LMFDB - Embedded newform 966.2.g.e.643.12

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			643.12
Root			$-0.691340 - 0.691340i$ of defining polynomial
Character	$\chi$	$=$	966.643
Dual form			966.2.g.e.643.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} -0.952834 q^{5} +1.00000i q^{6} +(-0.691340 + 2.55383i) q^{7} +1.00000 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} -0.952834 q^{5} +1.00000i q^{6} +(-0.691340 + 2.55383i) q^{7} +1.00000 q^{8} -1.00000 q^{9} -0.952834 q^{10} -1.02228i q^{11} +1.00000i q^{12} +5.28761i q^{13} +(-0.691340 + 2.55383i) q^{14} -0.952834i q^{15} +1.00000 q^{16} -1.38268 q^{17} -1.00000 q^{18} -5.99105 q^{19} -0.952834 q^{20} +(-2.55383 - 0.691340i) q^{21} -1.02228i q^{22} +(3.53113 + 3.24517i) q^{23} +1.00000i q^{24} -4.09211 q^{25} +5.28761i q^{26} -1.00000i q^{27} +(-0.691340 + 2.55383i) q^{28} +5.57914 q^{29} -0.952834i q^{30} +1.00000 q^{32} +1.02228 q^{33} -1.38268 q^{34} +(0.658732 - 2.43338i) q^{35} -1.00000 q^{36} -0.429846i q^{37} -5.99105 q^{38} -5.28761 q^{39} -0.952834 q^{40} +1.28761i q^{41} +(-2.55383 - 0.691340i) q^{42} +4.67781i q^{43} -1.02228i q^{44} +0.952834 q^{45} +(3.53113 + 3.24517i) q^{46} +7.09211i q^{47} +1.00000i q^{48} +(-6.04410 - 3.53113i) q^{49} -4.09211 q^{50} -1.38268i q^{51} +5.28761i q^{52} +8.75641i q^{53} -1.00000i q^{54} +0.974060i q^{55} +(-0.691340 + 2.55383i) q^{56} -5.99105i q^{57} +5.57914 q^{58} +1.70848i q^{59} -0.952834i q^{60} +7.37373 q^{61} +(0.691340 - 2.55383i) q^{63} +1.00000 q^{64} -5.03822i q^{65} +1.02228 q^{66} -11.6217i q^{67} -1.38268 q^{68} +(-3.24517 + 3.53113i) q^{69} +(0.658732 - 2.43338i) q^{70} -2.29152 q^{71} -1.00000 q^{72} -2.19551i q^{73} -0.429846i q^{74} -4.09211i q^{75} -5.99105 q^{76} +(2.61072 + 0.706741i) q^{77} -5.28761 q^{78} -9.77869i q^{79} -0.952834 q^{80} +1.00000 q^{81} +1.28761i q^{82} +5.46806 q^{83} +(-2.55383 - 0.691340i) q^{84} +1.31746 q^{85} +4.67781i q^{86} +5.57914i q^{87} -1.02228i q^{88} +8.69375 q^{89} +0.952834 q^{90} +(-13.5037 - 3.65554i) q^{91} +(3.53113 + 3.24517i) q^{92} +7.09211i q^{94} +5.70848 q^{95} +1.00000i q^{96} +19.2038 q^{97} +(-6.04410 - 3.53113i) q^{98} +1.02228i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−0.952834			−0.426120			−0.213060	−	0.977039i	$-0.568343\pi$
$5$	−0.952834			−0.426120			−0.213060	+	0.977039i	$0.568343\pi$
$6$			1.00000i			0.408248i
$7$	−0.691340	+	2.55383i	−0.261302	+	0.965257i
$7$	−0.691340	+	2.55383i	−0.261302	+	0.965257i
$8$	1.00000			0.353553
$9$	−1.00000			−0.333333
$10$	−0.952834			−0.301313
$11$		−	1.02228i		−	0.308228i	−0.988053	−	0.154114i	$-0.950748\pi$
$11$		−	1.02228i		−	0.308228i	0.988053	−	0.154114i	$-0.0492523\pi$
$12$			1.00000i			0.288675i
$13$			5.28761i			1.46652i	0.679948	+	0.733260i	$0.262002\pi$
$13$			5.28761i			1.46652i	−0.679948	+	0.733260i	$0.737998\pi$
$14$	−0.691340	+	2.55383i	−0.184768	+	0.682540i
$15$		−	0.952834i		−	0.246021i
$16$	1.00000			0.250000
$17$	−1.38268			−0.335349			−0.167675	−	0.985842i	$-0.553626\pi$
$17$	−1.38268			−0.335349			−0.167675	+	0.985842i	$0.553626\pi$
$18$	−1.00000			−0.235702
$19$	−5.99105			−1.37444			−0.687221	−	0.726449i	$-0.741169\pi$
$19$	−5.99105			−1.37444			−0.687221	+	0.726449i	$0.741169\pi$
$20$	−0.952834			−0.213060
$21$	−2.55383	−	0.691340i	−0.557291	−	0.150863i
$22$		−	1.02228i		−	0.217950i
$23$	3.53113	+	3.24517i	0.736291	+	0.676665i
$23$	3.53113	+	3.24517i	0.736291	+	0.676665i
$24$			1.00000i			0.204124i
$25$	−4.09211			−0.818422
$26$			5.28761i			1.03699i
$27$		−	1.00000i		−	0.192450i
$28$	−0.691340	+	2.55383i	−0.130651	+	0.482629i
$29$	5.57914			1.03602			0.518010	−	0.855375i	$-0.326673\pi$
$29$	5.57914			1.03602			0.518010	+	0.855375i	$0.326673\pi$
$30$		−	0.952834i		−	0.173963i
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$	1.00000			0.176777
$33$	1.02228			0.177956
$34$	−1.38268			−0.237128
$35$	0.658732	−	2.43338i	0.111346	−	0.411316i
$36$	−1.00000			−0.166667
$37$		−	0.429846i		−	0.0706662i	−0.999376	−	0.0353331i	$-0.988751\pi$
$37$		−	0.429846i		−	0.0706662i	0.999376	−	0.0353331i	$-0.0112492\pi$
$38$	−5.99105			−0.971877
$39$	−5.28761			−0.846696
$40$	−0.952834			−0.150656
$41$			1.28761i			0.201091i	0.994932	+	0.100546i	$0.0320589\pi$
$41$			1.28761i			0.201091i	−0.994932	+	0.100546i	$0.967941\pi$
$42$	−2.55383	−	0.691340i	−0.394065	−	0.106676i
$43$			4.67781i			0.713360i	0.934227	+	0.356680i	$0.116091\pi$
$43$			4.67781i			0.713360i	−0.934227	+	0.356680i	$0.883909\pi$
$44$		−	1.02228i		−	0.154114i
$45$	0.952834			0.142040
$46$	3.53113	+	3.24517i	0.520637	+	0.478474i
$47$			7.09211i			1.03449i	0.855837	+	0.517245i	$0.173042\pi$
$47$			7.09211i			1.03449i	−0.855837	+	0.517245i	$0.826958\pi$
$48$			1.00000i			0.144338i
$49$	−6.04410	−	3.53113i	−0.863443	−	0.504447i
$50$	−4.09211			−0.578711
$51$		−	1.38268i		−	0.193614i
$52$			5.28761i			0.733260i
$53$			8.75641i			1.20279i	0.798954	+	0.601393i	$0.205387\pi$
$53$			8.75641i			1.20279i	−0.798954	+	0.601393i	$0.794613\pi$
$54$		−	1.00000i		−	0.136083i
$55$			0.974060i			0.131342i
$56$	−0.691340	+	2.55383i	−0.0923842	+	0.341270i
$57$		−	5.99105i		−	0.793534i
$58$	5.57914			0.732577
$59$			1.70848i			0.222425i	0.993797	+	0.111212i	$0.0354734\pi$
$59$			1.70848i			0.222425i	−0.993797	+	0.111212i	$0.964527\pi$
$60$		−	0.952834i		−	0.123010i
$61$	7.37373			0.944109			0.472055	−	0.881569i	$-0.343512\pi$
$61$	7.37373			0.944109			0.472055	+	0.881569i	$0.343512\pi$
$62$		0			0
$63$	0.691340	−	2.55383i	0.0871006	−	0.321752i
$64$	1.00000			0.125000
$65$		−	5.03822i		−	0.624914i
$66$	1.02228			0.125834
$67$		−	11.6217i		−	1.41982i	−0.704294	−	0.709908i	$-0.748736\pi$
$67$		−	11.6217i		−	1.41982i	0.704294	−	0.709908i	$-0.251264\pi$
$68$	−1.38268			−0.167675
$69$	−3.24517	+	3.53113i	−0.390673	+	0.425098i
$70$	0.658732	−	2.43338i	0.0787335	−	0.290844i
$71$	−2.29152			−0.271954			−0.135977	−	0.990712i	$-0.543417\pi$
$71$	−2.29152			−0.271954			−0.135977	+	0.990712i	$0.543417\pi$
$72$	−1.00000			−0.117851
$73$		−	2.19551i		−	0.256965i	−0.991712	−	0.128482i	$-0.958989\pi$
$73$		−	2.19551i		−	0.256965i	0.991712	−	0.128482i	$-0.0410105\pi$
$74$		−	0.429846i		−	0.0499685i
$75$		−	4.09211i		−	0.472516i
$76$	−5.99105			−0.687221
$77$	2.61072	+	0.706741i	0.297519	+	0.0805406i
$78$	−5.28761			−0.598704
$79$		−	9.77869i		−	1.10019i	−0.835103	−	0.550094i	$-0.814592\pi$
$79$		−	9.77869i		−	1.10019i	0.835103	−	0.550094i	$-0.185408\pi$
$80$	−0.952834			−0.106530
$81$	1.00000			0.111111
$82$			1.28761i			0.142193i
$83$	5.46806			0.600198			0.300099	−	0.953908i	$-0.402980\pi$
$83$	5.46806			0.600198			0.300099	+	0.953908i	$0.402980\pi$
$84$	−2.55383	−	0.691340i	−0.278646	−	0.0754314i
$85$	1.31746			0.142899
$86$			4.67781i			0.504422i
$87$			5.57914i			0.598146i
$88$		−	1.02228i		−	0.108975i
$89$	8.69375			0.921536			0.460768	−	0.887521i	$-0.347574\pi$
$89$	8.69375			0.921536			0.460768	+	0.887521i	$0.347574\pi$
$90$	0.952834			0.100438
$91$	−13.5037	−	3.65554i	−1.41557	−	0.383204i
$92$	3.53113	+	3.24517i	0.368146	+	0.338332i
$93$		0			0
$94$			7.09211i			0.731495i
$95$	5.70848			0.585677
$96$			1.00000i			0.102062i
$97$	19.2038			1.94985			0.974923	−	0.222541i	$-0.0714353\pi$
$97$	19.2038			1.94985			0.974923	+	0.222541i	$0.0714353\pi$
$98$	−6.04410	−	3.53113i	−0.610546	−	0.356698i
$99$			1.02228i			0.102743i
$100$	−4.09211			−0.409211
$101$		−	15.8927i		−	1.58138i	−0.612216	−	0.790691i	$-0.709722\pi$
$101$		−	15.8927i		−	1.58138i	0.612216	−	0.790691i	$-0.290278\pi$
$102$		−	1.38268i		−	0.136906i
$103$	−1.74987			−0.172420			−0.0862099	−	0.996277i	$-0.527476\pi$
$103$	−1.74987			−0.172420			−0.0862099	+	0.996277i	$0.527476\pi$
$104$			5.28761i			0.518493i
$105$	2.43338	+	0.658732i	0.237473	+	0.0642856i
$106$			8.75641i			0.850498i
$107$			11.0987i			1.07295i	0.843915	+	0.536476i	$0.180245\pi$
$107$			11.0987i			1.07295i	−0.843915	+	0.536476i	$0.819755\pi$
$108$		−	1.00000i		−	0.0962250i
$109$			2.33551i			0.223702i	0.993725	+	0.111851i	$0.0356779\pi$
$109$			2.33551i			0.223702i	−0.993725	+	0.111851i	$0.964322\pi$
$110$			0.974060i			0.0928730i
$111$	0.429846			0.0407991
$112$	−0.691340	+	2.55383i	−0.0653255	+	0.241314i
$113$			10.2322i			0.962567i	0.876565	+	0.481284i	$0.159829\pi$
$113$			10.2322i			0.962567i	−0.876565	+	0.481284i	$0.840171\pi$
$114$		−	5.99105i		−	0.561113i
$115$	−3.36458	−	3.09211i	−0.313749	−	0.288341i
$116$	5.57914			0.518010
$117$		−	5.28761i		−	0.488840i
$118$			1.70848i			0.157278i
$119$	0.955901	−	3.53113i	0.0876273	−	0.323698i
$120$		−	0.952834i		−	0.0869814i
$121$	9.95495			0.904995
$122$	7.37373			0.667586
$123$	−1.28761			−0.116100
$124$		0			0
$125$	8.66327			0.774866
$126$	0.691340	−	2.55383i	0.0615894	−	0.227513i
$127$	−16.3499			−1.45082			−0.725408	−	0.688319i	$-0.758349\pi$
$127$	−16.3499			−1.45082			−0.725408	+	0.688319i	$0.758349\pi$
$128$	1.00000			0.0883883
$129$	−4.67781			−0.411859
$130$		−	5.03822i		−	0.441881i
$131$		−	11.1583i		−	0.974903i	−0.873150	−	0.487452i	$-0.837927\pi$
$131$		−	11.1583i		−	0.974903i	0.873150	−	0.487452i	$-0.162073\pi$
$132$	1.02228			0.0889778
$133$	4.14185	−	15.3001i	0.359144	−	1.32669i
$134$		−	11.6217i		−	1.00396i
$135$			0.952834i			0.0820069i
$136$	−1.38268			−0.118564
$137$			0.155798i			0.0133107i	0.999978	+	0.00665534i	$0.00211848\pi$
$137$			0.155798i			0.0133107i	−0.999978	+	0.00665534i	$0.997882\pi$
$138$	−3.24517	+	3.53113i	−0.276247	+	0.300590i
$139$			2.99609i			0.254125i	0.991895	+	0.127063i	$0.0405549\pi$
$139$			2.99609i			0.254125i	−0.991895	+	0.127063i	$0.959445\pi$
$140$	0.658732	−	2.43338i	0.0556730	−	0.205658i
$141$	−7.09211			−0.597263
$142$	−2.29152			−0.192300
$143$	5.40541			0.452023
$144$	−1.00000			−0.0833333
$145$	−5.31599			−0.441469
$146$		−	2.19551i		−	0.181701i
$147$	3.53113	−	6.04410i	0.291243	−	0.498509i
$148$		−	0.429846i		−	0.0353331i
$149$		−	2.17972i		−	0.178569i	−0.996006	−	0.0892846i	$-0.971542\pi$
$149$		−	2.17972i		−	0.178569i	0.996006	−	0.0892846i	$-0.0284581\pi$
$150$		−	4.09211i		−	0.334119i
$151$	1.38363			0.112598			0.0562992	−	0.998414i	$-0.482070\pi$
$151$	1.38363			0.112598			0.0562992	+	0.998414i	$0.482070\pi$
$152$	−5.99105			−0.485938
$153$	1.38268			0.111783
$154$	2.61072	+	0.706741i	0.210378	+	0.0569508i
$155$		0			0
$156$	−5.28761			−0.423348
$157$	11.1851			0.892665			0.446333	−	0.894867i	$-0.352730\pi$
$157$	11.1851			0.892665			0.446333	+	0.894867i	$0.352730\pi$
$158$		−	9.77869i		−	0.777951i
$159$	−8.75641			−0.694428
$160$	−0.952834			−0.0753281
$161$	−10.7288	+	6.77439i	−0.845550	+	0.533897i
$162$	1.00000			0.0785674
$163$	7.54929			0.591306			0.295653	−	0.955295i	$-0.404463\pi$
$163$	7.54929			0.591306			0.295653	+	0.955295i	$0.404463\pi$
$164$			1.28761i			0.100546i
$165$	−0.974060			−0.0758305
$166$	5.46806			0.424404
$167$			11.9290i			0.923094i	0.887116	+	0.461547i	$0.152706\pi$
$167$			11.9290i			0.923094i	−0.887116	+	0.461547i	$0.847294\pi$
$168$	−2.55383	−	0.691340i	−0.197032	−	0.0533380i
$169$	−14.9589			−1.15068
$170$	1.31746			0.101045
$171$	5.99105			0.458147
$172$			4.67781i			0.356680i
$173$		−	18.0882i		−	1.37522i	−0.726080	−	0.687610i	$-0.758660\pi$
$173$		−	18.0882i		−	1.37522i	0.726080	−	0.687610i	$-0.241340\pi$
$174$			5.57914i			0.422953i
$175$	2.82904	−	10.4505i	0.213855	−	0.789987i
$176$		−	1.02228i		−	0.0770571i
$177$	−1.70848			−0.128417
$178$	8.69375			0.651624
$179$	1.77464			0.132643			0.0663216	−	0.997798i	$-0.478874\pi$
$179$	1.77464			0.132643			0.0663216	+	0.997798i	$0.478874\pi$
$180$	0.952834			0.0710200
$181$	20.4933			1.52325			0.761627	−	0.648015i	$-0.224401\pi$
$181$	20.4933			1.52325			0.761627	+	0.648015i	$0.224401\pi$
$182$	−13.5037	−	3.65554i	−1.00096	−	0.270966i
$183$			7.37373i			0.545082i
$184$	3.53113	+	3.24517i	0.260318	+	0.239237i
$185$			0.409572i			0.0301123i
$186$		0			0
$187$			1.41348i			0.103364i
$188$			7.09211i			0.517245i
$189$	2.55383	+	0.691340i	0.185764	+	0.0502876i
$190$	5.70848			0.414136
$191$		−	1.68043i		−	0.121591i	−0.998150	−	0.0607957i	$-0.980636\pi$
$191$		−	1.68043i		−	0.121591i	0.998150	−	0.0607957i	$-0.0193638\pi$
$192$			1.00000i			0.0721688i
$193$	−4.71239			−0.339205			−0.169602	−	0.985513i	$-0.554248\pi$
$193$	−4.71239			−0.339205			−0.169602	+	0.985513i	$0.554248\pi$
$194$	19.2038			1.37875
$195$	5.03822			0.360794
$196$	−6.04410	−	3.53113i	−0.431721	−	0.252223i
$197$	24.9251			1.77584			0.887920	−	0.459998i	$-0.152150\pi$
$197$	24.9251			1.77584			0.887920	+	0.459998i	$0.152150\pi$
$198$			1.02228i			0.0726501i
$199$	8.60434			0.609945			0.304973	−	0.952361i	$-0.401353\pi$
$199$	8.60434			0.609945			0.304973	+	0.952361i	$0.401353\pi$
$200$	−4.09211			−0.289356
$201$	11.6217			0.819731
$202$		−	15.8927i		−	1.11821i
$203$	−3.85708	+	14.2482i	−0.270714	+	1.00003i
$204$		−	1.38268i		−	0.0968069i
$205$		−	1.22688i		−	0.0856892i
$206$	−1.74987			−0.121919
$207$	−3.53113	−	3.24517i	−0.245430	−	0.225555i
$208$			5.28761i			0.366630i
$209$			6.12452i			0.423642i
$210$	2.43338	+	0.658732i	0.167919	+	0.0454568i
$211$	−19.3460			−1.33183			−0.665915	−	0.746027i	$-0.731959\pi$
$211$	−19.3460			−1.33183			−0.665915	+	0.746027i	$0.731959\pi$
$212$			8.75641i			0.601393i
$213$		−	2.29152i		−	0.157013i
$214$			11.0987i			0.758692i
$215$		−	4.45718i		−	0.303977i
$216$		−	1.00000i		−	0.0680414i
$217$		0			0
$218$			2.33551i			0.158181i
$219$	2.19551			0.148359
$220$			0.974060i			0.0656711i
$221$		−	7.31108i		−	0.491796i
$222$	0.429846			0.0288494
$223$			17.7335i			1.18752i	0.804641	+	0.593762i	$0.202358\pi$
$223$			17.7335i			1.18752i	−0.804641	+	0.593762i	$0.797642\pi$
$224$	−0.691340	+	2.55383i	−0.0461921	+	0.170635i
$225$	4.09211			0.272807
$226$			10.2322i			0.680638i
$227$	9.92436			0.658703			0.329352	−	0.944207i	$-0.393170\pi$
$227$	9.92436			0.658703			0.329352	+	0.944207i	$0.393170\pi$
$228$		−	5.99105i		−	0.396767i
$229$	−15.8223			−1.04557			−0.522783	−	0.852466i	$-0.675106\pi$
$229$	−15.8223			−1.04557			−0.522783	+	0.852466i	$0.675106\pi$
$230$	−3.36458	−	3.09211i	−0.221854	−	0.203888i
$231$	−0.706741	+	2.61072i	−0.0465001	+	0.171773i
$232$	5.57914			0.366288
$233$	13.0259			0.853358			0.426679	−	0.904403i	$-0.359683\pi$
$233$	13.0259			0.853358			0.426679	+	0.904403i	$0.359683\pi$
$234$		−	5.28761i		−	0.345662i
$235$		−	6.75760i		−	0.440817i
$236$			1.70848i			0.111212i
$237$	9.77869			0.635194
$238$	0.955901	−	3.53113i	0.0619619	−	0.228889i
$239$	10.6712			0.690266			0.345133	−	0.938554i	$-0.387834\pi$
$239$	10.6712			0.690266			0.345133	+	0.938554i	$0.387834\pi$
$240$		−	0.952834i		−	0.0615052i
$241$	−19.2038			−1.23702			−0.618511	−	0.785776i	$-0.712264\pi$
$241$	−19.2038			−1.23702			−0.618511	+	0.785776i	$0.712264\pi$
$242$	9.95495			0.639928
$243$			1.00000i			0.0641500i
$244$	7.37373			0.472055
$245$	5.75902	+	3.36458i	0.367930	+	0.214955i
$246$	−1.28761			−0.0820953
$247$		−	31.6784i		−	2.01565i
$248$		0			0
$249$			5.46806i			0.346524i
$250$	8.66327			0.547913
$251$	−0.429846			−0.0271316			−0.0135658	−	0.999908i	$-0.504318\pi$
$251$	−0.429846			−0.0271316			−0.0135658	+	0.999908i	$0.504318\pi$
$252$	0.691340	−	2.55383i	0.0435503	−	0.160876i
$253$	3.31746	−	3.60979i	0.208567	−	0.226946i
$254$	−16.3499			−1.02588
$255$			1.31746i			0.0825028i
$256$	1.00000			0.0625000
$257$		−	21.2465i		−	1.32532i	−0.748921	−	0.662659i	$-0.769428\pi$
$257$		−	21.2465i		−	1.32532i	0.748921	−	0.662659i	$-0.230572\pi$
$258$	−4.67781			−0.291228
$259$	1.09775	+	0.297169i	0.0682111	+	0.0184652i
$260$		−	5.03822i		−	0.312457i
$261$	−5.57914			−0.345340
$262$		−	11.1583i		−	0.689361i
$263$			18.1188i			1.11725i	0.829419	+	0.558627i	$0.188672\pi$
$263$			18.1188i			1.11725i	−0.829419	+	0.558627i	$0.811328\pi$
$264$	1.02228			0.0629168
$265$		−	8.34340i		−	0.512531i
$266$	4.14185	−	15.3001i	0.253953	−	0.938111i
$267$			8.69375i			0.532049i
$268$		−	11.6217i		−	0.709908i
$269$		−	3.44198i		−	0.209861i	−0.994480	−	0.104931i	$-0.966538\pi$
$269$		−	3.44198i		−	0.209861i	0.994480	−	0.104931i	$-0.0334620\pi$
$270$			0.952834i			0.0579876i
$271$		−	2.57523i		−	0.156434i	−0.996936	−	0.0782170i	$-0.975077\pi$
$271$		−	2.57523i		−	0.156434i	0.996936	−	0.0782170i	$-0.0249227\pi$
$272$	−1.38268			−0.0838373
$273$	3.65554	−	13.5037i	0.221243	−	0.817279i
$274$			0.155798i			0.00941208i
$275$			4.18327i			0.252261i
$276$	−3.24517	+	3.53113i	−0.195336	+	0.212549i
$277$	−15.7335			−0.945335			−0.472667	−	0.881241i	$-0.656709\pi$
$277$	−15.7335			−0.945335			−0.472667	+	0.881241i	$0.656709\pi$
$278$			2.99609i			0.179694i
$279$		0			0
$280$	0.658732	−	2.43338i	0.0393668	−	0.145422i
$281$		−	24.2115i		−	1.44434i	−0.691717	−	0.722168i	$-0.743146\pi$
$281$		−	24.2115i		−	1.44434i	0.691717	−	0.722168i	$-0.256854\pi$
$282$	−7.09211			−0.422329
$283$	−24.2383			−1.44081			−0.720407	−	0.693551i	$-0.756045\pi$
$283$	−24.2383			−1.44081			−0.720407	+	0.693551i	$0.756045\pi$
$284$	−2.29152			−0.135977
$285$			5.70848i			0.338141i
$286$	5.40541			0.319628
$287$	−3.28835	−	0.890179i	−0.194105	−	0.0525456i
$288$	−1.00000			−0.0589256
$289$	−15.0882			−0.887541
$290$	−5.31599			−0.312166
$291$			19.2038i			1.12574i
$292$		−	2.19551i		−	0.128482i
$293$	27.2814			1.59380			0.796898	−	0.604114i	$-0.206473\pi$
$293$	27.2814			1.59380			0.796898	+	0.604114i	$0.206473\pi$
$294$	3.53113	−	6.04410i	0.205940	−	0.352499i
$295$		−	1.62789i		−	0.0947796i
$296$		−	0.429846i		−	0.0249843i
$297$	−1.02228			−0.0593185
$298$		−	2.17972i		−	0.126268i
$299$	−17.1592	+	18.6712i	−0.992343	+	1.07979i
$300$		−	4.09211i		−	0.236258i
$301$	−11.9463	−	3.23396i	−0.688576	−	0.186402i
$302$	1.38363			0.0796191
$303$	15.8927			0.913011
$304$	−5.99105			−0.343610
$305$	−7.02594			−0.402304
$306$	1.38268			0.0790425
$307$			25.1206i			1.43371i	0.697223	+	0.716854i	$0.254419\pi$
$307$			25.1206i			1.43371i	−0.697223	+	0.716854i	$0.745581\pi$
$308$	2.61072	+	0.706741i	0.148760	+	0.0402703i
$309$		−	1.74987i		−	0.0995466i
$310$		0			0
$311$			10.6712i			0.605111i	0.953132	+	0.302555i	$0.0978397\pi$
$311$			10.6712i			0.605111i	−0.953132	+	0.302555i	$0.902160\pi$
$312$	−5.28761			−0.299352
$313$	−9.21674			−0.520961			−0.260481	−	0.965479i	$-0.583881\pi$
$313$	−9.21674			−0.520961			−0.260481	+	0.965479i	$0.583881\pi$
$314$	11.1851			0.631210
$315$	−0.658732	+	2.43338i	−0.0371153	+	0.137105i
$316$		−	9.77869i		−	0.550094i
$317$	−25.3048			−1.42126			−0.710630	−	0.703566i	$-0.751590\pi$
$317$	−25.3048			−1.42126			−0.710630	+	0.703566i	$0.751590\pi$
$318$	−8.75641			−0.491035
$319$		−	5.70343i		−	0.319331i
$320$	−0.952834			−0.0532650
$321$	−11.0987			−0.619470
$322$	−10.7288	+	6.77439i	−0.597894	+	0.377522i
$323$	8.28370			0.460918
$324$	1.00000			0.0555556
$325$		−	21.6375i		−	1.20023i
$326$	7.54929			0.418116
$327$	−2.33551			−0.129154
$328$			1.28761i			0.0710966i
$329$	−18.1120	−	4.90306i	−0.998549	−	0.270314i
$330$	−0.974060			−0.0536203
$331$	−0.830434			−0.0456448			−0.0228224	−	0.999740i	$-0.507265\pi$
$331$	−0.830434			−0.0456448			−0.0228224	+	0.999740i	$0.507265\pi$
$332$	5.46806			0.300099
$333$			0.429846i			0.0235554i
$334$			11.9290i			0.652726i
$335$			11.0735i			0.605013i
$336$	−2.55383	−	0.691340i	−0.139323	−	0.0377157i
$337$			7.58885i			0.413391i	0.978405	+	0.206695i	$0.0662709\pi$
$337$			7.58885i			0.413391i	−0.978405	+	0.206695i	$0.933729\pi$
$338$	−14.9589			−0.813655
$339$	−10.2322			−0.555739
$340$	1.31746			0.0714495
$341$		0			0
$342$	5.99105			0.323959
$343$	13.1964	−	12.9944i	0.712540	−	0.701631i
$344$			4.67781i			0.252211i
$345$	3.09211	−	3.36458i	0.166473	−	0.181143i
$346$		−	18.0882i		−	0.972428i
$347$	30.1431			1.61817			0.809083	−	0.587695i	$-0.199965\pi$
$347$	30.1431			1.61817			0.809083	+	0.587695i	$0.199965\pi$
$348$			5.57914i			0.299073i
$349$			22.6115i			1.21037i	0.796086	+	0.605184i	$0.206901\pi$
$349$			22.6115i			1.21037i	−0.796086	+	0.605184i	$0.793099\pi$
$350$	2.82904	−	10.4505i	0.151218	−	0.558605i
$351$	5.28761			0.282232
$352$		−	1.02228i		−	0.0544876i
$353$		−	8.44589i		−	0.449529i	−0.974413	−	0.224765i	$-0.927839\pi$
$353$		−	8.44589i		−	0.449529i	0.974413	−	0.224765i	$-0.0721613\pi$
$354$	−1.70848			−0.0908045
$355$	2.18344			0.115885
$356$	8.69375			0.460768
$357$	3.53113	+	0.955901i	0.186887	+	0.0505917i
$358$	1.77464			0.0937928
$359$			18.7007i			0.986988i	0.869749	+	0.493494i	$0.164280\pi$
$359$			18.7007i			0.986988i	−0.869749	+	0.493494i	$0.835720\pi$
$360$	0.952834			0.0502188
$361$	16.8927			0.889089
$362$	20.4933			1.07710
$363$			9.95495i			0.522499i
$364$	−13.5037	−	3.65554i	−0.707785	−	0.191602i
$365$			2.09195i			0.109498i
$366$			7.37373i			0.385431i
$367$	−27.7112			−1.44651			−0.723257	−	0.690579i	$-0.757356\pi$
$367$	−27.7112			−1.44651			−0.723257	+	0.690579i	$0.757356\pi$
$368$	3.53113	+	3.24517i	0.184073	+	0.169166i
$369$		−	1.28761i		−	0.0670305i
$370$			0.409572i			0.0212926i
$371$	−22.3624	−	6.05365i	−1.16100	−	0.314290i
$372$		0			0
$373$		−	31.6157i		−	1.63700i	−0.574507	−	0.818500i	$-0.694806\pi$
$373$		−	31.6157i		−	1.63700i	0.574507	−	0.818500i	$-0.305194\pi$
$374$			1.41348i			0.0730894i
$375$			8.66327i			0.447369i
$376$			7.09211i			0.365748i
$377$			29.5003i			1.51934i
$378$	2.55383	+	0.691340i	0.131355	+	0.0355587i
$379$			31.2347i			1.60442i	0.597044	+	0.802209i	$0.296342\pi$
$379$			31.2347i			1.60442i	−0.597044	+	0.802209i	$0.703658\pi$
$380$	5.70848			0.292839
$381$		−	16.3499i		−	0.837629i
$382$		−	1.68043i		−	0.0859781i
$383$	−10.3880			−0.530804			−0.265402	−	0.964138i	$-0.585505\pi$
$383$	−10.3880			−0.530804			−0.265402	+	0.964138i	$0.585505\pi$
$384$			1.00000i			0.0510310i
$385$	−2.48758	−	0.673407i	−0.126779	−	0.0343200i
$386$	−4.71239			−0.239854
$387$		−	4.67781i		−	0.237787i
$388$	19.2038			0.974923
$389$		−	11.7081i		−	0.593622i	−0.954936	−	0.296811i	$-0.904077\pi$
$389$		−	11.7081i		−	0.593622i	0.954936	−	0.296811i	$-0.0959231\pi$
$390$	5.03822			0.255120
$391$	−4.88242	−	4.48703i	−0.246915	−	0.226919i
$392$	−6.04410	−	3.53113i	−0.305273	−	0.178349i
$393$	11.1583			0.562861
$394$	24.9251			1.25571
$395$			9.31746i			0.468812i
$396$			1.02228i			0.0513714i
$397$		−	5.35378i		−	0.268699i	−0.990934	−	0.134349i	$-0.957106\pi$
$397$		−	5.35378i		−	0.268699i	0.990934	−	0.134349i	$-0.0428944\pi$
$398$	8.60434			0.431297
$399$	15.3001	+	4.14185i	0.765964	+	0.207352i
$400$	−4.09211			−0.204605
$401$			34.9329i			1.74447i	0.489091	+	0.872233i	$0.337329\pi$
$401$			34.9329i			1.74447i	−0.489091	+	0.872233i	$0.662671\pi$
$402$	11.6217			0.579638
$403$		0			0
$404$		−	15.8927i		−	0.790691i
$405$	−0.952834			−0.0473467
$406$	−3.85708	+	14.2482i	−0.191424	+	0.707125i
$407$	−0.439422			−0.0217813
$408$		−	1.38268i		−	0.0684528i
$409$			22.1479i			1.09514i	0.836759	+	0.547572i	$0.184448\pi$
$409$			22.1479i			1.09514i	−0.836759	+	0.547572i	$0.815552\pi$
$410$		−	1.22688i		−	0.0605914i
$411$	−0.155798			−0.00768493
$412$	−1.74987			−0.0862099
$413$	−4.36316	−	1.18114i	−0.214697	−	0.0581200i
$414$	−3.53113	−	3.24517i	−0.173546	−	0.159491i
$415$	−5.21016			−0.255756
$416$			5.28761i			0.259247i
$417$	−2.99609			−0.146719
$418$			6.12452i			0.299560i
$419$	0.215119			0.0105092			0.00525462	−	0.999986i	$-0.498327\pi$
$419$	0.215119			0.0105092			0.00525462	+	0.999986i	$0.498327\pi$
$420$	2.43338	+	0.658732i	0.118737	+	0.0321428i
$421$		−	16.3757i		−	0.798105i	−0.916928	−	0.399053i	$-0.869339\pi$
$421$		−	16.3757i		−	0.798105i	0.916928	−	0.399053i	$-0.130661\pi$
$422$	−19.3460			−0.941747
$423$		−	7.09211i		−	0.344830i
$424$			8.75641i			0.425249i
$425$	5.65807			0.274457
$426$		−	2.29152i		−	0.111025i
$427$	−5.09775	+	18.8313i	−0.246698	+	0.911308i
$428$			11.0987i			0.536476i
$429$			5.40541i			0.260976i
$430$		−	4.45718i		−	0.214944i
$431$		−	17.1982i		−	0.828406i	−0.910184	−	0.414203i	$-0.864060\pi$
$431$		−	17.1982i		−	0.828406i	0.910184	−	0.414203i	$-0.135940\pi$
$432$		−	1.00000i		−	0.0481125i
$433$	3.99224			0.191855			0.0959274	−	0.995388i	$-0.469418\pi$
$433$	3.99224			0.191855			0.0959274	+	0.995388i	$0.469418\pi$
$434$		0			0
$435$		−	5.31599i		−	0.254882i
$436$			2.33551i			0.111851i
$437$	−21.1552	−	19.4420i	−1.01199	−	0.930036i
$438$	2.19551			0.104905
$439$		−	2.76726i		−	0.132074i	−0.997817	−	0.0660371i	$-0.978964\pi$
$439$		−	2.76726i		−	0.132074i	0.997817	−	0.0660371i	$-0.0210356\pi$
$440$			0.974060i			0.0464365i
$441$	6.04410	+	3.53113i	0.287814	+	0.168149i
$442$		−	7.31108i		−	0.347752i
$443$	−13.6673			−0.649355			−0.324677	−	0.945825i	$-0.605256\pi$
$443$	−13.6673			−0.649355			−0.324677	+	0.945825i	$0.605256\pi$
$444$	0.429846			0.0203996
$445$	−8.28370			−0.392685
$446$			17.7335i			0.839706i
$447$	2.17972			0.103097
$448$	−0.691340	+	2.55383i	−0.0326627	+	0.120657i
$449$	−11.6012			−0.547493			−0.273746	−	0.961802i	$-0.588263\pi$
$449$	−11.6012			−0.547493			−0.273746	+	0.961802i	$0.588263\pi$
$450$	4.09211			0.192904
$451$	1.31630			0.0619821
$452$			10.2322i			0.481284i
$453$			1.38363i			0.0650087i
$454$	9.92436			0.465773
$455$	12.8668	+	3.48312i	0.603203	+	0.163291i
$456$		−	5.99105i		−	0.280557i
$457$			26.1476i			1.22314i	0.791192	+	0.611568i	$0.209461\pi$
$457$			26.1476i			1.22314i	−0.791192	+	0.611568i	$0.790539\pi$
$458$	−15.8223			−0.739326
$459$			1.38268i			0.0645380i
$460$	−3.36458	−	3.09211i	−0.156874	−	0.144170i
$461$			5.44980i			0.253822i	0.991914	+	0.126911i	$0.0405063\pi$
$461$			5.44980i			0.253822i	−0.991914	+	0.126911i	$0.959494\pi$
$462$	−0.706741	+	2.61072i	−0.0328806	+	0.121462i
$463$	−34.0834			−1.58399			−0.791994	−	0.610528i	$-0.790957\pi$
$463$	−34.0834			−1.58399			−0.791994	+	0.610528i	$0.790957\pi$
$464$	5.57914			0.259005
$465$		0			0
$466$	13.0259			0.603415
$467$	−28.7609			−1.33090			−0.665449	−	0.746444i	$-0.731760\pi$
$467$	−28.7609			−1.33090			−0.665449	+	0.746444i	$0.731760\pi$
$468$		−	5.28761i		−	0.244420i
$469$	29.6798	+	8.03454i	1.37049	+	0.371001i
$470$		−	6.75760i		−	0.311705i
$471$			11.1851i			0.515381i
$472$			1.70848i			0.0786390i
$473$	4.78202			0.219878
$474$	9.77869			0.449150
$475$	24.5160			1.12487
$476$	0.955901	−	3.53113i	0.0438137	−	0.161849i
$477$		−	8.75641i		−	0.400928i
$478$	10.6712			0.488091
$479$	−39.5714			−1.80806			−0.904031	−	0.427468i	$-0.859406\pi$
$479$	−39.5714			−1.80806			−0.904031	+	0.427468i	$0.859406\pi$
$480$		−	0.952834i		−	0.0434907i
$481$	2.27286			0.103633
$482$	−19.2038			−0.874707
$483$	−6.77439	−	10.7288i	−0.308245	−	0.488178i
$484$	9.95495			0.452498
$485$	−18.2980			−0.830869
$486$			1.00000i			0.0453609i
$487$	−12.8006			−0.580050			−0.290025	−	0.957019i	$-0.593664\pi$
$487$	−12.8006			−0.580050			−0.290025	+	0.957019i	$0.593664\pi$
$488$	7.37373			0.333793
$489$			7.54929i			0.341391i
$490$	5.75902	+	3.36458i	0.260166	+	0.151996i
$491$	39.4670			1.78112			0.890561	−	0.454865i	$-0.150312\pi$
$491$	39.4670			1.78112			0.890561	+	0.454865i	$0.150312\pi$
$492$	−1.28761			−0.0580501
$493$	−7.71416			−0.347428
$494$		−	31.6784i		−	1.42528i
$495$		−	0.974060i		−	0.0437808i
$496$		0			0
$497$	1.58422	−	5.85216i	0.0710621	−	0.262505i
$498$			5.46806i			0.245030i
$499$	−8.58305			−0.384230			−0.192115	−	0.981372i	$-0.561535\pi$
$499$	−8.58305			−0.384230			−0.192115	+	0.981372i	$0.561535\pi$
$500$	8.66327			0.387433
$501$	−11.9290			−0.532949
$502$	−0.429846			−0.0191850
$503$	25.3794			1.13161			0.565807	−	0.824538i	$-0.308565\pi$
$503$	25.3794			1.13161			0.565807	+	0.824538i	$0.308565\pi$
$504$	0.691340	−	2.55383i	0.0307947	−	0.113757i
$505$			15.1431i			0.673859i
$506$	3.31746	−	3.60979i	0.147479	−	0.160475i
$507$		−	14.9589i		−	0.664346i
$508$	−16.3499			−0.725408
$509$			19.0623i			0.844920i	0.906382	+	0.422460i	$0.138833\pi$
$509$			19.0623i			0.844920i	−0.906382	+	0.422460i	$0.861167\pi$
$510$			1.31746i			0.0583383i
$511$	5.60695	+	1.51784i	0.248037	+	0.0671453i
$512$	1.00000			0.0441942
$513$			5.99105i			0.264511i
$514$		−	21.2465i		−	0.937142i
$515$	1.66734			0.0734716
$516$	−4.67781			−0.205929
$517$	7.25010			0.318859
$518$	1.09775	+	0.297169i	0.0482325	+	0.0130569i
$519$	18.0882			0.793984
$520$		−	5.03822i		−	0.220940i
$521$	26.9484			1.18063			0.590316	−	0.807173i	$-0.299003\pi$
$521$	26.9484			1.18063			0.590316	+	0.807173i	$0.299003\pi$
$522$	−5.57914			−0.244192
$523$	8.04918			0.351966			0.175983	−	0.984393i	$-0.443690\pi$
$523$	8.04918			0.351966			0.175983	+	0.984393i	$0.443690\pi$
$524$		−	11.1583i		−	0.487452i
$525$	10.4505	+	2.82904i	0.456099	+	0.123469i
$526$			18.1188i			0.790018i
$527$		0			0
$528$	1.02228			0.0444889
$529$	1.93774	+	22.9182i	0.0842497	+	0.996445i
$530$		−	8.34340i		−	0.362414i
$531$		−	1.70848i		−	0.0741415i
$532$	4.14185	−	15.3001i	0.179572	−	0.663345i
$533$	−6.80840			−0.294905
$534$			8.69375i			0.376216i
$535$		−	10.5752i		−	0.457207i
$536$		−	11.6217i		−	0.501981i
$537$			1.77464i			0.0765815i
$538$		−	3.44198i		−	0.148394i
$539$	−3.60979	+	6.17875i	−0.155485	+	0.266137i
$540$			0.952834i			0.0410034i
$541$	45.6184			1.96129			0.980644	−	0.195802i	$-0.0627308\pi$
$541$	45.6184			1.96129			0.980644	+	0.195802i	$0.0627308\pi$
$542$		−	2.57523i		−	0.110615i
$543$			20.4933i			0.879452i
$544$	−1.38268			−0.0592819
$545$		−	2.22536i		−	0.0953238i
$546$	3.65554	−	13.5037i	0.156443	−	0.577904i
$547$	16.7707			0.717065			0.358532	−	0.933517i	$-0.383277\pi$
$547$	16.7707			0.717065			0.358532	+	0.933517i	$0.383277\pi$
$548$			0.155798i			0.00665534i
$549$	−7.37373			−0.314703
$550$			4.18327i			0.178375i
$551$	−33.4249			−1.42395
$552$	−3.24517	+	3.53113i	−0.138124	+	0.150295i
$553$	24.9731	+	6.76040i	1.06196	+	0.287481i
$554$	−15.7335			−0.668453
$555$	−0.409572			−0.0173853
$556$			2.99609i			0.127063i
$557$		−	18.0646i		−	0.765423i	−0.923868	−	0.382712i	$-0.874990\pi$
$557$		−	18.0646i		−	0.765423i	0.923868	−	0.382712i	$-0.125010\pi$
$558$		0			0
$559$	−24.7345			−1.04616
$560$	0.658732	−	2.43338i	0.0278365	−	0.102829i
$561$	−1.41348			−0.0596773
$562$		−	24.2115i		−	1.02130i
$563$	5.55748			0.234220			0.117110	−	0.993119i	$-0.462637\pi$
$563$	5.55748			0.234220			0.117110	+	0.993119i	$0.462637\pi$
$564$	−7.09211			−0.298632
$565$		−	9.74962i		−	0.410169i
$566$	−24.2383			−1.01881
$567$	−0.691340	+	2.55383i	−0.0290335	+	0.107251i
$568$	−2.29152			−0.0961502
$569$			4.66769i			0.195680i	0.995202	+	0.0978399i	$0.0311933\pi$
$569$			4.66769i			0.195680i	−0.995202	+	0.0978399i	$0.968807\pi$
$570$			5.70848i			0.239102i
$571$			25.3232i			1.05974i	0.848078	+	0.529871i	$0.177760\pi$
$571$			25.3232i			1.05974i	−0.848078	+	0.529871i	$0.822240\pi$
$572$	5.40541			0.226011
$573$	1.68043			0.0702008
$574$	−3.28835	−	0.890179i	−0.137253	−	0.0371553i
$575$	−14.4498	−	13.2796i	−0.602597	−	0.553797i
$576$	−1.00000			−0.0416667
$577$		−	7.44198i		−	0.309814i	−0.987929	−	0.154907i	$-0.950492\pi$
$577$		−	7.44198i		−	0.309814i	0.987929	−	0.154907i	$-0.0495077\pi$
$578$	−15.0882			−0.627586
$579$		−	4.71239i		−	0.195840i
$580$	−5.31599			−0.220735
$581$	−3.78029	+	13.9645i	−0.156833	+	0.579345i
$582$			19.2038i			0.796021i
$583$	8.95148			0.370732
$584$		−	2.19551i		−	0.0908507i
$585$			5.03822i			0.208305i
$586$	27.2814			1.12698
$587$			13.6012i			0.561380i	0.959798	+	0.280690i	$0.0905633\pi$
$587$			13.6012i			0.561380i	−0.959798	+	0.280690i	$0.909437\pi$
$588$	3.53113	−	6.04410i	0.145621	−	0.249254i
$589$		0			0
$590$		−	1.62789i		−	0.0670193i
$591$			24.9251i			1.02528i
$592$		−	0.429846i		−	0.0176665i
$593$			25.9147i			1.06419i	0.846685	+	0.532095i	$0.178595\pi$
$593$			25.9147i			1.06419i	−0.846685	+	0.532095i	$0.821405\pi$
$594$	−1.02228			−0.0419445
$595$	−0.910815	+	3.36458i	−0.0373398	+	0.137934i
$596$		−	2.17972i		−	0.0892846i
$597$			8.60434i			0.352152i
$598$	−17.1592	+	18.6712i	−0.701692	+	0.763524i
$599$	8.09602			0.330794			0.165397	−	0.986227i	$-0.447109\pi$
$599$	8.09602			0.330794			0.165397	+	0.986227i	$0.447109\pi$
$600$		−	4.09211i		−	0.167060i
$601$			44.5924i			1.81896i	0.415744	+	0.909482i	$0.363521\pi$
$601$			44.5924i			1.81896i	−0.415744	+	0.909482i	$0.636479\pi$
$602$	−11.9463	−	3.23396i	−0.486897	−	0.131806i
$603$			11.6217i			0.473272i
$604$	1.38363			0.0562992
$605$	−9.48541			−0.385637
$606$	15.8927			0.645596
$607$		−	4.30873i		−	0.174886i	−0.996170	−	0.0874430i	$-0.972130\pi$
$607$		−	4.30873i		−	0.174886i	0.996170	−	0.0874430i	$-0.0278696\pi$
$608$	−5.99105			−0.242969
$609$	−14.2482	−	3.85708i	−0.577365	−	0.156297i
$610$	−7.02594			−0.284472
$611$	−37.5003			−1.51710
$612$	1.38268			0.0558915
$613$			3.10372i			0.125358i	0.998034	+	0.0626789i	$0.0199644\pi$
$613$			3.10372i			0.125358i	−0.998034	+	0.0626789i	$0.980036\pi$
$614$			25.1206i			1.01379i
$615$	1.22688			0.0494727
$616$	2.61072	+	0.706741i	0.105189	+	0.0284754i
$617$		−	27.8081i		−	1.11951i	−0.828658	−	0.559756i	$-0.810895\pi$
$617$		−	27.8081i		−	1.11951i	0.828658	−	0.559756i	$-0.189105\pi$
$618$		−	1.74987i		−	0.0703901i
$619$	−45.5624			−1.83131			−0.915654	−	0.401968i	$-0.868326\pi$
$619$	−45.5624			−1.83131			−0.915654	+	0.401968i	$0.868326\pi$
$620$		0			0
$621$	3.24517	−	3.53113i	0.130224	−	0.141699i
$622$			10.6712i			0.427878i
$623$	−6.01034	+	22.2024i	−0.240799	+	0.889519i
$624$	−5.28761			−0.211674
$625$	12.2059			0.488235
$626$	−9.21674			−0.368375
$627$	−6.12452			−0.244590
$628$	11.1851			0.446333
$629$			0.594339i			0.0236978i
$630$	−0.658732	+	2.43338i	−0.0262445	+	0.0969480i
$631$			9.09170i			0.361935i	0.983489	+	0.180968i	$0.0579229\pi$
$631$			9.09170i			0.361935i	−0.983489	+	0.180968i	$0.942077\pi$
$632$		−	9.77869i		−	0.388975i
$633$		−	19.3460i		−	0.768933i
$634$	−25.3048			−1.00498
$635$	15.5787			0.618222
$636$	−8.75641			−0.347214
$637$	18.6712	−	31.9589i	0.739782	−	1.26626i
$638$		−	5.70343i		−	0.225801i
$639$	2.29152			0.0906513
$640$	−0.952834			−0.0376641
$641$		−	45.7219i		−	1.80591i	−0.429738	−	0.902954i	$-0.641394\pi$
$641$		−	45.7219i		−	1.80591i	0.429738	−	0.902954i	$-0.358606\pi$
$642$	−11.0987			−0.438031
$643$	−33.7328			−1.33029			−0.665145	−	0.746714i	$-0.731630\pi$
$643$	−33.7328			−1.33029			−0.665145	+	0.746714i	$0.731630\pi$
$644$	−10.7288	+	6.77439i	−0.422775	+	0.266948i
$645$	4.45718			0.175501
$646$	8.28370			0.325918
$647$		−	18.6712i		−	0.734042i	−0.930213	−	0.367021i	$-0.880378\pi$
$647$		−	18.6712i		−	0.734042i	0.930213	−	0.367021i	$-0.119622\pi$
$648$	1.00000			0.0392837
$649$	1.74654			0.0685575
$650$		−	21.6375i		−	0.848692i
$651$		0			0
$652$	7.54929			0.295653
$653$	−25.3161			−0.990696			−0.495348	−	0.868695i	$-0.664959\pi$
$653$	−25.3161			−0.990696			−0.495348	+	0.868695i	$0.664959\pi$
$654$	−2.33551			−0.0913258
$655$			10.6320i			0.415426i
$656$			1.28761i			0.0502729i
$657$			2.19551i			0.0856548i
$658$	−18.1120	−	4.90306i	−0.706081	−	0.191141i
$659$		−	42.9498i		−	1.67309i	−0.547901	−	0.836543i	$-0.684573\pi$
$659$		−	42.9498i		−	1.67309i	0.547901	−	0.836543i	$-0.315427\pi$
$660$	−0.974060			−0.0379152
$661$	43.2862			1.68364			0.841819	−	0.539759i	$-0.181485\pi$
$661$	43.2862			1.68364			0.841819	+	0.539759i	$0.181485\pi$
$662$	−0.830434			−0.0322757
$663$	7.31108			0.283939
$664$	5.46806			0.212202
$665$	−3.94650	+	14.5785i	−0.153039	+	0.565329i
$666$			0.429846i			0.0166562i
$667$	19.7007	+	18.1053i	0.762812	+	0.701038i
$668$			11.9290i			0.461547i
$669$	−17.7335			−0.685617
$670$			11.0735i			0.427808i
$671$		−	7.53800i		−	0.291001i
$672$	−2.55383	−	0.691340i	−0.0985161	−	0.0266690i
$673$	−3.66734			−0.141365			−0.0706827	−	0.997499i	$-0.522518\pi$
$673$	−3.66734			−0.141365			−0.0706827	+	0.997499i	$0.522518\pi$
$674$			7.58885i			0.292312i
$675$			4.09211i			0.157505i
$676$	−14.9589			−0.575341
$677$	9.06801			0.348512			0.174256	−	0.984700i	$-0.444248\pi$
$677$	9.06801			0.348512			0.174256	+	0.984700i	$0.444248\pi$
$678$	−10.2322			−0.392966
$679$	−13.2763	+	49.0431i	−0.509499	+	1.88210i
$680$	1.31746			0.0505224
$681$			9.92436i			0.380302i
$682$		0			0
$683$	19.3823			0.741642			0.370821	−	0.928704i	$-0.379076\pi$
$683$	19.3823			0.741642			0.370821	+	0.928704i	$0.379076\pi$
$684$	5.99105			0.229074
$685$		−	0.148449i		−	0.00567195i
$686$	13.1964	−	12.9944i	0.503842	−	0.496128i
$687$		−	15.8223i		−	0.603657i
$688$			4.67781i			0.178340i
$689$	−46.3005			−1.76391
$690$	3.09211	−	3.36458i	0.117715	−	0.128087i
$691$		−	0.800584i		−	0.0304556i	−0.999884	−	0.0152278i	$-0.995153\pi$
$691$		−	0.800584i		−	0.0304556i	0.999884	−	0.0152278i	$-0.00484735\pi$
$692$		−	18.0882i		−	0.687610i
$693$	−2.61072	−	0.706741i	−0.0991732	−	0.0268469i
$694$	30.1431			1.14422
$695$		−	2.85478i		−	0.108288i
$696$			5.57914i			0.211477i
$697$		−	1.78036i		−	0.0674358i
$698$			22.6115i			0.855860i
$699$			13.0259i			0.492686i
$700$	2.82904	−	10.4505i	0.106928	−	0.394994i
$701$		−	43.0748i		−	1.62691i	−0.581625	−	0.813457i	$-0.697583\pi$
$701$		−	43.0748i		−	1.62691i	0.581625	−	0.813457i	$-0.302417\pi$
$702$	5.28761			0.199568
$703$			2.57523i			0.0971265i
$704$		−	1.02228i		−	0.0385285i
$705$	6.75760			0.254506
$706$		−	8.44589i		−	0.317865i
$707$	40.5872	+	10.9872i	1.52644	+	0.413218i
$708$	−1.70848			−0.0642085
$709$		−	3.01430i		−	0.113204i	−0.998397	−	0.0566022i	$-0.981973\pi$
$709$		−	3.01430i		−	0.113204i	0.998397	−	0.0566022i	$-0.0180267\pi$
$710$	2.18344			0.0819431
$711$			9.77869i			0.366729i
$712$	8.69375			0.325812
$713$		0			0
$714$	3.53113	+	0.955901i	0.132149	+	0.0357737i
$715$	−5.15046			−0.192616
$716$	1.77464			0.0663216
$717$			10.6712i			0.398525i
$718$			18.7007i			0.697906i
$719$			6.84472i			0.255265i	0.991822	+	0.127633i	$0.0407378\pi$
$719$			6.84472i			0.255265i	−0.991822	+	0.127633i	$0.959262\pi$
$720$	0.952834			0.0355100
$721$	1.20975	−	4.46887i	0.0450536	−	0.166429i
$722$	16.8927			0.628681
$723$		−	19.2038i		−	0.714196i
$724$	20.4933			0.761627
$725$	−22.8304			−0.847901
$726$			9.95495i			0.369463i
$727$	−10.8772			−0.403413			−0.201706	−	0.979446i	$-0.564649\pi$
$727$	−10.8772			−0.403413			−0.201706	+	0.979446i	$0.564649\pi$
$728$	−13.5037	−	3.65554i	−0.500479	−	0.135483i
$729$	−1.00000			−0.0370370
$730$			2.09195i			0.0774266i
$731$		−	6.46792i		−	0.239225i
$732$			7.37373i			0.272541i
$733$	0.0626552			0.00231422			0.00115711	−	0.999999i	$-0.499632\pi$
$733$	0.0626552			0.00231422			0.00115711	+	0.999999i	$0.499632\pi$
$734$	−27.7112			−1.02284
$735$	−3.36458	+	5.75902i	−0.124104	+	0.212425i
$736$	3.53113	+	3.24517i	0.130159	+	0.119619i
$737$	−11.8806			−0.437628
$738$		−	1.28761i		−	0.0473977i
$739$	38.9549			1.43298			0.716490	−	0.697597i	$-0.245747\pi$
$739$	38.9549			1.43298			0.716490	+	0.697597i	$0.245747\pi$
$740$			0.409572i			0.0150561i
$741$	31.6784			1.16373
$742$	−22.3624	−	6.05365i	−0.820949	−	0.222237i
$743$			5.61707i			0.206070i	0.994678	+	0.103035i	$0.0328554\pi$
$743$			5.61707i			0.206070i	−0.994678	+	0.103035i	$0.967145\pi$
$744$		0			0
$745$			2.07691i			0.0760920i
$746$		−	31.6157i		−	1.15753i
$747$	−5.46806			−0.200066
$748$			1.41348i			0.0516820i
$749$	−28.3442	−	7.67298i	−1.03568	−	0.280365i
$750$			8.66327i			0.316338i
$751$		−	20.8401i		−	0.760467i	−0.924891	−	0.380233i	$-0.875844\pi$
$751$		−	20.8401i		−	0.760467i	0.924891	−	0.380233i	$-0.124156\pi$
$752$			7.09211i			0.258623i
$753$		−	0.429846i		−	0.0156644i
$754$			29.5003i			1.07434i
$755$	−1.31837			−0.0479804
$756$	2.55383	+	0.691340i	0.0928819	+	0.0251438i
$757$			42.0037i			1.52665i	0.646014	+	0.763326i	$0.276435\pi$
$757$			42.0037i			1.52665i	−0.646014	+	0.763326i	$0.723565\pi$
$758$			31.2347i			1.13449i
$759$	3.60979	+	3.31746i	0.131027	+	0.120416i
$760$	5.70848			0.207068
$761$		−	2.34687i		−	0.0850741i	−0.999095	−	0.0425370i	$-0.986456\pi$
$761$		−	2.34687i		−	0.0850741i	0.999095	−	0.0425370i	$-0.0135440\pi$
$762$		−	16.3499i		−	0.592293i
$763$	−5.96450	−	1.61463i	−0.215930	−	0.0584536i
$764$		−	1.68043i		−	0.0607957i
$765$	−1.31746			−0.0476330
$766$	−10.3880			−0.375335
$767$	−9.03376			−0.326190
$768$			1.00000i			0.0360844i
$769$	0.553475			0.0199588			0.00997941	−	0.999950i	$-0.496823\pi$
$769$	0.553475			0.0199588			0.00997941	+	0.999950i	$0.496823\pi$
$770$	−2.48758	−	0.673407i	−0.0896463	−	0.0242679i
$771$	21.2465			0.765173
$772$	−4.71239			−0.169602
$773$	−24.1488			−0.868573			−0.434287	−	0.900775i	$-0.642999\pi$
$773$	−24.1488			−0.868573			−0.434287	+	0.900775i	$0.642999\pi$
$774$		−	4.67781i		−	0.168141i
$775$		0			0
$776$	19.2038			0.689375
$777$	−0.297169	+	1.09775i	−0.0106609	+	0.0393817i
$778$		−	11.7081i		−	0.419754i
$779$		−	7.71416i		−	0.276388i
$780$	5.03822			0.180397
$781$			2.34257i			0.0838239i
$782$	−4.88242	−	4.48703i	−0.174595	−	0.160456i
$783$		−	5.57914i		−	0.199382i
$784$	−6.04410	−	3.53113i	−0.215861	−	0.126112i
$785$	−10.6575			−0.380383
$786$	11.1583			0.398003
$787$	25.2842			0.901285			0.450643	−	0.892704i	$-0.351195\pi$
$787$	25.2842			0.901285			0.450643	+	0.892704i	$0.351195\pi$
$788$	24.9251			0.887920
$789$	−18.1188			−0.645047
$790$			9.31746i			0.331500i
$791$	−26.1314	−	7.07395i	−0.929125	−	0.251521i
$792$			1.02228i			0.0363250i
$793$			38.9894i			1.38456i
$794$		−	5.35378i		−	0.189999i
$795$	8.34340			0.295910
$796$	8.60434			0.304973
$797$	48.5161			1.71853			0.859265	−	0.511531i	$-0.170922\pi$
$797$	48.5161			1.71853			0.859265	+	0.511531i	$0.170922\pi$
$798$	15.3001	+	4.14185i	0.541619	+	0.146620i
$799$		−	9.80611i		−	0.346915i
$800$	−4.09211			−0.144678
$801$	−8.69375			−0.307179
$802$			34.9329i			1.23352i
$803$	−2.24442			−0.0792037
$804$	11.6217			0.409866
$805$	10.2228	−	6.45487i	0.360306	−	0.227504i
$806$		0			0
$807$	3.44198			0.121163
$808$		−	15.8927i		−	0.559103i
$809$	19.6738			0.691694			0.345847	−	0.938291i	$-0.387592\pi$
$809$	19.6738			0.691694			0.345847	+	0.938291i	$0.387592\pi$
$810$	−0.952834			−0.0334792
$811$		−	53.0496i		−	1.86282i	−0.363967	−	0.931412i	$-0.618578\pi$
$811$		−	53.0496i		−	1.86282i	0.363967	−	0.931412i	$-0.381422\pi$
$812$	−3.85708	+	14.2482i	−0.135357	+	0.500013i
$813$	2.57523			0.0903172
$814$	−0.439422			−0.0154017
$815$	−7.19322			−0.251967
$816$		−	1.38268i		−	0.0484035i
$817$		−	28.0250i		−	0.980472i
$818$			22.1479i			0.774383i
$819$	13.5037	+	3.65554i	0.471856	+	0.127735i
$820$		−	1.22688i		−	0.0428446i
$821$	−21.8080			−0.761103			−0.380552	−	0.924760i	$-0.624266\pi$
$821$	−21.8080			−0.761103			−0.380552	+	0.924760i	$0.624266\pi$
$822$	−0.155798			−0.00543406
$823$	−22.8084			−0.795051			−0.397525	−	0.917591i	$-0.630131\pi$
$823$	−22.8084			−0.795051			−0.397525	+	0.917591i	$0.630131\pi$
$824$	−1.74987			−0.0609596
$825$	−4.18327			−0.145643
$826$	−4.36316	−	1.18114i	−0.151814	−	0.0410970i
$827$			19.9503i			0.693741i	0.937913	+	0.346871i	$0.112756\pi$
$827$			19.9503i			0.693741i	−0.937913	+	0.346871i	$0.887244\pi$
$828$	−3.53113	−	3.24517i	−0.122715	−	0.112777i
$829$		−	18.2205i		−	0.632825i	−0.948622	−	0.316413i	$-0.897522\pi$
$829$		−	18.2205i		−	0.632825i	0.948622	−	0.316413i	$-0.102478\pi$
$830$	−5.21016			−0.180847
$831$		−	15.7335i		−	0.545789i
$832$			5.28761i			0.183315i
$833$	8.35705	+	4.88242i	0.289555	+	0.169166i
$834$	−2.99609			−0.103746
$835$		−	11.3664i		−	0.393349i
$836$			6.12452i			0.211821i
$837$		0			0
$838$	0.215119			0.00743116
$839$	−22.1838			−0.765871			−0.382936	−	0.923775i	$-0.625087\pi$
$839$	−22.1838			−0.765871			−0.382936	+	0.923775i	$0.625087\pi$
$840$	2.43338	+	0.658732i	0.0839594	+	0.0227284i
$841$	2.12678			0.0733372
$842$		−	16.3757i		−	0.564345i
$843$	24.2115			0.833888
$844$	−19.3460			−0.665915
$845$	14.2533			0.490329
$846$		−	7.09211i		−	0.243832i
$847$	−6.88225	+	25.4233i	−0.236477	+	0.873553i
$848$			8.75641i			0.300696i
$849$		−	24.2383i		−	0.831855i
$850$	5.65807			0.194070
$851$	1.39492	−	1.51784i	0.0478173	−	0.0520309i
$852$		−	2.29152i		−	0.0785063i
$853$		−	51.9476i		−	1.77865i	−0.457275	−	0.889325i	$-0.651174\pi$
$853$		−	51.9476i		−	1.77865i	0.457275	−	0.889325i	$-0.348826\pi$
$854$	−5.09775	+	18.8313i	−0.174442	+	0.644392i
$855$	−5.70848			−0.195226
$856$			11.0987i			0.379346i
$857$		−	35.7806i		−	1.22224i	−0.791538	−	0.611120i	$-0.790719\pi$
$857$		−	35.7806i		−	1.22224i	0.791538	−	0.611120i	$-0.209281\pi$
$858$			5.40541i			0.184538i
$859$		−	6.28506i		−	0.214443i	−0.994235	−	0.107222i	$-0.965805\pi$
$859$		−	6.28506i		−	0.214443i	0.994235	−	0.107222i	$-0.0341955\pi$
$860$		−	4.45718i		−	0.151989i
$861$	0.890179	−	3.28835i	0.0303372	−	0.112067i
$862$		−	17.1982i		−	0.585772i
$863$	20.4507			0.696150			0.348075	−	0.937467i	$-0.386835\pi$
$863$	20.4507			0.696150			0.348075	+	0.937467i	$0.386835\pi$
$864$		−	1.00000i		−	0.0340207i
$865$			17.2350i			0.586009i
$866$	3.99224			0.135662
$867$		−	15.0882i		−	0.512422i
$868$		0			0
$869$	−9.99653			−0.339109
$870$		−	5.31599i		−	0.180229i
$871$	61.4511			2.08219
$872$			2.33551i			0.0790905i
$873$	−19.2038			−0.649949
$874$	−21.1552	−	19.4420i	−0.715584	−	0.657635i
$875$	−5.98926	+	22.1245i	−0.202474	+	0.747945i
$876$	2.19551			0.0741793
$877$	16.8840			0.570131			0.285065	−	0.958508i	$-0.407985\pi$
$877$	16.8840			0.570131			0.285065	+	0.958508i	$0.407985\pi$
$878$		−	2.76726i		−	0.0933906i
$879$			27.2814i			0.920178i
$880$			0.974060i			0.0328356i
$881$	−54.6901			−1.84256			−0.921279	−	0.388903i	$-0.872854\pi$
$881$	−54.6901			−1.84256			−0.921279	+	0.388903i	$0.872854\pi$
$882$	6.04410	+	3.53113i	0.203515	+	0.118899i
$883$	13.2811			0.446946			0.223473	−	0.974710i	$-0.428261\pi$
$883$	13.2811			0.446946			0.223473	+	0.974710i	$0.428261\pi$
$884$		−	7.31108i		−	0.245898i
$885$	1.62789			0.0547210
$886$	−13.6673			−0.459163
$887$		−	50.9913i		−	1.71212i	−0.516877	−	0.856060i	$-0.672906\pi$
$887$		−	50.9913i		−	1.71212i	0.516877	−	0.856060i	$-0.327094\pi$
$888$	0.429846			0.0144247
$889$	11.3033	−	41.7548i	0.379101	−	1.40041i
$890$	−8.28370			−0.277670
$891$		−	1.02228i		−	0.0342476i
$892$			17.7335i			0.593762i
$893$		−	42.4892i		−	1.42185i
$894$	2.17972			0.0729006
$895$	−1.69094			−0.0565219
$896$	−0.691340	+	2.55383i	−0.0230960	+	0.0853175i
$897$	−18.6712	−	17.1592i	−0.623415	−	0.572929i
$898$	−11.6012			−0.387136
$899$		0			0
$900$	4.09211			0.136404
$901$		−	12.1073i		−	0.403353i
$902$	1.31630			0.0438279
$903$	3.23396	−	11.9463i	0.107619	−	0.397549i
$904$			10.2322i			0.340319i
$905$	−19.5267			−0.649090
$906$			1.38363i			0.0459681i
$907$		−	54.9286i		−	1.82387i	−0.410332	−	0.911936i	$-0.634587\pi$
$907$		−	54.9286i		−	1.82387i	0.410332	−	0.911936i	$-0.365413\pi$
$908$	9.92436			0.329352
$909$			15.8927i			0.527127i
$910$	12.8668	+	3.48312i	0.426529	+	0.115464i
$911$		−	0.862754i		−	0.0285843i	−0.999898	−	0.0142922i	$-0.995451\pi$
$911$		−	0.862754i		−	0.0285843i	0.999898	−	0.0142922i	$-0.00454949\pi$
$912$		−	5.99105i		−	0.198384i
$913$		−	5.58988i		−	0.184998i
$914$			26.1476i			0.864887i
$915$		−	7.02594i		−	0.232270i
$916$	−15.8223			−0.522783
$917$	28.4963	+	7.71416i	0.941032	+	0.254744i
$918$			1.38268i			0.0456352i
$919$		−	23.5411i		−	0.776551i	−0.921543	−	0.388275i	$-0.873071\pi$
$919$		−	23.5411i		−	0.776551i	0.921543	−	0.388275i	$-0.126929\pi$
$920$	−3.36458	−	3.09211i	−0.110927	−	0.101944i
$921$	−25.1206			−0.827752
$922$			5.44980i			0.179480i
$923$		−	12.1167i		−	0.398826i
$924$	−0.706741	+	2.61072i	−0.0232501	+	0.0858865i
$925$			1.75897i			0.0578347i
$926$	−34.0834			−1.12005
$927$	1.74987			0.0574733
$928$	5.57914			0.183144
$929$			50.0471i			1.64199i	0.570935	+	0.820995i	$0.306581\pi$
$929$			50.0471i			1.64199i	−0.570935	+	0.820995i	$0.693419\pi$
$930$		0			0
$931$	36.2105	+	21.1552i	1.18675	+	0.693333i
$932$	13.0259			0.426679
$933$	−10.6712			−0.349361
$934$	−28.7609			−0.941086
$935$		−	1.34681i		−	0.0440455i
$936$		−	5.28761i		−	0.172831i
$937$	57.6038			1.88184			0.940918	−	0.338636i	$-0.109965\pi$
$937$	57.6038			1.88184			0.940918	+	0.338636i	$0.109965\pi$
$938$	29.6798	+	8.03454i	0.969081	+	0.262337i
$939$		−	9.21674i		−	0.300777i
$940$		−	6.75760i		−	0.220409i
$941$	50.1440			1.63465			0.817324	−	0.576178i	$-0.195457\pi$
$941$	50.1440			1.63465			0.817324	+	0.576178i	$0.195457\pi$
$942$			11.1851i			0.364429i
$943$	−4.17853	+	4.54673i	−0.136072	+	0.148062i
$944$			1.70848i			0.0556062i
$945$	−2.43338	−	0.658732i	−0.0791577	−	0.0214285i
$946$	4.78202			0.155477
$947$	21.8187			0.709013			0.354506	−	0.935054i	$-0.384649\pi$
$947$	21.8187			0.709013			0.354506	+	0.935054i	$0.384649\pi$
$948$	9.77869			0.317597
$949$	11.6090			0.376844
$950$	24.5160			0.795405
$951$		−	25.3048i		−	0.820565i
$952$	0.955901	−	3.53113i	0.0309809	−	0.114445i
$953$			34.1070i			1.10483i	0.833568	+	0.552417i	$0.186295\pi$
$953$			34.1070i			1.10483i	−0.833568	+	0.552417i	$0.813705\pi$
$954$		−	8.75641i		−	0.283499i
$955$			1.60117i			0.0518126i
$956$	10.6712			0.345133
$957$	5.70343			0.184366
$958$	−39.5714			−1.27849
$959$	−0.397881	−	0.107709i	−0.0128482	−	0.00347811i
$960$		−	0.952834i		−	0.0307526i
$961$	31.0000			1.00000
$962$	2.27286			0.0732799
$963$		−	11.0987i		−	0.357651i
$964$	−19.2038			−0.618511
$965$	4.49012			0.144542
$966$	−6.77439	−	10.7288i	−0.217962	−	0.345194i
$967$	−16.7820			−0.539674			−0.269837	−	0.962906i	$-0.586970\pi$
$967$	−16.7820			−0.539674			−0.269837	+	0.962906i	$0.586970\pi$
$968$	9.95495			0.319964
$969$			8.28370i			0.266111i
$970$	−18.2980			−0.587513
$971$	55.1233			1.76899			0.884496	−	0.466549i	$-0.154503\pi$
$971$	55.1233			1.76899			0.884496	+	0.466549i	$0.154503\pi$
$972$			1.00000i			0.0320750i
$973$	−7.65150	−	2.07132i	−0.245296	−	0.0664033i
$974$	−12.8006			−0.410157
$975$	21.6375			0.692954
$976$	7.37373			0.236027
$977$		−	29.0350i		−	0.928911i	−0.885596	−	0.464456i	$-0.846250\pi$
$977$		−	29.0350i		−	0.928911i	0.885596	−	0.464456i	$-0.153750\pi$
$978$			7.54929i			0.241400i
$979$		−	8.88743i		−	0.284043i
$980$	5.75902	+	3.36458i	0.183965	+	0.107478i
$981$		−	2.33551i		−	0.0745672i
$982$	39.4670			1.25944
$983$	46.8899			1.49556			0.747778	−	0.663949i	$-0.231121\pi$
$983$	46.8899			1.49556			0.747778	+	0.663949i	$0.231121\pi$
$984$	−1.28761			−0.0410476
$985$	−23.7495			−0.756721
$986$	−7.71416			−0.245669
$987$	4.90306	−	18.1120i	0.156066	−	0.576513i
$988$		−	31.6784i		−	1.00782i
$989$	−15.1803	+	16.5180i	−0.482706	+	0.525241i
$990$		−	0.974060i		−	0.0309577i
$991$	21.9325			0.696708			0.348354	−	0.937363i	$-0.386741\pi$
$991$	21.9325			0.696708			0.348354	+	0.937363i	$0.386741\pi$
$992$		0			0
$993$		−	0.830434i		−	0.0263530i
$994$	1.58422	−	5.85216i	0.0502485	−	0.185619i
$995$	−8.19850			−0.259910
$996$			5.46806i			0.173262i
$997$		−	36.4714i		−	1.15506i	−0.816369	−	0.577530i	$-0.804017\pi$
$997$		−	36.4714i		−	1.15506i	0.816369	−	0.577530i	$-0.195983\pi$
$998$	−8.58305			−0.271692
$999$	−0.429846			−0.0135997

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.g.e.643.12	yes	16
3.2	odd	2		2898.2.g.j.2575.10		16
7.6	odd	2	inner	966.2.g.e.643.5	yes	16
21.20	even	2		2898.2.g.j.2575.8		16
23.22	odd	2	inner	966.2.g.e.643.13	yes	16
69.68	even	2		2898.2.g.j.2575.7		16
161.160	even	2	inner	966.2.g.e.643.4	✓	16
483.482	odd	2		2898.2.g.j.2575.9		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.g.e.643.4	✓	16	161.160	even	2	inner
966.2.g.e.643.5	yes	16	7.6	odd	2	inner
966.2.g.e.643.12	yes	16	1.1	even	1	trivial
966.2.g.e.643.13	yes	16	23.22	odd	2	inner
2898.2.g.j.2575.7		16	69.68	even	2
2898.2.g.j.2575.8		16	21.20	even	2
2898.2.g.j.2575.9		16	483.482	odd	2
2898.2.g.j.2575.10		16	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.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} -0.952834 q^{5} +1.00000i q^{6} +(-0.691340 + 2.55383i) q^{7} +1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} -0.952834 q^{5} +1.00000i q^{6} +(-0.691340 + 2.55383i) q^{7} +1.00000 q^{8} -1.00000 q^{9} -0.952834 q^{10} -1.02228i q^{11} +1.00000i q^{12} +5.28761i q^{13} +(-0.691340 + 2.55383i) q^{14} -0.952834i q^{15} +1.00000 q^{16} -1.38268 q^{17} -1.00000 q^{18} -5.99105 q^{19} -0.952834 q^{20} +(-2.55383 - 0.691340i) q^{21} -1.02228i q^{22} +(3.53113 + 3.24517i) q^{23} +1.00000i q^{24} -4.09211 q^{25} +5.28761i q^{26} -1.00000i q^{27} +(-0.691340 + 2.55383i) q^{28} +5.57914 q^{29} -0.952834i q^{30} +1.00000 q^{32} +1.02228 q^{33} -1.38268 q^{34} +(0.658732 - 2.43338i) q^{35} -1.00000 q^{36} -0.429846i q^{37} -5.99105 q^{38} -5.28761 q^{39} -0.952834 q^{40} +1.28761i q^{41} +(-2.55383 - 0.691340i) q^{42} +4.67781i q^{43} -1.02228i q^{44} +0.952834 q^{45} +(3.53113 + 3.24517i) q^{46} +7.09211i q^{47} +1.00000i q^{48} +(-6.04410 - 3.53113i) q^{49} -4.09211 q^{50} -1.38268i q^{51} +5.28761i q^{52} +8.75641i q^{53} -1.00000i q^{54} +0.974060i q^{55} +(-0.691340 + 2.55383i) q^{56} -5.99105i q^{57} +5.57914 q^{58} +1.70848i q^{59} -0.952834i q^{60} +7.37373 q^{61} +(0.691340 - 2.55383i) q^{63} +1.00000 q^{64} -5.03822i q^{65} +1.02228 q^{66} -11.6217i q^{67} -1.38268 q^{68} +(-3.24517 + 3.53113i) q^{69} +(0.658732 - 2.43338i) q^{70} -2.29152 q^{71} -1.00000 q^{72} -2.19551i q^{73} -0.429846i q^{74} -4.09211i q^{75} -5.99105 q^{76} +(2.61072 + 0.706741i) q^{77} -5.28761 q^{78} -9.77869i q^{79} -0.952834 q^{80} +1.00000 q^{81} +1.28761i q^{82} +5.46806 q^{83} +(-2.55383 - 0.691340i) q^{84} +1.31746 q^{85} +4.67781i q^{86} +5.57914i q^{87} -1.02228i q^{88} +8.69375 q^{89} +0.952834 q^{90} +(-13.5037 - 3.65554i) q^{91} +(3.53113 + 3.24517i) q^{92} +7.09211i q^{94} +5.70848 q^{95} +1.00000i q^{96} +19.2038 q^{97} +(-6.04410 - 3.53113i) q^{98} +1.02228i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} + 16 q^{4} + 16 q^{8} - 16 q^{9}+O(q^{10}) \) 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

L-functions

Modular forms

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