LMFDB - Embedded newform 1110.2.u.f.401.5

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			401.5
Character	$\chi$	$=$	1110.401
Dual form			1110.2.u.f.191.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(1.33218 - 1.10694i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(-0.159268 + 1.72471i) q^{6} -3.17089 q^{7} +(0.707107 + 0.707107i) q^{8} +(0.549384 - 2.94927i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(1.33218 - 1.10694i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(-0.159268 + 1.72471i) 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} +(1.72471 + 0.159268i) q^{15} -1.00000 q^{16} +(-4.17376 - 4.17376i) q^{17} +(1.69697 + 2.47392i) 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} +(1.72471 + 0.159268i) 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} +(0.105684 - 1.14445i) q^{39} +1.00000i q^{40} +6.28349 q^{41} +(0.505022 - 5.46888i) q^{42} +(2.94167 - 2.94167i) q^{43} -4.29438i q^{44} +(2.47392 - 1.69697i) 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} +(-10.1803 - 0.940094i) q^{51} +(-0.469209 - 0.469209i) q^{52} -10.4161i q^{53} +(4.99914 + 1.41725i) q^{54} +(3.03659 + 3.03659i) q^{55} +(-2.24216 - 2.24216i) q^{56} +(0.530030 - 5.73969i) q^{57} +4.64554i q^{58} +(5.42735 + 5.42735i) q^{59} +(0.159268 - 1.72471i) 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} +(-0.683958 + 7.40657i) q^{66} -7.22479i q^{67} +(-4.17376 + 4.17376i) q^{68} +(-5.94588 - 0.549071i) q^{69} +3.17089 q^{70} -8.00969i q^{71} +(2.47392 - 1.69697i) 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} +(0.739886 - 8.01221i) 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} +(-0.184534 - 0.0170408i) q^{93} +(0.392017 + 0.392017i) q^{94} +3.32791 q^{95} +(0.159268 - 1.72471i) 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
$6$	−0.159268	+	1.72471i	−0.0650209	+	0.704111i
$7$	−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	$-0.275855\pi$
$11$	4.29438			1.29480			0.647402	+	0.762149i	$0.275855\pi$
$12$	−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
$15$	1.72471	+	0.159268i	0.445319	+	0.0411229i
$16$	−1.00000			−0.250000
$17$	−4.17376	−	4.17376i	−1.01229	−	1.01229i	−0.999924	−	0.0123615i	$-0.996065\pi$
$17$	−4.17376	−	4.17376i	−1.01229	−	1.01229i	−0.0123615	−	0.999924i	$-0.503935\pi$
$18$	1.69697	+	2.47392i	0.399981	+	0.583108i
$19$	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	0.405704	−	0.914005i	$-0.367026\pi$
$23$	−2.43772	−	2.43772i	−0.508301	−	0.508301i	−0.914005	+	0.405704i	$0.867026\pi$
$24$	1.72471	+	0.159268i	0.352055	+	0.0325105i
$25$			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	−0.332954	−	0.942943i	$-0.608045\pi$
$29$	3.28489	−	3.28489i	0.609989	−	0.609989i	0.942943	+	0.332954i	$0.108045\pi$
$30$	−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
$39$	0.105684	−	1.14445i	0.0169230	−	0.183259i
$40$			1.00000i			0.158114i
$41$	6.28349			0.981316			0.490658	−	0.871352i	$-0.336756\pi$
$41$	6.28349			0.981316			0.490658	+	0.871352i	$0.336756\pi$
$42$	0.505022	−	5.46888i	0.0779266	−	0.843867i
$43$	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
$45$	2.47392	−	1.69697i	0.368790	−	0.252970i
$46$	3.44746			0.508301
$47$		−	0.554395i		−	0.0808669i	−0.999182	−	0.0404334i	$-0.987126\pi$
$47$		−	0.554395i		−	0.0808669i	0.999182	−	0.0404334i	$-0.0128739\pi$
$48$	−1.33218	+	1.10694i	−0.192283	+	0.159773i
$49$	3.05457			0.436367
$50$	−0.707107	−	0.707107i	−0.100000	−	0.100000i
$51$	−10.1803	−	0.940094i	−1.42552	−	0.131639i
$52$	−0.469209	−	0.469209i	−0.0650676	−	0.0650676i
$53$		−	10.4161i		−	1.43075i	−0.698738	−	0.715377i	$-0.746255\pi$
$53$		−	10.4161i		−	1.43075i	0.698738	−	0.715377i	$-0.253745\pi$
$54$	4.99914	+	1.41725i	0.680297	+	0.192864i
$55$	3.03659	+	3.03659i	0.409453	+	0.409453i
$56$	−2.24216	−	2.24216i	−0.299621	−	0.299621i
$57$	0.530030	−	5.73969i	0.0702043	−	0.760241i
$58$			4.64554i			0.609989i
$59$	5.42735	+	5.42735i	0.706580	+	0.706580i	0.965814	−	0.259234i	$-0.0834701\pi$
$59$	5.42735	+	5.42735i	0.706580	+	0.706580i	−0.259234	+	0.965814i	$0.583470\pi$
$60$	0.159268	−	1.72471i	0.0205614	−	0.222659i
$61$	−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
$66$	−0.683958	+	7.40657i	−0.0841894	+	0.911686i
$67$		−	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
$69$	−5.94588	−	0.549071i	−0.715800	−	0.0661004i
$70$	3.17089			0.378994
$71$		−	8.00969i		−	0.950575i	−0.879831	−	0.475287i	$-0.842344\pi$
$71$		−	8.00969i		−	0.950575i	0.879831	−	0.475287i	$-0.157656\pi$
$72$	2.47392	−	1.69697i	0.291554	−	0.199990i
$73$			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	$-0.807980\pi$
$83$		−	10.3371i		−	1.13464i	0.823496	−	0.567321i	$-0.192020\pi$
$84$	3.50998	+	4.22419i	0.382970	+	0.460897i
$85$		−	5.90259i		−	0.640225i
$86$			4.16015i			0.448600i
$87$	0.739886	−	8.01221i	0.0793241	−	0.859000i
$88$	3.03659	+	3.03659i	0.323701	+	0.323701i
$89$	2.62728	−	2.62728i	0.278491	−	0.278491i	−0.554016	−	0.832506i	$-0.686905\pi$
$89$	2.62728	−	2.62728i	0.278491	−	0.278491i	0.832506	+	0.554016i	$0.186905\pi$
$90$	−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
$93$	−0.184534	−	0.0170408i	−0.0191353	−	0.00176704i
$94$	0.392017	+	0.392017i	0.0404334	+	0.0404334i
$95$	3.32791			0.341437
$96$	0.159268	−	1.72471i	0.0162552	−	0.176028i
$97$	−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	$-0.776148\pi$
$101$	−15.3310			−1.52549			−0.762744	+	0.646700i	$0.776148\pi$
$102$	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
$105$	−5.46888	−	0.505022i	−0.533708	−	0.0492851i
$106$	7.36526	+	7.36526i	0.715377	+	0.715377i
$107$		−	0.283834i		−	0.0274393i	−0.999906	−	0.0137196i	$-0.995633\pi$
$107$		−	0.283834i		−	0.0274393i	0.999906	−	0.0137196i	$-0.00436724\pi$
$108$	−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
$111$	10.0931	+	3.02143i	0.957996	+	0.286782i
$112$	3.17089			0.299621
$113$	10.1290	−	10.1290i	0.952860	−	0.952860i	−0.0460778	−	0.998938i	$-0.514672\pi$
$113$	10.1290	−	10.1290i	0.952860	−	0.952860i	0.998938	+	0.0460778i	$0.0146722\pi$
$114$	3.68379	+	4.43336i	0.345018	+	0.415223i
$115$		−	3.44746i		−	0.321477i
$116$	−3.28489	−	3.28489i	−0.304994	−	0.304994i
$117$	−1.12605	−	1.64160i	−0.104103	−	0.151766i
$118$	−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
$126$	−5.38092	−	7.84454i	−0.479371	−	0.698847i
$127$	−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
$129$	0.662579	−	7.17506i	0.0583368	−	0.631728i
$130$	−0.469209	+	0.469209i	−0.0411524	+	0.0411524i
$131$	14.8606	−	14.8606i	1.29838	−	1.29838i	0.368917	−	0.929462i	$-0.379729\pi$
$131$	14.8606	−	14.8606i	1.29838	−	1.29838i	0.929462	−	0.368917i	$-0.120271\pi$
$132$	−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
$135$	1.41725	−	4.99914i	0.121978	−	0.430257i
$136$		−	5.90259i		−	0.506143i
$137$			20.7659i			1.77415i	0.461628	+	0.887074i	$0.347265\pi$
$137$			20.7659i			1.77415i	−0.461628	+	0.887074i	$0.652735\pi$
$138$	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	$0.185339\pi$
$149$			13.4251i			1.09982i	−0.835223	+	0.549911i	$0.814661\pi$
$150$	−1.72471	−	0.159268i	−0.140822	−	0.0130042i
$151$			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
$153$	−14.6025	+	10.0165i	−1.18054	+	0.809789i
$154$	9.62869	−	9.62869i	0.775902	−	0.775902i
$155$		−	0.106994i		−	0.00859397i
$156$	−1.14445	−	0.105684i	−0.0916296	−	0.00846151i
$157$	−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
$162$	8.22854	−	3.64570i	0.646495	−	0.286433i
$163$	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
$165$	7.40657	+	0.683958i	0.576601	+	0.0532461i
$166$	7.30943	+	7.30943i	0.567321	+	0.567321i
$167$	2.59545	+	2.59545i	0.200842	+	0.200842i	0.800361	−	0.599519i	$-0.204641\pi$
$167$	2.59545	+	2.59545i	0.200842	+	0.200842i	−0.599519	+	0.800361i	$0.704641\pi$
$168$	−5.46888	−	0.505022i	−0.421933	−	0.0389633i
$169$			12.5597i			0.966130i
$170$	4.17376	+	4.17376i	0.320113	+	0.320113i
$171$	−5.64738	−	8.23299i	−0.431866	−	0.629592i
$172$	−2.94167	−	2.94167i	−0.224300	−	0.224300i
$173$	5.26417			0.400228			0.200114	−	0.979773i	$-0.435869\pi$
$173$	5.26417			0.400228			0.200114	+	0.979773i	$0.435869\pi$
$174$	5.14231	+	6.18867i	0.389838	+	0.469162i
$175$		−	3.17089i		−	0.239697i
$176$	−4.29438			−0.323701
$177$	13.2379	+	1.22245i	0.995022	+	0.0918850i
$178$			3.71553i			0.278491i
$179$	9.64682	−	9.64682i	0.721037	−	0.721037i	−0.247780	−	0.968816i	$-0.579701\pi$
$179$	9.64682	−	9.64682i	0.721037	−	0.721037i	0.968816	+	0.247780i	$0.0797009\pi$
$180$	−1.69697	−	2.47392i	−0.126485	−	0.184395i
$181$	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
$183$	−9.28893	−	0.857784i	−0.686657	−	0.0634092i
$184$		−	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	$0.110224\pi$
$191$	17.6905	+	17.6905i	1.28004	+	1.28004i	0.339399	+	0.940643i	$0.389776\pi$
$192$	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	$0.331055\pi$
$197$			24.2094i			1.72485i	−0.506185	+	0.862425i	$0.668945\pi$
$198$	7.28745	+	10.6240i	0.517897	+	0.755011i
$199$	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
$204$	−0.940094	+	10.1803i	−0.0658197	+	0.712761i
$205$	4.44310	+	4.44310i	0.310320	+	0.310320i
$206$	−10.2172			−0.711863
$207$	−8.52874	+	5.85025i	−0.592789	+	0.406621i
$208$	−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
$216$	1.41725	−	4.99914i	0.0964319	−	0.340148i
$217$	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
$222$	−9.27339	+	5.00043i	−0.622389	+	0.335607i
$223$	−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	0.779385	−	0.626545i	$-0.215532\pi$
$227$	2.30277	+	2.30277i	0.152840	+	0.152840i	−0.626545	+	0.779385i	$0.715532\pi$
$228$	−5.73969	−	0.530030i	−0.380120	−	0.0351021i
$229$	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	$-0.640847\pi$
$233$	−13.0719			−0.856372			−0.428186	+	0.903691i	$0.640847\pi$
$234$	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
$237$	−0.533081	+	5.77273i	−0.0346273	+	0.374979i
$238$	−18.7165			−1.21321
$239$	6.64308	+	6.64308i	0.429705	+	0.429705i	0.888528	−	0.458823i	$-0.151729\pi$
$239$	6.64308	+	6.64308i	0.429705	+	0.429705i	−0.458823	+	0.888528i	$0.651729\pi$
$240$	−1.72471	−	0.159268i	−0.111330	−	0.0102807i
$241$	−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
$246$	−1.00076	+	10.8372i	−0.0638061	+	0.690956i
$247$		−	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	−0.810860	−	0.585240i	$-0.801000\pi$
$251$	−3.57449	+	3.57449i	−0.225620	+	0.225620i	0.585240	+	0.810860i	$0.301000\pi$
$252$	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	0.621778	−	0.783194i	$-0.286411\pi$
$257$	−2.58770	−	2.58770i	−0.161416	−	0.161416i	−0.783194	+	0.621778i	$0.786411\pi$
$258$	4.60502	+	5.54204i	0.286696	+	0.345033i
$259$	−10.6767	−	16.0632i	−0.663416	−	0.998121i
$260$		−	0.663562i		−	0.0411524i
$261$	−7.88335	−	11.4927i	−0.487967	−	0.711379i
$262$			21.0161i			1.29838i
$263$	−10.2023			−0.629102			−0.314551	−	0.949241i	$-0.601854\pi$
$263$	−10.2023			−0.629102			−0.314551	+	0.949241i	$0.601854\pi$
$264$	7.40657	+	0.683958i	0.455843	+	0.0420947i
$265$	7.36526	−	7.36526i	0.452444	−	0.452444i
$266$		−	10.5525i		−	0.647013i
$267$	0.591765	−	6.40822i	0.0362154	−	0.392177i
$268$	−7.22479			−0.441324
$269$			22.2257i			1.35513i	0.735465	+	0.677563i	$0.236964\pi$
$269$			22.2257i			1.35513i	−0.735465	+	0.677563i	$0.763036\pi$
$270$	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
$273$	−0.335114	+	3.62894i	−0.0202820	+	0.219633i
$274$	−14.6837	−	14.6837i	−0.887074	−	0.887074i
$275$			4.29438i			0.258961i
$276$	−0.549071	+	5.94588i	−0.0330502	+	0.357900i
$277$	−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
$279$	−0.264695	+	0.181566i	−0.0158469	+	0.0108701i
$280$		−	3.17089i		−	0.189497i
$281$	7.32785	+	7.32785i	0.437143	+	0.437143i	0.891049	−	0.453906i	$-0.149970\pi$
$281$	7.32785	+	7.32785i	0.437143	+	0.437143i	−0.453906	+	0.891049i	$0.649970\pi$
$282$	0.956173	+	0.0882975i	0.0569393	+	0.00525804i
$283$	−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
$288$	−1.69697	−	2.47392i	−0.0999952	−	0.145777i
$289$			17.8405i			1.04944i
$290$	−3.28489	+	3.28489i	−0.192895	+	0.192895i
$291$	−0.0294685	+	0.319114i	−0.00172747	+	0.0187068i
$292$	12.0206			0.703453
$293$		−	27.9995i		−	1.63575i	−0.575399	−	0.817873i	$-0.695153\pi$
$293$		−	27.9995i		−	1.63575i	0.575399	−	0.817873i	$-0.304847\pi$
$294$	−0.486495	+	5.26825i	−0.0283730	+	0.307251i
$295$			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
$309$	17.6216	+	1.62727i	1.00246	+	0.0925720i
$310$	0.0756563	+	0.0756563i	0.00429699	+	0.00429699i
$311$	10.9987	−	10.9987i	0.623678	−	0.623678i	−0.322792	−	0.946470i	$-0.604621\pi$
$311$	10.9987	−	10.9987i	0.623678	−	0.623678i	0.946470	+	0.322792i	$0.104621\pi$
$312$	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
$315$	−7.84454	+	5.38092i	−0.441990	+	0.303181i
$316$	2.36673	+	2.36673i	0.133139	+	0.133139i
$317$	−24.9951			−1.40386			−0.701932	−	0.712244i	$-0.747679\pi$
$317$	−24.9951			−1.40386			−0.701932	+	0.712244i	$0.747679\pi$
$318$	17.9647	+	1.65895i	1.00741	+	0.0930290i
$319$	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
$327$	−1.59744	+	17.2986i	−0.0883384	+	0.956615i
$328$	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
$333$	16.7903	−	7.14735i	0.920105	−	0.391673i
$334$	−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
$339$	2.28146	−	24.7059i	0.123912	−	1.34184i
$340$	−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	−0.519281	−	0.854603i	$-0.673800\pi$
$347$	6.24635	−	6.24635i	0.335322	−	0.335322i	0.854603	+	0.519281i	$0.173800\pi$
$348$	−8.01221	−	0.739886i	−0.429500	−	0.0396620i
$349$	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
$351$	−3.31724	−	0.940435i	−0.177061	−	0.0501967i
$352$	3.03659	−	3.03659i	0.161851	−	0.161851i
$353$	−13.3438	+	13.3438i	−0.710218	+	0.710218i	−0.966581	−	0.256362i	$-0.917476\pi$
$353$	−13.3438	+	13.3438i	−0.710218	+	0.710218i	0.256362	+	0.966581i	$0.417476\pi$
$354$	−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
$357$	32.2805	+	2.98094i	1.70847	+	0.157768i
$358$			13.6427i			0.721037i
$359$			0.209030i			0.0110322i	0.999985	+	0.00551610i	$0.00175584\pi$
$359$			0.209030i			0.0110322i	−0.999985	+	0.00551610i	$0.998244\pi$
$360$	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
$372$	−0.0170408	+	0.184534i	−0.000883522	+	0.00956765i
$373$			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
$375$	−0.159268	+	1.72471i	−0.00822457	+	0.0890638i
$376$	0.392017	−	0.392017i	0.0202167	−	0.0202167i
$377$		−	3.08260i		−	0.158762i
$378$	−15.8517	−	4.49396i	−0.815326	−	0.231144i
$379$	−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	0.918843	−	0.394622i	$-0.129125\pi$
$383$	10.2592	+	10.2592i	0.524221	+	0.524221i	−0.394622	+	0.918843i	$0.629125\pi$
$384$	−1.72471	−	0.159268i	−0.0880139	−	0.00812762i
$385$	−9.62869	−	9.62869i	−0.490723	−	0.490723i
$386$			3.26985i			0.166431i
$387$	−7.05966	−	10.2919i	−0.358863	−	0.523165i
$388$	0.130832	+	0.130832i	0.00664199	+	0.00664199i
$389$	11.2832	+	11.2832i	0.572079	+	0.572079i	0.932709	−	0.360630i	$-0.117438\pi$
$389$	11.2832	+	11.2832i	0.572079	+	0.572079i	−0.360630	+	0.932709i	$0.617438\pi$
$390$	−0.105684	+	1.14445i	−0.00535153	+	0.0579516i
$391$			20.3489i			1.02909i
$392$	2.15991	+	2.15991i	0.109092	+	0.109092i
$393$	3.34720	−	36.2467i	0.168844	−	1.82841i
$394$	−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
$399$	−1.68067	+	18.2000i	−0.0841388	+	0.911138i
$400$		−	1.00000i		−	0.0500000i
$401$	1.36032	−	1.36032i	0.0679314	−	0.0679314i	−0.672325	−	0.740256i	$-0.734704\pi$
$401$	1.36032	−	1.36032i	0.0679314	−	0.0679314i	0.740256	+	0.672325i	$0.234704\pi$
$402$	12.4607	+	1.15068i	0.621483	+	0.0573907i
$403$	−0.0709972			−0.00353662
$404$			15.3310i			0.762744i
$405$	−3.64570	−	8.22854i	−0.181156	−	0.408879i
$406$		−	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	$-0.733761\pi$
$419$		−	30.3868i		−	1.48449i	0.670128	−	0.742246i	$-0.266239\pi$
$420$	−0.505022	+	5.46888i	−0.0246426	+	0.266854i
$421$	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
$426$	13.8144	+	1.27569i	0.669310	+	0.0618073i
$427$	12.0758	+	12.0758i	0.584389	+	0.584389i
$428$	−0.283834			−0.0137196
$429$	0.453848	−	4.91472i	0.0219120	−	0.237285i
$430$	−2.94167	+	2.94167i	−0.141860	+	0.141860i
$431$	−13.1264	+	13.1264i	−0.632279	+	0.632279i	−0.948639	−	0.316360i	$-0.897539\pi$
$431$	−13.1264	+	13.1264i	−0.632279	+	0.632279i	0.316360	+	0.948639i	$0.397539\pi$
$432$	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
$438$	−20.7321	−	1.91450i	−0.990619	−	0.0914784i
$439$	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	$-0.0806295\pi$
$443$	40.7519			1.93618			0.968089	+	0.250605i	$0.0806295\pi$
$444$	3.02143	−	10.0931i	0.143391	−	0.478998i
$445$	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	0.979123	−	0.203269i	$-0.0651567\pi$
$449$	16.4400	+	16.4400i	0.775853	+	0.775853i	−0.203269	+	0.979123i	$0.565157\pi$
$450$	−2.47392	+	1.69697i	−0.116622	+	0.0799961i
$451$	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
$459$	−8.36546	+	29.5078i	−0.390466	+	1.37731i
$460$	−3.44746			−0.160739
$461$	−14.2992	−	14.2992i	−0.665979	−	0.665979i	0.290804	−	0.956783i	$-0.406077\pi$
$461$	−14.2992	−	14.2992i	−0.665979	−	0.665979i	−0.956783	+	0.290804i	$0.906077\pi$
$462$	2.16876	−	23.4855i	0.100900	−	1.09264i
$463$	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	$0.0618289\pi$
$467$	25.3750	+	25.3750i	1.17422	+	1.17422i	0.193022	+	0.981194i	$0.438171\pi$
$468$	−1.64160	+	1.12605i	−0.0758829	+	0.0520515i
$469$			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	$-0.879314\pi$
$479$	−28.4324	−	28.4324i	−1.29911	−	1.29911i	−0.370127	−	0.928981i	$-0.620686\pi$
$480$	1.33218	−	1.10694i	0.0608052	−	0.0505245i
$481$	3.95681	+	0.797069i	0.180415	+	0.0363432i
$482$		−	8.18905i		−	0.373001i
$483$	18.8538	+	1.74105i	0.857876	+	0.0792203i
$484$		−	7.44170i		−	0.338259i
$485$	−0.185024			−0.00840152
$486$	6.92630	−	13.9652i	0.314183	−	0.633474i
$487$	−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
$489$	31.2436	+	2.88518i	1.41288	+	0.130472i
$490$	−3.05457			−0.137991
$491$			21.3703i			0.964426i	0.876054	+	0.482213i	$0.160167\pi$
$491$			21.3703i			0.964426i	−0.876054	+	0.482213i	$0.839833\pi$
$492$	−6.95543	−	8.37071i	−0.313575	−	0.377381i
$493$	−27.4207			−1.23497
$494$	1.56149	+	1.56149i	0.0702546	+	0.0702546i
$495$	10.6240	−	7.28745i	0.477511	−	0.327547i
$496$	0.0756563	+	0.0756563i	0.00339707	+	0.00339707i
$497$			25.3979i			1.13925i
$498$	17.8285	+	1.64637i	0.798915	+	0.0737756i
$499$	−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
$501$	6.33060	+	0.584598i	0.282831	+	0.0261179i
$502$		−	5.05509i		−	0.225620i
$503$	17.4364	+	17.4364i	0.777452	+	0.777452i	0.979397	−	0.201945i	$-0.0647261\pi$
$503$	17.4364	+	17.4364i	0.777452	+	0.777452i	−0.201945	+	0.979397i	$0.564726\pi$
$504$	−7.84454	+	5.38092i	−0.349423	+	0.239685i
$505$	−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	$-0.706882\pi$
$509$	−27.3051			−1.21028			−0.605139	+	0.796120i	$0.706882\pi$
$510$	10.1803	+	0.940094i	0.450790	+	0.0416281i
$511$		−	38.1161i		−	1.68616i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−16.6367	−	4.71649i	−0.734528	−	0.208238i
$514$	3.65956			0.161416
$515$			10.2172i			0.450221i
$516$	−7.17506	−	0.662579i	−0.315864	−	0.0291684i
$517$		−	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	$-0.762863\pi$
$521$	−33.5578			−1.47019			−0.735097	+	0.677962i	$0.762863\pi$
$522$	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
$531$	18.9884	−	13.0250i	0.824026	−	0.565237i
$532$	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
$537$	2.17284	−	23.5297i	0.0937650	−	1.01538i
$538$	−15.7160	−	15.7160i	−0.677563	−	0.677563i
$539$	13.1175			0.565010
$540$	−4.99914	−	1.41725i	−0.215129	−	0.0609889i
$541$	−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
$549$	−13.3240	+	9.13954i	−0.568654	+	0.390066i
$550$	−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
$555$	5.00043	+	9.27339i	0.212257	+	0.393633i
$556$	−10.4767			−0.444309
$557$	−4.77952	+	4.77952i	−0.202515	+	0.202515i	−0.801077	−	0.598562i	$-0.795739\pi$
$557$	−4.77952	+	4.77952i	−0.202515	+	0.202515i	0.598562	+	0.801077i	$0.295739\pi$
$558$	0.0587808	−	0.315554i	0.00248839	−	0.0133585i
$559$		−	2.76051i		−	0.116757i
$560$	2.24216	+	2.24216i	0.0947486	+	0.0947486i
$561$	−43.7179	−	4.03712i	−1.84577	−	0.170447i
$562$	−10.3631			−0.437143
$563$	−20.9149	−	20.9149i	−0.881459	−	0.881459i	0.112224	−	0.993683i	$-0.464203\pi$
$563$	−20.9149	−	20.9149i	−0.881459	−	0.881459i	−0.993683	+	0.112224i	$0.964203\pi$
$564$	−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	−0.00505843	−	0.999987i	$-0.501610\pi$
$569$	23.7328	−	23.7328i	0.994929	−	0.994929i	0.999987	+	0.00505843i	$0.00161016\pi$
$570$	−0.530030	+	5.73969i	−0.0222005	+	0.240409i
$571$	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
$573$	43.1492	+	3.98460i	1.80258	+	0.166459i
$574$	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
$579$	0.520783	−	5.63955i	0.0216430	−	0.234372i
$580$		−	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	$-0.442056\pi$
$587$	28.2138	−	28.2138i	1.16451	−	1.16451i	0.983477	−	0.181033i	$-0.0579440\pi$
$588$	−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	$-0.955327\pi$
$593$		−	6.81280i		−	0.279768i	0.990168	−	0.139884i	$-0.0446730\pi$
$594$	21.4682	+	6.08622i	0.880851	+	0.249721i
$595$			18.7165i			0.767301i
$596$	13.4251			0.549911
$597$	37.6765	+	3.47923i	1.54200	+	0.142395i
$598$	1.61758	−	1.61758i	0.0661478	−	0.0661478i
$599$		−	35.3959i		−	1.44624i	−0.690724	−	0.723119i	$-0.742708\pi$
$599$		−	35.3959i		−	1.44624i	0.690724	−	0.723119i	$-0.257292\pi$
$600$	−0.159268	+	1.72471i	−0.00650209	+	0.0704111i
$601$	−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
$606$	2.44173	−	26.4415i	0.0991887	−	1.07411i
$607$	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
$609$	−2.34610	+	25.4059i	−0.0950688	+	1.02950i
$610$	3.80832	+	3.80832i	0.154195	+	0.154195i
$611$	−0.260127	−	0.260127i	−0.0105236	−	0.0105236i
$612$	10.0165	+	14.6025i	0.404894	+	0.590272i
$613$		−	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
$615$	10.8372	+	1.00076i	0.436999	+	0.0403545i
$616$	−9.62869	−	9.62869i	−0.387951	−	0.387951i
$617$	8.81089			0.354713			0.177357	−	0.984147i	$-0.443245\pi$
$617$	8.81089			0.354713			0.177357	+	0.984147i	$0.443245\pi$
$618$	−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
$621$	−4.88593	+	17.2343i	−0.196065	+	0.691590i
$622$			15.5545i			0.623678i
$623$	−8.33081	+	8.33081i	−0.333767	+	0.333767i
$624$	−0.105684	+	1.14445i	−0.00423076	+	0.0458148i
$625$	−1.00000			−0.0400000
$626$		−	34.8571i		−	1.39317i
$627$	2.27615	−	24.6484i	0.0909008	−	0.984363i
$628$			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	$-0.921683\pi$
$641$		−	12.3332i		−	0.487131i	0.969884	−	0.243565i	$-0.0783170\pi$
$642$	0.489532	+	0.0452057i	0.0193203	+	0.00178413i
$643$	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	−0.867634	−	0.497204i	$-0.834360\pi$
$647$	−9.42234	+	9.42234i	−0.370430	+	0.370430i	0.497204	+	0.867634i	$0.334360\pi$
$648$	−3.64570	−	8.22854i	−0.143217	−	0.323248i
$649$	23.3071	+	23.3071i	0.914883	+	0.914883i
$650$	−0.663562			−0.0260270
$651$	0.585138	+	0.0540344i	0.0229334	+	0.00211778i
$652$	12.8094	−	12.8094i	0.501655	−	0.501655i
$653$	5.72159	−	5.72159i	0.223903	−	0.223903i	−0.586237	−	0.810140i	$-0.699391\pi$
$653$	5.72159	−	5.72159i	0.223903	−	0.223903i	0.810140	+	0.586237i	$0.199391\pi$
$654$	−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	$-0.466309\pi$
$659$	5.42404			0.211291			0.105645	+	0.994404i	$0.466309\pi$
$660$	0.683958	−	7.40657i	0.0266230	−	0.288300i
$661$	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
$666$	−6.81862	+	16.9265i	−0.264216	+	0.655889i
$667$	−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
$672$	−0.505022	+	5.46888i	−0.0194817	+	0.210967i
$673$	−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	$-0.666358\pi$
$677$	−25.9755			−0.998319			−0.499160	+	0.866510i	$0.666358\pi$
$678$	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
$681$	5.61670	+	0.518673i	0.215233	+	0.0198756i
$682$	0.459473			0.0175941
$683$	−17.5140	−	17.5140i	−0.670156	−	0.670156i	0.287596	−	0.957752i	$-0.407144\pi$
$683$	−17.5140	−	17.5140i	−0.670156	−	0.670156i	−0.957752	+	0.287596i	$0.907144\pi$
$684$	−8.23299	+	5.64738i	−0.314796	+	0.215933i
$685$	−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
$690$	5.94588	+	0.549071i	0.226356	+	0.0209028i
$691$		−	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	0.710134	−	0.704067i	$-0.248634\pi$
$701$	0.160630	+	0.160630i	0.00606691	+	0.00606691i	−0.704067	+	0.710134i	$0.748634\pi$
$702$	3.01063	−	1.68065i	0.113629	−	0.0634322i
$703$	19.8443	+	3.99748i	0.748441	+	0.150768i
$704$			4.29438i			0.161851i
$705$	0.0882975	−	0.956173i	0.00332548	−	0.0360116i
$706$		−	18.8710i		−	0.710218i
$707$	48.6129			1.82828
$708$	1.22245	−	13.2379i	0.0459425	−	0.497511i
$709$	−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
$711$	5.67988	+	8.28037i	0.213012	+	0.310538i
$712$	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
$717$	16.2032	+	1.49628i	0.605120	+	0.0558797i
$718$	−0.147807	−	0.147807i	−0.00551610	−	0.00551610i
$719$			4.09595i			0.152753i	0.997079	+	0.0763766i	$0.0243351\pi$
$719$			4.09595i			0.152753i	−0.997079	+	0.0763766i	$0.975665\pi$
$720$	−2.47392	+	1.69697i	−0.0921975	+	0.0632425i
$721$	−22.9085	−	22.9085i	−0.853157	−	0.853157i
$722$	−5.60382	−	5.60382i	−0.208553	−	0.208553i
$723$	−1.30425	+	14.1238i	−0.0485057	+	0.525268i
$724$		−	1.74294i		−	0.0647760i
$725$	3.28489	+	3.28489i	0.121998	+	0.121998i
$726$	−1.18523	+	12.8348i	−0.0439879	+	0.476344i
$727$	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
$732$	−0.857784	+	9.28893i	−0.0317046	+	0.343329i
$733$		−	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
$735$	5.26825	+	0.486495i	0.194322	+	0.0179447i
$736$	−3.44746			−0.127075
$737$		−	31.0260i		−	1.14286i
$738$	10.6629	+	15.5449i	0.392508	+	0.572214i
$739$			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	$-0.240445\pi$
$743$	39.6883			1.45602			0.728012	+	0.685565i	$0.240445\pi$
$744$	−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
$753$	−0.805115	+	8.71858i	−0.0293400	+	0.317723i
$754$	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
$759$	−25.5339	−	2.35792i	−0.926821	−	0.0855870i
$760$	2.35319	+	2.35319i	0.0853592	+	0.0853592i
$761$	−1.71775			−0.0622685			−0.0311343	−	0.999515i	$-0.509912\pi$
$761$	−1.71775			−0.0622685			−0.0311343	+	0.999515i	$0.509912\pi$
$762$	1.89239	−	20.4927i	0.0685540	−	0.742371i
$763$	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
$771$	−6.31169	−	0.582851i	−0.227310	−	0.0209909i
$772$	−2.31213	−	2.31213i	−0.0832155	−	0.0832155i
$773$		−	23.3393i		−	0.839457i	−0.907650	−	0.419729i	$-0.862125\pi$
$773$		−	23.3393i		−	0.839457i	0.907650	−	0.419729i	$-0.137875\pi$
$774$	12.2694	+	2.28552i	0.441014	+	0.0821512i
$775$	0.0756563	−	0.0756563i	0.00271765	−	0.00271765i
$776$	−0.185024			−0.00664199
$777$	−32.0042	−	9.58065i	−1.14814	−	0.343704i
$778$	−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
$783$	−23.2237	−	6.58390i	−0.829947	−	0.235289i
$784$	−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
$792$	10.6240	−	7.28745i	0.377506	−	0.258948i
$793$	−3.57380			−0.126909
$794$	−10.9694	−	10.9694i	−0.389290	−	0.389290i
$795$	1.65895	−	17.9647i	0.0588367	−	0.637142i
$796$	15.4468	−	15.4468i	0.547498	−	0.547498i
$797$	25.0247	−	25.0247i	0.886420	−	0.886420i	−0.107757	−	0.994177i	$-0.534367\pi$
$797$	25.0247	−	25.0247i	0.886420	−	0.886420i	0.994177	+	0.107757i	$0.0343669\pi$
$798$	−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
$801$	−6.30515	−	9.19192i	−0.222782	−	0.324780i
$802$			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	$0.651492\pi$
$809$	−38.3135	+	38.3135i	−1.34703	+	1.34703i	−0.888868	+	0.458163i	$0.848508\pi$
$810$	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
$816$	10.1803	+	0.940094i	0.356381	+	0.0329099i
$817$		−	13.8446i		−	0.484361i
$818$	13.3383			0.466363
$819$	3.57058	+	5.20533i	0.124766	+	0.181889i
$820$	4.44310	−	4.44310i	0.155160	−	0.155160i
$821$			21.9003i			0.764325i	0.924095	+	0.382163i	$0.124821\pi$
$821$			21.9003i			0.764325i	−0.924095	+	0.382163i	$0.875179\pi$
$822$	−35.8151	−	3.30734i	−1.24920	−	0.115357i
$823$	−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	0.975321	−	0.220792i	$-0.0708643\pi$
$827$	21.6984	+	21.6984i	0.754529	+	0.754529i	−0.220792	+	0.975321i	$0.570864\pi$
$828$	5.85025	+	8.52874i	0.203310	+	0.296394i
$829$	−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
$831$	−12.7527	−	1.17765i	−0.442387	−	0.0408521i
$832$	0.469209	+	0.469209i	0.0162669	+	0.0162669i
$833$	−12.7490	−	12.7490i	−0.441728	−	0.441728i
$834$	18.0692	+	1.66860i	0.625686	+	0.0577788i
$835$			3.67053i			0.127024i
$836$	−10.1055	−	10.1055i	−0.349506	−	0.349506i
$837$	−0.151638	+	0.534878i	−0.00524137	+	0.0184881i
$838$	21.4867	+	21.4867i	0.742246	+	0.742246i
$839$	−1.48655			−0.0513213			−0.0256606	−	0.999671i	$-0.508169\pi$
$839$	−1.48655			−0.0513213			−0.0256606	+	0.999671i	$0.508169\pi$
$840$	−3.50998	−	4.22419i	−0.121106	−	0.145748i
$841$			7.41899i			0.255827i
$842$	−10.6565			−0.367246
$843$	17.8735	+	1.65052i	0.615594	+	0.0568469i
$844$			26.2503i			0.903571i
$845$	−8.88104	+	8.88104i	−0.305517	+	0.305517i
$846$	1.37153	−	0.940795i	0.0471542	−	0.0323452i
$847$	−23.5968			−0.810797
$848$			10.4161i			0.357689i
$849$	−17.2918	−	1.59681i	−0.593454	−	0.0548023i
$850$			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	0.658160	−	0.752878i	$-0.271335\pi$
$857$	−2.77286	−	2.77286i	−0.0947189	−	0.0947189i	−0.752878	+	0.658160i	$0.771335\pi$
$858$	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	$-0.903253\pi$
$863$		−	17.5839i		−	0.598563i	0.954165	−	0.299281i	$-0.0967469\pi$
$864$	−4.99914	−	1.41725i	−0.170074	−	0.0482159i
$865$	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
$870$	−0.739886	+	8.01221i	−0.0250845	+	0.271640i
$871$	−3.38994	−	3.38994i	−0.114864	−	0.114864i
$872$	−10.0299			−0.339654
$873$	0.313982	+	0.457735i	0.0106267	+	0.0154920i
$874$	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	$-0.285871\pi$
$881$	36.9896			1.24621			0.623105	+	0.782138i	$0.285871\pi$
$882$	5.18352	+	7.55676i	0.174538	+	0.254449i
$883$	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	$-0.639305\pi$
$887$	−25.2439			−0.847606			−0.423803	+	0.905754i	$0.639305\pi$
$888$	5.00043	+	9.27339i	0.167804	+	0.311194i
$889$	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
$894$	−23.1544	−	2.13818i	−0.774397	−	0.0715115i
$895$	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
$903$	−2.10097	+	22.7513i	−0.0699158	+	0.757117i
$904$	14.3246			0.476430
$905$	1.23245	+	1.23245i	0.0409679	+	0.0409679i
$906$	−20.1484	−	1.86060i	−0.669386	−	0.0618143i
$907$	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	0.942445	−	0.334361i	$-0.108521\pi$
$911$	18.3536	+	18.3536i	0.608083	+	0.608083i	−0.334361	+	0.942445i	$0.608521\pi$
$912$	−0.530030	+	5.73969i	−0.0175511	+	0.190060i
$913$		−	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
$927$	25.2764	−	17.3382i	0.830186	−	0.569462i
$928$		−	4.64554i		−	0.152497i
$929$	56.8147			1.86403			0.932015	−	0.362420i	$-0.118049\pi$
$929$	56.8147			1.86403			0.932015	+	0.362420i	$0.118049\pi$
$930$	0.184534	+	0.0170408i	0.00605111	+	0.000558788i
$931$	7.18798	−	7.18798i	0.235576	−	0.235576i
$932$			13.0719i			0.428186i
$933$	2.47733	−	26.8270i	0.0811043	−	0.878277i
$934$	−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
$939$	−5.55163	+	60.1185i	−0.181171	+	1.96189i
$940$	−0.392017	−	0.392017i	−0.0127862	−	0.0127862i
$941$		−	0.420330i		−	0.0137024i	−0.999977	−	0.00685118i	$-0.997819\pi$
$941$		−	0.420330i		−	0.0137024i	0.999977	−	0.00685118i	$-0.00218082\pi$
$942$	0.732240	−	7.92941i	0.0238577	−	0.258354i
$943$	−15.3174	−	15.3174i	−0.498804	−	0.498804i
$944$	−5.42735	−	5.42735i	−0.176645	−	0.176645i
$945$	−4.49396	+	15.8517i	−0.146188	+	0.515657i
$946$			17.8652i			0.580849i
$947$	14.3006	+	14.3006i	0.464707	+	0.464707i	0.900195	−	0.435488i	$-0.143424\pi$
$947$	14.3006	+	14.3006i	0.464707	+	0.464707i	−0.435488	+	0.900195i	$0.643424\pi$
$948$	5.77273	+	0.533081i	0.187489	+	0.0173137i
$949$	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	$-0.330945\pi$
$953$	31.2710			1.01297			0.506483	+	0.862250i	$0.330945\pi$
$954$	25.7685	−	17.6758i	0.834285	−	0.572274i
$955$			25.0182i			0.809569i
$956$	6.64308	−	6.64308i	0.214853	−	0.214853i
$957$	3.17735	−	34.4075i	0.102709	−	1.11224i
$958$	40.2094			1.29911
$959$		−	65.8463i		−	2.12629i
$960$	−0.159268	+	1.72471i	−0.00514036	+	0.0556649i
$961$		−	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	$-0.918676\pi$
$971$		−	15.7497i		−	0.505433i	0.967540	−	0.252716i	$-0.0813239\pi$
$972$	4.97724	+	14.7725i	0.159645	+	0.473829i
$973$			33.2203i			1.06500i
$974$		−	11.9449i		−	0.382739i
$975$	1.14445	+	0.105684i	0.0366518	+	0.00338460i
$976$	3.80832	+	3.80832i	0.121901	+	0.121901i
$977$	−33.7074	+	33.7074i	−1.07839	+	1.07839i	−0.0817411	+	0.996654i	$0.526048\pi$
$977$	−33.7074	+	33.7074i	−1.07839	+	1.07839i	−0.996654	+	0.0817411i	$0.973952\pi$
$978$	−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
$981$	17.0204	+	24.8130i	0.543419	+	0.792220i
$982$	−15.1111	−	15.1111i	−0.482213	−	0.482213i
$983$	1.64672			0.0525221			0.0262611	−	0.999655i	$-0.491640\pi$
$983$	1.64672			0.0525221			0.0262611	+	0.999655i	$0.491640\pi$
$984$	10.8372	+	1.00076i	0.345478	+	0.0319031i
$985$	−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
$993$	4.26890	−	46.2279i	0.135470	−	1.46700i
$994$	−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
$999$	14.4560	−	28.1074i	0.457368	−	0.889278i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.33218 - 1.10694i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(-0.159268 + 1.72471i) q^{6} -3.17089 q^{7} +(0.707107 + 0.707107i) q^{8} +(0.549384 - 2.94927i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.33218 - 1.10694i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(-0.159268 + 1.72471i) 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} +(1.72471 + 0.159268i) q^{15} -1.00000 q^{16} +(-4.17376 - 4.17376i) q^{17} +(1.69697 + 2.47392i) 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} +(1.72471 + 0.159268i) 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} +(0.105684 - 1.14445i) q^{39} +1.00000i q^{40} +6.28349 q^{41} +(0.505022 - 5.46888i) q^{42} +(2.94167 - 2.94167i) q^{43} -4.29438i q^{44} +(2.47392 - 1.69697i) 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} +(-10.1803 - 0.940094i) q^{51} +(-0.469209 - 0.469209i) q^{52} -10.4161i q^{53} +(4.99914 + 1.41725i) q^{54} +(3.03659 + 3.03659i) q^{55} +(-2.24216 - 2.24216i) q^{56} +(0.530030 - 5.73969i) q^{57} +4.64554i q^{58} +(5.42735 + 5.42735i) q^{59} +(0.159268 - 1.72471i) 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} +(-0.683958 + 7.40657i) q^{66} -7.22479i q^{67} +(-4.17376 + 4.17376i) q^{68} +(-5.94588 - 0.549071i) q^{69} +3.17089 q^{70} -8.00969i q^{71} +(2.47392 - 1.69697i) 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} +(0.739886 - 8.01221i) 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} +(-0.184534 - 0.0170408i) q^{93} +(0.392017 + 0.392017i) q^{94} +3.32791 q^{95} +(0.159268 - 1.72471i) 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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