LMFDB - Embedded newform 418.2.s.a.145.7

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			145.7
Character	$\chi$	$=$	418.145
Dual form			418.2.s.a.369.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.978148 - 0.207912i) q^{2} +(0.411849 - 0.925027i) q^{3} +(0.913545 - 0.406737i) q^{4} +(2.71323 - 3.01335i) q^{5} +(0.210525 - 0.990442i) q^{6} +(-2.18824 + 3.01185i) q^{7} +(0.809017 - 0.587785i) q^{8} +(1.32134 + 1.46749i) q^{9} +O(q^{10})$	\(q+(0.978148 - 0.207912i) q^{2} +(0.411849 - 0.925027i) q^{3} +(0.913545 - 0.406737i) q^{4} +(2.71323 - 3.01335i) q^{5} +(0.210525 - 0.990442i) q^{6} +(-2.18824 + 3.01185i) q^{7} +(0.809017 - 0.587785i) q^{8} +(1.32134 + 1.46749i) q^{9} +(2.02743 - 3.51161i) q^{10} +(2.69834 + 1.92846i) q^{11} -1.01257i q^{12} +(0.177449 + 0.197078i) q^{13} +(-1.51422 + 3.40099i) q^{14} +(-1.66999 - 3.75086i) q^{15} +(0.669131 - 0.743145i) q^{16} +(-4.88808 - 4.40125i) q^{17} +(1.59757 + 1.16070i) q^{18} +(-3.60843 - 2.44525i) q^{19} +(1.25302 - 3.85640i) q^{20} +(1.88482 + 3.26461i) q^{21} +(3.04033 + 1.32530i) q^{22} +(-2.75530 + 4.77232i) q^{23} +(-0.210525 - 0.990442i) q^{24} +(-1.19600 - 11.3792i) q^{25} +(0.214546 + 0.155877i) q^{26} +(4.79069 - 1.55659i) q^{27} +(-0.774024 + 3.64150i) q^{28} +(-3.14711 + 1.40118i) q^{29} +(-2.41334 - 3.32168i) q^{30} +(-4.09755 - 1.33137i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.89519 - 1.70181i) q^{33} +(-5.69633 - 3.28878i) q^{34} +(3.13856 + 14.7658i) q^{35} +(1.80398 + 0.803185i) q^{36} +(-3.71793 + 5.11729i) q^{37} +(-4.03797 - 1.64158i) q^{38} +(0.255384 - 0.0829794i) q^{39} +(0.423848 - 4.03265i) q^{40} +(8.42408 + 3.75064i) q^{41} +(2.52238 + 2.80139i) q^{42} +(-5.37762 + 3.10477i) q^{43} +(3.24943 + 0.664221i) q^{44} +8.00715 q^{45} +(-1.70287 + 5.24089i) q^{46} +(0.408211 + 3.88387i) q^{47} +(-0.411849 - 0.925027i) q^{48} +(-2.11974 - 6.52389i) q^{49} +(-3.53574 - 10.8819i) q^{50} +(-6.08442 + 2.70896i) q^{51} +(0.242267 + 0.107864i) q^{52} +(5.97857 - 5.38313i) q^{53} +(4.36237 - 2.51861i) q^{54} +(13.1323 - 2.89869i) q^{55} +3.72285i q^{56} +(-3.74805 + 2.33082i) q^{57} +(-2.78702 + 2.02489i) q^{58} +(7.69304 + 0.808571i) q^{59} +(-3.05122 - 2.74733i) q^{60} +(-0.831862 + 3.91360i) q^{61} +(-4.28482 - 0.450353i) q^{62} +(-7.31126 + 0.768444i) q^{63} +(0.309017 - 0.951057i) q^{64} +1.07533 q^{65} +(2.47809 - 2.26656i) q^{66} +(-2.05096 - 1.18412i) q^{67} +(-6.25563 - 2.03258i) q^{68} +(3.27976 + 4.51420i) q^{69} +(6.13995 + 13.7906i) q^{70} +(4.48434 + 4.03772i) q^{71} +(1.93155 + 0.410564i) q^{72} +(0.0391678 + 0.00411670i) q^{73} +(-2.57274 + 5.77847i) q^{74} +(-11.0187 - 3.58018i) q^{75} +(-4.29104 - 0.766166i) q^{76} +(-11.7128 + 3.90707i) q^{77} +(0.232551 - 0.134264i) q^{78} +(9.58320 - 2.03697i) q^{79} +(-0.423848 - 4.03265i) q^{80} +(-0.0860870 + 0.819063i) q^{81} +(9.01980 + 1.91722i) q^{82} +(-8.58249 + 2.78862i) q^{83} +(3.04970 + 2.21574i) q^{84} +(-26.5250 + 2.78789i) q^{85} +(-4.61458 + 4.15499i) q^{86} +3.48824i q^{87} +(3.31652 - 0.0258886i) q^{88} +(-8.93646 - 5.15947i) q^{89} +(7.83218 - 1.66478i) q^{90} +(-0.981870 + 0.103199i) q^{91} +(-0.576014 + 5.48041i) q^{92} +(-2.91913 + 3.24202i) q^{93} +(1.20679 + 3.71413i) q^{94} +(-17.1589 + 4.23893i) q^{95} +(-0.595173 - 0.819185i) q^{96} +(-1.80205 - 8.47797i) q^{97} +(-3.42981 - 5.94061i) q^{98} +(0.735415 + 6.50794i) 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 $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	0.978148	−	0.207912i	0.691655	−	0.147016i
$2$	0.978148	−	0.207912i	0.691655	−	0.147016i
$3$	0.411849	−	0.925027i	0.237781	−	0.534065i	−0.754756	−	0.656005i	$-0.772245\pi$
$3$	0.411849	−	0.925027i	0.237781	−	0.534065i	0.992537	+	0.121940i	$0.0389116\pi$
$4$	0.913545	−	0.406737i	0.456773	−	0.203368i
$5$	2.71323	−	3.01335i	1.21339	−	1.34761i	0.293248	−	0.956037i	$-0.405264\pi$
$5$	2.71323	−	3.01335i	1.21339	−	1.34761i	0.920147	−	0.391574i	$-0.128069\pi$
$6$	0.210525	−	0.990442i	0.0859464	−	0.404346i
$7$	−2.18824	+	3.01185i	−0.827076	+	1.13837i	0.161384	+	0.986892i	$0.448404\pi$
$7$	−2.18824	+	3.01185i	−0.827076	+	1.13837i	−0.988460	+	0.151481i	$0.951596\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	1.32134	+	1.46749i	0.440445	+	0.489164i
$10$	2.02743	−	3.51161i	0.641130	−	1.11047i
$11$	2.69834	+	1.92846i	0.813580	+	0.581452i
$11$	2.69834	+	1.92846i	0.813580	+	0.581452i
$12$		−	1.01257i		−	0.292303i
$13$	0.177449	+	0.197078i	0.0492156	+	0.0546595i	0.767250	−	0.641348i	$-0.221625\pi$
$13$	0.177449	+	0.197078i	0.0492156	+	0.0546595i	−0.718034	+	0.696008i	$0.754958\pi$
$14$	−1.51422	+	3.40099i	−0.404692	+	0.908954i
$15$	−1.66999	−	3.75086i	−0.431189	−	0.968467i
$16$	0.669131	−	0.743145i	0.167283	−	0.185786i
$17$	−4.88808	−	4.40125i	−1.18553	−	1.06746i	−0.996336	−	0.0855197i	$-0.972745\pi$
$17$	−4.88808	−	4.40125i	−1.18553	−	1.06746i	−0.189197	−	0.981939i	$-0.560588\pi$
$18$	1.59757	+	1.16070i	0.376551	+	0.273580i
$19$	−3.60843	−	2.44525i	−0.827830	−	0.560979i
$19$	−3.60843	−	2.44525i	−0.827830	−	0.560979i
$20$	1.25302	−	3.85640i	0.280184	−	0.862318i
$21$	1.88482	+	3.26461i	0.411302	+	0.712395i
$22$	3.04033	+	1.32530i	0.648199	+	0.282555i
$23$	−2.75530	+	4.77232i	−0.574519	+	0.995097i	0.421574	+	0.906794i	$0.361478\pi$
$23$	−2.75530	+	4.77232i	−0.574519	+	0.995097i	−0.996094	+	0.0883029i	$0.971856\pi$
$24$	−0.210525	−	0.990442i	−0.0429732	−	0.202173i
$25$	−1.19600	−	11.3792i	−0.239201	−	2.27584i
$26$	0.214546	+	0.155877i	0.0420760	+	0.0305700i
$27$	4.79069	−	1.55659i	0.921969	−	0.299566i
$28$	−0.774024	+	3.64150i	−0.146277	+	0.688178i
$29$	−3.14711	+	1.40118i	−0.584404	+	0.260193i	−0.677571	−	0.735457i	$-0.736967\pi$
$29$	−3.14711	+	1.40118i	−0.584404	+	0.260193i	0.0931675	+	0.995650i	$0.470301\pi$
$30$	−2.41334	−	3.32168i	−0.440614	−	0.606453i
$31$	−4.09755	−	1.33137i	−0.735942	−	0.239122i	−0.0830206	−	0.996548i	$-0.526457\pi$
$31$	−4.09755	−	1.33137i	−0.735942	−	0.239122i	−0.652921	+	0.757426i	$0.726457\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	2.89519	−	1.70181i	0.503987	−	0.296246i
$34$	−5.69633	−	3.28878i	−0.976913	−	0.564021i
$35$	3.13856	+	14.7658i	0.530514	+	2.49587i
$36$	1.80398	+	0.803185i	0.300664	+	0.133864i
$37$	−3.71793	+	5.11729i	−0.611224	+	0.841277i	−0.996677	−	0.0814498i	$-0.974045\pi$
$37$	−3.71793	+	5.11729i	−0.611224	+	0.841277i	0.385454	+	0.922727i	$0.374045\pi$
$38$	−4.03797	−	1.64158i	−0.655046	−	0.266299i
$39$	0.255384	−	0.0829794i	0.0408942	−	0.0132873i
$40$	0.423848	−	4.03265i	0.0670163	−	0.637618i
$41$	8.42408	+	3.75064i	1.31562	+	0.585752i	0.940049	−	0.341041i	$-0.110779\pi$
$41$	8.42408	+	3.75064i	1.31562	+	0.585752i	0.375573	+	0.926793i	$0.377446\pi$
$42$	2.52238	+	2.80139i	0.389212	+	0.432264i
$43$	−5.37762	+	3.10477i	−0.820079	+	0.473473i	−0.850444	−	0.526066i	$-0.823666\pi$
$43$	−5.37762	+	3.10477i	−0.820079	+	0.473473i	0.0303649	+	0.999539i	$0.490333\pi$
$44$	3.24943	+	0.664221i	0.489870	+	0.100135i
$45$	8.00715			1.19364
$46$	−1.70287	+	5.24089i	−0.251074	+	0.772727i
$47$	0.408211	+	3.88387i	0.0595437	+	0.566521i	0.983101	+	0.183061i	$0.0586007\pi$
$47$	0.408211	+	3.88387i	0.0595437	+	0.566521i	−0.923558	+	0.383459i	$0.874733\pi$
$48$	−0.411849	−	0.925027i	−0.0594452	−	0.133516i
$49$	−2.11974	−	6.52389i	−0.302820	−	0.931984i
$50$	−3.53574	−	10.8819i	−0.500029	−	1.53893i
$51$	−6.08442	+	2.70896i	−0.851989	+	0.379330i
$52$	0.242267	+	0.107864i	0.0335964	+	0.0149581i
$53$	5.97857	−	5.38313i	0.821219	−	0.739429i	−0.147106	−	0.989121i	$-0.546996\pi$
$53$	5.97857	−	5.38313i	0.821219	−	0.739429i	0.968325	+	0.249692i	$0.0803292\pi$
$54$	4.36237	−	2.51861i	0.593643	−	0.342740i
$55$	13.1323	−	2.89869i	1.77077	−	0.390859i
$56$			3.72285i			0.497487i
$57$	−3.74805	+	2.33082i	−0.496441	+	0.308725i
$58$	−2.78702	+	2.02489i	−0.365953	+	0.265881i
$59$	7.69304	+	0.808571i	1.00155	+	0.105267i	0.591084	−	0.806610i	$-0.298700\pi$
$59$	7.69304	+	0.808571i	1.00155	+	0.105267i	0.410464	+	0.911877i	$0.365367\pi$
$60$	−3.05122	−	2.74733i	−0.393911	−	0.354679i
$61$	−0.831862	+	3.91360i	−0.106509	+	0.501086i	0.892262	+	0.451518i	$0.149118\pi$
$61$	−0.831862	+	3.91360i	−0.106509	+	0.501086i	−0.998771	+	0.0495671i	$0.984216\pi$
$62$	−4.28482	−	0.450353i	−0.544172	−	0.0571948i
$63$	−7.31126	+	0.768444i	−0.921132	+	0.0968149i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	1.07533			0.133378
$66$	2.47809	−	2.26656i	0.305032	−	0.278994i
$67$	−2.05096	−	1.18412i	−0.250564	−	0.144663i	0.369458	−	0.929247i	$-0.379543\pi$
$67$	−2.05096	−	1.18412i	−0.250564	−	0.144663i	−0.620023	+	0.784584i	$0.712877\pi$
$68$	−6.25563	−	2.03258i	−0.758607	−	0.246486i
$69$	3.27976	+	4.51420i	0.394836	+	0.543446i
$70$	6.13995	+	13.7906i	0.733865	+	1.64829i
$71$	4.48434	+	4.03772i	0.532193	+	0.479189i	0.890861	−	0.454276i	$-0.150102\pi$
$71$	4.48434	+	4.03772i	0.532193	+	0.479189i	−0.358667	+	0.933465i	$0.616769\pi$
$72$	1.93155	+	0.410564i	0.227636	+	0.0483855i
$73$	0.0391678	+	0.00411670i	0.00458425	+	0.000481824i	0.106820	−	0.994278i	$-0.465933\pi$
$73$	0.0391678	+	0.00411670i	0.00458425	+	0.000481824i	−0.102236	+	0.994760i	$0.532600\pi$
$74$	−2.57274	+	5.77847i	−0.299075	+	0.671733i
$75$	−11.0187	−	3.58018i	−1.27233	−	0.413404i
$76$	−4.29104	−	0.766166i	−0.492216	−	0.0878852i
$77$	−11.7128	+	3.90707i	−1.33480	+	0.445252i
$78$	0.232551	−	0.134264i	0.0263313	−	0.0152024i
$79$	9.58320	−	2.03697i	1.07819	−	0.229177i	0.365613	−	0.930767i	$-0.380859\pi$
$79$	9.58320	−	2.03697i	1.07819	−	0.229177i	0.712581	+	0.701590i	$0.247526\pi$
$80$	−0.423848	−	4.03265i	−0.0473877	−	0.450864i
$81$	−0.0860870	+	0.819063i	−0.00956522	+	0.0910070i
$82$	9.01980	+	1.91722i	0.996070	+	0.211721i
$83$	−8.58249	+	2.78862i	−0.942051	+	0.306091i	−0.739481	−	0.673177i	$-0.764929\pi$
$83$	−8.58249	+	2.78862i	−0.942051	+	0.306091i	−0.202570	+	0.979268i	$0.564929\pi$
$84$	3.04970	+	2.21574i	0.332750	+	0.241757i
$85$	−26.5250	+	2.78789i	−2.87704	+	0.302389i
$86$	−4.61458	+	4.15499i	−0.497603	+	0.448044i
$87$			3.48824i			0.373979i
$88$	3.31652	−	0.0258886i	0.353543	−	0.00275973i
$89$	−8.93646	−	5.15947i	−0.947263	−	0.546903i	−0.0550335	−	0.998485i	$-0.517527\pi$
$89$	−8.93646	−	5.15947i	−0.947263	−	0.546903i	−0.892230	+	0.451582i	$0.850860\pi$
$90$	7.83218	−	1.66478i	0.825584	−	0.175483i
$91$	−0.981870	+	0.103199i	−0.102928	+	0.0108182i
$92$	−0.576014	+	5.48041i	−0.0600536	+	0.571372i
$93$	−2.91913	+	3.24202i	−0.302700	+	0.336182i
$94$	1.20679	+	3.71413i	0.124471	+	0.383083i
$95$	−17.1589	+	4.23893i	−1.76047	+	0.434905i
$96$	−0.595173	−	0.819185i	−0.0607446	−	0.0836077i
$97$	−1.80205	−	8.47797i	−0.182970	−	0.860807i	−0.969850	−	0.243701i	$-0.921638\pi$
$97$	−1.80205	−	8.47797i	−0.182970	−	0.860807i	0.786880	−	0.617106i	$-0.211695\pi$
$98$	−3.42981	−	5.94061i	−0.346463	−	0.600092i
$99$	0.735415	+	6.50794i	0.0739120	+	0.654072i
$100$	−5.72095	−	9.90898i	−0.572095	−	0.990898i
$101$	0.846402	−	0.762104i	0.0842202	−	0.0758322i	−0.625945	−	0.779867i	$-0.715287\pi$
$101$	0.846402	−	0.762104i	0.0842202	−	0.0758322i	0.710166	+	0.704035i	$0.248620\pi$
$102$	−5.38824	+	3.91478i	−0.533515	+	0.387621i
$103$	10.7599	−	14.8097i	1.06020	−	1.45924i	0.180585	−	0.983559i	$-0.442201\pi$
$103$	10.7599	−	14.8097i	1.06020	−	1.45924i	0.879617	−	0.475683i	$-0.157799\pi$
$104$	0.259399	+	0.0551369i	0.0254362	+	0.00540662i
$105$	14.9514	+	3.17801i	1.45910	+	0.310142i
$106$	4.72871	−	6.50851i	0.459293	−	0.632162i
$107$	−9.42929	+	6.85078i	−0.911564	+	0.662290i	−0.941410	−	0.337264i	$-0.890498\pi$
$107$	−9.42929	+	6.85078i	−0.911564	+	0.662290i	0.0298458	+	0.999555i	$0.490498\pi$
$108$	3.74339	−	3.37056i	0.360208	−	0.324333i
$109$	2.77499	+	4.80643i	0.265796	+	0.460373i	0.967772	−	0.251828i	$-0.0810318\pi$
$109$	2.77499	+	4.80643i	0.265796	+	0.460373i	−0.701976	+	0.712201i	$0.747699\pi$
$110$	12.2427	−	5.56571i	1.16730	−	0.530670i
$111$	3.20241	+	5.54674i	0.303959	+	0.526473i
$112$	0.774024	+	3.64150i	0.0731384	+	0.344089i
$113$	−1.92367	−	2.64770i	−0.180963	−	0.249075i	0.708892	−	0.705317i	$-0.249195\pi$
$113$	−1.92367	−	2.64770i	−0.180963	−	0.249075i	−0.889856	+	0.456242i	$0.849195\pi$
$114$	−3.18154	+	3.05915i	−0.297978	+	0.286516i
$115$	6.90489	+	21.2511i	0.643885	+	1.98167i
$116$	−2.30512	+	2.56009i	−0.214025	+	0.237698i
$117$	−0.0547395	+	0.520811i	−0.00506066	+	0.0481490i
$118$	7.69304	−	0.808571i	0.708202	−	0.0744350i
$119$	23.9522	−	5.09119i	2.19569	−	0.466709i
$120$	−3.55575	−	2.05291i	−0.324594	−	0.187404i
$121$	3.56209	+	10.4073i	0.323826	+	0.946117i
$122$			4.00104i			0.362237i
$123$	6.93890	−	6.24781i	0.625659	−	0.563346i
$124$	−4.28482	+	0.450353i	−0.384788	+	0.0404428i
$125$	−21.1323	−	15.3535i	−1.89013	−	1.37326i
$126$	−6.99172	+	2.27175i	−0.622872	+	0.202383i
$127$	14.1152	+	3.00028i	1.25252	+	0.266232i	0.785972	−	0.618262i	$-0.212163\pi$
$127$	14.1152	+	3.00028i	1.25252	+	0.266232i	0.466551	+	0.884494i	$0.345496\pi$
$128$	0.104528	−	0.994522i	0.00923910	−	0.0879041i
$129$	0.657231	+	6.25314i	0.0578660	+	0.550558i
$130$	1.05183	−	0.223573i	0.0922513	−	0.0196086i
$131$	8.23027	−	4.75175i	0.719082	−	0.415162i	−0.0953329	−	0.995445i	$-0.530392\pi$
$131$	8.23027	−	4.75175i	0.719082	−	0.415162i	0.814415	+	0.580283i	$0.197058\pi$
$132$	1.95270	−	2.73226i	0.169960	−	0.237812i
$133$	15.2608	−	5.51726i	1.32328	−	0.478407i
$134$	−2.25233	−	0.731827i	−0.194572	−	0.0632202i
$135$	8.30770	−	18.6594i	0.715013	−	1.60595i
$136$	−6.54153	−	0.687542i	−0.560931	−	0.0589562i
$137$	−6.65234	−	1.41400i	−0.568347	−	0.120806i	−0.0852296	−	0.996361i	$-0.527162\pi$
$137$	−6.65234	−	1.41400i	−0.568347	−	0.120806i	−0.483118	+	0.875555i	$0.660496\pi$
$138$	4.14664	+	3.73365i	0.352986	+	0.317830i
$139$	−7.49318	−	16.8300i	−0.635563	−	1.42750i	−0.887981	−	0.459880i	$-0.847892\pi$
$139$	−7.49318	−	16.8300i	−0.635563	−	1.42750i	0.252417	−	0.967618i	$-0.418774\pi$
$140$	8.87300	+	12.2126i	0.749905	+	1.03216i
$141$	3.76081	+	1.22196i	0.316717	+	0.102908i
$142$	5.22584	+	3.01714i	0.438542	+	0.253193i
$143$	0.0987630	+	0.873987i	0.00825898	+	0.0730864i
$144$	1.97470			0.164559
$145$	−4.31658	+	13.2851i	−0.358473	+	1.10327i
$146$	0.0391678	−	0.00411670i	0.00324155	−	0.000340701i
$147$	−6.90779	−	0.726038i	−0.569745	−	0.0598826i
$148$	−1.31511	+	6.18710i	−0.108101	+	0.508576i
$149$	−3.07996	−	2.77320i	−0.252320	−	0.227190i	0.533258	−	0.845953i	$-0.320968\pi$
$149$	−3.07996	−	2.77320i	−0.252320	−	0.227190i	−0.785578	+	0.618763i	$0.787634\pi$
$150$	−11.5222	−	1.21104i	−0.940787	−	0.0988807i
$151$	2.91865	−	2.12052i	0.237516	−	0.172566i	−0.462660	−	0.886536i	$-0.653105\pi$
$151$	2.91865	−	2.12052i	0.237516	−	0.172566i	0.700176	+	0.713970i	$0.253105\pi$
$152$	−4.35656	+	0.142733i	−0.353364	+	0.0115772i
$153$		−	12.9887i		−	1.05008i
$154$	−10.6446	+	6.25693i	−0.857763	+	0.504198i
$155$	−15.1295	+	8.73502i	−1.21523	+	0.701614i
$156$	0.199555	−	0.179680i	0.0159772	−	0.0143859i
$157$	0.572794	+	0.255025i	0.0457140	+	0.0203532i	0.429466	−	0.903083i	$-0.358702\pi$
$157$	0.572794	+	0.255025i	0.0457140	+	0.0203532i	−0.383752	+	0.923436i	$0.625368\pi$
$158$	8.95027	−	3.98492i	0.712046	−	0.317023i
$159$	−2.51727	−	7.74737i	−0.199633	−	0.614407i
$160$	−1.25302	−	3.85640i	−0.0990600	−	0.304875i
$161$	−8.34425	−	18.7415i	−0.657619	−	1.47704i
$162$	0.0860870	+	0.819063i	0.00676363	+	0.0643516i
$163$	−4.70096	+	14.4681i	−0.368207	+	1.13323i	0.579741	+	0.814801i	$0.303154\pi$
$163$	−4.70096	+	14.4681i	−0.368207	+	1.13323i	−0.947948	+	0.318425i	$0.896846\pi$
$164$	9.22131			0.720063
$165$	2.72718	−	13.3416i	0.212310	−	1.03864i
$166$	−7.81516	+	4.51208i	−0.606574	+	0.350206i
$167$	−11.4039	−	12.6654i	−0.882464	−	0.980076i	0.117451	−	0.993079i	$-0.462528\pi$
$167$	−11.4039	−	12.6654i	−0.882464	−	0.980076i	−0.999915	+	0.0130030i	$0.995861\pi$
$168$	3.44374	+	1.53325i	0.265690	+	0.118293i
$169$	1.35152	−	12.8588i	0.103963	−	0.989142i
$170$	−25.3657	+	8.24182i	−1.94546	+	0.632119i
$171$	−1.17956	−	8.52633i	−0.0902034	−	0.652025i
$172$	−3.64987	+	5.02362i	−0.278300	+	0.383047i
$173$	9.41469	+	4.19169i	0.715786	+	0.318688i	0.732118	−	0.681178i	$-0.238532\pi$
$173$	9.41469	+	4.19169i	0.715786	+	0.318688i	−0.0163319	+	0.999867i	$0.505199\pi$
$174$	0.725246	+	3.41201i	0.0549807	+	0.258664i
$175$	36.8896	+	21.2982i	2.78859	+	1.61000i
$176$	3.23867	−	0.714867i	0.244124	−	0.0538851i
$177$	3.91632	−	6.78326i	0.294369	−	0.509861i
$178$	−9.81389	−	3.18873i	−0.735582	−	0.239005i
$179$	−6.15109	−	8.46625i	−0.459754	−	0.632797i	0.514704	−	0.857368i	$-0.327902\pi$
$179$	−6.15109	−	8.46625i	−0.459754	−	0.632797i	−0.974458	+	0.224571i	$0.927902\pi$
$180$	7.31490	−	3.25680i	0.545220	−	0.242748i
$181$	−5.14048	+	24.1841i	−0.382089	+	1.79759i	0.194887	+	0.980826i	$0.437566\pi$
$181$	−5.14048	+	24.1841i	−0.382089	+	1.79759i	−0.576976	+	0.816761i	$0.695767\pi$
$182$	−0.938957	+	0.305086i	−0.0696001	+	0.0226145i
$183$	3.27759	+	2.38131i	0.242286	+	0.176031i
$184$	0.576014	+	5.48041i	0.0424643	+	0.404021i
$185$	5.33258	+	25.0878i	0.392059	+	1.84449i
$186$	−2.18129	+	3.77810i	−0.159940	+	0.277024i
$187$	−4.70208	−	21.3025i	−0.343850	−	1.55779i
$188$	1.95263	+	3.38206i	0.142410	+	0.246662i
$189$	−5.79495	+	17.8350i	−0.421521	+	1.29731i
$190$	−15.9026	+	7.71383i	−1.15370	+	0.559620i
$191$	−6.23259	−	4.52824i	−0.450974	−	0.327652i	0.339006	−	0.940784i	$-0.389909\pi$
$191$	−6.23259	−	4.52824i	−0.450974	−	0.327652i	−0.789980	+	0.613132i	$0.789909\pi$
$192$	−0.752485	−	0.677541i	−0.0543059	−	0.0488973i
$193$	2.35928	−	2.62025i	0.169825	−	0.188609i	−0.652225	−	0.758026i	$-0.726164\pi$
$193$	2.35928	−	2.62025i	0.169825	−	0.188609i	0.822049	+	0.569416i	$0.192831\pi$
$194$	−3.52534	−	7.91803i	−0.253104	−	0.568482i
$195$	0.442871	−	0.994705i	0.0317147	−	0.0712323i
$196$	−4.58998	−	5.09769i	−0.327856	−	0.364121i
$197$		−	20.3857i		−	1.45242i	−0.687474	−	0.726209i	$-0.741280\pi$
$197$		−	20.3857i		−	1.45242i	0.687474	−	0.726209i	$-0.258720\pi$
$198$	2.07242	+	6.21282i	0.147281	+	0.441526i
$199$	−4.09617	+	7.09477i	−0.290370	+	0.502935i	−0.973897	−	0.226990i	$-0.927112\pi$
$199$	−4.09617	+	7.09477i	−0.290370	+	0.502935i	0.683527	+	0.729925i	$0.260445\pi$
$200$	−7.65613	−	8.50299i	−0.541370	−	0.601252i
$201$	−1.94003	+	1.40951i	−0.136839	+	0.0994193i
$202$	0.669456	−	0.921427i	0.0471028	−	0.0648314i
$203$	2.66647	−	12.5447i	0.187149	−	0.880469i
$204$	−4.45656	+	4.94951i	−0.312022	+	0.346535i
$205$	34.1585	−	15.2083i	2.38573	−	1.06220i
$206$	7.44563	−	16.7232i	0.518762	−	1.16516i
$207$	−10.6440	+	2.26245i	−0.739810	+	0.157251i
$208$	0.265194			0.0183879
$209$	−5.02121	−	13.5568i	−0.347324	−	0.937745i
$210$	15.2854			1.05479
$211$	−0.586899	+	0.124749i	−0.0404038	+	0.00858809i	−0.228069	−	0.973645i	$-0.573241\pi$
$211$	−0.586899	+	0.124749i	−0.0404038	+	0.00858809i	0.187665	+	0.982233i	$0.439908\pi$
$212$	3.27218	−	7.34943i	0.224734	−	0.504761i
$213$	5.58187	−	2.48521i	0.382463	−	0.170284i
$214$	−7.79888	+	8.66154i	−0.533121	+	0.592090i
$215$	−5.23497	+	24.6286i	−0.357022	+	1.67966i
$216$	2.96081	−	4.07520i	0.201458	−	0.277283i
$217$	12.9763	−	9.42784i	0.880890	−	0.640004i
$218$	3.71367	+	4.12444i	0.251521	+	0.279343i
$219$	0.0199393	−	0.0345358i	0.00134737	−	0.00233372i
$220$	10.8180	−	7.98949i	0.729349	−	0.538651i
$221$		−	1.74433i		−	0.117336i
$222$	4.28566	+	4.75971i	0.287635	+	0.319451i
$223$	−7.12613	+	16.0055i	−0.477201	+	1.07181i	0.501245	+	0.865305i	$0.332876\pi$
$223$	−7.12613	+	16.0055i	−0.477201	+	1.07181i	−0.978446	+	0.206505i	$0.933791\pi$
$224$	1.51422	+	3.40099i	0.101173	+	0.227238i
$225$	15.1186	−	16.7909i	1.00791	−	1.11939i
$226$	−2.43212	−	2.18989i	−0.161782	−	0.145669i
$227$	0.945380	+	0.686859i	0.0627471	+	0.0455884i	0.618717	−	0.785614i	$-0.287653\pi$
$227$	0.945380	+	0.686859i	0.0627471	+	0.0455884i	−0.555970	+	0.831203i	$0.687653\pi$
$228$	−2.47598	+	3.65378i	−0.163976	+	0.241978i
$229$	4.00714	−	12.3327i	0.264799	−	0.814969i	−0.726940	−	0.686701i	$-0.759058\pi$
$229$	4.00714	−	12.3327i	0.264799	−	0.814969i	0.991740	−	0.128268i	$-0.0409418\pi$
$230$	11.1724	+	19.3511i	0.736683	+	1.27597i
$231$	−1.20977	+	12.4438i	−0.0795970	+	0.818743i
$232$	−1.72247	+	2.98341i	−0.113086	+	0.195870i
$233$	3.13214	+	14.7356i	0.205194	+	0.965360i	0.953357	+	0.301845i	$0.0976027\pi$
$233$	3.13214	+	14.7356i	0.205194	+	0.965360i	−0.748163	+	0.663515i	$0.769064\pi$
$234$	0.0547395	+	0.520811i	0.00357843	+	0.0340465i
$235$	12.8110	+	9.30776i	0.835699	+	0.607171i
$236$	7.35682	−	2.39037i	0.478888	−	0.155600i
$237$	2.06257	−	9.70365i	0.133979	−	0.630320i
$238$	22.3702	−	9.95987i	1.45005	−	0.645603i
$239$	2.61759	+	3.60281i	0.169318	+	0.233046i	0.885241	−	0.465134i	$-0.153994\pi$
$239$	2.61759	+	3.60281i	0.169318	+	0.233046i	−0.715923	+	0.698180i	$0.753994\pi$
$240$	−3.90487	−	1.26877i	−0.252058	−	0.0818987i
$241$	12.3647	−	21.4164i	0.796483	−	1.37955i	−0.125411	−	0.992105i	$-0.540025\pi$
$241$	12.3647	−	21.4164i	0.796483	−	1.37955i	0.921893	−	0.387444i	$-0.126642\pi$
$242$	5.64804	+	9.43926i	0.363070	+	0.606779i
$243$	13.8093	+	7.97281i	0.885867	+	0.511456i
$244$	0.831862	+	3.91360i	0.0532545	+	0.250543i
$245$	−25.4101	−	11.3133i	−1.62339	−	0.722780i
$246$	5.48827	−	7.55396i	0.349919	−	0.481623i
$247$	−0.158410	−	1.14505i	−0.0100794	−	0.0728577i
$248$	−4.09755	+	1.33137i	−0.260195	+	0.0845424i
$249$	−0.955138	+	9.08753i	−0.0605294	+	0.575899i
$250$	−23.8627	−	10.6244i	−1.50921	−	0.671944i
$251$	5.08837	+	5.65120i	0.321175	+	0.356701i	0.882013	−	0.471224i	$-0.156188\pi$
$251$	5.08837	+	5.65120i	0.321175	+	0.356701i	−0.560839	+	0.827925i	$0.689521\pi$
$252$	−6.36661	+	3.67577i	−0.401059	+	0.231552i
$253$	−16.6380	+	7.56386i	−1.04602	+	0.475536i
$254$	14.4306			0.905454
$255$	−8.34541	+	25.6845i	−0.522610	+	1.60843i
$256$	−0.104528	−	0.994522i	−0.00653303	−	0.0621576i
$257$	−9.55890	−	21.4696i	−0.596268	−	1.33924i	−0.919563	−	0.392941i	$-0.871457\pi$
$257$	−9.55890	−	21.4696i	−0.596268	−	1.33924i	0.323296	−	0.946298i	$-0.395209\pi$
$258$	1.94297	+	5.97984i	0.120964	+	0.372289i
$259$	−7.27680	−	22.3957i	−0.452158	−	1.39160i
$260$	0.982358	−	0.437374i	0.0609233	−	0.0271248i
$261$	−6.21462	−	2.76692i	−0.384675	−	0.171268i
$262$	7.06247	−	6.35908i	0.436321	−	0.392865i
$263$	0.232007	−	0.133950i	0.0143062	−	0.00825968i	−0.492830	−	0.870126i	$-0.664037\pi$
$263$	0.232007	−	0.133950i	0.0143062	−	0.00825968i	0.507136	+	0.861866i	$0.330704\pi$
$264$	1.34196	−	3.07854i	0.0825918	−	0.189471i
$265$		−	32.6212i		−	2.00390i
$266$	13.7802	−	8.56960i	0.844920	−	0.525436i
$267$	−8.45312	+	6.14155i	−0.517323	+	0.375857i
$268$	−2.35527	−	0.247549i	−0.143871	−	0.0151214i
$269$	4.81148	+	4.33227i	0.293361	+	0.264143i	0.802648	−	0.596454i	$-0.203424\pi$
$269$	4.81148	+	4.33227i	0.293361	+	0.264143i	−0.509287	+	0.860597i	$0.670091\pi$
$270$	4.24665	−	19.9789i	0.258443	−	1.21588i
$271$	−12.8322	−	1.34872i	−0.779501	−	0.0819289i	−0.293583	−	0.955933i	$-0.594848\pi$
$271$	−12.8322	−	1.34872i	−0.779501	−	0.0819289i	−0.485918	+	0.874005i	$0.661514\pi$
$272$	−6.54153	+	0.687542i	−0.396638	+	0.0416884i
$273$	−0.308920	+	0.950758i	−0.0186967	+	0.0575425i
$274$	−6.80095			−0.410861
$275$	18.7171	−	33.0115i	1.12869	−	1.99067i
$276$	4.83230	+	2.78993i	0.290870	+	0.167934i
$277$	19.1596	+	6.22532i	1.15119	+	0.374043i	0.821590	−	0.570079i	$-0.193087\pi$
$277$	19.1596	+	6.22532i	1.15119	+	0.374043i	0.329596	+	0.944122i	$0.393087\pi$
$278$	−10.8286	−	14.9043i	−0.649455	−	0.893899i
$279$	−3.46046	−	7.77231i	−0.207172	−	0.465316i
$280$	11.2183	+	10.1010i	0.670419	+	0.603648i
$281$	24.0197	+	5.10554i	1.43289	+	0.304571i	0.857997	−	0.513655i	$-0.171709\pi$
$281$	24.0197	+	5.10554i	1.43289	+	0.304571i	0.574897	+	0.818226i	$0.305042\pi$
$282$	3.93268	+	0.413342i	0.234188	+	0.0246141i
$283$	−4.30477	+	9.66868i	−0.255892	+	0.574743i	−0.995116	−	0.0987171i	$-0.968526\pi$
$283$	−4.30477	+	9.66868i	−0.255892	+	0.574743i	0.739223	+	0.673460i	$0.235193\pi$
$284$	5.73894	+	1.86469i	0.340543	+	0.110649i
$285$	−3.14574	+	17.6182i	−0.186338	+	1.04361i
$286$	0.278317	+	0.834354i	0.0164572	+	0.0493364i
$287$	−29.7303	+	17.1648i	−1.75492	+	1.01320i
$288$	1.93155	−	0.410564i	0.113818	−	0.0241927i
$289$	2.74536	+	26.1204i	0.161492	+	1.53649i
$290$	−1.46013	+	13.8922i	−0.0857420	+	0.815780i
$291$	−8.58452	−	1.82470i	−0.503234	−	0.106966i
$292$	0.0374560	−	0.0121702i	0.00219195	−	0.000712206i
$293$	5.94692	+	4.32069i	0.347423	+	0.252418i	0.747787	−	0.663939i	$-0.231116\pi$
$293$	5.94692	+	4.32069i	0.347423	+	0.252418i	−0.400364	+	0.916356i	$0.631116\pi$
$294$	−6.90779	+	0.726038i	−0.402870	+	0.0423434i
$295$	23.3095	−	20.9880i	1.35713	−	1.22197i
$296$			6.32532i			0.367652i
$297$	15.9287	+	5.03844i	0.924279	+	0.292360i
$298$	−3.58923	−	2.07224i	−0.207919	−	0.120042i
$299$	−1.42944	+	0.303837i	−0.0826668	+	0.0175714i
$300$	−11.5222	+	1.21104i	−0.665237	+	0.0699192i
$301$	2.41640	−	22.9905i	0.139279	−	1.32515i
$302$	2.41399	−	2.68101i	0.138910	−	0.154275i
$303$	−0.356377	−	1.09682i	−0.0204733	−	0.0630105i
$304$	−4.23168	+	1.04539i	−0.242704	+	0.0599575i
$305$	9.53602	+	13.1252i	0.546031	+	0.751547i
$306$	−2.70051	−	12.7049i	−0.154378	−	0.726291i
$307$	−5.63882	−	9.76671i	−0.321824	−	0.557416i	0.659040	−	0.752108i	$-0.270963\pi$
$307$	−5.63882	−	9.76671i	−0.321824	−	0.557416i	−0.980864	+	0.194692i	$0.937629\pi$
$308$	−9.11106	+	8.33333i	−0.519151	+	0.474835i
$309$	−9.26793	−	16.0525i	−0.527234	−	0.913197i
$310$	−12.9828	+	11.6897i	−0.737372	+	0.663933i
$311$	7.05854	−	5.12833i	0.400253	−	0.290801i	−0.369391	−	0.929274i	$-0.620434\pi$
$311$	7.05854	−	5.12833i	0.400253	−	0.290801i	0.769644	+	0.638473i	$0.220434\pi$
$312$	0.157836	−	0.217243i	0.00893572	−	0.0122990i
$313$	−26.8801	−	5.71354i	−1.51935	−	0.322948i	−0.628705	−	0.777644i	$-0.716415\pi$
$313$	−26.8801	−	5.71354i	−1.51935	−	0.322948i	−0.890647	+	0.454695i	$0.849748\pi$
$314$	0.613300	+	0.130361i	0.0346105	+	0.00735669i
$315$	−17.5216	+	24.1163i	−0.987228	+	1.35880i
$316$	7.92618	−	5.75871i	0.445882	−	0.323952i
$317$	−24.6683	+	22.2114i	−1.38551	+	1.24752i	−0.450557	+	0.892748i	$0.648775\pi$
$317$	−24.6683	+	22.2114i	−1.38551	+	1.24752i	−0.934953	+	0.354772i	$0.884559\pi$
$318$	−4.07303	−	7.05470i	−0.228404	−	0.395608i
$319$	−11.1941	−	2.28820i	−0.626750	−	0.128115i
$320$	−2.02743	−	3.51161i	−0.113337	−	0.196305i
$321$	2.45372	+	11.5438i	0.136953	+	0.644314i
$322$	−12.0585	−	16.5971i	−0.671993	−	0.924920i
$323$	6.87614	+	27.8341i	0.382599	+	1.54873i
$324$	0.254498	+	0.783266i	0.0141388	+	0.0435148i
$325$	2.03036	−	2.25494i	0.112624	−	0.125082i
$326$	−1.59015	+	15.1293i	−0.0880703	+	0.837933i
$327$	5.58896	−	0.587423i	0.309070	−	0.0324846i
$328$	9.01980	−	1.91722i	0.498035	−	0.105861i
$329$	−12.5909	−	7.26936i	−0.694159	−	0.400773i
$330$	−0.106294	−	13.6171i	−0.00585130	−	0.749595i
$331$		−	1.92984i		−	0.106074i	−0.998593	−	0.0530368i	$-0.983110\pi$
$331$		−	1.92984i		−	0.106074i	0.998593	−	0.0530368i	$-0.0168901\pi$
$332$	−6.70626	+	6.03835i	−0.368054	+	0.331397i
$333$	−12.4222	+	1.30563i	−0.680733	+	0.0715479i
$334$	−13.7880	−	10.0176i	−0.754447	−	0.548138i
$335$	−9.13289	+	2.96746i	−0.498983	+	0.162129i
$336$	3.68727	+	0.783753i	0.201157	+	0.0427572i
$337$	3.59993	−	34.2511i	0.196101	−	1.86577i	−0.246617	−	0.969113i	$-0.579319\pi$
$337$	3.59993	−	34.2511i	0.196101	−	1.86577i	0.442718	−	0.896661i	$-0.354014\pi$
$338$	−1.35152	−	12.8588i	−0.0735129	−	0.699429i
$339$	−3.24146	+	0.688993i	−0.176052	+	0.0374209i
$340$	−23.0978	+	13.3355i	−1.25266	+	0.723221i
$341$	−8.48909	−	11.4945i	−0.459710	−	0.622460i
$342$	−2.92651	−	8.09477i	−0.158248	−	0.437715i
$343$	−0.497031	−	0.161495i	−0.0268372	−	0.00871993i
$344$	−2.52565	+	5.67269i	−0.136174	+	0.305851i
$345$	22.5016	+	2.36501i	1.21145	+	0.127328i
$346$	10.0805	+	2.14267i	0.541929	+	0.115191i
$347$	−2.08509	−	1.87742i	−0.111933	−	0.100785i	0.611264	−	0.791427i	$-0.290662\pi$
$347$	−2.08509	−	1.87742i	−0.111933	−	0.100785i	−0.723197	+	0.690642i	$0.757328\pi$
$348$	1.41879	+	3.18667i	0.0760554	+	0.170823i
$349$	10.1025	+	13.9049i	0.540776	+	0.744315i	0.988725	−	0.149745i	$-0.0478452\pi$
$349$	10.1025	+	13.9049i	0.540776	+	0.744315i	−0.447949	+	0.894059i	$0.647845\pi$
$350$	40.5117	+	13.1630i	2.16544	+	0.703594i
$351$	1.15687	+	0.667922i	0.0617494	+	0.0356510i
$352$	3.01927	−	1.37260i	0.160927	−	0.0731599i
$353$	29.5744			1.57409			0.787043	−	0.616898i	$-0.211611\pi$
$353$	29.5744			1.57409			0.787043	+	0.616898i	$0.211611\pi$
$354$	2.42042	−	7.44928i	0.128644	−	0.395925i
$355$	24.3341	−	2.55762i	1.29152	−	0.135744i
$356$	−10.2624	−	1.07862i	−0.543907	−	0.0571669i
$357$	5.15518	−	24.2532i	0.272841	−	1.28362i
$358$	−7.77691	−	7.00236i	−0.411022	−	0.370086i
$359$	−25.3677	−	2.66625i	−1.33886	−	0.140720i	−0.592126	−	0.805846i	$-0.701711\pi$
$359$	−25.3677	−	2.66625i	−1.33886	−	0.140720i	−0.746731	+	0.665126i	$0.768378\pi$
$360$	6.47792	−	4.70649i	0.341417	−	0.248054i
$361$	7.04152	+	17.6470i	0.370606	+	0.928790i
$362$			24.7243i			1.29948i
$363$	11.0941	+	0.991197i	0.582287	+	0.0520243i
$364$	−0.855008	+	0.493639i	−0.0448146	+	0.0258737i
$365$	0.118676	−	0.106857i	0.00621181	−	0.00559314i
$366$	3.70107	+	1.64782i	0.193458	+	0.0861330i
$367$	−15.9980	+	7.12275i	−0.835087	+	0.371805i	−0.779310	−	0.626639i	$-0.784430\pi$
$367$	−15.9980	+	7.12275i	−0.835087	+	0.371805i	−0.0557768	+	0.998443i	$0.517764\pi$
$368$	1.70287	+	5.24089i	0.0887681	+	0.273200i
$369$	5.62700	+	17.3181i	0.292930	+	0.901546i
$370$	10.4321	+	23.4309i	0.542339	+	1.21811i
$371$	3.13065	+	29.7861i	0.162535	+	1.54642i
$372$	−1.34811	+	4.14905i	−0.0698962	+	0.215118i
$373$	11.5930			0.600263			0.300132	−	0.953898i	$-0.402969\pi$
$373$	11.5930			0.600263			0.300132	+	0.953898i	$0.402969\pi$
$374$	−9.02837	−	19.8594i	−0.466846	−	1.02690i
$375$	−22.9058	+	13.2247i	−1.18285	+	0.682918i
$376$	2.61313	+	2.90218i	0.134762	+	0.149668i
$377$	−0.834595	−	0.371586i	−0.0429838	−	0.0191376i
$378$	−1.96021	+	18.6501i	−0.100822	+	0.959259i
$379$	12.8834	−	4.18607i	0.661776	−	0.215024i	0.0411765	−	0.999152i	$-0.486889\pi$
$379$	12.8834	−	4.18607i	0.661776	−	0.215024i	0.620599	+	0.784128i	$0.286889\pi$
$380$	−13.9513	+	10.8516i	−0.715687	+	0.556676i
$381$	8.58868	−	11.8213i	0.440011	−	0.605624i
$382$	−7.03787	−	3.13346i	−0.360089	−	0.160322i
$383$	4.02191	+	18.9216i	0.205510	+	0.966848i	0.953092	+	0.302679i	$0.0978811\pi$
$383$	4.02191	+	18.9216i	0.205510	+	0.966848i	−0.747583	+	0.664169i	$0.768786\pi$
$384$	−0.876910	−	0.506284i	−0.0447496	−	0.0258362i
$385$	−20.0063	+	45.8957i	−1.01961	+	2.33906i
$386$	1.76294	−	3.05351i	0.0897315	−	0.155420i
$387$	−11.6619	−	3.78917i	−0.592805	−	0.192614i
$388$	−5.09455	−	7.01205i	−0.258637	−	0.355983i
$389$	3.87089	−	1.72343i	0.196262	−	0.0873813i	−0.306252	−	0.951950i	$-0.599075\pi$
$389$	3.87089	−	1.72343i	0.196262	−	0.0873813i	0.502514	+	0.864569i	$0.332408\pi$
$390$	0.226383	−	1.06505i	0.0114633	−	0.0539307i
$391$	34.4723	−	11.2007i	1.74334	−	0.566444i
$392$	−5.54955	−	4.03198i	−0.280295	−	0.203646i
$393$	−1.00587	−	9.57022i	−0.0507395	−	0.482754i
$394$	−4.23842	−	19.9402i	−0.213528	−	1.00457i
$395$	19.8633	−	34.4043i	0.999433	−	1.73107i
$396$	3.31885	+	5.64617i	0.166779	+	0.283731i
$397$	14.1864	+	24.5715i	0.711994	+	1.23321i	0.964108	+	0.265512i	$0.0855409\pi$
$397$	14.1864	+	24.5715i	0.711994	+	1.23321i	−0.252114	+	0.967698i	$0.581126\pi$
$398$	−2.53157	+	7.79138i	−0.126896	+	0.390546i
$399$	1.18153	−	16.3890i	0.0591505	−	0.820474i
$400$	−9.25669	−	6.72538i	−0.462835	−	0.336269i
$401$	−15.1022	−	13.5981i	−0.754168	−	0.679056i	0.199507	−	0.979896i	$-0.436066\pi$
$401$	−15.1022	−	13.5981i	−0.754168	−	0.679056i	−0.953674	+	0.300841i	$0.902733\pi$
$402$	−1.60458	+	1.78207i	−0.0800291	+	0.0888814i
$403$	−0.464724	−	1.04379i	−0.0231495	−	0.0519947i
$404$	0.463251	−	1.04048i	0.0230476	−	0.0517658i
$405$	2.23455	+	2.48172i	0.111036	+	0.123318i
$406$		−	12.8250i		−	0.636494i
$407$	−19.9007	+	6.63832i	−0.986442	+	0.329049i
$408$	−3.33011	+	5.76793i	−0.164865	+	0.285555i
$409$	5.76984	+	6.40806i	0.285300	+	0.316858i	0.868711	−	0.495319i	$-0.164949\pi$
$409$	5.76984	+	6.40806i	0.285300	+	0.316858i	−0.583411	+	0.812177i	$0.698282\pi$
$410$	30.2501	−	21.9780i	1.49394	−	1.08541i
$411$	−4.04774	+	5.57124i	−0.199660	+	0.274809i
$412$	3.80599	−	17.9058i	0.187508	−	0.882154i
$413$	−19.2695	+	21.4009i	−0.948190	+	1.05307i
$414$	−9.94102	+	4.42603i	−0.488574	+	0.217527i
$415$	−14.8832	+	33.4282i	−0.730588	+	1.64093i
$416$	0.259399	−	0.0551369i	0.0127181	−	0.00270331i
$417$	−18.6542			−0.913502
$418$	−7.73011	−	12.2166i	−0.378092	−	0.597534i
$419$	−3.94914			−0.192928			−0.0964641	−	0.995336i	$-0.530753\pi$
$419$	−3.94914			−0.192928			−0.0964641	+	0.995336i	$0.530753\pi$
$420$	14.9514	−	3.17801i	0.729551	−	0.155071i
$421$	8.86722	−	19.9161i	0.432162	−	0.970652i	−0.557886	−	0.829918i	$-0.688387\pi$
$421$	8.86722	−	19.9161i	0.432162	−	0.970652i	0.990047	−	0.140734i	$-0.0449461\pi$
$422$	−0.548137	+	0.244046i	−0.0266829	+	0.0118800i
$423$	−5.16016	+	5.73094i	−0.250896	+	0.278648i
$424$	1.67264	−	7.86915i	0.0812306	−	0.382160i
$425$	−44.2366	+	60.8864i	−2.14579	+	2.95343i
$426$	4.94319	−	3.59144i	0.239498	−	0.174006i
$427$	−9.96687	−	11.0693i	−0.482331	−	0.535683i
$428$	−5.82762	+	10.0937i	−0.281689	+	0.487899i
$429$	0.849137	+	0.268592i	0.0409967	+	0.0129677i
$430$			25.1788i			1.21423i
$431$	9.50841	+	10.5602i	0.458004	+	0.508665i	0.927271	−	0.374391i	$-0.122148\pi$
$431$	9.50841	+	10.5602i	0.458004	+	0.508665i	−0.469267	+	0.883056i	$0.655482\pi$
$432$	2.04883	−	4.60174i	0.0985742	−	0.221401i
$433$	6.72614	+	15.1072i	0.323238	+	0.726004i	0.999948	−	0.0102461i	$-0.00326148\pi$
$433$	6.72614	+	15.1072i	0.323238	+	0.726004i	−0.676710	+	0.736250i	$0.736595\pi$
$434$	10.7326	−	11.9198i	0.515181	−	0.572166i
$435$	10.5113	+	9.46440i	0.503977	+	0.453783i
$436$	4.49003	+	3.26220i	0.215034	+	0.156231i
$437$	21.6118	−	10.4832i	1.03383	−	0.501478i
$438$	0.0123231	−	0.0379268i	0.000588823	−	0.00181221i
$439$	−5.20671	−	9.01828i	−0.248503	−	0.430419i	0.714608	−	0.699525i	$-0.246605\pi$
$439$	−5.20671	−	9.01828i	−0.248503	−	0.430419i	−0.963111	+	0.269106i	$0.913272\pi$
$440$	8.92049	−	10.0641i	0.425267	−	0.479786i
$441$	6.77286	−	11.7309i	0.322517	−	0.558616i
$442$	−0.362666	−	1.70621i	−0.0172503	−	0.0811562i
$443$	−2.98615	−	28.4113i	−0.141876	−	1.34986i	−0.801378	−	0.598158i	$-0.795899\pi$
$443$	−2.98615	−	28.4113i	−0.141876	−	1.34986i	0.659502	−	0.751703i	$-0.270767\pi$
$444$	5.18161	+	3.76466i	0.245908	+	0.178663i
$445$	−39.7940	+	12.9298i	−1.88642	+	0.612934i
$446$	−3.64266	+	17.1374i	−0.172485	+	0.811479i
$447$	−3.83377	+	1.70690i	−0.181331	+	0.0807337i
$448$	2.18824	+	3.01185i	0.103384	+	0.142297i
$449$	25.4780	+	8.27831i	1.20238	+	0.390678i	0.840637	−	0.541599i	$-0.182181\pi$
$449$	25.4780	+	8.27831i	1.20238	+	0.390678i	0.361745	+	0.932277i	$0.382181\pi$
$450$	11.2972	−	19.5673i	0.532555	−	0.922412i
$451$	15.4981	+	26.3660i	0.729776	+	1.24153i
$452$	−2.83427	−	1.63637i	−0.133313	−	0.0769683i
$453$	−0.759500	−	3.57317i	−0.0356844	−	0.167882i
$454$	1.06753	+	0.475294i	0.0501015	+	0.0223066i
$455$	−2.35307	+	3.23872i	−0.110313	+	0.151833i
$456$	−1.66221	+	4.08872i	−0.0778402	+	0.191472i
$457$	−34.5630	+	11.2302i	−1.61679	+	0.525327i	−0.971181	−	0.238342i	$-0.923396\pi$
$457$	−34.5630	+	11.2302i	−1.61679	+	0.525327i	−0.645608	+	0.763669i	$0.723396\pi$
$458$	1.35546	−	12.8963i	0.0633365	−	0.602607i
$459$	−30.2682	−	13.4763i	−1.41280	−	0.629019i
$460$	14.9515	+	16.6054i	0.697118	+	0.774228i
$461$	−22.6442	+	13.0736i	−1.05465	+	0.608901i	−0.923947	−	0.382521i	$-0.875056\pi$
$461$	−22.6442	+	13.0736i	−1.05465	+	0.608901i	−0.130700	+	0.991422i	$0.541722\pi$
$462$	1.40388	+	12.4234i	0.0653145	+	0.577990i
$463$	−10.1571			−0.472040			−0.236020	−	0.971748i	$-0.575843\pi$
$463$	−10.1571			−0.472040			−0.236020	+	0.971748i	$0.575843\pi$
$464$	−1.06455	+	3.27633i	−0.0494203	+	0.152100i
$465$	1.84907	+	17.5927i	0.0857485	+	0.815843i
$466$	6.12740	+	13.7624i	0.283846	+	0.637529i
$467$	−6.27973	−	19.3270i	−0.290591	−	0.894348i	−0.984667	−	0.174446i	$-0.944187\pi$
$467$	−6.27973	−	19.3270i	−0.290591	−	0.894348i	0.694075	−	0.719902i	$-0.255813\pi$
$468$	0.161826	+	0.498049i	0.00748041	+	0.0230223i
$469$	8.05437	−	3.58604i	0.371916	−	0.165588i
$470$	14.4663	+	6.44080i	0.667279	+	0.297092i
$471$	0.471809	−	0.424819i	0.0217398	−	0.0195746i
$472$	6.69907	−	3.86771i	0.308350	−	0.178026i
$473$	−20.4981	−	1.99279i	−0.942502	−	0.0916286i
$474$		−	9.92043i		−	0.455661i
$475$	−23.5093	+	43.9856i	−1.07868	+	2.01820i
$476$	19.8106	−	14.3933i	0.908018	−	0.659714i
$477$	15.7994	+	1.66058i	0.723404	+	0.0760328i
$478$	3.30946	+	2.97985i	0.151371	+	0.136295i
$479$	2.98541	−	14.0453i	0.136407	−	0.641744i	−0.855817	−	0.517279i	$-0.826945\pi$
$479$	2.98541	−	14.0453i	0.136407	−	0.641744i	0.992224	−	0.124466i	$-0.0397217\pi$
$480$	−4.08333	−	0.429176i	−0.186378	−	0.0195891i
$481$	−1.66825	+	0.175340i	−0.0760655	+	0.00799481i
$482$	7.64183	−	23.5191i	0.348076	−	1.07127i
$483$	−20.7730			−0.945203
$484$	7.48715	+	8.05869i	0.340325	+	0.366304i
$485$	−30.4364	−	17.5725i	−1.38205	−	0.797926i
$486$	15.1652	+	4.92747i	0.687907	+	0.223514i
$487$	0.476131	+	0.655338i	0.0215756	+	0.0296962i	0.819669	−	0.572838i	$-0.194158\pi$
$487$	0.476131	+	0.655338i	0.0215756	+	0.0296962i	−0.798093	+	0.602534i	$0.794158\pi$
$488$	1.62737	+	3.65513i	0.0736675	+	0.165460i
$489$	11.4473	+	10.3072i	0.517663	+	0.466106i
$490$	−27.2070	−	5.78302i	−1.22909	−	0.261250i
$491$	−3.22810	−	0.339287i	−0.145682	−	0.0153118i	0.0314067	−	0.999507i	$-0.490001\pi$
$491$	−3.22810	−	0.339287i	−0.145682	−	0.0153118i	−0.177089	+	0.984195i	$0.556668\pi$
$492$	3.79778	−	8.52996i	0.171217	−	0.384560i
$493$	21.5503	+	7.00211i	0.970576	+	0.315359i
$494$	−0.393017	−	1.08709i	−0.0176827	−	0.0489105i
$495$	21.6060	+	15.4415i	0.971119	+	0.694043i
$496$	−3.73120	+	2.15421i	−0.167536	+	0.0967269i
$497$	−21.9738	+	4.67068i	−0.985660	+	0.209508i
$498$	0.955138	+	9.08753i	0.0428008	+	0.407222i
$499$	3.06187	−	29.1318i	0.137068	−	1.30412i	−0.682395	−	0.730984i	$-0.739061\pi$
$499$	3.06187	−	29.1318i	0.137068	−	1.30412i	0.819463	−	0.573132i	$-0.194272\pi$
$500$	−25.5502	−	5.43086i	−1.14264	−	0.242876i
$501$	−16.4125	+	5.33275i	−0.733257	+	0.238250i
$502$	6.15212	+	4.46978i	0.274583	+	0.199496i
$503$	11.0841	−	1.16498i	0.494214	−	0.0519440i	0.145857	−	0.989306i	$-0.453406\pi$
$503$	11.0841	−	1.16498i	0.494214	−	0.0519440i	0.348357	+	0.937362i	$0.386740\pi$
$504$	−5.46325	+	4.91914i	−0.243353	+	0.219116i
$505$		−	4.61827i		−	0.205510i
$506$	−14.7018	+	10.8578i	−0.653573	+	0.482688i
$507$	−11.3382	−	6.54609i	−0.503545	−	0.290722i
$508$	14.1152	−	3.00028i	0.626262	−	0.133116i
$509$	−15.1058	+	1.58769i	−0.669554	+	0.0703730i	−0.433205	−	0.901295i	$-0.642618\pi$
$509$	−15.1058	+	1.58769i	−0.669554	+	0.0703730i	−0.236349	+	0.971668i	$0.575951\pi$
$510$	−2.82293	+	26.8584i	−0.125001	+	1.18931i
$511$	−0.0981073	+	0.108959i	−0.00434001	+	0.00482007i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	−21.0931	−	6.09759i	−0.931284	−	0.269215i
$514$	−13.8138	−	19.0131i	−0.609301	−	0.838631i
$515$	−15.4328	−	72.6054i	−0.680048	−	3.19938i
$516$	3.14379	+	5.44520i	0.138398	+	0.239712i
$517$	−6.38839	+	11.2672i	−0.280961	+	0.495532i
$518$	−11.7741	−	20.3934i	−0.517325	−	0.896033i
$519$	7.75486	−	6.98250i	0.340400	−	0.306498i
$520$	0.869956	−	0.632060i	0.0381501	−	0.0277177i
$521$	6.61810	−	9.10903i	0.289944	−	0.399074i	−0.639052	−	0.769164i	$-0.720673\pi$
$521$	6.61810	−	9.10903i	0.289944	−	0.399074i	0.928996	+	0.370090i	$0.120673\pi$
$522$	−6.65409	−	1.41437i	−0.291241	−	0.0619053i
$523$	11.5170	+	2.44801i	0.503602	+	0.107044i	0.452706	−	0.891660i	$-0.350459\pi$
$523$	11.5170	+	2.44801i	0.503602	+	0.107044i	0.0508963	+	0.998704i	$0.483792\pi$
$524$	5.58601	−	7.68849i	0.244026	−	0.335873i
$525$	34.8944	−	25.3523i	1.52292	−	1.10646i
$526$	0.199088	−	0.179260i	0.00868064	−	0.00781609i
$527$	14.1694	+	24.5422i	0.617231	+	1.06907i
$528$	0.672569	−	3.29027i	0.0292698	−	0.143191i
$529$	−3.68334	−	6.37972i	−0.160145	−	0.277379i
$530$	−6.78232	−	31.9083i	−0.294605	−	1.38601i
$531$	8.97852	+	12.3579i	0.389634	+	0.536286i
$532$	11.6974	−	11.2474i	0.507146	−	0.487637i
$533$	0.755681	+	2.32575i	0.0327322	+	0.100739i
$534$	−6.99150	+	7.76485i	−0.302552	+	0.336018i
$535$	−4.94006	+	47.0015i	−0.213577	+	2.03205i
$536$	−2.35527	+	0.247549i	−0.101732	+	0.0106925i
$537$	−10.3648	+	2.20311i	−0.447276	+	0.0950714i
$538$	5.60706	+	3.23724i	0.241738	+	0.139567i
$539$	6.86127	−	21.6915i	0.295536	−	0.934319i
$540$		−	20.4253i		−	0.878964i
$541$	15.3887	−	13.8560i	0.661610	−	0.595717i	−0.268374	−	0.963315i	$-0.586486\pi$
$541$	15.3887	−	13.8560i	0.661610	−	0.595717i	0.929985	+	0.367598i	$0.119820\pi$
$542$	−12.8322	+	1.34872i	−0.551190	+	0.0579324i
$543$	20.2538	+	14.7153i	0.869174	+	0.631492i
$544$	−6.25563	+	2.03258i	−0.268208	+	0.0871460i
$545$	22.0127	+	4.67893i	0.942919	+	0.200424i
$546$	−0.104496	+	0.994210i	−0.00447200	+	0.0425483i
$547$	−3.04942	−	29.0133i	−0.130384	−	1.24052i	−0.842593	−	0.538551i	$-0.818972\pi$
$547$	−3.04942	−	29.0133i	−0.130384	−	1.24052i	0.712209	−	0.701967i	$-0.247695\pi$
$548$	−6.65234	+	1.41400i	−0.284174	+	0.0604030i
$549$	−6.84235	+	3.95043i	−0.292024	+	0.168600i
$550$	11.4447	−	36.1816i	0.488002	−	1.54279i
$551$	14.7824	+	2.63940i	0.629750	+	0.112442i
$552$	5.30676	+	1.72427i	0.225871	+	0.0733898i
$553$	−14.8353	+	33.3205i	−0.630859	+	1.41693i
$554$	20.0352	+	2.10578i	0.851214	+	0.0894662i
$555$	25.4031	+	5.39960i	1.07830	+	0.229200i
$556$	−13.6907	−	12.3272i	−0.580616	−	0.522789i
$557$	7.54810	+	16.9533i	0.319823	+	0.718335i	0.999890	−	0.0148152i	$-0.00471601\pi$
$557$	7.54810	+	16.9533i	0.319823	+	0.718335i	−0.680067	+	0.733150i	$0.738049\pi$
$558$	−5.00079	−	6.88300i	−0.211700	−	0.291381i
$559$	−1.56614	−	0.508868i	−0.0662405	−	0.0215228i
$560$	13.0732	+	7.54782i	0.552444	+	0.318954i
$561$	−21.6420	−	4.42387i	−0.913724	−	0.186776i
$562$	24.5563			1.03584
$563$	7.05392	−	21.7097i	0.297287	−	0.914957i	−0.685156	−	0.728396i	$-0.740266\pi$
$563$	7.05392	−	21.7097i	0.297287	−	0.914957i	0.982444	−	0.186560i	$-0.0597340\pi$
$564$	3.93268	−	0.413342i	0.165596	−	0.0174048i
$565$	−13.1978	−	1.38714i	−0.555236	−	0.0583576i
$566$	−2.20047	+	10.3524i	−0.0924927	+	0.435144i
$567$	−2.27852	−	2.05158i	−0.0956886	−	0.0861584i
$568$	6.00122	+	0.630754i	0.251806	+	0.0264658i
$569$	−24.1862	+	17.5723i	−1.01394	+	0.736669i	−0.965031	−	0.262135i	$-0.915573\pi$
$569$	−24.1862	+	17.5723i	−1.01394	+	0.736669i	−0.0489060	+	0.998803i	$0.515573\pi$
$570$	0.586039	+	17.8873i	0.0245465	+	0.749216i
$571$		−	7.16833i		−	0.299985i	−0.988687	−	0.149993i	$-0.952075\pi$
$571$		−	7.16833i		−	0.299985i	0.988687	−	0.149993i	$-0.0479250\pi$
$572$	0.445707	+	0.758256i	0.0186359	+	0.0317043i
$573$	−6.75563	+	3.90037i	−0.282221	+	0.162940i
$574$	−25.5118	+	22.9710i	−1.06484	+	0.958789i
$575$	57.6006	+	25.6454i	2.40211	+	1.06949i
$576$	1.80398	−	0.803185i	0.0751659	−	0.0334660i
$577$	−1.32360	−	4.07361i	−0.0551020	−	0.169587i	0.919718	−	0.392580i	$-0.128417\pi$
$577$	−1.32360	−	4.07361i	−0.0551020	−	0.169587i	−0.974820	+	0.222993i	$0.928417\pi$
$578$	8.11611	+	24.9788i	0.337586	+	1.03898i
$579$	−1.45213	−	3.26154i	−0.0603486	−	0.135545i
$580$	1.46013	+	13.8922i	0.0606287	+	0.576844i
$581$	10.3816	−	31.9513i	0.430702	−	1.32557i
$582$	−8.77630			−0.363790
$583$	26.5134	−	2.99609i	1.09807	−	0.124085i
$584$	0.0341072	−	0.0196918i	0.00141136	−	0.000814852i
$585$	1.42087	+	1.57803i	0.0587455	+	0.0652435i
$586$	6.71529	+	2.98984i	0.277406	+	0.123509i
$587$	0.885825	−	8.42806i	0.0365619	−	0.347863i	−0.960913	−	0.276849i	$-0.910710\pi$
$587$	0.885825	−	8.42806i	0.0365619	−	0.347863i	0.997475	−	0.0710141i	$-0.0226235\pi$
$588$	−6.60588	+	2.14638i	−0.272422	+	0.0885153i
$589$	11.5302	+	14.8237i	0.475093	+	0.610800i
$590$	18.4365	−	25.3757i	0.759018	−	1.04470i
$591$	−18.8573	−	8.39581i	−0.775685	−	0.345357i
$592$	1.31511	+	6.18710i	0.0540506	+	0.254288i
$593$	−9.18506	−	5.30300i	−0.377185	−	0.217768i	0.299408	−	0.954125i	$-0.403211\pi$
$593$	−9.18506	−	5.30300i	−0.377185	−	0.217768i	−0.676593	+	0.736357i	$0.736544\pi$
$594$	16.6282	+	1.61657i	0.682264	+	0.0663287i
$595$	49.6462	−	85.9898i	2.03530	−	3.52524i
$596$	−3.94164	−	1.28072i	−0.161456	−	0.0524602i
$597$	4.87586	+	6.71104i	0.199556	+	0.274665i
$598$	−1.33503	+	0.594396i	−0.0545936	+	0.0243066i
$599$	−3.76737	+	17.7241i	−0.153931	+	0.724187i	0.831694	+	0.555235i	$0.187372\pi$
$599$	−3.76737	+	17.7241i	−0.153931	+	0.724187i	−0.985624	+	0.168952i	$0.945962\pi$
$600$	−11.0187	+	3.58018i	−0.449835	+	0.146160i
$601$	−13.8637	−	10.0726i	−0.565514	−	0.410870i	0.267959	−	0.963430i	$-0.413651\pi$
$601$	−13.8637	−	10.0726i	−0.565514	−	0.410870i	−0.833473	+	0.552560i	$0.813651\pi$
$602$	−2.41640	−	22.9905i	−0.0984852	−	0.937024i
$603$	−0.972315	−	4.57438i	−0.0395957	−	0.186283i
$604$	1.80383	−	3.12432i	0.0733966	−	0.127127i
$605$	41.0255	+	17.5036i	1.66793	+	0.711621i
$606$	−0.576631	−	0.998754i	−0.0234240	−	0.0405716i
$607$	13.9579	−	42.9580i	0.566533	−	1.74361i	−0.0968185	−	0.995302i	$-0.530867\pi$
$607$	13.9579	−	42.9580i	0.566533	−	1.74361i	0.663352	−	0.748308i	$-0.269133\pi$
$608$	−3.92186	+	1.90237i	−0.159053	+	0.0771512i
$609$	−10.5061	−	7.63309i	−0.425727	−	0.309309i
$610$	12.0565	+	10.8557i	0.488154	+	0.439536i
$611$	−0.692987	+	0.769640i	−0.0280352	+	0.0311363i
$612$	−5.28300	−	11.8658i	−0.213552	−	0.479647i
$613$	15.9500	−	35.8243i	0.644215	−	1.44693i	−0.235712	−	0.971823i	$-0.575742\pi$
$613$	15.9500	−	35.8243i	0.644215	−	1.44693i	0.879927	−	0.475109i	$-0.157591\pi$
$614$	−7.54621	−	8.38091i	−0.304540	−	0.338226i
$615$		−	37.8611i		−	1.52671i
$616$	−7.17937	+	10.0455i	−0.289265	+	0.404746i
$617$	−16.0478	+	27.7956i	−0.646061	+	1.11901i	0.337994	+	0.941148i	$0.390251\pi$
$617$	−16.0478	+	27.7956i	−0.646061	+	1.11901i	−0.984055	+	0.177862i	$0.943082\pi$
$618$	−12.4029	−	13.7748i	−0.498918	−	0.554105i
$619$	−13.2779	+	9.64698i	−0.533685	+	0.387745i	−0.821734	−	0.569871i	$-0.806993\pi$
$619$	−13.2779	+	9.64698i	−0.533685	+	0.387745i	0.288049	+	0.957616i	$0.406993\pi$
$620$	−10.2686	+	14.1336i	−0.412398	+	0.567618i
$621$	−5.77124	+	27.1516i	−0.231592	+	1.08955i
$622$	5.83805	−	6.48381i	0.234085	−	0.259977i
$623$	35.0946	−	15.6251i	1.40604	−	0.626008i
$624$	0.109220	−	0.245312i	0.00437229	−	0.00982033i
$625$	−47.6432	+	10.1269i	−1.90573	+	0.405075i
$626$	−27.4806			−1.09835
$627$	−14.6084	−	0.938605i	−0.583404	−	0.0374843i
$628$	0.627002			0.0250201
$629$	40.6960	−	8.65020i	1.62266	−	0.344906i
$630$	−12.1246	+	27.2323i	−0.483055	+	1.08496i
$631$	4.69241	−	2.08919i	0.186802	−	0.0831695i	−0.311204	−	0.950343i	$-0.600732\pi$
$631$	4.69241	−	2.08919i	0.186802	−	0.0831695i	0.498006	+	0.867174i	$0.334066\pi$
$632$	6.55567	−	7.28081i	0.260771	−	0.289615i
$633$	−0.126317	+	0.594275i	−0.00502065	+	0.0236203i
$634$	−19.5112	+	26.8549i	−0.774890	+	1.06654i
$635$	47.3388	−	34.3936i	1.87858	−	1.36487i
$636$	−5.45078	−	6.05371i	−0.216138	−	0.240045i
$637$	0.909565	−	1.57541i	0.0360383	−	0.0624201i
$638$	−11.4252	+	0.0891847i	−0.452329	+	0.00353086i
$639$			11.9159i			0.471386i
$640$	−2.71323	−	3.01335i	−0.107250	−	0.119113i
$641$	18.1056	−	40.6658i	0.715127	−	1.60620i	−0.0778606	−	0.996964i	$-0.524809\pi$
$641$	18.1056	−	40.6658i	0.715127	−	1.60620i	0.792988	−	0.609238i	$-0.208524\pi$
$642$	4.80020	+	10.7814i	0.189449	+	0.425509i
$643$	14.6846	−	16.3089i	0.579104	−	0.643160i	−0.380411	−	0.924817i	$-0.624218\pi$
$643$	14.6846	−	16.3089i	0.579104	−	0.643160i	0.959515	+	0.281657i	$0.0908842\pi$
$644$	−15.2457	−	13.7273i	−0.600765	−	0.540931i
$645$	20.6261	+	14.9857i	0.812152	+	0.590063i
$646$	12.5129	+	25.7963i	0.492315	+	1.01494i
$647$	−14.7708	+	45.4599i	−0.580700	+	1.78721i	0.0351913	+	0.999381i	$0.488796\pi$
$647$	−14.7708	+	45.4599i	−0.580700	+	1.78721i	−0.615892	+	0.787831i	$0.711204\pi$
$648$	0.411787	+	0.713236i	0.0161765	+	0.0280186i
$649$	19.1991	+	17.0175i	0.753633	+	0.667996i
$650$	1.51716	−	2.62780i	0.0595080	−	0.103071i
$651$	−3.37674	−	15.8863i	−0.132345	−	0.622633i
$652$	1.59015	+	15.1293i	0.0622751	+	0.592508i
$653$	28.7309	+	20.8742i	1.12433	+	0.816870i	0.984859	−	0.173357i	$-0.0554614\pi$
$653$	28.7309	+	20.8742i	1.12433	+	0.816870i	0.139466	+	0.990227i	$0.455461\pi$
$654$	5.34469	−	1.73660i	0.208994	−	0.0679063i
$655$	8.01195	−	37.6933i	0.313053	−	1.47280i
$656$	8.42408	−	3.75064i	0.328905	−	0.146438i
$657$	0.0457126	+	0.0629180i	0.00178342	+	0.00245466i
$658$	−13.8271	−	4.49271i	−0.539038	−	0.175144i
$659$	−17.6744	+	30.6130i	−0.688498	+	1.19251i	0.283826	+	0.958876i	$0.408396\pi$
$659$	−17.6744	+	30.6130i	−0.688498	+	1.19251i	−0.972324	+	0.233637i	$0.924937\pi$
$660$	−2.93512	−	13.2974i	−0.114249	−	0.517601i
$661$	22.4131	+	12.9402i	0.871768	+	0.503316i	0.867935	−	0.496677i	$-0.165447\pi$
$661$	22.4131	+	12.9402i	0.871768	+	0.503316i	0.00383276	+	0.999993i	$0.498780\pi$
$662$	−0.401236	−	1.88767i	−0.0155945	−	0.0733663i
$663$	−1.61355	−	0.718400i	−0.0626652	−	0.0279003i
$664$	−5.30427	+	7.30071i	−0.205846	+	0.283322i
$665$	24.7807	−	60.9558i	0.960954	−	2.36376i
$666$	−11.8793	+	3.85982i	−0.460314	+	0.149565i
$667$	1.98434	−	18.8797i	0.0768338	−	0.731024i
$668$	−15.5695	−	6.93199i	−0.602402	−	0.268207i
$669$	11.8707	+	13.1837i	0.458947	+	0.509712i
$670$	−8.31634	+	4.80144i	−0.321288	+	0.185496i
$671$	−9.79187	+	8.95602i	−0.378011	+	0.345743i
$672$	3.76964			0.145417
$673$	4.96304	−	15.2747i	0.191311	−	0.588795i	−0.808689	−	0.588237i	$-0.799822\pi$
$673$	4.96304	−	15.2747i	0.191311	−	0.588795i	1.00000		0.000558478i	$-0.000177769\pi$
$674$	−3.59993	−	34.2511i	−0.138664	−	1.31930i
$675$	−23.4425	−	52.6526i	−0.902301	−	2.02660i
$676$	−3.99549	−	12.2968i	−0.153673	−	0.472956i
$677$	4.84287	+	14.9048i	0.186127	+	0.572839i	0.999966	−	0.00825098i	$-0.00262640\pi$
$677$	4.84287	+	14.9048i	0.186127	+	0.572839i	−0.813839	+	0.581090i	$0.802626\pi$
$678$	−3.02737	+	1.34787i	−0.116266	+	0.0517647i
$679$	29.4777	+	13.1243i	1.13125	+	0.503664i
$680$	−19.8205	+	17.8464i	−0.760081	+	0.684380i
$681$	1.02472	−	0.591620i	0.0392672	−	0.0226709i
$682$	−10.6934	−	9.47830i	−0.409472	−	0.362943i
$683$			8.45275i			0.323436i	0.986837	+	0.161718i	$0.0517034\pi$
$683$			8.45275i			0.323436i	−0.986837	+	0.161718i	$0.948297\pi$
$684$	−4.54556	−	7.30942i	−0.173804	−	0.279483i
$685$	−22.3102	+	16.2093i	−0.852429	+	0.619326i
$686$	−0.519747	−	0.0546276i	−0.0198440	−	0.00208569i
$687$	−9.75776	−	8.78593i	−0.372282	−	0.335204i
$688$	−1.29104	+	6.07384i	−0.0492203	+	0.231563i
$689$	2.12179	+	0.223009i	0.0808336	+	0.00849596i
$690$	22.5016	−	2.36501i	0.856621	−	0.0900345i
$691$	−10.1860	+	31.3493i	−0.387494	+	1.19258i	0.547162	+	0.837027i	$0.315708\pi$
$691$	−10.1860	+	31.3493i	−0.387494	+	1.19258i	−0.934655	+	0.355555i	$0.884292\pi$
$692$	10.3057			0.391762
$693$	−21.2102	−	12.0259i	−0.805708	−	0.456828i
$694$	−2.42986	−	1.40288i	−0.0922364	−	0.0532527i
$695$	−71.0453	−	23.0840i	−2.69490	−	0.875627i
$696$	2.05034	+	2.82205i	0.0777178	+	0.106969i
$697$	−24.6701	−	55.4099i	−0.934446	−	2.09880i
$698$	12.7728	+	11.5007i	0.483456	+	0.435306i
$699$	14.9208	+	3.17151i	0.564356	+	0.119958i
$700$	42.3631	+	4.45255i	1.60118	+	0.168290i
$701$	−15.0381	+	33.7762i	−0.567982	+	1.27571i	0.370002	+	0.929031i	$0.379357\pi$
$701$	−15.0381	+	33.7762i	−0.567982	+	1.27571i	−0.937984	+	0.346678i	$0.887310\pi$
$702$	1.27046	+	0.412798i	0.0479505	+	0.0155801i
$703$	25.9289	−	9.37412i	0.977928	−	0.353552i
$704$	2.66791	−	1.97035i	0.100551	−	0.0742603i
$705$	13.8861	−	8.01716i	0.522982	−	0.301944i
$706$	28.9281	−	6.14886i	1.08872	−	0.231416i
$707$	0.443214	+	4.21690i	0.0166688	+	0.158593i
$708$	0.818734	−	7.78973i	0.0307699	−	0.292756i
$709$	−1.38841	−	0.295116i	−0.0521429	−	0.0110833i	0.181766	−	0.983342i	$-0.441819\pi$
$709$	−1.38841	−	0.295116i	−0.0521429	−	0.0110833i	−0.233909	+	0.972258i	$0.575152\pi$
$710$	23.2706	−	7.56107i	0.873330	−	0.283762i
$711$	15.6519	+	11.3717i	0.586991	+	0.426474i
$712$	−10.2624	+	1.07862i	−0.384600	+	0.0404231i
$713$	17.6437	−	15.8865i	0.660762	−	0.594953i
$714$		−	24.7950i		−	0.927931i
$715$	2.90159	+	2.07372i	0.108513	+	0.0775528i
$716$	−9.06284	−	5.23243i	−0.338694	−	0.195545i
$717$	4.41075	−	0.937533i	0.164722	−	0.0350128i
$718$	−25.3677	+	2.66625i	−0.946715	+	0.0995037i
$719$	−3.24284	+	30.8536i	−0.120938	+	1.15065i	0.750751	+	0.660585i	$0.229692\pi$
$719$	−3.24284	+	30.8536i	−0.120938	+	1.15065i	−0.871689	+	0.490060i	$0.836975\pi$
$720$	5.35783	−	5.95048i	0.199675	−	0.221761i
$721$	21.0594	+	64.8142i	0.784294	+	2.41381i
$722$	10.5567	+	15.7974i	0.392878	+	0.587917i
$723$	−14.7183	−	20.2580i	−0.547380	−	0.753404i
$724$	5.14048	+	24.1841i	0.191044	+	0.898793i
$725$	19.7083	+	34.1358i	0.731949	+	1.26777i
$726$	11.0577	−	1.33705i	0.410390	−	0.0496225i
$727$	−15.7613	−	27.2994i	−0.584555	−	1.01248i	−0.994931	−	0.100562i	$-0.967936\pi$
$727$	−15.7613	−	27.2994i	−0.584555	−	1.01248i	0.410376	−	0.911916i	$-0.365398\pi$
$728$	−0.733690	+	0.660618i	−0.0271924	+	0.0244841i
$729$	11.0636	−	8.03814i	0.409761	−	0.297709i
$730$	0.0938663	−	0.129196i	0.00347415	−	0.00478175i
$731$	39.9511	+	8.49186i	1.47764	+	0.314083i
$732$	3.96279	+	0.842317i	0.146469	+	0.0311329i
$733$	7.39441	−	10.1775i	0.273119	−	0.375916i	−0.650321	−	0.759660i	$-0.725365\pi$
$733$	7.39441	−	10.1775i	0.273119	−	0.375916i	0.923440	+	0.383744i	$0.125365\pi$
$734$	−14.1675	+	10.2933i	−0.522931	+	0.379931i
$735$	−20.9302	+	18.8457i	−0.772023	+	0.695133i
$736$	2.75530	+	4.77232i	0.101562	+	0.175910i
$737$	−3.25065	−	7.15035i	−0.119739	−	0.263386i
$738$	9.10468	+	15.7698i	0.335148	+	0.580493i
$739$	−1.57886	−	7.42793i	−0.0580791	−	0.273241i	0.939520	−	0.342494i	$-0.111272\pi$
$739$	−1.57886	−	7.42793i	−0.0580791	−	0.273241i	−0.997599	+	0.0692533i	$0.977938\pi$
$740$	15.0757	+	20.7499i	0.554193	+	0.762782i
$741$	−1.12444	−	0.325053i	−0.0413074	−	0.0119411i
$742$	9.25511	+	28.4843i	0.339766	+	1.04569i
$743$	−7.47958	+	8.30691i	−0.274399	+	0.304751i	−0.864555	−	0.502538i	$-0.832400\pi$
$743$	−7.47958	+	8.30691i	−0.274399	+	0.304751i	0.590156	+	0.807289i	$0.299066\pi$
$744$	−0.456013	+	4.33867i	−0.0167182	+	0.159063i
$745$	−16.7133	+	1.75664i	−0.612327	+	0.0643581i
$746$	11.3397	−	2.41032i	0.415175	−	0.0882482i
$747$	−15.4326	−	8.91003i	−0.564651	−	0.326001i
$748$	−12.9601	−	17.5483i	−0.473867	−	0.641630i
$749$		−	43.3908i		−	1.58546i
$750$	−19.6557	+	17.6980i	−0.717724	+	0.646241i
$751$	38.2815	−	4.02355i	1.39691	−	0.146821i	0.624044	−	0.781389i	$-0.285489\pi$
$751$	38.2815	−	4.02355i	1.39691	−	0.146821i	0.772867	+	0.634568i	$0.218822\pi$
$752$	3.15942	+	2.29546i	0.115212	+	0.0837067i
$753$	7.32316	−	2.37944i	0.266871	−	0.0867115i
$754$	−0.893614	−	0.189944i	−0.0325435	−	0.00691734i
$755$	1.52910	−	14.5484i	0.0556495	−	0.529470i
$756$	1.96021	+	18.6501i	0.0712921	+	0.678299i
$757$	−31.5531	+	6.70682i	−1.14682	+	0.243764i	−0.741849	−	0.670567i	$-0.766051\pi$
$757$	−31.5531	+	6.70682i	−1.14682	+	0.243764i	−0.404969	+	0.914331i	$0.632718\pi$
$758$	11.7315	−	6.77320i	0.426108	−	0.246014i
$759$	0.144455	+	18.5057i	0.00524337	+	0.671715i
$760$	−11.3903	+	13.5151i	−0.413168	+	0.490245i
$761$	37.0891	+	12.0510i	1.34448	+	0.436847i	0.890831	−	0.454335i	$-0.150123\pi$
$761$	37.0891	+	12.0510i	1.34448	+	0.436847i	0.453646	+	0.891182i	$0.350123\pi$
$762$	5.94321	−	13.3487i	0.215300	−	0.483571i
$763$	−20.5486	−	2.15974i	−0.743909	−	0.0781880i
$764$	−7.53556	−	1.60173i	−0.272627	−	0.0579486i
$765$	−39.1396	−	35.2415i	−1.41510	−	1.27416i
$766$	7.86804	+	17.6719i	0.284284	+	0.638512i
$767$	1.20577	+	1.65961i	0.0435380	+	0.0599249i
$768$	−0.963010	−	0.312901i	−0.0347496	−	0.0112908i
$769$	26.5534	+	15.3306i	0.957541	+	0.552836i	0.895415	−	0.445232i	$-0.146879\pi$
$769$	26.5534	+	15.3306i	0.957541	+	0.552836i	0.0621253	+	0.998068i	$0.480212\pi$
$770$	−10.0268	+	49.0523i	−0.361342	+	1.76772i
$771$	−23.7968			−0.857022
$772$	1.08956	−	3.35332i	0.0392141	−	0.120689i
$773$	−0.968103	+	0.101752i	−0.0348203	+	0.00365976i	−0.121923	−	0.992540i	$-0.538906\pi$
$773$	−0.968103	+	0.101752i	−0.0348203	+	0.00365976i	0.0871023	+	0.996199i	$0.472239\pi$
$774$	−12.1948	−	1.28173i	−0.438334	−	0.0460708i
$775$	−10.2493	+	48.2193i	−0.368166	+	1.73209i
$776$	−6.44111	−	5.79960i	−0.231222	−	0.208194i
$777$	−23.7136	−	2.49240i	−0.850719	−	0.0894142i
$778$	3.42798	−	2.49057i	0.122899	−	0.0892913i
$779$	−21.2265	−	34.1329i	−0.760517	−	1.22294i
$780$		−	1.08884i		−	0.0389867i
$781$	4.31370	+	19.5430i	0.154356	+	0.699304i
$782$	31.3902	−	18.1231i	1.12251	−	0.648082i
$783$	−12.8958	+	11.6114i	−0.460857	+	0.414958i
$784$	−6.26658	−	2.79006i	−0.223806	−	0.0996450i
$785$	2.32260	−	1.03409i	0.0828972	−	0.0369082i
$786$	−2.97365	−	9.15196i	−0.106067	−	0.326440i
$787$	13.0410	+	40.1361i	0.464861	+	1.43070i	0.859157	+	0.511713i	$0.170989\pi$
$787$	13.0410	+	40.1361i	0.464861	+	1.43070i	−0.394295	+	0.918984i	$0.629011\pi$
$788$	−8.29159	−	18.6232i	−0.295376	−	0.663425i
$789$	−0.0283550	−	0.269780i	−0.00100947	−	0.00960443i
$790$	12.2762	−	37.7823i	0.436768	−	1.34423i
$791$	12.1839			0.433210
$792$	4.42023	+	4.83276i	0.157066	+	0.171725i
$793$	−0.918897	+	0.530525i	−0.0326310	+	0.0188395i
$794$	18.9851	+	21.0851i	0.673755	+	0.748281i
$795$	−30.1755	−	13.4350i	−1.07021	−	0.476490i
$796$	−0.856332	+	8.14746i	−0.0303519	+	0.288779i
$797$	−18.5945	+	6.04172i	−0.658651	+	0.214009i	−0.619225	−	0.785214i	$-0.712553\pi$
$797$	−18.5945	+	6.04172i	−0.658651	+	0.214009i	−0.0394260	+	0.999222i	$0.512553\pi$
$798$	−2.25174	−	16.2765i	−0.0797109	−	0.576181i
$799$	15.0985	−	20.7813i	0.534146	−	0.735190i
$800$	−10.4527	−	4.65384i	−0.369559	−	0.164538i
$801$	−4.23659	−	19.9316i	−0.149692	−	0.704248i
$802$	−17.5994	−	10.1610i	−0.621456	−	0.358798i
$803$	0.0977492	+	0.0866418i	0.00344949	+	0.00305752i
$804$	−1.19900	+	2.07673i	−0.0422856	+	0.0732408i
$805$	−79.1146	−	25.7059i	−2.78842	−	0.906014i
$806$	−0.671584	−	0.924356i	−0.0236555	−	0.0325591i
$807$	5.98907	−	2.66651i	0.210825	−	0.0938655i
$808$	0.236800	−	1.11406i	0.00833061	−	0.0391924i
$809$	−27.6138	+	8.97226i	−0.970848	+	0.315448i	−0.751158	−	0.660122i	$-0.770505\pi$
$809$	−27.6138	+	8.97226i	−0.970848	+	0.315448i	−0.219690	+	0.975570i	$0.570505\pi$
$810$	2.70170	+	1.96290i	0.0949279	+	0.0689692i
$811$	2.36218	+	22.4746i	0.0829473	+	0.789191i	0.954364	+	0.298647i	$0.0965353\pi$
$811$	2.36218	+	22.4746i	0.0829473	+	0.789191i	−0.871416	+	0.490544i	$0.836798\pi$
$812$	−2.66647	−	12.5447i	−0.0935747	−	0.440234i
$813$	−6.53253	+	11.3147i	−0.229106	+	0.396823i
$814$	−18.0857	+	10.6308i	−0.633902	+	0.372611i
$815$	30.8425	+	53.4208i	1.08037	+	1.87125i
$816$	−2.05812	+	6.33425i	−0.0720487	+	0.221743i
$817$	26.9967	+	1.94627i	0.944494	+	0.0680915i
$818$	6.97607	+	5.06841i	0.243913	+	0.177213i
$819$	−1.44882	−	1.30453i	−0.0506259	−	0.0455838i
$820$	25.0195	−	27.7870i	0.873721	−	0.970365i
$821$	6.10107	+	13.7032i	0.212929	+	0.478246i	0.988159	−	0.153433i	$-0.0490329\pi$
$821$	6.10107	+	13.7032i	0.212929	+	0.478246i	−0.775230	+	0.631679i	$0.782366\pi$
$822$	−2.80096	+	6.29107i	−0.0976948	+	0.219426i
$823$	−13.0880	−	14.5357i	−0.456220	−	0.506683i	0.470519	−	0.882390i	$-0.344067\pi$
$823$	−13.0880	−	14.5357i	−0.456220	−	0.506683i	−0.926739	+	0.375707i	$0.877400\pi$
$824$		−	18.3058i		−	0.637712i
$825$	−22.8279	−	30.9096i	−0.794765	−	1.07613i
$826$	−14.3989	+	24.9396i	−0.501002	+	0.867761i
$827$	0.558674	+	0.620470i	0.0194270	+	0.0215759i	0.752780	−	0.658272i	$-0.228712\pi$
$827$	0.558674	+	0.620470i	0.0194270	+	0.0215759i	−0.733353	+	0.679848i	$0.762046\pi$
$828$	−8.80356	+	6.39616i	−0.305945	+	0.222282i
$829$	−11.2439	+	15.4759i	−0.390516	+	0.537499i	−0.958332	−	0.285657i	$-0.907788\pi$
$829$	−11.2439	+	15.4759i	−0.390516	+	0.537499i	0.567816	+	0.823155i	$0.307788\pi$
$830$	−7.60785	+	35.7921i	−0.264072	+	1.24236i
$831$	13.6494	−	15.1592i	0.473493	−	0.525868i
$832$	0.242267	−	0.107864i	0.00839909	−	0.00373952i
$833$	−18.3518	+	41.2188i	−0.635851	+	1.42815i
$834$	−18.2466	+	3.87843i	−0.631828	+	0.134299i
$835$	−69.1067			−2.39154
$836$	−10.1012	−	10.3425i	−0.349356	−	0.357702i
$837$	−21.7025			−0.750148
$838$	−3.86284	+	0.821072i	−0.133440	+	0.0283635i
$839$	−10.0562	+	22.5866i	−0.347179	+	0.779776i	0.652578	+	0.757722i	$0.273687\pi$
$839$	−10.0562	+	22.5866i	−0.347179	+	0.779776i	−0.999757	+	0.0220547i	$0.992979\pi$
$840$	13.9639	−	6.21712i	0.481800	−	0.214511i
$841$	−11.4638	+	12.7318i	−0.395303	+	0.439029i
$842$	4.53266	−	21.3245i	0.156206	−	0.734890i
$843$	14.6152	−	20.1161i	0.503375	−	0.692837i
$844$	−0.485419	+	0.352677i	−0.0167088	+	0.0121396i
$845$	−35.0812	−	38.9616i	−1.20683	−	1.34032i
$846$	−3.85587	+	6.67857i	−0.132568	+	0.229614i
$847$	−39.1399	−	12.0451i	−1.34486	−	0.413875i
$848$		−	8.04496i		−	0.276265i
$849$	7.17088	+	7.96407i	0.246104	+	0.273326i
$850$	−30.6109	+	68.7532i	−1.04995	+	2.35822i
$851$	−14.1773	−	31.8428i	−0.485992	−	1.09156i
$852$	4.08847	−	4.54070i	0.140069	−	0.155562i
$853$	−12.6866	−	11.4231i	−0.434382	−	0.391119i	0.422725	−	0.906258i	$-0.361074\pi$
$853$	−12.6866	−	11.4231i	−0.434382	−	0.391119i	−0.857107	+	0.515139i	$0.827740\pi$
$854$	−12.0505	−	8.75521i	−0.412360	−	0.299597i
$855$	−28.8932	−	19.5795i	−0.988128	−	0.669604i
$856$	−3.60167	+	11.0848i	−0.123103	+	0.378871i
$857$	−0.517007	−	0.895483i	−0.0176606	−	0.0305891i	0.857060	−	0.515217i	$-0.172289\pi$
$857$	−0.517007	−	0.895483i	−0.0176606	−	0.0305891i	−0.874721	+	0.484627i	$0.838955\pi$
$858$	0.886425	+	0.0861769i	0.0302620	+	0.00294203i
$859$	−10.9723	+	19.0046i	−0.374371	+	0.648430i	−0.990233	−	0.139425i	$-0.955475\pi$
$859$	−10.9723	+	19.0046i	−0.374371	+	0.648430i	0.615862	+	0.787854i	$0.288808\pi$
$860$	5.23497	+	24.6286i	0.178511	+	0.839828i
$861$	3.63352	+	34.5706i	0.123830	+	1.17816i
$862$	11.4962	+	8.35249i	0.391562	+	0.284487i
$863$	−10.6302	+	3.45396i	−0.361856	+	0.117574i	−0.484302	−	0.874901i	$-0.660926\pi$
$863$	−10.6302	+	3.45396i	−0.361856	+	0.117574i	0.122446	+	0.992475i	$0.460926\pi$
$864$	1.04730	−	4.92715i	0.0356298	−	0.167625i
$865$	38.1753	−	16.9967i	1.29800	−	0.577906i
$866$	9.72011	+	13.3786i	0.330303	+	0.454623i
$867$	25.2928	+	8.21812i	0.858987	+	0.279102i
$868$	8.01980	−	13.8907i	0.272210	−	0.471481i
$869$	29.7870	+	12.9844i	1.01045	+	0.440464i
$870$	12.2493	+	7.07216i	0.415292	+	0.239769i
$871$	−0.130578	−	0.614319i	−0.00442445	−	0.0208154i
$872$	5.07017	+	2.25738i	0.171697	+	0.0764446i
$873$	10.0602	−	13.8467i	0.340487	−	0.468641i
$874$	18.9600	−	14.7474i	0.641330	−	0.498840i
$875$	92.4851	−	30.0502i	3.12657	−	1.01588i
$876$	0.00416844	−	0.0396601i	0.000140839	−	0.00133999i
$877$	7.17505	+	3.19454i	0.242284	+	0.107872i	0.524287	−	0.851542i	$-0.324332\pi$
$877$	7.17505	+	3.19454i	0.242284	+	0.107872i	−0.282002	+	0.959414i	$0.590999\pi$
$878$	−6.96793	−	7.73867i	−0.235156	−	0.261168i
$879$	6.44599	−	3.72160i	0.217418	−	0.125526i
$880$	6.63311	−	11.6988i	0.223602	−	0.394368i
$881$	52.1063			1.75551			0.877753	−	0.479114i	$-0.159042\pi$
$881$	52.1063			1.75551			0.877753	+	0.479114i	$0.159042\pi$
$882$	4.18586	−	12.8828i	0.140945	−	0.433785i
$883$	−3.03505	−	28.8766i	−0.102138	−	0.971774i	−0.918817	−	0.394683i	$-0.870855\pi$
$883$	−3.03505	−	28.8766i	−0.102138	−	0.971774i	0.816680	−	0.577091i	$-0.195812\pi$
$884$	−0.709483	−	1.59352i	−0.0238625	−	0.0535960i
$885$	−9.81446	−	30.2058i	−0.329909	−	1.01536i
$886$	−8.82793	−	27.1696i	−0.296580	−	0.912780i
$887$	12.9575	−	5.76904i	0.435070	−	0.193705i	−0.177502	−	0.984120i	$-0.556802\pi$
$887$	12.9575	−	5.76904i	0.435070	−	0.193705i	0.612572	+	0.790415i	$0.290135\pi$
$888$	5.85109	+	2.60507i	0.196350	+	0.0874206i
$889$	−39.9238	+	35.9476i	−1.33900	+	1.20564i
$890$	−36.2361	+	20.9209i	−1.21464	+	0.701271i
$891$	−1.81182	+	2.04410i	−0.0606983	+	0.0684798i
$892$			17.5202i			0.586621i
$893$	8.02403	−	15.0128i	0.268514	−	0.502386i
$894$	−3.39510	+	2.46669i	−0.113549	+	0.0824984i
$895$	−42.2011	−	4.43552i	−1.41063	−	0.148263i
$896$	2.76662	+	2.49107i	0.0924262	+	0.0832209i
$897$	−0.307656	+	1.44741i	−0.0102723	+	0.0483276i
$898$	26.6424	+	2.80023i	0.889069	+	0.0934449i
$899$	14.7609	−	1.55144i	0.492305	−	0.0517434i
$900$	6.98205	−	21.4885i	0.232735	−	0.716284i
$901$	−52.9162			−1.76289
$902$	20.6412	+	22.5676i	0.687278	+	0.751420i
$903$	−20.2717	−	11.7039i	−0.674600	−	0.389480i
$904$	−3.11256	−	1.01133i	−0.103522	−	0.0336364i
$905$	58.9277	+	81.1070i	1.95882	+	2.69609i
$906$	−1.48581	−	3.33718i	−0.0493626	−	0.110870i
$907$	−8.53437	−	7.68438i	−0.283379	−	0.255156i	0.515166	−	0.857090i	$-0.327730\pi$
$907$	−8.53437	−	7.68438i	−0.283379	−	0.255156i	−0.798545	+	0.601935i	$0.794397\pi$
$908$	1.14302	+	0.242956i	0.0379324	+	0.00806278i
$909$	2.23676	+	0.235093i	0.0741887	+	0.00779755i
$910$	−1.62828	+	3.65717i	−0.0539769	+	0.121234i
$911$	48.3108	+	15.6971i	1.60061	+	0.520070i	0.967258	−	0.253795i	$-0.0816787\pi$
$911$	48.3108	+	15.6971i	1.60061	+	0.520070i	0.633352	+	0.773864i	$0.281679\pi$
$912$	−0.775795	+	4.34497i	−0.0256891	+	0.143876i
$913$	−28.5362	−	9.02634i	−0.944412	−	0.298728i
$914$	−31.4728	+	18.1708i	−1.04103	+	0.601038i
$915$	16.0686	−	3.41548i	0.531211	−	0.112912i
$916$	−1.35546	−	12.8963i	−0.0447857	−	0.426107i
$917$	−3.69823	+	35.1863i	−0.122126	+	1.16195i
$918$	−32.4086	−	6.88867i	−1.06964	−	0.227360i
$919$	−6.35878	+	2.06609i	−0.209757	+	0.0681541i	−0.412011	−	0.911179i	$-0.635173\pi$
$919$	−6.35878	+	2.06609i	−0.209757	+	0.0681541i	0.202254	+	0.979333i	$0.435173\pi$
$920$	18.0772	+	13.1339i	0.595989	+	0.433011i
$921$	−11.3568	+	1.19365i	−0.374220	+	0.0393321i
$922$	−19.4312	+	17.4960i	−0.639933	+	0.576199i
$923$			1.60025i			0.0526730i
$924$	3.95618	+	11.8601i	0.130149	+	0.390167i
$925$	62.6774	+	36.1868i	2.06082	+	1.18982i
$926$	−9.93513	+	2.11178i	−0.326489	+	0.0693973i
$927$	35.9505	−	3.77855i	1.18077	−	0.124104i
$928$	−0.360094	+	3.42607i	−0.0118207	+	0.112466i
$929$	22.6096	−	25.1105i	0.741797	−	0.823849i	−0.247634	−	0.968854i	$-0.579653\pi$
$929$	22.6096	−	25.1105i	0.741797	−	0.823849i	0.989431	+	0.145005i	$0.0463198\pi$
$930$	5.46639	+	16.8238i	0.179250	+	0.551675i
$931$	−8.30360	+	28.7243i	−0.272139	+	0.941400i
$932$	8.85486	+	12.1877i	0.290051	+	0.399220i
$933$	−1.83679	−	8.64144i	−0.0601339	−	0.282908i
$934$	−10.1608	−	17.5991i	−0.332472	−	0.575859i
$935$	−76.9498	−	43.6297i	−2.51653	−	1.42684i
$936$	0.261840	+	0.453520i	0.00855851	+	0.0148238i
$937$	29.1742	−	26.2686i	0.953081	−	0.858158i	−0.0369057	−	0.999319i	$-0.511750\pi$
$937$	29.1742	−	26.2686i	0.953081	−	0.858158i	0.989987	+	0.141161i	$0.0450835\pi$
$938$	7.13278	−	5.18227i	0.232894	−	0.169207i
$939$	−16.3557	+	22.5117i	−0.533748	+	0.734642i
$940$	15.4893	+	3.29234i	0.505204	+	0.107384i
$941$	7.57795	+	1.61074i	0.247034	+	0.0525087i	0.329764	−	0.944063i	$-0.393031\pi$
$941$	7.57795	+	1.61074i	0.247034	+	0.0525087i	−0.0827304	+	0.996572i	$0.526364\pi$
$942$	0.373174	−	0.513630i	0.0121587	−	0.0167350i
$943$	−41.1101	+	29.8683i	−1.33873	+	0.972644i
$944$	5.74853	−	5.17600i	0.187099	−	0.168465i
$945$	38.0201	+	65.8528i	1.23679	+	2.14219i
$946$	−20.4645	+	2.31254i	−0.665357	+	0.0751872i
$947$	10.4967	+	18.1808i	0.341097	+	0.590798i	0.984637	−	0.174615i	$-0.0558681\pi$
$947$	10.4967	+	18.1808i	0.341097	+	0.590798i	−0.643539	+	0.765413i	$0.722535\pi$
$948$	−2.06257	−	9.70365i	−0.0669893	−	0.315160i
$949$	0.00613900	+	0.00844960i	0.000199280	+	0.000274286i
$950$	−13.8505	+	47.9123i	−0.449368	+	1.55448i
$951$	10.3866	+	31.9666i	0.336808	+	1.03659i
$952$	16.3852	−	18.1976i	0.531047	−	0.589787i
$953$	−2.88526	+	27.4515i	−0.0934629	+	0.889240i	0.842868	+	0.538121i	$0.180866\pi$
$953$	−2.88526	+	27.4515i	−0.0934629	+	0.889240i	−0.936331	+	0.351119i	$0.885801\pi$
$954$	15.7994	−	1.66058i	0.511524	−	0.0537633i
$955$	−30.5556	+	6.49480i	−0.988757	+	0.210167i
$956$	3.85668	+	2.22666i	0.124734	+	0.0720152i
$957$	−6.72693	+	9.41246i	−0.217451	+	0.304262i
$958$		−	14.3590i		−	0.463920i
$959$	18.8156	−	16.9417i	0.607589	−	0.547075i
$960$	−4.08333	+	0.429176i	−0.131789	+	0.0138516i
$961$	−10.0622	−	7.31059i	−0.324586	−	0.235825i
$962$	−1.59534	+	0.518356i	−0.0514357	+	0.0167125i
$963$	−22.5127	−	4.78523i	−0.725462	−	0.154202i
$964$	2.58493	−	24.5940i	0.0832551	−	0.792120i
$965$	−1.49444	−	14.2187i	−0.0481078	−	0.457715i
$966$	−20.3190	+	4.31894i	−0.653754	+	0.138960i
$967$	42.7224	−	24.6658i	1.37386	−	0.793198i	0.382448	−	0.923977i	$-0.375081\pi$
$967$	42.7224	−	24.6658i	1.37386	−	0.793198i	0.991412	+	0.130779i	$0.0417478\pi$
$968$	8.99904	+	6.32593i	0.289240	+	0.203323i
$969$	28.5793	+	5.10284i	0.918099	+	0.163927i
$970$	−33.4249	−	10.8604i	−1.07321	−	0.348706i
$971$	−7.16636	+	16.0959i	−0.229979	+	0.516542i	−0.991267	−	0.131873i	$-0.957901\pi$
$971$	−7.16636	+	16.0959i	−0.229979	+	0.516542i	0.761287	+	0.648415i	$0.224568\pi$
$972$	15.8583	+	1.66677i	0.508654	+	0.0534617i
$973$	67.0862	+	14.2596i	2.15068	+	0.457142i
$974$	0.601979	+	0.542025i	0.0192887	+	0.0173676i
$975$	−1.24968	−	2.80683i	−0.0400219	−	0.0898906i
$976$	2.35175	+	3.23691i	0.0752777	+	0.103611i
$977$	57.5789	+	18.7085i	1.84211	+	0.598539i	0.998059	+	0.0622815i	$0.0198377\pi$
$977$	57.5789	+	18.7085i	1.84211	+	0.598539i	0.844055	+	0.536257i	$0.180162\pi$
$978$	13.3401	+	7.70191i	0.426569	+	0.246280i
$979$	−14.1638	−	31.1556i	−0.452677	−	0.995738i
$980$	−27.8148			−0.888512
$981$	−3.38670	+	10.4232i	−0.108129	+	0.332787i
$982$	−3.22810	+	0.339287i	−0.103013	+	0.0108271i
$983$	−5.47181	−	0.575110i	−0.174524	−	0.0183432i	0.0168636	−	0.999858i	$-0.494632\pi$
$983$	−5.47181	−	0.575110i	−0.174524	−	0.0183432i	−0.191387	+	0.981515i	$0.561299\pi$
$984$	1.94131	−	9.13317i	0.0618868	−	0.291155i
$985$	−61.4291	−	55.3110i	−1.95729	−	1.76236i
$986$	22.5352	+	2.36854i	0.717666	+	0.0754298i
$987$	−11.9099	+	8.65305i	−0.379096	+	0.275430i
$988$	−0.610448	−	0.981623i	−0.0194209	−	0.0312296i
$989$		−	34.2182i		−	1.08808i
$990$	24.3444	+	10.6119i	0.773714	+	0.337268i
$991$	23.8528	−	13.7714i	0.757709	−	0.437463i	−0.0707638	−	0.997493i	$-0.522544\pi$
$991$	23.8528	−	13.7714i	0.757709	−	0.437463i	0.828472	+	0.560030i	$0.189210\pi$
$992$	−3.20178	+	2.88290i	−0.101657	+	0.0915320i
$993$	−1.78515	−	0.794802i	−0.0566502	−	0.0252223i
$994$	−20.5225	+	9.13722i	−0.650935	+	0.289815i
$995$	10.2652	+	31.5930i	0.325428	+	1.00156i
$996$	2.82367	+	8.69036i	0.0894714	+	0.275365i
$997$	19.2304	+	43.1921i	0.609032	+	1.36791i	0.910133	+	0.414315i	$0.135979\pi$
$997$	19.2304	+	43.1921i	0.609032	+	1.36791i	−0.301102	+	0.953592i	$0.597354\pi$
$998$	−3.06187	−	29.1318i	−0.0969218	−	0.922150i
$999$	−9.84593	+	30.3026i	−0.311511	+	0.958733i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.s.a.145.7	✓	80
11.6	odd	10		418.2.s.b.259.7	yes	80
19.8	odd	6		418.2.s.b.255.7	yes	80
209.160	even	30	inner	418.2.s.a.369.7	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.s.a.145.7	✓	80	1.1	even	1	trivial
418.2.s.a.369.7	yes	80	209.160	even	30	inner
418.2.s.b.255.7	yes	80	19.8	odd	6
418.2.s.b.259.7	yes	80	11.6	odd	10

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)

\(f(q)\)	\(=\)	\(q+(0.978148 - 0.207912i) q^{2} +(0.411849 - 0.925027i) q^{3} +(0.913545 - 0.406737i) q^{4} +(2.71323 - 3.01335i) q^{5} +(0.210525 - 0.990442i) q^{6} +(-2.18824 + 3.01185i) q^{7} +(0.809017 - 0.587785i) q^{8} +(1.32134 + 1.46749i) q^{9} +O(q^{10})\)	\(q+(0.978148 - 0.207912i) q^{2} +(0.411849 - 0.925027i) q^{3} +(0.913545 - 0.406737i) q^{4} +(2.71323 - 3.01335i) q^{5} +(0.210525 - 0.990442i) q^{6} +(-2.18824 + 3.01185i) q^{7} +(0.809017 - 0.587785i) q^{8} +(1.32134 + 1.46749i) q^{9} +(2.02743 - 3.51161i) q^{10} +(2.69834 + 1.92846i) q^{11} -1.01257i q^{12} +(0.177449 + 0.197078i) q^{13} +(-1.51422 + 3.40099i) q^{14} +(-1.66999 - 3.75086i) q^{15} +(0.669131 - 0.743145i) q^{16} +(-4.88808 - 4.40125i) q^{17} +(1.59757 + 1.16070i) q^{18} +(-3.60843 - 2.44525i) q^{19} +(1.25302 - 3.85640i) q^{20} +(1.88482 + 3.26461i) q^{21} +(3.04033 + 1.32530i) q^{22} +(-2.75530 + 4.77232i) q^{23} +(-0.210525 - 0.990442i) q^{24} +(-1.19600 - 11.3792i) q^{25} +(0.214546 + 0.155877i) q^{26} +(4.79069 - 1.55659i) q^{27} +(-0.774024 + 3.64150i) q^{28} +(-3.14711 + 1.40118i) q^{29} +(-2.41334 - 3.32168i) q^{30} +(-4.09755 - 1.33137i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.89519 - 1.70181i) q^{33} +(-5.69633 - 3.28878i) q^{34} +(3.13856 + 14.7658i) q^{35} +(1.80398 + 0.803185i) q^{36} +(-3.71793 + 5.11729i) q^{37} +(-4.03797 - 1.64158i) q^{38} +(0.255384 - 0.0829794i) q^{39} +(0.423848 - 4.03265i) q^{40} +(8.42408 + 3.75064i) q^{41} +(2.52238 + 2.80139i) q^{42} +(-5.37762 + 3.10477i) q^{43} +(3.24943 + 0.664221i) q^{44} +8.00715 q^{45} +(-1.70287 + 5.24089i) q^{46} +(0.408211 + 3.88387i) q^{47} +(-0.411849 - 0.925027i) q^{48} +(-2.11974 - 6.52389i) q^{49} +(-3.53574 - 10.8819i) q^{50} +(-6.08442 + 2.70896i) q^{51} +(0.242267 + 0.107864i) q^{52} +(5.97857 - 5.38313i) q^{53} +(4.36237 - 2.51861i) q^{54} +(13.1323 - 2.89869i) q^{55} +3.72285i q^{56} +(-3.74805 + 2.33082i) q^{57} +(-2.78702 + 2.02489i) q^{58} +(7.69304 + 0.808571i) q^{59} +(-3.05122 - 2.74733i) q^{60} +(-0.831862 + 3.91360i) q^{61} +(-4.28482 - 0.450353i) q^{62} +(-7.31126 + 0.768444i) q^{63} +(0.309017 - 0.951057i) q^{64} +1.07533 q^{65} +(2.47809 - 2.26656i) q^{66} +(-2.05096 - 1.18412i) q^{67} +(-6.25563 - 2.03258i) q^{68} +(3.27976 + 4.51420i) q^{69} +(6.13995 + 13.7906i) q^{70} +(4.48434 + 4.03772i) q^{71} +(1.93155 + 0.410564i) q^{72} +(0.0391678 + 0.00411670i) q^{73} +(-2.57274 + 5.77847i) q^{74} +(-11.0187 - 3.58018i) q^{75} +(-4.29104 - 0.766166i) q^{76} +(-11.7128 + 3.90707i) q^{77} +(0.232551 - 0.134264i) q^{78} +(9.58320 - 2.03697i) q^{79} +(-0.423848 - 4.03265i) q^{80} +(-0.0860870 + 0.819063i) q^{81} +(9.01980 + 1.91722i) q^{82} +(-8.58249 + 2.78862i) q^{83} +(3.04970 + 2.21574i) q^{84} +(-26.5250 + 2.78789i) q^{85} +(-4.61458 + 4.15499i) q^{86} +3.48824i q^{87} +(3.31652 - 0.0258886i) q^{88} +(-8.93646 - 5.15947i) q^{89} +(7.83218 - 1.66478i) q^{90} +(-0.981870 + 0.103199i) q^{91} +(-0.576014 + 5.48041i) q^{92} +(-2.91913 + 3.24202i) q^{93} +(1.20679 + 3.71413i) q^{94} +(-17.1589 + 4.23893i) q^{95} +(-0.595173 - 0.819185i) q^{96} +(-1.80205 - 8.47797i) q^{97} +(-3.42981 - 5.94061i) q^{98} +(0.735415 + 6.50794i) 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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