LMFDB - Embedded newform 966.2.g.e.643.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(643,966)]

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([0, 1, 1]))

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

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

chi := DirichletCharacter("966.643");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.g (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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 326x^{12} + 27081x^{8} + 96196x^{4} + 65536 $ x^16 + 326x^12 + 27081x^8 + 96196*x^4 + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			643.6
Root			$2.48351 - 2.48351i$ of defining polynomial
Character	$\chi$	$=$	966.643
Dual form			966.2.g.e.643.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +1.36314 q^{5} -1.00000i q^{6} +(2.48351 - 0.912244i) q^{7} +1.00000 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +1.36314 q^{5} -1.00000i q^{6} +(2.48351 - 0.912244i) q^{7} +1.00000 q^{8} -1.00000 q^{9} +1.36314 q^{10} -5.58196i q^{11} -1.00000i q^{12} +4.43338i q^{13} +(2.48351 - 0.912244i) q^{14} -1.36314i q^{15} +1.00000 q^{16} +4.96702 q^{17} -1.00000 q^{18} -4.68017 q^{19} +1.36314 q^{20} +(-0.912244 - 2.48351i) q^{21} -5.58196i q^{22} +(-4.53113 + 1.57126i) q^{23} -1.00000i q^{24} -3.14185 q^{25} +4.43338i q^{26} +1.00000i q^{27} +(2.48351 - 0.912244i) q^{28} +7.94635 q^{29} -1.36314i q^{30} +1.00000 q^{32} -5.58196 q^{33} +4.96702 q^{34} +(3.38537 - 1.24352i) q^{35} -1.00000 q^{36} -3.60388i q^{37} -4.68017 q^{38} +4.43338 q^{39} +1.36314 q^{40} +8.43338i q^{41} +(-0.912244 - 2.48351i) q^{42} -5.42836i q^{43} -5.58196i q^{44} -1.36314 q^{45} +(-4.53113 + 1.57126i) q^{46} -6.14185i q^{47} -1.00000i q^{48} +(5.33562 - 4.53113i) q^{49} -3.14185 q^{50} -4.96702i q^{51} +4.43338i q^{52} +5.25386i q^{53} +1.00000i q^{54} -7.60899i q^{55} +(2.48351 - 0.912244i) q^{56} +4.68017i q^{57} +7.94635 q^{58} +10.3797i q^{59} -1.36314i q^{60} -0.286847 q^{61} +(-2.48351 + 0.912244i) q^{63} +1.00000 q^{64} +6.04331i q^{65} -5.58196 q^{66} +8.74539i q^{67} +4.96702 q^{68} +(1.57126 + 4.53113i) q^{69} +(3.38537 - 1.24352i) q^{70} -14.3797 q^{71} -1.00000 q^{72} -6.57523i q^{73} -3.60388i q^{74} +3.14185i q^{75} -4.68017 q^{76} +(-5.09211 - 13.8628i) q^{77} +4.43338 q^{78} -10.8358i q^{79} +1.36314 q^{80} +1.00000 q^{81} +8.43338i q^{82} +2.43943 q^{83} +(-0.912244 - 2.48351i) q^{84} +6.77073 q^{85} -5.42836i q^{86} -7.94635i q^{87} -5.58196i q^{88} +17.0536 q^{89} -1.36314 q^{90} +(4.04432 + 11.0103i) q^{91} +(-4.53113 + 1.57126i) q^{92} -6.14185i q^{94} -6.37972 q^{95} -1.00000i q^{96} -4.19792 q^{97} +(5.33562 - 4.53113i) q^{98} +5.58196i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} + 16 q^{4} + 16 q^{8} - 16 q^{9}+O(q^{10}) $ 16 * q + 16 * q^2 + 16 * q^4 + 16 * q^8 - 16 * q^9	$ 16 q + 16 q^{2} + 16 q^{4} + 16 q^{8} - 16 q^{9} + 16 q^{16} - 16 q^{18} - 8 q^{23} + 36 q^{25} + 20 q^{29} + 16 q^{32} - 16 q^{35} - 16 q^{36} - 4 q^{39} - 8 q^{46} + 36 q^{50} + 20 q^{58} + 16 q^{64} - 16 q^{70} - 48 q^{71} - 16 q^{72} + 20 q^{77} - 4 q^{78} + 16 q^{81} - 32 q^{85} - 8 q^{92} + 80 q^{95}+O(q^{100}) $ 16 * q + 16 * q^2 + 16 * q^4 + 16 * q^8 - 16 * q^9 + 16 * q^16 - 16 * q^18 - 8 * q^23 + 36 * q^25 + 20 * q^29 + 16 * q^32 - 16 * q^35 - 16 * q^36 - 4 * q^39 - 8 * q^46 + 36 * q^50 + 20 * q^58 + 16 * q^64 - 16 * q^70 - 48 * q^71 - 16 * q^72 + 20 * q^77 - 4 * q^78 + 16 * q^81 - 32 * q^85 - 8 * q^92 + 80 * q^95

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.00000			0.500000
$5$	1.36314			0.609614			0.304807	−	0.952414i	$-0.401408\pi$
$5$	1.36314			0.609614			0.304807	+	0.952414i	$0.401408\pi$
$6$		−	1.00000i		−	0.408248i
$7$	2.48351	−	0.912244i	0.938678	−	0.344796i
$7$	2.48351	−	0.912244i	0.938678	−	0.344796i
$8$	1.00000			0.353553
$9$	−1.00000			−0.333333
$10$	1.36314			0.431062
$11$		−	5.58196i		−	1.68302i	−0.540238	−	0.841512i	$-0.681666\pi$
$11$		−	5.58196i		−	1.68302i	0.540238	−	0.841512i	$-0.318334\pi$
$12$		−	1.00000i		−	0.288675i
$13$			4.43338i			1.22960i	0.788684	+	0.614799i	$0.210763\pi$
$13$			4.43338i			1.22960i	−0.788684	+	0.614799i	$0.789237\pi$
$14$	2.48351	−	0.912244i	0.663745	−	0.243807i
$15$		−	1.36314i		−	0.351961i
$16$	1.00000			0.250000
$17$	4.96702			1.20468			0.602339	−	0.798240i	$-0.294235\pi$
$17$	4.96702			1.20468			0.602339	+	0.798240i	$0.294235\pi$
$18$	−1.00000			−0.235702
$19$	−4.68017			−1.07370			−0.536852	−	0.843676i	$-0.680387\pi$
$19$	−4.68017			−1.07370			−0.536852	+	0.843676i	$0.680387\pi$
$20$	1.36314			0.304807
$21$	−0.912244	−	2.48351i	−0.199068	−	0.541946i
$22$		−	5.58196i		−	1.19008i
$23$	−4.53113	+	1.57126i	−0.944806	+	0.327631i
$23$	−4.53113	+	1.57126i	−0.944806	+	0.327631i
$24$		−	1.00000i		−	0.204124i
$25$	−3.14185			−0.628370
$26$			4.43338i			0.869457i
$27$			1.00000i			0.192450i
$28$	2.48351	−	0.912244i	0.469339	−	0.172398i
$29$	7.94635			1.47560			0.737800	−	0.675020i	$-0.235865\pi$
$29$	7.94635			1.47560			0.737800	+	0.675020i	$0.235865\pi$
$30$		−	1.36314i		−	0.248874i
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$	1.00000			0.176777
$33$	−5.58196			−0.971694
$34$	4.96702			0.851836
$35$	3.38537	−	1.24352i	0.572231	−	0.210192i
$36$	−1.00000			−0.166667
$37$		−	3.60388i		−	0.592474i	−0.955115	−	0.296237i	$-0.904268\pi$
$37$		−	3.60388i		−	0.592474i	0.955115	−	0.296237i	$-0.0957318\pi$
$38$	−4.68017			−0.759224
$39$	4.43338			0.709908
$40$	1.36314			0.215531
$41$			8.43338i			1.31707i	0.752549	+	0.658536i	$0.228824\pi$
$41$			8.43338i			1.31707i	−0.752549	+	0.658536i	$0.771176\pi$
$42$	−0.912244	−	2.48351i	−0.140762	−	0.383214i
$43$		−	5.42836i		−	0.827818i	−0.910318	−	0.413909i	$-0.864163\pi$
$43$		−	5.42836i		−	0.827818i	0.910318	−	0.413909i	$-0.135837\pi$
$44$		−	5.58196i		−	0.841512i
$45$	−1.36314			−0.203205
$46$	−4.53113	+	1.57126i	−0.668079	+	0.231670i
$47$		−	6.14185i		−	0.895881i	−0.894063	−	0.447941i	$-0.852158\pi$
$47$		−	6.14185i		−	0.895881i	0.894063	−	0.447941i	$-0.147842\pi$
$48$		−	1.00000i		−	0.144338i
$49$	5.33562	−	4.53113i	0.762232	−	0.647304i
$50$	−3.14185			−0.444325
$51$		−	4.96702i		−	0.695521i
$52$			4.43338i			0.614799i
$53$			5.25386i			0.721674i	0.932629	+	0.360837i	$0.117509\pi$
$53$			5.25386i			0.721674i	−0.932629	+	0.360837i	$0.882491\pi$
$54$			1.00000i			0.136083i
$55$		−	7.60899i		−	1.02600i
$56$	2.48351	−	0.912244i	0.331873	−	0.121904i
$57$			4.68017i			0.619904i
$58$	7.94635			1.04341
$59$			10.3797i			1.35132i	0.737211	+	0.675662i	$0.236142\pi$
$59$			10.3797i			1.35132i	−0.737211	+	0.675662i	$0.763858\pi$
$60$		−	1.36314i		−	0.175981i
$61$	−0.286847			−0.0367270			−0.0183635	−	0.999831i	$-0.505846\pi$
$61$	−0.286847			−0.0367270			−0.0183635	+	0.999831i	$0.505846\pi$
$62$		0			0
$63$	−2.48351	+	0.912244i	−0.312893	+	0.114932i
$64$	1.00000			0.125000
$65$			6.04331i			0.749580i
$66$	−5.58196			−0.687092
$67$			8.74539i			1.06842i	0.845352	+	0.534210i	$0.179391\pi$
$67$			8.74539i			1.06842i	−0.845352	+	0.534210i	$0.820609\pi$
$68$	4.96702			0.602339
$69$	1.57126	+	4.53113i	0.189158	+	0.545484i
$70$	3.38537	−	1.24352i	0.404629	−	0.148628i
$71$	−14.3797			−1.70656			−0.853279	−	0.521454i	$-0.825390\pi$
$71$	−14.3797			−1.70656			−0.853279	+	0.521454i	$0.825390\pi$
$72$	−1.00000			−0.117851
$73$		−	6.57523i		−	0.769572i	−0.923006	−	0.384786i	$-0.874275\pi$
$73$		−	6.57523i		−	0.769572i	0.923006	−	0.384786i	$-0.125725\pi$
$74$		−	3.60388i		−	0.418942i
$75$			3.14185i			0.362790i
$76$	−4.68017			−0.536852
$77$	−5.09211	−	13.8628i	−0.580300	−	1.57982i
$78$	4.43338			0.501981
$79$		−	10.8358i		−	1.21913i	−0.792738	−	0.609563i	$-0.791345\pi$
$79$		−	10.8358i		−	1.21913i	0.792738	−	0.609563i	$-0.208655\pi$
$80$	1.36314			0.152404
$81$	1.00000			0.111111
$82$			8.43338i			0.931311i
$83$	2.43943			0.267762			0.133881	−	0.990997i	$-0.457256\pi$
$83$	2.43943			0.267762			0.133881	+	0.990997i	$0.457256\pi$
$84$	−0.912244	−	2.48351i	−0.0995339	−	0.270973i
$85$	6.77073			0.734389
$86$		−	5.42836i		−	0.585356i
$87$		−	7.94635i		−	0.851938i
$88$		−	5.58196i		−	0.595039i
$89$	17.0536			1.80768			0.903841	−	0.427869i	$-0.140736\pi$
$89$	17.0536			1.80768			0.903841	+	0.427869i	$0.140736\pi$
$90$	−1.36314			−0.143687
$91$	4.04432	+	11.0103i	0.423960	+	1.15420i
$92$	−4.53113	+	1.57126i	−0.472403	+	0.163816i
$93$		0			0
$94$		−	6.14185i		−	0.633484i
$95$	−6.37972			−0.654546
$96$		−	1.00000i		−	0.102062i
$97$	−4.19792			−0.426234			−0.213117	−	0.977027i	$-0.568362\pi$
$97$	−4.19792			−0.426234			−0.213117	+	0.977027i	$0.568362\pi$
$98$	5.33562	−	4.53113i	0.538979	−	0.457713i
$99$			5.58196i			0.561008i
$100$	−3.14185			−0.314185
$101$			1.90398i			0.189453i	0.995503	+	0.0947266i	$0.0301977\pi$
$101$			1.90398i			0.189453i	−0.995503	+	0.0947266i	$0.969802\pi$
$102$		−	4.96702i		−	0.491808i
$103$	−13.7366			−1.35351			−0.676754	−	0.736209i	$-0.736614\pi$
$103$	−13.7366			−1.35351			−0.676754	+	0.736209i	$0.736614\pi$
$104$			4.43338i			0.434728i
$105$	−1.24352	−	3.38537i	−0.121355	−	0.330378i
$106$			5.25386i			0.510300i
$107$		−	6.50466i		−	0.628829i	−0.949286	−	0.314414i	$-0.898192\pi$
$107$		−	6.50466i		−	0.628829i	0.949286	−	0.314414i	$-0.101808\pi$
$108$			1.00000i			0.0962250i
$109$			6.33015i			0.606319i	0.952940	+	0.303159i	$0.0980415\pi$
$109$			6.33015i			0.606319i	−0.952940	+	0.303159i	$0.901959\pi$
$110$		−	7.60899i		−	0.725489i
$111$	−3.60388			−0.342065
$112$	2.48351	−	0.912244i	0.234669	−	0.0861989i
$113$			4.37626i			0.411684i	0.978585	+	0.205842i	$0.0659933\pi$
$113$			4.37626i			0.411684i	−0.978585	+	0.205842i	$0.934007\pi$
$114$			4.68017i			0.438338i
$115$	−6.17656	+	2.14185i	−0.575967	+	0.199729i
$116$	7.94635			0.737800
$117$		−	4.43338i		−	0.409866i
$118$			10.3797i			0.955531i
$119$	12.3356	−	4.53113i	1.13080	−	0.415368i
$120$		−	1.36314i		−	0.124437i
$121$	−20.1583			−1.83257
$122$	−0.286847			−0.0259699
$123$	8.43338			0.760412
$124$		0			0
$125$	−11.0985			−0.992678
$126$	−2.48351	+	0.912244i	−0.221248	+	0.0812691i
$127$	9.49563			0.842601			0.421301	−	0.906921i	$-0.361574\pi$
$127$	9.49563			0.842601			0.421301	+	0.906921i	$0.361574\pi$
$128$	1.00000			0.0883883
$129$	−5.42836			−0.477941
$130$			6.04331i			0.530033i
$131$			15.8927i			1.38855i	0.719709	+	0.694275i	$0.244275\pi$
$131$			15.8927i			1.38855i	−0.719709	+	0.694275i	$0.755725\pi$
$132$	−5.58196			−0.485847
$133$	−11.6232	+	4.26945i	−1.00786	+	0.370209i
$134$			8.74539i			0.755487i
$135$			1.36314i			0.117320i
$136$	4.96702			0.425918
$137$			16.4629i			1.40652i	0.710933	+	0.703259i	$0.248273\pi$
$137$			16.4629i			1.40652i	−0.710933	+	0.703259i	$0.751727\pi$
$138$	1.57126	+	4.53113i	0.133755	+	0.385715i
$139$			18.8131i			1.59571i	0.602852	+	0.797853i	$0.294031\pi$
$139$			18.8131i			1.59571i	−0.602852	+	0.797853i	$0.705969\pi$
$140$	3.38537	−	1.24352i	0.286116	−	0.105096i
$141$	−6.14185			−0.517237
$142$	−14.3797			−1.20672
$143$	24.7469			2.06944
$144$	−1.00000			−0.0833333
$145$	10.8320			0.899547
$146$		−	6.57523i		−	0.544170i
$147$	−4.53113	−	5.33562i	−0.373721	−	0.440075i
$148$		−	3.60388i		−	0.296237i
$149$			10.1327i			0.830105i	0.909797	+	0.415053i	$0.136237\pi$
$149$			10.1327i			0.830105i	−0.909797	+	0.415053i	$0.863763\pi$
$150$			3.14185i			0.256531i
$151$	12.5216			1.01899			0.509496	−	0.860473i	$-0.329832\pi$
$151$	12.5216			1.01899			0.509496	+	0.860473i	$0.329832\pi$
$152$	−4.68017			−0.379612
$153$	−4.96702			−0.401559
$154$	−5.09211	−	13.8628i	−0.410334	−	1.11710i
$155$		0			0
$156$	4.43338			0.354954
$157$	−5.73940			−0.458054			−0.229027	−	0.973420i	$-0.573554\pi$
$157$	−5.73940			−0.458054			−0.229027	+	0.973420i	$0.573554\pi$
$158$		−	10.8358i		−	0.862052i
$159$	5.25386			0.416658
$160$	1.36314			0.107766
$161$	−9.81972	+	8.03574i	−0.773902	+	0.633305i
$162$	1.00000			0.0785674
$163$	−5.25776			−0.411820			−0.205910	−	0.978571i	$-0.566015\pi$
$163$	−5.25776			−0.411820			−0.205910	+	0.978571i	$0.566015\pi$
$164$			8.43338i			0.658536i
$165$	−7.60899			−0.592359
$166$	2.43943			0.189337
$167$			11.5493i			0.893711i	0.894606	+	0.446855i	$0.147456\pi$
$167$			11.5493i			0.893711i	−0.894606	+	0.446855i	$0.852544\pi$
$168$	−0.912244	−	2.48351i	−0.0703811	−	0.191607i
$169$	−6.65482			−0.511909
$170$	6.77073			0.519292
$171$	4.68017			0.357901
$172$		−	5.42836i		−	0.413909i
$173$		−	4.67125i		−	0.355148i	−0.984107	−	0.177574i	$-0.943175\pi$
$173$		−	4.67125i		−	0.355148i	0.984107	−	0.177574i	$-0.0568249\pi$
$174$		−	7.94635i		−	0.602411i
$175$	−7.80281	+	2.86613i	−0.589837	+	0.216659i
$176$		−	5.58196i		−	0.420756i
$177$	10.3797			0.780188
$178$	17.0536			1.27822
$179$	−4.62888			−0.345979			−0.172989	−	0.984924i	$-0.555343\pi$
$179$	−4.62888			−0.345979			−0.172989	+	0.984924i	$0.555343\pi$
$180$	−1.36314			−0.101602
$181$	−15.0095			−1.11565			−0.557825	−	0.829958i	$-0.688364\pi$
$181$	−15.0095			−1.11565			−0.557825	+	0.829958i	$0.688364\pi$
$182$	4.04432	+	11.0103i	0.299785	+	0.816140i
$183$			0.286847i			0.0212043i
$184$	−4.53113	+	1.57126i	−0.334039	+	0.115835i
$185$		−	4.91259i		−	0.361180i
$186$		0			0
$187$		−	27.7257i		−	2.02750i
$188$		−	6.14185i		−	0.447941i
$189$	0.912244	+	2.48351i	0.0663560	+	0.180649i
$190$	−6.37972			−0.462834
$191$			17.9554i			1.29921i	0.760272	+	0.649604i	$0.225065\pi$
$191$			17.9554i			1.29921i	−0.760272	+	0.649604i	$0.774935\pi$
$192$		−	1.00000i		−	0.0721688i
$193$	−14.4334			−1.03894			−0.519469	−	0.854490i	$-0.673870\pi$
$193$	−14.4334			−1.03894			−0.519469	+	0.854490i	$0.673870\pi$
$194$	−4.19792			−0.301393
$195$	6.04331			0.432770
$196$	5.33562	−	4.53113i	0.381116	−	0.323652i
$197$	−20.3624			−1.45076			−0.725380	−	0.688349i	$-0.758336\pi$
$197$	−20.3624			−1.45076			−0.725380	+	0.688349i	$0.758336\pi$
$198$			5.58196i			0.396693i
$199$	−18.5253			−1.31322			−0.656611	−	0.754230i	$-0.728011\pi$
$199$	−18.5253			−1.31322			−0.656611	+	0.754230i	$0.728011\pi$
$200$	−3.14185			−0.222162
$201$	8.74539			0.616853
$202$			1.90398i			0.133964i
$203$	19.7348	−	7.24900i	1.38511	−	0.508780i
$204$		−	4.96702i		−	0.347761i
$205$			11.4959i			0.802906i
$206$	−13.7366			−0.957074
$207$	4.53113	−	1.57126i	0.314935	−	0.109210i
$208$			4.43338i			0.307399i
$209$			26.1245i			1.80707i
$210$	−1.24352	−	3.38537i	−0.0858107	−	0.233613i
$211$	28.3087			1.94885			0.974427	−	0.224706i	$-0.0721420\pi$
$211$	28.3087			1.94885			0.974427	+	0.224706i	$0.0721420\pi$
$212$			5.25386i			0.360837i
$213$			14.3797i			0.985282i
$214$		−	6.50466i		−	0.444649i
$215$		−	7.39962i		−	0.504650i
$216$			1.00000i			0.0680414i
$217$		0			0
$218$			6.33015i			0.428732i
$219$	−6.57523			−0.444313
$220$		−	7.60899i		−	0.512998i
$221$			22.0206i			1.48127i
$222$	−3.60388			−0.241876
$223$		−	3.02594i		−	0.202632i	−0.994854	−	0.101316i	$-0.967695\pi$
$223$		−	3.02594i		−	0.202632i	0.994854	−	0.101316i	$-0.0323053\pi$
$224$	2.48351	−	0.912244i	0.165936	−	0.0609518i
$225$	3.14185			0.209457
$226$			4.37626i			0.291105i
$227$	−1.18479			−0.0786373			−0.0393186	−	0.999227i	$-0.512519\pi$
$227$	−1.18479			−0.0786373			−0.0393186	+	0.999227i	$0.512519\pi$
$228$			4.68017i			0.309952i
$229$	2.34924			0.155242			0.0776209	−	0.996983i	$-0.475268\pi$
$229$	2.34924			0.155242			0.0776209	+	0.996983i	$0.475268\pi$
$230$	−6.17656	+	2.14185i	−0.407270	+	0.141230i
$231$	−13.8628	+	5.09211i	−0.912108	+	0.335036i
$232$	7.94635			0.521703
$233$	6.39101			0.418689			0.209345	−	0.977842i	$-0.432867\pi$
$233$	6.39101			0.418689			0.209345	+	0.977842i	$0.432867\pi$
$234$		−	4.43338i		−	0.289819i
$235$		−	8.37220i		−	0.546142i
$236$			10.3797i			0.675662i
$237$	−10.8358			−0.703862
$238$	12.3356	−	4.53113i	0.799600	−	0.293709i
$239$	12.0882			0.781920			0.390960	−	0.920408i	$-0.372143\pi$
$239$	12.0882			0.781920			0.390960	+	0.920408i	$0.372143\pi$
$240$		−	1.36314i		−	0.0879903i
$241$	4.19792			0.270411			0.135206	−	0.990818i	$-0.456830\pi$
$241$	4.19792			0.270411			0.135206	+	0.990818i	$0.456830\pi$
$242$	−20.1583			−1.29582
$243$		−	1.00000i		−	0.0641500i
$244$	−0.286847			−0.0183635
$245$	7.27320	−	6.17656i	0.464667	−	0.394606i
$246$	8.43338			0.537692
$247$		−	20.7489i		−	1.32022i
$248$		0			0
$249$		−	2.43943i		−	0.154593i
$250$	−11.0985			−0.701929
$251$	3.60388			0.227475			0.113737	−	0.993511i	$-0.463718\pi$
$251$	3.60388			0.227475			0.113737	+	0.993511i	$0.463718\pi$
$252$	−2.48351	+	0.912244i	−0.156446	+	0.0574660i
$253$	8.77073	+	25.2926i	0.551411	+	1.59013i
$254$	9.49563			0.595809
$255$		−	6.77073i		−	0.424000i
$256$	1.00000			0.0625000
$257$			3.22145i			0.200948i	0.994940	+	0.100474i	$0.0320360\pi$
$257$			3.22145i			0.200948i	−0.994940	+	0.100474i	$0.967964\pi$
$258$	−5.42836			−0.337955
$259$	−3.28761	−	8.95026i	−0.204282	−	0.556142i
$260$			6.04331i			0.374790i
$261$	−7.94635			−0.491866
$262$			15.8927i			0.981854i
$263$		−	23.6915i		−	1.46088i	−0.682975	−	0.730441i	$-0.739314\pi$
$263$		−	23.6915i		−	1.46088i	0.682975	−	0.730441i	$-0.260686\pi$
$264$	−5.58196			−0.343546
$265$			7.16175i			0.439943i
$266$	−11.6232	+	4.26945i	−0.712666	+	0.261777i
$267$		−	17.0536i		−	1.04367i
$268$			8.74539i			0.534210i
$269$		−	23.3538i		−	1.42391i	−0.702228	−	0.711953i	$-0.747811\pi$
$269$		−	23.3538i		−	1.42391i	0.702228	−	0.711953i	$-0.252189\pi$
$270$			1.36314i			0.0829580i
$271$		−	16.8668i		−	1.02458i	−0.858812	−	0.512291i	$-0.828797\pi$
$271$		−	16.8668i		−	1.02458i	0.858812	−	0.512291i	$-0.171203\pi$
$272$	4.96702			0.301170
$273$	11.0103	−	4.04432i	0.666375	−	0.244773i
$274$			16.4629i			0.994559i
$275$			17.5377i			1.05756i
$276$	1.57126	+	4.53113i	0.0945790	+	0.272742i
$277$	−1.02594			−0.0616427			−0.0308214	−	0.999525i	$-0.509812\pi$
$277$	−1.02594			−0.0616427			−0.0308214	+	0.999525i	$0.509812\pi$
$278$			18.8131i			1.12833i
$279$		0			0
$280$	3.38537	−	1.24352i	0.202314	−	0.0743142i
$281$		−	26.3067i		−	1.56933i	−0.619922	−	0.784664i	$-0.712836\pi$
$281$		−	26.3067i		−	1.56933i	0.619922	−	0.784664i	$-0.287164\pi$
$282$	−6.14185			−0.365742
$283$	−31.5797			−1.87722			−0.938609	−	0.344984i	$-0.887884\pi$
$283$	−31.5797			−1.87722			−0.938609	+	0.344984i	$0.887884\pi$
$284$	−14.3797			−0.853279
$285$			6.37972i			0.377902i
$286$	24.7469			1.46332
$287$	7.69329	+	20.9444i	0.454121	+	1.23631i
$288$	−1.00000			−0.0589256
$289$	7.67125			0.451250
$290$	10.8320			0.636075
$291$			4.19792i			0.246086i
$292$		−	6.57523i		−	0.384786i
$293$	4.77037			0.278688			0.139344	−	0.990244i	$-0.455501\pi$
$293$	4.77037			0.278688			0.139344	+	0.990244i	$0.455501\pi$
$294$	−4.53113	−	5.33562i	−0.264261	−	0.311180i
$295$			14.1490i			0.823787i
$296$		−	3.60388i		−	0.209471i
$297$	5.58196			0.323898
$298$			10.1327i			0.586973i
$299$	−6.96600	−	20.0882i	−0.402854	−	1.16173i
$300$			3.14185i			0.181395i
$301$	−4.95199	−	13.4814i	−0.285428	−	0.777054i
$302$	12.5216			0.720536
$303$	1.90398			0.109381
$304$	−4.68017			−0.268426
$305$	−0.391012			−0.0223893
$306$	−4.96702			−0.283945
$307$			28.9376i			1.65156i	0.563995	+	0.825778i	$0.309264\pi$
$307$			28.9376i			1.65156i	−0.563995	+	0.825778i	$0.690736\pi$
$308$	−5.09211	−	13.8628i	−0.290150	−	0.789909i
$309$			13.7366i			0.781448i
$310$		0			0
$311$		−	12.0882i		−	0.685459i	−0.939434	−	0.342729i	$-0.888649\pi$
$311$		−	12.0882i		−	0.685459i	0.939434	−	0.342729i	$-0.111351\pi$
$312$	4.43338			0.250990
$313$	−19.2944			−1.09058			−0.545291	−	0.838247i	$-0.683581\pi$
$313$	−19.2944			−1.09058			−0.545291	+	0.838247i	$0.683581\pi$
$314$	−5.73940			−0.323893
$315$	−3.38537	+	1.24352i	−0.190744	+	0.0700641i
$316$		−	10.8358i		−	0.609563i
$317$	30.6539			1.72170			0.860848	−	0.508863i	$-0.169934\pi$
$317$	30.6539			1.72170			0.860848	+	0.508863i	$0.169934\pi$
$318$	5.25386			0.294622
$319$		−	44.3562i		−	2.48347i
$320$	1.36314			0.0762018
$321$	−6.50466			−0.363055
$322$	−9.81972	+	8.03574i	−0.547232	+	0.447814i
$323$	−23.2465			−1.29347
$324$	1.00000			0.0555556
$325$		−	13.9290i		−	0.772642i
$326$	−5.25776			−0.291201
$327$	6.33015			0.350058
$328$			8.43338i			0.465655i
$329$	−5.60287	−	15.2533i	−0.308896	−	0.840944i
$330$	−7.60899			−0.418861
$331$	−2.96624			−0.163039			−0.0815196	−	0.996672i	$-0.525977\pi$
$331$	−2.96624			−0.163039			−0.0815196	+	0.996672i	$0.525977\pi$
$332$	2.43943			0.133881
$333$			3.60388i			0.197491i
$334$			11.5493i			0.631949i
$335$			11.9212i			0.651324i
$336$	−0.912244	−	2.48351i	−0.0497670	−	0.135486i
$337$		−	5.14536i		−	0.280286i	−0.990131	−	0.140143i	$-0.955244\pi$
$337$		−	5.14536i		−	0.280286i	0.990131	−	0.140143i	$-0.0447562\pi$
$338$	−6.65482			−0.361975
$339$	4.37626			0.237686
$340$	6.77073			0.367195
$341$		0			0
$342$	4.68017			0.253075
$343$	9.11757	−	16.1205i	0.492302	−	0.870424i
$344$		−	5.42836i		−	0.292678i
$345$	2.14185	+	6.17656i	0.115313	+	0.332535i
$346$		−	4.67125i		−	0.251128i
$347$	19.9385			1.07036			0.535178	−	0.844739i	$-0.320245\pi$
$347$	19.9385			1.07036			0.535178	+	0.844739i	$0.320245\pi$
$348$		−	7.94635i		−	0.425969i
$349$			6.32002i			0.338303i	0.985590	+	0.169151i	$0.0541027\pi$
$349$			6.32002i			0.338303i	−0.985590	+	0.169151i	$0.945897\pi$
$350$	−7.80281	+	2.86613i	−0.417078	+	0.153201i
$351$	−4.43338			−0.236636
$352$		−	5.58196i		−	0.297519i
$353$			3.45932i			0.184121i	0.995753	+	0.0920604i	$0.0293453\pi$
$353$			3.45932i			0.184121i	−0.995753	+	0.0920604i	$0.970655\pi$
$354$	10.3797			0.551676
$355$	−19.6016			−1.04034
$356$	17.0536			0.903841
$357$	−4.53113	−	12.3356i	−0.239813	−	0.652870i
$358$	−4.62888			−0.244644
$359$		−	33.3591i		−	1.76062i	−0.474395	−	0.880312i	$-0.657333\pi$
$359$		−	33.3591i		−	1.76062i	0.474395	−	0.880312i	$-0.342667\pi$
$360$	−1.36314			−0.0718437
$361$	2.90398			0.152841
$362$	−15.0095			−0.788884
$363$			20.1583i			1.05804i
$364$	4.04432	+	11.0103i	0.211980	+	0.577098i
$365$		−	8.96295i		−	0.469142i
$366$			0.286847i			0.0149937i
$367$	−1.16649			−0.0608902			−0.0304451	−	0.999536i	$-0.509692\pi$
$367$	−1.16649			−0.0608902			−0.0304451	+	0.999536i	$0.509692\pi$
$368$	−4.53113	+	1.57126i	−0.236201	+	0.0819078i
$369$		−	8.43338i		−	0.439024i
$370$		−	4.91259i		−	0.255393i
$371$	4.79280	+	13.0480i	0.248830	+	0.677419i
$372$		0			0
$373$			1.55855i			0.0806985i	0.999186	+	0.0403492i	$0.0128470\pi$
$373$			1.55855i			0.0806985i	−0.999186	+	0.0403492i	$0.987153\pi$
$374$		−	27.7257i		−	1.43366i
$375$			11.0985i			0.573123i
$376$		−	6.14185i		−	0.316742i
$377$			35.2291i			1.81439i
$378$	0.912244	+	2.48351i	0.0469208	+	0.127738i
$379$		−	38.7031i		−	1.98805i	−0.109170	−	0.994023i	$-0.534819\pi$
$379$		−	38.7031i		−	1.98805i	0.109170	−	0.994023i	$-0.465181\pi$
$380$	−6.37972			−0.327273
$381$		−	9.49563i		−	0.486476i
$382$			17.9554i			0.918679i
$383$	20.8391			1.06483			0.532415	−	0.846483i	$-0.321284\pi$
$383$	20.8391			1.06483			0.532415	+	0.846483i	$0.321284\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	−6.94125	−	18.8970i	−0.353759	−	0.963079i
$386$	−14.4334			−0.734639
$387$			5.42836i			0.275939i
$388$	−4.19792			−0.213117
$389$		−	3.49867i		−	0.177389i	−0.996059	−	0.0886947i	$-0.971730\pi$
$389$		−	3.49867i		−	0.177389i	0.996059	−	0.0886947i	$-0.0282695\pi$
$390$	6.04331			0.306015
$391$	−22.5062	+	7.80449i	−1.13819	+	0.394690i
$392$	5.33562	−	4.53113i	0.269490	−	0.228857i
$393$	15.8927			0.801680
$394$	−20.3624			−1.02584
$395$		−	14.7707i		−	0.743196i
$396$			5.58196i			0.280504i
$397$			1.31746i			0.0661216i	0.999453	+	0.0330608i	$0.0105255\pi$
$397$			1.31746i			0.0661216i	−0.999453	+	0.0330608i	$0.989475\pi$
$398$	−18.5253			−0.928588
$399$	4.26945	+	11.6232i	0.213740	+	0.581890i
$400$	−3.14185			−0.157093
$401$			12.3918i			0.618815i	0.950930	+	0.309408i	$0.100131\pi$
$401$			12.3918i			0.618815i	−0.950930	+	0.309408i	$0.899869\pi$
$402$	8.74539			0.436181
$403$		0			0
$404$			1.90398i			0.0947266i
$405$	1.36314			0.0677349
$406$	19.7348	−	7.24900i	0.979422	−	0.359762i
$407$	−20.1167			−0.997148
$408$		−	4.96702i		−	0.245904i
$409$		−	29.7370i		−	1.47040i	−0.677851	−	0.735199i	$-0.737089\pi$
$409$		−	29.7370i		−	1.47040i	0.677851	−	0.735199i	$-0.262911\pi$
$410$			11.4959i			0.567740i
$411$	16.4629			0.812054
$412$	−13.7366			−0.676754
$413$	9.46884	+	25.7781i	0.465931	+	1.26846i
$414$	4.53113	−	1.57126i	0.222693	−	0.0772234i
$415$	3.32528			0.163232
$416$			4.43338i			0.217364i
$417$	18.8131			0.921281
$418$			26.1245i			1.27779i
$419$	5.43221			0.265381			0.132690	−	0.991158i	$-0.457638\pi$
$419$	5.43221			0.265381			0.132690	+	0.991158i	$0.457638\pi$
$420$	−1.24352	−	3.38537i	−0.0606773	−	0.165189i
$421$			28.0436i			1.36676i	0.730062	+	0.683381i	$0.239491\pi$
$421$			28.0436i			1.36676i	−0.730062	+	0.683381i	$0.760509\pi$
$422$	28.3087			1.37805
$423$			6.14185i			0.298627i
$424$			5.25386i			0.255150i
$425$	−15.6056			−0.756984
$426$			14.3797i			0.696700i
$427$	−0.712386	+	0.261674i	−0.0344748	+	0.0126633i
$428$		−	6.50466i		−	0.314414i
$429$		−	24.7469i		−	1.19479i
$430$		−	7.39962i		−	0.356841i
$431$		−	25.4049i		−	1.22371i	−0.790969	−	0.611856i	$-0.790423\pi$
$431$		−	25.4049i		−	1.22371i	0.790969	−	0.611856i	$-0.209577\pi$
$432$			1.00000i			0.0481125i
$433$	1.56183			0.0750569			0.0375285	−	0.999296i	$-0.488052\pi$
$433$	1.56183			0.0750569			0.0375285	+	0.999296i	$0.488052\pi$
$434$		0			0
$435$		−	10.8320i		−	0.519353i
$436$			6.33015i			0.303159i
$437$	21.2064	−	7.35378i	1.01444	−	0.351779i
$438$	−6.57523			−0.314177
$439$			25.0431i			1.19524i	0.801778	+	0.597622i	$0.203888\pi$
$439$			25.0431i			1.19524i	−0.801778	+	0.597622i	$0.796112\pi$
$440$		−	7.60899i		−	0.362744i
$441$	−5.33562	+	4.53113i	−0.254077	+	0.215768i
$442$			22.0206i			1.04742i
$443$	6.72490			0.319510			0.159755	−	0.987157i	$-0.448930\pi$
$443$	6.72490			0.319510			0.159755	+	0.987157i	$0.448930\pi$
$444$	−3.60388			−0.171032
$445$	23.2465			1.10199
$446$		−	3.02594i		−	0.143282i
$447$	10.1327			0.479261
$448$	2.48351	−	0.912244i	0.117335	−	0.0430995i
$449$	14.4757			0.683152			0.341576	−	0.939854i	$-0.389039\pi$
$449$	14.4757			0.683152			0.341576	+	0.939854i	$0.389039\pi$
$450$	3.14185			0.148108
$451$	47.0748			2.21666
$452$			4.37626i			0.205842i
$453$		−	12.5216i		−	0.588315i
$454$	−1.18479			−0.0556049
$455$	5.51297	+	15.0086i	0.258452	+	0.703614i
$456$			4.68017i			0.219169i
$457$			0.880885i			0.0412061i	0.999788	+	0.0206030i	$0.00655861\pi$
$457$			0.880885i			0.0412061i	−0.999788	+	0.0206030i	$0.993441\pi$
$458$	2.34924			0.109773
$459$			4.96702i			0.231840i
$460$	−6.17656	+	2.14185i	−0.287984	+	0.0998644i
$461$		−	22.2724i		−	1.03733i	−0.854978	−	0.518665i	$-0.826429\pi$
$461$		−	22.2724i		−	1.03733i	0.854978	−	0.518665i	$-0.173571\pi$
$462$	−13.8628	+	5.09211i	−0.644958	+	0.236906i
$463$	6.46969			0.300672			0.150336	−	0.988635i	$-0.451964\pi$
$463$	6.46969			0.300672			0.150336	+	0.988635i	$0.451964\pi$
$464$	7.94635			0.368900
$465$		0			0
$466$	6.39101			0.296058
$467$	24.0863			1.11458			0.557291	−	0.830317i	$-0.311841\pi$
$467$	24.0863			1.11458			0.557291	+	0.830317i	$0.311841\pi$
$468$		−	4.43338i		−	0.204933i
$469$	7.97793	+	21.7193i	0.368387	+	1.00290i
$470$		−	8.37220i		−	0.386181i
$471$			5.73940i			0.264458i
$472$			10.3797i			0.477765i
$473$	−30.3009			−1.39324
$474$	−10.8358			−0.497706
$475$	14.7044			0.674684
$476$	12.3356	−	4.53113i	0.565402	−	0.207684i
$477$		−	5.25386i		−	0.240558i
$478$	12.0882			0.552901
$479$	−10.9392			−0.499826			−0.249913	−	0.968268i	$-0.580402\pi$
$479$	−10.9392			−0.499826			−0.249913	+	0.968268i	$0.580402\pi$
$480$		−	1.36314i		−	0.0622185i
$481$	15.9773			0.728504
$482$	4.19792			0.191210
$483$	8.03574	+	9.81972i	0.365639	+	0.446813i
$484$	−20.1583			−0.916285
$485$	−5.72234			−0.259838
$486$		−	1.00000i		−	0.0453609i
$487$	0.237870			0.0107789			0.00538946	−	0.999985i	$-0.498284\pi$
$487$	0.237870			0.0107789			0.00538946	+	0.999985i	$0.498284\pi$
$488$	−0.286847			−0.0129849
$489$			5.25776i			0.237764i
$490$	7.27320	−	6.17656i	0.328570	−	0.279028i
$491$	10.0519			0.453635			0.226817	−	0.973937i	$-0.427168\pi$
$491$	10.0519			0.453635			0.226817	+	0.973937i	$0.427168\pi$
$492$	8.43338			0.380206
$493$	39.4696			1.77762
$494$		−	20.7489i		−	0.933539i
$495$			7.60899i			0.341999i
$496$		0			0
$497$	−35.7122	+	13.1178i	−1.60191	+	0.588414i
$498$		−	2.43943i		−	0.109314i
$499$	−32.7594			−1.46651			−0.733257	−	0.679952i	$-0.762001\pi$
$499$	−32.7594			−1.46651			−0.733257	+	0.679952i	$0.762001\pi$
$500$	−11.0985			−0.496339
$501$	11.5493			0.515984
$502$	3.60388			0.160849
$503$	−22.2376			−0.991527			−0.495764	−	0.868457i	$-0.665112\pi$
$503$	−22.2376			−0.991527			−0.495764	+	0.868457i	$0.665112\pi$
$504$	−2.48351	+	0.912244i	−0.110624	+	0.0406346i
$505$			2.59539i			0.115493i
$506$	8.77073	+	25.2926i	0.389907	+	1.12439i
$507$			6.65482i			0.295551i
$508$	9.49563			0.421301
$509$		−	2.93774i		−	0.130213i	−0.997878	−	0.0651066i	$-0.979261\pi$
$509$		−	2.93774i		−	0.130213i	0.997878	−	0.0651066i	$-0.0207387\pi$
$510$		−	6.77073i		−	0.299813i
$511$	−5.99821	−	16.3296i	−0.265345	−	0.722380i
$512$	1.00000			0.0441942
$513$		−	4.68017i		−	0.206635i
$514$			3.22145i			0.142092i
$515$	−18.7249			−0.825118
$516$	−5.42836			−0.238970
$517$	−34.2836			−1.50779
$518$	−3.28761	−	8.95026i	−0.144449	−	0.393252i
$519$	−4.67125			−0.205045
$520$			6.04331i			0.265017i
$521$	−15.5154			−0.679743			−0.339872	−	0.940472i	$-0.610384\pi$
$521$	−15.5154			−0.679743			−0.339872	+	0.940472i	$0.610384\pi$
$522$	−7.94635			−0.347802
$523$	29.6936			1.29841			0.649205	−	0.760613i	$-0.275102\pi$
$523$	29.6936			1.29841			0.649205	+	0.760613i	$0.275102\pi$
$524$			15.8927i			0.694275i
$525$	2.86613	+	7.80281i	0.125088	+	0.340543i
$526$		−	23.6915i		−	1.03300i
$527$		0			0
$528$	−5.58196			−0.242924
$529$	18.0623	−	14.2392i	0.785316	−	0.619096i
$530$			7.16175i			0.311086i
$531$		−	10.3797i		−	0.450442i
$532$	−11.6232	+	4.26945i	−0.503931	+	0.185104i
$533$	−37.3883			−1.61947
$534$		−	17.0536i		−	0.737983i
$535$		−	8.86675i		−	0.383343i
$536$			8.74539i			0.377743i
$537$			4.62888i			0.199751i
$538$		−	23.3538i		−	1.00685i
$539$	−25.2926	−	29.7832i	−1.08943	−	1.28285i
$540$			1.36314i			0.0586602i
$541$	−26.6963			−1.14776			−0.573881	−	0.818939i	$-0.694563\pi$
$541$	−26.6963			−1.14776			−0.573881	+	0.818939i	$0.694563\pi$
$542$		−	16.8668i		−	0.724489i
$543$			15.0095i			0.644121i
$544$	4.96702			0.212959
$545$			8.62888i			0.369621i
$546$	11.0103	−	4.04432i	0.471198	−	0.173081i
$547$	−11.4420			−0.489224			−0.244612	−	0.969621i	$-0.578661\pi$
$547$	−11.4420			−0.489224			−0.244612	+	0.969621i	$0.578661\pi$
$548$			16.4629i			0.703259i
$549$	0.286847			0.0122423
$550$			17.5377i			0.747810i
$551$	−37.1902			−1.58436
$552$	1.57126	+	4.53113i	0.0668774	+	0.192858i
$553$	−9.88491	−	26.9109i	−0.420349	−	1.14437i
$554$	−1.02594			−0.0435880
$555$	−4.91259			−0.208528
$556$			18.8131i			0.797853i
$557$		−	14.5240i		−	0.615402i	−0.951483	−	0.307701i	$-0.900440\pi$
$557$		−	14.5240i		−	0.615402i	0.951483	−	0.307701i	$-0.0995596\pi$
$558$		0			0
$559$	24.0660			1.01788
$560$	3.38537	−	1.24352i	0.143058	−	0.0525481i
$561$	−27.7257			−1.17058
$562$		−	26.3067i		−	1.10968i
$563$	38.0183			1.60228			0.801141	−	0.598476i	$-0.204227\pi$
$563$	38.0183			1.60228			0.801141	+	0.598476i	$0.204227\pi$
$564$	−6.14185			−0.258619
$565$			5.96546i			0.250969i
$566$	−31.5797			−1.32739
$567$	2.48351	−	0.912244i	0.104298	−	0.0383106i
$568$	−14.3797			−0.603360
$569$		−	31.5423i		−	1.32232i	−0.750244	−	0.661161i	$-0.770064\pi$
$569$		−	31.5423i		−	1.32232i	0.750244	−	0.661161i	$-0.229936\pi$
$570$			6.37972i			0.267217i
$571$		−	3.69023i		−	0.154431i	−0.997014	−	0.0772156i	$-0.975397\pi$
$571$		−	3.69023i		−	0.154431i	0.997014	−	0.0772156i	$-0.0246030\pi$
$572$	24.7469			1.03472
$573$	17.9554			0.750099
$574$	7.69329	+	20.9444i	0.321112	+	0.874201i
$575$	14.2361	−	4.93668i	0.593688	−	0.205874i
$576$	−1.00000			−0.0416667
$577$		−	19.3538i		−	0.805708i	−0.915264	−	0.402854i	$-0.868018\pi$
$577$		−	19.3538i		−	0.805708i	0.915264	−	0.402854i	$-0.131982\pi$
$578$	7.67125			0.319082
$579$			14.4334i			0.599831i
$580$	10.8320			0.449773
$581$	6.05835	−	2.22536i	0.251343	−	0.0923233i
$582$			4.19792i			0.174009i
$583$	29.3268			1.21459
$584$		−	6.57523i		−	0.272085i
$585$		−	6.04331i		−	0.249860i
$586$	4.77037			0.197062
$587$			12.4757i			0.514929i	0.966288	+	0.257464i	$0.0828870\pi$
$587$			12.4757i			0.514929i	−0.966288	+	0.257464i	$0.917113\pi$
$588$	−4.53113	−	5.33562i	−0.186861	−	0.220037i
$589$		0			0
$590$			14.1490i			0.582505i
$591$			20.3624i			0.837597i
$592$		−	3.60388i		−	0.148118i
$593$			16.5181i			0.678317i	0.940729	+	0.339159i	$0.110142\pi$
$593$			16.5181i			0.678317i	−0.940729	+	0.339159i	$0.889858\pi$
$594$	5.58196			0.229031
$595$	16.8152	−	6.17656i	0.689355	−	0.253214i
$596$			10.1327i			0.415053i
$597$			18.5253i			0.758189i
$598$	−6.96600	−	20.0882i	−0.284861	−	0.821467i
$599$	28.9549			1.18307			0.591534	−	0.806280i	$-0.298523\pi$
$599$	28.9549			1.18307			0.591534	+	0.806280i	$0.298523\pi$
$600$			3.14185i			0.128266i
$601$			21.0873i			0.860168i	0.902789	+	0.430084i	$0.141516\pi$
$601$			21.0873i			0.860168i	−0.902789	+	0.430084i	$0.858484\pi$
$602$	−4.95199	−	13.4814i	−0.201828	−	0.549460i
$603$		−	8.74539i		−	0.356140i
$604$	12.5216			0.509496
$605$	−27.4785			−1.11716
$606$	1.90398			0.0773440
$607$		−	29.8408i		−	1.21120i	−0.795769	−	0.605601i	$-0.792933\pi$
$607$		−	29.8408i		−	1.21120i	0.795769	−	0.605601i	$-0.207067\pi$
$608$	−4.68017			−0.189806
$609$	−7.24900	−	19.7348i	−0.293744	−	0.799695i
$610$	−0.391012			−0.0158316
$611$	27.2291			1.10157
$612$	−4.96702			−0.200780
$613$		−	15.0266i		−	0.606919i	−0.952844	−	0.303459i	$-0.901858\pi$
$613$		−	15.0266i		−	0.606919i	0.952844	−	0.303459i	$-0.0981417\pi$
$614$			28.9376i			1.16783i
$615$	11.4959			0.463558
$616$	−5.09211	−	13.8628i	−0.205167	−	0.558550i
$617$		−	22.7232i		−	0.914801i	−0.889261	−	0.457400i	$-0.848781\pi$
$617$		−	22.7232i		−	0.914801i	0.889261	−	0.457400i	$-0.151219\pi$
$618$			13.7366i			0.552567i
$619$	−15.6194			−0.627797			−0.313898	−	0.949457i	$-0.601635\pi$
$619$	−15.6194			−0.627797			−0.313898	+	0.949457i	$0.601635\pi$
$620$		0			0
$621$	−1.57126	−	4.53113i	−0.0630527	−	0.181828i
$622$		−	12.0882i		−	0.484693i
$623$	42.3528	−	15.5571i	1.69683	−	0.623281i
$624$	4.43338			0.177477
$625$	0.580491			0.0232196
$626$	−19.2944			−0.771158
$627$	26.1245			1.04331
$628$	−5.73940			−0.229027
$629$		−	17.9005i		−	0.713740i
$630$	−3.38537	+	1.24352i	−0.134876	+	0.0495428i
$631$			28.1162i			1.11929i	0.828733	+	0.559644i	$0.189062\pi$
$631$			28.1162i			1.11929i	−0.828733	+	0.559644i	$0.810938\pi$
$632$		−	10.8358i		−	0.431026i
$633$		−	28.3087i		−	1.12517i
$634$	30.6539			1.21742
$635$	12.9439			0.513662
$636$	5.25386			0.208329
$637$	20.0882	+	23.6548i	0.795923	+	0.937238i
$638$		−	44.3562i		−	1.75608i
$639$	14.3797			0.568853
$640$	1.36314			0.0538828
$641$		−	30.5778i		−	1.20775i	−0.797079	−	0.603875i	$-0.793623\pi$
$641$		−	30.5778i		−	1.20775i	0.797079	−	0.603875i	$-0.206377\pi$
$642$	−6.50466			−0.256718
$643$	−33.9988			−1.34078			−0.670390	−	0.742009i	$-0.733873\pi$
$643$	−33.9988			−1.34078			−0.670390	+	0.742009i	$0.733873\pi$
$644$	−9.81972	+	8.03574i	−0.386951	+	0.316653i
$645$	−7.39962			−0.291360
$646$	−23.2465			−0.914620
$647$			20.0882i			0.789749i	0.918735	+	0.394874i	$0.129212\pi$
$647$			20.0882i			0.789749i	−0.918735	+	0.394874i	$0.870788\pi$
$648$	1.00000			0.0392837
$649$	57.9392			2.27431
$650$		−	13.9290i		−	0.546341i
$651$		0			0
$652$	−5.25776			−0.205910
$653$	37.5128			1.46799			0.733995	−	0.679154i	$-0.237653\pi$
$653$	37.5128			1.46799			0.733995	+	0.679154i	$0.237653\pi$
$654$	6.33015			0.247529
$655$			21.6639i			0.846481i
$656$			8.43338i			0.329268i
$657$			6.57523i			0.256524i
$658$	−5.60287	−	15.2533i	−0.218422	−	0.594637i
$659$		−	38.7324i		−	1.50880i	−0.656415	−	0.754400i	$-0.727928\pi$
$659$		−	38.7324i		−	1.50880i	0.656415	−	0.754400i	$-0.272072\pi$
$660$	−7.60899			−0.296179
$661$	43.8446			1.70536			0.852680	−	0.522434i	$-0.174976\pi$
$661$	43.8446			1.70536			0.852680	+	0.522434i	$0.174976\pi$
$662$	−2.96624			−0.115286
$663$	22.0206			0.855211
$664$	2.43943			0.0946683
$665$	−15.8441	+	5.81986i	−0.614407	+	0.225685i
$666$			3.60388i			0.139647i
$667$	−36.0059	+	12.4858i	−1.39415	+	0.483452i
$668$			11.5493i			0.446855i
$669$	−3.02594			−0.116990
$670$			11.9212i			0.460556i
$671$			1.60117i			0.0618124i
$672$	−0.912244	−	2.48351i	−0.0351906	−	0.0958034i
$673$	16.7249			0.644698			0.322349	−	0.946621i	$-0.395528\pi$
$673$	16.7249			0.644698			0.322349	+	0.946621i	$0.395528\pi$
$674$		−	5.14536i		−	0.198192i
$675$		−	3.14185i		−	0.120930i
$676$	−6.65482			−0.255955
$677$	−38.1796			−1.46736			−0.733681	−	0.679494i	$-0.762199\pi$
$677$	−38.1796			−1.46736			−0.733681	+	0.679494i	$0.762199\pi$
$678$	4.37626			0.168069
$679$	−10.4256	+	3.82952i	−0.400096	+	0.146964i
$680$	6.77073			0.259646
$681$			1.18479i			0.0454013i
$682$		0			0
$683$	−37.7620			−1.44492			−0.722461	−	0.691411i	$-0.756989\pi$
$683$	−37.7620			−1.44492			−0.722461	+	0.691411i	$0.756989\pi$
$684$	4.68017			0.178951
$685$			22.4412i			0.857434i
$686$	9.11757	−	16.1205i	0.348110	−	0.615483i
$687$		−	2.34924i		−	0.0896289i
$688$		−	5.42836i		−	0.206954i
$689$	−23.2923			−0.887368
$690$	2.14185	+	6.17656i	0.0815389	+	0.235138i
$691$		−	12.2379i		−	0.465551i	−0.972531	−	0.232775i	$-0.925219\pi$
$691$		−	12.2379i		−	0.465551i	0.972531	−	0.232775i	$-0.0747807\pi$
$692$		−	4.67125i		−	0.177574i
$693$	5.09211	+	13.8628i	0.193433	+	0.526606i
$694$	19.9385			0.756856
$695$			25.6449i			0.972765i
$696$		−	7.94635i		−	0.301205i
$697$			41.8887i			1.58665i
$698$			6.32002i			0.239216i
$699$		−	6.39101i		−	0.241730i
$700$	−7.80281	+	2.86613i	−0.294919	+	0.108330i
$701$			8.67815i			0.327769i	0.986480	+	0.163885i	$0.0524025\pi$
$701$			8.67815i			0.327769i	−0.986480	+	0.163885i	$0.947598\pi$
$702$	−4.43338			−0.167327
$703$			16.8668i			0.636142i
$704$		−	5.58196i		−	0.210378i
$705$	−8.37220			−0.315315
$706$			3.45932i			0.130193i
$707$	1.73690	+	4.72855i	0.0653227	+	0.177836i
$708$	10.3797			0.390094
$709$		−	20.5523i		−	0.771858i	−0.922529	−	0.385929i	$-0.873881\pi$
$709$		−	20.5523i		−	0.771858i	0.922529	−	0.385929i	$-0.126119\pi$
$710$	−19.6016			−0.735633
$711$			10.8358i			0.406375i
$712$	17.0536			0.639112
$713$		0			0
$714$	−4.53113	−	12.3356i	−0.169573	−	0.461649i
$715$	33.7335			1.26156
$716$	−4.62888			−0.172989
$717$		−	12.0882i		−	0.451442i
$718$		−	33.3591i		−	1.24495i
$719$		−	27.9351i		−	1.04180i	−0.853617	−	0.520901i	$-0.825596\pi$
$719$		−	27.9351i		−	1.04180i	0.853617	−	0.520901i	$-0.174404\pi$
$720$	−1.36314			−0.0508012
$721$	−34.1150	+	12.5311i	−1.27051	+	0.466684i
$722$	2.90398			0.108075
$723$		−	4.19792i		−	0.156122i
$724$	−15.0095			−0.557825
$725$	−24.9662			−0.927223
$726$			20.1583i			0.748144i
$727$	2.54793			0.0944975			0.0472487	−	0.998883i	$-0.484955\pi$
$727$	2.54793			0.0944975			0.0472487	+	0.998883i	$0.484955\pi$
$728$	4.04432	+	11.0103i	0.149892	+	0.408070i
$729$	−1.00000			−0.0370370
$730$		−	8.96295i		−	0.331734i
$731$		−	26.9628i		−	0.997254i
$732$			0.286847i			0.0106022i
$733$	−22.3075			−0.823946			−0.411973	−	0.911196i	$-0.635160\pi$
$733$	−22.3075			−0.823946			−0.411973	+	0.911196i	$0.635160\pi$
$734$	−1.16649			−0.0430559
$735$	−6.17656	−	7.27320i	−0.227826	−	0.268276i
$736$	−4.53113	+	1.57126i	−0.167020	+	0.0579176i
$737$	48.8164			1.79818
$738$		−	8.43338i		−	0.310437i
$739$	8.84172			0.325248			0.162624	−	0.986688i	$-0.448004\pi$
$739$	8.84172			0.325248			0.162624	+	0.986688i	$0.448004\pi$
$740$		−	4.91259i		−	0.180590i
$741$	−20.7489			−0.762232
$742$	4.79280	+	13.0480i	0.175949	+	0.479007i
$743$			32.1121i			1.17808i	0.808104	+	0.589040i	$0.200494\pi$
$743$			32.1121i			1.17808i	−0.808104	+	0.589040i	$0.799506\pi$
$744$		0			0
$745$			13.8123i			0.506044i
$746$			1.55855i			0.0570624i
$747$	−2.43943			−0.0892541
$748$		−	27.7257i		−	1.01375i
$749$	−5.93383	−	16.1544i	−0.216817	−	0.590268i
$750$			11.0985i			0.405259i
$751$		−	50.5719i		−	1.84540i	−0.385523	−	0.922698i	$-0.625979\pi$
$751$		−	50.5719i		−	1.84540i	0.385523	−	0.922698i	$-0.374021\pi$
$752$		−	6.14185i		−	0.223970i
$753$		−	3.60388i		−	0.131333i
$754$			35.2291i			1.28297i
$755$	17.0686			0.621192
$756$	0.912244	+	2.48351i	0.0331780	+	0.0903243i
$757$			19.2806i			0.700765i	0.936607	+	0.350383i	$0.113948\pi$
$757$			19.2806i			0.700765i	−0.936607	+	0.350383i	$0.886052\pi$
$758$		−	38.7031i		−	1.40576i
$759$	25.2926	−	8.77073i	0.918062	−	0.318357i
$760$	−6.37972			−0.231417
$761$		−	49.3234i		−	1.78797i	−0.448096	−	0.893986i	$-0.647898\pi$
$761$		−	49.3234i		−	1.78797i	0.448096	−	0.893986i	$-0.352102\pi$
$762$		−	9.49563i		−	0.343991i
$763$	5.77464	+	15.7210i	0.209056	+	0.569138i
$764$			17.9554i			0.649604i
$765$	−6.77073			−0.244796
$766$	20.8391			0.752949
$767$	−46.0172			−1.66159
$768$		−	1.00000i		−	0.0360844i
$769$	30.3928			1.09599			0.547997	−	0.836480i	$-0.315391\pi$
$769$	30.3928			1.09599			0.547997	+	0.836480i	$0.315391\pi$
$770$	−6.94125	−	18.8970i	−0.250145	−	0.681000i
$771$	3.22145			0.116018
$772$	−14.4334			−0.519469
$773$	3.99922			0.143842			0.0719210	−	0.997410i	$-0.477087\pi$
$773$	3.99922			0.143842			0.0719210	+	0.997410i	$0.477087\pi$
$774$			5.42836i			0.195119i
$775$		0			0
$776$	−4.19792			−0.150696
$777$	−8.95026	+	3.28761i	−0.321089	+	0.117942i
$778$		−	3.49867i		−	0.125433i
$779$		−	39.4696i		−	1.41415i
$780$	6.04331			0.216385
$781$			80.2670i			2.87218i
$782$	−22.5062	+	7.80449i	−0.804820	+	0.279088i
$783$			7.94635i			0.283979i
$784$	5.33562	−	4.53113i	0.190558	−	0.161826i
$785$	−7.82361			−0.279236
$786$	15.8927			0.566874
$787$	36.0612			1.28544			0.642721	−	0.766101i	$-0.277806\pi$
$787$	36.0612			1.28544			0.642721	+	0.766101i	$0.277806\pi$
$788$	−20.3624			−0.725380
$789$	−23.6915			−0.843441
$790$		−	14.7707i		−	0.525519i
$791$	3.99222	+	10.8685i	0.141947	+	0.386439i
$792$			5.58196i			0.198346i
$793$		−	1.27170i		−	0.0451594i
$794$			1.31746i			0.0467550i
$795$	7.16175			0.254001
$796$	−18.5253			−0.656611
$797$	−46.7688			−1.65664			−0.828318	−	0.560258i	$-0.810702\pi$
$797$	−46.7688			−1.65664			−0.828318	+	0.560258i	$0.810702\pi$
$798$	4.26945	+	11.6232i	0.151137	+	0.411458i
$799$		−	30.5067i		−	1.07925i
$800$	−3.14185			−0.111081
$801$	−17.0536			−0.602560
$802$			12.3918i			0.437568i
$803$	−36.7027			−1.29521
$804$	8.74539			0.308426
$805$	−13.3856	+	10.9538i	−0.471782	+	0.386072i
$806$		0			0
$807$	−23.3538			−0.822092
$808$			1.90398i			0.0669818i
$809$	−25.3823			−0.892393			−0.446197	−	0.894935i	$-0.647222\pi$
$809$	−25.3823			−0.892393			−0.446197	+	0.894935i	$0.647222\pi$
$810$	1.36314			0.0478958
$811$		−	24.4869i		−	0.859851i	−0.902864	−	0.429926i	$-0.858540\pi$
$811$		−	24.4869i		−	0.859851i	0.902864	−	0.429926i	$-0.141460\pi$
$812$	19.7348	−	7.24900i	0.692556	−	0.254390i
$813$	−16.8668			−0.591543
$814$	−20.1167			−0.705090
$815$	−7.16706			−0.251051
$816$		−	4.96702i		−	0.173880i
$817$			25.4057i			0.888832i
$818$		−	29.7370i		−	1.03973i
$819$	−4.04432	−	11.0103i	−0.141320	−	0.384732i
$820$			11.4959i			0.401453i
$821$	19.9099			0.694860			0.347430	−	0.937706i	$-0.387054\pi$
$821$	19.9099			0.694860			0.347430	+	0.937706i	$0.387054\pi$
$822$	16.4629			0.574209
$823$	−53.3883			−1.86100			−0.930500	−	0.366292i	$-0.880627\pi$
$823$	−53.3883			−1.86100			−0.930500	+	0.366292i	$0.880627\pi$
$824$	−13.7366			−0.478537
$825$	17.5377			0.610584
$826$	9.46884	+	25.7781i	0.329463	+	0.896936i
$827$			57.0480i			1.98375i	0.127203	+	0.991877i	$0.459400\pi$
$827$			57.0480i			1.98375i	−0.127203	+	0.991877i	$0.540600\pi$
$828$	4.53113	−	1.57126i	0.157468	−	0.0546052i
$829$			6.83043i			0.237231i	0.992940	+	0.118615i	$0.0378456\pi$
$829$			6.83043i			0.237231i	−0.992940	+	0.118615i	$0.962154\pi$
$830$	3.32528			0.115422
$831$			1.02594i			0.0355895i
$832$			4.43338i			0.153700i
$833$	26.5021	−	22.5062i	0.918244	−	0.779793i
$834$	18.8131			0.651444
$835$			15.7433i			0.544819i
$836$			26.1245i			0.903535i
$837$		0			0
$838$	5.43221			0.187653
$839$	23.1680			0.799849			0.399925	−	0.916548i	$-0.369036\pi$
$839$	23.1680			0.799849			0.399925	+	0.916548i	$0.369036\pi$
$840$	−1.24352	−	3.38537i	−0.0429053	−	0.116806i
$841$	34.1444			1.17739
$842$			28.0436i			0.966447i
$843$	−26.3067			−0.906051
$844$	28.3087			0.974427
$845$	−9.07145			−0.312067
$846$			6.14185i			0.211161i
$847$	−50.0632	+	18.3893i	−1.72019	+	0.631862i
$848$			5.25386i			0.180418i
$849$			31.5797i			1.08381i
$850$	−15.6056			−0.535269
$851$	5.66264	+	16.3296i	0.194113	+	0.559772i
$852$			14.3797i			0.492641i
$853$			50.5138i			1.72956i	0.502153	+	0.864779i	$0.332542\pi$
$853$			50.5138i			1.72956i	−0.502153	+	0.864779i	$0.667458\pi$
$854$	−0.712386	+	0.261674i	−0.0243774	+	0.00895431i
$855$	6.37972			0.218182
$856$		−	6.50466i		−	0.222325i
$857$		−	9.99048i		−	0.341268i	−0.985334	−	0.170634i	$-0.945418\pi$
$857$		−	9.99048i		−	0.341268i	0.985334	−	0.170634i	$-0.0545816\pi$
$858$		−	24.7469i		−	0.844846i
$859$			43.0371i			1.46841i	0.678930	+	0.734203i	$0.262444\pi$
$859$			43.0371i			1.46841i	−0.678930	+	0.734203i	$0.737556\pi$
$860$		−	7.39962i		−	0.252325i
$861$	20.9444	−	7.69329i	0.713782	−	0.262187i
$862$		−	25.4049i		−	0.865295i
$863$	33.2578			1.13211			0.566054	−	0.824368i	$-0.308469\pi$
$863$	33.2578			1.13211			0.566054	+	0.824368i	$0.308469\pi$
$864$			1.00000i			0.0340207i
$865$		−	6.36756i		−	0.216503i
$866$	1.56183			0.0530733
$867$		−	7.67125i		−	0.260529i
$868$		0			0
$869$	−60.4851			−2.05182
$870$		−	10.8320i		−	0.367238i
$871$	−38.7716			−1.31373
$872$			6.33015i			0.214366i
$873$	4.19792			0.142078
$874$	21.2064	−	7.35378i	0.717319	−	0.248745i
$875$	−27.5632	+	10.1245i	−0.931805	+	0.342271i
$876$	−6.57523			−0.222156
$877$	−36.7076			−1.23953			−0.619763	−	0.784789i	$-0.712771\pi$
$877$	−36.7076			−1.23953			−0.619763	+	0.784789i	$0.712771\pi$
$878$			25.0431i			0.845165i
$879$		−	4.77037i		−	0.160900i
$880$		−	7.60899i		−	0.256499i
$881$	−13.8032			−0.465041			−0.232520	−	0.972592i	$-0.574697\pi$
$881$	−13.8032			−0.465041			−0.232520	+	0.972592i	$0.574697\pi$
$882$	−5.33562	+	4.53113i	−0.179660	+	0.152571i
$883$	28.2240			0.949813			0.474907	−	0.880036i	$-0.342482\pi$
$883$	28.2240			0.949813			0.474907	+	0.880036i	$0.342482\pi$
$884$			22.0206i			0.740635i
$885$	14.1490			0.475614
$886$	6.72490			0.225927
$887$			11.3885i			0.382387i	0.981552	+	0.191193i	$0.0612358\pi$
$887$			11.3885i			0.382387i	−0.981552	+	0.191193i	$0.938764\pi$
$888$	−3.60388			−0.120938
$889$	23.5825	−	8.66233i	0.790931	−	0.290525i
$890$	23.2465			0.779224
$891$		−	5.58196i		−	0.187003i
$892$		−	3.02594i		−	0.101316i
$893$			28.7449i			0.961912i
$894$	10.1327			0.338889
$895$	−6.30981			−0.210914
$896$	2.48351	−	0.912244i	0.0829682	−	0.0304759i
$897$	−20.0882	+	6.96600i	−0.670725	+	0.232588i
$898$	14.4757			0.483062
$899$		0			0
$900$	3.14185			0.104728
$901$			26.0960i			0.869384i
$902$	47.0748			1.56742
$903$	−13.4814	+	4.95199i	−0.448632	+	0.164792i
$904$			4.37626i			0.145552i
$905$	−20.4601			−0.680117
$906$		−	12.5216i		−	0.416001i
$907$			14.8305i			0.492439i	0.969214	+	0.246220i	$0.0791884\pi$
$907$			14.8305i			0.492439i	−0.969214	+	0.246220i	$0.920812\pi$
$908$	−1.18479			−0.0393186
$909$		−	1.90398i		−	0.0631511i
$910$	5.51297	+	15.0086i	0.182753	+	0.497530i
$911$			40.6152i			1.34564i	0.739805	+	0.672821i	$0.234918\pi$
$911$			40.6152i			1.34564i	−0.739805	+	0.672821i	$0.765082\pi$
$912$			4.68017i			0.154976i
$913$		−	13.6168i		−	0.450651i
$914$			0.880885i			0.0291371i
$915$			0.391012i			0.0129265i
$916$	2.34924			0.0776209
$917$	14.4980	+	39.4696i	0.478766	+	1.30340i
$918$			4.96702i			0.163936i
$919$			40.4132i			1.33311i	0.745456	+	0.666555i	$0.232232\pi$
$919$			40.4132i			1.33311i	−0.745456	+	0.666555i	$0.767768\pi$
$920$	−6.17656	+	2.14185i	−0.203635	+	0.0706148i
$921$	28.9376			0.953527
$922$		−	22.2724i		−	0.733503i
$923$		−	63.7507i		−	2.09838i
$924$	−13.8628	+	5.09211i	−0.456054	+	0.167518i
$925$			11.3228i			0.372293i
$926$	6.46969			0.212607
$927$	13.7366			0.451169
$928$	7.94635			0.260852
$929$		−	18.9836i		−	0.622831i	−0.950274	−	0.311415i	$-0.899197\pi$
$929$		−	18.9836i		−	0.622831i	0.950274	−	0.311415i	$-0.100803\pi$
$930$		0			0
$931$	−24.9716	+	21.2064i	−0.818412	+	0.695013i
$932$	6.39101			0.209345
$933$	−12.0882			−0.395750
$934$	24.0863			0.788129
$935$		−	37.7940i		−	1.23599i
$936$		−	4.43338i		−	0.144909i
$937$	46.8748			1.53133			0.765667	−	0.643237i	$-0.222409\pi$
$937$	46.8748			1.53133			0.765667	+	0.643237i	$0.222409\pi$
$938$	7.97793	+	21.7193i	0.260489	+	0.709159i
$939$			19.2944i			0.629648i
$940$		−	8.37220i		−	0.273071i
$941$	−32.6198			−1.06338			−0.531688	−	0.846940i	$-0.678442\pi$
$941$	−32.6198			−1.06338			−0.531688	+	0.846940i	$0.678442\pi$
$942$			5.73940i			0.187000i
$943$	−13.2511	−	38.2127i	−0.431514	−	1.24438i
$944$			10.3797i			0.337831i
$945$	1.24352	+	3.38537i	0.0404515	+	0.110126i
$946$	−30.3009			−0.985168
$947$	−41.4731			−1.34769			−0.673847	−	0.738871i	$-0.735359\pi$
$947$	−41.4731			−1.34769			−0.673847	+	0.738871i	$0.735359\pi$
$948$	−10.8358			−0.351931
$949$	29.1505			0.946264
$950$	14.7044			0.477074
$951$		−	30.6539i		−	0.994021i
$952$	12.3356	−	4.53113i	0.399800	−	0.146855i
$953$			21.2345i			0.687853i	0.938997	+	0.343926i	$0.111757\pi$
$953$			21.2345i			0.687853i	−0.938997	+	0.343926i	$0.888243\pi$
$954$		−	5.25386i		−	0.170100i
$955$			24.4757i			0.792016i
$956$	12.0882			0.390960
$957$	−44.3562			−1.43383
$958$	−10.9392			−0.353430
$959$	15.0182	+	40.8857i	0.484962	+	1.32027i
$960$		−	1.36314i		−	0.0439951i
$961$	31.0000			1.00000
$962$	15.9773			0.515130
$963$			6.50466i			0.209610i
$964$	4.19792			0.135206
$965$	−19.6747			−0.633351
$966$	8.03574	+	9.81972i	0.258546	+	0.315944i
$967$	18.3009			0.588518			0.294259	−	0.955726i	$-0.404927\pi$
$967$	18.3009			0.588518			0.294259	+	0.955726i	$0.404927\pi$
$968$	−20.1583			−0.647912
$969$			23.2465i			0.746784i
$970$	−5.72234			−0.183733
$971$	−34.0033			−1.09122			−0.545609	−	0.838040i	$-0.683702\pi$
$971$	−34.0033			−1.09122			−0.545609	+	0.838040i	$0.683702\pi$
$972$		−	1.00000i		−	0.0320750i
$973$	17.1621	+	46.7225i	0.550193	+	1.49785i
$974$	0.237870			0.00762184
$975$	−13.9290			−0.446085
$976$	−0.286847			−0.00918174
$977$		−	11.2273i		−	0.359194i	−0.983740	−	0.179597i	$-0.942521\pi$
$977$		−	11.2273i		−	0.359194i	0.983740	−	0.179597i	$-0.0574793\pi$
$978$			5.25776i			0.168125i
$979$		−	95.1927i		−	3.04237i
$980$	7.27320	−	6.17656i	0.232334	−	0.197303i
$981$		−	6.33015i		−	0.202106i
$982$	10.0519			0.320768
$983$	−26.5087			−0.845496			−0.422748	−	0.906247i	$-0.638934\pi$
$983$	−26.5087			−0.845496			−0.422748	+	0.906247i	$0.638934\pi$
$984$	8.43338			0.268846
$985$	−27.7568			−0.884404
$986$	39.4696			1.25697
$987$	−15.2533	+	5.60287i	−0.485519	+	0.178341i
$988$		−	20.7489i		−	0.660112i
$989$	8.52939	+	24.5966i	0.271219	+	0.782127i
$990$			7.60899i			0.241830i
$991$	−52.0344			−1.65293			−0.826464	−	0.562990i	$-0.809651\pi$
$991$	−52.0344			−1.65293			−0.826464	+	0.562990i	$0.809651\pi$
$992$		0			0
$993$			2.96624i			0.0941308i
$994$	−35.7122	+	13.1178i	−1.13272	+	0.416072i
$995$	−25.2525			−0.800559
$996$		−	2.43943i		−	0.0772963i
$997$		−	47.4479i		−	1.50269i	−0.659910	−	0.751345i	$-0.729405\pi$
$997$		−	47.4479i		−	1.50269i	0.659910	−	0.751345i	$-0.270595\pi$
$998$	−32.7594			−1.03698
$999$	3.60388			0.114022

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.g.e.643.6	yes	16
3.2	odd	2		2898.2.g.j.2575.5		16
7.6	odd	2	inner	966.2.g.e.643.11	yes	16
21.20	even	2		2898.2.g.j.2575.11		16
23.22	odd	2	inner	966.2.g.e.643.3	✓	16
69.68	even	2		2898.2.g.j.2575.12		16
161.160	even	2	inner	966.2.g.e.643.14	yes	16
483.482	odd	2		2898.2.g.j.2575.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.g.e.643.3	✓	16	23.22	odd	2	inner
966.2.g.e.643.6	yes	16	1.1	even	1	trivial
966.2.g.e.643.11	yes	16	7.6	odd	2	inner
966.2.g.e.643.14	yes	16	161.160	even	2	inner
2898.2.g.j.2575.5		16	3.2	odd	2
2898.2.g.j.2575.6		16	483.482	odd	2
2898.2.g.j.2575.11		16	21.20	even	2
2898.2.g.j.2575.12		16	69.68	even	2

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.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +1.36314 q^{5} -1.00000i q^{6} +(2.48351 - 0.912244i) q^{7} +1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +1.36314 q^{5} -1.00000i q^{6} +(2.48351 - 0.912244i) q^{7} +1.00000 q^{8} -1.00000 q^{9} +1.36314 q^{10} -5.58196i q^{11} -1.00000i q^{12} +4.43338i q^{13} +(2.48351 - 0.912244i) q^{14} -1.36314i q^{15} +1.00000 q^{16} +4.96702 q^{17} -1.00000 q^{18} -4.68017 q^{19} +1.36314 q^{20} +(-0.912244 - 2.48351i) q^{21} -5.58196i q^{22} +(-4.53113 + 1.57126i) q^{23} -1.00000i q^{24} -3.14185 q^{25} +4.43338i q^{26} +1.00000i q^{27} +(2.48351 - 0.912244i) q^{28} +7.94635 q^{29} -1.36314i q^{30} +1.00000 q^{32} -5.58196 q^{33} +4.96702 q^{34} +(3.38537 - 1.24352i) q^{35} -1.00000 q^{36} -3.60388i q^{37} -4.68017 q^{38} +4.43338 q^{39} +1.36314 q^{40} +8.43338i q^{41} +(-0.912244 - 2.48351i) q^{42} -5.42836i q^{43} -5.58196i q^{44} -1.36314 q^{45} +(-4.53113 + 1.57126i) q^{46} -6.14185i q^{47} -1.00000i q^{48} +(5.33562 - 4.53113i) q^{49} -3.14185 q^{50} -4.96702i q^{51} +4.43338i q^{52} +5.25386i q^{53} +1.00000i q^{54} -7.60899i q^{55} +(2.48351 - 0.912244i) q^{56} +4.68017i q^{57} +7.94635 q^{58} +10.3797i q^{59} -1.36314i q^{60} -0.286847 q^{61} +(-2.48351 + 0.912244i) q^{63} +1.00000 q^{64} +6.04331i q^{65} -5.58196 q^{66} +8.74539i q^{67} +4.96702 q^{68} +(1.57126 + 4.53113i) q^{69} +(3.38537 - 1.24352i) q^{70} -14.3797 q^{71} -1.00000 q^{72} -6.57523i q^{73} -3.60388i q^{74} +3.14185i q^{75} -4.68017 q^{76} +(-5.09211 - 13.8628i) q^{77} +4.43338 q^{78} -10.8358i q^{79} +1.36314 q^{80} +1.00000 q^{81} +8.43338i q^{82} +2.43943 q^{83} +(-0.912244 - 2.48351i) q^{84} +6.77073 q^{85} -5.42836i q^{86} -7.94635i q^{87} -5.58196i q^{88} +17.0536 q^{89} -1.36314 q^{90} +(4.04432 + 11.0103i) q^{91} +(-4.53113 + 1.57126i) q^{92} -6.14185i q^{94} -6.37972 q^{95} -1.00000i q^{96} -4.19792 q^{97} +(5.33562 - 4.53113i) q^{98} +5.58196i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} + 16 q^{4} + 16 q^{8} - 16 q^{9}+O(q^{10}) \) 16 * q + 16 * q^2 + 16 * q^4 + 16 * q^8 - 16 * q^9	\( 16 q + 16 q^{2} + 16 q^{4} + 16 q^{8} - 16 q^{9} + 16 q^{16} - 16 q^{18} - 8 q^{23} + 36 q^{25} + 20 q^{29} + 16 q^{32} - 16 q^{35} - 16 q^{36} - 4 q^{39} - 8 q^{46} + 36 q^{50} + 20 q^{58} + 16 q^{64} - 16 q^{70} - 48 q^{71} - 16 q^{72} + 20 q^{77} - 4 q^{78} + 16 q^{81} - 32 q^{85} - 8 q^{92} + 80 q^{95}+O(q^{100}) \) 16 * q + 16 * q^2 + 16 * q^4 + 16 * q^8 - 16 * q^9 + 16 * q^16 - 16 * q^18 - 8 * q^23 + 36 * q^25 + 20 * q^29 + 16 * q^32 - 16 * q^35 - 16 * q^36 - 4 * q^39 - 8 * q^46 + 36 * q^50 + 20 * q^58 + 16 * q^64 - 16 * q^70 - 48 * q^71 - 16 * q^72 + 20 * q^77 - 4 * q^78 + 16 * q^81 - 32 * q^85 - 8 * q^92 + 80 * q^95

Introduction

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