LMFDB - Embedded newform 33.8.d.b.32.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [33,8,Mod(32,33)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(33, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 8, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("33.32"); S:= CuspForms(chi, 8); N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	33.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$10.3087058410$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			32.3
Character	$\chi$	$=$	33.32
Dual form			33.8.d.b.32.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-17.1890 q^{2} +(-43.8101 - 16.3606i) q^{3} +167.460 q^{4} -90.8965i q^{5} +(753.051 + 281.222i) q^{6} +1506.19i q^{7} -678.279 q^{8} +(1651.66 + 1433.52i) q^{9} +1562.42i q^{10} +(981.685 - 4303.89i) q^{11} +(-7336.45 - 2739.76i) q^{12} +3566.16i q^{13} -25889.9i q^{14} +(-1487.13 + 3982.19i) q^{15} -9775.99 q^{16} -13457.6 q^{17} +(-28390.3 - 24640.8i) q^{18} -26772.8i q^{19} -15221.5i q^{20} +(24642.3 - 65986.6i) q^{21} +(-16874.1 + 73979.4i) q^{22} +40415.9i q^{23} +(29715.5 + 11097.1i) q^{24} +69862.8 q^{25} -61298.6i q^{26} +(-48906.0 - 89825.1i) q^{27} +252228. i q^{28} -142803. q^{29} +(25562.1 - 68449.7i) q^{30} -158528. q^{31} +254859. q^{32} +(-113422. + 172493. i) q^{33} +231322. q^{34} +136908. q^{35} +(276587. + 240058. i) q^{36} +286564. q^{37} +460197. i q^{38} +(58344.7 - 156234. i) q^{39} +61653.2i q^{40} -434415. q^{41} +(-423576. + 1.13424e6i) q^{42} -689840. i q^{43} +(164393. - 720730. i) q^{44} +(130302. - 150130. i) q^{45} -694707. i q^{46} -1.28647e6i q^{47} +(428288. + 159942. i) q^{48} -1.44508e6 q^{49} -1.20087e6 q^{50} +(589579. + 220175. i) q^{51} +597190. i q^{52} -406111. i q^{53} +(840643. + 1.54400e6i) q^{54} +(-391208. - 89231.7i) q^{55} -1.02162e6i q^{56} +(-438020. + 1.17292e6i) q^{57} +2.45463e6 q^{58} -622324. i q^{59} +(-249034. + 666858. i) q^{60} -901495. i q^{61} +2.72492e6 q^{62} +(-2.15917e6 + 2.48772e6i) q^{63} -3.12943e6 q^{64} +324151. q^{65} +(1.94961e6 - 2.96497e6i) q^{66} +2.03178e6 q^{67} -2.25361e6 q^{68} +(661230. - 1.77063e6i) q^{69} -2.35330e6 q^{70} -2.52259e6i q^{71} +(-1.12029e6 - 972330. i) q^{72} +1.13869e6i q^{73} -4.92573e6 q^{74} +(-3.06070e6 - 1.14300e6i) q^{75} -4.48338e6i q^{76} +(6.48250e6 + 1.47861e6i) q^{77} +(-1.00288e6 + 2.68550e6i) q^{78} +1.22674e6i q^{79} +888604. i q^{80} +(672982. + 4.73539e6i) q^{81} +7.46715e6 q^{82} -5.90164e6 q^{83} +(4.12661e6 - 1.10501e7i) q^{84} +1.22325e6i q^{85} +1.18576e7i q^{86} +(6.25621e6 + 2.33634e6i) q^{87} +(-665856. + 2.91924e6i) q^{88} -7.09843e6i q^{89} +(-2.23976e6 + 2.58058e6i) q^{90} -5.37133e6 q^{91} +6.76805e6i q^{92} +(6.94512e6 + 2.59362e6i) q^{93} +2.21131e7i q^{94} -2.43355e6 q^{95} +(-1.11654e7 - 4.16966e6i) q^{96} +8.09192e6 q^{97} +2.48394e7 q^{98} +(7.79114e6 - 5.70128e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 120 q^{3} + 1788 q^{4} - 5940 q^{9} - 6936 q^{12} + 23160 q^{15} + 5844 q^{16} - 17556 q^{22} - 34704 q^{25} + 7560 q^{27} + 131328 q^{31} + 28644 q^{33} - 436080 q^{34} - 302832 q^{36} + 1072488 q^{37}+ \cdots + 53650080 q^{99}+O(q^{100}) $ 24 * q + 120 * q^3 + 1788 * q^4 - 5940 * q^9 - 6936 * q^12 + 23160 * q^15 + 5844 * q^16 - 17556 * q^22 - 34704 * q^25 + 7560 * q^27 + 131328 * q^31 + 28644 * q^33 - 436080 * q^34 - 302832 * q^36 + 1072488 * q^37 - 100296 * q^42 - 1854252 * q^45 + 3172548 * q^48 - 1169304 * q^49 - 4401936 * q^55 - 2920440 * q^58 + 1981452 * q^60 + 14578596 * q^64 + 2895156 * q^66 + 7729200 * q^67 - 4614108 * q^69 - 6924504 * q^70 - 4375800 * q^75 - 26237448 * q^78 + 22367340 * q^81 - 23600232 * q^82 - 25179660 * q^88 + 9380640 * q^91 + 25396908 * q^93 + 72948360 * q^97 + 53650080 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−17.1890			−1.51930			−0.759652	−	0.650330i	$-0.774631\pi$
$2$	−17.1890			−1.51930			−0.759652	+	0.650330i	$0.774631\pi$
$3$	−43.8101	−	16.3606i	−0.936807	−	0.349845i
$3$	−43.8101	−	16.3606i	−0.936807	−	0.349845i
$4$	167.460			1.30828
$5$		−	90.8965i		−	0.325201i	−0.986692	−	0.162601i	$-0.948012\pi$
$5$		−	90.8965i		−	0.325201i	0.986692	−	0.162601i	$-0.0519882\pi$
$6$	753.051	+	281.222i	1.42329	+	0.531521i
$7$			1506.19i			1.65973i	0.557963	+	0.829866i	$0.311583\pi$
$7$			1506.19i			1.65973i	−0.557963	+	0.829866i	$0.688417\pi$
$8$	−678.279			−0.468375
$9$	1651.66	+	1433.52i	0.755216	+	0.655476i
$10$			1562.42i			0.494079i
$11$	981.685	−	4303.89i	0.222381	−	0.974960i
$11$	981.685	−	4303.89i	0.222381	−	0.974960i
$12$	−7336.45	−	2739.76i	−1.22561	−	0.457697i
$13$			3566.16i			0.450193i	0.974336	+	0.225097i	$0.0722698\pi$
$13$			3566.16i			0.450193i	−0.974336	+	0.225097i	$0.927730\pi$
$14$		−	25889.9i		−	2.52164i
$15$	−1487.13	+	3982.19i	−0.113770	+	0.304651i
$16$	−9775.99			−0.596679
$17$	−13457.6			−0.664349			−0.332174	−	0.943218i	$-0.607782\pi$
$17$	−13457.6			−0.664349			−0.332174	+	0.943218i	$0.607782\pi$
$18$	−28390.3	−	24640.8i	−1.14740	−	0.995866i
$19$		−	26772.8i		−	0.895481i	−0.894164	−	0.447740i	$-0.852229\pi$
$19$		−	26772.8i		−	0.895481i	0.894164	−	0.447740i	$-0.147771\pi$
$20$		−	15221.5i		−	0.425455i
$21$	24642.3	−	65986.6i	0.580650	−	1.55485i
$22$	−16874.1	+	73979.4i	−0.337864	+	1.48126i
$23$			40415.9i			0.692635i	0.938117	+	0.346318i	$0.112568\pi$
$23$			40415.9i			0.692635i	−0.938117	+	0.346318i	$0.887432\pi$
$24$	29715.5	+	11097.1i	0.438777	+	0.163859i
$25$	69862.8			0.894244
$26$		−	61298.6i		−	0.683980i
$27$	−48906.0	−	89825.1i	−0.478177	−	0.878263i
$28$			252228.i			2.17140i
$29$	−142803.			−1.08728			−0.543642	−	0.839317i	$-0.682955\pi$
$29$	−142803.			−1.08728			−0.543642	+	0.839317i	$0.682955\pi$
$30$	25562.1	−	68449.7i	0.172851	−	0.462857i
$31$	−158528.			−0.955739			−0.477869	−	0.878431i	$-0.658591\pi$
$31$	−158528.			−0.955739			−0.477869	+	0.878431i	$0.658591\pi$
$32$	254859.			1.37491
$33$	−113422.	+	172493.i	−0.549413	+	0.835551i
$34$	231322.			1.00935
$35$	136908.			0.539747
$36$	276587.	+	240058.i	0.988036	+	0.857547i
$37$	286564.			0.930069			0.465035	−	0.885292i	$-0.346042\pi$
$37$	286564.			0.930069			0.465035	+	0.885292i	$0.346042\pi$
$38$			460197.i			1.36051i
$39$	58344.7	−	156234.i	0.157498	−	0.421745i
$40$			61653.2i			0.152316i
$41$	−434415.			−0.984378			−0.492189	−	0.870488i	$-0.663803\pi$
$41$	−434415.			−0.984378			−0.492189	+	0.870488i	$0.663803\pi$
$42$	−423576.	+	1.13424e6i	−0.882183	+	2.36229i
$43$		−	689840.i		−	1.32315i	−0.749880	−	0.661574i	$-0.769889\pi$
$43$		−	689840.i		−	1.32315i	0.749880	−	0.661574i	$-0.230111\pi$
$44$	164393.	−	720730.i	0.290937	−	1.27552i
$45$	130302.	−	150130.i	0.213161	−	0.245597i
$46$		−	694707.i		−	1.05232i
$47$		−	1.28647e6i		−	1.80741i	−0.428155	−	0.903705i	$-0.640836\pi$
$47$		−	1.28647e6i		−	1.80741i	0.428155	−	0.903705i	$-0.359164\pi$
$48$	428288.	+	159942.i	0.558974	+	0.208746i
$49$	−1.44508e6			−1.75471
$50$	−1.20087e6			−1.35863
$51$	589579.	+	220175.i	0.622367	+	0.232419i
$52$			597190.i			0.588980i
$53$		−	406111.i		−	0.374696i	−0.982294	−	0.187348i	$-0.940011\pi$
$53$		−	406111.i		−	0.374696i	0.982294	−	0.187348i	$-0.0599892\pi$
$54$	840643.	+	1.54400e6i	0.726496	+	1.33435i
$55$	−391208.	−	89231.7i	−0.317058	−	0.0723186i
$56$		−	1.02162e6i		−	0.777377i
$57$	−438020.	+	1.17292e6i	−0.313280	+	0.838893i
$58$	2.45463e6			1.65192
$59$		−	622324.i		−	0.394489i	−0.980354	−	0.197244i	$-0.936801\pi$
$59$		−	622324.i		−	0.394489i	0.980354	−	0.197244i	$-0.0631993\pi$
$60$	−249034.	+	666858.i	−0.148843	+	0.398569i
$61$		−	901495.i		−	0.508521i	−0.967136	−	0.254261i	$-0.918168\pi$
$61$		−	901495.i		−	0.508521i	0.967136	−	0.254261i	$-0.0818321\pi$
$62$	2.72492e6			1.45206
$63$	−2.15917e6	+	2.48772e6i	−1.08791	+	1.25346i
$64$	−3.12943e6			−1.49223
$65$	324151.			0.146403
$66$	1.94961e6	−	2.96497e6i	0.834726	−	1.26945i
$67$	2.03178e6			0.825308			0.412654	−	0.910888i	$-0.364602\pi$
$67$	2.03178e6			0.825308			0.412654	+	0.910888i	$0.364602\pi$
$68$	−2.25361e6			−0.869156
$69$	661230.	−	1.77063e6i	0.242315	−	0.648866i
$70$	−2.35330e6			−0.820039
$71$		−	2.52259e6i		−	0.836455i	−0.908342	−	0.418228i	$-0.862651\pi$
$71$		−	2.52259e6i		−	0.836455i	0.908342	−	0.418228i	$-0.137349\pi$
$72$	−1.12029e6	−	972330.i	−0.353724	−	0.307008i
$73$			1.13869e6i			0.342589i	0.985220	+	0.171295i	$0.0547950\pi$
$73$			1.13869e6i			0.342589i	−0.985220	+	0.171295i	$0.945205\pi$
$74$	−4.92573e6			−1.41306
$75$	−3.06070e6	−	1.14300e6i	−0.837735	−	0.312847i
$76$		−	4.48338e6i		−	1.17154i
$77$	6.48250e6	+	1.47861e6i	1.61817	+	0.369093i
$78$	−1.00288e6	+	2.68550e6i	−0.239287	+	0.640758i
$79$			1.22674e6i			0.279934i	0.990156	+	0.139967i	$0.0446997\pi$
$79$			1.22674e6i			0.279934i	−0.990156	+	0.139967i	$0.955300\pi$
$80$			888604.i			0.194041i
$81$	672982.	+	4.73539e6i	0.140704	+	0.990052i
$82$	7.46715e6			1.49557
$83$	−5.90164e6			−1.13292			−0.566460	−	0.824089i	$-0.691687\pi$
$83$	−5.90164e6			−1.13292			−0.566460	+	0.824089i	$0.691687\pi$
$84$	4.12661e6	−	1.10501e7i	0.759654	−	2.03418i
$85$			1.22325e6i			0.216047i
$86$			1.18576e7i			2.01026i
$87$	6.25621e6	+	2.33634e6i	1.01858	+	0.380382i
$88$	−665856.	+	2.91924e6i	−0.104158	+	0.456646i
$89$		−	7.09843e6i		−	1.06733i	−0.845697	−	0.533664i	$-0.820815\pi$
$89$		−	7.09843e6i		−	1.06733i	0.845697	−	0.533664i	$-0.179185\pi$
$90$	−2.23976e6	+	2.58058e6i	−0.323857	+	0.373137i
$91$	−5.37133e6			−0.747200
$92$			6.76805e6i			0.906163i
$93$	6.94512e6	+	2.59362e6i	0.895343	+	0.334361i
$94$			2.21131e7i			2.74601i
$95$	−2.43355e6			−0.291211
$96$	−1.11654e7	−	4.16966e6i	−1.28803	−	0.481006i
$97$	8.09192e6			0.900224			0.450112	−	0.892972i	$-0.351384\pi$
$97$	8.09192e6			0.900224			0.450112	+	0.892972i	$0.351384\pi$
$98$	2.48394e7			2.66594
$99$	7.79114e6	−	5.70128e6i	0.807008	−	0.590540i
$100$	1.16992e7			1.16992
$101$	4.89863e6			0.473097			0.236548	−	0.971620i	$-0.423984\pi$
$101$	4.89863e6			0.473097			0.236548	+	0.971620i	$0.423984\pi$
$102$	−1.01343e7	−	3.78458e6i	−0.945564	−	0.353116i
$103$	−1.63269e7			−1.47223			−0.736113	−	0.676859i	$-0.763341\pi$
$103$	−1.63269e7			−1.47223			−0.736113	+	0.676859i	$0.763341\pi$
$104$		−	2.41885e6i		−	0.210859i
$105$	−5.99795e6	−	2.23990e6i	−0.505639	−	0.188828i
$106$			6.98062e6i			0.569276i
$107$	−2.11142e7			−1.66622			−0.833108	−	0.553111i	$-0.813441\pi$
$107$	−2.11142e7			−1.66622			−0.833108	+	0.553111i	$0.813441\pi$
$108$	−8.18981e6	−	1.50421e7i	−0.625591	−	1.14902i
$109$		−	2.46933e7i		−	1.82636i	−0.407559	−	0.913179i	$-0.633620\pi$
$109$		−	2.46933e7i		−	1.82636i	0.407559	−	0.913179i	$-0.366380\pi$
$110$	6.72446e6	+	1.53380e6i	0.481707	+	0.109874i
$111$	−1.25544e7	−	4.68837e6i	−0.871296	−	0.325380i
$112$		−	1.47246e7i		−	0.990328i
$113$			2.80165e7i			1.82658i	0.407308	+	0.913291i	$0.366468\pi$
$113$			2.80165e7i			1.82658i	−0.407308	+	0.913291i	$0.633532\pi$
$114$	7.52911e6	−	2.01613e7i	0.475967	−	1.27453i
$115$	3.67366e6			0.225246
$116$	−2.39138e7			−1.42248
$117$	−5.11218e6	+	5.89008e6i	−0.295091	+	0.339993i
$118$			1.06971e7i			0.599348i
$119$		−	2.02698e7i		−	1.10264i
$120$	1.00869e6	−	2.70103e6i	0.0532870	−	0.142691i
$121$	−1.75598e7	−	8.45013e6i	−0.901093	−	0.433625i
$122$			1.54958e7i			0.772598i
$123$	1.90318e7	+	7.10732e6i	0.922172	+	0.344380i
$124$	−2.65471e7			−1.25038
$125$		−	1.34516e7i		−	0.616010i
$126$	3.71138e7	−	4.27613e7i	1.65287	−	1.90438i
$127$		−	3.98549e7i		−	1.72651i	−0.504768	−	0.863255i	$-0.668422\pi$
$127$		−	3.98549e7i		−	1.72651i	0.504768	−	0.863255i	$-0.331578\pi$
$128$	2.11697e7			0.892236
$129$	−1.12862e7	+	3.02220e7i	−0.462897	+	1.23954i
$130$	−5.57182e6			−0.222431
$131$	1.80946e7			0.703232			0.351616	−	0.936144i	$-0.385632\pi$
$131$	1.80946e7			0.703232			0.351616	+	0.936144i	$0.385632\pi$
$132$	−1.89937e7	+	2.88857e7i	−0.718788	+	1.09314i
$133$	4.03251e7			1.48626
$134$	−3.49242e7			−1.25389
$135$	−8.16479e6	+	4.44538e6i	−0.285612	+	0.155504i
$136$	9.12800e6			0.311164
$137$			1.08842e7i			0.361638i	0.983516	+	0.180819i	$0.0578747\pi$
$137$			1.08842e7i			0.361638i	−0.983516	+	0.180819i	$0.942125\pi$
$138$	−1.13659e7	+	3.04352e7i	−0.368150	+	0.985824i
$139$			1.33599e6i			0.0421942i	0.999777	+	0.0210971i	$0.00671591\pi$
$139$			1.33599e6i			0.0421942i	−0.999777	+	0.0210971i	$0.993284\pi$
$140$	2.29266e7			0.706141
$141$	−2.10475e7	+	5.63604e7i	−0.632314	+	1.69320i
$142$			4.33607e7i			1.27083i
$143$	1.53484e7	+	3.50085e6i	0.438920	+	0.100114i
$144$	−1.61466e7	−	1.40141e7i	−0.450622	−	0.391109i
$145$			1.29803e7i			0.353586i
$146$		−	1.95728e7i		−	0.520497i
$147$	6.33092e7	+	2.36425e7i	1.64383	+	0.613878i
$148$	4.79880e7			1.21679
$149$	3.30097e7			0.817503			0.408752	−	0.912646i	$-0.365964\pi$
$149$	3.30097e7			0.817503			0.408752	+	0.912646i	$0.365964\pi$
$150$	5.26102e7	+	1.96470e7i	1.27277	+	0.475310i
$151$			7.90394e6i			0.186820i	0.995628	+	0.0934102i	$0.0297768\pi$
$151$			7.90394e6i			0.186820i	−0.995628	+	0.0934102i	$0.970223\pi$
$152$			1.81594e7i			0.419420i
$153$	−2.22274e7	−	1.92918e7i	−0.501727	−	0.435464i
$154$	−1.11427e8	−	2.54157e7i	−2.45849	−	0.560764i
$155$			1.44096e7i			0.310807i
$156$	9.77041e6	−	2.61630e7i	0.206052	−	0.551761i
$157$	5.79006e6			0.119408			0.0597041	−	0.998216i	$-0.480984\pi$
$157$	5.79006e6			0.119408			0.0597041	+	0.998216i	$0.480984\pi$
$158$		−	2.10863e7i		−	0.425305i
$159$	−6.64423e6	+	1.77918e7i	−0.131086	+	0.351018i
$160$		−	2.31658e7i		−	0.447123i
$161$	−6.08742e7			−1.14959
$162$	−1.15678e7	−	8.13963e7i	−0.213772	−	1.50419i
$163$	−1.67020e7			−0.302073			−0.151037	−	0.988528i	$-0.548261\pi$
$163$	−1.67020e7			−0.302073			−0.151037	+	0.988528i	$0.548261\pi$
$164$	−7.27473e7			−1.28784
$165$	1.56790e7	+	1.03097e7i	0.271722	+	0.178670i
$166$	1.01443e8			1.72125
$167$	−5.41613e7			−0.899873			−0.449936	−	0.893061i	$-0.648553\pi$
$167$	−5.41613e7			−0.899873			−0.449936	+	0.893061i	$0.648553\pi$
$168$	−1.67144e7	+	4.47573e7i	−0.271962	+	0.728252i
$169$	5.00310e7			0.797326
$170$		−	2.10264e7i		−	0.328241i
$171$	3.83795e7	−	4.42195e7i	0.586966	−	0.676282i
$172$		−	1.15521e8i		−	1.73105i
$173$	1.03863e8			1.52511			0.762554	−	0.646924i	$-0.223945\pi$
$173$	1.03863e8			1.52511			0.762554	+	0.646924i	$0.223945\pi$
$174$	−1.07538e8	−	4.01593e7i	−1.54753	−	0.577915i
$175$			1.05227e8i			1.48421i
$176$	−9.59695e6	+	4.20748e7i	−0.132690	+	0.581738i
$177$	−1.01816e7	+	2.72641e7i	−0.138010	+	0.369560i
$178$			1.22015e8i			1.62159i
$179$			1.48451e7i			0.193463i	0.995311	+	0.0967316i	$0.0308389\pi$
$179$			1.48451e7i			0.193463i	−0.995311	+	0.0967316i	$0.969161\pi$
$180$	2.18205e7	−	2.51408e7i	0.278875	−	0.321311i
$181$	−4.88799e7			−0.612710			−0.306355	−	0.951917i	$-0.599109\pi$
$181$	−4.88799e7			−0.612710			−0.306355	+	0.951917i	$0.599109\pi$
$182$	9.23276e7			1.13522
$183$	−1.47490e7	+	3.94946e7i	−0.177904	+	0.476386i
$184$		−	2.74132e7i		−	0.324413i
$185$		−	2.60476e7i		−	0.302460i
$186$	−1.19379e8	−	4.45815e7i	−1.36030	−	0.507995i
$187$	−1.32111e7	+	5.79200e7i	−0.147739	+	0.647714i
$188$		−	2.15432e8i		−	2.36460i
$189$	1.35294e8	−	7.36620e7i	1.45768	−	0.793646i
$190$	4.18302e7			0.442438
$191$		−	9.62151e7i		−	0.999140i	−0.866273	−	0.499570i	$-0.833491\pi$
$191$		−	9.62151e7i		−	0.999140i	0.866273	−	0.499570i	$-0.166509\pi$
$192$	1.37101e8	+	5.11995e7i	1.39793	+	0.522049i
$193$			1.60072e8i			1.60275i	0.598164	+	0.801374i	$0.295897\pi$
$193$			1.60072e8i			1.60275i	−0.598164	+	0.801374i	$0.704103\pi$
$194$	−1.39092e8			−1.36771
$195$	−1.42011e7	−	5.30333e6i	−0.137152	−	0.0512186i
$196$	−2.41993e8			−2.29566
$197$	−1.66964e7			−0.155593			−0.0777965	−	0.996969i	$-0.524788\pi$
$197$	−1.66964e7			−0.155593			−0.0777965	+	0.996969i	$0.524788\pi$
$198$	−1.33922e8	+	9.79991e7i	−1.22609	+	0.897210i
$199$	1.14515e8			1.03009			0.515045	−	0.857163i	$-0.327775\pi$
$199$	1.14515e8			1.03009			0.515045	+	0.857163i	$0.327775\pi$
$200$	−4.73865e7			−0.418841
$201$	−8.90128e7	−	3.32413e7i	−0.773154	−	0.288730i
$202$	−8.42023e7			−0.718777
$203$		−	2.15089e8i		−	1.80460i
$204$	9.87310e7	+	3.68705e7i	0.814232	+	0.304070i
$205$			3.94868e7i			0.320121i
$206$	2.80643e8			2.23676
$207$	−5.79372e7	+	6.67532e7i	−0.454005	+	0.523089i
$208$		−	3.48628e7i		−	0.268621i
$209$	−1.15227e8	−	2.62825e7i	−0.873058	−	0.199138i
$210$	1.03099e8	+	3.85016e7i	0.768219	+	0.286887i
$211$		−	1.51161e8i		−	1.10778i	−0.832591	−	0.553889i	$-0.813143\pi$
$211$		−	1.51161e8i		−	1.10778i	0.832591	−	0.553889i	$-0.186857\pi$
$212$		−	6.80073e7i		−	0.490208i
$213$	−4.12712e7	+	1.10515e8i	−0.292630	+	0.783597i
$214$	3.62931e8			2.53149
$215$	−6.27040e7			−0.430289
$216$	3.31719e7	+	6.09265e7i	0.223966	+	0.411356i
$217$		−	2.38774e8i		−	1.58627i
$218$			4.24451e8i			2.77479i
$219$	1.86296e7	−	4.98860e7i	0.119853	−	0.320940i
$220$	−6.55118e7	−	1.49428e7i	−0.414802	−	0.0946131i
$221$		−	4.79919e7i		−	0.299085i
$222$	2.15797e8	+	8.05882e7i	1.32376	+	0.494352i
$223$	−1.62697e8			−0.982457			−0.491228	−	0.871031i	$-0.663452\pi$
$223$	−1.62697e8			−0.982457			−0.491228	+	0.871031i	$0.663452\pi$
$224$			3.83867e8i			2.28199i
$225$	1.15390e8	+	1.00150e8i	0.675348	+	0.586155i
$226$		−	4.81574e8i		−	2.77513i
$227$	−2.43483e8			−1.38158			−0.690792	−	0.723053i	$-0.742738\pi$
$227$	−2.43483e8			−1.38158			−0.690792	+	0.723053i	$0.742738\pi$
$228$	−7.33510e7	+	1.96417e8i	−0.409858	+	1.09751i
$229$	−7.10138e7			−0.390767			−0.195384	−	0.980727i	$-0.562595\pi$
$229$	−7.10138e7			−0.390767			−0.195384	+	0.980727i	$0.562595\pi$
$230$	−6.31464e7			−0.342217
$231$	−2.59808e8	−	1.70836e8i	−1.38679	−	0.911879i
$232$	9.68600e7			0.509257
$233$	−3.81060e7			−0.197355			−0.0986774	−	0.995119i	$-0.531461\pi$
$233$	−3.81060e7			−0.197355			−0.0986774	+	0.995119i	$0.531461\pi$
$234$	8.78730e7	−	1.01244e8i	0.448332	−	0.516553i
$235$	−1.16936e8			−0.587772
$236$		−	1.04215e8i		−	0.516103i
$237$	2.00702e7	−	5.37435e7i	0.0979338	−	0.262245i
$238$			3.48416e8i			1.67525i
$239$	3.32792e8			1.57681			0.788406	−	0.615156i	$-0.210907\pi$
$239$	3.32792e8			1.57681			0.788406	+	0.615156i	$0.210907\pi$
$240$	1.45381e7	−	3.89299e7i	0.0678843	−	0.181779i
$241$		−	2.13039e7i		−	0.0980390i	−0.998798	−	0.0490195i	$-0.984390\pi$
$241$		−	2.13039e7i		−	0.0980390i	0.998798	−	0.0490195i	$-0.0156097\pi$
$242$	3.01834e8	+	1.45249e8i	1.36903	+	0.658808i
$243$	4.79906e7	−	2.18468e8i	0.214553	−	0.976712i
$244$		−	1.50965e8i		−	0.665289i
$245$			1.31353e8i			0.570634i
$246$	−3.27137e8	−	1.22167e8i	−1.40106	−	0.523218i
$247$	9.54761e7			0.403139
$248$	1.07526e8			0.447644
$249$	2.58552e8	+	9.65546e7i	1.06133	+	0.396347i
$250$			2.31218e8i			0.935907i
$251$		−	2.36907e8i		−	0.945629i	−0.881162	−	0.472814i	$-0.843238\pi$
$251$		−	2.36907e8i		−	0.945629i	0.881162	−	0.472814i	$-0.156762\pi$
$252$	−3.61575e8	+	4.16594e8i	−1.42330	+	1.63988i
$253$	1.73945e8	+	3.96757e7i	0.675292	+	0.154029i
$254$			6.85065e8i			2.62309i
$255$	2.00131e7	−	5.35907e7i	0.0755831	−	0.202394i
$256$	3.66821e7			0.136651
$257$		−	1.83527e8i		−	0.674425i	−0.941429	−	0.337212i	$-0.890516\pi$
$257$		−	1.83527e8i		−	0.674425i	0.941429	−	0.337212i	$-0.109484\pi$
$258$	1.93998e8	−	5.19484e8i	0.703282	−	1.88323i
$259$			4.31621e8i			1.54367i
$260$	5.42824e7			0.191537
$261$	−2.35861e8	−	2.04711e8i	−0.821135	−	0.712689i
$262$	−3.11027e8			−1.06842
$263$	3.47905e8			1.17928			0.589638	−	0.807667i	$-0.299270\pi$
$263$	3.47905e8			1.17928			0.589638	+	0.807667i	$0.299270\pi$
$264$	7.69319e7	−	1.16998e8i	0.257331	−	0.391351i
$265$	−3.69140e7			−0.121851
$266$	−6.93146e8			−2.25808
$267$	−1.16135e8	+	3.10983e8i	−0.373399	+	0.999880i
$268$	3.40243e8			1.07974
$269$			5.51585e8i			1.72774i	0.503711	+	0.863872i	$0.331968\pi$
$269$			5.51585e8i			1.72774i	−0.503711	+	0.863872i	$0.668032\pi$
$270$	1.40344e8	−	7.64115e7i	0.433932	−	0.236257i
$271$		−	2.83981e8i		−	0.866755i	−0.901213	−	0.433377i	$-0.857322\pi$
$271$		−	2.83981e8i		−	0.866755i	0.901213	−	0.433377i	$-0.142678\pi$
$272$	1.31561e8			0.396403
$273$	2.35319e8	+	8.78785e7i	0.699983	+	0.261405i
$274$		−	1.87088e8i		−	0.549437i
$275$	6.85833e7	−	3.00682e8i	0.198863	−	0.871852i
$276$	1.10730e8	−	2.96509e8i	0.317017	−	0.848900i
$277$			3.38232e8i			0.956170i	0.878313	+	0.478085i	$0.158669\pi$
$277$			3.38232e8i			0.956170i	−0.878313	+	0.478085i	$0.841331\pi$
$278$		−	2.29643e7i		−	0.0641058i
$279$	−2.61834e8	−	2.27253e8i	−0.721790	−	0.626463i
$280$	−9.28617e7			−0.252804
$281$	−3.57886e8			−0.962216			−0.481108	−	0.876661i	$-0.659765\pi$
$281$	−3.57886e8			−0.962216			−0.481108	+	0.876661i	$0.659765\pi$
$282$	3.61784e8	−	9.68776e8i	0.960677	−	2.57248i
$283$			1.65581e8i			0.434267i	0.976142	+	0.217134i	$0.0696707\pi$
$283$			1.65581e8i			0.434267i	−0.976142	+	0.217134i	$0.930329\pi$
$284$		−	4.22433e8i		−	1.09432i
$285$	1.06614e8	+	3.98145e7i	0.272809	+	0.101879i
$286$	−2.63822e8	−	6.01759e7i	−0.666853	−	0.152104i
$287$		−	6.54314e8i		−	1.63380i
$288$	4.20940e8	+	3.65346e8i	1.03836	+	0.901221i
$289$	−2.29232e8			−0.558640
$290$		−	2.23117e8i		−	0.537205i
$291$	−3.54508e8	−	1.32389e8i	−0.843337	−	0.314939i
$292$			1.90685e8i			0.448204i
$293$	−3.27097e8			−0.759695			−0.379847	−	0.925049i	$-0.624024\pi$
$293$	−3.27097e8			−0.759695			−0.379847	+	0.925049i	$0.624024\pi$
$294$	−1.08822e9	−	4.06389e8i	−2.49747	−	0.932666i
$295$	−5.65671e7			−0.128288
$296$	−1.94370e8			−0.435621
$297$	−4.34608e8	+	1.22306e8i	−0.962609	+	0.270895i
$298$	−5.67402e8			−1.24204
$299$	−1.44129e8			−0.311820
$300$	−5.12545e8	−	1.91407e8i	−1.09599	−	0.409293i
$301$	1.03903e9			2.19607
$302$		−	1.35860e8i		−	0.283837i
$303$	−2.14610e8	−	8.01448e7i	−0.443200	−	0.165511i
$304$			2.61731e8i			0.534315i
$305$	−8.19427e7			−0.165372
$306$	3.82065e8	+	3.31606e8i	0.762276	+	0.661603i
$307$		−	3.94124e8i		−	0.777408i	−0.921363	−	0.388704i	$-0.872923\pi$
$307$		−	3.94124e8i		−	0.777408i	0.921363	−	0.388704i	$-0.127077\pi$
$308$	1.08556e9	+	2.47608e8i	2.11703	+	0.482878i
$309$	7.15285e8	+	2.67119e8i	1.37919	+	0.515051i
$310$		−	2.47686e8i		−	0.472211i
$311$		−	1.72708e8i		−	0.325575i	−0.986661	−	0.162788i	$-0.947951\pi$
$311$		−	1.72708e8i		−	0.325575i	0.986661	−	0.162788i	$-0.0520485\pi$
$312$	−3.95740e7	+	1.05970e8i	−0.0737681	+	0.197534i
$313$	−2.48533e8			−0.458119			−0.229060	−	0.973412i	$-0.573565\pi$
$313$	−2.48533e8			−0.458119			−0.229060	+	0.973412i	$0.573565\pi$
$314$	−9.95251e7			−0.181417
$315$	2.26125e8	+	1.96261e8i	0.407626	+	0.353791i
$316$			2.05429e8i			0.366233i
$317$			6.99051e8i			1.23254i	0.787534	+	0.616271i	$0.211357\pi$
$317$			6.99051e8i			1.23254i	−0.787534	+	0.616271i	$0.788643\pi$
$318$	1.14207e8	−	3.05822e8i	0.199159	−	0.533302i
$319$	−1.40187e8	+	6.14607e8i	−0.241792	+	1.06006i
$320$			2.84454e8i			0.485274i
$321$	9.25016e8	+	3.45442e8i	1.56092	+	0.582918i
$322$	1.04636e9			1.74657
$323$			3.60298e8i			0.594912i
$324$	1.12698e8	+	7.92989e8i	0.184080	+	1.29527i
$325$			2.49142e8i			0.402583i
$326$	2.87090e8			0.458941
$327$	−4.03998e8	+	1.08182e9i	−0.638943	+	1.71095i
$328$	2.94655e8			0.461058
$329$	1.93767e9			2.99982
$330$	−2.69506e8	−	1.77213e8i	−0.412828	−	0.271454i
$331$	−6.14954e8			−0.932062			−0.466031	−	0.884768i	$-0.654317\pi$
$331$	−6.14954e8			−0.932062			−0.466031	+	0.884768i	$0.654317\pi$
$332$	−9.88289e8			−1.48218
$333$	4.73306e8	+	4.10796e8i	0.702404	+	0.609638i
$334$	9.30975e8			1.36718
$335$		−	1.84682e8i		−	0.268391i
$336$	−2.40903e8	+	6.45085e8i	−0.346462	+	0.927747i
$337$		−	3.16600e8i		−	0.450616i	−0.974288	−	0.225308i	$-0.927661\pi$
$337$		−	3.16600e8i		−	0.450616i	0.974288	−	0.225308i	$-0.0723388\pi$
$338$	−8.59981e8			−1.21138
$339$	4.58368e8	−	1.22741e9i	0.639021	−	1.71116i
$340$			2.04845e8i			0.282651i
$341$	−1.55624e8	+	6.82286e8i	−0.212538	+	0.931807i
$342$	−6.59703e8	+	7.60087e8i	−0.891779	+	1.02748i
$343$		−	9.36156e8i		−	1.25262i
$344$			4.67904e8i			0.619729i
$345$	−1.60944e8	−	6.01035e7i	−0.211012	−	0.0788012i
$346$	−1.78530e9			−2.31710
$347$	−1.05014e9			−1.34925			−0.674626	−	0.738160i	$-0.735695\pi$
$347$	−1.05014e9			−1.34925			−0.674626	+	0.738160i	$0.735695\pi$
$348$	1.04767e9	+	3.91245e8i	1.33259	+	0.497647i
$349$		−	8.07445e8i		−	1.01677i	−0.861129	−	0.508386i	$-0.830242\pi$
$349$		−	8.07445e8i		−	1.01677i	0.861129	−	0.508386i	$-0.169758\pi$
$350$		−	1.80874e9i		−	2.25496i
$351$	3.20331e8	−	1.74407e8i	0.395388	−	0.215272i
$352$	2.50191e8	−	1.09688e9i	0.305754	−	1.34048i
$353$			6.42480e8i			0.777406i	0.921363	+	0.388703i	$0.127077\pi$
$353$			6.42480e8i			0.777406i	−0.921363	+	0.388703i	$0.872923\pi$
$354$	1.75012e8	−	4.68642e8i	0.209679	−	0.561474i
$355$	−2.29295e8			−0.272016
$356$		−	1.18870e9i		−	1.39637i
$357$	−3.31626e8	+	8.88021e8i	−0.385754	+	1.03296i
$358$		−	2.55172e8i		−	0.293929i
$359$	−1.21411e9			−1.38493			−0.692464	−	0.721452i	$-0.743475\pi$
$359$	−1.21411e9			−1.38493			−0.692464	+	0.721452i	$0.743475\pi$
$360$	−8.83814e7	+	1.01830e8i	−0.0998394	+	0.115032i
$361$	1.77089e8			0.198114
$362$	8.40194e8			0.930892
$363$	6.31046e8	+	6.57490e8i	0.692449	+	0.721467i
$364$	−8.99484e8			−0.977549
$365$	1.03503e8			0.111410
$366$	2.53521e8	−	6.78871e8i	0.270290	−	0.723775i
$367$	2.98569e8			0.315292			0.157646	−	0.987496i	$-0.449609\pi$
$367$	2.98569e8			0.315292			0.157646	+	0.987496i	$0.449609\pi$
$368$		−	3.95105e8i		−	0.413281i
$369$	−7.17506e8	−	6.22745e8i	−0.743418	−	0.645235i
$370$			4.47732e8i			0.459528i
$371$	6.11682e8			0.621895
$372$	1.16303e9	+	4.34327e8i	1.17136	+	0.437438i
$373$		−	1.65310e9i		−	1.64937i	−0.565594	−	0.824684i	$-0.691353\pi$
$373$		−	1.65310e9i		−	1.64937i	0.565594	−	0.824684i	$-0.308647\pi$
$374$	2.27085e8	−	9.95584e8i	0.224460	−	0.984073i
$375$	−2.20076e8	+	5.89315e8i	−0.215508	+	0.577083i
$376$			8.72585e8i			0.846545i
$377$		−	5.09257e8i		−	0.489488i
$378$	−2.32557e9	+	1.26617e9i	−2.21466	+	1.20579i
$379$	−1.56573e8			−0.147734			−0.0738669	−	0.997268i	$-0.523534\pi$
$379$	−1.56573e8			−0.147734			−0.0738669	+	0.997268i	$0.523534\pi$
$380$	−4.07523e8			−0.380987
$381$	−6.52053e8	+	1.74605e9i	−0.604011	+	1.61741i
$382$			1.65384e9i			1.51800i
$383$			1.20689e9i			1.09767i	0.835932	+	0.548834i	$0.184928\pi$
$383$			1.20689e9i			1.09767i	−0.835932	+	0.548834i	$0.815072\pi$
$384$	−9.27447e8	−	3.46350e8i	−0.835853	−	0.312145i
$385$	1.34400e8	−	5.89236e8i	0.120030	−	0.526232i
$386$		−	2.75147e9i		−	2.43506i
$387$	9.88903e8	−	1.13938e9i	0.867292	−	0.999264i
$388$	1.35507e9			1.17775
$389$		−	8.41324e7i		−	0.0724669i	−0.999343	−	0.0362335i	$-0.988464\pi$
$389$		−	8.41324e7i		−	0.0724669i	0.999343	−	0.0362335i	$-0.0115360\pi$
$390$	2.44102e8	+	9.11587e7i	0.208375	+	0.0778165i
$391$		−	5.43901e8i		−	0.460151i
$392$	9.80167e8			0.821862
$393$	−7.92726e8	−	2.96039e8i	−0.658793	−	0.246023i
$394$	2.86993e8			0.236393
$395$	1.11506e8			0.0910350
$396$	1.30471e9	−	9.54738e8i	1.05579	−	0.772594i
$397$	2.75369e8			0.220876			0.110438	−	0.993883i	$-0.464775\pi$
$397$	2.75369e8			0.220876			0.110438	+	0.993883i	$0.464775\pi$
$398$	−1.96839e9			−1.56502
$399$	−1.76665e9	−	6.59744e8i	−1.39234	−	0.519961i
$400$	−6.82979e8			−0.533577
$401$		−	1.02279e8i		−	0.0792103i	−0.999215	−	0.0396051i	$-0.987390\pi$
$401$		−	1.02279e8i		−	0.0792103i	0.999215	−	0.0396051i	$-0.0126100\pi$
$402$	1.53004e9	+	5.71383e8i	1.17466	+	0.438668i
$403$		−	5.65335e8i		−	0.430267i
$404$	8.20325e8			0.618944
$405$	4.30430e8	−	6.11717e7i	0.321966	−	0.0457570i
$406$			3.69715e9i			2.74174i
$407$	2.81316e8	−	1.23334e9i	0.206830	−	0.906780i
$408$	−3.99899e8	−	1.49340e8i	−0.291501	−	0.108859i
$409$			2.21805e9i			1.60303i	0.597977	+	0.801513i	$0.295971\pi$
$409$			2.21805e9i			1.60303i	−0.597977	+	0.801513i	$0.704029\pi$
$410$		−	6.78737e8i		−	0.486360i
$411$	1.78072e8	−	4.76837e8i	0.126517	−	0.338785i
$412$	−2.73411e9			−1.92609
$413$	9.37342e8			0.654746
$414$	9.95879e8	−	1.14742e9i	0.689772	−	0.794732i
$415$			5.36438e8i			0.368427i
$416$			9.08867e8i			0.618976i
$417$	2.18577e7	−	5.85301e7i	0.0147614	−	0.0395278i
$418$	1.98063e9	+	4.51768e8i	1.32644	+	0.302551i
$419$			1.77010e9i			1.17557i	0.809016	+	0.587786i	$0.200000\pi$
$419$			1.77010e9i			1.17557i	−0.809016	+	0.587786i	$0.800000\pi$
$420$	−1.00442e9	−	3.75094e8i	−0.661519	−	0.247040i
$421$	−4.18994e7			−0.0273666			−0.0136833	−	0.999906i	$-0.504356\pi$
$421$	−4.18994e7			−0.0273666			−0.0136833	+	0.999906i	$0.504356\pi$
$422$			2.59831e9i			1.68305i
$423$	1.84419e9	−	2.12481e9i	1.18471	−	1.36499i
$424$			2.75456e8i			0.175498i
$425$	−9.40186e8			−0.594090
$426$	7.09409e8	−	1.89964e9i	0.444594	−	1.19052i
$427$	1.35783e9			0.844009
$428$	−3.53578e9			−2.17988
$429$	−6.15138e8	−	4.04482e8i	−0.376159	−	0.247342i
$430$	1.07782e9			0.653740
$431$	1.47449e9			0.887096			0.443548	−	0.896251i	$-0.353720\pi$
$431$	1.47449e9			0.887096			0.443548	+	0.896251i	$0.353720\pi$
$432$	4.78105e8	+	8.78130e8i	0.285319	+	0.524042i
$433$	−1.82639e9			−1.08115			−0.540575	−	0.841296i	$-0.681793\pi$
$433$	−1.82639e9			−1.08115			−0.540575	+	0.841296i	$0.681793\pi$
$434$			4.10427e9i			2.41003i
$435$	2.12365e8	−	5.68667e8i	0.123701	−	0.331242i
$436$		−	4.13514e9i		−	2.38939i
$437$	1.08205e9			0.620242
$438$	−3.20224e8	+	8.57488e8i	−0.182094	+	0.487606i
$439$			8.64064e8i			0.487439i	0.969846	+	0.243719i	$0.0783676\pi$
$439$			8.64064e8i			0.487439i	−0.969846	+	0.243719i	$0.921632\pi$
$440$	2.65348e8	+	6.05240e7i	0.148502	+	0.0338722i
$441$	−2.38678e9	−	2.07156e9i	−1.32519	−	1.15017i
$442$			8.24931e8i			0.454402i
$443$			1.93792e9i			1.05907i	0.848289	+	0.529533i	$0.177633\pi$
$443$			1.93792e9i			1.05907i	−0.848289	+	0.529533i	$0.822367\pi$
$444$	−2.10236e9	−	7.85115e8i	−1.13990	−	0.425690i
$445$	−6.45223e8			−0.347096
$446$	2.79660e9			1.49265
$447$	−1.44616e9	−	5.40060e8i	−0.765843	−	0.286000i
$448$		−	4.71353e9i		−	2.47670i
$449$		−	2.62445e9i		−	1.36828i	−0.729350	−	0.684141i	$-0.760177\pi$
$449$		−	2.62445e9i		−	1.36828i	0.729350	−	0.684141i	$-0.239823\pi$
$450$	−1.98343e9	−	1.72148e9i	−1.02606	−	0.890547i
$451$	−4.26459e8	+	1.86968e9i	−0.218907	+	0.959729i
$452$			4.69165e9i			2.38969i
$453$	1.29314e8	−	3.46273e8i	0.0653583	−	0.175015i
$454$	4.18521e9			2.09905
$455$			4.88235e8i			0.242990i
$456$	2.97100e8	−	7.95567e8i	0.146732	−	0.392916i
$457$		−	1.97630e8i		−	0.0968602i	−0.998827	−	0.0484301i	$-0.984578\pi$
$457$		−	1.97630e8i		−	0.0968602i	0.998827	−	0.0484301i	$-0.0154218\pi$
$458$	1.22065e9			0.593694
$459$	6.58157e8	+	1.20883e9i	0.317677	+	0.583473i
$460$	6.15192e8			0.294685
$461$	−2.12787e9			−1.01156			−0.505781	−	0.862662i	$-0.668795\pi$
$461$	−2.12787e9			−1.01156			−0.505781	+	0.862662i	$0.668795\pi$
$462$	4.46583e9	+	2.93649e9i	2.10696	+	1.38542i
$463$	−1.17054e9			−0.548091			−0.274045	−	0.961717i	$-0.588362\pi$
$463$	−1.17054e9			−0.548091			−0.274045	+	0.961717i	$0.588362\pi$
$464$	1.39604e9			0.648760
$465$	2.35751e8	−	6.31287e8i	0.108734	−	0.291167i
$466$	6.55002e8			0.299842
$467$			9.29267e8i			0.422213i	0.977463	+	0.211107i	$0.0677067\pi$
$467$			9.29267e8i			0.422213i	−0.977463	+	0.211107i	$0.932293\pi$
$468$	−8.56086e8	+	9.86353e8i	−0.386062	+	0.444807i
$469$			3.06026e9i			1.36979i
$470$	2.01000e9			0.893004
$471$	−2.53663e8	−	9.47292e7i	−0.111863	−	0.0417744i
$472$			4.22110e8i			0.184769i
$473$	−2.96899e9	−	6.77206e8i	−1.29002	−	0.294243i
$474$	−3.44986e8	+	9.23795e8i	−0.148791	+	0.398429i
$475$		−	1.87042e9i		−	0.800778i
$476$		−	3.39438e9i		−	1.44257i
$477$	5.82170e8	−	6.70756e8i	0.245604	−	0.282976i
$478$	−5.72034e9			−2.39565
$479$	2.34570e9			0.975209			0.487605	−	0.873065i	$-0.337871\pi$
$479$	2.34570e9			0.975209			0.487605	+	0.873065i	$0.337871\pi$
$480$	−3.79007e8	+	1.01490e9i	−0.156424	+	0.418868i
$481$			1.02193e9i			0.418711i
$482$			3.66191e8i			0.148951i
$483$	2.66691e9	+	9.95941e8i	1.07694	+	0.402178i
$484$	−2.94056e9	−	1.41506e9i	−1.17888	−	0.567304i
$485$		−	7.35527e8i		−	0.292754i
$486$	−8.24908e8	+	3.75524e9i	−0.325971	+	1.48392i
$487$	2.47213e9			0.969882			0.484941	−	0.874547i	$-0.338841\pi$
$487$	2.47213e9			0.969882			0.484941	+	0.874547i	$0.338841\pi$
$488$			6.11465e8i			0.238178i
$489$	7.31718e8	+	2.73256e8i	0.282985	+	0.105679i
$490$		−	2.25782e9i		−	0.866966i
$491$	−4.41850e9			−1.68457			−0.842287	−	0.539030i	$-0.818791\pi$
$491$	−4.41850e9			−1.68457			−0.842287	+	0.539030i	$0.818791\pi$
$492$	3.18707e9	+	1.19019e9i	1.20646	+	0.450546i
$493$	1.92178e9			0.722337
$494$	−1.64113e9			−0.612491
$495$	−5.18227e8	−	7.08187e8i	−0.192044	−	0.262440i
$496$	1.54977e9			0.570270
$497$	3.79951e9			1.38829
$498$	−4.44423e9	−	1.65967e9i	−1.61248	−	0.602171i
$499$	2.81853e9			1.01548			0.507740	−	0.861510i	$-0.330481\pi$
$499$	2.81853e9			1.01548			0.507740	+	0.861510i	$0.330481\pi$
$500$		−	2.25260e9i		−	0.805916i
$501$	2.37281e9	+	8.86113e8i	0.843008	+	0.314816i
$502$			4.07219e9i			1.43670i
$503$	1.28396e9			0.449844			0.224922	−	0.974377i	$-0.427787\pi$
$503$	1.28396e9			0.449844			0.224922	+	0.974377i	$0.427787\pi$
$504$	1.46452e9	−	1.68737e9i	0.509551	−	0.587088i
$505$		−	4.45268e8i		−	0.153852i
$506$	−2.98994e9	−	6.81983e8i	−1.02597	−	0.234017i
$507$	−2.19187e9	−	8.18540e8i	−0.746941	−	0.278941i
$508$		−	6.67411e9i		−	2.25876i
$509$		−	6.98994e8i		−	0.234942i	−0.993076	−	0.117471i	$-0.962521\pi$
$509$		−	6.98994e8i		−	0.234942i	0.993076	−	0.117471i	$-0.0374788\pi$
$510$	−3.44005e8	+	9.21168e8i	−0.114834	+	0.307499i
$511$	−1.71508e9			−0.568607
$512$	−3.34025e9			−1.09985
$513$	−2.40487e9	+	1.30935e9i	−0.786468	+	0.428199i
$514$			3.15463e9i			1.02466i
$515$			1.48406e9i			0.478769i
$516$	−1.88999e9	+	5.06098e9i	−0.605601	+	1.62166i
$517$	−5.53682e9	−	1.26291e9i	−1.76215	−	0.401934i
$518$		−	7.41911e9i		−	2.34530i
$519$	−4.55027e9	−	1.69927e9i	−1.42873	−	0.533552i
$520$	−2.19865e8			−0.0685716
$521$		−	2.63160e9i		−	0.815245i	−0.913151	−	0.407622i	$-0.866358\pi$
$521$		−	2.63160e9i		−	0.815245i	0.913151	−	0.407622i	$-0.133642\pi$
$522$	4.05421e9	+	3.51877e9i	1.24755	+	1.08279i
$523$			8.06360e8i			0.246475i	0.992377	+	0.123238i	$0.0393277\pi$
$523$			8.06360e8i			0.246475i	−0.992377	+	0.123238i	$0.960672\pi$
$524$	3.03012e9			0.920027
$525$	1.72158e9	−	4.61001e9i	0.519243	−	1.39042i
$526$	−5.98013e9			−1.79168
$527$	2.13340e9			0.634944
$528$	1.10881e9	−	1.68629e9i	0.327824	−	0.498556i
$529$	1.77138e9			0.520256
$530$	6.34513e8			0.185129
$531$	8.92118e8	−	1.02787e9i	0.258578	−	0.297925i
$532$	6.75284e9			1.94445
$533$		−	1.54919e9i		−	0.443160i
$534$	1.99624e9	−	5.34548e9i	0.567307	−	1.51912i
$535$			1.91921e9i			0.541855i
$536$	−1.37812e9			−0.386553
$537$	2.42876e8	−	6.50367e8i	0.0676822	−	0.181238i
$538$		−	9.48117e9i		−	2.62497i
$539$	−1.41861e9	+	6.21947e9i	−0.390215	+	1.71077i
$540$	−1.36728e9	+	7.44425e8i	−0.373662	+	0.203443i
$541$		−	6.85116e8i		−	0.186026i	−0.995665	−	0.0930130i	$-0.970350\pi$
$541$		−	6.85116e8i		−	0.186026i	0.995665	−	0.0930130i	$-0.0296498\pi$
$542$			4.88133e9i			1.31686i
$543$	2.14143e9	+	7.99706e8i	0.573991	+	0.214354i
$544$	−3.42979e9			−0.913421
$545$	−2.24453e9			−0.593934
$546$	−4.04489e9	−	1.51054e9i	−1.06349	−	0.397153i
$547$		−	3.43701e9i		−	0.897893i	−0.893559	−	0.448946i	$-0.851799\pi$
$547$		−	3.43701e9i		−	0.897893i	0.893559	−	0.448946i	$-0.148201\pi$
$548$			1.82267e9i			0.473124i
$549$	1.29232e9	−	1.48896e9i	0.333323	−	0.384043i
$550$	−1.17888e9	+	5.16841e9i	−0.302133	+	1.32461i
$551$			3.82323e9i			0.973643i
$552$	−4.48498e8	+	1.20098e9i	−0.113494	+	0.303912i
$553$	−1.84770e9			−0.464616
$554$		−	5.81385e9i		−	1.45271i
$555$	−4.26156e8	+	1.14115e9i	−0.105814	+	0.283346i
$556$			2.23726e8i			0.0552019i
$557$	4.55366e9			1.11652			0.558261	−	0.829665i	$-0.311469\pi$
$557$	4.55366e9			1.11652			0.558261	+	0.829665i	$0.311469\pi$
$558$	4.50064e9	+	3.90625e9i	1.09662	+	0.951788i
$559$	2.46008e9			0.595673
$560$	−1.33841e9			−0.322056
$561$	1.52639e9	−	2.32134e9i	0.365002	−	0.555097i
$562$	6.15168e9			1.46190
$563$	1.43713e9			0.339405			0.169702	−	0.985495i	$-0.445719\pi$
$563$	1.43713e9			0.339405			0.169702	+	0.985495i	$0.445719\pi$
$564$	−3.52461e9	+	9.43812e9i	−0.827246	+	2.21518i
$565$	2.54660e9			0.594007
$566$		−	2.84616e9i		−	0.659784i
$567$	−7.13242e9	+	1.01364e9i	−1.64322	+	0.233531i
$568$			1.71102e9i			0.391774i
$569$	−4.72921e9			−1.07621			−0.538103	−	0.842879i	$-0.680859\pi$
$569$	−4.72921e9			−1.07621			−0.538103	+	0.842879i	$0.680859\pi$
$570$	−1.83259e9	−	6.84370e8i	−0.414480	−	0.154785i
$571$			5.46491e9i			1.22845i	0.789132	+	0.614224i	$0.210531\pi$
$571$			5.46491e9i			1.22845i	−0.789132	+	0.614224i	$0.789469\pi$
$572$	2.57024e9	+	5.86252e8i	0.574232	+	0.130978i
$573$	−1.57414e9	+	4.21520e9i	−0.349545	+	0.936002i
$574$			1.12470e10i			2.48224i
$575$			2.82357e9i			0.619385i
$576$	−5.16875e9	−	4.48612e9i	−1.12696	−	0.978119i
$577$	1.40691e9			0.304896			0.152448	−	0.988311i	$-0.451284\pi$
$577$	1.40691e9			0.304896			0.152448	+	0.988311i	$0.451284\pi$
$578$	3.94025e9			0.848744
$579$	2.61888e9	−	7.01278e9i	0.560714	−	1.50147i
$580$			2.17368e9i			0.462591i
$581$		−	8.88902e9i		−	1.88034i
$582$	6.09363e9	+	2.27563e9i	1.28128	+	0.478488i
$583$	−1.74785e9	−	3.98673e8i	−0.365313	−	0.0833252i
$584$		−	7.72347e8i		−	0.160460i
$585$	5.35387e8	+	4.64679e8i	0.110566	+	0.0959638i
$586$	5.62245e9			1.15421
$587$			2.19542e9i			0.448007i	0.974588	+	0.224003i	$0.0719127\pi$
$587$			2.19542e9i			0.448007i	−0.974588	+	0.224003i	$0.928087\pi$
$588$	1.06018e10	+	3.95917e9i	2.15059	+	0.803125i
$589$			4.24423e9i			0.855846i
$590$	9.72329e8			0.194909
$591$	7.31470e8	+	2.73163e8i	0.145761	+	0.0544335i
$592$	−2.80145e9			−0.554953
$593$	−3.84584e9			−0.757355			−0.378677	−	0.925529i	$-0.623621\pi$
$593$	−3.84584e9			−0.757355			−0.378677	+	0.925529i	$0.623621\pi$
$594$	7.47045e9	−	2.10231e9i	1.46250	−	0.411571i
$595$	−1.84245e9			−0.358580
$596$	5.52781e9			1.06953
$597$	−5.01690e9	−	1.87353e9i	−0.964996	−	0.360372i
$598$	2.47744e9			0.473749
$599$		−	3.80221e9i		−	0.722840i	−0.932403	−	0.361420i	$-0.882292\pi$
$599$		−	3.80221e9i		−	0.722840i	0.932403	−	0.361420i	$-0.117708\pi$
$600$	2.07601e9	+	7.75274e8i	0.392374	+	0.146530i
$601$		−	2.11400e9i		−	0.397233i	−0.980077	−	0.198616i	$-0.936355\pi$
$601$		−	2.11400e9i		−	0.397233i	0.980077	−	0.198616i	$-0.0636448\pi$
$602$	−1.78599e10			−3.33650
$603$	3.35581e9	+	2.91261e9i	0.623286	+	0.540969i
$604$			1.32360e9i			0.244414i
$605$	−7.68087e8	+	1.59612e9i	−0.141015	+	0.293037i
$606$	3.68892e9	+	1.37760e9i	0.673356	+	0.251461i
$607$		−	4.49197e9i		−	0.815223i	−0.913155	−	0.407611i	$-0.866362\pi$
$607$		−	4.49197e9i		−	0.815223i	0.913155	−	0.407611i	$-0.133638\pi$
$608$		−	6.82329e9i		−	1.23121i
$609$	−3.51899e9	+	9.42307e9i	−0.631332	+	1.69056i
$610$	1.40851e9			0.251250
$611$	4.58776e9			0.813684
$612$	−3.72220e9	−	3.23061e9i	−0.656401	−	0.569711i
$613$			9.04115e8i			0.158530i	0.996854	+	0.0792651i	$0.0252574\pi$
$613$			9.04115e8i			0.158530i	−0.996854	+	0.0792651i	$0.974743\pi$
$614$			6.77458e9i			1.18112i
$615$	6.46030e8	−	1.72992e9i	0.111993	−	0.299891i
$616$	−4.39694e9	−	1.00291e9i	−0.757911	−	0.172874i
$617$			1.22475e9i			0.209918i	0.994477	+	0.104959i	$0.0334712\pi$
$617$			1.22475e9i			0.209918i	−0.994477	+	0.104959i	$0.966529\pi$
$618$	−1.22950e10	−	4.59150e9i	−2.09541	−	0.782519i
$619$	−6.43876e9			−1.09115			−0.545576	−	0.838062i	$-0.683689\pi$
$619$	−6.43876e9			−1.09115			−0.545576	+	0.838062i	$0.683689\pi$
$620$			2.41304e9i			0.406624i
$621$	3.63036e9	−	1.97658e9i	0.608316	−	0.331202i
$622$			2.96867e9i			0.494648i
$623$	1.06916e10			1.77148
$624$	−5.70377e8	+	1.52734e9i	−0.0939758	+	0.251646i
$625$	4.23533e9			0.693917
$626$	4.27202e9			0.696022
$627$	4.61812e9	+	3.03663e9i	0.748220	+	0.491989i
$628$	9.69605e8			0.156220
$629$	−3.85646e9			−0.617891
$630$	−3.88685e9	−	3.37352e9i	−0.619307	−	0.537516i
$631$	1.66316e9			0.263530			0.131765	−	0.991281i	$-0.457936\pi$
$631$	1.66316e9			0.263530			0.131765	+	0.991281i	$0.457936\pi$
$632$		−	8.32069e8i		−	0.131114i
$633$	−2.47310e9	+	6.62241e9i	−0.387551	+	1.03777i
$634$		−	1.20160e10i		−	1.87260i
$635$	−3.62267e9			−0.561463
$636$	−1.11264e9	+	2.97941e9i	−0.171497	+	0.459230i
$637$		−	5.15339e9i		−	0.789959i
$638$	2.40967e9	−	1.05645e10i	0.367355	−	1.61055i
$639$	3.61620e9	−	4.16646e9i	0.548276	−	0.631705i
$640$		−	1.92425e9i		−	0.290156i
$641$		−	2.73222e9i		−	0.409744i	−0.978789	−	0.204872i	$-0.934322\pi$
$641$		−	2.73222e9i		−	0.409744i	0.978789	−	0.204872i	$-0.0656778\pi$
$642$	−1.59001e10	−	5.93778e9i	−2.37152	−	0.885629i
$643$	1.02739e10			1.52405			0.762023	−	0.647550i	$-0.224206\pi$
$643$	1.02739e10			1.52405			0.762023	+	0.647550i	$0.224206\pi$
$644$	−1.01940e10			−1.50399
$645$	2.74707e9	+	1.02588e9i	0.403098	+	0.150535i
$646$		−	6.19314e9i		−	0.903851i
$647$			4.55706e9i			0.661485i	0.943721	+	0.330742i	$0.107299\pi$
$647$			4.55706e9i			0.661485i	−0.943721	+	0.330742i	$0.892701\pi$
$648$	−4.56469e8	−	3.21191e9i	−0.0659021	−	0.463715i
$649$	−2.67842e9	−	6.10927e8i	−0.384611	−	0.0877269i
$650$		−	4.28249e9i		−	0.611645i
$651$	−3.90649e9	+	1.04607e10i	−0.554949	+	1.48603i
$652$	−2.79692e9			−0.395197
$653$		−	3.74412e8i		−	0.0526203i	−0.999654	−	0.0263101i	$-0.991624\pi$
$653$		−	3.74412e8i		−	0.0526203i	0.999654	−	0.0263101i	$-0.00837574\pi$
$654$	6.94430e9	−	1.85953e10i	0.970748	−	2.59944i
$655$		−	1.64473e9i		−	0.228692i
$656$	4.24684e9			0.587358
$657$	−1.63233e9	+	1.88072e9i	−0.224559	+	0.258729i
$658$	−3.33066e10			−4.55763
$659$	1.99436e9			0.271459			0.135730	−	0.990746i	$-0.456662\pi$
$659$	1.99436e9			0.271459			0.135730	+	0.990746i	$0.456662\pi$
$660$	2.62561e9	+	1.72646e9i	0.355489	+	0.233751i
$661$	−3.02625e9			−0.407567			−0.203784	−	0.979016i	$-0.565324\pi$
$661$	−3.02625e9			−0.407567			−0.203784	+	0.979016i	$0.565324\pi$
$662$	1.05704e10			1.41609
$663$	−7.85179e8	+	2.10253e9i	−0.104634	+	0.280186i
$664$	4.00296e9			0.530631
$665$		−	3.66541e9i		−	0.483333i
$666$	−8.13563e9	−	7.06116e9i	−1.06716	−	0.926225i
$667$		−	5.77149e9i		−	0.753092i
$668$	−9.06985e9			−1.17729
$669$	7.12780e9	+	2.66183e9i	0.920373	+	0.343708i
$670$			3.17449e9i			0.407767i
$671$	−3.87994e9	−	8.84984e8i	−0.495788	−	0.113085i
$672$	6.28031e9	−	1.68173e10i	0.798342	−	2.13778i
$673$			7.32088e9i			0.925786i	0.886414	+	0.462893i	$0.153189\pi$
$673$			7.32088e9i			0.925786i	−0.886414	+	0.462893i	$0.846811\pi$
$674$			5.44202e9i			0.684622i
$675$	−3.41671e9	−	6.27544e9i	−0.427607	−	0.785382i
$676$	8.37820e9			1.04313
$677$	−7.83766e9			−0.970792			−0.485396	−	0.874295i	$-0.661324\pi$
$677$	−7.83766e9			−0.970792			−0.485396	+	0.874295i	$0.661324\pi$
$678$	−7.87887e9	+	2.10978e10i	−0.970867	+	2.59976i
$679$			1.21880e10i			1.49413i
$680$		−	8.29704e8i		−	0.101191i
$681$	1.06670e10	+	3.98353e9i	1.29428	+	0.483341i
$682$	2.67502e9	−	1.17278e10i	0.322910	−	1.41570i
$683$			9.04868e9i			1.08671i	0.839504	+	0.543354i	$0.182846\pi$
$683$			9.04868e9i			1.08671i	−0.839504	+	0.543354i	$0.817154\pi$
$684$	6.42703e9	−	7.40501e9i	0.767917	−	0.884768i
$685$	9.89333e8			0.117605
$686$			1.60915e10i			1.90311i
$687$	3.11112e9	+	1.16183e9i	0.366074	+	0.136708i
$688$			6.74387e9i			0.789496i
$689$	1.44826e9			0.168686
$690$	2.76645e9	+	1.03312e9i	0.320591	+	0.119723i
$691$	−3.93165e9			−0.453316			−0.226658	−	0.973974i	$-0.572780\pi$
$691$	−3.93165e9			−0.453316			−0.226658	+	0.973974i	$0.572780\pi$
$692$	1.73930e10			1.99527
$693$	8.58725e9	+	1.17350e10i	0.980139	+	1.33942i
$694$	1.80508e10			2.04992
$695$	1.21437e8			0.0137216
$696$	−4.24345e9	−	1.58469e9i	−0.477075	−	0.178161i
$697$	5.84619e9			0.653970
$698$			1.38791e10i			1.54479i
$699$	1.66943e9	+	6.23439e8i	0.184883	+	0.0690437i
$700$			1.76213e10i			1.94176i
$701$	5.21221e9			0.571490			0.285745	−	0.958306i	$-0.407759\pi$
$701$	5.21221e9			0.571490			0.285745	+	0.958306i	$0.407759\pi$
$702$	−5.50615e9	+	2.99787e9i	−0.600715	+	0.327064i
$703$		−	7.67212e9i		−	0.832859i
$704$	−3.07211e9	+	1.34687e10i	−0.331843	+	1.45486i
$705$	5.12296e9	+	1.91314e9i	0.550629	+	0.205629i
$706$		−	1.10436e10i		−	1.18112i
$707$			7.37829e9i			0.785214i
$708$	−1.70502e9	+	4.56566e9i	−0.180556	+	0.483489i
$709$	−7.80610e8			−0.0822569			−0.0411285	−	0.999154i	$-0.513095\pi$
$709$	−7.80610e8			−0.0822569			−0.0411285	+	0.999154i	$0.513095\pi$
$710$	3.94134e9			0.413275
$711$	−1.75856e9	+	2.02615e9i	−0.183490	+	0.211411i
$712$			4.81472e9i			0.499909i
$713$		−	6.40703e9i		−	0.661978i
$714$	5.70031e9	−	1.52642e10i	0.586077	−	1.56938i
$715$	3.18215e8	−	1.39511e9i	0.0325574	−	0.142737i
$716$			2.48597e9i			0.253105i
$717$	−1.45797e10	−	5.44469e9i	−1.47717	−	0.551640i
$718$	2.08693e10			2.10413
$719$		−	1.70514e10i		−	1.71084i	−0.517936	−	0.855419i	$-0.673300\pi$
$719$		−	1.70514e10i		−	1.71084i	0.517936	−	0.855419i	$-0.326700\pi$
$720$	−1.27384e9	+	1.46767e9i	−0.127189	+	0.146543i
$721$		−	2.45915e10i		−	2.44350i
$722$	−3.04397e9			−0.300996
$723$	−3.48545e8	+	9.33326e8i	−0.0342985	+	0.0918437i
$724$	−8.18543e9			−0.801598
$725$	−9.97660e9			−0.972298
$726$	−1.08470e10	−	1.13016e10i	−1.05204	−	1.09613i
$727$	−1.69760e10			−1.63857			−0.819285	−	0.573386i	$-0.805630\pi$
$727$	−1.69760e10			−1.63857			−0.819285	+	0.573386i	$0.805630\pi$
$728$	3.64326e9			0.349970
$729$	−5.67676e9	+	8.78598e9i	−0.542693	+	0.839931i
$730$	−1.77910e9			−0.169266
$731$			9.28358e9i			0.879032i
$732$	−2.46988e9	+	6.61378e9i	−0.232748	+	0.623248i
$733$			2.18459e7i			0.00204883i	0.999999	+	0.00102442i	$0.000326082\pi$
$733$			2.18459e7i			0.00204883i	−0.999999	+	0.00102442i	$0.999674\pi$
$734$	−5.13209e9			−0.479025
$735$	2.14902e9	−	5.75458e9i	0.199634	−	0.534574i
$736$			1.03003e10i			0.952312i
$737$	1.99457e9	−	8.74458e9i	0.183533	−	0.804642i
$738$	1.23332e10	+	1.07043e10i	1.12948	+	0.980308i
$739$		−	3.00892e9i		−	0.274256i	−0.990553	−	0.137128i	$-0.956213\pi$
$739$		−	3.00892e9i		−	0.274256i	0.990553	−	0.137128i	$-0.0437871\pi$
$740$		−	4.36194e9i		−	0.395703i
$741$	−4.18282e9	−	1.56205e9i	−0.377664	−	0.141036i
$742$	−1.05142e10			−0.944846
$743$	4.99839e9			0.447063			0.223532	−	0.974697i	$-0.428241\pi$
$743$	4.99839e9			0.447063			0.223532	+	0.974697i	$0.428241\pi$
$744$	−4.71073e9	−	1.75919e9i	−0.419356	−	0.156606i
$745$		−	3.00047e9i		−	0.265853i
$746$			2.84150e10i			2.50589i
$747$	−9.74749e9	−	8.46014e9i	−0.855600	−	0.742601i
$748$	−2.21234e9	+	9.69929e9i	−0.193284	+	0.847392i
$749$		−	3.18021e10i		−	2.76547i
$750$	3.78288e9	−	1.01297e10i	0.327423	−	0.876764i
$751$	−9.37269e9			−0.807467			−0.403733	−	0.914877i	$-0.632288\pi$
$751$	−9.37269e9			−0.807467			−0.403733	+	0.914877i	$0.632288\pi$
$752$			1.25765e10i			1.07844i
$753$	−3.87596e9	+	1.03790e10i	−0.330824	+	0.885872i
$754$			8.75360e9i			0.743681i
$755$	7.18440e8			0.0607542
$756$	2.26564e10	−	1.23354e10i	1.90706	−	1.03831i
$757$	−3.29570e9			−0.276129			−0.138064	−	0.990423i	$-0.544088\pi$
$757$	−3.29570e9			−0.276129			−0.138064	+	0.990423i	$0.544088\pi$
$758$	2.69133e9			0.224452
$759$	−6.97146e9	−	4.58406e9i	−0.578732	−	0.380543i
$760$	1.65063e9			0.136396
$761$	7.79377e9			0.641064			0.320532	−	0.947238i	$-0.396138\pi$
$761$	7.79377e9			0.641064			0.320532	+	0.947238i	$0.396138\pi$
$762$	1.12081e10	−	3.00128e10i	0.917677	−	2.45733i
$763$	3.71929e10			3.03126
$764$		−	1.61122e10i		−	1.30716i
$765$	−1.75356e9	+	2.02039e9i	−0.141614	+	0.163162i
$766$		−	2.07451e10i		−	1.66769i
$767$	2.21931e9			0.177596
$768$	−1.60705e9	−	6.00143e8i	−0.128016	−	0.0478069i
$769$			1.81737e10i			1.44112i	0.693392	+	0.720560i	$0.256115\pi$
$769$			1.81737e10i			1.44112i	−0.693392	+	0.720560i	$0.743885\pi$
$770$	−2.31020e9	+	1.01284e10i	−0.182361	+	0.799505i
$771$	−3.00262e9	+	8.04033e9i	−0.235944	+	0.631806i
$772$			2.68057e10i			2.09685i
$773$		−	6.21890e9i		−	0.484268i	−0.970243	−	0.242134i	$-0.922153\pi$
$773$		−	6.21890e9i		−	0.484268i	0.970243	−	0.242134i	$-0.0778473\pi$
$774$	−1.69982e10	+	1.95847e10i	−1.31768	+	1.51818i
$775$	−1.10752e10			−0.854664
$776$	−5.48858e9			−0.421642
$777$	7.06160e9	−	1.89094e10i	0.540045	−	1.44612i
$778$			1.44615e9i			0.110099i
$779$			1.16305e10i			0.881491i
$780$	−2.37812e9	−	8.88096e8i	−0.179433	−	0.0670083i
$781$	−1.08570e10	−	2.47639e9i	−0.815510	−	0.186012i
$782$			9.34908e9i			0.699110i
$783$	6.98391e9	+	1.28273e10i	0.519915	+	0.954922i
$784$	1.41271e10			1.04700
$785$		−	5.26296e8i		−	0.0388317i
$786$	1.36261e10	+	5.08860e9i	1.00091	+	0.373783i
$787$			1.00229e9i			0.0732965i	0.999328	+	0.0366482i	$0.0116681\pi$
$787$			1.00229e9i			0.0732965i	−0.999328	+	0.0366482i	$0.988332\pi$
$788$	−2.79598e9			−0.203560
$789$	−1.52418e10	−	5.69195e9i	−1.10476	−	0.412565i
$790$	−1.91667e9			−0.138310
$791$	−4.21983e10			−3.03164
$792$	−5.28457e9	+	3.86706e9i	−0.377982	+	0.276594i
$793$	3.21488e9			0.228933
$794$	−4.73331e9			−0.335578
$795$	1.61721e9	+	6.03937e8i	0.114151	+	0.0426292i
$796$	1.91766e10			1.34765
$797$		−	1.31177e10i		−	0.917814i	−0.888484	−	0.458907i	$-0.848241\pi$
$797$		−	1.31177e10i		−	0.917814i	0.888484	−	0.458907i	$-0.151759\pi$
$798$	3.03668e10	+	1.13403e10i	2.11538	+	0.789978i
$799$			1.73128e10i			1.20075i
$800$	1.78052e10			1.22951
$801$	1.01758e10	−	1.17242e10i	0.699607	−	0.806063i
$802$			1.75807e9i			0.120344i
$803$	4.90078e9	+	1.11783e9i	0.334011	+	0.0761854i
$804$	−1.49061e10	−	5.56660e9i	−1.01150	−	0.377740i
$805$			5.53325e9i			0.373848i
$806$			9.71752e9i			0.653706i
$807$	9.02429e9	−	2.41650e10i	0.604443	−	1.61856i
$808$	−3.32264e9			−0.221586
$809$	2.43034e10			1.61379			0.806895	−	0.590695i	$-0.201146\pi$
$809$	2.43034e10			1.61379			0.806895	+	0.590695i	$0.201146\pi$
$810$	−7.39864e9	+	1.05148e9i	−0.489164	+	0.0695188i
$811$		−	1.74656e10i		−	1.14977i	−0.818234	−	0.574886i	$-0.805046\pi$
$811$		−	1.74656e10i		−	1.14977i	0.818234	−	0.574886i	$-0.194954\pi$
$812$		−	3.60188e10i		−	2.36093i
$813$	−4.64611e9	+	1.24412e10i	−0.303230	+	0.811982i
$814$	−4.83552e9	+	2.11998e10i	−0.314237	+	1.37767i
$815$			1.51815e9i			0.0982346i
$816$	−5.76372e9	−	2.15243e9i	−0.371354	−	0.138680i
$817$	−1.84689e10			−1.18485
$818$		−	3.81260e10i		−	2.43548i
$819$	−8.87161e9	−	7.69994e9i	−0.564298	−	0.489772i
$820$			6.61247e9i			0.418808i
$821$	−6.87118e9			−0.433341			−0.216671	−	0.976245i	$-0.569520\pi$
$821$	−6.87118e9			−0.433341			−0.216671	+	0.976245i	$0.569520\pi$
$822$	−3.06087e9	+	8.19633e9i	−0.192218	+	0.514717i
$823$	1.42413e9			0.0890534			0.0445267	−	0.999008i	$-0.485822\pi$
$823$	1.42413e9			0.0890534			0.0445267	+	0.999008i	$0.485822\pi$
$824$	1.10742e10			0.689553
$825$	−7.92400e9	+	1.20509e10i	−0.491310	+	0.747186i
$826$	−1.61119e10			−0.994758
$827$	−5.57924e9			−0.343009			−0.171505	−	0.985183i	$-0.554863\pi$
$827$	−5.57924e9			−0.343009			−0.171505	+	0.985183i	$0.554863\pi$
$828$	−9.70217e9	+	1.11785e10i	−0.593967	+	0.684349i
$829$	−2.23224e10			−1.36082			−0.680408	−	0.732834i	$-0.738197\pi$
$829$	−2.23224e10			−1.36082			−0.680408	+	0.732834i	$0.738197\pi$
$830$		−	9.22081e9i		−	0.559752i
$831$	5.53369e9	−	1.48180e10i	0.334512	−	0.895748i
$832$		−	1.11600e10i		−	0.671791i
$833$	1.94473e10			1.16574
$834$	−3.75712e8	+	1.00607e9i	−0.0224271	+	0.0600548i
$835$			4.92307e9i			0.292640i
$836$	−1.92960e10	−	4.40127e9i	−1.14221	−	0.260529i
$837$	7.75295e9	+	1.42398e10i	0.457013	+	0.839390i
$838$		−	3.04262e10i		−	1.78605i
$839$		−	7.88538e9i		−	0.460952i	−0.973078	−	0.230476i	$-0.925972\pi$
$839$		−	7.88538e9i		−	0.460952i	0.973078	−	0.230476i	$-0.0740283\pi$
$840$	4.06828e9	+	1.51928e9i	0.236828	+	0.0884422i
$841$	3.14273e9			0.182188
$842$	7.20206e8			0.0415781
$843$	1.56790e10	+	5.85525e9i	0.901411	+	0.336627i
$844$		−	2.53135e10i		−	1.44929i
$845$		−	4.54764e9i		−	0.259291i
$846$	−3.16996e10	+	3.65232e10i	−1.79994	+	2.07383i
$847$	1.27275e10	−	2.64484e10i	0.719702	−	1.49557i
$848$			3.97013e9i			0.223573i
$849$	2.70901e9	−	7.25411e9i	0.151926	−	0.406825i
$850$	1.61608e10			0.902603
$851$			1.15817e10i			0.644199i
$852$	−6.91129e9	+	1.85069e10i	−0.382843	+	1.02517i
$853$		−	2.40175e9i		−	0.132497i	−0.997803	−	0.0662485i	$-0.978897\pi$
$853$		−	2.40175e9i		−	0.132497i	0.997803	−	0.0662485i	$-0.0211030\pi$
$854$	−2.33396e10			−1.28231
$855$	−4.01940e9	−	3.48856e9i	−0.219928	−	0.190882i
$856$	1.43213e10			0.780413
$857$	−2.70670e10			−1.46895			−0.734476	−	0.678635i	$-0.762572\pi$
$857$	−2.70670e10			−1.46895			−0.734476	+	0.678635i	$0.762572\pi$
$858$	1.05736e10	+	6.95262e9i	0.571500	+	0.375788i
$859$	1.53100e10			0.824137			0.412068	−	0.911153i	$-0.364806\pi$
$859$	1.53100e10			0.824137			0.412068	+	0.911153i	$0.364806\pi$
$860$	−1.05004e10			−0.562940
$861$	−1.07050e10	+	2.86656e10i	−0.571579	+	1.53056i
$862$	−2.53449e10			−1.34777
$863$			6.06233e9i			0.321071i	0.987030	+	0.160536i	$0.0513222\pi$
$863$			6.06233e9i			0.321071i	−0.987030	+	0.160536i	$0.948678\pi$
$864$	−1.24641e10	−	2.28927e10i	−0.657452	−	1.20753i
$865$		−	9.44081e9i		−	0.495967i
$866$	3.13937e10			1.64259
$867$	1.00427e10	+	3.75038e9i	0.523339	+	0.195438i
$868$		−	3.99851e10i		−	2.07529i
$869$	5.27974e9	+	1.20427e9i	0.272925	+	0.0622521i
$870$	−3.65034e9	+	9.77479e9i	−0.187939	+	0.503257i
$871$			7.24567e9i			0.371548i
$872$			1.67489e10i			0.855419i
$873$	1.33651e10	+	1.16000e10i	0.679864	+	0.590075i
$874$	−1.85992e10			−0.942335
$875$	2.02607e10			1.02241
$876$	3.11972e9	−	8.35392e9i	0.156802	−	0.419881i
$877$			3.16536e10i			1.58462i	0.610120	+	0.792309i	$0.291121\pi$
$877$			3.16536e10i			1.58462i	−0.610120	+	0.792309i	$0.708879\pi$
$878$		−	1.48524e10i		−	0.740567i
$879$	1.43301e10	+	5.35151e9i	0.711688	+	0.265776i
$880$	3.82445e9	+	8.72329e8i	0.189182	+	0.0431510i
$881$			1.48267e10i			0.730513i	0.930907	+	0.365256i	$0.119019\pi$
$881$			1.48267e10i			0.730513i	−0.930907	+	0.365256i	$0.880981\pi$
$882$	4.10262e10	+	3.56079e10i	2.01336	+	1.74746i
$883$	−1.66978e10			−0.816201			−0.408100	−	0.912937i	$-0.633809\pi$
$883$	−1.66978e10			−0.816201			−0.408100	+	0.912937i	$0.633809\pi$
$884$		−	8.03674e9i		−	0.391288i
$885$	2.47821e9	+	9.25475e8i	0.120181	+	0.0448811i
$886$		−	3.33108e10i		−	1.60904i
$887$	−6.88613e9			−0.331316			−0.165658	−	0.986183i	$-0.552975\pi$
$887$	−6.88613e9			−0.331316			−0.165658	+	0.986183i	$0.552975\pi$
$888$	8.51539e9	+	3.18002e9i	0.408093	+	0.152400i
$889$	6.00293e10			2.86554
$890$	1.10907e10			0.527344
$891$	2.10412e10	+	1.75222e9i	0.996551	+	0.0829883i
$892$	−2.72453e10			−1.28533
$893$	−3.44424e10			−1.61850
$894$	2.48580e10	+	9.28307e9i	1.16355	+	0.434520i
$895$	1.34937e9			0.0629145
$896$			3.18857e10i			1.48087i
$897$	6.31433e9	+	2.35805e9i	0.292115	+	0.109089i
$898$			4.51115e10i			2.07884i
$899$	2.26382e10			1.03916
$900$	1.93231e10	+	1.67712e10i	0.883546	+	0.766857i
$901$			5.46527e9i			0.248929i
$902$	7.33039e9	−	3.21378e10i	0.332586	−	1.45812i
$903$	−4.55202e10	−	1.69993e10i	−2.05730	−	0.768286i
$904$		−	1.90030e10i		−	0.855525i
$905$			4.44301e9i			0.199254i
$906$	−2.22277e9	+	5.95207e9i	−0.0992990	+	0.265901i
$907$	2.35867e9			0.104964			0.0524822	−	0.998622i	$-0.483287\pi$
$907$	2.35867e9			0.104964			0.0524822	+	0.998622i	$0.483287\pi$
$908$	−4.07736e10			−1.80750
$909$	8.09086e9	+	7.02231e9i	0.357290	+	0.310103i
$910$		−	8.39225e9i		−	0.369176i
$911$		−	2.01599e10i		−	0.883433i	−0.897155	−	0.441716i	$-0.854370\pi$
$911$		−	2.01599e10i		−	0.883433i	0.897155	−	0.441716i	$-0.145630\pi$
$912$	4.28209e9	−	1.14665e10i	0.186928	−	0.500550i
$913$	−5.79355e9	+	2.54000e10i	−0.251940	+	1.10455i
$914$			3.39705e9i			0.147160i
$915$	3.58992e9	+	1.34064e9i	0.154921	+	0.0578545i
$916$	−1.18920e10			−0.511234
$917$			2.72540e10i			1.16718i
$918$	−1.13130e10	−	2.07785e10i	−0.482647	−	0.886473i
$919$			3.33135e10i			1.41585i	0.706289	+	0.707923i	$0.250368\pi$
$919$			3.33135e10i			1.41585i	−0.706289	+	0.707923i	$0.749632\pi$
$920$	−2.49177e9			−0.105499
$921$	−6.44813e9	+	1.72666e10i	−0.271972	+	0.728281i
$922$	3.65759e10			1.53687
$923$	8.99596e9			0.376567
$924$	−4.35075e10	−	2.86082e10i	−1.81431	−	1.19300i
$925$	2.00202e10			0.831709
$926$	2.01204e10			0.832716
$927$	−2.69665e10	−	2.34051e10i	−1.11185	−	0.965008i
$928$	−3.63945e10			−1.49492
$929$			3.78936e10i			1.55064i	0.631568	+	0.775320i	$0.282412\pi$
$929$			3.78936e10i			1.55064i	−0.631568	+	0.775320i	$0.717588\pi$
$930$	−4.05231e9	+	1.08512e10i	−0.165201	+	0.442370i
$931$			3.86888e10i			1.57131i
$932$	−6.38124e9			−0.258196
$933$	−2.82562e9	+	7.56637e9i	−0.113901	+	0.305001i
$934$		−	1.59731e10i		−	0.641470i
$935$	5.26473e9	+	1.20084e9i	0.210637	+	0.0480448i
$936$	3.46748e9	−	3.99512e9i	0.138213	−	0.159244i
$937$		−	2.43061e10i		−	0.965221i	−0.875835	−	0.482611i	$-0.839689\pi$
$937$		−	2.43061e10i		−	0.965221i	0.875835	−	0.482611i	$-0.160311\pi$
$938$		−	5.26027e10i		−	2.08113i
$939$	1.08883e10	+	4.06616e9i	0.429170	+	0.160271i
$940$	−1.95820e10			−0.768972
$941$	3.55368e10			1.39032			0.695160	−	0.718855i	$-0.255334\pi$
$941$	3.55368e10			1.39032			0.695160	+	0.718855i	$0.255334\pi$
$942$	4.36021e9	+	1.62830e9i	0.169953	+	0.0634680i
$943$		−	1.75573e10i		−	0.681815i
$944$			6.08384e9i			0.235383i
$945$	−6.69561e9	−	1.22978e10i	−0.258095	−	0.474040i
$946$	5.10339e10	+	1.16405e10i	1.95993	+	0.447045i
$947$			1.39578e10i			0.534061i	0.963688	+	0.267031i	$0.0860425\pi$
$947$			1.39578e10i			0.534061i	−0.963688	+	0.267031i	$0.913957\pi$
$948$	3.36096e9	−	8.99990e9i	0.128125	−	0.343090i
$949$	−4.06074e9			−0.154231
$950$			3.21506e10i			1.21663i
$951$	1.14369e10	−	3.06255e10i	0.431199	−	1.15465i
$952$			1.37486e10i			0.516449i
$953$	−1.58704e10			−0.593968			−0.296984	−	0.954882i	$-0.595981\pi$
$953$	−1.58704e10			−0.593968			−0.296984	+	0.954882i	$0.595981\pi$
$954$	−1.00069e10	+	1.15296e10i	−0.373147	+	0.429927i
$955$	−8.74562e9			−0.324922
$956$	5.57293e10			2.06291
$957$	1.61970e10	−	2.46325e10i	0.597369	−	0.908482i
$958$	−4.03201e10			−1.48164
$959$	−1.63937e10			−0.600221
$960$	4.65385e9	−	1.24620e10i	0.169771	−	0.454609i
$961$	−2.38159e9			−0.0865637
$962$		−	1.75660e10i		−	0.636149i
$963$	−3.48734e10	−	3.02677e10i	−1.25835	−	1.09216i
$964$		−	3.56755e9i		−	0.128263i
$965$	1.45500e10			0.521215
$966$	−4.58413e10	−	1.71192e10i	−1.63620	−	0.611031i
$967$			1.26468e10i			0.449767i	0.974386	+	0.224884i	$0.0722002\pi$
$967$			1.26468e10i			0.449767i	−0.974386	+	0.224884i	$0.927800\pi$
$968$	1.19104e10	+	5.73155e9i	0.422049	+	0.203099i
$969$	5.89470e9	−	1.57847e10i	0.208127	−	0.557318i
$970$			1.26429e10i			0.444782i
$971$			4.37988e10i			1.53531i	0.640866	+	0.767653i	$0.278575\pi$
$971$			4.37988e10i			1.53531i	−0.640866	+	0.767653i	$0.721425\pi$
$972$	8.03651e9	−	3.65848e10i	0.280696	−	1.27782i
$973$	−2.01227e9			−0.0700311
$974$	−4.24932e10			−1.47355
$975$	4.07613e9	−	1.09149e10i	0.140842	−	0.377143i
$976$			8.81301e9i			0.303424i
$977$		−	1.33767e10i		−	0.458899i	−0.973321	−	0.229450i	$-0.926307\pi$
$977$		−	1.33767e10i		−	0.458899i	0.973321	−	0.229450i	$-0.0736926\pi$
$978$	−1.25775e10	−	4.69698e9i	−0.429939	−	0.160558i
$979$	−3.05509e10	−	6.96843e9i	−1.04060	−	0.237353i
$980$			2.19963e10i			0.746551i
$981$	3.53984e10	−	4.07848e10i	1.19713	−	1.37930i
$982$	7.59494e10			2.55938
$983$		−	3.86027e10i		−	1.29623i	−0.761544	−	0.648113i	$-0.775559\pi$
$983$		−	3.86027e10i		−	1.29623i	0.761544	−	0.648113i	$-0.224441\pi$
$984$	−1.29089e10	−	4.82074e9i	−0.431922	−	0.161299i
$985$			1.51764e9i			0.0505990i
$986$	−3.30334e10			−1.09745
$987$	−8.48898e10	−	3.17016e10i	−2.81025	−	1.04947i
$988$	1.59884e10			0.527420
$989$	2.78805e10			0.916459
$990$	8.90778e9	+	1.21730e10i	0.291774	+	0.398726i
$991$	4.44473e9			0.145073			0.0725366	−	0.997366i	$-0.476891\pi$
$991$	4.44473e9			0.145073			0.0725366	+	0.997366i	$0.476891\pi$
$992$	−4.04022e10			−1.31406
$993$	2.69412e10	+	1.00611e10i	0.873163	+	0.326078i
$994$	−6.53097e10			−2.10924
$995$		−	1.04090e10i		−	0.334987i
$996$	4.32971e10	+	1.61690e10i	1.38852	+	0.518533i
$997$		−	5.59898e10i		−	1.78927i	−0.446799	−	0.894634i	$-0.647436\pi$
$997$		−	5.59898e10i		−	1.78927i	0.446799	−	0.894634i	$-0.352564\pi$
$998$	−4.84477e10			−1.54282
$999$	−1.40147e10	−	2.57406e10i	−0.444738	−	0.816846i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.8.d.b.32.3	✓	24
3.2	odd	2	inner	33.8.d.b.32.22	yes	24
11.10	odd	2	inner	33.8.d.b.32.21	yes	24
33.32	even	2	inner	33.8.d.b.32.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.8.d.b.32.3	✓	24	1.1	even	1	trivial
33.8.d.b.32.4	yes	24	33.32	even	2	inner
33.8.d.b.32.21	yes	24	11.10	odd	2	inner
33.8.d.b.32.22	yes	24	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	33.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-17.1890 q^{2} +(-43.8101 - 16.3606i) q^{3} +167.460 q^{4} -90.8965i q^{5} +(753.051 + 281.222i) q^{6} +1506.19i q^{7} -678.279 q^{8} +(1651.66 + 1433.52i) q^{9} +1562.42i q^{10} +(981.685 - 4303.89i) q^{11} +(-7336.45 - 2739.76i) q^{12} +3566.16i q^{13} -25889.9i q^{14} +(-1487.13 + 3982.19i) q^{15} -9775.99 q^{16} -13457.6 q^{17} +(-28390.3 - 24640.8i) q^{18} -26772.8i q^{19} -15221.5i q^{20} +(24642.3 - 65986.6i) q^{21} +(-16874.1 + 73979.4i) q^{22} +40415.9i q^{23} +(29715.5 + 11097.1i) q^{24} +69862.8 q^{25} -61298.6i q^{26} +(-48906.0 - 89825.1i) q^{27} +252228. i q^{28} -142803. q^{29} +(25562.1 - 68449.7i) q^{30} -158528. q^{31} +254859. q^{32} +(-113422. + 172493. i) q^{33} +231322. q^{34} +136908. q^{35} +(276587. + 240058. i) q^{36} +286564. q^{37} +460197. i q^{38} +(58344.7 - 156234. i) q^{39} +61653.2i q^{40} -434415. q^{41} +(-423576. + 1.13424e6i) q^{42} -689840. i q^{43} +(164393. - 720730. i) q^{44} +(130302. - 150130. i) q^{45} -694707. i q^{46} -1.28647e6i q^{47} +(428288. + 159942. i) q^{48} -1.44508e6 q^{49} -1.20087e6 q^{50} +(589579. + 220175. i) q^{51} +597190. i q^{52} -406111. i q^{53} +(840643. + 1.54400e6i) q^{54} +(-391208. - 89231.7i) q^{55} -1.02162e6i q^{56} +(-438020. + 1.17292e6i) q^{57} +2.45463e6 q^{58} -622324. i q^{59} +(-249034. + 666858. i) q^{60} -901495. i q^{61} +2.72492e6 q^{62} +(-2.15917e6 + 2.48772e6i) q^{63} -3.12943e6 q^{64} +324151. q^{65} +(1.94961e6 - 2.96497e6i) q^{66} +2.03178e6 q^{67} -2.25361e6 q^{68} +(661230. - 1.77063e6i) q^{69} -2.35330e6 q^{70} -2.52259e6i q^{71} +(-1.12029e6 - 972330. i) q^{72} +1.13869e6i q^{73} -4.92573e6 q^{74} +(-3.06070e6 - 1.14300e6i) q^{75} -4.48338e6i q^{76} +(6.48250e6 + 1.47861e6i) q^{77} +(-1.00288e6 + 2.68550e6i) q^{78} +1.22674e6i q^{79} +888604. i q^{80} +(672982. + 4.73539e6i) q^{81} +7.46715e6 q^{82} -5.90164e6 q^{83} +(4.12661e6 - 1.10501e7i) q^{84} +1.22325e6i q^{85} +1.18576e7i q^{86} +(6.25621e6 + 2.33634e6i) q^{87} +(-665856. + 2.91924e6i) q^{88} -7.09843e6i q^{89} +(-2.23976e6 + 2.58058e6i) q^{90} -5.37133e6 q^{91} +6.76805e6i q^{92} +(6.94512e6 + 2.59362e6i) q^{93} +2.21131e7i q^{94} -2.43355e6 q^{95} +(-1.11654e7 - 4.16966e6i) q^{96} +8.09192e6 q^{97} +2.48394e7 q^{98} +(7.79114e6 - 5.70128e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 120 q^{3} + 1788 q^{4} - 5940 q^{9} - 6936 q^{12} + 23160 q^{15} + 5844 q^{16} - 17556 q^{22} - 34704 q^{25} + 7560 q^{27} + 131328 q^{31} + 28644 q^{33} - 436080 q^{34} - 302832 q^{36} + 1072488 q^{37}+ \cdots + 53650080 q^{99}+O(q^{100}) \) 24 * q + 120 * q^3 + 1788 * q^4 - 5940 * q^9 - 6936 * q^12 + 23160 * q^15 + 5844 * q^16 - 17556 * q^22 - 34704 * q^25 + 7560 * q^27 + 131328 * q^31 + 28644 * q^33 - 436080 * q^34 - 302832 * q^36 + 1072488 * q^37 - 100296 * q^42 - 1854252 * q^45 + 3172548 * q^48 - 1169304 * q^49 - 4401936 * q^55 - 2920440 * q^58 + 1981452 * q^60 + 14578596 * q^64 + 2895156 * q^66 + 7729200 * q^67 - 4614108 * q^69 - 6924504 * q^70 - 4375800 * q^75 - 26237448 * q^78 + 22367340 * q^81 - 23600232 * q^82 - 25179660 * q^88 + 9380640 * q^91 + 25396908 * q^93 + 72948360 * q^97 + 53650080 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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