LMFDB - Embedded newform 418.2.s.a.107.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(107,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([9, 25]))

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

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

chi := DirichletCharacter("418.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.s (of order $30$, degree $8$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			107.10
Character	$\chi$	$=$	418.107
Dual form			418.2.s.a.293.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.913545 - 0.406737i) q^{2} +(2.22316 + 2.00174i) q^{3} +(0.669131 + 0.743145i) q^{4} +(-0.155938 + 1.48365i) q^{5} +(-1.21677 - 2.73292i) q^{6} +(-4.91364 - 1.59654i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.621881 + 5.91681i) q^{9} +O(q^{10})$	\(q+(-0.913545 - 0.406737i) q^{2} +(2.22316 + 2.00174i) q^{3} +(0.669131 + 0.743145i) q^{4} +(-0.155938 + 1.48365i) q^{5} +(-1.21677 - 2.73292i) q^{6} +(-4.91364 - 1.59654i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.621881 + 5.91681i) q^{9} +(0.745913 - 1.29196i) q^{10} +(-3.31335 - 0.147244i) q^{11} +2.99155i q^{12} +(0.431546 + 4.10589i) q^{13} +(3.83946 + 3.45707i) q^{14} +(-3.31656 + 2.98625i) q^{15} +(-0.104528 + 0.994522i) q^{16} +(4.10657 + 0.431618i) q^{17} +(1.83846 - 5.65821i) q^{18} +(0.997602 + 4.24321i) q^{19} +(-1.20691 + 0.876873i) q^{20} +(-7.72795 - 13.3852i) q^{21} +(2.96701 + 1.48218i) q^{22} +(-1.80940 + 3.13397i) q^{23} +(1.21677 - 2.73292i) q^{24} +(2.71383 + 0.576842i) q^{25} +(1.27578 - 3.92644i) q^{26} +(-5.18619 + 7.13818i) q^{27} +(-2.10141 - 4.71984i) q^{28} +(-1.96655 - 2.18407i) q^{29} +(4.24445 - 1.37911i) q^{30} +(-3.78920 - 5.21539i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-7.07137 - 6.95982i) q^{33} +(-3.57598 - 2.06459i) q^{34} +(3.13494 - 7.04118i) q^{35} +(-3.98092 + 4.42126i) q^{36} +(5.75599 + 1.87023i) q^{37} +(0.814512 - 4.28212i) q^{38} +(-7.25953 + 9.99189i) q^{39} +(1.45923 - 0.310168i) q^{40} +(0.785878 - 0.872806i) q^{41} +(1.61558 + 15.3712i) q^{42} +(8.52452 - 4.92163i) q^{43} +(-2.10764 - 2.56083i) q^{44} -8.87546 q^{45} +(2.92766 - 2.12707i) q^{46} +(1.65228 + 0.351203i) q^{47} +(-2.22316 + 2.00174i) q^{48} +(15.9318 + 11.5752i) q^{49} +(-2.24458 - 1.63078i) q^{50} +(8.26556 + 9.17984i) q^{51} +(-2.76251 + 3.06808i) q^{52} +(-5.74462 + 0.603784i) q^{53} +(7.64119 - 4.41164i) q^{54} +(0.735137 - 4.89291i) q^{55} +5.16651i q^{56} +(-6.27597 + 11.4303i) q^{57} +(0.908189 + 2.79512i) q^{58} +(-0.0109047 - 0.0513028i) q^{59} +(-4.43843 - 0.466498i) q^{60} +(2.05060 + 4.60572i) q^{61} +(1.34032 + 6.30571i) q^{62} +(6.39071 - 30.0659i) q^{63} +(-0.809017 + 0.587785i) q^{64} -6.15901 q^{65} +(3.62920 + 9.23430i) q^{66} +(-3.71315 - 2.14379i) q^{67} +(2.42708 + 3.34058i) q^{68} +(-10.2960 + 3.34536i) q^{69} +(-5.72781 + 5.15735i) q^{70} +(3.04708 + 0.320261i) q^{71} +(5.43504 - 2.41984i) q^{72} +(-0.412672 - 1.94147i) q^{73} +(-4.49767 - 4.04972i) q^{74} +(4.87858 + 6.71479i) q^{75} +(-2.48579 + 3.58062i) q^{76} +(16.0456 + 6.01340i) q^{77} +(10.6960 - 6.17533i) q^{78} +(11.4269 + 5.08758i) q^{79} +(-1.45923 - 0.310168i) q^{80} +(-8.36036 + 1.77705i) q^{81} +(-1.07294 + 0.477702i) q^{82} +(0.381900 - 0.525640i) q^{83} +(4.77613 - 14.6994i) q^{84} +(-1.28074 + 6.02542i) q^{85} +(-9.78935 + 1.02890i) q^{86} -8.79206i q^{87} +(0.883846 + 3.19669i) q^{88} +(1.73365 + 1.00092i) q^{89} +(8.10814 + 3.60998i) q^{90} +(4.43475 - 20.8639i) q^{91} +(-3.53971 + 0.752389i) q^{92} +(2.01586 - 19.1796i) q^{93} +(-1.36659 - 0.992884i) q^{94} +(-6.45101 + 0.818418i) q^{95} +(2.84514 - 0.924441i) q^{96} +(-0.591993 + 1.32964i) q^{97} +(-9.84641 - 17.0545i) q^{98} +(-1.18930 - 19.6960i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 10 q^{2} - 3 q^{3} + 10 q^{4} - 2 q^{5} + 7 q^{6} - 10 q^{7} + 20 q^{8} - 11 q^{9}+O(q^{10}) $ 80 * q - 10 * q^2 - 3 * q^3 + 10 * q^4 - 2 * q^5 + 7 * q^6 - 10 * q^7 + 20 * q^8 - 11 * q^9	\( 80 q - 10 q^{2} - 3 q^{3} + 10 q^{4} - 2 q^{5} + 7 q^{6} - 10 q^{7} + 20 q^{8} - 11 q^{9} + 2 q^{10} - q^{11} + 5 q^{13} - 4 q^{14} - 27 q^{15} + 10 q^{16} - 6 q^{17} - 17 q^{18} - 2 q^{19} + 4 q^{20} + 24 q^{21} - 2 q^{22} - 6 q^{23} - 7 q^{24} - 10 q^{26} - 45 q^{27} + 6 q^{28} - 65 q^{29} + 30 q^{30} + 40 q^{32} + 3 q^{33} + 24 q^{34} - 13 q^{35} - q^{36} + 22 q^{38} - 30 q^{39} - 3 q^{40} - 14 q^{41} - 14 q^{42} + 12 q^{43} + 24 q^{44} - 12 q^{45} - 2 q^{46} - q^{47} + 3 q^{48} + 32 q^{49} + 30 q^{50} - 28 q^{51} - 5 q^{52} - q^{53} - 27 q^{54} - 23 q^{55} + 28 q^{57} - 10 q^{58} + 56 q^{59} - 28 q^{60} + 28 q^{61} + 15 q^{62} + 88 q^{63} - 20 q^{64} + 8 q^{65} - 57 q^{66} - 27 q^{67} - 60 q^{69} + 17 q^{70} + 2 q^{71} + 11 q^{72} - q^{73} + 12 q^{74} - 35 q^{75} - 11 q^{76} - 8 q^{77} - 6 q^{79} + 3 q^{80} + 43 q^{81} - 16 q^{82} - 25 q^{83} + 52 q^{84} - 33 q^{85} - 43 q^{86} - 9 q^{88} - 36 q^{89} + 74 q^{90} + 38 q^{91} - 11 q^{92} + 15 q^{93} - 2 q^{94} - 61 q^{95} - 24 q^{97} - 44 q^{98} + 37 q^{99}+O(q^{100}) \) 80 * q - 10 * q^2 - 3 * q^3 + 10 * q^4 - 2 * q^5 + 7 * q^6 - 10 * q^7 + 20 * q^8 - 11 * q^9 + 2 * q^10 - q^11 + 5 * q^13 - 4 * q^14 - 27 * q^15 + 10 * q^16 - 6 * q^17 - 17 * q^18 - 2 * q^19 + 4 * q^20 + 24 * q^21 - 2 * q^22 - 6 * q^23 - 7 * q^24 - 10 * q^26 - 45 * q^27 + 6 * q^28 - 65 * q^29 + 30 * q^30 + 40 * q^32 + 3 * q^33 + 24 * q^34 - 13 * q^35 - q^36 + 22 * q^38 - 30 * q^39 - 3 * q^40 - 14 * q^41 - 14 * q^42 + 12 * q^43 + 24 * q^44 - 12 * q^45 - 2 * q^46 - q^47 + 3 * q^48 + 32 * q^49 + 30 * q^50 - 28 * q^51 - 5 * q^52 - q^53 - 27 * q^54 - 23 * q^55 + 28 * q^57 - 10 * q^58 + 56 * q^59 - 28 * q^60 + 28 * q^61 + 15 * q^62 + 88 * q^63 - 20 * q^64 + 8 * q^65 - 57 * q^66 - 27 * q^67 - 60 * q^69 + 17 * q^70 + 2 * q^71 + 11 * q^72 - q^73 + 12 * q^74 - 35 * q^75 - 11 * q^76 - 8 * q^77 - 6 * q^79 + 3 * q^80 + 43 * q^81 - 16 * q^82 - 25 * q^83 + 52 * q^84 - 33 * q^85 - 43 * q^86 - 9 * q^88 - 36 * q^89 + 74 * q^90 + 38 * q^91 - 11 * q^92 + 15 * q^93 - 2 * q^94 - 61 * q^95 - 24 * q^97 - 44 * q^98 + 37 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.913545	−	0.406737i	−0.645974	−	0.287606i
$2$	−0.913545	−	0.406737i	−0.645974	−	0.287606i
$3$	2.22316	+	2.00174i	1.28354	+	1.15571i	0.979146	+	0.203160i	$0.0651210\pi$
$3$	2.22316	+	2.00174i	1.28354	+	1.15571i	0.304395	+	0.952546i	$0.401546\pi$
$4$	0.669131	+	0.743145i	0.334565	+	0.371572i
$5$	−0.155938	+	1.48365i	−0.0697377	+	0.663510i	0.902688	+	0.430296i	$0.141591\pi$
$5$	−0.155938	+	1.48365i	−0.0697377	+	0.663510i	−0.972425	+	0.233214i	$0.925076\pi$
$6$	−1.21677	−	2.73292i	−0.496746	−	1.11571i
$7$	−4.91364	−	1.59654i	−1.85718	−	0.603435i	−0.995360	−	0.0962257i	$-0.969323\pi$
$7$	−4.91364	−	1.59654i	−1.85718	−	0.603435i	−0.861823	−	0.507209i	$-0.830677\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	0.621881	+	5.91681i	0.207294	+	1.97227i
$10$	0.745913	−	1.29196i	0.235878	−	0.408553i
$11$	−3.31335	−	0.147244i	−0.999014	−	0.0443956i
$11$	−3.31335	−	0.147244i	−0.999014	−	0.0443956i
$12$			2.99155i			0.863587i
$13$	0.431546	+	4.10589i	0.119689	+	1.13877i	0.875243	+	0.483683i	$0.160701\pi$
$13$	0.431546	+	4.10589i	0.119689	+	1.13877i	−0.755554	+	0.655086i	$0.772632\pi$
$14$	3.83946	+	3.45707i	1.02614	+	0.923941i
$15$	−3.31656	+	2.98625i	−0.856333	+	0.771046i
$16$	−0.104528	+	0.994522i	−0.0261321	+	0.248630i
$17$	4.10657	+	0.431618i	0.995989	+	0.104683i	0.588474	−	0.808516i	$-0.299729\pi$
$17$	4.10657	+	0.431618i	0.995989	+	0.104683i	0.407515	+	0.913199i	$0.366396\pi$
$18$	1.83846	−	5.65821i	0.433330	−	1.33365i
$19$	0.997602	+	4.24321i	0.228866	+	0.973458i
$19$	0.997602	+	4.24321i	0.228866	+	0.973458i
$20$	−1.20691	+	0.876873i	−0.269874	+	0.196075i
$21$	−7.72795	−	13.3852i	−1.68638	−	2.92089i
$22$	2.96701	+	1.48218i	0.632569	+	0.316001i
$23$	−1.80940	+	3.13397i	−0.377285	+	0.653477i	−0.990666	−	0.136310i	$-0.956476\pi$
$23$	−1.80940	+	3.13397i	−0.377285	+	0.653477i	0.613381	+	0.789787i	$0.289809\pi$
$24$	1.21677	−	2.73292i	0.248373	−	0.557855i
$25$	2.71383	+	0.576842i	0.542765	+	0.115368i
$26$	1.27578	−	3.92644i	0.250201	−	0.770039i
$27$	−5.18619	+	7.13818i	−0.998084	+	1.37374i
$28$	−2.10141	−	4.71984i	−0.397129	−	0.891966i
$29$	−1.96655	−	2.18407i	−0.365179	−	0.405572i	0.532352	−	0.846523i	$-0.321308\pi$
$29$	−1.96655	−	2.18407i	−0.365179	−	0.405572i	−0.897531	+	0.440950i	$0.854641\pi$
$30$	4.24445	−	1.37911i	0.774927	−	0.251789i
$31$	−3.78920	−	5.21539i	−0.680561	−	0.936712i	0.319379	−	0.947627i	$-0.396526\pi$
$31$	−3.78920	−	5.21539i	−0.680561	−	0.936712i	−0.999940	+	0.0109149i	$0.996526\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−7.07137	−	6.95982i	−1.23097	−	1.21155i
$34$	−3.57598	−	2.06459i	−0.613276	−	0.354075i
$35$	3.13494	−	7.04118i	0.529901	−	1.19018i
$36$	−3.98092	+	4.42126i	−0.663487	+	0.736877i
$37$	5.75599	+	1.87023i	0.946279	+	0.307465i	0.741203	−	0.671281i	$-0.234256\pi$
$37$	5.75599	+	1.87023i	0.946279	+	0.307465i	0.205076	+	0.978746i	$0.434256\pi$
$38$	0.814512	−	4.28212i	0.132131	−	0.694652i
$39$	−7.25953	+	9.99189i	−1.16246	+	1.59998i
$40$	1.45923	−	0.310168i	0.230724	−	0.0490419i
$41$	0.785878	−	0.872806i	0.122733	−	0.136309i	−0.678646	−	0.734465i	$-0.737433\pi$
$41$	0.785878	−	0.872806i	0.122733	−	0.136309i	0.801380	+	0.598156i	$0.204100\pi$
$42$	1.61558	+	15.3712i	0.249290	+	2.37183i
$43$	8.52452	−	4.92163i	1.29998	−	0.750542i	0.319577	−	0.947560i	$-0.396459\pi$
$43$	8.52452	−	4.92163i	1.29998	−	0.750542i	0.980400	+	0.197018i	$0.0631257\pi$
$44$	−2.10764	−	2.56083i	−0.317739	−	0.386059i
$45$	−8.87546			−1.32308
$46$	2.92766	−	2.12707i	0.431661	−	0.313620i
$47$	1.65228	+	0.351203i	0.241010	+	0.0512283i	0.326833	−	0.945082i	$-0.394019\pi$
$47$	1.65228	+	0.351203i	0.241010	+	0.0512283i	−0.0858228	+	0.996310i	$0.527352\pi$
$48$	−2.22316	+	2.00174i	−0.320885	+	0.288926i
$49$	15.9318	+	11.5752i	2.27598	+	1.65359i
$50$	−2.24458	−	1.63078i	−0.317432	−	0.230628i
$51$	8.26556	+	9.17984i	1.15741	+	1.28543i
$52$	−2.76251	+	3.06808i	−0.383091	+	0.425466i
$53$	−5.74462	+	0.603784i	−0.789084	+	0.0829361i	−0.490493	−	0.871445i	$-0.663183\pi$
$53$	−5.74462	+	0.603784i	−0.789084	+	0.0829361i	−0.298591	+	0.954381i	$0.596517\pi$
$54$	7.64119	−	4.41164i	1.03983	−	0.600348i
$55$	0.735137	−	4.89291i	0.0991259	−	0.659760i
$56$			5.16651i			0.690404i
$57$	−6.27597	+	11.4303i	−0.831272	+	1.51397i
$58$	0.908189	+	2.79512i	0.119251	+	0.367017i
$59$	−0.0109047	−	0.0513028i	−0.00141968	−	0.00667905i	0.977432	−	0.211250i	$-0.0677534\pi$
$59$	−0.0109047	−	0.0513028i	−0.00141968	−	0.00667905i	−0.978852	+	0.204571i	$0.934420\pi$
$60$	−4.43843	−	0.466498i	−0.572999	−	0.0602246i
$61$	2.05060	+	4.60572i	0.262552	+	0.589702i	0.995931	−	0.0901183i	$-0.0287245\pi$
$61$	2.05060	+	4.60572i	0.262552	+	0.589702i	−0.733379	+	0.679820i	$0.762058\pi$
$62$	1.34032	+	6.30571i	0.170221	+	0.800825i
$63$	6.39071	−	30.0659i	0.805154	−	3.78795i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−6.15901			−0.763931
$66$	3.62920	+	9.23430i	0.446724	+	1.13666i
$67$	−3.71315	−	2.14379i	−0.453634	−	0.261905i	0.255730	−	0.966748i	$-0.417684\pi$
$67$	−3.71315	−	2.14379i	−0.453634	−	0.261905i	−0.709364	+	0.704843i	$0.751018\pi$
$68$	2.42708	+	3.34058i	0.294326	+	0.405105i
$69$	−10.2960	+	3.34536i	−1.23949	+	0.402734i
$70$	−5.72781	+	5.15735i	−0.684605	+	0.616421i
$71$	3.04708	+	0.320261i	0.361622	+	0.0380080i	0.283597	−	0.958943i	$-0.408472\pi$
$71$	3.04708	+	0.320261i	0.361622	+	0.0380080i	0.0780244	+	0.996951i	$0.475139\pi$
$72$	5.43504	−	2.41984i	0.640526	−	0.285181i
$73$	−0.412672	−	1.94147i	−0.0482996	−	0.227232i	0.947377	−	0.320120i	$-0.103723\pi$
$73$	−0.412672	−	1.94147i	−0.0482996	−	0.227232i	−0.995677	+	0.0928885i	$0.970390\pi$
$74$	−4.49767	−	4.04972i	−0.522843	−	0.470770i
$75$	4.87858	+	6.71479i	0.563330	+	0.775357i
$76$	−2.48579	+	3.58062i	−0.285140	+	0.410725i
$77$	16.0456	+	6.01340i	1.82856	+	0.685291i
$78$	10.6960	−	6.17533i	1.21108	−	0.699218i
$79$	11.4269	+	5.08758i	1.28563	+	0.572398i	0.931820	−	0.362921i	$-0.118221\pi$
$79$	11.4269	+	5.08758i	1.28563	+	0.572398i	0.353806	+	0.935319i	$0.384887\pi$
$80$	−1.45923	−	0.310168i	−0.163146	−	0.0346778i
$81$	−8.36036	+	1.77705i	−0.928929	+	0.197450i
$82$	−1.07294	+	0.477702i	−0.118486	+	0.0527534i
$83$	0.381900	−	0.525640i	0.0419190	−	0.0576965i	−0.787543	−	0.616260i	$-0.788647\pi$
$83$	0.381900	−	0.525640i	0.0419190	−	0.0576965i	0.829462	+	0.558563i	$0.188647\pi$
$84$	4.77613	−	14.6994i	0.521119	−	1.60384i
$85$	−1.28074	+	6.02542i	−0.138916	+	0.653548i
$86$	−9.78935	+	1.02890i	−1.05561	+	0.110949i
$87$		−	8.79206i		−	0.942608i
$88$	0.883846	+	3.19669i	0.0942183	+	0.340768i
$89$	1.73365	+	1.00092i	0.183767	+	0.106098i	0.589061	−	0.808088i	$-0.299498\pi$
$89$	1.73365	+	1.00092i	0.183767	+	0.106098i	−0.405295	+	0.914186i	$0.632831\pi$
$90$	8.10814	+	3.60998i	0.854673	+	0.380525i
$91$	4.43475	−	20.8639i	0.464888	−	2.18713i
$92$	−3.53971	+	0.752389i	−0.369041	+	0.0784420i
$93$	2.01586	−	19.1796i	0.209035	−	1.98884i
$94$	−1.36659	−	0.992884i	−0.140953	−	0.102408i
$95$	−6.45101	+	0.818418i	−0.661860	+	0.0839679i
$96$	2.84514	−	0.924441i	0.290381	−	0.0943504i
$97$	−0.591993	+	1.32964i	−0.0601078	+	0.135004i	−0.941102	−	0.338123i	$-0.890208\pi$
$97$	−0.591993	+	1.32964i	−0.0601078	+	0.135004i	0.880994	+	0.473127i	$0.156875\pi$
$98$	−9.84641	−	17.0545i	−0.994638	−	1.72276i
$99$	−1.18930	−	19.6960i	−0.119529	−	1.97953i
$100$	1.38723	+	2.40275i	0.138723	+	0.240275i
$101$	−18.9399	+	1.99066i	−1.88459	+	0.198078i	−0.975723	−	0.219006i	$-0.929718\pi$
$101$	−18.9399	+	1.99066i	−1.88459	+	0.198078i	−0.908868	+	0.417085i	$0.863052\pi$
$102$	−3.81719	−	11.7481i	−0.377958	−	1.16324i
$103$	11.6028	+	3.76997i	1.14326	+	0.371466i	0.818599	−	0.574366i	$-0.194751\pi$
$103$	11.6028	+	3.76997i	1.14326	+	0.371466i	0.324657	+	0.945832i	$0.394751\pi$
$104$	3.77158	−	1.67921i	0.369834	−	0.164661i
$105$	21.0641	−	9.37833i	2.05564	−	0.915231i
$106$	5.49355	+	1.78496i	0.533581	+	0.173371i
$107$	−4.53023	−	13.9426i	−0.437954	−	1.34788i	−0.890029	−	0.455903i	$-0.849316\pi$
$107$	−4.53023	−	13.9426i	−0.437954	−	1.34788i	0.452076	−	0.891980i	$-0.350684\pi$
$108$	−8.77495	+	0.922284i	−0.844370	+	0.0887468i
$109$	−0.486492	−	0.842629i	−0.0465975	−	0.0807092i	0.841786	−	0.539811i	$-0.181504\pi$
$109$	−0.486492	−	0.842629i	−0.0465975	−	0.0807092i	−0.888383	+	0.459102i	$0.848171\pi$
$110$	−2.66171	+	4.17089i	−0.253784	+	0.397679i
$111$	9.05275	+	15.6798i	0.859249	+	1.48826i
$112$	2.10141	−	4.71984i	0.198564	−	0.445983i
$113$	2.96822	−	0.964432i	0.279226	−	0.0907261i	−0.166056	−	0.986116i	$-0.553103\pi$
$113$	2.96822	−	0.964432i	0.279226	−	0.0907261i	0.445282	+	0.895390i	$0.353103\pi$
$114$	10.3825	−	7.88939i	0.972409	−	0.738909i
$115$	−4.36757	−	3.17322i	−0.407278	−	0.295904i
$116$	0.307205	−	2.92286i	0.0285233	−	0.271381i
$117$	−24.0254	+	5.10675i	−2.22115	+	0.472119i
$118$	−0.0109047	+	0.0513028i	−0.00100386	+	0.00472280i
$119$	−19.4891	−	8.67711i	−1.78656	−	0.795430i
$120$	3.86497	+	2.23144i	0.352821	+	0.203702i
$121$	10.9566	+	0.975741i	0.996058	+	0.0887037i
$122$		−	5.04159i		−	0.456444i
$123$	3.49426	−	0.367262i	0.315067	−	0.0331149i
$124$	1.34032	−	6.30571i	0.120364	−	0.566269i
$125$	−3.58402	+	11.0305i	−0.320565	+	0.986596i
$126$	−18.0671	+	24.8673i	−1.60955	+	2.21535i
$127$	6.39514	−	2.84730i	0.567477	−	0.252657i	−0.102883	−	0.994694i	$-0.532807\pi$
$127$	6.39514	−	2.84730i	0.567477	−	0.252657i	0.670359	+	0.742036i	$0.266140\pi$
$128$	0.978148	−	0.207912i	0.0864569	−	0.0183770i
$129$	28.8032	+	6.12231i	2.53598	+	0.539039i
$130$	5.62654	+	2.50510i	0.493480	+	0.219711i
$131$	−15.9757	+	9.22359i	−1.39581	+	0.805869i	−0.993950	−	0.109833i	$-0.964968\pi$
$131$	−15.9757	+	9.22359i	−1.39581	+	0.805869i	−0.401856	+	0.915703i	$0.631635\pi$
$132$	0.440487	−	9.91208i	0.0383395	−	0.862736i
$133$	1.87258	−	22.4423i	0.162374	−	1.94599i
$134$	2.52017	+	3.46872i	0.217710	+	0.299652i
$135$	−9.78187	−	8.80763i	−0.841889	−	0.758040i
$136$	−0.858506	−	4.03896i	−0.0736163	−	0.346338i
$137$	7.33354	−	3.26510i	0.626547	−	0.278957i	−0.0688005	−	0.997630i	$-0.521917\pi$
$137$	7.33354	−	3.26510i	0.626547	−	0.278957i	0.695347	+	0.718674i	$0.255251\pi$
$138$	10.7665	+	1.13161i	0.916506	+	0.0963287i
$139$	−9.71351	+	8.74608i	−0.823889	+	0.741833i	−0.968862	−	0.247603i	$-0.920357\pi$
$139$	−9.71351	+	8.74608i	−0.823889	+	0.741833i	0.144973	+	0.989436i	$0.453691\pi$
$140$	7.33030	−	2.38176i	0.619523	−	0.201295i
$141$	2.97027	+	4.08822i	0.250141	+	0.344290i
$142$	−2.65338	−	1.53193i	−0.222667	−	0.128557i
$143$	−0.825300	−	13.6678i	−0.0690151	−	1.14296i
$144$	−5.94940			−0.495783
$145$	3.54707	−	2.57710i	0.294568	−	0.214016i
$146$	−0.412672	+	1.94147i	−0.0341530	+	0.160677i
$147$	12.2485	+	57.6248i	1.01024	+	4.75281i
$148$	2.46165	+	5.52897i	0.202347	+	0.454478i
$149$	1.24709	+	0.131075i	0.102166	+	0.0107381i	0.155473	−	0.987840i	$-0.450310\pi$
$149$	1.24709	+	0.131075i	0.102166	+	0.0107381i	−0.0533076	+	0.998578i	$0.516976\pi$
$150$	−1.72565	−	8.11856i	−0.140899	−	0.662878i
$151$	5.42541	+	16.6977i	0.441514	+	1.35884i	0.886262	+	0.463184i	$0.153293\pi$
$151$	5.42541	+	16.6977i	0.441514	+	1.35884i	−0.444749	+	0.895655i	$0.646707\pi$
$152$	3.72725	−	2.26000i	0.302320	−	0.183310i
$153$			24.5662i			1.98606i
$154$	−12.2125	−	12.0198i	−0.984109	−	0.968586i
$155$	8.32872	−	4.80859i	0.668979	−	0.386235i
$156$	−12.2830	+	1.29099i	−0.983426	+	0.103362i
$157$	8.79020	−	9.76251i	0.701535	−	0.779133i	−0.282085	−	0.959389i	$-0.591026\pi$
$157$	8.79020	−	9.76251i	0.701535	−	0.779133i	0.983620	+	0.180256i	$0.0576927\pi$
$158$	−8.36968	−	9.29547i	−0.665856	−	0.739508i
$159$	−13.9798	−	10.1569i	−1.10867	−	0.805497i
$160$	1.20691	+	0.876873i	0.0954148	+	0.0693229i
$161$	13.8942	−	12.5104i	1.09502	−	0.985959i
$162$	8.36036	+	1.77705i	0.656852	+	0.139618i
$163$	6.45122	−	4.68708i	0.505298	−	0.367121i	−0.305739	−	0.952115i	$-0.598903\pi$
$163$	6.45122	−	4.68708i	0.505298	−	0.367121i	0.811037	+	0.584995i	$0.198903\pi$
$164$	1.17448			0.0917112
$165$	11.4287	−	9.40616i	0.889720	−	0.732268i
$166$	−0.562680	+	0.324863i	−0.0436724	+	0.0252143i
$167$	2.10279	+	20.0067i	0.162718	+	1.54816i	0.705756	+	0.708455i	$0.250607\pi$
$167$	2.10279	+	20.0067i	0.162718	+	1.54816i	−0.543038	+	0.839708i	$0.682726\pi$
$168$	−10.3420	+	11.4860i	−0.797904	+	0.886162i
$169$	−3.95618	+	0.840912i	−0.304322	+	0.0646856i
$170$	3.62077	−	4.98357i	0.277701	−	0.382222i
$171$	−24.4858	+	8.54139i	−1.87248	+	0.653176i
$172$	9.36150	+	3.04174i	0.713808	+	0.231930i
$173$	−1.34659	+	1.49554i	−0.102379	+	0.113704i	−0.792157	−	0.610318i	$-0.791042\pi$
$173$	−1.34659	+	1.49554i	−0.102379	+	0.113704i	0.689777	+	0.724022i	$0.257708\pi$
$174$	−3.57605	+	8.03195i	−0.271100	+	0.608900i
$175$	−12.4138	−	7.16713i	−0.938397	−	0.541784i
$176$	0.492777	−	3.27981i	0.0371445	−	0.247225i
$177$	0.0784519	−	0.135883i	0.00589681	−	0.0102136i
$178$	−1.17666	−	1.61953i	−0.0881941	−	0.121389i
$179$	−14.6264	+	4.75241i	−1.09323	+	0.355212i	−0.799494	−	0.600675i	$-0.794899\pi$
$179$	−14.6264	+	4.75241i	−1.09323	+	0.355212i	−0.293736	+	0.955887i	$0.594899\pi$
$180$	−5.93884	−	6.59575i	−0.442655	−	0.491619i
$181$	−7.42176	−	16.6695i	−0.551655	−	1.23904i	−0.947215	−	0.320598i	$-0.896116\pi$
$181$	−7.42176	−	16.6695i	−0.551655	−	1.23904i	0.395560	−	0.918440i	$-0.370550\pi$
$182$	−12.5374	+	17.2563i	−0.929337	+	1.27912i
$183$	−4.66065	+	14.3440i	−0.344525	+	1.06034i
$184$	3.53971	+	0.752389i	0.260951	+	0.0554669i
$185$	−3.67236	+	8.24825i	−0.269997	+	0.606424i
$186$	−9.64265	+	16.7016i	−0.707033	+	1.22462i
$187$	−13.5430	−	2.03477i	−0.990359	−	0.148797i
$188$	0.844597	+	1.46289i	0.0615986	+	0.106692i
$189$	36.8795	−	26.7945i	2.68259	−	1.94901i
$190$	6.22617	+	1.87620i	0.451694	+	0.136114i
$191$	7.56602	−	23.2858i	0.547458	−	1.68490i	−0.167616	−	0.985852i	$-0.553607\pi$
$191$	7.56602	−	23.2858i	0.547458	−	1.68490i	0.715074	−	0.699049i	$-0.246393\pi$
$192$	−2.97517	−	0.312703i	−0.214714	−	0.0225674i
$193$	−2.68807	+	25.5753i	−0.193492	+	1.84095i	0.279815	+	0.960054i	$0.409727\pi$
$193$	−2.68807	+	25.5753i	−0.193492	+	1.84095i	−0.473307	+	0.880898i	$0.656940\pi$
$194$	1.08162	−	0.973899i	0.0776561	−	0.0699219i
$195$	−13.6925	−	12.3287i	−0.980537	−	0.882880i
$196$	2.05846	+	19.5849i	0.147033	+	1.39892i
$197$		−	9.42108i		−	0.671224i	−0.942000	−	0.335612i	$-0.891057\pi$
$197$		−	9.42108i		−	0.671224i	0.942000	−	0.335612i	$-0.108943\pi$
$198$	−6.92462	+	18.4770i	−0.492111	+	1.31310i
$199$	6.92906	−	12.0015i	0.491188	−	0.850763i	−0.508760	−	0.860908i	$-0.669896\pi$
$199$	6.92906	−	12.0015i	0.491188	−	0.850763i	0.999949	+	0.0101454i	$0.00322944\pi$
$200$	−0.290010	−	2.75926i	−0.0205068	−	0.195109i
$201$	−3.96361	−	12.1987i	−0.279572	−	0.860433i
$202$	18.1121	+	5.88499i	1.27437	+	0.414067i
$203$	6.17596	+	13.8714i	0.433467	+	0.973584i
$204$	−1.29121	+	12.2850i	−0.0904026	+	0.860123i
$205$	1.17239	+	1.30207i	0.0818835	+	0.0909408i
$206$	−9.06628	−	8.16331i	−0.631677	−	0.568765i
$207$	−19.6683	−	8.75689i	−1.36704	−	0.608646i
$208$	−4.12851			−0.286260
$209$	−2.68062	−	14.2061i	−0.185423	−	0.982659i
$210$	−23.0575			−1.59112
$211$	−3.30552	−	1.47171i	−0.227562	−	0.101317i	0.289789	−	0.957091i	$-0.406415\pi$
$211$	−3.30552	−	1.47171i	−0.227562	−	0.101317i	−0.517350	+	0.855774i	$0.673082\pi$
$212$	−4.29260	−	3.86507i	−0.294817	−	0.265454i
$213$	6.13306	+	6.81145i	0.420230	+	0.466713i
$214$	−1.53240	+	14.5798i	−0.104753	+	0.996656i
$215$	5.97270	+	13.4149i	0.407335	+	0.914889i
$216$	8.39144	+	2.72654i	0.570965	+	0.185518i
$217$	10.2922	+	31.6762i	0.698681	+	2.15032i
$218$	0.101705	+	0.967654i	0.00688830	+	0.0655378i
$219$	2.96888	−	5.14225i	0.200618	−	0.347481i
$220$	4.12804	−	2.72768i	0.278313	−	0.183900i
$221$			17.0474i			1.14673i
$222$	−1.89254	−	18.0063i	−0.127019	−	1.20850i
$223$	0.175608	+	0.158118i	0.0117596	+	0.0105884i	0.674989	−	0.737827i	$-0.264148\pi$
$223$	0.175608	+	0.158118i	0.0117596	+	0.0105884i	−0.663230	+	0.748416i	$0.730815\pi$
$224$	−3.83946	+	3.45707i	−0.256535	+	0.230985i
$225$	−1.72538	+	16.4159i	−0.115025	+	1.09439i
$226$	−3.10387	−	0.326230i	−0.206466	−	0.0217005i
$227$	0.414263	−	1.27497i	0.0274956	−	0.0846228i	−0.936367	−	0.351022i	$-0.885834\pi$
$227$	0.414263	−	1.27497i	0.0274956	−	0.0846228i	0.963863	+	0.266400i	$0.0858341\pi$
$228$	−12.6938	+	2.98438i	−0.840666	+	0.197645i
$229$	−6.88828	+	5.00463i	−0.455190	+	0.330715i	−0.791642	−	0.610986i	$-0.790773\pi$
$229$	−6.88828	+	5.00463i	−0.455190	+	0.330715i	0.336451	+	0.941701i	$0.390773\pi$
$230$	2.69930	+	4.67533i	0.177987	+	0.308282i
$231$	23.6345	+	45.4878i	1.55504	+	2.99288i
$232$	−1.46948	+	2.54521i	−0.0964761	+	0.167102i
$233$	3.28607	−	7.38063i	0.215278	−	0.483521i	−0.773336	−	0.633996i	$-0.781414\pi$
$233$	3.28607	−	7.38063i	0.215278	−	0.483521i	0.988614	+	0.150475i	$0.0480802\pi$
$234$	24.0254	+	5.10675i	1.57059	+	0.333839i
$235$	−0.778718	+	2.39665i	−0.0507980	+	0.156340i
$236$	0.0308287	−	0.0424321i	0.00200678	−	0.00276209i
$237$	15.2198	+	34.1842i	0.988631	+	2.22050i
$238$	14.2749	+	15.8539i	0.925304	+	1.02765i
$239$	−7.74763	+	2.51736i	−0.501152	+	0.162834i	−0.548675	−	0.836036i	$-0.684867\pi$
$239$	−7.74763	+	2.51736i	−0.501152	+	0.162834i	0.0475224	+	0.998870i	$0.484867\pi$
$240$	−2.62321	−	3.61054i	−0.169328	−	0.233060i
$241$	−6.84481	+	11.8556i	−0.440913	+	0.763684i	−0.997757	−	0.0669327i	$-0.978679\pi$
$241$	−6.84481	+	11.8556i	−0.440913	+	0.763684i	0.556844	+	0.830617i	$0.312012\pi$
$242$	−9.61252	−	5.34785i	−0.617916	−	0.343773i
$243$	0.779966	+	0.450314i	0.0500349	+	0.0288876i
$244$	−2.05060	+	4.60572i	−0.131276	+	0.294851i
$245$	−19.6579	+	21.8323i	−1.25590	+	1.39481i
$246$	−3.34154	−	1.08573i	−0.213049	−	0.0692239i
$247$	−16.9916	+	5.92718i	−1.08115	+	0.377138i
$248$	−3.78920	+	5.21539i	−0.240615	+	0.331178i
$249$	1.90122	−	0.404117i	0.120485	−	0.0256098i
$250$	7.76067	−	8.61909i	0.490828	−	0.545119i
$251$	0.600102	+	5.70959i	0.0378781	+	0.360386i	0.997001	+	0.0773945i	$0.0246601\pi$
$251$	0.600102	+	5.70959i	0.0378781	+	0.360386i	−0.959122	+	0.282991i	$0.908673\pi$
$252$	26.6196	−	15.3688i	1.67687	−	0.968144i
$253$	6.45663	−	10.1175i	0.405925	−	0.636083i
$254$	−7.00035			−0.439241
$255$	−14.9086	+	10.8317i	−0.933614	+	0.678310i
$256$	−0.978148	−	0.207912i	−0.0611342	−	0.0129945i
$257$	12.6971	−	11.4325i	0.792024	−	0.713142i	−0.170197	−	0.985410i	$-0.554440\pi$
$257$	12.6971	−	11.4325i	0.792024	−	0.713142i	0.962221	+	0.272268i	$0.0877738\pi$
$258$	−23.8229	−	17.3083i	−1.48315	−	1.07757i
$259$	−25.2970	−	18.3793i	−1.57188	−	1.14204i
$260$	−4.12118	−	4.57704i	−0.255585	−	0.283856i
$261$	11.6998	−	12.9939i	0.724198	−	0.804304i
$262$	18.3461	−	1.92826i	1.13343	−	0.119128i
$263$	14.8665	−	8.58320i	0.916710	−	0.529263i	0.0341257	−	0.999418i	$-0.489135\pi$
$263$	14.8665	−	8.58320i	0.916710	−	0.529263i	0.882584	+	0.470155i	$0.155802\pi$
$264$	−4.43401	+	8.87597i	−0.272895	+	0.546278i
$265$		−	8.61718i		−	0.529349i
$266$	−10.8388	+	19.7404i	−0.664569	+	1.21036i
$267$	1.85059	+	5.69553i	0.113254	+	0.348561i
$268$	−0.891437	−	4.19388i	−0.0544532	−	0.256182i
$269$	−24.0984	−	2.53285i	−1.46931	−	0.154430i	−0.664198	−	0.747557i	$-0.731227\pi$
$269$	−24.0984	−	2.53285i	−1.46931	−	0.154430i	−0.805109	+	0.593127i	$0.797893\pi$
$270$	5.35379	+	12.0248i	0.325821	+	0.731807i
$271$	−4.48429	−	21.0969i	−0.272401	−	1.28155i	−0.875242	−	0.483685i	$-0.839298\pi$
$271$	−4.48429	−	21.0969i	−0.272401	−	1.28155i	0.602841	−	0.797861i	$-0.294035\pi$
$272$	−0.858506	+	4.03896i	−0.0520546	+	0.244898i
$273$	51.6232	−	37.5064i	3.12438	−	2.26999i
$274$	−8.02756			−0.484963
$275$	−8.90694	−	2.31088i	−0.537108	−	0.139351i
$276$	−9.37543	−	5.41291i	−0.564335	−	0.325819i
$277$	−7.88075	−	10.8469i	−0.473509	−	0.651729i	0.503733	−	0.863860i	$-0.331960\pi$
$277$	−7.88075	−	10.8469i	−0.473509	−	0.651729i	−0.977241	+	0.212131i	$0.931960\pi$
$278$	12.4311	−	4.03910i	0.745567	−	0.242249i
$279$	28.5020	−	25.6633i	1.70637	−	1.53642i
$280$	−7.66531	−	0.805656i	−0.458090	−	0.0481472i
$281$	27.1606	−	12.0927i	1.62027	−	0.721390i	0.622161	−	0.782889i	$-0.286255\pi$
$281$	27.1606	−	12.0927i	1.62027	−	0.721390i	0.998107	+	0.0614993i	$0.0195882\pi$
$282$	−1.05064	−	4.94289i	−0.0625649	−	0.294345i
$283$	7.95310	+	7.16100i	0.472763	+	0.425677i	0.870759	−	0.491709i	$-0.163628\pi$
$283$	7.95310	+	7.16100i	0.472763	+	0.425677i	−0.397997	+	0.917387i	$0.630294\pi$
$284$	1.80089	+	2.47872i	0.106863	+	0.147085i
$285$	−15.9799	−	11.0938i	−0.946566	−	0.657139i
$286$	−4.80525	+	12.8218i	−0.284140	+	0.758172i
$287$	−5.25499	+	3.03397i	−0.310192	+	0.179090i
$288$	5.43504	+	2.41984i	0.320263	+	0.142590i
$289$	0.0490953	+	0.0104355i	0.00288796	+	0.000613855i
$290$	−4.28861	+	0.911572i	−0.251836	+	0.0535293i
$291$	−3.97768	+	1.77098i	−0.233176	+	0.103817i
$292$	1.16666	−	1.60577i	0.0682737	−	0.0939706i
$293$	8.08825	−	24.8931i	0.472520	−	1.45427i	−0.376752	−	0.926314i	$-0.622959\pi$
$293$	8.08825	−	24.8931i	0.472520	−	1.45427i	0.849273	−	0.527954i	$-0.177041\pi$
$294$	12.2485	−	57.6248i	0.714348	−	3.36075i
$295$	0.0778160	−	0.00817879i	0.00453062	−	0.000476188i
$296$		−	6.05221i		−	0.351777i
$297$	18.2348	−	22.8877i	1.05809	−	1.32808i
$298$	−1.08596	−	0.626981i	−0.0629082	−	0.0363201i
$299$	−13.6486	−	6.07673i	−0.789316	−	0.351426i
$300$	−1.72565	+	8.11856i	−0.0996307	+	0.468725i
$301$	−49.7440	+	10.5734i	−2.86720	+	0.609442i
$302$	1.83521	−	17.4608i	0.105604	−	1.00476i
$303$	−46.0912	−	33.4872i	−2.64787	−	1.92379i
$304$	−4.32424	+	0.548601i	−0.248012	+	0.0314644i
$305$	−7.15306	+	2.32417i	−0.409583	+	0.133082i
$306$	9.99196	−	22.4423i	0.571203	−	1.28294i
$307$	−4.94090	−	8.55788i	−0.281992	−	0.488424i	0.689883	−	0.723921i	$-0.257662\pi$
$307$	−4.94090	−	8.55788i	−0.281992	−	0.488424i	−0.971875	+	0.235496i	$0.924328\pi$
$308$	6.26775	+	15.9479i	0.357138	+	0.908718i
$309$	18.2483	+	31.6070i	1.03811	+	1.79806i
$310$	−9.56449	+	1.00527i	−0.543226	+	0.0570954i
$311$	3.72166	+	11.4541i	0.211036	+	0.649501i	0.999411	+	0.0343070i	$0.0109224\pi$
$311$	3.72166	+	11.4541i	0.211036	+	0.649501i	−0.788376	+	0.615194i	$0.789078\pi$
$312$	11.7462	+	3.81656i	0.664996	+	0.216070i
$313$	−24.4819	+	10.9000i	−1.38380	+	0.616106i	−0.957489	−	0.288471i	$-0.906853\pi$
$313$	−24.4819	+	10.9000i	−1.38380	+	0.616106i	−0.426309	+	0.904578i	$0.640186\pi$
$314$	−12.0010	+	5.34320i	−0.677257	+	0.301534i
$315$	43.6109	+	14.1700i	2.45719	+	0.798391i
$316$	3.86528	+	11.8961i	0.217439	+	0.669208i
$317$	19.0048	−	1.99749i	1.06742	−	0.112190i	0.445507	−	0.895278i	$-0.353023\pi$
$317$	19.0048	−	1.99749i	1.06742	−	0.112190i	0.621911	+	0.783088i	$0.286357\pi$
$318$	8.64000	+	14.9649i	0.484507	+	0.839191i
$319$	6.19428	+	7.52617i	0.346813	+	0.421385i
$320$	−0.745913	−	1.29196i	−0.0416978	−	0.0722227i
$321$	17.8381	−	40.0650i	0.995624	−	2.23621i
$322$	−17.7815	+	5.77754i	−0.990922	+	0.321970i
$323$	2.26528	+	17.8556i	0.126043	+	0.993512i
$324$	−6.91478	−	5.02388i	−0.384154	−	0.279104i
$325$	−1.19731	+	11.3916i	−0.0664146	+	0.631893i
$326$	−7.79989	+	1.65792i	−0.431996	+	0.0918236i
$327$	0.605176	−	2.84713i	0.0334663	−	0.157447i
$328$	−1.07294	−	0.477702i	−0.0592430	−	0.0263767i
$329$	−7.55801	−	4.36362i	−0.416687	−	0.240574i
$330$	−14.2664	+	3.94450i	−0.785341	+	0.217137i
$331$		−	11.3909i		−	0.626098i	−0.949737	−	0.313049i	$-0.898650\pi$
$331$		−	11.3909i		−	0.626098i	0.949737	−	0.313049i	$-0.101350\pi$
$332$	0.646168	−	0.0679150i	0.0354631	−	0.00372732i
$333$	−7.48627	+	35.2201i	−0.410245	+	1.93005i
$334$	6.21646	−	19.1323i	0.340149	−	1.04687i
$335$	3.75966	−	5.17473i	0.205412	−	0.282726i
$336$	14.1197	−	6.28648i	0.770291	−	0.342956i
$337$	6.07172	−	1.29058i	0.330748	−	0.0703026i	−0.0395448	−	0.999218i	$-0.512591\pi$
$337$	6.07172	−	1.29058i	0.330748	−	0.0703026i	0.370292	+	0.928915i	$0.379257\pi$
$338$	3.95618	+	0.840912i	0.215188	+	0.0457396i
$339$	8.52936	+	3.79751i	0.463251	+	0.206253i
$340$	−5.33474	+	3.08001i	−0.289317	+	0.167037i
$341$	11.7870	+	17.8384i	0.638304	+	0.966003i
$342$	25.8430	+	2.15634i	1.39743	+	0.116601i
$343$	−38.5455	−	53.0534i	−2.08126	−	2.86461i
$344$	−7.31497	−	6.58643i	−0.394397	−	0.355117i
$345$	−3.35782	−	15.7973i	−0.180779	−	0.850498i
$346$	1.83846	−	0.818536i	0.0988363	−	0.0440048i
$347$	−5.65116	−	0.593961i	−0.303370	−	0.0318855i	−0.0483797	−	0.998829i	$-0.515406\pi$
$347$	−5.65116	−	0.593961i	−0.303370	−	0.0318855i	−0.254991	+	0.966944i	$0.582072\pi$
$348$	6.53378	−	5.88304i	0.350247	−	0.315364i
$349$	−7.05816	+	2.29333i	−0.377814	+	0.122759i	−0.491767	−	0.870727i	$-0.663649\pi$
$349$	−7.05816	+	2.29333i	−0.377814	+	0.122759i	0.113953	+	0.993486i	$0.463649\pi$
$350$	8.42546	+	11.5967i	0.450360	+	0.619867i
$351$	−31.5467	−	18.2135i	−1.68384	−	0.972164i
$352$	−1.78419	+	2.79583i	−0.0950979	+	0.149018i
$353$	20.0973			1.06967			0.534834	−	0.844957i	$-0.320374\pi$
$353$	20.0973			1.06967			0.534834	+	0.844957i	$0.320374\pi$
$354$	−0.126938	+	0.0922257i	−0.00674667	+	0.00490174i
$355$	−0.950312	+	4.47087i	−0.0504373	+	0.237289i
$356$	0.416207	+	1.95810i	0.0220590	+	0.103779i
$357$	−25.9581	−	58.3027i	−1.37385	−	3.08571i
$358$	15.2949	+	1.60756i	0.808359	+	0.0849620i
$359$	1.49501	+	7.03345i	0.0789034	+	0.371211i	0.999828	−	0.0185286i	$-0.00589819\pi$
$359$	1.49501	+	7.03345i	0.0789034	+	0.371211i	−0.920925	+	0.389740i	$0.872565\pi$
$360$	2.74267	+	8.44107i	0.144551	+	0.444883i
$361$	−17.0096	+	8.46606i	−0.895241	+	0.445582i
$362$			18.2471i			0.959046i
$363$	22.4052	+	24.1016i	1.17597	+	1.26500i
$364$	18.4723	−	10.6650i	0.968211	−	0.558997i
$365$	2.94482	−	0.309513i	0.154139	−	0.0162006i
$366$	10.0919	−	11.2082i	0.527515	−	0.585864i
$367$	−7.39270	−	8.21042i	−0.385896	−	0.428580i	0.518631	−	0.854998i	$-0.326442\pi$
$367$	−7.39270	−	8.21042i	−0.385896	−	0.428580i	−0.904526	+	0.426418i	$0.859775\pi$
$368$	−2.92766	−	2.12707i	−0.152615	−	0.110881i
$369$	5.65294	+	4.10710i	0.294281	+	0.213807i
$370$	6.70973	−	6.04147i	0.348822	−	0.314081i
$371$	29.1910	+	6.20473i	1.51552	+	0.322134i
$372$	15.6021	−	11.3356i	0.808933	−	0.587724i
$373$	33.0785			1.71274			0.856370	−	0.516362i	$-0.172714\pi$
$373$	33.0785			1.71274			0.856370	+	0.516362i	$0.172714\pi$
$374$	11.5445	+	7.36727i	0.596952	+	0.380953i
$375$	−30.0480	+	17.3482i	−1.55167	+	0.895858i
$376$	−0.176569	−	1.67994i	−0.00910585	−	0.0866363i
$377$	8.11891	−	9.01696i	0.418145	−	0.464397i
$378$	−44.5894	+	9.47777i	−2.29343	+	0.487484i
$379$	−6.37266	+	8.77122i	−0.327342	+	0.450547i	−0.940691	−	0.339265i	$-0.889822\pi$
$379$	−6.37266	+	8.77122i	−0.327342	+	0.450547i	0.613349	+	0.789812i	$0.289822\pi$
$380$	−4.92477	−	4.24641i	−0.252635	−	0.217836i
$381$	19.9170	+	6.47141i	1.02038	+	0.331541i
$382$	−16.3831	+	18.1953i	−0.838232	+	0.930951i
$383$	0.481032	−	1.08041i	0.0245796	−	0.0552066i	−0.900839	−	0.434154i	$-0.857047\pi$
$383$	0.481032	−	1.08041i	0.0245796	−	0.0552066i	0.925418	+	0.378948i	$0.123714\pi$
$384$	2.59076	+	1.49578i	0.132209	+	0.0763311i
$385$	−11.4239	+	22.8683i	−0.582217	+	1.16548i
$386$	12.8581	−	22.2709i	0.654460	−	1.13356i
$387$	34.4216	+	47.3773i	1.74975	+	2.40832i
$388$	−1.38423	+	0.449765i	−0.0702738	+	0.0228333i
$389$	2.00790	+	2.23000i	0.101805	+	0.113065i	0.791894	−	0.610659i	$-0.209095\pi$
$389$	2.00790	+	2.23000i	0.101805	+	0.113065i	−0.690089	+	0.723724i	$0.742429\pi$
$390$	7.49413	+	16.8321i	0.379480	+	0.852326i
$391$	−8.78308	+	12.0889i	−0.444180	+	0.611361i
$392$	6.08542	−	18.7290i	0.307360	−	0.945957i
$393$	−53.9798	−	11.4738i	−2.72292	−	0.578775i
$394$	−3.83190	+	8.60659i	−0.193048	+	0.433594i
$395$	−9.33010	+	16.1602i	−0.469448	+	0.813108i
$396$	13.8412	−	14.0630i	0.695547	−	0.706695i
$397$	−9.71655	−	16.8296i	−0.487659	−	0.844651i	0.512240	−	0.858842i	$-0.328816\pi$
$397$	−9.71655	−	16.8296i	−0.487659	−	0.844651i	−0.999899	+	0.0141914i	$0.995483\pi$
$398$	−11.2115	+	8.14560i	−0.561980	+	0.408302i
$399$	49.0867	−	46.1444i	2.45741	−	2.31011i
$400$	−0.857354	+	2.63866i	−0.0428677	+	0.131933i
$401$	11.6400	+	1.22342i	0.581275	+	0.0610945i	0.390603	−	0.920559i	$-0.372267\pi$
$401$	11.6400	+	1.22342i	0.581275	+	0.0610945i	0.190672	+	0.981654i	$0.438933\pi$
$402$	−1.34074	+	12.7563i	−0.0668698	+	0.636224i
$403$	19.7786	−	17.8087i	0.985243	−	0.887117i
$404$	−14.1526	−	12.7431i	−0.704119	−	0.633992i
$405$	−1.33283	−	12.6810i	−0.0662286	−	0.630123i
$406$		−	15.1842i		−	0.753578i
$407$	−18.7963	−	7.04428i	−0.931696	−	0.349172i
$408$	6.17634	−	10.6977i	0.305775	−	0.529617i
$409$	2.25123	+	21.4190i	0.111316	+	1.05910i	0.897472	+	0.441072i	$0.145402\pi$
$409$	2.25123	+	21.4190i	0.111316	+	1.05910i	−0.786156	+	0.618029i	$0.787932\pi$
$410$	−0.541433	−	1.66636i	−0.0267395	−	0.0822956i
$411$	22.8395	+	7.42101i	1.12659	+	0.366051i
$412$	4.96214	+	11.1451i	0.244467	+	0.549082i
$413$	−0.0283249	+	0.269493i	−0.00139378	+	0.0132609i
$414$	14.4061	+	15.9996i	0.708023	+	0.786339i
$415$	0.720315	+	0.648574i	0.0353589	+	0.0318373i
$416$	3.77158	+	1.67921i	0.184917	+	0.0823303i
$417$	−39.1020			−1.91484
$418$	−3.32928	+	14.0683i	−0.162841	+	0.688101i
$419$	−26.0104			−1.27069			−0.635346	−	0.772227i	$-0.719143\pi$
$419$	−26.0104			−1.27069			−0.635346	+	0.772227i	$0.719143\pi$
$420$	21.0641	+	9.37833i	1.02782	+	0.457616i
$421$	15.3679	+	13.8374i	0.748988	+	0.674392i	0.952451	−	0.304691i	$-0.0985531\pi$
$421$	15.3679	+	13.8374i	0.748988	+	0.674392i	−0.203463	+	0.979083i	$0.565220\pi$
$422$	2.42115	+	2.68896i	0.117860	+	0.130896i
$423$	−1.05048	+	9.99464i	−0.0510760	+	0.485956i
$424$	2.34942	+	5.27688i	0.114098	+	0.256268i
$425$	10.8955	+	3.54018i	0.528511	+	0.171724i
$426$	−2.83236	−	8.71711i	−0.137228	−	0.422345i
$427$	−2.72270	−	25.9047i	−0.131760	−	1.25362i
$428$	7.33006	−	12.6960i	0.354312	−	0.613686i
$429$	25.5246	−	32.0377i	1.23234	−	1.54680i
$430$		−	14.6844i		−	0.708147i
$431$	1.15458	+	10.9851i	0.0556141	+	0.529132i	0.986493	+	0.163804i	$0.0523765\pi$
$431$	1.15458	+	10.9851i	0.0556141	+	0.529132i	−0.930879	+	0.365328i	$0.880957\pi$
$432$	−6.55698	−	5.90393i	−0.315473	−	0.284053i
$433$	−8.11822	+	7.30968i	−0.390137	+	0.351281i	−0.840736	−	0.541446i	$-0.817877\pi$
$433$	−8.11822	+	7.30968i	−0.390137	+	0.351281i	0.450599	+	0.892726i	$0.351210\pi$
$434$	3.48146	−	33.1239i	0.167115	−	1.59000i
$435$	13.0444	+	1.37102i	0.625430	+	0.0657353i
$436$	0.300669	−	0.925363i	0.0143994	−	0.0443169i
$437$	−15.1031	−	4.55119i	−0.722480	−	0.217713i
$438$	−4.80375	+	3.49013i	−0.229532	+	0.166765i
$439$	7.73361	+	13.3950i	0.369105	+	0.639309i	0.989426	−	0.145039i	$-0.0463309\pi$
$439$	7.73361	+	13.3950i	0.369105	+	0.639309i	−0.620321	+	0.784348i	$0.712998\pi$
$440$	−4.88060	+	0.812835i	−0.232674	+	0.0387504i
$441$	−58.5802	+	101.464i	−2.78953	+	4.83161i
$442$	6.93379	−	15.5736i	0.329807	−	0.740758i
$443$	−12.6787	−	2.69494i	−0.602382	−	0.128040i	−0.103381	−	0.994642i	$-0.532966\pi$
$443$	−12.6787	−	2.69494i	−0.602382	−	0.128040i	−0.499001	+	0.866601i	$0.666300\pi$
$444$	−5.59491	+	17.2194i	−0.265523	+	0.817194i
$445$	−1.75537	+	2.41605i	−0.0832123	+	0.114532i
$446$	−0.0961134	−	0.215874i	−0.00455110	−	0.0102219i
$447$	2.51011	+	2.78776i	0.118724	+	0.131856i
$448$	4.91364	−	1.59654i	0.232148	−	0.0754294i
$449$	−8.27907	−	11.3952i	−0.390713	−	0.537771i	0.567670	−	0.823256i	$-0.307845\pi$
$449$	−8.27907	−	11.3952i	−0.390713	−	0.537771i	−0.958383	+	0.285486i	$0.907845\pi$
$450$	8.25317	−	14.2949i	0.389058	−	0.673869i
$451$	−2.73241	+	2.77620i	−0.128664	+	0.130726i
$452$	2.70284	+	1.56048i	0.127131	+	0.0733990i
$453$	−21.3629	+	47.9819i	−1.00372	+	2.25439i
$454$	−0.897025	+	0.996248i	−0.0420995	+	0.0467562i
$455$	30.2632	+	9.83310i	1.41876	+	0.460983i
$456$	12.8102	+	2.43666i	0.599893	+	0.114107i
$457$	12.3312	−	16.9725i	0.576830	−	0.793938i	−0.416514	−	0.909129i	$-0.636748\pi$
$457$	12.3312	−	16.9725i	0.576830	−	0.793938i	0.993343	+	0.115191i	$0.0367482\pi$
$458$	8.32832	−	1.77024i	0.389157	−	0.0827178i
$459$	−24.3784	+	27.0750i	−1.13789	+	1.26375i
$460$	−0.564308	−	5.36903i	−0.0263110	−	0.250332i
$461$	−18.3058	+	10.5689i	−0.852587	+	0.492241i	−0.861523	−	0.507719i	$-0.830489\pi$
$461$	−18.3058	+	10.5689i	−0.852587	+	0.492241i	0.00893599	+	0.999960i	$0.497156\pi$
$462$	−3.08968	−	51.1682i	−0.143745	−	2.38056i
$463$	−3.46809			−0.161176			−0.0805880	−	0.996748i	$-0.525680\pi$
$463$	−3.46809			−0.161176			−0.0805880	+	0.996748i	$0.525680\pi$
$464$	2.37767	−	1.72748i	0.110381	−	0.0801962i
$465$	28.1416	+	5.98168i	1.30504	+	0.277394i
$466$	−6.00395	+	5.40598i	−0.278128	+	0.250427i
$467$	25.9860	+	18.8799i	1.20249	+	0.873659i	0.994527	−	0.104478i	$-0.0333171\pi$
$467$	25.9860	+	18.8799i	1.20249	+	0.873659i	0.207961	+	0.978137i	$0.433317\pi$
$468$	−19.8712	−	14.4373i	−0.918545	−	0.667362i
$469$	14.8225	+	16.4620i	0.684437	+	0.760145i
$470$	1.68620	−	1.87271i	0.0777785	−	0.0863818i
$471$	39.0840	−	4.10790i	1.80090	−	0.189282i
$472$	−0.0454221	+	0.0262245i	−0.00209072	+	0.00120708i
$473$	−28.9694	+	15.0519i	−1.33202	+	0.692089i
$474$		−	37.4192i		−	1.71872i
$475$	0.259662	+	12.0908i	0.0119141	+	0.554763i
$476$	−6.59241	−	20.2894i	−0.302163	−	0.929961i
$477$	−7.14494	−	33.6143i	−0.327144	−	1.53909i
$478$	8.10171	+	0.851524i	0.370564	+	0.0389478i
$479$	−6.71649	−	15.0855i	−0.306884	−	0.689273i	0.692602	−	0.721320i	$-0.256464\pi$
$479$	−6.71649	−	15.0855i	−0.306884	−	0.689273i	−0.999486	+	0.0320467i	$0.989797\pi$
$480$	0.927884	+	4.36535i	0.0423519	+	0.199250i
$481$	−5.19500	+	24.4406i	−0.236872	+	1.11439i
$482$	11.0751	−	8.04656i	0.504459	−	0.366511i
$483$	55.9317			2.54498
$484$	6.60631	+	8.79527i	0.300287	+	0.399785i
$485$	−1.88041	−	1.08565i	−0.0853849	−	0.0492970i
$486$	−0.529376	−	0.728623i	−0.0240130	−	0.0330510i
$487$	0.385452	−	0.125241i	0.0174665	−	0.00567521i	−0.300271	−	0.953854i	$-0.597077\pi$
$487$	0.385452	−	0.125241i	0.0174665	−	0.00567521i	0.317737	+	0.948179i	$0.397077\pi$
$488$	3.74663	−	3.37348i	0.169602	−	0.152710i
$489$	23.7244	+	2.49354i	1.07285	+	0.112762i
$490$	26.8384	−	11.9492i	1.21243	−	0.539810i
$491$	−1.87016	−	8.79839i	−0.0843989	−	0.397066i	0.915588	−	0.402117i	$-0.131725\pi$
$491$	−1.87016	−	8.79839i	−0.0843989	−	0.397066i	−0.999987	+	0.00505121i	$0.998392\pi$
$492$	2.61105	+	2.35100i	0.117715	+	0.105991i
$493$	−7.13308	−	9.81784i	−0.321258	−	0.442173i
$494$	17.9334	+	1.49636i	0.806863	+	0.0673246i
$495$	29.4076	+	1.30686i	1.32177	+	0.0587388i
$496$	5.58290	−	3.22329i	0.250680	−	0.144730i
$497$	−14.4609	−	6.43843i	−0.648662	−	0.288803i
$498$	−1.90122	−	0.404117i	−0.0851957	−	0.0181089i
$499$	12.8612	−	2.73374i	0.575747	−	0.122379i	0.0891699	−	0.996016i	$-0.471579\pi$
$499$	12.8612	−	2.73374i	0.575747	−	0.122379i	0.486577	+	0.873638i	$0.338245\pi$
$500$	−10.5954	+	4.71739i	−0.473842	+	0.210968i
$501$	−35.3733	+	48.6872i	−1.58036	+	2.17518i
$502$	1.77408	−	5.46005i	0.0791810	−	0.243694i
$503$	−6.78736	+	31.9320i	−0.302633	+	1.42378i	0.519494	+	0.854474i	$0.326121\pi$
$503$	−6.78736	+	31.9320i	−0.302633	+	1.42378i	−0.822127	+	0.569304i	$0.807213\pi$
$504$	−30.5692	+	3.21296i	−1.36166	+	0.143116i
$505$		−	28.4107i		−	1.26426i
$506$	−10.0136	+	6.61667i	−0.445158	+	0.294147i
$507$	−10.4785	−	6.04977i	−0.465367	−	0.268680i
$508$	6.39514	+	2.84730i	0.283738	+	0.126329i
$509$	−0.960808	+	4.52025i	−0.0425871	+	0.200356i	−0.994298	−	0.106640i	$-0.965991\pi$
$509$	−0.960808	+	4.52025i	−0.0425871	+	0.200356i	0.951711	+	0.306997i	$0.0993240\pi$
$510$	18.0254	−	3.83141i	0.798176	−	0.169658i
$511$	−1.07191	+	10.1985i	−0.0474184	+	0.451156i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	−35.4625	−	14.8850i	−1.56571	−	0.657190i
$514$	−16.2494	+	5.27976i	−0.716731	+	0.232880i
$515$	−7.40265	+	16.6266i	−0.326200	+	0.732656i
$516$	14.7233	+	25.5016i	0.648159	+	1.12264i
$517$	−5.42288	−	1.40695i	−0.238498	−	0.0618776i
$518$	15.6344	+	27.0796i	0.686936	+	1.18981i
$519$	−5.98736	+	0.629297i	−0.262816	+	0.0276231i
$520$	1.90324	+	5.85757i	0.0834626	+	0.256871i
$521$	−30.2752	−	9.83702i	−1.32638	−	0.430968i	−0.441700	−	0.897163i	$-0.645624\pi$
$521$	−30.2752	−	9.83702i	−1.32638	−	0.430968i	−0.884682	+	0.466195i	$0.845624\pi$
$522$	−15.9734	+	7.11181i	−0.699136	+	0.311275i
$523$	8.44923	−	3.76184i	0.369459	−	0.164494i	−0.213605	−	0.976920i	$-0.568520\pi$
$523$	8.44923	−	3.76184i	0.369459	−	0.164494i	0.583064	+	0.812426i	$0.301854\pi$
$524$	−17.5443	−	5.70049i	−0.766427	−	0.249027i
$525$	−13.2512	−	40.7829i	−0.578329	−	1.77991i
$526$	−17.0724	+	1.79438i	−0.744390	+	0.0782385i
$527$	−13.3096	−	23.0528i	−0.579774	−	1.00420i
$528$	7.66085	−	6.30513i	0.333396	−	0.274396i
$529$	4.95217	+	8.57741i	0.215312	+	0.372931i
$530$	−3.50492	+	7.87218i	−0.152244	+	0.341946i
$531$	0.296767	−	0.0964255i	0.0128786	−	0.00418451i
$532$	17.9309	−	13.6252i	0.777403	−	0.590729i
$533$	3.92279	+	2.85007i	0.169915	+	0.123450i
$534$	0.625983	−	5.95583i	0.0270889	−	0.257734i
$535$	21.3924	−	4.54710i	0.924876	−	0.196588i
$536$	−0.891437	+	4.19388i	−0.0385042	+	0.181148i
$537$	−42.0299	−	18.7129i	−1.81373	−	0.807523i
$538$	20.9848	+	12.1156i	0.904719	+	0.522340i
$539$	−51.0834	−	40.6984i	−2.20032	−	1.75301i
$540$		−	13.1628i		−	0.566437i
$541$	11.0032	−	1.15648i	0.473065	−	0.0497211i	0.135003	−	0.990845i	$-0.456895\pi$
$541$	11.0032	−	1.15648i	0.473065	−	0.0497211i	0.338061	+	0.941124i	$0.390229\pi$
$542$	−4.48429	+	21.0969i	−0.192617	+	0.906190i
$543$	16.8684	−	51.9155i	0.723891	−	2.22791i
$544$	2.42708	−	3.34058i	0.104060	−	0.143226i
$545$	1.32603	−	0.590388i	0.0568010	−	0.0252894i
$546$	−62.4154	+	13.2668i	−2.67113	+	0.567766i
$547$	−26.0841	−	5.54435i	−1.11528	−	0.237059i	−0.386823	−	0.922154i	$-0.626427\pi$
$547$	−26.0841	−	5.54435i	−1.11528	−	0.237059i	−0.728454	+	0.685095i	$0.759761\pi$
$548$	7.33354	+	3.26510i	0.313273	+	0.139478i
$549$	−25.9759	+	14.9972i	−1.10862	+	0.640065i
$550$	7.19697	+	5.73387i	0.306880	+	0.244493i
$551$	7.30564	−	10.5233i	0.311231	−	0.448308i
$552$	6.36325	+	8.75827i	0.270838	+	0.372777i
$553$	−48.0252	−	43.2420i	−2.04224	−	1.83884i
$554$	2.78758	+	13.1145i	0.118433	+	0.557184i
$555$	−24.6751	+	10.9861i	−1.04740	+	0.466332i
$556$	−12.9992	−	1.36627i	−0.551289	−	0.0579428i
$557$	16.8898	−	15.2076i	0.715644	−	0.644369i	−0.228636	−	0.973512i	$-0.573427\pi$
$557$	16.8898	−	15.2076i	0.715644	−	0.644369i	0.944280	+	0.329143i	$0.106760\pi$
$558$	−36.4761	+	11.8518i	−1.54416	+	0.501727i
$559$	23.8864	+	32.8768i	1.01029	+	1.39054i
$560$	6.67492	+	3.85377i	0.282067	+	0.162851i
$561$	−26.0351	−	31.6331i	−1.09920	−	1.33555i
$562$	−29.7310			−1.25413
$563$	15.7686	−	11.4566i	0.664568	−	0.482837i	−0.203634	−	0.979047i	$-0.565275\pi$
$563$	15.7686	−	11.4566i	0.664568	−	0.482837i	0.868203	+	0.496210i	$0.165275\pi$
$564$	−1.05064	+	4.94289i	−0.0442401	+	0.208133i
$565$	0.968024	+	4.55420i	0.0407251	+	0.191596i
$566$	−4.35288	−	9.77672i	−0.182965	−	0.410946i
$567$	43.9169	+	4.61586i	1.84434	+	0.193848i
$568$	−0.637013	−	2.99691i	−0.0267285	−	0.125748i
$569$	0.761149	+	2.34258i	0.0319090	+	0.0982059i	0.965743	−	0.259502i	$-0.0835584\pi$
$569$	0.761149	+	2.34258i	0.0319090	+	0.0982059i	−0.933834	+	0.357708i	$0.883558\pi$
$570$	10.0861	+	16.6343i	0.422460	+	0.696733i
$571$		−	29.6570i		−	1.24111i	−0.784165	−	0.620553i	$-0.786908\pi$
$571$		−	29.6570i		−	1.24111i	0.784165	−	0.620553i	$-0.213092\pi$
$572$	9.60493	−	9.75887i	0.401602	−	0.408039i
$573$	63.4326	−	36.6228i	2.64993	−	1.52994i
$574$	6.03470	−	0.634273i	0.251884	−	0.0264740i
$575$	−6.71819	+	7.46131i	−0.280168	+	0.311158i
$576$	−3.98092	−	4.42126i	−0.165872	−	0.184219i
$577$	13.1268	+	9.53719i	0.546477	+	0.397039i	0.826485	−	0.562959i	$-0.190337\pi$
$577$	13.1268	+	9.53719i	0.546477	+	0.397039i	−0.280008	+	0.959998i	$0.590337\pi$
$578$	−0.0406063	−	0.0295022i	−0.00168900	−	0.00122713i
$579$	−57.1712	+	51.4771i	−2.37595	+	2.13932i
$580$	4.28861	+	0.911572i	0.178075	+	0.0378510i
$581$	−2.71572	+	1.97309i	−0.112667	+	0.0818575i
$582$	4.35412			0.180484
$583$	19.1229	−	1.15469i	0.791988	−	0.0478224i
$584$	−1.71892	+	0.992421i	−0.0711296	+	0.0410667i
$585$	−3.83017	−	36.4417i	−0.158358	−	1.50668i
$586$	−17.5139	+	19.4512i	−0.723493	+	0.803520i
$587$	0.836362	−	0.177774i	0.0345204	−	0.00733753i	−0.190619	−	0.981664i	$-0.561050\pi$
$587$	0.836362	−	0.177774i	0.0345204	−	0.00733753i	0.225139	+	0.974327i	$0.427716\pi$
$588$	−34.6277	+	47.6609i	−1.42802	+	1.96550i
$589$	18.3499	−	21.2813i	0.756093	−	0.876879i
$590$	−0.0744151	−	0.0241789i	−0.00306362	−	0.000995431i
$591$	18.8586	−	20.9446i	0.775737	−	0.861544i
$592$	−2.46165	+	5.52897i	−0.101173	+	0.227239i
$593$	29.7115	+	17.1540i	1.22011	+	0.704429i	0.964941	−	0.262469i	$-0.0845366\pi$
$593$	29.7115	+	17.1540i	1.22011	+	0.704429i	0.255166	+	0.966897i	$0.417870\pi$
$594$	−25.9675	+	13.4922i	−1.06546	+	0.553592i
$595$	15.9129	−	27.5620i	0.652366	−	1.12993i
$596$	0.737061	+	1.01448i	0.0301912	+	0.0415546i
$597$	39.4283	−	12.8110i	1.61369	−	0.524320i
$598$	9.99695	+	11.1027i	0.408806	+	0.454025i
$599$	1.62517	+	3.65019i	0.0664025	+	0.149143i	0.943698	−	0.330808i	$-0.107321\pi$
$599$	1.62517	+	3.65019i	0.0664025	+	0.149143i	−0.877296	+	0.479951i	$0.840655\pi$
$600$	4.87858	−	6.71479i	0.199167	−	0.274130i
$601$	−8.05824	+	24.8007i	−0.328702	+	1.01164i	0.641039	+	0.767508i	$0.278504\pi$
$601$	−8.05824	+	24.8007i	−0.328702	+	1.01164i	−0.969742	+	0.244134i	$0.921496\pi$
$602$	49.7440	+	10.5734i	2.02742	+	0.430940i
$603$	10.3752	−	23.3032i	0.422512	−	0.948978i
$604$	−8.77850	+	15.2048i	−0.357192	+	0.618675i
$605$	−3.15622	+	16.1037i	−0.128319	+	0.654708i
$606$	28.4859	+	49.3391i	1.15716	+	2.00426i
$607$	22.3713	−	16.2537i	0.908024	−	0.659718i	−0.0324901	−	0.999472i	$-0.510344\pi$
$607$	22.3713	−	16.2537i	0.908024	−	0.659718i	0.940514	+	0.339754i	$0.110344\pi$
$608$	4.17352	+	1.25765i	0.169259	+	0.0510046i
$609$	−14.0369	+	43.2011i	−0.568803	+	1.75059i
$610$	7.47997	+	0.786176i	0.302855	+	0.0318313i
$611$	−0.728966	+	6.93565i	−0.0294908	+	0.280586i
$612$	−18.2562	+	16.4380i	−0.737964	+	0.664466i
$613$	13.1525	+	11.8425i	0.531223	+	0.478315i	0.890543	−	0.454899i	$-0.150325\pi$
$613$	13.1525	+	11.8425i	0.531223	+	0.478315i	−0.359320	+	0.933214i	$0.616991\pi$
$614$	1.03293	+	9.82766i	0.0416856	+	0.396612i
$615$			5.24154i			0.211359i
$616$	0.760736	−	17.1185i	0.0306509	−	0.689723i
$617$	6.10380	−	10.5721i	0.245730	−	0.425616i	−0.716607	−	0.697477i	$-0.754306\pi$
$617$	6.10380	−	10.5721i	0.245730	−	0.425616i	0.962337	+	0.271861i	$0.0876391\pi$
$618$	−3.81493	−	36.2967i	−0.153459	−	1.46007i
$619$	7.17259	+	22.0750i	0.288291	+	0.887267i	0.985393	+	0.170296i	$0.0544723\pi$
$619$	7.17259	+	22.0750i	0.288291	+	0.887267i	−0.697102	+	0.716972i	$0.745528\pi$
$620$	9.14648	+	2.97187i	0.367331	+	0.119353i
$621$	−12.9869	−	29.1692i	−0.521148	−	1.17052i
$622$	1.25889	−	11.9776i	0.0504770	−	0.480256i
$623$	−6.92053	−	7.68602i	−0.277265	−	0.307934i
$624$	−9.17832	−	8.26420i	−0.367427	−	0.330833i
$625$	−3.13356	−	1.39515i	−0.125343	−	0.0558061i
$626$	26.7988			1.07109
$627$	22.4775	−	36.9484i	0.897667	−	1.47558i
$628$	13.1368			0.524213
$629$	22.8301	+	10.1646i	0.910297	+	0.405290i
$630$	−34.0770	−	30.6831i	−1.35766	−	1.22244i
$631$	−4.81633	−	5.34908i	−0.191735	−	0.212943i	0.639611	−	0.768699i	$-0.279096\pi$
$631$	−4.81633	−	5.34908i	−0.191735	−	0.212943i	−0.831346	+	0.555756i	$0.812429\pi$
$632$	1.30747	−	12.4398i	0.0520085	−	0.494828i
$633$	−4.40271	−	9.88866i	−0.174992	−	0.393039i
$634$	−18.1742	−	5.90517i	−0.721791	−	0.234524i
$635$	3.22716	+	9.93218i	0.128066	+	0.394146i
$636$	−1.80625	−	17.1853i	−0.0716226	−	0.681443i
$637$	−40.6510	+	70.4095i	−1.61065	+	2.78973i
$638$	−2.59759	−	9.39494i	−0.102840	−	0.371949i
$639$			18.2281i			0.721094i
$640$	0.155938	+	1.48365i	0.00616400	+	0.0586465i
$641$	−9.17594	−	8.26206i	−0.362428	−	0.326332i	0.467718	−	0.883878i	$-0.345076\pi$
$641$	−9.17594	−	8.26206i	−0.362428	−	0.326332i	−0.830146	+	0.557546i	$0.811743\pi$
$642$	−32.5918	+	29.3458i	−1.28630	+	1.15819i
$643$	4.63778	−	44.1255i	0.182896	−	1.74014i	−0.390270	−	0.920701i	$-0.627618\pi$
$643$	4.63778	−	44.1255i	0.182896	−	1.74014i	0.573166	−	0.819439i	$-0.305715\pi$
$644$	18.5941	+	1.95432i	0.732710	+	0.0770110i
$645$	−13.5749	+	41.7793i	−0.534511	+	1.64506i
$646$	5.19309	−	17.2333i	0.204319	−	0.678034i
$647$	−7.66287	+	5.56740i	−0.301259	+	0.218877i	−0.728137	−	0.685432i	$-0.759613\pi$
$647$	−7.66287	+	5.56740i	−0.301259	+	0.218877i	0.426878	+	0.904309i	$0.359613\pi$
$648$	4.27357	+	7.40204i	0.167882	+	0.290779i
$649$	0.0285773	+	0.171590i	0.00112176	+	0.00673550i
$650$	5.72718	−	9.91977i	0.224638	−	0.389085i
$651$	−40.5263	+	91.0235i	−1.58835	+	3.56749i
$652$	7.79989	+	1.65792i	0.305467	+	0.0649291i
$653$	0.386776	−	1.19037i	0.0151357	−	0.0465830i	−0.943203	−	0.332216i	$-0.892204\pi$
$653$	0.386776	−	1.19037i	0.0151357	−	0.0465830i	0.958339	+	0.285633i	$0.0922038\pi$
$654$	−1.71089	+	2.35483i	−0.0669010	+	0.0920813i
$655$	−11.1934	−	25.1408i	−0.437362	−	0.982331i
$656$	0.785878	+	0.872806i	0.0306834	+	0.0340773i
$657$	11.2307	−	3.64906i	0.438150	−	0.142363i
$658$	5.12974	+	7.06049i	0.199978	+	0.275246i
$659$	16.5110	−	28.5979i	0.643178	−	1.11402i	−0.341541	−	0.939867i	$-0.610949\pi$
$659$	16.5110	−	28.5979i	0.643178	−	1.11402i	0.984719	−	0.174150i	$-0.0557178\pi$
$660$	14.6374	+	2.19920i	0.569760	+	0.0856039i
$661$	−4.95670	−	2.86175i	−0.192793	−	0.111309i	0.400496	−	0.916298i	$-0.368838\pi$
$661$	−4.95670	−	2.86175i	−0.192793	−	0.111309i	−0.593290	+	0.804989i	$0.702171\pi$
$662$	−4.63308	+	10.4061i	−0.180070	+	0.404443i
$663$	−34.1244	+	37.8990i	−1.32528	+	1.47188i
$664$	−0.617927	−	0.200777i	−0.0239802	−	0.00779165i
$665$	33.0046	+	6.27788i	1.27986	+	0.243446i
$666$	21.1644	−	29.1303i	0.820103	−	1.12877i
$667$	10.4031	−	2.21124i	0.402809	−	0.0856197i
$668$	−13.4608	+	14.9498i	−0.520815	+	0.578423i
$669$	0.0738928	+	0.703043i	0.00285686	+	0.0271812i
$670$	−5.53937	+	3.19816i	−0.214005	+	0.123556i
$671$	−6.11620	−	15.5623i	−0.236113	−	0.600777i
$672$	−15.4559			−0.596224
$673$	30.2465	−	21.9754i	1.16592	−	0.847089i	0.175403	−	0.984497i	$-0.443877\pi$
$673$	30.2465	−	21.9754i	1.16592	−	0.847089i	0.990515	+	0.137408i	$0.0438771\pi$
$674$	−6.07172	−	1.29058i	−0.233874	−	0.0497114i
$675$	−18.1920	+	16.3802i	−0.700212	+	0.630474i
$676$	−3.27212	−	2.37734i	−0.125851	−	0.0914360i
$677$	26.2107	+	19.0432i	1.00736	+	0.731889i	0.963653	−	0.267156i	$-0.0860838\pi$
$677$	26.2107	+	19.0432i	1.00736	+	0.731889i	0.0437051	+	0.999044i	$0.486084\pi$
$678$	−6.24737	−	6.93840i	−0.239929	−	0.266468i
$679$	5.03166	−	5.58822i	0.193097	−	0.214456i
$680$	6.12628	−	0.643898i	0.234932	−	0.0246924i
$681$	3.47313	−	2.00521i	0.133091	−	0.0768400i
$682$	−3.51248	−	21.0904i	−0.134500	−	0.807593i
$683$		−	28.5897i		−	1.09396i	−0.837147	−	0.546978i	$-0.815778\pi$
$683$		−	28.5897i		−	1.09396i	0.837147	−	0.546978i	$-0.184222\pi$
$684$	−22.7317	−	12.4812i	−0.869169	−	0.477231i
$685$	3.70070	+	11.3896i	0.141397	+	0.435174i
$686$	13.6343	+	64.1446i	0.520562	+	2.44905i
$687$	−25.3317	−	2.66247i	−0.966465	−	0.101580i
$688$	4.00362	+	8.99227i	0.152637	+	0.342827i
$689$	−4.95814	−	23.3262i	−0.188890	−	0.888658i
$690$	−3.35782	+	15.7973i	−0.127830	+	0.601393i
$691$	−13.7149	+	9.96445i	−0.521739	+	0.379066i	−0.817259	−	0.576271i	$-0.804507\pi$
$691$	−13.7149	+	9.96445i	−0.521739	+	0.379066i	0.295520	+	0.955337i	$0.404507\pi$
$692$	−2.01245			−0.0765017
$693$	−25.6017	+	98.6781i	−0.972528	+	3.74847i
$694$	4.92101	+	2.84115i	0.186799	+	0.107848i
$695$	−11.4614	−	15.7753i	−0.434757	−	0.598392i
$696$	−8.36175	+	2.71690i	−0.316951	+	0.102984i
$697$	3.60398	−	3.24504i	0.136510	−	0.122915i
$698$	7.38073	+	0.775746i	0.279365	+	0.0293624i
$699$	22.0796	−	9.83046i	0.835126	−	0.371822i
$700$	−2.98026	−	14.0210i	−0.112643	−	0.529945i
$701$	−21.5498	−	19.4035i	−0.813925	−	0.732862i	0.152916	−	0.988239i	$-0.451134\pi$
$701$	−21.5498	−	19.4035i	−0.813925	−	0.732862i	−0.966841	+	0.255377i	$0.917800\pi$
$702$	21.4112	+	29.4700i	0.808115	+	1.11228i
$703$	−2.19360	+	26.2896i	−0.0827332	+	0.991531i
$704$	2.76711	−	1.82842i	0.104289	−	0.0689111i
$705$	−6.52868	+	3.76933i	−0.245884	+	0.141961i
$706$	−18.3598	−	8.17429i	−0.690978	−	0.307643i
$707$	96.2421	+	20.4569i	3.61956	+	0.769361i
$708$	0.153475	−	0.0326221i	0.00576795	−	0.00122601i
$709$	45.8629	−	20.4195i	1.72242	−	0.766870i	0.725517	−	0.688205i	$-0.241601\pi$
$709$	45.8629	−	20.4195i	1.72242	−	0.766870i	0.996901	−	0.0786651i	$-0.0250658\pi$
$710$	2.68662	−	3.69781i	0.100827	−	0.138776i
$711$	−22.9961	+	70.7746i	−0.862420	+	2.65425i
$712$	0.416207	−	1.95810i	0.0155980	−	0.0733830i
$713$	23.2010	−	2.43853i	0.868886	−	0.0913236i
$714$			63.8203i			2.38841i
$715$	20.4070	+	0.906876i	0.763178	+	0.0339152i
$716$	−13.3187	−	7.68956i	−0.497744	−	0.287372i
$717$	−22.2633	−	9.91226i	−0.831438	−	0.370180i
$718$	1.49501	−	7.03345i	0.0557931	−	0.262486i
$719$	40.2807	−	8.56193i	1.50222	−	0.319306i	0.617924	−	0.786238i	$-0.287974\pi$
$719$	40.2807	−	8.56193i	1.50222	−	0.319306i	0.884293	+	0.466932i	$0.154641\pi$
$720$	0.927739	−	8.82684i	0.0345748	−	0.328957i
$721$	−50.9930	−	37.0486i	−1.89908	−	1.37976i
$722$	18.9825	−	0.815711i	0.706455	−	0.0303576i
$723$	−38.9489	+	12.6553i	−1.44852	+	0.470654i
$724$	7.42176	−	16.6695i	0.275828	−	0.619519i
$725$	−4.07701	−	7.06159i	−0.151416	−	0.262261i
$726$	−10.6651	−	31.1309i	−0.395820	−	1.15538i
$727$	−5.37530	−	9.31029i	−0.199359	−	0.345300i	0.748962	−	0.662613i	$-0.230553\pi$
$727$	−5.37530	−	9.31029i	−0.199359	−	0.345300i	−0.948321	+	0.317313i	$0.897219\pi$
$728$	−21.2131	+	2.22959i	−0.786211	+	0.0826341i
$729$	8.75621	+	26.9488i	0.324304	+	0.998105i
$730$	−2.81611	−	0.915011i	−0.104229	−	0.0338661i
$731$	37.1308	−	16.5317i	1.37333	−	0.611447i
$732$	−13.7783	+	6.13448i	−0.509259	+	0.226737i
$733$	−47.8510	−	15.5477i	−1.76742	−	0.574268i	−0.769491	−	0.638657i	$-0.779490\pi$
$733$	−47.8510	−	15.5477i	−1.76742	−	0.574268i	−0.997925	+	0.0643890i	$0.979490\pi$
$734$	3.41408	+	10.5075i	0.126016	+	0.387838i
$735$	−87.4052	+	9.18666i	−3.22399	+	0.338855i
$736$	1.80940	+	3.13397i	0.0666952	+	0.115520i
$737$	11.9873	+	7.64987i	0.441559	+	0.281787i
$738$	−3.49371	−	6.05129i	−0.128605	−	0.222751i
$739$	5.81919	−	13.0701i	0.214062	−	0.480792i	−0.774317	−	0.632797i	$-0.781907\pi$
$739$	5.81919	−	13.0701i	0.214062	−	0.480792i	0.988380	+	0.152006i	$0.0485733\pi$
$740$	−8.58693	+	2.79006i	−0.315662	+	0.102565i
$741$	−49.6397	−	20.8358i	−1.82356	−	0.765420i
$742$	−24.1436	−	17.5413i	−0.886339	−	0.643963i
$743$	−4.45775	+	42.4126i	−0.163539	+	1.55597i	0.537758	+	0.843099i	$0.319272\pi$
$743$	−4.45775	+	42.4126i	−0.163539	+	1.55597i	−0.701297	+	0.712870i	$0.747395\pi$
$744$	−18.8639	+	4.00964i	−0.691583	+	0.147000i
$745$	−0.388939	+	1.82981i	−0.0142496	+	0.0670392i
$746$	−30.2187	−	13.4542i	−1.10639	−	0.492595i
$747$	3.34761	+	1.93274i	0.122483	+	0.0707153i
$748$	−7.54988	−	11.4259i	−0.276051	−	0.417773i
$749$			75.7417i			2.76754i
$750$	34.5064	−	3.62677i	1.25999	−	0.132431i
$751$	−0.696454	+	3.27656i	−0.0254140	+	0.119563i	−0.989026	−	0.147741i	$-0.952800\pi$
$751$	−0.696454	+	3.27656i	−0.0254140	+	0.119563i	0.963612	+	0.267305i	$0.0861330\pi$
$752$	−0.521990	+	1.60652i	−0.0190350	+	0.0585837i
$753$	−10.0950	+	13.8946i	−0.367882	+	0.506346i
$754$	−11.0845	+	4.93515i	−0.403674	+	0.179727i
$755$	−25.6196	+	5.44562i	−0.932394	+	0.198186i
$756$	44.5894	+	9.47777i	1.62170	+	0.344703i
$757$	3.19980	+	1.42464i	0.116299	+	0.0517796i	0.464061	−	0.885803i	$-0.346392\pi$
$757$	3.19980	+	1.42464i	0.116299	+	0.0517796i	−0.347762	+	0.937583i	$0.613058\pi$
$758$	9.38929	−	5.42091i	0.341034	−	0.196896i
$759$	34.6068	−	9.56835i	1.25615	−	0.347309i
$760$	2.77183	+	5.88237i	0.100545	+	0.213376i
$761$	−10.9557	−	15.0792i	−0.397144	−	0.546621i	0.562881	−	0.826538i	$-0.309693\pi$
$761$	−10.9557	−	15.0792i	−0.397144	−	0.546621i	−0.960024	+	0.279917i	$0.909693\pi$
$762$	−15.5629	−	14.0129i	−0.563784	−	0.507633i
$763$	1.04516	+	4.91708i	0.0378373	+	0.178010i
$764$	22.3674	−	9.95860i	0.809223	−	0.360289i
$765$	−36.4477	−	3.83081i	−1.31777	−	0.138503i
$766$	−0.878888	+	0.791355i	−0.0317555	+	0.0285928i
$767$	0.205938	−	0.0669132i	0.00743598	−	0.00241610i
$768$	−1.75839	−	2.42022i	−0.0634505	−	0.0873321i
$769$	−25.3605	−	14.6419i	−0.914522	−	0.527999i	−0.0326384	−	0.999467i	$-0.510391\pi$
$769$	−25.3605	−	14.6419i	−0.914522	−	0.527999i	−0.881883	+	0.471468i	$0.843724\pi$
$770$	19.7377	−	16.2447i	0.711296	−	0.585419i
$771$	51.1127			1.84078
$772$	−20.8048	+	15.1156i	−0.748782	+	0.544022i
$773$	6.30094	−	29.6436i	0.226629	−	1.06621i	−0.706792	−	0.707422i	$-0.749858\pi$
$773$	6.30094	−	29.6436i	0.226629	−	1.06621i	0.933421	−	0.358784i	$-0.116808\pi$
$774$	−12.1756	−	57.2818i	−0.437644	−	2.05895i
$775$	−7.27479	−	16.3394i	−0.261318	−	0.586930i
$776$	1.44750	+	0.152138i	0.0519621	+	0.00546144i
$777$	−19.4485	−	91.4981i	−0.697712	−	3.28248i
$778$	−0.927285	−	2.85389i	−0.0332448	−	0.102317i
$779$	4.48749	+	2.46393i	0.160781	+	0.0882794i
$780$		−	18.4250i		−	0.659722i
$781$	−10.0489	−	1.50980i	−0.359578	−	0.0540249i
$782$	12.9407	−	7.47134i	0.462760	−	0.267174i
$783$	25.7892	−	2.71056i	0.921632	−	0.0968674i
$784$	−13.1771	+	14.6346i	−0.470610	+	0.522665i
$785$	13.1135	+	14.5640i	0.468039	+	0.519810i
$786$	44.6462	+	32.4374i	1.59248	+	1.15700i
$787$	−5.50974	−	4.00306i	−0.196401	−	0.142694i	0.485239	−	0.874382i	$-0.338733\pi$
$787$	−5.50974	−	4.00306i	−0.196401	−	0.142694i	−0.681640	+	0.731688i	$0.738733\pi$
$788$	7.00123	−	6.30393i	0.249408	−	0.224568i
$789$	50.2320	+	10.6771i	1.78831	+	0.380116i
$790$	15.0964	−	10.9682i	0.537106	−	0.390231i
$791$	−16.1245			−0.573321
$792$	−18.3645	+	7.21750i	−0.652555	+	0.256463i
$793$	−18.0256	+	10.4071i	−0.640109	+	0.369567i
$794$	2.03131	+	19.3266i	0.0720885	+	0.685877i
$795$	17.2494	−	19.1573i	0.611771	−	0.679441i
$796$	13.5553	−	2.88127i	0.480454	−	0.102124i
$797$	−27.7020	+	38.1285i	−0.981254	+	1.35058i	−0.0451029	+	0.998982i	$0.514362\pi$
$797$	−27.7020	+	38.1285i	−0.981254	+	1.35058i	−0.936151	+	0.351598i	$0.885638\pi$
$798$	−63.6116	+	22.1896i	−2.25182	+	0.785504i
$799$	6.63362	+	2.15539i	0.234681	+	0.0762524i
$800$	1.85647	−	2.06182i	0.0656362	−	0.0728964i
$801$	−4.84415	+	10.8801i	−0.171159	+	0.384431i
$802$	−10.1361	−	5.85207i	−0.357918	−	0.206644i
$803$	1.08146	+	6.49354i	0.0381639	+	0.229152i
$804$	6.41326	−	11.1081i	0.226178	−	0.391752i
$805$	16.3945	+	22.5651i	0.577830	+	0.795314i
$806$	−25.3121	+	8.22441i	−0.891582	+	0.289692i
$807$	−48.5045	−	53.8697i	−1.70744	−	1.89630i
$808$	7.74599	+	17.3978i	0.272503	+	0.612051i
$809$	−25.6014	+	35.2372i	−0.900096	+	1.23888i	0.0703420	+	0.997523i	$0.477591\pi$
$809$	−25.6014	+	35.2372i	−0.900096	+	1.23888i	−0.970438	+	0.241352i	$0.922409\pi$
$810$	−3.94022	+	12.1268i	−0.138445	+	0.426091i
$811$	52.2423	+	11.1044i	1.83447	+	0.389930i	0.989459	−	0.144812i	$-0.0462578\pi$
$811$	52.2423	+	11.1044i	1.83447	+	0.389930i	0.845015	+	0.534742i	$0.179591\pi$
$812$	−6.17596	+	13.8714i	−0.216734	+	0.486792i
$813$	32.2613	−	55.8781i	1.13145	−	1.95973i
$814$	14.3061	+	14.0804i	0.501427	+	0.493518i
$815$	5.94802	+	10.3023i	0.208350	+	0.360873i
$816$	−9.99354	+	7.26073i	−0.349844	+	0.254176i
$817$	29.3876	+	31.2615i	1.02814	+	1.09370i
$818$	6.65529	−	20.4829i	0.232697	−	0.716167i
$819$	126.205	+	13.2647i	4.40997	+	0.463506i
$820$	−0.183146	+	1.74252i	−0.00639573	+	0.0608513i
$821$	17.9614	−	16.1725i	0.626856	−	0.564424i	−0.293278	−	0.956027i	$-0.594746\pi$
$821$	17.9614	−	16.1725i	0.626856	−	0.564424i	0.920134	+	0.391603i	$0.128079\pi$
$822$	−17.8465	−	16.0691i	−0.622470	−	0.560474i
$823$	−1.60093	−	15.2318i	−0.0558047	−	0.530947i	−0.986337	−	0.164738i	$-0.947322\pi$
$823$	−1.60093	−	15.2318i	−0.0558047	−	0.530947i	0.930533	−	0.366209i	$-0.119344\pi$
$824$		−	12.1999i		−	0.425003i
$825$	−15.1758	−	22.9668i	−0.528352	−	0.799602i
$826$	0.135489	−	0.234674i	0.00471426	−	0.00816534i
$827$	1.08365	+	10.3102i	0.0376821	+	0.358521i	0.997074	+	0.0764443i	$0.0243567\pi$
$827$	1.08365	+	10.3102i	0.0376821	+	0.358521i	−0.959392	+	0.282077i	$0.908977\pi$
$828$	−6.65302	−	20.4759i	−0.231208	−	0.711587i
$829$	17.2050	+	5.59024i	0.597554	+	0.194157i	0.592149	−	0.805828i	$-0.298280\pi$
$829$	17.2050	+	5.59024i	0.597554	+	0.194157i	0.00540457	+	0.999985i	$0.498280\pi$
$830$	−0.394241	−	0.885481i	−0.0136843	−	0.0307355i
$831$	4.19257	−	39.8896i	0.145439	−	1.38376i
$832$	−2.76251	−	3.06808i	−0.0957728	−	0.106366i
$833$	60.4291	+	54.4106i	2.09374	+	1.88522i
$834$	35.7215	+	15.9042i	1.23693	+	0.550719i
$835$	−30.0109			−1.03857
$836$	8.76353	−	11.4979i	0.303093	−	0.397662i
$837$	56.8800			1.96606
$838$	23.7617	+	10.5794i	0.820835	+	0.365459i
$839$	28.6471	+	25.7939i	0.989007	+	0.890506i	0.993989	−	0.109482i	$-0.0349192\pi$
$839$	28.6471	+	25.7939i	0.989007	+	0.890506i	−0.00498209	+	0.999988i	$0.501586\pi$
$840$	−15.4285	−	17.1351i	−0.532333	−	0.591216i
$841$	2.12846	−	20.2510i	0.0733952	−	0.698309i
$842$	−8.41116	−	18.8918i	−0.289868	−	0.651053i
$843$	84.5889	+	27.4846i	2.91339	+	0.946619i
$844$	−1.11813	−	3.44125i	−0.0384876	−	0.118453i
$845$	−0.630702	−	6.00073i	−0.0216968	−	0.206431i
$846$	5.02484	−	8.70329i	0.172758	−	0.299225i
$847$	−52.2792	−	22.2871i	−1.79633	−	0.765795i
$848$		−	5.77626i		−	0.198358i
$849$	3.34653	+	31.8401i	0.114853	+	1.09275i
$850$	−8.51365	−	7.66573i	−0.292016	−	0.262932i
$851$	−16.2761	+	14.6551i	−0.557938	+	0.502370i
$852$	−0.958078	+	9.11550i	−0.0328232	+	0.312292i
$853$	14.1971	+	1.49218i	0.486101	+	0.0510912i	0.344409	−	0.938820i	$-0.388079\pi$
$853$	14.1971	+	1.49218i	0.486101	+	0.0510912i	0.141691	+	0.989911i	$0.454746\pi$
$854$	−8.04909	+	24.7726i	−0.275434	+	0.847699i
$855$	−8.85418	−	37.6604i	−0.302807	−	1.28796i
$856$	−11.8603	+	8.61701i	−0.405376	+	0.294523i
$857$	−10.4529	−	18.1049i	−0.357064	−	0.618453i	0.630405	−	0.776266i	$-0.282889\pi$
$857$	−10.4529	−	18.1049i	−0.357064	−	0.618453i	−0.987469	+	0.157814i	$0.949555\pi$
$858$	−36.3488	+	18.8861i	−1.24093	+	0.644762i
$859$	2.59875	−	4.50117i	0.0886683	−	0.153578i	−0.818280	−	0.574820i	$-0.805072\pi$
$859$	2.59875	−	4.50117i	0.0886683	−	0.153578i	0.906948	+	0.421242i	$0.138406\pi$
$860$	−5.97270	+	13.4149i	−0.203667	+	0.457444i
$861$	−17.7559	−	3.77413i	−0.605119	−	0.128622i
$862$	3.41327	−	10.5050i	0.116257	−	0.357801i
$863$	−15.0225	+	20.6767i	−0.511373	+	0.703844i	−0.984150	−	0.177338i	$-0.943252\pi$
$863$	−15.0225	+	20.6767i	−0.511373	+	0.703844i	0.472777	+	0.881182i	$0.343252\pi$
$864$	3.58875	+	8.06047i	0.122092	+	0.274223i
$865$	−2.00888	−	2.23108i	−0.0683039	−	0.0758591i
$866$	10.3895	−	3.37574i	0.353049	−	0.114712i
$867$	0.0882575	+	0.121476i	0.00299738	+	0.00412554i
$868$	−16.6532	+	28.8441i	−0.565245	+	0.979033i
$869$	−37.1122	−	18.5395i	−1.25895	−	0.628910i
$870$	−11.3590	−	6.55811i	−0.385106	−	0.222341i
$871$	7.19976	−	16.1709i	0.243955	−	0.547931i
$872$	−0.651054	+	0.723068i	−0.0220475	+	0.0244862i
$873$	−8.23536	−	2.67583i	−0.278725	−	0.0905631i
$874$	11.9462	+	10.3007i	0.404088	+	0.348427i
$875$	35.2212	−	48.4778i	1.19069	−	1.63885i
$876$	5.80801	−	1.23453i	0.196234	−	0.0417109i
$877$	0.0222722	−	0.0247358i	0.000752079	−	0.000835268i	−0.742769	−	0.669548i	$-0.766488\pi$
$877$	0.0222722	−	0.0247358i	0.000752079	−	0.000835268i	0.743521	+	0.668713i	$0.233154\pi$
$878$	−1.61677	−	15.3825i	−0.0545632	−	0.519134i
$879$	67.8109	−	39.1506i	2.28721	−	1.32052i
$880$	4.78926	+	1.24256i	0.161446	+	0.0418866i
$881$	−18.6715			−0.629057			−0.314529	−	0.949248i	$-0.601846\pi$
$881$	−18.6715			−0.629057			−0.314529	+	0.949248i	$0.601846\pi$
$882$	94.7848	−	68.8652i	3.19157	−	2.31881i
$883$	−30.2413	−	6.42798i	−1.01770	−	0.216319i	−0.331287	−	0.943530i	$-0.607483\pi$
$883$	−30.2413	−	6.42798i	−1.01770	−	0.216319i	−0.686414	+	0.727211i	$0.740816\pi$
$884$	−12.6687	+	11.4069i	−0.426094	+	0.383656i
$885$	0.189369	+	0.137585i	0.00636557	+	0.00462486i
$886$	10.4864	+	7.61883i	0.352298	+	0.255960i
$887$	−5.79309	−	6.43387i	−0.194513	−	0.216028i	0.637997	−	0.770039i	$-0.279763\pi$
$887$	−5.79309	−	6.43387i	−0.194513	−	0.216028i	−0.832510	+	0.554011i	$0.813097\pi$
$888$	12.1149	−	13.4550i	0.406551	−	0.451521i
$889$	−35.9693	+	3.78052i	−1.20637	+	0.126795i
$890$	2.58630	−	1.49320i	0.0866931	−	0.0500523i
$891$	27.9625	−	4.65698i	0.936779	−	0.156015i
$892$			0.236304i			0.00791203i
$893$	0.158092	+	7.36133i	0.00529034	+	0.246338i
$894$	−1.15921	−	3.56770i	−0.0387699	−	0.119322i
$895$	−4.77011	−	22.4416i	−0.159447	−	0.750140i
$896$	−5.13821	−	0.540047i	−0.171655	−	0.0180417i
$897$	−18.1789	−	40.8304i	−0.606975	−	1.36329i
$898$	2.92848	+	13.7774i	0.0977245	+	0.459758i
$899$	−3.93915	+	18.5322i	−0.131378	+	0.618084i
$900$	−13.3539	+	9.70218i	−0.445130	+	0.323406i
$901$	−23.8513			−0.794601
$902$	3.62536	−	1.42481i	0.120711	−	0.0474411i
$903$	−131.754	−	76.0683i	−4.38450	−	2.53139i
$904$	−1.83446	−	2.52492i	−0.0610132	−	0.0839774i
$905$	25.8892	−	8.41190i	0.860585	−	0.279621i
$906$	39.0320	−	35.1446i	1.29675	−	1.16760i
$907$	−38.0776	−	4.00212i	−1.26435	−	0.132888i	−0.551480	−	0.834188i	$-0.685937\pi$
$907$	−38.0776	−	4.00212i	−1.26435	−	0.132888i	−0.712866	+	0.701300i	$0.752603\pi$
$908$	1.22468	−	0.545264i	0.0406426	−	0.0180952i
$909$	−23.5567	−	110.826i	−0.781328	−	3.67586i
$910$	−23.6473	−	21.2921i	−0.783901	−	0.705827i
$911$	3.87549	+	5.33416i	0.128401	+	0.176728i	0.868377	−	0.495904i	$-0.165163\pi$
$911$	3.87549	+	5.33416i	0.128401	+	0.176728i	−0.739976	+	0.672633i	$0.765163\pi$
$912$	−10.7116	−	7.43638i	−0.354697	−	0.246243i
$913$	−1.34277	+	1.68540i	−0.0444391	+	0.0557786i
$914$	−18.1684	+	10.4896i	−0.600959	+	0.346964i
$915$	−20.5548	−	9.15157i	−0.679519	−	0.302542i
$916$	−8.32832	−	1.77024i	−0.275175	−	0.0584903i
$917$	93.2249	−	19.8156i	3.07856	−	0.654367i
$918$	33.2832	−	14.8186i	1.09851	−	0.489088i
$919$	−6.67184	+	9.18300i	−0.220084	+	0.302919i	−0.904755	−	0.425933i	$-0.859946\pi$
$919$	−6.67184	+	9.18300i	−0.220084	+	0.302919i	0.684671	+	0.728852i	$0.259946\pi$
$920$	−1.66826	+	5.13438i	−0.0550009	+	0.169276i
$921$	6.14627	−	28.9159i	0.202526	−	0.952812i
$922$	21.0219	−	2.20950i	0.692321	−	0.0727658i
$923$			12.6492i			0.416353i
$924$	−17.9894	+	48.0012i	−0.591809	+	1.57912i
$925$	14.5419	+	8.39579i	0.478136	+	0.276052i
$926$	3.16826	+	1.41060i	0.104115	+	0.0463552i
$927$	−15.0906	+	70.9958i	−0.495641	+	2.33181i
$928$	−2.87474	+	0.611044i	−0.0943679	+	0.0200585i
$929$	4.92711	−	46.8783i	0.161653	−	1.53803i	−0.549801	−	0.835295i	$-0.685297\pi$
$929$	4.92711	−	46.8783i	0.161653	−	1.53803i	0.711455	−	0.702732i	$-0.248037\pi$
$930$	−23.2757	−	16.9108i	−0.763239	−	0.554526i
$931$	−33.2221	+	79.1494i	−1.08881	+	2.59402i
$932$	7.68369	−	2.49658i	0.251688	−	0.0817783i
$933$	−14.6543	+	32.9140i	−0.479759	+	1.07756i
$934$	−16.0602	−	27.8171i	−0.525507	−	0.910204i
$935$	5.13076	−	19.7758i	0.167794	−	0.646737i
$936$	12.2811	+	21.2714i	0.401419	+	0.695278i
$937$	16.8350	−	1.76943i	0.549975	−	0.0578047i	0.174534	−	0.984651i	$-0.444158\pi$
$937$	16.8350	−	1.76943i	0.549975	−	0.0578047i	0.375441	+	0.926846i	$0.377491\pi$
$938$	−6.84528	−	21.0676i	−0.223506	−	0.687882i
$939$	−76.2461	−	24.7739i	−2.48820	−	0.808465i
$940$	−2.30212	+	1.02497i	−0.0750869	+	0.0334308i
$941$	14.7025	−	6.54596i	0.479287	−	0.213392i	−0.152850	−	0.988249i	$-0.548845\pi$
$941$	14.7025	−	6.54596i	0.479287	−	0.213392i	0.632136	+	0.774857i	$0.282178\pi$
$942$	−37.3759	−	12.1442i	−1.21777	−	0.395678i
$943$	1.31338	+	4.04217i	0.0427695	+	0.131631i
$944$	0.0521616	−	0.00548241i	0.00169772	−	0.000178437i
$945$	34.0029	+	58.8947i	1.10611	+	1.91584i
$946$	32.5871	−	1.96770i	1.05950	−	0.0639754i
$947$	4.12993	+	7.15326i	0.134205	+	0.232450i	0.925293	−	0.379252i	$-0.123819\pi$
$947$	4.12993	+	7.15326i	0.134205	+	0.232450i	−0.791089	+	0.611702i	$0.790485\pi$
$948$	−15.2198	+	34.1842i	−0.494315	+	1.11025i
$949$	7.79337	−	2.53222i	0.252983	−	0.0821993i
$950$	4.68055	−	11.1511i	0.151857	−	0.361789i
$951$	46.2492	+	33.6020i	1.49973	+	1.08962i
$952$	−2.22996	+	21.2166i	−0.0722733	+	0.687635i
$953$	45.1514	−	9.59722i	1.46260	−	0.310885i	0.593222	−	0.805039i	$-0.297855\pi$
$953$	45.1514	−	9.59722i	1.46260	−	0.310885i	0.869374	+	0.494154i	$0.164522\pi$
$954$	−7.14494	+	33.6143i	−0.231326	+	1.08830i
$955$	33.3682	+	14.8565i	1.07977	+	0.480745i
$956$	−7.05493	−	4.07317i	−0.228173	−	0.131736i
$957$	−1.29458	+	29.1312i	−0.0418477	+	0.941679i
$958$			16.5131i			0.533514i
$959$	−41.2473	+	4.33526i	−1.33194	+	0.139993i
$960$	0.927884	−	4.36535i	0.0299473	−	0.140891i
$961$	−3.26272	+	10.0416i	−0.105249	+	0.323923i
$962$	14.6867	−	20.2146i	0.473519	−	0.651744i
$963$	79.6785	−	35.4751i	2.56760	−	1.14317i
$964$	−13.3905	+	2.84623i	−0.431278	+	0.0916710i
$965$	−37.5257	−	7.97634i	−1.20800	−	0.256767i
$966$	−51.0961	−	22.7495i	−1.64399	−	0.731952i
$967$	−3.28627	+	1.89733i	−0.105679	+	0.0610139i	−0.551908	−	0.833905i	$-0.686100\pi$
$967$	−3.28627	+	1.89733i	−0.105679	+	0.0610139i	0.446229	+	0.894919i	$0.352767\pi$
$968$	−2.45780	−	10.7219i	−0.0789968	−	0.344615i
$969$	−30.7062	+	44.2303i	−0.986425	+	1.42088i
$970$	1.27626	+	1.75662i	0.0409783	+	0.0564018i
$971$	−10.1355	−	9.12601i	−0.325262	−	0.292867i	0.490280	−	0.871565i	$-0.336895\pi$
$971$	−10.1355	−	9.12601i	−0.325262	−	0.292867i	−0.815542	+	0.578698i	$0.803561\pi$
$972$	0.187251	+	0.880947i	0.00600608	+	0.0282564i
$973$	61.6922	−	27.4671i	1.97776	−	0.880556i
$974$	−0.403068	−	0.0423642i	−0.0129151	−	0.00135744i
$975$	−25.4649	+	22.9287i	−0.815528	+	0.734305i
$976$	−4.79483	+	1.55794i	−0.153479	+	0.0498683i
$977$	−12.6380	−	17.3947i	−0.404325	−	0.556506i	0.557498	−	0.830179i	$-0.311762\pi$
$977$	−12.6380	−	17.3947i	−0.404325	−	0.556506i	−0.961823	+	0.273673i	$0.911762\pi$
$978$	−20.6591	−	11.9275i	−0.660605	−	0.381401i
$979$	−5.59682	−	3.57168i	−0.178875	−	0.114152i
$980$	−29.3783			−0.938454
$981$	4.68313	−	3.40250i	0.149521	−	0.108633i
$982$	−1.87016	+	8.79839i	−0.0596791	+	0.280768i
$983$	4.34859	+	20.4585i	0.138698	+	0.652524i	0.991480	+	0.130257i	$0.0415803\pi$
$983$	4.34859	+	20.4585i	0.138698	+	0.652524i	−0.852782	+	0.522267i	$0.825086\pi$
$984$	−1.42907	−	3.20975i	−0.0455572	−	0.102323i
$985$	13.9776	+	1.46911i	0.445364	+	0.0468096i
$986$	2.52312	+	11.8703i	0.0803524	+	0.378028i
$987$	−8.06782	−	24.8302i	−0.256802	−	0.790354i
$988$	−15.7744	−	8.66118i	−0.501850	−	0.275549i
$989$			35.6207i			1.13267i
$990$	−26.3336	−	13.1550i	−0.836937	−	0.418093i
$991$	15.6511	−	9.03618i	0.497175	−	0.287044i	−0.230371	−	0.973103i	$-0.573994\pi$
$991$	15.6511	−	9.03618i	0.497175	−	0.287044i	0.727546	+	0.686059i	$0.240661\pi$
$992$	−6.41126	+	0.673851i	−0.203558	+	0.0213948i
$993$	22.8015	−	25.3237i	0.723585	−	0.803623i
$994$	10.5920	+	11.7636i	0.335957	+	0.373119i
$995$	16.7255	+	12.1518i	0.530235	+	0.385238i
$996$	1.57248	+	1.14247i	0.0498260	+	0.0362007i
$997$	37.9223	−	34.1454i	1.20101	−	1.08140i	0.206321	−	0.978484i	$-0.433851\pi$
$997$	37.9223	−	34.1454i	1.20101	−	1.08140i	0.994691	−	0.102911i	$-0.0328156\pi$
$998$	−12.8612	−	2.73374i	−0.407115	−	0.0865349i
$999$	−43.2018	+	31.3879i	−1.36684	+	0.993070i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.s.a.107.10	✓	80
11.7	odd	10		418.2.s.b.183.1	yes	80
19.8	odd	6		418.2.s.b.217.1	yes	80
209.84	even	30	inner	418.2.s.a.293.10	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.s.a.107.10	✓	80	1.1	even	1	trivial
418.2.s.a.293.10	yes	80	209.84	even	30	inner
418.2.s.b.183.1	yes	80	11.7	odd	10
418.2.s.b.217.1	yes	80	19.8	odd	6

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.s (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.913545 - 0.406737i) q^{2} +(2.22316 + 2.00174i) q^{3} +(0.669131 + 0.743145i) q^{4} +(-0.155938 + 1.48365i) q^{5} +(-1.21677 - 2.73292i) q^{6} +(-4.91364 - 1.59654i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.621881 + 5.91681i) q^{9} +O(q^{10})\)	\(q+(-0.913545 - 0.406737i) q^{2} +(2.22316 + 2.00174i) q^{3} +(0.669131 + 0.743145i) q^{4} +(-0.155938 + 1.48365i) q^{5} +(-1.21677 - 2.73292i) q^{6} +(-4.91364 - 1.59654i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.621881 + 5.91681i) q^{9} +(0.745913 - 1.29196i) q^{10} +(-3.31335 - 0.147244i) q^{11} +2.99155i q^{12} +(0.431546 + 4.10589i) q^{13} +(3.83946 + 3.45707i) q^{14} +(-3.31656 + 2.98625i) q^{15} +(-0.104528 + 0.994522i) q^{16} +(4.10657 + 0.431618i) q^{17} +(1.83846 - 5.65821i) q^{18} +(0.997602 + 4.24321i) q^{19} +(-1.20691 + 0.876873i) q^{20} +(-7.72795 - 13.3852i) q^{21} +(2.96701 + 1.48218i) q^{22} +(-1.80940 + 3.13397i) q^{23} +(1.21677 - 2.73292i) q^{24} +(2.71383 + 0.576842i) q^{25} +(1.27578 - 3.92644i) q^{26} +(-5.18619 + 7.13818i) q^{27} +(-2.10141 - 4.71984i) q^{28} +(-1.96655 - 2.18407i) q^{29} +(4.24445 - 1.37911i) q^{30} +(-3.78920 - 5.21539i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-7.07137 - 6.95982i) q^{33} +(-3.57598 - 2.06459i) q^{34} +(3.13494 - 7.04118i) q^{35} +(-3.98092 + 4.42126i) q^{36} +(5.75599 + 1.87023i) q^{37} +(0.814512 - 4.28212i) q^{38} +(-7.25953 + 9.99189i) q^{39} +(1.45923 - 0.310168i) q^{40} +(0.785878 - 0.872806i) q^{41} +(1.61558 + 15.3712i) q^{42} +(8.52452 - 4.92163i) q^{43} +(-2.10764 - 2.56083i) q^{44} -8.87546 q^{45} +(2.92766 - 2.12707i) q^{46} +(1.65228 + 0.351203i) q^{47} +(-2.22316 + 2.00174i) q^{48} +(15.9318 + 11.5752i) q^{49} +(-2.24458 - 1.63078i) q^{50} +(8.26556 + 9.17984i) q^{51} +(-2.76251 + 3.06808i) q^{52} +(-5.74462 + 0.603784i) q^{53} +(7.64119 - 4.41164i) q^{54} +(0.735137 - 4.89291i) q^{55} +5.16651i q^{56} +(-6.27597 + 11.4303i) q^{57} +(0.908189 + 2.79512i) q^{58} +(-0.0109047 - 0.0513028i) q^{59} +(-4.43843 - 0.466498i) q^{60} +(2.05060 + 4.60572i) q^{61} +(1.34032 + 6.30571i) q^{62} +(6.39071 - 30.0659i) q^{63} +(-0.809017 + 0.587785i) q^{64} -6.15901 q^{65} +(3.62920 + 9.23430i) q^{66} +(-3.71315 - 2.14379i) q^{67} +(2.42708 + 3.34058i) q^{68} +(-10.2960 + 3.34536i) q^{69} +(-5.72781 + 5.15735i) q^{70} +(3.04708 + 0.320261i) q^{71} +(5.43504 - 2.41984i) q^{72} +(-0.412672 - 1.94147i) q^{73} +(-4.49767 - 4.04972i) q^{74} +(4.87858 + 6.71479i) q^{75} +(-2.48579 + 3.58062i) q^{76} +(16.0456 + 6.01340i) q^{77} +(10.6960 - 6.17533i) q^{78} +(11.4269 + 5.08758i) q^{79} +(-1.45923 - 0.310168i) q^{80} +(-8.36036 + 1.77705i) q^{81} +(-1.07294 + 0.477702i) q^{82} +(0.381900 - 0.525640i) q^{83} +(4.77613 - 14.6994i) q^{84} +(-1.28074 + 6.02542i) q^{85} +(-9.78935 + 1.02890i) q^{86} -8.79206i q^{87} +(0.883846 + 3.19669i) q^{88} +(1.73365 + 1.00092i) q^{89} +(8.10814 + 3.60998i) q^{90} +(4.43475 - 20.8639i) q^{91} +(-3.53971 + 0.752389i) q^{92} +(2.01586 - 19.1796i) q^{93} +(-1.36659 - 0.992884i) q^{94} +(-6.45101 + 0.818418i) q^{95} +(2.84514 - 0.924441i) q^{96} +(-0.591993 + 1.32964i) q^{97} +(-9.84641 - 17.0545i) q^{98} +(-1.18930 - 19.6960i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 10 q^{2} - 3 q^{3} + 10 q^{4} - 2 q^{5} + 7 q^{6} - 10 q^{7} + 20 q^{8} - 11 q^{9}+O(q^{10}) \) 80 * q - 10 * q^2 - 3 * q^3 + 10 * q^4 - 2 * q^5 + 7 * q^6 - 10 * q^7 + 20 * q^8 - 11 * q^9	\( 80 q - 10 q^{2} - 3 q^{3} + 10 q^{4} - 2 q^{5} + 7 q^{6} - 10 q^{7} + 20 q^{8} - 11 q^{9} + 2 q^{10} - q^{11} + 5 q^{13} - 4 q^{14} - 27 q^{15} + 10 q^{16} - 6 q^{17} - 17 q^{18} - 2 q^{19} + 4 q^{20} + 24 q^{21} - 2 q^{22} - 6 q^{23} - 7 q^{24} - 10 q^{26} - 45 q^{27} + 6 q^{28} - 65 q^{29} + 30 q^{30} + 40 q^{32} + 3 q^{33} + 24 q^{34} - 13 q^{35} - q^{36} + 22 q^{38} - 30 q^{39} - 3 q^{40} - 14 q^{41} - 14 q^{42} + 12 q^{43} + 24 q^{44} - 12 q^{45} - 2 q^{46} - q^{47} + 3 q^{48} + 32 q^{49} + 30 q^{50} - 28 q^{51} - 5 q^{52} - q^{53} - 27 q^{54} - 23 q^{55} + 28 q^{57} - 10 q^{58} + 56 q^{59} - 28 q^{60} + 28 q^{61} + 15 q^{62} + 88 q^{63} - 20 q^{64} + 8 q^{65} - 57 q^{66} - 27 q^{67} - 60 q^{69} + 17 q^{70} + 2 q^{71} + 11 q^{72} - q^{73} + 12 q^{74} - 35 q^{75} - 11 q^{76} - 8 q^{77} - 6 q^{79} + 3 q^{80} + 43 q^{81} - 16 q^{82} - 25 q^{83} + 52 q^{84} - 33 q^{85} - 43 q^{86} - 9 q^{88} - 36 q^{89} + 74 q^{90} + 38 q^{91} - 11 q^{92} + 15 q^{93} - 2 q^{94} - 61 q^{95} - 24 q^{97} - 44 q^{98} + 37 q^{99}+O(q^{100}) \) 80 * q - 10 * q^2 - 3 * q^3 + 10 * q^4 - 2 * q^5 + 7 * q^6 - 10 * q^7 + 20 * q^8 - 11 * q^9 + 2 * q^10 - q^11 + 5 * q^13 - 4 * q^14 - 27 * q^15 + 10 * q^16 - 6 * q^17 - 17 * q^18 - 2 * q^19 + 4 * q^20 + 24 * q^21 - 2 * q^22 - 6 * q^23 - 7 * q^24 - 10 * q^26 - 45 * q^27 + 6 * q^28 - 65 * q^29 + 30 * q^30 + 40 * q^32 + 3 * q^33 + 24 * q^34 - 13 * q^35 - q^36 + 22 * q^38 - 30 * q^39 - 3 * q^40 - 14 * q^41 - 14 * q^42 + 12 * q^43 + 24 * q^44 - 12 * q^45 - 2 * q^46 - q^47 + 3 * q^48 + 32 * q^49 + 30 * q^50 - 28 * q^51 - 5 * q^52 - q^53 - 27 * q^54 - 23 * q^55 + 28 * q^57 - 10 * q^58 + 56 * q^59 - 28 * q^60 + 28 * q^61 + 15 * q^62 + 88 * q^63 - 20 * q^64 + 8 * q^65 - 57 * q^66 - 27 * q^67 - 60 * q^69 + 17 * q^70 + 2 * q^71 + 11 * q^72 - q^73 + 12 * q^74 - 35 * q^75 - 11 * q^76 - 8 * q^77 - 6 * q^79 + 3 * q^80 + 43 * q^81 - 16 * q^82 - 25 * q^83 + 52 * q^84 - 33 * q^85 - 43 * q^86 - 9 * q^88 - 36 * q^89 + 74 * q^90 + 38 * q^91 - 11 * q^92 + 15 * q^93 - 2 * q^94 - 61 * q^95 - 24 * q^97 - 44 * q^98 + 37 * q^99

Introduction

L-functions

Modular forms

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