LMFDB - Embedded newform 325.10.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,10,Mod(1,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("325.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	325.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:	$167.386646753$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 1602x^{2} + 1544x + 342272 $ x^4 - x^3 - 1602x^2 + 1544x + 342272
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 13)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-15.3567$ of defining polynomial
Character	$\chi$	$=$	325.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-7.35673 q^{2} -42.6243 q^{3} -457.879 q^{4} +313.575 q^{6} -892.010 q^{7} +7135.13 q^{8} -17866.2 q^{9} +O(q^{10})$	\(q-7.35673 q^{2} -42.6243 q^{3} -457.879 q^{4} +313.575 q^{6} -892.010 q^{7} +7135.13 q^{8} -17866.2 q^{9} -27149.8 q^{11} +19516.8 q^{12} +28561.0 q^{13} +6562.27 q^{14} +181943. q^{16} +34643.4 q^{17} +131437. q^{18} +428885. q^{19} +38021.3 q^{21} +199734. q^{22} -2.03704e6 q^{23} -304130. q^{24} -210115. q^{26} +1.60051e6 q^{27} +408432. q^{28} -5.26400e6 q^{29} -4.15910e6 q^{31} -4.99169e6 q^{32} +1.15724e6 q^{33} -254862. q^{34} +8.18054e6 q^{36} +7.58854e6 q^{37} -3.15519e6 q^{38} -1.21739e6 q^{39} -4.92536e6 q^{41} -279712. q^{42} -1.71882e7 q^{43} +1.24313e7 q^{44} +1.49859e7 q^{46} +2.95568e7 q^{47} -7.75518e6 q^{48} -3.95579e7 q^{49} -1.47665e6 q^{51} -1.30775e7 q^{52} +2.72331e7 q^{53} -1.17745e7 q^{54} -6.36461e6 q^{56} -1.82809e7 q^{57} +3.87258e7 q^{58} -1.13602e8 q^{59} -3.76868e7 q^{61} +3.05973e7 q^{62} +1.59368e7 q^{63} -5.64321e7 q^{64} -8.51352e6 q^{66} -1.90094e8 q^{67} -1.58625e7 q^{68} +8.68273e7 q^{69} +6.87130e7 q^{71} -1.27477e8 q^{72} -3.61495e8 q^{73} -5.58268e7 q^{74} -1.96377e8 q^{76} +2.42179e7 q^{77} +8.95603e6 q^{78} -1.42229e8 q^{79} +2.83439e8 q^{81} +3.62346e7 q^{82} +5.80240e7 q^{83} -1.74091e7 q^{84} +1.26449e8 q^{86} +2.24374e8 q^{87} -1.93718e8 q^{88} -8.59928e8 q^{89} -2.54767e7 q^{91} +9.32716e8 q^{92} +1.77279e8 q^{93} -2.17442e8 q^{94} +2.12767e8 q^{96} -1.46970e9 q^{97} +2.91017e8 q^{98} +4.85064e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 33 q^{2} + 163 q^{3} + 1429 q^{4} - 4529 q^{6} + 11241 q^{7} + 45543 q^{8} - 29953 q^{9}+O(q^{10}) $ 4 * q + 33 * q^2 + 163 * q^3 + 1429 * q^4 - 4529 * q^6 + 11241 * q^7 + 45543 * q^8 - 29953 * q^9	\( 4 q + 33 q^{2} + 163 q^{3} + 1429 q^{4} - 4529 q^{6} + 11241 q^{7} + 45543 q^{8} - 29953 q^{9} - 40140 q^{11} + 155479 q^{12} + 114244 q^{13} - 277653 q^{14} + 726609 q^{16} - 78717 q^{17} - 1691026 q^{18} + 209664 q^{19} + 1138431 q^{21} - 1364090 q^{22} + 4257444 q^{23} + 3561573 q^{24} + 942513 q^{26} + 2077801 q^{27} - 4035181 q^{28} - 1647936 q^{29} - 11366002 q^{31} + 29458959 q^{32} + 14413222 q^{33} + 26257659 q^{34} - 11587714 q^{36} - 4636891 q^{37} - 25172466 q^{38} + 4655443 q^{39} + 13859538 q^{41} - 75564923 q^{42} + 33368081 q^{43} + 66489222 q^{44} + 71369332 q^{46} + 3943005 q^{47} + 620787 q^{48} + 23294923 q^{49} - 19664471 q^{51} + 40813669 q^{52} + 171019326 q^{53} - 64946915 q^{54} - 281552967 q^{56} + 47829030 q^{57} - 79964734 q^{58} - 63389388 q^{59} + 77050190 q^{61} + 95878740 q^{62} + 155695476 q^{63} + 768962465 q^{64} - 42396374 q^{66} + 41174072 q^{67} + 717615423 q^{68} + 546642556 q^{69} + 252460989 q^{71} - 562579254 q^{72} - 594415068 q^{73} - 957058539 q^{74} - 326897170 q^{76} - 561950454 q^{77} - 129352769 q^{78} + 115998984 q^{79} + 437803700 q^{81} + 875148240 q^{82} + 79577862 q^{83} + 108899441 q^{84} - 589924887 q^{86} + 1087526510 q^{87} + 2327564370 q^{88} - 1152240276 q^{89} + 321054201 q^{91} + 4213481460 q^{92} - 1618266556 q^{93} + 1859909503 q^{94} + 3171454029 q^{96} - 1049098084 q^{97} - 420532254 q^{98} + 2132181050 q^{99}+O(q^{100}) \) 4 * q + 33 * q^2 + 163 * q^3 + 1429 * q^4 - 4529 * q^6 + 11241 * q^7 + 45543 * q^8 - 29953 * q^9 - 40140 * q^11 + 155479 * q^12 + 114244 * q^13 - 277653 * q^14 + 726609 * q^16 - 78717 * q^17 - 1691026 * q^18 + 209664 * q^19 + 1138431 * q^21 - 1364090 * q^22 + 4257444 * q^23 + 3561573 * q^24 + 942513 * q^26 + 2077801 * q^27 - 4035181 * q^28 - 1647936 * q^29 - 11366002 * q^31 + 29458959 * q^32 + 14413222 * q^33 + 26257659 * q^34 - 11587714 * q^36 - 4636891 * q^37 - 25172466 * q^38 + 4655443 * q^39 + 13859538 * q^41 - 75564923 * q^42 + 33368081 * q^43 + 66489222 * q^44 + 71369332 * q^46 + 3943005 * q^47 + 620787 * q^48 + 23294923 * q^49 - 19664471 * q^51 + 40813669 * q^52 + 171019326 * q^53 - 64946915 * q^54 - 281552967 * q^56 + 47829030 * q^57 - 79964734 * q^58 - 63389388 * q^59 + 77050190 * q^61 + 95878740 * q^62 + 155695476 * q^63 + 768962465 * q^64 - 42396374 * q^66 + 41174072 * q^67 + 717615423 * q^68 + 546642556 * q^69 + 252460989 * q^71 - 562579254 * q^72 - 594415068 * q^73 - 957058539 * q^74 - 326897170 * q^76 - 561950454 * q^77 - 129352769 * q^78 + 115998984 * q^79 + 437803700 * q^81 + 875148240 * q^82 + 79577862 * q^83 + 108899441 * q^84 - 589924887 * q^86 + 1087526510 * q^87 + 2327564370 * q^88 - 1152240276 * q^89 + 321054201 * q^91 + 4213481460 * q^92 - 1618266556 * q^93 + 1859909503 * q^94 + 3171454029 * q^96 - 1049098084 * q^97 - 420532254 * q^98 + 2132181050 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−7.35673	−0.325124	−0.162562	−	0.986698i	$-0.551976\pi$
$2$	−7.35673	−0.325124	−0.162562	+	0.986698i	$0.551976\pi$
$3$	−42.6243	−0.303817	−0.151908	−	0.988395i	$-0.548542\pi$
$3$	−42.6243	−0.303817	−0.151908	+	0.988395i	$0.548542\pi$
$4$	−457.879	−0.894294
$5$	0	0
$5$	0	0
$6$	313.575	0.0987782
$7$	−892.010	−0.140420	−0.0702099	−	0.997532i	$-0.522367\pi$
$7$	−892.010	−0.140420	−0.0702099	+	0.997532i	$0.522367\pi$
$8$	7135.13	0.615881
$9$	−17866.2	−0.907695
$10$	0	0
$11$	−27149.8	−0.559114	−0.279557	−	0.960129i	$-0.590188\pi$
$11$	−27149.8	−0.559114	−0.279557	+	0.960129i	$0.590188\pi$
$12$	19516.8	0.271702
$13$	28561.0	0.277350
$13$	28561.0	0.277350
$14$	6562.27	0.0456539
$15$	0	0
$16$	181943.	0.694056
$17$	34643.4	0.100601	0.0503003	−	0.998734i	$-0.483982\pi$
$17$	34643.4	0.100601	0.0503003	+	0.998734i	$0.483982\pi$
$18$	131437.	0.295114
$19$	428885.	0.755004	0.377502	−	0.926009i	$-0.376783\pi$
$19$	428885.	0.755004	0.377502	+	0.926009i	$0.376783\pi$
$20$	0	0
$21$	38021.3	0.0426619
$22$	199734.	0.181782
$23$	−2.03704e6	−1.51783	−0.758916	−	0.651188i	$-0.774271\pi$
$23$	−2.03704e6	−1.51783	−0.758916	+	0.651188i	$0.774271\pi$
$24$	−304130.	−0.187115
$25$	0	0
$26$	−210115.	−0.0901733
$27$	1.60051e6	0.579590
$28$	408432.	0.125577
$29$	−5.26400e6	−1.38205	−0.691026	−	0.722830i	$-0.742841\pi$
$29$	−5.26400e6	−1.38205	−0.691026	+	0.722830i	$0.742841\pi$
$30$	0	0
$31$	−4.15910e6	−0.808856	−0.404428	−	0.914570i	$-0.632529\pi$
$31$	−4.15910e6	−0.808856	−0.404428	+	0.914570i	$0.632529\pi$
$32$	−4.99169e6	−0.841536
$33$	1.15724e6	0.169868
$34$	−254862.	−0.0327077
$35$	0	0
$36$	8.18054e6	0.811747
$37$	7.58854e6	0.665657	0.332829	−	0.942987i	$-0.391997\pi$
$37$	7.58854e6	0.665657	0.332829	+	0.942987i	$0.391997\pi$
$38$	−3.15519e6	−0.245470
$39$	−1.21739e6	−0.0842636
$40$	0	0
$41$	−4.92536e6	−0.272214	−0.136107	−	0.990694i	$-0.543459\pi$
$41$	−4.92536e6	−0.272214	−0.136107	+	0.990694i	$0.543459\pi$
$42$	−279712.	−0.0138704
$43$	−1.71882e7	−0.766696	−0.383348	−	0.923604i	$-0.625229\pi$
$43$	−1.71882e7	−0.766696	−0.383348	+	0.923604i	$0.625229\pi$
$44$	1.24313e7	0.500012
$45$	0	0
$46$	1.49859e7	0.493484
$47$	2.95568e7	0.883522	0.441761	−	0.897133i	$-0.354354\pi$
$47$	2.95568e7	0.883522	0.441761	+	0.897133i	$0.354354\pi$
$48$	−7.75518e6	−0.210866
$49$	−3.95579e7	−0.980282
$50$	0	0
$51$	−1.47665e6	−0.0305642
$52$	−1.30775e7	−0.248033
$53$	2.72331e7	0.474084	0.237042	−	0.971499i	$-0.423822\pi$
$53$	2.72331e7	0.474084	0.237042	+	0.971499i	$0.423822\pi$
$54$	−1.17745e7	−0.188439
$55$	0	0
$56$	−6.36461e6	−0.0864819
$57$	−1.82809e7	−0.229383
$58$	3.87258e7	0.449339
$59$	−1.13602e8	−1.22054	−0.610272	−	0.792192i	$-0.708940\pi$
$59$	−1.13602e8	−1.22054	−0.610272	+	0.792192i	$0.708940\pi$
$60$	0	0
$61$	−3.76868e7	−0.348502	−0.174251	−	0.984701i	$-0.555750\pi$
$61$	−3.76868e7	−0.348502	−0.174251	+	0.984701i	$0.555750\pi$
$62$	3.05973e7	0.262979
$63$	1.59368e7	0.127458
$64$	−5.64321e7	−0.420452
$65$	0	0
$66$	−8.51352e6	−0.0552283
$67$	−1.90094e8	−1.15247	−0.576237	−	0.817283i	$-0.695479\pi$
$67$	−1.90094e8	−1.15247	−0.576237	+	0.817283i	$0.695479\pi$
$68$	−1.58625e7	−0.0899666
$69$	8.68273e7	0.461143
$70$	0	0
$71$	6.87130e7	0.320905	0.160453	−	0.987044i	$-0.448705\pi$
$71$	6.87130e7	0.320905	0.160453	+	0.987044i	$0.448705\pi$
$72$	−1.27477e8	−0.559033
$73$	−3.61495e8	−1.48987	−0.744937	−	0.667135i	$-0.767520\pi$
$73$	−3.61495e8	−1.48987	−0.744937	+	0.667135i	$0.767520\pi$
$74$	−5.58268e7	−0.216421
$75$	0	0
$76$	−1.96377e8	−0.675196
$77$	2.42179e7	0.0785107
$78$	8.95603e6	0.0273962
$79$	−1.42229e8	−0.410834	−0.205417	−	0.978675i	$-0.565855\pi$
$79$	−1.42229e8	−0.410834	−0.205417	+	0.978675i	$0.565855\pi$
$80$	0	0
$81$	2.83439e8	0.731606
$82$	3.62346e7	0.0885035
$83$	5.80240e7	0.134201	0.0671006	−	0.997746i	$-0.478625\pi$
$83$	5.80240e7	0.134201	0.0671006	+	0.997746i	$0.478625\pi$
$84$	−1.74091e7	−0.0381523
$85$	0	0
$86$	1.26449e8	0.249272
$87$	2.24374e8	0.419891
$88$	−1.93718e8	−0.344348
$89$	−8.59928e8	−1.45280	−0.726402	−	0.687270i	$-0.758809\pi$
$89$	−8.59928e8	−1.45280	−0.726402	+	0.687270i	$0.758809\pi$
$90$	0	0
$91$	−2.54767e7	−0.0389454
$92$	9.32716e8	1.35739
$93$	1.77279e8	0.245744
$94$	−2.17442e8	−0.287255
$95$	0	0
$96$	2.12767e8	0.255673
$97$	−1.46970e9	−1.68560	−0.842802	−	0.538223i	$-0.819096\pi$
$97$	−1.46970e9	−1.68560	−0.842802	+	0.538223i	$0.819096\pi$
$98$	2.91017e8	0.318714
$99$	4.85064e8	0.507505
$100$	0	0
$101$	−4.15100e8	−0.396923	−0.198462	−	0.980109i	$-0.563595\pi$
$101$	−4.15100e8	−0.396923	−0.198462	+	0.980109i	$0.563595\pi$
$102$	1.08633e7	0.00993716
$103$	−1.86377e9	−1.63164	−0.815821	−	0.578305i	$-0.803714\pi$
$103$	−1.86377e9	−1.63164	−0.815821	+	0.578305i	$0.803714\pi$
$104$	2.03786e8	0.170815
$105$	0	0
$106$	−2.00346e8	−0.154136
$107$	7.50777e8	0.553712	0.276856	−	0.960911i	$-0.410707\pi$
$107$	7.50777e8	0.553712	0.276856	+	0.960911i	$0.410707\pi$
$108$	−7.32838e8	−0.518324
$109$	2.07010e9	1.40467	0.702333	−	0.711849i	$-0.252142\pi$
$109$	2.07010e9	1.40467	0.702333	+	0.711849i	$0.252142\pi$
$110$	0	0
$111$	−3.23456e8	−0.202238
$112$	−1.62295e8	−0.0974592
$113$	2.10155e9	1.21251	0.606257	−	0.795268i	$-0.292670\pi$
$113$	2.10155e9	1.21251	0.606257	+	0.795268i	$0.292670\pi$
$114$	1.34488e8	0.0745780
$115$	0	0
$116$	2.41027e9	1.23596
$117$	−5.10276e8	−0.251749
$118$	8.35741e8	0.396828
$119$	−3.09023e7	−0.0141263
$120$	0	0
$121$	−1.62083e9	−0.687392
$122$	2.77251e8	0.113306
$123$	2.09940e8	0.0827033
$124$	1.90436e9	0.723356
$125$	0	0
$126$	−1.17243e8	−0.0414398
$127$	4.77696e9	1.62943	0.814713	−	0.579865i	$-0.196895\pi$
$127$	4.77696e9	1.62943	0.814713	+	0.579865i	$0.196895\pi$
$128$	2.97090e9	0.978235
$129$	7.32636e8	0.232935
$130$	0	0
$131$	−4.62884e9	−1.37326	−0.686628	−	0.727009i	$-0.740910\pi$
$131$	−4.62884e9	−1.37326	−0.686628	+	0.727009i	$0.740910\pi$
$132$	−5.29877e8	−0.151912
$133$	−3.82569e8	−0.106018
$134$	1.39847e9	0.374697
$135$	0	0
$136$	2.47186e8	0.0619581
$137$	−3.85972e9	−0.936080	−0.468040	−	0.883707i	$-0.655040\pi$
$137$	−3.85972e9	−0.936080	−0.468040	+	0.883707i	$0.655040\pi$
$138$	−6.38765e8	−0.149929
$139$	−8.38068e9	−1.90420	−0.952100	−	0.305786i	$-0.901081\pi$
$139$	−8.38068e9	−1.90420	−0.952100	+	0.305786i	$0.901081\pi$
$140$	0	0
$141$	−1.25984e9	−0.268429
$142$	−5.05503e8	−0.104334
$143$	−7.75427e8	−0.155070
$144$	−3.25062e9	−0.629991
$145$	0	0
$146$	2.65942e9	0.484394
$147$	1.68613e9	0.297826
$148$	−3.47463e9	−0.595293
$149$	3.96089e9	0.658347	0.329174	−	0.944269i	$-0.393230\pi$
$149$	3.96089e9	0.658347	0.329174	+	0.944269i	$0.393230\pi$
$150$	0	0
$151$	1.11419e10	1.74407	0.872036	−	0.489442i	$-0.162799\pi$
$151$	1.11419e10	1.74407	0.872036	+	0.489442i	$0.162799\pi$
$152$	3.06015e9	0.464993
$153$	−6.18946e8	−0.0913148
$154$	−1.78165e8	−0.0255257
$155$	0	0
$156$	5.57418e8	0.0753564
$157$	7.39104e9	0.970861	0.485430	−	0.874275i	$-0.338663\pi$
$157$	7.39104e9	0.970861	0.485430	+	0.874275i	$0.338663\pi$
$158$	1.04634e9	0.133572
$159$	−1.16079e9	−0.144035
$160$	0	0
$161$	1.81706e9	0.213134
$162$	−2.08519e9	−0.237863
$163$	7.32911e8	0.0813218	0.0406609	−	0.999173i	$-0.487054\pi$
$163$	7.32911e8	0.0813218	0.0406609	+	0.999173i	$0.487054\pi$
$164$	2.25522e9	0.243440
$165$	0	0
$166$	−4.26867e8	−0.0436321
$167$	1.23516e10	1.22885	0.614427	−	0.788974i	$-0.289387\pi$
$167$	1.23516e10	1.22885	0.614427	+	0.788974i	$0.289387\pi$
$168$	2.71287e8	0.0262747
$169$	8.15731e8	0.0769231
$170$	0	0
$171$	−7.66252e9	−0.685314
$172$	7.87012e9	0.685651
$173$	−1.12727e10	−0.956794	−0.478397	−	0.878144i	$-0.658782\pi$
$173$	−1.12727e10	−0.956794	−0.478397	+	0.878144i	$0.658782\pi$
$174$	−1.65066e9	−0.136517
$175$	0	0
$176$	−4.93971e9	−0.388056
$177$	4.84222e9	0.370822
$178$	6.32626e9	0.472342
$179$	−3.32764e9	−0.242269	−0.121134	−	0.992636i	$-0.538653\pi$
$179$	−3.32764e9	−0.242269	−0.121134	+	0.992636i	$0.538653\pi$
$180$	0	0
$181$	1.56098e10	1.08104	0.540521	−	0.841330i	$-0.318227\pi$
$181$	1.56098e10	1.08104	0.540521	+	0.841330i	$0.318227\pi$
$182$	1.87425e8	0.0126621
$183$	1.60637e9	0.105881
$184$	−1.45345e10	−0.934805
$185$	0	0
$186$	−1.30419e9	−0.0798974
$187$	−9.40564e8	−0.0562472
$188$	−1.35334e10	−0.790129
$189$	−1.42767e9	−0.0813859
$190$	0	0
$191$	2.64757e10	1.43945	0.719725	−	0.694259i	$-0.244268\pi$
$191$	2.64757e10	1.43945	0.719725	+	0.694259i	$0.244268\pi$
$192$	2.40538e9	0.127740
$193$	2.67204e9	0.138623	0.0693114	−	0.997595i	$-0.477920\pi$
$193$	2.67204e9	0.138623	0.0693114	+	0.997595i	$0.477920\pi$
$194$	1.08122e10	0.548031
$195$	0	0
$196$	1.81127e10	0.876661
$197$	−1.38233e10	−0.653903	−0.326951	−	0.945041i	$-0.606021\pi$
$197$	−1.38233e10	−0.653903	−0.326951	+	0.945041i	$0.606021\pi$
$198$	−3.56848e9	−0.165002
$199$	−1.21811e10	−0.550616	−0.275308	−	0.961356i	$-0.588780\pi$
$199$	−1.21811e10	−0.550616	−0.275308	+	0.961356i	$0.588780\pi$
$200$	0	0
$201$	8.10261e9	0.350141
$202$	3.05378e9	0.129049
$203$	4.69554e9	0.194068
$204$	6.76128e8	0.0273334
$205$	0	0
$206$	1.37112e10	0.530486
$207$	3.63941e10	1.37773
$208$	5.19646e9	0.192497
$209$	−1.16441e10	−0.422133
$210$	0	0
$211$	−3.16880e9	−0.110058	−0.0550292	−	0.998485i	$-0.517525\pi$
$211$	−3.16880e9	−0.110058	−0.0550292	+	0.998485i	$0.517525\pi$
$212$	−1.24695e10	−0.423971
$213$	−2.92885e9	−0.0974963
$214$	−5.52326e9	−0.180025
$215$	0	0
$216$	1.14198e10	0.356959
$217$	3.70996e9	0.113579
$218$	−1.52292e10	−0.456691
$219$	1.54085e10	0.452648
$220$	0	0
$221$	9.89451e8	0.0279016
$222$	2.37958e9	0.0657524
$223$	1.00184e10	0.271285	0.135642	−	0.990758i	$-0.456690\pi$
$223$	1.00184e10	0.271285	0.135642	+	0.990758i	$0.456690\pi$
$224$	4.45264e9	0.118168
$225$	0	0
$226$	−1.54605e10	−0.394218
$227$	5.23965e10	1.30974	0.654871	−	0.755741i	$-0.272723\pi$
$227$	5.23965e10	1.30974	0.654871	+	0.755741i	$0.272723\pi$
$228$	8.37044e9	0.205136
$229$	−2.94853e10	−0.708510	−0.354255	−	0.935149i	$-0.615266\pi$
$229$	−2.94853e10	−0.708510	−0.354255	+	0.935149i	$0.615266\pi$
$230$	0	0
$231$	−1.03227e9	−0.0238529
$232$	−3.75593e10	−0.851180
$233$	6.67468e10	1.48364	0.741820	−	0.670599i	$-0.233963\pi$
$233$	6.67468e10	1.48364	0.741820	+	0.670599i	$0.233963\pi$
$234$	3.75396e9	0.0818499
$235$	0	0
$236$	5.20161e10	1.09152
$237$	6.06241e9	0.124818
$238$	2.27340e8	0.00459281
$239$	−7.42940e10	−1.47286	−0.736432	−	0.676511i	$-0.763491\pi$
$239$	−7.42940e10	−1.47286	−0.736432	+	0.676511i	$0.763491\pi$
$240$	0	0
$241$	9.01496e10	1.72142	0.860711	−	0.509095i	$-0.170020\pi$
$241$	9.01496e10	1.72142	0.860711	+	0.509095i	$0.170020\pi$
$242$	1.19240e10	0.223488
$243$	−4.35842e10	−0.801864
$244$	1.72560e10	0.311663
$245$	0	0
$246$	−1.54447e9	−0.0268889
$247$	1.22494e10	0.209400
$248$	−2.96757e10	−0.498160
$249$	−2.47323e9	−0.0407726
$250$	0	0
$251$	3.62007e10	0.575685	0.287843	−	0.957678i	$-0.407062\pi$
$251$	3.62007e10	0.575685	0.287843	+	0.957678i	$0.407062\pi$
$252$	−7.29712e9	−0.113985
$253$	5.53053e10	0.848641
$254$	−3.51428e10	−0.529766
$255$	0	0
$256$	7.03715e9	0.102404
$257$	1.97638e10	0.282600	0.141300	−	0.989967i	$-0.454872\pi$
$257$	1.97638e10	0.282600	0.141300	+	0.989967i	$0.454872\pi$
$258$	−5.38980e9	−0.0757329
$259$	−6.76905e9	−0.0934714
$260$	0	0
$261$	9.40474e10	1.25448
$262$	3.40531e10	0.446479
$263$	1.70457e10	0.219692	0.109846	−	0.993949i	$-0.464964\pi$
$263$	1.70457e10	0.219692	0.109846	+	0.993949i	$0.464964\pi$
$264$	8.25708e9	0.104619
$265$	0	0
$266$	2.81446e9	0.0344689
$267$	3.66539e10	0.441386
$268$	8.70398e10	1.03065
$269$	6.56819e10	0.764822	0.382411	−	0.923992i	$-0.375094\pi$
$269$	6.56819e10	0.764822	0.382411	+	0.923992i	$0.375094\pi$
$270$	0	0
$271$	1.52442e11	1.71689	0.858447	−	0.512902i	$-0.171430\pi$
$271$	1.52442e11	1.71689	0.858447	+	0.512902i	$0.171430\pi$
$272$	6.30312e9	0.0698225
$273$	1.08593e9	0.0118323
$274$	2.83949e10	0.304343
$275$	0	0
$276$	−3.97564e10	−0.412397
$277$	1.21612e11	1.24113	0.620566	−	0.784154i	$-0.286903\pi$
$277$	1.21612e11	1.24113	0.620566	+	0.784154i	$0.286903\pi$
$278$	6.16544e10	0.619102
$279$	7.43071e10	0.734195
$280$	0	0
$281$	−2.03083e11	−1.94310	−0.971548	−	0.236842i	$-0.923888\pi$
$281$	−2.03083e11	−1.94310	−0.971548	+	0.236842i	$0.923888\pi$
$282$	9.26829e9	0.0872728
$283$	−3.09567e10	−0.286891	−0.143445	−	0.989658i	$-0.545818\pi$
$283$	−3.09567e10	−0.286891	−0.143445	+	0.989658i	$0.545818\pi$
$284$	−3.14622e10	−0.286984
$285$	0	0
$286$	5.70460e9	0.0504171
$287$	4.39347e9	0.0382243
$288$	8.91824e10	0.763858
$289$	−1.17388e11	−0.989880
$290$	0	0
$291$	6.26449e10	0.512115
$292$	1.65521e11	1.33238
$293$	7.81733e10	0.619661	0.309831	−	0.950792i	$-0.399728\pi$
$293$	7.81733e10	0.619661	0.309831	+	0.950792i	$0.399728\pi$
$294$	−1.24044e10	−0.0968306
$295$	0	0
$296$	5.41452e10	0.409966
$297$	−4.34535e10	−0.324057
$298$	−2.91392e10	−0.214045
$299$	−5.81798e10	−0.420971
$300$	0	0
$301$	1.53321e10	0.107659
$302$	−8.19682e10	−0.567040
$303$	1.76933e10	0.120592
$304$	7.80324e10	0.524015
$305$	0	0
$306$	4.55341e9	0.0296887
$307$	−1.19962e11	−0.770766	−0.385383	−	0.922757i	$-0.625931\pi$
$307$	−1.19962e11	−0.770766	−0.385383	+	0.922757i	$0.625931\pi$
$308$	−1.10889e10	−0.0702116
$309$	7.94419e10	0.495720
$310$	0	0
$311$	1.16227e11	0.704504	0.352252	−	0.935905i	$-0.385416\pi$
$311$	1.16227e11	0.704504	0.352252	+	0.935905i	$0.385416\pi$
$312$	−8.68626e9	−0.0518964
$313$	−9.92344e10	−0.584403	−0.292202	−	0.956357i	$-0.594388\pi$
$313$	−9.92344e10	−0.584403	−0.292202	+	0.956357i	$0.594388\pi$
$314$	−5.43738e10	−0.315651
$315$	0	0
$316$	6.51236e10	0.367406
$317$	2.98194e11	1.65856	0.829281	−	0.558832i	$-0.188750\pi$
$317$	2.98194e11	1.65856	0.829281	+	0.558832i	$0.188750\pi$
$318$	8.53963e9	0.0468292
$319$	1.42917e11	0.772725
$320$	0	0
$321$	−3.20014e10	−0.168227
$322$	−1.33676e10	−0.0692950
$323$	1.48580e10	0.0759539
$324$	−1.29781e11	−0.654271
$325$	0	0
$326$	−5.39183e9	−0.0264397
$327$	−8.82367e10	−0.426761
$328$	−3.51431e10	−0.167652
$329$	−2.63650e10	−0.124064
$330$	0	0
$331$	6.87707e10	0.314904	0.157452	−	0.987527i	$-0.449672\pi$
$331$	6.87707e10	0.314904	0.157452	+	0.987527i	$0.449672\pi$
$332$	−2.65680e10	−0.120015
$333$	−1.35578e11	−0.604214
$334$	−9.08675e10	−0.399530
$335$	0	0
$336$	6.91769e9	0.0296097
$337$	1.56091e11	0.659239	0.329619	−	0.944114i	$-0.393080\pi$
$337$	1.56091e11	0.659239	0.329619	+	0.944114i	$0.393080\pi$
$338$	−6.00111e9	−0.0250096
$339$	−8.95772e10	−0.368382
$340$	0	0
$341$	1.12919e11	0.452243
$342$	5.63711e10	0.222812
$343$	7.12819e10	0.278071
$344$	−1.22640e11	−0.472194
$345$	0	0
$346$	8.29298e10	0.311077
$347$	1.65467e11	0.612673	0.306337	−	0.951923i	$-0.400897\pi$
$347$	1.65467e11	0.612673	0.306337	+	0.951923i	$0.400897\pi$
$348$	−1.02736e11	−0.375506
$349$	−4.02009e11	−1.45051	−0.725257	−	0.688478i	$-0.758279\pi$
$349$	−4.02009e11	−1.45051	−0.725257	+	0.688478i	$0.758279\pi$
$350$	0	0
$351$	4.57121e10	0.160749
$352$	1.35524e11	0.470514
$353$	−2.74001e11	−0.939217	−0.469609	−	0.882875i	$-0.655605\pi$
$353$	−2.74001e11	−0.939217	−0.469609	+	0.882875i	$0.655605\pi$
$354$	−3.56229e10	−0.120563
$355$	0	0
$356$	3.93743e11	1.29923
$357$	1.31719e9	0.00429182
$358$	2.44805e10	0.0787675
$359$	8.26405e10	0.262584	0.131292	−	0.991344i	$-0.458087\pi$
$359$	8.26405e10	0.262584	0.131292	+	0.991344i	$0.458087\pi$
$360$	0	0
$361$	−1.38746e11	−0.429969
$362$	−1.14837e11	−0.351473
$363$	6.90869e10	0.208841
$364$	1.16652e10	0.0348287
$365$	0	0
$366$	−1.18176e10	−0.0344244
$367$	−4.83059e10	−0.138996	−0.0694980	−	0.997582i	$-0.522140\pi$
$367$	−4.83059e10	−0.138996	−0.0694980	+	0.997582i	$0.522140\pi$
$368$	−3.70624e11	−1.05346
$369$	8.79974e10	0.247088
$370$	0	0
$371$	−2.42922e10	−0.0665708
$372$	−8.11721e10	−0.219768
$373$	−8.53749e10	−0.228371	−0.114185	−	0.993459i	$-0.536426\pi$
$373$	−8.53749e10	−0.228371	−0.114185	+	0.993459i	$0.536426\pi$
$374$	6.91947e9	0.0182873
$375$	0	0
$376$	2.10892e11	0.544145
$377$	−1.50345e11	−0.383312
$378$	1.05030e10	0.0264605
$379$	−2.25085e11	−0.560365	−0.280182	−	0.959947i	$-0.590395\pi$
$379$	−2.25085e11	−0.560365	−0.280182	+	0.959947i	$0.590395\pi$
$380$	0	0
$381$	−2.03614e11	−0.495047
$382$	−1.94774e11	−0.468001
$383$	−6.84152e11	−1.62464	−0.812322	−	0.583210i	$-0.801797\pi$
$383$	−6.84152e11	−1.62464	−0.812322	+	0.583210i	$0.801797\pi$
$384$	−1.26633e11	−0.297204
$385$	0	0
$386$	−1.96574e10	−0.0450696
$387$	3.07088e11	0.695926
$388$	6.72944e11	1.50743
$389$	7.47317e11	1.65475	0.827374	−	0.561652i	$-0.189834\pi$
$389$	7.47317e11	1.65475	0.827374	+	0.561652i	$0.189834\pi$
$390$	0	0
$391$	−7.05700e10	−0.152695
$392$	−2.82251e11	−0.603738
$393$	1.97301e11	0.417218
$394$	1.01694e11	0.212600
$395$	0	0
$396$	−2.22100e11	−0.453859
$397$	−1.63235e11	−0.329804	−0.164902	−	0.986310i	$-0.552731\pi$
$397$	−1.63235e11	−0.329804	−0.164902	+	0.986310i	$0.552731\pi$
$398$	8.96133e10	0.179019
$399$	1.63067e10	0.0322099
$400$	0	0
$401$	−7.33836e11	−1.41726	−0.708629	−	0.705581i	$-0.750686\pi$
$401$	−7.33836e11	−1.41726	−0.708629	+	0.705581i	$0.750686\pi$
$402$	−5.96087e10	−0.113839
$403$	−1.18788e11	−0.224336
$404$	1.90065e11	0.354966
$405$	0	0
$406$	−3.45438e10	−0.0630961
$407$	−2.06028e11	−0.372178
$408$	−1.05361e10	−0.0188239
$409$	7.45800e11	1.31785	0.658927	−	0.752207i	$-0.271010\pi$
$409$	7.45800e11	1.31785	0.658927	+	0.752207i	$0.271010\pi$
$410$	0	0
$411$	1.64518e11	0.284397
$412$	8.53380e11	1.45917
$413$	1.01334e11	0.171388
$414$	−2.67741e11	−0.447934
$415$	0	0
$416$	−1.42568e11	−0.233400
$417$	3.57221e11	0.578528
$418$	8.56628e10	0.137246
$419$	−5.46254e11	−0.865828	−0.432914	−	0.901435i	$-0.642515\pi$
$419$	−5.46254e11	−0.865828	−0.432914	+	0.901435i	$0.642515\pi$
$420$	0	0
$421$	−2.95449e11	−0.458366	−0.229183	−	0.973383i	$-0.573606\pi$
$421$	−2.95449e11	−0.458366	−0.229183	+	0.973383i	$0.573606\pi$
$422$	2.33120e10	0.0357827
$423$	−5.28067e11	−0.801969
$424$	1.94312e11	0.291980
$425$	0	0
$426$	2.15467e10	0.0316984
$427$	3.36170e10	0.0489365
$428$	−3.43765e11	−0.495182
$429$	3.30520e10	0.0471129
$430$	0	0
$431$	−5.49479e11	−0.767014	−0.383507	−	0.923538i	$-0.625284\pi$
$431$	−5.49479e11	−0.767014	−0.383507	+	0.923538i	$0.625284\pi$
$432$	2.91201e11	0.402268
$433$	7.54093e11	1.03093	0.515465	−	0.856910i	$-0.327619\pi$
$433$	7.54093e11	1.03093	0.515465	+	0.856910i	$0.327619\pi$
$434$	−2.72931e10	−0.0369275
$435$	0	0
$436$	−9.47856e11	−1.25618
$437$	−8.73654e11	−1.14597
$438$	−1.13356e11	−0.147167
$439$	9.98220e10	0.128273	0.0641366	−	0.997941i	$-0.479571\pi$
$439$	9.98220e10	0.128273	0.0641366	+	0.997941i	$0.479571\pi$
$440$	0	0
$441$	7.06749e11	0.889798
$442$	−7.27912e9	−0.00907149
$443$	1.08040e12	1.33281	0.666404	−	0.745591i	$-0.267832\pi$
$443$	1.08040e12	1.33281	0.666404	+	0.745591i	$0.267832\pi$
$444$	1.48104e11	0.180860
$445$	0	0
$446$	−7.37024e10	−0.0882013
$447$	−1.68830e11	−0.200017
$448$	5.03380e10	0.0590398
$449$	1.02947e12	1.19538	0.597688	−	0.801729i	$-0.296086\pi$
$449$	1.02947e12	1.19538	0.597688	+	0.801729i	$0.296086\pi$
$450$	0	0
$451$	1.33723e11	0.152199
$452$	−9.62256e11	−1.08435
$453$	−4.74917e11	−0.529878
$454$	−3.85466e11	−0.425829
$455$	0	0
$456$	−1.30437e11	−0.141273
$457$	−1.06106e12	−1.13793	−0.568966	−	0.822361i	$-0.692657\pi$
$457$	−1.06106e12	−1.13793	−0.568966	+	0.822361i	$0.692657\pi$
$458$	2.16915e11	0.230354
$459$	5.54471e10	0.0583071
$460$	0	0
$461$	−7.20760e11	−0.743253	−0.371626	−	0.928382i	$-0.621200\pi$
$461$	−7.20760e11	−0.743253	−0.371626	+	0.928382i	$0.621200\pi$
$462$	7.59414e9	0.00775514
$463$	−1.41179e11	−0.142776	−0.0713880	−	0.997449i	$-0.522743\pi$
$463$	−1.41179e11	−0.142776	−0.0713880	+	0.997449i	$0.522743\pi$
$464$	−9.57745e11	−0.959222
$465$	0	0
$466$	−4.91038e11	−0.482368
$467$	5.23104e11	0.508935	0.254467	−	0.967081i	$-0.418100\pi$
$467$	5.23104e11	0.508935	0.254467	+	0.967081i	$0.418100\pi$
$468$	2.33644e11	0.225138
$469$	1.69565e11	0.161830
$470$	0	0
$471$	−3.15038e11	−0.294964
$472$	−8.10568e11	−0.751710
$473$	4.66658e11	0.428670
$474$	−4.45995e10	−0.0405814
$475$	0	0
$476$	1.41495e10	0.0126331
$477$	−4.86551e11	−0.430324
$478$	5.46560e11	0.478864
$479$	1.22387e12	1.06224	0.531122	−	0.847295i	$-0.321770\pi$
$479$	1.22387e12	1.06224	0.531122	+	0.847295i	$0.321770\pi$
$480$	0	0
$481$	2.16736e11	0.184620
$482$	−6.63206e11	−0.559676
$483$	−7.74508e10	−0.0647536
$484$	7.42145e11	0.614730
$485$	0	0
$486$	3.20637e11	0.260706
$487$	3.77344e11	0.303988	0.151994	−	0.988381i	$-0.451431\pi$
$487$	3.77344e11	0.303988	0.151994	+	0.988381i	$0.451431\pi$
$488$	−2.68900e11	−0.214636
$489$	−3.12398e10	−0.0247069
$490$	0	0
$491$	−2.35736e12	−1.83046	−0.915229	−	0.402934i	$-0.867990\pi$
$491$	−2.35736e12	−1.83046	−0.915229	+	0.402934i	$0.867990\pi$
$492$	−9.61271e10	−0.0739610
$493$	−1.82363e11	−0.139035
$494$	−9.01153e10	−0.0680812
$495$	0	0
$496$	−7.56717e11	−0.561392
$497$	−6.12927e10	−0.0450614
$498$	1.81949e10	0.0132562
$499$	−2.64345e12	−1.90862	−0.954309	−	0.298822i	$-0.903406\pi$
$499$	−2.64345e12	−1.90862	−0.954309	+	0.298822i	$0.903406\pi$
$500$	0	0
$501$	−5.26480e11	−0.373346
$502$	−2.66319e11	−0.187169
$503$	−1.53328e11	−0.106799	−0.0533994	−	0.998573i	$-0.517006\pi$
$503$	−1.53328e11	−0.106799	−0.0533994	+	0.998573i	$0.517006\pi$
$504$	1.13711e11	0.0784993
$505$	0	0
$506$	−4.06866e11	−0.275914
$507$	−3.47700e10	−0.0233705
$508$	−2.18727e12	−1.45719
$509$	−6.36840e11	−0.420533	−0.210267	−	0.977644i	$-0.567433\pi$
$509$	−6.36840e11	−0.420533	−0.210267	+	0.977644i	$0.567433\pi$
$510$	0	0
$511$	3.22457e11	0.209208
$512$	−1.57287e12	−1.01153
$513$	6.86433e11	0.437593
$514$	−1.45397e11	−0.0918801
$515$	0	0
$516$	−3.35458e11	−0.208312
$517$	−8.02463e11	−0.493989
$518$	4.97981e10	0.0303899
$519$	4.80489e11	0.290690
$520$	0	0
$521$	1.84033e12	1.09427	0.547137	−	0.837043i	$-0.315718\pi$
$521$	1.84033e12	1.09427	0.547137	+	0.837043i	$0.315718\pi$
$522$	−6.91881e11	−0.407863
$523$	1.13176e10	0.00661447	0.00330724	−	0.999995i	$-0.498947\pi$
$523$	1.13176e10	0.00661447	0.00330724	+	0.999995i	$0.498947\pi$
$524$	2.11945e12	1.22809
$525$	0	0
$526$	−1.25401e11	−0.0714272
$527$	−1.44085e11	−0.0813715
$528$	2.10552e11	0.117898
$529$	2.34837e12	1.30382
$530$	0	0
$531$	2.02964e12	1.10788
$532$	1.75170e11	0.0948108
$533$	−1.40673e11	−0.0754987
$534$	−2.69652e11	−0.143506
$535$	0	0
$536$	−1.35634e12	−0.709787
$537$	1.41838e11	0.0736053
$538$	−4.83203e11	−0.248662
$539$	1.07399e12	0.548089
$540$	0	0
$541$	−2.25189e12	−1.13021	−0.565107	−	0.825018i	$-0.691165\pi$
$541$	−2.25189e12	−1.13021	−0.565107	+	0.825018i	$0.691165\pi$
$542$	−1.12148e12	−0.558204
$543$	−6.65356e11	−0.328439
$544$	−1.72929e11	−0.0846591
$545$	0	0
$546$	−7.98886e9	−0.00384696
$547$	−1.92777e11	−0.0920686	−0.0460343	−	0.998940i	$-0.514658\pi$
$547$	−1.92777e11	−0.0920686	−0.0460343	+	0.998940i	$0.514658\pi$
$548$	1.76728e12	0.837131
$549$	6.73318e11	0.316333
$550$	0	0
$551$	−2.25765e12	−1.04346
$552$	6.19524e11	0.284009
$553$	1.26870e11	0.0576892
$554$	−8.94667e11	−0.403522
$555$	0	0
$556$	3.83733e12	1.70292
$557$	−3.00574e12	−1.32313	−0.661566	−	0.749887i	$-0.730108\pi$
$557$	−3.00574e12	−1.32313	−0.661566	+	0.749887i	$0.730108\pi$
$558$	−5.46657e11	−0.238705
$559$	−4.90913e11	−0.212643
$560$	0	0
$561$	4.00909e10	0.0170888
$562$	1.49402e12	0.631748
$563$	1.64962e11	0.0691984	0.0345992	−	0.999401i	$-0.488985\pi$
$563$	1.64962e11	0.0691984	0.0345992	+	0.999401i	$0.488985\pi$
$564$	5.76854e11	0.240054
$565$	0	0
$566$	2.27740e11	0.0932751
$567$	−2.52831e11	−0.102732
$568$	4.90277e11	0.197639
$569$	−2.35127e11	−0.0940368	−0.0470184	−	0.998894i	$-0.514972\pi$
$569$	−2.35127e11	−0.0940368	−0.0470184	+	0.998894i	$0.514972\pi$
$570$	0	0
$571$	−2.71697e12	−1.06960	−0.534801	−	0.844978i	$-0.679613\pi$
$571$	−2.71697e12	−1.06960	−0.534801	+	0.844978i	$0.679613\pi$
$572$	3.55051e11	0.138678
$573$	−1.12851e12	−0.437329
$574$	−3.23216e10	−0.0124276
$575$	0	0
$576$	1.00823e12	0.381643
$577$	3.01507e12	1.13242	0.566209	−	0.824262i	$-0.308410\pi$
$577$	3.01507e12	1.13242	0.566209	+	0.824262i	$0.308410\pi$
$578$	8.63589e11	0.321834
$579$	−1.13894e11	−0.0421159
$580$	0	0
$581$	−5.17580e10	−0.0188445
$582$	−4.60862e11	−0.166501
$583$	−7.39374e11	−0.265067
$584$	−2.57931e12	−0.917585
$585$	0	0
$586$	−5.75100e11	−0.201467
$587$	9.84708e11	0.342323	0.171161	−	0.985243i	$-0.445248\pi$
$587$	9.84708e11	0.342323	0.171161	+	0.985243i	$0.445248\pi$
$588$	−7.72042e11	−0.266344
$589$	−1.78377e12	−0.610690
$590$	0	0
$591$	5.89208e11	0.198667
$592$	1.38068e12	0.462003
$593$	−1.01065e12	−0.335625	−0.167812	−	0.985819i	$-0.553670\pi$
$593$	−1.01065e12	−0.335625	−0.167812	+	0.985819i	$0.553670\pi$
$594$	3.19676e11	0.105359
$595$	0	0
$596$	−1.81361e12	−0.588756
$597$	5.19213e11	0.167286
$598$	4.28013e11	0.136868
$599$	5.47507e12	1.73768	0.868839	−	0.495095i	$-0.164867\pi$
$599$	5.47507e12	1.73768	0.868839	+	0.495095i	$0.164867\pi$
$600$	0	0
$601$	9.94557e11	0.310953	0.155476	−	0.987840i	$-0.450309\pi$
$601$	9.94557e11	0.310953	0.155476	+	0.987840i	$0.450309\pi$
$602$	−1.12794e11	−0.0350027
$603$	3.39624e12	1.04609
$604$	−5.10165e12	−1.55971
$605$	0	0
$606$	−1.30165e11	−0.0392074
$607$	−4.57629e12	−1.36825	−0.684124	−	0.729366i	$-0.739815\pi$
$607$	−4.57629e12	−1.36825	−0.684124	+	0.729366i	$0.739815\pi$
$608$	−2.14086e12	−0.635363
$609$	−2.00144e11	−0.0589610
$610$	0	0
$611$	8.44173e11	0.245045
$612$	2.83402e11	0.0816623
$613$	−2.27107e12	−0.649617	−0.324809	−	0.945780i	$-0.605300\pi$
$613$	−2.27107e12	−0.649617	−0.324809	+	0.945780i	$0.605300\pi$
$614$	8.82531e11	0.250595
$615$	0	0
$616$	1.72798e11	0.0483532
$617$	−3.53862e12	−0.982994	−0.491497	−	0.870879i	$-0.663550\pi$
$617$	−3.53862e12	−0.982994	−0.491497	+	0.870879i	$0.663550\pi$
$618$	−5.84432e11	−0.161171
$619$	1.97957e12	0.541956	0.270978	−	0.962586i	$-0.412653\pi$
$619$	1.97957e12	0.541956	0.270978	+	0.962586i	$0.412653\pi$
$620$	0	0
$621$	−3.26029e12	−0.879720
$622$	−8.55047e11	−0.229052
$623$	7.67065e11	0.204003
$624$	−2.21496e11	−0.0584837
$625$	0	0
$626$	7.30040e11	0.190004
$627$	4.96324e11	0.128251
$628$	−3.38420e12	−0.868235
$629$	2.62893e11	0.0669656
$630$	0	0
$631$	3.71649e11	0.0933256	0.0466628	−	0.998911i	$-0.485141\pi$
$631$	3.71649e11	0.0933256	0.0466628	+	0.998911i	$0.485141\pi$
$632$	−1.01482e12	−0.253025
$633$	1.35068e11	0.0334376
$634$	−2.19373e12	−0.539239
$635$	0	0
$636$	5.31502e11	0.128809
$637$	−1.12981e12	−0.271881
$638$	−1.05140e12	−0.251232
$639$	−1.22764e12	−0.291284
$640$	0	0
$641$	1.07772e12	0.252143	0.126071	−	0.992021i	$-0.459763\pi$
$641$	1.07772e12	0.252143	0.126071	+	0.992021i	$0.459763\pi$
$642$	2.35425e11	0.0546947
$643$	6.69209e12	1.54388	0.771938	−	0.635698i	$-0.219288\pi$
$643$	6.69209e12	1.54388	0.771938	+	0.635698i	$0.219288\pi$
$644$	−8.31992e11	−0.190604
$645$	0	0
$646$	−1.09307e11	−0.0246945
$647$	−1.58975e12	−0.356664	−0.178332	−	0.983970i	$-0.557070\pi$
$647$	−1.58975e12	−0.356664	−0.178332	+	0.983970i	$0.557070\pi$
$648$	2.02238e12	0.450583
$649$	3.08429e12	0.682423
$650$	0	0
$651$	−1.58134e11	−0.0345073
$652$	−3.35584e11	−0.0727256
$653$	1.96565e12	0.423055	0.211527	−	0.977372i	$-0.432156\pi$
$653$	1.96565e12	0.423055	0.211527	+	0.977372i	$0.432156\pi$
$654$	6.49133e11	0.138750
$655$	0	0
$656$	−8.96134e11	−0.188932
$657$	6.45853e12	1.35235
$658$	1.93960e11	0.0403362
$659$	1.09426e11	0.0226014	0.0113007	−	0.999936i	$-0.496403\pi$
$659$	1.09426e11	0.0226014	0.0113007	+	0.999936i	$0.496403\pi$
$660$	0	0
$661$	−2.69590e12	−0.549285	−0.274643	−	0.961546i	$-0.588560\pi$
$661$	−2.69590e12	−0.549285	−0.274643	+	0.961546i	$0.588560\pi$
$662$	−5.05927e11	−0.102383
$663$	−4.21747e10	−0.00847698
$664$	4.14009e11	0.0826520
$665$	0	0
$666$	9.97411e11	0.196445
$667$	1.07230e13	2.09772
$668$	−5.65555e12	−1.09896
$669$	−4.27026e11	−0.0824208
$670$	0	0
$671$	1.02319e12	0.194852
$672$	−1.89790e11	−0.0359015
$673$	6.37187e12	1.19729	0.598644	−	0.801015i	$-0.295706\pi$
$673$	6.37187e12	1.19729	0.598644	+	0.801015i	$0.295706\pi$
$674$	−1.14832e12	−0.214335
$675$	0	0
$676$	−3.73506e11	−0.0687919
$677$	6.61270e12	1.20985	0.604923	−	0.796284i	$-0.293204\pi$
$677$	6.61270e12	1.20985	0.604923	+	0.796284i	$0.293204\pi$
$678$	6.58995e11	0.119770
$679$	1.31099e12	0.236692
$680$	0	0
$681$	−2.23336e12	−0.397921
$682$	−8.30713e11	−0.147035
$683$	−3.52480e12	−0.619785	−0.309893	−	0.950772i	$-0.600293\pi$
$683$	−3.52480e12	−0.619785	−0.309893	+	0.950772i	$0.600293\pi$
$684$	3.50851e12	0.612872
$685$	0	0
$686$	−5.24401e11	−0.0904076
$687$	1.25679e12	0.215257
$688$	−3.12727e12	−0.532130
$689$	7.77804e11	0.131487
$690$	0	0
$691$	1.21020e12	0.201932	0.100966	−	0.994890i	$-0.467807\pi$
$691$	1.21020e12	0.201932	0.100966	+	0.994890i	$0.467807\pi$
$692$	5.16151e12	0.855656
$693$	−4.32681e11	−0.0712638
$694$	−1.21730e12	−0.199195
$695$	0	0
$696$	1.60094e12	0.258603
$697$	−1.70632e11	−0.0273849
$698$	2.95747e12	0.471597
$699$	−2.84503e12	−0.450755
$700$	0	0
$701$	3.34752e12	0.523591	0.261796	−	0.965123i	$-0.415685\pi$
$701$	3.34752e12	0.523591	0.261796	+	0.965123i	$0.415685\pi$
$702$	−3.36291e11	−0.0522635
$703$	3.25461e12	0.502574
$704$	1.53212e12	0.235081
$705$	0	0
$706$	2.01575e12	0.305362
$707$	3.70273e11	0.0557359
$708$	−2.21715e12	−0.331624
$709$	1.09345e13	1.62514	0.812568	−	0.582866i	$-0.198069\pi$
$709$	1.09345e13	1.62514	0.812568	+	0.582866i	$0.198069\pi$
$710$	0	0
$711$	2.54109e12	0.372912
$712$	−6.13570e12	−0.894755
$713$	8.47224e12	1.22771
$714$	−9.69020e9	−0.00139537
$715$	0	0
$716$	1.52365e12	0.216660
$717$	3.16673e12	0.447481
$718$	−6.07964e11	−0.0853724
$719$	4.73071e12	0.660156	0.330078	−	0.943954i	$-0.392925\pi$
$719$	4.73071e12	0.660156	0.330078	+	0.943954i	$0.392925\pi$
$720$	0	0
$721$	1.66250e12	0.229115
$722$	1.02071e12	0.139793
$723$	−3.84256e12	−0.522997
$724$	−7.14738e12	−0.966770
$725$	0	0
$726$	−5.08254e11	−0.0678994
$727$	−1.40402e13	−1.86410	−0.932049	−	0.362333i	$-0.881980\pi$
$727$	−1.40402e13	−1.86410	−0.932049	+	0.362333i	$0.881980\pi$
$728$	−1.81780e11	−0.0239858
$729$	−3.72119e12	−0.487987
$730$	0	0
$731$	−5.95459e11	−0.0771301
$732$	−7.35524e11	−0.0946884
$733$	1.78493e12	0.228377	0.114188	−	0.993459i	$-0.463573\pi$
$733$	1.78493e12	0.228377	0.114188	+	0.993459i	$0.463573\pi$
$734$	3.55373e11	0.0451910
$735$	0	0
$736$	1.01683e13	1.27731
$737$	5.16101e12	0.644364
$738$	−6.47373e11	−0.0803342
$739$	−1.24956e13	−1.54119	−0.770595	−	0.637325i	$-0.780041\pi$
$739$	−1.24956e13	−1.54119	−0.770595	+	0.637325i	$0.780041\pi$
$740$	0	0
$741$	−5.22121e11	−0.0636194
$742$	1.78711e11	0.0216438
$743$	−4.21591e12	−0.507506	−0.253753	−	0.967269i	$-0.581665\pi$
$743$	−4.21591e12	−0.507506	−0.253753	+	0.967269i	$0.581665\pi$
$744$	1.26491e12	0.151349
$745$	0	0
$746$	6.28080e11	0.0742489
$747$	−1.03667e12	−0.121814
$748$	4.30664e11	0.0503016
$749$	−6.69701e11	−0.0777522
$750$	0	0
$751$	9.94988e12	1.14140	0.570701	−	0.821158i	$-0.306672\pi$
$751$	9.94988e12	1.14140	0.570701	+	0.821158i	$0.306672\pi$
$752$	5.37765e12	0.613214
$753$	−1.54303e12	−0.174903
$754$	1.10605e12	0.124624
$755$	0	0
$756$	6.53699e11	0.0727829
$757$	1.61992e13	1.79293	0.896465	−	0.443115i	$-0.146127\pi$
$757$	1.61992e13	1.79293	0.896465	+	0.443115i	$0.146127\pi$
$758$	1.65589e12	0.182188
$759$	−2.35735e12	−0.257831
$760$	0	0
$761$	4.79250e12	0.518001	0.259001	−	0.965877i	$-0.416607\pi$
$761$	4.79250e12	0.518001	0.259001	+	0.965877i	$0.416607\pi$
$762$	1.49794e12	0.160952
$763$	−1.84655e12	−0.197243
$764$	−1.21226e13	−1.28729
$765$	0	0
$766$	5.03312e12	0.528211
$767$	−3.24460e12	−0.338518
$768$	−2.99954e11	−0.0311121
$769$	−8.41625e11	−0.0867861	−0.0433930	−	0.999058i	$-0.513817\pi$
$769$	−8.41625e11	−0.0867861	−0.0433930	+	0.999058i	$0.513817\pi$
$770$	0	0
$771$	−8.42419e11	−0.0858585
$772$	−1.22347e12	−0.123970
$773$	−3.90333e12	−0.393213	−0.196607	−	0.980482i	$-0.562992\pi$
$773$	−3.90333e12	−0.393213	−0.196607	+	0.980482i	$0.562992\pi$
$774$	−2.25916e12	−0.226263
$775$	0	0
$776$	−1.04865e13	−1.03813
$777$	2.88526e11	0.0283982
$778$	−5.49781e12	−0.537999
$779$	−2.11241e12	−0.205523
$780$	0	0
$781$	−1.86555e12	−0.179422
$782$	5.19164e11	0.0496449
$783$	−8.42507e12	−0.801024
$784$	−7.19727e12	−0.680371
$785$	0	0
$786$	−1.45149e12	−0.135648
$787$	1.42677e13	1.32577	0.662884	−	0.748723i	$-0.269332\pi$
$787$	1.42677e13	1.32577	0.662884	+	0.748723i	$0.269332\pi$
$788$	6.32939e12	0.584782
$789$	−7.26562e11	−0.0667461
$790$	0	0
$791$	−1.87460e12	−0.170261
$792$	3.46099e12	0.312563
$793$	−1.07637e12	−0.0966570
$794$	1.20087e12	0.107227
$795$	0	0
$796$	5.57748e12	0.492413
$797$	−1.77300e13	−1.55649	−0.778245	−	0.627960i	$-0.783890\pi$
$797$	−1.77300e13	−1.55649	−0.778245	+	0.627960i	$0.783890\pi$
$798$	−1.19964e11	−0.0104722
$799$	1.02395e12	0.0888829
$800$	0	0
$801$	1.53636e13	1.31870
$802$	5.39863e12	0.460785
$803$	9.81453e12	0.833009
$804$	−3.71001e12	−0.313129
$805$	0	0
$806$	8.73891e11	0.0729372
$807$	−2.79964e12	−0.232366
$808$	−2.96179e12	−0.244458
$809$	6.57374e12	0.539565	0.269783	−	0.962921i	$-0.413048\pi$
$809$	6.57374e12	0.539565	0.269783	+	0.962921i	$0.413048\pi$
$810$	0	0
$811$	1.30848e13	1.06212	0.531060	−	0.847334i	$-0.321794\pi$
$811$	1.30848e13	1.06212	0.531060	+	0.847334i	$0.321794\pi$
$812$	−2.14999e12	−0.173553
$813$	−6.49774e12	−0.521621
$814$	1.51569e12	0.121004
$815$	0	0
$816$	−2.68666e11	−0.0212132
$817$	−7.37177e12	−0.578858
$818$	−5.48665e12	−0.428467
$819$	4.55171e11	0.0353506
$820$	0	0
$821$	4.25638e12	0.326961	0.163480	−	0.986547i	$-0.447728\pi$
$821$	4.25638e12	0.326961	0.163480	+	0.986547i	$0.447728\pi$
$822$	−1.21031e12	−0.0924644
$823$	4.41691e12	0.335598	0.167799	−	0.985821i	$-0.446334\pi$
$823$	4.41691e12	0.335598	0.167799	+	0.985821i	$0.446334\pi$
$824$	−1.32982e13	−1.00490
$825$	0	0
$826$	−7.45489e11	−0.0557226
$827$	1.65971e13	1.23384	0.616919	−	0.787026i	$-0.288380\pi$
$827$	1.65971e13	1.23384	0.616919	+	0.787026i	$0.288380\pi$
$828$	−1.66641e13	−1.23210
$829$	−1.79742e13	−1.32176	−0.660882	−	0.750490i	$-0.729817\pi$
$829$	−1.79742e13	−1.32176	−0.660882	+	0.750490i	$0.729817\pi$
$830$	0	0
$831$	−5.18363e12	−0.377077
$832$	−1.61176e12	−0.116612
$833$	−1.37042e12	−0.0986171
$834$	−2.62798e12	−0.188094
$835$	0	0
$836$	5.33161e12	0.377511
$837$	−6.65667e12	−0.468805
$838$	4.01864e12	0.281502
$839$	3.10688e12	0.216469	0.108234	−	0.994125i	$-0.465480\pi$
$839$	3.10688e12	0.216469	0.108234	+	0.994125i	$0.465480\pi$
$840$	0	0
$841$	1.32025e13	0.910070
$842$	2.17354e12	0.149026
$843$	8.65626e12	0.590345
$844$	1.45092e12	0.0984246
$845$	0	0
$846$	3.88485e12	0.260740
$847$	1.44580e12	0.0965234
$848$	4.95486e12	0.329041
$849$	1.31951e12	0.0871622
$850$	0	0
$851$	−1.54581e13	−1.01036
$852$	1.34106e12	0.0871904
$853$	−1.20700e13	−0.780613	−0.390306	−	0.920685i	$-0.627631\pi$
$853$	−1.20700e13	−0.780613	−0.390306	+	0.920685i	$0.627631\pi$
$854$	−2.47311e11	−0.0159105
$855$	0	0
$856$	5.35690e12	0.341021
$857$	6.31368e12	0.399824	0.199912	−	0.979814i	$-0.435934\pi$
$857$	6.31368e12	0.399824	0.199912	+	0.979814i	$0.435934\pi$
$858$	−2.43155e11	−0.0153176
$859$	1.86663e13	1.16974	0.584870	−	0.811127i	$-0.301146\pi$
$859$	1.86663e13	1.16974	0.584870	+	0.811127i	$0.301146\pi$
$860$	0	0
$861$	−1.87269e11	−0.0116132
$862$	4.04237e12	0.249375
$863$	1.78712e13	1.09675	0.548373	−	0.836234i	$-0.315247\pi$
$863$	1.78712e13	1.09675	0.548373	+	0.836234i	$0.315247\pi$
$864$	−7.98924e12	−0.487746
$865$	0	0
$866$	−5.54766e12	−0.335181
$867$	5.00357e12	0.300742
$868$	−1.69871e12	−0.101573
$869$	3.86149e12	0.229703
$870$	0	0
$871$	−5.42926e12	−0.319639
$872$	1.47705e13	0.865107
$873$	2.62579e13	1.53002
$874$	6.42723e12	0.372583
$875$	0	0
$876$	−7.05521e12	−0.404801
$877$	3.76100e12	0.214687	0.107343	−	0.994222i	$-0.465766\pi$
$877$	3.76100e12	0.214687	0.107343	+	0.994222i	$0.465766\pi$
$878$	−7.34363e11	−0.0417047
$879$	−3.33208e12	−0.188263
$880$	0	0
$881$	2.05824e13	1.15108	0.575539	−	0.817775i	$-0.304792\pi$
$881$	2.05824e13	1.15108	0.575539	+	0.817775i	$0.304792\pi$
$882$	−5.19936e12	−0.289295
$883$	3.01536e13	1.66923	0.834616	−	0.550833i	$-0.185690\pi$
$883$	3.01536e13	1.66923	0.834616	+	0.550833i	$0.185690\pi$
$884$	−4.53049e11	−0.0249522
$885$	0	0
$886$	−7.94821e12	−0.433329
$887$	3.34317e13	1.81343	0.906717	−	0.421739i	$-0.138580\pi$
$887$	3.34317e13	1.81343	0.906717	+	0.421739i	$0.138580\pi$
$888$	−2.30790e12	−0.124554
$889$	−4.26109e12	−0.228804
$890$	0	0
$891$	−7.69533e12	−0.409051
$892$	−4.58720e12	−0.242608
$893$	1.26765e13	0.667063
$894$	1.24204e12	0.0650304
$895$	0	0
$896$	−2.65007e12	−0.137364
$897$	2.47988e12	0.127898
$898$	−7.57351e12	−0.388646
$899$	2.18935e13	1.11788
$900$	0	0
$901$	9.43448e11	0.0476932
$902$	−9.83762e11	−0.0494835
$903$	−6.53519e11	−0.0327087
$904$	1.49948e13	0.746765
$905$	0	0
$906$	3.49384e12	0.172276
$907$	−2.03004e13	−0.996030	−0.498015	−	0.867169i	$-0.665937\pi$
$907$	−2.03004e13	−0.996030	−0.498015	+	0.867169i	$0.665937\pi$
$908$	−2.39912e13	−1.17129
$909$	7.41625e12	0.360285
$910$	0	0
$911$	1.74407e13	0.838940	0.419470	−	0.907769i	$-0.362216\pi$
$911$	1.74407e13	0.838940	0.419470	+	0.907769i	$0.362216\pi$
$912$	−3.32608e12	−0.159205
$913$	−1.57534e12	−0.0750337
$914$	7.80592e12	0.369970
$915$	0	0
$916$	1.35007e13	0.633617
$917$	4.12897e12	0.192832
$918$	−4.07909e11	−0.0189571
$919$	1.69619e13	0.784430	0.392215	−	0.919874i	$-0.371709\pi$
$919$	1.69619e13	0.784430	0.392215	+	0.919874i	$0.371709\pi$
$920$	0	0
$921$	5.11332e12	0.234172
$922$	5.30243e12	0.241650
$923$	1.96251e12	0.0890031
$924$	4.72655e11	0.0213315
$925$	0	0
$926$	1.03861e12	0.0464200
$927$	3.32984e13	1.48103
$928$	2.62762e13	1.16305
$929$	4.90922e12	0.216243	0.108121	−	0.994138i	$-0.465516\pi$
$929$	4.90922e12	0.216243	0.108121	+	0.994138i	$0.465516\pi$
$930$	0	0
$931$	−1.69658e13	−0.740117
$932$	−3.05619e13	−1.32681
$933$	−4.95408e12	−0.214040
$934$	−3.84833e12	−0.165467
$935$	0	0
$936$	−3.64088e12	−0.155048
$937$	−1.13139e13	−0.479497	−0.239749	−	0.970835i	$-0.577065\pi$
$937$	−1.13139e13	−0.479497	−0.239749	+	0.970835i	$0.577065\pi$
$938$	−1.24745e12	−0.0526149
$939$	4.22980e12	0.177552
$940$	0	0
$941$	7.23052e11	0.0300619	0.0150310	−	0.999887i	$-0.495215\pi$
$941$	7.23052e11	0.0300619	0.0150310	+	0.999887i	$0.495215\pi$
$942$	2.31765e12	0.0958999
$943$	1.00332e13	0.413176
$944$	−2.06691e13	−0.847126
$945$	0	0
$946$	−3.43307e12	−0.139371
$947$	−4.04364e13	−1.63380	−0.816898	−	0.576782i	$-0.804308\pi$
$947$	−4.04364e13	−1.63380	−0.816898	+	0.576782i	$0.804308\pi$
$948$	−2.77585e12	−0.111624
$949$	−1.03247e13	−0.413216
$950$	0	0
$951$	−1.27103e13	−0.503899
$952$	−2.20492e11	−0.00870014
$953$	−4.03093e13	−1.58302	−0.791511	−	0.611155i	$-0.790705\pi$
$953$	−4.03093e13	−1.58302	−0.791511	+	0.611155i	$0.790705\pi$
$954$	3.57942e12	0.139909
$955$	0	0
$956$	3.40176e13	1.31717
$957$	−6.09172e12	−0.234767
$958$	−9.00366e12	−0.345362
$959$	3.44291e12	0.131444
$960$	0	0
$961$	−9.14153e12	−0.345751
$962$	−1.59447e12	−0.0600245
$963$	−1.34135e13	−0.502602
$964$	−4.12776e13	−1.53946
$965$	0	0
$966$	5.69784e11	0.0210530
$967$	−1.74415e13	−0.641451	−0.320726	−	0.947172i	$-0.603927\pi$
$967$	−1.74415e13	−0.641451	−0.320726	+	0.947172i	$0.603927\pi$
$968$	−1.15649e13	−0.423352
$969$	−6.33314e11	−0.0230761
$970$	0	0
$971$	−5.09597e13	−1.83967	−0.919836	−	0.392303i	$-0.871678\pi$
$971$	−5.09597e13	−1.83967	−0.919836	+	0.392303i	$0.871678\pi$
$972$	1.99563e13	0.717102
$973$	7.47565e12	0.267388
$974$	−2.77601e12	−0.0988340
$975$	0	0
$976$	−6.85683e12	−0.241880
$977$	−3.19652e13	−1.12241	−0.561205	−	0.827677i	$-0.689662\pi$
$977$	−3.19652e13	−1.12241	−0.561205	+	0.827677i	$0.689662\pi$
$978$	2.29823e11	0.00803283
$979$	2.33469e13	0.812283
$980$	0	0
$981$	−3.69848e13	−1.27501
$982$	1.73425e13	0.595127
$983$	5.12376e13	1.75024	0.875121	−	0.483904i	$-0.160782\pi$
$983$	5.12376e13	1.75024	0.875121	+	0.483904i	$0.160782\pi$
$984$	1.49795e12	0.0509354
$985$	0	0
$986$	1.34159e12	0.0452038
$987$	1.12379e12	0.0376927
$988$	−5.60873e12	−0.187266
$989$	3.50131e13	1.16372
$990$	0	0
$991$	−1.90444e13	−0.627243	−0.313622	−	0.949548i	$-0.601542\pi$
$991$	−1.90444e13	−0.627243	−0.313622	+	0.949548i	$0.601542\pi$
$992$	2.07609e13	0.680682
$993$	−2.93130e12	−0.0956730
$994$	4.50914e11	0.0146506
$995$	0	0
$996$	1.13244e12	0.0364627
$997$	−4.27709e13	−1.37095	−0.685473	−	0.728098i	$-0.740405\pi$
$997$	−4.27709e13	−1.37095	−0.685473	+	0.728098i	$0.740405\pi$
$998$	1.94471e13	0.620538
$999$	1.21455e13	0.385808

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.10.a.a.1.2		4
5.4	even	2		13.10.a.a.1.3	✓	4
15.14	odd	2		117.10.a.c.1.2		4
20.19	odd	2		208.10.a.g.1.2		4
65.64	even	2		169.10.a.a.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.10.a.a.1.3	✓	4	5.4	even	2
117.10.a.c.1.2		4	15.14	odd	2
169.10.a.a.1.2		4	65.64	even	2
208.10.a.g.1.2		4	20.19	odd	2
325.10.a.a.1.2		4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	325.a (trivial)

\(f(q)\)	\(=\)	\(q-7.35673 q^{2} -42.6243 q^{3} -457.879 q^{4} +313.575 q^{6} -892.010 q^{7} +7135.13 q^{8} -17866.2 q^{9} +O(q^{10})\)	\(q-7.35673 q^{2} -42.6243 q^{3} -457.879 q^{4} +313.575 q^{6} -892.010 q^{7} +7135.13 q^{8} -17866.2 q^{9} -27149.8 q^{11} +19516.8 q^{12} +28561.0 q^{13} +6562.27 q^{14} +181943. q^{16} +34643.4 q^{17} +131437. q^{18} +428885. q^{19} +38021.3 q^{21} +199734. q^{22} -2.03704e6 q^{23} -304130. q^{24} -210115. q^{26} +1.60051e6 q^{27} +408432. q^{28} -5.26400e6 q^{29} -4.15910e6 q^{31} -4.99169e6 q^{32} +1.15724e6 q^{33} -254862. q^{34} +8.18054e6 q^{36} +7.58854e6 q^{37} -3.15519e6 q^{38} -1.21739e6 q^{39} -4.92536e6 q^{41} -279712. q^{42} -1.71882e7 q^{43} +1.24313e7 q^{44} +1.49859e7 q^{46} +2.95568e7 q^{47} -7.75518e6 q^{48} -3.95579e7 q^{49} -1.47665e6 q^{51} -1.30775e7 q^{52} +2.72331e7 q^{53} -1.17745e7 q^{54} -6.36461e6 q^{56} -1.82809e7 q^{57} +3.87258e7 q^{58} -1.13602e8 q^{59} -3.76868e7 q^{61} +3.05973e7 q^{62} +1.59368e7 q^{63} -5.64321e7 q^{64} -8.51352e6 q^{66} -1.90094e8 q^{67} -1.58625e7 q^{68} +8.68273e7 q^{69} +6.87130e7 q^{71} -1.27477e8 q^{72} -3.61495e8 q^{73} -5.58268e7 q^{74} -1.96377e8 q^{76} +2.42179e7 q^{77} +8.95603e6 q^{78} -1.42229e8 q^{79} +2.83439e8 q^{81} +3.62346e7 q^{82} +5.80240e7 q^{83} -1.74091e7 q^{84} +1.26449e8 q^{86} +2.24374e8 q^{87} -1.93718e8 q^{88} -8.59928e8 q^{89} -2.54767e7 q^{91} +9.32716e8 q^{92} +1.77279e8 q^{93} -2.17442e8 q^{94} +2.12767e8 q^{96} -1.46970e9 q^{97} +2.91017e8 q^{98} +4.85064e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 33 q^{2} + 163 q^{3} + 1429 q^{4} - 4529 q^{6} + 11241 q^{7} + 45543 q^{8} - 29953 q^{9}+O(q^{10}) \) 4 * q + 33 * q^2 + 163 * q^3 + 1429 * q^4 - 4529 * q^6 + 11241 * q^7 + 45543 * q^8 - 29953 * q^9	\( 4 q + 33 q^{2} + 163 q^{3} + 1429 q^{4} - 4529 q^{6} + 11241 q^{7} + 45543 q^{8} - 29953 q^{9} - 40140 q^{11} + 155479 q^{12} + 114244 q^{13} - 277653 q^{14} + 726609 q^{16} - 78717 q^{17} - 1691026 q^{18} + 209664 q^{19} + 1138431 q^{21} - 1364090 q^{22} + 4257444 q^{23} + 3561573 q^{24} + 942513 q^{26} + 2077801 q^{27} - 4035181 q^{28} - 1647936 q^{29} - 11366002 q^{31} + 29458959 q^{32} + 14413222 q^{33} + 26257659 q^{34} - 11587714 q^{36} - 4636891 q^{37} - 25172466 q^{38} + 4655443 q^{39} + 13859538 q^{41} - 75564923 q^{42} + 33368081 q^{43} + 66489222 q^{44} + 71369332 q^{46} + 3943005 q^{47} + 620787 q^{48} + 23294923 q^{49} - 19664471 q^{51} + 40813669 q^{52} + 171019326 q^{53} - 64946915 q^{54} - 281552967 q^{56} + 47829030 q^{57} - 79964734 q^{58} - 63389388 q^{59} + 77050190 q^{61} + 95878740 q^{62} + 155695476 q^{63} + 768962465 q^{64} - 42396374 q^{66} + 41174072 q^{67} + 717615423 q^{68} + 546642556 q^{69} + 252460989 q^{71} - 562579254 q^{72} - 594415068 q^{73} - 957058539 q^{74} - 326897170 q^{76} - 561950454 q^{77} - 129352769 q^{78} + 115998984 q^{79} + 437803700 q^{81} + 875148240 q^{82} + 79577862 q^{83} + 108899441 q^{84} - 589924887 q^{86} + 1087526510 q^{87} + 2327564370 q^{88} - 1152240276 q^{89} + 321054201 q^{91} + 4213481460 q^{92} - 1618266556 q^{93} + 1859909503 q^{94} + 3171454029 q^{96} - 1049098084 q^{97} - 420532254 q^{98} + 2132181050 q^{99}+O(q^{100}) \) 4 * q + 33 * q^2 + 163 * q^3 + 1429 * q^4 - 4529 * q^6 + 11241 * q^7 + 45543 * q^8 - 29953 * q^9 - 40140 * q^11 + 155479 * q^12 + 114244 * q^13 - 277653 * q^14 + 726609 * q^16 - 78717 * q^17 - 1691026 * q^18 + 209664 * q^19 + 1138431 * q^21 - 1364090 * q^22 + 4257444 * q^23 + 3561573 * q^24 + 942513 * q^26 + 2077801 * q^27 - 4035181 * q^28 - 1647936 * q^29 - 11366002 * q^31 + 29458959 * q^32 + 14413222 * q^33 + 26257659 * q^34 - 11587714 * q^36 - 4636891 * q^37 - 25172466 * q^38 + 4655443 * q^39 + 13859538 * q^41 - 75564923 * q^42 + 33368081 * q^43 + 66489222 * q^44 + 71369332 * q^46 + 3943005 * q^47 + 620787 * q^48 + 23294923 * q^49 - 19664471 * q^51 + 40813669 * q^52 + 171019326 * q^53 - 64946915 * q^54 - 281552967 * q^56 + 47829030 * q^57 - 79964734 * q^58 - 63389388 * q^59 + 77050190 * q^61 + 95878740 * q^62 + 155695476 * q^63 + 768962465 * q^64 - 42396374 * q^66 + 41174072 * q^67 + 717615423 * q^68 + 546642556 * q^69 + 252460989 * q^71 - 562579254 * q^72 - 594415068 * q^73 - 957058539 * q^74 - 326897170 * q^76 - 561950454 * q^77 - 129352769 * q^78 + 115998984 * q^79 + 437803700 * q^81 + 875148240 * q^82 + 79577862 * q^83 + 108899441 * q^84 - 589924887 * q^86 + 1087526510 * q^87 + 2327564370 * q^88 - 1152240276 * q^89 + 321054201 * q^91 + 4213481460 * q^92 - 1618266556 * q^93 + 1859909503 * q^94 + 3171454029 * q^96 - 1049098084 * q^97 - 420532254 * q^98 + 2132181050 * q^99

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