LMFDB - Embedded newform 13.10.a.b.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [13,10,Mod(1,13)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(13, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("13.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	13.a (trivial)

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:	yes
Analytic conductor:	$6.69546587013$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 1438x^{3} - 4164x^{2} + 396957x - 59580 $ x^5 - 1438x^3 - 4164x^2 + 396957*x - 59580
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$35.1685$ of defining polynomial
Character	$\chi$	$=$	13.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+38.1685 q^{2} +47.8784 q^{3} +944.833 q^{4} -109.762 q^{5} +1827.45 q^{6} +5947.44 q^{7} +16520.6 q^{8} -17390.7 q^{9} -4189.45 q^{10} -25205.7 q^{11} +45237.1 q^{12} +28561.0 q^{13} +227005. q^{14} -5255.24 q^{15} +146811. q^{16} +109318. q^{17} -663775. q^{18} -904609. q^{19} -103707. q^{20} +284754. q^{21} -962062. q^{22} -435749. q^{23} +790979. q^{24} -1.94108e6 q^{25} +1.09013e6 q^{26} -1.77503e6 q^{27} +5.61934e6 q^{28} +6.44791e6 q^{29} -200584. q^{30} +6.62308e6 q^{31} -2.85499e6 q^{32} -1.20681e6 q^{33} +4.17250e6 q^{34} -652804. q^{35} -1.64313e7 q^{36} +4.14357e6 q^{37} -3.45275e7 q^{38} +1.36745e6 q^{39} -1.81333e6 q^{40} +1.49568e7 q^{41} +1.08686e7 q^{42} +4.01789e7 q^{43} -2.38151e7 q^{44} +1.90884e6 q^{45} -1.66319e7 q^{46} +6.30151e6 q^{47} +7.02907e6 q^{48} -4.98153e6 q^{49} -7.40880e7 q^{50} +5.23397e6 q^{51} +2.69854e7 q^{52} +1.53111e7 q^{53} -6.77501e7 q^{54} +2.76663e6 q^{55} +9.82552e7 q^{56} -4.33112e7 q^{57} +2.46107e8 q^{58} -1.52760e8 q^{59} -4.96532e6 q^{60} +8.66321e7 q^{61} +2.52793e8 q^{62} -1.03430e8 q^{63} -1.84138e8 q^{64} -3.13492e6 q^{65} -4.60620e7 q^{66} -1.01034e8 q^{67} +1.03287e8 q^{68} -2.08630e7 q^{69} -2.49165e7 q^{70} +4.13122e8 q^{71} -2.87304e8 q^{72} -3.14453e8 q^{73} +1.58154e8 q^{74} -9.29357e7 q^{75} -8.54704e8 q^{76} -1.49909e8 q^{77} +5.21937e7 q^{78} -2.00580e8 q^{79} -1.61143e7 q^{80} +2.57315e8 q^{81} +5.70879e8 q^{82} +6.34578e7 q^{83} +2.69045e8 q^{84} -1.19990e7 q^{85} +1.53357e9 q^{86} +3.08715e8 q^{87} -4.16412e8 q^{88} +3.47074e7 q^{89} +7.28574e7 q^{90} +1.69865e8 q^{91} -4.11710e8 q^{92} +3.17102e8 q^{93} +2.40519e8 q^{94} +9.92918e7 q^{95} -1.36692e8 q^{96} -1.25403e9 q^{97} -1.90137e8 q^{98} +4.38343e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 15 q^{2} + 161 q^{3} + 361 q^{4} + 1803 q^{5} + 5693 q^{6} + 10099 q^{7} + 23151 q^{8} + 61060 q^{9} + 84505 q^{10} + 121746 q^{11} + 113389 q^{12} + 142805 q^{13} + 8475 q^{14} + 105973 q^{15} - 322463 q^{16}+ \cdots + 3016199848 q^{99}+O(q^{100}) $ 5 * q + 15 * q^2 + 161 * q^3 + 361 * q^4 + 1803 * q^5 + 5693 * q^6 + 10099 * q^7 + 23151 * q^8 + 61060 * q^9 + 84505 * q^10 + 121746 * q^11 + 113389 * q^12 + 142805 * q^13 + 8475 * q^14 + 105973 * q^15 - 322463 * q^16 - 495669 * q^17 - 656228 * q^18 - 840738 * q^19 - 1595607 * q^20 - 1599467 * q^21 - 2023594 * q^22 - 592152 * q^23 - 2295657 * q^24 + 1670362 * q^25 + 428415 * q^26 + 6847883 * q^27 + 2587955 * q^28 + 10678182 * q^29 + 5491201 * q^30 + 12885296 * q^31 + 3282927 * q^32 + 17278298 * q^33 - 9934079 * q^34 + 8380731 * q^35 - 20483302 * q^36 + 7171823 * q^37 - 25568814 * q^38 + 4598321 * q^39 - 54359445 * q^40 + 9294012 * q^41 - 69520457 * q^42 + 12831975 * q^43 - 41479074 * q^44 + 26135198 * q^45 - 59319696 * q^46 + 43354215 * q^47 - 86874671 * q^48 + 25249488 * q^49 - 16270770 * q^50 + 16905901 * q^51 + 10310521 * q^52 + 93231780 * q^53 + 58983719 * q^54 + 99448846 * q^55 + 199599225 * q^56 + 90173382 * q^57 + 151020970 * q^58 + 246496182 * q^59 + 90097913 * q^60 - 132232612 * q^61 + 158135724 * q^62 - 416955202 * q^63 + 91019105 * q^64 + 51495483 * q^65 - 323733130 * q^66 - 369388534 * q^67 + 238172073 * q^68 - 579986760 * q^69 - 144857425 * q^70 + 212150457 * q^71 - 415774278 * q^72 - 252729806 * q^73 + 192105957 * q^74 - 752457788 * q^75 - 953775990 * q^76 + 449666118 * q^77 + 162597773 * q^78 - 1247271728 * q^79 + 900649725 * q^80 - 317713115 * q^81 + 169559388 * q^82 + 1696894296 * q^83 + 1247983739 * q^84 - 775363765 * q^85 + 3291621459 * q^86 - 614530466 * q^87 - 220227222 * q^88 - 753854382 * q^89 + 2296265882 * q^90 + 288437539 * q^91 + 13876128 * q^92 - 892784668 * q^93 + 272071215 * q^94 + 1442632962 * q^95 + 930612847 * q^96 + 3824606 * q^97 + 1570614816 * q^98 + 3016199848 * q^99

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 $

$2$	38.1685	1.68682	0.843412	−	0.537267i	$-0.180543\pi$
$2$	38.1685	1.68682	0.843412	+	0.537267i	$0.180543\pi$
$3$	47.8784	0.341267	0.170633	−	0.985335i	$-0.445419\pi$
$3$	47.8784	0.341267	0.170633	+	0.985335i	$0.445419\pi$
$4$	944.833	1.84538
$5$	−109.762	−0.0785394	−0.0392697	−	0.999229i	$-0.512503\pi$
$5$	−109.762	−0.0785394	−0.0392697	+	0.999229i	$0.512503\pi$
$6$	1827.45	0.575657
$7$	5947.44	0.936244	0.468122	−	0.883664i	$-0.344931\pi$
$7$	5947.44	0.936244	0.468122	+	0.883664i	$0.344931\pi$
$8$	16520.6	1.42600
$9$	−17390.7	−0.883537
$10$	−4189.45	−0.132482
$11$	−25205.7	−0.519076	−0.259538	−	0.965733i	$-0.583570\pi$
$11$	−25205.7	−0.519076	−0.259538	+	0.965733i	$0.583570\pi$
$12$	45237.1	0.629766
$13$	28561.0	0.277350
$13$	28561.0	0.277350
$14$	227005.	1.57928
$15$	−5255.24	−0.0268029
$16$	146811.	0.560039
$17$	109318.	0.317447	0.158724	−	0.987323i	$-0.449262\pi$
$17$	109318.	0.317447	0.158724	+	0.987323i	$0.449262\pi$
$18$	−663775.	−1.49037
$19$	−904609.	−1.59246	−0.796232	−	0.604992i	$-0.793176\pi$
$19$	−904609.	−1.59246	−0.796232	+	0.604992i	$0.793176\pi$
$20$	−103707.	−0.144935
$21$	284754.	0.319509
$22$	−962062.	−0.875590
$23$	−435749.	−0.324684	−0.162342	−	0.986735i	$-0.551905\pi$
$23$	−435749.	−0.324684	−0.162342	+	0.986735i	$0.551905\pi$
$24$	790979.	0.486647
$25$	−1.94108e6	−0.993832
$26$	1.09013e6	0.467841
$27$	−1.77503e6	−0.642789
$28$	5.61934e6	1.72772
$29$	6.44791e6	1.69289	0.846443	−	0.532479i	$-0.178740\pi$
$29$	6.44791e6	1.69289	0.846443	+	0.532479i	$0.178740\pi$
$30$	−200584.	−0.0452118
$31$	6.62308e6	1.28805	0.644024	−	0.765005i	$-0.277264\pi$
$31$	6.62308e6	1.28805	0.644024	+	0.765005i	$0.277264\pi$
$32$	−2.85499e6	−0.481315
$33$	−1.20681e6	−0.177143
$34$	4.17250e6	0.535477
$35$	−652804.	−0.0735320
$36$	−1.64313e7	−1.63046
$37$	4.14357e6	0.363469	0.181734	−	0.983348i	$-0.441829\pi$
$37$	4.14357e6	0.363469	0.181734	+	0.983348i	$0.441829\pi$
$38$	−3.45275e7	−2.68621
$39$	1.36745e6	0.0946504
$40$	−1.81333e6	−0.111997
$41$	1.49568e7	0.826632	0.413316	−	0.910588i	$-0.364370\pi$
$41$	1.49568e7	0.826632	0.413316	+	0.910588i	$0.364370\pi$
$42$	1.08686e7	0.538956
$43$	4.01789e7	1.79221	0.896107	−	0.443838i	$-0.146384\pi$
$43$	4.01789e7	1.79221	0.896107	+	0.443838i	$0.146384\pi$
$44$	−2.38151e7	−0.957891
$45$	1.90884e6	0.0693925
$46$	−1.66319e7	−0.547685
$47$	6.30151e6	0.188367	0.0941834	−	0.995555i	$-0.469976\pi$
$47$	6.30151e6	0.188367	0.0941834	+	0.995555i	$0.469976\pi$
$48$	7.02907e6	0.191123
$49$	−4.98153e6	−0.123447
$50$	−7.40880e7	−1.67642
$51$	5.23397e6	0.108334
$52$	2.69854e7	0.511815
$53$	1.53111e7	0.266542	0.133271	−	0.991080i	$-0.457452\pi$
$53$	1.53111e7	0.266542	0.133271	+	0.991080i	$0.457452\pi$
$54$	−6.77501e7	−1.08427
$55$	2.76663e6	0.0407679
$56$	9.82552e7	1.33509
$57$	−4.33112e7	−0.543455
$58$	2.46107e8	2.85560
$59$	−1.52760e8	−1.64126	−0.820629	−	0.571462i	$-0.806376\pi$
$59$	−1.52760e8	−1.64126	−0.820629	+	0.571462i	$0.806376\pi$
$60$	−4.96532e6	−0.0494614
$61$	8.66321e7	0.801114	0.400557	−	0.916272i	$-0.368817\pi$
$61$	8.66321e7	0.801114	0.400557	+	0.916272i	$0.368817\pi$
$62$	2.52793e8	2.17271
$63$	−1.03430e8	−0.827206
$64$	−1.84138e8	−1.37193
$65$	−3.13492e6	−0.0217829
$66$	−4.60620e7	−0.298810
$67$	−1.01034e8	−0.612537	−0.306268	−	0.951945i	$-0.599080\pi$
$67$	−1.01034e8	−0.612537	−0.306268	+	0.951945i	$0.599080\pi$
$68$	1.03287e8	0.585809
$69$	−2.08630e7	−0.110804
$70$	−2.49165e7	−0.124036
$71$	4.13122e8	1.92937	0.964685	−	0.263406i	$-0.0848458\pi$
$71$	4.13122e8	1.92937	0.964685	+	0.263406i	$0.0848458\pi$
$72$	−2.87304e8	−1.25993
$73$	−3.14453e8	−1.29599	−0.647997	−	0.761643i	$-0.724393\pi$
$73$	−3.14453e8	−1.29599	−0.647997	+	0.761643i	$0.724393\pi$
$74$	1.58154e8	0.613108
$75$	−9.29357e7	−0.339162
$76$	−8.54704e8	−2.93870
$77$	−1.49909e8	−0.485982
$78$	5.21937e7	0.159659
$79$	−2.00580e8	−0.579383	−0.289692	−	0.957120i	$-0.593553\pi$
$79$	−2.00580e8	−0.579383	−0.289692	+	0.957120i	$0.593553\pi$
$80$	−1.61143e7	−0.0439851
$81$	2.57315e8	0.664175
$82$	5.70879e8	1.39438
$83$	6.34578e7	0.146769	0.0733843	−	0.997304i	$-0.476620\pi$
$83$	6.34578e7	0.146769	0.0733843	+	0.997304i	$0.476620\pi$
$84$	2.69045e8	0.589614
$85$	−1.19990e7	−0.0249321
$86$	1.53357e9	3.02315
$87$	3.08715e8	0.577726
$88$	−4.16412e8	−0.740204
$89$	3.47074e7	0.0586364	0.0293182	−	0.999570i	$-0.490666\pi$
$89$	3.47074e7	0.0586364	0.0293182	+	0.999570i	$0.490666\pi$
$90$	7.28574e7	0.117053
$91$	1.69865e8	0.259667
$92$	−4.11710e8	−0.599164
$93$	3.17102e8	0.439568
$94$	2.40519e8	0.317742
$95$	9.92918e7	0.125071
$96$	−1.36692e8	−0.164257
$97$	−1.25403e9	−1.43825	−0.719127	−	0.694879i	$-0.755458\pi$
$97$	−1.25403e9	−1.43825	−0.719127	+	0.694879i	$0.755458\pi$
$98$	−1.90137e8	−0.208233
$99$	4.38343e8	0.458623
$100$	−1.83399e9	−1.83399
$101$	−9.06459e8	−0.866766	−0.433383	−	0.901210i	$-0.642680\pi$
$101$	−9.06459e8	−0.866766	−0.433383	+	0.901210i	$0.642680\pi$
$102$	1.99773e8	0.182741
$103$	−4.17013e8	−0.365075	−0.182537	−	0.983199i	$-0.558431\pi$
$103$	−4.17013e8	−0.365075	−0.182537	+	0.983199i	$0.558431\pi$
$104$	4.71844e8	0.395502
$105$	−3.12552e7	−0.0250940
$106$	5.84402e8	0.449610
$107$	6.71636e8	0.495344	0.247672	−	0.968844i	$-0.420334\pi$
$107$	6.71636e8	0.495344	0.247672	+	0.968844i	$0.420334\pi$
$108$	−1.67710e9	−1.18619
$109$	1.66748e9	1.13147	0.565734	−	0.824588i	$-0.308593\pi$
$109$	1.66748e9	1.13147	0.565734	+	0.824588i	$0.308593\pi$
$110$	1.05598e8	0.0687683
$111$	1.98387e8	0.124040
$112$	8.73149e8	0.524333
$113$	−1.84580e9	−1.06496	−0.532478	−	0.846444i	$-0.678739\pi$
$113$	−1.84580e9	−1.06496	−0.532478	+	0.846444i	$0.678739\pi$
$114$	−1.65312e9	−0.916713
$115$	4.78287e7	0.0255005
$116$	6.09219e9	3.12401
$117$	−4.96695e8	−0.245049
$118$	−5.83063e9	−2.76851
$119$	6.50162e8	0.297208
$120$	−8.68195e7	−0.0382210
$121$	−1.72262e9	−0.730560
$122$	3.30661e9	1.35134
$123$	7.16109e8	0.282102
$124$	6.25770e9	2.37694
$125$	4.27436e8	0.156594
$126$	−3.94776e9	−1.39535
$127$	1.87922e9	0.641006	0.320503	−	0.947248i	$-0.396148\pi$
$127$	1.87922e9	0.641006	0.320503	+	0.947248i	$0.396148\pi$
$128$	−5.56650e9	−1.83290
$129$	1.92370e9	0.611623
$130$	−1.19655e8	−0.0367439
$131$	3.46045e9	1.02663	0.513313	−	0.858201i	$-0.328418\pi$
$131$	3.46045e9	1.02663	0.513313	+	0.858201i	$0.328418\pi$
$132$	−1.14023e9	−0.326896
$133$	−5.38011e9	−1.49093
$134$	−3.85632e9	−1.03324
$135$	1.94831e8	0.0504842
$136$	1.80600e9	0.452680
$137$	5.04786e9	1.22424	0.612118	−	0.790766i	$-0.290318\pi$
$137$	5.04786e9	1.22424	0.612118	+	0.790766i	$0.290318\pi$
$138$	−7.96307e8	−0.186907
$139$	3.59716e9	0.817322	0.408661	−	0.912686i	$-0.365996\pi$
$139$	3.59716e9	0.817322	0.408661	+	0.912686i	$0.365996\pi$
$140$	−6.16791e8	−0.135694
$141$	3.01706e8	0.0642833
$142$	1.57682e10	3.25451
$143$	−7.19899e8	−0.143966
$144$	−2.55314e9	−0.494815
$145$	−7.07736e8	−0.132958
$146$	−1.20022e10	−2.18611
$147$	−2.38508e8	−0.0421283
$148$	3.91498e9	0.670736
$149$	1.27561e9	0.212022	0.106011	−	0.994365i	$-0.466192\pi$
$149$	1.27561e9	0.212022	0.106011	+	0.994365i	$0.466192\pi$
$150$	−3.54721e9	−0.572106
$151$	4.35273e9	0.681342	0.340671	−	0.940183i	$-0.389346\pi$
$151$	4.35273e9	0.681342	0.340671	+	0.940183i	$0.389346\pi$
$152$	−1.49447e10	−2.27086
$153$	−1.90111e9	−0.280476
$154$	−5.72181e9	−0.819766
$155$	−7.26963e8	−0.101163
$156$	1.29202e9	0.174666
$157$	−1.41002e10	−1.85215	−0.926075	−	0.377339i	$-0.876839\pi$
$157$	−1.41002e10	−1.85215	−0.926075	+	0.377339i	$0.876839\pi$
$158$	−7.65584e9	−0.977318
$159$	7.33072e8	0.0909619
$160$	3.13370e8	0.0378022
$161$	−2.59159e9	−0.303983
$162$	9.82132e9	1.12035
$163$	7.24812e8	0.0804231	0.0402116	−	0.999191i	$-0.487197\pi$
$163$	7.24812e8	0.0804231	0.0402116	+	0.999191i	$0.487197\pi$
$164$	1.41317e10	1.52545
$165$	1.32462e8	0.0139127
$166$	2.42209e9	0.247573
$167$	−8.33031e8	−0.0828776	−0.0414388	−	0.999141i	$-0.513194\pi$
$167$	−8.33031e8	−0.0828776	−0.0414388	+	0.999141i	$0.513194\pi$
$168$	4.70430e9	0.455621
$169$	8.15731e8	0.0769231
$170$	−4.57983e8	−0.0420561
$171$	1.57317e10	1.40700
$172$	3.79623e10	3.30731
$173$	5.77955e8	0.0490553	0.0245277	−	0.999699i	$-0.492192\pi$
$173$	5.77955e8	0.0490553	0.0245277	+	0.999699i	$0.492192\pi$
$174$	1.17832e10	0.974522
$175$	−1.15444e10	−0.930469
$176$	−3.70046e9	−0.290703
$177$	−7.31392e9	−0.560106
$178$	1.32473e9	0.0989094
$179$	−1.56569e10	−1.13990	−0.569952	−	0.821678i	$-0.693038\pi$
$179$	−1.56569e10	−1.13990	−0.569952	+	0.821678i	$0.693038\pi$
$180$	1.80353e9	0.128055
$181$	−2.18552e10	−1.51356	−0.756781	−	0.653668i	$-0.773229\pi$
$181$	−2.18552e10	−1.51356	−0.756781	+	0.653668i	$0.773229\pi$
$182$	6.48349e9	0.438013
$183$	4.14780e9	0.273394
$184$	−7.19882e9	−0.463000
$185$	−4.54807e8	−0.0285466
$186$	1.21033e10	0.741474
$187$	−2.75543e9	−0.164779
$188$	5.95388e9	0.347608
$189$	−1.05569e10	−0.601807
$190$	3.78982e9	0.210973
$191$	1.67784e10	0.912222	0.456111	−	0.889923i	$-0.349242\pi$
$191$	1.67784e10	0.912222	0.456111	+	0.889923i	$0.349242\pi$
$192$	−8.81622e9	−0.468195
$193$	−2.70036e10	−1.40092	−0.700462	−	0.713690i	$-0.747023\pi$
$193$	−2.70036e10	−1.40092	−0.700462	+	0.713690i	$0.747023\pi$
$194$	−4.78645e10	−2.42608
$195$	−1.50095e8	−0.00743378
$196$	−4.70671e9	−0.227806
$197$	1.58277e10	0.748720	0.374360	−	0.927283i	$-0.377862\pi$
$197$	1.58277e10	0.748720	0.374360	+	0.927283i	$0.377862\pi$
$198$	1.67309e10	0.773616
$199$	8.80397e9	0.397960	0.198980	−	0.980004i	$-0.436237\pi$
$199$	8.80397e9	0.397960	0.198980	+	0.980004i	$0.436237\pi$
$200$	−3.20677e10	−1.41721
$201$	−4.83736e9	−0.209038
$202$	−3.45982e10	−1.46208
$203$	3.83485e10	1.58495
$204$	4.94523e9	0.199917
$205$	−1.64169e9	−0.0649232
$206$	−1.59167e10	−0.615817
$207$	7.57796e9	0.286870
$208$	4.19306e9	0.155327
$209$	2.28013e10	0.826610
$210$	−1.19296e9	−0.0423292
$211$	−1.82054e10	−0.632308	−0.316154	−	0.948708i	$-0.602392\pi$
$211$	−1.82054e10	−0.632308	−0.316154	+	0.948708i	$0.602392\pi$
$212$	1.44665e10	0.491870
$213$	1.97796e10	0.658430
$214$	2.56353e10	0.835558
$215$	−4.41012e9	−0.140759
$216$	−2.93245e10	−0.916618
$217$	3.93904e10	1.20593
$218$	6.36453e10	1.90859
$219$	−1.50555e10	−0.442280
$220$	2.61400e9	0.0752322
$221$	3.12223e9	0.0880440
$222$	7.57215e9	0.209233
$223$	1.53511e10	0.415688	0.207844	−	0.978162i	$-0.433355\pi$
$223$	1.53511e10	0.415688	0.207844	+	0.978162i	$0.433355\pi$
$224$	−1.69799e10	−0.450628
$225$	3.37566e10	0.878087
$226$	−7.04514e10	−1.79639
$227$	4.20620e10	1.05141	0.525707	−	0.850666i	$-0.323801\pi$
$227$	4.20620e10	1.05141	0.525707	+	0.850666i	$0.323801\pi$
$228$	−4.09219e10	−1.00288
$229$	−6.68760e10	−1.60698	−0.803490	−	0.595318i	$-0.797026\pi$
$229$	−6.68760e10	−1.60698	−0.803490	+	0.595318i	$0.797026\pi$
$230$	1.82555e9	0.0430148
$231$	−7.17741e9	−0.165849
$232$	1.06523e11	2.41406
$233$	−5.19268e10	−1.15422	−0.577112	−	0.816665i	$-0.695820\pi$
$233$	−5.19268e10	−1.15422	−0.577112	+	0.816665i	$0.695820\pi$
$234$	−1.89581e10	−0.413355
$235$	−6.91668e8	−0.0147942
$236$	−1.44333e11	−3.02874
$237$	−9.60345e9	−0.197724
$238$	2.48157e10	0.501338
$239$	7.45881e10	1.47870	0.739348	−	0.673323i	$-0.235134\pi$
$239$	7.45881e10	1.47870	0.739348	+	0.673323i	$0.235134\pi$
$240$	−7.71525e8	−0.0150107
$241$	5.74852e10	1.09769	0.548845	−	0.835924i	$-0.315068\pi$
$241$	5.74852e10	1.09769	0.548845	+	0.835924i	$0.315068\pi$
$242$	−6.57499e10	−1.23233
$243$	4.72577e10	0.869449
$244$	8.18528e10	1.47836
$245$	5.46784e8	0.00969545
$246$	2.73328e10	0.475857
$247$	−2.58365e10	−0.441670
$248$	1.09417e11	1.83676
$249$	3.03826e9	0.0500873
$250$	1.63146e10	0.264147
$251$	−1.07873e11	−1.71546	−0.857732	−	0.514097i	$-0.828127\pi$
$251$	−1.07873e11	−1.71546	−0.857732	+	0.514097i	$0.828127\pi$
$252$	−9.77240e10	−1.52651
$253$	1.09833e10	0.168536
$254$	7.17272e10	1.08126
$255$	−5.74492e8	−0.00850850
$256$	−1.18186e11	−1.71984
$257$	−6.64074e10	−0.949550	−0.474775	−	0.880107i	$-0.657470\pi$
$257$	−6.64074e10	−0.949550	−0.474775	+	0.880107i	$0.657470\pi$
$258$	7.34247e10	1.03170
$259$	2.46436e10	0.340295
$260$	−2.96197e9	−0.0401977
$261$	−1.12133e11	−1.49573
$262$	1.32080e11	1.73174
$263$	−8.15356e10	−1.05086	−0.525432	−	0.850836i	$-0.676096\pi$
$263$	−8.15356e10	−1.05086	−0.525432	+	0.850836i	$0.676096\pi$
$264$	−1.99371e10	−0.252607
$265$	−1.68058e9	−0.0209340
$266$	−2.05351e11	−2.51494
$267$	1.66174e9	0.0200107
$268$	−9.54605e10	−1.13036
$269$	1.00568e11	1.17105	0.585523	−	0.810656i	$-0.300889\pi$
$269$	1.00568e11	1.17105	0.585523	+	0.810656i	$0.300889\pi$
$270$	7.43640e9	0.0851580
$271$	−2.98757e10	−0.336477	−0.168239	−	0.985746i	$-0.553808\pi$
$271$	−2.98757e10	−0.336477	−0.168239	+	0.985746i	$0.553808\pi$
$272$	1.60491e10	0.177783
$273$	8.13286e9	0.0886158
$274$	1.92669e11	2.06507
$275$	4.89261e10	0.515874
$276$	−1.97120e10	−0.204475
$277$	−3.17195e10	−0.323718	−0.161859	−	0.986814i	$-0.551749\pi$
$277$	−3.17195e10	−0.323718	−0.161859	+	0.986814i	$0.551749\pi$
$278$	1.37298e11	1.37868
$279$	−1.15180e11	−1.13804
$280$	−1.07847e10	−0.104857
$281$	9.86953e10	0.944318	0.472159	−	0.881513i	$-0.343475\pi$
$281$	9.86953e10	0.944318	0.472159	+	0.881513i	$0.343475\pi$
$282$	1.15157e10	0.108435
$283$	−1.06164e11	−0.983871	−0.491935	−	0.870632i	$-0.663710\pi$
$283$	−1.06164e11	−0.983871	−0.491935	+	0.870632i	$0.663710\pi$
$284$	3.90331e11	3.56042
$285$	4.75393e9	0.0426826
$286$	−2.74774e10	−0.242845
$287$	8.89549e10	0.773929
$288$	4.96501e10	0.425260
$289$	−1.06637e11	−0.899227
$290$	−2.70132e10	−0.224277
$291$	−6.00410e10	−0.490828
$292$	−2.97106e11	−2.39160
$293$	2.26355e11	1.79426	0.897132	−	0.441763i	$-0.145647\pi$
$293$	2.26355e11	1.79426	0.897132	+	0.441763i	$0.145647\pi$
$294$	−9.10348e9	−0.0710631
$295$	1.67673e10	0.128903
$296$	6.84541e10	0.518307
$297$	4.47407e10	0.333656
$298$	4.86881e10	0.357643
$299$	−1.24454e10	−0.0900511
$300$	−8.78087e10	−0.625881
$301$	2.38962e11	1.67795
$302$	1.66137e11	1.14930
$303$	−4.33998e10	−0.295798
$304$	−1.32806e11	−0.891841
$305$	−9.50892e9	−0.0629190
$306$	−7.25625e10	−0.473114
$307$	−2.23009e10	−0.143285	−0.0716424	−	0.997430i	$-0.522824\pi$
$307$	−2.23009e10	−0.143285	−0.0716424	+	0.997430i	$0.522824\pi$
$308$	−1.41639e11	−0.896820
$309$	−1.99659e10	−0.124588
$310$	−2.77471e10	−0.170643
$311$	−2.71805e11	−1.64754	−0.823770	−	0.566925i	$-0.808133\pi$
$311$	−2.71805e11	−1.64754	−0.823770	+	0.566925i	$0.808133\pi$
$312$	2.25911e10	0.134972
$313$	−7.90775e10	−0.465697	−0.232849	−	0.972513i	$-0.574805\pi$
$313$	−7.90775e10	−0.465697	−0.232849	+	0.972513i	$0.574805\pi$
$314$	−5.38183e11	−3.12425
$315$	1.13527e10	0.0649683
$316$	−1.89515e11	−1.06918
$317$	2.03032e11	1.12927	0.564636	−	0.825340i	$-0.309017\pi$
$317$	2.03032e11	1.12927	0.564636	+	0.825340i	$0.309017\pi$
$318$	2.79802e10	0.153437
$319$	−1.62524e11	−0.878736
$320$	2.02114e10	0.107751
$321$	3.21568e10	0.169044
$322$	−9.89171e10	−0.512767
$323$	−9.88899e10	−0.505523
$324$	2.43120e11	1.22565
$325$	−5.54391e10	−0.275639
$326$	2.76650e10	0.135660
$327$	7.98365e10	0.386132
$328$	2.47095e11	1.17878
$329$	3.74779e10	0.176357
$330$	5.05586e9	0.0234683
$331$	3.24137e11	1.48424	0.742118	−	0.670270i	$-0.233822\pi$
$331$	3.24137e11	1.48424	0.742118	+	0.670270i	$0.233822\pi$
$332$	5.99570e10	0.270844
$333$	−7.20594e10	−0.321138
$334$	−3.17955e10	−0.139800
$335$	1.10897e10	0.0481083
$336$	4.18050e10	0.178937
$337$	2.68510e11	1.13403	0.567017	−	0.823706i	$-0.308097\pi$
$337$	2.68510e11	1.13403	0.567017	+	0.823706i	$0.308097\pi$
$338$	3.11352e10	0.129756
$339$	−8.83739e10	−0.363434
$340$	−1.13370e10	−0.0460091
$341$	−1.66939e11	−0.668595
$342$	6.00457e11	2.37336
$343$	−2.69628e11	−1.05182
$344$	6.63778e11	2.55570
$345$	2.28996e9	0.00870247
$346$	2.20597e10	0.0827478
$347$	2.74715e11	1.01719	0.508593	−	0.861007i	$-0.330166\pi$
$347$	2.74715e11	1.01719	0.508593	+	0.861007i	$0.330166\pi$
$348$	2.91684e11	1.06612
$349$	−3.54006e11	−1.27731	−0.638655	−	0.769494i	$-0.720509\pi$
$349$	−3.54006e11	−1.27731	−0.638655	+	0.769494i	$0.720509\pi$
$350$	−4.40634e11	−1.56954
$351$	−5.06966e10	−0.178277
$352$	7.19619e10	0.249839
$353$	−2.25650e11	−0.773481	−0.386741	−	0.922189i	$-0.626399\pi$
$353$	−2.25650e11	−0.773481	−0.386741	+	0.922189i	$0.626399\pi$
$354$	−2.79161e11	−0.944801
$355$	−4.53451e10	−0.151532
$356$	3.27927e10	0.108206
$357$	3.11287e10	0.101427
$358$	−5.97602e11	−1.92282
$359$	3.39022e10	0.107722	0.0538608	−	0.998548i	$-0.482847\pi$
$359$	3.39022e10	0.107722	0.0538608	+	0.998548i	$0.482847\pi$
$360$	3.15351e10	0.0989538
$361$	4.95629e11	1.53594
$362$	−8.34178e11	−2.55312
$363$	−8.24764e10	−0.249316
$364$	1.60494e11	0.479184
$365$	3.45150e10	0.101787
$366$	1.58315e11	0.461167
$367$	−7.74387e10	−0.222823	−0.111412	−	0.993774i	$-0.535537\pi$
$367$	−7.74387e10	−0.222823	−0.111412	+	0.993774i	$0.535537\pi$
$368$	−6.39726e10	−0.181836
$369$	−2.60109e11	−0.730360
$370$	−1.73593e10	−0.0481531
$371$	9.10620e10	0.249548
$372$	2.99609e11	0.811169
$373$	6.50821e11	1.74089	0.870446	−	0.492264i	$-0.163831\pi$
$373$	6.50821e11	1.74089	0.870446	+	0.492264i	$0.163831\pi$
$374$	−1.05171e11	−0.277954
$375$	2.04649e10	0.0534404
$376$	1.04105e11	0.268612
$377$	1.84159e11	0.469522
$378$	−4.02940e11	−1.01514
$379$	1.93989e11	0.482948	0.241474	−	0.970407i	$-0.422369\pi$
$379$	1.93989e11	0.482948	0.241474	+	0.970407i	$0.422369\pi$
$380$	9.38141e10	0.230803
$381$	8.99743e10	0.218754
$382$	6.40406e11	1.53876
$383$	4.44645e11	1.05589	0.527946	−	0.849278i	$-0.322963\pi$
$383$	4.44645e11	1.05589	0.527946	+	0.849278i	$0.322963\pi$
$384$	−2.66515e11	−0.625506
$385$	1.64544e10	0.0381687
$386$	−1.03069e12	−2.36311
$387$	−6.98737e11	−1.58349
$388$	−1.18485e12	−2.65412
$389$	−1.69623e11	−0.375589	−0.187794	−	0.982208i	$-0.560134\pi$
$389$	−1.69623e11	−0.375589	−0.187794	+	0.982208i	$0.560134\pi$
$390$	−5.72889e9	−0.0125395
$391$	−4.76352e10	−0.103070
$392$	−8.22978e10	−0.176036
$393$	1.65681e11	0.350353
$394$	6.04119e11	1.26296
$395$	2.20161e10	0.0455044
$396$	4.14161e11	0.846332
$397$	2.94468e11	0.594951	0.297476	−	0.954729i	$-0.403855\pi$
$397$	2.94468e11	0.594951	0.297476	+	0.954729i	$0.403855\pi$
$398$	3.36034e11	0.671289
$399$	−2.57591e11	−0.508806
$400$	−2.84971e11	−0.556584
$401$	4.43362e11	0.856265	0.428133	−	0.903716i	$-0.359172\pi$
$401$	4.43362e11	0.856265	0.428133	+	0.903716i	$0.359172\pi$
$402$	−1.84635e11	−0.352611
$403$	1.89162e11	0.357240
$404$	−8.56452e11	−1.59951
$405$	−2.82434e10	−0.0521639
$406$	1.46371e12	2.67354
$407$	−1.04441e11	−0.188668
$408$	8.64682e10	0.154485
$409$	−1.01253e11	−0.178918	−0.0894592	−	0.995990i	$-0.528514\pi$
$409$	−1.01253e11	−0.178918	−0.0894592	+	0.995990i	$0.528514\pi$
$410$	−6.26610e10	−0.109514
$411$	2.41684e11	0.417791
$412$	−3.94007e11	−0.673700
$413$	−9.08533e11	−1.53662
$414$	2.89239e11	0.483900
$415$	−6.96526e9	−0.0115271
$416$	−8.15413e10	−0.133493
$417$	1.72226e11	0.278925
$418$	8.70289e11	1.39435
$419$	7.93982e10	0.125848	0.0629242	−	0.998018i	$-0.479957\pi$
$419$	7.93982e10	0.125848	0.0629242	+	0.998018i	$0.479957\pi$
$420$	−2.95310e10	−0.0463080
$421$	−6.06765e11	−0.941350	−0.470675	−	0.882307i	$-0.655990\pi$
$421$	−6.06765e11	−0.941350	−0.470675	+	0.882307i	$0.655990\pi$
$422$	−6.94871e11	−1.06659
$423$	−1.09587e11	−0.166429
$424$	2.52949e11	0.380089
$425$	−2.12195e11	−0.315489
$426$	7.54958e11	1.11066
$427$	5.15239e11	0.750038
$428$	6.34583e11	0.914096
$429$	−3.44676e10	−0.0491307
$430$	−1.68328e11	−0.237436
$431$	−2.72544e11	−0.380442	−0.190221	−	0.981741i	$-0.560920\pi$
$431$	−2.72544e11	−0.380442	−0.190221	+	0.981741i	$0.560920\pi$
$432$	−2.60593e11	−0.359987
$433$	−1.15522e12	−1.57931	−0.789655	−	0.613551i	$-0.789740\pi$
$433$	−1.15522e12	−1.57931	−0.789655	+	0.613551i	$0.789740\pi$
$434$	1.50347e12	2.03419
$435$	−3.38853e10	−0.0453742
$436$	1.57549e12	2.08799
$437$	3.94182e11	0.517047
$438$	−5.74646e11	−0.746048
$439$	1.78053e11	0.228801	0.114401	−	0.993435i	$-0.463505\pi$
$439$	1.78053e11	0.228801	0.114401	+	0.993435i	$0.463505\pi$
$440$	4.57063e10	0.0581351
$441$	8.66321e10	0.109070
$442$	1.19171e11	0.148515
$443$	−6.55260e10	−0.0808345	−0.0404173	−	0.999183i	$-0.512869\pi$
$443$	−6.55260e10	−0.0808345	−0.0404173	+	0.999183i	$0.512869\pi$
$444$	1.87443e11	0.228900
$445$	−3.80956e9	−0.00460527
$446$	5.85928e11	0.701192
$447$	6.10742e10	0.0723559
$448$	−1.09515e12	−1.28446
$449$	−7.98150e11	−0.926779	−0.463390	−	0.886155i	$-0.653367\pi$
$449$	−7.98150e11	−0.926779	−0.463390	+	0.886155i	$0.653367\pi$
$450$	1.28844e12	1.48118
$451$	−3.76997e11	−0.429085
$452$	−1.74397e12	−1.96525
$453$	2.08402e11	0.232519
$454$	1.60544e12	1.77355
$455$	−1.86447e10	−0.0203941
$456$	−7.15526e11	−0.774968
$457$	−8.92736e11	−0.957415	−0.478708	−	0.877974i	$-0.658895\pi$
$457$	−8.92736e11	−0.957415	−0.478708	+	0.877974i	$0.658895\pi$
$458$	−2.55256e12	−2.71069
$459$	−1.94042e11	−0.204051
$460$	4.51901e10	0.0470580
$461$	2.32490e11	0.239745	0.119872	−	0.992789i	$-0.461751\pi$
$461$	2.32490e11	0.239745	0.119872	+	0.992789i	$0.461751\pi$
$462$	−2.73951e11	−0.279759
$463$	−1.54421e12	−1.56168	−0.780841	−	0.624730i	$-0.785209\pi$
$463$	−1.54421e12	−1.56168	−0.780841	+	0.624730i	$0.785209\pi$
$464$	9.46622e11	0.948082
$465$	−3.48058e10	−0.0345234
$466$	−1.98197e12	−1.94697
$467$	1.63317e12	1.58893	0.794465	−	0.607310i	$-0.207751\pi$
$467$	1.63317e12	1.58893	0.794465	+	0.607310i	$0.207751\pi$
$468$	−4.69293e11	−0.452208
$469$	−6.00895e11	−0.573484
$470$	−2.63999e10	−0.0249553
$471$	−6.75094e11	−0.632077
$472$	−2.52369e12	−2.34044
$473$	−1.01274e12	−0.930295
$474$	−3.66549e11	−0.333526
$475$	1.75592e12	1.58264
$476$	6.14295e11	0.548461
$477$	−2.66271e11	−0.235500
$478$	2.84692e12	2.49430
$479$	1.54414e12	1.34022	0.670112	−	0.742260i	$-0.266246\pi$
$479$	1.54414e12	1.34022	0.670112	+	0.742260i	$0.266246\pi$
$480$	1.50036e10	0.0129006
$481$	1.18344e11	0.100808
$482$	2.19412e12	1.85161
$483$	−1.24081e11	−0.103739
$484$	−1.62759e12	−1.34816
$485$	1.37645e11	0.112960
$486$	1.80375e12	1.46661
$487$	2.55439e11	0.205782	0.102891	−	0.994693i	$-0.467191\pi$
$487$	2.55439e11	0.205782	0.102891	+	0.994693i	$0.467191\pi$
$488$	1.43121e12	1.14239
$489$	3.47028e10	0.0274457
$490$	2.08699e10	0.0163545
$491$	1.58407e12	1.23000	0.615002	−	0.788526i	$-0.289155\pi$
$491$	1.58407e12	1.23000	0.615002	+	0.788526i	$0.289155\pi$
$492$	6.76603e11	0.520584
$493$	7.04872e11	0.537402
$494$	−9.86141e11	−0.745020
$495$	−4.81135e10	−0.0360200
$496$	9.72340e11	0.721357
$497$	2.45702e12	1.80636
$498$	1.15966e11	0.0844884
$499$	−6.29948e11	−0.454833	−0.227417	−	0.973798i	$-0.573028\pi$
$499$	−6.29948e11	−0.454833	−0.227417	+	0.973798i	$0.573028\pi$
$500$	4.03856e11	0.288976
$501$	−3.98842e10	−0.0282834
$502$	−4.11736e12	−2.89369
$503$	5.49263e11	0.382582	0.191291	−	0.981533i	$-0.438733\pi$
$503$	5.49263e11	0.382582	0.191291	+	0.981533i	$0.438733\pi$
$504$	−1.70872e12	−1.17960
$505$	9.94949e10	0.0680753
$506$	4.19217e11	0.284290
$507$	3.90559e10	0.0262513
$508$	1.77555e12	1.18290
$509$	1.36923e11	0.0904165	0.0452083	−	0.998978i	$-0.485605\pi$
$509$	1.36923e11	0.0904165	0.0452083	+	0.998978i	$0.485605\pi$
$510$	−2.19275e10	−0.0143523
$511$	−1.87019e12	−1.21337
$512$	−1.66095e12	−1.06817
$513$	1.60570e12	1.02362
$514$	−2.53467e12	−1.60172
$515$	4.57722e10	0.0286727
$516$	1.81758e12	1.12867
$517$	−1.58834e11	−0.0977767
$518$	9.40610e11	0.574018
$519$	2.76715e10	0.0167410
$520$	−5.17906e10	−0.0310625
$521$	−1.66627e12	−0.990779	−0.495389	−	0.868671i	$-0.664975\pi$
$521$	−1.66627e12	−0.990779	−0.495389	+	0.868671i	$0.664975\pi$
$522$	−4.27996e12	−2.52303
$523$	1.97187e12	1.15244	0.576222	−	0.817293i	$-0.304526\pi$
$523$	1.97187e12	1.15244	0.576222	+	0.817293i	$0.304526\pi$
$524$	3.26955e12	1.89451
$525$	−5.52730e11	−0.317538
$526$	−3.11209e12	−1.77262
$527$	7.24021e11	0.408887
$528$	−1.77172e11	−0.0992072
$529$	−1.61128e12	−0.894580
$530$	−6.41452e10	−0.0353121
$531$	2.65660e12	1.45011
$532$	−5.08330e12	−2.75134
$533$	4.27182e11	0.229266
$534$	6.34260e10	0.0337545
$535$	−7.37202e10	−0.0389040
$536$	−1.66914e12	−0.873479
$537$	−7.49629e11	−0.389011
$538$	3.83852e12	1.97535
$539$	1.25563e11	0.0640784
$540$	1.84083e11	0.0931624
$541$	1.54916e12	0.777513	0.388756	−	0.921341i	$-0.372905\pi$
$541$	1.54916e12	0.777513	0.388756	+	0.921341i	$0.372905\pi$
$542$	−1.14031e12	−0.567578
$543$	−1.04639e12	−0.516529
$544$	−3.12101e11	−0.152792
$545$	−1.83027e11	−0.0888648
$546$	3.10419e11	0.149479
$547$	1.98052e12	0.945879	0.472939	−	0.881095i	$-0.343193\pi$
$547$	1.98052e12	0.945879	0.472939	+	0.881095i	$0.343193\pi$
$548$	4.76939e12	2.25918
$549$	−1.50659e12	−0.707814
$550$	1.86744e12	0.870189
$551$	−5.83283e12	−2.69586
$552$	−3.44668e11	−0.158007
$553$	−1.19294e12	−0.542444
$554$	−1.21068e12	−0.546056
$555$	−2.17754e10	−0.00974200
$556$	3.39871e12	1.50827
$557$	8.86577e11	0.390273	0.195136	−	0.980776i	$-0.437485\pi$
$557$	8.86577e11	0.390273	0.195136	+	0.980776i	$0.437485\pi$
$558$	−4.39623e12	−1.91967
$559$	1.14755e12	0.497071
$560$	−9.58387e10	−0.0411808
$561$	−1.31926e11	−0.0562336
$562$	3.76705e12	1.59290
$563$	3.89786e12	1.63508	0.817539	−	0.575873i	$-0.195338\pi$
$563$	3.89786e12	1.63508	0.817539	+	0.575873i	$0.195338\pi$
$564$	2.85062e11	0.118627
$565$	2.02599e11	0.0836410
$566$	−4.05212e12	−1.65962
$567$	1.53037e12	0.621830
$568$	6.82501e12	2.75129
$569$	−2.26590e12	−0.906223	−0.453112	−	0.891454i	$-0.649686\pi$
$569$	−2.26590e12	−0.906223	−0.453112	+	0.891454i	$0.649686\pi$
$570$	1.81450e11	0.0719981
$571$	−3.09546e12	−1.21860	−0.609302	−	0.792938i	$-0.708550\pi$
$571$	−3.09546e12	−1.21860	−0.609302	+	0.792938i	$0.708550\pi$
$572$	−6.80184e11	−0.265671
$573$	8.03323e11	0.311311
$574$	3.39527e12	1.30548
$575$	8.45822e11	0.322681
$576$	3.20228e12	1.21215
$577$	−3.23415e12	−1.21470	−0.607350	−	0.794434i	$-0.707767\pi$
$577$	−3.23415e12	−1.21470	−0.607350	+	0.794434i	$0.707767\pi$
$578$	−4.07019e12	−1.51684
$579$	−1.29289e12	−0.478089
$580$	−6.68692e11	−0.245358
$581$	3.77411e11	0.137411
$582$	−2.29167e12	−0.827941
$583$	−3.85927e11	−0.138356
$584$	−5.19495e12	−1.84809
$585$	5.45183e10	0.0192460
$586$	8.63964e12	3.02661
$587$	−8.78491e11	−0.305398	−0.152699	−	0.988273i	$-0.548796\pi$
$587$	−8.78491e11	−0.305398	−0.152699	+	0.988273i	$0.548796\pi$
$588$	−2.25350e11	−0.0777427
$589$	−5.99129e12	−2.05117
$590$	6.39983e11	0.217437
$591$	7.57805e11	0.255513
$592$	6.08321e11	0.203556
$593$	−1.91730e12	−0.636712	−0.318356	−	0.947971i	$-0.603131\pi$
$593$	−1.91730e12	−0.636712	−0.318356	+	0.947971i	$0.603131\pi$
$594$	1.70769e12	0.562819
$595$	−7.13632e10	−0.0233425
$596$	1.20524e12	0.391260
$597$	4.21520e11	0.135811
$598$	−4.75023e11	−0.151900
$599$	−5.10464e12	−1.62011	−0.810054	−	0.586355i	$-0.800562\pi$
$599$	−5.10464e12	−1.62011	−0.810054	+	0.586355i	$0.800562\pi$
$600$	−1.53535e12	−0.483645
$601$	3.00419e12	0.939273	0.469636	−	0.882860i	$-0.344385\pi$
$601$	3.00419e12	0.939273	0.469636	+	0.882860i	$0.344385\pi$
$602$	9.12080e12	2.83041
$603$	1.75705e12	0.541199
$604$	4.11260e12	1.25733
$605$	1.89079e11	0.0573778
$606$	−1.65650e12	−0.498960
$607$	1.18434e12	0.354101	0.177051	−	0.984202i	$-0.443344\pi$
$607$	1.18434e12	0.354101	0.177051	+	0.984202i	$0.443344\pi$
$608$	2.58265e12	0.766477
$609$	1.83607e12	0.540892
$610$	−3.62941e11	−0.106133
$611$	1.79978e11	0.0522436
$612$	−1.79623e12	−0.517584
$613$	6.42597e11	0.183809	0.0919045	−	0.995768i	$-0.470705\pi$
$613$	6.42597e11	0.183809	0.0919045	+	0.995768i	$0.470705\pi$
$614$	−8.51193e11	−0.241696
$615$	−7.86017e10	−0.0221561
$616$	−2.47659e12	−0.693011
$617$	5.05474e12	1.40416	0.702078	−	0.712100i	$-0.252256\pi$
$617$	5.05474e12	1.40416	0.702078	+	0.712100i	$0.252256\pi$
$618$	−7.62068e11	−0.210158
$619$	−3.09492e11	−0.0847308	−0.0423654	−	0.999102i	$-0.513489\pi$
$619$	−3.09492e11	−0.0847308	−0.0423654	+	0.999102i	$0.513489\pi$
$620$	−6.86859e11	−0.186683
$621$	7.73466e11	0.208703
$622$	−1.03744e13	−2.77911
$623$	2.06421e11	0.0548980
$624$	2.00757e11	0.0530079
$625$	3.74425e12	0.981533
$626$	−3.01827e12	−0.785549
$627$	1.09169e12	0.282094
$628$	−1.33223e13	−3.41792
$629$	4.52966e11	0.115382
$630$	4.33315e11	0.109590
$631$	−7.94237e11	−0.199443	−0.0997214	−	0.995015i	$-0.531795\pi$
$631$	−7.94237e11	−0.199443	−0.0997214	+	0.995015i	$0.531795\pi$
$632$	−3.31370e12	−0.826202
$633$	−8.71644e11	−0.215786
$634$	7.74944e12	1.90488
$635$	−2.06268e11	−0.0503442
$636$	6.92631e11	0.167859
$637$	−1.42278e11	−0.0342380
$638$	−6.20328e12	−1.48227
$639$	−7.18446e12	−1.70467
$640$	6.10991e11	0.143954
$641$	2.30298e12	0.538802	0.269401	−	0.963028i	$-0.413174\pi$
$641$	2.30298e12	0.538802	0.269401	+	0.963028i	$0.413174\pi$
$642$	1.22738e12	0.285148
$643$	−2.54593e12	−0.587350	−0.293675	−	0.955905i	$-0.594878\pi$
$643$	−2.54593e12	−0.587350	−0.293675	+	0.955905i	$0.594878\pi$
$644$	−2.44862e12	−0.560964
$645$	−2.11149e11	−0.0480365
$646$	−3.77448e12	−0.852728
$647$	−2.74568e11	−0.0616001	−0.0308000	−	0.999526i	$-0.509806\pi$
$647$	−2.74568e11	−0.0616001	−0.0308000	+	0.999526i	$0.509806\pi$
$648$	4.25099e12	0.947115
$649$	3.85043e12	0.851937
$650$	−2.11603e12	−0.464955
$651$	1.88595e12	0.411543
$652$	6.84826e11	0.148411
$653$	−6.05719e12	−1.30365	−0.651826	−	0.758369i	$-0.725997\pi$
$653$	−6.05719e12	−1.30365	−0.651826	+	0.758369i	$0.725997\pi$
$654$	3.04724e12	0.651338
$655$	−3.79827e11	−0.0806306
$656$	2.19582e12	0.462946
$657$	5.46855e12	1.14506
$658$	1.43047e12	0.297484
$659$	4.97718e12	1.02801	0.514007	−	0.857786i	$-0.328160\pi$
$659$	4.97718e12	1.02801	0.514007	+	0.857786i	$0.328160\pi$
$660$	1.25154e11	0.0256742
$661$	1.79834e12	0.366409	0.183204	−	0.983075i	$-0.441353\pi$
$661$	1.79834e12	0.366409	0.183204	+	0.983075i	$0.441353\pi$
$662$	1.23718e13	2.50364
$663$	1.49487e11	0.0300465
$664$	1.04836e12	0.209292
$665$	5.90532e11	0.117097
$666$	−2.75040e12	−0.541703
$667$	−2.80967e12	−0.549653
$668$	−7.87076e11	−0.152940
$669$	7.34986e11	0.141860
$670$	4.23278e11	0.0811502
$671$	−2.18362e12	−0.415839
$672$	−8.12969e11	−0.153784
$673$	1.37693e12	0.258728	0.129364	−	0.991597i	$-0.458706\pi$
$673$	1.37693e12	0.258728	0.129364	+	0.991597i	$0.458706\pi$
$674$	1.02486e13	1.91292
$675$	3.44547e12	0.638824
$676$	7.70729e11	0.141952
$677$	6.49642e11	0.118857	0.0594285	−	0.998233i	$-0.481072\pi$
$677$	6.49642e11	0.118857	0.0594285	+	0.998233i	$0.481072\pi$
$678$	−3.37310e12	−0.613049
$679$	−7.45828e12	−1.34656
$680$	−1.98230e11	−0.0355532
$681$	2.01386e12	0.358813
$682$	−6.37181e12	−1.12780
$683$	−1.10011e12	−0.193438	−0.0967190	−	0.995312i	$-0.530835\pi$
$683$	−1.10011e12	−0.193438	−0.0967190	+	0.995312i	$0.530835\pi$
$684$	1.48639e13	2.59645
$685$	−5.54064e11	−0.0961507
$686$	−1.02913e13	−1.77424
$687$	−3.20192e12	−0.548409
$688$	5.89869e12	1.00371
$689$	4.37301e11	0.0739254
$690$	8.74044e10	0.0146795
$691$	7.72289e12	1.28863	0.644315	−	0.764760i	$-0.277142\pi$
$691$	7.72289e12	1.28863	0.644315	+	0.764760i	$0.277142\pi$
$692$	5.46071e11	0.0905256
$693$	2.60702e12	0.429383
$694$	1.04855e13	1.71581
$695$	−3.94832e11	−0.0641920
$696$	5.10016e12	0.823838
$697$	1.63505e12	0.262412
$698$	−1.35119e13	−2.15460
$699$	−2.48617e12	−0.393898
$700$	−1.09076e13	−1.71707
$701$	1.40436e12	0.219658	0.109829	−	0.993950i	$-0.464970\pi$
$701$	1.40436e12	0.219658	0.109829	+	0.993950i	$0.464970\pi$
$702$	−1.93501e12	−0.300723
$703$	−3.74831e12	−0.578810
$704$	4.64131e12	0.712137
$705$	−3.31159e10	−0.00504877
$706$	−8.61273e12	−1.30473
$707$	−5.39111e12	−0.811505
$708$	−6.91043e12	−1.03361
$709$	5.19764e12	0.772499	0.386250	−	0.922394i	$-0.373770\pi$
$709$	5.19764e12	0.772499	0.386250	+	0.922394i	$0.373770\pi$
$710$	−1.73075e12	−0.255607
$711$	3.48822e12	0.511907
$712$	5.73387e11	0.0836157
$713$	−2.88600e12	−0.418209
$714$	1.18814e12	0.171090
$715$	7.90176e10	0.0113070
$716$	−1.47932e13	−2.10355
$717$	3.57116e12	0.504630
$718$	1.29400e12	0.181707
$719$	−1.27042e13	−1.77284	−0.886418	−	0.462886i	$-0.846814\pi$
$719$	−1.27042e13	−1.77284	−0.886418	+	0.462886i	$0.846814\pi$
$720$	2.80238e11	0.0388625
$721$	−2.48016e12	−0.341799
$722$	1.89174e13	2.59086
$723$	2.75230e12	0.374605
$724$	−2.06495e13	−2.79309
$725$	−1.25159e13	−1.68244
$726$	−3.14800e12	−0.420552
$727$	9.91998e11	0.131706	0.0658531	−	0.997829i	$-0.479023\pi$
$727$	9.91998e11	0.131706	0.0658531	+	0.997829i	$0.479023\pi$
$728$	2.80627e12	0.370286
$729$	−2.80211e12	−0.367461
$730$	1.31739e12	0.171696
$731$	4.39227e12	0.568933
$732$	3.91898e12	0.504514
$733$	5.54849e12	0.709916	0.354958	−	0.934882i	$-0.384495\pi$
$733$	5.54849e12	0.709916	0.354958	+	0.934882i	$0.384495\pi$
$734$	−2.95572e12	−0.375864
$735$	2.61791e10	0.00330873
$736$	1.24406e12	0.156275
$737$	2.54663e12	0.317953
$738$	−9.92797e12	−1.23199
$739$	8.78597e12	1.08365	0.541826	−	0.840491i	$-0.317733\pi$
$739$	8.78597e12	1.08365	0.541826	+	0.840491i	$0.317733\pi$
$740$	−4.29717e11	−0.0526792
$741$	−1.23701e12	−0.150727
$742$	3.47570e12	0.420944
$743$	4.04326e12	0.486724	0.243362	−	0.969936i	$-0.421750\pi$
$743$	4.04326e12	0.486724	0.243362	+	0.969936i	$0.421750\pi$
$744$	5.23871e12	0.626825
$745$	−1.40014e11	−0.0166521
$746$	2.48408e13	2.93658
$747$	−1.10357e12	−0.129676
$748$	−2.60342e12	−0.304080
$749$	3.99451e12	0.463763
$750$	7.81116e11	0.0901446
$751$	−2.52936e11	−0.0290156	−0.0145078	−	0.999895i	$-0.504618\pi$
$751$	−2.52936e11	−0.0290156	−0.0145078	+	0.999895i	$0.504618\pi$
$752$	9.25130e11	0.105493
$753$	−5.16479e12	−0.585431
$754$	7.02906e12	0.792001
$755$	−4.77765e11	−0.0535122
$756$	−9.97448e12	−1.11056
$757$	9.99638e12	1.10640	0.553199	−	0.833049i	$-0.313407\pi$
$757$	9.99638e12	1.10640	0.553199	+	0.833049i	$0.313407\pi$
$758$	7.40426e12	0.814649
$759$	5.25864e11	0.0575156
$760$	1.64036e12	0.178352
$761$	−2.98848e12	−0.323013	−0.161507	−	0.986872i	$-0.551635\pi$
$761$	−2.98848e12	−0.323013	−0.161507	+	0.986872i	$0.551635\pi$
$762$	3.43418e12	0.369000
$763$	9.91726e12	1.05933
$764$	1.58528e13	1.68339
$765$	2.08670e11	0.0220284
$766$	1.69714e13	1.78110
$767$	−4.36299e12	−0.455203
$768$	−5.65858e12	−0.586924
$769$	1.54887e13	1.59715	0.798576	−	0.601894i	$-0.205587\pi$
$769$	1.54887e13	1.59715	0.798576	+	0.601894i	$0.205587\pi$
$770$	6.28038e11	0.0643839
$771$	−3.17948e12	−0.324050
$772$	−2.55139e13	−2.58523
$773$	1.07589e13	1.08383	0.541915	−	0.840434i	$-0.317700\pi$
$773$	1.07589e13	1.08383	0.541915	+	0.840434i	$0.317700\pi$
$774$	−2.66697e13	−2.67106
$775$	−1.28559e13	−1.28010
$776$	−2.07173e13	−2.05095
$777$	1.17990e12	0.116131
$778$	−6.47427e12	−0.633552
$779$	−1.35301e13	−1.31638
$780$	−1.41814e11	−0.0137181
$781$	−1.04130e13	−1.00149
$782$	−1.81816e12	−0.173861
$783$	−1.14452e13	−1.08817
$784$	−7.31343e11	−0.0691351
$785$	1.54767e12	0.145467
$786$	6.32379e12	0.590985
$787$	1.29304e13	1.20151	0.600755	−	0.799433i	$-0.294867\pi$
$787$	1.29304e13	1.20151	0.600755	+	0.799433i	$0.294867\pi$
$788$	1.49545e13	1.38167
$789$	−3.90379e12	−0.358625
$790$	8.40321e11	0.0767579
$791$	−1.09778e13	−0.997059
$792$	7.24168e12	0.653997
$793$	2.47430e12	0.222189
$794$	1.12394e13	1.00358
$795$	−8.04635e10	−0.00714409
$796$	8.31828e12	0.734387
$797$	1.24713e13	1.09484	0.547418	−	0.836859i	$-0.315611\pi$
$797$	1.24713e13	1.09484	0.547418	+	0.836859i	$0.315611\pi$
$798$	−9.83185e12	−0.858267
$799$	6.88868e11	0.0597965
$800$	5.54175e12	0.478346
$801$	−6.03585e11	−0.0518075
$802$	1.69224e13	1.44437
$803$	7.92600e12	0.672719
$804$	−4.57049e12	−0.385755
$805$	2.84459e11	0.0238747
$806$	7.22002e12	0.602602
$807$	4.81502e12	0.399639
$808$	−1.49752e13	−1.23601
$809$	−2.40763e13	−1.97616	−0.988079	−	0.153948i	$-0.950801\pi$
$809$	−2.40763e13	−1.97616	−0.988079	+	0.153948i	$0.950801\pi$
$810$	−1.07801e12	−0.0879913
$811$	1.14686e13	0.930928	0.465464	−	0.885067i	$-0.345888\pi$
$811$	1.14686e13	0.930928	0.465464	+	0.885067i	$0.345888\pi$
$812$	3.62330e13	2.92484
$813$	−1.43040e12	−0.114829
$814$	−3.98637e12	−0.318249
$815$	−7.95569e10	−0.00631638
$816$	7.68403e11	0.0606713
$817$	−3.63462e13	−2.85403
$818$	−3.86469e12	−0.301804
$819$	−2.95406e12	−0.229426
$820$	−1.55113e12	−0.119808
$821$	−2.50113e13	−1.92129	−0.960643	−	0.277786i	$-0.910399\pi$
$821$	−2.50113e13	−1.92129	−0.960643	+	0.277786i	$0.910399\pi$
$822$	9.22470e12	0.704740
$823$	1.29351e13	0.982808	0.491404	−	0.870932i	$-0.336484\pi$
$823$	1.29351e13	0.982808	0.491404	+	0.870932i	$0.336484\pi$
$824$	−6.88929e12	−0.520597
$825$	2.34250e12	0.176051
$826$	−3.46773e13	−2.59200
$827$	1.00464e13	0.746851	0.373425	−	0.927660i	$-0.378183\pi$
$827$	1.00464e13	0.746851	0.373425	+	0.927660i	$0.378183\pi$
$828$	7.15990e12	0.529384
$829$	8.77304e12	0.645141	0.322570	−	0.946545i	$-0.395453\pi$
$829$	8.77304e12	0.645141	0.322570	+	0.946545i	$0.395453\pi$
$830$	−2.65853e11	−0.0194442
$831$	−1.51868e12	−0.110474
$832$	−5.25916e12	−0.380506
$833$	−5.44571e11	−0.0391879
$834$	6.57361e12	0.470497
$835$	9.14353e10	0.00650916
$836$	2.15434e13	1.52541
$837$	−1.17561e13	−0.827943
$838$	3.03051e12	0.212284
$839$	−1.54259e13	−1.07478	−0.537392	−	0.843332i	$-0.680590\pi$
$839$	−1.54259e13	−1.07478	−0.537392	+	0.843332i	$0.680590\pi$
$840$	−5.16354e11	−0.0357842
$841$	2.70683e13	1.86586
$842$	−2.31593e13	−1.58789
$843$	4.72537e12	0.322264
$844$	−1.72010e13	−1.16685
$845$	−8.95364e10	−0.00604149
$846$	−4.18279e12	−0.280737
$847$	−1.02452e13	−0.683983
$848$	2.24784e12	0.149274
$849$	−5.08296e12	−0.335762
$850$	−8.09914e12	−0.532174
$851$	−1.80556e12	−0.118012
$852$	1.86884e13	1.21505
$853$	−1.84928e12	−0.119600	−0.0598002	−	0.998210i	$-0.519046\pi$
$853$	−1.84928e12	−0.119600	−0.0598002	+	0.998210i	$0.519046\pi$
$854$	1.96659e13	1.26518
$855$	−1.72675e12	−0.110505
$856$	1.10958e13	0.706361
$857$	−2.34715e13	−1.48637	−0.743185	−	0.669086i	$-0.766686\pi$
$857$	−2.34715e13	−1.48637	−0.743185	+	0.669086i	$0.766686\pi$
$858$	−1.31558e12	−0.0828749
$859$	1.25121e12	0.0784079	0.0392039	−	0.999231i	$-0.487518\pi$
$859$	1.25121e12	0.0784079	0.0392039	+	0.999231i	$0.487518\pi$
$860$	−4.16683e12	−0.259754
$861$	4.25902e12	0.264116
$862$	−1.04026e13	−0.641739
$863$	2.38217e13	1.46192	0.730961	−	0.682419i	$-0.239072\pi$
$863$	2.38217e13	1.46192	0.730961	+	0.682419i	$0.239072\pi$
$864$	5.06768e12	0.309384
$865$	−6.34375e10	−0.00385278
$866$	−4.40928e13	−2.66402
$867$	−5.10563e12	−0.306876
$868$	3.72173e13	2.22539
$869$	5.05575e12	0.300744
$870$	−1.29335e12	−0.0765383
$871$	−2.88564e12	−0.169887
$872$	2.75478e13	1.61348
$873$	2.18084e13	1.27075
$874$	1.50453e13	0.872168
$875$	2.54215e12	0.146611
$876$	−1.42249e13	−0.816173
$877$	−1.35717e13	−0.774707	−0.387353	−	0.921931i	$-0.626611\pi$
$877$	−1.35717e13	−0.774707	−0.387353	+	0.921931i	$0.626611\pi$
$878$	6.79601e12	0.385948
$879$	1.08375e13	0.612323
$880$	4.06171e11	0.0228316
$881$	2.38436e12	0.133346	0.0666730	−	0.997775i	$-0.478762\pi$
$881$	2.38436e12	0.133346	0.0666730	+	0.997775i	$0.478762\pi$
$882$	3.30662e12	0.183982
$883$	−5.99779e11	−0.0332023	−0.0166011	−	0.999862i	$-0.505285\pi$
$883$	−5.99779e11	−0.0332023	−0.0166011	+	0.999862i	$0.505285\pi$
$884$	2.94999e12	0.162474
$885$	8.02792e11	0.0439904
$886$	−2.50103e12	−0.136354
$887$	1.02483e13	0.555897	0.277949	−	0.960596i	$-0.410346\pi$
$887$	1.02483e13	0.555897	0.277949	+	0.960596i	$0.410346\pi$
$888$	3.27747e12	0.176881
$889$	1.11766e13	0.600138
$890$	−1.45405e11	−0.00776828
$891$	−6.48579e12	−0.344757
$892$	1.45042e13	0.767101
$893$	−5.70040e12	−0.299967
$894$	2.33111e12	0.122052
$895$	1.71854e12	0.0895274
$896$	−3.31065e13	−1.71604
$897$	−5.95867e11	−0.0307315
$898$	−3.04642e13	−1.56331
$899$	4.27050e13	2.18052
$900$	3.18944e13	1.62040
$901$	1.67378e12	0.0846130
$902$	−1.43894e13	−0.723791
$903$	1.14411e13	0.572628
$904$	−3.04937e13	−1.51863
$905$	2.39887e12	0.118874
$906$	7.95437e12	0.392219
$907$	−2.43855e13	−1.19646	−0.598231	−	0.801323i	$-0.704130\pi$
$907$	−2.43855e13	−1.19646	−0.598231	+	0.801323i	$0.704130\pi$
$908$	3.97416e13	1.94026
$909$	1.57639e13	0.765820
$910$	−7.11641e11	−0.0344013
$911$	2.90386e13	1.39683	0.698415	−	0.715693i	$-0.253889\pi$
$911$	2.90386e13	1.39683	0.698415	+	0.715693i	$0.253889\pi$
$912$	−6.35855e12	−0.304356
$913$	−1.59949e12	−0.0761841
$914$	−3.40744e13	−1.61499
$915$	−4.55272e11	−0.0214722
$916$	−6.31867e13	−2.96549
$917$	2.05809e13	0.961173
$918$	−7.40630e12	−0.344199
$919$	−1.41793e13	−0.655746	−0.327873	−	0.944722i	$-0.606332\pi$
$919$	−1.41793e13	−0.655746	−0.327873	+	0.944722i	$0.606332\pi$
$920$	7.90158e11	0.0363638
$921$	−1.06773e12	−0.0488984
$922$	8.87378e12	0.404408
$923$	1.17992e13	0.535111
$924$	−6.78146e12	−0.306055
$925$	−8.04299e12	−0.361226
$926$	−5.89402e13	−2.63428
$927$	7.25212e12	0.322557
$928$	−1.84087e13	−0.814812
$929$	−3.56246e13	−1.56920	−0.784601	−	0.620001i	$-0.787132\pi$
$929$	−3.56246e13	−1.56920	−0.784601	+	0.620001i	$0.787132\pi$
$930$	−1.32849e12	−0.0582349
$931$	4.50634e12	0.196585
$932$	−4.90621e13	−2.12998
$933$	−1.30136e13	−0.562250
$934$	6.23355e13	2.68025
$935$	3.02442e11	0.0129417
$936$	−8.20568e12	−0.349441
$937$	9.35575e12	0.396506	0.198253	−	0.980151i	$-0.436473\pi$
$937$	9.35575e12	0.396506	0.198253	+	0.980151i	$0.436473\pi$
$938$	−2.29353e13	−0.967366
$939$	−3.78610e12	−0.158927
$940$	−6.53510e11	−0.0273009
$941$	1.23413e13	0.513106	0.256553	−	0.966530i	$-0.417413\pi$
$941$	1.23413e13	0.513106	0.256553	+	0.966530i	$0.417413\pi$
$942$	−2.57673e13	−1.06620
$943$	−6.51742e12	−0.268394
$944$	−2.24269e13	−0.919168
$945$	1.15875e12	0.0472656
$946$	−3.86546e13	−1.56924
$947$	2.93722e12	0.118676	0.0593379	−	0.998238i	$-0.481101\pi$
$947$	2.93722e12	0.118676	0.0593379	+	0.998238i	$0.481101\pi$
$948$	−9.07366e12	−0.364876
$949$	−8.98110e12	−0.359444
$950$	6.70206e13	2.66964
$951$	9.72086e12	0.385383
$952$	1.07411e13	0.423819
$953$	−3.90544e12	−0.153374	−0.0766870	−	0.997055i	$-0.524434\pi$
$953$	−3.90544e12	−0.153374	−0.0766870	+	0.997055i	$0.524434\pi$
$954$	−1.01631e13	−0.397247
$955$	−1.84163e12	−0.0716454
$956$	7.04733e13	2.72875
$957$	−7.78137e12	−0.299883
$958$	5.89375e13	2.26072
$959$	3.00219e13	1.14618
$960$	9.67687e11	0.0367718
$961$	1.74255e13	0.659069
$962$	4.51703e12	0.170045
$963$	−1.16802e13	−0.437655
$964$	5.43139e13	2.02565
$965$	2.96398e12	0.110028
$966$	−4.73599e12	−0.174990
$967$	−1.06697e13	−0.392405	−0.196203	−	0.980563i	$-0.562861\pi$
$967$	−1.06697e13	−0.392405	−0.196203	+	0.980563i	$0.562861\pi$
$968$	−2.84587e13	−1.04178
$969$	−4.73469e12	−0.172518
$970$	5.25371e12	0.190543
$971$	−3.10264e12	−0.112007	−0.0560034	−	0.998431i	$-0.517836\pi$
$971$	−3.10264e12	−0.112007	−0.0560034	+	0.998431i	$0.517836\pi$
$972$	4.46506e13	1.60446
$973$	2.13939e13	0.765213
$974$	9.74972e12	0.347118
$975$	−2.65434e12	−0.0940665
$976$	1.27185e13	0.448655
$977$	−4.66167e13	−1.63688	−0.818438	−	0.574594i	$-0.805160\pi$
$977$	−4.66167e13	−1.63688	−0.818438	+	0.574594i	$0.805160\pi$
$978$	1.32455e12	0.0462961
$979$	−8.74824e11	−0.0304368
$980$	5.16619e11	0.0178918
$981$	−2.89986e13	−0.999694
$982$	6.04614e13	2.07480
$983$	−3.22316e13	−1.10101	−0.550505	−	0.834832i	$-0.685565\pi$
$983$	−3.22316e13	−1.10101	−0.550505	+	0.834832i	$0.685565\pi$
$984$	1.18305e13	0.402278
$985$	−1.73728e12	−0.0588040
$986$	2.69039e13	0.906502
$987$	1.79438e12	0.0601849
$988$	−2.44112e13	−0.815047
$989$	−1.75079e13	−0.581903
$990$	−1.83642e12	−0.0607594
$991$	−2.25008e13	−0.741081	−0.370540	−	0.928816i	$-0.620828\pi$
$991$	−2.25008e13	−0.741081	−0.370540	+	0.928816i	$0.620828\pi$
$992$	−1.89088e13	−0.619957
$993$	1.55192e13	0.506520
$994$	9.37807e13	3.04701
$995$	−9.66342e11	−0.0312556
$996$	2.87064e12	0.0924299
$997$	−3.13756e13	−1.00569	−0.502844	−	0.864377i	$-0.667713\pi$
$997$	−3.13756e13	−1.00569	−0.502844	+	0.864377i	$0.667713\pi$
$998$	−2.40442e13	−0.767224
$999$	−7.35495e12	−0.233633

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.10.a.b.1.5	✓	5
3.2	odd	2		117.10.a.e.1.1		5
4.3	odd	2		208.10.a.h.1.3		5
5.4	even	2		325.10.a.b.1.1		5
13.12	even	2		169.10.a.b.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.10.a.b.1.5	✓	5	1.1	even	1	trivial
117.10.a.e.1.1		5	3.2	odd	2
169.10.a.b.1.1		5	13.12	even	2
208.10.a.h.1.3		5	4.3	odd	2
325.10.a.b.1.1		5	5.4	even	2

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:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	13.a (trivial)

\(f(q)\)	\(=\)	\(q+38.1685 q^{2} +47.8784 q^{3} +944.833 q^{4} -109.762 q^{5} +1827.45 q^{6} +5947.44 q^{7} +16520.6 q^{8} -17390.7 q^{9} -4189.45 q^{10} -25205.7 q^{11} +45237.1 q^{12} +28561.0 q^{13} +227005. q^{14} -5255.24 q^{15} +146811. q^{16} +109318. q^{17} -663775. q^{18} -904609. q^{19} -103707. q^{20} +284754. q^{21} -962062. q^{22} -435749. q^{23} +790979. q^{24} -1.94108e6 q^{25} +1.09013e6 q^{26} -1.77503e6 q^{27} +5.61934e6 q^{28} +6.44791e6 q^{29} -200584. q^{30} +6.62308e6 q^{31} -2.85499e6 q^{32} -1.20681e6 q^{33} +4.17250e6 q^{34} -652804. q^{35} -1.64313e7 q^{36} +4.14357e6 q^{37} -3.45275e7 q^{38} +1.36745e6 q^{39} -1.81333e6 q^{40} +1.49568e7 q^{41} +1.08686e7 q^{42} +4.01789e7 q^{43} -2.38151e7 q^{44} +1.90884e6 q^{45} -1.66319e7 q^{46} +6.30151e6 q^{47} +7.02907e6 q^{48} -4.98153e6 q^{49} -7.40880e7 q^{50} +5.23397e6 q^{51} +2.69854e7 q^{52} +1.53111e7 q^{53} -6.77501e7 q^{54} +2.76663e6 q^{55} +9.82552e7 q^{56} -4.33112e7 q^{57} +2.46107e8 q^{58} -1.52760e8 q^{59} -4.96532e6 q^{60} +8.66321e7 q^{61} +2.52793e8 q^{62} -1.03430e8 q^{63} -1.84138e8 q^{64} -3.13492e6 q^{65} -4.60620e7 q^{66} -1.01034e8 q^{67} +1.03287e8 q^{68} -2.08630e7 q^{69} -2.49165e7 q^{70} +4.13122e8 q^{71} -2.87304e8 q^{72} -3.14453e8 q^{73} +1.58154e8 q^{74} -9.29357e7 q^{75} -8.54704e8 q^{76} -1.49909e8 q^{77} +5.21937e7 q^{78} -2.00580e8 q^{79} -1.61143e7 q^{80} +2.57315e8 q^{81} +5.70879e8 q^{82} +6.34578e7 q^{83} +2.69045e8 q^{84} -1.19990e7 q^{85} +1.53357e9 q^{86} +3.08715e8 q^{87} -4.16412e8 q^{88} +3.47074e7 q^{89} +7.28574e7 q^{90} +1.69865e8 q^{91} -4.11710e8 q^{92} +3.17102e8 q^{93} +2.40519e8 q^{94} +9.92918e7 q^{95} -1.36692e8 q^{96} -1.25403e9 q^{97} -1.90137e8 q^{98} +4.38343e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 15 q^{2} + 161 q^{3} + 361 q^{4} + 1803 q^{5} + 5693 q^{6} + 10099 q^{7} + 23151 q^{8} + 61060 q^{9} + 84505 q^{10} + 121746 q^{11} + 113389 q^{12} + 142805 q^{13} + 8475 q^{14} + 105973 q^{15} - 322463 q^{16}+ \cdots + 3016199848 q^{99}+O(q^{100}) \) 5 * q + 15 * q^2 + 161 * q^3 + 361 * q^4 + 1803 * q^5 + 5693 * q^6 + 10099 * q^7 + 23151 * q^8 + 61060 * q^9 + 84505 * q^10 + 121746 * q^11 + 113389 * q^12 + 142805 * q^13 + 8475 * q^14 + 105973 * q^15 - 322463 * q^16 - 495669 * q^17 - 656228 * q^18 - 840738 * q^19 - 1595607 * q^20 - 1599467 * q^21 - 2023594 * q^22 - 592152 * q^23 - 2295657 * q^24 + 1670362 * q^25 + 428415 * q^26 + 6847883 * q^27 + 2587955 * q^28 + 10678182 * q^29 + 5491201 * q^30 + 12885296 * q^31 + 3282927 * q^32 + 17278298 * q^33 - 9934079 * q^34 + 8380731 * q^35 - 20483302 * q^36 + 7171823 * q^37 - 25568814 * q^38 + 4598321 * q^39 - 54359445 * q^40 + 9294012 * q^41 - 69520457 * q^42 + 12831975 * q^43 - 41479074 * q^44 + 26135198 * q^45 - 59319696 * q^46 + 43354215 * q^47 - 86874671 * q^48 + 25249488 * q^49 - 16270770 * q^50 + 16905901 * q^51 + 10310521 * q^52 + 93231780 * q^53 + 58983719 * q^54 + 99448846 * q^55 + 199599225 * q^56 + 90173382 * q^57 + 151020970 * q^58 + 246496182 * q^59 + 90097913 * q^60 - 132232612 * q^61 + 158135724 * q^62 - 416955202 * q^63 + 91019105 * q^64 + 51495483 * q^65 - 323733130 * q^66 - 369388534 * q^67 + 238172073 * q^68 - 579986760 * q^69 - 144857425 * q^70 + 212150457 * q^71 - 415774278 * q^72 - 252729806 * q^73 + 192105957 * q^74 - 752457788 * q^75 - 953775990 * q^76 + 449666118 * q^77 + 162597773 * q^78 - 1247271728 * q^79 + 900649725 * q^80 - 317713115 * q^81 + 169559388 * q^82 + 1696894296 * q^83 + 1247983739 * q^84 - 775363765 * q^85 + 3291621459 * q^86 - 614530466 * q^87 - 220227222 * q^88 - 753854382 * q^89 + 2296265882 * q^90 + 288437539 * q^91 + 13876128 * q^92 - 892784668 * q^93 + 272071215 * q^94 + 1442632962 * q^95 + 930612847 * q^96 + 3824606 * q^97 + 1570614816 * q^98 + 3016199848 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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