LMFDB - Embedded newform 625.2.e.c.124.2

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			124.2
Root			$0.587785 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	625.124
Dual form			625.2.e.c.499.2

$q$-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 $\left(\mathbb{Z}/625\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{10}\right)$

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	$-0.329881\pi$
$2$	0.587785	+	0.190983i	0.415627	+	0.135045i	−0.0937362	+	0.995597i	$0.529881\pi$
$3$	−0.587785	+	0.809017i	−0.339358	+	0.467086i	−0.944254	−	0.329218i	$-0.893215\pi$
$3$	−0.587785	+	0.809017i	−0.339358	+	0.467086i	0.604896	+	0.796305i	$0.293215\pi$
$4$	−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	−0.980317	−	0.197430i	$-0.936740\pi$
$11$	−0.236068	+	0.726543i	−0.0711772	+	0.219061i	0.909140	+	0.416491i	$0.136740\pi$
$12$	1.53884	−	0.500000i	0.444225	−	0.144338i
$13$	−4.61653	+	1.50000i	−1.28039	+	0.416025i	−0.868719	−	0.495306i	$-0.835056\pi$
$13$	−4.61653	+	1.50000i	−1.28039	+	0.416025i	−0.411675	+	0.911331i	$0.635056\pi$
$14$	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	$-0.170469\pi$
$17$	0.449028	+	0.618034i	0.108905	+	0.149895i	−0.751085	+	0.660205i	$0.770469\pi$
$18$			1.23607i			0.291344i
$19$	−4.73607	+	3.44095i	−1.08653	+	0.789409i	−0.978810	−	0.204772i	$-0.934355\pi$
$19$	−4.73607	+	3.44095i	−1.08653	+	0.789409i	−0.107719	+	0.994181i	$0.534355\pi$
$20$		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	$-0.728708\pi$
$23$	−7.83297	−	2.54508i	−1.63329	−	0.530687i	−0.975024	+	0.222101i	$0.928708\pi$
$24$	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	0.479120	−	0.877750i	$-0.340956\pi$
$29$	−1.11803	−	0.812299i	−0.207614	−	0.150840i	−0.686733	+	0.726909i	$0.740956\pi$
$30$		0			0
$31$	2.42705	−	1.76336i	0.435911	−	0.316708i	−0.348097	−	0.937459i	$-0.613172\pi$
$31$	2.42705	−	1.76336i	0.435911	−	0.316708i	0.784008	+	0.620750i	$0.213172\pi$
$32$			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	$-0.713208\pi$
$37$	−4.02874	+	1.30902i	−0.662321	+	0.215201i	−0.0414819	+	0.999139i	$0.513208\pi$
$38$	−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	−0.994275	−	0.106850i	$-0.965924\pi$
$41$	−1.61803	−	4.97980i	−0.252694	−	0.777714i	0.741581	−	0.670864i	$-0.234076\pi$
$42$	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	$-0.837651\pi$
$47$	−0.951057	+	1.30902i	−0.138726	+	0.190940i	0.734001	+	0.679148i	$0.237651\pi$
$48$	−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	$-0.922642\pi$
$53$	−3.21644	+	4.42705i	−0.441812	+	0.608102i	0.528801	+	0.848746i	$0.322642\pi$
$54$	−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	0.999164	−	0.0408847i	$-0.0130176\pi$
$59$	1.28115	+	3.94298i	0.166792	+	0.513333i	−0.832372	+	0.554217i	$0.813018\pi$
$60$		0			0
$61$	−1.45492	+	4.47777i	−0.186283	+	0.573319i	−0.999968	−	0.00798614i	$-0.997458\pi$
$61$	−1.45492	+	4.47777i	−0.186283	+	0.573319i	0.813685	+	0.581306i	$0.197458\pi$
$62$	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	$-0.390809\pi$
$67$	−5.42882	−	7.47214i	−0.663236	−	0.912867i	−0.999583	+	0.0288716i	$0.990809\pi$
$68$		−	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	0.777929	−	0.628352i	$-0.216270\pi$
$71$	3.54508	+	2.57565i	0.420724	+	0.305674i	−0.357205	+	0.934026i	$0.616270\pi$
$72$	2.62866	−	3.61803i	0.309790	−	0.426389i
$73$	8.55951	+	2.78115i	1.00181	+	0.325509i	0.763590	−	0.645701i	$-0.223435\pi$
$73$	8.55951	+	2.78115i	1.00181	+	0.325509i	0.238224	+	0.971210i	$0.423435\pi$
$74$	−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	0.719472	−	0.694521i	$-0.244384\pi$
$79$	2.50000	+	1.81636i	0.281272	+	0.204356i	−0.438200	+	0.898877i	$0.644384\pi$
$80$		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	$-0.230863\pi$
$83$	−1.03681	−	1.42705i	−0.113805	−	0.156639i	−0.862120	+	0.506705i	$0.830863\pi$
$84$	−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	0.690918	+	0.722934i	$0.257207\pi$
$89$	−2.76393	+	8.50651i	−0.292976	+	0.901688i	−0.983894	+	0.178754i	$0.942793\pi$
$90$		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	$-0.753716\pi$
$97$	1.67760	−	2.30902i	0.170334	−	0.234445i	0.885647	+	0.464360i	$0.153716\pi$
$98$	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	$-0.607085\pi$
$103$	6.79615	−	9.35410i	0.669645	−	0.921687i	0.999752	+	0.0222563i	$0.00708499\pi$
$104$	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	−0.982889	−	0.184199i	$-0.941031\pi$
$109$	−3.09017	−	9.51057i	−0.295985	−	0.910947i	0.686904	−	0.726748i	$-0.258969\pi$
$110$		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	$-0.441643\pi$
$113$	9.64932	−	3.13525i	0.907732	−	0.294940i	0.725425	+	0.688302i	$0.241643\pi$
$114$	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	$-0.649026\pi$
$127$	−15.1109	−	4.90983i	−1.34088	−	0.435677i	−0.889613	+	0.456714i	$0.849026\pi$
$128$	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	0.259402	−	0.965769i	$-0.416475\pi$
$131$	14.3992	−	10.4616i	1.25806	−	0.914036i	0.998661	+	0.0517333i	$0.0164746\pi$
$132$			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	$-0.681722\pi$
$137$	−5.65334	+	1.83688i	−0.482997	+	0.156935i	0.0573898	+	0.998352i	$0.481722\pi$
$138$	4.84104	−	1.57295i	0.412097	−	0.133898i
$139$	−1.54508	+	4.75528i	−0.131052	+	0.403338i	−0.994955	−	0.100321i	$-0.968013\pi$
$139$	−1.54508	+	4.75528i	−0.131052	+	0.403338i	0.863903	+	0.503659i	$0.168013\pi$
$140$		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	$-0.458234\pi$
$163$	10.4616	−	3.39919i	0.819417	−	0.266245i	0.688581	+	0.725159i	$0.258234\pi$
$164$	−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	$-0.130956\pi$
$167$	3.26944	+	4.50000i	0.252997	+	0.348220i	−0.663561	+	0.748122i	$0.730956\pi$
$168$		−	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	$-0.178102\pi$
$173$	16.0620	+	5.21885i	1.22117	+	0.396782i	0.373661	+	0.927565i	$0.378102\pi$
$174$	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	0.263341	−	0.964703i	$-0.415175\pi$
$179$	−7.66312	−	5.56758i	−0.572768	−	0.416141i	−0.836110	+	0.548562i	$0.815175\pi$
$180$		0			0
$181$	−11.0902	+	8.05748i	−0.824326	+	0.598908i	−0.917948	−	0.396700i	$-0.870155\pi$
$181$	−11.0902	+	8.05748i	−0.824326	+	0.598908i	0.0936225	+	0.995608i	$0.470155\pi$
$182$			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	−0.731080	−	0.682292i	$-0.760984\pi$
$191$	−7.47214	−	22.9969i	−0.540665	−	1.66400i	0.190415	−	0.981704i	$-0.439016\pi$
$192$	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	$-0.912406\pi$
$197$	−5.70634	+	7.85410i	−0.406560	+	0.559582i	0.555815	+	0.831306i	$0.312406\pi$
$198$	−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	−0.707348	−	0.706865i	$-0.750109\pi$
$211$	4.07295	−	12.5352i	0.280393	−	0.862962i	0.987742	−	0.156097i	$-0.0498912\pi$
$212$	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	$-0.666433\pi$
$223$	−21.0948	−	6.85410i	−1.41261	−	0.458985i	−0.913246	+	0.407408i	$0.866433\pi$
$224$	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	$-0.179608\pi$
$227$	18.2946	+	5.94427i	1.21425	+	0.394535i	0.369268	+	0.929323i	$0.379608\pi$
$228$	−5.56758	+	7.66312i	−0.368722	+	0.507502i
$229$	6.70820	+	4.87380i	0.443291	+	0.322069i	0.786941	−	0.617028i	$-0.211664\pi$
$229$	6.70820	+	4.87380i	0.443291	+	0.322069i	−0.343650	+	0.939098i	$0.611664\pi$
$230$		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	$-0.0371735\pi$
$233$	8.78402	+	12.0902i	0.575460	+	0.792053i	−0.417728	+	0.908572i	$0.637174\pi$
$234$	−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	0.00700219	−	0.999975i	$-0.497771\pi$
$239$	9.10739	−	28.0297i	0.589108	−	1.81309i	0.582106	−	0.813113i	$-0.302229\pi$
$240$		0			0
$241$	3.54508	+	10.9106i	0.228359	+	0.702817i	0.997933	+	0.0642594i	$0.0204685\pi$
$241$	3.54508	+	10.9106i	0.228359	+	0.702817i	−0.769574	+	0.638557i	$0.779532\pi$
$242$	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	$-0.838485\pi$
$263$	−21.0090	+	6.82624i	−1.29547	+	0.420924i	−0.421467	+	0.906844i	$0.638485\pi$
$264$	−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	−0.925200	−	0.379479i	$-0.876103\pi$
$269$	−13.9443	+	10.1311i	−0.850197	+	0.617704i	0.0750032	+	0.997183i	$0.476103\pi$
$270$		0			0
$271$	6.47214	+	4.70228i	0.393154	+	0.285643i	0.766747	−	0.641950i	$-0.221874\pi$
$271$	6.47214	+	4.70228i	0.393154	+	0.285643i	−0.373593	+	0.927593i	$0.621874\pi$
$272$	−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	$-0.510166\pi$
$277$	−10.7391	−	3.48936i	−0.645252	−	0.209655i	−0.613320	+	0.789835i	$0.710166\pi$
$278$	−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	−0.561168	−	0.827702i	$-0.689648\pi$
$281$	0.881966	−	0.640786i	0.0526137	−	0.0382261i	0.613781	+	0.789476i	$0.289648\pi$
$282$		−	1.00000i		−	0.0595491i
$283$	−13.6048	−	18.7254i	−0.808722	−	1.11311i	−0.991519	−	0.129960i	$-0.958515\pi$
$283$	−13.6048	−	18.7254i	−0.808722	−	1.11311i	0.182797	−	0.983151i	$-0.441485\pi$
$284$	−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	0.262510	+	0.964929i	$0.415450\pi$
$311$	−9.11803	+	28.0624i	−0.517036	+	1.59127i	−0.779546	+	0.626345i	$0.784550\pi$
$312$	−10.3229	+	3.35410i	−0.584417	+	0.189889i
$313$	−20.1967	+	6.56231i	−1.14159	+	0.370923i	−0.817967	−	0.575265i	$-0.804899\pi$
$313$	−20.1967	+	6.56231i	−1.14159	+	0.370923i	−0.323618	+	0.946188i	$0.604899\pi$
$314$	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	0.995188	+	0.0979842i	$0.0312395\pi$
$317$	13.9026	+	19.1353i	0.780846	+	1.07474i	−0.214341	+	0.976759i	$0.568761\pi$
$318$		−	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	−0.899367	−	0.437194i	$-0.855972\pi$
$331$	−13.8541	+	10.0656i	−0.761490	+	0.553255i	0.137877	+	0.990449i	$0.455972\pi$
$332$			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	$-0.609936\pi$
$337$	−1.08981	+	0.354102i	−0.0593659	+	0.0192892i	0.279183	+	0.960238i	$0.409936\pi$
$338$	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	−0.0447390	+	0.998999i	$0.514246\pi$
$347$	−18.2743	+	25.1525i	−0.981018	+	1.35026i	−0.936279	+	0.351257i	$0.885754\pi$
$348$	−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	0.244063	+	0.969759i	$0.421520\pi$
$353$	−14.1598	+	19.4894i	−0.753653	+	1.03731i	−0.997716	+	0.0675544i	$0.978480\pi$
$354$	−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	0.854176	+	0.519984i	$0.174062\pi$
$359$	8.88197	+	27.3359i	0.468772	+	1.44273i	−0.385403	+	0.922748i	$0.625938\pi$
$360$		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	$-0.154672\pi$
$367$	3.19620	+	4.39919i	0.166840	+	0.229636i	−0.717408	+	0.696653i	$0.754672\pi$
$368$		−	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	$-0.443569\pi$
$373$	−5.01255	−	1.62868i	−0.259540	−	0.0843297i	−0.435897	+	0.899997i	$0.643569\pi$
$374$	−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	−0.988513	−	0.151133i	$-0.951708\pi$
$379$	−27.9894	−	20.3355i	−1.43772	−	1.04456i	−0.449203	−	0.893430i	$-0.648292\pi$
$380$		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	$-0.293739\pi$
$383$	−6.67764	−	9.19098i	−0.341211	−	0.469637i	−0.944795	+	0.327663i	$0.893739\pi$
$384$	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	0.762102	+	0.647456i	$0.224167\pi$
$389$	−4.63525	+	14.2658i	−0.235017	+	0.723307i	−0.997119	+	0.0758507i	$0.975833\pi$
$390$		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	$-0.800275\pi$
$397$	−0.0202444	+	0.0278640i	−0.00101604	+	0.00139846i	0.808509	+	0.588484i	$0.200275\pi$
$398$	−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	−0.893904	−	0.448258i	$-0.852045\pi$
$409$	−8.78115	−	27.0256i	−0.434200	−	1.33633i	0.459704	−	0.888072i	$-0.347955\pi$
$410$		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	−0.598168	−	0.801371i	$-0.704104\pi$
$419$	−0.427051	+	0.310271i	−0.0208628	+	0.0151577i	0.577305	+	0.816529i	$0.304104\pi$
$420$		0			0
$421$	−25.8885	−	18.8091i	−1.26173	−	0.916701i	−0.262889	−	0.964826i	$-0.584675\pi$
$421$	−25.8885	−	18.8091i	−1.26173	−	0.916701i	−0.998841	+	0.0481252i	$0.984675\pi$
$422$	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	−0.945684	−	0.325087i	$-0.894606\pi$
$431$	−19.2812	+	14.0086i	−0.928740	+	0.674769i	0.0169437	+	0.999856i	$0.494606\pi$
$432$		−	9.27051i		−	0.446028i
$433$	11.8415	+	16.2984i	0.569064	+	0.783250i	0.992443	−	0.122703i	$-0.0391562\pi$
$433$	11.8415	+	16.2984i	0.569064	+	0.783250i	−0.423379	+	0.905953i	$0.639156\pi$
$434$	−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	−0.985416	−	0.170164i	$-0.945570\pi$
$439$	−1.84752	+	5.68609i	−0.0881775	+	0.271382i	0.897238	+	0.441547i	$0.145570\pi$
$440$		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	−0.633778	−	0.773515i	$-0.718497\pi$
$461$	7.16312	−	22.0458i	0.333620	−	1.02678i	0.967398	−	0.253261i	$-0.0815032\pi$
$462$	−0.726543	+	0.236068i	−0.0338018	+	0.0109829i
$463$	15.3354	−	4.98278i	0.712697	−	0.231569i	0.0698431	−	0.997558i	$-0.477750\pi$
$463$	15.3354	−	4.98278i	0.712697	−	0.231569i	0.642854	+	0.765989i	$0.277750\pi$
$464$	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	0.995934	+	0.0900830i	$0.0287132\pi$
$467$	16.7230	+	23.0172i	0.773848	+	1.06511i	−0.222087	+	0.975027i	$0.571287\pi$
$468$			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	0.508516	−	0.861052i	$-0.330194\pi$
$479$	−3.35410	−	2.43690i	−0.153253	−	0.111345i	−0.661769	+	0.749708i	$0.730194\pi$
$480$		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	$-0.530328\pi$
$487$	9.11454	−	2.96149i	0.413019	−	0.134198i	0.508154	+	0.861266i	$0.330328\pi$
$488$	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	0.775002	+	0.631958i	$0.217749\pi$
$491$	11.5106	+	35.4261i	0.519468	+	1.59876i	−0.255534	+	0.966800i	$0.582251\pi$
$492$	−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	$-0.724180\pi$
$503$	6.22088	−	8.56231i	0.277375	−	0.381774i	0.924862	+	0.380302i	$0.124180\pi$
$504$	−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	0.977949	−	0.208844i	$-0.0669701\pi$
$509$	1.44427	+	4.44501i	0.0640162	+	0.197022i	−0.913933	+	0.405866i	$0.866970\pi$
$510$		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	0.825731	−	0.564064i	$-0.190763\pi$
$521$	12.4271	+	9.02878i	0.544439	+	0.395558i	−0.281292	+	0.959622i	$0.590763\pi$
$522$	1.00406	−	1.38197i	0.0439464	−	0.0604870i
$523$	18.8824	+	6.13525i	0.825669	+	0.268276i	0.691220	−	0.722645i	$-0.257074\pi$
$523$	18.8824	+	6.13525i	0.825669	+	0.268276i	0.134449	+	0.990921i	$0.457074\pi$
$524$	−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	0.825235	−	0.564790i	$-0.191043\pi$
$541$	−4.05573	−	12.4822i	−0.174369	−	0.536654i	−0.999604	+	0.0281362i	$0.991043\pi$
$542$	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	0.106217	+	0.994343i	$0.466126\pi$
$547$	−20.4010	+	28.0795i	−0.872283	+	1.20059i	−0.978499	+	0.206251i	$0.933874\pi$
$548$	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	$-0.535036\pi$
$563$	9.14729	−	2.97214i	0.385512	−	0.125261i	0.495360	+	0.868688i	$0.335036\pi$
$564$	−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	0.0375739	−	0.999294i	$-0.488037\pi$
$569$	23.8435	−	17.3233i	0.999570	−	0.726230i	0.961996	+	0.273064i	$0.0880370\pi$
$570$		0			0
$571$	−25.9894	−	18.8824i	−1.08762	−	0.790203i	−0.108625	−	0.994083i	$-0.534645\pi$
$571$	−25.9894	−	18.8824i	−1.08762	−	0.790203i	−0.978996	+	0.203880i	$0.934645\pi$
$572$	−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	$-0.111973\pi$
$577$	35.9281	+	11.6738i	1.49571	+	0.485985i	0.556945	+	0.830549i	$0.311973\pi$
$578$	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	$-0.726173\pi$
$587$	−17.7926	+	5.78115i	−0.734378	+	0.238614i	−0.0821320	+	0.996621i	$0.526173\pi$
$588$	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	$-0.376522\pi$
$613$	30.4136	−	9.88197i	1.22839	−	0.399129i	0.850132	+	0.526570i	$0.176522\pi$
$614$	−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	$-0.262971\pi$
$617$	−5.73910	−	7.89919i	−0.231047	−	0.318009i	−0.908761	+	0.417316i	$0.862971\pi$
$618$			7.14590i			0.287450i
$619$	31.9336	−	23.2011i	1.28352	−	0.932533i	0.283868	−	0.958863i	$-0.408382\pi$
$619$	31.9336	−	23.2011i	1.28352	−	0.932533i	0.999653	+	0.0263310i	$0.00838237\pi$
$620$		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	−0.491086	−	0.871111i	$-0.663400\pi$
$631$	4.66312	−	3.38795i	0.185636	−	0.134872i	0.676722	+	0.736239i	$0.263400\pi$
$632$		−	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	0.993560	−	0.113304i	$-0.0361433\pi$
$641$	3.11803	+	9.59632i	0.123155	+	0.379032i	−0.870405	+	0.492336i	$0.836143\pi$
$642$	−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	−0.294129	−	0.955766i	$-0.595030\pi$
$647$	17.9516	−	24.7082i	0.705749	−	0.971380i	0.999878	−	0.0156141i	$-0.00497033\pi$
$648$	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	$-0.849463\pi$
$653$	−4.64928	+	6.39919i	−0.181940	+	0.250420i	0.708299	+	0.705913i	$0.249463\pi$
$654$	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	−0.983360	−	0.181666i	$-0.941851\pi$
$659$	−7.56231	−	23.2744i	−0.294586	−	0.906641i	0.688775	−	0.724975i	$-0.258149\pi$
$660$		0			0
$661$	−12.5729	+	38.6956i	−0.489031	+	1.50508i	0.337025	+	0.941496i	$0.390579\pi$
$661$	−12.5729	+	38.6956i	−0.489031	+	1.50508i	−0.826057	+	0.563587i	$0.809421\pi$
$662$	−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	$-0.337136\pi$
$673$	9.68208	+	3.14590i	0.373217	+	0.121265i	−0.116402	+	0.993202i	$0.537136\pi$
$674$	−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	$-0.348505\pi$
$677$	7.97172	+	2.59017i	0.306378	+	0.0995483i	−0.151793	+	0.988412i	$0.548505\pi$
$678$	−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	$-0.227609\pi$
$683$	−2.66141	−	3.66312i	−0.101836	−	0.140165i	−0.856894	+	0.515493i	$0.827609\pi$
$684$	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	0.965817	−	0.259224i	$-0.0834668\pi$
$691$	0.843459	+	2.59590i	0.0320867	+	0.0987527i	−0.933731	+	0.357977i	$0.883467\pi$
$692$	−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	−0.933345	−	0.358980i	$-0.883125\pi$
$709$	−10.3647	−	31.8994i	−0.389256	−	1.19801i	0.544089	−	0.839027i	$-0.316875\pi$
$710$		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	−0.982273	−	0.187455i	$-0.939976\pi$
$719$	−29.6976	+	21.5765i	−1.10753	+	0.804669i	−0.125259	+	0.992124i	$0.539976\pi$
$720$		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	$-0.373776\pi$
$727$	4.22050	+	1.37132i	0.156530	+	0.0508596i	−0.229704	+	0.973261i	$0.573776\pi$
$728$	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	$-0.0339796\pi$
$733$	15.8577	+	21.8262i	0.585717	+	0.806170i	−0.408590	+	0.912718i	$0.633980\pi$
$734$	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	−0.605499	−	0.795846i	$-0.707026\pi$
$739$	9.57295	−	29.4625i	0.352147	−	1.08380i	0.957646	−	0.287950i	$-0.0929736\pi$
$740$		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	−0.488627	−	0.872493i	$-0.662502\pi$
$761$	11.5729	−	35.6179i	0.419519	−	1.29115i	0.908146	−	0.418654i	$-0.137498\pi$
$762$	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	−0.766033	−	0.642802i	$-0.777772\pi$
$769$	−10.8541	+	7.88597i	−0.391409	+	0.284375i	0.374624	+	0.927177i	$0.377772\pi$
$770$		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	$-0.603373\pi$
$773$	−31.5361	−	10.2467i	−1.13428	−	0.368549i	−0.815199	+	0.579180i	$0.803373\pi$
$774$	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	$-0.391491\pi$
$787$	32.5074	−	10.5623i	1.15876	−	0.376506i	0.824438	+	0.565952i	$0.191491\pi$
$788$	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	$-0.718868\pi$
$797$	8.36775	−	11.5172i	0.296401	−	0.407961i	0.931080	+	0.364815i	$0.118868\pi$
$798$	−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	0.999567	−	0.0294328i	$-0.00937011\pi$
$809$	4.93769	+	15.1967i	0.173600	+	0.534286i	−0.825967	+	0.563719i	$0.809370\pi$
$810$		0			0
$811$	−0.399187	+	1.22857i	−0.0140173	+	0.0431410i	−0.957821	−	0.287367i	$-0.907220\pi$
$811$	−0.399187	+	1.22857i	−0.0140173	+	0.0431410i	0.943803	+	0.330508i	$0.107220\pi$
$812$	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	0.274083	−	0.961706i	$-0.411626\pi$
$821$	−15.9271	−	11.5717i	−0.555858	−	0.403854i	−0.829941	+	0.557852i	$0.811626\pi$
$822$	2.15938	−	2.97214i	0.0753171	−	0.103665i
$823$	−32.6134	−	10.5967i	−1.13683	−	0.369379i	−0.320664	−	0.947193i	$-0.603906\pi$
$823$	−32.6134	−	10.5967i	−1.13683	−	0.369379i	−0.816169	+	0.577814i	$0.803906\pi$
$824$	−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	$-0.574889\pi$
$827$	−28.5645	−	9.28115i	−0.993283	−	0.322737i	−0.760178	+	0.649714i	$0.774889\pi$
$828$	−15.6659	+	21.5623i	−0.544429	+	0.749342i
$829$	−23.5795	−	17.1315i	−0.818951	−	0.595003i	0.0974610	−	0.995239i	$-0.468928\pi$
$829$	−23.5795	−	17.1315i	−0.818951	−	0.595003i	−0.916412	+	0.400237i	$0.868928\pi$
$830$		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	−0.970733	−	0.240161i	$-0.922800\pi$
$839$	−1.28115	+	3.94298i	−0.0442303	+	0.136127i	0.926503	+	0.376288i	$0.122800\pi$
$840$		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	−0.00141065	+	0.999999i	$0.500449\pi$
$853$	−27.8052	+	38.2705i	−0.952030	+	1.31036i	−0.950620	+	0.310358i	$0.899551\pi$
$854$	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	0.981634	+	0.190773i	$0.0610995\pi$
$859$	8.78115	+	27.0256i	0.299609	+	0.922102i	−0.682025	+	0.731329i	$0.738901\pi$
$860$		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	$-0.850131\pi$
$863$	−39.5281	+	12.8435i	−1.34555	+	0.437196i	−0.454358	+	0.890819i	$0.650131\pi$
$864$	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	$-0.227551\pi$
$877$	29.0462	+	9.43769i	0.980822	+	0.318688i	0.225645	+	0.974210i	$0.427551\pi$
$878$	−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	−0.645626	−	0.763654i	$-0.723403\pi$
$881$	−3.52786	+	2.56314i	−0.118857	+	0.0863545i	0.526769	+	0.850009i	$0.323403\pi$
$882$			5.41641i			0.182380i
$883$	−27.8707	−	38.3607i	−0.937923	−	1.29094i	−0.956688	−	0.291116i	$-0.905974\pi$
$883$	−27.8707	−	38.3607i	−0.937923	−	1.29094i	0.0187653	−	0.999824i	$-0.494026\pi$
$884$	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	$-0.568481\pi$
$887$	5.60034	−	1.81966i	0.188041	−	0.0610982i	0.401524	+	0.915849i	$0.368481\pi$
$888$	−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	0.583095	+	0.812404i	$0.301842\pi$
$911$	−11.0517	+	34.0135i	−0.366158	+	1.12692i	−0.949253	+	0.314514i	$0.898158\pi$
$912$	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	−0.611351	−	0.791359i	$-0.709374\pi$
$919$	−1.44427	+	1.04932i	−0.0476421	+	0.0346140i	0.563709	+	0.825973i	$0.309374\pi$
$920$		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	−0.0163263	−	0.999867i	$-0.505197\pi$
$929$	−29.6353	−	21.5313i	−0.972301	−	0.706418i	−0.955975	+	0.293449i	$0.905197\pi$
$930$		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	$-0.915965\pi$
$937$	−48.7612	+	15.8435i	−1.59296	+	0.517583i	−0.627605	+	0.778532i	$0.715965\pi$
$938$	−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	−0.999942	−	0.0107294i	$-0.996585\pi$
$941$	−6.05166	−	18.6251i	−0.197279	−	0.607161i	0.802664	−	0.596432i	$-0.203415\pi$
$942$	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	$-0.954140\pi$
$947$	−16.8415	+	23.1803i	−0.547275	+	0.753260i	0.442364	+	0.896836i	$0.354140\pi$
$948$	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	$-0.990242\pi$
$953$	−20.4212	+	28.1074i	−0.661508	+	0.910488i	0.338022	+	0.941138i	$0.390242\pi$
$954$	−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	−0.997692	−	0.0679046i	$-0.978369\pi$
$967$	−23.4459	−	32.2705i	−0.753969	−	1.03775i	0.243723	−	0.969845i	$-0.421631\pi$
$968$		−	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	0.543017	−	0.839722i	$-0.317282\pi$
$971$	−2.73607	−	1.98787i	−0.0878046	−	0.0637938i	−0.630821	+	0.775928i	$0.717282\pi$
$972$	−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	$-0.580940\pi$
$977$	−32.0054	−	10.3992i	−1.02394	−	0.332699i	−0.772393	+	0.635145i	$0.780940\pi$
$978$	−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	$-0.162440\pi$
$983$	4.33901	+	5.97214i	0.138393	+	0.190482i	−0.734195	+	0.678939i	$0.762440\pi$
$984$	−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	0.985418	+	0.170153i	$0.0544264\pi$
$991$	9.07295	+	27.9237i	0.288212	+	0.887024i	−0.697206	+	0.716871i	$0.745574\pi$
$992$	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	$-0.855159\pi$
$997$	−6.40013	+	8.80902i	−0.202694	+	0.278984i	0.695554	+	0.718474i	$0.255159\pi$
$998$	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.124.2		8
5.2	odd	4		625.2.d.b.501.1		4
5.3	odd	4		625.2.d.h.501.1		4
5.4	even	2	inner	625.2.e.c.124.1		8
25.2	odd	20		125.2.d.a.76.1		4
25.3	odd	20		25.2.d.a.11.1	✓	4
25.4	even	10		125.2.e.a.74.2		8
25.6	even	5	inner	625.2.e.c.499.1		8
25.8	odd	20		625.2.d.h.126.1		4
25.9	even	10		625.2.b.a.624.2		4
25.11	even	5		125.2.e.a.49.2		8
25.12	odd	20		625.2.a.c.1.1		2
25.13	odd	20		625.2.a.b.1.2		2
25.14	even	10		125.2.e.a.49.1		8
25.16	even	5		625.2.b.a.624.3		4
25.17	odd	20		625.2.d.b.126.1		4
25.19	even	10	inner	625.2.e.c.499.2		8
25.21	even	5		125.2.e.a.74.1		8
25.22	odd	20		125.2.d.a.51.1		4
25.23	odd	20		25.2.d.a.16.1	yes	4
75.23	even	20		225.2.h.b.91.1		4
75.38	even	20		5625.2.a.f.1.1		2
75.53	even	20		225.2.h.b.136.1		4
75.62	even	20		5625.2.a.d.1.2		2
100.3	even	20		400.2.u.b.161.1		4
100.23	even	20		400.2.u.b.241.1		4
100.63	even	20		10000.2.a.c.1.2		2
100.87	even	20		10000.2.a.l.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.2.d.a.11.1	✓	4	25.3	odd	20
25.2.d.a.16.1	yes	4	25.23	odd	20
125.2.d.a.51.1		4	25.22	odd	20
125.2.d.a.76.1		4	25.2	odd	20
125.2.e.a.49.1		8	25.14	even	10
125.2.e.a.49.2		8	25.11	even	5
125.2.e.a.74.1		8	25.21	even	5
125.2.e.a.74.2		8	25.4	even	10
225.2.h.b.91.1		4	75.23	even	20
225.2.h.b.136.1		4	75.53	even	20
400.2.u.b.161.1		4	100.3	even	20
400.2.u.b.241.1		4	100.23	even	20
625.2.a.b.1.2		2	25.13	odd	20
625.2.a.c.1.1		2	25.12	odd	20
625.2.b.a.624.2		4	25.9	even	10
625.2.b.a.624.3		4	25.16	even	5
625.2.d.b.126.1		4	25.17	odd	20
625.2.d.b.501.1		4	5.2	odd	4
625.2.d.h.126.1		4	25.8	odd	20
625.2.d.h.501.1		4	5.3	odd	4
625.2.e.c.124.1		8	5.4	even	2	inner
625.2.e.c.124.2		8	1.1	even	1	trivial
625.2.e.c.499.1		8	25.6	even	5	inner
625.2.e.c.499.2		8	25.19	even	10	inner
5625.2.a.d.1.2		2	75.62	even	20
5625.2.a.f.1.1		2	75.38	even	20
10000.2.a.c.1.2		2	100.63	even	20
10000.2.a.l.1.1		2	100.87	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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