LMFDB - Embedded newform 354.5.d.a.235.4

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			235.4
Character	$\chi$	$=$	354.235
Dual form			354.5.d.a.235.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.82843i q^{2} -5.19615 q^{3} -8.00000 q^{4} +21.2806 q^{5} -14.6969i q^{6} -81.9829 q^{7} -22.6274i q^{8} +27.0000 q^{9} +O(q^{10})$	\(q+2.82843i q^{2} -5.19615 q^{3} -8.00000 q^{4} +21.2806 q^{5} -14.6969i q^{6} -81.9829 q^{7} -22.6274i q^{8} +27.0000 q^{9} +60.1907i q^{10} +167.036i q^{11} +41.5692 q^{12} +16.7521i q^{13} -231.883i q^{14} -110.577 q^{15} +64.0000 q^{16} -400.019 q^{17} +76.3675i q^{18} +475.320 q^{19} -170.245 q^{20} +425.996 q^{21} -472.448 q^{22} +339.573i q^{23} +117.576i q^{24} -172.135 q^{25} -47.3822 q^{26} -140.296 q^{27} +655.863 q^{28} +158.559 q^{29} -312.760i q^{30} -1045.16i q^{31} +181.019i q^{32} -867.942i q^{33} -1131.42i q^{34} -1744.65 q^{35} -216.000 q^{36} -2013.43i q^{37} +1344.41i q^{38} -87.0467i q^{39} -481.525i q^{40} -1226.52 q^{41} +1204.90i q^{42} -1633.79i q^{43} -1336.28i q^{44} +574.577 q^{45} -960.456 q^{46} +982.626i q^{47} -332.554 q^{48} +4320.20 q^{49} -486.872i q^{50} +2078.56 q^{51} -134.017i q^{52} -1481.67 q^{53} -396.817i q^{54} +3554.62i q^{55} +1855.06i q^{56} -2469.84 q^{57} +448.471i q^{58} +(2502.22 - 2419.97i) q^{59} +884.619 q^{60} -3223.51i q^{61} +2956.17 q^{62} -2213.54 q^{63} -512.000 q^{64} +356.496i q^{65} +2454.91 q^{66} +2608.02i q^{67} +3200.15 q^{68} -1764.47i q^{69} -4934.61i q^{70} +4800.52 q^{71} -610.940i q^{72} -5505.27i q^{73} +5694.83 q^{74} +894.441 q^{75} -3802.56 q^{76} -13694.1i q^{77} +246.205 q^{78} +12209.4 q^{79} +1361.96 q^{80} +729.000 q^{81} -3469.13i q^{82} -4329.44i q^{83} -3407.97 q^{84} -8512.64 q^{85} +4621.06 q^{86} -823.895 q^{87} +3779.58 q^{88} -15005.6i q^{89} +1625.15i q^{90} -1373.39i q^{91} -2716.58i q^{92} +5430.82i q^{93} -2779.29 q^{94} +10115.1 q^{95} -940.604i q^{96} -4372.22i q^{97} +12219.4i q^{98} +4509.96i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	21.2806			0.851225			0.425612	−	0.904906i	$-0.360059\pi$
$5$	21.2806			0.851225			0.425612	+	0.904906i	$0.360059\pi$
$6$		−	14.6969i		−	0.408248i
$7$	−81.9829			−1.67312			−0.836561	−	0.547874i	$-0.815437\pi$
$7$	−81.9829			−1.67312			−0.836561	+	0.547874i	$0.815437\pi$
$8$		−	22.6274i		−	0.353553i
$9$	27.0000			0.333333
$10$			60.1907i			0.601907i
$11$			167.036i			1.38046i	0.723591	+	0.690229i	$0.242490\pi$
$11$			167.036i			1.38046i	−0.723591	+	0.690229i	$0.757510\pi$
$12$	41.5692			0.288675
$13$			16.7521i			0.0991251i	0.998771	+	0.0495626i	$0.0157827\pi$
$13$			16.7521i			0.0991251i	−0.998771	+	0.0495626i	$0.984217\pi$
$14$		−	231.883i		−	1.18308i
$15$	−110.577			−0.491455
$16$	64.0000			0.250000
$17$	−400.019			−1.38415			−0.692074	−	0.721827i	$-0.743303\pi$
$17$	−400.019			−1.38415			−0.692074	+	0.721827i	$0.743303\pi$
$18$			76.3675i			0.235702i
$19$	475.320			1.31668			0.658338	−	0.752722i	$-0.271260\pi$
$19$	475.320			1.31668			0.658338	+	0.752722i	$0.271260\pi$
$20$	−170.245			−0.425612
$21$	425.996			0.965977
$22$	−472.448			−0.976132
$23$			339.573i			0.641914i	0.947094	+	0.320957i	$0.104005\pi$
$23$			339.573i			0.641914i	−0.947094	+	0.320957i	$0.895995\pi$
$24$			117.576i			0.204124i
$25$	−172.135			−0.275416
$26$	−47.3822			−0.0700921
$27$	−140.296			−0.192450
$28$	655.863			0.836561
$29$	158.559			0.188536			0.0942679	−	0.995547i	$-0.469949\pi$
$29$	158.559			0.188536			0.0942679	+	0.995547i	$0.469949\pi$
$30$		−	312.760i		−	0.347511i
$31$		−	1045.16i		−	1.08758i	−0.839222	−	0.543789i	$-0.816989\pi$
$31$		−	1045.16i		−	1.08758i	0.839222	−	0.543789i	$-0.183011\pi$
$32$			181.019i			0.176777i
$33$		−	867.942i		−	0.797008i
$34$		−	1131.42i		−	0.978740i
$35$	−1744.65			−1.42420
$36$	−216.000			−0.166667
$37$		−	2013.43i		−	1.47073i	−0.677672	−	0.735364i	$-0.737011\pi$
$37$		−	2013.43i		−	1.47073i	0.677672	−	0.735364i	$-0.262989\pi$
$38$			1344.41i			0.931031i
$39$		−	87.0467i		−	0.0572299i
$40$		−	481.525i		−	0.300953i
$41$	−1226.52			−0.729639			−0.364820	−	0.931078i	$-0.618869\pi$
$41$	−1226.52			−0.729639			−0.364820	+	0.931078i	$0.618869\pi$
$42$			1204.90i			0.683049i
$43$		−	1633.79i		−	0.883608i	−0.897112	−	0.441804i	$-0.854339\pi$
$43$		−	1633.79i		−	0.883608i	0.897112	−	0.441804i	$-0.145661\pi$
$44$		−	1336.28i		−	0.690229i
$45$	574.577			0.283742
$46$	−960.456			−0.453902
$47$			982.626i			0.444828i	0.974952	+	0.222414i	$0.0713937\pi$
$47$			982.626i			0.444828i	−0.974952	+	0.222414i	$0.928606\pi$
$48$	−332.554			−0.144338
$49$	4320.20			1.79933
$50$		−	486.872i		−	0.194749i
$51$	2078.56			0.799138
$52$		−	134.017i		−	0.0495626i
$53$	−1481.67			−0.527471			−0.263736	−	0.964595i	$-0.584955\pi$
$53$	−1481.67			−0.527471			−0.263736	+	0.964595i	$0.584955\pi$
$54$		−	396.817i		−	0.136083i
$55$			3554.62i			1.17508i
$56$			1855.06i			0.591538i
$57$	−2469.84			−0.760184
$58$			448.471i			0.133315i
$59$	2502.22	−	2419.97i	0.718822	−	0.695194i
$59$	2502.22	−	2419.97i	0.718822	−	0.695194i
$60$	884.619			0.245727
$61$		−	3223.51i		−	0.866302i	−0.901321	−	0.433151i	$-0.857402\pi$
$61$		−	3223.51i		−	0.866302i	0.901321	−	0.433151i	$-0.142598\pi$
$62$	2956.17			0.769034
$63$	−2213.54			−0.557707
$64$	−512.000			−0.125000
$65$			356.496i			0.0843778i
$66$	2454.91			0.563570
$67$			2608.02i			0.580979i	0.956878	+	0.290490i	$0.0938181\pi$
$67$			2608.02i			0.580979i	−0.956878	+	0.290490i	$0.906182\pi$
$68$	3200.15			0.692074
$69$		−	1764.47i		−	0.370609i
$70$		−	4934.61i		−	1.00706i
$71$	4800.52			0.952295			0.476147	−	0.879365i	$-0.342033\pi$
$71$	4800.52			0.952295			0.476147	+	0.879365i	$0.342033\pi$
$72$		−	610.940i		−	0.117851i
$73$		−	5505.27i		−	1.03308i	−0.856264	−	0.516539i	$-0.827220\pi$
$73$		−	5505.27i		−	1.03308i	0.856264	−	0.516539i	$-0.172780\pi$
$74$	5694.83			1.03996
$75$	894.441			0.159012
$76$	−3802.56			−0.658338
$77$		−	13694.1i		−	2.30968i
$78$	246.205			0.0404677
$79$	12209.4			1.95632			0.978158	−	0.207862i	$-0.0666503\pi$
$79$	12209.4			1.95632			0.978158	+	0.207862i	$0.0666503\pi$
$80$	1361.96			0.212806
$81$	729.000			0.111111
$82$		−	3469.13i		−	0.515933i
$83$		−	4329.44i		−	0.628458i	−0.949347	−	0.314229i	$-0.898254\pi$
$83$		−	4329.44i		−	0.628458i	0.949347	−	0.314229i	$-0.101746\pi$
$84$	−3407.97			−0.482988
$85$	−8512.64			−1.17822
$86$	4621.06			0.624805
$87$	−823.895			−0.108851
$88$	3779.58			0.488066
$89$		−	15005.6i		−	1.89440i	−0.320642	−	0.947201i	$-0.603899\pi$
$89$		−	15005.6i		−	1.89440i	0.320642	−	0.947201i	$-0.396101\pi$
$90$			1625.15i			0.200636i
$91$		−	1373.39i		−	0.165848i
$92$		−	2716.58i		−	0.320957i
$93$			5430.82i			0.627913i
$94$	−2779.29			−0.314541
$95$	10115.1			1.12079
$96$		−	940.604i		−	0.102062i
$97$		−	4372.22i		−	0.464685i	−0.972634	−	0.232342i	$-0.925361\pi$
$97$		−	4372.22i		−	0.464685i	0.972634	−	0.232342i	$-0.0746390\pi$
$98$			12219.4i			1.27232i
$99$			4509.96i			0.460153i
$100$	1377.08			0.137708
$101$			12784.8i			1.25329i	0.779304	+	0.626646i	$0.215573\pi$
$101$			12784.8i			1.25329i	−0.779304	+	0.626646i	$0.784427\pi$
$102$			5879.05i			0.565076i
$103$			18166.7i			1.71239i	0.516656	+	0.856193i	$0.327176\pi$
$103$			18166.7i			1.71239i	−0.516656	+	0.856193i	$0.672824\pi$
$104$	379.058			0.0350460
$105$	9065.46			0.822264
$106$		−	4190.79i		−	0.372978i
$107$	5406.76			0.472248			0.236124	−	0.971723i	$-0.424123\pi$
$107$	5406.76			0.472248			0.236124	+	0.971723i	$0.424123\pi$
$108$	1122.37			0.0962250
$109$		−	18214.4i		−	1.53307i	−0.642204	−	0.766534i	$-0.721980\pi$
$109$		−	18214.4i		−	1.53307i	0.642204	−	0.766534i	$-0.278020\pi$
$110$	−10054.0			−0.830908
$111$			10462.1i			0.849125i
$112$	−5246.91			−0.418280
$113$			4742.14i			0.371379i	0.982608	+	0.185690i	$0.0594519\pi$
$113$			4742.14i			0.371379i	−0.982608	+	0.185690i	$0.940548\pi$
$114$		−	6985.75i		−	0.537531i
$115$			7226.32i			0.546413i
$116$	−1268.47			−0.0942679
$117$			452.308i			0.0330417i
$118$	6844.71	+	7077.35i	0.491576	+	0.508284i
$119$	32794.7			2.31585
$120$			2502.08i			0.173756i
$121$	−13259.9			−0.905667
$122$	9117.46			0.612568
$123$	6373.20			0.421257
$124$			8361.30i			0.543789i
$125$	−16963.5			−1.08567
$126$		−	6260.83i		−	0.394358i
$127$	−14055.7			−0.871452			−0.435726	−	0.900079i	$-0.643508\pi$
$127$	−14055.7			−0.871452			−0.435726	+	0.900079i	$0.643508\pi$
$128$		−	1448.15i		−	0.0883883i
$129$			8489.43i			0.510151i
$130$	−1008.32			−0.0596641
$131$		−	5797.33i		−	0.337820i	−0.985631	−	0.168910i	$-0.945975\pi$
$131$		−	5797.33i		−	0.337820i	0.985631	−	0.168910i	$-0.0540248\pi$
$132$			6943.54i			0.398504i
$133$	−38968.2			−2.20296
$134$	−7376.58			−0.410814
$135$	−2985.59			−0.163818
$136$			9051.39i			0.489370i
$137$	−5360.01			−0.285578			−0.142789	−	0.989753i	$-0.545607\pi$
$137$	−5360.01			−0.285578			−0.142789	+	0.989753i	$0.545607\pi$
$138$	4990.68			0.262060
$139$	−23632.3			−1.22314			−0.611570	−	0.791190i	$-0.709462\pi$
$139$	−23632.3			−1.22314			−0.611570	+	0.791190i	$0.709462\pi$
$140$	13957.2			0.712101
$141$		−	5105.88i		−	0.256822i
$142$			13577.9i			0.673374i
$143$	−2798.20			−0.136838
$144$	1728.00			0.0833333
$145$	3374.23			0.160486
$146$	15571.2			0.730496
$147$	−22448.4			−1.03885
$148$			16107.4i			0.735364i
$149$		−	24452.4i		−	1.10141i	−0.834699	−	0.550706i	$-0.814359\pi$
$149$		−	24452.4i		−	1.10141i	0.834699	−	0.550706i	$-0.185641\pi$
$150$			2529.86i			0.112438i
$151$		−	39834.9i		−	1.74707i	−0.486763	−	0.873534i	$-0.661822\pi$
$151$		−	39834.9i		−	1.74707i	0.486763	−	0.873534i	$-0.338178\pi$
$152$		−	10755.3i		−	0.465516i
$153$	−10800.5			−0.461383
$154$	38732.7			1.63319
$155$		−	22241.7i		−	0.925773i
$156$			696.374i			0.0286150i
$157$			23234.3i			0.942605i	0.881972	+	0.471303i	$0.156216\pi$
$157$			23234.3i			0.942605i	−0.881972	+	0.471303i	$0.843784\pi$
$158$			34533.3i			1.38332i
$159$	7698.96			0.304536
$160$			3852.20i			0.150477i
$161$		−	27839.2i		−	1.07400i
$162$			2061.92i			0.0785674i
$163$	−26110.0			−0.982723			−0.491361	−	0.870956i	$-0.663501\pi$
$163$	−26110.0			−0.982723			−0.491361	+	0.870956i	$0.663501\pi$
$164$	9812.19			0.364820
$165$		−	18470.3i		−	0.678433i
$166$	12245.5			0.444387
$167$	14299.5			0.512729			0.256365	−	0.966580i	$-0.417475\pi$
$167$	14299.5			0.512729			0.256365	+	0.966580i	$0.417475\pi$
$168$		−	9639.19i		−	0.341524i
$169$	28280.4			0.990174
$170$		−	24077.4i		−	0.833128i
$171$	12833.6			0.438892
$172$			13070.3i			0.441804i
$173$			4687.85i			0.156632i	0.996929	+	0.0783161i	$0.0249543\pi$
$173$			4687.85i			0.156632i	−0.996929	+	0.0783161i	$0.975046\pi$
$174$		−	2330.33i		−	0.0769694i
$175$	14112.1			0.460805
$176$			10690.3i			0.345115i
$177$	−13001.9	+	12574.5i	−0.415012	+	0.401370i
$178$	42442.1			1.33954
$179$			24812.3i			0.774391i	0.921998	+	0.387195i	$0.126556\pi$
$179$			24812.3i			0.774391i	−0.921998	+	0.387195i	$0.873444\pi$
$180$	−4596.61			−0.141871
$181$	−47654.7			−1.45462			−0.727308	−	0.686311i	$-0.759229\pi$
$181$	−47654.7			−1.45462			−0.727308	+	0.686311i	$0.759229\pi$
$182$	3884.53			0.117272
$183$			16749.8i			0.500160i
$184$	7683.65			0.226951
$185$		−	42847.0i		−	1.25192i
$186$	−15360.7			−0.444002
$187$		−	66817.3i		−	1.91076i
$188$		−	7861.01i		−	0.222414i
$189$	11501.9			0.321992
$190$			28609.9i			0.792517i
$191$			34175.8i			0.936810i	0.883514	+	0.468405i	$0.155171\pi$
$191$			34175.8i			0.936810i	−0.883514	+	0.468405i	$0.844829\pi$
$192$	2660.43			0.0721688
$193$	42645.4			1.14487			0.572437	−	0.819949i	$-0.305998\pi$
$193$	42645.4			1.14487			0.572437	+	0.819949i	$0.305998\pi$
$194$	12366.5			0.328582
$195$		−	1852.41i		−	0.0487155i
$196$	−34561.6			−0.899667
$197$	−68831.8			−1.77360			−0.886802	−	0.462149i	$-0.847079\pi$
$197$	−68831.8			−1.77360			−0.886802	+	0.462149i	$0.847079\pi$
$198$	−12756.1			−0.325377
$199$	−72298.8			−1.82568			−0.912840	−	0.408316i	$-0.866116\pi$
$199$	−72298.8			−1.82568			−0.912840	+	0.408316i	$0.866116\pi$
$200$			3894.97i			0.0973744i
$201$		−	13551.6i		−	0.335428i
$202$	−36161.0			−0.886211
$203$	−12999.1			−0.315443
$204$	−16628.5			−0.399569
$205$	−26101.2			−0.621087
$206$	−51383.2			−1.21084
$207$			9168.46i			0.213971i
$208$			1072.14i			0.0247813i
$209$			79395.4i			1.81762i
$210$			25641.0i			0.581428i
$211$		−	8866.11i		−	0.199144i	−0.995030	−	0.0995722i	$-0.968253\pi$
$211$		−	8866.11i		−	0.199144i	0.995030	−	0.0995722i	$-0.0317474\pi$
$212$	11853.3			0.263736
$213$	−24944.2			−0.549808
$214$			15292.6i			0.333930i
$215$		−	34768.1i		−	0.752149i
$216$			3174.54i			0.0680414i
$217$			85685.5i			1.81965i
$218$	51518.0			1.08404
$219$			28606.2i			0.596447i
$220$		−	28437.0i		−	0.587540i
$221$		−	6701.17i		−	0.137204i
$222$	−29591.2			−0.600422
$223$	−61252.9			−1.23173			−0.615867	−	0.787850i	$-0.711194\pi$
$223$	−61252.9			−1.23173			−0.615867	+	0.787850i	$0.711194\pi$
$224$		−	14840.5i		−	0.295769i
$225$	−4647.65			−0.0918054
$226$	−13412.8			−0.262605
$227$		−	39332.5i		−	0.763308i	−0.924305	−	0.381654i	$-0.875355\pi$
$227$		−	39332.5i		−	0.763308i	0.924305	−	0.381654i	$-0.124645\pi$
$228$	19758.7			0.380092
$229$		−	89783.3i		−	1.71208i	−0.516908	−	0.856041i	$-0.672917\pi$
$229$		−	89783.3i		−	1.71208i	0.516908	−	0.856041i	$-0.327083\pi$
$230$	−20439.1			−0.386373
$231$			71156.4i			1.33349i
$232$		−	3587.77i		−	0.0666575i
$233$			35773.3i			0.658942i	0.944166	+	0.329471i	$0.106870\pi$
$233$			35773.3i			0.658942i	−0.944166	+	0.329471i	$0.893130\pi$
$234$	−1279.32			−0.0233640
$235$			20910.9i			0.378649i
$236$	−20017.8	+	19359.8i	−0.359411	+	0.347597i
$237$	−63441.8			−1.12948
$238$			92757.4i			1.63755i
$239$	−22082.8			−0.386597			−0.193299	−	0.981140i	$-0.561919\pi$
$239$	−22082.8			−0.386597			−0.193299	+	0.981140i	$0.561919\pi$
$240$	−7076.95			−0.122864
$241$	16649.8			0.286665			0.143332	−	0.989675i	$-0.454218\pi$
$241$	16649.8			0.286665			0.143332	+	0.989675i	$0.454218\pi$
$242$		−	37504.6i		−	0.640403i
$243$	−3788.00			−0.0641500
$244$			25788.1i			0.433151i
$245$	91936.6			1.53164
$246$			18026.1i			0.297874i
$247$			7962.64i			0.130516i
$248$	−23649.3			−0.384517
$249$			22496.5i			0.362840i
$250$		−	47980.1i		−	0.767682i
$251$	53391.6			0.847472			0.423736	−	0.905786i	$-0.360718\pi$
$251$	53391.6			0.847472			0.423736	+	0.905786i	$0.360718\pi$
$252$	17708.3			0.278854
$253$	−56720.7			−0.886136
$254$		−	39755.4i		−	0.616210i
$255$	44233.0			0.680246
$256$	4096.00			0.0625000
$257$	63598.2			0.962895			0.481447	−	0.876475i	$-0.340111\pi$
$257$	63598.2			0.962895			0.481447	+	0.876475i	$0.340111\pi$
$258$	−24011.7			−0.360731
$259$			165067.i			2.46071i
$260$		−	2851.97i		−	0.0421889i
$261$	4281.08			0.0628453
$262$	16397.3			0.238875
$263$	87845.5			1.27001			0.635006	−	0.772507i	$-0.280997\pi$
$263$	87845.5			1.27001			0.635006	+	0.772507i	$0.280997\pi$
$264$	−19639.3			−0.281785
$265$	−31530.8			−0.448996
$266$		−	110219.i		−	1.55773i
$267$			77971.1i			1.09373i
$268$		−	20864.1i		−	0.290490i
$269$			20651.3i			0.285392i	0.989767	+	0.142696i	$0.0455772\pi$
$269$			20651.3i			0.285392i	−0.989767	+	0.142696i	$0.954423\pi$
$270$		−	8444.52i		−	0.115837i
$271$	−62656.5			−0.853154			−0.426577	−	0.904451i	$-0.640281\pi$
$271$	−62656.5			−0.853154			−0.426577	+	0.904451i	$0.640281\pi$
$272$	−25601.2			−0.346037
$273$			7136.34i			0.0957526i
$274$		−	15160.4i		−	0.201934i
$275$		−	28752.7i		−	0.380201i
$276$			14115.8i			0.185305i
$277$	58797.1			0.766295			0.383148	−	0.923687i	$-0.374840\pi$
$277$	58797.1			0.766295			0.383148	+	0.923687i	$0.374840\pi$
$278$		−	66842.2i		−	0.864891i
$279$		−	28219.4i		−	0.362526i
$280$			39476.9i			0.503532i
$281$	8921.95			0.112992			0.0564959	−	0.998403i	$-0.482007\pi$
$281$	8921.95			0.112992			0.0564959	+	0.998403i	$0.482007\pi$
$282$	14441.6			0.181600
$283$		−	9099.73i		−	0.113620i	−0.998385	−	0.0568101i	$-0.981907\pi$
$283$		−	9099.73i		−	0.113620i	0.998385	−	0.0568101i	$-0.0180930\pi$
$284$	−38404.2			−0.476147
$285$	−52559.7			−0.647087
$286$		−	7914.52i		−	0.0967592i
$287$	100554.			1.22077
$288$			4887.52i			0.0589256i
$289$	76493.9			0.915864
$290$			9543.75i			0.113481i
$291$			22718.7i			0.268286i
$292$			44042.1i			0.516539i
$293$	50490.9			0.588136			0.294068	−	0.955784i	$-0.404991\pi$
$293$	50490.9			0.588136			0.294068	+	0.955784i	$0.404991\pi$
$294$		−	63493.7i		−	0.734575i
$295$	53248.8	−	51498.5i	0.611879	−	0.591766i
$296$	−45558.6			−0.519981
$297$		−	23434.4i		−	0.265669i
$298$	69162.0			0.778816
$299$	−5688.57			−0.0636298
$300$	−7155.53			−0.0795058
$301$			133943.i			1.47838i
$302$	112670.			1.23536
$303$		−	66431.9i		−	0.723588i
$304$	30420.5			0.329169
$305$		−	68598.3i		−	0.737418i
$306$		−	30548.4i		−	0.326247i
$307$	93671.2			0.993869			0.496935	−	0.867788i	$-0.334459\pi$
$307$	93671.2			0.993869			0.496935	+	0.867788i	$0.334459\pi$
$308$			109553.i			1.15484i
$309$		−	94396.9i		−	0.988646i
$310$	62909.0			0.654621
$311$	−95271.5			−0.985013			−0.492507	−	0.870309i	$-0.663919\pi$
$311$	−95271.5			−0.985013			−0.492507	+	0.870309i	$0.663919\pi$
$312$	−1969.64			−0.0202338
$313$		−	82270.6i		−	0.839761i	−0.907579	−	0.419881i	$-0.862072\pi$
$313$		−	82270.6i		−	0.839761i	0.907579	−	0.419881i	$-0.137928\pi$
$314$	−65716.5			−0.666523
$315$	−47105.5			−0.474734
$316$	−97675.0			−0.978158
$317$	−31959.0			−0.318034			−0.159017	−	0.987276i	$-0.550833\pi$
$317$	−31959.0			−0.318034			−0.159017	+	0.987276i	$0.550833\pi$
$318$			21776.0i			0.215339i
$319$			26484.9i			0.260266i
$320$	−10895.7			−0.106403
$321$	−28094.4			−0.272652
$322$	78741.0			0.759433
$323$	−190137.			−1.82247
$324$	−5832.00			−0.0555556
$325$		−	2883.63i		−	0.0273007i
$326$		−	73850.1i		−	0.694890i
$327$			94644.7i			0.885117i
$328$			27753.1i			0.257966i
$329$		−	80558.6i		−	0.744252i
$330$	52242.0			0.479725
$331$	82912.6			0.756771			0.378385	−	0.925648i	$-0.376479\pi$
$331$	82912.6			0.756771			0.378385	+	0.925648i	$0.376479\pi$
$332$			34635.6i			0.314229i
$333$		−	54362.5i		−	0.490243i
$334$			40445.1i			0.362554i
$335$			55500.2i			0.494544i
$336$	27263.7			0.241494
$337$		−	28035.3i		−	0.246857i	−0.992353	−	0.123428i	$-0.960611\pi$
$337$		−	28035.3i		−	0.246857i	0.992353	−	0.123428i	$-0.0393889\pi$
$338$			79989.0i			0.700159i
$339$		−	24640.9i		−	0.214416i
$340$	68101.2			0.589110
$341$	174579.			1.50136
$342$			36299.0i			0.310344i
$343$	−157342.			−1.33738
$344$	−36968.5			−0.312403
$345$		−	37549.0i		−	0.315472i
$346$	−13259.2			−0.110756
$347$		−	30014.0i		−	0.249267i	−0.992203	−	0.124634i	$-0.960224\pi$
$347$		−	30014.0i		−	0.249267i	0.992203	−	0.124634i	$-0.0397756\pi$
$348$	6591.16			0.0544256
$349$			241740.i			1.98471i	0.123406	+	0.992356i	$0.460618\pi$
$349$			241740.i			1.98471i	−0.123406	+	0.992356i	$0.539382\pi$
$350$			39915.2i			0.325838i
$351$		−	2350.26i		−	0.0190766i
$352$	−30236.7			−0.244033
$353$		−	139673.i		−	1.12089i	−0.828191	−	0.560446i	$-0.810630\pi$
$353$		−	139673.i		−	1.12089i	0.828191	−	0.560446i	$-0.189370\pi$
$354$	−35566.1	−	36775.0i	−0.283812	−	0.293458i
$355$	102158.			0.810617
$356$			120044.i			0.947201i
$357$	−170406.			−1.33705
$358$	−70179.7			−0.547577
$359$	71107.8			0.551732			0.275866	−	0.961196i	$-0.411035\pi$
$359$	71107.8			0.551732			0.275866	+	0.961196i	$0.411035\pi$
$360$		−	13001.2i		−	0.100318i
$361$	95608.4			0.733638
$362$		−	134788.i		−	1.02857i
$363$	68900.3			0.522887
$364$			10987.1i			0.0829242i
$365$		−	117156.i		−	0.879381i
$366$	−47375.7			−0.353666
$367$		−	24687.9i		−	0.183295i	−0.995791	−	0.0916477i	$-0.970787\pi$
$367$		−	24687.9i		−	0.183295i	0.995791	−	0.0916477i	$-0.0292134\pi$
$368$			21732.6i			0.160479i
$369$	−33116.1			−0.243213
$370$	121190.			0.885241
$371$	121471.			0.882523
$372$		−	43446.6i		−	0.313957i
$373$	−48445.2			−0.348203			−0.174102	−	0.984728i	$-0.555702\pi$
$373$	−48445.2			−0.348203			−0.174102	+	0.984728i	$0.555702\pi$
$374$	188988.			1.35111
$375$	88145.1			0.626810
$376$	22234.3			0.157271
$377$			2656.20i			0.0186886i
$378$			32532.3i			0.227683i
$379$	−13161.9			−0.0916306			−0.0458153	−	0.998950i	$-0.514589\pi$
$379$	−13161.9			−0.0916306			−0.0458153	+	0.998950i	$0.514589\pi$
$380$	−80920.9			−0.560394
$381$	73035.3			0.503133
$382$	−96663.6			−0.662425
$383$	−252365.			−1.72041			−0.860206	−	0.509947i	$-0.829665\pi$
$383$	−252365.			−1.72041			−0.860206	+	0.509947i	$0.829665\pi$
$384$			7524.83i			0.0510310i
$385$		−	291418.i		−	1.96605i
$386$			120619.i			0.809548i
$387$		−	44112.4i		−	0.294536i
$388$			34977.7i			0.232342i
$389$	15401.2			0.101779			0.0508893	−	0.998704i	$-0.483794\pi$
$389$	15401.2			0.101779			0.0508893	+	0.998704i	$0.483794\pi$
$390$	5239.40			0.0344471
$391$		−	135835.i		−	0.888504i
$392$		−	97755.0i		−	0.636161i
$393$			30123.8i			0.195041i
$394$		−	194686.i		−	1.25413i
$395$	259823.			1.66527
$396$		−	36079.7i		−	0.230076i
$397$			103315.i			0.655514i	0.944762	+	0.327757i	$0.106293\pi$
$397$			103315.i			0.655514i	−0.944762	+	0.327757i	$0.893707\pi$
$398$		−	204492.i		−	1.29095i
$399$	202484.			1.27188
$400$	−11016.7			−0.0688541
$401$			16885.5i			0.105009i	0.998621	+	0.0525043i	$0.0167203\pi$
$401$			16885.5i			0.105009i	−0.998621	+	0.0525043i	$0.983280\pi$
$402$	38329.8			0.237184
$403$	17508.7			0.107806
$404$		−	102279.i		−	0.626646i
$405$	15513.6			0.0945805
$406$		−	36767.0i		−	0.223052i
$407$	336314.			2.03028
$408$		−	47032.4i		−	0.282538i
$409$			246666.i			1.47456i	0.675587	+	0.737280i	$0.263890\pi$
$409$			246666.i			1.47456i	−0.675587	+	0.737280i	$0.736110\pi$
$410$		−	73825.3i		−	0.439175i
$411$	27851.4			0.164878
$412$		−	145334.i		−	0.856193i
$413$	−205139.	+	198396.i	−1.20268	+	1.16314i
$414$	−25932.3			−0.151301
$415$		−	92133.3i		−	0.534959i
$416$	−3032.46			−0.0175230
$417$	122797.			0.706180
$418$	−224564.			−1.28525
$419$		−	250583.i		−	1.42733i	−0.700489	−	0.713663i	$-0.747035\pi$
$419$		−	250583.i		−	1.42733i	0.700489	−	0.713663i	$-0.252965\pi$
$420$	−72523.6			−0.411132
$421$		−	271576.i		−	1.53224i	−0.642697	−	0.766120i	$-0.722185\pi$
$421$		−	271576.i		−	1.53224i	0.642697	−	0.766120i	$-0.277815\pi$
$422$	25077.1			0.140816
$423$			26530.9i			0.148276i
$424$			33526.3i			0.186489i
$425$	68857.3			0.381217
$426$		−	70552.9i		−	0.388773i
$427$			264273.i			1.44943i
$428$	−43254.1			−0.236124
$429$	14539.9			0.0790036
$430$	98339.0			0.531850
$431$			324034.i			1.74436i	0.489186	+	0.872180i	$0.337294\pi$
$431$			324034.i			1.74436i	−0.489186	+	0.872180i	$0.662706\pi$
$432$	−8978.95			−0.0481125
$433$	−316700.			−1.68917			−0.844583	−	0.535424i	$-0.820152\pi$
$433$	−316700.			−1.68917			−0.844583	+	0.535424i	$0.820152\pi$
$434$	−242355.			−1.28669
$435$	−17533.0			−0.0926568
$436$			145715.i			0.766534i
$437$			161406.i			0.845194i
$438$	−80910.6			−0.421752
$439$	171136.			0.887997			0.443998	−	0.896028i	$-0.353560\pi$
$439$	171136.			0.887997			0.443998	+	0.896028i	$0.353560\pi$
$440$	80431.9			0.415454
$441$	116645.			0.599778
$442$	18953.8			0.0970177
$443$		−	112858.i		−	0.575077i	−0.957769	−	0.287539i	$-0.907163\pi$
$443$		−	112858.i		−	0.575077i	0.957769	−	0.287539i	$-0.0928369\pi$
$444$		−	83696.6i		−	0.424563i
$445$		−	319327.i		−	1.61256i
$446$		−	173249.i		−	0.870968i
$447$			127059.i			0.635901i
$448$	41975.3			0.209140
$449$	−287485.			−1.42601			−0.713004	−	0.701160i	$-0.752666\pi$
$449$	−287485.			−1.42601			−0.713004	+	0.701160i	$0.752666\pi$
$450$		−	13145.5i		−	0.0649162i
$451$		−	204873.i		−	1.00724i
$452$		−	37937.1i		−	0.185690i
$453$			206988.i			1.00867i
$454$	111249.			0.539740
$455$		−	29226.6i		−	0.141174i
$456$			55886.0i			0.268766i
$457$			7922.27i			0.0379330i	0.999820	+	0.0189665i	$0.00603759\pi$
$457$			7922.27i			0.0379330i	−0.999820	+	0.0189665i	$0.993962\pi$
$458$	253946.			1.21063
$459$	56121.1			0.266379
$460$		−	57810.5i		−	0.273207i
$461$	84230.1			0.396338			0.198169	−	0.980168i	$-0.436501\pi$
$461$	84230.1			0.396338			0.198169	+	0.980168i	$0.436501\pi$
$462$	−201261.			−0.942921
$463$		−	158383.i		−	0.738832i	−0.929264	−	0.369416i	$-0.879558\pi$
$463$		−	158383.i		−	0.738832i	0.929264	−	0.369416i	$-0.120442\pi$
$464$	10147.8			0.0471340
$465$			115571.i			0.534495i
$466$	−101182.			−0.465942
$467$			79110.3i			0.362743i	0.983415	+	0.181372i	$0.0580537\pi$
$467$			79110.3i			0.362743i	−0.983415	+	0.181372i	$0.941946\pi$
$468$		−	3618.46i		−	0.0165209i
$469$		−	213813.i		−	0.972048i
$470$	−59144.9			−0.267745
$471$		−	120729.i		−	0.544213i
$472$	−54757.7	−	56618.8i	−0.245788	−	0.254142i
$473$	272901.			1.21978
$474$		−	179440.i		−	0.798663i
$475$	−81819.4			−0.362634
$476$	−262358.			−1.15792
$477$	−40005.0			−0.175824
$478$		−	62459.7i		−	0.273366i
$479$	87520.5			0.381451			0.190726	−	0.981643i	$-0.438916\pi$
$479$	87520.5			0.381451			0.190726	+	0.981643i	$0.438916\pi$
$480$		−	20016.6i		−	0.0868778i
$481$	33729.2			0.145786
$482$			47092.7i			0.202703i
$483$			144657.i			0.620074i
$484$	106079.			0.452833
$485$		−	93043.5i		−	0.395551i
$486$		−	10714.1i		−	0.0453609i
$487$	120894.			0.509737			0.254869	−	0.966976i	$-0.417968\pi$
$487$	120894.			0.509737			0.254869	+	0.966976i	$0.417968\pi$
$488$	−72939.7			−0.306284
$489$	135671.			0.567375
$490$			260036.i			1.08303i
$491$	−76565.2			−0.317591			−0.158796	−	0.987311i	$-0.550761\pi$
$491$	−76565.2			−0.317591			−0.158796	+	0.987311i	$0.550761\pi$
$492$	−50985.6			−0.210629
$493$	−63426.4			−0.260961
$494$	−22521.7			−0.0922886
$495$			95974.7i			0.391694i
$496$		−	66890.4i		−	0.271894i
$497$	−393561.			−1.59330
$498$	−63629.6			−0.256567
$499$	36622.8			0.147079			0.0735396	−	0.997292i	$-0.476570\pi$
$499$	36622.8			0.147079			0.0735396	+	0.997292i	$0.476570\pi$
$500$	135708.			0.542833
$501$	−74302.4			−0.296024
$502$			151014.i			0.599253i
$503$		−	143892.i		−	0.568722i	−0.958717	−	0.284361i	$-0.908219\pi$
$503$		−	143892.i		−	0.568722i	0.958717	−	0.284361i	$-0.0917814\pi$
$504$			50086.7i			0.197179i
$505$			272069.i			1.06683i
$506$		−	160430.i		−	0.626593i
$507$	−146949.			−0.571677
$508$	112445.			0.435726
$509$		−	392489.i		−	1.51493i	−0.652878	−	0.757463i	$-0.726439\pi$
$509$		−	392489.i		−	1.51493i	0.652878	−	0.757463i	$-0.273561\pi$
$510$			125110.i			0.481007i
$511$			451338.i			1.72846i
$512$			11585.2i			0.0441942i
$513$	−66685.6			−0.253395
$514$			179883.i			0.680869i
$515$			386599.i			1.45763i
$516$		−	67915.4i		−	0.255076i
$517$	−164133.			−0.614067
$518$	−466879.			−1.73998
$519$		−	24358.8i		−	0.0904317i
$520$	8066.59			0.0298320
$521$	293168.			1.08004			0.540021	−	0.841651i	$-0.318416\pi$
$521$	293168.			1.08004			0.540021	+	0.841651i	$0.318416\pi$
$522$			12108.7i			0.0444383i
$523$	94020.1			0.343730			0.171865	−	0.985121i	$-0.445021\pi$
$523$	94020.1			0.343730			0.171865	+	0.985121i	$0.445021\pi$
$524$			46378.7i			0.168910i
$525$	−73328.9			−0.266046
$526$			248465.i			0.898035i
$527$			418084.i			1.50537i
$528$		−	55548.3i		−	0.199252i
$529$	164531.			0.587946
$530$		−	89182.5i		−	0.317488i
$531$	67560.0	−	65339.2i	0.239607	−	0.231731i
$532$	311745.			1.10148
$533$		−	20546.9i		−	0.0723256i
$534$	−220536.			−0.773386
$535$	115059.			0.401989
$536$	59012.6			0.205407
$537$		−	128928.i		−	0.447095i
$538$	−58410.6			−0.201803
$539$			721627.i			2.48391i
$540$	23884.7			0.0819091
$541$		−	566394.i		−	1.93519i	−0.252501	−	0.967597i	$-0.581253\pi$
$541$		−	566394.i		−	1.93519i	0.252501	−	0.967597i	$-0.418747\pi$
$542$		−	177219.i		−	0.603271i
$543$	247621.			0.839823
$544$		−	72411.1i		−	0.244685i
$545$		−	387613.i		−	1.30499i
$546$	−20184.6			−0.0677073
$547$	−2933.56			−0.00980438			−0.00490219	−	0.999988i	$-0.501560\pi$
$547$	−2933.56			−0.00980438			−0.00490219	+	0.999988i	$0.501560\pi$
$548$	42880.1			0.142789
$549$		−	87034.8i		−	0.288767i
$550$	81324.9			0.268843
$551$	75366.1			0.248241
$552$	−39925.4			−0.131030
$553$	−1.00096e6			−3.27315
$554$			166303.i			0.541852i
$555$			222639.i			0.722796i
$556$	189058.			0.611570
$557$	14238.3			0.0458932			0.0229466	−	0.999737i	$-0.492695\pi$
$557$	14238.3			0.0458932			0.0229466	+	0.999737i	$0.492695\pi$
$558$	79816.5			0.256345
$559$	27369.5			0.0875878
$560$	−111657.			−0.356051
$561$			347193.i			1.10318i
$562$			25235.1i			0.0798973i
$563$			465445.i			1.46842i	0.678920	+	0.734212i	$0.262448\pi$
$563$			465445.i			1.46842i	−0.678920	+	0.734212i	$0.737552\pi$
$564$			40847.0i			0.128411i
$565$			100916.i			0.316127i
$566$	25737.9			0.0803417
$567$	−59765.6			−0.185902
$568$		−	108623.i		−	0.336687i
$569$			625304.i			1.93138i	0.259704	+	0.965688i	$0.416375\pi$
$569$			625304.i			1.93138i	−0.259704	+	0.965688i	$0.583625\pi$
$570$		−	148661.i		−	0.457560i
$571$		−	93202.8i		−	0.285862i	−0.989733	−	0.142931i	$-0.954347\pi$
$571$		−	93202.8i		−	0.285862i	0.989733	−	0.142931i	$-0.0456527\pi$
$572$	22385.6			0.0684191
$573$		−	177582.i		−	0.540867i
$574$			284410.i			0.863218i
$575$		−	58452.4i		−	0.176794i
$576$	−13824.0			−0.0416667
$577$	−198746.			−0.596962			−0.298481	−	0.954416i	$-0.596480\pi$
$577$	−198746.			−0.596962			−0.298481	+	0.954416i	$0.596480\pi$
$578$			216357.i			0.647614i
$579$	−221592.			−0.660993
$580$	−26993.8			−0.0802432
$581$			354941.i			1.05149i
$582$	−64258.2			−0.189707
$583$		−	247491.i		−	0.728152i
$584$	−124570.			−0.365248
$585$			9625.39i			0.0281259i
$586$			142810.i			0.415875i
$587$		−	505766.i		−	1.46782i	−0.679246	−	0.733911i	$-0.737693\pi$
$587$		−	505766.i		−	1.46782i	0.679246	−	0.733911i	$-0.262307\pi$
$588$	179587.			0.519423
$589$		−	496787.i		−	1.43199i
$590$	145660.	+	150610.i	0.418442	+	0.432664i
$591$	357661.			1.02399
$592$		−	128859.i		−	0.367682i
$593$	−332924.			−0.946751			−0.473375	−	0.880861i	$-0.656965\pi$
$593$	−332924.			−0.946751			−0.473375	+	0.880861i	$0.656965\pi$
$594$	66282.6			0.187857
$595$	697892.			1.97131
$596$			195620.i			0.550706i
$597$	375676.			1.05406
$598$		−	16089.7i		−	0.0449931i
$599$	−465357.			−1.29698			−0.648488	−	0.761225i	$-0.724598\pi$
$599$	−465357.			−1.29698			−0.648488	+	0.761225i	$0.724598\pi$
$600$		−	20238.9i		−	0.0562191i
$601$			124281.i			0.344078i	0.985090	+	0.172039i	$0.0550355\pi$
$601$			124281.i			0.344078i	−0.985090	+	0.172039i	$0.944964\pi$
$602$	−378848.			−1.04537
$603$			70416.4i			0.193660i
$604$			318679.i			0.873534i
$605$	−282178.			−0.770926
$606$	187898.			0.511654
$607$	−248772.			−0.675187			−0.337593	−	0.941292i	$-0.609613\pi$
$607$	−248772.			−0.675187			−0.337593	+	0.941292i	$0.609613\pi$
$608$			86042.2i			0.232758i
$609$	67545.3			0.182121
$610$	194025.			0.521433
$611$	−16461.1			−0.0440937
$612$	86404.0			0.230691
$613$		−	100500.i		−	0.267451i	−0.991018	−	0.133725i	$-0.957306\pi$
$613$		−	100500.i		−	0.267451i	0.991018	−	0.133725i	$-0.0426940\pi$
$614$			264942.i			0.702772i
$615$	135626.			0.358585
$616$	−309861.			−0.816593
$617$	459590.			1.20726			0.603629	−	0.797265i	$-0.293721\pi$
$617$	459590.			1.20726			0.603629	+	0.797265i	$0.293721\pi$
$618$	266995.			0.699079
$619$	−626666.			−1.63552			−0.817758	−	0.575563i	$-0.804783\pi$
$619$	−626666.			−1.63552			−0.817758	+	0.575563i	$0.804783\pi$
$620$			177934.i			0.462887i
$621$		−	47640.7i		−	0.123536i
$622$		−	269468.i		−	0.696510i
$623$			1.23020e6i			3.16956i
$624$		−	5570.99i		−	0.0143075i
$625$	−253410.			−0.648730
$626$	232696.			0.593801
$627$		−	412550.i		−	1.04940i
$628$		−	185874.i		−	0.471303i
$629$			805408.i			2.03570i
$630$		−	133234.i		−	0.335688i
$631$	−41503.3			−0.104237			−0.0521187	−	0.998641i	$-0.516597\pi$
$631$	−41503.3			−0.104237			−0.0521187	+	0.998641i	$0.516597\pi$
$632$		−	276267.i		−	0.691662i
$633$			46069.6i			0.114976i
$634$		−	90393.6i		−	0.224884i
$635$	−299113.			−0.741802
$636$	−61591.7			−0.152268
$637$			72372.7i			0.178359i
$638$	−74910.7			−0.184036
$639$	129614.			0.317432
$640$		−	30817.6i		−	0.0752384i
$641$	−201212.			−0.489709			−0.244855	−	0.969560i	$-0.578740\pi$
$641$	−201212.			−0.489709			−0.244855	+	0.969560i	$0.578740\pi$
$642$		−	79462.9i		−	0.192794i
$643$	−285557.			−0.690670			−0.345335	−	0.938479i	$-0.612235\pi$
$643$	−285557.			−0.690670			−0.345335	+	0.938479i	$0.612235\pi$
$644$			222713.i			0.537000i
$645$			180660.i			0.434253i
$646$		−	537789.i		−	1.28868i
$647$	−665151.			−1.58896			−0.794478	−	0.607293i	$-0.792255\pi$
$647$	−665151.			−1.58896			−0.794478	+	0.607293i	$0.792255\pi$
$648$		−	16495.4i		−	0.0392837i
$649$	404221.	+	417960.i	0.959686	+	0.992305i
$650$	8156.15			0.0193045
$651$		−	445235.i		−	1.05058i
$652$	208880.			0.491361
$653$	389637.			0.913763			0.456881	−	0.889528i	$-0.348966\pi$
$653$	389637.			0.913763			0.456881	+	0.889528i	$0.348966\pi$
$654$	−267696.			−0.625872
$655$		−	123371.i		−	0.287561i
$656$	−78497.5			−0.182410
$657$		−	148642.i		−	0.344359i
$658$	227854.			0.526266
$659$		−	53636.8i		−	0.123507i	−0.998091	−	0.0617535i	$-0.980331\pi$
$659$		−	53636.8i		−	0.123507i	0.998091	−	0.0617535i	$-0.0196693\pi$
$660$			147763.i			0.339217i
$661$	111107.			0.254295			0.127148	−	0.991884i	$-0.459418\pi$
$661$	111107.			0.254295			0.127148	+	0.991884i	$0.459418\pi$
$662$			234512.i			0.535118i
$663$			34820.3i			0.0792147i
$664$	−97964.1			−0.222193
$665$	−829267.			−1.87521
$666$	153760.			0.346654
$667$			53842.2i			0.121024i
$668$	−114396.			−0.256365
$669$	318280.			0.711142
$670$	−156978.			−0.349695
$671$	538441.			1.19589
$672$			77113.5i			0.170762i
$673$		−	251708.i		−	0.555734i	−0.960620	−	0.277867i	$-0.910373\pi$
$673$		−	251708.i		−	0.555734i	0.960620	−	0.277867i	$-0.0896274\pi$
$674$	79295.7			0.174554
$675$	24149.9			0.0530039
$676$	−226243.			−0.495087
$677$	189199.			0.412802			0.206401	−	0.978467i	$-0.433825\pi$
$677$	189199.			0.412802			0.206401	+	0.978467i	$0.433825\pi$
$678$	69694.9			0.151615
$679$			358447.i			0.777474i
$680$			192619.i			0.416564i
$681$			204378.i			0.440696i
$682$			493785.i			1.06162i
$683$		−	866154.i		−	1.85675i	−0.371644	−	0.928375i	$-0.621206\pi$
$683$		−	866154.i		−	1.85675i	0.371644	−	0.928375i	$-0.378794\pi$
$684$	−102669.			−0.219446
$685$	−114064.			−0.243091
$686$		−	445030.i		−	0.945673i
$687$			466528.i			0.988471i
$688$		−	104563.i		−	0.220902i
$689$		−	24821.1i		−	0.0522856i
$690$	106205.			0.223072
$691$			111777.i			0.234098i	0.993126	+	0.117049i	$0.0373434\pi$
$691$			111777.i			0.234098i	−0.993126	+	0.117049i	$0.962657\pi$
$692$		−	37502.8i		−	0.0783161i
$693$		−	369740.i		−	0.769892i
$694$	84892.5			0.176259
$695$	−502910.			−1.04117
$696$			18642.6i			0.0384847i
$697$	490632.			1.00993
$698$	−683744.			−1.40340
$699$		−	185884.i		−	0.380440i
$700$	−112897.			−0.230402
$701$		−	97970.6i		−	0.199370i	−0.995019	−	0.0996850i	$-0.968216\pi$
$701$		−	97970.6i		−	0.199370i	0.995019	−	0.0996850i	$-0.0317835\pi$
$702$	6647.54			0.0134892
$703$		−	957023.i		−	1.93647i
$704$		−	85522.2i		−	0.172557i
$705$		−	108656.i		−	0.218613i
$706$	395056.			0.792591
$707$		−	1.04814e6i		−	2.09691i
$708$	104015.	−	100596.i	0.207506	−	0.200685i
$709$	−62691.5			−0.124714			−0.0623571	−	0.998054i	$-0.519862\pi$
$709$	−62691.5			−0.124714			−0.0623571	+	0.998054i	$0.519862\pi$
$710$			288947.i			0.573193i
$711$	329653.			0.652106
$712$	−339537.			−0.669772
$713$	354909.			0.698132
$714$		−	481982.i		−	0.945440i
$715$	−59547.5			−0.116480
$716$		−	198498.i		−	0.387195i
$717$	114746.			0.223202
$718$			201123.i			0.390134i
$719$			782462.i			1.51358i	0.653657	+	0.756791i	$0.273234\pi$
$719$			782462.i			1.51358i	−0.653657	+	0.756791i	$0.726766\pi$
$720$	36772.9			0.0709354
$721$		−	1.48936e6i		−	2.86503i
$722$			270421.i			0.518760i
$723$	−86514.8			−0.165506
$724$	381238.			0.727308
$725$	−27293.5			−0.0519258
$726$			194879.i			0.369737i
$727$	87872.1			0.166258			0.0831290	−	0.996539i	$-0.473509\pi$
$727$	87872.1			0.166258			0.0831290	+	0.996539i	$0.473509\pi$
$728$	−31076.3			−0.0586362
$729$	19683.0			0.0370370
$730$	331366.			0.621816
$731$			653547.i			1.22304i
$732$		−	133999.i		−	0.250080i
$733$	443363.			0.825185			0.412592	−	0.910916i	$-0.364623\pi$
$733$	443363.			0.825185			0.412592	+	0.910916i	$0.364623\pi$
$734$	69827.9			0.129609
$735$	−477716.			−0.884292
$736$	−61469.2			−0.113475
$737$	−435631.			−0.802018
$738$		−	93666.6i		−	0.171978i
$739$		−	38536.6i		−	0.0705642i	−0.999377	−	0.0352821i	$-0.988767\pi$
$739$		−	38536.6i		−	0.0705642i	0.999377	−	0.0352821i	$-0.0112330\pi$
$740$			342776.i			0.625960i
$741$		−	41375.1i		−	0.0753533i
$742$			343573.i			0.624038i
$743$	1.00787e6			1.82570			0.912849	−	0.408298i	$-0.133878\pi$
$743$	1.00787e6			1.82570			0.912849	+	0.408298i	$0.133878\pi$
$744$	122886.			0.222001
$745$		−	520363.i		−	0.937549i
$746$		−	137024.i		−	0.246217i
$747$		−	116895.i		−	0.209486i
$748$			534539.i			0.955379i
$749$	−443262.			−0.790128
$750$			249312.i			0.443221i
$751$		−	35298.8i		−	0.0625864i	−0.999510	−	0.0312932i	$-0.990037\pi$
$751$		−	35298.8i		−	0.0625864i	0.999510	−	0.0312932i	$-0.00996256\pi$
$752$			62888.1i			0.111207i
$753$	−277431.			−0.489288
$754$	−7512.86			−0.0132149
$755$		−	847712.i		−	1.48715i
$756$	−92015.1			−0.160996
$757$	−233857.			−0.408092			−0.204046	−	0.978961i	$-0.565409\pi$
$757$	−233857.			−0.408092			−0.204046	+	0.978961i	$0.565409\pi$
$758$		−	37227.5i		−	0.0647927i
$759$	294729.			0.511611
$760$		−	228879.i		−	0.396258i
$761$	−636217.			−1.09859			−0.549296	−	0.835628i	$-0.685104\pi$
$761$	−636217.			−1.09859			−0.549296	+	0.835628i	$0.685104\pi$
$762$			206575.i			0.355769i
$763$			1.49327e6i			2.56501i
$764$		−	273406.i		−	0.468405i
$765$	−229841.			−0.392740
$766$		−	713797.i		−	1.21651i
$767$	40539.7	+	41917.6i	0.0689112	+	0.0712534i
$768$	−21283.4			−0.0360844
$769$			1.11250e6i			1.88125i	0.339452	+	0.940623i	$0.389758\pi$
$769$			1.11250e6i			1.88125i	−0.339452	+	0.940623i	$0.610242\pi$
$770$	824255.			1.39021
$771$	−330466.			−0.555928
$772$	−341163.			−0.572437
$773$		−	712849.i		−	1.19300i	−0.802615	−	0.596498i	$-0.796558\pi$
$773$		−	712849.i		−	1.19300i	0.802615	−	0.596498i	$-0.203442\pi$
$774$	124769.			0.208268
$775$			179909.i			0.299537i
$776$	−98932.0			−0.164291
$777$		−	857711.i		−	1.42069i
$778$			43561.3i			0.0719683i
$779$	−582992.			−0.960699
$780$			14819.3i			0.0243578i
$781$			801857.i			1.31460i
$782$	384200.			0.628267
$783$	−22245.2			−0.0362837
$784$	276493.			0.449834
$785$			494440.i			0.802369i
$786$	−85203.0			−0.137915
$787$	−808306.			−1.30505			−0.652523	−	0.757769i	$-0.726290\pi$
$787$	−808306.			−1.30505			−0.652523	+	0.757769i	$0.726290\pi$
$788$	550655.			0.886802
$789$	−456459.			−0.733242
$790$			734890.i			1.17752i
$791$		−	388774.i		−	0.621362i
$792$	102049.			0.162689
$793$	54000.7			0.0858723
$794$	−292218.			−0.463518
$795$	163839.			0.259228
$796$	578390.			0.912840
$797$		−	102636.i		−	0.161578i	−0.996731	−	0.0807890i	$-0.974256\pi$
$797$		−	102636.i		−	0.161578i	0.996731	−	0.0807890i	$-0.0257440\pi$
$798$			572713.i			0.899355i
$799$		−	393069.i		−	0.615708i
$800$		−	31159.8i		−	0.0486872i
$801$		−	405150.i		−	0.631467i
$802$	−47759.3			−0.0742522
$803$	919575.			1.42612
$804$			108413.i			0.167714i
$805$		−	592435.i		−	0.914216i
$806$			49522.1i			0.0762306i
$807$		−	107307.i		−	0.164771i
$808$	289288.			0.443106
$809$		−	270769.i		−	0.413716i	−0.978371	−	0.206858i	$-0.933676\pi$
$809$		−	270769.i		−	0.413716i	0.978371	−	0.206858i	$-0.0663238\pi$
$810$			43879.0i			0.0668785i
$811$			644898.i			0.980504i	0.871581	+	0.490252i	$0.163095\pi$
$811$			644898.i			0.980504i	−0.871581	+	0.490252i	$0.836905\pi$
$812$	103993.			0.157722
$813$	325573.			0.492569
$814$			951239.i			1.43562i
$815$	−555636.			−0.836518
$816$	133028.			0.199784
$817$		−	776574.i		−	1.16343i
$818$	−697676.			−1.04267
$819$		−	37081.5i		−	0.0552828i
$820$	208809.			0.310544
$821$		−	874246.i		−	1.29702i	−0.761205	−	0.648511i	$-0.775392\pi$
$821$		−	874246.i		−	1.29702i	0.761205	−	0.648511i	$-0.224608\pi$
$822$			78775.8i			0.116587i
$823$		−	1.01745e6i		−	1.50215i	−0.660219	−	0.751073i	$-0.729537\pi$
$823$		−	1.01745e6i		−	1.50215i	0.660219	−	0.751073i	$-0.270463\pi$
$824$	411065.			0.605420
$825$			149403.i			0.219509i
$826$	−561149.	−	580222.i	−0.822467	−	0.850421i
$827$	−29940.3			−0.0437769			−0.0218884	−	0.999760i	$-0.506968\pi$
$827$	−29940.3			−0.0437769			−0.0218884	+	0.999760i	$0.506968\pi$
$828$		−	73347.7i		−	0.106986i
$829$	−768590.			−1.11837			−0.559185	−	0.829043i	$-0.688886\pi$
$829$	−768590.			−1.11837			−0.559185	+	0.829043i	$0.688886\pi$
$830$	260592.			0.378273
$831$	−305518.			−0.442421
$832$		−	8577.10i		−	0.0123906i
$833$	−1.72816e6			−2.49054
$834$			347322.i			0.499345i
$835$	304302.			0.436448
$836$		−	635163.i		−	0.908809i
$837$			146632.i			0.209304i
$838$	708755.			1.00927
$839$			1.04424e6i			1.48346i	0.670697	+	0.741732i	$0.265995\pi$
$839$			1.04424e6i			1.48346i	−0.670697	+	0.741732i	$0.734005\pi$
$840$		−	205128.i		−	0.290714i
$841$	−682140.			−0.964454
$842$	768133.			1.08346
$843$	−46359.8			−0.0652359
$844$			70928.8i			0.0995722i
$845$	601824.			0.842861
$846$	−75040.7			−0.104847
$847$	1.08708e6			1.51529
$848$	−94826.6			−0.131868
$849$			47283.6i			0.0655987i
$850$			194758.i			0.269561i
$851$	683705.			0.944081
$852$	199554.			0.274904
$853$	−611563.			−0.840510			−0.420255	−	0.907406i	$-0.638059\pi$
$853$	−611563.			−0.840510			−0.420255	+	0.907406i	$0.638059\pi$
$854$	−747476.			−1.02490
$855$	273108.			0.373596
$856$		−	122341.i		−	0.166965i
$857$		−	854600.i		−	1.16359i	−0.813334	−	0.581796i	$-0.802350\pi$
$857$		−	854600.i		−	1.16359i	0.813334	−	0.581796i	$-0.197650\pi$
$858$			41125.0i			0.0558640i
$859$		−	608743.i		−	0.824989i	−0.910960	−	0.412494i	$-0.864658\pi$
$859$		−	608743.i		−	0.824989i	0.910960	−	0.412494i	$-0.135342\pi$
$860$			278145.i			0.376075i
$861$	−522494.			−0.704815
$862$	−916506.			−1.23345
$863$		−	956261.i		−	1.28397i	−0.766717	−	0.641985i	$-0.778111\pi$
$863$		−	956261.i		−	1.28397i	0.766717	−	0.641985i	$-0.221889\pi$
$864$		−	25396.3i		−	0.0340207i
$865$			99760.3i			0.133329i
$866$		−	895763.i		−	1.19442i
$867$	−397474.			−0.528775
$868$		−	685484.i		−	0.909825i
$869$			2.03940e6i			2.70061i
$870$		−	49590.8i		−	0.0655183i
$871$	−43689.9			−0.0575896
$872$	−412144.			−0.542021
$873$		−	118050.i		−	0.154895i
$874$	−456524.			−0.597642
$875$	1.39072e6			1.81645
$876$		−	228850.i		−	0.298224i
$877$	374399.			0.486783			0.243391	−	0.969928i	$-0.421740\pi$
$877$	374399.			0.486783			0.243391	+	0.969928i	$0.421740\pi$
$878$			484045.i			0.627908i
$879$	−262358.			−0.339561
$880$			227496.i			0.293770i
$881$		−	1.25055e6i		−	1.61120i	−0.592460	−	0.805600i	$-0.701843\pi$
$881$		−	1.25055e6i		−	1.61120i	0.592460	−	0.805600i	$-0.298157\pi$
$882$			329923.i			0.424107i
$883$	−827453.			−1.06126			−0.530630	−	0.847604i	$-0.678045\pi$
$883$	−827453.			−1.06126			−0.530630	+	0.847604i	$0.678045\pi$
$884$			53609.4i			0.0686019i
$885$	−276689.	+	267594.i	−0.353269	+	0.341656i
$886$	319212.			0.406641
$887$			160264.i			0.203699i	0.994800	+	0.101849i	$0.0324760\pi$
$887$			160264.i			0.203699i	−0.994800	+	0.101849i	$0.967524\pi$
$888$	236730.			0.300211
$889$	1.15232e6			1.45805
$890$	903194.			1.14025
$891$			121769.i			0.153384i
$892$	490023.			0.615867
$893$			467062.i			0.585695i
$894$	−359376.			−0.449650
$895$			528020.i			0.659181i
$896$			118724.i			0.147884i
$897$	29558.7			0.0367367
$898$		−	813130.i		−	1.00834i
$899$		−	165720.i		−	0.205047i
$900$	37181.2			0.0459027
$901$	592694.			0.730098
$902$	579468.			0.712224
$903$		−	695988.i		−	0.853545i
$904$	107302.			0.131302
$905$	−1.01412e6			−1.23821
$906$	−585451.			−0.713238
$907$	751589.			0.913621			0.456810	−	0.889564i	$-0.348992\pi$
$907$	751589.			0.913621			0.456810	+	0.889564i	$0.348992\pi$
$908$			314660.i			0.381654i
$909$			345190.i			0.417764i
$910$	82665.3			0.0998253
$911$	1.06138e6			1.27889			0.639445	−	0.768837i	$-0.279164\pi$
$911$	1.06138e6			1.27889			0.639445	+	0.768837i	$0.279164\pi$
$912$	−158070.			−0.190046
$913$	723171.			0.867560
$914$	−22407.6			−0.0268227
$915$			356447.i			0.425748i
$916$			718267.i			0.856041i
$917$			475282.i			0.565214i
$918$			158734.i			0.188359i
$919$		−	546322.i		−	0.646871i	−0.946250	−	0.323435i	$-0.895162\pi$
$919$		−	546322.i		−	0.646871i	0.946250	−	0.323435i	$-0.104838\pi$
$920$	163513.			0.193186
$921$	−486730.			−0.573811
$922$			238239.i			0.280253i
$923$			80419.0i			0.0943964i
$924$		−	569252.i		−	0.666746i
$925$			346582.i			0.405063i
$926$	447974.			0.522433
$927$			490501.i			0.570795i
$928$			28702.2i			0.0333287i
$929$		−	322208.i		−	0.373340i	−0.982423	−	0.186670i	$-0.940231\pi$
$929$		−	322208.i		−	0.373340i	0.982423	−	0.186670i	$-0.0597695\pi$
$930$	−326885.			−0.377945
$931$	2.05348e6			2.36914
$932$		−	286186.i		−	0.329471i
$933$	495045.			0.568698
$934$	−223758.			−0.256498
$935$		−	1.42191e6i		−	1.62649i
$936$	10234.6			0.0116820
$937$		−	1.41751e6i		−	1.61453i	−0.590191	−	0.807264i	$-0.700947\pi$
$937$		−	1.41751e6i		−	1.61453i	0.590191	−	0.807264i	$-0.299053\pi$
$938$	604754.			0.687342
$939$			427490.i			0.484836i
$940$		−	167287.i		−	0.189325i
$941$		−	1.56169e6i		−	1.76366i	−0.471565	−	0.881831i	$-0.656311\pi$
$941$		−	1.56169e6i		−	1.76366i	0.471565	−	0.881831i	$-0.343689\pi$
$942$	341473.			0.384817
$943$		−	416494.i		−	0.468366i
$944$	160142.	−	154878.i	0.179706	−	0.173798i
$945$	244767.			0.274088
$946$			771881.i			0.862518i
$947$	645471.			0.719742			0.359871	−	0.933002i	$-0.382821\pi$
$947$	645471.			0.719742			0.359871	+	0.933002i	$0.382821\pi$
$948$	507534.			0.564740
$949$	92225.1			0.102404
$950$		−	231420.i		−	0.256421i
$951$	166064.			0.183617
$952$		−	742059.i		−	0.818775i
$953$	264893.			0.291665			0.145833	−	0.989309i	$-0.453414\pi$
$953$	264893.			0.291665			0.145833	+	0.989309i	$0.453414\pi$
$954$		−	113151.i		−	0.124326i
$955$			727281.i			0.797436i
$956$	176663.			0.193299
$957$		−	137620.i		−	0.150265i
$958$			247545.i			0.269727i
$959$	439430.			0.477806
$960$	56615.6			0.0614319
$961$	−168843.			−0.182826
$962$			95400.6i			0.103086i
$963$	145983.			0.157416
$964$	−133198.			−0.143332
$965$	907521.			0.974545
$966$	−409150.			−0.438459
$967$			222959.i			0.238436i	0.992868	+	0.119218i	$0.0380387\pi$
$967$			222959.i			0.238436i	−0.992868	+	0.119218i	$0.961961\pi$
$968$			300037.i			0.320202i
$969$	987981.			1.05221
$970$	263167.			0.279697
$971$	985936.			1.04571			0.522854	−	0.852422i	$-0.324867\pi$
$971$	985936.			1.04571			0.522854	+	0.852422i	$0.324867\pi$
$972$	30304.0			0.0320750
$973$	1.93744e6			2.04646
$974$			341940.i			0.360439i
$975$			14983.8i			0.0157621i
$976$		−	206305.i		−	0.216575i
$977$		−	1.86930e6i		−	1.95835i	−0.203020	−	0.979175i	$-0.565076\pi$
$977$		−	1.86930e6i		−	1.95835i	0.203020	−	0.979175i	$-0.434924\pi$
$978$			383736.i			0.401195i
$979$	2.50646e6			2.61514
$980$	−735493.			−0.765819
$981$		−	491788.i		−	0.511023i
$982$		−	216559.i		−	0.224571i
$983$			627248.i			0.649131i	0.945863	+	0.324565i	$0.105218\pi$
$983$			627248.i			0.649131i	−0.945863	+	0.324565i	$0.894782\pi$
$984$		−	144209.i		−	0.148937i
$985$	−1.46478e6			−1.50974
$986$		−	179397.i		−	0.184528i
$987$			418595.i			0.429694i
$988$		−	63701.1i		−	0.0652579i
$989$	554791.			0.567201
$990$	−271458.			−0.276969
$991$			426818.i			0.434606i	0.976104	+	0.217303i	$0.0697260\pi$
$991$			426818.i			0.434606i	−0.976104	+	0.217303i	$0.930274\pi$
$992$	189195.			0.192258
$993$	−430826.			−0.436922
$994$		−	1.11316e6i		−	1.12664i
$995$	−1.53856e6			−1.55406
$996$		−	179972.i		−	0.181420i
$997$	−1.61060e6			−1.62030			−0.810152	−	0.586220i	$-0.800615\pi$
$997$	−1.61060e6			−1.62030			−0.810152	+	0.586220i	$0.800615\pi$
$998$			103585.i			0.104001i
$999$			282476.i			0.283042i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.5.d.a.235.4	yes	40
3.2	odd	2		1062.5.d.b.235.35		40
59.58	odd	2	inner	354.5.d.a.235.3	✓	40
177.176	even	2		1062.5.d.b.235.36		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.5.d.a.235.3	✓	40	59.58	odd	2	inner
354.5.d.a.235.4	yes	40	1.1	even	1	trivial
1062.5.d.b.235.35		40	3.2	odd	2
1062.5.d.b.235.36		40	177.176	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+2.82843i q^{2} -5.19615 q^{3} -8.00000 q^{4} +21.2806 q^{5} -14.6969i q^{6} -81.9829 q^{7} -22.6274i q^{8} +27.0000 q^{9} +O(q^{10})\)	\(q+2.82843i q^{2} -5.19615 q^{3} -8.00000 q^{4} +21.2806 q^{5} -14.6969i q^{6} -81.9829 q^{7} -22.6274i q^{8} +27.0000 q^{9} +60.1907i q^{10} +167.036i q^{11} +41.5692 q^{12} +16.7521i q^{13} -231.883i q^{14} -110.577 q^{15} +64.0000 q^{16} -400.019 q^{17} +76.3675i q^{18} +475.320 q^{19} -170.245 q^{20} +425.996 q^{21} -472.448 q^{22} +339.573i q^{23} +117.576i q^{24} -172.135 q^{25} -47.3822 q^{26} -140.296 q^{27} +655.863 q^{28} +158.559 q^{29} -312.760i q^{30} -1045.16i q^{31} +181.019i q^{32} -867.942i q^{33} -1131.42i q^{34} -1744.65 q^{35} -216.000 q^{36} -2013.43i q^{37} +1344.41i q^{38} -87.0467i q^{39} -481.525i q^{40} -1226.52 q^{41} +1204.90i q^{42} -1633.79i q^{43} -1336.28i q^{44} +574.577 q^{45} -960.456 q^{46} +982.626i q^{47} -332.554 q^{48} +4320.20 q^{49} -486.872i q^{50} +2078.56 q^{51} -134.017i q^{52} -1481.67 q^{53} -396.817i q^{54} +3554.62i q^{55} +1855.06i q^{56} -2469.84 q^{57} +448.471i q^{58} +(2502.22 - 2419.97i) q^{59} +884.619 q^{60} -3223.51i q^{61} +2956.17 q^{62} -2213.54 q^{63} -512.000 q^{64} +356.496i q^{65} +2454.91 q^{66} +2608.02i q^{67} +3200.15 q^{68} -1764.47i q^{69} -4934.61i q^{70} +4800.52 q^{71} -610.940i q^{72} -5505.27i q^{73} +5694.83 q^{74} +894.441 q^{75} -3802.56 q^{76} -13694.1i q^{77} +246.205 q^{78} +12209.4 q^{79} +1361.96 q^{80} +729.000 q^{81} -3469.13i q^{82} -4329.44i q^{83} -3407.97 q^{84} -8512.64 q^{85} +4621.06 q^{86} -823.895 q^{87} +3779.58 q^{88} -15005.6i q^{89} +1625.15i q^{90} -1373.39i q^{91} -2716.58i q^{92} +5430.82i q^{93} -2779.29 q^{94} +10115.1 q^{95} -940.604i q^{96} -4372.22i q^{97} +12219.4i q^{98} +4509.96i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 320 q^{4} - 80 q^{7} + 1080 q^{9}+O(q^{10}) \) 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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