LMFDB - Embedded newform 966.2.f.b.461.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(461,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("966.461");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.f (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			461.5
Character	$\chi$	$=$	966.461
Dual form			966.2.f.b.461.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.740879 - 1.56560i) q^{3} -1.00000 q^{4} -3.67536 q^{5} +(-1.56560 + 0.740879i) q^{6} +(-0.229372 - 2.63579i) q^{7} +1.00000i q^{8} +(-1.90220 + 2.31984i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.740879 - 1.56560i) q^{3} -1.00000 q^{4} -3.67536 q^{5} +(-1.56560 + 0.740879i) q^{6} +(-0.229372 - 2.63579i) q^{7} +1.00000i q^{8} +(-1.90220 + 2.31984i) q^{9} +3.67536i q^{10} -3.25510i q^{11} +(0.740879 + 1.56560i) q^{12} +0.990814i q^{13} +(-2.63579 + 0.229372i) q^{14} +(2.72300 + 5.75414i) q^{15} +1.00000 q^{16} -6.53395 q^{17} +(2.31984 + 1.90220i) q^{18} +1.80051i q^{19} +3.67536 q^{20} +(-3.95665 + 2.31190i) q^{21} -3.25510 q^{22} +1.00000i q^{23} +(1.56560 - 0.740879i) q^{24} +8.50828 q^{25} +0.990814 q^{26} +(5.04123 + 1.25936i) q^{27} +(0.229372 + 2.63579i) q^{28} +1.83336i q^{29} +(5.75414 - 2.72300i) q^{30} -7.84167i q^{31} -1.00000i q^{32} +(-5.09618 + 2.41164i) q^{33} +6.53395i q^{34} +(0.843024 + 9.68748i) q^{35} +(1.90220 - 2.31984i) q^{36} -0.190892 q^{37} +1.80051 q^{38} +(1.55122 - 0.734073i) q^{39} -3.67536i q^{40} +2.12529 q^{41} +(2.31190 + 3.95665i) q^{42} +6.53847 q^{43} +3.25510i q^{44} +(6.99126 - 8.52624i) q^{45} +1.00000 q^{46} +11.1772 q^{47} +(-0.740879 - 1.56560i) q^{48} +(-6.89478 + 1.20915i) q^{49} -8.50828i q^{50} +(4.84087 + 10.2295i) q^{51} -0.990814i q^{52} +7.60949i q^{53} +(1.25936 - 5.04123i) q^{54} +11.9637i q^{55} +(2.63579 - 0.229372i) q^{56} +(2.81887 - 1.33396i) q^{57} +1.83336 q^{58} +4.25613 q^{59} +(-2.72300 - 5.75414i) q^{60} +3.34953i q^{61} -7.84167 q^{62} +(6.55091 + 4.48169i) q^{63} -1.00000 q^{64} -3.64160i q^{65} +(2.41164 + 5.09618i) q^{66} -3.26593 q^{67} +6.53395 q^{68} +(1.56560 - 0.740879i) q^{69} +(9.68748 - 0.843024i) q^{70} -2.80632i q^{71} +(-2.31984 - 1.90220i) q^{72} +0.439240i q^{73} +0.190892i q^{74} +(-6.30360 - 13.3206i) q^{75} -1.80051i q^{76} +(-8.57977 + 0.746629i) q^{77} +(-0.734073 - 1.55122i) q^{78} -5.24291 q^{79} -3.67536 q^{80} +(-1.76329 - 8.82558i) q^{81} -2.12529i q^{82} -16.5597 q^{83} +(3.95665 - 2.31190i) q^{84} +24.0146 q^{85} -6.53847i q^{86} +(2.87030 - 1.35829i) q^{87} +3.25510 q^{88} -8.22000 q^{89} +(-8.52624 - 6.99126i) q^{90} +(2.61158 - 0.227265i) q^{91} -1.00000i q^{92} +(-12.2769 + 5.80972i) q^{93} -11.1772i q^{94} -6.61752i q^{95} +(-1.56560 + 0.740879i) q^{96} +12.5797i q^{97} +(1.20915 + 6.89478i) q^{98} +(7.55131 + 6.19185i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{4} - 4 q^{7} + 8 q^{9}+O(q^{10}) $ 24 * q - 24 * q^4 - 4 * q^7 + 8 * q^9	$ 24 q - 24 q^{4} - 4 q^{7} + 8 q^{9} + 24 q^{16} + 16 q^{18} - 28 q^{21} + 8 q^{22} - 24 q^{25} + 4 q^{28} + 24 q^{30} - 8 q^{36} + 40 q^{37} + 72 q^{39} + 64 q^{43} + 24 q^{46} - 24 q^{51} + 16 q^{58} + 12 q^{63} - 24 q^{64} - 64 q^{67} + 16 q^{70} - 16 q^{72} - 32 q^{78} + 88 q^{79} + 48 q^{81} + 28 q^{84} + 64 q^{85} - 8 q^{88} - 56 q^{91} + 8 q^{93} - 8 q^{99}+O(q^{100}) $ 24 * q - 24 * q^4 - 4 * q^7 + 8 * q^9 + 24 * q^16 + 16 * q^18 - 28 * q^21 + 8 * q^22 - 24 * q^25 + 4 * q^28 + 24 * q^30 - 8 * q^36 + 40 * q^37 + 72 * q^39 + 64 * q^43 + 24 * q^46 - 24 * q^51 + 16 * q^58 + 12 * q^63 - 24 * q^64 - 64 * q^67 + 16 * q^70 - 16 * q^72 - 32 * q^78 + 88 * q^79 + 48 * q^81 + 28 * q^84 + 64 * q^85 - 8 * q^88 - 56 * q^91 + 8 * q^93 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−0.740879	−	1.56560i	−0.427747	−	0.903899i
$3$	−0.740879	−	1.56560i	−0.427747	−	0.903899i
$4$	−1.00000			−0.500000
$5$	−3.67536			−1.64367			−0.821836	−	0.569725i	$-0.807050\pi$
$5$	−3.67536			−1.64367			−0.821836	+	0.569725i	$0.807050\pi$
$6$	−1.56560	+	0.740879i	−0.639153	+	0.302462i
$7$	−0.229372	−	2.63579i	−0.0866944	−	0.996235i
$7$	−0.229372	−	2.63579i	−0.0866944	−	0.996235i
$8$			1.00000i			0.353553i
$9$	−1.90220	+	2.31984i	−0.634066	+	0.773279i
$10$			3.67536i			1.16225i
$11$		−	3.25510i		−	0.981450i	−0.871314	−	0.490725i	$-0.836732\pi$
$11$		−	3.25510i		−	0.981450i	0.871314	−	0.490725i	$-0.163268\pi$
$12$	0.740879	+	1.56560i	0.213873	+	0.451949i
$13$			0.990814i			0.274802i	0.990515	+	0.137401i	$0.0438750\pi$
$13$			0.990814i			0.274802i	−0.990515	+	0.137401i	$0.956125\pi$
$14$	−2.63579	+	0.229372i	−0.704444	+	0.0613022i
$15$	2.72300	+	5.75414i	0.703075	+	1.48571i
$16$	1.00000			0.250000
$17$	−6.53395			−1.58472			−0.792358	−	0.610056i	$-0.791147\pi$
$17$	−6.53395			−1.58472			−0.792358	+	0.610056i	$0.791147\pi$
$18$	2.31984	+	1.90220i	0.546791	+	0.448352i
$19$			1.80051i			0.413065i	0.978440	+	0.206533i	$0.0662179\pi$
$19$			1.80051i			0.413065i	−0.978440	+	0.206533i	$0.933782\pi$
$20$	3.67536			0.821836
$21$	−3.95665	+	2.31190i	−0.863412	+	0.504499i
$22$	−3.25510			−0.693990
$23$			1.00000i			0.208514i
$23$			1.00000i			0.208514i
$24$	1.56560	−	0.740879i	0.319576	−	0.151231i
$25$	8.50828			1.70166
$26$	0.990814			0.194315
$27$	5.04123	+	1.25936i	0.970185	+	0.242364i
$28$	0.229372	+	2.63579i	0.0433472	+	0.498117i
$29$			1.83336i			0.340446i	0.985406	+	0.170223i	$0.0544487\pi$
$29$			1.83336i			0.340446i	−0.985406	+	0.170223i	$0.945551\pi$
$30$	5.75414	−	2.72300i	1.05056	−	0.497149i
$31$		−	7.84167i		−	1.40840i	−0.709999	−	0.704202i	$-0.751305\pi$
$31$		−	7.84167i		−	1.40840i	0.709999	−	0.704202i	$-0.248695\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−5.09618	+	2.41164i	−0.887132	+	0.419812i
$34$			6.53395i			1.12056i
$35$	0.843024	+	9.68748i	0.142497	+	1.63748i
$36$	1.90220	−	2.31984i	0.317033	−	0.386640i
$37$	−0.190892			−0.0313824			−0.0156912	−	0.999877i	$-0.504995\pi$
$37$	−0.190892			−0.0313824			−0.0156912	+	0.999877i	$0.504995\pi$
$38$	1.80051			0.292081
$39$	1.55122	−	0.734073i	0.248394	−	0.117546i
$40$		−	3.67536i		−	0.581126i
$41$	2.12529			0.331914			0.165957	−	0.986133i	$-0.446929\pi$
$41$	2.12529			0.331914			0.165957	+	0.986133i	$0.446929\pi$
$42$	2.31190	+	3.95665i	0.356735	+	0.610525i
$43$	6.53847			0.997107			0.498553	−	0.866859i	$-0.333865\pi$
$43$	6.53847			0.997107			0.498553	+	0.866859i	$0.333865\pi$
$44$			3.25510i			0.490725i
$45$	6.99126	−	8.52624i	1.04220	−	1.27102i
$46$	1.00000			0.147442
$47$	11.1772			1.63036			0.815178	−	0.579211i	$-0.196639\pi$
$47$	11.1772			1.63036			0.815178	+	0.579211i	$0.196639\pi$
$48$	−0.740879	−	1.56560i	−0.106937	−	0.225975i
$49$	−6.89478	+	1.20915i	−0.984968	+	0.172736i
$50$		−	8.50828i		−	1.20325i
$51$	4.84087	+	10.2295i	0.677857	+	1.43242i
$52$		−	0.990814i		−	0.137401i
$53$			7.60949i			1.04524i	0.852565	+	0.522622i	$0.175046\pi$
$53$			7.60949i			1.04524i	−0.852565	+	0.522622i	$0.824954\pi$
$54$	1.25936	−	5.04123i	0.171377	−	0.686025i
$55$			11.9637i			1.61318i
$56$	2.63579	−	0.229372i	0.352222	−	0.0306511i
$57$	2.81887	−	1.33396i	0.373369	−	0.176687i
$58$	1.83336			0.240731
$59$	4.25613			0.554101			0.277051	−	0.960855i	$-0.410643\pi$
$59$	4.25613			0.554101			0.277051	+	0.960855i	$0.410643\pi$
$60$	−2.72300	−	5.75414i	−0.351537	−	0.742856i
$61$			3.34953i			0.428864i	0.976739	+	0.214432i	$0.0687900\pi$
$61$			3.34953i			0.428864i	−0.976739	+	0.214432i	$0.931210\pi$
$62$	−7.84167			−0.995893
$63$	6.55091	+	4.48169i	0.825338	+	0.564640i
$64$	−1.00000			−0.125000
$65$		−	3.64160i		−	0.451685i
$66$	2.41164	+	5.09618i	0.296852	+	0.627297i
$67$	−3.26593			−0.398996			−0.199498	−	0.979898i	$-0.563931\pi$
$67$	−3.26593			−0.398996			−0.199498	+	0.979898i	$0.563931\pi$
$68$	6.53395			0.792358
$69$	1.56560	−	0.740879i	0.188476	−	0.0891913i
$70$	9.68748	−	0.843024i	1.15788	−	0.100761i
$71$		−	2.80632i		−	0.333049i	−0.986037	−	0.166524i	$-0.946746\pi$
$71$		−	2.80632i		−	0.333049i	0.986037	−	0.166524i	$-0.0532545\pi$
$72$	−2.31984	−	1.90220i	−0.273395	−	0.224176i
$73$			0.439240i			0.0514092i	0.999670	+	0.0257046i	$0.00818293\pi$
$73$			0.439240i			0.0514092i	−0.999670	+	0.0257046i	$0.991817\pi$
$74$			0.190892i			0.0221907i
$75$	−6.30360	−	13.3206i	−0.727877	−	1.53812i
$76$		−	1.80051i		−	0.206533i
$77$	−8.57977	+	0.746629i	−0.977755	+	0.0850862i
$78$	−0.734073	−	1.55122i	−0.0831174	−	0.175641i
$79$	−5.24291			−0.589874			−0.294937	−	0.955517i	$-0.595299\pi$
$79$	−5.24291			−0.589874			−0.294937	+	0.955517i	$0.595299\pi$
$80$	−3.67536			−0.410918
$81$	−1.76329	−	8.82558i	−0.195921	−	0.980620i
$82$		−	2.12529i		−	0.234699i
$83$	−16.5597			−1.81766			−0.908831	−	0.417165i	$-0.863024\pi$
$83$	−16.5597			−1.81766			−0.908831	+	0.417165i	$0.863024\pi$
$84$	3.95665	−	2.31190i	0.431706	−	0.252250i
$85$	24.0146			2.60475
$86$		−	6.53847i		−	0.705061i
$87$	2.87030	−	1.35829i	0.307728	−	0.145624i
$88$	3.25510			0.346995
$89$	−8.22000			−0.871318			−0.435659	−	0.900112i	$-0.643485\pi$
$89$	−8.22000			−0.871318			−0.435659	+	0.900112i	$0.643485\pi$
$90$	−8.52624	−	6.99126i	−0.898745	−	0.736944i
$91$	2.61158	−	0.227265i	0.273768	−	0.0238238i
$92$		−	1.00000i		−	0.104257i
$93$	−12.2769	+	5.80972i	−1.27306	+	0.602440i
$94$		−	11.1772i		−	1.15284i
$95$		−	6.61752i		−	0.678944i
$96$	−1.56560	+	0.740879i	−0.159788	+	0.0756156i
$97$			12.5797i			1.27727i	0.769509	+	0.638636i	$0.220501\pi$
$97$			12.5797i			1.27727i	−0.769509	+	0.638636i	$0.779499\pi$
$98$	1.20915	+	6.89478i	0.122143	+	0.696478i
$99$	7.55131	+	6.19185i	0.758935	+	0.622304i
$100$	−8.50828			−0.850828
$101$	−13.9089			−1.38399			−0.691993	−	0.721904i	$-0.743267\pi$
$101$	−13.9089			−1.38399			−0.691993	+	0.721904i	$0.743267\pi$
$102$	10.2295	−	4.84087i	1.01288	−	0.479317i
$103$			15.1470i			1.49248i	0.665675	+	0.746241i	$0.268144\pi$
$103$			15.1470i			1.49248i	−0.665675	+	0.746241i	$0.731856\pi$
$104$	−0.990814			−0.0971573
$105$	14.5421	−	8.49709i	1.41917	−	0.829231i
$106$	7.60949			0.739099
$107$			0.0273799i			0.00264692i	0.999999	+	0.00132346i	$0.000421270\pi$
$107$			0.0273799i			0.00264692i	−0.999999	+	0.00132346i	$0.999579\pi$
$108$	−5.04123	−	1.25936i	−0.485093	−	0.121182i
$109$	−6.00594			−0.575265			−0.287633	−	0.957741i	$-0.592868\pi$
$109$	−6.00594			−0.575265			−0.287633	+	0.957741i	$0.592868\pi$
$110$	11.9637			1.14069
$111$	0.141428	+	0.298860i	0.0134237	+	0.0283665i
$112$	−0.229372	−	2.63579i	−0.0216736	−	0.249059i
$113$		−	0.521029i		−	0.0490143i	−0.999700	−	0.0245072i	$-0.992198\pi$
$113$		−	0.521029i		−	0.0490143i	0.999700	−	0.0245072i	$-0.00780165\pi$
$114$	−1.33396	−	2.81887i	−0.124937	−	0.264012i
$115$		−	3.67536i		−	0.342729i
$116$		−	1.83336i		−	0.170223i
$117$	−2.29853	−	1.88472i	−0.212499	−	0.174243i
$118$		−	4.25613i		−	0.391809i
$119$	1.49870	+	17.2221i	0.137386	+	1.57875i
$120$	−5.75414	+	2.72300i	−0.525279	+	0.248574i
$121$	0.404309			0.0367553
$122$	3.34953			0.303253
$123$	−1.57458	−	3.32735i	−0.141975	−	0.300017i
$124$			7.84167i			0.704202i
$125$	−12.8942			−1.15329
$126$	4.48169	−	6.55091i	0.399260	−	0.583602i
$127$	−18.3214			−1.62576			−0.812881	−	0.582430i	$-0.802102\pi$
$127$	−18.3214			−1.62576			−0.812881	+	0.582430i	$0.802102\pi$
$128$			1.00000i			0.0883883i
$129$	−4.84421	−	10.2366i	−0.426509	−	0.901284i
$130$	−3.64160			−0.319389
$131$	18.6407			1.62864			0.814322	−	0.580414i	$-0.197109\pi$
$131$	18.6407			1.62864			0.814322	+	0.580414i	$0.197109\pi$
$132$	5.09618	−	2.41164i	0.443566	−	0.209906i
$133$	4.74576	−	0.412986i	0.411510	−	0.0358104i
$134$			3.26593i			0.282133i
$135$	−18.5283	−	4.62860i	−1.59467	−	0.398366i
$136$		−	6.53395i		−	0.560282i
$137$		−	19.4381i		−	1.66071i	−0.557234	−	0.830356i	$-0.688137\pi$
$137$		−	19.4381i		−	1.66071i	0.557234	−	0.830356i	$-0.311863\pi$
$138$	−0.740879	−	1.56560i	−0.0630678	−	0.133273i
$139$			6.92135i			0.587062i	0.955950	+	0.293531i	$0.0948303\pi$
$139$			6.92135i			0.587062i	−0.955950	+	0.293531i	$0.905170\pi$
$140$	−0.843024	−	9.68748i	−0.0712485	−	0.818741i
$141$	−8.28092	−	17.4989i	−0.697379	−	1.47368i
$142$	−2.80632			−0.235501
$143$	3.22520			0.269705
$144$	−1.90220	+	2.31984i	−0.158516	+	0.193320i
$145$		−	6.73824i		−	0.559581i
$146$	0.439240			0.0363518
$147$	7.00124	+	9.89862i	0.577453	+	0.816424i
$148$	0.190892			0.0156912
$149$		−	0.390513i		−	0.0319921i	−0.999872	−	0.0159960i	$-0.994908\pi$
$149$		−	0.390513i		−	0.0319921i	0.999872	−	0.0159960i	$-0.00509191\pi$
$150$	−13.3206	+	6.30360i	−1.08762	+	0.514687i
$151$	−20.9019			−1.70097			−0.850487	−	0.525995i	$-0.823693\pi$
$151$	−20.9019			−1.70097			−0.850487	+	0.525995i	$0.823693\pi$
$152$	−1.80051			−0.146041
$153$	12.4289	−	15.1577i	1.00481	−	1.22543i
$154$	0.746629	+	8.57977i	0.0601651	+	0.691377i
$155$			28.8210i			2.31495i
$156$	−1.55122	+	0.734073i	−0.124197	+	0.0587729i
$157$			23.7614i			1.89637i	0.317726	+	0.948183i	$0.397081\pi$
$157$			23.7614i			1.89637i	−0.317726	+	0.948183i	$0.602919\pi$
$158$			5.24291i			0.417104i
$159$	11.9134	−	5.63771i	0.944794	−	0.447099i
$160$			3.67536i			0.290563i
$161$	2.63579	−	0.229372i	0.207729	−	0.0180770i
$162$	−8.82558	+	1.76329i	−0.693403	+	0.138537i
$163$	4.89757			0.383607			0.191803	−	0.981433i	$-0.438566\pi$
$163$	4.89757			0.383607			0.191803	+	0.981433i	$0.438566\pi$
$164$	−2.12529			−0.165957
$165$	18.7303	−	8.86363i	1.45815	−	0.690033i
$166$			16.5597i			1.28528i
$167$	−15.5771			−1.20539			−0.602696	−	0.797971i	$-0.705907\pi$
$167$	−15.5771			−1.20539			−0.602696	+	0.797971i	$0.705907\pi$
$168$	−2.31190	−	3.95665i	−0.178367	−	0.305262i
$169$	12.0183			0.924484
$170$		−	24.0146i		−	1.84184i
$171$	−4.17689	−	3.42492i	−0.319415	−	0.261911i
$172$	−6.53847			−0.498553
$173$	9.71016			0.738249			0.369125	−	0.929380i	$-0.379658\pi$
$173$	9.71016			0.738249			0.369125	+	0.929380i	$0.379658\pi$
$174$	−1.35829	−	2.87030i	−0.102972	−	0.217597i
$175$	−1.95156	−	22.4260i	−0.147524	−	1.69525i
$176$		−	3.25510i		−	0.245363i
$177$	−3.15328	−	6.66340i	−0.237015	−	0.500852i
$178$			8.22000i			0.616115i
$179$			10.3095i			0.770570i	0.922798	+	0.385285i	$0.125897\pi$
$179$			10.3095i			0.770570i	−0.922798	+	0.385285i	$0.874103\pi$
$180$	−6.99126	+	8.52624i	−0.521098	+	0.635508i
$181$			22.9161i			1.70334i	0.524076	+	0.851671i	$0.324411\pi$
$181$			22.9161i			1.70334i	−0.524076	+	0.851671i	$0.675589\pi$
$182$	−0.227265	−	2.61158i	−0.0168460	−	0.193583i
$183$	5.24403	−	2.48160i	0.387650	−	0.183445i
$184$	−1.00000			−0.0737210
$185$	0.701596			0.0515824
$186$	5.80972	+	12.2769i	0.425990	+	0.900186i
$187$			21.2687i			1.55532i
$188$	−11.1772			−0.815178
$189$	2.16309	−	13.5765i	0.157342	−	0.987544i
$190$	−6.61752			−0.480086
$191$		−	16.1579i		−	1.16914i	−0.811342	−	0.584572i	$-0.801262\pi$
$191$		−	16.1579i		−	1.16914i	0.811342	−	0.584572i	$-0.198738\pi$
$192$	0.740879	+	1.56560i	0.0534683	+	0.112987i
$193$	−2.58052			−0.185750			−0.0928750	−	0.995678i	$-0.529606\pi$
$193$	−2.58052			−0.185750			−0.0928750	+	0.995678i	$0.529606\pi$
$194$	12.5797			0.903167
$195$	−5.70128	+	2.69798i	−0.408277	+	0.193207i
$196$	6.89478	−	1.20915i	0.492484	−	0.0863680i
$197$			18.7519i			1.33601i	0.744155	+	0.668007i	$0.232853\pi$
$197$			18.7519i			1.33601i	−0.744155	+	0.668007i	$0.767147\pi$
$198$	6.19185	−	7.55131i	0.440035	−	0.536648i
$199$		−	19.7966i		−	1.40334i	−0.712500	−	0.701672i	$-0.752437\pi$
$199$		−	19.7966i		−	1.40334i	0.712500	−	0.701672i	$-0.247563\pi$
$200$			8.50828i			0.601626i
$201$	2.41966	+	5.11313i	0.170669	+	0.360652i
$202$			13.9089i			0.978626i
$203$	4.83234	−	0.420520i	0.339164	−	0.0295147i
$204$	−4.84087	−	10.2295i	−0.338928	−	0.716211i
$205$	−7.81120			−0.545558
$206$	15.1470			1.05534
$207$	−2.31984	−	1.90220i	−0.161240	−	0.132212i
$208$			0.990814i			0.0687006i
$209$	5.86084			0.405403
$210$	−8.49709	−	14.5421i	−0.586355	−	1.00350i
$211$	−16.2725			−1.12025			−0.560123	−	0.828409i	$-0.689246\pi$
$211$	−16.2725			−1.12025			−0.560123	+	0.828409i	$0.689246\pi$
$212$		−	7.60949i		−	0.522622i
$213$	−4.39357	+	2.07914i	−0.301042	+	0.142460i
$214$	0.0273799			0.00187165
$215$	−24.0312			−1.63892
$216$	−1.25936	+	5.04123i	−0.0856885	+	0.343012i
$217$	−20.6690	+	1.79866i	−1.40310	+	0.122101i
$218$			6.00594i			0.406774i
$219$	0.687674	−	0.325424i	0.0464687	−	0.0219901i
$220$		−	11.9637i		−	0.806591i
$221$		−	6.47393i		−	0.435484i
$222$	0.298860	−	0.141428i	0.0200582	−	0.00949201i
$223$			29.5230i			1.97701i	0.151200	+	0.988503i	$0.451686\pi$
$223$			29.5230i			1.97701i	−0.151200	+	0.988503i	$0.548314\pi$
$224$	−2.63579	+	0.229372i	−0.176111	+	0.0153255i
$225$	−16.1844	+	19.7378i	−1.07896	+	1.31586i
$226$	−0.521029			−0.0346583
$227$	7.59289			0.503958			0.251979	−	0.967733i	$-0.418919\pi$
$227$	7.59289			0.503958			0.251979	+	0.967733i	$0.418919\pi$
$228$	−2.81887	+	1.33396i	−0.186685	+	0.0883436i
$229$		−	17.1975i		−	1.13644i	−0.822875	−	0.568222i	$-0.807631\pi$
$229$		−	17.1975i		−	1.13644i	0.822875	−	0.568222i	$-0.192369\pi$
$230$	−3.67536			−0.242346
$231$	7.52549	+	12.8793i	0.495141	+	0.847396i
$232$	−1.83336			−0.120366
$233$			9.84118i			0.644717i	0.946618	+	0.322359i	$0.104476\pi$
$233$			9.84118i			0.644717i	−0.946618	+	0.322359i	$0.895524\pi$
$234$	−1.88472	+	2.29853i	−0.123208	+	0.150259i
$235$	−41.0801			−2.67977
$236$	−4.25613			−0.277051
$237$	3.88436	+	8.20829i	0.252316	+	0.533186i
$238$	17.2221	−	1.49870i	1.11634	−	0.0971466i
$239$		−	13.4039i		−	0.867028i	−0.901147	−	0.433514i	$-0.857274\pi$
$239$		−	13.4039i		−	0.867028i	0.901147	−	0.433514i	$-0.142726\pi$
$240$	2.72300	+	5.75414i	0.175769	+	0.371428i
$241$		−	7.75964i		−	0.499842i	−0.968266	−	0.249921i	$-0.919595\pi$
$241$		−	7.75964i		−	0.499842i	0.968266	−	0.249921i	$-0.0804047\pi$
$242$		−	0.404309i		−	0.0259899i
$243$	−12.5109	+	9.29929i	−0.802576	+	0.596550i
$244$		−	3.34953i		−	0.214432i
$245$	25.3408	−	4.44407i	1.61896	−	0.283921i
$246$	−3.32735	+	1.57458i	−0.212144	+	0.100392i
$247$	−1.78397			−0.113511
$248$	7.84167			0.497946
$249$	12.2687	+	25.9258i	0.777498	+	1.64298i
$250$			12.8942i			0.815501i
$251$	0.348605			0.0220038			0.0110019	−	0.999939i	$-0.496498\pi$
$251$	0.348605			0.0220038			0.0110019	+	0.999939i	$0.496498\pi$
$252$	−6.55091	−	4.48169i	−0.412669	−	0.282320i
$253$	3.25510			0.204647
$254$			18.3214i			1.14959i
$255$	−17.7919	−	37.5973i	−1.11417	−	2.35443i
$256$	1.00000			0.0625000
$257$	22.3150			1.39197			0.695986	−	0.718056i	$-0.254968\pi$
$257$	22.3150			1.39197			0.695986	+	0.718056i	$0.254968\pi$
$258$	−10.2366	+	4.84421i	−0.637304	+	0.301587i
$259$	0.0437852	+	0.503151i	0.00272068	+	0.0312643i
$260$			3.64160i			0.225842i
$261$	−4.25309	−	3.48740i	−0.263259	−	0.215865i
$262$		−	18.6407i		−	1.15163i
$263$			17.0199i			1.04949i	0.851259	+	0.524746i	$0.175840\pi$
$263$			17.0199i			1.04949i	−0.851259	+	0.524746i	$0.824160\pi$
$264$	−2.41164	−	5.09618i	−0.148426	−	0.313648i
$265$		−	27.9676i		−	1.71804i
$266$	−0.412986	−	4.74576i	−0.0253218	−	0.290982i
$267$	6.09002	+	12.8692i	0.372703	+	0.787584i
$268$	3.26593			0.199498
$269$	−0.881138			−0.0537239			−0.0268620	−	0.999639i	$-0.508551\pi$
$269$	−0.881138			−0.0537239			−0.0268620	+	0.999639i	$0.508551\pi$
$270$	−4.62860	+	18.5283i	−0.281688	+	1.12760i
$271$		−	32.7329i		−	1.98838i	−0.107626	−	0.994191i	$-0.534325\pi$
$271$		−	32.7329i		−	1.98838i	0.107626	−	0.994191i	$-0.465675\pi$
$272$	−6.53395			−0.396179
$273$	−2.29067	−	3.92031i	−0.138638	−	0.237268i
$274$	−19.4381			−1.17430
$275$		−	27.6953i		−	1.67009i
$276$	−1.56560	+	0.740879i	−0.0942380	+	0.0445957i
$277$	−2.03058			−0.122006			−0.0610029	−	0.998138i	$-0.519430\pi$
$277$	−2.03058			−0.122006			−0.0610029	+	0.998138i	$0.519430\pi$
$278$	6.92135			0.415115
$279$	18.1914	+	14.9164i	1.08909	+	0.893021i
$280$	−9.68748	+	0.843024i	−0.578938	+	0.0503803i
$281$		−	20.8700i		−	1.24500i	−0.782620	−	0.622500i	$-0.786117\pi$
$281$		−	20.8700i		−	1.24500i	0.782620	−	0.622500i	$-0.213883\pi$
$282$	−17.4989	+	8.28092i	−1.04205	+	0.493121i
$283$		−	1.94986i		−	0.115907i	−0.998319	−	0.0579537i	$-0.981542\pi$
$283$		−	1.94986i		−	0.115907i	0.998319	−	0.0579537i	$-0.0184576\pi$
$284$			2.80632i			0.166524i
$285$	−10.3604	+	4.90278i	−0.613696	+	0.290416i
$286$		−	3.22520i		−	0.190710i
$287$	−0.487481	−	5.60181i	−0.0287751	−	0.330665i
$288$	2.31984	+	1.90220i	0.136698	+	0.112088i
$289$	25.6925			1.51133
$290$	−6.73824			−0.395683
$291$	19.6947	−	9.32001i	1.15452	−	0.546349i
$292$		−	0.439240i		−	0.0257046i
$293$	−25.4240			−1.48528			−0.742642	−	0.669689i	$-0.766428\pi$
$293$	−25.4240			−1.48528			−0.742642	+	0.669689i	$0.766428\pi$
$294$	9.89862	−	7.00124i	0.577299	−	0.408321i
$295$	−15.6428			−0.910761
$296$		−	0.190892i		−	0.0110954i
$297$	4.09934	−	16.4097i	0.237868	−	0.952189i
$298$	−0.390513			−0.0226218
$299$	−0.990814			−0.0573003
$300$	6.30360	+	13.3206i	0.363939	+	0.769062i
$301$	−1.49974	−	17.2340i	−0.0864436	−	0.993353i
$302$			20.9019i			1.20277i
$303$	10.3048	+	21.7757i	0.591996	+	1.25098i
$304$			1.80051i			0.103266i
$305$		−	12.3107i		−	0.704911i
$306$	−15.1577	−	12.4289i	−0.866508	−	0.710511i
$307$			9.82966i			0.561008i	0.959853	+	0.280504i	$0.0905016\pi$
$307$			9.82966i			0.561008i	−0.959853	+	0.280504i	$0.909498\pi$
$308$	8.57977	−	0.746629i	0.488878	−	0.0425431i
$309$	23.7142	−	11.2221i	1.34905	−	0.638404i
$310$	28.8210			1.63692
$311$	−24.9333			−1.41384			−0.706919	−	0.707294i	$-0.749916\pi$
$311$	−24.9333			−1.41384			−0.706919	+	0.707294i	$0.749916\pi$
$312$	0.734073	+	1.55122i	0.0415587	+	0.0878204i
$313$		−	17.5159i		−	0.990059i	−0.868876	−	0.495030i	$-0.835157\pi$
$313$		−	17.5159i		−	0.990059i	0.868876	−	0.495030i	$-0.164843\pi$
$314$	23.7614			1.34093
$315$	−24.0770	−	16.4718i	−1.35658	−	0.928082i
$316$	5.24291			0.294937
$317$		−	15.4380i		−	0.867082i	−0.901134	−	0.433541i	$-0.857264\pi$
$317$		−	15.4380i		−	0.867082i	0.901134	−	0.433541i	$-0.142736\pi$
$318$	−5.63771	−	11.9134i	−0.316147	−	0.668070i
$319$	5.96776			0.334130
$320$	3.67536			0.205459
$321$	0.0428659	−	0.0202852i	0.00239254	−	0.00113221i
$322$	−0.229372	−	2.63579i	−0.0127824	−	0.146887i
$323$		−	11.7644i		−	0.654591i
$324$	1.76329	+	8.82558i	0.0979606	+	0.490310i
$325$			8.43012i			0.467619i
$326$		−	4.89757i		−	0.271251i
$327$	4.44968	+	9.40290i	0.246068	+	0.519981i
$328$			2.12529i			0.117349i
$329$	−2.56372	−	29.4606i	−0.141343	−	1.62422i
$330$	−8.86363	−	18.7303i	−0.487927	−	1.03107i
$331$	−10.8470			−0.596203			−0.298101	−	0.954534i	$-0.596353\pi$
$331$	−10.8470			−0.596203			−0.298101	+	0.954534i	$0.596353\pi$
$332$	16.5597			0.908831
$333$	0.363114	−	0.442838i	0.0198985	−	0.0242674i
$334$			15.5771i			0.852340i
$335$	12.0035			0.655819
$336$	−3.95665	+	2.31190i	−0.215853	+	0.126125i
$337$	−24.5820			−1.33907			−0.669535	−	0.742781i	$-0.733506\pi$
$337$	−24.5820			−1.33907			−0.669535	+	0.742781i	$0.733506\pi$
$338$		−	12.0183i		−	0.653709i
$339$	−0.815723	+	0.386020i	−0.0443040	+	0.0209657i
$340$	−24.0146			−1.30238
$341$	−25.5254			−1.38228
$342$	−3.42492	+	4.17689i	−0.185199	+	0.225860i
$343$	4.76854	+	17.8958i	0.257477	+	0.966284i
$344$			6.53847i			0.352531i
$345$	−5.75414	+	2.72300i	−0.309792	+	0.146601i
$346$		−	9.71016i		−	0.522021i
$347$		−	3.59690i		−	0.193092i	−0.995329	−	0.0965458i	$-0.969221\pi$
$347$		−	3.59690i		−	0.193092i	0.995329	−	0.0965458i	$-0.0307794\pi$
$348$	−2.87030	+	1.35829i	−0.153864	+	0.0728122i
$349$			3.00054i			0.160615i	0.996770	+	0.0803075i	$0.0255902\pi$
$349$			3.00054i			0.160615i	−0.996770	+	0.0803075i	$0.974410\pi$
$350$	−22.4260	+	1.95156i	−1.19872	+	0.104315i
$351$	−1.24779	+	4.99492i	−0.0666021	+	0.266609i
$352$	−3.25510			−0.173498
$353$	24.9982			1.33052			0.665260	−	0.746611i	$-0.268321\pi$
$353$	24.9982			1.33052			0.665260	+	0.746611i	$0.268321\pi$
$354$	−6.66340	+	3.15328i	−0.354156	+	0.167595i
$355$			10.3142i			0.547423i
$356$	8.22000			0.435659
$357$	25.8526	−	15.1059i	1.36826	−	0.799488i
$358$	10.3095			0.544875
$359$			5.79636i			0.305920i	0.988232	+	0.152960i	$0.0488806\pi$
$359$			5.79636i			0.305920i	−0.988232	+	0.152960i	$0.951119\pi$
$360$	8.52624	+	6.99126i	0.449372	+	0.368472i
$361$	15.7582			0.829377
$362$	22.9161			1.20445
$363$	−0.299544	−	0.632985i	−0.0157220	−	0.0332231i
$364$	−2.61158	+	0.227265i	−0.136884	+	0.0119119i
$365$		−	1.61437i		−	0.0844998i
$366$	−2.48160	−	5.24403i	−0.129715	−	0.274110i
$367$			9.65508i			0.503991i	0.967728	+	0.251996i	$0.0810868\pi$
$367$			9.65508i			0.503991i	−0.967728	+	0.251996i	$0.918913\pi$
$368$			1.00000i			0.0521286i
$369$	−4.04272	+	4.93032i	−0.210456	+	0.256662i
$370$		−	0.701596i		−	0.0364743i
$371$	20.0570	−	1.74540i	1.04131	−	0.0906167i
$372$	12.2769	−	5.80972i	0.636528	−	0.301220i
$373$	5.05219			0.261592			0.130796	−	0.991409i	$-0.458247\pi$
$373$	5.05219			0.261592			0.130796	+	0.991409i	$0.458247\pi$
$374$	21.2687			1.09978
$375$	9.55304	+	20.1871i	0.493317	+	1.04246i
$376$			11.1772i			0.576418i
$377$	−1.81651			−0.0935552
$378$	−13.5765	−	2.16309i	−0.698299	−	0.111257i
$379$	35.3245			1.81450			0.907250	−	0.420592i	$-0.138178\pi$
$379$	35.3245			1.81450			0.907250	+	0.420592i	$0.138178\pi$
$380$			6.61752i			0.339472i
$381$	13.5739	+	28.6840i	0.695414	+	1.46952i
$382$	−16.1579			−0.826710
$383$	−19.8941			−1.01654			−0.508271	−	0.861197i	$-0.669715\pi$
$383$	−19.8941			−1.01654			−0.508271	+	0.861197i	$0.669715\pi$
$384$	1.56560	−	0.740879i	0.0798941	−	0.0378078i
$385$	31.5337	−	2.74413i	1.60711	−	0.139854i
$386$			2.58052i			0.131345i
$387$	−12.4375	+	15.1682i	−0.632231	+	0.771042i
$388$		−	12.5797i		−	0.638636i
$389$			30.1103i			1.52665i	0.646014	+	0.763326i	$0.276435\pi$
$389$			30.1103i			1.52665i	−0.646014	+	0.763326i	$0.723565\pi$
$390$	2.69798	+	5.70128i	0.136618	+	0.288696i
$391$		−	6.53395i		−	0.330436i
$392$	−1.20915	−	6.89478i	−0.0610714	−	0.348239i
$393$	−13.8105	−	29.1838i	−0.696647	−	1.47213i
$394$	18.7519			0.944705
$395$	19.2696			0.969558
$396$	−7.55131	−	6.19185i	−0.379468	−	0.311152i
$397$			1.78727i			0.0897004i	0.998994	+	0.0448502i	$0.0142811\pi$
$397$			1.78727i			0.0897004i	−0.998994	+	0.0448502i	$0.985719\pi$
$398$	−19.7966			−0.992314
$399$	−4.16261	−	7.12399i	−0.208391	−	0.356646i
$400$	8.50828			0.425414
$401$			9.59796i			0.479299i	0.970859	+	0.239650i	$0.0770326\pi$
$401$			9.59796i			0.479299i	−0.970859	+	0.239650i	$0.922967\pi$
$402$	5.11313	−	2.41966i	0.255020	−	0.120681i
$403$	7.76963			0.387033
$404$	13.9089			0.691993
$405$	6.48073	+	32.4372i	0.322030	+	1.61182i
$406$	−0.420520	−	4.83234i	−0.0208701	−	0.239825i
$407$			0.621372i			0.0308003i
$408$	−10.2295	+	4.84087i	−0.506438	+	0.239659i
$409$		−	1.66743i		−	0.0824493i	−0.999150	−	0.0412246i	$-0.986874\pi$
$409$		−	1.66743i		−	0.0824493i	0.999150	−	0.0412246i	$-0.0131259\pi$
$410$			7.81120i			0.385768i
$411$	−30.4323	+	14.4013i	−1.50111	+	0.710364i
$412$		−	15.1470i		−	0.746241i
$413$	−0.976237	−	11.2183i	−0.0480375	−	0.552015i
$414$	−1.90220	+	2.31984i	−0.0934879	+	0.114014i
$415$	60.8628			2.98764
$416$	0.990814			0.0485787
$417$	10.8361	−	5.12788i	0.530644	−	0.251114i
$418$		−	5.86084i		−	0.286663i
$419$	0.229830			0.0112279			0.00561396	−	0.999984i	$-0.498213\pi$
$419$	0.229830			0.0112279			0.00561396	+	0.999984i	$0.498213\pi$
$420$	−14.5421	+	8.49709i	−0.709583	+	0.414615i
$421$	−24.1797			−1.17845			−0.589223	−	0.807970i	$-0.700566\pi$
$421$	−24.1797			−1.17845			−0.589223	+	0.807970i	$0.700566\pi$
$422$			16.2725i			0.792134i
$423$	−21.2612	+	25.9292i	−1.03375	+	1.26072i
$424$	−7.60949			−0.369549
$425$	−55.5927			−2.69664
$426$	2.07914	+	4.39357i	0.100735	+	0.212869i
$427$	8.82867	−	0.768289i	0.427249	−	0.0371801i
$428$		−	0.0273799i		−	0.00132346i
$429$	−2.38948	−	5.04937i	−0.115365	−	0.243786i
$430$			24.0312i			1.15889i
$431$			31.7602i			1.52984i	0.644128	+	0.764918i	$0.277220\pi$
$431$			31.7602i			1.52984i	−0.644128	+	0.764918i	$0.722780\pi$
$432$	5.04123	+	1.25936i	0.242546	+	0.0605909i
$433$		−	16.6374i		−	0.799542i	−0.916615	−	0.399771i	$-0.869090\pi$
$433$		−	16.6374i		−	0.799542i	0.916615	−	0.399771i	$-0.130910\pi$
$434$	1.79866	+	20.6690i	0.0863383	+	0.992143i
$435$	−10.5494	+	4.99222i	−0.505804	+	0.239359i
$436$	6.00594			0.287633
$437$	−1.80051			−0.0861300
$438$	−0.325424	−	0.687674i	−0.0155493	−	0.0328583i
$439$			7.23914i			0.345505i	0.984965	+	0.172753i	$0.0552661\pi$
$439$			7.23914i			0.345505i	−0.984965	+	0.172753i	$0.944734\pi$
$440$	−11.9637			−0.570346
$441$	10.3102	−	18.2948i	0.490961	−	0.871181i
$442$	−6.47393			−0.307934
$443$			34.8927i			1.65780i	0.559395	+	0.828901i	$0.311034\pi$
$443$			34.8927i			1.65780i	−0.559395	+	0.828901i	$0.688966\pi$
$444$	−0.141428	−	0.298860i	−0.00671186	−	0.0141833i
$445$	30.2115			1.43216
$446$	29.5230			1.39795
$447$	−0.611387	+	0.289323i	−0.0289176	+	0.0136845i
$448$	0.229372	+	2.63579i	0.0108368	+	0.124529i
$449$		−	26.1806i		−	1.23554i	−0.786359	−	0.617769i	$-0.788036\pi$
$449$		−	26.1806i		−	1.23554i	0.786359	−	0.617769i	$-0.211964\pi$
$450$	19.7378	+	16.1844i	0.930450	+	0.762941i
$451$		−	6.91803i		−	0.325757i
$452$			0.521029i			0.0245072i
$453$	15.4858	+	32.7240i	0.727586	+	1.53751i
$454$		−	7.59289i		−	0.356352i
$455$	−9.59849	+	0.835280i	−0.449984	+	0.0391585i
$456$	1.33396	+	2.81887i	0.0624684	+	0.132006i
$457$	−22.7852			−1.06585			−0.532923	−	0.846164i	$-0.678906\pi$
$457$	−22.7852			−1.06585			−0.532923	+	0.846164i	$0.678906\pi$
$458$	−17.1975			−0.803588
$459$	−32.9392	−	8.22859i	−1.53747	−	0.384078i
$460$			3.67536i			0.171365i
$461$	1.19278			0.0555534			0.0277767	−	0.999614i	$-0.491157\pi$
$461$	1.19278			0.0555534			0.0277767	+	0.999614i	$0.491157\pi$
$462$	12.8793	−	7.52549i	0.599200	−	0.350117i
$463$	−32.2261			−1.49767			−0.748837	−	0.662754i	$-0.769387\pi$
$463$	−32.2261			−1.49767			−0.748837	+	0.662754i	$0.769387\pi$
$464$			1.83336i			0.0851114i
$465$	45.1220	−	21.3528i	2.09248	−	0.990214i
$466$	9.84118			0.455884
$467$	−11.4195			−0.528432			−0.264216	−	0.964464i	$-0.585113\pi$
$467$	−11.4195			−0.528432			−0.264216	+	0.964464i	$0.585113\pi$
$468$	2.29853	+	1.88472i	0.106249	+	0.0871214i
$469$	0.749112	+	8.60830i	0.0345908	+	0.397494i
$470$			41.0801i			1.89488i
$471$	37.2008	−	17.6043i	1.71412	−	0.811164i
$472$			4.25613i			0.195904i
$473$		−	21.2834i		−	0.978611i
$474$	8.20829	−	3.88436i	0.377019	−	0.178415i
$475$			15.3192i			0.702895i
$476$	−1.49870	−	17.2221i	−0.0686930	−	0.789375i
$477$	−17.6528	−	14.4747i	−0.808265	−	0.662753i
$478$	−13.4039			−0.613081
$479$	18.3392			0.837940			0.418970	−	0.908000i	$-0.362391\pi$
$479$	18.3392			0.837940			0.418970	+	0.908000i	$0.362391\pi$
$480$	5.75414	−	2.72300i	0.262639	−	0.124287i
$481$		−	0.189138i		−	0.00862397i
$482$	−7.75964			−0.353442
$483$	−2.31190	−	3.95665i	−0.105195	−	0.180034i
$484$	−0.404309			−0.0183777
$485$		−	46.2348i		−	2.09941i
$486$	9.29929	+	12.5109i	0.421824	+	0.567507i
$487$	36.5849			1.65782			0.828910	−	0.559382i	$-0.188962\pi$
$487$	36.5849			1.65782			0.828910	+	0.559382i	$0.188962\pi$
$488$	−3.34953			−0.151626
$489$	−3.62850	−	7.66762i	−0.164087	−	0.346742i
$490$	−4.44407	−	25.3408i	−0.200763	−	1.14478i
$491$		−	11.6650i		−	0.526433i	−0.964737	−	0.263217i	$-0.915217\pi$
$491$		−	11.6650i		−	0.526433i	0.964737	−	0.263217i	$-0.0847834\pi$
$492$	1.57458	+	3.32735i	0.0709876	+	0.150008i
$493$		−	11.9791i		−	0.539510i
$494$			1.78397i			0.0802646i
$495$	−27.7538	−	22.7573i	−1.24744	−	1.02286i
$496$		−	7.84167i		−	0.352101i
$497$	−7.39687	+	0.643691i	−0.331795	+	0.0288735i
$498$	25.9258	−	12.2687i	1.16176	−	0.549774i
$499$	29.4161			1.31685			0.658424	−	0.752647i	$-0.271224\pi$
$499$	29.4161			1.31685			0.658424	+	0.752647i	$0.271224\pi$
$500$	12.8942			0.576646
$501$	11.5407	+	24.3875i	0.515602	+	1.08955i
$502$		−	0.348605i		−	0.0155590i
$503$	38.4715			1.71536			0.857679	−	0.514186i	$-0.171906\pi$
$503$	38.4715			1.71536			0.857679	+	0.514186i	$0.171906\pi$
$504$	−4.48169	+	6.55091i	−0.199630	+	0.291801i
$505$	51.1202			2.27482
$506$		−	3.25510i		−	0.144707i
$507$	−8.90409	−	18.8158i	−0.395445	−	0.835640i
$508$	18.3214			0.812881
$509$	1.24092			0.0550026			0.0275013	−	0.999622i	$-0.491245\pi$
$509$	1.24092			0.0550026			0.0275013	+	0.999622i	$0.491245\pi$
$510$	−37.5973	+	17.7919i	−1.66484	+	0.787840i
$511$	1.15775	−	0.100749i	0.0512156	−	0.00445689i
$512$		−	1.00000i		−	0.0441942i
$513$	−2.26749	+	9.07679i	−0.100112	+	0.400750i
$514$		−	22.3150i		−	0.984272i
$515$		−	55.6709i		−	2.45315i
$516$	4.84421	+	10.2366i	0.213255	+	0.450642i
$517$		−	36.3828i		−	1.60011i
$518$	0.503151	−	0.0437852i	0.0221072	−	0.00192381i
$519$	−7.19405	−	15.2022i	−0.315784	−	0.667303i
$520$	3.64160			0.159695
$521$	7.78062			0.340875			0.170438	−	0.985368i	$-0.445482\pi$
$521$	7.78062			0.340875			0.170438	+	0.985368i	$0.445482\pi$
$522$	−3.48740	+	4.25309i	−0.152640	+	0.186153i
$523$			8.10593i			0.354448i	0.984171	+	0.177224i	$0.0567117\pi$
$523$			8.10593i			0.354448i	−0.984171	+	0.177224i	$0.943288\pi$
$524$	−18.6407			−0.814322
$525$	−33.6643	+	19.6703i	−1.46923	+	0.858484i
$526$	17.0199			0.742103
$527$			51.2371i			2.23192i
$528$	−5.09618	+	2.41164i	−0.221783	+	0.104953i
$529$	−1.00000			−0.0434783
$530$	−27.9676			−1.21484
$531$	−8.09601	+	9.87354i	−0.351337	+	0.428475i
$532$	−4.74576	+	0.412986i	−0.205755	+	0.0179052i
$533$			2.10577i			0.0912108i
$534$	12.8692	−	6.09002i	0.556906	−	0.263541i
$535$		−	0.100631i		−	0.00435066i
$536$		−	3.26593i		−	0.141067i
$537$	16.1406	−	7.63810i	0.696517	−	0.329608i
$538$			0.881138i			0.0379885i
$539$	3.93591	+	22.4432i	0.169532	+	0.966697i
$540$	18.5283	+	4.62860i	0.797333	+	0.199183i
$541$	−6.04900			−0.260067			−0.130033	−	0.991510i	$-0.541508\pi$
$541$	−6.04900			−0.260067			−0.130033	+	0.991510i	$0.541508\pi$
$542$	−32.7329			−1.40600
$543$	35.8775	−	16.9781i	1.53965	−	0.728599i
$544$			6.53395i			0.280141i
$545$	22.0740			0.945547
$546$	−3.92031	+	2.29067i	−0.167774	+	0.0980315i
$547$	−10.7577			−0.459964			−0.229982	−	0.973195i	$-0.573867\pi$
$547$	−10.7577			−0.459964			−0.229982	+	0.973195i	$0.573867\pi$
$548$			19.4381i			0.830356i
$549$	−7.77038	−	6.37148i	−0.331632	−	0.271928i
$550$	−27.6953			−1.18093
$551$	−3.30097			−0.140626
$552$	0.740879	+	1.56560i	0.0315339	+	0.0666363i
$553$	1.20258	+	13.8192i	0.0511387	+	0.587653i
$554$			2.03058i			0.0862711i
$555$	−0.519798	−	1.09842i	−0.0220642	−	0.0466253i
$556$		−	6.92135i		−	0.293531i
$557$			17.3697i			0.735977i	0.929830	+	0.367989i	$0.119953\pi$
$557$			17.3697i			0.735977i	−0.929830	+	0.367989i	$0.880047\pi$
$558$	14.9164	−	18.1914i	0.631461	−	0.770103i
$559$			6.47841i			0.274007i
$560$	0.843024	+	9.68748i	0.0356243	+	0.409371i
$561$	33.2982	−	15.7575i	1.40585	−	0.665283i
$562$	−20.8700			−0.880348
$563$	−34.1642			−1.43985			−0.719924	−	0.694053i	$-0.755823\pi$
$563$	−34.1642			−1.43985			−0.719924	+	0.694053i	$0.755823\pi$
$564$	8.28092	+	17.4989i	0.348689	+	0.736838i
$565$			1.91497i			0.0805634i
$566$	−1.94986			−0.0819589
$567$	−22.8579	+	6.67200i	−0.959942	+	0.280198i
$568$	2.80632			0.117751
$569$		−	30.3249i		−	1.27129i	−0.771983	−	0.635644i	$-0.780735\pi$
$569$		−	30.3249i		−	1.27129i	0.771983	−	0.635644i	$-0.219265\pi$
$570$	4.90278	+	10.3604i	0.205355	+	0.433949i
$571$	−10.1504			−0.424780			−0.212390	−	0.977185i	$-0.568125\pi$
$571$	−10.1504			−0.424780			−0.212390	+	0.977185i	$0.568125\pi$
$572$	−3.22520			−0.134852
$573$	−25.2968	+	11.9710i	−1.05679	+	0.500097i
$574$	−5.60181	+	0.487481i	−0.233815	+	0.0203471i
$575$			8.50828i			0.354820i
$576$	1.90220	−	2.31984i	0.0792582	−	0.0966599i
$577$			18.0400i			0.751015i	0.926819	+	0.375508i	$0.122532\pi$
$577$			18.0400i			0.751015i	−0.926819	+	0.375508i	$0.877468\pi$
$578$		−	25.6925i		−	1.06867i
$579$	1.91185	+	4.04006i	0.0794539	+	0.167899i
$580$			6.73824i			0.279790i
$581$	3.79832	+	43.6479i	0.157581	+	1.81082i
$582$	−9.32001	−	19.6947i	−0.386327	−	0.816372i
$583$	24.7697			1.02585
$584$	−0.439240			−0.0181759
$585$	8.44792	+	6.92704i	0.349278	+	0.286398i
$586$			25.4240i			1.05025i
$587$	−8.54650			−0.352752			−0.176376	−	0.984323i	$-0.556437\pi$
$587$	−8.54650			−0.352752			−0.176376	+	0.984323i	$0.556437\pi$
$588$	−7.00124	−	9.89862i	−0.288726	−	0.408212i
$589$	14.1190			0.581763
$590$			15.6428i			0.644005i
$591$	29.3579	−	13.8929i	1.20762	−	0.571476i
$592$	−0.190892			−0.00784561
$593$	−6.16800			−0.253289			−0.126645	−	0.991948i	$-0.540421\pi$
$593$	−6.16800			−0.253289			−0.126645	+	0.991948i	$0.540421\pi$
$594$	−16.4097	−	4.09934i	−0.673299	−	0.168198i
$595$	−5.50828	−	63.2975i	−0.225817	−	2.59495i
$596$			0.390513i			0.0159960i
$597$	−30.9935	+	14.6669i	−1.26848	+	0.600276i
$598$			0.990814i			0.0405174i
$599$		−	8.87592i		−	0.362660i	−0.983422	−	0.181330i	$-0.941960\pi$
$599$		−	8.87592i		−	0.362660i	0.983422	−	0.181330i	$-0.0580402\pi$
$600$	13.3206	−	6.30360i	0.543809	−	0.257344i
$601$			35.1069i			1.43204i	0.698080	+	0.716020i	$0.254038\pi$
$601$			35.1069i			1.43204i	−0.698080	+	0.716020i	$0.745962\pi$
$602$	−17.2340	+	1.49974i	−0.702407	+	0.0611248i
$603$	6.21244	−	7.57642i	0.252990	−	0.308536i
$604$	20.9019			0.850487
$605$	−1.48598			−0.0604137
$606$	21.7757	−	10.3048i	0.884579	−	0.418604i
$607$		−	45.9118i		−	1.86350i	−0.363099	−	0.931751i	$-0.618281\pi$
$607$		−	45.9118i		−	1.86350i	0.363099	−	0.931751i	$-0.381719\pi$
$608$	1.80051			0.0730203
$609$	−4.23854	−	7.25395i	−0.171754	−	0.293945i
$610$	−12.3107			−0.498448
$611$			11.0745i			0.448026i
$612$	−12.4289	+	15.1577i	−0.502407	+	0.612714i
$613$	−3.94171			−0.159204			−0.0796021	−	0.996827i	$-0.525365\pi$
$613$	−3.94171			−0.159204			−0.0796021	+	0.996827i	$0.525365\pi$
$614$	9.82966			0.396693
$615$	5.78715	+	12.2292i	0.233361	+	0.493129i
$616$	−0.746629	−	8.57977i	−0.0300825	−	0.345689i
$617$		−	0.0338202i		−	0.00136155i	−1.00000		0.000680774i	$-0.999783\pi$
$617$		−	0.0338202i		−	0.00136155i	1.00000		0.000680774i	$-0.000216697\pi$
$618$	−11.2221	−	23.7142i	−0.451420	−	0.953925i
$619$		−	5.86070i		−	0.235562i	−0.993040	−	0.117781i	$-0.962422\pi$
$619$		−	5.86070i		−	0.235562i	0.993040	−	0.117781i	$-0.0375780\pi$
$620$		−	28.8210i		−	1.15748i
$621$	−1.25936	+	5.04123i	−0.0505363	+	0.202298i
$622$			24.9333i			0.999735i
$623$	1.88544	+	21.6662i	0.0755384	+	0.868038i
$624$	1.55122	−	0.734073i	0.0620984	−	0.0293864i
$625$	4.84943			0.193977
$626$	−17.5159			−0.700078
$627$	−4.34217	−	9.17573i	−0.173410	−	0.366443i
$628$		−	23.7614i		−	0.948183i
$629$	1.24728			0.0497322
$630$	−16.4718	+	24.0770i	−0.656253	+	0.959250i
$631$	−14.1405			−0.562923			−0.281462	−	0.959572i	$-0.590819\pi$
$631$	−14.1405			−0.562923			−0.281462	+	0.959572i	$0.590819\pi$
$632$		−	5.24291i		−	0.208552i
$633$	12.0560	+	25.4762i	0.479182	+	1.01259i
$634$	−15.4380			−0.613120
$635$	67.3378			2.67222
$636$	−11.9134	+	5.63771i	−0.472397	+	0.223550i
$637$	−1.19804	−	6.83144i	−0.0474683	−	0.270672i
$638$		−	5.96776i		−	0.236266i
$639$	6.51020	+	5.33817i	0.257540	+	0.211175i
$640$		−	3.67536i		−	0.145281i
$641$		−	7.93823i		−	0.313541i	−0.987635	−	0.156771i	$-0.949892\pi$
$641$		−	7.93823i		−	0.313541i	0.987635	−	0.156771i	$-0.0501083\pi$
$642$	−0.0202852	−	0.0428659i	−0.000800593	−	0.00169178i
$643$		−	24.8397i		−	0.979582i	−0.871840	−	0.489791i	$-0.837073\pi$
$643$		−	24.8397i		−	0.979582i	0.871840	−	0.489791i	$-0.162927\pi$
$644$	−2.63579	+	0.229372i	−0.103865	+	0.00903851i
$645$	17.8042	+	37.6233i	0.701041	+	1.48141i
$646$	−11.7644			−0.462866
$647$	2.13059			0.0837620			0.0418810	−	0.999123i	$-0.486665\pi$
$647$	2.13059			0.0837620			0.0418810	+	0.999123i	$0.486665\pi$
$648$	8.82558	−	1.76329i	0.346701	−	0.0692686i
$649$		−	13.8542i		−	0.543823i
$650$	8.43012			0.330657
$651$	18.1292	+	31.0267i	0.710539	+	1.21603i
$652$	−4.89757			−0.191803
$653$			16.8241i			0.658377i	0.944264	+	0.329189i	$0.106775\pi$
$653$			16.8241i			0.658377i	−0.944264	+	0.329189i	$0.893225\pi$
$654$	9.40290	−	4.44968i	0.367682	−	0.173996i
$655$	−68.5112			−2.67696
$656$	2.12529			0.0829786
$657$	−1.01897	−	0.835522i	−0.0397536	−	0.0325968i
$658$	−29.4606	+	2.56372i	−1.14849	+	0.0999444i
$659$			21.5641i			0.840019i	0.907520	+	0.420010i	$0.137973\pi$
$659$			21.5641i			0.840019i	−0.907520	+	0.420010i	$0.862027\pi$
$660$	−18.7303	+	8.86363i	−0.729077	+	0.345016i
$661$		−	13.5757i		−	0.528035i	−0.964518	−	0.264017i	$-0.914952\pi$
$661$		−	13.5757i		−	0.528035i	0.964518	−	0.264017i	$-0.0850477\pi$
$662$			10.8470i			0.421579i
$663$	−10.1356	+	4.79640i	−0.393633	+	0.186277i
$664$		−	16.5597i		−	0.642640i
$665$	−17.4424	+	1.51787i	−0.676387	+	0.0588606i
$666$	−0.442838	−	0.363114i	−0.0171596	−	0.0140704i
$667$	−1.83336			−0.0709878
$668$	15.5771			0.602696
$669$	46.2212	−	21.8730i	1.78701	−	0.845658i
$670$		−	12.0035i		−	0.463734i
$671$	10.9031			0.420909
$672$	2.31190	+	3.95665i	0.0891837	+	0.152631i
$673$	45.4517			1.75203			0.876017	−	0.482280i	$-0.160191\pi$
$673$	45.4517			1.75203			0.876017	+	0.482280i	$0.160191\pi$
$674$			24.5820i			0.946865i
$675$	42.8922	+	10.7150i	1.65092	+	0.412420i
$676$	−12.0183			−0.462242
$677$	−4.79217			−0.184178			−0.0920891	−	0.995751i	$-0.529354\pi$
$677$	−4.79217			−0.184178			−0.0920891	+	0.995751i	$0.529354\pi$
$678$	0.386020	+	0.815723i	0.0148250	+	0.0313276i
$679$	33.1574	−	2.88542i	1.27246	−	0.110732i
$680$			24.0146i			0.920919i
$681$	−5.62541	−	11.8874i	−0.215566	−	0.455527i
$682$			25.5254i			0.977419i
$683$			20.0552i			0.767389i	0.923460	+	0.383695i	$0.125348\pi$
$683$			20.0552i			0.767389i	−0.923460	+	0.383695i	$0.874652\pi$
$684$	4.17689	+	3.42492i	0.159707	+	0.130955i
$685$			71.4421i			2.72966i
$686$	17.8958	−	4.76854i	0.683266	−	0.182064i
$687$	−26.9244	+	12.7413i	−1.02723	+	0.486110i
$688$	6.53847			0.249277
$689$	−7.53959			−0.287235
$690$	2.72300	+	5.75414i	0.103663	+	0.219056i
$691$			11.0515i			0.420418i	0.977656	+	0.210209i	$0.0674145\pi$
$691$			11.0515i			0.420418i	−0.977656	+	0.210209i	$0.932585\pi$
$692$	−9.71016			−0.369125
$693$	14.5884	−	21.3239i	0.554166	−	0.810028i
$694$	−3.59690			−0.136536
$695$		−	25.4385i		−	0.964936i
$696$	1.35829	+	2.87030i	0.0514860	+	0.108798i
$697$	−13.8865			−0.525990
$698$	3.00054			0.113572
$699$	15.4073	−	7.29112i	0.582759	−	0.275776i
$700$	1.95156	+	22.4260i	0.0737620	+	0.847625i
$701$			12.3196i			0.465305i	0.972560	+	0.232652i	$0.0747404\pi$
$701$			12.3196i			0.465305i	−0.972560	+	0.232652i	$0.925260\pi$
$702$	4.99492	+	1.24779i	0.188521	+	0.0470948i
$703$		−	0.343703i		−	0.0129630i
$704$			3.25510i			0.122681i
$705$	30.4354	+	64.3149i	1.14626	+	2.42224i
$706$		−	24.9982i		−	0.940820i
$707$	3.19031	+	36.6609i	0.119984	+	1.37878i
$708$	3.15328	+	6.66340i	0.118508	+	0.250426i
$709$	−29.9536			−1.12493			−0.562466	−	0.826821i	$-0.690147\pi$
$709$	−29.9536			−1.12493			−0.562466	+	0.826821i	$0.690147\pi$
$710$	10.3142			0.387086
$711$	9.97305	−	12.1627i	0.374019	−	0.456137i
$712$		−	8.22000i		−	0.308058i
$713$	7.84167			0.293673
$714$	−15.1059	−	25.8526i	−0.565323	−	0.967508i
$715$	−11.8538			−0.443306
$716$		−	10.3095i		−	0.385285i
$717$	−20.9852	+	9.93068i	−0.783705	+	0.370868i
$718$	5.79636			0.216318
$719$	−39.0111			−1.45487			−0.727433	−	0.686178i	$-0.759287\pi$
$719$	−39.0111			−1.45487			−0.727433	+	0.686178i	$0.759287\pi$
$720$	6.99126	−	8.52624i	0.260549	−	0.317754i
$721$	39.9244	−	3.47431i	1.48686	−	0.129390i
$722$		−	15.7582i		−	0.586458i
$723$	−12.1485	+	5.74895i	−0.451807	+	0.213806i
$724$		−	22.9161i		−	0.851671i
$725$			15.5987i			0.579321i
$726$	−0.632985	+	0.299544i	−0.0234923	+	0.0111171i
$727$		−	7.11904i		−	0.264030i	−0.991248	−	0.132015i	$-0.957855\pi$
$727$		−	7.11904i		−	0.264030i	0.991248	−	0.132015i	$-0.0421448\pi$
$728$	0.227265	+	2.61158i	0.00842299	+	0.0967915i
$729$	23.8280	+	12.6974i	0.882520	+	0.470276i
$730$	−1.61437			−0.0597504
$731$	−42.7220			−1.58013
$732$	−5.24403	+	2.48160i	−0.193825	+	0.0917225i
$733$		−	13.5301i		−	0.499744i	−0.968279	−	0.249872i	$-0.919611\pi$
$733$		−	13.5301i		−	0.499744i	0.968279	−	0.249872i	$-0.0803886\pi$
$734$	9.65508			0.356376
$735$	−25.7321	−	36.3810i	−0.949142	−	1.34193i
$736$	1.00000			0.0368605
$737$			10.6309i			0.391595i
$738$	4.93032	+	4.04272i	0.181488	+	0.148815i
$739$	−1.76310			−0.0648566			−0.0324283	−	0.999474i	$-0.510324\pi$
$739$	−1.76310			−0.0648566			−0.0324283	+	0.999474i	$0.510324\pi$
$740$	−0.701596			−0.0257912
$741$	1.32171	+	2.79298i	0.0485541	+	0.102603i
$742$	−1.74540	−	20.0570i	−0.0640757	−	0.736316i
$743$		−	26.2525i		−	0.963111i	−0.876416	−	0.481555i	$-0.840072\pi$
$743$		−	26.2525i		−	0.963111i	0.876416	−	0.481555i	$-0.159928\pi$
$744$	−5.80972	−	12.2769i	−0.212995	−	0.450093i
$745$			1.43528i			0.0525845i
$746$		−	5.05219i		−	0.184974i
$747$	31.4998	−	38.4158i	1.15252	−	1.40556i
$748$		−	21.2687i		−	0.777660i
$749$	0.0721677	−	0.00628018i	0.00263695	−	0.000229473i
$750$	20.1871	−	9.55304i	0.737130	−	0.348828i
$751$	−28.4321			−1.03750			−0.518752	−	0.854925i	$-0.673603\pi$
$751$	−28.4321			−1.03750			−0.518752	+	0.854925i	$0.673603\pi$
$752$	11.1772			0.407589
$753$	−0.258274	−	0.545776i	−0.00941204	−	0.0198892i
$754$			1.81651i			0.0661536i
$755$	76.8221			2.79584
$756$	−2.16309	+	13.5765i	−0.0786708	+	0.493772i
$757$	−45.9609			−1.67048			−0.835238	−	0.549889i	$-0.814670\pi$
$757$	−45.9609			−1.67048			−0.835238	+	0.549889i	$0.814670\pi$
$758$		−	35.3245i		−	1.28305i
$759$	−2.41164	−	5.09618i	−0.0875369	−	0.184980i
$760$	6.61752			0.240043
$761$	−43.0644			−1.56108			−0.780542	−	0.625103i	$-0.785057\pi$
$761$	−43.0644			−1.56108			−0.780542	+	0.625103i	$0.785057\pi$
$762$	28.6840	−	13.5739i	1.03911	−	0.491732i
$763$	1.37759	+	15.8304i	0.0498723	+	0.573099i
$764$			16.1579i			0.584572i
$765$	−45.6806	+	55.7100i	−1.65158	+	2.01420i
$766$			19.8941i			0.718804i
$767$			4.21704i			0.152268i
$768$	−0.740879	−	1.56560i	−0.0267342	−	0.0564937i
$769$			15.6167i			0.563154i	0.959539	+	0.281577i	$0.0908574\pi$
$769$			15.6167i			0.563154i	−0.959539	+	0.281577i	$0.909143\pi$
$770$	−2.74413	−	31.5337i	−0.0988916	−	1.13640i
$771$	−16.5327	−	34.9363i	−0.595411	−	1.25820i
$772$	2.58052			0.0928750
$773$	12.3667			0.444801			0.222401	−	0.974955i	$-0.428611\pi$
$773$	12.3667			0.444801			0.222401	+	0.974955i	$0.428611\pi$
$774$	15.1682	+	12.4375i	0.545209	+	0.447055i
$775$		−	66.7191i		−	2.39662i
$776$	−12.5797			−0.451584
$777$	0.755293	−	0.441324i	0.0270960	−	0.0158324i
$778$	30.1103			1.07951
$779$			3.82660i			0.137102i
$780$	5.70128	−	2.69798i	0.204139	−	0.0966033i
$781$	−9.13486			−0.326871
$782$	−6.53395			−0.233654
$783$	−2.30885	+	9.24237i	−0.0825117	+	0.330295i
$784$	−6.89478	+	1.20915i	−0.246242	+	0.0431840i
$785$		−	87.3317i		−	3.11700i
$786$	−29.1838	+	13.8105i	−1.04095	+	0.492604i
$787$		−	37.2348i		−	1.32728i	−0.748054	−	0.663638i	$-0.769011\pi$
$787$		−	37.2348i		−	1.32728i	0.748054	−	0.663638i	$-0.230989\pi$
$788$		−	18.7519i		−	0.668007i
$789$	26.6463	−	12.6097i	0.948635	−	0.448917i
$790$		−	19.2696i		−	0.685581i
$791$	−1.37332	+	0.119509i	−0.0488298	+	0.00424927i
$792$	−6.19185	+	7.55131i	−0.220018	+	0.268324i
$793$	−3.31877			−0.117853
$794$	1.78727			0.0634278
$795$	−43.7861	+	20.7206i	−1.55293	+	0.734884i
$796$			19.7966i			0.701672i
$797$	−37.9457			−1.34411			−0.672053	−	0.740503i	$-0.734587\pi$
$797$	−37.9457			−1.34411			−0.672053	+	0.740503i	$0.734587\pi$
$798$	−7.12399	+	4.16261i	−0.252186	+	0.147355i
$799$	−73.0310			−2.58365
$800$		−	8.50828i		−	0.300813i
$801$	15.6361	−	19.0691i	0.552473	−	0.673772i
$802$	9.59796			0.338916
$803$	1.42977			0.0504556
$804$	−2.41966	−	5.11313i	−0.0853347	−	0.180326i
$805$	−9.68748	+	0.843024i	−0.341439	+	0.0297127i
$806$		−	7.76963i		−	0.273674i
$807$	0.652816	+	1.37951i	0.0229802	+	0.0485610i
$808$		−	13.9089i		−	0.489313i
$809$			9.63624i			0.338792i	0.985548	+	0.169396i	$0.0541817\pi$
$809$			9.63624i			0.338792i	−0.985548	+	0.169396i	$0.945818\pi$
$810$	32.4372	−	6.48073i	1.13973	−	0.227710i
$811$			3.80152i			0.133490i	0.997770	+	0.0667448i	$0.0212613\pi$
$811$			3.80152i			0.133490i	−0.997770	+	0.0667448i	$0.978739\pi$
$812$	−4.83234	+	0.420520i	−0.169582	+	0.0147574i
$813$	−51.2466	+	24.2511i	−1.79730	+	0.850524i
$814$	0.621372			0.0217791
$815$	−18.0003			−0.630524
$816$	4.84087	+	10.2295i	0.169464	+	0.358106i
$817$			11.7726i			0.411870i
$818$	−1.66743			−0.0583005
$819$	−4.44052	+	6.49074i	−0.155164	+	0.226805i
$820$	7.81120			0.272779
$821$			34.4800i			1.20336i	0.798738	+	0.601680i	$0.205502\pi$
$821$			34.4800i			1.20336i	−0.798738	+	0.601680i	$0.794498\pi$
$822$	14.4013	+	30.4323i	0.502303	+	1.06145i
$823$	−31.1473			−1.08573			−0.542863	−	0.839822i	$-0.682660\pi$
$823$	−31.1473			−1.08573			−0.542863	+	0.839822i	$0.682660\pi$
$824$	−15.1470			−0.527672
$825$	−43.3598	+	20.5189i	−1.50959	+	0.714376i
$826$	−11.2183	+	0.976237i	−0.390334	+	0.0339676i
$827$		−	27.6761i		−	0.962392i	−0.876613	−	0.481196i	$-0.840203\pi$
$827$		−	27.6761i		−	0.962392i	0.876613	−	0.481196i	$-0.159797\pi$
$828$	2.31984	+	1.90220i	0.0806199	+	0.0661059i
$829$		−	36.4145i		−	1.26473i	−0.774672	−	0.632363i	$-0.782085\pi$
$829$		−	36.4145i		−	1.26473i	0.774672	−	0.632363i	$-0.217915\pi$
$830$		−	60.8628i		−	2.11258i
$831$	1.50441	+	3.17907i	0.0521875	+	0.110281i
$832$		−	0.990814i		−	0.0343503i
$833$	45.0501	−	7.90054i	1.56090	−	0.273737i
$834$	−5.12788	−	10.8361i	−0.177564	−	0.375222i
$835$	57.2514			1.98127
$836$	−5.86084			−0.202701
$837$	9.87547	−	39.5317i	0.341346	−	1.36641i
$838$		−	0.229830i		−	0.00793934i
$839$	43.0659			1.48680			0.743399	−	0.668848i	$-0.233212\pi$
$839$	43.0659			1.48680			0.743399	+	0.668848i	$0.233212\pi$
$840$	8.49709	+	14.5421i	0.293177	+	0.501751i
$841$	25.6388			0.884097
$842$			24.1797i			0.833287i
$843$	−32.6740	+	15.4621i	−1.12535	+	0.532544i
$844$	16.2725			0.560123
$845$	−44.1715			−1.51955
$846$	25.9292	+	21.2612i	0.891464	+	0.730973i
$847$	−0.0927370	−	1.06567i	−0.00318648	−	0.0366169i
$848$			7.60949i			0.261311i
$849$	−3.05270	+	1.44461i	−0.104769	+	0.0495790i
$850$			55.5927i			1.90681i
$851$		−	0.190892i		−	0.00654369i
$852$	4.39357	−	2.07914i	0.150521	−	0.0712302i
$853$			36.0299i			1.23364i	0.787104	+	0.616820i	$0.211579\pi$
$853$			36.0299i			1.23364i	−0.787104	+	0.616820i	$0.788421\pi$
$854$	−0.768289	−	8.82867i	−0.0262903	−	0.302111i
$855$	15.3516	+	12.5878i	0.525013	+	0.430495i
$856$	−0.0273799			−0.000935826
$857$	24.6141			0.840802			0.420401	−	0.907338i	$-0.361889\pi$
$857$	24.6141			0.840802			0.420401	+	0.907338i	$0.361889\pi$
$858$	−5.04937	+	2.38948i	−0.172383	+	0.0815756i
$859$			42.7730i			1.45940i	0.683769	+	0.729698i	$0.260339\pi$
$859$			42.7730i			1.45940i	−0.683769	+	0.729698i	$0.739661\pi$
$860$	24.0312			0.819458
$861$	−8.40903	+	4.91347i	−0.286579	+	0.167450i
$862$	31.7602			1.08176
$863$		−	4.39713i		−	0.149680i	−0.997196	−	0.0748400i	$-0.976155\pi$
$863$		−	4.39713i		−	0.149680i	0.997196	−	0.0748400i	$-0.0238446\pi$
$864$	1.25936	−	5.04123i	0.0428443	−	0.171506i
$865$	−35.6883			−1.21344
$866$	−16.6374			−0.565362
$867$	−19.0351	−	40.2242i	−0.646464	−	1.36609i
$868$	20.6690	−	1.79866i	0.701551	−	0.0610504i
$869$			17.0662i			0.578932i
$870$	4.99222	+	10.5494i	0.169252	+	0.357658i
$871$		−	3.23593i		−	0.109645i
$872$		−	6.00594i		−	0.203387i
$873$	−29.1828	−	23.9290i	−0.987687	−	0.809874i
$874$			1.80051i			0.0609031i
$875$	2.95756	+	33.9864i	0.0999839	+	1.14895i
$876$	−0.687674	+	0.325424i	−0.0232343	+	0.0109951i
$877$	−22.1258			−0.747135			−0.373568	−	0.927603i	$-0.621866\pi$
$877$	−22.1258			−0.747135			−0.373568	+	0.927603i	$0.621866\pi$
$878$	7.23914			0.244309
$879$	18.8361	+	39.8037i	0.635325	+	1.34255i
$880$			11.9637i			0.403295i
$881$	−50.8507			−1.71320			−0.856602	−	0.515978i	$-0.827429\pi$
$881$	−50.8507			−1.71320			−0.856602	+	0.515978i	$0.827429\pi$
$882$	−18.2948	−	10.3102i	−0.616018	−	0.347162i
$883$	33.5258			1.12823			0.564116	−	0.825696i	$-0.309217\pi$
$883$	33.5258			1.12823			0.564116	+	0.825696i	$0.309217\pi$
$884$			6.47393i			0.217742i
$885$	11.5894	+	24.4904i	0.389575	+	0.823236i
$886$	34.8927			1.17224
$887$	−46.7315			−1.56909			−0.784545	−	0.620072i	$-0.787103\pi$
$887$	−46.7315			−1.56909			−0.784545	+	0.620072i	$0.787103\pi$
$888$	−0.298860	+	0.141428i	−0.0100291	+	0.00474600i
$889$	4.20241	+	48.2914i	0.140944	+	1.61964i
$890$		−	30.2115i		−	1.01269i
$891$	−28.7282	+	5.73969i	−0.962429	+	0.192287i
$892$		−	29.5230i		−	0.988503i
$893$			20.1246i			0.673443i
$894$	0.289323	+	0.611387i	0.00967640	+	0.0204478i
$895$		−	37.8912i		−	1.26656i
$896$	2.63579	−	0.229372i	0.0880556	−	0.00766277i
$897$	0.734073	+	1.55122i	0.0245100	+	0.0517936i
$898$	−26.1806			−0.873658
$899$	14.3766			0.479485
$900$	16.1844	−	19.7378i	0.539481	−	0.657928i
$901$		−	49.7200i		−	1.65641i
$902$	−6.91803			−0.230345
$903$	−25.8704	+	15.1163i	−0.860914	+	0.503039i
$904$	0.521029			0.0173292
$905$		−	84.2251i		−	2.79974i
$906$	32.7240	−	15.4858i	1.08718	−	0.514481i
$907$	−25.0178			−0.830703			−0.415351	−	0.909661i	$-0.636341\pi$
$907$	−25.0178			−0.830703			−0.415351	+	0.909661i	$0.636341\pi$
$908$	−7.59289			−0.251979
$909$	26.4575	−	32.2664i	0.877539	−	1.07021i
$910$	0.835280	+	9.59849i	0.0276893	+	0.318187i
$911$			6.00508i			0.198957i	0.995040	+	0.0994786i	$0.0317175\pi$
$911$			6.00508i			0.198957i	−0.995040	+	0.0994786i	$0.968283\pi$
$912$	2.81887	−	1.33396i	0.0933423	−	0.0441718i
$913$			53.9035i			1.78394i
$914$			22.7852i			0.753667i
$915$	−19.2737	+	9.12077i	−0.637169	+	0.301523i
$916$			17.1975i			0.568222i
$917$	−4.27565	−	49.1329i	−0.141194	−	1.62251i
$918$	−8.22859	+	32.9392i	−0.271584	+	1.08715i
$919$	56.6028			1.86715			0.933577	−	0.358376i	$-0.116670\pi$
$919$	56.6028			1.86715			0.933577	+	0.358376i	$0.116670\pi$
$920$	3.67536			0.121173
$921$	15.3893	−	7.28258i	0.507095	−	0.239969i
$922$		−	1.19278i		−	0.0392822i
$923$	2.78054			0.0915226
$924$	−7.52549	−	12.8793i	−0.247570	−	0.423698i
$925$	−1.62416			−0.0534021
$926$			32.2261i			1.05902i
$927$	−35.1387	−	28.8127i	−1.15411	−	0.946332i
$928$	1.83336			0.0601828
$929$	5.70514			0.187180			0.0935898	−	0.995611i	$-0.470166\pi$
$929$	5.70514			0.187180			0.0935898	+	0.995611i	$0.470166\pi$
$930$	−21.3528	−	45.1220i	−0.700187	−	1.47961i
$931$	−2.17709	−	12.4141i	−0.0713512	−	0.406856i
$932$		−	9.84118i		−	0.322359i
$933$	18.4726	+	39.0356i	0.604765	+	1.27797i
$934$			11.4195i			0.373658i
$935$		−	78.1701i		−	2.55644i
$936$	1.88472	−	2.29853i	0.0616041	−	0.0751297i
$937$		−	43.6968i		−	1.42751i	−0.700395	−	0.713755i	$-0.746993\pi$
$937$		−	43.6968i		−	1.42751i	0.700395	−	0.713755i	$-0.253007\pi$
$938$	8.60830	−	0.749112i	0.281071	−	0.0244594i
$939$	−27.4229	+	12.9772i	−0.894913	+	0.423495i
$940$	41.0801			1.33988
$941$	17.0823			0.556867			0.278434	−	0.960456i	$-0.410185\pi$
$941$	17.0823			0.556867			0.278434	+	0.960456i	$0.410185\pi$
$942$	−17.6043	−	37.2008i	−0.573579	−	1.21207i
$943$			2.12529i			0.0692089i
$944$	4.25613			0.138525
$945$	−7.95013	+	49.8985i	−0.258618	+	1.62320i
$946$	−21.2834			−0.691982
$947$		−	47.6408i		−	1.54812i	−0.633114	−	0.774059i	$-0.718223\pi$
$947$		−	47.6408i		−	1.54812i	0.633114	−	0.774059i	$-0.281777\pi$
$948$	−3.88436	−	8.20829i	−0.126158	−	0.266593i
$949$	−0.435205			−0.0141274
$950$	15.3192			0.497022
$951$	−24.1697	+	11.4377i	−0.783755	+	0.370892i
$952$	−17.2221	+	1.49870i	−0.558172	+	0.0485733i
$953$			38.7681i			1.25582i	0.778285	+	0.627911i	$0.216090\pi$
$953$			38.7681i			1.25582i	−0.778285	+	0.627911i	$0.783910\pi$
$954$	−14.4747	+	17.6528i	−0.468637	+	0.571530i
$955$			59.3861i			1.92169i
$956$			13.4039i			0.433514i
$957$	−4.42139	−	9.34312i	−0.142923	−	0.302020i
$958$		−	18.3392i		−	0.592513i
$959$	−51.2348	+	4.45856i	−1.65446	+	0.143974i
$960$	−2.72300	−	5.75414i	−0.0878844	−	0.185714i
$961$	−30.4917			−0.983604
$962$	−0.189138			−0.00609806
$963$	−0.0635169	−	0.0520820i	−0.00204680	−	0.00167832i
$964$			7.75964i			0.249921i
$965$	9.48435			0.305312
$966$	−3.95665	+	2.31190i	−0.127303	+	0.0743843i
$967$	−36.7557			−1.18198			−0.590992	−	0.806677i	$-0.701264\pi$
$967$	−36.7557			−1.18198			−0.590992	+	0.806677i	$0.701264\pi$
$968$			0.404309i			0.0129950i
$969$	−18.4184	+	8.71603i	−0.591684	+	0.279999i
$970$	−46.2348			−1.48451
$971$	−32.0346			−1.02804			−0.514020	−	0.857778i	$-0.671844\pi$
$971$	−32.0346			−1.02804			−0.514020	+	0.857778i	$0.671844\pi$
$972$	12.5109	−	9.29929i	0.401288	−	0.298275i
$973$	18.2432	−	1.58756i	0.584851	−	0.0508949i
$974$		−	36.5849i		−	1.17226i
$975$	13.1982	−	6.24570i	0.422680	−	0.200022i
$976$			3.34953i			0.107216i
$977$			44.0219i			1.40839i	0.710009	+	0.704193i	$0.248691\pi$
$977$			44.0219i			1.40839i	−0.710009	+	0.704193i	$0.751309\pi$
$978$	−7.66762	+	3.62850i	−0.245184	+	0.116027i
$979$			26.7569i			0.855156i
$980$	−25.3408	+	4.44407i	−0.809482	+	0.141961i
$981$	11.4245	−	13.9328i	0.364756	−	0.444841i
$982$	−11.6650			−0.372245
$983$	−12.6070			−0.402102			−0.201051	−	0.979581i	$-0.564436\pi$
$983$	−12.6070			−0.402102			−0.201051	+	0.979581i	$0.564436\pi$
$984$	3.32735	−	1.57458i	0.106072	−	0.0501958i
$985$		−	68.9199i		−	2.19597i
$986$	−11.9791			−0.381491
$987$	−44.2241	+	25.8405i	−1.40767	+	0.822513i
$988$	1.78397			0.0567557
$989$			6.53847i			0.207911i
$990$	−22.7573	+	27.7538i	−0.723274	+	0.882073i
$991$	33.2013			1.05468			0.527338	−	0.849656i	$-0.323190\pi$
$991$	33.2013			1.05468			0.527338	+	0.849656i	$0.323190\pi$
$992$	−7.84167			−0.248973
$993$	8.03628	+	16.9820i	0.255024	+	0.538907i
$994$	0.643691	+	7.39687i	0.0204166	+	0.234614i
$995$			72.7597i			2.30664i
$996$	−12.2687	−	25.9258i	−0.388749	−	0.821491i
$997$		−	1.60287i		−	0.0507634i	−0.999678	−	0.0253817i	$-0.991920\pi$
$997$		−	1.60287i		−	0.0507634i	0.999678	−	0.0253817i	$-0.00808011\pi$
$998$		−	29.4161i		−	0.931152i
$999$	−0.962330	−	0.240401i	−0.0304468	−	0.00760596i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.f.b.461.5	✓	24
3.2	odd	2	inner	966.2.f.b.461.20	yes	24
7.6	odd	2	inner	966.2.f.b.461.8	yes	24
21.20	even	2	inner	966.2.f.b.461.17	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.f.b.461.5	✓	24	1.1	even	1	trivial
966.2.f.b.461.8	yes	24	7.6	odd	2	inner
966.2.f.b.461.17	yes	24	21.20	even	2	inner
966.2.f.b.461.20	yes	24	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.740879 - 1.56560i) q^{3} -1.00000 q^{4} -3.67536 q^{5} +(-1.56560 + 0.740879i) q^{6} +(-0.229372 - 2.63579i) q^{7} +1.00000i q^{8} +(-1.90220 + 2.31984i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.740879 - 1.56560i) q^{3} -1.00000 q^{4} -3.67536 q^{5} +(-1.56560 + 0.740879i) q^{6} +(-0.229372 - 2.63579i) q^{7} +1.00000i q^{8} +(-1.90220 + 2.31984i) q^{9} +3.67536i q^{10} -3.25510i q^{11} +(0.740879 + 1.56560i) q^{12} +0.990814i q^{13} +(-2.63579 + 0.229372i) q^{14} +(2.72300 + 5.75414i) q^{15} +1.00000 q^{16} -6.53395 q^{17} +(2.31984 + 1.90220i) q^{18} +1.80051i q^{19} +3.67536 q^{20} +(-3.95665 + 2.31190i) q^{21} -3.25510 q^{22} +1.00000i q^{23} +(1.56560 - 0.740879i) q^{24} +8.50828 q^{25} +0.990814 q^{26} +(5.04123 + 1.25936i) q^{27} +(0.229372 + 2.63579i) q^{28} +1.83336i q^{29} +(5.75414 - 2.72300i) q^{30} -7.84167i q^{31} -1.00000i q^{32} +(-5.09618 + 2.41164i) q^{33} +6.53395i q^{34} +(0.843024 + 9.68748i) q^{35} +(1.90220 - 2.31984i) q^{36} -0.190892 q^{37} +1.80051 q^{38} +(1.55122 - 0.734073i) q^{39} -3.67536i q^{40} +2.12529 q^{41} +(2.31190 + 3.95665i) q^{42} +6.53847 q^{43} +3.25510i q^{44} +(6.99126 - 8.52624i) q^{45} +1.00000 q^{46} +11.1772 q^{47} +(-0.740879 - 1.56560i) q^{48} +(-6.89478 + 1.20915i) q^{49} -8.50828i q^{50} +(4.84087 + 10.2295i) q^{51} -0.990814i q^{52} +7.60949i q^{53} +(1.25936 - 5.04123i) q^{54} +11.9637i q^{55} +(2.63579 - 0.229372i) q^{56} +(2.81887 - 1.33396i) q^{57} +1.83336 q^{58} +4.25613 q^{59} +(-2.72300 - 5.75414i) q^{60} +3.34953i q^{61} -7.84167 q^{62} +(6.55091 + 4.48169i) q^{63} -1.00000 q^{64} -3.64160i q^{65} +(2.41164 + 5.09618i) q^{66} -3.26593 q^{67} +6.53395 q^{68} +(1.56560 - 0.740879i) q^{69} +(9.68748 - 0.843024i) q^{70} -2.80632i q^{71} +(-2.31984 - 1.90220i) q^{72} +0.439240i q^{73} +0.190892i q^{74} +(-6.30360 - 13.3206i) q^{75} -1.80051i q^{76} +(-8.57977 + 0.746629i) q^{77} +(-0.734073 - 1.55122i) q^{78} -5.24291 q^{79} -3.67536 q^{80} +(-1.76329 - 8.82558i) q^{81} -2.12529i q^{82} -16.5597 q^{83} +(3.95665 - 2.31190i) q^{84} +24.0146 q^{85} -6.53847i q^{86} +(2.87030 - 1.35829i) q^{87} +3.25510 q^{88} -8.22000 q^{89} +(-8.52624 - 6.99126i) q^{90} +(2.61158 - 0.227265i) q^{91} -1.00000i q^{92} +(-12.2769 + 5.80972i) q^{93} -11.1772i q^{94} -6.61752i q^{95} +(-1.56560 + 0.740879i) q^{96} +12.5797i q^{97} +(1.20915 + 6.89478i) q^{98} +(7.55131 + 6.19185i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4} - 4 q^{7} + 8 q^{9}+O(q^{10}) \) 24 * q - 24 * q^4 - 4 * q^7 + 8 * q^9	\( 24 q - 24 q^{4} - 4 q^{7} + 8 q^{9} + 24 q^{16} + 16 q^{18} - 28 q^{21} + 8 q^{22} - 24 q^{25} + 4 q^{28} + 24 q^{30} - 8 q^{36} + 40 q^{37} + 72 q^{39} + 64 q^{43} + 24 q^{46} - 24 q^{51} + 16 q^{58} + 12 q^{63} - 24 q^{64} - 64 q^{67} + 16 q^{70} - 16 q^{72} - 32 q^{78} + 88 q^{79} + 48 q^{81} + 28 q^{84} + 64 q^{85} - 8 q^{88} - 56 q^{91} + 8 q^{93} - 8 q^{99}+O(q^{100}) \) 24 * q - 24 * q^4 - 4 * q^7 + 8 * q^9 + 24 * q^16 + 16 * q^18 - 28 * q^21 + 8 * q^22 - 24 * q^25 + 4 * q^28 + 24 * q^30 - 8 * q^36 + 40 * q^37 + 72 * q^39 + 64 * q^43 + 24 * q^46 - 24 * q^51 + 16 * q^58 + 12 * q^63 - 24 * q^64 - 64 * q^67 + 16 * q^70 - 16 * q^72 - 32 * q^78 + 88 * q^79 + 48 * q^81 + 28 * q^84 + 64 * q^85 - 8 * q^88 - 56 * q^91 + 8 * q^93 - 8 * q^99

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