LMFDB - Embedded newform 930.2.z.a.469.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(109,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 2]))

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

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

chi := DirichletCharacter("930.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.z (of order $10$, degree $4$, 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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			469.1
Root			$0.951057 + 0.309017i$ of defining polynomial
Character	$\chi$	$=$	930.469
Dual form			930.2.z.a.349.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 + 0.309017i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.809017 - 0.587785i) q^{4} -2.23607 q^{5} -1.00000 q^{6} +(-0.726543 - 1.00000i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.951057 + 0.309017i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.809017 - 0.587785i) q^{4} -2.23607 q^{5} -1.00000 q^{6} +(-0.726543 - 1.00000i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.809017 + 0.587785i) q^{9} +(2.12663 - 0.690983i) q^{10} +(1.92705 - 1.40008i) q^{11} +(0.951057 - 0.309017i) q^{12} +(-0.138757 - 0.0450850i) q^{13} +(1.00000 + 0.726543i) q^{14} +(-2.12663 - 0.690983i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-1.08981 + 1.50000i) q^{17} +(-0.951057 - 0.309017i) q^{18} +(-1.38197 - 4.25325i) q^{19} +(-1.80902 + 1.31433i) q^{20} +(-0.381966 - 1.17557i) q^{21} +(-1.40008 + 1.92705i) q^{22} +(-3.44095 + 4.73607i) q^{23} +(-0.809017 + 0.587785i) q^{24} +5.00000 q^{25} +0.145898 q^{26} +(0.587785 + 0.809017i) q^{27} +(-1.17557 - 0.381966i) q^{28} +(-2.11803 - 6.51864i) q^{29} +2.23607 q^{30} +(-2.19098 - 5.11855i) q^{31} +1.00000i q^{32} +(2.26538 - 0.736068i) q^{33} +(0.572949 - 1.76336i) q^{34} +(1.62460 + 2.23607i) q^{35} +1.00000 q^{36} -10.8541i q^{37} +(2.62866 + 3.61803i) q^{38} +(-0.118034 - 0.0857567i) q^{39} +(1.31433 - 1.80902i) q^{40} +(-2.38197 - 7.33094i) q^{41} +(0.726543 + 1.00000i) q^{42} +(3.80423 - 1.23607i) q^{43} +(0.736068 - 2.26538i) q^{44} +(-1.80902 - 1.31433i) q^{45} +(1.80902 - 5.56758i) q^{46} +(-2.93893 - 0.954915i) q^{47} +(0.587785 - 0.809017i) q^{48} +(1.69098 - 5.20431i) q^{49} +(-4.75528 + 1.54508i) q^{50} +(-1.50000 + 1.08981i) q^{51} +(-0.138757 + 0.0450850i) q^{52} +(-4.53077 + 6.23607i) q^{53} +(-0.809017 - 0.587785i) q^{54} +(-4.30902 + 3.13068i) q^{55} +1.23607 q^{56} -4.47214i q^{57} +(4.02874 + 5.54508i) q^{58} +(0.972136 - 2.99193i) q^{59} +(-2.12663 + 0.690983i) q^{60} +2.76393 q^{61} +(3.66547 + 4.19098i) q^{62} -1.23607i q^{63} +(-0.309017 - 0.951057i) q^{64} +(0.310271 + 0.100813i) q^{65} +(-1.92705 + 1.40008i) q^{66} -8.00000i q^{67} +1.85410i q^{68} +(-4.73607 + 3.44095i) q^{69} +(-2.23607 - 1.62460i) q^{70} +(3.23607 + 2.35114i) q^{71} +(-0.951057 + 0.309017i) q^{72} +(1.73060 + 2.38197i) q^{73} +(3.35410 + 10.3229i) q^{74} +(4.75528 + 1.54508i) q^{75} +(-3.61803 - 2.62866i) q^{76} +(-2.80017 - 0.909830i) q^{77} +(0.138757 + 0.0450850i) q^{78} +(4.92705 + 3.57971i) q^{79} +(-0.690983 + 2.12663i) q^{80} +(0.309017 + 0.951057i) q^{81} +(4.53077 + 6.23607i) q^{82} +(-2.62866 + 0.854102i) q^{83} +(-1.00000 - 0.726543i) q^{84} +(2.43690 - 3.35410i) q^{85} +(-3.23607 + 2.35114i) q^{86} -6.85410i q^{87} +2.38197i q^{88} +(1.85410 - 1.34708i) q^{89} +(2.12663 + 0.690983i) q^{90} +(0.0557281 + 0.171513i) q^{91} +5.85410i q^{92} +(-0.502029 - 5.54508i) q^{93} +3.09017 q^{94} +(3.09017 + 9.51057i) q^{95} +(-0.309017 + 0.951057i) q^{96} +(0.555029 + 0.763932i) q^{97} +5.47214i q^{98} +2.38197 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4} - 8 q^{6} + 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^4 - 8 * q^6 + 2 * q^9	$ 8 q + 2 q^{4} - 8 q^{6} + 2 q^{9} + 2 q^{11} + 8 q^{14} - 2 q^{16} - 20 q^{19} - 10 q^{20} - 12 q^{21} - 2 q^{24} + 40 q^{25} + 28 q^{26} - 8 q^{29} - 22 q^{31} + 18 q^{34} + 8 q^{36} + 8 q^{39} - 28 q^{41} - 12 q^{44} - 10 q^{45} + 10 q^{46} + 18 q^{49} - 12 q^{51} - 2 q^{54} - 30 q^{55} - 8 q^{56} - 28 q^{59} + 40 q^{61} + 2 q^{64} - 2 q^{66} - 20 q^{69} + 8 q^{71} - 20 q^{76} + 26 q^{79} - 10 q^{80} - 2 q^{81} - 8 q^{84} - 8 q^{86} - 12 q^{89} + 72 q^{91} - 20 q^{94} - 20 q^{95} + 2 q^{96} + 28 q^{99}+O(q^{100}) $ 8 * q + 2 * q^4 - 8 * q^6 + 2 * q^9 + 2 * q^11 + 8 * q^14 - 2 * q^16 - 20 * q^19 - 10 * q^20 - 12 * q^21 - 2 * q^24 + 40 * q^25 + 28 * q^26 - 8 * q^29 - 22 * q^31 + 18 * q^34 + 8 * q^36 + 8 * q^39 - 28 * q^41 - 12 * q^44 - 10 * q^45 + 10 * q^46 + 18 * q^49 - 12 * q^51 - 2 * q^54 - 30 * q^55 - 8 * q^56 - 28 * q^59 + 40 * q^61 + 2 * q^64 - 2 * q^66 - 20 * q^69 + 8 * q^71 - 20 * q^76 + 26 * q^79 - 10 * q^80 - 2 * q^81 - 8 * q^84 - 8 * q^86 - 12 * q^89 + 72 * q^91 - 20 * q^94 - 20 * q^95 + 2 * q^96 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.951057	+	0.309017i	−0.672499	+	0.218508i
$2$	−0.951057	+	0.309017i	−0.672499	+	0.218508i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	−2.23607			−1.00000
$5$	−2.23607			−1.00000
$6$	−1.00000			−0.408248
$7$	−0.726543	−	1.00000i	−0.274607	−	0.377964i	0.649331	−	0.760506i	$-0.275049\pi$
$7$	−0.726543	−	1.00000i	−0.274607	−	0.377964i	−0.923938	+	0.382541i	$0.875049\pi$
$8$	−0.587785	+	0.809017i	−0.207813	+	0.286031i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$	2.12663	−	0.690983i	0.672499	−	0.218508i
$11$	1.92705	−	1.40008i	0.581028	−	0.422141i	−0.258067	−	0.966127i	$-0.583085\pi$
$11$	1.92705	−	1.40008i	0.581028	−	0.422141i	0.839094	+	0.543986i	$0.183085\pi$
$12$	0.951057	−	0.309017i	0.274546	−	0.0892055i
$13$	−0.138757	−	0.0450850i	−0.0384843	−	0.0125043i	0.289712	−	0.957114i	$-0.406441\pi$
$13$	−0.138757	−	0.0450850i	−0.0384843	−	0.0125043i	−0.328196	+	0.944610i	$0.606441\pi$
$14$	1.00000	+	0.726543i	0.267261	+	0.194177i
$15$	−2.12663	−	0.690983i	−0.549093	−	0.178411i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−1.08981	+	1.50000i	−0.264319	+	0.363803i	−0.920461	−	0.390833i	$-0.872187\pi$
$17$	−1.08981	+	1.50000i	−0.264319	+	0.363803i	0.656143	+	0.754637i	$0.272187\pi$
$18$	−0.951057	−	0.309017i	−0.224166	−	0.0728360i
$19$	−1.38197	−	4.25325i	−0.317045	−	0.975763i	−0.974905	−	0.222623i	$-0.928538\pi$
$19$	−1.38197	−	4.25325i	−0.317045	−	0.975763i	0.657860	−	0.753140i	$-0.271462\pi$
$20$	−1.80902	+	1.31433i	−0.404508	+	0.293893i
$21$	−0.381966	−	1.17557i	−0.0833518	−	0.256531i
$22$	−1.40008	+	1.92705i	−0.298499	+	0.410849i
$23$	−3.44095	+	4.73607i	−0.717489	+	0.987538i	0.282115	+	0.959381i	$0.408964\pi$
$23$	−3.44095	+	4.73607i	−0.717489	+	0.987538i	−0.999603	+	0.0281578i	$0.991036\pi$
$24$	−0.809017	+	0.587785i	−0.165140	+	0.119981i
$25$	5.00000			1.00000
$26$	0.145898			0.0286130
$27$	0.587785	+	0.809017i	0.113119	+	0.155695i
$28$	−1.17557	−	0.381966i	−0.222162	−	0.0721848i
$29$	−2.11803	−	6.51864i	−0.393309	−	1.21048i	−0.930271	−	0.366874i	$-0.880428\pi$
$29$	−2.11803	−	6.51864i	−0.393309	−	1.21048i	0.536962	−	0.843607i	$-0.319572\pi$
$30$	2.23607			0.408248
$31$	−2.19098	−	5.11855i	−0.393512	−	0.919319i
$31$	−2.19098	−	5.11855i	−0.393512	−	0.919319i
$32$			1.00000i			0.176777i
$33$	2.26538	−	0.736068i	0.394353	−	0.128133i
$34$	0.572949	−	1.76336i	0.0982599	−	0.302413i
$35$	1.62460	+	2.23607i	0.274607	+	0.377964i
$36$	1.00000			0.166667
$37$		−	10.8541i		−	1.78440i	−0.451637	−	0.892202i	$-0.649160\pi$
$37$		−	10.8541i		−	1.78440i	0.451637	−	0.892202i	$-0.350840\pi$
$38$	2.62866	+	3.61803i	0.426424	+	0.586923i
$39$	−0.118034	−	0.0857567i	−0.0189006	−	0.0137321i
$40$	1.31433	−	1.80902i	0.207813	−	0.286031i
$41$	−2.38197	−	7.33094i	−0.372001	−	1.14490i	−0.945480	−	0.325680i	$-0.894407\pi$
$41$	−2.38197	−	7.33094i	−0.372001	−	1.14490i	0.573479	−	0.819220i	$-0.305593\pi$
$42$	0.726543	+	1.00000i	0.112108	+	0.154303i
$43$	3.80423	−	1.23607i	0.580139	−	0.188499i	−0.00422383	−	0.999991i	$-0.501344\pi$
$43$	3.80423	−	1.23607i	0.580139	−	0.188499i	0.584363	+	0.811492i	$0.301344\pi$
$44$	0.736068	−	2.26538i	0.110966	−	0.341520i
$45$	−1.80902	−	1.31433i	−0.269672	−	0.195928i
$46$	1.80902	−	5.56758i	0.266725	−	0.820895i
$47$	−2.93893	−	0.954915i	−0.428686	−	0.139289i	0.0867235	−	0.996232i	$-0.472360\pi$
$47$	−2.93893	−	0.954915i	−0.428686	−	0.139289i	−0.515410	+	0.856944i	$0.672360\pi$
$48$	0.587785	−	0.809017i	0.0848395	−	0.116772i
$49$	1.69098	−	5.20431i	0.241569	−	0.743473i
$50$	−4.75528	+	1.54508i	−0.672499	+	0.218508i
$51$	−1.50000	+	1.08981i	−0.210042	+	0.152604i
$52$	−0.138757	+	0.0450850i	−0.0192422	+	0.00625216i
$53$	−4.53077	+	6.23607i	−0.622349	+	0.856590i	−0.997521	−	0.0703653i	$-0.977584\pi$
$53$	−4.53077	+	6.23607i	−0.622349	+	0.856590i	0.375172	+	0.926955i	$0.377584\pi$
$54$	−0.809017	−	0.587785i	−0.110093	−	0.0799874i
$55$	−4.30902	+	3.13068i	−0.581028	+	0.422141i
$56$	1.23607			0.165177
$57$		−	4.47214i		−	0.592349i
$58$	4.02874	+	5.54508i	0.528999	+	0.728105i
$59$	0.972136	−	2.99193i	0.126561	−	0.389516i	−0.867621	−	0.497226i	$-0.834352\pi$
$59$	0.972136	−	2.99193i	0.126561	−	0.389516i	0.994182	+	0.107710i	$0.0343519\pi$
$60$	−2.12663	+	0.690983i	−0.274546	+	0.0892055i
$61$	2.76393			0.353885			0.176943	−	0.984221i	$-0.443379\pi$
$61$	2.76393			0.353885			0.176943	+	0.984221i	$0.443379\pi$
$62$	3.66547	+	4.19098i	0.465515	+	0.532255i
$63$		−	1.23607i		−	0.155730i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	0.310271	+	0.100813i	0.0384843	+	0.0125043i
$66$	−1.92705	+	1.40008i	−0.237204	+	0.172338i
$67$		−	8.00000i		−	0.977356i	−0.872464	−	0.488678i	$-0.837479\pi$
$67$		−	8.00000i		−	0.977356i	0.872464	−	0.488678i	$-0.162521\pi$
$68$			1.85410i			0.224843i
$69$	−4.73607	+	3.44095i	−0.570156	+	0.414242i
$70$	−2.23607	−	1.62460i	−0.267261	−	0.194177i
$71$	3.23607	+	2.35114i	0.384051	+	0.279029i	0.763013	−	0.646383i	$-0.223719\pi$
$71$	3.23607	+	2.35114i	0.384051	+	0.279029i	−0.378963	+	0.925412i	$0.623719\pi$
$72$	−0.951057	+	0.309017i	−0.112083	+	0.0364180i
$73$	1.73060	+	2.38197i	0.202551	+	0.278788i	0.898193	−	0.439601i	$-0.144880\pi$
$73$	1.73060	+	2.38197i	0.202551	+	0.278788i	−0.695642	+	0.718389i	$0.744880\pi$
$74$	3.35410	+	10.3229i	0.389906	+	1.20001i
$75$	4.75528	+	1.54508i	0.549093	+	0.178411i
$76$	−3.61803	−	2.62866i	−0.415017	−	0.301527i
$77$	−2.80017	−	0.909830i	−0.319109	−	0.103685i
$78$	0.138757	+	0.0450850i	0.0157112	+	0.00510487i
$79$	4.92705	+	3.57971i	0.554337	+	0.402749i	0.829382	−	0.558682i	$-0.188693\pi$
$79$	4.92705	+	3.57971i	0.554337	+	0.402749i	−0.275045	+	0.961431i	$0.588693\pi$
$80$	−0.690983	+	2.12663i	−0.0772542	+	0.237764i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	4.53077	+	6.23607i	0.500340	+	0.688659i
$83$	−2.62866	+	0.854102i	−0.288532	+	0.0937499i	−0.449707	−	0.893176i	$-0.648472\pi$
$83$	−2.62866	+	0.854102i	−0.288532	+	0.0937499i	0.161175	+	0.986926i	$0.448472\pi$
$84$	−1.00000	−	0.726543i	−0.109109	−	0.0792723i
$85$	2.43690	−	3.35410i	0.264319	−	0.363803i
$86$	−3.23607	+	2.35114i	−0.348954	+	0.253530i
$87$		−	6.85410i		−	0.734837i
$88$			2.38197i			0.253918i
$89$	1.85410	−	1.34708i	0.196534	−	0.142791i	−0.485166	−	0.874422i	$-0.661241\pi$
$89$	1.85410	−	1.34708i	0.196534	−	0.142791i	0.681700	+	0.731632i	$0.261241\pi$
$90$	2.12663	+	0.690983i	0.224166	+	0.0728360i
$91$	0.0557281	+	0.171513i	0.00584189	+	0.0179795i
$92$			5.85410i			0.610332i
$93$	−0.502029	−	5.54508i	−0.0520579	−	0.574999i
$94$	3.09017			0.318727
$95$	3.09017	+	9.51057i	0.317045	+	0.975763i
$96$	−0.309017	+	0.951057i	−0.0315389	+	0.0970668i
$97$	0.555029	+	0.763932i	0.0563547	+	0.0775655i	0.836264	−	0.548327i	$-0.184735\pi$
$97$	0.555029	+	0.763932i	0.0563547	+	0.0775655i	−0.779910	+	0.625892i	$0.784735\pi$
$98$			5.47214i			0.552769i
$99$	2.38197			0.239397
$100$	4.04508	−	2.93893i	0.404508	−	0.293893i
$101$	−6.16312	−	4.47777i	−0.613253	−	0.445555i	0.237305	−	0.971435i	$-0.423736\pi$
$101$	−6.16312	−	4.47777i	−0.613253	−	0.445555i	−0.850558	+	0.525881i	$0.823736\pi$
$102$	1.08981	−	1.50000i	0.107908	−	0.148522i
$103$	−7.77997	+	2.52786i	−0.766583	+	0.249078i	−0.666102	−	0.745861i	$-0.732038\pi$
$103$	−7.77997	+	2.52786i	−0.766583	+	0.249078i	−0.100481	+	0.994939i	$0.532038\pi$
$104$	0.118034	−	0.0857567i	0.0115742	−	0.00840914i
$105$	0.854102	+	2.62866i	0.0833518	+	0.256531i
$106$	2.38197	−	7.33094i	0.231357	−	0.712044i
$107$	9.23305	−	12.7082i	0.892593	−	1.22855i	−0.0801784	−	0.996781i	$-0.525549\pi$
$107$	9.23305	−	12.7082i	0.892593	−	1.22855i	0.972771	−	0.231768i	$-0.0744510\pi$
$108$	0.951057	+	0.309017i	0.0915155	+	0.0297352i
$109$	−3.85410	+	11.8617i	−0.369156	+	1.13615i	0.578181	+	0.815908i	$0.303763\pi$
$109$	−3.85410	+	11.8617i	−0.369156	+	1.13615i	−0.947337	+	0.320237i	$0.896237\pi$
$110$	3.13068	−	4.30902i	0.298499	−	0.410849i
$111$	3.35410	−	10.3229i	0.318357	−	0.979803i
$112$	−1.17557	+	0.381966i	−0.111081	+	0.0360924i
$113$	−4.97980	−	6.85410i	−0.468460	−	0.644780i	0.507776	−	0.861489i	$-0.330468\pi$
$113$	−4.97980	−	6.85410i	−0.468460	−	0.644780i	−0.976236	+	0.216709i	$0.930468\pi$
$114$	1.38197	+	4.25325i	0.129433	+	0.398354i
$115$	7.69421	−	10.5902i	0.717489	−	0.987538i
$116$	−5.54508	−	4.02874i	−0.514848	−	0.374059i
$117$	−0.0857567	−	0.118034i	−0.00792821	−	0.0109122i
$118$			3.14590i			0.289603i
$119$	2.29180			0.210089
$120$	1.80902	−	1.31433i	0.165140	−	0.119981i
$121$	−1.64590	+	5.06555i	−0.149627	+	0.460505i
$122$	−2.62866	+	0.854102i	−0.237987	+	0.0773268i
$123$		−	7.70820i		−	0.695025i
$124$	−4.78115	−	2.85317i	−0.429360	−	0.256222i
$125$	−11.1803			−1.00000
$126$	0.381966	+	1.17557i	0.0340282	+	0.104728i
$127$	−15.9434	−	5.18034i	−1.41475	−	0.459681i	−0.500821	−	0.865551i	$-0.666969\pi$
$127$	−15.9434	−	5.18034i	−1.41475	−	0.459681i	−0.913931	+	0.405870i	$0.866969\pi$
$128$	0.587785	+	0.809017i	0.0519534	+	0.0715077i
$129$	4.00000			0.352180
$130$	−0.326238			−0.0286130
$131$	4.69098	−	3.40820i	0.409853	−	0.297776i	−0.363689	−	0.931520i	$-0.618483\pi$
$131$	4.69098	−	3.40820i	0.409853	−	0.297776i	0.773542	+	0.633745i	$0.218483\pi$
$132$	1.40008	−	1.92705i	0.121862	−	0.167728i
$133$	−3.24920	+	4.47214i	−0.281741	+	0.387783i
$134$	2.47214	+	7.60845i	0.213560	+	0.657270i
$135$	−1.31433	−	1.80902i	−0.113119	−	0.155695i
$136$	−0.572949	−	1.76336i	−0.0491300	−	0.151207i
$137$	8.95554	+	2.90983i	0.765123	+	0.248604i	0.665476	−	0.746419i	$-0.268229\pi$
$137$	8.95554	+	2.90983i	0.765123	+	0.248604i	0.0996471	+	0.995023i	$0.468229\pi$
$138$	3.44095	−	4.73607i	0.292914	−	0.403161i
$139$	−0.909830	+	2.80017i	−0.0771708	+	0.237507i	−0.982199	−	0.187845i	$-0.939850\pi$
$139$	−0.909830	+	2.80017i	−0.0771708	+	0.237507i	0.905028	+	0.425352i	$0.139850\pi$
$140$	2.62866	+	0.854102i	0.222162	+	0.0721848i
$141$	−2.50000	−	1.81636i	−0.210538	−	0.152965i
$142$	−3.80423	−	1.23607i	−0.319244	−	0.103729i
$143$	−0.330515	+	0.107391i	−0.0276391	+	0.00898048i
$144$	0.809017	−	0.587785i	0.0674181	−	0.0489821i
$145$	4.73607	+	14.5761i	0.393309	+	1.21048i
$146$	−2.38197	−	1.73060i	−0.197133	−	0.143225i
$147$	3.21644	−	4.42705i	0.265288	−	0.365137i
$148$	−6.37988	−	8.78115i	−0.524423	−	0.721806i
$149$	14.6180			1.19756			0.598778	−	0.800915i	$-0.295653\pi$
$149$	14.6180			1.19756			0.598778	+	0.800915i	$0.295653\pi$
$150$	−5.00000			−0.408248
$151$	14.4721	−	10.5146i	1.17773	−	0.855668i	0.185812	−	0.982585i	$-0.440508\pi$
$151$	14.4721	−	10.5146i	1.17773	−	0.855668i	0.991913	+	0.126917i	$0.0405083\pi$
$152$	4.25325	+	1.38197i	0.344984	+	0.112092i
$153$	−1.76336	+	0.572949i	−0.142559	+	0.0463202i
$154$	2.94427			0.237256
$155$	4.89919	+	11.4454i	0.393512	+	0.919319i
$156$	−0.145898			−0.0116812
$157$	16.2537	−	5.28115i	1.29719	−	0.421482i	0.422586	−	0.906323i	$-0.361123\pi$
$157$	16.2537	−	5.28115i	1.29719	−	0.421482i	0.874602	+	0.484841i	$0.161123\pi$
$158$	−5.79210	−	1.88197i	−0.460794	−	0.149721i
$159$	−6.23607	+	4.53077i	−0.494552	+	0.359313i
$160$		−	2.23607i		−	0.176777i
$161$	7.23607			0.570282
$162$	−0.587785	−	0.809017i	−0.0461808	−	0.0635624i
$163$	−7.66145	+	10.5451i	−0.600091	+	0.825955i	−0.995717	−	0.0924572i	$-0.970528\pi$
$163$	−7.66145	+	10.5451i	−0.600091	+	0.825955i	0.395625	+	0.918412i	$0.370528\pi$
$164$	−6.23607	−	4.53077i	−0.486955	−	0.353794i
$165$	−5.06555	+	1.64590i	−0.394353	+	0.128133i
$166$	2.23607	−	1.62460i	0.173553	−	0.126093i
$167$	−13.4005	+	4.35410i	−1.03697	+	0.336931i	−0.777541	−	0.628833i	$-0.783533\pi$
$167$	−13.4005	+	4.35410i	−1.03697	+	0.336931i	−0.259425	+	0.965763i	$0.583533\pi$
$168$	1.17557	+	0.381966i	0.0906972	+	0.0294693i
$169$	−10.5000	−	7.62870i	−0.807692	−	0.586823i
$170$	−1.28115	+	3.94298i	−0.0982599	+	0.302413i
$171$	1.38197	−	4.25325i	0.105682	−	0.325254i
$172$	2.35114	−	3.23607i	0.179273	−	0.246748i
$173$	11.5842	+	3.76393i	0.880730	+	0.286166i	0.714260	−	0.699880i	$-0.246763\pi$
$173$	11.5842	+	3.76393i	0.880730	+	0.286166i	0.166469	+	0.986047i	$0.446763\pi$
$174$	2.11803	+	6.51864i	0.160568	+	0.494177i
$175$	−3.63271	−	5.00000i	−0.274607	−	0.377964i
$176$	−0.736068	−	2.26538i	−0.0554832	−	0.170760i
$177$	1.84911	−	2.54508i	0.138988	−	0.191300i
$178$	−1.34708	+	1.85410i	−0.100968	+	0.138971i
$179$	−16.5902	+	12.0535i	−1.24001	+	0.900918i	−0.997599	−	0.0692560i	$-0.977937\pi$
$179$	−16.5902	+	12.0535i	−1.24001	+	0.900918i	−0.242409	+	0.970174i	$0.577937\pi$
$180$	−2.23607			−0.166667
$181$	−13.2361			−0.983829			−0.491915	−	0.870643i	$-0.663703\pi$
$181$	−13.2361			−0.983829			−0.491915	+	0.870643i	$0.663703\pi$
$182$	−0.106001	−	0.145898i	−0.00785733	−	0.0108147i
$183$	2.62866	+	0.854102i	0.194316	+	0.0631370i
$184$	−1.80902	−	5.56758i	−0.133363	−	0.410448i
$185$			24.2705i			1.78440i
$186$	2.19098	+	5.11855i	0.160651	+	0.375311i
$187$			4.41641i			0.322960i
$188$	−2.93893	+	0.954915i	−0.214343	+	0.0696443i
$189$	0.381966	−	1.17557i	0.0277839	−	0.0855102i
$190$	−5.87785	−	8.09017i	−0.426424	−	0.586923i
$191$	−7.23607			−0.523584			−0.261792	−	0.965124i	$-0.584313\pi$
$191$	−7.23607			−0.523584			−0.261792	+	0.965124i	$0.584313\pi$
$192$		−	1.00000i		−	0.0721688i
$193$	10.4086	+	14.3262i	0.749229	+	1.03123i	0.998034	+	0.0626716i	$0.0199621\pi$
$193$	10.4086	+	14.3262i	0.749229	+	1.03123i	−0.248805	+	0.968554i	$0.580038\pi$
$194$	−0.763932	−	0.555029i	−0.0548471	−	0.0398488i
$195$	0.263932	+	0.191758i	0.0189006	+	0.0137321i
$196$	−1.69098	−	5.20431i	−0.120785	−	0.371736i
$197$	−4.08174	−	5.61803i	−0.290812	−	0.400268i	0.638466	−	0.769650i	$-0.279569\pi$
$197$	−4.08174	−	5.61803i	−0.290812	−	0.400268i	−0.929278	+	0.369382i	$0.879569\pi$
$198$	−2.26538	+	0.736068i	−0.160994	+	0.0523101i
$199$	−7.29837	+	22.4621i	−0.517368	+	1.59229i	0.261564	+	0.965186i	$0.415762\pi$
$199$	−7.29837	+	22.4621i	−0.517368	+	1.59229i	−0.778932	+	0.627109i	$0.784238\pi$
$200$	−2.93893	+	4.04508i	−0.207813	+	0.286031i
$201$	2.47214	−	7.60845i	0.174371	−	0.536659i
$202$	7.24518	+	2.35410i	0.509769	+	0.165634i
$203$	−4.97980	+	6.85410i	−0.349513	+	0.481064i
$204$	−0.572949	+	1.76336i	−0.0401145	+	0.123460i
$205$	5.32624	+	16.3925i	0.372001	+	1.14490i
$206$	6.61803	−	4.80828i	0.461100	−	0.335009i
$207$	−5.56758	+	1.80902i	−0.386974	+	0.125735i
$208$	−0.0857567	+	0.118034i	−0.00594616	+	0.00818418i
$209$	−8.61803	−	6.26137i	−0.596122	−	0.433108i
$210$	−1.62460	−	2.23607i	−0.112108	−	0.154303i
$211$	12.6525			0.871032			0.435516	−	0.900181i	$-0.356566\pi$
$211$	12.6525			0.871032			0.435516	+	0.900181i	$0.356566\pi$
$212$			7.70820i			0.529402i
$213$	2.35114	+	3.23607i	0.161098	+	0.221732i
$214$	−4.85410	+	14.9394i	−0.331820	+	1.02124i
$215$	−8.50651	+	2.76393i	−0.580139	+	0.188499i
$216$	−1.00000			−0.0680414
$217$	−3.52671	+	5.90983i	−0.239409	+	0.401185i
$218$		−	12.4721i		−	0.844720i
$219$	0.909830	+	2.80017i	0.0614806	+	0.189218i
$220$	−1.64590	+	5.06555i	−0.110966	+	0.341520i
$221$	0.218847	−	0.159002i	0.0147212	−	0.0106956i
$222$			10.8541i			0.728480i
$223$		−	25.8885i		−	1.73363i	−0.498634	−	0.866813i	$-0.666165\pi$
$223$		−	25.8885i		−	1.73363i	0.498634	−	0.866813i	$-0.333835\pi$
$224$	1.00000	−	0.726543i	0.0668153	−	0.0485442i
$225$	4.04508	+	2.93893i	0.269672	+	0.195928i
$226$	6.85410	+	4.97980i	0.455928	+	0.331251i
$227$	−5.42882	+	1.76393i	−0.360324	+	0.117076i	−0.483584	−	0.875298i	$-0.660665\pi$
$227$	−5.42882	+	1.76393i	−0.360324	+	0.117076i	0.123260	+	0.992374i	$0.460665\pi$
$228$	−2.62866	−	3.61803i	−0.174087	−	0.239610i
$229$	7.90983	+	24.3440i	0.522696	+	1.60869i	0.768827	+	0.639457i	$0.220841\pi$
$229$	7.90983	+	24.3440i	0.522696	+	1.60869i	−0.246131	+	0.969237i	$0.579159\pi$
$230$	−4.04508	+	12.4495i	−0.266725	+	0.820895i
$231$	−2.38197	−	1.73060i	−0.156722	−	0.113865i
$232$	6.51864	+	2.11803i	0.427970	+	0.139056i
$233$	12.0005	+	3.89919i	0.786176	+	0.255444i	0.674475	−	0.738298i	$-0.264370\pi$
$233$	12.0005	+	3.89919i	0.786176	+	0.255444i	0.111701	+	0.993742i	$0.464370\pi$
$234$	0.118034	+	0.0857567i	0.00771612	+	0.00560609i
$235$	6.57164	+	2.13525i	0.428686	+	0.139289i
$236$	−0.972136	−	2.99193i	−0.0632807	−	0.194758i
$237$	3.57971	+	4.92705i	0.232527	+	0.320046i
$238$	−2.17963	+	0.708204i	−0.141284	+	0.0459060i
$239$	12.2361	+	8.89002i	0.791485	+	0.575048i	0.908404	−	0.418094i	$-0.137302\pi$
$239$	12.2361	+	8.89002i	0.791485	+	0.575048i	−0.116918	+	0.993142i	$0.537302\pi$
$240$	−1.31433	+	1.80902i	−0.0848395	+	0.116772i
$241$	−5.97214	+	4.33901i	−0.384699	+	0.279500i	−0.763280	−	0.646068i	$-0.776412\pi$
$241$	−5.97214	+	4.33901i	−0.384699	+	0.279500i	0.378581	+	0.925568i	$0.376412\pi$
$242$		−	5.32624i		−	0.342384i
$243$			1.00000i			0.0641500i
$244$	2.23607	−	1.62460i	0.143150	−	0.104004i
$245$	−3.78115	+	11.6372i	−0.241569	+	0.743473i
$246$	2.38197	+	7.33094i	0.151869	+	0.467404i
$247$			0.652476i			0.0415160i
$248$	5.42882	+	1.23607i	0.344731	+	0.0784904i
$249$	−2.76393			−0.175157
$250$	10.6331	−	3.45492i	0.672499	−	0.218508i
$251$	−4.04508	+	12.4495i	−0.255323	+	0.785805i	0.738442	+	0.674317i	$0.235562\pi$
$251$	−4.04508	+	12.4495i	−0.255323	+	0.785805i	−0.993766	+	0.111488i	$0.964438\pi$
$252$	−0.726543	−	1.00000i	−0.0457679	−	0.0629941i
$253$			13.9443i			0.876669i
$254$	16.7639			1.05186
$255$	3.35410	−	2.43690i	0.210042	−	0.152604i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−8.00448	+	11.0172i	−0.499306	+	0.687235i	−0.982070	−	0.188515i	$-0.939633\pi$
$257$	−8.00448	+	11.0172i	−0.499306	+	0.687235i	0.482765	+	0.875750i	$0.339633\pi$
$258$	−3.80423	+	1.23607i	−0.236841	+	0.0769542i
$259$	−10.8541	+	7.88597i	−0.674441	+	0.490010i
$260$	0.310271	−	0.100813i	0.0192422	−	0.00625216i
$261$	2.11803	−	6.51864i	0.131103	−	0.403494i
$262$	−3.40820	+	4.69098i	−0.210559	+	0.289810i
$263$	−6.34712	−	2.06231i	−0.391380	−	0.127167i	0.106714	−	0.994290i	$-0.465967\pi$
$263$	−6.34712	−	2.06231i	−0.391380	−	0.127167i	−0.498095	+	0.867122i	$0.665967\pi$
$264$	−0.736068	+	2.26538i	−0.0453019	+	0.139425i
$265$	10.1311	−	13.9443i	0.622349	−	0.856590i
$266$	1.70820	−	5.25731i	0.104737	−	0.322346i
$267$	2.17963	−	0.708204i	0.133391	−	0.0433414i
$268$	−4.70228	−	6.47214i	−0.287238	−	0.395349i
$269$	−3.10081	−	9.54332i	−0.189060	−	0.581867i	0.810935	−	0.585137i	$-0.198959\pi$
$269$	−3.10081	−	9.54332i	−0.189060	−	0.581867i	−0.999995	+	0.00327003i	$0.998959\pi$
$270$	1.80902	+	1.31433i	0.110093	+	0.0799874i
$271$	−16.2082	−	11.7759i	−0.984578	−	0.715338i	−0.0258512	−	0.999666i	$-0.508230\pi$
$271$	−16.2082	−	11.7759i	−0.984578	−	0.715338i	−0.958727	+	0.284328i	$0.908230\pi$
$272$	1.08981	+	1.50000i	0.0660797	+	0.0909509i
$273$			0.180340i			0.0109147i
$274$	−9.41641			−0.568866
$275$	9.63525	−	7.00042i	0.581028	−	0.422141i
$276$	−1.80902	+	5.56758i	−0.108890	+	0.335129i
$277$	3.38795	−	1.10081i	0.203562	−	0.0661414i	−0.205461	−	0.978665i	$-0.565869\pi$
$277$	3.38795	−	1.10081i	0.203562	−	0.0661414i	0.409024	+	0.912524i	$0.365869\pi$
$278$		−	2.94427i		−	0.176586i
$279$	1.23607	−	5.42882i	0.0740015	−	0.325015i
$280$	−2.76393			−0.165177
$281$	−3.81966	−	11.7557i	−0.227862	−	0.701287i	−0.997988	−	0.0633956i	$-0.979807\pi$
$281$	−3.81966	−	11.7557i	−0.227862	−	0.701287i	0.770127	−	0.637891i	$-0.220193\pi$
$282$	2.93893	+	0.954915i	0.175011	+	0.0568644i
$283$	6.06961	+	8.35410i	0.360801	+	0.496600i	0.950372	−	0.311117i	$-0.100703\pi$
$283$	6.06961	+	8.35410i	0.360801	+	0.496600i	−0.589571	+	0.807717i	$0.700703\pi$
$284$	4.00000			0.237356
$285$			10.0000i			0.592349i
$286$	0.281153	−	0.204270i	0.0166249	−	0.0120787i
$287$	−5.60034	+	7.70820i	−0.330577	+	0.455001i
$288$	−0.587785	+	0.809017i	−0.0346356	+	0.0476718i
$289$	4.19098	+	12.8985i	0.246528	+	0.758736i
$290$	−9.00854	−	12.3992i	−0.528999	−	0.728105i
$291$	0.291796	+	0.898056i	0.0171054	+	0.0526450i
$292$	2.80017	+	0.909830i	0.163867	+	0.0532438i
$293$	−3.97574	+	5.47214i	−0.232265	+	0.319686i	−0.909202	−	0.416356i	$-0.863307\pi$
$293$	−3.97574	+	5.47214i	−0.232265	+	0.319686i	0.676937	+	0.736041i	$0.263307\pi$
$294$	−1.69098	+	5.20431i	−0.0986201	+	0.303522i
$295$	−2.17376	+	6.69015i	−0.126561	+	0.389516i
$296$	8.78115	+	6.37988i	0.510394	+	0.370823i
$297$	2.26538	+	0.736068i	0.131451	+	0.0427110i
$298$	−13.9026	+	4.51722i	−0.805355	+	0.261676i
$299$	0.690983	−	0.502029i	0.0399606	−	0.0290331i
$300$	4.75528	−	1.54508i	0.274546	−	0.0892055i
$301$	−4.00000	−	2.90617i	−0.230556	−	0.167509i
$302$	−10.5146	+	14.4721i	−0.605049	+	0.832778i
$303$	−4.47777	−	6.16312i	−0.257241	−	0.354062i
$304$	−4.47214			−0.256495
$305$	−6.18034			−0.353885
$306$	1.50000	−	1.08981i	0.0857493	−	0.0623005i
$307$	−6.96767	−	2.26393i	−0.397666	−	0.129209i	0.103355	−	0.994644i	$-0.467042\pi$
$307$	−6.96767	−	2.26393i	−0.397666	−	0.129209i	−0.501021	+	0.865435i	$0.667042\pi$
$308$	−2.80017	+	0.909830i	−0.159554	+	0.0518424i
$309$	−8.18034			−0.465363
$310$	−8.19624	−	9.37132i	−0.465515	−	0.532255i
$311$	13.4164			0.760775			0.380387	−	0.924827i	$-0.375791\pi$
$311$	13.4164			0.760775			0.380387	+	0.924827i	$0.375791\pi$
$312$	0.138757	−	0.0450850i	0.00785558	−	0.00255243i
$313$	4.97980	+	1.61803i	0.281475	+	0.0914567i	0.446352	−	0.894857i	$-0.352723\pi$
$313$	4.97980	+	1.61803i	0.281475	+	0.0914567i	−0.164877	+	0.986314i	$0.552723\pi$
$314$	−13.8262	+	10.0453i	−0.780260	+	0.566892i
$315$			2.76393i			0.155730i
$316$	6.09017			0.342599
$317$	10.4086	+	14.3262i	0.584606	+	0.804642i	0.994191	−	0.107630i	$-0.0343263\pi$
$317$	10.4086	+	14.3262i	0.584606	+	0.804642i	−0.409585	+	0.912272i	$0.634326\pi$
$318$	4.53077	−	6.23607i	0.254073	−	0.349701i
$319$	−13.2082	−	9.59632i	−0.739517	−	0.537291i
$320$	0.690983	+	2.12663i	0.0386271	+	0.118882i
$321$	12.7082	−	9.23305i	0.709303	−	0.515339i
$322$	−6.88191	+	2.23607i	−0.383514	+	0.124611i
$323$	7.88597	+	2.56231i	0.438787	+	0.142571i
$324$	0.809017	+	0.587785i	0.0449454	+	0.0326547i
$325$	−0.693786	−	0.225425i	−0.0384843	−	0.0125043i
$326$	4.02786	−	12.3965i	0.223083	−	0.686578i
$327$	−7.33094	+	10.0902i	−0.405402	+	0.557988i
$328$	7.33094	+	2.38197i	0.404783	+	0.131522i
$329$	1.18034	+	3.63271i	0.0650742	+	0.200278i
$330$	4.30902	−	3.13068i	0.237204	−	0.172338i
$331$	4.09017	+	12.5882i	0.224816	+	0.691913i	0.998310	+	0.0581093i	$0.0185072\pi$
$331$	4.09017	+	12.5882i	0.224816	+	0.691913i	−0.773494	+	0.633803i	$0.781493\pi$
$332$	−1.62460	+	2.23607i	−0.0891614	+	0.122720i
$333$	6.37988	−	8.78115i	0.349615	−	0.481204i
$334$	11.3992	−	8.28199i	0.623736	−	0.453171i
$335$			17.8885i			0.977356i
$336$	−1.23607			−0.0674330
$337$	−5.60034	−	7.70820i	−0.305070	−	0.419893i	0.628766	−	0.777595i	$-0.283560\pi$
$337$	−5.60034	−	7.70820i	−0.305070	−	0.419893i	−0.933836	+	0.357702i	$0.883560\pi$
$338$	12.3435	+	4.01064i	0.671397	+	0.218150i
$339$	−2.61803	−	8.05748i	−0.142192	−	0.437622i
$340$		−	4.14590i		−	0.224843i
$341$	−11.3885	−	6.79615i	−0.616724	−	0.368032i
$342$			4.47214i			0.241825i
$343$	−14.6619	+	4.76393i	−0.791667	+	0.257228i
$344$	−1.23607	+	3.80423i	−0.0666443	+	0.205110i
$345$	10.5902	−	7.69421i	0.570156	−	0.414242i
$346$	−12.1803			−0.654819
$347$		−	8.00000i		−	0.429463i	−0.976673	−	0.214731i	$-0.931112\pi$
$347$		−	8.00000i		−	0.429463i	0.976673	−	0.214731i	$-0.0688876\pi$
$348$	−4.02874	−	5.54508i	−0.215963	−	0.297248i
$349$	7.85410	+	5.70634i	0.420420	+	0.305453i	0.777807	−	0.628503i	$-0.216332\pi$
$349$	7.85410	+	5.70634i	0.420420	+	0.305453i	−0.357387	+	0.933957i	$0.616332\pi$
$350$	5.00000	+	3.63271i	0.267261	+	0.194177i
$351$	−0.0450850	−	0.138757i	−0.00240646	−	0.00740632i
$352$	1.40008	+	1.92705i	0.0746248	+	0.102712i
$353$	25.2623	−	8.20820i	1.34457	−	0.436879i	0.453710	−	0.891149i	$-0.350100\pi$
$353$	25.2623	−	8.20820i	1.34457	−	0.436879i	0.890864	+	0.454271i	$0.150100\pi$
$354$	−0.972136	+	2.99193i	−0.0516684	+	0.159019i
$355$	−7.23607	−	5.25731i	−0.384051	−	0.279029i
$356$	0.708204	−	2.17963i	0.0375347	−	0.115520i
$357$	2.17963	+	0.708204i	0.115358	+	0.0374821i
$358$	12.0535	−	16.5902i	0.637045	−	0.876818i
$359$	9.32624	−	28.7032i	0.492220	−	1.51490i	−0.329025	−	0.944321i	$-0.606720\pi$
$359$	9.32624	−	28.7032i	0.492220	−	1.51490i	0.821245	−	0.570576i	$-0.193280\pi$
$360$	2.12663	−	0.690983i	0.112083	−	0.0364180i
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	12.5882	−	4.09017i	0.661624	−	0.214975i
$363$	−3.13068	+	4.30902i	−0.164318	+	0.226165i
$364$	0.145898	+	0.106001i	0.00764713	+	0.00555597i
$365$	−3.86974	−	5.32624i	−0.202551	−	0.278788i
$366$	−2.76393			−0.144473
$367$		−	20.7639i		−	1.08387i	−0.840421	−	0.541934i	$-0.817692\pi$
$367$		−	20.7639i		−	1.08387i	0.840421	−	0.541934i	$-0.182308\pi$
$368$	3.44095	+	4.73607i	0.179372	+	0.246885i
$369$	2.38197	−	7.33094i	0.124000	−	0.381633i
$370$	−7.50000	−	23.0826i	−0.389906	−	1.20001i
$371$	9.52786			0.494662
$372$	−3.66547	−	4.19098i	−0.190046	−	0.217292i
$373$			38.0344i			1.96935i	0.174403	+	0.984674i	$0.444200\pi$
$373$			38.0344i			1.96935i	−0.174403	+	0.984674i	$0.555800\pi$
$374$	−1.36475	−	4.20025i	−0.0705693	−	0.217190i
$375$	−10.6331	−	3.45492i	−0.549093	−	0.178411i
$376$	2.50000	−	1.81636i	0.128928	−	0.0936714i
$377$			1.00000i			0.0515026i
$378$			1.23607i			0.0635765i
$379$	5.85410	−	4.25325i	0.300705	−	0.218475i	−0.427193	−	0.904161i	$-0.640497\pi$
$379$	5.85410	−	4.25325i	0.300705	−	0.218475i	0.727898	+	0.685686i	$0.240497\pi$
$380$	8.09017	+	5.87785i	0.415017	+	0.301527i
$381$	−13.5623	−	9.85359i	−0.694818	−	0.504815i
$382$	6.88191	−	2.23607i	0.352109	−	0.114407i
$383$	−19.8007	−	27.2533i	−1.01177	−	1.39258i	−0.917818	−	0.397001i	$-0.870051\pi$
$383$	−19.8007	−	27.2533i	−1.01177	−	1.39258i	−0.0939490	−	0.995577i	$-0.529949\pi$
$384$	0.309017	+	0.951057i	0.0157695	+	0.0485334i
$385$	6.26137	+	2.03444i	0.319109	+	0.103685i
$386$	−14.3262	−	10.4086i	−0.729186	−	0.529785i
$387$	3.80423	+	1.23607i	0.193380	+	0.0628329i
$388$	0.898056	+	0.291796i	0.0455919	+	0.0148137i
$389$	11.3262	+	8.22899i	0.574263	+	0.417227i	0.836651	−	0.547736i	$-0.184510\pi$
$389$	11.3262	+	8.22899i	0.574263	+	0.417227i	−0.262388	+	0.964962i	$0.584510\pi$
$390$	−0.310271	−	0.100813i	−0.0157112	−	0.00510487i
$391$	−3.35410	−	10.3229i	−0.169624	−	0.522050i
$392$	3.21644	+	4.42705i	0.162455	+	0.223600i
$393$	5.51458	−	1.79180i	0.278174	−	0.0903842i
$394$	5.61803	+	4.08174i	0.283032	+	0.205635i
$395$	−11.0172	−	8.00448i	−0.554337	−	0.402749i
$396$	1.92705	−	1.40008i	0.0968380	−	0.0703569i
$397$			6.61803i			0.332150i	0.986113	+	0.166075i	$0.0531093\pi$
$397$			6.61803i			0.332150i	−0.986113	+	0.166075i	$0.946891\pi$
$398$		−	23.6180i		−	1.18387i
$399$	−4.47214	+	3.24920i	−0.223887	+	0.162663i
$400$	1.54508	−	4.75528i	0.0772542	−	0.237764i
$401$	−3.32624	−	10.2371i	−0.166104	−	0.511217i	0.833012	−	0.553256i	$-0.186615\pi$
$401$	−3.32624	−	10.2371i	−0.166104	−	0.511217i	−0.999116	+	0.0420388i	$0.986615\pi$
$402$			8.00000i			0.399004i
$403$	0.0732450	+	0.809017i	0.00364859	+	0.0403000i
$404$	−7.61803			−0.379011
$405$	−0.690983	−	2.12663i	−0.0343352	−	0.105673i
$406$	2.61803	−	8.05748i	0.129931	−	0.399886i
$407$	−15.1967	−	20.9164i	−0.753270	−	1.03679i
$408$		−	1.85410i		−	0.0917917i
$409$	30.5623			1.51121			0.755604	−	0.655028i	$-0.227343\pi$
$409$	30.5623			1.51121			0.755604	+	0.655028i	$0.227343\pi$
$410$	−10.1311	−	13.9443i	−0.500340	−	0.688659i
$411$	7.61803	+	5.53483i	0.375770	+	0.273013i
$412$	−4.80828	+	6.61803i	−0.236887	+	0.326047i
$413$	−3.69822	+	1.20163i	−0.181978	+	0.0591282i
$414$	4.73607	−	3.44095i	0.232765	−	0.169114i
$415$	5.87785	−	1.90983i	0.288532	−	0.0937499i
$416$	0.0450850	−	0.138757i	0.00221047	−	0.00680314i
$417$	−1.73060	+	2.38197i	−0.0847478	+	0.116645i
$418$	10.1311	+	3.29180i	0.495529	+	0.161007i
$419$	11.9336	−	36.7279i	0.582996	−	1.79428i	−0.0241776	−	0.999708i	$-0.507697\pi$
$419$	11.9336	−	36.7279i	0.582996	−	1.79428i	0.607174	−	0.794569i	$-0.292303\pi$
$420$	2.23607	+	1.62460i	0.109109	+	0.0792723i
$421$	7.14590	−	21.9928i	0.348270	−	1.07186i	−0.611540	−	0.791213i	$-0.709450\pi$
$421$	7.14590	−	21.9928i	0.348270	−	1.07186i	0.959810	−	0.280651i	$-0.0905503\pi$
$422$	−12.0332	+	3.90983i	−0.585768	+	0.190328i
$423$	−1.81636	−	2.50000i	−0.0883143	−	0.121554i
$424$	−2.38197	−	7.33094i	−0.115678	−	0.356022i
$425$	−5.44907	+	7.50000i	−0.264319	+	0.363803i
$426$	−3.23607	−	2.35114i	−0.156788	−	0.113913i
$427$	−2.00811	−	2.76393i	−0.0971795	−	0.133756i
$428$		−	15.7082i		−	0.759285i
$429$	−0.347524			−0.0167786
$430$	7.23607	−	5.25731i	0.348954	−	0.253530i
$431$	−7.18034	+	22.0988i	−0.345865	+	1.06446i	0.615254	+	0.788329i	$0.289053\pi$
$431$	−7.18034	+	22.0988i	−0.345865	+	1.06446i	−0.961119	+	0.276134i	$0.910947\pi$
$432$	0.951057	−	0.309017i	0.0457577	−	0.0148676i
$433$			10.7639i			0.517282i	0.965974	+	0.258641i	$0.0832746\pi$
$433$			10.7639i			0.517282i	−0.965974	+	0.258641i	$0.916725\pi$
$434$	1.52786	−	6.71040i	0.0733398	−	0.322109i
$435$			15.3262i			0.734837i
$436$	3.85410	+	11.8617i	0.184578	+	0.568073i
$437$	24.8990	+	8.09017i	1.19108	+	0.387005i
$438$	−1.73060	−	2.38197i	−0.0826912	−	0.113815i
$439$	−27.0344			−1.29028			−0.645142	−	0.764063i	$-0.723202\pi$
$439$	−27.0344			−1.29028			−0.645142	+	0.764063i	$0.723202\pi$
$440$		−	5.32624i		−	0.253918i
$441$	4.42705	−	3.21644i	0.210812	−	0.153164i
$442$	−0.159002	+	0.218847i	−0.00756294	+	0.0104095i
$443$	20.5397	−	28.2705i	0.975872	−	1.34317i	0.0368479	−	0.999321i	$-0.488268\pi$
$443$	20.5397	−	28.2705i	0.975872	−	1.34317i	0.939024	−	0.343852i	$-0.111732\pi$
$444$	−3.35410	−	10.3229i	−0.159179	−	0.489901i
$445$	−4.14590	+	3.01217i	−0.196534	+	0.142791i
$446$	8.00000	+	24.6215i	0.378811	+	1.16586i
$447$	13.9026	+	4.51722i	0.657569	+	0.213657i
$448$	−0.726543	+	1.00000i	−0.0343259	+	0.0472456i
$449$	2.47214	−	7.60845i	0.116667	−	0.359065i	−0.875624	−	0.482994i	$-0.839549\pi$
$449$	2.47214	−	7.60845i	0.116667	−	0.359065i	0.992291	+	0.123929i	$0.0395494\pi$
$450$	−4.75528	−	1.54508i	−0.224166	−	0.0728360i
$451$	−14.8541	−	10.7921i	−0.699452	−	0.508182i
$452$	−8.05748	−	2.61803i	−0.378992	−	0.123142i
$453$	17.0130	−	5.52786i	0.799341	−	0.259722i
$454$	4.61803	−	3.35520i	0.216735	−	0.157467i
$455$	−0.124612	−	0.383516i	−0.00584189	−	0.0179795i
$456$	3.61803	+	2.62866i	0.169430	+	0.123098i
$457$	15.6659	−	21.5623i	0.732821	−	1.00864i	−0.266178	−	0.963924i	$-0.585761\pi$
$457$	15.6659	−	21.5623i	0.732821	−	1.00864i	0.999000	−	0.0447183i	$-0.0142390\pi$
$458$	−15.0454	−	20.7082i	−0.703025	−	0.967631i
$459$	−1.85410			−0.0865421
$460$		−	13.0902i		−	0.610332i
$461$	10.5623	−	7.67396i	0.491936	−	0.357412i	−0.313993	−	0.949425i	$-0.601667\pi$
$461$	10.5623	−	7.67396i	0.491936	−	0.357412i	0.805928	+	0.592013i	$0.201667\pi$
$462$	2.80017	+	0.909830i	0.130276	+	0.0423291i
$463$	−24.0664	+	7.81966i	−1.11846	+	0.363410i	−0.809181	−	0.587560i	$-0.800089\pi$
$463$	−24.0664	+	7.81966i	−1.11846	+	0.363410i	−0.309282	+	0.950970i	$0.600089\pi$
$464$	−6.85410			−0.318194
$465$	1.12257	+	12.3992i	0.0520579	+	0.574999i
$466$	−12.6180			−0.584519
$467$	25.1765	−	8.18034i	1.16503	−	0.378541i	0.338244	−	0.941058i	$-0.390167\pi$
$467$	25.1765	−	8.18034i	1.16503	−	0.378541i	0.826785	+	0.562517i	$0.190167\pi$
$468$	−0.138757	−	0.0450850i	−0.00641406	−	0.00208405i
$469$	−8.00000	+	5.81234i	−0.369406	+	0.268389i
$470$	−6.90983			−0.318727
$471$	17.0902			0.787473
$472$	1.84911	+	2.54508i	0.0851123	+	0.117147i
$473$	5.60034	−	7.70820i	0.257504	−	0.354424i
$474$	−4.92705	−	3.57971i	−0.226307	−	0.164422i
$475$	−6.90983	−	21.2663i	−0.317045	−	0.975763i
$476$	1.85410	−	1.34708i	0.0849826	−	0.0617435i
$477$	−7.33094	+	2.38197i	−0.335661	+	0.109063i
$478$	−14.3844	−	4.67376i	−0.657925	−	0.213773i
$479$	14.4721	+	10.5146i	0.661249	+	0.480425i	0.867084	−	0.498161i	$-0.165991\pi$
$479$	14.4721	+	10.5146i	0.661249	+	0.480425i	−0.205836	+	0.978587i	$0.565991\pi$
$480$	0.690983	−	2.12663i	0.0315389	−	0.0970668i
$481$	−0.489357	+	1.50609i	−0.0223128	+	0.0686716i
$482$	4.33901	−	5.97214i	0.197637	−	0.272023i
$483$	6.88191	+	2.23607i	0.313138	+	0.101745i
$484$	1.64590	+	5.06555i	0.0748135	+	0.230252i
$485$	−1.24108	−	1.70820i	−0.0563547	−	0.0775655i
$486$	−0.309017	−	0.951057i	−0.0140173	−	0.0431408i
$487$	−5.32282	+	7.32624i	−0.241200	+	0.331984i	−0.912405	−	0.409288i	$-0.865777\pi$
$487$	−5.32282	+	7.32624i	−0.241200	+	0.331984i	0.671205	+	0.741272i	$0.265777\pi$
$488$	−1.62460	+	2.23607i	−0.0735421	+	0.101222i
$489$	−10.5451	+	7.66145i	−0.476865	+	0.346463i
$490$		−	12.2361i		−	0.552769i
$491$	−10.0344			−0.452848			−0.226424	−	0.974029i	$-0.572703\pi$
$491$	−10.0344			−0.452848			−0.226424	+	0.974029i	$0.572703\pi$
$492$	−4.53077	−	6.23607i	−0.204263	−	0.281144i
$493$	12.0862	+	3.92705i	0.544336	+	0.176865i
$494$	−0.201626	−	0.620541i	−0.00907159	−	0.0279195i
$495$	−5.32624			−0.239397
$496$	−5.54508	+	0.502029i	−0.248982	+	0.0225417i
$497$		−	4.94427i		−	0.221781i
$498$	2.62866	−	0.854102i	0.117793	−	0.0382732i
$499$	−1.18034	+	3.63271i	−0.0528393	+	0.162623i	−0.973994	−	0.226574i	$-0.927247\pi$
$499$	−1.18034	+	3.63271i	−0.0528393	+	0.162623i	0.921155	+	0.389197i	$0.127247\pi$
$500$	−9.04508	+	6.57164i	−0.404508	+	0.293893i
$501$	−14.0902			−0.629502
$502$		−	13.0902i		−	0.584243i
$503$	−12.1190	−	16.6803i	−0.540358	−	0.743740i	0.448306	−	0.893880i	$-0.352027\pi$
$503$	−12.1190	−	16.6803i	−0.540358	−	0.743740i	−0.988665	+	0.150140i	$0.952027\pi$
$504$	1.00000	+	0.726543i	0.0445435	+	0.0323628i
$505$	13.7812	+	10.0126i	0.613253	+	0.445555i
$506$	−4.30902	−	13.2618i	−0.191559	−	0.589559i
$507$	−7.62870	−	10.5000i	−0.338802	−	0.466321i
$508$	−15.9434	+	5.18034i	−0.707376	+	0.229840i
$509$	1.59017	−	4.89404i	0.0704830	−	0.216925i	−0.909610	−	0.415463i	$-0.863620\pi$
$509$	1.59017	−	4.89404i	0.0704830	−	0.216925i	0.980093	+	0.198539i	$0.0636195\pi$
$510$	−2.43690	+	3.35410i	−0.107908	+	0.148522i
$511$	1.12461	−	3.46120i	0.0497499	−	0.153114i
$512$	0.951057	+	0.309017i	0.0420312	+	0.0136568i
$513$	2.62866	−	3.61803i	0.116058	−	0.159740i
$514$	4.20820	−	12.9515i	0.185616	−	0.571267i
$515$	17.3965	−	5.65248i	0.766583	−	0.249078i
$516$	3.23607	−	2.35114i	0.142460	−	0.103503i
$517$	−7.00042	+	2.27458i	−0.307878	+	0.100036i
$518$	7.88597	−	10.8541i	0.346489	−	0.476902i
$519$	9.85410	+	7.15942i	0.432547	+	0.314264i
$520$	−0.263932	+	0.191758i	−0.0115742	+	0.00840914i
$521$	−24.4721			−1.07214			−0.536072	−	0.844172i	$-0.680092\pi$
$521$	−24.4721			−1.07214			−0.536072	+	0.844172i	$0.680092\pi$
$522$			6.85410i			0.299996i
$523$	−4.44501	−	6.11803i	−0.194367	−	0.267523i	0.700699	−	0.713457i	$-0.252872\pi$
$523$	−4.44501	−	6.11803i	−0.194367	−	0.267523i	−0.895066	+	0.445934i	$0.852872\pi$
$524$	1.79180	−	5.51458i	0.0782750	−	0.240906i
$525$	−1.90983	−	5.87785i	−0.0833518	−	0.256531i
$526$	6.67376			0.290990
$527$	10.0656	+	2.29180i	0.438464	+	0.0998322i
$528$		−	2.38197i		−	0.103662i
$529$	−3.48278	−	10.7189i	−0.151425	−	0.466039i
$530$	−5.32624	+	16.3925i	−0.231357	+	0.712044i
$531$	2.54508	−	1.84911i	0.110447	−	0.0802446i
$532$			5.52786i			0.239663i
$533$			1.12461i			0.0487123i
$534$	−1.85410	+	1.34708i	−0.0802348	+	0.0582940i
$535$	−20.6457	+	28.4164i	−0.892593	+	1.22855i
$536$	6.47214	+	4.70228i	0.279554	+	0.203108i
$537$	−19.5029	+	6.33688i	−0.841613	+	0.273457i
$538$	5.89810	+	8.11803i	0.254285	+	0.349993i
$539$	−4.02786	−	12.3965i	−0.173492	−	0.533955i
$540$	−2.12663	−	0.690983i	−0.0915155	−	0.0297352i
$541$	36.1803	+	26.2866i	1.55551	+	1.13015i	0.939570	+	0.342358i	$0.111226\pi$
$541$	36.1803	+	26.2866i	1.55551	+	1.13015i	0.615945	+	0.787789i	$0.288774\pi$
$542$	19.0539	+	6.19098i	0.818435	+	0.265925i
$543$	−12.5882	−	4.09017i	−0.540213	−	0.175526i
$544$	−1.50000	−	1.08981i	−0.0643120	−	0.0467254i
$545$	8.61803	−	26.5236i	0.369156	−	1.13615i
$546$	−0.0557281	−	0.171513i	−0.00238494	−	0.00734010i
$547$	6.58415	+	9.06231i	0.281518	+	0.387476i	0.926236	−	0.376944i	$-0.123025\pi$
$547$	6.58415	+	9.06231i	0.281518	+	0.387476i	−0.644718	+	0.764421i	$0.723025\pi$
$548$	8.95554	−	2.90983i	0.382562	−	0.124302i
$549$	2.23607	+	1.62460i	0.0954331	+	0.0693362i
$550$	−7.00042	+	9.63525i	−0.298499	+	0.410849i
$551$	−24.7984	+	18.0171i	−1.05645	+	0.767553i
$552$		−	5.85410i		−	0.249167i
$553$		−	7.52786i		−	0.320117i
$554$	−2.88197	+	2.09387i	−0.122443	+	0.0889600i
$555$	−7.50000	+	23.0826i	−0.318357	+	0.979803i
$556$	0.909830	+	2.80017i	0.0385854	+	0.118754i
$557$		−	8.65248i		−	0.366617i	−0.983055	−	0.183309i	$-0.941319\pi$
$557$		−	8.65248i		−	0.366617i	0.983055	−	0.183309i	$-0.0586808\pi$
$558$	0.502029	+	5.54508i	0.0212526	+	0.234742i
$559$	−0.583592			−0.0246833
$560$	2.62866	−	0.854102i	0.111081	−	0.0360924i
$561$	−1.36475	+	4.20025i	−0.0576196	+	0.177335i
$562$	7.26543	+	10.0000i	0.306473	+	0.421825i
$563$		−	10.0000i		−	0.421450i	−0.977545	−	0.210725i	$-0.932418\pi$
$563$		−	10.0000i		−	0.421450i	0.977545	−	0.210725i	$-0.0675824\pi$
$564$	−3.09017			−0.130120
$565$	11.1352	+	15.3262i	0.468460	+	0.644780i
$566$	−8.35410	−	6.06961i	−0.351149	−	0.255125i
$567$	0.726543	−	1.00000i	0.0305119	−	0.0419961i
$568$	−3.80423	+	1.23607i	−0.159622	+	0.0518643i
$569$	0.618034	−	0.449028i	0.0259093	−	0.0188242i	−0.574755	−	0.818325i	$-0.694903\pi$
$569$	0.618034	−	0.449028i	0.0259093	−	0.0188242i	0.600665	+	0.799501i	$0.294903\pi$
$570$	−3.09017	−	9.51057i	−0.129433	−	0.398354i
$571$	8.65248	−	26.6296i	0.362095	−	1.11441i	−0.589685	−	0.807633i	$-0.700748\pi$
$571$	8.65248	−	26.6296i	0.362095	−	1.11441i	0.951780	−	0.306780i	$-0.0992517\pi$
$572$	−0.204270	+	0.281153i	−0.00854094	+	0.0117556i
$573$	−6.88191	−	2.23607i	−0.287496	−	0.0934131i
$574$	2.94427	−	9.06154i	0.122892	−	0.378221i
$575$	−17.2048	+	23.6803i	−0.717489	+	0.987538i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	−18.7436	+	6.09017i	−0.780307	+	0.253537i	−0.671971	−	0.740577i	$-0.734552\pi$
$577$	−18.7436	+	6.09017i	−0.780307	+	0.253537i	−0.108336	+	0.994114i	$0.534552\pi$
$578$	−7.97172	−	10.9721i	−0.331580	−	0.456381i
$579$	5.47214	+	16.8415i	0.227414	+	0.699909i
$580$	12.3992	+	9.00854i	0.514848	+	0.374059i
$581$	2.76393	+	2.00811i	0.114667	+	0.0833106i
$582$	−0.555029	−	0.763932i	−0.0230067	−	0.0316660i
$583$			18.3607i			0.760422i
$584$	−2.94427			−0.121835
$585$	0.191758	+	0.263932i	0.00792821	+	0.0109122i
$586$	2.09017	−	6.43288i	0.0863441	−	0.265740i
$587$	−24.0009	+	7.79837i	−0.990624	+	0.321873i	−0.759113	−	0.650959i	$-0.774367\pi$
$587$	−24.0009	+	7.79837i	−0.990624	+	0.321873i	−0.231511	+	0.972832i	$0.574367\pi$
$588$		−	5.47214i		−	0.225667i
$589$	−18.7426	+	16.3925i	−0.772277	+	0.675440i
$590$		−	7.03444i		−	0.289603i
$591$	−2.14590	−	6.60440i	−0.0882705	−	0.271669i
$592$	−10.3229	−	3.35410i	−0.424267	−	0.137853i
$593$	−1.64484	−	2.26393i	−0.0675456	−	0.0929685i	0.773908	−	0.633298i	$-0.218299\pi$
$593$	−1.64484	−	2.26393i	−0.0675456	−	0.0929685i	−0.841453	+	0.540330i	$0.818299\pi$
$594$	−2.38197			−0.0977332
$595$	−5.12461			−0.210089
$596$	11.8262	−	8.59226i	0.484422	−	0.351953i
$597$	−13.8823	+	19.1074i	−0.568166	+	0.782013i
$598$	−0.502029	+	0.690983i	−0.0205295	+	0.0282564i
$599$	−10.7984	−	33.2340i	−0.441210	−	1.35790i	−0.886588	−	0.462561i	$-0.846931\pi$
$599$	−10.7984	−	33.2340i	−0.441210	−	1.35790i	0.445378	−	0.895343i	$-0.353069\pi$
$600$	−4.04508	+	2.93893i	−0.165140	+	0.119981i
$601$	7.91641	+	24.3642i	0.322917	+	0.993836i	0.972372	+	0.233436i	$0.0749971\pi$
$601$	7.91641	+	24.3642i	0.322917	+	0.993836i	−0.649455	+	0.760400i	$0.725003\pi$
$602$	4.70228	+	1.52786i	0.191651	+	0.0622711i
$603$	4.70228	−	6.47214i	0.191492	−	0.263566i
$604$	5.52786	−	17.0130i	0.224926	−	0.692250i
$605$	3.68034	−	11.3269i	0.149627	−	0.460505i
$606$	6.16312	+	4.47777i	0.250360	+	0.181897i
$607$	10.5801	+	3.43769i	0.429434	+	0.139532i	0.515756	−	0.856736i	$-0.327511\pi$
$607$	10.5801	+	3.43769i	0.429434	+	0.139532i	−0.0863214	+	0.996267i	$0.527511\pi$
$608$	4.25325	−	1.38197i	0.172492	−	0.0560461i
$609$	−6.85410	+	4.97980i	−0.277742	+	0.201792i
$610$	5.87785	−	1.90983i	0.237987	−	0.0773268i
$611$	0.364745	+	0.265003i	0.0147560	+	0.0107209i
$612$	−1.08981	+	1.50000i	−0.0440531	+	0.0606339i
$613$	22.3888	+	30.8156i	0.904277	+	1.24463i	0.969084	+	0.246732i	$0.0793568\pi$
$613$	22.3888	+	30.8156i	0.904277	+	1.24463i	−0.0648069	+	0.997898i	$0.520643\pi$
$614$	7.32624			0.295663
$615$			17.2361i			0.695025i
$616$	2.38197	−	1.73060i	0.0959721	−	0.0697278i
$617$	−9.09429	−	2.95492i	−0.366122	−	0.118960i	0.120177	−	0.992752i	$-0.461654\pi$
$617$	−9.09429	−	2.95492i	−0.366122	−	0.118960i	−0.486300	+	0.873792i	$0.661654\pi$
$618$	7.77997	−	2.52786i	0.312956	−	0.101686i
$619$	−6.65248			−0.267386			−0.133693	−	0.991023i	$-0.542684\pi$
$619$	−6.65248			−0.267386			−0.133693	+	0.991023i	$0.542684\pi$
$620$	10.6910	+	6.37988i	0.429360	+	0.256222i
$621$	−5.85410			−0.234917
$622$	−12.7598	+	4.14590i	−0.511620	+	0.166235i
$623$	−2.69417	−	0.875388i	−0.107940	−	0.0350717i
$624$	−0.118034	+	0.0857567i	−0.00472514	+	0.00343302i
$625$	25.0000			1.00000
$626$	−5.23607			−0.209275
$627$	−6.26137	−	8.61803i	−0.250055	−	0.344171i
$628$	10.0453	−	13.8262i	0.400853	−	0.551727i
$629$	16.2812	+	11.8290i	0.649172	+	0.471651i
$630$	−0.854102	−	2.62866i	−0.0340282	−	0.104728i
$631$	23.2082	−	16.8617i	0.923904	−	0.671256i	−0.0205887	−	0.999788i	$-0.506554\pi$
$631$	23.2082	−	16.8617i	0.923904	−	0.671256i	0.944493	+	0.328532i	$0.106554\pi$
$632$	−5.79210	+	1.88197i	−0.230397	+	0.0748606i
$633$	12.0332	+	3.90983i	0.478278	+	0.155402i
$634$	−14.3262	−	10.4086i	−0.568968	−	0.413379i
$635$	35.6506	+	11.5836i	1.41475	+	0.459681i
$636$	−2.38197	+	7.33094i	−0.0944511	+	0.290691i
$637$	−0.469272	+	0.645898i	−0.0185932	+	0.0255914i
$638$	15.5272	+	5.04508i	0.614727	+	0.199737i
$639$	1.23607	+	3.80423i	0.0488981	+	0.150493i
$640$	−1.31433	−	1.80902i	−0.0519534	−	0.0715077i
$641$	3.88854	+	11.9677i	0.153588	+	0.472696i	0.998015	−	0.0629748i	$-0.0200588\pi$
$641$	3.88854	+	11.9677i	0.153588	+	0.472696i	−0.844427	+	0.535671i	$0.820059\pi$
$642$	−9.23305	+	12.7082i	−0.364399	+	0.501553i
$643$	−6.65740	+	9.16312i	−0.262542	+	0.361358i	−0.919854	−	0.392260i	$-0.871693\pi$
$643$	−6.65740	+	9.16312i	−0.262542	+	0.361358i	0.657312	+	0.753618i	$0.271693\pi$
$644$	5.85410	−	4.25325i	0.230684	−	0.167602i
$645$	−8.94427			−0.352180
$646$	−8.29180			−0.326236
$647$	−13.4005	−	18.4443i	−0.526830	−	0.725119i	0.459813	−	0.888016i	$-0.347916\pi$
$647$	−13.4005	−	18.4443i	−0.526830	−	0.725119i	−0.986643	+	0.162896i	$0.947916\pi$
$648$	−0.951057	−	0.309017i	−0.0373610	−	0.0121393i
$649$	−2.31559	−	7.12667i	−0.0908950	−	0.279746i
$650$	0.729490			0.0286130
$651$	−5.18034	+	4.53077i	−0.203034	+	0.177575i
$652$			13.0344i			0.510468i
$653$	43.3651	−	14.0902i	1.69701	−	0.551391i	0.708920	−	0.705289i	$-0.249183\pi$
$653$	43.3651	−	14.0902i	1.69701	−	0.551391i	0.988087	+	0.153898i	$0.0491827\pi$
$654$	3.85410	−	11.8617i	0.150707	−	0.463829i
$655$	−10.4894	+	7.62096i	−0.409853	+	0.297776i
$656$	−7.70820			−0.300955
$657$			2.94427i			0.114867i
$658$	−2.24514	−	3.09017i	−0.0875247	−	0.120467i
$659$	12.8262	+	9.31881i	0.499639	+	0.363009i	0.808879	−	0.587975i	$-0.200075\pi$
$659$	12.8262	+	9.31881i	0.499639	+	0.363009i	−0.309240	+	0.950984i	$0.600075\pi$
$660$	−3.13068	+	4.30902i	−0.121862	+	0.167728i
$661$	−8.70820	−	26.8011i	−0.338710	−	1.04244i	−0.964866	−	0.262744i	$-0.915373\pi$
$661$	−8.70820	−	26.8011i	−0.338710	−	1.04244i	0.626156	−	0.779698i	$-0.284627\pi$
$662$	−7.77997	−	10.7082i	−0.302377	−	0.416186i
$663$	0.257270	−	0.0835921i	0.00999154	−	0.00324645i
$664$	0.854102	−	2.62866i	0.0331456	−	0.102012i
$665$	7.26543	−	10.0000i	0.281741	−	0.387783i
$666$	−3.35410	+	10.3229i	−0.129969	+	0.400003i
$667$	38.1608	+	12.3992i	1.47759	+	0.480098i
$668$	−8.28199	+	11.3992i	−0.320440	+	0.441048i
$669$	8.00000	−	24.6215i	0.309298	−	0.951921i
$670$	−5.52786	−	17.0130i	−0.213560	−	0.657270i
$671$	5.32624	−	3.86974i	0.205617	−	0.149390i
$672$	1.17557	−	0.381966i	0.0453486	−	0.0147347i
$673$	−25.7970	+	35.5066i	−0.994403	+	1.36868i	−0.0657056	+	0.997839i	$0.520930\pi$
$673$	−25.7970	+	35.5066i	−0.994403	+	1.36868i	−0.928697	+	0.370839i	$0.879070\pi$
$674$	7.70820	+	5.60034i	0.296909	+	0.215717i
$675$	2.93893	+	4.04508i	0.113119	+	0.155695i
$676$	−12.9787			−0.499181
$677$		−	20.9443i		−	0.804954i	−0.915430	−	0.402477i	$-0.868149\pi$
$677$		−	20.9443i		−	0.804954i	0.915430	−	0.402477i	$-0.131851\pi$
$678$	4.97980	+	6.85410i	0.191248	+	0.263230i
$679$	0.360680	−	1.11006i	0.0138416	−	0.0426001i
$680$	1.28115	+	3.94298i	0.0491300	+	0.151207i
$681$	−5.70820			−0.218739
$682$	12.9313	+	2.94427i	0.495164	+	0.112742i
$683$		−	8.58359i		−	0.328442i	−0.986424	−	0.164221i	$-0.947489\pi$
$683$		−	8.58359i		−	0.328442i	0.986424	−	0.164221i	$-0.0525110\pi$
$684$	−1.38197	−	4.25325i	−0.0528408	−	0.162627i
$685$	−20.0252	−	6.50658i	−0.765123	−	0.248604i
$686$	12.4721	−	9.06154i	0.476188	−	0.345971i
$687$			25.5967i			0.976577i
$688$		−	4.00000i		−	0.152499i
$689$	0.909830	−	0.661030i	0.0346618	−	0.0251832i
$690$	−7.69421	+	10.5902i	−0.292914	+	0.403161i
$691$	7.76393	+	5.64083i	0.295354	+	0.214587i	0.725587	−	0.688131i	$-0.241569\pi$
$691$	7.76393	+	5.64083i	0.295354	+	0.214587i	−0.430233	+	0.902718i	$0.641569\pi$
$692$	11.5842	−	3.76393i	0.440365	−	0.143083i
$693$	−1.73060	−	2.38197i	−0.0657400	−	0.0904834i
$694$	2.47214	+	7.60845i	0.0938410	+	0.288813i
$695$	2.03444	−	6.26137i	0.0771708	−	0.237507i
$696$	5.54508	+	4.02874i	0.210186	+	0.152709i
$697$	13.5923	+	4.41641i	0.514845	+	0.167283i
$698$	−9.23305	−	3.00000i	−0.349476	−	0.113552i
$699$	10.2082	+	7.41669i	0.386110	+	0.280525i
$700$	−5.87785	−	1.90983i	−0.222162	−	0.0721848i
$701$	3.17376	+	9.76784i	0.119871	+	0.368926i	0.992932	−	0.118686i	$-0.0378681\pi$
$701$	3.17376	+	9.76784i	0.119871	+	0.368926i	−0.873061	+	0.487612i	$0.837868\pi$
$702$	0.0857567	+	0.118034i	0.00323668	+	0.00445491i
$703$	−46.1653	+	15.0000i	−1.74116	+	0.565736i
$704$	−1.92705	−	1.40008i	−0.0726285	−	0.0527677i
$705$	5.59017	+	4.06150i	0.210538	+	0.152965i
$706$	−21.4894	+	15.6129i	−0.808763	+	0.587600i
$707$			9.41641i			0.354140i
$708$		−	3.14590i		−	0.118230i
$709$	31.2705	−	22.7194i	1.17439	−	0.853243i	0.182861	−	0.983139i	$-0.441464\pi$
$709$	31.2705	−	22.7194i	1.17439	−	0.853243i	0.991528	+	0.129895i	$0.0414642\pi$
$710$	8.50651	+	2.76393i	0.319244	+	0.103729i
$711$	1.88197	+	5.79210i	0.0705792	+	0.217221i
$712$			2.29180i			0.0858887i
$713$	31.7809	+	7.23607i	1.19020	+	0.270993i
$714$	−2.29180			−0.0857683
$715$	0.739054	−	0.240133i	0.0276391	−	0.00898048i
$716$	−6.33688	+	19.5029i	−0.236820	+	0.728858i
$717$	8.89002	+	12.2361i	0.332004	+	0.456964i
$718$			30.1803i			1.12632i
$719$	−3.88854			−0.145018			−0.0725091	−	0.997368i	$-0.523101\pi$
$719$	−3.88854			−0.145018			−0.0725091	+	0.997368i	$0.523101\pi$
$720$	−1.80902	+	1.31433i	−0.0674181	+	0.0489821i
$721$	8.18034	+	5.94336i	0.304652	+	0.221342i
$722$	0.587785	−	0.809017i	0.0218751	−	0.0301085i
$723$	−7.02067	+	2.28115i	−0.261101	+	0.0848370i
$724$	−10.7082	+	7.77997i	−0.397967	+	0.289140i
$725$	−10.5902	−	32.5932i	−0.393309	−	1.21048i
$726$	1.64590	−	5.06555i	0.0610850	−	0.188000i
$727$	21.3723	−	29.4164i	0.792654	−	1.09099i	−0.201119	−	0.979567i	$-0.564458\pi$
$727$	21.3723	−	29.4164i	0.792654	−	1.09099i	0.993773	−	0.111427i	$-0.0355422\pi$
$728$	−0.171513	−	0.0557281i	−0.00635671	−	0.00206542i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	5.32624	+	3.86974i	0.197133	+	0.143225i
$731$	−2.29180	+	7.05342i	−0.0847651	+	0.260880i
$732$	2.62866	−	0.854102i	0.0971579	−	0.0315685i
$733$	−23.7109	−	32.6353i	−0.875782	−	1.20541i	−0.977571	−	0.210605i	$-0.932457\pi$
$733$	−23.7109	−	32.6353i	−0.875782	−	1.20541i	0.101789	−	0.994806i	$-0.467543\pi$
$734$	6.41641	+	19.7477i	0.236834	+	0.728900i
$735$	−7.19218	+	9.89919i	−0.265288	+	0.365137i
$736$	−4.73607	−	3.44095i	−0.174574	−	0.126835i
$737$	−11.2007	−	15.4164i	−0.412582	−	0.567871i
$738$			7.70820i			0.283743i
$739$	18.4721			0.679509			0.339754	−	0.940514i	$-0.389656\pi$
$739$	18.4721			0.679509			0.339754	+	0.940514i	$0.389656\pi$
$740$	14.2658	+	19.6353i	0.524423	+	0.721806i
$741$	−0.201626	+	0.620541i	−0.00740692	+	0.0227962i
$742$	−9.06154	+	2.94427i	−0.332659	+	0.108088i
$743$		−	11.9787i		−	0.439456i	−0.975561	−	0.219728i	$-0.929483\pi$
$743$		−	11.9787i		−	0.439456i	0.975561	−	0.219728i	$-0.0705170\pi$
$744$	4.78115	+	2.85317i	0.175286	+	0.104602i
$745$	−32.6869			−1.19756
$746$	−11.7533	−	36.1729i	−0.430318	−	1.32438i
$747$	−2.62866	−	0.854102i	−0.0961775	−	0.0312500i
$748$	2.59590	+	3.57295i	0.0949155	+	0.130640i
$749$	−19.4164			−0.709460
$750$	11.1803			0.408248
$751$	−14.3090	+	10.3961i	−0.522143	+	0.379359i	−0.817411	−	0.576055i	$-0.804591\pi$
$751$	−14.3090	+	10.3961i	−0.522143	+	0.379359i	0.295267	+	0.955415i	$0.404591\pi$
$752$	−1.81636	+	2.50000i	−0.0662357	+	0.0911656i
$753$	−7.69421	+	10.5902i	−0.280393	+	0.385927i
$754$	−0.309017	−	0.951057i	−0.0112537	−	0.0346354i
$755$	−32.3607	+	23.5114i	−1.17773	+	0.855668i
$756$	−0.381966	−	1.17557i	−0.0138920	−	0.0427551i
$757$	−44.4347	−	14.4377i	−1.61500	−	0.524747i	−0.644249	−	0.764816i	$-0.722830\pi$
$757$	−44.4347	−	14.4377i	−1.61500	−	0.524747i	−0.970756	+	0.240069i	$0.922830\pi$
$758$	−4.25325	+	5.85410i	−0.154485	+	0.212631i
$759$	−4.30902	+	13.2618i	−0.156407	+	0.481373i
$760$	−9.51057	−	3.09017i	−0.344984	−	0.112092i
$761$	31.7426	+	23.0624i	1.15067	+	0.836011i	0.988570	−	0.150764i	$-0.0481732\pi$
$761$	31.7426	+	23.0624i	1.15067	+	0.836011i	0.162100	+	0.986774i	$0.448173\pi$
$762$	15.9434	+	5.18034i	0.577570	+	0.187664i
$763$	14.6619	−	4.76393i	0.530796	−	0.172466i
$764$	−5.85410	+	4.25325i	−0.211794	+	0.153877i
$765$	3.94298	−	1.28115i	0.142559	−	0.0463202i
$766$	27.2533	+	19.8007i	0.984701	+	0.715427i
$767$	−0.269782	+	0.371323i	−0.00974126	+	0.0134077i
$768$	−0.587785	−	0.809017i	−0.0212099	−	0.0291929i
$769$	36.0902			1.30144			0.650722	−	0.759316i	$-0.274466\pi$
$769$	36.0902			1.30144			0.650722	+	0.759316i	$0.274466\pi$
$770$	−6.58359			−0.237256
$771$	−11.0172	+	8.00448i	−0.396776	+	0.288274i
$772$	16.8415	+	5.47214i	0.606139	+	0.196946i
$773$	−30.2218	+	9.81966i	−1.08700	+	0.353189i	−0.797088	−	0.603864i	$-0.793627\pi$
$773$	−30.2218	+	9.81966i	−1.08700	+	0.353189i	−0.289915	+	0.957052i	$0.593627\pi$
$774$	−4.00000			−0.143777
$775$	−10.9549	−	25.5928i	−0.393512	−	0.919319i
$776$	−0.944272			−0.0338974
$777$	−12.7598	+	4.14590i	−0.457754	+	0.148733i
$778$	−13.3148	−	4.32624i	−0.477358	−	0.155103i
$779$	−27.8885	+	20.2622i	−0.999211	+	0.725969i
$780$	0.326238			0.0116812
$781$	9.52786			0.340934
$782$	6.37988	+	8.78115i	0.228144	+	0.314013i
$783$	4.02874	−	5.54508i	0.143975	−	0.198165i
$784$	−4.42705	−	3.21644i	−0.158109	−	0.114873i
$785$	−36.3444	+	11.8090i	−1.29719	+	0.421482i
$786$	−4.69098	+	3.40820i	−0.167322	+	0.121566i
$787$	14.4046	−	4.68034i	0.513469	−	0.166836i	−0.0408105	−	0.999167i	$-0.512994\pi$
$787$	14.4046	−	4.68034i	0.513469	−	0.166836i	0.554279	+	0.832331i	$0.312994\pi$
$788$	−6.60440	−	2.14590i	−0.235272	−	0.0764445i
$789$	−5.39919	−	3.92274i	−0.192216	−	0.139653i
$790$	12.9515	+	4.20820i	0.460794	+	0.149721i
$791$	−3.23607	+	9.95959i	−0.115061	+	0.354122i
$792$	−1.40008	+	1.92705i	−0.0497498	+	0.0684748i
$793$	−0.383516	−	0.124612i	−0.0136190	−	0.00442509i
$794$	−2.04508	−	6.29412i	−0.0725773	−	0.223370i
$795$	13.9443	−	10.1311i	0.494552	−	0.359313i
$796$	7.29837	+	22.4621i	0.258684	+	0.796147i
$797$	14.9394	−	20.5623i	0.529180	−	0.728354i	−0.457825	−	0.889042i	$-0.651371\pi$
$797$	14.9394	−	20.5623i	0.529180	−	0.728354i	0.987005	+	0.160688i	$0.0513713\pi$
$798$	3.24920	−	4.47214i	0.115020	−	0.158312i
$799$	4.63525	−	3.36771i	0.163984	−	0.119141i
$800$			5.00000i			0.176777i
$801$	2.29180			0.0809766
$802$	6.32688	+	8.70820i	0.223410	+	0.307497i
$803$	6.66991	+	2.16718i	0.235376	+	0.0764783i
$804$	−2.47214	−	7.60845i	−0.0871855	−	0.268329i
$805$	−16.1803			−0.570282
$806$	−0.319660	−	0.746787i	−0.0112595	−	0.0263044i
$807$		−	10.0344i		−	0.353229i
$808$	7.24518	−	2.35410i	0.254885	−	0.0828170i
$809$	−4.90983	+	15.1109i	−0.172620	+	0.531271i	−0.999517	−	0.0310833i	$-0.990104\pi$
$809$	−4.90983	+	15.1109i	−0.172620	+	0.531271i	0.826896	+	0.562354i	$0.190104\pi$
$810$	1.31433	+	1.80902i	0.0461808	+	0.0635624i
$811$	−34.3607			−1.20657			−0.603283	−	0.797527i	$-0.706141\pi$
$811$	−34.3607			−1.20657			−0.603283	+	0.797527i	$0.706141\pi$
$812$			8.47214i			0.297314i
$813$	−11.7759	−	16.2082i	−0.413001	−	0.568447i
$814$	20.9164	+	15.1967i	0.733120	+	0.532643i
$815$	17.1315	−	23.5795i	0.600091	−	0.825955i
$816$	0.572949	+	1.76336i	0.0200572	+	0.0617298i
$817$	−10.5146	−	14.4721i	−0.367860	−	0.506316i
$818$	−29.0665	+	9.44427i	−1.01629	+	0.330211i
$819$	−0.0557281	+	0.171513i	−0.00194730	+	0.00599316i
$820$	13.9443	+	10.1311i	0.486955	+	0.353794i
$821$	−13.3926	+	41.2182i	−0.467405	+	1.43853i	0.388527	+	0.921437i	$0.372984\pi$
$821$	−13.3926	+	41.2182i	−0.467405	+	1.43853i	−0.855932	+	0.517088i	$0.827016\pi$
$822$	−8.95554	−	2.90983i	−0.312360	−	0.101492i
$823$	11.2412	−	15.4721i	0.391842	−	0.539325i	−0.566831	−	0.823834i	$-0.691831\pi$
$823$	11.2412	−	15.4721i	0.391842	−	0.539325i	0.958673	+	0.284509i	$0.0918307\pi$
$824$	2.52786	−	7.77997i	0.0880623	−	0.271028i
$825$	11.3269	−	3.68034i	0.394353	−	0.128133i
$826$	3.14590	−	2.28563i	0.109460	−	0.0795272i
$827$	15.2824	−	4.96556i	0.531422	−	0.172669i	−0.0310008	−	0.999519i	$-0.509869\pi$
$827$	15.2824	−	4.96556i	0.531422	−	0.172669i	0.562423	+	0.826850i	$0.309869\pi$
$828$	−3.44095	+	4.73607i	−0.119581	+	0.164590i
$829$	−11.0000	−	7.99197i	−0.382046	−	0.277573i	0.380142	−	0.924928i	$-0.375875\pi$
$829$	−11.0000	−	7.99197i	−0.382046	−	0.277573i	−0.762188	+	0.647355i	$0.775875\pi$
$830$	−5.00000	+	3.63271i	−0.173553	+	0.126093i
$831$	3.56231			0.123575
$832$			0.145898i			0.00505810i
$833$	5.96361	+	8.20820i	0.206627	+	0.284397i
$834$	0.909830	−	2.80017i	0.0315048	−	0.0969619i
$835$	29.9645	−	9.73607i	1.03697	−	0.336931i
$836$	−10.6525			−0.368424
$837$	2.85317	−	4.78115i	0.0986200	−	0.165261i
$838$			38.6180i			1.33404i
$839$	−1.52786	−	4.70228i	−0.0527477	−	0.162341i	0.921212	−	0.389060i	$-0.127200\pi$
$839$	−1.52786	−	4.70228i	−0.0527477	−	0.162341i	−0.973960	+	0.226719i	$0.927200\pi$
$840$	−2.62866	−	0.854102i	−0.0906972	−	0.0294693i
$841$	−14.5451	+	10.5676i	−0.501555	+	0.364401i
$842$			23.1246i			0.796927i
$843$		−	12.3607i		−	0.425724i
$844$	10.2361	−	7.43694i	0.352340	−	0.255990i
$845$	23.4787	+	17.0583i	0.807692	+	0.586823i
$846$	2.50000	+	1.81636i	0.0859518	+	0.0624476i
$847$	6.26137	−	2.03444i	0.215143	−	0.0699042i
$848$	4.53077	+	6.23607i	0.155587	+	0.214147i
$849$	3.19098	+	9.82084i	0.109514	+	0.337050i
$850$	2.86475	−	8.81678i	0.0982599	−	0.302413i
$851$	51.4058	+	37.3485i	1.76217	+	1.28029i
$852$	3.80423	+	1.23607i	0.130331	+	0.0423470i
$853$	28.4459	+	9.24265i	0.973970	+	0.316462i	0.752418	−	0.658686i	$-0.228888\pi$
$853$	28.4459	+	9.24265i	0.973970	+	0.316462i	0.221553	+	0.975148i	$0.428888\pi$
$854$	2.76393	+	2.00811i	0.0945798	+	0.0687163i
$855$	−3.09017	+	9.51057i	−0.105682	+	0.325254i
$856$	4.85410	+	14.9394i	0.165910	+	0.510618i
$857$	−32.0382	−	44.0967i	−1.09440	−	1.50632i	−0.842602	−	0.538537i	$-0.818977\pi$
$857$	−32.0382	−	44.0967i	−1.09440	−	1.50632i	−0.251801	−	0.967779i	$-0.581023\pi$
$858$	0.330515	−	0.107391i	0.0112836	−	0.00366626i
$859$	7.32624	+	5.32282i	0.249968	+	0.181612i	0.705713	−	0.708498i	$-0.250627\pi$
$859$	7.32624	+	5.32282i	0.249968	+	0.181612i	−0.455745	+	0.890111i	$0.650627\pi$
$860$	−5.25731	+	7.23607i	−0.179273	+	0.246748i
$861$	−7.70820	+	5.60034i	−0.262695	+	0.190859i
$862$		−	23.2361i		−	0.791424i
$863$		−	6.83282i		−	0.232592i	−0.993215	−	0.116296i	$-0.962898\pi$
$863$		−	6.83282i		−	0.232592i	0.993215	−	0.116296i	$-0.0371021\pi$
$864$	−0.809017	+	0.587785i	−0.0275233	+	0.0199969i
$865$	−25.9030	−	8.41641i	−0.880730	−	0.286166i
$866$	−3.32624	−	10.2371i	−0.113030	−	0.347871i
$867$			13.5623i			0.460600i
$868$	0.620541	+	6.85410i	0.0210625	+	0.232643i
$869$	14.5066			0.492102
$870$	−4.73607	−	14.5761i	−0.160568	−	0.494177i
$871$	−0.360680	+	1.11006i	−0.0122212	+	0.0376129i
$872$	−7.33094	−	10.0902i	−0.248257	−	0.341696i
$873$			0.944272i			0.0319588i
$874$	−26.1803			−0.885563
$875$	8.12299	+	11.1803i	0.274607	+	0.377964i
$876$	2.38197	+	1.73060i	0.0804792	+	0.0584715i
$877$	3.52671	−	4.85410i	0.119089	−	0.163911i	−0.745311	−	0.666717i	$-0.767699\pi$
$877$	3.52671	−	4.85410i	0.119089	−	0.163911i	0.864399	+	0.502806i	$0.167699\pi$
$878$	25.7113	−	8.35410i	0.867714	−	0.281937i
$879$	−5.47214	+	3.97574i	−0.184571	+	0.134098i
$880$	1.64590	+	5.06555i	0.0554832	+	0.170760i
$881$	−7.18034	+	22.0988i	−0.241912	+	0.744528i	0.754217	+	0.656625i	$0.228017\pi$
$881$	−7.18034	+	22.0988i	−0.241912	+	0.744528i	−0.996129	+	0.0879030i	$0.971983\pi$
$882$	−3.21644	+	4.42705i	−0.108303	+	0.149067i
$883$	−35.5524	−	11.5517i	−1.19643	−	0.388744i	−0.357985	−	0.933727i	$-0.616536\pi$
$883$	−35.5524	−	11.5517i	−1.19643	−	0.388744i	−0.838447	+	0.544983i	$0.816536\pi$
$884$	0.0835921	−	0.257270i	0.00281151	−	0.00865293i
$885$	−4.13474	+	5.69098i	−0.138988	+	0.191300i
$886$	−10.7984	+	33.2340i	−0.362778	+	1.11652i
$887$	−34.2178	+	11.1180i	−1.14892	+	0.373307i	−0.820737	−	0.571307i	$-0.806437\pi$
$887$	−34.2178	+	11.1180i	−1.14892	+	0.373307i	−0.328184	+	0.944614i	$0.606437\pi$
$888$	6.37988	+	8.78115i	0.214095	+	0.294676i
$889$	6.40325	+	19.7072i	0.214758	+	0.660958i
$890$	3.01217	−	4.14590i	0.100968	−	0.138971i
$891$	1.92705	+	1.40008i	0.0645586	+	0.0469046i
$892$	−15.2169	−	20.9443i	−0.509500	−	0.701266i
$893$			13.8197i			0.462457i
$894$	−14.6180			−0.488900
$895$	37.0967	−	26.9524i	1.24001	−	0.900918i
$896$	0.381966	−	1.17557i	0.0127606	−	0.0392731i
$897$	0.812299	−	0.263932i	0.0271219	−	0.00881243i
$898$			8.00000i			0.266963i
$899$	−28.7254	+	25.1235i	−0.958047	+	0.837916i
$900$	5.00000			0.166667
$901$	−4.41641	−	13.5923i	−0.147132	−	0.452825i
$902$	17.4620	+	5.67376i	0.581422	+	0.188916i
$903$	−2.90617	−	4.00000i	−0.0967113	−	0.133112i
$904$	8.47214			0.281779
$905$	29.5967			0.983829
$906$	−14.4721	+	10.5146i	−0.480805	+	0.349325i
$907$	2.26538	−	3.11803i	0.0752209	−	0.103533i	−0.769749	−	0.638347i	$-0.779618\pi$
$907$	2.26538	−	3.11803i	0.0752209	−	0.103533i	0.844970	+	0.534814i	$0.179618\pi$
$908$	−3.35520	+	4.61803i	−0.111346	+	0.153255i
$909$	−2.35410	−	7.24518i	−0.0780806	−	0.240307i
$910$	0.237026	+	0.326238i	0.00785733	+	0.0108147i
$911$	16.5623	+	50.9735i	0.548734	+	1.68883i	0.711943	+	0.702237i	$0.247815\pi$
$911$	16.5623	+	50.9735i	0.548734	+	1.68883i	−0.163209	+	0.986591i	$0.552185\pi$
$912$	−4.25325	−	1.38197i	−0.140839	−	0.0457615i
$913$	−3.86974	+	5.32624i	−0.128070	+	0.176273i
$914$	−8.23607	+	25.3480i	−0.272425	+	0.838438i
$915$	−5.87785	−	1.90983i	−0.194316	−	0.0631370i
$916$	20.7082	+	15.0454i	0.684218	+	0.497114i
$917$	−6.81640	−	2.21478i	−0.225097	−	0.0731385i
$918$	1.76336	−	0.572949i	0.0581994	−	0.0189101i
$919$	19.6803	−	14.2986i	0.649195	−	0.471667i	−0.213802	−	0.976877i	$-0.568585\pi$
$919$	19.6803	−	14.2986i	0.649195	−	0.471667i	0.862997	+	0.505210i	$0.168585\pi$
$920$	4.04508	+	12.4495i	0.133363	+	0.410448i
$921$	−5.92705	−	4.30625i	−0.195303	−	0.141896i
$922$	−7.67396	+	10.5623i	−0.252729	+	0.347851i
$923$	−0.343027	−	0.472136i	−0.0112909	−	0.0155405i
$924$	−2.94427			−0.0968594
$925$		−	54.2705i		−	1.78440i
$926$	20.4721	−	14.8739i	0.672756	−	0.488786i
$927$	−7.77997	−	2.52786i	−0.255528	−	0.0830259i
$928$	6.51864	−	2.11803i	0.213985	−	0.0695279i
$929$	−53.4164			−1.75254			−0.876268	−	0.481824i	$-0.839974\pi$
$929$	−53.4164			−1.75254			−0.876268	+	0.481824i	$0.839974\pi$
$930$	−4.89919	−	11.4454i	−0.160651	−	0.375311i
$931$	−24.4721			−0.802042
$932$	12.0005	−	3.89919i	0.393088	−	0.127722i
$933$	12.7598	+	4.14590i	0.417736	+	0.135731i
$934$	−21.4164	+	15.5599i	−0.700766	+	0.509136i
$935$		−	9.87539i		−	0.322960i
$936$	0.145898			0.00476883
$937$	−3.11817	−	4.29180i	−0.101866	−	0.140207i	0.755041	−	0.655678i	$-0.227617\pi$
$937$	−3.11817	−	4.29180i	−0.101866	−	0.140207i	−0.856907	+	0.515471i	$0.827617\pi$
$938$	5.81234	−	8.00000i	0.189780	−	0.261209i
$939$	4.23607	+	3.07768i	0.138239	+	0.100436i
$940$	6.57164	−	2.13525i	0.214343	−	0.0696443i
$941$	−35.4336	+	25.7440i	−1.15510	+	0.839232i	−0.989151	−	0.146902i	$-0.953070\pi$
$941$	−35.4336	+	25.7440i	−1.15510	+	0.839232i	−0.165952	+	0.986134i	$0.553070\pi$
$942$	−16.2537	+	5.28115i	−0.529575	+	0.172069i
$943$	42.9161	+	13.9443i	1.39754	+	0.454088i
$944$	−2.54508	−	1.84911i	−0.0828355	−	0.0601835i
$945$	−0.854102	+	2.62866i	−0.0277839	+	0.0855102i
$946$	−2.94427	+	9.06154i	−0.0957265	+	0.294616i
$947$	−25.1765	+	34.6525i	−0.818126	+	1.12605i	0.171892	+	0.985116i	$0.445012\pi$
$947$	−25.1765	+	34.6525i	−0.818126	+	1.12605i	−0.990018	+	0.140938i	$0.954988\pi$
$948$	5.79210	+	1.88197i	0.188119	+	0.0611234i
$949$	−0.132742	−	0.408539i	−0.00430900	−	0.0132617i
$950$	13.1433	+	18.0902i	0.426424	+	0.586923i
$951$	5.47214	+	16.8415i	0.177446	+	0.546123i
$952$	−1.34708	+	1.85410i	−0.0436592	+	0.0600918i
$953$	19.8662	−	27.3435i	0.643529	−	0.885742i	−0.355269	−	0.934764i	$-0.615611\pi$
$953$	19.8662	−	27.3435i	0.643529	−	0.885742i	0.998798	+	0.0490227i	$0.0156107\pi$
$954$	6.23607	−	4.53077i	0.201900	−	0.146689i
$955$	16.1803			0.523584
$956$	15.1246			0.489165
$957$	−9.59632	−	13.2082i	−0.310205	−	0.426961i
$958$	−17.0130	−	5.52786i	−0.549666	−	0.178597i
$959$	−3.59675	−	11.0697i	−0.116145	−	0.357458i
$960$			2.23607i			0.0721688i
$961$	−21.3992	+	22.4293i	−0.690296	+	0.723527i
$962$		−	1.58359i		−	0.0510571i
$963$	14.9394	−	4.85410i	0.481415	−	0.156421i
$964$	−2.28115	+	7.02067i	−0.0734710	+	0.226120i
$965$	−23.2744	−	32.0344i	−0.749229	−	1.03123i
$966$	−7.23607			−0.232817
$967$		−	53.5967i		−	1.72356i	−0.507286	−	0.861778i	$-0.669351\pi$
$967$		−	53.5967i		−	1.72356i	0.507286	−	0.861778i	$-0.330649\pi$
$968$	−3.13068	−	4.30902i	−0.100624	−	0.138497i
$969$	6.70820	+	4.87380i	0.215499	+	0.156569i
$970$	1.70820	+	1.24108i	0.0548471	+	0.0398488i
$971$	−12.0836	−	37.1895i	−0.387781	−	1.19347i	−0.934443	−	0.356113i	$-0.884102\pi$
$971$	−12.0836	−	37.1895i	−0.387781	−	1.19347i	0.546662	−	0.837353i	$-0.315898\pi$
$972$	0.587785	+	0.809017i	0.0188532	+	0.0259492i
$973$	3.46120	−	1.12461i	0.110961	−	0.0360534i
$974$	2.79837	−	8.61251i	0.0896657	−	0.275963i
$975$	−0.590170	−	0.428784i	−0.0189006	−	0.0137321i
$976$	0.854102	−	2.62866i	0.0273391	−	0.0841412i
$977$	−0.983813	−	0.319660i	−0.0314750	−	0.0102268i	0.293237	−	0.956040i	$-0.405267\pi$
$977$	−0.983813	−	0.319660i	−0.0314750	−	0.0102268i	−0.324712	+	0.945813i	$0.605267\pi$
$978$	7.66145	−	10.5451i	0.244986	−	0.337195i
$979$	1.68692	−	5.19180i	0.0539141	−	0.165931i
$980$	3.78115	+	11.6372i	0.120785	+	0.371736i
$981$	−10.0902	+	7.33094i	−0.322154	+	0.234059i
$982$	9.54332	−	3.10081i	0.304540	−	0.0989509i
$983$	12.8533	−	17.6910i	0.409955	−	0.564255i	−0.553252	−	0.833014i	$-0.686613\pi$
$983$	12.8533	−	17.6910i	0.409955	−	0.564255i	0.963207	+	0.268759i	$0.0866135\pi$
$984$	6.23607	+	4.53077i	0.198799	+	0.144436i
$985$	9.12705	+	12.5623i	0.290812	+	0.400268i
$986$	−12.7082			−0.404712
$987$			3.81966i			0.121581i
$988$	0.383516	+	0.527864i	0.0122013	+	0.0167936i
$989$	−7.23607	+	22.2703i	−0.230094	+	0.708155i
$990$	5.06555	−	1.64590i	0.160994	−	0.0523101i
$991$	−19.4164			−0.616783			−0.308391	−	0.951260i	$-0.599791\pi$
$991$	−19.4164			−0.616783			−0.308391	+	0.951260i	$0.599791\pi$
$992$	5.11855	−	2.19098i	0.162514	−	0.0695638i
$993$			13.2361i			0.420034i
$994$	1.52786	+	4.70228i	0.0484609	+	0.149147i
$995$	16.3197	−	50.2267i	0.517368	−	1.59229i
$996$	−2.23607	+	1.62460i	−0.0708525	+	0.0514774i
$997$		−	36.1459i		−	1.14475i	−0.819991	−	0.572376i	$-0.806022\pi$
$997$		−	36.1459i		−	1.14475i	0.819991	−	0.572376i	$-0.193978\pi$
$998$		−	3.81966i		−	0.120909i
$999$	8.78115	−	6.37988i	0.277823	−	0.201851i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.z.a.469.1	yes	8
5.4	even	2	inner	930.2.z.a.469.2	yes	8
31.8	even	5	inner	930.2.z.a.349.2	yes	8
155.39	even	10	inner	930.2.z.a.349.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.z.a.349.1	✓	8	155.39	even	10	inner
930.2.z.a.349.2	yes	8	31.8	even	5	inner
930.2.z.a.469.1	yes	8	1.1	even	1	trivial
930.2.z.a.469.2	yes	8	5.4	even	2	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.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 + 0.309017i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.809017 - 0.587785i) q^{4} -2.23607 q^{5} -1.00000 q^{6} +(-0.726543 - 1.00000i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.951057 + 0.309017i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.809017 - 0.587785i) q^{4} -2.23607 q^{5} -1.00000 q^{6} +(-0.726543 - 1.00000i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.809017 + 0.587785i) q^{9} +(2.12663 - 0.690983i) q^{10} +(1.92705 - 1.40008i) q^{11} +(0.951057 - 0.309017i) q^{12} +(-0.138757 - 0.0450850i) q^{13} +(1.00000 + 0.726543i) q^{14} +(-2.12663 - 0.690983i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-1.08981 + 1.50000i) q^{17} +(-0.951057 - 0.309017i) q^{18} +(-1.38197 - 4.25325i) q^{19} +(-1.80902 + 1.31433i) q^{20} +(-0.381966 - 1.17557i) q^{21} +(-1.40008 + 1.92705i) q^{22} +(-3.44095 + 4.73607i) q^{23} +(-0.809017 + 0.587785i) q^{24} +5.00000 q^{25} +0.145898 q^{26} +(0.587785 + 0.809017i) q^{27} +(-1.17557 - 0.381966i) q^{28} +(-2.11803 - 6.51864i) q^{29} +2.23607 q^{30} +(-2.19098 - 5.11855i) q^{31} +1.00000i q^{32} +(2.26538 - 0.736068i) q^{33} +(0.572949 - 1.76336i) q^{34} +(1.62460 + 2.23607i) q^{35} +1.00000 q^{36} -10.8541i q^{37} +(2.62866 + 3.61803i) q^{38} +(-0.118034 - 0.0857567i) q^{39} +(1.31433 - 1.80902i) q^{40} +(-2.38197 - 7.33094i) q^{41} +(0.726543 + 1.00000i) q^{42} +(3.80423 - 1.23607i) q^{43} +(0.736068 - 2.26538i) q^{44} +(-1.80902 - 1.31433i) q^{45} +(1.80902 - 5.56758i) q^{46} +(-2.93893 - 0.954915i) q^{47} +(0.587785 - 0.809017i) q^{48} +(1.69098 - 5.20431i) q^{49} +(-4.75528 + 1.54508i) q^{50} +(-1.50000 + 1.08981i) q^{51} +(-0.138757 + 0.0450850i) q^{52} +(-4.53077 + 6.23607i) q^{53} +(-0.809017 - 0.587785i) q^{54} +(-4.30902 + 3.13068i) q^{55} +1.23607 q^{56} -4.47214i q^{57} +(4.02874 + 5.54508i) q^{58} +(0.972136 - 2.99193i) q^{59} +(-2.12663 + 0.690983i) q^{60} +2.76393 q^{61} +(3.66547 + 4.19098i) q^{62} -1.23607i q^{63} +(-0.309017 - 0.951057i) q^{64} +(0.310271 + 0.100813i) q^{65} +(-1.92705 + 1.40008i) q^{66} -8.00000i q^{67} +1.85410i q^{68} +(-4.73607 + 3.44095i) q^{69} +(-2.23607 - 1.62460i) q^{70} +(3.23607 + 2.35114i) q^{71} +(-0.951057 + 0.309017i) q^{72} +(1.73060 + 2.38197i) q^{73} +(3.35410 + 10.3229i) q^{74} +(4.75528 + 1.54508i) q^{75} +(-3.61803 - 2.62866i) q^{76} +(-2.80017 - 0.909830i) q^{77} +(0.138757 + 0.0450850i) q^{78} +(4.92705 + 3.57971i) q^{79} +(-0.690983 + 2.12663i) q^{80} +(0.309017 + 0.951057i) q^{81} +(4.53077 + 6.23607i) q^{82} +(-2.62866 + 0.854102i) q^{83} +(-1.00000 - 0.726543i) q^{84} +(2.43690 - 3.35410i) q^{85} +(-3.23607 + 2.35114i) q^{86} -6.85410i q^{87} +2.38197i q^{88} +(1.85410 - 1.34708i) q^{89} +(2.12663 + 0.690983i) q^{90} +(0.0557281 + 0.171513i) q^{91} +5.85410i q^{92} +(-0.502029 - 5.54508i) q^{93} +3.09017 q^{94} +(3.09017 + 9.51057i) q^{95} +(-0.309017 + 0.951057i) q^{96} +(0.555029 + 0.763932i) q^{97} +5.47214i q^{98} +2.38197 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} - 8 q^{6} + 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^4 - 8 * q^6 + 2 * q^9	\( 8 q + 2 q^{4} - 8 q^{6} + 2 q^{9} + 2 q^{11} + 8 q^{14} - 2 q^{16} - 20 q^{19} - 10 q^{20} - 12 q^{21} - 2 q^{24} + 40 q^{25} + 28 q^{26} - 8 q^{29} - 22 q^{31} + 18 q^{34} + 8 q^{36} + 8 q^{39} - 28 q^{41} - 12 q^{44} - 10 q^{45} + 10 q^{46} + 18 q^{49} - 12 q^{51} - 2 q^{54} - 30 q^{55} - 8 q^{56} - 28 q^{59} + 40 q^{61} + 2 q^{64} - 2 q^{66} - 20 q^{69} + 8 q^{71} - 20 q^{76} + 26 q^{79} - 10 q^{80} - 2 q^{81} - 8 q^{84} - 8 q^{86} - 12 q^{89} + 72 q^{91} - 20 q^{94} - 20 q^{95} + 2 q^{96} + 28 q^{99}+O(q^{100}) \) 8 * q + 2 * q^4 - 8 * q^6 + 2 * q^9 + 2 * q^11 + 8 * q^14 - 2 * q^16 - 20 * q^19 - 10 * q^20 - 12 * q^21 - 2 * q^24 + 40 * q^25 + 28 * q^26 - 8 * q^29 - 22 * q^31 + 18 * q^34 + 8 * q^36 + 8 * q^39 - 28 * q^41 - 12 * q^44 - 10 * q^45 + 10 * q^46 + 18 * q^49 - 12 * q^51 - 2 * q^54 - 30 * q^55 - 8 * q^56 - 28 * q^59 + 40 * q^61 + 2 * q^64 - 2 * q^66 - 20 * q^69 + 8 * q^71 - 20 * q^76 + 26 * q^79 - 10 * q^80 - 2 * q^81 - 8 * q^84 - 8 * q^86 - 12 * q^89 + 72 * q^91 - 20 * q^94 - 20 * q^95 + 2 * q^96 + 28 * q^99

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