LMFDB - Embedded newform 7.9.d.a.3.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7,9,Mod(3,7)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("7.3");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	7.d (of order $6$, degree $2$, 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:	$2.85165027043$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 592x^{6} - 1176x^{5} + 336397x^{4} - 348096x^{3} + 8673408x^{2} + 8271396x + 197880489 $ x^8 + 592x^6 - 1176x^5 + 336397x^4 - 348096x^3 + 8673408x^2 + 8271396x + 197880489
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4}\cdot 3\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			3.4
Root			$11.6264 - 20.1376i$ of defining polynomial
Character	$\chi$	$=$	7.3
Dual form			7.9.d.a.5.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(11.1264 + 19.2716i) q^{2} +(31.2153 + 18.0222i) q^{3} +(-119.595 + 207.145i) q^{4} +(-305.183 + 176.198i) q^{5} +802.090i q^{6} +(2236.80 - 872.649i) q^{7} +374.058 q^{8} +(-2630.90 - 4556.86i) q^{9} +O(q^{10})$	\(q+(11.1264 + 19.2716i) q^{2} +(31.2153 + 18.0222i) q^{3} +(-119.595 + 207.145i) q^{4} +(-305.183 + 176.198i) q^{5} +802.090i q^{6} +(2236.80 - 872.649i) q^{7} +374.058 q^{8} +(-2630.90 - 4556.86i) q^{9} +(-6791.21 - 3920.91i) q^{10} +(6599.36 - 11430.4i) q^{11} +(-7466.41 + 4310.73i) q^{12} +25343.6i q^{13} +(41705.0 + 33397.2i) q^{14} -12701.9 q^{15} +(34778.3 + 60237.8i) q^{16} +(-129613. - 74832.2i) q^{17} +(58545.2 - 101403. i) q^{18} +(-88694.6 + 51207.9i) q^{19} -84289.7i q^{20} +(85549.5 + 13072.0i) q^{21} +293709. q^{22} +(-79908.8 - 138406. i) q^{23} +(11676.3 + 6741.33i) q^{24} +(-133221. + 230746. i) q^{25} +(-488410. + 281984. i) q^{26} -426145. i q^{27} +(-86746.0 + 567707. i) q^{28} +651182. q^{29} +(-141326. - 244785. i) q^{30} +(699138. + 403648. i) q^{31} +(-726038. + 1.25754e6i) q^{32} +(412002. - 237869. i) q^{33} -3.33046e6i q^{34} +(-528876. + 660437. i) q^{35} +1.25857e6 q^{36} +(-524495. - 908452. i) q^{37} +(-1.97371e6 - 1.13952e6i) q^{38} +(-456746. + 791107. i) q^{39} +(-114156. + 65908.1i) q^{40} +1.60644e6i q^{41} +(699943. + 1.79412e6i) q^{42} +2.42701e6 q^{43} +(1.57850e6 + 2.73405e6i) q^{44} +(1.60582e6 + 927118. i) q^{45} +(1.77820e6 - 3.07993e6i) q^{46} +(-7.13909e6 + 4.12175e6i) q^{47} +2.50712e6i q^{48} +(4.24177e6 - 3.90389e6i) q^{49} -5.92911e6 q^{50} +(-2.69728e6 - 4.67182e6i) q^{51} +(-5.24979e6 - 3.03097e6i) q^{52} +(4.30300e6 - 7.45301e6i) q^{53} +(8.21248e6 - 4.74148e6i) q^{54} +4.65116e6i q^{55} +(836693. - 326421. i) q^{56} -3.69151e6 q^{57} +(7.24533e6 + 1.25493e7i) q^{58} +(-241746. - 139572. i) q^{59} +(1.51908e6 - 2.63113e6i) q^{60} +(3.61375e6 - 2.08640e6i) q^{61} +1.79646e7i q^{62} +(-9.86135e6 - 7.89693e6i) q^{63} -1.45064e7 q^{64} +(-4.46548e6 - 7.73443e6i) q^{65} +(9.16823e6 + 5.29328e6i) q^{66} +(-1.64700e7 + 2.85269e7i) q^{67} +(3.10022e7 - 1.78992e7i) q^{68} -5.76052e6i q^{69} +(-1.86122e7 - 2.84395e6i) q^{70} -4.27665e6 q^{71} +(-984109. - 1.70453e6i) q^{72} +(4.46928e7 + 2.58034e7i) q^{73} +(1.16715e7 - 2.02157e7i) q^{74} +(-8.31708e6 + 4.80187e6i) q^{75} -2.44969e7i q^{76} +(4.78671e6 - 3.13265e7i) q^{77} -2.03278e7 q^{78} +(-1.54593e7 - 2.67762e7i) q^{79} +(-2.12275e7 - 1.22557e7i) q^{80} +(-9.58130e6 + 1.65953e7i) q^{81} +(-3.09586e7 + 1.78739e7i) q^{82} +1.80611e7i q^{83} +(-1.29391e7 + 1.61578e7i) q^{84} +5.27410e7 q^{85} +(2.70039e7 + 4.67722e7i) q^{86} +(2.03268e7 + 1.17357e7i) q^{87} +(2.46854e6 - 4.27563e6i) q^{88} +(1.47398e7 - 8.51001e6i) q^{89} +4.12621e7i q^{90} +(2.21160e7 + 5.66885e7i) q^{91} +3.82269e7 q^{92} +(1.45492e7 + 2.52000e7i) q^{93} +(-1.58865e8 - 9.17209e7i) q^{94} +(1.80454e7 - 3.12556e7i) q^{95} +(-4.53270e7 + 2.61696e7i) q^{96} -1.20359e8i q^{97} +(1.22430e8 + 3.83091e7i) q^{98} -6.94491e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 84 q^{3} - 164 q^{4} - 840 q^{5} - 140 q^{7} + 6544 q^{8} + 396 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 - 84 * q^3 - 164 * q^4 - 840 * q^5 - 140 * q^7 + 6544 * q^8 + 396 * q^9	\( 8 q - 4 q^{2} - 84 q^{3} - 164 q^{4} - 840 q^{5} - 140 q^{7} + 6544 q^{8} + 396 q^{9} + 5796 q^{10} + 1784 q^{11} - 40908 q^{12} - 9856 q^{14} + 131808 q^{15} - 8584 q^{16} - 141456 q^{17} - 121944 q^{18} - 257544 q^{19} + 474012 q^{21} + 1706256 q^{22} - 348940 q^{23} - 895104 q^{24} - 557752 q^{25} - 2913120 q^{26} + 1485092 q^{28} + 4983176 q^{29} - 551112 q^{30} - 2376696 q^{31} - 332016 q^{32} - 5719140 q^{33} + 2491272 q^{35} + 13269408 q^{36} + 492740 q^{37} - 7088088 q^{38} - 2850372 q^{39} - 7601832 q^{40} + 3586128 q^{42} + 4448432 q^{43} - 3678804 q^{44} + 3328164 q^{45} - 226560 q^{46} + 2704128 q^{47} - 3811024 q^{49} - 15628912 q^{50} - 350856 q^{51} + 11135208 q^{52} + 2281460 q^{53} + 24553368 q^{54} - 6573392 q^{56} - 43638408 q^{57} + 11442696 q^{58} + 25291140 q^{59} + 17679564 q^{60} + 59368764 q^{61} - 60081756 q^{63} - 114153056 q^{64} + 16923396 q^{65} + 463428 q^{66} - 107108 q^{67} + 44316972 q^{68} + 19120080 q^{70} - 82809760 q^{71} + 13297584 q^{72} + 116758404 q^{73} + 72690340 q^{74} + 79832424 q^{75} - 58244200 q^{77} - 44122512 q^{78} - 50628092 q^{79} - 93591624 q^{80} - 96868872 q^{81} - 91061712 q^{82} + 154096572 q^{84} + 119231208 q^{85} + 39093088 q^{86} + 26702676 q^{87} + 41392848 q^{88} - 2322516 q^{89} - 151794552 q^{91} + 253819128 q^{92} - 57693204 q^{93} - 345566088 q^{94} - 172787052 q^{95} - 416455200 q^{96} + 373659692 q^{98} + 672244008 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 84 * q^3 - 164 * q^4 - 840 * q^5 - 140 * q^7 + 6544 * q^8 + 396 * q^9 + 5796 * q^10 + 1784 * q^11 - 40908 * q^12 - 9856 * q^14 + 131808 * q^15 - 8584 * q^16 - 141456 * q^17 - 121944 * q^18 - 257544 * q^19 + 474012 * q^21 + 1706256 * q^22 - 348940 * q^23 - 895104 * q^24 - 557752 * q^25 - 2913120 * q^26 + 1485092 * q^28 + 4983176 * q^29 - 551112 * q^30 - 2376696 * q^31 - 332016 * q^32 - 5719140 * q^33 + 2491272 * q^35 + 13269408 * q^36 + 492740 * q^37 - 7088088 * q^38 - 2850372 * q^39 - 7601832 * q^40 + 3586128 * q^42 + 4448432 * q^43 - 3678804 * q^44 + 3328164 * q^45 - 226560 * q^46 + 2704128 * q^47 - 3811024 * q^49 - 15628912 * q^50 - 350856 * q^51 + 11135208 * q^52 + 2281460 * q^53 + 24553368 * q^54 - 6573392 * q^56 - 43638408 * q^57 + 11442696 * q^58 + 25291140 * q^59 + 17679564 * q^60 + 59368764 * q^61 - 60081756 * q^63 - 114153056 * q^64 + 16923396 * q^65 + 463428 * q^66 - 107108 * q^67 + 44316972 * q^68 + 19120080 * q^70 - 82809760 * q^71 + 13297584 * q^72 + 116758404 * q^73 + 72690340 * q^74 + 79832424 * q^75 - 58244200 * q^77 - 44122512 * q^78 - 50628092 * q^79 - 93591624 * q^80 - 96868872 * q^81 - 91061712 * q^82 + 154096572 * q^84 + 119231208 * q^85 + 39093088 * q^86 + 26702676 * q^87 + 41392848 * q^88 - 2322516 * q^89 - 151794552 * q^91 + 253819128 * q^92 - 57693204 * q^93 - 345566088 * q^94 - 172787052 * q^95 - 416455200 * q^96 + 373659692 * q^98 + 672244008 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/7\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	11.1264	+	19.2716i	0.695402	+	1.20447i	0.970045	+	0.242926i	$0.0781072\pi$
$2$	11.1264	+	19.2716i	0.695402	+	1.20447i	−0.274642	+	0.961546i	$0.588559\pi$
$3$	31.2153	+	18.0222i	0.385374	+	0.222496i	0.680154	−	0.733069i	$-0.261913\pi$
$3$	31.2153	+	18.0222i	0.385374	+	0.222496i	−0.294780	+	0.955565i	$0.595246\pi$
$4$	−119.595	+	207.145i	−0.467169	+	0.809161i
$5$	−305.183	+	176.198i	−0.488293	+	0.281916i	−0.723866	−	0.689940i	$-0.757637\pi$
$5$	−305.183	+	176.198i	−0.488293	+	0.281916i	0.235573	+	0.971857i	$0.424303\pi$
$6$			802.090i			0.618897i
$7$	2236.80	−	872.649i	0.931613	−	0.363452i
$7$	2236.80	−	872.649i	0.931613	−	0.363452i
$8$	374.058			0.0913226
$9$	−2630.90	−	4556.86i	−0.400991	−	0.694537i
$10$	−6791.21	−	3920.91i	−0.679121	−	0.392091i
$11$	6599.36	−	11430.4i	0.450745	−	0.780713i	−0.547688	−	0.836683i	$-0.684492\pi$
$11$	6599.36	−	11430.4i	0.450745	−	0.780713i	0.998432	+	0.0559699i	$0.0178251\pi$
$12$	−7466.41	+	4310.73i	−0.360070	+	0.207886i
$13$			25343.6i			0.887348i	0.896188	+	0.443674i	$0.146325\pi$
$13$			25343.6i			0.887348i	−0.896188	+	0.443674i	$0.853675\pi$
$14$	41705.0	+	33397.2i	1.08561	+	0.869356i
$15$	−12701.9			−0.250901
$16$	34778.3	+	60237.8i	0.530675	+	0.919156i
$17$	−129613.	−	74832.2i	−1.55186	−	0.895968i	−0.997990	−	0.0633671i	$-0.979816\pi$
$17$	−129613.	−	74832.2i	−1.55186	−	0.895968i	−0.553873	−	0.832601i	$-0.686851\pi$
$18$	58545.2	−	101403.i	0.557701	−	0.965966i
$19$	−88694.6	+	51207.9i	−0.680586	+	0.392936i	−0.800076	−	0.599899i	$-0.795207\pi$
$19$	−88694.6	+	51207.9i	−0.680586	+	0.392936i	0.119490	+	0.992835i	$0.461874\pi$
$20$		−	84289.7i		−	0.526810i
$21$	85549.5	+	13072.0i	0.439886	+	0.0672148i
$22$	293709.			1.25380
$23$	−79908.8	−	138406.i	−0.285551	−	0.494588i	0.687192	−	0.726476i	$-0.258843\pi$
$23$	−79908.8	−	138406.i	−0.285551	−	0.494588i	−0.972743	+	0.231888i	$0.925510\pi$
$24$	11676.3	+	6741.33i	0.0351934	+	0.0203189i
$25$	−133221.	+	230746.i	−0.341046	+	0.590710i
$26$	−488410.	+	281984.i	−1.06879	+	0.617064i
$27$		−	426145.i		−	0.801867i
$28$	−86746.0	+	567707.i	−0.141129	+	0.923618i
$29$	651182.			0.920683			0.460342	−	0.887742i	$-0.347727\pi$
$29$	651182.			0.920683			0.460342	+	0.887742i	$0.347727\pi$
$30$	−141326.	−	244785.i	−0.174477	−	0.302203i
$31$	699138.	+	403648.i	0.757036	+	0.437075i	0.828230	−	0.560388i	$-0.189348\pi$
$31$	699138.	+	403648.i	0.757036	+	0.437075i	−0.0711947	+	0.997462i	$0.522681\pi$
$32$	−726038.	+	1.25754e6i	−0.692404	+	1.19928i
$33$	412002.	−	237869.i	0.347411	−	0.200578i
$34$		−	3.33046e6i		−	2.49223i
$35$	−528876.	+	660437.i	−0.352437	+	0.440108i
$36$	1.25857e6			0.749323
$37$	−524495.	−	908452.i	−0.279856	−	0.484725i	0.691493	−	0.722383i	$-0.256953\pi$
$37$	−524495.	−	908452.i	−0.279856	−	0.484725i	−0.971349	+	0.237659i	$0.923620\pi$
$38$	−1.97371e6	−	1.13952e6i	−0.946562	−	0.546498i
$39$	−456746.	+	791107.i	−0.197431	+	0.341961i
$40$	−114156.	+	65908.1i	−0.0445922	+	0.0257453i
$41$			1.60644e6i			0.568498i	0.958751	+	0.284249i	$0.0917442\pi$
$41$			1.60644e6i			0.568498i	−0.958751	+	0.284249i	$0.908256\pi$
$42$	699943.	+	1.79412e6i	0.224939	+	0.576572i
$43$	2.42701e6			0.709900			0.354950	−	0.934885i	$-0.384498\pi$
$43$	2.42701e6			0.709900			0.354950	+	0.934885i	$0.384498\pi$
$44$	1.57850e6	+	2.73405e6i	0.421148	+	0.729450i
$45$	1.60582e6	+	927118.i	0.391603	+	0.226092i
$46$	1.77820e6	−	3.07993e6i	0.397145	−	0.687876i
$47$	−7.13909e6	+	4.12175e6i	−1.46302	+	0.844677i	−0.999150	−	0.0412246i	$-0.986874\pi$
$47$	−7.13909e6	+	4.12175e6i	−1.46302	+	0.844677i	−0.463873	+	0.885902i	$0.653541\pi$
$48$			2.50712e6i			0.472292i
$49$	4.24177e6	−	3.90389e6i	0.735805	−	0.677194i
$50$	−5.92911e6			−0.948658
$51$	−2.69728e6	−	4.67182e6i	−0.398699	−	0.690566i
$52$	−5.24979e6	−	3.03097e6i	−0.718007	−	0.414542i
$53$	4.30300e6	−	7.45301e6i	0.545341	−	0.944558i	−0.453245	−	0.891386i	$-0.649734\pi$
$53$	4.30300e6	−	7.45301e6i	0.545341	−	0.944558i	0.998585	−	0.0531716i	$-0.0169330\pi$
$54$	8.21248e6	−	4.74148e6i	0.965827	−	0.557620i
$55$			4.65116e6i			0.508289i
$56$	836693.	−	326421.i	0.0850773	−	0.0331914i
$57$	−3.69151e6			−0.349707
$58$	7.24533e6	+	1.25493e7i	0.640245	+	1.10894i
$59$	−241746.	−	139572.i	−0.0199504	−	0.0115184i	0.489992	−	0.871727i	$-0.337000\pi$
$59$	−241746.	−	139572.i	−0.0199504	−	0.0115184i	−0.509942	+	0.860209i	$0.670333\pi$
$60$	1.51908e6	−	2.63113e6i	0.117213	−	0.203019i
$61$	3.61375e6	−	2.08640e6i	0.260999	−	0.150688i	−0.363791	−	0.931481i	$-0.618518\pi$
$61$	3.61375e6	−	2.08640e6i	0.260999	−	0.150688i	0.624790	+	0.780793i	$0.285185\pi$
$62$			1.79646e7i			1.21577i
$63$	−9.86135e6	−	7.89693e6i	−0.626000	−	0.501298i
$64$	−1.45064e7			−0.864648
$65$	−4.46548e6	−	7.73443e6i	−0.250158	−	0.433286i
$66$	9.16823e6	+	5.29328e6i	0.483181	+	0.278964i
$67$	−1.64700e7	+	2.85269e7i	−0.817324	+	1.41565i	0.0903235	+	0.995912i	$0.471210\pi$
$67$	−1.64700e7	+	2.85269e7i	−0.817324	+	1.41565i	−0.907647	+	0.419734i	$0.862123\pi$
$68$	3.10022e7	−	1.78992e7i	1.44996	−	0.837138i
$69$		−	5.76052e6i		−	0.254135i
$70$	−1.86122e7	−	2.84395e6i	−0.775184	−	0.118448i
$71$	−4.27665e6			−0.168295			−0.0841473	−	0.996453i	$-0.526817\pi$
$71$	−4.27665e6			−0.168295			−0.0841473	+	0.996453i	$0.526817\pi$
$72$	−984109.	−	1.70453e6i	−0.0366196	−	0.0634270i
$73$	4.46928e7	+	2.58034e7i	1.57379	+	0.908626i	0.995699	+	0.0926512i	$0.0295342\pi$
$73$	4.46928e7	+	2.58034e7i	1.57379	+	0.908626i	0.578088	+	0.815975i	$0.303799\pi$
$74$	1.16715e7	−	2.02157e7i	0.389225	−	0.674158i
$75$	−8.31708e6	+	4.80187e6i	−0.262861	+	0.151763i
$76$		−	2.44969e7i		−	0.734271i
$77$	4.78671e6	−	3.13265e7i	0.136168	−	0.891147i
$78$	−2.03278e7			−0.549177
$79$	−1.54593e7	−	2.67762e7i	−0.396899	−	0.687449i	0.596442	−	0.802656i	$-0.296580\pi$
$79$	−1.54593e7	−	2.67762e7i	−0.396899	−	0.687449i	−0.993342	+	0.115206i	$0.963247\pi$
$80$	−2.12275e7	−	1.22557e7i	−0.518250	−	0.299212i
$81$	−9.58130e6	+	1.65953e7i	−0.222579	+	0.385518i
$82$	−3.09586e7	+	1.78739e7i	−0.684740	+	0.395335i
$83$			1.80611e7i			0.380567i	0.981729	+	0.190284i	$0.0609408\pi$
$83$			1.80611e7i			0.380567i	−0.981729	+	0.190284i	$0.939059\pi$
$84$	−1.29391e7	+	1.61578e7i	−0.259889	+	0.324538i
$85$	5.27410e7			1.01035
$86$	2.70039e7	+	4.67722e7i	0.493666	+	0.855055i
$87$	2.03268e7	+	1.17357e7i	0.354807	+	0.204848i
$88$	2.46854e6	−	4.27563e6i	0.0411632	−	0.0712968i
$89$	1.47398e7	−	8.51001e6i	0.234926	−	0.135635i	−0.377917	−	0.925840i	$-0.623359\pi$
$89$	1.47398e7	−	8.51001e6i	0.234926	−	0.135635i	0.612842	+	0.790205i	$0.290026\pi$
$90$			4.12621e7i			0.628899i
$91$	2.21160e7	+	5.66885e7i	0.322509	+	0.826665i
$92$	3.82269e7			0.533602
$93$	1.45492e7	+	2.52000e7i	0.194495	+	0.336875i
$94$	−1.58865e8	−	9.17209e7i	−2.03478	−	1.17478i
$95$	1.80454e7	−	3.12556e7i	0.221550	−	0.383737i
$96$	−4.53270e7	+	2.61696e7i	−0.533669	+	0.308114i
$97$		−	1.20359e8i		−	1.35954i	−0.733424	−	0.679772i	$-0.762079\pi$
$97$		−	1.20359e8i		−	1.35954i	0.733424	−	0.679772i	$-0.237921\pi$
$98$	1.22430e8	+	3.83091e7i	1.32734	+	0.415334i
$99$	−6.94491e7			−0.722979
$100$	−3.18653e7	−	5.51923e7i	−0.318653	−	0.551923i
$101$	−4.31829e7	−	2.49317e7i	−0.414979	−	0.239588i	0.277948	−	0.960596i	$-0.410346\pi$
$101$	−4.31829e7	−	2.49317e7i	−0.414979	−	0.239588i	−0.692927	+	0.721008i	$0.743679\pi$
$102$	6.00221e7	−	1.03961e8i	0.554512	−	0.960443i
$103$	−5.60837e7	+	3.23799e7i	−0.498296	+	0.287691i	−0.728010	−	0.685567i	$-0.759554\pi$
$103$	−5.60837e7	+	3.23799e7i	−0.498296	+	0.287691i	0.229713	+	0.973258i	$0.426221\pi$
$104$			9.47995e6i			0.0810350i
$105$	−2.84115e7	+	1.10843e7i	−0.233742	+	0.0911905i
$106$	1.91508e8			1.51692
$107$	−8.29211e6	−	1.43624e7i	−0.0632601	−	0.109570i	0.832661	−	0.553783i	$-0.186816\pi$
$107$	−8.29211e6	−	1.43624e7i	−0.0632601	−	0.109570i	−0.895921	+	0.444214i	$0.853483\pi$
$108$	8.82739e7	+	5.09650e7i	0.648839	+	0.374608i
$109$	−8.10512e7	+	1.40385e8i	−0.574187	+	0.994521i	0.421943	+	0.906623i	$0.361348\pi$
$109$	−8.10512e7	+	1.40385e8i	−0.574187	+	0.994521i	−0.996129	+	0.0878983i	$0.971985\pi$
$110$	−8.96352e7	+	5.17509e7i	−0.612220	+	0.353466i
$111$		−	3.78102e7i		−	0.249067i
$112$	1.30359e8	+	1.04391e8i	0.828453	+	0.663423i
$113$	−1.74676e7			−0.107132			−0.0535660	−	0.998564i	$-0.517059\pi$
$113$	−1.74676e7			−0.107132			−0.0535660	+	0.998564i	$0.517059\pi$
$114$	−4.10733e7	−	7.11411e7i	−0.243187	−	0.421212i
$115$	4.87736e7	+	2.81595e7i	0.278865	+	0.161003i
$116$	−7.78783e7	+	1.34889e8i	−0.430115	+	0.744981i
$117$	1.15487e8	−	6.66764e7i	0.616296	−	0.355819i
$118$		−	6.21176e6i		−	0.0320396i
$119$	−3.55221e8	−	5.42780e7i	−1.77138	−	0.270667i
$120$	−4.75122e6			−0.0229129
$121$	2.00764e7	+	3.47734e7i	0.0936581	+	0.162221i
$122$	8.04163e7	+	4.64284e7i	0.362999	+	0.209577i
$123$	−2.89515e7	+	5.01455e7i	−0.126488	+	0.219084i
$124$	−1.67227e8	+	9.65487e7i	−0.707327	+	0.408376i
$125$		−	2.31548e8i		−	0.948419i
$126$	4.24645e7	−	2.77908e8i	0.168478	−	1.10260i
$127$	3.19294e8			1.22737			0.613685	−	0.789551i	$-0.289687\pi$
$127$	3.19294e8			1.22737			0.613685	+	0.789551i	$0.289687\pi$
$128$	2.44614e7	+	4.23684e7i	0.0911258	+	0.157834i
$129$	7.57597e7	+	4.37399e7i	0.273577	+	0.157950i
$130$	9.93697e7	−	1.72113e8i	0.347921	−	0.602617i
$131$	4.95946e8	−	2.86335e8i	1.68403	−	0.972274i	0.725093	−	0.688651i	$-0.241797\pi$
$131$	4.95946e8	−	2.86335e8i	1.68403	−	0.972274i	0.958936	−	0.283624i	$-0.0915366\pi$
$132$			1.13792e8i			0.374815i
$133$	−1.53706e8	+	1.91941e8i	−0.491229	+	0.613425i
$134$	−7.33009e8			−2.27348
$135$	7.50858e7	+	1.30052e8i	0.226059	+	0.391546i
$136$	−4.84828e7	−	2.79915e7i	−0.141720	−	0.0818222i
$137$	−1.19167e8	+	2.06403e8i	−0.338278	+	0.585915i	−0.984109	−	0.177566i	$-0.943178\pi$
$137$	−1.19167e8	+	2.06403e8i	−0.338278	+	0.585915i	0.645831	+	0.763480i	$0.276511\pi$
$138$	1.11014e8	−	6.40940e7i	0.306099	−	0.176726i
$139$		−	1.39444e8i		−	0.373542i	−0.982403	−	0.186771i	$-0.940198\pi$
$139$		−	1.39444e8i		−	0.373542i	0.982403	−	0.186771i	$-0.0598022\pi$
$140$	−7.35553e7	−	1.88539e8i	−0.191470	−	0.490783i
$141$	−2.97132e8			−0.751748
$142$	−4.75839e7	−	8.24177e7i	−0.117032	−	0.202706i
$143$	2.89687e8	+	1.67251e8i	0.692764	+	0.399968i
$144$	1.82997e8	−	3.16960e8i	0.425592	−	0.737147i
$145$	−1.98730e8	+	1.14737e8i	−0.449563	+	0.259556i
$146$			1.14840e9i			2.52744i
$147$	2.02765e8	−	4.54152e7i	0.434233	−	0.0972595i
$148$	2.50909e8			0.522960
$149$	8.28009e7	+	1.43415e8i	0.167993	+	0.290972i	0.937714	−	0.347408i	$-0.112938\pi$
$149$	8.28009e7	+	1.43415e8i	0.167993	+	0.290972i	−0.769721	+	0.638380i	$0.779605\pi$
$150$	−1.85079e8	−	1.06855e8i	−0.365588	−	0.211072i
$151$	9.53528e7	−	1.65156e8i	0.183411	−	0.317677i	−0.759629	−	0.650357i	$-0.774619\pi$
$151$	9.53528e7	−	1.65156e8i	0.183411	−	0.317677i	0.943040	+	0.332680i	$0.107953\pi$
$152$	−3.31769e7	+	1.91547e7i	−0.0621529	+	0.0358840i
$153$			7.87505e8i			1.43710i
$154$	6.56970e8	−	2.56305e8i	1.16805	−	0.455695i
$155$	−2.84487e8			−0.492874
$156$	−1.09249e8	−	1.89225e8i	−0.184468	−	0.319507i
$157$	−4.60267e8	−	2.65736e8i	−0.757551	−	0.437372i	0.0708650	−	0.997486i	$-0.477424\pi$
$157$	−4.60267e8	−	2.65736e8i	−0.757551	−	0.437372i	−0.828416	+	0.560114i	$0.810757\pi$
$158$	3.44013e8	−	5.95848e8i	0.552009	−	0.956108i
$159$	2.68639e8	−	1.55099e8i	0.420320	−	0.242672i
$160$		−	5.11705e8i		−	0.780800i
$161$	−2.99520e8	−	2.39855e8i	−0.445782	−	0.356981i
$162$	−4.26423e8			−0.619128
$163$	−2.07441e8	−	3.59298e8i	−0.293863	−	0.508985i	0.680857	−	0.732416i	$-0.261607\pi$
$163$	−2.07441e8	−	3.59298e8i	−0.293863	−	0.508985i	−0.974720	+	0.223431i	$0.928274\pi$
$164$	−3.32766e8	−	1.92122e8i	−0.460006	−	0.265584i
$165$	−8.38241e7	+	1.45188e8i	−0.113092	+	0.195882i
$166$	−3.48065e8	+	2.00956e8i	−0.458383	+	0.264648i
$167$		−	7.35036e8i		−	0.945023i	−0.881324	−	0.472512i	$-0.843347\pi$
$167$		−	7.35036e8i		−	0.945023i	0.881324	−	0.472512i	$-0.156653\pi$
$168$	3.20004e7	+	4.88968e6i	0.0401716	+	0.00613824i
$169$	1.73435e8			0.212613
$170$	5.86820e8	+	1.01640e9i	0.702602	+	1.21694i
$171$	4.66694e8	+	2.69446e8i	0.545818	+	0.315128i
$172$	−2.90259e8	+	5.02743e8i	−0.331643	+	0.574423i
$173$	4.55455e8	−	2.62957e8i	0.508465	−	0.293562i	−0.223738	−	0.974649i	$-0.571826\pi$
$173$	4.55455e8	−	2.62957e8i	0.508465	−	0.293562i	0.732202	+	0.681087i	$0.238493\pi$
$174$			5.22306e8i			0.569808i
$175$	−9.66293e7	+	6.32389e8i	−0.103028	+	0.674267i
$176$	9.18058e8			0.956796
$177$	−5.03078e6	−	8.71357e6i	−0.00512557	−	0.00887775i
$178$	3.28002e8	+	1.89372e8i	0.326736	+	0.188641i
$179$	−1.22450e7	+	2.12090e7i	−0.0119274	+	0.0206589i	−0.871928	−	0.489635i	$-0.837130\pi$
$179$	−1.22450e7	+	2.12090e7i	−0.0119274	+	0.0206589i	0.860000	+	0.510294i	$0.170463\pi$
$180$	−3.84096e8	+	2.21758e8i	−0.365889	+	0.211246i
$181$		−	9.24794e8i		−	0.861650i	−0.902436	−	0.430825i	$-0.858223\pi$
$181$		−	9.24794e8i		−	0.861650i	0.902436	−	0.430825i	$-0.141777\pi$
$182$	−8.46403e8	+	1.05695e9i	−0.771422	+	0.963318i
$183$	1.50406e8			0.134110
$184$	−2.98905e7	−	5.17718e7i	−0.0260772	−	0.0451671i
$185$	3.20134e8	+	1.84830e8i	0.273304	+	0.157792i
$186$	−3.23762e8	+	5.60772e8i	−0.270504	+	0.468527i
$187$	−1.71073e9	+	9.87688e8i	−1.39899	+	0.807706i
$188$		−	1.97177e9i		−	1.57843i
$189$	−3.71875e8	−	9.53202e8i	−0.291441	−	0.747030i
$190$	8.03125e8			0.616267
$191$	−5.77301e8	−	9.99915e8i	−0.433780	−	0.751328i	0.563416	−	0.826174i	$-0.309487\pi$
$191$	−5.77301e8	−	9.99915e8i	−0.433780	−	0.751328i	−0.997195	+	0.0748453i	$0.976154\pi$
$192$	−4.52821e8	−	2.61437e8i	−0.333213	−	0.192381i
$193$	−6.39922e8	+	1.10838e9i	−0.461209	+	0.798838i	−0.999022	−	0.0442267i	$-0.985918\pi$
$193$	−6.39922e8	+	1.10838e9i	−0.461209	+	0.798838i	0.537812	+	0.843065i	$0.319251\pi$
$194$	2.31951e9	−	1.33917e9i	1.63753	−	0.945430i
$195$		−	3.21910e8i		−	0.222636i
$196$	3.01376e8	+	1.34555e9i	0.204213	+	0.911748i
$197$	1.03937e9			0.690088			0.345044	−	0.938587i	$-0.387864\pi$
$197$	1.03937e9			0.690088			0.345044	+	0.938587i	$0.387864\pi$
$198$	−7.72721e8	−	1.33839e9i	−0.502761	−	0.870808i
$199$	1.05379e9	+	6.08407e8i	0.671959	+	0.387956i	0.796818	−	0.604219i	$-0.206515\pi$
$199$	1.05379e9	+	6.08407e8i	0.671959	+	0.387956i	−0.124860	+	0.992174i	$0.539848\pi$
$200$	−4.98324e7	+	8.63123e7i	−0.0311453	+	0.0539452i
$201$	−1.02823e9	+	5.93650e8i	−0.629951	+	0.363702i
$202$		−	1.10960e9i		−	0.666441i
$203$	1.45656e9	−	5.68253e8i	0.857720	−	0.334624i
$204$	1.29033e9			0.745039
$205$	−2.83051e8	−	4.90258e8i	−0.160269	−	0.277594i
$206$	−1.24802e9	−	7.20547e8i	−0.693033	−	0.400123i
$207$	−4.20464e8	+	7.28266e8i	−0.229007	+	0.396651i
$208$	−1.52664e9	+	8.81406e8i	−0.815612	+	0.470894i
$209$			1.35176e9i			0.708456i
$210$	−5.29730e8	−	4.24206e8i	−0.272381	−	0.218122i
$211$	−2.74826e8			−0.138652			−0.0693262	−	0.997594i	$-0.522085\pi$
$211$	−2.74826e8			−0.138652			−0.0693262	+	0.997594i	$0.522085\pi$
$212$	1.02924e9	+	1.78269e9i	0.509533	+	0.882536i
$213$	−1.33497e8	−	7.70745e7i	−0.0648564	−	0.0374448i
$214$	1.84523e8	−	3.19604e8i	0.0879824	−	0.152390i
$215$	−7.40682e8	+	4.27633e8i	−0.346639	+	0.200132i
$216$		−	1.59403e8i		−	0.0732286i
$217$	1.91608e9	+	2.92778e8i	0.864120	+	0.132038i
$218$	−3.60724e9			−1.59716
$219$	9.30065e8	+	1.61092e9i	0.404331	+	0.700322i
$220$	−9.63466e8	−	5.56257e8i	−0.411288	−	0.237457i
$221$	1.89651e9	−	3.28486e9i	0.795036	−	1.37704i
$222$	7.28661e8	−	4.20692e8i	0.299995	−	0.173202i
$223$			3.35379e9i			1.35618i	0.734980	+	0.678088i	$0.237191\pi$
$223$			3.35379e9i			1.35618i	−0.734980	+	0.678088i	$0.762809\pi$
$224$	−5.26617e8	+	3.44644e9i	−0.209172	+	1.36892i
$225$	1.40197e9			0.547026
$226$	−1.94352e8	−	3.36628e8i	−0.0744999	−	0.129038i
$227$	−3.08485e9	−	1.78104e9i	−1.16180	−	0.670764i	−0.210063	−	0.977688i	$-0.567367\pi$
$227$	−3.08485e9	−	1.78104e9i	−1.16180	−	0.670764i	−0.951734	+	0.306924i	$0.900700\pi$
$228$	4.41487e8	−	7.64678e8i	0.163372	−	0.282969i
$229$	2.52928e9	−	1.46028e9i	0.919720	−	0.531000i	0.0361740	−	0.999346i	$-0.488483\pi$
$229$	2.52928e9	−	1.46028e9i	0.919720	−	0.531000i	0.883546	+	0.468345i	$0.155150\pi$
$230$			1.25326e9i			0.447847i
$231$	7.13990e8	−	8.91600e8i	0.250752	−	0.313128i
$232$	2.43579e8			0.0840792
$233$	4.79545e8	+	8.30596e8i	0.162707	+	0.281816i	0.935839	−	0.352429i	$-0.114644\pi$
$233$	4.79545e8	+	8.30596e8i	0.162707	+	0.281816i	−0.773132	+	0.634245i	$0.781311\pi$
$234$	2.56992e9	+	1.48374e9i	0.857148	+	0.494875i
$235$	1.45249e9	−	2.51578e9i	0.476256	−	0.824900i
$236$	5.78233e7	−	3.33843e7i	0.0186404	−	0.0107620i
$237$		−	1.11444e9i		−	0.353234i
$238$	−2.90633e9	−	7.44959e9i	−0.905809	−	2.32180i
$239$	−3.39709e9			−1.04116			−0.520578	−	0.853814i	$-0.674284\pi$
$239$	−3.39709e9			−1.04116			−0.520578	+	0.853814i	$0.674284\pi$
$240$	−4.41749e8	−	7.65132e8i	−0.133147	−	0.230617i
$241$	4.57409e8	+	2.64085e8i	0.135593	+	0.0782845i	0.566262	−	0.824225i	$-0.308389\pi$
$241$	4.57409e8	+	2.64085e8i	0.135593	+	0.0782845i	−0.430669	+	0.902510i	$0.641722\pi$
$242$	−4.46759e8	+	7.73809e8i	−0.130260	+	0.225617i
$243$	−3.01952e9	+	1.74332e9i	−0.865990	+	0.499979i
$244$			9.98094e8i			0.281587i
$245$	−6.06661e8	+	1.93879e9i	−0.168377	+	0.538105i
$246$	−1.28851e9			−0.351841
$247$	−1.29779e9	−	2.24784e9i	−0.348672	−	0.603917i
$248$	2.61518e8	+	1.50987e8i	0.0691345	+	0.0399148i
$249$	−3.25500e8	+	5.63782e8i	−0.0846747	+	0.146661i
$250$	4.46228e9	−	2.57630e9i	1.14234	−	0.659533i
$251$			2.08656e9i			0.525698i	0.964837	+	0.262849i	$0.0846621\pi$
$251$			2.08656e9i			0.525698i	−0.964837	+	0.262849i	$0.915338\pi$
$252$	2.81518e9	−	1.09829e9i	0.698079	−	0.272343i
$253$	−2.10939e9			−0.514842
$254$	3.55260e9	+	6.15329e9i	0.853516	+	1.47833i
$255$	1.64633e9	+	9.50507e8i	0.389364	+	0.224799i
$256$	−2.40115e9	+	4.15892e9i	−0.559062	+	0.968324i
$257$	1.41437e9	−	8.16587e8i	0.324213	−	0.187184i	−0.329056	−	0.944310i	$-0.606730\pi$
$257$	1.41437e9	−	8.16587e8i	0.324213	−	0.187184i	0.653269	+	0.757126i	$0.273397\pi$
$258$			1.94668e9i			0.439355i
$259$	−1.96595e9	−	1.57433e9i	−0.436892	−	0.349862i
$260$	2.13620e9			0.467464
$261$	−1.71320e9	−	2.96734e9i	−0.369186	−	0.639449i
$262$	1.10362e10	+	6.37177e9i	2.34216	+	1.35224i
$263$	−1.94576e9	+	3.37015e9i	−0.406692	+	0.704412i	−0.994517	−	0.104577i	$-0.966651\pi$
$263$	−1.94576e9	+	3.37015e9i	−0.406692	+	0.704412i	0.587825	+	0.808988i	$0.299985\pi$
$264$	1.54112e8	−	8.89768e7i	0.0317265	−	0.0183173i
$265$			3.03271e9i			0.614962i
$266$	−5.40920e9	−	8.26529e8i	−1.08046	−	0.165094i
$267$	6.13476e8			0.120712
$268$	−3.93947e9	−	6.82336e9i	−0.763657	−	1.32269i
$269$	−6.58669e9	−	3.80282e9i	−1.25793	−	0.726268i	−0.285261	−	0.958450i	$-0.592080\pi$
$269$	−6.58669e9	−	3.80282e9i	−1.25793	−	0.726268i	−0.972673	+	0.232181i	$0.925414\pi$
$270$	−1.67087e9	+	2.89404e9i	−0.314405	+	0.544565i
$271$	2.06731e9	−	1.19356e9i	0.383291	−	0.221293i	−0.295958	−	0.955201i	$-0.595639\pi$
$271$	2.06731e9	−	1.19356e9i	0.383291	−	0.221293i	0.679249	+	0.733908i	$0.262306\pi$
$272$		−	1.04102e10i		−	1.90187i
$273$	−3.31291e8	+	2.16813e9i	−0.0596430	+	0.390332i
$274$	−5.30362e9			−0.940957
$275$	1.75835e9	+	3.04555e9i	0.307450	+	0.532519i
$276$	1.19326e9	+	6.88931e8i	0.205636	+	0.118724i
$277$	3.43465e9	−	5.94898e9i	0.583395	−	1.01047i	−0.411678	−	0.911329i	$-0.635057\pi$
$277$	3.43465e9	−	5.94898e9i	0.583395	−	1.01047i	0.995073	−	0.0991409i	$-0.0316095\pi$
$278$	2.68729e9	−	1.55151e9i	0.449921	−	0.259762i
$279$		−	4.24783e9i		−	0.701053i
$280$	−1.97830e8	+	2.47042e8i	−0.0321855	+	0.0401918i
$281$	1.48540e9			0.238242			0.119121	−	0.992880i	$-0.461992\pi$
$281$	1.48540e9			0.238242			0.119121	+	0.992880i	$0.461992\pi$
$282$	−3.30602e9	−	5.72619e9i	−0.522768	−	0.905460i
$283$	−7.19267e8	−	4.15269e8i	−0.112136	−	0.0647416i	0.442883	−	0.896579i	$-0.353956\pi$
$283$	−7.19267e8	−	4.15269e8i	−0.112136	−	0.0647416i	−0.555019	+	0.831838i	$0.687289\pi$
$284$	5.11467e8	−	8.85887e8i	0.0786220	−	0.136177i
$285$	1.12659e9	−	6.50435e8i	0.170760	−	0.0985881i
$286$			7.44364e9i			1.11255i
$287$	1.40186e9	+	3.59328e9i	0.206622	+	0.529620i
$288$	7.64055e9			1.11059
$289$	7.71183e9	+	1.33573e10i	1.10552	+	1.91482i
$290$	−4.42231e9	−	2.55322e9i	−0.625255	−	0.360991i
$291$	2.16914e9	−	3.75705e9i	0.302493	−	0.523933i
$292$	−1.06901e10	+	6.17193e9i	−1.47045	+	0.848964i
$293$		−	4.57596e9i		−	0.620886i	−0.950592	−	0.310443i	$-0.899523\pi$
$293$		−	4.57596e9i		−	0.620886i	0.950592	−	0.310443i	$-0.100477\pi$
$294$	3.13127e9	+	3.40228e9i	0.419113	+	0.455387i
$295$	9.83691e7			0.0129888
$296$	−1.96191e8	−	3.39813e8i	−0.0255572	−	0.0442664i
$297$	−4.87102e9	−	2.81228e9i	−0.626028	−	0.361438i
$298$	−1.84256e9	+	3.19140e9i	−0.233645	+	0.404685i
$299$	3.50770e9	−	2.02517e9i	0.438872	−	0.253383i
$300$		−	2.29712e9i		−	0.283596i
$301$	5.42873e9	−	2.11793e9i	0.661352	−	0.258015i
$302$	4.24375e9			0.510178
$303$	−8.98645e8	−	1.55650e9i	−0.106615	−	0.184662i
$304$	−6.16930e9	−	3.56185e9i	−0.722340	−	0.417043i
$305$	−7.35237e8	+	1.27347e9i	−0.0849627	+	0.147160i
$306$	−1.51764e10	+	8.76213e9i	−1.73095	+	0.999364i
$307$			1.11742e10i			1.25795i	0.777427	+	0.628973i	$0.216524\pi$
$307$			1.11742e10i			1.25795i	−0.777427	+	0.628973i	$0.783476\pi$
$308$	5.91667e9	+	4.73805e9i	0.657467	+	0.526498i
$309$	−2.33423e9			−0.256041
$310$	−3.16533e9	−	5.48251e9i	−0.342746	−	0.593653i
$311$	−7.11909e8	−	4.11021e8i	−0.0760997	−	0.0439362i	0.461467	−	0.887157i	$-0.347323\pi$
$311$	−7.11909e8	−	4.11021e8i	−0.0760997	−	0.0439362i	−0.537567	+	0.843221i	$0.680656\pi$
$312$	−1.70849e8	+	2.95919e8i	−0.0180299	+	0.0312288i
$313$	−7.09380e9	+	4.09561e9i	−0.739097	+	0.426718i	−0.821741	−	0.569861i	$-0.806997\pi$
$313$	−7.09380e9	+	4.09561e9i	−0.739097	+	0.426718i	0.0826439	+	0.996579i	$0.473664\pi$
$314$		−	1.18268e10i		−	1.21660i
$315$	4.40094e9	+	6.72466e8i	0.446996	+	0.0683012i
$316$	7.39542e9			0.741676
$317$	3.35989e9	+	5.81950e9i	0.332727	+	0.576300i	0.983046	−	0.183361i	$-0.0586979\pi$
$317$	3.35989e9	+	5.81950e9i	0.332727	+	0.576300i	−0.650318	+	0.759662i	$0.725365\pi$
$318$	5.97799e9	+	3.45139e9i	0.584584	+	0.337509i
$319$	4.29738e9	−	7.44328e9i	0.414993	−	0.718789i
$320$	4.42711e9	−	2.55599e9i	0.422202	−	0.243758i
$321$		−	5.97767e8i		−	0.0563004i
$322$	1.28978e9	−	8.44095e9i	0.119975	−	0.785177i
$323$	1.53280e10			1.40823
$324$	−2.29176e9	−	3.96944e9i	−0.207964	−	0.360204i
$325$	−5.84792e9	−	3.37630e9i	−0.524165	−	0.302627i
$326$	4.61616e9	−	7.99543e9i	0.408706	−	0.707899i
$327$	−5.06007e9	+	2.92143e9i	−0.442554	+	0.255508i
$328$			6.00900e8i			0.0519167i
$329$	−1.23719e10	+	1.54495e10i	−1.05597	+	1.31865i
$330$	−3.73065e9			−0.314579
$331$	−7.29999e9	−	1.26439e10i	−0.608149	−	1.05335i	−0.991545	−	0.129761i	$-0.958579\pi$
$331$	−7.29999e9	−	1.26439e10i	−0.608149	−	1.05335i	0.383396	−	0.923584i	$-0.374754\pi$
$332$	−3.74127e9	−	2.16002e9i	−0.307940	−	0.177789i
$333$	−2.75979e9	+	4.78010e9i	−0.224440	+	0.388741i
$334$	1.41653e10	−	8.17833e9i	1.13825	−	0.657171i
$335$		−	1.16079e10i		−	0.921668i
$336$	2.18784e9	+	5.60794e9i	0.171656	+	0.439993i
$337$	−2.23598e10			−1.73360			−0.866798	−	0.498660i	$-0.833826\pi$
$337$	−2.23598e10			−1.73360			−0.866798	+	0.498660i	$0.833826\pi$
$338$	1.92971e9	+	3.34236e9i	0.147852	+	0.256087i
$339$	−5.45256e8	−	3.14804e8i	−0.0412859	−	0.0238364i
$340$	−6.30758e9	+	1.09250e10i	−0.472005	+	0.817537i
$341$	9.22773e9	−	5.32763e9i	0.682460	−	0.394018i
$342$			1.19919e10i			0.876564i
$343$	6.08127e9	−	1.24338e10i	0.439357	−	0.898312i
$344$	9.07840e8			0.0648299
$345$	1.01499e9	+	1.75801e9i	0.0716449	+	0.124093i
$346$	1.01352e10	+	5.85155e9i	0.707175	+	0.408288i
$347$	−1.02338e10	+	1.77255e10i	−0.705863	+	1.22259i	0.260517	+	0.965469i	$0.416107\pi$
$347$	−1.02338e10	+	1.77255e10i	−0.705863	+	1.22259i	−0.966379	+	0.257121i	$0.917226\pi$
$348$	−4.86199e9	+	2.80707e9i	−0.331510	+	0.191397i
$349$		−	1.36302e10i		−	0.918756i	−0.888241	−	0.459378i	$-0.848072\pi$
$349$		−	1.36302e10i		−	0.918756i	0.888241	−	0.459378i	$-0.151928\pi$
$350$	−1.32623e10	+	5.17404e9i	−0.883782	+	0.344792i
$351$	1.08000e10			0.711535
$352$	9.58277e9	+	1.65978e10i	0.624195	+	1.08114i
$353$	2.22641e10	+	1.28542e10i	1.43386	+	0.827839i	0.997412	−	0.0718917i	$-0.0229036\pi$
$353$	2.22641e10	+	1.28542e10i	1.43386	+	0.827839i	0.436446	+	0.899730i	$0.356237\pi$
$354$	1.11949e8	−	1.93902e8i	0.00712867	−	0.0123472i
$355$	1.30516e9	−	7.53536e8i	0.0821771	−	0.0474450i
$356$			4.07103e9i			0.253457i
$357$	−1.01101e10	−	8.09616e9i	−0.622421	−	0.498432i
$358$	−5.44974e8			−0.0331775
$359$	−1.07964e9	−	1.86999e9i	−0.0649982	−	0.112580i	0.831695	−	0.555233i	$-0.187371\pi$
$359$	−1.07964e9	−	1.86999e9i	−0.0649982	−	0.112580i	−0.896693	+	0.442653i	$0.854038\pi$
$360$	6.00667e8	+	3.46795e8i	0.0357622	+	0.0206473i
$361$	−3.24729e9	+	5.62447e9i	−0.191202	+	0.331171i
$362$	1.78222e10	−	1.02897e10i	1.03783	−	0.599193i
$363$			1.44728e9i			0.0833542i
$364$	−1.43877e10	−	2.19845e9i	−0.819571	−	0.125231i
$365$	−1.81860e10			−1.02463
$366$	1.67348e9	+	2.89855e9i	0.0932602	+	0.161531i
$367$	1.28869e10	+	7.44023e9i	0.710367	+	0.410130i	0.811197	−	0.584773i	$-0.198816\pi$
$367$	1.28869e10	+	7.44023e9i	0.710367	+	0.410130i	−0.100830	+	0.994904i	$0.532150\pi$
$368$	5.55819e9	−	9.62706e9i	0.303069	−	0.524931i
$369$	7.32031e9	−	4.22638e9i	0.394843	−	0.227962i
$370$			8.22599e9i			0.438916i
$371$	3.12109e9	−	2.04259e10i	0.164745	−	1.07817i
$372$	−6.96007e9			−0.363448
$373$	−1.41578e10	−	2.45220e10i	−0.731407	−	1.26683i	−0.956282	−	0.292447i	$-0.905530\pi$
$373$	−1.41578e10	−	2.45220e10i	−0.731407	−	1.26683i	0.224874	−	0.974388i	$-0.427803\pi$
$374$	−3.80686e10	−	2.19789e10i	−1.94572	−	1.12336i
$375$	4.17299e9	−	7.22783e9i	0.211019	−	0.365496i
$376$	−2.67043e9	+	1.54177e9i	−0.133607	+	0.0771381i
$377$			1.65033e10i			0.816967i
$378$	1.42320e10	−	1.77724e10i	0.697108	−	0.870518i
$379$	7.26160e9			0.351946			0.175973	−	0.984395i	$-0.443693\pi$
$379$	7.26160e9			0.351946			0.175973	+	0.984395i	$0.443693\pi$
$380$	4.31629e9	+	7.47604e9i	0.207003	+	0.358540i
$381$	9.96685e9	+	5.75436e9i	0.472997	+	0.273085i
$382$	1.28466e10	−	2.22510e10i	0.603303	−	1.04495i
$383$	−2.39383e10	+	1.38208e10i	−1.11250	+	0.642299i	−0.939474	−	0.342619i	$-0.888686\pi$
$383$	−2.39383e10	+	1.38208e10i	−1.11250	+	0.642299i	−0.173021	+	0.984918i	$0.555353\pi$
$384$			1.76339e9i			0.0811004i
$385$	4.05884e9	+	1.04037e10i	0.184739	+	0.473529i
$386$	−2.84802e10			−1.28290
$387$	−6.38522e9	−	1.10595e10i	−0.284664	−	0.493052i
$388$	2.49319e10	+	1.43944e10i	1.10009	+	0.635137i
$389$	2.18007e9	−	3.77599e9i	0.0952077	−	0.164905i	−0.814488	−	0.580181i	$-0.802982\pi$
$389$	2.18007e9	−	3.77599e9i	0.0952077	−	0.164905i	0.909695	+	0.415276i	$0.136315\pi$
$390$	6.20371e9	−	3.58171e9i	0.268159	−	0.154822i
$391$			2.39190e10i			1.02338i
$392$	1.58667e9	−	1.46028e9i	0.0671956	−	0.0618431i
$393$	2.06415e10			0.865308
$394$	1.15645e10	+	2.00302e10i	0.479889	+	0.831192i
$395$	9.43581e9	+	5.44777e9i	0.387606	+	0.223785i
$396$	8.30578e9	−	1.43860e10i	0.337753	−	0.585006i
$397$	5.27066e9	−	3.04302e9i	0.212179	−	0.122502i	−0.390145	−	0.920754i	$-0.627575\pi$
$397$	5.27066e9	−	3.04302e9i	0.212179	−	0.122502i	0.602324	+	0.798252i	$0.294242\pi$
$398$			2.70776e10i			1.07914i
$399$	−8.25717e9	+	3.22139e9i	−0.325791	+	0.127102i
$400$	−1.85328e10			−0.723939
$401$	1.52329e10	+	2.63842e10i	0.589122	+	1.02039i	0.994348	+	0.106173i	$0.0338596\pi$
$401$	1.52329e10	+	2.63842e10i	0.589122	+	1.02039i	−0.405226	+	0.914217i	$0.632807\pi$
$402$	−2.28811e10	−	1.32104e10i	−0.876139	−	0.505839i
$403$	−1.02299e10	+	1.77187e10i	−0.387838	+	0.671754i
$404$	1.03289e10	−	5.96342e9i	0.387731	−	0.223856i
$405$		−	6.75281e9i		−	0.250995i
$406$	2.71575e10	+	2.17476e10i	0.999507	+	0.800402i
$407$	−1.38453e10			−0.504575
$408$	−1.00894e9	−	1.74753e9i	−0.0364102	−	0.0630643i
$409$	−3.84688e10	−	2.22100e10i	−1.37472	−	0.793697i	−0.383206	−	0.923663i	$-0.625180\pi$
$409$	−3.84688e10	−	2.22100e10i	−1.37472	−	0.793697i	−0.991519	+	0.129966i	$0.958513\pi$
$410$	6.29869e9	−	1.09097e10i	0.222902	−	0.386078i
$411$	−7.43967e9	+	4.29529e9i	−0.260727	+	0.150531i
$412$		−	1.54899e10i		−	0.537602i
$413$	−6.62535e8	−	1.01236e8i	−0.0227724	−	0.00347963i
$414$	−1.87131e10			−0.637007
$415$	−3.18232e9	−	5.51194e9i	−0.107288	−	0.185829i
$416$	−3.18704e10	−	1.84004e10i	−1.06418	−	0.614404i
$417$	2.51307e9	−	4.35277e9i	0.0831115	−	0.143953i
$418$	−2.60504e10	+	1.50402e10i	−0.853316	+	0.492662i
$419$		−	5.46453e9i		−	0.177295i	−0.996063	−	0.0886476i	$-0.971746\pi$
$419$		−	5.46453e9i		−	0.177295i	0.996063	−	0.0886476i	$-0.0282545\pi$
$420$	1.10183e9	−	7.21094e9i	0.0354095	−	0.231737i
$421$	5.14972e10			1.63929			0.819644	−	0.572874i	$-0.194171\pi$
$421$	5.14972e10			1.63929			0.819644	+	0.572874i	$0.194171\pi$
$422$	−3.05783e9	−	5.29632e9i	−0.0964193	−	0.167003i
$423$	3.75645e10	+	2.16879e10i	1.17332	+	0.677416i
$424$	1.60957e9	−	2.78786e9i	0.0498019	−	0.0862595i
$425$	3.45345e10	−	1.99385e10i	1.05851	−	0.611134i
$426$		−	3.43026e9i		−	0.104157i
$427$	6.26255e9	−	7.82040e9i	0.188382	−	0.235243i
$428$	3.96679e9			0.118213
$429$	6.02845e9	+	1.04416e10i	0.177982	+	0.308274i
$430$	−1.64823e10	−	9.51606e9i	−0.482108	−	0.278345i
$431$	−6.47466e9	+	1.12144e10i	−0.187632	+	0.324989i	−0.944460	−	0.328625i	$-0.893415\pi$
$431$	−6.47466e9	+	1.12144e10i	−0.187632	+	0.324989i	0.756828	+	0.653614i	$0.226748\pi$
$432$	2.56701e10	−	1.48206e10i	0.737041	−	0.425531i
$433$		−	5.03186e10i		−	1.43145i	−0.698381	−	0.715726i	$-0.746096\pi$
$433$		−	5.03186e10i		−	1.43145i	0.698381	−	0.715726i	$-0.253904\pi$
$434$	1.56768e10	+	4.01834e10i	0.441875	+	1.13263i
$435$	−8.27121e9			−0.231000
$436$	−1.93867e10	−	3.35787e10i	−0.536485	−	0.929219i
$437$	1.41750e10	+	8.18392e9i	0.388683	+	0.224407i
$438$	−2.06966e10	+	3.58476e10i	−0.562346	+	0.974011i
$439$	−3.07074e10	+	1.77289e10i	−0.826771	+	0.477336i	−0.852746	−	0.522326i	$-0.825064\pi$
$439$	−3.07074e10	+	1.77289e10i	−0.826771	+	0.477336i	0.0259748	+	0.999663i	$0.491731\pi$
$440$			1.73980e9i			0.0464183i
$441$	−2.89491e10	−	9.05838e9i	−0.765387	−	0.239495i
$442$	8.44058e10			2.21148
$443$	−3.29533e10	−	5.70767e10i	−0.855625	−	1.48199i	−0.876064	−	0.482195i	$-0.839840\pi$
$443$	−3.29533e10	−	5.70767e10i	−0.855625	−	1.48199i	0.0204385	−	0.999791i	$-0.493494\pi$
$444$	7.83219e9	+	4.52192e9i	0.201535	+	0.116357i
$445$	−2.99889e9	+	5.19423e9i	−0.0764752	+	0.132459i
$446$	−6.46327e10	+	3.73157e10i	−1.63348	+	0.943089i
$447$			5.96901e9i			0.149511i
$448$	−3.24479e10	+	1.26590e10i	−0.805517	+	0.314258i
$449$	−5.46203e9			−0.134390			−0.0671952	−	0.997740i	$-0.521405\pi$
$449$	−5.46203e9			−0.134390			−0.0671952	+	0.997740i	$0.521405\pi$
$450$	1.55989e10	+	2.70181e10i	0.380404	+	0.658878i
$451$	1.83623e10	+	1.06015e10i	0.443833	+	0.256247i
$452$	2.08904e9	−	3.61833e9i	0.0500488	−	0.0866870i
$453$	5.95293e9	−	3.43693e9i	0.141364	−	0.0816164i
$454$		−	7.92664e10i		−	1.86580i
$455$	−1.67378e10	−	1.34036e10i	−0.390529	−	0.312734i
$456$	−1.38084e9			−0.0319362
$457$	1.16117e10	+	2.01120e10i	0.266214	+	0.461096i	0.967881	−	0.251409i	$-0.0808939\pi$
$457$	1.16117e10	+	2.01120e10i	0.266214	+	0.461096i	−0.701667	+	0.712505i	$0.747561\pi$
$458$	5.62838e10	+	3.24955e10i	1.27915	+	0.738518i
$459$	−3.18894e10	+	5.52340e10i	−0.718448	+	1.24439i
$460$	−1.16662e10	+	6.73548e9i	−0.260554	+	0.150431i
$461$		−	2.39964e10i		−	0.531302i	−0.964069	−	0.265651i	$-0.914413\pi$
$461$		−	2.39964e10i		−	0.531302i	0.964069	−	0.265651i	$-0.0855869\pi$
$462$	2.51267e10	+	3.83937e9i	0.551528	+	0.0842737i
$463$	−8.39640e9			−0.182713			−0.0913564	−	0.995818i	$-0.529120\pi$
$463$	−8.39640e9			−0.182713			−0.0913564	+	0.995818i	$0.529120\pi$
$464$	2.26470e10	+	3.92258e10i	0.488584	+	0.846252i
$465$	−8.88035e9	−	5.12707e9i	−0.189941	−	0.109662i
$466$	−1.06713e10	+	1.84831e10i	−0.226293	+	0.391951i
$467$	−1.03242e10	+	5.96067e9i	−0.217064	+	0.125322i	−0.604590	−	0.796537i	$-0.706663\pi$
$467$	−1.03242e10	+	5.96067e9i	−0.217064	+	0.125322i	0.387526	+	0.921859i	$0.373330\pi$
$468$			3.18968e10i			0.664910i
$469$	−1.19462e10	+	7.81815e10i	−0.246909	+	1.61589i
$470$	6.46440e10			1.32476
$471$	−9.57826e9	−	1.65900e10i	−0.194627	−	0.337104i
$472$	−9.04269e7	−	5.22080e7i	−0.00182192	−	0.00105189i
$473$	1.60167e10	−	2.77417e10i	0.319984	−	0.554228i
$474$	2.14769e10	−	1.23997e10i	0.425460	−	0.245640i
$475$		−	2.72879e10i		−	0.536038i
$476$	5.37262e10	−	6.70910e10i	1.04655	−	1.30688i
$477$	−4.52831e10			−0.874707
$478$	−3.77976e10	−	6.54673e10i	−0.724023	−	1.25404i
$479$	−1.43061e10	−	8.25964e9i	−0.271756	−	0.156899i	0.357929	−	0.933749i	$-0.383483\pi$
$479$	−1.43061e10	−	8.25964e9i	−0.271756	−	0.156899i	−0.629686	+	0.776850i	$0.716816\pi$
$480$	9.22203e9	−	1.59730e10i	0.173725	−	0.300900i
$481$	2.30234e10	−	1.32926e10i	0.430120	−	0.248330i
$482$			1.17533e10i			0.217757i
$483$	−5.02691e9	−	1.28851e10i	−0.0923661	−	0.236756i
$484$	−9.60419e9			−0.175017
$485$	2.12070e10	+	3.67317e10i	0.383277	+	0.663856i
$486$	−6.71930e10	−	3.87939e10i	−1.20442	−	0.695374i
$487$	1.36996e10	−	2.37284e10i	0.243552	−	0.421845i	−0.718171	−	0.695866i	$-0.755021\pi$
$487$	1.36996e10	−	2.37284e10i	0.243552	−	0.421845i	0.961724	+	0.274022i	$0.0883540\pi$
$488$	1.35175e9	−	7.80433e8i	0.0238351	−	0.0137612i
$489$		−	1.49541e10i		−	0.261533i
$490$	−4.41135e10	+	9.88054e9i	−0.765222	+	0.171394i
$491$	−1.34157e10			−0.230828			−0.115414	−	0.993317i	$-0.536820\pi$
$491$	−1.34157e10			−0.230828			−0.115414	+	0.993317i	$0.536820\pi$
$492$	−6.92492e9	−	1.19943e10i	−0.118183	−	0.204699i
$493$	−8.44017e10	−	4.87293e10i	−1.42877	−	0.824903i
$494$	2.88796e10	−	5.00209e10i	0.484934	−	0.839930i
$495$	2.11947e10	−	1.22368e10i	0.353026	−	0.203820i
$496$			5.61528e10i			0.927779i
$497$	−9.56602e9	+	3.73201e9i	−0.156785	+	0.0611671i
$498$	−1.44866e10			−0.235532
$499$	5.32201e10	+	9.21799e10i	0.858368	+	1.48674i	0.873485	+	0.486851i	$0.161855\pi$
$499$	5.32201e10	+	9.21799e10i	0.858368	+	1.48674i	−0.0151167	+	0.999886i	$0.504812\pi$
$500$	4.79639e10	+	2.76920e10i	0.767423	+	0.443072i
$501$	1.32469e10	−	2.29444e10i	0.210264	−	0.364187i
$502$	−4.02113e10	+	2.32160e10i	−0.633189	+	0.365572i
$503$			3.23033e10i			0.504633i	0.967645	+	0.252316i	$0.0811924\pi$
$503$			3.23033e10i			0.504633i	−0.967645	+	0.252316i	$0.918808\pi$
$504$	−3.68871e9	−	2.95391e9i	−0.0571679	−	0.0457799i
$505$	1.75716e10			0.270175
$506$	−2.34700e10	−	4.06511e10i	−0.358022	−	0.620113i
$507$	5.41383e9	+	3.12567e9i	0.0819356	+	0.0473055i
$508$	−3.81860e10	+	6.61401e10i	−0.573389	+	0.993139i
$509$	1.03047e11	−	5.94943e10i	1.53520	−	0.886349i	0.536091	−	0.844160i	$-0.319900\pi$
$509$	1.03047e11	−	5.94943e10i	1.53520	−	0.886349i	0.999110	−	0.0421883i	$-0.0134329\pi$
$510$			4.23031e10i			0.625304i
$511$	1.22486e11	+	1.87160e10i	1.79640	+	0.274491i
$512$	−9.43410e10			−1.37284
$513$	2.18220e10	+	3.77968e10i	0.315083	+	0.545740i
$514$	3.14738e10	+	1.81714e10i	0.450917	+	0.260337i
$515$	1.14105e10	−	1.97636e10i	0.162210	−	0.280956i
$516$	−1.81210e10	+	1.04622e10i	−0.255614	+	0.147579i
$517$			1.08804e11i			1.52294i
$518$	8.46570e9	−	5.54036e10i	0.117583	−	0.769519i
$519$	1.89562e10			0.261266
$520$	−1.67034e9	−	2.89312e9i	−0.0228451	−	0.0395688i
$521$	−9.37730e9	−	5.41399e9i	−0.127270	−	0.0734795i	0.435013	−	0.900424i	$-0.356744\pi$
$521$	−9.37730e9	−	5.41399e9i	−0.127270	−	0.0734795i	−0.562283	+	0.826945i	$0.690077\pi$
$522$	3.81235e10	−	6.60319e10i	0.513465	−	0.889348i
$523$	−5.28582e10	+	3.05177e10i	−0.706489	+	0.407892i	−0.809760	−	0.586762i	$-0.800403\pi$
$523$	−5.28582e10	+	3.05177e10i	−0.706489	+	0.407892i	0.103271	+	0.994653i	$0.467069\pi$
$524$			1.36977e11i			1.81687i
$525$	−1.44133e10	+	1.79987e10i	−0.189726	+	0.236922i
$526$	−8.65974e10			−1.13126
$527$	−6.04117e10	−	1.04636e11i	−0.783210	−	1.35656i
$528$	2.86575e10	+	1.65454e10i	0.368725	+	0.212883i
$529$	2.63847e10	−	4.56996e10i	0.336922	−	0.583565i
$530$	−5.84451e10	+	3.37433e10i	−0.740704	+	0.427646i
$531$			1.46880e9i			0.0184750i
$532$	−2.13772e10	−	5.47947e10i	−0.266873	−	0.684056i
$533$	−4.07129e10			−0.504455
$534$	6.82580e9	+	1.18226e10i	0.0839438	+	0.145395i
$535$	5.06123e9	+	2.92210e9i	0.0617790	+	0.0356681i
$536$	−6.16072e9	+	1.06707e10i	−0.0746402	+	0.129281i
$537$	−7.64464e8	+	4.41363e8i	−0.00919305	+	0.00530761i
$538$		−	1.69248e11i		−	2.02020i
$539$	−1.66301e10	−	7.42483e10i	−0.197034	−	0.879694i
$540$	−3.59196e10			−0.422432
$541$	5.51898e10	+	9.55916e10i	0.644273	+	1.11591i	0.984469	+	0.175559i	$0.0561732\pi$
$541$	5.51898e10	+	9.55916e10i	0.644273	+	1.11591i	−0.340196	+	0.940355i	$0.610493\pi$
$542$	4.60036e10	+	2.65602e10i	0.533082	+	0.307775i
$543$	1.66668e10	−	2.88677e10i	0.191713	−	0.332057i
$544$	1.88208e11	−	1.08662e11i	2.14903	−	1.24074i
$545$		−	5.71241e10i		−	0.647491i
$546$	−4.54693e10	+	1.77391e10i	−0.511620	+	0.199600i
$547$	1.16310e10			0.129918			0.0649590	−	0.997888i	$-0.479308\pi$
$547$	1.16310e10			0.129918			0.0649590	+	0.997888i	$0.479308\pi$
$548$	−2.85036e10	−	4.93697e10i	−0.316066	−	0.547443i
$549$	−1.90149e10	−	1.09782e10i	−0.209317	−	0.120849i
$550$	−3.91283e10	+	6.77723e10i	−0.427603	+	0.740630i
$551$	−5.77563e10	+	3.33456e10i	−0.626604	+	0.361770i
$552$		−	2.15476e9i		−	0.0232083i
$553$	−5.79455e10	−	4.64026e10i	−0.619611	−	0.496183i
$554$	1.52862e11			1.62278
$555$	6.66206e9	+	1.15390e10i	0.0702161	+	0.121618i
$556$	2.88851e10	+	1.66768e10i	0.302255	+	0.174507i
$557$	−8.60407e10	+	1.49027e11i	−0.893888	+	1.54826i	−0.0587140	+	0.998275i	$0.518700\pi$
$557$	−8.60407e10	+	1.49027e11i	−0.893888	+	1.54826i	−0.835174	+	0.549985i	$0.814633\pi$
$558$	8.18624e10	−	4.72633e10i	0.844398	−	0.487514i
$559$			6.15090e10i			0.629928i
$560$	−5.81767e10	−	8.88943e9i	−0.591558	−	0.0903903i
$561$	−7.12011e10			−0.718845
$562$	1.65272e10	+	2.86260e10i	0.165674	+	0.286956i
$563$	9.97053e10	+	5.75649e10i	0.992395	+	0.572960i	0.905989	−	0.423300i	$-0.139129\pi$
$563$	9.97053e10	+	5.75649e10i	0.992395	+	0.572960i	0.0864057	+	0.996260i	$0.472462\pi$
$564$	3.55356e10	−	6.15494e10i	0.351194	−	0.608285i
$565$	5.33082e9	−	3.07775e9i	0.0523118	−	0.0302023i
$566$		−	1.84819e10i		−	0.180086i
$567$	−6.94960e9	+	4.54815e10i	−0.0672400	+	0.440051i
$568$	−1.59971e9			−0.0153691
$569$	−1.64702e10	−	2.85272e10i	−0.157126	−	0.272151i	0.776705	−	0.629865i	$-0.216890\pi$
$569$	−1.64702e10	−	2.85272e10i	−0.157126	−	0.272151i	−0.933831	+	0.357714i	$0.883556\pi$
$570$	2.50698e10	+	1.44740e10i	0.237493	+	0.137117i
$571$	8.47351e10	−	1.46765e11i	0.797111	−	1.38064i	−0.124379	−	0.992235i	$-0.539694\pi$
$571$	8.47351e10	−	1.46765e11i	0.797111	−	1.38064i	0.921490	−	0.388402i	$-0.126973\pi$
$572$	−6.92905e10	+	4.00049e10i	−0.647276	+	0.373705i
$573$		−	4.16169e10i		−	0.386057i
$574$	−5.36505e10	+	6.69964e10i	−0.494227	+	0.617169i
$575$	4.25822e10			0.389544
$576$	3.81649e10	+	6.61036e10i	0.346716	+	0.600530i
$577$	−1.57863e11	−	9.11425e10i	−1.42422	−	0.822276i	−0.427567	−	0.903983i	$-0.640629\pi$
$577$	−1.57863e11	−	9.11425e10i	−1.42422	−	0.822276i	−0.996656	+	0.0817075i	$0.973963\pi$
$578$	−1.71610e11	+	2.97238e11i	−1.53756	+	2.66313i
$579$	−3.99507e10	+	2.30656e10i	−0.355476	+	0.205234i
$580$		−	5.48879e10i		−	0.485025i
$581$	1.57610e10	+	4.03991e10i	0.138318	+	0.354541i
$582$	9.65391e10			0.841417
$583$	−5.67941e10	−	9.83702e10i	−0.491619	−	0.851509i
$584$	1.67177e10	+	9.65195e9i	0.143722	+	0.0829781i
$585$	−2.34965e10	+	4.06971e10i	−0.200622	+	0.347488i
$586$	8.81859e10	−	5.09141e10i	0.747840	−	0.431766i
$587$			2.23062e10i			0.187876i	0.995578	+	0.0939382i	$0.0299456\pi$
$587$			2.23062e10i			0.187876i	−0.995578	+	0.0939382i	$0.970054\pi$
$588$	−1.48422e10	+	4.74331e10i	−0.124162	+	0.396801i
$589$	−8.26798e10			−0.686971
$590$	1.09450e9	+	1.89573e9i	0.00903247	+	0.0156447i
$591$	3.24442e10	+	1.87317e10i	0.265942	+	0.153542i
$592$	3.64821e10	−	6.31889e10i	0.297025	−	0.514463i
$593$	−3.95146e10	+	2.28138e10i	−0.319550	+	0.184492i	−0.651192	−	0.758913i	$-0.725731\pi$
$593$	−3.95146e10	+	2.28138e10i	−0.319550	+	0.184492i	0.331642	+	0.943405i	$0.392397\pi$
$594$		−	1.25163e11i		−	1.00538i
$595$	1.17971e11	−	4.60244e10i	0.941257	−	0.367215i
$596$	−3.96104e10			−0.313924
$597$	2.19296e10	+	3.79832e10i	0.172637	+	0.299016i
$598$	7.80565e10	+	4.50659e10i	0.610385	+	0.352406i
$599$	3.98067e10	−	6.89472e10i	0.309207	−	0.535562i	−0.668982	−	0.743278i	$-0.733270\pi$
$599$	3.98067e10	−	6.89472e10i	0.309207	−	0.535562i	0.978189	+	0.207717i	$0.0666032\pi$
$600$	−3.11107e9	+	1.79618e9i	−0.0240052	+	0.0138594i
$601$			5.38298e10i			0.412596i	0.978489	+	0.206298i	$0.0661416\pi$
$601$			5.38298e10i			0.412596i	−0.978489	+	0.206298i	$0.933858\pi$
$602$	1.01218e11	+	8.10552e10i	0.770677	+	0.617156i
$603$	1.73324e11			1.31096
$604$	2.28075e10	+	3.95037e10i	0.171368	+	0.296818i
$605$	−1.22540e10	−	7.07485e9i	−0.0914652	−	0.0528075i
$606$	1.99974e10	−	3.46366e10i	0.148280	−	0.256829i
$607$	−7.84469e10	+	4.52913e10i	−0.577858	+	0.333626i	−0.760282	−	0.649594i	$-0.774939\pi$
$607$	−7.84469e10	+	4.52913e10i	−0.577858	+	0.333626i	0.182424	+	0.983220i	$0.441606\pi$
$608$		−	1.48716e11i		−	1.08828i
$609$	5.57083e10	+	8.51225e9i	0.404996	+	0.0618836i
$610$	−3.27223e10			−0.236333
$611$	−1.04460e11	−	1.80930e11i	−0.749523	−	1.29821i
$612$	−1.63128e11	−	9.41819e10i	−1.16285	−	0.671370i
$613$	3.92430e10	−	6.79709e10i	0.277920	−	0.481372i	−0.692947	−	0.720988i	$-0.743688\pi$
$613$	3.92430e10	−	6.79709e10i	0.277920	−	0.481372i	0.970868	+	0.239616i	$0.0770215\pi$
$614$	−2.15344e11	+	1.24329e11i	−1.51516	+	0.874778i
$615$		−	2.04047e10i		−	0.142636i
$616$	1.79050e9	−	1.17179e10i	0.0124352	−	0.0813819i
$617$	1.46941e11			1.01392			0.506958	−	0.861971i	$-0.330770\pi$
$617$	1.46941e11			1.01392			0.506958	+	0.861971i	$0.330770\pi$
$618$	−2.59716e10	−	4.49842e10i	−0.178051	−	0.308394i
$619$	−4.23698e10	−	2.44622e10i	−0.288599	−	0.166622i	0.348711	−	0.937230i	$-0.386619\pi$
$619$	−4.23698e10	−	2.44622e10i	−0.288599	−	0.166622i	−0.637310	+	0.770608i	$0.719953\pi$
$620$	3.40233e10	−	5.89301e10i	0.230256	−	0.398814i
$621$	−5.89811e10	+	3.40527e10i	−0.396594	+	0.228974i
$622$		−	1.82928e10i		−	0.122213i
$623$	2.55437e10	−	3.18979e10i	0.169563	−	0.211743i
$624$	−6.35394e10			−0.419088
$625$	−1.12414e10	−	1.94707e10i	−0.0736718	−	0.127603i
$626$	−1.57857e11	−	9.11390e10i	−1.02794	−	0.593481i
$627$	−2.43616e10	+	4.21955e10i	−0.157629	+	0.273021i
$628$	1.10092e11	−	6.35614e10i	0.707809	−	0.408653i
$629$			1.56997e11i			1.00297i
$630$	3.60073e10	+	9.22951e10i	0.228575	+	0.585891i
$631$	−2.11090e10			−0.133153			−0.0665765	−	0.997781i	$-0.521208\pi$
$631$	−2.11090e10			−0.133153			−0.0665765	+	0.997781i	$0.521208\pi$
$632$	−5.78265e9	−	1.00158e10i	−0.0362459	−	0.0627797i
$633$	−8.57877e9	−	4.95295e9i	−0.0534331	−	0.0308496i
$634$	−7.47673e10	+	1.29501e11i	−0.462758	+	0.801521i
$635$	−9.74431e10	+	5.62588e10i	−0.599316	+	0.346016i
$636$			7.41963e10i			0.453476i
$637$	9.89384e10	+	1.07501e11i	0.600907	+	0.652915i
$638$	1.91258e11			1.15435
$639$	1.12514e10	+	1.94881e10i	0.0674847	+	0.116887i
$640$	−1.49304e10	−	8.62008e9i	−0.0889922	−	0.0513797i
$641$	1.28983e11	−	2.23405e11i	0.764011	−	1.32331i	−0.176757	−	0.984254i	$-0.556561\pi$
$641$	1.28983e11	−	2.23405e11i	0.764011	−	1.32331i	0.940768	−	0.339051i	$-0.110106\pi$
$642$	1.15199e10	−	6.65102e9i	0.0678123	−	0.0391515i
$643$			2.70867e11i			1.58457i	0.610151	+	0.792285i	$0.291109\pi$
$643$			2.70867e11i			1.58457i	−0.610151	+	0.792285i	$0.708891\pi$
$644$	8.55059e10	−	3.33586e10i	0.497110	−	0.193939i
$645$	−3.08275e10			−0.178114
$646$	1.70546e11	+	2.95394e11i	0.979290	+	1.69618i
$647$	4.22990e10	+	2.44213e10i	0.241386	+	0.139365i	0.615814	−	0.787892i	$-0.288827\pi$
$647$	4.22990e10	+	2.44213e10i	0.241386	+	0.139365i	−0.374427	+	0.927256i	$0.622161\pi$
$648$	−3.58396e9	+	6.20760e9i	−0.0203265	+	0.0352065i
$649$	−3.19073e9	+	1.84217e9i	−0.0179851	+	0.0103837i
$650$		−	1.50265e11i		−	0.841790i
$651$	5.45344e10	+	4.36710e10i	0.303632	+	0.243147i
$652$	9.92359e10			0.549134
$653$	1.52491e11	+	2.64122e11i	0.838669	+	1.45262i	0.891007	+	0.453989i	$0.149999\pi$
$653$	1.52491e11	+	2.64122e11i	0.838669	+	1.45262i	−0.0523379	+	0.998629i	$0.516667\pi$
$654$	−1.12601e11	−	6.50103e10i	−0.615506	−	0.355362i
$655$	−1.00903e11	+	1.74769e11i	−0.548200	+	0.949510i
$656$	−9.67683e10	+	5.58692e10i	−0.522538	+	0.301687i
$657$		−	2.71545e11i		−	1.45740i
$658$	−4.35390e11	−	6.65279e10i	−2.32260	−	0.354895i
$659$	−1.52413e11			−0.808127			−0.404063	−	0.914731i	$-0.632402\pi$
$659$	−1.52413e11			−0.808127			−0.404063	+	0.914731i	$0.632402\pi$
$660$	−2.00499e10	−	3.47275e10i	−0.105666	−	0.183020i
$661$	−2.51592e10	−	1.45257e10i	−0.131793	−	0.0760905i	0.432654	−	0.901560i	$-0.357577\pi$
$661$	−2.51592e10	−	1.45257e10i	−0.131793	−	0.0760905i	−0.564447	+	0.825469i	$0.690910\pi$
$662$	1.62446e11	−	2.81364e11i	0.845817	−	1.46500i
$663$	1.18400e11	−	6.83586e10i	0.612773	−	0.353784i
$664$			6.75589e9i			0.0347544i
$665$	1.30889e10	−	8.56599e10i	0.0669292	−	0.438017i
$666$	−1.22827e11			−0.624303
$667$	−5.20351e10	−	9.01275e10i	−0.262902	−	0.455359i
$668$	1.52259e11	+	8.79068e10i	0.764676	+	0.441486i
$669$	−6.04425e10	+	1.04690e11i	−0.301744	+	0.522635i
$670$	2.23702e11	−	1.29155e11i	1.11012	−	0.640930i
$671$		−	5.50756e10i		−	0.271687i
$672$	−7.85507e10	+	9.80907e10i	−0.385188	+	0.481006i
$673$	−1.50544e11			−0.733843			−0.366922	−	0.930252i	$-0.619588\pi$
$673$	−1.50544e11			−0.733843			−0.366922	+	0.930252i	$0.619588\pi$
$674$	−2.48785e11	−	4.30908e11i	−1.20555	−	2.08807i
$675$	9.83313e10	+	5.67716e10i	0.473671	+	0.273474i
$676$	−2.07420e10	+	3.59262e10i	−0.0993262	+	0.172038i
$677$	1.13475e11	−	6.55149e10i	0.540189	−	0.311878i	−0.204966	−	0.978769i	$-0.565709\pi$
$677$	1.13475e11	−	6.55149e10i	0.540189	−	0.311878i	0.745156	+	0.666891i	$0.232375\pi$
$678$		−	1.40106e10i		−	0.0663036i
$679$	−1.05032e11	−	2.69220e11i	−0.494129	−	1.26657i
$680$	1.97282e10			0.0922680
$681$	−6.41963e10	−	1.11191e11i	−0.298484	−	0.516990i
$682$	2.05343e11	+	1.18555e11i	0.949169	+	0.548003i
$683$	−1.38351e11	+	2.39631e11i	−0.635771	+	1.10119i	0.350581	+	0.936533i	$0.385984\pi$
$683$	−1.38351e11	+	2.39631e11i	−0.635771	+	1.10119i	−0.986351	+	0.164654i	$0.947349\pi$
$684$	−1.11629e11	+	6.44489e10i	−0.509979	+	0.294436i
$685$		−	8.39878e10i		−	0.381464i
$686$	3.07282e11	−	2.11483e10i	1.38752	−	0.0954949i
$687$	1.05270e11			0.472582
$688$	8.44072e10	+	1.46198e11i	0.376726	+	0.652509i
$689$	1.88886e11	+	1.09053e11i	0.838152	+	0.483907i
$690$	−2.25864e10	+	3.91209e10i	−0.0996441	+	0.172589i
$691$	5.95148e9	−	3.43609e9i	0.0261043	−	0.0150713i	−0.486891	−	0.873463i	$-0.661869\pi$
$691$	5.95148e9	−	3.43609e9i	0.0261043	−	0.0150713i	0.512995	+	0.858391i	$0.328536\pi$
$692$			1.25794e11i			0.548573i
$693$	−1.55344e11	+	6.06047e10i	−0.673536	+	0.262768i
$694$	−4.55464e11			−1.96343
$695$	2.45696e10	+	4.25558e10i	0.105308	+	0.182398i
$696$	7.60340e9	+	4.38983e9i	0.0324020	+	0.0187073i
$697$	1.20213e11	−	2.08215e11i	0.509356	−	0.882230i
$698$	2.62675e11	−	1.51655e11i	1.10662	−	0.638905i
$699$			3.45697e10i			0.144806i
$700$	−1.19440e11	−	9.56470e10i	−0.497459	−	0.398363i
$701$	2.66001e11			1.10157			0.550784	−	0.834648i	$-0.314329\pi$
$701$	2.66001e11			1.10157			0.550784	+	0.834648i	$0.314329\pi$
$702$	1.20166e11	+	2.08133e11i	0.494804	+	0.857025i
$703$	9.30398e10	+	5.37166e10i	0.380932	+	0.219931i
$704$	−9.57328e10	+	1.65814e11i	−0.389736	+	0.675042i
$705$	9.06796e10	−	5.23539e10i	0.367074	−	0.211930i
$706$			5.72085e11i			2.30272i
$707$	−1.18348e11	−	1.80837e10i	−0.473679	−	0.0723784i
$708$	2.40663e9			0.00957804
$709$	−1.10139e11	−	1.90766e11i	−0.435868	−	0.754945i	0.561498	−	0.827478i	$-0.310225\pi$
$709$	−1.10139e11	−	1.90766e11i	−0.435868	−	0.754945i	−0.997366	+	0.0725326i	$0.976892\pi$
$710$	2.90436e10	+	1.67683e10i	0.114292	+	0.0659867i
$711$	−8.13436e10	+	1.40891e11i	−0.318306	+	0.551322i
$712$	5.51352e9	−	3.18323e9i	0.0214541	−	0.0123865i
$713$		−	1.29020e11i		−	0.499228i
$714$	4.35358e10	−	2.84919e11i	0.167515	−	1.09630i
$715$	−1.17877e11			−0.451030
$716$	−2.92889e9	−	5.07299e9i	−0.0111443	−	0.0193024i
$717$	−1.06041e11	−	6.12230e10i	−0.401235	−	0.231653i
$718$	2.40251e10	−	4.16127e10i	0.0903998	−	0.156577i
$719$	−2.09040e11	+	1.20689e11i	−0.782194	+	0.451600i	−0.837207	−	0.546886i	$-0.815813\pi$
$719$	−2.09040e11	+	1.20689e11i	−0.782194	+	0.451600i	0.0550134	+	0.998486i	$0.482480\pi$
$720$			1.28974e11i			0.479925i
$721$	−9.71918e10	+	1.21369e11i	−0.359657	+	0.449124i
$722$	−1.44523e11			−0.531849
$723$	9.51877e9	+	1.64870e10i	0.0348360	+	0.0603377i
$724$	1.91567e11	+	1.10601e11i	0.697213	+	0.402536i
$725$	−8.67512e10	+	1.50258e11i	−0.313996	+	0.543856i
$726$	−2.78914e10	+	1.61031e10i	−0.100398	+	0.0579647i
$727$		−	1.26784e11i		−	0.453865i	−0.973910	−	0.226933i	$-0.927130\pi$
$727$		−	1.26784e11i		−	0.453865i	0.973910	−	0.226933i	$-0.0728697\pi$
$728$	8.27267e9	+	2.12048e10i	0.0294524	+	0.0754932i
$729$	5.21646e7			0.000184700
$730$	−2.02345e11	−	3.50472e11i	−0.712527	−	1.23413i
$731$	−3.14572e11	−	1.81618e11i	−1.10167	−	0.636048i
$732$	−1.79878e10	+	3.11558e10i	−0.0626519	+	0.108516i
$733$	3.58437e11	−	2.06944e11i	1.24164	−	0.716864i	0.272216	−	0.962236i	$-0.412244\pi$
$733$	3.58437e11	−	2.06944e11i	1.24164	−	0.716864i	0.969429	+	0.245372i	$0.0789102\pi$
$734$			3.31133e11i			1.14082i
$735$	−5.38783e10	+	4.95866e10i	−0.184614	+	0.169908i
$736$	2.32067e11			0.790866
$737$	2.17383e11	+	3.76518e11i	0.736809	+	1.27619i
$738$	1.62898e11	+	9.40492e10i	0.549149	+	0.317051i
$739$	2.22802e11	−	3.85905e11i	0.747036	−	1.29390i	−0.202201	−	0.979344i	$-0.564809\pi$
$739$	2.22802e11	−	3.85905e11i	0.747036	−	1.29390i	0.949237	−	0.314561i	$-0.101857\pi$
$740$	−7.65731e10	+	4.42095e10i	−0.255358	+	0.147431i
$741$		−	9.35559e10i		−	0.310312i
$742$	4.28366e11	−	1.67120e11i	1.41319	−	0.551330i
$743$	−4.60776e11			−1.51194			−0.755971	−	0.654605i	$-0.772835\pi$
$743$	−4.60776e11			−1.51194			−0.755971	+	0.654605i	$0.772835\pi$
$744$	5.44224e9	+	9.42624e9i	0.0177618	+	0.0307643i
$745$	−5.05389e10	−	2.91787e10i	−0.164059	−	0.0947197i
$746$	3.15051e11	−	5.45684e11i	1.01725	−	1.76192i
$747$	8.23018e10	−	4.75170e10i	0.264318	−	0.152604i
$748$		−	4.72492e11i		−	1.50934i
$749$	−3.10811e10	−	2.48896e10i	−0.0987573	−	0.0790845i
$750$	1.85722e11			0.586973
$751$	2.73796e11	+	4.74229e11i	0.860731	+	1.49083i	0.871225	+	0.490885i	$0.163326\pi$
$751$	2.73796e11	+	4.74229e11i	0.860731	+	1.49083i	−0.0104937	+	0.999945i	$0.503340\pi$
$752$	−4.96571e11	−	2.86695e11i	−1.55278	−	0.896498i
$753$	−3.76044e10	+	6.51327e10i	−0.116966	+	0.202590i
$754$	−3.18043e11	+	1.83622e11i	−0.984014	+	0.568121i
$755$			6.72037e10i			0.206826i
$756$	2.41926e11	+	3.69664e10i	0.740619	+	0.113167i
$757$	−2.69991e11			−0.822176			−0.411088	−	0.911596i	$-0.634851\pi$
$757$	−2.69991e11			−0.822176			−0.411088	+	0.911596i	$0.634851\pi$
$758$	8.07957e10	+	1.39942e11i	0.244744	+	0.423909i
$759$	−6.58451e10	−	3.80157e10i	−0.198407	−	0.114550i
$760$	6.75002e9	−	1.16914e10i	0.0202326	−	0.0350438i
$761$	1.11052e11	−	6.41158e10i	0.331121	−	0.191173i	−0.325217	−	0.945639i	$-0.605438\pi$
$761$	1.11052e11	−	6.41158e10i	0.331121	−	0.191173i	0.656339	+	0.754466i	$0.272104\pi$
$762$			2.56102e11i			0.759615i
$763$	−5.87888e10	+	3.84742e11i	−0.173459	+	1.13520i
$764$	2.76170e11			0.810594
$765$	−1.38757e11	−	2.40333e11i	−0.405142	−	0.701727i
$766$	−5.32696e11	−	3.07552e11i	−1.54726	−	0.893313i
$767$	3.53725e9	−	6.12670e9i	0.0102208	−	0.0177029i
$768$	−1.49906e11	+	8.65480e10i	−0.430896	+	0.248778i
$769$			2.57274e10i			0.0735682i	0.999323	+	0.0367841i	$0.0117114\pi$
$769$			2.57274e10i			0.0735682i	−0.999323	+	0.0367841i	$0.988289\pi$
$770$	−1.55336e11	+	1.93977e11i	−0.441884	+	0.551806i
$771$	5.88666e10			0.166591
$772$	−1.53063e11	−	2.65114e11i	−0.430926	−	0.746385i
$773$	3.81272e11	+	2.20128e11i	1.06787	+	0.616533i	0.927598	−	0.373580i	$-0.121870\pi$
$773$	3.81272e11	+	2.20128e11i	1.06787	+	0.616533i	0.140269	+	0.990113i	$0.455203\pi$
$774$	1.42090e11	−	2.46106e11i	0.395912	−	0.685739i
$775$	−1.86280e11	+	1.07549e11i	−0.516369	+	0.298126i
$776$		−	4.50213e10i		−	0.124157i
$777$	−3.29950e10	−	8.45739e10i	−0.0905241	−	0.232034i
$778$	9.70257e10			0.264831
$779$	−8.22623e10	−	1.42482e11i	−0.223383	−	0.386911i
$780$	6.66821e10	+	3.84989e10i	0.180149	+	0.104009i
$781$	−2.82231e10	+	4.88839e10i	−0.0758579	+	0.131390i
$782$	−4.60956e11	+	2.66133e11i	−1.23263	+	0.711659i
$783$		−	2.77498e11i		−	0.738266i
$784$	3.82683e11	+	1.19744e11i	1.01292	+	0.316950i
$785$	1.87288e11			0.493209
$786$	2.29666e11	+	3.97794e11i	0.601737	+	1.04224i
$787$	1.61357e11	+	9.31592e10i	0.420618	+	0.242844i	0.695342	−	0.718679i	$-0.255253\pi$
$787$	1.61357e11	+	9.31592e10i	0.420618	+	0.242844i	−0.274724	+	0.961523i	$0.588586\pi$
$788$	−1.24304e11	+	2.15300e11i	−0.322388	+	0.558392i
$789$	−1.21475e11	+	7.01335e10i	−0.313457	+	0.180975i
$790$			2.42457e11i			0.622482i
$791$	−3.90715e10	+	1.52431e10i	−0.0998055	+	0.0389374i
$792$	−2.59779e10			−0.0660243
$793$	5.28768e10	+	9.15853e10i	0.133713	+	0.231597i
$794$	1.17287e11	+	6.77159e10i	0.295100	+	0.170376i
$795$	−5.46561e10	+	9.46671e10i	−0.136826	+	0.236990i
$796$	−2.52057e11	+	1.45525e11i	−0.627837	+	0.362482i
$797$			2.65830e11i			0.658826i	0.944186	+	0.329413i	$0.106851\pi$
$797$			2.65830e11i			0.658826i	−0.944186	+	0.329413i	$0.893149\pi$
$798$	−1.53954e11	−	1.23286e11i	−0.379647	−	0.304020i
$799$	1.23376e12			3.02722
$800$	−1.93448e11	−	3.35061e11i	−0.472284	−	0.818020i
$801$	−7.75579e10	−	4.47780e10i	−0.188406	−	0.108777i
$802$	−3.38976e11	+	5.87124e11i	−0.819354	+	1.41916i
$803$	5.89887e11	−	3.40571e11i	1.41875	−	0.819117i
$804$		−	2.83991e11i		−	0.679642i
$805$	1.33670e11	+	2.04249e10i	0.318311	+	0.0486381i
$806$	−4.55288e11			−1.07881
$807$	−1.37070e11	−	2.37413e11i	−0.323183	−	0.559770i
$808$	−1.61529e10	−	9.32587e9i	−0.0378970	−	0.0218798i
$809$	−2.14660e11	+	3.71802e11i	−0.501138	+	0.867996i	0.498861	+	0.866682i	$0.333752\pi$
$809$	−2.14660e11	+	3.71802e11i	−0.501138	+	0.867996i	−0.999999	+	0.00131446i	$0.999582\pi$
$810$	1.30137e11	−	7.51347e10i	0.302316	−	0.174542i
$811$		−	5.96056e11i		−	1.37785i	−0.724830	−	0.688927i	$-0.758082\pi$
$811$		−	5.96056e11i		−	1.37785i	0.724830	−	0.688927i	$-0.241918\pi$
$812$	−5.64874e10	+	3.69681e11i	−0.129935	+	0.850360i
$813$	8.60422e10			0.196947
$814$	−1.54049e11	−	2.66821e11i	−0.350882	−	0.607746i
$815$	1.26615e11	+	7.31013e10i	0.286982	+	0.165689i
$816$	1.87613e11	−	3.24956e11i	0.423159	−	0.732933i
$817$	−2.15262e11	+	1.24282e11i	−0.483148	+	0.278946i
$818$		−	9.88472e11i		−	2.20776i
$819$	2.00136e11	−	2.49922e11i	0.444826	−	0.555480i
$820$	1.35406e11			0.299490
$821$	−2.40274e11	−	4.16166e11i	−0.528851	−	0.915997i	−0.999434	−	0.0336410i	$-0.989290\pi$
$821$	−2.40274e11	−	4.16166e11i	−0.528851	−	0.915997i	0.470583	−	0.882356i	$-0.344044\pi$
$822$	−1.65554e11	−	9.55827e10i	−0.362621	−	0.209359i
$823$	−3.19735e11	+	5.53798e11i	−0.696933	+	1.20712i	0.272592	+	0.962130i	$0.412119\pi$
$823$	−3.19735e11	+	5.53798e11i	−0.696933	+	1.20712i	−0.969525	+	0.244994i	$0.921214\pi$
$824$	−2.09785e10	+	1.21120e10i	−0.0455057	+	0.0262727i
$825$			1.26757e11i			0.273625i
$826$	−5.42069e9	−	1.38945e10i	−0.0116449	−	0.0298485i
$827$	−4.42304e11			−0.945581			−0.472791	−	0.881175i	$-0.656753\pi$
$827$	−4.42304e11			−0.945581			−0.472791	+	0.881175i	$0.656753\pi$
$828$	−1.00571e11	−	1.74194e11i	−0.213970	−	0.370606i
$829$	9.55946e10	+	5.51916e10i	0.202402	+	0.116857i	0.597776	−	0.801664i	$-0.296051\pi$
$829$	9.55946e10	+	5.51916e10i	0.202402	+	0.116857i	−0.395373	+	0.918521i	$0.629385\pi$
$830$	7.08158e10	−	1.22657e11i	0.149217	−	0.258451i
$831$	2.14427e11	−	1.23800e11i	0.449651	−	0.259606i
$832$		−	3.67643e11i		−	0.767244i
$833$	−8.41925e11	+	1.88574e11i	−1.74861	+	0.391654i
$834$	1.11846e11			0.231184
$835$	1.29512e11	+	2.24321e11i	0.266417	+	0.461448i
$836$	−2.80010e11	−	1.61664e11i	−0.573255	−	0.330969i
$837$	1.72013e11	−	2.97934e11i	0.350476	−	0.607042i
$838$	1.05310e11	−	6.08008e10i	0.213547	−	0.123291i
$839$		−	1.25793e11i		−	0.253868i	−0.991911	−	0.126934i	$-0.959486\pi$
$839$		−	1.25793e11i		−	0.253868i	0.991911	−	0.126934i	$-0.0405137\pi$
$840$	−1.06275e10	+	4.14615e9i	−0.0213460	+	0.00832776i
$841$	−7.62089e10			−0.152343
$842$	5.72980e11	+	9.92431e11i	1.13996	+	1.97448i
$843$	4.63672e10	+	2.67701e10i	0.0918123	+	0.0530079i
$844$	3.28679e10	−	5.69288e10i	0.0647741	−	0.112192i
$845$	−5.29295e10	+	3.05588e10i	−0.103818	+	0.0599391i
$846$			9.65235e11i			1.88431i
$847$	7.52520e10	+	6.02616e10i	0.146213	+	0.117087i
$848$	5.98605e11			1.15759
$849$	−1.49681e10	−	2.59255e10i	−0.0288095	−	0.0498995i
$850$	7.68491e11	+	4.43688e11i	1.47219	+	0.849968i
$851$	−8.38235e10	+	1.45187e11i	−0.159826	+	0.276827i
$852$	3.19312e10	−	1.84355e10i	0.0605978	−	0.0349862i
$853$		−	5.12517e11i		−	0.968083i	−0.875045	−	0.484041i	$-0.839168\pi$
$853$		−	5.12517e11i		−	0.968083i	0.875045	−	0.484041i	$-0.160832\pi$
$854$	2.20391e11	+	3.36759e10i	0.414346	+	0.0633122i
$855$	−1.89903e11			−0.355359
$856$	−3.10172e9	−	5.37235e9i	−0.00577708	−	0.0100062i
$857$	2.40655e11	+	1.38942e11i	0.446141	+	0.257580i	0.706199	−	0.708013i	$-0.250408\pi$
$857$	2.40655e11	+	1.38942e11i	0.446141	+	0.257580i	−0.260058	+	0.965593i	$0.583742\pi$
$858$	−1.34150e11	+	2.32355e11i	−0.247539	+	0.428750i
$859$	−3.49390e11	+	2.01720e11i	−0.641708	+	0.370490i	−0.785272	−	0.619151i	$-0.787477\pi$
$859$	−3.49390e11	+	2.01720e11i	−0.641708	+	0.370490i	0.143564	+	0.989641i	$0.454144\pi$
$860$		−	2.04572e11i		−	0.373983i
$861$	−2.09994e10	+	1.37430e11i	−0.0382115	+	0.250074i
$862$	−2.88160e11			−0.521920
$863$	−1.18345e9	−	2.04979e9i	−0.00213357	−	0.00369545i	0.864957	−	0.501847i	$-0.167346\pi$
$863$	−1.18345e9	−	2.04979e9i	−0.00213357	−	0.00369545i	−0.867090	+	0.498151i	$0.834012\pi$
$864$	5.35893e11	+	3.09398e11i	0.961663	+	0.555216i
$865$	−9.26648e10	+	1.60500e11i	−0.165520	+	0.286689i
$866$	9.69718e11	−	5.59867e11i	1.72414	−	0.995435i
$867$			5.55936e11i			0.983894i
$868$	−2.89801e11	+	3.61891e11i	−0.510530	+	0.637528i
$869$	−4.08084e11			−0.715601
$870$	−9.20292e10	−	1.59399e11i	−0.160638	−	0.278233i
$871$	−7.22972e11	−	4.17408e11i	−1.25617	−	0.725251i
$872$	−3.03178e10	+	5.25120e10i	−0.0524363	+	0.0908223i
$873$	−5.48461e11	+	3.16654e11i	−0.944253	+	0.545165i
$874$			3.64231e11i			0.624211i
$875$	−2.02060e11	−	5.17926e11i	−0.344705	−	0.883559i
$876$	−4.44926e11			−0.755564
$877$	−3.82331e11	−	6.62217e11i	−0.646311	−	1.11944i	−0.983997	−	0.178185i	$-0.942978\pi$
$877$	−3.82331e11	−	6.62217e11i	−0.646311	−	1.11944i	0.337686	−	0.941259i	$-0.390356\pi$
$878$	−6.83328e11	−	3.94520e11i	−1.14988	−	0.663882i
$879$	8.24687e10	−	1.42840e11i	0.138145	−	0.239273i
$880$	−2.80176e11	+	1.61760e11i	−0.467197	+	0.269736i
$881$			9.22930e11i			1.53202i	0.642828	+	0.766011i	$0.277761\pi$
$881$			9.22930e11i			1.53202i	−0.642828	+	0.766011i	$0.722239\pi$
$882$	−1.47532e11	−	6.58683e11i	−0.243787	−	1.08843i
$883$	1.92656e11			0.316912			0.158456	−	0.987366i	$-0.449348\pi$
$883$	1.92656e11			0.316912			0.158456	+	0.987366i	$0.449348\pi$
$884$	4.53628e11	+	7.85707e11i	0.742833	+	1.28662i
$885$	3.07062e9	+	1.77282e9i	0.00500556	+	0.00288996i
$886$	7.33305e11	−	1.27012e12i	1.19001	−	2.06115i
$887$	7.29885e11	−	4.21399e11i	1.17913	−	0.680768i	0.223313	−	0.974747i	$-0.428313\pi$
$887$	7.29885e11	−	4.21399e11i	1.17913	−	0.680768i	0.955812	+	0.293978i	$0.0949794\pi$
$888$		−	1.41432e10i		−	0.0227455i
$889$	7.14197e11	−	2.78631e11i	1.14343	−	0.446091i
$890$	−1.33468e11			−0.212724
$891$	1.26461e11	+	2.19037e11i	0.200653	+	0.347541i
$892$	−6.94721e11	−	4.01097e11i	−1.09736	−	0.633564i
$893$	4.22133e11	−	7.31155e11i	0.663809	−	1.14975i
$894$	−1.15032e11	+	6.64138e10i	−0.180081	+	0.103970i
$895$		−	8.63017e9i		−	0.0134502i
$896$	9.16880e10	+	7.34234e10i	0.142259	+	0.113921i
$897$	1.45992e11			0.225507
$898$	−6.07729e10	−	1.05262e11i	−0.0934554	−	0.161870i
$899$	4.55266e11	+	2.62848e11i	0.696990	+	0.402407i
$900$	−1.67669e11	+	2.90411e11i	−0.255554	+	0.442632i
$901$	−1.11545e12	+	6.44006e11i	−1.69259	+	0.977216i
$902$			4.71826e11i			0.712780i
$903$	2.07629e11	+	3.17258e10i	0.312275	+	0.0477158i
$904$	−6.53388e9			−0.00978358
$905$	1.62947e11	+	2.82232e11i	0.242913	+	0.420738i
$906$	1.32470e11	+	7.64815e10i	0.196609	+	0.113512i
$907$	4.52506e11	−	7.83764e11i	0.668645	−	1.15813i	−0.309638	−	0.950854i	$-0.600208\pi$
$907$	4.52506e11	−	7.83764e11i	0.668645	−	1.15813i	0.978283	−	0.207272i	$-0.0664587\pi$
$908$	7.37866e11	−	4.26007e11i	1.08551	−	0.626720i
$909$			2.62371e11i			0.384291i
$910$	7.20758e10	−	4.71698e11i	0.105105	−	0.687858i
$911$	−2.90481e11			−0.421740			−0.210870	−	0.977514i	$-0.567630\pi$
$911$	−2.90481e11			−0.421740			−0.210870	+	0.977514i	$0.567630\pi$
$912$	−1.28384e11	−	2.22368e11i	−0.185581	−	0.321435i
$913$	2.06446e11	+	1.19192e11i	0.297114	+	0.171539i
$914$	−2.58394e11	+	4.47551e11i	−0.370252	+	0.641295i
$915$	−4.59013e10	+	2.65011e10i	−0.0654848	+	0.0378077i
$916$			6.98571e11i			0.992268i
$917$	8.59464e11	−	1.07326e12i	1.21549	−	1.51785i
$918$	−1.41926e12			−1.99844
$919$	−1.97689e11	−	3.42407e11i	−0.277153	−	0.480043i	0.693523	−	0.720435i	$-0.256058\pi$
$919$	−1.97689e11	−	3.42407e11i	−0.277153	−	0.480043i	−0.970676	+	0.240391i	$0.922724\pi$
$920$	1.82441e10	+	1.05333e10i	0.0254667	+	0.0147032i
$921$	−2.01383e11	+	3.48805e11i	−0.279888	+	0.484780i
$922$	4.62447e11	−	2.66994e11i	0.639939	−	0.369469i
$923$		−	1.08385e11i		−	0.149336i
$924$	9.93007e10	+	2.54531e11i	0.136227	+	0.349182i
$925$	2.79496e11			0.381776
$926$	−9.34220e10	−	1.61812e11i	−0.127059	−	0.220072i
$927$	2.95101e11	+	1.70377e11i	0.399625	+	0.230723i
$928$	−4.72783e11	+	8.18884e11i	−0.637485	+	1.10416i
$929$	−2.41713e10	+	1.39553e10i	−0.0324517	+	0.0187360i	−0.516138	−	0.856505i	$-0.672631\pi$
$929$	−2.41713e10	+	1.39553e10i	−0.0324517	+	0.0187360i	0.483686	+	0.875241i	$0.339298\pi$
$930$		−	2.28184e11i		−	0.305038i
$931$	−1.76312e11	+	5.63466e11i	−0.234684	+	0.750013i
$932$	−2.29405e11			−0.304046
$933$	−1.48150e10	−	2.56603e10i	−0.0195512	−	0.0338638i
$934$	−2.29743e11	−	1.32642e11i	−0.301894	−	0.174298i
$935$	3.48057e11	−	6.02852e11i	0.455411	−	0.788795i
$936$	4.31988e10	−	2.49408e10i	0.0562818	−	0.0324943i
$937$			3.87006e11i			0.502064i	0.967979	+	0.251032i	$0.0807699\pi$
$937$			3.87006e11i			0.502064i	−0.967979	+	0.251032i	$0.919230\pi$
$938$	−1.63960e12	+	6.39660e11i	−2.11800	+	0.826300i
$939$	−2.95247e11			−0.379772
$940$	3.47421e11	+	6.01751e11i	0.444985	+	0.770736i
$941$	−5.29404e11	−	3.05652e11i	−0.675195	−	0.389824i	0.122847	−	0.992426i	$-0.460797\pi$
$941$	−5.29404e11	−	3.05652e11i	−0.675195	−	0.389824i	−0.798042	+	0.602602i	$0.794131\pi$
$942$	2.13144e11	−	3.69176e11i	0.270688	−	0.468846i
$943$	2.22341e11	−	1.28368e11i	0.281172	−	0.162335i
$944$		−	1.94163e10i		−	0.0244500i
$945$	2.81442e11	+	2.25378e11i	0.352908	+	0.282608i
$946$	7.12834e11			0.890070
$947$	5.18078e11	+	8.97338e11i	0.644163	+	1.11572i	0.984494	+	0.175417i	$0.0561274\pi$
$947$	5.18078e11	+	8.97338e11i	0.644163	+	1.11572i	−0.340331	+	0.940306i	$0.610539\pi$
$948$	2.30850e11	+	1.33281e11i	0.285823	+	0.165020i
$949$	−6.53949e11	+	1.13267e12i	−0.806268	+	1.39650i
$950$	5.25881e11	−	3.03617e11i	0.645643	−	0.372762i
$951$			2.42210e11i			0.296122i
$952$	−1.32873e11	−	2.03031e10i	−0.161767	−	0.0247181i
$953$	−2.05636e11			−0.249303			−0.124652	−	0.992201i	$-0.539781\pi$
$953$	−2.05636e11			−0.249303			−0.124652	+	0.992201i	$0.539781\pi$
$954$	−5.03840e11	−	8.72676e11i	−0.608273	−	1.05356i
$955$	3.52366e11	+	2.03438e11i	0.423623	+	0.244579i
$956$	4.06277e11	−	7.03692e11i	0.486396	−	0.842463i
$957$	2.68288e11	−	1.54896e11i	0.319855	−	0.184669i
$958$		−	3.67602e11i		−	0.436431i
$959$	−8.64353e10	+	5.65674e11i	−0.102192	+	0.668794i
$960$	1.84258e11			0.216941
$961$	−1.00583e11	−	1.74214e11i	−0.117931	−	0.204263i
$962$	5.12337e11	+	2.95798e11i	0.598213	+	0.345378i
$963$	−4.36315e10	+	7.55719e10i	−0.0507335	+	0.0878730i
$964$	−1.09408e11	+	6.31667e10i	−0.126690	+	0.0731442i
$965$		−	4.51011e11i		−	0.520090i
$966$	1.92385e11	−	2.40242e11i	0.220934	−	0.275893i
$967$	−1.54263e11			−0.176424			−0.0882118	−	0.996102i	$-0.528115\pi$
$967$	−1.54263e11			−0.176424			−0.0882118	+	0.996102i	$0.528115\pi$
$968$	7.50975e9	+	1.30073e10i	0.00855310	+	0.0148144i
$969$	4.78468e11	+	2.76244e11i	0.542697	+	0.313326i
$970$	−4.71918e11	+	8.17385e11i	−0.533064	+	0.923294i
$971$	−1.19043e11	+	6.87297e10i	−0.133915	+	0.0773157i	−0.565461	−	0.824775i	$-0.691302\pi$
$971$	−1.19043e11	+	6.87297e10i	−0.133915	+	0.0773157i	0.431546	+	0.902091i	$0.357968\pi$
$972$		−	8.33972e11i		−	0.934300i
$973$	−1.21685e11	−	3.11908e11i	−0.135765	−	0.347996i
$974$	6.09711e11			0.677467
$975$	−1.21696e11	−	2.10784e11i	−0.134666	−	0.233249i
$976$	2.51360e11	+	1.45123e11i	0.277011	+	0.159933i
$977$	1.91236e11	−	3.31231e11i	0.209890	−	0.363541i	−0.741789	−	0.670633i	$-0.766023\pi$
$977$	1.91236e11	−	3.31231e11i	0.209890	−	0.363541i	0.951680	+	0.307092i	$0.0993560\pi$
$978$	2.88190e11	−	1.66386e11i	0.315009	−	0.181871i
$979$		−	2.24642e11i		−	0.244546i
$980$	−3.29057e11	−	3.57537e11i	−0.356753	−	0.387630i
$981$	8.52951e11			0.920976
$982$	−1.49269e11	−	2.58542e11i	−0.160519	−	0.278026i
$983$	−1.25776e12	−	7.26165e11i	−1.34705	−	0.777717i	−0.359215	−	0.933255i	$-0.616956\pi$
$983$	−1.25776e12	−	7.26165e11i	−1.34705	−	0.777717i	−0.987830	+	0.155538i	$0.950289\pi$
$984$	−1.08295e10	+	1.87573e10i	−0.0115512	+	0.0200073i
$985$	−3.17198e11	+	1.83134e11i	−0.336965	+	0.194547i
$986$		−	2.16874e12i		−	2.29456i
$987$	−6.64625e11	+	2.59292e11i	−0.700338	+	0.273225i
$988$	6.20838e11			0.651554
$989$	−1.93939e11	−	3.35912e11i	−0.202712	−	0.351108i
$990$	4.71643e11	+	2.72303e11i	0.490990	+	0.283473i
$991$	−9.97800e10	+	1.72824e11i	−0.103454	+	0.179188i	−0.913106	−	0.407723i	$-0.866323\pi$
$991$	−9.97800e10	+	1.72824e11i	−0.103454	+	0.179188i	0.809651	+	0.586911i	$0.199656\pi$
$992$	−1.01520e12	+	5.86128e11i	−1.04835	+	0.605265i
$993$		−	5.26246e11i		−	0.541243i
$994$	−1.78357e11	−	1.42828e11i	−0.182703	−	0.146308i
$995$	−4.28800e11			−0.437484
$996$	−7.78565e10	−	1.34851e11i	−0.0791148	−	0.137031i
$997$	2.13092e11	+	1.23029e11i	0.215668	+	0.124516i	0.603943	−	0.797027i	$-0.293595\pi$
$997$	2.13092e11	+	1.23029e11i	0.215668	+	0.124516i	−0.388275	+	0.921544i	$0.626929\pi$
$998$	−1.18430e12	+	2.05127e12i	−1.19382	+	2.06776i
$999$	−3.87133e11	+	2.23511e11i	−0.388685	+	0.224407i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.9.d.a.3.4	✓	8
3.2	odd	2		63.9.m.b.10.1		8
4.3	odd	2		112.9.s.a.17.2		8
7.2	even	3		49.9.d.c.19.4		8
7.3	odd	6		49.9.b.a.48.2		8
7.4	even	3		49.9.b.a.48.1		8
7.5	odd	6	inner	7.9.d.a.5.4	yes	8
7.6	odd	2		49.9.d.c.31.4		8
21.5	even	6		63.9.m.b.19.1		8
28.19	even	6		112.9.s.a.33.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.9.d.a.3.4	✓	8	1.1	even	1	trivial
7.9.d.a.5.4	yes	8	7.5	odd	6	inner
49.9.b.a.48.1		8	7.4	even	3
49.9.b.a.48.2		8	7.3	odd	6
49.9.d.c.19.4		8	7.2	even	3
49.9.d.c.31.4		8	7.6	odd	2
63.9.m.b.10.1		8	3.2	odd	2
63.9.m.b.19.1		8	21.5	even	6
112.9.s.a.17.2		8	4.3	odd	2
112.9.s.a.33.2		8	28.19	even	6

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:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	7.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(11.1264 + 19.2716i) q^{2} +(31.2153 + 18.0222i) q^{3} +(-119.595 + 207.145i) q^{4} +(-305.183 + 176.198i) q^{5} +802.090i q^{6} +(2236.80 - 872.649i) q^{7} +374.058 q^{8} +(-2630.90 - 4556.86i) q^{9} +O(q^{10})\)	\(q+(11.1264 + 19.2716i) q^{2} +(31.2153 + 18.0222i) q^{3} +(-119.595 + 207.145i) q^{4} +(-305.183 + 176.198i) q^{5} +802.090i q^{6} +(2236.80 - 872.649i) q^{7} +374.058 q^{8} +(-2630.90 - 4556.86i) q^{9} +(-6791.21 - 3920.91i) q^{10} +(6599.36 - 11430.4i) q^{11} +(-7466.41 + 4310.73i) q^{12} +25343.6i q^{13} +(41705.0 + 33397.2i) q^{14} -12701.9 q^{15} +(34778.3 + 60237.8i) q^{16} +(-129613. - 74832.2i) q^{17} +(58545.2 - 101403. i) q^{18} +(-88694.6 + 51207.9i) q^{19} -84289.7i q^{20} +(85549.5 + 13072.0i) q^{21} +293709. q^{22} +(-79908.8 - 138406. i) q^{23} +(11676.3 + 6741.33i) q^{24} +(-133221. + 230746. i) q^{25} +(-488410. + 281984. i) q^{26} -426145. i q^{27} +(-86746.0 + 567707. i) q^{28} +651182. q^{29} +(-141326. - 244785. i) q^{30} +(699138. + 403648. i) q^{31} +(-726038. + 1.25754e6i) q^{32} +(412002. - 237869. i) q^{33} -3.33046e6i q^{34} +(-528876. + 660437. i) q^{35} +1.25857e6 q^{36} +(-524495. - 908452. i) q^{37} +(-1.97371e6 - 1.13952e6i) q^{38} +(-456746. + 791107. i) q^{39} +(-114156. + 65908.1i) q^{40} +1.60644e6i q^{41} +(699943. + 1.79412e6i) q^{42} +2.42701e6 q^{43} +(1.57850e6 + 2.73405e6i) q^{44} +(1.60582e6 + 927118. i) q^{45} +(1.77820e6 - 3.07993e6i) q^{46} +(-7.13909e6 + 4.12175e6i) q^{47} +2.50712e6i q^{48} +(4.24177e6 - 3.90389e6i) q^{49} -5.92911e6 q^{50} +(-2.69728e6 - 4.67182e6i) q^{51} +(-5.24979e6 - 3.03097e6i) q^{52} +(4.30300e6 - 7.45301e6i) q^{53} +(8.21248e6 - 4.74148e6i) q^{54} +4.65116e6i q^{55} +(836693. - 326421. i) q^{56} -3.69151e6 q^{57} +(7.24533e6 + 1.25493e7i) q^{58} +(-241746. - 139572. i) q^{59} +(1.51908e6 - 2.63113e6i) q^{60} +(3.61375e6 - 2.08640e6i) q^{61} +1.79646e7i q^{62} +(-9.86135e6 - 7.89693e6i) q^{63} -1.45064e7 q^{64} +(-4.46548e6 - 7.73443e6i) q^{65} +(9.16823e6 + 5.29328e6i) q^{66} +(-1.64700e7 + 2.85269e7i) q^{67} +(3.10022e7 - 1.78992e7i) q^{68} -5.76052e6i q^{69} +(-1.86122e7 - 2.84395e6i) q^{70} -4.27665e6 q^{71} +(-984109. - 1.70453e6i) q^{72} +(4.46928e7 + 2.58034e7i) q^{73} +(1.16715e7 - 2.02157e7i) q^{74} +(-8.31708e6 + 4.80187e6i) q^{75} -2.44969e7i q^{76} +(4.78671e6 - 3.13265e7i) q^{77} -2.03278e7 q^{78} +(-1.54593e7 - 2.67762e7i) q^{79} +(-2.12275e7 - 1.22557e7i) q^{80} +(-9.58130e6 + 1.65953e7i) q^{81} +(-3.09586e7 + 1.78739e7i) q^{82} +1.80611e7i q^{83} +(-1.29391e7 + 1.61578e7i) q^{84} +5.27410e7 q^{85} +(2.70039e7 + 4.67722e7i) q^{86} +(2.03268e7 + 1.17357e7i) q^{87} +(2.46854e6 - 4.27563e6i) q^{88} +(1.47398e7 - 8.51001e6i) q^{89} +4.12621e7i q^{90} +(2.21160e7 + 5.66885e7i) q^{91} +3.82269e7 q^{92} +(1.45492e7 + 2.52000e7i) q^{93} +(-1.58865e8 - 9.17209e7i) q^{94} +(1.80454e7 - 3.12556e7i) q^{95} +(-4.53270e7 + 2.61696e7i) q^{96} -1.20359e8i q^{97} +(1.22430e8 + 3.83091e7i) q^{98} -6.94491e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 84 q^{3} - 164 q^{4} - 840 q^{5} - 140 q^{7} + 6544 q^{8} + 396 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 - 84 * q^3 - 164 * q^4 - 840 * q^5 - 140 * q^7 + 6544 * q^8 + 396 * q^9	\( 8 q - 4 q^{2} - 84 q^{3} - 164 q^{4} - 840 q^{5} - 140 q^{7} + 6544 q^{8} + 396 q^{9} + 5796 q^{10} + 1784 q^{11} - 40908 q^{12} - 9856 q^{14} + 131808 q^{15} - 8584 q^{16} - 141456 q^{17} - 121944 q^{18} - 257544 q^{19} + 474012 q^{21} + 1706256 q^{22} - 348940 q^{23} - 895104 q^{24} - 557752 q^{25} - 2913120 q^{26} + 1485092 q^{28} + 4983176 q^{29} - 551112 q^{30} - 2376696 q^{31} - 332016 q^{32} - 5719140 q^{33} + 2491272 q^{35} + 13269408 q^{36} + 492740 q^{37} - 7088088 q^{38} - 2850372 q^{39} - 7601832 q^{40} + 3586128 q^{42} + 4448432 q^{43} - 3678804 q^{44} + 3328164 q^{45} - 226560 q^{46} + 2704128 q^{47} - 3811024 q^{49} - 15628912 q^{50} - 350856 q^{51} + 11135208 q^{52} + 2281460 q^{53} + 24553368 q^{54} - 6573392 q^{56} - 43638408 q^{57} + 11442696 q^{58} + 25291140 q^{59} + 17679564 q^{60} + 59368764 q^{61} - 60081756 q^{63} - 114153056 q^{64} + 16923396 q^{65} + 463428 q^{66} - 107108 q^{67} + 44316972 q^{68} + 19120080 q^{70} - 82809760 q^{71} + 13297584 q^{72} + 116758404 q^{73} + 72690340 q^{74} + 79832424 q^{75} - 58244200 q^{77} - 44122512 q^{78} - 50628092 q^{79} - 93591624 q^{80} - 96868872 q^{81} - 91061712 q^{82} + 154096572 q^{84} + 119231208 q^{85} + 39093088 q^{86} + 26702676 q^{87} + 41392848 q^{88} - 2322516 q^{89} - 151794552 q^{91} + 253819128 q^{92} - 57693204 q^{93} - 345566088 q^{94} - 172787052 q^{95} - 416455200 q^{96} + 373659692 q^{98} + 672244008 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 84 * q^3 - 164 * q^4 - 840 * q^5 - 140 * q^7 + 6544 * q^8 + 396 * q^9 + 5796 * q^10 + 1784 * q^11 - 40908 * q^12 - 9856 * q^14 + 131808 * q^15 - 8584 * q^16 - 141456 * q^17 - 121944 * q^18 - 257544 * q^19 + 474012 * q^21 + 1706256 * q^22 - 348940 * q^23 - 895104 * q^24 - 557752 * q^25 - 2913120 * q^26 + 1485092 * q^28 + 4983176 * q^29 - 551112 * q^30 - 2376696 * q^31 - 332016 * q^32 - 5719140 * q^33 + 2491272 * q^35 + 13269408 * q^36 + 492740 * q^37 - 7088088 * q^38 - 2850372 * q^39 - 7601832 * q^40 + 3586128 * q^42 + 4448432 * q^43 - 3678804 * q^44 + 3328164 * q^45 - 226560 * q^46 + 2704128 * q^47 - 3811024 * q^49 - 15628912 * q^50 - 350856 * q^51 + 11135208 * q^52 + 2281460 * q^53 + 24553368 * q^54 - 6573392 * q^56 - 43638408 * q^57 + 11442696 * q^58 + 25291140 * q^59 + 17679564 * q^60 + 59368764 * q^61 - 60081756 * q^63 - 114153056 * q^64 + 16923396 * q^65 + 463428 * q^66 - 107108 * q^67 + 44316972 * q^68 + 19120080 * q^70 - 82809760 * q^71 + 13297584 * q^72 + 116758404 * q^73 + 72690340 * q^74 + 79832424 * q^75 - 58244200 * q^77 - 44122512 * q^78 - 50628092 * q^79 - 93591624 * q^80 - 96868872 * q^81 - 91061712 * q^82 + 154096572 * q^84 + 119231208 * q^85 + 39093088 * q^86 + 26702676 * q^87 + 41392848 * q^88 - 2322516 * q^89 - 151794552 * q^91 + 253819128 * q^92 - 57693204 * q^93 - 345566088 * q^94 - 172787052 * q^95 - 416455200 * q^96 + 373659692 * q^98 + 672244008 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more