LMFDB - Embedded newform 1110.2.u.f.401.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(191,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("1110.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.u (of order $4$, degree $2$, 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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			401.11
Character	$\chi$	$=$	1110.401
Dual form			1110.2.u.f.191.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-1.33218 - 1.10694i) q^{3} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.72471 + 0.159268i) q^{6} -3.17089 q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.549384 + 2.94927i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-1.33218 - 1.10694i) q^{3} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.72471 + 0.159268i) q^{6} -3.17089 q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.549384 + 2.94927i) q^{9} -1.00000 q^{10} -4.29438 q^{11} +(-1.10694 + 1.33218i) q^{12} +(0.469209 - 0.469209i) q^{13} +(-2.24216 + 2.24216i) q^{14} +(0.159268 + 1.72471i) q^{15} -1.00000 q^{16} +(4.17376 + 4.17376i) q^{17} +(2.47392 + 1.69697i) q^{18} +(2.35319 - 2.35319i) q^{19} +(-0.707107 + 0.707107i) q^{20} +(4.22419 + 3.50998i) q^{21} +(-3.03659 + 3.03659i) q^{22} +(2.43772 + 2.43772i) q^{23} +(0.159268 + 1.72471i) q^{24} +1.00000i q^{25} -0.663562i q^{26} +(2.53278 - 4.53707i) q^{27} +3.17089i q^{28} +(-3.28489 + 3.28489i) q^{29} +(1.33218 + 1.10694i) q^{30} +(-0.0756563 - 0.0756563i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(5.72087 + 4.75361i) q^{33} +5.90259 q^{34} +(2.24216 + 2.24216i) q^{35} +(2.94927 - 0.549384i) q^{36} +(3.36709 + 5.06584i) q^{37} -3.32791i q^{38} +(-1.14445 + 0.105684i) q^{39} +1.00000i q^{40} -6.28349 q^{41} +(5.46888 - 0.505022i) q^{42} +(2.94167 - 2.94167i) q^{43} +4.29438i q^{44} +(1.69697 - 2.47392i) q^{45} +3.44746 q^{46} +0.554395i q^{47} +(1.33218 + 1.10694i) q^{48} +3.05457 q^{49} +(0.707107 + 0.707107i) q^{50} +(-0.940094 - 10.1803i) q^{51} +(-0.469209 - 0.469209i) q^{52} +10.4161i q^{53} +(-1.41725 - 4.99914i) q^{54} +(3.03659 + 3.03659i) q^{55} +(2.24216 + 2.24216i) q^{56} +(-5.73969 + 0.530030i) q^{57} +4.64554i q^{58} +(-5.42735 - 5.42735i) q^{59} +(1.72471 - 0.159268i) q^{60} +(-3.80832 - 3.80832i) q^{61} -0.106994 q^{62} +(-1.74204 - 9.35181i) q^{63} +1.00000i q^{64} -0.663562 q^{65} +(7.40657 - 0.683958i) q^{66} -7.22479i q^{67} +(4.17376 - 4.17376i) q^{68} +(-0.549071 - 5.94588i) q^{69} +3.17089 q^{70} +8.00969i q^{71} +(1.69697 - 2.47392i) q^{72} +12.0206i q^{73} +(5.96298 + 1.20120i) q^{74} +(1.10694 - 1.33218i) q^{75} +(-2.35319 - 2.35319i) q^{76} +13.6170 q^{77} +(-0.734521 + 0.883981i) q^{78} +(-2.36673 + 2.36673i) q^{79} +(0.707107 + 0.707107i) q^{80} +(-8.39636 + 3.24056i) q^{81} +(-4.44310 + 4.44310i) q^{82} +10.3371i q^{83} +(3.50998 - 4.22419i) q^{84} -5.90259i q^{85} -4.16015i q^{86} +(8.01221 - 0.739886i) q^{87} +(3.03659 + 3.03659i) q^{88} +(-2.62728 + 2.62728i) q^{89} +(-0.549384 - 2.94927i) q^{90} +(-1.48781 + 1.48781i) q^{91} +(2.43772 - 2.43772i) q^{92} +(0.0170408 + 0.184534i) q^{93} +(0.392017 + 0.392017i) q^{94} -3.32791 q^{95} +(1.72471 - 0.159268i) q^{96} +(-0.130832 + 0.130832i) q^{97} +(2.15991 - 2.15991i) q^{98} +(-2.35926 - 12.6653i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 24 q^{7} - 8 q^{9}+O(q^{10}) $ 40 * q + 24 * q^7 - 8 * q^9	$ 40 q + 24 q^{7} - 8 q^{9} - 40 q^{10} + 16 q^{13} - 40 q^{16} + 8 q^{18} + 16 q^{19} - 16 q^{22} - 8 q^{31} + 24 q^{33} + 24 q^{34} + 32 q^{37} + 16 q^{39} + 12 q^{42} + 32 q^{43} + 8 q^{45} - 56 q^{46} - 32 q^{49} - 44 q^{51} - 16 q^{52} - 24 q^{54} + 16 q^{55} + 8 q^{57} - 72 q^{61} + 24 q^{63} - 28 q^{66} + 16 q^{69} - 24 q^{70} + 8 q^{72} - 16 q^{76} - 48 q^{79} + 120 q^{81} - 24 q^{82} - 24 q^{84} + 20 q^{87} + 16 q^{88} + 8 q^{90} - 92 q^{93} - 8 q^{94} - 40 q^{97}+O(q^{100}) $ 40 * q + 24 * q^7 - 8 * q^9 - 40 * q^10 + 16 * q^13 - 40 * q^16 + 8 * q^18 + 16 * q^19 - 16 * q^22 - 8 * q^31 + 24 * q^33 + 24 * q^34 + 32 * q^37 + 16 * q^39 + 12 * q^42 + 32 * q^43 + 8 * q^45 - 56 * q^46 - 32 * q^49 - 44 * q^51 - 16 * q^52 - 24 * q^54 + 16 * q^55 + 8 * q^57 - 72 * q^61 + 24 * q^63 - 28 * q^66 + 16 * q^69 - 24 * q^70 + 8 * q^72 - 16 * q^76 - 48 * q^79 + 120 * q^81 - 24 * q^82 - 24 * q^84 + 20 * q^87 + 16 * q^88 + 8 * q^90 - 92 * q^93 - 8 * q^94 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−1.33218	−	1.10694i	−0.769132	−	0.639090i
$3$	−1.33218	−	1.10694i	−0.769132	−	0.639090i
$4$		−	1.00000i		−	0.500000i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$6$	−1.72471	+	0.159268i	−0.704111	+	0.0650209i
$7$	−3.17089			−1.19849			−0.599243	−	0.800567i	$-0.704532\pi$
$7$	−3.17089			−1.19849			−0.599243	+	0.800567i	$0.704532\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.549384	+	2.94927i	0.183128	+	0.983089i
$10$	−1.00000			−0.316228
$11$	−4.29438			−1.29480			−0.647402	−	0.762149i	$-0.724145\pi$
$11$	−4.29438			−1.29480			−0.647402	+	0.762149i	$0.724145\pi$
$12$	−1.10694	+	1.33218i	−0.319545	+	0.384566i
$13$	0.469209	−	0.469209i	0.130135	−	0.130135i	−0.639039	−	0.769174i	$-0.720668\pi$
$13$	0.469209	−	0.469209i	0.130135	−	0.130135i	0.769174	+	0.639039i	$0.220668\pi$
$14$	−2.24216	+	2.24216i	−0.599243	+	0.599243i
$15$	0.159268	+	1.72471i	0.0411229	+	0.445319i
$16$	−1.00000			−0.250000
$17$	4.17376	+	4.17376i	1.01229	+	1.01229i	0.999924	+	0.0123615i	$0.00393489\pi$
$17$	4.17376	+	4.17376i	1.01229	+	1.01229i	0.0123615	+	0.999924i	$0.496065\pi$
$18$	2.47392	+	1.69697i	0.583108	+	0.399981i
$19$	2.35319	−	2.35319i	0.539859	−	0.539859i	−0.383629	−	0.923487i	$-0.625326\pi$
$19$	2.35319	−	2.35319i	0.539859	−	0.539859i	0.923487	+	0.383629i	$0.125326\pi$
$20$	−0.707107	+	0.707107i	−0.158114	+	0.158114i
$21$	4.22419	+	3.50998i	0.921793	+	0.765940i
$22$	−3.03659	+	3.03659i	−0.647402	+	0.647402i
$23$	2.43772	+	2.43772i	0.508301	+	0.508301i	0.914005	−	0.405704i	$-0.132974\pi$
$23$	2.43772	+	2.43772i	0.508301	+	0.508301i	−0.405704	+	0.914005i	$0.632974\pi$
$24$	0.159268	+	1.72471i	0.0325105	+	0.352055i
$25$			1.00000i			0.200000i
$26$		−	0.663562i		−	0.130135i
$27$	2.53278	−	4.53707i	0.487433	−	0.873160i
$28$			3.17089i			0.599243i
$29$	−3.28489	+	3.28489i	−0.609989	+	0.609989i	−0.942943	−	0.332954i	$-0.891955\pi$
$29$	−3.28489	+	3.28489i	−0.609989	+	0.609989i	0.332954	+	0.942943i	$0.391955\pi$
$30$	1.33218	+	1.10694i	0.243221	+	0.202098i
$31$	−0.0756563	−	0.0756563i	−0.0135883	−	0.0135883i	0.700280	−	0.713868i	$-0.253058\pi$
$31$	−0.0756563	−	0.0756563i	−0.0135883	−	0.0135883i	−0.713868	+	0.700280i	$0.753058\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	5.72087	+	4.75361i	0.995875	+	0.827497i
$34$	5.90259			1.01229
$35$	2.24216	+	2.24216i	0.378994	+	0.378994i
$36$	2.94927	−	0.549384i	0.491545	−	0.0915639i
$37$	3.36709	+	5.06584i	0.553546	+	0.832819i
$37$	3.36709	+	5.06584i	0.553546	+	0.832819i
$38$		−	3.32791i		−	0.539859i
$39$	−1.14445	+	0.105684i	−0.183259	+	0.0169230i
$40$			1.00000i			0.158114i
$41$	−6.28349			−0.981316			−0.490658	−	0.871352i	$-0.663244\pi$
$41$	−6.28349			−0.981316			−0.490658	+	0.871352i	$0.663244\pi$
$42$	5.46888	−	0.505022i	0.843867	−	0.0779266i
$43$	2.94167	−	2.94167i	0.448600	−	0.448600i	−0.446289	−	0.894889i	$-0.647255\pi$
$43$	2.94167	−	2.94167i	0.448600	−	0.448600i	0.894889	+	0.446289i	$0.147255\pi$
$44$			4.29438i			0.647402i
$45$	1.69697	−	2.47392i	0.252970	−	0.368790i
$46$	3.44746			0.508301
$47$			0.554395i			0.0808669i	0.999182	+	0.0404334i	$0.0128739\pi$
$47$			0.554395i			0.0808669i	−0.999182	+	0.0404334i	$0.987126\pi$
$48$	1.33218	+	1.10694i	0.192283	+	0.159773i
$49$	3.05457			0.436367
$50$	0.707107	+	0.707107i	0.100000	+	0.100000i
$51$	−0.940094	−	10.1803i	−0.131639	−	1.42552i
$52$	−0.469209	−	0.469209i	−0.0650676	−	0.0650676i
$53$			10.4161i			1.43075i	0.698738	+	0.715377i	$0.253745\pi$
$53$			10.4161i			1.43075i	−0.698738	+	0.715377i	$0.746255\pi$
$54$	−1.41725	−	4.99914i	−0.192864	−	0.680297i
$55$	3.03659	+	3.03659i	0.409453	+	0.409453i
$56$	2.24216	+	2.24216i	0.299621	+	0.299621i
$57$	−5.73969	+	0.530030i	−0.760241	+	0.0702043i
$58$			4.64554i			0.609989i
$59$	−5.42735	−	5.42735i	−0.706580	−	0.706580i	0.259234	−	0.965814i	$-0.416530\pi$
$59$	−5.42735	−	5.42735i	−0.706580	−	0.706580i	−0.965814	+	0.259234i	$0.916530\pi$
$60$	1.72471	−	0.159268i	0.222659	−	0.0205614i
$61$	−3.80832	−	3.80832i	−0.487606	−	0.487606i	0.419944	−	0.907550i	$-0.362050\pi$
$61$	−3.80832	−	3.80832i	−0.487606	−	0.487606i	−0.907550	+	0.419944i	$0.862050\pi$
$62$	−0.106994			−0.0135883
$63$	−1.74204	−	9.35181i	−0.219476	−	1.17822i
$64$			1.00000i			0.125000i
$65$	−0.663562			−0.0823047
$66$	7.40657	−	0.683958i	0.911686	−	0.0841894i
$67$		−	7.22479i		−	0.882649i	−0.897348	−	0.441324i	$-0.854509\pi$
$67$		−	7.22479i		−	0.882649i	0.897348	−	0.441324i	$-0.145491\pi$
$68$	4.17376	−	4.17376i	0.506143	−	0.506143i
$69$	−0.549071	−	5.94588i	−0.0661004	−	0.715800i
$70$	3.17089			0.378994
$71$			8.00969i			0.950575i	0.879831	+	0.475287i	$0.157656\pi$
$71$			8.00969i			0.950575i	−0.879831	+	0.475287i	$0.842344\pi$
$72$	1.69697	−	2.47392i	0.199990	−	0.291554i
$73$			12.0206i			1.40691i	0.710741	+	0.703453i	$0.248360\pi$
$73$			12.0206i			1.40691i	−0.710741	+	0.703453i	$0.751640\pi$
$74$	5.96298	+	1.20120i	0.693182	+	0.139636i
$75$	1.10694	−	1.33218i	0.127818	−	0.153826i
$76$	−2.35319	−	2.35319i	−0.269929	−	0.269929i
$77$	13.6170			1.55180
$78$	−0.734521	+	0.883981i	−0.0831681	+	0.100091i
$79$	−2.36673	+	2.36673i	−0.266278	+	0.266278i	−0.827599	−	0.561320i	$-0.810294\pi$
$79$	−2.36673	+	2.36673i	−0.266278	+	0.266278i	0.561320	+	0.827599i	$0.310294\pi$
$80$	0.707107	+	0.707107i	0.0790569	+	0.0790569i
$81$	−8.39636	+	3.24056i	−0.932928	+	0.360062i
$82$	−4.44310	+	4.44310i	−0.490658	+	0.490658i
$83$			10.3371i			1.13464i	0.823496	+	0.567321i	$0.192020\pi$
$83$			10.3371i			1.13464i	−0.823496	+	0.567321i	$0.807980\pi$
$84$	3.50998	−	4.22419i	0.382970	−	0.460897i
$85$		−	5.90259i		−	0.640225i
$86$		−	4.16015i		−	0.448600i
$87$	8.01221	−	0.739886i	0.859000	−	0.0793241i
$88$	3.03659	+	3.03659i	0.323701	+	0.323701i
$89$	−2.62728	+	2.62728i	−0.278491	+	0.278491i	−0.832506	−	0.554016i	$-0.813095\pi$
$89$	−2.62728	+	2.62728i	−0.278491	+	0.278491i	0.554016	+	0.832506i	$0.313095\pi$
$90$	−0.549384	−	2.94927i	−0.0579101	−	0.310880i
$91$	−1.48781	+	1.48781i	−0.155965	+	0.155965i
$92$	2.43772	−	2.43772i	0.254150	−	0.254150i
$93$	0.0170408	+	0.184534i	0.00176704	+	0.0191353i
$94$	0.392017	+	0.392017i	0.0404334	+	0.0404334i
$95$	−3.32791			−0.341437
$96$	1.72471	−	0.159268i	0.176028	−	0.0162552i
$97$	−0.130832	+	0.130832i	−0.0132840	+	0.0132840i	−0.713718	−	0.700434i	$-0.752990\pi$
$97$	−0.130832	+	0.130832i	−0.0132840	+	0.0132840i	0.700434	+	0.713718i	$0.252990\pi$
$98$	2.15991	−	2.15991i	0.218183	−	0.218183i
$99$	−2.35926	−	12.6653i	−0.237115	−	1.27291i
$100$	1.00000			0.100000
$101$	15.3310			1.52549			0.762744	−	0.646700i	$-0.223852\pi$
$101$	15.3310			1.52549			0.762744	+	0.646700i	$0.223852\pi$
$102$	−7.86328	−	6.53379i	−0.778581	−	0.646941i
$103$	7.22462	+	7.22462i	0.711863	+	0.711863i	0.966925	−	0.255062i	$-0.0820959\pi$
$103$	7.22462	+	7.22462i	0.711863	+	0.711863i	−0.255062	+	0.966925i	$0.582096\pi$
$104$	−0.663562			−0.0650676
$105$	−0.505022	−	5.46888i	−0.0492851	−	0.533708i
$106$	7.36526	+	7.36526i	0.715377	+	0.715377i
$107$			0.283834i			0.0274393i	0.999906	+	0.0137196i	$0.00436724\pi$
$107$			0.283834i			0.0274393i	−0.999906	+	0.0137196i	$0.995633\pi$
$108$	−4.53707	−	2.53278i	−0.436580	−	0.243716i
$109$	−7.09218	+	7.09218i	−0.679307	+	0.679307i	−0.959843	−	0.280536i	$-0.909488\pi$
$109$	−7.09218	+	7.09218i	−0.679307	+	0.679307i	0.280536	+	0.959843i	$0.409488\pi$
$110$	4.29438			0.409453
$111$	1.12201	−	10.4757i	0.106496	−	0.994313i
$112$	3.17089			0.299621
$113$	−10.1290	+	10.1290i	−0.952860	+	0.952860i	−0.998938	−	0.0460778i	$-0.985328\pi$
$113$	−10.1290	+	10.1290i	−0.952860	+	0.952860i	0.0460778	+	0.998938i	$0.485328\pi$
$114$	−3.68379	+	4.43336i	−0.345018	+	0.415223i
$115$		−	3.44746i		−	0.321477i
$116$	3.28489	+	3.28489i	0.304994	+	0.304994i
$117$	1.64160	+	1.12605i	0.151766	+	0.104103i
$118$	−7.67543			−0.706580
$119$	−13.2345	−	13.2345i	−1.21321	−	1.21321i
$120$	1.10694	−	1.33218i	0.101049	−	0.121610i
$121$	7.44170			0.676518
$122$	−5.38578			−0.487606
$123$	8.37071	+	6.95543i	0.754762	+	0.627150i
$124$	−0.0756563	+	0.0756563i	−0.00679413	+	0.00679413i
$125$	0.707107	−	0.707107i	0.0632456	−	0.0632456i
$126$	−7.84454	−	5.38092i	−0.698847	−	0.479371i
$127$	−11.8818			−1.05434			−0.527169	−	0.849761i	$-0.676747\pi$
$127$	−11.8818			−1.05434			−0.527169	+	0.849761i	$0.676747\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−7.17506	+	0.662579i	−0.631728	+	0.0583368i
$130$	−0.469209	+	0.469209i	−0.0411524	+	0.0411524i
$131$	−14.8606	+	14.8606i	−1.29838	+	1.29838i	−0.368917	+	0.929462i	$0.620271\pi$
$131$	−14.8606	+	14.8606i	−1.29838	+	1.29838i	−0.929462	+	0.368917i	$0.879729\pi$
$132$	4.75361	−	5.72087i	0.413748	−	0.497938i
$133$	−7.46172	+	7.46172i	−0.647013	+	0.647013i
$134$	−5.10870	−	5.10870i	−0.441324	−	0.441324i
$135$	−4.99914	+	1.41725i	−0.430257	+	0.121978i
$136$		−	5.90259i		−	0.506143i
$137$		−	20.7659i		−	1.77415i	−0.461628	−	0.887074i	$-0.652735\pi$
$137$		−	20.7659i		−	1.77415i	0.461628	−	0.887074i	$-0.347265\pi$
$138$	−4.59262	−	3.81612i	−0.390950	−	0.324850i
$139$		−	10.4767i		−	0.888618i	−0.895874	−	0.444309i	$-0.853449\pi$
$139$		−	10.4767i		−	0.888618i	0.895874	−	0.444309i	$-0.146551\pi$
$140$	2.24216	−	2.24216i	0.189497	−	0.189497i
$141$	0.613680	−	0.738552i	0.0516812	−	0.0621973i
$142$	5.66370	+	5.66370i	0.475287	+	0.475287i
$143$	−2.01496	+	2.01496i	−0.168500	+	0.168500i
$144$	−0.549384	−	2.94927i	−0.0457820	−	0.245772i
$145$	4.64554			0.385791
$146$	8.49986	+	8.49986i	0.703453	+	0.703453i
$147$	−4.06922	−	3.38121i	−0.335624	−	0.278878i
$148$	5.06584	−	3.36709i	0.416409	−	0.276773i
$149$		−	13.4251i		−	1.09982i	−0.835223	−	0.549911i	$-0.814661\pi$
$149$		−	13.4251i		−	1.09982i	0.835223	−	0.549911i	$-0.185339\pi$
$150$	−0.159268	−	1.72471i	−0.0130042	−	0.140822i
$151$			11.6822i			0.950682i	0.879802	+	0.475341i	$0.157675\pi$
$151$			11.6822i			0.950682i	−0.879802	+	0.475341i	$0.842325\pi$
$152$	−3.32791			−0.269929
$153$	−10.0165	+	14.6025i	−0.809789	+	1.18054i
$154$	9.62869	−	9.62869i	0.775902	−	0.775902i
$155$			0.106994i			0.00859397i
$156$	0.105684	+	1.14445i	0.00846151	+	0.0916296i
$157$	−4.59753			−0.366923			−0.183461	−	0.983027i	$-0.558730\pi$
$157$	−4.59753			−0.366923			−0.183461	+	0.983027i	$0.558730\pi$
$158$			3.34706i			0.266278i
$159$	11.5299	−	13.8760i	0.914381	−	1.10044i
$160$	1.00000			0.0790569
$161$	−7.72976	−	7.72976i	−0.609191	−	0.609191i
$162$	−3.64570	+	8.22854i	−0.286433	+	0.646495i
$163$	12.8094	+	12.8094i	1.00331	+	1.00331i	0.999995	+	0.00331536i	$0.00105531\pi$
$163$	12.8094	+	12.8094i	1.00331	+	1.00331i	0.00331536	+	0.999995i	$0.498945\pi$
$164$			6.28349i			0.490658i
$165$	−0.683958	−	7.40657i	−0.0532461	−	0.576601i
$166$	7.30943	+	7.30943i	0.567321	+	0.567321i
$167$	−2.59545	−	2.59545i	−0.200842	−	0.200842i	0.599519	−	0.800361i	$-0.295359\pi$
$167$	−2.59545	−	2.59545i	−0.200842	−	0.200842i	−0.800361	+	0.599519i	$0.795359\pi$
$168$	−0.505022	−	5.46888i	−0.0389633	−	0.421933i
$169$			12.5597i			0.966130i
$170$	−4.17376	−	4.17376i	−0.320113	−	0.320113i
$171$	8.23299	+	5.64738i	0.629592	+	0.431866i
$172$	−2.94167	−	2.94167i	−0.224300	−	0.224300i
$173$	−5.26417			−0.400228			−0.200114	−	0.979773i	$-0.564131\pi$
$173$	−5.26417			−0.400228			−0.200114	+	0.979773i	$0.564131\pi$
$174$	5.14231	−	6.18867i	0.389838	−	0.469162i
$175$		−	3.17089i		−	0.239697i
$176$	4.29438			0.323701
$177$	1.22245	+	13.2379i	0.0918850	+	0.995022i
$178$			3.71553i			0.278491i
$179$	−9.64682	+	9.64682i	−0.721037	+	0.721037i	−0.968816	−	0.247780i	$-0.920299\pi$
$179$	−9.64682	+	9.64682i	−0.721037	+	0.721037i	0.247780	+	0.968816i	$0.420299\pi$
$180$	−2.47392	−	1.69697i	−0.184395	−	0.126485i
$181$	1.74294			0.129552			0.0647760	−	0.997900i	$-0.479367\pi$
$181$	1.74294			0.129552			0.0647760	+	0.997900i	$0.479367\pi$
$182$			2.10408i			0.155965i
$183$	0.857784	+	9.28893i	0.0634092	+	0.686657i
$184$		−	3.44746i		−	0.254150i
$185$	1.20120	−	5.96298i	0.0883139	−	0.438407i
$186$	0.142535	+	0.118436i	0.0104512	+	0.00868413i
$187$	−17.9237	−	17.9237i	−1.31071	−	1.31071i
$188$	0.554395			0.0404334
$189$	−8.03116	+	14.3866i	−0.584181	+	1.04647i
$190$	−2.35319	+	2.35319i	−0.170718	+	0.170718i
$191$	−17.6905	−	17.6905i	−1.28004	−	1.28004i	−0.940643	−	0.339399i	$-0.889776\pi$
$191$	−17.6905	−	17.6905i	−1.28004	−	1.28004i	−0.339399	−	0.940643i	$-0.610224\pi$
$192$	1.10694	−	1.33218i	0.0798863	−	0.0961415i
$193$	2.31213	−	2.31213i	0.166431	−	0.166431i	−0.618978	−	0.785409i	$-0.712453\pi$
$193$	2.31213	−	2.31213i	0.166431	−	0.166431i	0.785409	+	0.618978i	$0.212453\pi$
$194$			0.185024i			0.0132840i
$195$	0.883981	+	0.734521i	0.0633032	+	0.0526001i
$196$		−	3.05457i		−	0.218183i
$197$		−	24.2094i		−	1.72485i	−0.506185	−	0.862425i	$-0.668945\pi$
$197$		−	24.2094i		−	1.72485i	0.506185	−	0.862425i	$-0.331055\pi$
$198$	−10.6240	−	7.28745i	−0.755011	−	0.517897i
$199$	15.4468	+	15.4468i	1.09500	+	1.09500i	0.994986	+	0.100010i	$0.0318874\pi$
$199$	15.4468	+	15.4468i	1.09500	+	1.09500i	0.100010	+	0.994986i	$0.468113\pi$
$200$	0.707107	−	0.707107i	0.0500000	−	0.0500000i
$201$	−7.99739	+	9.62469i	−0.564092	+	0.678873i
$202$	10.8406	−	10.8406i	0.762744	−	0.762744i
$203$	10.4160	−	10.4160i	0.731063	−	0.731063i
$204$	−10.1803	+	0.940094i	−0.712761	+	0.0658197i
$205$	4.44310	+	4.44310i	0.310320	+	0.310320i
$206$	10.2172			0.711863
$207$	−5.85025	+	8.52874i	−0.406621	+	0.592789i
$208$	−0.469209	+	0.469209i	−0.0325338	+	0.0325338i
$209$	−10.1055	+	10.1055i	−0.699011	+	0.699011i
$210$	−4.22419	−	3.50998i	−0.291497	−	0.242211i
$211$	−26.2503			−1.80714			−0.903571	−	0.428437i	$-0.859064\pi$
$211$	−26.2503			−1.80714			−0.903571	+	0.428437i	$0.859064\pi$
$212$	10.4161			0.715377
$213$	8.86621	−	10.6703i	0.607503	−	0.731117i
$214$	0.200701	+	0.200701i	0.0137196	+	0.0137196i
$215$	−4.16015			−0.283720
$216$	−4.99914	+	1.41725i	−0.340148	+	0.0964319i
$217$	0.239898	+	0.239898i	0.0162853	+	0.0162853i
$218$			10.0299i			0.679307i
$219$	13.3061	−	16.0136i	0.899140	−	1.08210i
$220$	3.03659	−	3.03659i	0.204727	−	0.204727i
$221$	3.91673			0.263468
$222$	−6.61409	−	8.20085i	−0.443908	−	0.550405i
$223$	−16.7598			−1.12232			−0.561160	−	0.827707i	$-0.689645\pi$
$223$	−16.7598			−1.12232			−0.561160	+	0.827707i	$0.689645\pi$
$224$	2.24216	−	2.24216i	0.149811	−	0.149811i
$225$	−2.94927	+	0.549384i	−0.196618	+	0.0366256i
$226$			14.3246i			0.952860i
$227$	−2.30277	−	2.30277i	−0.152840	−	0.152840i	0.626545	−	0.779385i	$-0.284468\pi$
$227$	−2.30277	−	2.30277i	−0.152840	−	0.152840i	−0.779385	+	0.626545i	$0.784468\pi$
$228$	0.530030	+	5.73969i	0.0351021	+	0.380120i
$229$	2.83286			0.187200			0.0936002	−	0.995610i	$-0.470162\pi$
$229$	2.83286			0.187200			0.0936002	+	0.995610i	$0.470162\pi$
$230$	−2.43772	−	2.43772i	−0.160739	−	0.160739i
$231$	−18.1403	−	15.0732i	−1.19354	−	0.991742i
$232$	4.64554			0.304994
$233$	13.0719			0.856372			0.428186	−	0.903691i	$-0.359153\pi$
$233$	13.0719			0.856372			0.428186	+	0.903691i	$0.359153\pi$
$234$	1.95702	−	0.364550i	0.127934	−	0.0238314i
$235$	0.392017	−	0.392017i	0.0255724	−	0.0255724i
$236$	−5.42735	+	5.42735i	−0.353290	+	0.353290i
$237$	5.77273	−	0.533081i	0.374979	−	0.0346273i
$238$	−18.7165			−1.21321
$239$	−6.64308	−	6.64308i	−0.429705	−	0.429705i	0.458823	−	0.888528i	$-0.348271\pi$
$239$	−6.64308	−	6.64308i	−0.429705	−	0.429705i	−0.888528	+	0.458823i	$0.848271\pi$
$240$	−0.159268	−	1.72471i	−0.0102807	−	0.111330i
$241$	−5.79053	+	5.79053i	−0.373001	+	0.373001i	−0.868569	−	0.495568i	$-0.834960\pi$
$241$	−5.79053	+	5.79053i	−0.373001	+	0.373001i	0.495568	+	0.868569i	$0.334960\pi$
$242$	5.26208	−	5.26208i	0.338259	−	0.338259i
$243$	14.7725	+	4.97724i	0.947657	+	0.319290i
$244$	−3.80832	+	3.80832i	−0.243803	+	0.243803i
$245$	−2.15991	−	2.15991i	−0.137991	−	0.137991i
$246$	10.8372	−	1.00076i	0.690956	−	0.0638061i
$247$		−	2.20828i		−	0.140509i
$248$			0.106994i			0.00679413i
$249$	11.4425	−	13.7708i	0.725139	−	0.872690i
$250$		−	1.00000i		−	0.0632456i
$251$	3.57449	−	3.57449i	0.225620	−	0.225620i	−0.585240	−	0.810860i	$-0.699000\pi$
$251$	3.57449	−	3.57449i	0.225620	−	0.225620i	0.810860	+	0.585240i	$0.199000\pi$
$252$	−9.35181	+	1.74204i	−0.589109	+	0.109738i
$253$	−10.4685	−	10.4685i	−0.658150	−	0.658150i
$254$	−8.40169	+	8.40169i	−0.527169	+	0.527169i
$255$	−6.53379	+	7.86328i	−0.409162	+	0.492418i
$256$	1.00000			0.0625000
$257$	2.58770	+	2.58770i	0.161416	+	0.161416i	0.783194	−	0.621778i	$-0.213589\pi$
$257$	2.58770	+	2.58770i	0.161416	+	0.161416i	−0.621778	+	0.783194i	$0.713589\pi$
$258$	−4.60502	+	5.54204i	−0.286696	+	0.345033i
$259$	−10.6767	−	16.0632i	−0.663416	−	0.998121i
$260$			0.663562i			0.0411524i
$261$	−11.4927	−	7.88335i	−0.711379	−	0.487967i
$262$			21.0161i			1.29838i
$263$	10.2023			0.629102			0.314551	−	0.949241i	$-0.398146\pi$
$263$	10.2023			0.629102			0.314551	+	0.949241i	$0.398146\pi$
$264$	−0.683958	−	7.40657i	−0.0420947	−	0.455843i
$265$	7.36526	−	7.36526i	0.452444	−	0.452444i
$266$			10.5525i			0.647013i
$267$	6.40822	−	0.591765i	0.392177	−	0.0362154i
$268$	−7.22479			−0.441324
$269$		−	22.2257i		−	1.35513i	−0.735465	−	0.677563i	$-0.763036\pi$
$269$		−	22.2257i		−	1.35513i	0.735465	−	0.677563i	$-0.236964\pi$
$270$	−2.53278	+	4.53707i	−0.154140	+	0.276118i
$271$	−0.400523			−0.0243300			−0.0121650	−	0.999926i	$-0.503872\pi$
$271$	−0.400523			−0.0243300			−0.0121650	+	0.999926i	$0.503872\pi$
$272$	−4.17376	−	4.17376i	−0.253071	−	0.253071i
$273$	3.62894	−	0.335114i	0.219633	−	0.0202820i
$274$	−14.6837	−	14.6837i	−0.887074	−	0.887074i
$275$		−	4.29438i		−	0.258961i
$276$	−5.94588	+	0.549071i	−0.357900	+	0.0330502i
$277$	−5.22843	−	5.22843i	−0.314146	−	0.314146i	0.532367	−	0.846513i	$-0.321302\pi$
$277$	−5.22843	−	5.22843i	−0.314146	−	0.314146i	−0.846513	+	0.532367i	$0.821302\pi$
$278$	−7.40811	−	7.40811i	−0.444309	−	0.444309i
$279$	0.181566	−	0.264695i	0.0108701	−	0.0158469i
$280$		−	3.17089i		−	0.189497i
$281$	−7.32785	−	7.32785i	−0.437143	−	0.437143i	0.453906	−	0.891049i	$-0.350030\pi$
$281$	−7.32785	−	7.32785i	−0.437143	−	0.437143i	−0.891049	+	0.453906i	$0.850030\pi$
$282$	−0.0882975	−	0.956173i	−0.00525804	−	0.0569393i
$283$	−7.08939	−	7.08939i	−0.421421	−	0.421421i	0.464272	−	0.885693i	$-0.346316\pi$
$283$	−7.08939	−	7.08939i	−0.421421	−	0.421421i	−0.885693	+	0.464272i	$0.846316\pi$
$284$	8.00969			0.475287
$285$	4.43336	+	3.68379i	0.262610	+	0.218209i
$286$			2.84959i			0.168500i
$287$	19.9243			1.17609
$288$	−2.47392	−	1.69697i	−0.145777	−	0.0999952i
$289$			17.8405i			1.04944i
$290$	3.28489	−	3.28489i	0.192895	−	0.192895i
$291$	0.319114	−	0.0294685i	0.0187068	−	0.00172747i
$292$	12.0206			0.703453
$293$			27.9995i			1.63575i	0.575399	+	0.817873i	$0.304847\pi$
$293$			27.9995i			1.63575i	−0.575399	+	0.817873i	$0.695153\pi$
$294$	−5.26825	+	0.486495i	−0.307251	+	0.0283730i
$295$			7.67543i			0.446881i
$296$	1.20120	−	5.96298i	0.0698182	−	0.346591i
$297$	−10.8767	+	19.4839i	−0.631130	+	1.13057i
$298$	−9.49294	−	9.49294i	−0.549911	−	0.549911i
$299$	2.28760			0.132296
$300$	−1.33218	−	1.10694i	−0.0769132	−	0.0639090i
$301$	−9.32772	+	9.32772i	−0.537641	+	0.537641i
$302$	8.26055	+	8.26055i	0.475341	+	0.475341i
$303$	−20.4235	−	16.9704i	−1.17330	−	0.974924i
$304$	−2.35319	+	2.35319i	−0.134965	+	0.134965i
$305$			5.38578i			0.308389i
$306$	3.24278	+	17.4083i	0.185378	+	0.995166i
$307$			12.1710i			0.694637i	0.937747	+	0.347319i	$0.112908\pi$
$307$			12.1710i			0.694637i	−0.937747	+	0.347319i	$0.887092\pi$
$308$		−	13.6170i		−	0.775902i
$309$	−1.62727	−	17.6216i	−0.0925720	−	1.00246i
$310$	0.0756563	+	0.0756563i	0.00429699	+	0.00429699i
$311$	−10.9987	+	10.9987i	−0.623678	+	0.623678i	−0.946470	−	0.322792i	$-0.895379\pi$
$311$	−10.9987	+	10.9987i	−0.623678	+	0.623678i	0.322792	+	0.946470i	$0.395379\pi$
$312$	0.883981	+	0.734521i	0.0500456	+	0.0415840i
$313$	−24.6477	+	24.6477i	−1.39317	+	1.39317i	−0.575057	+	0.818113i	$0.695020\pi$
$313$	−24.6477	+	24.6477i	−1.39317	+	1.39317i	−0.818113	+	0.575057i	$0.804980\pi$
$314$	−3.25094	+	3.25094i	−0.183461	+	0.183461i
$315$	−5.38092	+	7.84454i	−0.303181	+	0.441990i
$316$	2.36673	+	2.36673i	0.133139	+	0.133139i
$317$	24.9951			1.40386			0.701932	−	0.712244i	$-0.252321\pi$
$317$	24.9951			1.40386			0.701932	+	0.712244i	$0.252321\pi$
$318$	−1.65895	−	17.9647i	−0.0930290	−	1.00741i
$319$	14.1066	−	14.1066i	0.789816	−	0.789816i
$320$	0.707107	−	0.707107i	0.0395285	−	0.0395285i
$321$	0.314186	−	0.378117i	0.0175362	−	0.0211044i
$322$	−10.9315			−0.609191
$323$	19.6433			1.09298
$324$	3.24056	+	8.39636i	0.180031	+	0.466464i
$325$	0.469209	+	0.469209i	0.0260270	+	0.0260270i
$326$	18.1152			1.00331
$327$	17.2986	−	1.59744i	0.956615	−	0.0883384i
$328$	4.44310	+	4.44310i	0.245329	+	0.245329i
$329$		−	1.75793i		−	0.0969178i
$330$	−5.72087	−	4.75361i	−0.314923	−	0.261677i
$331$	18.9528	−	18.9528i	1.04174	−	1.04174i	0.0426473	−	0.999090i	$-0.486421\pi$
$331$	18.9528	−	18.9528i	1.04174	−	1.04174i	0.999090	−	0.0426473i	$-0.0135792\pi$
$332$	10.3371			0.567321
$333$	−13.0907	+	12.7135i	−0.717365	+	0.696697i
$334$	−3.67053			−0.200842
$335$	−5.10870	+	5.10870i	−0.279118	+	0.279118i
$336$	−4.22419	−	3.50998i	−0.230448	−	0.191485i
$337$			3.52403i			0.191966i	0.995383	+	0.0959832i	$0.0305995\pi$
$337$			3.52403i			0.191966i	−0.995383	+	0.0959832i	$0.969400\pi$
$338$	8.88104	+	8.88104i	0.483065	+	0.483065i
$339$	24.7059	−	2.28146i	1.34184	−	0.123912i
$340$	−5.90259			−0.320113
$341$	0.324897	+	0.324897i	0.0175941	+	0.0175941i
$342$	9.81490	−	1.82830i	0.530729	−	0.0988632i
$343$	12.5105			0.675506
$344$	−4.16015			−0.224300
$345$	−3.81612	+	4.59262i	−0.205453	+	0.247259i
$346$	−3.72233	+	3.72233i	−0.200114	+	0.200114i
$347$	−6.24635	+	6.24635i	−0.335322	+	0.335322i	−0.854603	−	0.519281i	$-0.826200\pi$
$347$	−6.24635	+	6.24635i	−0.335322	+	0.335322i	0.519281	+	0.854603i	$0.326200\pi$
$348$	−0.739886	−	8.01221i	−0.0396620	−	0.429500i
$349$	32.9526			1.76391			0.881957	−	0.471330i	$-0.156226\pi$
$349$	32.9526			1.76391			0.881957	+	0.471330i	$0.156226\pi$
$350$	−2.24216	−	2.24216i	−0.119849	−	0.119849i
$351$	−0.940435	−	3.31724i	−0.0501967	−	0.177061i
$352$	3.03659	−	3.03659i	0.161851	−	0.161851i
$353$	13.3438	−	13.3438i	0.710218	−	0.710218i	−0.256362	−	0.966581i	$-0.582524\pi$
$353$	13.3438	−	13.3438i	0.710218	−	0.710218i	0.966581	+	0.256362i	$0.0825240\pi$
$354$	10.2250	+	8.49621i	0.543453	+	0.451568i
$355$	5.66370	−	5.66370i	0.300598	−	0.300598i
$356$	2.62728	+	2.62728i	0.139245	+	0.139245i
$357$	2.98094	+	32.2805i	0.157768	+	1.70847i
$358$			13.6427i			0.721037i
$359$		−	0.209030i		−	0.0110322i	−0.999985	−	0.00551610i	$-0.998244\pi$
$359$		−	0.209030i		−	0.0110322i	0.999985	−	0.00551610i	$-0.00175584\pi$
$360$	−2.94927	+	0.549384i	−0.155440	+	0.0289551i
$361$			7.92500i			0.417105i
$362$	1.23245	−	1.23245i	0.0647760	−	0.0647760i
$363$	−9.91365	−	8.23749i	−0.520332	−	0.432356i
$364$	1.48781	+	1.48781i	0.0779825	+	0.0779825i
$365$	8.49986	−	8.49986i	0.444903	−	0.444903i
$366$	7.17481	+	5.96172i	0.375033	+	0.311624i
$367$	14.8095			0.773048			0.386524	−	0.922279i	$-0.373676\pi$
$367$	14.8095			0.773048			0.386524	+	0.922279i	$0.373676\pi$
$368$	−2.43772	−	2.43772i	−0.127075	−	0.127075i
$369$	−3.45205	−	18.5317i	−0.179706	−	0.964722i
$370$	−3.36709	−	5.06584i	−0.175047	−	0.263360i
$371$		−	33.0282i		−	1.71474i
$372$	0.184534	−	0.0170408i	0.00956765	−	0.000883522i
$373$			3.56845i			0.184767i	0.995723	+	0.0923836i	$0.0294486\pi$
$373$			3.56845i			0.184767i	−0.995723	+	0.0923836i	$0.970551\pi$
$374$	−25.3479			−1.31071
$375$	−1.72471	+	0.159268i	−0.0890638	+	0.00822457i
$376$	0.392017	−	0.392017i	0.0202167	−	0.0202167i
$377$			3.08260i			0.158762i
$378$	4.49396	+	15.8517i	0.231144	+	0.815326i
$379$	−6.69408			−0.343852			−0.171926	−	0.985110i	$-0.554999\pi$
$379$	−6.69408			−0.343852			−0.171926	+	0.985110i	$0.554999\pi$
$380$			3.32791i			0.170718i
$381$	15.8286	+	13.1524i	0.810925	+	0.673817i
$382$	−25.0182			−1.28004
$383$	−10.2592	−	10.2592i	−0.524221	−	0.524221i	0.394622	−	0.918843i	$-0.370875\pi$
$383$	−10.2592	−	10.2592i	−0.524221	−	0.524221i	−0.918843	+	0.394622i	$0.870875\pi$
$384$	−0.159268	−	1.72471i	−0.00812762	−	0.0880139i
$385$	−9.62869	−	9.62869i	−0.490723	−	0.490723i
$386$		−	3.26985i		−	0.166431i
$387$	10.2919	+	7.05966i	0.523165	+	0.358863i
$388$	0.130832	+	0.130832i	0.00664199	+	0.00664199i
$389$	−11.2832	−	11.2832i	−0.572079	−	0.572079i	0.360630	−	0.932709i	$-0.382562\pi$
$389$	−11.2832	−	11.2832i	−0.572079	−	0.572079i	−0.932709	+	0.360630i	$0.882562\pi$
$390$	1.14445	−	0.105684i	0.0579516	−	0.00535153i
$391$			20.3489i			1.02909i
$392$	−2.15991	−	2.15991i	−0.109092	−	0.109092i
$393$	36.2467	−	3.34720i	1.82841	−	0.168844i
$394$	−17.1186	−	17.1186i	−0.862425	−	0.862425i
$395$	3.34706			0.168409
$396$	−12.6653	+	2.35926i	−0.636454	+	0.118557i
$397$			15.5131i			0.778580i	0.921115	+	0.389290i	$0.127280\pi$
$397$			15.5131i			0.778580i	−0.921115	+	0.389290i	$0.872720\pi$
$398$	21.8451			1.09500
$399$	18.2000	−	1.68067i	0.911138	−	0.0841388i
$400$		−	1.00000i		−	0.0500000i
$401$	−1.36032	+	1.36032i	−0.0679314	+	0.0679314i	−0.740256	−	0.672325i	$-0.765296\pi$
$401$	−1.36032	+	1.36032i	−0.0679314	+	0.0679314i	0.672325	+	0.740256i	$0.265296\pi$
$402$	1.15068	+	12.4607i	0.0573907	+	0.621483i
$403$	−0.0709972			−0.00353662
$404$		−	15.3310i		−	0.762744i
$405$	8.22854	+	3.64570i	0.408879	+	0.181156i
$406$		−	14.7305i		−	0.731063i
$407$	−14.4596	−	21.7546i	−0.716733	−	1.07834i
$408$	−6.53379	+	7.86328i	−0.323471	+	0.389290i
$409$	−9.43162	−	9.43162i	−0.466363	−	0.466363i	0.434371	−	0.900734i	$-0.356971\pi$
$409$	−9.43162	−	9.43162i	−0.466363	−	0.466363i	−0.900734	+	0.434371i	$0.856971\pi$
$410$	6.28349			0.310320
$411$	−22.9865	+	27.6638i	−1.13384	+	1.36455i
$412$	7.22462	−	7.22462i	0.355931	−	0.355931i
$413$	17.2095	+	17.2095i	0.846826	+	0.846826i
$414$	1.89398	+	10.1675i	0.0930840	+	0.499705i
$415$	7.30943	−	7.30943i	0.358806	−	0.358806i
$416$			0.663562i			0.0325338i
$417$	−11.5970	+	13.9567i	−0.567907	+	0.683464i
$418$			14.2913i			0.699011i
$419$			30.3868i			1.48449i	0.670128	+	0.742246i	$0.266239\pi$
$419$			30.3868i			1.48449i	−0.670128	+	0.742246i	$0.733761\pi$
$420$	−5.46888	+	0.505022i	−0.266854	+	0.0246426i
$421$	7.53525	+	7.53525i	0.367246	+	0.367246i	0.866472	−	0.499226i	$-0.166382\pi$
$421$	7.53525	+	7.53525i	0.367246	+	0.367246i	−0.499226	+	0.866472i	$0.666382\pi$
$422$	−18.5617	+	18.5617i	−0.903571	+	0.903571i
$423$	−1.63506	+	0.304576i	−0.0794994	+	0.0148090i
$424$	7.36526	−	7.36526i	0.357689	−	0.357689i
$425$	−4.17376	+	4.17376i	−0.202457	+	0.202457i
$426$	−1.27569	−	13.8144i	−0.0618073	−	0.669310i
$427$	12.0758	+	12.0758i	0.584389	+	0.584389i
$428$	0.283834			0.0137196
$429$	4.91472	−	0.453848i	0.237285	−	0.0219120i
$430$	−2.94167	+	2.94167i	−0.141860	+	0.141860i
$431$	13.1264	−	13.1264i	0.632279	−	0.632279i	−0.316360	−	0.948639i	$-0.602461\pi$
$431$	13.1264	−	13.1264i	0.632279	−	0.632279i	0.948639	+	0.316360i	$0.102461\pi$
$432$	−2.53278	+	4.53707i	−0.121858	+	0.218290i
$433$	21.3135			1.02426			0.512131	−	0.858907i	$-0.328856\pi$
$433$	21.3135			1.02426			0.512131	+	0.858907i	$0.328856\pi$
$434$	0.339267			0.0162853
$435$	−6.18867	−	5.14231i	−0.296724	−	0.246555i
$436$	7.09218	+	7.09218i	0.339654	+	0.339654i
$437$	11.4729			0.548821
$438$	−1.91450	−	20.7321i	−0.0914784	−	0.990619i
$439$	1.95249	+	1.95249i	0.0931874	+	0.0931874i	0.752164	−	0.658976i	$-0.229010\pi$
$439$	1.95249	+	1.95249i	0.0931874	+	0.0931874i	−0.658976	+	0.752164i	$0.729010\pi$
$440$		−	4.29438i		−	0.204727i
$441$	1.67813	+	9.00874i	0.0799109	+	0.428987i
$442$	2.76955	−	2.76955i	0.131734	−	0.131734i
$443$	−40.7519			−1.93618			−0.968089	−	0.250605i	$-0.919371\pi$
$443$	−40.7519			−1.93618			−0.968089	+	0.250605i	$0.919371\pi$
$444$	−10.4757	−	1.12201i	−0.497157	−	0.0532482i
$445$	3.71553			0.176133
$446$	−11.8510	+	11.8510i	−0.561160	+	0.561160i
$447$	−14.8607	+	17.8845i	−0.702886	+	0.845909i
$448$		−	3.17089i		−	0.149811i
$449$	−16.4400	−	16.4400i	−0.775853	−	0.775853i	0.203269	−	0.979123i	$-0.434843\pi$
$449$	−16.4400	−	16.4400i	−0.775853	−	0.775853i	−0.979123	+	0.203269i	$0.934843\pi$
$450$	−1.69697	+	2.47392i	−0.0799961	+	0.116622i
$451$	26.9837			1.27061
$452$	10.1290	+	10.1290i	0.476430	+	0.476430i
$453$	12.9314	−	15.5627i	0.607572	−	0.731200i
$454$	−3.25660			−0.152840
$455$	2.10408			0.0986410
$456$	4.43336	+	3.68379i	0.207611	+	0.172509i
$457$	−13.7781	+	13.7781i	−0.644512	+	0.644512i	−0.951661	−	0.307149i	$-0.900625\pi$
$457$	−13.7781	+	13.7781i	−0.644512	+	0.644512i	0.307149	+	0.951661i	$0.400625\pi$
$458$	2.00313	−	2.00313i	0.0936002	−	0.0936002i
$459$	29.5078	−	8.36546i	1.37731	−	0.390466i
$460$	−3.44746			−0.160739
$461$	14.2992	+	14.2992i	0.665979	+	0.665979i	0.956783	−	0.290804i	$-0.0939226\pi$
$461$	14.2992	+	14.2992i	0.665979	+	0.665979i	−0.290804	+	0.956783i	$0.593923\pi$
$462$	−23.4855	+	2.16876i	−1.09264	+	0.100900i
$463$	22.7343	−	22.7343i	1.05655	−	1.05655i	0.0582522	−	0.998302i	$-0.481447\pi$
$463$	22.7343	−	22.7343i	1.05655	−	1.05655i	0.998302	−	0.0582522i	$-0.0185528\pi$
$464$	3.28489	−	3.28489i	0.152497	−	0.152497i
$465$	0.118436	−	0.142535i	0.00549232	−	0.00660990i
$466$	9.24326	−	9.24326i	0.428186	−	0.428186i
$467$	−25.3750	−	25.3750i	−1.17422	−	1.17422i	−0.981194	−	0.193022i	$-0.938171\pi$
$467$	−25.3750	−	25.3750i	−1.17422	−	1.17422i	−0.193022	−	0.981194i	$-0.561829\pi$
$468$	1.12605	−	1.64160i	0.0520515	−	0.0758829i
$469$			22.9090i			1.05784i
$470$		−	0.554395i		−	0.0255724i
$471$	6.12471	+	5.08917i	0.282212	+	0.234497i
$472$			7.67543i			0.353290i
$473$	−12.6326	+	12.6326i	−0.580849	+	0.580849i
$474$	3.70499	−	4.45888i	0.170176	−	0.204803i
$475$	2.35319	+	2.35319i	0.107972	+	0.107972i
$476$	−13.2345	+	13.2345i	−0.606604	+	0.606604i
$477$	−30.7197	+	5.72241i	−1.40656	+	0.262011i
$478$	−9.39473			−0.429705
$479$	28.4324	+	28.4324i	1.29911	+	1.29911i	0.928981	+	0.370127i	$0.120686\pi$
$479$	28.4324	+	28.4324i	1.29911	+	1.29911i	0.370127	+	0.928981i	$0.379314\pi$
$480$	−1.33218	−	1.10694i	−0.0608052	−	0.0505245i
$481$	3.95681	+	0.797069i	0.180415	+	0.0363432i
$482$			8.18905i			0.373001i
$483$	1.74105	+	18.8538i	0.0792203	+	0.857876i
$484$		−	7.44170i		−	0.338259i
$485$	0.185024			0.00840152
$486$	13.9652	−	6.92630i	0.633474	−	0.314183i
$487$	−8.44631	+	8.44631i	−0.382739	+	0.382739i	−0.872088	−	0.489349i	$-0.837234\pi$
$487$	−8.44631	+	8.44631i	−0.382739	+	0.382739i	0.489349	+	0.872088i	$0.337234\pi$
$488$			5.38578i			0.243803i
$489$	−2.88518	−	31.2436i	−0.130472	−	1.41288i
$490$	−3.05457			−0.137991
$491$		−	21.3703i		−	0.964426i	−0.876054	−	0.482213i	$-0.839833\pi$
$491$		−	21.3703i		−	0.964426i	0.876054	−	0.482213i	$-0.160167\pi$
$492$	6.95543	−	8.37071i	0.313575	−	0.377381i
$493$	−27.4207			−1.23497
$494$	−1.56149	−	1.56149i	−0.0702546	−	0.0702546i
$495$	−7.28745	+	10.6240i	−0.327547	+	0.477511i
$496$	0.0756563	+	0.0756563i	0.00339707	+	0.00339707i
$497$		−	25.3979i		−	1.13925i
$498$	−1.64637	−	17.8285i	−0.0737756	−	0.798915i
$499$	−23.8771	−	23.8771i	−1.06888	−	1.06888i	−0.997445	−	0.0714387i	$-0.977241\pi$
$499$	−23.8771	−	23.8771i	−1.06888	−	1.06888i	−0.0714387	−	0.997445i	$-0.522759\pi$
$500$	−0.707107	−	0.707107i	−0.0316228	−	0.0316228i
$501$	0.584598	+	6.33060i	0.0261179	+	0.282831i
$502$		−	5.05509i		−	0.225620i
$503$	−17.4364	−	17.4364i	−0.777452	−	0.777452i	0.201945	−	0.979397i	$-0.435274\pi$
$503$	−17.4364	−	17.4364i	−0.777452	−	0.777452i	−0.979397	+	0.201945i	$0.935274\pi$
$504$	−5.38092	+	7.84454i	−0.239685	+	0.349423i
$505$	−10.8406	−	10.8406i	−0.482402	−	0.482402i
$506$	−14.8047			−0.658150
$507$	13.9028	−	16.7317i	0.617444	−	0.743081i
$508$			11.8818i			0.527169i
$509$	27.3051			1.21028			0.605139	−	0.796120i	$-0.293118\pi$
$509$	27.3051			1.21028			0.605139	+	0.796120i	$0.293118\pi$
$510$	0.940094	+	10.1803i	0.0416281	+	0.450790i
$511$		−	38.1161i		−	1.68616i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−4.71649	−	16.6367i	−0.208238	−	0.734528i
$514$	3.65956			0.161416
$515$		−	10.2172i		−	0.450221i
$516$	0.662579	+	7.17506i	0.0291684	+	0.315864i
$517$		−	2.38078i		−	0.104707i
$518$	−18.9080	−	3.80887i	−0.830769	−	0.167352i
$519$	7.01280	+	5.82710i	0.307828	+	0.255781i
$520$	0.469209	+	0.469209i	0.0205762	+	0.0205762i
$521$	33.5578			1.47019			0.735097	−	0.677962i	$-0.237137\pi$
$521$	33.5578			1.47019			0.735097	+	0.677962i	$0.237137\pi$
$522$	−13.7009	+	2.55218i	−0.599673	+	0.111706i
$523$	−3.03654	+	3.03654i	−0.132779	+	0.132779i	−0.770373	−	0.637594i	$-0.779930\pi$
$523$	−3.03654	+	3.03654i	−0.132779	+	0.132779i	0.637594	+	0.770373i	$0.279930\pi$
$524$	14.8606	+	14.8606i	0.649190	+	0.649190i
$525$	−3.50998	+	4.22419i	−0.153188	+	0.184359i
$526$	7.21413	−	7.21413i	0.314551	−	0.314551i
$527$		−	0.631542i		−	0.0275104i
$528$	−5.72087	−	4.75361i	−0.248969	−	0.206874i
$529$		−	11.1150i		−	0.483261i
$530$		−	10.4161i		−	0.452444i
$531$	13.0250	−	18.9884i	0.565237	−	0.824026i
$532$	7.46172	+	7.46172i	0.323506	+	0.323506i
$533$	−2.94827	+	2.94827i	−0.127704	+	0.127704i
$534$	4.11285	−	4.94974i	0.177981	−	0.214196i
$535$	0.200701	−	0.200701i	0.00867707	−	0.00867707i
$536$	−5.10870	+	5.10870i	−0.220662	+	0.220662i
$537$	23.5297	−	2.17284i	1.01538	−	0.0937650i
$538$	−15.7160	−	15.7160i	−0.677563	−	0.677563i
$539$	−13.1175			−0.565010
$540$	1.41725	+	4.99914i	0.0609889	+	0.215129i
$541$	−5.18238	+	5.18238i	−0.222808	+	0.222808i	−0.809680	−	0.586872i	$-0.800359\pi$
$541$	−5.18238	+	5.18238i	−0.222808	+	0.222808i	0.586872	+	0.809680i	$0.300359\pi$
$542$	−0.283212	+	0.283212i	−0.0121650	+	0.0121650i
$543$	−2.32191	−	1.92933i	−0.0996425	−	0.0827953i
$544$	−5.90259			−0.253071
$545$	10.0299			0.429632
$546$	2.32909	−	2.80301i	0.0996757	−	0.119958i
$547$	−2.14503	−	2.14503i	−0.0917148	−	0.0917148i	0.659761	−	0.751476i	$-0.270658\pi$
$547$	−2.14503	−	2.14503i	−0.0917148	−	0.0917148i	−0.751476	+	0.659761i	$0.770658\pi$
$548$	−20.7659			−0.887074
$549$	9.13954	−	13.3240i	0.390066	−	0.568654i
$550$	−3.03659	−	3.03659i	−0.129480	−	0.129480i
$551$			15.4599i			0.658616i
$552$	−3.81612	+	4.59262i	−0.162425	+	0.195475i
$553$	7.50466	−	7.50466i	0.319130	−	0.319130i
$554$	−7.39412			−0.314146
$555$	−8.20085	+	6.61409i	−0.348107	+	0.280752i
$556$	−10.4767			−0.444309
$557$	4.77952	−	4.77952i	0.202515	−	0.202515i	−0.598562	−	0.801077i	$-0.704261\pi$
$557$	4.77952	−	4.77952i	0.202515	−	0.202515i	0.801077	+	0.598562i	$0.204261\pi$
$558$	−0.0587808	−	0.315554i	−0.00248839	−	0.0133585i
$559$		−	2.76051i		−	0.116757i
$560$	−2.24216	−	2.24216i	−0.0947486	−	0.0947486i
$561$	4.03712	+	43.7179i	0.170447	+	1.84577i
$562$	−10.3631			−0.437143
$563$	20.9149	+	20.9149i	0.881459	+	0.881459i	0.993683	−	0.112224i	$-0.0357973\pi$
$563$	20.9149	+	20.9149i	0.881459	+	0.881459i	−0.112224	+	0.993683i	$0.535797\pi$
$564$	−0.738552	−	0.613680i	−0.0310987	−	0.0258406i
$565$	14.3246			0.602642
$566$	−10.0259			−0.421421
$567$	26.6240	−	10.2755i	1.11810	−	0.431529i
$568$	5.66370	−	5.66370i	0.237644	−	0.237644i
$569$	−23.7328	+	23.7328i	−0.994929	+	0.994929i	−0.999987	−	0.00505843i	$-0.998390\pi$
$569$	−23.7328	+	23.7328i	−0.994929	+	0.994929i	0.00505843	+	0.999987i	$0.498390\pi$
$570$	5.73969	−	0.530030i	0.240409	−	0.0222005i
$571$	47.2125			1.97578			0.987890	−	0.155154i	$-0.0495873\pi$
$571$	47.2125			1.97578			0.987890	+	0.155154i	$0.0495873\pi$
$572$	2.01496	+	2.01496i	0.0842498	+	0.0842498i
$573$	3.98460	+	43.1492i	0.166459	+	1.80258i
$574$	14.0886	−	14.0886i	0.588047	−	0.588047i
$575$	−2.43772	+	2.43772i	−0.101660	+	0.101660i
$576$	−2.94927	+	0.549384i	−0.122886	+	0.0228910i
$577$	13.8837	−	13.8837i	0.577985	−	0.577985i	−0.356363	−	0.934348i	$-0.615983\pi$
$577$	13.8837	−	13.8837i	0.577985	−	0.577985i	0.934348	+	0.356363i	$0.115983\pi$
$578$	12.6152	+	12.6152i	0.524721	+	0.524721i
$579$	−5.63955	+	0.520783i	−0.234372	+	0.0216430i
$580$		−	4.64554i		−	0.192895i
$581$		−	32.7778i		−	1.35985i
$582$	0.204810	−	0.246485i	0.00848965	−	0.0102171i
$583$		−	44.7305i		−	1.85255i
$584$	8.49986	−	8.49986i	0.351727	−	0.351727i
$585$	−0.364550	−	1.95702i	−0.0150723	−	0.0809129i
$586$	19.7986	+	19.7986i	0.817873	+	0.817873i
$587$	−28.2138	+	28.2138i	−1.16451	+	1.16451i	−0.181033	+	0.983477i	$0.557944\pi$
$587$	−28.2138	+	28.2138i	−1.16451	+	1.16451i	−0.983477	+	0.181033i	$0.942056\pi$
$588$	−3.38121	+	4.06922i	−0.139439	+	0.167812i
$589$	−0.356067			−0.0146715
$590$	5.42735	+	5.42735i	0.223440	+	0.223440i
$591$	−26.7983	+	32.2512i	−1.10233	+	1.32664i
$592$	−3.36709	−	5.06584i	−0.138386	−	0.208205i
$593$			6.81280i			0.279768i	0.990168	+	0.139884i	$0.0446730\pi$
$593$			6.81280i			0.279768i	−0.990168	+	0.139884i	$0.955327\pi$
$594$	6.08622	+	21.4682i	0.249721	+	0.880851i
$595$			18.7165i			0.767301i
$596$	−13.4251			−0.549911
$597$	−3.47923	−	37.6765i	−0.142395	−	1.54200i
$598$	1.61758	−	1.61758i	0.0661478	−	0.0661478i
$599$			35.3959i			1.44624i	0.690724	+	0.723119i	$0.257292\pi$
$599$			35.3959i			1.44624i	−0.690724	+	0.723119i	$0.742708\pi$
$600$	−1.72471	+	0.159268i	−0.0704111	+	0.00650209i
$601$	−9.54349			−0.389287			−0.194643	−	0.980874i	$-0.562355\pi$
$601$	−9.54349			−0.389287			−0.194643	+	0.980874i	$0.562355\pi$
$602$			13.1914i			0.537641i
$603$	21.3078	−	3.96918i	0.867722	−	0.161638i
$604$	11.6822			0.475341
$605$	−5.26208	−	5.26208i	−0.213934	−	0.213934i
$606$	−26.4415	+	2.44173i	−1.07411	+	0.0991887i
$607$	14.5767	+	14.5767i	0.591650	+	0.591650i	0.938077	−	0.346427i	$-0.112605\pi$
$607$	14.5767	+	14.5767i	0.591650	+	0.591650i	−0.346427	+	0.938077i	$0.612605\pi$
$608$			3.32791i			0.134965i
$609$	−25.4059	+	2.34610i	−1.02950	+	0.0950688i
$610$	3.80832	+	3.80832i	0.154195	+	0.154195i
$611$	0.260127	+	0.260127i	0.0105236	+	0.0105236i
$612$	14.6025	+	10.0165i	0.590272	+	0.404894i
$613$		−	46.0780i		−	1.86107i	−0.366198	−	0.930537i	$-0.619341\pi$
$613$		−	46.0780i		−	1.86107i	0.366198	−	0.930537i	$-0.380659\pi$
$614$	8.60622	+	8.60622i	0.347319	+	0.347319i
$615$	−1.00076	−	10.8372i	−0.0403545	−	0.436999i
$616$	−9.62869	−	9.62869i	−0.387951	−	0.387951i
$617$	−8.81089			−0.354713			−0.177357	−	0.984147i	$-0.556755\pi$
$617$	−8.81089			−0.354713			−0.177357	+	0.984147i	$0.556755\pi$
$618$	−13.6110	−	11.3097i	−0.547516	−	0.454944i
$619$		−	31.5228i		−	1.26701i	−0.773740	−	0.633504i	$-0.781616\pi$
$619$		−	31.5228i		−	1.26701i	0.773740	−	0.633504i	$-0.218384\pi$
$620$	0.106994			0.00429699
$621$	17.2343	−	4.88593i	0.691590	−	0.196065i
$622$			15.5545i			0.623678i
$623$	8.33081	−	8.33081i	0.333767	−	0.333767i
$624$	1.14445	−	0.105684i	0.0458148	−	0.00423076i
$625$	−1.00000			−0.0400000
$626$			34.8571i			1.39317i
$627$	24.6484	−	2.27615i	0.984363	−	0.0909008i
$628$			4.59753i			0.183461i
$629$	−7.09018	+	35.1970i	−0.282704	+	1.40340i
$630$	1.74204	+	9.35181i	0.0694044	+	0.372585i
$631$	−18.7269	−	18.7269i	−0.745504	−	0.745504i	0.228127	−	0.973631i	$-0.426740\pi$
$631$	−18.7269	−	18.7269i	−0.745504	−	0.745504i	−0.973631	+	0.228127i	$0.926740\pi$
$632$	3.34706			0.133139
$633$	34.9700	+	29.0574i	1.38993	+	1.15493i
$634$	17.6742	−	17.6742i	0.701932	−	0.701932i
$635$	8.40169	+	8.40169i	0.333411	+	0.333411i
$636$	−13.8760	−	11.5299i	−0.550220	−	0.457191i
$637$	1.43323	−	1.43323i	0.0567867	−	0.0567867i
$638$		−	19.9497i		−	0.789816i
$639$	−23.6227	+	4.40039i	−0.934500	+	0.174077i
$640$		−	1.00000i		−	0.0395285i
$641$			12.3332i			0.487131i	0.969884	+	0.243565i	$0.0783170\pi$
$641$			12.3332i			0.487131i	−0.969884	+	0.243565i	$0.921683\pi$
$642$	−0.0452057	−	0.489532i	−0.00178413	−	0.0193203i
$643$	17.2628	+	17.2628i	0.680776	+	0.680776i	0.960175	−	0.279399i	$-0.0901351\pi$
$643$	17.2628	+	17.2628i	0.680776	+	0.680776i	−0.279399	+	0.960175i	$0.590135\pi$
$644$	−7.72976	+	7.72976i	−0.304595	+	0.304595i
$645$	5.54204	+	4.60502i	0.218218	+	0.181322i
$646$	13.8899	−	13.8899i	0.546491	−	0.546491i
$647$	9.42234	−	9.42234i	0.370430	−	0.370430i	−0.497204	−	0.867634i	$-0.665640\pi$
$647$	9.42234	−	9.42234i	0.370430	−	0.370430i	0.867634	+	0.497204i	$0.165640\pi$
$648$	8.22854	+	3.64570i	0.323248	+	0.143217i
$649$	23.3071	+	23.3071i	0.914883	+	0.914883i
$650$	0.663562			0.0260270
$651$	−0.0540344	−	0.585138i	−0.00211778	−	0.0229334i
$652$	12.8094	−	12.8094i	0.501655	−	0.501655i
$653$	−5.72159	+	5.72159i	−0.223903	+	0.223903i	−0.810140	−	0.586237i	$-0.800609\pi$
$653$	−5.72159	+	5.72159i	−0.223903	+	0.223903i	0.586237	+	0.810140i	$0.300609\pi$
$654$	11.1024	−	13.3615i	0.434138	−	0.522477i
$655$	21.0161			0.821167
$656$	6.28349			0.245329
$657$	−35.4520	+	6.60393i	−1.38311	+	0.257644i
$658$	−1.24304	−	1.24304i	−0.0484589	−	0.0484589i
$659$	−5.42404			−0.211291			−0.105645	−	0.994404i	$-0.533691\pi$
$659$	−5.42404			−0.211291			−0.105645	+	0.994404i	$0.533691\pi$
$660$	−7.40657	+	0.683958i	−0.288300	+	0.0266230i
$661$	11.0748	+	11.0748i	0.430758	+	0.430758i	0.888886	−	0.458128i	$-0.151480\pi$
$661$	11.0748	+	11.0748i	0.430758	+	0.430758i	−0.458128	+	0.888886i	$0.651480\pi$
$662$		−	26.8032i		−	1.04174i
$663$	−5.21777	−	4.33557i	−0.202641	−	0.168380i
$664$	7.30943	−	7.30943i	0.283661	−	0.283661i
$665$	10.5525			0.409207
$666$	−0.266692	+	18.2463i	−0.0103341	+	0.707031i
$667$	−16.0153			−0.620115
$668$	−2.59545	+	2.59545i	−0.100421	+	0.100421i
$669$	22.3270	+	18.5520i	0.863212	+	0.717264i
$670$			7.22479i			0.279118i
$671$	16.3544	+	16.3544i	0.631354	+	0.631354i
$672$	−5.46888	+	0.505022i	−0.210967	+	0.0194817i
$673$	−24.4076			−0.940843			−0.470422	−	0.882442i	$-0.655898\pi$
$673$	−24.4076			−0.940843			−0.470422	+	0.882442i	$0.655898\pi$
$674$	2.49187	+	2.49187i	0.0959832	+	0.0959832i
$675$	4.53707	+	2.53278i	0.174632	+	0.0974866i
$676$	12.5597			0.483065
$677$	25.9755			0.998319			0.499160	−	0.866510i	$-0.333642\pi$
$677$	25.9755			0.998319			0.499160	+	0.866510i	$0.333642\pi$
$678$	15.8565	−	19.0829i	0.608963	−	0.732875i
$679$	0.414854	−	0.414854i	0.0159206	−	0.0159206i
$680$	−4.17376	+	4.17376i	−0.160056	+	0.160056i
$681$	0.518673	+	5.61670i	0.0198756	+	0.215233i
$682$	0.459473			0.0175941
$683$	17.5140	+	17.5140i	0.670156	+	0.670156i	0.957752	−	0.287596i	$-0.0928561\pi$
$683$	17.5140	+	17.5140i	0.670156	+	0.670156i	−0.287596	+	0.957752i	$0.592856\pi$
$684$	5.64738	−	8.23299i	0.215933	−	0.314796i
$685$	−14.6837	+	14.6837i	−0.561035	+	0.561035i
$686$	8.84629	−	8.84629i	0.337753	−	0.337753i
$687$	−3.77386	−	3.13579i	−0.143982	−	0.119638i
$688$	−2.94167	+	2.94167i	−0.112150	+	0.112150i
$689$	4.88731	+	4.88731i	0.186192	+	0.186192i
$690$	0.549071	+	5.94588i	0.0209028	+	0.226356i
$691$		−	27.6376i		−	1.05138i	−0.850675	−	0.525692i	$-0.823807\pi$
$691$		−	27.6376i		−	1.05138i	0.850675	−	0.525692i	$-0.176193\pi$
$692$			5.26417i			0.200114i
$693$	7.48097	+	40.1602i	0.284179	+	1.52556i
$694$			8.83368i			0.335322i
$695$	−7.40811	+	7.40811i	−0.281006	+	0.281006i
$696$	−6.18867	−	5.14231i	−0.234581	−	0.194919i
$697$	−26.2258	−	26.2258i	−0.993372	−	0.993372i
$698$	23.3010	−	23.3010i	0.881957	−	0.881957i
$699$	−17.4141	−	14.4698i	−0.658663	−	0.547299i
$700$	−3.17089			−0.119849
$701$	−0.160630	−	0.160630i	−0.00606691	−	0.00606691i	0.704067	−	0.710134i	$-0.251366\pi$
$701$	−0.160630	−	0.160630i	−0.00606691	−	0.00606691i	−0.710134	+	0.704067i	$0.751366\pi$
$702$	−3.01063	−	1.68065i	−0.113629	−	0.0634322i
$703$	19.8443	+	3.99748i	0.748441	+	0.150768i
$704$		−	4.29438i		−	0.161851i
$705$	−0.956173	+	0.0882975i	−0.0360116	+	0.00332548i
$706$		−	18.8710i		−	0.710218i
$707$	−48.6129			−1.82828
$708$	13.2379	−	1.22245i	0.497511	−	0.0459425i
$709$	−9.93985	+	9.93985i	−0.373299	+	0.373299i	−0.868677	−	0.495378i	$-0.835029\pi$
$709$	−9.93985	+	9.93985i	−0.373299	+	0.373299i	0.495378	+	0.868677i	$0.335029\pi$
$710$		−	8.00969i		−	0.300598i
$711$	−8.28037	−	5.67988i	−0.310538	−	0.213012i
$712$	3.71553			0.139245
$713$		−	0.368858i		−	0.0138138i
$714$	24.9336	+	20.7179i	0.933118	+	0.775350i
$715$	2.84959			0.106568
$716$	9.64682	+	9.64682i	0.360518	+	0.360518i
$717$	1.49628	+	16.2032i	0.0558797	+	0.605120i
$718$	−0.147807	−	0.147807i	−0.00551610	−	0.00551610i
$719$		−	4.09595i		−	0.152753i	−0.997079	−	0.0763766i	$-0.975665\pi$
$719$		−	4.09595i		−	0.152753i	0.997079	−	0.0763766i	$-0.0243351\pi$
$720$	−1.69697	+	2.47392i	−0.0632425	+	0.0921975i
$721$	−22.9085	−	22.9085i	−0.853157	−	0.853157i
$722$	5.60382	+	5.60382i	0.208553	+	0.208553i
$723$	14.1238	−	1.30425i	0.525268	−	0.0485057i
$724$		−	1.74294i		−	0.0647760i
$725$	−3.28489	−	3.28489i	−0.121998	−	0.121998i
$726$	−12.8348	+	1.18523i	−0.476344	+	0.0439879i
$727$	18.7410	+	18.7410i	0.695066	+	0.695066i	0.963342	−	0.268276i	$-0.0864540\pi$
$727$	18.7410	+	18.7410i	0.695066	+	0.695066i	−0.268276	+	0.963342i	$0.586454\pi$
$728$	2.10408			0.0779825
$729$	−14.1701	−	22.9828i	−0.524818	−	0.851214i
$730$		−	12.0206i		−	0.444903i
$731$	24.5556			0.908222
$732$	9.28893	−	0.857784i	0.343329	−	0.0317046i
$733$		−	16.3805i		−	0.605026i	−0.953145	−	0.302513i	$-0.902174\pi$
$733$		−	16.3805i		−	0.605026i	0.953145	−	0.302513i	$-0.0978255\pi$
$734$	10.4719	−	10.4719i	0.386524	−	0.386524i
$735$	0.486495	+	5.26825i	0.0179447	+	0.194322i
$736$	−3.44746			−0.127075
$737$			31.0260i			1.14286i
$738$	−15.5449	−	10.6629i	−0.572214	−	0.392508i
$739$			46.1239i			1.69670i	0.529439	+	0.848348i	$0.322403\pi$
$739$			46.1239i			1.69670i	−0.529439	+	0.848348i	$0.677597\pi$
$740$	−5.96298	−	1.20120i	−0.219203	−	0.0441569i
$741$	−2.44442	+	2.94181i	−0.0897980	+	0.108070i
$742$	−23.3545	−	23.3545i	−0.857369	−	0.857369i
$743$	−39.6883			−1.45602			−0.728012	−	0.685565i	$-0.759555\pi$
$743$	−39.6883			−1.45602			−0.728012	+	0.685565i	$0.759555\pi$
$744$	0.118436	−	0.142535i	0.00434206	−	0.00522558i
$745$	−9.49294	+	9.49294i	−0.347795	+	0.347795i
$746$	2.52327	+	2.52327i	0.0923836	+	0.0923836i
$747$	−30.4868	+	5.67903i	−1.11546	+	0.207785i
$748$	−17.9237	+	17.9237i	−0.655356	+	0.655356i
$749$		−	0.900008i		−	0.0328856i
$750$	−1.10694	+	1.33218i	−0.0404196	+	0.0486442i
$751$			46.3282i			1.69054i	0.534339	+	0.845270i	$0.320560\pi$
$751$			46.3282i			1.69054i	−0.534339	+	0.845270i	$0.679440\pi$
$752$		−	0.554395i		−	0.0202167i
$753$	−8.71858	+	0.805115i	−0.317723	+	0.0293400i
$754$	2.17973	+	2.17973i	0.0793810	+	0.0793810i
$755$	8.26055	−	8.26055i	0.300632	−	0.300632i
$756$	14.3866	+	8.03116i	0.523235	+	0.292091i
$757$	6.01198	−	6.01198i	0.218509	−	0.218509i	−0.589361	−	0.807870i	$-0.700620\pi$
$757$	6.01198	−	6.01198i	0.218509	−	0.218509i	0.807870	+	0.589361i	$0.200620\pi$
$758$	−4.73343	+	4.73343i	−0.171926	+	0.171926i
$759$	2.35792	+	25.5339i	0.0855870	+	0.926821i
$760$	2.35319	+	2.35319i	0.0853592	+	0.0853592i
$761$	1.71775			0.0622685			0.0311343	−	0.999515i	$-0.490088\pi$
$761$	1.71775			0.0622685			0.0311343	+	0.999515i	$0.490088\pi$
$762$	20.4927	−	1.89239i	0.742371	−	0.0685540i
$763$	22.4885	−	22.4885i	0.814140	−	0.814140i
$764$	−17.6905	+	17.6905i	−0.640021	+	0.640021i
$765$	17.4083	−	3.24278i	0.629399	−	0.117243i
$766$	−14.5087			−0.524221
$767$	−5.09312			−0.183902
$768$	−1.33218	−	1.10694i	−0.0480707	−	0.0399431i
$769$	−28.0211	−	28.0211i	−1.01047	−	1.01047i	−0.999945	−	0.0105221i	$-0.996651\pi$
$769$	−28.0211	−	28.0211i	−1.01047	−	1.01047i	−0.0105221	−	0.999945i	$-0.503349\pi$
$770$	−13.6170			−0.490723
$771$	−0.582851	−	6.31169i	−0.0209909	−	0.227310i
$772$	−2.31213	−	2.31213i	−0.0832155	−	0.0832155i
$773$			23.3393i			0.839457i	0.907650	+	0.419729i	$0.137875\pi$
$773$			23.3393i			0.839457i	−0.907650	+	0.419729i	$0.862125\pi$
$774$	12.2694	−	2.28552i	0.441014	−	0.0821512i
$775$	0.0756563	−	0.0756563i	0.00271765	−	0.00271765i
$776$	0.185024			0.00664199
$777$	−3.55777	+	33.2175i	−0.127634	+	1.19167i
$778$	−15.9568			−0.572079
$779$	−14.7862	+	14.7862i	−0.529772	+	0.529772i
$780$	0.734521	−	0.883981i	0.0263001	−	0.0316516i
$781$		−	34.3966i		−	1.23081i
$782$	14.3889	+	14.3889i	0.514545	+	0.514545i
$783$	6.58390	+	23.2237i	0.235289	+	0.829947i
$784$	−3.05457			−0.109092
$785$	3.25094	+	3.25094i	0.116031	+	0.116031i
$786$	23.2635	−	27.9971i	0.829781	−	0.998625i
$787$	−5.24375			−0.186919			−0.0934597	−	0.995623i	$-0.529793\pi$
$787$	−5.24375			−0.186919			−0.0934597	+	0.995623i	$0.529793\pi$
$788$	−24.2094			−0.862425
$789$	−13.5913	−	11.2933i	−0.483863	−	0.402053i
$790$	2.36673	−	2.36673i	0.0842046	−	0.0842046i
$791$	32.1181	−	32.1181i	1.14199	−	1.14199i
$792$	−7.28745	+	10.6240i	−0.258948	+	0.377506i
$793$	−3.57380			−0.126909
$794$	10.9694	+	10.9694i	0.389290	+	0.389290i
$795$	−17.9647	+	1.65895i	−0.637142	+	0.0588367i
$796$	15.4468	−	15.4468i	0.547498	−	0.547498i
$797$	−25.0247	+	25.0247i	−0.886420	+	0.886420i	−0.994177	−	0.107757i	$-0.965633\pi$
$797$	−25.0247	+	25.0247i	−0.886420	+	0.886420i	0.107757	+	0.994177i	$0.465633\pi$
$798$	11.6809	−	14.0577i	0.413499	−	0.497638i
$799$	−2.31391	+	2.31391i	−0.0818603	+	0.0818603i
$800$	−0.707107	−	0.707107i	−0.0250000	−	0.0250000i
$801$	−9.19192	−	6.30515i	−0.324780	−	0.222782i
$802$			1.92379i			0.0679314i
$803$		−	51.6211i		−	1.82167i
$804$	9.62469	+	7.99739i	0.339437	+	0.282046i
$805$			10.9315i			0.385286i
$806$	−0.0502026	+	0.0502026i	−0.00176831	+	0.00176831i
$807$	−24.6025	+	29.6086i	−0.866048	+	1.04227i
$808$	−10.8406	−	10.8406i	−0.381372	−	0.381372i
$809$	38.3135	−	38.3135i	1.34703	−	1.34703i	0.458163	−	0.888868i	$-0.348508\pi$
$809$	38.3135	−	38.3135i	1.34703	−	1.34703i	0.888868	−	0.458163i	$-0.151492\pi$
$810$	8.39636	−	3.24056i	0.295018	−	0.113862i
$811$	−3.89006			−0.136599			−0.0682993	−	0.997665i	$-0.521757\pi$
$811$	−3.89006			−0.136599			−0.0682993	+	0.997665i	$0.521757\pi$
$812$	−10.4160	−	10.4160i	−0.365531	−	0.365531i
$813$	0.533566	+	0.443353i	0.0187130	+	0.0155491i
$814$	−25.6073	−	5.15840i	−0.897535	−	0.180802i
$815$		−	18.1152i		−	0.634549i
$816$	0.940094	+	10.1803i	0.0329099	+	0.356381i
$817$		−	13.8446i		−	0.484361i
$818$	−13.3383			−0.466363
$819$	−5.20533	−	3.57058i	−0.181889	−	0.124766i
$820$	4.44310	−	4.44310i	0.155160	−	0.155160i
$821$		−	21.9003i		−	0.764325i	−0.924095	−	0.382163i	$-0.875179\pi$
$821$		−	21.9003i		−	0.764325i	0.924095	−	0.382163i	$-0.124821\pi$
$822$	3.30734	+	35.8151i	0.115357	+	1.24920i
$823$	−6.96342			−0.242729			−0.121365	−	0.992608i	$-0.538727\pi$
$823$	−6.96342			−0.242729			−0.121365	+	0.992608i	$0.538727\pi$
$824$		−	10.2172i		−	0.355931i
$825$	−4.75361	+	5.72087i	−0.165499	+	0.199175i
$826$	24.3380			0.846826
$827$	−21.6984	−	21.6984i	−0.754529	−	0.754529i	0.220792	−	0.975321i	$-0.429136\pi$
$827$	−21.6984	−	21.6984i	−0.754529	−	0.754529i	−0.975321	+	0.220792i	$0.929136\pi$
$828$	8.52874	+	5.85025i	0.296394	+	0.203310i
$829$	−12.8924	−	12.8924i	−0.447770	−	0.447770i	0.446843	−	0.894613i	$-0.352548\pi$
$829$	−12.8924	−	12.8924i	−0.447770	−	0.447770i	−0.894613	+	0.446843i	$0.852548\pi$
$830$		−	10.3371i		−	0.358806i
$831$	1.17765	+	12.7527i	0.0408521	+	0.442387i
$832$	0.469209	+	0.469209i	0.0162669	+	0.0162669i
$833$	12.7490	+	12.7490i	0.441728	+	0.441728i
$834$	1.66860	+	18.0692i	0.0577788	+	0.625686i
$835$			3.67053i			0.127024i
$836$	10.1055	+	10.1055i	0.349506	+	0.349506i
$837$	−0.534878	+	0.151638i	−0.0184881	+	0.00524137i
$838$	21.4867	+	21.4867i	0.742246	+	0.742246i
$839$	1.48655			0.0513213			0.0256606	−	0.999671i	$-0.491831\pi$
$839$	1.48655			0.0513213			0.0256606	+	0.999671i	$0.491831\pi$
$840$	−3.50998	+	4.22419i	−0.121106	+	0.145748i
$841$			7.41899i			0.255827i
$842$	10.6565			0.367246
$843$	1.65052	+	17.8735i	0.0568469	+	0.615594i
$844$			26.2503i			0.903571i
$845$	8.88104	−	8.88104i	0.305517	−	0.305517i
$846$	−0.940795	+	1.37153i	−0.0323452	+	0.0471542i
$847$	−23.5968			−0.810797
$848$		−	10.4161i		−	0.357689i
$849$	1.59681	+	17.2918i	0.0548023	+	0.593454i
$850$			5.90259i			0.202457i
$851$	−4.14109	+	20.5571i	−0.141955	+	0.704690i
$852$	−10.6703	−	8.86621i	−0.365559	−	0.303751i
$853$	35.9111	+	35.9111i	1.22957	+	1.22957i	0.964125	+	0.265449i	$0.0855201\pi$
$853$	35.9111	+	35.9111i	1.22957	+	1.22957i	0.265449	+	0.964125i	$0.414480\pi$
$854$	17.0777			0.584389
$855$	−1.82830	−	9.81490i	−0.0625266	−	0.335663i
$856$	0.200701	−	0.200701i	0.00685982	−	0.00685982i
$857$	2.77286	+	2.77286i	0.0947189	+	0.0947189i	0.752878	−	0.658160i	$-0.228665\pi$
$857$	2.77286	+	2.77286i	0.0947189	+	0.0947189i	−0.658160	+	0.752878i	$0.728665\pi$
$858$	3.15431	−	3.79615i	0.107686	−	0.129598i
$859$	−22.6656	+	22.6656i	−0.773339	+	0.773339i	−0.978689	−	0.205349i	$-0.934167\pi$
$859$	−22.6656	+	22.6656i	−0.773339	+	0.773339i	0.205349	+	0.978689i	$0.434167\pi$
$860$			4.16015i			0.141860i
$861$	−26.5426	−	22.0549i	−0.904571	−	0.751629i
$862$		−	18.5636i		−	0.632279i
$863$			17.5839i			0.598563i	0.954165	+	0.299281i	$0.0967469\pi$
$863$			17.5839i			0.598563i	−0.954165	+	0.299281i	$0.903253\pi$
$864$	1.41725	+	4.99914i	0.0482159	+	0.170074i
$865$	3.72233	+	3.72233i	0.126563	+	0.126563i
$866$	15.0709	−	15.0709i	0.512131	−	0.512131i
$867$	19.7483	−	23.7667i	0.670688	−	0.807160i
$868$	0.239898	−	0.239898i	0.00814267	−	0.00814267i
$869$	10.1636	−	10.1636i	0.344778	−	0.344778i
$870$	−8.01221	+	0.739886i	−0.271640	+	0.0250845i
$871$	−3.38994	−	3.38994i	−0.114864	−	0.114864i
$872$	10.0299			0.339654
$873$	−0.457735	−	0.313982i	−0.0154920	−	0.0106267i
$874$	8.11253	−	8.11253i	0.274410	−	0.274410i
$875$	−2.24216	+	2.24216i	−0.0757989	+	0.0757989i
$876$	−16.0136	−	13.3061i	−0.541049	−	0.449570i
$877$	10.1063			0.341265			0.170633	−	0.985335i	$-0.445419\pi$
$877$	10.1063			0.341265			0.170633	+	0.985335i	$0.445419\pi$
$878$	2.76124			0.0931874
$879$	30.9936	−	37.3002i	1.04539	−	1.25810i
$880$	−3.03659	−	3.03659i	−0.102363	−	0.102363i
$881$	−36.9896			−1.24621			−0.623105	−	0.782138i	$-0.714129\pi$
$881$	−36.9896			−1.24621			−0.623105	+	0.782138i	$0.714129\pi$
$882$	7.55676	+	5.18352i	0.254449	+	0.174538i
$883$	30.1940	+	30.1940i	1.01611	+	1.01611i	0.999868	+	0.0162393i	$0.00516936\pi$
$883$	30.1940	+	30.1940i	1.01611	+	1.01611i	0.0162393	+	0.999868i	$0.494831\pi$
$884$		−	3.91673i		−	0.131734i
$885$	8.49621	−	10.2250i	0.285597	−	0.343710i
$886$	−28.8159	+	28.8159i	−0.968089	+	0.968089i
$887$	25.2439			0.847606			0.423803	−	0.905754i	$-0.360695\pi$
$887$	25.2439			0.847606			0.423803	+	0.905754i	$0.360695\pi$
$888$	−8.20085	+	6.61409i	−0.275202	+	0.221954i
$889$	37.6759			1.26361
$890$	2.62728	−	2.62728i	0.0880665	−	0.0880665i
$891$	36.0571	−	13.9162i	1.20796	−	0.466210i
$892$			16.7598i			0.561160i
$893$	1.30460	+	1.30460i	0.0436567	+	0.0436567i
$894$	2.13818	+	23.1544i	0.0715115	+	0.774397i
$895$	13.6427			0.456024
$896$	−2.24216	−	2.24216i	−0.0749053	−	0.0749053i
$897$	−3.04749	−	2.53223i	−0.101753	−	0.0845488i
$898$	−23.2497			−0.775853
$899$	0.497045			0.0165774
$900$	0.549384	+	2.94927i	0.0183128	+	0.0983089i
$901$	−43.4741	+	43.4741i	−1.44833	+	1.44833i
$902$	19.0804	−	19.0804i	0.635306	−	0.635306i
$903$	22.7513	−	2.10097i	0.757117	−	0.0699158i
$904$	14.3246			0.476430
$905$	−1.23245	−	1.23245i	−0.0409679	−	0.0409679i
$906$	−1.86060	−	20.1484i	−0.0618143	−	0.669386i
$907$	33.7526	−	33.7526i	1.12074	−	1.12074i	0.129104	−	0.991631i	$-0.458790\pi$
$907$	33.7526	−	33.7526i	1.12074	−	1.12074i	0.991631	−	0.129104i	$-0.0412101\pi$
$908$	−2.30277	+	2.30277i	−0.0764200	+	0.0764200i
$909$	8.42258	+	45.2151i	0.279359	+	1.49969i
$910$	1.48781	−	1.48781i	0.0493205	−	0.0493205i
$911$	−18.3536	−	18.3536i	−0.608083	−	0.608083i	0.334361	−	0.942445i	$-0.391479\pi$
$911$	−18.3536	−	18.3536i	−0.608083	−	0.608083i	−0.942445	+	0.334361i	$0.891479\pi$
$912$	5.73969	−	0.530030i	0.190060	−	0.0175511i
$913$		−	44.3914i		−	1.46914i
$914$			19.4852i			0.644512i
$915$	5.96172	−	7.17481i	0.197088	−	0.237192i
$916$		−	2.83286i		−	0.0936002i
$917$	47.1215	−	47.1215i	1.55609	−	1.55609i
$918$	14.9499	−	26.7805i	0.493421	−	0.883887i
$919$	−26.0543	−	26.0543i	−0.859450	−	0.859450i	0.131823	−	0.991273i	$-0.457917\pi$
$919$	−26.0543	−	26.0543i	−0.859450	−	0.859450i	−0.991273	+	0.131823i	$0.957917\pi$
$920$	−2.43772	+	2.43772i	−0.0803694	+	0.0803694i
$921$	13.4726	−	16.2139i	0.443936	−	0.534268i
$922$	20.2221			0.665979
$923$	3.75822	+	3.75822i	0.123703	+	0.123703i
$924$	−15.0732	+	18.1403i	−0.495871	+	0.596771i
$925$	−5.06584	+	3.36709i	−0.166564	+	0.110709i
$926$		−	32.1512i		−	1.05655i
$927$	−17.3382	+	25.2764i	−0.569462	+	0.830186i
$928$		−	4.64554i		−	0.152497i
$929$	−56.8147			−1.86403			−0.932015	−	0.362420i	$-0.881951\pi$
$929$	−56.8147			−1.86403			−0.932015	+	0.362420i	$0.881951\pi$
$930$	−0.0170408	−	0.184534i	−0.000558788	−	0.00605111i
$931$	7.18798	−	7.18798i	0.235576	−	0.235576i
$932$		−	13.0719i		−	0.428186i
$933$	26.8270	−	2.47733i	0.878277	−	0.0811043i
$934$	−35.8857			−1.17422
$935$			25.3479i			0.828967i
$936$	−0.364550	−	1.95702i	−0.0119157	−	0.0639672i
$937$	−52.7386			−1.72289			−0.861447	−	0.507848i	$-0.830441\pi$
$937$	−52.7386			−1.72289			−0.861447	+	0.507848i	$0.830441\pi$
$938$	16.1991	+	16.1991i	0.528921	+	0.528921i
$939$	60.1185	−	5.55163i	1.96189	−	0.181171i
$940$	−0.392017	−	0.392017i	−0.0127862	−	0.0127862i
$941$			0.420330i			0.0137024i	0.999977	+	0.00685118i	$0.00218082\pi$
$941$			0.420330i			0.0137024i	−0.999977	+	0.00685118i	$0.997819\pi$
$942$	7.92941	−	0.732240i	0.258354	−	0.0238577i
$943$	−15.3174	−	15.3174i	−0.498804	−	0.498804i
$944$	5.42735	+	5.42735i	0.176645	+	0.176645i
$945$	15.8517	−	4.49396i	0.515657	−	0.146188i
$946$			17.8652i			0.580849i
$947$	−14.3006	−	14.3006i	−0.464707	−	0.464707i	0.435488	−	0.900195i	$-0.356576\pi$
$947$	−14.3006	−	14.3006i	−0.464707	−	0.464707i	−0.900195	+	0.435488i	$0.856576\pi$
$948$	−0.533081	−	5.77273i	−0.0173137	−	0.187489i
$949$	5.64018	+	5.64018i	0.183088	+	0.183088i
$950$	3.32791			0.107972
$951$	−33.2978	−	27.6680i	−1.07976	−	0.897195i
$952$			18.7165i			0.606604i
$953$	−31.2710			−1.01297			−0.506483	−	0.862250i	$-0.669055\pi$
$953$	−31.2710			−1.01297			−0.506483	+	0.862250i	$0.669055\pi$
$954$	−17.6758	+	25.7685i	−0.572274	+	0.834285i
$955$			25.0182i			0.809569i
$956$	−6.64308	+	6.64308i	−0.214853	+	0.214853i
$957$	−34.4075	+	3.17735i	−1.11224	+	0.102709i
$958$	40.2094			1.29911
$959$			65.8463i			2.12629i
$960$	−1.72471	+	0.159268i	−0.0556649	+	0.00514036i
$961$		−	30.9886i		−	0.999631i
$962$	3.36150	−	2.23427i	0.108379	−	0.0720358i
$963$	−0.837103	+	0.155934i	−0.0269753	+	0.00502490i
$964$	5.79053	+	5.79053i	0.186500	+	0.186500i
$965$	−3.26985			−0.105260
$966$	14.5627	+	12.1005i	0.468548	+	0.389328i
$967$	−34.4721	+	34.4721i	−1.10855	+	1.10855i	−0.115207	+	0.993342i	$0.536753\pi$
$967$	−34.4721	+	34.4721i	−1.10855	+	1.10855i	−0.993342	+	0.115207i	$0.963247\pi$
$968$	−5.26208	−	5.26208i	−0.169130	−	0.169130i
$969$	−26.1683	−	21.7439i	−0.840647	−	0.698514i
$970$	0.130832	−	0.130832i	0.00420076	−	0.00420076i
$971$			15.7497i			0.505433i	0.967540	+	0.252716i	$0.0813239\pi$
$971$			15.7497i			0.505433i	−0.967540	+	0.252716i	$0.918676\pi$
$972$	4.97724	−	14.7725i	0.159645	−	0.473829i
$973$			33.2203i			1.06500i
$974$			11.9449i			0.382739i
$975$	−0.105684	−	1.14445i	−0.00338460	−	0.0366518i
$976$	3.80832	+	3.80832i	0.121901	+	0.121901i
$977$	33.7074	−	33.7074i	1.07839	−	1.07839i	0.0817411	−	0.996654i	$-0.473952\pi$
$977$	33.7074	−	33.7074i	1.07839	−	1.07839i	0.996654	−	0.0817411i	$-0.0260481\pi$
$978$	−24.1327	−	20.0524i	−0.771678	−	0.641205i
$979$	11.2825	−	11.2825i	0.360591	−	0.360591i
$980$	−2.15991	+	2.15991i	−0.0689957	+	0.0689957i
$981$	−24.8130	−	17.0204i	−0.792220	−	0.543419i
$982$	−15.1111	−	15.1111i	−0.482213	−	0.482213i
$983$	−1.64672			−0.0525221			−0.0262611	−	0.999655i	$-0.508360\pi$
$983$	−1.64672			−0.0525221			−0.0262611	+	0.999655i	$0.508360\pi$
$984$	−1.00076	−	10.8372i	−0.0319031	−	0.345478i
$985$	−17.1186	+	17.1186i	−0.545445	+	0.545445i
$986$	−19.3893	+	19.3893i	−0.617483	+	0.617483i
$987$	−1.94592	+	2.34187i	−0.0619392	+	0.0745425i
$988$	−2.20828			−0.0702546
$989$	14.3419			0.456047
$990$	2.35926	+	12.6653i	0.0749823	+	0.402529i
$991$	16.4951	+	16.4951i	0.523985	+	0.523985i	0.918772	−	0.394788i	$-0.129182\pi$
$991$	16.4951	+	16.4951i	0.523985	+	0.523985i	−0.394788	+	0.918772i	$0.629182\pi$
$992$	0.106994			0.00339707
$993$	−46.2279	+	4.26890i	−1.46700	+	0.135470i
$994$	−17.9590	−	17.9590i	−0.569625	−	0.569625i
$995$		−	21.8451i		−	0.692536i
$996$	−13.7708	−	11.4425i	−0.436345	−	0.362570i
$997$	26.1157	−	26.1157i	0.827092	−	0.827092i	−0.160022	−	0.987114i	$-0.551156\pi$
$997$	26.1157	−	26.1157i	0.827092	−	0.827092i	0.987114	+	0.160022i	$0.0511564\pi$
$998$	−33.7673			−1.06888
$999$	31.5122	−	2.44609i	0.997001	−	0.0773909i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.u.f.401.11	yes	40
3.2	odd	2	inner	1110.2.u.f.401.5	yes	40
37.6	odd	4	inner	1110.2.u.f.191.5	✓	40
111.80	even	4	inner	1110.2.u.f.191.11	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.u.f.191.5	✓	40	37.6	odd	4	inner
1110.2.u.f.191.11	yes	40	111.80	even	4	inner
1110.2.u.f.401.5	yes	40	3.2	odd	2	inner
1110.2.u.f.401.11	yes	40	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.33218 - 1.10694i) q^{3} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.72471 + 0.159268i) q^{6} -3.17089 q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.549384 + 2.94927i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.33218 - 1.10694i) q^{3} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.72471 + 0.159268i) q^{6} -3.17089 q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.549384 + 2.94927i) q^{9} -1.00000 q^{10} -4.29438 q^{11} +(-1.10694 + 1.33218i) q^{12} +(0.469209 - 0.469209i) q^{13} +(-2.24216 + 2.24216i) q^{14} +(0.159268 + 1.72471i) q^{15} -1.00000 q^{16} +(4.17376 + 4.17376i) q^{17} +(2.47392 + 1.69697i) q^{18} +(2.35319 - 2.35319i) q^{19} +(-0.707107 + 0.707107i) q^{20} +(4.22419 + 3.50998i) q^{21} +(-3.03659 + 3.03659i) q^{22} +(2.43772 + 2.43772i) q^{23} +(0.159268 + 1.72471i) q^{24} +1.00000i q^{25} -0.663562i q^{26} +(2.53278 - 4.53707i) q^{27} +3.17089i q^{28} +(-3.28489 + 3.28489i) q^{29} +(1.33218 + 1.10694i) q^{30} +(-0.0756563 - 0.0756563i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(5.72087 + 4.75361i) q^{33} +5.90259 q^{34} +(2.24216 + 2.24216i) q^{35} +(2.94927 - 0.549384i) q^{36} +(3.36709 + 5.06584i) q^{37} -3.32791i q^{38} +(-1.14445 + 0.105684i) q^{39} +1.00000i q^{40} -6.28349 q^{41} +(5.46888 - 0.505022i) q^{42} +(2.94167 - 2.94167i) q^{43} +4.29438i q^{44} +(1.69697 - 2.47392i) q^{45} +3.44746 q^{46} +0.554395i q^{47} +(1.33218 + 1.10694i) q^{48} +3.05457 q^{49} +(0.707107 + 0.707107i) q^{50} +(-0.940094 - 10.1803i) q^{51} +(-0.469209 - 0.469209i) q^{52} +10.4161i q^{53} +(-1.41725 - 4.99914i) q^{54} +(3.03659 + 3.03659i) q^{55} +(2.24216 + 2.24216i) q^{56} +(-5.73969 + 0.530030i) q^{57} +4.64554i q^{58} +(-5.42735 - 5.42735i) q^{59} +(1.72471 - 0.159268i) q^{60} +(-3.80832 - 3.80832i) q^{61} -0.106994 q^{62} +(-1.74204 - 9.35181i) q^{63} +1.00000i q^{64} -0.663562 q^{65} +(7.40657 - 0.683958i) q^{66} -7.22479i q^{67} +(4.17376 - 4.17376i) q^{68} +(-0.549071 - 5.94588i) q^{69} +3.17089 q^{70} +8.00969i q^{71} +(1.69697 - 2.47392i) q^{72} +12.0206i q^{73} +(5.96298 + 1.20120i) q^{74} +(1.10694 - 1.33218i) q^{75} +(-2.35319 - 2.35319i) q^{76} +13.6170 q^{77} +(-0.734521 + 0.883981i) q^{78} +(-2.36673 + 2.36673i) q^{79} +(0.707107 + 0.707107i) q^{80} +(-8.39636 + 3.24056i) q^{81} +(-4.44310 + 4.44310i) q^{82} +10.3371i q^{83} +(3.50998 - 4.22419i) q^{84} -5.90259i q^{85} -4.16015i q^{86} +(8.01221 - 0.739886i) q^{87} +(3.03659 + 3.03659i) q^{88} +(-2.62728 + 2.62728i) q^{89} +(-0.549384 - 2.94927i) q^{90} +(-1.48781 + 1.48781i) q^{91} +(2.43772 - 2.43772i) q^{92} +(0.0170408 + 0.184534i) q^{93} +(0.392017 + 0.392017i) q^{94} -3.32791 q^{95} +(1.72471 - 0.159268i) q^{96} +(-0.130832 + 0.130832i) q^{97} +(2.15991 - 2.15991i) q^{98} +(-2.35926 - 12.6653i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 24 q^{7} - 8 q^{9}+O(q^{10}) \) 40 * q + 24 * q^7 - 8 * q^9	\( 40 q + 24 q^{7} - 8 q^{9} - 40 q^{10} + 16 q^{13} - 40 q^{16} + 8 q^{18} + 16 q^{19} - 16 q^{22} - 8 q^{31} + 24 q^{33} + 24 q^{34} + 32 q^{37} + 16 q^{39} + 12 q^{42} + 32 q^{43} + 8 q^{45} - 56 q^{46} - 32 q^{49} - 44 q^{51} - 16 q^{52} - 24 q^{54} + 16 q^{55} + 8 q^{57} - 72 q^{61} + 24 q^{63} - 28 q^{66} + 16 q^{69} - 24 q^{70} + 8 q^{72} - 16 q^{76} - 48 q^{79} + 120 q^{81} - 24 q^{82} - 24 q^{84} + 20 q^{87} + 16 q^{88} + 8 q^{90} - 92 q^{93} - 8 q^{94} - 40 q^{97}+O(q^{100}) \) 40 * q + 24 * q^7 - 8 * q^9 - 40 * q^10 + 16 * q^13 - 40 * q^16 + 8 * q^18 + 16 * q^19 - 16 * q^22 - 8 * q^31 + 24 * q^33 + 24 * q^34 + 32 * q^37 + 16 * q^39 + 12 * q^42 + 32 * q^43 + 8 * q^45 - 56 * q^46 - 32 * q^49 - 44 * q^51 - 16 * q^52 - 24 * q^54 + 16 * q^55 + 8 * q^57 - 72 * q^61 + 24 * q^63 - 28 * q^66 + 16 * q^69 - 24 * q^70 + 8 * q^72 - 16 * q^76 - 48 * q^79 + 120 * q^81 - 24 * q^82 - 24 * q^84 + 20 * q^87 + 16 * q^88 + 8 * q^90 - 92 * q^93 - 8 * q^94 - 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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