LMFDB - Embedded newform 630.2.p.d.433.4

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			433.4
Root			$1.57567 - 1.19896i$ of defining polynomial
Character	$\chi$	$=$	630.433
Dual form			630.2.p.d.307.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(2.20245 + 0.386289i) q^{5} +(-2.12393 + 1.57763i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(2.20245 + 0.386289i) q^{5} +(-2.12393 + 1.57763i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.83051 + 1.28422i) q^{10} -1.41421 q^{11} +(-3.66103 + 3.66103i) q^{13} +(0.386289 - 2.61740i) q^{14} -1.00000 q^{16} +(2.58874 + 2.58874i) q^{17} -4.75362 q^{19} +(0.386289 - 2.20245i) q^{20} +(1.00000 - 1.00000i) q^{22} +(3.82059 + 3.82059i) q^{23} +(4.70156 + 1.70156i) q^{25} -5.17748i q^{26} +(1.57763 + 2.12393i) q^{28} -8.06323i q^{29} +9.89049i q^{31} +(0.707107 - 0.707107i) q^{32} -3.66103 q^{34} +(-5.28727 + 2.65421i) q^{35} +(-0.701562 + 0.701562i) q^{37} +(3.36131 - 3.36131i) q^{38} +(1.28422 + 1.83051i) q^{40} +10.3550i q^{41} +(-2.00000 - 2.00000i) q^{43} +1.41421i q^{44} -5.40312 q^{46} +(-1.54515 - 1.54515i) q^{47} +(2.02214 - 6.70156i) q^{49} +(-4.52769 + 2.12132i) q^{50} +(3.66103 + 3.66103i) q^{52} +(6.64901 + 6.64901i) q^{53} +(-3.11473 - 0.546295i) q^{55} +(-2.61740 - 0.386289i) q^{56} +(5.70156 + 5.70156i) q^{58} -7.49521 q^{59} -6.22947i q^{61} +(-6.99364 - 6.99364i) q^{62} +1.00000i q^{64} +(-9.47744 + 6.64901i) q^{65} +(-4.00000 + 4.00000i) q^{67} +(2.58874 - 2.58874i) q^{68} +(1.86185 - 5.61547i) q^{70} -0.992159 q^{71} +(-4.59058 + 4.59058i) q^{73} -0.992159i q^{74} +4.75362i q^{76} +(3.00369 - 2.23111i) q^{77} -7.40312i q^{79} +(-2.20245 - 0.386289i) q^{80} +(-7.32206 - 7.32206i) q^{82} +(-8.03722 + 8.03722i) q^{83} +(4.70156 + 6.70156i) q^{85} +2.82843 q^{86} +(-1.00000 - 1.00000i) q^{88} +12.4421 q^{89} +(2.00000 - 13.5515i) q^{91} +(3.82059 - 3.82059i) q^{92} +2.18518 q^{94} +(-10.4696 - 1.83627i) q^{95} +(1.63888 + 1.63888i) q^{97} +(3.30885 + 6.16859i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	−2.12393	+	1.57763i	−0.802769	+	0.596289i
$7$	−2.12393	+	1.57763i	−0.802769	+	0.596289i
$8$	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	$0.504936\pi$
$13$	−3.66103	+	3.66103i	−1.01539	+	1.01539i	−0.999880	+	0.0155066i	$0.995064\pi$
$14$	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	0.947529	−	0.319668i	$-0.103572\pi$
$17$	2.58874	+	2.58874i	0.627861	+	0.627861i	−0.319668	+	0.947529i	$0.603572\pi$
$18$		0			0
$19$	−4.75362			−1.09055			−0.545277	−	0.838256i	$-0.683576\pi$
$19$	−4.75362			−1.09055			−0.545277	+	0.838256i	$0.683576\pi$
$20$	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
$28$	1.57763	+	2.12393i	0.298145	+	0.401385i
$29$		−	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	$0.348039\pi$
$31$			9.89049i			1.77639i	−0.459471	+	0.888193i	$0.651961\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$	−3.66103			−0.627861
$35$	−5.28727	+	2.65421i	−0.893711	+	0.448643i
$36$		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	$0.299767\pi$
$41$			10.3550i			1.61717i	−0.588378	+	0.808586i	$0.700233\pi$
$42$		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	0.585377	−	0.810761i	$-0.300946\pi$
$47$	−1.54515	−	1.54515i	−0.225384	−	0.225384i	−0.810761	+	0.585377i	$0.800946\pi$
$48$		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	$-0.662236\pi$
$59$	−7.49521			−0.975793			−0.487896	+	0.872902i	$0.662236\pi$
$60$		0			0
$61$		−	6.22947i		−	0.797601i	−0.917038	−	0.398801i	$-0.869427\pi$
$61$		−	6.22947i		−	0.797601i	0.917038	−	0.398801i	$-0.130573\pi$
$62$	−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
$70$	1.86185	−	5.61547i	0.222534	−	0.671177i
$71$	−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	−0.922731	−	0.385444i	$-0.874048\pi$
$73$	−4.59058	+	4.59058i	−0.537287	+	0.537287i	0.385444	+	0.922731i	$0.374048\pi$
$74$		−	0.992159i		−	0.115336i
$75$		0			0
$76$			4.75362i			0.545277i
$77$	3.00369	−	2.23111i	0.342302	−	0.254259i
$78$		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	−0.993758	−	0.111559i	$-0.964416\pi$
$83$	−8.03722	+	8.03722i	−0.882199	+	0.882199i	0.111559	+	0.993758i	$0.464416\pi$
$84$		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	$-0.270797\pi$
$89$	12.4421			1.31886			0.659431	+	0.751765i	$0.270797\pi$
$90$		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	0.785396	−	0.618993i	$-0.212459\pi$
$97$	1.63888	+	1.63888i	0.166403	+	0.166403i	−0.618993	+	0.785396i	$0.712459\pi$
$98$	3.30885	+	6.16859i	0.334244	+	0.623122i
$99$		0			0
$100$	1.70156	−	4.70156i	0.170156	−	0.470156i
$101$		−	8.03722i		−	0.799733i	−0.916573	−	0.399867i	$-0.869056\pi$
$101$		−	8.03722i		−	0.799733i	0.916573	−	0.399867i	$-0.130944\pi$
$102$		0			0
$103$	11.9126	−	11.9126i	1.17379	−	1.17379i	0.192488	−	0.981299i	$-0.438344\pi$
$103$	11.9126	−	11.9126i	1.17379	−	1.17379i	0.981299	−	0.192488i	$-0.0616555\pi$
$104$	−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
$112$	2.12393	−	1.57763i	0.200692	−	0.149072i
$113$	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	$0.0616365\pi$
$131$			4.40490i			0.384858i	−0.981311	+	0.192429i	$0.938364\pi$
$132$		0			0
$133$	10.0963	−	7.49947i	0.875464	−	0.650286i
$134$		−	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	$-0.328859\pi$
$139$	12.0757			1.02425			0.512123	+	0.858912i	$0.328859\pi$
$140$	2.65421	+	5.28727i	0.224322	+	0.446856i
$141$		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	$0.0166587\pi$
$157$	13.1683	+	13.1683i	1.05094	+	1.05094i	0.0523109	+	0.998631i	$0.483341\pi$
$158$	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	0.833539	−	0.552461i	$-0.186311\pi$
$167$	3.63232	+	3.63232i	0.281077	+	0.281077i	−0.552461	+	0.833539i	$0.686311\pi$
$168$		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	$-0.486058\pi$
$173$	13.7163	−	13.7163i	1.04283	−	1.04283i	0.999041	−	0.0437875i	$-0.0139424\pi$
$174$		0			0
$175$	−12.6702	+	3.80335i	−0.957779	+	0.287506i
$176$	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	$-0.961128\pi$
$181$		−	3.27777i		−	0.243635i	0.992553	−	0.121817i	$-0.0388722\pi$
$182$	8.16816	+	10.9966i	0.605464	+	0.815121i
$183$		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	$-0.636727\pi$
$199$	−11.7496			−0.832907			−0.416454	+	0.909157i	$0.636727\pi$
$200$	2.12132	+	4.52769i	0.150000	+	0.320156i
$201$		0			0
$202$	5.68317	+	5.68317i	0.399867	+	0.399867i
$203$	12.7208	+	17.1257i	0.892826	+	1.20199i
$204$		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
$217$	−15.6036	−	21.0067i	−1.05924	−	1.42603i
$218$	−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	−0.833804	−	0.552061i	$-0.813842\pi$
$223$	−4.20732	+	4.20732i	−0.281743	+	0.281743i	0.552061	+	0.833804i	$0.313842\pi$
$224$	−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	$-0.954041\pi$
$227$	−17.0776	−	17.0776i	−1.13348	−	1.13348i	−0.143884	−	0.989595i	$-0.545959\pi$
$228$		0			0
$229$	1.85911			0.122853			0.0614267	−	0.998112i	$-0.480435\pi$
$229$	1.85911			0.122853			0.0614267	+	0.998112i	$0.480435\pi$
$230$	−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
$238$	7.77576	−	5.77576i	0.504028	−	0.374387i
$239$		−	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	$0.278430\pi$
$241$			23.8253i			1.53472i	−0.641216	+	0.767360i	$0.721570\pi$
$242$	6.36396	−	6.36396i	0.409091	−	0.409091i
$243$		0			0
$244$	−6.22947			−0.398801
$245$	7.04241	−	13.9787i	0.449923	−	0.893067i
$246$		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	$-0.997684\pi$
$251$		−	0.230566i		−	0.0145532i	0.999974	−	0.00727661i	$-0.00231624\pi$
$252$		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	0.906547	−	0.422104i	$-0.138708\pi$
$257$	7.76621	+	7.76621i	0.484443	+	0.484443i	−0.422104	+	0.906547i	$0.638708\pi$
$258$		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	$-0.462428\pi$
$269$	3.86289			0.235524			0.117762	+	0.993042i	$0.462428\pi$
$270$		0			0
$271$		−	13.1683i		−	0.799915i	−0.916534	−	0.399957i	$-0.869025\pi$
$271$		−	13.1683i		−	0.799915i	0.916534	−	0.399957i	$-0.130975\pi$
$272$	−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
$280$	−5.61547	−	1.86185i	−0.335589	−	0.111267i
$281$	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	$0.590712\pi$
$283$	−20.8736	+	20.8736i	−1.24081	+	1.24081i	−0.959667	+	0.281138i	$0.909288\pi$
$284$			0.992159i			0.0588738i
$285$		0			0
$286$			7.32206i			0.432962i
$287$	−16.3363	−	21.9932i	−0.964302	−	1.29822i
$288$		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	−0.0613973	−	0.998113i	$-0.519556\pi$
$293$	16.0340	−	16.0340i	0.936716	−	0.936716i	0.998113	+	0.0613973i	$0.0195557\pi$
$294$		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	0.717959	−	0.696085i	$-0.245076\pi$
$307$	0.383260	+	0.383260i	0.0218738	+	0.0218738i	−0.696085	+	0.717959i	$0.745076\pi$
$308$	−2.23111	−	3.00369i	−0.127129	−	0.171151i
$309$		0			0
$310$	−12.7016	−	18.1047i	−0.721400	−	1.02828i
$311$		−	19.1647i		−	1.08673i	−0.839496	−	0.543367i	$-0.817149\pi$
$311$		−	19.1647i		−	1.08673i	0.839496	−	0.543367i	$-0.182851\pi$
$312$		0			0
$313$	−10.0535	+	10.0535i	−0.568259	+	0.568259i	−0.931640	−	0.363381i	$-0.881622\pi$
$313$	−10.0535	+	10.0535i	−0.568259	+	0.568259i	0.363381	+	0.931640i	$0.381622\pi$
$314$	−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
$322$	11.4758	−	8.52415i	0.639524	−	0.475032i
$323$	−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
$343$	6.27772	+	17.4238i	0.338965	+	0.940799i
$344$		−	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	$-0.711714\pi$
$349$	−23.0588			−1.23431			−0.617153	+	0.786843i	$0.711714\pi$
$350$	6.26983	−	11.6486i	0.335136	−	0.622642i
$351$		0			0
$352$	−1.00000	+	1.00000i	−0.0533002	+	0.0533002i
$353$	−14.4888	+	14.4888i	−0.771163	+	0.771163i	−0.978310	−	0.207147i	$-0.933582\pi$
$353$	−14.4888	+	14.4888i	−0.771163	+	0.771163i	0.207147	+	0.978310i	$0.433582\pi$
$354$		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	0.888877	−	0.458146i	$-0.151486\pi$
$367$	8.25161	+	8.25161i	0.430731	+	0.430731i	−0.458146	+	0.888877i	$0.651486\pi$
$368$	−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	$0.528680\pi$
$383$	−21.2519	+	21.2519i	−1.08592	+	1.08592i	−0.995944	+	0.0899782i	$0.971320\pi$
$384$		0			0
$385$	7.47732	−	3.75362i	0.381080	−	0.191302i
$386$	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
$392$	6.16859	−	3.30885i	0.311561	−	0.167122i
$393$		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	0.577684	−	0.816261i	$-0.303957\pi$
$397$	−4.75362	−	4.75362i	−0.238577	−	0.238577i	−0.816261	+	0.577684i	$0.803957\pi$
$398$	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	$-0.450780\pi$
$409$	6.22947			0.308027			0.154014	+	0.988069i	$0.450780\pi$
$410$	−13.2980	−	18.9549i	−0.656743	−	0.936115i
$411$		0			0
$412$	−11.9126	−	11.9126i	−0.586894	−	0.586894i
$413$	15.9193	−	11.8247i	0.783337	−	0.581855i
$414$		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	$-0.304719\pi$
$419$	23.5696			1.15145			0.575726	+	0.817643i	$0.304719\pi$
$420$		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
$427$	9.82782	+	13.2309i	0.475601	+	0.640290i
$428$	−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	−0.458209	−	0.888844i	$-0.651509\pi$
$433$	8.96094	−	8.96094i	0.430635	−	0.430635i	0.888844	+	0.458209i	$0.151509\pi$
$434$	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	$-0.511213\pi$
$439$	−1.47585			−0.0704384			−0.0352192	+	0.999380i	$0.511213\pi$
$440$	−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
$448$	−1.57763	−	2.12393i	−0.0745362	−	0.100346i
$449$		−	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
$455$	9.63970	−	29.0740i	0.451916	−	1.36301i
$456$		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	$0.00974602\pi$
$461$			1.31459i			0.0612265i	−0.999531	+	0.0306132i	$0.990254\pi$
$462$		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	0.821075	−	0.570821i	$-0.193375\pi$
$467$	5.40804	+	5.40804i	0.250254	+	0.250254i	−0.570821	+	0.821075i	$0.693375\pi$
$468$		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	$-0.533772\pi$
$479$	−4.63546			−0.211800			−0.105900	+	0.994377i	$0.533772\pi$
$480$		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
$490$	4.90471	+	14.8642i	0.221572	+	0.671495i
$491$	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
$497$	2.10727	−	1.56526i	0.0945242	−	0.0702116i
$498$		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	−0.322804	−	0.946466i	$-0.604626\pi$
$503$	13.9873	−	13.9873i	0.623662	−	0.623662i	0.946466	+	0.322804i	$0.104626\pi$
$504$		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	$-0.346383\pi$
$509$	20.9405			0.928170			0.464085	+	0.885791i	$0.346383\pi$
$510$		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
$518$	1.56526	+	2.10727i	0.0687737	+	0.0925883i
$519$		0			0
$520$	−11.4031	−	2.00000i	−0.500060	−	0.0877058i
$521$			39.3326i			1.72319i	0.507593	+	0.861597i	$0.330535\pi$
$521$			39.3326i			1.72319i	−0.507593	+	0.861597i	$0.669465\pi$
$522$		0			0
$523$	5.84621	−	5.84621i	0.255637	−	0.255637i	−0.567640	−	0.823277i	$-0.692143\pi$
$523$	5.84621	−	5.84621i	0.255637	−	0.255637i	0.823277	+	0.567640i	$0.192143\pi$
$524$	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
$532$	−7.49947	−	10.0963i	−0.325143	−	0.437732i
$533$	−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
$553$	11.6794	+	15.7237i	0.496659	+	0.668640i
$554$		−	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
$560$	5.28727	−	2.65421i	0.223428	−	0.112161i
$561$		0			0
$562$	−14.0000	+	14.0000i	−0.590554	+	0.590554i
$563$	14.5293	−	14.5293i	0.612336	−	0.612336i	−0.331218	−	0.943554i	$-0.607460\pi$
$563$	14.5293	−	14.5293i	0.612336	−	0.612336i	0.943554	+	0.331218i	$0.107460\pi$
$564$		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	0.445057	−	0.895502i	$-0.353183\pi$
$577$	−10.8200	−	10.8200i	−0.450445	−	0.450445i	−0.895502	+	0.445057i	$0.853183\pi$
$578$	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	0.905659	−	0.424006i	$-0.139376\pi$
$587$	11.6695	+	11.6695i	0.481653	+	0.481653i	−0.424006	+	0.905659i	$0.639376\pi$
$588$		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	−0.980727	−	0.195385i	$-0.937404\pi$
$593$	−19.1243	+	19.1243i	−0.785341	+	0.785341i	0.195385	+	0.980727i	$0.437404\pi$
$594$		0			0
$595$	−20.5584	−	6.81630i	−0.842812	−	0.279441i
$596$	−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	$-0.807558\pi$
$601$		−	27.8696i		−	1.13682i	0.822744	−	0.568412i	$-0.192442\pi$
$602$	−6.00738	+	4.46222i	−0.244842	+	0.181867i
$603$		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	0.664877	−	0.746953i	$-0.268484\pi$
$607$	−2.02214	−	2.02214i	−0.0820763	−	0.0820763i	−0.746953	+	0.664877i	$0.768484\pi$
$608$	−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	$-0.253391\pi$
$619$	34.8084			1.39907			0.699533	+	0.714600i	$0.253391\pi$
$620$	21.7833	+	3.82059i	0.874839	+	0.153438i
$621$		0			0
$622$	13.5515	+	13.5515i	0.543367	+	0.543367i
$623$	−26.4262	+	19.6291i	−1.05874	+	0.786423i
$624$		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
$637$	17.1315	+	31.9377i	0.678774	+	1.26542i
$638$	−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	−0.456561	−	0.889692i	$-0.650919\pi$
$643$	10.9831	−	10.9831i	0.433131	−	0.433131i	0.889692	+	0.456561i	$0.150919\pi$
$644$	−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	0.995102	−	0.0988565i	$-0.0315185\pi$
$647$	22.7971	+	22.7971i	0.896245	+	0.896245i	−0.0988565	+	0.995102i	$0.531518\pi$
$648$		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
$658$	−4.64116	+	3.44741i	−0.180931	+	0.134394i
$659$			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	$-0.792875\pi$
$661$		−	31.1473i		−	1.21149i	0.795659	−	0.605745i	$-0.207125\pi$
$662$	−18.1108	+	18.1108i	−0.703895	+	0.703895i
$663$		0			0
$664$	−11.3663			−0.441100
$665$	25.1336	−	12.6171i	0.974641	−	0.489270i
$666$		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	0.260232	−	0.965546i	$-0.416201\pi$
$677$	−18.3517	−	18.3517i	−0.705314	−	0.705314i	−0.965546	+	0.260232i	$0.916201\pi$
$678$		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	$0.139763\pi$
$691$			22.3494i			0.850212i	−0.905144	+	0.425106i	$0.860237\pi$
$692$	−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
$700$	3.80335	+	12.6702i	0.143753	+	0.478889i
$701$	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
$707$	12.6798	+	17.0705i	0.476872	+	0.642001i
$708$		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	$-0.524802\pi$
$719$	−4.17433			−0.155676			−0.0778381	+	0.996966i	$0.524802\pi$
$720$		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	0.209662	−	0.977774i	$-0.432764\pi$
$727$	−20.7105	−	20.7105i	−0.768111	−	0.768111i	−0.977774	+	0.209662i	$0.932764\pi$
$728$	10.9966	−	8.16816i	0.407561	−	0.302732i
$729$		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	−0.673046	−	0.739601i	$-0.735014\pi$
$733$	1.80192	−	1.80192i	0.0665554	−	0.0665554i	0.739601	+	0.673046i	$0.235014\pi$
$734$	−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
$742$	19.9716	−	14.8347i	0.733179	−	0.544598i
$743$	−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	$0.0151744\pi$
$761$			2.62918i			0.0953076i	−0.998864	+	0.0476538i	$0.984826\pi$
$762$		0			0
$763$	−0.941651	−	1.26772i	−0.0340901	−	0.0458946i
$764$			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	$-0.671933\pi$
$769$	−28.5217			−1.02852			−0.514259	+	0.857635i	$0.671933\pi$
$770$	−2.63306	+	7.94147i	−0.0948888	+	0.286191i
$771$		0			0
$772$	−11.0000	+	11.0000i	−0.395899	+	0.395899i
$773$	−14.2583	+	14.2583i	−0.512835	+	0.512835i	−0.915394	−	0.402559i	$-0.868121\pi$
$773$	−14.2583	+	14.2583i	−0.512835	+	0.512835i	0.402559	+	0.915394i	$0.368121\pi$
$774$		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	$-0.903757\pi$
$787$	−35.1344	−	35.1344i	−1.25241	−	1.25241i	−0.297769	−	0.954638i	$-0.596243\pi$
$788$	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	0.407950	−	0.913004i	$-0.366244\pi$
$797$	−14.2583	−	14.2583i	−0.505054	−	0.505054i	−0.913004	+	0.407950i	$0.866244\pi$
$798$		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
$805$	−30.3411	−	10.0598i	−1.06938	−	0.354562i
$806$	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	$0.128354\pi$
$811$			22.3494i			0.784794i	−0.919796	+	0.392397i	$0.871646\pi$
$812$	17.1257	−	12.7208i	0.600995	−	0.446413i
$813$		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	$-0.639750\pi$
$829$	−24.4774			−0.850136			−0.425068	+	0.905161i	$0.639750\pi$
$830$	4.39069	−	25.0338i	0.152403	−	0.868936i
$831$		0			0
$832$	−3.66103	−	3.66103i	−0.126923	−	0.126923i
$833$	22.5834	−	12.1138i	0.782468	−	0.419718i
$834$		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	$-0.365236\pi$
$839$	23.8002			0.821674			0.410837	+	0.911709i	$0.365236\pi$
$840$		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
$847$	19.1154	−	14.1987i	0.656811	−	0.487873i
$848$	−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	−0.999947	−	0.0102603i	$-0.996734\pi$
$853$	−28.9050	+	28.9050i	−0.989687	+	0.989687i	0.0102603	+	0.999947i	$0.496734\pi$
$854$	−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	0.774178	−	0.632967i	$-0.218163\pi$
$857$	4.13389	+	4.13389i	0.141211	+	0.141211i	−0.632967	+	0.774178i	$0.718163\pi$
$858$		0			0
$859$	9.12397			0.311306			0.155653	−	0.987812i	$-0.450252\pi$
$859$	9.12397			0.311306			0.155653	+	0.987812i	$0.450252\pi$
$860$	−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
$868$	−21.0067	+	15.6036i	−0.713014	+	0.529620i
$869$			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
$875$	−29.3747	+	3.48231i	−0.993046	+	0.117724i
$876$		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	$0.261831\pi$
$881$			43.5070i			1.46579i	−0.680343	+	0.732893i	$0.738169\pi$
$882$		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	0.995686	−	0.0927904i	$-0.0295786\pi$
$887$	26.8905	+	26.8905i	0.902895	+	0.902895i	−0.0927904	+	0.995686i	$0.529579\pi$
$888$		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
$910$	13.7421	+	27.3747i	0.455546	+	0.907462i
$911$	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
$917$	−6.94932	−	9.35569i	−0.229487	−	0.308952i
$918$		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	$-0.409176\pi$
$929$	17.1585			0.562951			0.281475	+	0.959568i	$0.409176\pi$
$930$		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	$0.0453333\pi$
$937$	34.6453	+	34.6453i	1.13181	+	1.13181i	0.141938	+	0.989876i	$0.454667\pi$
$938$	8.92444	+	12.0148i	0.291393	+	0.392296i
$939$		0			0
$940$	−4.00000	+	2.80625i	−0.130466	+	0.0915297i
$941$		−	25.1148i		−	0.818719i	−0.912373	−	0.409360i	$-0.865752\pi$
$941$		−	25.1148i		−	0.818719i	0.912373	−	0.409360i	$-0.134248\pi$
$942$		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
$952$	−5.77576	−	7.77576i	−0.187193	−	0.252014i
$953$	−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	$-0.810132\pi$
$971$		−	35.0086i		−	1.12348i	0.827314	−	0.561740i	$-0.189868\pi$
$972$		0			0
$973$	−25.6479	+	19.0510i	−0.822233	+	0.610747i
$974$			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
$980$	−13.9787	−	7.04241i	−0.446534	−	0.224961i
$981$		0			0
$982$	−28.4031	+	28.4031i	−0.906380	+	0.906380i
$983$	35.2392	−	35.2392i	1.12396	−	1.12396i	0.132814	−	0.991141i	$-0.457599\pi$
$983$	35.2392	−	35.2392i	1.12396	−	1.12396i	0.991141	−	0.132814i	$-0.0424014\pi$
$984$		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	0.420872	−	0.907120i	$-0.361724\pi$
$997$	−15.3534	−	15.3534i	−0.486248	−	0.486248i	−0.907120	+	0.420872i	$0.861724\pi$
$998$	−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.433.4	yes	16
3.2	odd	2	inner	630.2.p.d.433.5	yes	16
5.2	odd	4	inner	630.2.p.d.307.1	✓	16
7.6	odd	2	inner	630.2.p.d.433.1	yes	16
15.2	even	4	inner	630.2.p.d.307.8	yes	16
21.20	even	2	inner	630.2.p.d.433.8	yes	16
35.27	even	4	inner	630.2.p.d.307.4	yes	16
105.62	odd	4	inner	630.2.p.d.307.5	yes	16

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

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(2.20245 + 0.386289i) q^{5} +(-2.12393 + 1.57763i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(2.20245 + 0.386289i) q^{5} +(-2.12393 + 1.57763i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.83051 + 1.28422i) q^{10} -1.41421 q^{11} +(-3.66103 + 3.66103i) q^{13} +(0.386289 - 2.61740i) q^{14} -1.00000 q^{16} +(2.58874 + 2.58874i) q^{17} -4.75362 q^{19} +(0.386289 - 2.20245i) q^{20} +(1.00000 - 1.00000i) q^{22} +(3.82059 + 3.82059i) q^{23} +(4.70156 + 1.70156i) q^{25} -5.17748i q^{26} +(1.57763 + 2.12393i) q^{28} -8.06323i q^{29} +9.89049i q^{31} +(0.707107 - 0.707107i) q^{32} -3.66103 q^{34} +(-5.28727 + 2.65421i) q^{35} +(-0.701562 + 0.701562i) q^{37} +(3.36131 - 3.36131i) q^{38} +(1.28422 + 1.83051i) q^{40} +10.3550i q^{41} +(-2.00000 - 2.00000i) q^{43} +1.41421i q^{44} -5.40312 q^{46} +(-1.54515 - 1.54515i) q^{47} +(2.02214 - 6.70156i) q^{49} +(-4.52769 + 2.12132i) q^{50} +(3.66103 + 3.66103i) q^{52} +(6.64901 + 6.64901i) q^{53} +(-3.11473 - 0.546295i) q^{55} +(-2.61740 - 0.386289i) q^{56} +(5.70156 + 5.70156i) q^{58} -7.49521 q^{59} -6.22947i q^{61} +(-6.99364 - 6.99364i) q^{62} +1.00000i q^{64} +(-9.47744 + 6.64901i) q^{65} +(-4.00000 + 4.00000i) q^{67} +(2.58874 - 2.58874i) q^{68} +(1.86185 - 5.61547i) q^{70} -0.992159 q^{71} +(-4.59058 + 4.59058i) q^{73} -0.992159i q^{74} +4.75362i q^{76} +(3.00369 - 2.23111i) q^{77} -7.40312i q^{79} +(-2.20245 - 0.386289i) q^{80} +(-7.32206 - 7.32206i) q^{82} +(-8.03722 + 8.03722i) q^{83} +(4.70156 + 6.70156i) q^{85} +2.82843 q^{86} +(-1.00000 - 1.00000i) q^{88} +12.4421 q^{89} +(2.00000 - 13.5515i) q^{91} +(3.82059 - 3.82059i) q^{92} +2.18518 q^{94} +(-10.4696 - 1.83627i) q^{95} +(1.63888 + 1.63888i) q^{97} +(3.30885 + 6.16859i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{7}+O(q^{10}) \) 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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