LMFDB - Embedded newform 630.2.p.d.433.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(307,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("630.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.p (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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 44 x^{14} - 160 x^{13} + 468 x^{12} - 1060 x^{11} + 2038 x^{10} - 3208 x^{9} + \cdots + 2468 $ x^16 - 8x^15 + 44x^14 - 160x^13 + 468x^12 - 1060x^11 + 2038x^10 - 3208x^9 + 4381x^8 - 3980x^7 - 390x^6 + 9000x^5 - 10018x^4 - 2304x^3 + 9396x^2 - 4200*x + 2468
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			433.1
Root			$0.131441 + 0.491850i$ of defining polynomial
Character	$\chi$	$=$	630.433
Dual form			630.2.p.d.307.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-2.20245 - 0.386289i) q^{5} +(-1.57763 + 2.12393i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-2.20245 - 0.386289i) q^{5} +(-1.57763 + 2.12393i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.83051 - 1.28422i) q^{10} -1.41421 q^{11} +(3.66103 - 3.66103i) q^{13} +(-0.386289 - 2.61740i) q^{14} -1.00000 q^{16} +(-2.58874 - 2.58874i) q^{17} +4.75362 q^{19} +(-0.386289 + 2.20245i) q^{20} +(1.00000 - 1.00000i) q^{22} +(3.82059 + 3.82059i) q^{23} +(4.70156 + 1.70156i) q^{25} +5.17748i q^{26} +(2.12393 + 1.57763i) q^{28} -8.06323i q^{29} -9.89049i q^{31} +(0.707107 - 0.707107i) q^{32} +3.66103 q^{34} +(4.29511 - 4.06842i) q^{35} +(-0.701562 + 0.701562i) q^{37} +(-3.36131 + 3.36131i) q^{38} +(-1.28422 - 1.83051i) q^{40} -10.3550i q^{41} +(-2.00000 - 2.00000i) q^{43} +1.41421i q^{44} -5.40312 q^{46} +(1.54515 + 1.54515i) q^{47} +(-2.02214 - 6.70156i) q^{49} +(-4.52769 + 2.12132i) q^{50} +(-3.66103 - 3.66103i) q^{52} +(6.64901 + 6.64901i) q^{53} +(3.11473 + 0.546295i) q^{55} +(-2.61740 + 0.386289i) q^{56} +(5.70156 + 5.70156i) q^{58} +7.49521 q^{59} +6.22947i q^{61} +(6.99364 + 6.99364i) q^{62} +1.00000i q^{64} +(-9.47744 + 6.64901i) q^{65} +(-4.00000 + 4.00000i) q^{67} +(-2.58874 + 2.58874i) q^{68} +(-0.160291 + 5.91391i) q^{70} -0.992159 q^{71} +(4.59058 - 4.59058i) q^{73} -0.992159i q^{74} -4.75362i q^{76} +(2.23111 - 3.00369i) q^{77} -7.40312i q^{79} +(2.20245 + 0.386289i) q^{80} +(7.32206 + 7.32206i) q^{82} +(8.03722 - 8.03722i) q^{83} +(4.70156 + 6.70156i) q^{85} +2.82843 q^{86} +(-1.00000 - 1.00000i) q^{88} -12.4421 q^{89} +(2.00000 + 13.5515i) q^{91} +(3.82059 - 3.82059i) q^{92} -2.18518 q^{94} +(-10.4696 - 1.83627i) q^{95} +(-1.63888 - 1.63888i) q^{97} +(6.16859 + 3.30885i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{7}+O(q^{10}) $ 16 * q - 4 * q^7	$ 16 q - 4 q^{7} - 16 q^{16} + 16 q^{22} + 24 q^{25} + 4 q^{28} + 40 q^{37} - 32 q^{43} + 16 q^{46} + 40 q^{58} - 64 q^{67} - 12 q^{70} + 24 q^{85} - 16 q^{88} + 32 q^{91}+O(q^{100}) $ 16 * q - 4 * q^7 - 16 * q^16 + 16 * q^22 + 24 * q^25 + 4 * q^28 + 40 * q^37 - 32 * q^43 + 16 * q^46 + 40 * q^58 - 64 * q^67 - 12 * q^70 + 24 * q^85 - 16 * q^88 + 32 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	−2.20245	−	0.386289i	−0.984965	−	0.172754i
$5$	−2.20245	−	0.386289i	−0.984965	−	0.172754i
$6$		0			0
$7$	−1.57763	+	2.12393i	−0.596289	+	0.802769i
$7$	−1.57763	+	2.12393i	−0.596289	+	0.802769i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	1.83051	−	1.28422i	0.578859	−	0.406106i
$11$	−1.41421			−0.426401			−0.213201	−	0.977008i	$-0.568389\pi$
$11$	−1.41421			−0.426401			−0.213201	+	0.977008i	$0.568389\pi$
$12$		0			0
$13$	3.66103	−	3.66103i	1.01539	−	1.01539i	0.0155066	−	0.999880i	$-0.495064\pi$
$13$	3.66103	−	3.66103i	1.01539	−	1.01539i	0.999880	−	0.0155066i	$-0.00493612\pi$
$14$	−0.386289	−	2.61740i	−0.103240	−	0.699529i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−2.58874	−	2.58874i	−0.627861	−	0.627861i	0.319668	−	0.947529i	$-0.396428\pi$
$17$	−2.58874	−	2.58874i	−0.627861	−	0.627861i	−0.947529	+	0.319668i	$0.896428\pi$
$18$		0			0
$19$	4.75362			1.09055			0.545277	−	0.838256i	$-0.316424\pi$
$19$	4.75362			1.09055			0.545277	+	0.838256i	$0.316424\pi$
$20$	−0.386289	+	2.20245i	−0.0863768	+	0.492483i
$21$		0			0
$22$	1.00000	−	1.00000i	0.213201	−	0.213201i
$23$	3.82059	+	3.82059i	0.796647	+	0.796647i	0.982565	−	0.185918i	$-0.0595259\pi$
$23$	3.82059	+	3.82059i	0.796647	+	0.796647i	−0.185918	+	0.982565i	$0.559526\pi$
$24$		0			0
$25$	4.70156	+	1.70156i	0.940312	+	0.340312i
$26$			5.17748i			1.01539i
$27$		0			0
$28$	2.12393	+	1.57763i	0.401385	+	0.298145i
$29$		−	8.06323i		−	1.49730i	−0.662963	−	0.748652i	$-0.730702\pi$
$29$		−	8.06323i		−	1.49730i	0.662963	−	0.748652i	$-0.269298\pi$
$30$		0			0
$31$		−	9.89049i		−	1.77639i	−0.459471	−	0.888193i	$-0.651961\pi$
$31$		−	9.89049i		−	1.77639i	0.459471	−	0.888193i	$-0.348039\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$	3.66103			0.627861
$35$	4.29511	−	4.06842i	0.726006	−	0.687689i
$36$		0			0
$37$	−0.701562	+	0.701562i	−0.115336	+	0.115336i	−0.762419	−	0.647083i	$-0.775989\pi$
$37$	−0.701562	+	0.701562i	−0.115336	+	0.115336i	0.647083	+	0.762419i	$0.275989\pi$
$38$	−3.36131	+	3.36131i	−0.545277	+	0.545277i
$39$		0			0
$40$	−1.28422	−	1.83051i	−0.203053	−	0.289430i
$41$		−	10.3550i		−	1.61717i	−0.588378	−	0.808586i	$-0.700233\pi$
$41$		−	10.3550i		−	1.61717i	0.588378	−	0.808586i	$-0.299767\pi$
$42$		0			0
$43$	−2.00000	−	2.00000i	−0.304997	−	0.304997i	0.537968	−	0.842965i	$-0.319192\pi$
$43$	−2.00000	−	2.00000i	−0.304997	−	0.304997i	−0.842965	+	0.537968i	$0.819192\pi$
$44$			1.41421i			0.213201i
$45$		0			0
$46$	−5.40312			−0.796647
$47$	1.54515	+	1.54515i	0.225384	+	0.225384i	0.810761	−	0.585377i	$-0.199054\pi$
$47$	1.54515	+	1.54515i	0.225384	+	0.225384i	−0.585377	+	0.810761i	$0.699054\pi$
$48$		0			0
$49$	−2.02214	−	6.70156i	−0.288878	−	0.957366i
$50$	−4.52769	+	2.12132i	−0.640312	+	0.300000i
$51$		0			0
$52$	−3.66103	−	3.66103i	−0.507693	−	0.507693i
$53$	6.64901	+	6.64901i	0.913312	+	0.913312i	0.996531	−	0.0832191i	$-0.0265201\pi$
$53$	6.64901	+	6.64901i	0.913312	+	0.913312i	−0.0832191	+	0.996531i	$0.526520\pi$
$54$		0			0
$55$	3.11473	+	0.546295i	0.419991	+	0.0736624i
$56$	−2.61740	+	0.386289i	−0.349765	+	0.0516200i
$57$		0			0
$58$	5.70156	+	5.70156i	0.748652	+	0.748652i
$59$	7.49521			0.975793			0.487896	−	0.872902i	$-0.337764\pi$
$59$	7.49521			0.975793			0.487896	+	0.872902i	$0.337764\pi$
$60$		0			0
$61$			6.22947i			0.797601i	0.917038	+	0.398801i	$0.130573\pi$
$61$			6.22947i			0.797601i	−0.917038	+	0.398801i	$0.869427\pi$
$62$	6.99364	+	6.99364i	0.888193	+	0.888193i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−9.47744	+	6.64901i	−1.17553	+	0.824709i
$66$		0			0
$67$	−4.00000	+	4.00000i	−0.488678	+	0.488678i	−0.907889	−	0.419211i	$-0.862307\pi$
$67$	−4.00000	+	4.00000i	−0.488678	+	0.488678i	0.419211	+	0.907889i	$0.362307\pi$
$68$	−2.58874	+	2.58874i	−0.313931	+	0.313931i
$69$		0			0
$70$	−0.160291	+	5.91391i	−0.0191584	+	0.706847i
$71$	−0.992159			−0.117748			−0.0588738	−	0.998265i	$-0.518751\pi$
$71$	−0.992159			−0.117748			−0.0588738	+	0.998265i	$0.518751\pi$
$72$		0			0
$73$	4.59058	−	4.59058i	0.537287	−	0.537287i	−0.385444	−	0.922731i	$-0.625952\pi$
$73$	4.59058	−	4.59058i	0.537287	−	0.537287i	0.922731	+	0.385444i	$0.125952\pi$
$74$		−	0.992159i		−	0.115336i
$75$		0			0
$76$		−	4.75362i		−	0.545277i
$77$	2.23111	−	3.00369i	0.254259	−	0.342302i
$78$		0			0
$79$		−	7.40312i		−	0.832917i	−0.909155	−	0.416458i	$-0.863271\pi$
$79$		−	7.40312i		−	0.832917i	0.909155	−	0.416458i	$-0.136729\pi$
$80$	2.20245	+	0.386289i	0.246241	+	0.0431884i
$81$		0			0
$82$	7.32206	+	7.32206i	0.808586	+	0.808586i
$83$	8.03722	−	8.03722i	0.882199	−	0.882199i	−0.111559	−	0.993758i	$-0.535584\pi$
$83$	8.03722	−	8.03722i	0.882199	−	0.882199i	0.993758	+	0.111559i	$0.0355843\pi$
$84$		0			0
$85$	4.70156	+	6.70156i	0.509956	+	0.726886i
$86$	2.82843			0.304997
$87$		0			0
$88$	−1.00000	−	1.00000i	−0.106600	−	0.106600i
$89$	−12.4421			−1.31886			−0.659431	−	0.751765i	$-0.729203\pi$
$89$	−12.4421			−1.31886			−0.659431	+	0.751765i	$0.729203\pi$
$90$		0			0
$91$	2.00000	+	13.5515i	0.209657	+	1.42059i
$92$	3.82059	−	3.82059i	0.398324	−	0.398324i
$93$		0			0
$94$	−2.18518			−0.225384
$95$	−10.4696	−	1.83627i	−1.07416	−	0.188397i
$96$		0			0
$97$	−1.63888	−	1.63888i	−0.166403	−	0.166403i	0.618993	−	0.785396i	$-0.287541\pi$
$97$	−1.63888	−	1.63888i	−0.166403	−	0.166403i	−0.785396	+	0.618993i	$0.787541\pi$
$98$	6.16859	+	3.30885i	0.623122	+	0.334244i
$99$		0			0
$100$	1.70156	−	4.70156i	0.170156	−	0.470156i
$101$			8.03722i			0.799733i	0.916573	+	0.399867i	$0.130944\pi$
$101$			8.03722i			0.799733i	−0.916573	+	0.399867i	$0.869056\pi$
$102$		0			0
$103$	−11.9126	+	11.9126i	−1.17379	+	1.17379i	−0.192488	+	0.981299i	$0.561656\pi$
$103$	−11.9126	+	11.9126i	−1.17379	+	1.17379i	−0.981299	+	0.192488i	$0.938344\pi$
$104$	5.17748			0.507693
$105$		0			0
$106$	−9.40312			−0.913312
$107$	9.47744	−	9.47744i	0.916219	−	0.916219i	−0.0805332	−	0.996752i	$-0.525662\pi$
$107$	9.47744	−	9.47744i	0.916219	−	0.916219i	0.996752	+	0.0805332i	$0.0256623\pi$
$108$		0			0
$109$			0.596876i			0.0571703i	0.999591	+	0.0285852i	$0.00910018\pi$
$109$			0.596876i			0.0571703i	−0.999591	+	0.0285852i	$0.990900\pi$
$110$	−2.58874	+	1.81616i	−0.246826	+	0.173164i
$111$		0			0
$112$	1.57763	−	2.12393i	0.149072	−	0.200692i
$113$	6.22696	+	6.22696i	0.585783	+	0.585783i	0.936487	−	0.350704i	$-0.114058\pi$
$113$	6.22696	+	6.22696i	0.585783	+	0.585783i	−0.350704	+	0.936487i	$0.614058\pi$
$114$		0			0
$115$	−6.93880	−	9.89049i	−0.647046	−	0.922293i
$116$	−8.06323			−0.748652
$117$		0			0
$118$	−5.29991	+	5.29991i	−0.487896	+	0.487896i
$119$	9.58237	−	1.41421i	0.878415	−	0.129641i
$120$		0			0
$121$	−9.00000			−0.818182
$122$	−4.40490	−	4.40490i	−0.398801	−	0.398801i
$123$		0			0
$124$	−9.89049			−0.888193
$125$	−9.69766	−	5.56376i	−0.867385	−	0.497638i
$126$		0			0
$127$	−5.70156	+	5.70156i	−0.505932	+	0.505932i	−0.913275	−	0.407343i	$-0.866455\pi$
$127$	−5.70156	+	5.70156i	−0.505932	+	0.505932i	0.407343	+	0.913275i	$0.366455\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	2.00000	−	11.4031i	0.175412	−	1.00012i
$131$		−	4.40490i		−	0.384858i	−0.981311	−	0.192429i	$-0.938364\pi$
$131$		−	4.40490i		−	0.384858i	0.981311	−	0.192429i	$-0.0616365\pi$
$132$		0			0
$133$	−7.49947	+	10.0963i	−0.650286	+	0.875464i
$134$		−	5.65685i		−	0.488678i
$135$		0			0
$136$		−	3.66103i		−	0.313931i
$137$	11.8838	−	11.8838i	1.01530	−	1.01530i	0.0154215	−	0.999881i	$-0.495091\pi$
$137$	11.8838	−	11.8838i	1.01530	−	1.01530i	0.999881	−	0.0154215i	$-0.00490902\pi$
$138$		0			0
$139$	−12.0757			−1.02425			−0.512123	−	0.858912i	$-0.671141\pi$
$139$	−12.0757			−1.02425			−0.512123	+	0.858912i	$0.671141\pi$
$140$	−4.06842	−	4.29511i	−0.343844	−	0.363003i
$141$		0			0
$142$	0.701562	−	0.701562i	0.0588738	−	0.0588738i
$143$	−5.17748	+	5.17748i	−0.432962	+	0.432962i
$144$		0			0
$145$	−3.11473	+	17.7588i	−0.258665	+	1.47479i
$146$			6.49206i			0.537287i
$147$		0			0
$148$	0.701562	+	0.701562i	0.0576681	+	0.0576681i
$149$		−	10.0475i		−	0.823127i	−0.911381	−	0.411563i	$-0.864983\pi$
$149$		−	10.0475i		−	0.823127i	0.911381	−	0.411563i	$-0.135017\pi$
$150$		0			0
$151$	18.8062			1.53043			0.765215	−	0.643774i	$-0.222632\pi$
$151$	18.8062			1.53043			0.765215	+	0.643774i	$0.222632\pi$
$152$	3.36131	+	3.36131i	0.272639	+	0.272639i
$153$		0			0
$154$	0.546295	+	3.70156i	0.0440217	+	0.298280i
$155$	−3.82059	+	21.7833i	−0.306877	+	1.74968i
$156$		0			0
$157$	−13.1683	−	13.1683i	−1.05094	−	1.05094i	−0.998631	−	0.0523109i	$-0.983341\pi$
$157$	−13.1683	−	13.1683i	−1.05094	−	1.05094i	−0.0523109	−	0.998631i	$-0.516659\pi$
$158$	5.23480	+	5.23480i	0.416458	+	0.416458i
$159$		0			0
$160$	−1.83051	+	1.28422i	−0.144715	+	0.101526i
$161$	−14.1421	+	2.08717i	−1.11456	+	0.164492i
$162$		0			0
$163$	−1.40312	−	1.40312i	−0.109901	−	0.109901i	0.650018	−	0.759919i	$-0.274761\pi$
$163$	−1.40312	−	1.40312i	−0.109901	−	0.109901i	−0.759919	+	0.650018i	$0.774761\pi$
$164$	−10.3550			−0.808586
$165$		0			0
$166$			11.3663i			0.882199i
$167$	−3.63232	−	3.63232i	−0.281077	−	0.281077i	0.552461	−	0.833539i	$-0.313689\pi$
$167$	−3.63232	−	3.63232i	−0.281077	−	0.281077i	−0.833539	+	0.552461i	$0.813689\pi$
$168$		0			0
$169$		−	13.8062i		−	1.06202i
$170$	−8.06323	−	1.41421i	−0.618421	−	0.108465i
$171$		0			0
$172$	−2.00000	+	2.00000i	−0.152499	+	0.152499i
$173$	−13.7163	+	13.7163i	−1.04283	+	1.04283i	−0.0437875	+	0.999041i	$0.513942\pi$
$173$	−13.7163	+	13.7163i	−1.04283	+	1.04283i	−0.999041	+	0.0437875i	$0.986058\pi$
$174$		0			0
$175$	−11.0313	+	7.30134i	−0.833891	+	0.551929i
$176$	1.41421			0.106600
$177$		0			0
$178$	8.79790	−	8.79790i	0.659431	−	0.659431i
$179$		−	3.39853i		−	0.254018i	−0.991902	−	0.127009i	$-0.959462\pi$
$179$		−	3.39853i		−	0.254018i	0.991902	−	0.127009i	$-0.0405377\pi$
$180$		0			0
$181$			3.27777i			0.243635i	0.992553	+	0.121817i	$0.0388722\pi$
$181$			3.27777i			0.243635i	−0.992553	+	0.121817i	$0.961128\pi$
$182$	−10.9966	−	8.16816i	−0.815121	−	0.605464i
$183$		0			0
$184$			5.40312i			0.398324i
$185$	1.81616	−	1.27415i	0.133527	−	0.0936773i
$186$		0			0
$187$	3.66103	+	3.66103i	0.267721	+	0.267721i
$188$	1.54515	−	1.54515i	0.112692	−	0.112692i
$189$		0			0
$190$	8.70156	−	6.10469i	0.631278	−	0.442880i
$191$	−2.97648			−0.215370			−0.107685	−	0.994185i	$-0.534344\pi$
$191$	−2.97648			−0.215370			−0.107685	+	0.994185i	$0.534344\pi$
$192$		0			0
$193$	−11.0000	−	11.0000i	−0.791797	−	0.791797i	0.189989	−	0.981786i	$-0.439155\pi$
$193$	−11.0000	−	11.0000i	−0.791797	−	0.791797i	−0.981786	+	0.189989i	$0.939155\pi$
$194$	2.31773			0.166403
$195$		0			0
$196$	−6.70156	+	2.02214i	−0.478683	+	0.144439i
$197$	−7.49312	+	7.49312i	−0.533863	+	0.533863i	−0.921720	−	0.387857i	$-0.873216\pi$
$197$	−7.49312	+	7.49312i	−0.533863	+	0.533863i	0.387857	+	0.921720i	$0.373216\pi$
$198$		0			0
$199$	11.7496			0.832907			0.416454	−	0.909157i	$-0.363273\pi$
$199$	11.7496			0.832907			0.416454	+	0.909157i	$0.363273\pi$
$200$	2.12132	+	4.52769i	0.150000	+	0.320156i
$201$		0			0
$202$	−5.68317	−	5.68317i	−0.399867	−	0.399867i
$203$	17.1257	+	12.7208i	1.20199	+	0.892826i
$204$		0			0
$205$	−4.00000	+	22.8062i	−0.279372	+	1.59286i
$206$		−	16.8470i		−	1.17379i
$207$		0			0
$208$	−3.66103	+	3.66103i	−0.253847	+	0.253847i
$209$	−6.72263			−0.465014
$210$		0			0
$211$	14.8062			1.01930			0.509652	−	0.860381i	$-0.329774\pi$
$211$	14.8062			1.01930			0.509652	+	0.860381i	$0.329774\pi$
$212$	6.64901	−	6.64901i	0.456656	−	0.456656i
$213$		0			0
$214$			13.4031i			0.916219i
$215$	3.63232	+	5.17748i	0.247722	+	0.353101i
$216$		0			0
$217$	21.0067	+	15.6036i	1.42603	+	1.05924i
$218$	−0.422055	−	0.422055i	−0.0285852	−	0.0285852i
$219$		0			0
$220$	0.546295	−	3.11473i	0.0368312	−	0.209995i
$221$	−18.9549			−1.27504
$222$		0			0
$223$	4.20732	−	4.20732i	0.281743	−	0.281743i	−0.552061	−	0.833804i	$-0.686158\pi$
$223$	4.20732	−	4.20732i	0.281743	−	0.281743i	0.833804	+	0.552061i	$0.186158\pi$
$224$	0.386289	+	2.61740i	0.0258100	+	0.174882i
$225$		0			0
$226$	−8.80625			−0.585783
$227$	17.0776	+	17.0776i	1.13348	+	1.13348i	0.989595	+	0.143884i	$0.0459593\pi$
$227$	17.0776	+	17.0776i	1.13348	+	1.13348i	0.143884	+	0.989595i	$0.454041\pi$
$228$		0			0
$229$	−1.85911			−0.122853			−0.0614267	−	0.998112i	$-0.519565\pi$
$229$	−1.85911			−0.122853			−0.0614267	+	0.998112i	$0.519565\pi$
$230$	11.9001	+	2.08717i	0.784670	+	0.137624i
$231$		0			0
$232$	5.70156	−	5.70156i	0.374326	−	0.374326i
$233$	−4.24264	−	4.24264i	−0.277945	−	0.277945i	0.554343	−	0.832288i	$-0.312969\pi$
$233$	−4.24264	−	4.24264i	−0.277945	−	0.277945i	−0.832288	+	0.554343i	$0.812969\pi$
$234$		0			0
$235$	−2.80625	−	4.00000i	−0.183059	−	0.260931i
$236$		−	7.49521i		−	0.487896i
$237$		0			0
$238$	−5.77576	+	7.77576i	−0.374387	+	0.504028i
$239$		−	23.6196i		−	1.52782i	−0.645321	−	0.763912i	$-0.723276\pi$
$239$		−	23.6196i		−	1.52782i	0.645321	−	0.763912i	$-0.276724\pi$
$240$		0			0
$241$		−	23.8253i		−	1.53472i	−0.641216	−	0.767360i	$-0.721570\pi$
$241$		−	23.8253i		−	1.53472i	0.641216	−	0.767360i	$-0.278430\pi$
$242$	6.36396	−	6.36396i	0.409091	−	0.409091i
$243$		0			0
$244$	6.22947			0.398801
$245$	1.86493	+	15.5410i	0.119146	+	0.992877i
$246$		0			0
$247$	17.4031	−	17.4031i	1.10733	−	1.10733i
$248$	6.99364	−	6.99364i	0.444096	−	0.444096i
$249$		0			0
$250$	10.7915	−	2.92310i	0.682511	−	0.184873i
$251$			0.230566i			0.0145532i	0.999974	+	0.00727661i	$0.00231624\pi$
$251$			0.230566i			0.0145532i	−0.999974	+	0.00727661i	$0.997684\pi$
$252$		0			0
$253$	−5.40312	−	5.40312i	−0.339692	−	0.339692i
$254$		−	8.06323i		−	0.505932i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−7.76621	−	7.76621i	−0.484443	−	0.484443i	0.422104	−	0.906547i	$-0.361292\pi$
$257$	−7.76621	−	7.76621i	−0.484443	−	0.484443i	−0.906547	+	0.422104i	$0.861292\pi$
$258$		0			0
$259$	−0.383260	−	2.59688i	−0.0238146	−	0.161362i
$260$	6.64901	+	9.47744i	0.412354	+	0.587766i
$261$		0			0
$262$	3.11473	+	3.11473i	0.192429	+	0.192429i
$263$	11.3137	+	11.3137i	0.697633	+	0.697633i	0.963899	−	0.266266i	$-0.0857901\pi$
$263$	11.3137	+	11.3137i	0.697633	+	0.697633i	−0.266266	+	0.963899i	$0.585790\pi$
$264$		0			0
$265$	−12.0757	−	17.2125i	−0.741803	−	1.05736i
$266$	−1.83627	−	12.4421i	−0.112589	−	0.762875i
$267$		0			0
$268$	4.00000	+	4.00000i	0.244339	+	0.244339i
$269$	−3.86289			−0.235524			−0.117762	−	0.993042i	$-0.537572\pi$
$269$	−3.86289			−0.235524			−0.117762	+	0.993042i	$0.537572\pi$
$270$		0			0
$271$			13.1683i			0.799915i	0.916534	+	0.399957i	$0.130975\pi$
$271$			13.1683i			0.799915i	−0.916534	+	0.399957i	$0.869025\pi$
$272$	2.58874	+	2.58874i	0.156965	+	0.156965i
$273$		0			0
$274$			16.8062i			1.01530i
$275$	−6.64901	−	2.40637i	−0.400951	−	0.145110i
$276$		0			0
$277$	−14.1047	+	14.1047i	−0.847468	+	0.847468i	−0.989817	−	0.142348i	$-0.954535\pi$
$277$	−14.1047	+	14.1047i	−0.847468	+	0.847468i	0.142348	+	0.989817i	$0.454535\pi$
$278$	8.53879	−	8.53879i	0.512123	−	0.512123i
$279$		0			0
$280$	5.91391	+	0.160291i	0.353424	+	0.00957921i
$281$	19.7990			1.18111			0.590554	−	0.806998i	$-0.298909\pi$
$281$	19.7990			1.18111			0.590554	+	0.806998i	$0.298909\pi$
$282$		0			0
$283$	20.8736	−	20.8736i	1.24081	−	1.24081i	0.281138	−	0.959667i	$-0.409288\pi$
$283$	20.8736	−	20.8736i	1.24081	−	1.24081i	0.959667	−	0.281138i	$-0.0907119\pi$
$284$			0.992159i			0.0588738i
$285$		0			0
$286$		−	7.32206i		−	0.432962i
$287$	21.9932	+	16.3363i	1.29822	+	0.964302i
$288$		0			0
$289$		−	3.59688i		−	0.211581i
$290$	−10.3550	−	14.7598i	−0.608064	−	0.866728i
$291$		0			0
$292$	−4.59058	−	4.59058i	−0.268643	−	0.268643i
$293$	−16.0340	+	16.0340i	−0.936716	+	0.936716i	−0.998113	−	0.0613973i	$-0.980444\pi$
$293$	−16.0340	+	16.0340i	−0.936716	+	0.936716i	0.0613973	+	0.998113i	$0.480444\pi$
$294$		0			0
$295$	−16.5078	−	2.89531i	−0.961122	−	0.168572i
$296$	−0.992159			−0.0576681
$297$		0			0
$298$	7.10469	+	7.10469i	0.411563	+	0.411563i
$299$	27.9745			1.61781
$300$		0			0
$301$	7.40312	−	1.09259i	0.426709	−	0.0629758i
$302$	−13.2980	+	13.2980i	−0.765215	+	0.765215i
$303$		0			0
$304$	−4.75362			−0.272639
$305$	2.40637	−	13.7201i	0.137788	−	0.785610i
$306$		0			0
$307$	−0.383260	−	0.383260i	−0.0218738	−	0.0218738i	0.696085	−	0.717959i	$-0.254924\pi$
$307$	−0.383260	−	0.383260i	−0.0218738	−	0.0218738i	−0.717959	+	0.696085i	$0.754924\pi$
$308$	−3.00369	−	2.23111i	−0.171151	−	0.127129i
$309$		0			0
$310$	−12.7016	−	18.1047i	−0.721400	−	1.02828i
$311$			19.1647i			1.08673i	0.839496	+	0.543367i	$0.182851\pi$
$311$			19.1647i			1.08673i	−0.839496	+	0.543367i	$0.817149\pi$
$312$		0			0
$313$	10.0535	−	10.0535i	0.568259	−	0.568259i	−0.363381	−	0.931640i	$-0.618378\pi$
$313$	10.0535	−	10.0535i	0.568259	−	0.568259i	0.931640	+	0.363381i	$0.118378\pi$
$314$	18.6227			1.05094
$315$		0			0
$316$	−7.40312			−0.416458
$317$	1.41421	−	1.41421i	0.0794301	−	0.0794301i	−0.666276	−	0.745706i	$-0.732113\pi$
$317$	1.41421	−	1.41421i	0.0794301	−	0.0794301i	0.745706	+	0.666276i	$0.232113\pi$
$318$		0			0
$319$			11.4031i			0.638452i
$320$	0.386289	−	2.20245i	0.0215942	−	0.123121i
$321$		0			0
$322$	8.52415	−	11.4758i	0.475032	−	0.639524i
$323$	−12.3059	−	12.3059i	−0.684717	−	0.684717i
$324$		0			0
$325$	23.4420	−	10.9831i	1.30033	−	0.609232i
$326$	1.98432			0.109901
$327$		0			0
$328$	7.32206	−	7.32206i	0.404293	−	0.404293i
$329$	−5.71949	+	0.844110i	−0.315325	+	0.0465373i
$330$		0			0
$331$	25.6125			1.40779			0.703895	−	0.710304i	$-0.251443\pi$
$331$	25.6125			1.40779			0.703895	+	0.710304i	$0.251443\pi$
$332$	−8.03722	−	8.03722i	−0.441100	−	0.441100i
$333$		0			0
$334$	5.13688			0.281077
$335$	10.3550	−	7.26464i	0.565751	−	0.396910i
$336$		0			0
$337$	−1.00000	+	1.00000i	−0.0544735	+	0.0544735i	−0.733819	−	0.679345i	$-0.762264\pi$
$337$	−1.00000	+	1.00000i	−0.0544735	+	0.0544735i	0.679345	+	0.733819i	$0.262264\pi$
$338$	9.76249	+	9.76249i	0.531010	+	0.531010i
$339$		0			0
$340$	6.70156	−	4.70156i	0.363443	−	0.254978i
$341$			13.9873i			0.757453i
$342$		0			0
$343$	17.4238	+	6.27772i	0.940799	+	0.338965i
$344$		−	2.82843i		−	0.152499i
$345$		0			0
$346$		−	19.3977i		−	1.04283i
$347$	−10.0475	+	10.0475i	−0.539380	+	0.539380i	−0.923347	−	0.383967i	$-0.874558\pi$
$347$	−10.0475	+	10.0475i	−0.539380	+	0.539380i	0.383967	+	0.923347i	$0.374558\pi$
$348$		0			0
$349$	23.0588			1.23431			0.617153	−	0.786843i	$-0.288286\pi$
$349$	23.0588			1.23431			0.617153	+	0.786843i	$0.288286\pi$
$350$	2.63751	−	12.9632i	0.140981	−	0.692910i
$351$		0			0
$352$	−1.00000	+	1.00000i	−0.0533002	+	0.0533002i
$353$	14.4888	−	14.4888i	0.771163	−	0.771163i	−0.207147	−	0.978310i	$-0.566418\pi$
$353$	14.4888	−	14.4888i	0.771163	−	0.771163i	0.978310	+	0.207147i	$0.0664177\pi$
$354$		0			0
$355$	2.18518	+	0.383260i	0.115977	+	0.0203413i
$356$			12.4421i			0.659431i
$357$		0			0
$358$	2.40312	+	2.40312i	0.127009	+	0.127009i
$359$			28.4323i			1.50060i	0.661097	+	0.750300i	$0.270091\pi$
$359$			28.4323i			1.50060i	−0.661097	+	0.750300i	$0.729909\pi$
$360$		0			0
$361$	3.59688			0.189309
$362$	−2.31773	−	2.31773i	−0.121817	−	0.121817i
$363$		0			0
$364$	13.5515	−	2.00000i	0.710293	−	0.104828i
$365$	−11.8838	+	8.33723i	−0.622027	+	0.436391i
$366$		0			0
$367$	−8.25161	−	8.25161i	−0.430731	−	0.430731i	0.458146	−	0.888877i	$-0.348514\pi$
$367$	−8.25161	−	8.25161i	−0.430731	−	0.430731i	−0.888877	+	0.458146i	$0.848514\pi$
$368$	−3.82059	−	3.82059i	−0.199162	−	0.199162i
$369$		0			0
$370$	−0.383260	+	2.18518i	−0.0199247	+	0.113602i
$371$	−24.6117	+	3.63232i	−1.27778	+	0.188581i
$372$		0			0
$373$	2.70156	+	2.70156i	0.139882	+	0.139882i	0.773580	−	0.633699i	$-0.218464\pi$
$373$	2.70156	+	2.70156i	0.139882	+	0.139882i	−0.633699	+	0.773580i	$0.718464\pi$
$374$	−5.17748			−0.267721
$375$		0			0
$376$			2.18518i			0.112692i
$377$	−29.5197	−	29.5197i	−1.52034	−	1.52034i
$378$		0			0
$379$			33.6125i			1.72656i	0.504727	+	0.863279i	$0.331593\pi$
$379$			33.6125i			1.72656i	−0.504727	+	0.863279i	$0.668407\pi$
$380$	−1.83627	+	10.4696i	−0.0941986	+	0.537079i
$381$		0			0
$382$	2.10469	−	2.10469i	0.107685	−	0.107685i
$383$	21.2519	−	21.2519i	1.08592	−	1.08592i	0.0899782	−	0.995944i	$-0.471320\pi$
$383$	21.2519	−	21.2519i	1.08592	−	1.08592i	0.995944	−	0.0899782i	$-0.0286797\pi$
$384$		0			0
$385$	−6.07420	+	5.75362i	−0.309570	+	0.293231i
$386$	15.5563			0.791797
$387$		0			0
$388$	−1.63888	+	1.63888i	−0.0832017	+	0.0832017i
$389$			22.2054i			1.12586i	0.826506	+	0.562928i	$0.190325\pi$
$389$			22.2054i			1.12586i	−0.826506	+	0.562928i	$0.809675\pi$
$390$		0			0
$391$		−	19.7810i		−	1.00037i
$392$	3.30885	−	6.16859i	0.167122	−	0.311561i
$393$		0			0
$394$		−	10.5969i		−	0.533863i
$395$	−2.85974	+	16.3050i	−0.143889	+	0.820394i
$396$		0			0
$397$	4.75362	+	4.75362i	0.238577	+	0.238577i	0.816261	−	0.577684i	$-0.196043\pi$
$397$	4.75362	+	4.75362i	0.238577	+	0.238577i	−0.577684	+	0.816261i	$0.696043\pi$
$398$	−8.30822	+	8.30822i	−0.416454	+	0.416454i
$399$		0			0
$400$	−4.70156	−	1.70156i	−0.235078	−	0.0850781i
$401$	31.4088			1.56848			0.784240	−	0.620457i	$-0.213053\pi$
$401$	31.4088			1.56848			0.784240	+	0.620457i	$0.213053\pi$
$402$		0			0
$403$	−36.2094	−	36.2094i	−1.80372	−	1.80372i
$404$	8.03722			0.399867
$405$		0			0
$406$	−21.1047	+	3.11473i	−1.04741	+	0.154582i
$407$	0.992159	−	0.992159i	0.0491795	−	0.0491795i
$408$		0			0
$409$	−6.22947			−0.308027			−0.154014	−	0.988069i	$-0.549220\pi$
$409$	−6.22947			−0.308027			−0.154014	+	0.988069i	$0.549220\pi$
$410$	−13.2980	−	18.9549i	−0.656743	−	0.936115i
$411$		0			0
$412$	11.9126	+	11.9126i	0.586894	+	0.586894i
$413$	−11.8247	+	15.9193i	−0.581855	+	0.783337i
$414$		0			0
$415$	−20.8062	+	14.5969i	−1.02134	+	0.716532i
$416$		−	5.17748i		−	0.253847i
$417$		0			0
$418$	4.75362	−	4.75362i	0.232507	−	0.232507i
$419$	−23.5696			−1.15145			−0.575726	−	0.817643i	$-0.695281\pi$
$419$	−23.5696			−1.15145			−0.575726	+	0.817643i	$0.695281\pi$
$420$		0			0
$421$	19.4031			0.945650			0.472825	−	0.881156i	$-0.343234\pi$
$421$	19.4031			0.945650			0.472825	+	0.881156i	$0.343234\pi$
$422$	−10.4696	+	10.4696i	−0.509652	+	0.509652i
$423$		0			0
$424$			9.40312i			0.456656i
$425$	−7.76621	−	16.5760i	−0.376717	−	0.804055i
$426$		0			0
$427$	−13.2309	−	9.82782i	−0.640290	−	0.475601i
$428$	−9.47744	−	9.47744i	−0.458109	−	0.458109i
$429$		0			0
$430$	−6.22947	−	1.09259i	−0.300412	−	0.0526893i
$431$	0.148049			0.00713126			0.00356563	−	0.999994i	$-0.498865\pi$
$431$	0.148049			0.00713126			0.00356563	+	0.999994i	$0.498865\pi$
$432$		0			0
$433$	−8.96094	+	8.96094i	−0.430635	+	0.430635i	−0.888844	−	0.458209i	$-0.848491\pi$
$433$	−8.96094	+	8.96094i	−0.430635	+	0.430635i	0.458209	+	0.888844i	$0.348491\pi$
$434$	−25.8874	+	3.82059i	−1.24263	+	0.183394i
$435$		0			0
$436$	0.596876			0.0285852
$437$	18.1616	+	18.1616i	0.868787	+	0.868787i
$438$		0			0
$439$	1.47585			0.0704384			0.0352192	−	0.999380i	$-0.488787\pi$
$439$	1.47585			0.0704384			0.0352192	+	0.999380i	$0.488787\pi$
$440$	1.81616	+	2.58874i	0.0865820	+	0.123413i
$441$		0			0
$442$	13.4031	−	13.4031i	0.637522	−	0.637522i
$443$	−16.5485	−	16.5485i	−0.786243	−	0.786243i	0.194633	−	0.980876i	$-0.437648\pi$
$443$	−16.5485	−	16.5485i	−0.786243	−	0.786243i	−0.980876	+	0.194633i	$0.937648\pi$
$444$		0			0
$445$	27.4031	+	4.80625i	1.29903	+	0.227838i
$446$			5.95005i			0.281743i
$447$		0			0
$448$	−2.12393	−	1.57763i	−0.100346	−	0.0745362i
$449$		−	17.8147i		−	0.840726i	−0.907356	−	0.420363i	$-0.861903\pi$
$449$		−	17.8147i		−	0.840726i	0.907356	−	0.420363i	$-0.138097\pi$
$450$		0			0
$451$			14.6441i			0.689564i
$452$	6.22696	−	6.22696i	0.292891	−	0.292891i
$453$		0			0
$454$	−24.1513			−1.13348
$455$	0.829902	−	30.6191i	0.0389064	−	1.43545i
$456$		0			0
$457$	−5.80625	+	5.80625i	−0.271605	+	0.271605i	−0.829746	−	0.558141i	$-0.811515\pi$
$457$	−5.80625	+	5.80625i	−0.271605	+	0.271605i	0.558141	+	0.829746i	$0.311515\pi$
$458$	1.31459	−	1.31459i	0.0614267	−	0.0614267i
$459$		0			0
$460$	−9.89049	+	6.93880i	−0.461147	+	0.323523i
$461$		−	1.31459i		−	0.0612265i	−0.999531	−	0.0306132i	$-0.990254\pi$
$461$		−	1.31459i		−	0.0612265i	0.999531	−	0.0306132i	$-0.00974602\pi$
$462$		0			0
$463$	−13.1047	−	13.1047i	−0.609026	−	0.609026i	0.333665	−	0.942692i	$-0.391714\pi$
$463$	−13.1047	−	13.1047i	−0.609026	−	0.609026i	−0.942692	+	0.333665i	$0.891714\pi$
$464$			8.06323i			0.374326i
$465$		0			0
$466$	6.00000			0.277945
$467$	−5.40804	−	5.40804i	−0.250254	−	0.250254i	0.570821	−	0.821075i	$-0.306625\pi$
$467$	−5.40804	−	5.40804i	−0.250254	−	0.250254i	−0.821075	+	0.570821i	$0.806625\pi$
$468$		0			0
$469$	−2.18518	−	14.8062i	−0.100902	−	0.683689i
$470$	4.81274	+	0.844110i	0.221995	+	0.0389359i
$471$		0			0
$472$	5.29991	+	5.29991i	0.243948	+	0.243948i
$473$	2.82843	+	2.82843i	0.130051	+	0.130051i
$474$		0			0
$475$	22.3494	+	8.08857i	1.02546	+	0.371129i
$476$	−1.41421	−	9.58237i	−0.0648204	−	0.439207i
$477$		0			0
$478$	16.7016	+	16.7016i	0.763912	+	0.763912i
$479$	4.63546			0.211800			0.105900	−	0.994377i	$-0.466228\pi$
$479$	4.63546			0.211800			0.105900	+	0.994377i	$0.466228\pi$
$480$		0			0
$481$			5.13688i			0.234221i
$482$	16.8470	+	16.8470i	0.767360	+	0.767360i
$483$		0			0
$484$			9.00000i			0.409091i
$485$	2.97648	+	4.24264i	0.135155	+	0.192648i
$486$		0			0
$487$	16.5078	−	16.5078i	0.748040	−	0.748040i	−0.226071	−	0.974111i	$-0.572588\pi$
$487$	16.5078	−	16.5078i	0.748040	−	0.748040i	0.974111	+	0.226071i	$0.0725880\pi$
$488$	−4.40490	+	4.40490i	−0.199400	+	0.199400i
$489$		0			0
$490$	−12.3078	−	9.67043i	−0.556011	−	0.436865i
$491$	40.1681			1.81276			0.906380	−	0.422463i	$-0.138834\pi$
$491$	40.1681			1.81276			0.906380	+	0.422463i	$0.138834\pi$
$492$		0			0
$493$	−20.8736	+	20.8736i	−0.940099	+	0.940099i
$494$			24.6117i			1.10733i
$495$		0			0
$496$			9.89049i			0.444096i
$497$	1.56526	−	2.10727i	0.0702116	−	0.0945242i
$498$		0			0
$499$			8.00000i			0.358129i	0.983837	+	0.179065i	$0.0573071\pi$
$499$			8.00000i			0.358129i	−0.983837	+	0.179065i	$0.942693\pi$
$500$	−5.56376	+	9.69766i	−0.248819	+	0.433692i
$501$		0			0
$502$	−0.163035	−	0.163035i	−0.00727661	−	0.00727661i
$503$	−13.9873	+	13.9873i	−0.623662	+	0.623662i	−0.946466	−	0.322804i	$-0.895374\pi$
$503$	−13.9873	+	13.9873i	−0.623662	+	0.623662i	0.322804	+	0.946466i	$0.395374\pi$
$504$		0			0
$505$	3.10469	−	17.7016i	0.138157	−	0.787709i
$506$	7.64117			0.339692
$507$		0			0
$508$	5.70156	+	5.70156i	0.252966	+	0.252966i
$509$	−20.9405			−0.928170			−0.464085	−	0.885791i	$-0.653617\pi$
$509$	−20.9405			−0.928170			−0.464085	+	0.885791i	$0.653617\pi$
$510$		0			0
$511$	2.50781	+	16.9923i	0.110939	+	0.751696i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$	10.9831			0.484443
$515$	30.8387	−	21.6353i	1.35892	−	0.953363i
$516$		0			0
$517$	−2.18518	−	2.18518i	−0.0961041	−	0.0961041i
$518$	2.10727	+	1.56526i	0.0925883	+	0.0687737i
$519$		0			0
$520$	−11.4031	−	2.00000i	−0.500060	−	0.0877058i
$521$		−	39.3326i		−	1.72319i	−0.507593	−	0.861597i	$-0.669465\pi$
$521$		−	39.3326i		−	1.72319i	0.507593	−	0.861597i	$-0.330535\pi$
$522$		0			0
$523$	−5.84621	+	5.84621i	−0.255637	+	0.255637i	−0.823277	−	0.567640i	$-0.807857\pi$
$523$	−5.84621	+	5.84621i	−0.255637	+	0.255637i	0.567640	+	0.823277i	$0.307857\pi$
$524$	−4.40490			−0.192429
$525$		0			0
$526$	−16.0000			−0.697633
$527$	−25.6039	+	25.6039i	−1.11532	+	1.11532i
$528$		0			0
$529$			6.19375i			0.269294i
$530$	20.7099	+	3.63232i	0.899581	+	0.157778i
$531$		0			0
$532$	10.0963	+	7.49947i	0.437732	+	0.325143i
$533$	−37.9098	−	37.9098i	−1.64205	−	1.64205i
$534$		0			0
$535$	−24.5346	+	17.2125i	−1.06072	+	0.744163i
$536$	−5.65685			−0.244339
$537$		0			0
$538$	2.73147	−	2.73147i	0.117762	−	0.117762i
$539$	2.85974	+	9.47744i	0.123178	+	0.408222i
$540$		0			0
$541$	−18.0000			−0.773880			−0.386940	−	0.922105i	$-0.626468\pi$
$541$	−18.0000			−0.773880			−0.386940	+	0.922105i	$0.626468\pi$
$542$	−9.31137	−	9.31137i	−0.399957	−	0.399957i
$543$		0			0
$544$	−3.66103			−0.156965
$545$	0.230566	−	1.31459i	0.00987638	−	0.0563108i
$546$		0			0
$547$	−16.5969	+	16.5969i	−0.709631	+	0.709631i	−0.966458	−	0.256826i	$-0.917323\pi$
$547$	−16.5969	+	16.5969i	−0.709631	+	0.709631i	0.256826	+	0.966458i	$0.417323\pi$
$548$	−11.8838	−	11.8838i	−0.507651	−	0.507651i
$549$		0			0
$550$	6.40312	−	3.00000i	0.273030	−	0.127920i
$551$		−	38.3295i		−	1.63289i
$552$		0			0
$553$	15.7237	+	11.6794i	0.668640	+	0.496659i
$554$		−	19.9470i		−	0.847468i
$555$		0			0
$556$			12.0757i			0.512123i
$557$	1.83627	−	1.83627i	0.0778052	−	0.0778052i	−0.667133	−	0.744938i	$-0.732479\pi$
$557$	1.83627	−	1.83627i	0.0778052	−	0.0778052i	0.744938	+	0.667133i	$0.232479\pi$
$558$		0			0
$559$	−14.6441			−0.619380
$560$	−4.29511	+	4.06842i	−0.181501	+	0.171922i
$561$		0			0
$562$	−14.0000	+	14.0000i	−0.590554	+	0.590554i
$563$	−14.5293	+	14.5293i	−0.612336	+	0.612336i	−0.943554	−	0.331218i	$-0.892540\pi$
$563$	−14.5293	+	14.5293i	−0.612336	+	0.612336i	0.331218	+	0.943554i	$0.392540\pi$
$564$		0			0
$565$	−11.3092	−	16.1200i	−0.475780	−	0.678172i
$566$			29.5197i			1.24081i
$567$		0			0
$568$	−0.701562	−	0.701562i	−0.0294369	−	0.0294369i
$569$			8.78138i			0.368135i	0.982914	+	0.184067i	$0.0589264\pi$
$569$			8.78138i			0.368135i	−0.982914	+	0.184067i	$0.941074\pi$
$570$		0			0
$571$		0			0			−	1.00000i	$-0.5\pi$
$571$		0			0				1.00000i	$0.5\pi$
$572$	5.17748	+	5.17748i	0.216481	+	0.216481i
$573$		0			0
$574$	−27.1030	+	4.00000i	−1.13126	+	0.166957i
$575$	11.4618	+	24.4637i	0.477988	+	1.02021i
$576$		0			0
$577$	10.8200	+	10.8200i	0.450445	+	0.450445i	0.895502	−	0.445057i	$-0.146817\pi$
$577$	10.8200	+	10.8200i	0.450445	+	0.450445i	−0.445057	+	0.895502i	$0.646817\pi$
$578$	2.54338	+	2.54338i	0.105790	+	0.105790i
$579$		0			0
$580$	17.7588	+	3.11473i	0.737396	+	0.129332i
$581$	4.39069	+	29.7503i	0.182156	+	1.23425i
$582$		0			0
$583$	−9.40312	−	9.40312i	−0.389438	−	0.389438i
$584$	6.49206			0.268643
$585$		0			0
$586$		−	22.6755i		−	0.936716i
$587$	−11.6695	−	11.6695i	−0.481653	−	0.481653i	0.424006	−	0.905659i	$-0.360624\pi$
$587$	−11.6695	−	11.6695i	−0.481653	−	0.481653i	−0.905659	+	0.424006i	$0.860624\pi$
$588$		0			0
$589$		−	47.0156i		−	1.93724i
$590$	13.7201	−	9.62549i	0.564847	−	0.396275i
$591$		0			0
$592$	0.701562	−	0.701562i	0.0288340	−	0.0288340i
$593$	19.1243	−	19.1243i	0.785341	−	0.785341i	−0.195385	−	0.980727i	$-0.562596\pi$
$593$	19.1243	−	19.1243i	0.785341	−	0.785341i	0.980727	+	0.195385i	$0.0625958\pi$
$594$		0			0
$595$	−21.6510	−	0.586829i	−0.887604	−	0.0240576i
$596$	−10.0475			−0.411563
$597$		0			0
$598$	−19.7810	+	19.7810i	−0.808905	+	0.808905i
$599$			20.7911i			0.849503i	0.905310	+	0.424752i	$0.139639\pi$
$599$			20.7911i			0.849503i	−0.905310	+	0.424752i	$0.860361\pi$
$600$		0			0
$601$			27.8696i			1.13682i	0.822744	+	0.568412i	$0.192442\pi$
$601$			27.8696i			1.13682i	−0.822744	+	0.568412i	$0.807558\pi$
$602$	−4.46222	+	6.00738i	−0.181867	+	0.244842i
$603$		0			0
$604$		−	18.8062i		−	0.765215i
$605$	19.8220	+	3.47660i	0.805881	+	0.141344i
$606$		0			0
$607$	2.02214	+	2.02214i	0.0820763	+	0.0820763i	0.746953	−	0.664877i	$-0.231516\pi$
$607$	2.02214	+	2.02214i	0.0820763	+	0.0820763i	−0.664877	+	0.746953i	$0.731516\pi$
$608$	3.36131	−	3.36131i	0.136319	−	0.136319i
$609$		0			0
$610$	8.00000	+	11.4031i	0.323911	+	0.461699i
$611$	11.3137			0.457704
$612$		0			0
$613$	−15.2984	−	15.2984i	−0.617898	−	0.617898i	0.327094	−	0.944992i	$-0.393931\pi$
$613$	−15.2984	−	15.2984i	−0.617898	−	0.617898i	−0.944992	+	0.327094i	$0.893931\pi$
$614$	0.542011			0.0218738
$615$		0			0
$616$	3.70156	−	0.546295i	0.149140	−	0.0220108i
$617$	−30.8387	+	30.8387i	−1.24152	+	1.24152i	−0.282148	+	0.959371i	$0.591047\pi$
$617$	−30.8387	+	30.8387i	−1.24152	+	1.24152i	−0.959371	+	0.282148i	$0.908953\pi$
$618$		0			0
$619$	−34.8084			−1.39907			−0.699533	−	0.714600i	$-0.746609\pi$
$619$	−34.8084			−1.39907			−0.699533	+	0.714600i	$0.746609\pi$
$620$	21.7833	+	3.82059i	0.874839	+	0.153438i
$621$		0			0
$622$	−13.5515	−	13.5515i	−0.543367	−	0.543367i
$623$	19.6291	−	26.4262i	0.786423	−	1.05874i
$624$		0			0
$625$	19.2094	+	16.0000i	0.768375	+	0.640000i
$626$			14.2178i			0.568259i
$627$		0			0
$628$	−13.1683	+	13.1683i	−0.525471	+	0.525471i
$629$	3.63232			0.144830
$630$		0			0
$631$	8.59688			0.342236			0.171118	−	0.985251i	$-0.445262\pi$
$631$	8.59688			0.342236			0.171118	+	0.985251i	$0.445262\pi$
$632$	5.23480	−	5.23480i	0.208229	−	0.208229i
$633$		0			0
$634$			2.00000i			0.0794301i
$635$	14.7598	−	10.3550i	0.585727	−	0.410924i
$636$		0			0
$637$	−31.9377	−	17.1315i	−1.26542	−	0.678774i
$638$	−8.06323	−	8.06323i	−0.319226	−	0.319226i
$639$		0			0
$640$	1.28422	+	1.83051i	0.0507632	+	0.0723574i
$641$	−47.2392			−1.86583			−0.932917	−	0.360091i	$-0.882746\pi$
$641$	−47.2392			−1.86583			−0.932917	+	0.360091i	$0.882746\pi$
$642$		0			0
$643$	−10.9831	+	10.9831i	−0.433131	+	0.433131i	−0.889692	−	0.456561i	$-0.849081\pi$
$643$	−10.9831	+	10.9831i	−0.433131	+	0.433131i	0.456561	+	0.889692i	$0.349081\pi$
$644$	2.08717	+	14.1421i	0.0822459	+	0.557278i
$645$		0			0
$646$	17.4031			0.684717
$647$	−22.7971	−	22.7971i	−0.896245	−	0.896245i	0.0988565	−	0.995102i	$-0.468482\pi$
$647$	−22.7971	−	22.7971i	−0.896245	−	0.896245i	−0.995102	+	0.0988565i	$0.968482\pi$
$648$		0			0
$649$	−10.5998			−0.416079
$650$	−8.80980	+	24.3422i	−0.345549	+	0.954780i
$651$		0			0
$652$	−1.40312	+	1.40312i	−0.0549506	+	0.0549506i
$653$	−0.570104	−	0.570104i	−0.0223099	−	0.0223099i	0.695864	−	0.718174i	$-0.255022\pi$
$653$	−0.570104	−	0.570104i	−0.0223099	−	0.0223099i	−0.718174	+	0.695864i	$0.755022\pi$
$654$		0			0
$655$	−1.70156	+	9.70156i	−0.0664855	+	0.379071i
$656$			10.3550i			0.404293i
$657$		0			0
$658$	3.44741	−	4.64116i	0.134394	−	0.180931i
$659$			15.8524i			0.617524i	0.951139	+	0.308762i	$0.0999146\pi$
$659$			15.8524i			0.617524i	−0.951139	+	0.308762i	$0.900085\pi$
$660$		0			0
$661$			31.1473i			1.21149i	0.795659	+	0.605745i	$0.207125\pi$
$661$			31.1473i			1.21149i	−0.795659	+	0.605745i	$0.792875\pi$
$662$	−18.1108	+	18.1108i	−0.703895	+	0.703895i
$663$		0			0
$664$	11.3663			0.441100
$665$	20.4173	−	19.3397i	0.791749	−	0.749962i
$666$		0			0
$667$	30.8062	−	30.8062i	1.19282	−	1.19282i
$668$	−3.63232	+	3.63232i	−0.140539	+	0.140539i
$669$		0			0
$670$	−2.18518	+	12.4589i	−0.0844208	+	0.481331i
$671$		−	8.80980i		−	0.340098i
$672$		0			0
$673$	33.8062	+	33.8062i	1.30314	+	1.30314i	0.926267	+	0.376868i	$0.122999\pi$
$673$	33.8062	+	33.8062i	1.30314	+	1.30314i	0.376868	+	0.926267i	$0.377001\pi$
$674$		−	1.41421i		−	0.0544735i
$675$		0			0
$676$	−13.8062			−0.531010
$677$	18.3517	+	18.3517i	0.705314	+	0.705314i	0.965546	−	0.260232i	$-0.0837990\pi$
$677$	18.3517	+	18.3517i	0.705314	+	0.705314i	−0.260232	+	0.965546i	$0.583799\pi$
$678$		0			0
$679$	6.06643	−	0.895314i	0.232808	−	0.0343590i
$680$	−1.41421	+	8.06323i	−0.0542326	+	0.309211i
$681$		0			0
$682$	−9.89049	−	9.89049i	−0.378727	−	0.378727i
$683$	−12.4539	−	12.4539i	−0.476536	−	0.476536i	0.427486	−	0.904022i	$-0.359399\pi$
$683$	−12.4539	−	12.4539i	−0.476536	−	0.476536i	−0.904022	+	0.427486i	$0.859399\pi$
$684$		0			0
$685$	−30.7641	+	21.5829i	−1.17543	+	0.824640i
$686$	−16.7595	+	7.88150i	−0.639882	+	0.300917i
$687$		0			0
$688$	2.00000	+	2.00000i	0.0762493	+	0.0762493i
$689$	48.6844			1.85473
$690$		0			0
$691$		−	22.3494i		−	0.850212i	−0.905144	−	0.425106i	$-0.860237\pi$
$691$		−	22.3494i		−	0.850212i	0.905144	−	0.425106i	$-0.139763\pi$
$692$	13.7163	+	13.7163i	0.521414	+	0.521414i
$693$		0			0
$694$		−	14.2094i		−	0.539380i
$695$	26.5961	+	4.66470i	1.00885	+	0.176942i
$696$		0			0
$697$	−26.8062	+	26.8062i	−1.01536	+	1.01536i
$698$	−16.3050	+	16.3050i	−0.617153	+	0.617153i
$699$		0			0
$700$	7.30134	+	11.0313i	0.275965	+	0.416945i
$701$	52.4740			1.98191			0.990957	−	0.134181i	$-0.0428403\pi$
$701$	52.4740			1.98191			0.990957	+	0.134181i	$0.0428403\pi$
$702$		0			0
$703$	−3.33496	+	3.33496i	−0.125780	+	0.125780i
$704$		−	1.41421i		−	0.0533002i
$705$		0			0
$706$			20.4903i			0.771163i
$707$	−17.0705	−	12.6798i	−0.642001	−	0.476872i
$708$		0			0
$709$		−	41.0156i		−	1.54037i	−0.637818	−	0.770187i	$-0.720163\pi$
$709$		−	41.0156i		−	1.54037i	0.637818	−	0.770187i	$-0.279837\pi$
$710$	−1.81616	+	1.27415i	−0.0681593	+	0.0478180i
$711$		0			0
$712$	−8.79790	−	8.79790i	−0.329715	−	0.329715i
$713$	37.7875	−	37.7875i	1.41515	−	1.41515i
$714$		0			0
$715$	13.4031	−	9.40312i	0.501248	−	0.351657i
$716$	−3.39853			−0.127009
$717$		0			0
$718$	−20.1047	−	20.1047i	−0.750300	−	0.750300i
$719$	4.17433			0.155676			0.0778381	−	0.996966i	$-0.475198\pi$
$719$	4.17433			0.155676			0.0778381	+	0.996966i	$0.475198\pi$
$720$		0			0
$721$	−6.50781	−	44.0954i	−0.242364	−	1.64220i
$722$	−2.54338	+	2.54338i	−0.0946546	+	0.0946546i
$723$		0			0
$724$	3.27777			0.121817
$725$	13.7201	−	37.9098i	0.509551	−	1.40793i
$726$		0			0
$727$	20.7105	+	20.7105i	0.768111	+	0.768111i	0.977774	−	0.209662i	$-0.0672365\pi$
$727$	20.7105	+	20.7105i	0.768111	+	0.768111i	−0.209662	+	0.977774i	$0.567236\pi$
$728$	−8.16816	+	10.9966i	−0.302732	+	0.407561i
$729$		0			0
$730$	2.50781	−	14.2984i	0.0928182	−	0.529209i
$731$			10.3550i			0.382992i
$732$		0			0
$733$	−1.80192	+	1.80192i	−0.0665554	+	0.0665554i	−0.739601	−	0.673046i	$-0.764986\pi$
$733$	−1.80192	+	1.80192i	−0.0665554	+	0.0665554i	0.673046	+	0.739601i	$0.264986\pi$
$734$	11.6695			0.430731
$735$		0			0
$736$	5.40312			0.199162
$737$	5.65685	−	5.65685i	0.208373	−	0.208373i
$738$		0			0
$739$			34.8062i			1.28037i	0.768221	+	0.640184i	$0.221142\pi$
$739$			34.8062i			1.28037i	−0.768221	+	0.640184i	$0.778858\pi$
$740$	−1.27415	−	1.81616i	−0.0468387	−	0.0667634i
$741$		0			0
$742$	14.8347	−	19.9716i	0.544598	−	0.733179i
$743$	−22.6274	−	22.6274i	−0.830119	−	0.830119i	0.157413	−	0.987533i	$-0.449684\pi$
$743$	−22.6274	−	22.6274i	−0.830119	−	0.830119i	−0.987533	+	0.157413i	$0.949684\pi$
$744$		0			0
$745$	−3.88125	+	22.1292i	−0.142198	+	0.810751i
$746$	−3.82059			−0.139882
$747$		0			0
$748$	3.66103	−	3.66103i	0.133860	−	0.133860i
$749$	5.17748	+	35.0813i	0.189181	+	1.28184i
$750$		0			0
$751$	−34.2094			−1.24832			−0.624159	−	0.781297i	$-0.714558\pi$
$751$	−34.2094			−1.24832			−0.624159	+	0.781297i	$0.714558\pi$
$752$	−1.54515	−	1.54515i	−0.0563460	−	0.0563460i
$753$		0			0
$754$	41.7472			1.52034
$755$	−41.4198	−	7.26464i	−1.50742	−	0.264387i
$756$		0			0
$757$	−31.5078	+	31.5078i	−1.14517	+	1.14517i	−0.157681	+	0.987490i	$0.550402\pi$
$757$	−31.5078	+	31.5078i	−1.14517	+	1.14517i	−0.987490	+	0.157681i	$0.949598\pi$
$758$	−23.7676	−	23.7676i	−0.863279	−	0.863279i
$759$		0			0
$760$	−6.10469	−	8.70156i	−0.221440	−	0.315639i
$761$		−	2.62918i		−	0.0953076i	−0.998864	−	0.0476538i	$-0.984826\pi$
$761$		−	2.62918i		−	0.0953076i	0.998864	−	0.0476538i	$-0.0151744\pi$
$762$		0			0
$763$	−1.26772	−	0.941651i	−0.0458946	−	0.0340901i
$764$			2.97648i			0.107685i
$765$		0			0
$766$			30.0547i			1.08592i
$767$	27.4402	−	27.4402i	0.990807	−	0.990807i
$768$		0			0
$769$	28.5217			1.02852			0.514259	−	0.857635i	$-0.328067\pi$
$769$	28.5217			1.02852			0.514259	+	0.857635i	$0.328067\pi$
$770$	0.226685	−	8.36353i	0.00816918	−	0.301401i
$771$		0			0
$772$	−11.0000	+	11.0000i	−0.395899	+	0.395899i
$773$	14.2583	−	14.2583i	0.512835	−	0.512835i	−0.402559	−	0.915394i	$-0.631879\pi$
$773$	14.2583	−	14.2583i	0.512835	−	0.512835i	0.915394	+	0.402559i	$0.131879\pi$
$774$		0			0
$775$	16.8293	−	46.5008i	0.604526	−	1.67036i
$776$		−	2.31773i		−	0.0832017i
$777$		0			0
$778$	−15.7016	−	15.7016i	−0.562928	−	0.562928i
$779$		−	49.2235i		−	1.76361i
$780$		0			0
$781$	1.40312			0.0502077
$782$	13.9873	+	13.9873i	0.500184	+	0.500184i
$783$		0			0
$784$	2.02214	+	6.70156i	0.0722194	+	0.239342i
$785$	23.9157	+	34.0892i	0.853587	+	1.21669i
$786$		0			0
$787$	35.1344	+	35.1344i	1.25241	+	1.25241i	0.954638	+	0.297769i	$0.0962426\pi$
$787$	35.1344	+	35.1344i	1.25241	+	1.25241i	0.297769	+	0.954638i	$0.403757\pi$
$788$	7.49312	+	7.49312i	0.266931	+	0.266931i
$789$		0			0
$790$	−9.50723	−	13.5515i	−0.338252	−	0.482142i
$791$	−23.0495	+	3.40175i	−0.819545	+	0.120952i
$792$		0			0
$793$	22.8062	+	22.8062i	0.809874	+	0.809874i
$794$	−6.72263			−0.238577
$795$		0			0
$796$		−	11.7496i		−	0.416454i
$797$	14.2583	+	14.2583i	0.505054	+	0.505054i	0.913004	−	0.407950i	$-0.133756\pi$
$797$	14.2583	+	14.2583i	0.505054	+	0.505054i	−0.407950	+	0.913004i	$0.633756\pi$
$798$		0			0
$799$		−	8.00000i		−	0.283020i
$800$	4.52769	−	2.12132i	0.160078	−	0.0750000i
$801$		0			0
$802$	−22.2094	+	22.2094i	−0.784240	+	0.784240i
$803$	−6.49206	+	6.49206i	−0.229100	+	0.229100i
$804$		0			0
$805$	31.9536	+	0.866071i	1.12622	+	0.0305250i
$806$	51.2078			1.80372
$807$		0			0
$808$	−5.68317	+	5.68317i	−0.199933	+	0.199933i
$809$			34.2372i			1.20372i	0.798603	+	0.601858i	$0.205573\pi$
$809$			34.2372i			1.20372i	−0.798603	+	0.601858i	$0.794427\pi$
$810$		0			0
$811$		−	22.3494i		−	0.784794i	−0.919796	−	0.392397i	$-0.871646\pi$
$811$		−	22.3494i		−	0.784794i	0.919796	−	0.392397i	$-0.128354\pi$
$812$	12.7208	−	17.1257i	0.446413	−	0.600995i
$813$		0			0
$814$			1.40312i			0.0491795i
$815$	2.54830	+	3.63232i	0.0892630	+	0.127235i
$816$		0			0
$817$	−9.50723	−	9.50723i	−0.332616	−	0.332616i
$818$	4.40490	−	4.40490i	0.154014	−	0.154014i
$819$		0			0
$820$	22.8062	+	4.00000i	0.796429	+	0.139686i
$821$	−16.8446			−0.587881			−0.293940	−	0.955824i	$-0.594967\pi$
$821$	−16.8446			−0.587881			−0.293940	+	0.955824i	$0.594967\pi$
$822$		0			0
$823$	27.9109	+	27.9109i	0.972914	+	0.972914i	0.999643	−	0.0267287i	$-0.00850902\pi$
$823$	27.9109	+	27.9109i	0.972914	+	0.972914i	−0.0267287	+	0.999643i	$0.508509\pi$
$824$	−16.8470			−0.586894
$825$		0			0
$826$	−2.89531	−	19.6180i	−0.100741	−	0.682596i
$827$	−26.0259	+	26.0259i	−0.905011	+	0.905011i	−0.995864	−	0.0908534i	$-0.971041\pi$
$827$	−26.0259	+	26.0259i	−0.905011	+	0.905011i	0.0908534	+	0.995864i	$0.471041\pi$
$828$		0			0
$829$	24.4774			0.850136			0.425068	−	0.905161i	$-0.360250\pi$
$829$	24.4774			0.850136			0.425068	+	0.905161i	$0.360250\pi$
$830$	4.39069	−	25.0338i	0.152403	−	0.868936i
$831$		0			0
$832$	3.66103	+	3.66103i	0.126923	+	0.126923i
$833$	−12.1138	+	22.5834i	−0.419718	+	0.782468i
$834$		0			0
$835$	6.59688	+	9.40312i	0.228294	+	0.325409i
$836$			6.72263i			0.232507i
$837$		0			0
$838$	16.6663	−	16.6663i	0.575726	−	0.575726i
$839$	−23.8002			−0.821674			−0.410837	−	0.911709i	$-0.634764\pi$
$839$	−23.8002			−0.821674			−0.410837	+	0.911709i	$0.634764\pi$
$840$		0			0
$841$	−36.0156			−1.24192
$842$	−13.7201	+	13.7201i	−0.472825	+	0.472825i
$843$		0			0
$844$		−	14.8062i		−	0.509652i
$845$	−5.33320	+	30.4076i	−0.183468	+	1.04605i
$846$		0			0
$847$	14.1987	−	19.1154i	0.487873	−	0.656811i
$848$	−6.64901	−	6.64901i	−0.228328	−	0.228328i
$849$		0			0
$850$	17.2125	+	6.22947i	0.590386	+	0.213669i
$851$	−5.36076			−0.183764
$852$		0			0
$853$	28.9050	−	28.9050i	0.989687	−	0.989687i	−0.0102603	−	0.999947i	$-0.503266\pi$
$853$	28.9050	−	28.9050i	0.989687	−	0.989687i	0.999947	+	0.0102603i	$0.00326601\pi$
$854$	16.3050	−	2.40637i	0.557946	−	0.0823444i
$855$		0			0
$856$	13.4031			0.458109
$857$	−4.13389	−	4.13389i	−0.141211	−	0.141211i	0.632967	−	0.774178i	$-0.281837\pi$
$857$	−4.13389	−	4.13389i	−0.141211	−	0.141211i	−0.774178	+	0.632967i	$0.781837\pi$
$858$		0			0
$859$	−9.12397			−0.311306			−0.155653	−	0.987812i	$-0.549748\pi$
$859$	−9.12397			−0.311306			−0.155653	+	0.987812i	$0.549748\pi$
$860$	5.17748	−	3.63232i	0.176550	−	0.123861i
$861$		0			0
$862$	−0.104686	+	0.104686i	−0.00356563	+	0.00356563i
$863$	−25.6039	−	25.6039i	−0.871567	−	0.871567i	0.121077	−	0.992643i	$-0.461365\pi$
$863$	−25.6039	−	25.6039i	−0.871567	−	0.871567i	−0.992643	+	0.121077i	$0.961365\pi$
$864$		0			0
$865$	35.5078	−	24.9109i	1.20730	−	0.846997i
$866$		−	12.6727i		−	0.430635i
$867$		0			0
$868$	15.6036	−	21.0067i	0.529620	−	0.713014i
$869$			10.4696i			0.355157i
$870$		0			0
$871$			29.2882i			0.992394i
$872$	−0.422055	+	0.422055i	−0.0142926	+	0.0142926i
$873$		0			0
$874$	−25.6844			−0.868787
$875$	27.1164	−	11.8195i	0.916701	−	0.399574i
$876$		0			0
$877$	6.49219	−	6.49219i	0.219226	−	0.219226i	−0.588946	−	0.808172i	$-0.700457\pi$
$877$	6.49219	−	6.49219i	0.219226	−	0.219226i	0.808172	+	0.588946i	$0.200457\pi$
$878$	−1.04358	+	1.04358i	−0.0352192	+	0.0352192i
$879$		0			0
$880$	−3.11473	−	0.546295i	−0.104998	−	0.0184156i
$881$		−	43.5070i		−	1.46579i	−0.680343	−	0.732893i	$-0.738169\pi$
$881$		−	43.5070i		−	1.46579i	0.680343	−	0.732893i	$-0.261831\pi$
$882$		0			0
$883$	−1.19375	−	1.19375i	−0.0401729	−	0.0401729i	0.686735	−	0.726908i	$-0.259043\pi$
$883$	−1.19375	−	1.19375i	−0.0401729	−	0.0401729i	−0.726908	+	0.686735i	$0.759043\pi$
$884$			18.9549i			0.637522i
$885$		0			0
$886$	23.4031			0.786243
$887$	−26.8905	−	26.8905i	−0.902895	−	0.902895i	0.0927904	−	0.995686i	$-0.470421\pi$
$887$	−26.8905	−	26.8905i	−0.902895	−	0.902895i	−0.995686	+	0.0927904i	$0.970421\pi$
$888$		0			0
$889$	−3.11473	−	21.1047i	−0.104465	−	0.707828i
$890$	−22.7755	+	15.9784i	−0.763435	+	0.535597i
$891$		0			0
$892$	−4.20732	−	4.20732i	−0.140872	−	0.140872i
$893$	7.34507	+	7.34507i	0.245794	+	0.245794i
$894$		0			0
$895$	−1.31281	+	7.48509i	−0.0438825	+	0.250199i
$896$	2.61740	−	0.386289i	0.0874412	−	0.0129050i
$897$		0			0
$898$	12.5969	+	12.5969i	0.420363	+	0.420363i
$899$	−79.7493			−2.65979
$900$		0			0
$901$		−	34.4251i		−	1.14687i
$902$	−10.3550	−	10.3550i	−0.344782	−	0.344782i
$903$		0			0
$904$			8.80625i			0.292891i
$905$	1.26616	−	7.21912i	0.0420887	−	0.239972i
$906$		0			0
$907$	16.5969	−	16.5969i	0.551090	−	0.551090i	−0.375665	−	0.926755i	$-0.622586\pi$
$907$	16.5969	−	16.5969i	0.551090	−	0.551090i	0.926755	+	0.375665i	$0.122586\pi$
$908$	17.0776	−	17.0776i	0.566739	−	0.566739i
$909$		0			0
$910$	21.0642	+	22.2378i	0.698270	+	0.737176i
$911$	30.1205			0.997938			0.498969	−	0.866620i	$-0.333712\pi$
$911$	30.1205			0.997938			0.498969	+	0.866620i	$0.333712\pi$
$912$		0			0
$913$	−11.3663	+	11.3663i	−0.376171	+	0.376171i
$914$		−	8.21128i		−	0.271605i
$915$		0			0
$916$			1.85911i			0.0614267i
$917$	9.35569	+	6.94932i	0.308952	+	0.229487i
$918$		0			0
$919$			39.8219i			1.31360i	0.754064	+	0.656801i	$0.228091\pi$
$919$			39.8219i			1.31360i	−0.754064	+	0.656801i	$0.771909\pi$
$920$	2.08717	−	11.9001i	0.0688118	−	0.392335i
$921$		0			0
$922$	0.929554	+	0.929554i	0.0306132	+	0.0306132i
$923$	−3.63232	+	3.63232i	−0.119559	+	0.119559i
$924$		0			0
$925$	−4.49219	+	2.10469i	−0.147702	+	0.0692017i
$926$	18.5328			0.609026
$927$		0			0
$928$	−5.70156	−	5.70156i	−0.187163	−	0.187163i
$929$	−17.1585			−0.562951			−0.281475	−	0.959568i	$-0.590824\pi$
$929$	−17.1585			−0.562951			−0.281475	+	0.959568i	$0.590824\pi$
$930$		0			0
$931$	−9.61250	−	31.8567i	−0.315037	−	1.04406i
$932$	−4.24264	+	4.24264i	−0.138972	+	0.138972i
$933$		0			0
$934$	7.64813			0.250254
$935$	−6.64901	−	9.47744i	−0.217446	−	0.309945i
$936$		0			0
$937$	−34.6453	−	34.6453i	−1.13181	−	1.13181i	−0.989876	−	0.141938i	$-0.954667\pi$
$937$	−34.6453	−	34.6453i	−1.13181	−	1.13181i	−0.141938	−	0.989876i	$-0.545333\pi$
$938$	12.0148	+	8.92444i	0.392296	+	0.291393i
$939$		0			0
$940$	−4.00000	+	2.80625i	−0.130466	+	0.0915297i
$941$			25.1148i			0.818719i	0.912373	+	0.409360i	$0.134248\pi$
$941$			25.1148i			0.818719i	−0.912373	+	0.409360i	$0.865752\pi$
$942$		0			0
$943$	39.5620	−	39.5620i	1.28832	−	1.28832i
$944$	−7.49521			−0.243948
$945$		0			0
$946$	−4.00000			−0.130051
$947$	−1.26616	+	1.26616i	−0.0411448	+	0.0411448i	−0.727380	−	0.686235i	$-0.759262\pi$
$947$	−1.26616	+	1.26616i	−0.0411448	+	0.0411448i	0.686235	+	0.727380i	$0.259262\pi$
$948$		0			0
$949$		−	33.6125i		−	1.09111i
$950$	−21.5229	+	10.0839i	−0.698296	+	0.327166i
$951$		0			0
$952$	7.77576	+	5.77576i	0.252014	+	0.187193i
$953$	−32.5269	−	32.5269i	−1.05365	−	1.05365i	−0.998477	−	0.0551732i	$-0.982429\pi$
$953$	−32.5269	−	32.5269i	−1.05365	−	1.05365i	−0.0551732	−	0.998477i	$-0.517571\pi$
$954$		0			0
$955$	6.55554	+	1.14978i	0.212132	+	0.0372060i
$956$	−23.6196			−0.763912
$957$		0			0
$958$	−3.27777	+	3.27777i	−0.105900	+	0.105900i
$959$	6.49206	+	43.9887i	0.209640	+	1.42047i
$960$		0			0
$961$	−66.8219			−2.15554
$962$	−3.63232	−	3.63232i	−0.117111	−	0.117111i
$963$		0			0
$964$	−23.8253			−0.767360
$965$	19.9778	+	28.4761i	0.643107	+	0.916679i
$966$		0			0
$967$	15.1047	−	15.1047i	0.485734	−	0.485734i	−0.421223	−	0.906957i	$-0.638399\pi$
$967$	15.1047	−	15.1047i	0.485734	−	0.485734i	0.906957	+	0.421223i	$0.138399\pi$
$968$	−6.36396	−	6.36396i	−0.204545	−	0.204545i
$969$		0			0
$970$	−5.10469	−	0.895314i	−0.163902	−	0.0287468i
$971$			35.0086i			1.12348i	0.827314	+	0.561740i	$0.189868\pi$
$971$			35.0086i			1.12348i	−0.827314	+	0.561740i	$0.810132\pi$
$972$		0			0
$973$	19.0510	−	25.6479i	0.610747	−	0.822233i
$974$			23.3456i			0.748040i
$975$		0			0
$976$		−	6.22947i		−	0.199400i
$977$	−8.21128	+	8.21128i	−0.262702	+	0.262702i	−0.826151	−	0.563449i	$-0.809474\pi$
$977$	−8.21128	+	8.21128i	−0.262702	+	0.262702i	0.563449	+	0.826151i	$0.309474\pi$
$978$		0			0
$979$	17.5958			0.562364
$980$	15.5410	−	1.86493i	0.496438	−	0.0595730i
$981$		0			0
$982$	−28.4031	+	28.4031i	−0.906380	+	0.906380i
$983$	−35.2392	+	35.2392i	−1.12396	+	1.12396i	−0.132814	+	0.991141i	$0.542401\pi$
$983$	−35.2392	+	35.2392i	−1.12396	+	1.12396i	−0.991141	+	0.132814i	$0.957599\pi$
$984$		0			0
$985$	19.3977	−	13.6087i	0.618063	−	0.433610i
$986$		−	29.5197i		−	0.940099i
$987$		0			0
$988$	−17.4031	−	17.4031i	−0.553667	−	0.553667i
$989$		−	15.2823i		−	0.485950i
$990$		0			0
$991$	2.80625			0.0891434			0.0445717	−	0.999006i	$-0.485808\pi$
$991$	2.80625			0.0891434			0.0445717	+	0.999006i	$0.485808\pi$
$992$	−6.99364	−	6.99364i	−0.222048	−	0.222048i
$993$		0			0
$994$	0.383260	+	2.59688i	0.0121563	+	0.0823679i
$995$	−25.8779	−	4.53874i	−0.820385	−	0.143888i
$996$		0			0
$997$	15.3534	+	15.3534i	0.486248	+	0.486248i	0.907120	−	0.420872i	$-0.138276\pi$
$997$	15.3534	+	15.3534i	0.486248	+	0.486248i	−0.420872	+	0.907120i	$0.638276\pi$
$998$	−5.65685	−	5.65685i	−0.179065	−	0.179065i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.p.d.433.1	yes	16
3.2	odd	2	inner	630.2.p.d.433.8	yes	16
5.2	odd	4	inner	630.2.p.d.307.4	yes	16
7.6	odd	2	inner	630.2.p.d.433.4	yes	16
15.2	even	4	inner	630.2.p.d.307.5	yes	16
21.20	even	2	inner	630.2.p.d.433.5	yes	16
35.27	even	4	inner	630.2.p.d.307.1	✓	16
105.62	odd	4	inner	630.2.p.d.307.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.p.d.307.1	✓	16	35.27	even	4	inner
630.2.p.d.307.4	yes	16	5.2	odd	4	inner
630.2.p.d.307.5	yes	16	15.2	even	4	inner
630.2.p.d.307.8	yes	16	105.62	odd	4	inner
630.2.p.d.433.1	yes	16	1.1	even	1	trivial
630.2.p.d.433.4	yes	16	7.6	odd	2	inner
630.2.p.d.433.5	yes	16	21.20	even	2	inner
630.2.p.d.433.8	yes	16	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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-2.20245 - 0.386289i) q^{5} +(-1.57763 + 2.12393i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-2.20245 - 0.386289i) q^{5} +(-1.57763 + 2.12393i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.83051 - 1.28422i) q^{10} -1.41421 q^{11} +(3.66103 - 3.66103i) q^{13} +(-0.386289 - 2.61740i) q^{14} -1.00000 q^{16} +(-2.58874 - 2.58874i) q^{17} +4.75362 q^{19} +(-0.386289 + 2.20245i) q^{20} +(1.00000 - 1.00000i) q^{22} +(3.82059 + 3.82059i) q^{23} +(4.70156 + 1.70156i) q^{25} +5.17748i q^{26} +(2.12393 + 1.57763i) q^{28} -8.06323i q^{29} -9.89049i q^{31} +(0.707107 - 0.707107i) q^{32} +3.66103 q^{34} +(4.29511 - 4.06842i) q^{35} +(-0.701562 + 0.701562i) q^{37} +(-3.36131 + 3.36131i) q^{38} +(-1.28422 - 1.83051i) q^{40} -10.3550i q^{41} +(-2.00000 - 2.00000i) q^{43} +1.41421i q^{44} -5.40312 q^{46} +(1.54515 + 1.54515i) q^{47} +(-2.02214 - 6.70156i) q^{49} +(-4.52769 + 2.12132i) q^{50} +(-3.66103 - 3.66103i) q^{52} +(6.64901 + 6.64901i) q^{53} +(3.11473 + 0.546295i) q^{55} +(-2.61740 + 0.386289i) q^{56} +(5.70156 + 5.70156i) q^{58} +7.49521 q^{59} +6.22947i q^{61} +(6.99364 + 6.99364i) q^{62} +1.00000i q^{64} +(-9.47744 + 6.64901i) q^{65} +(-4.00000 + 4.00000i) q^{67} +(-2.58874 + 2.58874i) q^{68} +(-0.160291 + 5.91391i) q^{70} -0.992159 q^{71} +(4.59058 - 4.59058i) q^{73} -0.992159i q^{74} -4.75362i q^{76} +(2.23111 - 3.00369i) q^{77} -7.40312i q^{79} +(2.20245 + 0.386289i) q^{80} +(7.32206 + 7.32206i) q^{82} +(8.03722 - 8.03722i) q^{83} +(4.70156 + 6.70156i) q^{85} +2.82843 q^{86} +(-1.00000 - 1.00000i) q^{88} -12.4421 q^{89} +(2.00000 + 13.5515i) q^{91} +(3.82059 - 3.82059i) q^{92} -2.18518 q^{94} +(-10.4696 - 1.83627i) q^{95} +(-1.63888 - 1.63888i) q^{97} +(6.16859 + 3.30885i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{7}+O(q^{10}) \) 16 * q - 4 * q^7	\( 16 q - 4 q^{7} - 16 q^{16} + 16 q^{22} + 24 q^{25} + 4 q^{28} + 40 q^{37} - 32 q^{43} + 16 q^{46} + 40 q^{58} - 64 q^{67} - 12 q^{70} + 24 q^{85} - 16 q^{88} + 32 q^{91}+O(q^{100}) \) 16 * q - 4 * q^7 - 16 * q^16 + 16 * q^22 + 24 * q^25 + 4 * q^28 + 40 * q^37 - 32 * q^43 + 16 * q^46 + 40 * q^58 - 64 * q^67 - 12 * q^70 + 24 * q^85 - 16 * q^88 + 32 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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