LMFDB - Embedded newform 429.2.bs.a.349.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [429,2,Mod(7,429)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(429, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([0, 42, 55])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("429.7"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bs (of order $60$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [224,0,-28] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$14$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			349.14
Character	$\chi$	$=$	429.349
Dual form			429.2.bs.a.370.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.31335 - 0.888012i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(3.07673 - 2.77030i) q^{4} +(-0.569220 - 3.59392i) q^{5} +(-0.888012 + 2.31335i) q^{6} +(-0.0796919 + 1.52061i) q^{7} +(2.40758 - 4.72514i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(-4.50825 - 7.80851i) q^{10} +(1.22542 - 3.08194i) q^{11} +4.14015i q^{12} +(-0.672825 + 3.54222i) q^{13} +(1.16597 + 3.58847i) q^{14} +(3.05168 + 1.98179i) q^{15} +(0.508066 - 4.83393i) q^{16} +(0.760974 - 0.338807i) q^{17} +(-1.12496 - 2.20785i) q^{18} +(-1.21707 + 0.790378i) q^{19} +(-11.7076 - 9.48061i) q^{20} +(-1.07671 - 1.07671i) q^{21} +(0.0980370 - 8.21779i) q^{22} +(4.79612 - 2.76904i) q^{23} +(1.90048 + 4.95092i) q^{24} +(-7.83694 + 2.54638i) q^{25} +(1.58905 + 8.79187i) q^{26} +(0.809017 + 0.587785i) q^{27} +(3.96736 + 4.89929i) q^{28} +(1.67365 + 7.87389i) q^{29} +(8.81946 + 1.87463i) q^{30} +(2.65472 + 0.420467i) q^{31} +(-0.372136 - 1.38883i) q^{32} +(1.47036 + 2.97289i) q^{33} +(1.45953 - 1.45953i) q^{34} +(5.51031 - 0.579157i) q^{35} +(-3.07673 - 2.77030i) q^{36} +(-0.299601 + 0.461346i) q^{37} +(-2.11365 + 2.90920i) q^{38} +(-2.18217 - 2.87021i) q^{39} +(-18.3522 - 5.96300i) q^{40} +(0.310875 + 5.93186i) q^{41} +(-3.44694 - 1.53468i) q^{42} +(-1.22704 + 2.12529i) q^{43} +(-4.76760 - 12.8771i) q^{44} +(-3.51473 + 0.941769i) q^{45} +(8.63616 - 10.6648i) q^{46} +(-8.93000 - 4.55006i) q^{47} +(3.25235 + 3.61210i) q^{48} +(4.65574 + 0.489338i) q^{49} +(-15.8684 + 12.8500i) q^{50} +(-0.257408 + 0.792220i) q^{51} +(7.74291 + 12.7624i) q^{52} +(3.56475 - 2.58994i) q^{53} +(2.39350 + 0.641336i) q^{54} +(-11.7738 - 2.64977i) q^{55} +(6.99324 + 4.03755i) q^{56} +(0.227017 - 1.43333i) q^{57} +(10.8638 + 16.7288i) q^{58} +(-10.8155 - 0.566816i) q^{59} +(14.8794 - 2.35666i) q^{60} +(4.43970 + 9.97172i) q^{61} +(6.51468 - 1.38474i) q^{62} +(1.52061 - 0.0796919i) q^{63} +(3.61975 + 4.98215i) q^{64} +(13.1134 + 0.401775i) q^{65} +(6.04141 + 5.57163i) q^{66} +(1.46898 - 5.48229i) q^{67} +(1.40271 - 3.15055i) q^{68} +(-1.15143 + 5.41706i) q^{69} +(12.2330 - 6.23302i) q^{70} +(1.22442 + 0.470012i) q^{71} +(-4.95092 - 1.90048i) q^{72} +(-12.6472 + 6.44410i) q^{73} +(-0.283402 + 1.33330i) q^{74} +(3.35161 - 7.52784i) q^{75} +(-1.55503 + 5.80345i) q^{76} +(4.58877 + 2.10900i) q^{77} +(-7.59691 - 4.70201i) q^{78} +(-8.29617 - 11.4187i) q^{79} +(-17.6619 + 0.925623i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(5.98672 + 13.4464i) q^{82} +(-3.06953 + 0.486166i) q^{83} +(-6.29556 - 0.329936i) q^{84} +(-1.65081 - 2.54202i) q^{85} +(-0.951284 + 6.00617i) q^{86} +(-6.97133 - 4.02490i) q^{87} +(-11.6123 - 13.2103i) q^{88} +(3.02281 + 0.809960i) q^{89} +(-7.29449 + 5.29976i) q^{90} +(-5.33272 - 1.30539i) q^{91} +(7.08529 - 21.8063i) q^{92} +(-2.08882 + 1.69150i) q^{93} +(-24.6987 - 2.59594i) q^{94} +(3.53333 + 3.92417i) q^{95} +(1.28111 + 0.652758i) q^{96} +(11.7354 - 14.4921i) q^{97} +(11.2049 - 3.00235i) q^{98} +(-3.19315 - 0.896560i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 28 q^{3} - 6 q^{5} + 28 q^{9} - 16 q^{11} - 10 q^{13} - 36 q^{14} + 8 q^{15} - 24 q^{16} + 50 q^{20} + 10 q^{22} - 48 q^{23} - 30 q^{24} + 10 q^{26} + 56 q^{27} + 20 q^{29} + 12 q^{31} - 32 q^{33}+ \cdots - 6 q^{99}+O(q^{100}) $ 224 * q - 28 * q^3 - 6 * q^5 + 28 * q^9 - 16 * q^11 - 10 * q^13 - 36 * q^14 + 8 * q^15 - 24 * q^16 + 50 * q^20 + 10 * q^22 - 48 * q^23 - 30 * q^24 + 10 * q^26 + 56 * q^27 + 20 * q^29 + 12 * q^31 - 32 * q^33 - 104 * q^34 + 20 * q^35 + 12 * q^37 + 20 * q^39 - 80 * q^40 + 190 * q^41 + 32 * q^42 - 24 * q^44 + 4 * q^45 - 40 * q^46 - 10 * q^47 + 44 * q^48 - 24 * q^49 - 180 * q^50 - 110 * q^52 + 28 * q^53 - 62 * q^55 - 72 * q^56 + 20 * q^58 - 118 * q^59 + 88 * q^60 - 20 * q^61 + 120 * q^62 - 20 * q^66 - 156 * q^67 - 60 * q^68 + 12 * q^69 - 20 * q^70 + 64 * q^71 - 30 * q^72 + 10 * q^73 - 60 * q^74 - 12 * q^75 + 84 * q^78 + 200 * q^79 + 188 * q^80 + 28 * q^81 - 138 * q^82 - 80 * q^83 - 60 * q^84 + 40 * q^85 - 42 * q^86 - 18 * q^88 + 216 * q^89 - 88 * q^91 + 16 * q^92 + 12 * q^93 - 40 * q^94 - 300 * q^95 - 100 * q^96 + 18 * q^97 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{3}{10}\right)$	$1$

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 $

$2$	2.31335	−	0.888012i	1.63579	−	0.627919i	0.645101	−	0.764097i	$-0.276815\pi$
$2$	2.31335	−	0.888012i	1.63579	−	0.627919i	0.990684	+	0.136178i	$0.0434820\pi$
$3$	−0.669131	+	0.743145i	−0.386323	+	0.429055i
$3$	−0.669131	+	0.743145i	−0.386323	+	0.429055i
$4$	3.07673	−	2.77030i	1.53837	−	1.38515i
$5$	−0.569220	−	3.59392i	−0.254563	−	1.60725i	−0.701491	−	0.712678i	$-0.747482\pi$
$5$	−0.569220	−	3.59392i	−0.254563	−	1.60725i	0.446928	−	0.894570i	$-0.352518\pi$
$6$	−0.888012	+	2.31335i	−0.362529	+	0.944421i
$7$	−0.0796919	+	1.52061i	−0.0301207	+	0.574737i	0.941329	+	0.337491i	$0.109578\pi$
$7$	−0.0796919	+	1.52061i	−0.0301207	+	0.574737i	−0.971450	+	0.237246i	$0.923755\pi$
$8$	2.40758	−	4.72514i	0.851209	−	1.67059i
$9$	−0.104528	−	0.994522i	−0.0348428	−	0.331507i
$10$	−4.50825	−	7.80851i	−1.42563	−	2.46927i
$11$	1.22542	−	3.08194i	0.369479	−	0.929239i
$11$	1.22542	−	3.08194i	0.369479	−	0.929239i
$12$			4.14015i			1.19516i
$13$	−0.672825	+	3.54222i	−0.186608	+	0.982434i
$13$	−0.672825	+	3.54222i	−0.186608	+	0.982434i
$14$	1.16597	+	3.58847i	0.311617	+	0.959060i
$15$	3.05168	+	1.98179i	0.787941	+	0.511695i
$16$	0.508066	−	4.83393i	0.127017	−	1.20848i
$17$	0.760974	−	0.338807i	0.184563	−	0.0821729i	−0.312375	−	0.949959i	$-0.601124\pi$
$17$	0.760974	−	0.338807i	0.184563	−	0.0821729i	0.496938	+	0.867786i	$0.334458\pi$
$18$	−1.12496	−	2.20785i	−0.265155	−	0.520396i
$19$	−1.21707	+	0.790378i	−0.279216	+	0.181325i	−0.676648	−	0.736307i	$-0.736568\pi$
$19$	−1.21707	+	0.790378i	−0.279216	+	0.181325i	0.397432	+	0.917632i	$0.369901\pi$
$20$	−11.7076	−	9.48061i	−2.61789	−	2.11993i
$21$	−1.07671	−	1.07671i	−0.234957	−	0.234957i
$22$	0.0980370	−	8.21779i	0.0209016	−	1.75204i
$23$	4.79612	−	2.76904i	1.00006	−	0.577385i	0.0917936	−	0.995778i	$-0.470740\pi$
$23$	4.79612	−	2.76904i	1.00006	−	0.577385i	0.908266	+	0.418393i	$0.137407\pi$
$24$	1.90048	+	4.95092i	0.387934	+	1.01060i
$25$	−7.83694	+	2.54638i	−1.56739	+	0.509275i
$26$	1.58905	+	8.79187i	0.311638	+	1.72423i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	3.96736	+	4.89929i	0.749761	+	0.925878i
$29$	1.67365	+	7.87389i	0.310788	+	1.46214i	0.805245	+	0.592942i	$0.202034\pi$
$29$	1.67365	+	7.87389i	0.310788	+	1.46214i	−0.494456	+	0.869202i	$0.664633\pi$
$30$	8.81946	+	1.87463i	1.61021	+	0.342260i
$31$	2.65472	+	0.420467i	0.476802	+	0.0755181i	0.390210	−	0.920726i	$-0.372402\pi$
$31$	2.65472	+	0.420467i	0.476802	+	0.0755181i	0.0865921	+	0.996244i	$0.472402\pi$
$32$	−0.372136	−	1.38883i	−0.0657850	−	0.245513i
$33$	1.47036	+	2.97289i	0.255956	+	0.517513i
$34$	1.45953	−	1.45953i	0.250308	−	0.250308i
$35$	5.51031	−	0.579157i	0.931413	−	0.0978954i
$36$	−3.07673	−	2.77030i	−0.512789	−	0.461717i
$37$	−0.299601	+	0.461346i	−0.0492542	+	0.0758448i	−0.862440	−	0.506160i	$-0.831065\pi$
$37$	−0.299601	+	0.461346i	−0.0492542	+	0.0758448i	0.813186	+	0.582004i	$0.197731\pi$
$38$	−2.11365	+	2.90920i	−0.342880	+	0.471934i
$39$	−2.18217	−	2.87021i	−0.349427	−	0.459602i
$40$	−18.3522	−	5.96300i	−2.90174	−	0.942833i
$41$	0.310875	+	5.93186i	0.0485506	+	0.926400i	0.908982	+	0.416835i	$0.136861\pi$
$41$	0.310875	+	5.93186i	0.0485506	+	0.926400i	−0.860432	+	0.509566i	$0.829806\pi$
$42$	−3.44694	−	1.53468i	−0.531874	−	0.236806i
$43$	−1.22704	+	2.12529i	−0.187122	+	0.324104i	−0.944289	−	0.329116i	$-0.893249\pi$
$43$	−1.22704	+	2.12529i	−0.187122	+	0.324104i	0.757168	+	0.653220i	$0.226582\pi$
$44$	−4.76760	−	12.8771i	−0.718742	−	1.94129i
$45$	−3.51473	+	0.941769i	−0.523945	+	0.140391i
$46$	8.63616	−	10.6648i	1.27333	−	1.57243i
$47$	−8.93000	−	4.55006i	−1.30257	−	0.663695i	−0.341473	−	0.939892i	$-0.610926\pi$
$47$	−8.93000	−	4.55006i	−1.30257	−	0.663695i	−0.961101	+	0.276197i	$0.910926\pi$
$48$	3.25235	+	3.61210i	0.469436	+	0.521361i
$49$	4.65574	+	0.489338i	0.665106	+	0.0699055i
$50$	−15.8684	+	12.8500i	−2.24413	+	1.81726i
$51$	−0.257408	+	0.792220i	−0.0360443	+	0.110933i
$52$	7.74291	+	12.7624i	1.07375	+	1.76982i
$53$	3.56475	−	2.58994i	0.489656	−	0.355756i	−0.315396	−	0.948960i	$-0.602137\pi$
$53$	3.56475	−	2.58994i	0.489656	−	0.355756i	0.805052	+	0.593204i	$0.202137\pi$
$54$	2.39350	+	0.641336i	0.325714	+	0.0872748i
$55$	−11.7738	−	2.64977i	−1.58757	−	0.357295i
$56$	6.99324	+	4.03755i	0.934512	+	0.539541i
$57$	0.227017	−	1.43333i	0.0300691	−	0.189849i
$58$	10.8638	+	16.7288i	1.42649	+	2.19660i
$59$	−10.8155	−	0.566816i	−1.40806	−	0.0737932i	−0.666912	−	0.745137i	$-0.732384\pi$
$59$	−10.8155	−	0.566816i	−1.40806	−	0.0737932i	−0.741146	+	0.671344i	$0.765718\pi$
$60$	14.8794	−	2.35666i	1.92092	−	0.304243i
$61$	4.43970	+	9.97172i	0.568445	+	1.27675i	0.937708	+	0.347423i	$0.112943\pi$
$61$	4.43970	+	9.97172i	0.568445	+	1.27675i	−0.369264	+	0.929325i	$0.620390\pi$
$62$	6.51468	−	1.38474i	0.827366	−	0.175862i
$63$	1.52061	−	0.0796919i	0.191579	−	0.0100402i
$64$	3.61975	+	4.98215i	0.452468	+	0.622769i
$65$	13.1134	+	0.401775i	1.62652	+	0.0498341i
$66$	6.04141	+	5.57163i	0.743646	+	0.685820i
$67$	1.46898	−	5.48229i	0.179464	−	0.669769i	−0.816284	−	0.577651i	$-0.803970\pi$
$67$	1.46898	−	5.48229i	0.179464	−	0.669769i	0.995748	−	0.0921181i	$-0.0293637\pi$
$68$	1.40271	−	3.15055i	0.170104	−	0.382060i
$69$	−1.15143	+	5.41706i	−0.138616	+	0.652137i
$70$	12.2330	−	6.23302i	1.46212	−	0.744988i
$71$	1.22442	+	0.470012i	0.145312	+	0.0557802i	0.429937	−	0.902859i	$-0.358536\pi$
$71$	1.22442	+	0.470012i	0.145312	+	0.0557802i	−0.284625	+	0.958639i	$0.591869\pi$
$72$	−4.95092	−	1.90048i	−0.583472	−	0.223974i
$73$	−12.6472	+	6.44410i	−1.48025	+	0.754224i	−0.992896	−	0.118981i	$-0.962037\pi$
$73$	−12.6472	+	6.44410i	−1.48025	+	0.754224i	−0.487352	+	0.873206i	$0.662037\pi$
$74$	−0.283402	+	1.33330i	−0.0329449	+	0.154993i
$75$	3.35161	−	7.52784i	0.387011	−	0.869240i
$76$	−1.55503	+	5.80345i	−0.178374	+	0.665701i
$77$	4.58877	+	2.10900i	0.522939	+	0.240343i
$78$	−7.59691	−	4.70201i	−0.860181	−	0.532398i
$79$	−8.29617	−	11.4187i	−0.933392	−	1.28470i	−0.958522	−	0.285020i	$-0.908000\pi$
$79$	−8.29617	−	11.4187i	−0.933392	−	1.28470i	0.0251295	−	0.999684i	$-0.492000\pi$
$80$	−17.6619	+	0.925623i	−1.97466	+	0.103488i
$81$	−0.978148	+	0.207912i	−0.108683	+	0.0231013i
$82$	5.98672	+	13.4464i	0.661123	+	1.48491i
$83$	−3.06953	+	0.486166i	−0.336925	+	0.0533637i	−0.322605	−	0.946534i	$-0.604558\pi$
$83$	−3.06953	+	0.486166i	−0.336925	+	0.0533637i	−0.0143202	+	0.999897i	$0.504558\pi$
$84$	−6.29556	−	0.329936i	−0.686902	−	0.0359990i
$85$	−1.65081	−	2.54202i	−0.179055	−	0.275721i
$86$	−0.951284	+	6.00617i	−0.102580	+	0.647662i
$87$	−6.97133	−	4.02490i	−0.747405	−	0.431514i
$88$	−11.6123	−	13.2103i	−1.23787	−	1.40822i
$89$	3.02281	+	0.809960i	0.320417	+	0.0858556i	0.415443	−	0.909619i	$-0.363627\pi$
$89$	3.02281	+	0.809960i	0.320417	+	0.0858556i	−0.0950256	+	0.995475i	$0.530293\pi$
$90$	−7.29449	+	5.29976i	−0.768907	+	0.558644i
$91$	−5.33272	−	1.30539i	−0.559021	−	0.136842i
$92$	7.08529	−	21.8063i	0.738693	−	2.27346i
$93$	−2.08882	+	1.69150i	−0.216601	+	0.175400i
$94$	−24.6987	−	2.59594i	−2.54748	−	0.267751i
$95$	3.53333	+	3.92417i	0.362512	+	0.402611i
$96$	1.28111	+	0.652758i	0.130753	+	0.0666219i
$97$	11.7354	−	14.4921i	1.19155	−	1.47145i	0.345441	−	0.938441i	$-0.387729\pi$
$97$	11.7354	−	14.4921i	1.19155	−	1.47145i	0.846112	−	0.533005i	$-0.178937\pi$
$98$	11.2049	−	3.00235i	1.13187	−	0.303283i
$99$	−3.19315	−	0.896560i	−0.320923	−	0.0901077i
$100$	−17.0579	+	29.5452i	−1.70579	+	2.95452i
$101$	−13.8660	−	6.17354i	−1.37972	−	0.614290i	−0.423220	−	0.906027i	$-0.639100\pi$
$101$	−13.8660	−	6.17354i	−1.37972	−	0.614290i	−0.956499	+	0.291736i	$0.905767\pi$
$102$	0.108026	+	2.06126i	0.0106962	+	0.204096i
$103$	13.3410	+	4.33474i	1.31452	+	0.427115i	0.880611	−	0.473840i	$-0.157132\pi$
$103$	13.3410	+	4.33474i	1.31452	+	0.427115i	0.433913	+	0.900955i	$0.357132\pi$
$104$	15.1176	+	11.7074i	1.48240	+	1.14800i
$105$	−3.25672	+	4.48249i	−0.317823	+	0.437446i
$106$	5.94662	−	9.15699i	0.577586	−	0.889405i
$107$	5.78221	+	5.20633i	0.558988	+	0.503315i	0.899497	−	0.436926i	$-0.143933\pi$
$107$	5.78221	+	5.20633i	0.558988	+	0.503315i	−0.340510	+	0.940241i	$0.610600\pi$
$108$	4.11747	−	0.432764i	0.396204	−	0.0416427i
$109$	−12.6249	+	12.6249i	−1.20924	+	1.20924i	−0.237972	+	0.971272i	$0.576483\pi$
$109$	−12.6249	+	12.6249i	−1.20924	+	1.20924i	−0.971272	+	0.237972i	$0.923517\pi$
$110$	−29.5899	+	4.32540i	−2.82128	+	0.412410i
$111$	−0.142374	−	0.531348i	−0.0135136	−	0.0504333i
$112$	7.31004	+	1.15780i	0.690734	+	0.109401i
$113$	−6.27401	−	1.33358i	−0.590209	−	0.125453i	−0.0968809	−	0.995296i	$-0.530887\pi$
$113$	−6.27401	−	1.33358i	−0.590209	−	0.125453i	−0.493328	+	0.869843i	$0.664220\pi$
$114$	−0.747643	−	3.51738i	−0.0700232	−	0.329433i
$115$	−12.6817	−	15.6606i	−1.18258	−	1.46036i
$116$	26.9624	+	19.5893i	2.50340	+	1.81883i
$117$	3.59314	+	0.298877i	0.332186	+	0.0276312i
$118$	−25.5234	+	8.29305i	−2.34962	+	0.763437i
$119$	0.454551	+	1.18415i	0.0416686	+	0.108550i
$120$	16.7114	−	9.64833i	1.52554	−	0.880768i
$121$	−7.99667	−	7.55336i	−0.726970	−	0.686669i
$122$	19.1256	+	19.1256i	1.73155	+	1.73155i
$123$	−4.61624	−	3.73816i	−0.416233	−	0.337059i
$124$	9.33270	−	6.06072i	0.838101	−	0.544269i
$125$	5.35270	+	10.5053i	0.478760	+	0.939619i
$126$	3.44694	−	1.53468i	0.307078	−	0.136720i
$127$	1.60983	−	15.3165i	0.142849	−	1.35912i	−0.654712	−	0.755879i	$-0.727210\pi$
$127$	1.60983	−	15.3165i	0.142849	−	1.35912i	0.797561	−	0.603239i	$-0.206123\pi$
$128$	15.2097	+	9.87728i	1.34436	+	0.873036i
$129$	−0.758351	−	2.33397i	−0.0667691	−	0.205494i
$130$	30.6927	−	10.7154i	2.69193	−	0.939805i
$131$			12.8688i			1.12435i	0.827019	+	0.562174i	$0.190035\pi$
$131$			12.8688i			1.12435i	−0.827019	+	0.562174i	$0.809965\pi$
$132$	12.7597	+	5.07344i	1.11059	+	0.441586i
$133$	−1.10487	−	1.91368i	−0.0958041	−	0.165937i
$134$	−1.47009	−	13.9869i	−0.126996	−	1.20829i
$135$	1.65194	−	3.24212i	0.142177	−	0.279037i
$136$	0.231193	−	4.41142i	0.0198246	−	0.378276i
$137$	8.04195	−	20.9500i	0.687070	−	1.78988i	0.0777251	−	0.996975i	$-0.475234\pi$
$137$	8.04195	−	20.9500i	0.687070	−	1.78988i	0.609345	−	0.792905i	$-0.291432\pi$
$138$	2.14675	+	13.5540i	0.182743	+	1.15380i
$139$	2.36737	−	2.13159i	0.200797	−	0.180799i	−0.562597	−	0.826731i	$-0.690198\pi$
$139$	2.36737	−	2.13159i	0.200797	−	0.180799i	0.763395	+	0.645932i	$0.223531\pi$
$140$	15.3493	−	17.0471i	1.29725	−	1.44075i
$141$	9.35669	−	3.59170i	0.787975	−	0.302475i
$142$	3.24990			0.272725
$143$	10.0924	+	6.41432i	0.843969	+	0.536393i
$144$	−4.86056			−0.405046
$145$	27.3454	−	10.4969i	2.27091	−	0.871722i
$146$	−23.5351	+	26.1384i	−1.94778	+	2.16323i
$147$	−3.47895	+	3.13246i	−0.286939	+	0.258361i
$148$	0.356274	+	2.24942i	0.0292855	+	0.184902i
$149$	−0.121291	+	0.315974i	−0.00993656	+	0.0258856i	−0.938459	−	0.345391i	$-0.887746\pi$
$149$	−0.121291	+	0.315974i	−0.00993656	+	0.0258856i	0.928522	+	0.371276i	$0.121080\pi$
$150$	1.06864	−	20.3908i	0.0872538	−	1.66490i
$151$	4.93826	−	9.69189i	0.401870	−	0.788715i	−0.598049	−	0.801460i	$-0.704057\pi$
$151$	4.93826	−	9.69189i	0.401870	−	0.788715i	0.999919	+	0.0127452i	$0.00405703\pi$
$152$	0.804442	+	7.65375i	0.0652488	+	0.620801i
$153$	−0.416495	−	0.721390i	−0.0336716	−	0.0583209i
$154$	12.4883	+	0.803967i	1.00633	+	0.0647855i
$155$		−	9.78019i		−	0.785564i
$156$	−14.6653	−	2.78560i	−1.17417	−	0.223026i
$157$	−0.827156	−	2.54572i	−0.0660142	−	0.203171i	0.912608	−	0.408835i	$-0.134065\pi$
$157$	−0.827156	−	2.54572i	−0.0660142	−	0.203171i	−0.978623	+	0.205664i	$0.934065\pi$
$158$	−29.3319	−	19.0483i	−2.33352	−	1.51541i
$159$	−0.460581	+	4.38214i	−0.0365265	+	0.347526i
$160$	−4.77951	+	2.12798i	−0.377854	+	0.168231i
$161$	3.82842	+	7.51370i	0.301722	+	0.592163i
$162$	−2.07817	+	1.34958i	−0.163276	+	0.106033i
$163$	−3.22264	−	2.60964i	−0.252417	−	0.204403i	0.494758	−	0.869031i	$-0.335257\pi$
$163$	−3.22264	−	2.60964i	−0.252417	−	0.204403i	−0.747175	+	0.664628i	$0.768590\pi$
$164$	17.3895	+	17.3895i	1.35789	+	1.35789i
$165$	9.84734	−	6.97657i	0.766615	−	0.543125i
$166$	−6.66918	+	3.85045i	−0.517629	+	0.298853i
$167$	−5.98213	−	15.5840i	−0.462911	−	1.20592i	−0.944203	−	0.329364i	$-0.893166\pi$
$167$	−5.98213	−	15.5840i	−0.462911	−	1.20592i	0.481292	−	0.876560i	$-0.340168\pi$
$168$	−7.67988	+	2.49534i	−0.592516	+	0.192520i
$169$	−12.0946	−	4.76659i	−0.930355	−	0.366661i
$170$	−6.07624	−	4.41465i	−0.466026	−	0.338588i
$171$	0.913267	+	1.12779i	0.0698393	+	0.0862443i
$172$	2.11243	+	9.93822i	0.161072	+	0.757782i
$173$	7.70977	+	1.63876i	0.586163	+	0.124593i	0.491441	−	0.870911i	$-0.336470\pi$
$173$	7.70977	+	1.63876i	0.586163	+	0.124593i	0.0947222	+	0.995504i	$0.469804\pi$
$174$	−19.7013	−	3.12038i	−1.49355	−	0.236555i
$175$	−3.24751	−	12.1199i	−0.245489	−	0.916176i
$176$	−14.2753	−	7.48944i	−1.07604	−	0.564538i
$177$	7.65821	−	7.65821i	0.575626	−	0.575626i
$178$	7.71207	−	0.810572i	0.578044	−	0.0607549i
$179$	17.6940	+	15.9317i	1.32251	+	1.19079i	0.966606	+	0.256269i	$0.0824933\pi$
$179$	17.6940	+	15.9317i	1.32251	+	1.19079i	0.355903	+	0.934523i	$0.384173\pi$
$180$	−8.20490	+	12.6344i	−0.611557	+	0.941715i
$181$	−3.81149	+	5.24606i	−0.283306	+	0.389937i	−0.926825	−	0.375493i	$-0.877473\pi$
$181$	−3.81149	+	5.24606i	−0.283306	+	0.389937i	0.643520	+	0.765430i	$0.277473\pi$
$182$	−13.4956	+	1.71569i	−1.00036	+	0.127175i
$183$	−10.3812	−	3.37305i	−0.767398	−	0.249343i
$184$	−1.53707	−	29.3290i	−0.113314	−	2.16216i
$185$	1.82858	+	0.814135i	0.134440	+	0.0598564i
$186$	−3.33011	+	5.76792i	−0.244176	+	0.422925i
$187$	−0.111668	−	2.76046i	−0.00816595	−	0.201865i
$188$	−40.0803	+	10.7395i	−2.92315	+	0.783257i
$189$	−0.958265	+	1.18336i	−0.0697035	+	0.0860767i
$190$	11.6585	+	5.94032i	0.845800	+	0.430956i
$191$	7.96664	+	8.84785i	0.576446	+	0.640208i	0.958892	−	0.283770i	$-0.0915851\pi$
$191$	7.96664	+	8.84785i	0.576446	+	0.640208i	−0.382447	+	0.923978i	$0.624918\pi$
$192$	−6.12454	−	0.643716i	−0.442001	−	0.0464562i
$193$	−7.91759	+	6.41154i	−0.569921	+	0.461513i	−0.870448	−	0.492261i	$-0.836171\pi$
$193$	−7.91759	+	6.41154i	−0.569921	+	0.461513i	0.300527	+	0.953773i	$0.402837\pi$
$194$	14.2791	−	43.9464i	1.02518	−	3.15517i
$195$	−9.07317	+	9.47633i	−0.649743	+	0.678614i
$196$	15.6801	−	11.3923i	1.12001	−	0.813733i
$197$	4.27973	+	1.14675i	0.304918	+	0.0817026i	0.408034	−	0.912967i	$-0.366214\pi$
$197$	4.27973	+	1.14675i	0.304918	+	0.0817026i	−0.103116	+	0.994669i	$0.532881\pi$
$198$	−8.18302	+	0.761493i	−0.581542	+	0.0541169i
$199$	−9.25141	−	5.34130i	−0.655815	−	0.378635i	0.134866	−	0.990864i	$-0.456940\pi$
$199$	−9.25141	−	5.34130i	−0.655815	−	0.378635i	−0.790681	+	0.612229i	$0.790273\pi$
$200$	−6.83607	+	43.1613i	−0.483383	+	3.05196i
$201$	3.09120	+	4.76003i	0.218037	+	0.335747i
$202$	−37.5591	−	1.96839i	−2.64265	−	0.138495i
$203$	−12.1065	+	1.91748i	−0.849710	+	0.134581i
$204$	1.40271	+	3.15055i	0.0982096	+	0.220582i
$205$	21.1416	−	4.49379i	1.47660	−	0.313860i
$206$	34.7116	−	1.81916i	2.41847	−	0.126747i
$207$	−3.25520	−	4.48040i	−0.226252	−	0.311409i
$208$	16.7810	+	5.05207i	1.16355	+	0.350298i
$209$	0.944462	+	4.71950i	0.0653298	+	0.326454i
$210$	−3.55343	+	13.2616i	−0.245210	+	0.915136i
$211$	4.40561	−	9.89516i	0.303294	−	0.681211i	−0.696028	−	0.718015i	$-0.745051\pi$
$211$	4.40561	−	9.89516i	0.303294	−	0.681211i	0.999323	+	0.0368040i	$0.0117177\pi$
$212$	3.79286	−	17.8440i	0.260495	−	1.22553i
$213$	−1.16859	+	0.595425i	−0.0800703	+	0.0407978i
$214$	17.9996	+	6.90939i	1.23043	+	0.472316i
$215$	8.33658	+	3.20011i	0.568550	+	0.218246i
$216$	4.72514	−	2.40758i	0.321505	−	0.163815i
$217$	−0.850927	+	4.00330i	−0.0577647	+	0.271761i
$218$	−17.9947	+	40.4168i	−1.21876	+	2.73737i
$219$	3.67377	−	13.7107i	0.248250	−	0.926482i
$220$	−43.5654	+	24.4642i	−2.93718	+	1.64938i
$221$	0.688127	+	2.92349i	0.0462884	+	0.196655i
$222$	−0.801204	−	1.10276i	−0.0537733	−	0.0740126i
$223$	−12.2588	+	0.642454i	−0.820907	+	0.0430219i	−0.458164	−	0.888867i	$-0.651493\pi$
$223$	−12.2588	+	0.642454i	−0.820907	+	0.0430219i	−0.362743	+	0.931889i	$0.618160\pi$
$224$	2.14153	−	0.455196i	0.143087	−	0.0304141i
$225$	3.35161	+	7.52784i	0.223441	+	0.501856i
$226$	−15.6982	+	2.48635i	−1.04423	+	0.165390i
$227$	−11.4806	−	0.601675i	−0.761997	−	0.0399346i	−0.332621	−	0.943061i	$-0.607933\pi$
$227$	−11.4806	−	0.601675i	−0.761997	−	0.0399346i	−0.429376	+	0.903126i	$0.641266\pi$
$228$	−3.27228	−	5.03887i	−0.216712	−	0.333708i
$229$	−2.19070	+	13.8315i	−0.144765	+	0.914012i	0.803216	+	0.595687i	$0.203120\pi$
$229$	−2.19070	+	13.8315i	−0.144765	+	0.914012i	−0.947982	+	0.318325i	$0.896880\pi$
$230$	−43.2441	−	24.9670i	−2.85143	−	1.64628i
$231$	−4.63778	+	1.99893i	−0.305144	+	0.131520i
$232$	41.2347	+	11.0488i	2.70719	+	0.725390i
$233$	0.585832	−	0.425632i	0.0383791	−	0.0278841i	−0.568430	−	0.822731i	$-0.692449\pi$
$233$	0.585832	−	0.425632i	0.0383791	−	0.0278841i	0.606809	+	0.794847i	$0.292449\pi$
$234$	8.57760	−	2.49935i	0.560735	−	0.163387i
$235$	−11.2694	+	34.6836i	−0.735135	+	2.26251i
$236$	−34.8467	+	28.2183i	−2.26832	+	1.83685i
$237$	14.0370	+	1.47534i	0.911799	+	0.0958339i
$238$	2.10307	+	2.33570i	0.136322	+	0.151401i
$239$	−9.24396	−	4.71003i	−0.597942	−	0.304667i	0.128699	−	0.991684i	$-0.458920\pi$
$239$	−9.24396	−	4.71003i	−0.597942	−	0.304667i	−0.726641	+	0.687017i	$0.758920\pi$
$240$	11.1303	−	13.7447i	0.718456	−	0.887219i
$241$	−22.3017	+	5.97572i	−1.43658	+	0.384930i	−0.891334	−	0.453348i	$-0.850230\pi$
$241$	−22.3017	+	5.97572i	−1.43658	+	0.384930i	−0.545244	+	0.838278i	$0.683563\pi$
$242$	−25.2066	−	10.3724i	−1.62034	−	0.666764i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	41.2844	+	18.3810i	2.64297	+	1.17672i
$245$	−0.891503	−	17.0109i	−0.0569561	−	1.08679i
$246$	−13.9985	−	4.54839i	−0.892513	−	0.289995i
$247$	−1.98081	−	4.84293i	−0.126036	−	0.308148i
$248$	8.37823	−	11.5316i	0.532018	−	0.732260i
$249$	1.69263	−	2.60642i	0.107266	−	0.165175i
$250$	21.7115	+	19.5491i	1.37315	+	1.23639i
$251$	−24.9815	+	2.62566i	−1.57682	+	0.165730i	−0.852124	−	0.523341i	$-0.824686\pi$
$251$	−24.9815	+	2.62566i	−1.57682	+	0.165730i	−0.724694	+	0.689071i	$0.758019\pi$
$252$	4.45774	−	4.45774i	0.280812	−	0.280812i
$253$	−2.65673	−	18.1746i	−0.167027	−	1.14263i
$254$	−9.87712	−	36.8619i	−0.619745	−	2.31292i
$255$	2.99370	+	0.474155i	0.187472	+	0.0296927i
$256$	31.9090	+	6.78247i	1.99431	+	0.423904i
$257$	−2.27807	−	10.7175i	−0.142102	−	0.668537i	−0.990310	−	0.138874i	$-0.955652\pi$
$257$	−2.27807	−	10.7175i	−0.142102	−	0.668537i	0.848208	−	0.529663i	$-0.177682\pi$
$258$	−3.82692	−	4.72585i	−0.238254	−	0.294219i
$259$	−0.677652	−	0.492343i	−0.0421072	−	0.0305927i
$260$	41.4595	−	35.0920i	2.57121	−	2.17631i
$261$	7.65581	−	2.48752i	0.473883	−	0.153974i
$262$	11.4276	+	29.7699i	0.706000	+	1.83919i
$263$	11.3281	−	6.54029i	0.698522	−	0.403292i	−0.108275	−	0.994121i	$-0.534533\pi$
$263$	11.3281	−	6.54029i	0.698522	−	0.403292i	0.806797	+	0.590829i	$0.201199\pi$
$264$	17.5873	+	0.209814i	1.08242	+	0.0129132i
$265$	−11.3372	−	11.3372i	−0.696437	−	0.696437i
$266$	−4.25532	−	3.44589i	−0.260910	−	0.211281i
$267$	−2.62457	+	1.70442i	−0.160621	+	0.104309i
$268$	−10.6680	−	20.9371i	−0.651650	−	1.27893i
$269$	17.3459	−	7.72290i	1.05760	−	0.470874i	0.197131	−	0.980377i	$-0.436838\pi$
$269$	17.3459	−	7.72290i	1.05760	−	0.470874i	0.860469	+	0.509503i	$0.170171\pi$
$270$	0.942480	−	8.96710i	0.0573575	−	0.545720i
$271$	−3.87197	−	2.51449i	−0.235206	−	0.152744i	0.421655	−	0.906756i	$-0.361449\pi$
$271$	−3.87197	−	2.51449i	−0.235206	−	0.152744i	−0.656861	+	0.754012i	$0.728116\pi$
$272$	−1.25115	−	3.85063i	−0.0758619	−	0.233479i
$273$	4.53838	−	3.08950i	0.274675	−	0.186985i
$274$		−	55.6060i		−	3.35928i
$275$	−1.75580	+	27.2733i	−0.105879	+	1.64464i
$276$	11.4642	+	19.8567i	0.690066	+	1.19523i
$277$	0.456681	+	4.34503i	0.0274393	+	0.261068i	0.999638	+	0.0269097i	$0.00856665\pi$
$277$	0.456681	+	4.34503i	0.0274393	+	0.261068i	−0.972199	+	0.234158i	$0.924767\pi$
$278$	3.58367	−	7.03336i	0.214935	−	0.421833i
$279$	0.140669	−	2.68413i	0.00842166	−	0.160695i
$280$	10.5299	−	27.4314i	0.629283	−	1.63934i
$281$	2.07194	+	13.0817i	0.123601	+	0.780388i	0.969147	+	0.246485i	$0.0792755\pi$
$281$	2.07194	+	13.0817i	0.123601	+	0.780388i	−0.845545	+	0.533904i	$0.820724\pi$
$282$	18.4558	−	16.6177i	1.09903	−	0.989570i
$283$	−10.2404	+	11.3731i	−0.608730	+	0.676063i	−0.966180	−	0.257869i	$-0.916980\pi$
$283$	−10.2404	+	11.3731i	−0.608730	+	0.676063i	0.357450	+	0.933932i	$0.383646\pi$
$284$	5.06930	−	1.94592i	0.300808	−	0.115469i
$285$	−5.28049			−0.312789
$286$	29.0432	+	5.87641i	1.71736	+	0.347479i
$287$	−9.04482			−0.533899
$288$	−1.34232	+	0.515270i	−0.0790972	+	0.0303626i
$289$	−10.9109	+	12.1178i	−0.641819	+	0.712813i
$290$	53.9381	−	48.5661i	3.16736	−	2.85190i
$291$	2.91716	+	18.4182i	0.171007	+	1.07969i
$292$	−21.0601	+	54.8635i	−1.23245	+	3.21064i
$293$	0.993722	−	18.9613i	0.0580538	−	1.10773i	−0.801932	−	0.597415i	$-0.796194\pi$
$293$	0.993722	−	18.9613i	0.0580538	−	1.10773i	0.859986	−	0.510318i	$-0.170472\pi$
$294$	−5.26637	+	10.3358i	−0.307141	+	0.602798i
$295$	4.11931	+	39.1926i	0.239836	+	2.28188i
$296$	1.45861	+	2.52639i	0.0847800	+	0.146843i
$297$	2.80291	−	1.77305i	0.162641	−	0.102883i
$298$			0.838667i			0.0485827i
$299$	6.58159	+	18.8520i	0.380623	+	1.09024i
$300$	−10.5424	−	32.4461i	−0.608665	−	1.87328i
$301$	−3.13396	−	2.03522i	−0.180638	−	0.117308i
$302$	2.81742	−	26.8060i	0.162124	−	1.54251i
$303$	13.8660	−	6.17354i	0.796581	−	0.354661i
$304$	3.20227	+	6.28482i	0.183663	+	0.360459i
$305$	33.3104	−	21.6320i	1.90735	−	1.23864i
$306$	−1.60410	−	1.29898i	−0.0917004	−	0.0742575i
$307$	12.4627	+	12.4627i	0.711285	+	0.711285i	0.966804	−	0.255519i	$-0.0822465\pi$
$307$	12.4627	+	12.4627i	0.711285	+	0.711285i	−0.255519	+	0.966804i	$0.582246\pi$
$308$	19.9610	−	6.22346i	1.13738	−	0.354615i
$309$	−12.1482	+	7.01376i	−0.691086	+	0.398999i
$310$	−8.68493	−	22.6250i	−0.493271	−	1.28501i
$311$	−1.91088	+	0.620884i	−0.108356	+	0.0352071i	−0.362693	−	0.931909i	$-0.618143\pi$
$311$	−1.91088	+	0.620884i	−0.108356	+	0.0352071i	0.254337	+	0.967116i	$0.418143\pi$
$312$	−18.8159	+	3.40081i	−1.06524	+	0.192533i
$313$	22.4613	+	16.3191i	1.26959	+	0.922409i	0.999186	−	0.0403387i	$-0.0128437\pi$
$313$	22.4613	+	16.3191i	1.26959	+	0.922409i	0.270401	+	0.962748i	$0.412844\pi$
$314$	−4.17413	−	5.15463i	−0.235560	−	0.290892i
$315$	−1.15197	−	5.41959i	−0.0649061	−	0.305359i
$316$	−57.1584	−	12.1494i	−3.21541	−	0.683456i
$317$	−22.3877	−	3.54587i	−1.25742	−	0.199156i	−0.508061	−	0.861321i	$-0.669638\pi$
$317$	−22.3877	−	3.54587i	−1.25742	−	0.199156i	−0.749358	+	0.662165i	$0.769638\pi$
$318$	2.82590	+	10.5464i	0.158469	+	0.591414i
$319$	26.3178	+	4.49078i	1.47351	+	0.251435i
$320$	15.8450	−	15.8450i	0.885763	−	0.885763i
$321$	−7.73811	+	0.813309i	−0.431899	+	0.0453945i
$322$	15.5287	+	13.9821i	0.865382	+	0.779194i
$323$	−0.658376	+	1.01381i	−0.0366330	+	0.0564099i
$324$	−2.43352	+	3.34945i	−0.135196	+	0.186081i
$325$	−3.74693	−	29.4734i	−0.207842	−	1.63489i
$326$	−9.77249	−	3.17528i	−0.541248	−	0.175862i
$327$	−0.934420	−	17.8298i	−0.0516736	−	0.985990i
$328$	28.7773	+	12.8125i	1.58896	+	0.707452i
$329$	7.63052	−	13.2165i	0.420684	−	0.728647i
$330$	16.5851	−	24.8838i	0.912979	−	1.36981i
$331$	−22.7814	+	6.10426i	−1.25218	+	0.335520i	−0.823178	−	0.567784i	$-0.807801\pi$
$331$	−22.7814	+	6.10426i	−1.25218	+	0.335520i	−0.429001	+	0.903304i	$0.641134\pi$
$332$	−8.09730	+	9.99934i	−0.444397	+	0.548785i
$333$	0.490135	+	0.249736i	0.0268592	+	0.0136855i
$334$	−27.6775	−	30.7390i	−1.51445	−	1.68196i
$335$	−20.5391	−	2.15874i	−1.12217	−	0.117945i
$336$	−5.75178	+	4.65770i	−0.313785	+	0.254098i
$337$	−5.98656	+	18.4247i	−0.326108	+	1.00366i	0.644829	+	0.764327i	$0.276928\pi$
$337$	−5.98656	+	18.4247i	−0.326108	+	1.00366i	−0.970938	+	0.239332i	$0.923072\pi$
$338$	−32.2119	−	0.286627i	−1.75209	−	0.0155904i
$339$	5.18918	−	3.77016i	0.281837	−	0.204767i
$340$	−12.1213	−	3.24788i	−0.657368	−	0.176141i
$341$	4.54901	−	7.66644i	0.246343	−	0.415161i
$342$	3.11420	+	1.79798i	0.168396	+	0.0972237i
$343$	−2.78254	+	17.5682i	−0.150243	+	0.948596i
$344$	7.08812	+	10.9147i	0.382166	+	0.588484i
$345$	20.1239	+	1.05465i	1.08343	+	0.0567803i
$346$	19.2906	−	3.05534i	1.03707	−	0.164256i
$347$	−6.15902	−	13.8334i	−0.330633	−	0.742615i	0.669367	−	0.742932i	$-0.266566\pi$
$347$	−6.15902	−	13.8334i	−0.330633	−	0.742615i	−1.00000		0.000317550i	$0.999899\pi$
$348$	−32.5991	+	6.92915i	−1.74750	+	0.371442i
$349$	20.8114	−	1.09068i	1.11401	−	0.0583828i	0.513567	−	0.858050i	$-0.328324\pi$
$349$	20.8114	−	1.09068i	1.11401	−	0.0583828i	0.600444	+	0.799667i	$0.294990\pi$
$350$	−18.2752	−	25.1537i	−0.976851	−	1.34452i
$351$	−2.62639	+	2.47024i	−0.140186	+	0.131852i
$352$	−4.73631	−	0.555006i	−0.252446	−	0.0295819i
$353$	−0.360145	+	1.34408i	−0.0191686	+	0.0715381i	−0.974848	−	0.222873i	$-0.928457\pi$
$353$	−0.360145	+	1.34408i	−0.0191686	+	0.0715381i	0.955679	+	0.294411i	$0.0951233\pi$
$354$	10.9155	−	24.5167i	0.580154	−	1.30305i
$355$	0.992218	−	4.66802i	0.0526615	−	0.247753i
$356$	11.5442	−	5.88207i	0.611842	−	0.311749i
$357$	−1.18415	−	0.454551i	−0.0626716	−	0.0240574i
$358$	55.0799	+	21.1432i	2.91106	+	1.11745i
$359$	−16.5799	+	8.44786i	−0.875052	+	0.445861i	−0.833012	−	0.553255i	$-0.813386\pi$
$359$	−16.5799	+	8.44786i	−0.875052	+	0.445861i	−0.0420398	+	0.999116i	$0.513386\pi$
$360$	−4.01200	+	18.8750i	−0.211451	+	0.994799i
$361$	−6.87142	+	15.4335i	−0.361654	+	0.812288i
$362$	−4.15874	+	15.5206i	−0.218578	+	0.815745i
$363$	10.9641	−	0.888504i	0.575464	−	0.0466344i
$364$	−20.0237	+	10.7569i	−1.04953	+	0.563815i
$365$	30.3586	+	41.7850i	1.58904	+	2.18713i
$366$	−27.0106	+	1.41556i	−1.41187	+	0.0739927i
$367$	−3.08117	+	0.654922i	−0.160836	+	0.0341867i	−0.287626	−	0.957743i	$-0.592866\pi$
$367$	−3.08117	+	0.654922i	−0.160836	+	0.0341867i	0.126790	+	0.991930i	$0.459533\pi$
$368$	−10.9486	−	24.5909i	−0.570735	−	1.28189i
$369$	5.86686	−	0.929220i	0.305417	−	0.0483733i
$370$	4.95310	+	0.259581i	0.257499	+	0.0134950i
$371$	3.65422	+	5.62700i	0.189717	+	0.292139i
$372$	−1.74080	+	10.9910i	−0.0902561	+	0.569855i
$373$	10.6533	+	6.15070i	0.551609	+	0.318471i	0.749771	−	0.661698i	$-0.230164\pi$
$373$	10.6533	+	6.15070i	0.551609	+	0.318471i	−0.198162	+	0.980169i	$0.563497\pi$
$374$	−2.70964	−	6.28674i	−0.140112	−	0.325080i
$375$	−11.3886	−	3.05156i	−0.588104	−	0.157582i
$376$	−42.9994	+	31.2409i	−2.21752	+	1.61113i
$377$	−29.0171	+	0.630669i	−1.49446	+	0.0324811i
$378$	−1.16597	+	3.58847i	−0.0599708	+	0.184571i
$379$	9.30224	−	7.53281i	0.477824	−	0.386934i	−0.359932	−	0.932978i	$-0.617200\pi$
$379$	9.30224	−	7.53281i	0.477824	−	0.386934i	0.837756	+	0.546044i	$0.183867\pi$
$380$	21.7423	+	2.28520i	1.11535	+	0.117228i
$381$	10.3052	+	11.4451i	0.527950	+	0.586348i
$382$	26.2866	+	13.3937i	1.34494	+	0.685281i
$383$	23.4911	−	29.0090i	1.20034	−	1.48229i	0.366379	−	0.930466i	$-0.380597\pi$
$383$	23.4911	−	29.0090i	1.20034	−	1.48229i	0.833958	−	0.551827i	$-0.186069\pi$
$384$	−17.5175	+	4.69380i	−0.893936	+	0.239530i
$385$	4.96754	−	17.6921i	0.253169	−	0.901675i
$386$	−12.6226	+	21.8630i	−0.642475	+	1.11280i
$387$	2.24191	+	0.998163i	0.113963	+	0.0507395i
$388$	−4.04058	−	77.0989i	−0.205129	−	3.91410i
$389$	−23.1597	−	7.52503i	−1.17424	−	0.381534i	−0.344017	−	0.938963i	$-0.611788\pi$
$389$	−23.1597	−	7.52503i	−1.17424	−	0.381534i	−0.830224	+	0.557429i	$0.811788\pi$
$390$	−12.5743	+	29.9791i	−0.636725	+	1.51805i
$391$	2.71155	−	3.73213i	0.137129	−	0.188742i
$392$	13.5213	−	20.8209i	0.682928	−	1.05162i
$393$	−9.56335	−	8.61087i	−0.482407	−	0.434361i
$394$	10.9188	−	1.14762i	0.550084	−	0.0578161i
$395$	−36.3155	+	36.3155i	−1.82723	+	1.82723i
$396$	−12.3082	+	6.08750i	−0.618510	+	0.305909i
$397$	3.70047	+	13.8103i	0.185721	+	0.693122i	0.994475	+	0.104974i	$0.0334759\pi$
$397$	3.70047	+	13.8103i	0.185721	+	0.693122i	−0.808754	+	0.588148i	$0.799857\pi$
$398$	−26.1449	−	4.14094i	−1.31052	−	0.207567i
$399$	2.16144	+	0.459429i	0.108208	+	0.0230002i
$400$	8.32731	+	39.1769i	0.416366	+	1.95885i
$401$	24.5937	+	30.3707i	1.22815	+	1.51664i	0.784092	+	0.620645i	$0.213129\pi$
$401$	24.5937	+	30.3707i	1.22815	+	1.51664i	0.444061	+	0.895997i	$0.353537\pi$
$402$	11.3780	+	8.26660i	0.567483	+	0.412300i
$403$	−3.27555	+	9.12071i	−0.163167	+	0.454335i
$404$	−59.7646	+	19.4187i	−2.97340	+	0.966116i
$405$	1.30400	+	3.39703i	0.0647962	+	0.168800i
$406$	−26.3038	+	15.1865i	−1.30544	+	0.753695i
$407$	1.05470	+	1.48870i	0.0522795	+	0.0737920i
$408$	3.12362	+	3.12362i	0.154642	+	0.154642i
$409$	9.90613	+	8.02182i	0.489826	+	0.396654i	0.842166	−	0.539219i	$-0.181280\pi$
$409$	9.90613	+	8.02182i	0.489826	+	0.396654i	−0.352339	+	0.935872i	$0.614614\pi$
$410$	44.9175	−	29.1697i	2.21832	−	1.44059i
$411$	10.1878	+	19.9946i	0.502526	+	0.986262i
$412$	53.0551	−	23.6217i	2.61384	−	1.16376i
$413$	1.72381	−	16.4010i	0.0848234	−	0.807041i
$414$	−11.5091	−	7.47407i	−0.565640	−	0.367331i
$415$	3.49448	+	10.7549i	0.171537	+	0.527938i
$416$	5.16992	−	0.383746i	0.253476	−	0.0188147i
$417$			3.18561i			0.156000i
$418$	6.37584	+	10.0791i	0.311852	+	0.492987i
$419$	3.69565	+	6.40106i	0.180545	+	0.312712i	0.942066	−	0.335427i	$-0.108881\pi$
$419$	3.69565	+	6.40106i	0.180545	+	0.312712i	−0.761522	+	0.648140i	$0.775547\pi$
$420$	2.39780	+	22.8135i	0.117001	+	1.11319i
$421$	7.78535	−	15.2796i	0.379435	−	0.744683i	−0.619761	−	0.784791i	$-0.712770\pi$
$421$	7.78535	−	15.2796i	0.379435	−	0.744683i	0.999195	+	0.0401083i	$0.0127703\pi$
$422$	1.40470	−	26.8032i	0.0683795	−	1.30476i
$423$	−3.59170	+	9.35669i	−0.174634	+	0.454938i
$424$	−3.65543	−	23.0795i	−0.177523	−	1.12084i
$425$	−5.10098	+	4.59294i	−0.247434	+	0.222790i
$426$	−2.17461	+	2.41515i	−0.105360	+	0.117014i
$427$	−15.5169	+	5.95639i	−0.750916	+	0.288250i
$428$	32.2134			1.55710
$429$	−11.5199	+	3.20809i	−0.556186	+	0.154888i
$430$	22.1272			1.06707
$431$	6.65076	−	2.55299i	0.320356	−	0.122973i	−0.192876	−	0.981223i	$-0.561781\pi$
$431$	6.65076	−	2.55299i	0.320356	−	0.122973i	0.513232	+	0.858250i	$0.328448\pi$
$432$	3.25235	−	3.61210i	0.156479	−	0.173787i
$433$	0.945788	−	0.851592i	0.0454517	−	0.0409249i	−0.646092	−	0.763260i	$-0.723598\pi$
$433$	0.945788	−	0.851592i	0.0454517	−	0.0409249i	0.691543	+	0.722335i	$0.256931\pi$
$434$	1.58648	+	10.0167i	0.0761536	+	0.480815i
$435$	−10.4969	+	27.3454i	−0.503289	+	1.31111i
$436$	−3.86864	+	73.8181i	−0.185274	+	3.53525i
$437$	−3.64865	+	7.16087i	−0.174538	+	0.342551i
$438$	−3.67654	−	34.9799i	−0.175672	−	1.67141i
$439$	−11.8719	−	20.5628i	−0.566616	−	0.981408i	−0.996897	−	0.0787129i	$-0.974919\pi$
$439$	−11.8719	−	20.5628i	−0.566616	−	0.981408i	0.430281	−	0.902695i	$-0.358414\pi$
$440$	−40.8668	+	49.2532i	−1.94825	+	2.34805i
$441$		−	4.68139i		−	0.222923i
$442$	4.18798	+	6.15200i	0.199202	+	0.292621i
$443$	9.87434	+	30.3901i	0.469144	+	1.44388i	0.853695	+	0.520773i	$0.174356\pi$
$443$	9.87434	+	30.3901i	0.469144	+	1.44388i	−0.384551	+	0.923104i	$0.625644\pi$
$444$	−1.91004	−	1.24040i	−0.0906466	−	0.0588666i
$445$	1.19028	−	11.3248i	0.0564248	−	0.536846i
$446$	−27.7883	+	12.3721i	−1.31581	+	0.585838i
$447$	−0.153655	−	0.301565i	−0.00726764	−	0.0142635i
$448$	−7.86438	+	5.10719i	−0.371557	+	0.241292i
$449$	15.0184	+	12.1616i	0.708761	+	0.573944i	0.914462	−	0.404671i	$-0.132614\pi$
$449$	15.0184	+	12.1616i	0.708761	+	0.573944i	−0.205701	+	0.978615i	$0.565947\pi$
$450$	14.4383	+	14.4383i	0.680626	+	0.680626i
$451$	18.6626	+	6.31094i	0.878786	+	0.297170i
$452$	−22.9979	+	13.2778i	−1.08173	+	0.624537i
$453$	3.89813	+	10.1550i	0.183150	+	0.477123i
$454$	−27.0930	+	8.80306i	−1.27154	+	0.413148i
$455$	−1.65598	+	19.9084i	−0.0776334	+	0.933320i
$456$	−6.22612	−	4.52354i	−0.291565	−	0.211834i
$457$	−6.18782	−	7.64133i	−0.289454	−	0.357446i	0.611589	−	0.791176i	$-0.290531\pi$
$457$	−6.18782	−	7.64133i	−0.289454	−	0.357446i	−0.901043	+	0.433730i	$0.857197\pi$
$458$	7.21470	+	33.9425i	0.337121	+	1.58603i
$459$	0.814787	+	0.173188i	0.0380310	+	0.00808374i
$460$	−82.4031	−	13.0514i	−3.84206	−	0.608523i
$461$	−4.30184	−	16.0547i	−0.200357	−	0.747741i	−0.990815	−	0.135225i	$-0.956824\pi$
$461$	−4.30184	−	16.0547i	−0.200357	−	0.747741i	0.790458	−	0.612516i	$-0.209842\pi$
$462$	−8.95374	+	8.74262i	−0.416565	+	0.406744i
$463$	19.8721	−	19.8721i	0.923535	−	0.923535i	−0.0737425	−	0.997277i	$-0.523494\pi$
$463$	19.8721	−	19.8721i	0.923535	−	0.923535i	0.997277	+	0.0737425i	$0.0234943\pi$
$464$	38.9122	−	4.08983i	1.80645	−	0.189866i
$465$	7.26810	+	6.54423i	0.337050	+	0.303481i
$466$	0.977268	−	1.50486i	0.0452711	−	0.0697113i
$467$	10.5740	−	14.5538i	0.489305	−	0.673470i	−0.490955	−	0.871185i	$-0.663352\pi$
$467$	10.5740	−	14.5538i	0.489305	−	0.673470i	0.980260	+	0.197715i	$0.0633520\pi$
$468$	11.8831	−	9.03453i	0.549297	−	0.417621i
$469$	8.21937	+	2.67064i	0.379535	+	0.123319i
$470$	4.72942	+	90.2428i	0.218152	+	4.16259i
$471$	2.44532	+	1.08873i	0.112674	+	0.0501658i
$472$	−28.7175	+	49.7401i	−1.32183	+	2.28948i
$473$	5.04638	+	6.38604i	0.232033	+	0.293630i
$474$	33.7825	−	9.05201i	1.55168	−	0.415772i
$475$	7.52554	−	9.29327i	0.345296	−	0.426404i
$476$	4.67897	+	2.38406i	0.214460	+	0.109273i
$477$	−2.94837	−	3.27450i	−0.134997	−	0.149929i
$478$	−25.5671	−	2.68721i	−1.16941	−	0.122910i
$479$	27.3441	−	22.1428i	1.24939	−	1.01173i	0.250335	−	0.968159i	$-0.419459\pi$
$479$	27.3441	−	22.1428i	1.24939	−	1.01173i	0.999050	−	0.0435732i	$-0.0138742\pi$
$480$	1.61672	−	4.97577i	0.0737930	−	0.227112i
$481$	−1.43261	−	1.37166i	−0.0653213	−	0.0625422i
$482$	−46.2851	+	33.6281i	−2.10823	+	1.53172i
$483$	−8.14548	−	2.18258i	−0.370632	−	0.0993106i
$484$	−45.5287	−	1.08646i	−2.06949	−	0.0493844i
$485$	−58.7633	−	33.9270i	−2.66830	−	1.54055i
$486$	0.387634	−	2.44743i	0.0175834	−	0.111017i
$487$	−11.0067	−	16.9489i	−0.498762	−	0.768026i	0.496208	−	0.868204i	$-0.334725\pi$
$487$	−11.0067	−	16.9489i	−0.498762	−	0.768026i	−0.994970	+	0.100178i	$0.968059\pi$
$488$	57.8067	+	3.02952i	2.61679	+	0.137140i
$489$	4.09571	−	0.648697i	0.185215	−	0.0293351i
$490$	−17.1682	−	38.5605i	−0.775582	−	1.74199i
$491$	−2.61042	+	0.554861i	−0.117806	+	0.0250405i	−0.266438	−	0.963852i	$-0.585847\pi$
$491$	−2.61042	+	0.554861i	−0.117806	+	0.0250405i	0.148631	+	0.988893i	$0.452513\pi$
$492$	−24.5588	+	1.28707i	−1.10720	+	0.0580257i
$493$	3.94133	+	5.42478i	0.177509	+	0.244320i
$494$	−8.88289	−	9.44441i	−0.399660	−	0.424924i
$495$	−1.40456	+	11.9862i	−0.0631303	+	0.538741i
$496$	3.38128	−	12.6191i	0.151824	−	0.566615i
$497$	−0.812283	+	1.82442i	−0.0364359	+	0.0818363i
$498$	1.60111	−	7.53262i	0.0717474	−	0.337545i
$499$	13.4461	−	6.85115i	0.601932	−	0.306700i	−0.126341	−	0.991987i	$-0.540323\pi$
$499$	13.4461	−	6.85115i	0.601932	−	0.306700i	0.728273	+	0.685287i	$0.240323\pi$
$500$	45.5716	+	17.4933i	2.03802	+	0.782324i
$501$	15.5840	+	5.98213i	0.696240	+	0.267262i
$502$	−55.4593	+	28.2579i	−2.47527	+	1.26121i
$503$	−4.49247	+	21.1354i	−0.200309	+	0.942381i	0.757022	+	0.653389i	$0.226653\pi$
$503$	−4.49247	+	21.1354i	−0.200309	+	0.942381i	−0.957331	+	0.288992i	$0.906680\pi$
$504$	3.28444	−	7.37697i	0.146301	−	0.328597i
$505$	−14.2944	+	53.3474i	−0.636092	+	2.37393i
$506$	−22.2852	−	39.6849i	−0.990697	−	1.76421i
$507$	11.6351	−	5.79858i	0.516735	−	0.257524i
$508$	−37.4783	−	51.5844i	−1.66283	−	2.28869i
$509$	3.18647	−	0.166996i	0.141238	−	0.00740195i	0.0184139	−	0.999830i	$-0.494138\pi$
$509$	3.18647	−	0.166996i	0.141238	−	0.00740195i	0.122824	+	0.992428i	$0.460805\pi$
$510$	7.34652	−	1.56155i	0.325309	−	0.0691466i
$511$	−8.79108	−	19.7451i	−0.388895	−	0.873472i
$512$	44.0153	−	6.97133i	1.94522	−	0.308092i
$513$	−1.44921	−	0.0759497i	−0.0639840	−	0.00335326i
$514$	−14.7872	−	22.7703i	−0.652235	−	1.00435i
$515$	7.98475	−	50.4137i	0.351850	−	2.22149i
$516$	−8.79903	−	5.08012i	−0.387356	−	0.223640i
$517$	−24.9660	+	21.9459i	−1.09800	+	0.965181i
$518$	−2.00485	−	0.537198i	−0.0880881	−	0.0236031i
$519$	−6.37668	+	4.63293i	−0.279905	+	0.203363i
$520$	33.4701	−	60.9955i	1.46776	−	2.67483i
$521$	−1.68597	+	5.18889i	−0.0738638	+	0.227329i	−0.981172	−	0.193137i	$-0.938134\pi$
$521$	−1.68597	+	5.18889i	−0.0738638	+	0.227329i	0.907308	+	0.420467i	$0.138134\pi$
$522$	15.5016	−	12.5530i	0.678488	−	0.549428i
$523$	−5.47099	−	0.575025i	−0.239230	−	0.0251441i	−0.0158453	−	0.999874i	$-0.505044\pi$
$523$	−5.47099	−	0.575025i	−0.239230	−	0.0251441i	−0.223385	+	0.974730i	$0.571711\pi$
$524$	35.6503	+	39.5937i	1.55739	+	1.72966i
$525$	11.1798	+	5.69640i	0.487927	+	0.248611i
$526$	20.3980	−	25.1895i	0.889397	−	1.09831i
$527$	2.16263	−	0.579476i	0.0942058	−	0.0252424i
$528$	15.1178	−	5.59718i	0.657916	−	0.243586i
$529$	3.83516	−	6.64269i	0.166746	−	0.288812i
$530$	−36.2944	−	16.1593i	−1.57653	−	0.701915i
$531$	0.566816	+	10.8155i	0.0245977	+	0.469353i
$532$	−8.70086	−	2.82708i	−0.377230	−	0.122570i
$533$	−21.2211	−	2.88991i	−0.919187	−	0.125176i
$534$	−4.55801	+	6.27357i	−0.197244	+	0.271484i
$535$	15.4198	−	23.7443i	0.666654	−	1.02656i
$536$	−22.3679	−	20.1402i	−0.966148	−	0.869924i
$537$	−23.6791	+	2.48878i	−1.02183	+	0.107399i
$538$	33.2692	−	33.2692i	1.43434	−	1.43434i
$539$	7.21337	−	13.7491i	0.310702	−	0.592214i
$540$	−3.89907	−	14.5515i	−0.167789	−	0.626197i
$541$	32.0705	+	5.07947i	1.37882	+	0.218383i	0.801431	−	0.598087i	$-0.204072\pi$
$541$	32.0705	+	5.07947i	1.37882	+	0.218383i	0.577387	+	0.816471i	$0.304072\pi$
$542$	−11.1901	−	2.37853i	−0.480657	−	0.102167i
$543$	−1.34820	−	6.34279i	−0.0578568	−	0.272195i
$544$	−0.753732	−	0.930782i	−0.0323160	−	0.0399069i
$545$	52.5591	+	38.1864i	2.25138	+	1.63573i
$546$	7.75534	−	11.1772i	0.331898	−	0.478342i
$547$	−12.2405	+	3.97719i	−0.523367	+	0.170052i	−0.558773	−	0.829321i	$-0.688728\pi$
$547$	−12.2405	+	3.97719i	−0.523367	+	0.170052i	0.0354058	+	0.999373i	$0.488728\pi$
$548$	−33.2949	−	86.7362i	−1.42229	−	3.70519i
$549$	9.45302	−	5.45770i	0.403445	−	0.232929i
$550$	20.1573	+	64.6520i	0.859509	+	2.75677i
$551$	−8.26030	−	8.26030i	−0.351901	−	0.351901i
$552$	22.8242	+	18.4827i	0.971463	+	0.786675i
$553$	18.0245	−	11.7053i	0.766482	−	0.497759i
$554$	4.91490	+	9.64604i	0.208814	+	0.409821i
$555$	−1.82858	+	0.814135i	−0.0776188	+	0.0345581i
$556$	1.37862	−	13.1166i	0.0584663	−	0.556270i
$557$	1.91771	+	1.24538i	0.0812560	+	0.0527683i	0.584628	−	0.811302i	$-0.301241\pi$
$557$	1.91771	+	1.24538i	0.0812560	+	0.0527683i	−0.503372	+	0.864070i	$0.667907\pi$
$558$	−2.05812	−	6.33425i	−0.0871273	−	0.268150i
$559$	−6.70267	−	5.77639i	−0.283493	−	0.244315i
$560$		−	26.9307i		−	1.13803i
$561$	2.12614	+	1.76412i	0.0897657	+	0.0744812i
$562$	16.4098	+	28.4226i	0.692206	+	1.19894i
$563$	−1.34387	−	12.7861i	−0.0566373	−	0.538868i	−0.985648	−	0.168815i	$-0.946006\pi$
$563$	−1.34387	−	12.7861i	−0.0566373	−	0.538868i	0.929011	−	0.370053i	$-0.120661\pi$
$564$	18.8379	−	36.9715i	0.793221	−	1.55678i
$565$	−1.22149	+	23.3074i	−0.0513884	+	0.980549i
$566$	−13.5902	+	35.4037i	−0.571239	+	1.48813i
$567$	−0.238202	−	1.50395i	−0.0100036	−	0.0631600i
$568$	5.16878	−	4.65399i	0.216877	−	0.195277i
$569$	27.9989	−	31.0959i	1.17378	−	1.30361i	0.229935	−	0.973206i	$-0.426148\pi$
$569$	27.9989	−	31.0959i	1.17378	−	1.30361i	0.943840	−	0.330404i	$-0.107185\pi$
$570$	−12.2156	+	4.68913i	−0.511656	+	0.196406i
$571$	20.8613			0.873018			0.436509	−	0.899700i	$-0.356215\pi$
$571$	20.8613			0.873018			0.436509	+	0.899700i	$0.356215\pi$
$572$	48.8212	−	8.22383i	2.04132	−	0.343856i
$573$	−11.9060			−0.497378
$574$	−20.9238	+	8.03191i	−0.873344	+	0.335245i
$575$	−30.5359	+	33.9135i	−1.27343	+	1.41429i
$576$	4.57649	−	4.12069i	0.190687	−	0.171696i
$577$	3.24444	+	20.4846i	0.135068	+	0.852785i	0.958442	+	0.285286i	$0.0920887\pi$
$577$	3.24444	+	20.4846i	0.135068	+	0.852785i	−0.823375	+	0.567498i	$0.807911\pi$
$578$	−14.4800	+	37.7218i	−0.602290	+	1.56902i
$579$	0.533201	−	10.1741i	0.0221591	−	0.422820i
$580$	55.0549	−	108.051i	2.28603	−	4.48659i
$581$	−0.494653	−	4.70631i	−0.0205217	−	0.195251i
$582$	23.1040	+	40.0173i	0.957691	+	1.65877i
$583$	−3.61371	−	14.1601i	−0.149665	−	0.586452i
$584$			75.2748i			3.11489i
$585$	−0.971151	−	13.0836i	−0.0401522	−	0.540939i
$586$	−14.5391	−	44.7467i	−0.600603	−	1.84847i
$587$	−6.38699	−	4.14776i	−0.263619	−	0.171196i	0.406061	−	0.913846i	$-0.366902\pi$
$587$	−6.38699	−	4.14776i	−0.263619	−	0.171196i	−0.669680	+	0.742650i	$0.733569\pi$
$588$	−2.02594	+	19.2755i	−0.0835482	+	0.794908i
$589$	−3.56332	+	1.58649i	−0.146824	+	0.0653704i
$590$	44.3329	+	87.0083i	1.82516	+	3.58207i
$591$	−3.71590	+	2.41314i	−0.152852	+	0.0992631i
$592$	2.07789	+	1.68265i	0.0854010	+	0.0691563i
$593$	2.65737	+	2.65737i	0.109125	+	0.109125i	0.759561	−	0.650436i	$-0.225414\pi$
$593$	2.65737	+	2.65737i	0.109125	+	0.109125i	−0.650436	+	0.759561i	$0.725414\pi$
$594$	4.90961	−	6.59071i	0.201444	−	0.270420i
$595$	3.99698	−	2.30766i	0.163860	−	0.0946048i
$596$	0.502164	+	1.30818i	0.0205694	+	0.0535852i
$597$	10.1598	−	3.30111i	0.415811	−	0.135105i
$598$	31.9663	+	37.7667i	1.30720	+	1.54439i
$599$	−24.5498	−	17.8365i	−1.00308	−	0.728779i	−0.0403319	−	0.999186i	$-0.512842\pi$
$599$	−24.5498	−	17.8365i	−1.00308	−	0.728779i	−0.962746	+	0.270408i	$0.912842\pi$
$600$	−27.5009	−	33.9607i	−1.12272	−	1.38644i
$601$	−5.34831	−	25.1618i	−0.218162	−	1.02637i	−0.941795	−	0.336187i	$-0.890862\pi$
$601$	−5.34831	−	25.1618i	−0.218162	−	1.02637i	0.723633	−	0.690185i	$-0.242471\pi$
$602$	−9.05724	−	1.92518i	−0.369146	−	0.0784643i
$603$	−5.60581	−	0.887873i	−0.228286	−	0.0361570i
$604$	−11.6557	−	43.4998i	−0.474266	−	1.76998i
$605$	−22.5943	+	33.0389i	−0.918587	+	1.34322i
$606$	26.5947	−	26.5947i	1.08034	−	1.08034i
$607$	15.6510	−	1.64499i	0.635255	−	0.0667680i	0.218573	−	0.975821i	$-0.429860\pi$
$607$	15.6510	−	1.64499i	0.635255	−	0.0667680i	0.416681	+	0.909053i	$0.363193\pi$
$608$	1.55062	+	1.39618i	0.0628859	+	0.0566227i
$609$	6.67587	−	10.2799i	0.270520	−	0.416564i
$610$	57.8490	−	79.6224i	2.34224	−	3.22382i
$611$	22.1256	−	28.5706i	0.895107	−	1.15584i
$612$	−3.27991	−	1.06571i	−0.132583	−	0.0430787i
$613$	−0.223245	−	4.25977i	−0.00901679	−	0.172051i	−0.999426	−	0.0338839i	$-0.989212\pi$
$613$	−0.223245	−	4.25977i	−0.00901679	−	0.172051i	0.990409	−	0.138167i	$-0.0441210\pi$
$614$	39.8976	+	17.7636i	1.61014	+	0.716880i
$615$	−10.8070	+	18.7182i	−0.435779	+	0.754792i
$616$	21.0132	−	16.6050i	0.846645	−	0.669036i
$617$	11.4180	−	3.05943i	0.459670	−	0.123168i	−0.0215506	−	0.999768i	$-0.506860\pi$
$617$	11.4180	−	3.05943i	0.459670	−	0.123168i	0.481221	+	0.876600i	$0.340194\pi$
$618$	−21.8747	+	27.0130i	−0.879930	+	1.08662i
$619$	5.33290	+	2.71725i	0.214347	+	0.109215i	0.557868	−	0.829930i	$-0.311620\pi$
$619$	5.33290	+	2.71725i	0.214347	+	0.109215i	−0.343521	+	0.939145i	$0.611620\pi$
$620$	−27.0941	−	30.0910i	−1.08812	−	1.20849i
$621$	5.50774	+	0.578887i	0.221018	+	0.0232299i
$622$	−3.86919	+	3.13321i	−0.155140	+	0.125630i
$623$	−1.47253	+	4.53197i	−0.0589956	+	0.181570i
$624$	−14.9831	+	9.09021i	−0.599804	+	0.363900i
$625$	1.37567	−	0.999481i	0.0550267	−	0.0399793i
$626$	66.4524	+	17.8059i	2.65597	+	0.711665i
$627$	−4.13924	−	2.45609i	−0.165305	−	0.0980867i
$628$	−9.59737	−	5.54104i	−0.382977	−	0.221112i
$629$	−0.0716815	+	0.452579i	−0.00285813	+	0.0180455i
$630$	−7.47757	−	11.5144i	−0.297913	−	0.458746i
$631$	10.5456	+	0.552674i	0.419815	+	0.0220016i	0.261074	−	0.965319i	$-0.415923\pi$
$631$	10.5456	+	0.552674i	0.419815	+	0.0220016i	0.158741	+	0.987320i	$0.449257\pi$
$632$	−73.9287	+	11.7092i	−2.94073	+	0.465765i
$633$	4.40561	+	9.89516i	0.175107	+	0.393297i
$634$	−54.9394	+	11.6777i	−2.18192	+	0.463782i
$635$	−55.9625	+	2.93287i	−2.22080	+	0.116387i
$636$	10.7228	+	14.7586i	0.425185	+	0.585217i
$637$	−4.86585	+	16.1624i	−0.192792	+	0.640378i
$638$	64.8701	−	12.9817i	2.56823	−	0.513952i
$639$	0.339450	−	1.26685i	0.0134285	−	0.0501157i
$640$	26.8404	−	60.2846i	1.06096	−	2.38296i
$641$	0.0963730	−	0.453399i	0.00380650	−	0.0179082i	−0.976203	−	0.216857i	$-0.930419\pi$
$641$	0.0963730	−	0.453399i	0.00380650	−	0.0179082i	0.980010	+	0.198949i	$0.0637528\pi$
$642$	−17.1787	+	8.75300i	−0.677991	+	0.345453i
$643$	−32.6763	−	12.5432i	−1.28863	−	0.494657i	−0.384975	−	0.922927i	$-0.625790\pi$
$643$	−32.6763	−	12.5432i	−1.28863	−	0.494657i	−0.903651	+	0.428270i	$0.859123\pi$
$644$	32.5943	+	12.5118i	1.28439	+	0.493032i
$645$	−7.95641	+	4.05399i	−0.313283	+	0.159626i
$646$	−0.622779	+	2.92994i	−0.0245029	+	0.115277i
$647$	8.50772	−	19.1087i	0.334473	−	0.751239i	−0.665515	−	0.746384i	$-0.731788\pi$
$647$	8.50772	−	19.1087i	0.334473	−	0.751239i	0.999988	−	0.00485455i	$-0.00154526\pi$
$648$	−1.37256	+	5.12245i	−0.0539191	+	0.201229i
$649$	−15.0005	+	32.6381i	−0.588820	+	1.28116i
$650$	−34.8407	−	64.8550i	−1.36656	−	2.54382i
$651$	−2.40565	−	3.31109i	−0.0942847	−	0.129772i
$652$	−17.1447	+	0.898516i	−0.671439	+	0.0351886i
$653$	−8.13728	+	1.72963i	−0.318436	+	0.0676857i	−0.364357	−	0.931259i	$-0.618711\pi$
$653$	−8.13728	+	1.72963i	−0.318436	+	0.0676857i	0.0459206	+	0.998945i	$0.485378\pi$
$654$	−17.9947	−	40.4168i	−0.703649	−	1.58042i
$655$	46.2492	−	7.32516i	1.80711	−	0.286218i
$656$	28.8321	+	1.51103i	1.12570	+	0.0589957i
$657$	7.73079	+	11.9044i	0.301607	+	0.464434i
$658$	5.91570	−	37.3503i	0.230618	−	1.45607i
$659$	−26.8475	−	15.5004i	−1.04583	−	0.603809i	−0.124350	−	0.992238i	$-0.539684\pi$
$659$	−26.8475	−	15.5004i	−1.04583	−	0.603809i	−0.921479	+	0.388429i	$0.873018\pi$
$660$	10.9704	−	48.7452i	0.427024	−	1.89740i
$661$	13.9882	+	3.74812i	0.544077	+	0.145785i	0.520381	−	0.853934i	$-0.325790\pi$
$661$	13.9882	+	3.74812i	0.544077	+	0.145785i	0.0236960	+	0.999719i	$0.492457\pi$
$662$	−47.2807	+	34.3514i	−1.83762	+	1.33511i
$663$	−2.63303	−	1.44482i	−0.102258	−	0.0561122i
$664$	−5.09294	+	15.6745i	−0.197645	+	0.608287i
$665$	−6.24871	+	5.06010i	−0.242315	+	0.196222i
$666$	1.35562	+	0.142482i	0.0525293	+	0.00552106i
$667$	29.8301	+	33.1297i	1.15503	+	1.28279i
$668$	−61.5777	−	31.3754i	−2.38251	−	1.21395i
$669$	7.72527	−	9.53992i	0.298676	−	0.368834i
$670$	−49.4311	+	13.2450i	−1.90969	+	0.511699i
$671$	36.1727	−	1.46328i	1.39643	−	0.0564894i
$672$	−1.09469	+	1.89605i	−0.0422284	+	0.0731418i
$673$	−12.1349	−	5.40282i	−0.467767	−	0.208263i	0.159297	−	0.987231i	$-0.449077\pi$
$673$	−12.1349	−	5.40282i	−0.467767	−	0.208263i	−0.627065	+	0.778967i	$0.715744\pi$
$674$	2.51237	+	47.9390i	0.0967731	+	1.84654i
$675$	−7.83694	−	2.54638i	−0.301644	−	0.0980101i
$676$	−50.4168	+	18.8402i	−1.93911	+	0.724624i
$677$	−4.24565	+	5.84363i	−0.163174	+	0.224589i	−0.882772	−	0.469801i	$-0.844326\pi$
$677$	−4.24565	+	5.84363i	−0.163174	+	0.224589i	0.719599	+	0.694390i	$0.244326\pi$
$678$	8.65644	−	13.3297i	0.332449	−	0.511926i
$679$	21.1016	+	18.9999i	0.809804	+	0.729151i
$680$	−15.9859	+	1.68018i	−0.613030	+	0.0644321i
$681$	8.12918	−	8.12918i	0.311511	−	0.311511i
$682$	3.71557	−	21.7747i	0.142277	−	0.833798i
$683$	3.92813	+	14.6600i	0.150306	+	0.560949i	0.999462	+	0.0328068i	$0.0104446\pi$
$683$	3.92813	+	14.6600i	0.150306	+	0.560949i	−0.849156	+	0.528142i	$0.822889\pi$
$684$	5.93420	+	0.939885i	0.226900	+	0.0359374i
$685$	−79.8702	−	16.9769i	−3.05168	−	0.648655i
$686$	9.16383	+	43.1124i	0.349877	+	1.64604i
$687$	−8.81296	−	10.8831i	−0.336235	−	0.415216i
$688$	9.65010	+	7.01120i	0.367906	+	0.267300i
$689$	6.77569	+	14.3697i	0.258133	+	0.547442i
$690$	47.4901	−	15.4305i	1.80792	−	0.587428i
$691$	10.6309	+	27.6945i	0.404420	+	1.05355i	0.972976	+	0.230905i	$0.0741687\pi$
$691$	10.6309	+	27.6945i	0.404420	+	1.05355i	−0.568557	+	0.822644i	$0.692498\pi$
$692$	28.2608	−	16.3164i	1.07431	−	0.620255i
$693$	1.61779	−	4.78409i	0.0614547	−	0.181732i
$694$	−26.5322	−	26.5322i	−1.00715	−	1.00715i
$695$	−9.00830	−	7.29478i	−0.341704	−	0.276707i
$696$	−35.8023	+	23.2503i	−1.35708	+	0.881299i
$697$	2.24632	+	4.40866i	0.0850856	+	0.166990i
$698$	47.1756	−	21.0039i	1.78562	−	0.795011i
$699$	−0.0756920	+	0.720161i	−0.00286293	+	0.0272390i
$700$	−43.5674	−	28.2930i	−1.64669	−	1.06938i
$701$	−1.64593	−	5.06566i	−0.0621660	−	0.191327i	0.915150	−	0.403113i	$-0.132072\pi$
$701$	−1.64593	−	5.06566i	−0.0621660	−	0.191327i	−0.977316	+	0.211786i	$0.932072\pi$
$702$	−3.88216	+	8.04679i	−0.146523	+	0.303706i
$703$		−	0.798290i		−	0.0301081i
$704$	19.7904	−	5.05058i	0.745879	−	0.190351i
$705$	−18.2343	−	31.5827i	−0.686742	−	1.18947i
$706$	0.360417	+	3.42914i	0.0135645	+	0.129057i
$707$	10.4926	−	20.5928i	0.394614	−	0.774473i
$708$	2.34671	−	44.7778i	0.0881946	−	1.68285i
$709$	−7.16409	+	18.6631i	−0.269053	+	0.700907i	0.730780	+	0.682614i	$0.239157\pi$
$709$	−7.16409	+	18.6631i	−0.269053	+	0.700907i	−0.999833	+	0.0182938i	$0.994177\pi$
$710$	−1.84991	−	11.6799i	−0.0694258	−	0.438337i
$711$	−10.4890	+	9.44430i	−0.393367	+	0.354189i
$712$	11.1048	−	12.3332i	0.416171	−	0.462205i
$713$	13.8967	−	5.33443i	0.520434	−	0.199776i
$714$	−3.14299			−0.117623
$715$	17.3077	−	39.9224i	0.647273	−	1.49301i
$716$	98.5752			3.68393
$717$	9.68566	−	3.71798i	0.361717	−	0.138850i
$718$	−30.8532	+	34.2660i	−1.15143	+	1.27880i
$719$	−8.77951	+	7.90511i	−0.327420	+	0.294811i	−0.816403	−	0.577483i	$-0.804035\pi$
$719$	−8.77951	+	7.90511i	−0.327420	+	0.294811i	0.488982	+	0.872294i	$0.337368\pi$
$720$	2.76673	+	17.4684i	0.103110	+	0.651010i
$721$	−7.65462	+	19.9410i	−0.285073	+	0.742641i
$722$	−2.19090	+	41.8049i	−0.0815369	+	1.55582i
$723$	10.4819	−	20.5719i	0.389827	−	0.765078i
$724$	2.80625	+	26.6997i	0.104293	+	0.992286i
$725$	−33.1662	−	57.4455i	−1.23176	−	2.13347i
$726$	24.5747	−	11.7916i	0.912053	−	0.437629i
$727$		−	8.95660i		−	0.332182i	−0.986110	−	0.166091i	$-0.946885\pi$
$727$		−	8.95660i		−	0.332182i	0.986110	−	0.166091i	$-0.0531145\pi$
$728$	−19.0071	+	22.0550i	−0.704451	+	0.817414i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	107.336	+	69.7046i	3.97267	+	2.57988i
$731$	−0.213679	+	2.03302i	−0.00790321	+	0.0751940i
$732$	−41.2844	+	18.3810i	−1.52592	+	0.679382i
$733$	4.35350	+	8.54423i	0.160800	+	0.315588i	0.957323	−	0.289020i	$-0.0933295\pi$
$733$	4.35350	+	8.54423i	0.160800	+	0.315588i	−0.796523	+	0.604609i	$0.793330\pi$
$734$	−6.54624	+	4.25118i	−0.241626	+	0.156914i
$735$	13.2381	+	10.7200i	0.488294	+	0.395413i
$736$	−5.63054	−	5.63054i	−0.207544	−	0.207544i
$737$	−15.0960	−	11.2454i	−0.556067	−	0.414231i
$738$	12.7470	−	7.35946i	0.469222	−	0.270905i
$739$	4.09656	+	10.6719i	0.150694	+	0.392572i	0.988060	−	0.154071i	$-0.0492386\pi$
$739$	4.09656	+	10.6719i	0.150694	+	0.392572i	−0.837365	+	0.546644i	$0.815905\pi$
$740$	7.88144	−	2.56084i	0.289728	−	0.0941382i
$741$	4.92442	+	1.76852i	0.180903	+	0.0649683i
$742$	13.4503	+	9.77223i	0.493777	+	0.358750i
$743$	−4.10842	−	5.07347i	−0.150723	−	0.186128i	0.696192	−	0.717856i	$-0.254876\pi$
$743$	−4.10842	−	5.07347i	−0.150723	−	0.186128i	−0.846915	+	0.531728i	$0.821543\pi$
$744$	2.96355	+	13.9424i	0.108649	+	0.511154i
$745$	1.20463	+	0.256051i	0.0441341	+	0.00938100i
$746$	30.1068	+	4.76845i	1.10229	+	0.174585i
$747$	0.804356	+	3.00190i	0.0294299	+	0.109834i
$748$	−7.99087	−	8.18383i	−0.292175	−	0.299231i
$749$	−8.37760	+	8.37760i	−0.306111	+	0.306111i
$750$	−29.0556	+	3.05387i	−1.06096	+	0.111511i
$751$	11.4349	+	10.2961i	0.417267	+	0.375708i	0.850853	−	0.525403i	$-0.176086\pi$
$751$	11.4349	+	10.2961i	0.417267	+	0.375708i	−0.433587	+	0.901112i	$0.642752\pi$
$752$	−26.5317	+	40.8552i	−0.967512	+	1.48984i
$753$	14.7646	−	20.3218i	0.538053	−	0.740567i
$754$	−66.5667	+	27.2265i	−2.42422	+	0.991530i
$755$	−37.6428	−	12.2309i	−1.36996	−	0.445127i
$756$	0.329936	+	6.29556i	0.0119997	+	0.228967i
$757$	−32.4264	−	14.4372i	−1.17856	−	0.524727i	−0.278473	−	0.960444i	$-0.589828\pi$
$757$	−32.4264	−	14.4372i	−1.17856	−	0.524727i	−0.900084	+	0.435716i	$0.856495\pi$
$758$	14.8301	−	25.6865i	0.538654	−	0.932976i
$759$	15.2840	+	10.1868i	0.554776	+	0.369759i
$760$	27.0490	−	7.24777i	0.981172	−	0.262904i
$761$	26.4717	−	32.6899i	0.959599	−	1.18501i	−0.0230876	−	0.999733i	$-0.507350\pi$
$761$	26.4717	−	32.6899i	0.959599	−	1.18501i	0.982687	−	0.185273i	$-0.0593170\pi$
$762$	34.0028	+	17.3253i	1.23179	+	0.627629i
$763$	−18.1914	−	20.2036i	−0.658574	−	0.731421i
$764$	49.0224	+	5.15246i	1.77357	+	0.186410i
$765$	−2.35554	+	1.90748i	−0.0851647	+	0.0689650i
$766$	28.5827	−	87.9684i	1.03273	−	3.17843i
$767$	9.28473	−	37.9295i	0.335252	−	1.36955i
$768$	−26.3917	+	19.1747i	−0.952327	+	0.691906i
$769$	21.7084	+	5.81675i	0.782825	+	0.209757i	0.628030	−	0.778189i	$-0.283862\pi$
$769$	21.7084	+	5.81675i	0.782825	+	0.209757i	0.154795	+	0.987947i	$0.450528\pi$
$770$	−4.21918	−	45.3394i	−0.152049	−	1.63392i
$771$	9.48895	+	5.47845i	0.341736	+	0.197301i
$772$	−6.59841	+	41.6607i	−0.237482	+	1.49940i
$773$	6.45634	+	9.94189i	0.232218	+	0.357585i	0.935500	−	0.353326i	$-0.114949\pi$
$773$	6.45634	+	9.94189i	0.232218	+	0.357585i	−0.703282	+	0.710911i	$0.748283\pi$
$774$	6.07270	+	0.318257i	0.218279	+	0.0114395i
$775$	−21.8756	+	3.46475i	−0.785794	+	0.124458i
$776$	−40.2230	−	90.3424i	−1.44392	−	3.24310i
$777$	0.819320	−	0.174152i	0.0293929	−	0.00624766i
$778$	−60.2587	+	3.15803i	−2.16038	+	0.113221i
$779$	−5.06676	−	6.97380i	−0.181536	−	0.249862i
$780$	−1.66341	+	54.2916i	−0.0595597	+	1.94395i
$781$	2.94899	−	3.19763i	0.105523	−	0.114420i
$782$	2.95859	−	11.0416i	0.105799	−	0.394847i
$783$	−3.27415	+	7.35386i	−0.117009	+	0.262805i
$784$	4.73085	−	22.2569i	0.168959	−	0.794890i
$785$	−8.67829	+	4.42181i	−0.309741	+	0.157821i
$786$	−29.7699	−	11.4276i	−1.06186	−	0.407609i
$787$	−27.4617	−	10.5416i	−0.978904	−	0.375766i	−0.184284	−	0.982873i	$-0.558997\pi$
$787$	−27.4617	−	10.5416i	−0.978904	−	0.375766i	−0.794620	+	0.607107i	$0.792330\pi$
$788$	16.3444	−	8.32791i	0.582247	−	0.296669i
$789$	−2.71961	+	12.7947i	−0.0968205	+	0.455505i
$790$	−51.7619	+	116.259i	−1.84160	+	4.13631i
$791$	2.52785	−	9.43406i	0.0898799	−	0.335436i
$792$	−11.9241	+	12.9295i	−0.423706	+	0.459431i
$793$	−38.3091	+	9.01714i	−1.36040	+	0.320208i
$794$	20.8242	+	28.6621i	0.739025	+	1.01718i
$795$	16.0112	−	0.839112i	0.567859	−	0.0297602i
$796$	−43.2611	+	9.19544i	−1.53335	+	0.325924i
$797$	−16.6468	−	37.3893i	−0.589660	−	1.32440i	−0.924161	−	0.382002i	$-0.875235\pi$
$797$	−16.6468	−	37.3893i	−0.589660	−	1.32440i	0.334502	−	0.942395i	$-0.391432\pi$
$798$	5.40816	−	0.856568i	0.191447	−	0.0303222i
$799$	−8.33709	−	0.436928i	−0.294945	−	0.0154574i
$800$	6.45289	+	9.93659i	0.228144	+	0.351311i
$801$	0.489553	−	3.09092i	0.0172975	−	0.109212i
$802$	83.8635	+	48.4186i	2.96132	+	1.70972i
$803$	4.36206	+	46.8748i	0.153934	+	1.65417i
$804$	22.6975	+	6.08178i	0.800480	+	0.214488i
$805$	24.8244	−	18.0360i	0.874945	−	0.635685i
$806$	0.521802	+	24.0081i	0.0183797	+	0.845650i
$807$	−5.86745	+	18.0582i	−0.206544	+	0.635677i
$808$	−62.5544	+	50.6556i	−2.20066	+	1.78206i
$809$	−12.0460	−	1.26609i	−0.423516	−	0.0445133i	−0.109627	−	0.993973i	$-0.534966\pi$
$809$	−12.0460	−	1.26609i	−0.423516	−	0.0445133i	−0.313890	+	0.949460i	$0.601632\pi$
$810$	6.03321	+	6.70056i	0.211985	+	0.235434i
$811$	5.07351	+	2.58508i	0.178155	+	0.0907745i	0.540794	−	0.841155i	$-0.318124\pi$
$811$	5.07351	+	2.58508i	0.178155	+	0.0907745i	−0.362639	+	0.931930i	$0.618124\pi$
$812$	−31.9365	+	39.4383i	−1.12075	+	1.38401i
$813$	4.45948	−	1.19491i	0.156401	−	0.0419075i
$814$	3.76187	+	2.50729i	0.131853	+	0.0878805i
$815$	−7.54445	+	13.0674i	−0.264271	+	0.457730i
$816$	3.69876	+	1.64679i	0.129482	+	0.0576493i
$817$	−0.186386	−	3.55646i	−0.00652083	−	0.124425i
$818$	30.0398	+	9.76053i	1.05032	+	0.341269i
$819$	−0.740820	+	5.43996i	−0.0258863	+	0.190087i
$820$	52.5980	−	72.3949i	1.83680	−	2.52814i
$821$	9.85780	−	15.1797i	0.344040	−	0.529775i	−0.623721	−	0.781647i	$-0.714380\pi$
$821$	9.85780	−	15.1797i	0.344040	−	0.529775i	0.967760	+	0.251873i	$0.0810464\pi$
$822$	41.3233	+	37.2077i	1.44132	+	1.29777i
$823$	7.52283	−	0.790681i	0.262229	−	0.0275614i	0.0274986	−	0.999622i	$-0.491246\pi$
$823$	7.52283	−	0.790681i	0.262229	−	0.0275614i	0.234731	+	0.972060i	$0.424579\pi$
$824$	52.6017	−	52.6017i	1.83247	−	1.83247i
$825$	−19.0932	−	19.5542i	−0.664739	−	0.680791i
$826$	−10.5765	−	39.4720i	−0.368003	−	1.37341i
$827$	−30.9088	−	4.89547i	−1.07480	−	0.170232i	−0.406150	−	0.913806i	$-0.633129\pi$
$827$	−30.9088	−	4.89547i	−1.07480	−	0.170232i	−0.668653	+	0.743574i	$0.733129\pi$
$828$	−22.4274	−	4.76710i	−0.779408	−	0.165668i
$829$	−5.09801	−	23.9842i	−0.177061	−	0.833007i	−0.973572	−	0.228382i	$-0.926656\pi$
$829$	−5.09801	−	23.9842i	−0.177061	−	0.833007i	0.796510	−	0.604625i	$-0.206677\pi$
$830$	17.6344	+	21.7767i	0.612100	+	0.755881i
$831$	−3.53457	−	2.56801i	−0.122613	−	0.0890834i
$832$	−20.0833	+	9.46981i	−0.696264	+	0.328307i
$833$	3.70869	−	1.20503i	0.128499	−	0.0417517i
$834$	2.82886	+	7.36942i	0.0979553	+	0.255182i
$835$	−52.6023	+	30.3700i	−1.82038	+	1.05100i
$836$	15.9803	+	11.9042i	0.552690	+	0.411715i
$837$	1.90057	+	1.90057i	0.0656934	+	0.0656934i
$838$	14.2336	+	11.5261i	0.491690	+	0.398163i
$839$	36.8345	−	23.9206i	1.27167	−	0.825831i	0.280683	−	0.959800i	$-0.409439\pi$
$839$	36.8345	−	23.9206i	1.27167	−	0.825831i	0.990986	+	0.133969i	$0.0427723\pi$
$840$	13.3396	+	26.1804i	0.460260	+	0.903311i
$841$	−32.7042	+	14.5609i	−1.12773	+	0.502099i
$842$	4.44176	−	42.2606i	0.153073	−	1.45640i
$843$	−11.1080	−	7.21361i	−0.382579	−	0.248450i
$844$	−13.8577	−	42.6496i	−0.477002	−	1.46806i
$845$	−10.2462	+	46.1803i	−0.352481	+	1.58865i
$846$			24.8348i			0.853837i
$847$	12.1230	−	11.5579i	0.416551	−	0.397134i
$848$	−10.7085	−	18.5476i	−0.367730	−	0.636928i
$849$	−1.59971	−	15.2202i	−0.0549020	−	0.522357i
$850$	−7.72176	+	15.1548i	−0.264854	+	0.519805i
$851$	−0.159439	+	3.04228i	−0.00546550	+	0.104288i
$852$	−1.94592	+	5.06930i	−0.0666662	+	0.173671i
$853$	−4.10950	−	25.9463i	−0.140706	−	0.888385i	−0.952522	−	0.304471i	$-0.901520\pi$
$853$	−4.10950	−	25.9463i	−0.140706	−	0.888385i	0.811815	−	0.583914i	$-0.198480\pi$
$854$	−30.6067	+	27.5584i	−1.04734	+	0.943030i
$855$	3.53333	−	3.92417i	0.120837	−	0.134204i
$856$	38.5218	−	14.7871i	1.31665	−	0.505414i
$857$	8.63480			0.294959			0.147480	−	0.989065i	$-0.452884\pi$
$857$	8.63480			0.294959			0.147480	+	0.989065i	$0.452884\pi$
$858$	−23.8007	+	17.6512i	−0.812544	+	0.602604i
$859$	−13.5711			−0.463039			−0.231520	−	0.972830i	$-0.574370\pi$
$859$	−13.5711			−0.463039			−0.231520	+	0.972830i	$0.574370\pi$
$860$	34.5147	−	13.2490i	1.17694	−	0.451786i
$861$	6.05217	−	6.72161i	0.206257	−	0.229072i
$862$	13.1185	−	11.8119i	0.446816	−	0.402315i
$863$	0.0152803	+	0.0964759i	0.000520147	+	0.00328408i	0.987947	−	0.154792i	$-0.0494708\pi$
$863$	0.0152803	+	0.0964759i	0.000520147	+	0.00328408i	−0.987427	+	0.158076i	$0.949471\pi$
$864$	0.515270	−	1.34232i	0.0175298	−	0.0456668i
$865$	1.50102	−	28.6411i	0.0510361	−	0.973826i
$866$	1.43172	−	2.80990i	0.0486517	−	0.0954843i
$867$	−1.70445	−	16.2168i	−0.0578863	−	0.550751i
$868$	8.47227	+	14.6744i	0.287567	+	0.498081i
$869$	−45.3580	+	11.5755i	−1.53867	+	0.392673i
$870$			72.5809i			2.46072i
$871$	18.4311	+	8.89206i	0.624514	+	0.301296i
$872$	29.2589	+	90.0498i	0.990833	+	3.04947i
$873$	−15.6394	−	10.1563i	−0.529312	−	0.343739i
$874$	−2.08166	+	19.8056i	−0.0704131	+	0.669936i
$875$	−16.4010	+	7.30219i	−0.554455	+	0.246859i
$876$	−26.6795	−	52.3615i	−0.901418	−	1.76913i
$877$	31.8694	−	20.6962i	1.07615	−	0.698862i	0.120309	−	0.992736i	$-0.461611\pi$
$877$	31.8694	−	20.6962i	1.07615	−	0.698862i	0.955844	+	0.293874i	$0.0949447\pi$
$878$	−45.7239	−	37.0265i	−1.54311	−	1.24958i
$879$	13.4261	+	13.4261i	0.452851	+	0.452851i
$880$	−18.7906	+	55.5673i	−0.633432	+	1.87317i
$881$	−23.7353	+	13.7036i	−0.799661	+	0.461685i	−0.843353	−	0.537361i	$-0.819421\pi$
$881$	−23.7353	+	13.7036i	−0.799661	+	0.461685i	0.0436915	+	0.999045i	$0.486088\pi$
$882$	−4.15713	−	10.8297i	−0.139978	−	0.364655i
$883$	11.4641	−	3.72493i	0.385799	−	0.125354i	−0.109694	−	0.993965i	$-0.534987\pi$
$883$	11.4641	−	3.72493i	0.385799	−	0.125354i	0.495494	+	0.868612i	$0.334987\pi$
$884$	10.2161	+	7.08849i	0.343606	+	0.238412i
$885$	−31.8822	−	23.1638i	−1.07171	−	0.778641i
$886$	49.8295	+	61.5344i	1.67406	+	2.06729i
$887$	−0.735971	−	3.46247i	−0.0247115	−	0.116258i	0.964063	−	0.265673i	$-0.0855943\pi$
$887$	−0.735971	−	3.46247i	−0.0247115	−	0.116258i	−0.988775	+	0.149415i	$0.952261\pi$
$888$	−2.85347	−	0.606524i	−0.0957563	−	0.0203536i
$889$	23.1621	+	3.66852i	0.776832	+	0.123038i
$890$	−7.30300	−	27.2552i	−0.244797	−	0.913595i
$891$	−0.557874	+	3.26937i	−0.0186895	+	0.109528i
$892$	−35.9371	+	35.9371i	−1.20326	+	1.20326i
$893$	14.4647	−	1.52031i	0.484044	−	0.0508751i
$894$	−0.623251	−	0.561178i	−0.0208446	−	0.0187686i
$895$	47.1855	−	72.6593i	1.57724	−	2.42873i
$896$	−16.2316	+	22.3409i	−0.542259	+	0.746356i
$897$	−18.4137	−	7.72335i	−0.614815	−	0.257875i
$898$	45.5425	+	14.7976i	1.51977	+	0.493804i
$899$	1.13236	+	21.6067i	0.0377663	+	0.720624i
$900$	31.1664	+	13.8762i	1.03888	+	0.462539i
$901$	1.83519	−	3.17864i	0.0611391	−	0.105896i
$902$	48.7772	−	1.97317i	1.62410	−	0.0656993i
$903$	3.60949	−	0.967160i	0.120116	−	0.0321851i
$904$	−21.4066	+	26.4349i	−0.711972	+	0.879212i
$905$	21.0235	+	10.7120i	0.698844	+	0.356079i
$906$	18.0355	+	20.0304i	0.599189	+	0.665467i
$907$	−19.0417	−	2.00136i	−0.632268	−	0.0664541i	−0.217027	−	0.976166i	$-0.569636\pi$
$907$	−19.0417	−	2.00136i	−0.632268	−	0.0664541i	−0.415241	+	0.909711i	$0.636303\pi$
$908$	−36.9897	+	29.9537i	−1.22755	+	0.994047i
$909$	−4.69033	+	14.4354i	−0.155568	+	0.478790i
$910$	13.8480	+	47.5256i	0.459058	+	1.57546i
$911$	10.2343	−	7.43565i	0.339077	−	0.246354i	−0.405195	−	0.914230i	$-0.632796\pi$
$911$	10.2343	−	7.43565i	0.339077	−	0.246354i	0.744272	+	0.667876i	$0.232796\pi$
$912$	−6.81327	−	1.82561i	−0.225610	−	0.0604520i
$913$	−2.26314	+	10.0559i	−0.0748991	+	0.332801i
$914$	−21.1002	−	12.1822i	−0.697932	−	0.402951i
$915$	−6.21327	+	39.2291i	−0.205404	+	1.29687i
$916$	31.5773	+	48.6248i	1.04334	+	1.60661i
$917$	−19.5684	−	1.02553i	−0.646205	−	0.0338661i
$918$	2.03868	−	0.322895i	0.0672865	−	0.0106571i
$919$	−8.04341	−	18.0658i	−0.265328	−	0.595936i	0.730922	−	0.682461i	$-0.239090\pi$
$919$	−8.04341	−	18.0658i	−0.265328	−	0.595936i	−0.996250	+	0.0865252i	$0.972424\pi$
$920$	−104.531	+	22.2188i	−3.44629	+	0.732532i
$921$	−17.6008	+	0.922418i	−0.579965	+	0.0303947i
$922$	−24.2084	−	33.3200i	−0.797262	−	1.09734i
$923$	−2.48871	+	4.02094i	−0.0819169	+	0.132351i
$924$	−8.73158	+	18.9982i	−0.287248	+	0.624995i
$925$	1.17320	−	4.37844i	0.0385745	−	0.143962i
$926$	28.3245	−	63.6178i	0.930800	−	2.09061i
$927$	2.91649	−	13.7210i	0.0957899	−	0.450656i
$928$	10.3127	−	5.25457i	0.338530	−	0.172490i
$929$	46.7246	+	17.9359i	1.53298	+	0.588458i	0.971082	−	0.238746i	$-0.0767362\pi$
$929$	46.7246	+	17.9359i	1.53298	+	0.588458i	0.561903	+	0.827203i	$0.310070\pi$
$930$	22.6250	+	8.68493i	0.741903	+	0.284790i
$931$	−6.05315	+	3.08423i	−0.198384	+	0.101082i
$932$	0.623319	−	2.93249i	0.0204175	−	0.0960568i
$933$	0.817224	−	1.83551i	0.0267547	−	0.0600921i
$934$	11.5373	−	43.0579i	0.377513	−	1.40890i
$935$	−9.85729	+	1.97263i	−0.322368	+	0.0645120i
$936$	10.0630	−	16.2585i	0.328920	−	0.531427i
$937$	−9.03143	−	12.4307i	−0.295044	−	0.406093i	0.635600	−	0.772018i	$-0.280753\pi$
$937$	−9.03143	−	12.4307i	−0.295044	−	0.406093i	−0.930644	+	0.365925i	$0.880753\pi$
$938$	21.3858	−	1.12078i	0.698272	−	0.0365949i
$939$	−27.1570	+	5.77239i	−0.886234	+	0.188375i
$940$	61.4113	+	137.932i	2.00301	+	4.49884i
$941$	−10.4338	+	1.65255i	−0.340133	+	0.0538717i	−0.324164	−	0.946001i	$-0.605083\pi$
$941$	−10.4338	+	1.65255i	−0.340133	+	0.0538717i	−0.0159683	+	0.999872i	$0.505083\pi$
$942$	6.62368	+	0.347132i	0.215811	+	0.0113102i
$943$	17.9165	+	27.5890i	0.583443	+	0.898423i
$944$	−8.23494	+	51.9934i	−0.268025	+	1.69224i
$945$	4.79836	+	2.77033i	0.156091	+	0.0901189i
$946$	17.3449	+	10.2919i	0.563932	+	0.334618i
$947$	2.98932	+	0.800987i	0.0971400	+	0.0260286i	0.307062	−	0.951690i	$-0.400654\pi$
$947$	2.98932	+	0.800987i	0.0971400	+	0.0260286i	−0.209922	+	0.977718i	$0.567321\pi$
$948$	47.2752	−	34.3474i	1.53543	−	1.11555i
$949$	−14.3170	−	49.1351i	−0.464749	−	1.59499i
$950$	9.15668	−	28.1814i	0.297082	−	0.914324i
$951$	17.6154	−	14.2647i	0.571218	−	0.462563i
$952$	6.68963	+	0.703108i	0.216812	+	0.0227879i
$953$	14.1487	+	15.7137i	0.458321	+	0.509017i	0.927365	−	0.374158i	$-0.122068\pi$
$953$	14.1487	+	15.7137i	0.458321	+	0.509017i	−0.469044	+	0.883175i	$0.655401\pi$
$954$	−9.72841	−	4.95687i	−0.314969	−	0.160485i
$955$	27.2636	−	33.6678i	0.882231	−	1.08946i
$956$	−41.4894	+	11.1171i	−1.34186	+	0.359551i
$957$	−20.9473	+	16.5530i	−0.677131	+	0.535082i
$958$	43.5934	−	75.5061i	1.40844	−	2.43949i
$959$	31.2159	+	13.8982i	1.00802	+	0.448797i
$960$	1.17276	+	22.3775i	0.0378505	+	0.722231i
$961$	−22.6120	−	7.34708i	−0.729419	−	0.237003i
$962$	−4.53217	−	1.90095i	−0.146123	−	0.0612892i
$963$	4.57340	−	6.29475i	0.147376	−	0.202845i
$964$	−52.0618	+	80.1681i	−1.67680	+	2.58204i
$965$	27.5494	+	24.8056i	0.886846	+	0.798520i
$966$	−20.7815	+	2.18422i	−0.668634	+	0.0702762i
$967$	9.51852	−	9.51852i	0.306095	−	0.306095i	−0.537298	−	0.843393i	$-0.680555\pi$
$967$	9.51852	−	9.51852i	0.306095	−	0.306095i	0.843393	+	0.537298i	$0.180555\pi$
$968$	−54.9433	+	19.6001i	−1.76595	+	0.629972i
$969$	−0.312868	−	1.16764i	−0.0100508	−	0.0375100i
$970$	−166.068	−	26.3025i	−5.33211	−	0.844523i
$971$	6.73838	+	1.43229i	0.216245	+	0.0459643i	0.314760	−	0.949171i	$-0.398076\pi$
$971$	6.73838	+	1.43229i	0.216245	+	0.0459643i	−0.0985151	+	0.995136i	$0.531409\pi$
$972$	−0.860786	−	4.04968i	−0.0276097	−	0.129894i
$973$	3.05266	+	3.76972i	0.0978637	+	0.120852i
$974$	−40.5132	−	29.4345i	−1.29813	−	0.943143i
$975$	24.4102	+	16.9371i	0.781752	+	0.542420i
$976$	50.4582	−	16.3949i	1.61513	−	0.524787i
$977$	−11.8289	−	30.8154i	−0.378441	−	0.985872i	−0.982055	−	0.188596i	$-0.939606\pi$
$977$	−11.8289	−	30.8154i	−0.378441	−	0.985872i	0.603614	−	0.797277i	$-0.293727\pi$
$978$	8.89876	−	5.13770i	0.284551	−	0.164286i
$979$	6.20047	−	8.32357i	0.198168	−	0.266022i
$980$	−49.8683	−	49.8683i	−1.59298	−	1.59298i
$981$	13.8754	+	11.2361i	0.443007	+	0.358740i
$982$	−5.54608	+	3.60167i	−0.176983	+	0.114934i
$983$	−4.36488	−	8.56657i	−0.139218	−	0.273231i	0.810862	−	0.585238i	$-0.198999\pi$
$983$	−4.36488	−	8.56657i	−0.139218	−	0.273231i	−0.950080	+	0.312007i	$0.898999\pi$
$984$	−28.7773	+	12.8125i	−0.917388	+	0.408447i
$985$	1.68522	−	16.0338i	0.0536954	−	0.510878i
$986$	13.9350	+	9.04947i	0.443779	+	0.288194i
$987$	4.71592	+	14.5141i	0.150109	+	0.461989i
$988$	−19.5108	−	9.41295i	−0.620721	−	0.299466i
$989$			13.5909i			0.432164i
$990$	7.39468	+	28.9756i	0.235018	+	0.920906i
$991$	16.6268	+	28.7985i	0.528169	+	0.914815i	0.999461	+	0.0328380i	$0.0104546\pi$
$991$	16.6268	+	28.7985i	0.528169	+	0.914815i	−0.471292	+	0.881977i	$0.656212\pi$
$992$	−0.403961	−	3.84343i	−0.0128258	−	0.122029i
$993$	10.7074	−	21.0144i	0.339788	−	0.666872i
$994$	−0.258990	+	4.94183i	−0.00821468	+	0.156745i
$995$	−13.9301	+	36.2892i	−0.441614	+	1.15044i
$996$	−2.01280	−	12.7083i	−0.0637781	−	0.402679i
$997$	40.9041	−	36.8303i	1.29545	−	1.16643i	0.319702	−	0.947518i	$-0.396417\pi$
$997$	40.9041	−	36.8303i	1.29545	−	1.16643i	0.975746	−	0.218908i	$-0.0702493\pi$
$998$	25.0217	−	27.7894i	0.792049	−	0.879659i
$999$	−0.513555	+	0.197135i	−0.0162482	+	0.00623708i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bs.a.349.14	yes	224
11.7	odd	10	inner	429.2.bs.a.271.1	yes	224
13.6	odd	12	inner	429.2.bs.a.19.1	✓	224
143.84	even	60	inner	429.2.bs.a.370.14	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bs.a.19.1	✓	224	13.6	odd	12	inner
429.2.bs.a.271.1	yes	224	11.7	odd	10	inner
429.2.bs.a.349.14	yes	224	1.1	even	1	trivial
429.2.bs.a.370.14	yes	224	143.84	even	60	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bs (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(2.31335 - 0.888012i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(3.07673 - 2.77030i) q^{4} +(-0.569220 - 3.59392i) q^{5} +(-0.888012 + 2.31335i) q^{6} +(-0.0796919 + 1.52061i) q^{7} +(2.40758 - 4.72514i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(-4.50825 - 7.80851i) q^{10} +(1.22542 - 3.08194i) q^{11} +4.14015i q^{12} +(-0.672825 + 3.54222i) q^{13} +(1.16597 + 3.58847i) q^{14} +(3.05168 + 1.98179i) q^{15} +(0.508066 - 4.83393i) q^{16} +(0.760974 - 0.338807i) q^{17} +(-1.12496 - 2.20785i) q^{18} +(-1.21707 + 0.790378i) q^{19} +(-11.7076 - 9.48061i) q^{20} +(-1.07671 - 1.07671i) q^{21} +(0.0980370 - 8.21779i) q^{22} +(4.79612 - 2.76904i) q^{23} +(1.90048 + 4.95092i) q^{24} +(-7.83694 + 2.54638i) q^{25} +(1.58905 + 8.79187i) q^{26} +(0.809017 + 0.587785i) q^{27} +(3.96736 + 4.89929i) q^{28} +(1.67365 + 7.87389i) q^{29} +(8.81946 + 1.87463i) q^{30} +(2.65472 + 0.420467i) q^{31} +(-0.372136 - 1.38883i) q^{32} +(1.47036 + 2.97289i) q^{33} +(1.45953 - 1.45953i) q^{34} +(5.51031 - 0.579157i) q^{35} +(-3.07673 - 2.77030i) q^{36} +(-0.299601 + 0.461346i) q^{37} +(-2.11365 + 2.90920i) q^{38} +(-2.18217 - 2.87021i) q^{39} +(-18.3522 - 5.96300i) q^{40} +(0.310875 + 5.93186i) q^{41} +(-3.44694 - 1.53468i) q^{42} +(-1.22704 + 2.12529i) q^{43} +(-4.76760 - 12.8771i) q^{44} +(-3.51473 + 0.941769i) q^{45} +(8.63616 - 10.6648i) q^{46} +(-8.93000 - 4.55006i) q^{47} +(3.25235 + 3.61210i) q^{48} +(4.65574 + 0.489338i) q^{49} +(-15.8684 + 12.8500i) q^{50} +(-0.257408 + 0.792220i) q^{51} +(7.74291 + 12.7624i) q^{52} +(3.56475 - 2.58994i) q^{53} +(2.39350 + 0.641336i) q^{54} +(-11.7738 - 2.64977i) q^{55} +(6.99324 + 4.03755i) q^{56} +(0.227017 - 1.43333i) q^{57} +(10.8638 + 16.7288i) q^{58} +(-10.8155 - 0.566816i) q^{59} +(14.8794 - 2.35666i) q^{60} +(4.43970 + 9.97172i) q^{61} +(6.51468 - 1.38474i) q^{62} +(1.52061 - 0.0796919i) q^{63} +(3.61975 + 4.98215i) q^{64} +(13.1134 + 0.401775i) q^{65} +(6.04141 + 5.57163i) q^{66} +(1.46898 - 5.48229i) q^{67} +(1.40271 - 3.15055i) q^{68} +(-1.15143 + 5.41706i) q^{69} +(12.2330 - 6.23302i) q^{70} +(1.22442 + 0.470012i) q^{71} +(-4.95092 - 1.90048i) q^{72} +(-12.6472 + 6.44410i) q^{73} +(-0.283402 + 1.33330i) q^{74} +(3.35161 - 7.52784i) q^{75} +(-1.55503 + 5.80345i) q^{76} +(4.58877 + 2.10900i) q^{77} +(-7.59691 - 4.70201i) q^{78} +(-8.29617 - 11.4187i) q^{79} +(-17.6619 + 0.925623i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(5.98672 + 13.4464i) q^{82} +(-3.06953 + 0.486166i) q^{83} +(-6.29556 - 0.329936i) q^{84} +(-1.65081 - 2.54202i) q^{85} +(-0.951284 + 6.00617i) q^{86} +(-6.97133 - 4.02490i) q^{87} +(-11.6123 - 13.2103i) q^{88} +(3.02281 + 0.809960i) q^{89} +(-7.29449 + 5.29976i) q^{90} +(-5.33272 - 1.30539i) q^{91} +(7.08529 - 21.8063i) q^{92} +(-2.08882 + 1.69150i) q^{93} +(-24.6987 - 2.59594i) q^{94} +(3.53333 + 3.92417i) q^{95} +(1.28111 + 0.652758i) q^{96} +(11.7354 - 14.4921i) q^{97} +(11.2049 - 3.00235i) q^{98} +(-3.19315 - 0.896560i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 28 q^{3} - 6 q^{5} + 28 q^{9} - 16 q^{11} - 10 q^{13} - 36 q^{14} + 8 q^{15} - 24 q^{16} + 50 q^{20} + 10 q^{22} - 48 q^{23} - 30 q^{24} + 10 q^{26} + 56 q^{27} + 20 q^{29} + 12 q^{31} - 32 q^{33}+ \cdots - 6 q^{99}+O(q^{100}) \) 224 * q - 28 * q^3 - 6 * q^5 + 28 * q^9 - 16 * q^11 - 10 * q^13 - 36 * q^14 + 8 * q^15 - 24 * q^16 + 50 * q^20 + 10 * q^22 - 48 * q^23 - 30 * q^24 + 10 * q^26 + 56 * q^27 + 20 * q^29 + 12 * q^31 - 32 * q^33 - 104 * q^34 + 20 * q^35 + 12 * q^37 + 20 * q^39 - 80 * q^40 + 190 * q^41 + 32 * q^42 - 24 * q^44 + 4 * q^45 - 40 * q^46 - 10 * q^47 + 44 * q^48 - 24 * q^49 - 180 * q^50 - 110 * q^52 + 28 * q^53 - 62 * q^55 - 72 * q^56 + 20 * q^58 - 118 * q^59 + 88 * q^60 - 20 * q^61 + 120 * q^62 - 20 * q^66 - 156 * q^67 - 60 * q^68 + 12 * q^69 - 20 * q^70 + 64 * q^71 - 30 * q^72 + 10 * q^73 - 60 * q^74 - 12 * q^75 + 84 * q^78 + 200 * q^79 + 188 * q^80 + 28 * q^81 - 138 * q^82 - 80 * q^83 - 60 * q^84 + 40 * q^85 - 42 * q^86 - 18 * q^88 + 216 * q^89 - 88 * q^91 + 16 * q^92 + 12 * q^93 - 40 * q^94 - 300 * q^95 - 100 * q^96 + 18 * q^97 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more