LMFDB - Embedded newform 62.2.g.b.59.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [62,2,Mod(7,62)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(62, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([28]))

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

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

chi := DirichletCharacter("62.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	62.g (of order $15$, 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:	$0.495072492532$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			59.1
Root			$0.913545 + 0.406737i$ of defining polynomial
Character	$\chi$	$=$	62.59
Dual form			62.2.g.b.41.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(0.0399263 - 0.379874i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.604528 + 1.04707i) q^{5} +(-0.190983 - 0.330792i) q^{6} +(-3.01807 + 0.641511i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(2.79173 + 0.593401i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(0.0399263 - 0.379874i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.604528 + 1.04707i) q^{5} +(-0.190983 - 0.330792i) q^{6} +(-3.01807 + 0.641511i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(2.79173 + 0.593401i) q^{9} +(0.126381 + 1.20243i) q^{10} +(0.115699 + 0.128496i) q^{11} +(-0.348943 - 0.155360i) q^{12} +(-4.27222 + 1.90211i) q^{13} +(-2.06460 + 2.29297i) q^{14} +(0.373619 + 0.271450i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(1.91588 - 2.12780i) q^{17} +(2.60735 - 1.16087i) q^{18} +(-0.269091 - 0.119807i) q^{19} +(0.809017 + 0.898504i) q^{20} +(0.123193 + 1.17210i) q^{21} +(0.169131 + 0.0359498i) q^{22} +(-1.53440 - 4.72241i) q^{23} +(-0.373619 + 0.0794152i) q^{24} +(1.76909 + 3.06415i) q^{25} +(-2.33826 + 4.04999i) q^{26} +(0.690983 - 2.12663i) q^{27} +(-0.322523 + 3.06860i) q^{28} +(6.82614 - 4.95948i) q^{29} +0.461819 q^{30} +(-3.10735 - 4.62000i) q^{31} -1.00000 q^{32} +(0.0534318 - 0.0388205i) q^{33} +(0.299290 - 2.84755i) q^{34} +(1.15280 - 3.54796i) q^{35} +(1.42705 - 2.47172i) q^{36} +(4.00973 + 6.94505i) q^{37} +(-0.288120 + 0.0612417i) q^{38} +(0.551989 + 1.69885i) q^{39} +(1.18264 + 0.251377i) q^{40} +(-0.196341 - 1.86806i) q^{41} +(0.788608 + 0.875838i) q^{42} +(-4.41667 - 1.96643i) q^{43} +(0.157960 - 0.0703285i) q^{44} +(-2.30902 + 2.56442i) q^{45} +(-4.01712 - 2.91861i) q^{46} +(8.11787 + 5.89798i) q^{47} +(-0.255585 + 0.283856i) q^{48} +(2.30242 - 1.02510i) q^{49} +(3.23229 + 1.43911i) q^{50} +(-0.731801 - 0.812748i) q^{51} +(0.488830 + 4.65090i) q^{52} +(-8.21139 - 1.74539i) q^{53} +(-0.690983 - 2.12663i) q^{54} +(-0.204489 + 0.0434654i) q^{55} +(1.54275 + 2.67212i) q^{56} +(-0.0562553 + 0.0974370i) q^{57} +(2.60735 - 8.02460i) q^{58} +(-1.54653 + 14.7142i) q^{59} +(0.373619 - 0.271450i) q^{60} -12.5623 q^{61} +(-5.22947 - 1.91120i) q^{62} -8.80633 q^{63} +(-0.809017 + 0.587785i) q^{64} +(0.591023 - 5.62321i) q^{65} +(0.0204091 - 0.0628129i) q^{66} +(-4.60075 + 7.96873i) q^{67} +(-1.43162 - 2.47964i) q^{68} +(-1.85518 + 0.394331i) q^{69} +(-1.15280 - 3.54796i) q^{70} +(9.97420 + 2.12008i) q^{71} +(-0.298335 - 2.83847i) q^{72} +(1.57384 + 1.74793i) q^{73} +(7.32614 + 3.26181i) q^{74} +(1.23462 - 0.549690i) q^{75} +(-0.197097 + 0.218898i) q^{76} +(-0.431619 - 0.313590i) q^{77} +(1.44512 + 1.04994i) q^{78} +(4.94240 - 5.48910i) q^{79} +(1.10453 - 0.491768i) q^{80} +(7.04179 + 3.13521i) q^{81} +(-1.25686 - 1.39589i) q^{82} +(-0.582676 - 5.54379i) q^{83} +(1.15280 + 0.245036i) q^{84} +(1.06976 + 3.29239i) q^{85} +(-4.72900 + 1.00518i) q^{86} +(-1.61143 - 2.79108i) q^{87} +(0.0864545 - 0.149744i) q^{88} +(0.590233 - 1.81655i) q^{89} +(-0.360704 + 3.43187i) q^{90} +(11.6736 - 8.48139i) q^{91} -4.96543 q^{92} +(-1.87908 + 0.995941i) q^{93} +10.0342 q^{94} +(0.288120 - 0.209331i) q^{95} +(-0.0399263 + 0.379874i) q^{96} +(5.32614 - 16.3922i) q^{97} +(1.26015 - 2.18265i) q^{98} +(0.246750 + 0.427384i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + q^{3} - 2 q^{4} - 3 q^{5} - 6 q^{6} - 16 q^{7} + 2 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 + q^3 - 2 * q^4 - 3 * q^5 - 6 * q^6 - 16 * q^7 + 2 * q^8 + 8 * q^9	\( 8 q + 2 q^{2} + q^{3} - 2 q^{4} - 3 q^{5} - 6 q^{6} - 16 q^{7} + 2 q^{8} + 8 q^{9} + 8 q^{10} + 3 q^{11} + q^{12} - 14 q^{14} - 4 q^{15} - 2 q^{16} - 2 q^{17} + 7 q^{18} + 3 q^{19} + 2 q^{20} - 31 q^{21} - 3 q^{22} + 15 q^{23} + 4 q^{24} + 9 q^{25} - 10 q^{26} + 10 q^{27} + 9 q^{28} + 13 q^{29} + 14 q^{30} - 11 q^{31} - 8 q^{32} - 6 q^{33} + 22 q^{34} + 24 q^{35} - 2 q^{36} + 8 q^{37} - 18 q^{38} - 30 q^{39} - 2 q^{40} + 13 q^{41} + 21 q^{42} - 7 q^{44} - 14 q^{45} + 5 q^{46} + 9 q^{47} - 4 q^{48} + 9 q^{49} - 9 q^{50} + 28 q^{51} - 51 q^{53} - 10 q^{54} + q^{55} + q^{56} + 18 q^{57} + 7 q^{58} - 18 q^{59} - 4 q^{60} - 20 q^{61} - 19 q^{62} - 14 q^{63} - 2 q^{64} + 10 q^{65} - 19 q^{66} - 18 q^{67} + 3 q^{68} + 35 q^{69} - 24 q^{70} + 7 q^{71} + 7 q^{72} - 13 q^{73} + 17 q^{74} - 36 q^{75} - 12 q^{76} + 11 q^{77} - 10 q^{78} + 9 q^{79} + 7 q^{80} + 16 q^{81} + 7 q^{82} + 6 q^{83} + 24 q^{84} - 17 q^{85} + 15 q^{86} + q^{87} + 7 q^{88} + 28 q^{89} + 19 q^{90} + 20 q^{91} - 20 q^{92} + 32 q^{93} + 6 q^{94} + 18 q^{95} - q^{96} + q^{97} + 11 q^{98} - 11 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + q^3 - 2 * q^4 - 3 * q^5 - 6 * q^6 - 16 * q^7 + 2 * q^8 + 8 * q^9 + 8 * q^10 + 3 * q^11 + q^12 - 14 * q^14 - 4 * q^15 - 2 * q^16 - 2 * q^17 + 7 * q^18 + 3 * q^19 + 2 * q^20 - 31 * q^21 - 3 * q^22 + 15 * q^23 + 4 * q^24 + 9 * q^25 - 10 * q^26 + 10 * q^27 + 9 * q^28 + 13 * q^29 + 14 * q^30 - 11 * q^31 - 8 * q^32 - 6 * q^33 + 22 * q^34 + 24 * q^35 - 2 * q^36 + 8 * q^37 - 18 * q^38 - 30 * q^39 - 2 * q^40 + 13 * q^41 + 21 * q^42 - 7 * q^44 - 14 * q^45 + 5 * q^46 + 9 * q^47 - 4 * q^48 + 9 * q^49 - 9 * q^50 + 28 * q^51 - 51 * q^53 - 10 * q^54 + q^55 + q^56 + 18 * q^57 + 7 * q^58 - 18 * q^59 - 4 * q^60 - 20 * q^61 - 19 * q^62 - 14 * q^63 - 2 * q^64 + 10 * q^65 - 19 * q^66 - 18 * q^67 + 3 * q^68 + 35 * q^69 - 24 * q^70 + 7 * q^71 + 7 * q^72 - 13 * q^73 + 17 * q^74 - 36 * q^75 - 12 * q^76 + 11 * q^77 - 10 * q^78 + 9 * q^79 + 7 * q^80 + 16 * q^81 + 7 * q^82 + 6 * q^83 + 24 * q^84 - 17 * q^85 + 15 * q^86 + q^87 + 7 * q^88 + 28 * q^89 + 19 * q^90 + 20 * q^91 - 20 * q^92 + 32 * q^93 + 6 * q^94 + 18 * q^95 - q^96 + q^97 + 11 * q^98 - 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{8}{15}\right)$

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 $

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	0.0399263	−	0.379874i	0.0230515	−	0.219320i	−0.976932	−	0.213551i	$-0.931497\pi$
$3$	0.0399263	−	0.379874i	0.0230515	−	0.219320i	0.999983	−	0.00576897i	$-0.00183633\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−0.604528	+	1.04707i	−0.270353	+	0.468266i	−0.968952	−	0.247248i	$-0.920474\pi$
$5$	−0.604528	+	1.04707i	−0.270353	+	0.468266i	0.698599	+	0.715513i	$0.253807\pi$
$6$	−0.190983	−	0.330792i	−0.0779685	−	0.135045i
$7$	−3.01807	+	0.641511i	−1.14072	+	0.242469i	−0.739269	−	0.673410i	$-0.764829\pi$
$7$	−3.01807	+	0.641511i	−1.14072	+	0.242469i	−0.401456	+	0.915879i	$0.631496\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	2.79173	+	0.593401i	0.930578	+	0.197800i
$10$	0.126381	+	1.20243i	0.0399651	+	0.380243i
$11$	0.115699	+	0.128496i	0.0348845	+	0.0387431i	0.760335	−	0.649532i	$-0.225035\pi$
$11$	0.115699	+	0.128496i	0.0348845	+	0.0387431i	−0.725450	+	0.688275i	$0.758368\pi$
$12$	−0.348943	−	0.155360i	−0.100731	−	0.0448484i
$13$	−4.27222	+	1.90211i	−1.18490	+	0.527551i	−0.902058	−	0.431615i	$-0.857944\pi$
$13$	−4.27222	+	1.90211i	−1.18490	+	0.527551i	−0.282842	+	0.959167i	$0.591277\pi$
$14$	−2.06460	+	2.29297i	−0.551788	+	0.612823i
$15$	0.373619	+	0.271450i	0.0964680	+	0.0700881i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	1.91588	−	2.12780i	0.464669	−	0.516068i	−0.464575	−	0.885534i	$-0.653793\pi$
$17$	1.91588	−	2.12780i	0.464669	−	0.516068i	0.929244	+	0.369466i	$0.120459\pi$
$18$	2.60735	−	1.16087i	0.614559	−	0.273619i
$19$	−0.269091	−	0.119807i	−0.0617336	−	0.0274856i	0.375638	−	0.926767i	$-0.377424\pi$
$19$	−0.269091	−	0.119807i	−0.0617336	−	0.0274856i	−0.437371	+	0.899281i	$0.644090\pi$
$20$	0.809017	+	0.898504i	0.180902	+	0.200912i
$21$	0.123193	+	1.17210i	0.0268828	+	0.255773i
$22$	0.169131	+	0.0359498i	0.0360588	+	0.00766453i
$23$	−1.53440	−	4.72241i	−0.319945	−	0.984690i	−0.973671	−	0.227958i	$-0.926795\pi$
$23$	−1.53440	−	4.72241i	−0.319945	−	0.984690i	0.653726	−	0.756732i	$-0.273205\pi$
$24$	−0.373619	+	0.0794152i	−0.0762647	+	0.0162106i
$25$	1.76909	+	3.06415i	0.353818	+	0.612831i
$26$	−2.33826	+	4.04999i	−0.458571	+	0.794268i
$27$	0.690983	−	2.12663i	0.132980	−	0.409270i
$28$	−0.322523	+	3.06860i	−0.0609510	+	0.579910i
$29$	6.82614	−	4.95948i	1.26758	−	0.920952i	0.268478	−	0.963286i	$-0.413479\pi$
$29$	6.82614	−	4.95948i	1.26758	−	0.920952i	0.999104	+	0.0423338i	$0.0134793\pi$
$30$	0.461819			0.0843162
$31$	−3.10735	−	4.62000i	−0.558097	−	0.829776i
$31$	−3.10735	−	4.62000i	−0.558097	−	0.829776i
$32$	−1.00000			−0.176777
$33$	0.0534318	−	0.0388205i	0.00930129	−	0.00675778i
$34$	0.299290	−	2.84755i	0.0513278	−	0.488351i
$35$	1.15280	−	3.54796i	0.194859	−	0.599714i
$36$	1.42705	−	2.47172i	0.237842	−	0.411954i
$37$	4.00973	+	6.94505i	0.659195	+	1.14176i	0.980824	+	0.194894i	$0.0624362\pi$
$37$	4.00973	+	6.94505i	0.659195	+	1.14176i	−0.321629	+	0.946866i	$0.604230\pi$
$38$	−0.288120	+	0.0612417i	−0.0467392	+	0.00993472i
$39$	0.551989	+	1.69885i	0.0883889	+	0.272033i
$40$	1.18264	+	0.251377i	0.186991	+	0.0397462i
$41$	−0.196341	−	1.86806i	−0.0306634	−	0.291742i	−0.999098	−	0.0424732i	$-0.986476\pi$
$41$	−0.196341	−	1.86806i	−0.0306634	−	0.291742i	0.968434	−	0.249269i	$-0.0801904\pi$
$42$	0.788608	+	0.875838i	0.121685	+	0.135145i
$43$	−4.41667	−	1.96643i	−0.673536	−	0.299878i	0.0413234	−	0.999146i	$-0.486843\pi$
$43$	−4.41667	−	1.96643i	−0.673536	−	0.299878i	−0.714859	+	0.699268i	$0.753509\pi$
$44$	0.157960	−	0.0703285i	0.0238134	−	0.0106024i
$45$	−2.30902	+	2.56442i	−0.344208	+	0.382282i
$46$	−4.01712	−	2.91861i	−0.592292	−	0.430325i
$47$	8.11787	+	5.89798i	1.18411	+	0.860308i	0.992630	−	0.121188i	$-0.0386702\pi$
$47$	8.11787	+	5.89798i	1.18411	+	0.860308i	0.191483	+	0.981496i	$0.438670\pi$
$48$	−0.255585	+	0.283856i	−0.0368905	+	0.0409711i
$49$	2.30242	−	1.02510i	0.328916	−	0.146443i
$50$	3.23229	+	1.43911i	0.457115	+	0.203521i
$51$	−0.731801	−	0.812748i	−0.102473	−	0.113807i
$52$	0.488830	+	4.65090i	0.0677885	+	0.644964i
$53$	−8.21139	−	1.74539i	−1.12792	−	0.239747i	−0.394085	−	0.919074i	$-0.628939\pi$
$53$	−8.21139	−	1.74539i	−1.12792	−	0.239747i	−0.733836	+	0.679327i	$0.762272\pi$
$54$	−0.690983	−	2.12663i	−0.0940309	−	0.289397i
$55$	−0.204489	+	0.0434654i	−0.0275732	+	0.00586087i
$56$	1.54275	+	2.67212i	0.206159	+	0.357077i
$57$	−0.0562553	+	0.0974370i	−0.00745119	+	0.0129058i
$58$	2.60735	−	8.02460i	0.342362	−	1.05368i
$59$	−1.54653	+	14.7142i	−0.201341	+	1.91563i	0.167031	+	0.985952i	$0.446582\pi$
$59$	−1.54653	+	14.7142i	−0.201341	+	1.91563i	−0.368372	+	0.929678i	$0.620085\pi$
$60$	0.373619	−	0.271450i	0.0482340	−	0.0350441i
$61$	−12.5623			−1.60844			−0.804219	−	0.594333i	$-0.797416\pi$
$61$	−12.5623			−1.60844			−0.804219	+	0.594333i	$0.797416\pi$
$62$	−5.22947	−	1.91120i	−0.664143	−	0.242723i
$63$	−8.80633			−1.10949
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	0.591023	−	5.62321i	0.0733074	−	0.697473i
$66$	0.0204091	−	0.0628129i	0.00251219	−	0.00773173i
$67$	−4.60075	+	7.96873i	−0.562071	+	0.973536i	0.435244	+	0.900312i	$0.356662\pi$
$67$	−4.60075	+	7.96873i	−0.562071	+	0.973536i	−0.997316	+	0.0732234i	$0.976671\pi$
$68$	−1.43162	−	2.47964i	−0.173609	−	0.300700i
$69$	−1.85518	+	0.394331i	−0.223337	+	0.0474718i
$70$	−1.15280	−	3.54796i	−0.137786	−	0.424062i
$71$	9.97420	+	2.12008i	1.18372	+	0.251608i	0.757392	−	0.652961i	$-0.226473\pi$
$71$	9.97420	+	2.12008i	1.18372	+	0.251608i	0.426329	+	0.904568i	$0.359807\pi$
$72$	−0.298335	−	2.83847i	−0.0351591	−	0.334517i
$73$	1.57384	+	1.74793i	0.184204	+	0.204579i	0.828173	−	0.560472i	$-0.189380\pi$
$73$	1.57384	+	1.74793i	0.184204	+	0.204579i	−0.643969	+	0.765051i	$0.722714\pi$
$74$	7.32614	+	3.26181i	0.851646	+	0.379177i
$75$	1.23462	−	0.549690i	0.142562	−	0.0634728i
$76$	−0.197097	+	0.218898i	−0.0226085	+	0.0251093i
$77$	−0.431619	−	0.313590i	−0.0491876	−	0.0357369i
$78$	1.44512	+	1.04994i	0.163628	+	0.118883i
$79$	4.94240	−	5.48910i	0.556064	−	0.617571i	−0.397923	−	0.917419i	$-0.630269\pi$
$79$	4.94240	−	5.48910i	0.556064	−	0.617571i	0.953987	+	0.299847i	$0.0969357\pi$
$80$	1.10453	−	0.491768i	0.123490	−	0.0549813i
$81$	7.04179	+	3.13521i	0.782422	+	0.348357i
$82$	−1.25686	−	1.39589i	−0.138797	−	0.154150i
$83$	−0.582676	−	5.54379i	−0.0639570	−	0.608510i	−0.978817	−	0.204738i	$-0.934366\pi$
$83$	−0.582676	−	5.54379i	−0.0639570	−	0.608510i	0.914860	−	0.403772i	$-0.132301\pi$
$84$	1.15280	+	0.245036i	0.125781	+	0.0267356i
$85$	1.06976	+	3.29239i	0.116032	+	0.357109i
$86$	−4.72900	+	1.00518i	−0.509941	+	0.108391i
$87$	−1.61143	−	2.79108i	−0.172764	−	0.299235i
$88$	0.0864545	−	0.149744i	0.00921609	−	0.0159627i
$89$	0.590233	−	1.81655i	0.0625646	−	0.192554i	−0.914889	−	0.403707i	$-0.867722\pi$
$89$	0.590233	−	1.81655i	0.0625646	−	0.192554i	0.977453	+	0.211153i	$0.0677217\pi$
$90$	−0.360704	+	3.43187i	−0.0380215	+	0.361751i
$91$	11.6736	−	8.48139i	1.22373	−	0.889092i
$92$	−4.96543			−0.517682
$93$	−1.87908	+	0.995941i	−0.194851	+	0.103274i
$94$	10.0342			1.03495
$95$	0.288120	−	0.209331i	0.0295605	−	0.0214769i
$96$	−0.0399263	+	0.379874i	−0.00407496	+	0.0387707i
$97$	5.32614	−	16.3922i	0.540787	−	1.66437i	−0.190014	−	0.981781i	$-0.560853\pi$
$97$	5.32614	−	16.3922i	0.540787	−	1.66437i	0.730801	−	0.682590i	$-0.239147\pi$
$98$	1.26015	−	2.18265i	0.127295	−	0.220481i
$99$	0.246750	+	0.427384i	0.0247993	+	0.0429537i
$100$	3.46086	−	0.735629i	0.346086	−	0.0735629i
$101$	0.184381	+	0.567467i	0.0183466	+	0.0564650i	0.959811	−	0.280648i	$-0.0905494\pi$
$101$	0.184381	+	0.567467i	0.0183466	+	0.0564650i	−0.941464	+	0.337113i	$0.890549\pi$
$102$	−1.06976	−	0.227385i	−0.105922	−	0.0225144i
$103$	1.50329	+	14.3029i	0.148124	+	1.40930i	0.775874	+	0.630887i	$0.217309\pi$
$103$	1.50329	+	14.3029i	0.148124	+	1.40930i	−0.627751	+	0.778414i	$0.716024\pi$
$104$	3.12920	+	3.47533i	0.306844	+	0.340784i
$105$	−1.30175	−	0.579576i	−0.127038	−	0.0565608i
$106$	−7.66907	+	3.41449i	−0.744886	+	0.331644i
$107$	1.36623	−	1.51735i	0.132078	−	0.146688i	−0.673478	−	0.739208i	$-0.735200\pi$
$107$	1.36623	−	1.51735i	0.132078	−	0.146688i	0.805556	+	0.592520i	$0.201867\pi$
$108$	−1.80902	−	1.31433i	−0.174073	−	0.126471i
$109$	6.22522	+	4.52289i	0.596268	+	0.433214i	0.844552	−	0.535473i	$-0.179867\pi$
$109$	6.22522	+	4.52289i	0.596268	+	0.433214i	−0.248284	+	0.968687i	$0.579867\pi$
$110$	−0.139886	+	0.155360i	−0.0133376	+	0.0148130i
$111$	2.79833	−	1.24590i	0.265606	−	0.118255i
$112$	2.81874	+	1.25499i	0.266346	+	0.118585i
$113$	−8.25969	−	9.17331i	−0.777006	−	0.862953i	0.216553	−	0.976271i	$-0.430519\pi$
$113$	−8.25969	−	9.17331i	−0.777006	−	0.862953i	−0.993559	+	0.113318i	$0.963852\pi$
$114$	0.0117606	+	0.111894i	0.00110148	+	0.0104799i
$115$	5.87230	+	1.24820i	0.547595	+	0.116395i
$116$	−2.60735	−	8.02460i	−0.242087	−	0.745066i
$117$	−13.0556	+	2.77505i	−1.20699	+	0.256554i
$118$	7.39764	+	12.8131i	0.681008	+	1.17954i
$119$	−4.41726	+	7.65092i	−0.404930	+	0.701359i
$120$	0.142710	−	0.439216i	0.0130276	−	0.0400947i
$121$	1.14669	−	10.9100i	0.104244	−	0.991819i
$122$	−10.1631	+	7.38394i	−0.920126	+	0.668510i
$123$	−0.717467			−0.0646918
$124$	−5.35410	+	1.52761i	−0.480813	+	0.137183i
$125$	−10.3231			−0.923330
$126$	−7.12447	+	5.17623i	−0.634698	+	0.461135i
$127$	1.61320	−	15.3486i	0.143148	−	1.36196i	−0.653227	−	0.757162i	$-0.726585\pi$
$127$	1.61320	−	15.3486i	0.143148	−	1.36196i	0.796376	−	0.604802i	$-0.206748\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	−0.923336	+	1.59926i	−0.0812952	+	0.140807i
$130$	−2.82709	−	4.89667i	−0.247952	−	0.429466i
$131$	−10.6768	+	2.26943i	−0.932838	+	0.198281i	−0.649172	−	0.760642i	$-0.724884\pi$
$131$	−10.6768	+	2.26943i	−0.932838	+	0.198281i	−0.283667	+	0.958923i	$0.591551\pi$
$132$	−0.0204091	−	0.0628129i	−0.00177639	−	0.00546716i
$133$	0.888993	+	0.188961i	0.0770855	+	0.0163850i
$134$	0.961819	+	9.15109i	0.0830885	+	0.790534i
$135$	1.80902	+	2.00912i	0.155695	+	0.172917i
$136$	−2.61570	−	1.16458i	−0.224294	−	0.0998623i
$137$	−6.69975	+	2.98292i	−0.572399	+	0.254848i	−0.672461	−	0.740133i	$-0.734763\pi$
$137$	−6.69975	+	2.98292i	−0.572399	+	0.254848i	0.100062	+	0.994981i	$0.468096\pi$
$138$	−1.26909	+	1.40947i	−0.108032	+	0.119982i
$139$	9.77455	+	7.10163i	0.829067	+	0.602352i	0.919295	−	0.393569i	$-0.128760\pi$
$139$	9.77455	+	7.10163i	0.829067	+	0.602352i	−0.0902285	+	0.995921i	$0.528760\pi$
$140$	−3.01807	−	2.19276i	−0.255074	−	0.185322i
$141$	2.56460	−	2.84828i	0.215978	−	0.239868i
$142$	9.31545	−	4.14751i	0.781736	−	0.348051i
$143$	−0.738705	−	0.328893i	−0.0617736	−	0.0275034i
$144$	−1.90977	−	2.12101i	−0.159147	−	0.176751i
$145$	1.06635	+	10.1456i	0.0885553	+	0.842547i
$146$	2.30067	+	0.489023i	0.190405	+	0.0404718i
$147$	−0.297482	−	0.915555i	−0.0245359	−	0.0755137i
$148$	7.84421	−	1.66734i	0.644790	−	0.137054i
$149$	−4.67206	−	8.09224i	−0.382750	−	0.662942i	0.608704	−	0.793397i	$-0.291690\pi$
$149$	−4.67206	−	8.09224i	−0.382750	−	0.662942i	−0.991454	+	0.130455i	$0.958356\pi$
$150$	0.675733	−	1.17040i	0.0551733	−	0.0955630i
$151$	−5.87782	+	18.0901i	−0.478330	+	1.47215i	0.363083	+	0.931757i	$0.381724\pi$
$151$	−5.87782	+	18.0901i	−0.478330	+	1.47215i	−0.841413	+	0.540393i	$0.818276\pi$
$152$	−0.0307895	+	0.292943i	−0.00249736	+	0.0237608i
$153$	6.61127	−	4.80337i	0.534489	−	0.388329i
$154$	−0.533511			−0.0429915
$155$	6.71596	−	0.460708i	0.539439	−	0.0370050i
$156$	1.78627			0.143016
$157$	−2.98272	+	2.16707i	−0.238047	+	0.172951i	−0.700413	−	0.713738i	$-0.747001\pi$
$157$	−2.98272	+	2.16707i	−0.238047	+	0.172951i	0.462366	+	0.886689i	$0.347001\pi$
$158$	0.772079	−	7.34584i	0.0614233	−	0.584404i
$159$	−0.990876	+	3.04960i	−0.0785816	+	0.241849i
$160$	0.604528	−	1.04707i	0.0477922	−	0.0827785i
$161$	7.66042	+	13.2682i	0.603726	+	1.04568i
$162$	7.53976	−	1.60263i	0.592380	−	0.125914i
$163$	−2.90977	−	8.95534i	−0.227911	−	0.701437i	−0.997983	−	0.0634802i	$-0.979780\pi$
$163$	−2.90977	−	8.95534i	−0.227911	−	0.701437i	0.770073	−	0.637956i	$-0.220220\pi$
$164$	−1.83731	−	0.390531i	−0.143470	−	0.0304954i
$165$	0.00834687	+	0.0794152i	0.000649803	+	0.00618246i
$166$	−3.72995	−	4.14253i	−0.289501	−	0.321523i
$167$	2.99856	+	1.33504i	0.232035	+	0.103309i	0.519461	−	0.854494i	$-0.326133\pi$
$167$	2.99856	+	1.33504i	0.232035	+	0.103309i	−0.287426	+	0.957803i	$0.592799\pi$
$168$	1.07666	−	0.479362i	0.0830665	−	0.0369836i
$169$	5.93510	−	6.59159i	0.456546	−	0.507046i
$170$	2.80067	+	2.03481i	0.214802	+	0.156062i
$171$	−0.680136	−	0.494148i	−0.0520113	−	0.0377884i
$172$	−3.23501	+	3.59284i	−0.246667	+	0.273952i
$173$	−0.912653	+	0.406340i	−0.0693878	+	0.0308934i	−0.441137	−	0.897440i	$-0.645425\pi$
$173$	−0.912653	+	0.406340i	−0.0693878	+	0.0308934i	0.371749	+	0.928333i	$0.378758\pi$
$174$	−2.94423	−	1.31086i	−0.223202	−	0.0993758i
$175$	−7.30494	−	8.11295i	−0.552201	−	0.613282i
$176$	−0.0180739	−	0.171962i	−0.00136237	−	0.0129621i
$177$	5.52780	+	1.17497i	0.415495	+	0.0883162i
$178$	−0.590233	−	1.81655i	−0.0442398	−	0.136156i
$179$	11.8087	−	2.51001i	0.882623	−	0.187607i	0.255763	−	0.966739i	$-0.417673\pi$
$179$	11.8087	−	2.51001i	0.882623	−	0.187607i	0.626860	+	0.779132i	$0.284340\pi$
$180$	1.72539	+	2.98846i	0.128603	+	0.222746i
$181$	5.82236	−	10.0846i	0.432772	−	0.749584i	−0.564338	−	0.825544i	$-0.690869\pi$
$181$	5.82236	−	10.0846i	0.432772	−	0.749584i	0.997111	+	0.0759597i	$0.0242020\pi$
$182$	4.45893	−	13.7232i	0.330518	−	1.01723i
$183$	−0.501567	+	4.77209i	−0.0370769	+	0.352763i
$184$	−4.01712	+	2.91861i	−0.296146	+	0.215163i
$185$	−9.69598			−0.712862
$186$	−0.934808	+	1.91023i	−0.0685434	+	0.140065i
$187$	0.495080			0.0362038
$188$	8.11787	−	5.89798i	0.592056	−	0.430154i
$189$	−0.721182	+	6.86159i	−0.0524583	+	0.499107i
$190$	0.110052	−	0.338705i	0.00798400	−	0.0245722i
$191$	3.88936	−	6.73657i	0.281424	−	0.487441i	−0.690312	−	0.723512i	$-0.742527\pi$
$191$	3.88936	−	6.73657i	0.281424	−	0.487441i	0.971736	+	0.236071i	$0.0758599\pi$
$192$	0.190983	+	0.330792i	0.0137830	+	0.0238729i
$193$	−8.13324	+	1.72877i	−0.585444	+	0.124440i	−0.491105	−	0.871100i	$-0.663407\pi$
$193$	−8.13324	+	1.72877i	−0.585444	+	0.124440i	−0.0943385	+	0.995540i	$0.530074\pi$
$194$	−5.32614	−	16.3922i	−0.382394	−	1.17689i
$195$	−2.11251	−	0.449028i	−0.151280	−	0.0321556i
$196$	−0.263444	−	2.50650i	−0.0188174	−	0.179036i
$197$	6.75648	+	7.50383i	0.481379	+	0.534626i	0.934093	−	0.357030i	$-0.116211\pi$
$197$	6.75648	+	7.50383i	0.481379	+	0.534626i	−0.452714	+	0.891656i	$0.649544\pi$
$198$	0.450835	+	0.200725i	0.0320394	+	0.0142649i
$199$	−1.43978	+	0.641031i	−0.102063	+	0.0454415i	−0.457133	−	0.889398i	$-0.651124\pi$
$199$	−1.43978	+	0.641031i	−0.102063	+	0.0454415i	0.355070	+	0.934840i	$0.384457\pi$
$200$	2.36751	−	2.62938i	0.167408	−	0.185925i
$201$	2.84342	+	2.06587i	0.200559	+	0.145715i
$202$	0.482716	+	0.350714i	0.0339638	+	0.0246761i
$203$	−17.4202	+	19.3471i	−1.22266	+	1.35790i
$204$	−0.999108	+	0.444832i	−0.0699516	+	0.0311444i
$205$	2.07469	+	0.923713i	0.144903	+	0.0645149i
$206$	9.62319	+	10.6876i	0.670480	+	0.744643i
$207$	−1.48136	−	14.0942i	−0.102962	−	0.979616i
$208$	4.57433	+	0.972304i	0.317173	+	0.0674171i
$209$	−0.0157387	−	0.0484387i	−0.00108867	−	0.00335058i
$210$	−1.39380	+	0.296262i	−0.0961815	+	0.0204440i
$211$	−4.02307	−	6.96816i	−0.276959	−	0.479708i	0.693668	−	0.720295i	$-0.255993\pi$
$211$	−4.02307	−	6.96816i	−0.276959	−	0.479708i	−0.970628	+	0.240587i	$0.922660\pi$
$212$	−4.19742	+	7.27014i	−0.288280	+	0.499316i
$213$	1.20360	−	3.70429i	0.0824691	−	0.253814i
$214$	0.213426	−	2.03061i	0.0145895	−	0.138810i
$215$	4.72900	−	3.43582i	0.322515	−	0.234321i
$216$	−2.23607			−0.152145
$217$	12.3420	+	11.9501i	0.837829	+	0.811225i
$218$	7.69480			0.521157
$219$	0.726829	−	0.528072i	0.0491146	−	0.0356838i
$220$	−0.0218524	+	0.207912i	−0.00147329	+	0.0140174i
$221$	−4.13774	+	12.7346i	−0.278334	+	0.856625i
$222$	1.53158	−	2.65277i	0.102793	−	0.178042i
$223$	0.818319	+	1.41737i	0.0547987	+	0.0949141i	0.892123	−	0.451792i	$-0.149215\pi$
$223$	0.818319	+	1.41737i	0.0547987	+	0.0949141i	−0.837325	+	0.546706i	$0.815882\pi$
$224$	3.01807	−	0.641511i	0.201654	−	0.0428628i
$225$	3.12056	+	9.60408i	0.208037	+	0.640272i
$226$	−12.0742	−	2.56644i	−0.803161	−	0.170717i
$227$	−1.87143	−	17.8054i	−0.124211	−	1.18179i	−0.862054	−	0.506816i	$-0.830822\pi$
$227$	−1.87143	−	17.8054i	−0.124211	−	1.18179i	0.737843	−	0.674972i	$-0.235844\pi$
$228$	0.0752842	+	0.0836116i	0.00498582	+	0.00553732i
$229$	2.05626	+	0.915504i	0.135881	+	0.0604982i	0.473551	−	0.880766i	$-0.342972\pi$
$229$	2.05626	+	0.915504i	0.135881	+	0.0604982i	−0.337670	+	0.941265i	$0.609639\pi$
$230$	5.48446	−	2.44184i	0.361635	−	0.161010i
$231$	−0.136357	+	0.151440i	−0.00897166	+	0.00996404i
$232$	−6.82614	−	4.95948i	−0.448158	−	0.325606i
$233$	3.22539	+	2.34338i	0.211302	+	0.153520i	0.688403	−	0.725329i	$-0.258312\pi$
$233$	3.22539	+	2.34338i	0.211302	+	0.153520i	−0.477101	+	0.878849i	$0.658312\pi$
$234$	−8.93107	+	9.91896i	−0.583842	+	0.648422i
$235$	−11.0831	+	4.93451i	−0.722982	+	0.321892i
$236$	13.5162	+	6.01778i	0.879827	+	0.391724i
$237$	−1.88783	−	2.09665i	−0.122628	−	0.136192i
$238$	0.923459	+	8.78613i	0.0598590	+	0.569520i
$239$	−21.5117	−	4.57246i	−1.39148	−	0.295768i	−0.549597	−	0.835430i	$-0.685219\pi$
$239$	−21.5117	−	4.57246i	−1.39148	−	0.295768i	−0.841882	+	0.539662i	$0.818552\pi$
$240$	−0.142710	−	0.439216i	−0.00921188	−	0.0283512i
$241$	−3.92610	+	0.834517i	−0.252902	+	0.0537560i	−0.332618	−	0.943062i	$-0.607932\pi$
$241$	−3.92610	+	0.834517i	−0.252902	+	0.0537560i	0.0797160	+	0.996818i	$0.474599\pi$
$242$	−5.48505	−	9.50039i	−0.352592	−	0.610708i
$243$	4.82624	−	8.35929i	0.309603	−	0.536249i
$244$	−3.88197	+	11.9475i	−0.248517	+	0.764858i
$245$	−0.318519	+	3.03050i	−0.0203494	+	0.193612i
$246$	−0.580443	+	0.421716i	−0.0370077	+	0.0268877i
$247$	1.37750			0.0876482
$248$	−3.43365	+	4.38292i	−0.218037	+	0.278316i
$249$	−2.12920			−0.134933
$250$	−8.35160	+	6.06779i	−0.528202	+	0.383761i
$251$	−1.61820	+	15.3961i	−0.102140	+	0.971796i	0.816673	+	0.577101i	$0.195816\pi$
$251$	−1.61820	+	15.3961i	−0.102140	+	0.971796i	−0.918812	+	0.394694i	$0.870850\pi$
$252$	−2.72131	+	8.37532i	−0.171426	+	0.527595i
$253$	0.429284	−	0.743542i	0.0269889	−	0.0467461i
$254$	−7.71655	−	13.3655i	−0.484179	−	0.838623i
$255$	1.29340	−	0.274921i	0.0809960	−	0.0172162i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−1.60075	−	0.340250i	−0.0998520	−	0.0212242i	0.157715	−	0.987485i	$-0.449587\pi$
$257$	−1.60075	−	0.340250i	−0.0998520	−	0.0212242i	−0.257567	+	0.966261i	$0.582921\pi$
$258$	0.193030	+	1.83655i	0.0120175	+	0.114339i
$259$	−16.5570	−	18.3884i	−1.02880	−	1.14260i
$260$	−5.16535	−	2.29976i	−0.320342	−	0.142625i
$261$	21.9997	−	9.79490i	1.36175	−	0.606289i
$262$	−7.30380	+	8.11169i	−0.451230	+	0.501142i
$263$	23.7356	+	17.2449i	1.46360	+	1.06337i	0.982407	+	0.186750i	$0.0597955\pi$
$263$	23.7356	+	17.2449i	1.46360	+	1.06337i	0.481191	+	0.876616i	$0.340204\pi$
$264$	−0.0534318	−	0.0388205i	−0.00328850	−	0.00238924i
$265$	6.79157	−	7.54280i	0.417203	−	0.463351i
$266$	0.830279	−	0.369664i	0.0509077	−	0.0226656i
$267$	−0.666494	−	0.296742i	−0.0407887	−	0.0181603i
$268$	6.15701	+	6.83805i	0.376099	+	0.417700i
$269$	−1.78095	−	16.9446i	−0.108586	−	1.03313i	−0.904137	−	0.427243i	$-0.859485\pi$
$269$	−1.78095	−	16.9446i	−0.108586	−	1.03313i	0.795550	−	0.605887i	$-0.207182\pi$
$270$	2.64445	+	0.562096i	0.160936	+	0.0342081i
$271$	−2.51476	−	7.73964i	−0.152761	−	0.470150i	0.845166	−	0.534504i	$-0.179501\pi$
$271$	−2.51476	−	7.73964i	−0.152761	−	0.470150i	−0.997927	+	0.0643538i	$0.979501\pi$
$272$	−2.80067	+	0.595301i	−0.169816	+	0.0360954i
$273$	−2.75577	−	4.77314i	−0.166787	−	0.288883i
$274$	−3.66690	+	6.35125i	−0.221525	+	0.383693i
$275$	−0.189052	+	0.581841i	−0.0114002	+	0.0350863i
$276$	−0.198251	+	1.88624i	−0.0119333	+	0.113538i
$277$	−15.0659	+	10.9460i	−0.905219	+	0.657680i	−0.939801	−	0.341722i	$-0.888990\pi$
$277$	−15.0659	+	10.9460i	−0.905219	+	0.657680i	0.0345819	+	0.999402i	$0.488990\pi$
$278$	12.0820			0.724631
$279$	−5.93339	−	14.7417i	−0.355223	−	0.882563i
$280$	−3.73054			−0.222943
$281$	−1.94842	+	1.41561i	−0.116233	+	0.0844480i	−0.644383	−	0.764703i	$-0.722886\pi$
$281$	−1.94842	+	1.41561i	−0.116233	+	0.0844480i	0.528150	+	0.849151i	$0.322886\pi$
$282$	0.400630	−	3.81174i	0.0238572	−	0.226986i
$283$	−5.09011	+	15.6657i	−0.302575	+	0.931231i	0.677995	+	0.735066i	$0.262849\pi$
$283$	−5.09011	+	15.6657i	−0.302575	+	0.931231i	−0.980571	+	0.196165i	$0.937151\pi$
$284$	5.09852	−	8.83089i	0.302541	−	0.524017i
$285$	−0.0680158	−	0.117807i	−0.00402891	−	0.00697828i
$286$	−0.790943	+	0.168120i	−0.0467694	+	0.00994115i
$287$	1.79096	+	5.51200i	0.105717	+	0.325363i
$288$	−2.79173	−	0.593401i	−0.164504	−	0.0349665i
$289$	0.920045	+	8.75365i	0.0541203	+	0.514920i
$290$	6.82614	+	7.58119i	0.400844	+	0.445183i
$291$	−6.01430	−	2.67774i	−0.352564	−	0.156972i
$292$	2.14872	−	0.956672i	0.125744	−	0.0559850i
$293$	12.3062	−	13.6675i	0.718938	−	0.798461i	−0.267332	−	0.963605i	$-0.586142\pi$
$293$	12.3062	−	13.6675i	0.718938	−	0.798461i	0.986270	+	0.165143i	$0.0528086\pi$
$294$	−0.778818	−	0.565844i	−0.0454216	−	0.0330007i
$295$	−14.4720	−	10.5145i	−0.842591	−	0.612178i
$296$	5.36606	−	5.95962i	0.311896	−	0.346396i
$297$	0.353210	−	0.157259i	0.0204953	−	0.00912511i
$298$	−8.53627	−	3.80059i	−0.494493	−	0.220162i
$299$	15.5379	+	17.2565i	0.898577	+	0.997971i
$300$	−0.141267	−	1.34406i	−0.00815603	−	0.0775994i
$301$	14.5913	+	3.10148i	0.841030	+	0.178766i
$302$	5.87782	+	18.0901i	0.338231	+	1.04097i
$303$	0.222927	−	0.0473846i	0.0128068	−	0.00272218i
$304$	0.147278	+	0.255093i	0.00844698	+	0.0146306i
$305$	7.59427	−	13.1537i	0.434847	−	0.753177i
$306$	2.52528	−	7.77201i	0.144361	−	0.444296i
$307$	2.75332	−	26.1961i	0.157140	−	1.49509i	−0.577365	−	0.816486i	$-0.695919\pi$
$307$	2.75332	−	26.1961i	0.157140	−	1.49509i	0.734506	−	0.678603i	$-0.237414\pi$
$308$	−0.431619	+	0.313590i	−0.0245938	+	0.0178684i
$309$	5.49330			0.312503
$310$	5.16253	−	4.32026i	0.293212	−	0.245374i
$311$	19.7294			1.11875			0.559377	−	0.828913i	$-0.311040\pi$
$311$	19.7294			1.11875			0.559377	+	0.828913i	$0.311040\pi$
$312$	1.44512	−	1.04994i	0.0818141	−	0.0594414i
$313$	−1.13534	+	10.8020i	−0.0641732	+	0.610567i	0.914421	+	0.404765i	$0.132647\pi$
$313$	−1.13534	+	10.8020i	−0.0641732	+	0.610567i	−0.978594	+	0.205802i	$0.934020\pi$
$314$	−1.13930	+	3.50639i	−0.0642942	+	0.197877i
$315$	5.32368	−	9.22088i	0.299955	−	0.519538i
$316$	−3.69315	−	6.39673i	−0.207756	−	0.359844i
$317$	29.1091	−	6.18733i	1.63493	−	0.347515i	0.703291	−	0.710902i	$-0.251713\pi$
$317$	29.1091	−	6.18733i	1.63493	−	0.347515i	0.931638	+	0.363387i	$0.118380\pi$
$318$	0.990876	+	3.04960i	0.0555656	+	0.171013i
$319$	1.42705	+	0.303329i	0.0798995	+	0.0169832i
$320$	−0.126381	−	1.20243i	−0.00706490	−	0.0672181i
$321$	−0.521852	−	0.579576i	−0.0291270	−	0.0323488i
$322$	13.9963	+	6.23155i	0.779982	+	0.347270i
$323$	−0.770471	+	0.343036i	−0.0428701	+	0.0190870i
$324$	5.15780	−	5.72831i	0.286544	−	0.318240i
$325$	−13.3863	−	9.72572i	−0.742539	−	0.539486i
$326$	−7.61787	−	5.53471i	−0.421915	−	0.306539i
$327$	1.96668	−	2.18421i	0.108757	−	0.120787i
$328$	−1.71596	+	0.763995i	−0.0947481	+	0.0421846i
$329$	−28.2839	−	12.5928i	−1.55934	−	0.694265i
$330$	0.0534318	+	0.0593421i	0.00294133	+	0.00326667i
$331$	0.862546	+	8.20658i	0.0474098	+	0.451074i	0.992316	+	0.123732i	$0.0394864\pi$
$331$	0.862546	+	8.20658i	0.0474098	+	0.451074i	−0.944906	+	0.327342i	$0.893847\pi$
$332$	−5.45252	−	1.15897i	−0.299246	−	0.0636066i
$333$	7.07289	+	21.7681i	0.387592	+	1.19288i
$334$	3.21060	−	0.682435i	0.175676	−	0.0373412i
$335$	−5.56257	−	9.63465i	−0.303916	−	0.526397i
$336$	0.589278	−	1.02066i	0.0321477	−	0.0556815i
$337$	−10.1245	+	31.1601i	−0.551519	+	1.69740i	0.153446	+	0.988157i	$0.450963\pi$
$337$	−10.1245	+	31.1601i	−0.551519	+	1.69740i	−0.704965	+	0.709242i	$0.749037\pi$
$338$	0.927153	−	8.82127i	0.0504305	−	0.479814i
$339$	−3.81448	+	2.77138i	−0.207174	+	0.150521i
$340$	3.46182			0.187743
$341$	0.234137	−	0.933812i	0.0126792	−	0.0505687i
$342$	−0.840694			−0.0454595
$343$	11.1823	−	8.12442i	0.603788	−	0.438677i
$344$	−0.505358	+	4.80816i	−0.0272471	+	0.259239i
$345$	0.708616	−	2.18090i	0.0381506	−	0.117415i
$346$	−0.499512	+	0.865180i	−0.0268539	+	0.0465124i
$347$	1.86878	+	3.23683i	0.100322	+	0.173762i	0.911817	−	0.410597i	$-0.134680\pi$
$347$	1.86878	+	3.23683i	0.100322	+	0.173762i	−0.811496	+	0.584359i	$0.801346\pi$
$348$	−3.15244	+	0.670071i	−0.168988	+	0.0359196i
$349$	5.25577	+	16.1756i	0.281335	+	0.865860i	0.987473	+	0.157786i	$0.0504357\pi$
$349$	5.25577	+	16.1756i	0.281335	+	0.865860i	−0.706138	+	0.708074i	$0.749564\pi$
$350$	−10.6785	−	2.26978i	−0.570789	−	0.121325i
$351$	1.09306	+	10.3997i	0.0583430	+	0.555097i
$352$	−0.115699	−	0.128496i	−0.00616676	−	0.00684889i
$353$	1.49281	+	0.664641i	0.0794541	+	0.0353753i	0.446079	−	0.894994i	$-0.352820\pi$
$353$	1.49281	+	0.664641i	0.0794541	+	0.0353753i	−0.366625	+	0.930369i	$0.619487\pi$
$354$	5.16272	−	2.29859i	0.274395	−	0.122169i
$355$	−8.24957	+	9.16208i	−0.437842	+	0.486273i
$356$	−1.54525	−	1.12269i	−0.0818981	−	0.0595024i
$357$	2.73002	+	1.98347i	0.144488	+	0.104977i
$358$	8.07808	−	8.97162i	0.426940	−	0.474165i
$359$	−28.1923	+	12.5520i	−1.48793	+	0.662469i	−0.980012	−	0.198936i	$-0.936251\pi$
$359$	−28.1923	+	12.5520i	−1.48793	+	0.662469i	−0.507918	+	0.861405i	$0.669585\pi$
$360$	3.15244	+	1.40356i	0.166148	+	0.0739739i
$361$	−12.6554	−	14.0553i	−0.666075	−	0.739751i
$362$	−1.21720	−	11.5809i	−0.0639748	−	0.608680i
$363$	−4.09864	−	0.871193i	−0.215123	−	0.0457258i
$364$	−4.45893	−	13.7232i	−0.233712	−	0.719290i
$365$	−2.78164	+	0.591256i	−0.145598	+	0.0309478i
$366$	2.39919	+	4.15551i	0.125408	+	0.217212i
$367$	−4.66216	+	8.07510i	−0.243363	+	0.421517i	−0.961670	−	0.274209i	$-0.911584\pi$
$367$	−4.66216	+	8.07510i	−0.243363	+	0.421517i	0.718307	+	0.695726i	$0.244917\pi$
$368$	−1.53440	+	4.72241i	−0.0799863	+	0.246172i
$369$	0.560378	−	5.33164i	0.0291721	−	0.277554i
$370$	−7.84421	+	5.69915i	−0.407801	+	0.296285i
$371$	25.9023			1.34478
$372$	0.366529	+	2.09487i	0.0190036	+	0.108614i
$373$	−2.91508			−0.150937			−0.0754685	−	0.997148i	$-0.524045\pi$
$373$	−2.91508			−0.150937			−0.0754685	+	0.997148i	$0.524045\pi$
$374$	0.400528	−	0.291001i	0.0207108	−	0.0150473i
$375$	−0.412165	+	3.92149i	−0.0212841	+	0.202505i
$376$	3.10075	−	9.54313i	0.159909	−	0.492149i
$377$	−19.7292	+	34.1720i	−1.01611	+	1.75995i
$378$	3.44969	+	5.97504i	0.177433	+	0.307323i
$379$	−14.8615	+	3.15892i	−0.763385	+	0.162263i	−0.573122	−	0.819470i	$-0.694268\pi$
$379$	−14.8615	+	3.15892i	−0.763385	+	0.162263i	−0.190264	+	0.981733i	$0.560934\pi$
$380$	−0.110052	−	0.338705i	−0.00564554	−	0.0173752i
$381$	−5.76610	−	1.22562i	−0.295406	−	0.0627906i
$382$	−0.813097	−	7.73610i	−0.0416017	−	0.395813i
$383$	−6.95463	−	7.72390i	−0.355365	−	0.394673i	0.538783	−	0.842445i	$-0.318884\pi$
$383$	−6.95463	−	7.72390i	−0.355365	−	0.394673i	−0.894148	+	0.447772i	$0.852218\pi$
$384$	0.348943	+	0.155360i	0.0178069	+	0.00792816i
$385$	0.589278	−	0.262363i	0.0300324	−	0.0133713i
$386$	−5.56378	+	6.17921i	−0.283189	+	0.314513i
$387$	−11.1633	−	8.11060i	−0.567462	−	0.412285i
$388$	−13.9440	−	10.1309i	−0.707900	−	0.514319i
$389$	3.37085	−	3.74371i	0.170909	−	0.189814i	−0.651605	−	0.758558i	$-0.725904\pi$
$389$	3.37085	−	3.74371i	0.170909	−	0.189814i	0.822514	+	0.568745i	$0.192571\pi$
$390$	−1.97299	+	0.878431i	−0.0999062	+	0.0444811i
$391$	−12.9881	−	5.78266i	−0.656835	−	0.292442i
$392$	−1.68641	−	1.87295i	−0.0851768	−	0.0945984i
$393$	0.435810	+	4.14645i	0.0219837	+	0.209161i
$394$	9.87674	+	2.09937i	0.497583	+	0.105765i
$395$	2.75967	+	8.49338i	0.138854	+	0.427348i
$396$	0.482716	−	0.102604i	0.0242574	−	0.00515607i
$397$	5.06645	+	8.77535i	0.254278	+	0.440422i	0.964699	−	0.263355i	$-0.0848289\pi$
$397$	5.06645	+	8.77535i	0.254278	+	0.440422i	−0.710421	+	0.703777i	$0.751496\pi$
$398$	−0.788018	+	1.36489i	−0.0394998	+	0.0684156i
$399$	0.107276	−	0.330160i	0.00537050	−	0.0165287i
$400$	0.369841	−	3.51880i	0.0184920	−	0.175940i
$401$	−29.3562	+	21.3285i	−1.46598	+	1.06510i	−0.484226	+	0.874943i	$0.660899\pi$
$401$	−29.3562	+	21.3285i	−1.46598	+	1.06510i	−0.981754	+	0.190154i	$0.939101\pi$
$402$	3.51466			0.175295
$403$	22.0630	+	13.8271i	1.09904	+	0.688776i
$404$	0.596670			0.0296854
$405$	−7.53976	+	5.47796i	−0.374654	+	0.272202i
$406$	−2.72131	+	25.8915i	−0.135056	+	1.28497i
$407$	−0.428494	+	1.31877i	−0.0212397	+	0.0653690i
$408$	−0.546830	+	0.947137i	−0.0270721	+	0.0468903i
$409$	−19.0880	−	33.0613i	−0.943839	−	1.63478i	−0.758060	−	0.652185i	$-0.773852\pi$
$409$	−19.0880	−	33.0613i	−0.943839	−	1.63478i	−0.185779	−	0.982592i	$-0.559481\pi$
$410$	2.22141	−	0.472175i	0.109708	−	0.0233191i
$411$	0.865637	+	2.66416i	0.0426987	+	0.131413i
$412$	14.0674	+	2.99011i	0.693049	+	0.147312i
$413$	−4.77181	−	45.4008i	−0.234806	−	2.23403i
$414$	−9.48282	−	10.5317i	−0.466055	−	0.517607i
$415$	6.15701	+	2.74128i	0.302236	+	0.134564i
$416$	4.27222	−	1.90211i	0.209463	−	0.0932588i
$417$	3.08798	−	3.42955i	0.151219	−	0.167946i
$418$	−0.0412044	−	0.0299368i	−0.00201537	−	0.00146426i
$419$	−0.0687037	−	0.0499161i	−0.00335639	−	0.00243856i	0.586106	−	0.810235i	$-0.300660\pi$
$419$	−0.0687037	−	0.0499161i	−0.00335639	−	0.00243856i	−0.589462	+	0.807796i	$0.700660\pi$
$420$	−0.953472	+	1.05894i	−0.0465247	+	0.0516709i
$421$	10.3419	−	4.60453i	0.504035	−	0.224411i	−0.138936	−	0.990301i	$-0.544368\pi$
$421$	10.3419	−	4.60453i	0.504035	−	0.224411i	0.642971	+	0.765890i	$0.277702\pi$
$422$	−7.35051	−	3.27266i	−0.357817	−	0.159310i
$423$	19.1631	+	21.2827i	0.931740	+	1.03480i
$424$	0.877500	+	8.34885i	0.0426152	+	0.405456i
$425$	9.90928	+	2.10628i	0.480671	+	0.102170i
$426$	−1.20360	−	3.70429i	−0.0583144	−	0.179473i
$427$	37.9140	−	8.05886i	1.83479	−	0.389996i
$428$	−1.02090	−	1.76825i	−0.0493469	−	0.0854714i
$429$	−0.154431	+	0.267483i	−0.00745602	+	0.0129142i
$430$	1.80632	−	5.55927i	0.0871083	−	0.268092i
$431$	0.107806	−	1.02570i	0.00519281	−	0.0494063i	−0.991619	−	0.129199i	$-0.958759\pi$
$431$	0.107806	−	1.02570i	0.00519281	−	0.0494063i	0.996811	+	0.0797931i	$0.0254260\pi$
$432$	−1.80902	+	1.31433i	−0.0870364	+	0.0632356i
$433$	32.9911			1.58545			0.792724	−	0.609580i	$-0.208662\pi$
$433$	32.9911			1.58545			0.792724	+	0.609580i	$0.208662\pi$
$434$	17.0090	+	2.41338i	0.816457	+	0.115846i
$435$	3.89663			0.186829
$436$	6.22522	−	4.52289i	0.298134	−	0.216607i
$437$	−0.152883	+	1.45459i	−0.00731340	+	0.0695824i
$438$	0.277624	−	0.854439i	0.0132654	−	0.0408267i
$439$	1.73887	−	3.01181i	0.0829917	−	0.143746i	−0.821542	−	0.570148i	$-0.806886\pi$
$439$	1.73887	−	3.01181i	0.0829917	−	0.143746i	0.904534	+	0.426402i	$0.140219\pi$
$440$	0.104528	+	0.181049i	0.00498320	+	0.00863115i
$441$	7.03602	−	1.49555i	0.335049	−	0.0712168i
$442$	4.13774	+	12.7346i	0.196812	+	0.605725i
$443$	−11.6239	−	2.47074i	−0.552269	−	0.117388i	−0.0766795	−	0.997056i	$-0.524432\pi$
$443$	−11.6239	−	2.47074i	−0.552269	−	0.117388i	−0.475589	+	0.879667i	$0.657765\pi$
$444$	−0.320187	−	3.04638i	−0.0151954	−	0.144575i
$445$	1.54525	+	1.71617i	0.0732519	+	0.0813545i
$446$	1.49514	+	0.665681i	0.0707971	+	0.0315209i
$447$	−3.26057	+	1.45170i	−0.154219	+	0.0686629i
$448$	2.06460	−	2.29297i	0.0975433	−	0.108333i
$449$	−27.9054	−	20.2745i	−1.31694	−	0.956811i	−0.999965	−	0.00837591i	$-0.997334\pi$
$449$	−27.9054	−	20.2745i	−1.31694	−	0.956811i	−0.316972	−	0.948435i	$-0.602666\pi$
$450$	8.16972	+	5.93565i	0.385124	+	0.279809i
$451$	0.217323	−	0.241362i	0.0102333	−	0.0113653i
$452$	−11.2767	+	5.02072i	−0.530412	+	0.236155i
$453$	6.63726	+	2.95510i	0.311846	+	0.138843i
$454$	−11.9798	−	13.3049i	−0.562240	−	0.624430i
$455$	1.82360	+	17.3504i	0.0854917	+	0.813399i
$456$	0.110052	+	0.0233923i	0.00515365	+	0.00109544i
$457$	7.48925	+	23.0496i	0.350333	+	1.07821i	0.958667	+	0.284532i	$0.0918381\pi$
$457$	7.48925	+	23.0496i	0.350333	+	1.07821i	−0.608334	+	0.793681i	$0.708162\pi$
$458$	2.20167	−	0.467978i	0.102877	−	0.0218672i
$459$	−3.20120	−	5.54464i	−0.149419	−	0.258802i
$460$	3.00174	−	5.19917i	0.139957	−	0.242413i
$461$	7.16703	−	22.0579i	0.333802	−	1.02734i	−0.633507	−	0.773737i	$-0.718385\pi$
$461$	7.16703	−	22.0579i	0.333802	−	1.02734i	0.967309	−	0.253600i	$-0.0816148\pi$
$462$	−0.0213011	+	0.202667i	−0.000991018	+	0.00942891i
$463$	11.5518	−	8.39287i	0.536857	−	0.390050i	−0.286059	−	0.958212i	$-0.592345\pi$
$463$	11.5518	−	8.39287i	0.536857	−	0.390050i	0.822916	+	0.568162i	$0.192345\pi$
$464$	−8.43757			−0.391704
$465$	0.0931327	−	2.56961i	0.00431893	−	0.119163i
$466$	3.98680			0.184685
$467$	18.5900	−	13.5064i	0.860243	−	0.625003i	−0.0677082	−	0.997705i	$-0.521569\pi$
$467$	18.5900	−	13.5064i	0.860243	−	0.625003i	0.927951	+	0.372702i	$0.121569\pi$
$468$	−1.39517	+	13.2742i	−0.0644917	+	0.613598i
$469$	8.77337	−	27.0017i	0.405117	−	1.24682i
$470$	−6.06598	+	10.5066i	−0.279803	+	0.484633i
$471$	0.704124	+	1.21958i	0.0324443	+	0.0561952i
$472$	14.4720	−	3.07611i	0.666126	−	0.141590i
$473$	−0.258324	−	0.795040i	−0.0118778	−	0.0365560i
$474$	−2.75967	−	0.586585i	−0.126756	−	0.0269427i
$475$	−0.108939	−	1.03648i	−0.00499846	−	0.0475572i
$476$	5.91145	+	6.56533i	0.270951	+	0.300921i
$477$	−21.8883	−	9.74530i	−1.00220	−	0.446207i
$478$	−20.0910	+	8.94508i	−0.918940	+	0.409138i
$479$	−1.42094	+	1.57811i	−0.0649243	+	0.0721057i	−0.774732	−	0.632290i	$-0.782115\pi$
$479$	−1.42094	+	1.57811i	−0.0649243	+	0.0721057i	0.709808	+	0.704396i	$0.248782\pi$
$480$	−0.373619	−	0.271450i	−0.0170533	−	0.0123899i
$481$	−30.3407	−	22.0438i	−1.38342	−	1.00511i
$482$	−2.68576	+	2.98284i	−0.122333	+	0.135865i
$483$	5.34610	−	2.38024i	0.243256	−	0.108305i
$484$	−10.0217	−	4.46194i	−0.455531	−	0.202816i
$485$	13.9440	+	15.4864i	0.633165	+	0.703201i
$486$	−1.00896	−	9.59960i	−0.0457673	−	0.435447i
$487$	24.6947	+	5.24902i	1.11902	+	0.237856i	0.730050	−	0.683393i	$-0.239497\pi$
$487$	24.6947	+	5.24902i	1.11902	+	0.237856i	0.388973	+	0.921249i	$0.372830\pi$
$488$	3.88197	+	11.9475i	0.175728	+	0.540836i
$489$	−3.51807	+	0.747790i	−0.159093	+	0.0338162i
$490$	1.52360	+	2.63895i	0.0688291	+	0.119216i
$491$	8.86239	−	15.3501i	0.399954	−	0.692740i	−0.593766	−	0.804638i	$-0.702359\pi$
$491$	8.86239	−	15.3501i	0.399954	−	0.692740i	0.993720	+	0.111897i	$0.0356928\pi$
$492$	−0.221709	+	0.682352i	−0.00999543	+	0.0307628i
$493$	2.52528	−	24.0264i	0.113733	−	1.08210i
$494$	1.11442	−	0.809674i	0.0501402	−	0.0364290i
$495$	−0.596670			−0.0268183
$496$	−0.201665	+	5.56411i	−0.00905503	+	0.249836i
$497$	−31.4629			−1.41131
$498$	−1.72256	+	1.25151i	−0.0771899	+	0.0560817i
$499$	−2.92958	+	27.8731i	−0.131146	+	1.24777i	0.708921	+	0.705288i	$0.249182\pi$
$499$	−2.92958	+	27.8731i	−0.131146	+	1.24777i	−0.840067	+	0.542483i	$0.817484\pi$
$500$	−3.19003	+	9.81790i	−0.142662	+	0.439070i
$501$	0.626869	−	1.08577i	0.0280064	−	0.0485086i
$502$	7.74047	+	13.4069i	0.345474	+	0.598379i
$503$	−2.84310	+	0.604319i	−0.126767	+	0.0269452i	−0.270858	−	0.962619i	$-0.587308\pi$
$503$	−2.84310	+	0.604319i	−0.126767	+	0.0269452i	0.144091	+	0.989564i	$0.453974\pi$
$504$	2.72131	+	8.37532i	0.121217	+	0.373066i
$505$	−0.705643	−	0.149989i	−0.0314007	−	0.00667443i
$506$	−0.0897448	−	0.853865i	−0.00398964	−	0.0379589i
$507$	−2.26700	−	2.51776i	−0.100681	−	0.111818i
$508$	−14.0988	−	6.27721i	−0.625535	−	0.278506i
$509$	30.3548	−	13.5148i	1.34545	−	0.599034i	0.397546	−	0.917582i	$-0.369862\pi$
$509$	30.3548	−	13.5148i	1.34545	−	0.599034i	0.947907	+	0.318548i	$0.103195\pi$
$510$	0.884789	−	0.982658i	0.0391791	−	0.0435128i
$511$	−5.87128	−	4.26574i	−0.259730	−	0.188705i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	−0.440722	+	0.489471i	−0.0194583	+	0.0216107i
$514$	−1.49503	+	0.665629i	−0.0659429	+	0.0293596i
$515$	−15.8849	−	7.07242i	−0.699973	−	0.311648i
$516$	1.23566	+	1.37234i	0.0543971	+	0.0604141i
$517$	0.181358	+	1.72551i	0.00797612	+	0.0758877i
$518$	−24.2033	−	5.14457i	−1.06343	−	0.226039i
$519$	0.117919	+	0.362917i	0.00517606	+	0.0159303i
$520$	−5.53062	+	1.17557i	−0.242534	+	0.0515522i
$521$	14.0372	+	24.3131i	0.614979	+	1.06518i	0.990388	+	0.138316i	$0.0441689\pi$
$521$	14.0372	+	24.3131i	0.614979	+	1.06518i	−0.375409	+	0.926859i	$0.622498\pi$
$522$	12.0408	−	20.8553i	0.527013	−	0.912814i
$523$	−2.24525	+	6.91018i	−0.0981781	+	0.302161i	−0.988069	−	0.154012i	$-0.950780\pi$
$523$	−2.24525	+	6.91018i	−0.0981781	+	0.302161i	0.889891	+	0.456174i	$0.150780\pi$
$524$	−1.14096	+	10.8556i	−0.0498433	+	0.474227i
$525$	−3.37356	+	2.45103i	−0.147234	+	0.106972i
$526$	29.3388			1.27923
$527$	−15.7837	−	2.23953i	−0.687551	−	0.0975557i
$528$	−0.0660454			−0.00287426
$529$	−1.33934	+	0.973087i	−0.0582322	+	0.0423081i
$530$	1.06095	−	10.0942i	0.0460846	−	0.438466i
$531$	−13.0489	+	40.1605i	−0.566276	+	1.74282i
$532$	0.454427	−	0.787090i	0.0197019	−	0.0341247i
$533$	4.39208	+	7.60730i	0.190242	+	0.329509i
$534$	−0.713625	+	0.151686i	−0.0308816	+	0.00656408i
$535$	0.762854	+	2.34782i	0.0329810	+	0.101505i
$536$	9.00043	+	1.91310i	0.388759	+	0.0826333i
$537$	−0.482010	−	4.58602i	−0.0208003	−	0.197902i
$538$	−11.4006	−	12.6617i	−0.491515	−	0.545883i
$539$	0.398108	+	0.177249i	0.0171477	+	0.00763467i
$540$	2.46980	−	1.09963i	0.106283	−	0.0473204i
$541$	−6.01013	+	6.67493i	−0.258396	+	0.286978i	−0.858358	−	0.513050i	$-0.828515\pi$
$541$	−6.01013	+	6.67493i	−0.258396	+	0.286978i	0.599963	+	0.800028i	$0.295182\pi$
$542$	−6.58373	−	4.78336i	−0.282796	−	0.205463i
$543$	−3.59841	−	2.61440i	−0.154423	−	0.112195i
$544$	−1.91588	+	2.12780i	−0.0821427	+	0.0912287i
$545$	−8.49912	+	3.78405i	−0.364062	+	0.162091i
$546$	−5.03505	−	2.24175i	−0.215480	−	0.0959379i
$547$	4.16611	+	4.62694i	0.178130	+	0.197834i	0.825597	−	0.564260i	$-0.190838\pi$
$547$	4.16611	+	4.62694i	0.178130	+	0.197834i	−0.647467	+	0.762093i	$0.724172\pi$
$548$	0.766590	+	7.29362i	0.0327471	+	0.311568i
$549$	−35.0706	−	7.45449i	−1.49678	−	0.318150i
$550$	0.189052	+	0.581841i	0.00806119	+	0.0248098i
$551$	−2.43103	+	0.516731i	−0.103565	+	0.0220135i
$552$	0.948313	+	1.64253i	0.0403629	+	0.0699106i
$553$	−11.3952	+	19.7371i	−0.484574	+	0.839307i
$554$	−5.75464	+	17.7110i	−0.244491	+	0.752467i
$555$	−0.387125	+	3.68325i	−0.0164325	+	0.156345i
$556$	9.77455	−	7.10163i	0.414533	−	0.301176i
$557$	0.755772			0.0320231			0.0160115	−	0.999872i	$-0.494903\pi$
$557$	0.755772			0.0320231			0.0160115	+	0.999872i	$0.494903\pi$
$558$	−13.4652	−	8.43873i	−0.570026	−	0.357240i
$559$	22.6093			0.956273
$560$	−3.01807	+	2.19276i	−0.127537	+	0.0926610i
$561$	0.0197667	−	0.188068i	0.000834552	−	0.00794023i
$562$	−0.744228	+	2.29050i	−0.0313934	+	0.0966189i
$563$	22.0150	−	38.1311i	0.927822	−	1.60703i	0.140863	−	0.990029i	$-0.455012\pi$
$563$	22.0150	−	38.1311i	0.927822	−	1.60703i	0.786959	−	0.617006i	$-0.211655\pi$
$564$	−1.91637	−	3.31925i	−0.0806937	−	0.139766i
$565$	14.5984	−	3.10298i	0.614157	−	0.130543i
$566$	5.09011	+	15.6657i	0.213953	+	0.658480i
$567$	−23.2639	−	4.94490i	−0.976993	−	0.207666i
$568$	−1.06588	−	10.1412i	−0.0447233	−	0.425514i
$569$	12.3358	+	13.7003i	0.517145	+	0.574348i	0.943989	−	0.329978i	$-0.107041\pi$
$569$	12.3358	+	13.7003i	0.517145	+	0.574348i	−0.426844	+	0.904325i	$0.640375\pi$
$570$	−0.124271	−	0.0553291i	−0.00520514	−	0.00231748i
$571$	−14.3166	+	6.37418i	−0.599133	+	0.266751i	−0.683813	−	0.729657i	$-0.739680\pi$
$571$	−14.3166	+	6.37418i	−0.599133	+	0.266751i	0.0846803	+	0.996408i	$0.473013\pi$
$572$	−0.541068	+	0.600917i	−0.0226232	+	0.0251256i
$573$	−2.40376	−	1.74643i	−0.100418	−	0.0729582i
$574$	4.68878	+	3.40660i	0.195706	+	0.142189i
$575$	11.7557	−	13.0560i	0.490246	−	0.544473i
$576$	−2.60735	+	1.16087i	−0.108640	+	0.0483695i
$577$	9.63359	+	4.28915i	0.401052	+	0.178560i	0.597343	−	0.801986i	$-0.296223\pi$
$577$	9.63359	+	4.28915i	0.401052	+	0.178560i	−0.196291	+	0.980546i	$0.562890\pi$
$578$	5.88960	+	6.54106i	0.244975	+	0.272072i
$579$	0.331985	+	3.15863i	0.0137968	+	0.131268i
$580$	9.97857	+	2.12101i	0.414338	+	0.0880702i
$581$	5.31497	+	16.3578i	0.220502	+	0.678635i
$582$	−6.43960	+	1.36878i	−0.266930	+	0.0567377i
$583$	−0.725772	−	1.25707i	−0.0300584	−	0.0520627i
$584$	1.17603	−	2.03695i	0.0486646	−	0.0842896i
$585$	4.98680	−	15.3478i	0.206179	−	0.634553i
$586$	1.92242	−	18.2906i	0.0794145	−	0.755579i
$587$	−16.0235	+	11.6417i	−0.661360	+	0.480506i	−0.867122	−	0.498096i	$-0.834033\pi$
$587$	−16.0235	+	11.6417i	−0.661360	+	0.480506i	0.205762	+	0.978602i	$0.434033\pi$
$588$	−0.962672			−0.0396999
$589$	0.282652	+	1.61548i	0.0116465	+	0.0665647i
$590$	−17.8883			−0.736451
$591$	3.12027	−	2.26701i	0.128351	−	0.0932522i
$592$	0.838261	−	7.97552i	0.0344523	−	0.327792i
$593$	−2.93767	+	9.04122i	−0.120636	+	0.371278i	−0.993081	−	0.117434i	$-0.962533\pi$
$593$	−2.93767	+	9.04122i	−0.120636	+	0.371278i	0.872445	+	0.488712i	$0.162533\pi$
$594$	0.193318	−	0.334837i	0.00793194	−	0.0137385i
$595$	−5.34072	−	9.25040i	−0.218948	−	0.379229i
$596$	−9.13992	+	1.94275i	−0.374386	+	0.0795781i
$597$	0.186026	+	0.572528i	0.00761353	+	0.0234320i
$598$	22.7135	+	4.82791i	0.928825	+	0.197428i
$599$	1.78911	+	17.0222i	0.0731010	+	0.695510i	0.968291	+	0.249825i	$0.0803731\pi$
$599$	1.78911	+	17.0222i	0.0731010	+	0.695510i	−0.895190	+	0.445685i	$0.852960\pi$
$600$	−0.904307	−	1.00433i	−0.0369182	−	0.0410018i
$601$	−0.542774	−	0.241658i	−0.0221402	−	0.00985746i	0.395637	−	0.918407i	$-0.370524\pi$
$601$	−0.542774	−	0.241658i	−0.0221402	−	0.00985746i	−0.417777	+	0.908550i	$0.637191\pi$
$602$	13.6276	−	6.06741i	0.555421	−	0.247289i
$603$	−17.5727	+	19.5165i	−0.715617	+	0.794773i
$604$	15.3883	+	11.1803i	0.626143	+	0.454919i
$605$	10.7304	+	7.79608i	0.436252	+	0.316956i
$606$	0.152500	−	0.169368i	0.00619489	−	0.00688012i
$607$	2.19322	−	0.976483i	0.0890199	−	0.0396342i	−0.361744	−	0.932278i	$-0.617818\pi$
$607$	2.19322	−	0.976483i	0.0890199	−	0.0396342i	0.450764	+	0.892643i	$0.351152\pi$
$608$	0.269091	+	0.119807i	0.0109131	+	0.00485881i
$609$	6.65393	+	7.38994i	0.269631	+	0.299455i
$610$	−1.58764	−	15.1053i	−0.0642815	−	0.611597i
$611$	−45.8999	−	9.75633i	−1.85691	−	0.394699i
$612$	−2.52528	−	7.77201i	−0.102078	−	0.314165i
$613$	−29.6658	+	6.30567i	−1.19819	+	0.254684i	−0.763447	−	0.645870i	$-0.776495\pi$
$613$	−29.6658	+	6.30567i	−1.19819	+	0.254684i	−0.434745	+	0.900554i	$0.643161\pi$
$614$	−13.1702	−	22.8114i	−0.531505	−	0.920594i
$615$	0.433729	−	0.751241i	0.0174896	−	0.0302930i
$616$	−0.164864	+	0.507399i	−0.00664256	+	0.0204437i
$617$	1.14784	−	10.9210i	0.0462104	−	0.439663i	−0.946816	−	0.321774i	$-0.895721\pi$
$617$	1.14784	−	10.9210i	0.0462104	−	0.439663i	0.993027	−	0.117888i	$-0.0376125\pi$
$618$	4.44417	−	3.22888i	0.178771	−	0.129885i
$619$	31.8590			1.28052			0.640261	−	0.768157i	$-0.278826\pi$
$619$	31.8590			1.28052			0.640261	+	0.768157i	$0.278826\pi$
$620$	1.63719	−	6.52962i	0.0657510	−	0.262236i
$621$	−11.1030			−0.445550
$622$	15.9615	−	11.5967i	0.639996	−	0.464984i
$623$	−0.616029	+	5.86112i	−0.0246807	+	0.234821i
$624$	0.551989	−	1.69885i	0.0220972	−	0.0680083i
$625$	−2.60482	+	4.51168i	−0.104193	+	0.180467i
$626$	5.43077	+	9.40636i	0.217057	+	0.375954i
$627$	−0.0190290	+	0.00404473i	−0.000759944	+	0.000161531i
$628$	1.13930	+	3.50639i	0.0454629	+	0.139920i
$629$	22.4598	+	4.77399i	0.895533	+	0.190351i
$630$	−1.11295	−	10.5890i	−0.0443411	−	0.421877i
$631$	7.21761	+	8.01597i	0.287328	+	0.319111i	0.869478	−	0.493971i	$-0.164455\pi$
$631$	7.21761	+	8.01597i	0.287328	+	0.319111i	−0.582150	+	0.813081i	$0.697788\pi$
$632$	−6.74773	−	3.00428i	−0.268410	−	0.119504i
$633$	−2.80764	+	1.25004i	−0.111594	+	0.0496848i
$634$	19.9129	−	22.1156i	0.790844	−	0.878321i
$635$	15.0959	+	10.9678i	0.599061	+	0.435243i
$636$	2.59415	+	1.88476i	0.102865	+	0.0747356i
$637$	−7.88656	+	8.75891i	−0.312477	+	0.347041i
$638$	1.33280	−	0.593401i	0.0527661	−	0.0234930i
$639$	26.5873	+	11.8374i	1.05178	+	0.468281i
$640$	−0.809017	−	0.898504i	−0.0319792	−	0.0355165i
$641$	−2.50387	−	23.8228i	−0.0988971	−	0.940943i	−0.925651	−	0.378379i	$-0.876482\pi$
$641$	−2.50387	−	23.8228i	−0.0988971	−	0.940943i	0.826754	−	0.562564i	$-0.190185\pi$
$642$	−0.762854	−	0.162150i	−0.0301074	−	0.00639953i
$643$	−11.2746	−	34.6997i	−0.444627	−	1.36842i	−0.882892	−	0.469576i	$-0.844407\pi$
$643$	−11.2746	−	34.6997i	−0.444627	−	1.36842i	0.438265	−	0.898846i	$-0.355593\pi$
$644$	14.9860	−	3.18538i	0.590533	−	0.125522i
$645$	−1.11637	−	1.93360i	−0.0439568	−	0.0761355i
$646$	−0.421693	+	0.730393i	−0.0165913	+	0.0287369i
$647$	12.9866	−	39.9686i	0.510556	−	1.57133i	−0.280670	−	0.959804i	$-0.590557\pi$
$647$	12.9866	−	39.9686i	0.510556	−	1.57133i	0.791226	−	0.611524i	$-0.209443\pi$
$648$	0.805727	−	7.66598i	0.0316519	−	0.301148i
$649$	−2.06966	+	1.50370i	−0.0812412	+	0.0590252i
$650$	−16.5464			−0.649003
$651$	5.03229	−	4.21128i	0.197231	−	0.165053i
$652$	−9.41620			−0.368767
$653$	−1.54525	+	1.12269i	−0.0604703	+	0.0439343i	−0.617610	−	0.786485i	$-0.711899\pi$
$653$	−1.54525	+	1.12269i	−0.0604703	+	0.0439343i	0.557139	+	0.830419i	$0.311899\pi$
$654$	0.307225	−	2.92305i	0.0120134	−	0.114300i
$655$	4.07818	−	12.5514i	0.159348	−	0.490422i
$656$	−0.939176	+	1.62670i	−0.0366687	+	0.0635120i
$657$	3.35652	+	5.81367i	0.130950	+	0.226813i
$658$	−30.2841	+	6.43708i	−1.18060	+	0.250943i
$659$	2.97622	+	9.15985i	0.115937	+	0.356817i	0.992141	−	0.125123i	$-0.0399324\pi$
$659$	2.97622	+	9.15985i	0.115937	+	0.356817i	−0.876204	+	0.481940i	$0.839932\pi$
$660$	0.0781077	+	0.0166023i	0.00304034	+	0.000646244i
$661$	0.844175	+	8.03179i	0.0328346	+	0.312400i	0.998596	+	0.0529691i	$0.0168685\pi$
$661$	0.844175	+	8.03179i	0.0328346	+	0.312400i	−0.965762	+	0.259431i	$0.916465\pi$
$662$	5.52152	+	6.13227i	0.214600	+	0.238338i
$663$	4.67235	+	2.08026i	0.181459	+	0.0807908i
$664$	−5.09240	+	2.26728i	−0.197624	+	0.0879877i
$665$	−0.735278	+	0.816609i	−0.0285129	+	0.0316667i
$666$	18.5171	+	13.4534i	0.717521	+	0.521310i
$667$	−33.8947	−	24.6260i	−1.31241	−	0.953521i
$668$	2.19631	−	2.43925i	0.0849777	−	0.0943773i
$669$	0.571094	−	0.254267i	0.0220798	−	0.00983054i
$670$	−10.1633	−	4.52500i	−0.392643	−	0.174816i
$671$	−1.45344	−	1.61421i	−0.0561096	−	0.0623160i
$672$	−0.123193	−	1.17210i	−0.00475226	−	0.0452147i
$673$	38.3620	+	8.15410i	1.47875	+	0.314317i	0.875493	−	0.483231i	$-0.160537\pi$
$673$	38.3620	+	8.15410i	1.47875	+	0.314317i	0.603254	+	0.797549i	$0.293870\pi$
$674$	10.1245	+	31.1601i	0.389982	+	1.20024i
$675$	7.73873	−	1.64492i	0.297864	−	0.0633129i
$676$	−4.43493	−	7.68153i	−0.170574	−	0.295443i
$677$	4.51806	−	7.82551i	0.173643	−	0.300759i	−0.766048	−	0.642784i	$-0.777779\pi$
$677$	4.51806	−	7.82551i	0.173643	−	0.300759i	0.939691	+	0.342025i	$0.111113\pi$
$678$	−1.45700	+	4.48419i	−0.0559558	+	0.172214i
$679$	−5.55891	+	52.8895i	−0.213332	+	2.02971i
$680$	2.80067	−	2.03481i	0.107401	−	0.0780312i
$681$	−6.83854			−0.262053
$682$	−0.359460	−	0.893091i	−0.0137644	−	0.0341982i
$683$	42.6651			1.63254			0.816268	−	0.577673i	$-0.196039\pi$
$683$	42.6651			1.63254			0.816268	+	0.577673i	$0.196039\pi$
$684$	−0.680136	+	0.494148i	−0.0260056	+	0.0188942i
$685$	0.926851	−	8.81840i	0.0354132	−	0.336934i
$686$	4.27126	−	13.1456i	0.163077	−	0.501901i
$687$	0.429874	−	0.744564i	0.0164007	−	0.0284069i
$688$	2.41732	+	4.18693i	0.0921596	+	0.159625i
$689$	38.4008	−	8.16233i	1.46295	−	0.310960i
$690$	−0.708616	−	2.18090i	−0.0269765	−	0.0830253i
$691$	−21.6776	−	4.60772i	−0.824655	−	0.175286i	−0.223791	−	0.974637i	$-0.571843\pi$
$691$	−21.6776	−	4.60772i	−0.824655	−	0.175286i	−0.600864	+	0.799351i	$0.705177\pi$
$692$	0.104426	+	0.993551i	0.00396970	+	0.0377691i
$693$	−1.01888	−	1.13158i	−0.0387041	−	0.0429853i
$694$	3.41444	+	1.52021i	0.129610	+	0.0577062i
$695$	−13.3449	+	5.94154i	−0.506202	+	0.225376i
$696$	−2.15652	+	2.39505i	−0.0817426	+	0.0907843i
$697$	−4.35103	−	3.16121i	−0.164807	−	0.119739i
$698$	13.7598	+	9.99707i	0.520816	+	0.378395i
$699$	1.01897	−	1.13168i	0.0385408	−	0.0428039i
$700$	−9.97323	+	4.44037i	−0.376953	+	0.167830i
$701$	17.7200	+	7.88947i	0.669277	+	0.297981i	0.713104	−	0.701058i	$-0.247289\pi$
$701$	17.7200	+	7.88947i	0.669277	+	0.297981i	−0.0438277	+	0.999039i	$0.513955\pi$
$702$	6.99711	+	7.77108i	0.264089	+	0.293301i
$703$	−0.246915	−	2.34924i	−0.00931258	−	0.0886033i
$704$	−0.169131	−	0.0359498i	−0.00637435	−	0.00135491i
$705$	1.43198	+	4.40719i	0.0539316	+	0.165985i
$706$	1.59837	−	0.339745i	0.0601556	−	0.0127865i
$707$	−0.920512	−	1.59437i	−0.0346194	−	0.0599626i
$708$	2.82565	−	4.89417i	0.106194	−	0.183934i
$709$	−1.98261	+	6.10186i	−0.0744586	+	0.229160i	−0.981358	−	0.192186i	$-0.938442\pi$
$709$	−1.98261	+	6.10186i	−0.0744586	+	0.229160i	0.906900	+	0.421346i	$0.138442\pi$
$710$	−1.28871	+	12.2613i	−0.0483644	+	0.460157i
$711$	17.0551	−	12.3913i	0.639616	−	0.464709i
$712$	−1.91003			−0.0715816
$713$	−17.0496	+	21.7631i	−0.638511	+	0.815035i
$714$	3.37449			0.126287
$715$	0.790943	−	0.574654i	0.0295796	−	0.0214908i
$716$	1.26192	−	12.0064i	0.0471602	−	0.448699i
$717$	−2.59584	+	7.98918i	−0.0969435	+	0.298361i
$718$	−15.4301	+	26.7258i	−0.575848	+	0.997397i
$719$	−21.5071	−	37.2513i	−0.802078	−	1.38924i	−0.918246	−	0.396010i	$-0.870394\pi$
$719$	−21.5071	−	37.2513i	−0.802078	−	1.38924i	0.116168	−	0.993230i	$-0.462939\pi$
$720$	3.37536	−	0.717456i	0.125792	−	0.0267380i
$721$	−13.7125	−	42.2027i	−0.510680	−	1.57171i
$722$	−18.4999	−	3.93228i	−0.688496	−	0.146344i
$723$	0.160257	+	1.52474i	0.00596001	+	0.0567057i
$724$	−7.79184	−	8.65371i	−0.289581	−	0.321613i
$725$	27.2727	+	12.1426i	1.01288	+	0.450964i
$726$	−3.82794	+	1.70431i	−0.142068	+	0.0632529i
$727$	−8.36883	+	9.29453i	−0.310383	+	0.344715i	−0.878072	−	0.478528i	$-0.841171\pi$
$727$	−8.36883	+	9.29453i	−0.310383	+	0.344715i	0.567690	+	0.823243i	$0.307837\pi$
$728$	−11.6736	−	8.48139i	−0.432654	−	0.314341i
$729$	15.7254	+	11.4252i	0.582423	+	0.423155i
$730$	−1.90286	+	2.11334i	−0.0704281	+	0.0782184i
$731$	−12.6460	+	5.63035i	−0.467729	+	0.208246i
$732$	4.38353	+	1.95167i	0.162020	+	0.0721360i
$733$	−14.2494	−	15.8255i	−0.526313	−	0.584530i	0.420105	−	0.907476i	$-0.361993\pi$
$733$	−14.2494	−	15.8255i	−0.526313	−	0.584530i	−0.946417	+	0.322946i	$0.895327\pi$
$734$	0.974658	+	9.27325i	0.0359753	+	0.342282i
$735$	1.13849	+	0.241994i	0.0419938	+	0.00892607i
$736$	1.53440	+	4.72241i	0.0565588	+	0.174070i
$737$	−1.55626	+	0.330792i	−0.0573254	+	0.0121849i
$738$	−2.68051	−	4.64277i	−0.0986708	−	0.170903i
$739$	−18.3029	+	31.7016i	−0.673285	+	1.16616i	0.303683	+	0.952773i	$0.401784\pi$
$739$	−18.3029	+	31.7016i	−0.673285	+	1.16616i	−0.976967	+	0.213390i	$0.931550\pi$
$740$	−2.99622	+	9.22142i	−0.110143	+	0.338986i
$741$	0.0549985	−	0.523276i	0.00202042	−	0.0192230i
$742$	20.9554	−	15.2250i	0.769296	−	0.558926i
$743$	−39.5536			−1.45108			−0.725541	−	0.688179i	$-0.758410\pi$
$743$	−39.5536			−1.45108			−0.725541	+	0.688179i	$0.758410\pi$
$744$	1.52786	+	1.47935i	0.0560142	+	0.0542355i
$745$	11.2976			0.413911
$746$	−2.35835	+	1.71344i	−0.0863452	+	0.0627335i
$747$	1.66302	−	15.8225i	0.0608466	−	0.578917i
$748$	0.152988	−	0.470849i	0.00559380	−	0.0172159i
$749$	−3.14998	+	5.45592i	−0.115098	+	0.199355i
$750$	1.97155	+	3.41482i	0.0719907	+	0.124691i
$751$	−48.4490	+	10.2981i	−1.76793	+	0.375785i	−0.972979	−	0.230892i	$-0.925835\pi$
$751$	−48.4490	+	10.2981i	−1.76793	+	0.375785i	−0.794948	+	0.606677i	$0.792502\pi$
$752$	−3.10075	−	9.54313i	−0.113073	−	0.348002i
$753$	5.78398	+	1.22942i	0.210780	+	0.0448026i
$754$	4.12453	+	39.2423i	0.150207	+	1.42912i
$755$	−15.3883	−	17.0905i	−0.560039	−	0.621986i
$756$	6.30290	+	2.80623i	0.229234	+	0.102062i
$757$	−26.8857	+	11.9703i	−0.977177	+	0.435067i	−0.832265	−	0.554377i	$-0.812956\pi$
$757$	−26.8857	+	11.9703i	−0.977177	+	0.435067i	−0.144912	+	0.989445i	$0.546290\pi$
$758$	−10.1665	+	11.2910i	−0.369263	+	0.410108i
$759$	−0.265312	−	0.192761i	−0.00963022	−	0.00699677i
$760$	−0.288120	−	0.209331i	−0.0104512	−	0.00759324i
$761$	−13.2355	+	14.6995i	−0.479787	+	0.532858i	−0.933637	−	0.358221i	$-0.883384\pi$
$761$	−13.2355	+	14.6995i	−0.479787	+	0.532858i	0.453850	+	0.891078i	$0.350050\pi$
$762$	−5.38528	+	2.39768i	−0.195088	+	0.0868588i
$763$	−21.6897	−	9.65686i	−0.785218	−	0.349602i
$764$	−5.20498	−	5.78071i	−0.188309	−	0.209139i
$765$	1.03278	+	9.82626i	0.0373403	+	0.355269i
$766$	−10.1664	−	2.16094i	−0.367327	−	0.0780778i
$767$	−21.3810	−	65.8041i	−0.772024	−	2.37605i
$768$	0.373619	−	0.0794152i	0.0134818	−	0.00286565i
$769$	18.3511	+	31.7850i	0.661757	+	1.14620i	0.980154	+	0.198239i	$0.0635221\pi$
$769$	18.3511	+	31.7850i	0.661757	+	1.14620i	−0.318397	+	0.947957i	$0.603145\pi$
$770$	0.322523	−	0.558625i	0.0116229	−	0.0201315i
$771$	−0.193164	+	0.594498i	−0.00695663	+	0.0214103i
$772$	−0.869148	+	8.26939i	−0.0312813	+	0.297622i
$773$	−15.3479	+	11.1509i	−0.552024	+	0.401069i	−0.828531	−	0.559943i	$-0.810823\pi$
$773$	−15.3479	+	11.1509i	−0.552024	+	0.401069i	0.276507	+	0.961012i	$0.410823\pi$
$774$	−13.7986			−0.495980
$775$	8.65920	−	17.6946i	0.311048	−	0.635609i
$776$	−17.2357			−0.618727
$777$	−7.64632	+	5.55538i	−0.274310	+	0.199298i
$778$	0.526579	−	5.01006i	0.0188788	−	0.179619i
$779$	−0.170973	+	0.526201i	−0.00612575	+	0.0188531i
$780$	−1.07985	+	1.87036i	−0.0386649	+	0.0669696i
$781$	0.881580	+	1.52694i	0.0315454	+	0.0546382i
$782$	−13.9065	+	2.95593i	−0.497297	+	0.105704i
$783$	−5.83022	−	17.9436i	−0.208355	−	0.641251i
$784$	−2.46523	−	0.524001i	−0.0880440	−	0.0187143i
$785$	−0.465946	−	4.43318i	−0.0166303	−	0.158227i
$786$	2.78980	+	3.09839i	0.0995089	+	0.110516i
$787$	18.7177	+	8.33367i	0.667215	+	0.297063i	0.712254	−	0.701922i	$-0.247675\pi$
$787$	18.7177	+	8.33367i	0.667215	+	0.297063i	−0.0450389	+	0.998985i	$0.514341\pi$
$788$	9.22443	−	4.10698i	0.328607	−	0.146305i
$789$	7.49856	−	8.32799i	0.266956	−	0.296484i
$790$	7.22490	+	5.24920i	0.257050	+	0.186758i
$791$	30.8131	+	22.3870i	1.09559	+	0.795992i
$792$	0.330216	−	0.366742i	0.0117337	−	0.0130316i
$793$	53.6689	−	23.8949i	1.90584	−	0.848534i
$794$	9.25686	+	4.12142i	0.328514	+	0.146264i
$795$	−2.59415	−	2.88109i	−0.0920050	−	0.102182i
$796$	0.164741	+	1.56740i	0.00583907	+	0.0555551i
$797$	41.0825	+	8.73236i	1.45522	+	0.309316i	0.866563	−	0.499068i	$-0.166324\pi$
$797$	41.0825	+	8.73236i	1.45522	+	0.309316i	0.588655	+	0.808384i	$0.299658\pi$
$798$	−0.107276	−	0.330160i	−0.00379752	−	0.0116876i
$799$	28.1026	−	5.97339i	0.994198	−	0.211323i
$800$	−1.76909	−	3.06415i	−0.0625468	−	0.108334i
$801$	2.72572	−	4.72108i	0.0963084	−	0.166811i
$802$	−11.2131	+	34.5103i	−0.395948	+	1.21860i
$803$	−0.0425111	+	0.404466i	−0.00150018	+	0.0142733i
$804$	2.84342	−	2.06587i	0.100280	−	0.0728575i
$805$	−18.5238			−0.652877
$806$	25.9767	−	1.78198i	0.914991	−	0.0627675i
$807$	−6.50791			−0.229089
$808$	0.482716	−	0.350714i	0.0169819	−	0.0123381i
$809$	1.11211	−	10.5810i	0.0390997	−	0.372009i	−0.957423	−	0.288689i	$-0.906781\pi$
$809$	1.11211	−	10.5810i	0.0390997	−	0.372009i	0.996523	−	0.0833206i	$-0.0265526\pi$
$810$	−2.87993	+	8.86352i	−0.101191	+	0.311432i
$811$	−4.24539	+	7.35323i	−0.149076	+	0.258207i	−0.930886	−	0.365309i	$-0.880963\pi$
$811$	−4.24539	+	7.35323i	−0.149076	+	0.258207i	0.781810	+	0.623516i	$0.214297\pi$
$812$	13.0171	+	22.5462i	0.456809	+	0.791217i
$813$	−3.04049	+	0.646276i	−0.106635	+	0.0226659i
$814$	0.428494	+	1.31877i	0.0150187	+	0.0462229i
$815$	11.1359	+	2.36702i	0.390075	+	0.0829130i
$816$	0.114319	+	1.08767i	0.00400195	+	0.0380760i
$817$	0.952893	+	1.05830i	0.0333375	+	0.0370251i
$818$	−34.8754	−	15.5275i	−1.21939	−	0.542908i
$819$	37.6225	−	16.7506i	1.31464	−	0.585315i
$820$	1.51962	−	1.68771i	0.0530674	−	0.0589373i
$821$	0.753352	+	0.547342i	0.0262922	+	0.0191024i	0.600854	−	0.799359i	$-0.294827\pi$
$821$	0.753352	+	0.547342i	0.0262922	+	0.0191024i	−0.574562	+	0.818461i	$0.694827\pi$
$822$	2.26627	+	1.64654i	0.0790451	+	0.0574297i
$823$	−14.0411	+	15.5942i	−0.489442	+	0.543580i	−0.936381	−	0.350984i	$-0.885847\pi$
$823$	−14.0411	+	15.5942i	−0.489442	+	0.543580i	0.446940	+	0.894564i	$0.352514\pi$
$824$	13.1383	−	5.84954i	0.457694	−	0.203778i
$825$	0.213478	+	0.0950465i	0.00743234	+	0.00330909i
$826$	−30.5464	−	33.9252i	−1.06284	−	1.18041i
$827$	0.996907	+	9.48493i	0.0346658	+	0.329823i	0.998087	+	0.0618303i	$0.0196938\pi$
$827$	0.996907	+	9.48493i	0.0346658	+	0.329823i	−0.963421	+	0.267993i	$0.913640\pi$
$828$	−13.8622	−	2.94649i	−0.481743	−	0.102398i
$829$	−4.20816	−	12.9514i	−0.146156	−	0.449821i	0.851002	−	0.525162i	$-0.175995\pi$
$829$	−4.20816	−	12.9514i	−0.146156	−	0.449821i	−0.997158	+	0.0753414i	$0.975995\pi$
$830$	6.59240	−	1.40126i	0.228826	−	0.0486384i
$831$	3.55657	+	6.16015i	0.123376	+	0.213693i
$832$	2.33826	−	4.04999i	0.0810646	−	0.140408i
$833$	2.22994	−	6.86305i	0.0772629	−	0.237791i
$834$	0.482390	−	4.58964i	0.0167038	−	0.158926i
$835$	−3.21060	+	2.33264i	−0.111107	+	0.0807243i
$836$	−0.0509315			−0.00176150
$837$	−11.9721	+	3.41584i	−0.413818	+	0.118069i
$838$	−0.0849224			−0.00293360
$839$	−38.1645	+	27.7282i	−1.31759	+	0.957283i	−0.317628	+	0.948216i	$0.602886\pi$
$839$	−38.1645	+	27.7282i	−1.31759	+	0.957283i	−0.999959	+	0.00906710i	$0.997114\pi$
$840$	−0.148947	+	1.41714i	−0.00513916	+	0.0488958i
$841$	13.0382	−	40.1275i	0.449594	−	1.38371i
$842$	5.66033	−	9.80398i	0.195068	−	0.337867i
$843$	0.459958	+	0.796671i	0.0158418	+	0.0274388i
$844$	−7.87031	+	1.67289i	−0.270907	+	0.0575831i
$845$	3.31395	+	10.1993i	0.114003	+	0.350866i
$846$	28.0129	+	5.95433i	0.963104	+	0.204714i
$847$	3.53811	+	33.6628i	0.121571	+	1.15667i
$848$	5.61724	+	6.23858i	0.192897	+	0.214234i
$849$	5.74777	+	2.55907i	0.197263	+	0.0878271i
$850$	9.25482	−	4.12051i	0.317438	−	0.141332i
$851$	26.6448	−	29.5921i	0.913373	−	1.01440i
$852$	−3.15106	−	2.28938i	−0.107953	−	0.0784328i
$853$	−1.78567	−	1.29736i	−0.0611400	−	0.0444208i	0.556795	−	0.830650i	$-0.312031\pi$
$853$	−1.78567	−	1.29736i	−0.0611400	−	0.0444208i	−0.617935	+	0.786229i	$0.712031\pi$
$854$	25.9362	−	28.8050i	0.887517	−	0.985688i
$855$	0.928570	−	0.413426i	0.0317564	−	0.0141389i
$856$	−1.86527	−	0.830473i	−0.0637537	−	0.0283850i
$857$	−15.4138	−	17.1188i	−0.526526	−	0.584766i	0.419947	−	0.907548i	$-0.362048\pi$
$857$	−15.4138	−	17.1188i	−0.526526	−	0.584766i	−0.946473	+	0.322782i	$0.895382\pi$
$858$	0.0322850	+	0.307171i	0.00110219	+	0.0104866i
$859$	33.3273	+	7.08394i	1.13711	+	0.241701i	0.737739	−	0.675087i	$-0.235894\pi$
$859$	33.3273	+	7.08394i	1.13711	+	0.241701i	0.399375	+	0.916788i	$0.369227\pi$
$860$	−1.80632	−	5.55927i	−0.0615949	−	0.189570i
$861$	2.16537	−	0.460263i	0.0737955	−	0.0156857i
$862$	−0.515676	−	0.893176i	−0.0175640	−	0.0304217i
$863$	−11.0442	+	19.1292i	−0.375951	+	0.651166i	−0.990469	−	0.137737i	$-0.956017\pi$
$863$	−11.0442	+	19.1292i	−0.375951	+	0.651166i	0.614518	+	0.788903i	$0.289350\pi$
$864$	−0.690983	+	2.12663i	−0.0235077	+	0.0723493i
$865$	0.126257	−	1.20126i	0.00429288	−	0.0408440i
$866$	26.6903	−	19.3917i	0.906974	−	0.658955i
$867$	3.36201			0.114180
$868$	15.1791	−	8.04516i	0.515212	−	0.273070i
$869$	1.27716			0.0433247
$870$	3.15244	−	2.29038i	0.106878	−	0.0776511i
$871$	4.49797	−	42.7953i	0.152408	−	1.45006i
$872$	2.37782	−	7.31819i	0.0805232	−	0.247825i
$873$	24.5963	−	42.6020i	0.832458	−	1.44186i
$874$	0.731300	+	1.26665i	0.0247366	+	0.0428450i
$875$	31.1560	−	6.62242i	1.05327	−	0.223879i
$876$	−0.277624	−	0.854439i	−0.00938005	−	0.0288688i
$877$	−11.2057	−	2.38184i	−0.378389	−	0.0804290i	0.0147912	−	0.999891i	$-0.495292\pi$
$877$	−11.2057	−	2.38184i	−0.378389	−	0.0804290i	−0.393180	+	0.919462i	$0.628625\pi$
$878$	−0.363523	−	3.45869i	−0.0122683	−	0.116725i
$879$	−4.70056	−	5.22050i	−0.158546	−	0.176083i
$880$	0.190983	+	0.0850311i	0.00643804	+	0.00286640i
$881$	−44.8343	+	19.9615i	−1.51051	+	0.672520i	−0.984084	−	0.177703i	$-0.943133\pi$
$881$	−44.8343	+	19.9615i	−1.51051	+	0.672520i	−0.526421	+	0.850224i	$0.676467\pi$
$882$	4.81320	−	5.34560i	0.162069	−	0.179996i
$883$	21.4848	+	15.6097i	0.723023	+	0.525307i	0.887348	−	0.461099i	$-0.152545\pi$
$883$	21.4848	+	15.6097i	0.723023	+	0.525307i	−0.164326	+	0.986406i	$0.552545\pi$
$884$	10.8327	+	7.87044i	0.364344	+	0.264712i
$885$	−4.57199	+	5.07771i	−0.153686	+	0.170685i
$886$	−10.8562	+	4.83350i	−0.364721	+	0.162384i
$887$	37.4485	+	16.6732i	1.25740	+	0.559830i	0.923796	−	0.382884i	$-0.125069\pi$
$887$	37.4485	+	16.6732i	1.25740	+	0.559830i	0.333602	+	0.942714i	$0.391736\pi$
$888$	−2.04965	−	2.27637i	−0.0687819	−	0.0763900i
$889$	4.97752	+	47.3580i	0.166941	+	1.58834i
$890$	2.25888	+	0.480139i	0.0757177	+	0.0160943i
$891$	0.411864	+	1.26759i	0.0137979	+	0.0424657i
$892$	1.60087	−	0.340276i	0.0536012	−	0.0113933i
$893$	−1.47782	−	2.55967i	−0.0494535	−	0.0856560i
$894$	−1.78457	+	3.09096i	−0.0596848	+	0.103377i
$895$	−4.51052	+	13.8819i	−0.150770	+	0.464022i
$896$	0.322523	−	3.06860i	0.0107747	−	0.102515i
$897$	7.17567	−	5.21343i	0.239589	−	0.174071i
$898$	−34.4930			−1.15105
$899$	−44.1240	−	16.1259i	−1.47162	−	0.537828i
$900$	10.0983			0.336611
$901$	−19.4459	+	14.1283i	−0.647836	+	0.470681i
$902$	0.0339492	−	0.323005i	0.00113038	−	0.0107549i
$903$	1.76075	−	5.41903i	0.0585941	−	0.180334i
$904$	−6.17195	+	10.6901i	−0.205276	+	0.355549i
$905$	7.03956	+	12.1929i	0.234003	+	0.405305i
$906$	7.10662	−	1.51056i	0.236102	−	0.0501850i
$907$	−6.21212	−	19.1189i	−0.206270	−	0.634834i	−0.999659	−	0.0261187i	$-0.991685\pi$
$907$	−6.21212	−	19.1189i	−0.206270	−	0.634834i	0.793389	−	0.608715i	$-0.208315\pi$
$908$	−17.5123	−	3.72235i	−0.581166	−	0.123531i
$909$	0.178007	+	1.69363i	0.00590413	+	0.0561741i
$910$	11.6736	+	12.9649i	0.386977	+	0.429782i
$911$	18.2136	+	8.10920i	0.603443	+	0.268670i	0.685634	−	0.727947i	$-0.259525\pi$
$911$	18.2136	+	8.10920i	0.603443	+	0.268670i	−0.0821913	+	0.996617i	$0.526192\pi$
$912$	0.102783	−	0.0457622i	0.00340350	−	0.00151534i
$913$	0.644943	−	0.716282i	0.0213445	−	0.0237055i
$914$	19.6071	+	14.2454i	0.648546	+	0.471196i
$915$	−4.69352	−	3.41004i	−0.155163	−	0.112732i
$916$	1.50611	−	1.67271i	0.0497634	−	0.0552679i
$917$	30.7676	−	13.6986i	1.01604	−	0.452368i
$918$	−5.84888	−	2.60409i	−0.193042	−	0.0859478i
$919$	−14.6299	−	16.2482i	−0.482596	−	0.535977i	0.451844	−	0.892097i	$-0.350766\pi$
$919$	−14.6299	−	16.2482i	−0.482596	−	0.535977i	−0.934440	+	0.356120i	$0.884100\pi$
$920$	−0.627536	−	5.97060i	−0.0206892	−	0.196845i
$921$	−9.84126	−	2.09183i	−0.324281	−	0.0689280i
$922$	−7.16703	−	22.0579i	−0.236034	−	0.726437i
$923$	−46.6446	+	9.91461i	−1.53533	+	0.326343i
$924$	0.101892	+	0.176481i	0.00335198	+	0.00580581i
$925$	−14.1871	+	24.5728i	−0.466470	+	0.807950i
$926$	4.41239	−	13.5799i	0.145000	−	0.446265i
$927$	−4.29054	+	40.8218i	−0.140920	+	1.34076i
$928$	−6.82614	+	4.95948i	−0.224079	+	0.162803i
$929$	−42.7555			−1.40276			−0.701382	−	0.712786i	$-0.747433\pi$
$929$	−42.7555			−1.40276			−0.701382	+	0.712786i	$0.747433\pi$
$930$	−1.43503	−	2.13360i	−0.0470566	−	0.0699635i
$931$	−0.742373			−0.0243303
$932$	3.22539	−	2.34338i	0.105651	−	0.0767600i
$933$	0.787724	−	7.49469i	0.0257889	−	0.245365i
$934$	7.10075	−	21.8539i	0.232344	−	0.715080i
$935$	−0.299290	+	0.518385i	−0.00978783	+	0.0169530i
$936$	6.67364	+	11.5591i	0.218135	+	0.377820i
$937$	−1.58518	+	0.336940i	−0.0517855	+	0.0110073i	−0.233732	−	0.972301i	$-0.575094\pi$
$937$	−1.58518	+	0.336940i	−0.0517855	+	0.0110073i	0.181946	+	0.983309i	$0.441760\pi$
$938$	−8.77337	−	27.0017i	−0.286461	−	0.881635i
$939$	4.05808	+	0.862571i	0.132430	+	0.0281489i
$940$	1.26814	+	12.0655i	0.0413620	+	0.393533i
$941$	18.1253	+	20.1302i	0.590868	+	0.656226i	0.962222	−	0.272266i	$-0.0877730\pi$
$941$	18.1253	+	20.1302i	0.590868	+	0.656226i	−0.371354	+	0.928491i	$0.621106\pi$
$942$	1.28650	+	0.572786i	0.0419164	+	0.0186624i
$943$	−8.52049	+	3.79356i	−0.277465	+	0.123535i
$944$	9.89998	−	10.9950i	0.322217	−	0.357858i
$945$	−6.74862	−	4.90316i	−0.219533	−	0.159500i
$946$	−0.676301	−	0.491362i	−0.0219885	−	0.0159755i
$947$	−19.4449	+	21.5957i	−0.631873	+	0.701766i	−0.971028	−	0.238964i	$-0.923192\pi$
$947$	−19.4449	+	21.5957i	−0.631873	+	0.701766i	0.339155	+	0.940730i	$0.389859\pi$
$948$	−2.57740	+	1.14753i	−0.0837101	+	0.0372702i
$949$	−10.0485	−	4.47390i	−0.326190	−	0.145229i
$950$	−0.697364	−	0.774501i	−0.0226255	−	0.0251281i
$951$	−1.18818	−	11.3048i	−0.0385295	−	0.366584i
$952$	8.64147	+	1.83680i	0.280072	+	0.0595310i
$953$	1.91530	+	5.89470i	0.0620428	+	0.190948i	0.977274	−	0.211982i	$-0.0679918\pi$
$953$	1.91530	+	5.89470i	0.0620428	+	0.190948i	−0.915231	+	0.402930i	$0.867992\pi$
$954$	−23.4362	+	4.98151i	−0.758773	+	0.161282i
$955$	4.70246	+	8.14489i	0.152168	+	0.263562i
$956$	−10.9962	+	19.0459i	−0.355641	+	0.615989i
$957$	0.172204	−	0.529988i	0.00556655	−	0.0171321i
$958$	−0.221972	+	2.11192i	−0.00717160	+	0.0682332i
$959$	18.3068	−	13.3007i	0.591157	−	0.429500i
$960$	−0.461819			−0.0149051
$961$	−11.6887	+	28.7119i	−0.377056	+	0.926191i
$962$	−37.5032			−1.20915
$963$	4.71454	−	3.42531i	0.151924	−	0.110379i
$964$	−0.419557	+	3.99182i	−0.0135130	+	0.128568i
$965$	3.10662	−	9.56120i	0.100006	−	0.307786i
$966$	2.92602	−	5.06801i	0.0941431	−	0.163061i
$967$	−5.43592	−	9.41529i	−0.174807	−	0.302775i	0.765287	−	0.643689i	$-0.222597\pi$
$967$	−5.43592	−	9.41529i	−0.174807	−	0.302775i	−0.940095	+	0.340914i	$0.889264\pi$
$968$	−10.7304	+	2.28081i	−0.344887	+	0.0733081i
$969$	0.0995481	+	0.306378i	0.00319795	+	0.00984227i
$970$	20.3836	+	4.33267i	0.654478	+	0.139114i
$971$	0.424304	+	4.03698i	0.0136166	+	0.129553i	0.999218	−	0.0395301i	$-0.0125861\pi$
$971$	0.424304	+	4.03698i	0.0136166	+	0.129553i	−0.985602	+	0.169083i	$0.945919\pi$
$972$	−6.45877	−	7.17319i	−0.207165	−	0.230080i
$973$	−34.0561	−	15.1627i	−1.09179	−	0.486095i
$974$	23.0637	−	10.2686i	0.739009	−	0.329028i
$975$	−4.22901	+	4.69679i	−0.135437	+	0.150418i
$976$	10.1631	+	7.38394i	0.325314	+	0.236354i
$977$	22.4159	+	16.2861i	0.717147	+	0.521038i	0.885472	−	0.464694i	$-0.153836\pi$
$977$	22.4159	+	16.2861i	0.717147	+	0.521038i	−0.168324	+	0.985732i	$0.553836\pi$
$978$	−2.40664	+	2.67285i	−0.0769559	+	0.0854682i
$979$	0.301710	−	0.134330i	0.00964268	−	0.00429320i
$980$	2.78375	+	1.23941i	0.0889237	+	0.0395914i
$981$	14.6953	+	16.3207i	0.469184	+	0.521081i
$982$	−1.85274	−	17.6277i	−0.0591234	−	0.562522i
$983$	−20.1222	−	4.27711i	−0.641799	−	0.136419i	−0.124495	−	0.992220i	$-0.539731\pi$
$983$	−20.1222	−	4.27711i	−0.641799	−	0.136419i	−0.517304	+	0.855802i	$0.673064\pi$
$984$	0.221709	+	0.682352i	0.00706784	+	0.0217526i
$985$	−11.9415	+	2.53825i	−0.380489	+	0.0808755i
$986$	−12.0794	−	20.9221i	−0.384686	−	0.666296i
$987$	−5.91296	+	10.2415i	−0.188211	+	0.325992i
$988$	0.425671	−	1.31008i	0.0135424	−	0.0416792i
$989$	−2.50932	+	23.8746i	−0.0797918	+	0.759168i
$990$	−0.482716	+	0.350714i	−0.0153417	+	0.0111464i
$991$	−34.9964			−1.11170			−0.555849	−	0.831283i	$-0.687607\pi$
$991$	−34.9964			−1.11170			−0.555849	+	0.831283i	$0.687607\pi$
$992$	3.10735	+	4.62000i	0.0986585	+	0.146685i
$993$	3.15190			0.100023
$994$	−25.4541	+	18.4935i	−0.807354	+	0.586577i
$995$	0.199181	−	1.89508i	0.00631445	−	0.0600780i
$996$	−0.657960	+	2.02499i	−0.0208483	+	0.0641644i
$997$	−3.30900	+	5.73135i	−0.104797	+	0.181514i	−0.913655	−	0.406490i	$-0.866753\pi$
$997$	−3.30900	+	5.73135i	−0.104797	+	0.181514i	0.808858	+	0.588004i	$0.200086\pi$
$998$	14.0133	+	24.2718i	0.443584	+	0.768310i
$999$	17.5402	−	3.72828i	0.554947	−	0.117958i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.2.g.b.59.1	yes	8
3.2	odd	2		558.2.ba.c.307.1		8
4.3	odd	2		496.2.bg.b.369.1		8
31.10	even	15	inner	62.2.g.b.41.1	✓	8
31.14	even	15		1922.2.a.h.1.4		4
31.17	odd	30		1922.2.a.m.1.2		4
93.41	odd	30		558.2.ba.c.289.1		8
124.103	odd	30		496.2.bg.b.289.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.2.g.b.41.1	✓	8	31.10	even	15	inner
62.2.g.b.59.1	yes	8	1.1	even	1	trivial
496.2.bg.b.289.1		8	124.103	odd	30
496.2.bg.b.369.1		8	4.3	odd	2
558.2.ba.c.289.1		8	93.41	odd	30
558.2.ba.c.307.1		8	3.2	odd	2
1922.2.a.h.1.4		4	31.14	even	15
1922.2.a.m.1.2		4	31.17	odd	30

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:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	62.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.0399263 - 0.379874i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.604528 + 1.04707i) q^{5} +(-0.190983 - 0.330792i) q^{6} +(-3.01807 + 0.641511i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(2.79173 + 0.593401i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.0399263 - 0.379874i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.604528 + 1.04707i) q^{5} +(-0.190983 - 0.330792i) q^{6} +(-3.01807 + 0.641511i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(2.79173 + 0.593401i) q^{9} +(0.126381 + 1.20243i) q^{10} +(0.115699 + 0.128496i) q^{11} +(-0.348943 - 0.155360i) q^{12} +(-4.27222 + 1.90211i) q^{13} +(-2.06460 + 2.29297i) q^{14} +(0.373619 + 0.271450i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(1.91588 - 2.12780i) q^{17} +(2.60735 - 1.16087i) q^{18} +(-0.269091 - 0.119807i) q^{19} +(0.809017 + 0.898504i) q^{20} +(0.123193 + 1.17210i) q^{21} +(0.169131 + 0.0359498i) q^{22} +(-1.53440 - 4.72241i) q^{23} +(-0.373619 + 0.0794152i) q^{24} +(1.76909 + 3.06415i) q^{25} +(-2.33826 + 4.04999i) q^{26} +(0.690983 - 2.12663i) q^{27} +(-0.322523 + 3.06860i) q^{28} +(6.82614 - 4.95948i) q^{29} +0.461819 q^{30} +(-3.10735 - 4.62000i) q^{31} -1.00000 q^{32} +(0.0534318 - 0.0388205i) q^{33} +(0.299290 - 2.84755i) q^{34} +(1.15280 - 3.54796i) q^{35} +(1.42705 - 2.47172i) q^{36} +(4.00973 + 6.94505i) q^{37} +(-0.288120 + 0.0612417i) q^{38} +(0.551989 + 1.69885i) q^{39} +(1.18264 + 0.251377i) q^{40} +(-0.196341 - 1.86806i) q^{41} +(0.788608 + 0.875838i) q^{42} +(-4.41667 - 1.96643i) q^{43} +(0.157960 - 0.0703285i) q^{44} +(-2.30902 + 2.56442i) q^{45} +(-4.01712 - 2.91861i) q^{46} +(8.11787 + 5.89798i) q^{47} +(-0.255585 + 0.283856i) q^{48} +(2.30242 - 1.02510i) q^{49} +(3.23229 + 1.43911i) q^{50} +(-0.731801 - 0.812748i) q^{51} +(0.488830 + 4.65090i) q^{52} +(-8.21139 - 1.74539i) q^{53} +(-0.690983 - 2.12663i) q^{54} +(-0.204489 + 0.0434654i) q^{55} +(1.54275 + 2.67212i) q^{56} +(-0.0562553 + 0.0974370i) q^{57} +(2.60735 - 8.02460i) q^{58} +(-1.54653 + 14.7142i) q^{59} +(0.373619 - 0.271450i) q^{60} -12.5623 q^{61} +(-5.22947 - 1.91120i) q^{62} -8.80633 q^{63} +(-0.809017 + 0.587785i) q^{64} +(0.591023 - 5.62321i) q^{65} +(0.0204091 - 0.0628129i) q^{66} +(-4.60075 + 7.96873i) q^{67} +(-1.43162 - 2.47964i) q^{68} +(-1.85518 + 0.394331i) q^{69} +(-1.15280 - 3.54796i) q^{70} +(9.97420 + 2.12008i) q^{71} +(-0.298335 - 2.83847i) q^{72} +(1.57384 + 1.74793i) q^{73} +(7.32614 + 3.26181i) q^{74} +(1.23462 - 0.549690i) q^{75} +(-0.197097 + 0.218898i) q^{76} +(-0.431619 - 0.313590i) q^{77} +(1.44512 + 1.04994i) q^{78} +(4.94240 - 5.48910i) q^{79} +(1.10453 - 0.491768i) q^{80} +(7.04179 + 3.13521i) q^{81} +(-1.25686 - 1.39589i) q^{82} +(-0.582676 - 5.54379i) q^{83} +(1.15280 + 0.245036i) q^{84} +(1.06976 + 3.29239i) q^{85} +(-4.72900 + 1.00518i) q^{86} +(-1.61143 - 2.79108i) q^{87} +(0.0864545 - 0.149744i) q^{88} +(0.590233 - 1.81655i) q^{89} +(-0.360704 + 3.43187i) q^{90} +(11.6736 - 8.48139i) q^{91} -4.96543 q^{92} +(-1.87908 + 0.995941i) q^{93} +10.0342 q^{94} +(0.288120 - 0.209331i) q^{95} +(-0.0399263 + 0.379874i) q^{96} +(5.32614 - 16.3922i) q^{97} +(1.26015 - 2.18265i) q^{98} +(0.246750 + 0.427384i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + q^{3} - 2 q^{4} - 3 q^{5} - 6 q^{6} - 16 q^{7} + 2 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 + q^3 - 2 * q^4 - 3 * q^5 - 6 * q^6 - 16 * q^7 + 2 * q^8 + 8 * q^9	\( 8 q + 2 q^{2} + q^{3} - 2 q^{4} - 3 q^{5} - 6 q^{6} - 16 q^{7} + 2 q^{8} + 8 q^{9} + 8 q^{10} + 3 q^{11} + q^{12} - 14 q^{14} - 4 q^{15} - 2 q^{16} - 2 q^{17} + 7 q^{18} + 3 q^{19} + 2 q^{20} - 31 q^{21} - 3 q^{22} + 15 q^{23} + 4 q^{24} + 9 q^{25} - 10 q^{26} + 10 q^{27} + 9 q^{28} + 13 q^{29} + 14 q^{30} - 11 q^{31} - 8 q^{32} - 6 q^{33} + 22 q^{34} + 24 q^{35} - 2 q^{36} + 8 q^{37} - 18 q^{38} - 30 q^{39} - 2 q^{40} + 13 q^{41} + 21 q^{42} - 7 q^{44} - 14 q^{45} + 5 q^{46} + 9 q^{47} - 4 q^{48} + 9 q^{49} - 9 q^{50} + 28 q^{51} - 51 q^{53} - 10 q^{54} + q^{55} + q^{56} + 18 q^{57} + 7 q^{58} - 18 q^{59} - 4 q^{60} - 20 q^{61} - 19 q^{62} - 14 q^{63} - 2 q^{64} + 10 q^{65} - 19 q^{66} - 18 q^{67} + 3 q^{68} + 35 q^{69} - 24 q^{70} + 7 q^{71} + 7 q^{72} - 13 q^{73} + 17 q^{74} - 36 q^{75} - 12 q^{76} + 11 q^{77} - 10 q^{78} + 9 q^{79} + 7 q^{80} + 16 q^{81} + 7 q^{82} + 6 q^{83} + 24 q^{84} - 17 q^{85} + 15 q^{86} + q^{87} + 7 q^{88} + 28 q^{89} + 19 q^{90} + 20 q^{91} - 20 q^{92} + 32 q^{93} + 6 q^{94} + 18 q^{95} - q^{96} + q^{97} + 11 q^{98} - 11 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + q^3 - 2 * q^4 - 3 * q^5 - 6 * q^6 - 16 * q^7 + 2 * q^8 + 8 * q^9 + 8 * q^10 + 3 * q^11 + q^12 - 14 * q^14 - 4 * q^15 - 2 * q^16 - 2 * q^17 + 7 * q^18 + 3 * q^19 + 2 * q^20 - 31 * q^21 - 3 * q^22 + 15 * q^23 + 4 * q^24 + 9 * q^25 - 10 * q^26 + 10 * q^27 + 9 * q^28 + 13 * q^29 + 14 * q^30 - 11 * q^31 - 8 * q^32 - 6 * q^33 + 22 * q^34 + 24 * q^35 - 2 * q^36 + 8 * q^37 - 18 * q^38 - 30 * q^39 - 2 * q^40 + 13 * q^41 + 21 * q^42 - 7 * q^44 - 14 * q^45 + 5 * q^46 + 9 * q^47 - 4 * q^48 + 9 * q^49 - 9 * q^50 + 28 * q^51 - 51 * q^53 - 10 * q^54 + q^55 + q^56 + 18 * q^57 + 7 * q^58 - 18 * q^59 - 4 * q^60 - 20 * q^61 - 19 * q^62 - 14 * q^63 - 2 * q^64 + 10 * q^65 - 19 * q^66 - 18 * q^67 + 3 * q^68 + 35 * q^69 - 24 * q^70 + 7 * q^71 + 7 * q^72 - 13 * q^73 + 17 * q^74 - 36 * q^75 - 12 * q^76 + 11 * q^77 - 10 * q^78 + 9 * q^79 + 7 * q^80 + 16 * q^81 + 7 * q^82 + 6 * q^83 + 24 * q^84 - 17 * q^85 + 15 * q^86 + q^87 + 7 * q^88 + 28 * q^89 + 19 * q^90 + 20 * q^91 - 20 * q^92 + 32 * q^93 + 6 * q^94 + 18 * q^95 - q^96 + q^97 + 11 * q^98 - 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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