LMFDB - Embedded newform 13.10.a.b.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [13,10,Mod(1,13)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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			1.4
Root			$16.7176$ 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)

$f(q)$	$=$	\(q+19.7176 q^{2} +250.479 q^{3} -123.217 q^{4} +1555.58 q^{5} +4938.84 q^{6} -8329.39 q^{7} -12524.9 q^{8} +43056.6 q^{9} +30672.3 q^{10} +30751.5 q^{11} -30863.2 q^{12} +28561.0 q^{13} -164236. q^{14} +389640. q^{15} -183875. q^{16} -637455. q^{17} +848973. q^{18} +105834. q^{19} -191674. q^{20} -2.08634e6 q^{21} +606345. q^{22} -511169. q^{23} -3.13723e6 q^{24} +466710. q^{25} +563154. q^{26} +5.85460e6 q^{27} +1.02632e6 q^{28} +781868. q^{29} +7.68276e6 q^{30} -2.83285e6 q^{31} +2.78721e6 q^{32} +7.70259e6 q^{33} -1.25691e7 q^{34} -1.29571e7 q^{35} -5.30530e6 q^{36} +1.22183e7 q^{37} +2.08680e6 q^{38} +7.15392e6 q^{39} -1.94836e7 q^{40} -6.83367e6 q^{41} -4.11375e7 q^{42} +3.84656e7 q^{43} -3.78910e6 q^{44} +6.69781e7 q^{45} -1.00790e7 q^{46} -1.30402e7 q^{47} -4.60567e7 q^{48} +2.90252e7 q^{49} +9.20238e6 q^{50} -1.59669e8 q^{51} -3.51920e6 q^{52} -2.42871e7 q^{53} +1.15439e8 q^{54} +4.78364e7 q^{55} +1.04325e8 q^{56} +2.65092e7 q^{57} +1.54166e7 q^{58} +1.63738e8 q^{59} -4.80103e7 q^{60} +1.90751e7 q^{61} -5.58569e7 q^{62} -3.58636e8 q^{63} +1.49101e8 q^{64} +4.44290e7 q^{65} +1.51876e8 q^{66} -7.22869e7 q^{67} +7.85452e7 q^{68} -1.28037e8 q^{69} -2.55482e8 q^{70} +2.65461e7 q^{71} -5.39282e8 q^{72} +2.42850e8 q^{73} +2.40916e8 q^{74} +1.16901e8 q^{75} -1.30406e7 q^{76} -2.56141e8 q^{77} +1.41058e8 q^{78} -4.64290e8 q^{79} -2.86032e8 q^{80} +6.18969e8 q^{81} -1.34744e8 q^{82} +5.46643e8 q^{83} +2.57072e8 q^{84} -9.91613e8 q^{85} +7.58449e8 q^{86} +1.95841e8 q^{87} -3.85160e8 q^{88} +3.65672e8 q^{89} +1.32065e9 q^{90} -2.37896e8 q^{91} +6.29847e7 q^{92} -7.09568e8 q^{93} -2.57121e8 q^{94} +1.64634e8 q^{95} +6.98137e8 q^{96} +9.98914e7 q^{97} +5.72307e8 q^{98} +1.32405e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	19.7176	0.871402	0.435701	−	0.900091i	$-0.356500\pi$
$2$	19.7176	0.871402	0.435701	+	0.900091i	$0.356500\pi$
$3$	250.479	1.78536	0.892679	−	0.450693i	$-0.148823\pi$
$3$	250.479	1.78536	0.892679	+	0.450693i	$0.148823\pi$
$4$	−123.217	−0.240658
$5$	1555.58	1.11308	0.556542	−	0.830820i	$-0.312128\pi$
$5$	1555.58	1.11308	0.556542	+	0.830820i	$0.312128\pi$
$6$	4938.84	1.55577
$7$	−8329.39	−1.31121	−0.655605	−	0.755104i	$-0.727586\pi$
$7$	−8329.39	−1.31121	−0.655605	+	0.755104i	$0.727586\pi$
$8$	−12524.9	−1.08111
$9$	43056.6	2.18750
$10$	30672.3	0.969944
$11$	30751.5	0.633284	0.316642	−	0.948545i	$-0.397445\pi$
$11$	30751.5	0.633284	0.316642	+	0.948545i	$0.397445\pi$
$12$	−30863.2	−0.429661
$13$	28561.0	0.277350
$13$	28561.0	0.277350
$14$	−164236.	−1.14259
$15$	389640.	1.98725
$16$	−183875.	−0.701426
$17$	−637455.	−1.85110	−0.925549	−	0.378629i	$-0.876396\pi$
$17$	−637455.	−1.85110	−0.925549	+	0.378629i	$0.876396\pi$
$18$	848973.	1.90620
$19$	105834.	0.186310	0.0931548	−	0.995652i	$-0.470305\pi$
$19$	105834.	0.186310	0.0931548	+	0.995652i	$0.470305\pi$
$20$	−191674.	−0.267872
$21$	−2.08634e6	−2.34098
$22$	606345.	0.551845
$23$	−511169.	−0.380881	−0.190441	−	0.981699i	$-0.560992\pi$
$23$	−511169.	−0.380881	−0.190441	+	0.981699i	$0.560992\pi$
$24$	−3.13723e6	−1.93017
$25$	466710.	0.238955
$26$	563154.	0.241684
$27$	5.85460e6	2.12012
$28$	1.02632e6	0.315553
$29$	781868.	0.205278	0.102639	−	0.994719i	$-0.467271\pi$
$29$	781868.	0.205278	0.102639	+	0.994719i	$0.467271\pi$
$30$	7.68276e6	1.73170
$31$	−2.83285e6	−0.550929	−0.275464	−	0.961311i	$-0.588832\pi$
$31$	−2.83285e6	−0.550929	−0.275464	+	0.961311i	$0.588832\pi$
$32$	2.78721e6	0.469888
$33$	7.70259e6	1.13064
$34$	−1.25691e7	−1.61305
$35$	−1.29571e7	−1.45949
$36$	−5.30530e6	−0.526440
$37$	1.22183e7	1.07178	0.535889	−	0.844289i	$-0.319977\pi$
$37$	1.22183e7	1.07178	0.535889	+	0.844289i	$0.319977\pi$
$38$	2.08680e6	0.162351
$39$	7.15392e6	0.495169
$40$	−1.94836e7	−1.20337
$41$	−6.83367e6	−0.377682	−0.188841	−	0.982008i	$-0.560473\pi$
$41$	−6.83367e6	−0.377682	−0.188841	+	0.982008i	$0.560473\pi$
$42$	−4.11375e7	−2.03993
$43$	3.84656e7	1.71579	0.857896	−	0.513823i	$-0.171771\pi$
$43$	3.84656e7	1.71579	0.857896	+	0.513823i	$0.171771\pi$
$44$	−3.78910e6	−0.152405
$45$	6.69781e7	2.43487
$46$	−1.00790e7	−0.331901
$47$	−1.30402e7	−0.389802	−0.194901	−	0.980823i	$-0.562439\pi$
$47$	−1.30402e7	−0.389802	−0.194901	+	0.980823i	$0.562439\pi$
$48$	−4.60567e7	−1.25230
$49$	2.90252e7	0.719272
$50$	9.20238e6	0.208226
$51$	−1.59669e8	−3.30487
$52$	−3.51920e6	−0.0667465
$53$	−2.42871e7	−0.422800	−0.211400	−	0.977400i	$-0.567802\pi$
$53$	−2.42871e7	−0.422800	−0.211400	+	0.977400i	$0.567802\pi$
$54$	1.15439e8	1.84748
$55$	4.78364e7	0.704898
$56$	1.04325e8	1.41757
$57$	2.65092e7	0.332629
$58$	1.54166e7	0.178880
$59$	1.63738e8	1.75920	0.879599	−	0.475716i	$-0.157811\pi$
$59$	1.63738e8	1.75920	0.879599	+	0.475716i	$0.157811\pi$
$60$	−4.80103e7	−0.478248
$61$	1.90751e7	0.176394	0.0881968	−	0.996103i	$-0.471890\pi$
$61$	1.90751e7	0.176394	0.0881968	+	0.996103i	$0.471890\pi$
$62$	−5.58569e7	−0.480081
$63$	−3.58636e8	−2.86828
$64$	1.49101e8	1.11089
$65$	4.44290e7	0.308714
$66$	1.51876e8	0.985242
$67$	−7.22869e7	−0.438251	−0.219125	−	0.975697i	$-0.570320\pi$
$67$	−7.22869e7	−0.438251	−0.219125	+	0.975697i	$0.570320\pi$
$68$	7.85452e7	0.445481
$69$	−1.28037e8	−0.680009
$70$	−2.55482e8	−1.27180
$71$	2.65461e7	0.123976	0.0619880	−	0.998077i	$-0.480256\pi$
$71$	2.65461e7	0.123976	0.0619880	+	0.998077i	$0.480256\pi$
$72$	−5.39282e8	−2.36494
$73$	2.42850e8	1.00089	0.500445	−	0.865769i	$-0.333170\pi$
$73$	2.42850e8	1.00089	0.500445	+	0.865769i	$0.333170\pi$
$74$	2.40916e8	0.933950
$75$	1.16901e8	0.426621
$76$	−1.30406e7	−0.0448369
$77$	−2.56141e8	−0.830369
$78$	1.41058e8	0.431492
$79$	−4.64290e8	−1.34112	−0.670560	−	0.741855i	$-0.733946\pi$
$79$	−4.64290e8	−1.34112	−0.670560	+	0.741855i	$0.733946\pi$
$80$	−2.86032e8	−0.780746
$81$	6.18969e8	1.59767
$82$	−1.34744e8	−0.329113
$83$	5.46643e8	1.26431	0.632153	−	0.774843i	$-0.282171\pi$
$83$	5.46643e8	1.26431	0.632153	+	0.774843i	$0.282171\pi$
$84$	2.57072e8	0.563375
$85$	−9.91613e8	−2.06043
$86$	7.58449e8	1.49515
$87$	1.95841e8	0.366495
$88$	−3.85160e8	−0.684651
$89$	3.65672e8	0.617783	0.308892	−	0.951097i	$-0.400042\pi$
$89$	3.65672e8	0.617783	0.308892	+	0.951097i	$0.400042\pi$
$90$	1.32065e9	2.12176
$91$	−2.37896e8	−0.363664
$92$	6.29847e7	0.0916621
$93$	−7.09568e8	−0.983605
$94$	−2.57121e8	−0.339674
$95$	1.64634e8	0.207378
$96$	6.98137e8	0.838919
$97$	9.98914e7	0.114566	0.0572830	−	0.998358i	$-0.481756\pi$
$97$	9.98914e7	0.114566	0.0572830	+	0.998358i	$0.481756\pi$
$98$	5.72307e8	0.626775
$99$	1.32405e9	1.38531
$100$	−5.75065e7	−0.0575065
$101$	−6.76155e8	−0.646547	−0.323273	−	0.946306i	$-0.604783\pi$
$101$	−6.76155e8	−0.646547	−0.323273	+	0.946306i	$0.604783\pi$
$102$	−3.14829e9	−2.87987
$103$	−1.73267e8	−0.151687	−0.0758434	−	0.997120i	$-0.524165\pi$
$103$	−1.73267e8	−0.151687	−0.0758434	+	0.997120i	$0.524165\pi$
$104$	−3.57725e8	−0.299847
$105$	−3.24547e9	−2.60571
$106$	−4.78883e8	−0.368429
$107$	1.23684e9	0.912191	0.456095	−	0.889931i	$-0.349248\pi$
$107$	1.23684e9	0.912191	0.456095	+	0.889931i	$0.349248\pi$
$108$	−7.21385e8	−0.510223
$109$	−1.04481e9	−0.708956	−0.354478	−	0.935064i	$-0.615341\pi$
$109$	−1.04481e9	−0.708956	−0.354478	+	0.935064i	$0.615341\pi$
$110$	9.43218e8	0.614250
$111$	3.06044e9	1.91351
$112$	1.53156e9	0.919716
$113$	−1.17492e9	−0.677884	−0.338942	−	0.940807i	$-0.610069\pi$
$113$	−1.17492e9	−0.677884	−0.338942	+	0.940807i	$0.610069\pi$
$114$	5.22698e8	0.289854
$115$	−7.95166e8	−0.423953
$116$	−9.63394e7	−0.0494018
$117$	1.22974e9	0.606704
$118$	3.22851e9	1.53297
$119$	5.30961e9	2.42718
$120$	−4.88022e9	−2.14844
$121$	−1.41230e9	−0.598951
$122$	3.76115e8	0.153710
$123$	−1.71169e9	−0.674298
$124$	3.49055e8	0.132585
$125$	−2.31224e9	−0.847106
$126$	−7.07143e9	−2.49942
$127$	6.34961e8	0.216586	0.108293	−	0.994119i	$-0.465462\pi$
$127$	6.34961e8	0.216586	0.108293	+	0.994119i	$0.465462\pi$
$128$	1.51286e9	0.498142
$129$	9.63482e9	3.06330
$130$	8.76032e8	0.269014
$131$	−5.68611e9	−1.68692	−0.843459	−	0.537193i	$-0.819485\pi$
$131$	−5.68611e9	−1.68692	−0.843459	+	0.537193i	$0.819485\pi$
$132$	−9.49089e8	−0.272097
$133$	−8.81536e8	−0.244291
$134$	−1.42532e9	−0.381893
$135$	9.10731e9	2.35987
$136$	7.98408e9	2.00124
$137$	4.47162e9	1.08448	0.542241	−	0.840223i	$-0.317576\pi$
$137$	4.47162e9	1.08448	0.542241	+	0.840223i	$0.317576\pi$
$138$	−2.52458e9	−0.592562
$139$	−8.63285e9	−1.96150	−0.980748	−	0.195275i	$-0.937440\pi$
$139$	−8.63285e9	−1.96150	−0.980748	+	0.195275i	$0.937440\pi$
$140$	1.59653e9	0.351237
$141$	−3.26629e9	−0.695936
$142$	5.23424e8	0.108033
$143$	8.78292e8	0.175641
$144$	−7.91702e9	−1.53437
$145$	1.21626e9	0.228492
$146$	4.78842e9	0.872177
$147$	7.27020e9	1.28416
$148$	−1.50551e9	−0.257932
$149$	−6.88630e9	−1.14458	−0.572292	−	0.820050i	$-0.693946\pi$
$149$	−6.88630e9	−1.14458	−0.572292	+	0.820050i	$0.693946\pi$
$150$	2.30500e9	0.371758
$151$	4.01063e9	0.627792	0.313896	−	0.949457i	$-0.398366\pi$
$151$	4.01063e9	0.627792	0.313896	+	0.949457i	$0.398366\pi$
$152$	−1.32557e9	−0.201422
$153$	−2.74467e10	−4.04928
$154$	−5.05048e9	−0.723585
$155$	−4.40672e9	−0.613230
$156$	−8.81484e8	−0.119166
$157$	9.39913e9	1.23464	0.617318	−	0.786714i	$-0.288219\pi$
$157$	9.39913e9	1.23464	0.617318	+	0.786714i	$0.288219\pi$
$158$	−9.15469e9	−1.16866
$159$	−6.08341e9	−0.754849
$160$	4.33573e9	0.523025
$161$	4.25773e9	0.499415
$162$	1.22046e10	1.39221
$163$	3.72144e9	0.412920	0.206460	−	0.978455i	$-0.433806\pi$
$163$	3.72144e9	0.412920	0.206460	+	0.978455i	$0.433806\pi$
$164$	8.42024e8	0.0908923
$165$	1.19820e10	1.25850
$166$	1.07785e10	1.10172
$167$	−4.48607e9	−0.446315	−0.223158	−	0.974782i	$-0.571636\pi$
$167$	−4.48607e9	−0.446315	−0.223158	+	0.974782i	$0.571636\pi$
$168$	2.61312e10	2.53086
$169$	8.15731e8	0.0769231
$170$	−1.95522e10	−1.79546
$171$	4.55687e9	0.407553
$172$	−4.73962e9	−0.412919
$173$	−1.69286e10	−1.43686	−0.718428	−	0.695602i	$-0.755138\pi$
$173$	−1.69286e10	−1.43686	−0.718428	+	0.695602i	$0.755138\pi$
$174$	3.86152e9	0.319364
$175$	−3.88741e9	−0.313321
$176$	−5.65441e9	−0.444202
$177$	4.10128e10	3.14080
$178$	7.21016e9	0.538338
$179$	1.23127e10	0.896428	0.448214	−	0.893926i	$-0.352060\pi$
$179$	1.23127e10	0.896428	0.448214	+	0.893926i	$0.352060\pi$
$180$	−8.25283e9	−0.585972
$181$	−2.43748e10	−1.68806	−0.844030	−	0.536295i	$-0.819823\pi$
$181$	−2.43748e10	−1.68806	−0.844030	+	0.536295i	$0.819823\pi$
$182$	−4.69073e9	−0.316898
$183$	4.77791e9	0.314926
$184$	6.40237e9	0.411775
$185$	1.90066e10	1.19298
$186$	−1.39910e10	−0.857116
$187$	−1.96027e10	−1.17227
$188$	1.60677e9	0.0938089
$189$	−4.87653e10	−2.77992
$190$	3.24618e9	0.180710
$191$	−8.67702e9	−0.471759	−0.235880	−	0.971782i	$-0.575797\pi$
$191$	−8.67702e9	−0.471759	−0.235880	+	0.971782i	$0.575797\pi$
$192$	3.73466e10	1.98333
$193$	−2.33509e10	−1.21142	−0.605712	−	0.795684i	$-0.707112\pi$
$193$	−2.33509e10	−1.21142	−0.605712	+	0.795684i	$0.707112\pi$
$194$	1.96962e9	0.0998330
$195$	1.11285e10	0.551165
$196$	−3.57640e9	−0.173098
$197$	−2.62332e9	−0.124095	−0.0620473	−	0.998073i	$-0.519763\pi$
$197$	−2.62332e9	−0.124095	−0.0620473	+	0.998073i	$0.519763\pi$
$198$	2.61071e10	1.20716
$199$	8.36775e9	0.378242	0.189121	−	0.981954i	$-0.439436\pi$
$199$	8.36775e9	0.378242	0.189121	+	0.981954i	$0.439436\pi$
$200$	−5.84551e9	−0.258337
$201$	−1.81063e10	−0.782435
$202$	−1.33321e10	−0.563403
$203$	−6.51249e9	−0.269163
$204$	1.96739e10	0.795344
$205$	−1.06303e10	−0.420392
$206$	−3.41640e9	−0.132180
$207$	−2.20092e10	−0.833179
$208$	−5.25164e9	−0.194541
$209$	3.25456e9	0.117987
$210$	−6.39928e10	−2.27062
$211$	3.66318e10	1.27229	0.636147	−	0.771568i	$-0.280527\pi$
$211$	3.66318e10	1.27229	0.636147	+	0.771568i	$0.280527\pi$
$212$	2.99258e9	0.101750
$213$	6.64923e9	0.221342
$214$	2.43874e10	0.794885
$215$	5.98364e10	1.90982
$216$	−7.33285e10	−2.29209
$217$	2.35959e10	0.722383
$218$	−2.06012e10	−0.617786
$219$	6.08289e10	1.78695
$220$	−5.89425e9	−0.169639
$221$	−1.82063e10	−0.513402
$222$	6.03444e10	1.66743
$223$	6.22383e10	1.68533	0.842667	−	0.538435i	$-0.180984\pi$
$223$	6.22383e10	1.68533	0.842667	+	0.538435i	$0.180984\pi$
$224$	−2.32158e10	−0.616122
$225$	2.00949e10	0.522715
$226$	−2.31666e10	−0.590710
$227$	4.00531e10	1.00120	0.500599	−	0.865679i	$-0.333113\pi$
$227$	4.00531e10	1.00120	0.500599	+	0.865679i	$0.333113\pi$
$228$	−3.26639e9	−0.0800499
$229$	4.61622e10	1.10924	0.554621	−	0.832103i	$-0.312863\pi$
$229$	4.61622e10	1.10924	0.554621	+	0.832103i	$0.312863\pi$
$230$	−1.56787e10	−0.369433
$231$	−6.41579e10	−1.48251
$232$	−9.79285e9	−0.221929
$233$	−2.82042e10	−0.626920	−0.313460	−	0.949601i	$-0.601488\pi$
$233$	−2.82042e10	−0.626920	−0.313460	+	0.949601i	$0.601488\pi$
$234$	2.42475e10	0.528683
$235$	−2.02851e10	−0.433882
$236$	−2.01753e10	−0.423365
$237$	−1.16295e11	−2.39438
$238$	1.04693e11	2.11505
$239$	7.93923e9	0.157394	0.0786969	−	0.996899i	$-0.474924\pi$
$239$	7.93923e9	0.157394	0.0786969	+	0.996899i	$0.474924\pi$
$240$	−7.16449e10	−1.39391
$241$	−4.33069e10	−0.826953	−0.413476	−	0.910515i	$-0.635686\pi$
$241$	−4.33069e10	−0.826953	−0.413476	+	0.910515i	$0.635686\pi$
$242$	−2.78471e10	−0.521927
$243$	3.98026e10	0.732290
$244$	−2.35037e9	−0.0424505
$245$	4.51511e10	0.800610
$246$	−3.37504e10	−0.587585
$247$	3.02273e9	0.0516730
$248$	3.54812e10	0.595616
$249$	1.36922e11	2.25724
$250$	−4.55918e10	−0.738171
$251$	3.48447e10	0.554121	0.277061	−	0.960852i	$-0.410640\pi$
$251$	3.48447e10	0.554121	0.277061	+	0.960852i	$0.410640\pi$
$252$	4.41900e10	0.690274
$253$	−1.57192e10	−0.241206
$254$	1.25199e10	0.188733
$255$	−2.48378e11	−3.67860
$256$	−4.65097e10	−0.676806
$257$	6.17149e10	0.882452	0.441226	−	0.897396i	$-0.354544\pi$
$257$	6.17149e10	0.882452	0.441226	+	0.897396i	$0.354544\pi$
$258$	1.89975e11	2.66937
$259$	−1.01771e11	−1.40533
$260$	−5.47440e9	−0.0742945
$261$	3.36646e10	0.449046
$262$	−1.12116e11	−1.46999
$263$	−1.78558e10	−0.230132	−0.115066	−	0.993358i	$-0.536708\pi$
$263$	−1.78558e10	−0.230132	−0.115066	+	0.993358i	$0.536708\pi$
$264$	−9.64745e10	−1.22235
$265$	−3.77806e10	−0.470611
$266$	−1.73818e10	−0.212876
$267$	9.15930e10	1.10296
$268$	8.90696e9	0.105469
$269$	−5.24399e10	−0.610628	−0.305314	−	0.952252i	$-0.598761\pi$
$269$	−5.24399e10	−0.610628	−0.305314	+	0.952252i	$0.598761\pi$
$270$	1.79574e11	2.05640
$271$	−5.03988e10	−0.567621	−0.283811	−	0.958880i	$-0.591599\pi$
$271$	−5.03988e10	−0.567621	−0.283811	+	0.958880i	$0.591599\pi$
$272$	1.17212e11	1.29841
$273$	−5.95879e10	−0.649271
$274$	8.81695e10	0.945020
$275$	1.43520e10	0.151327
$276$	1.57763e10	0.163650
$277$	−1.58677e11	−1.61941	−0.809703	−	0.586840i	$-0.800372\pi$
$277$	−1.58677e11	−1.61941	−0.809703	+	0.586840i	$0.800372\pi$
$278$	−1.70219e11	−1.70925
$279$	−1.21973e11	−1.20516
$280$	1.62286e11	1.57787
$281$	3.04536e10	0.291381	0.145690	−	0.989330i	$-0.453460\pi$
$281$	3.04536e10	0.291381	0.145690	+	0.989330i	$0.453460\pi$
$282$	−6.44034e10	−0.606440
$283$	4.21589e10	0.390706	0.195353	−	0.980733i	$-0.437415\pi$
$283$	4.21589e10	0.390706	0.195353	+	0.980733i	$0.437415\pi$
$284$	−3.27092e9	−0.0298358
$285$	4.12373e10	0.370244
$286$	1.73178e10	0.153054
$287$	5.69204e10	0.495221
$288$	1.20008e11	1.02788
$289$	2.87761e11	2.42656
$290$	2.39817e10	0.199108
$291$	2.50207e10	0.204541
$292$	−2.99233e10	−0.240872
$293$	9.73493e10	0.771665	0.385832	−	0.922569i	$-0.373914\pi$
$293$	9.73493e10	0.771665	0.385832	+	0.922569i	$0.373914\pi$
$294$	1.43351e11	1.11902
$295$	2.54707e11	1.95813
$296$	−1.53034e11	−1.15871
$297$	1.80037e11	1.34264
$298$	−1.35781e11	−0.997393
$299$	−1.45995e10	−0.105637
$300$	−1.44042e10	−0.102670
$301$	−3.20395e11	−2.24976
$302$	7.90799e10	0.547060
$303$	−1.69362e11	−1.15432
$304$	−1.94602e10	−0.130682
$305$	2.96729e10	0.196341
$306$	−5.41182e11	−3.52855
$307$	−1.62669e11	−1.04516	−0.522578	−	0.852591i	$-0.675030\pi$
$307$	−1.62669e11	−1.04516	−0.522578	+	0.852591i	$0.675030\pi$
$308$	3.15609e10	0.199835
$309$	−4.33996e10	−0.270815
$310$	−8.68900e10	−0.534370
$311$	1.80301e11	1.09289	0.546445	−	0.837495i	$-0.315981\pi$
$311$	1.80301e11	1.09289	0.546445	+	0.837495i	$0.315981\pi$
$312$	−8.96025e10	−0.535334
$313$	−6.08927e10	−0.358605	−0.179302	−	0.983794i	$-0.557384\pi$
$313$	−6.08927e10	−0.358605	−0.179302	+	0.983794i	$0.557384\pi$
$314$	1.85328e11	1.07586
$315$	−5.57887e11	−3.19263
$316$	5.72084e10	0.322751
$317$	4.75152e10	0.264281	0.132140	−	0.991231i	$-0.457815\pi$
$317$	4.75152e10	0.264281	0.132140	+	0.991231i	$0.457815\pi$
$318$	−1.19950e11	−0.657777
$319$	2.40436e10	0.129999
$320$	2.31938e11	1.23651
$321$	3.09802e11	1.62859
$322$	8.39522e10	0.435192
$323$	−6.74646e10	−0.344877
$324$	−7.62674e10	−0.384491
$325$	1.33297e10	0.0662743
$326$	7.33777e10	0.359820
$327$	−2.61704e11	−1.26574
$328$	8.55914e10	0.408317
$329$	1.08617e11	0.511112
$330$	2.36256e11	1.09666
$331$	−8.96236e10	−0.410390	−0.205195	−	0.978721i	$-0.565783\pi$
$331$	−8.96236e10	−0.410390	−0.205195	+	0.978721i	$0.565783\pi$
$332$	−6.73557e10	−0.304265
$333$	5.26081e11	2.34452
$334$	−8.84544e10	−0.388920
$335$	−1.12448e11	−0.487810
$336$	3.83624e11	1.64202
$337$	2.05747e11	0.868957	0.434478	−	0.900682i	$-0.356933\pi$
$337$	2.05747e11	0.868957	0.434478	+	0.900682i	$0.356933\pi$
$338$	1.60842e10	0.0670309
$339$	−2.94293e11	−1.21027
$340$	1.22183e11	0.495858
$341$	−8.71142e10	−0.348894
$342$	8.98504e10	0.355143
$343$	9.43587e10	0.368094
$344$	−4.81780e11	−1.85496
$345$	−1.99172e11	−0.756907
$346$	−3.33791e11	−1.25208
$347$	3.41311e11	1.26377	0.631884	−	0.775063i	$-0.282282\pi$
$347$	3.41311e11	1.26377	0.631884	+	0.775063i	$0.282282\pi$
$348$	−2.41310e10	−0.0881999
$349$	−4.15352e11	−1.49866	−0.749328	−	0.662198i	$-0.769624\pi$
$349$	−4.15352e11	−1.49866	−0.749328	+	0.662198i	$0.769624\pi$
$350$	−7.66503e10	−0.273028
$351$	1.67213e11	0.588015
$352$	8.57107e10	0.297573
$353$	−1.00300e11	−0.343806	−0.171903	−	0.985114i	$-0.554992\pi$
$353$	−1.00300e11	−0.343806	−0.171903	+	0.985114i	$0.554992\pi$
$354$	8.08674e11	2.73690
$355$	4.12946e10	0.137996
$356$	−4.50569e10	−0.148675
$357$	1.32995e12	4.33338
$358$	2.42777e11	0.781149
$359$	−3.35856e11	−1.06716	−0.533578	−	0.845751i	$-0.679153\pi$
$359$	−3.35856e11	−1.06716	−0.533578	+	0.845751i	$0.679153\pi$
$360$	−8.38897e11	−2.63237
$361$	−3.11487e11	−0.965289
$362$	−4.80613e11	−1.47098
$363$	−3.53750e11	−1.06934
$364$	2.93128e10	0.0875187
$365$	3.77774e11	1.11407
$366$	9.42088e10	0.274427
$367$	3.43252e11	0.987679	0.493839	−	0.869553i	$-0.335593\pi$
$367$	3.43252e11	0.987679	0.493839	+	0.869553i	$0.335593\pi$
$368$	9.39910e10	0.267160
$369$	−2.94235e11	−0.826182
$370$	3.74765e11	1.03956
$371$	2.02297e11	0.554379
$372$	8.74308e10	0.236712
$373$	−3.20544e11	−0.857428	−0.428714	−	0.903440i	$-0.641033\pi$
$373$	−3.20544e11	−0.857428	−0.428714	+	0.903440i	$0.641033\pi$
$374$	−3.86517e11	−1.02152
$375$	−5.79167e11	−1.51239
$376$	1.63328e11	0.421420
$377$	2.23309e10	0.0569339
$378$	−9.61533e11	−2.42243
$379$	5.59129e11	1.39199	0.695994	−	0.718047i	$-0.254964\pi$
$379$	5.59129e11	1.39199	0.695994	+	0.718047i	$0.254964\pi$
$380$	−2.02857e10	−0.0499072
$381$	1.59044e11	0.386683
$382$	−1.71090e11	−0.411092
$383$	−1.14158e11	−0.271089	−0.135544	−	0.990771i	$-0.543278\pi$
$383$	−1.14158e11	−0.271089	−0.135544	+	0.990771i	$0.543278\pi$
$384$	3.78938e11	0.889361
$385$	−3.98448e11	−0.924270
$386$	−4.60424e11	−1.05564
$387$	1.65620e12	3.75330
$388$	−1.23083e10	−0.0275712
$389$	−1.10883e11	−0.245522	−0.122761	−	0.992436i	$-0.539175\pi$
$389$	−1.10883e11	−0.245522	−0.122761	+	0.992436i	$0.539175\pi$
$390$	2.19427e11	0.480286
$391$	3.25847e11	0.705048
$392$	−3.63539e11	−0.777613
$393$	−1.42425e12	−3.01175
$394$	−5.17255e10	−0.108136
$395$	−7.22242e11	−1.49278
$396$	−1.63146e11	−0.333386
$397$	2.31687e11	0.468107	0.234053	−	0.972224i	$-0.424801\pi$
$397$	2.31687e11	0.468107	0.234053	+	0.972224i	$0.424801\pi$
$398$	1.64992e11	0.329601
$399$	−2.20806e11	−0.436147
$400$	−8.58160e10	−0.167609
$401$	5.44480e10	0.105156	0.0525778	−	0.998617i	$-0.483256\pi$
$401$	5.44480e10	0.105156	0.0525778	+	0.998617i	$0.483256\pi$
$402$	−3.57013e11	−0.681815
$403$	−8.09089e10	−0.152800
$404$	8.33137e10	0.155597
$405$	9.62857e11	1.77834
$406$	−1.28411e11	−0.234549
$407$	3.75732e11	0.678740
$408$	1.99984e12	3.57294
$409$	2.35793e11	0.416654	0.208327	−	0.978059i	$-0.433198\pi$
$409$	2.35793e11	0.416654	0.208327	+	0.978059i	$0.433198\pi$
$410$	−2.09605e11	−0.366331
$411$	1.12005e12	1.93619
$412$	2.13494e10	0.0365046
$413$	−1.36384e12	−2.30668
$414$	−4.33969e11	−0.726034
$415$	8.50348e11	1.40728
$416$	7.96055e10	0.130324
$417$	−2.16235e12	−3.50197
$418$	6.41721e10	0.102814
$419$	5.43639e11	0.861682	0.430841	−	0.902428i	$-0.358217\pi$
$419$	5.43639e11	0.861682	0.430841	+	0.902428i	$0.358217\pi$
$420$	3.99896e11	0.627084
$421$	2.70622e11	0.419849	0.209925	−	0.977718i	$-0.432678\pi$
$421$	2.70622e11	0.419849	0.209925	+	0.977718i	$0.432678\pi$
$422$	7.22291e11	1.10868
$423$	−5.61467e11	−0.852693
$424$	3.04195e11	0.457094
$425$	−2.97506e11	−0.442329
$426$	1.31107e11	0.192878
$427$	−1.58884e11	−0.231289
$428$	−1.52399e11	−0.219526
$429$	2.19994e11	0.313583
$430$	1.17983e12	1.66422
$431$	−1.07553e12	−1.50132	−0.750662	−	0.660687i	$-0.770265\pi$
$431$	−1.07553e12	−1.50132	−0.750662	+	0.660687i	$0.770265\pi$
$432$	−1.07651e12	−1.48711
$433$	−2.63085e11	−0.359667	−0.179833	−	0.983697i	$-0.557556\pi$
$433$	−2.63085e11	−0.359667	−0.179833	+	0.983697i	$0.557556\pi$
$434$	4.65254e11	0.629486
$435$	3.04647e11	0.407939
$436$	1.28739e11	0.170616
$437$	−5.40992e10	−0.0709618
$438$	1.19940e12	1.55715
$439$	−8.20045e11	−1.05377	−0.526887	−	0.849935i	$-0.676641\pi$
$439$	−8.20045e11	−1.05377	−0.526887	+	0.849935i	$0.676641\pi$
$440$	−5.99148e11	−0.762074
$441$	1.24973e12	1.57341
$442$	−3.58985e11	−0.447380
$443$	−1.77977e10	−0.0219557	−0.0109779	−	0.999940i	$-0.503494\pi$
$443$	−1.77977e10	−0.0219557	−0.0109779	+	0.999940i	$0.503494\pi$
$444$	−3.77098e11	−0.460501
$445$	5.68832e11	0.687645
$446$	1.22719e12	1.46860
$447$	−1.72487e12	−2.04349
$448$	−1.24192e12	−1.45661
$449$	1.15873e12	1.34547	0.672734	−	0.739885i	$-0.265120\pi$
$449$	1.15873e12	1.34547	0.672734	+	0.739885i	$0.265120\pi$
$450$	3.96224e11	0.455495
$451$	−2.10145e11	−0.239180
$452$	1.44770e11	0.163138
$453$	1.00458e12	1.12083
$454$	7.89751e11	0.872446
$455$	−3.70066e11	−0.404789
$456$	−3.32027e11	−0.359610
$457$	−9.23583e11	−0.990497	−0.495249	−	0.868751i	$-0.664923\pi$
$457$	−9.23583e11	−0.990497	−0.495249	+	0.868751i	$0.664923\pi$
$458$	9.10207e11	0.966597
$459$	−3.73204e12	−3.92455
$460$	9.79778e10	0.102028
$461$	6.32718e11	0.652464	0.326232	−	0.945290i	$-0.394221\pi$
$461$	6.32718e11	0.652464	0.326232	+	0.945290i	$0.394221\pi$
$462$	−1.26504e12	−1.29186
$463$	2.14607e11	0.217035	0.108517	−	0.994095i	$-0.465390\pi$
$463$	2.14607e11	0.217035	0.108517	+	0.994095i	$0.465390\pi$
$464$	−1.43766e11	−0.143987
$465$	−1.10379e12	−1.09483
$466$	−5.56119e11	−0.546300
$467$	5.49922e11	0.535026	0.267513	−	0.963554i	$-0.413798\pi$
$467$	5.49922e11	0.535026	0.267513	+	0.963554i	$0.413798\pi$
$468$	−1.51525e11	−0.146008
$469$	6.02106e11	0.574639
$470$	−3.99973e11	−0.378086
$471$	2.35428e12	2.20427
$472$	−2.05081e12	−1.90189
$473$	1.18287e12	1.08658
$474$	−2.29305e12	−2.08647
$475$	4.93939e10	0.0445197
$476$	−6.54234e11	−0.584120
$477$	−1.04572e12	−0.924875
$478$	1.56542e11	0.137153
$479$	1.60843e12	1.39602	0.698010	−	0.716088i	$-0.254069\pi$
$479$	1.60843e12	1.39602	0.698010	+	0.716088i	$0.254069\pi$
$480$	1.08601e12	0.933787
$481$	3.48968e11	0.297258
$482$	−8.53908e11	−0.720609
$483$	1.06647e12	0.891635
$484$	1.74019e11	0.144142
$485$	1.55389e11	0.127521
$486$	7.84810e11	0.638119
$487$	−1.40030e12	−1.12808	−0.564040	−	0.825747i	$-0.690754\pi$
$487$	−1.40030e12	−1.12808	−0.564040	+	0.825747i	$0.690754\pi$
$488$	−2.38915e11	−0.190701
$489$	9.32141e11	0.737211
$490$	8.90270e11	0.697653
$491$	1.31274e12	1.01932	0.509661	−	0.860376i	$-0.329771\pi$
$491$	1.31274e12	1.01932	0.509661	+	0.860376i	$0.329771\pi$
$492$	2.10909e11	0.162275
$493$	−4.98406e11	−0.379990
$494$	5.96010e10	0.0450280
$495$	2.05967e12	1.54197
$496$	5.20888e11	0.386436
$497$	−2.21113e11	−0.162559
$498$	2.69978e12	1.96696
$499$	−3.50247e11	−0.252885	−0.126442	−	0.991974i	$-0.540356\pi$
$499$	−3.50247e11	−0.252885	−0.126442	+	0.991974i	$0.540356\pi$
$500$	2.84907e11	0.203863
$501$	−1.12366e12	−0.796833
$502$	6.87053e11	0.482863
$503$	2.62962e12	1.83163	0.915815	−	0.401601i	$-0.131546\pi$
$503$	2.62962e12	1.83163	0.915815	+	0.401601i	$0.131546\pi$
$504$	4.49189e12	3.10093
$505$	−1.05181e12	−0.719661
$506$	−3.09945e11	−0.210187
$507$	2.04323e11	0.137335
$508$	−7.82379e10	−0.0521231
$509$	4.07673e11	0.269204	0.134602	−	0.990900i	$-0.457024\pi$
$509$	4.07673e11	0.269204	0.134602	+	0.990900i	$0.457024\pi$
$510$	−4.89741e12	−3.20554
$511$	−2.02280e12	−1.31238
$512$	−1.69164e12	−1.08791
$513$	6.19617e11	0.394998
$514$	1.21687e12	0.768970
$515$	−2.69531e11	−0.168840
$516$	−1.18717e12	−0.737209
$517$	−4.01005e11	−0.246855
$518$	−2.00669e12	−1.22460
$519$	−4.24025e12	−2.56530
$520$	−5.56470e11	−0.333754
$521$	−1.90638e12	−1.13355	−0.566773	−	0.823874i	$-0.691808\pi$
$521$	−1.90638e12	−1.13355	−0.566773	+	0.823874i	$0.691808\pi$
$522$	6.63785e11	0.391300
$523$	−6.84980e11	−0.400332	−0.200166	−	0.979762i	$-0.564148\pi$
$523$	−6.84980e11	−0.400332	−0.200166	+	0.979762i	$0.564148\pi$
$524$	7.00624e11	0.405971
$525$	−9.73713e11	−0.559389
$526$	−3.52073e11	−0.200538
$527$	1.80581e12	1.01982
$528$	−1.41631e12	−0.793059
$529$	−1.53986e12	−0.854930
$530$	−7.44942e11	−0.410092
$531$	7.04999e12	3.84825
$532$	1.08620e11	0.0587906
$533$	−1.95177e11	−0.104750
$534$	1.80599e12	0.961126
$535$	1.92400e12	1.01534
$536$	9.05389e11	0.473798
$537$	3.08407e12	1.60044
$538$	−1.03399e12	−0.532103
$539$	8.92568e11	0.455503
$540$	−1.12217e12	−0.567921
$541$	−1.99962e12	−1.00360	−0.501798	−	0.864985i	$-0.667328\pi$
$541$	−1.99962e12	−1.00360	−0.501798	+	0.864985i	$0.667328\pi$
$542$	−9.93743e11	−0.494626
$543$	−6.10538e12	−3.01379
$544$	−1.77672e12	−0.869809
$545$	−1.62529e12	−0.789128
$546$	−1.17493e12	−0.565776
$547$	2.19967e12	1.05055	0.525273	−	0.850933i	$-0.323963\pi$
$547$	2.19967e12	1.05055	0.525273	+	0.850933i	$0.323963\pi$
$548$	−5.50979e11	−0.260989
$549$	8.21310e11	0.385861
$550$	2.82987e11	0.131866
$551$	8.27485e10	0.0382453
$552$	1.60366e12	0.735166
$553$	3.86726e12	1.75849
$554$	−3.12873e12	−1.41115
$555$	4.76076e12	2.12989
$556$	1.06371e12	0.472050
$557$	2.10846e12	0.928148	0.464074	−	0.885797i	$-0.346387\pi$
$557$	2.10846e12	0.928148	0.464074	+	0.885797i	$0.346387\pi$
$558$	−2.40501e12	−1.05018
$559$	1.09862e12	0.475875
$560$	2.38247e12	1.02372
$561$	−4.91005e12	−2.09292
$562$	6.00472e11	0.253910
$563$	2.49136e12	1.04508	0.522540	−	0.852615i	$-0.324985\pi$
$563$	2.49136e12	1.04508	0.522540	+	0.852615i	$0.324985\pi$
$564$	4.02462e11	0.167483
$565$	−1.82769e12	−0.754542
$566$	8.31272e11	0.340462
$567$	−5.15564e12	−2.09488
$568$	−3.32488e11	−0.134032
$569$	6.91496e11	0.276557	0.138278	−	0.990393i	$-0.455843\pi$
$569$	6.91496e11	0.276557	0.138278	+	0.990393i	$0.455843\pi$
$570$	8.13100e11	0.322632
$571$	−2.70238e11	−0.106386	−0.0531930	−	0.998584i	$-0.516940\pi$
$571$	−2.70238e11	−0.106386	−0.0531930	+	0.998584i	$0.516940\pi$
$572$	−1.08220e11	−0.0422695
$573$	−2.17341e12	−0.842259
$574$	1.12233e12	0.431537
$575$	−2.38568e11	−0.0910136
$576$	6.41978e12	2.43007
$577$	−3.66686e12	−1.37722	−0.688610	−	0.725132i	$-0.741779\pi$
$577$	−3.66686e12	−1.37722	−0.688610	+	0.725132i	$0.741779\pi$
$578$	5.67395e12	2.11451
$579$	−5.84891e12	−2.16283
$580$	−1.49864e11	−0.0549883
$581$	−4.55321e12	−1.65777
$582$	4.93347e11	0.178238
$583$	−7.46864e11	−0.267752
$584$	−3.04169e12	−1.08207
$585$	1.91296e12	0.675313
$586$	1.91949e12	0.672431
$587$	1.16732e12	0.405806	0.202903	−	0.979199i	$-0.434962\pi$
$587$	1.16732e12	0.405806	0.202903	+	0.979199i	$0.434962\pi$
$588$	−8.95811e11	−0.309043
$589$	−2.99812e11	−0.102643
$590$	5.02221e12	1.70632
$591$	−6.57085e11	−0.221553
$592$	−2.24664e12	−0.751773
$593$	3.14463e12	1.04430	0.522148	−	0.852855i	$-0.325131\pi$
$593$	3.14463e12	1.04430	0.522148	+	0.852855i	$0.325131\pi$
$594$	3.54990e12	1.16998
$595$	8.25954e12	2.70165
$596$	8.48508e11	0.275453
$597$	2.09594e12	0.675297
$598$	−2.87867e11	−0.0920527
$599$	2.09251e12	0.664120	0.332060	−	0.943258i	$-0.392256\pi$
$599$	2.09251e12	0.664120	0.332060	+	0.943258i	$0.392256\pi$
$600$	−1.46418e12	−0.461225
$601$	4.34608e12	1.35882	0.679410	−	0.733758i	$-0.262236\pi$
$601$	4.34608e12	1.35882	0.679410	+	0.733758i	$0.262236\pi$
$602$	−6.31742e12	−1.96045
$603$	−3.11243e12	−0.958675
$604$	−4.94177e11	−0.151083
$605$	−2.19694e12	−0.666683
$606$	−3.33942e12	−1.00588
$607$	1.73690e12	0.519310	0.259655	−	0.965701i	$-0.416391\pi$
$607$	1.73690e12	0.519310	0.259655	+	0.965701i	$0.416391\pi$
$608$	2.94982e11	0.0875447
$609$	−1.63124e12	−0.480552
$610$	5.85078e11	0.171092
$611$	−3.72441e11	−0.108112
$612$	3.38189e12	0.974492
$613$	4.02259e12	1.15062	0.575312	−	0.817934i	$-0.304881\pi$
$613$	4.02259e12	1.15062	0.575312	+	0.817934i	$0.304881\pi$
$614$	−3.20744e12	−0.910752
$615$	−2.66267e12	−0.750551
$616$	3.20815e12	0.897722
$617$	−5.03083e12	−1.39752	−0.698758	−	0.715358i	$-0.746263\pi$
$617$	−5.03083e12	−1.39752	−0.698758	+	0.715358i	$0.746263\pi$
$618$	−8.55736e11	−0.235989
$619$	−4.77626e12	−1.30761	−0.653807	−	0.756661i	$-0.726829\pi$
$619$	−4.77626e12	−1.30761	−0.653807	+	0.756661i	$0.726829\pi$
$620$	5.42983e11	0.147579
$621$	−2.99269e12	−0.807513
$622$	3.55510e12	0.952348
$623$	−3.04582e12	−0.810044
$624$	−1.31542e12	−0.347324
$625$	−4.50842e12	−1.18186
$626$	−1.20066e12	−0.312489
$627$	8.15198e11	0.210649
$628$	−1.15813e12	−0.297125
$629$	−7.78864e12	−1.98396
$630$	−1.10002e13	−2.78207
$631$	−3.04417e12	−0.764428	−0.382214	−	0.924074i	$-0.624838\pi$
$631$	−3.04417e12	−0.764428	−0.382214	+	0.924074i	$0.624838\pi$
$632$	5.81521e12	1.44990
$633$	9.17549e12	2.27150
$634$	9.36884e11	0.230295
$635$	9.87734e11	0.241078
$636$	7.49579e11	0.181660
$637$	8.28989e11	0.199490
$638$	4.74081e11	0.113282
$639$	1.14298e12	0.271198
$640$	2.35337e12	0.554473
$641$	−1.53417e12	−0.358932	−0.179466	−	0.983764i	$-0.557437\pi$
$641$	−1.53417e12	−0.358932	−0.179466	+	0.983764i	$0.557437\pi$
$642$	6.10854e12	1.41915
$643$	3.17074e12	0.731494	0.365747	−	0.930714i	$-0.380814\pi$
$643$	3.17074e12	0.731494	0.365747	+	0.930714i	$0.380814\pi$
$644$	−5.24624e11	−0.120188
$645$	1.49878e13	3.40971
$646$	−1.33024e12	−0.300527
$647$	−6.75140e12	−1.51469	−0.757347	−	0.653013i	$-0.773505\pi$
$647$	−6.75140e12	−1.51469	−0.757347	+	0.653013i	$0.773505\pi$
$648$	−7.75255e12	−1.72726
$649$	5.03517e12	1.11407
$650$	2.62829e11	0.0577516
$651$	5.91027e12	1.28971
$652$	−4.58544e11	−0.0993726
$653$	−3.96591e12	−0.853559	−0.426780	−	0.904356i	$-0.640352\pi$
$653$	−3.96591e12	−0.853559	−0.426780	+	0.904356i	$0.640352\pi$
$654$	−5.16016e12	−1.10297
$655$	−8.84520e12	−1.87768
$656$	1.25654e12	0.264916
$657$	1.04563e13	2.18945
$658$	2.14166e12	0.445384
$659$	−1.08932e12	−0.224993	−0.112497	−	0.993652i	$-0.535885\pi$
$659$	−1.08932e12	−0.224993	−0.112497	+	0.993652i	$0.535885\pi$
$660$	−1.47639e12	−0.302867
$661$	−9.01775e12	−1.83735	−0.918674	−	0.395017i	$-0.870739\pi$
$661$	−9.01775e12	−1.83735	−0.918674	+	0.395017i	$0.870739\pi$
$662$	−1.76716e12	−0.357615
$663$	−4.56030e12	−0.916606
$664$	−6.84667e12	−1.36686
$665$	−1.37130e12	−0.271916
$666$	1.03730e13	2.04302
$667$	−3.99667e11	−0.0781865
$668$	5.52759e11	0.107409
$669$	1.55894e13	3.00893
$670$	−2.21721e12	−0.425079
$671$	5.86587e11	0.111707
$672$	−5.81506e12	−1.10000
$673$	6.77812e12	1.27362	0.636812	−	0.771019i	$-0.280253\pi$
$673$	6.77812e12	1.27362	0.636812	+	0.771019i	$0.280253\pi$
$674$	4.05683e12	0.757211
$675$	2.73240e12	0.506613
$676$	−1.00512e11	−0.0185122
$677$	−9.77011e12	−1.78752	−0.893759	−	0.448548i	$-0.851941\pi$
$677$	−9.77011e12	−1.78752	−0.893759	+	0.448548i	$0.851941\pi$
$678$	−5.80274e12	−1.05463
$679$	−8.32035e11	−0.150220
$680$	1.24199e13	2.22755
$681$	1.00325e13	1.78750
$682$	−1.71768e12	−0.304027
$683$	7.99180e12	1.40524	0.702621	−	0.711564i	$-0.252013\pi$
$683$	7.99180e12	1.40524	0.702621	+	0.711564i	$0.252013\pi$
$684$	−5.61483e11	−0.0980809
$685$	6.95597e12	1.20712
$686$	1.86053e12	0.320758
$687$	1.15626e13	1.98040
$688$	−7.07285e12	−1.20350
$689$	−6.93664e11	−0.117264
$690$	−3.92719e12	−0.659571
$691$	−7.13265e12	−1.19014	−0.595072	−	0.803672i	$-0.702877\pi$
$691$	−7.13265e12	−1.19014	−0.595072	+	0.803672i	$0.702877\pi$
$692$	2.08589e12	0.345791
$693$	−1.10286e13	−1.81643
$694$	6.72982e12	1.10125
$695$	−1.34291e13	−2.18331
$696$	−2.45290e12	−0.396222
$697$	4.35616e12	0.699127
$698$	−8.18974e12	−1.30593
$699$	−7.06456e12	−1.11928
$700$	4.78994e11	0.0754031
$701$	1.19764e13	1.87325	0.936626	−	0.350330i	$-0.113931\pi$
$701$	1.19764e13	1.87325	0.936626	+	0.350330i	$0.113931\pi$
$702$	3.29704e12	0.512398
$703$	1.29312e12	0.199683
$704$	4.58507e12	0.703507
$705$	−5.08099e12	−0.774635
$706$	−1.97767e12	−0.299594
$707$	5.63196e12	0.847759
$708$	−5.05347e12	−0.755858
$709$	−6.13692e12	−0.912099	−0.456050	−	0.889954i	$-0.650736\pi$
$709$	−6.13692e12	−0.912099	−0.456050	+	0.889954i	$0.650736\pi$
$710$	8.14229e11	0.120250
$711$	−1.99908e13	−2.93371
$712$	−4.58002e12	−0.667893
$713$	1.44806e12	0.209838
$714$	2.62233e13	3.77612
$715$	1.36626e12	0.195504
$716$	−1.51713e12	−0.215733
$717$	1.98861e12	0.281004
$718$	−6.62226e12	−0.929922
$719$	4.74258e12	0.661812	0.330906	−	0.943664i	$-0.392646\pi$
$719$	4.74258e12	0.661812	0.330906	+	0.943664i	$0.392646\pi$
$720$	−1.23156e13	−1.70788
$721$	1.44321e12	0.198893
$722$	−6.14177e12	−0.841155
$723$	−1.08475e13	−1.47641
$724$	3.00339e12	0.406245
$725$	3.64905e11	0.0490523
$726$	−6.97510e12	−0.931827
$727$	−9.67795e12	−1.28493	−0.642464	−	0.766316i	$-0.722088\pi$
$727$	−9.67795e12	−1.28493	−0.642464	+	0.766316i	$0.722088\pi$
$728$	2.97963e12	0.393162
$729$	−2.21347e12	−0.290268
$730$	7.44878e12	0.970806
$731$	−2.45201e13	−3.17610
$732$	−5.88719e11	−0.0757894
$733$	1.50341e13	1.92357	0.961787	−	0.273798i	$-0.0882801\pi$
$733$	1.50341e13	1.92357	0.961787	+	0.273798i	$0.0882801\pi$
$734$	6.76810e12	0.860666
$735$	1.13094e13	1.42937
$736$	−1.42474e12	−0.178972
$737$	−2.22293e12	−0.277537
$738$	−5.80160e12	−0.719937
$739$	−2.14842e12	−0.264983	−0.132492	−	0.991184i	$-0.542298\pi$
$739$	−2.14842e12	−0.264983	−0.132492	+	0.991184i	$0.542298\pi$
$740$	−2.34194e12	−0.287100
$741$	7.57131e11	0.0922548
$742$	3.98881e12	0.483087
$743$	5.22310e12	0.628751	0.314376	−	0.949299i	$-0.398205\pi$
$743$	5.22310e12	0.628751	0.314376	+	0.949299i	$0.398205\pi$
$744$	8.88730e12	1.06339
$745$	−1.07122e13	−1.27402
$746$	−6.32035e12	−0.747165
$747$	2.35366e13	2.76567
$748$	2.41538e12	0.282116
$749$	−1.03021e13	−1.19607
$750$	−1.14198e13	−1.31790
$751$	1.65523e13	1.89880	0.949399	−	0.314071i	$-0.101693\pi$
$751$	1.65523e13	1.89880	0.949399	+	0.314071i	$0.101693\pi$
$752$	2.39776e12	0.273417
$753$	8.72786e12	0.989305
$754$	4.40312e11	0.0496123
$755$	6.23886e12	0.698786
$756$	6.00870e12	0.669010
$757$	1.59809e13	1.76877	0.884384	−	0.466761i	$-0.154579\pi$
$757$	1.59809e13	1.76877	0.884384	+	0.466761i	$0.154579\pi$
$758$	1.10247e13	1.21298
$759$	−3.93733e12	−0.430639
$760$	−2.06203e12	−0.224199
$761$	3.31655e12	0.358473	0.179236	−	0.983806i	$-0.442637\pi$
$761$	3.31655e12	0.358473	0.179236	+	0.983806i	$0.442637\pi$
$762$	3.13597e12	0.336957
$763$	8.70266e12	0.929591
$764$	1.06916e12	0.113533
$765$	−4.26955e13	−4.50719
$766$	−2.25092e12	−0.236227
$767$	4.67651e12	0.487914
$768$	−1.16497e13	−1.20834
$769$	−2.26842e12	−0.233913	−0.116956	−	0.993137i	$-0.537314\pi$
$769$	−2.26842e12	−0.233913	−0.116956	+	0.993137i	$0.537314\pi$
$770$	−7.85644e12	−0.805411
$771$	1.54583e13	1.57549
$772$	2.87723e12	0.291539
$773$	1.45998e13	1.47075	0.735375	−	0.677661i	$-0.237006\pi$
$773$	1.45998e13	1.47075	0.735375	+	0.677661i	$0.237006\pi$
$774$	3.26563e13	3.27064
$775$	−1.32212e12	−0.131647
$776$	−1.25113e12	−0.123859
$777$	−2.54916e13	−2.50901
$778$	−2.18634e12	−0.213949
$779$	−7.23237e11	−0.0703659
$780$	−1.37122e12	−0.132642
$781$	8.16330e11	0.0785120
$782$	6.42492e12	0.614380
$783$	4.57752e12	0.435214
$784$	−5.33700e12	−0.504516
$785$	1.46211e13	1.37425
$786$	−2.80828e13	−2.62445
$787$	−1.26923e13	−1.17938	−0.589692	−	0.807628i	$-0.700751\pi$
$787$	−1.26923e13	−1.17938	−0.589692	+	0.807628i	$0.700751\pi$
$788$	3.23237e11	0.0298643
$789$	−4.47249e12	−0.410869
$790$	−1.42409e13	−1.30081
$791$	9.78638e12	0.888849
$792$	−1.65837e13	−1.49768
$793$	5.44804e11	0.0489228
$794$	4.56831e12	0.407909
$795$	−9.46324e12	−0.840210
$796$	−1.03105e12	−0.0910270
$797$	−1.22392e13	−1.07446	−0.537230	−	0.843436i	$-0.680529\pi$
$797$	−1.22392e13	−1.07446	−0.537230	+	0.843436i	$0.680529\pi$
$798$	−4.35376e12	−0.380059
$799$	8.31254e12	0.721561
$800$	1.30082e12	0.112282
$801$	1.57446e13	1.35140
$802$	1.07358e12	0.0916328
$803$	7.46801e12	0.633847
$804$	2.23101e12	0.188299
$805$	6.62325e12	0.555891
$806$	−1.59533e12	−0.133150
$807$	−1.31351e13	−1.09019
$808$	8.46880e12	0.698990
$809$	−4.89425e12	−0.401714	−0.200857	−	0.979621i	$-0.564373\pi$
$809$	−4.89425e12	−0.401714	−0.200857	+	0.979621i	$0.564373\pi$
$810$	1.89852e13	1.54965
$811$	−3.11178e12	−0.252590	−0.126295	−	0.991993i	$-0.540309\pi$
$811$	−3.11178e12	−0.252590	−0.126295	+	0.991993i	$0.540309\pi$
$812$	8.02449e11	0.0647761
$813$	−1.26238e13	−1.01341
$814$	7.40853e12	0.591456
$815$	5.78900e12	0.459615
$816$	2.93590e13	2.31812
$817$	4.07098e12	0.319669
$818$	4.64926e12	0.363073
$819$	−1.02430e13	−0.795517
$820$	1.30984e12	0.101171
$821$	3.48502e12	0.267708	0.133854	−	0.991001i	$-0.457265\pi$
$821$	3.48502e12	0.267708	0.133854	+	0.991001i	$0.457265\pi$
$822$	2.20846e13	1.68720
$823$	−4.38954e12	−0.333518	−0.166759	−	0.985998i	$-0.553330\pi$
$823$	−4.38954e12	−0.333518	−0.166759	+	0.985998i	$0.553330\pi$
$824$	2.17016e12	0.163990
$825$	3.59487e12	0.270172
$826$	−2.68916e13	−2.01004
$827$	−1.21660e13	−0.904424	−0.452212	−	0.891910i	$-0.649365\pi$
$827$	−1.21660e13	−0.904424	−0.452212	+	0.891910i	$0.649365\pi$
$828$	2.71191e12	0.200511
$829$	−1.35524e12	−0.0996600	−0.0498300	−	0.998758i	$-0.515868\pi$
$829$	−1.35524e12	−0.0996600	−0.0498300	+	0.998758i	$0.515868\pi$
$830$	1.67668e13	1.22631
$831$	−3.97453e13	−2.89122
$832$	4.25847e12	0.308105
$833$	−1.85023e13	−1.33144
$834$	−4.26362e13	−3.05163
$835$	−6.97845e12	−0.496786
$836$	−4.01017e11	−0.0283945
$837$	−1.65852e13	−1.16803
$838$	1.07192e13	0.750872
$839$	−1.12215e13	−0.781847	−0.390924	−	0.920423i	$-0.627844\pi$
$839$	−1.12215e13	−0.781847	−0.390924	+	0.920423i	$0.627844\pi$
$840$	4.06493e13	2.81706
$841$	−1.38958e13	−0.957861
$842$	5.33601e12	0.365858
$843$	7.62799e12	0.520219
$844$	−4.51366e12	−0.306188
$845$	1.26894e12	0.0856218
$846$	−1.10708e13	−0.743038
$847$	1.17636e13	0.785351
$848$	4.46578e12	0.296563
$849$	1.05599e13	0.697551
$850$	−5.86610e12	−0.385447
$851$	−6.24564e12	−0.408220
$852$	−8.19297e11	−0.0532676
$853$	7.91778e11	0.0512074	0.0256037	−	0.999672i	$-0.491849\pi$
$853$	7.91778e11	0.0512074	0.0256037	+	0.999672i	$0.491849\pi$
$854$	−3.13281e12	−0.201546
$855$	7.08858e12	0.453640
$856$	−1.54913e13	−0.986180
$857$	1.76782e13	1.11950	0.559751	−	0.828661i	$-0.310897\pi$
$857$	1.76782e13	1.11950	0.559751	+	0.828661i	$0.310897\pi$
$858$	4.33774e12	0.273257
$859$	4.03561e12	0.252895	0.126448	−	0.991973i	$-0.459642\pi$
$859$	4.03561e12	0.252895	0.126448	+	0.991973i	$0.459642\pi$
$860$	−7.37286e12	−0.459614
$861$	1.42573e13	0.884147
$862$	−2.12068e13	−1.30826
$863$	−7.74540e11	−0.0475330	−0.0237665	−	0.999718i	$-0.507566\pi$
$863$	−7.74540e11	−0.0475330	−0.0237665	+	0.999718i	$0.507566\pi$
$864$	1.63180e13	0.996219
$865$	−2.63338e13	−1.59934
$866$	−5.18739e12	−0.313414
$867$	7.20780e13	4.33228
$868$	−2.90741e12	−0.173847
$869$	−1.42776e13	−0.849311
$870$	6.00691e12	0.355479
$871$	−2.06459e12	−0.121549
$872$	1.30862e13	0.766461
$873$	4.30099e12	0.250613
$874$	−1.06671e12	−0.0618363
$875$	1.92596e13	1.11073
$876$	−7.49515e12	−0.430043
$877$	−2.57530e13	−1.47004	−0.735020	−	0.678046i	$-0.762827\pi$
$877$	−2.57530e13	−1.47004	−0.735020	+	0.678046i	$0.762827\pi$
$878$	−1.61693e13	−0.918261
$879$	2.43839e13	1.37770
$880$	−8.79590e12	−0.494434
$881$	1.93336e12	0.108124	0.0540620	−	0.998538i	$-0.482783\pi$
$881$	1.93336e12	0.108124	0.0540620	+	0.998538i	$0.482783\pi$
$882$	2.46416e13	1.37107
$883$	2.94334e13	1.62936	0.814681	−	0.579910i	$-0.196912\pi$
$883$	2.94334e13	1.62936	0.814681	+	0.579910i	$0.196912\pi$
$884$	2.24333e12	0.123554
$885$	6.37988e13	3.49597
$886$	−3.50928e11	−0.0191323
$887$	4.07138e12	0.220844	0.110422	−	0.993885i	$-0.464780\pi$
$887$	4.07138e12	0.220844	0.110422	+	0.993885i	$0.464780\pi$
$888$	−3.83318e13	−2.06872
$889$	−5.28884e12	−0.283990
$890$	1.12160e13	0.599215
$891$	1.90342e13	1.01178
$892$	−7.66881e12	−0.405589
$893$	−1.38010e12	−0.0726238
$894$	−3.40103e13	−1.78070
$895$	1.91534e13	0.997799
$896$	−1.26012e13	−0.653168
$897$	−3.65687e12	−0.188601
$898$	2.28473e13	1.17244
$899$	−2.21491e12	−0.113094
$900$	−2.47604e12	−0.125796
$901$	1.54819e13	0.782643
$902$	−4.14356e12	−0.208422
$903$	−8.02523e13	−4.01664
$904$	1.47158e13	0.732869
$905$	−3.79170e13	−1.87895
$906$	1.98078e13	0.976698
$907$	−5.11710e12	−0.251068	−0.125534	−	0.992089i	$-0.540064\pi$
$907$	−5.11710e12	−0.251068	−0.125534	+	0.992089i	$0.540064\pi$
$908$	−4.93522e12	−0.240946
$909$	−2.91130e13	−1.41432
$910$	−7.29682e12	−0.352734
$911$	−1.65675e13	−0.796937	−0.398468	−	0.917182i	$-0.630458\pi$
$911$	−1.65675e13	−0.796937	−0.398468	+	0.917182i	$0.630458\pi$
$912$	−4.87438e12	−0.233315
$913$	1.68101e13	0.800665
$914$	−1.82108e13	−0.863121
$915$	7.43243e12	0.350539
$916$	−5.68796e12	−0.266948
$917$	4.73618e13	2.21191
$918$	−7.35868e13	−3.41986
$919$	2.46210e13	1.13864	0.569319	−	0.822117i	$-0.307207\pi$
$919$	2.46210e13	1.13864	0.569319	+	0.822117i	$0.307207\pi$
$920$	9.95940e12	0.458340
$921$	−4.07451e13	−1.86598
$922$	1.24757e13	0.568558
$923$	7.58182e11	0.0343848
$924$	7.90534e12	0.356777
$925$	5.70242e12	0.256107
$926$	4.23153e12	0.189125
$927$	−7.46028e12	−0.331815
$928$	2.17923e12	0.0964577
$929$	2.10967e13	0.929272	0.464636	−	0.885502i	$-0.346185\pi$
$929$	2.10967e13	0.929272	0.464636	+	0.885502i	$0.346185\pi$
$930$	−2.17641e13	−0.954041
$931$	3.07186e12	0.134007
$932$	3.47524e12	0.150873
$933$	4.51616e13	1.95120
$934$	1.08431e13	0.466223
$935$	−3.04935e13	−1.30484
$936$	−1.54024e13	−0.655915
$937$	−3.29230e13	−1.39531	−0.697656	−	0.716433i	$-0.745774\pi$
$937$	−3.29230e13	−1.39531	−0.697656	+	0.716433i	$0.745774\pi$
$938$	1.18721e13	0.500742
$939$	−1.52523e13	−0.640238
$940$	2.49947e12	0.104417
$941$	3.85496e13	1.60275	0.801376	−	0.598161i	$-0.204102\pi$
$941$	3.85496e13	1.60275	0.801376	+	0.598161i	$0.204102\pi$
$942$	4.64208e13	1.92080
$943$	3.49316e12	0.143852
$944$	−3.01072e13	−1.23395
$945$	−7.58583e13	−3.09428
$946$	2.33234e13	0.946852
$947$	1.22394e13	0.494521	0.247261	−	0.968949i	$-0.420470\pi$
$947$	1.22394e13	0.494521	0.247261	+	0.968949i	$0.420470\pi$
$948$	1.43295e13	0.576227
$949$	6.93605e12	0.277597
$950$	9.73928e11	0.0387945
$951$	1.19015e13	0.471836
$952$	−6.65026e13	−2.62405
$953$	3.26425e13	1.28194	0.640968	−	0.767568i	$-0.278533\pi$
$953$	3.26425e13	1.28194	0.640968	+	0.767568i	$0.278533\pi$
$954$	−2.06191e13	−0.805939
$955$	−1.34978e13	−0.525108
$956$	−9.78247e11	−0.0378781
$957$	6.02241e12	0.232095
$958$	3.17143e13	1.21649
$959$	−3.72459e13	−1.42198
$960$	5.80957e13	2.20761
$961$	−1.84146e13	−0.696478
$962$	6.88081e12	0.259031
$963$	5.32540e13	1.99542
$964$	5.33614e12	0.199013
$965$	−3.63243e13	−1.34842
$966$	2.10282e13	0.776973
$967$	−1.28552e13	−0.472780	−0.236390	−	0.971658i	$-0.575964\pi$
$967$	−1.28552e13	−0.472780	−0.236390	+	0.971658i	$0.575964\pi$
$968$	1.76889e13	0.647533
$969$	−1.68984e13	−0.615729
$970$	3.06390e12	0.111122
$971$	−4.30846e13	−1.55538	−0.777689	−	0.628650i	$-0.783608\pi$
$971$	−4.30846e13	−1.55538	−0.777689	+	0.628650i	$0.783608\pi$
$972$	−4.90435e12	−0.176231
$973$	7.19064e13	2.57193
$974$	−2.76105e13	−0.983012
$975$	3.33880e12	0.118323
$976$	−3.50743e12	−0.123727
$977$	3.58870e13	1.26012	0.630059	−	0.776547i	$-0.283031\pi$
$977$	3.58870e13	1.26012	0.630059	+	0.776547i	$0.283031\pi$
$978$	1.83796e13	0.642407
$979$	1.12449e13	0.391233
$980$	−5.56338e12	−0.192673
$981$	−4.49861e13	−1.55084
$982$	2.58840e13	0.888239
$983$	4.49637e12	0.153593	0.0767964	−	0.997047i	$-0.475531\pi$
$983$	4.49637e12	0.153593	0.0767964	+	0.997047i	$0.475531\pi$
$984$	2.14388e13	0.728992
$985$	−4.08078e12	−0.138128
$986$	−9.82735e12	−0.331124
$987$	2.72062e13	0.912518
$988$	−3.72452e11	−0.0124355
$989$	−1.96624e13	−0.653513
$990$	4.06118e13	1.34367
$991$	1.56221e13	0.514526	0.257263	−	0.966341i	$-0.417179\pi$
$991$	1.56221e13	0.514526	0.257263	+	0.966341i	$0.417179\pi$
$992$	−7.89573e12	−0.258875
$993$	−2.24488e13	−0.732693
$994$	−4.35981e12	−0.141654
$995$	1.30167e13	0.421015
$996$	−1.68712e13	−0.543223
$997$	−3.76783e13	−1.20771	−0.603856	−	0.797094i	$-0.706370\pi$
$997$	−3.76783e13	−1.20771	−0.603856	+	0.797094i	$0.706370\pi$
$998$	−6.90603e12	−0.220364
$999$	7.15335e13	2.27230

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.10.a.b.1.4	✓	5
3.2	odd	2		117.10.a.e.1.2		5
4.3	odd	2		208.10.a.h.1.1		5
5.4	even	2		325.10.a.b.1.2		5
13.12	even	2		169.10.a.b.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.10.a.b.1.4	✓	5	1.1	even	1	trivial
117.10.a.e.1.2		5	3.2	odd	2
169.10.a.b.1.2		5	13.12	even	2
208.10.a.h.1.1		5	4.3	odd	2
325.10.a.b.1.2		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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+19.7176 q^{2} +250.479 q^{3} -123.217 q^{4} +1555.58 q^{5} +4938.84 q^{6} -8329.39 q^{7} -12524.9 q^{8} +43056.6 q^{9} +30672.3 q^{10} +30751.5 q^{11} -30863.2 q^{12} +28561.0 q^{13} -164236. q^{14} +389640. q^{15} -183875. q^{16} -637455. q^{17} +848973. q^{18} +105834. q^{19} -191674. q^{20} -2.08634e6 q^{21} +606345. q^{22} -511169. q^{23} -3.13723e6 q^{24} +466710. q^{25} +563154. q^{26} +5.85460e6 q^{27} +1.02632e6 q^{28} +781868. q^{29} +7.68276e6 q^{30} -2.83285e6 q^{31} +2.78721e6 q^{32} +7.70259e6 q^{33} -1.25691e7 q^{34} -1.29571e7 q^{35} -5.30530e6 q^{36} +1.22183e7 q^{37} +2.08680e6 q^{38} +7.15392e6 q^{39} -1.94836e7 q^{40} -6.83367e6 q^{41} -4.11375e7 q^{42} +3.84656e7 q^{43} -3.78910e6 q^{44} +6.69781e7 q^{45} -1.00790e7 q^{46} -1.30402e7 q^{47} -4.60567e7 q^{48} +2.90252e7 q^{49} +9.20238e6 q^{50} -1.59669e8 q^{51} -3.51920e6 q^{52} -2.42871e7 q^{53} +1.15439e8 q^{54} +4.78364e7 q^{55} +1.04325e8 q^{56} +2.65092e7 q^{57} +1.54166e7 q^{58} +1.63738e8 q^{59} -4.80103e7 q^{60} +1.90751e7 q^{61} -5.58569e7 q^{62} -3.58636e8 q^{63} +1.49101e8 q^{64} +4.44290e7 q^{65} +1.51876e8 q^{66} -7.22869e7 q^{67} +7.85452e7 q^{68} -1.28037e8 q^{69} -2.55482e8 q^{70} +2.65461e7 q^{71} -5.39282e8 q^{72} +2.42850e8 q^{73} +2.40916e8 q^{74} +1.16901e8 q^{75} -1.30406e7 q^{76} -2.56141e8 q^{77} +1.41058e8 q^{78} -4.64290e8 q^{79} -2.86032e8 q^{80} +6.18969e8 q^{81} -1.34744e8 q^{82} +5.46643e8 q^{83} +2.57072e8 q^{84} -9.91613e8 q^{85} +7.58449e8 q^{86} +1.95841e8 q^{87} -3.85160e8 q^{88} +3.65672e8 q^{89} +1.32065e9 q^{90} -2.37896e8 q^{91} +6.29847e7 q^{92} -7.09568e8 q^{93} -2.57121e8 q^{94} +1.64634e8 q^{95} +6.98137e8 q^{96} +9.98914e7 q^{97} +5.72307e8 q^{98} +1.32405e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 15 q^{2} + 161 q^{3} + 361 q^{4} + 1803 q^{5} + 5693 q^{6} + 10099 q^{7} + 23151 q^{8} + 61060 q^{9} + 84505 q^{10} + 121746 q^{11} + 113389 q^{12} + 142805 q^{13} + 8475 q^{14} + 105973 q^{15} - 322463 q^{16}+ \cdots + 3016199848 q^{99}+O(q^{100}) \) 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

Groups

Database

Properties

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