LMFDB - Embedded newform 69.6.e.a.58.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,6,Mod(4,69)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("69.4");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	69.e (of order $11$, degree $10$, 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:	$11.0664835671$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$10$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			58.9
Character	$\chi$	$=$	69.58
Dual form			69.6.e.a.25.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(7.27132 - 4.67299i) q^{2} +(1.28083 - 8.90839i) q^{3} +(17.7420 - 38.8495i) q^{4} +(-64.7474 + 19.0116i) q^{5} +(-32.3155 - 70.7611i) q^{6} +(-107.029 - 123.518i) q^{7} +(-13.1730 - 91.6202i) q^{8} +(-77.7189 - 22.8203i) q^{9} +O(q^{10})$	\(q+(7.27132 - 4.67299i) q^{2} +(1.28083 - 8.90839i) q^{3} +(17.7420 - 38.8495i) q^{4} +(-64.7474 + 19.0116i) q^{5} +(-32.3155 - 70.7611i) q^{6} +(-107.029 - 123.518i) q^{7} +(-13.1730 - 91.6202i) q^{8} +(-77.7189 - 22.8203i) q^{9} +(-381.958 + 440.803i) q^{10} +(-320.315 - 205.854i) q^{11} +(-323.362 - 207.812i) q^{12} +(686.300 - 792.032i) q^{13} +(-1355.44 - 397.994i) q^{14} +(86.4317 + 601.146i) q^{15} +(371.064 + 428.231i) q^{16} +(194.789 + 426.529i) q^{17} +(-671.759 + 197.246i) q^{18} +(547.898 - 1199.73i) q^{19} +(-410.157 + 2852.70i) q^{20} +(-1237.44 + 795.252i) q^{21} -3291.07 q^{22} +(2515.59 + 328.870i) q^{23} -833.062 q^{24} +(1201.87 - 772.395i) q^{25} +(1289.14 - 8966.20i) q^{26} +(-302.838 + 663.122i) q^{27} +(-6697.52 + 1966.57i) q^{28} +(-1523.56 - 3336.12i) q^{29} +(3437.62 + 3967.23i) q^{30} +(719.526 + 5004.41i) q^{31} +(7541.26 + 2214.31i) q^{32} +(-2244.10 + 2589.83i) q^{33} +(3409.54 + 2191.18i) q^{34} +(9278.13 + 5962.69i) q^{35} +(-2265.44 + 2614.46i) q^{36} +(-12986.9 - 3813.31i) q^{37} +(-1622.39 - 11283.9i) q^{38} +(-6176.70 - 7128.29i) q^{39} +(2594.76 + 5681.73i) q^{40} +(10758.2 - 3158.89i) q^{41} +(-5281.58 + 11565.1i) q^{42} +(2444.11 - 16999.2i) q^{43} +(-13680.3 + 8791.81i) q^{44} +5465.95 q^{45} +(19828.5 - 9364.02i) q^{46} -17155.4 q^{47} +(4290.12 - 2757.09i) q^{48} +(-1409.63 + 9804.18i) q^{49} +(5129.78 - 11232.7i) q^{50} +(4049.18 - 1188.95i) q^{51} +(-18593.7 - 40714.6i) q^{52} +(16322.8 + 18837.5i) q^{53} +(896.735 + 6236.93i) q^{54} +(24653.2 + 7238.82i) q^{55} +(-9906.88 + 11433.1i) q^{56} +(-9985.90 - 6417.55i) q^{57} +(-26668.0 - 17138.5i) q^{58} +(9665.15 - 11154.2i) q^{59} +(24887.7 + 7307.68i) q^{60} +(1197.82 + 8331.05i) q^{61} +(28617.5 + 33026.3i) q^{62} +(5499.46 + 12042.1i) q^{63} +(47784.7 - 14030.9i) q^{64} +(-29378.4 + 64329.7i) q^{65} +(-4215.31 + 29318.1i) q^{66} +(33887.8 - 21778.4i) q^{67} +20026.3 q^{68} +(6151.75 - 21988.6i) q^{69} +95327.9 q^{70} +(15164.0 - 9745.34i) q^{71} +(-1067.01 + 7421.24i) q^{72} +(-16496.2 + 36121.7i) q^{73} +(-112252. + 32960.1i) q^{74} +(-5341.40 - 11696.0i) q^{75} +(-36888.1 - 42571.1i) q^{76} +(8856.33 + 61597.1i) q^{77} +(-78223.2 - 22968.4i) q^{78} +(36870.9 - 42551.3i) q^{79} +(-32166.8 - 20672.3i) q^{80} +(5519.46 + 3547.14i) q^{81} +(63464.9 - 73242.4i) q^{82} +(-64883.4 - 19051.5i) q^{83} +(8940.57 + 62183.0i) q^{84} +(-20721.1 - 23913.4i) q^{85} +(-61665.1 - 135028. i) q^{86} +(-31670.9 + 9299.42i) q^{87} +(-14640.9 + 32059.1i) q^{88} +(-9630.70 + 66983.0i) q^{89} +(39744.7 - 25542.3i) q^{90} -171285. q^{91} +(57407.9 - 91894.5i) q^{92} +45502.9 q^{93} +(-124742. + 80167.1i) q^{94} +(-12666.3 + 88095.8i) q^{95} +(29385.1 - 64344.3i) q^{96} +(-108476. + 31851.5i) q^{97} +(35565.0 + 77876.5i) q^{98} +(20196.9 + 23308.4i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - 8 q^{2} + 90 q^{3} - 148 q^{4} + 6 q^{5} + 171 q^{6} + 118 q^{7} + 1616 q^{8} - 810 q^{9}+O(q^{10}) $ 100 * q - 8 * q^2 + 90 * q^3 - 148 * q^4 + 6 * q^5 + 171 * q^6 + 118 * q^7 + 1616 * q^8 - 810 * q^9	\( 100 q - 8 q^{2} + 90 q^{3} - 148 q^{4} + 6 q^{5} + 171 q^{6} + 118 q^{7} + 1616 q^{8} - 810 q^{9} - 262 q^{10} + 724 q^{11} + 1332 q^{12} + 2730 q^{13} + 328 q^{14} - 1143 q^{15} - 8596 q^{16} - 5699 q^{17} - 648 q^{18} + 1993 q^{19} + 28263 q^{20} - 1062 q^{21} - 19378 q^{22} + 9084 q^{23} + 1296 q^{24} - 4752 q^{25} - 7828 q^{26} + 7290 q^{27} - 29888 q^{28} - 37644 q^{29} + 2358 q^{30} - 2471 q^{31} + 42352 q^{32} + 1305 q^{33} + 47233 q^{34} + 9062 q^{35} - 21789 q^{36} + 1170 q^{37} - 133648 q^{38} - 24570 q^{39} + 135509 q^{40} - 8556 q^{41} - 17208 q^{42} + 39714 q^{43} + 108207 q^{44} - 44064 q^{45} + 87076 q^{46} + 56898 q^{47} + 60237 q^{48} + 35646 q^{49} + 12207 q^{50} - 48600 q^{51} - 368495 q^{52} + 11912 q^{53} - 34263 q^{54} - 231697 q^{55} + 235302 q^{56} + 4437 q^{57} - 201743 q^{58} + 116756 q^{59} + 209349 q^{60} - 191952 q^{61} - 91633 q^{62} + 9558 q^{63} + 383796 q^{64} + 120963 q^{65} + 92925 q^{66} - 7699 q^{67} - 486648 q^{68} + 9522 q^{69} + 340272 q^{70} + 60029 q^{71} + 130896 q^{72} + 110721 q^{73} - 290458 q^{74} + 48906 q^{75} + 30961 q^{76} - 325750 q^{77} + 51444 q^{78} - 267838 q^{79} - 519366 q^{80} - 65610 q^{81} - 739402 q^{82} - 236288 q^{83} - 382428 q^{84} + 72669 q^{85} + 643772 q^{86} + 62784 q^{87} + 976500 q^{88} + 455688 q^{89} - 21222 q^{90} + 267512 q^{91} + 70711 q^{92} - 12906 q^{93} + 1298755 q^{94} + 1815505 q^{95} + 461520 q^{96} + 271324 q^{97} - 1533115 q^{98} - 11745 q^{99}+O(q^{100}) \) 100 * q - 8 * q^2 + 90 * q^3 - 148 * q^4 + 6 * q^5 + 171 * q^6 + 118 * q^7 + 1616 * q^8 - 810 * q^9 - 262 * q^10 + 724 * q^11 + 1332 * q^12 + 2730 * q^13 + 328 * q^14 - 1143 * q^15 - 8596 * q^16 - 5699 * q^17 - 648 * q^18 + 1993 * q^19 + 28263 * q^20 - 1062 * q^21 - 19378 * q^22 + 9084 * q^23 + 1296 * q^24 - 4752 * q^25 - 7828 * q^26 + 7290 * q^27 - 29888 * q^28 - 37644 * q^29 + 2358 * q^30 - 2471 * q^31 + 42352 * q^32 + 1305 * q^33 + 47233 * q^34 + 9062 * q^35 - 21789 * q^36 + 1170 * q^37 - 133648 * q^38 - 24570 * q^39 + 135509 * q^40 - 8556 * q^41 - 17208 * q^42 + 39714 * q^43 + 108207 * q^44 - 44064 * q^45 + 87076 * q^46 + 56898 * q^47 + 60237 * q^48 + 35646 * q^49 + 12207 * q^50 - 48600 * q^51 - 368495 * q^52 + 11912 * q^53 - 34263 * q^54 - 231697 * q^55 + 235302 * q^56 + 4437 * q^57 - 201743 * q^58 + 116756 * q^59 + 209349 * q^60 - 191952 * q^61 - 91633 * q^62 + 9558 * q^63 + 383796 * q^64 + 120963 * q^65 + 92925 * q^66 - 7699 * q^67 - 486648 * q^68 + 9522 * q^69 + 340272 * q^70 + 60029 * q^71 + 130896 * q^72 + 110721 * q^73 - 290458 * q^74 + 48906 * q^75 + 30961 * q^76 - 325750 * q^77 + 51444 * q^78 - 267838 * q^79 - 519366 * q^80 - 65610 * q^81 - 739402 * q^82 - 236288 * q^83 - 382428 * q^84 + 72669 * q^85 + 643772 * q^86 + 62784 * q^87 + 976500 * q^88 + 455688 * q^89 - 21222 * q^90 + 267512 * q^91 + 70711 * q^92 - 12906 * q^93 + 1298755 * q^94 + 1815505 * q^95 + 461520 * q^96 + 271324 * q^97 - 1533115 * q^98 - 11745 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{10}{11}\right)$	$1$

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 $

$2$	7.27132	−	4.67299i	1.28540	−	0.826076i	0.293856	−	0.955850i	$-0.405061\pi$
$2$	7.27132	−	4.67299i	1.28540	−	0.826076i	0.991544	+	0.129773i	$0.0414249\pi$
$3$	1.28083	−	8.90839i	0.0821655	−	0.571474i
$3$	1.28083	−	8.90839i	0.0821655	−	0.571474i
$4$	17.7420	−	38.8495i	0.554436	−	1.21405i
$5$	−64.7474	+	19.0116i	−1.15824	+	0.340089i	−0.803747	−	0.594971i	$-0.797164\pi$
$5$	−64.7474	+	19.0116i	−1.15824	+	0.340089i	−0.354490	+	0.935060i	$0.615345\pi$
$6$	−32.3155	−	70.7611i	−0.366465	−	0.802447i
$7$	−107.029	−	123.518i	−0.825576	−	0.952765i	0.173912	−	0.984761i	$-0.444359\pi$
$7$	−107.029	−	123.518i	−0.825576	−	0.952765i	−0.999488	+	0.0319958i	$0.989814\pi$
$8$	−13.1730	−	91.6202i	−0.0727712	−	0.506135i
$9$	−77.7189	−	22.8203i	−0.319831	−	0.0939109i
$10$	−381.958	+	440.803i	−1.20786	+	1.39394i
$11$	−320.315	−	205.854i	−0.798170	−	0.512953i	0.0768479	−	0.997043i	$-0.475514\pi$
$11$	−320.315	−	205.854i	−0.798170	−	0.512953i	−0.875018	+	0.484090i	$0.839151\pi$
$12$	−323.362	−	207.812i	−0.648240	−	0.416598i
$13$	686.300	−	792.032i	1.12630	−	1.29982i	0.177442	−	0.984131i	$-0.443218\pi$
$13$	686.300	−	792.032i	1.12630	−	1.29982i	0.948862	−	0.315692i	$-0.102237\pi$
$14$	−1355.44	−	397.994i	−1.84825	−	0.542696i
$15$	86.4317	+	601.146i	0.0991848	+	0.689845i
$16$	371.064	+	428.231i	0.362367	+	0.418194i
$17$	194.789	+	426.529i	0.163472	+	0.357953i	0.973587	−	0.228318i	$-0.0733226\pi$
$17$	194.789	+	426.529i	0.163472	+	0.357953i	−0.810115	+	0.586271i	$0.800595\pi$
$18$	−671.759	+	197.246i	−0.488688	+	0.143492i
$19$	547.898	−	1199.73i	0.348190	−	0.762429i	−0.651802	−	0.758389i	$-0.725987\pi$
$19$	547.898	−	1199.73i	0.348190	−	0.762429i	0.999992	−	0.00404012i	$-0.00128601\pi$
$20$	−410.157	+	2852.70i	−0.229285	+	1.59471i
$21$	−1237.44	+	795.252i	−0.612314	+	0.393510i
$22$	−3291.07			−1.44971
$23$	2515.59	+	328.870i	0.991562	+	0.129630i
$23$	2515.59	+	328.870i	0.991562	+	0.129630i
$24$	−833.062			−0.295222
$25$	1201.87	−	772.395i	0.384598	−	0.247166i
$26$	1289.14	−	8966.20i	0.373997	−	2.60121i
$27$	−302.838	+	663.122i	−0.0799467	+	0.175059i
$28$	−6697.52	+	1966.57i	−1.61443	+	0.474039i
$29$	−1523.56	−	3336.12i	−0.336406	−	0.736626i	0.663528	−	0.748152i	$-0.269058\pi$
$29$	−1523.56	−	3336.12i	−0.336406	−	0.736626i	−0.999934	+	0.0115256i	$0.996331\pi$
$30$	3437.62	+	3967.23i	0.697357	+	0.804793i
$31$	719.526	+	5004.41i	0.134475	+	0.935295i	0.939621	+	0.342218i	$0.111178\pi$
$31$	719.526	+	5004.41i	0.134475	+	0.935295i	−0.805145	+	0.593077i	$0.797913\pi$
$32$	7541.26	+	2214.31i	1.30187	+	0.382265i
$33$	−2244.10	+	2589.83i	−0.358721	+	0.413986i
$34$	3409.54	+	2191.18i	0.505823	+	0.325073i
$35$	9278.13	+	5962.69i	1.28024	+	0.822759i
$36$	−2265.44	+	2614.46i	−0.291338	+	0.336222i
$37$	−12986.9	−	3813.31i	−1.55956	−	0.457928i	−0.615620	−	0.788043i	$-0.711094\pi$
$37$	−12986.9	−	3813.31i	−1.55956	−	0.457928i	−0.943941	+	0.330115i	$0.892912\pi$
$38$	−1622.39	−	11283.9i	−0.182262	−	1.26766i
$39$	−6176.70	−	7128.29i	−0.650272	−	0.750454i
$40$	2594.76	+	5681.73i	0.256417	+	0.561476i
$41$	10758.2	−	3158.89i	0.999494	−	0.293478i	0.259246	−	0.965811i	$-0.416526\pi$
$41$	10758.2	−	3158.89i	0.999494	−	0.293478i	0.740248	+	0.672333i	$0.234708\pi$
$42$	−5281.58	+	11565.1i	−0.461999	+	1.01164i
$43$	2444.11	−	16999.2i	0.201581	−	1.40203i	−0.598013	−	0.801487i	$-0.704043\pi$
$43$	2444.11	−	16999.2i	0.201581	−	1.40203i	0.799594	−	0.600541i	$-0.205048\pi$
$44$	−13680.3	+	8791.81i	−1.06528	+	0.684616i
$45$	5465.95			0.402378
$46$	19828.5	−	9364.02i	1.38164	−	0.652481i
$47$	−17155.4			−1.13281			−0.566404	−	0.824128i	$-0.691666\pi$
$47$	−17155.4			−1.13281			−0.566404	+	0.824128i	$0.691666\pi$
$48$	4290.12	−	2757.09i	0.268761	−	0.172722i
$49$	−1409.63	+	9804.18i	−0.0838715	+	0.583339i
$50$	5129.78	−	11232.7i	0.290184	−	0.635415i
$51$	4049.18	−	1188.95i	0.217992	−	0.0640083i
$52$	−18593.7	−	40714.6i	−0.953582	−	2.08805i
$53$	16322.8	+	18837.5i	0.798188	+	0.921159i	0.998280	−	0.0586185i	$-0.0186696\pi$
$53$	16322.8	+	18837.5i	0.798188	+	0.921159i	−0.200092	+	0.979777i	$0.564124\pi$
$54$	896.735	+	6236.93i	0.0418485	+	0.291063i
$55$	24653.2	+	7238.82i	1.09892	+	0.322672i
$56$	−9906.88	+	11433.1i	−0.422150	+	0.487187i
$57$	−9985.90	−	6417.55i	−0.407099	−	0.261627i
$58$	−26668.0	−	17138.5i	−1.04093	−	0.668962i
$59$	9665.15	−	11154.2i	0.361475	−	0.417165i	−0.545658	−	0.838008i	$-0.683720\pi$
$59$	9665.15	−	11154.2i	0.361475	−	0.417165i	0.907133	+	0.420843i	$0.138266\pi$
$60$	24887.7	+	7307.68i	0.892495	+	0.262060i
$61$	1197.82	+	8331.05i	0.0412162	+	0.286665i	0.999997	+	0.00251778i	$0.000801435\pi$
$61$	1197.82	+	8331.05i	0.0412162	+	0.286665i	−0.958781	+	0.284147i	$0.908289\pi$
$62$	28617.5	+	33026.3i	0.945480	+	1.09114i
$63$	5499.46	+	12042.1i	0.174570	+	0.382254i
$64$	47784.7	−	14030.9i	1.45827	−	0.428188i
$65$	−29378.4	+	64329.7i	−0.862471	+	1.88855i
$66$	−4215.31	+	29318.1i	−0.119116	+	0.828469i
$67$	33887.8	−	21778.4i	0.922267	−	0.592705i	0.00895226	−	0.999960i	$-0.497150\pi$
$67$	33887.8	−	21778.4i	0.922267	−	0.592705i	0.913314	+	0.407255i	$0.133514\pi$
$68$	20026.3			0.525206
$69$	6151.75	−	21988.6i	0.155552	−	0.556001i
$70$	95327.9			2.32528
$71$	15164.0	−	9745.34i	0.357001	−	0.229431i	−0.349830	−	0.936813i	$-0.613761\pi$
$71$	15164.0	−	9745.34i	0.357001	−	0.229431i	0.706831	+	0.707383i	$0.250124\pi$
$72$	−1067.01	+	7421.24i	−0.0242571	+	0.168712i
$73$	−16496.2	+	36121.7i	−0.362308	+	0.793343i	0.637432	+	0.770507i	$0.279997\pi$
$73$	−16496.2	+	36121.7i	−0.362308	+	0.793343i	−0.999739	+	0.0228362i	$0.992730\pi$
$74$	−112252.	+	32960.1i	−2.38294	+	0.699695i
$75$	−5341.40	−	11696.0i	−0.109648	−	0.240096i
$76$	−36888.1	−	42571.1i	−0.732575	−	0.845436i
$77$	8856.33	+	61597.1i	0.170226	+	1.18395i
$78$	−78223.2	−	22968.4i	−1.45579	−	0.427459i
$79$	36870.9	−	42551.3i	0.664685	−	0.767087i	−0.318850	−	0.947805i	$-0.603297\pi$
$79$	36870.9	−	42551.3i	0.664685	−	0.767087i	0.983535	+	0.180718i	$0.0578421\pi$
$80$	−32166.8	−	20672.3i	−0.561930	−	0.361131i
$81$	5519.46	+	3547.14i	0.0934726	+	0.0600712i
$82$	63464.9	−	73242.4i	1.04231	−	1.20290i
$83$	−64883.4	−	19051.5i	−1.03380	−	0.303552i	−0.279547	−	0.960132i	$-0.590184\pi$
$83$	−64883.4	−	19051.5i	−1.03380	−	0.303552i	−0.754257	+	0.656580i	$0.772003\pi$
$84$	8940.57	+	62183.0i	0.138251	+	0.961554i
$85$	−20721.1	−	23913.4i	−0.311075	−	0.358999i
$86$	−61665.1	−	135028.i	−0.899070	−	1.96869i
$87$	−31670.9	+	9299.42i	−0.448603	+	0.131722i
$88$	−14640.9	+	32059.1i	−0.201540	+	0.441310i
$89$	−9630.70	+	66983.0i	−0.128879	+	0.896375i	0.818099	+	0.575077i	$0.195028\pi$
$89$	−9630.70	+	66983.0i	−0.128879	+	0.896375i	−0.946978	+	0.321298i	$0.895881\pi$
$90$	39744.7	−	25542.3i	0.517217	−	0.332395i
$91$	−171285.			−2.16828
$92$	57407.9	−	91894.5i	0.707134	−	1.13193i
$93$	45502.9			0.545546
$94$	−124742.	+	80167.1i	−1.45611	+	0.935786i
$95$	−12666.3	+	88095.8i	−0.143992	+	1.00149i
$96$	29385.1	−	64344.3i	0.325423	−	0.712578i
$97$	−108476.	+	31851.5i	−1.17059	+	0.343716i	−0.808539	−	0.588442i	$-0.799742\pi$
$97$	−108476.	+	31851.5i	−1.17059	+	0.343716i	−0.362051	+	0.932158i	$0.617923\pi$
$98$	35565.0	+	77876.5i	0.374074	+	0.819108i
$99$	20196.9	+	23308.4i	0.207108	+	0.239015i
$100$	−8683.60	−	60395.8i	−0.0868360	−	0.603958i
$101$	−64071.4	−	18813.0i	−0.624972	−	0.183508i	−0.0461133	−	0.998936i	$-0.514684\pi$
$101$	−64071.4	−	18813.0i	−0.624972	−	0.183508i	−0.578859	+	0.815428i	$0.696502\pi$
$102$	23886.9	−	27567.0i	0.227332	−	0.262355i
$103$	−28193.5	−	18118.9i	−0.261852	−	0.168282i	0.403127	−	0.915144i	$-0.367923\pi$
$103$	−28193.5	−	18118.9i	−0.261852	−	0.168282i	−0.664979	+	0.746862i	$0.731560\pi$
$104$	−81606.8	−	52445.5i	−0.739849	−	0.475472i
$105$	65001.8	−	75016.0i	0.575376	−	0.664020i
$106$	206716.	+	60697.3i	1.78694	+	0.524693i
$107$	19069.3	+	132630.i	0.161018	+	1.11991i	0.896719	+	0.442601i	$0.145944\pi$
$107$	19069.3	+	132630.i	0.161018	+	1.11991i	−0.735700	+	0.677307i	$0.763147\pi$
$108$	20389.0	+	23530.1i	0.168204	+	0.194118i
$109$	−52888.6	−	115810.i	−0.426379	−	0.933640i	−0.993900	−	0.110282i	$-0.964825\pi$
$109$	−52888.6	−	115810.i	−0.426379	−	0.933640i	0.567521	−	0.823359i	$-0.307903\pi$
$110$	213088.	−	62568.3i	1.67910	−	0.493029i
$111$	−50604.5	+	110808.i	−0.389836	+	0.853622i
$112$	13179.6	−	91666.3i	0.0992792	−	0.690502i
$113$	−401.819	+	258.233i	−0.00296029	+	0.00190246i	−0.542120	−	0.840301i	$-0.682378\pi$
$113$	−401.819	+	258.233i	−0.00296029	+	0.00190246i	0.539160	+	0.842203i	$0.318742\pi$
$114$	−102600.			−0.739409
$115$	−169130.	+	26531.8i	−1.19255	+	0.187078i
$116$	−156637.			−1.08081
$117$	−71412.9	+	45894.3i	−0.482294	+	0.309952i
$118$	18155.0	−	126271.i	0.120030	−	0.834830i
$119$	31835.9	−	69711.0i	0.206087	−	0.451267i
$120$	53938.6	−	15837.8i	0.341937	−	0.100402i
$121$	−6677.13	−	14620.9i	−0.0414597	−	0.0907842i
$122$	47640.7	+	54980.3i	0.289787	+	0.334432i
$123$	−14361.2	−	99884.4i	−0.0855910	−	0.595298i
$124$	207184.	+	60834.8i	1.21005	+	0.355302i
$125$	74962.0	−	86510.7i	0.429107	−	0.495216i
$126$	96261.2	+	61863.3i	0.540163	+	0.347142i
$127$	255693.	+	164324.i	1.40673	+	0.904050i	0.999955	−	0.00947955i	$-0.00301748\pi$
$127$	255693.	+	164324.i	1.40673	+	0.904050i	0.406773	+	0.913529i	$0.366654\pi$
$128$	117189.	−	135243.i	0.632211	−	0.729610i
$129$	−148305.	−	43546.2i	−0.784659	−	0.230397i
$130$	86992.6	+	605047.i	0.451465	+	3.14001i
$131$	165899.	+	191458.i	0.844630	+	0.974754i	0.999914	−	0.0131154i	$-0.00417487\pi$
$131$	165899.	+	191458.i	0.844630	+	0.974754i	−0.155284	+	0.987870i	$0.549629\pi$
$132$	60798.7	+	133131.i	0.303710	+	0.665033i
$133$	−206830.	+	60730.7i	−1.01387	+	0.297700i
$134$	144639.	−	316715.i	0.695862	−	1.52373i
$135$	7000.97	−	48692.8i	0.0330616	−	0.229948i
$136$	36512.7	−	23465.3i	0.169276	−	0.108787i
$137$	270866.			1.23297			0.616487	−	0.787365i	$-0.288555\pi$
$137$	270866.			1.23297			0.616487	+	0.787365i	$0.288555\pi$
$138$	−58021.4	−	188633.i	−0.259352	−	0.843181i
$139$	79088.3			0.347196			0.173598	−	0.984817i	$-0.444461\pi$
$139$	79088.3			0.347196			0.173598	+	0.984817i	$0.444461\pi$
$140$	396260.	−	254661.i	1.70868	−	1.09810i
$141$	−21973.2	+	152827.i	−0.0930777	+	0.647370i
$142$	64722.7	−	141723.i	0.269362	−	0.589820i
$143$	−382875.	+	112422.i	−1.56573	+	0.459740i
$144$	−19066.3	−	41749.4i	−0.0766233	−	0.167782i
$145$	162071.	+	187040.i	0.640156	+	0.738780i
$146$	48847.1	+	339739.i	0.189652	+	1.31906i
$147$	85534.0	+	25115.0i	0.326471	+	0.0958607i
$148$	−378558.	+	436880.i	−1.42062	+	1.63949i
$149$	194947.	+	125285.i	0.719366	+	0.462308i	0.848416	−	0.529330i	$-0.177557\pi$
$149$	194947.	+	125285.i	0.719366	+	0.462308i	−0.129050	+	0.991638i	$0.541193\pi$
$150$	−93494.6	−	60085.3i	−0.339280	−	0.218042i
$151$	194281.	−	224212.i	0.693407	−	0.800234i	−0.294439	−	0.955670i	$-0.595133\pi$
$151$	194281.	−	224212.i	0.693407	−	0.800234i	0.987846	+	0.155436i	$0.0496784\pi$
$152$	−117137.	−	34394.5i	−0.411230	−	0.120748i
$153$	−5405.27	−	37594.5i	−0.0186676	−	0.129836i
$154$	352240.	+	406507.i	1.19684	+	1.38123i
$155$	−141729.	−	310343.i	−0.473838	−	1.03756i
$156$	−386517.	+	113492.i	−1.27162	+	0.373381i
$157$	−142155.	+	311276.i	−0.460270	+	1.00785i	0.527156	+	0.849768i	$0.323258\pi$
$157$	−142155.	+	311276.i	−0.460270	+	1.00785i	−0.987426	+	0.158082i	$0.949469\pi$
$158$	69258.2	−	481701.i	0.220713	−	1.53509i
$159$	188719.	−	121282.i	0.592001	−	0.380456i
$160$	−530374.			−1.63788
$161$	−228620.	−	345920.i	−0.695104	−	1.05175i
$162$	56709.6			0.169773
$163$	517452.	−	332546.i	1.52546	−	0.980354i	0.534654	−	0.845071i	$-0.320442\pi$
$163$	517452.	−	332546.i	1.52546	−	0.980354i	0.990807	−	0.135283i	$-0.0431942\pi$
$164$	68150.3	−	473996.i	0.197860	−	1.37615i
$165$	96062.9	−	210348.i	0.274692	−	0.601491i
$166$	−560815.	+	164670.i	−1.57961	+	0.463815i
$167$	130178.	+	285051.i	0.361200	+	0.790918i	0.999772	+	0.0213558i	$0.00679829\pi$
$167$	130178.	+	285051.i	0.361200	+	0.790918i	−0.638572	+	0.769562i	$0.720474\pi$
$168$	89161.9	+	102898.i	0.243728	+	0.281277i
$169$	−103467.	−	719629.i	−0.278667	−	1.93817i
$170$	−262417.	−	77052.4i	−0.696416	−	0.204486i
$171$	−69960.3	+	80738.5i	−0.182962	+	0.211150i
$172$	−617045.	−	396551.i	−1.59036	−	1.02206i
$173$	−465712.	−	299295.i	−1.18305	−	0.760298i	−0.207103	−	0.978319i	$-0.566403\pi$
$173$	−465712.	−	299295.i	−1.18305	−	0.760298i	−0.975944	+	0.218021i	$0.930040\pi$
$174$	−186833.	+	215617.i	−0.467823	+	0.539896i
$175$	−224040.	−	65784.1i	−0.553007	−	0.162377i
$176$	−30704.4	−	213554.i	−0.0747169	−	0.519667i
$177$	−86986.3	−	100388.i	−0.208698	−	0.240850i
$178$	242983.	+	532059.i	0.574813	+	1.25866i
$179$	489231.	−	143651.i	1.14125	−	0.335102i	0.344131	−	0.938922i	$-0.388174\pi$
$179$	489231.	−	143651.i	1.14125	−	0.335102i	0.797120	+	0.603820i	$0.206356\pi$
$180$	96976.6	−	212349.i	0.223093	−	0.488505i
$181$	9717.26	−	67585.0i	0.0220469	−	0.153339i	−0.975824	−	0.218557i	$-0.929865\pi$
$181$	9717.26	−	67585.0i	0.0220469	−	0.153339i	0.997871	+	0.0652175i	$0.0207741\pi$
$182$	−1.24546e6	+	800412.i	−2.78710	+	1.79116i
$183$	75750.5			0.167208
$184$	−3006.75	−	234811.i	−0.00654716	−	0.511298i
$185$	913367.			1.96208
$186$	330866.	−	212635.i	0.701245	−	0.450663i
$187$	25408.7	−	176722.i	0.0531348	−	0.369561i
$188$	−304370.	+	666478.i	−0.628069	+	1.37528i
$189$	114320.	−	33567.4i	0.232792	−	0.0683539i
$190$	319571.	+	699762.i	0.642219	+	1.40626i
$191$	464257.	+	535781.i	0.920821	+	1.06268i	0.997842	+	0.0656545i	$0.0209135\pi$
$191$	464257.	+	535781.i	0.920821	+	1.06268i	−0.0770215	+	0.997029i	$0.524541\pi$
$192$	−63788.1	−	443656.i	−0.124878	−	0.868547i
$193$	−398510.	−	117013.i	−0.770098	−	0.226121i	−0.126998	−	0.991903i	$-0.540534\pi$
$193$	−398510.	−	117013.i	−0.770098	−	0.226121i	−0.643100	+	0.765782i	$0.722352\pi$
$194$	−639923.	+	738511.i	−1.22074	+	1.40881i
$195$	535445.	+	344110.i	1.00839	+	0.648053i
$196$	355877.	+	228708.i	0.661699	+	0.425248i
$197$	234155.	−	270230.i	0.429871	−	0.496098i	−0.498948	−	0.866632i	$-0.666280\pi$
$197$	234155.	−	270230.i	0.429871	−	0.496098i	0.928819	+	0.370534i	$0.120825\pi$
$198$	255778.	+	75103.3i	0.463661	+	0.136143i
$199$	−76331.9	−	530900.i	−0.136639	−	0.950343i	−0.936627	−	0.350327i	$-0.886070\pi$
$199$	−76331.9	−	530900.i	−0.136639	−	0.950343i	0.799989	−	0.600015i	$-0.204839\pi$
$200$	−86599.2	−	99940.9i	−0.153087	−	0.176672i
$201$	−150606.	−	329780.i	−0.262937	−	0.575751i
$202$	−553797.	+	162609.i	−0.954931	+	0.280393i
$203$	−249007.	+	545249.i	−0.424103	+	0.928657i
$204$	25650.4	−	178403.i	0.0431538	−	0.300141i
$205$	−636511.	+	409060.i	−1.05784	+	0.679834i
$206$	−289673.			−0.475599
$207$	−188004.	−	82966.0i	−0.304959	−	0.134578i
$208$	593834.			0.951714
$209$	−422469.	+	271505.i	−0.669005	+	0.429943i
$210$	122099.	−	849219.i	0.191058	−	1.32884i
$211$	−382939.	+	838519.i	−0.592138	+	1.29660i	0.342003	+	0.939699i	$0.388895\pi$
$211$	−382939.	+	838519.i	−0.592138	+	1.29660i	−0.934141	+	0.356903i	$0.883833\pi$
$212$	1.02143e6	−	299918.i	1.56087	−	0.458314i
$213$	−67392.7	−	147569.i	−0.101780	−	0.222868i
$214$	758438.	+	875285.i	1.13210	+	1.30652i
$215$	164931.	+	1.14712e6i	0.243336	+	1.69244i
$216$	64744.7	+	19010.7i	0.0944212	+	0.0277246i
$217$	541126.	−	624492.i	0.780098	−	0.900281i
$218$	−925749.	−	594943.i	−1.31933	−	0.847879i
$219$	300657.	+	193221.i	0.423606	+	0.272235i
$220$	718620.	−	829331.i	1.00102	−	1.15524i
$221$	471508.	+	138447.i	0.649394	+	0.190679i
$222$	149846.	+	1.04220e6i	0.204062	+	1.41928i
$223$	−750212.	−	865791.i	−1.01023	−	1.16587i	−0.986098	−	0.166163i	$-0.946862\pi$
$223$	−750212.	−	865791.i	−1.01023	−	1.16587i	−0.0241355	−	0.999709i	$-0.507683\pi$
$224$	−533627.	−	1.16848e6i	−0.710587	−	1.55597i
$225$	−111034.	+	32602.6i	−0.146218	+	0.0429335i
$226$	−1715.03	+	3755.40i	−0.00223358	+	0.00489085i
$227$	−8505.64	+	59158.0i	−0.0109558	+	0.0761990i	−0.994566	−	0.104110i	$-0.966801\pi$
$227$	−8505.64	+	59158.0i	−0.0109558	+	0.0761990i	0.983610	+	0.180309i	$0.0577097\pi$
$228$	−426488.	+	274087.i	−0.543337	+	0.349182i
$229$	1.04919e6			1.32210			0.661051	−	0.750341i	$-0.270110\pi$
$229$	1.04919e6			1.32210			0.661051	+	0.750341i	$0.270110\pi$
$230$	−1.10582e6	+	983266.i	−1.37836	+	1.22561i
$231$	560075.			0.690583
$232$	−285587.	+	183535.i	−0.348352	+	0.223872i
$233$	105995.	−	737209.i	0.127907	−	0.889613i	−0.820294	−	0.571942i	$-0.806190\pi$
$233$	105995.	−	737209.i	0.127907	−	0.889613i	0.948201	−	0.317671i	$-0.102901\pi$
$234$	−304803.	+	667424.i	−0.363897	+	0.796824i
$235$	1.11077e6	−	326151.i	1.31206	−	0.385255i
$236$	−261855.	−	573383.i	−0.306042	−	0.670138i
$237$	−331838.	−	382961.i	−0.383756	−	0.442878i
$238$	−94269.7	−	655660.i	−0.107877	−	0.750303i
$239$	−551744.	−	162007.i	−0.624803	−	0.183459i	−0.0460203	−	0.998941i	$-0.514654\pi$
$239$	−551744.	−	162007.i	−0.624803	−	0.183459i	−0.578783	+	0.815482i	$0.696472\pi$
$240$	−225357.	+	260076.i	−0.252548	+	0.291456i
$241$	−178893.	−	114968.i	−0.198404	−	0.127507i	0.437666	−	0.899137i	$-0.355805\pi$
$241$	−178893.	−	114968.i	−0.198404	−	0.127507i	−0.636071	+	0.771631i	$0.719441\pi$
$242$	−116875.	−	75110.9i	−0.128287	−	0.0824451i
$243$	38668.9	−	44626.3i	0.0420093	−	0.0484814i
$244$	344908.	+	101274.i	0.370876	+	0.108899i
$245$	−95122.9	−	661594.i	−0.101244	−	0.704168i
$246$	−571184.	−	659181.i	−0.601781	−	0.694492i
$247$	−574202.	−	1.25733e6i	−0.598856	−	1.31131i
$248$	449027.	−	131846.i	0.463600	−	0.136125i
$249$	−252823.	+	553605.i	−0.258415	+	0.565850i
$250$	140808.	−	979344.i	0.142488	−	0.991027i
$251$	145943.	−	93791.8i	0.146217	−	0.0939681i	−0.465487	−	0.885055i	$-0.654121\pi$
$251$	145943.	−	93791.8i	0.146217	−	0.0939681i	0.611704	+	0.791087i	$0.290484\pi$
$252$	565402.			0.560862
$253$	−738082.	−	623186.i	−0.724942	−	0.612091i
$254$	2.62712e6			2.55502
$255$	−239570.	+	153962.i	−0.230718	+	0.148274i
$256$	−6674.62	+	46423.0i	−0.00636541	+	0.0442724i
$257$	294068.	−	643920.i	0.277725	−	0.608134i	−0.718443	−	0.695585i	$-0.755145\pi$
$257$	294068.	−	643920.i	0.277725	−	0.608134i	0.996169	+	0.0874518i	$0.0278724\pi$
$258$	−1.28186e6	+	376389.i	−1.19893	+	0.352036i
$259$	918967.	+	2.01226e6i	0.851237	+	1.86395i
$260$	1.97794e6	+	2.28267e6i	1.81460	+	2.09416i
$261$	42277.7	+	294048.i	0.0384158	+	0.267188i
$262$	2.10099e6	+	616906.i	1.89091	+	0.555221i
$263$	−77077.2	+	88951.8i	−0.0687126	+	0.0792986i	−0.789065	−	0.614310i	$-0.789435\pi$
$263$	−77077.2	+	88951.8i	−0.0687126	+	0.0792986i	0.720352	+	0.693608i	$0.243980\pi$
$264$	266842.	+	171489.i	0.235638	+	0.151435i
$265$	−1.41499e6	−	909359.i	−1.23777	−	0.795465i
$266$	−1.22013e6	+	1.40811e6i	−1.05731	+	1.22020i
$267$	584376.	+	171588.i	0.501665	+	0.147302i
$268$	−244842.	−	1.70291e6i	−0.208233	−	1.44829i
$269$	74903.7	+	86443.5i	0.0631136	+	0.0728369i	0.786428	−	0.617681i	$-0.211928\pi$
$269$	74903.7	+	86443.5i	0.0631136	+	0.0728369i	−0.723315	+	0.690518i	$0.757382\pi$
$270$	−176635.	−	386777.i	−0.147458	−	0.322887i
$271$	−1.31335e6	+	385636.i	−1.08632	+	0.318973i	−0.775405	−	0.631464i	$-0.782454\pi$
$271$	−1.31335e6	+	385636.i	−1.08632	+	0.318973i	−0.310917	+	0.950437i	$0.600636\pi$
$272$	−110373.	+	241684.i	−0.0904570	+	0.198073i
$273$	−219387.	+	1.52587e6i	−0.178158	+	1.23911i
$274$	1.96956e6	−	1.26576e6i	1.58486	−	1.01853i
$275$	−543978.			−0.433760
$276$	−745102.	−	629113.i	−0.588767	−	0.497114i
$277$	−1.69853e6			−1.33007			−0.665035	−	0.746812i	$-0.731584\pi$
$277$	−1.69853e6			−1.33007			−0.665035	+	0.746812i	$0.731584\pi$
$278$	575076.	−	369579.i	0.446286	−	0.286811i
$279$	58281.6	−	405357.i	0.0448251	−	0.311765i
$280$	424083.	−	928611.i	0.323263	−	0.707846i
$281$	81912.7	−	24051.7i	0.0618850	−	0.0181711i	−0.250644	−	0.968079i	$-0.580642\pi$
$281$	81912.7	−	24051.7i	0.0618850	−	0.0181711i	0.312529	+	0.949908i	$0.398824\pi$
$282$	554385.	+	1.21393e6i	0.415135	+	0.909018i
$283$	951741.	+	1.09837e6i	0.706403	+	0.815233i	0.989603	−	0.143828i	$-0.0459413\pi$
$283$	951741.	+	1.09837e6i	0.706403	+	0.815233i	−0.283199	+	0.959061i	$0.591396\pi$
$284$	−109561.	−	762016.i	−0.0806050	−	0.560620i
$285$	768569.	+	225672.i	0.560493	+	0.164576i
$286$	−2.25866e6	+	2.60663e6i	−1.63281	+	1.88436i
$287$	−1.54162e6	−	990741.i	−1.10477	−	0.709995i
$288$	−535567.	−	344188.i	−0.380481	−	0.244520i
$289$	785825.	−	906890.i	0.553453	−	0.638719i
$290$	2.05251e6	+	602671.i	1.43315	+	0.420809i
$291$	144806.	+	1.00714e6i	0.100243	+	0.697203i
$292$	1.11063e6	+	1.28174e6i	0.762278	+	0.879716i
$293$	−95542.9	−	209210.i	−0.0650174	−	0.142368i	0.874334	−	0.485325i	$-0.161299\pi$
$293$	−95542.9	−	209210.i	−0.0650174	−	0.142368i	−0.939351	+	0.342957i	$0.888571\pi$
$294$	739307.	−	217080.i	0.498835	−	0.146471i
$295$	−413735.	+	905953.i	−0.276801	+	0.606109i
$296$	−178299.	+	1.24010e6i	−0.118282	+	0.822672i
$297$	233510.	−	150068.i	0.153608	−	0.0987178i
$298$	2.00297e6			1.30657
$299$	1.98692e6	−	1.76672e6i	1.28530	−	1.14285i
$300$	−549152.			−0.352281
$301$	−2.36130e6	+	1.51751e6i	−1.50222	+	0.965421i
$302$	364937.	−	2.53819e6i	0.230251	−	1.60143i
$303$	−249659.	+	546676.i	−0.156221	+	0.342077i
$304$	717066.	−	210550.i	0.445016	−	0.130668i
$305$	−235942.	−	516641.i	−0.145230	−	0.318009i
$306$	−214982.	−	248103.i	−0.131250	−	0.151471i
$307$	−126658.	−	880928.i	−0.0766986	−	0.533451i	−0.991557	−	0.129675i	$-0.958607\pi$
$307$	−126658.	−	880928.i	−0.0766986	−	0.533451i	0.914858	−	0.403776i	$-0.132302\pi$
$308$	2.55014e6	+	748790.i	1.53175	+	0.449762i
$309$	−197521.	+	227952.i	−0.117684	+	0.135815i
$310$	−2.48079e6	−	1.59431e6i	−1.46617	−	0.942253i
$311$	−786682.	−	505570.i	−0.461210	−	0.296401i	0.289327	−	0.957230i	$-0.406569\pi$
$311$	−786682.	−	505570.i	−0.461210	−	0.296401i	−0.750537	+	0.660829i	$0.770205\pi$
$312$	−571730.	+	659812.i	−0.332510	+	0.383737i
$313$	2.02776e6	+	595404.i	1.16992	+	0.343519i	0.808279	−	0.588799i	$-0.200399\pi$
$313$	2.02776e6	+	595404.i	1.16992	+	0.343519i	0.361639	+	0.932318i	$0.382217\pi$
$314$	420936.	+	2.92767e6i	0.240930	+	1.67571i
$315$	−585016.	−	675144.i	−0.332194	−	0.383372i
$316$	−998932.	−	2.18736e6i	−0.562754	−	1.23226i
$317$	−1.88629e6	+	553863.i	−1.05429	+	0.309567i	−0.762549	−	0.646931i	$-0.776052\pi$
$317$	−1.88629e6	+	553863.i	−1.05429	+	0.309567i	−0.291740	+	0.956498i	$0.594234\pi$
$318$	805485.	−	1.76377e6i	0.446673	−	0.978077i
$319$	−198736.	+	1.38224e6i	−0.109345	+	0.760514i
$320$	−2.82719e6	+	1.81692e6i	−1.54340	+	0.991885i
$321$	1.20595e6			0.653228
$322$	−3.27885e6	−	1.44695e6i	−1.76231	−	0.777705i
$323$	618444.			0.329833
$324$	235731.	−	151495.i	0.124754	−	0.0801744i
$325$	213081.	−	1.48201e6i	0.111902	−	0.778294i
$326$	2.20857e6	−	4.83610e6i	1.15098	−	2.52029i
$327$	−1.09942e6	+	322819.i	−0.568585	+	0.166951i
$328$	−431137.	−	944058.i	−0.221274	−	0.484522i
$329$	1.83613e6	+	2.11900e6i	0.935218	+	1.07930i
$330$	−284453.	−	1.97841e6i	−0.143789	−	1.00007i
$331$	2.70646e6	+	794689.i	1.35779	+	0.398682i	0.877983	−	0.478693i	$-0.158889\pi$
$331$	2.70646e6	+	794689.i	1.35779	+	0.398682i	0.479805	+	0.877375i	$0.340707\pi$
$332$	−1.89130e6	+	2.18267e6i	−0.941704	+	1.08678i
$333$	922309.	+	592732.i	0.455791	+	0.292919i
$334$	2.27861e6	+	1.46437e6i	1.11765	+	0.718267i
$335$	−1.78011e6	+	2.05435e6i	−0.866631	+	1.00015i
$336$	−799719.	−	234819.i	−0.386446	−	0.113471i
$337$	−204262.	−	1.42068e6i	−0.0979747	−	0.681429i	−0.978321	−	0.207096i	$-0.933599\pi$
$337$	−204262.	−	1.42068e6i	−0.0979747	−	0.681429i	0.880346	−	0.474332i	$-0.157310\pi$
$338$	−4.11517e6	−	4.74915e6i	−1.95928	−	2.26112i
$339$	1785.78	+	3910.32i	0.000843974	+	0.00184805i
$340$	−1.29665e6	+	380732.i	−0.608312	+	0.178617i
$341$	799703.	−	1.75111e6i	0.372428	−	0.815504i
$342$	−131413.	+	914000.i	−0.0607539	+	0.422553i
$343$	−948976.	+	609870.i	−0.435532	+	0.279899i
$344$	−1.58966e6			−0.724285
$345$	19728.1	+	1.54066e6i	0.00892357	+	0.696882i
$346$	−4.78494e6			−2.14875
$347$	−2.72864e6	+	1.75359e6i	−1.21653	+	0.781815i	−0.981739	−	0.190231i	$-0.939076\pi$
$347$	−2.72864e6	+	1.75359e6i	−1.21653	+	0.781815i	−0.234789	+	0.972046i	$0.575440\pi$
$348$	−200626.	+	1.39539e6i	−0.0888056	+	0.617656i
$349$	−748102.	+	1.63811e6i	−0.328774	+	0.719914i	−0.999768	−	0.0215486i	$-0.993140\pi$
$349$	−748102.	+	1.63811e6i	−0.328774	+	0.719914i	0.670994	+	0.741463i	$0.265868\pi$
$350$	−1.93648e6	+	568600.i	−0.844971	+	0.248106i
$351$	317376.	+	694957.i	0.137501	+	0.301086i
$352$	−1.95975e6	−	2.26168e6i	−0.843033	−	0.972912i
$353$	243933.	+	1.69659e6i	0.104192	+	0.724670i	0.973215	+	0.229898i	$0.0738393\pi$
$353$	243933.	+	1.69659e6i	0.104192	+	0.724670i	−0.869023	+	0.494772i	$0.835252\pi$
$354$	−1.10162e6	−	323464.i	−0.467221	−	0.137188i
$355$	−796559.	+	919278.i	−0.335465	+	0.387147i
$356$	2.43139e6	+	1.56256e6i	1.01678	+	0.653448i
$357$	−580236.	−	372895.i	−0.240954	−	0.154852i
$358$	2.88607e6	−	3.33071e6i	1.19014	−	1.37350i
$359$	2.99176e6	+	878461.i	1.22515	+	0.359738i	0.829419	−	0.558627i	$-0.188672\pi$
$359$	2.99176e6	+	878461.i	1.22515	+	0.359738i	0.395735	+	0.918365i	$0.370490\pi$
$360$	−72003.0	−	500792.i	−0.0292816	−	0.203658i
$361$	482340.	+	556650.i	0.194799	+	0.224809i
$362$	−245167.	−	536841.i	−0.0983311	−	0.215315i
$363$	−138801.	+	40755.6i	−0.0552873	+	0.0162338i
$364$	−3.03892e6	+	6.65431e6i	−1.20217	+	2.63239i
$365$	381358.	−	2.65241e6i	0.149831	−	1.04210i
$366$	550806.	−	353981.i	0.214929	−	0.138127i
$367$	−5485.86			−0.00212608			−0.00106304	−	0.999999i	$-0.500338\pi$
$367$	−5485.86			−0.00212608			−0.00106304	+	0.999999i	$0.500338\pi$
$368$	792612.	+	1.19928e6i	0.305099	+	0.461639i
$369$	−908203.			−0.347230
$370$	6.64138e6	−	4.26816e6i	2.52205	−	1.62083i
$371$	579762.	−	4.03233e6i	0.218683	−	1.52097i
$372$	807309.	−	1.76776e6i	0.302470	−	0.662317i
$373$	−854206.	+	250818.i	−0.317900	+	0.0933439i	−0.436790	−	0.899564i	$-0.643885\pi$
$373$	−854206.	+	250818.i	−0.317900	+	0.0933439i	0.118890	+	0.992907i	$0.462066\pi$
$374$	−641064.	−	1.40373e6i	−0.236986	−	0.518927i
$375$	−674658.	−	778597.i	−0.247745	−	0.285913i
$376$	225988.	+	1.57178e6i	0.0824358	+	0.573354i
$377$	−3.68793e6	−	1.08288e6i	−1.33638	−	0.392396i
$378$	674398.	−	778296.i	0.242765	−	0.280166i
$379$	781151.	+	502015.i	0.279342	+	0.179522i	0.672809	−	0.739817i	$-0.265088\pi$
$379$	781151.	+	502015.i	0.279342	+	0.179522i	−0.393466	+	0.919339i	$0.628724\pi$
$380$	3.19775e6	+	2.05507e6i	1.13602	+	0.730075i
$381$	1.79137e6	−	2.06735e6i	0.632225	−	0.729627i
$382$	5.87947e6	+	1.72637e6i	2.06148	+	0.605306i
$383$	−391639.	−	2.72391e6i	−0.136423	−	0.948845i	−0.936929	−	0.349520i	$-0.886345\pi$
$383$	−391639.	−	2.72391e6i	−0.136423	−	0.948845i	0.800506	−	0.599325i	$-0.204564\pi$
$384$	−1.05470e6	−	1.21719e6i	−0.365007	−	0.421241i
$385$	−1.74448e6	−	3.81988e6i	−0.599811	−	1.31340i
$386$	−3.44450e6	+	1.01140e6i	−1.17668	+	0.345504i
$387$	−577881.	+	1.26538e6i	−0.196138	+	0.429481i
$388$	−687166.	+	4.77935e6i	−0.231730	+	1.61172i
$389$	4.50142e6	−	2.89289e6i	1.50826	−	0.969298i	0.514530	−	0.857472i	$-0.327966\pi$
$389$	4.50142e6	−	2.89289e6i	1.50826	−	0.969298i	0.993728	−	0.111826i	$-0.0356699\pi$
$390$	5.50142e6			1.83153
$391$	349737.	+	1.13703e6i	0.115691	+	0.376123i
$392$	916830.			0.301352
$393$	1.91807e6	−	1.23267e6i	0.626446	−	0.402592i
$394$	439837.	−	3.05913e6i	0.142742	−	0.992790i
$395$	−1.57833e6	+	3.45606e6i	−0.508985	+	1.11452i
$396$	1.26385e6	−	371101.i	0.405003	−	0.118920i
$397$	−1.19592e6	−	2.61870e6i	−0.380825	−	0.833891i	−0.998860	−	0.0477400i	$-0.984798\pi$
$397$	−1.19592e6	−	2.61870e6i	−0.380825	−	0.833891i	0.618035	−	0.786151i	$-0.287929\pi$
$398$	−3.03593e6	−	3.50365e6i	−0.960691	−	1.10870i
$399$	276098.	+	1.92031e6i	0.0868223	+	0.603863i
$400$	776734.	+	228070.i	0.242729	+	0.0712717i
$401$	−4.16180e6	+	4.80297e6i	−1.29247	+	1.49159i	−0.523973	+	0.851735i	$0.675551\pi$
$401$	−4.16180e6	+	4.80297e6i	−1.29247	+	1.49159i	−0.768496	+	0.639855i	$0.778995\pi$
$402$	−2.63616e6	−	1.69416e6i	−0.813593	−	0.522865i
$403$	4.45747e6	+	2.86464e6i	1.36718	+	0.878633i
$404$	−1.86763e6	+	2.15536e6i	−0.569294	+	0.657001i
$405$	−424808.	−	124735.i	−0.128693	−	0.0377877i
$406$	737337.	+	5.12829e6i	0.221999	+	1.54404i
$407$	3.37493e6	+	3.89487e6i	1.00990	+	1.16549i
$408$	−162271.	−	355325.i	−0.0482604	−	0.105676i
$409$	4.23602e6	−	1.24381e6i	1.25213	−	0.367659i	0.412571	−	0.910926i	$-0.364631\pi$
$409$	4.23602e6	−	1.24381e6i	1.25213	−	0.367659i	0.839560	+	0.543267i	$0.182813\pi$
$410$	−2.71674e6	+	5.94882e6i	−0.798156	+	1.74772i
$411$	346935.	−	2.41298e6i	0.101308	−	0.704612i
$412$	−1.20412e6	+	773839.i	−0.349482	+	0.224599i
$413$	−2.41220e6			−0.695885
$414$	−1.75474e6	+	275269.i	−0.503166	+	0.0789327i
$415$	4.56323e6			1.30062
$416$	6.92937e6	−	4.45324e6i	1.96318	−	1.26166i
$417$	101299.	−	704550.i	0.0285276	−	0.198414i
$418$	−1.80317e6	+	3.94839e6i	−0.504773	+	1.10530i
$419$	1.35742e6	−	398575.i	0.377728	−	0.110911i	−0.0873567	−	0.996177i	$-0.527842\pi$
$419$	1.35742e6	−	398575.i	0.377728	−	0.110911i	0.465085	+	0.885266i	$0.346024\pi$
$420$	−1.76107e6	−	3.85621e6i	−0.487141	−	1.06669i
$421$	−1.44701e6	−	1.66994e6i	−0.397893	−	0.459193i	0.521083	−	0.853506i	$-0.325528\pi$
$421$	−1.44701e6	−	1.66994e6i	−0.397893	−	0.459193i	−0.918976	+	0.394313i	$0.870983\pi$
$422$	1.13392e6	+	7.88661e6i	0.309958	+	2.15580i
$423$	1.33330e6	+	391492.i	0.362307	+	0.106383i
$424$	1.51088e6	−	1.74365e6i	0.408146	−	0.471025i
$425$	563560.	+	362178.i	0.151345	+	0.0972634i
$426$	−1.17963e6	−	758099.i	−0.314934	−	0.202396i
$427$	900834.	−	1.03962e6i	0.239098	−	0.275933i
$428$	5.49093e6	+	1.61228e6i	1.44889	+	0.425434i
$429$	511103.	+	3.55480e6i	0.134080	+	0.932549i
$430$	6.55974e6	+	7.57035e6i	1.71086	+	1.97444i
$431$	906427.	+	1.98480e6i	0.235039	+	0.514663i	0.989993	−	0.141114i	$-0.0450684\pi$
$431$	906427.	+	1.98480e6i	0.235039	+	0.514663i	−0.754955	+	0.655777i	$0.772341\pi$
$432$	−396341.	+	116376.i	−0.102179	+	0.0300023i
$433$	−87938.5	+	192558.i	−0.0225403	+	0.0493563i	−0.920567	−	0.390584i	$-0.872273\pi$
$433$	−87938.5	+	192558.i	−0.0225403	+	0.0493563i	0.898027	+	0.439940i	$0.145000\pi$
$434$	1.01645e6	−	7.06956e6i	0.259037	−	1.80164i
$435$	1.87381e6	−	1.20423e6i	0.474792	−	0.305130i
$436$	−5.43750e6			−1.36988
$437$	1.77284e6	−	2.83784e6i	0.444085	−	0.710861i
$438$	3.08910e6			0.769389
$439$	−6.18561e6	+	3.97525e6i	−1.53187	+	0.984472i	−0.542336	+	0.840162i	$0.682460\pi$
$439$	−6.18561e6	+	3.97525e6i	−1.53187	+	0.984472i	−0.989532	+	0.144311i	$0.953904\pi$
$440$	338467.	−	2.35409e6i	0.0833459	−	0.579683i
$441$	333289.	−	729802.i	0.0816065	−	0.178693i
$442$	4.07545e6	−	1.19666e6i	0.992247	−	0.291350i
$443$	415805.	+	910486.i	0.100665	+	0.220427i	0.953263	−	0.302141i	$-0.0977014\pi$
$443$	415805.	+	910486.i	0.100665	+	0.220427i	−0.852598	+	0.522568i	$0.824974\pi$
$444$	3.40703e6	+	3.93192e6i	0.820197	+	0.946557i
$445$	−649888.	−	4.52007e6i	−0.155575	−	1.08204i
$446$	−9.50087e6	−	2.78971e6i	−2.26165	−	0.664082i
$447$	1.36578e6	−	1.57619e6i	0.323304	−	0.373113i
$448$	−6.84742e6	−	4.40057e6i	−1.61188	−	1.03589i
$449$	−3.65616e6	−	2.34967e6i	−0.855874	−	0.550037i	0.0375276	−	0.999296i	$-0.488052\pi$
$449$	−3.65616e6	−	2.34967e6i	−0.855874	−	0.550037i	−0.893402	+	0.449259i	$0.851688\pi$
$450$	−655015.	+	755927.i	−0.152482	+	0.175974i
$451$	−4.09629e6	−	1.20278e6i	−0.948307	−	0.278448i
$452$	2903.17	+	20192.0i	0.000668385	+	0.00464872i
$453$	−1.74853e6	−	2.01791e6i	−0.400338	−	0.462015i
$454$	214598.	+	469904.i	0.0488637	+	0.106996i
$455$	1.10902e7	−	3.25638e6i	2.51138	−	0.737407i
$456$	−456433.	+	999449.i	−0.102793	+	0.225086i
$457$	−485563.	+	3.37716e6i	−0.108756	+	0.756418i	0.860337	+	0.509725i	$0.170253\pi$
$457$	−485563.	+	3.37716e6i	−0.108756	+	0.756418i	−0.969094	+	0.246693i	$0.920656\pi$
$458$	7.62899e6	−	4.90286e6i	1.69943	−	1.09216i
$459$	−341830.			−0.0757318
$460$	−1.96995e6	+	7.04134e6i	−0.434072	+	1.55153i
$461$	−8.46634e6			−1.85542			−0.927712	−	0.373295i	$-0.878228\pi$
$461$	−8.46634e6			−1.85542			−0.927712	+	0.373295i	$0.878228\pi$
$462$	4.07248e6	−	2.61723e6i	0.887676	−	0.570475i
$463$	−242049.	+	1.68349e6i	−0.0524748	+	0.364970i	0.946617	+	0.322360i	$0.104476\pi$
$463$	−242049.	+	1.68349e6i	−0.0524748	+	0.364970i	−0.999092	+	0.0426097i	$0.986433\pi$
$464$	863293.	−	1.89035e6i	0.186150	−	0.407612i
$465$	−2.94619e6	+	865080.i	−0.631871	+	0.185534i
$466$	−2.67425e6	−	5.85580e6i	−0.570477	−	1.24917i
$467$	4.15180e6	+	4.79143e6i	0.880935	+	1.01665i	0.999718	+	0.0237333i	$0.00755526\pi$
$467$	4.15180e6	+	4.79143e6i	0.880935	+	1.01665i	−0.118783	+	0.992920i	$0.537899\pi$
$468$	515964.	+	3.58861e6i	0.108894	+	0.757376i
$469$	−6.31701e6	−	1.85484e6i	−1.32611	−	0.389381i
$470$	6.55264e6	−	7.56216e6i	1.36827	−	1.57907i
$471$	2.59089e6	+	1.66506e6i	0.538141	+	0.345842i
$472$	−1.14927e6	−	738589.i	−0.237447	−	0.152598i
$473$	−4.28223e6	+	4.94196e6i	−0.880070	+	1.01566i
$474$	−4.20248e6	−	1.23396e6i	−0.859131	−	0.252264i
$475$	−268163.	−	1.86511e6i	−0.0545336	−	0.379290i
$476$	−2.14340e6	−	2.47362e6i	−0.433597	−	0.500398i
$477$	−838713.	−	1.83653e6i	−0.168779	−	0.369574i
$478$	−4.76897e6	+	1.40030e6i	−0.954673	+	0.280317i
$479$	−3.30363e6	+	7.23393e6i	−0.657888	+	1.44057i	0.226588	+	0.973991i	$0.427243\pi$
$479$	−3.30363e6	+	7.23393e6i	−0.657888	+	1.44057i	−0.884477	+	0.466584i	$0.845484\pi$
$480$	−679321.	+	4.72478e6i	−0.134577	+	0.936007i
$481$	−1.19332e7	+	7.66900e6i	−2.35176	+	1.51139i
$482$	−1.83803e6			−0.360359
$483$	−3.37441e6	+	1.59357e6i	−0.658158	+	0.310816i
$484$	−686479.			−0.133203
$485$	6.41800e6	−	4.12460e6i	1.23893	−	0.796210i
$486$	72635.5	−	505191.i	0.0139495	−	0.0970209i
$487$	54447.3	−	119223.i	0.0104029	−	0.0227791i	−0.904359	−	0.426772i	$-0.859651\pi$
$487$	54447.3	−	119223.i	0.0104029	−	0.0227791i	0.914762	+	0.403993i	$0.132378\pi$
$488$	747514.	−	219490.i	0.142092	−	0.0417220i
$489$	−2.29968e6	−	5.03560e6i	−0.434906	−	0.952312i
$490$	−3.78329e6	−	4.36615e6i	−0.711836	−	0.821503i
$491$	−1.05176e6	−	7.31513e6i	−0.196884	−	1.36936i	−0.813256	−	0.581906i	$-0.802307\pi$
$491$	−1.05176e6	−	7.31513e6i	−0.196884	−	1.36936i	0.616371	−	0.787456i	$-0.288602\pi$
$492$	−4.13525e6	−	1.21422e6i	−0.770174	−	0.226144i
$493$	1.12618e6	−	1.29968e6i	0.208685	−	0.240835i
$494$	−1.00507e7	−	6.45919e6i	−1.85301	−	1.19086i
$495$	−1.75083e6	−	1.12519e6i	−0.321166	−	0.206401i
$496$	−1.87605e6	+	2.16508e6i	−0.342405	+	0.395157i
$497$	−2.82672e6	−	830001.i	−0.513325	−	0.150726i
$498$	748636.	+	5.20688e6i	0.135269	+	0.940815i
$499$	86881.0	+	100266.i	0.0156197	+	0.0180261i	0.763506	−	0.645801i	$-0.223476\pi$
$499$	86881.0	+	100266.i	0.0156197	+	0.0180261i	−0.747886	+	0.663827i	$0.768931\pi$
$500$	−2.03092e6	−	4.44710e6i	−0.363303	−	0.795522i
$501$	2.70608e6	−	794578.i	0.481667	−	0.141430i
$502$	622909.	−	1.36398e6i	0.110323	−	0.241573i
$503$	188556.	−	1.31144e6i	0.0332292	−	0.231114i	−0.966438	−	0.256899i	$-0.917299\pi$
$503$	188556.	−	1.31144e6i	0.0332292	−	0.231114i	0.999668	+	0.0257844i	$0.00820835\pi$
$504$	1.03086e6	−	662493.i	0.180769	−	0.116173i
$505$	4.50612e6			0.786275
$506$	−8.27897e6	−	1.08233e6i	−1.43747	−	0.187925i
$507$	−6.54327e6			−1.13051
$508$	1.09204e7	−	7.01812e6i	1.87750	−	1.20659i
$509$	121691.	−	846381.i	0.0208192	−	0.144801i	−0.976760	−	0.214334i	$-0.931242\pi$
$509$	121691.	−	846381.i	0.0208192	−	0.144801i	0.997580	+	0.0695332i	$0.0221510\pi$
$510$	−1.02253e6	+	2.23902e6i	−0.174080	+	0.381182i
$511$	6.22727e6	−	1.82849e6i	1.05498	−	0.309771i
$512$	2.54727e6	+	5.57774e6i	0.429437	+	0.940336i
$513$	629643.	+	726647.i	0.105633	+	0.121907i
$514$	−870768.	−	6.05633e6i	−0.145377	−	1.01112i
$515$	2.16992e6	+	637147.i	0.360518	+	0.105858i
$516$	−4.32296e6	+	4.98897e6i	−0.714755	+	0.824871i
$517$	5.49513e6	+	3.53151e6i	0.904173	+	0.581077i
$518$	1.60854e7	+	1.03374e7i	2.63395	+	1.69273i
$519$	−3.26273e6	+	3.76540e6i	−0.531696	+	0.613610i
$520$	6.28090e6	+	1.84424e6i	1.01862	+	0.299095i
$521$	1.19923e6	+	8.34081e6i	0.193556	+	1.34621i	0.822501	+	0.568763i	$0.192578\pi$
$521$	1.19923e6	+	8.34081e6i	0.193556	+	1.34621i	−0.628945	+	0.777450i	$0.716513\pi$
$522$	1.68150e6	+	1.94055e6i	0.270097	+	0.311709i
$523$	1.59198e6	+	3.48595e6i	0.254497	+	0.557271i	0.993154	−	0.116810i	$-0.0372670\pi$
$523$	1.59198e6	+	3.48595e6i	0.254497	+	0.557271i	−0.738657	+	0.674081i	$0.764540\pi$
$524$	1.03814e7	−	3.04826e6i	1.65169	−	0.484980i
$525$	−872988.	+	1.91158e6i	−0.138232	+	0.302687i
$526$	−144782.	+	1.00698e6i	−0.0228165	+	0.158692i
$527$	−1.99437e6	+	1.28170e6i	−0.312809	+	0.201030i
$528$	−1.94175e6			−0.303115
$529$	6.22003e6	+	1.65460e6i	0.966392	+	0.257072i
$530$	−1.45383e7			−2.24814
$531$	−1.00571e6	+	646329.i	−0.154787	+	0.0994757i
$532$	−1.31021e6	+	9.11270e6i	−0.200706	+	1.39594i
$533$	4.88141e6	−	1.06888e7i	0.744264	−	1.62971i
$534$	5.05101e6	−	1.48311e6i	0.766523	−	0.225072i
$535$	−3.75619e6	−	8.22491e6i	−0.567366	−	1.24236i
$536$	−2.44174e6	−	2.81792e6i	−0.367103	−	0.423660i
$537$	−653077.	−	4.54225e6i	−0.0977302	−	0.679729i
$538$	948599.	+	278534.i	0.141295	+	0.0414880i
$539$	2.46975e6	−	2.85025e6i	0.366169	−	0.422582i
$540$	−1.76748e6	−	1.13589e6i	−0.260837	−	0.167630i
$541$	1.06965e7	+	6.87421e6i	1.57126	+	1.00979i	0.978956	+	0.204071i	$0.0654173\pi$
$541$	1.06965e7	+	6.87421e6i	1.57126	+	1.00979i	0.592302	+	0.805716i	$0.298219\pi$
$542$	−7.74775e6	+	8.94138e6i	−1.13286	+	1.30739i
$543$	−589628.	−	173130.i	−0.0858180	−	0.0251984i
$544$	524487.	+	3.64789e6i	0.0759867	+	0.528499i
$545$	5.62613e6	+	6.49290e6i	0.811369	+	0.936370i
$546$	5.53515e6	+	1.21203e7i	0.794598	+	1.73993i
$547$	8.95049e6	−	2.62810e6i	1.27902	−	0.375555i	0.429481	−	0.903076i	$-0.358697\pi$
$547$	8.95049e6	−	2.62810e6i	1.27902	−	0.375555i	0.849542	+	0.527521i	$0.176878\pi$
$548$	4.80570e6	−	1.05230e7i	0.683605	−	1.49689i
$549$	97023.7	−	674815.i	0.0137387	−	0.0955551i
$550$	−3.95544e6	+	2.54200e6i	−0.557555	+	0.358319i
$551$	−4.83720e6			−0.678758
$552$	−2.09564e6	−	273969.i	−0.292731	−	0.0382695i
$553$	−9.20212e6			−1.27960
$554$	−1.23506e7	+	7.93724e6i	−1.70967	+	1.09874i
$555$	1.16987e6	−	8.13663e6i	0.161215	−	1.12128i
$556$	1.40318e6	−	3.07254e6i	0.192498	−	0.421512i
$557$	−1.02993e7	+	3.02414e6i	−1.40660	+	0.413014i	−0.894944	−	0.446179i	$-0.852784\pi$
$557$	−1.02993e7	+	3.02414e6i	−1.40660	+	0.413014i	−0.511652	+	0.859193i	$0.670966\pi$
$558$	−1.47045e6	−	3.21983e6i	−0.199924	−	0.437772i
$559$	−1.17865e7	−	1.36023e7i	−1.59535	−	1.84113i
$560$	889372.	+	6.18572e6i	0.119843	+	0.833528i
$561$	−1.54176e6	−	452702.i	−0.206828	−	0.0607303i
$562$	483220.	−	557666.i	0.0645363	−	0.0744789i
$563$	6.94888e6	+	4.46577e6i	0.923940	+	0.593780i	0.913798	−	0.406168i	$-0.133135\pi$
$563$	6.94888e6	+	4.46577e6i	0.923940	+	0.593780i	0.0101417	+	0.999949i	$0.496772\pi$
$564$	5.54740e6	+	3.56510e6i	0.734331	+	0.471926i
$565$	21107.3	−	24359.1i	0.00278171	−	0.00321027i
$566$	1.20531e7	+	3.53910e6i	1.58146	+	0.464357i
$567$	−152607.	−	1.06140e6i	−0.0199350	−	0.138651i
$568$	−1.09263e6	−	1.26096e6i	−0.142102	−	0.163995i
$569$	−3.18764e6	−	6.97995e6i	−0.412751	−	0.903799i	−0.995817	−	0.0913736i	$-0.970874\pi$
$569$	−3.18764e6	−	6.97995e6i	−0.412751	−	0.903799i	0.583066	−	0.812425i	$-0.301853\pi$
$570$	6.64307e6	−	1.95058e6i	0.856410	−	0.251465i
$571$	629134.	−	1.37761e6i	0.0807520	−	0.176822i	−0.864949	−	0.501859i	$-0.832650\pi$
$571$	629134.	−	1.37761e6i	0.0807520	−	0.176822i	0.945701	+	0.325037i	$0.105377\pi$
$572$	−2.42541e6	+	1.68691e7i	−0.309952	+	2.15576i
$573$	5.36759e6	−	3.44954e6i	0.682956	−	0.438909i
$574$	−1.58394e7			−2.00659
$575$	3.27743e6	−	1.54777e6i	0.413393	−	0.195226i
$576$	−4.03396e6			−0.506612
$577$	9.64866e6	−	6.20082e6i	1.20650	−	0.775370i	0.226431	−	0.974027i	$-0.427294\pi$
$577$	9.64866e6	−	6.20082e6i	1.20650	−	0.775370i	0.980069	+	0.198657i	$0.0636579\pi$
$578$	1.47609e6	−	1.02664e7i	0.183778	−	1.27820i
$579$	−1.55282e6	+	3.40021e6i	−0.192498	+	0.421511i
$580$	1.01419e7	−	2.97792e6i	1.25184	−	0.367573i
$581$	4.59121e6	+	1.00533e7i	0.564270	+	1.23558i
$582$	5.75931e6	+	6.64660e6i	0.704795	+	0.813377i
$583$	−1.35066e6	−	9.39406e6i	−0.164579	−	1.14467i
$584$	3.52678e6	+	1.03556e6i	0.427904	+	0.125644i
$585$	3.75128e6	−	4.32921e6i	0.453200	−	0.523021i
$586$	−1.67236e6	−	1.07476e6i	−0.201180	−	0.129291i
$587$	−3.54523e6	−	2.27838e6i	−0.424667	−	0.272917i	0.310803	−	0.950474i	$-0.399402\pi$
$587$	−3.54523e6	−	2.27838e6i	−0.424667	−	0.272917i	−0.735470	+	0.677557i	$0.763038\pi$
$588$	2.49324e6	−	2.87736e6i	0.297387	−	0.343203i
$589$	6.39817e6	+	1.87867e6i	0.759919	+	0.223132i
$590$	1.22511e6	+	8.52086e6i	0.144893	+	1.00775i
$591$	−2.10740e6	−	2.43207e6i	−0.248186	−	0.286422i
$592$	−3.18601e6	−	6.97638e6i	−0.373631	−	0.818137i
$593$	−320228.	+	94027.5i	−0.0373958	+	0.0109804i	−0.300377	−	0.953821i	$-0.597112\pi$
$593$	−320228.	+	94027.5i	−0.0373958	+	0.0109804i	0.262981	+	0.964801i	$0.415294\pi$
$594$	996659.	−	2.18238e6i	0.115899	−	0.253784i
$595$	−735981.	+	5.11886e6i	−0.0852264	+	0.592762i
$596$	8.32597e6	−	5.35077e6i	0.960106	−	0.617022i
$597$	−4.82724e6			−0.554323
$598$	6.19167e6	−	2.21313e7i	0.708035	−	2.53078i
$599$	−9.24157e6			−1.05239			−0.526197	−	0.850362i	$-0.676383\pi$
$599$	−9.24157e6			−1.05239			−0.526197	+	0.850362i	$0.676383\pi$
$600$	−1.00123e6	+	643452.i	−0.113542	+	0.0729690i
$601$	−747658.	+	5.20008e6i	−0.0844339	+	0.587251i	0.903051	+	0.429534i	$0.141322\pi$
$601$	−747658.	+	5.20008e6i	−0.0844339	+	0.587251i	−0.987484	+	0.157716i	$0.949587\pi$
$602$	−1.00784e7	+	2.20687e7i	−1.13345	+	2.48190i
$603$	−3.13071e6	+	919261.i	−0.350631	+	0.102955i
$604$	−5.26360e6	−	1.15257e7i	−0.587071	−	1.28551i
$605$	710293.	+	819721.i	0.0788949	+	0.0910496i
$606$	739267.	+	5.14171e6i	0.0817748	+	0.568757i
$607$	1.60961e7	+	4.72624e6i	1.77316	+	0.520648i	0.994307	−	0.106554i	$-0.0339818\pi$
$607$	1.60961e7	+	4.72624e6i	1.77316	+	0.520648i	0.778857	+	0.627202i	$0.215800\pi$
$608$	6.78842e6	−	7.83426e6i	0.744749	−	0.859486i
$609$	4.53836e6	+	2.91663e6i	0.495856	+	0.318667i
$610$	−4.12987e6	−	2.65411e6i	−0.449378	−	0.288798i
$611$	−1.17737e7	+	1.35876e7i	−1.27589	+	1.47245i
$612$	−1.55643e6	−	457008.i	−0.167977	−	0.0493225i
$613$	−1.46118e6	−	1.01627e7i	−0.157056	−	1.09235i	−0.904023	−	0.427484i	$-0.859400\pi$
$613$	−1.46118e6	−	1.01627e7i	−0.157056	−	1.09235i	0.746967	−	0.664861i	$-0.231509\pi$
$614$	−5.03754e6	−	5.81363e6i	−0.539260	−	0.622339i
$615$	2.82881e6	+	6.19422e6i	0.301589	+	0.660388i
$616$	5.52688e6	−	1.62284e6i	0.586851	−	0.172315i
$617$	6.74041e6	−	1.47594e7i	0.712809	−	1.56083i	−0.110906	−	0.993831i	$-0.535375\pi$
$617$	6.74041e6	−	1.47594e7i	0.712809	−	1.56083i	0.823715	−	0.567004i	$-0.191897\pi$
$618$	−371024.	+	2.58053e6i	−0.0390778	+	0.271792i
$619$	6.00868e6	−	3.86155e6i	0.630308	−	0.405074i	−0.186116	−	0.982528i	$-0.559590\pi$
$619$	6.00868e6	−	3.86155e6i	0.630308	−	0.405074i	0.816424	+	0.577454i	$0.195954\pi$
$620$	−1.45712e7			−1.52236
$621$	−979895.	+	1.56855e6i	−0.101965	+	0.163218i
$622$	−8.08274e6			−0.837689
$623$	9.30439e6	−	5.97957e6i	0.960435	−	0.617234i
$624$	760602.	−	5.29010e6i	0.0781981	−	0.543879i
$625$	−5.06354e6	+	1.10876e7i	−0.518507	+	1.13537i
$626$	1.75268e7	−	5.14633e6i	1.78759	−	0.524882i
$627$	1.87756e6	+	4.11127e6i	0.190732	+	0.417645i
$628$	9.57078e6	+	1.10453e7i	0.968386	+	1.11758i
$629$	−903228.	−	6.28209e6i	−0.0910271	−	0.633107i
$630$	−7.40878e6	−	2.17542e6i	−0.743696	−	0.218369i
$631$	520584.	−	600786.i	0.0520496	−	0.0600684i	−0.729128	−	0.684378i	$-0.760074\pi$
$631$	520584.	−	600786.i	0.0520496	−	0.0600684i	0.781177	+	0.624309i	$0.214619\pi$
$632$	−4.38426e6	−	2.81759e6i	−0.436620	−	0.280598i
$633$	6.97937e6	+	4.48537e6i	0.692320	+	0.444927i
$634$	−1.11276e7	+	1.28419e7i	−1.09946	+	1.26884i
$635$	−1.96795e7	−	5.77844e6i	−1.93678	−	0.568691i
$636$	−1.36351e6	−	9.48342e6i	−0.133664	−	0.929655i
$637$	6.79780e6	+	7.84507e6i	0.663773	+	0.766035i
$638$	5.01413e6	+	1.09794e7i	0.487690	+	1.06789i
$639$	−1.40093e6	+	411349.i	−0.135726	+	0.0398527i
$640$	−5.01650e6	+	1.09846e7i	−0.484117	+	1.06007i
$641$	−2.95291e6	+	2.05379e7i	−0.283860	+	1.97429i	−0.0692101	+	0.997602i	$0.522048\pi$
$641$	−2.95291e6	+	2.05379e7i	−0.283860	+	1.97429i	−0.214650	+	0.976691i	$0.568861\pi$
$642$	8.76881e6	−	5.63537e6i	0.839660	−	0.539616i
$643$	1.12440e7			1.07249			0.536245	−	0.844062i	$-0.319842\pi$
$643$	1.12440e7			1.07249			0.536245	+	0.844062i	$0.319842\pi$
$644$	−1.74950e7	+	2.74447e6i	−1.66226	+	0.260762i
$645$	1.04302e7			0.987176
$646$	4.49690e6	−	2.88998e6i	0.423967	−	0.272467i
$647$	−1.87982e6	+	1.30744e7i	−0.176545	+	1.22790i	0.688139	+	0.725579i	$0.258428\pi$
$647$	−1.87982e6	+	1.30744e7i	−0.176545	+	1.22790i	−0.864684	+	0.502317i	$0.832481\pi$
$648$	252282.	−	552421.i	0.0236020	−	0.0516812i
$649$	−5.39202e6	+	1.58324e6i	−0.502505	+	0.147549i
$650$	−5.37606e6	−	1.17719e7i	−0.499092	−	1.09286i
$651$	−4.87013e6	−	5.62043e6i	−0.450390	−	0.519777i
$652$	−3.73863e6	−	2.60027e7i	−0.344424	−	2.39552i
$653$	673994.	+	197902.i	0.0618547	+	0.0181622i	0.312514	−	0.949913i	$-0.398829\pi$
$653$	673994.	+	197902.i	0.0618547	+	0.0181622i	−0.250659	+	0.968075i	$0.580647\pi$
$654$	−6.48572e6	+	7.48492e6i	−0.592944	+	0.684294i
$655$	−1.43815e7	−	9.24240e6i	−1.30978	−	0.841747i
$656$	5.34472e6	+	3.43484e6i	0.484915	+	0.311636i
$657$	2.10638e6	−	2.43089e6i	0.190381	−	0.219711i
$658$	2.32532e7	+	6.82775e6i	2.09371	+	0.614770i
$659$	−1.31808e6	−	9.16742e6i	−0.118230	−	0.822306i	−0.959504	−	0.281697i	$-0.909103\pi$
$659$	−1.31808e6	−	9.16742e6i	−0.118230	−	0.822306i	0.841274	−	0.540609i	$-0.181806\pi$
$660$	−6.46758e6	−	7.46398e6i	−0.577939	−	0.666977i
$661$	−2.14688e6	−	4.70102e6i	−0.191119	−	0.418493i	0.789678	−	0.613521i	$-0.210247\pi$
$661$	−2.14688e6	−	4.70102e6i	−0.191119	−	0.418493i	−0.980798	+	0.195028i	$0.937520\pi$
$662$	2.33931e7	−	6.86884e6i	2.07464	−	0.609170i
$663$	1.83727e6	−	4.02305e6i	0.162326	−	0.355444i
$664$	−890792.	+	6.19560e6i	−0.0784072	+	0.545334i
$665$	1.22371e7	−	7.86431e6i	1.07306	−	0.689614i
$666$	9.47624e6			0.827848
$667$	−2.73549e6	−	8.89337e6i	−0.238079	−	0.774019i
$668$	1.33837e7			1.16047
$669$	−8.67370e6	+	5.57425e6i	−0.749272	+	0.481528i
$670$	−3.34375e6	+	2.32563e7i	−0.287771	+	2.00149i
$671$	1.33130e6	−	2.91514e6i	0.114148	−	0.249950i
$672$	−1.10928e7	+	3.25713e6i	−0.947581	+	0.278235i
$673$	301436.	+	660053.i	0.0256541	+	0.0561747i	0.922025	−	0.387130i	$-0.126533\pi$
$673$	301436.	+	660053.i	0.0256541	+	0.0561747i	−0.896371	+	0.443304i	$0.853806\pi$
$674$	−8.12407e6	−	9.37568e6i	−0.688849	−	0.794974i
$675$	148220.	+	1.03090e6i	0.0125213	+	0.0870874i
$676$	−2.97929e7	−	8.74799e6i	−2.50753	−	0.736277i
$677$	4.93641e6	−	5.69692e6i	0.413942	−	0.477715i	−0.510040	−	0.860151i	$-0.670369\pi$
$677$	4.93641e6	−	5.69692e6i	0.413942	−	0.477715i	0.923982	+	0.382436i	$0.124915\pi$
$678$	31257.9	+	20088.2i	0.00261147	+	0.00167829i
$679$	1.55443e7	+	9.98975e6i	1.29389	+	0.831534i
$680$	−1.91799e6	+	2.21348e6i	−0.159065	+	0.183571i
$681$	516109.	+	151543.i	0.0426455	+	0.0125219i
$682$	−2.36801e6	−	1.64699e7i	−0.194950	−	1.35590i
$683$	−1.29115e7	−	1.49006e7i	−1.05907	−	1.22223i	−0.974165	−	0.225839i	$-0.927488\pi$
$683$	−1.29115e7	−	1.49006e7i	−1.05907	−	1.22223i	−0.0849020	−	0.996389i	$-0.527058\pi$
$684$	1.89541e6	+	4.15038e6i	0.154904	+	0.339194i
$685$	−1.75379e7	+	5.14959e6i	−1.42807	+	0.419321i
$686$	−4.05039e6	+	8.86912e6i	−0.328615	+	0.719565i
$687$	1.34384e6	−	9.34659e6i	0.108631	−	0.755547i
$688$	8.18649e6	−	5.26114e6i	0.659366	−	0.423749i
$689$	2.61223e7			2.09635
$690$	7.34295e6	+	1.11105e7i	0.587148	+	0.888401i
$691$	8.37497e6			0.667249			0.333625	−	0.942706i	$-0.391728\pi$
$691$	8.37497e6			0.667249			0.333625	+	0.942706i	$0.391728\pi$
$692$	−1.98901e7	+	1.27826e7i	−1.57896	+	1.01474i
$693$	717363.	−	4.98937e6i	0.0567421	−	0.394650i
$694$	−1.16463e7	+	2.55018e7i	−0.917886	+	2.00989i
$695$	−5.12076e6	+	1.50359e6i	−0.402136	+	0.118078i
$696$	1.26922e6	+	2.77920e6i	0.0993145	+	0.217468i
$697$	3.44294e6	+	3.97337e6i	0.268440	+	0.309797i
$698$	2.21521e6	+	1.54071e7i	0.172098	+	1.19697i
$699$	−6.43159e6	−	1.88849e6i	−0.497881	−	0.146191i
$700$	−6.53058e6	+	7.53669e6i	−0.503740	+	0.581347i
$701$	−4.73482e6	−	3.04288e6i	−0.363922	−	0.233878i	0.345882	−	0.938278i	$-0.387580\pi$
$701$	−4.73482e6	−	3.04288e6i	−0.363922	−	0.233878i	−0.709803	+	0.704400i	$0.751216\pi$
$702$	5.55528e6	+	3.57016e6i	0.425464	+	0.273429i
$703$	−1.16905e7	+	1.34915e7i	−0.892161	+	1.02961i
$704$	−1.81945e7	−	5.34238e6i	−1.38359	−	0.406259i
$705$	−1.48277e6	−	1.03129e7i	−0.112357	−	0.781462i
$706$	9.70187e6	+	1.11966e7i	0.732561	+	0.845420i
$707$	4.53375e6	+	9.92753e6i	0.341121	+	0.746952i
$708$	−5.44331e6	+	1.59830e6i	−0.408113	+	0.119833i
$709$	−4.69605e6	+	1.02829e7i	−0.350846	+	0.768246i	0.649125	+	0.760682i	$0.275135\pi$
$709$	−4.69605e6	+	1.02829e7i	−0.350846	+	0.768246i	−0.999971	+	0.00756461i	$0.997592\pi$
$710$	−1.49625e6	+	1.04067e7i	−0.111393	+	0.774758i
$711$	−3.83660e6	+	2.46563e6i	−0.284625	+	0.182917i
$712$	6.26387e6			0.463066
$713$	164233.	+	1.28257e7i	0.0120986	+	0.944836i
$714$	−5.96162e6			−0.437642
$715$	2.26528e7	−	1.45581e7i	1.65713	−	1.06498i
$716$	3.09914e6	−	2.15550e7i	0.225922	−	1.57132i
$717$	−2.14991e6	+	4.70765e6i	−0.156179	+	0.341985i
$718$	2.58591e7	−	7.59292e6i	1.87198	−	0.549664i
$719$	−138469.	−	303205.i	−0.00998921	−	0.0218733i	0.904572	−	0.426322i	$-0.140191\pi$
$719$	−138469.	−	303205.i	−0.00998921	−	0.0218733i	−0.914561	+	0.404448i	$0.867464\pi$
$720$	2.02822e6	+	2.34069e6i	0.145809	+	0.168272i
$721$	779517.	+	5.42166e6i	0.0558454	+	0.388413i
$722$	6.10848e6	+	1.79361e6i	0.436104	+	0.128052i
$723$	−1.25331e6	+	1.44640e6i	−0.0891688	+	0.102906i
$724$	−2.45324e6	−	1.57660e6i	−0.173938	−	0.111783i
$725$	−4.40792e6	−	2.83280e6i	−0.311450	−	0.200157i
$726$	−818815.	+	944963.i	−0.0576560	+	0.0665385i
$727$	1.25629e7	+	3.68881e6i	0.881567	+	0.258851i	0.691028	−	0.722828i	$-0.257158\pi$
$727$	1.25629e7	+	3.68881e6i	0.881567	+	0.258851i	0.190539	+	0.981680i	$0.438976\pi$
$728$	2.25633e6	+	1.56931e7i	0.157788	+	1.09744i
$729$	−348020.	−	401636.i	−0.0242541	−	0.0279907i
$730$	−9.62170e6	−	2.10686e7i	−0.668259	−	1.46328i
$731$	7.72672e6	−	2.26877e6i	0.534813	−	0.157035i
$732$	1.34396e6	−	2.94286e6i	0.0927062	−	0.202998i
$733$	−993268.	+	6.90833e6i	−0.0682820	+	0.474912i	0.926776	+	0.375615i	$0.122568\pi$
$733$	−993268.	+	6.90833e6i	−0.0682820	+	0.474912i	−0.995058	+	0.0992970i	$0.968341\pi$
$734$	−39889.4	+	25635.4i	−0.00273286	+	0.00175630i
$735$	−6.01558e6			−0.410732
$736$	1.82425e7	+	8.05039e6i	1.24134	+	0.547801i
$737$	−1.53379e7			−1.04016
$738$	−6.60384e6	+	4.24403e6i	−0.446329	+	0.286839i
$739$	−1.02317e6	+	7.11630e6i	−0.0689186	+	0.479339i	0.925908	+	0.377750i	$0.123302\pi$
$739$	−1.02317e6	+	7.11630e6i	−0.0689186	+	0.479339i	−0.994826	+	0.101590i	$0.967607\pi$
$740$	1.62049e7	−	3.54838e7i	1.08785	−	2.38205i
$741$	−1.19362e7	+	3.50479e6i	−0.798586	+	0.234486i
$742$	−1.46274e7	−	3.20296e7i	−0.975345	−	2.13571i
$743$	−5.75838e6	−	6.64553e6i	−0.382674	−	0.441629i	0.531435	−	0.847099i	$-0.321653\pi$
$743$	−5.75838e6	−	6.64553e6i	−0.382674	−	0.441629i	−0.914108	+	0.405471i	$0.867108\pi$
$744$	−599409.	−	4.16898e6i	−0.0397001	−	0.276120i
$745$	−1.50041e7	−	4.40561e6i	−0.990422	−	0.290814i
$746$	−5.03914e6	+	5.81547e6i	−0.331520	+	0.382594i
$747$	4.60790e6	+	2.96132e6i	0.302136	+	0.194171i
$748$	−6.41474e6	−	4.12250e6i	−0.419204	−	0.269406i
$749$	1.43413e7	−	1.65507e7i	0.934077	−	1.07798i
$750$	−8.54403e6	−	2.50875e6i	−0.554638	−	0.162856i
$751$	−1.73264e6	−	1.20508e7i	−0.112101	−	0.779678i	−0.965870	−	0.259026i	$-0.916598\pi$
$751$	−1.73264e6	−	1.20508e7i	−0.112101	−	0.779678i	0.853770	−	0.520651i	$-0.174311\pi$
$752$	−6.36575e6	−	7.34646e6i	−0.410492	−	0.473733i
$753$	−648606.	−	1.42025e6i	−0.0416863	−	0.0912803i
$754$	−3.18764e7	+	9.35976e6i	−2.04193	+	0.599565i
$755$	−8.31657e6	+	1.82107e7i	−0.530978	+	1.16268i
$756$	724186.	−	5.03682e6i	0.0460835	−	0.320518i
$757$	−2.24128e7	+	1.44038e7i	−1.42153	+	0.913562i	−0.421553	+	0.906804i	$0.638515\pi$
$757$	−2.24128e7	+	1.44038e7i	−1.42153	+	0.913562i	−0.999977	+	0.00675806i	$0.997849\pi$
$758$	8.02591e6			0.507366
$759$	−6.49694e6	+	5.77693e6i	−0.409359	+	0.363992i
$760$	8.23821e6			0.517367
$761$	−293372.	+	188539.i	−0.0183636	+	0.0118016i	−0.549790	−	0.835303i	$-0.685292\pi$
$761$	−293372.	+	188539.i	−0.0183636	+	0.0118016i	0.531427	+	0.847104i	$0.321656\pi$
$762$	3.36490e6	−	2.34034e7i	0.209935	−	1.46013i
$763$	−8.64401e6	+	1.89278e7i	−0.537532	+	1.17703i
$764$	2.90516e7	−	8.53033e6i	1.80068	−	0.528728i
$765$	1.06471e6	+	2.33138e6i	0.0657774	+	0.144032i
$766$	−1.55765e7	−	1.79763e7i	−0.959177	−	1.10695i
$767$	−2.20128e6	−	1.53102e7i	−0.135110	−	0.939708i
$768$	405005.	+	118920.i	0.0247775	+	0.00727533i
$769$	−1.22300e7	+	1.41142e7i	−0.745780	+	0.860676i	−0.994152	−	0.107989i	$-0.965559\pi$
$769$	−1.22300e7	+	1.41142e7i	−0.745780	+	0.860676i	0.248372	+	0.968665i	$0.420104\pi$
$770$	−3.05350e7	−	1.96236e7i	−1.85597	−	1.19276i
$771$	−5.35964e6	−	3.44443e6i	−0.324713	−	0.208680i
$772$	−1.16162e7	+	1.34059e7i	−0.701491	+	0.809564i
$773$	1.54526e6	+	453730.i	0.0930151	+	0.0273117i	0.327909	−	0.944709i	$-0.393656\pi$
$773$	1.54526e6	+	453730.i	0.0930151	+	0.0273117i	−0.234894	+	0.972021i	$0.575474\pi$
$774$	1.71117e6	+	1.19014e7i	0.102669	+	0.714080i
$775$	4.73016e6	+	5.45889e6i	0.282892	+	0.326475i
$776$	4.34720e6	+	9.51903e6i	0.259152	+	0.567464i
$777$	1.91030e7	−	5.60916e6i	1.13514	−	0.333307i
$778$	1.92128e7	−	4.20702e7i	1.13800	−	2.49187i
$779$	2.10458e6	−	1.46377e7i	0.124257	−	0.864230i
$780$	2.28683e7	−	1.46966e7i	1.34585	−	0.864927i
$781$	−6.86339e6			−0.402635
$782$	7.85639e6	+	6.63340e6i	0.459416	+	0.387899i
$783$	2.67365e6			0.155847
$784$	−4.72151e6	+	3.03433e6i	−0.274341	+	0.176308i
$785$	3.28632e6	−	2.28569e7i	0.190343	−	1.32386i
$786$	8.18666e6	−	1.79263e7i	0.472662	−	1.03498i
$787$	2.22134e6	−	652243.i	0.127843	−	0.0375381i	−0.217185	−	0.976130i	$-0.569688\pi$
$787$	2.22134e6	−	652243.i	0.127843	−	0.0375381i	0.345028	+	0.938592i	$0.387869\pi$
$788$	−6.34390e6	−	1.38912e7i	−0.363949	−	0.796938i
$789$	693694.	+	800566.i	0.0396712	+	0.0457830i
$790$	4.67360e6	+	3.25056e7i	0.266431	+	1.85307i
$791$	74902.9	+	21993.5i	0.00425655	+	0.00124983i
$792$	1.86947e6	−	2.15749e6i	0.105902	−	0.122218i
$793$	7.42052e6	+	4.76888e6i	0.419036	+	0.269298i
$794$	−2.09331e7	−	1.34529e7i	−1.17837	−	0.757293i
$795$	−9.91330e6	+	1.14406e7i	−0.556289	+	0.641992i
$796$	−2.19795e7	−	6.45375e6i	−1.22952	−	0.361019i
$797$	−1.22729e6	−	8.53596e6i	−0.0684384	−	0.476000i	−0.995001	−	0.0998603i	$-0.968160\pi$
$797$	−1.22729e6	−	8.53596e6i	−0.0684384	−	0.476000i	0.926563	−	0.376140i	$-0.122749\pi$
$798$	1.09812e7	+	1.26730e7i	0.610438	+	0.704483i
$799$	−3.34168e6	−	7.31727e6i	−0.185182	−	0.405492i
$800$	1.07739e7	−	3.16351e6i	0.595182	−	0.174761i
$801$	2.27706e6	−	4.98607e6i	0.125399	−	0.274585i
$802$	−7.81752e6	+	5.43720e7i	−0.429174	+	2.98497i
$803$	1.27198e7	−	8.17451e6i	0.696131	−	0.447376i
$804$	−1.54838e7			−0.844770
$805$	2.13790e7	+	1.80510e7i	1.16278	+	0.981773i
$806$	4.57981e7			2.48319
$807$	866012.	−	556552.i	0.0468101	−	0.0300831i
$808$	−879644.	+	6.11806e6i	−0.0474000	+	0.329674i
$809$	−1.65279e6	+	3.61912e6i	−0.0887866	+	0.194416i	−0.948816	−	0.315828i	$-0.897718\pi$
$809$	−1.65279e6	+	3.61912e6i	−0.0887866	+	0.194416i	0.860030	+	0.510244i	$0.170445\pi$
$810$	−3.67180e6	+	1.07814e6i	−0.196637	+	0.0577380i
$811$	1.20487e7	+	2.63830e7i	0.643264	+	1.40855i	0.897328	+	0.441364i	$0.145505\pi$
$811$	1.20487e7	+	2.63830e7i	0.643264	+	1.40855i	−0.254064	+	0.967187i	$0.581767\pi$
$812$	1.67648e7	+	1.93476e7i	0.892293	+	1.02976i
$813$	1.75321e6	+	1.21938e7i	0.0930264	+	0.647013i
$814$	4.27409e7	+	1.25499e7i	2.26091	+	0.663862i
$815$	−2.71814e7	+	3.13691e7i	−1.43344	+	1.65427i
$816$	2.01165e6	+	1.29281e6i	0.105761	+	0.0679686i
$817$	−1.90553e7	−	1.22461e7i	−0.998758	−	0.641863i
$818$	2.49892e7	−	2.88390e7i	1.30577	−	1.50694i
$819$	1.33120e7	+	3.90877e6i	0.693482	+	0.203625i
$820$	4.59884e6	+	3.19856e7i	0.238844	+	1.66119i
$821$	1.10443e7	+	1.27458e7i	0.571848	+	0.659948i	0.965832	−	0.259169i	$-0.0834487\pi$
$821$	1.10443e7	+	1.27458e7i	0.571848	+	0.659948i	−0.393983	+	0.919118i	$0.628903\pi$
$822$	−8.75318e6	−	1.91668e7i	−0.451842	−	0.989396i
$823$	−1.57153e7	+	4.61442e6i	−0.808765	+	0.237475i	−0.659871	−	0.751379i	$-0.729389\pi$
$823$	−1.57153e7	+	4.61442e6i	−0.808765	+	0.237475i	−0.148893	+	0.988853i	$0.547571\pi$
$824$	−1.28866e6	+	2.82178e6i	−0.0661182	+	0.144779i
$825$	−696745.	+	4.84597e6i	−0.0356401	+	0.247882i
$826$	−1.75399e7	+	1.12722e7i	−0.894491	+	0.574854i
$827$	1.25013e7			0.635610			0.317805	−	0.948156i	$-0.397054\pi$
$827$	1.25013e7			0.635610			0.317805	+	0.948156i	$0.397054\pi$
$828$	−6.55874e6	+	5.83187e6i	−0.332464	+	0.295619i
$829$	8.73646e6			0.441519			0.220759	−	0.975328i	$-0.429146\pi$
$829$	8.73646e6			0.441519			0.220759	+	0.975328i	$0.429146\pi$
$830$	3.31807e7	−	2.13239e7i	1.67182	−	1.07442i
$831$	−2.17554e6	+	1.51312e7i	−0.109286	+	0.760100i
$832$	2.16817e7	−	4.74764e7i	1.08589	−	2.37777i
$833$	−4.45634e6	+	1.30850e6i	−0.222518	+	0.0653373i
$834$	−2.55578e6	−	5.59638e6i	−0.127235	−	0.278607i
$835$	−1.38480e7	−	1.59814e7i	−0.687338	−	0.793230i
$836$	3.05237e6	+	2.12297e7i	0.151050	+	1.05058i
$837$	−3.53643e6	−	1.03839e6i	−0.174482	−	0.0512327i
$838$	8.00770e6	−	9.24138e6i	0.393911	−	0.454597i
$839$	960152.	+	617052.i	0.0470907	+	0.0302634i	0.563974	−	0.825792i	$-0.309272\pi$
$839$	960152.	+	617052.i	0.0470907	+	0.0302634i	−0.516884	+	0.856056i	$0.672908\pi$
$840$	−7.72926e6	−	4.96729e6i	−0.377954	−	0.242897i
$841$	4.62345e6	−	5.33575e6i	0.225412	−	0.260139i
$842$	−1.83253e7	−	5.38079e6i	−0.890780	−	0.261557i
$843$	−109346.	−	760517.i	−0.00529948	−	0.0368587i
$844$	2.57819e7	+	2.97539e7i	1.24583	+	1.43777i
$845$	2.03805e7	+	4.46271e7i	0.981913	+	2.15009i
$846$	1.15243e7	−	3.38383e6i	0.553590	−	0.162549i
$847$	−1.09130e6	+	2.38961e6i	−0.0522679	+	0.114451i
$848$	−2.01000e6	+	1.39799e7i	−0.0959857	+	0.667595i
$849$	1.10037e7	−	7.07166e6i	0.523926	−	0.336707i
$850$	5.79028e6			0.274886
$851$	−3.14157e7	−	1.38637e7i	−1.48704	−	0.656230i
$852$	−6.92867e6			−0.327002
$853$	−1.77520e6	+	1.14085e6i	−0.0835364	+	0.0536856i	−0.581742	−	0.813373i	$-0.697629\pi$
$853$	−1.77520e6	+	1.14085e6i	−0.0835364	+	0.0536856i	0.498206	+	0.867059i	$0.333992\pi$
$854$	1.69213e6	−	1.17690e7i	0.0793940	−	0.552198i
$855$	2.99478e6	−	6.55766e6i	0.140104	−	0.306785i
$856$	1.19004e7	−	3.49427e6i	0.555107	−	0.162994i
$857$	1.12159e7	+	2.45594e7i	0.521653	+	1.14226i	0.968810	+	0.247806i	$0.0797095\pi$
$857$	1.12159e7	+	2.45594e7i	0.521653	+	1.14226i	−0.447156	+	0.894456i	$0.647563\pi$
$858$	2.03279e7	+	2.34597e7i	0.942703	+	1.08794i
$859$	1.54794e6	+	1.07662e7i	0.0715766	+	0.497826i	0.993801	+	0.111172i	$0.0354604\pi$
$859$	1.54794e6	+	1.07662e7i	0.0715766	+	0.497826i	−0.922225	+	0.386655i	$0.873631\pi$
$860$	4.74911e7	+	1.39447e7i	2.18961	+	0.642927i
$861$	−1.08005e7	+	1.24644e7i	−0.496518	+	0.573012i
$862$	1.58659e7	+	1.01964e7i	0.727270	+	0.467388i
$863$	−5.05579e6	−	3.24916e6i	−0.231080	−	0.148506i	0.419978	−	0.907535i	$-0.362038\pi$
$863$	−5.05579e6	−	3.24916e6i	−0.231080	−	0.148506i	−0.651057	+	0.759028i	$0.725674\pi$
$864$	−3.75214e6	+	4.33020e6i	−0.170999	+	0.197344i
$865$	3.58437e7	+	1.05247e7i	1.62882	+	0.478264i
$866$	260395.	+	1.81109e6i	0.0117988	+	0.0820626i
$867$	−7.07242e6	−	8.16201e6i	−0.319536	−	0.368765i
$868$	−1.46606e7	−	3.21022e7i	−0.660467	−	1.44622i
$869$	−2.05696e7	+	6.03979e6i	−0.924012	+	0.271314i
$870$	7.99775e6	−	1.75126e7i	0.358237	−	0.784429i
$871$	6.00803e6	−	4.17867e7i	0.268341	−	1.86635i
$872$	−9.91383e6	+	6.37123e6i	−0.441520	+	0.283748i
$873$	9.15751e6			0.406670
$874$	−370312.	−	2.89193e7i	−0.0163979	−	1.28059i
$875$	−1.87088e7			−0.826086
$876$	1.28408e7	−	8.25226e6i	0.565368	−	0.363340i
$877$	3.20243e6	−	2.22734e7i	0.140598	−	0.977883i	−0.790330	−	0.612681i	$-0.790091\pi$
$877$	3.20243e6	−	2.22734e7i	0.140598	−	0.977883i	0.930929	−	0.365201i	$-0.119000\pi$
$878$	−2.64013e7	+	5.78107e7i	−1.15581	+	2.53088i
$879$	−1.98610e6	+	583171.i	−0.0867018	+	0.0254580i
$880$	6.04802e6	+	1.32433e7i	0.263273	+	0.576487i
$881$	−2.33881e7	−	2.69913e7i	−1.01521	−	1.17161i	−0.985086	−	0.172065i	$-0.944956\pi$
$881$	−2.33881e7	−	2.69913e7i	−1.01521	−	1.17161i	−0.0301213	−	0.999546i	$-0.509589\pi$
$882$	−986906.	−	6.86408e6i	−0.0427174	−	0.297106i
$883$	1.72423e6	+	506279.i	0.0744205	+	0.0218518i	0.318731	−	0.947845i	$-0.396743\pi$
$883$	1.72423e6	+	506279.i	0.0744205	+	0.0218518i	−0.244310	+	0.969697i	$0.578562\pi$
$884$	1.37441e7	−	1.58615e7i	0.591541	−	0.682675i
$885$	7.54066e6	+	4.84609e6i	0.323632	+	0.207986i
$886$	7.27815e6	+	4.67738e6i	0.311485	+	0.200179i
$887$	−1.69574e7	+	1.95699e7i	−0.723686	+	0.835178i	−0.991745	−	0.128225i	$-0.959072\pi$
$887$	−1.69574e7	+	1.95699e7i	−0.723686	+	0.835178i	0.268059	+	0.963402i	$0.413618\pi$
$888$	1.08189e7	+	3.17672e6i	0.460417	+	0.135191i
$889$	−7.06962e6	−	4.91703e7i	−0.300014	−	2.08664i
$890$	−2.58478e7	−	2.98300e7i	−1.09383	−	1.26234i
$891$	−1.03777e6	−	2.27241e6i	−0.0437934	−	0.0958941i
$892$	−4.69457e7	+	1.37845e7i	−1.97553	+	0.580068i
$893$	−9.39941e6	+	2.05818e7i	−0.394432	+	0.863685i
$894$	2.56547e6	−	1.78433e7i	0.107355	−	0.746673i
$895$	−2.89454e7	+	1.86021e7i	−1.20787	+	0.776254i
$896$	−2.92477e7			−1.21709
$897$	−1.31938e7	−	1.99632e7i	−0.547504	−	0.828416i
$898$	−3.75652e7			−1.55451
$899$	1.55991e7	−	1.00249e7i	0.643725	−	0.413697i
$900$	−703372.	+	4.89206e6i	−0.0289453	+	0.201319i
$901$	−4.85524e6	+	1.06315e7i	−0.199250	+	0.436297i
$902$	−3.54060e7	+	1.03961e7i	−1.44897	+	0.425457i
$903$	1.04942e7	+	2.29791e7i	0.428282	+	0.937806i
$904$	28952.6	+	33413.0i	0.00117833	+	0.00135986i
$905$	655729.	+	4.56069e6i	0.0266136	+	0.185101i
$906$	−2.21438e7	−	6.50201e6i	−0.896255	−	0.263164i
$907$	1.86541e7	−	2.15280e7i	0.752934	−	0.868932i	−0.241916	−	0.970297i	$-0.577776\pi$
$907$	1.86541e7	−	2.15280e7i	0.752934	−	0.868932i	0.994849	+	0.101365i	$0.0323211\pi$
$908$	2.14735e6	+	1.38002e6i	0.0864348	+	0.0555483i
$909$	4.55024e6	+	2.92426e6i	0.182652	+	0.117383i
$910$	6.54235e7	−	7.55028e7i	2.61897	−	3.02245i
$911$	−3.02914e7	−	8.89436e6i	−1.20927	−	0.355074i	−0.385880	−	0.922549i	$-0.626102\pi$
$911$	−3.02914e7	−	8.89436e6i	−1.20927	−	0.355074i	−0.823391	+	0.567475i	$0.807920\pi$
$912$	−957217.	−	6.65759e6i	−0.0381086	−	0.265051i
$913$	1.68613e7	+	1.94590e7i	0.669444	+	0.772579i
$914$	1.22508e7	+	2.68255e7i	0.485063	+	1.06214i
$915$	−4.90465e6	+	1.44013e6i	−0.193667	+	0.0568657i
$916$	1.86147e7	−	4.07604e7i	0.733021	−	1.60509i
$917$	5.89249e6	−	4.09832e7i	0.231407	−	1.60947i
$918$	−2.48555e6	+	1.59737e6i	−0.0973456	+	0.0625602i
$919$	−1.10189e7			−0.430378			−0.215189	−	0.976572i	$-0.569037\pi$
$919$	−1.10189e7			−0.430378			−0.215189	+	0.976572i	$0.569037\pi$
$920$	4.65880e6	+	1.51462e7i	0.181470	+	0.589977i
$921$	−8.00988e6			−0.311155
$922$	−6.15615e7	+	3.95632e7i	−2.38496	+	1.53272i
$923$	2.68846e6	−	1.86986e7i	0.103872	−	0.722447i
$924$	9.93682e6	−	2.17586e7i	0.382884	−	0.838400i
$925$	−1.85540e7	+	5.44794e6i	−0.712989	+	0.209352i
$926$	6.10691e6	+	1.33723e7i	0.234042	+	0.512481i
$927$	1.77769e6	+	2.05157e6i	0.0679449	+	0.0784126i
$928$	−4.10231e6	−	2.85322e7i	−0.156372	−	1.08759i
$929$	4.84305e6	+	1.42205e6i	0.184111	+	0.0540599i	0.372488	−	0.928037i	$-0.378505\pi$
$929$	4.84305e6	+	1.42205e6i	0.184111	+	0.0540599i	−0.188377	+	0.982097i	$0.560323\pi$
$930$	−1.73802e7	+	2.00578e7i	−0.658942	+	0.760460i
$931$	1.09900e7	+	7.06286e6i	0.415551	+	0.267059i
$932$	−2.67596e7	−	1.71974e7i	−1.00911	−	0.648518i
$933$	−5.51142e6	+	6.36052e6i	−0.207281	+	0.239215i
$934$	5.25794e7	+	1.54387e7i	1.97219	+	0.579087i
$935$	1.71460e6	+	1.19253e7i	0.0641408	+	0.446109i
$936$	5.14557e6	+	5.93830e6i	0.191975	+	0.221551i
$937$	−9.31795e6	−	2.04035e7i	−0.346714	−	0.759198i	−0.999998	−	0.00208493i	$-0.999336\pi$
$937$	−9.31795e6	−	2.04035e7i	−0.346714	−	0.759198i	0.653284	−	0.757113i	$-0.273391\pi$
$938$	−5.46007e7	+	1.60322e7i	−2.02624	+	0.594958i
$939$	7.90131e6	−	1.73015e7i	0.292439	−	0.640352i
$940$	7.03640e6	−	4.89393e7i	0.259735	−	1.80650i
$941$	−1.07811e7	+	6.92857e6i	−0.396906	+	0.255076i	−0.723835	−	0.689973i	$-0.757622\pi$
$941$	−1.07811e7	+	6.92857e6i	−0.396906	+	0.255076i	0.326929	+	0.945049i	$0.393986\pi$
$942$	2.66200e7			0.977419
$943$	2.81021e7	−	4.40843e6i	1.02910	−	0.161438i
$944$	8.36295e6			0.305442
$945$	−6.76376e6	+	4.34680e6i	−0.246382	+	0.158340i
$946$	−8.04374e6	+	5.59454e7i	−0.292234	+	2.03253i
$947$	9.07601e6	−	1.98737e7i	0.328867	−	0.720118i	−0.670904	−	0.741545i	$-0.734094\pi$
$947$	9.07601e6	−	1.98737e7i	0.328867	−	0.720118i	0.999770	+	0.0214267i	$0.00682084\pi$
$948$	−2.07653e7	+	6.09724e6i	−0.750442	+	0.220350i
$949$	1.72882e7	+	3.78559e7i	0.623138	+	1.36448i
$950$	−1.06656e7	−	1.23087e7i	−0.383420	−	0.442490i
$951$	2.51802e6	+	1.75132e7i	0.0902832	+	0.627934i
$952$	−6.80631e6	−	1.99851e6i	−0.243399	−	0.0714685i
$953$	1.01631e7	−	1.17289e7i	0.362489	−	0.418335i	−0.544983	−	0.838447i	$-0.683464\pi$
$953$	1.01631e7	−	1.17289e7i	0.362489	−	0.418335i	0.907472	+	0.420112i	$0.138009\pi$
$954$	−1.46806e7	−	9.43466e6i	−0.522244	−	0.335626i
$955$	−4.02455e7	−	2.58642e7i	−1.42794	−	0.917679i
$956$	−1.60829e7	+	1.85607e7i	−0.569141	+	0.656823i
$957$	1.20590e7	+	3.54084e6i	0.425629	+	0.124976i
$958$	9.78240e6	+	6.80381e7i	0.344375	+	2.39518i
$959$	−2.89906e7	−	3.34569e7i	−1.01791	−	1.17473i
$960$	1.25647e7	+	2.75129e7i	0.440022	+	0.963513i
$961$	2.94306e6	−	864159.i	0.102799	−	0.0301846i
$962$	−5.09329e7	+	1.11527e8i	−1.77444	+	3.88548i
$963$	1.54461e6	−	1.07430e7i	0.0536728	−	0.373303i
$964$	−7.64035e6	+	4.91016e6i	−0.264802	+	0.170178i
$965$	2.80271e7			0.968857
$966$	−1.70897e7	+	2.73560e7i	−0.589239	+	0.943212i
$967$	1.11384e7			0.383052			0.191526	−	0.981488i	$-0.438656\pi$
$967$	1.11384e7			0.383052			0.191526	+	0.981488i	$0.438656\pi$
$968$	−1.25161e6	+	804361.i	−0.0429320	+	0.0275907i
$969$	792124.	−	5.50934e6i	0.0271009	−	0.188491i
$970$	2.73931e7	−	5.99826e7i	0.934786	−	2.04690i
$971$	−3.89846e6	+	1.14469e6i	−0.132692	+	0.0389619i	−0.347404	−	0.937715i	$-0.612937\pi$
$971$	−3.89846e6	+	1.14469e6i	−0.132692	+	0.0389619i	0.214712	+	0.976677i	$0.431119\pi$
$972$	−1.04764e6	−	2.29402e6i	−0.0355671	−	0.0778811i
$973$	−8.46476e6	−	9.76885e6i	−0.286637	−	0.330797i
$974$	−161224.	−	1.12134e6i	−0.00544544	−	0.0378739i
$975$	−1.29294e7	−	3.79643e6i	−0.435580	−	0.127898i
$976$	−3.12314e6	+	3.60430e6i	−0.104946	+	0.121114i
$977$	3.77946e7	+	2.42891e7i	1.26676	+	0.814096i	0.989194	−	0.146611i	$-0.0468367\pi$
$977$	3.77946e7	+	2.42891e7i	1.26676	+	0.814096i	0.277564	+	0.960707i	$0.410473\pi$
$978$	−4.02531e7	−	2.58691e7i	−1.34571	−	0.864836i
$979$	1.68736e7	−	1.94732e7i	0.562666	−	0.649351i
$980$	−2.73902e7	−	8.04250e6i	−0.911026	−	0.267501i
$981$	1.46763e6	+	1.02076e7i	0.0486903	+	0.338649i
$982$	−4.18312e7	−	4.82758e7i	−1.38427	−	1.59754i
$983$	−1.93872e7	−	4.24521e7i	−0.639930	−	1.40125i	−0.900098	−	0.435687i	$-0.856505\pi$
$983$	−1.93872e7	−	4.24521e7i	−0.639930	−	1.40125i	0.260168	−	0.965563i	$-0.416222\pi$
$984$	−8.96225e6	+	2.63155e6i	−0.295073	+	0.0866412i
$985$	−1.00235e7	+	2.19483e7i	−0.329175	+	0.720793i
$986$	2.11541e6	−	1.47130e7i	0.0692952	−	0.481959i
$987$	2.12287e7	−	1.36429e7i	0.693634	−	0.445772i
$988$	−5.90340e7			−1.92402
$989$	1.17389e7	−	4.19591e7i	0.381625	−	1.36407i
$990$	−1.79888e7			−0.583330
$991$	3.31321e7	−	2.12927e7i	1.07168	−	0.688727i	0.119060	−	0.992887i	$-0.462012\pi$
$991$	3.31321e7	−	2.12927e7i	1.07168	−	0.688727i	0.952621	+	0.304160i	$0.0983757\pi$
$992$	−5.65521e6	+	3.93328e7i	−0.182461	+	1.26904i
$993$	1.05459e7	−	2.30924e7i	0.339400	−	0.743182i
$994$	−2.44326e7	+	7.17406e6i	−0.784339	+	0.230303i
$995$	1.50355e7	+	3.29232e7i	0.481461	+	1.05425i
$996$	1.70217e7	+	1.96441e7i	0.543693	+	0.627455i
$997$	2.91776e6	+	2.02935e7i	0.0929634	+	0.646575i	0.982020	+	0.188777i	$0.0604524\pi$
$997$	2.91776e6	+	2.02935e7i	0.0929634	+	0.646575i	−0.889057	+	0.457797i	$0.848639\pi$
$998$	1.10028e6	+	323072.i	0.0349686	+	0.0102677i
$999$	6.46162e6	−	7.45710e6i	0.204846	−	0.236405i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.6.e.a.58.9	yes	100
23.2	even	11	inner	69.6.e.a.25.9	✓	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.6.e.a.25.9	✓	100	23.2	even	11	inner
69.6.e.a.58.9	yes	100	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:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	69.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(7.27132 - 4.67299i) q^{2} +(1.28083 - 8.90839i) q^{3} +(17.7420 - 38.8495i) q^{4} +(-64.7474 + 19.0116i) q^{5} +(-32.3155 - 70.7611i) q^{6} +(-107.029 - 123.518i) q^{7} +(-13.1730 - 91.6202i) q^{8} +(-77.7189 - 22.8203i) q^{9} +O(q^{10})\)	\(q+(7.27132 - 4.67299i) q^{2} +(1.28083 - 8.90839i) q^{3} +(17.7420 - 38.8495i) q^{4} +(-64.7474 + 19.0116i) q^{5} +(-32.3155 - 70.7611i) q^{6} +(-107.029 - 123.518i) q^{7} +(-13.1730 - 91.6202i) q^{8} +(-77.7189 - 22.8203i) q^{9} +(-381.958 + 440.803i) q^{10} +(-320.315 - 205.854i) q^{11} +(-323.362 - 207.812i) q^{12} +(686.300 - 792.032i) q^{13} +(-1355.44 - 397.994i) q^{14} +(86.4317 + 601.146i) q^{15} +(371.064 + 428.231i) q^{16} +(194.789 + 426.529i) q^{17} +(-671.759 + 197.246i) q^{18} +(547.898 - 1199.73i) q^{19} +(-410.157 + 2852.70i) q^{20} +(-1237.44 + 795.252i) q^{21} -3291.07 q^{22} +(2515.59 + 328.870i) q^{23} -833.062 q^{24} +(1201.87 - 772.395i) q^{25} +(1289.14 - 8966.20i) q^{26} +(-302.838 + 663.122i) q^{27} +(-6697.52 + 1966.57i) q^{28} +(-1523.56 - 3336.12i) q^{29} +(3437.62 + 3967.23i) q^{30} +(719.526 + 5004.41i) q^{31} +(7541.26 + 2214.31i) q^{32} +(-2244.10 + 2589.83i) q^{33} +(3409.54 + 2191.18i) q^{34} +(9278.13 + 5962.69i) q^{35} +(-2265.44 + 2614.46i) q^{36} +(-12986.9 - 3813.31i) q^{37} +(-1622.39 - 11283.9i) q^{38} +(-6176.70 - 7128.29i) q^{39} +(2594.76 + 5681.73i) q^{40} +(10758.2 - 3158.89i) q^{41} +(-5281.58 + 11565.1i) q^{42} +(2444.11 - 16999.2i) q^{43} +(-13680.3 + 8791.81i) q^{44} +5465.95 q^{45} +(19828.5 - 9364.02i) q^{46} -17155.4 q^{47} +(4290.12 - 2757.09i) q^{48} +(-1409.63 + 9804.18i) q^{49} +(5129.78 - 11232.7i) q^{50} +(4049.18 - 1188.95i) q^{51} +(-18593.7 - 40714.6i) q^{52} +(16322.8 + 18837.5i) q^{53} +(896.735 + 6236.93i) q^{54} +(24653.2 + 7238.82i) q^{55} +(-9906.88 + 11433.1i) q^{56} +(-9985.90 - 6417.55i) q^{57} +(-26668.0 - 17138.5i) q^{58} +(9665.15 - 11154.2i) q^{59} +(24887.7 + 7307.68i) q^{60} +(1197.82 + 8331.05i) q^{61} +(28617.5 + 33026.3i) q^{62} +(5499.46 + 12042.1i) q^{63} +(47784.7 - 14030.9i) q^{64} +(-29378.4 + 64329.7i) q^{65} +(-4215.31 + 29318.1i) q^{66} +(33887.8 - 21778.4i) q^{67} +20026.3 q^{68} +(6151.75 - 21988.6i) q^{69} +95327.9 q^{70} +(15164.0 - 9745.34i) q^{71} +(-1067.01 + 7421.24i) q^{72} +(-16496.2 + 36121.7i) q^{73} +(-112252. + 32960.1i) q^{74} +(-5341.40 - 11696.0i) q^{75} +(-36888.1 - 42571.1i) q^{76} +(8856.33 + 61597.1i) q^{77} +(-78223.2 - 22968.4i) q^{78} +(36870.9 - 42551.3i) q^{79} +(-32166.8 - 20672.3i) q^{80} +(5519.46 + 3547.14i) q^{81} +(63464.9 - 73242.4i) q^{82} +(-64883.4 - 19051.5i) q^{83} +(8940.57 + 62183.0i) q^{84} +(-20721.1 - 23913.4i) q^{85} +(-61665.1 - 135028. i) q^{86} +(-31670.9 + 9299.42i) q^{87} +(-14640.9 + 32059.1i) q^{88} +(-9630.70 + 66983.0i) q^{89} +(39744.7 - 25542.3i) q^{90} -171285. q^{91} +(57407.9 - 91894.5i) q^{92} +45502.9 q^{93} +(-124742. + 80167.1i) q^{94} +(-12666.3 + 88095.8i) q^{95} +(29385.1 - 64344.3i) q^{96} +(-108476. + 31851.5i) q^{97} +(35565.0 + 77876.5i) q^{98} +(20196.9 + 23308.4i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 8 q^{2} + 90 q^{3} - 148 q^{4} + 6 q^{5} + 171 q^{6} + 118 q^{7} + 1616 q^{8} - 810 q^{9}+O(q^{10}) \) 100 * q - 8 * q^2 + 90 * q^3 - 148 * q^4 + 6 * q^5 + 171 * q^6 + 118 * q^7 + 1616 * q^8 - 810 * q^9	\( 100 q - 8 q^{2} + 90 q^{3} - 148 q^{4} + 6 q^{5} + 171 q^{6} + 118 q^{7} + 1616 q^{8} - 810 q^{9} - 262 q^{10} + 724 q^{11} + 1332 q^{12} + 2730 q^{13} + 328 q^{14} - 1143 q^{15} - 8596 q^{16} - 5699 q^{17} - 648 q^{18} + 1993 q^{19} + 28263 q^{20} - 1062 q^{21} - 19378 q^{22} + 9084 q^{23} + 1296 q^{24} - 4752 q^{25} - 7828 q^{26} + 7290 q^{27} - 29888 q^{28} - 37644 q^{29} + 2358 q^{30} - 2471 q^{31} + 42352 q^{32} + 1305 q^{33} + 47233 q^{34} + 9062 q^{35} - 21789 q^{36} + 1170 q^{37} - 133648 q^{38} - 24570 q^{39} + 135509 q^{40} - 8556 q^{41} - 17208 q^{42} + 39714 q^{43} + 108207 q^{44} - 44064 q^{45} + 87076 q^{46} + 56898 q^{47} + 60237 q^{48} + 35646 q^{49} + 12207 q^{50} - 48600 q^{51} - 368495 q^{52} + 11912 q^{53} - 34263 q^{54} - 231697 q^{55} + 235302 q^{56} + 4437 q^{57} - 201743 q^{58} + 116756 q^{59} + 209349 q^{60} - 191952 q^{61} - 91633 q^{62} + 9558 q^{63} + 383796 q^{64} + 120963 q^{65} + 92925 q^{66} - 7699 q^{67} - 486648 q^{68} + 9522 q^{69} + 340272 q^{70} + 60029 q^{71} + 130896 q^{72} + 110721 q^{73} - 290458 q^{74} + 48906 q^{75} + 30961 q^{76} - 325750 q^{77} + 51444 q^{78} - 267838 q^{79} - 519366 q^{80} - 65610 q^{81} - 739402 q^{82} - 236288 q^{83} - 382428 q^{84} + 72669 q^{85} + 643772 q^{86} + 62784 q^{87} + 976500 q^{88} + 455688 q^{89} - 21222 q^{90} + 267512 q^{91} + 70711 q^{92} - 12906 q^{93} + 1298755 q^{94} + 1815505 q^{95} + 461520 q^{96} + 271324 q^{97} - 1533115 q^{98} - 11745 q^{99}+O(q^{100}) \) 100 * q - 8 * q^2 + 90 * q^3 - 148 * q^4 + 6 * q^5 + 171 * q^6 + 118 * q^7 + 1616 * q^8 - 810 * q^9 - 262 * q^10 + 724 * q^11 + 1332 * q^12 + 2730 * q^13 + 328 * q^14 - 1143 * q^15 - 8596 * q^16 - 5699 * q^17 - 648 * q^18 + 1993 * q^19 + 28263 * q^20 - 1062 * q^21 - 19378 * q^22 + 9084 * q^23 + 1296 * q^24 - 4752 * q^25 - 7828 * q^26 + 7290 * q^27 - 29888 * q^28 - 37644 * q^29 + 2358 * q^30 - 2471 * q^31 + 42352 * q^32 + 1305 * q^33 + 47233 * q^34 + 9062 * q^35 - 21789 * q^36 + 1170 * q^37 - 133648 * q^38 - 24570 * q^39 + 135509 * q^40 - 8556 * q^41 - 17208 * q^42 + 39714 * q^43 + 108207 * q^44 - 44064 * q^45 + 87076 * q^46 + 56898 * q^47 + 60237 * q^48 + 35646 * q^49 + 12207 * q^50 - 48600 * q^51 - 368495 * q^52 + 11912 * q^53 - 34263 * q^54 - 231697 * q^55 + 235302 * q^56 + 4437 * q^57 - 201743 * q^58 + 116756 * q^59 + 209349 * q^60 - 191952 * q^61 - 91633 * q^62 + 9558 * q^63 + 383796 * q^64 + 120963 * q^65 + 92925 * q^66 - 7699 * q^67 - 486648 * q^68 + 9522 * q^69 + 340272 * q^70 + 60029 * q^71 + 130896 * q^72 + 110721 * q^73 - 290458 * q^74 + 48906 * q^75 + 30961 * q^76 - 325750 * q^77 + 51444 * q^78 - 267838 * q^79 - 519366 * q^80 - 65610 * q^81 - 739402 * q^82 - 236288 * q^83 - 382428 * q^84 + 72669 * q^85 + 643772 * q^86 + 62784 * q^87 + 976500 * q^88 + 455688 * q^89 - 21222 * q^90 + 267512 * q^91 + 70711 * q^92 - 12906 * q^93 + 1298755 * q^94 + 1815505 * q^95 + 461520 * q^96 + 271324 * q^97 - 1533115 * q^98 - 11745 * q^99

Introduction

L-functions

Modular forms

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Database

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