LMFDB - Embedded newform 966.2.h.a.827.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(827,966)]

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, 0, 1]))

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

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

chi := DirichletCharacter("966.827");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.h (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			827.8
Character	$\chi$	$=$	966.827
Dual form			966.2.h.a.827.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.696580 + 1.58580i) q^{3} -1.00000 q^{4} -3.16093 q^{5} +(1.58580 - 0.696580i) q^{6} +1.00000i q^{7} +1.00000i q^{8} +(-2.02955 + 2.20928i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.696580 + 1.58580i) q^{3} -1.00000 q^{4} -3.16093 q^{5} +(1.58580 - 0.696580i) q^{6} +1.00000i q^{7} +1.00000i q^{8} +(-2.02955 + 2.20928i) q^{9} +3.16093i q^{10} -1.43736 q^{11} +(-0.696580 - 1.58580i) q^{12} +2.73688 q^{13} +1.00000 q^{14} +(-2.20184 - 5.01261i) q^{15} +1.00000 q^{16} -0.955308 q^{17} +(2.20928 + 2.02955i) q^{18} -7.49148i q^{19} +3.16093 q^{20} +(-1.58580 + 0.696580i) q^{21} +1.43736i q^{22} +(-1.60694 - 4.51860i) q^{23} +(-1.58580 + 0.696580i) q^{24} +4.99145 q^{25} -2.73688i q^{26} +(-4.91723 - 1.67954i) q^{27} -1.00000i q^{28} -8.82668i q^{29} +(-5.01261 + 2.20184i) q^{30} -2.94042 q^{31} -1.00000i q^{32} +(-1.00124 - 2.27938i) q^{33} +0.955308i q^{34} -3.16093i q^{35} +(2.02955 - 2.20928i) q^{36} -2.44558i q^{37} -7.49148 q^{38} +(1.90645 + 4.34016i) q^{39} -3.16093i q^{40} +3.05089i q^{41} +(0.696580 + 1.58580i) q^{42} -2.41150i q^{43} +1.43736 q^{44} +(6.41527 - 6.98336i) q^{45} +(-4.51860 + 1.60694i) q^{46} +8.46091i q^{47} +(0.696580 + 1.58580i) q^{48} -1.00000 q^{49} -4.99145i q^{50} +(-0.665448 - 1.51493i) q^{51} -2.73688 q^{52} -12.4211 q^{53} +(-1.67954 + 4.91723i) q^{54} +4.54340 q^{55} -1.00000 q^{56} +(11.8800 - 5.21841i) q^{57} -8.82668 q^{58} +4.28580i q^{59} +(2.20184 + 5.01261i) q^{60} -3.13255i q^{61} +2.94042i q^{62} +(-2.20928 - 2.02955i) q^{63} -1.00000 q^{64} -8.65107 q^{65} +(-2.27938 + 1.00124i) q^{66} +2.67907i q^{67} +0.955308 q^{68} +(6.04626 - 5.69586i) q^{69} -3.16093 q^{70} -12.6591i q^{71} +(-2.20928 - 2.02955i) q^{72} -4.14418 q^{73} -2.44558 q^{74} +(3.47694 + 7.91546i) q^{75} +7.49148i q^{76} -1.43736i q^{77} +(4.34016 - 1.90645i) q^{78} +4.98085i q^{79} -3.16093 q^{80} +(-0.761822 - 8.96770i) q^{81} +3.05089 q^{82} -5.69587 q^{83} +(1.58580 - 0.696580i) q^{84} +3.01966 q^{85} -2.41150 q^{86} +(13.9974 - 6.14848i) q^{87} -1.43736i q^{88} +11.4395 q^{89} +(-6.98336 - 6.41527i) q^{90} +2.73688i q^{91} +(1.60694 + 4.51860i) q^{92} +(-2.04824 - 4.66294i) q^{93} +8.46091 q^{94} +23.6800i q^{95} +(1.58580 - 0.696580i) q^{96} -4.71539i q^{97} +1.00000i q^{98} +(2.91721 - 3.17554i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{3} - 24 q^{4} - 4 q^{5} - 4 q^{9}+O(q^{10}) $ 24 * q + 4 * q^3 - 24 * q^4 - 4 * q^5 - 4 * q^9	$ 24 q + 4 q^{3} - 24 q^{4} - 4 q^{5} - 4 q^{9} - 4 q^{12} + 8 q^{13} + 24 q^{14} - 4 q^{15} + 24 q^{16} + 32 q^{17} + 4 q^{18} + 4 q^{20} - 8 q^{23} - 12 q^{25} + 16 q^{27} - 4 q^{30} - 16 q^{31} + 20 q^{33} + 4 q^{36} - 8 q^{39} + 4 q^{42} + 24 q^{45} - 4 q^{46} + 4 q^{48} - 24 q^{49} + 24 q^{51} - 8 q^{52} + 24 q^{53} - 12 q^{54} + 16 q^{55} - 24 q^{56} + 4 q^{57} + 4 q^{58} + 4 q^{60} - 4 q^{63} - 24 q^{64} - 12 q^{66} - 32 q^{68} - 24 q^{69} - 4 q^{70} - 4 q^{72} - 32 q^{73} - 16 q^{74} + 48 q^{75} + 12 q^{78} - 4 q^{80} - 8 q^{81} - 8 q^{82} + 16 q^{83} - 16 q^{85} + 16 q^{86} + 20 q^{87} + 24 q^{89} - 28 q^{90} + 8 q^{92} + 16 q^{93} + 8 q^{94} - 48 q^{99}+O(q^{100}) $ 24 * q + 4 * q^3 - 24 * q^4 - 4 * q^5 - 4 * q^9 - 4 * q^12 + 8 * q^13 + 24 * q^14 - 4 * q^15 + 24 * q^16 + 32 * q^17 + 4 * q^18 + 4 * q^20 - 8 * q^23 - 12 * q^25 + 16 * q^27 - 4 * q^30 - 16 * q^31 + 20 * q^33 + 4 * q^36 - 8 * q^39 + 4 * q^42 + 24 * q^45 - 4 * q^46 + 4 * q^48 - 24 * q^49 + 24 * q^51 - 8 * q^52 + 24 * q^53 - 12 * q^54 + 16 * q^55 - 24 * q^56 + 4 * q^57 + 4 * q^58 + 4 * q^60 - 4 * q^63 - 24 * q^64 - 12 * q^66 - 32 * q^68 - 24 * q^69 - 4 * q^70 - 4 * q^72 - 32 * q^73 - 16 * q^74 + 48 * q^75 + 12 * q^78 - 4 * q^80 - 8 * q^81 - 8 * q^82 + 16 * q^83 - 16 * q^85 + 16 * q^86 + 20 * q^87 + 24 * q^89 - 28 * q^90 + 8 * q^92 + 16 * q^93 + 8 * q^94 - 48 * 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
$3$	0.696580	+	1.58580i	0.402170	+	0.915565i
$3$	0.696580	+	1.58580i	0.402170	+	0.915565i
$4$	−1.00000			−0.500000
$5$	−3.16093			−1.41361			−0.706804	−	0.707409i	$-0.749864\pi$
$5$	−3.16093			−1.41361			−0.706804	+	0.707409i	$0.749864\pi$
$6$	1.58580	−	0.696580i	0.647402	−	0.284377i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$			1.00000i			0.353553i
$9$	−2.02955	+	2.20928i	−0.676518	+	0.736426i
$10$			3.16093i			0.999572i
$11$	−1.43736			−0.433382			−0.216691	−	0.976240i	$-0.569526\pi$
$11$	−1.43736			−0.433382			−0.216691	+	0.976240i	$0.569526\pi$
$12$	−0.696580	−	1.58580i	−0.201085	−	0.457782i
$13$	2.73688			0.759074			0.379537	−	0.925177i	$-0.376083\pi$
$13$	2.73688			0.759074			0.379537	+	0.925177i	$0.376083\pi$
$14$	1.00000			0.267261
$15$	−2.20184	−	5.01261i	−0.568512	−	1.29425i
$16$	1.00000			0.250000
$17$	−0.955308			−0.231696			−0.115848	−	0.993267i	$-0.536959\pi$
$17$	−0.955308			−0.231696			−0.115848	+	0.993267i	$0.536959\pi$
$18$	2.20928	+	2.02955i	0.520732	+	0.478370i
$19$		−	7.49148i		−	1.71866i	−0.511418	−	0.859332i	$-0.670880\pi$
$19$		−	7.49148i		−	1.71866i	0.511418	−	0.859332i	$-0.329120\pi$
$20$	3.16093			0.706804
$21$	−1.58580	+	0.696580i	−0.346051	+	0.152006i
$22$			1.43736i			0.306447i
$23$	−1.60694	−	4.51860i	−0.335070	−	0.942193i
$23$	−1.60694	−	4.51860i	−0.335070	−	0.942193i
$24$	−1.58580	+	0.696580i	−0.323701	+	0.142189i
$25$	4.99145			0.998290
$26$		−	2.73688i		−	0.536746i
$27$	−4.91723	−	1.67954i	−0.946321	−	0.323227i
$28$		−	1.00000i		−	0.188982i
$29$		−	8.82668i		−	1.63907i	−0.573027	−	0.819537i	$-0.694231\pi$
$29$		−	8.82668i		−	1.63907i	0.573027	−	0.819537i	$-0.305769\pi$
$30$	−5.01261	+	2.20184i	−0.915173	+	0.401998i
$31$	−2.94042			−0.528115			−0.264058	−	0.964507i	$-0.585061\pi$
$31$	−2.94042			−0.528115			−0.264058	+	0.964507i	$0.585061\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−1.00124	−	2.27938i	−0.174293	−	0.396789i
$34$			0.955308i			0.163834i
$35$		−	3.16093i		−	0.534294i
$36$	2.02955	−	2.20928i	0.338259	−	0.368213i
$37$		−	2.44558i		−	0.402051i	−0.979586	−	0.201026i	$-0.935573\pi$
$37$		−	2.44558i		−	0.402051i	0.979586	−	0.201026i	$-0.0644275\pi$
$38$	−7.49148			−1.21528
$39$	1.90645	+	4.34016i	0.305277	+	0.694981i
$40$		−	3.16093i		−	0.499786i
$41$			3.05089i			0.476469i	0.971208	+	0.238234i	$0.0765686\pi$
$41$			3.05089i			0.476469i	−0.971208	+	0.238234i	$0.923431\pi$
$42$	0.696580	+	1.58580i	0.107485	+	0.244695i
$43$		−	2.41150i		−	0.367750i	−0.982950	−	0.183875i	$-0.941136\pi$
$43$		−	2.41150i		−	0.367750i	0.982950	−	0.183875i	$-0.0588642\pi$
$44$	1.43736			0.216691
$45$	6.41527	−	6.98336i	0.956332	−	1.04102i
$46$	−4.51860	+	1.60694i	−0.666231	+	0.236930i
$47$			8.46091i			1.23415i	0.786904	+	0.617075i	$0.211683\pi$
$47$			8.46091i			1.23415i	−0.786904	+	0.617075i	$0.788317\pi$
$48$	0.696580	+	1.58580i	0.100543	+	0.228891i
$49$	−1.00000			−0.142857
$50$		−	4.99145i		−	0.705897i
$51$	−0.665448	−	1.51493i	−0.0931813	−	0.212133i
$52$	−2.73688			−0.379537
$53$	−12.4211			−1.70616			−0.853082	−	0.521777i	$-0.825269\pi$
$53$	−12.4211			−1.70616			−0.853082	+	0.521777i	$0.825269\pi$
$54$	−1.67954	+	4.91723i	−0.228556	+	0.669150i
$55$	4.54340			0.612632
$56$	−1.00000			−0.133631
$57$	11.8800	−	5.21841i	1.57355	−	0.691196i
$58$	−8.82668			−1.15900
$59$			4.28580i			0.557964i	0.960296	+	0.278982i	$0.0899970\pi$
$59$			4.28580i			0.557964i	−0.960296	+	0.278982i	$0.910003\pi$
$60$	2.20184	+	5.01261i	0.284256	+	0.647125i
$61$		−	3.13255i		−	0.401082i	−0.979685	−	0.200541i	$-0.935730\pi$
$61$		−	3.13255i		−	0.401082i	0.979685	−	0.200541i	$-0.0642700\pi$
$62$			2.94042i			0.373434i
$63$	−2.20928	−	2.02955i	−0.278343	−	0.255700i
$64$	−1.00000			−0.125000
$65$	−8.65107			−1.07303
$66$	−2.27938	+	1.00124i	−0.280572	+	0.123244i
$67$			2.67907i			0.327301i	0.986518	+	0.163650i	$0.0523269\pi$
$67$			2.67907i			0.327301i	−0.986518	+	0.163650i	$0.947673\pi$
$68$	0.955308			0.115848
$69$	6.04626	−	5.69586i	0.727884	−	0.685700i
$70$	−3.16093			−0.377803
$71$		−	12.6591i		−	1.50235i	−0.660101	−	0.751177i	$-0.729487\pi$
$71$		−	12.6591i		−	1.50235i	0.660101	−	0.751177i	$-0.270513\pi$
$72$	−2.20928	−	2.02955i	−0.260366	−	0.239185i
$73$	−4.14418			−0.485040			−0.242520	−	0.970146i	$-0.577974\pi$
$73$	−4.14418			−0.485040			−0.242520	+	0.970146i	$0.577974\pi$
$74$	−2.44558			−0.284293
$75$	3.47694	+	7.91546i	0.401483	+	0.913999i
$76$			7.49148i			0.859332i
$77$		−	1.43736i		−	0.163803i
$78$	4.34016	−	1.90645i	0.491426	−	0.215863i
$79$			4.98085i			0.560389i	0.959943	+	0.280195i	$0.0903990\pi$
$79$			4.98085i			0.560389i	−0.959943	+	0.280195i	$0.909601\pi$
$80$	−3.16093			−0.353402
$81$	−0.761822	−	8.96770i	−0.0846469	−	0.996411i
$82$	3.05089			0.336914
$83$	−5.69587			−0.625202			−0.312601	−	0.949884i	$-0.601200\pi$
$83$	−5.69587			−0.625202			−0.312601	+	0.949884i	$0.601200\pi$
$84$	1.58580	−	0.696580i	0.173025	−	0.0760031i
$85$	3.01966			0.327528
$86$	−2.41150			−0.260039
$87$	13.9974	−	6.14848i	1.50068	−	0.659187i
$88$		−	1.43736i		−	0.153224i
$89$	11.4395			1.21258			0.606290	−	0.795244i	$-0.292657\pi$
$89$	11.4395			1.21258			0.606290	+	0.795244i	$0.292657\pi$
$90$	−6.98336	−	6.41527i	−0.736111	−	0.676229i
$91$			2.73688i			0.286903i
$92$	1.60694	+	4.51860i	0.167535	+	0.471097i
$93$	−2.04824	−	4.66294i	−0.212392	−	0.483524i
$94$	8.46091			0.872676
$95$			23.6800i			2.42952i
$96$	1.58580	−	0.696580i	0.161851	−	0.0710944i
$97$		−	4.71539i		−	0.478776i	−0.970924	−	0.239388i	$-0.923053\pi$
$97$		−	4.71539i		−	0.478776i	0.970924	−	0.239388i	$-0.0769467\pi$
$98$			1.00000i			0.101015i
$99$	2.91721	−	3.17554i	0.293190	−	0.319153i
$100$	−4.99145			−0.499145
$101$		−	16.4580i		−	1.63763i	−0.574057	−	0.818815i	$-0.694631\pi$
$101$		−	16.4580i		−	1.63763i	0.574057	−	0.818815i	$-0.305369\pi$
$102$	−1.51493	+	0.665448i	−0.150001	+	0.0658892i
$103$		−	5.39758i		−	0.531839i	−0.963995	−	0.265920i	$-0.914324\pi$
$103$		−	5.39758i		−	0.531839i	0.963995	−	0.265920i	$-0.0856755\pi$
$104$			2.73688i			0.268373i
$105$	5.01261	−	2.20184i	0.489181	−	0.214877i
$106$			12.4211i			1.20644i
$107$	17.5408			1.69573			0.847865	−	0.530213i	$-0.177888\pi$
$107$	17.5408			1.69573			0.847865	+	0.530213i	$0.177888\pi$
$108$	4.91723	+	1.67954i	0.473161	+	0.161614i
$109$			3.72374i			0.356670i	0.983970	+	0.178335i	$0.0570710\pi$
$109$			3.72374i			0.356670i	−0.983970	+	0.178335i	$0.942929\pi$
$110$		−	4.54340i		−	0.433196i
$111$	3.87822	−	1.70354i	0.368104	−	0.161693i
$112$			1.00000i			0.0944911i
$113$	−17.5621			−1.65210			−0.826051	−	0.563595i	$-0.809418\pi$
$113$	−17.5621			−1.65210			−0.826051	+	0.563595i	$0.809418\pi$
$114$	−5.21841	−	11.8800i	−0.488749	−	1.11267i
$115$	5.07941	+	14.2830i	0.473658	+	1.33189i
$116$			8.82668i			0.819537i
$117$	−5.55464	+	6.04653i	−0.513527	+	0.559002i
$118$	4.28580			0.394540
$119$		−	0.955308i		−	0.0875729i
$120$	5.01261	−	2.20184i	0.457587	−	0.200999i
$121$	−8.93398			−0.812180
$122$	−3.13255			−0.283608
$123$	−4.83811	+	2.12519i	−0.436238	+	0.191622i
$124$	2.94042			0.264058
$125$	0.0270313			0.00241776
$126$	−2.02955	+	2.20928i	−0.180807	+	0.196818i
$127$	−7.88472			−0.699655			−0.349828	−	0.936814i	$-0.613760\pi$
$127$	−7.88472			−0.699655			−0.349828	+	0.936814i	$0.613760\pi$
$128$			1.00000i			0.0883883i
$129$	3.82417	−	1.67980i	0.336699	−	0.147898i
$130$			8.65107i			0.758749i
$131$			10.5721i			0.923688i	0.886961	+	0.461844i	$0.152812\pi$
$131$			10.5721i			0.923688i	−0.886961	+	0.461844i	$0.847188\pi$
$132$	1.00124	+	2.27938i	0.0871466	+	0.198394i
$133$	7.49148			0.649594
$134$	2.67907			0.231437
$135$	15.5430	+	5.30889i	1.33773	+	0.456917i
$136$		−	0.955308i		−	0.0819170i
$137$	−4.41592			−0.377277			−0.188639	−	0.982047i	$-0.560407\pi$
$137$	−4.41592			−0.377277			−0.188639	+	0.982047i	$0.560407\pi$
$138$	−5.69586	−	6.04626i	−0.484863	−	0.514692i
$139$	11.6934			0.991825			0.495913	−	0.868372i	$-0.334834\pi$
$139$	11.6934			0.991825			0.495913	+	0.868372i	$0.334834\pi$
$140$			3.16093i			0.267147i
$141$	−13.4174	+	5.89370i	−1.12994	+	0.496339i
$142$	−12.6591			−1.06232
$143$	−3.93389			−0.328968
$144$	−2.02955	+	2.20928i	−0.169129	+	0.184107i
$145$			27.9005i			2.31701i
$146$			4.14418i			0.342975i
$147$	−0.696580	−	1.58580i	−0.0574529	−	0.130795i
$148$			2.44558i			0.201026i
$149$	3.18337			0.260792			0.130396	−	0.991462i	$-0.458375\pi$
$149$	3.18337			0.260792			0.130396	+	0.991462i	$0.458375\pi$
$150$	7.91546	−	3.47694i	0.646295	−	0.283891i
$151$	−5.57408			−0.453613			−0.226806	−	0.973940i	$-0.572828\pi$
$151$	−5.57408			−0.453613			−0.226806	+	0.973940i	$0.572828\pi$
$152$	7.49148			0.607639
$153$	1.93885	−	2.11054i	0.156747	−	0.170627i
$154$	−1.43736			−0.115826
$155$	9.29446			0.746549
$156$	−1.90645	−	4.34016i	−0.152638	−	0.347491i
$157$			24.0388i			1.91850i	0.282554	+	0.959251i	$0.408818\pi$
$157$			24.0388i			1.91850i	−0.282554	+	0.959251i	$0.591182\pi$
$158$	4.98085			0.396255
$159$	−8.65226	−	19.6974i	−0.686169	−	1.56210i
$160$			3.16093i			0.249893i
$161$	4.51860	−	1.60694i	0.356116	−	0.126645i
$162$	−8.96770	+	0.761822i	−0.704569	+	0.0598544i
$163$	−23.8869			−1.87097			−0.935485	−	0.353368i	$-0.885037\pi$
$163$	−23.8869			−1.87097			−0.935485	+	0.353368i	$0.885037\pi$
$164$		−	3.05089i		−	0.238234i
$165$	3.16484	+	7.20495i	0.246382	+	0.560904i
$166$			5.69587i			0.442085i
$167$		−	4.36843i		−	0.338039i	−0.985613	−	0.169020i	$-0.945940\pi$
$167$		−	4.36843i		−	0.338039i	0.985613	−	0.169020i	$-0.0540601\pi$
$168$	−0.696580	−	1.58580i	−0.0537423	−	0.122347i
$169$	−5.50950			−0.423807
$170$		−	3.01966i		−	0.231597i
$171$	16.5508	+	15.2044i	1.26567	+	1.16271i
$172$			2.41150i			0.183875i
$173$		−	7.06727i		−	0.537315i	−0.963236	−	0.268657i	$-0.913420\pi$
$173$		−	7.06727i		−	0.537315i	0.963236	−	0.268657i	$-0.0865799\pi$
$174$	−6.14848	−	13.9974i	−0.466115	−	1.06114i
$175$			4.99145i			0.377318i
$176$	−1.43736			−0.108345
$177$	−6.79644	+	2.98540i	−0.510852	+	0.224397i
$178$		−	11.4395i		−	0.857423i
$179$			9.61154i			0.718400i	0.933261	+	0.359200i	$0.116950\pi$
$179$			9.61154i			0.718400i	−0.933261	+	0.359200i	$0.883050\pi$
$180$	−6.41527	+	6.98336i	−0.478166	+	0.520509i
$181$			18.0382i			1.34077i	0.742012	+	0.670386i	$0.233872\pi$
$181$			18.0382i			1.34077i	−0.742012	+	0.670386i	$0.766128\pi$
$182$	2.73688			0.202871
$183$	4.96761	−	2.18207i	0.367216	−	0.161303i
$184$	4.51860	−	1.60694i	0.333116	−	0.118465i
$185$			7.73031i			0.568343i
$186$	−4.66294	+	2.04824i	−0.341903	+	0.150184i
$187$	1.37312			0.100413
$188$		−	8.46091i		−	0.617075i
$189$	1.67954	−	4.91723i	0.122168	−	0.357676i
$190$	23.6800			1.71793
$191$	−2.22287			−0.160841			−0.0804205	−	0.996761i	$-0.525626\pi$
$191$	−2.22287			−0.160841			−0.0804205	+	0.996761i	$0.525626\pi$
$192$	−0.696580	−	1.58580i	−0.0502713	−	0.114446i
$193$	0.558094			0.0401725			0.0200863	−	0.999798i	$-0.493606\pi$
$193$	0.558094			0.0401725			0.0200863	+	0.999798i	$0.493606\pi$
$194$	−4.71539			−0.338545
$195$	−6.02616	−	13.7189i	−0.431542	−	0.982431i
$196$	1.00000			0.0714286
$197$		−	12.3603i		−	0.880637i	−0.897842	−	0.440318i	$-0.854866\pi$
$197$		−	12.3603i		−	0.880637i	0.897842	−	0.440318i	$-0.145134\pi$
$198$	−3.17554	−	2.91721i	−0.225676	−	0.207317i
$199$		−	8.80742i		−	0.624342i	−0.950026	−	0.312171i	$-0.898944\pi$
$199$		−	8.80742i		−	0.624342i	0.950026	−	0.312171i	$-0.101056\pi$
$200$			4.99145i			0.352949i
$201$	−4.24849	+	1.86619i	−0.299665	+	0.131631i
$202$	−16.4580			−1.15798
$203$	8.82668			0.619511
$204$	0.665448	+	1.51493i	0.0465907	+	0.106066i
$205$		−	9.64363i		−	0.673540i
$206$	−5.39758			−0.376067
$207$	13.2442	+	5.62057i	0.920537	+	0.390656i
$208$	2.73688			0.189768
$209$			10.7680i			0.744837i
$210$	−2.20184	−	5.01261i	−0.151941	−	0.345903i
$211$	−10.3245			−0.710770			−0.355385	−	0.934720i	$-0.615650\pi$
$211$	−10.3245			−0.710770			−0.355385	+	0.934720i	$0.615650\pi$
$212$	12.4211			0.853082
$213$	20.0748	−	8.81804i	1.37550	−	0.604202i
$214$		−	17.5408i		−	1.19906i
$215$			7.62257i			0.519855i
$216$	1.67954	−	4.91723i	0.114278	−	0.334575i
$217$		−	2.94042i		−	0.199609i
$218$	3.72374			0.252204
$219$	−2.88675	−	6.57187i	−0.195069	−	0.444086i
$220$	−4.54340			−0.306316
$221$	−2.61456			−0.175874
$222$	−1.70354	−	3.87822i	−0.114334	−	0.260289i
$223$	−24.4011			−1.63402			−0.817008	−	0.576626i	$-0.804369\pi$
$223$	−24.4011			−1.63402			−0.817008	+	0.576626i	$0.804369\pi$
$224$	1.00000			0.0668153
$225$	−10.1304	+	11.0275i	−0.675361	+	0.735167i
$226$			17.5621i			1.16821i
$227$	22.2351			1.47580			0.737899	−	0.674911i	$-0.235818\pi$
$227$	22.2351			1.47580			0.737899	+	0.674911i	$0.235818\pi$
$228$	−11.8800	+	5.21841i	−0.786774	+	0.345598i
$229$			8.65227i			0.571758i	0.958266	+	0.285879i	$0.0922856\pi$
$229$			8.65227i			0.571758i	−0.958266	+	0.285879i	$0.907714\pi$
$230$	14.2830	−	5.07941i	0.941790	−	0.334927i
$231$	2.27938	−	1.00124i	0.149972	−	0.0658766i
$232$	8.82668			0.579500
$233$			8.55688i			0.560580i	0.959915	+	0.280290i	$0.0904306\pi$
$233$			8.55688i			0.560580i	−0.959915	+	0.280290i	$0.909569\pi$
$234$	6.04653	+	5.55464i	0.395274	+	0.363118i
$235$		−	26.7443i		−	1.74461i
$236$		−	4.28580i		−	0.278982i
$237$	−7.89865	+	3.46956i	−0.513073	+	0.225372i
$238$	−0.955308			−0.0619234
$239$		−	23.8378i		−	1.54194i	−0.636871	−	0.770971i	$-0.719772\pi$
$239$		−	23.8378i		−	1.54194i	0.636871	−	0.770971i	$-0.280228\pi$
$240$	−2.20184	−	5.01261i	−0.142128	−	0.323563i
$241$		−	23.4908i		−	1.51317i	−0.653893	−	0.756587i	$-0.726865\pi$
$241$		−	23.4908i		−	1.51317i	0.653893	−	0.756587i	$-0.273135\pi$
$242$			8.93398i			0.574298i
$243$	13.6904	−	7.45482i	0.878236	−	0.478227i
$244$			3.13255i			0.200541i
$245$	3.16093			0.201944
$246$	2.12519	+	4.83811i	0.135497	+	0.308467i
$247$		−	20.5033i		−	1.30459i
$248$		−	2.94042i		−	0.186717i
$249$	−3.96762	−	9.03253i	−0.251438	−	0.572413i
$250$		−	0.0270313i		−	0.00170961i
$251$	12.4989			0.788924			0.394462	−	0.918912i	$-0.370931\pi$
$251$	12.4989			0.788924			0.394462	+	0.918912i	$0.370931\pi$
$252$	2.20928	+	2.02955i	0.139171	+	0.127850i
$253$	2.30976	+	6.49487i	0.145213	+	0.408329i
$254$			7.88472i			0.494731i
$255$	2.10343	+	4.78859i	0.131722	+	0.299873i
$256$	1.00000			0.0625000
$257$			30.8343i			1.92339i	0.274115	+	0.961697i	$0.411615\pi$
$257$			30.8343i			1.92339i	−0.274115	+	0.961697i	$0.588385\pi$
$258$	−1.67980	−	3.82417i	−0.104580	−	0.238082i
$259$	2.44558			0.151961
$260$	8.65107			0.536517
$261$	19.5006	+	17.9142i	1.20706	+	1.10886i
$262$	10.5721			0.653146
$263$	3.14039			0.193645			0.0968223	−	0.995302i	$-0.469132\pi$
$263$	3.14039			0.193645			0.0968223	+	0.995302i	$0.469132\pi$
$264$	2.27938	−	1.00124i	0.140286	−	0.0616220i
$265$	39.2621			2.41185
$266$		−	7.49148i		−	0.459332i
$267$	7.96849	+	18.1407i	0.487664	+	1.11020i
$268$		−	2.67907i		−	0.163650i
$269$		−	12.2235i		−	0.745279i	−0.927976	−	0.372640i	$-0.878453\pi$
$269$		−	12.2235i		−	0.745279i	0.927976	−	0.372640i	$-0.121547\pi$
$270$	5.30889	−	15.5430i	0.323089	−	0.945917i
$271$	3.88654			0.236090			0.118045	−	0.993008i	$-0.462337\pi$
$271$	3.88654			0.236090			0.118045	+	0.993008i	$0.462337\pi$
$272$	−0.955308			−0.0579240
$273$	−4.34016	+	1.90645i	−0.262678	+	0.115384i
$274$			4.41592i			0.266775i
$275$	−7.17453			−0.432640
$276$	−6.04626	+	5.69586i	−0.363942	+	0.342850i
$277$	−6.26285			−0.376298			−0.188149	−	0.982140i	$-0.560249\pi$
$277$	−6.26285			−0.376298			−0.188149	+	0.982140i	$0.560249\pi$
$278$		−	11.6934i		−	0.701326i
$279$	5.96775	−	6.49621i	0.357280	−	0.388918i
$280$	3.16093			0.188901
$281$	−27.6788			−1.65118			−0.825589	−	0.564272i	$-0.809157\pi$
$281$	−27.6788			−1.65118			−0.825589	+	0.564272i	$0.809157\pi$
$282$	5.89370	+	13.4174i	0.350965	+	0.798992i
$283$			19.1248i			1.13685i	0.822734	+	0.568427i	$0.192448\pi$
$283$			19.1248i			1.13685i	−0.822734	+	0.568427i	$0.807552\pi$
$284$			12.6591i			0.751177i
$285$	−37.5519	+	16.4950i	−2.22438	+	0.977080i
$286$			3.93389i			0.232616i
$287$	−3.05089			−0.180088
$288$	2.20928	+	2.02955i	0.130183	+	0.119593i
$289$	−16.0874			−0.946317
$290$	27.9005			1.63837
$291$	7.47769	−	3.28465i	0.438350	−	0.192549i
$292$	4.14418			0.242520
$293$	17.3761			1.01512			0.507561	−	0.861616i	$-0.330547\pi$
$293$	17.3761			1.01512			0.507561	+	0.861616i	$0.330547\pi$
$294$	−1.58580	+	0.696580i	−0.0924860	+	0.0406253i
$295$		−	13.5471i		−	0.788743i
$296$	2.44558			0.142147
$297$	7.06785	+	2.41411i	0.410118	+	0.140081i
$298$		−	3.18337i		−	0.184407i
$299$	−4.39800	−	12.3669i	−0.254343	−	0.715194i
$300$	−3.47694	−	7.91546i	−0.200741	−	0.456999i
$301$	2.41150			0.138997
$302$			5.57408i			0.320753i
$303$	26.0992	−	11.4643i	1.49936	−	0.658607i
$304$		−	7.49148i		−	0.429666i
$305$			9.90175i			0.566973i
$306$	−2.11054	−	1.93885i	−0.120652	−	0.110837i
$307$	−4.36673			−0.249222			−0.124611	−	0.992206i	$-0.539768\pi$
$307$	−4.36673			−0.249222			−0.124611	+	0.992206i	$0.539768\pi$
$308$			1.43736i			0.0819014i
$309$	8.55950	−	3.75984i	0.486933	−	0.213890i
$310$		−	9.29446i		−	0.527890i
$311$			16.1558i			0.916111i	0.888924	+	0.458056i	$0.151454\pi$
$311$			16.1558i			0.916111i	−0.888924	+	0.458056i	$0.848546\pi$
$312$	−4.34016	+	1.90645i	−0.245713	+	0.107932i
$313$			9.82356i			0.555260i	0.960688	+	0.277630i	$0.0895490\pi$
$313$			9.82356i			0.555260i	−0.960688	+	0.277630i	$0.910451\pi$
$314$	24.0388			1.35659
$315$	6.98336	+	6.41527i	0.393468	+	0.361459i
$316$		−	4.98085i		−	0.280195i
$317$		−	20.6564i		−	1.16018i	−0.814553	−	0.580090i	$-0.803018\pi$
$317$		−	20.6564i		−	1.16018i	0.814553	−	0.580090i	$-0.196982\pi$
$318$	−19.6974	+	8.65226i	−1.10457	+	0.485195i
$319$			12.6872i			0.710344i
$320$	3.16093			0.176701
$321$	12.2185	+	27.8162i	0.681972	+	1.55255i
$322$	−1.60694	−	4.51860i	−0.0895512	−	0.251812i
$323$			7.15667i			0.398208i
$324$	0.761822	+	8.96770i	0.0423235	+	0.498206i
$325$	13.6610			0.757775
$326$			23.8869i			1.32297i
$327$	−5.90512	+	2.59388i	−0.326554	+	0.143442i
$328$	−3.05089			−0.168457
$329$	−8.46091			−0.466465
$330$	7.20495	−	3.16484i	0.396619	−	0.174219i
$331$	29.9075			1.64386			0.821932	−	0.569585i	$-0.192896\pi$
$331$	29.9075			1.64386			0.821932	+	0.569585i	$0.192896\pi$
$332$	5.69587			0.312601
$333$	5.40297	+	4.96344i	0.296081	+	0.271995i
$334$	−4.36843			−0.239030
$335$		−	8.46835i		−	0.462675i
$336$	−1.58580	+	0.696580i	−0.0865127	+	0.0380015i
$337$			26.5522i			1.44639i	0.690643	+	0.723196i	$0.257328\pi$
$337$			26.5522i			1.44639i	−0.690643	+	0.723196i	$0.742672\pi$
$338$			5.50950i			0.299677i
$339$	−12.2334	−	27.8500i	−0.664427	−	1.51261i
$340$	−3.01966			−0.163764
$341$	4.22646			0.228876
$342$	15.2044	−	16.5508i	0.822158	−	0.894963i
$343$		−	1.00000i		−	0.0539949i
$344$	2.41150			0.130019
$345$	−19.1118	+	18.0042i	−1.02894	+	0.969312i
$346$	−7.06727			−0.379939
$347$		−	9.30442i		−	0.499488i	−0.968312	−	0.249744i	$-0.919654\pi$
$347$		−	9.30442i		−	0.499488i	0.968312	−	0.249744i	$-0.0803464\pi$
$348$	−13.9974	+	6.14848i	−0.750339	+	0.329593i
$349$	−3.90929			−0.209260			−0.104630	−	0.994511i	$-0.533366\pi$
$349$	−3.90929			−0.209260			−0.104630	+	0.994511i	$0.533366\pi$
$350$	4.99145			0.266804
$351$	−13.4579	−	4.59669i	−0.718328	−	0.245353i
$352$			1.43736i			0.0766118i
$353$		−	16.4595i		−	0.876053i	−0.898962	−	0.438026i	$-0.855678\pi$
$353$		−	16.4595i		−	0.876053i	0.898962	−	0.438026i	$-0.144322\pi$
$354$	2.98540	+	6.79644i	0.158672	+	0.361227i
$355$			40.0143i			2.12374i
$356$	−11.4395			−0.606290
$357$	1.51493	−	0.665448i	0.0801787	−	0.0352192i
$358$	9.61154			0.507985
$359$	21.2177			1.11983			0.559913	−	0.828552i	$-0.310835\pi$
$359$	21.2177			1.11983			0.559913	+	0.828552i	$0.310835\pi$
$360$	6.98336	+	6.41527i	0.368056	+	0.338114i
$361$	−37.1223			−1.95381
$362$	18.0382			0.948069
$363$	−6.22323	−	14.1676i	−0.326635	−	0.743604i
$364$		−	2.73688i		−	0.143451i
$365$	13.0995			0.685657
$366$	−2.18207	−	4.96761i	−0.114059	−	0.259661i
$367$		−	35.0833i		−	1.83133i	−0.401939	−	0.915666i	$-0.631664\pi$
$367$		−	35.0833i		−	1.83133i	0.401939	−	0.915666i	$-0.368336\pi$
$368$	−1.60694	−	4.51860i	−0.0837675	−	0.235548i
$369$	−6.74026	−	6.19194i	−0.350884	−	0.322340i
$370$	7.73031			0.401879
$371$		−	12.4211i		−	0.644869i
$372$	2.04824	+	4.66294i	0.106196	+	0.241762i
$373$		−	14.9339i		−	0.773248i	−0.922238	−	0.386624i	$-0.873641\pi$
$373$		−	14.9339i		−	0.773248i	0.922238	−	0.386624i	$-0.126359\pi$
$374$		−	1.37312i		−	0.0710026i
$375$	0.0188295	+	0.0428664i	0.000972350	+	0.00221361i
$376$	−8.46091			−0.436338
$377$		−	24.1575i		−	1.24418i
$378$	−4.91723	−	1.67954i	−0.252915	−	0.0863861i
$379$		−	27.7891i		−	1.42743i	−0.700436	−	0.713715i	$-0.747011\pi$
$379$		−	27.7891i		−	1.42743i	0.700436	−	0.713715i	$-0.252989\pi$
$380$		−	23.6800i		−	1.21476i
$381$	−5.49233	−	12.5036i	−0.281381	−	0.640580i
$382$			2.22287i			0.113732i
$383$	−8.51042			−0.434862			−0.217431	−	0.976076i	$-0.569768\pi$
$383$	−8.51042			−0.434862			−0.217431	+	0.976076i	$0.569768\pi$
$384$	−1.58580	+	0.696580i	−0.0809253	+	0.0355472i
$385$			4.54340i			0.231553i
$386$		−	0.558094i		−	0.0284062i
$387$	5.32768	+	4.89427i	0.270821	+	0.248790i
$388$			4.71539i			0.239388i
$389$	−35.9378			−1.82212			−0.911059	−	0.412275i	$-0.864734\pi$
$389$	−35.9378			−1.82212			−0.911059	+	0.412275i	$0.864734\pi$
$390$	−13.7189	+	6.02616i	−0.694684	+	0.305146i
$391$	1.53512	+	4.31665i	0.0776344	+	0.218303i
$392$		−	1.00000i		−	0.0505076i
$393$	−16.7653	+	7.36430i	−0.845696	+	0.371480i
$394$	−12.3603			−0.622704
$395$		−	15.7441i		−	0.792171i
$396$	−2.91721	+	3.17554i	−0.146595	+	0.159577i
$397$	−0.792101			−0.0397544			−0.0198772	−	0.999802i	$-0.506328\pi$
$397$	−0.792101			−0.0397544			−0.0198772	+	0.999802i	$0.506328\pi$
$398$	−8.80742			−0.441476
$399$	5.21841	+	11.8800i	0.261247	+	0.594745i
$400$	4.99145			0.249572
$401$	−9.59257			−0.479030			−0.239515	−	0.970893i	$-0.576988\pi$
$401$	−9.59257			−0.479030			−0.239515	+	0.970893i	$0.576988\pi$
$402$	1.86619	+	4.24849i	0.0930770	+	0.211895i
$403$	−8.04758			−0.400879
$404$			16.4580i			0.818815i
$405$	2.40806	+	28.3462i	0.119658	+	1.40854i
$406$		−	8.82668i		−	0.438061i
$407$			3.51519i			0.174242i
$408$	1.51493	−	0.665448i	0.0750003	−	0.0329446i
$409$	−18.3665			−0.908167			−0.454083	−	0.890959i	$-0.650033\pi$
$409$	−18.3665			−0.908167			−0.454083	+	0.890959i	$0.650033\pi$
$410$	−9.64363			−0.476265
$411$	−3.07604	−	7.00278i	−0.151730	−	0.345422i
$412$			5.39758i			0.265920i
$413$	−4.28580			−0.210890
$414$	5.62057	−	13.2442i	0.276236	−	0.650918i
$415$	18.0042			0.883792
$416$		−	2.73688i		−	0.134187i
$417$	8.14541	+	18.5435i	0.398883	+	0.908080i
$418$	10.7680			0.526679
$419$	−22.7727			−1.11252			−0.556261	−	0.831008i	$-0.687764\pi$
$419$	−22.7727			−1.11252			−0.556261	+	0.831008i	$0.687764\pi$
$420$	−5.01261	+	2.20184i	−0.244590	+	0.107439i
$421$		−	24.4294i		−	1.19062i	−0.803497	−	0.595309i	$-0.797030\pi$
$421$		−	24.4294i		−	1.19062i	0.803497	−	0.595309i	$-0.202970\pi$
$422$			10.3245i			0.502590i
$423$	−18.6925	−	17.1719i	−0.908861	−	0.834925i
$424$		−	12.4211i		−	0.603220i
$425$	−4.76837			−0.231300
$426$	−8.81804	−	20.0748i	−0.427235	−	0.972627i
$427$	3.13255			0.151595
$428$	−17.5408			−0.847865
$429$	−2.74027	−	6.23838i	−0.132301	−	0.301192i
$430$	7.62257			0.367593
$431$	30.7337			1.48039			0.740195	−	0.672393i	$-0.234733\pi$
$431$	30.7337			1.48039			0.740195	+	0.672393i	$0.234733\pi$
$432$	−4.91723	−	1.67954i	−0.236580	−	0.0808068i
$433$			3.51132i			0.168743i	0.996434	+	0.0843717i	$0.0268883\pi$
$433$			3.51132i			0.168743i	−0.996434	+	0.0843717i	$0.973112\pi$
$434$	−2.94042			−0.141145
$435$	−44.2447	+	19.4349i	−2.12137	+	0.931832i
$436$		−	3.72374i		−	0.178335i
$437$	−33.8510	+	12.0384i	−1.61931	+	0.575873i
$438$	−6.57187	+	2.88675i	−0.314016	+	0.137934i
$439$	35.6882			1.70331			0.851653	−	0.524107i	$-0.175601\pi$
$439$	35.6882			1.70331			0.851653	+	0.524107i	$0.175601\pi$
$440$			4.54340i			0.216598i
$441$	2.02955	−	2.20928i	0.0966454	−	0.105204i
$442$			2.61456i			0.124362i
$443$			1.80797i			0.0858994i	0.999077	+	0.0429497i	$0.0136755\pi$
$443$			1.80797i			0.0858994i	−0.999077	+	0.0429497i	$0.986324\pi$
$444$	−3.87822	+	1.70354i	−0.184052	+	0.0808466i
$445$	−36.1593			−1.71411
$446$			24.4011i			1.15542i
$447$	2.21747	+	5.04820i	0.104883	+	0.238772i
$448$		−	1.00000i		−	0.0472456i
$449$			14.7943i			0.698186i	0.937088	+	0.349093i	$0.113510\pi$
$449$			14.7943i			0.698186i	−0.937088	+	0.349093i	$0.886490\pi$
$450$	11.0275	+	10.1304i	0.519841	+	0.477552i
$451$		−	4.38524i		−	0.206493i
$452$	17.5621			0.826051
$453$	−3.88279	−	8.83941i	−0.182430	−	0.415312i
$454$		−	22.2351i		−	1.04355i
$455$		−	8.65107i		−	0.405568i
$456$	5.21841	+	11.8800i	0.244375	+	0.556333i
$457$			20.8221i			0.974015i	0.873398	+	0.487007i	$0.161912\pi$
$457$			20.8221i			0.974015i	−0.873398	+	0.487007i	$0.838088\pi$
$458$	8.65227			0.404294
$459$	4.69747	+	1.60448i	0.219259	+	0.0748905i
$460$	−5.07941	−	14.2830i	−0.236829	−	0.665946i
$461$		−	13.0151i		−	0.606176i	−0.952963	−	0.303088i	$-0.901982\pi$
$461$		−	13.0151i		−	0.606176i	0.952963	−	0.303088i	$-0.0980176\pi$
$462$	−1.00124	−	2.27938i	−0.0465818	−	0.106046i
$463$	2.04658			0.0951127			0.0475564	−	0.998869i	$-0.484857\pi$
$463$	2.04658			0.0951127			0.0475564	+	0.998869i	$0.484857\pi$
$464$		−	8.82668i		−	0.409768i
$465$	6.47433	+	14.7392i	0.300240	+	0.683514i
$466$	8.55688			0.396390
$467$	−20.1564			−0.932725			−0.466362	−	0.884594i	$-0.654436\pi$
$467$	−20.1564			−0.932725			−0.466362	+	0.884594i	$0.654436\pi$
$468$	5.55464	−	6.04653i	0.256763	−	0.279501i
$469$	−2.67907			−0.123708
$470$	−26.7443			−1.23362
$471$	−38.1208	+	16.7449i	−1.75651	+	0.771565i
$472$	−4.28580			−0.197270
$473$			3.46620i			0.159376i
$474$	3.46956	+	7.89865i	0.159362	+	0.362797i
$475$		−	37.3933i		−	1.71572i
$476$			0.955308i			0.0437865i
$477$	25.2092	−	27.4416i	1.15425	−	1.25646i
$478$	−23.8378			−1.09032
$479$	−16.2560			−0.742757			−0.371379	−	0.928482i	$-0.621115\pi$
$479$	−16.2560			−0.742757			−0.371379	+	0.928482i	$0.621115\pi$
$480$	−5.01261	+	2.20184i	−0.228793	+	0.100500i
$481$		−	6.69326i		−	0.305187i
$482$	−23.4908			−1.06998
$483$	5.69586	+	6.04626i	0.259170	+	0.275114i
$484$	8.93398			0.406090
$485$			14.9050i			0.676801i
$486$	−7.45482	−	13.6904i	−0.338157	−	0.621007i
$487$	7.11067			0.322215			0.161108	−	0.986937i	$-0.448493\pi$
$487$	7.11067			0.322215			0.161108	+	0.986937i	$0.448493\pi$
$488$	3.13255			0.141804
$489$	−16.6392	−	37.8800i	−0.752448	−	1.71299i
$490$		−	3.16093i		−	0.142796i
$491$		−	8.71633i		−	0.393362i	−0.980468	−	0.196681i	$-0.936984\pi$
$491$		−	8.71633i		−	0.393362i	0.980468	−	0.196681i	$-0.0630164\pi$
$492$	4.83811	−	2.12519i	0.218119	−	0.0958108i
$493$			8.43219i			0.379767i
$494$	−20.5033			−0.922486
$495$	−9.22107	+	10.0376i	−0.414456	+	0.451158i
$496$	−2.94042			−0.132029
$497$	12.6591			0.567836
$498$	−9.03253	+	3.96762i	−0.404757	+	0.177793i
$499$	7.71385			0.345319			0.172660	−	0.984982i	$-0.444764\pi$
$499$	7.71385			0.345319			0.172660	+	0.984982i	$0.444764\pi$
$500$	−0.0270313			−0.00120888
$501$	6.92748	−	3.04296i	0.309497	−	0.135949i
$502$		−	12.4989i		−	0.557854i
$503$	−12.6605			−0.564503			−0.282252	−	0.959340i	$-0.591081\pi$
$503$	−12.6605			−0.564503			−0.282252	+	0.959340i	$0.591081\pi$
$504$	2.02955	−	2.20928i	0.0904035	−	0.0984091i
$505$			52.0225i			2.31497i
$506$	6.49487	−	2.30976i	0.288732	−	0.102681i
$507$	−3.83780	−	8.73698i	−0.170443	−	0.388023i
$508$	7.88472			0.349828
$509$		−	2.61552i		−	0.115931i	−0.998319	−	0.0579655i	$-0.981539\pi$
$509$		−	2.61552i		−	0.115931i	0.998319	−	0.0579655i	$-0.0184613\pi$
$510$	4.78859	−	2.10343i	0.212042	−	0.0931415i
$511$		−	4.14418i		−	0.183328i
$512$		−	1.00000i		−	0.0441942i
$513$	−12.5822	+	36.8373i	−0.555519	+	1.62641i
$514$	30.8343			1.36004
$515$			17.0613i			0.751812i
$516$	−3.82417	+	1.67980i	−0.168350	+	0.0739491i
$517$		−	12.1614i		−	0.534858i
$518$		−	2.44558i		−	0.107453i
$519$	11.2073	−	4.92292i	0.491946	−	0.216092i
$520$		−	8.65107i		−	0.379374i
$521$	−23.7977			−1.04260			−0.521298	−	0.853375i	$-0.674552\pi$
$521$	−23.7977			−1.04260			−0.521298	+	0.853375i	$0.674552\pi$
$522$	17.9142	−	19.5006i	0.784084	−	0.853518i
$523$		−	16.1736i		−	0.707221i	−0.935393	−	0.353611i	$-0.884954\pi$
$523$		−	16.1736i		−	0.707221i	0.935393	−	0.353611i	$-0.115046\pi$
$524$		−	10.5721i		−	0.461844i
$525$	−7.91546	+	3.47694i	−0.345459	+	0.151746i
$526$		−	3.14039i		−	0.136927i
$527$	2.80901			0.122362
$528$	−1.00124	−	2.27938i	−0.0435733	−	0.0991972i
$529$	−17.8355	+	14.5222i	−0.775456	+	0.631401i
$530$		−	39.2621i		−	1.70543i
$531$	−9.46853	−	8.69826i	−0.410899	−	0.377473i
$532$	−7.49148			−0.324797
$533$			8.34991i			0.361675i
$534$	18.1407	−	7.96849i	0.785027	−	0.344830i
$535$	−55.4450			−2.39710
$536$	−2.67907			−0.115718
$537$	−15.2420	+	6.69520i	−0.657742	+	0.288919i
$538$	−12.2235			−0.526992
$539$	1.43736			0.0619116
$540$	−15.5430	−	5.30889i	−0.668864	−	0.228458i
$541$	30.4963			1.31114			0.655569	−	0.755135i	$-0.272429\pi$
$541$	30.4963			1.31114			0.655569	+	0.755135i	$0.272429\pi$
$542$		−	3.88654i		−	0.166941i
$543$	−28.6051	+	12.5651i	−1.22756	+	0.539219i
$544$			0.955308i			0.0409585i
$545$		−	11.7705i		−	0.504191i
$546$	1.90645	+	4.34016i	0.0815887	+	0.185742i
$547$	21.3948			0.914774			0.457387	−	0.889268i	$-0.348785\pi$
$547$	21.3948			0.914774			0.457387	+	0.889268i	$0.348785\pi$
$548$	4.41592			0.188639
$549$	6.92067	+	6.35768i	0.295367	+	0.271339i
$550$			7.17453i			0.305923i
$551$	−66.1249			−2.81702
$552$	5.69586	+	6.04626i	0.242432	+	0.257346i
$553$	−4.98085			−0.211807
$554$			6.26285i			0.266083i
$555$	−12.2588	+	5.38477i	−0.520355	+	0.228571i
$556$	−11.6934			−0.495913
$557$	2.57053			0.108917			0.0544585	−	0.998516i	$-0.482657\pi$
$557$	2.57053			0.108917			0.0544585	+	0.998516i	$0.482657\pi$
$558$	−6.49621	−	5.96775i	−0.275007	−	0.252635i
$559$		−	6.59998i		−	0.279150i
$560$		−	3.16093i		−	0.133573i
$561$	0.956491	+	2.17751i	0.0403831	+	0.0919345i
$562$			27.6788i			1.16756i
$563$	3.60599			0.151974			0.0759871	−	0.997109i	$-0.475789\pi$
$563$	3.60599			0.151974			0.0759871	+	0.997109i	$0.475789\pi$
$564$	13.4174	−	5.89370i	0.564972	−	0.248169i
$565$	55.5124			2.33543
$566$	19.1248			0.803877
$567$	8.96770	−	0.761822i	0.376608	−	0.0319935i
$568$	12.6591			0.531162
$569$	−32.4780			−1.36155			−0.680774	−	0.732493i	$-0.738356\pi$
$569$	−32.4780			−1.36155			−0.680774	+	0.732493i	$0.738356\pi$
$570$	16.4950	+	37.5519i	0.690900	+	1.57288i
$571$			32.9643i			1.37951i	0.724040	+	0.689757i	$0.242283\pi$
$571$			32.9643i			1.37951i	−0.724040	+	0.689757i	$0.757717\pi$
$572$	3.93389			0.164484
$573$	−1.54840	−	3.52503i	−0.0646855	−	0.147260i
$574$			3.05089i			0.127342i
$575$	−8.02095	−	22.5544i	−0.334497	−	0.940582i
$576$	2.02955	−	2.20928i	0.0845647	−	0.0920533i
$577$	−4.64339			−0.193307			−0.0966534	−	0.995318i	$-0.530814\pi$
$577$	−4.64339			−0.193307			−0.0966534	+	0.995318i	$0.530814\pi$
$578$			16.0874i			0.669147i
$579$	0.388757	+	0.885029i	0.0161562	+	0.0367805i
$580$		−	27.9005i		−	1.15850i
$581$		−	5.69587i		−	0.236304i
$582$	−3.28465	−	7.47769i	−0.136153	−	0.309960i
$583$	17.8536			0.739420
$584$		−	4.14418i		−	0.171488i
$585$	17.5578	−	19.1126i	0.725926	−	0.790210i
$586$		−	17.3761i		−	0.717800i
$587$			37.7274i			1.55718i	0.627534	+	0.778589i	$0.284064\pi$
$587$			37.7274i			1.55718i	−0.627534	+	0.778589i	$0.715936\pi$
$588$	0.696580	+	1.58580i	0.0287265	+	0.0653975i
$589$			22.0281i			0.907653i
$590$	−13.5471			−0.557725
$591$	19.6011	−	8.60995i	0.806280	−	0.354166i
$592$		−	2.44558i		−	0.100513i
$593$			16.5595i			0.680018i	0.940422	+	0.340009i	$0.110430\pi$
$593$			16.5595i			0.680018i	−0.940422	+	0.340009i	$0.889570\pi$
$594$	2.41411	−	7.06785i	0.0990520	−	0.289997i
$595$			3.01966i			0.123794i
$596$	−3.18337			−0.130396
$597$	13.9669	−	6.13507i	0.571625	−	0.251092i
$598$	−12.3669	+	4.39800i	−0.505719	+	0.179847i
$599$			6.99970i			0.286000i	0.989723	+	0.143000i	$0.0456749\pi$
$599$			6.99970i			0.286000i	−0.989723	+	0.143000i	$0.954325\pi$
$600$	−7.91546	+	3.47694i	−0.323147	+	0.141946i
$601$	44.4297			1.81233			0.906163	−	0.422929i	$-0.138998\pi$
$601$	44.4297			1.81233			0.906163	+	0.422929i	$0.138998\pi$
$602$		−	2.41150i		−	0.0982854i
$603$	−5.91882	−	5.43732i	−0.241033	−	0.221425i
$604$	5.57408			0.226806
$605$	28.2397			1.14811
$606$	−11.4643	−	26.0992i	−0.465705	−	1.06021i
$607$	7.73439			0.313929			0.156965	−	0.987604i	$-0.449829\pi$
$607$	7.73439			0.313929			0.156965	+	0.987604i	$0.449829\pi$
$608$	−7.49148			−0.303820
$609$	6.14848	+	13.9974i	0.249149	+	0.567203i
$610$	9.90175			0.400910
$611$			23.1565i			0.936811i
$612$	−1.93885	+	2.11054i	−0.0783733	+	0.0853136i
$613$		−	34.4121i		−	1.38989i	−0.719063	−	0.694945i	$-0.755429\pi$
$613$		−	34.4121i		−	1.38989i	0.719063	−	0.694945i	$-0.244571\pi$
$614$			4.36673i			0.176227i
$615$	15.2929	−	6.71756i	0.616670	−	0.270878i
$616$	1.43736			0.0579130
$617$	28.4641			1.14592			0.572962	−	0.819582i	$-0.305794\pi$
$617$	28.4641			1.14592			0.572962	+	0.819582i	$0.305794\pi$
$618$	−3.75984	−	8.55950i	−0.151243	−	0.344314i
$619$		−	13.5907i		−	0.546255i	−0.961978	−	0.273128i	$-0.911942\pi$
$619$		−	13.5907i		−	0.546255i	0.961978	−	0.273128i	$-0.0880581\pi$
$620$	−9.29446			−0.373274
$621$	0.312528	+	24.9179i	0.0125413	+	0.999921i
$622$	16.1558			0.647788
$623$			11.4395i			0.458312i
$624$	1.90645	+	4.34016i	0.0763192	+	0.173745i
$625$	−25.0427			−1.00171
$626$	9.82356			0.392628
$627$	−17.0759	+	7.50076i	−0.681947	+	0.299551i
$628$		−	24.0388i		−	0.959251i
$629$			2.33628i			0.0931538i
$630$	6.41527	−	6.98336i	0.255590	−	0.278224i
$631$		−	36.4553i		−	1.45126i	−0.688084	−	0.725631i	$-0.741548\pi$
$631$		−	36.4553i		−	1.45126i	0.688084	−	0.725631i	$-0.258452\pi$
$632$	−4.98085			−0.198128
$633$	−7.19185	−	16.3727i	−0.285851	−	0.650756i
$634$	−20.6564			−0.820371
$635$	24.9230			0.989039
$636$	8.65226	+	19.6974i	0.343084	+	0.781052i
$637$	−2.73688			−0.108439
$638$	12.6872			0.502289
$639$	27.9674	+	25.6922i	1.10637	+	1.01637i
$640$		−	3.16093i		−	0.124947i
$641$	−24.6276			−0.972730			−0.486365	−	0.873756i	$-0.661677\pi$
$641$	−24.6276			−0.972730			−0.486365	+	0.873756i	$0.661677\pi$
$642$	27.8162	−	12.2185i	1.09782	−	0.482227i
$643$			37.4725i			1.47777i	0.673832	+	0.738885i	$0.264647\pi$
$643$			37.4725i			1.47777i	−0.673832	+	0.738885i	$0.735353\pi$
$644$	−4.51860	+	1.60694i	−0.178058	+	0.0633223i
$645$	−12.0879	+	5.30973i	−0.475961	+	0.209070i
$646$	7.15667			0.281575
$647$		−	14.9430i		−	0.587470i	−0.955887	−	0.293735i	$-0.905102\pi$
$647$		−	14.9430i		−	0.587470i	0.955887	−	0.293735i	$-0.0948983\pi$
$648$	8.96770	−	0.761822i	0.352284	−	0.0299272i
$649$		−	6.16026i		−	0.241811i
$650$		−	13.6610i		−	0.535828i
$651$	4.66294	−	2.04824i	0.182755	−	0.0802768i
$652$	23.8869			0.935485
$653$			47.3585i			1.85328i	0.375946	+	0.926641i	$0.377318\pi$
$653$			47.3585i			1.85328i	−0.375946	+	0.926641i	$0.622682\pi$
$654$	2.59388	+	5.90512i	0.101429	+	0.230909i
$655$		−	33.4176i		−	1.30573i
$656$			3.05089i			0.119117i
$657$	8.41084	−	9.15566i	0.328138	−	0.357196i
$658$			8.46091i			0.329841i
$659$	37.8228			1.47337			0.736683	−	0.676239i	$-0.236391\pi$
$659$	37.8228			1.47337			0.736683	+	0.676239i	$0.236391\pi$
$660$	−3.16484	−	7.20495i	−0.123191	−	0.280452i
$661$			6.55736i			0.255052i	0.991835	+	0.127526i	$0.0407036\pi$
$661$			6.55736i			0.255052i	−0.991835	+	0.127526i	$0.959296\pi$
$662$		−	29.9075i		−	1.16239i
$663$	−1.82125	−	4.14618i	−0.0707315	−	0.161024i
$664$		−	5.69587i		−	0.221042i
$665$	−23.6800			−0.918272
$666$	4.96344	−	5.40297i	0.192329	−	0.209361i
$667$	−39.8842	+	14.1839i	−1.54432	+	0.549204i
$668$			4.36843i			0.169020i
$669$	−16.9973	−	38.6953i	−0.657153	−	1.49605i
$670$	−8.46835			−0.327161
$671$			4.50261i			0.173821i
$672$	0.696580	+	1.58580i	0.0268711	+	0.0611737i
$673$	11.2750			0.434619			0.217309	−	0.976103i	$-0.430272\pi$
$673$	11.2750			0.434619			0.217309	+	0.976103i	$0.430272\pi$
$674$	26.5522			1.02275
$675$	−24.5441	−	8.38333i	−0.944703	−	0.322674i
$676$	5.50950			0.211904
$677$	29.9218			1.14999			0.574994	−	0.818158i	$-0.305004\pi$
$677$	29.9218			1.14999			0.574994	+	0.818158i	$0.305004\pi$
$678$	−27.8500	+	12.2334i	−1.06957	+	0.469821i
$679$	4.71539			0.180960
$680$			3.01966i			0.115799i
$681$	15.4885	+	35.2606i	0.593522	+	1.35119i
$682$		−	4.22646i		−	0.161839i
$683$		−	14.0318i		−	0.536914i	−0.963292	−	0.268457i	$-0.913486\pi$
$683$		−	14.0318i		−	0.536914i	0.963292	−	0.268457i	$-0.0865136\pi$
$684$	−16.5508	−	15.2044i	−0.632834	−	0.581353i
$685$	13.9584			0.533322
$686$	−1.00000			−0.0381802
$687$	−13.7208	+	6.02700i	−0.523482	+	0.229944i
$688$		−	2.41150i		−	0.0919376i
$689$	−33.9949			−1.29510
$690$	18.0042	+	19.1118i	0.685407	+	0.727573i
$691$	26.7544			1.01779			0.508893	−	0.860830i	$-0.330055\pi$
$691$	26.7544			1.01779			0.508893	+	0.860830i	$0.330055\pi$
$692$			7.06727i			0.268657i
$693$	3.17554	+	2.91721i	0.120629	+	0.110816i
$694$	−9.30442			−0.353191
$695$	−36.9621			−1.40205
$696$	6.14848	+	13.9974i	0.233058	+	0.530570i
$697$		−	2.91454i		−	0.110396i
$698$			3.90929i			0.147969i
$699$	−13.5695	+	5.96055i	−0.513247	+	0.225449i
$700$		−	4.99145i		−	0.188659i
$701$	29.4751			1.11326			0.556630	−	0.830760i	$-0.312094\pi$
$701$	29.4751			1.11326			0.556630	+	0.830760i	$0.312094\pi$
$702$	−4.59669	+	13.4579i	−0.173491	+	0.507934i
$703$	−18.3210			−0.690991
$704$	1.43736			0.0541727
$705$	42.4112	−	18.6295i	1.59730	−	0.701629i
$706$	−16.4595			−0.619463
$707$	16.4580			0.618966
$708$	6.79644	−	2.98540i	0.255426	−	0.112198i
$709$		−	18.5469i		−	0.696544i	−0.937394	−	0.348272i	$-0.886769\pi$
$709$		−	18.5469i		−	0.696544i	0.937394	−	0.348272i	$-0.113231\pi$
$710$	40.0143			1.50171
$711$	−11.0041	−	10.1089i	−0.412685	−	0.379113i
$712$			11.4395i			0.428712i
$713$	4.72508	+	13.2866i	0.176956	+	0.497587i
$714$	−0.665448	−	1.51493i	−0.0249038	−	0.0566949i
$715$	12.4347			0.465033
$716$		−	9.61154i		−	0.359200i
$717$	37.8021	−	16.6049i	1.41175	−	0.620123i
$718$		−	21.2177i		−	0.791836i
$719$			0.520739i			0.0194203i	0.999953	+	0.00971014i	$0.00309088\pi$
$719$			0.520739i			0.0194203i	−0.999953	+	0.00971014i	$0.996909\pi$
$720$	6.41527	−	6.98336i	0.239083	−	0.260255i
$721$	5.39758			0.201016
$722$			37.1223i			1.38155i
$723$	37.2518	−	16.3632i	1.38541	−	0.608554i
$724$		−	18.0382i		−	0.670386i
$725$		−	44.0579i		−	1.63627i
$726$	−14.1676	+	6.22323i	−0.525807	+	0.230966i
$727$		−	6.56581i		−	0.243513i	−0.992560	−	0.121756i	$-0.961147\pi$
$727$		−	6.56581i		−	0.243513i	0.992560	−	0.121756i	$-0.0388526\pi$
$728$	−2.73688			−0.101435
$729$	21.3583	+	16.5174i	0.791048	+	0.611754i
$730$		−	13.0995i		−	0.484833i
$731$			2.30372i			0.0852063i
$732$	−4.96761	+	2.18207i	−0.183608	+	0.0806516i
$733$		−	48.6685i		−	1.79761i	−0.438346	−	0.898806i	$-0.644435\pi$
$733$		−	48.6685i		−	1.79761i	0.438346	−	0.898806i	$-0.355565\pi$
$734$	−35.0833			−1.29495
$735$	2.20184	+	5.01261i	0.0812159	+	0.184893i
$736$	−4.51860	+	1.60694i	−0.166558	+	0.0592326i
$737$		−	3.85080i		−	0.141846i
$738$	−6.19194	+	6.74026i	−0.227929	+	0.248112i
$739$	−20.6702			−0.760365			−0.380182	−	0.924912i	$-0.624139\pi$
$739$	−20.6702			−0.760365			−0.380182	+	0.924912i	$0.624139\pi$
$740$		−	7.73031i		−	0.284172i
$741$	32.5142	−	14.2822i	1.19444	−	0.524668i
$742$	−12.4211			−0.455992
$743$	33.2398			1.21945			0.609725	−	0.792613i	$-0.291280\pi$
$743$	33.2398			1.21945			0.609725	+	0.792613i	$0.291280\pi$
$744$	4.66294	−	2.04824i	0.170952	−	0.0750921i
$745$	−10.0624			−0.368657
$746$	−14.9339			−0.546769
$747$	11.5601	−	12.5838i	0.422961	−	0.460415i
$748$	−1.37312			−0.0502064
$749$			17.5408i			0.640925i
$750$	0.0428664	−	0.0188295i	0.00156526	−	0.000687555i
$751$		−	49.7801i		−	1.81650i	−0.418424	−	0.908252i	$-0.637417\pi$
$751$		−	49.7801i		−	1.81650i	0.418424	−	0.908252i	$-0.362583\pi$
$752$			8.46091i			0.308538i
$753$	8.70648	+	19.8208i	0.317282	+	0.722311i
$754$	−24.1575			−0.879766
$755$	17.6193			0.641231
$756$	−1.67954	+	4.91723i	−0.0610842	+	0.178838i
$757$		−	16.7959i		−	0.610458i	−0.952279	−	0.305229i	$-0.901267\pi$
$757$		−	16.7959i		−	0.610458i	0.952279	−	0.305229i	$-0.0987330\pi$
$758$	−27.7891			−1.00935
$759$	−8.69067	+	8.18702i	−0.315451	+	0.297170i
$760$	−23.6800			−0.858964
$761$		−	17.3845i		−	0.630186i	−0.949061	−	0.315093i	$-0.897964\pi$
$761$		−	17.3845i		−	0.630186i	0.949061	−	0.315093i	$-0.102036\pi$
$762$	−12.5036	+	5.49233i	−0.452958	+	0.198966i
$763$	−3.72374			−0.134808
$764$	2.22287			0.0804205
$765$	−6.12855	+	6.67126i	−0.221578	+	0.241200i
$766$			8.51042i			0.307494i
$767$			11.7297i			0.423536i
$768$	0.696580	+	1.58580i	0.0251356	+	0.0572228i
$769$			3.89998i			0.140637i	0.997525	+	0.0703184i	$0.0224015\pi$
$769$			3.89998i			0.140637i	−0.997525	+	0.0703184i	$0.977598\pi$
$770$	4.54340			0.163733
$771$	−48.8973	+	21.4786i	−1.76099	+	0.773532i
$772$	−0.558094			−0.0200863
$773$	−37.5592			−1.35091			−0.675455	−	0.737401i	$-0.736053\pi$
$773$	−37.5592			−1.35091			−0.675455	+	0.737401i	$0.736053\pi$
$774$	4.89427	−	5.32768i	0.175921	−	0.191499i
$775$	−14.6770			−0.527212
$776$	4.71539			0.169273
$777$	1.70354	+	3.87822i	0.0611143	+	0.139130i
$778$			35.9378i			1.28843i
$779$	22.8557			0.818890
$780$	6.02616	+	13.7189i	0.215771	+	0.491216i
$781$			18.1957i			0.651092i
$782$	4.31665	−	1.53512i	0.154363	−	0.0548958i
$783$	−14.8247	+	43.4028i	−0.529793	+	1.55109i
$784$	−1.00000			−0.0357143
$785$		−	75.9848i		−	2.71201i
$786$	7.36430	+	16.7653i	0.262676	+	0.597998i
$787$		−	13.1094i		−	0.467299i	−0.972321	−	0.233649i	$-0.924933\pi$
$787$		−	13.1094i		−	0.467299i	0.972321	−	0.233649i	$-0.0750668\pi$
$788$			12.3603i			0.440318i
$789$	2.18753	+	4.98004i	0.0778781	+	0.177294i
$790$	−15.7441			−0.560150
$791$		−	17.5621i		−	0.624436i
$792$	3.17554	+	2.91721i	0.112838	+	0.103658i
$793$		−	8.57341i		−	0.304451i
$794$			0.792101i			0.0281106i
$795$	27.3491	+	62.2620i	0.969974	+	2.20820i
$796$			8.80742i			0.312171i
$797$	−6.39797			−0.226628			−0.113314	−	0.993559i	$-0.536147\pi$
$797$	−6.39797			−0.226628			−0.113314	+	0.993559i	$0.536147\pi$
$798$	11.8800	−	5.21841i	0.420548	−	0.184730i
$799$		−	8.08277i		−	0.285948i
$800$		−	4.99145i		−	0.176474i
$801$	−23.2170	+	25.2729i	−0.820332	+	0.892976i
$802$			9.59257i			0.338725i
$803$	5.95670			0.210207
$804$	4.24849	−	1.86619i	0.149833	−	0.0658154i
$805$	−14.2830	+	5.07941i	−0.503408	+	0.179026i
$806$			8.04758i			0.283464i
$807$	19.3841	−	8.51463i	0.682351	−	0.299729i
$808$	16.4580			0.578990
$809$		−	24.4886i		−	0.860972i	−0.902597	−	0.430486i	$-0.858342\pi$
$809$		−	24.4886i		−	0.860972i	0.902597	−	0.430486i	$-0.141658\pi$
$810$	28.3462	−	2.40806i	0.995985	−	0.0846107i
$811$	22.6766			0.796285			0.398142	−	0.917324i	$-0.369655\pi$
$811$	22.6766			0.796285			0.398142	+	0.917324i	$0.369655\pi$
$812$	−8.82668			−0.309756
$813$	2.70728	+	6.16329i	0.0949486	+	0.216156i
$814$	3.51519			0.123207
$815$	75.5048			2.64482
$816$	−0.665448	−	1.51493i	−0.0232953	−	0.0530332i
$817$	−18.0657			−0.632039
$818$			18.3665i			0.642171i
$819$	−6.04653	−	5.55464i	−0.211283	−	0.194095i
$820$			9.64363i			0.336770i
$821$		−	8.16844i		−	0.285081i	−0.989789	−	0.142540i	$-0.954473\pi$
$821$		−	8.16844i		−	0.285081i	0.989789	−	0.142540i	$-0.0455270\pi$
$822$	−7.00278	+	3.07604i	−0.244250	+	0.107289i
$823$	35.3945			1.23378			0.616888	−	0.787051i	$-0.288393\pi$
$823$	35.3945			1.23378			0.616888	+	0.787051i	$0.288393\pi$
$824$	5.39758			0.188034
$825$	−4.99763	−	11.3774i	−0.173995	−	0.396110i
$826$			4.28580i			0.149122i
$827$	27.8741			0.969276			0.484638	−	0.874715i	$-0.338951\pi$
$827$	27.8741			0.969276			0.484638	+	0.874715i	$0.338951\pi$
$828$	−13.2442	−	5.62057i	−0.460268	−	0.195328i
$829$	−21.8553			−0.759067			−0.379534	−	0.925178i	$-0.623916\pi$
$829$	−21.8553			−0.759067			−0.379534	+	0.925178i	$0.623916\pi$
$830$		−	18.0042i		−	0.624935i
$831$	−4.36258	−	9.93167i	−0.151336	−	0.344526i
$832$	−2.73688			−0.0948842
$833$	0.955308			0.0330994
$834$	18.5435	−	8.14541i	0.642110	−	0.282053i
$835$			13.8083i			0.477855i
$836$		−	10.7680i		−	0.372419i
$837$	14.4587	+	4.93855i	0.499767	+	0.170701i
$838$			22.7727i			0.786671i
$839$	29.7400			1.02674			0.513370	−	0.858167i	$-0.328397\pi$
$839$	29.7400			1.02674			0.513370	+	0.858167i	$0.328397\pi$
$840$	2.20184	+	5.01261i	0.0759706	+	0.172951i
$841$	−48.9103			−1.68656
$842$	−24.4294			−0.841894
$843$	−19.2805	−	43.8932i	−0.664055	−	1.51176i
$844$	10.3245			0.355385
$845$	17.4151			0.599098
$846$	−17.1719	+	18.6925i	−0.590381	+	0.642662i
$847$		−	8.93398i		−	0.306975i
$848$	−12.4211			−0.426541
$849$	−30.3283	+	13.3220i	−1.04086	+	0.457209i
$850$			4.76837i			0.163554i
$851$	−11.0506	+	3.92990i	−0.378810	+	0.134715i
$852$	−20.0748	+	8.81804i	−0.687751	+	0.302101i
$853$	19.0667			0.652831			0.326415	−	0.945226i	$-0.394159\pi$
$853$	19.0667			0.652831			0.326415	+	0.945226i	$0.394159\pi$
$854$		−	3.13255i		−	0.107194i
$855$	−52.3157	−	48.0599i	−1.78916	−	1.64361i
$856$			17.5408i			0.599531i
$857$			39.8550i			1.36142i	0.732553	+	0.680710i	$0.238329\pi$
$857$			39.8550i			1.36142i	−0.732553	+	0.680710i	$0.761671\pi$
$858$	−6.23838	+	2.74027i	−0.212975	+	0.0935512i
$859$	56.9500			1.94311			0.971554	−	0.236818i	$-0.0761045\pi$
$859$	56.9500			1.94311			0.971554	+	0.236818i	$0.0761045\pi$
$860$		−	7.62257i		−	0.259928i
$861$	−2.12519	−	4.83811i	−0.0724262	−	0.164882i
$862$		−	30.7337i		−	1.04679i
$863$		−	2.03872i		−	0.0693988i	−0.999398	−	0.0346994i	$-0.988953\pi$
$863$		−	2.03872i		−	0.0693988i	0.999398	−	0.0346994i	$-0.0110474\pi$
$864$	−1.67954	+	4.91723i	−0.0571390	+	0.167288i
$865$			22.3391i			0.759553i
$866$	3.51132			0.119320
$867$	−11.2061	−	25.5115i	−0.380581	−	0.866414i
$868$			2.94042i			0.0998044i
$869$		−	7.15929i		−	0.242862i
$870$	19.4349	+	44.2447i	0.658905	+	1.50004i
$871$			7.33230i			0.248445i
$872$	−3.72374			−0.126102
$873$	10.4176	+	9.57014i	0.352583	+	0.323900i
$874$	12.0384	+	33.8510i	0.407203	+	1.14503i
$875$			0.0270313i			0.000913826i
$876$	2.88675	+	6.57187i	0.0975344	+	0.222043i
$877$	21.7647			0.734940			0.367470	−	0.930035i	$-0.380224\pi$
$877$	21.7647			0.734940			0.367470	+	0.930035i	$0.380224\pi$
$878$		−	35.6882i		−	1.20442i
$879$	12.1038	+	27.5551i	0.408252	+	0.929411i
$880$	4.54340			0.153158
$881$	−25.3830			−0.855175			−0.427587	−	0.903974i	$-0.640636\pi$
$881$	−25.3830			−0.855175			−0.427587	+	0.903974i	$0.640636\pi$
$882$	−2.20928	−	2.02955i	−0.0743903	−	0.0683386i
$883$	25.0321			0.842399			0.421199	−	0.906968i	$-0.361609\pi$
$883$	25.0321			0.842399			0.421199	+	0.906968i	$0.361609\pi$
$884$	2.61456			0.0879372
$885$	21.4831	−	9.43663i	0.722145	−	0.317209i
$886$	1.80797			0.0607401
$887$		−	31.6088i		−	1.06132i	−0.847585	−	0.530659i	$-0.821944\pi$
$887$		−	31.6088i		−	1.06132i	0.847585	−	0.530659i	$-0.178056\pi$
$888$	1.70354	+	3.87822i	0.0571672	+	0.130144i
$889$		−	7.88472i		−	0.264445i
$890$			36.1593i			1.21206i
$891$	1.09502	+	12.8898i	0.0366844	+	0.431826i
$892$	24.4011			0.817008
$893$	63.3848			2.12109
$894$	5.04820	−	2.21747i	0.168837	−	0.0741632i
$895$		−	30.3813i		−	1.01554i
$896$	−1.00000			−0.0334077
$897$	16.5479	−	15.5889i	0.552517	−	0.520497i
$898$	14.7943			0.493692
$899$			25.9542i			0.865620i
$900$	10.1304	−	11.0275i	0.337680	−	0.367583i
$901$	11.8659			0.395312
$902$	−4.38524			−0.146012
$903$	1.67980	+	3.82417i	0.0559003	+	0.127260i
$904$		−	17.5621i		−	0.584106i
$905$		−	57.0176i		−	1.89533i
$906$	−8.83941	+	3.88279i	−0.293670	+	0.128997i
$907$		−	20.4248i		−	0.678194i	−0.940751	−	0.339097i	$-0.889878\pi$
$907$		−	20.4248i		−	0.678194i	0.940751	−	0.339097i	$-0.110122\pi$
$908$	−22.2351			−0.737899
$909$	36.3603	+	33.4024i	1.20599	+	1.10789i
$910$	−8.65107			−0.286780
$911$	−19.5011			−0.646101			−0.323051	−	0.946382i	$-0.604708\pi$
$911$	−19.5011			−0.646101			−0.323051	+	0.946382i	$0.604708\pi$
$912$	11.8800	−	5.21841i	0.393387	−	0.172799i
$913$	8.18703			0.270951
$914$	20.8221			0.688732
$915$	−15.7022	+	6.89736i	−0.519100	+	0.228020i
$916$		−	8.65227i		−	0.285879i
$917$	−10.5721			−0.349121
$918$	1.60448	−	4.69747i	0.0529556	−	0.155040i
$919$			56.2065i			1.85408i	0.374963	+	0.927040i	$0.377656\pi$
$919$			56.2065i			1.85408i	−0.374963	+	0.927040i	$0.622344\pi$
$920$	−14.2830	+	5.07941i	−0.470895	+	0.167463i
$921$	−3.04177	−	6.92478i	−0.100230	−	0.228179i
$922$	−13.0151			−0.428631
$923$		−	34.6463i		−	1.14040i
$924$	−2.27938	+	1.00124i	−0.0749861	+	0.0329383i
$925$		−	12.2070i		−	0.401364i
$926$		−	2.04658i		−	0.0672549i
$927$	11.9248	+	10.9547i	0.391660	+	0.359799i
$928$	−8.82668			−0.289750
$929$			13.9413i			0.457398i	0.973497	+	0.228699i	$0.0734472\pi$
$929$			13.9413i			0.457398i	−0.973497	+	0.228699i	$0.926553\pi$
$930$	14.7392	−	6.47433i	0.483317	−	0.212302i
$931$			7.49148i			0.245523i
$932$		−	8.55688i		−	0.280290i
$933$	−25.6199	+	11.2538i	−0.838759	+	0.368433i
$934$			20.1564i			0.659536i
$935$	−4.34034			−0.141944
$936$	−6.04653	−	5.55464i	−0.197637	−	0.181559i
$937$			43.3848i			1.41732i	0.705551	+	0.708659i	$0.250700\pi$
$937$			43.3848i			1.41732i	−0.705551	+	0.708659i	$0.749300\pi$
$938$			2.67907i			0.0874748i
$939$	−15.5782	+	6.84289i	−0.508377	+	0.223309i
$940$			26.7443i			0.872303i
$941$	4.73452			0.154341			0.0771705	−	0.997018i	$-0.475411\pi$
$941$	4.73452			0.154341			0.0771705	+	0.997018i	$0.475411\pi$
$942$	16.7449	+	38.1208i	0.545579	+	1.24204i
$943$	13.7857	−	4.90259i	0.448926	−	0.159650i
$944$			4.28580i			0.139491i
$945$	−5.30889	+	15.5430i	−0.172698	+	0.505614i
$946$	3.46620			0.112696
$947$			15.6253i			0.507754i	0.967237	+	0.253877i	$0.0817058\pi$
$947$			15.6253i			0.507754i	−0.967237	+	0.253877i	$0.918294\pi$
$948$	7.89865	−	3.46956i	0.256536	−	0.112686i
$949$	−11.3421			−0.368181
$950$	−37.3933			−1.21320
$951$	32.7570	−	14.3888i	1.06222	−	0.466590i
$952$	0.955308			0.0309617
$953$	−15.1466			−0.490645			−0.245323	−	0.969441i	$-0.578894\pi$
$953$	−15.1466			−0.490645			−0.245323	+	0.969441i	$0.578894\pi$
$954$	−27.4416	−	25.2092i	−0.888454	−	0.816179i
$955$	7.02631			0.227366
$956$			23.8378i			0.770971i
$957$	−20.1193	+	8.83761i	−0.650366	+	0.285679i
$958$			16.2560i			0.525209i
$959$		−	4.41592i		−	0.142597i
$960$	2.20184	+	5.01261i	0.0710639	+	0.161781i
$961$	−22.3539			−0.721094
$962$	−6.69326			−0.215799
$963$	−35.5999	+	38.7524i	−1.14719	+	1.24878i
$964$			23.4908i			0.756587i
$965$	−1.76409			−0.0567882
$966$	6.04626	−	5.69586i	0.194535	−	0.183261i
$967$	56.9433			1.83117			0.915587	−	0.402121i	$-0.131727\pi$
$967$	56.9433			1.83117			0.915587	+	0.402121i	$0.131727\pi$
$968$		−	8.93398i		−	0.287149i
$969$	−11.3491	+	4.98519i	−0.364585	+	0.160147i
$970$	14.9050			0.478571
$971$	−16.4715			−0.528597			−0.264298	−	0.964441i	$-0.585140\pi$
$971$	−16.4715			−0.528597			−0.264298	+	0.964441i	$0.585140\pi$
$972$	−13.6904	+	7.45482i	−0.439118	+	0.239113i
$973$			11.6934i			0.374875i
$974$		−	7.11067i		−	0.227841i
$975$	9.51597	+	21.6637i	0.304755	+	0.693792i
$976$		−	3.13255i		−	0.100270i
$977$	48.1456			1.54032			0.770158	−	0.637853i	$-0.220177\pi$
$977$	48.1456			1.54032			0.770158	+	0.637853i	$0.220177\pi$
$978$	−37.8800	+	16.6392i	−1.21127	+	0.532061i
$979$	−16.4427			−0.525510
$980$	−3.16093			−0.100972
$981$	−8.22678	−	7.55753i	−0.262661	−	0.241293i
$982$	−8.71633			−0.278149
$983$	16.2780			0.519187			0.259594	−	0.965718i	$-0.416411\pi$
$983$	16.2780			0.519187			0.259594	+	0.965718i	$0.416411\pi$
$984$	−2.12519	−	4.83811i	−0.0677485	−	0.154233i
$985$			39.0701i			1.24488i
$986$	8.43219			0.268536
$987$	−5.89370	−	13.4174i	−0.187598	−	0.427079i
$988$			20.5033i			0.652296i
$989$	−10.8966	+	3.87513i	−0.346492	+	0.123222i
$990$	10.0376	+	9.22107i	0.319017	+	0.293065i
$991$	−39.4499			−1.25317			−0.626584	−	0.779354i	$-0.715547\pi$
$991$	−39.4499			−1.25317			−0.626584	+	0.779354i	$0.715547\pi$
$992$			2.94042i			0.0933585i
$993$	20.8330	+	47.4275i	0.661114	+	1.50506i
$994$		−	12.6591i		−	0.401521i
$995$			27.8396i			0.882575i
$996$	3.96762	+	9.03253i	0.125719	+	0.286207i
$997$	6.46064			0.204611			0.102305	−	0.994753i	$-0.467378\pi$
$997$	6.46064			0.204611			0.102305	+	0.994753i	$0.467378\pi$
$998$		−	7.71385i		−	0.244178i
$999$	−4.10745	+	12.0255i	−0.129954	+	0.380470i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.h.a.827.8	✓	24
3.2	odd	2		966.2.h.b.827.20	yes	24
23.22	odd	2		966.2.h.b.827.8	yes	24
69.68	even	2	inner	966.2.h.a.827.20	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.h.a.827.8	✓	24	1.1	even	1	trivial
966.2.h.a.827.20	yes	24	69.68	even	2	inner
966.2.h.b.827.8	yes	24	23.22	odd	2
966.2.h.b.827.20	yes	24	3.2	odd	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.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.696580 + 1.58580i) q^{3} -1.00000 q^{4} -3.16093 q^{5} +(1.58580 - 0.696580i) q^{6} +1.00000i q^{7} +1.00000i q^{8} +(-2.02955 + 2.20928i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.696580 + 1.58580i) q^{3} -1.00000 q^{4} -3.16093 q^{5} +(1.58580 - 0.696580i) q^{6} +1.00000i q^{7} +1.00000i q^{8} +(-2.02955 + 2.20928i) q^{9} +3.16093i q^{10} -1.43736 q^{11} +(-0.696580 - 1.58580i) q^{12} +2.73688 q^{13} +1.00000 q^{14} +(-2.20184 - 5.01261i) q^{15} +1.00000 q^{16} -0.955308 q^{17} +(2.20928 + 2.02955i) q^{18} -7.49148i q^{19} +3.16093 q^{20} +(-1.58580 + 0.696580i) q^{21} +1.43736i q^{22} +(-1.60694 - 4.51860i) q^{23} +(-1.58580 + 0.696580i) q^{24} +4.99145 q^{25} -2.73688i q^{26} +(-4.91723 - 1.67954i) q^{27} -1.00000i q^{28} -8.82668i q^{29} +(-5.01261 + 2.20184i) q^{30} -2.94042 q^{31} -1.00000i q^{32} +(-1.00124 - 2.27938i) q^{33} +0.955308i q^{34} -3.16093i q^{35} +(2.02955 - 2.20928i) q^{36} -2.44558i q^{37} -7.49148 q^{38} +(1.90645 + 4.34016i) q^{39} -3.16093i q^{40} +3.05089i q^{41} +(0.696580 + 1.58580i) q^{42} -2.41150i q^{43} +1.43736 q^{44} +(6.41527 - 6.98336i) q^{45} +(-4.51860 + 1.60694i) q^{46} +8.46091i q^{47} +(0.696580 + 1.58580i) q^{48} -1.00000 q^{49} -4.99145i q^{50} +(-0.665448 - 1.51493i) q^{51} -2.73688 q^{52} -12.4211 q^{53} +(-1.67954 + 4.91723i) q^{54} +4.54340 q^{55} -1.00000 q^{56} +(11.8800 - 5.21841i) q^{57} -8.82668 q^{58} +4.28580i q^{59} +(2.20184 + 5.01261i) q^{60} -3.13255i q^{61} +2.94042i q^{62} +(-2.20928 - 2.02955i) q^{63} -1.00000 q^{64} -8.65107 q^{65} +(-2.27938 + 1.00124i) q^{66} +2.67907i q^{67} +0.955308 q^{68} +(6.04626 - 5.69586i) q^{69} -3.16093 q^{70} -12.6591i q^{71} +(-2.20928 - 2.02955i) q^{72} -4.14418 q^{73} -2.44558 q^{74} +(3.47694 + 7.91546i) q^{75} +7.49148i q^{76} -1.43736i q^{77} +(4.34016 - 1.90645i) q^{78} +4.98085i q^{79} -3.16093 q^{80} +(-0.761822 - 8.96770i) q^{81} +3.05089 q^{82} -5.69587 q^{83} +(1.58580 - 0.696580i) q^{84} +3.01966 q^{85} -2.41150 q^{86} +(13.9974 - 6.14848i) q^{87} -1.43736i q^{88} +11.4395 q^{89} +(-6.98336 - 6.41527i) q^{90} +2.73688i q^{91} +(1.60694 + 4.51860i) q^{92} +(-2.04824 - 4.66294i) q^{93} +8.46091 q^{94} +23.6800i q^{95} +(1.58580 - 0.696580i) q^{96} -4.71539i q^{97} +1.00000i q^{98} +(2.91721 - 3.17554i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{3} - 24 q^{4} - 4 q^{5} - 4 q^{9}+O(q^{10}) \) 24 * q + 4 * q^3 - 24 * q^4 - 4 * q^5 - 4 * q^9	\( 24 q + 4 q^{3} - 24 q^{4} - 4 q^{5} - 4 q^{9} - 4 q^{12} + 8 q^{13} + 24 q^{14} - 4 q^{15} + 24 q^{16} + 32 q^{17} + 4 q^{18} + 4 q^{20} - 8 q^{23} - 12 q^{25} + 16 q^{27} - 4 q^{30} - 16 q^{31} + 20 q^{33} + 4 q^{36} - 8 q^{39} + 4 q^{42} + 24 q^{45} - 4 q^{46} + 4 q^{48} - 24 q^{49} + 24 q^{51} - 8 q^{52} + 24 q^{53} - 12 q^{54} + 16 q^{55} - 24 q^{56} + 4 q^{57} + 4 q^{58} + 4 q^{60} - 4 q^{63} - 24 q^{64} - 12 q^{66} - 32 q^{68} - 24 q^{69} - 4 q^{70} - 4 q^{72} - 32 q^{73} - 16 q^{74} + 48 q^{75} + 12 q^{78} - 4 q^{80} - 8 q^{81} - 8 q^{82} + 16 q^{83} - 16 q^{85} + 16 q^{86} + 20 q^{87} + 24 q^{89} - 28 q^{90} + 8 q^{92} + 16 q^{93} + 8 q^{94} - 48 q^{99}+O(q^{100}) \) 24 * q + 4 * q^3 - 24 * q^4 - 4 * q^5 - 4 * q^9 - 4 * q^12 + 8 * q^13 + 24 * q^14 - 4 * q^15 + 24 * q^16 + 32 * q^17 + 4 * q^18 + 4 * q^20 - 8 * q^23 - 12 * q^25 + 16 * q^27 - 4 * q^30 - 16 * q^31 + 20 * q^33 + 4 * q^36 - 8 * q^39 + 4 * q^42 + 24 * q^45 - 4 * q^46 + 4 * q^48 - 24 * q^49 + 24 * q^51 - 8 * q^52 + 24 * q^53 - 12 * q^54 + 16 * q^55 - 24 * q^56 + 4 * q^57 + 4 * q^58 + 4 * q^60 - 4 * q^63 - 24 * q^64 - 12 * q^66 - 32 * q^68 - 24 * q^69 - 4 * q^70 - 4 * q^72 - 32 * q^73 - 16 * q^74 + 48 * q^75 + 12 * q^78 - 4 * q^80 - 8 * q^81 - 8 * q^82 + 16 * q^83 - 16 * q^85 + 16 * q^86 + 20 * q^87 + 24 * q^89 - 28 * q^90 + 8 * q^92 + 16 * q^93 + 8 * q^94 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more