LMFDB - Embedded newform 354.5.d.a.235.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,5,Mod(235,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("354.235");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	354.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$36.5929669317$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			235.9
Character	$\chi$	$=$	354.235
Dual form			354.5.d.a.235.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.82843i q^{2} -5.19615 q^{3} -8.00000 q^{4} -44.0140 q^{5} +14.6969i q^{6} +46.8163 q^{7} +22.6274i q^{8} +27.0000 q^{9} +O(q^{10})$	\(q-2.82843i q^{2} -5.19615 q^{3} -8.00000 q^{4} -44.0140 q^{5} +14.6969i q^{6} +46.8163 q^{7} +22.6274i q^{8} +27.0000 q^{9} +124.490i q^{10} +137.116i q^{11} +41.5692 q^{12} -10.0301i q^{13} -132.416i q^{14} +228.703 q^{15} +64.0000 q^{16} +42.3457 q^{17} -76.3675i q^{18} +73.9872 q^{19} +352.112 q^{20} -243.264 q^{21} +387.822 q^{22} -110.466i q^{23} -117.576i q^{24} +1312.23 q^{25} -28.3693 q^{26} -140.296 q^{27} -374.530 q^{28} +404.115 q^{29} -646.871i q^{30} -2.67049i q^{31} -181.019i q^{32} -712.474i q^{33} -119.772i q^{34} -2060.57 q^{35} -216.000 q^{36} +1809.15i q^{37} -209.267i q^{38} +52.1178i q^{39} -995.923i q^{40} -1940.22 q^{41} +688.056i q^{42} -669.686i q^{43} -1096.93i q^{44} -1188.38 q^{45} -312.445 q^{46} -1472.47i q^{47} -332.554 q^{48} -209.237 q^{49} -3711.56i q^{50} -220.035 q^{51} +80.2406i q^{52} -5203.70 q^{53} +396.817i q^{54} -6035.01i q^{55} +1059.33i q^{56} -384.449 q^{57} -1143.01i q^{58} +(-1674.14 - 3051.99i) q^{59} -1829.63 q^{60} +1786.60i q^{61} -7.55328 q^{62} +1264.04 q^{63} -512.000 q^{64} +441.464i q^{65} -2015.18 q^{66} -5770.61i q^{67} -338.765 q^{68} +573.999i q^{69} +5828.18i q^{70} +1559.38 q^{71} +610.940i q^{72} -3040.70i q^{73} +5117.05 q^{74} -6818.56 q^{75} -591.897 q^{76} +6419.25i q^{77} +147.411 q^{78} +5843.07 q^{79} -2816.90 q^{80} +729.000 q^{81} +5487.76i q^{82} +3170.91i q^{83} +1946.12 q^{84} -1863.80 q^{85} -1894.16 q^{86} -2099.84 q^{87} -3102.57 q^{88} +5247.04i q^{89} +3361.24i q^{90} -469.571i q^{91} +883.729i q^{92} +13.8763i q^{93} -4164.77 q^{94} -3256.47 q^{95} +940.604i q^{96} -7138.62i q^{97} +591.813i q^{98} +3702.12i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 320 q^{4} - 80 q^{7} + 1080 q^{9}+O(q^{10}) $ 40 * q - 320 * q^4 - 80 * q^7 + 1080 * q^9	$ 40 q - 320 q^{4} - 80 q^{7} + 1080 q^{9} - 144 q^{15} + 2560 q^{16} + 480 q^{17} - 792 q^{19} - 1024 q^{22} + 3400 q^{25} + 768 q^{26} + 640 q^{28} + 1608 q^{29} - 5760 q^{35} - 8640 q^{36} + 6264 q^{41} + 7040 q^{46} + 17912 q^{49} + 1296 q^{51} - 1104 q^{53} + 5040 q^{57} + 13584 q^{59} + 1152 q^{60} - 12288 q^{62} - 2160 q^{63} - 20480 q^{64} + 1152 q^{66} - 3840 q^{68} + 35352 q^{71} + 4608 q^{74} + 3168 q^{75} + 6336 q^{76} - 12672 q^{78} - 15720 q^{79} + 29160 q^{81} - 26872 q^{85} + 18432 q^{86} + 7776 q^{87} + 8192 q^{88} - 18432 q^{94} - 19128 q^{95}+O(q^{100}) $ 40 * q - 320 * q^4 - 80 * q^7 + 1080 * q^9 - 144 * q^15 + 2560 * q^16 + 480 * q^17 - 792 * q^19 - 1024 * q^22 + 3400 * q^25 + 768 * q^26 + 640 * q^28 + 1608 * q^29 - 5760 * q^35 - 8640 * q^36 + 6264 * q^41 + 7040 * q^46 + 17912 * q^49 + 1296 * q^51 - 1104 * q^53 + 5040 * q^57 + 13584 * q^59 + 1152 * q^60 - 12288 * q^62 - 2160 * q^63 - 20480 * q^64 + 1152 * q^66 - 3840 * q^68 + 35352 * q^71 + 4608 * q^74 + 3168 * q^75 + 6336 * q^76 - 12672 * q^78 - 15720 * q^79 + 29160 * q^81 - 26872 * q^85 + 18432 * q^86 + 7776 * q^87 + 8192 * q^88 - 18432 * q^94 - 19128 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	2.82843i		−	0.707107i
$2$		−	2.82843i		−	0.707107i
$3$	−5.19615			−0.577350
$3$	−5.19615			−0.577350
$4$	−8.00000			−0.500000
$5$	−44.0140			−1.76056			−0.880280	−	0.474454i	$-0.842645\pi$
$5$	−44.0140			−1.76056			−0.880280	+	0.474454i	$0.842645\pi$
$6$			14.6969i			0.408248i
$7$	46.8163			0.955434			0.477717	−	0.878514i	$-0.341464\pi$
$7$	46.8163			0.955434			0.477717	+	0.878514i	$0.341464\pi$
$8$			22.6274i			0.353553i
$9$	27.0000			0.333333
$10$			124.490i			1.24490i
$11$			137.116i			1.13319i	0.823997	+	0.566594i	$0.191739\pi$
$11$			137.116i			1.13319i	−0.823997	+	0.566594i	$0.808261\pi$
$12$	41.5692			0.288675
$13$		−	10.0301i		−	0.0593496i	−0.999560	−	0.0296748i	$-0.990553\pi$
$13$		−	10.0301i		−	0.0593496i	0.999560	−	0.0296748i	$-0.00944717\pi$
$14$		−	132.416i		−	0.675594i
$15$	228.703			1.01646
$16$	64.0000			0.250000
$17$	42.3457			0.146525			0.0732624	−	0.997313i	$-0.476659\pi$
$17$	42.3457			0.146525			0.0732624	+	0.997313i	$0.476659\pi$
$18$		−	76.3675i		−	0.235702i
$19$	73.9872			0.204951			0.102475	−	0.994736i	$-0.467324\pi$
$19$	73.9872			0.204951			0.102475	+	0.994736i	$0.467324\pi$
$20$	352.112			0.880280
$21$	−243.264			−0.551620
$22$	387.822			0.801285
$23$		−	110.466i		−	0.208821i	−0.994534	−	0.104410i	$-0.966704\pi$
$23$		−	110.466i		−	0.208821i	0.994534	−	0.104410i	$-0.0332955\pi$
$24$		−	117.576i		−	0.204124i
$25$	1312.23			2.09957
$26$	−28.3693			−0.0419665
$27$	−140.296			−0.192450
$28$	−374.530			−0.477717
$29$	404.115			0.480517			0.240259	−	0.970709i	$-0.422768\pi$
$29$	404.115			0.480517			0.240259	+	0.970709i	$0.422768\pi$
$30$		−	646.871i		−	0.718746i
$31$		−	2.67049i		−	0.00277886i	−0.999999	−	0.00138943i	$-0.999558\pi$
$31$		−	2.67049i		−	0.00277886i	0.999999	−	0.00138943i	$-0.000442270\pi$
$32$		−	181.019i		−	0.176777i
$33$		−	712.474i		−	0.654246i
$34$		−	119.772i		−	0.103609i
$35$	−2060.57			−1.68210
$36$	−216.000			−0.166667
$37$			1809.15i			1.32151i	0.750601	+	0.660756i	$0.229764\pi$
$37$			1809.15i			1.32151i	−0.750601	+	0.660756i	$0.770236\pi$
$38$		−	209.267i		−	0.144922i
$39$			52.1178i			0.0342655i
$40$		−	995.923i		−	0.622452i
$41$	−1940.22			−1.15420			−0.577102	−	0.816672i	$-0.695816\pi$
$41$	−1940.22			−1.15420			−0.577102	+	0.816672i	$0.695816\pi$
$42$			688.056i			0.390054i
$43$		−	669.686i		−	0.362188i	−0.983466	−	0.181094i	$-0.942036\pi$
$43$		−	669.686i		−	0.362188i	0.983466	−	0.181094i	$-0.0579639\pi$
$44$		−	1096.93i		−	0.566594i
$45$	−1188.38			−0.586853
$46$	−312.445			−0.147658
$47$		−	1472.47i		−	0.666576i	−0.942825	−	0.333288i	$-0.891842\pi$
$47$		−	1472.47i		−	0.666576i	0.942825	−	0.333288i	$-0.108158\pi$
$48$	−332.554			−0.144338
$49$	−209.237			−0.0871459
$50$		−	3711.56i		−	1.48462i
$51$	−220.035			−0.0845961
$52$			80.2406i			0.0296748i
$53$	−5203.70			−1.85251			−0.926255	−	0.376897i	$-0.876991\pi$
$53$	−5203.70			−1.85251			−0.926255	+	0.376897i	$0.876991\pi$
$54$			396.817i			0.136083i
$55$		−	6035.01i		−	1.99505i
$56$			1059.33i			0.337797i
$57$	−384.449			−0.118328
$58$		−	1143.01i		−	0.339777i
$59$	−1674.14	−	3051.99i	−0.480937	−	0.876755i
$59$	−1674.14	−	3051.99i	−0.480937	−	0.876755i
$60$	−1829.63			−0.508230
$61$			1786.60i			0.480140i	0.970756	+	0.240070i	$0.0771705\pi$
$61$			1786.60i			0.480140i	−0.970756	+	0.240070i	$0.922830\pi$
$62$	−7.55328			−0.00196495
$63$	1264.04			0.318478
$64$	−512.000			−0.125000
$65$			441.464i			0.104489i
$66$	−2015.18			−0.462622
$67$		−	5770.61i		−	1.28550i	−0.766076	−	0.642750i	$-0.777793\pi$
$67$		−	5770.61i		−	1.28550i	0.766076	−	0.642750i	$-0.222207\pi$
$68$	−338.765			−0.0732624
$69$			573.999i			0.120563i
$70$			5828.18i			1.18942i
$71$	1559.38			0.309340			0.154670	−	0.987966i	$-0.450569\pi$
$71$	1559.38			0.309340			0.154670	+	0.987966i	$0.450569\pi$
$72$			610.940i			0.117851i
$73$		−	3040.70i		−	0.570595i	−0.958439	−	0.285298i	$-0.907908\pi$
$73$		−	3040.70i		−	0.570595i	0.958439	−	0.285298i	$-0.0920925\pi$
$74$	5117.05			0.934449
$75$	−6818.56			−1.21219
$76$	−591.897			−0.102475
$77$			6419.25i			1.08269i
$78$	147.411			0.0242294
$79$	5843.07			0.936240			0.468120	−	0.883665i	$-0.344931\pi$
$79$	5843.07			0.936240			0.468120	+	0.883665i	$0.344931\pi$
$80$	−2816.90			−0.440140
$81$	729.000			0.111111
$82$			5487.76i			0.816145i
$83$			3170.91i			0.460285i	0.973157	+	0.230143i	$0.0739193\pi$
$83$			3170.91i			0.460285i	−0.973157	+	0.230143i	$0.926081\pi$
$84$	1946.12			0.275810
$85$	−1863.80			−0.257966
$86$	−1894.16			−0.256106
$87$	−2099.84			−0.277427
$88$	−3102.57			−0.400642
$89$			5247.04i			0.662421i	0.943557	+	0.331211i	$0.107457\pi$
$89$			5247.04i			0.662421i	−0.943557	+	0.331211i	$0.892543\pi$
$90$			3361.24i			0.414968i
$91$		−	469.571i		−	0.0567046i
$92$			883.729i			0.104410i
$93$			13.8763i			0.00160438i
$94$	−4164.77			−0.471341
$95$	−3256.47			−0.360828
$96$			940.604i			0.102062i
$97$		−	7138.62i		−	0.758701i	−0.925253	−	0.379351i	$-0.876147\pi$
$97$		−	7138.62i		−	0.758701i	0.925253	−	0.379351i	$-0.123853\pi$
$98$			591.813i			0.0616215i
$99$			3702.12i			0.377729i
$100$	−10497.9			−1.04979
$101$		−	6627.37i		−	0.649679i	−0.945769	−	0.324839i	$-0.894690\pi$
$101$		−	6627.37i		−	0.649679i	0.945769	−	0.324839i	$-0.105310\pi$
$102$			622.352i			0.0598185i
$103$		−	18501.5i		−	1.74395i	−0.489554	−	0.871973i	$-0.662840\pi$
$103$		−	18501.5i		−	1.74395i	0.489554	−	0.871973i	$-0.337160\pi$
$104$	226.955			0.0209832
$105$	10707.0			0.971160
$106$			14718.3i			1.30992i
$107$	−1033.48			−0.0902684			−0.0451342	−	0.998981i	$-0.514372\pi$
$107$	−1033.48			−0.0902684			−0.0451342	+	0.998981i	$0.514372\pi$
$108$	1122.37			0.0962250
$109$		−	18706.7i		−	1.57451i	−0.616629	−	0.787254i	$-0.711502\pi$
$109$		−	18706.7i		−	1.57451i	0.616629	−	0.787254i	$-0.288498\pi$
$110$	−17069.6			−1.41071
$111$		−	9400.61i		−	0.762975i
$112$	2996.24			0.238858
$113$		−	4110.37i		−	0.321902i	−0.986962	−	0.160951i	$-0.948544\pi$
$113$		−	4110.37i		−	0.321902i	0.986962	−	0.160951i	$-0.0514562\pi$
$114$			1087.38i			0.0836707i
$115$			4862.05i			0.367641i
$116$	−3232.92			−0.240259
$117$		−	270.812i		−	0.0197832i
$118$	−8632.32	+	4735.18i	−0.619960	+	0.340074i
$119$	1982.47			0.139995
$120$			5174.97i			0.359373i
$121$	−4159.72			−0.284115
$122$	5053.28			0.339511
$123$	10081.7			0.666380
$124$			21.3639i			0.00138943i
$125$	−30247.9			−1.93586
$126$		−	3575.24i		−	0.225198i
$127$	−5297.18			−0.328426			−0.164213	−	0.986425i	$-0.552508\pi$
$127$	−5297.18			−0.328426			−0.164213	+	0.986425i	$0.552508\pi$
$128$			1448.15i			0.0883883i
$129$			3479.79i			0.209110i
$130$	1248.65			0.0738845
$131$			2657.02i			0.154829i	0.996999	+	0.0774144i	$0.0246665\pi$
$131$			2657.02i			0.154829i	−0.996999	+	0.0774144i	$0.975334\pi$
$132$			5699.79i			0.327123i
$133$	3463.80			0.195817
$134$	−16321.7			−0.908986
$135$	6174.99			0.338820
$136$			958.173i			0.0518043i
$137$	2585.00			0.137727			0.0688636	−	0.997626i	$-0.478063\pi$
$137$	2585.00			0.137727			0.0688636	+	0.997626i	$0.478063\pi$
$138$	1623.51			0.0852506
$139$	−6099.40			−0.315688			−0.157844	−	0.987464i	$-0.550454\pi$
$139$	−6099.40			−0.315688			−0.157844	+	0.987464i	$0.550454\pi$
$140$	16484.6			0.841050
$141$			7651.16i			0.384848i
$142$		−	4410.61i		−	0.218737i
$143$	1375.28			0.0672542
$144$	1728.00			0.0833333
$145$	−17786.7			−0.845980
$146$	−8600.41			−0.403472
$147$	1087.23			0.0503137
$148$		−	14473.2i		−	0.660756i
$149$			31529.8i			1.42020i	0.704102	+	0.710098i	$0.251350\pi$
$149$			31529.8i			1.42020i	−0.704102	+	0.710098i	$0.748650\pi$
$150$			19285.8i			0.857147i
$151$		−	17991.1i		−	0.789047i	−0.918886	−	0.394524i	$-0.870910\pi$
$151$		−	17991.1i		−	0.789047i	0.918886	−	0.394524i	$-0.129090\pi$
$152$			1674.14i			0.0724610i
$153$	1143.33			0.0488416
$154$	18156.4			0.765575
$155$			117.539i			0.00489236i
$156$		−	416.943i		−	0.0171327i
$157$			23314.6i			0.945864i	0.881099	+	0.472932i	$0.156804\pi$
$157$			23314.6i			0.945864i	−0.881099	+	0.472932i	$0.843196\pi$
$158$		−	16526.7i		−	0.662022i
$159$	27039.2			1.06955
$160$			7967.39i			0.311226i
$161$		−	5171.61i		−	0.199514i
$162$		−	2061.92i		−	0.0785674i
$163$	20161.4			0.758833			0.379417	−	0.925226i	$-0.376125\pi$
$163$	20161.4			0.758833			0.379417	+	0.925226i	$0.376125\pi$
$164$	15521.7			0.577102
$165$			31358.8i			1.15184i
$166$	8968.67			0.325471
$167$	−14199.1			−0.509130			−0.254565	−	0.967056i	$-0.581932\pi$
$167$	−14199.1			−0.509130			−0.254565	+	0.967056i	$0.581932\pi$
$168$		−	5504.45i		−	0.195027i
$169$	28460.4			0.996478
$170$			5271.63i			0.182409i
$171$	1997.65			0.0683169
$172$			5357.49i			0.181094i
$173$		−	58222.5i		−	1.94535i	−0.232161	−	0.972677i	$-0.574580\pi$
$173$		−	58222.5i		−	1.94535i	0.232161	−	0.972677i	$-0.425420\pi$
$174$			5939.25i			0.196170i
$175$	61433.8			2.00600
$176$			8775.41i			0.283297i
$177$	8699.09	+	15858.6i	0.277669	+	0.506195i
$178$	14840.9			0.468402
$179$			13262.0i			0.413906i	0.978351	+	0.206953i	$0.0663547\pi$
$179$			13262.0i			0.413906i	−0.978351	+	0.206953i	$0.933645\pi$
$180$	9507.03			0.293427
$181$	13307.4			0.406197			0.203098	−	0.979158i	$-0.434899\pi$
$181$	13307.4			0.406197			0.203098	+	0.979158i	$0.434899\pi$
$182$	−1328.15			−0.0400962
$183$		−	9283.46i		−	0.277209i
$184$	2499.56			0.0738292
$185$		−	79627.9i		−	2.32660i
$186$	39.2480			0.00113447
$187$			5806.26i			0.166040i
$188$			11779.7i			0.333288i
$189$	−6568.14			−0.183873
$190$			9210.69i			0.255144i
$191$		−	37595.0i		−	1.03054i	−0.857029	−	0.515268i	$-0.827692\pi$
$191$		−	37595.0i		−	1.03054i	0.857029	−	0.515268i	$-0.172308\pi$
$192$	2660.43			0.0721688
$193$	45971.3			1.23416			0.617081	−	0.786900i	$-0.288315\pi$
$193$	45971.3			1.23416			0.617081	+	0.786900i	$0.288315\pi$
$194$	−20191.1			−0.536483
$195$		−	2293.91i		−	0.0603265i
$196$	1673.90			0.0435730
$197$	−43905.7			−1.13133			−0.565664	−	0.824636i	$-0.691380\pi$
$197$	−43905.7			−1.13133			−0.565664	+	0.824636i	$0.691380\pi$
$198$	10471.2			0.267095
$199$	30023.0			0.758137			0.379069	−	0.925369i	$-0.376244\pi$
$199$	30023.0			0.758137			0.379069	+	0.925369i	$0.376244\pi$
$200$			29692.4i			0.742311i
$201$			29985.0i			0.742184i
$202$	−18745.0			−0.459392
$203$	18919.2			0.459103
$204$	1760.28			0.0422981
$205$	85396.7			2.03204
$206$	−52330.2			−1.23316
$207$		−	2982.58i		−	0.0696069i
$208$		−	641.925i		−	0.0148374i
$209$			10144.8i			0.232248i
$210$		−	30284.1i		−	0.686714i
$211$			27527.0i			0.618293i	0.951014	+	0.309146i	$0.100043\pi$
$211$			27527.0i			0.618293i	−0.951014	+	0.309146i	$0.899957\pi$
$212$	41629.6			0.926255
$213$	−8102.80			−0.178598
$214$			2923.13i			0.0638294i
$215$			29475.6i			0.637654i
$216$		−	3174.54i		−	0.0680414i
$217$		−	125.022i		−	0.00265502i
$218$	−52910.6			−1.11334
$219$			15800.0i			0.329433i
$220$			48280.1i			0.997523i
$221$		−	424.730i		−	0.00869618i
$222$	−26588.9			−0.539505
$223$	−69912.9			−1.40588			−0.702939	−	0.711250i	$-0.748129\pi$
$223$	−69912.9			−1.40588			−0.702939	+	0.711250i	$0.748129\pi$
$224$		−	8474.65i		−	0.168898i
$225$	35430.3			0.699858
$226$	−11625.9			−0.227619
$227$		−	45752.7i		−	0.887903i	−0.896051	−	0.443951i	$-0.853576\pi$
$227$		−	45752.7i		−	0.887903i	0.896051	−	0.443951i	$-0.146424\pi$
$228$	3075.59			0.0591641
$229$		−	77469.6i		−	1.47727i	−0.674105	−	0.738636i	$-0.735470\pi$
$229$		−	77469.6i		−	1.47727i	0.674105	−	0.738636i	$-0.264530\pi$
$230$	13752.0			0.259962
$231$		−	33355.4i		−	0.625089i
$232$			9144.08i			0.169889i
$233$		−	56078.4i		−	1.03296i	−0.856299	−	0.516480i	$-0.827242\pi$
$233$		−	56078.4i		−	1.03296i	0.856299	−	0.516480i	$-0.172758\pi$
$234$	−765.972			−0.0139888
$235$			64809.2i			1.17355i
$236$	13393.1	+	24415.9i	0.240468	+	0.438378i
$237$	−30361.5			−0.540539
$238$		−	5607.26i		−	0.0989912i
$239$	−18432.4			−0.322691			−0.161345	−	0.986898i	$-0.551583\pi$
$239$	−18432.4			−0.322691			−0.161345	+	0.986898i	$0.551583\pi$
$240$	14637.0			0.254115
$241$	−51595.3			−0.888334			−0.444167	−	0.895944i	$-0.646500\pi$
$241$	−51595.3			−0.888334			−0.444167	+	0.895944i	$0.646500\pi$
$242$			11765.5i			0.200900i
$243$	−3788.00			−0.0641500
$244$		−	14292.8i		−	0.240070i
$245$	9209.37			0.153426
$246$		−	28515.2i		−	0.471201i
$247$		−	742.097i		−	0.0121637i
$248$	60.4263			0.000982477
$249$		−	16476.5i		−	0.265746i
$250$			85553.9i			1.36886i
$251$	−35881.2			−0.569534			−0.284767	−	0.958597i	$-0.591916\pi$
$251$	−35881.2			−0.569534			−0.284767	+	0.958597i	$0.591916\pi$
$252$	−10112.3			−0.159239
$253$	15146.6			0.236633
$254$			14982.7i			0.232232i
$255$	9684.60			0.148937
$256$	4096.00			0.0625000
$257$	114840.			1.73870			0.869352	−	0.494194i	$-0.164537\pi$
$257$	114840.			1.73870			0.869352	+	0.494194i	$0.164537\pi$
$258$	9842.34			0.147863
$259$			84697.6i			1.26262i
$260$		−	3531.71i		−	0.0522443i
$261$	10911.1			0.160172
$262$	7515.18			0.109481
$263$	−56149.7			−0.811776			−0.405888	−	0.913923i	$-0.633038\pi$
$263$	−56149.7			−0.811776			−0.405888	+	0.913923i	$0.633038\pi$
$264$	16121.5			0.231311
$265$	229036.			3.26146
$266$		−	9797.11i		−	0.138463i
$267$		−	27264.4i		−	0.382449i
$268$			46164.9i			0.642750i
$269$		−	80261.4i		−	1.10918i	−0.832124	−	0.554590i	$-0.812875\pi$
$269$		−	80261.4i		−	1.10918i	0.832124	−	0.554590i	$-0.187125\pi$
$270$		−	17465.5i		−	0.239582i
$271$	4312.63			0.0587223			0.0293612	−	0.999569i	$-0.490653\pi$
$271$	4312.63			0.0587223			0.0293612	+	0.999569i	$0.490653\pi$
$272$	2710.12			0.0366312
$273$			2439.96i			0.0327384i
$274$		−	7311.49i		−	0.0973878i
$275$			179928.i			2.37921i
$276$		−	4591.99i		−	0.0602813i
$277$	−21426.6			−0.279251			−0.139625	−	0.990204i	$-0.544590\pi$
$277$	−21426.6			−0.279251			−0.139625	+	0.990204i	$0.544590\pi$
$278$			17251.7i			0.223225i
$279$		−	72.1032i		−	0.000926288i
$280$		−	46625.4i		−	0.594712i
$281$	37213.9			0.471295			0.235648	−	0.971839i	$-0.424279\pi$
$281$	37213.9			0.471295			0.235648	+	0.971839i	$0.424279\pi$
$282$	21640.8			0.272129
$283$		−	33844.7i		−	0.422589i	−0.977422	−	0.211295i	$-0.932232\pi$
$283$		−	33844.7i		−	0.422589i	0.977422	−	0.211295i	$-0.0677679\pi$
$284$	−12475.1			−0.154670
$285$	16921.1			0.208324
$286$		−	3889.88i		−	0.0475559i
$287$	−90833.6			−1.10276
$288$		−	4887.52i		−	0.0589256i
$289$	−81727.8			−0.978530
$290$			50308.4i			0.598198i
$291$			37093.4i			0.438036i
$292$			24325.6i			0.285298i
$293$	−99141.4			−1.15483			−0.577417	−	0.816449i	$-0.695939\pi$
$293$	−99141.4			−1.15483			−0.577417	+	0.816449i	$0.695939\pi$
$294$		−	3075.15i		−	0.0355772i
$295$	73685.6	+	134330.i	0.846718	+	1.54358i
$296$	−40936.4			−0.467225
$297$		−	19236.8i		−	0.218082i
$298$	89179.7			1.00423
$299$	−1107.98			−0.0123934
$300$	54548.5			0.606094
$301$		−	31352.2i		−	0.346047i
$302$	−50886.4			−0.557941
$303$			34436.8i			0.375092i
$304$	4735.18			0.0512377
$305$		−	78635.5i		−	0.845316i
$306$		−	3233.83i		−	0.0345362i
$307$	−148130.			−1.57168			−0.785842	−	0.618428i	$-0.787770\pi$
$307$	−148130.			−1.57168			−0.785842	+	0.618428i	$0.787770\pi$
$308$		−	51354.0i		−	0.541343i
$309$			96136.7i			1.00687i
$310$	332.450			0.00345942
$311$	54948.8			0.568116			0.284058	−	0.958807i	$-0.408319\pi$
$311$	54948.8			0.568116			0.284058	+	0.958807i	$0.408319\pi$
$312$	−1179.29			−0.0121147
$313$			48169.0i			0.491676i	0.969311	+	0.245838i	$0.0790632\pi$
$313$			48169.0i			0.491676i	−0.969311	+	0.245838i	$0.920937\pi$
$314$	65943.7			0.668827
$315$	−55635.4			−0.560700
$316$	−46744.6			−0.468120
$317$	70531.6			0.701884			0.350942	−	0.936397i	$-0.385861\pi$
$317$	70531.6			0.701884			0.350942	+	0.936397i	$0.385861\pi$
$318$		−	76478.5i		−	0.756284i
$319$			55410.5i			0.544516i
$320$	22535.2			0.220070
$321$	5370.13			0.0521165
$322$	−14627.5			−0.141078
$323$	3133.04			0.0300303
$324$	−5832.00			−0.0555556
$325$		−	13161.8i		−	0.124609i
$326$		−	57025.2i		−	0.536576i
$327$			97203.0i			0.909042i
$328$		−	43902.1i		−	0.408072i
$329$		−	68935.4i		−	0.636870i
$330$	88696.2			0.814474
$331$	−18263.7			−0.166699			−0.0833495	−	0.996520i	$-0.526562\pi$
$331$	−18263.7			−0.166699			−0.0833495	+	0.996520i	$0.526562\pi$
$332$		−	25367.2i		−	0.230143i
$333$			48847.0i			0.440504i
$334$			40161.2i			0.360009i
$335$			253988.i			2.26320i
$336$	−15568.9			−0.137905
$337$		−	75695.1i		−	0.666512i	−0.942836	−	0.333256i	$-0.891853\pi$
$337$		−	75695.1i		−	0.666512i	0.942836	−	0.333256i	$-0.108147\pi$
$338$		−	80498.2i		−	0.704616i
$339$			21358.1i			0.185850i
$340$	14910.4			0.128983
$341$	366.166			0.00314898
$342$		−	5650.22i		−	0.0483073i
$343$	−122202.			−1.03870
$344$	15153.3			0.128053
$345$		−	25264.0i		−	0.212258i
$346$	−164678.			−1.37557
$347$			38223.5i			0.317447i	0.987323	+	0.158723i	$0.0507378\pi$
$347$			38223.5i			0.317447i	−0.987323	+	0.158723i	$0.949262\pi$
$348$	16798.7			0.138713
$349$		−	23777.2i		−	0.195213i	−0.995225	−	0.0976067i	$-0.968881\pi$
$349$		−	23777.2i		−	0.195213i	0.995225	−	0.0976067i	$-0.0311187\pi$
$350$		−	173761.i		−	1.41846i
$351$			1407.18i			0.0114218i
$352$	24820.6			0.200321
$353$		−	135017.i		−	1.08353i	−0.840531	−	0.541764i	$-0.817757\pi$
$353$		−	135017.i		−	1.08353i	0.840531	−	0.541764i	$-0.182243\pi$
$354$	44854.8	−	24604.7i	0.357934	−	0.196342i
$355$	−68634.8			−0.544612
$356$		−	41976.3i		−	0.331211i
$357$	−10301.2			−0.0808260
$358$	37510.5			0.292676
$359$	−224773.			−1.74403			−0.872017	−	0.489476i	$-0.837188\pi$
$359$	−224773.			−1.74403			−0.872017	+	0.489476i	$0.837188\pi$
$360$		−	26889.9i		−	0.207484i
$361$	−124847.			−0.957995
$362$		−	37639.0i		−	0.287225i
$363$	21614.6			0.164034
$364$			3756.57i			0.0283523i
$365$			133834.i			1.00457i
$366$	−26257.6			−0.196017
$367$		−	241338.i		−	1.79182i	−0.444237	−	0.895909i	$-0.646525\pi$
$367$		−	241338.i		−	1.79182i	0.444237	−	0.895909i	$-0.353475\pi$
$368$		−	7069.83i		−	0.0522051i
$369$	−52385.8			−0.384734
$370$	−225222.			−1.64515
$371$	−243618.			−1.76995
$372$		−	111.010i		−	0.000802189i
$373$	−167438.			−1.20347			−0.601736	−	0.798695i	$-0.705524\pi$
$373$	−167438.			−1.20347			−0.601736	+	0.798695i	$0.705524\pi$
$374$	16422.6			0.117408
$375$	157173.			1.11767
$376$	33318.1			0.235670
$377$		−	4053.31i		−	0.0285185i
$378$			18577.5i			0.130018i
$379$	14138.9			0.0984325			0.0492162	−	0.998788i	$-0.484328\pi$
$379$	14138.9			0.0984325			0.0492162	+	0.998788i	$0.484328\pi$
$380$	26051.8			0.180414
$381$	27525.0			0.189617
$382$	−106335.			−0.728700
$383$	202652.			1.38151			0.690755	−	0.723089i	$-0.257278\pi$
$383$	202652.			1.38151			0.690755	+	0.723089i	$0.257278\pi$
$384$		−	7524.83i		−	0.0510310i
$385$		−	282537.i		−	1.90613i
$386$		−	130026.i		−	0.872684i
$387$		−	18081.5i		−	0.120729i
$388$			57109.0i			0.379351i
$389$	22776.6			0.150518			0.0752591	−	0.997164i	$-0.476022\pi$
$389$	22776.6			0.150518			0.0752591	+	0.997164i	$0.476022\pi$
$390$	−6488.17			−0.0426573
$391$		−	4677.76i		−	0.0305974i
$392$		−	4734.50i		−	0.0308107i
$393$		−	13806.3i		−	0.0893905i
$394$			124184.i			0.799970i
$395$	−257177.			−1.64831
$396$		−	29617.0i		−	0.188865i
$397$			24242.5i			0.153814i	0.997038	+	0.0769072i	$0.0245045\pi$
$397$			24242.5i			0.153814i	−0.997038	+	0.0769072i	$0.975495\pi$
$398$		−	84917.8i		−	0.536084i
$399$	−17998.4			−0.113055
$400$	83982.9			0.524893
$401$		−	245235.i		−	1.52508i	−0.646939	−	0.762541i	$-0.723951\pi$
$401$		−	245235.i		−	1.52508i	0.646939	−	0.762541i	$-0.276049\pi$
$402$	84810.3			0.524803
$403$	−26.7852			−0.000164924
$404$			53019.0i			0.324839i
$405$	−32086.2			−0.195618
$406$		−	53511.5i		−	0.324635i
$407$	−248063.			−1.49752
$408$		−	4978.81i		−	0.0299092i
$409$			308643.i			1.84506i	0.385929	+	0.922528i	$0.373881\pi$
$409$			308643.i			1.84506i	−0.385929	+	0.922528i	$0.626119\pi$
$410$		−	241538.i		−	1.43687i
$411$	−13432.1			−0.0795168
$412$			148012.i			0.871973i
$413$	−78377.0	−	142883.i	−0.459503	−	0.837682i
$414$	−8436.02			−0.0492195
$415$		−	139564.i		−	0.810360i
$416$	−1815.64			−0.0104916
$417$	31693.4			0.182262
$418$	28693.8			0.164224
$419$			277308.i			1.57955i	0.613394	+	0.789777i	$0.289804\pi$
$419$			277308.i			1.57955i	−0.613394	+	0.789777i	$0.710196\pi$
$420$	−85656.3			−0.485580
$421$			195586.i			1.10350i	0.834008	+	0.551752i	$0.186040\pi$
$421$			195586.i			1.10350i	−0.834008	+	0.551752i	$0.813960\pi$
$422$	77858.1			0.437199
$423$		−	39756.6i		−	0.222192i
$424$		−	117746.i		−	0.654961i
$425$	55567.4			0.307639
$426$			22918.2i			0.126288i
$427$			83642.1i			0.458743i
$428$	8267.86			0.0451342
$429$	−7146.17			−0.0388292
$430$	83369.5			0.450890
$431$		−	266003.i		−	1.43196i	−0.698119	−	0.715982i	$-0.745979\pi$
$431$		−	266003.i		−	1.43196i	0.698119	−	0.715982i	$-0.254021\pi$
$432$	−8978.95			−0.0481125
$433$	−93517.5			−0.498789			−0.249395	−	0.968402i	$-0.580232\pi$
$433$	−93517.5			−0.498789			−0.249395	+	0.968402i	$0.580232\pi$
$434$	−353.616			−0.00187738
$435$	92422.5			0.488427
$436$			149654.i			0.787254i
$437$		−	8173.07i		−	0.0427979i
$438$	44689.0			0.232945
$439$	355060.			1.84235			0.921176	−	0.389146i	$-0.127230\pi$
$439$	355060.			1.84235			0.921176	+	0.389146i	$0.127230\pi$
$440$	136557.			0.705355
$441$	−5649.41			−0.0290486
$442$	−1201.32			−0.00614913
$443$			380102.i			1.93684i	0.249331	+	0.968418i	$0.419789\pi$
$443$			380102.i			1.93684i	−0.249331	+	0.968418i	$0.580211\pi$
$444$			75204.9i			0.381487i
$445$		−	230943.i		−	1.16623i
$446$			197744.i			0.994106i
$447$		−	163834.i		−	0.819951i
$448$	−23969.9			−0.119429
$449$	−19388.6			−0.0961731			−0.0480865	−	0.998843i	$-0.515312\pi$
$449$	−19388.6			−0.0961731			−0.0480865	+	0.998843i	$0.515312\pi$
$450$		−	100212.i		−	0.494874i
$451$		−	266034.i		−	1.30793i
$452$			32883.0i			0.160951i
$453$			93484.3i			0.455557i
$454$	−129408.			−0.627842
$455$			20667.7i			0.0998319i
$456$		−	8699.08i		−	0.0418354i
$457$		−	312091.i		−	1.49434i	−0.664633	−	0.747170i	$-0.731412\pi$
$457$		−	312091.i		−	1.49434i	0.664633	−	0.747170i	$-0.268588\pi$
$458$	−219117.			−1.04459
$459$	−5940.93			−0.0281987
$460$		−	38896.4i		−	0.183821i
$461$	154238.			0.725755			0.362877	−	0.931837i	$-0.381794\pi$
$461$	154238.			0.725755			0.362877	+	0.931837i	$0.381794\pi$
$462$	−94343.3			−0.442005
$463$			128426.i			0.599091i	0.954082	+	0.299545i	$0.0968350\pi$
$463$			128426.i			0.599091i	−0.954082	+	0.299545i	$0.903165\pi$
$464$	25863.4			0.120129
$465$		−	610.750i		−	0.00282460i
$466$	−158614.			−0.730413
$467$			118773.i			0.544608i	0.962211	+	0.272304i	$0.0877856\pi$
$467$			118773.i			0.544608i	−0.962211	+	0.272304i	$0.912214\pi$
$468$			2166.50i			0.00989160i
$469$		−	270158.i		−	1.22821i
$470$	183308.			0.829824
$471$		−	121146.i		−	0.546095i
$472$	69058.5	−	37881.5i	0.309980	−	0.170037i
$473$	91824.5			0.410427
$474$			85875.3i			0.382218i
$475$	97088.4			0.430309
$476$	−15859.7			−0.0699974
$477$	−140500.			−0.617503
$478$			52134.7i			0.228177i
$479$	−46356.2			−0.202040			−0.101020	−	0.994884i	$-0.532211\pi$
$479$	−46356.2			−0.202040			−0.101020	+	0.994884i	$0.532211\pi$
$480$		−	41399.8i		−	0.179686i
$481$	18145.9			0.0784311
$482$			145934.i			0.628147i
$483$			26872.5i			0.115190i
$484$	33277.8			0.142057
$485$			314199.i			1.33574i
$486$			10714.1i			0.0453609i
$487$	373894.			1.57649			0.788245	−	0.615362i	$-0.210990\pi$
$487$	373894.			1.57649			0.788245	+	0.615362i	$0.210990\pi$
$488$	−40426.2			−0.169755
$489$	−104762.			−0.438113
$490$		−	26048.0i		−	0.108488i
$491$	59038.2			0.244889			0.122445	−	0.992475i	$-0.460927\pi$
$491$	59038.2			0.244889			0.122445	+	0.992475i	$0.460927\pi$
$492$	−80653.2			−0.333190
$493$	17112.5			0.0704077
$494$	−2098.97			−0.00860106
$495$		−	162945.i		−	0.665015i
$496$		−	170.911i		−	0.000694716i
$497$	73004.6			0.295554
$498$	−46602.6			−0.187911
$499$	102779.			0.412764			0.206382	−	0.978472i	$-0.433831\pi$
$499$	102779.			0.412764			0.206382	+	0.978472i	$0.433831\pi$
$500$	241983.			0.967932
$501$	73780.9			0.293946
$502$			101487.i			0.402721i
$503$		−	439823.i		−	1.73837i	−0.494487	−	0.869185i	$-0.664644\pi$
$503$		−	439823.i		−	1.73837i	0.494487	−	0.869185i	$-0.335356\pi$
$504$			28601.9i			0.112599i
$505$			291697.i			1.14380i
$506$		−	42841.2i		−	0.167325i
$507$	−147885.			−0.575317
$508$	42377.5			0.164213
$509$		−	339254.i		−	1.30945i	−0.755866	−	0.654726i	$-0.772784\pi$
$509$		−	339254.i		−	1.30945i	0.755866	−	0.654726i	$-0.227216\pi$
$510$		−	27392.2i		−	0.105314i
$511$		−	142354.i		−	0.545166i
$512$		−	11585.2i		−	0.0441942i
$513$	−10380.1			−0.0394428
$514$		−	324815.i		−	1.22945i
$515$			814326.i			3.07032i
$516$		−	27838.3i		−	0.104555i
$517$	201898.			0.755356
$518$	239561.			0.892805
$519$			302533.i			1.12315i
$520$	−9989.19			−0.0369423
$521$	−188480.			−0.694368			−0.347184	−	0.937797i	$-0.612862\pi$
$521$	−188480.			−0.694368			−0.347184	+	0.937797i	$0.612862\pi$
$522$		−	30861.3i		−	0.113259i
$523$	−152454.			−0.557359			−0.278680	−	0.960384i	$-0.589897\pi$
$523$	−152454.			−0.557359			−0.278680	+	0.960384i	$0.589897\pi$
$524$		−	21256.1i		−	0.0774144i
$525$	−319220.			−1.15817
$526$			158815.i			0.574012i
$527$		−	113.084i		−	0.000407172i
$528$		−	45598.4i		−	0.163562i
$529$	267638.			0.956394
$530$		−	647811.i		−	2.30620i
$531$	−45201.8	−	82403.6i	−0.160312	−	0.292252i
$532$	−27710.4			−0.0979084
$533$			19460.5i			0.0685015i
$534$	−77115.4			−0.270432
$535$	45487.7			0.158923
$536$	130574.			0.454493
$537$		−	68911.2i		−	0.238969i
$538$	−227013.			−0.784309
$539$		−	28689.7i		−	0.0987527i
$540$	−49400.0			−0.169410
$541$			106435.i			0.363654i	0.983331	+	0.181827i	$0.0582011\pi$
$541$			106435.i			0.363654i	−0.983331	+	0.181827i	$0.941799\pi$
$542$		−	12198.0i		−	0.0415230i
$543$	−69147.3			−0.234518
$544$		−	7665.38i		−	0.0259022i
$545$			823358.i			2.77201i
$546$	6901.25			0.0231496
$547$	−13393.2			−0.0447620			−0.0223810	−	0.999750i	$-0.507125\pi$
$547$	−13393.2			−0.0447620			−0.0223810	+	0.999750i	$0.507125\pi$
$548$	−20680.0			−0.0688636
$549$			48238.3i			0.160047i
$550$	508913.			1.68236
$551$	29899.3			0.0984823
$552$	−12988.1			−0.0426253
$553$	273551.			0.894516
$554$			60603.7i			0.197460i
$555$			413759.i			1.34326i
$556$	48795.2			0.157844
$557$	273966.			0.883052			0.441526	−	0.897249i	$-0.354437\pi$
$557$	273966.			0.883052			0.441526	+	0.897249i	$0.354437\pi$
$558$	−203.939			−0.000654985
$559$	−6717.01			−0.0214957
$560$	−131877.			−0.420525
$561$		−	30170.2i		−	0.0958633i
$562$		−	105257.i		−	0.333256i
$563$			556932.i			1.75706i	0.477691	+	0.878528i	$0.341474\pi$
$563$			556932.i			1.75706i	−0.477691	+	0.878528i	$0.658526\pi$
$564$		−	61209.3i		−	0.192424i
$565$			180914.i			0.566728i
$566$	−95727.4			−0.298816
$567$	34129.1			0.106159
$568$			35284.8i			0.109368i
$569$			229502.i			0.708863i	0.935082	+	0.354431i	$0.115326\pi$
$569$			229502.i			0.708863i	−0.935082	+	0.354431i	$0.884674\pi$
$570$		−	47860.2i		−	0.147307i
$571$			584197.i			1.79179i	0.444267	+	0.895894i	$0.353464\pi$
$571$			584197.i			1.79179i	−0.444267	+	0.895894i	$0.646536\pi$
$572$	−11002.3			−0.0336271
$573$			195349.i			0.594981i
$574$			256916.i			0.779773i
$575$		−	144957.i		−	0.438434i
$576$	−13824.0			−0.0416667
$577$	−576335.			−1.73111			−0.865553	−	0.500817i	$-0.833033\pi$
$577$	−576335.			−1.73111			−0.865553	+	0.500817i	$0.833033\pi$
$578$			231161.i			0.691926i
$579$	−238874.			−0.712544
$580$	142294.			0.422990
$581$			148450.i			0.439772i
$582$	104916.			0.309739
$583$		−	713509.i		−	2.09924i
$584$	68803.2			0.201736
$585$			11919.5i			0.0348295i
$586$			280414.i			0.816591i
$587$		−	428988.i		−	1.24500i	−0.782620	−	0.622499i	$-0.786117\pi$
$587$		−	428988.i		−	1.24500i	0.782620	−	0.622499i	$-0.213883\pi$
$588$	−8697.83			−0.0251569
$589$		−	197.582i		−	0.000569530i
$590$	379943.	−	208414.i	1.09148	−	0.598720i
$591$	228141.			0.653173
$592$			115786.i			0.330378i
$593$	285143.			0.810875			0.405438	−	0.914123i	$-0.367119\pi$
$593$	285143.			0.810875			0.405438	+	0.914123i	$0.367119\pi$
$594$	−54409.9			−0.154207
$595$	−87256.3			−0.246469
$596$		−	252238.i		−	0.710098i
$597$	−156004.			−0.437711
$598$			3133.85i			0.00876347i
$599$	456615.			1.27261			0.636307	−	0.771436i	$-0.280461\pi$
$599$	456615.			1.27261			0.636307	+	0.771436i	$0.280461\pi$
$600$		−	154286.i		−	0.428573i
$601$		−	376817.i		−	1.04323i	−0.853180	−	0.521617i	$-0.825329\pi$
$601$		−	376817.i		−	1.04323i	0.853180	−	0.521617i	$-0.174671\pi$
$602$	−88677.4			−0.244692
$603$		−	155806.i		−	0.428500i
$604$			143929.i			0.394524i
$605$	183086.			0.500201
$606$	97402.1			0.265230
$607$	−451640.			−1.22579			−0.612894	−	0.790165i	$-0.709995\pi$
$607$	−451640.			−1.22579			−0.612894	+	0.790165i	$0.709995\pi$
$608$		−	13393.1i		−	0.0362305i
$609$	−98306.8			−0.265063
$610$	−222415.			−0.597729
$611$	−14769.0			−0.0395610
$612$	−9146.66			−0.0244208
$613$			675214.i			1.79689i	0.439090	+	0.898443i	$0.355301\pi$
$613$			675214.i			1.79689i	−0.439090	+	0.898443i	$0.644699\pi$
$614$			418974.i			1.11135i
$615$	−443734.			−1.17320
$616$	−145251.			−0.382787
$617$	−440909.			−1.15819			−0.579094	−	0.815261i	$-0.696594\pi$
$617$	−440909.			−1.15819			−0.579094	+	0.815261i	$0.696594\pi$
$618$	271916.			0.711963
$619$	−687057.			−1.79313			−0.896565	−	0.442912i	$-0.853945\pi$
$619$	−687057.			−1.79313			−0.896565	+	0.442912i	$0.853945\pi$
$620$		−	940.311i		−	0.00244618i
$621$			15498.0i			0.0401875i
$622$		−	155419.i		−	0.401719i
$623$			245647.i			0.632900i
$624$			3335.54i			0.00856637i
$625$	511185.			1.30863
$626$	136243.			0.347668
$627$		−	52714.0i		−	0.134088i
$628$		−	186517.i		−	0.472932i
$629$			76609.6i			0.193634i
$630$			157361.i			0.396475i
$631$	71943.3			0.180689			0.0903445	−	0.995911i	$-0.471203\pi$
$631$	71943.3			0.180689			0.0903445	+	0.995911i	$0.471203\pi$
$632$			132214.i			0.331011i
$633$		−	143035.i		−	0.356971i
$634$		−	199494.i		−	0.496307i
$635$	233150.			0.578214
$636$	−216314.			−0.534774
$637$			2098.67i			0.00517207i
$638$	156725.			0.385031
$639$	42103.4			0.103113
$640$		−	63739.1i		−	0.155613i
$641$	−125964.			−0.306570			−0.153285	−	0.988182i	$-0.548985\pi$
$641$	−125964.			−0.306570			−0.153285	+	0.988182i	$0.548985\pi$
$642$		−	15189.0i		−	0.0368519i
$643$	745563.			1.80328			0.901639	−	0.432489i	$-0.142365\pi$
$643$	745563.			1.80328			0.901639	+	0.432489i	$0.142365\pi$
$644$			41372.9i			0.0997571i
$645$		−	153160.i		−	0.368150i
$646$		−	8861.56i		−	0.0212347i
$647$	594216.			1.41950			0.709750	−	0.704453i	$-0.248808\pi$
$647$	594216.			1.41950			0.709750	+	0.704453i	$0.248808\pi$
$648$			16495.4i			0.0392837i
$649$	418475.	−	229551.i	0.993529	−	0.544992i
$650$	−37227.2			−0.0881117
$651$			649.635i			0.00153288i
$652$	−161292.			−0.379417
$653$	747092.			1.75205			0.876027	−	0.482262i	$-0.160185\pi$
$653$	747092.			1.75205			0.876027	+	0.482262i	$0.160185\pi$
$654$	274931.			0.642790
$655$		−	116946.i		−	0.272586i
$656$	−124174.			−0.288551
$657$		−	82099.0i		−	0.190198i
$658$	−194979.			−0.450335
$659$			187379.i			0.431470i	0.976452	+	0.215735i	$0.0692147\pi$
$659$			187379.i			0.431470i	−0.976452	+	0.215735i	$0.930785\pi$
$660$		−	250871.i		−	0.575920i
$661$	−521254.			−1.19302			−0.596509	−	0.802607i	$-0.703446\pi$
$661$	−521254.			−1.19302			−0.596509	+	0.802607i	$0.703446\pi$
$662$			51657.6i			0.117874i
$663$			2206.96i			0.00502074i
$664$	−71749.4			−0.162735
$665$	−152456.			−0.344747
$666$	138160.			0.311483
$667$		−	44641.0i		−	0.100342i
$668$	113593.			0.254565
$669$	363278.			0.811684
$670$	718386.			1.60032
$671$	−244971.			−0.544089
$672$			44035.6i			0.0975136i
$673$		−	46497.1i		−	0.102659i	−0.998682	−	0.0513293i	$-0.983654\pi$
$673$		−	46497.1i		−	0.102659i	0.998682	−	0.0513293i	$-0.0163458\pi$
$674$	−214098.			−0.471295
$675$	−184101.			−0.404063
$676$	−227683.			−0.498239
$677$	697302.			1.52140			0.760700	−	0.649104i	$-0.224856\pi$
$677$	697302.			1.52140			0.760700	+	0.649104i	$0.224856\pi$
$678$	60409.9			0.131416
$679$		−	334204.i		−	0.724889i
$680$		−	42173.0i		−	0.0912047i
$681$			237738.i			0.512631i
$682$		−	1035.67i		−	0.00222666i
$683$			148315.i			0.317940i	0.987283	+	0.158970i	$0.0508173\pi$
$683$			148315.i			0.317940i	−0.987283	+	0.158970i	$0.949183\pi$
$684$	−15981.2			−0.0341584
$685$	−113776.			−0.242477
$686$			345638.i			0.734469i
$687$			402544.i			0.852903i
$688$		−	42859.9i		−	0.0905471i
$689$			52193.5i			0.109946i
$690$	−71457.3			−0.150089
$691$		−	490423.i		−	1.02711i	−0.858058	−	0.513553i	$-0.828329\pi$
$691$		−	490423.i		−	1.02711i	0.858058	−	0.513553i	$-0.171671\pi$
$692$			465780.i			0.972677i
$693$			173320.i			0.360895i
$694$	108112.			0.224469
$695$	268459.			0.555787
$696$		−	47514.0i		−	0.0980852i
$697$	−82159.7			−0.169119
$698$	−67252.0			−0.138037
$699$			291392.i			0.596380i
$700$	−491471.			−1.00300
$701$		−	754901.i		−	1.53622i	−0.640316	−	0.768111i	$-0.721197\pi$
$701$		−	754901.i		−	1.53622i	0.640316	−	0.768111i	$-0.278803\pi$
$702$	3980.11			0.00807646
$703$			133854.i			0.270845i
$704$		−	70203.3i		−	0.141648i
$705$		−	336758.i		−	0.677548i
$706$	−381887.			−0.766170
$707$		−	310269.i		−	0.620725i
$708$	−69592.7	−	126869.i	−0.138834	−	0.253097i
$709$	−771119.			−1.53401			−0.767006	−	0.641640i	$-0.778254\pi$
$709$	−771119.			−1.53401			−0.767006	+	0.641640i	$0.778254\pi$
$710$			194128.i			0.385099i
$711$	157763.			0.312080
$712$	−118727.			−0.234201
$713$	−294.998			−0.000580284
$714$			29136.2i			0.0571526i
$715$	−60531.7			−0.118405
$716$		−	106096.i		−	0.206953i
$717$	95777.6			0.186306
$718$			635754.i			1.23322i
$719$			355475.i			0.687625i	0.939038	+	0.343812i	$0.111718\pi$
$719$			355475.i			0.687625i	−0.939038	+	0.343812i	$0.888282\pi$
$720$	−76056.2			−0.146713
$721$		−	866172.i		−	1.66623i
$722$			353120.i			0.677405i
$723$	268097.			0.512880
$724$	−106459.			−0.203098
$725$	530293.			1.00888
$726$		−	61135.2i		−	0.115989i
$727$	12350.4			0.0233676			0.0116838	−	0.999932i	$-0.496281\pi$
$727$	12350.4			0.0233676			0.0116838	+	0.999932i	$0.496281\pi$
$728$	10625.2			0.0200481
$729$	19683.0			0.0370370
$730$	378538.			0.710337
$731$		−	28358.3i		−	0.0530696i
$732$			74267.7i			0.138605i
$733$	406766.			0.757071			0.378536	−	0.925587i	$-0.376428\pi$
$733$	406766.			0.757071			0.378536	+	0.925587i	$0.376428\pi$
$734$	−682608.			−1.26701
$735$	−47853.3			−0.0885803
$736$	−19996.5			−0.0369146
$737$	791241.			1.45671
$738$			148169.i			0.272048i
$739$		−	511731.i		−	0.937029i	−0.883456	−	0.468515i	$-0.844789\pi$
$739$		−	511731.i		−	0.937029i	0.883456	−	0.468515i	$-0.155211\pi$
$740$			637023.i			1.16330i
$741$			3856.05i			0.00702274i
$742$			689055.i			1.25154i
$743$	47524.3			0.0860871			0.0430435	−	0.999073i	$-0.486295\pi$
$743$	47524.3			0.0860871			0.0430435	+	0.999073i	$0.486295\pi$
$744$	−313.984			−0.000567233
$745$		−	1.38775e6i		−	2.50034i
$746$			473586.i			0.850984i
$747$			85614.4i			0.153428i
$748$		−	46450.1i		−	0.0830201i
$749$	−48383.8			−0.0862455
$750$		−	444551.i		−	0.790313i
$751$			778410.i			1.38016i	0.723735	+	0.690078i	$0.242424\pi$
$751$			778410.i			1.38016i	−0.723735	+	0.690078i	$0.757576\pi$
$752$		−	94237.9i		−	0.166644i
$753$	186444.			0.328821
$754$	−11464.5			−0.0201656
$755$			791859.i			1.38917i
$756$	52545.1			0.0919367
$757$	269630.			0.470518			0.235259	−	0.971933i	$-0.424406\pi$
$757$	269630.			0.470518			0.235259	+	0.971933i	$0.424406\pi$
$758$		−	39991.0i		−	0.0696023i
$759$	−78704.2			−0.136620
$760$		−	73685.6i		−	0.127572i
$761$	−170885.			−0.295077			−0.147538	−	0.989056i	$-0.547135\pi$
$761$	−170885.			−0.295077			−0.147538	+	0.989056i	$0.547135\pi$
$762$		−	77852.4i		−	0.134079i
$763$		−	875779.i		−	1.50434i
$764$			300760.i			0.515268i
$765$	−50322.7			−0.0859886
$766$		−	573187.i		−	0.976875i
$767$	−30611.7	+	16791.8i	−0.0520351	+	0.0285434i
$768$	−21283.4			−0.0360844
$769$		−	478548.i		−	0.809232i	−0.914487	−	0.404616i	$-0.867405\pi$
$769$		−	478548.i		−	0.809232i	0.914487	−	0.404616i	$-0.132595\pi$
$770$	−799135.			−1.34784
$771$	−596724.			−1.00384
$772$	−367770.			−0.617081
$773$		−	218197.i		−	0.365166i	−0.983190	−	0.182583i	$-0.941554\pi$
$773$		−	218197.i		−	0.365166i	0.983190	−	0.182583i	$-0.0584458\pi$
$774$	−51142.3			−0.0853686
$775$		−	3504.30i		−	0.00583443i
$776$	161529.			0.268241
$777$		−	440102.i		−	0.728972i
$778$		−	64421.8i		−	0.106432i
$779$	−143551.			−0.236555
$780$			18351.3i			0.0301632i
$781$			213816.i			0.350541i
$782$	−13230.7			−0.0216356
$783$	−56695.8			−0.0924756
$784$	−13391.2			−0.0217865
$785$		−	1.02617e6i		−	1.66525i
$786$	−39050.0			−0.0632086
$787$	−63545.9			−0.102598			−0.0512989	−	0.998683i	$-0.516336\pi$
$787$	−63545.9			−0.102598			−0.0512989	+	0.998683i	$0.516336\pi$
$788$	351246.			0.565664
$789$	291762.			0.468679
$790$			727407.i			1.16553i
$791$		−	192432.i		−	0.307556i
$792$	−83769.5			−0.133547
$793$	17919.8			0.0284961
$794$	68568.2			0.108763
$795$	−1.19010e6			−1.88300
$796$	−240184.			−0.379069
$797$		−	1.10517e6i		−	1.73985i	−0.493181	−	0.869927i	$-0.664166\pi$
$797$		−	1.10517e6i		−	1.73985i	0.493181	−	0.869927i	$-0.335834\pi$
$798$			50907.3i			0.0799419i
$799$		−	62352.6i		−	0.0976699i
$800$		−	237540.i		−	0.371156i
$801$			141670.i			0.220807i
$802$	−693629.			−1.07840
$803$	416928.			0.646592
$804$		−	239880.i		−	0.371092i
$805$			227623.i			0.351257i
$806$			75.7600i			0.000116619i
$807$			417050.i			0.640385i
$808$	149960.			0.229696
$809$		−	60667.5i		−	0.0926957i	−0.998925	−	0.0463478i	$-0.985242\pi$
$809$		−	60667.5i		−	0.0926957i	0.998925	−	0.0463478i	$-0.0147583\pi$
$810$			90753.5i			0.138323i
$811$		−	428837.i		−	0.652004i	−0.945369	−	0.326002i	$-0.894298\pi$
$811$		−	428837.i		−	0.652004i	0.945369	−	0.326002i	$-0.105702\pi$
$812$	−151353.			−0.229551
$813$	−22409.1			−0.0339034
$814$			701627.i			1.05891i
$815$	−887386.			−1.33597
$816$	−14082.2			−0.0211490
$817$		−	49548.2i		−	0.0742307i
$818$	872974.			1.30465
$819$		−	12678.4i		−	0.0189015i
$820$	−683173.			−1.01602
$821$		−	1.08674e6i		−	1.61227i	−0.591732	−	0.806135i	$-0.701556\pi$
$821$		−	1.08674e6i		−	1.61227i	0.591732	−	0.806135i	$-0.298444\pi$
$822$			37991.6i			0.0562269i
$823$		−	188769.i		−	0.278697i	−0.990243	−	0.139348i	$-0.955499\pi$
$823$		−	188769.i		−	0.278697i	0.990243	−	0.139348i	$-0.0445008\pi$
$824$	418642.			0.616578
$825$		−	934932.i		−	1.37364i
$826$	−404133.	+	221684.i	−0.592330	+	0.324918i
$827$	785862.			1.14904			0.574520	−	0.818490i	$-0.305189\pi$
$827$	785862.			1.14904			0.574520	+	0.818490i	$0.305189\pi$
$828$			23860.7i			0.0348034i
$829$	−929243.			−1.35214			−0.676068	−	0.736840i	$-0.736317\pi$
$829$	−929243.			−1.35214			−0.676068	+	0.736840i	$0.736317\pi$
$830$	−394747.			−0.573011
$831$	111336.			0.161226
$832$			5135.40i			0.00741870i
$833$	−8860.29			−0.0127690
$834$		−	89642.6i		−	0.128879i
$835$	624961.			0.896354
$836$		−	81158.4i		−	0.116124i
$837$			374.659i			0.000534793i
$838$	784346.			1.11691
$839$			91782.8i			0.130388i	0.997873	+	0.0651940i	$0.0207666\pi$
$839$			91782.8i			0.130388i	−0.997873	+	0.0651940i	$0.979233\pi$
$840$			242273.i			0.343357i
$841$	−543972.			−0.769103
$842$	553201.			0.780295
$843$	−193369.			−0.272102
$844$		−	220216.i		−	0.309146i
$845$	−1.25266e6			−1.75436
$846$	−112449.			−0.157114
$847$	−194743.			−0.271453
$848$	−333037.			−0.463127
$849$			175862.i			0.243982i
$850$		−	157168.i		−	0.217534i
$851$	199850.			0.275959
$852$	64822.4			0.0892989
$853$	673997.			0.926318			0.463159	−	0.886275i	$-0.346716\pi$
$853$	673997.			0.926318			0.463159	+	0.886275i	$0.346716\pi$
$854$	236575.			0.324380
$855$	−87924.7			−0.120276
$856$		−	23385.0i		−	0.0319147i
$857$		−	185621.i		−	0.252735i	−0.991984	−	0.126367i	$-0.959668\pi$
$857$		−	185621.i		−	0.252735i	0.991984	−	0.126367i	$-0.0403318\pi$
$858$			20212.4i			0.0274564i
$859$			839192.i			1.13730i	0.822579	+	0.568650i	$0.192534\pi$
$859$			839192.i			1.13730i	−0.822579	+	0.568650i	$0.807466\pi$
$860$		−	235805.i		−	0.318827i
$861$	471985.			0.636682
$862$	−752370.			−1.01255
$863$		−	1.28770e6i		−	1.72900i	−0.502634	−	0.864499i	$-0.667636\pi$
$863$		−	1.28770e6i		−	1.72900i	0.502634	−	0.864499i	$-0.332364\pi$
$864$			25396.3i			0.0340207i
$865$			2.56261e6i			3.42491i
$866$			264507.i			0.352697i
$867$	424670.			0.564955
$868$			1000.18i			0.00132751i
$869$			801178.i			1.06094i
$870$		−	261410.i		−	0.345370i
$871$	−57879.7			−0.0762939
$872$	423285.			0.556672
$873$		−	192743.i		−	0.252900i
$874$	−23116.9			−0.0302627
$875$	−1.41609e6			−1.84959
$876$		−	126400.i		−	0.164717i
$877$	225619.			0.293344			0.146672	−	0.989185i	$-0.453144\pi$
$877$	225619.			0.293344			0.146672	+	0.989185i	$0.453144\pi$
$878$		−	1.00426e6i		−	1.30274i
$879$	515154.			0.666744
$880$		−	386241.i		−	0.498761i
$881$		−	117049.i		−	0.150805i	−0.997153	−	0.0754023i	$-0.975976\pi$
$881$		−	117049.i		−	0.150805i	0.997153	−	0.0754023i	$-0.0240241\pi$
$882$			15978.9i			0.0205405i
$883$	225659.			0.289422			0.144711	−	0.989474i	$-0.453775\pi$
$883$	225659.			0.289422			0.144711	+	0.989474i	$0.453775\pi$
$884$			3397.84i			0.00434809i
$885$	−382882.	−	698000.i	−0.488853	−	0.891187i
$886$	1.07509e6			1.36955
$887$			191517.i			0.243422i	0.992566	+	0.121711i	$0.0388382\pi$
$887$			191517.i			0.243422i	−0.992566	+	0.121711i	$0.961162\pi$
$888$	212712.			0.269752
$889$	−247994.			−0.313789
$890$	−653206.			−0.824651
$891$			99957.4i			0.125910i
$892$	559303.			0.702939
$893$		−	108944.i		−	0.136615i
$894$	−463391.			−0.579793
$895$		−	583712.i		−	0.728707i
$896$			67797.2i			0.0844492i
$897$	5757.25			0.00715534
$898$			54839.2i			0.0680046i
$899$		−	1079.18i		−	0.00133529i
$900$	−283442.			−0.349929
$901$	−220354.			−0.271439
$902$	−752458.			−0.924846
$903$			162911.i			0.199790i
$904$	93007.1			0.113810
$905$	−585713.			−0.715134
$906$	264414.			0.322127
$907$	−596315.			−0.724872			−0.362436	−	0.932009i	$-0.618055\pi$
$907$	−596315.			−0.724872			−0.362436	+	0.932009i	$0.618055\pi$
$908$			366022.i			0.443951i
$909$		−	178939.i		−	0.216560i
$910$	58457.1			0.0705918
$911$	88396.9			0.106512			0.0532562	−	0.998581i	$-0.483040\pi$
$911$	88396.9			0.106512			0.0532562	+	0.998581i	$0.483040\pi$
$912$	−24604.7			−0.0295821
$913$	−434781.			−0.521590
$914$	−882728.			−1.05666
$915$			408602.i			0.488044i
$916$			619757.i			0.738636i
$917$			124392.i			0.147929i
$918$			16803.5i			0.0199395i
$919$			938106.i			1.11076i	0.831596	+	0.555381i	$0.187427\pi$
$919$			938106.i			1.11076i	−0.831596	+	0.555381i	$0.812573\pi$
$920$	−110016.			−0.129981
$921$	769704.			0.907412
$922$		−	436251.i		−	0.513186i
$923$		−	15640.8i		−	0.0183592i
$924$			266843.i			0.312545i
$925$			2.37402e6i			2.77461i
$926$	363245.			0.423621
$927$		−	499541.i		−	0.581315i
$928$		−	73152.6i		−	0.0849443i
$929$		−	447256.i		−	0.518232i	−0.965846	−	0.259116i	$-0.916569\pi$
$929$		−	447256.i		−	0.518232i	0.965846	−	0.259116i	$-0.0834313\pi$
$930$	−1727.46			−0.00199730
$931$	−15480.9			−0.0178606
$932$			448627.i			0.516480i
$933$	−285522.			−0.328002
$934$	335941.			0.385096
$935$		−	255557.i		−	0.292324i
$936$	6127.78			0.00699442
$937$		−	1.06041e6i		−	1.20780i	−0.797059	−	0.603901i	$-0.793612\pi$
$937$		−	1.06041e6i		−	1.20780i	0.797059	−	0.603901i	$-0.206388\pi$
$938$	−764123.			−0.868476
$939$		−	250294.i		−	0.283870i
$940$		−	518473.i		−	0.586774i
$941$		−	487573.i		−	0.550631i	−0.961354	−	0.275315i	$-0.911218\pi$
$941$		−	487573.i		−	0.550631i	0.961354	−	0.275315i	$-0.0887823\pi$
$942$	−342653.			−0.386147
$943$			214328.i			0.241021i
$944$	−107145.	−	195327.i	−0.120234	−	0.219189i
$945$	289090.			0.323720
$946$		−	259719.i		−	0.290216i
$947$	621810.			0.693358			0.346679	−	0.937984i	$-0.387309\pi$
$947$	621810.			0.693358			0.346679	+	0.937984i	$0.387309\pi$
$948$	242892.			0.270269
$949$	−30498.5			−0.0338646
$950$		−	274607.i		−	0.304274i
$951$	−366493.			−0.405233
$952$			44858.1i			0.0494956i
$953$	1.03888e6			1.14388			0.571939	−	0.820296i	$-0.306191\pi$
$953$	1.03888e6			1.14388			0.571939	+	0.820296i	$0.306191\pi$
$954$			397394.i			0.436641i
$955$			1.65471e6i			1.81432i
$956$	147459.			0.161345
$957$		−	287922.i		−	0.314377i
$958$			131115.i			0.142864i
$959$	121020.			0.131589
$960$	−117096.			−0.127057
$961$	923514.			0.999992
$962$		−	51324.4i		−	0.0554592i
$963$	−27904.0			−0.0300895
$964$	412763.			0.444167
$965$	−2.02338e6			−2.17282
$966$	76006.8			0.0814514
$967$			1.26806e6i			1.35609i	0.735021	+	0.678044i	$0.237172\pi$
$967$			1.26806e6i			1.35609i	−0.735021	+	0.678044i	$0.762828\pi$
$968$		−	94123.8i		−	0.100450i
$969$	−16279.7			−0.0173380
$970$	888690.			0.944511
$971$	−349296.			−0.370472			−0.185236	−	0.982694i	$-0.559305\pi$
$971$	−349296.			−0.370472			−0.185236	+	0.982694i	$0.559305\pi$
$972$	30304.0			0.0320750
$973$	−285551.			−0.301619
$974$		−	1.05753e6i		−	1.11475i
$975$			68390.7i			0.0719429i
$976$			114343.i			0.120035i
$977$			1.16397e6i			1.21942i	0.792625	+	0.609709i	$0.208714\pi$
$977$			1.16397e6i			1.21942i	−0.792625	+	0.609709i	$0.791286\pi$
$978$			296311.i			0.309792i
$979$	−719451.			−0.750648
$980$	−73675.0			−0.0767128
$981$		−	505081.i		−	0.524836i
$982$		−	166985.i		−	0.173163i
$983$			1.30717e6i			1.35277i	0.736547	+	0.676386i	$0.236455\pi$
$983$			1.30717e6i			1.35277i	−0.736547	+	0.676386i	$0.763545\pi$
$984$			228122.i			0.235601i
$985$	1.93247e6			1.99177
$986$		−	48401.5i		−	0.0497858i
$987$			358199.i			0.367697i
$988$			5936.78i			0.00608187i
$989$	−73977.6			−0.0756324
$990$	−460879.			−0.470237
$991$			590472.i			0.601246i	0.953743	+	0.300623i	$0.0971946\pi$
$991$			590472.i			0.601246i	−0.953743	+	0.300623i	$0.902805\pi$
$992$	−483.410			−0.000491238
$993$	94901.1			0.0962437
$994$		−	206488.i		−	0.208988i
$995$	−1.32143e6			−1.33475
$996$			131812.i			0.132873i
$997$	−531952.			−0.535159			−0.267579	−	0.963536i	$-0.586224\pi$
$997$	−531952.			−0.535159			−0.267579	+	0.963536i	$0.586224\pi$
$998$		−	290702.i		−	0.291868i
$999$		−	253817.i		−	0.254325i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.5.d.a.235.9	✓	40
3.2	odd	2		1062.5.d.b.235.30		40
59.58	odd	2	inner	354.5.d.a.235.10	yes	40
177.176	even	2		1062.5.d.b.235.29		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.5.d.a.235.9	✓	40	1.1	even	1	trivial
354.5.d.a.235.10	yes	40	59.58	odd	2	inner
1062.5.d.b.235.29		40	177.176	even	2
1062.5.d.b.235.30		40	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	354.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.82843i q^{2} -5.19615 q^{3} -8.00000 q^{4} -44.0140 q^{5} +14.6969i q^{6} +46.8163 q^{7} +22.6274i q^{8} +27.0000 q^{9} +O(q^{10})\)	\(q-2.82843i q^{2} -5.19615 q^{3} -8.00000 q^{4} -44.0140 q^{5} +14.6969i q^{6} +46.8163 q^{7} +22.6274i q^{8} +27.0000 q^{9} +124.490i q^{10} +137.116i q^{11} +41.5692 q^{12} -10.0301i q^{13} -132.416i q^{14} +228.703 q^{15} +64.0000 q^{16} +42.3457 q^{17} -76.3675i q^{18} +73.9872 q^{19} +352.112 q^{20} -243.264 q^{21} +387.822 q^{22} -110.466i q^{23} -117.576i q^{24} +1312.23 q^{25} -28.3693 q^{26} -140.296 q^{27} -374.530 q^{28} +404.115 q^{29} -646.871i q^{30} -2.67049i q^{31} -181.019i q^{32} -712.474i q^{33} -119.772i q^{34} -2060.57 q^{35} -216.000 q^{36} +1809.15i q^{37} -209.267i q^{38} +52.1178i q^{39} -995.923i q^{40} -1940.22 q^{41} +688.056i q^{42} -669.686i q^{43} -1096.93i q^{44} -1188.38 q^{45} -312.445 q^{46} -1472.47i q^{47} -332.554 q^{48} -209.237 q^{49} -3711.56i q^{50} -220.035 q^{51} +80.2406i q^{52} -5203.70 q^{53} +396.817i q^{54} -6035.01i q^{55} +1059.33i q^{56} -384.449 q^{57} -1143.01i q^{58} +(-1674.14 - 3051.99i) q^{59} -1829.63 q^{60} +1786.60i q^{61} -7.55328 q^{62} +1264.04 q^{63} -512.000 q^{64} +441.464i q^{65} -2015.18 q^{66} -5770.61i q^{67} -338.765 q^{68} +573.999i q^{69} +5828.18i q^{70} +1559.38 q^{71} +610.940i q^{72} -3040.70i q^{73} +5117.05 q^{74} -6818.56 q^{75} -591.897 q^{76} +6419.25i q^{77} +147.411 q^{78} +5843.07 q^{79} -2816.90 q^{80} +729.000 q^{81} +5487.76i q^{82} +3170.91i q^{83} +1946.12 q^{84} -1863.80 q^{85} -1894.16 q^{86} -2099.84 q^{87} -3102.57 q^{88} +5247.04i q^{89} +3361.24i q^{90} -469.571i q^{91} +883.729i q^{92} +13.8763i q^{93} -4164.77 q^{94} -3256.47 q^{95} +940.604i q^{96} -7138.62i q^{97} +591.813i q^{98} +3702.12i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 320 q^{4} - 80 q^{7} + 1080 q^{9}+O(q^{10}) \) 40 * q - 320 * q^4 - 80 * q^7 + 1080 * q^9	\( 40 q - 320 q^{4} - 80 q^{7} + 1080 q^{9} - 144 q^{15} + 2560 q^{16} + 480 q^{17} - 792 q^{19} - 1024 q^{22} + 3400 q^{25} + 768 q^{26} + 640 q^{28} + 1608 q^{29} - 5760 q^{35} - 8640 q^{36} + 6264 q^{41} + 7040 q^{46} + 17912 q^{49} + 1296 q^{51} - 1104 q^{53} + 5040 q^{57} + 13584 q^{59} + 1152 q^{60} - 12288 q^{62} - 2160 q^{63} - 20480 q^{64} + 1152 q^{66} - 3840 q^{68} + 35352 q^{71} + 4608 q^{74} + 3168 q^{75} + 6336 q^{76} - 12672 q^{78} - 15720 q^{79} + 29160 q^{81} - 26872 q^{85} + 18432 q^{86} + 7776 q^{87} + 8192 q^{88} - 18432 q^{94} - 19128 q^{95}+O(q^{100}) \) 40 * q - 320 * q^4 - 80 * q^7 + 1080 * q^9 - 144 * q^15 + 2560 * q^16 + 480 * q^17 - 792 * q^19 - 1024 * q^22 + 3400 * q^25 + 768 * q^26 + 640 * q^28 + 1608 * q^29 - 5760 * q^35 - 8640 * q^36 + 6264 * q^41 + 7040 * q^46 + 17912 * q^49 + 1296 * q^51 - 1104 * q^53 + 5040 * q^57 + 13584 * q^59 + 1152 * q^60 - 12288 * q^62 - 2160 * q^63 - 20480 * q^64 + 1152 * q^66 - 3840 * q^68 + 35352 * q^71 + 4608 * q^74 + 3168 * q^75 + 6336 * q^76 - 12672 * q^78 - 15720 * q^79 + 29160 * q^81 - 26872 * q^85 + 18432 * q^86 + 7776 * q^87 + 8192 * q^88 - 18432 * q^94 - 19128 * q^95

Introduction

L-functions

Modular forms

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