LMFDB - Embedded newform 17.12.d.a.15.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,12,Mod(2,17)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([7]))

N = Newforms(chi, 12, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("17.2");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	17.d (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.0618340695$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$15$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			15.7
Character	$\chi$	$=$	17.15
Dual form			17.12.d.a.8.7

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-9.05999 - 9.05999i) q^{2} +(-110.206 - 266.060i) q^{3} -1883.83i q^{4} +(-9907.96 + 4104.01i) q^{5} +(-1412.04 + 3408.96i) q^{6} +(-5252.05 - 2175.47i) q^{7} +(-35622.4 + 35622.4i) q^{8} +(66619.3 - 66619.3i) q^{9} +O(q^{10})$	\(q+(-9.05999 - 9.05999i) q^{2} +(-110.206 - 266.060i) q^{3} -1883.83i q^{4} +(-9907.96 + 4104.01i) q^{5} +(-1412.04 + 3408.96i) q^{6} +(-5252.05 - 2175.47i) q^{7} +(-35622.4 + 35622.4i) q^{8} +(66619.3 - 66619.3i) q^{9} +(126948. + 52583.7i) q^{10} +(169417. - 409009. i) q^{11} +(-501212. + 207609. i) q^{12} +2.35308e6i q^{13} +(27873.8 + 67293.2i) q^{14} +(2.18382e6 + 2.18382e6i) q^{15} -3.21261e6 q^{16} +(5.74399e6 + 1.13070e6i) q^{17} -1.20714e6 q^{18} +(1.13456e6 + 1.13456e6i) q^{19} +(7.73127e6 + 1.86649e7i) q^{20} +1.63711e6i q^{21} +(-5.24053e6 + 2.17070e6i) q^{22} +(-2.16872e7 + 5.23575e7i) q^{23} +(1.34035e7 + 5.55190e6i) q^{24} +(4.67980e7 - 4.67980e7i) q^{25} +(2.13189e7 - 2.13189e7i) q^{26} +(-7.21982e7 - 2.99055e7i) q^{27} +(-4.09822e6 + 9.89399e6i) q^{28} +(-1.29173e7 + 5.35054e6i) q^{29} -3.95708e7i q^{30} +(-6.00324e7 - 1.44931e8i) q^{31} +(1.02061e8 + 1.02061e8i) q^{32} -1.27492e8 q^{33} +(-4.17963e7 - 6.22846e7i) q^{34} +6.09652e7 q^{35} +(-1.25500e8 - 1.25500e8i) q^{36} +(-1.20882e8 - 2.91836e8i) q^{37} -2.05582e7i q^{38} +(6.26061e8 - 2.59323e8i) q^{39} +(2.06750e8 - 4.99139e8i) q^{40} +(2.41279e8 + 9.99412e7i) q^{41} +(1.48322e7 - 1.48322e7i) q^{42} +(-8.72587e8 + 8.72587e8i) q^{43} +(-7.70505e8 - 3.19153e8i) q^{44} +(-3.86655e8 + 9.33467e8i) q^{45} +(6.70844e8 - 2.77873e8i) q^{46} +1.94347e9i q^{47} +(3.54048e8 + 8.54748e8i) q^{48} +(-1.37533e9 - 1.37533e9i) q^{49} -8.47978e8 q^{50} +(-3.32185e8 - 1.65285e9i) q^{51} +4.43282e9 q^{52} +(2.38756e9 + 2.38756e9i) q^{53} +(3.83172e8 + 9.25058e8i) q^{54} +4.74773e9i q^{55} +(2.64586e8 - 1.09595e8i) q^{56} +(1.76826e8 - 4.26897e8i) q^{57} +(1.65507e8 + 6.85552e7i) q^{58} +(-2.71935e9 + 2.71935e9i) q^{59} +(4.11396e9 - 4.11396e9i) q^{60} +(-4.39113e9 - 1.81887e9i) q^{61} +(-7.69181e8 + 1.85697e9i) q^{62} +(-4.94816e8 + 2.04960e8i) q^{63} +4.73010e9i q^{64} +(-9.65708e9 - 2.33143e10i) q^{65} +(1.15507e9 + 1.15507e9i) q^{66} -1.60345e10 q^{67} +(2.13005e9 - 1.08207e10i) q^{68} +1.63203e10 q^{69} +(-5.52344e8 - 5.52344e8i) q^{70} +(1.77078e9 + 4.27503e9i) q^{71} +4.74627e9i q^{72} +(1.95618e10 - 8.10278e9i) q^{73} +(-1.54884e9 + 3.73922e9i) q^{74} +(-1.76085e10 - 7.29367e9i) q^{75} +(2.13733e9 - 2.13733e9i) q^{76} +(-1.77957e9 + 1.77957e9i) q^{77} +(-8.02157e9 - 3.32264e9i) q^{78} +(-8.31421e9 + 2.00723e10i) q^{79} +(3.18304e10 - 1.31846e10i) q^{80} +5.81510e9i q^{81} +(-1.28052e9 - 3.09145e9i) q^{82} +(8.40193e8 + 8.40193e8i) q^{83} +3.08404e9 q^{84} +(-6.15516e10 + 1.23704e10i) q^{85} +1.58112e10 q^{86} +(2.84713e9 + 2.84713e9i) q^{87} +(8.53482e9 + 2.06049e10i) q^{88} +8.40715e10i q^{89} +(1.19603e10 - 4.95411e9i) q^{90} +(5.11907e9 - 1.23585e10i) q^{91} +(9.86329e10 + 4.08551e10i) q^{92} +(-3.19445e10 + 3.19445e10i) q^{93} +(1.76078e10 - 1.76078e10i) q^{94} +(-1.58975e10 - 6.58494e9i) q^{95} +(1.59066e10 - 3.84020e10i) q^{96} +(-4.16581e10 + 1.72553e10i) q^{97} +2.49209e10i q^{98} +(-1.59614e10 - 3.85343e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 4 q^{2} - 4 q^{3} + 10120 q^{5} - 44716 q^{6} - 4 q^{7} + 8188 q^{8} + 621728 q^{9}+O(q^{10}) $ 60 * q - 4 * q^2 - 4 * q^3 + 10120 * q^5 - 44716 * q^6 - 4 * q^7 + 8188 * q^8 + 621728 * q^9	\( 60 q - 4 q^{2} - 4 q^{3} + 10120 q^{5} - 44716 q^{6} - 4 q^{7} + 8188 q^{8} + 621728 q^{9} + 1216764 q^{10} - 2477204 q^{11} + 3940328 q^{12} - 5240148 q^{14} + 268504 q^{15} - 37748744 q^{16} - 8506952 q^{17} - 49606536 q^{18} - 30493864 q^{19} - 4030468 q^{20} - 36263996 q^{22} + 41885892 q^{23} + 274044968 q^{24} - 149009884 q^{25} - 149388276 q^{26} + 372604808 q^{27} + 4552772 q^{28} - 405222844 q^{29} - 314352908 q^{31} + 158198620 q^{32} + 1579932656 q^{33} + 1442610972 q^{34} - 1930639352 q^{35} - 366488740 q^{36} - 548749688 q^{37} + 1410218272 q^{39} + 4273406456 q^{40} + 589469732 q^{41} - 2429156064 q^{42} - 1054826472 q^{43} + 1709288236 q^{44} + 1506858388 q^{45} - 5816026300 q^{46} - 9522665340 q^{48} + 5648484080 q^{49} - 1244607984 q^{50} + 11680434460 q^{51} - 8594677768 q^{52} - 778073292 q^{53} - 21008154412 q^{54} - 30926853276 q^{56} - 6110953360 q^{57} + 18118173496 q^{58} + 37531292320 q^{59} + 27234822368 q^{60} - 18404313464 q^{61} - 33465767324 q^{62} - 71416360044 q^{63} + 32319214364 q^{65} + 127830372436 q^{66} - 30146193488 q^{67} + 115331418852 q^{68} - 3167366672 q^{69} + 94186059512 q^{70} - 125576765420 q^{71} - 106477971796 q^{73} + 99841309980 q^{74} + 49903675300 q^{75} + 122143021712 q^{76} + 12932381888 q^{77} - 41324166360 q^{78} - 59932259908 q^{79} - 303074713864 q^{80} - 148956007488 q^{82} + 92931722448 q^{83} + 352647150176 q^{84} + 281879722956 q^{85} - 719170979232 q^{86} + 53292447280 q^{87} - 526424624472 q^{88} - 276922392380 q^{90} + 302957259936 q^{91} + 302729734572 q^{92} + 184432247152 q^{93} + 526721876024 q^{94} - 580598088 q^{95} - 523924088028 q^{96} - 283776169328 q^{97} - 276595143092 q^{99}+O(q^{100}) \) 60 * q - 4 * q^2 - 4 * q^3 + 10120 * q^5 - 44716 * q^6 - 4 * q^7 + 8188 * q^8 + 621728 * q^9 + 1216764 * q^10 - 2477204 * q^11 + 3940328 * q^12 - 5240148 * q^14 + 268504 * q^15 - 37748744 * q^16 - 8506952 * q^17 - 49606536 * q^18 - 30493864 * q^19 - 4030468 * q^20 - 36263996 * q^22 + 41885892 * q^23 + 274044968 * q^24 - 149009884 * q^25 - 149388276 * q^26 + 372604808 * q^27 + 4552772 * q^28 - 405222844 * q^29 - 314352908 * q^31 + 158198620 * q^32 + 1579932656 * q^33 + 1442610972 * q^34 - 1930639352 * q^35 - 366488740 * q^36 - 548749688 * q^37 + 1410218272 * q^39 + 4273406456 * q^40 + 589469732 * q^41 - 2429156064 * q^42 - 1054826472 * q^43 + 1709288236 * q^44 + 1506858388 * q^45 - 5816026300 * q^46 - 9522665340 * q^48 + 5648484080 * q^49 - 1244607984 * q^50 + 11680434460 * q^51 - 8594677768 * q^52 - 778073292 * q^53 - 21008154412 * q^54 - 30926853276 * q^56 - 6110953360 * q^57 + 18118173496 * q^58 + 37531292320 * q^59 + 27234822368 * q^60 - 18404313464 * q^61 - 33465767324 * q^62 - 71416360044 * q^63 + 32319214364 * q^65 + 127830372436 * q^66 - 30146193488 * q^67 + 115331418852 * q^68 - 3167366672 * q^69 + 94186059512 * q^70 - 125576765420 * q^71 - 106477971796 * q^73 + 99841309980 * q^74 + 49903675300 * q^75 + 122143021712 * q^76 + 12932381888 * q^77 - 41324166360 * q^78 - 59932259908 * q^79 - 303074713864 * q^80 - 148956007488 * q^82 + 92931722448 * q^83 + 352647150176 * q^84 + 281879722956 * q^85 - 719170979232 * q^86 + 53292447280 * q^87 - 526424624472 * q^88 - 276922392380 * q^90 + 302957259936 * q^91 + 302729734572 * q^92 + 184432247152 * q^93 + 526721876024 * q^94 - 580598088 * q^95 - 523924088028 * q^96 - 283776169328 * q^97 - 276595143092 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/17\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{3}{8}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−9.05999	−	9.05999i	−0.200199	−	0.200199i	0.599886	−	0.800085i	$-0.295213\pi$
$2$	−9.05999	−	9.05999i	−0.200199	−	0.200199i	−0.800085	+	0.599886i	$0.795213\pi$
$3$	−110.206	−	266.060i	−0.261840	−	0.632139i	0.737212	−	0.675662i	$-0.236142\pi$
$3$	−110.206	−	266.060i	−0.261840	−	0.632139i	−0.999052	+	0.0435227i	$0.986142\pi$
$4$		−	1883.83i		−	0.919840i
$5$	−9907.96	+	4104.01i	−1.41791	+	0.587318i	−0.954335	−	0.298739i	$-0.903434\pi$
$5$	−9907.96	+	4104.01i	−1.41791	+	0.587318i	−0.463576	+	0.886057i	$0.653434\pi$
$6$	−1412.04	+	3408.96i	−0.0741335	+	0.178974i
$7$	−5252.05	−	2175.47i	−0.118111	−	0.0489231i	0.322845	−	0.946452i	$-0.395361\pi$
$7$	−5252.05	−	2175.47i	−0.118111	−	0.0489231i	−0.440956	+	0.897529i	$0.645361\pi$
$8$	−35622.4	+	35622.4i	−0.384351	+	0.384351i
$9$	66619.3	−	66619.3i	0.376068	−	0.376068i
$10$	126948.	+	52583.7i	0.401445	+	0.166284i
$11$	169417.	−	409009.i	0.317174	−	0.765725i	−0.682228	−	0.731140i	$-0.738989\pi$
$11$	169417.	−	409009.i	0.317174	−	0.765725i	0.999402	−	0.0345857i	$-0.0110112\pi$
$12$	−501212.	+	207609.i	−0.581467	+	0.240851i
$13$			2.35308e6i			1.75772i	0.477082	+	0.878859i	$0.341694\pi$
$13$			2.35308e6i			1.75772i	−0.477082	+	0.878859i	$0.658306\pi$
$14$	27873.8	+	67293.2i	0.0138513	+	0.0334401i
$15$	2.18382e6	+	2.18382e6i	0.742533	+	0.742533i
$16$	−3.21261e6			−0.765947
$17$	5.74399e6	+	1.13070e6i	0.981171	+	0.193143i
$17$	5.74399e6	+	1.13070e6i	0.981171	+	0.193143i
$18$	−1.20714e6			−0.150577
$19$	1.13456e6	+	1.13456e6i	0.105120	+	0.105120i	0.757710	−	0.652591i	$-0.226318\pi$
$19$	1.13456e6	+	1.13456e6i	0.105120	+	0.105120i	−0.652591	+	0.757710i	$0.726318\pi$
$20$	7.73127e6	+	1.86649e7i	0.540239	+	1.30425i
$21$			1.63711e6i			0.0874725i
$22$	−5.24053e6	+	2.17070e6i	−0.216796	+	0.0897997i
$23$	−2.16872e7	+	5.23575e7i	−0.702588	+	1.69620i	0.0151523	+	0.999885i	$0.495177\pi$
$23$	−2.16872e7	+	5.23575e7i	−0.702588	+	1.69620i	−0.717740	+	0.696311i	$0.754823\pi$
$24$	1.34035e7	+	5.55190e6i	0.343602	+	0.142324i
$25$	4.67980e7	−	4.67980e7i	0.958423	−	0.958423i
$26$	2.13189e7	−	2.13189e7i	0.351894	−	0.351894i
$27$	−7.21982e7	−	2.99055e7i	−0.968336	−	0.401098i
$28$	−4.09822e6	+	9.89399e6i	−0.0450015	+	0.108643i
$29$	−1.29173e7	+	5.35054e6i	−0.116946	+	0.0484405i	−0.440389	−	0.897807i	$-0.645159\pi$
$29$	−1.29173e7	+	5.35054e6i	−0.116946	+	0.0484405i	0.323443	+	0.946248i	$0.395159\pi$
$30$		−	3.95708e7i		−	0.297309i
$31$	−6.00324e7	−	1.44931e8i	−0.376614	−	0.909227i	−0.992596	−	0.121466i	$-0.961240\pi$
$31$	−6.00324e7	−	1.44931e8i	−0.376614	−	0.909227i	0.615981	−	0.787761i	$-0.288760\pi$
$32$	1.02061e8	+	1.02061e8i	0.537693	+	0.537693i
$33$	−1.27492e8			−0.567094
$34$	−4.17963e7	−	6.22846e7i	−0.157763	−	0.235097i
$35$	6.09652e7			0.196204
$36$	−1.25500e8	−	1.25500e8i	−0.345922	−	0.345922i
$37$	−1.20882e8	−	2.91836e8i	−0.286585	−	0.691878i	0.713375	−	0.700782i	$-0.247166\pi$
$37$	−1.20882e8	−	2.91836e8i	−0.286585	−	0.691878i	−0.999960	+	0.00890437i	$0.997166\pi$
$38$		−	2.05582e7i		−	0.0420897i
$39$	6.26061e8	−	2.59323e8i	1.11112	−	0.460242i
$40$	2.06750e8	−	4.99139e8i	0.319239	−	0.770711i
$41$	2.41279e8	+	9.99412e7i	0.325244	+	0.134720i	0.539330	−	0.842094i	$-0.318677\pi$
$41$	2.41279e8	+	9.99412e7i	0.325244	+	0.134720i	−0.214086	+	0.976815i	$0.568677\pi$
$42$	1.48322e7	−	1.48322e7i	0.0175119	−	0.0175119i
$43$	−8.72587e8	+	8.72587e8i	−0.905174	+	0.905174i	−0.995878	−	0.0907038i	$-0.971088\pi$
$43$	−8.72587e8	+	8.72587e8i	−0.905174	+	0.905174i	0.0907038	+	0.995878i	$0.471088\pi$
$44$	−7.70505e8	−	3.19153e8i	−0.704345	−	0.291749i
$45$	−3.86655e8	+	9.33467e8i	−0.312359	+	0.754102i
$46$	6.70844e8	−	2.77873e8i	0.480235	−	0.198920i
$47$			1.94347e9i			1.23606i	0.786154	+	0.618031i	$0.212069\pi$
$47$			1.94347e9i			1.23606i	−0.786154	+	0.618031i	$0.787931\pi$
$48$	3.54048e8	+	8.54748e8i	0.200556	+	0.484185i
$49$	−1.37533e9	−	1.37533e9i	−0.695550	−	0.695550i
$50$	−8.47978e8			−0.383751
$51$	−3.32185e8	−	1.65285e9i	−0.134817	−	0.670809i
$52$	4.43282e9			1.61682
$53$	2.38756e9	+	2.38756e9i	0.784218	+	0.784218i	0.980540	−	0.196321i	$-0.0628995\pi$
$53$	2.38756e9	+	2.38756e9i	0.784218	+	0.784218i	−0.196321	+	0.980540i	$0.562900\pi$
$54$	3.83172e8	+	9.25058e8i	0.113561	+	0.274160i
$55$			4.74773e9i			1.27201i
$56$	2.64586e8	−	1.09595e8i	0.0641996	−	0.0265923i
$57$	1.76826e8	−	4.26897e8i	0.0389256	−	0.0939748i
$58$	1.65507e8	+	6.85552e7i	0.0331102	+	0.0137147i
$59$	−2.71935e9	+	2.71935e9i	−0.495198	+	0.495198i	−0.909939	−	0.414741i	$-0.863872\pi$
$59$	−2.71935e9	+	2.71935e9i	−0.495198	+	0.495198i	0.414741	+	0.909939i	$0.363872\pi$
$60$	4.11396e9	−	4.11396e9i	0.683012	−	0.683012i
$61$	−4.39113e9	−	1.81887e9i	−0.665675	−	0.275732i	0.0241494	−	0.999708i	$-0.492312\pi$
$61$	−4.39113e9	−	1.81887e9i	−0.665675	−	0.275732i	−0.689824	+	0.723977i	$0.742312\pi$
$62$	−7.69181e8	+	1.85697e9i	−0.106629	+	0.257425i
$63$	−4.94816e8	+	2.04960e8i	−0.0628161	+	0.0260193i
$64$			4.73010e9i			0.550656i
$65$	−9.65708e9	−	2.33143e10i	−1.03234	−	2.49229i
$66$	1.15507e9	+	1.15507e9i	0.113532	+	0.113532i
$67$	−1.60345e10			−1.45092			−0.725461	−	0.688264i	$-0.758373\pi$
$67$	−1.60345e10			−1.45092			−0.725461	+	0.688264i	$0.758373\pi$
$68$	2.13005e9	−	1.08207e10i	0.177661	−	0.902520i
$69$	1.63203e10			1.25620
$70$	−5.52344e8	−	5.52344e8i	−0.0392799	−	0.0392799i
$71$	1.77078e9	+	4.27503e9i	0.116478	+	0.281202i	0.971357	−	0.237625i	$-0.0763689\pi$
$71$	1.77078e9	+	4.27503e9i	0.116478	+	0.281202i	−0.854879	+	0.518827i	$0.826369\pi$
$72$			4.74627e9i			0.289084i
$73$	1.95618e10	−	8.10278e9i	1.10442	−	0.457466i	0.245407	−	0.969420i	$-0.421078\pi$
$73$	1.95618e10	−	8.10278e9i	1.10442	−	0.457466i	0.859013	+	0.511954i	$0.171078\pi$
$74$	−1.54884e9	+	3.73922e9i	−0.0811393	+	0.195888i
$75$	−1.76085e10	−	7.29367e9i	−0.856810	−	0.354902i
$76$	2.13733e9	−	2.13733e9i	0.0966933	−	0.0966933i
$77$	−1.77957e9	+	1.77957e9i	−0.0749233	+	0.0749233i
$78$	−8.02157e9	−	3.32264e9i	−0.314586	−	0.130306i
$79$	−8.31421e9	+	2.00723e10i	−0.303999	+	0.733918i	0.695877	+	0.718161i	$0.255016\pi$
$79$	−8.31421e9	+	2.00723e10i	−0.303999	+	0.733918i	−0.999876	+	0.0157571i	$0.994984\pi$
$80$	3.18304e10	−	1.31846e10i	1.08604	−	0.449855i
$81$			5.81510e9i			0.185306i
$82$	−1.28052e9	−	3.09145e9i	−0.0381426	−	0.0920845i
$83$	8.40193e8	+	8.40193e8i	0.0234126	+	0.0234126i	0.718716	−	0.695304i	$-0.244730\pi$
$83$	8.40193e8	+	8.40193e8i	0.0234126	+	0.0234126i	−0.695304	+	0.718716i	$0.744730\pi$
$84$	3.08404e9			0.0804607
$85$	−6.15516e10	+	1.23704e10i	−1.50465	+	0.302399i
$86$	1.58112e10			0.362430
$87$	2.84713e9	+	2.84713e9i	0.0612423	+	0.0612423i
$88$	8.53482e9	+	2.06049e10i	0.172401	+	0.416213i
$89$			8.40715e10i			1.59589i	0.602728	+	0.797947i	$0.294080\pi$
$89$			8.40715e10i			1.59589i	−0.602728	+	0.797947i	$0.705920\pi$
$90$	1.19603e10	−	4.95411e9i	0.213505	−	0.0884366i
$91$	5.11907e9	−	1.23585e10i	0.0859930	−	0.207605i
$92$	9.86329e10	+	4.08551e10i	1.56023	+	0.646269i
$93$	−3.19445e10	+	3.19445e10i	−0.476145	+	0.476145i
$94$	1.76078e10	−	1.76078e10i	0.247459	−	0.247459i
$95$	−1.58975e10	−	6.58494e9i	−0.210789	−	0.0873116i
$96$	1.59066e10	−	3.84020e10i	0.199107	−	0.480686i
$97$	−4.16581e10	+	1.72553e10i	−0.492555	+	0.204023i	−0.615114	−	0.788438i	$-0.710890\pi$
$97$	−4.16581e10	+	1.72553e10i	−0.492555	+	0.204023i	0.122559	+	0.992461i	$0.460890\pi$
$98$			2.49209e10i			0.278497i
$99$	−1.59614e10	−	3.85343e10i	−0.168686	−	0.407243i
$100$	−8.81596e10	−	8.81596e10i	−0.881596	−	0.881596i
$101$	1.19855e11			1.13472			0.567362	−	0.823468i	$-0.307964\pi$
$101$	1.19855e11			1.13472			0.567362	+	0.823468i	$0.307964\pi$
$102$	−1.19652e10	+	1.79844e10i	−0.107305	+	0.161286i
$103$	5.21146e10			0.442950			0.221475	−	0.975166i	$-0.428913\pi$
$103$	5.21146e10			0.442950			0.221475	+	0.975166i	$0.428913\pi$
$104$	−8.38224e10	−	8.38224e10i	−0.675580	−	0.675580i
$105$	−6.71871e9	−	1.62204e10i	−0.0513742	−	0.124028i
$106$		−	4.32625e10i		−	0.314000i
$107$	−1.38334e11	+	5.73000e10i	−0.953498	+	0.394952i	−0.804544	−	0.593893i	$-0.797590\pi$
$107$	−1.38334e11	+	5.73000e10i	−0.953498	+	0.394952i	−0.148953	+	0.988844i	$0.547590\pi$
$108$	−5.63370e10	+	1.36009e11i	−0.368946	+	0.890714i
$109$	6.12428e10	+	2.53676e10i	0.381249	+	0.157919i	0.565074	−	0.825041i	$-0.308848\pi$
$109$	6.12428e10	+	2.53676e10i	0.381249	+	0.157919i	−0.183824	+	0.982959i	$0.558848\pi$
$110$	4.30144e10	−	4.30144e10i	0.254656	−	0.254656i
$111$	−6.43240e10	+	6.43240e10i	−0.362323	+	0.362323i
$112$	1.68728e10	+	6.98895e9i	0.0904666	+	0.0374725i
$113$	8.98812e10	−	2.16992e11i	0.458920	−	1.10793i	−0.509915	−	0.860225i	$-0.670323\pi$
$113$	8.98812e10	−	2.16992e11i	0.458920	−	1.10793i	0.968835	−	0.247707i	$-0.0796769\pi$
$114$	−5.46972e9	+	2.26563e9i	−0.0266066	+	0.0110208i
$115$		−	6.07761e11i		−	2.81770i
$116$	1.00795e10	+	2.43341e10i	0.0445575	+	0.107571i
$117$	1.56761e11	+	1.56761e11i	0.661021	+	0.661021i
$118$	4.92745e10			0.198277
$119$	−2.77079e10	−	1.84344e10i	−0.106438	−	0.0708142i
$120$	−1.55586e11			−0.570786
$121$	6.31597e10	+	6.31597e10i	0.221371	+	0.221371i
$122$	2.33047e10	+	5.62625e10i	0.0780664	+	0.188469i
$123$		−	7.52088e10i		−	0.240874i
$124$	−2.73026e11	+	1.13091e11i	−0.836344	+	0.346425i
$125$	−7.12219e10	+	1.71945e11i	−0.208741	+	0.503946i
$126$	6.33996e9	+	2.62610e9i	0.0177848	+	0.00736669i
$127$	−1.66992e11	+	1.66992e11i	−0.448514	+	0.448514i	−0.894860	−	0.446346i	$-0.852725\pi$
$127$	−1.66992e11	+	1.66992e11i	−0.448514	+	0.448514i	0.446346	+	0.894860i	$0.352725\pi$
$128$	2.51875e11	−	2.51875e11i	0.647934	−	0.647934i
$129$	3.28324e11	+	1.35996e11i	0.809207	+	0.335185i
$130$	−1.23734e11	+	2.98720e11i	−0.292281	+	0.705628i
$131$	−2.39114e11	+	9.90441e10i	−0.541517	+	0.224304i	−0.636639	−	0.771162i	$-0.719676\pi$
$131$	−2.39114e11	+	9.90441e10i	−0.541517	+	0.224304i	0.0951220	+	0.995466i	$0.469676\pi$
$132$			2.40173e11i			0.521636i
$133$	−3.49057e9	−	8.42699e9i	−0.00727299	−	0.0175585i
$134$	1.45272e11	+	1.45272e11i	0.290473	+	0.290473i
$135$	8.38069e11			1.60859
$136$	−2.44893e11	+	1.64336e11i	−0.451348	+	0.302879i
$137$	−6.69247e11			−1.18474			−0.592371	−	0.805666i	$-0.701808\pi$
$137$	−6.69247e11			−1.18474			−0.592371	+	0.805666i	$0.701808\pi$
$138$	−1.47862e11	−	1.47862e11i	−0.251490	−	0.251490i
$139$	−3.74452e10	−	9.04007e10i	−0.0612089	−	0.147771i	0.890316	−	0.455343i	$-0.150484\pi$
$139$	−3.74452e10	−	9.04007e10i	−0.0612089	−	0.147771i	−0.951525	+	0.307572i	$0.900484\pi$
$140$		−	1.14848e11i		−	0.180476i
$141$	5.17080e11	−	2.14182e11i	0.781363	−	0.323651i
$142$	2.26885e10	−	5.47750e10i	0.0329777	−	0.0796152i
$143$	9.62432e11	+	3.98653e11i	1.34593	+	0.557502i
$144$	−2.14022e11	+	2.14022e11i	−0.288048	+	0.288048i
$145$	1.06026e11	−	1.06026e11i	0.137369	−	0.137369i
$146$	−2.50641e11	−	1.03819e11i	−0.312688	−	0.129520i
$147$	−2.14351e11	+	5.17489e11i	−0.257561	+	0.621807i
$148$	−5.49771e11	+	2.27722e11i	−0.636417	+	0.263613i
$149$			6.59897e11i			0.736125i	0.929801	+	0.368062i	$0.119979\pi$
$149$			6.59897e11i			0.736125i	−0.929801	+	0.368062i	$0.880021\pi$
$150$	9.34520e10	+	2.25613e11i	0.100482	+	0.242584i
$151$	−6.01268e11	−	6.01268e11i	−0.623297	−	0.623297i	0.323076	−	0.946373i	$-0.395283\pi$
$151$	−6.01268e11	−	6.01268e11i	−0.623297	−	0.623297i	−0.946373	+	0.323076i	$0.895283\pi$
$152$	−8.08316e10			−0.0808056
$153$	4.57987e11	−	3.07334e11i	0.441621	−	0.296352i
$154$	3.22458e10			0.0299992
$155$	1.18960e12	+	1.18960e12i	1.06801	+	1.06801i
$156$	−4.88521e11	−	1.17940e12i	−0.423349	−	1.02205i
$157$		−	1.38372e12i		−	1.15771i	−0.815431	−	0.578854i	$-0.803500\pi$
$157$		−	1.38372e12i		−	1.15771i	0.815431	−	0.578854i	$-0.196500\pi$
$158$	2.57181e11	−	1.06528e11i	0.207790	−	0.0860695i
$159$	3.72111e11	−	8.98356e11i	0.290395	−	0.701075i
$160$	−1.43007e12	−	5.92355e11i	−1.07820	−	0.446604i
$161$	2.27805e11	−	2.27805e11i	0.165966	−	0.165966i
$162$	5.26847e10	−	5.26847e10i	0.0370982	−	0.0370982i
$163$	−1.39449e12	−	5.77616e11i	−0.949255	−	0.393194i	−0.146304	−	0.989240i	$-0.546738\pi$
$163$	−1.39449e12	−	5.77616e11i	−0.949255	−	0.393194i	−0.802951	+	0.596046i	$0.796738\pi$
$164$	1.88273e11	−	4.54530e11i	0.123921	−	0.299172i
$165$	1.26318e12	−	5.23227e11i	0.804088	−	0.333064i
$166$		−	1.52243e10i		−	0.00937437i
$167$	−3.37877e11	−	8.15706e11i	−0.201288	−	0.485952i	0.790712	−	0.612188i	$-0.209710\pi$
$167$	−3.37877e11	−	8.15706e11i	−0.201288	−	0.485952i	−0.992000	+	0.126236i	$0.959710\pi$
$168$	−5.83177e10	−	5.83177e10i	−0.0336201	−	0.0336201i
$169$	−3.74485e12			−2.08957
$170$	6.69733e11	+	4.45581e11i	0.361770	+	0.240690i
$171$	1.51168e11			0.0790642
$172$	1.64381e12	+	1.64381e12i	0.832616	+	0.832616i
$173$	−2.94660e11	−	7.11372e11i	−0.144566	−	0.349014i	0.834966	−	0.550302i	$-0.185487\pi$
$173$	−2.94660e11	−	7.11372e11i	−0.144566	−	0.349014i	−0.979532	+	0.201288i	$0.935487\pi$
$174$		−	5.15899e10i		−	0.0245213i
$175$	−3.47593e11	+	1.43978e11i	−0.160089	+	0.0663111i
$176$	−5.44272e11	+	1.31399e12i	−0.242938	+	0.586505i
$177$	1.02320e12	+	4.23822e11i	0.442697	+	0.183371i
$178$	7.61687e11	−	7.61687e11i	0.319497	−	0.319497i
$179$	−8.36450e11	+	8.36450e11i	−0.340211	+	0.340211i	−0.856447	−	0.516236i	$-0.827333\pi$
$179$	−8.36450e11	+	8.36450e11i	−0.340211	+	0.340211i	0.516236	+	0.856447i	$0.327333\pi$
$180$	1.75850e12	+	7.28393e11i	0.693654	+	0.287321i
$181$	−6.53455e11	+	1.57758e12i	−0.250025	+	0.603614i	−0.998206	−	0.0598814i	$-0.980928\pi$
$181$	−6.53455e11	+	1.57758e12i	−0.250025	+	0.603614i	0.748180	+	0.663495i	$0.230928\pi$
$182$	−1.58347e11	+	6.55893e10i	−0.0587782	+	0.0243467i
$183$			1.36875e12i			0.492997i
$184$	−1.09255e12	−	2.63765e12i	−0.381894	−	0.921974i
$185$	2.39540e12	+	2.39540e12i	0.812705	+	0.812705i
$186$	5.78833e11			0.190648
$187$	1.43560e12	−	2.15778e12i	0.459096	−	0.690047i
$188$	3.66118e12			1.13698
$189$	3.14130e11	+	3.14130e11i	0.0947480	+	0.0947480i
$190$	8.43712e10	+	2.03690e11i	0.0247201	+	0.0596795i
$191$		−	4.35801e11i		−	0.124052i	−0.998075	−	0.0620262i	$-0.980244\pi$
$191$		−	4.35801e11i		−	0.124052i	0.998075	−	0.0620262i	$-0.0197562\pi$
$192$	1.25849e12	−	5.21283e11i	0.348091	−	0.144184i
$193$	−5.83138e11	+	1.40782e12i	−0.156750	+	0.378427i	−0.982671	−	0.185358i	$-0.940655\pi$
$193$	−5.83138e11	+	1.40782e12i	−0.156750	+	0.378427i	0.825921	+	0.563785i	$0.190655\pi$
$194$	5.33755e11	+	2.21089e11i	0.139454	+	0.0577639i
$195$	−5.13872e12	+	5.13872e12i	−1.30516	+	1.30516i
$196$	−2.59089e12	+	2.59089e12i	−0.639795	+	0.639795i
$197$	−6.32755e12	−	2.62096e12i	−1.51940	−	0.629355i	−0.541926	−	0.840426i	$-0.682305\pi$
$197$	−6.32755e12	−	2.62096e12i	−1.51940	−	0.629355i	−0.977471	+	0.211072i	$0.932305\pi$
$198$	−2.04510e11	+	4.93731e11i	−0.0477591	+	0.115301i
$199$	6.97018e12	−	2.88714e12i	1.58326	−	0.655808i	0.594334	−	0.804218i	$-0.297416\pi$
$199$	6.97018e12	−	2.88714e12i	1.58326	−	0.655808i	0.988926	+	0.148410i	$0.0474156\pi$
$200$			3.33411e12i			0.736741i
$201$	1.76709e12	+	4.26613e12i	0.379910	+	0.917184i
$202$	−1.08589e12	−	1.08589e12i	−0.227171	−	0.227171i
$203$	7.94825e10			0.0161824
$204$	−3.11370e12	+	6.25782e11i	−0.617037	+	0.124010i
$205$	−2.80075e12			−0.540291
$206$	−4.72158e11	−	4.72158e11i	−0.0886783	−	0.0886783i
$207$	2.04324e12	+	4.93281e12i	0.373664	+	0.902105i
$208$		−	7.55955e12i		−	1.34632i
$209$	6.56261e11	−	2.71832e11i	0.113834	−	0.0471516i
$210$	−8.60852e10	+	2.07828e11i	−0.0145453	+	0.0351154i
$211$	−7.46801e12	−	3.09335e12i	−1.22928	−	0.509185i	−0.328933	−	0.944353i	$-0.606689\pi$
$211$	−7.46801e12	−	3.09335e12i	−1.22928	−	0.509185i	−0.900349	+	0.435168i	$0.856689\pi$
$212$	4.49777e12	−	4.49777e12i	0.721356	−	0.721356i
$213$	9.42265e11	−	9.42265e11i	0.147260	−	0.147260i
$214$	1.77245e12	+	7.34171e11i	0.269959	+	0.111821i
$215$	5.06445e12	−	1.22267e13i	0.751831	−	1.81508i
$216$	3.63717e12	−	1.50657e12i	0.526343	−	0.218018i
$217$			8.91785e11i			0.125815i
$218$	−3.25029e11	−	7.84688e11i	−0.0447106	−	0.107941i
$219$	−4.31165e12	−	4.31165e12i	−0.578364	−	0.578364i
$220$	8.94393e12			1.17005
$221$	−2.66064e12	+	1.35161e13i	−0.339491	+	1.72462i
$222$	1.16555e12			0.145074
$223$	−2.29572e12	−	2.29572e12i	−0.278767	−	0.278767i	0.553849	−	0.832617i	$-0.313158\pi$
$223$	−2.29572e12	−	2.29572e12i	−0.278767	−	0.278767i	−0.832617	+	0.553849i	$0.813158\pi$
$224$	−3.13998e11	−	7.58059e11i	−0.0372017	−	0.0898129i
$225$		−	6.23530e12i		−	0.720864i
$226$	−2.78027e12	+	1.15163e12i	−0.313683	+	0.129932i
$227$	1.82338e12	−	4.40204e12i	0.200787	−	0.484743i	−0.791127	−	0.611651i	$-0.790505\pi$
$227$	1.82338e12	−	4.40204e12i	0.200787	−	0.484743i	0.991914	+	0.126909i	$0.0405055\pi$
$228$	−8.04203e11	−	3.33112e11i	−0.0864418	−	0.0358054i
$229$	−1.05508e13	+	1.05508e13i	−1.10710	+	1.10710i	−0.113575	+	0.993529i	$0.536230\pi$
$229$	−1.05508e13	+	1.05508e13i	−1.10710	+	1.10710i	−0.993529	+	0.113575i	$0.963770\pi$
$230$	−5.50630e12	+	5.50630e12i	−0.564101	+	0.564101i
$231$	6.69592e11	+	2.77354e11i	0.0669799	+	0.0277440i
$232$	2.69547e11	−	6.50745e11i	0.0263300	−	0.0635663i
$233$	2.20707e12	−	9.14199e11i	0.210552	−	0.0872134i	−0.274915	−	0.961469i	$-0.588650\pi$
$233$	2.20707e12	−	9.14199e11i	0.210552	−	0.0872134i	0.485467	+	0.874255i	$0.338650\pi$
$234$		−	2.84050e12i		−	0.264672i
$235$	−7.97603e12	−	1.92558e13i	−0.725962	−	1.75263i
$236$	5.12280e12	+	5.12280e12i	0.455503	+	0.455503i
$237$	6.25670e12			0.543537
$238$	8.40180e10	+	4.18049e11i	0.00713180	+	0.0354857i
$239$	−4.24779e11			−0.0352351			−0.0176175	−	0.999845i	$-0.505608\pi$
$239$	−4.24779e11			−0.0352351			−0.0176175	+	0.999845i	$0.505608\pi$
$240$	−7.01579e12	−	7.01579e12i	−0.568741	−	0.568741i
$241$	1.81131e12	+	4.37290e12i	0.143516	+	0.346478i	0.979250	−	0.202657i	$-0.0649575\pi$
$241$	1.81131e12	+	4.37290e12i	0.143516	+	0.346478i	−0.835734	+	0.549134i	$0.814958\pi$
$242$		−	1.14445e12i		−	0.0886366i
$243$	−1.12425e13	+	4.65681e12i	−0.851196	+	0.352577i
$244$	−3.42644e12	+	8.27216e12i	−0.253629	+	0.612315i
$245$	1.92711e13	+	7.98234e12i	1.39474	+	0.577719i
$246$	−6.81391e11	+	6.81391e11i	−0.0482229	+	0.0482229i
$247$	−2.66972e12	+	2.66972e12i	−0.184771	+	0.184771i
$248$	7.30129e12	+	3.02429e12i	0.494214	+	0.204710i
$249$	1.30948e11	−	3.16136e11i	0.00866964	−	0.0209304i
$250$	2.20309e12	−	9.12549e11i	0.142680	−	0.0590998i
$251$		−	1.74760e13i		−	1.10723i	−0.832773	−	0.553614i	$-0.813248\pi$
$251$		−	1.74760e13i		−	1.10723i	0.832773	−	0.553614i	$-0.186752\pi$
$252$	3.86110e11	+	9.32151e11i	0.0239336	+	0.0577808i
$253$	1.77405e13	+	1.77405e13i	1.07598	+	1.07598i
$254$	3.02590e12			0.179584
$255$	1.00746e13	+	1.50131e13i	0.585136	+	0.871967i
$256$	5.12327e12			0.291224
$257$	1.48043e13	+	1.48043e13i	0.823672	+	0.823672i	0.986633	−	0.162961i	$-0.0521043\pi$
$257$	1.48043e13	+	1.48043e13i	0.823672	+	0.823672i	−0.162961	+	0.986633i	$0.552104\pi$
$258$	−1.74249e12	−	4.20674e12i	−0.0948990	−	0.229106i
$259$			1.79571e12i			0.0957389i
$260$	−4.39202e13	+	1.81923e13i	−2.29251	+	0.949587i
$261$	−5.04095e11	+	1.21699e12i	−0.0257626	+	0.0621964i
$262$	3.06370e12	+	1.26903e12i	0.153317	+	0.0635059i
$263$	−4.17300e12	+	4.17300e12i	−0.204499	+	0.204499i	−0.801925	−	0.597425i	$-0.796190\pi$
$263$	−4.17300e12	+	4.17300e12i	−0.204499	+	0.204499i	0.597425	+	0.801925i	$0.296190\pi$
$264$	4.54155e12	−	4.54155e12i	0.217963	−	0.217963i
$265$	−3.34544e13	−	1.38573e13i	−1.57254	−	0.651366i
$266$	−4.47239e10	+	1.07973e11i	−0.00205916	+	0.00497126i
$267$	2.23681e13	−	9.26515e12i	1.00883	−	0.417869i
$268$			3.02063e13i			1.33462i
$269$	−3.40092e12	−	8.21055e12i	−0.147217	−	0.355414i	0.833019	−	0.553245i	$-0.186611\pi$
$269$	−3.40092e12	−	8.21055e12i	−0.147217	−	0.355414i	−0.980236	+	0.197830i	$0.936611\pi$
$270$	−7.59290e12	−	7.59290e12i	−0.322038	−	0.322038i
$271$	2.99248e13			1.24366			0.621828	−	0.783154i	$-0.286390\pi$
$271$	2.99248e13			1.24366			0.621828	+	0.783154i	$0.286390\pi$
$272$	−1.84532e13	−	3.63251e12i	−0.751525	−	0.147937i
$273$	−3.85226e12			−0.153752
$274$	6.06337e12	+	6.06337e12i	0.237184	+	0.237184i
$275$	−1.12124e13	−	2.70692e13i	−0.429902	−	1.03788i
$276$		−	3.07447e13i		−	1.15550i
$277$	2.20411e13	−	9.12974e12i	0.812073	−	0.336372i	0.0622924	−	0.998058i	$-0.480159\pi$
$277$	2.20411e13	−	9.12974e12i	0.812073	−	0.336372i	0.749781	+	0.661686i	$0.230159\pi$
$278$	−4.79776e11	+	1.15828e12i	−0.0173298	+	0.0418377i
$279$	−1.36545e13	−	5.65589e12i	−0.483563	−	0.200299i
$280$	−2.17173e12	+	2.17173e12i	−0.0754112	+	0.0754112i
$281$	1.61622e13	−	1.61622e13i	0.550319	−	0.550319i	−0.376214	−	0.926533i	$-0.622774\pi$
$281$	1.61622e13	−	1.61622e13i	0.550319	−	0.550319i	0.926533	+	0.376214i	$0.122774\pi$
$282$	−6.62522e12	−	2.74426e12i	−0.221223	−	0.0916336i
$283$	−2.04093e13	+	4.92725e13i	−0.668349	+	1.61354i	0.116024	+	0.993246i	$0.462985\pi$
$283$	−2.04093e13	+	4.92725e13i	−0.668349	+	1.61354i	−0.784372	+	0.620290i	$0.787015\pi$
$284$	8.05345e12	−	3.33585e12i	0.258661	−	0.107141i
$285$			4.95537e12i			0.156110i
$286$	−5.10784e12	−	1.23314e13i	−0.157842	−	0.381065i
$287$	−1.04979e12	−	1.04979e12i	−0.0318239	−	0.0318239i
$288$	1.35984e13			0.404418
$289$	3.17149e13	+	1.29895e13i	0.925391	+	0.379013i
$290$	−1.92119e12			−0.0550022
$291$	9.18191e12	+	9.18191e12i	0.257942	+	0.257942i
$292$	−1.52643e13	−	3.68513e13i	−0.420795	−	1.01589i
$293$		−	2.48911e13i		−	0.673398i	−0.941612	−	0.336699i	$-0.890690\pi$
$293$		−	2.48911e13i		−	0.673398i	0.941612	−	0.336699i	$-0.109310\pi$
$294$	6.63046e12	−	2.74643e12i	0.176049	−	0.0729219i
$295$	1.57830e13	−	3.81034e13i	0.411308	−	0.992986i
$296$	1.47020e13	+	6.08977e12i	0.376073	+	0.155775i
$297$	−2.44632e13	+	2.44632e13i	−0.614261	+	0.614261i
$298$	5.97865e12	−	5.97865e12i	0.147372	−	0.147372i
$299$	−1.23202e14	−	5.10318e13i	−2.98143	−	1.23495i
$300$	−1.37401e13	+	3.31714e13i	−0.326454	+	0.788129i
$301$	6.48116e12	−	2.68458e12i	0.151195	−	0.0626269i
$302$			1.08950e13i			0.249567i
$303$	−1.32087e13	−	3.18887e13i	−0.297117	−	0.717303i
$304$	−3.64491e12	−	3.64491e12i	−0.0805161	−	0.0805161i
$305$	5.09718e13			1.10581
$306$	−6.93379e12	−	1.36492e12i	−0.147742	−	0.0290829i
$307$	7.32387e13			1.53278			0.766390	−	0.642376i	$-0.222051\pi$
$307$	7.32387e13			1.53278			0.766390	+	0.642376i	$0.222051\pi$
$308$	3.35242e12	+	3.35242e12i	0.0689175	+	0.0689175i
$309$	−5.74332e12	−	1.38656e13i	−0.115982	−	0.280006i
$310$		−	2.15555e13i		−	0.427630i
$311$	−5.10087e13	+	2.11285e13i	−0.994173	+	0.411800i	−0.819657	−	0.572855i	$-0.805836\pi$
$311$	−5.10087e13	+	2.11285e13i	−0.994173	+	0.411800i	−0.174516	+	0.984654i	$0.555836\pi$
$312$	−1.30641e13	+	3.15395e13i	−0.250166	+	0.603954i
$313$	3.00073e13	+	1.24294e13i	0.564591	+	0.233861i	0.646677	−	0.762764i	$-0.276158\pi$
$313$	3.00073e13	+	1.24294e13i	0.564591	+	0.233861i	−0.0820861	+	0.996625i	$0.526158\pi$
$314$	−1.25365e13	+	1.25365e13i	−0.231772	+	0.231772i
$315$	4.06146e12	−	4.06146e12i	0.0737860	−	0.0737860i
$316$	3.78128e13	+	1.56626e13i	0.675088	+	0.279630i
$317$	−4.29914e13	+	1.03790e14i	−0.754320	+	1.82109i	−0.220756	+	0.975329i	$0.570853\pi$
$317$	−4.29914e13	+	1.03790e14i	−0.754320	+	1.82109i	−0.533563	+	0.845760i	$0.679147\pi$
$318$	−1.15104e13	+	4.76777e12i	−0.198492	+	0.0822179i
$319$			6.18978e12i			0.104912i
$320$	−1.94124e13	−	4.68656e13i	−0.323410	−	0.780781i
$321$	3.04905e13	+	3.04905e13i	0.499329	+	0.499329i
$322$	−4.12781e12			−0.0664527
$323$	5.23406e12	+	7.79977e12i	0.0828372	+	0.123443i
$324$	1.09547e13			0.170452
$325$	1.10120e14	+	1.10120e14i	1.68464	+	1.68464i
$326$	7.40085e12	+	1.78672e13i	0.111323	+	0.268757i
$327$		−	1.90899e13i		−	0.282352i
$328$	−1.21551e13	+	5.03480e12i	−0.176788	+	0.0732278i
$329$	4.22797e12	−	1.02072e13i	0.0604720	−	0.145992i
$330$	−1.61848e13	−	6.70397e12i	−0.227657	−	0.0942987i
$331$	1.49179e12	−	1.49179e12i	0.0206373	−	0.0206373i	−0.696713	−	0.717350i	$-0.745355\pi$
$331$	1.49179e12	−	1.49179e12i	0.0206373	−	0.0206373i	0.717350	+	0.696713i	$0.245355\pi$
$332$	1.58278e12	−	1.58278e12i	0.0215358	−	0.0215358i
$333$	−2.74950e13	−	1.13888e13i	−0.367968	−	0.152418i
$334$	−4.32913e12	+	1.04514e13i	−0.0569895	+	0.137585i
$335$	1.58869e14	−	6.58057e13i	2.05728	−	0.852152i
$336$		−	5.25940e12i		−	0.0669993i
$337$	−4.00701e13	−	9.67379e13i	−0.502177	−	1.21236i	−0.948296	−	0.317388i	$-0.897194\pi$
$337$	−4.00701e13	−	9.67379e13i	−0.502177	−	1.21236i	0.446119	−	0.894974i	$-0.352806\pi$
$338$	3.39282e13	+	3.39282e13i	0.418331	+	0.418331i
$339$	−6.76384e13			−0.820530
$340$	2.33038e13	+	1.15953e14i	0.278159	+	1.38404i
$341$	−6.94486e13			−0.815670
$342$	−1.36958e12	−	1.36958e12i	−0.0158286	−	0.0158286i
$343$	8.53293e12	+	2.06003e13i	0.0970466	+	0.234291i
$344$		−	6.21672e13i		−	0.695809i
$345$	−1.61701e14	+	6.69786e13i	−1.78118	+	0.737787i
$346$	−3.77541e12	+	9.11463e12i	−0.0409303	+	0.0988145i
$347$	−1.50459e13	−	6.23220e12i	−0.160548	−	0.0665011i	0.300962	−	0.953636i	$-0.402692\pi$
$347$	−1.50459e13	−	6.23220e12i	−0.160548	−	0.0665011i	−0.461510	+	0.887135i	$0.652692\pi$
$348$	5.36352e12	−	5.36352e12i	0.0563331	−	0.0563331i
$349$	−6.91792e13	+	6.91792e13i	−0.715214	+	0.715214i	−0.967621	−	0.252407i	$-0.918778\pi$
$349$	−6.91792e13	+	6.91792e13i	−0.715214	+	0.715214i	0.252407	+	0.967621i	$0.418778\pi$
$350$	4.45363e12	+	1.84475e12i	0.0453252	+	0.0187743i
$351$	7.03701e13	−	1.69889e14i	0.705016	−	1.70206i
$352$	5.90346e13	−	2.44529e13i	0.582267	−	0.241183i
$353$			9.79391e13i			0.951032i	0.879707	+	0.475516i	$0.157739\pi$
$353$			9.79391e13i			0.951032i	−0.879707	+	0.475516i	$0.842261\pi$
$354$	−5.43033e12	−	1.31100e13i	−0.0519169	−	0.125338i
$355$	−3.50896e13	−	3.50896e13i	−0.330310	−	0.330310i
$356$	1.58377e14			1.46797
$357$	−1.85108e12	+	9.40354e12i	−0.0168947	+	0.0858254i
$358$	1.51565e13			0.136220
$359$	−8.96470e13	−	8.96470e13i	−0.793444	−	0.793444i	0.188608	−	0.982052i	$-0.439602\pi$
$359$	−8.96470e13	−	8.96470e13i	−0.793444	−	0.793444i	−0.982052	+	0.188608i	$0.939602\pi$
$360$	−1.94787e13	−	4.70258e13i	−0.169784	−	0.409895i
$361$		−	1.13916e14i		−	0.977900i
$362$	2.02131e13	−	8.37256e12i	0.170898	−	0.0707882i
$363$	9.84371e12	−	2.37648e13i	0.0819733	−	0.197901i
$364$	−2.32814e13	−	9.64347e12i	−0.190964	−	0.0790998i
$365$	−1.60564e14	+	1.60564e14i	−1.29729	+	1.29729i
$366$	1.24009e13	−	1.24009e13i	0.0986976	−	0.0986976i
$367$	−1.21254e14	−	5.02252e13i	−0.950679	−	0.393784i	−0.147193	−	0.989108i	$-0.547024\pi$
$367$	−1.21254e14	−	5.02252e13i	−0.950679	−	0.393784i	−0.803486	+	0.595323i	$0.797024\pi$
$368$	6.96726e13	−	1.68205e14i	0.538145	−	1.29920i
$369$	2.27319e13	−	9.41585e12i	0.172978	−	0.0716497i
$370$		−	4.34045e13i		−	0.325406i
$371$	−7.34552e12	−	1.77337e13i	−0.0542583	−	0.130991i
$372$	6.01780e13	+	6.01780e13i	0.437977	+	0.437977i
$373$	1.51734e14			1.08814			0.544068	−	0.839041i	$-0.316883\pi$
$373$	1.51734e14			1.08814			0.544068	+	0.839041i	$0.316883\pi$
$374$	−3.25560e13	+	6.54299e12i	−0.230058	+	0.0462362i
$375$	5.35967e13			0.373221
$376$	−6.92311e13	−	6.92311e13i	−0.475081	−	0.475081i
$377$	−1.25903e13	−	3.03956e13i	−0.0851447	−	0.205558i
$378$		−	5.69203e12i		−	0.0379370i
$379$	5.54484e13	−	2.29675e13i	0.364228	−	0.150868i	−0.193061	−	0.981187i	$-0.561841\pi$
$379$	5.54484e13	−	2.29675e13i	0.364228	−	0.150868i	0.557289	+	0.830318i	$0.311841\pi$
$380$	−1.24049e13	+	2.99482e13i	−0.0803128	+	0.193892i
$381$	6.28334e13	+	2.60265e13i	0.400962	+	0.166084i
$382$	−3.94835e12	+	3.94835e12i	−0.0248352	+	0.0248352i
$383$	−5.96890e13	+	5.96890e13i	−0.370084	+	0.370084i	−0.867508	−	0.497424i	$-0.834280\pi$
$383$	−5.96890e13	+	5.96890e13i	−0.370084	+	0.370084i	0.497424	+	0.867508i	$0.334280\pi$
$384$	−9.47719e13	−	3.92558e13i	−0.579239	−	0.239929i
$385$	1.03285e13	−	2.49353e13i	0.0622308	−	0.150238i
$386$	1.80381e13	−	7.47161e12i	0.107142	−	0.0443796i
$387$			1.16262e14i			0.680814i
$388$	3.25062e13	+	7.84769e13i	0.187669	+	0.453072i
$389$	2.41154e13	+	2.41154e13i	0.137269	+	0.137269i	0.772402	−	0.635134i	$-0.219055\pi$
$389$	2.41154e13	+	2.41154e13i	0.137269	+	0.137269i	−0.635134	+	0.772402i	$0.719055\pi$
$390$	9.31135e13			0.522586
$391$	−1.83772e14	+	2.76219e14i	−1.01697	+	1.52856i
$392$	9.79850e13			0.534670
$393$	5.27033e13	+	5.27033e13i	0.283582	+	0.283582i
$394$	3.35817e13	+	8.10733e13i	0.178186	+	0.430178i
$395$		−	2.32997e14i		−	1.21917i
$396$	−7.25922e13	+	3.00687e13i	−0.374599	+	0.155164i
$397$	−5.70519e13	+	1.37735e14i	−0.290350	+	0.700967i	−0.999994	−	0.00359372i	$-0.998856\pi$
$397$	−5.70519e13	+	1.37735e14i	−0.290350	+	0.700967i	0.709643	+	0.704561i	$0.248856\pi$
$398$	−8.93073e13	−	3.69923e13i	−0.448260	−	0.185675i
$399$	−1.85740e12	+	1.85740e12i	−0.00919508	+	0.00919508i
$400$	−1.50344e14	+	1.50344e14i	−0.734101	+	0.734101i
$401$	1.93903e14	+	8.03174e13i	0.933880	+	0.386826i	0.797149	−	0.603782i	$-0.206340\pi$
$401$	1.93903e14	+	8.03174e13i	0.933880	+	0.386826i	0.136731	+	0.990608i	$0.456340\pi$
$402$	2.26413e13	−	5.46609e13i	0.107562	−	0.259677i
$403$	3.41035e14	−	1.41261e14i	1.59816	−	0.661981i
$404$		−	2.25788e14i		−	1.04377i
$405$	−2.38652e13	−	5.76158e13i	−0.108834	−	0.262748i
$406$	−7.20110e11	−	7.20110e11i	−0.00323971	−	0.00323971i
$407$	−1.39843e14			−0.620686
$408$	7.07118e13	+	4.70454e13i	0.309643	+	0.206009i
$409$	−2.01361e14			−0.869957			−0.434978	−	0.900441i	$-0.643244\pi$
$409$	−2.01361e14			−0.869957			−0.434978	+	0.900441i	$0.643244\pi$
$410$	2.53747e13	+	2.53747e13i	0.108166	+	0.108166i
$411$	7.37548e13	+	1.78060e14i	0.310213	+	0.748921i
$412$		−	9.81753e13i		−	0.407443i
$413$	2.01980e13	−	8.36630e12i	0.0827149	−	0.0342616i
$414$	2.61795e13	−	6.32028e13i	0.105794	−	0.255408i
$415$	−1.17728e13	−	4.87643e12i	−0.0469476	−	0.0194463i
$416$	−2.40158e14	+	2.40158e14i	−0.945112	+	0.945112i
$417$	−1.99253e13	+	1.99253e13i	−0.0773851	+	0.0773851i
$418$	−8.40851e12	−	3.48292e12i	−0.0322292	−	0.0133498i
$419$	−7.58688e13	+	1.83164e14i	−0.287003	+	0.692886i	−0.999965	−	0.00831584i	$-0.997353\pi$
$419$	−7.58688e13	+	1.83164e14i	−0.287003	+	0.692886i	0.712963	+	0.701202i	$0.247353\pi$
$420$	−3.05565e13	+	1.26569e13i	−0.114086	+	0.0472560i
$421$			1.80693e14i			0.665870i	0.942950	+	0.332935i	$0.108039\pi$
$421$			1.80693e14i			0.665870i	−0.942950	+	0.332935i	$0.891961\pi$
$422$	3.96344e13	+	9.56858e13i	0.144163	+	0.348040i
$423$	1.29473e14	+	1.29473e14i	0.464843	+	0.464843i
$424$	−1.70101e14			−0.602830
$425$	3.21722e14	−	2.15893e14i	1.12549	−	0.755264i
$426$	−1.70738e13			−0.0589628
$427$	1.91056e13	+	1.91056e13i	0.0651338	+	0.0651338i
$428$	1.07944e14	+	2.60599e14i	0.363293	+	0.877066i
$429$		−	2.99998e14i		−	0.996790i
$430$	−1.56657e14	+	6.48895e13i	−0.513894	+	0.212862i
$431$	−7.97756e13	+	1.92595e14i	−0.258372	+	0.623765i	−0.998831	−	0.0483366i	$-0.984608\pi$
$431$	−7.97756e13	+	1.92595e14i	−0.258372	+	0.623765i	0.740459	+	0.672101i	$0.234608\pi$
$432$	2.31945e14	+	9.60748e13i	0.741694	+	0.307220i
$433$	2.42237e14	−	2.42237e14i	0.764817	−	0.764817i	−0.212372	−	0.977189i	$-0.568119\pi$
$433$	2.42237e14	−	2.42237e14i	0.764817	−	0.764817i	0.977189	+	0.212372i	$0.0681189\pi$
$434$	8.07956e12	−	8.07956e12i	0.0251880	−	0.0251880i
$435$	−3.98939e13	−	1.65246e13i	−0.122805	−	0.0508674i
$436$	4.77883e13	−	1.15371e14i	0.145260	−	0.350688i
$437$	−8.40084e13	+	3.47974e13i	−0.252159	+	0.104448i
$438$			7.81270e13i			0.231576i
$439$	−2.33298e14	−	5.63232e14i	−0.682900	−	1.64867i	−0.758617	−	0.651537i	$-0.774125\pi$
$439$	−2.33298e14	−	5.63232e14i	−0.682900	−	1.64867i	0.0757174	−	0.997129i	$-0.475875\pi$
$440$	−1.69125e14	−	1.69125e14i	−0.488899	−	0.488899i
$441$	−1.83247e14			−0.523148
$442$	1.46561e14	−	9.83502e13i	0.413234	−	0.277302i
$443$	7.11947e14			1.98256			0.991282	−	0.131757i	$-0.0420620\pi$
$443$	7.11947e14			1.98256			0.991282	+	0.131757i	$0.0420620\pi$
$444$	1.21176e14	+	1.21176e14i	0.333280	+	0.333280i
$445$	−3.45030e14	−	8.32977e14i	−0.937297	−	2.26283i
$446$			4.15984e13i			0.111618i
$447$	1.75572e14	−	7.27243e13i	0.465333	−	0.192747i
$448$	1.02902e13	−	2.48427e13i	0.0269398	−	0.0650384i
$449$	−1.62882e14	−	6.74678e13i	−0.421228	−	0.174478i	0.161993	−	0.986792i	$-0.448208\pi$
$449$	−1.62882e14	−	6.74678e13i	−0.421228	−	0.174478i	−0.583221	+	0.812314i	$0.698208\pi$
$450$	−5.64917e13	+	5.64917e13i	−0.144316	+	0.144316i
$451$	8.17537e13	−	8.17537e13i	0.206318	−	0.206318i
$452$	−4.08777e14	−	1.69321e14i	−1.01912	−	0.422133i
$453$	−9.37101e13	+	2.26236e14i	−0.230806	+	0.557214i
$454$	−5.64022e13	+	2.33626e13i	−0.137243	+	0.0568478i
$455$			1.43456e14i			0.344871i
$456$	8.90810e12	+	2.15060e13i	0.0211582	+	0.0510804i
$457$	−1.86397e14	−	1.86397e14i	−0.437422	−	0.437422i	0.453721	−	0.891144i	$-0.350096\pi$
$457$	−1.86397e14	−	1.86397e14i	−0.437422	−	0.437422i	−0.891144	+	0.453721i	$0.850096\pi$
$458$	1.91179e14			0.443283
$459$	−3.80892e14	−	2.53412e14i	−0.872633	−	0.580573i
$460$	−1.14492e15			−2.59183
$461$	5.72366e14	+	5.72366e14i	1.28032	+	1.28032i	0.940484	+	0.339837i	$0.110372\pi$
$461$	5.72366e14	+	5.72366e14i	1.28032	+	1.28032i	0.339837	+	0.940484i	$0.389628\pi$
$462$	−3.55367e12	−	8.57932e12i	−0.00785500	−	0.0189637i
$463$			5.28154e14i			1.15363i	0.816876	+	0.576814i	$0.195704\pi$
$463$			5.28154e14i			1.15363i	−0.816876	+	0.576814i	$0.804296\pi$
$464$	4.14985e13	−	1.71892e13i	0.0895742	−	0.0371029i
$465$	1.85404e14	−	4.47605e14i	0.395483	−	0.954780i
$466$	−2.82787e13	−	1.17134e13i	−0.0596124	−	0.0246922i
$467$	1.34525e14	−	1.34525e14i	0.280259	−	0.280259i	−0.552953	−	0.833212i	$-0.686499\pi$
$467$	1.34525e14	−	1.34525e14i	0.280259	−	0.280259i	0.833212	+	0.552953i	$0.186499\pi$
$468$	2.95311e14	−	2.95311e14i	0.608034	−	0.608034i
$469$	8.42140e13	+	3.48826e13i	0.171369	+	0.0709836i
$470$	−1.02195e14	+	2.46720e14i	−0.205538	+	0.496211i
$471$	−3.68152e14	+	1.52493e14i	−0.731833	+	0.303135i
$472$		−	1.93739e14i		−	0.380660i
$473$	2.09065e14	+	5.04727e14i	0.406017	+	0.980212i
$474$	−5.66856e13	−	5.66856e13i	−0.108816	−	0.108816i
$475$	1.06191e14			0.201498
$476$	−3.47273e13	+	5.21971e13i	−0.0651378	+	0.0979057i
$477$	3.18115e14			0.589838
$478$	3.84849e12	+	3.84849e12i	0.00705403	+	0.00705403i
$479$	−1.93581e14	−	4.67346e14i	−0.350766	−	0.846824i	−0.996526	−	0.0832837i	$-0.973459\pi$
$479$	−1.93581e14	−	4.67346e14i	−0.350766	−	0.846824i	0.645760	−	0.763541i	$-0.276541\pi$
$480$			4.45766e14i			0.798509i
$481$	6.86715e14	−	2.84447e14i	1.21613	−	0.503736i
$482$	2.32079e13	−	5.60288e13i	0.0406328	−	0.0980964i
$483$	−8.57150e13	−	3.55043e13i	−0.148371	−	0.0614571i
$484$	1.18982e14	−	1.18982e14i	0.203626	−	0.203626i
$485$	3.41930e14	−	3.41930e14i	0.578573	−	0.578573i
$486$	1.44048e14	+	5.96666e13i	0.240995	+	0.0998232i
$487$	−2.71202e14	+	6.54739e14i	−0.448625	+	1.08308i	0.524212	+	0.851588i	$0.324360\pi$
$487$	−2.71202e14	+	6.54739e14i	−0.448625	+	1.08308i	−0.972837	+	0.231489i	$0.925640\pi$
$488$	2.21215e14	−	9.16301e13i	0.361830	−	0.149875i
$489$			4.34674e14i			0.703015i
$490$	−1.02276e14	−	2.46916e14i	−0.163566	−	0.394884i
$491$	1.50623e14	+	1.50623e14i	0.238200	+	0.238200i	0.816105	−	0.577904i	$-0.196129\pi$
$491$	1.50623e14	+	1.50623e14i	0.238200	+	0.238200i	−0.577904	+	0.816105i	$0.696129\pi$
$492$	−1.41681e14			−0.221566
$493$	−8.02470e13	+	1.61278e13i	−0.124100	+	0.0249411i
$494$	4.83753e13			0.0739819
$495$	3.16290e14	+	3.16290e14i	0.478363	+	0.478363i
$496$	1.92861e14	+	4.65608e14i	0.288467	+	0.696420i
$497$		−	2.63050e13i		−	0.0389115i
$498$	−4.05057e12	+	1.67780e12i	−0.00592590	+	0.00245459i
$499$	−2.11843e14	+	5.11434e14i	−0.306522	+	0.740009i	0.693291	+	0.720658i	$0.256160\pi$
$499$	−2.11843e14	+	5.11434e14i	−0.306522	+	0.740009i	−0.999813	+	0.0193510i	$0.993840\pi$
$500$	3.23916e14	+	1.34170e14i	0.463550	+	0.192009i
$501$	−1.79791e14	+	1.79791e14i	−0.254484	+	0.254484i
$502$	−1.58333e14	+	1.58333e14i	−0.221666	+	0.221666i
$503$	−1.97969e14	−	8.20013e13i	−0.274140	−	0.113553i	0.241378	−	0.970431i	$-0.422401\pi$
$503$	−1.97969e14	−	8.20013e13i	−0.274140	−	0.113553i	−0.515518	+	0.856879i	$0.672401\pi$
$504$	1.03254e13	−	2.49277e13i	0.0141429	−	0.0341439i
$505$	−1.18752e15	+	4.91888e14i	−1.60894	+	0.666444i
$506$		−	3.21458e14i		−	0.430820i
$507$	4.12703e14	+	9.96353e14i	0.547134	+	1.32090i
$508$	3.14586e14	+	3.14586e14i	0.412561	+	0.412561i
$509$	−5.46825e14			−0.709415			−0.354707	−	0.934977i	$-0.615420\pi$
$509$	−5.46825e14			−0.709415			−0.354707	+	0.934977i	$0.615420\pi$
$510$	4.47428e13	−	2.27294e14i	0.0574232	−	0.291711i
$511$	−1.20367e14			−0.152825
$512$	−5.62257e14	−	5.62257e14i	−0.706236	−	0.706236i
$513$	−4.79838e13	−	1.15843e14i	−0.0596278	−	0.143954i
$514$		−	2.68253e14i		−	0.329797i
$515$	−5.16349e14	+	2.13879e14i	−0.628064	+	0.260153i
$516$	2.56195e14	−	6.18508e14i	0.308316	−	0.744341i
$517$	7.94898e14	+	3.29257e14i	0.946484	+	0.392046i
$518$	1.62691e13	−	1.62691e13i	0.0191669	−	0.0191669i
$519$	−1.56794e14	+	1.56794e14i	−0.182772	+	0.182772i
$520$	1.17452e15	+	4.86501e14i	1.35469	+	0.561132i
$521$	2.52197e14	−	6.08858e14i	0.287828	−	0.694878i	−0.712147	−	0.702031i	$-0.752277\pi$
$521$	2.52197e14	−	6.08858e14i	0.287828	−	0.694878i	0.999974	+	0.00715301i	$0.00227689\pi$
$522$	1.55930e13	−	6.45885e12i	0.0176093	−	0.00729403i
$523$		−	7.34382e14i		−	0.820659i	−0.911937	−	0.410330i	$-0.865414\pi$
$523$		−	7.34382e14i		−	0.820659i	0.911937	−	0.410330i	$-0.134586\pi$
$524$	1.86583e14	+	4.50450e14i	0.206324	+	0.498109i
$525$	7.66134e13	+	7.66134e13i	0.0838356	+	0.0838356i
$526$	7.56147e13			0.0818813
$527$	−1.80952e14	−	9.00362e14i	−0.193912	−	0.964847i
$528$	4.09581e14			0.434364
$529$	−1.59724e15	−	1.59724e15i	−1.67635	−	1.67635i
$530$	1.77550e14	+	4.28643e14i	0.184418	+	0.445224i
$531$			3.62322e14i			0.372456i
$532$	−1.58750e13	+	6.57566e12i	−0.0161511	+	0.00668999i
$533$	−2.35170e14	+	5.67751e14i	−0.236800	+	0.571687i
$534$	−2.86596e14	−	1.18712e14i	−0.285623	−	0.118309i
$535$	1.13545e15	−	1.13545e15i	1.12001	−	1.12001i
$536$	5.71186e14	−	5.71186e14i	0.557662	−	0.557662i
$537$	3.14727e14	+	1.30364e14i	0.304142	+	0.125980i
$538$	−4.35752e13	+	1.05200e14i	−0.0416809	+	0.100627i
$539$	−7.95526e14	+	3.29518e14i	−0.753210	+	0.311990i
$540$		−	1.57878e15i		−	1.47964i
$541$	−6.83874e14	−	1.65102e15i	−0.634441	−	1.53168i	−0.833985	−	0.551787i	$-0.813946\pi$
$541$	−6.83874e14	−	1.65102e15i	−0.634441	−	1.53168i	0.199544	−	0.979889i	$-0.436054\pi$
$542$	−2.71118e14	−	2.71118e14i	−0.248979	−	0.248979i
$543$	4.91745e14			0.447035
$544$	4.70836e14	+	7.01637e14i	0.423717	+	0.631420i
$545$	−7.10899e14			−0.633326
$546$	3.49014e13	+	3.49014e13i	0.0307810	+	0.0307810i
$547$	7.77097e14	+	1.87608e15i	0.678492	+	1.63803i	0.766764	+	0.641929i	$0.221866\pi$
$547$	7.77097e14	+	1.87608e15i	0.678492	+	1.63803i	−0.0882720	+	0.996096i	$0.528134\pi$
$548$			1.26075e15i			1.08977i
$549$	−4.13705e14	+	1.71362e14i	−0.354033	+	0.146645i
$550$	−1.43662e14	+	3.46831e14i	−0.121716	+	0.293848i
$551$	−2.07261e13	−	8.58502e12i	−0.0173853	−	0.00720124i
$552$	−5.81367e14	+	5.81367e14i	−0.482820	+	0.482820i
$553$	8.73333e13	−	8.73333e13i	0.0718111	−	0.0718111i
$554$	−2.82408e14	−	1.16977e14i	−0.229918	−	0.0952351i
$555$	3.73333e14	−	9.01305e14i	0.300943	−	0.726541i
$556$	−1.70300e14	+	7.05405e13i	−0.135926	+	0.0563025i
$557$		−	4.17813e14i		−	0.330201i	−0.986277	−	0.165101i	$-0.947205\pi$
$557$		−	4.17813e14i		−	0.330201i	0.986277	−	0.165101i	$-0.0527949\pi$
$558$	7.24675e13	+	1.74952e14i	0.0567094	+	0.136909i
$559$	−2.05327e15	−	2.05327e15i	−1.59104	−	1.59104i
$560$	−1.95858e14			−0.150282
$561$	−7.32310e14	−	1.44155e14i	−0.556416	−	0.109530i
$562$	−2.92858e14			−0.220347
$563$	−7.63824e14	−	7.63824e14i	−0.569111	−	0.569111i	0.362768	−	0.931879i	$-0.381832\pi$
$563$	−7.63824e14	−	7.63824e14i	−0.569111	−	0.569111i	−0.931879	+	0.362768i	$0.881832\pi$
$564$	−4.03482e14	−	9.74093e14i	−0.297707	−	0.718729i
$565$			2.51882e15i			1.84048i
$566$	6.31316e14	−	2.61500e14i	0.456832	−	0.189226i
$567$	1.26506e13	−	3.05412e13i	0.00906575	−	0.0218867i
$568$	−2.15366e14	−	8.92075e13i	−0.152849	−	0.0633119i
$569$	1.12721e15	−	1.12721e15i	0.792299	−	0.792299i	−0.189569	−	0.981867i	$-0.560709\pi$
$569$	1.12721e15	−	1.12721e15i	0.792299	−	0.792299i	0.981867	+	0.189569i	$0.0607090\pi$
$570$	4.48956e13	−	4.48956e13i	0.0312530	−	0.0312530i
$571$	2.49729e15	+	1.03441e15i	1.72175	+	0.713173i	0.999774	+	0.0212577i	$0.00676705\pi$
$571$	2.49729e15	+	1.03441e15i	1.72175	+	0.713173i	0.721978	+	0.691916i	$0.243233\pi$
$572$	7.50995e14	−	1.81306e15i	0.512813	−	1.23804i
$573$	−1.15949e14	+	4.80277e13i	−0.0784183	+	0.0324819i
$574$			1.90222e13i			0.0127422i
$575$	1.43531e15	+	3.46515e15i	0.952297	+	2.29905i
$576$	3.15116e14	+	3.15116e14i	0.207084	+	0.207084i
$577$	5.02585e14			0.327146			0.163573	−	0.986531i	$-0.447698\pi$
$577$	5.02585e14			0.327146			0.163573	+	0.986531i	$0.447698\pi$
$578$	−1.69652e14	−	4.05021e14i	−0.109385	−	0.261141i
$579$	4.38830e14			0.280262
$580$	−1.99735e14	−	1.99735e14i	−0.126357	−	0.126357i
$581$	−2.58492e12	−	6.24055e12i	−0.00161986	−	0.00391070i
$582$		−	1.66376e14i		−	0.103280i
$583$	1.38103e15	−	5.72040e14i	0.849229	−	0.351762i
$584$	−4.08199e14	+	9.85479e14i	−0.248657	+	0.600312i
$585$	−2.19653e15	−	9.09831e14i	−1.32550	−	0.549039i
$586$	−2.25513e14	+	2.25513e14i	−0.134814	+	0.134814i
$587$	−1.90440e15	+	1.90440e15i	−1.12784	+	1.12784i	−0.137316	+	0.990527i	$0.543848\pi$
$587$	−1.90440e15	+	1.90440e15i	−1.12784	+	1.12784i	−0.990527	+	0.137316i	$0.956152\pi$
$588$	9.74863e14	+	4.03802e14i	0.571964	+	0.236915i
$589$	9.63229e13	−	2.32544e14i	0.0559881	−	0.135167i
$590$	−4.88210e14	+	2.02223e14i	−0.281139	+	0.116451i
$591$			1.97235e15i			1.12526i
$592$	3.88349e14	+	9.37557e14i	0.219509	+	0.529942i
$593$	1.82360e15	+	1.82360e15i	1.02124	+	1.02124i	0.999769	+	0.0214715i	$0.00683510\pi$
$593$	1.82360e15	+	1.82360e15i	1.02124	+	1.02124i	0.0214715	+	0.999769i	$0.493165\pi$
$594$	4.43273e14			0.245949
$595$	3.50184e14	+	6.89335e13i	0.192510	+	0.0378955i
$596$	1.24314e15			0.677117
$597$	−1.53631e15	−	1.53631e15i	−0.829123	−	0.829123i
$598$	6.53858e14	+	1.57855e15i	0.349645	+	0.844117i
$599$			1.58139e15i			0.837898i	0.908010	+	0.418949i	$0.137601\pi$
$599$			1.58139e15i			0.837898i	−0.908010	+	0.418949i	$0.862399\pi$
$600$	8.87073e14	−	3.67438e14i	0.465723	−	0.192909i
$601$	1.45478e15	−	3.51214e15i	0.756809	−	1.82710i	0.240635	−	0.970616i	$-0.422644\pi$
$601$	1.45478e15	−	3.51214e15i	0.756809	−	1.82710i	0.516174	−	0.856484i	$-0.327356\pi$
$602$	−8.30415e13	−	3.43969e13i	−0.0428070	−	0.0177312i
$603$	−1.06821e15	+	1.06821e15i	−0.545645	+	0.545645i
$604$	−1.13269e15	+	1.13269e15i	−0.573333	+	0.573333i
$605$	−8.84991e14	−	3.66575e14i	−0.443899	−	0.183869i
$606$	−1.69240e14	+	4.08582e14i	−0.0841210	+	0.203086i
$607$	6.66773e14	−	2.76186e14i	0.328428	−	0.136039i	−0.212376	−	0.977188i	$-0.568120\pi$
$607$	6.66773e14	−	2.76186e14i	0.328428	−	0.136039i	0.540804	+	0.841149i	$0.318120\pi$
$608$			2.31589e14i			0.113044i
$609$	−8.75942e12	−	2.11471e13i	−0.00423721	−	0.0102295i
$610$	−4.61803e14	−	4.61803e14i	−0.221382	−	0.221382i
$611$	−4.57316e15			−2.17265
$612$	−5.78966e14	−	8.62771e14i	−0.272596	−	0.406221i
$613$	−1.92675e15			−0.899071			−0.449535	−	0.893263i	$-0.648410\pi$
$613$	−1.92675e15			−0.899071			−0.449535	+	0.893263i	$0.648410\pi$
$614$	−6.63542e14	−	6.63542e14i	−0.306861	−	0.306861i
$615$	3.08658e14	+	7.45166e14i	0.141470	+	0.341539i
$616$		−	1.26785e14i		−	0.0575937i
$617$	5.20232e14	−	2.15487e14i	0.234223	−	0.0970182i	−0.262485	−	0.964936i	$-0.584542\pi$
$617$	5.20232e14	−	2.15487e14i	0.234223	−	0.0970182i	0.496708	+	0.867918i	$0.334542\pi$
$618$	−7.35878e13	+	1.77657e14i	−0.0328374	+	0.0792766i
$619$	8.57803e14	+	3.55313e14i	0.379393	+	0.157150i	0.564226	−	0.825620i	$-0.309175\pi$
$619$	8.57803e14	+	3.55313e14i	0.379393	+	0.157150i	−0.184834	+	0.982770i	$0.559175\pi$
$620$	2.24100e15	−	2.24100e15i	0.982400	−	0.982400i
$621$	3.13156e15	−	3.13156e15i	1.36068	−	1.36068i
$622$	6.53561e14	+	2.70714e14i	0.281475	+	0.116591i
$623$	1.82895e14	−	4.41548e14i	0.0780760	−	0.188492i
$624$	−2.01129e15	+	8.33105e14i	−0.851060	+	0.352521i
$625$			1.23564e15i			0.518266i
$626$	−1.59255e14	−	3.84477e14i	−0.0662118	−	0.159849i
$627$	−1.44647e14	−	1.44647e14i	−0.0596127	−	0.0596127i
$628$	−2.60669e15			−1.06491
$629$	−3.64368e14	−	1.81299e15i	−0.147558	−	0.734202i
$630$	−7.35935e13			−0.0295438
$631$	3.09637e15	+	3.09637e15i	1.23223	+	1.23223i	0.963106	+	0.269123i	$0.0867339\pi$
$631$	3.09637e15	+	3.09637e15i	1.23223	+	1.23223i	0.269123	+	0.963106i	$0.413266\pi$
$632$	−4.18850e14	−	1.01119e15i	−0.165240	−	0.398924i
$633$			2.32784e15i			0.910402i
$634$	1.32984e15	−	5.50838e14i	0.515595	−	0.213566i
$635$	9.69214e14	−	2.33989e15i	0.372533	−	0.899373i
$636$	−1.69235e15	−	7.00996e14i	−0.644877	−	0.267117i
$637$	3.23627e15	−	3.23627e15i	1.22258	−	1.22258i
$638$	5.60793e13	−	5.60793e13i	0.0210034	−	0.0210034i
$639$	4.02767e14	+	1.66832e14i	0.149555	+	0.0619475i
$640$	−1.46187e15	+	3.52927e15i	−0.538169	+	1.29926i
$641$	3.36717e14	−	1.39473e14i	0.122898	−	0.0509061i	−0.320387	−	0.947287i	$-0.603813\pi$
$641$	3.36717e14	−	1.39473e14i	0.122898	−	0.0509061i	0.443285	+	0.896381i	$0.353813\pi$
$642$		−	5.52486e14i		−	0.199930i
$643$	3.67518e14	+	8.87267e14i	0.131862	+	0.318342i	0.975996	−	0.217790i	$-0.0698848\pi$
$643$	3.67518e14	+	8.87267e14i	0.131862	+	0.318342i	−0.844134	+	0.536132i	$0.819885\pi$
$644$	−4.29146e14	−	4.29146e14i	−0.152663	−	0.152663i
$645$	−3.81115e15			−1.34424
$646$	2.32453e13	−	1.18086e14i	0.00812935	−	0.0412972i
$647$	2.26151e15			0.784195			0.392098	−	0.919924i	$-0.371750\pi$
$647$	2.26151e15			0.784195			0.392098	+	0.919924i	$0.371750\pi$
$648$	−2.07148e14	−	2.07148e14i	−0.0712225	−	0.0712225i
$649$	6.51534e14	+	1.57294e15i	0.222122	+	0.536250i
$650$		−	1.99536e15i		−	0.674526i
$651$	2.37268e14	−	9.82797e13i	0.0795324	−	0.0329434i
$652$	−1.08813e15	+	2.62698e15i	−0.361676	+	0.873163i
$653$	−2.22382e15	−	9.21137e14i	−0.732955	−	0.303600i	−0.0151896	−	0.999885i	$-0.504835\pi$
$653$	−2.22382e15	−	9.21137e14i	−0.732955	−	0.303600i	−0.717766	+	0.696285i	$0.754835\pi$
$654$	−1.72954e14	+	1.72954e14i	−0.0565267	+	0.0565267i
$655$	1.96265e15	−	1.96265e15i	0.636085	−	0.636085i
$656$	−7.75138e14	−	3.21073e14i	−0.249120	−	0.103189i
$657$	7.63395e14	−	1.84300e15i	0.243299	−	0.587375i
$658$	−1.30783e14	+	5.41719e13i	−0.0413340	+	0.0171211i
$659$		−	5.03063e15i		−	1.57671i	−0.615220	−	0.788356i	$-0.710933\pi$
$659$		−	5.03063e15i		−	1.57671i	0.615220	−	0.788356i	$-0.289067\pi$
$660$	−9.85672e14	−	2.37962e15i	−0.306366	−	0.739633i
$661$	−1.64670e15	−	1.64670e15i	−0.507583	−	0.507583i	0.406201	−	0.913784i	$-0.366853\pi$
$661$	−1.64670e15	−	1.64670e15i	−0.507583	−	0.507583i	−0.913784	+	0.406201i	$0.866853\pi$
$662$	−2.70311e13			−0.00826313
$663$	3.88931e15	−	7.81660e14i	1.17909	−	0.236970i
$664$	−5.98593e13			−0.0179973
$665$	6.91689e13	+	6.91689e13i	0.0206249	+	0.0206249i
$666$	1.45922e14	+	3.52287e14i	0.0431531	+	0.104181i
$667$		−	7.92359e14i		−	0.232397i
$668$	−1.53665e15	+	6.36503e14i	−0.446998	+	0.185153i
$669$	−3.57798e14	+	8.63800e14i	−0.103227	+	0.249212i
$670$	−2.03555e15	−	8.43152e14i	−0.582466	−	0.241265i
$671$	−1.48786e15	+	1.48786e15i	−0.422269	+	0.422269i
$672$	−1.67085e14	+	1.67085e14i	−0.0470333	+	0.0470333i
$673$	8.90664e13	+	3.68925e13i	0.0248674	+	0.0103004i	0.395082	−	0.918646i	$-0.370716\pi$
$673$	8.90664e13	+	3.68925e13i	0.0248674	+	0.0103004i	−0.370215	+	0.928946i	$0.620716\pi$
$674$	−5.13409e14	+	1.23948e15i	−0.142179	+	0.343249i
$675$	−4.77825e15	+	1.97922e15i	−1.31250	+	0.543654i
$676$			7.05466e15i			1.92207i
$677$	2.46345e15	+	5.94729e15i	0.665741	+	1.60724i	0.788663	+	0.614825i	$0.210773\pi$
$677$	2.46345e15	+	5.94729e15i	0.665741	+	1.60724i	−0.122922	+	0.992416i	$0.539227\pi$
$678$	6.12802e14	+	6.12802e14i	0.164270	+	0.164270i
$679$	2.56329e14			0.0681575
$680$	1.75195e15	−	2.63328e15i	0.462086	−	0.694540i
$681$	−1.37215e15			−0.358999
$682$	6.29204e14	+	6.29204e14i	0.163297	+	0.163297i
$683$	−2.60150e15	−	6.28057e15i	−0.669745	−	1.61691i	−0.782036	−	0.623233i	$-0.785819\pi$
$683$	−2.60150e15	−	6.28057e15i	−0.669745	−	1.61691i	0.112291	−	0.993675i	$-0.464181\pi$
$684$		−	2.84774e14i		−	0.0727264i
$685$	6.63087e15	−	2.74660e15i	1.67986	−	0.695820i
$686$	1.09330e14	−	2.63947e14i	0.0274763	−	0.0663336i
$687$	3.96989e15	+	1.64438e15i	0.989728	+	0.409959i
$688$	2.80329e15	−	2.80329e15i	0.693315	−	0.693315i
$689$	−5.61813e15	+	5.61813e15i	−1.37843	+	1.37843i
$690$	2.07183e15	+	8.58181e14i	0.504295	+	0.208886i
$691$	−1.28629e15	+	3.10537e15i	−0.310605	+	0.749868i	0.689078	+	0.724688i	$0.258016\pi$
$691$	−1.28629e15	+	3.10537e15i	−0.310605	+	0.749868i	−0.999683	+	0.0251801i	$0.991984\pi$
$692$	−1.34011e15	+	5.55090e14i	−0.321037	+	0.132978i
$693$			2.37108e14i			0.0563525i
$694$	7.98516e13	+	1.92779e14i	0.0188281	+	0.0454551i
$695$	7.42011e14	+	7.42011e14i	0.173578	+	0.173578i
$696$	−2.02843e14			−0.0470770
$697$	1.27290e15	+	8.46876e14i	0.293099	+	0.195002i
$698$	1.25353e15			0.286371
$699$	−4.86463e14	−	4.86463e14i	−0.110262	−	0.110262i
$700$	2.71230e14	+	6.54807e14i	0.0609956	+	0.147256i
$701$			3.43802e15i			0.767113i	0.923517	+	0.383557i	$0.125301\pi$
$701$			3.43802e15i			0.767113i	−0.923517	+	0.383557i	$0.874699\pi$
$702$	−2.17674e15	+	9.01635e14i	−0.481895	+	0.199607i
$703$	1.93958e14	−	4.68255e14i	0.0426042	−	0.102856i
$704$	1.93465e15	+	8.01359e14i	0.421651	+	0.174654i
$705$	−4.24420e15	+	4.24420e15i	−0.917817	+	0.917817i
$706$	8.87327e14	−	8.87327e14i	0.190396	−	0.190396i
$707$	−6.29487e14	−	2.60742e14i	−0.134023	−	0.0555142i
$708$	7.98411e14	−	1.92753e15i	0.168672	−	0.407211i
$709$	4.93915e15	−	2.04586e15i	1.03538	−	0.428867i	0.200726	−	0.979648i	$-0.435670\pi$
$709$	4.93915e15	−	2.04586e15i	1.03538	−	0.428867i	0.834650	+	0.550781i	$0.185670\pi$
$710$			6.35822e14i			0.132256i
$711$	7.83314e14	+	1.89109e15i	0.161679	+	0.390327i
$712$	−2.99482e15	−	2.99482e15i	−0.613383	−	0.613383i
$713$	8.89017e15			1.80683
$714$	1.01967e14	−	6.84251e13i	0.0205645	−	0.0137999i
$715$	−1.11718e16			−2.23584
$716$	1.57573e15	+	1.57573e15i	0.312940	+	0.312940i
$717$	4.68131e13	+	1.13017e14i	0.00922596	+	0.0222734i
$718$			1.62440e15i			0.317694i
$719$	1.59773e15	−	6.61800e14i	0.310094	−	0.128445i	−0.222209	−	0.974999i	$-0.571327\pi$
$719$	1.59773e15	−	6.61800e14i	0.310094	−	0.128445i	0.532303	+	0.846554i	$0.321327\pi$
$720$	1.24217e15	−	2.99887e15i	0.239251	−	0.577602i
$721$	−2.73709e14	−	1.13374e14i	−0.0523172	−	0.0216705i
$722$	−1.03208e15	+	1.03208e15i	−0.195775	+	0.195775i
$723$	9.63835e14	−	9.63835e14i	0.181444	−	0.181444i
$724$	2.97190e15	+	1.23100e15i	0.555229	+	0.229983i
$725$	−3.54111e14	+	8.54901e14i	−0.0656570	+	0.158510i
$726$	−3.04493e14	+	1.26125e14i	−0.0560306	+	0.0232086i
$727$		−	6.21193e15i		−	1.13445i	−0.823561	−	0.567227i	$-0.808016\pi$
$727$		−	6.21193e15i		−	1.13445i	0.823561	−	0.567227i	$-0.191984\pi$
$728$	2.57886e14	+	6.22593e14i	0.0467418	+	0.112845i
$729$	3.20639e15	+	3.20639e15i	0.576787	+	0.576787i
$730$	2.90942e15			0.519434
$731$	−5.99876e15	+	4.02549e15i	−1.06296	+	0.713302i
$732$	2.57850e15			0.453478
$733$	−1.90481e15	−	1.90481e15i	−0.332491	−	0.332491i	0.521041	−	0.853532i	$-0.325544\pi$
$733$	−1.90481e15	−	1.90481e15i	−0.332491	−	0.332491i	−0.853532	+	0.521041i	$0.825544\pi$
$734$	6.43523e14	+	1.55360e15i	0.111490	+	0.269161i
$735$		−	6.00696e15i		−	1.03294i
$736$	−7.55707e15	+	3.13024e15i	−1.28981	+	0.534256i
$737$	−2.71652e15	+	6.55825e15i	−0.460194	+	1.11101i
$738$	−2.91258e14	−	1.20643e14i	−0.0489742	−	0.0202858i
$739$	1.51829e15	−	1.51829e15i	0.253402	−	0.253402i	−0.568962	−	0.822364i	$-0.692655\pi$
$739$	1.51829e15	−	1.51829e15i	0.253402	−	0.253402i	0.822364	+	0.568962i	$0.192655\pi$
$740$	4.51253e15	−	4.51253e15i	0.747559	−	0.747559i
$741$	1.00452e15	+	4.16088e14i	0.165181	+	0.0684203i
$742$	−9.41163e13	+	2.27217e14i	−0.0153619	+	0.0370868i
$743$	−3.32646e15	+	1.37786e15i	−0.538944	+	0.223238i	−0.635515	−	0.772088i	$-0.719212\pi$
$743$	−3.32646e15	+	1.37786e15i	−0.538944	+	0.223238i	0.0965714	+	0.995326i	$0.469212\pi$
$744$		−	2.27587e15i		−	0.366013i
$745$	−2.70822e15	−	6.53823e15i	−0.432339	−	1.04376i
$746$	−1.37471e15	−	1.37471e15i	−0.217844	−	0.217844i
$747$	1.11946e14			0.0176094
$748$	−4.06490e15	−	2.70443e15i	−0.634733	−	0.422295i
$749$	8.51194e14			0.131941
$750$	−4.85585e14	−	4.85585e14i	−0.0747186	−	0.0747186i
$751$	−1.16042e15	−	2.80151e15i	−0.177254	−	0.427929i	0.810135	−	0.586244i	$-0.199394\pi$
$751$	−1.16042e15	−	2.80151e15i	−0.177254	−	0.427929i	−0.987389	+	0.158315i	$0.949394\pi$
$752$		−	6.24363e15i		−	0.946758i
$753$	−4.64967e15	+	1.92596e15i	−0.699922	+	0.289917i
$754$	−1.61316e14	+	3.89451e14i	−0.0241066	+	0.0581984i
$755$	8.42494e15	+	3.48973e15i	1.24985	+	0.517706i
$756$	5.91769e14	−	5.91769e14i	0.0871530	−	0.0871530i
$757$	6.19273e14	−	6.19273e14i	0.0905430	−	0.0905430i	−0.660385	−	0.750928i	$-0.729607\pi$
$757$	6.19273e14	−	6.19273e14i	0.0905430	−	0.0905430i	0.750928	+	0.660385i	$0.229607\pi$
$758$	−7.10447e14	−	2.94277e14i	−0.103122	−	0.0427145i
$759$	2.76494e15	−	6.67514e15i	0.398433	−	0.961902i
$760$	8.00876e14	−	3.31734e14i	0.114575	−	0.0474586i
$761$		−	9.19588e15i		−	1.30610i	−0.757313	−	0.653052i	$-0.773488\pi$
$761$		−	9.19588e15i		−	1.30610i	0.757313	−	0.653052i	$-0.226512\pi$
$762$	−3.33471e14	−	8.05069e14i	−0.0470224	−	0.113522i
$763$	−2.66464e14	−	2.66464e14i	−0.0373038	−	0.0373038i
$764$	−8.20977e14			−0.114108
$765$	−3.27641e15	+	4.92463e15i	−0.452127	+	0.679573i
$766$	1.08156e15			0.148181
$767$	−6.39886e15	−	6.39886e15i	−0.870419	−	0.870419i
$768$	−5.64613e14	−	1.36310e15i	−0.0762542	−	0.184094i
$769$			3.65462e15i			0.490058i	0.969516	+	0.245029i	$0.0787975\pi$
$769$			3.65462e15i			0.490058i	−0.969516	+	0.245029i	$0.921203\pi$
$770$	−3.19490e14	+	1.32337e14i	−0.0425362	+	0.0176191i
$771$	2.30731e15	−	5.57033e15i	0.305004	−	0.736346i
$772$	2.65210e15	+	1.09854e15i	0.348092	+	0.144185i
$773$	−4.82706e15	+	4.82706e15i	−0.629065	+	0.629065i	−0.947833	−	0.318768i	$-0.896731\pi$
$773$	−4.82706e15	+	4.82706e15i	−0.629065	+	0.629065i	0.318768	+	0.947833i	$0.396731\pi$
$774$	1.05333e15	−	1.05333e15i	0.136298	−	0.136298i
$775$	−9.59188e15	−	3.97309e15i	−1.23238	−	0.510468i
$776$	8.69283e14	−	2.09864e15i	0.110898	−	0.267730i
$777$	4.77768e14	−	1.97898e14i	0.0605203	−	0.0250683i
$778$		−	4.36970e14i		−	0.0549622i
$779$	1.60357e14	+	3.87136e14i	0.0200277	+	0.0483513i
$780$	9.68050e15	+	9.68050e15i	1.20054	+	1.20054i
$781$	2.04853e15			0.252267
$782$	4.16751e15	−	8.37573e14i	0.509612	−	0.102420i
$783$	1.09262e15			0.132672
$784$	4.41840e15	+	4.41840e15i	0.532755	+	0.532755i
$785$	5.67879e15	+	1.37098e16i	0.679943	+	1.64153i
$786$		−	9.54983e14i		−	0.113546i
$787$	−5.06753e15	+	2.09904e15i	−0.598323	+	0.247833i	−0.661227	−	0.750186i	$-0.729964\pi$
$787$	−5.06753e15	+	2.09904e15i	−0.598323	+	0.247833i	0.0629038	+	0.998020i	$0.479964\pi$
$788$	−4.93744e15	+	1.19200e16i	−0.578906	+	1.39760i
$789$	1.57016e15	+	6.50380e14i	0.182818	+	0.0757258i
$790$	−2.11095e15	+	2.11095e15i	−0.244078	+	0.244078i
$791$	−9.44121e14	+	9.44121e14i	−0.108407	+	0.108407i
$792$	1.94127e15	+	8.04099e14i	0.221359	+	0.0916898i
$793$	4.27994e15	−	1.03327e16i	0.484658	−	1.17007i
$794$	1.76477e15	−	7.30992e14i	0.198461	−	0.0822053i
$795$			1.04280e16i			1.16462i
$796$	−5.43890e15	−	1.31307e16i	−0.603239	−	1.45635i
$797$	−4.34473e15	−	4.34473e15i	−0.478567	−	0.478567i	0.426106	−	0.904673i	$-0.359885\pi$
$797$	−4.34473e15	−	4.34473e15i	−0.478567	−	0.478567i	−0.904673	+	0.426106i	$0.859885\pi$
$798$	3.36561e13			0.00368170
$799$	−2.19749e15	+	1.11633e16i	−0.238737	+	1.21279i
$800$	9.55248e15			1.03067
$801$	5.60078e15	+	5.60078e15i	0.600164	+	0.600164i
$802$	−1.02909e15	−	2.48444e15i	−0.109520	−	0.264404i
$803$		−	9.37372e15i		−	0.990778i
$804$	8.03669e15	−	3.32890e15i	0.843663	−	0.349456i
$805$	−1.32217e15	+	3.19199e15i	−0.137851	+	0.332801i
$806$	−4.36960e15	−	1.80995e15i	−0.452480	−	0.187423i
$807$	−1.80970e15	+	1.80970e15i	−0.186124	+	0.186124i
$808$	−4.26953e15	+	4.26953e15i	−0.436132	+	0.436132i
$809$	−2.52367e15	−	1.04534e15i	−0.256045	−	0.106057i	0.250969	−	0.967995i	$-0.419251\pi$
$809$	−2.52367e15	−	1.04534e15i	−0.256045	−	0.106057i	−0.507014	+	0.861938i	$0.669251\pi$
$810$	−3.05779e14	+	7.38217e14i	−0.0308135	+	0.0743903i
$811$	4.16211e14	−	1.72400e14i	0.0416581	−	0.0172553i	−0.361757	−	0.932272i	$-0.617823\pi$
$811$	4.16211e14	−	1.72400e14i	0.0416581	−	0.0172553i	0.403415	+	0.915017i	$0.367823\pi$
$812$		−	1.49732e14i		−	0.0148852i
$813$	−3.29788e15	−	7.96179e15i	−0.325640	−	0.786164i
$814$	1.26698e15	+	1.26698e15i	0.124261	+	0.124261i
$815$	1.61871e16			1.57689
$816$	1.06718e15	+	5.30999e15i	0.103263	+	0.513804i
$817$	−1.98001e15			−0.190303
$818$	1.82433e15	+	1.82433e15i	0.174165	+	0.174165i
$819$	−4.82287e14	−	1.16434e15i	−0.0457345	−	0.110413i
$820$			5.27614e15i			0.496981i
$821$	−6.48532e15	+	2.68631e15i	−0.606798	+	0.251344i	−0.664859	−	0.746969i	$-0.731508\pi$
$821$	−6.48532e15	+	2.68631e15i	−0.606798	+	0.251344i	0.0580606	+	0.998313i	$0.481508\pi$
$822$	9.45002e14	−	2.28144e15i	0.0878290	−	0.212038i
$823$	−2.58349e15	−	1.07012e15i	−0.238510	−	0.0987943i	0.260227	−	0.965548i	$-0.416203\pi$
$823$	−2.58349e15	−	1.07012e15i	−0.238510	−	0.0987943i	−0.498737	+	0.866753i	$0.666203\pi$
$824$	−1.85645e15	+	1.85645e15i	−0.170248	+	0.170248i
$825$	−5.96635e15	+	5.96635e15i	−0.543515	+	0.543515i
$826$	−2.58792e14	−	1.07195e14i	−0.0234186	−	0.00970031i
$827$	−6.05839e15	+	1.46262e16i	−0.544599	+	1.31478i	0.376849	+	0.926275i	$0.377008\pi$
$827$	−6.05839e15	+	1.46262e16i	−0.544599	+	1.31478i	−0.921447	+	0.388503i	$0.872992\pi$
$828$	9.29259e15	−	3.84911e15i	0.829793	−	0.343711i
$829$			1.13188e16i			1.00404i	0.864855	+	0.502021i	$0.167410\pi$
$829$			1.13188e16i			1.00404i	−0.864855	+	0.502021i	$0.832590\pi$
$830$	6.24805e13	+	1.50841e14i	0.00550573	+	0.0132920i
$831$	−4.85811e15	−	4.85811e15i	−0.425267	−	0.425267i
$832$	−1.11303e16			−0.967897
$833$	−6.34479e15	−	9.45497e15i	−0.548113	−	0.816794i
$834$	3.61046e14			0.0309849
$835$	6.69533e15	+	6.69533e15i	0.570817	+	0.570817i
$836$	−5.12086e14	−	1.23629e15i	−0.0433719	−	0.104709i
$837$			1.22591e16i			1.03150i
$838$	2.34683e15	−	9.72089e14i	0.196173	−	0.0812576i
$839$	2.25228e15	−	5.43750e15i	0.187039	−	0.451552i	−0.802348	−	0.596857i	$-0.796416\pi$
$839$	2.25228e15	−	5.43750e15i	0.187039	−	0.451552i	0.989387	+	0.145304i	$0.0464161\pi$
$840$	8.17145e14	+	3.38473e14i	0.0674160	+	0.0279246i
$841$	−8.48883e15	+	8.48883e15i	−0.695777	+	0.695777i
$842$	1.63708e15	−	1.63708e15i	0.133307	−	0.133307i
$843$	−6.08126e15	−	2.51894e15i	−0.491974	−	0.203782i
$844$	−5.82736e15	+	1.40685e16i	−0.468369	+	1.13074i
$845$	3.71038e16	−	1.53689e16i	2.96283	−	1.22724i
$846$		−	2.34604e15i		−	0.186122i
$847$	−1.94316e14	−	4.69120e14i	−0.0153161	−	0.0369765i
$848$	−7.67031e15	−	7.67031e15i	−0.600670	−	0.600670i
$849$	1.53586e16			1.19498
$850$	−4.87078e15	−	9.58811e14i	−0.376525	−	0.0741189i
$851$	1.79014e16			1.37491
$852$	−1.77507e15	−	1.77507e15i	−0.135456	−	0.135456i
$853$	−7.82106e15	−	1.88817e16i	−0.592988	−	1.43160i	−0.880603	−	0.473854i	$-0.842862\pi$
$853$	−7.82106e15	−	1.88817e16i	−0.592988	−	1.43160i	0.287615	−	0.957746i	$-0.407138\pi$
$854$		−	3.46192e14i		−	0.0260795i
$855$	−1.49776e15	+	6.20393e14i	−0.112106	+	0.0464358i
$856$	2.88664e15	−	6.96896e15i	0.214678	−	0.518277i
$857$	6.83384e14	+	2.83067e14i	0.0504975	+	0.0209168i	0.407789	−	0.913076i	$-0.366300\pi$
$857$	6.83384e14	+	2.83067e14i	0.0504975	+	0.0209168i	−0.357292	+	0.933993i	$0.616300\pi$
$858$	−2.71798e15	+	2.71798e15i	−0.199557	+	0.199557i
$859$	3.42278e15	−	3.42278e15i	0.249699	−	0.249699i	−0.571148	−	0.820847i	$-0.693502\pi$
$859$	3.42278e15	−	3.42278e15i	0.249699	−	0.249699i	0.820847	+	0.571148i	$0.193502\pi$
$860$	−2.30330e16	−	9.54057e15i	−1.66959	−	0.691565i
$861$	−1.63615e14	+	3.95001e14i	−0.0117843	+	0.0284499i
$862$	2.46768e15	−	1.02214e15i	0.176603	−	0.0731514i
$863$			9.62144e15i			0.684196i	0.939664	+	0.342098i	$0.111138\pi$
$863$			9.62144e15i			0.684196i	−0.939664	+	0.342098i	$0.888862\pi$
$864$	−4.31643e15	−	1.04208e16i	−0.305000	−	0.736334i
$865$	5.83896e15	+	5.83896e15i	0.409965	+	0.409965i
$866$	−4.38933e15			−0.306231
$867$	−3.91816e13	−	9.86958e15i	−0.00271630	−	0.684217i
$868$	1.67997e15			0.115729
$869$	6.80117e15	+	6.80117e15i	0.465559	+	0.465559i
$870$	2.11725e14	+	5.11150e14i	0.0144018	+	0.0347690i
$871$		−	3.77305e16i		−	2.55031i
$872$	−3.08526e15	+	1.27796e15i	−0.207230	+	0.0858373i
$873$	−1.62569e15	+	3.92477e15i	−0.108508	+	0.261961i
$874$	1.07638e15	+	4.45851e14i	0.0713925	+	0.0295717i
$875$	7.48122e14	−	7.48122e14i	0.0493092	−	0.0493092i
$876$	−8.12243e15	+	8.12243e15i	−0.532002	+	0.532002i
$877$	−8.96486e15	−	3.71337e15i	−0.583507	−	0.241696i	0.0713476	−	0.997452i	$-0.477270\pi$
$877$	−8.96486e15	−	3.71337e15i	−0.583507	−	0.241696i	−0.654854	+	0.755755i	$0.727270\pi$
$878$	−2.98920e15	+	7.21656e15i	−0.193346	+	0.466778i
$879$	−6.62252e15	+	2.74314e15i	−0.425681	+	0.176323i
$880$		−	1.52526e16i		−	0.974294i
$881$	−2.32651e15	−	5.61670e15i	−0.147685	−	0.356544i	0.832674	−	0.553764i	$-0.186809\pi$
$881$	−2.32651e15	−	5.61670e15i	−0.147685	−	0.356544i	−0.980359	+	0.197219i	$0.936809\pi$
$882$	1.66021e15	+	1.66021e15i	0.104734	+	0.104734i
$883$	−8.53864e15			−0.535309			−0.267655	−	0.963515i	$-0.586249\pi$
$883$	−8.53864e15			−0.535309			−0.267655	+	0.963515i	$0.586249\pi$
$884$	2.54621e16	+	5.01220e15i	1.58638	+	0.312278i
$885$	−1.18772e16			−0.735402
$886$	−6.45023e15	−	6.45023e15i	−0.396908	−	0.396908i
$887$	6.80545e14	+	1.64298e15i	0.0416176	+	0.100474i	0.943321	−	0.331880i	$-0.107683\pi$
$887$	6.80545e14	+	1.64298e15i	0.0416176	+	0.100474i	−0.901704	+	0.432354i	$0.857683\pi$
$888$		−	4.58274e15i		−	0.278518i
$889$	1.24034e15	−	5.13765e14i	0.0749171	−	0.0310317i
$890$	−4.42079e15	+	1.06727e16i	−0.265372	+	0.640664i
$891$	2.37843e15	+	9.85177e14i	0.141894	+	0.0587742i
$892$	−4.32475e15	+	4.32475e15i	−0.256422	+	0.256422i
$893$	−2.20499e15	+	2.20499e15i	−0.129934	+	0.129934i
$894$	−2.24956e15	−	9.31799e14i	−0.131747	−	0.0545715i
$895$	4.85471e15	−	1.17203e16i	0.282577	−	0.682201i
$896$	−1.87081e15	+	7.74914e14i	−0.108227	+	0.0448291i
$897$			3.84030e16i			2.20804i
$898$	8.64448e14	+	2.08696e15i	0.0493991	+	0.119260i
$899$	1.55092e15	+	1.55092e15i	0.0880869	+	0.0880869i
$900$	−1.17463e16			−0.663080
$901$	1.10145e16	+	1.64137e16i	0.617986	+	0.920918i
$902$	−1.48137e15			−0.0826093
$903$	−1.42852e15	−	1.42852e15i	−0.0791778	−	0.0791778i
$904$	4.52800e15	+	1.09316e16i	0.249448	+	0.602221i
$905$		−	1.83124e16i		−	1.00272i
$906$	2.89871e15	−	1.20068e15i	0.157761	−	0.0653468i
$907$	9.41981e15	−	2.27414e16i	0.509568	−	1.23021i	−0.434565	−	0.900641i	$-0.643098\pi$
$907$	9.41981e15	−	2.27414e16i	0.509568	−	1.23021i	0.944133	−	0.329565i	$-0.106902\pi$
$908$	−8.29270e15	−	3.43495e15i	−0.445886	−	0.184692i
$909$	7.98468e15	−	7.98468e15i	0.426733	−	0.426733i
$910$	1.29971e15	−	1.29971e15i	0.0690430	−	0.0690430i
$911$	3.64134e15	+	1.50829e15i	0.192270	+	0.0796407i	0.476741	−	0.879044i	$-0.341818\pi$
$911$	3.64134e15	+	1.50829e15i	0.192270	+	0.0796407i	−0.284471	+	0.958685i	$0.591818\pi$
$912$	−5.68075e14	+	1.37146e15i	−0.0298150	+	0.0719797i
$913$	4.85989e14	−	2.01303e14i	0.0253535	−	0.0105017i
$914$			3.37752e15i			0.175143i
$915$	−5.61737e15	−	1.35615e16i	−0.289546	−	0.699025i
$916$	1.98759e16	+	1.98759e16i	1.01836	+	1.01836i
$917$	1.47130e15			0.0749327
$918$	1.15497e15	+	5.74678e15i	0.0584703	+	0.290931i
$919$	3.10515e16			1.56260			0.781298	−	0.624158i	$-0.214558\pi$
$919$	3.10515e16			1.56260			0.781298	+	0.624158i	$0.214558\pi$
$920$	2.16499e16	+	2.16499e16i	1.08298	+	1.08298i
$921$	−8.07132e15	−	1.94859e16i	−0.401344	−	0.968930i
$922$		−	1.03713e16i		−	0.512639i
$923$	−1.00595e16	+	4.16679e15i	−0.494274	+	0.204735i
$924$	5.22489e14	−	1.26140e15i	0.0255200	−	0.0616108i
$925$	−1.93144e16	−	8.00029e15i	−0.937782	−	0.388442i
$926$	4.78507e15	−	4.78507e15i	0.230955	−	0.230955i
$927$	3.47184e15	−	3.47184e15i	0.166579	−	0.166579i
$928$	−1.86444e15	−	7.72275e14i	−0.0889270	−	0.0368348i
$929$	−3.91292e15	+	9.44662e15i	−0.185530	+	0.447909i	−0.989090	−	0.147315i	$-0.952937\pi$
$929$	−3.91292e15	+	9.44662e15i	−0.185530	+	0.447909i	0.803560	+	0.595224i	$0.202937\pi$
$930$	−5.73505e15	+	2.37553e15i	−0.270322	+	0.111971i
$931$		−	3.12080e15i		−	0.146232i
$932$	−1.72220e15	−	4.15775e15i	−0.0802224	−	0.193674i
$933$	1.12429e16	+	1.12429e16i	0.520629	+	0.520629i
$934$	−2.43759e15			−0.112215
$935$	−5.36827e15	+	2.72709e16i	−0.245680	+	1.24806i
$936$	−1.11684e16			−0.508128
$937$	1.40563e16	+	1.40563e16i	0.635773	+	0.635773i	0.949510	−	0.313737i	$-0.101581\pi$
$937$	1.40563e16	+	1.40563e16i	0.635773	+	0.635773i	−0.313737	+	0.949510i	$0.601581\pi$
$938$	−4.46942e14	−	1.07901e15i	−0.0200972	−	0.0485189i
$939$		−	9.35355e15i		−	0.418134i
$940$	−3.62748e16	+	1.50255e16i	−1.61214	+	0.667769i
$941$	−1.04817e16	+	2.53052e16i	−0.463117	+	1.11806i	0.503994	+	0.863707i	$0.331863\pi$
$941$	−1.04817e16	+	2.53052e16i	−0.463117	+	1.11806i	−0.967111	+	0.254355i	$0.918137\pi$
$942$	4.71704e15	+	1.95386e15i	0.207200	+	0.0858250i
$943$	−1.04654e16	+	1.04654e16i	−0.457025	+	0.457025i
$944$	8.73622e15	−	8.73622e15i	0.379296	−	0.379296i
$945$	−4.40158e15	−	1.82320e15i	−0.189991	−	0.0786970i
$946$	2.67869e15	−	6.46694e15i	0.114953	−	0.277522i
$947$	2.93974e15	−	1.21768e15i	0.125425	−	0.0519527i	−0.319088	−	0.947725i	$-0.603377\pi$
$947$	2.93974e15	−	1.21768e15i	0.125425	−	0.0519527i	0.444513	+	0.895772i	$0.353377\pi$
$948$		−	1.17866e16i		−	0.499968i
$949$	1.90665e16	+	4.60307e16i	0.804095	+	1.94126i
$950$	−9.62085e14	−	9.62085e14i	−0.0403398	−	0.0403398i
$951$	3.23523e16			1.34869
$952$	1.64370e15	−	3.30345e14i	0.0681269	−	0.0136919i
$953$	−4.19334e16			−1.72802			−0.864010	−	0.503475i	$-0.832055\pi$
$953$	−4.19334e16			−1.72802			−0.864010	+	0.503475i	$0.832055\pi$
$954$	−2.88212e15	−	2.88212e15i	−0.118085	−	0.118085i
$955$	1.78853e15	+	4.31790e15i	0.0728582	+	0.175895i
$956$			8.00214e14i			0.0324106i
$957$	1.64685e15	−	6.82149e14i	0.0663192	−	0.0274703i
$958$	−2.48031e15	+	5.98799e15i	−0.0993105	+	0.239757i
$959$	3.51492e15	+	1.45593e15i	0.139931	+	0.0579612i
$960$	−1.03297e16	+	1.03297e16i	−0.408880	+	0.408880i
$961$	5.65363e14	−	5.65363e14i	0.0222510	−	0.0222510i
$962$	−8.79871e15	−	3.64455e15i	−0.344315	−	0.142620i
$963$	−5.39846e15	+	1.30330e16i	−0.210051	+	0.507108i
$964$	8.23781e15	−	3.41221e15i	0.318704	−	0.132012i
$965$		−	1.63418e16i		−	0.628637i
$966$	4.54908e14	+	1.09825e15i	0.0174000	+	0.0420073i
$967$	−9.82593e15	−	9.82593e15i	−0.373704	−	0.373704i	0.495120	−	0.868824i	$-0.335124\pi$
$967$	−9.82593e15	−	9.82593e15i	−0.373704	−	0.373704i	−0.868824	+	0.495120i	$0.835124\pi$
$968$	−4.49979e15			−0.170168
$969$	1.49838e15	−	2.25215e15i	0.0563433	−	0.0846871i
$970$	−6.19577e15			−0.231660
$971$	−3.00099e16	−	3.00099e16i	−1.11573	−	1.11573i	−0.992361	−	0.123367i	$-0.960631\pi$
$971$	−3.00099e16	−	3.00099e16i	−1.11573	−	1.11573i	−0.123367	−	0.992361i	$-0.539369\pi$
$972$	8.77266e15	+	2.11791e16i	0.324315	+	0.782965i
$973$			5.56250e14i			0.0204479i
$974$	8.38902e15	−	3.47484e15i	0.306646	−	0.127017i
$975$	1.71626e16	−	4.14342e16i	0.623818	−	1.50603i
$976$	1.41070e16	+	5.84331e15i	0.509872	+	0.211196i
$977$	1.46546e16	−	1.46546e16i	0.526689	−	0.526689i	−0.392894	−	0.919584i	$-0.628526\pi$
$977$	1.46546e16	−	1.46546e16i	0.526689	−	0.526689i	0.919584	+	0.392894i	$0.128526\pi$
$978$	3.93814e15	−	3.93814e15i	0.140743	−	0.140743i
$979$	3.43860e16	+	1.42431e16i	1.22202	+	0.506175i
$980$	1.50374e16	−	3.63035e16i	0.531409	−	1.28294i
$981$	5.76992e15	−	2.38998e15i	0.202764	−	0.0839874i
$982$		−	2.72928e15i		−	0.0953750i
$983$	−9.29222e14	−	2.24334e15i	−0.0322905	−	0.0779562i	0.906912	−	0.421321i	$-0.138433\pi$
$983$	−9.29222e14	−	2.24334e15i	−0.0322905	−	0.0779562i	−0.939202	+	0.343365i	$0.888433\pi$
$984$	2.67912e15	+	2.67912e15i	0.0925803	+	0.0925803i
$985$	7.34495e16			2.52400
$986$	8.73154e14	+	5.80919e14i	0.0298379	+	0.0198515i
$987$	−3.18168e15			−0.108121
$988$	5.02931e15	+	5.02931e15i	0.169959	+	0.169959i
$989$	−2.67625e16	−	6.46105e16i	−0.899389	−	2.17132i
$990$		−	5.73117e15i		−	0.191536i
$991$	−2.82995e16	+	1.17221e16i	−0.940533	+	0.389582i	−0.799665	−	0.600447i	$-0.794990\pi$
$991$	−2.82995e16	+	1.17221e16i	−0.940533	+	0.389582i	−0.140869	+	0.990028i	$0.544990\pi$
$992$	8.66483e15	−	2.09188e16i	0.286382	−	0.691388i
$993$	−5.61307e14	−	2.32501e14i	−0.0184493	−	0.00764195i
$994$	−2.38323e14	+	2.38323e14i	−0.00779005	+	0.00779005i
$995$	−5.72114e16	+	5.72114e16i	−1.85975	+	1.85975i
$996$	−5.95547e14	−	2.46683e14i	−0.0192526	−	0.00797469i
$997$	−1.92418e15	+	4.64538e15i	−0.0618618	+	0.149348i	−0.951788	−	0.306758i	$-0.900756\pi$
$997$	−1.92418e15	+	4.64538e15i	−0.0618618	+	0.149348i	0.889926	+	0.456105i	$0.150756\pi$
$998$	6.55288e15	−	2.71429e15i	0.209515	−	0.0867838i
$999$			2.46851e16i			0.784919i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.12.d.a.15.7	yes	60
17.8	even	8	inner	17.12.d.a.8.7	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.12.d.a.8.7	✓	60	17.8	even	8	inner
17.12.d.a.15.7	yes	60	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	17.d (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-9.05999 - 9.05999i) q^{2} +(-110.206 - 266.060i) q^{3} -1883.83i q^{4} +(-9907.96 + 4104.01i) q^{5} +(-1412.04 + 3408.96i) q^{6} +(-5252.05 - 2175.47i) q^{7} +(-35622.4 + 35622.4i) q^{8} +(66619.3 - 66619.3i) q^{9} +O(q^{10})\)	\(q+(-9.05999 - 9.05999i) q^{2} +(-110.206 - 266.060i) q^{3} -1883.83i q^{4} +(-9907.96 + 4104.01i) q^{5} +(-1412.04 + 3408.96i) q^{6} +(-5252.05 - 2175.47i) q^{7} +(-35622.4 + 35622.4i) q^{8} +(66619.3 - 66619.3i) q^{9} +(126948. + 52583.7i) q^{10} +(169417. - 409009. i) q^{11} +(-501212. + 207609. i) q^{12} +2.35308e6i q^{13} +(27873.8 + 67293.2i) q^{14} +(2.18382e6 + 2.18382e6i) q^{15} -3.21261e6 q^{16} +(5.74399e6 + 1.13070e6i) q^{17} -1.20714e6 q^{18} +(1.13456e6 + 1.13456e6i) q^{19} +(7.73127e6 + 1.86649e7i) q^{20} +1.63711e6i q^{21} +(-5.24053e6 + 2.17070e6i) q^{22} +(-2.16872e7 + 5.23575e7i) q^{23} +(1.34035e7 + 5.55190e6i) q^{24} +(4.67980e7 - 4.67980e7i) q^{25} +(2.13189e7 - 2.13189e7i) q^{26} +(-7.21982e7 - 2.99055e7i) q^{27} +(-4.09822e6 + 9.89399e6i) q^{28} +(-1.29173e7 + 5.35054e6i) q^{29} -3.95708e7i q^{30} +(-6.00324e7 - 1.44931e8i) q^{31} +(1.02061e8 + 1.02061e8i) q^{32} -1.27492e8 q^{33} +(-4.17963e7 - 6.22846e7i) q^{34} +6.09652e7 q^{35} +(-1.25500e8 - 1.25500e8i) q^{36} +(-1.20882e8 - 2.91836e8i) q^{37} -2.05582e7i q^{38} +(6.26061e8 - 2.59323e8i) q^{39} +(2.06750e8 - 4.99139e8i) q^{40} +(2.41279e8 + 9.99412e7i) q^{41} +(1.48322e7 - 1.48322e7i) q^{42} +(-8.72587e8 + 8.72587e8i) q^{43} +(-7.70505e8 - 3.19153e8i) q^{44} +(-3.86655e8 + 9.33467e8i) q^{45} +(6.70844e8 - 2.77873e8i) q^{46} +1.94347e9i q^{47} +(3.54048e8 + 8.54748e8i) q^{48} +(-1.37533e9 - 1.37533e9i) q^{49} -8.47978e8 q^{50} +(-3.32185e8 - 1.65285e9i) q^{51} +4.43282e9 q^{52} +(2.38756e9 + 2.38756e9i) q^{53} +(3.83172e8 + 9.25058e8i) q^{54} +4.74773e9i q^{55} +(2.64586e8 - 1.09595e8i) q^{56} +(1.76826e8 - 4.26897e8i) q^{57} +(1.65507e8 + 6.85552e7i) q^{58} +(-2.71935e9 + 2.71935e9i) q^{59} +(4.11396e9 - 4.11396e9i) q^{60} +(-4.39113e9 - 1.81887e9i) q^{61} +(-7.69181e8 + 1.85697e9i) q^{62} +(-4.94816e8 + 2.04960e8i) q^{63} +4.73010e9i q^{64} +(-9.65708e9 - 2.33143e10i) q^{65} +(1.15507e9 + 1.15507e9i) q^{66} -1.60345e10 q^{67} +(2.13005e9 - 1.08207e10i) q^{68} +1.63203e10 q^{69} +(-5.52344e8 - 5.52344e8i) q^{70} +(1.77078e9 + 4.27503e9i) q^{71} +4.74627e9i q^{72} +(1.95618e10 - 8.10278e9i) q^{73} +(-1.54884e9 + 3.73922e9i) q^{74} +(-1.76085e10 - 7.29367e9i) q^{75} +(2.13733e9 - 2.13733e9i) q^{76} +(-1.77957e9 + 1.77957e9i) q^{77} +(-8.02157e9 - 3.32264e9i) q^{78} +(-8.31421e9 + 2.00723e10i) q^{79} +(3.18304e10 - 1.31846e10i) q^{80} +5.81510e9i q^{81} +(-1.28052e9 - 3.09145e9i) q^{82} +(8.40193e8 + 8.40193e8i) q^{83} +3.08404e9 q^{84} +(-6.15516e10 + 1.23704e10i) q^{85} +1.58112e10 q^{86} +(2.84713e9 + 2.84713e9i) q^{87} +(8.53482e9 + 2.06049e10i) q^{88} +8.40715e10i q^{89} +(1.19603e10 - 4.95411e9i) q^{90} +(5.11907e9 - 1.23585e10i) q^{91} +(9.86329e10 + 4.08551e10i) q^{92} +(-3.19445e10 + 3.19445e10i) q^{93} +(1.76078e10 - 1.76078e10i) q^{94} +(-1.58975e10 - 6.58494e9i) q^{95} +(1.59066e10 - 3.84020e10i) q^{96} +(-4.16581e10 + 1.72553e10i) q^{97} +2.49209e10i q^{98} +(-1.59614e10 - 3.85343e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 4 q^{2} - 4 q^{3} + 10120 q^{5} - 44716 q^{6} - 4 q^{7} + 8188 q^{8} + 621728 q^{9}+O(q^{10}) \) 60 * q - 4 * q^2 - 4 * q^3 + 10120 * q^5 - 44716 * q^6 - 4 * q^7 + 8188 * q^8 + 621728 * q^9	\( 60 q - 4 q^{2} - 4 q^{3} + 10120 q^{5} - 44716 q^{6} - 4 q^{7} + 8188 q^{8} + 621728 q^{9} + 1216764 q^{10} - 2477204 q^{11} + 3940328 q^{12} - 5240148 q^{14} + 268504 q^{15} - 37748744 q^{16} - 8506952 q^{17} - 49606536 q^{18} - 30493864 q^{19} - 4030468 q^{20} - 36263996 q^{22} + 41885892 q^{23} + 274044968 q^{24} - 149009884 q^{25} - 149388276 q^{26} + 372604808 q^{27} + 4552772 q^{28} - 405222844 q^{29} - 314352908 q^{31} + 158198620 q^{32} + 1579932656 q^{33} + 1442610972 q^{34} - 1930639352 q^{35} - 366488740 q^{36} - 548749688 q^{37} + 1410218272 q^{39} + 4273406456 q^{40} + 589469732 q^{41} - 2429156064 q^{42} - 1054826472 q^{43} + 1709288236 q^{44} + 1506858388 q^{45} - 5816026300 q^{46} - 9522665340 q^{48} + 5648484080 q^{49} - 1244607984 q^{50} + 11680434460 q^{51} - 8594677768 q^{52} - 778073292 q^{53} - 21008154412 q^{54} - 30926853276 q^{56} - 6110953360 q^{57} + 18118173496 q^{58} + 37531292320 q^{59} + 27234822368 q^{60} - 18404313464 q^{61} - 33465767324 q^{62} - 71416360044 q^{63} + 32319214364 q^{65} + 127830372436 q^{66} - 30146193488 q^{67} + 115331418852 q^{68} - 3167366672 q^{69} + 94186059512 q^{70} - 125576765420 q^{71} - 106477971796 q^{73} + 99841309980 q^{74} + 49903675300 q^{75} + 122143021712 q^{76} + 12932381888 q^{77} - 41324166360 q^{78} - 59932259908 q^{79} - 303074713864 q^{80} - 148956007488 q^{82} + 92931722448 q^{83} + 352647150176 q^{84} + 281879722956 q^{85} - 719170979232 q^{86} + 53292447280 q^{87} - 526424624472 q^{88} - 276922392380 q^{90} + 302957259936 q^{91} + 302729734572 q^{92} + 184432247152 q^{93} + 526721876024 q^{94} - 580598088 q^{95} - 523924088028 q^{96} - 283776169328 q^{97} - 276595143092 q^{99}+O(q^{100}) \) 60 * q - 4 * q^2 - 4 * q^3 + 10120 * q^5 - 44716 * q^6 - 4 * q^7 + 8188 * q^8 + 621728 * q^9 + 1216764 * q^10 - 2477204 * q^11 + 3940328 * q^12 - 5240148 * q^14 + 268504 * q^15 - 37748744 * q^16 - 8506952 * q^17 - 49606536 * q^18 - 30493864 * q^19 - 4030468 * q^20 - 36263996 * q^22 + 41885892 * q^23 + 274044968 * q^24 - 149009884 * q^25 - 149388276 * q^26 + 372604808 * q^27 + 4552772 * q^28 - 405222844 * q^29 - 314352908 * q^31 + 158198620 * q^32 + 1579932656 * q^33 + 1442610972 * q^34 - 1930639352 * q^35 - 366488740 * q^36 - 548749688 * q^37 + 1410218272 * q^39 + 4273406456 * q^40 + 589469732 * q^41 - 2429156064 * q^42 - 1054826472 * q^43 + 1709288236 * q^44 + 1506858388 * q^45 - 5816026300 * q^46 - 9522665340 * q^48 + 5648484080 * q^49 - 1244607984 * q^50 + 11680434460 * q^51 - 8594677768 * q^52 - 778073292 * q^53 - 21008154412 * q^54 - 30926853276 * q^56 - 6110953360 * q^57 + 18118173496 * q^58 + 37531292320 * q^59 + 27234822368 * q^60 - 18404313464 * q^61 - 33465767324 * q^62 - 71416360044 * q^63 + 32319214364 * q^65 + 127830372436 * q^66 - 30146193488 * q^67 + 115331418852 * q^68 - 3167366672 * q^69 + 94186059512 * q^70 - 125576765420 * q^71 - 106477971796 * q^73 + 99841309980 * q^74 + 49903675300 * q^75 + 122143021712 * q^76 + 12932381888 * q^77 - 41324166360 * q^78 - 59932259908 * q^79 - 303074713864 * q^80 - 148956007488 * q^82 + 92931722448 * q^83 + 352647150176 * q^84 + 281879722956 * q^85 - 719170979232 * q^86 + 53292447280 * q^87 - 526424624472 * q^88 - 276922392380 * q^90 + 302957259936 * q^91 + 302729734572 * q^92 + 184432247152 * q^93 + 526721876024 * q^94 - 580598088 * q^95 - 523924088028 * q^96 - 283776169328 * q^97 - 276595143092 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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