LMFDB - Embedded newform 431.2.g.a.10.29

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [431,2,Mod(5,431)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(431, base_ring=CyclotomicField(430))

chi = DirichletCharacter(H, H._module([342]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("431.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	431.g (of order $215$, degree $168$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.44155232712$
Analytic rank:	$0$
Dimension:	$5880$
Relative dimension:	$35$ over $\Q(\zeta_{215})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{215}]$

Embedding invariants

Embedding label			10.29
Character	$\chi$	$=$	431.10
Dual form			431.2.g.a.388.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.207615 - 1.88687i) q^{2} +(-2.00526 + 0.295114i) q^{3} +(-1.56502 - 0.348624i) q^{4} +(-2.79353 + 0.122536i) q^{5} +(0.140519 + 3.84494i) q^{6} +(0.622702 + 0.897816i) q^{7} +(0.243090 - 0.712556i) q^{8} +(1.06119 - 0.319264i) q^{9} +(-0.348769 + 5.29648i) q^{10} +(2.84839 + 4.37446i) q^{11} +(3.24117 + 0.237223i) q^{12} +(0.667179 + 0.733758i) q^{13} +(1.82334 - 0.988558i) q^{14} +(5.56561 - 1.07013i) q^{15} +(-4.19759 - 1.96775i) q^{16} +(-0.151861 + 2.96679i) q^{17} +(-0.382091 - 2.06861i) q^{18} +(-0.898608 - 3.24283i) q^{19} +(4.41467 + 0.782120i) q^{20} +(-1.51364 - 1.61659i) q^{21} +(8.84540 - 4.46633i) q^{22} +(7.56657 + 1.80196i) q^{23} +(-0.277175 + 1.50060i) q^{24} +(2.80802 - 0.246818i) q^{25} +(1.52302 - 1.10654i) q^{26} +(3.47192 - 1.62757i) q^{27} +(-0.661543 - 1.62219i) q^{28} +(7.58494 + 3.28888i) q^{29} +(-0.863689 - 10.7238i) q^{30} +(-6.07649 - 2.22284i) q^{31} +(-3.79996 + 6.22647i) q^{32} +(-7.00273 - 7.93134i) q^{33} +(5.56643 + 0.902492i) q^{34} +(-1.84955 - 2.43177i) q^{35} +(-1.77209 + 0.129700i) q^{36} +(5.35443 + 5.08736i) q^{37} +(-6.30537 + 1.02230i) q^{38} +(-1.55441 - 1.27448i) q^{39} +(-0.591767 + 2.02034i) q^{40} +(-5.24661 + 5.60345i) q^{41} +(-3.36455 + 2.52041i) q^{42} +(0.400137 + 6.07656i) q^{43} +(-2.93275 - 7.83915i) q^{44} +(-2.92534 + 1.02191i) q^{45} +(4.97100 - 13.9030i) q^{46} +(-4.35711 + 6.09012i) q^{47} +(8.99799 + 2.70709i) q^{48} +(2.03447 - 5.43806i) q^{49} +(0.117272 - 5.34961i) q^{50} +(-0.571020 - 5.99402i) q^{51} +(-0.788345 - 1.38094i) q^{52} +(-7.91691 + 10.7309i) q^{53} +(-2.35019 - 6.88897i) q^{54} +(-8.49309 - 11.8712i) q^{55} +(0.791117 - 0.225460i) q^{56} +(2.75895 + 6.23754i) q^{57} +(7.78043 - 13.6290i) q^{58} +(7.82232 + 3.52847i) q^{59} +(-9.08338 - 0.265529i) q^{60} +(1.25318 - 1.15630i) q^{61} +(-5.45578 + 11.0041i) q^{62} +(0.947443 + 0.753944i) q^{63} +(3.62098 + 2.79603i) q^{64} +(-1.95370 - 1.96802i) q^{65} +(-16.4193 + 11.5666i) q^{66} +(-4.41498 + 9.24172i) q^{67} +(1.27196 - 4.59016i) q^{68} +(-15.7047 - 1.38041i) q^{69} +(-4.97244 + 2.98500i) q^{70} +(-0.0200249 - 2.74083i) q^{71} +(0.0304711 - 0.833765i) q^{72} +(6.42015 - 4.11394i) q^{73} +(10.7108 - 9.04690i) q^{74} +(-5.55797 + 1.32362i) q^{75} +(0.275814 + 5.38839i) q^{76} +(-2.15376 + 5.28131i) q^{77} +(-2.72751 + 2.66837i) q^{78} +(-17.6302 + 0.515374i) q^{79} +(11.9672 + 4.98262i) q^{80} +(-9.25443 + 6.12268i) q^{81} +(9.48372 + 11.0630i) q^{82} +(-2.70229 - 1.41440i) q^{83} +(1.80530 + 3.05769i) q^{84} +(0.0606882 - 8.30645i) q^{85} +(11.5488 + 0.506578i) q^{86} +(-16.1804 - 4.35665i) q^{87} +(3.80946 - 0.966246i) q^{88} +(7.90724 - 3.84868i) q^{89} +(1.32086 + 5.73190i) q^{90} +(-0.243326 + 1.05592i) q^{91} +(-11.2137 - 5.45800i) q^{92} +(12.8410 + 2.66413i) q^{93} +(10.5867 + 9.48569i) q^{94} +(2.90766 + 8.94885i) q^{95} +(5.78241 - 13.6071i) q^{96} +(3.35161 + 11.4426i) q^{97} +(-9.83854 - 4.96780i) q^{98} +(4.41928 + 3.73273i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5880 q - 166 q^{2} - 164 q^{3} - 302 q^{4} - 169 q^{5} - 148 q^{6} - 171 q^{7} - 160 q^{8} - 300 q^{9} - 157 q^{10} - 83 q^{11} - 142 q^{12} - 177 q^{13} - 164 q^{14} - 166 q^{15} - 298 q^{16} - 176 q^{17}+ \cdots - 72 q^{99}+O(q^{100}) $ 5880 * q - 166 * q^2 - 164 * q^3 - 302 * q^4 - 169 * q^5 - 148 * q^6 - 171 * q^7 - 160 * q^8 - 300 * q^9 - 157 * q^10 - 83 * q^11 - 142 * q^12 - 177 * q^13 - 164 * q^14 - 166 * q^15 - 298 * q^16 - 176 * q^17 - 174 * q^18 - 175 * q^19 - 166 * q^20 - 43 * q^21 - 180 * q^22 - 186 * q^23 - 116 * q^24 - 120 * q^25 + 104 * q^26 - 104 * q^27 - 172 * q^28 - 173 * q^29 + 42 * q^30 - 172 * q^31 - 172 * q^32 - 63 * q^33 - 193 * q^34 - 199 * q^35 - 258 * q^36 - 184 * q^37 - 113 * q^38 - 180 * q^39 - 118 * q^40 - 126 * q^41 - 107 * q^42 - 163 * q^43 - 181 * q^44 - 138 * q^45 - 142 * q^46 - 46 * q^47 - 78 * q^48 - 156 * q^49 - 223 * q^50 - 223 * q^51 + 86 * q^52 - 156 * q^53 + 447 * q^54 - 232 * q^55 + 267 * q^56 - 134 * q^57 - 183 * q^58 - 194 * q^59 - 107 * q^60 + 107 * q^61 - 143 * q^62 - 19 * q^63 - 352 * q^64 - 219 * q^65 - 116 * q^66 + 11 * q^67 - 251 * q^68 - 109 * q^69 + 1000 * q^70 + 137 * q^71 - 106 * q^72 - 189 * q^73 - 175 * q^74 - 189 * q^75 - 124 * q^76 - 26 * q^77 + 165 * q^78 + 249 * q^79 - 146 * q^80 - 328 * q^81 + 13 * q^82 - 139 * q^83 + 307 * q^84 - 227 * q^85 - 130 * q^86 - 106 * q^87 + 208 * q^88 - 166 * q^89 - 150 * q^90 - 181 * q^91 - 80 * q^92 + 23 * q^93 + 22 * q^94 - 90 * q^95 + 226 * q^96 - 191 * q^97 - 171 * q^98 - 72 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/431\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{66}{215}\right)$

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 $

$2$	0.207615	−	1.88687i	0.146806	−	1.33422i	−0.663484	−	0.748190i	$-0.730923\pi$
$2$	0.207615	−	1.88687i	0.146806	−	1.33422i	0.810290	−	0.586029i	$-0.199309\pi$
$3$	−2.00526	+	0.295114i	−1.15774	+	0.170384i	−0.696946	−	0.717124i	$-0.745458\pi$
$3$	−2.00526	+	0.295114i	−1.15774	+	0.170384i	−0.460793	+	0.887507i	$0.652435\pi$
$4$	−1.56502	−	0.348624i	−0.782512	−	0.174312i
$5$	−2.79353	+	0.122536i	−1.24931	+	0.0547999i	−0.658853	−	0.752272i	$-0.728958\pi$
$5$	−2.79353	+	0.122536i	−1.24931	+	0.0547999i	−0.590453	+	0.807072i	$0.701051\pi$
$6$	0.140519	+	3.84494i	0.0573666	+	1.56969i
$7$	0.622702	+	0.897816i	0.235359	+	0.339342i	0.921676	−	0.387960i	$-0.126820\pi$
$7$	0.622702	+	0.897816i	0.235359	+	0.339342i	−0.686317	+	0.727303i	$0.740774\pi$
$8$	0.243090	−	0.712556i	0.0859454	−	0.251927i
$9$	1.06119	−	0.319264i	0.353729	−	0.106421i
$10$	−0.348769	+	5.29648i	−0.110290	+	1.67489i
$11$	2.84839	+	4.37446i	0.858821	+	1.31895i	0.946468	+	0.322797i	$0.104623\pi$
$11$	2.84839	+	4.37446i	0.858821	+	1.31895i	−0.0876475	+	0.996152i	$0.527935\pi$
$12$	3.24117	+	0.237223i	0.935645	+	0.0684804i
$13$	0.667179	+	0.733758i	0.185042	+	0.203508i	0.825368	−	0.564596i	$-0.190968\pi$
$13$	0.667179	+	0.733758i	0.185042	+	0.203508i	−0.640325	+	0.768104i	$0.721201\pi$
$14$	1.82334	−	0.988558i	0.487309	−	0.264203i
$15$	5.56561	−	1.07013i	1.43703	−	0.276306i
$16$	−4.19759	−	1.96775i	−1.04940	−	0.491938i
$17$	−0.151861	+	2.96679i	−0.0368317	+	0.719553i	0.913221	+	0.407464i	$0.133587\pi$
$17$	−0.151861	+	2.96679i	−0.0368317	+	0.719553i	−0.950053	+	0.312089i	$0.898971\pi$
$18$	−0.382091	−	2.06861i	−0.0900597	−	0.487575i
$19$	−0.898608	−	3.24283i	−0.206155	−	0.743957i	−0.992077	−	0.125631i	$-0.959904\pi$
$19$	−0.898608	−	3.24283i	−0.206155	−	0.743957i	0.785922	−	0.618325i	$-0.212189\pi$
$20$	4.41467	+	0.782120i	0.987149	+	0.174887i
$21$	−1.51364	−	1.61659i	−0.330303	−	0.352769i
$22$	8.84540	−	4.46633i	1.88585	−	0.952225i
$23$	7.56657	+	1.80196i	1.57774	+	0.375735i	0.924429	−	0.381355i	$-0.124543\pi$
$23$	7.56657	+	1.80196i	1.57774	+	0.375735i	0.653310	+	0.757090i	$0.273380\pi$
$24$	−0.277175	+	1.50060i	−0.0565781	+	0.306309i
$25$	2.80802	−	0.246818i	0.561603	−	0.0493636i
$26$	1.52302	−	1.10654i	0.298689	−	0.217010i
$27$	3.47192	−	1.62757i	0.668171	−	0.313226i
$28$	−0.661543	−	1.62219i	−0.125020	−	0.306565i
$29$	7.58494	+	3.28888i	1.40849	+	0.610729i	0.959218	−	0.282667i	$-0.0912191\pi$
$29$	7.58494	+	3.28888i	1.40849	+	0.610729i	0.449270	+	0.893396i	$0.351684\pi$
$30$	−0.863689	−	10.7238i	−0.157687	−	1.95788i
$31$	−6.07649	−	2.22284i	−1.09137	−	0.399234i	−0.266085	−	0.963950i	$-0.585730\pi$
$31$	−6.07649	−	2.22284i	−1.09137	−	0.399234i	−0.825286	+	0.564716i	$0.808986\pi$
$32$	−3.79996	+	6.22647i	−0.671745	+	1.10070i
$33$	−7.00273	−	7.93134i	−1.21902	−	1.38067i
$34$	5.56643	+	0.902492i	0.954634	+	0.154776i
$35$	−1.84955	−	2.43177i	−0.312632	−	0.411045i
$36$	−1.77209	+	0.129700i	−0.295348	+	0.0216167i
$37$	5.35443	+	5.08736i	0.880262	+	0.836357i	0.987458	−	0.157881i	$-0.0504662\pi$
$37$	5.35443	+	5.08736i	0.880262	+	0.836357i	−0.107196	+	0.994238i	$0.534187\pi$
$38$	−6.30537	+	1.02230i	−1.02287	+	0.165839i
$39$	−1.55441	−	1.27448i	−0.248905	−	0.204081i
$40$	−0.591767	+	2.02034i	−0.0935666	+	0.319443i
$41$	−5.24661	+	5.60345i	−0.819382	+	0.875112i	−0.993984	−	0.109527i	$-0.965066\pi$
$41$	−5.24661	+	5.60345i	−0.819382	+	0.875112i	0.174602	+	0.984639i	$0.444136\pi$
$42$	−3.36455	+	2.52041i	−0.519161	+	0.388908i
$43$	0.400137	+	6.07656i	0.0610203	+	0.926667i	0.914255	+	0.405140i	$0.132777\pi$
$43$	0.400137	+	6.07656i	0.0610203	+	0.926667i	−0.853235	+	0.521527i	$0.825362\pi$
$44$	−2.93275	−	7.83915i	−0.442129	−	1.18180i
$45$	−2.92534	+	1.02191i	−0.436084	+	0.152337i
$46$	4.97100	−	13.9030i	0.732934	−	2.04989i
$47$	−4.35711	+	6.09012i	−0.635549	+	0.888335i	−0.999064	−	0.0432535i	$-0.986228\pi$
$47$	−4.35711	+	6.09012i	−0.635549	+	0.888335i	0.363515	+	0.931588i	$0.381577\pi$
$48$	8.99799	+	2.70709i	1.29875	+	0.390735i
$49$	2.03447	−	5.43806i	0.290638	−	0.776866i
$50$	0.117272	−	5.34961i	0.0165848	−	0.756549i
$51$	−0.571020	−	5.99402i	−0.0799588	−	0.839331i
$52$	−0.788345	−	1.38094i	−0.109324	−	0.191502i
$53$	−7.91691	+	10.7309i	−1.08747	+	1.47401i	−0.220674	+	0.975348i	$0.570826\pi$
$53$	−7.91691	+	10.7309i	−1.08747	+	1.47401i	−0.866797	+	0.498661i	$0.833825\pi$
$54$	−2.35019	−	6.88897i	−0.319820	−	0.937470i
$55$	−8.49309	−	11.8712i	−1.14521	−	1.60071i
$56$	0.791117	−	0.225460i	0.105717	−	0.0301283i
$57$	2.75895	+	6.23754i	0.365432	+	0.826182i
$58$	7.78043	−	13.6290i	1.02162	−	1.78957i
$59$	7.82232	+	3.52847i	1.01838	+	0.459368i	0.850240	−	0.526395i	$-0.176457\pi$
$59$	7.82232	+	3.52847i	1.01838	+	0.459368i	0.168139	+	0.985763i	$0.446224\pi$
$60$	−9.08338	−	0.265529i	−1.17266	−	0.0342797i
$61$	1.25318	−	1.15630i	0.160453	−	0.148049i	−0.593851	−	0.804575i	$-0.702393\pi$
$61$	1.25318	−	1.15630i	0.160453	−	0.148049i	0.754304	+	0.656526i	$0.227975\pi$
$62$	−5.45578	+	11.0041i	−0.692885	+	1.39752i
$63$	0.947443	+	0.753944i	0.119367	+	0.0949880i
$64$	3.62098	+	2.79603i	0.452622	+	0.349503i
$65$	−1.95370	−	1.96802i	−0.242326	−	0.244103i
$66$	−16.4193	+	11.5666i	−2.02107	+	1.42375i
$67$	−4.41498	+	9.24172i	−0.539376	+	1.12906i	0.434226	+	0.900804i	$0.357022\pi$
$67$	−4.41498	+	9.24172i	−0.539376	+	1.12906i	−0.973602	+	0.228252i	$0.926699\pi$
$68$	1.27196	−	4.59016i	0.154248	−	0.556639i
$69$	−15.7047	−	1.38041i	−1.89063	−	0.166182i
$70$	−4.97244	+	2.98500i	−0.594320	+	0.356775i
$71$	−0.0200249	−	2.74083i	−0.00237652	−	0.325276i	−0.987847	−	0.155430i	$-0.950324\pi$
$71$	−0.0200249	−	2.74083i	−0.00237652	−	0.325276i	0.985470	−	0.169847i	$-0.0543273\pi$
$72$	0.0304711	−	0.833765i	0.00359106	−	0.0982602i
$73$	6.42015	−	4.11394i	0.751422	−	0.481501i	−0.107118	−	0.994246i	$-0.534162\pi$
$73$	6.42015	−	4.11394i	0.751422	−	0.481501i	0.858541	+	0.512746i	$0.171372\pi$
$74$	10.7108	−	9.04690i	1.24511	−	1.05168i
$75$	−5.55797	+	1.32362i	−0.641780	+	0.152838i
$76$	0.275814	+	5.38839i	0.0316381	+	0.618090i
$77$	−2.15376	+	5.28131i	−0.245444	+	0.601861i
$78$	−2.72751	+	2.66837i	−0.308829	+	0.302133i
$79$	−17.6302	+	0.515374i	−1.98355	+	0.0579841i	−0.995419	−	0.0956106i	$-0.969520\pi$
$79$	−17.6302	+	0.515374i	−1.98355	+	0.0579841i	−0.988134	+	0.153595i	$0.950915\pi$
$80$	11.9672	+	4.98262i	1.33798	+	0.557074i
$81$	−9.25443	+	6.12268i	−1.02827	+	0.680297i
$82$	9.48372	+	11.0630i	1.04730	+	1.22171i
$83$	−2.70229	−	1.41440i	−0.296615	−	0.155251i	0.308877	−	0.951102i	$-0.400047\pi$
$83$	−2.70229	−	1.41440i	−0.296615	−	0.155251i	−0.605492	+	0.795851i	$0.707024\pi$
$84$	1.80530	+	3.05769i	0.196974	+	0.333621i
$85$	0.0606882	−	8.30645i	0.00658256	−	0.900961i
$86$	11.5488	+	0.506578i	1.24533	+	0.0546257i
$87$	−16.1804	−	4.35665i	−1.73472	−	0.467082i
$88$	3.80946	−	0.966246i	0.406090	−	0.103002i
$89$	7.90724	−	3.84868i	0.838166	−	0.407959i	0.0318850	−	0.999492i	$-0.489849\pi$
$89$	7.90724	−	3.84868i	0.838166	−	0.407959i	0.806281	+	0.591533i	$0.201477\pi$
$90$	1.32086	+	5.73190i	0.139231	+	0.604195i
$91$	−0.243326	+	1.05592i	−0.0255075	+	0.110690i
$92$	−11.2137	−	5.45800i	−1.16910	−	0.569036i
$93$	12.8410	+	2.66413i	1.33155	+	0.276257i
$94$	10.5867	+	9.48569i	1.09193	+	0.978374i
$95$	2.90766	+	8.94885i	0.298319	+	0.918132i
$96$	5.78241	−	13.6071i	0.590164	−	1.38877i
$97$	3.35161	+	11.4426i	0.340304	+	1.16182i	0.934041	+	0.357165i	$0.116257\pi$
$97$	3.35161	+	11.4426i	0.340304	+	1.16182i	−0.593737	+	0.804659i	$0.702348\pi$
$98$	−9.83854	−	4.96780i	−0.993842	−	0.501823i
$99$	4.41928	+	3.73273i	0.444154	+	0.375154i
$100$	−4.48066	−	0.592666i	−0.448066	−	0.0592666i
$101$	5.75154	−	4.44119i	0.572300	−	0.441915i	−0.283684	−	0.958918i	$-0.591557\pi$
$101$	5.75154	−	4.44119i	0.572300	−	0.441915i	0.855984	+	0.517002i	$0.172952\pi$
$102$	−11.4285	−	0.167006i	−1.13159	−	0.0165360i
$103$	−4.47676	−	8.40311i	−0.441109	−	0.827983i	0.558890	−	0.829241i	$-0.311227\pi$
$103$	−4.47676	−	8.40311i	−0.441109	−	0.827983i	−0.999999	+	0.00125878i	$0.999599\pi$
$104$	0.685028	−	0.297033i	0.0671726	−	0.0291265i
$105$	4.42649	+	4.33052i	0.431981	+	0.422615i
$106$	18.6042	+	17.1661i	1.80700	+	1.66732i
$107$	8.70688	−	3.33010i	0.841726	−	0.321933i	0.101953	−	0.994789i	$-0.467491\pi$
$107$	8.70688	−	3.33010i	0.841726	−	0.321933i	0.739773	+	0.672857i	$0.234933\pi$
$108$	−6.00104	+	1.33679i	−0.577451	+	0.128633i
$109$	8.46984	−	2.28054i	0.811263	−	0.218436i	0.169689	−	0.985498i	$-0.445724\pi$
$109$	8.46984	−	2.28054i	0.811263	−	0.218436i	0.641574	+	0.767061i	$0.278282\pi$
$110$	−24.1626	+	13.5607i	−2.30382	+	1.29296i
$111$	−12.2384	−	8.62133i	−1.16162	−	0.818301i
$112$	−0.847172	−	4.99399i	−0.0800502	−	0.471887i
$113$	−2.91091	−	1.98759i	−0.273835	−	0.186977i	0.419173	−	0.907906i	$-0.362320\pi$
$113$	−2.91091	−	1.98759i	−0.273835	−	0.186977i	−0.693009	+	0.720929i	$0.743715\pi$
$114$	12.3422	−	3.91078i	1.15596	−	0.366278i
$115$	−21.3583	−	4.10666i	−1.99167	−	0.382948i
$116$	−10.7240	−	7.79146i	−0.995701	−	0.723419i
$117$	0.942264	+	0.565649i	0.0871123	+	0.0522942i
$118$	8.28180	−	14.0271i	0.762401	−	1.29130i
$119$	−2.75820	+	1.71109i	−0.252844	+	0.156855i
$120$	0.590420	−	4.22594i	0.0538977	−	0.385774i
$121$	−6.57297	+	14.8604i	−0.597543	+	1.35095i
$122$	−1.92162	−	2.60464i	−0.173975	−	0.235813i
$123$	8.86717	−	12.7847i	0.799526	−	1.15276i
$124$	8.73492	+	5.59721i	0.784419	+	0.502644i
$125$	6.04633	−	0.799760i	0.540800	−	0.0715327i
$126$	1.61930	−	1.63117i	0.144259	−	0.145316i
$127$	0.524592	−	3.09241i	0.0465500	−	0.274407i	−0.953046	−	0.302825i	$-0.902070\pi$
$127$	0.524592	−	3.09241i	0.0465500	−	0.274407i	0.999596	+	0.0284180i	$0.00904694\pi$
$128$	−4.09824	+	4.25075i	−0.362237	+	0.375717i
$129$	−2.59565	−	12.0670i	−0.228535	−	1.06244i
$130$	−4.11902	+	3.27778i	−0.361262	+	0.287481i
$131$	−6.47253	+	0.0945837i	−0.565507	+	0.00826381i	−0.296769	−	0.954949i	$-0.595909\pi$
$131$	−6.47253	+	0.0945837i	−0.565507	+	0.00826381i	−0.268738	+	0.963213i	$0.586607\pi$
$132$	8.19438	+	14.8541i	0.713229	+	1.29288i
$133$	2.35190	−	2.82610i	0.203936	−	0.245054i
$134$	16.5213	+	10.2492i	1.42722	+	0.885397i
$135$	−9.49948	+	4.97210i	−0.817585	+	0.427930i
$136$	2.07709	+	0.829408i	0.178109	+	0.0711212i
$137$	0.619362	+	0.206258i	0.0529156	+	0.0176218i	0.342292	−	0.939594i	$-0.388797\pi$
$137$	0.619362	+	0.206258i	0.0529156	+	0.0176218i	−0.289376	+	0.957215i	$0.593448\pi$
$138$	−5.86519	+	29.3462i	−0.499278	+	2.49812i
$139$	−6.61905	+	2.42132i	−0.561421	+	0.205373i	−0.608550	−	0.793515i	$-0.708249\pi$
$139$	−6.61905	+	2.42132i	−0.561421	+	0.205373i	0.0471293	+	0.998889i	$0.484993\pi$
$140$	2.04682	+	4.45058i	0.172988	+	0.376143i
$141$	6.93987	−	13.4981i	0.584442	−	1.13675i
$142$	−5.17575	−	0.531252i	−0.434339	−	0.0445817i
$143$	−1.30941	+	5.00857i	−0.109499	+	0.418838i
$144$	−5.08266	−	0.748013i	−0.423555	−	0.0623344i
$145$	−21.5918	−	8.25816i	−1.79310	−	0.685803i
$146$	−6.42956	−	12.9681i	−0.532114	−	1.07325i
$147$	−2.47480	+	11.5052i	−0.204118	+	0.948929i
$148$	−6.60623	−	9.82852i	−0.543029	−	0.807900i
$149$	14.8327	+	9.81319i	1.21514	+	0.803928i	0.985554	−	0.169361i	$-0.0541703\pi$
$149$	14.8327	+	9.81319i	1.21514	+	0.803928i	0.229584	+	0.973289i	$0.426263\pi$
$150$	1.34358	+	10.7620i	0.109703	+	0.878712i
$151$	10.2433	−	3.41117i	0.833585	−	0.277597i	0.132955	−	0.991122i	$-0.457554\pi$
$151$	10.2433	−	3.41117i	0.833585	−	0.277597i	0.700630	+	0.713525i	$0.252902\pi$
$152$	−2.52914	−	0.147992i	−0.205141	−	0.0120038i
$153$	0.786037	+	3.19681i	0.0635473	+	0.258447i
$154$	9.51799	+	5.16035i	0.766982	+	0.415833i
$155$	17.2473	+	5.46499i	1.38533	+	0.438959i
$156$	1.98837	+	2.53650i	0.159197	+	0.203083i
$157$	2.44158	−	5.30894i	0.194859	−	0.423700i	−0.786051	−	0.618162i	$-0.787878\pi$
$157$	2.44158	−	5.30894i	0.194859	−	0.423700i	0.980910	+	0.194462i	$0.0622962\pi$
$158$	−2.68785	+	33.3729i	−0.213834	+	2.65501i
$159$	12.7086	−	23.8548i	1.00786	−	1.89181i
$160$	9.85235	−	17.8595i	0.778897	−	1.41192i
$161$	3.09389	+	7.91547i	0.243833	+	0.623826i
$162$	9.63134	+	18.7331i	0.756709	+	1.47181i
$163$	−3.05876	+	3.90196i	−0.239581	+	0.305625i	−0.891822	−	0.452386i	$-0.850573\pi$
$163$	−3.05876	+	3.90196i	−0.239581	+	0.305625i	0.652241	+	0.758011i	$0.273829\pi$
$164$	10.1646	−	6.94045i	0.793719	−	0.541958i
$165$	20.5342	+	21.2984i	1.59859	+	1.65808i
$166$	−3.22983	+	4.80522i	−0.250683	+	0.372958i
$167$	−9.87626	+	4.11203i	−0.764248	+	0.318199i	−0.732021	−	0.681282i	$-0.761423\pi$
$167$	−9.87626	+	4.11203i	−0.764248	+	0.318199i	−0.0322272	+	0.999481i	$0.510260\pi$
$168$	−1.51986	+	0.685575i	−0.117260	+	0.0528933i
$169$	1.13959	−	11.9623i	0.0876608	−	0.920178i
$170$	−15.6606	−	1.83905i	−1.20111	−	0.141049i
$171$	−1.98891	−	3.15436i	−0.152096	−	0.241220i
$172$	1.49221	−	9.64946i	0.113780	−	0.735764i
$173$	4.38074	−	0.449651i	0.333062	−	0.0341863i	0.0658656	−	0.997829i	$-0.479019\pi$
$173$	4.38074	−	0.449651i	0.333062	−	0.0341863i	0.267196	+	0.963642i	$0.413903\pi$
$174$	−11.5797	+	29.6258i	−0.877856	+	2.24593i
$175$	1.97015	+	2.36739i	0.148930	+	0.178958i
$176$	−3.34852	−	23.9671i	−0.252404	−	1.80659i
$177$	−16.7271	−	4.76704i	−1.25729	−	0.358313i
$178$	−5.62029	−	15.7190i	−0.421259	−	1.17819i
$179$	−7.58079	−	9.38483i	−0.566615	−	0.701455i	0.411053	−	0.911611i	$-0.365161\pi$
$179$	−7.58079	−	9.38483i	−0.566615	−	0.701455i	−0.977668	+	0.210156i	$0.932603\pi$
$180$	4.93449	−	0.579466i	0.367795	−	0.0431909i
$181$	−0.181787	−	8.29258i	−0.0135121	−	0.616382i	−0.957828	−	0.287342i	$-0.907228\pi$
$181$	−0.181787	−	8.29258i	−0.0135121	−	0.616382i	0.944316	−	0.329040i	$-0.106725\pi$
$182$	1.94186	+	0.678349i	0.143940	+	0.0502825i
$183$	−2.17171	+	2.68852i	−0.160537	+	0.198741i
$184$	3.12336	−	4.95356i	0.230257	−	0.365182i
$185$	−15.5812	−	13.5556i	−1.14555	−	0.996628i
$186$	7.69283	−	23.6761i	0.564066	−	1.73602i
$187$	−13.4107	+	7.78627i	−0.980686	+	0.569388i
$188$	8.94213	−	8.01219i	0.652172	−	0.584349i
$189$	3.62323	+	2.10365i	0.263551	+	0.153018i
$190$	17.4890	−	3.62846i	1.26878	−	0.263236i
$191$	−9.29864	−	2.35854i	−0.672826	−	0.170658i	−0.105837	−	0.994383i	$-0.533752\pi$
$191$	−9.29864	−	2.35854i	−0.672826	−	0.170658i	−0.566989	+	0.823725i	$0.691892\pi$
$192$	−8.08616	−	4.53817i	−0.583568	−	0.327514i
$193$	−0.0977651	−	0.204648i	−0.00703729	−	0.0147309i	0.898774	−	0.438412i	$-0.144459\pi$
$193$	−0.0977651	−	0.204648i	−0.00703729	−	0.0147309i	−0.905812	+	0.423681i	$0.860738\pi$
$194$	22.2866	−	3.94839i	1.60009	−	0.283478i
$195$	4.49847	+	3.36984i	0.322142	+	0.241320i
$196$	−5.07983	+	7.80144i	−0.362845	+	0.557246i
$197$	4.06020	−	5.33831i	0.289277	−	0.380339i	−0.628250	−	0.778011i	$-0.716229\pi$
$197$	4.06020	−	5.33831i	0.289277	−	0.380339i	0.917527	+	0.397673i	$0.130182\pi$
$198$	7.96069	−	7.56363i	0.565742	−	0.537524i
$199$	−1.83884	+	2.02235i	−0.130352	+	0.143360i	−0.801573	−	0.597898i	$-0.796003\pi$
$199$	−1.83884	+	2.02235i	−0.130352	+	0.143360i	0.671220	+	0.741258i	$0.265770\pi$
$200$	0.506730	−	2.06087i	0.0358312	−	0.145725i
$201$	6.12584	−	19.8350i	0.432084	−	1.39905i
$202$	−7.18585	−	11.7745i	−0.505595	−	0.828449i
$203$	1.77035	+	8.85787i	0.124254	+	0.621700i
$204$	−1.19600	+	9.57986i	−0.0837366	+	0.670724i
$205$	13.9699	−	16.2963i	0.975703	−	1.13819i
$206$	−16.7850	+	6.70247i	−1.16947	+	0.466983i
$207$	8.60485	−	0.503512i	0.598078	−	0.0349965i
$208$	−1.35669	−	4.39286i	−0.0940696	−	0.304590i
$209$	11.6261	−	13.1678i	0.804191	−	0.910833i
$210$	9.09013	−	7.45314i	0.627279	−	0.514315i
$211$	1.06685	+	2.51052i	0.0734453	+	0.172831i	0.953003	−	0.302961i	$-0.0979753\pi$
$211$	1.06685	+	2.51052i	0.0734453	+	0.172831i	−0.879558	+	0.475792i	$0.842161\pi$
$212$	16.1312	−	14.0342i	1.10790	−	0.963870i
$213$	0.849011	+	5.49017i	0.0581733	+	0.376180i
$214$	−4.47579	−	17.1201i	−0.305959	−	1.17031i
$215$	−1.86239	−	16.9260i	−0.127014	−	1.15435i
$216$	−0.315744	−	2.86958i	−0.0214836	−	0.195250i
$217$	−1.78814	−	6.83974i	−0.121387	−	0.464312i
$218$	−2.54463	−	16.4550i	−0.172344	−	1.11447i
$219$	−11.6600	+	10.1442i	−0.787911	+	0.685482i
$220$	9.15332	+	21.5396i	0.617117	+	1.45220i
$221$	−2.27823	+	1.86795i	−0.153250	+	0.125652i
$222$	−18.8082	+	21.3023i	−1.26232	+	1.42972i
$223$	1.50596	+	4.87619i	0.100847	+	0.326534i	0.991841	−	0.127481i	$-0.0406891\pi$
$223$	1.50596	+	4.87619i	0.100847	+	0.326534i	−0.890994	+	0.454014i	$0.849991\pi$
$224$	−7.95647	+	0.465572i	−0.531614	+	0.0311073i
$225$	2.90103	−	1.15842i	0.193402	−	0.0772279i
$226$	−4.35468	+	5.07985i	−0.289669	+	0.337907i
$227$	1.89966	−	15.2161i	0.126085	−	1.00993i	−0.791161	−	0.611607i	$-0.790523\pi$
$227$	1.89966	−	15.2161i	0.126085	−	1.00993i	0.917246	−	0.398321i	$-0.130407\pi$
$228$	−2.14327	−	10.7237i	−0.141941	−	0.710197i
$229$	3.12608	+	5.12227i	0.206577	+	0.338489i	0.939935	−	0.341353i	$-0.110885\pi$
$229$	3.12608	+	5.12227i	0.206577	+	0.338489i	−0.733358	+	0.679843i	$0.762048\pi$
$230$	−12.1830	+	39.4477i	−0.803325	+	2.60110i
$231$	2.76027	−	11.2260i	0.181613	−	0.738618i
$232$	4.18734	−	4.60520i	0.274912	−	0.302346i
$233$	0.289438	−	0.275001i	0.0189617	−	0.0180159i	−0.679256	−	0.733901i	$-0.737698\pi$
$233$	0.289438	−	0.275001i	0.0189617	−	0.0180159i	0.698218	+	0.715885i	$0.253977\pi$
$234$	1.26293	−	1.66049i	0.0825606	−	0.108550i
$235$	11.4255	−	17.5468i	0.745315	−	1.14463i
$236$	−11.0120	−	8.24919i	−0.716820	−	0.536977i
$237$	35.2011	−	6.23637i	2.28656	−	0.405096i
$238$	2.65595	+	5.55961i	0.172160	+	0.360376i
$239$	−7.98508	−	4.48145i	−0.516512	−	0.289881i	0.209207	−	0.977871i	$-0.432912\pi$
$239$	−7.98508	−	4.48145i	−0.516512	−	0.289881i	−0.725720	+	0.687991i	$0.758493\pi$
$240$	−25.4679	−	6.45977i	−1.64395	−	0.416976i
$241$	−21.9104	+	4.54577i	−1.41137	+	0.292819i	−0.846513	−	0.532368i	$-0.821302\pi$
$241$	−21.9104	+	4.54577i	−1.41137	+	0.292819i	−0.564859	+	0.825187i	$0.691070\pi$
$242$	26.6750	+	15.4876i	1.71474	+	0.995580i
$243$	8.18326	−	7.33223i	0.524956	−	0.470363i
$244$	−2.36436	+	1.37275i	−0.151363	+	0.0878816i
$245$	−5.01699	+	15.4407i	−0.320524	+	0.986471i
$246$	−22.2822	−	19.3855i	−1.42066	−	1.23597i
$247$	1.77992	−	2.82291i	0.113254	−	0.179617i
$248$	−3.06104	+	3.78949i	−0.194376	+	0.240633i
$249$	5.83622	+	2.03876i	0.369855	+	0.129201i
$250$	−0.253735	−	11.5747i	−0.0160476	−	0.732047i
$251$	−11.9727	+	1.40598i	−0.755711	+	0.0887446i	−0.485715	−	0.874117i	$-0.661441\pi$
$251$	−11.9727	+	1.40598i	−0.755711	+	0.0887446i	−0.269996	+	0.962862i	$0.587022\pi$
$252$	−1.21993	−	1.51024i	−0.0768482	−	0.0951363i
$253$	13.6699	+	38.2323i	0.859419	+	2.40365i
$254$	−5.72607	−	1.63187i	−0.359285	−	0.102392i
$255$	2.32965	+	16.6745i	0.145888	+	1.04420i
$256$	13.0226	+	15.6483i	0.813911	+	0.978016i
$257$	−6.40204	+	16.3791i	−0.399348	+	1.02170i	0.579109	+	0.815250i	$0.303401\pi$
$257$	−6.40204	+	16.3791i	−0.399348	+	1.02170i	−0.978457	+	0.206451i	$0.933809\pi$
$258$	−23.3078	+	2.39237i	−1.45108	+	0.148943i
$259$	−1.23330	+	7.97520i	−0.0766335	+	0.495555i
$260$	2.37148	+	3.76111i	0.147073	+	0.233254i
$261$	9.09906	+	1.06852i	0.563218	+	0.0661397i
$262$	−1.16532	+	12.2325i	−0.0719940	+	0.755724i
$263$	22.8387	−	10.3020i	1.40830	−	0.635250i	0.443026	−	0.896509i	$-0.353905\pi$
$263$	22.8387	−	10.3020i	1.40830	−	0.635250i	0.965269	+	0.261258i	$0.0841374\pi$
$264$	−7.35382	+	3.06180i	−0.452596	+	0.188441i
$265$	20.8012	−	30.9474i	1.27781	−	1.90108i
$266$	−4.84420	−	5.02447i	−0.297017	−	0.308070i
$267$	−14.7203	+	10.0511i	−0.900868	+	0.615120i
$268$	10.1314	−	12.9243i	0.618876	−	0.789480i
$269$	7.73471	+	15.0441i	0.471594	+	0.917255i	0.997761	+	0.0668747i	$0.0213028\pi$
$269$	7.73471	+	15.0441i	0.471594	+	0.917255i	−0.526168	+	0.850381i	$0.676372\pi$
$270$	7.40948	+	18.9566i	0.450927	+	1.15366i
$271$	13.5294	−	24.5249i	0.821852	−	1.48978i	−0.0493090	−	0.998784i	$-0.515702\pi$
$271$	13.5294	−	24.5249i	0.821852	−	1.48978i	0.871161	−	0.490998i	$-0.163368\pi$
$272$	6.47536	−	12.1546i	0.392626	−	0.736979i
$273$	0.176318	−	2.18920i	0.0106712	−	0.132496i
$274$	0.517770	−	1.12583i	0.0312796	−	0.0680140i
$275$	9.07801	+	11.5805i	0.547425	+	0.698332i
$276$	24.0971	+	7.63543i	1.45047	+	0.459599i
$277$	2.06129	+	1.11756i	0.123851	+	0.0671478i	0.537365	−	0.843350i	$-0.319420\pi$
$277$	2.06129	+	1.11756i	0.123851	+	0.0671478i	−0.413514	+	0.910498i	$0.635699\pi$
$278$	3.19450	+	12.9920i	0.191593	+	0.779208i
$279$	−7.15797	−	0.418848i	−0.428536	−	0.0250757i
$280$	−2.18238	+	0.726770i	−0.130422	+	0.0434328i
$281$	1.09529	+	8.77323i	0.0653398	+	0.523367i	0.989840	+	0.142185i	$0.0454129\pi$
$281$	1.09529	+	8.77323i	0.0653398	+	0.523367i	−0.924500	+	0.381181i	$0.875517\pi$
$282$	−24.0284	−	15.8970i	−1.43087	−	0.946655i
$283$	15.5709	+	23.1658i	0.925593	+	1.37707i	0.926186	+	0.377066i	$0.123067\pi$
$283$	15.5709	+	23.1658i	0.925593	+	1.37707i	−0.000592777		1.00000i	$0.500189\pi$
$284$	−0.924179	+	4.29644i	−0.0548399	+	0.254947i
$285$	−8.47154	−	17.0867i	−0.501811	−	1.01213i
$286$	9.17867	+	3.51054i	0.542746	+	0.207583i
$287$	−8.29794	−	1.22120i	−0.489812	−	0.0720854i
$288$	−2.04458	+	7.82064i	−0.120478	+	0.460836i
$289$	8.13234	+	0.834725i	0.478373	+	0.0491015i
$290$	−20.0649	+	39.0264i	−1.17825	+	2.29171i
$291$	−10.0977	−	21.9564i	−0.591940	−	1.28711i
$292$	−11.4819	+	4.20020i	−0.671928	+	0.245798i
$293$	−0.435209	+	2.17755i	−0.0254252	+	0.127214i	−0.991254	−	0.131966i	$-0.957871\pi$
$293$	−0.435209	+	2.17755i	−0.0254252	+	0.127214i	0.965829	+	0.259180i	$0.0834523\pi$
$294$	21.1949	+	7.05826i	1.23611	+	0.411646i
$295$	−22.2843	−	8.89839i	−1.29744	−	0.518084i
$296$	4.92664	−	2.57864i	0.286355	−	0.149880i
$297$	17.0091	+	10.5518i	0.986968	+	0.612279i
$298$	21.5957	−	25.9499i	1.25101	−	1.50324i
$299$	3.72605	+	6.75426i	0.215483	+	0.390609i
$300$	9.15981	−	0.133853i	0.528842	−	0.00772802i
$301$	−5.20647	+	4.14313i	−0.300096	+	0.238806i
$302$	−4.30979	−	20.0359i	−0.248001	−	1.15294i
$303$	−10.2227	+	10.6031i	−0.587278	+	0.609133i
$304$	−2.60909	+	15.3803i	−0.149642	+	0.882122i
$305$	−3.35910	+	3.38373i	−0.192341	+	0.193752i
$306$	6.19515	−	0.819445i	0.354153	−	0.0468445i
$307$	4.74640	+	3.04142i	0.270891	+	0.173583i	0.667942	−	0.744214i	$-0.267176\pi$
$307$	4.74640	+	3.04142i	0.270891	+	0.173583i	−0.397051	+	0.917797i	$0.629966\pi$
$308$	5.21188	−	7.51452i	0.296974	−	0.428180i
$309$	11.4570	+	15.5293i	0.651764	+	0.883430i
$310$	13.8925	−	31.4087i	0.789042	−	1.78390i
$311$	−2.78707	+	19.9485i	−0.158040	+	1.13118i	0.733977	+	0.679174i	$0.237662\pi$
$311$	−2.78707	+	19.9485i	−0.158040	+	1.13118i	−0.892017	+	0.452001i	$0.850710\pi$
$312$	−1.28600	+	0.797790i	−0.0728056	+	0.0451660i
$313$	1.55021	−	2.62563i	0.0876228	−	0.148409i	−0.814099	−	0.580726i	$-0.802769\pi$
$313$	1.55021	−	2.62563i	0.0876228	−	0.148409i	0.901722	+	0.432316i	$0.142304\pi$
$314$	−9.51038	−	5.70916i	−0.536702	−	0.322186i
$315$	−2.73910	−	1.99007i	−0.154331	−	0.112128i
$316$	27.7714	+	5.33974i	1.56226	+	0.300384i
$317$	−26.3238	+	8.34099i	−1.47849	+	0.468477i	−0.929962	−	0.367655i	$-0.880161\pi$
$317$	−26.3238	+	8.34099i	−1.47849	+	0.468477i	−0.548529	+	0.836132i	$0.684812\pi$
$318$	−42.3723	−	28.9322i	−2.37612	−	1.62244i
$319$	7.21777	+	42.5480i	0.404118	+	2.38223i
$320$	−10.4579	−	7.36709i	−0.584616	−	0.411833i
$321$	−16.4768	+	9.24724i	−0.919647	+	0.516131i
$322$	15.5778	−	4.19440i	0.868117	−	0.233745i
$323$	9.75728	−	2.17353i	0.542910	−	0.120938i
$324$	16.6179	−	6.35582i	0.923218	−	0.353101i
$325$	2.05455	+	1.89573i	0.113966	+	0.105156i
$326$	6.72745	+	6.58159i	0.372599	+	0.364521i
$327$	−16.3112	+	7.07266i	−0.902013	+	0.391119i
$328$	2.71737	+	5.10065i	0.150042	+	0.281636i
$329$	−8.18098	−	0.119549i	−0.451032	−	0.00659098i
$330$	44.4505	−	34.3236i	2.44692	−	1.88945i
$331$	−33.8244	−	4.47402i	−1.85916	−	0.245914i	−0.884009	−	0.467470i	$-0.845166\pi$
$331$	−33.8244	−	4.47402i	−1.85916	−	0.245914i	−0.975148	+	0.221556i	$0.928887\pi$
$332$	3.73606	+	3.15565i	0.205043	+	0.173189i
$333$	7.30626	+	3.68917i	0.400380	+	0.202165i
$334$	5.70841	+	19.4889i	0.312351	+	1.06639i
$335$	11.2010	−	26.3580i	0.611973	−	1.44009i
$336$	3.17260	+	9.76425i	0.173079	+	0.532683i
$337$	−2.31807	−	2.07700i	−0.126273	−	0.113141i	0.601780	−	0.798662i	$-0.294458\pi$
$337$	−2.31807	−	2.07700i	−0.126273	−	0.113141i	−0.728053	+	0.685521i	$0.759575\pi$
$338$	−22.3347	−	4.63381i	−1.21485	−	0.252046i
$339$	6.42370	+	3.12660i	0.348888	+	0.169813i
$340$	−2.99080	+	12.9786i	−0.162199	+	0.703865i
$341$	−7.58447	−	32.9129i	−0.410722	−	1.78233i
$342$	−6.36479	+	3.09792i	−0.344169	+	0.167517i
$343$	13.5629	−	3.44013i	0.732326	−	0.185750i
$344$	4.42716	+	1.19203i	0.238696	+	0.0642701i
$345$	44.0409	+	1.93182i	2.37108	+	0.104006i
$346$	0.0610740	−	8.35925i	0.00328336	−	0.449396i
$347$	−6.08087	−	10.2994i	−0.326438	−	0.552899i	0.652313	−	0.757950i	$-0.273799\pi$
$347$	−6.08087	−	10.2994i	−0.326438	−	0.552899i	−0.978751	+	0.205051i	$0.934264\pi$
$348$	23.8039	+	12.4591i	1.27602	+	0.667879i
$349$	21.2563	+	24.7960i	1.13782	+	1.32730i	0.937666	+	0.347537i	$0.112982\pi$
$349$	21.2563	+	24.7960i	1.13782	+	1.32730i	0.200155	+	0.979764i	$0.435855\pi$
$350$	4.87599	−	3.22592i	0.260632	−	0.172433i
$351$	3.51063	+	1.46167i	0.187384	+	0.0780181i
$352$	−38.0612	+	1.11262i	−2.02867	+	0.0593029i
$353$	−5.69858	+	5.57503i	−0.303305	+	0.296729i	−0.835048	−	0.550177i	$-0.814560\pi$
$353$	−5.69858	+	5.57503i	−0.303305	+	0.296729i	0.531743	+	0.846906i	$0.321537\pi$
$354$	−12.4676	+	30.5722i	−0.662645	+	1.62489i
$355$	0.391791	+	7.65414i	0.0207941	+	0.406240i
$356$	−13.7168	+	3.26662i	−0.726987	+	0.173130i
$357$	5.02595	−	4.24516i	0.266001	−	0.224678i
$358$	−19.2818	+	12.3555i	−1.01908	+	0.653010i
$359$	1.21064	−	33.1261i	0.0638952	−	1.74833i	−0.452306	−	0.891863i	$-0.649399\pi$
$359$	1.21064	−	33.1261i	0.0638952	−	1.74833i	0.516201	−	0.856467i	$-0.327346\pi$
$360$	0.0170444	+	2.33288i	0.000898320	+	0.122954i
$361$	6.58168	−	3.95104i	0.346404	−	0.207949i
$362$	−15.6848	−	1.37865i	−0.824373	−	0.0724604i
$363$	8.79502	−	31.7388i	0.461619	−	1.66586i
$364$	0.748929	−	1.56770i	0.0392545	−	0.0821701i
$365$	−17.4308	+	12.2791i	−0.912370	+	0.642719i
$366$	4.62201	+	4.65590i	0.241596	+	0.243368i
$367$	−0.515550	−	0.398095i	−0.0269115	−	0.0207804i	0.597630	−	0.801772i	$-0.296109\pi$
$367$	−0.515550	−	0.398095i	−0.0269115	−	0.0207804i	−0.624541	+	0.780992i	$0.714714\pi$
$368$	−28.2156	−	22.4530i	−1.47084	−	1.17044i
$369$	−3.77865	+	7.62136i	−0.196709	+	0.396752i
$370$	−28.8125	+	26.5853i	−1.49789	+	1.38210i
$371$	−14.5643	−	0.425750i	−0.756140	−	0.0221038i
$372$	−19.1676	−	8.64609i	−0.993795	−	0.448279i
$373$	−17.4417	+	30.5526i	−0.903096	+	1.58195i	−0.0929922	+	0.995667i	$0.529643\pi$
$373$	−17.4417	+	30.5526i	−0.903096	+	1.58195i	−0.810104	+	0.586286i	$0.800589\pi$
$374$	11.9074	+	26.9208i	0.615718	+	1.39204i
$375$	−11.8885	+	3.38808i	−0.613917	+	0.174960i
$376$	3.28038	+	4.58513i	0.169173	+	0.236460i
$377$	2.64727	+	7.75978i	0.136341	+	0.399649i
$378$	4.72155	−	6.39981i	0.242851	−	0.329171i
$379$	−2.82631	−	4.95085i	−0.145178	−	0.254308i	0.786503	−	0.617587i	$-0.211890\pi$
$379$	−2.82631	−	4.95085i	−0.145178	−	0.254308i	−0.931680	+	0.363279i	$0.881657\pi$
$380$	−1.43077	−	15.0188i	−0.0733970	−	0.770450i
$381$	−0.139332	+	6.35591i	−0.00713818	+	0.325623i
$382$	−6.38080	+	17.0557i	−0.326470	+	0.872644i
$383$	3.17070	+	0.953923i	0.162015	+	0.0487432i	0.368074	−	0.929796i	$-0.380017\pi$
$383$	3.17070	+	0.953923i	0.162015	+	0.0487432i	−0.206059	+	0.978540i	$0.566064\pi$
$384$	6.96359	−	9.73332i	0.355359	−	0.496701i
$385$	5.36945	−	15.0174i	0.273653	−	0.765359i
$386$	−0.406442	+	0.141982i	−0.0206873	+	0.00722670i
$387$	2.36464	+	6.32062i	0.120202	+	0.321295i
$388$	−1.25617	−	19.0765i	−0.0637723	−	0.968460i
$389$	10.9535	−	8.20539i	0.555366	−	0.416030i	−0.284618	−	0.958641i	$-0.591867\pi$
$389$	10.9535	−	8.20539i	0.555366	−	0.416030i	0.839984	+	0.542611i	$0.182564\pi$
$390$	7.29241	−	7.78840i	0.369265	−	0.394381i
$391$	−6.49512	+	22.1748i	−0.328472	+	1.12143i
$392$	−3.38037	−	2.77161i	−0.170734	−	0.139988i
$393$	12.9512	−	2.09980i	0.653302	−	0.105921i
$394$	−9.22974	−	8.76938i	−0.464988	−	0.441795i
$395$	49.1874	−	3.60005i	2.47489	−	0.181138i
$396$	−5.61495	−	7.38248i	−0.282162	−	0.370984i
$397$	13.3195	+	2.15951i	0.668486	+	0.108383i	0.484831	−	0.874608i	$-0.338881\pi$
$397$	13.3195	+	2.15951i	0.668486	+	0.108383i	0.183656	+	0.982991i	$0.441207\pi$
$398$	3.43413	+	3.88953i	0.172138	+	0.194964i
$399$	−3.88216	+	6.36116i	−0.194351	+	0.318456i
$400$	−12.2726	−	4.48944i	−0.613630	−	0.224472i
$401$	1.70804	+	21.2074i	0.0852953	+	1.05905i	0.887136	+	0.461508i	$0.152691\pi$
$401$	1.70804	+	21.2074i	0.0852953	+	1.05905i	−0.801841	+	0.597538i	$0.796146\pi$
$402$	−36.1543	−	15.6767i	−1.80321	−	0.781883i
$403$	−2.42308	−	5.94171i	−0.120702	−	0.295978i
$404$	−10.5496	+	4.94545i	−0.524862	+	0.246045i
$405$	25.1023	−	18.2379i	1.24734	−	0.906249i
$406$	17.0812	−	1.50140i	0.847726	−	0.0745131i
$407$	−7.00298	+	37.9135i	−0.347125	+	1.87930i
$408$	−4.40988	−	1.05020i	−0.218322	−	0.0519929i
$409$	−17.0767	+	8.62257i	−0.844387	+	0.426359i	−0.819326	−	0.573327i	$-0.805652\pi$
$409$	−17.0767	+	8.62257i	−0.844387	+	0.426359i	−0.0250609	+	0.999686i	$0.507978\pi$
$410$	−27.8487	−	29.7428i	−1.37535	−	1.46889i
$411$	−1.30285	−	0.230819i	−0.0642650	−	0.0113854i
$412$	4.07672	+	14.7118i	0.200846	+	0.724797i
$413$	1.70305	+	9.22018i	0.0838018	+	0.453696i
$414$	0.836432	−	16.3408i	0.0411084	−	0.803105i
$415$	7.72226	+	3.62005i	0.379071	+	0.177701i
$416$	−7.10398	+	1.36592i	−0.348301	+	0.0669696i
$417$	12.5584	−	6.80875i	0.614987	−	0.333426i
$418$	−22.4321	−	24.6707i	−1.09719	−	1.20668i
$419$	−27.6623	−	2.02462i	−1.35139	−	0.0989093i	−0.622008	−	0.783011i	$-0.713683\pi$
$419$	−27.6623	−	2.02462i	−1.35139	−	0.0989093i	−0.729386	+	0.684102i	$0.760194\pi$
$420$	−5.41784	−	8.32055i	−0.264364	−	0.406001i
$421$	1.15061	−	17.4733i	0.0560771	−	0.851598i	−0.874390	−	0.485223i	$-0.838738\pi$
$421$	1.15061	−	17.4733i	0.0560771	−	0.851598i	0.930467	−	0.366375i	$-0.119401\pi$
$422$	4.95852	−	1.49180i	0.241377	−	0.0726195i
$423$	−2.67935	+	7.85382i	−0.130274	+	0.381866i
$424$	5.72187	+	8.24983i	0.277879	+	0.400647i
$425$	0.305831	+	8.36829i	0.0148350	+	0.405922i
$426$	10.5355	−	0.462133i	0.510447	−	0.0223904i
$427$	1.81850	+	0.405088i	0.0880034	+	0.0196036i
$428$	−14.7874	+	2.17626i	−0.714777	+	0.105193i
$429$	1.14762	−	10.4299i	0.0554076	−	0.503562i
$430$	−32.3239			−1.55880
$431$	−15.1484	−	14.1960i	−0.729671	−	0.683798i
$431$	−15.1484	−	14.1960i	−0.729671	−	0.683798i
$432$	−17.7763			−0.855265
$433$	−2.05468	+	18.6736i	−0.0987415	+	0.897394i	0.837595	+	0.546291i	$0.183961\pi$
$433$	−2.05468	+	18.6736i	−0.0987415	+	0.897394i	−0.936337	+	0.351103i	$0.885807\pi$
$434$	−13.2769	+	1.95396i	−0.637314	+	0.0937931i
$435$	45.7343	+	10.1878i	2.19279	+	0.488465i
$436$	−14.0506	+	0.616317i	−0.672899	+	0.0295162i
$437$	−0.955921	−	26.1564i	−0.0457279	−	1.25123i
$438$	16.7200	+	24.1070i	0.798914	+	1.15188i
$439$	5.51510	−	16.1661i	0.263221	−	0.771565i	−0.732635	−	0.680622i	$-0.761710\pi$
$439$	5.51510	−	16.1661i	0.263221	−	0.771565i	0.995856	−	0.0909428i	$-0.0289880\pi$
$440$	−10.5235	+	3.16604i	−0.501686	+	0.150935i
$441$	0.422774	−	6.42033i	0.0201321	−	0.305730i
$442$	3.05159	+	4.68653i	0.145149	+	0.222916i
$443$	−13.7629	−	1.00731i	−0.653894	−	0.0478588i	−0.257985	−	0.966149i	$-0.583059\pi$
$443$	−13.7629	−	1.00731i	−0.653894	−	0.0478588i	−0.395908	+	0.918290i	$0.629570\pi$
$444$	16.1478	+	17.7592i	0.766339	+	0.842814i
$445$	−21.6175	+	11.7203i	−1.02477	+	0.555597i
$446$	9.51339	−	1.82919i	0.450472	−	0.0866146i
$447$	−32.6394	−	15.3007i	−1.54379	−	0.723699i
$448$	−0.255528	+	4.99206i	−0.0120726	+	0.235853i
$449$	−6.17878	−	33.4514i	−0.291595	−	1.57867i	−0.732279	−	0.681005i	$-0.761543\pi$
$449$	−6.17878	−	33.4514i	−0.291595	−	1.57867i	0.440684	−	0.897662i	$-0.354736\pi$
$450$	−1.58349	−	5.71437i	−0.0746463	−	0.269378i
$451$	−39.4564	−	6.99026i	−1.85793	−	0.329159i
$452$	3.86272	+	4.12544i	0.181687	+	0.194044i
$453$	−19.5338	+	9.86323i	−0.917776	+	0.463415i
$454$	−28.3164	−	6.74349i	−1.32896	−	0.316488i
$455$	0.550351	−	2.97955i	0.0258009	−	0.139684i
$456$	5.11527	−	0.449620i	0.239545	−	0.0210554i
$457$	29.8668	−	21.6995i	1.39711	−	1.01506i	0.402068	−	0.915610i	$-0.368292\pi$
$457$	29.8668	−	21.6995i	1.39711	−	1.01506i	0.995043	−	0.0994501i	$-0.0317084\pi$
$458$	10.3141	−	4.83504i	0.481946	−	0.225927i
$459$	4.30141	+	10.5476i	0.200773	+	0.492321i
$460$	31.9945	+	13.8730i	1.49175	+	0.646833i
$461$	3.38810	+	42.0673i	0.157799	+	1.95927i	0.262935	+	0.964814i	$0.415310\pi$
$461$	3.38810	+	42.0673i	0.157799	+	1.95927i	−0.105135	+	0.994458i	$0.533528\pi$
$462$	−20.6090	−	7.53897i	−0.958816	−	0.350744i
$463$	6.35839	−	10.4186i	0.295500	−	0.484194i	−0.670792	−	0.741646i	$-0.734046\pi$
$463$	6.35839	−	10.4186i	0.295500	−	0.484194i	0.966291	+	0.257451i	$0.0828827\pi$
$464$	−25.3668	−	28.7306i	−1.17762	−	1.33379i
$465$	−36.1981	−	5.86884i	−1.67865	−	0.272161i
$466$	−0.458801	−	0.603226i	−0.0212535	−	0.0279439i
$467$	37.9474	−	2.77739i	1.75600	−	0.128522i	0.843374	−	0.537326i	$-0.180566\pi$
$467$	37.9474	−	2.77739i	1.75600	−	0.128522i	0.912622	+	0.408804i	$0.134054\pi$
$468$	−1.27747	−	1.21375i	−0.0590509	−	0.0561056i
$469$	−11.0466	+	1.79100i	−0.510084	+	0.0827005i
$470$	−30.7365	−	25.2013i	−1.41777	−	1.16245i
$471$	−3.32927	+	11.3664i	−0.153405	+	0.523735i
$472$	4.41576	−	4.71610i	0.203252	−	0.217076i
$473$	−25.4419	+	19.0588i	−1.16982	+	0.876323i
$474$	−4.45896	−	67.7147i	−0.204807	−	3.11024i
$475$	−3.32370	−	8.88414i	−0.152502	−	0.407632i
$476$	4.91317	−	1.71632i	0.225195	−	0.0786672i
$477$	−4.97533	+	13.9151i	−0.227805	+	0.637130i
$478$	−10.1137	+	14.1364i	−0.462591	+	0.646584i
$479$	32.6153	+	9.81249i	1.49023	+	0.448344i	0.926080	−	0.377327i	$-0.123157\pi$
$479$	32.6153	+	9.81249i	1.49023	+	0.448344i	0.564152	+	0.825671i	$0.309203\pi$
$480$	−14.4860	+	38.7205i	−0.661191	+	1.76734i
$481$	−0.160533	+	7.32303i	−0.00731966	+	0.333902i
$482$	4.02836	+	42.2858i	0.183487	+	1.92607i
$483$	−8.54002	−	14.9596i	−0.388584	−	0.680683i
$484$	15.4676	−	20.9654i	0.703071	−	0.952974i
$485$	−10.7650	−	31.5547i	−0.488812	−	1.43283i
$486$	−12.1360	−	16.9630i	−0.550501	−	0.769459i
$487$	36.8352	−	10.4976i	1.66916	−	0.475693i	0.698394	−	0.715714i	$-0.253898\pi$
$487$	36.8352	−	10.4976i	1.66916	−	0.475693i	0.970768	+	0.240021i	$0.0771543\pi$
$488$	−0.519296	−	1.17404i	−0.0235074	−	0.0531464i
$489$	4.98210	−	8.72715i	0.225298	−	0.394655i
$490$	28.0930	+	12.6721i	1.26911	+	0.572469i
$491$	−17.4069	−	0.508846i	−0.785563	−	0.0229639i	−0.365912	−	0.930649i	$-0.619243\pi$
$491$	−17.4069	−	0.508846i	−0.785563	−	0.0229639i	−0.419651	+	0.907686i	$0.637848\pi$
$492$	−18.3344	+	16.9171i	−0.826579	+	0.762683i
$493$	−10.9093	+	22.0035i	−0.491329	+	0.990988i
$494$	−4.95693	−	3.94456i	−0.223023	−	0.177474i
$495$	−12.8028	−	9.88599i	−0.575443	−	0.444342i
$496$	21.1326	+	21.2876i	0.948884	+	0.955842i
$497$	2.44829	−	1.72470i	0.109821	−	0.0773633i
$498$	5.05856	−	10.5889i	0.226680	−	0.474500i
$499$	10.9841	−	39.6386i	0.491715	−	1.77447i	−0.130315	−	0.991473i	$-0.541599\pi$
$499$	10.9841	−	39.6386i	0.491715	−	1.77447i	0.622030	−	0.782993i	$-0.286308\pi$
$500$	−9.74146	−	0.856252i	−0.435652	−	0.0382928i
$501$	18.5910	−	11.1603i	0.830584	−	0.498607i
$502$	0.167186	+	22.8829i	0.00746187	+	1.02131i
$503$	−0.154946	+	4.23972i	−0.00690872	+	0.189040i	0.991398	+	0.130878i	$0.0417797\pi$
$503$	−0.154946	+	4.23972i	−0.00690872	+	0.189040i	−0.998307	+	0.0581616i	$0.981476\pi$
$504$	0.767542	−	0.491830i	0.0341890	−	0.0219078i
$505$	−15.5229	+	13.1114i	−0.690760	+	0.583450i
$506$	74.9775	−	17.8557i	3.33316	−	0.793784i
$507$	1.24506	+	24.3239i	0.0552952	+	1.08026i
$508$	−1.89909	+	4.65681i	−0.0842584	+	0.206613i
$509$	16.2728	−	15.9200i	0.721280	−	0.705642i	−0.243147	−	0.969989i	$-0.578180\pi$
$509$	16.2728	−	15.9200i	0.721280	−	0.705642i	0.964427	+	0.264348i	$0.0851566\pi$
$510$	31.9463	−	0.933869i	1.41461	−	0.0413524i
$511$	7.69140	+	3.20236i	0.340248	+	0.141664i
$512$	22.3810	−	14.8072i	0.989111	−	0.654390i
$513$	−8.39782	−	9.79630i	−0.370773	−	0.432517i
$514$	29.5761	+	15.4804i	1.30455	+	0.682809i
$515$	13.5357	+	22.9258i	0.596453	+	1.01023i
$516$	−0.144589	+	19.7901i	−0.00636520	+	0.871210i
$517$	−39.0517	−	1.71297i	−1.71749	−	0.0753365i
$518$	14.7921	+	3.98285i	0.649928	+	0.174996i
$519$	−8.65184	+	2.19449i	−0.379774	+	0.0963272i
$520$	−1.87725	+	0.913712i	−0.0823230	+	0.0400689i
$521$	−2.60907	−	11.3221i	−0.114305	−	0.496029i	−0.999524	−	0.0308539i	$-0.990177\pi$
$521$	−2.60907	−	11.3221i	−0.114305	−	0.496029i	0.885219	−	0.465175i	$-0.154009\pi$
$522$	3.90526	−	16.9469i	0.170928	−	0.741746i
$523$	−8.82571	−	4.29572i	−0.385921	−	0.187839i	0.234484	−	0.972120i	$-0.424660\pi$
$523$	−8.82571	−	4.29572i	−0.385921	−	0.187839i	−0.620406	+	0.784281i	$0.713032\pi$
$524$	10.1626	+	2.10845i	0.443957	+	0.0921081i
$525$	−4.64933	−	4.16582i	−0.202913	−	0.181811i
$526$	−14.6969	−	45.2325i	−0.640817	−	1.97223i
$527$	7.51749	−	17.6901i	0.327467	−	0.770594i
$528$	13.7877	+	47.0722i	0.600032	+	2.04855i
$529$	33.4747	+	16.9025i	1.45542	+	0.734891i
$530$	−54.0750	−	45.6744i	−2.34887	−	1.98397i
$531$	9.42745	+	1.24699i	0.409117	+	0.0541146i
$532$	−4.66603	+	3.60299i	−0.202298	+	0.156209i
$533$	−7.61200	−	0.111235i	−0.329712	−	0.00481812i
$534$	15.9091	+	29.8621i	0.688452	+	1.29226i
$535$	−23.9149	+	10.3696i	−1.03393	+	0.448319i
$536$	5.51200	+	5.39249i	0.238082	+	0.232920i
$537$	17.9711	+	16.5819i	0.775509	+	0.715561i
$538$	29.9921	−	11.4710i	1.29305	−	0.494550i
$539$	29.5835	−	6.59001i	1.27425	−	0.283852i
$540$	16.6003	−	4.46971i	0.714364	−	0.192346i
$541$	20.7226	−	11.6301i	0.890934	−	0.500016i	0.0247224	−	0.999694i	$-0.492130\pi$
$541$	20.7226	−	11.6301i	0.890934	−	0.500016i	0.866211	+	0.499678i	$0.166548\pi$
$542$	−43.4664	−	30.6199i	−1.86704	−	1.31524i
$543$	2.81178	+	16.5752i	0.120665	+	0.711308i
$544$	−17.8956	−	12.2193i	−0.767267	−	0.523896i
$545$	−23.3813	+	7.40864i	−1.00155	+	0.317351i
$546$	−4.09413	−	0.787198i	−0.175213	−	0.0336890i
$547$	−14.9084	−	10.8316i	−0.637435	−	0.463124i	0.221533	−	0.975153i	$-0.428894\pi$
$547$	−14.9084	−	10.8316i	−0.637435	−	0.463124i	−0.858968	+	0.512029i	$0.828894\pi$
$548$	−0.897409	−	0.538722i	−0.0383354	−	0.0230131i
$549$	0.960688	−	1.62715i	0.0410012	−	0.0694449i
$550$	23.7357	−	14.7247i	1.01209	−	0.627865i
$551$	3.84939	−	27.5521i	0.163990	−	1.17376i
$552$	−4.80129	+	10.8549i	−0.204357	+	0.462017i
$553$	−11.4411	−	15.5077i	−0.486524	−	0.659457i
$554$	2.53665	−	3.65736i	0.107772	−	0.155386i
$555$	35.2448	+	22.5843i	1.49606	+	0.958652i
$556$	11.2031	−	1.48186i	0.475117	−	0.0628447i
$557$	−8.81933	+	8.88400i	−0.373687	+	0.376427i	−0.871116	−	0.491078i	$-0.836603\pi$
$557$	−8.81933	+	8.88400i	−0.373687	+	0.376427i	0.497429	+	0.867505i	$0.334278\pi$
$558$	−2.27641	+	13.4192i	−0.0963681	+	0.568080i
$559$	−4.19176	+	4.34776i	−0.177293	+	0.183890i
$560$	2.97855	+	13.8471i	0.125867	+	0.585145i
$561$	24.5941	−	19.5712i	1.03836	−	0.826296i
$562$	16.7813	−	0.245227i	0.707878	−	0.0103443i
$563$	15.9405	+	28.8955i	0.671810	+	1.21780i	0.965126	+	0.261784i	$0.0843108\pi$
$563$	15.9405	+	28.8955i	0.671810	+	1.21780i	−0.293316	+	0.956015i	$0.594759\pi$
$564$	−15.5668	+	18.7055i	−0.655482	+	0.787643i
$565$	8.37527	+	5.19571i	0.352350	+	0.218585i
$566$	46.9437	−	24.5707i	1.97319	−	1.03278i
$567$	−11.2598	−	4.49617i	−0.472867	−	0.188822i
$568$	−1.95786	−	0.652000i	−0.0821500	−	0.0273573i
$569$	0.549586	−	2.74983i	0.0230398	−	0.115279i	−0.967391	−	0.253286i	$-0.918488\pi$
$569$	0.549586	−	2.74983i	0.0230398	−	0.115279i	0.990431	+	0.138008i	$0.0440699\pi$
$570$	−33.9992	+	12.4373i	−1.42407	+	0.520939i
$571$	4.45731	+	9.69193i	0.186533	+	0.405595i	0.978869	−	0.204491i	$-0.0655538\pi$
$571$	4.45731	+	9.69193i	0.186533	+	0.405595i	−0.792336	+	0.610085i	$0.791135\pi$
$572$	3.79537	−	7.38204i	0.158692	−	0.308659i
$573$	19.3423	+	1.98534i	0.808035	+	0.0829388i
$574$	−4.02703	+	15.4036i	−0.168085	+	0.642934i
$575$	21.6918	+	3.19237i	0.904611	+	0.133131i
$576$	4.73520	+	1.81106i	0.197300	+	0.0754609i
$577$	−17.5705	−	35.4388i	−0.731468	−	1.47534i	−0.874195	−	0.485574i	$-0.838611\pi$
$577$	−17.5705	−	35.4388i	−0.731468	−	1.47534i	0.142728	−	0.989762i	$-0.454413\pi$
$578$	3.26341	−	15.1714i	0.135740	−	0.631046i
$579$	0.256439	+	0.381521i	0.0106573	+	0.0158555i
$580$	30.9127	+	20.4516i	1.28358	+	0.849208i
$581$	−0.412852	−	3.30691i	−0.0171280	−	0.137194i
$582$	−43.5253	+	14.4946i	−1.80418	+	0.600822i
$583$	−69.4925	−	4.06634i	−2.87808	−	0.168411i
$584$	−1.37074	−	5.57478i	−0.0567215	−	0.230686i
$585$	−2.70156	−	1.46470i	−0.111696	−	0.0605578i
$586$	4.01840	+	1.27327i	0.165998	+	0.0525985i
$587$	15.7351	+	20.0727i	0.649456	+	0.828489i	0.993896	−	0.110319i	$-0.0351872\pi$
$587$	15.7351	+	20.0727i	0.649456	+	0.828489i	−0.344441	+	0.938808i	$0.611931\pi$
$588$	7.88408	−	17.1431i	0.325134	−	0.706968i
$589$	−1.74792	+	21.7025i	−0.0720216	+	0.894236i
$590$	−21.4166	+	40.2001i	−0.881709	+	1.65501i
$591$	−6.56636	+	11.9029i	−0.270104	+	0.489621i
$592$	−12.4650	−	31.8909i	−0.512310	−	1.31071i
$593$	9.95089	+	19.3546i	0.408634	+	0.794798i	0.999932	−	0.0116548i	$-0.00370991\pi$
$593$	9.95089	+	19.3546i	0.408634	+	0.794798i	−0.591298	+	0.806453i	$0.701384\pi$
$594$	23.4413	−	29.9032i	0.961806	−	1.22694i
$595$	7.49545	−	5.11795i	0.307283	−	0.209816i
$596$	−19.7923	−	20.5289i	−0.810726	−	0.840896i
$597$	3.09054	−	4.59800i	0.126487	−	0.188184i
$598$	13.5180	−	5.62829i	0.552792	−	0.230158i
$599$	−5.65590	+	2.55125i	−0.231094	+	0.104241i	−0.523412	−	0.852080i	$-0.675341\pi$
$599$	−5.65590	+	2.55125i	−0.231094	+	0.104241i	0.292318	+	0.956321i	$0.405574\pi$
$600$	−0.407937	+	4.28213i	−0.0166540	+	0.174817i
$601$	−41.0214	−	4.81722i	−1.67330	−	0.196499i	−0.773803	−	0.633426i	$-0.781648\pi$
$601$	−41.0214	−	4.81722i	−1.67330	−	0.196499i	−0.899497	+	0.436928i	$0.856067\pi$
$602$	6.73662	+	10.6841i	0.274564	+	0.435451i
$603$	−1.73458	+	11.2167i	−0.0706375	+	0.456781i
$604$	−17.2202	+	1.76752i	−0.700679	+	0.0719195i
$605$	16.5409	−	42.3185i	0.672482	−	1.72049i
$606$	17.8843	+	21.4903i	0.726501	+	0.872982i
$607$	0.234711	+	1.67995i	0.00952663	+	0.0681871i	0.994557	−	0.104194i	$-0.0332262\pi$
$607$	0.234711	+	1.67995i	0.00952663	+	0.0681871i	−0.985030	+	0.172381i	$0.944854\pi$
$608$	23.6061	+	6.72748i	0.957353	+	0.272835i
$609$	−6.16410	−	17.2399i	−0.249782	−	0.698596i
$610$	5.68726	+	7.04069i	0.230270	+	0.285069i
$611$	−7.37564	+	0.866135i	−0.298386	+	0.0350401i
$612$	−0.115683	−	5.27711i	−0.00467620	−	0.213315i
$613$	23.5204	+	8.21636i	0.949979	+	0.331856i	0.759993	−	0.649931i	$-0.225202\pi$
$613$	23.5204	+	8.21636i	0.949979	+	0.331856i	0.189986	+	0.981787i	$0.439156\pi$
$614$	6.72419	−	8.32439i	0.271366	−	0.335945i
$615$	−23.2041	+	36.8012i	−0.935681	+	1.48397i
$616$	3.23967	+	2.81851i	0.130530	+	0.113561i
$617$	11.4263	−	35.1665i	0.460005	−	1.41575i	−0.405152	−	0.914249i	$-0.632781\pi$
$617$	11.4263	−	35.1665i	0.460005	−	1.41575i	0.865157	−	0.501501i	$-0.167219\pi$
$618$	31.6804	−	18.3937i	1.27437	−	0.739903i
$619$	16.2934	−	14.5989i	0.654886	−	0.586780i	−0.271921	−	0.962320i	$-0.587659\pi$
$619$	16.2934	−	14.5989i	0.654886	−	0.586780i	0.926806	+	0.375539i	$0.122543\pi$
$620$	−25.0872	−	14.5656i	−1.00752	−	0.584971i
$621$	29.2033	−	6.05884i	1.17189	−	0.243133i
$622$	37.0616	+	9.40043i	1.48603	+	0.376923i
$623$	8.37926	+	4.70267i	0.335708	+	0.188408i
$624$	4.01692	+	8.40846i	0.160805	+	0.336608i
$625$	−30.6707	+	5.43375i	−1.22683	+	0.217350i
$626$	−4.63238	−	3.47016i	−0.185147	−	0.138695i
$627$	−19.4273	+	29.8358i	−0.775852	+	1.19153i
$628$	−5.67195	+	7.45743i	−0.226336	+	0.297584i
$629$	−15.9063	+	15.1129i	−0.634225	+	0.602591i
$630$	−4.32369	+	4.75516i	−0.172260	+	0.189450i
$631$	−10.5020	+	42.7115i	−0.418077	+	1.70032i	0.260236	+	0.965545i	$0.416200\pi$
$631$	−10.5020	+	42.7115i	−0.418077	+	1.70032i	−0.678313	+	0.734773i	$0.737289\pi$
$632$	−3.91850	+	12.6878i	−0.155870	+	0.504693i
$633$	−2.88021	−	4.71941i	−0.114478	−	0.187580i
$634$	10.2732	+	51.4013i	0.407999	+	2.04141i
$635$	−1.08653	+	8.70304i	−0.0431177	+	0.345369i
$636$	−28.2057	+	32.9027i	−1.11843	+	1.30468i
$637$	5.34758	−	2.13535i	0.211879	−	0.0846058i
$638$	81.7811	−	4.78541i	3.23774	−	0.189456i
$639$	−0.896297	−	2.90214i	−0.0354570	−	0.114807i
$640$	10.9277	−	12.3768i	0.431955	−	0.489236i
$641$	19.4023	−	15.9082i	0.766345	−	0.628338i	−0.167559	−	0.985862i	$-0.553588\pi$
$641$	19.4023	−	15.9082i	0.766345	−	0.628338i	0.933904	+	0.357524i	$0.116379\pi$
$642$	14.0275	+	33.0095i	0.553622	+	1.30278i
$643$	−12.5735	+	10.9390i	−0.495852	+	0.431391i	−0.867838	−	0.496848i	$-0.834491\pi$
$643$	−12.5735	+	10.9390i	−0.495852	+	0.431391i	0.371986	+	0.928238i	$0.378677\pi$
$644$	−2.08249	−	13.4665i	−0.0820614	−	0.530655i
$645$	8.72970	+	33.3916i	0.343731	+	1.31479i
$646$	−2.07541	−	18.8620i	−0.0816558	−	0.742115i
$647$	0.338489	+	3.07630i	0.0133074	+	0.120942i	0.998814	−	0.0486978i	$-0.0155071\pi$
$647$	0.338489	+	3.07630i	0.0133074	+	0.120942i	−0.985506	+	0.169639i	$0.945740\pi$
$648$	2.11309	+	8.08266i	0.0830098	+	0.317517i
$649$	6.84582	+	44.2688i	0.268722	+	1.73770i
$650$	4.00356	−	3.48310i	0.157033	−	0.136618i
$651$	5.60419	+	13.1878i	0.219646	+	0.516869i
$652$	6.14736	−	5.04031i	0.240749	−	0.197394i
$653$	16.3812	−	18.5534i	0.641044	−	0.726052i	−0.335339	−	0.942097i	$-0.608851\pi$
$653$	16.3812	−	18.5534i	0.641044	−	0.726052i	0.976383	+	0.216046i	$0.0693160\pi$
$654$	9.95873	+	32.2456i	0.389417	+	1.26090i
$655$	18.0696	−	1.05734i	0.706039	−	0.0413138i
$656$	33.0493	−	13.1970i	1.29036	−	0.515256i
$657$	5.49955	−	6.41538i	0.214558	−	0.250288i
$658$	−1.92407	+	15.4116i	−0.0750079	+	0.600808i
$659$	−0.585399	−	2.92902i	−0.0228039	−	0.114098i	0.967544	−	0.252703i	$-0.0813196\pi$
$659$	−0.585399	−	2.92902i	−0.0228039	−	0.114098i	−0.990348	+	0.138605i	$0.955738\pi$
$660$	−24.7114	−	40.4912i	−0.961891	−	1.57612i
$661$	3.32132	−	10.7542i	0.129184	−	0.418288i	−0.867707	−	0.497076i	$-0.834407\pi$
$661$	3.32132	−	10.7542i	0.129184	−	0.418288i	0.996891	+	0.0787875i	$0.0251048\pi$
$662$	−15.4643	+	62.8934i	−0.601038	+	2.44442i
$663$	4.01719	−	4.41807i	0.156015	−	0.171584i
$664$	−1.66474	+	1.58171i	−0.0646045	+	0.0613821i
$665$	−6.22381	+	8.18301i	−0.241349	+	0.317323i
$666$	8.47787	−	13.0200i	0.328511	−	0.504516i
$667$	51.4655	+	38.5533i	1.99275	+	1.49279i
$668$	16.8901	−	2.99233i	0.653499	−	0.115777i
$669$	−4.45888	−	9.33361i	−0.172390	−	0.360858i
$670$	−47.4087	−	26.6071i	−1.83156	−	1.02792i
$671$	8.62772	+	2.18837i	0.333070	+	0.0844810i
$672$	15.8174	−	3.28166i	0.610170	−	0.126593i
$673$	−10.8286	−	6.28710i	−0.417411	−	0.242350i	0.278561	−	0.960419i	$-0.410143\pi$
$673$	−10.8286	−	6.28710i	−0.417411	−	0.242350i	−0.695972	+	0.718069i	$0.745026\pi$
$674$	−4.40029	+	3.94268i	−0.169493	+	0.151866i
$675$	9.34749	−	5.42717i	0.359785	−	0.208892i
$676$	−5.95383	+	18.3240i	−0.228994	+	0.704770i
$677$	19.5141	+	16.9772i	0.749987	+	0.652489i	0.944537	−	0.328404i	$-0.106511\pi$
$677$	19.5141	+	16.9772i	0.749987	+	0.652489i	−0.194550	+	0.980893i	$0.562325\pi$
$678$	7.23314	−	11.4716i	0.277787	−	0.440563i
$679$	−8.18633	+	10.1345i	−0.314162	+	0.388926i
$680$	−5.90406	−	2.06246i	−0.226410	−	0.0790918i
$681$	0.681168	+	31.0729i	0.0261024	+	1.19072i
$682$	−63.6770	+	7.47770i	−2.43832	+	0.286336i
$683$	−14.0991	−	17.4543i	−0.539487	−	0.667872i	0.432847	−	0.901467i	$-0.357509\pi$
$683$	−14.0991	−	17.4543i	−0.539487	−	0.667872i	−0.972334	+	0.233595i	$0.924951\pi$
$684$	2.01301	+	5.63003i	0.0769692	+	0.215270i
$685$	−1.75548	−	0.500293i	−0.0670735	−	0.0191152i
$686$	−3.67524	−	26.3056i	−0.140321	−	1.00435i
$687$	−7.78026	−	9.34896i	−0.296835	−	0.356685i
$688$	10.2775	−	26.2943i	0.391828	−	1.00246i
$689$	−13.1559	+	1.35036i	−0.501200	+	0.0514445i
$690$	12.7886	−	82.6984i	0.486855	−	3.14827i
$691$	−21.7414	−	34.4812i	−0.827080	−	1.31173i	−0.947743	−	0.319034i	$-0.896641\pi$
$691$	−21.7414	−	34.4812i	−0.827080	−	1.31173i	0.120663	−	0.992694i	$-0.461498\pi$
$692$	−7.01273	−	0.823517i	−0.266584	−	0.0313054i
$693$	−0.599415	+	6.29207i	−0.0227699	+	0.239016i
$694$	−20.6960	+	9.33552i	−0.785611	+	0.354372i
$695$	18.1938	−	7.57510i	0.690132	−	0.287340i
$696$	−7.03765	+	10.4704i	−0.266762	+	0.396879i
$697$	−15.8275	−	16.4165i	−0.599511	−	0.621821i
$698$	51.2000	−	34.9598i	1.93795	−	1.32325i
$699$	−0.499243	+	0.636867i	−0.0188831	+	0.0240885i
$700$	−2.25801	−	4.39186i	−0.0853448	−	0.165997i
$701$	0.535100	+	1.36901i	0.0202105	+	0.0517069i	0.941128	−	0.338052i	$-0.109768\pi$
$701$	0.535100	+	1.36901i	0.0202105	+	0.0517069i	−0.920917	+	0.389758i	$0.872559\pi$
$702$	3.48684	−	6.32064i	0.131602	−	0.238557i
$703$	11.6859	−	21.9351i	0.440743	−	0.827296i
$704$	−1.91717	+	23.8040i	−0.0722560	+	0.897146i
$705$	−17.7327	+	38.5579i	−0.667854	+	1.45217i
$706$	9.33625	+	11.9099i	0.351374	+	0.448237i
$707$	7.56887	+	2.39828i	0.284657	+	0.0901967i
$708$	24.5164	+	13.2920i	0.921383	+	0.499544i
$709$	−8.62839	−	35.0916i	−0.324046	−	1.31789i	−0.875310	−	0.483562i	$-0.839343\pi$
$709$	−8.62839	−	35.0916i	−0.324046	−	1.31789i	0.551264	−	0.834331i	$-0.314146\pi$
$710$	14.5237	+	0.849853i	0.545065	+	0.0318944i
$711$	−18.5444	+	6.17559i	−0.695469	+	0.231603i
$712$	−0.820224	−	6.56993i	−0.0307392	−	0.246219i
$713$	−41.9727	−	27.7689i	−1.57189	−	1.03995i
$714$	−6.96660	−	10.3647i	−0.260719	−	0.387888i
$715$	3.04415	−	14.1521i	0.113845	−	0.529257i
$716$	8.59233	+	17.3303i	0.321111	+	0.647665i
$717$	17.3347	+	6.62997i	0.647377	+	0.247601i
$718$	−62.2533	−	9.16179i	−2.32327	−	0.341915i
$719$	−1.24895	+	4.77728i	−0.0465778	+	0.178163i	−0.986663	−	0.162778i	$-0.947955\pi$
$719$	−1.24895	+	4.77728i	−0.0465778	+	0.178163i	0.940085	+	0.340940i	$0.110745\pi$
$720$	14.2902	+	1.46679i	0.532566	+	0.0546640i
$721$	4.75675	−	9.25194i	0.177151	−	0.344560i
$722$	−6.08865	−	13.2391i	−0.226596	−	0.492708i
$723$	42.5946	−	15.5815i	1.58411	−	0.579483i
$724$	−2.60649	+	13.0415i	−0.0968695	+	0.484682i
$725$	22.1104	+	7.36312i	0.821159	+	0.273460i
$726$	−58.0611	−	23.1845i	−2.15485	−	0.860458i
$727$	−20.5675	+	10.7652i	−0.762805	+	0.399258i	−0.799961	−	0.600052i	$-0.795147\pi$
$727$	−20.5675	+	10.7652i	−0.762805	+	0.399258i	0.0371566	+	0.999309i	$0.488170\pi$
$728$	0.693249	+	0.430066i	0.0256935	+	0.0159393i
$729$	7.04859	−	8.46976i	0.261059	−	0.313695i
$730$	19.5502	+	35.4390i	0.723587	+	1.31166i
$731$	−18.0887	+	0.264332i	−0.669034	+	0.00977665i
$732$	4.33605	−	3.45049i	0.160265	−	0.127534i
$733$	−1.11794	−	5.19720i	−0.0412919	−	0.191963i	0.952269	−	0.305259i	$-0.0987430\pi$
$733$	−1.11794	−	5.19720i	−0.0412919	−	0.191963i	−0.993561	+	0.113296i	$0.963859\pi$
$734$	−0.858190	+	0.890126i	−0.0316764	+	0.0328552i
$735$	5.50362	−	32.4433i	0.203004	−	1.19669i
$736$	−39.9725	+	40.2657i	−1.47341	+	1.48421i
$737$	−53.0031	+	7.01082i	−1.95239	+	0.258247i
$738$	13.5960	+	8.71213i	0.500476	+	0.320698i
$739$	9.53752	−	13.7513i	0.350843	−	0.505848i	−0.606389	−	0.795168i	$-0.707383\pi$
$739$	9.53752	−	13.7513i	0.350843	−	0.505848i	0.957232	+	0.289320i	$0.0934291\pi$
$740$	19.6591	+	26.6468i	0.722682	+	0.979556i
$741$	−2.73613	+	6.18596i	−0.100514	+	0.227247i
$742$	−3.82710	+	27.3925i	−0.140497	+	1.00561i
$743$	−18.9587	+	11.7613i	−0.695525	+	0.431479i	−0.828759	−	0.559606i	$-0.810952\pi$
$743$	−18.9587	+	11.7613i	−0.695525	+	0.431479i	0.133233	+	0.991085i	$0.457464\pi$
$744$	5.01985	−	8.50228i	0.184037	−	0.311709i
$745$	−42.6380	−	25.5959i	−1.56214	−	0.937763i
$746$	54.0276	+	39.2534i	1.97809	+	1.43717i
$747$	−3.31920	−	0.638200i	−0.121443	−	0.0233505i
$748$	23.7025	−	7.51041i	0.866650	−	0.274608i
$749$	8.41160	+	5.74351i	0.307353	+	0.209863i
$750$	3.92465	+	23.1354i	0.143308	+	0.844785i
$751$	42.5616	+	29.9825i	1.55309	+	1.09408i	0.956578	+	0.291477i	$0.0941467\pi$
$751$	42.5616	+	29.9825i	1.55309	+	1.09408i	0.596517	+	0.802601i	$0.296551\pi$
$752$	30.2732	−	16.9901i	1.10395	−	0.619567i
$753$	23.5935	−	6.35267i	0.859796	−	0.231504i
$754$	15.1913	−	3.38401i	0.553235	−	0.123238i
$755$	−28.1969	+	10.7844i	−1.02619	+	0.392484i
$756$	−4.93705	−	4.55541i	−0.179559	−	0.165679i
$757$	0.200843	+	0.196489i	0.00729978	+	0.00714151i	0.702956	−	0.711233i	$-0.251863\pi$
$757$	0.200843	+	0.196489i	0.00729978	+	0.00714151i	−0.695656	+	0.718375i	$0.744886\pi$
$758$	−9.92839	+	4.30501i	−0.360615	+	0.156365i
$759$	−38.6946	−	72.6317i	−1.40453	−	2.63636i
$760$	7.08338	+	0.103510i	0.256941	+	0.00375471i
$761$	−21.1985	+	16.3690i	−0.768446	+	0.593375i	−0.918554	−	0.395295i	$-0.870642\pi$
$761$	−21.1985	+	16.3690i	−0.768446	+	0.593375i	0.150108	+	0.988670i	$0.452038\pi$
$762$	11.9639	+	1.58248i	0.433405	+	0.0573273i
$763$	7.32169	+	6.18425i	0.265063	+	0.223885i
$764$	13.7304	+	6.93290i	0.496747	+	0.250824i
$765$	−2.58754	−	8.83407i	−0.0935529	−	0.319396i
$766$	2.45821	−	5.78466i	0.0888189	−	0.209008i
$767$	2.62984	+	8.09381i	0.0949580	+	0.292251i
$768$	−30.7317	−	27.5357i	−1.10893	−	0.993610i
$769$	−24.3186	−	5.04542i	−0.876953	−	0.181942i	−0.256839	−	0.966454i	$-0.582681\pi$
$769$	−24.3186	−	5.04542i	−0.876953	−	0.181942i	−0.620114	+	0.784512i	$0.712914\pi$
$770$	−27.2212	−	13.2493i	−0.980983	−	0.477472i
$771$	8.00407	−	34.7338i	0.288260	−	1.25091i
$772$	0.0816595	+	0.354362i	0.00293899	+	0.0127538i
$773$	13.3300	−	6.48807i	0.479446	−	0.233360i	−0.182078	−	0.983284i	$-0.558282\pi$
$773$	13.3300	−	6.48807i	0.479446	−	0.233360i	0.661523	+	0.749924i	$0.269910\pi$
$774$	12.4171	−	3.14952i	0.446324	−	0.113207i
$775$	−17.6115	−	4.74199i	−0.632625	−	0.170337i
$776$	8.96826	+	0.393386i	0.321942	+	0.0141218i
$777$	0.119502	−	16.3563i	0.00428711	−	0.586780i
$778$	−13.2084	−	22.3715i	−0.473544	−	0.802056i
$779$	22.8857	+	11.9786i	0.819965	+	0.429176i
$780$	−5.86540	−	6.84216i	−0.210015	−	0.244989i
$781$	11.9326	−	7.89453i	0.426982	−	0.282489i
$782$	40.4925	+	16.8593i	1.44801	+	0.602886i
$783$	31.6872	−	0.926293i	1.13241	−	0.0331030i
$784$	−19.2406	+	18.8235i	−0.687165	+	0.672266i
$785$	−6.17010	+	15.1299i	−0.220220	+	0.540009i
$786$	−1.27318	−	24.8732i	−0.0454128	−	0.887197i
$787$	16.0406	−	3.82003i	0.571785	−	0.136169i	0.0644539	−	0.997921i	$-0.479469\pi$
$787$	16.0406	−	3.82003i	0.571785	−	0.136169i	0.507331	+	0.861751i	$0.330632\pi$
$788$	−8.21537	+	6.93910i	−0.292661	+	0.247195i
$789$	−42.7574	+	27.3983i	−1.52220	+	0.975405i
$790$	3.41920	−	93.5577i	0.121650	−	3.32863i
$791$	−0.0281370	−	3.85114i	−0.00100044	−	0.136931i
$792$	3.73406	−	2.24159i	0.132684	−	0.0796514i
$793$	1.68454	+	0.148067i	0.0598197	+	0.00525801i
$794$	6.84003	−	24.6838i	0.242744	−	0.875996i
$795$	−32.5790	+	68.1963i	−1.15546	+	2.41867i
$796$	3.58287	−	2.52395i	0.126992	−	0.0894592i
$797$	−33.1713	−	33.4146i	−1.17499	−	1.18361i	−0.979187	−	0.202962i	$-0.934943\pi$
$797$	−33.1713	−	33.4146i	−1.17499	−	1.18361i	−0.195802	−	0.980643i	$-0.562731\pi$
$798$	11.1967	+	8.64580i	0.396358	+	0.306058i
$799$	−17.4065	−	13.8515i	−0.615796	−	0.490030i
$800$	−9.13355	+	18.4219i	−0.322920	+	0.651314i
$801$	7.16232	−	6.60866i	0.253068	−	0.233506i
$802$	40.3702	+	1.18012i	1.42552	+	0.0416714i
$803$	36.2833	+	16.3666i	1.28041	+	0.577565i
$804$	−16.5020	+	28.9066i	−0.581982	+	1.01946i
$805$	−9.61281	−	21.7330i	−0.338807	−	0.765988i
$806$	−11.7143	+	3.33845i	−0.412619	+	0.117592i
$807$	−19.9498	−	27.8848i	−0.702268	−	0.981591i
$808$	−1.76646	−	5.17791i	−0.0621437	−	0.182158i
$809$	−8.28203	+	11.2258i	−0.291181	+	0.394679i	−0.925719	−	0.378212i	$-0.876539\pi$
$809$	−8.28203	+	11.2258i	−0.291181	+	0.394679i	0.634538	+	0.772891i	$0.281190\pi$
$810$	−29.2009	−	51.1513i	−1.02602	−	1.79727i
$811$	−2.32951	−	24.4529i	−0.0818000	−	0.858657i	−0.939055	−	0.343766i	$-0.888297\pi$
$811$	−2.32951	−	24.4529i	−0.0818000	−	0.858657i	0.857255	−	0.514892i	$-0.172168\pi$
$812$	0.317424	−	14.4800i	0.0111394	−	0.508147i
$813$	−19.8923	+	53.1716i	−0.697655	+	1.86481i
$814$	70.0839	+	21.0851i	2.45644	+	0.739033i
$815$	8.06662	−	11.2751i	0.282562	−	0.394949i
$816$	−9.39783	+	26.2841i	−0.328990	+	0.920127i
$817$	19.3457	−	6.75802i	0.676820	−	0.236433i
$818$	12.7243	+	34.0116i	0.444895	+	1.18919i
$819$	0.0789011	+	1.19821i	0.00275703	+	0.0418688i
$820$	−27.5446	+	20.6339i	−0.961899	+	0.720567i
$821$	−16.1101	+	17.2058i	−0.562246	+	0.600487i	−0.946486	−	0.322746i	$-0.895394\pi$
$821$	−16.1101	+	17.2058i	−0.562246	+	0.600487i	0.384239	+	0.923233i	$0.374464\pi$
$822$	−0.706016	+	2.41039i	−0.0246251	+	0.0840721i
$823$	−19.3000	−	15.8243i	−0.672755	−	0.551602i	0.234535	−	0.972108i	$-0.424643\pi$
$823$	−19.3000	−	15.8243i	−0.672755	−	0.551602i	−0.907290	+	0.420506i	$0.861853\pi$
$824$	−7.07594	+	1.14723i	−0.246502	+	0.0399657i
$825$	−21.6214	−	20.5429i	−0.752760	−	0.715214i
$826$	17.7509	−	1.29920i	0.617632	−	0.0452048i
$827$	−26.2508	−	34.5143i	−0.912830	−	1.20018i	−0.979305	−	0.202392i	$-0.935129\pi$
$827$	−26.2508	−	34.5143i	−0.912830	−	1.20018i	0.0664746	−	0.997788i	$-0.478825\pi$
$828$	−13.6423	−	2.21185i	−0.474104	−	0.0768670i
$829$	−30.0702	−	34.0578i	−1.04438	−	1.18288i	−0.982781	−	0.184775i	$-0.940844\pi$
$829$	−30.0702	−	34.0578i	−1.04438	−	1.18288i	−0.0616014	−	0.998101i	$-0.519621\pi$
$830$	8.43381	−	13.8193i	0.292742	−	0.479676i
$831$	−4.46323	−	1.63269i	−0.154828	−	0.0566375i
$832$	0.364231	+	4.52237i	0.0126274	+	0.156785i
$833$	15.8247	+	6.86167i	0.548292	+	0.237743i
$834$	−10.2399	−	25.1096i	−0.354579	−	0.869475i
$835$	27.0858	−	12.6973i	0.937343	−	0.439408i
$836$	−22.7856	+	16.5547i	−0.788058	+	0.572558i
$837$	−24.7149	+	2.17238i	−0.854272	+	0.0750885i
$838$	−9.56331	+	51.7749i	−0.330359	+	1.78854i
$839$	48.5248	+	11.5561i	1.67526	+	0.398960i	0.955437	−	0.295194i	$-0.0953844\pi$
$839$	48.5248	+	11.5561i	1.67526	+	0.398960i	0.719826	+	0.694155i	$0.244222\pi$
$840$	4.16177	−	2.10142i	0.143595	−	0.0725057i
$841$	26.8936	+	28.7228i	0.927367	+	0.990442i
$842$	−32.7310	−	5.79877i	−1.12799	−	0.199839i
$843$	−4.78545	−	17.2694i	−0.164820	−	0.594789i
$844$	−0.794426	−	4.30095i	−0.0273453	−	0.148045i
$845$	−1.71766	+	33.5568i	−0.0590895	+	1.15439i
$846$	14.2629	+	6.68616i	0.490367	+	0.229875i
$847$	−17.4349	+	3.35230i	−0.599071	+	0.115186i
$848$	54.3478	−	29.4656i	1.86631	−	1.01185i
$849$	−38.0603	−	41.8584i	−1.30623	−	1.43658i
$850$	15.8534	+	1.16032i	0.543766	+	0.0397986i
$851$	31.3474	+	48.1423i	1.07458	+	1.65030i
$852$	0.585283	−	8.88824i	0.0200515	−	0.304506i
$853$	24.3573	−	7.32803i	0.833979	−	0.250907i	0.157639	−	0.987497i	$-0.449612\pi$
$853$	24.3573	−	7.32803i	0.833979	−	0.250907i	0.676340	+	0.736590i	$0.263565\pi$
$854$	1.14190	−	3.34717i	0.0390749	−	0.114538i
$855$	5.94261	+	8.56809i	0.203233	+	0.293023i
$856$	−0.256324	−	7.01365i	−0.00876097	−	0.239722i
$857$	5.33900	−	0.234192i	0.182377	−	0.00799983i	0.0475492	−	0.998869i	$-0.484859\pi$
$857$	5.33900	−	0.234192i	0.182377	−	0.00799983i	0.134828	+	0.990869i	$0.456952\pi$
$858$	−19.4417	−	4.33082i	−0.663727	−	0.147852i
$859$	42.5983	−	6.26917i	1.45344	−	0.213901i	0.627919	−	0.778279i	$-0.283907\pi$
$859$	42.5983	−	6.26917i	1.45344	−	0.213901i	0.825517	+	0.564377i	$0.190884\pi$
$860$	−2.98613	+	27.1389i	−0.101826	+	0.925430i
$861$	16.9999			0.579357
$862$	−29.9311	+	25.6357i	−1.01946	+	0.873155i
$863$	−3.27816			−0.111590			−0.0557949	−	0.998442i	$-0.517769\pi$
$863$	−3.27816			−0.111590			−0.0557949	+	0.998442i	$0.517769\pi$
$864$	−3.05914	+	27.8025i	−0.104074	+	0.945860i
$865$	−12.1827	+	1.79291i	−0.414223	+	0.0609609i
$866$	34.8080	+	7.75382i	1.18282	+	0.263485i
$867$	−16.5538	+	0.726122i	−0.562198	+	0.0246604i
$868$	0.413988	+	11.3277i	0.0140517	+	0.384489i
$869$	−52.4721	−	75.6546i	−1.77999	−	2.56641i
$870$	28.7181	−	84.1796i	0.973634	−	2.85396i
$871$	−9.72677	+	2.92635i	−0.329579	+	0.0991555i
$872$	0.433921	−	6.58961i	0.0146944	−	0.223152i
$873$	7.20990	+	11.0727i	0.244018	+	0.374755i
$874$	−49.5521	−	3.62675i	−1.67613	−	0.122677i
$875$	4.48310	+	4.93048i	0.151556	+	0.166681i
$876$	21.7847	−	11.8110i	0.736038	−	0.399056i
$877$	43.9638	−	8.45314i	1.48455	−	0.285442i	0.618654	−	0.785663i	$-0.287678\pi$
$877$	43.9638	−	8.45314i	1.48455	−	0.285442i	0.865898	+	0.500221i	$0.166748\pi$
$878$	−29.3583	−	13.7626i	−0.990794	−	0.464465i
$879$	0.230085	−	4.49499i	0.00776056	−	0.151612i
$880$	12.2910	+	66.5426i	0.414331	+	2.24315i
$881$	6.40894	+	23.1281i	0.215923	+	0.779206i	0.989379	+	0.145357i	$0.0464329\pi$
$881$	6.40894	+	23.1281i	0.215923	+	0.779206i	−0.773457	+	0.633849i	$0.781474\pi$
$882$	−12.0266	−	2.13068i	−0.404956	−	0.0717436i
$883$	−23.1301	−	24.7033i	−0.778389	−	0.831331i	0.210869	−	0.977514i	$-0.432371\pi$
$883$	−23.1301	−	24.7033i	−0.778389	−	0.831331i	−0.989257	+	0.146184i	$0.953301\pi$
$884$	4.21669	−	2.12915i	0.141823	−	0.0716109i
$885$	47.3119	+	11.2672i	1.59037	+	0.378743i
$886$	−4.75804	+	25.7596i	−0.159850	+	0.865411i
$887$	2.86075	−	0.251453i	0.0960545	−	0.00844296i	−0.0394310	−	0.999222i	$-0.512555\pi$
$887$	2.86075	−	0.251453i	0.0960545	−	0.00844296i	0.135485	+	0.990779i	$0.456741\pi$
$888$	−9.11822	+	6.62477i	−0.305987	+	0.222313i
$889$	3.10308	−	1.45466i	0.104074	−	0.0487879i
$890$	17.6266	+	43.2228i	0.590846	+	1.44883i
$891$	−53.1436	−	23.0434i	−1.78038	−	0.771983i
$892$	−0.656912	−	8.15637i	−0.0219950	−	0.273095i
$893$	23.6646	+	8.65673i	0.791904	+	0.289686i
$894$	−35.6469	+	58.4096i	−1.19221	+	1.95351i
$895$	22.3272	+	25.2879i	0.746315	+	0.845282i
$896$	−6.36837	−	1.03251i	−0.212752	−	0.0344938i
$897$	−9.46499	−	12.4445i	−0.316027	−	0.415509i
$898$	−64.4012	+	4.71356i	−2.14910	+	0.157293i
$899$	−38.7792	−	36.8450i	−1.29336	−	1.22885i
$900$	−4.94404	+	0.801583i	−0.164801	+	0.0267194i
$901$	−30.6342	−	25.1175i	−1.02057	−	0.836784i
$902$	−21.3815	+	72.9979i	−0.711925	+	2.43056i
$903$	9.21764	−	9.84458i	0.306744	−	0.327607i
$904$	−2.12388	+	1.59102i	−0.0706393	+	0.0529166i
$905$	1.52397	+	23.1433i	0.0506584	+	0.769310i
$906$	14.5551	+	38.9054i	0.483562	+	1.29255i
$907$	11.2106	−	3.91620i	0.372242	−	0.130035i	−0.137193	−	0.990544i	$-0.543808\pi$
$907$	11.2106	−	3.91620i	0.372242	−	0.130035i	0.509435	+	0.860509i	$0.329854\pi$
$908$	−8.27771	+	23.1513i	−0.274705	+	0.768303i
$909$	4.68555	−	6.54920i	0.155410	−	0.217223i
$910$	−5.50777	−	1.65704i	−0.182581	−	0.0549304i
$911$	5.27921	−	14.1111i	0.174908	−	0.467523i	−0.819506	−	0.573070i	$-0.805752\pi$
$911$	5.27921	−	14.1111i	0.174908	−	0.467523i	0.994414	+	0.105547i	$0.0336593\pi$
$912$	0.692977	−	31.6116i	0.0229467	−	1.04676i
$913$	−1.50993	−	15.8498i	−0.0499715	−	0.524553i
$914$	−34.7434	−	60.8599i	−1.14921	−	2.01307i
$915$	5.73729	−	7.77658i	0.189669	−	0.257086i
$916$	−3.10664	−	9.10631i	−0.102646	−	0.300881i
$917$	−4.11537	−	5.75224i	−0.135902	−	0.189956i
$918$	20.7950	−	5.92636i	0.686339	−	0.195599i
$919$	−11.8671	−	26.8295i	−0.391458	−	0.885024i	−0.996075	−	0.0885079i	$-0.971790\pi$
$919$	−11.8671	−	26.8295i	−0.391458	−	0.885024i	0.604617	−	0.796516i	$-0.293326\pi$
$920$	−8.11821	+	14.2207i	−0.267650	+	0.468842i
$921$	−10.4153	−	4.69813i	−0.343197	−	0.154809i
$922$	80.0790	+	2.34091i	2.63726	+	0.0770936i
$923$	1.99774	−	1.84332i	0.0657566	−	0.0606735i
$924$	−8.23355	+	16.6067i	−0.270864	+	0.546320i
$925$	16.2910	+	12.9638i	0.535644	+	0.426248i
$926$	−18.3385	−	14.1605i	−0.602640	−	0.465344i
$927$	−7.43349	−	7.48800i	−0.244148	−	0.245938i
$928$	−49.3006	+	34.7298i	−1.61837	+	1.14006i
$929$	7.17111	−	15.0110i	0.235276	−	0.492495i	−0.750434	−	0.660946i	$-0.770155\pi$
$929$	7.17111	−	15.0110i	0.235276	−	0.492495i	0.985710	+	0.168450i	$0.0538763\pi$
$930$	−18.5890	+	67.0826i	−0.609557	+	2.19973i
$931$	−19.4629	−	1.71075i	−0.637871	−	0.0560674i
$932$	−0.548849	+	0.329479i	−0.0179782	+	0.0107924i
$933$	−0.298270	−	40.8245i	−0.00976493	−	1.33653i
$934$	2.63786	−	72.1785i	0.0863135	−	2.36175i
$935$	36.5091	−	23.3945i	1.19397	−	0.765082i
$936$	0.632112	−	0.533912i	0.0206612	−	0.0174515i
$937$	−13.7069	+	3.26428i	−0.447786	+	0.106639i	−0.449343	−	0.893360i	$-0.648342\pi$
$937$	−13.7069	+	3.26428i	−0.447786	+	0.106639i	0.00155659	+	0.999999i	$0.499505\pi$
$938$	1.08594	+	21.2153i	0.0354573	+	0.692704i
$939$	−2.33371	+	5.72257i	−0.0761578	+	0.186749i
$940$	−23.9984	+	23.4781i	−0.782740	+	0.765770i
$941$	46.7268	−	1.36594i	1.52325	−	0.0445283i	0.742701	−	0.669624i	$-0.233545\pi$
$941$	46.7268	−	1.36594i	1.52325	−	0.0445283i	0.780548	+	0.625095i	$0.214940\pi$
$942$	20.7557	+	8.64172i	0.676256	+	0.281563i
$943$	−49.7960	+	32.9447i	−1.62158	+	1.07283i
$944$	−25.8917	−	30.2035i	−0.842705	−	0.983039i
$945$	−10.3794	−	5.43265i	−0.337641	−	0.176724i
$946$	30.6793	+	51.9625i	0.997470	+	1.68945i
$947$	0.00171124	−	0.234219i	5.56080e−5	−	0.00761111i	−0.999938	−	0.0111115i	$-0.996463\pi$
$947$	0.00171124	−	0.234219i	5.56080e−5	−	0.00761111i	0.999994	+	0.00350036i	$0.00111420\pi$
$948$	−57.2647	−	2.51188i	−1.85987	−	0.0815819i
$949$	7.30203	+	1.96611i	0.237034	+	0.0638225i
$950$	−17.4533	+	4.42691i	−0.566259	+	0.143628i
$951$	50.3246	−	24.4944i	1.63189	−	0.794285i
$952$	0.548753	+	2.38132i	0.0177852	+	0.0771790i
$953$	5.94422	−	25.7950i	0.192552	−	0.835582i	−0.784079	−	0.620661i	$-0.786864\pi$
$953$	5.94422	−	25.7950i	0.192552	−	0.835582i	0.976631	−	0.214922i	$-0.0689496\pi$
$954$	25.2231	+	12.2768i	0.816627	+	0.397475i
$955$	26.2651	+	5.44924i	0.849918	+	0.176333i
$956$	10.9345	+	9.79736i	0.353647	+	0.316869i
$957$	−27.0300	−	83.1899i	−0.873757	−	2.68915i
$958$	25.2863	−	59.5037i	0.816964	−	1.92248i
$959$	0.200496	+	0.684509i	0.00647437	+	0.0221040i
$960$	23.1450	+	11.6867i	0.747003	+	0.377186i
$961$	8.30018	+	7.01073i	0.267748	+	0.226153i
$962$	13.7843	+	1.82327i	0.444423	+	0.0587847i
$963$	8.17645	−	6.31365i	0.263482	−	0.203454i
$964$	35.8750	+	0.524246i	1.15546	+	0.0168848i
$965$	0.298187	+	0.559711i	0.00959898	+	0.0180177i
$966$	−29.9998	+	13.0081i	−0.965227	+	0.418528i
$967$	−0.806217	−	0.788737i	−0.0259262	−	0.0253641i	0.686237	−	0.727378i	$-0.259261\pi$
$967$	−0.806217	−	0.788737i	−0.0259262	−	0.0253641i	−0.712163	+	0.702014i	$0.752284\pi$
$968$	8.99106	+	8.29603i	0.288984	+	0.266645i
$969$	−18.9245	+	7.23800i	−0.607942	+	0.232518i
$970$	−61.7746	+	13.7609i	−1.98346	+	0.441835i
$971$	−17.1574	+	4.61972i	−0.550608	+	0.148254i	−0.524508	−	0.851406i	$-0.675751\pi$
$971$	−17.1574	+	4.61972i	−0.550608	+	0.148254i	−0.0261001	+	0.999659i	$0.508309\pi$
$972$	−15.3632	+	8.62224i	−0.492775	+	0.276559i
$973$	−6.29559	−	4.43493i	−0.201827	−	0.142177i
$974$	−12.1601	−	71.6827i	−0.389636	−	2.29686i
$975$	−4.67938	−	3.19512i	−0.149860	−	0.102326i
$976$	−7.53563	+	2.38775i	−0.241210	+	0.0764301i
$977$	−4.46653	−	0.858802i	−0.142897	−	0.0274755i	0.116868	−	0.993148i	$-0.462715\pi$
$977$	−4.46653	−	0.858802i	−0.142897	−	0.0274755i	−0.259764	+	0.965672i	$0.583645\pi$
$978$	−15.4326	−	11.2125i	−0.493481	−	0.358535i
$979$	39.3588	+	23.6274i	1.25791	+	0.755135i
$980$	13.2347	−	22.4160i	0.422767	−	0.716054i
$981$	8.25999	−	5.12419i	0.263721	−	0.163603i
$982$	−4.57406	+	32.7389i	−0.145964	+	1.04474i
$983$	−18.0661	+	40.8446i	−0.576219	+	1.30274i	0.353832	+	0.935309i	$0.384879\pi$
$983$	−18.0661	+	40.8446i	−0.576219	+	1.30274i	−0.930051	+	0.367430i	$0.880238\pi$
$984$	−6.95432	−	9.42620i	−0.221696	−	0.300496i
$985$	−10.6882	+	15.4103i	−0.340553	+	0.491012i
$986$	39.2528	+	25.1526i	1.25006	+	0.801023i
$987$	16.4403	−	2.17459i	0.523301	−	0.0692180i
$988$	−3.76976	+	3.79740i	−0.119932	+	0.120811i
$989$	−7.92207	+	46.6997i	−0.251907	+	1.48497i
$990$	−21.3116	+	22.1047i	−0.677328	+	0.702534i
$991$	−1.17550	−	5.46483i	−0.0373411	−	0.173596i	0.955107	−	0.296261i	$-0.0957398\pi$
$991$	−1.17550	−	5.46483i	−0.0373411	−	0.173596i	−0.992448	+	0.122665i	$0.960856\pi$
$992$	36.9309	−	29.3884i	1.17256	−	0.933083i
$993$	69.1472	−	1.01045i	2.19432	−	0.0320658i
$994$	−2.74598	−	4.97768i	−0.0870972	−	0.157882i
$995$	4.88906	−	5.87482i	0.154994	−	0.186244i
$996$	−8.42306	−	5.22536i	−0.266895	−	0.165572i
$997$	19.5507	−	10.2330i	0.619177	−	0.324082i	−0.124907	−	0.992169i	$-0.539863\pi$
$997$	19.5507	−	10.2330i	0.619177	−	0.324082i	0.744084	+	0.668086i	$0.232886\pi$
$998$	−72.5124	−	28.9551i	−2.29534	−	0.916558i
$999$	26.8702	+	8.94820i	0.850134	+	0.283109i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	431.2.g.a.10.29	✓	5880
431.388	even	215	inner	431.2.g.a.388.29	yes	5880

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
431.2.g.a.10.29	✓	5880	1.1	even	1	trivial
431.2.g.a.388.29	yes	5880	431.388	even	215	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	431.g (of order \(215\), degree \(168\), minimal)

\(f(q)\)	\(=\)	\(q+(0.207615 - 1.88687i) q^{2} +(-2.00526 + 0.295114i) q^{3} +(-1.56502 - 0.348624i) q^{4} +(-2.79353 + 0.122536i) q^{5} +(0.140519 + 3.84494i) q^{6} +(0.622702 + 0.897816i) q^{7} +(0.243090 - 0.712556i) q^{8} +(1.06119 - 0.319264i) q^{9} +(-0.348769 + 5.29648i) q^{10} +(2.84839 + 4.37446i) q^{11} +(3.24117 + 0.237223i) q^{12} +(0.667179 + 0.733758i) q^{13} +(1.82334 - 0.988558i) q^{14} +(5.56561 - 1.07013i) q^{15} +(-4.19759 - 1.96775i) q^{16} +(-0.151861 + 2.96679i) q^{17} +(-0.382091 - 2.06861i) q^{18} +(-0.898608 - 3.24283i) q^{19} +(4.41467 + 0.782120i) q^{20} +(-1.51364 - 1.61659i) q^{21} +(8.84540 - 4.46633i) q^{22} +(7.56657 + 1.80196i) q^{23} +(-0.277175 + 1.50060i) q^{24} +(2.80802 - 0.246818i) q^{25} +(1.52302 - 1.10654i) q^{26} +(3.47192 - 1.62757i) q^{27} +(-0.661543 - 1.62219i) q^{28} +(7.58494 + 3.28888i) q^{29} +(-0.863689 - 10.7238i) q^{30} +(-6.07649 - 2.22284i) q^{31} +(-3.79996 + 6.22647i) q^{32} +(-7.00273 - 7.93134i) q^{33} +(5.56643 + 0.902492i) q^{34} +(-1.84955 - 2.43177i) q^{35} +(-1.77209 + 0.129700i) q^{36} +(5.35443 + 5.08736i) q^{37} +(-6.30537 + 1.02230i) q^{38} +(-1.55441 - 1.27448i) q^{39} +(-0.591767 + 2.02034i) q^{40} +(-5.24661 + 5.60345i) q^{41} +(-3.36455 + 2.52041i) q^{42} +(0.400137 + 6.07656i) q^{43} +(-2.93275 - 7.83915i) q^{44} +(-2.92534 + 1.02191i) q^{45} +(4.97100 - 13.9030i) q^{46} +(-4.35711 + 6.09012i) q^{47} +(8.99799 + 2.70709i) q^{48} +(2.03447 - 5.43806i) q^{49} +(0.117272 - 5.34961i) q^{50} +(-0.571020 - 5.99402i) q^{51} +(-0.788345 - 1.38094i) q^{52} +(-7.91691 + 10.7309i) q^{53} +(-2.35019 - 6.88897i) q^{54} +(-8.49309 - 11.8712i) q^{55} +(0.791117 - 0.225460i) q^{56} +(2.75895 + 6.23754i) q^{57} +(7.78043 - 13.6290i) q^{58} +(7.82232 + 3.52847i) q^{59} +(-9.08338 - 0.265529i) q^{60} +(1.25318 - 1.15630i) q^{61} +(-5.45578 + 11.0041i) q^{62} +(0.947443 + 0.753944i) q^{63} +(3.62098 + 2.79603i) q^{64} +(-1.95370 - 1.96802i) q^{65} +(-16.4193 + 11.5666i) q^{66} +(-4.41498 + 9.24172i) q^{67} +(1.27196 - 4.59016i) q^{68} +(-15.7047 - 1.38041i) q^{69} +(-4.97244 + 2.98500i) q^{70} +(-0.0200249 - 2.74083i) q^{71} +(0.0304711 - 0.833765i) q^{72} +(6.42015 - 4.11394i) q^{73} +(10.7108 - 9.04690i) q^{74} +(-5.55797 + 1.32362i) q^{75} +(0.275814 + 5.38839i) q^{76} +(-2.15376 + 5.28131i) q^{77} +(-2.72751 + 2.66837i) q^{78} +(-17.6302 + 0.515374i) q^{79} +(11.9672 + 4.98262i) q^{80} +(-9.25443 + 6.12268i) q^{81} +(9.48372 + 11.0630i) q^{82} +(-2.70229 - 1.41440i) q^{83} +(1.80530 + 3.05769i) q^{84} +(0.0606882 - 8.30645i) q^{85} +(11.5488 + 0.506578i) q^{86} +(-16.1804 - 4.35665i) q^{87} +(3.80946 - 0.966246i) q^{88} +(7.90724 - 3.84868i) q^{89} +(1.32086 + 5.73190i) q^{90} +(-0.243326 + 1.05592i) q^{91} +(-11.2137 - 5.45800i) q^{92} +(12.8410 + 2.66413i) q^{93} +(10.5867 + 9.48569i) q^{94} +(2.90766 + 8.94885i) q^{95} +(5.78241 - 13.6071i) q^{96} +(3.35161 + 11.4426i) q^{97} +(-9.83854 - 4.96780i) q^{98} +(4.41928 + 3.73273i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5880 q - 166 q^{2} - 164 q^{3} - 302 q^{4} - 169 q^{5} - 148 q^{6} - 171 q^{7} - 160 q^{8} - 300 q^{9} - 157 q^{10} - 83 q^{11} - 142 q^{12} - 177 q^{13} - 164 q^{14} - 166 q^{15} - 298 q^{16} - 176 q^{17}+ \cdots - 72 q^{99}+O(q^{100}) \) 5880 * q - 166 * q^2 - 164 * q^3 - 302 * q^4 - 169 * q^5 - 148 * q^6 - 171 * q^7 - 160 * q^8 - 300 * q^9 - 157 * q^10 - 83 * q^11 - 142 * q^12 - 177 * q^13 - 164 * q^14 - 166 * q^15 - 298 * q^16 - 176 * q^17 - 174 * q^18 - 175 * q^19 - 166 * q^20 - 43 * q^21 - 180 * q^22 - 186 * q^23 - 116 * q^24 - 120 * q^25 + 104 * q^26 - 104 * q^27 - 172 * q^28 - 173 * q^29 + 42 * q^30 - 172 * q^31 - 172 * q^32 - 63 * q^33 - 193 * q^34 - 199 * q^35 - 258 * q^36 - 184 * q^37 - 113 * q^38 - 180 * q^39 - 118 * q^40 - 126 * q^41 - 107 * q^42 - 163 * q^43 - 181 * q^44 - 138 * q^45 - 142 * q^46 - 46 * q^47 - 78 * q^48 - 156 * q^49 - 223 * q^50 - 223 * q^51 + 86 * q^52 - 156 * q^53 + 447 * q^54 - 232 * q^55 + 267 * q^56 - 134 * q^57 - 183 * q^58 - 194 * q^59 - 107 * q^60 + 107 * q^61 - 143 * q^62 - 19 * q^63 - 352 * q^64 - 219 * q^65 - 116 * q^66 + 11 * q^67 - 251 * q^68 - 109 * q^69 + 1000 * q^70 + 137 * q^71 - 106 * q^72 - 189 * q^73 - 175 * q^74 - 189 * q^75 - 124 * q^76 - 26 * q^77 + 165 * q^78 + 249 * q^79 - 146 * q^80 - 328 * q^81 + 13 * q^82 - 139 * q^83 + 307 * q^84 - 227 * q^85 - 130 * q^86 - 106 * q^87 + 208 * q^88 - 166 * q^89 - 150 * q^90 - 181 * q^91 - 80 * q^92 + 23 * q^93 + 22 * q^94 - 90 * q^95 + 226 * q^96 - 191 * q^97 - 171 * q^98 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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