LMFDB - Embedded newform 350.10.c.k.99.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [350,10,Mod(99,350)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(350, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 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("350.99"); S:= CuspForms(chi, 10); N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	350.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,0,-1536,0,-2112] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$180.262542657$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 747x^{4} + 133865x^{2} + 6927424 $ x^6 + 747x^4 + 133865x^2 + 6927424
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{6}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.5
Root			$22.6263i$ of defining polynomial
Character	$\chi$	$=$	350.99
Dual form			350.10.c.k.99.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+16.0000i q^{2} +47.7937i q^{3} -256.000 q^{4} -764.699 q^{6} -2401.00i q^{7} -4096.00i q^{8} +17398.8 q^{9} +46788.5 q^{11} -12235.2i q^{12} -30219.1i q^{13} +38416.0 q^{14} +65536.0 q^{16} +296290. i q^{17} +278380. i q^{18} -184250. q^{19} +114753. q^{21} +748616. i q^{22} +21163.1i q^{23} +195763. q^{24} +483506. q^{26} +1.77227e6i q^{27} +614656. i q^{28} -2.53606e6 q^{29} -141632. q^{31} +1.04858e6i q^{32} +2.23620e6i q^{33} -4.74064e6 q^{34} -4.45408e6 q^{36} +1.47783e7i q^{37} -2.94800e6i q^{38} +1.44428e6 q^{39} +2.09468e7 q^{41} +1.83604e6i q^{42} -4.06298e7i q^{43} -1.19779e7 q^{44} -338610. q^{46} -5.11479e7i q^{47} +3.13221e6i q^{48} -5.76480e6 q^{49} -1.41608e7 q^{51} +7.73610e6i q^{52} +3.08865e6i q^{53} -2.83564e7 q^{54} -9.83450e6 q^{56} -8.80600e6i q^{57} -4.05770e7i q^{58} -6.45486e6 q^{59} +8.87555e7 q^{61} -2.26611e6i q^{62} -4.17744e7i q^{63} -1.67772e7 q^{64} -3.57791e7 q^{66} -4.97555e6i q^{67} -7.58502e7i q^{68} -1.01146e6 q^{69} +2.42378e8 q^{71} -7.12653e7i q^{72} +6.13812e6i q^{73} -2.36452e8 q^{74} +4.71681e7 q^{76} -1.12339e8i q^{77} +2.31086e7i q^{78} -3.41226e7 q^{79} +2.57756e8 q^{81} +3.35149e8i q^{82} -1.22298e8i q^{83} -2.93767e7 q^{84} +6.50077e8 q^{86} -1.21208e8i q^{87} -1.91646e8i q^{88} +6.48556e8 q^{89} -7.25562e7 q^{91} -5.41776e6i q^{92} -6.76910e6i q^{93} +8.18366e8 q^{94} -5.01153e7 q^{96} -5.98893e8i q^{97} -9.22368e7i q^{98} +8.14062e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 1536 q^{4} - 2112 q^{6} - 102258 q^{9} - 138252 q^{11} + 230496 q^{14} + 393216 q^{16} - 3450888 q^{19} + 316932 q^{21} + 540672 q^{24} - 291456 q^{26} - 13467528 q^{29} + 1570800 q^{31} - 17506560 q^{34}+ \cdots + 9978709104 q^{99}+O(q^{100}) $ 6 * q - 1536 * q^4 - 2112 * q^6 - 102258 * q^9 - 138252 * q^11 + 230496 * q^14 + 393216 * q^16 - 3450888 * q^19 + 316932 * q^21 + 540672 * q^24 - 291456 * q^26 - 13467528 * q^29 + 1570800 * q^31 - 17506560 * q^34 + 26178048 * q^36 - 168686172 * q^39 - 54174012 * q^41 + 35392512 * q^44 + 79516800 * q^46 - 34588806 * q^49 + 271643892 * q^51 + 14544576 * q^54 - 59006976 * q^56 + 280516080 * q^59 - 15470796 * q^61 - 100663296 * q^64 + 320082240 * q^66 - 389691000 * q^69 + 445467648 * q^71 + 80645568 * q^74 + 883427328 * q^76 - 1154709636 * q^79 + 1035637974 * q^81 - 81134592 * q^84 + 271343616 * q^86 + 312138444 * q^89 + 43736616 * q^91 - 901608384 * q^94 - 138412032 * q^96 + 9978709104 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$	16.0000i	0.707107i
$2$	16.0000i	0.707107i
$3$	47.7937i	0.340663i	0.985387	+	0.170332i	$0.0544839\pi$
$3$	47.7937i	0.340663i	−0.985387	+	0.170332i	$0.945516\pi$
$4$	−256.000	−0.500000
$5$	0	0
$5$	0	0
$6$	−764.699	−0.240885
$7$	− 2401.00i	− 0.377964i
$7$	− 2401.00i	− 0.377964i
$8$	− 4096.00i	− 0.353553i
$9$	17398.8	0.883949
$10$	0	0
$11$	46788.5	0.963545	0.481773	−	0.876296i	$-0.339993\pi$
$11$	46788.5	0.963545	0.481773	+	0.876296i	$0.339993\pi$
$12$	− 12235.2i	− 0.170332i
$13$	− 30219.1i	− 0.293452i	−0.989177	−	0.146726i	$-0.953126\pi$
$13$	− 30219.1i	− 0.293452i	0.989177	−	0.146726i	$-0.0468736\pi$
$14$	38416.0	0.267261
$15$	0	0
$16$	65536.0	0.250000
$17$	296290.i	0.860393i	0.902735	+	0.430196i	$0.141556\pi$
$17$	296290.i	0.860393i	−0.902735	+	0.430196i	$0.858444\pi$
$18$	278380.i	0.625046i
$19$	−184250.	−0.324352	−0.162176	−	0.986762i	$-0.551851\pi$
$19$	−184250.	−0.324352	−0.162176	+	0.986762i	$0.551851\pi$
$20$	0	0
$21$	114753.	0.128759
$22$	748616.i	0.681329i
$23$	21163.1i	0.0157690i	0.999969	+	0.00788450i	$0.00250974\pi$
$23$	21163.1i	0.0157690i	−0.999969	+	0.00788450i	$0.997490\pi$
$24$	195763.	0.120443
$25$	0	0
$26$	483506.	0.207502
$27$	1.77227e6i	0.641792i
$28$	614656.i	0.188982i
$29$	−2.53606e6	−0.665838	−0.332919	−	0.942955i	$-0.608034\pi$
$29$	−2.53606e6	−0.665838	−0.332919	+	0.942955i	$0.608034\pi$
$30$	0	0
$31$	−141632.	−0.0275443	−0.0137722	−	0.999905i	$-0.504384\pi$
$31$	−141632.	−0.0275443	−0.0137722	+	0.999905i	$0.504384\pi$
$32$	1.04858e6i	0.176777i
$33$	2.23620e6i	0.328244i
$34$	−4.74064e6	−0.608390
$35$	0	0
$36$	−4.45408e6	−0.441974
$37$	1.47783e7i	1.29633i	0.761500	+	0.648165i	$0.224463\pi$
$37$	1.47783e7i	1.29633i	−0.761500	+	0.648165i	$0.775537\pi$
$38$	− 2.94800e6i	− 0.229352i
$39$	1.44428e6	0.0999683
$40$	0	0
$41$	2.09468e7	1.15769	0.578843	−	0.815439i	$-0.303504\pi$
$41$	2.09468e7	1.15769	0.578843	+	0.815439i	$0.303504\pi$
$42$	1.83604e6i	0.0910460i
$43$	− 4.06298e7i	− 1.81233i	−0.422927	−	0.906164i	$-0.638997\pi$
$43$	− 4.06298e7i	− 1.81233i	0.422927	−	0.906164i	$-0.361003\pi$
$44$	−1.19779e7	−0.481773
$45$	0	0
$46$	−338610.	−0.0111504
$47$	− 5.11479e7i	− 1.52893i	−0.644666	−	0.764464i	$-0.723004\pi$
$47$	− 5.11479e7i	− 1.52893i	0.644666	−	0.764464i	$-0.276996\pi$
$48$	3.13221e6i	0.0851658i
$49$	−5.76480e6	−0.142857
$50$	0	0
$51$	−1.41608e7	−0.293104
$52$	7.73610e6i	0.146726i
$53$	3.08865e6i	0.0537684i	0.999639	+	0.0268842i	$0.00855854\pi$
$53$	3.08865e6i	0.0537684i	−0.999639	+	0.0268842i	$0.991441\pi$
$54$	−2.83564e7	−0.453815
$55$	0	0
$56$	−9.83450e6	−0.133631
$57$	− 8.80600e6i	− 0.110495i
$58$	− 4.05770e7i	− 0.470819i
$59$	−6.45486e6	−0.0693510	−0.0346755	−	0.999399i	$-0.511040\pi$
$59$	−6.45486e6	−0.0693510	−0.0346755	+	0.999399i	$0.511040\pi$
$60$	0	0
$61$	8.87555e7	0.820750	0.410375	−	0.911917i	$-0.365398\pi$
$61$	8.87555e7	0.820750	0.410375	+	0.911917i	$0.365398\pi$
$62$	− 2.26611e6i	− 0.0194768i
$63$	− 4.17744e7i	− 0.334101i
$64$	−1.67772e7	−0.125000
$65$	0	0
$66$	−3.57791e7	−0.232104
$67$	− 4.97555e6i	− 0.0301651i	−0.999886	−	0.0150825i	$-0.995199\pi$
$67$	− 4.97555e6i	− 0.0301651i	0.999886	−	0.0150825i	$-0.00480111\pi$
$68$	− 7.58502e7i	− 0.430196i
$69$	−1.01146e6	−0.00537192
$70$	0	0
$71$	2.42378e8	1.13196	0.565978	−	0.824420i	$-0.308499\pi$
$71$	2.42378e8	1.13196	0.565978	+	0.824420i	$0.308499\pi$
$72$	− 7.12653e7i	− 0.312523i
$73$	6.13812e6i	0.0252978i	0.999920	+	0.0126489i	$0.00402637\pi$
$73$	6.13812e6i	0.0252978i	−0.999920	+	0.0126489i	$0.995974\pi$
$74$	−2.36452e8	−0.916644
$75$	0	0
$76$	4.71681e7	0.162176
$77$	− 1.12339e8i	− 0.364186i
$78$	2.31086e7i	0.0706882i
$79$	−3.41226e7	−0.0985645	−0.0492822	−	0.998785i	$-0.515693\pi$
$79$	−3.41226e7	−0.0985645	−0.0492822	+	0.998785i	$0.515693\pi$
$80$	0	0
$81$	2.57756e8	0.665314
$82$	3.35149e8i	0.818608i
$83$	− 1.22298e8i	− 0.282857i	−0.989948	−	0.141429i	$-0.954830\pi$
$83$	− 1.22298e8i	− 0.282857i	0.989948	−	0.141429i	$-0.0451696\pi$
$84$	−2.93767e7	−0.0643793
$85$	0	0
$86$	6.50077e8	1.28151
$87$	− 1.21208e8i	− 0.226827i
$88$	− 1.91646e8i	− 0.340665i
$89$	6.48556e8	1.09570	0.547851	−	0.836576i	$-0.315446\pi$
$89$	6.48556e8	1.09570	0.547851	+	0.836576i	$0.315446\pi$
$90$	0	0
$91$	−7.25562e7	−0.110914
$92$	− 5.41776e6i	− 0.00788450i
$93$	− 6.76910e6i	− 0.00938334i
$94$	8.18366e8	1.08112
$95$	0	0
$96$	−5.01153e7	−0.0602213
$97$	− 5.98893e8i	− 0.686873i	−0.939176	−	0.343436i	$-0.888409\pi$
$97$	− 5.98893e8i	− 0.686873i	0.939176	−	0.343436i	$-0.111591\pi$
$98$	− 9.22368e7i	− 0.101015i
$99$	8.14062e8	0.851725
$100$	0	0
$101$	−1.47791e9	−1.41319	−0.706595	−	0.707618i	$-0.749770\pi$
$101$	−1.47791e9	−1.41319	−0.706595	+	0.707618i	$0.749770\pi$
$102$	− 2.26573e8i	− 0.207256i
$103$	1.71199e9i	1.49877i	0.662136	+	0.749384i	$0.269650\pi$
$103$	1.71199e9i	1.49877i	−0.662136	+	0.749384i	$0.730350\pi$
$104$	−1.23778e8	−0.103751
$105$	0	0
$106$	−4.94184e7	−0.0380200
$107$	4.38056e8i	0.323075i	0.986867	+	0.161537i	$0.0516452\pi$
$107$	4.38056e8i	0.323075i	−0.986867	+	0.161537i	$0.948355\pi$
$108$	− 4.53702e8i	− 0.320896i
$109$	6.73291e8	0.456860	0.228430	−	0.973560i	$-0.426641\pi$
$109$	6.73291e8	0.456860	0.228430	+	0.973560i	$0.426641\pi$
$110$	0	0
$111$	−7.06308e8	−0.441612
$112$	− 1.57352e8i	− 0.0944911i
$113$	− 5.93891e8i	− 0.342652i	−0.985214	−	0.171326i	$-0.945195\pi$
$113$	− 5.93891e8i	− 0.342652i	0.985214	−	0.171326i	$-0.0548052\pi$
$114$	1.40896e8	0.0781316
$115$	0	0
$116$	6.49232e8	0.332919
$117$	− 5.25776e8i	− 0.259397i
$118$	− 1.03278e8i	− 0.0490386i
$119$	7.11392e8	0.325198
$120$	0	0
$121$	−1.68783e8	−0.0715806
$122$	1.42009e9i	0.580358i
$123$	1.00113e9i	0.394381i
$124$	3.62577e7	0.0137722
$125$	0	0
$126$	6.68391e8	0.236245
$127$	− 4.41326e9i	− 1.50537i	−0.658381	−	0.752685i	$-0.728759\pi$
$127$	− 4.41326e9i	− 1.50537i	0.658381	−	0.752685i	$-0.271241\pi$
$128$	− 2.68435e8i	− 0.0883883i
$129$	1.94185e9	0.617393
$130$	0	0
$131$	1.12810e9	0.334678	0.167339	−	0.985899i	$-0.446483\pi$
$131$	1.12810e9	0.334678	0.167339	+	0.985899i	$0.446483\pi$
$132$	− 5.72466e8i	− 0.164122i
$133$	4.42385e8i	0.122594i
$134$	7.96088e7	0.0213299
$135$	0	0
$136$	1.21360e9	0.304195
$137$	2.67934e9i	0.649808i	0.945747	+	0.324904i	$0.105332\pi$
$137$	2.67934e9i	0.649808i	−0.945747	+	0.324904i	$0.894668\pi$
$138$	− 1.61834e7i	− 0.00379852i
$139$	−1.39668e8	−0.0317344	−0.0158672	−	0.999874i	$-0.505051\pi$
$139$	−1.39668e8	−0.0317344	−0.0158672	+	0.999874i	$0.505051\pi$
$140$	0	0
$141$	2.44455e9	0.520850
$142$	3.87804e9i	0.800414i
$143$	− 1.41391e9i	− 0.282754i
$144$	1.14025e9	0.220987
$145$	0	0
$146$	−9.82098e7	−0.0178882
$147$	− 2.75521e8i	− 0.0486661i
$148$	− 3.78323e9i	− 0.648165i
$149$	3.82858e9	0.636355	0.318177	−	0.948031i	$-0.396929\pi$
$149$	3.82858e9	0.636355	0.318177	+	0.948031i	$0.396929\pi$
$150$	0	0
$151$	1.16205e10	1.81899	0.909495	−	0.415715i	$-0.136469\pi$
$151$	1.16205e10	1.81899	0.909495	+	0.415715i	$0.136469\pi$
$152$	7.54689e8i	0.114676i
$153$	5.15508e9i	0.760543i
$154$	1.79743e9	0.257518
$155$	0	0
$156$	−3.69737e8	−0.0499841
$157$	1.13647e10i	1.49283i	0.665481	+	0.746415i	$0.268226\pi$
$157$	1.13647e10i	1.49283i	−0.665481	+	0.746415i	$0.731774\pi$
$158$	− 5.45962e8i	− 0.0696956i
$159$	−1.47618e8	−0.0183169
$160$	0	0
$161$	5.08126e7	0.00596012
$162$	4.12410e9i	0.470448i
$163$	− 9.92895e9i	− 1.10169i	−0.834608	−	0.550845i	$-0.814306\pi$
$163$	− 9.92895e9i	− 1.10169i	0.834608	−	0.550845i	$-0.185694\pi$
$164$	−5.36239e9	−0.578843
$165$	0	0
$166$	1.95677e9	0.200010
$167$	− 1.98206e9i	− 0.197193i	−0.995127	−	0.0985966i	$-0.968565\pi$
$167$	− 1.98206e9i	− 0.197193i	0.995127	−	0.0985966i	$-0.0314353\pi$
$168$	− 4.70027e8i	− 0.0455230i
$169$	9.69130e9	0.913886
$170$	0	0
$171$	−3.20573e9	−0.286711
$172$	1.04012e10i	0.906164i
$173$	− 1.26158e10i	− 1.07080i	−0.844599	−	0.535400i	$-0.820161\pi$
$173$	− 1.26158e10i	− 1.07080i	0.844599	−	0.535400i	$-0.179839\pi$
$174$	1.93932e9	0.160391
$175$	0	0
$176$	3.06633e9	0.240886
$177$	− 3.08502e8i	− 0.0236253i
$178$	1.03769e10i	0.774779i
$179$	−1.67410e10	−1.21883	−0.609414	−	0.792852i	$-0.708595\pi$
$179$	−1.67410e10	−1.21883	−0.609414	+	0.792852i	$0.708595\pi$
$180$	0	0
$181$	−6.03185e8	−0.0417731	−0.0208866	−	0.999782i	$-0.506649\pi$
$181$	−6.03185e8	−0.0417731	−0.0208866	+	0.999782i	$0.506649\pi$
$182$	− 1.16090e9i	− 0.0784284i
$183$	4.24195e9i	0.279599i
$184$	8.66841e7	0.00557518
$185$	0	0
$186$	1.08306e8	0.00663502
$187$	1.38630e10i	0.829027i
$188$	1.30939e10i	0.764464i
$189$	4.25523e9	0.242574
$190$	0	0
$191$	1.41557e10	0.769627	0.384814	−	0.922994i	$-0.374266\pi$
$191$	1.41557e10	0.769627	0.384814	+	0.922994i	$0.374266\pi$
$192$	− 8.01845e8i	− 0.0425829i
$193$	9.33468e8i	0.0484274i	0.999707	+	0.0242137i	$0.00770822\pi$
$193$	9.33468e8i	0.0484274i	−0.999707	+	0.0242137i	$0.992292\pi$
$194$	9.58229e9	0.485692
$195$	0	0
$196$	1.47579e9	0.0714286
$197$	− 3.59986e9i	− 0.170289i	−0.996369	−	0.0851446i	$-0.972865\pi$
$197$	− 3.59986e9i	− 0.170289i	0.996369	−	0.0851446i	$-0.0271352\pi$
$198$	1.30250e10i	0.602260i
$199$	−1.51610e10	−0.685315	−0.342657	−	0.939460i	$-0.611327\pi$
$199$	−1.51610e10	−0.685315	−0.342657	+	0.939460i	$0.611327\pi$
$200$	0	0
$201$	2.37800e8	0.0102761
$202$	− 2.36465e10i	− 0.999277i
$203$	6.08908e9i	0.251663i
$204$	3.62516e9	0.146552
$205$	0	0
$206$	−2.73919e10	−1.05979
$207$	3.68212e8i	0.0139390i
$208$	− 1.98044e9i	− 0.0733630i
$209$	−8.62079e9	−0.312528
$210$	0	0
$211$	3.64707e10	1.26670	0.633350	−	0.773866i	$-0.281679\pi$
$211$	3.64707e10	1.26670	0.633350	+	0.773866i	$0.281679\pi$
$212$	− 7.90695e8i	− 0.0268842i
$213$	1.15841e10i	0.385616i
$214$	−7.00890e9	−0.228448
$215$	0	0
$216$	7.25924e9	0.226908
$217$	3.40057e8i	0.0104108i
$218$	1.07727e10i	0.323049i
$219$	−2.93363e8	−0.00861801
$220$	0	0
$221$	8.95363e9	0.252484
$222$	− 1.13009e10i	− 0.312267i
$223$	7.07764e10i	1.91653i	0.285874	+	0.958267i	$0.407716\pi$
$223$	7.07764e10i	1.91653i	−0.285874	+	0.958267i	$0.592284\pi$
$224$	2.51763e9	0.0668153
$225$	0	0
$226$	9.50226e9	0.242292
$227$	− 4.82157e9i	− 0.120524i	−0.998183	−	0.0602619i	$-0.980806\pi$
$227$	− 4.82157e9i	− 0.120524i	0.998183	−	0.0602619i	$-0.0191936\pi$
$228$	2.25434e9i	0.0552474i
$229$	−3.22729e10	−0.775494	−0.387747	−	0.921766i	$-0.626747\pi$
$229$	−3.22729e10	−0.775494	−0.387747	+	0.921766i	$0.626747\pi$
$230$	0	0
$231$	5.36911e9	0.124065
$232$	1.03877e10i	0.235409i
$233$	4.99119e10i	1.10944i	0.832038	+	0.554718i	$0.187174\pi$
$233$	4.99119e10i	1.10944i	−0.832038	+	0.554718i	$0.812826\pi$
$234$	8.41241e9	0.183421
$235$	0	0
$236$	1.65244e9	0.0346755
$237$	− 1.63085e9i	− 0.0335773i
$238$	1.13823e10i	0.229950i
$239$	−5.20511e10	−1.03190	−0.515952	−	0.856617i	$-0.672562\pi$
$239$	−5.20511e10	−1.03190	−0.515952	+	0.856617i	$0.672562\pi$
$240$	0	0
$241$	4.83303e10	0.922876	0.461438	−	0.887173i	$-0.347334\pi$
$241$	4.83303e10	0.922876	0.461438	+	0.887173i	$0.347334\pi$
$242$	− 2.70053e9i	− 0.0506151i
$243$	4.72028e10i	0.868440i
$244$	−2.27214e10	−0.410375
$245$	0	0
$246$	−1.60180e10	−0.278870
$247$	5.56788e9i	0.0951818i
$248$	5.80123e8i	0.00973840i
$249$	5.84507e9	0.0963591
$250$	0	0
$251$	7.61018e9	0.121022	0.0605108	−	0.998168i	$-0.480727\pi$
$251$	7.61018e9	0.121022	0.0605108	+	0.998168i	$0.480727\pi$
$252$	1.06943e10i	0.167051i
$253$	9.90190e8i	0.0151941i
$254$	7.06122e10	1.06446
$255$	0	0
$256$	4.29497e9	0.0625000
$257$	− 3.96631e10i	− 0.567136i	−0.958952	−	0.283568i	$-0.908482\pi$
$257$	− 3.96631e10i	− 0.567136i	0.958952	−	0.283568i	$-0.0915182\pi$
$258$	3.10696e10i	0.436563i
$259$	3.54826e10	0.489967
$260$	0	0
$261$	−4.41243e10	−0.588567
$262$	1.80496e10i	0.236653i
$263$	5.27510e10i	0.679877i	0.940448	+	0.339938i	$0.110406\pi$
$263$	5.27510e10i	0.679877i	−0.940448	+	0.339938i	$0.889594\pi$
$264$	9.15946e9	0.116052
$265$	0	0
$266$	−7.07816e9	−0.0866868
$267$	3.09969e10i	0.373265i
$268$	1.27374e9i	0.0150825i
$269$	−7.78415e9	−0.0906413	−0.0453206	−	0.998972i	$-0.514431\pi$
$269$	−7.78415e9	−0.0906413	−0.0453206	+	0.998972i	$0.514431\pi$
$270$	0	0
$271$	6.73788e10	0.758859	0.379430	−	0.925221i	$-0.376120\pi$
$271$	6.73788e10	0.758859	0.379430	+	0.925221i	$0.376120\pi$
$272$	1.94177e10i	0.215098i
$273$	− 3.46773e9i	− 0.0377844i
$274$	−4.28694e10	−0.459483
$275$	0	0
$276$	2.58935e8	0.00268596
$277$	1.03616e11i	1.05747i	0.848788	+	0.528734i	$0.177333\pi$
$277$	1.03616e11i	1.05747i	−0.848788	+	0.528734i	$0.822667\pi$
$278$	− 2.23468e9i	− 0.0224396i
$279$	−2.46421e9	−0.0243478
$280$	0	0
$281$	1.99578e11	1.90956	0.954781	−	0.297311i	$-0.0960898\pi$
$281$	1.99578e11	1.90956	0.954781	+	0.297311i	$0.0960898\pi$
$282$	3.91127e10i	0.368296i
$283$	1.14421e11i	1.06040i	0.847874	+	0.530199i	$0.177883\pi$
$283$	1.14421e11i	1.06040i	−0.847874	+	0.530199i	$0.822117\pi$
$284$	−6.20487e10	−0.565978
$285$	0	0
$286$	2.26225e10	0.199937
$287$	− 5.02933e10i	− 0.437564i
$288$	1.82439e10i	0.156262i
$289$	3.08002e10	0.259724
$290$	0	0
$291$	2.86233e10	0.233992
$292$	− 1.57136e9i	− 0.0126489i
$293$	1.85827e11i	1.47300i	0.676436	+	0.736501i	$0.263523\pi$
$293$	1.85827e11i	1.47300i	−0.676436	+	0.736501i	$0.736477\pi$
$294$	4.40834e9	0.0344122
$295$	0	0
$296$	6.05318e10	0.458322
$297$	8.29221e10i	0.618395i
$298$	6.12572e10i	0.449971i
$299$	6.39531e8	0.00462745
$300$	0	0
$301$	−9.75522e10	−0.684995
$302$	1.85929e11i	1.28622i
$303$	− 7.06346e10i	− 0.481422i
$304$	−1.20750e10	−0.0810881
$305$	0	0
$306$	−8.24812e10	−0.537785
$307$	− 4.40731e10i	− 0.283172i	−0.989926	−	0.141586i	$-0.954780\pi$
$307$	− 4.40731e10i	− 0.283172i	0.989926	−	0.141586i	$-0.0452202\pi$
$308$	2.87588e10i	0.182093i
$309$	−8.18225e10	−0.510575
$310$	0	0
$311$	2.34014e11	1.41847	0.709234	−	0.704973i	$-0.249041\pi$
$311$	2.34014e11	1.41847	0.709234	+	0.704973i	$0.249041\pi$
$312$	− 5.91579e9i	− 0.0353441i
$313$	2.91468e11i	1.71649i	0.513238	+	0.858246i	$0.328446\pi$
$313$	2.91468e11i	1.71649i	−0.513238	+	0.858246i	$0.671554\pi$
$314$	−1.81835e11	−1.05559
$315$	0	0
$316$	8.73539e9	0.0492822
$317$	− 5.48144e10i	− 0.304879i	−0.988313	−	0.152440i	$-0.951287\pi$
$317$	− 5.48144e10i	− 0.304879i	0.988313	−	0.152440i	$-0.0487129\pi$
$318$	− 2.36189e9i	− 0.0129520i
$319$	−1.18659e11	−0.641565
$320$	0	0
$321$	−2.09363e10	−0.110060
$322$	8.13002e8i	0.00421444i
$323$	− 5.45915e10i	− 0.279070i
$324$	−6.59856e10	−0.332657
$325$	0	0
$326$	1.58863e11	0.779012
$327$	3.21791e10i	0.155635i
$328$	− 8.57982e10i	− 0.409304i
$329$	−1.22806e11	−0.577881
$330$	0	0
$331$	3.33423e11	1.52676	0.763378	−	0.645952i	$-0.223539\pi$
$331$	3.33423e11	1.52676	0.763378	+	0.645952i	$0.223539\pi$
$332$	3.13083e10i	0.141429i
$333$	2.57123e11i	1.14589i
$334$	3.17129e10	0.139437
$335$	0	0
$336$	7.52043e9	0.0321896
$337$	1.74864e10i	0.0738527i	0.999318	+	0.0369263i	$0.0117567\pi$
$337$	1.74864e10i	0.0738527i	−0.999318	+	0.0369263i	$0.988243\pi$
$338$	1.55061e11i	0.646215i
$339$	2.83842e10	0.116729
$340$	0	0
$341$	−6.62673e9	−0.0265402
$342$	− 5.12916e10i	− 0.202735i
$343$	1.38413e10i	0.0539949i
$344$	−1.66420e11	−0.640755
$345$	0	0
$346$	2.01853e11	0.757169
$347$	5.82899e10i	0.215829i	0.994160	+	0.107915i	$0.0344173\pi$
$347$	5.82899e10i	0.215829i	−0.994160	+	0.107915i	$0.965583\pi$
$348$	3.10292e10i	0.113413i
$349$	3.27438e11	1.18145	0.590724	−	0.806874i	$-0.298842\pi$
$349$	3.27438e11	1.18145	0.590724	+	0.806874i	$0.298842\pi$
$350$	0	0
$351$	5.35566e10	0.188335
$352$	4.90613e10i	0.170332i
$353$	− 5.05786e11i	− 1.73373i	−0.498545	−	0.866864i	$-0.666132\pi$
$353$	− 5.05786e11i	− 1.73373i	0.498545	−	0.866864i	$-0.333868\pi$
$354$	4.93603e9	0.0167056
$355$	0	0
$356$	−1.66030e11	−0.547851
$357$	3.40001e10i	0.110783i
$358$	− 2.67856e11i	− 0.861841i
$359$	3.40768e11	1.08276	0.541382	−	0.840776i	$-0.317901\pi$
$359$	3.40768e11	1.08276	0.541382	+	0.840776i	$0.317901\pi$
$360$	0	0
$361$	−2.88740e11	−0.894796
$362$	− 9.65096e9i	− 0.0295381i
$363$	− 8.06678e9i	− 0.0243849i
$364$	1.85744e10	0.0554572
$365$	0	0
$366$	−6.78713e10	−0.197707
$367$	1.48153e11i	0.426298i	0.977020	+	0.213149i	$0.0683720\pi$
$367$	1.48153e11i	0.426298i	−0.977020	+	0.213149i	$0.931628\pi$
$368$	1.38695e9i	0.00394225i
$369$	3.64449e11	1.02334
$370$	0	0
$371$	7.41585e9	0.0203226
$372$	1.73289e9i	0.00469167i
$373$	6.68098e11i	1.78711i	0.448958	+	0.893553i	$0.351795\pi$
$373$	6.68098e11i	1.78711i	−0.448958	+	0.893553i	$0.648205\pi$
$374$	−2.21807e11	−0.586211
$375$	0	0
$376$	−2.09502e11	−0.540558
$377$	7.66376e10i	0.195392i
$378$	6.80837e10i	0.171526i
$379$	−6.37388e11	−1.58682	−0.793410	−	0.608687i	$-0.791696\pi$
$379$	−6.37388e11	−1.58682	−0.793410	+	0.608687i	$0.791696\pi$
$380$	0	0
$381$	2.10926e11	0.512824
$382$	2.26491e11i	0.544209i
$383$	5.84553e10i	0.138813i	0.997588	+	0.0694064i	$0.0221105\pi$
$383$	5.84553e10i	0.138813i	−0.997588	+	0.0694064i	$0.977889\pi$
$384$	1.28295e10	0.0301106
$385$	0	0
$386$	−1.49355e10	−0.0342434
$387$	− 7.06908e11i	− 1.60200i
$388$	1.53317e11i	0.343436i
$389$	4.40338e11	0.975018	0.487509	−	0.873118i	$-0.337906\pi$
$389$	4.40338e11	0.975018	0.487509	+	0.873118i	$0.337906\pi$
$390$	0	0
$391$	−6.27042e9	−0.0135675
$392$	2.36126e10i	0.0505076i
$393$	5.39162e10i	0.114013i
$394$	5.75977e10	0.120413
$395$	0	0
$396$	−2.08400e11	−0.425862
$397$	− 8.55630e11i	− 1.72874i	−0.502859	−	0.864368i	$-0.667719\pi$
$397$	− 8.55630e11i	− 1.72874i	0.502859	−	0.864368i	$-0.332281\pi$
$398$	− 2.42577e11i	− 0.484591i
$399$	−2.11432e10	−0.0417631
$400$	0	0
$401$	−3.72657e11	−0.719713	−0.359857	−	0.933008i	$-0.617174\pi$
$401$	−3.72657e11	−0.719713	−0.359857	+	0.933008i	$0.617174\pi$
$402$	3.80480e9i	0.00726632i
$403$	4.27999e9i	0.00808294i
$404$	3.78344e11	0.706595
$405$	0	0
$406$	−9.74253e10	−0.177953
$407$	6.91453e11i	1.24907i
$408$	5.80026e10i	0.103628i
$409$	5.39642e11	0.953566	0.476783	−	0.879021i	$-0.341803\pi$
$409$	5.39642e11	0.953566	0.476783	+	0.879021i	$0.341803\pi$
$410$	0	0
$411$	−1.28055e11	−0.221365
$412$	− 4.38270e11i	− 0.749384i
$413$	1.54981e10i	0.0262122i
$414$	−5.89139e9	−0.00985635
$415$	0	0
$416$	3.16871e10	0.0518755
$417$	− 6.67524e9i	− 0.0108107i
$418$	− 1.37933e11i	− 0.220991i
$419$	5.16016e11	0.817900	0.408950	−	0.912557i	$-0.365895\pi$
$419$	5.16016e11	0.817900	0.408950	+	0.912557i	$0.365895\pi$
$420$	0	0
$421$	4.17716e11	0.648055	0.324028	−	0.946048i	$-0.394963\pi$
$421$	4.17716e11	0.648055	0.324028	+	0.946048i	$0.394963\pi$
$422$	5.83532e11i	0.895692i
$423$	− 8.89910e11i	− 1.35149i
$424$	1.26511e10	0.0190100
$425$	0	0
$426$	−1.85346e11	−0.272672
$427$	− 2.13102e11i	− 0.310214i
$428$	− 1.12142e11i	− 0.161537i
$429$	6.75759e10	0.0963239
$430$	0	0
$431$	8.43198e11	1.17702	0.588508	−	0.808492i	$-0.299716\pi$
$431$	8.43198e11	1.17702	0.588508	+	0.808492i	$0.299716\pi$
$432$	1.16148e11i	0.160448i
$433$	3.77330e11i	0.515853i	0.966164	+	0.257927i	$0.0830393\pi$
$433$	3.77330e11i	0.515853i	−0.966164	+	0.257927i	$0.916961\pi$
$434$	−5.44092e9	−0.00736154
$435$	0	0
$436$	−1.72362e11	−0.228430
$437$	− 3.89931e9i	− 0.00511471i
$438$	− 4.69381e9i	− 0.00609386i
$439$	4.84525e11	0.622624	0.311312	−	0.950308i	$-0.399232\pi$
$439$	4.84525e11	0.622624	0.311312	+	0.950308i	$0.399232\pi$
$440$	0	0
$441$	−1.00300e11	−0.126278
$442$	1.43258e11i	0.178533i
$443$	− 1.11440e12i	− 1.37475i	−0.726301	−	0.687376i	$-0.758762\pi$
$443$	− 1.11440e12i	− 1.37475i	0.726301	−	0.687376i	$-0.241238\pi$
$444$	1.80815e11	0.220806
$445$	0	0
$446$	−1.13242e12	−1.35519
$447$	1.82982e11i	0.216783i
$448$	4.02821e10i	0.0472456i
$449$	−1.02272e12	−1.18754	−0.593770	−	0.804635i	$-0.702361\pi$
$449$	−1.02272e12	−1.18754	−0.593770	+	0.804635i	$0.702361\pi$
$450$	0	0
$451$	9.80071e11	1.11548
$452$	1.52036e11i	0.171326i
$453$	5.55389e11i	0.619662i
$454$	7.71452e10	0.0852231
$455$	0	0
$456$	−3.60694e10	−0.0390658
$457$	− 1.20876e12i	− 1.29634i	−0.761497	−	0.648168i	$-0.775535\pi$
$457$	− 1.20876e12i	− 1.29634i	0.761497	−	0.648168i	$-0.224465\pi$
$458$	− 5.16366e11i	− 0.548357i
$459$	−5.25107e11	−0.552193
$460$	0	0
$461$	1.07621e12	1.10980	0.554898	−	0.831919i	$-0.312757\pi$
$461$	1.07621e12	1.10980	0.554898	+	0.831919i	$0.312757\pi$
$462$	8.59057e10i	0.0877270i
$463$	− 7.86233e11i	− 0.795127i	−0.917575	−	0.397564i	$-0.869856\pi$
$463$	− 7.86233e11i	− 0.795127i	0.917575	−	0.397564i	$-0.130144\pi$
$464$	−1.66203e11	−0.166460
$465$	0	0
$466$	−7.98590e11	−0.784490
$467$	1.25725e12i	1.22319i	0.791170	+	0.611597i	$0.209472\pi$
$467$	1.25725e12i	1.22319i	−0.791170	+	0.611597i	$0.790528\pi$
$468$	1.34599e11i	0.129698i
$469$	−1.19463e10	−0.0114013
$470$	0	0
$471$	−5.43162e11	−0.508552
$472$	2.64391e10i	0.0245193i
$473$	− 1.90101e12i	− 1.74626i
$474$	2.60935e10	0.0237427
$475$	0	0
$476$	−1.82116e11	−0.162599
$477$	5.37387e10i	0.0475285i
$478$	− 8.32818e11i	− 0.729666i
$479$	−1.24726e12	−1.08255	−0.541274	−	0.840846i	$-0.682058\pi$
$479$	−1.24726e12	−1.08255	−0.541274	+	0.840846i	$0.682058\pi$
$480$	0	0
$481$	4.46586e11	0.380411
$482$	7.73286e11i	0.652572i
$483$	2.42852e9i	0.00203039i
$484$	4.32085e10	0.0357903
$485$	0	0
$486$	−7.55245e11	−0.614080
$487$	1.79336e11i	0.144474i	0.997388	+	0.0722368i	$0.0230137\pi$
$487$	1.79336e11i	0.144474i	−0.997388	+	0.0722368i	$0.976986\pi$
$488$	− 3.63542e11i	− 0.290179i
$489$	4.74541e11	0.375305
$490$	0	0
$491$	4.94081e11	0.383647	0.191823	−	0.981429i	$-0.438560\pi$
$491$	4.94081e11	0.383647	0.191823	+	0.981429i	$0.438560\pi$
$492$	− 2.56288e11i	− 0.197191i
$493$	− 7.51410e11i	− 0.572883i
$494$	−8.90862e10	−0.0673037
$495$	0	0
$496$	−9.28197e9	−0.00688609
$497$	− 5.81949e11i	− 0.427840i
$498$	9.35211e10i	0.0681362i
$499$	6.73453e11	0.486245	0.243122	−	0.969996i	$-0.421828\pi$
$499$	6.73453e11	0.486245	0.243122	+	0.969996i	$0.421828\pi$
$500$	0	0
$501$	9.47298e10	0.0671764
$502$	1.21763e11i	0.0855752i
$503$	3.69632e11i	0.257462i	0.991680	+	0.128731i	$0.0410904\pi$
$503$	3.69632e11i	0.257462i	−0.991680	+	0.128731i	$0.958910\pi$
$504$	−1.71108e11	−0.118123
$505$	0	0
$506$	−1.58430e10	−0.0107439
$507$	4.63183e11i	0.311327i
$508$	1.12980e12i	0.752685i
$509$	1.87204e11	0.123619	0.0618094	−	0.998088i	$-0.480313\pi$
$509$	1.87204e11	0.123619	0.0618094	+	0.998088i	$0.480313\pi$
$510$	0	0
$511$	1.47376e10	0.00956166
$512$	6.87195e10i	0.0441942i
$513$	− 3.26542e11i	− 0.208167i
$514$	6.34609e11	0.401026
$515$	0	0
$516$	−4.97113e11	−0.308697
$517$	− 2.39313e12i	− 1.47319i
$518$	5.67722e11i	0.346459i
$519$	6.02957e11	0.364782
$520$	0	0
$521$	−1.46566e12	−0.871494	−0.435747	−	0.900069i	$-0.643516\pi$
$521$	−1.46566e12	−0.871494	−0.435747	+	0.900069i	$0.643516\pi$
$522$	− 7.05989e11i	− 0.416180i
$523$	2.21909e11i	0.129693i	0.997895	+	0.0648467i	$0.0206558\pi$
$523$	2.21909e11i	0.129693i	−0.997895	+	0.0648467i	$0.979344\pi$
$524$	−2.88794e11	−0.167339
$525$	0	0
$526$	−8.44017e11	−0.480745
$527$	− 4.19640e10i	− 0.0236990i
$528$	1.46551e11i	0.0820611i
$529$	1.80070e12	0.999751
$530$	0	0
$531$	−1.12307e11	−0.0613027
$532$	− 1.13251e11i	− 0.0612968i
$533$	− 6.32995e11i	− 0.339725i
$534$	−4.95950e11	−0.263938
$535$	0	0
$536$	−2.03799e10	−0.0106650
$537$	− 8.00114e11i	− 0.415210i
$538$	− 1.24546e11i	− 0.0640931i
$539$	−2.69726e11	−0.137649
$540$	0	0
$541$	−1.75400e12	−0.880323	−0.440162	−	0.897919i	$-0.645079\pi$
$541$	−1.75400e12	−0.880323	−0.440162	+	0.897919i	$0.645079\pi$
$542$	1.07806e12i	0.536594i
$543$	− 2.88284e10i	− 0.0142306i
$544$	−3.10683e11	−0.152097
$545$	0	0
$546$	5.54836e10	0.0267176
$547$	− 2.01155e12i	− 0.960701i	−0.877077	−	0.480351i	$-0.840509\pi$
$547$	− 2.01155e12i	− 0.960701i	0.877077	−	0.480351i	$-0.159491\pi$
$548$	− 6.85910e11i	− 0.324904i
$549$	1.54424e12	0.725501
$550$	0	0
$551$	4.67270e11	0.215966
$552$	4.14295e9i	0.00189926i
$553$	8.19284e10i	0.0372539i
$554$	−1.65785e12	−0.747743
$555$	0	0
$556$	3.57550e10	0.0158672
$557$	− 6.62452e11i	− 0.291613i	−0.989313	−	0.145806i	$-0.953422\pi$
$557$	− 6.62452e11i	− 0.291613i	0.989313	−	0.145806i	$-0.0465776\pi$
$558$	− 3.94274e10i	− 0.0172165i
$559$	−1.22780e12	−0.531831
$560$	0	0
$561$	−6.62562e11	−0.282419
$562$	3.19324e12i	1.35026i
$563$	− 1.14706e12i	− 0.481171i	−0.970628	−	0.240585i	$-0.922661\pi$
$563$	− 1.14706e12i	− 0.481171i	0.970628	−	0.240585i	$-0.0773394\pi$
$564$	−6.25804e11	−0.260425
$565$	0	0
$566$	−1.83074e12	−0.749814
$567$	− 6.18873e11i	− 0.251465i
$568$	− 9.92779e11i	− 0.400207i
$569$	1.08600e12	0.434333	0.217167	−	0.976135i	$-0.430319\pi$
$569$	1.08600e12	0.434333	0.217167	+	0.976135i	$0.430319\pi$
$570$	0	0
$571$	−7.48876e11	−0.294813	−0.147407	−	0.989076i	$-0.547093\pi$
$571$	−7.48876e11	−0.294813	−0.147407	+	0.989076i	$0.547093\pi$
$572$	3.61961e11i	0.141377i
$573$	6.76552e11i	0.262184i
$574$	8.04694e11	0.309405
$575$	0	0
$576$	−2.91903e11	−0.110494
$577$	− 3.40755e12i	− 1.27983i	−0.768447	−	0.639914i	$-0.778970\pi$
$577$	− 3.40755e12i	− 1.27983i	0.768447	−	0.639914i	$-0.221030\pi$
$578$	4.92803e11i	0.183653i
$579$	−4.46139e10	−0.0164974
$580$	0	0
$581$	−2.93637e11	−0.106910
$582$	4.57973e11i	0.165457i
$583$	1.44513e11i	0.0518083i
$584$	2.51417e10	0.00894411
$585$	0	0
$586$	−2.97322e12	−1.04157
$587$	− 3.56830e12i	− 1.24048i	−0.784412	−	0.620241i	$-0.787035\pi$
$587$	− 3.56830e12i	− 1.24048i	0.784412	−	0.620241i	$-0.212965\pi$
$588$	7.05334e10i	0.0243331i
$589$	2.60957e10	0.00893407
$590$	0	0
$591$	1.72051e11	0.0580113
$592$	9.68508e11i	0.324082i
$593$	− 5.06024e12i	− 1.68045i	−0.542240	−	0.840224i	$-0.682424\pi$
$593$	− 5.06024e12i	− 1.68045i	0.542240	−	0.840224i	$-0.317576\pi$
$594$	−1.32675e12	−0.437272
$595$	0	0
$596$	−9.80116e11	−0.318177
$597$	− 7.24602e11i	− 0.233461i
$598$	1.02325e10i	0.00327210i
$599$	−3.96760e12	−1.25924	−0.629618	−	0.776905i	$-0.716789\pi$
$599$	−3.96760e12	−1.25924	−0.629618	+	0.776905i	$0.716789\pi$
$600$	0	0
$601$	−3.08383e12	−0.964173	−0.482086	−	0.876124i	$-0.660121\pi$
$601$	−3.08383e12	−0.964173	−0.482086	+	0.876124i	$0.660121\pi$
$602$	− 1.56083e12i	− 0.484365i
$603$	− 8.65684e10i	− 0.0266644i
$604$	−2.97486e12	−0.909495
$605$	0	0
$606$	1.13015e12	0.340417
$607$	− 2.30191e11i	− 0.0688239i	−0.999408	−	0.0344120i	$-0.989044\pi$
$607$	− 2.30191e11i	− 0.0688239i	0.999408	−	0.0344120i	$-0.0109558\pi$
$608$	− 1.93200e11i	− 0.0573379i
$609$	−2.91020e11	−0.0857324
$610$	0	0
$611$	−1.54565e12	−0.448667
$612$	− 1.31970e12i	− 0.380272i
$613$	3.21533e12i	0.919716i	0.887992	+	0.459858i	$0.152100\pi$
$613$	3.21533e12i	0.919716i	−0.887992	+	0.459858i	$0.847900\pi$
$614$	7.05170e11	0.200233
$615$	0	0
$616$	−4.60141e11	−0.128759
$617$	− 5.58117e12i	− 1.55039i	−0.631720	−	0.775196i	$-0.717651\pi$
$617$	− 5.58117e12i	− 1.55039i	0.631720	−	0.775196i	$-0.282349\pi$
$618$	− 1.30916e12i	− 0.361031i
$619$	3.95942e11	0.108398	0.0541992	−	0.998530i	$-0.482739\pi$
$619$	3.95942e11	0.108398	0.0541992	+	0.998530i	$0.482739\pi$
$620$	0	0
$621$	−3.75068e10	−0.0101204
$622$	3.74422e12i	1.00301i
$623$	− 1.55718e12i	− 0.414137i
$624$	9.46526e10	0.0249921
$625$	0	0
$626$	−4.66349e12	−1.21374
$627$	− 4.12020e11i	− 0.106467i
$628$	− 2.90937e12i	− 0.746415i
$629$	−4.37865e12	−1.11535
$630$	0	0
$631$	−2.03177e12	−0.510203	−0.255102	−	0.966914i	$-0.582109\pi$
$631$	−2.03177e12	−0.510203	−0.255102	+	0.966914i	$0.582109\pi$
$632$	1.39766e11i	0.0348478i
$633$	1.74307e12i	0.431518i
$634$	8.77030e11	0.215582
$635$	0	0
$636$	3.77902e10	0.00915846
$637$	1.74207e11i	0.0419217i
$638$	− 1.89854e12i	− 0.453655i
$639$	4.21707e12	1.00059
$640$	0	0
$641$	5.58429e12	1.30649	0.653246	−	0.757146i	$-0.273407\pi$
$641$	5.58429e12	1.30649	0.653246	+	0.757146i	$0.273407\pi$
$642$	− 3.34981e11i	− 0.0778239i
$643$	6.16637e12i	1.42259i	0.702893	+	0.711296i	$0.251891\pi$
$643$	6.16637e12i	1.42259i	−0.702893	+	0.711296i	$0.748109\pi$
$644$	−1.30080e10	−0.00298006
$645$	0	0
$646$	8.73464e11	0.197332
$647$	− 1.02974e11i	− 0.0231025i	−0.999933	−	0.0115512i	$-0.996323\pi$
$647$	− 1.02974e11i	− 0.0231025i	0.999933	−	0.0115512i	$-0.00367696\pi$
$648$	− 1.05577e12i	− 0.235224i
$649$	−3.02013e11	−0.0668228
$650$	0	0
$651$	−1.62526e10	−0.00354657
$652$	2.54181e12i	0.550845i
$653$	− 2.82592e12i	− 0.608207i	−0.952639	−	0.304103i	$-0.901643\pi$
$653$	− 2.82592e12i	− 0.608207i	0.952639	−	0.304103i	$-0.0983568\pi$
$654$	−5.14865e11	−0.110051
$655$	0	0
$656$	1.37277e12	0.289422
$657$	1.06796e11i	0.0223619i
$658$	− 1.96490e12i	− 0.408623i
$659$	5.44052e12	1.12371	0.561857	−	0.827234i	$-0.310087\pi$
$659$	5.44052e12	1.12371	0.561857	+	0.827234i	$0.310087\pi$
$660$	0	0
$661$	3.62012e12	0.737592	0.368796	−	0.929510i	$-0.379770\pi$
$661$	3.62012e12	0.737592	0.368796	+	0.929510i	$0.379770\pi$
$662$	5.33477e12i	1.07958i
$663$	4.27927e11i	0.0860120i
$664$	−5.00932e11	−0.100005
$665$	0	0
$666$	−4.11398e12	−0.810266
$667$	− 5.36710e10i	− 0.0104996i
$668$	5.07406e11i	0.0985966i
$669$	−3.38267e12	−0.652892
$670$	0	0
$671$	4.15274e12	0.790830
$672$	1.20327e11i	0.0227615i
$673$	1.96230e12i	0.368721i	0.982859	+	0.184361i	$0.0590214\pi$
$673$	1.96230e12i	0.368721i	−0.982859	+	0.184361i	$0.940979\pi$
$674$	−2.79783e11	−0.0522217
$675$	0	0
$676$	−2.48097e12	−0.456943
$677$	6.57309e12i	1.20260i	0.799024	+	0.601299i	$0.205350\pi$
$677$	6.57309e12i	1.20260i	−0.799024	+	0.601299i	$0.794650\pi$
$678$	4.54148e11i	0.0825399i
$679$	−1.43794e12	−0.259614
$680$	0	0
$681$	2.30441e11	0.0410580
$682$	− 1.06028e11i	− 0.0187668i
$683$	2.98633e12i	0.525103i	0.964918	+	0.262551i	$0.0845640\pi$
$683$	2.98633e12i	0.525103i	−0.964918	+	0.262551i	$0.915436\pi$
$684$	8.20666e11	0.143355
$685$	0	0
$686$	−2.21461e11	−0.0381802
$687$	− 1.54244e12i	− 0.264182i
$688$	− 2.66272e12i	− 0.453082i
$689$	9.33364e10	0.0157785
$690$	0	0
$691$	4.56733e12	0.762098	0.381049	−	0.924555i	$-0.375563\pi$
$691$	4.56733e12	0.762098	0.381049	+	0.924555i	$0.375563\pi$
$692$	3.22965e12i	0.535400i
$693$	− 1.95456e12i	− 0.321922i
$694$	−9.32638e11	−0.152614
$695$	0	0
$696$	−4.96467e11	−0.0801953
$697$	6.20634e12i	0.996065i
$698$	5.23901e12i	0.835410i
$699$	−2.38547e12	−0.377944
$700$	0	0
$701$	−6.84995e12	−1.07141	−0.535706	−	0.844405i	$-0.679954\pi$
$701$	−6.84995e12	−1.07141	−0.535706	+	0.844405i	$0.679954\pi$
$702$	8.56906e11i	0.133173i
$703$	− 2.72290e12i	− 0.420467i
$704$	−7.84981e11	−0.120443
$705$	0	0
$706$	8.09258e12	1.22593
$707$	3.54845e12i	0.534136i
$708$	7.89764e10i	0.0118127i
$709$	8.40144e12	1.24866	0.624332	−	0.781159i	$-0.285371\pi$
$709$	8.40144e12	1.24866	0.624332	+	0.781159i	$0.285371\pi$
$710$	0	0
$711$	−5.93691e11	−0.0871260
$712$	− 2.65649e12i	− 0.387389i
$713$	− 2.99736e9i	0 0.000434347i
$714$	−5.44001e11	−0.0783353
$715$	0	0
$716$	4.28569e12	0.609414
$717$	− 2.48771e12i	− 0.351532i
$718$	5.45229e12i	0.765630i
$719$	−4.28211e12	−0.597555	−0.298777	−	0.954323i	$-0.596579\pi$
$719$	−4.28211e12	−0.597555	−0.298777	+	0.954323i	$0.596579\pi$
$720$	0	0
$721$	4.11049e12	0.566481
$722$	− 4.61983e12i	− 0.632716i
$723$	2.30989e12i	0.314390i
$724$	1.54415e11	0.0208866
$725$	0	0
$726$	1.29068e11	0.0172427
$727$	4.03989e12i	0.536370i	0.963367	+	0.268185i	$0.0864238\pi$
$727$	4.03989e12i	0.536370i	−0.963367	+	0.268185i	$0.913576\pi$
$728$	2.97190e11i	0.0392142i
$729$	2.81742e12	0.369469
$730$	0	0
$731$	1.20382e13	1.55931
$732$	− 1.08594e12i	− 0.139800i
$733$	− 8.78598e12i	− 1.12415i	−0.827088	−	0.562073i	$-0.810004\pi$
$733$	− 8.78598e12i	− 1.12415i	0.827088	−	0.562073i	$-0.189996\pi$
$734$	−2.37045e12	−0.301439
$735$	0	0
$736$	−2.21911e10	−0.00278759
$737$	− 2.32799e11i	− 0.0290654i
$738$	5.83118e12i	0.723608i
$739$	1.26308e13	1.55787	0.778935	−	0.627105i	$-0.215760\pi$
$739$	1.26308e13	1.55787	0.778935	+	0.627105i	$0.215760\pi$
$740$	0	0
$741$	−2.66110e11	−0.0324249
$742$	1.18654e11i	0.0143702i
$743$	1.72613e12i	0.207790i	0.994588	+	0.103895i	$0.0331306\pi$
$743$	1.72613e12i	0.207790i	−0.994588	+	0.103895i	$0.966869\pi$
$744$	−2.77262e10	−0.00331751
$745$	0	0
$746$	−1.06896e13	−1.26367
$747$	− 2.12783e12i	− 0.250031i
$748$	− 3.54892e12i	− 0.414514i
$749$	1.05177e12	0.122111
$750$	0	0
$751$	3.06753e12	0.351892	0.175946	−	0.984400i	$-0.443702\pi$
$751$	3.06753e12	0.351892	0.175946	+	0.984400i	$0.443702\pi$
$752$	− 3.35203e12i	− 0.382232i
$753$	3.63718e11i	0.0412276i
$754$	−1.22620e12	−0.138163
$755$	0	0
$756$	−1.08934e12	−0.121287
$757$	6.51793e12i	0.721403i	0.932681	+	0.360702i	$0.117463\pi$
$757$	6.51793e12i	0.721403i	−0.932681	+	0.360702i	$0.882537\pi$
$758$	− 1.01982e13i	− 1.12205i
$759$	−4.73249e10	−0.00517608
$760$	0	0
$761$	−4.75019e11	−0.0513428	−0.0256714	−	0.999670i	$-0.508172\pi$
$761$	−4.75019e11	−0.0513428	−0.0256714	+	0.999670i	$0.508172\pi$
$762$	3.37482e12i	0.362621i
$763$	− 1.61657e12i	− 0.172677i
$764$	−3.62385e12	−0.384814
$765$	0	0
$766$	−9.35285e11	−0.0981555
$767$	1.95060e11i	0.0203512i
$768$	2.05272e11i	0.0212914i
$769$	−7.10887e12	−0.733048	−0.366524	−	0.930409i	$-0.619452\pi$
$769$	−7.10887e12	−0.733048	−0.366524	+	0.930409i	$0.619452\pi$
$770$	0	0
$771$	1.89564e12	0.193202
$772$	− 2.38968e11i	− 0.0242137i
$773$	6.83668e12i	0.688712i	0.938839	+	0.344356i	$0.111903\pi$
$773$	6.83668e12i	0.688712i	−0.938839	+	0.344356i	$0.888097\pi$
$774$	1.13105e13	1.13279
$775$	0	0
$776$	−2.45307e12	−0.242846
$777$	1.69584e12i	0.166914i
$778$	7.04540e12i	0.689442i
$779$	−3.85946e12	−0.375498
$780$	0	0
$781$	1.13405e13	1.09069
$782$	− 1.00327e11i	− 0.00959370i
$783$	− 4.49460e12i	− 0.427330i
$784$	−3.77802e11	−0.0357143
$785$	0	0
$786$	−8.62659e11	−0.0806190
$787$	− 6.09938e12i	− 0.566760i	−0.959008	−	0.283380i	$-0.908544\pi$
$787$	− 6.09938e12i	− 0.566760i	0.959008	−	0.283380i	$-0.0914558\pi$
$788$	9.21564e11i	0.0851446i
$789$	−2.52117e12	−0.231609
$790$	0	0
$791$	−1.42593e12	−0.129510
$792$	− 3.33440e12i	− 0.301130i
$793$	− 2.68211e12i	− 0.240851i
$794$	1.36901e13	1.22240
$795$	0	0
$796$	3.88122e12	0.342657
$797$	6.20696e12i	0.544900i	0.962170	+	0.272450i	$0.0878339\pi$
$797$	6.20696e12i	0.544900i	−0.962170	+	0.272450i	$0.912166\pi$
$798$	− 3.38291e11i	− 0.0295310i
$799$	1.51546e13	1.31548
$800$	0	0
$801$	1.12841e13	0.968545
$802$	− 5.96251e12i	− 0.508914i
$803$	2.87193e11i	0.0243755i
$804$	−6.08768e10	−0.00513807
$805$	0	0
$806$	−6.84798e10	−0.00571550
$807$	− 3.72033e11i	− 0.0308781i
$808$	6.05351e12i	0.499638i
$809$	1.43675e13	1.17927	0.589633	−	0.807671i	$-0.299272\pi$
$809$	1.43675e13	1.17927	0.589633	+	0.807671i	$0.299272\pi$
$810$	0	0
$811$	1.78668e13	1.45028	0.725140	−	0.688602i	$-0.241775\pi$
$811$	1.78668e13	1.45028	0.725140	+	0.688602i	$0.241775\pi$
$812$	− 1.55881e12i	− 0.125832i
$813$	3.22028e12i	0.258515i
$814$	−1.10632e13	−0.883228
$815$	0	0
$816$	−9.28042e11	−0.0732760
$817$	7.48605e12i	0.587832i
$818$	8.63427e12i	0.674273i
$819$	−1.26239e12	−0.0980427
$820$	0	0
$821$	−8.35383e12	−0.641714	−0.320857	−	0.947128i	$-0.603971\pi$
$821$	−8.35383e12	−0.641714	−0.320857	+	0.947128i	$0.603971\pi$
$822$	− 2.04889e12i	− 0.156529i
$823$	1.49432e13i	1.13539i	0.823239	+	0.567696i	$0.192165\pi$
$823$	1.49432e13i	1.13539i	−0.823239	+	0.567696i	$0.807835\pi$
$824$	7.01232e12	0.529894
$825$	0	0
$826$	−2.47970e11	−0.0185348
$827$	− 1.86653e13i	− 1.38758i	−0.720175	−	0.693792i	$-0.755938\pi$
$827$	− 1.86653e13i	− 1.38758i	0.720175	−	0.693792i	$-0.244062\pi$
$828$	− 9.42622e10i	− 0.00696949i
$829$	−1.50539e13	−1.10701	−0.553506	−	0.832845i	$-0.686711\pi$
$829$	−1.50539e13	−1.10701	−0.553506	+	0.832845i	$0.686711\pi$
$830$	0	0
$831$	−4.95219e12	−0.360240
$832$	5.06993e11i	0.0366815i
$833$	− 1.70805e12i	− 0.122913i
$834$	1.06804e11	0.00764433
$835$	0	0
$836$	2.20692e12	0.156264
$837$	− 2.51010e11i	− 0.0176777i
$838$	8.25626e12i	0.578342i
$839$	1.47923e13	1.03064	0.515320	−	0.856998i	$-0.327673\pi$
$839$	1.47923e13	1.03064	0.515320	+	0.856998i	$0.327673\pi$
$840$	0	0
$841$	−8.07554e12	−0.556659
$842$	6.68346e12i	0.458244i
$843$	9.53856e12i	0.650517i
$844$	−9.33651e12	−0.633350
$845$	0	0
$846$	1.42386e13	0.955651
$847$	4.05249e11i	0.0270549i
$848$	2.02418e11i	0.0134421i
$849$	−5.46863e12	−0.361238
$850$	0	0
$851$	−3.12754e11	−0.0204418
$852$	− 2.96554e12i	− 0.192808i
$853$	2.80780e13i	1.81591i	0.419064	+	0.907957i	$0.362358\pi$
$853$	2.80780e13i	1.81591i	−0.419064	+	0.907957i	$0.637642\pi$
$854$	3.40963e12	0.219355
$855$	0	0
$856$	1.79428e12	0.114224
$857$	1.40734e13i	0.891218i	0.895228	+	0.445609i	$0.147013\pi$
$857$	1.40734e13i	0.891218i	−0.895228	+	0.445609i	$0.852987\pi$
$858$	1.08121e12i	0.0681113i
$859$	4.08045e12	0.255705	0.127852	−	0.991793i	$-0.459192\pi$
$859$	4.08045e12	0.255705	0.127852	+	0.991793i	$0.459192\pi$
$860$	0	0
$861$	2.40371e12	0.149062
$862$	1.34912e13i	0.832275i
$863$	2.65684e13i	1.63048i	0.579121	+	0.815242i	$0.303396\pi$
$863$	2.65684e13i	1.63048i	−0.579121	+	0.815242i	$0.696604\pi$
$864$	−1.85836e12	−0.113454
$865$	0	0
$866$	−6.03729e12	−0.364763
$867$	1.47205e12i	0.0884785i
$868$	− 8.70547e10i	− 0.00520539i
$869$	−1.59655e12	−0.0949714
$870$	0	0
$871$	−1.50357e11	−0.00885201
$872$	− 2.75780e12i	− 0.161524i
$873$	− 1.04200e13i	− 0.607160i
$874$	6.23889e10	0.00361665
$875$	0	0
$876$	7.51010e10	0.00430901
$877$	− 2.30661e13i	− 1.31667i	−0.752727	−	0.658333i	$-0.771262\pi$
$877$	− 2.30661e13i	− 1.31667i	0.752727	−	0.658333i	$-0.228738\pi$
$878$	7.75240e12i	0.440262i
$879$	−8.88134e12	−0.501797
$880$	0	0
$881$	3.49096e13	1.95233	0.976164	−	0.217033i	$-0.0696381\pi$
$881$	3.49096e13	1.95233	0.976164	+	0.217033i	$0.0696381\pi$
$882$	− 1.60481e12i	− 0.0892923i
$883$	− 7.37648e12i	− 0.408344i	−0.978935	−	0.204172i	$-0.934550\pi$
$883$	− 7.37648e12i	− 0.408344i	0.978935	−	0.204172i	$-0.0654501\pi$
$884$	−2.29213e12	−0.126242
$885$	0	0
$886$	1.78304e13	0.972097
$887$	1.87675e13i	1.01800i	0.860765	+	0.509002i	$0.169985\pi$
$887$	1.87675e13i	1.01800i	−0.860765	+	0.509002i	$0.830015\pi$
$888$	2.89304e12i	0.156133i
$889$	−1.05962e13	−0.568976
$890$	0	0
$891$	1.20600e13	0.641060
$892$	− 1.81188e13i	− 0.958267i
$893$	9.42401e12i	0.495911i
$894$	−2.92771e12	−0.153288
$895$	0	0
$896$	−6.44514e11	−0.0334077
$897$	3.05656e10i	0.00157640i
$898$	− 1.63635e13i	− 0.839718i
$899$	3.59186e11	0.0183401
$900$	0	0
$901$	−9.15136e11	−0.0462620
$902$	1.56811e13i	0.788766i
$903$	− 4.66238e12i	− 0.233353i
$904$	−2.43258e12	−0.121146
$905$	0	0
$906$	−8.88622e12	−0.438168
$907$	− 1.37618e12i	− 0.0675215i	−0.999430	−	0.0337607i	$-0.989252\pi$
$907$	− 1.37618e12i	− 0.0675215i	0.999430	−	0.0337607i	$-0.0107484\pi$
$908$	1.23432e12i	0.0602619i
$909$	−2.57137e13	−1.24919
$910$	0	0
$911$	−3.17846e13	−1.52892	−0.764458	−	0.644674i	$-0.776993\pi$
$911$	−3.17846e13	−1.52892	−0.764458	+	0.644674i	$0.776993\pi$
$912$	− 5.77110e11i	− 0.0276237i
$913$	− 5.72214e12i	− 0.272546i
$914$	1.93402e13	0.916649
$915$	0	0
$916$	8.26186e12	0.387747
$917$	− 2.70857e12i	− 0.126497i
$918$	− 8.40171e12i	− 0.390459i
$919$	−4.52221e12	−0.209137	−0.104569	−	0.994518i	$-0.533346\pi$
$919$	−4.52221e12	−0.209137	−0.104569	+	0.994518i	$0.533346\pi$
$920$	0	0
$921$	2.10642e12	0.0964664
$922$	1.72194e13i	0.784744i
$923$	− 7.32444e12i	− 0.332175i
$924$	−1.37449e12	−0.0620323
$925$	0	0
$926$	1.25797e13	0.562240
$927$	2.97866e13i	1.32483i
$928$	− 2.65925e12i	− 0.117705i
$929$	−3.69672e13	−1.62834	−0.814171	−	0.580626i	$-0.802808\pi$
$929$	−3.69672e13	−1.62834	−0.814171	+	0.580626i	$0.802808\pi$
$930$	0	0
$931$	1.06217e12	0.0463360
$932$	− 1.27774e13i	− 0.554718i
$933$	1.11844e13i	0.483220i
$934$	−2.01160e13	−0.864928
$935$	0	0
$936$	−2.15358e12	−0.0917105
$937$	1.20574e13i	0.511005i	0.966808	+	0.255502i	$0.0822409\pi$
$937$	1.20574e13i	0.511005i	−0.966808	+	0.255502i	$0.917759\pi$
$938$	− 1.91141e11i	− 0.00806196i
$939$	−1.39304e13	−0.584746
$940$	0	0
$941$	−2.75798e13	−1.14667	−0.573335	−	0.819321i	$-0.694351\pi$
$941$	−2.75798e13	−1.14667	−0.573335	+	0.819321i	$0.694351\pi$
$942$	− 8.69059e12i	− 0.359600i
$943$	4.43300e11i	0.0182556i
$944$	−4.23026e11	−0.0173378
$945$	0	0
$946$	3.04161e13	1.23479
$947$	8.81700e12i	0.356243i	0.984009	+	0.178121i	$0.0570020\pi$
$947$	8.81700e12i	0.356243i	−0.984009	+	0.178121i	$0.942998\pi$
$948$	4.17497e11i	0.0167886i
$949$	1.85489e11	0.00742368
$950$	0	0
$951$	2.61978e12	0.103861
$952$	− 2.91386e12i	− 0.114975i
$953$	− 2.00605e13i	− 0.787813i	−0.919151	−	0.393907i	$-0.871123\pi$
$953$	− 2.00605e13i	− 0.787813i	0.919151	−	0.393907i	$-0.128877\pi$
$954$	−8.59819e11	−0.0336078
$955$	0	0
$956$	1.33251e13	0.515952
$957$	− 5.67113e12i	− 0.218558i
$958$	− 1.99562e13i	− 0.765477i
$959$	6.43309e12	0.245604
$960$	0	0
$961$	−2.64196e13	−0.999241
$962$	7.14538e12i	0.268991i
$963$	7.62163e12i	0.285581i
$964$	−1.23726e13	−0.461438
$965$	0	0
$966$	−3.88564e10	−0.00143570
$967$	− 3.57232e12i	− 0.131380i	−0.997840	−	0.0656902i	$-0.979075\pi$
$967$	− 3.57232e12i	− 0.131380i	0.997840	−	0.0656902i	$-0.0209249\pi$
$968$	6.91337e11i	0.0253076i
$969$	2.60913e12	0.0950689
$970$	0	0
$971$	−4.97663e13	−1.79659	−0.898295	−	0.439394i	$-0.855193\pi$
$971$	−4.97663e13	−1.79659	−0.898295	+	0.439394i	$0.855193\pi$
$972$	− 1.20839e13i	− 0.434220i
$973$	3.35342e11i	0.0119945i
$974$	−2.86938e12	−0.102158
$975$	0	0
$976$	5.81668e12	0.205188
$977$	2.14940e13i	0.754730i	0.926065	+	0.377365i	$0.123170\pi$
$977$	2.14940e13i	0.754730i	−0.926065	+	0.377365i	$0.876830\pi$
$978$	7.59266e12i	0.265381i
$979$	3.03450e13	1.05576
$980$	0	0
$981$	1.17144e13	0.403841
$982$	7.90530e12i	0.271279i
$983$	3.03607e13i	1.03710i	0.855047	+	0.518551i	$0.173528\pi$
$983$	3.03607e13i	1.03710i	−0.855047	+	0.518551i	$0.826472\pi$
$984$	4.10061e12	0.139435
$985$	0	0
$986$	1.20226e13	0.405089
$987$	− 5.86936e12i	− 0.196863i
$988$	− 1.42538e12i	− 0.0475909i
$989$	8.59853e11	0.0285786
$990$	0	0
$991$	4.36370e13	1.43722	0.718610	−	0.695413i	$-0.244779\pi$
$991$	4.36370e13	1.43722	0.718610	+	0.695413i	$0.244779\pi$
$992$	− 1.48511e11i	− 0.00486920i
$993$	1.59355e13i	0.520109i
$994$	9.31118e12	0.302528
$995$	0	0
$996$	−1.49634e12	−0.0481795
$997$	1.08721e13i	0.348485i	0.984703	+	0.174243i	$0.0557477\pi$
$997$	1.08721e13i	0.348485i	−0.984703	+	0.174243i	$0.944252\pi$
$998$	1.07752e13i	0.343827i
$999$	−2.61911e13	−0.831974

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.10.c.k.99.5		6
5.2	odd	4		350.10.a.l.1.2		3
5.3	odd	4		70.10.a.h.1.2	✓	3
5.4	even	2	inner	350.10.c.k.99.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.10.a.h.1.2	✓	3	5.3	odd	4
350.10.a.l.1.2		3	5.2	odd	4
350.10.c.k.99.2		6	5.4	even	2	inner
350.10.c.k.99.5		6	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	350.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+16.0000i q^{2} +47.7937i q^{3} -256.000 q^{4} -764.699 q^{6} -2401.00i q^{7} -4096.00i q^{8} +17398.8 q^{9} +46788.5 q^{11} -12235.2i q^{12} -30219.1i q^{13} +38416.0 q^{14} +65536.0 q^{16} +296290. i q^{17} +278380. i q^{18} -184250. q^{19} +114753. q^{21} +748616. i q^{22} +21163.1i q^{23} +195763. q^{24} +483506. q^{26} +1.77227e6i q^{27} +614656. i q^{28} -2.53606e6 q^{29} -141632. q^{31} +1.04858e6i q^{32} +2.23620e6i q^{33} -4.74064e6 q^{34} -4.45408e6 q^{36} +1.47783e7i q^{37} -2.94800e6i q^{38} +1.44428e6 q^{39} +2.09468e7 q^{41} +1.83604e6i q^{42} -4.06298e7i q^{43} -1.19779e7 q^{44} -338610. q^{46} -5.11479e7i q^{47} +3.13221e6i q^{48} -5.76480e6 q^{49} -1.41608e7 q^{51} +7.73610e6i q^{52} +3.08865e6i q^{53} -2.83564e7 q^{54} -9.83450e6 q^{56} -8.80600e6i q^{57} -4.05770e7i q^{58} -6.45486e6 q^{59} +8.87555e7 q^{61} -2.26611e6i q^{62} -4.17744e7i q^{63} -1.67772e7 q^{64} -3.57791e7 q^{66} -4.97555e6i q^{67} -7.58502e7i q^{68} -1.01146e6 q^{69} +2.42378e8 q^{71} -7.12653e7i q^{72} +6.13812e6i q^{73} -2.36452e8 q^{74} +4.71681e7 q^{76} -1.12339e8i q^{77} +2.31086e7i q^{78} -3.41226e7 q^{79} +2.57756e8 q^{81} +3.35149e8i q^{82} -1.22298e8i q^{83} -2.93767e7 q^{84} +6.50077e8 q^{86} -1.21208e8i q^{87} -1.91646e8i q^{88} +6.48556e8 q^{89} -7.25562e7 q^{91} -5.41776e6i q^{92} -6.76910e6i q^{93} +8.18366e8 q^{94} -5.01153e7 q^{96} -5.98893e8i q^{97} -9.22368e7i q^{98} +8.14062e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 1536 q^{4} - 2112 q^{6} - 102258 q^{9} - 138252 q^{11} + 230496 q^{14} + 393216 q^{16} - 3450888 q^{19} + 316932 q^{21} + 540672 q^{24} - 291456 q^{26} - 13467528 q^{29} + 1570800 q^{31} - 17506560 q^{34}+ \cdots + 9978709104 q^{99}+O(q^{100}) \) 6 * q - 1536 * q^4 - 2112 * q^6 - 102258 * q^9 - 138252 * q^11 + 230496 * q^14 + 393216 * q^16 - 3450888 * q^19 + 316932 * q^21 + 540672 * q^24 - 291456 * q^26 - 13467528 * q^29 + 1570800 * q^31 - 17506560 * q^34 + 26178048 * q^36 - 168686172 * q^39 - 54174012 * q^41 + 35392512 * q^44 + 79516800 * q^46 - 34588806 * q^49 + 271643892 * q^51 + 14544576 * q^54 - 59006976 * q^56 + 280516080 * q^59 - 15470796 * q^61 - 100663296 * q^64 + 320082240 * q^66 - 389691000 * q^69 + 445467648 * q^71 + 80645568 * q^74 + 883427328 * q^76 - 1154709636 * q^79 + 1035637974 * q^81 - 81134592 * q^84 + 271343616 * q^86 + 312138444 * q^89 + 43736616 * q^91 - 901608384 * q^94 - 138412032 * q^96 + 9978709104 * q^99

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