LMFDB - Embedded newform 930.2.br.a.11.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(11,930)]

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([15, 0, 23]))

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

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

chi := DirichletCharacter("930.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.br (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$22$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			11.4
Character	$\chi$	$=$	930.11
Dual form			930.2.br.a.761.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 + 0.309017i) q^{2} +(-1.00587 + 1.41004i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(0.520913 - 1.65186i) q^{6} +(-0.0129897 - 0.123589i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(-0.976447 - 2.83664i) q^{9} +O(q^{10})$	\(q+(-0.951057 + 0.309017i) q^{2} +(-1.00587 + 1.41004i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(0.520913 - 1.65186i) q^{6} +(-0.0129897 - 0.123589i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(-0.976447 - 2.83664i) q^{9} +(-0.669131 + 0.743145i) q^{10} +(-1.53643 - 0.684064i) q^{11} +(0.0150361 + 1.73199i) q^{12} +(0.248847 + 1.17073i) q^{13} +(0.0505449 + 0.113526i) q^{14} +(-0.166088 + 1.72407i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.251322 + 0.111896i) q^{17} +(1.80523 + 2.39607i) q^{18} +(4.89527 + 1.04052i) q^{19} +(0.406737 - 0.913545i) q^{20} +(0.187331 + 0.105998i) q^{21} +(1.67262 + 0.175800i) q^{22} +(2.82606 + 2.05325i) q^{23} +(-0.549513 - 1.64257i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-0.598443 - 1.03653i) q^{26} +(4.98197 + 1.47647i) q^{27} +(-0.0831524 - 0.0923502i) q^{28} +(-2.71830 - 8.36606i) q^{29} +(-0.374808 - 1.69101i) q^{30} +(3.31997 + 4.46965i) q^{31} +1.00000i q^{32} +(2.51001 - 1.47836i) q^{33} +(0.204444 - 0.184082i) q^{34} +(-0.0730437 - 0.100536i) q^{35} +(-2.45730 - 1.72095i) q^{36} +(8.89048 + 5.13292i) q^{37} +(-4.97721 + 0.523126i) q^{38} +(-1.90109 - 0.826721i) q^{39} +(-0.104528 + 0.994522i) q^{40} +(-4.07719 - 3.67112i) q^{41} +(-0.210918 - 0.0429217i) q^{42} +(0.901877 - 4.24300i) q^{43} +(-1.64508 + 0.349673i) q^{44} +(-2.26395 - 1.96838i) q^{45} +(-3.32223 - 1.07946i) q^{46} +(2.81695 + 0.915281i) q^{47} +(1.03020 + 1.39237i) q^{48} +(6.83193 - 1.45217i) q^{49} +(-0.207912 + 0.978148i) q^{50} +(0.0950198 - 0.466929i) q^{51} +(0.889460 + 0.800874i) q^{52} +(-0.920365 + 8.75669i) q^{53} +(-5.19439 + 0.135312i) q^{54} +(-1.67262 + 0.175800i) q^{55} +(0.107620 + 0.0621347i) q^{56} +(-6.39119 + 5.85591i) q^{57} +(5.17051 + 7.11659i) q^{58} +(-0.903708 + 0.813702i) q^{59} +(0.879014 + 1.49243i) q^{60} +3.06126i q^{61} +(-4.53868 - 3.22496i) q^{62} +(-0.337893 + 0.157525i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(0.800874 + 0.889460i) q^{65} +(-1.93033 + 2.18164i) q^{66} +(3.27663 + 5.67529i) q^{67} +(-0.137553 + 0.238249i) q^{68} +(-5.73783 + 1.91956i) q^{69} +(0.100536 + 0.0730437i) q^{70} +(15.0775 + 1.58471i) q^{71} +(2.86883 + 0.877376i) q^{72} +(-2.31783 + 5.20592i) q^{73} +(-10.0415 - 2.13439i) q^{74} +(0.718198 + 1.57613i) q^{75} +(4.57196 - 2.03557i) q^{76} +(-0.0645848 + 0.198771i) q^{77} +(2.06352 + 0.198789i) q^{78} +(3.84839 + 8.64362i) q^{79} +(-0.207912 - 0.978148i) q^{80} +(-7.09310 + 5.53966i) q^{81} +(5.01207 + 2.23152i) q^{82} +(3.69418 - 4.10280i) q^{83} +(0.213858 - 0.0243562i) q^{84} +(-0.161704 + 0.222566i) q^{85} +(0.453423 + 4.31403i) q^{86} +(14.5308 + 4.58226i) q^{87} +(1.45651 - 0.840918i) q^{88} +(-7.19218 + 5.22542i) q^{89} +(2.76141 + 1.17244i) q^{90} +(0.141457 - 0.0459621i) q^{91} +3.49320 q^{92} +(-9.64187 + 0.185417i) q^{93} -2.96191 q^{94} +(4.75968 - 1.54652i) q^{95} +(-1.41004 - 1.00587i) q^{96} +(3.57622 - 2.59827i) q^{97} +(-6.04880 + 3.49228i) q^{98} +(-0.440201 + 5.02627i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9	$ 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9} - 22 q^{10} - 38 q^{13} - 44 q^{16} + 12 q^{18} + 8 q^{19} - 18 q^{21} - 4 q^{22} + 88 q^{25} - 90 q^{27} + 36 q^{28} + 24 q^{31} + 18 q^{33} + 14 q^{34} + 4 q^{36} - 42 q^{37} - 42 q^{39} + 22 q^{40} - 12 q^{42} - 34 q^{43} - 8 q^{45} + 10 q^{46} + 22 q^{49} + 26 q^{51} - 2 q^{52} + 4 q^{55} + 114 q^{57} + 32 q^{63} + 44 q^{64} - 42 q^{66} + 20 q^{67} + 16 q^{69} + 8 q^{70} - 12 q^{72} - 28 q^{73} + 12 q^{76} - 92 q^{78} - 56 q^{79} - 124 q^{81} - 32 q^{82} - 12 q^{84} - 36 q^{87} - 6 q^{88} + 24 q^{90} - 140 q^{91} - 104 q^{93} - 36 q^{94} + 88 q^{97} - 60 q^{99}+O(q^{100}) $ 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9 - 22 * q^10 - 38 * q^13 - 44 * q^16 + 12 * q^18 + 8 * q^19 - 18 * q^21 - 4 * q^22 + 88 * q^25 - 90 * q^27 + 36 * q^28 + 24 * q^31 + 18 * q^33 + 14 * q^34 + 4 * q^36 - 42 * q^37 - 42 * q^39 + 22 * q^40 - 12 * q^42 - 34 * q^43 - 8 * q^45 + 10 * q^46 + 22 * q^49 + 26 * q^51 - 2 * q^52 + 4 * q^55 + 114 * q^57 + 32 * q^63 + 44 * q^64 - 42 * q^66 + 20 * q^67 + 16 * q^69 + 8 * q^70 - 12 * q^72 - 28 * q^73 + 12 * q^76 - 92 * q^78 - 56 * q^79 - 124 * q^81 - 32 * q^82 - 12 * q^84 - 36 * q^87 - 6 * q^88 + 24 * q^90 - 140 * q^91 - 104 * q^93 - 36 * q^94 + 88 * q^97 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{23}{30}\right)$

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
$3$	−1.00587	+	1.41004i	−0.580740	+	0.814089i
$3$	−1.00587	+	1.41004i	−0.580740	+	0.814089i
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$6$	0.520913	−	1.65186i	0.212662	−	0.674370i
$7$	−0.0129897	−	0.123589i	−0.00490964	−	0.0467121i	0.991793	−	0.127856i	$-0.0408094\pi$
$7$	−0.0129897	−	0.123589i	−0.00490964	−	0.0467121i	−0.996702	+	0.0811436i	$0.974143\pi$
$8$	−0.587785	+	0.809017i	−0.207813	+	0.286031i
$9$	−0.976447	−	2.83664i	−0.325482	−	0.945548i
$10$	−0.669131	+	0.743145i	−0.211598	+	0.235003i
$11$	−1.53643	−	0.684064i	−0.463252	−	0.206253i	0.161820	−	0.986820i	$-0.448264\pi$
$11$	−1.53643	−	0.684064i	−0.463252	−	0.206253i	−0.625072	+	0.780567i	$0.714930\pi$
$12$	0.0150361	+	1.73199i	0.00434056	+	0.499981i
$13$	0.248847	+	1.17073i	0.0690177	+	0.324703i	0.999089	−	0.0426765i	$-0.0135885\pi$
$13$	0.248847	+	1.17073i	0.0690177	+	0.324703i	−0.930071	+	0.367379i	$0.880255\pi$
$14$	0.0505449	+	0.113526i	0.0135087	+	0.0303410i
$15$	−0.166088	+	1.72407i	−0.0428837	+	0.445153i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−0.251322	+	0.111896i	−0.0609547	+	0.0271388i	−0.436988	−	0.899468i	$-0.643955\pi$
$17$	−0.251322	+	0.111896i	−0.0609547	+	0.0271388i	0.376033	+	0.926606i	$0.377288\pi$
$18$	1.80523	+	2.39607i	0.425496	+	0.564759i
$19$	4.89527	+	1.04052i	1.12305	+	0.238712i	0.731765	−	0.681557i	$-0.238697\pi$
$19$	4.89527	+	1.04052i	1.12305	+	0.238712i	0.391286	+	0.920269i	$0.372030\pi$
$20$	0.406737	−	0.913545i	0.0909491	−	0.204275i
$21$	0.187331	+	0.105998i	0.0408790	+	0.0231307i
$22$	1.67262	+	0.175800i	0.356604	+	0.0374806i
$23$	2.82606	+	2.05325i	0.589274	+	0.428133i	0.842056	−	0.539391i	$-0.181345\pi$
$23$	2.82606	+	2.05325i	0.589274	+	0.428133i	−0.252782	+	0.967523i	$0.581345\pi$
$24$	−0.549513	−	1.64257i	−0.112169	−	0.335288i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−0.598443	−	1.03653i	−0.117364	−	0.203281i
$27$	4.98197	+	1.47647i	0.958781	+	0.284146i
$28$	−0.0831524	−	0.0923502i	−0.0157143	−	0.0174525i
$29$	−2.71830	−	8.36606i	−0.504775	−	1.55354i	−0.801148	−	0.598466i	$-0.795777\pi$
$29$	−2.71830	−	8.36606i	−0.504775	−	1.55354i	0.296373	−	0.955072i	$-0.404223\pi$
$30$	−0.374808	−	1.69101i	−0.0684302	−	0.308735i
$31$	3.31997	+	4.46965i	0.596285	+	0.802773i
$31$	3.31997	+	4.46965i	0.596285	+	0.802773i
$32$			1.00000i			0.176777i
$33$	2.51001	−	1.47836i	0.436937	−	0.257349i
$34$	0.204444	−	0.184082i	0.0350619	−	0.0315699i
$35$	−0.0730437	−	0.100536i	−0.0123466	−	0.0169937i
$36$	−2.45730	−	1.72095i	−0.409550	−	0.286825i
$37$	8.89048	+	5.13292i	1.46159	+	0.843847i	0.999085	−	0.0427714i	$-0.0136187\pi$
$37$	8.89048	+	5.13292i	1.46159	+	0.843847i	0.462501	+	0.886619i	$0.346952\pi$
$38$	−4.97721	+	0.523126i	−0.807410	+	0.0848623i
$39$	−1.90109	−	0.826721i	−0.304418	−	0.132381i
$40$	−0.104528	+	0.994522i	−0.0165274	+	0.157248i
$41$	−4.07719	−	3.67112i	−0.636750	−	0.573332i	0.286239	−	0.958158i	$-0.407595\pi$
$41$	−4.07719	−	3.67112i	−0.636750	−	0.573332i	−0.922989	+	0.384826i	$0.874261\pi$
$42$	−0.210918	−	0.0429217i	−0.0325453	−	0.00662296i
$43$	0.901877	−	4.24300i	0.137535	−	0.647051i	−0.854327	−	0.519736i	$-0.826030\pi$
$43$	0.901877	−	4.24300i	0.137535	−	0.647051i	0.991862	−	0.127316i	$-0.0406362\pi$
$44$	−1.64508	+	0.349673i	−0.248006	+	0.0527152i
$45$	−2.26395	−	1.96838i	−0.337490	−	0.293429i
$46$	−3.32223	−	1.07946i	−0.489836	−	0.159157i
$47$	2.81695	+	0.915281i	0.410894	+	0.133507i	0.507168	−	0.861847i	$-0.330692\pi$
$47$	2.81695	+	0.915281i	0.410894	+	0.133507i	−0.0962739	+	0.995355i	$0.530692\pi$
$48$	1.03020	+	1.39237i	0.148697	+	0.200971i
$49$	6.83193	−	1.45217i	0.975990	−	0.207453i
$50$	−0.207912	+	0.978148i	−0.0294032	+	0.138331i
$51$	0.0950198	−	0.466929i	0.0133054	−	0.0653831i
$52$	0.889460	+	0.800874i	0.123346	+	0.111061i
$53$	−0.920365	+	8.75669i	−0.126422	+	1.20282i	0.728861	+	0.684662i	$0.240050\pi$
$53$	−0.920365	+	8.75669i	−0.126422	+	1.20282i	−0.855283	+	0.518162i	$0.826617\pi$
$54$	−5.19439	+	0.135312i	−0.706867	+	0.0184136i
$55$	−1.67262	+	0.175800i	−0.225536	+	0.0237048i
$56$	0.107620	+	0.0621347i	0.0143814	+	0.00830310i
$57$	−6.39119	+	5.85591i	−0.846533	+	0.775634i
$58$	5.17051	+	7.11659i	0.678921	+	0.934455i
$59$	−0.903708	+	0.813702i	−0.117653	+	0.105935i	−0.725857	−	0.687845i	$-0.758557\pi$
$59$	−0.903708	+	0.813702i	−0.117653	+	0.105935i	0.608205	+	0.793780i	$0.291890\pi$
$60$	0.879014	+	1.49243i	0.113480	+	0.192671i
$61$			3.06126i			0.391954i	0.980609	+	0.195977i	$0.0627878\pi$
$61$			3.06126i			0.391954i	−0.980609	+	0.195977i	$0.937212\pi$
$62$	−4.53868	−	3.22496i	−0.576413	−	0.409571i
$63$	−0.337893	+	0.157525i	−0.0425705	+	0.0198463i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	0.800874	+	0.889460i	0.0993361	+	0.110324i
$66$	−1.93033	+	2.18164i	−0.237607	+	0.268541i
$67$	3.27663	+	5.67529i	0.400304	+	0.693347i	0.993762	−	0.111518i	$-0.0355712\pi$
$67$	3.27663	+	5.67529i	0.400304	+	0.693347i	−0.593458	+	0.804865i	$0.702238\pi$
$68$	−0.137553	+	0.238249i	−0.0166808	+	0.0288920i
$69$	−5.73783	+	1.91956i	−0.690753	+	0.231088i
$70$	0.100536	+	0.0730437i	0.0120164	+	0.00873039i
$71$	15.0775	+	1.58471i	1.78937	+	0.188071i	0.940333	−	0.340255i	$-0.110513\pi$
$71$	15.0775	+	1.58471i	1.78937	+	0.188071i	0.849042	+	0.528326i	$0.177180\pi$
$72$	2.86883	+	0.877376i	0.338095	+	0.103400i
$73$	−2.31783	+	5.20592i	−0.271281	+	0.609307i	−0.996890	−	0.0787997i	$-0.974891\pi$
$73$	−2.31783	+	5.20592i	−0.271281	+	0.609307i	0.725609	+	0.688107i	$0.241558\pi$
$74$	−10.0415	−	2.13439i	−1.16730	−	0.248118i
$75$	0.718198	+	1.57613i	0.0829304	+	0.181996i
$76$	4.57196	−	2.03557i	0.524439	−	0.233495i
$77$	−0.0645848	+	0.198771i	−0.00736012	+	0.0226521i
$78$	2.06352	+	0.198789i	0.233647	+	0.0225084i
$79$	3.84839	+	8.64362i	0.432977	+	0.972483i	0.989880	+	0.141905i	$0.0453229\pi$
$79$	3.84839	+	8.64362i	0.432977	+	0.972483i	−0.556903	+	0.830578i	$0.688010\pi$
$80$	−0.207912	−	0.978148i	−0.0232452	−	0.109360i
$81$	−7.09310	+	5.53966i	−0.788123	+	0.615518i
$82$	5.01207	+	2.23152i	0.553491	+	0.246430i
$83$	3.69418	−	4.10280i	0.405489	−	0.450341i	−0.505466	−	0.862846i	$-0.668679\pi$
$83$	3.69418	−	4.10280i	0.405489	−	0.450341i	0.910955	+	0.412505i	$0.135346\pi$
$84$	0.213858	−	0.0243562i	0.0233339	−	0.00265748i
$85$	−0.161704	+	0.222566i	−0.0175392	+	0.0241407i
$86$	0.453423	+	4.31403i	0.0488938	+	0.465194i
$87$	14.5308	+	4.58226i	1.55786	+	0.491270i
$88$	1.45651	−	0.840918i	0.155265	−	0.0896421i
$89$	−7.19218	+	5.22542i	−0.762369	+	0.553894i	−0.899636	−	0.436640i	$-0.856168\pi$
$89$	−7.19218	+	5.22542i	−0.762369	+	0.553894i	0.137267	+	0.990534i	$0.456168\pi$
$90$	2.76141	+	1.17244i	0.291078	+	0.123586i
$91$	0.141457	−	0.0459621i	0.0148287	−	0.00481813i
$92$	3.49320			0.364191
$93$	−9.64187	+	0.185417i	−0.999815	+	0.0192268i
$94$	−2.96191			−0.305498
$95$	4.75968	−	1.54652i	0.488333	−	0.158669i
$96$	−1.41004	−	1.00587i	−0.143912	−	0.102661i
$97$	3.57622	−	2.59827i	0.363110	−	0.263815i	−0.391238	−	0.920289i	$-0.627953\pi$
$97$	3.57622	−	2.59827i	0.363110	−	0.263815i	0.754348	+	0.656475i	$0.227953\pi$
$98$	−6.04880	+	3.49228i	−0.611021	+	0.352773i
$99$	−0.440201	+	5.02627i	−0.0442419	+	0.505159i
$100$	−0.104528	−	0.994522i	−0.0104528	−	0.0994522i
$101$	−4.55186	+	6.26510i	−0.452927	+	0.623400i	−0.973023	−	0.230707i	$-0.925896\pi$
$101$	−4.55186	+	6.26510i	−0.452927	+	0.623400i	0.520096	+	0.854108i	$0.325896\pi$
$102$	0.0539197	+	0.473438i	0.00533884	+	0.0468774i
$103$	−6.85675	+	7.61520i	−0.675616	+	0.750348i	−0.979298	−	0.202426i	$-0.935117\pi$
$103$	−6.85675	+	7.61520i	−0.675616	+	0.750348i	0.303682	+	0.952774i	$0.401784\pi$
$104$	−1.09341	−	0.486818i	−0.107218	−	0.0477364i
$105$	0.215233	−	0.00186853i	0.0210046	−	0.000182350i
$106$	−1.83065	−	8.61251i	−0.177808	−	0.836521i
$107$	6.40126	+	14.3775i	0.618833	+	1.38992i	0.902371	+	0.430961i	$0.141825\pi$
$107$	6.40126	+	14.3775i	0.618833	+	1.38992i	−0.283537	+	0.958961i	$0.591508\pi$
$108$	4.89835	−	1.73384i	0.471343	−	0.166839i
$109$	5.38767	−	16.5815i	0.516045	−	1.58822i	−0.265326	−	0.964159i	$-0.585480\pi$
$109$	5.38767	−	16.5815i	0.516045	−	1.58822i	0.781372	−	0.624066i	$-0.214520\pi$
$110$	1.53643	−	0.684064i	0.146493	−	0.0652230i
$111$	−16.1803	+	7.37291i	−1.53577	+	0.699806i
$112$	−0.121554	−	0.0258371i	−0.0114858	−	0.00244137i
$113$	−1.06107	+	2.38320i	−0.0998169	+	0.224192i	−0.956550	−	0.291567i	$-0.905823\pi$
$113$	−1.06107	+	2.38320i	−0.0998169	+	0.224192i	0.856734	+	0.515759i	$0.172490\pi$
$114$	4.26880	−	7.54428i	0.399810	−	0.706587i
$115$	3.47406	+	0.365139i	0.323958	+	0.0340494i
$116$	−7.11659	−	5.17051i	−0.660759	−	0.480070i
$117$	3.07796	−	1.84905i	0.284558	−	0.170944i
$118$	0.608029	−	1.05314i	0.0559736	−	0.0969492i
$119$	0.0170937	+	0.0296071i	0.00156697	+	0.00271408i
$120$	−1.29718	−	1.14775i	−0.118416	−	0.104775i
$121$	−5.46775	−	6.07256i	−0.497069	−	0.552051i
$122$	−0.945980	−	2.91143i	−0.0856450	−	0.263588i
$123$	9.27756	−	2.05634i	0.836529	−	0.185414i
$124$	5.31311	+	1.66459i	0.477131	+	0.149485i
$125$		−	1.00000i		−	0.0894427i
$126$	0.272678	−	0.254230i	0.0242921	−	0.0226486i
$127$	4.00873	−	3.60948i	0.355717	−	0.320289i	−0.471826	−	0.881692i	$-0.656405\pi$
$127$	4.00873	−	3.60948i	0.355717	−	0.320289i	0.827543	+	0.561403i	$0.189738\pi$
$128$	0.587785	+	0.809017i	0.0519534	+	0.0715077i
$129$	5.07564	+	5.53960i	0.446885	+	0.487734i
$130$	−1.03653	−	0.598443i	−0.0909101	−	0.0524870i
$131$	−1.63964	+	0.172333i	−0.143256	+	0.0150568i	−0.175885	−	0.984411i	$-0.556279\pi$
$131$	−1.63964	+	0.172333i	−0.143256	+	0.0150568i	0.0326290	+	0.999468i	$0.489612\pi$
$132$	1.16169	−	2.67137i	0.101112	−	0.232513i
$133$	0.0650086	−	0.618515i	0.00563696	−	0.0536321i
$134$	−4.87002	−	4.38499i	−0.420706	−	0.378805i
$135$	5.05275	−	1.21233i	0.434871	−	0.104341i
$136$	0.0571979	−	0.269095i	0.00490468	−	0.0230747i
$137$	13.4550	−	2.85994i	1.14953	−	0.244341i	0.406537	−	0.913635i	$-0.366736\pi$
$137$	13.4550	−	2.85994i	1.14953	−	0.244341i	0.742998	+	0.669293i	$0.233403\pi$
$138$	4.86382	−	3.59870i	0.414036	−	0.306341i
$139$	−3.15726	−	1.02586i	−0.267796	−	0.0870121i	0.172041	−	0.985090i	$-0.444964\pi$
$139$	−3.15726	−	1.02586i	−0.267796	−	0.0870121i	−0.439837	+	0.898078i	$0.644964\pi$
$140$	−0.118187	−	0.0384014i	−0.00998864	−	0.00324551i
$141$	−4.12407	+	3.05136i	−0.347309	+	0.256971i
$142$	−14.8293	+	3.15206i	−1.24445	+	0.264515i
$143$	0.418519	−	1.96898i	0.0349983	−	0.164654i
$144$	−2.99955	+	0.0520847i	−0.249962	+	0.00434039i
$145$	−6.53714	−	5.88607i	−0.542880	−	0.488812i
$146$	0.595665	−	5.66737i	0.0492976	−	0.469035i
$147$	−4.82441	+	11.0940i	−0.397911	+	0.915019i
$148$	10.2096	−	1.07307i	0.839224	−	0.0882060i
$149$	−0.401614	−	0.231872i	−0.0329015	−	0.0189957i	0.483459	−	0.875367i	$-0.339380\pi$
$149$	−0.401614	−	0.231872i	−0.0329015	−	0.0189957i	−0.516361	+	0.856371i	$0.672714\pi$
$150$	−1.17010	−	1.27705i	−0.0955381	−	0.104271i
$151$	−0.529925	−	0.729379i	−0.0431247	−	0.0593560i	0.786910	−	0.617068i	$-0.211680\pi$
$151$	−0.529925	−	0.729379i	−0.0431247	−	0.0593560i	−0.830035	+	0.557712i	$0.811680\pi$
$152$	−3.71916	+	3.34875i	−0.301664	+	0.271619i
$153$	0.562812	+	0.603652i	0.0455007	+	0.0488024i
$154$		−	0.209001i		−	0.0168418i
$155$	5.11001	+	2.21084i	0.410446	+	0.177579i
$156$	−2.02395	+	0.448602i	−0.162046	+	0.0359169i
$157$	−1.66784	−	5.13309i	−0.133108	−	0.409666i	0.862183	−	0.506598i	$-0.169097\pi$
$157$	−1.66784	−	5.13309i	−0.133108	−	0.409666i	−0.995291	+	0.0969321i	$0.969097\pi$
$158$	−6.33106	−	7.03135i	−0.503672	−	0.559384i
$159$	−11.4215	−	10.1059i	−0.905787	−	0.801446i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	0.217049	−	0.375940i	0.0171059	−	0.0296282i
$162$	5.03409	−	7.46042i	0.395516	−	0.586146i
$163$	−11.1246	−	8.08251i	−0.871348	−	0.633071i	0.0596005	−	0.998222i	$-0.481017\pi$
$163$	−11.1246	−	8.08251i	−0.871348	−	0.633071i	−0.930948	+	0.365151i	$0.881017\pi$
$164$	−5.45634	−	0.573485i	−0.426069	−	0.0447816i
$165$	1.43456	−	2.53530i	0.111680	−	0.197373i
$166$	−2.24554	+	5.04356i	−0.174288	+	0.391457i
$167$	4.95913	+	1.05409i	0.383749	+	0.0815683i	0.395747	−	0.918360i	$-0.370486\pi$
$167$	4.95913	+	1.05409i	0.383749	+	0.0815683i	−0.0119980	+	0.999928i	$0.503819\pi$
$168$	−0.195865	+	0.0892500i	−0.0151113	+	0.00688579i
$169$	10.5674	−	4.70491i	0.812877	−	0.361916i
$170$	0.0850126	−	0.261642i	0.00652017	−	0.0200670i
$171$	−1.82838	−	14.9021i	−0.139820	−	1.13960i
$172$	−1.76434	−	3.96277i	−0.134530	−	0.302158i
$173$	−4.89946	−	23.0502i	−0.372499	−	1.75247i	−0.620972	−	0.783833i	$-0.713262\pi$
$173$	−4.89946	−	23.0502i	−0.372499	−	1.75247i	0.248473	−	0.968639i	$-0.420071\pi$
$174$	−15.2356	+	0.132267i	−1.15501	+	0.0100271i
$175$	−0.113526	−	0.0505449i	−0.00858174	−	0.00382084i
$176$	−1.12537	+	1.24985i	−0.0848278	+	0.0942108i
$177$	−0.238342	−	2.09275i	−0.0179149	−	0.157300i
$178$	5.22542	−	7.19218i	0.391662	−	0.539077i
$179$	0.00672597	+	0.0639933i	0.000502723	+	0.00478309i	0.994770	−	0.102137i	$-0.0325679\pi$
$179$	0.00672597	+	0.0639933i	0.000502723	+	0.00478309i	−0.994268	+	0.106920i	$0.965901\pi$
$180$	−2.98856	−	0.261739i	−0.222754	−	0.0195089i
$181$	−13.7532	+	7.94044i	−1.02227	+	0.590208i	−0.914761	−	0.403996i	$-0.867621\pi$
$181$	−13.7532	+	7.94044i	−1.02227	+	0.590208i	−0.107509	+	0.994204i	$0.534288\pi$
$182$	−0.120330	+	0.0874251i	−0.00891947	+	0.00648038i
$183$	−4.31651	−	3.07923i	−0.319085	−	0.227623i
$184$	−3.32223	+	1.07946i	−0.244918	+	0.0795787i
$185$	10.2658			0.754760
$186$	9.11266	−	3.15584i	0.668173	−	0.231398i
$187$	0.462684			0.0338348
$188$	2.81695	−	0.915281i	0.205447	−	0.0667537i
$189$	0.117760	−	0.634894i	0.00856579	−	0.0461817i
$190$	−4.04883	+	2.94165i	−0.293733	+	0.213409i
$191$	20.5622	−	11.8716i	1.48783	−	0.858999i	0.487927	−	0.872885i	$-0.337753\pi$
$191$	20.5622	−	11.8716i	1.48783	−	0.858999i	0.999904	+	0.0138856i	$0.00442007\pi$
$192$	1.65186	+	0.520913i	0.119213	+	0.0375936i
$193$	−1.23626	−	11.7622i	−0.0889880	−	0.846664i	−0.944418	−	0.328746i	$-0.893374\pi$
$193$	−1.23626	−	11.7622i	−0.0889880	−	0.846664i	0.855430	−	0.517918i	$-0.173293\pi$
$194$	−2.59827	+	3.57622i	−0.186545	+	0.256757i
$195$	−2.05975	+	0.234584i	−0.147502	+	0.0167989i
$196$	4.67358	−	5.19054i	0.333827	−	0.370753i
$197$	5.64299	+	2.51242i	0.402047	+	0.179003i	0.597790	−	0.801652i	$-0.296045\pi$
$197$	5.64299	+	2.51242i	0.402047	+	0.179003i	−0.195744	+	0.980655i	$0.562712\pi$
$198$	−1.13455	−	4.91629i	−0.0806286	−	0.349386i
$199$	3.92159	+	18.4496i	0.277994	+	1.30786i	0.866424	+	0.499310i	$0.166413\pi$
$199$	3.92159	+	18.4496i	0.277994	+	1.30786i	−0.588430	+	0.808548i	$0.700254\pi$
$200$	0.406737	+	0.913545i	0.0287606	+	0.0645974i
$201$	−11.2983	−	1.08842i	−0.796919	−	0.0767711i
$202$	2.39305	−	7.36506i	0.168375	−	0.518204i
$203$	−0.998640	+	0.444623i	−0.0700908	+	0.0312064i
$204$	−0.197581	−	0.433604i	−0.0138334	−	0.0303584i
$205$	−5.36651	−	1.14069i	−0.374813	−	0.0796690i
$206$	4.16794	−	9.36134i	0.290394	−	0.652235i
$207$	3.06485	−	10.0214i	0.213022	−	0.696536i
$208$	1.19033	+	0.125109i	0.0825345	+	0.00867473i
$209$	−6.80946	−	4.94737i	−0.471021	−	0.342216i
$210$	−0.204121	+	0.0682877i	−0.0140857	+	0.00471230i
$211$	10.6534	−	18.4522i	0.733409	−	1.27030i	−0.222009	−	0.975045i	$-0.571261\pi$
$211$	10.6534	−	18.4522i	0.733409	−	1.27030i	0.955418	−	0.295257i	$-0.0954053\pi$
$212$	4.40246	+	7.62529i	0.302362	+	0.523707i
$213$	−17.4006	+	19.6660i	−1.19227	+	1.34749i
$214$	−10.5308	−	11.6957i	−0.719874	−	0.799501i
$215$	−1.34045	−	4.12548i	−0.0914180	−	0.281356i
$216$	−4.12282	+	3.16266i	−0.280522	+	0.215191i
$217$	0.509272	−	0.468370i	0.0345717	−	0.0317951i
$218$			17.4349i			1.18084i
$219$	−5.00914	−	8.50472i	−0.338487	−	0.574696i
$220$	−1.24985	+	1.12537i	−0.0842647	+	0.0758723i
$221$	−0.193541	−	0.266386i	−0.0130190	−	0.0179191i
$222$	13.1100	−	12.0120i	0.879889	−	0.806196i
$223$	−11.8236	−	6.82639i	−0.791770	−	0.457129i	0.0488153	−	0.998808i	$-0.484455\pi$
$223$	−11.8236	−	6.82639i	−0.791770	−	0.457129i	−0.840585	+	0.541679i	$0.817789\pi$
$224$	0.123589	−	0.0129897i	0.00825761	−	0.000867910i
$225$	−2.94483	−	0.572695i	−0.196322	−	0.0381796i
$226$	0.272687	−	2.59445i	0.0181389	−	0.172580i
$227$	7.21742	+	6.49860i	0.479037	+	0.431327i	0.872942	−	0.487824i	$-0.162209\pi$
$227$	7.21742	+	6.49860i	0.479037	+	0.431327i	−0.393905	+	0.919151i	$0.628876\pi$
$228$	−1.72856	+	8.49417i	−0.114477	+	0.562540i
$229$	2.50829	−	11.8006i	0.165753	−	0.779805i	−0.814202	−	0.580582i	$-0.802825\pi$
$229$	2.50829	−	11.8006i	0.165753	−	0.779805i	0.979954	−	0.199223i	$-0.0638417\pi$
$230$	−3.41687	+	0.726277i	−0.225301	+	0.0478893i
$231$	−0.215312	−	0.291006i	−0.0141665	−	0.0191468i
$232$	8.36606	+	2.71830i	0.549259	+	0.178465i
$233$	−20.9613	−	6.81073i	−1.37322	−	0.446186i	−0.472785	−	0.881178i	$-0.656751\pi$
$233$	−20.9613	−	6.81073i	−1.37322	−	0.446186i	−0.900434	+	0.434992i	$0.856751\pi$
$234$	−2.35593	+	2.70969i	−0.154012	+	0.177138i
$235$	2.89719	−	0.615816i	0.188992	−	0.0401714i
$236$	−0.252833	+	1.18948i	−0.0164580	+	0.0774289i
$237$	−16.0589	−	3.26797i	−1.04314	−	0.212278i
$238$	−0.0254061	−	0.0228758i	−0.00164684	−	0.00148282i
$239$	−0.432890	+	4.11868i	−0.0280013	+	0.266415i	0.971560	+	0.236794i	$0.0760967\pi$
$239$	−0.432890	+	4.11868i	−0.0280013	+	0.266415i	−0.999561	+	0.0296209i	$0.990570\pi$
$240$	1.58836	+	0.690726i	0.102528	+	0.0445862i
$241$	22.4566	−	2.36028i	1.44656	−	0.152039i	0.651534	−	0.758620i	$-0.274126\pi$
$241$	22.4566	−	2.36028i	1.44656	−	0.152039i	0.795022	+	0.606580i	$0.207459\pi$
$242$	7.07667	+	4.08571i	0.454905	+	0.262640i
$243$	−0.676422	−	15.5738i	−0.0433925	−	0.999058i
$244$	1.79936	+	2.47661i	0.115192	+	0.158549i
$245$	5.19054	−	4.67358i	0.331611	−	0.298584i
$246$	−8.18804	+	4.82262i	−0.522050	+	0.307479i
$247$			5.98997i			0.381133i
$248$	−5.56745	+	0.0587210i	−0.353534	+	0.00372879i
$249$	2.06926	+	9.33585i	0.131134	+	0.591636i
$250$	0.309017	+	0.951057i	0.0195440	+	0.0601501i
$251$	−4.81886	−	5.35188i	−0.304164	−	0.337808i	0.571614	−	0.820523i	$-0.306317\pi$
$251$	−4.81886	−	5.35188i	−0.304164	−	0.337808i	−0.875778	+	0.482715i	$0.839651\pi$
$252$	−0.180771	+	0.326049i	−0.0113875	+	0.0205392i
$253$	−2.93749	−	5.08789i	−0.184679	−	0.319873i
$254$	−2.69714	+	4.67158i	−0.169233	+	0.293121i
$255$	−0.151175	−	0.451882i	−0.00946693	−	0.0282979i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	5.78764	+	0.608305i	0.361023	+	0.0379450i	0.283304	−	0.959030i	$-0.408570\pi$
$257$	5.78764	+	0.608305i	0.361023	+	0.0379450i	0.0777192	+	0.996975i	$0.475236\pi$
$258$	−6.53905	−	3.70001i	−0.407104	−	0.230353i
$259$	0.518886	−	1.16544i	0.0322420	−	0.0724168i
$260$	1.17073	+	0.248847i	0.0726057	+	0.0154328i
$261$	−21.0773	+	15.8799i	−1.30465	+	0.982938i
$262$	1.50614	−	0.670575i	0.0930494	−	0.0414282i
$263$	1.69580	−	5.21912i	0.104567	−	0.321825i	−0.885061	−	0.465474i	$-0.845884\pi$
$263$	1.69580	−	5.21912i	0.104567	−	0.321825i	0.989629	+	0.143649i	$0.0458838\pi$
$264$	−0.279333	+	2.89960i	−0.0171917	+	0.178458i
$265$	3.58128	+	8.04370i	0.219997	+	0.494120i
$266$	0.129305	+	0.608332i	0.00792819	+	0.0372992i
$267$	−0.133672	−	15.3974i	−0.00818057	−	0.942305i
$268$	5.98670	+	2.66545i	0.365696	+	0.162818i
$269$	−12.1147	+	13.4547i	−0.738646	+	0.820350i	−0.989017	−	0.147800i	$-0.952781\pi$
$269$	−12.1147	+	13.4547i	−0.738646	+	0.820350i	0.250371	+	0.968150i	$0.419447\pi$
$270$	−4.43082	+	2.71438i	−0.269651	+	0.165192i
$271$	4.46470	−	6.14513i	0.271211	−	0.373290i	−0.651587	−	0.758574i	$-0.725896\pi$
$271$	4.46470	−	6.14513i	0.271211	−	0.373290i	0.922798	+	0.385284i	$0.125896\pi$
$272$	0.0287565	+	0.273600i	0.00174362	+	0.0165894i
$273$	−0.0774787	+	0.245692i	−0.00468922	+	0.0148700i
$274$	−11.9127	+	6.87778i	−0.719670	+	0.415502i
$275$	−1.36063	+	0.988558i	−0.0820493	+	0.0596123i
$276$	−3.51371	+	4.92557i	−0.211500	+	0.296484i
$277$	−13.5789	+	4.41204i	−0.815875	+	0.265094i	−0.687084	−	0.726578i	$-0.741110\pi$
$277$	−13.5789	+	4.41204i	−0.815875	+	0.265094i	−0.128791	+	0.991672i	$0.541110\pi$
$278$	3.31974			0.199105
$279$	9.43703	−	13.7820i	0.564980	−	0.825104i
$280$	0.124269			0.00742652
$281$	25.7156	−	8.35549i	1.53406	−	0.498447i	0.584331	−	0.811516i	$-0.301357\pi$
$281$	25.7156	−	8.35549i	1.53406	−	0.498447i	0.949730	+	0.313069i	$0.101357\pi$
$282$	2.97930	−	4.17643i	0.177415	−	0.248703i
$283$	−23.6717	+	17.1985i	−1.40714	+	1.02235i	−0.413407	+	0.910546i	$0.635661\pi$
$283$	−23.6717	+	17.1985i	−1.40714	+	1.02235i	−0.993731	+	0.111799i	$0.964339\pi$
$284$	13.1295	−	7.58030i	0.779090	−	0.449808i
$285$	−2.60697	+	8.26696i	−0.154424	+	0.489692i
$286$	0.210412	+	2.00194i	0.0124419	+	0.118377i
$287$	−0.400747	+	0.551581i	−0.0236553	+	0.0325588i
$288$	2.83664	−	0.976447i	0.167151	−	0.0575377i
$289$	−11.3246	+	12.5772i	−0.666152	+	0.739836i
$290$	8.03609	+	3.57790i	0.471895	+	0.210101i
$291$	0.0664664	+	7.65615i	0.00389633	+	0.448811i
$292$	1.18480	+	5.57406i	0.0693354	+	0.326197i
$293$	−2.60346	−	5.84747i	−0.152096	−	0.341613i	0.821388	−	0.570370i	$-0.193200\pi$
$293$	−2.60346	−	5.84747i	−0.152096	−	0.341613i	−0.973483	+	0.228758i	$0.926534\pi$
$294$	1.16005	−	12.0419i	0.0676556	−	0.702296i
$295$	−0.375783	+	1.15654i	−0.0218789	+	0.0673364i
$296$	−9.37832	+	4.17549i	−0.545103	+	0.242696i
$297$	−6.64447	−	5.67648i	−0.385551	−	0.329383i
$298$	0.453609	+	0.0964177i	0.0262769	+	0.00558533i
$299$	−1.70055	+	3.81950i	−0.0983454	+	0.220887i
$300$	1.50746	+	0.852971i	0.0870333	+	0.0492463i
$301$	−0.536102	−	0.0563466i	−0.0309004	−	0.00324776i
$302$	0.729379	+	0.529925i	0.0419710	+	0.0304937i
$303$	−4.25548	−	12.7202i	−0.244471	−	0.730756i
$304$	2.50231	−	4.33414i	0.143518	−	0.248580i
$305$	1.53063	+	2.65113i	0.0876435	+	0.151803i
$306$	−0.721805	−	0.400189i	−0.0412628	−	0.0228773i
$307$	1.48907	+	1.65377i	0.0849854	+	0.0943859i	0.784138	−	0.620587i	$-0.213106\pi$
$307$	1.48907	+	1.65377i	0.0849854	+	0.0943859i	−0.699152	+	0.714973i	$0.746439\pi$
$308$	0.0645848	+	0.198771i	0.00368006	+	0.0113261i
$309$	−3.84075	−	17.3282i	−0.218493	−	0.985768i
$310$	−5.54309	−	0.523558i	−0.314827	−	0.0297361i
$311$		−	7.43836i		−	0.421791i	−0.977509	−	0.210895i	$-0.932362\pi$
$311$		−	7.43836i		−	0.421791i	0.977509	−	0.210895i	$-0.0676380\pi$
$312$	1.78626	−	1.05208i	0.101127	−	0.0595623i
$313$	−8.28003	+	7.45537i	−0.468015	+	0.421403i	−0.869099	−	0.494639i	$-0.835300\pi$
$313$	−8.28003	+	7.45537i	−0.468015	+	0.421403i	0.401084	+	0.916041i	$0.368634\pi$
$314$	3.17243	+	4.36647i	0.179030	+	0.246414i
$315$	−0.213862	+	0.305367i	−0.0120497	+	0.0172055i
$316$	8.19400	+	4.73081i	0.460949	+	0.266129i
$317$	−26.6629	+	2.80238i	−1.49754	+	0.157397i	−0.817563	−	0.575839i	$-0.804675\pi$
$317$	−26.6629	+	2.80238i	−1.49754	+	0.157397i	−0.679973	+	0.733237i	$0.738009\pi$
$318$	13.9854	+	6.08179i	0.784263	+	0.341050i
$319$	−1.54644	+	14.7134i	−0.0865839	+	0.823791i
$320$	−0.743145	−	0.669131i	−0.0415431	−	0.0374055i
$321$	−26.7117	−	5.43582i	−1.49090	−	0.303398i
$322$	−0.0902540	+	0.424612i	−0.00502966	+	0.0236627i
$323$	−1.34672	+	0.286254i	−0.0749335	+	0.0159276i
$324$	−2.48231	+	8.65090i	−0.137906	+	0.480606i
$325$	1.13831	+	0.369858i	0.0631419	+	0.0205160i
$326$	13.0778	+	4.24923i	0.724311	+	0.235343i
$327$	17.9614	+	24.2758i	0.993268	+	1.34245i
$328$	5.36651	−	1.14069i	0.296316	−	0.0629839i
$329$	0.0765271	−	0.360032i	0.00421908	−	0.0198492i
$330$	−0.580893	+	2.85452i	−0.0319771	+	0.157136i
$331$	1.27327	+	1.14646i	0.0699852	+	0.0630150i	0.703381	−	0.710813i	$-0.251673\pi$
$331$	1.27327	+	1.14646i	0.0699852	+	0.0630150i	−0.633396	+	0.773828i	$0.718339\pi$
$332$	0.577088	−	5.49062i	0.0316718	−	0.301337i
$333$	5.87919	−	30.2312i	0.322178	−	1.65666i
$334$	−5.04214	+	0.529951i	−0.275894	+	0.0289976i
$335$	5.67529	+	3.27663i	0.310074	+	0.179021i
$336$	0.158699	−	0.145407i	0.00865773	−	0.00793263i
$337$	8.03190	+	11.0550i	0.437525	+	0.602202i	0.969660	−	0.244458i	$-0.0786100\pi$
$337$	8.03190	+	11.0550i	0.437525	+	0.602202i	−0.532135	+	0.846660i	$0.678610\pi$
$338$	−8.59630	+	7.74014i	−0.467577	+	0.421008i
$339$	−2.29312	−	3.89334i	−0.124545	−	0.211457i
$340$			0.275107i			0.0149198i
$341$	−2.04339	−	9.13839i	−0.110656	−	0.494872i
$342$	6.34391	+	13.6078i	0.343039	+	0.735824i
$343$	−0.537026	−	1.65280i	−0.0289967	−	0.0892426i
$344$	2.90255	+	3.22361i	0.156495	+	0.173805i
$345$	−4.00932	+	4.53130i	−0.215855	+	0.243957i
$346$	11.7826	+	20.4080i	0.633434	+	1.09714i
$347$	−3.02143	+	5.23328i	−0.162199	+	0.280937i	−0.935657	−	0.352911i	$-0.885192\pi$
$347$	−3.02143	+	5.23328i	−0.162199	+	0.280937i	0.773458	+	0.633848i	$0.218525\pi$
$348$	14.4490	−	4.83384i	0.774549	−	0.259121i
$349$	−1.72120	−	1.25052i	−0.0921337	−	0.0669391i	0.540765	−	0.841174i	$-0.318135\pi$
$349$	−1.72120	−	1.25052i	−0.0921337	−	0.0669391i	−0.632898	+	0.774235i	$0.718135\pi$
$350$	0.123589	+	0.0129897i	0.00660609	+	0.000694328i
$351$	−0.488798	+	6.19997i	−0.0260901	+	0.330930i
$352$	0.684064	−	1.53643i	0.0364607	−	0.0818922i
$353$	−5.89876	−	1.25382i	−0.313959	−	0.0667341i	0.0482371	−	0.998836i	$-0.484640\pi$
$353$	−5.89876	−	1.25382i	−0.313959	−	0.0667341i	−0.362196	+	0.932102i	$0.617973\pi$
$354$	0.873371	+	1.91667i	0.0464191	+	0.101870i
$355$	13.8499	−	6.16637i	0.735076	−	0.327277i
$356$	−2.74717	+	8.45491i	−0.145600	+	0.448110i
$357$	−0.0589413	−	0.00567811i	−0.00311951	−	0.000300517i
$358$	−0.0261718	−	0.0587828i	−0.00138322	−	0.00310677i
$359$	1.19671	+	5.63006i	0.0631598	+	0.297143i	0.998378	−	0.0569276i	$-0.0181304\pi$
$359$	1.19671	+	5.63006i	0.0631598	+	0.297143i	−0.935219	+	0.354071i	$0.884797\pi$
$360$	2.92317	−	0.674588i	0.154065	−	0.0355539i
$361$	5.52357	+	2.45925i	0.290714	+	0.129434i
$362$	10.6264	−	11.8018i	0.558510	−	0.620288i
$363$	14.0624	−	1.60156i	0.738086	−	0.0840603i
$364$	0.0874251	−	0.120330i	0.00458232	−	0.00630702i
$365$	0.595665	+	5.66737i	0.0311785	+	0.296644i
$366$	5.05678	+	1.59465i	0.264322	+	0.0833536i
$367$	21.3598	−	12.3321i	1.11497	−	0.643730i	0.174860	−	0.984593i	$-0.444053\pi$
$367$	21.3598	−	12.3321i	1.11497	−	0.643730i	0.940113	+	0.340863i	$0.110719\pi$
$368$	2.82606	−	2.05325i	0.147318	−	0.107033i
$369$	−6.43250	+	15.1502i	−0.334862	+	0.788687i
$370$	−9.76340	+	3.17232i	−0.507575	+	0.164921i
$371$	1.09418			0.0568071
$372$	−7.69145	+	5.81735i	−0.398783	+	0.301616i
$373$	16.1225			0.834790			0.417395	−	0.908725i	$-0.362943\pi$
$373$	16.1225			0.834790			0.417395	+	0.908725i	$0.362943\pi$
$374$	−0.440039	+	0.142977i	−0.0227539	+	0.00739318i
$375$	1.41004	+	1.00587i	0.0728143	+	0.0519430i
$376$	−2.39624	+	1.74097i	−0.123577	+	0.0897836i
$377$	9.11797	−	5.26426i	0.469599	−	0.271123i
$378$	0.0841965	+	0.640210i	0.00433060	+	0.0329288i
$379$	−2.74840	−	26.1492i	−0.141176	−	1.34320i	−0.804093	−	0.594504i	$-0.797348\pi$
$379$	−2.74840	−	26.1492i	−0.141176	−	1.34320i	0.662917	−	0.748693i	$-0.269318\pi$
$380$	2.94165	−	4.04883i	0.150903	−	0.207701i
$381$	1.05725	+	9.28315i	0.0541648	+	0.475590i
$382$	−15.8873	+	17.6446i	−0.812865	+	0.902778i
$383$	3.47460	+	1.54699i	0.177544	+	0.0790475i	0.493584	−	0.869698i	$-0.335687\pi$
$383$	3.47460	+	1.54699i	0.177544	+	0.0790475i	−0.316040	+	0.948746i	$0.602353\pi$
$384$	−1.73199	+	0.0150361i	−0.0883850	+	0.000767309i
$385$	0.0434537	+	0.204433i	0.00221460	+	0.0104189i
$386$	4.81049	+	10.8045i	0.244847	+	0.549936i
$387$	−12.9165	+	1.58476i	−0.656583	+	0.0805578i
$388$	1.36599	−	4.20409i	0.0693478	−	0.213430i
$389$	17.3903	−	7.74267i	0.881725	−	0.392569i	0.0846221	−	0.996413i	$-0.473032\pi$
$389$	17.3903	−	7.74267i	0.881725	−	0.392569i	0.797102	+	0.603844i	$0.206365\pi$
$390$	1.88645	−	0.859602i	0.0955242	−	0.0435276i
$391$	−0.940003	−	0.199804i	−0.0475380	−	0.0101045i
$392$	−2.84088	+	6.38071i	−0.143486	+	0.322275i
$393$	1.40627	−	2.48531i	0.0709369	−	0.125367i
$394$	−6.14319	−	0.645675i	−0.309489	−	0.0325286i
$395$	7.65461	+	5.56140i	0.385145	+	0.279824i
$396$	2.59823	+	4.32508i	0.130566	+	0.217343i
$397$	9.29443	−	16.0984i	0.466474	−	0.807957i	−0.532793	−	0.846246i	$-0.678857\pi$
$397$	9.29443	−	16.0984i	0.466474	−	0.807957i	0.999267	+	0.0382892i	$0.0121908\pi$
$398$	−9.43089	−	16.3348i	−0.472728	−	0.818789i
$399$	0.806743	+	0.713811i	0.0403877	+	0.0357353i
$400$	−0.669131	−	0.743145i	−0.0334565	−	0.0371572i
$401$	−3.91850	−	12.0599i	−0.195681	−	0.602243i	−0.999968	−	0.00800254i	$-0.997453\pi$
$401$	−3.91850	−	12.0599i	−0.195681	−	0.602243i	0.804287	−	0.594241i	$-0.202547\pi$
$402$	11.0816	−	2.45621i	0.552702	−	0.122505i
$403$	−4.40660	+	4.99906i	−0.219508	+	0.249021i
$404$			7.74408i			0.385283i
$405$	−3.37298	+	8.34404i	−0.167604	+	0.414619i
$406$	0.812367	−	0.731458i	0.0403171	−	0.0363017i
$407$	−10.1484	−	13.9681i	−0.503037	−	0.692371i
$408$	0.321902	+	0.351326i	0.0159365	+	0.0173932i
$409$	22.6265	+	13.0634i	1.11881	+	0.645945i	0.941097	−	0.338137i	$-0.109797\pi$
$409$	22.6265	+	13.0634i	1.11881	+	0.645945i	0.177713	+	0.984082i	$0.443130\pi$
$410$	5.45634	−	0.573485i	0.269470	−	0.0283224i
$411$	−9.50131	+	21.8488i	−0.468665	+	1.07772i
$412$	−1.07113	+	10.1911i	−0.0527708	+	0.502081i
$413$	0.112303	+	0.101118i	0.00552608	+	0.00497570i
$414$	0.181942	+	10.4780i	0.00894198	+	0.514967i
$415$	1.14785	−	5.40022i	0.0563459	−	0.265087i
$416$	−1.17073	+	0.248847i	−0.0573999	+	0.0122007i
$417$	4.62230	−	3.42000i	0.226355	−	0.167478i
$418$	8.00501	+	2.60098i	0.391538	+	0.127218i
$419$	13.6334	+	4.42977i	0.666037	+	0.216408i	0.622472	−	0.782642i	$-0.286128\pi$
$419$	13.6334	+	4.42977i	0.666037	+	0.216408i	0.0435648	+	0.999051i	$0.486128\pi$
$420$	0.173029	−	0.128022i	0.00844294	−	0.00624685i
$421$	−9.58059	+	2.03642i	−0.466929	+	0.0992489i	−0.435367	−	0.900253i	$-0.643382\pi$
$421$	−9.58059	+	2.03642i	−0.466929	+	0.0992489i	−0.0315620	+	0.999502i	$0.510048\pi$
$422$	−4.42992	+	20.8412i	−0.215645	+	1.01453i
$423$	−0.154270	−	8.88440i	−0.00750088	−	0.431974i
$424$	−6.54333	−	5.89164i	−0.317772	−	0.286123i
$425$	−0.0287565	+	0.273600i	−0.00139489	+	0.0132715i
$426$	10.4718	−	24.0805i	0.507361	−	1.16671i
$427$	0.378337	−	0.0397648i	0.0183090	−	0.00192435i
$428$	13.6296	+	7.86905i	0.658811	+	0.380365i
$429$	2.35537	+	2.57067i	0.113718	+	0.124113i
$430$	2.54969	+	3.50935i	0.122957	+	0.169236i
$431$	−8.09919	+	7.29255i	−0.390124	+	0.351270i	−0.840731	−	0.541453i	$-0.817874\pi$
$431$	−8.09919	+	7.29255i	−0.390124	+	0.351270i	0.450607	+	0.892723i	$0.351208\pi$
$432$	2.94372	−	4.28188i	0.141630	−	0.206012i
$433$			3.03249i			0.145732i	0.997342	+	0.0728661i	$0.0232146\pi$
$433$			3.03249i			0.145732i	−0.997342	+	0.0728661i	$0.976785\pi$
$434$	−0.339613	+	0.602821i	−0.0163019	+	0.0289363i
$435$	14.8751	−	3.29703i	0.713208	−	0.158080i
$436$	−5.38767	−	16.5815i	−0.258023	−	0.794112i
$437$	11.6979	+	12.9918i	0.559584	+	0.621481i
$438$	7.39208	+	6.54056i	0.353207	+	0.312520i
$439$	−9.00073	−	15.5897i	−0.429581	−	0.744057i	0.567255	−	0.823542i	$-0.308006\pi$
$439$	−9.00073	−	15.5897i	−0.429581	−	0.744057i	−0.996836	+	0.0794858i	$0.974672\pi$
$440$	0.840918	−	1.45651i	0.0400892	−	0.0694365i
$441$	−10.7903	−	17.9618i	−0.513824	−	0.855323i
$442$	0.266386	+	0.193541i	0.0126707	+	0.00920580i
$443$	−15.7085	−	1.65103i	−0.746332	−	0.0784427i	−0.276275	−	0.961079i	$-0.589100\pi$
$443$	−15.7085	−	1.65103i	−0.746332	−	0.0784427i	−0.470057	+	0.882636i	$0.655767\pi$
$444$	−8.75647	+	15.4754i	−0.415564	+	0.734428i
$445$	−3.61590	+	8.12144i	−0.171410	+	0.384993i
$446$	13.3544	+	2.83857i	0.632350	+	0.134410i
$447$	0.730921	−	0.333060i	0.0345714	−	0.0157532i
$448$	−0.113526	+	0.0505449i	−0.00536359	+	0.00238802i
$449$	−1.72422	+	5.30661i	−0.0813710	+	0.250434i	−0.983463	−	0.181110i	$-0.942031\pi$
$449$	−1.72422	+	5.30661i	−0.0813710	+	0.250434i	0.902092	+	0.431544i	$0.142031\pi$
$450$	2.97767	−	0.365338i	0.140369	−	0.0172222i
$451$	3.75305	+	8.42948i	0.176724	+	0.396929i
$452$	0.542387	+	2.55173i	0.0255117	+	0.120023i
$453$	1.56149	−	0.0135560i	0.0733653	−	0.000636917i
$454$	−8.87235	−	3.95023i	−0.416400	−	0.185393i
$455$	0.0995241	−	0.110533i	0.00466576	−	0.00518185i
$456$	−0.980885	−	8.61259i	−0.0459341	−	0.403322i
$457$	2.77355	−	3.81747i	0.129741	−	0.178574i	−0.739204	−	0.673481i	$-0.764798\pi$
$457$	2.77355	−	3.81747i	0.129741	−	0.178574i	0.868946	+	0.494908i	$0.164798\pi$
$458$	1.26105	+	11.9981i	0.0589252	+	0.560636i
$459$	−1.41729	+	0.186394i	−0.0661535	+	0.00870011i
$460$	3.02520	−	1.74660i	0.141051	−	0.0814357i
$461$	−13.5073	+	9.81364i	−0.629098	+	0.457067i	−0.856088	−	0.516831i	$-0.827112\pi$
$461$	−13.5073	+	9.81364i	−0.629098	+	0.457067i	0.226989	+	0.973897i	$0.427112\pi$
$462$	0.294700	+	0.210228i	0.0137107	+	0.00978068i
$463$	−27.7025	+	9.00108i	−1.28744	+	0.418316i	−0.871196	−	0.490935i	$-0.836655\pi$
$463$	−27.7025	+	9.00108i	−1.28744	+	0.418316i	−0.416248	+	0.909251i	$0.636655\pi$
$464$	−8.79659			−0.408372
$465$	−8.25739	+	4.98151i	−0.382927	+	0.231012i
$466$	22.0400			1.02098
$467$	1.25164	−	0.406683i	0.0579191	−	0.0188191i	−0.279914	−	0.960025i	$-0.590306\pi$
$467$	1.25164	−	0.406683i	0.0579191	−	0.0188191i	0.337833	+	0.941206i	$0.390306\pi$
$468$	1.40328	−	3.30509i	0.0648668	−	0.152778i
$469$	0.658839	−	0.478674i	0.0304223	−	0.0221031i
$470$	−2.56509	+	1.48096i	−0.118319	+	0.0683114i
$471$	8.91552	+	2.81150i	0.410806	+	0.129547i
$472$	−0.127113	−	1.20940i	−0.00585084	−	0.0556670i
$473$	−4.28816	+	5.90214i	−0.197170	+	0.271381i
$474$	16.2827	−	1.85444i	0.747891	−	0.0851770i
$475$	3.34875	−	3.71916i	0.153651	−	0.170647i
$476$	0.0312317	+	0.0139052i	0.00143150	+	0.000637346i
$477$	25.7383	−	5.93969i	1.17848	−	0.271960i
$478$	−0.861038	−	4.05086i	−0.0393829	−	0.185282i
$479$	−3.73826	−	8.39627i	−0.170805	−	0.383635i	0.807778	−	0.589487i	$-0.200670\pi$
$479$	−3.73826	−	8.39627i	−0.170805	−	0.383635i	−0.978583	+	0.205852i	$0.934003\pi$
$480$	−1.72407	−	0.166088i	−0.0786926	−	0.00758085i
$481$	−3.79691	+	11.6857i	−0.173124	+	0.532821i
$482$	−20.6281	+	9.18423i	−0.939585	+	0.418330i
$483$	0.311768	+	0.684195i	0.0141859	+	0.0311320i
$484$	−7.99286	−	1.69894i	−0.363312	−	0.0772244i
$485$	1.79796	−	4.03828i	0.0816410	−	0.183369i
$486$	5.45588	+	14.6025i	0.247484	+	0.662383i
$487$	−20.6178	−	2.16702i	−0.934283	−	0.0981971i	−0.374862	−	0.927081i	$-0.622310\pi$
$487$	−20.6178	−	2.16702i	−0.934283	−	0.0981971i	−0.559421	+	0.828884i	$0.688977\pi$
$488$	−2.47661	−	1.79936i	−0.112111	−	0.0814533i
$489$	22.5866	−	7.55624i	1.02140	−	0.341705i
$490$	−3.49228	+	6.04880i	−0.157765	+	0.273257i
$491$	7.89383	+	13.6725i	0.356244	+	0.617032i	0.987330	−	0.158680i	$-0.0507239\pi$
$491$	7.89383	+	13.6725i	0.356244	+	0.617032i	−0.631086	+	0.775713i	$0.717391\pi$
$492$	6.29702	−	7.11683i	0.283891	−	0.320851i
$493$	1.61930	+	1.79841i	0.0729295	+	0.0809964i
$494$	−1.85100	−	5.69680i	−0.0832806	−	0.256311i
$495$	2.13191	+	4.57298i	0.0958221	+	0.205540i
$496$	5.27682	−	1.77629i	0.236936	−	0.0797576i
$497$		−	1.88400i		−	0.0845088i
$498$	−4.85292	−	8.23948i	−0.217465	−	0.369220i
$499$	−11.2739	+	10.1511i	−0.504691	+	0.454425i	−0.881718	−	0.471777i	$-0.843613\pi$
$499$	−11.2739	+	10.1511i	−0.504691	+	0.454425i	0.377028	+	0.926202i	$0.376946\pi$
$500$	−0.587785	−	0.809017i	−0.0262866	−	0.0361803i
$501$	−6.47456	+	5.93230i	−0.289262	+	0.265036i
$502$	6.23683	+	3.60084i	0.278363	+	0.160713i
$503$	24.0689	−	2.52974i	1.07318	−	0.112796i	0.448581	−	0.893742i	$-0.351930\pi$
$503$	24.0689	−	2.52974i	1.07318	−	0.112796i	0.624598	+	0.780947i	$0.285263\pi$
$504$	0.0711684	−	0.365952i	0.00317009	−	0.0163008i
$505$	−0.809477	+	7.70166i	−0.0360213	+	0.342719i
$506$	4.36597	+	3.93113i	0.194091	+	0.174760i
$507$	−3.99531	+	19.6330i	−0.177438	+	0.871934i
$508$	1.12153	−	5.27640i	0.0497600	−	0.234102i
$509$	−39.4882	+	8.39348i	−1.75029	+	0.372035i	−0.968013	−	0.250901i	$-0.919273\pi$
$509$	−39.4882	+	8.39348i	−1.75029	+	0.372035i	−0.782273	+	0.622936i	$0.785940\pi$
$510$	0.283415	+	0.383050i	0.0125498	+	0.0169617i
$511$	0.673501	+	0.218834i	0.0297939	+	0.00968063i
$512$	0.951057	+	0.309017i	0.0420312	+	0.0136568i
$513$	22.8518	+	12.4115i	1.00893	+	0.547983i
$514$	−5.69235	+	1.20995i	−0.251079	+	0.0533684i
$515$	−2.13052	+	10.0233i	−0.0938821	+	0.441681i
$516$	7.36238	+	1.49824i	0.324111	+	0.0659564i
$517$	−3.70194	−	3.33324i	−0.162811	−	0.146596i
$518$	−0.133350	+	1.26874i	−0.00585907	+	0.0557453i
$519$	37.4300	+	16.2770i	1.64299	+	0.714483i
$520$	−1.19033	+	0.125109i	−0.0521994	+	0.00548638i
$521$	34.0699	+	19.6703i	1.49263	+	0.861771i	0.999964	−	0.00844794i	$-0.00268909\pi$
$521$	34.0699	+	19.6703i	1.49263	+	0.861771i	0.492666	+	0.870218i	$0.336022\pi$
$522$	15.1385	−	21.6159i	0.662595	−	0.946101i
$523$	6.17550	+	8.49984i	0.270036	+	0.371672i	0.922402	−	0.386232i	$-0.126224\pi$
$523$	6.17550	+	8.49984i	0.270036	+	0.371672i	−0.652366	+	0.757904i	$0.726224\pi$
$524$	−1.22520	+	1.10318i	−0.0535232	+	0.0481925i
$525$	0.185463	−	0.109235i	0.00809426	−	0.00476739i
$526$			5.48771i			0.239276i
$527$	−1.33452	−	0.751832i	−0.0581326	−	0.0327503i
$528$	−0.630365	−	2.84400i	−0.0274331	−	0.123769i
$529$	−3.33663	−	10.2691i	−0.145071	−	0.446482i
$530$	−5.89164	−	6.54333i	−0.255917	−	0.284224i
$531$	3.19061	+	1.76896i	0.138460	+	0.0767663i
$532$	−0.310961	−	0.538600i	−0.0134819	−	0.0233513i
$533$	3.28330	−	5.68684i	0.142215	−	0.246324i
$534$	4.88518	+	14.6025i	0.211403	+	0.631911i
$535$	12.7324	+	9.25062i	0.550469	+	0.399939i
$536$	−6.51736	−	0.685002i	−0.281507	−	0.0295876i
$537$	−0.0969989	−	0.0548851i	−0.00418581	−	0.00236847i
$538$	7.36402	−	16.5399i	0.317486	−	0.713084i
$539$	−11.4902	−	2.44231i	−0.494917	−	0.105198i
$540$	3.37517	−	3.95073i	0.145244	−	0.170012i
$541$	6.23714	−	2.77695i	0.268155	−	0.119391i	−0.268254	−	0.963348i	$-0.586447\pi$
$541$	6.23714	−	2.77695i	0.268155	−	0.119391i	0.536410	+	0.843958i	$0.319780\pi$
$542$	−2.34723	+	7.22404i	−0.100822	+	0.310299i
$543$	2.63762	−	27.3797i	0.113191	−	1.17498i
$544$	−0.111896	−	0.251322i	−0.00479750	−	0.0107754i
$545$	−3.62491	−	17.0539i	−0.155274	−	0.730508i
$546$	−0.00223642	−	0.257609i	−9.57099e−5	−	0.0110247i
$547$	0.792438	+	0.352816i	0.0338822	+	0.0150853i	0.423608	−	0.905846i	$-0.360763\pi$
$547$	0.792438	+	0.352816i	0.0338822	+	0.0150853i	−0.389726	+	0.920931i	$0.627430\pi$
$548$	9.20426	−	10.2224i	0.393187	−	0.436678i
$549$	8.68370	−	2.98915i	0.370611	−	0.127574i
$550$	0.988558	−	1.36063i	0.0421523	−	0.0580176i
$551$	−4.60173	−	43.7825i	−0.196040	−	1.86520i
$552$	1.81965	−	5.77029i	0.0774496	−	0.245600i
$553$	1.01826	−	0.587895i	0.0433010	−	0.0249998i
$554$	11.5509	−	8.39220i	0.490750	−	0.356550i
$555$	−10.3261	+	14.4753i	−0.438319	+	0.614442i
$556$	−3.15726	+	1.02586i	−0.133898	+	0.0435060i
$557$	−26.2553			−1.11247			−0.556236	−	0.831025i	$-0.687755\pi$
$557$	−26.2553			−1.11247			−0.556236	+	0.831025i	$0.687755\pi$
$558$	−4.71629	+	16.0236i	−0.199656	+	0.678334i
$559$	5.19184			0.219592
$560$	−0.118187	+	0.0384014i	−0.00499432	+	0.00162275i
$561$	−0.465401	+	0.652405i	−0.0196492	+	0.0275446i
$562$	−21.8750	+	15.8931i	−0.922739	+	0.670409i
$563$	−22.6377	+	13.0699i	−0.954065	+	0.550829i	−0.894341	−	0.447386i	$-0.852355\pi$
$563$	−22.6377	+	13.0699i	−0.954065	+	0.550829i	−0.0597234	+	0.998215i	$0.519022\pi$
$564$	−1.54290	+	4.89267i	−0.0649677	+	0.206019i
$565$	0.272687	+	2.59445i	0.0114720	+	0.109149i
$566$	17.1985	−	23.6717i	0.722907	−	0.994997i
$567$	0.776777	+	0.804668i	0.0326216	+	0.0337929i
$568$	−10.1444	+	11.2665i	−0.425650	+	0.472732i
$569$	38.3574	+	17.0778i	1.60802	+	0.715938i	0.997125	−	0.0757705i	$-0.0241416\pi$
$569$	38.3574	+	17.0778i	1.60802	+	0.715938i	0.610899	+	0.791709i	$0.290808\pi$
$570$	−0.0752502	−	8.66794i	−0.00315189	−	0.363060i
$571$	4.52829	+	21.3039i	0.189503	+	0.891541i	0.965419	+	0.260704i	$0.0839548\pi$
$571$	4.52829	+	21.3039i	0.189503	+	0.891541i	−0.775916	+	0.630836i	$0.782712\pi$
$572$	−0.818747	−	1.83894i	−0.0342335	−	0.0768898i
$573$	−3.94346	+	40.9349i	−0.164741	+	1.71008i
$574$	0.210685	−	0.648422i	0.00879383	−	0.0270646i
$575$	3.19120	−	1.42081i	0.133082	−	0.0592520i
$576$	−2.39607	+	1.80523i	−0.0998363	+	0.0752178i
$577$	−39.4837	−	8.39252i	−1.64373	−	0.349385i	−0.709127	−	0.705081i	$-0.750911\pi$
$577$	−39.4837	−	8.39252i	−1.64373	−	0.349385i	−0.934602	+	0.355696i	$0.884244\pi$
$578$	6.88374	−	15.4611i	0.286326	−	0.643098i
$579$	17.8288	+	10.0881i	0.740939	+	0.419248i
$580$	−8.74840	−	0.919494i	−0.363258	−	0.0381799i
$581$	−0.555046	−	0.403265i	−0.0230272	−	0.0167302i
$582$	−2.42909	−	7.26089i	−0.100689	−	0.300974i
$583$	7.40421	−	12.8245i	0.306651	−	0.531135i
$584$	−2.84930	−	4.93512i	−0.117905	−	0.204217i
$585$	1.74107	−	3.14030i	0.0719845	−	0.129836i
$586$	4.28300	+	4.75676i	0.176929	+	0.196500i
$587$	−5.14243	−	15.8268i	−0.212251	−	0.653240i	−0.999337	−	0.0363979i	$-0.988412\pi$
$587$	−5.14243	−	15.8268i	−0.212251	−	0.653240i	0.787087	−	0.616842i	$-0.211588\pi$
$588$	2.61787	+	11.8110i	0.107959	+	0.487076i
$589$	11.6014	+	25.3346i	0.478027	+	1.04390i
$590$		−	1.21606i		−	0.0500643i
$591$	−9.21875	+	5.42969i	−0.379209	+	0.223348i
$592$	7.62901	−	6.86919i	0.313550	−	0.282322i
$593$	6.76870	+	9.31632i	0.277957	+	0.382575i	0.925056	−	0.379831i	$-0.124018\pi$
$593$	6.76870	+	9.31632i	0.277957	+	0.382575i	−0.647099	+	0.762406i	$0.724018\pi$
$594$	8.07339	+	3.34540i	0.331255	+	0.137263i
$595$	0.0296071	+	0.0170937i	0.00121377	+	0.000700772i
$596$	−0.461203	+	0.0484744i	−0.0188916	+	0.00198559i
$597$	−29.9594	−	13.0283i	−1.22616	−	0.533214i
$598$	0.437030	−	4.15806i	0.0178715	−	0.170036i
$599$	−23.5745	−	21.2266i	−0.963229	−	0.867295i	0.0279788	−	0.999609i	$-0.491093\pi$
$599$	−23.5745	−	21.2266i	−0.963229	−	0.867295i	−0.991208	+	0.132313i	$0.957760\pi$
$600$	−1.69726	−	0.345392i	−0.0692905	−	0.0141006i
$601$	1.28262	−	6.03427i	0.0523193	−	0.246143i	−0.944215	−	0.329331i	$-0.893177\pi$
$601$	1.28262	−	6.03427i	0.0523193	−	0.246143i	0.996534	+	0.0831880i	$0.0265102\pi$
$602$	0.527275	−	0.112076i	0.0214901	−	0.00456787i
$603$	12.8993	−	14.8362i	0.525301	−	0.604179i
$604$	−0.857436	−	0.278598i	−0.0348886	−	0.0113360i
$605$	−7.77149	−	2.52511i	−0.315956	−	0.102660i
$606$	7.97796	+	10.7826i	0.324082	+	0.438014i
$607$	2.00971	−	0.427176i	0.0815714	−	0.0173385i	−0.166945	−	0.985966i	$-0.553390\pi$
$607$	2.00971	−	0.427176i	0.0815714	−	0.0173385i	0.248517	+	0.968628i	$0.420057\pi$
$608$	−1.04052	+	4.89527i	−0.0421987	+	0.198529i
$609$	0.377565	−	1.85536i	0.0152997	−	0.0751829i
$610$	−2.27496	−	2.04838i	−0.0921103	−	0.0829365i
$611$	−0.370561	+	3.52565i	−0.0149913	+	0.142633i
$612$	0.810142	+	0.157552i	0.0327481	+	0.00636867i
$613$	−6.91022	+	0.726293i	−0.279101	+	0.0293347i	−0.243045	−	0.970015i	$-0.578146\pi$
$613$	−6.91022	+	0.726293i	−0.279101	+	0.0293347i	−0.0360562	+	0.999350i	$0.511480\pi$
$614$	−1.92723	−	1.11269i	−0.0777766	−	0.0449044i
$615$	7.00643	−	6.41963i	0.282527	−	0.258864i
$616$	−0.122847	−	0.169085i	−0.00494967	−	0.00681263i
$617$	−19.4144	+	17.4808i	−0.781594	+	0.703750i	−0.959936	−	0.280218i	$-0.909593\pi$
$617$	−19.4144	+	17.4808i	−0.781594	+	0.703750i	0.178343	+	0.983968i	$0.442926\pi$
$618$	9.00749	+	15.2933i	0.362334	+	0.615185i
$619$		−	1.16221i		−	0.0467132i	−0.999727	−	0.0233566i	$-0.992565\pi$
$619$		−	1.16221i		−	0.0467132i	0.999727	−	0.0233566i	$-0.00743531\pi$
$620$	5.43358	−	1.21498i	0.218218	−	0.0487946i
$621$	11.0478	+	14.4018i	0.443332	+	0.577925i
$622$	2.29858	+	7.07430i	0.0921647	+	0.283654i
$623$	0.739227	+	0.820995i	0.0296165	+	0.0328925i
$624$	−1.37373	+	1.55257i	−0.0549931	+	0.0621527i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	5.57094	−	9.64915i	0.222660	−	0.385658i
$627$	13.8254	−	4.62523i	0.552135	−	0.184714i
$628$	−4.36647	−	3.17243i	−0.174241	−	0.126594i
$629$	−2.80873	−	0.295210i	−0.111991	−	0.0117708i
$630$	0.109031	−	0.356508i	0.00434390	−	0.0142036i
$631$	8.12469	−	18.2484i	0.323439	−	0.726455i	−0.676511	−	0.736432i	$-0.736509\pi$
$631$	8.12469	−	18.2484i	0.323439	−	0.726455i	0.999950	+	0.00997672i	$0.00317574\pi$
$632$	−9.25486	−	1.96718i	−0.368139	−	0.0782503i
$633$	15.3025	+	33.5823i	0.608219	+	1.33478i
$634$	24.4919	−	10.9045i	0.972698	−	0.433073i
$635$	1.66692	−	5.13026i	0.0661498	−	0.203588i
$636$	−15.1803	−	1.46239i	−0.601938	−	0.0579876i
$637$	3.40021	+	7.63699i	0.134721	+	0.302588i
$638$	−3.07593	−	14.4711i	−0.121777	−	0.572917i
$639$	−10.2271	−	44.3170i	−0.404580	−	1.75315i
$640$	0.913545	+	0.406737i	0.0361111	+	0.0160777i
$641$	2.57987	−	2.86524i	0.101899	−	0.113170i	−0.690038	−	0.723773i	$-0.742406\pi$
$641$	2.57987	−	2.86524i	0.101899	−	0.113170i	0.791937	+	0.610603i	$0.209073\pi$
$642$	27.0841	−	3.08460i	1.06892	−	0.121739i
$643$	−10.5228	+	14.4834i	−0.414978	+	0.571168i	−0.964424	−	0.264362i	$-0.914839\pi$
$643$	−10.5228	+	14.4834i	−0.414978	+	0.571168i	0.549446	+	0.835529i	$0.314839\pi$
$644$	−0.0453756	−	0.431720i	−0.00178805	−	0.0170121i
$645$	7.16543	+	2.25961i	0.282139	+	0.0889721i
$646$	1.19235	−	0.688403i	0.0469124	−	0.0270849i
$647$	−22.4104	+	16.2821i	−0.881044	+	0.640116i	−0.933527	−	0.358506i	$-0.883286\pi$
$647$	−22.4104	+	16.2821i	−0.881044	+	0.640116i	0.0524834	+	0.998622i	$0.483286\pi$
$648$	−0.312461	−	8.99457i	−0.0122746	−	0.353340i
$649$	1.94511	−	0.632005i	0.0763523	−	0.0248084i
$650$	−1.19689			−0.0469458
$651$	0.148160	+	1.18922i	0.00580686	+	0.0466091i
$652$	−13.7508			−0.538523
$653$	36.5076	−	11.8621i	1.42865	−	0.464198i	0.510314	−	0.859988i	$-0.329529\pi$
$653$	36.5076	−	11.8621i	1.42865	−	0.464198i	0.918341	+	0.395790i	$0.129529\pi$
$654$	−24.5839	−	17.5372i	−0.961308	−	0.685760i
$655$	−1.33380	+	0.969064i	−0.0521160	+	0.0378645i
$656$	−4.75136	+	2.74320i	−0.185509	+	0.107104i
$657$	17.0306	+	1.49154i	0.664426	+	0.0581906i
$658$	0.0384743	+	0.366059i	0.00149988	+	0.0142705i
$659$	−21.2648	+	29.2685i	−0.828360	+	1.14014i	0.159866	+	0.987139i	$0.448894\pi$
$659$	−21.2648	+	29.2685i	−0.828360	+	1.14014i	−0.988226	+	0.153001i	$0.951106\pi$
$660$	−0.329632	−	2.89431i	−0.0128309	−	0.112661i
$661$	−33.7537	+	37.4873i	−1.31287	+	1.45809i	−0.512355	+	0.858774i	$0.671227\pi$
$661$	−33.7537	+	37.4873i	−1.31287	+	1.45809i	−0.800514	+	0.599315i	$0.795440\pi$
$662$	−1.56523	−	0.696884i	−0.0608342	−	0.0270852i
$663$	0.570294	−	0.00495097i	0.0221484	−	0.000192280i
$664$	1.14785	+	5.40022i	0.0445453	+	0.209569i
$665$	−0.252959	−	0.568154i	−0.00980931	−	0.0220321i
$666$	3.75050	+	30.5683i	0.145329	+	1.18450i
$667$	9.49556	−	29.2243i	0.367669	−	1.13157i
$668$	4.63160	−	2.06212i	0.179202	−	0.0797859i
$669$	21.5186	−	9.80540i	0.831956	−	0.379098i
$670$	−6.41005	−	1.36250i	−0.247642	−	0.0526379i
$671$	2.09410	−	4.70342i	0.0808417	−	0.181573i
$672$	−0.105998	+	0.187331i	−0.00408897	+	0.00722646i
$673$	−50.7707	−	5.33621i	−1.95707	−	0.205696i	−0.959864	−	0.280465i	$-0.909511\pi$
$673$	−50.7707	−	5.33621i	−1.95707	−	0.205696i	−0.997201	+	0.0747694i	$0.976178\pi$
$674$	−11.0550	−	8.03190i	−0.425821	−	0.309377i
$675$	3.76964	−	3.57628i	0.145094	−	0.137651i
$676$	5.78373	−	10.0177i	0.222451	−	0.385297i
$677$	−18.6373	−	32.2808i	−0.716291	−	1.24065i	−0.962460	−	0.271425i	$-0.912505\pi$
$677$	−18.6373	−	32.2808i	−0.716291	−	1.24065i	0.246169	−	0.969227i	$-0.420828\pi$
$678$	3.38399	+	2.99418i	0.129961	+	0.114991i
$679$	−0.367571	−	0.408229i	−0.0141061	−	0.0156664i
$680$	−0.0850126	−	0.261642i	−0.00326009	−	0.0100335i
$681$	−16.4231	+	3.64013i	−0.629335	+	0.139490i
$682$	4.76730	+	8.05969i	0.182549	+	0.308621i
$683$			32.4671i			1.24232i	0.783685	+	0.621159i	$0.213338\pi$
$683$			32.4671i			1.24232i	−0.783685	+	0.621159i	$0.786662\pi$
$684$	−10.2384	−	10.9814i	−0.391477	−	0.419884i
$685$	10.2224	−	9.20426i	0.390577	−	0.351677i
$686$	1.02148	+	1.40595i	0.0390004	+	0.0536795i
$687$	14.1163	+	15.4067i	0.538572	+	0.587801i
$688$	−3.75664	−	2.16890i	−0.143220	−	0.0826884i
$689$	−10.4808	+	1.10157i	−0.399285	+	0.0419666i
$690$	2.41284	−	5.54847i	0.0918554	−	0.211227i
$691$	−1.28238	+	12.2010i	−0.0487841	+	0.464149i	0.942673	+	0.333717i	$0.108303\pi$
$691$	−1.28238	+	12.2010i	−0.0487841	+	0.464149i	−0.991457	+	0.130432i	$0.958364\pi$
$692$	−17.5123	−	15.7681i	−0.665718	−	0.599415i
$693$	0.626907	−	0.0108857i	0.0238142	−	0.000413515i
$694$	1.25638	−	5.91082i	0.0476916	−	0.224372i
$695$	−3.24720	+	0.690213i	−0.123173	+	0.0261813i
$696$	−12.2481	+	9.06225i	−0.464263	+	0.343504i
$697$	1.43547	+	0.466413i	0.0543724	+	0.0176667i
$698$	2.02339	+	0.657440i	0.0765865	+	0.0248845i
$699$	30.6878	−	22.7056i	1.16072	−	0.858805i
$700$	−0.121554	+	0.0258371i	−0.00459430	+	0.000976549i
$701$	10.5165	−	49.4760i	0.397201	−	1.86868i	−0.0908443	−	0.995865i	$-0.528957\pi$
$701$	10.5165	−	49.4760i	0.397201	−	1.86868i	0.488045	−	0.872818i	$-0.337710\pi$
$702$	−1.45102	−	6.04757i	−0.0547652	−	0.228251i
$703$	38.1804	+	34.3777i	1.44000	+	1.29658i
$704$	−0.175800	+	1.67262i	−0.00662570	+	0.0630393i
$705$	−2.04587	+	4.70459i	−0.0770519	+	0.177185i
$706$	5.99751	−	0.630363i	0.225719	−	0.0237240i
$707$	0.833422	+	0.481176i	0.0313441	+	0.0180965i
$708$	−1.42291	−	1.55297i	−0.0534762	−	0.0583643i
$709$	12.7615	+	17.5646i	0.479267	+	0.659654i	0.978364	−	0.206892i	$-0.0663349\pi$
$709$	12.7615	+	17.5646i	0.479267	+	0.659654i	−0.499097	+	0.866546i	$0.666335\pi$
$710$	−11.2665	+	10.1444i	−0.422825	+	0.380713i
$711$	20.7611	−	19.3565i	0.778603	−	0.725927i
$712$		−	8.89002i		−	0.333168i
$713$	0.205124	+	19.4482i	0.00768196	+	0.728342i
$714$	0.0578112	−	0.0128137i	0.00216353	−	0.000479540i
$715$	−0.622041	−	1.91444i	−0.0232630	−	0.0715962i
$716$	0.0430558	+	0.0478183i	0.00160907	+	0.00178705i
$717$	−5.37208	−	4.75325i	−0.200624	−	0.177513i
$718$	−2.87792	−	4.98471i	−0.107403	−	0.186028i
$719$	−12.0315	+	20.8391i	−0.448698	+	0.777168i	−0.998302	−	0.0582576i	$-0.981446\pi$
$719$	−12.0315	+	20.8391i	−0.448698	+	0.777168i	0.549603	+	0.835426i	$0.314779\pi$
$720$	−2.57164	+	1.54488i	−0.0958394	+	0.0575743i
$721$	1.03022	+	0.748498i	0.0383674	+	0.0278755i
$722$	−6.01318	−	0.632011i	−0.223788	−	0.0235210i
$723$	−19.2603	+	34.0389i	−0.716299	+	1.26592i
$724$	−6.45933	+	14.5079i	−0.240059	+	0.539182i
$725$	−8.60437	−	1.82891i	−0.319558	−	0.0679242i
$726$	−12.8793	+	5.86871i	−0.477994	+	0.217808i
$727$	−18.1407	+	8.07676i	−0.672801	+	0.299551i	−0.714557	−	0.699577i	$-0.753372\pi$
$727$	−18.1407	+	8.07676i	−0.672801	+	0.299551i	0.0417554	+	0.999128i	$0.486705\pi$
$728$	−0.0459621	+	0.141457i	−0.00170347	+	0.00524273i
$729$	22.6401	+	14.7114i	0.838522	+	0.544868i
$730$	−2.31783	−	5.20592i	−0.0857866	−	0.192680i
$731$	0.248113	+	1.16728i	0.00917677	+	0.0431733i
$732$	−5.30205	+	0.0460295i	−0.195970	+	0.00170130i
$733$	−29.3208	−	13.0545i	−1.08299	−	0.482178i	−0.213912	−	0.976853i	$-0.568620\pi$
$733$	−29.3208	−	13.0545i	−1.08299	−	0.482178i	−0.869078	+	0.494675i	$0.835287\pi$
$734$	−16.5036	+	18.3291i	−0.609157	+	0.676538i
$735$	1.36894	+	12.0199i	0.0504942	+	0.443361i
$736$	−2.05325	+	2.82606i	−0.0756839	+	0.104170i
$737$	−1.15206	−	10.9611i	−0.0424367	−	0.403758i
$738$	1.43600	−	16.3964i	0.0528600	−	0.603561i
$739$	−27.1759	+	15.6900i	−0.999682	+	0.577167i	−0.908154	−	0.418636i	$-0.862508\pi$
$739$	−27.1759	+	15.6900i	−0.999682	+	0.577167i	−0.0915279	+	0.995803i	$0.529175\pi$
$740$	8.30524	−	6.03411i	0.305307	−	0.221818i
$741$	−8.44612	−	6.02514i	−0.310276	−	0.221339i
$742$	−1.04063	+	0.338121i	−0.0382027	+	0.0124128i
$743$	6.01158			0.220543			0.110272	−	0.993901i	$-0.464828\pi$
$743$	6.01158			0.220543			0.110272	+	0.993901i	$0.464828\pi$
$744$	5.51734	−	7.90942i	0.202276	−	0.289973i
$745$	−0.463743			−0.0169902
$746$	−15.3334	+	4.98212i	−0.561395	+	0.182408i
$747$	−15.2454	−	6.47291i	−0.557799	−	0.236831i
$748$	0.374319	−	0.271959i	0.0136865	−	0.00994380i
$749$	1.69374	−	0.977882i	0.0618879	−	0.0357310i
$750$	−1.65186	−	0.520913i	−0.0603175	−	0.0190210i
$751$	−3.89234	−	37.0332i	−0.142034	−	1.35136i	−0.800764	−	0.598980i	$-0.795573\pi$
$751$	−3.89234	−	37.0332i	−0.142034	−	1.35136i	0.658731	−	0.752379i	$-0.271094\pi$
$752$	1.74097	−	2.39624i	0.0634866	−	0.0873818i
$753$	12.3935	−	1.41150i	0.451646	−	0.0514378i
$754$	−7.04496	+	7.82422i	−0.256562	+	0.284941i
$755$	−0.823618	−	0.366698i	−0.0299745	−	0.0133455i
$756$	−0.277911	−	0.582858i	−0.0101075	−	0.0211983i
$757$	−10.6619	−	50.1601i	−0.387512	−	1.82310i	−0.548509	−	0.836144i	$-0.684805\pi$
$757$	−10.6619	−	50.1601i	−0.387512	−	1.82310i	0.160998	−	0.986955i	$-0.448529\pi$
$758$	10.6944	+	24.0201i	0.388440	+	0.872450i
$759$	10.1289	+	0.975765i	0.367655	+	0.0354180i
$760$	−1.54652	+	4.75968i	−0.0560980	+	0.172652i
$761$	−6.71094	+	2.98790i	−0.243271	+	0.108311i	−0.524751	−	0.851256i	$-0.675842\pi$
$761$	−6.71094	+	2.98790i	−0.243271	+	0.108311i	0.281479	+	0.959567i	$0.409175\pi$
$762$	−3.87416	−	8.50209i	−0.140346	−	0.307998i
$763$	−2.11928	−	0.450466i	−0.0767229	−	0.0163080i
$764$	9.65723	−	21.6905i	0.349386	−	0.784735i
$765$	0.789236	+	0.241372i	0.0285349	+	0.00872682i
$766$	−3.78259	−	0.397566i	−0.136670	−	0.0143646i
$767$	−1.17751	−	0.855512i	−0.0425175	−	0.0308908i
$768$	1.64257	−	0.549513i	0.0592711	−	0.0198288i
$769$	2.58049	−	4.46955i	0.0930550	−	0.161176i	−0.815740	−	0.578418i	$-0.803670\pi$
$769$	2.58049	−	4.46955i	0.0930550	−	0.161176i	0.908795	+	0.417242i	$0.137003\pi$
$770$	−0.104500	−	0.181000i	−0.00376593	−	0.00652278i
$771$	−6.67935	+	7.54894i	−0.240551	+	0.271869i
$772$	−7.91383	−	8.78919i	−0.284825	−	0.316330i
$773$	12.2154	+	37.5953i	0.439359	+	1.35221i	0.888553	+	0.458774i	$0.151711\pi$
$773$	12.2154	+	37.5953i	0.439359	+	1.35221i	−0.449194	+	0.893434i	$0.648289\pi$
$774$	11.7946	−	5.49862i	0.423949	−	0.197644i
$775$	5.53082	−	0.640357i	0.198673	−	0.0230023i
$776$			4.42045i			0.158685i
$777$	1.12139	+	1.90393i	0.0402295	+	0.0683032i
$778$	−14.1466	+	12.7376i	−0.507179	+	0.456666i
$779$	−16.1390	−	22.2135i	−0.578241	−	0.795881i
$780$	−1.52849	+	1.40048i	−0.0547287	+	0.0501451i
$781$	−22.0816	−	12.7488i	−0.790141	−	0.456188i
$782$	0.955738	−	0.100452i	0.0341771	−	0.00359216i
$783$	−1.19028	−	45.6929i	−0.0425372	−	1.63293i
$784$	0.730085	−	6.94629i	0.0260745	−	0.248082i
$785$	−4.01094	−	3.61147i	−0.143157	−	0.128899i
$786$	−0.569438	+	2.79823i	−0.0203112	+	0.0998095i
$787$	2.49955	−	11.7594i	0.0890993	−	0.419179i	−0.910880	−	0.412672i	$-0.864595\pi$
$787$	2.49955	−	11.7594i	0.0890993	−	0.419179i	0.999979	−	0.00650678i	$-0.00207119\pi$
$788$	6.04204	−	1.28428i	0.215239	−	0.0457504i
$789$	5.65344	+	7.64091i	0.201268	+	0.272024i
$790$	−8.99853	−	2.92380i	−0.320153	−	0.104024i
$791$	0.308319	+	0.100179i	0.0109626	+	0.00356195i
$792$	−3.80759	−	3.31050i	−0.135297	−	0.117633i
$793$	−3.58391	+	0.761784i	−0.127268	+	0.0270517i
$794$	−3.86484	+	18.1826i	−0.137158	+	0.645278i
$795$	−14.9443	−	3.04115i	−0.530019	−	0.107859i
$796$	14.0170	+	12.6210i	0.496821	+	0.447339i
$797$	1.73849	−	16.5406i	0.0615805	−	0.585899i	−0.919607	−	0.392840i	$-0.871493\pi$
$797$	1.73849	−	16.5406i	0.0615805	−	0.585899i	0.981187	−	0.193059i	$-0.0618408\pi$
$798$	−0.987838	−	0.429578i	−0.0349691	−	0.0152069i
$799$	−0.810378	+	0.0851742i	−0.0286691	+	0.00301325i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$	21.8455	+	15.2993i	0.771871	+	0.540574i
$802$	7.45343	+	10.2588i	0.263190	+	0.362250i
$803$	7.12237	−	6.41301i	0.251343	−	0.226310i
$804$	−9.78025	+	5.76041i	−0.344923	+	0.203154i
$805$		−	0.434098i		−	0.0152999i
$806$	2.64613	−	6.11610i	0.0932059	−	0.215430i
$807$	−6.78594	−	30.6160i	−0.238877	−	1.07773i
$808$	−2.39305	−	7.36506i	−0.0841873	−	0.259102i
$809$	−1.44725	−	1.60733i	−0.0508824	−	0.0565107i	0.717166	−	0.696902i	$-0.245439\pi$
$809$	−1.44725	−	1.60733i	−0.0508824	−	0.0565107i	−0.768049	+	0.640391i	$0.778772\pi$
$810$	0.629439	−	8.97796i	0.0221162	−	0.315453i
$811$	−13.2592	−	22.9656i	−0.465593	−	0.806430i	0.533635	−	0.845715i	$-0.320826\pi$
$811$	−13.2592	−	22.9656i	−0.465593	−	0.806430i	−0.999228	+	0.0392844i	$0.987492\pi$
$812$	−0.546574	+	0.946693i	−0.0191810	+	0.0332224i
$813$	4.17399	+	12.4766i	0.146388	+	0.437575i
$814$	13.9681	+	10.1484i	0.489580	+	0.355701i
$815$	−13.6755	−	1.43735i	−0.479031	−	0.0503481i
$816$	−0.414713	−	0.234658i	−0.0145179	−	0.00821468i
$817$	8.82986	−	19.8322i	0.308918	−	0.693840i
$818$	−25.5559	−	5.43208i	−0.893542	−	0.189928i
$819$	−0.268503	−	0.356383i	−0.00938225	−	0.0124530i
$820$	−5.01207	+	2.23152i	−0.175029	+	0.0779280i
$821$	9.99795	−	30.7705i	0.348931	−	1.07390i	−0.610515	−	0.792005i	$-0.709037\pi$
$821$	9.99795	−	30.7705i	0.348931	−	1.07390i	0.959446	−	0.281894i	$-0.0909625\pi$
$822$	2.28463	−	23.7155i	0.0796857	−	0.827174i
$823$	18.5622	+	41.6914i	0.647038	+	1.45327i	0.877204	+	0.480119i	$0.159406\pi$
$823$	18.5622	+	41.6914i	0.647038	+	1.45327i	−0.230166	+	0.973151i	$0.573927\pi$
$824$	−2.13052	−	10.0233i	−0.0742203	−	0.349179i
$825$	−0.0252883	−	2.91291i	−0.000880426	−	0.101415i
$826$	−0.138054	−	0.0614656i	−0.00480351	−	0.00213866i
$827$	−25.5012	+	28.3220i	−0.886764	+	0.984852i	−0.999962	−	0.00872083i	$-0.997224\pi$
$827$	−25.5012	+	28.3220i	−0.886764	+	0.984852i	0.113198	+	0.993573i	$0.463891\pi$
$828$	−3.41092	−	9.90897i	−0.118538	−	0.344360i
$829$	12.3239	−	16.9624i	0.428026	−	0.589127i	−0.539473	−	0.842003i	$-0.681376\pi$
$829$	12.3239	−	16.9624i	0.428026	−	0.589127i	0.967499	+	0.252876i	$0.0813764\pi$
$830$	0.577088	+	5.49062i	0.0200310	+	0.190582i
$831$	7.43742	−	23.5847i	0.258001	−	0.818145i
$832$	1.03653	−	0.598443i	0.0359354	−	0.0207473i
$833$	−1.55452	+	1.12943i	−0.0538611	+	0.0391324i
$834$	−3.33923	+	4.68098i	−0.115628	+	0.162089i
$835$	4.82178	−	1.56669i	0.166864	−	0.0542176i
$836$	−8.41696			−0.291107
$837$	9.94073	+	27.1695i	0.343602	+	0.939115i
$838$	−14.3350			−0.495196
$839$	52.5623	−	17.0785i	1.81465	−	0.589616i	0.814700	−	0.579883i	$-0.196902\pi$
$839$	52.5623	−	17.0785i	1.81465	−	0.589616i	0.999953	−	0.00973293i	$-0.00309814\pi$
$840$	−0.124999	+	0.175225i	−0.00431287	+	0.00604585i
$841$	−39.1403	+	28.4371i	−1.34967	+	0.980589i
$842$	8.48239	−	4.89731i	0.292323	−	0.168773i
$843$	−14.0849	+	44.6646i	−0.485111	+	1.53833i
$844$	−2.22716	−	21.1900i	−0.0766621	−	0.729391i
$845$	6.79918	−	9.35827i	0.233899	−	0.321934i
$846$	2.89215	+	8.40189i	0.0994342	+	0.288863i
$847$	−0.679474	+	0.754633i	−0.0233470	+	0.0259295i
$848$	8.04370	+	3.58128i	0.276222	+	0.122982i
$849$	−0.439955	−	50.6777i	−0.0150992	−	1.73925i
$850$	−0.0571979	−	0.269095i	−0.00196187	−	0.00922988i
$851$	14.5858	+	32.7603i	0.499996	+	1.12301i
$852$	−2.51799	+	26.1379i	−0.0862650	+	0.895470i
$853$	13.3136	−	40.9752i	0.455850	−	1.40296i	−0.414284	−	0.910148i	$-0.635968\pi$
$853$	13.3136	−	40.9752i	0.455850	−	1.40296i	0.870134	−	0.492815i	$-0.164032\pi$
$854$	−0.347531	+	0.154731i	−0.0118923	+	0.00529478i
$855$	−9.03449	−	11.9914i	−0.308973	−	0.410099i
$856$	−15.3942	−	3.27213i	−0.526162	−	0.111839i
$857$	−7.13751	+	16.0311i	−0.243813	+	0.547612i	−0.993454	−	0.114232i	$-0.963559\pi$
$857$	−7.13751	+	16.0311i	−0.243813	+	0.547612i	0.749641	+	0.661844i	$0.230226\pi$
$858$	−3.03447	−	1.71700i	−0.103595	−	0.0586175i
$859$	−30.9436	−	3.25231i	−1.05578	−	0.110967i	−0.439304	−	0.898338i	$-0.644775\pi$
$859$	−30.9436	−	3.25231i	−1.05578	−	0.110967i	−0.616479	+	0.787371i	$0.711442\pi$
$860$	−3.50935	−	2.54969i	−0.119668	−	0.0869437i
$861$	−0.374653	−	1.11989i	−0.0127681	−	0.0381657i
$862$	5.44927	−	9.43841i	0.185603	−	0.321474i
$863$	−19.7844	−	34.2677i	−0.673470	−	1.16649i	−0.976913	−	0.213635i	$-0.931470\pi$
$863$	−19.7844	−	34.2677i	−0.673470	−	1.16649i	0.303443	−	0.952850i	$-0.401864\pi$
$864$	−1.47647	+	4.98197i	−0.0502304	+	0.169490i
$865$	−15.7681	−	17.5123i	−0.536133	−	0.595436i
$866$	−0.937091	−	2.88407i	−0.0318437	−	0.0980047i
$867$	−6.34336	−	28.6192i	−0.215432	−	0.971959i
$868$	0.136709	−	0.678262i	0.00464020	−	0.0230217i
$869$		−	15.9129i		−	0.539808i
$870$	−13.1283	+	7.73233i	−0.445090	+	0.262151i
$871$	−5.82886	+	5.24833i	−0.197503	+	0.177833i
$872$	10.2480	+	14.1051i	0.347040	+	0.477659i
$873$	−10.8624	−	7.60738i	−0.367635	−	0.257471i
$874$	−15.1400	−	8.74108i	−0.512118	−	0.295672i
$875$	−0.123589	+	0.0129897i	−0.00417806	+	0.000439132i
$876$	−9.05143	−	3.93616i	−0.305820	−	0.132991i
$877$	−2.46664	+	23.4685i	−0.0832924	+	0.792474i	0.870533	+	0.492111i	$0.163775\pi$
$877$	−2.46664	+	23.4685i	−0.0832924	+	0.792474i	−0.953825	+	0.300363i	$0.902892\pi$
$878$	13.3777	+	12.0453i	0.451475	+	0.406510i
$879$	10.8639	+	2.21081i	0.366431	+	0.0745686i
$880$	−0.349673	+	1.64508i	−0.0117875	+	0.0554557i
$881$	24.6479	−	5.23908i	0.830410	−	0.176509i	0.226954	−	0.973906i	$-0.427123\pi$
$881$	24.6479	−	5.23908i	0.830410	−	0.176509i	0.603456	+	0.797396i	$0.293790\pi$
$882$	15.8127	+	13.7483i	0.532441	+	0.462929i
$883$	−21.1389	−	6.86846i	−0.711382	−	0.231142i	−0.0690992	−	0.997610i	$-0.522012\pi$
$883$	−21.1389	−	6.86846i	−0.711382	−	0.231142i	−0.642283	+	0.766468i	$0.722012\pi$
$884$	−0.313156	−	0.101751i	−0.0105326	−	0.00342224i
$885$	−1.25278	−	1.69320i	−0.0421119	−	0.0569163i
$886$	15.4498	−	3.28397i	0.519048	−	0.110327i
$887$	2.68731	−	12.6428i	0.0902311	−	0.424504i	−0.909726	−	0.415210i	$-0.863708\pi$
$887$	2.68731	−	12.6428i	0.0902311	−	0.424504i	0.999957	−	0.00929426i	$-0.00295850\pi$
$888$	3.54575	−	17.4238i	0.118987	−	0.584706i
$889$	−0.498162	−	0.448547i	−0.0167078	−	0.0150438i
$890$	0.929260	−	8.84132i	0.0311489	−	0.296362i
$891$	14.6876	−	3.65919i	0.492052	−	0.122587i
$892$	−13.5780	+	1.42710i	−0.454624	+	0.0477829i
$893$	12.8373	+	7.41163i	0.429585	+	0.248021i
$894$	−0.592226	+	0.542625i	−0.0198070	+	0.0181481i
$895$	0.0378215	+	0.0520569i	0.00126423	+	0.00174007i
$896$	0.0923502	−	0.0831524i	0.00308520	−	0.00277793i
$897$	−3.67513	−	6.23978i	−0.122709	−	0.208340i
$898$		−	5.57970i		−	0.186197i
$899$	28.3687	−	39.9249i	0.946148	−	1.33157i
$900$	−2.71904	+	1.26761i	−0.0906346	+	0.0422536i
$901$	−0.748530	−	2.30374i	−0.0249371	−	0.0767486i
$902$	−6.17421	−	6.85716i	−0.205579	−	0.228318i
$903$	0.618700	−	0.699249i	0.0205891	−	0.0232696i
$904$	−1.30437	−	2.25923i	−0.0433826	−	0.0751409i
$905$	−7.94044	+	13.7532i	−0.263949	+	0.457173i
$906$	−1.48088	+	0.495420i	−0.0491989	+	0.0164592i
$907$	−19.4424	−	14.1258i	−0.645575	−	0.469038i	0.216186	−	0.976352i	$-0.430638\pi$
$907$	−19.4424	−	14.1258i	−0.645575	−	0.469038i	−0.861761	+	0.507314i	$0.830638\pi$
$908$	9.65880	+	1.01518i	0.320538	+	0.0336899i
$909$	22.2165	+	6.79447i	0.736875	+	0.225358i
$910$	−0.0604965	+	0.135877i	−0.00200544	+	0.00450429i
$911$	38.0181	+	8.08100i	1.25960	+	0.267735i	0.788879	−	0.614549i	$-0.210662\pi$
$911$	38.0181	+	8.08100i	1.25960	+	0.267735i	0.470717	+	0.882284i	$0.343995\pi$
$912$	3.59431	+	7.88795i	0.119020	+	0.261196i
$913$	−8.48245	+	3.77663i	−0.280728	+	0.124988i
$914$	−1.45814	+	4.48770i	−0.0482311	+	0.148440i
$915$	−5.27782	−	0.508438i	−0.174479	−	0.0168084i
$916$	−4.90696	−	11.0212i	−0.162131	−	0.364151i
$917$	0.0425968	+	0.200402i	0.00140667	+	0.00661786i
$918$	1.29033	−	0.615238i	0.0425871	−	0.0203059i
$919$	−33.7014	−	15.0048i	−1.11171	−	0.494963i	−0.233072	−	0.972460i	$-0.574878\pi$
$919$	−33.7014	−	15.0048i	−1.11171	−	0.494963i	−0.878634	+	0.477496i	$0.841544\pi$
$920$	−2.33741	+	2.59595i	−0.0770620	+	0.0855861i
$921$	−3.82970	+	0.436163i	−0.126193	+	0.0143721i
$922$	9.81364	−	13.5073i	0.323195	−	0.444840i
$923$	1.89672	+	18.0461i	0.0624314	+	0.593995i
$924$	−0.345240	−	0.108871i	−0.0113576	−	0.00358160i
$925$	8.89048	−	5.13292i	0.292317	−	0.168769i
$926$	23.5651	−	17.1211i	0.774399	−	0.562634i
$927$	28.2969	+	12.0143i	0.929391	+	0.394603i
$928$	8.36606	−	2.71830i	0.274629	−	0.0892325i
$929$	13.5110			0.443281			0.221641	−	0.975128i	$-0.428859\pi$
$929$	13.5110			0.443281			0.221641	+	0.975128i	$0.428859\pi$
$930$	6.31388	−	7.28937i	0.207040	−	0.239028i
$931$	34.9551			1.14561
$932$	−20.9613	+	6.81073i	−0.686610	+	0.223093i
$933$	10.4884	+	7.48203i	0.343375	+	0.244951i
$934$	−1.06471	+	0.773558i	−0.0348384	+	0.0253116i
$935$	0.400696	−	0.231342i	0.0131042	−	0.00756570i
$936$	−0.313272	+	3.57697i	−0.0102396	+	0.116917i
$937$	−4.61474	−	43.9064i	−0.150757	−	1.43436i	−0.764384	−	0.644762i	$-0.776957\pi$
$937$	−4.61474	−	43.9064i	−0.150757	−	1.43436i	0.613626	−	0.789596i	$-0.289710\pi$
$938$	−0.478674	+	0.658839i	−0.0156293	+	0.0215118i
$939$	−2.18376	−	19.1743i	−0.0712643	−	0.625731i
$940$	1.98191	−	2.20113i	0.0646426	−	0.0717929i
$941$	38.2044	+	17.0097i	1.24543	+	0.554500i	0.920316	−	0.391176i	$-0.127931\pi$
$941$	38.2044	+	17.0097i	1.24543	+	0.554500i	0.325112	+	0.945676i	$0.394598\pi$
$942$	−9.34797	+	0.0811538i	−0.304573	+	0.00264413i
$943$	−3.98465	−	18.7463i	−0.129758	−	0.610463i
$944$	0.494616	+	1.11092i	0.0160984	+	0.0361575i
$945$	−0.215464	−	0.608714i	−0.00700904	−	0.0198015i
$946$	2.25442	−	6.93839i	0.0732975	−	0.225586i
$947$	−32.5613	+	14.4972i	−1.05810	+	0.471097i	−0.860640	−	0.509214i	$-0.829936\pi$
$947$	−32.5613	+	14.4972i	−1.05810	+	0.471097i	−0.197461	+	0.980311i	$0.563269\pi$
$948$	−14.9128	+	6.79532i	−0.484344	+	0.220702i
$949$	−6.67152	−	1.41808i	−0.216567	−	0.0460327i
$950$	−2.03557	+	4.57196i	−0.0660425	+	0.148334i
$951$	22.8679	−	40.4146i	0.741543	−	1.31053i
$952$	−0.0340001	−	0.00357355i	−0.00110195	−	0.000115819i
$953$	5.94338	+	4.31812i	0.192525	+	0.139878i	0.679872	−	0.733331i	$-0.262035\pi$
$953$	5.94338	+	4.31812i	0.192525	+	0.139878i	−0.487347	+	0.873208i	$0.662035\pi$
$954$	−22.6431	+	13.6026i	−0.733098	+	0.440399i
$955$	11.8716	−	20.5622i	0.384156	−	0.665378i
$956$	2.07068	+	3.58653i	0.0669706	+	0.115997i
$957$	−19.1910	−	16.9803i	−0.620357	−	0.548895i
$958$	6.14988	+	6.83014i	0.198694	+	0.220672i
$959$	−0.528232	−	1.62573i	−0.0170575	−	0.0524976i
$960$	1.69101	−	0.374808i	0.0545772	−	0.0120969i
$961$	−8.95554	+	29.6782i	−0.288889	+	0.957363i
$962$		−	12.2871i		−	0.396150i
$963$	34.5333	−	32.1969i	1.11282	−	1.03753i
$964$	16.7804	−	15.1092i	0.540461	−	0.486633i
$965$	−6.95175	−	9.56827i	−0.223785	−	0.308013i
$966$	−0.507937	−	0.554367i	−0.0163426	−	0.0178365i
$967$	39.4726	+	22.7895i	1.26935	+	0.732861i	0.974866	−	0.222794i	$-0.0715178\pi$
$967$	39.4726	+	22.7895i	1.26935	+	0.732861i	0.294487	+	0.955655i	$0.404851\pi$
$968$	8.12667	−	0.854147i	0.261201	−	0.0274533i
$969$	0.950996	−	2.18687i	0.0305504	−	0.0702524i
$970$	−0.462062	+	4.39623i	−0.0148359	+	0.141154i
$971$	25.3012	+	22.7813i	0.811954	+	0.731087i	0.966436	−	0.256909i	$-0.0827040\pi$
$971$	25.3012	+	22.7813i	0.811954	+	0.731087i	−0.154481	+	0.987996i	$0.549371\pi$
$972$	−9.70127	−	12.2019i	−0.311168	−	0.391375i
$973$	−0.0857724	+	0.403527i	−0.00274974	+	0.0129365i
$974$	20.2784	−	4.31030i	0.649761	−	0.138111i
$975$	−1.66651	+	1.23303i	−0.0533709	+	0.0394887i
$976$	2.91143	+	0.945980i	0.0931926	+	0.0302801i
$977$	−24.4559	−	7.94621i	−0.782415	−	0.254222i	−0.109544	−	0.993982i	$-0.534939\pi$
$977$	−24.4559	−	7.94621i	−0.782415	−	0.254222i	−0.672871	+	0.739760i	$0.734939\pi$
$978$	−19.1462	+	14.1661i	−0.612227	+	0.452981i
$979$	14.6248	−	3.10860i	0.467412	−	0.0993514i
$980$	1.45217	−	6.83193i	0.0463879	−	0.218238i
$981$	−52.2967	+	0.908091i	−1.66971	+	0.0289931i
$982$	−11.7325	−	10.5640i	−0.374400	−	0.337111i
$983$	0.523066	−	4.97664i	0.0166832	−	0.158730i	−0.983008	−	0.183560i	$-0.941238\pi$
$983$	0.523066	−	4.97664i	0.0166832	−	0.158730i	0.999692	+	0.0248300i	$0.00790443\pi$
$984$	−3.78960	+	8.71439i	−0.120808	+	0.277805i
$985$	6.14319	−	0.645675i	0.195738	−	0.0205729i
$986$	−2.09578	−	1.21000i	−0.0667433	−	0.0385343i
$987$	0.430684	+	0.470052i	0.0137088	+	0.0149619i
$988$	3.52082	+	4.84599i	0.112012	+	0.154171i
$989$	11.2607	−	10.1392i	0.358070	−	0.322407i
$990$	−3.44069	−	3.69036i	−0.109352	−	0.117287i
$991$		−	38.3856i		−	1.21936i	−0.792648	−	0.609680i	$-0.791298\pi$
$991$		−	38.3856i		−	1.21936i	0.792648	−	0.609680i	$-0.208702\pi$
$992$	−4.46965	+	3.31997i	−0.141912	+	0.105409i
$993$	−2.89730	+	0.642178i	−0.0919430	+	0.0203789i
$994$	0.582187	+	1.79179i	0.0184659	+	0.0568321i
$995$	12.6210	+	14.0170i	0.400112	+	0.444370i
$996$	7.16155	+	6.33658i	0.226922	+	0.200782i
$997$	15.6204	+	27.0553i	0.494702	+	0.856849i	0.999981	−	0.00610716i	$-0.00194398\pi$
$997$	15.6204	+	27.0553i	0.494702	+	0.856849i	−0.505280	+	0.862956i	$0.668611\pi$
$998$	7.58529	−	13.1381i	0.240108	−	0.415879i
$999$	36.7135	+	38.6986i	1.16157	+	1.22437i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.br.a.11.4	✓	176
3.2	odd	2	inner	930.2.br.a.11.13	yes	176
31.17	odd	30	inner	930.2.br.a.761.13	yes	176
93.17	even	30	inner	930.2.br.a.761.4	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.br.a.11.4	✓	176	1.1	even	1	trivial
930.2.br.a.11.13	yes	176	3.2	odd	2	inner
930.2.br.a.761.4	yes	176	93.17	even	30	inner
930.2.br.a.761.13	yes	176	31.17	odd	30	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.br (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 + 0.309017i) q^{2} +(-1.00587 + 1.41004i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(0.520913 - 1.65186i) q^{6} +(-0.0129897 - 0.123589i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(-0.976447 - 2.83664i) q^{9} +O(q^{10})\)	\(q+(-0.951057 + 0.309017i) q^{2} +(-1.00587 + 1.41004i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(0.520913 - 1.65186i) q^{6} +(-0.0129897 - 0.123589i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(-0.976447 - 2.83664i) q^{9} +(-0.669131 + 0.743145i) q^{10} +(-1.53643 - 0.684064i) q^{11} +(0.0150361 + 1.73199i) q^{12} +(0.248847 + 1.17073i) q^{13} +(0.0505449 + 0.113526i) q^{14} +(-0.166088 + 1.72407i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.251322 + 0.111896i) q^{17} +(1.80523 + 2.39607i) q^{18} +(4.89527 + 1.04052i) q^{19} +(0.406737 - 0.913545i) q^{20} +(0.187331 + 0.105998i) q^{21} +(1.67262 + 0.175800i) q^{22} +(2.82606 + 2.05325i) q^{23} +(-0.549513 - 1.64257i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-0.598443 - 1.03653i) q^{26} +(4.98197 + 1.47647i) q^{27} +(-0.0831524 - 0.0923502i) q^{28} +(-2.71830 - 8.36606i) q^{29} +(-0.374808 - 1.69101i) q^{30} +(3.31997 + 4.46965i) q^{31} +1.00000i q^{32} +(2.51001 - 1.47836i) q^{33} +(0.204444 - 0.184082i) q^{34} +(-0.0730437 - 0.100536i) q^{35} +(-2.45730 - 1.72095i) q^{36} +(8.89048 + 5.13292i) q^{37} +(-4.97721 + 0.523126i) q^{38} +(-1.90109 - 0.826721i) q^{39} +(-0.104528 + 0.994522i) q^{40} +(-4.07719 - 3.67112i) q^{41} +(-0.210918 - 0.0429217i) q^{42} +(0.901877 - 4.24300i) q^{43} +(-1.64508 + 0.349673i) q^{44} +(-2.26395 - 1.96838i) q^{45} +(-3.32223 - 1.07946i) q^{46} +(2.81695 + 0.915281i) q^{47} +(1.03020 + 1.39237i) q^{48} +(6.83193 - 1.45217i) q^{49} +(-0.207912 + 0.978148i) q^{50} +(0.0950198 - 0.466929i) q^{51} +(0.889460 + 0.800874i) q^{52} +(-0.920365 + 8.75669i) q^{53} +(-5.19439 + 0.135312i) q^{54} +(-1.67262 + 0.175800i) q^{55} +(0.107620 + 0.0621347i) q^{56} +(-6.39119 + 5.85591i) q^{57} +(5.17051 + 7.11659i) q^{58} +(-0.903708 + 0.813702i) q^{59} +(0.879014 + 1.49243i) q^{60} +3.06126i q^{61} +(-4.53868 - 3.22496i) q^{62} +(-0.337893 + 0.157525i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(0.800874 + 0.889460i) q^{65} +(-1.93033 + 2.18164i) q^{66} +(3.27663 + 5.67529i) q^{67} +(-0.137553 + 0.238249i) q^{68} +(-5.73783 + 1.91956i) q^{69} +(0.100536 + 0.0730437i) q^{70} +(15.0775 + 1.58471i) q^{71} +(2.86883 + 0.877376i) q^{72} +(-2.31783 + 5.20592i) q^{73} +(-10.0415 - 2.13439i) q^{74} +(0.718198 + 1.57613i) q^{75} +(4.57196 - 2.03557i) q^{76} +(-0.0645848 + 0.198771i) q^{77} +(2.06352 + 0.198789i) q^{78} +(3.84839 + 8.64362i) q^{79} +(-0.207912 - 0.978148i) q^{80} +(-7.09310 + 5.53966i) q^{81} +(5.01207 + 2.23152i) q^{82} +(3.69418 - 4.10280i) q^{83} +(0.213858 - 0.0243562i) q^{84} +(-0.161704 + 0.222566i) q^{85} +(0.453423 + 4.31403i) q^{86} +(14.5308 + 4.58226i) q^{87} +(1.45651 - 0.840918i) q^{88} +(-7.19218 + 5.22542i) q^{89} +(2.76141 + 1.17244i) q^{90} +(0.141457 - 0.0459621i) q^{91} +3.49320 q^{92} +(-9.64187 + 0.185417i) q^{93} -2.96191 q^{94} +(4.75968 - 1.54652i) q^{95} +(-1.41004 - 1.00587i) q^{96} +(3.57622 - 2.59827i) q^{97} +(-6.04880 + 3.49228i) q^{98} +(-0.440201 + 5.02627i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9	\( 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9} - 22 q^{10} - 38 q^{13} - 44 q^{16} + 12 q^{18} + 8 q^{19} - 18 q^{21} - 4 q^{22} + 88 q^{25} - 90 q^{27} + 36 q^{28} + 24 q^{31} + 18 q^{33} + 14 q^{34} + 4 q^{36} - 42 q^{37} - 42 q^{39} + 22 q^{40} - 12 q^{42} - 34 q^{43} - 8 q^{45} + 10 q^{46} + 22 q^{49} + 26 q^{51} - 2 q^{52} + 4 q^{55} + 114 q^{57} + 32 q^{63} + 44 q^{64} - 42 q^{66} + 20 q^{67} + 16 q^{69} + 8 q^{70} - 12 q^{72} - 28 q^{73} + 12 q^{76} - 92 q^{78} - 56 q^{79} - 124 q^{81} - 32 q^{82} - 12 q^{84} - 36 q^{87} - 6 q^{88} + 24 q^{90} - 140 q^{91} - 104 q^{93} - 36 q^{94} + 88 q^{97} - 60 q^{99}+O(q^{100}) \) 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9 - 22 * q^10 - 38 * q^13 - 44 * q^16 + 12 * q^18 + 8 * q^19 - 18 * q^21 - 4 * q^22 + 88 * q^25 - 90 * q^27 + 36 * q^28 + 24 * q^31 + 18 * q^33 + 14 * q^34 + 4 * q^36 - 42 * q^37 - 42 * q^39 + 22 * q^40 - 12 * q^42 - 34 * q^43 - 8 * q^45 + 10 * q^46 + 22 * q^49 + 26 * q^51 - 2 * q^52 + 4 * q^55 + 114 * q^57 + 32 * q^63 + 44 * q^64 - 42 * q^66 + 20 * q^67 + 16 * q^69 + 8 * q^70 - 12 * q^72 - 28 * q^73 + 12 * q^76 - 92 * q^78 - 56 * q^79 - 124 * q^81 - 32 * q^82 - 12 * q^84 - 36 * q^87 - 6 * q^88 + 24 * q^90 - 140 * q^91 - 104 * q^93 - 36 * q^94 + 88 * q^97 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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