LMFDB - Embedded newform 930.2.bg.d.391.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(121,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 0, 16]))

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

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

chi := DirichletCharacter("930.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bg (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 21x^{14} + 167x^{12} + 653x^{10} + 1350x^{8} + 1472x^{6} + 777x^{4} + 149x^{2} + 1 $ x^16 + 21x^14 + 167x^12 + 653x^10 + 1350x^8 + 1472x^6 + 777x^4 + 149*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			391.1
Root			$-2.07247i$ of defining polynomial
Character	$\chi$	$=$	930.391
Dual form			930.2.bg.d.421.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(0.913545 + 0.406737i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-1.16565 + 1.29459i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.669131 + 0.743145i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(0.913545 + 0.406737i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-1.16565 + 1.29459i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.669131 + 0.743145i) q^{9} +(-0.913545 + 0.406737i) q^{10} +(-4.27916 - 0.909564i) q^{11} +(-0.104528 + 0.994522i) q^{12} +(0.507131 + 4.82503i) q^{13} +(1.70397 - 0.362190i) q^{14} +(0.809017 - 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-5.11700 + 1.08765i) q^{17} +(-0.104528 - 0.994522i) q^{18} +(-0.132978 + 1.26520i) q^{19} +(0.978148 + 0.207912i) q^{20} +(-1.59143 + 0.708550i) q^{21} +(2.92729 + 3.25108i) q^{22} +(-0.898984 + 2.76679i) q^{23} +(0.669131 - 0.743145i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(2.42580 - 4.20162i) q^{26} +(0.309017 + 0.951057i) q^{27} +(-1.59143 - 0.708550i) q^{28} +(1.88671 + 1.37077i) q^{29} -1.00000 q^{30} +(-4.96249 + 2.52462i) q^{31} +1.00000 q^{32} +(-3.53926 - 2.57142i) q^{33} +(4.77904 + 2.12777i) q^{34} +(0.538319 + 1.65678i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(2.26066 + 3.91558i) q^{37} +(0.851248 - 0.945407i) q^{38} +(-1.49923 + 4.61415i) q^{39} +(-0.669131 - 0.743145i) q^{40} +(-2.29312 + 1.02096i) q^{41} +(1.70397 + 0.362190i) q^{42} +(0.805153 - 7.66052i) q^{43} +(-0.457287 - 4.35080i) q^{44} +(0.978148 - 0.207912i) q^{45} +(2.35357 - 1.70997i) q^{46} +(5.28976 - 3.84324i) q^{47} +(-0.978148 + 0.207912i) q^{48} +(0.414487 + 3.94358i) q^{49} +(-0.104528 + 0.994522i) q^{50} +(-5.11700 - 1.08765i) q^{51} +(-4.43216 + 1.97333i) q^{52} +(4.00911 + 4.45257i) q^{53} +(0.309017 - 0.951057i) q^{54} +(-2.92729 + 3.25108i) q^{55} +(0.871018 + 1.50865i) q^{56} +(-0.636085 + 1.10173i) q^{57} +(-0.720657 - 2.21795i) q^{58} +(-11.8990 - 5.29779i) q^{59} +(0.809017 + 0.587785i) q^{60} -5.21012 q^{61} +(5.49867 + 0.874412i) q^{62} -1.74204 q^{63} +(-0.809017 - 0.587785i) q^{64} +(4.43216 + 1.97333i) q^{65} +(1.35188 + 4.16065i) q^{66} +(-5.26759 + 9.12373i) q^{67} +(-2.61566 - 4.53045i) q^{68} +(-1.94662 + 2.16194i) q^{69} +(0.538319 - 1.65678i) q^{70} +(1.42988 + 1.58804i) q^{71} +(0.913545 - 0.406737i) q^{72} +(1.54177 + 0.327713i) q^{73} +(0.472607 - 4.49656i) q^{74} +(-0.104528 - 0.994522i) q^{75} +(-1.24437 + 0.264499i) q^{76} +(6.16552 - 4.47951i) q^{77} +(3.92503 - 2.85170i) q^{78} +(1.48077 - 0.314747i) q^{79} +(0.104528 + 0.994522i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(2.45528 + 0.521886i) q^{82} +(8.73828 - 3.89053i) q^{83} +(-1.16565 - 1.29459i) q^{84} +(-1.61656 + 4.97527i) q^{85} +(-5.15412 + 5.72423i) q^{86} +(1.16605 + 2.01965i) q^{87} +(-2.18738 + 3.78866i) q^{88} +(0.697694 + 2.14728i) q^{89} +(-0.913545 - 0.406737i) q^{90} +(-6.83755 - 4.96777i) q^{91} -2.90917 q^{92} +(-5.56031 + 0.287935i) q^{93} -6.53851 q^{94} +(1.02921 + 0.747763i) q^{95} +(0.913545 + 0.406737i) q^{96} +(5.20234 + 16.0112i) q^{97} +(1.98265 - 3.43406i) q^{98} +(-2.18738 - 3.78866i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 8 * q^5 - 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9	\( 16 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9} - 2 q^{10} - 4 q^{11} + 2 q^{12} - 20 q^{13} - 4 q^{14} + 4 q^{15} - 4 q^{16} - 12 q^{17} + 2 q^{18} - 7 q^{19} - 2 q^{20} - 4 q^{21} + 11 q^{22} + 11 q^{23} + 2 q^{24} - 8 q^{25} + 5 q^{26} - 4 q^{27} - 4 q^{28} + 23 q^{29} - 16 q^{30} - 17 q^{31} + 16 q^{32} - 2 q^{33} - 2 q^{34} + 7 q^{35} - 8 q^{36} + 17 q^{37} - 2 q^{38} - 5 q^{39} - 2 q^{40} + 8 q^{41} - 4 q^{42} + 32 q^{43} + q^{44} - 2 q^{45} + 11 q^{46} - 7 q^{47} + 2 q^{48} - q^{49} + 2 q^{50} - 12 q^{51} + 10 q^{52} + 54 q^{53} - 4 q^{54} - 11 q^{55} + q^{56} + 18 q^{57} - 22 q^{58} - 38 q^{59} + 4 q^{60} - 28 q^{61} - 27 q^{62} - 2 q^{63} - 4 q^{64} - 10 q^{65} - 7 q^{66} + q^{67} - 2 q^{68} - 13 q^{69} + 7 q^{70} - 11 q^{71} + 2 q^{72} + 53 q^{73} + 2 q^{74} + 2 q^{75} - 2 q^{76} + 44 q^{77} + 10 q^{78} + 48 q^{79} - 2 q^{80} + 2 q^{81} + 8 q^{82} + 56 q^{83} + 11 q^{84} - 24 q^{85} - 13 q^{86} + q^{87} - 9 q^{88} - 43 q^{89} - 2 q^{90} - 50 q^{91} - 44 q^{92} - 22 q^{93} - 72 q^{94} - 14 q^{95} + 2 q^{96} + 17 q^{97} + 29 q^{98} - 9 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 8 * q^5 - 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9 - 2 * q^10 - 4 * q^11 + 2 * q^12 - 20 * q^13 - 4 * q^14 + 4 * q^15 - 4 * q^16 - 12 * q^17 + 2 * q^18 - 7 * q^19 - 2 * q^20 - 4 * q^21 + 11 * q^22 + 11 * q^23 + 2 * q^24 - 8 * q^25 + 5 * q^26 - 4 * q^27 - 4 * q^28 + 23 * q^29 - 16 * q^30 - 17 * q^31 + 16 * q^32 - 2 * q^33 - 2 * q^34 + 7 * q^35 - 8 * q^36 + 17 * q^37 - 2 * q^38 - 5 * q^39 - 2 * q^40 + 8 * q^41 - 4 * q^42 + 32 * q^43 + q^44 - 2 * q^45 + 11 * q^46 - 7 * q^47 + 2 * q^48 - q^49 + 2 * q^50 - 12 * q^51 + 10 * q^52 + 54 * q^53 - 4 * q^54 - 11 * q^55 + q^56 + 18 * q^57 - 22 * q^58 - 38 * q^59 + 4 * q^60 - 28 * q^61 - 27 * q^62 - 2 * q^63 - 4 * q^64 - 10 * q^65 - 7 * q^66 + q^67 - 2 * q^68 - 13 * q^69 + 7 * q^70 - 11 * q^71 + 2 * q^72 + 53 * q^73 + 2 * q^74 + 2 * q^75 - 2 * q^76 + 44 * q^77 + 10 * q^78 + 48 * q^79 - 2 * q^80 + 2 * q^81 + 8 * q^82 + 56 * q^83 + 11 * q^84 - 24 * q^85 - 13 * q^86 + q^87 - 9 * q^88 - 43 * q^89 - 2 * q^90 - 50 * q^91 - 44 * q^92 - 22 * q^93 - 72 * q^94 - 14 * q^95 + 2 * q^96 + 17 * q^97 + 29 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{15}\right)$

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
$3$	0.913545	+	0.406737i	0.527436	+	0.234830i
$3$	0.913545	+	0.406737i	0.527436	+	0.234830i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	−1.16565	+	1.29459i	−0.440574	+	0.489307i	−0.922006	−	0.387176i	$-0.873450\pi$
$7$	−1.16565	+	1.29459i	−0.440574	+	0.489307i	0.481431	+	0.876484i	$0.340117\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	0.669131	+	0.743145i	0.223044	+	0.247715i
$10$	−0.913545	+	0.406737i	−0.288888	+	0.128621i
$11$	−4.27916	−	0.909564i	−1.29022	−	0.274244i	−0.488824	−	0.872383i	$-0.662574\pi$
$11$	−4.27916	−	0.909564i	−1.29022	−	0.274244i	−0.801393	+	0.598139i	$0.795907\pi$
$12$	−0.104528	+	0.994522i	−0.0301748	+	0.287094i
$13$	0.507131	+	4.82503i	0.140653	+	1.33822i	0.806101	+	0.591778i	$0.201574\pi$
$13$	0.507131	+	4.82503i	0.140653	+	1.33822i	−0.665448	+	0.746444i	$0.731759\pi$
$14$	1.70397	−	0.362190i	0.455405	−	0.0967993i
$15$	0.809017	−	0.587785i	0.208887	−	0.151765i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−5.11700	+	1.08765i	−1.24105	+	0.263794i	−0.781245	−	0.624224i	$-0.785415\pi$
$17$	−5.11700	+	1.08765i	−1.24105	+	0.263794i	−0.459808	+	0.888018i	$0.652082\pi$
$18$	−0.104528	−	0.994522i	−0.0246376	−	0.234411i
$19$	−0.132978	+	1.26520i	−0.0305072	+	0.290257i	0.968622	+	0.248538i	$0.0799501\pi$
$19$	−0.132978	+	1.26520i	−0.0305072	+	0.290257i	−0.999129	+	0.0417190i	$0.986717\pi$
$20$	0.978148	+	0.207912i	0.218720	+	0.0464905i
$21$	−1.59143	+	0.708550i	−0.347278	+	0.154618i
$22$	2.92729	+	3.25108i	0.624100	+	0.693133i
$23$	−0.898984	+	2.76679i	−0.187451	+	0.576915i	−0.999982	−	0.00600293i	$-0.998089\pi$
$23$	−0.898984	+	2.76679i	−0.187451	+	0.576915i	0.812531	+	0.582918i	$0.198089\pi$
$24$	0.669131	−	0.743145i	0.136586	−	0.151694i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	2.42580	−	4.20162i	0.475739	−	0.824005i
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	−1.59143	−	0.708550i	−0.300752	−	0.133903i
$29$	1.88671	+	1.37077i	0.350352	+	0.254546i	0.749017	−	0.662551i	$-0.230526\pi$
$29$	1.88671	+	1.37077i	0.350352	+	0.254546i	−0.398664	+	0.917097i	$0.630526\pi$
$30$	−1.00000			−0.182574
$31$	−4.96249	+	2.52462i	−0.891289	+	0.453436i
$31$	−4.96249	+	2.52462i	−0.891289	+	0.453436i
$32$	1.00000			0.176777
$33$	−3.53926	−	2.57142i	−0.616106	−	0.447627i
$34$	4.77904	+	2.12777i	0.819599	+	0.364909i
$35$	0.538319	+	1.65678i	0.0909925	+	0.280046i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	2.26066	+	3.91558i	0.371651	+	0.643718i	0.989820	−	0.142328i	$-0.0454586\pi$
$37$	2.26066	+	3.91558i	0.371651	+	0.643718i	−0.618169	+	0.786045i	$0.712125\pi$
$38$	0.851248	−	0.945407i	0.138091	−	0.153365i
$39$	−1.49923	+	4.61415i	−0.240069	+	0.738856i
$40$	−0.669131	−	0.743145i	−0.105799	−	0.117502i
$41$	−2.29312	+	1.02096i	−0.358125	+	0.159448i	−0.577909	−	0.816101i	$-0.696131\pi$
$41$	−2.29312	+	1.02096i	−0.358125	+	0.159448i	0.219784	+	0.975548i	$0.429465\pi$
$42$	1.70397	+	0.362190i	0.262928	+	0.0558871i
$43$	0.805153	−	7.66052i	0.122785	−	1.16822i	−0.743524	−	0.668709i	$-0.766847\pi$
$43$	0.805153	−	7.66052i	0.122785	−	1.16822i	0.866309	−	0.499509i	$-0.166486\pi$
$44$	−0.457287	−	4.35080i	−0.0689386	−	0.655907i
$45$	0.978148	−	0.207912i	0.145814	−	0.0309936i
$46$	2.35357	−	1.70997i	0.347015	−	0.252121i
$47$	5.28976	−	3.84324i	0.771591	−	0.560594i	−0.130852	−	0.991402i	$-0.541771\pi$
$47$	5.28976	−	3.84324i	0.771591	−	0.560594i	0.902444	+	0.430808i	$0.141771\pi$
$48$	−0.978148	+	0.207912i	−0.141183	+	0.0300095i
$49$	0.414487	+	3.94358i	0.0592125	+	0.563369i
$50$	−0.104528	+	0.994522i	−0.0147826	+	0.140647i
$51$	−5.11700	−	1.08765i	−0.716523	−	0.152302i
$52$	−4.43216	+	1.97333i	−0.614631	+	0.273651i
$53$	4.00911	+	4.45257i	0.550694	+	0.611608i	0.952657	−	0.304048i	$-0.0983384\pi$
$53$	4.00911	+	4.45257i	0.550694	+	0.611608i	−0.401962	+	0.915656i	$0.631672\pi$
$54$	0.309017	−	0.951057i	0.0420519	−	0.129422i
$55$	−2.92729	+	3.25108i	−0.394715	+	0.438376i
$56$	0.871018	+	1.50865i	0.116395	+	0.201602i
$57$	−0.636085	+	1.10173i	−0.0842515	+	0.145928i
$58$	−0.720657	−	2.21795i	−0.0946269	−	0.291232i
$59$	−11.8990	−	5.29779i	−1.54912	−	0.689714i	−0.558903	−	0.829233i	$-0.688778\pi$
$59$	−11.8990	−	5.29779i	−1.54912	−	0.689714i	−0.990219	+	0.139519i	$0.955444\pi$
$60$	0.809017	+	0.587785i	0.104444	+	0.0758827i
$61$	−5.21012			−0.667088			−0.333544	−	0.942735i	$-0.608245\pi$
$61$	−5.21012			−0.667088			−0.333544	+	0.942735i	$0.608245\pi$
$62$	5.49867	+	0.874412i	0.698332	+	0.111050i
$63$	−1.74204			−0.219476
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	4.43216	+	1.97333i	0.549742	+	0.244761i
$66$	1.35188	+	4.16065i	0.166404	+	0.512140i
$67$	−5.26759	+	9.12373i	−0.643539	+	1.11464i	0.341098	+	0.940028i	$0.389201\pi$
$67$	−5.26759	+	9.12373i	−0.643539	+	1.11464i	−0.984637	+	0.174614i	$0.944132\pi$
$68$	−2.61566	−	4.53045i	−0.317195	−	0.549398i
$69$	−1.94662	+	2.16194i	−0.234345	+	0.260267i
$70$	0.538319	−	1.65678i	0.0643414	−	0.198023i
$71$	1.42988	+	1.58804i	0.169695	+	0.188466i	0.821994	−	0.569496i	$-0.192862\pi$
$71$	1.42988	+	1.58804i	0.169695	+	0.188466i	−0.652298	+	0.757962i	$0.726195\pi$
$72$	0.913545	−	0.406737i	0.107662	−	0.0479344i
$73$	1.54177	+	0.327713i	0.180450	+	0.0383559i	0.297250	−	0.954800i	$-0.403930\pi$
$73$	1.54177	+	0.327713i	0.180450	+	0.0383559i	−0.116800	+	0.993155i	$0.537264\pi$
$74$	0.472607	−	4.49656i	0.0549395	−	0.522714i
$75$	−0.104528	−	0.994522i	−0.0120699	−	0.114837i
$76$	−1.24437	+	0.264499i	−0.142739	+	0.0303401i
$77$	6.16552	−	4.47951i	0.702626	−	0.510488i
$78$	3.92503	−	2.85170i	0.444423	−	0.322892i
$79$	1.48077	−	0.314747i	0.166599	−	0.0354117i	−0.123857	−	0.992300i	$-0.539526\pi$
$79$	1.48077	−	0.314747i	0.166599	−	0.0354117i	0.290456	+	0.956888i	$0.406193\pi$
$80$	0.104528	+	0.994522i	0.0116866	+	0.111191i
$81$	−0.104528	+	0.994522i	−0.0116143	+	0.110502i
$82$	2.45528	+	0.521886i	0.271140	+	0.0576326i
$83$	8.73828	−	3.89053i	0.959151	−	0.427041i	0.133391	−	0.991063i	$-0.457413\pi$
$83$	8.73828	−	3.89053i	0.959151	−	0.427041i	0.825760	+	0.564022i	$0.190747\pi$
$84$	−1.16565	−	1.29459i	−0.127183	−	0.141251i
$85$	−1.61656	+	4.97527i	−0.175341	+	0.539644i
$86$	−5.15412	+	5.72423i	−0.555783	+	0.617260i
$87$	1.16605	+	2.01965i	0.125013	+	0.216530i
$88$	−2.18738	+	3.78866i	−0.233176	+	0.403872i
$89$	0.697694	+	2.14728i	0.0739554	+	0.227611i	0.981201	−	0.192991i	$-0.0618188\pi$
$89$	0.697694	+	2.14728i	0.0739554	+	0.227611i	−0.907245	+	0.420602i	$0.861819\pi$
$90$	−0.913545	−	0.406737i	−0.0962961	−	0.0428738i
$91$	−6.83755	−	4.96777i	−0.716770	−	0.520764i
$92$	−2.90917			−0.303302
$93$	−5.56031	+	0.287935i	−0.576578	+	0.0298574i
$94$	−6.53851			−0.674396
$95$	1.02921	+	0.747763i	0.105594	+	0.0767188i
$96$	0.913545	+	0.406737i	0.0932383	+	0.0415124i
$97$	5.20234	+	16.0112i	0.528218	+	1.62569i	0.757863	+	0.652413i	$0.226243\pi$
$97$	5.20234	+	16.0112i	0.528218	+	1.62569i	−0.229645	+	0.973274i	$0.573757\pi$
$98$	1.98265	−	3.43406i	0.200278	−	0.346892i
$99$	−2.18738	−	3.78866i	−0.219840	−	0.380774i
$100$	0.669131	−	0.743145i	0.0669131	−	0.0743145i
$101$	2.40771	−	7.41016i	0.239576	−	0.737338i	−0.756906	−	0.653524i	$-0.773290\pi$
$101$	2.40771	−	7.41016i	0.239576	−	0.737338i	0.996481	−	0.0838142i	$-0.0267102\pi$
$102$	3.50043	+	3.88762i	0.346594	+	0.384932i
$103$	−11.4992	+	5.11979i	−1.13305	+	0.504468i	−0.885608	−	0.464434i	$-0.846258\pi$
$103$	−11.4992	+	5.11979i	−1.13305	+	0.504468i	−0.247445	+	0.968902i	$0.579591\pi$
$104$	4.74559	+	1.00871i	0.465343	+	0.0989118i
$105$	−0.182092	+	1.73249i	−0.0177704	+	0.169074i
$106$	−0.626285	−	5.95871i	−0.0608302	−	0.578761i
$107$	17.5621	−	3.73294i	1.69779	−	0.360876i	0.745603	−	0.666391i	$-0.232162\pi$
$107$	17.5621	−	3.73294i	1.69779	−	0.360876i	0.952188	+	0.305514i	$0.0988284\pi$
$108$	−0.809017	+	0.587785i	−0.0778477	+	0.0565597i
$109$	−8.30171	+	6.03154i	−0.795160	+	0.577717i	−0.909490	−	0.415726i	$-0.863528\pi$
$109$	−8.30171	+	6.03154i	−0.795160	+	0.577717i	0.114331	+	0.993443i	$0.463528\pi$
$110$	4.27916	−	0.909564i	0.408002	−	0.0867235i
$111$	0.472607	+	4.49656i	0.0448579	+	0.426794i
$112$	0.182092	−	1.73249i	0.0172061	−	0.163705i
$113$	−13.2387	−	2.81398i	−1.24540	−	0.264717i	−0.462359	−	0.886693i	$-0.652997\pi$
$113$	−13.2387	−	2.81398i	−1.24540	−	0.264717i	−0.783037	+	0.621976i	$0.786330\pi$
$114$	1.16219	−	0.517438i	0.108849	−	0.0484625i
$115$	1.94662	+	2.16194i	0.181523	+	0.201602i
$116$	−0.720657	+	2.21795i	−0.0669113	+	0.205932i
$117$	−3.24636	+	3.60545i	−0.300126	+	0.333324i
$118$	6.51256	+	11.2801i	0.599530	+	1.03842i
$119$	4.55657	−	7.89221i	0.417700	−	0.723478i
$120$	−0.309017	−	0.951057i	−0.0282093	−	0.0868192i
$121$	7.43493	+	3.31024i	0.675903	+	0.300931i
$122$	4.21508	+	3.06243i	0.381615	+	0.277260i
$123$	−2.51013			−0.226331
$124$	−3.93455	−	3.93945i	−0.353333	−	0.353773i
$125$	−1.00000			−0.0894427
$126$	1.40934	+	1.02394i	0.125554	+	0.0912201i
$127$	16.0333	+	7.13848i	1.42272	+	0.633438i	0.966556	−	0.256455i	$-0.0825547\pi$
$127$	16.0333	+	7.13848i	1.42272	+	0.633438i	0.456169	+	0.889893i	$0.349221\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	3.85136	−	6.67075i	0.339093	−	0.587326i
$130$	−2.42580	−	4.20162i	−0.212757	−	0.368506i
$131$	−9.53250	+	10.5869i	−0.832858	+	0.924983i	−0.998121	−	0.0612666i	$-0.980486\pi$
$131$	−9.53250	+	10.5869i	−0.832858	+	0.924983i	0.165263	+	0.986250i	$0.447153\pi$
$132$	1.35188	−	4.16065i	0.117666	−	0.362138i
$133$	−1.48291	−	1.64693i	−0.128584	−	0.142807i
$134$	9.62437	−	4.28504i	0.831419	−	0.370171i
$135$	0.978148	+	0.207912i	0.0841855	+	0.0178942i
$136$	−0.546821	+	5.20265i	−0.0468895	+	0.446124i
$137$	1.16204	+	11.0561i	0.0992801	+	0.944587i	0.924861	+	0.380304i	$0.124181\pi$
$137$	1.16204	+	11.0561i	0.0992801	+	0.944587i	−0.825581	+	0.564283i	$0.809153\pi$
$138$	2.84560	−	0.604851i	0.242234	−	0.0514884i
$139$	12.1094	−	8.79797i	1.02710	−	0.746234i	0.0593760	−	0.998236i	$-0.481089\pi$
$139$	12.1094	−	8.79797i	1.02710	−	0.746234i	0.967727	+	0.252002i	$0.0810889\pi$
$140$	−1.40934	+	1.02394i	−0.119111	+	0.0865390i
$141$	6.39563	−	1.35943i	0.538609	−	0.114485i
$142$	−0.223369	−	2.12521i	−0.0187447	−	0.178344i
$143$	2.21858	−	21.1084i	0.185527	−	1.76517i
$144$	−0.978148	−	0.207912i	−0.0815123	−	0.0173260i
$145$	2.13048	−	0.948549i	0.176926	−	0.0787727i
$146$	−1.05469	−	1.17135i	−0.0872869	−	0.0969419i
$147$	−1.22535	+	3.77123i	−0.101065	+	0.311046i
$148$	−3.02536	+	3.36000i	−0.248683	+	0.276190i
$149$	2.55003	+	4.41678i	0.208906	+	0.361837i	0.951370	−	0.308050i	$-0.0996763\pi$
$149$	2.55003	+	4.41678i	0.208906	+	0.361837i	−0.742464	+	0.669886i	$0.766343\pi$
$150$	−0.500000	+	0.866025i	−0.0408248	+	0.0707107i
$151$	−7.10030	−	21.8525i	−0.577814	−	1.77833i	−0.626391	−	0.779509i	$-0.715469\pi$
$151$	−7.10030	−	21.8525i	−0.577814	−	1.77833i	0.0485774	−	0.998819i	$-0.484531\pi$
$152$	1.16219	+	0.517438i	0.0942657	+	0.0419698i
$153$	−4.23222	−	3.07489i	−0.342155	−	0.248590i
$154$	−7.62100			−0.614117
$155$	−0.294854	+	5.55995i	−0.0236832	+	0.446586i
$156$	−4.85161			−0.388440
$157$	1.80664	+	1.31260i	0.144185	+	0.104757i	0.657539	−	0.753420i	$-0.271597\pi$
$157$	1.80664	+	1.31260i	0.144185	+	0.104757i	−0.513354	+	0.858177i	$0.671597\pi$
$158$	−1.38297	−	0.615737i	−0.110023	−	0.0489854i
$159$	1.85148	+	5.69828i	0.146832	+	0.451903i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−2.53394	−	4.38892i	−0.199703	−	0.345895i
$162$	0.669131	−	0.743145i	0.0525719	−	0.0583870i
$163$	−0.588424	+	1.81098i	−0.0460889	+	0.141847i	−0.971453	−	0.237233i	$-0.923760\pi$
$163$	−0.588424	+	1.81098i	−0.0460889	+	0.141847i	0.925364	+	0.379080i	$0.123760\pi$
$164$	−1.67961	−	1.86539i	−0.131155	−	0.145663i
$165$	−3.99654	+	1.77938i	−0.311131	+	0.138524i
$166$	−9.35621	−	1.98872i	−0.726183	−	0.154355i
$167$	2.48315	−	23.6256i	0.192152	−	1.82820i	−0.295705	−	0.955279i	$-0.595554\pi$
$167$	2.48315	−	23.6256i	0.192152	−	1.82820i	0.487857	−	0.872924i	$-0.337779\pi$
$168$	0.182092	+	1.73249i	0.0140487	+	0.133665i
$169$	−10.3078	+	2.19099i	−0.792909	+	0.168538i
$170$	4.23222	−	3.07489i	0.324596	−	0.235833i
$171$	−1.02921	+	0.747763i	−0.0787054	+	0.0571829i
$172$	7.53439	−	1.60148i	0.574492	−	0.122112i
$173$	0.985224	+	9.37378i	0.0749052	+	0.712675i	0.965945	+	0.258749i	$0.0833103\pi$
$173$	0.985224	+	9.37378i	0.0749052	+	0.712675i	−0.891039	+	0.453926i	$0.850023\pi$
$174$	0.243770	−	2.31932i	0.0184802	−	0.175827i
$175$	1.70397	+	0.362190i	0.128808	+	0.0273790i
$176$	3.99654	−	1.77938i	0.301251	−	0.134126i
$177$	−8.71551	−	9.67955i	−0.655097	−	0.727559i
$178$	0.697694	−	2.14728i	0.0522943	−	0.160945i
$179$	−3.72094	+	4.13252i	−0.278116	+	0.308879i	−0.865978	−	0.500082i	$-0.833303\pi$
$179$	−3.72094	+	4.13252i	−0.278116	+	0.308879i	0.587862	+	0.808961i	$0.299970\pi$
$180$	0.500000	+	0.866025i	0.0372678	+	0.0645497i
$181$	5.32796	−	9.22829i	0.396024	−	0.685934i	−0.597207	−	0.802087i	$-0.703723\pi$
$181$	5.32796	−	9.22829i	0.396024	−	0.685934i	0.993231	+	0.116153i	$0.0370564\pi$
$182$	2.61171	+	8.03803i	0.193593	+	0.595818i
$183$	−4.75968	−	2.11915i	−0.351846	−	0.156652i
$184$	2.35357	+	1.70997i	0.173508	+	0.126061i
$185$	4.52132			0.332414
$186$	4.66763	+	3.03533i	0.342247	+	0.222561i
$187$	22.8857			1.67357
$188$	5.28976	+	3.84324i	0.385796	+	0.280297i
$189$	−1.59143	−	0.708550i	−0.115759	−	0.0515394i
$190$	−0.393122	−	1.20991i	−0.0285201	−	0.0877758i
$191$	−5.04380	+	8.73611i	−0.364956	+	0.632123i	−0.988769	−	0.149451i	$-0.952249\pi$
$191$	−5.04380	+	8.73611i	−0.364956	+	0.632123i	0.623813	+	0.781574i	$0.285583\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	2.71976	−	3.02060i	0.195772	−	0.217427i	−0.637264	−	0.770646i	$-0.719934\pi$
$193$	2.71976	−	3.02060i	0.195772	−	0.217427i	0.833036	+	0.553218i	$0.186601\pi$
$194$	5.20234	−	16.0112i	0.373506	−	1.14953i
$195$	3.24636	+	3.60545i	0.232477	+	0.258191i
$196$	−3.62249	+	1.61284i	−0.258749	+	0.115203i
$197$	6.89826	+	1.46627i	0.491480	+	0.104467i	0.446984	−	0.894542i	$-0.352498\pi$
$197$	6.89826	+	1.46627i	0.491480	+	0.104467i	0.0444968	+	0.999010i	$0.485832\pi$
$198$	−0.457287	+	4.35080i	−0.0324980	+	0.309198i
$199$	0.507449	+	4.82805i	0.0359721	+	0.342252i	0.997675	+	0.0681564i	$0.0217117\pi$
$199$	0.507449	+	4.82805i	0.0359721	+	0.342252i	−0.961703	+	0.274095i	$0.911622\pi$
$200$	−0.978148	+	0.207912i	−0.0691655	+	0.0147016i
$201$	−8.52314	+	6.19242i	−0.601176	+	0.436780i
$202$	−6.30346	+	4.57973i	−0.443510	+	0.322229i
$203$	−3.97382	+	0.844661i	−0.278907	+	0.0592836i
$204$	−0.546821	−	5.20265i	−0.0382851	−	0.364259i
$205$	−0.262380	+	2.49638i	−0.0183254	+	0.174355i
$206$	12.3124	+	2.61708i	0.857846	+	0.182341i
$207$	−2.65766	+	1.18327i	−0.184720	+	0.0822428i
$208$	−3.24636	−	3.60545i	−0.225095	−	0.249993i
$209$	1.71982	−	5.29305i	0.118962	−	0.366128i
$210$	1.16565	−	1.29459i	0.0804375	−	0.0893349i
$211$	−0.158475	−	0.274486i	−0.0109098	−	0.0188964i	0.860519	−	0.509418i	$-0.170139\pi$
$211$	−0.158475	−	0.274486i	−0.0109098	−	0.0188964i	−0.871429	+	0.490522i	$0.836806\pi$
$212$	−2.99576	+	5.18882i	−0.205750	+	0.356369i
$213$	0.660345	+	2.03233i	0.0452461	+	0.139253i
$214$	−16.4022	−	7.30272i	−1.12123	−	0.499204i
$215$	−6.23163	−	4.52754i	−0.424993	−	0.308776i
$216$	1.00000			0.0680414
$217$	2.51618	−	9.36719i	0.170809	−	0.635887i
$218$	10.2615			0.694995
$219$	1.27518	+	0.926474i	0.0861688	+	0.0626053i
$220$	−3.99654	−	1.77938i	−0.269447	−	0.119966i
$221$	−7.84294	−	24.1381i	−0.527573	−	1.62370i
$222$	2.26066	−	3.91558i	0.151726	−	0.262797i
$223$	−5.70345	−	9.87866i	−0.381931	−	0.661524i	0.609407	−	0.792857i	$-0.291407\pi$
$223$	−5.70345	−	9.87866i	−0.381931	−	0.661524i	−0.991338	+	0.131334i	$0.958074\pi$
$224$	−1.16565	+	1.29459i	−0.0778833	+	0.0864981i
$225$	0.309017	−	0.951057i	0.0206011	−	0.0634038i
$226$	9.05635	+	10.0581i	0.602419	+	0.669055i
$227$	−12.5292	+	5.57835i	−0.831592	+	0.370248i	−0.777961	−	0.628312i	$-0.783746\pi$
$227$	−12.5292	+	5.57835i	−0.831592	+	0.370248i	−0.0536305	+	0.998561i	$0.517079\pi$
$228$	−1.24437	−	0.264499i	−0.0824104	−	0.0175169i
$229$	2.57558	−	24.5050i	0.170199	−	1.61934i	−0.492404	−	0.870366i	$-0.663882\pi$
$229$	2.57558	−	24.5050i	0.170199	−	1.61934i	0.662604	−	0.748970i	$-0.269451\pi$
$230$	−0.304091	−	2.89324i	−0.0200512	−	0.190774i
$231$	7.45446	−	1.58449i	0.490467	−	0.104252i
$232$	1.88671	−	1.37077i	0.123868	−	0.0899956i
$233$	19.5969	−	14.2380i	1.28384	−	0.932761i	0.284174	−	0.958773i	$-0.408281\pi$
$233$	19.5969	−	14.2380i	1.28384	−	0.932761i	0.999662	+	0.0260114i	$0.00828062\pi$
$234$	4.74559	−	1.00871i	0.310229	−	0.0659412i
$235$	−0.683460	−	6.50269i	−0.0445840	−	0.424189i
$236$	1.36150	−	12.9538i	0.0886258	−	0.843218i
$237$	1.48077	+	0.314747i	0.0961861	+	0.0204450i
$238$	−8.32527	+	3.70665i	−0.539647	+	0.240266i
$239$	−0.505547	−	0.561467i	−0.0327011	−	0.0363183i	0.726572	−	0.687090i	$-0.241112\pi$
$239$	−0.505547	−	0.561467i	−0.0327011	−	0.0363183i	−0.759273	+	0.650772i	$0.774446\pi$
$240$	−0.309017	+	0.951057i	−0.0199470	+	0.0613904i
$241$	10.8250	−	12.0224i	0.697300	−	0.774430i	−0.285644	−	0.958336i	$-0.592207\pi$
$241$	10.8250	−	12.0224i	0.697300	−	0.774430i	0.982944	+	0.183906i	$0.0588741\pi$
$242$	−4.06927	−	7.04819i	−0.261583	−	0.453074i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−1.61002	−	4.95512i	−0.103071	−	0.317219i
$245$	3.62249	+	1.61284i	0.231432	+	0.103040i
$246$	2.03074	+	1.47542i	0.129475	+	0.0940692i
$247$	−6.17207			−0.392719
$248$	0.867568	+	5.49976i	0.0550906	+	0.349235i
$249$	9.56524			0.606172
$250$	0.809017	+	0.587785i	0.0511667	+	0.0371748i
$251$	−2.27123	−	1.01121i	−0.143358	−	0.0638273i	0.333803	−	0.942643i	$-0.391668\pi$
$251$	−2.27123	−	1.01121i	−0.143358	−	0.0638273i	−0.477162	+	0.878815i	$0.658334\pi$
$252$	−0.538319	−	1.65678i	−0.0339109	−	0.104367i
$253$	6.36347	−	11.0219i	0.400068	−	0.692938i
$254$	−8.77531	−	15.1993i	−0.550612	−	0.953688i
$255$	−3.50043	+	3.88762i	−0.219205	+	0.243452i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−5.83092	−	6.47590i	−0.363723	−	0.403955i	0.533309	−	0.845920i	$-0.320948\pi$
$257$	−5.83092	−	6.47590i	−0.363723	−	0.403955i	−0.897032	+	0.441965i	$0.854282\pi$
$258$	−7.03678	+	3.13298i	−0.438091	+	0.195051i
$259$	−7.70420	−	1.63758i	−0.478715	−	0.101754i
$260$	−0.507131	+	4.82503i	−0.0314509	+	0.299236i
$261$	0.243770	+	2.31932i	0.0150890	+	0.143562i
$262$	13.9348	−	2.96193i	0.860894	−	0.182989i
$263$	−7.78018	+	5.65263i	−0.479747	+	0.348556i	−0.801228	−	0.598360i	$-0.795819\pi$
$263$	−7.78018	+	5.65263i	−0.479747	+	0.348556i	0.321481	+	0.946916i	$0.395819\pi$
$264$	−3.53926	+	2.57142i	−0.217826	+	0.158260i
$265$	5.86060	−	1.24571i	0.360014	−	0.0765233i
$266$	0.231653	+	2.20403i	0.0142035	+	0.135138i
$267$	−0.236003	+	2.24542i	−0.0144431	+	0.137417i
$268$	−10.3050	−	2.19039i	−0.629476	−	0.133799i
$269$	−7.60295	+	3.38505i	−0.463560	+	0.206390i	−0.625208	−	0.780458i	$-0.714986\pi$
$269$	−7.60295	+	3.38505i	−0.463560	+	0.206390i	0.161648	+	0.986849i	$0.448319\pi$
$270$	−0.669131	−	0.743145i	−0.0407220	−	0.0452264i
$271$	7.99175	−	24.5961i	0.485464	−	1.49410i	−0.345844	−	0.938292i	$-0.612407\pi$
$271$	7.99175	−	24.5961i	0.485464	−	1.49410i	0.831308	−	0.555812i	$-0.187593\pi$
$272$	3.50043	−	3.88762i	0.212245	−	0.235722i
$273$	−4.22584	−	7.31937i	−0.255759	−	0.442988i
$274$	5.55851	−	9.62761i	0.335802	−	0.581625i
$275$	1.35188	+	4.16065i	0.0815212	+	0.250896i
$276$	−2.65766	−	1.18327i	−0.159972	−	0.0712243i
$277$	−5.43002	−	3.94514i	−0.326258	−	0.237041i	0.412583	−	0.910920i	$-0.364627\pi$
$277$	−5.43002	−	3.94514i	−0.326258	−	0.237041i	−0.738841	+	0.673879i	$0.764627\pi$
$278$	−14.9680			−0.897721
$279$	−5.19671	−	1.99854i	−0.311119	−	0.119650i
$280$	1.74204			0.104107
$281$	−19.5516	−	14.2051i	−1.16635	−	0.847403i	−0.175783	−	0.984429i	$-0.556246\pi$
$281$	−19.5516	−	14.2051i	−1.16635	−	0.847403i	−0.990568	+	0.137025i	$0.956246\pi$
$282$	−5.97322	−	2.65945i	−0.355700	−	0.158368i
$283$	−5.53983	−	17.0498i	−0.329309	−	1.01351i	−0.969458	−	0.245257i	$-0.921127\pi$
$283$	−5.53983	−	17.0498i	−0.329309	−	1.01351i	0.640149	−	0.768251i	$-0.278873\pi$
$284$	−1.06846	+	1.85063i	−0.0634014	+	0.109815i
$285$	0.636085	+	1.10173i	0.0376784	+	0.0652610i
$286$	−14.2021	+	15.7730i	−0.839785	+	0.932676i
$287$	1.35125	−	4.15872i	0.0797619	−	0.245482i
$288$	0.669131	+	0.743145i	0.0394289	+	0.0437902i
$289$	9.47038	−	4.21649i	0.557081	−	0.248029i
$290$	−2.28113	−	0.484870i	−0.133953	−	0.0284725i
$291$	−1.75975	+	16.7429i	−0.103158	+	0.981487i
$292$	0.164759	+	1.56758i	0.00964179	+	0.0917355i
$293$	2.40128	−	0.510407i	0.140284	−	0.0298183i	−0.137234	−	0.990539i	$-0.543821\pi$
$293$	2.40128	−	0.510407i	0.140284	−	0.0298183i	0.277518	+	0.960720i	$0.410488\pi$
$294$	3.20800	−	2.33075i	0.187094	−	0.135932i
$295$	−10.5375	+	7.65597i	−0.613519	+	0.445748i
$296$	4.42252	−	0.940036i	0.257054	−	0.0546385i
$297$	−0.457287	−	4.35080i	−0.0265345	−	0.252459i
$298$	0.533101	−	5.07212i	0.0308817	−	0.293820i
$299$	−13.8057	−	2.93450i	−0.798407	−	0.169707i
$300$	0.913545	−	0.406737i	0.0527436	−	0.0234830i
$301$	8.97867	+	9.97182i	0.517522	+	0.574766i
$302$	−7.10030	+	21.8525i	−0.408576	+	1.25747i
$303$	5.21353	−	5.79021i	0.299510	−	0.332639i
$304$	−0.636085	−	1.10173i	−0.0364820	−	0.0631886i
$305$	−2.60506	+	4.51210i	−0.149165	+	0.258362i
$306$	1.61656	+	4.97527i	0.0924128	+	0.284417i
$307$	14.9410	+	6.65216i	0.852728	+	0.379659i	0.786085	−	0.618118i	$-0.212105\pi$
$307$	14.9410	+	6.65216i	0.852728	+	0.379659i	0.0666428	+	0.997777i	$0.478771\pi$
$308$	6.16552	+	4.47951i	0.351313	+	0.255244i
$309$	−12.5875			−0.716076
$310$	3.50660	−	4.32478i	0.199161	−	0.245631i
$311$	18.1973			1.03188			0.515938	−	0.856626i	$-0.327444\pi$
$311$	18.1973			1.03188			0.515938	+	0.856626i	$0.327444\pi$
$312$	3.92503	+	2.85170i	0.222211	+	0.161446i
$313$	24.3484	+	10.8406i	1.37625	+	0.612747i	0.955652	−	0.294499i	$-0.0951527\pi$
$313$	24.3484	+	10.8406i	1.37625	+	0.612747i	0.420601	+	0.907246i	$0.361819\pi$
$314$	−0.690074	−	2.12383i	−0.0389431	−	0.119855i
$315$	−0.871018	+	1.50865i	−0.0490763	+	0.0850027i
$316$	0.756924	+	1.31103i	0.0425803	+	0.0737512i
$317$	−5.20155	+	5.77690i	−0.292148	+	0.324463i	−0.871295	−	0.490760i	$-0.836719\pi$
$317$	−5.20155	+	5.77690i	−0.292148	+	0.324463i	0.579147	+	0.815223i	$0.303386\pi$
$318$	1.85148	−	5.69828i	0.103826	−	0.319544i
$319$	−6.82671	−	7.58183i	−0.382223	−	0.424501i
$320$	−0.913545	+	0.406737i	−0.0510687	+	0.0227373i
$321$	17.5621	+	3.73294i	0.980220	+	0.208352i
$322$	−0.529739	+	5.04013i	−0.0295212	+	0.280875i
$323$	−0.695649	−	6.61866i	−0.0387070	−	0.368272i
$324$	−0.978148	+	0.207912i	−0.0543415	+	0.0115506i
$325$	3.92503	−	2.85170i	0.217722	−	0.158184i
$326$	1.54051	−	1.11925i	0.0853212	−	0.0619895i
$327$	−10.0372	+	2.13348i	−0.555061	+	0.117982i
$328$	0.262380	+	2.49638i	0.0144875	+	0.137840i
$329$	−1.19061	+	11.3279i	−0.0656406	+	0.624529i
$330$	4.27916	+	0.909564i	0.235560	+	0.0500699i
$331$	−2.76578	+	1.23140i	−0.152021	+	0.0676841i	−0.481337	−	0.876536i	$-0.659849\pi$
$331$	−2.76578	+	1.23140i	−0.152021	+	0.0676841i	0.329316	+	0.944220i	$0.393182\pi$
$332$	6.40039	+	7.10836i	0.351267	+	0.390122i
$333$	−1.39717	+	4.30003i	−0.0765642	+	0.235640i
$334$	−15.8957	+	17.6539i	−0.869773	+	0.965981i
$335$	5.26759	+	9.12373i	0.287799	+	0.498483i
$336$	0.871018	−	1.50865i	0.0475180	−	0.0823035i
$337$	9.27352	+	28.5409i	0.505161	+	1.55472i	0.800500	+	0.599332i	$0.204567\pi$
$337$	9.27352	+	28.5409i	0.505161	+	1.55472i	−0.295340	+	0.955392i	$0.595433\pi$
$338$	9.62704	+	4.28623i	0.523642	+	0.233140i
$339$	−10.9496	−	7.95538i	−0.594703	−	0.432077i
$340$	−5.23131			−0.283708
$341$	23.5316	−	6.28958i	1.27431	−	0.340600i
$342$	1.27217			0.0687911
$343$	−15.4538	−	11.2279i	−0.834428	−	0.606247i
$344$	−7.03678	−	3.13298i	−0.379398	−	0.168919i
$345$	0.898984	+	2.76679i	0.0483997	+	0.148959i
$346$	4.71271	−	8.16265i	0.253357	−	0.438827i
$347$	7.62382	+	13.2048i	0.409268	+	0.708873i	0.994808	−	0.101771i	$-0.0324508\pi$
$347$	7.62382	+	13.2048i	0.409268	+	0.708873i	−0.585540	+	0.810644i	$0.699117\pi$
$348$	−1.56048	+	1.73308i	−0.0836503	+	0.0929031i
$349$	−8.63797	+	26.5849i	−0.462380	+	1.42306i	0.399868	+	0.916573i	$0.369056\pi$
$349$	−8.63797	+	26.5849i	−0.462380	+	1.42306i	−0.862248	+	0.506486i	$0.830944\pi$
$350$	−1.16565	−	1.29459i	−0.0623066	−	0.0691985i
$351$	−4.43216	+	1.97333i	−0.236571	+	0.105328i
$352$	−4.27916	−	0.909564i	−0.228080	−	0.0484799i
$353$	−1.30629	+	12.4285i	−0.0695268	+	0.661503i	0.903148	+	0.429330i	$0.141250\pi$
$353$	−1.30629	+	12.4285i	−0.0695268	+	0.661503i	−0.972674	+	0.232173i	$0.925416\pi$
$354$	1.36150	+	12.9538i	0.0723627	+	0.688485i
$355$	2.09022	−	0.444291i	0.110938	−	0.0235805i
$356$	−1.82659	+	1.32709i	−0.0968088	+	0.0703357i
$357$	7.37268	−	5.35657i	0.390204	−	0.283500i
$358$	5.43933	−	1.15617i	0.287478	−	0.0611053i
$359$	0.765092	+	7.27937i	0.0403800	+	0.384190i	0.995984	+	0.0895351i	$0.0285381\pi$
$359$	0.765092	+	7.27937i	0.0403800	+	0.384190i	−0.955604	+	0.294655i	$0.904795\pi$
$360$	0.104528	−	0.994522i	0.00550913	−	0.0524159i
$361$	17.0018	+	3.61383i	0.894829	+	0.190202i
$362$	−9.73466	+	4.33415i	−0.511642	+	0.227798i
$363$	5.44575	+	6.04812i	0.285828	+	0.317444i
$364$	2.61171	−	8.03803i	0.136891	−	0.421307i
$365$	1.05469	−	1.17135i	0.0552051	−	0.0613114i
$366$	2.60506	+	4.51210i	0.136169	+	0.235851i
$367$	−4.69508	+	8.13212i	−0.245081	+	0.424493i	−0.962154	−	0.272505i	$-0.912148\pi$
$367$	−4.69508	+	8.13212i	−0.245081	+	0.424493i	0.717073	+	0.696998i	$0.245481\pi$
$368$	−0.898984	−	2.76679i	−0.0468628	−	0.144229i
$369$	−2.29312	−	1.02096i	−0.119375	−	0.0531492i
$370$	−3.65783	−	2.65757i	−0.190161	−	0.138160i
$371$	−10.4375			−0.541886
$372$	−1.99207	−	5.19920i	−0.103284	−	0.269566i
$373$	29.1941			1.51161			0.755806	−	0.654796i	$-0.227245\pi$
$373$	29.1941			1.51161			0.755806	+	0.654796i	$0.227245\pi$
$374$	−18.5150	−	13.4519i	−0.957386	−	0.695581i
$375$	−0.913545	−	0.406737i	−0.0471753	−	0.0210038i
$376$	−2.02051	−	6.21849i	−0.104200	−	0.320694i
$377$	−5.65721	+	9.79857i	−0.291361	+	0.504652i
$378$	0.871018	+	1.50865i	0.0448004	+	0.0775965i
$379$	−22.7070	+	25.2187i	−1.16638	+	1.29540i	−0.218843	+	0.975760i	$0.570228\pi$
$379$	−22.7070	+	25.2187i	−1.16638	+	1.29540i	−0.947539	+	0.319639i	$0.896438\pi$
$380$	−0.393122	+	1.20991i	−0.0201667	+	0.0620669i
$381$	11.7437	+	13.0427i	0.601646	+	0.668196i
$382$	9.21548	−	4.10299i	0.471505	−	0.209927i
$383$	−8.38559	−	1.78241i	−0.428483	−	0.0910770i	−0.0113784	−	0.999935i	$-0.503622\pi$
$383$	−8.38559	−	1.78241i	−0.428483	−	0.0910770i	−0.417105	+	0.908858i	$0.636955\pi$
$384$	−0.104528	+	0.994522i	−0.00533420	+	0.0507515i
$385$	−0.796611	−	7.57925i	−0.0405991	−	0.386274i
$386$	−3.97579	+	0.845081i	−0.202362	+	0.0430135i
$387$	6.23163	−	4.52754i	0.316771	−	0.230148i
$388$	−13.6199	+	9.89545i	−0.691446	+	0.502365i
$389$	31.0456	−	6.59894i	1.57407	−	0.334579i	0.663580	−	0.748105i	$-0.269036\pi$
$389$	31.0456	−	6.59894i	1.57407	−	0.334579i	0.910492	+	0.413526i	$0.135703\pi$
$390$	−0.507131	−	4.82503i	−0.0256796	−	0.244325i
$391$	1.59080	−	15.1354i	0.0804501	−	0.765431i
$392$	3.87866	+	0.824434i	0.195902	+	0.0416402i
$393$	−13.0145	+	5.79441i	−0.656493	+	0.292289i
$394$	−4.71895	−	5.24093i	−0.237737	−	0.264034i
$395$	0.467804	−	1.43975i	0.0235378	−	0.0724419i
$396$	2.92729	−	3.25108i	0.147102	−	0.163373i
$397$	13.1561	+	22.7870i	0.660284	+	1.14365i	0.980541	+	0.196315i	$0.0628976\pi$
$397$	13.1561	+	22.7870i	0.660284	+	1.14365i	−0.320256	+	0.947331i	$0.603769\pi$
$398$	2.42732	−	4.20425i	0.121671	−	0.210740i
$399$	−0.684833	−	2.10770i	−0.0342846	−	0.105517i
$400$	0.913545	+	0.406737i	0.0456773	+	0.0203368i
$401$	−2.83865	−	2.06240i	−0.141756	−	0.102991i	0.514647	−	0.857402i	$-0.327923\pi$
$401$	−2.83865	−	2.06240i	−0.141756	−	0.102991i	−0.656403	+	0.754411i	$0.727923\pi$
$402$	10.5352			0.525447
$403$	−14.6980	−	22.6638i	−0.732161	−	1.12897i
$404$	7.79150			0.387642
$405$	0.809017	+	0.587785i	0.0402004	+	0.0292073i
$406$	3.71137	+	1.65241i	0.184192	+	0.0820076i
$407$	−6.11227	−	18.8116i	−0.302974	−	0.932458i
$408$	−2.61566	+	4.53045i	−0.129494	+	0.224291i
$409$	10.6406	+	18.4301i	0.526144	+	0.911308i	0.999536	+	0.0304561i	$0.00969598\pi$
$409$	10.6406	+	18.4301i	0.526144	+	0.911308i	−0.473392	+	0.880852i	$0.656971\pi$
$410$	1.67961	−	1.86539i	0.0829498	−	0.0921251i
$411$	−3.43535	+	10.5729i	−0.169453	+	0.521523i
$412$	−8.42267	−	9.35432i	−0.414955	−	0.460854i
$413$	20.7286	−	9.22895i	1.01999	−	0.454127i
$414$	2.84560	+	0.604851i	0.139854	+	0.0297268i
$415$	0.999840	−	9.51284i	0.0490802	−	0.466967i
$416$	0.507131	+	4.82503i	0.0248642	+	0.236567i
$417$	14.6409	−	3.11202i	0.716968	−	0.152396i
$418$	−4.50254	+	3.27128i	−0.220226	+	0.160004i
$419$	−1.26378	+	0.918189i	−0.0617397	+	0.0448565i	−0.618227	−	0.786000i	$-0.712149\pi$
$419$	−1.26378	+	0.918189i	−0.0617397	+	0.0448565i	0.556487	+	0.830856i	$0.312149\pi$
$420$	−1.70397	+	0.362190i	−0.0831452	+	0.0176731i
$421$	−0.894689	−	8.51239i	−0.0436045	−	0.414869i	−0.994451	−	0.105205i	$-0.966450\pi$
$421$	−0.894689	−	8.51239i	−0.0436045	−	0.414869i	0.950846	−	0.309664i	$-0.100217\pi$
$422$	−0.0331302	+	0.315213i	−0.00161275	+	0.0153443i
$423$	6.39563	+	1.35943i	0.310966	+	0.0660979i
$424$	5.47353	−	2.43697i	0.265818	−	0.118350i
$425$	3.50043	+	3.88762i	0.169796	+	0.188577i
$426$	0.660345	−	2.03233i	0.0319938	−	0.0984668i
$427$	6.07318	−	6.74495i	0.293902	−	0.326411i
$428$	8.97721	+	15.5490i	0.433930	+	0.751589i
$429$	10.6123	−	18.3811i	0.512367	−	0.887446i
$430$	2.38027	+	7.32572i	0.114787	+	0.353277i
$431$	−23.3639	−	10.4023i	−1.12540	−	0.501059i	−0.242278	−	0.970207i	$-0.577895\pi$
$431$	−23.3639	−	10.4023i	−1.12540	−	0.501059i	−0.883120	+	0.469148i	$0.844561\pi$
$432$	−0.809017	−	0.587785i	−0.0389238	−	0.0282798i
$433$	7.88624			0.378988			0.189494	−	0.981882i	$-0.439315\pi$
$433$	7.88624			0.378988			0.189494	+	0.981882i	$0.439315\pi$
$434$	−7.54153	+	6.09925i	−0.362005	+	0.292773i
$435$	2.33210			0.111815
$436$	−8.30171	−	6.03154i	−0.397580	−	0.288859i
$437$	−3.38100	−	1.50532i	−0.161735	−	0.0720091i
$438$	−0.487076	−	1.49907i	−0.0232734	−	0.0716281i
$439$	3.60326	−	6.24103i	0.171974	−	0.297868i	−0.767136	−	0.641485i	$-0.778319\pi$
$439$	3.60326	−	6.24103i	0.171974	−	0.297868i	0.939110	+	0.343617i	$0.111652\pi$
$440$	2.18738	+	3.78866i	0.104279	+	0.180617i
$441$	−2.65331	+	2.94680i	−0.126348	+	0.140324i
$442$	−7.84294	+	24.1381i	−0.373050	+	1.14813i
$443$	24.3712	+	27.0670i	1.15791	+	1.28599i	0.951543	+	0.307515i	$0.0994974\pi$
$443$	24.3712	+	27.0670i	1.15791	+	1.28599i	0.206367	+	0.978475i	$0.433836\pi$
$444$	−4.13043	+	1.83899i	−0.196022	+	0.0872745i
$445$	2.20845	+	0.469420i	0.104690	+	0.0222526i
$446$	−1.19234	+	11.3444i	−0.0564592	+	0.537173i
$447$	0.533101	+	5.07212i	0.0252148	+	0.239903i
$448$	1.70397	−	0.362190i	0.0805050	−	0.0171119i
$449$	−29.3745	+	21.3418i	−1.38627	+	1.00718i	−0.390003	+	0.920814i	$0.627526\pi$
$449$	−29.3745	+	21.3418i	−1.38627	+	1.00718i	−0.996263	+	0.0863678i	$0.972474\pi$
$450$	−0.809017	+	0.587785i	−0.0381374	+	0.0277085i
$451$	10.7413	−	2.28313i	0.505786	−	0.107508i
$452$	−1.41474	−	13.4604i	−0.0665438	−	0.633122i
$453$	2.40175	−	22.8512i	0.112844	−	1.07364i
$454$	13.4152	+	2.85149i	0.629607	+	0.133827i
$455$	−7.72099	+	3.43761i	−0.361966	+	0.161158i
$456$	0.851248	+	0.945407i	0.0398633	+	0.0442727i
$457$	−9.20438	+	28.3282i	−0.430563	+	1.32514i	0.467004	+	0.884255i	$0.345334\pi$
$457$	−9.20438	+	28.3282i	−0.430563	+	1.32514i	−0.897566	+	0.440880i	$0.854666\pi$
$458$	−16.4874	+	18.3111i	−0.770404	+	0.855621i
$459$	−2.61566	−	4.53045i	−0.122088	−	0.211463i
$460$	−1.45459	+	2.51942i	−0.0678205	+	0.117468i
$461$	9.06664	+	27.9043i	0.422276	+	1.29963i	0.905579	+	0.424178i	$0.139437\pi$
$461$	9.06664	+	27.9043i	0.422276	+	1.29963i	−0.483303	+	0.875453i	$0.660563\pi$
$462$	−6.96213	−	3.09974i	−0.323907	−	0.144213i
$463$	6.34760	+	4.61180i	0.294998	+	0.214328i	0.725433	−	0.688293i	$-0.241640\pi$
$463$	6.34760	+	4.61180i	0.294998	+	0.214328i	−0.430435	+	0.902622i	$0.641640\pi$
$464$	−2.33210			−0.108265
$465$	−2.53080	+	4.95934i	−0.117363	+	0.229984i
$466$	−24.2231			−1.12211
$467$	5.17239	+	3.75796i	0.239350	+	0.173898i	0.700993	−	0.713168i	$-0.252740\pi$
$467$	5.17239	+	3.75796i	0.239350	+	0.173898i	−0.461644	+	0.887065i	$0.652740\pi$
$468$	−4.43216	−	1.97333i	−0.204877	−	0.0912171i
$469$	−5.67129	−	17.4544i	−0.261876	−	0.805971i
$470$	−3.26925	+	5.66251i	−0.150799	+	0.261192i
$471$	1.11656	+	1.93394i	0.0514485	+	0.0891114i
$472$	−8.71551	+	9.67955i	−0.401164	+	0.445537i
$473$	−10.4131	+	32.0483i	−0.478795	+	1.47358i
$474$	−1.01296	−	1.12501i	−0.0465269	−	0.0516733i
$475$	1.16219	−	0.517438i	0.0533247	−	0.0237417i
$476$	8.91399	+	1.89473i	0.408572	+	0.0868447i
$477$	−0.626285	+	5.95871i	−0.0286756	+	0.272830i
$478$	0.0789742	+	0.751389i	0.00361220	+	0.0343677i
$479$	0.440893	−	0.0937148i	0.0201449	−	0.00428194i	−0.197828	−	0.980237i	$-0.563389\pi$
$479$	0.440893	−	0.0937148i	0.0201449	−	0.00428194i	0.217973	+	0.975955i	$0.430055\pi$
$480$	0.809017	−	0.587785i	0.0369264	−	0.0268286i
$481$	−17.7463	+	12.8935i	−0.809164	+	0.587892i
$482$	−15.8242	+	3.36354i	−0.720772	+	0.153205i
$483$	−0.529739	−	5.04013i	−0.0241039	−	0.229334i
$484$	−0.850709	+	8.09396i	−0.0386686	+	0.367907i
$485$	16.4672	+	3.50022i	0.747739	+	0.158937i
$486$	0.913545	−	0.406737i	0.0414393	−	0.0184499i
$487$	3.23986	+	3.59823i	0.146812	+	0.163051i	0.812066	−	0.583566i	$-0.198343\pi$
$487$	3.23986	+	3.59823i	0.146812	+	0.163051i	−0.665253	+	0.746618i	$0.731676\pi$
$488$	−1.61002	+	4.95512i	−0.0728820	+	0.224308i
$489$	−1.27415	+	1.41508i	−0.0576189	+	0.0639922i
$490$	−1.98265	−	3.43406i	−0.0895672	−	0.155135i
$491$	−13.9346	+	24.1355i	−0.628860	+	1.08922i	0.358920	+	0.933368i	$0.383145\pi$
$491$	−13.9346	+	24.1355i	−0.628860	+	1.08922i	−0.987781	+	0.155850i	$0.950188\pi$
$492$	−0.775673	−	2.38728i	−0.0349701	−	0.107627i
$493$	−11.1452	−	4.96216i	−0.501954	−	0.223484i
$494$	4.99331	+	3.62785i	0.224660	+	0.163225i
$495$	−4.37476			−0.196631
$496$	2.53080	−	4.95934i	0.113636	−	0.222681i
$497$	−3.72259			−0.166981
$498$	−7.73844	−	5.62231i	−0.346768	−	0.251942i
$499$	3.62173	+	1.61250i	0.162131	+	0.0721853i	0.486198	−	0.873849i	$-0.338384\pi$
$499$	3.62173	+	1.61250i	0.162131	+	0.0721853i	−0.324067	+	0.946034i	$0.605050\pi$
$500$	−0.309017	−	0.951057i	−0.0138197	−	0.0425325i
$501$	11.8779	−	20.5731i	0.530664	−	0.919137i
$502$	1.24308	+	2.15308i	0.0554815	+	0.0960968i
$503$	−26.0041	+	28.8805i	−1.15947	+	1.28772i	−0.208639	+	0.977993i	$0.566903\pi$
$503$	−26.0041	+	28.8805i	−1.15947	+	1.28772i	−0.950827	+	0.309724i	$0.899763\pi$
$504$	−0.538319	+	1.65678i	−0.0239786	+	0.0737986i
$505$	−5.21353	−	5.79021i	−0.231999	−	0.257661i
$506$	−11.6266	+	5.17651i	−0.516867	+	0.230124i
$507$	−10.3078	−	2.19099i	−0.457786	−	0.0973055i
$508$	−1.83454	+	17.4545i	−0.0813946	+	0.774417i
$509$	−1.68807	−	16.0609i	−0.0748225	−	0.711889i	−0.966054	−	0.258340i	$-0.916825\pi$
$509$	−1.68807	−	16.0609i	−0.0748225	−	0.711889i	0.891232	−	0.453549i	$-0.149842\pi$
$510$	5.11700	−	1.08765i	0.226584	−	0.0481620i
$511$	−2.22141	+	1.61395i	−0.0982696	+	0.0713970i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−1.24437	+	0.264499i	−0.0549403	+	0.0116779i
$514$	0.910880	+	8.66644i	0.0401772	+	0.382260i
$515$	−1.31575	+	12.5185i	−0.0579789	+	0.551632i
$516$	7.53439	+	1.60148i	0.331683	+	0.0705014i
$517$	−26.1314	+	11.6345i	−1.14926	+	0.511683i
$518$	5.27028	+	5.85324i	0.231563	+	0.257177i
$519$	−2.91261	+	8.96410i	−0.127850	+	0.393480i
$520$	3.24636	−	3.60545i	0.142362	−	0.158109i
$521$	16.0195	+	27.7466i	0.701827	+	1.21560i	0.967824	+	0.251627i	$0.0809655\pi$
$521$	16.0195	+	27.7466i	0.701827	+	1.21560i	−0.265997	+	0.963974i	$0.585701\pi$
$522$	1.16605	−	2.01965i	0.0510365	−	0.0883979i
$523$	1.31653	+	4.05186i	0.0575679	+	0.177176i	0.975706	−	0.219086i	$-0.0703074\pi$
$523$	1.31653	+	4.05186i	0.0575679	+	0.177176i	−0.918138	+	0.396261i	$0.870307\pi$
$524$	−13.0145	−	5.79441i	−0.568539	−	0.253130i
$525$	1.40934	+	1.02394i	0.0615085	+	0.0446886i
$526$	9.61684			0.419314
$527$	22.6471	−	18.3159i	0.986524	−	0.797855i
$528$	4.37476			0.190387
$529$	11.7604	+	8.54446i	0.511324	+	0.371498i
$530$	−5.47353	−	2.43697i	−0.237755	−	0.105855i
$531$	−4.02498	−	12.3876i	−0.174669	−	0.537577i
$532$	1.10808	−	1.91926i	0.0480415	−	0.0832104i
$533$	−6.08909	−	10.5466i	−0.263748	−	0.456824i
$534$	1.51075	−	1.67786i	0.0653767	−	0.0726081i
$535$	5.54822	−	17.0757i	0.239871	−	0.738246i
$536$	7.04941	+	7.82916i	0.304488	+	0.338168i
$537$	−5.08009	+	2.26180i	−0.219222	+	0.0976040i
$538$	8.14060	+	1.73034i	0.350966	+	0.0746001i
$539$	1.81328	−	17.2522i	0.0781037	−	0.743107i
$540$	0.104528	+	0.994522i	0.00449819	+	0.0427974i
$541$	9.46406	−	2.01165i	0.406892	−	0.0864875i	8.09926e−5	−	1.00000i	$-0.499974\pi$
$541$	9.46406	−	2.01165i	0.406892	−	0.0864875i	0.406811	+	0.913513i	$0.366641\pi$
$542$	−20.9227	+	15.2012i	−0.898705	+	0.652948i
$543$	8.62082	−	6.26339i	0.369955	−	0.268788i
$544$	−5.11700	+	1.08765i	−0.219389	+	0.0466326i
$545$	1.07262	+	10.2053i	0.0459458	+	0.437145i
$546$	−0.883441	+	8.40538i	−0.0378078	+	0.359717i
$547$	−20.4128	−	4.33887i	−0.872788	−	0.185517i	−0.250321	−	0.968163i	$-0.580536\pi$
$547$	−20.4128	−	4.33887i	−0.872788	−	0.185517i	−0.622467	+	0.782646i	$0.713869\pi$
$548$	−10.1559	+	4.52170i	−0.433838	+	0.193157i
$549$	−3.48625	−	3.87187i	−0.148790	−	0.165248i
$550$	1.35188	−	4.16065i	0.0576442	−	0.177411i
$551$	−1.98519	+	2.20478i	−0.0845720	+	0.0939267i
$552$	1.45459	+	2.51942i	0.0619113	+	0.107234i
$553$	−1.31859	+	2.28386i	−0.0560721	+	0.0971197i
$554$	2.07408	+	6.38337i	0.0881194	+	0.271204i
$555$	4.13043	+	1.83899i	0.175327	+	0.0780607i
$556$	12.1094	+	8.79797i	0.513551	+	0.373117i
$557$	−31.3611			−1.32881			−0.664406	−	0.747372i	$-0.731315\pi$
$557$	−31.3611			−1.32881			−0.664406	+	0.747372i	$0.731315\pi$
$558$	3.02952	+	4.67141i	0.128250	+	0.197756i
$559$	37.3705			1.58061
$560$	−1.40934	−	1.02394i	−0.0595554	−	0.0432695i
$561$	20.9072	+	9.30847i	0.882701	+	0.393004i
$562$	7.46805	+	22.9843i	0.315021	+	0.969534i
$563$	−0.109548	+	0.189743i	−0.00461691	+	0.00799673i	−0.868325	−	0.495996i	$-0.834803\pi$
$563$	−0.109548	+	0.189743i	−0.00461691	+	0.00799673i	0.863708	+	0.503993i	$0.168136\pi$
$564$	3.26925	+	5.66251i	0.137660	+	0.238435i
$565$	−9.05635	+	10.0581i	−0.381003	+	0.423147i
$566$	−5.53983	+	17.0498i	−0.232856	+	0.716658i
$567$	−1.16565	−	1.29459i	−0.0489527	−	0.0543675i
$568$	1.95217	−	0.869164i	0.0819114	−	0.0364693i
$569$	14.6498	+	3.11392i	0.614153	+	0.130542i	0.504477	−	0.863425i	$-0.331685\pi$
$569$	14.6498	+	3.11392i	0.614153	+	0.130542i	0.109676	+	0.993967i	$0.465019\pi$
$570$	0.132978	−	1.26520i	0.00556984	−	0.0529934i
$571$	−1.96069	−	18.6548i	−0.0820525	−	0.780678i	−0.955744	−	0.294198i	$-0.904947\pi$
$571$	−1.96069	−	18.6548i	−0.0820525	−	0.780678i	0.873692	−	0.486480i	$-0.161719\pi$
$572$	20.7608	−	4.41285i	0.868054	−	0.184510i
$573$	−8.16104	+	5.92934i	−0.340932	+	0.247702i
$574$	−3.53762	+	2.57023i	−0.147658	+	0.107279i
$575$	2.84560	−	0.604851i	0.118670	−	0.0252240i
$576$	−0.104528	−	0.994522i	−0.00435535	−	0.0414384i
$577$	1.45467	−	13.8402i	0.0605585	−	0.576176i	−0.921603	−	0.388135i	$-0.873119\pi$
$577$	1.45467	−	13.8402i	0.0605585	−	0.576176i	0.982161	−	0.188041i	$-0.0602139\pi$
$578$	−10.1401	−	2.15534i	−0.421772	−	0.0896504i
$579$	3.71321	−	1.65323i	0.154316	−	0.0687058i
$580$	1.56048	+	1.73308i	0.0647953	+	0.0719624i
$581$	−5.14915	+	15.8475i	−0.213623	+	0.657463i
$582$	11.2649	−	12.5109i	0.466945	−	0.518595i
$583$	−13.1058	−	22.6998i	−0.542785	−	0.940131i
$584$	0.788106	−	1.36504i	0.0326120	−	0.0564857i
$585$	1.49923	+	4.61415i	0.0619855	+	0.190772i
$586$	−2.24268	−	0.998506i	−0.0926443	−	0.0412479i
$587$	−23.4262	−	17.0201i	−0.966901	−	0.702495i	−0.0121577	−	0.999926i	$-0.503870\pi$
$587$	−23.4262	−	17.0201i	−0.966901	−	0.702495i	−0.954743	+	0.297432i	$0.903870\pi$
$588$	−3.96531			−0.163527
$589$	−2.53426	−	6.61426i	−0.104422	−	0.272536i
$590$	13.0251			0.536236
$591$	5.70548	+	4.14528i	0.234692	+	0.170514i
$592$	−4.13043	−	1.83899i	−0.169760	−	0.0755819i
$593$	−9.94754	−	30.6154i	−0.408496	−	1.25722i	−0.917940	−	0.396719i	$-0.870149\pi$
$593$	−9.94754	−	30.6154i	−0.408496	−	1.25722i	0.509444	−	0.860504i	$-0.329851\pi$
$594$	−2.18738	+	3.78866i	−0.0897493	+	0.155450i
$595$	−4.55657	−	7.89221i	−0.186801	−	0.323549i
$596$	−3.41260	+	3.79008i	−0.139786	+	0.155248i
$597$	−1.50017	+	4.61704i	−0.0613978	+	0.188963i
$598$	9.44422	+	10.4889i	0.386203	+	0.428922i
$599$	−19.1823	+	8.54050i	−0.783767	+	0.348955i	−0.759296	−	0.650745i	$-0.774457\pi$
$599$	−19.1823	+	8.54050i	−0.783767	+	0.348955i	−0.0244706	+	0.999701i	$0.507790\pi$
$600$	−0.978148	−	0.207912i	−0.0399327	−	0.00848796i
$601$	−0.105572	+	1.00445i	−0.00430637	+	0.0409724i	−0.996464	−	0.0840201i	$-0.973224\pi$
$601$	−0.105572	+	1.00445i	−0.00430637	+	0.0409724i	0.992158	+	0.124992i	$0.0398907\pi$
$602$	−1.40261	−	13.3449i	−0.0571659	−	0.543898i
$603$	−10.3050	+	2.19039i	−0.419650	+	0.0891995i
$604$	18.5888	−	13.5056i	0.756368	−	0.549534i
$605$	6.58422	−	4.78372i	0.267687	−	0.194486i
$606$	−7.62124	+	1.61994i	−0.309592	+	0.0658057i
$607$	−3.83154	−	36.4546i	−0.155517	−	1.47965i	−0.742390	−	0.669968i	$-0.766308\pi$
$607$	−3.83154	−	36.4546i	−0.155517	−	1.47965i	0.586872	−	0.809679i	$-0.300359\pi$
$608$	−0.132978	+	1.26520i	−0.00539297	+	0.0513107i
$609$	−3.97382	−	0.844661i	−0.161027	−	0.0342274i
$610$	4.75968	−	2.11915i	0.192714	−	0.0858018i
$611$	21.2264	+	23.5742i	0.858726	+	0.953712i
$612$	1.61656	−	4.97527i	0.0653457	−	0.201114i
$613$	15.2700	−	16.9591i	0.616750	−	0.684970i	−0.351146	−	0.936321i	$-0.614208\pi$
$613$	15.2700	−	16.9591i	0.616750	−	0.684970i	0.967896	+	0.251350i	$0.0808746\pi$
$614$	−8.17748	−	14.1638i	−0.330016	−	0.571605i
$615$	−1.25507	+	2.17384i	−0.0506091	+	0.0876576i
$616$	−2.35502	−	7.24800i	−0.0948864	−	0.292030i
$617$	−22.7588	−	10.1329i	−0.916235	−	0.407934i	−0.106219	−	0.994343i	$-0.533875\pi$
$617$	−22.7588	−	10.1329i	−0.916235	−	0.407934i	−0.810015	+	0.586409i	$0.800541\pi$
$618$	10.1835	+	7.39873i	0.409640	+	0.297621i
$619$	26.5117			1.06560			0.532798	−	0.846242i	$-0.321141\pi$
$619$	26.5117			1.06560			0.532798	+	0.846242i	$0.321141\pi$
$620$	−5.37894	+	1.43770i	−0.216024	+	0.0577393i
$621$	−2.90917			−0.116741
$622$	−14.7219	−	10.6961i	−0.590296	−	0.428875i
$623$	−3.59311	−	1.59975i	−0.143955	−	0.0640928i
$624$	−1.49923	−	4.61415i	−0.0600172	−	0.184714i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−13.3263	−	23.0819i	−0.532627	−	0.922537i
$627$	3.72401	−	4.13593i	0.148723	−	0.165173i
$628$	−0.690074	+	2.12383i	−0.0275369	+	0.0847500i
$629$	−15.8266	−	17.5772i	−0.631047	−	0.700849i
$630$	1.59143	−	0.708550i	0.0634041	−	0.0282293i
$631$	2.84162	+	0.604006i	0.113123	+	0.0240451i	0.264125	−	0.964488i	$-0.414917\pi$
$631$	2.84162	+	0.604006i	0.113123	+	0.0240451i	−0.151002	+	0.988533i	$0.548250\pi$
$632$	0.158240	−	1.50555i	0.00629445	−	0.0598877i
$633$	−0.0331302	−	0.315213i	−0.00131681	−	0.0125286i
$634$	7.60372	−	1.61622i	0.301982	−	0.0641883i
$635$	14.1988	−	10.3160i	0.563460	−	0.409378i
$636$	−4.84725	+	3.52173i	−0.192206	+	0.139646i
$637$	−18.8177	+	3.99983i	−0.745585	+	0.158479i
$638$	1.06644	+	10.1465i	0.0422207	+	0.401703i
$639$	−0.223369	+	2.12521i	−0.00883634	+	0.0840722i
$640$	0.978148	+	0.207912i	0.0386647	+	0.00821843i
$641$	14.4624	−	6.43906i	0.571229	−	0.254327i	−0.100733	−	0.994914i	$-0.532119\pi$
$641$	14.4624	−	6.43906i	0.571229	−	0.254327i	0.671961	+	0.740586i	$0.265452\pi$
$642$	−12.0139	−	13.3427i	−0.474149	−	0.526596i
$643$	−11.8378	+	36.4331i	−0.466839	+	1.43678i	0.389817	+	0.920892i	$0.372538\pi$
$643$	−11.8378	+	36.4331i	−0.466839	+	1.43678i	−0.856655	+	0.515889i	$0.827462\pi$
$644$	3.39108	−	3.76617i	0.133627	−	0.148408i
$645$	−3.85136	−	6.67075i	−0.151647	−	0.262660i
$646$	−3.32756	+	5.76350i	−0.130921	+	0.226762i
$647$	−12.1152	−	37.2869i	−0.476300	−	1.46590i	−0.844197	−	0.536033i	$-0.819922\pi$
$647$	−12.1152	−	37.2869i	−0.476300	−	1.46590i	0.367898	−	0.929866i	$-0.380078\pi$
$648$	0.913545	+	0.406737i	0.0358875	+	0.0159781i
$649$	46.0992	+	33.4931i	1.80955	+	1.31472i
$650$	−4.85161			−0.190296
$651$	6.10863	−	7.53393i	0.239416	−	0.295278i
$652$	−1.90418			−0.0745735
$653$	−20.7136	−	15.0493i	−0.810585	−	0.588924i	0.103415	−	0.994638i	$-0.467023\pi$
$653$	−20.7136	−	15.0493i	−0.810585	−	0.588924i	−0.914000	+	0.405714i	$0.867023\pi$
$654$	9.37433	+	4.17372i	0.366565	+	0.163205i
$655$	4.40229	+	13.5488i	0.172012	+	0.529397i
$656$	1.25507	−	2.17384i	0.0490021	−	0.0848741i
$657$	0.788106	+	1.36504i	0.0307469	+	0.0532552i
$658$	7.62161	−	8.46466i	0.297121	−	0.329987i
$659$	−15.5130	+	47.7441i	−0.604300	+	1.85984i	−0.102768	+	0.994705i	$0.532770\pi$
$659$	−15.5130	+	47.7441i	−0.604300	+	1.85984i	−0.501532	+	0.865139i	$0.667230\pi$
$660$	−2.92729	−	3.25108i	−0.113944	−	0.126548i
$661$	−14.9339	+	6.64898i	−0.580860	+	0.258615i	−0.676065	−	0.736842i	$-0.736316\pi$
$661$	−14.9339	+	6.64898i	−0.580860	+	0.258615i	0.0952050	+	0.995458i	$0.469649\pi$
$662$	2.96136	+	0.629458i	0.115097	+	0.0244646i
$663$	2.65296	−	25.2412i	0.103032	−	0.980289i
$664$	−0.999840	−	9.51284i	−0.0388013	−	0.369170i
$665$	−2.16774	+	0.460767i	−0.0840613	+	0.0178678i
$666$	3.65783	−	2.65757i	0.141738	−	0.102979i
$667$	−5.48875	+	3.98781i	−0.212525	+	0.154409i
$668$	23.2366	−	4.93909i	0.899051	−	0.191099i
$669$	−1.19234	−	11.3444i	−0.0460987	−	0.438600i
$670$	1.10123	−	10.4775i	0.0425441	−	0.404780i
$671$	22.2950	+	4.73894i	0.860687	+	0.182945i
$672$	−1.59143	+	0.708550i	−0.0613907	+	0.0273329i
$673$	−2.95382	−	3.28055i	−0.113861	−	0.126456i	0.683520	−	0.729932i	$-0.260448\pi$
$673$	−2.95382	−	3.28055i	−0.113861	−	0.126456i	−0.797381	+	0.603476i	$0.793782\pi$
$674$	9.27352	−	28.5409i	0.357202	−	1.09936i
$675$	0.669131	−	0.743145i	0.0257548	−	0.0286037i
$676$	−5.26905	−	9.12626i	−0.202656	−	0.351010i
$677$	−10.6252	+	18.4034i	−0.408359	+	0.707299i	−0.994706	−	0.102761i	$-0.967232\pi$
$677$	−10.6252	+	18.4034i	−0.408359	+	0.707299i	0.586347	+	0.810060i	$0.300566\pi$
$678$	4.18239	+	12.8721i	0.160624	+	0.494349i
$679$	−26.7919	−	11.9285i	−1.02818	−	0.457775i
$680$	4.23222	+	3.07489i	0.162298	+	0.117917i
$681$	−13.7149			−0.525556
$682$	−22.7344	−	8.74315i	−0.870545	−	0.334792i
$683$	5.09419			0.194924			0.0974619	−	0.995239i	$-0.468928\pi$
$683$	5.09419			0.194924			0.0974619	+	0.995239i	$0.468928\pi$
$684$	−1.02921	−	0.747763i	−0.0393527	−	0.0285914i
$685$	10.1559	+	4.52170i	0.388037	+	0.172765i
$686$	5.90283	+	18.1671i	0.225371	+	0.693621i
$687$	12.3200	−	21.3389i	0.470037	−	0.814128i
$688$	3.85136	+	6.67075i	0.146832	+	0.254320i
$689$	−19.4507	+	21.6021i	−0.741011	+	0.822976i
$690$	0.898984	−	2.76679i	0.0342237	−	0.105330i
$691$	−16.6034	−	18.4400i	−0.631624	−	0.701490i	0.339354	−	0.940659i	$-0.389792\pi$
$691$	−16.6034	−	18.4400i	−0.631624	−	0.701490i	−0.970978	+	0.239169i	$0.923125\pi$
$692$	−8.61054	+	3.83366i	−0.327324	+	0.145734i
$693$	7.45446	+	1.58449i	0.283172	+	0.0601900i
$694$	1.59381	−	15.1641i	0.0605003	−	0.575621i
$695$	−1.56458	−	14.8860i	−0.0593480	−	0.564658i
$696$	2.28113	−	0.484870i	0.0864662	−	0.0183789i
$697$	10.6234	−	7.71837i	0.402391	−	0.292354i
$698$	22.6145	−	16.4304i	0.855971	−	0.621900i
$699$	23.6938	−	5.03627i	0.896181	−	0.190489i
$700$	0.182092	+	1.73249i	0.00688245	+	0.0654821i
$701$	1.49585	−	14.2321i	0.0564975	−	0.537538i	−0.929267	−	0.369408i	$-0.879561\pi$
$701$	1.49585	−	14.2321i	0.0564975	−	0.537538i	0.985765	−	0.168130i	$-0.0537728\pi$
$702$	4.74559	+	1.00871i	0.179111	+	0.0380712i
$703$	−5.25462	+	2.33951i	−0.198182	+	0.0882361i
$704$	2.92729	+	3.25108i	0.110326	+	0.122530i
$705$	2.02051	−	6.21849i	0.0760968	−	0.234202i
$706$	8.36211	−	9.28706i	0.314712	−	0.349523i
$707$	6.78654	+	11.7546i	0.255234	+	0.442079i
$708$	6.51256	−	11.2801i	0.244757	−	0.423931i
$709$	−1.31841	−	4.05764i	−0.0495138	−	0.152388i	0.923243	−	0.384218i	$-0.125529\pi$
$709$	−1.31841	−	4.05764i	−0.0495138	−	0.152388i	−0.972756	+	0.231830i	$0.925529\pi$
$710$	−1.95217	−	0.869164i	−0.0732638	−	0.0326191i
$711$	1.22473	+	0.889817i	0.0459309	+	0.0333707i
$712$	2.25778			0.0846140
$713$	−2.52391	−	15.9997i	−0.0945210	−	0.599195i
$714$	−9.11314			−0.341051
$715$	−17.1711	−	12.4755i	−0.642162	−	0.466558i
$716$	−5.08009	−	2.26180i	−0.189852	−	0.0845275i
$717$	−0.233471	−	0.718550i	−0.00871913	−	0.0268347i
$718$	3.65973	−	6.33884i	0.136580	−	0.236564i
$719$	25.5868	+	44.3177i	0.954228	+	1.65277i	0.736124	+	0.676847i	$0.236654\pi$
$719$	25.5868	+	44.3177i	0.954228	+	1.65277i	0.218105	+	0.975925i	$0.430013\pi$
$720$	−0.669131	+	0.743145i	−0.0249370	+	0.0276954i
$721$	6.77608	−	20.8546i	0.252354	−	0.776667i
$722$	−11.6305	−	12.9170i	−0.432844	−	0.480722i
$723$	14.7791	−	6.58007i	0.549640	−	0.244715i
$724$	10.4231	+	2.21549i	0.387370	+	0.0823380i
$725$	0.243770	−	2.31932i	0.00905341	−	0.0861374i
$726$	−0.850709	−	8.09396i	−0.0315728	−	0.300395i
$727$	23.0514	−	4.89973i	0.854929	−	0.181721i	0.240458	−	0.970660i	$-0.422703\pi$
$727$	23.0514	−	4.89973i	0.854929	−	0.181721i	0.614472	+	0.788939i	$0.289369\pi$
$728$	−6.83755	+	4.96777i	−0.253417	+	0.184118i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−1.54177	+	0.327713i	−0.0570634	+	0.0121292i
$731$	4.21201	+	40.0746i	0.155787	+	1.48221i
$732$	0.544606	−	5.18158i	0.0201292	−	0.191517i
$733$	51.2502	+	10.8936i	1.89297	+	0.402363i	0.998956	−	0.0456754i	$-0.0145440\pi$
$733$	51.2502	+	10.8936i	1.89297	+	0.402363i	0.894014	+	0.448039i	$0.147877\pi$
$734$	8.57834	−	3.81932i	0.316632	−	0.140974i
$735$	2.65331	+	2.94680i	0.0978688	+	0.108694i
$736$	−0.898984	+	2.76679i	−0.0331370	+	0.101985i
$737$	30.8395	−	34.2507i	1.13599	−	1.26164i
$738$	1.25507	+	2.17384i	0.0461996	+	0.0800201i
$739$	−15.1281	+	26.2027i	−0.556497	+	0.963882i	0.441288	+	0.897366i	$0.354522\pi$
$739$	−15.1281	+	26.2027i	−0.556497	+	0.963882i	−0.997785	+	0.0665162i	$0.978812\pi$
$740$	1.39717	+	4.30003i	0.0513608	+	0.158072i
$741$	−5.63847	−	2.51041i	−0.207134	−	0.0922221i
$742$	8.44408	+	6.13499i	0.309992	+	0.225222i
$743$	−4.43812			−0.162819			−0.0814094	−	0.996681i	$-0.525942\pi$
$743$	−4.43812			−0.162819			−0.0814094	+	0.996681i	$0.525942\pi$
$744$	−1.44439	+	5.37715i	−0.0529539	+	0.197136i
$745$	5.10006			0.186852
$746$	−23.6185	−	17.1598i	−0.864735	−	0.628267i
$747$	8.73828	+	3.89053i	0.319717	+	0.142347i
$748$	7.07208	+	21.7656i	0.258581	+	0.795831i
$749$	−15.6386	+	27.0869i	−0.571423	+	0.989734i
$750$	0.500000	+	0.866025i	0.0182574	+	0.0316228i
$751$	−9.89764	+	10.9924i	−0.361170	+	0.401120i	−0.896155	−	0.443742i	$-0.853651\pi$
$751$	−9.89764	+	10.9924i	−0.361170	+	0.401120i	0.534985	+	0.844862i	$0.320317\pi$
$752$	−2.02051	+	6.21849i	−0.0736804	+	0.226765i
$753$	−1.66357	−	1.84758i	−0.0606238	−	0.0673296i
$754$	10.3362	−	4.60199i	0.376423	−	0.167594i
$755$	−22.4749	−	4.77720i	−0.817947	−	0.173860i
$756$	0.182092	−	1.73249i	0.00662264	−	0.0630102i
$757$	0.917906	+	8.73329i	0.0333619	+	0.317417i	0.998458	+	0.0555196i	$0.0176815\pi$
$757$	0.917906	+	8.73329i	0.0333619	+	0.317417i	−0.965096	+	0.261897i	$0.915652\pi$
$758$	33.1936	−	7.05551i	1.20565	−	0.256268i
$759$	10.2963	−	7.48071i	0.373732	−	0.271533i
$760$	1.02921	−	0.747763i	0.0373333	−	0.0271242i
$761$	−16.9251	+	3.59755i	−0.613536	+	0.130411i	−0.504190	−	0.863593i	$-0.668209\pi$
$761$	−16.9251	+	3.59755i	−0.613536	+	0.130411i	−0.109346	+	0.994004i	$0.534876\pi$
$762$	−1.83454	−	17.4545i	−0.0664584	−	0.632309i
$763$	1.86854	−	17.7779i	0.0676456	−	0.643605i
$764$	−9.86716	−	2.09733i	−0.356981	−	0.0758787i
$765$	−4.77904	+	2.12777i	−0.172787	+	0.0769296i
$766$	5.73641	+	6.37093i	0.207265	+	0.230191i
$767$	19.5276	−	60.0999i	0.705102	−	2.17008i
$768$	0.669131	−	0.743145i	0.0241452	−	0.0268159i
$769$	15.3742	+	26.6289i	0.554409	+	0.960264i	0.997949	+	0.0640098i	$0.0203889\pi$
$769$	15.3742	+	26.6289i	0.554409	+	0.960264i	−0.443540	+	0.896254i	$0.646278\pi$
$770$	−3.81050	+	6.59998i	−0.137321	+	0.237847i
$771$	−2.69283	−	8.28768i	−0.0969799	−	0.298473i
$772$	3.71321	+	1.65323i	0.133641	+	0.0595009i
$773$	5.36876	+	3.90063i	0.193101	+	0.140296i	0.680135	−	0.733087i	$-0.261921\pi$
$773$	5.36876	+	3.90063i	0.193101	+	0.140296i	−0.487034	+	0.873383i	$0.661921\pi$
$774$	−7.70271			−0.276868
$775$	4.66763	+	3.03533i	0.167666	+	0.109032i
$776$	16.8351			0.604346
$777$	−6.37207	−	4.62958i	−0.228597	−	0.166085i
$778$	−28.9951	−	12.9095i	−1.03953	−	0.462827i
$779$	−0.986788	−	3.03702i	−0.0353554	−	0.108813i
$780$	−2.42580	+	4.20162i	−0.0868577	+	0.150442i
$781$	−4.67426	−	8.09605i	−0.167258	−	0.289700i
$782$	−10.1834	+	11.3098i	−0.364156	+	0.404436i
$783$	−0.720657	+	2.21795i	−0.0257542	+	0.0792632i
$784$	−2.65331	−	2.94680i	−0.0947610	−	0.105243i
$785$	2.04006	−	0.908294i	0.0728129	−	0.0324184i
$786$	13.9348	+	2.96193i	0.497037	+	0.105649i
$787$	0.935024	−	8.89616i	0.0333300	−	0.317114i	−0.965136	−	0.261748i	$-0.915701\pi$
$787$	0.935024	−	8.89616i	0.0333300	−	0.317114i	0.998466	−	0.0553654i	$-0.0176324\pi$
$788$	0.737173	+	7.01373i	0.0262607	+	0.249854i
$789$	−9.40669	+	1.99945i	−0.334887	+	0.0711824i
$790$	−1.22473	+	0.889817i	−0.0435739	+	0.0316583i
$791$	19.0747	−	13.8586i	0.678218	−	0.492754i
$792$	−4.27916	+	0.909564i	−0.152053	+	0.0323200i
$793$	−2.64221	−	25.1390i	−0.0938278	−	0.892712i
$794$	2.75037	−	26.1680i	0.0976069	−	0.928668i
$795$	5.86060	+	1.24571i	0.207854	+	0.0441807i
$796$	−4.43494	+	1.97456i	−0.157192	+	0.0699865i
$797$	−17.2198	−	19.1245i	−0.609957	−	0.677426i	0.356488	−	0.934300i	$-0.383974\pi$
$797$	−17.2198	−	19.1245i	−0.609957	−	0.677426i	−0.966445	+	0.256874i	$0.917307\pi$
$798$	−0.684833	+	2.10770i	−0.0242428	+	0.0746118i
$799$	−22.8876	+	25.4193i	−0.809705	+	0.899269i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	−1.12889	+	1.95530i	−0.0398874	+	0.0690871i
$802$	1.08427	+	3.33704i	0.0382869	+	0.117835i
$803$	−6.29940	−	2.80467i	−0.222301	−	0.0989747i
$804$	−8.52314	−	6.19242i	−0.300588	−	0.218390i
$805$	−5.06789			−0.178620
$806$	−1.43052	+	26.9747i	−0.0503878	+	0.950144i
$807$	−8.32246			−0.292965
$808$	−6.30346	−	4.57973i	−0.221755	−	0.161114i
$809$	15.5455	+	6.92130i	0.546551	+	0.243340i	0.661388	−	0.750044i	$-0.269968\pi$
$809$	15.5455	+	6.92130i	0.546551	+	0.243340i	−0.114837	+	0.993384i	$0.536635\pi$
$810$	−0.309017	−	0.951057i	−0.0108578	−	0.0334167i
$811$	3.33536	−	5.77701i	0.117120	−	0.202858i	−0.801505	−	0.597988i	$-0.795967\pi$
$811$	3.33536	−	5.77701i	0.117120	−	0.202858i	0.918625	+	0.395130i	$0.129300\pi$
$812$	−2.03130	−	3.51831i	−0.0712846	−	0.123469i
$813$	17.3049	−	19.2191i	0.606911	−	0.674043i
$814$	−6.11227	+	18.8116i	−0.214235	+	0.659347i
$815$	1.27415	+	1.41508i	0.0446314	+	0.0495682i
$816$	4.77904	−	2.12777i	0.167300	−	0.0744867i
$817$	9.58503	+	2.03736i	0.335338	+	0.0712782i
$818$	2.22449	−	21.1646i	0.0777775	−	0.740004i
$819$	−0.883441	−	8.40538i	−0.0308699	−	0.293708i
$820$	−2.45528	+	0.521886i	−0.0857421	+	0.0182250i
$821$	29.5177	−	21.4459i	1.03018	−	0.748467i	0.0618319	−	0.998087i	$-0.480306\pi$
$821$	29.5177	−	21.4459i	1.03018	−	0.748467i	0.968344	+	0.249620i	$0.0803057\pi$
$822$	8.99385	−	6.53442i	0.313697	−	0.227914i
$823$	−23.4343	+	4.98112i	−0.816869	+	0.173631i	−0.597353	−	0.801978i	$-0.703781\pi$
$823$	−23.4343	+	4.98112i	−0.816869	+	0.173631i	−0.219515	+	0.975609i	$0.570448\pi$
$824$	1.31575	+	12.5185i	0.0458363	+	0.436103i
$825$	−0.457287	+	4.35080i	−0.0159207	+	0.151475i
$826$	−22.1944	−	4.71757i	−0.772242	−	0.164145i
$827$	−12.8778	+	5.73359i	−0.447807	+	0.199376i	−0.618234	−	0.785994i	$-0.712152\pi$
$827$	−12.8778	+	5.73359i	−0.447807	+	0.199376i	0.170428	+	0.985370i	$0.445485\pi$
$828$	−1.94662	−	2.16194i	−0.0676496	−	0.0751325i
$829$	9.21428	−	28.3587i	0.320025	−	0.984937i	−0.653611	−	0.756831i	$-0.726747\pi$
$829$	9.21428	−	28.3587i	0.320025	−	0.984937i	0.973636	−	0.228106i	$-0.0732533\pi$
$830$	−6.40039	+	7.10836i	−0.222161	+	0.246735i
$831$	−3.35594	−	5.81266i	−0.116416	−	0.201639i
$832$	2.42580	−	4.20162i	0.0840996	−	0.145665i
$833$	−6.41017	−	19.7285i	−0.222099	−	0.683552i
$834$	−13.6739	−	6.08803i	−0.473490	−	0.210811i
$835$	−19.2188	−	13.9633i	−0.665094	−	0.483219i
$836$	5.56544			0.192485
$837$	−3.93455	−	3.93945i	−0.135998	−	0.136167i
$838$	1.56212			0.0539624
$839$	18.4446	+	13.4008i	0.636779	+	0.462647i	0.858742	−	0.512408i	$-0.171247\pi$
$839$	18.4446	+	13.4008i	0.636779	+	0.462647i	−0.221963	+	0.975055i	$0.571247\pi$
$840$	1.59143	+	0.708550i	0.0549095	+	0.0244473i
$841$	−7.28085	−	22.4082i	−0.251064	−	0.772695i
$842$	−4.27964	+	7.41256i	−0.147486	+	0.255454i
$843$	−12.0836	−	20.9293i	−0.416180	−	0.720844i
$844$	0.212081	−	0.235539i	0.00730011	−	0.00810760i
$845$	−3.25645	+	10.0223i	−0.112025	+	0.344779i
$846$	−4.37512	−	4.85906i	−0.150420	−	0.167058i
$847$	−12.9519	+	5.76657i	−0.445033	+	0.198142i
$848$	−5.86060	−	1.24571i	−0.201254	−	0.0427778i
$849$	1.87391	−	17.8291i	0.0643124	−	0.611892i
$850$	−0.546821	−	5.20265i	−0.0187558	−	0.178450i
$851$	−12.8659	+	2.73473i	−0.441037	+	0.0937453i
$852$	−1.72880	+	1.25605i	−0.0592279	+	0.0430316i
$853$	−31.6390	+	22.9871i	−1.08330	+	0.787064i	−0.978255	−	0.207404i	$-0.933499\pi$
$853$	−31.6390	+	22.9871i	−1.08330	+	0.787064i	−0.105045	+	0.994467i	$0.533499\pi$
$854$	−8.87789	+	1.88705i	−0.303795	+	0.0645736i
$855$	0.132978	+	1.26520i	0.00454775	+	0.0432690i
$856$	1.87675	−	17.8561i	0.0641459	−	0.610308i
$857$	3.31745	+	0.705145i	0.113322	+	0.0240873i	0.264223	−	0.964461i	$-0.414884\pi$
$857$	3.31745	+	0.705145i	0.113322	+	0.0240873i	−0.150902	+	0.988549i	$0.548218\pi$
$858$	−19.3897	+	8.63284i	−0.661952	+	0.294720i
$859$	28.2781	+	31.4060i	0.964837	+	1.07156i	0.997398	+	0.0720905i	$0.0229670\pi$
$859$	28.2781	+	31.4060i	0.964837	+	1.07156i	−0.0325609	+	0.999470i	$0.510366\pi$
$860$	2.38027	−	7.32572i	0.0811665	−	0.249805i
$861$	2.92594	−	3.24958i	0.0997156	−	0.110745i
$862$	12.7875	+	22.1485i	0.435543	+	0.754382i
$863$	20.4009	−	35.3355i	0.694456	−	1.20283i	−0.275907	−	0.961184i	$-0.588978\pi$
$863$	20.4009	−	35.3355i	0.694456	−	1.20283i	0.970364	−	0.241649i	$-0.0776884\pi$
$864$	0.309017	+	0.951057i	0.0105130	+	0.0323556i
$865$	8.61054	+	3.83366i	0.292767	+	0.130348i
$866$	−6.38010	−	4.63541i	−0.216805	−	0.157518i
$867$	10.3666			0.352069
$868$	9.68627	−	0.501593i	0.328774	−	0.0170252i
$869$	−6.62272			−0.224660
$870$	−1.88671	−	1.37077i	−0.0639653	−	0.0464735i
$871$	−46.6937	−	20.7894i	−1.58215	−	0.704420i
$872$	3.17097	+	9.75924i	0.107383	+	0.330490i
$873$	−8.41757	+	14.5797i	−0.284892	+	0.493447i
$874$	1.85048	+	3.20513i	0.0625935	+	0.108415i
$875$	1.16565	−	1.29459i	0.0394062	−	0.0437650i
$876$	−0.487076	+	1.49907i	−0.0164568	+	0.0506487i
$877$	30.4871	+	33.8594i	1.02948	+	1.14335i	0.989556	+	0.144146i	$0.0460436\pi$
$877$	30.4871	+	33.8594i	1.02948	+	1.14335i	0.0399199	+	0.999203i	$0.487290\pi$
$878$	−6.58349	+	2.93116i	−0.222182	+	0.0989217i
$879$	2.40128	+	0.510407i	0.0809930	+	0.0172156i
$880$	0.457287	−	4.35080i	0.0154151	−	0.146665i
$881$	0.897848	+	8.54246i	0.0302493	+	0.287803i	0.999181	+	0.0404729i	$0.0128864\pi$
$881$	0.897848	+	8.54246i	0.0302493	+	0.287803i	−0.968931	+	0.247330i	$0.920447\pi$
$882$	3.87866	−	0.824434i	0.130601	−	0.0277601i
$883$	−6.68153	+	4.85442i	−0.224851	+	0.163364i	−0.694508	−	0.719485i	$-0.744378\pi$
$883$	−6.68153	+	4.85442i	−0.224851	+	0.163364i	0.469656	+	0.882849i	$0.344378\pi$
$884$	20.5331	−	14.9182i	0.690602	−	0.501752i
$885$	−12.7405	+	2.70807i	−0.428267	+	0.0910309i
$886$	−3.80715	−	36.2227i	−0.127904	−	1.21692i
$887$	−5.84494	+	55.6109i	−0.196254	+	1.86723i	0.244564	+	0.969633i	$0.421355\pi$
$887$	−5.84494	+	55.6109i	−0.196254	+	1.86723i	−0.440818	+	0.897597i	$0.645312\pi$
$888$	4.42252	+	0.940036i	0.148410	+	0.0315455i
$889$	−27.9306	+	12.4355i	−0.936762	+	0.417073i
$890$	−1.51075	−	1.67786i	−0.0506405	−	0.0562420i
$891$	1.35188	−	4.16065i	0.0452895	−	0.139387i
$892$	7.63270	−	8.47697i	0.255562	−	0.283830i
$893$	4.15905	+	7.20368i	0.139177	+	0.241062i
$894$	2.55003	−	4.41678i	0.0852857	−	0.147719i
$895$	1.71840	+	5.28869i	0.0574397	+	0.176781i
$896$	−1.59143	−	0.708550i	−0.0531659	−	0.0236710i
$897$	−11.4186	−	8.29610i	−0.381256	−	0.276999i
$898$	36.3088			1.21164
$899$	−12.8234	−	2.03921i	−0.427685	−	0.0680115i
$900$	1.00000			0.0333333
$901$	−25.3575	−	18.4233i	−0.844780	−	0.613768i
$902$	−10.0319	−	4.46647i	−0.334024	−	0.148717i
$903$	4.14652	+	12.7617i	0.137987	+	0.424682i
$904$	−6.76725	+	11.7212i	−0.225075	+	0.389842i
$905$	−5.32796	−	9.22829i	−0.177107	−	0.306759i
$906$	−15.3746	+	17.0753i	−0.510788	+	0.567288i
$907$	−8.07008	+	24.8372i	−0.267963	+	0.824705i	0.723033	+	0.690813i	$0.242747\pi$
$907$	−8.07008	+	24.8372i	−0.267963	+	0.824705i	−0.990996	+	0.133891i	$0.957253\pi$
$908$	−9.17706	−	10.1922i	−0.304552	−	0.338239i
$909$	7.11789	−	3.16909i	0.236086	−	0.105112i
$910$	8.26699	+	1.75720i	0.274048	+	0.0582507i
$911$	−0.557935	+	5.30840i	−0.0184852	+	0.175875i	−0.999869	−	0.0161815i	$-0.994849\pi$
$911$	−0.557935	+	5.30840i	−0.0184852	+	0.175875i	0.981384	+	0.192057i	$0.0615157\pi$
$912$	−0.132978	−	1.26520i	−0.00440334	−	0.0418950i
$913$	−40.9312	+	8.70020i	−1.35463	+	0.287935i
$914$	24.0974	−	17.5078i	0.797070	−	0.579105i
$915$	−4.21508	+	3.06243i	−0.139346	+	0.101241i
$916$	24.1015	−	5.12294i	0.796338	−	0.169267i
$917$	−2.59411	−	24.6813i	−0.0856650	−	0.815048i
$918$	−0.546821	+	5.20265i	−0.0180478	+	0.171713i
$919$	17.5832	+	3.73742i	0.580015	+	0.123286i	0.488571	−	0.872524i	$-0.337518\pi$
$919$	17.5832	+	3.73742i	0.580015	+	0.123286i	0.0914441	+	0.995810i	$0.470852\pi$
$920$	2.65766	−	1.18327i	0.0876205	−	0.0390112i
$921$	10.9436	+	12.1541i	0.360604	+	0.400492i
$922$	9.06664	−	27.9043i	0.298594	−	0.918978i
$923$	−6.93721	+	7.70455i	−0.228341	+	0.253598i
$924$	3.81050	+	6.59998i	0.125356	+	0.217123i
$925$	2.26066	−	3.91558i	0.0743301	−	0.128744i
$926$	−2.42457	−	7.46205i	−0.0796762	−	0.245218i
$927$	−11.4992	−	5.11979i	−0.377684	−	0.168156i
$928$	1.88671	+	1.37077i	0.0619341	+	0.0449978i
$929$	11.0641			0.363002			0.181501	−	0.983391i	$-0.441904\pi$
$929$	11.0641			0.363002			0.181501	+	0.983391i	$0.441904\pi$
$930$	4.96249	−	2.52462i	0.162726	−	0.0827857i
$931$	−5.04455			−0.165328
$932$	19.5969	+	14.2380i	0.641918	+	0.466381i
$933$	16.6241	+	7.40152i	0.544248	+	0.242315i
$934$	−1.97568	−	6.08051i	−0.0646461	−	0.198960i
$935$	11.4429	−	19.8196i	0.374222	−	0.648171i
$936$	2.42580	+	4.20162i	0.0792899	+	0.137334i
$937$	18.1626	−	20.1717i	0.593348	−	0.658980i	−0.369435	−	0.929257i	$-0.620449\pi$
$937$	18.1626	−	20.1717i	0.593348	−	0.658980i	0.962783	+	0.270277i	$0.0871153\pi$
$938$	−5.67129	+	17.4544i	−0.185174	+	0.569907i
$939$	17.8341	+	19.8068i	0.581994	+	0.646369i
$940$	5.97322	−	2.65945i	0.194825	−	0.0867417i
$941$	−26.5824	−	5.65026i	−0.866561	−	0.184193i	−0.246879	−	0.969046i	$-0.579405\pi$
$941$	−26.5824	−	5.65026i	−0.866561	−	0.184193i	−0.619682	+	0.784853i	$0.712738\pi$
$942$	0.233425	−	2.22089i	0.00760540	−	0.0723606i
$943$	−0.763310	−	7.26241i	−0.0248568	−	0.236496i
$944$	12.7405	−	2.70807i	0.414668	−	0.0881403i
$945$	−1.40934	+	1.02394i	−0.0458458	+	0.0333089i
$946$	27.2619	−	19.8069i	0.886360	−	0.643978i
$947$	−3.40114	+	0.722934i	−0.110522	+	0.0234922i	−0.262841	−	0.964839i	$-0.584659\pi$
$947$	−3.40114	+	0.722934i	−0.110522	+	0.0234922i	0.152319	+	0.988331i	$0.451326\pi$
$948$	0.158240	+	1.50555i	0.00513940	+	0.0488981i
$949$	−0.799346	+	7.60527i	−0.0259479	+	0.246877i
$950$	−1.24437	−	0.264499i	−0.0403727	−	0.00858148i
$951$	−7.10153	+	3.16180i	−0.230283	+	0.102528i
$952$	−6.09788	−	6.77238i	−0.197633	−	0.219494i
$953$	5.21013	−	16.0351i	0.168773	−	0.519428i	−0.830522	−	0.556986i	$-0.811958\pi$
$953$	5.21013	−	16.0351i	0.168773	−	0.519428i	0.999294	+	0.0375575i	$0.0119577\pi$
$954$	4.00911	−	4.45257i	0.129800	−	0.144157i
$955$	5.04380	+	8.73611i	0.163213	+	0.282694i
$956$	0.377764	−	0.654306i	0.0122178	−	0.0211618i
$957$	−3.15270	−	9.70303i	−0.101912	−	0.313654i
$958$	−0.411774	−	0.183334i	−0.0133038	−	0.00592324i
$959$	−15.6676	−	11.3832i	−0.505934	−	0.367582i
$960$	−1.00000			−0.0322749
$961$	18.2525	−	25.0568i	0.588792	−	0.808285i
$962$	21.9357			0.707235
$963$	14.5254	+	10.5533i	0.468076	+	0.340077i
$964$	14.7791	+	6.58007i	0.476002	+	0.211930i
$965$	−1.25603	−	3.86568i	−0.0404332	−	0.124441i
$966$	−2.53394	+	4.38892i	−0.0815283	+	0.141211i
$967$	−27.0718	−	46.8897i	−0.870569	−	1.50787i	−0.861409	−	0.507912i	$-0.830417\pi$
$967$	−27.0718	−	46.8897i	−0.870569	−	1.50787i	−0.00916043	−	0.999958i	$-0.502916\pi$
$968$	5.44575	−	6.04812i	0.175033	−	0.194394i
$969$	2.05654	−	6.32939i	0.0660657	−	0.203329i
$970$	−11.2649	−	12.5109i	−0.361694	−	0.401702i
$971$	−47.5005	+	21.1486i	−1.52436	+	0.678691i	−0.986413	−	0.164285i	$-0.947468\pi$
$971$	−47.5005	+	21.1486i	−1.52436	+	0.678691i	−0.537951	+	0.842976i	$0.680802\pi$
$972$	−0.978148	−	0.207912i	−0.0313741	−	0.00666877i
$973$	−2.72556	+	25.9320i	−0.0873774	+	0.831340i
$974$	−0.506116	−	4.81537i	−0.0162170	−	0.154295i
$975$	4.74559	−	1.00871i	0.151980	−	0.0323044i
$976$	4.21508	−	3.06243i	0.134921	−	0.0980261i
$977$	−22.7125	+	16.5016i	−0.726639	+	0.527934i	−0.888498	−	0.458880i	$-0.848251\pi$
$977$	−22.7125	+	16.5016i	−0.726639	+	0.527934i	0.161860	+	0.986814i	$0.448251\pi$
$978$	1.86257	−	0.395901i	0.0595584	−	0.0126595i
$979$	−1.03246	−	9.82316i	−0.0329974	−	0.313950i
$980$	−0.414487	+	3.94358i	−0.0132403	+	0.125973i
$981$	−10.0372	−	2.13348i	−0.320464	−	0.0681168i
$982$	25.4598	−	11.3354i	0.812455	−	0.361728i
$983$	18.8678	+	20.9548i	0.601789	+	0.668354i	0.964664	−	0.263484i	$-0.0848716\pi$
$983$	18.8678	+	20.9548i	0.601789	+	0.668354i	−0.362875	+	0.931838i	$0.618205\pi$
$984$	−0.775673	+	2.38728i	−0.0247276	+	0.0761036i
$985$	4.71895	−	5.24093i	0.150358	−	0.166990i
$986$	6.09996	+	10.5654i	0.194262	+	0.336472i
$987$	−5.69516	+	9.86431i	−0.181279	+	0.313984i
$988$	−1.90727	−	5.86999i	−0.0606785	−	0.186749i
$989$	20.4712	+	9.11437i	0.650947	+	0.289820i
$990$	3.53926	+	2.57142i	0.112485	+	0.0817251i
$991$	−3.56878			−0.113366			−0.0566830	−	0.998392i	$-0.518052\pi$
$991$	−3.56878			−0.113366			−0.0566830	+	0.998392i	$0.518052\pi$
$992$	−4.96249	+	2.52462i	−0.157559	+	0.0801569i
$993$	−3.02752			−0.0960756
$994$	3.01164	+	2.18809i	0.0955235	+	0.0694019i
$995$	4.43494	+	1.97456i	0.140597	+	0.0625979i
$996$	2.95582	+	9.09708i	0.0936588	+	0.288252i
$997$	−23.9484	+	41.4799i	−0.758454	+	1.31368i	0.185184	+	0.982704i	$0.440712\pi$
$997$	−23.9484	+	41.4799i	−0.758454	+	1.31368i	−0.943639	+	0.330978i	$0.892622\pi$
$998$	−1.98224	−	3.43334i	−0.0627467	−	0.108680i
$999$	−3.02536	+	3.36000i	−0.0957180	+	0.106306i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.d.391.1	✓	16
31.18	even	15	inner	930.2.bg.d.421.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.d.391.1	✓	16	1.1	even	1	trivial
930.2.bg.d.421.1	yes	16	31.18	even	15	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.913545 + 0.406737i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-1.16565 + 1.29459i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.669131 + 0.743145i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.913545 + 0.406737i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-1.16565 + 1.29459i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.669131 + 0.743145i) q^{9} +(-0.913545 + 0.406737i) q^{10} +(-4.27916 - 0.909564i) q^{11} +(-0.104528 + 0.994522i) q^{12} +(0.507131 + 4.82503i) q^{13} +(1.70397 - 0.362190i) q^{14} +(0.809017 - 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-5.11700 + 1.08765i) q^{17} +(-0.104528 - 0.994522i) q^{18} +(-0.132978 + 1.26520i) q^{19} +(0.978148 + 0.207912i) q^{20} +(-1.59143 + 0.708550i) q^{21} +(2.92729 + 3.25108i) q^{22} +(-0.898984 + 2.76679i) q^{23} +(0.669131 - 0.743145i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(2.42580 - 4.20162i) q^{26} +(0.309017 + 0.951057i) q^{27} +(-1.59143 - 0.708550i) q^{28} +(1.88671 + 1.37077i) q^{29} -1.00000 q^{30} +(-4.96249 + 2.52462i) q^{31} +1.00000 q^{32} +(-3.53926 - 2.57142i) q^{33} +(4.77904 + 2.12777i) q^{34} +(0.538319 + 1.65678i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(2.26066 + 3.91558i) q^{37} +(0.851248 - 0.945407i) q^{38} +(-1.49923 + 4.61415i) q^{39} +(-0.669131 - 0.743145i) q^{40} +(-2.29312 + 1.02096i) q^{41} +(1.70397 + 0.362190i) q^{42} +(0.805153 - 7.66052i) q^{43} +(-0.457287 - 4.35080i) q^{44} +(0.978148 - 0.207912i) q^{45} +(2.35357 - 1.70997i) q^{46} +(5.28976 - 3.84324i) q^{47} +(-0.978148 + 0.207912i) q^{48} +(0.414487 + 3.94358i) q^{49} +(-0.104528 + 0.994522i) q^{50} +(-5.11700 - 1.08765i) q^{51} +(-4.43216 + 1.97333i) q^{52} +(4.00911 + 4.45257i) q^{53} +(0.309017 - 0.951057i) q^{54} +(-2.92729 + 3.25108i) q^{55} +(0.871018 + 1.50865i) q^{56} +(-0.636085 + 1.10173i) q^{57} +(-0.720657 - 2.21795i) q^{58} +(-11.8990 - 5.29779i) q^{59} +(0.809017 + 0.587785i) q^{60} -5.21012 q^{61} +(5.49867 + 0.874412i) q^{62} -1.74204 q^{63} +(-0.809017 - 0.587785i) q^{64} +(4.43216 + 1.97333i) q^{65} +(1.35188 + 4.16065i) q^{66} +(-5.26759 + 9.12373i) q^{67} +(-2.61566 - 4.53045i) q^{68} +(-1.94662 + 2.16194i) q^{69} +(0.538319 - 1.65678i) q^{70} +(1.42988 + 1.58804i) q^{71} +(0.913545 - 0.406737i) q^{72} +(1.54177 + 0.327713i) q^{73} +(0.472607 - 4.49656i) q^{74} +(-0.104528 - 0.994522i) q^{75} +(-1.24437 + 0.264499i) q^{76} +(6.16552 - 4.47951i) q^{77} +(3.92503 - 2.85170i) q^{78} +(1.48077 - 0.314747i) q^{79} +(0.104528 + 0.994522i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(2.45528 + 0.521886i) q^{82} +(8.73828 - 3.89053i) q^{83} +(-1.16565 - 1.29459i) q^{84} +(-1.61656 + 4.97527i) q^{85} +(-5.15412 + 5.72423i) q^{86} +(1.16605 + 2.01965i) q^{87} +(-2.18738 + 3.78866i) q^{88} +(0.697694 + 2.14728i) q^{89} +(-0.913545 - 0.406737i) q^{90} +(-6.83755 - 4.96777i) q^{91} -2.90917 q^{92} +(-5.56031 + 0.287935i) q^{93} -6.53851 q^{94} +(1.02921 + 0.747763i) q^{95} +(0.913545 + 0.406737i) q^{96} +(5.20234 + 16.0112i) q^{97} +(1.98265 - 3.43406i) q^{98} +(-2.18738 - 3.78866i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 8 * q^5 - 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9	\( 16 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9} - 2 q^{10} - 4 q^{11} + 2 q^{12} - 20 q^{13} - 4 q^{14} + 4 q^{15} - 4 q^{16} - 12 q^{17} + 2 q^{18} - 7 q^{19} - 2 q^{20} - 4 q^{21} + 11 q^{22} + 11 q^{23} + 2 q^{24} - 8 q^{25} + 5 q^{26} - 4 q^{27} - 4 q^{28} + 23 q^{29} - 16 q^{30} - 17 q^{31} + 16 q^{32} - 2 q^{33} - 2 q^{34} + 7 q^{35} - 8 q^{36} + 17 q^{37} - 2 q^{38} - 5 q^{39} - 2 q^{40} + 8 q^{41} - 4 q^{42} + 32 q^{43} + q^{44} - 2 q^{45} + 11 q^{46} - 7 q^{47} + 2 q^{48} - q^{49} + 2 q^{50} - 12 q^{51} + 10 q^{52} + 54 q^{53} - 4 q^{54} - 11 q^{55} + q^{56} + 18 q^{57} - 22 q^{58} - 38 q^{59} + 4 q^{60} - 28 q^{61} - 27 q^{62} - 2 q^{63} - 4 q^{64} - 10 q^{65} - 7 q^{66} + q^{67} - 2 q^{68} - 13 q^{69} + 7 q^{70} - 11 q^{71} + 2 q^{72} + 53 q^{73} + 2 q^{74} + 2 q^{75} - 2 q^{76} + 44 q^{77} + 10 q^{78} + 48 q^{79} - 2 q^{80} + 2 q^{81} + 8 q^{82} + 56 q^{83} + 11 q^{84} - 24 q^{85} - 13 q^{86} + q^{87} - 9 q^{88} - 43 q^{89} - 2 q^{90} - 50 q^{91} - 44 q^{92} - 22 q^{93} - 72 q^{94} - 14 q^{95} + 2 q^{96} + 17 q^{97} + 29 q^{98} - 9 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 8 * q^5 - 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9 - 2 * q^10 - 4 * q^11 + 2 * q^12 - 20 * q^13 - 4 * q^14 + 4 * q^15 - 4 * q^16 - 12 * q^17 + 2 * q^18 - 7 * q^19 - 2 * q^20 - 4 * q^21 + 11 * q^22 + 11 * q^23 + 2 * q^24 - 8 * q^25 + 5 * q^26 - 4 * q^27 - 4 * q^28 + 23 * q^29 - 16 * q^30 - 17 * q^31 + 16 * q^32 - 2 * q^33 - 2 * q^34 + 7 * q^35 - 8 * q^36 + 17 * q^37 - 2 * q^38 - 5 * q^39 - 2 * q^40 + 8 * q^41 - 4 * q^42 + 32 * q^43 + q^44 - 2 * q^45 + 11 * q^46 - 7 * q^47 + 2 * q^48 - q^49 + 2 * q^50 - 12 * q^51 + 10 * q^52 + 54 * q^53 - 4 * q^54 - 11 * q^55 + q^56 + 18 * q^57 - 22 * q^58 - 38 * q^59 + 4 * q^60 - 28 * q^61 - 27 * q^62 - 2 * q^63 - 4 * q^64 - 10 * q^65 - 7 * q^66 + q^67 - 2 * q^68 - 13 * q^69 + 7 * q^70 - 11 * q^71 + 2 * q^72 + 53 * q^73 + 2 * q^74 + 2 * q^75 - 2 * q^76 + 44 * q^77 + 10 * q^78 + 48 * q^79 - 2 * q^80 + 2 * q^81 + 8 * q^82 + 56 * q^83 + 11 * q^84 - 24 * q^85 - 13 * q^86 + q^87 - 9 * q^88 - 43 * q^89 - 2 * q^90 - 50 * q^91 - 44 * q^92 - 22 * q^93 - 72 * q^94 - 14 * q^95 + 2 * q^96 + 17 * q^97 + 29 * q^98 - 9 * q^99

Introduction

L-functions

Modular forms

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Database

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