LMFDB - Embedded newform 625.2.e.c.499.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [625,2,Mod(124,625)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(625, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("625.124");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 625 = 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	625.e (of order $10$, degree $4$, not 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:	$4.99065012633$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			499.1
Root			$-0.587785 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	625.499
Dual form			625.2.e.c.124.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 + 0.190983i) q^{2} +(0.587785 + 0.809017i) q^{3} +(-1.30902 + 0.951057i) q^{4} +(-0.500000 - 0.363271i) q^{6} -1.61803i q^{7} +(1.31433 - 1.80902i) q^{8} +(0.618034 - 1.90211i) q^{9} +O(q^{10})$	\(q+(-0.587785 + 0.190983i) q^{2} +(0.587785 + 0.809017i) q^{3} +(-1.30902 + 0.951057i) q^{4} +(-0.500000 - 0.363271i) q^{6} -1.61803i q^{7} +(1.31433 - 1.80902i) q^{8} +(0.618034 - 1.90211i) q^{9} +(-0.236068 - 0.726543i) q^{11} +(-1.53884 - 0.500000i) q^{12} +(4.61653 + 1.50000i) q^{13} +(0.309017 + 0.951057i) q^{14} +(0.572949 - 1.76336i) q^{16} +(-0.449028 + 0.618034i) q^{17} +1.23607i q^{18} +(-4.73607 - 3.44095i) q^{19} +(1.30902 - 0.951057i) q^{21} +(0.277515 + 0.381966i) q^{22} +(7.83297 - 2.54508i) q^{23} +2.23607 q^{24} -3.00000 q^{26} +(4.75528 - 1.54508i) q^{27} +(1.53884 + 2.11803i) q^{28} +(-1.11803 + 0.812299i) q^{29} +(2.42705 + 1.76336i) q^{31} +5.61803i q^{32} +(0.449028 - 0.618034i) q^{33} +(0.145898 - 0.449028i) q^{34} +(1.00000 + 3.07768i) q^{36} +(4.02874 + 1.30902i) q^{37} +(3.44095 + 1.11803i) q^{38} +(1.50000 + 4.61653i) q^{39} +(-1.61803 + 4.97980i) q^{41} +(-0.587785 + 0.809017i) q^{42} -1.85410i q^{43} +(1.00000 + 0.726543i) q^{44} +(-4.11803 + 2.99193i) q^{46} +(0.951057 + 1.30902i) q^{47} +(1.76336 - 0.572949i) q^{48} +4.38197 q^{49} -0.763932 q^{51} +(-7.46969 + 2.42705i) q^{52} +(3.21644 + 4.42705i) q^{53} +(-2.50000 + 1.81636i) q^{54} +(-2.92705 - 2.12663i) q^{56} -5.85410i q^{57} +(0.502029 - 0.690983i) q^{58} +(1.28115 - 3.94298i) q^{59} +(-1.45492 - 4.47777i) q^{61} +(-1.76336 - 0.572949i) q^{62} +(-3.07768 - 1.00000i) q^{63} +(0.0729490 + 0.224514i) q^{64} +(-0.145898 + 0.449028i) q^{66} +(5.42882 - 7.47214i) q^{67} -1.23607i q^{68} +(6.66312 + 4.84104i) q^{69} +(3.54508 - 2.57565i) q^{71} +(-2.62866 - 3.61803i) q^{72} +(-8.55951 + 2.78115i) q^{73} -2.61803 q^{74} +9.47214 q^{76} +(-1.17557 + 0.381966i) q^{77} +(-1.76336 - 2.42705i) q^{78} +(2.50000 - 1.81636i) q^{79} +(-0.809017 - 0.587785i) q^{81} -3.23607i q^{82} +(1.03681 - 1.42705i) q^{83} +(-0.809017 + 2.48990i) q^{84} +(0.354102 + 1.08981i) q^{86} +(-1.31433 - 0.427051i) q^{87} +(-1.62460 - 0.527864i) q^{88} +(-2.76393 - 8.50651i) q^{89} +(2.42705 - 7.46969i) q^{91} +(-7.83297 + 10.7812i) q^{92} +3.00000i q^{93} +(-0.809017 - 0.587785i) q^{94} +(-4.54508 + 3.30220i) q^{96} +(-1.67760 - 2.30902i) q^{97} +(-2.57565 + 0.836881i) q^{98} -1.52786 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{4} - 4 q^{6} - 4 q^{9}+O(q^{10}) $ 8 * q - 6 * q^4 - 4 * q^6 - 4 * q^9	$ 8 q - 6 q^{4} - 4 q^{6} - 4 q^{9} + 16 q^{11} - 2 q^{14} + 18 q^{16} - 20 q^{19} + 6 q^{21} - 24 q^{26} + 6 q^{31} + 28 q^{34} + 8 q^{36} + 12 q^{39} - 4 q^{41} + 8 q^{44} - 24 q^{46} + 44 q^{49} - 24 q^{51} - 20 q^{54} - 10 q^{56} - 30 q^{59} - 34 q^{61} + 14 q^{64} - 28 q^{66} + 22 q^{69} + 6 q^{71} - 12 q^{74} + 40 q^{76} + 20 q^{79} - 2 q^{81} - 2 q^{84} - 24 q^{86} - 40 q^{89} + 6 q^{91} - 2 q^{94} - 14 q^{96} - 48 q^{99}+O(q^{100}) $ 8 * q - 6 * q^4 - 4 * q^6 - 4 * q^9 + 16 * q^11 - 2 * q^14 + 18 * q^16 - 20 * q^19 + 6 * q^21 - 24 * q^26 + 6 * q^31 + 28 * q^34 + 8 * q^36 + 12 * q^39 - 4 * q^41 + 8 * q^44 - 24 * q^46 + 44 * q^49 - 24 * q^51 - 20 * q^54 - 10 * q^56 - 30 * q^59 - 34 * q^61 + 14 * q^64 - 28 * q^66 + 22 * q^69 + 6 * q^71 - 12 * q^74 + 40 * q^76 + 20 * q^79 - 2 * q^81 - 2 * q^84 - 24 * q^86 - 40 * q^89 + 6 * q^91 - 2 * q^94 - 14 * q^96 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/625\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{9}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.587785	+	0.190983i	−0.415627	+	0.135045i	−0.509363	−	0.860552i	$-0.670119\pi$
$2$	−0.587785	+	0.190983i	−0.415627	+	0.135045i	0.0937362	+	0.995597i	$0.470119\pi$
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i	0.944254	−	0.329218i	$-0.106785\pi$
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i	−0.604896	+	0.796305i	$0.706785\pi$
$4$	−1.30902	+	0.951057i	−0.654508	+	0.475528i
$5$		0			0
$5$		0			0
$6$	−0.500000	−	0.363271i	−0.204124	−	0.148305i
$7$		−	1.61803i		−	0.611559i	−0.952102	−	0.305780i	$-0.901083\pi$
$7$		−	1.61803i		−	0.611559i	0.952102	−	0.305780i	$-0.0989171\pi$
$8$	1.31433	−	1.80902i	0.464685	−	0.639584i
$9$	0.618034	−	1.90211i	0.206011	−	0.634038i
$10$		0			0
$11$	−0.236068	−	0.726543i	−0.0711772	−	0.219061i	0.909140	−	0.416491i	$-0.136740\pi$
$11$	−0.236068	−	0.726543i	−0.0711772	−	0.219061i	−0.980317	+	0.197430i	$0.936740\pi$
$12$	−1.53884	−	0.500000i	−0.444225	−	0.144338i
$13$	4.61653	+	1.50000i	1.28039	+	0.416025i	0.868719	−	0.495306i	$-0.164944\pi$
$13$	4.61653	+	1.50000i	1.28039	+	0.416025i	0.411675	+	0.911331i	$0.364944\pi$
$14$	0.309017	+	0.951057i	0.0825883	+	0.254181i
$15$		0			0
$16$	0.572949	−	1.76336i	0.143237	−	0.440839i
$17$	−0.449028	+	0.618034i	−0.108905	+	0.149895i	−0.859991	−	0.510310i	$-0.829531\pi$
$17$	−0.449028	+	0.618034i	−0.108905	+	0.149895i	0.751085	+	0.660205i	$0.229531\pi$
$18$			1.23607i			0.291344i
$19$	−4.73607	−	3.44095i	−1.08653	−	0.789409i	−0.107719	−	0.994181i	$-0.534355\pi$
$19$	−4.73607	−	3.44095i	−1.08653	−	0.789409i	−0.978810	+	0.204772i	$0.934355\pi$
$20$		0			0
$21$	1.30902	−	0.951057i	0.285651	−	0.207538i
$22$	0.277515	+	0.381966i	0.0591663	+	0.0814354i
$23$	7.83297	−	2.54508i	1.63329	−	0.530687i	0.658263	−	0.752788i	$-0.271292\pi$
$23$	7.83297	−	2.54508i	1.63329	−	0.530687i	0.975024	+	0.222101i	$0.0712916\pi$
$24$	2.23607			0.456435
$25$		0			0
$26$	−3.00000			−0.588348
$27$	4.75528	−	1.54508i	0.915155	−	0.297352i
$28$	1.53884	+	2.11803i	0.290814	+	0.400271i
$29$	−1.11803	+	0.812299i	−0.207614	+	0.150840i	−0.686733	−	0.726909i	$-0.740956\pi$
$29$	−1.11803	+	0.812299i	−0.207614	+	0.150840i	0.479120	+	0.877750i	$0.340956\pi$
$30$		0			0
$31$	2.42705	+	1.76336i	0.435911	+	0.316708i	0.784008	−	0.620750i	$-0.213172\pi$
$31$	2.42705	+	1.76336i	0.435911	+	0.316708i	−0.348097	+	0.937459i	$0.613172\pi$
$32$			5.61803i			0.993137i
$33$	0.449028	−	0.618034i	0.0781657	−	0.107586i
$34$	0.145898	−	0.449028i	0.0250213	−	0.0770077i
$35$		0			0
$36$	1.00000	+	3.07768i	0.166667	+	0.512947i
$37$	4.02874	+	1.30902i	0.662321	+	0.215201i	0.620839	−	0.783938i	$-0.286792\pi$
$37$	4.02874	+	1.30902i	0.662321	+	0.215201i	0.0414819	+	0.999139i	$0.486792\pi$
$38$	3.44095	+	1.11803i	0.558197	+	0.181369i
$39$	1.50000	+	4.61653i	0.240192	+	0.739236i
$40$		0			0
$41$	−1.61803	+	4.97980i	−0.252694	+	0.777714i	0.741581	+	0.670864i	$0.234076\pi$
$41$	−1.61803	+	4.97980i	−0.252694	+	0.777714i	−0.994275	+	0.106850i	$0.965924\pi$
$42$	−0.587785	+	0.809017i	−0.0906972	+	0.124834i
$43$		−	1.85410i		−	0.282748i	−0.989956	−	0.141374i	$-0.954848\pi$
$43$		−	1.85410i		−	0.282748i	0.989956	−	0.141374i	$-0.0451520\pi$
$44$	1.00000	+	0.726543i	0.150756	+	0.109530i
$45$		0			0
$46$	−4.11803	+	2.99193i	−0.607171	+	0.441136i
$47$	0.951057	+	1.30902i	0.138726	+	0.190940i	0.872727	−	0.488208i	$-0.162349\pi$
$47$	0.951057	+	1.30902i	0.138726	+	0.190940i	−0.734001	+	0.679148i	$0.762349\pi$
$48$	1.76336	−	0.572949i	0.254518	−	0.0826981i
$49$	4.38197			0.625995
$50$		0			0
$51$	−0.763932			−0.106972
$52$	−7.46969	+	2.42705i	−1.03586	+	0.336571i
$53$	3.21644	+	4.42705i	0.441812	+	0.608102i	0.970614	−	0.240643i	$-0.0773584\pi$
$53$	3.21644	+	4.42705i	0.441812	+	0.608102i	−0.528801	+	0.848746i	$0.677358\pi$
$54$	−2.50000	+	1.81636i	−0.340207	+	0.247175i
$55$		0			0
$56$	−2.92705	−	2.12663i	−0.391144	−	0.284182i
$57$		−	5.85410i		−	0.775395i
$58$	0.502029	−	0.690983i	0.0659196	−	0.0907305i
$59$	1.28115	−	3.94298i	0.166792	−	0.513333i	−0.832372	−	0.554217i	$-0.813018\pi$
$59$	1.28115	−	3.94298i	0.166792	−	0.513333i	0.999164	+	0.0408847i	$0.0130176\pi$
$60$		0			0
$61$	−1.45492	−	4.47777i	−0.186283	−	0.573319i	0.813685	−	0.581306i	$-0.197458\pi$
$61$	−1.45492	−	4.47777i	−0.186283	−	0.573319i	−0.999968	+	0.00798614i	$0.997458\pi$
$62$	−1.76336	−	0.572949i	−0.223946	−	0.0727646i
$63$	−3.07768	−	1.00000i	−0.387752	−	0.125988i
$64$	0.0729490	+	0.224514i	0.00911863	+	0.0280642i
$65$		0			0
$66$	−0.145898	+	0.449028i	−0.0179588	+	0.0552715i
$67$	5.42882	−	7.47214i	0.663236	−	0.912867i	−0.336347	−	0.941738i	$-0.609191\pi$
$67$	5.42882	−	7.47214i	0.663236	−	0.912867i	0.999583	+	0.0288716i	$0.00919138\pi$
$68$		−	1.23607i		−	0.149895i
$69$	6.66312	+	4.84104i	0.802145	+	0.582793i
$70$		0			0
$71$	3.54508	−	2.57565i	0.420724	−	0.305674i	−0.357205	−	0.934026i	$-0.616270\pi$
$71$	3.54508	−	2.57565i	0.420724	−	0.305674i	0.777929	+	0.628352i	$0.216270\pi$
$72$	−2.62866	−	3.61803i	−0.309790	−	0.426389i
$73$	−8.55951	+	2.78115i	−1.00181	+	0.325509i	−0.763590	−	0.645701i	$-0.776565\pi$
$73$	−8.55951	+	2.78115i	−1.00181	+	0.325509i	−0.238224	+	0.971210i	$0.576565\pi$
$74$	−2.61803			−0.304340
$75$		0			0
$76$	9.47214			1.08653
$77$	−1.17557	+	0.381966i	−0.133969	+	0.0435291i
$78$	−1.76336	−	2.42705i	−0.199661	−	0.274809i
$79$	2.50000	−	1.81636i	0.281272	−	0.204356i	−0.438200	−	0.898877i	$-0.644384\pi$
$79$	2.50000	−	1.81636i	0.281272	−	0.204356i	0.719472	+	0.694521i	$0.244384\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$		−	3.23607i		−	0.357364i
$83$	1.03681	−	1.42705i	0.113805	−	0.156639i	−0.748315	−	0.663344i	$-0.769137\pi$
$83$	1.03681	−	1.42705i	0.113805	−	0.156639i	0.862120	+	0.506705i	$0.169137\pi$
$84$	−0.809017	+	2.48990i	−0.0882710	+	0.271670i
$85$		0			0
$86$	0.354102	+	1.08981i	0.0381838	+	0.117518i
$87$	−1.31433	−	0.427051i	−0.140911	−	0.0457847i
$88$	−1.62460	−	0.527864i	−0.173183	−	0.0562705i
$89$	−2.76393	−	8.50651i	−0.292976	−	0.901688i	−0.983894	−	0.178754i	$-0.942793\pi$
$89$	−2.76393	−	8.50651i	−0.292976	−	0.901688i	0.690918	−	0.722934i	$-0.257207\pi$
$90$		0			0
$91$	2.42705	−	7.46969i	0.254424	−	0.783037i
$92$	−7.83297	+	10.7812i	−0.816643	+	1.12401i
$93$			3.00000i			0.311086i
$94$	−0.809017	−	0.587785i	−0.0834437	−	0.0606254i
$95$		0			0
$96$	−4.54508	+	3.30220i	−0.463881	+	0.337029i
$97$	−1.67760	−	2.30902i	−0.170334	−	0.234445i	0.715312	−	0.698805i	$-0.246284\pi$
$97$	−1.67760	−	2.30902i	−0.170334	−	0.234445i	−0.885647	+	0.464360i	$0.846284\pi$
$98$	−2.57565	+	0.836881i	−0.260180	+	0.0845378i
$99$	−1.52786			−0.153556
$100$		0			0
$101$	−7.47214			−0.743505			−0.371753	−	0.928332i	$-0.621243\pi$
$101$	−7.47214			−0.743505			−0.371753	+	0.928332i	$0.621243\pi$
$102$	0.449028	−	0.145898i	0.0444604	−	0.0144461i
$103$	−6.79615	−	9.35410i	−0.669645	−	0.921687i	0.330107	−	0.943943i	$-0.392915\pi$
$103$	−6.79615	−	9.35410i	−0.669645	−	0.921687i	−0.999752	+	0.0222563i	$0.992915\pi$
$104$	8.78115	−	6.37988i	0.861063	−	0.625599i
$105$		0			0
$106$	−2.73607	−	1.98787i	−0.265750	−	0.193079i
$107$			10.4164i			1.00699i	0.863998	+	0.503496i	$0.167953\pi$
$107$			10.4164i			1.00699i	−0.863998	+	0.503496i	$0.832047\pi$
$108$	−4.75528	+	6.54508i	−0.457577	+	0.629801i
$109$	−3.09017	+	9.51057i	−0.295985	+	0.910947i	0.686904	+	0.726748i	$0.258969\pi$
$109$	−3.09017	+	9.51057i	−0.295985	+	0.910947i	−0.982889	+	0.184199i	$0.941031\pi$
$110$		0			0
$111$	1.30902	+	4.02874i	0.124246	+	0.382391i
$112$	−2.85317	−	0.927051i	−0.269599	−	0.0875981i
$113$	−9.64932	−	3.13525i	−0.907732	−	0.294940i	−0.182307	−	0.983242i	$-0.558357\pi$
$113$	−9.64932	−	3.13525i	−0.907732	−	0.294940i	−0.725425	+	0.688302i	$0.758357\pi$
$114$	1.11803	+	3.44095i	0.104713	+	0.322275i
$115$		0			0
$116$	0.690983	−	2.12663i	0.0641562	−	0.197452i
$117$	5.70634	−	7.85410i	0.527551	−	0.726112i
$118$			2.56231i			0.235879i
$119$	1.00000	+	0.726543i	0.0916698	+	0.0666020i
$120$		0			0
$121$	8.42705	−	6.12261i	0.766096	−	0.556601i
$122$	1.71036	+	2.35410i	0.154848	+	0.213130i
$123$	−4.97980	+	1.61803i	−0.449013	+	0.145893i
$124$	−4.85410			−0.435911
$125$		0			0
$126$	2.00000			0.178174
$127$	15.1109	−	4.90983i	1.34088	−	0.435677i	0.451262	−	0.892391i	$-0.350974\pi$
$127$	15.1109	−	4.90983i	1.34088	−	0.435677i	0.889613	+	0.456714i	$0.150974\pi$
$128$	−6.69015	−	9.20820i	−0.591331	−	0.813898i
$129$	1.50000	−	1.08981i	0.132068	−	0.0959528i
$130$		0			0
$131$	14.3992	+	10.4616i	1.25806	+	0.914036i	0.998661	−	0.0517333i	$-0.0164746\pi$
$131$	14.3992	+	10.4616i	1.25806	+	0.914036i	0.259402	+	0.965769i	$0.416475\pi$
$132$			1.23607i			0.107586i
$133$	−5.56758	+	7.66312i	−0.482771	+	0.664477i
$134$	−1.76393	+	5.42882i	−0.152381	+	0.468979i
$135$		0			0
$136$	0.527864	+	1.62460i	0.0452640	+	0.139308i
$137$	5.65334	+	1.83688i	0.482997	+	0.156935i	0.540387	−	0.841417i	$-0.318278\pi$
$137$	5.65334	+	1.83688i	0.482997	+	0.156935i	−0.0573898	+	0.998352i	$0.518278\pi$
$138$	−4.84104	−	1.57295i	−0.412097	−	0.133898i
$139$	−1.54508	−	4.75528i	−0.131052	−	0.403338i	0.863903	−	0.503659i	$-0.168013\pi$
$139$	−1.54508	−	4.75528i	−0.131052	−	0.403338i	−0.994955	+	0.100321i	$0.968013\pi$
$140$		0			0
$141$	−0.500000	+	1.53884i	−0.0421076	+	0.129594i
$142$	−1.59184	+	2.19098i	−0.133584	+	0.183863i
$143$		−	3.70820i		−	0.310096i
$144$	−3.00000	−	2.17963i	−0.250000	−	0.181636i
$145$		0			0
$146$	4.50000	−	3.26944i	0.372423	−	0.270581i
$147$	2.57565	+	3.54508i	0.212436	+	0.292394i
$148$	−6.51864	+	2.11803i	−0.535829	+	0.174101i
$149$	−13.9443			−1.14236			−0.571180	−	0.820825i	$-0.693514\pi$
$149$	−13.9443			−1.14236			−0.571180	+	0.820825i	$0.693514\pi$
$150$		0			0
$151$	−5.56231			−0.452654			−0.226327	−	0.974051i	$-0.572672\pi$
$151$	−5.56231			−0.452654			−0.226327	+	0.974051i	$0.572672\pi$
$152$	−12.4495	+	4.04508i	−1.00979	+	0.328100i
$153$	0.898056	+	1.23607i	0.0726035	+	0.0999302i
$154$	0.618034	−	0.449028i	0.0498026	−	0.0361837i
$155$		0			0
$156$	−6.35410	−	4.61653i	−0.508735	−	0.369618i
$157$		−	9.18034i		−	0.732671i	−0.930483	−	0.366335i	$-0.880612\pi$
$157$		−	9.18034i		−	0.732671i	0.930483	−	0.366335i	$-0.119388\pi$
$158$	−1.12257	+	1.54508i	−0.0893069	+	0.122920i
$159$	−1.69098	+	5.20431i	−0.134104	+	0.412729i
$160$		0			0
$161$	−4.11803	−	12.6740i	−0.324547	−	0.998852i
$162$	0.587785	+	0.190983i	0.0461808	+	0.0150050i
$163$	−10.4616	−	3.39919i	−0.819417	−	0.266245i	−0.130836	−	0.991404i	$-0.541766\pi$
$163$	−10.4616	−	3.39919i	−0.819417	−	0.266245i	−0.688581	+	0.725159i	$0.741766\pi$
$164$	−2.61803	−	8.05748i	−0.204434	−	0.629183i
$165$		0			0
$166$	−0.336881	+	1.03681i	−0.0261470	+	0.0804723i
$167$	−3.26944	+	4.50000i	−0.252997	+	0.348220i	−0.916558	−	0.399902i	$-0.869044\pi$
$167$	−3.26944	+	4.50000i	−0.252997	+	0.348220i	0.663561	+	0.748122i	$0.269044\pi$
$168$		−	3.61803i		−	0.279137i
$169$	8.54508	+	6.20837i	0.657314	+	0.477567i
$170$		0			0
$171$	−9.47214	+	6.88191i	−0.724352	+	0.526273i
$172$	1.76336	+	2.42705i	0.134455	+	0.185061i
$173$	−16.0620	+	5.21885i	−1.22117	+	0.396782i	−0.847507	−	0.530784i	$-0.821898\pi$
$173$	−16.0620	+	5.21885i	−1.22117	+	0.396782i	−0.373661	+	0.927565i	$0.621898\pi$
$174$	0.854102			0.0647493
$175$		0			0
$176$	−1.41641			−0.106766
$177$	3.94298	−	1.28115i	0.296373	−	0.0962974i
$178$	3.24920	+	4.47214i	0.243538	+	0.335201i
$179$	−7.66312	+	5.56758i	−0.572768	+	0.416141i	−0.836110	−	0.548562i	$-0.815175\pi$
$179$	−7.66312	+	5.56758i	−0.572768	+	0.416141i	0.263341	+	0.964703i	$0.415175\pi$
$180$		0			0
$181$	−11.0902	−	8.05748i	−0.824326	−	0.598908i	0.0936225	−	0.995608i	$-0.470155\pi$
$181$	−11.0902	−	8.05748i	−0.824326	−	0.598908i	−0.917948	+	0.396700i	$0.870155\pi$
$182$			4.85410i			0.359810i
$183$	2.76741	−	3.80902i	0.204573	−	0.281571i
$184$	5.69098	−	17.5150i	0.419545	−	1.29123i
$185$		0			0
$186$	−0.572949	−	1.76336i	−0.0420107	−	0.129296i
$187$	0.555029	+	0.180340i	0.0405877	+	0.0131878i
$188$	−2.48990	−	0.809017i	−0.181594	−	0.0590036i
$189$	−2.50000	−	7.69421i	−0.181848	−	0.559671i
$190$		0			0
$191$	−7.47214	+	22.9969i	−0.540665	+	1.66400i	0.190415	+	0.981704i	$0.439016\pi$
$191$	−7.47214	+	22.9969i	−0.540665	+	1.66400i	−0.731080	+	0.682292i	$0.760984\pi$
$192$	−0.138757	+	0.190983i	−0.0100139	+	0.0137830i
$193$			5.70820i			0.410886i	0.978669	+	0.205443i	$0.0658634\pi$
$193$			5.70820i			0.410886i	−0.978669	+	0.205443i	$0.934137\pi$
$194$	1.42705	+	1.03681i	0.102456	+	0.0744389i
$195$		0			0
$196$	−5.73607	+	4.16750i	−0.409719	+	0.297678i
$197$	5.70634	+	7.85410i	0.406560	+	0.559582i	0.962375	−	0.271724i	$-0.0875938\pi$
$197$	5.70634	+	7.85410i	0.406560	+	0.559582i	−0.555815	+	0.831306i	$0.687594\pi$
$198$	0.898056	−	0.291796i	0.0638221	−	0.0207370i
$199$	−2.56231			−0.181637			−0.0908185	−	0.995867i	$-0.528948\pi$
$199$	−2.56231			−0.181637			−0.0908185	+	0.995867i	$0.528948\pi$
$200$		0			0
$201$	9.23607			0.651462
$202$	4.39201	−	1.42705i	0.309021	−	0.100407i
$203$	1.31433	+	1.80902i	0.0922477	+	0.126968i
$204$	1.00000	−	0.726543i	0.0700140	−	0.0508682i
$205$		0			0
$206$	5.78115	+	4.20025i	0.402792	+	0.292646i
$207$		−	16.4721i		−	1.14489i
$208$	5.29007	−	7.28115i	0.366800	−	0.504857i
$209$	−1.38197	+	4.25325i	−0.0955926	+	0.294204i
$210$		0			0
$211$	4.07295	+	12.5352i	0.280393	+	0.862962i	0.987742	+	0.156097i	$0.0498912\pi$
$211$	4.07295	+	12.5352i	0.280393	+	0.862962i	−0.707348	+	0.706865i	$0.750109\pi$
$212$	−8.42075	−	2.73607i	−0.578340	−	0.187914i
$213$	4.16750	+	1.35410i	0.285552	+	0.0927815i
$214$	−1.98936	−	6.12261i	−0.135990	−	0.418533i
$215$		0			0
$216$	3.45492	−	10.6331i	0.235077	−	0.723493i
$217$	2.85317	−	3.92705i	0.193686	−	0.266586i
$218$		−	6.18034i		−	0.418585i
$219$	−7.28115	−	5.29007i	−0.492015	−	0.357470i
$220$		0			0
$221$	−3.00000	+	2.17963i	−0.201802	+	0.146618i
$222$	−1.53884	−	2.11803i	−0.103280	−	0.142153i
$223$	21.0948	−	6.85410i	1.41261	−	0.458985i	0.499363	−	0.866393i	$-0.333567\pi$
$223$	21.0948	−	6.85410i	1.41261	−	0.458985i	0.913246	+	0.407408i	$0.133567\pi$
$224$	9.09017			0.607363
$225$		0			0
$226$	6.27051			0.417108
$227$	−18.2946	+	5.94427i	−1.21425	+	0.394535i	−0.844986	−	0.534788i	$-0.820392\pi$
$227$	−18.2946	+	5.94427i	−1.21425	+	0.394535i	−0.369268	+	0.929323i	$0.620392\pi$
$228$	5.56758	+	7.66312i	0.368722	+	0.507502i
$229$	6.70820	−	4.87380i	0.443291	−	0.322069i	−0.343650	−	0.939098i	$-0.611664\pi$
$229$	6.70820	−	4.87380i	0.443291	−	0.322069i	0.786941	+	0.617028i	$0.211664\pi$
$230$		0			0
$231$	−1.00000	−	0.726543i	−0.0657952	−	0.0478030i
$232$			3.09017i			0.202880i
$233$	−8.78402	+	12.0902i	−0.575460	+	0.792053i	−0.993188	−	0.116519i	$-0.962826\pi$
$233$	−8.78402	+	12.0902i	−0.575460	+	0.792053i	0.417728	+	0.908572i	$0.362826\pi$
$234$	−1.85410	+	5.70634i	−0.121206	+	0.373035i
$235$		0			0
$236$	2.07295	+	6.37988i	0.134937	+	0.415295i
$237$	2.93893	+	0.954915i	0.190904	+	0.0620284i
$238$	−0.726543	−	0.236068i	−0.0470948	−	0.0153020i
$239$	9.10739	+	28.0297i	0.589108	+	1.81309i	0.582106	+	0.813113i	$0.302229\pi$
$239$	9.10739	+	28.0297i	0.589108	+	1.81309i	0.00700219	+	0.999975i	$0.497771\pi$
$240$		0			0
$241$	3.54508	−	10.9106i	0.228359	−	0.702817i	−0.769574	−	0.638557i	$-0.779532\pi$
$241$	3.54508	−	10.9106i	0.228359	−	0.702817i	0.997933	−	0.0642594i	$-0.0204685\pi$
$242$	−3.78398	+	5.20820i	−0.243244	+	0.334796i
$243$		−	16.0000i		−	1.02640i
$244$	6.16312	+	4.47777i	0.394553	+	0.286660i
$245$		0			0
$246$	2.61803	−	1.90211i	0.166920	−	0.121274i
$247$	−16.7027	−	22.9894i	−1.06277	−	1.46278i
$248$	6.37988	−	2.07295i	0.405123	−	0.131632i
$249$	1.76393			0.111785
$250$		0			0
$251$	−6.81966			−0.430453			−0.215227	−	0.976564i	$-0.569049\pi$
$251$	−6.81966			−0.430453			−0.215227	+	0.976564i	$0.569049\pi$
$252$	4.97980	−	1.61803i	0.313698	−	0.101927i
$253$	−3.69822	−	5.09017i	−0.232505	−	0.320016i
$254$	−7.94427	+	5.77185i	−0.498468	+	0.362158i
$255$		0			0
$256$	5.30902	+	3.85723i	0.331814	+	0.241077i
$257$			16.1459i			1.00715i	0.863951	+	0.503577i	$0.167983\pi$
$257$			16.1459i			1.00715i	−0.863951	+	0.503577i	$0.832017\pi$
$258$	−0.673542	+	0.927051i	−0.0419329	+	0.0577157i
$259$	2.11803	−	6.51864i	0.131608	−	0.405048i
$260$		0			0
$261$	0.854102	+	2.62866i	0.0528676	+	0.162710i
$262$	−10.4616	−	3.39919i	−0.646321	−	0.210002i
$263$	21.0090	+	6.82624i	1.29547	+	0.420924i	0.874003	−	0.485920i	$-0.161515\pi$
$263$	21.0090	+	6.82624i	1.29547	+	0.420924i	0.421467	+	0.906844i	$0.361515\pi$
$264$	−0.527864	−	1.62460i	−0.0324878	−	0.0999871i
$265$		0			0
$266$	1.80902	−	5.56758i	0.110918	−	0.341370i
$267$	5.25731	−	7.23607i	0.321742	−	0.442840i
$268$			14.9443i			0.912867i
$269$	−13.9443	−	10.1311i	−0.850197	−	0.617704i	0.0750032	−	0.997183i	$-0.476103\pi$
$269$	−13.9443	−	10.1311i	−0.850197	−	0.617704i	−0.925200	+	0.379479i	$0.876103\pi$
$270$		0			0
$271$	6.47214	−	4.70228i	0.393154	−	0.285643i	−0.373593	−	0.927593i	$-0.621874\pi$
$271$	6.47214	−	4.70228i	0.393154	−	0.285643i	0.766747	+	0.641950i	$0.221874\pi$
$272$	0.832544	+	1.14590i	0.0504804	+	0.0694803i
$273$	7.46969	−	2.42705i	0.452086	−	0.146892i
$274$	−3.67376			−0.221940
$275$		0			0
$276$	−13.3262			−0.802145
$277$	10.7391	−	3.48936i	0.645252	−	0.209655i	0.0319326	−	0.999490i	$-0.489834\pi$
$277$	10.7391	−	3.48936i	0.645252	−	0.209655i	0.613320	+	0.789835i	$0.289834\pi$
$278$	1.81636	+	2.50000i	0.108938	+	0.149940i
$279$	4.85410	−	3.52671i	0.290607	−	0.211139i
$280$		0			0
$281$	0.881966	+	0.640786i	0.0526137	+	0.0382261i	0.613781	−	0.789476i	$-0.289648\pi$
$281$	0.881966	+	0.640786i	0.0526137	+	0.0382261i	−0.561168	+	0.827702i	$0.689648\pi$
$282$		−	1.00000i		−	0.0595491i
$283$	13.6048	−	18.7254i	0.808722	−	1.11311i	−0.182797	−	0.983151i	$-0.558515\pi$
$283$	13.6048	−	18.7254i	0.808722	−	1.11311i	0.991519	−	0.129960i	$-0.0414850\pi$
$284$	−2.19098	+	6.74315i	−0.130011	+	0.400132i
$285$		0			0
$286$	0.708204	+	2.17963i	0.0418770	+	0.128884i
$287$	8.05748	+	2.61803i	0.475618	+	0.154538i
$288$	10.6861	+	3.47214i	0.629687	+	0.204598i
$289$	5.07295	+	15.6129i	0.298409	+	0.918408i
$290$		0			0
$291$	0.881966	−	2.71441i	0.0517018	−	0.159122i
$292$	8.55951	−	11.7812i	0.500907	−	0.689440i
$293$			28.4721i			1.66336i	0.555255	+	0.831680i	$0.312621\pi$
$293$			28.4721i			1.66336i	−0.555255	+	0.831680i	$0.687379\pi$
$294$	−2.19098	−	1.59184i	−0.127781	−	0.0928381i
$295$		0			0
$296$	7.66312	−	5.56758i	0.445410	−	0.323609i
$297$	−2.24514	−	3.09017i	−0.130276	−	0.179310i
$298$	8.19624	−	2.66312i	0.474795	−	0.154270i
$299$	39.9787			2.31203
$300$		0			0
$301$	−3.00000			−0.172917
$302$	3.26944	−	1.06231i	0.188135	−	0.0611288i
$303$	−4.39201	−	6.04508i	−0.252314	−	0.347281i
$304$	−8.78115	+	6.37988i	−0.503634	+	0.365911i
$305$		0			0
$306$	−0.763932	−	0.555029i	−0.0436711	−	0.0317289i
$307$			4.76393i			0.271892i	0.990716	+	0.135946i	$0.0434074\pi$
$307$			4.76393i			0.271892i	−0.990716	+	0.135946i	$0.956593\pi$
$308$	1.17557	−	1.61803i	0.0669843	−	0.0921960i
$309$	3.57295	−	10.9964i	0.203258	−	0.625564i
$310$		0			0
$311$	−9.11803	−	28.0624i	−0.517036	−	1.59127i	−0.779546	−	0.626345i	$-0.784550\pi$
$311$	−9.11803	−	28.0624i	−0.517036	−	1.59127i	0.262510	−	0.964929i	$-0.415450\pi$
$312$	10.3229	+	3.35410i	0.584417	+	0.189889i
$313$	20.1967	+	6.56231i	1.14159	+	0.370923i	0.817967	−	0.575265i	$-0.195101\pi$
$313$	20.1967	+	6.56231i	1.14159	+	0.370923i	0.323618	+	0.946188i	$0.395101\pi$
$314$	1.75329	+	5.39607i	0.0989438	+	0.304518i
$315$		0			0
$316$	−1.54508	+	4.75528i	−0.0869178	+	0.267506i
$317$	−13.9026	+	19.1353i	−0.780846	+	1.07474i	0.214341	+	0.976759i	$0.431239\pi$
$317$	−13.9026	+	19.1353i	−0.780846	+	1.07474i	−0.995188	+	0.0979842i	$0.968761\pi$
$318$		−	3.38197i		−	0.189651i
$319$	0.854102	+	0.620541i	0.0478205	+	0.0347436i
$320$		0			0
$321$	−8.42705	+	6.12261i	−0.470352	+	0.341731i
$322$	4.84104	+	6.66312i	0.269781	+	0.371321i
$323$	4.25325	−	1.38197i	0.236657	−	0.0768946i
$324$	1.61803			0.0898908
$325$		0			0
$326$	6.79837			0.376527
$327$	−9.51057	+	3.09017i	−0.525935	+	0.170887i
$328$	6.88191	+	9.47214i	0.379990	+	0.523011i
$329$	2.11803	−	1.53884i	0.116771	−	0.0848391i
$330$		0			0
$331$	−13.8541	−	10.0656i	−0.761490	−	0.553255i	0.137877	−	0.990449i	$-0.455972\pi$
$331$	−13.8541	−	10.0656i	−0.761490	−	0.553255i	−0.899367	+	0.437194i	$0.855972\pi$
$332$			2.85410i			0.156639i
$333$	4.97980	−	6.85410i	0.272891	−	0.375602i
$334$	1.06231	−	3.26944i	0.0581268	−	0.178896i
$335$		0			0
$336$	−0.927051	−	2.85317i	−0.0505748	−	0.155653i
$337$	1.08981	+	0.354102i	0.0593659	+	0.0192892i	0.338549	−	0.940949i	$-0.390064\pi$
$337$	1.08981	+	0.354102i	0.0593659	+	0.0192892i	−0.279183	+	0.960238i	$0.590064\pi$
$338$	−6.20837	−	2.01722i	−0.337691	−	0.109722i
$339$	−3.13525	−	9.64932i	−0.170284	−	0.524079i
$340$		0			0
$341$	0.708204	−	2.17963i	0.0383514	−	0.118033i
$342$	4.25325	−	5.85410i	0.229990	−	0.316554i
$343$		−	18.4164i		−	0.994393i
$344$	−3.35410	−	2.43690i	−0.180841	−	0.131389i
$345$		0			0
$346$	8.44427	−	6.13512i	0.453967	−	0.329826i
$347$	18.2743	+	25.1525i	0.981018	+	1.35026i	0.936279	+	0.351257i	$0.114246\pi$
$347$	18.2743	+	25.1525i	0.981018	+	1.35026i	0.0447390	+	0.998999i	$0.485754\pi$
$348$	2.12663	−	0.690983i	0.113999	−	0.0370406i
$349$	−8.29180			−0.443850			−0.221925	−	0.975064i	$-0.571234\pi$
$349$	−8.29180			−0.443850			−0.221925	+	0.975064i	$0.571234\pi$
$350$		0			0
$351$	24.2705			1.29546
$352$	4.08174	−	1.32624i	0.217558	−	0.0706887i
$353$	14.1598	+	19.4894i	0.753653	+	1.03731i	0.997716	+	0.0675544i	$0.0215196\pi$
$353$	14.1598	+	19.4894i	0.753653	+	1.03731i	−0.244063	+	0.969759i	$0.578480\pi$
$354$	−2.07295	+	1.50609i	−0.110176	+	0.0800475i
$355$		0			0
$356$	11.7082	+	8.50651i	0.620534	+	0.450844i
$357$			1.23607i			0.0654197i
$358$	3.44095	−	4.73607i	0.181860	−	0.250309i
$359$	8.88197	−	27.3359i	0.468772	−	1.44273i	−0.385403	−	0.922748i	$-0.625938\pi$
$359$	8.88197	−	27.3359i	0.468772	−	1.44273i	0.854176	−	0.519984i	$-0.174062\pi$
$360$		0			0
$361$	4.71885	+	14.5231i	0.248360	+	0.764375i
$362$	8.05748	+	2.61803i	0.423492	+	0.137601i
$363$	9.90659	+	3.21885i	0.519961	+	0.168946i
$364$	3.92705	+	12.0862i	0.205833	+	0.633490i
$365$		0			0
$366$	−0.899187	+	2.76741i	−0.0470013	+	0.144655i
$367$	−3.19620	+	4.39919i	−0.166840	+	0.229636i	−0.884248	−	0.467018i	$-0.845328\pi$
$367$	−3.19620	+	4.39919i	−0.166840	+	0.229636i	0.717408	+	0.696653i	$0.245328\pi$
$368$		−	15.2705i		−	0.796030i
$369$	8.47214	+	6.15537i	0.441042	+	0.320436i
$370$		0			0
$371$	7.16312	−	5.20431i	0.371891	−	0.270194i
$372$	−2.85317	−	3.92705i	−0.147930	−	0.203608i
$373$	5.01255	−	1.62868i	0.259540	−	0.0843297i	−0.176357	−	0.984326i	$-0.556431\pi$
$373$	5.01255	−	1.62868i	0.259540	−	0.0843297i	0.435897	+	0.899997i	$0.356431\pi$
$374$	−0.360680			−0.0186503
$375$		0			0
$376$	3.61803			0.186586
$377$	−6.37988	+	2.07295i	−0.328581	+	0.106762i
$378$	2.93893	+	4.04508i	0.151162	+	0.208057i
$379$	−27.9894	+	20.3355i	−1.43772	+	1.04456i	−0.449203	+	0.893430i	$0.648292\pi$
$379$	−27.9894	+	20.3355i	−1.43772	+	1.04456i	−0.988513	+	0.151133i	$0.951708\pi$
$380$		0			0
$381$	12.8541	+	9.33905i	0.658536	+	0.478454i
$382$		−	14.9443i		−	0.764615i
$383$	6.67764	−	9.19098i	0.341211	−	0.469637i	−0.603583	−	0.797300i	$-0.706261\pi$
$383$	6.67764	−	9.19098i	0.341211	−	0.469637i	0.944795	+	0.327663i	$0.106261\pi$
$384$	3.51722	−	10.8249i	0.179487	−	0.552406i
$385$		0			0
$386$	−1.09017	−	3.35520i	−0.0554882	−	0.170775i
$387$	−3.52671	−	1.14590i	−0.179273	−	0.0582493i
$388$	4.39201	+	1.42705i	0.222971	+	0.0724475i
$389$	−4.63525	−	14.2658i	−0.235017	−	0.723307i	−0.997119	−	0.0758507i	$-0.975833\pi$
$389$	−4.63525	−	14.2658i	−0.235017	−	0.723307i	0.762102	−	0.647456i	$-0.224167\pi$
$390$		0			0
$391$	−1.94427	+	5.98385i	−0.0983261	+	0.302616i
$392$	5.75934	−	7.92705i	0.290891	−	0.400377i
$393$			17.7984i			0.897809i
$394$	−4.85410	−	3.52671i	−0.244546	−	0.177673i
$395$		0			0
$396$	2.00000	−	1.45309i	0.100504	−	0.0730203i
$397$	0.0202444	+	0.0278640i	0.00101604	+	0.00139846i	0.809525	−	0.587086i	$-0.199725\pi$
$397$	0.0202444	+	0.0278640i	0.00101604	+	0.00139846i	−0.808509	+	0.588484i	$0.799725\pi$
$398$	1.50609	−	0.489357i	0.0754933	−	0.0245292i
$399$	−9.47214			−0.474200
$400$		0			0
$401$	−22.5967			−1.12843			−0.564214	−	0.825629i	$-0.690821\pi$
$401$	−22.5967			−1.12843			−0.564214	+	0.825629i	$0.690821\pi$
$402$	−5.42882	+	1.76393i	−0.270765	+	0.0879769i
$403$	8.55951	+	11.7812i	0.426379	+	0.586861i
$404$	9.78115	−	7.10642i	0.486631	−	0.353558i
$405$		0			0
$406$	−1.11803	−	0.812299i	−0.0554871	−	0.0403137i
$407$		−	3.23607i		−	0.160406i
$408$	−1.00406	+	1.38197i	−0.0497082	+	0.0684175i
$409$	−8.78115	+	27.0256i	−0.434200	+	1.33633i	0.459704	+	0.888072i	$0.347955\pi$
$409$	−8.78115	+	27.0256i	−0.434200	+	1.33633i	−0.893904	+	0.448258i	$0.852045\pi$
$410$		0			0
$411$	1.83688	+	5.65334i	0.0906067	+	0.278859i
$412$	17.7926	+	5.78115i	0.876576	+	0.284817i
$413$	−6.37988	−	2.07295i	−0.313933	−	0.102003i
$414$	3.14590	+	9.68208i	0.154612	+	0.475848i
$415$		0			0
$416$	−8.42705	+	25.9358i	−0.413170	+	1.27161i
$417$	2.93893	−	4.04508i	0.143920	−	0.198089i
$418$		−	2.76393i		−	0.135188i
$419$	−0.427051	−	0.310271i	−0.0208628	−	0.0151577i	0.577305	−	0.816529i	$-0.304104\pi$
$419$	−0.427051	−	0.310271i	−0.0208628	−	0.0151577i	−0.598168	+	0.801371i	$0.704104\pi$
$420$		0			0
$421$	−25.8885	+	18.8091i	−1.26173	+	0.916701i	−0.998841	−	0.0481252i	$-0.984675\pi$
$421$	−25.8885	+	18.8091i	−1.26173	+	0.916701i	−0.262889	+	0.964826i	$0.584675\pi$
$422$	−4.78804	−	6.59017i	−0.233078	−	0.320804i
$423$	3.07768	−	1.00000i	0.149642	−	0.0486217i
$424$	12.2361			0.594236
$425$		0			0
$426$	−2.70820			−0.131213
$427$	−7.24518	+	2.35410i	−0.350619	+	0.113923i
$428$	−9.90659	−	13.6353i	−0.478853	−	0.659085i
$429$	3.00000	−	2.17963i	0.144841	−	0.105233i
$430$		0			0
$431$	−19.2812	−	14.0086i	−0.928740	−	0.674769i	0.0169437	−	0.999856i	$-0.494606\pi$
$431$	−19.2812	−	14.0086i	−0.928740	−	0.674769i	−0.945684	+	0.325087i	$0.894606\pi$
$432$		−	9.27051i		−	0.446028i
$433$	−11.8415	+	16.2984i	−0.569064	+	0.783250i	−0.992443	−	0.122703i	$-0.960844\pi$
$433$	−11.8415	+	16.2984i	−0.569064	+	0.783250i	0.423379	+	0.905953i	$0.360844\pi$
$434$	−0.927051	+	2.85317i	−0.0444999	+	0.136957i
$435$		0			0
$436$	−5.00000	−	15.3884i	−0.239457	−	0.736972i
$437$	−45.8550	−	14.8992i	−2.19354	−	0.712725i
$438$	5.29007	+	1.71885i	0.252769	+	0.0821297i
$439$	−1.84752	−	5.68609i	−0.0881775	−	0.271382i	0.897238	−	0.441547i	$-0.145570\pi$
$439$	−1.84752	−	5.68609i	−0.0881775	−	0.271382i	−0.985416	+	0.170164i	$0.945570\pi$
$440$		0			0
$441$	2.70820	−	8.33499i	0.128962	−	0.396905i
$442$	1.34708	−	1.85410i	0.0640742	−	0.0881906i
$443$		−	12.0557i		−	0.572785i	−0.958112	−	0.286392i	$-0.907544\pi$
$443$		−	12.0557i		−	0.572785i	0.958112	−	0.286392i	$-0.0924561\pi$
$444$	−5.54508	−	4.02874i	−0.263158	−	0.191196i
$445$		0			0
$446$	−11.0902	+	8.05748i	−0.525135	+	0.381533i
$447$	−8.19624	−	11.2812i	−0.387669	−	0.533580i
$448$	0.363271	−	0.118034i	0.0171630	−	0.00557658i
$449$	−20.3262			−0.959254			−0.479627	−	0.877472i	$-0.659228\pi$
$449$	−20.3262			−0.959254			−0.479627	+	0.877472i	$0.659228\pi$
$450$		0			0
$451$	4.00000			0.188353
$452$	15.6129	−	5.07295i	0.734371	−	0.238611i
$453$	−3.26944	−	4.50000i	−0.153612	−	0.211428i
$454$	9.61803	−	6.98791i	0.451397	−	0.327959i
$455$		0			0
$456$	−10.5902	−	7.69421i	−0.495930	−	0.360314i
$457$			5.41641i			0.253369i	0.991943	+	0.126684i	$0.0404336\pi$
$457$			5.41641i			0.253369i	−0.991943	+	0.126684i	$0.959566\pi$
$458$	−3.01217	+	4.14590i	−0.140750	+	0.193725i
$459$	−1.18034	+	3.63271i	−0.0550935	+	0.169561i
$460$		0			0
$461$	7.16312	+	22.0458i	0.333620	+	1.02678i	0.967398	+	0.253261i	$0.0815032\pi$
$461$	7.16312	+	22.0458i	0.333620	+	1.02678i	−0.633778	+	0.773515i	$0.718497\pi$
$462$	0.726543	+	0.236068i	0.0338018	+	0.0109829i
$463$	−15.3354	−	4.98278i	−0.712697	−	0.231569i	−0.0698431	−	0.997558i	$-0.522250\pi$
$463$	−15.3354	−	4.98278i	−0.712697	−	0.231569i	−0.642854	+	0.765989i	$0.722250\pi$
$464$	0.791796	+	2.43690i	0.0367582	+	0.113130i
$465$		0			0
$466$	2.85410	−	8.78402i	0.132214	−	0.406912i
$467$	−16.7230	+	23.0172i	−0.773848	+	1.06511i	0.222087	+	0.975027i	$0.428713\pi$
$467$	−16.7230	+	23.0172i	−0.773848	+	1.06511i	−0.995934	+	0.0900830i	$0.971287\pi$
$468$			15.7082i			0.726112i
$469$	−12.0902	−	8.78402i	−0.558272	−	0.405608i
$470$		0			0
$471$	7.42705	−	5.39607i	0.342220	−	0.248638i
$472$	−5.44907	−	7.50000i	−0.250814	−	0.345215i
$473$	−1.34708	+	0.437694i	−0.0619390	+	0.0201252i
$474$	−1.90983			−0.0877214
$475$		0			0
$476$	−2.00000			−0.0916698
$477$	10.4086	−	3.38197i	0.476578	−	0.154850i
$478$	−10.7064	−	14.7361i	−0.489698	−	0.674012i
$479$	−3.35410	+	2.43690i	−0.153253	+	0.111345i	−0.661769	−	0.749708i	$-0.730194\pi$
$479$	−3.35410	+	2.43690i	−0.153253	+	0.111345i	0.508516	+	0.861052i	$0.330194\pi$
$480$		0			0
$481$	16.6353	+	12.0862i	0.758502	+	0.551084i
$482$			7.09017i			0.322948i
$483$	7.83297	−	10.7812i	0.356412	−	0.490559i
$484$	−5.20820	+	16.0292i	−0.236737	+	0.728600i
$485$		0			0
$486$	3.05573	+	9.40456i	0.138611	+	0.426600i
$487$	−9.11454	−	2.96149i	−0.413019	−	0.134198i	0.0951346	−	0.995464i	$-0.469672\pi$
$487$	−9.11454	−	2.96149i	−0.413019	−	0.134198i	−0.508154	+	0.861266i	$0.669672\pi$
$488$	−10.0126	−	3.25329i	−0.453249	−	0.147269i
$489$	−3.39919	−	10.4616i	−0.153717	−	0.473091i
$490$		0			0
$491$	11.5106	−	35.4261i	0.519468	−	1.59876i	−0.255534	−	0.966800i	$-0.582251\pi$
$491$	11.5106	−	35.4261i	0.519468	−	1.59876i	0.775002	−	0.631958i	$-0.217749\pi$
$492$	4.97980	−	6.85410i	0.224507	−	0.309007i
$493$		−	1.05573i		−	0.0475476i
$494$	14.2082	+	10.3229i	0.639257	+	0.464448i
$495$		0			0
$496$	4.50000	−	3.26944i	0.202056	−	0.146802i
$497$	−4.16750	−	5.73607i	−0.186938	−	0.257298i
$498$	−1.03681	+	0.336881i	−0.0464607	+	0.0150960i
$499$	12.5623			0.562366			0.281183	−	0.959654i	$-0.409273\pi$
$499$	12.5623			0.562366			0.281183	+	0.959654i	$0.409273\pi$
$500$		0			0
$501$	−5.56231			−0.248506
$502$	4.00850	−	1.30244i	0.178908	−	0.0581307i
$503$	−6.22088	−	8.56231i	−0.277375	−	0.381774i	0.647487	−	0.762076i	$-0.275820\pi$
$503$	−6.22088	−	8.56231i	−0.277375	−	0.381774i	−0.924862	+	0.380302i	$0.875820\pi$
$504$	−5.85410	+	4.25325i	−0.260762	+	0.189455i
$505$		0			0
$506$	3.14590	+	2.28563i	0.139852	+	0.101609i
$507$			10.5623i			0.469088i
$508$	−15.1109	+	20.7984i	−0.670438	+	0.922779i
$509$	1.44427	−	4.44501i	0.0640162	−	0.197022i	−0.913933	−	0.405866i	$-0.866970\pi$
$509$	1.44427	−	4.44501i	0.0640162	−	0.197022i	0.977949	+	0.208844i	$0.0669701\pi$
$510$		0			0
$511$	4.50000	+	13.8496i	0.199068	+	0.612669i
$512$	17.7926	+	5.78115i	0.786327	+	0.255493i
$513$	−27.8379	−	9.04508i	−1.22907	−	0.399350i
$514$	−3.08359	−	9.49032i	−0.136011	−	0.418600i
$515$		0			0
$516$	−0.927051	+	2.85317i	−0.0408111	+	0.125604i
$517$	0.726543	−	1.00000i	0.0319533	−	0.0439799i
$518$			4.23607i			0.186122i
$519$	−13.6631	−	9.92684i	−0.599744	−	0.435740i
$520$		0			0
$521$	12.4271	−	9.02878i	0.544439	−	0.395558i	−0.281292	−	0.959622i	$-0.590763\pi$
$521$	12.4271	−	9.02878i	0.544439	−	0.395558i	0.825731	+	0.564064i	$0.190763\pi$
$522$	−1.00406	−	1.38197i	−0.0439464	−	0.0604870i
$523$	−18.8824	+	6.13525i	−0.825669	+	0.268276i	−0.691220	−	0.722645i	$-0.742926\pi$
$523$	−18.8824	+	6.13525i	−0.825669	+	0.268276i	−0.134449	+	0.990921i	$0.542926\pi$
$524$	−28.7984			−1.25806
$525$		0			0
$526$	−13.6525			−0.595276
$527$	−2.17963	+	0.708204i	−0.0949461	+	0.0308498i
$528$	−0.832544	−	1.14590i	−0.0362318	−	0.0498688i
$529$	36.2705	−	26.3521i	1.57698	−	1.14574i
$530$		0			0
$531$	−6.70820	−	4.87380i	−0.291111	−	0.211505i
$532$		−	15.3262i		−	0.664477i
$533$	−14.9394	+	20.5623i	−0.647097	+	0.890652i
$534$	−1.70820	+	5.25731i	−0.0739212	+	0.227506i
$535$		0			0
$536$	−6.38197	−	19.6417i	−0.275659	−	0.848391i
$537$	−9.00854	−	2.92705i	−0.388747	−	0.126312i
$538$	10.1311	+	3.29180i	0.436783	+	0.141919i
$539$	−1.03444	−	3.18368i	−0.0445566	−	0.137131i
$540$		0			0
$541$	−4.05573	+	12.4822i	−0.174369	+	0.536654i	−0.999604	−	0.0281362i	$-0.991043\pi$
$541$	−4.05573	+	12.4822i	−0.174369	+	0.536654i	0.825235	+	0.564790i	$0.191043\pi$
$542$	−2.90617	+	4.00000i	−0.124831	+	0.171815i
$543$		−	13.7082i		−	0.588275i
$544$	−3.47214	−	2.52265i	−0.148867	−	0.108158i
$545$		0			0
$546$	−3.92705	+	2.85317i	−0.168062	+	0.122104i
$547$	20.4010	+	28.0795i	0.872283	+	1.20059i	0.978499	+	0.206251i	$0.0661263\pi$
$547$	20.4010	+	28.0795i	0.872283	+	1.20059i	−0.106217	+	0.994343i	$0.533874\pi$
$548$	−9.14729	+	2.97214i	−0.390753	+	0.126963i
$549$	−9.41641			−0.401882
$550$		0			0
$551$	8.09017			0.344653
$552$	17.5150	−	5.69098i	0.745490	−	0.242224i
$553$	−2.93893	−	4.04508i	−0.124976	−	0.172015i
$554$	−5.64590	+	4.10199i	−0.239871	+	0.174277i
$555$		0			0
$556$	6.54508	+	4.75528i	0.277573	+	0.201669i
$557$			9.23607i			0.391345i	0.980669	+	0.195672i	$0.0626889\pi$
$557$			9.23607i			0.391345i	−0.980669	+	0.195672i	$0.937311\pi$
$558$	−2.17963	+	3.00000i	−0.0922710	+	0.127000i
$559$	2.78115	−	8.55951i	0.117630	−	0.362029i
$560$		0			0
$561$	0.180340	+	0.555029i	0.00761396	+	0.0234333i
$562$	−0.640786	−	0.208204i	−0.0270299	−	0.00878255i
$563$	−9.14729	−	2.97214i	−0.385512	−	0.125261i	0.109847	−	0.993948i	$-0.464964\pi$
$563$	−9.14729	−	2.97214i	−0.385512	−	0.125261i	−0.495360	+	0.868688i	$0.664964\pi$
$564$	−0.809017	−	2.48990i	−0.0340658	−	0.104844i
$565$		0			0
$566$	−4.42047	+	13.6048i	−0.185806	+	0.571853i
$567$	−0.951057	+	1.30902i	−0.0399406	+	0.0549735i
$568$		−	9.79837i		−	0.411131i
$569$	23.8435	+	17.3233i	0.999570	+	0.726230i	0.961996	−	0.273064i	$-0.0880370\pi$
$569$	23.8435	+	17.3233i	0.999570	+	0.726230i	0.0375739	+	0.999294i	$0.488037\pi$
$570$		0			0
$571$	−25.9894	+	18.8824i	−1.08762	+	0.790203i	−0.978996	−	0.203880i	$-0.934645\pi$
$571$	−25.9894	+	18.8824i	−1.08762	+	0.790203i	−0.108625	+	0.994083i	$0.534645\pi$
$572$	3.52671	+	4.85410i	0.147459	+	0.202960i
$573$	−22.9969	+	7.47214i	−0.960708	+	0.312153i
$574$	−5.23607			−0.218549
$575$		0			0
$576$	0.472136			0.0196723
$577$	−35.9281	+	11.6738i	−1.49571	+	0.485985i	−0.938763	−	0.344564i	$-0.888027\pi$
$577$	−35.9281	+	11.6738i	−1.49571	+	0.485985i	−0.556945	+	0.830549i	$0.688027\pi$
$578$	−5.96361	−	8.20820i	−0.248053	−	0.341416i
$579$	−4.61803	+	3.35520i	−0.191919	+	0.139437i
$580$		0			0
$581$	−2.30902	−	1.67760i	−0.0957942	−	0.0695985i
$582$			1.76393i			0.0731173i
$583$	2.45714	−	3.38197i	0.101764	−	0.140067i
$584$	−6.21885	+	19.1396i	−0.257338	+	0.792004i
$585$		0			0
$586$	−5.43769	−	16.7355i	−0.224629	−	0.691337i
$587$	17.7926	+	5.78115i	0.734378	+	0.238614i	0.652246	−	0.758008i	$-0.273827\pi$
$587$	17.7926	+	5.78115i	0.734378	+	0.238614i	0.0821320	+	0.996621i	$0.473827\pi$
$588$	−6.74315	−	2.19098i	−0.278083	−	0.0903546i
$589$	−5.42705	−	16.7027i	−0.223618	−	0.688225i
$590$		0			0
$591$	−3.00000	+	9.23305i	−0.123404	+	0.379797i
$592$	4.61653	−	6.35410i	0.189738	−	0.261152i
$593$			22.0902i			0.907135i	0.891222	+	0.453567i	$0.149849\pi$
$593$			22.0902i			0.907135i	−0.891222	+	0.453567i	$0.850151\pi$
$594$	1.90983	+	1.38757i	0.0783613	+	0.0569328i
$595$		0			0
$596$	18.2533	−	13.2618i	0.747684	−	0.543224i
$597$	−1.50609	−	2.07295i	−0.0616400	−	0.0848402i
$598$	−23.4989	+	7.63525i	−0.960941	+	0.312229i
$599$	0.527864			0.0215679			0.0107840	−	0.999942i	$-0.496567\pi$
$599$	0.527864			0.0215679			0.0107840	+	0.999942i	$0.496567\pi$
$600$		0			0
$601$	36.2705			1.47950			0.739752	−	0.672879i	$-0.234943\pi$
$601$	36.2705			1.47950			0.739752	+	0.672879i	$0.234943\pi$
$602$	1.76336	−	0.572949i	0.0718690	−	0.0233517i
$603$	−10.8576	−	14.9443i	−0.442158	−	0.608578i
$604$	7.28115	−	5.29007i	0.296266	−	0.215250i
$605$		0			0
$606$	3.73607	+	2.71441i	0.151767	+	0.110265i
$607$		−	15.4377i		−	0.626597i	−0.949655	−	0.313298i	$-0.898566\pi$
$607$		−	15.4377i		−	0.626597i	0.949655	−	0.313298i	$-0.101434\pi$
$608$	19.3314	−	26.6074i	0.783992	−	1.07907i
$609$	−0.690983	+	2.12663i	−0.0280000	+	0.0861753i
$610$		0			0
$611$	2.42705	+	7.46969i	0.0981880	+	0.302192i
$612$	−2.35114	−	0.763932i	−0.0950392	−	0.0308801i
$613$	−30.4136	−	9.88197i	−1.22839	−	0.399129i	−0.378261	−	0.925699i	$-0.623478\pi$
$613$	−30.4136	−	9.88197i	−1.22839	−	0.399129i	−0.850132	+	0.526570i	$0.823478\pi$
$614$	−0.909830	−	2.80017i	−0.0367178	−	0.113006i
$615$		0			0
$616$	−0.854102	+	2.62866i	−0.0344127	+	0.105912i
$617$	5.73910	−	7.89919i	0.231047	−	0.318009i	−0.677714	−	0.735326i	$-0.737029\pi$
$617$	5.73910	−	7.89919i	0.231047	−	0.318009i	0.908761	+	0.417316i	$0.137029\pi$
$618$			7.14590i			0.287450i
$619$	31.9336	+	23.2011i	1.28352	+	0.932533i	0.999653	−	0.0263310i	$-0.00838237\pi$
$619$	31.9336	+	23.2011i	1.28352	+	0.932533i	0.283868	+	0.958863i	$0.408382\pi$
$620$		0			0
$621$	33.3156	−	24.2052i	1.33691	−	0.971321i
$622$	10.7189	+	14.7533i	0.429788	+	0.591553i
$623$	−13.7638	+	4.47214i	−0.551436	+	0.179172i
$624$	9.00000			0.360288
$625$		0			0
$626$	−13.1246			−0.524565
$627$	−4.25325	+	1.38197i	−0.169859	+	0.0551904i
$628$	8.73102	+	12.0172i	0.348406	+	0.479539i
$629$	−2.61803	+	1.90211i	−0.104388	+	0.0758422i
$630$		0			0
$631$	4.66312	+	3.38795i	0.185636	+	0.134872i	0.676722	−	0.736239i	$-0.263400\pi$
$631$	4.66312	+	3.38795i	0.185636	+	0.134872i	−0.491086	+	0.871111i	$0.663400\pi$
$632$		−	6.90983i		−	0.274858i
$633$	−7.74721	+	10.6631i	−0.307924	+	0.423821i
$634$	4.51722	−	13.9026i	0.179402	−	0.552142i
$635$		0			0
$636$	−2.73607	−	8.42075i	−0.108492	−	0.333905i
$637$	20.2295	+	6.57295i	0.801520	+	0.260430i
$638$	−0.620541	−	0.201626i	−0.0245675	−	0.00798245i
$639$	−2.70820	−	8.33499i	−0.107135	−	0.329727i
$640$		0			0
$641$	3.11803	−	9.59632i	0.123155	−	0.379032i	−0.870405	−	0.492336i	$-0.836143\pi$
$641$	3.11803	−	9.59632i	0.123155	−	0.379032i	0.993560	+	0.113304i	$0.0361433\pi$
$642$	3.78398	−	5.20820i	0.149342	−	0.205551i
$643$		−	22.8328i		−	0.900438i	−0.892918	−	0.450219i	$-0.851346\pi$
$643$		−	22.8328i		−	0.900438i	0.892918	−	0.450219i	$-0.148654\pi$
$644$	17.4443	+	12.6740i	0.687401	+	0.499426i
$645$		0			0
$646$	−2.23607	+	1.62460i	−0.0879769	+	0.0639190i
$647$	−17.9516	−	24.7082i	−0.705749	−	0.971380i	−0.999878	−	0.0156141i	$-0.995030\pi$
$647$	−17.9516	−	24.7082i	−0.705749	−	0.971380i	0.294129	−	0.955766i	$-0.404970\pi$
$648$	−2.12663	+	0.690983i	−0.0835418	+	0.0271444i
$649$	−3.16718			−0.124323
$650$		0			0
$651$	4.85410			0.190247
$652$	16.9273	−	5.50000i	0.662923	−	0.215397i
$653$	4.64928	+	6.39919i	0.181940	+	0.250420i	0.890239	−	0.455493i	$-0.150537\pi$
$653$	4.64928	+	6.39919i	0.181940	+	0.250420i	−0.708299	+	0.705913i	$0.750537\pi$
$654$	5.00000	−	3.63271i	0.195515	−	0.142050i
$655$		0			0
$656$	7.85410	+	5.70634i	0.306651	+	0.222795i
$657$			18.0000i			0.702247i
$658$	−0.951057	+	1.30902i	−0.0370760	+	0.0510308i
$659$	−7.56231	+	23.2744i	−0.294586	+	0.906641i	0.688775	+	0.724975i	$0.258149\pi$
$659$	−7.56231	+	23.2744i	−0.294586	+	0.906641i	−0.983360	+	0.181666i	$0.941851\pi$
$660$		0			0
$661$	−12.5729	−	38.6956i	−0.489031	−	1.50508i	−0.826057	−	0.563587i	$-0.809421\pi$
$661$	−12.5729	−	38.6956i	−0.489031	−	1.50508i	0.337025	−	0.941496i	$-0.390579\pi$
$662$	10.0656	+	3.27051i	0.391210	+	0.127112i
$663$	−3.52671	−	1.14590i	−0.136966	−	0.0445030i
$664$	−1.21885	−	3.75123i	−0.0473004	−	0.145576i
$665$		0			0
$666$	−1.61803	+	4.97980i	−0.0626975	+	0.192963i
$667$	−6.69015	+	9.20820i	−0.259044	+	0.356543i
$668$		−	9.00000i		−	0.348220i
$669$	17.9443	+	13.0373i	0.693766	+	0.504050i
$670$		0			0
$671$	−2.90983	+	2.11412i	−0.112333	+	0.0816145i
$672$	5.34307	+	7.35410i	0.206113	+	0.283691i
$673$	−9.68208	+	3.14590i	−0.373217	+	0.121265i	−0.489619	−	0.871937i	$-0.662864\pi$
$673$	−9.68208	+	3.14590i	−0.373217	+	0.121265i	0.116402	+	0.993202i	$0.462864\pi$
$674$	−0.708204			−0.0272790
$675$		0			0
$676$	−17.0902			−0.657314
$677$	−7.97172	+	2.59017i	−0.306378	+	0.0995483i	−0.458171	−	0.888864i	$-0.651495\pi$
$677$	−7.97172	+	2.59017i	−0.306378	+	0.0995483i	0.151793	+	0.988412i	$0.451495\pi$
$678$	3.68571	+	5.07295i	0.141549	+	0.194825i
$679$	−3.73607	+	2.71441i	−0.143377	+	0.104170i
$680$		0			0
$681$	−15.5623	−	11.3067i	−0.596349	−	0.433273i
$682$			1.41641i			0.0542371i
$683$	2.66141	−	3.66312i	0.101836	−	0.140165i	−0.755058	−	0.655658i	$-0.772391\pi$
$683$	2.66141	−	3.66312i	0.101836	−	0.140165i	0.856894	+	0.515493i	$0.172391\pi$
$684$	5.85410	−	18.0171i	0.223837	−	0.688900i
$685$		0			0
$686$	3.51722	+	10.8249i	0.134288	+	0.413296i
$687$	7.88597	+	2.56231i	0.300868	+	0.0977581i
$688$	−3.26944	−	1.06231i	−0.124646	−	0.0405000i
$689$	8.20820	+	25.2623i	0.312708	+	0.962415i
$690$		0			0
$691$	0.843459	−	2.59590i	0.0320867	−	0.0987527i	−0.933731	−	0.357977i	$-0.883467\pi$
$691$	0.843459	−	2.59590i	0.0320867	−	0.0987527i	0.965817	+	0.259224i	$0.0834668\pi$
$692$	16.0620	−	22.1074i	0.610584	−	0.840397i
$693$			2.47214i			0.0939087i
$694$	−15.5451	−	11.2942i	−0.590083	−	0.428721i
$695$		0			0
$696$	−2.50000	+	1.81636i	−0.0947623	+	0.0688488i
$697$	−2.35114	−	3.23607i	−0.0890558	−	0.122575i
$698$	4.87380	−	1.58359i	0.184476	−	0.0599398i
$699$	−14.9443			−0.565244
$700$		0			0
$701$	35.0132			1.32243			0.661214	−	0.750197i	$-0.270041\pi$
$701$	35.0132			1.32243			0.661214	+	0.750197i	$0.270041\pi$
$702$	−14.2658	+	4.63525i	−0.538430	+	0.174946i
$703$	−14.5761	−	20.0623i	−0.549749	−	0.756664i
$704$	0.145898	−	0.106001i	0.00549874	−	0.00399507i
$705$		0			0
$706$	−12.0451	−	8.75127i	−0.453323	−	0.329358i
$707$			12.0902i			0.454698i
$708$	−3.94298	+	5.42705i	−0.148186	+	0.203961i
$709$	−10.3647	+	31.8994i	−0.389256	+	1.19801i	0.544089	+	0.839027i	$0.316875\pi$
$709$	−10.3647	+	31.8994i	−0.389256	+	1.19801i	−0.933345	+	0.358980i	$0.883125\pi$
$710$		0			0
$711$	−1.90983	−	5.87785i	−0.0716242	−	0.220437i
$712$	−19.0211	−	6.18034i	−0.712847	−	0.231618i
$713$	23.4989	+	7.63525i	0.880041	+	0.285943i
$714$	−0.236068	−	0.726543i	−0.00883462	−	0.0271902i
$715$		0			0
$716$	4.73607	−	14.5761i	0.176995	−	0.544735i
$717$	−17.3233	+	23.8435i	−0.646950	+	0.890450i
$718$			17.7639i			0.662944i
$719$	−29.6976	−	21.5765i	−1.10753	−	0.804669i	−0.125259	−	0.992124i	$-0.539976\pi$
$719$	−29.6976	−	21.5765i	−1.10753	−	0.804669i	−0.982273	+	0.187455i	$0.939976\pi$
$720$		0			0
$721$	−15.1353	+	10.9964i	−0.563666	+	0.409528i
$722$	−5.54734	−	7.63525i	−0.206451	−	0.284155i
$723$	10.9106	−	3.54508i	0.405771	−	0.131843i
$724$	22.1803			0.824326
$725$		0			0
$726$	−6.43769			−0.238925
$727$	−4.22050	+	1.37132i	−0.156530	+	0.0508596i	−0.386234	−	0.922401i	$-0.626224\pi$
$727$	−4.22050	+	1.37132i	−0.156530	+	0.0508596i	0.229704	+	0.973261i	$0.426224\pi$
$728$	−10.3229	−	14.2082i	−0.382591	−	0.526591i
$729$	10.5172	−	7.64121i	0.389527	−	0.283008i
$730$		0			0
$731$	1.14590	+	0.832544i	0.0423826	+	0.0307927i
$732$			7.61803i			0.281571i
$733$	−15.8577	+	21.8262i	−0.585717	+	0.806170i	−0.994308	−	0.106547i	$-0.966020\pi$
$733$	−15.8577	+	21.8262i	−0.585717	+	0.806170i	0.408590	+	0.912718i	$0.366020\pi$
$734$	1.03851	−	3.19620i	0.0383320	−	0.117974i
$735$		0			0
$736$	14.2984	+	44.0059i	0.527045	+	1.62208i
$737$	−6.71040	−	2.18034i	−0.247181	−	0.0803139i
$738$	−6.15537	−	2.00000i	−0.226582	−	0.0736210i
$739$	9.57295	+	29.4625i	0.352147	+	1.08380i	0.957646	+	0.287950i	$0.0929736\pi$
$739$	9.57295	+	29.4625i	0.352147	+	1.08380i	−0.605499	+	0.795846i	$0.707026\pi$
$740$		0			0
$741$	8.78115	−	27.0256i	0.322584	−	0.992811i
$742$	−3.21644	+	4.42705i	−0.118079	+	0.162522i
$743$			16.3607i			0.600215i	0.953905	+	0.300108i	$0.0970226\pi$
$743$			16.3607i			0.600215i	−0.953905	+	0.300108i	$0.902977\pi$
$744$	5.42705	+	3.94298i	0.198965	+	0.144557i
$745$		0			0
$746$	−2.63525	+	1.91462i	−0.0964835	+	0.0700994i
$747$	−2.07363	−	2.85410i	−0.0758700	−	0.104426i
$748$	−0.898056	+	0.291796i	−0.0328362	+	0.0106691i
$749$	16.8541			0.615835
$750$		0			0
$751$	−40.8885			−1.49204			−0.746022	−	0.665921i	$-0.768039\pi$
$751$	−40.8885			−1.49204			−0.746022	+	0.665921i	$0.768039\pi$
$752$	2.85317	−	0.927051i	0.104044	−	0.0338061i
$753$	−4.00850	−	5.51722i	−0.146078	−	0.201059i
$754$	3.35410	−	2.43690i	0.122149	−	0.0887466i
$755$		0			0
$756$	10.5902	+	7.69421i	0.385161	+	0.279836i
$757$			3.58359i			0.130248i	0.997877	+	0.0651239i	$0.0207443\pi$
$757$			3.58359i			0.130248i	−0.997877	+	0.0651239i	$0.979256\pi$
$758$	12.5680	−	17.2984i	0.456490	−	0.628305i
$759$	1.94427	−	5.98385i	0.0705726	−	0.217200i
$760$		0			0
$761$	11.5729	+	35.6179i	0.419519	+	1.29115i	0.908146	+	0.418654i	$0.137498\pi$
$761$	11.5729	+	35.6179i	0.419519	+	1.29115i	−0.488627	+	0.872493i	$0.662502\pi$
$762$	−9.33905	−	3.03444i	−0.338318	−	0.109926i
$763$	15.3884	+	5.00000i	0.557098	+	0.181012i
$764$	−12.0902	−	37.2097i	−0.437407	−	1.34620i
$765$		0			0
$766$	−2.16970	+	6.67764i	−0.0783943	+	0.241273i
$767$	11.8290	−	16.2812i	0.427119	−	0.587878i
$768$			6.56231i			0.236797i
$769$	−10.8541	−	7.88597i	−0.391409	−	0.284375i	0.374624	−	0.927177i	$-0.377772\pi$
$769$	−10.8541	−	7.88597i	−0.391409	−	0.284375i	−0.766033	+	0.642802i	$0.777772\pi$
$770$		0			0
$771$	−13.0623	+	9.49032i	−0.470427	+	0.341786i
$772$	−5.42882	−	7.47214i	−0.195388	−	0.268928i
$773$	31.5361	−	10.2467i	1.13428	−	0.368549i	0.319076	−	0.947729i	$-0.396627\pi$
$773$	31.5361	−	10.2467i	1.13428	−	0.368549i	0.815199	+	0.579180i	$0.196627\pi$
$774$	2.29180			0.0823769
$775$		0			0
$776$	−6.38197			−0.229099
$777$	6.51864	−	2.11803i	0.233855	−	0.0759840i
$778$	5.44907	+	7.50000i	0.195359	+	0.268888i
$779$	24.7984	−	18.0171i	0.888494	−	0.645529i
$780$		0			0
$781$	−2.70820	−	1.96763i	−0.0969072	−	0.0704072i
$782$		−	3.88854i		−	0.139054i
$783$	−4.06150	+	5.59017i	−0.145146	+	0.199776i
$784$	2.51064	−	7.72696i	0.0896658	−	0.275963i
$785$		0			0
$786$	−3.39919	−	10.4616i	−0.121245	−	0.373154i
$787$	−32.5074	−	10.5623i	−1.15876	−	0.376506i	−0.334327	−	0.942457i	$-0.608509\pi$
$787$	−32.5074	−	10.5623i	−1.15876	−	0.376506i	−0.824438	+	0.565952i	$0.808509\pi$
$788$	−14.9394	−	4.85410i	−0.532194	−	0.172920i
$789$	6.82624	+	21.0090i	0.243021	+	0.747940i
$790$		0			0
$791$	−5.07295	+	15.6129i	−0.180373	+	0.555132i
$792$	−2.00811	+	2.76393i	−0.0713552	+	0.0982120i
$793$		−	22.8541i		−	0.811573i
$794$	−0.0172209	−	0.0125117i	−0.000611148	−	0.000444025i
$795$		0			0
$796$	3.35410	−	2.43690i	0.118883	−	0.0863735i
$797$	−8.36775	−	11.5172i	−0.296401	−	0.407961i	0.634679	−	0.772776i	$-0.281132\pi$
$797$	−8.36775	−	11.5172i	−0.296401	−	0.407961i	−0.931080	+	0.364815i	$0.881132\pi$
$798$	5.56758	−	1.80902i	0.197090	−	0.0640385i
$799$	−1.23607			−0.0437289
$800$		0			0
$801$	−17.8885			−0.632061
$802$	13.2820	−	4.31559i	0.469005	−	0.152389i
$803$	4.04125	+	5.56231i	0.142613	+	0.196290i
$804$	−12.0902	+	8.78402i	−0.426387	+	0.309789i
$805$		0			0
$806$	−7.28115	−	5.29007i	−0.256468	−	0.186335i
$807$		−	17.2361i		−	0.606738i
$808$	−9.82084	+	13.5172i	−0.345496	+	0.475534i
$809$	4.93769	−	15.1967i	0.173600	−	0.534286i	−0.825967	−	0.563719i	$-0.809370\pi$
$809$	4.93769	−	15.1967i	0.173600	−	0.534286i	0.999567	+	0.0294328i	$0.00937011\pi$
$810$		0			0
$811$	−0.399187	−	1.22857i	−0.0140173	−	0.0431410i	0.943803	−	0.330508i	$-0.107220\pi$
$811$	−0.399187	−	1.22857i	−0.0140173	−	0.0431410i	−0.957821	+	0.287367i	$0.907220\pi$
$812$	−3.44095	−	1.11803i	−0.120754	−	0.0392353i
$813$	7.60845	+	2.47214i	0.266840	+	0.0867016i
$814$	0.618034	+	1.90211i	0.0216621	+	0.0666690i
$815$		0			0
$816$	−0.437694	+	1.34708i	−0.0153224	+	0.0471574i
$817$	−6.37988	+	8.78115i	−0.223204	+	0.307214i
$818$		−	17.5623i		−	0.614052i
$819$	−12.7082	−	9.23305i	−0.444061	−	0.322629i
$820$		0			0
$821$	−15.9271	+	11.5717i	−0.555858	+	0.403854i	−0.829941	−	0.557852i	$-0.811626\pi$
$821$	−15.9271	+	11.5717i	−0.555858	+	0.403854i	0.274083	+	0.961706i	$0.411626\pi$
$822$	−2.15938	−	2.97214i	−0.0753171	−	0.103665i
$823$	32.6134	−	10.5967i	1.13683	−	0.369379i	0.320664	−	0.947193i	$-0.396094\pi$
$823$	32.6134	−	10.5967i	1.13683	−	0.369379i	0.816169	+	0.577814i	$0.196094\pi$
$824$	−25.8541			−0.900670
$825$		0			0
$826$	4.14590			0.144254
$827$	28.5645	−	9.28115i	0.993283	−	0.322737i	0.233105	−	0.972452i	$-0.425111\pi$
$827$	28.5645	−	9.28115i	0.993283	−	0.322737i	0.760178	+	0.649714i	$0.225111\pi$
$828$	15.6659	+	21.5623i	0.544429	+	0.749342i
$829$	−23.5795	+	17.1315i	−0.818951	+	0.595003i	−0.916412	−	0.400237i	$-0.868928\pi$
$829$	−23.5795	+	17.1315i	−0.818951	+	0.595003i	0.0974610	+	0.995239i	$0.468928\pi$
$830$		0			0
$831$	9.13525	+	6.63715i	0.316898	+	0.230240i
$832$			1.14590i			0.0397269i
$833$	−1.96763	+	2.70820i	−0.0681742	+	0.0938337i
$834$	−0.954915	+	2.93893i	−0.0330660	+	0.101767i
$835$		0			0
$836$	−2.23607	−	6.88191i	−0.0773360	−	0.238016i
$837$	14.2658	+	4.63525i	0.493100	+	0.160218i
$838$	0.310271	+	0.100813i	0.0107181	+	0.00348253i
$839$	−1.28115	−	3.94298i	−0.0442303	−	0.136127i	0.926503	−	0.376288i	$-0.122800\pi$
$839$	−1.28115	−	3.94298i	−0.0442303	−	0.136127i	−0.970733	+	0.240161i	$0.922800\pi$
$840$		0			0
$841$	−8.37132	+	25.7643i	−0.288666	+	0.888424i
$842$	11.6247	−	16.0000i	0.400613	−	0.551396i
$843$			1.09017i			0.0375474i
$844$	−17.2533	−	12.5352i	−0.593883	−	0.431481i
$845$		0			0
$846$	−1.61803	+	1.17557i	−0.0556292	+	0.0404169i
$847$	−9.90659	−	13.6353i	−0.340395	−	0.468513i
$848$	9.64932	−	3.13525i	0.331359	−	0.107665i
$849$	23.1459			0.794365
$850$		0			0
$851$	34.8885			1.19596
$852$	−6.74315	+	2.19098i	−0.231017	+	0.0750618i
$853$	27.8052	+	38.2705i	0.952030	+	1.31036i	0.950620	+	0.310358i	$0.100449\pi$
$853$	27.8052	+	38.2705i	0.952030	+	1.31036i	0.00141065	+	0.999999i	$0.499551\pi$
$854$	3.80902	−	2.76741i	0.130342	−	0.0946989i
$855$		0			0
$856$	18.8435	+	13.6906i	0.644056	+	0.467934i
$857$		−	40.6869i		−	1.38984i	−0.719088	−	0.694919i	$-0.755440\pi$
$857$		−	40.6869i		−	1.38984i	0.719088	−	0.694919i	$-0.244560\pi$
$858$	−1.34708	+	1.85410i	−0.0459887	+	0.0632980i
$859$	8.78115	−	27.0256i	0.299609	−	0.922102i	−0.682025	−	0.731329i	$-0.738901\pi$
$859$	8.78115	−	27.0256i	0.299609	−	0.922102i	0.981634	−	0.190773i	$-0.0610995\pi$
$860$		0			0
$861$	2.61803	+	8.05748i	0.0892224	+	0.274598i
$862$	14.0086	+	4.55166i	0.477134	+	0.155030i
$863$	39.5281	+	12.8435i	1.34555	+	0.437196i	0.891194	−	0.453623i	$-0.149869\pi$
$863$	39.5281	+	12.8435i	1.34555	+	0.437196i	0.454358	+	0.890819i	$0.349869\pi$
$864$	8.68034	+	26.7153i	0.295311	+	0.908874i
$865$		0			0
$866$	3.84752	−	11.8415i	0.130744	−	0.402389i
$867$	−9.64932	+	13.2812i	−0.327708	+	0.451052i
$868$			7.85410i			0.266586i
$869$	−1.90983	−	1.38757i	−0.0647865	−	0.0470702i
$870$		0			0
$871$	36.2705	−	26.3521i	1.22898	−	0.892906i
$872$	13.1433	+	18.0902i	0.445088	+	0.612610i
$873$	−5.42882	+	1.76393i	−0.183738	+	0.0597001i
$874$	29.7984			1.00795
$875$		0			0
$876$	14.5623			0.492015
$877$	−29.0462	+	9.43769i	−0.980822	+	0.318688i	−0.755177	−	0.655521i	$-0.772449\pi$
$877$	−29.0462	+	9.43769i	−0.980822	+	0.318688i	−0.225645	+	0.974210i	$0.572449\pi$
$878$	2.17189	+	2.98936i	0.0732979	+	0.100886i
$879$	−23.0344	+	16.7355i	−0.776932	+	0.564474i
$880$		0			0
$881$	−3.52786	−	2.56314i	−0.118857	−	0.0863545i	0.526769	−	0.850009i	$-0.323403\pi$
$881$	−3.52786	−	2.56314i	−0.118857	−	0.0863545i	−0.645626	+	0.763654i	$0.723403\pi$
$882$			5.41641i			0.182380i
$883$	27.8707	−	38.3607i	0.937923	−	1.29094i	−0.0187653	−	0.999824i	$-0.505974\pi$
$883$	27.8707	−	38.3607i	0.937923	−	1.29094i	0.956688	−	0.291116i	$-0.0940265\pi$
$884$	1.85410	−	5.70634i	0.0623602	−	0.191925i
$885$		0			0
$886$	2.30244	+	7.08618i	0.0773520	+	0.238065i
$887$	−5.60034	−	1.81966i	−0.188041	−	0.0610982i	0.213483	−	0.976947i	$-0.431519\pi$
$887$	−5.60034	−	1.81966i	−0.188041	−	0.0610982i	−0.401524	+	0.915849i	$0.631519\pi$
$888$	9.00854	+	2.92705i	0.302307	+	0.0982254i
$889$	−7.94427	−	24.4500i	−0.266442	−	0.820025i
$890$		0			0
$891$	−0.236068	+	0.726543i	−0.00790857	+	0.0243401i
$892$	−21.0948	+	29.0344i	−0.706305	+	0.972145i
$893$		−	9.47214i		−	0.316973i
$894$	6.97214	+	5.06555i	0.233183	+	0.169417i
$895$		0			0
$896$	−14.8992	+	10.8249i	−0.497747	+	0.361634i
$897$	23.4989	+	32.3435i	0.784605	+	1.07992i
$898$	11.9475	−	3.88197i	0.398692	−	0.129543i
$899$	−4.14590			−0.138273
$900$		0			0
$901$	−4.18034			−0.139267
$902$	−2.35114	+	0.763932i	−0.0782844	+	0.0254362i
$903$	−1.76336	−	2.42705i	−0.0586808	−	0.0807672i
$904$	−18.3541	+	13.3350i	−0.610448	+	0.443517i
$905$		0			0
$906$	2.78115	+	2.02063i	0.0923976	+	0.0671308i
$907$			47.2492i			1.56888i	0.620202	+	0.784442i	$0.287051\pi$
$907$			47.2492i			1.56888i	−0.620202	+	0.784442i	$0.712949\pi$
$908$	18.2946	−	25.1803i	0.607127	−	0.835639i
$909$	−4.61803	+	14.2128i	−0.153171	+	0.471410i
$910$		0			0
$911$	−11.0517	−	34.0135i	−0.366158	−	1.12692i	−0.949253	−	0.314514i	$-0.898158\pi$
$911$	−11.0517	−	34.0135i	−0.366158	−	1.12692i	0.583095	−	0.812404i	$-0.301842\pi$
$912$	−10.3229	−	3.35410i	−0.341824	−	0.111065i
$913$	−1.28157	−	0.416408i	−0.0424138	−	0.0137811i
$914$	−1.03444	−	3.18368i	−0.0342163	−	0.105307i
$915$		0			0
$916$	−4.14590	+	12.7598i	−0.136984	+	0.421594i
$917$	16.9273	−	23.2984i	0.558987	−	0.769380i
$918$		−	2.36068i		−	0.0779140i
$919$	−1.44427	−	1.04932i	−0.0476421	−	0.0346140i	0.563709	−	0.825973i	$-0.309374\pi$
$919$	−1.44427	−	1.04932i	−0.0476421	−	0.0346140i	−0.611351	+	0.791359i	$0.709374\pi$
$920$		0			0
$921$	−3.85410	+	2.80017i	−0.126997	+	0.0922687i
$922$	−8.42075	−	11.5902i	−0.277323	−	0.381702i
$923$	20.2295	−	6.57295i	0.665861	−	0.216351i
$924$	2.00000			0.0657952
$925$		0			0
$926$	9.96556			0.327489
$927$	−21.9928	+	7.14590i	−0.722339	+	0.234702i
$928$	−4.56352	−	6.28115i	−0.149805	−	0.206189i
$929$	−29.6353	+	21.5313i	−0.972301	+	0.706418i	−0.955975	−	0.293449i	$-0.905197\pi$
$929$	−29.6353	+	21.5313i	−0.972301	+	0.706418i	−0.0163263	+	0.999867i	$0.505197\pi$
$930$		0			0
$931$	−20.7533	−	15.0781i	−0.680162	−	0.494166i
$932$		−	24.1803i		−	0.792053i
$933$	17.3435	−	23.8713i	0.567802	−	0.781512i
$934$	5.43363	−	16.7230i	0.177794	−	0.547193i
$935$		0			0
$936$	−6.70820	−	20.6457i	−0.219265	−	0.674827i
$937$	48.7612	+	15.8435i	1.59296	+	0.517583i	0.965353	−	0.260949i	$-0.0840354\pi$
$937$	48.7612	+	15.8435i	1.59296	+	0.517583i	0.627605	+	0.778532i	$0.284035\pi$
$938$	8.78402	+	2.85410i	0.286809	+	0.0931897i
$939$	6.56231	+	20.1967i	0.214153	+	0.659094i
$940$		0			0
$941$	−6.05166	+	18.6251i	−0.197279	+	0.607161i	0.802664	+	0.596432i	$0.203415\pi$
$941$	−6.05166	+	18.6251i	−0.197279	+	0.607161i	−0.999942	+	0.0107294i	$0.996585\pi$
$942$	−3.33495	+	4.59017i	−0.108659	+	0.149556i
$943$			43.1246i			1.40433i
$944$	−6.21885	−	4.51826i	−0.202406	−	0.147057i
$945$		0			0
$946$	0.708204	−	0.514540i	0.0230257	−	0.0167291i
$947$	16.8415	+	23.1803i	0.547275	+	0.753260i	0.989639	−	0.143576i	$-0.0458601\pi$
$947$	16.8415	+	23.1803i	0.547275	+	0.753260i	−0.442364	+	0.896836i	$0.645860\pi$
$948$	−4.75528	+	1.54508i	−0.154444	+	0.0501820i
$949$	−43.6869			−1.41814
$950$		0			0
$951$	−23.6525			−0.766984
$952$	2.62866	−	0.854102i	0.0851952	−	0.0276816i
$953$	20.4212	+	28.1074i	0.661508	+	0.910488i	0.999530	−	0.0306505i	$-0.00975787\pi$
$953$	20.4212	+	28.1074i	0.661508	+	0.910488i	−0.338022	+	0.941138i	$0.609758\pi$
$954$	−5.47214	+	3.97574i	−0.177167	+	0.128719i
$955$		0			0
$956$	−38.5795	−	28.0297i	−1.24775	−	0.906544i
$957$			1.05573i			0.0341268i
$958$	1.50609	−	2.07295i	0.0486594	−	0.0669739i
$959$	2.97214	−	9.14729i	0.0959753	−	0.295382i
$960$		0			0
$961$	−6.79837	−	20.9232i	−0.219302	−	0.674943i
$962$	−12.0862	−	3.92705i	−0.389675	−	0.126613i
$963$	19.8132	+	6.43769i	0.638471	+	0.207452i
$964$	5.73607	+	17.6538i	0.184746	+	0.568591i
$965$		0			0
$966$	−2.54508	+	7.83297i	−0.0818868	+	0.252022i
$967$	23.4459	−	32.2705i	0.753969	−	1.03775i	−0.243723	−	0.969845i	$-0.578369\pi$
$967$	23.4459	−	32.2705i	0.753969	−	1.03775i	0.997692	−	0.0679046i	$-0.0216314\pi$
$968$		−	23.2918i		−	0.748627i
$969$	3.61803	+	2.62866i	0.116228	+	0.0844446i
$970$		0			0
$971$	−2.73607	+	1.98787i	−0.0878046	+	0.0637938i	−0.630821	−	0.775928i	$-0.717282\pi$
$971$	−2.73607	+	1.98787i	−0.0878046	+	0.0637938i	0.543017	+	0.839722i	$0.317282\pi$
$972$	15.2169	+	20.9443i	0.488082	+	0.671788i
$973$	−7.69421	+	2.50000i	−0.246665	+	0.0801463i
$974$	5.92299			0.189785
$975$		0			0
$976$	−8.72949			−0.279424
$977$	32.0054	−	10.3992i	1.02394	−	0.332699i	0.251551	−	0.967844i	$-0.419060\pi$
$977$	32.0054	−	10.3992i	1.02394	−	0.332699i	0.772393	+	0.635145i	$0.219060\pi$
$978$	3.99598	+	5.50000i	0.127777	+	0.175871i
$979$	−5.52786	+	4.01623i	−0.176671	+	0.128359i
$980$		0			0
$981$	16.1803	+	11.7557i	0.516598	+	0.375331i
$982$			23.0213i			0.734639i
$983$	−4.33901	+	5.97214i	−0.138393	+	0.190482i	−0.872588	−	0.488457i	$-0.837560\pi$
$983$	−4.33901	+	5.97214i	−0.138393	+	0.190482i	0.734195	+	0.678939i	$0.237560\pi$
$984$	−3.61803	+	11.1352i	−0.115339	+	0.354976i
$985$		0			0
$986$	0.201626	+	0.620541i	0.00642108	+	0.0197621i
$987$	2.48990	+	0.809017i	0.0792543	+	0.0257513i
$988$	43.7284	+	14.2082i	1.39118	+	0.452023i
$989$	−4.71885	−	14.5231i	−0.150051	−	0.461808i
$990$		0			0
$991$	9.07295	−	27.9237i	0.288212	−	0.887024i	−0.697206	−	0.716871i	$-0.745574\pi$
$991$	9.07295	−	27.9237i	0.288212	−	0.887024i	0.985418	−	0.170153i	$-0.0544264\pi$
$992$	−9.90659	+	13.6353i	−0.314535	+	0.432920i
$993$		−	17.1246i		−	0.543433i
$994$	3.54508	+	2.57565i	0.112443	+	0.0816948i
$995$		0			0
$996$	−2.30902	+	1.67760i	−0.0731640	+	0.0531568i
$997$	6.40013	+	8.80902i	0.202694	+	0.278984i	0.898248	−	0.439490i	$-0.144841\pi$
$997$	6.40013	+	8.80902i	0.202694	+	0.278984i	−0.695554	+	0.718474i	$0.744841\pi$
$998$	−7.38394	+	2.39919i	−0.233734	+	0.0759449i
$999$	21.1803			0.670116

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.e.c.499.1		8
5.2	odd	4		625.2.d.b.126.1		4
5.3	odd	4		625.2.d.h.126.1		4
5.4	even	2	inner	625.2.e.c.499.2		8
25.2	odd	20		625.2.a.c.1.1		2
25.3	odd	20		625.2.d.h.501.1		4
25.4	even	10	inner	625.2.e.c.124.1		8
25.6	even	5		125.2.e.a.49.2		8
25.8	odd	20		25.2.d.a.16.1	yes	4
25.9	even	10		125.2.e.a.74.2		8
25.11	even	5		625.2.b.a.624.3		4
25.12	odd	20		125.2.d.a.51.1		4
25.13	odd	20		25.2.d.a.11.1	✓	4
25.14	even	10		625.2.b.a.624.2		4
25.16	even	5		125.2.e.a.74.1		8
25.17	odd	20		125.2.d.a.76.1		4
25.19	even	10		125.2.e.a.49.1		8
25.21	even	5	inner	625.2.e.c.124.2		8
25.22	odd	20		625.2.d.b.501.1		4
25.23	odd	20		625.2.a.b.1.2		2
75.2	even	20		5625.2.a.d.1.2		2
75.8	even	20		225.2.h.b.91.1		4
75.23	even	20		5625.2.a.f.1.1		2
75.38	even	20		225.2.h.b.136.1		4
100.23	even	20		10000.2.a.c.1.2		2
100.27	even	20		10000.2.a.l.1.1		2
100.63	even	20		400.2.u.b.161.1		4
100.83	even	20		400.2.u.b.241.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.2.d.a.11.1	✓	4	25.13	odd	20
25.2.d.a.16.1	yes	4	25.8	odd	20
125.2.d.a.51.1		4	25.12	odd	20
125.2.d.a.76.1		4	25.17	odd	20
125.2.e.a.49.1		8	25.19	even	10
125.2.e.a.49.2		8	25.6	even	5
125.2.e.a.74.1		8	25.16	even	5
125.2.e.a.74.2		8	25.9	even	10
225.2.h.b.91.1		4	75.8	even	20
225.2.h.b.136.1		4	75.38	even	20
400.2.u.b.161.1		4	100.63	even	20
400.2.u.b.241.1		4	100.83	even	20
625.2.a.b.1.2		2	25.23	odd	20
625.2.a.c.1.1		2	25.2	odd	20
625.2.b.a.624.2		4	25.14	even	10
625.2.b.a.624.3		4	25.11	even	5
625.2.d.b.126.1		4	5.2	odd	4
625.2.d.b.501.1		4	25.22	odd	20
625.2.d.h.126.1		4	5.3	odd	4
625.2.d.h.501.1		4	25.3	odd	20
625.2.e.c.124.1		8	25.4	even	10	inner
625.2.e.c.124.2		8	25.21	even	5	inner
625.2.e.c.499.1		8	1.1	even	1	trivial
625.2.e.c.499.2		8	5.4	even	2	inner
5625.2.a.d.1.2		2	75.2	even	20
5625.2.a.f.1.1		2	75.23	even	20
10000.2.a.c.1.2		2	100.23	even	20
10000.2.a.l.1.1		2	100.27	even	20

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:	\( N \)	\(=\)	\( 625 = 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	625.e (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 + 0.190983i) q^{2} +(0.587785 + 0.809017i) q^{3} +(-1.30902 + 0.951057i) q^{4} +(-0.500000 - 0.363271i) q^{6} -1.61803i q^{7} +(1.31433 - 1.80902i) q^{8} +(0.618034 - 1.90211i) q^{9} +O(q^{10})\)	\(q+(-0.587785 + 0.190983i) q^{2} +(0.587785 + 0.809017i) q^{3} +(-1.30902 + 0.951057i) q^{4} +(-0.500000 - 0.363271i) q^{6} -1.61803i q^{7} +(1.31433 - 1.80902i) q^{8} +(0.618034 - 1.90211i) q^{9} +(-0.236068 - 0.726543i) q^{11} +(-1.53884 - 0.500000i) q^{12} +(4.61653 + 1.50000i) q^{13} +(0.309017 + 0.951057i) q^{14} +(0.572949 - 1.76336i) q^{16} +(-0.449028 + 0.618034i) q^{17} +1.23607i q^{18} +(-4.73607 - 3.44095i) q^{19} +(1.30902 - 0.951057i) q^{21} +(0.277515 + 0.381966i) q^{22} +(7.83297 - 2.54508i) q^{23} +2.23607 q^{24} -3.00000 q^{26} +(4.75528 - 1.54508i) q^{27} +(1.53884 + 2.11803i) q^{28} +(-1.11803 + 0.812299i) q^{29} +(2.42705 + 1.76336i) q^{31} +5.61803i q^{32} +(0.449028 - 0.618034i) q^{33} +(0.145898 - 0.449028i) q^{34} +(1.00000 + 3.07768i) q^{36} +(4.02874 + 1.30902i) q^{37} +(3.44095 + 1.11803i) q^{38} +(1.50000 + 4.61653i) q^{39} +(-1.61803 + 4.97980i) q^{41} +(-0.587785 + 0.809017i) q^{42} -1.85410i q^{43} +(1.00000 + 0.726543i) q^{44} +(-4.11803 + 2.99193i) q^{46} +(0.951057 + 1.30902i) q^{47} +(1.76336 - 0.572949i) q^{48} +4.38197 q^{49} -0.763932 q^{51} +(-7.46969 + 2.42705i) q^{52} +(3.21644 + 4.42705i) q^{53} +(-2.50000 + 1.81636i) q^{54} +(-2.92705 - 2.12663i) q^{56} -5.85410i q^{57} +(0.502029 - 0.690983i) q^{58} +(1.28115 - 3.94298i) q^{59} +(-1.45492 - 4.47777i) q^{61} +(-1.76336 - 0.572949i) q^{62} +(-3.07768 - 1.00000i) q^{63} +(0.0729490 + 0.224514i) q^{64} +(-0.145898 + 0.449028i) q^{66} +(5.42882 - 7.47214i) q^{67} -1.23607i q^{68} +(6.66312 + 4.84104i) q^{69} +(3.54508 - 2.57565i) q^{71} +(-2.62866 - 3.61803i) q^{72} +(-8.55951 + 2.78115i) q^{73} -2.61803 q^{74} +9.47214 q^{76} +(-1.17557 + 0.381966i) q^{77} +(-1.76336 - 2.42705i) q^{78} +(2.50000 - 1.81636i) q^{79} +(-0.809017 - 0.587785i) q^{81} -3.23607i q^{82} +(1.03681 - 1.42705i) q^{83} +(-0.809017 + 2.48990i) q^{84} +(0.354102 + 1.08981i) q^{86} +(-1.31433 - 0.427051i) q^{87} +(-1.62460 - 0.527864i) q^{88} +(-2.76393 - 8.50651i) q^{89} +(2.42705 - 7.46969i) q^{91} +(-7.83297 + 10.7812i) q^{92} +3.00000i q^{93} +(-0.809017 - 0.587785i) q^{94} +(-4.54508 + 3.30220i) q^{96} +(-1.67760 - 2.30902i) q^{97} +(-2.57565 + 0.836881i) q^{98} -1.52786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{4} - 4 q^{6} - 4 q^{9}+O(q^{10}) \) 8 * q - 6 * q^4 - 4 * q^6 - 4 * q^9	\( 8 q - 6 q^{4} - 4 q^{6} - 4 q^{9} + 16 q^{11} - 2 q^{14} + 18 q^{16} - 20 q^{19} + 6 q^{21} - 24 q^{26} + 6 q^{31} + 28 q^{34} + 8 q^{36} + 12 q^{39} - 4 q^{41} + 8 q^{44} - 24 q^{46} + 44 q^{49} - 24 q^{51} - 20 q^{54} - 10 q^{56} - 30 q^{59} - 34 q^{61} + 14 q^{64} - 28 q^{66} + 22 q^{69} + 6 q^{71} - 12 q^{74} + 40 q^{76} + 20 q^{79} - 2 q^{81} - 2 q^{84} - 24 q^{86} - 40 q^{89} + 6 q^{91} - 2 q^{94} - 14 q^{96} - 48 q^{99}+O(q^{100}) \) 8 * q - 6 * q^4 - 4 * q^6 - 4 * q^9 + 16 * q^11 - 2 * q^14 + 18 * q^16 - 20 * q^19 + 6 * q^21 - 24 * q^26 + 6 * q^31 + 28 * q^34 + 8 * q^36 + 12 * q^39 - 4 * q^41 + 8 * q^44 - 24 * q^46 + 44 * q^49 - 24 * q^51 - 20 * q^54 - 10 * q^56 - 30 * q^59 - 34 * q^61 + 14 * q^64 - 28 * q^66 + 22 * q^69 + 6 * q^71 - 12 * q^74 + 40 * q^76 + 20 * q^79 - 2 * q^81 - 2 * q^84 - 24 * q^86 - 40 * q^89 + 6 * q^91 - 2 * q^94 - 14 * q^96 - 48 * q^99

Introduction

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