LMFDB - Embedded newform 630.2.k.h.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(361,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("630.361");

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.k (of order $3$, 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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	630.361
Dual form			630.2.k.h.541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} +(-0.500000 + 0.866025i) q^{11} +7.00000 q^{13} +(2.50000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} +(-0.500000 - 0.866025i) q^{19} -1.00000 q^{20} -1.00000 q^{22} +(0.500000 + 0.866025i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(3.50000 + 6.06218i) q^{26} +(0.500000 + 2.59808i) q^{28} +8.00000 q^{29} +(-3.00000 + 5.19615i) q^{31} +(0.500000 - 0.866025i) q^{32} -4.00000 q^{34} +(2.50000 + 0.866025i) q^{35} +(1.50000 + 2.59808i) q^{37} +(0.500000 - 0.866025i) q^{38} +(-0.500000 - 0.866025i) q^{40} -9.00000 q^{41} -4.00000 q^{43} +(-0.500000 - 0.866025i) q^{44} +(-0.500000 + 0.866025i) q^{46} +(-1.50000 - 2.59808i) q^{47} +(1.00000 - 6.92820i) q^{49} -1.00000 q^{50} +(-3.50000 + 6.06218i) q^{52} +(-0.500000 + 0.866025i) q^{53} -1.00000 q^{55} +(-2.00000 + 1.73205i) q^{56} +(4.00000 + 6.92820i) q^{58} +(6.00000 - 10.3923i) q^{59} +(2.00000 + 3.46410i) q^{61} -6.00000 q^{62} +1.00000 q^{64} +(3.50000 + 6.06218i) q^{65} +(-6.00000 + 10.3923i) q^{67} +(-2.00000 - 3.46410i) q^{68} +(0.500000 + 2.59808i) q^{70} +14.0000 q^{71} +(7.00000 - 12.1244i) q^{73} +(-1.50000 + 2.59808i) q^{74} +1.00000 q^{76} +(0.500000 + 2.59808i) q^{77} +(-2.00000 - 3.46410i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-4.50000 - 7.79423i) q^{82} -12.0000 q^{83} -4.00000 q^{85} +(-2.00000 - 3.46410i) q^{86} +(0.500000 - 0.866025i) q^{88} +(-1.00000 - 1.73205i) q^{89} +(14.0000 - 12.1244i) q^{91} -1.00000 q^{92} +(1.50000 - 2.59808i) q^{94} +(0.500000 - 0.866025i) q^{95} -16.0000 q^{97} +(6.50000 - 2.59808i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} + q^{5} + 4 q^{7} - 2 q^{8}+O(q^{10}) $ 2 * q + q^2 - q^4 + q^5 + 4 * q^7 - 2 * q^8	$ 2 q + q^{2} - q^{4} + q^{5} + 4 q^{7} - 2 q^{8} - q^{10} - q^{11} + 14 q^{13} + 5 q^{14} - q^{16} - 4 q^{17} - q^{19} - 2 q^{20} - 2 q^{22} + q^{23} - q^{25} + 7 q^{26} + q^{28} + 16 q^{29} - 6 q^{31} + q^{32} - 8 q^{34} + 5 q^{35} + 3 q^{37} + q^{38} - q^{40} - 18 q^{41} - 8 q^{43} - q^{44} - q^{46} - 3 q^{47} + 2 q^{49} - 2 q^{50} - 7 q^{52} - q^{53} - 2 q^{55} - 4 q^{56} + 8 q^{58} + 12 q^{59} + 4 q^{61} - 12 q^{62} + 2 q^{64} + 7 q^{65} - 12 q^{67} - 4 q^{68} + q^{70} + 28 q^{71} + 14 q^{73} - 3 q^{74} + 2 q^{76} + q^{77} - 4 q^{79} + q^{80} - 9 q^{82} - 24 q^{83} - 8 q^{85} - 4 q^{86} + q^{88} - 2 q^{89} + 28 q^{91} - 2 q^{92} + 3 q^{94} + q^{95} - 32 q^{97} + 13 q^{98}+O(q^{100}) $ 2 * q + q^2 - q^4 + q^5 + 4 * q^7 - 2 * q^8 - q^10 - q^11 + 14 * q^13 + 5 * q^14 - q^16 - 4 * q^17 - q^19 - 2 * q^20 - 2 * q^22 + q^23 - q^25 + 7 * q^26 + q^28 + 16 * q^29 - 6 * q^31 + q^32 - 8 * q^34 + 5 * q^35 + 3 * q^37 + q^38 - q^40 - 18 * q^41 - 8 * q^43 - q^44 - q^46 - 3 * q^47 + 2 * q^49 - 2 * q^50 - 7 * q^52 - q^53 - 2 * q^55 - 4 * q^56 + 8 * q^58 + 12 * q^59 + 4 * q^61 - 12 * q^62 + 2 * q^64 + 7 * q^65 - 12 * q^67 - 4 * q^68 + q^70 + 28 * q^71 + 14 * q^73 - 3 * q^74 + 2 * q^76 + q^77 - 4 * q^79 + q^80 - 9 * q^82 - 24 * q^83 - 8 * q^85 - 4 * q^86 + q^88 - 2 * q^89 + 28 * q^91 - 2 * q^92 + 3 * q^94 + q^95 - 32 * q^97 + 13 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	2.00000	−	1.73205i	0.755929	−	0.654654i
$7$	2.00000	−	1.73205i	0.755929	−	0.654654i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i	−0.931505	−	0.363727i	$-0.881504\pi$
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i	0.780750	+	0.624844i	$0.214837\pi$
$12$		0			0
$13$	7.00000			1.94145			0.970725	−	0.240192i	$-0.0772105\pi$
$13$	7.00000			1.94145			0.970725	+	0.240192i	$0.0772105\pi$
$14$	2.50000	+	0.866025i	0.668153	+	0.231455i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	−0.999853	−	0.0171533i	$-0.994540\pi$
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	0.514782	+	0.857321i	$0.327873\pi$
$18$		0			0
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	0.802955	−	0.596040i	$-0.203260\pi$
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	−0.917663	+	0.397360i	$0.869927\pi$
$20$	−1.00000			−0.223607
$21$		0			0
$22$	−1.00000			−0.213201
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i	0.913434	−	0.406986i	$-0.133420\pi$
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i	−0.809177	+	0.587565i	$0.800087\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	3.50000	+	6.06218i	0.686406	+	1.18889i
$27$		0			0
$28$	0.500000	+	2.59808i	0.0944911	+	0.490990i
$29$	8.00000			1.48556			0.742781	−	0.669534i	$-0.233506\pi$
$29$	8.00000			1.48556			0.742781	+	0.669534i	$0.233506\pi$
$30$		0			0
$31$	−3.00000	+	5.19615i	−0.538816	+	0.933257i	0.460152	+	0.887840i	$0.347795\pi$
$31$	−3.00000	+	5.19615i	−0.538816	+	0.933257i	−0.998968	+	0.0454165i	$0.985539\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	−4.00000			−0.685994
$35$	2.50000	+	0.866025i	0.422577	+	0.146385i
$36$		0			0
$37$	1.50000	+	2.59808i	0.246598	+	0.427121i	0.962580	−	0.270998i	$-0.0873538\pi$
$37$	1.50000	+	2.59808i	0.246598	+	0.427121i	−0.715981	+	0.698119i	$0.754020\pi$
$38$	0.500000	−	0.866025i	0.0811107	−	0.140488i
$39$		0			0
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	−9.00000			−1.40556			−0.702782	−	0.711405i	$-0.748059\pi$
$41$	−9.00000			−1.40556			−0.702782	+	0.711405i	$0.748059\pi$
$42$		0			0
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$	−0.500000	−	0.866025i	−0.0753778	−	0.130558i
$45$		0			0
$46$	−0.500000	+	0.866025i	−0.0737210	+	0.127688i
$47$	−1.50000	−	2.59808i	−0.218797	−	0.378968i	0.735643	−	0.677369i	$-0.236880\pi$
$47$	−1.50000	−	2.59808i	−0.218797	−	0.378968i	−0.954441	+	0.298401i	$0.903547\pi$
$48$		0			0
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$	−1.00000			−0.141421
$51$		0			0
$52$	−3.50000	+	6.06218i	−0.485363	+	0.840673i
$53$	−0.500000	+	0.866025i	−0.0686803	+	0.118958i	−0.898321	−	0.439340i	$-0.855212\pi$
$53$	−0.500000	+	0.866025i	−0.0686803	+	0.118958i	0.829640	+	0.558298i	$0.188546\pi$
$54$		0			0
$55$	−1.00000			−0.134840
$56$	−2.00000	+	1.73205i	−0.267261	+	0.231455i
$57$		0			0
$58$	4.00000	+	6.92820i	0.525226	+	0.909718i
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	−0.150148	−	0.988663i	$-0.547975\pi$
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	0.931282	−	0.364299i	$-0.118692\pi$
$60$		0			0
$61$	2.00000	+	3.46410i	0.256074	+	0.443533i	0.965187	−	0.261562i	$-0.0842377\pi$
$61$	2.00000	+	3.46410i	0.256074	+	0.443533i	−0.709113	+	0.705095i	$0.750904\pi$
$62$	−6.00000			−0.762001
$63$		0			0
$64$	1.00000			0.125000
$65$	3.50000	+	6.06218i	0.434122	+	0.751921i
$66$		0			0
$67$	−6.00000	+	10.3923i	−0.733017	+	1.26962i	0.222571	+	0.974916i	$0.428555\pi$
$67$	−6.00000	+	10.3923i	−0.733017	+	1.26962i	−0.955588	+	0.294706i	$0.904778\pi$
$68$	−2.00000	−	3.46410i	−0.242536	−	0.420084i
$69$		0			0
$70$	0.500000	+	2.59808i	0.0597614	+	0.310530i
$71$	14.0000			1.66149			0.830747	−	0.556650i	$-0.187914\pi$
$71$	14.0000			1.66149			0.830747	+	0.556650i	$0.187914\pi$
$72$		0			0
$73$	7.00000	−	12.1244i	0.819288	−	1.41905i	−0.0869195	−	0.996215i	$-0.527702\pi$
$73$	7.00000	−	12.1244i	0.819288	−	1.41905i	0.906208	−	0.422833i	$-0.138964\pi$
$74$	−1.50000	+	2.59808i	−0.174371	+	0.302020i
$75$		0			0
$76$	1.00000			0.114708
$77$	0.500000	+	2.59808i	0.0569803	+	0.296078i
$78$		0			0
$79$	−2.00000	−	3.46410i	−0.225018	−	0.389742i	0.731307	−	0.682048i	$-0.238911\pi$
$79$	−2.00000	−	3.46410i	−0.225018	−	0.389742i	−0.956325	+	0.292306i	$0.905577\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$		0			0
$82$	−4.50000	−	7.79423i	−0.496942	−	0.860729i
$83$	−12.0000			−1.31717			−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000			−1.31717			−0.658586	+	0.752506i	$0.728845\pi$
$84$		0			0
$85$	−4.00000			−0.433861
$86$	−2.00000	−	3.46410i	−0.215666	−	0.373544i
$87$		0			0
$88$	0.500000	−	0.866025i	0.0533002	−	0.0923186i
$89$	−1.00000	−	1.73205i	−0.106000	−	0.183597i	0.808146	−	0.588982i	$-0.200471\pi$
$89$	−1.00000	−	1.73205i	−0.106000	−	0.183597i	−0.914146	+	0.405385i	$0.867138\pi$
$90$		0			0
$91$	14.0000	−	12.1244i	1.46760	−	1.27098i
$92$	−1.00000			−0.104257
$93$		0			0
$94$	1.50000	−	2.59808i	0.154713	−	0.267971i
$95$	0.500000	−	0.866025i	0.0512989	−	0.0888523i
$96$		0			0
$97$	−16.0000			−1.62455			−0.812277	−	0.583272i	$-0.801772\pi$
$97$	−16.0000			−1.62455			−0.812277	+	0.583272i	$0.801772\pi$
$98$	6.50000	−	2.59808i	0.656599	−	0.262445i
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$		0			0
$103$	−8.00000	−	13.8564i	−0.788263	−	1.36531i	−0.927030	−	0.374987i	$-0.877647\pi$
$103$	−8.00000	−	13.8564i	−0.788263	−	1.36531i	0.138767	−	0.990325i	$-0.455686\pi$
$104$	−7.00000			−0.686406
$105$		0			0
$106$	−1.00000			−0.0971286
$107$	−9.00000	−	15.5885i	−0.870063	−	1.50699i	−0.861931	−	0.507026i	$-0.830745\pi$
$107$	−9.00000	−	15.5885i	−0.870063	−	1.50699i	−0.00813215	−	0.999967i	$-0.502589\pi$
$108$		0			0
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	−0.520794	−	0.853682i	$-0.674364\pi$
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	0.999708	+	0.0241802i	$0.00769755\pi$
$110$	−0.500000	−	0.866025i	−0.0476731	−	0.0825723i
$111$		0			0
$112$	−2.50000	−	0.866025i	−0.236228	−	0.0818317i
$113$	6.00000			0.564433			0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000			0.564433			0.282216	+	0.959351i	$0.408930\pi$
$114$		0			0
$115$	−0.500000	+	0.866025i	−0.0466252	+	0.0807573i
$116$	−4.00000	+	6.92820i	−0.371391	+	0.643268i
$117$		0			0
$118$	12.0000			1.10469
$119$	2.00000	+	10.3923i	0.183340	+	0.952661i
$120$		0			0
$121$	5.00000	+	8.66025i	0.454545	+	0.787296i
$122$	−2.00000	+	3.46410i	−0.181071	+	0.313625i
$123$		0			0
$124$	−3.00000	−	5.19615i	−0.269408	−	0.466628i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	5.00000			0.443678			0.221839	−	0.975083i	$-0.428794\pi$
$127$	5.00000			0.443678			0.221839	+	0.975083i	$0.428794\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−3.50000	+	6.06218i	−0.306970	+	0.531688i
$131$	−6.50000	−	11.2583i	−0.567908	−	0.983645i	−0.996773	−	0.0802763i	$-0.974420\pi$
$131$	−6.50000	−	11.2583i	−0.567908	−	0.983645i	0.428865	−	0.903369i	$-0.358914\pi$
$132$		0			0
$133$	−2.50000	−	0.866025i	−0.216777	−	0.0750939i
$134$	−12.0000			−1.03664
$135$		0			0
$136$	2.00000	−	3.46410i	0.171499	−	0.297044i
$137$	−1.00000	+	1.73205i	−0.0854358	+	0.147979i	−0.905577	−	0.424182i	$-0.860562\pi$
$137$	−1.00000	+	1.73205i	−0.0854358	+	0.147979i	0.820141	+	0.572161i	$0.193895\pi$
$138$		0			0
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$	−2.00000	+	1.73205i	−0.169031	+	0.146385i
$141$		0			0
$142$	7.00000	+	12.1244i	0.587427	+	1.01745i
$143$	−3.50000	+	6.06218i	−0.292685	+	0.506945i
$144$		0			0
$145$	4.00000	+	6.92820i	0.332182	+	0.575356i
$146$	14.0000			1.15865
$147$		0			0
$148$	−3.00000			−0.246598
$149$	−2.00000	−	3.46410i	−0.163846	−	0.283790i	0.772399	−	0.635138i	$-0.219057\pi$
$149$	−2.00000	−	3.46410i	−0.163846	−	0.283790i	−0.936245	+	0.351348i	$0.885723\pi$
$150$		0			0
$151$	1.00000	−	1.73205i	0.0813788	−	0.140952i	−0.822464	−	0.568818i	$-0.807401\pi$
$151$	1.00000	−	1.73205i	0.0813788	−	0.140952i	0.903842	+	0.427865i	$0.140734\pi$
$152$	0.500000	+	0.866025i	0.0405554	+	0.0702439i
$153$		0			0
$154$	−2.00000	+	1.73205i	−0.161165	+	0.139573i
$155$	−6.00000			−0.481932
$156$		0			0
$157$	−7.50000	+	12.9904i	−0.598565	+	1.03675i	0.394468	+	0.918910i	$0.370929\pi$
$157$	−7.50000	+	12.9904i	−0.598565	+	1.03675i	−0.993033	+	0.117836i	$0.962404\pi$
$158$	2.00000	−	3.46410i	0.159111	−	0.275589i
$159$		0			0
$160$	1.00000			0.0790569
$161$	2.50000	+	0.866025i	0.197028	+	0.0682524i
$162$		0			0
$163$	−4.00000	−	6.92820i	−0.313304	−	0.542659i	0.665771	−	0.746156i	$-0.268103\pi$
$163$	−4.00000	−	6.92820i	−0.313304	−	0.542659i	−0.979076	+	0.203497i	$0.934769\pi$
$164$	4.50000	−	7.79423i	0.351391	−	0.608627i
$165$		0			0
$166$	−6.00000	−	10.3923i	−0.465690	−	0.806599i
$167$	5.00000			0.386912			0.193456	−	0.981109i	$-0.438030\pi$
$167$	5.00000			0.386912			0.193456	+	0.981109i	$0.438030\pi$
$168$		0			0
$169$	36.0000			2.76923
$170$	−2.00000	−	3.46410i	−0.153393	−	0.265684i
$171$		0			0
$172$	2.00000	−	3.46410i	0.152499	−	0.264135i
$173$	−10.5000	−	18.1865i	−0.798300	−	1.38270i	−0.920722	−	0.390218i	$-0.872399\pi$
$173$	−10.5000	−	18.1865i	−0.798300	−	1.38270i	0.122422	−	0.992478i	$-0.460934\pi$
$174$		0			0
$175$	0.500000	+	2.59808i	0.0377964	+	0.196396i
$176$	1.00000			0.0753778
$177$		0			0
$178$	1.00000	−	1.73205i	0.0749532	−	0.129823i
$179$	6.50000	−	11.2583i	0.485833	−	0.841487i	−0.514035	−	0.857769i	$-0.671850\pi$
$179$	6.50000	−	11.2583i	0.485833	−	0.841487i	0.999867	+	0.0162823i	$0.00518305\pi$
$180$		0			0
$181$	−12.0000			−0.891953			−0.445976	−	0.895045i	$-0.647144\pi$
$181$	−12.0000			−0.891953			−0.445976	+	0.895045i	$0.647144\pi$
$182$	17.5000	+	6.06218i	1.29719	+	0.449359i
$183$		0			0
$184$	−0.500000	−	0.866025i	−0.0368605	−	0.0638442i
$185$	−1.50000	+	2.59808i	−0.110282	+	0.191014i
$186$		0			0
$187$	−2.00000	−	3.46410i	−0.146254	−	0.253320i
$188$	3.00000			0.218797
$189$		0			0
$190$	1.00000			0.0725476
$191$	−5.00000	−	8.66025i	−0.361787	−	0.626634i	0.626468	−	0.779447i	$-0.284500\pi$
$191$	−5.00000	−	8.66025i	−0.361787	−	0.626634i	−0.988255	+	0.152813i	$0.951167\pi$
$192$		0			0
$193$	−13.0000	+	22.5167i	−0.935760	+	1.62078i	−0.162488	+	0.986710i	$0.551952\pi$
$193$	−13.0000	+	22.5167i	−0.935760	+	1.62078i	−0.773272	+	0.634074i	$0.781381\pi$
$194$	−8.00000	−	13.8564i	−0.574367	−	0.994832i
$195$		0			0
$196$	5.50000	+	4.33013i	0.392857	+	0.309295i
$197$	3.00000			0.213741			0.106871	−	0.994273i	$-0.465917\pi$
$197$	3.00000			0.213741			0.106871	+	0.994273i	$0.465917\pi$
$198$		0			0
$199$	6.00000	−	10.3923i	0.425329	−	0.736691i	−0.571122	−	0.820865i	$-0.693492\pi$
$199$	6.00000	−	10.3923i	0.425329	−	0.736691i	0.996451	+	0.0841740i	$0.0268252\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$		0			0
$202$		0			0
$203$	16.0000	−	13.8564i	1.12298	−	0.972529i
$204$		0			0
$205$	−4.50000	−	7.79423i	−0.314294	−	0.544373i
$206$	8.00000	−	13.8564i	0.557386	−	0.965422i
$207$		0			0
$208$	−3.50000	−	6.06218i	−0.242681	−	0.420336i
$209$	1.00000			0.0691714
$210$		0			0
$211$	−15.0000			−1.03264			−0.516321	−	0.856395i	$-0.672699\pi$
$211$	−15.0000			−1.03264			−0.516321	+	0.856395i	$0.672699\pi$
$212$	−0.500000	−	0.866025i	−0.0343401	−	0.0594789i
$213$		0			0
$214$	9.00000	−	15.5885i	0.615227	−	1.06561i
$215$	−2.00000	−	3.46410i	−0.136399	−	0.236250i
$216$		0			0
$217$	3.00000	+	15.5885i	0.203653	+	1.05821i
$218$	10.0000			0.677285
$219$		0			0
$220$	0.500000	−	0.866025i	0.0337100	−	0.0583874i
$221$	−14.0000	+	24.2487i	−0.941742	+	1.63114i
$222$		0			0
$223$	−4.00000			−0.267860			−0.133930	−	0.990991i	$-0.542760\pi$
$223$	−4.00000			−0.267860			−0.133930	+	0.990991i	$0.542760\pi$
$224$	−0.500000	−	2.59808i	−0.0334077	−	0.173591i
$225$		0			0
$226$	3.00000	+	5.19615i	0.199557	+	0.345643i
$227$	−10.0000	+	17.3205i	−0.663723	+	1.14960i	0.315906	+	0.948790i	$0.397691\pi$
$227$	−10.0000	+	17.3205i	−0.663723	+	1.14960i	−0.979630	+	0.200812i	$0.935642\pi$
$228$		0			0
$229$	11.0000	+	19.0526i	0.726900	+	1.25903i	0.958187	+	0.286143i	$0.0923732\pi$
$229$	11.0000	+	19.0526i	0.726900	+	1.25903i	−0.231287	+	0.972886i	$0.574293\pi$
$230$	−1.00000			−0.0659380
$231$		0			0
$232$	−8.00000			−0.525226
$233$	13.0000	+	22.5167i	0.851658	+	1.47512i	0.879711	+	0.475509i	$0.157736\pi$
$233$	13.0000	+	22.5167i	0.851658	+	1.47512i	−0.0280525	+	0.999606i	$0.508931\pi$
$234$		0			0
$235$	1.50000	−	2.59808i	0.0978492	−	0.169480i
$236$	6.00000	+	10.3923i	0.390567	+	0.676481i
$237$		0			0
$238$	−8.00000	+	6.92820i	−0.518563	+	0.449089i
$239$	6.00000			0.388108			0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000			0.388108			0.194054	+	0.980991i	$0.437836\pi$
$240$		0			0
$241$	−3.50000	+	6.06218i	−0.225455	+	0.390499i	−0.956456	−	0.291877i	$-0.905720\pi$
$241$	−3.50000	+	6.06218i	−0.225455	+	0.390499i	0.731001	+	0.682376i	$0.239053\pi$
$242$	−5.00000	+	8.66025i	−0.321412	+	0.556702i
$243$		0			0
$244$	−4.00000			−0.256074
$245$	6.50000	−	2.59808i	0.415270	−	0.165985i
$246$		0			0
$247$	−3.50000	−	6.06218i	−0.222700	−	0.385727i
$248$	3.00000	−	5.19615i	0.190500	−	0.329956i
$249$		0			0
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	3.00000			0.189358			0.0946792	−	0.995508i	$-0.469817\pi$
$251$	3.00000			0.189358			0.0946792	+	0.995508i	$0.469817\pi$
$252$		0			0
$253$	−1.00000			−0.0628695
$254$	2.50000	+	4.33013i	0.156864	+	0.271696i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−4.00000	−	6.92820i	−0.249513	−	0.432169i	0.713878	−	0.700270i	$-0.246937\pi$
$257$	−4.00000	−	6.92820i	−0.249513	−	0.432169i	−0.963391	+	0.268101i	$0.913604\pi$
$258$		0			0
$259$	7.50000	+	2.59808i	0.466027	+	0.161437i
$260$	−7.00000			−0.434122
$261$		0			0
$262$	6.50000	−	11.2583i	0.401571	−	0.695542i
$263$	−8.00000	+	13.8564i	−0.493301	+	0.854423i	−0.999970	−	0.00771799i	$-0.997543\pi$
$263$	−8.00000	+	13.8564i	−0.493301	+	0.854423i	0.506669	+	0.862141i	$0.330877\pi$
$264$		0			0
$265$	−1.00000			−0.0614295
$266$	−0.500000	−	2.59808i	−0.0306570	−	0.159298i
$267$		0			0
$268$	−6.00000	−	10.3923i	−0.366508	−	0.634811i
$269$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$269$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$270$		0			0
$271$	−8.00000	−	13.8564i	−0.485965	−	0.841717i	0.513905	−	0.857847i	$-0.328199\pi$
$271$	−8.00000	−	13.8564i	−0.485965	−	0.841717i	−0.999870	+	0.0161307i	$0.994865\pi$
$272$	4.00000			0.242536
$273$		0			0
$274$	−2.00000			−0.120824
$275$	−0.500000	−	0.866025i	−0.0301511	−	0.0522233i
$276$		0			0
$277$	1.00000	−	1.73205i	0.0600842	−	0.104069i	−0.834419	−	0.551131i	$-0.814196\pi$
$277$	1.00000	−	1.73205i	0.0600842	−	0.104069i	0.894503	+	0.447062i	$0.147530\pi$
$278$	−2.00000	−	3.46410i	−0.119952	−	0.207763i
$279$		0			0
$280$	−2.50000	−	0.866025i	−0.149404	−	0.0517549i
$281$	−3.00000			−0.178965			−0.0894825	−	0.995988i	$-0.528521\pi$
$281$	−3.00000			−0.178965			−0.0894825	+	0.995988i	$0.528521\pi$
$282$		0			0
$283$	1.00000	−	1.73205i	0.0594438	−	0.102960i	−0.834772	−	0.550596i	$-0.814401\pi$
$283$	1.00000	−	1.73205i	0.0594438	−	0.102960i	0.894216	+	0.447636i	$0.147734\pi$
$284$	−7.00000	+	12.1244i	−0.415374	+	0.719448i
$285$		0			0
$286$	−7.00000			−0.413919
$287$	−18.0000	+	15.5885i	−1.06251	+	0.920158i
$288$		0			0
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$	−4.00000	+	6.92820i	−0.234888	+	0.406838i
$291$		0			0
$292$	7.00000	+	12.1244i	0.409644	+	0.709524i
$293$	−9.00000			−0.525786			−0.262893	−	0.964825i	$-0.584677\pi$
$293$	−9.00000			−0.525786			−0.262893	+	0.964825i	$0.584677\pi$
$294$		0			0
$295$	12.0000			0.698667
$296$	−1.50000	−	2.59808i	−0.0871857	−	0.151010i
$297$		0			0
$298$	2.00000	−	3.46410i	0.115857	−	0.200670i
$299$	3.50000	+	6.06218i	0.202410	+	0.350585i
$300$		0			0
$301$	−8.00000	+	6.92820i	−0.461112	+	0.399335i
$302$	2.00000			0.115087
$303$		0			0
$304$	−0.500000	+	0.866025i	−0.0286770	+	0.0496700i
$305$	−2.00000	+	3.46410i	−0.114520	+	0.198354i
$306$		0			0
$307$	8.00000			0.456584			0.228292	−	0.973593i	$-0.426686\pi$
$307$	8.00000			0.456584			0.228292	+	0.973593i	$0.426686\pi$
$308$	−2.50000	−	0.866025i	−0.142451	−	0.0493464i
$309$		0			0
$310$	−3.00000	−	5.19615i	−0.170389	−	0.295122i
$311$	8.00000	−	13.8564i	0.453638	−	0.785725i	−0.544970	−	0.838455i	$-0.683459\pi$
$311$	8.00000	−	13.8564i	0.453638	−	0.785725i	0.998609	+	0.0527306i	$0.0167924\pi$
$312$		0			0
$313$	12.0000	+	20.7846i	0.678280	+	1.17482i	0.975499	+	0.220006i	$0.0706077\pi$
$313$	12.0000	+	20.7846i	0.678280	+	1.17482i	−0.297218	+	0.954810i	$0.596059\pi$
$314$	−15.0000			−0.846499
$315$		0			0
$316$	4.00000			0.225018
$317$	5.00000	+	8.66025i	0.280828	+	0.486408i	0.971589	−	0.236675i	$-0.0760576\pi$
$317$	5.00000	+	8.66025i	0.280828	+	0.486408i	−0.690761	+	0.723083i	$0.742724\pi$
$318$		0			0
$319$	−4.00000	+	6.92820i	−0.223957	+	0.387905i
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$		0			0
$322$	0.500000	+	2.59808i	0.0278639	+	0.144785i
$323$	4.00000			0.222566
$324$		0			0
$325$	−3.50000	+	6.06218i	−0.194145	+	0.336269i
$326$	4.00000	−	6.92820i	0.221540	−	0.383718i
$327$		0			0
$328$	9.00000			0.496942
$329$	−7.50000	−	2.59808i	−0.413488	−	0.143237i
$330$		0			0
$331$	4.50000	+	7.79423i	0.247342	+	0.428410i	0.962788	−	0.270259i	$-0.0871094\pi$
$331$	4.50000	+	7.79423i	0.247342	+	0.428410i	−0.715445	+	0.698669i	$0.753776\pi$
$332$	6.00000	−	10.3923i	0.329293	−	0.570352i
$333$		0			0
$334$	2.50000	+	4.33013i	0.136794	+	0.236934i
$335$	−12.0000			−0.655630
$336$		0			0
$337$		0			0			−	1.00000i	$-0.5\pi$
$337$		0			0				1.00000i	$0.5\pi$
$338$	18.0000	+	31.1769i	0.979071	+	1.69580i
$339$		0			0
$340$	2.00000	−	3.46410i	0.108465	−	0.187867i
$341$	−3.00000	−	5.19615i	−0.162459	−	0.281387i
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	4.00000			0.215666
$345$		0			0
$346$	10.5000	−	18.1865i	0.564483	−	0.977714i
$347$	−17.0000	+	29.4449i	−0.912608	+	1.58068i	−0.102241	+	0.994760i	$0.532601\pi$
$347$	−17.0000	+	29.4449i	−0.912608	+	1.58068i	−0.810366	+	0.585923i	$0.800732\pi$
$348$		0			0
$349$	−28.0000			−1.49881			−0.749403	−	0.662114i	$-0.769659\pi$
$349$	−28.0000			−1.49881			−0.749403	+	0.662114i	$0.769659\pi$
$350$	−2.00000	+	1.73205i	−0.106904	+	0.0925820i
$351$		0			0
$352$	0.500000	+	0.866025i	0.0266501	+	0.0461593i
$353$	−4.00000	+	6.92820i	−0.212899	+	0.368751i	−0.952620	−	0.304162i	$-0.901624\pi$
$353$	−4.00000	+	6.92820i	−0.212899	+	0.368751i	0.739722	+	0.672913i	$0.234957\pi$
$354$		0			0
$355$	7.00000	+	12.1244i	0.371521	+	0.643494i
$356$	2.00000			0.106000
$357$		0			0
$358$	13.0000			0.687071
$359$	18.0000	+	31.1769i	0.950004	+	1.64545i	0.745409	+	0.666608i	$0.232254\pi$
$359$	18.0000	+	31.1769i	0.950004	+	1.64545i	0.204595	+	0.978847i	$0.434412\pi$
$360$		0			0
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$	−6.00000	−	10.3923i	−0.315353	−	0.546207i
$363$		0			0
$364$	3.50000	+	18.1865i	0.183450	+	0.953233i
$365$	14.0000			0.732793
$366$		0			0
$367$	−9.50000	+	16.4545i	−0.495896	+	0.858917i	−0.999989	−	0.00473247i	$-0.998494\pi$
$367$	−9.50000	+	16.4545i	−0.495896	+	0.858917i	0.504093	+	0.863649i	$0.331827\pi$
$368$	0.500000	−	0.866025i	0.0260643	−	0.0451447i
$369$		0			0
$370$	−3.00000			−0.155963
$371$	0.500000	+	2.59808i	0.0259587	+	0.134885i
$372$		0			0
$373$	−13.0000	−	22.5167i	−0.673114	−	1.16587i	−0.977016	−	0.213165i	$-0.931623\pi$
$373$	−13.0000	−	22.5167i	−0.673114	−	1.16587i	0.303902	−	0.952703i	$-0.401711\pi$
$374$	2.00000	−	3.46410i	0.103418	−	0.179124i
$375$		0			0
$376$	1.50000	+	2.59808i	0.0773566	+	0.133986i
$377$	56.0000			2.88415
$378$		0			0
$379$	1.00000			0.0513665			0.0256833	−	0.999670i	$-0.491824\pi$
$379$	1.00000			0.0513665			0.0256833	+	0.999670i	$0.491824\pi$
$380$	0.500000	+	0.866025i	0.0256495	+	0.0444262i
$381$		0			0
$382$	5.00000	−	8.66025i	0.255822	−	0.443097i
$383$	6.50000	+	11.2583i	0.332134	+	0.575274i	0.982930	−	0.183979i	$-0.0588979\pi$
$383$	6.50000	+	11.2583i	0.332134	+	0.575274i	−0.650796	+	0.759253i	$0.725565\pi$
$384$		0			0
$385$	−2.00000	+	1.73205i	−0.101929	+	0.0882735i
$386$	−26.0000			−1.32337
$387$		0			0
$388$	8.00000	−	13.8564i	0.406138	−	0.703452i
$389$	−7.00000	+	12.1244i	−0.354914	+	0.614729i	−0.987103	−	0.160085i	$-0.948823\pi$
$389$	−7.00000	+	12.1244i	−0.354914	+	0.614729i	0.632189	+	0.774814i	$0.282157\pi$
$390$		0			0
$391$	−4.00000			−0.202289
$392$	−1.00000	+	6.92820i	−0.0505076	+	0.349927i
$393$		0			0
$394$	1.50000	+	2.59808i	0.0755689	+	0.130889i
$395$	2.00000	−	3.46410i	0.100631	−	0.174298i
$396$		0			0
$397$	−9.00000	−	15.5885i	−0.451697	−	0.782362i	0.546795	−	0.837267i	$-0.315848\pi$
$397$	−9.00000	−	15.5885i	−0.451697	−	0.782362i	−0.998492	+	0.0549046i	$0.982515\pi$
$398$	12.0000			0.601506
$399$		0			0
$400$	1.00000			0.0500000
$401$	−8.50000	−	14.7224i	−0.424470	−	0.735203i	0.571901	−	0.820323i	$-0.306206\pi$
$401$	−8.50000	−	14.7224i	−0.424470	−	0.735203i	−0.996371	+	0.0851195i	$0.972873\pi$
$402$		0			0
$403$	−21.0000	+	36.3731i	−1.04608	+	1.81187i
$404$		0			0
$405$		0			0
$406$	20.0000	+	6.92820i	0.992583	+	0.343841i
$407$	−3.00000			−0.148704
$408$		0			0
$409$	−5.00000	+	8.66025i	−0.247234	+	0.428222i	−0.962757	−	0.270367i	$-0.912855\pi$
$409$	−5.00000	+	8.66025i	−0.247234	+	0.428222i	0.715523	+	0.698589i	$0.246188\pi$
$410$	4.50000	−	7.79423i	0.222239	−	0.384930i
$411$		0			0
$412$	16.0000			0.788263
$413$	−6.00000	−	31.1769i	−0.295241	−	1.53412i
$414$		0			0
$415$	−6.00000	−	10.3923i	−0.294528	−	0.510138i
$416$	3.50000	−	6.06218i	0.171602	−	0.297223i
$417$		0			0
$418$	0.500000	+	0.866025i	0.0244558	+	0.0423587i
$419$	−11.0000			−0.537385			−0.268693	−	0.963226i	$-0.586592\pi$
$419$	−11.0000			−0.537385			−0.268693	+	0.963226i	$0.586592\pi$
$420$		0			0
$421$	−14.0000			−0.682318			−0.341159	−	0.940006i	$-0.610819\pi$
$421$	−14.0000			−0.682318			−0.341159	+	0.940006i	$0.610819\pi$
$422$	−7.50000	−	12.9904i	−0.365094	−	0.632362i
$423$		0			0
$424$	0.500000	−	0.866025i	0.0242821	−	0.0420579i
$425$	−2.00000	−	3.46410i	−0.0970143	−	0.168034i
$426$		0			0
$427$	10.0000	+	3.46410i	0.483934	+	0.167640i
$428$	18.0000			0.870063
$429$		0			0
$430$	2.00000	−	3.46410i	0.0964486	−	0.167054i
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	−0.973574	−	0.228373i	$-0.926659\pi$
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	0.684564	+	0.728953i	$0.259993\pi$
$432$		0			0
$433$	40.0000			1.92228			0.961139	−	0.276066i	$-0.0890309\pi$
$433$	40.0000			1.92228			0.961139	+	0.276066i	$0.0890309\pi$
$434$	−12.0000	+	10.3923i	−0.576018	+	0.498847i
$435$		0			0
$436$	5.00000	+	8.66025i	0.239457	+	0.414751i
$437$	0.500000	−	0.866025i	0.0239182	−	0.0414276i
$438$		0			0
$439$	−8.00000	−	13.8564i	−0.381819	−	0.661330i	0.609503	−	0.792784i	$-0.291369\pi$
$439$	−8.00000	−	13.8564i	−0.381819	−	0.661330i	−0.991322	+	0.131453i	$0.958036\pi$
$440$	1.00000			0.0476731
$441$		0			0
$442$	−28.0000			−1.33182
$443$	−18.0000	−	31.1769i	−0.855206	−	1.48126i	−0.876454	−	0.481486i	$-0.840097\pi$
$443$	−18.0000	−	31.1769i	−0.855206	−	1.48126i	0.0212481	−	0.999774i	$-0.493236\pi$
$444$		0			0
$445$	1.00000	−	1.73205i	0.0474045	−	0.0821071i
$446$	−2.00000	−	3.46410i	−0.0947027	−	0.164030i
$447$		0			0
$448$	2.00000	−	1.73205i	0.0944911	−	0.0818317i
$449$	25.0000			1.17982			0.589911	−	0.807468i	$-0.299163\pi$
$449$	25.0000			1.17982			0.589911	+	0.807468i	$0.299163\pi$
$450$		0			0
$451$	4.50000	−	7.79423i	0.211897	−	0.367016i
$452$	−3.00000	+	5.19615i	−0.141108	+	0.244406i
$453$		0			0
$454$	−20.0000			−0.938647
$455$	17.5000	+	6.06218i	0.820413	+	0.284199i
$456$		0			0
$457$	−5.00000	−	8.66025i	−0.233890	−	0.405110i	0.725059	−	0.688686i	$-0.241812\pi$
$457$	−5.00000	−	8.66025i	−0.233890	−	0.405110i	−0.958950	+	0.283577i	$0.908479\pi$
$458$	−11.0000	+	19.0526i	−0.513996	+	0.890268i
$459$		0			0
$460$	−0.500000	−	0.866025i	−0.0233126	−	0.0403786i
$461$	28.0000			1.30409			0.652045	−	0.758180i	$-0.273911\pi$
$461$	28.0000			1.30409			0.652045	+	0.758180i	$0.273911\pi$
$462$		0			0
$463$	33.0000			1.53364			0.766820	−	0.641862i	$-0.221838\pi$
$463$	33.0000			1.53364			0.766820	+	0.641862i	$0.221838\pi$
$464$	−4.00000	−	6.92820i	−0.185695	−	0.321634i
$465$		0			0
$466$	−13.0000	+	22.5167i	−0.602213	+	1.04306i
$467$	6.00000	+	10.3923i	0.277647	+	0.480899i	0.970799	−	0.239892i	$-0.0771121\pi$
$467$	6.00000	+	10.3923i	0.277647	+	0.480899i	−0.693153	+	0.720791i	$0.743779\pi$
$468$		0			0
$469$	6.00000	+	31.1769i	0.277054	+	1.43962i
$470$	3.00000			0.138380
$471$		0			0
$472$	−6.00000	+	10.3923i	−0.276172	+	0.478345i
$473$	2.00000	−	3.46410i	0.0919601	−	0.159280i
$474$		0			0
$475$	1.00000			0.0458831
$476$	−10.0000	−	3.46410i	−0.458349	−	0.158777i
$477$		0			0
$478$	3.00000	+	5.19615i	0.137217	+	0.237666i
$479$	13.0000	−	22.5167i	0.593985	−	1.02881i	−0.399704	−	0.916644i	$-0.630887\pi$
$479$	13.0000	−	22.5167i	0.593985	−	1.02881i	0.993689	−	0.112168i	$-0.0357796\pi$
$480$		0			0
$481$	10.5000	+	18.1865i	0.478759	+	0.829235i
$482$	−7.00000			−0.318841
$483$		0			0
$484$	−10.0000			−0.454545
$485$	−8.00000	−	13.8564i	−0.363261	−	0.629187i
$486$		0			0
$487$	4.00000	−	6.92820i	0.181257	−	0.313947i	−0.761052	−	0.648691i	$-0.775317\pi$
$487$	4.00000	−	6.92820i	0.181257	−	0.313947i	0.942309	+	0.334744i	$0.108650\pi$
$488$	−2.00000	−	3.46410i	−0.0905357	−	0.156813i
$489$		0			0
$490$	5.50000	+	4.33013i	0.248465	+	0.195615i
$491$	12.0000			0.541552			0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000			0.541552			0.270776	+	0.962642i	$0.412720\pi$
$492$		0			0
$493$	−16.0000	+	27.7128i	−0.720604	+	1.24812i
$494$	3.50000	−	6.06218i	0.157472	−	0.272750i
$495$		0			0
$496$	6.00000			0.269408
$497$	28.0000	−	24.2487i	1.25597	−	1.08770i
$498$		0			0
$499$	−12.0000	−	20.7846i	−0.537194	−	0.930447i	−0.999054	−	0.0434940i	$-0.986151\pi$
$499$	−12.0000	−	20.7846i	−0.537194	−	0.930447i	0.461860	−	0.886953i	$-0.347182\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$		0			0
$502$	1.50000	+	2.59808i	0.0669483	+	0.115958i
$503$	−28.0000			−1.24846			−0.624229	−	0.781241i	$-0.714587\pi$
$503$	−28.0000			−1.24846			−0.624229	+	0.781241i	$0.714587\pi$
$504$		0			0
$505$		0			0
$506$	−0.500000	−	0.866025i	−0.0222277	−	0.0384995i
$507$		0			0
$508$	−2.50000	+	4.33013i	−0.110920	+	0.192118i
$509$	15.0000	+	25.9808i	0.664863	+	1.15158i	0.979322	+	0.202306i	$0.0648436\pi$
$509$	15.0000	+	25.9808i	0.664863	+	1.15158i	−0.314459	+	0.949271i	$0.601823\pi$
$510$		0			0
$511$	−7.00000	−	36.3731i	−0.309662	−	1.60905i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	4.00000	−	6.92820i	0.176432	−	0.305590i
$515$	8.00000	−	13.8564i	0.352522	−	0.610586i
$516$		0			0
$517$	3.00000			0.131940
$518$	1.50000	+	7.79423i	0.0659062	+	0.342459i
$519$		0			0
$520$	−3.50000	−	6.06218i	−0.153485	−	0.265844i
$521$	−10.5000	+	18.1865i	−0.460013	+	0.796766i	−0.998961	−	0.0455727i	$-0.985489\pi$
$521$	−10.5000	+	18.1865i	−0.460013	+	0.796766i	0.538948	+	0.842339i	$0.318822\pi$
$522$		0			0
$523$	7.00000	+	12.1244i	0.306089	+	0.530161i	0.977503	−	0.210921i	$-0.0676463\pi$
$523$	7.00000	+	12.1244i	0.306089	+	0.530161i	−0.671414	+	0.741082i	$0.734313\pi$
$524$	13.0000			0.567908
$525$		0			0
$526$	−16.0000			−0.697633
$527$	−12.0000	−	20.7846i	−0.522728	−	0.905392i
$528$		0			0
$529$	11.0000	−	19.0526i	0.478261	−	0.828372i
$530$	−0.500000	−	0.866025i	−0.0217186	−	0.0376177i
$531$		0			0
$532$	2.00000	−	1.73205i	0.0867110	−	0.0750939i
$533$	−63.0000			−2.72883
$534$		0			0
$535$	9.00000	−	15.5885i	0.389104	−	0.673948i
$536$	6.00000	−	10.3923i	0.259161	−	0.448879i
$537$		0			0
$538$		0			0
$539$	5.50000	+	4.33013i	0.236902	+	0.186512i
$540$		0			0
$541$	−1.00000	−	1.73205i	−0.0429934	−	0.0744667i	0.843728	−	0.536771i	$-0.180356\pi$
$541$	−1.00000	−	1.73205i	−0.0429934	−	0.0744667i	−0.886721	+	0.462304i	$0.847023\pi$
$542$	8.00000	−	13.8564i	0.343629	−	0.595184i
$543$		0			0
$544$	2.00000	+	3.46410i	0.0857493	+	0.148522i
$545$	10.0000			0.428353
$546$		0			0
$547$	36.0000			1.53925			0.769624	−	0.638497i	$-0.220443\pi$
$547$	36.0000			1.53925			0.769624	+	0.638497i	$0.220443\pi$
$548$	−1.00000	−	1.73205i	−0.0427179	−	0.0739895i
$549$		0			0
$550$	0.500000	−	0.866025i	0.0213201	−	0.0369274i
$551$	−4.00000	−	6.92820i	−0.170406	−	0.295151i
$552$		0			0
$553$	−10.0000	−	3.46410i	−0.425243	−	0.147309i
$554$	2.00000			0.0849719
$555$		0			0
$556$	2.00000	−	3.46410i	0.0848189	−	0.146911i
$557$	22.5000	−	38.9711i	0.953356	−	1.65126i	0.215268	−	0.976555i	$-0.430937\pi$
$557$	22.5000	−	38.9711i	0.953356	−	1.65126i	0.738087	−	0.674705i	$-0.235729\pi$
$558$		0			0
$559$	−28.0000			−1.18427
$560$	−0.500000	−	2.59808i	−0.0211289	−	0.109789i
$561$		0			0
$562$	−1.50000	−	2.59808i	−0.0632737	−	0.109593i
$563$	7.00000	−	12.1244i	0.295015	−	0.510981i	−0.679974	−	0.733237i	$-0.738009\pi$
$563$	7.00000	−	12.1244i	0.295015	−	0.510981i	0.974988	+	0.222256i	$0.0713421\pi$
$564$		0			0
$565$	3.00000	+	5.19615i	0.126211	+	0.218604i
$566$	2.00000			0.0840663
$567$		0			0
$568$	−14.0000			−0.587427
$569$	−18.5000	−	32.0429i	−0.775560	−	1.34331i	−0.934479	−	0.356018i	$-0.884134\pi$
$569$	−18.5000	−	32.0429i	−0.775560	−	1.34331i	0.158919	−	0.987292i	$-0.449199\pi$
$570$		0			0
$571$	4.00000	−	6.92820i	0.167395	−	0.289936i	−0.770108	−	0.637913i	$-0.779798\pi$
$571$	4.00000	−	6.92820i	0.167395	−	0.289936i	0.937503	+	0.347977i	$0.113131\pi$
$572$	−3.50000	−	6.06218i	−0.146342	−	0.253472i
$573$		0			0
$574$	−22.5000	−	7.79423i	−0.939132	−	0.325325i
$575$	−1.00000			−0.0417029
$576$		0			0
$577$	7.00000	−	12.1244i	0.291414	−	0.504744i	−0.682730	−	0.730670i	$-0.739208\pi$
$577$	7.00000	−	12.1244i	0.291414	−	0.504744i	0.974144	+	0.225927i	$0.0725410\pi$
$578$	−0.500000	+	0.866025i	−0.0207973	+	0.0360219i
$579$		0			0
$580$	−8.00000			−0.332182
$581$	−24.0000	+	20.7846i	−0.995688	+	0.862291i
$582$		0			0
$583$	−0.500000	−	0.866025i	−0.0207079	−	0.0358671i
$584$	−7.00000	+	12.1244i	−0.289662	+	0.501709i
$585$		0			0
$586$	−4.50000	−	7.79423i	−0.185893	−	0.321977i
$587$	−42.0000			−1.73353			−0.866763	−	0.498721i	$-0.833803\pi$
$587$	−42.0000			−1.73353			−0.866763	+	0.498721i	$0.833803\pi$
$588$		0			0
$589$	6.00000			0.247226
$590$	6.00000	+	10.3923i	0.247016	+	0.427844i
$591$		0			0
$592$	1.50000	−	2.59808i	0.0616496	−	0.106780i
$593$	6.00000	+	10.3923i	0.246390	+	0.426761i	0.962522	−	0.271205i	$-0.0874221\pi$
$593$	6.00000	+	10.3923i	0.246390	+	0.426761i	−0.716131	+	0.697966i	$0.754089\pi$
$594$		0			0
$595$	−8.00000	+	6.92820i	−0.327968	+	0.284029i
$596$	4.00000			0.163846
$597$		0			0
$598$	−3.50000	+	6.06218i	−0.143126	+	0.247901i
$599$	3.00000	−	5.19615i	0.122577	−	0.212309i	−0.798206	−	0.602384i	$-0.794218\pi$
$599$	3.00000	−	5.19615i	0.122577	−	0.212309i	0.920783	+	0.390075i	$0.127551\pi$
$600$		0			0
$601$	22.0000			0.897399			0.448699	−	0.893683i	$-0.351887\pi$
$601$	22.0000			0.897399			0.448699	+	0.893683i	$0.351887\pi$
$602$	−10.0000	−	3.46410i	−0.407570	−	0.141186i
$603$		0			0
$604$	1.00000	+	1.73205i	0.0406894	+	0.0704761i
$605$	−5.00000	+	8.66025i	−0.203279	+	0.352089i
$606$		0			0
$607$	−12.5000	−	21.6506i	−0.507359	−	0.878772i	−0.999964	−	0.00851879i	$-0.997288\pi$
$607$	−12.5000	−	21.6506i	−0.507359	−	0.878772i	0.492604	−	0.870253i	$-0.336045\pi$
$608$	−1.00000			−0.0405554
$609$		0			0
$610$	−4.00000			−0.161955
$611$	−10.5000	−	18.1865i	−0.424785	−	0.735748i
$612$		0			0
$613$	7.50000	−	12.9904i	0.302922	−	0.524677i	−0.673874	−	0.738846i	$-0.735371\pi$
$613$	7.50000	−	12.9904i	0.302922	−	0.524677i	0.976797	+	0.214169i	$0.0687045\pi$
$614$	4.00000	+	6.92820i	0.161427	+	0.279600i
$615$		0			0
$616$	−0.500000	−	2.59808i	−0.0201456	−	0.104679i
$617$	−8.00000			−0.322068			−0.161034	−	0.986949i	$-0.551483\pi$
$617$	−8.00000			−0.322068			−0.161034	+	0.986949i	$0.551483\pi$
$618$		0			0
$619$	3.50000	−	6.06218i	0.140677	−	0.243659i	−0.787075	−	0.616858i	$-0.788405\pi$
$619$	3.50000	−	6.06218i	0.140677	−	0.243659i	0.927752	+	0.373198i	$0.121739\pi$
$620$	3.00000	−	5.19615i	0.120483	−	0.208683i
$621$		0			0
$622$	16.0000			0.641542
$623$	−5.00000	−	1.73205i	−0.200321	−	0.0693932i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−12.0000	+	20.7846i	−0.479616	+	0.830720i
$627$		0			0
$628$	−7.50000	−	12.9904i	−0.299283	−	0.518373i
$629$	−12.0000			−0.478471
$630$		0			0
$631$	14.0000			0.557331			0.278666	−	0.960388i	$-0.410108\pi$
$631$	14.0000			0.557331			0.278666	+	0.960388i	$0.410108\pi$
$632$	2.00000	+	3.46410i	0.0795557	+	0.137795i
$633$		0			0
$634$	−5.00000	+	8.66025i	−0.198575	+	0.343943i
$635$	2.50000	+	4.33013i	0.0992095	+	0.171836i
$636$		0			0
$637$	7.00000	−	48.4974i	0.277350	−	1.92154i
$638$	−8.00000			−0.316723
$639$		0			0
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−11.5000	+	19.9186i	−0.454223	+	0.786737i	−0.998643	−	0.0520757i	$-0.983416\pi$
$641$	−11.5000	+	19.9186i	−0.454223	+	0.786737i	0.544420	+	0.838812i	$0.316750\pi$
$642$		0			0
$643$	26.0000			1.02534			0.512670	−	0.858586i	$-0.328656\pi$
$643$	26.0000			1.02534			0.512670	+	0.858586i	$0.328656\pi$
$644$	−2.00000	+	1.73205i	−0.0788110	+	0.0682524i
$645$		0			0
$646$	2.00000	+	3.46410i	0.0786889	+	0.136293i
$647$	−7.50000	+	12.9904i	−0.294855	+	0.510705i	−0.974951	−	0.222419i	$-0.928605\pi$
$647$	−7.50000	+	12.9904i	−0.294855	+	0.510705i	0.680096	+	0.733123i	$0.261938\pi$
$648$		0			0
$649$	6.00000	+	10.3923i	0.235521	+	0.407934i
$650$	−7.00000			−0.274563
$651$		0			0
$652$	8.00000			0.313304
$653$	14.5000	+	25.1147i	0.567429	+	0.982816i	0.996819	+	0.0796966i	$0.0253951\pi$
$653$	14.5000	+	25.1147i	0.567429	+	0.982816i	−0.429390	+	0.903119i	$0.641272\pi$
$654$		0			0
$655$	6.50000	−	11.2583i	0.253976	−	0.439899i
$656$	4.50000	+	7.79423i	0.175695	+	0.304314i
$657$		0			0
$658$	−1.50000	−	7.79423i	−0.0584761	−	0.303851i
$659$	12.0000			0.467454			0.233727	−	0.972302i	$-0.424908\pi$
$659$	12.0000			0.467454			0.233727	+	0.972302i	$0.424908\pi$
$660$		0			0
$661$	−4.00000	+	6.92820i	−0.155582	+	0.269476i	−0.933271	−	0.359174i	$-0.883059\pi$
$661$	−4.00000	+	6.92820i	−0.155582	+	0.269476i	0.777689	+	0.628649i	$0.216392\pi$
$662$	−4.50000	+	7.79423i	−0.174897	+	0.302931i
$663$		0			0
$664$	12.0000			0.465690
$665$	−0.500000	−	2.59808i	−0.0193892	−	0.100749i
$666$		0			0
$667$	4.00000	+	6.92820i	0.154881	+	0.268261i
$668$	−2.50000	+	4.33013i	−0.0967279	+	0.167538i
$669$		0			0
$670$	−6.00000	−	10.3923i	−0.231800	−	0.401490i
$671$	−4.00000			−0.154418
$672$		0			0
$673$	−12.0000			−0.462566			−0.231283	−	0.972887i	$-0.574292\pi$
$673$	−12.0000			−0.462566			−0.231283	+	0.972887i	$0.574292\pi$
$674$		0			0
$675$		0			0
$676$	−18.0000	+	31.1769i	−0.692308	+	1.19911i
$677$	0.500000	+	0.866025i	0.0192166	+	0.0332841i	0.875474	−	0.483266i	$-0.160549\pi$
$677$	0.500000	+	0.866025i	0.0192166	+	0.0332841i	−0.856257	+	0.516550i	$0.827216\pi$
$678$		0			0
$679$	−32.0000	+	27.7128i	−1.22805	+	1.06352i
$680$	4.00000			0.153393
$681$		0			0
$682$	3.00000	−	5.19615i	0.114876	−	0.198971i
$683$	6.00000	−	10.3923i	0.229584	−	0.397650i	−0.728101	−	0.685470i	$-0.759597\pi$
$683$	6.00000	−	10.3923i	0.229584	−	0.397650i	0.957685	+	0.287819i	$0.0929302\pi$
$684$		0			0
$685$	−2.00000			−0.0764161
$686$	8.50000	−	16.4545i	0.324532	−	0.628235i
$687$		0			0
$688$	2.00000	+	3.46410i	0.0762493	+	0.132068i
$689$	−3.50000	+	6.06218i	−0.133339	+	0.230951i
$690$		0			0
$691$	−6.00000	−	10.3923i	−0.228251	−	0.395342i	0.729039	−	0.684472i	$-0.239967\pi$
$691$	−6.00000	−	10.3923i	−0.228251	−	0.395342i	−0.957290	+	0.289130i	$0.906634\pi$
$692$	21.0000			0.798300
$693$		0			0
$694$	−34.0000			−1.29062
$695$	−2.00000	−	3.46410i	−0.0758643	−	0.131401i
$696$		0			0
$697$	18.0000	−	31.1769i	0.681799	−	1.18091i
$698$	−14.0000	−	24.2487i	−0.529908	−	0.917827i
$699$		0			0
$700$	−2.50000	−	0.866025i	−0.0944911	−	0.0327327i
$701$	−6.00000			−0.226617			−0.113308	−	0.993560i	$-0.536145\pi$
$701$	−6.00000			−0.226617			−0.113308	+	0.993560i	$0.536145\pi$
$702$		0			0
$703$	1.50000	−	2.59808i	0.0565736	−	0.0979883i
$704$	−0.500000	+	0.866025i	−0.0188445	+	0.0326396i
$705$		0			0
$706$	−8.00000			−0.301084
$707$		0			0
$708$		0			0
$709$	−2.00000	−	3.46410i	−0.0751116	−	0.130097i	0.826023	−	0.563636i	$-0.190598\pi$
$709$	−2.00000	−	3.46410i	−0.0751116	−	0.130097i	−0.901135	+	0.433539i	$0.857265\pi$
$710$	−7.00000	+	12.1244i	−0.262705	+	0.455019i
$711$		0			0
$712$	1.00000	+	1.73205i	0.0374766	+	0.0649113i
$713$	−6.00000			−0.224702
$714$		0			0
$715$	−7.00000			−0.261785
$716$	6.50000	+	11.2583i	0.242916	+	0.420744i
$717$		0			0
$718$	−18.0000	+	31.1769i	−0.671754	+	1.16351i
$719$	13.0000	+	22.5167i	0.484818	+	0.839730i	0.999848	−	0.0174426i	$-0.00555244\pi$
$719$	13.0000	+	22.5167i	0.484818	+	0.839730i	−0.515030	+	0.857172i	$0.672219\pi$
$720$		0			0
$721$	−40.0000	−	13.8564i	−1.48968	−	0.516040i
$722$	18.0000			0.669891
$723$		0			0
$724$	6.00000	−	10.3923i	0.222988	−	0.386227i
$725$	−4.00000	+	6.92820i	−0.148556	+	0.257307i
$726$		0			0
$727$	17.0000			0.630495			0.315248	−	0.949009i	$-0.397912\pi$
$727$	17.0000			0.630495			0.315248	+	0.949009i	$0.397912\pi$
$728$	−14.0000	+	12.1244i	−0.518875	+	0.449359i
$729$		0			0
$730$	7.00000	+	12.1244i	0.259082	+	0.448743i
$731$	8.00000	−	13.8564i	0.295891	−	0.512498i
$732$		0			0
$733$	−18.5000	−	32.0429i	−0.683313	−	1.18353i	−0.973964	−	0.226704i	$-0.927205\pi$
$733$	−18.5000	−	32.0429i	−0.683313	−	1.18353i	0.290651	−	0.956829i	$-0.406128\pi$
$734$	−19.0000			−0.701303
$735$		0			0
$736$	1.00000			0.0368605
$737$	−6.00000	−	10.3923i	−0.221013	−	0.382805i
$738$		0			0
$739$	−20.5000	+	35.5070i	−0.754105	+	1.30615i	0.191714	+	0.981451i	$0.438596\pi$
$739$	−20.5000	+	35.5070i	−0.754105	+	1.30615i	−0.945818	+	0.324697i	$0.894738\pi$
$740$	−1.50000	−	2.59808i	−0.0551411	−	0.0955072i
$741$		0			0
$742$	−2.00000	+	1.73205i	−0.0734223	+	0.0635856i
$743$	9.00000			0.330178			0.165089	−	0.986279i	$-0.447209\pi$
$743$	9.00000			0.330178			0.165089	+	0.986279i	$0.447209\pi$
$744$		0			0
$745$	2.00000	−	3.46410i	0.0732743	−	0.126915i
$746$	13.0000	−	22.5167i	0.475964	−	0.824394i
$747$		0			0
$748$	4.00000			0.146254
$749$	−45.0000	−	15.5885i	−1.64426	−	0.569590i
$750$		0			0
$751$	13.0000	+	22.5167i	0.474377	+	0.821645i	0.999570	−	0.0293387i	$-0.00934013\pi$
$751$	13.0000	+	22.5167i	0.474377	+	0.821645i	−0.525193	+	0.850983i	$0.676007\pi$
$752$	−1.50000	+	2.59808i	−0.0546994	+	0.0947421i
$753$		0			0
$754$	28.0000	+	48.4974i	1.01970	+	1.76617i
$755$	2.00000			0.0727875
$756$		0			0
$757$	−2.00000			−0.0726912			−0.0363456	−	0.999339i	$-0.511572\pi$
$757$	−2.00000			−0.0726912			−0.0363456	+	0.999339i	$0.511572\pi$
$758$	0.500000	+	0.866025i	0.0181608	+	0.0314555i
$759$		0			0
$760$	−0.500000	+	0.866025i	−0.0181369	+	0.0314140i
$761$	−8.50000	−	14.7224i	−0.308125	−	0.533688i	0.669827	−	0.742517i	$-0.266368\pi$
$761$	−8.50000	−	14.7224i	−0.308125	−	0.533688i	−0.977952	+	0.208829i	$0.933035\pi$
$762$		0			0
$763$	−5.00000	−	25.9808i	−0.181012	−	0.940567i
$764$	10.0000			0.361787
$765$		0			0
$766$	−6.50000	+	11.2583i	−0.234855	+	0.406780i
$767$	42.0000	−	72.7461i	1.51653	−	2.62671i
$768$		0			0
$769$	−29.0000			−1.04577			−0.522883	−	0.852404i	$-0.675144\pi$
$769$	−29.0000			−1.04577			−0.522883	+	0.852404i	$0.675144\pi$
$770$	−2.50000	−	0.866025i	−0.0900937	−	0.0312094i
$771$		0			0
$772$	−13.0000	−	22.5167i	−0.467880	−	0.810392i
$773$	21.5000	−	37.2391i	0.773301	−	1.33940i	−0.162443	−	0.986718i	$-0.551937\pi$
$773$	21.5000	−	37.2391i	0.773301	−	1.33940i	0.935744	−	0.352679i	$-0.114729\pi$
$774$		0			0
$775$	−3.00000	−	5.19615i	−0.107763	−	0.186651i
$776$	16.0000			0.574367
$777$		0			0
$778$	−14.0000			−0.501924
$779$	4.50000	+	7.79423i	0.161229	+	0.279257i
$780$		0			0
$781$	−7.00000	+	12.1244i	−0.250480	+	0.433844i
$782$	−2.00000	−	3.46410i	−0.0715199	−	0.123876i
$783$		0			0
$784$	−6.50000	+	2.59808i	−0.232143	+	0.0927884i
$785$	−15.0000			−0.535373
$786$		0			0
$787$	11.0000	−	19.0526i	0.392108	−	0.679150i	−0.600620	−	0.799535i	$-0.705079\pi$
$787$	11.0000	−	19.0526i	0.392108	−	0.679150i	0.992727	+	0.120384i	$0.0384127\pi$
$788$	−1.50000	+	2.59808i	−0.0534353	+	0.0925526i
$789$		0			0
$790$	4.00000			0.142314
$791$	12.0000	−	10.3923i	0.426671	−	0.369508i
$792$		0			0
$793$	14.0000	+	24.2487i	0.497155	+	0.861097i
$794$	9.00000	−	15.5885i	0.319398	−	0.553214i
$795$		0			0
$796$	6.00000	+	10.3923i	0.212664	+	0.368345i
$797$	6.00000			0.212531			0.106265	−	0.994338i	$-0.466111\pi$
$797$	6.00000			0.212531			0.106265	+	0.994338i	$0.466111\pi$
$798$		0			0
$799$	12.0000			0.424529
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$		0			0
$802$	8.50000	−	14.7224i	0.300145	−	0.519867i
$803$	7.00000	+	12.1244i	0.247025	+	0.427859i
$804$		0			0
$805$	0.500000	+	2.59808i	0.0176227	+	0.0915702i
$806$	−42.0000			−1.47939
$807$		0			0
$808$		0			0
$809$	26.5000	−	45.8993i	0.931690	−	1.61374i	0.151259	−	0.988494i	$-0.451667\pi$
$809$	26.5000	−	45.8993i	0.931690	−	1.61374i	0.780432	−	0.625241i	$-0.214999\pi$
$810$		0			0
$811$	37.0000			1.29925			0.649623	−	0.760257i	$-0.274927\pi$
$811$	37.0000			1.29925			0.649623	+	0.760257i	$0.274927\pi$
$812$	4.00000	+	20.7846i	0.140372	+	0.729397i
$813$		0			0
$814$	−1.50000	−	2.59808i	−0.0525750	−	0.0910625i
$815$	4.00000	−	6.92820i	0.140114	−	0.242684i
$816$		0			0
$817$	2.00000	+	3.46410i	0.0699711	+	0.121194i
$818$	−10.0000			−0.349642
$819$		0			0
$820$	9.00000			0.314294
$821$	17.0000	+	29.4449i	0.593304	+	1.02763i	0.993784	+	0.111327i	$0.0355102\pi$
$821$	17.0000	+	29.4449i	0.593304	+	1.02763i	−0.400480	+	0.916306i	$0.631157\pi$
$822$		0			0
$823$	−24.0000	+	41.5692i	−0.836587	+	1.44901i	0.0561440	+	0.998423i	$0.482119\pi$
$823$	−24.0000	+	41.5692i	−0.836587	+	1.44901i	−0.892731	+	0.450589i	$0.851214\pi$
$824$	8.00000	+	13.8564i	0.278693	+	0.482711i
$825$		0			0
$826$	24.0000	−	20.7846i	0.835067	−	0.723189i
$827$	−10.0000			−0.347734			−0.173867	−	0.984769i	$-0.555626\pi$
$827$	−10.0000			−0.347734			−0.173867	+	0.984769i	$0.555626\pi$
$828$		0			0
$829$	−6.00000	+	10.3923i	−0.208389	+	0.360940i	−0.951207	−	0.308553i	$-0.900155\pi$
$829$	−6.00000	+	10.3923i	−0.208389	+	0.360940i	0.742818	+	0.669493i	$0.233489\pi$
$830$	6.00000	−	10.3923i	0.208263	−	0.360722i
$831$		0			0
$832$	7.00000			0.242681
$833$	22.0000	+	17.3205i	0.762255	+	0.600120i
$834$		0			0
$835$	2.50000	+	4.33013i	0.0865161	+	0.149850i
$836$	−0.500000	+	0.866025i	−0.0172929	+	0.0299521i
$837$		0			0
$838$	−5.50000	−	9.52628i	−0.189994	−	0.329080i
$839$	−44.0000			−1.51905			−0.759524	−	0.650479i	$-0.774568\pi$
$839$	−44.0000			−1.51905			−0.759524	+	0.650479i	$0.774568\pi$
$840$		0			0
$841$	35.0000			1.20690
$842$	−7.00000	−	12.1244i	−0.241236	−	0.417833i
$843$		0			0
$844$	7.50000	−	12.9904i	0.258161	−	0.447147i
$845$	18.0000	+	31.1769i	0.619219	+	1.07252i
$846$		0			0
$847$	25.0000	+	8.66025i	0.859010	+	0.297570i
$848$	1.00000			0.0343401
$849$		0			0
$850$	2.00000	−	3.46410i	0.0685994	−	0.118818i
$851$	−1.50000	+	2.59808i	−0.0514193	+	0.0890609i
$852$		0			0
$853$	1.00000			0.0342393			0.0171197	−	0.999853i	$-0.494550\pi$
$853$	1.00000			0.0342393			0.0171197	+	0.999853i	$0.494550\pi$
$854$	2.00000	+	10.3923i	0.0684386	+	0.355617i
$855$		0			0
$856$	9.00000	+	15.5885i	0.307614	+	0.532803i
$857$	−11.0000	+	19.0526i	−0.375753	+	0.650823i	−0.990439	−	0.137948i	$-0.955949\pi$
$857$	−11.0000	+	19.0526i	−0.375753	+	0.650823i	0.614687	+	0.788771i	$0.289283\pi$
$858$		0			0
$859$	10.0000	+	17.3205i	0.341196	+	0.590968i	0.984655	−	0.174512i	$-0.0558348\pi$
$859$	10.0000	+	17.3205i	0.341196	+	0.590968i	−0.643459	+	0.765480i	$0.722501\pi$
$860$	4.00000			0.136399
$861$		0			0
$862$	−12.0000			−0.408722
$863$	14.5000	+	25.1147i	0.493586	+	0.854916i	0.999973	−	0.00739078i	$-0.00235258\pi$
$863$	14.5000	+	25.1147i	0.493586	+	0.854916i	−0.506387	+	0.862306i	$0.669019\pi$
$864$		0			0
$865$	10.5000	−	18.1865i	0.357011	−	0.618361i
$866$	20.0000	+	34.6410i	0.679628	+	1.17715i
$867$		0			0
$868$	−15.0000	−	5.19615i	−0.509133	−	0.176369i
$869$	4.00000			0.135691
$870$		0			0
$871$	−42.0000	+	72.7461i	−1.42312	+	2.46491i
$872$	−5.00000	+	8.66025i	−0.169321	+	0.293273i
$873$		0			0
$874$	1.00000			0.0338255
$875$	−2.00000	+	1.73205i	−0.0676123	+	0.0585540i
$876$		0			0
$877$	−11.5000	−	19.9186i	−0.388327	−	0.672603i	0.603897	−	0.797062i	$-0.293614\pi$
$877$	−11.5000	−	19.9186i	−0.388327	−	0.672603i	−0.992225	+	0.124459i	$0.960280\pi$
$878$	8.00000	−	13.8564i	0.269987	−	0.467631i
$879$		0			0
$880$	0.500000	+	0.866025i	0.0168550	+	0.0291937i
$881$	25.0000			0.842271			0.421136	−	0.906998i	$-0.361632\pi$
$881$	25.0000			0.842271			0.421136	+	0.906998i	$0.361632\pi$
$882$		0			0
$883$	−58.0000			−1.95186			−0.975928	−	0.218094i	$-0.930016\pi$
$883$	−58.0000			−1.95186			−0.975928	+	0.218094i	$0.930016\pi$
$884$	−14.0000	−	24.2487i	−0.470871	−	0.815572i
$885$		0			0
$886$	18.0000	−	31.1769i	0.604722	−	1.04741i
$887$	10.0000	+	17.3205i	0.335767	+	0.581566i	0.983632	−	0.180190i	$-0.0576711\pi$
$887$	10.0000	+	17.3205i	0.335767	+	0.581566i	−0.647865	+	0.761755i	$0.724338\pi$
$888$		0			0
$889$	10.0000	−	8.66025i	0.335389	−	0.290456i
$890$	2.00000			0.0670402
$891$		0			0
$892$	2.00000	−	3.46410i	0.0669650	−	0.115987i
$893$	−1.50000	+	2.59808i	−0.0501956	+	0.0869413i
$894$		0			0
$895$	13.0000			0.434542
$896$	2.50000	+	0.866025i	0.0835191	+	0.0289319i
$897$		0			0
$898$	12.5000	+	21.6506i	0.417130	+	0.722491i
$899$	−24.0000	+	41.5692i	−0.800445	+	1.38641i
$900$		0			0
$901$	−2.00000	−	3.46410i	−0.0666297	−	0.115406i
$902$	9.00000			0.299667
$903$		0			0
$904$	−6.00000			−0.199557
$905$	−6.00000	−	10.3923i	−0.199447	−	0.345452i
$906$		0			0
$907$	−23.0000	+	39.8372i	−0.763702	+	1.32277i	0.177227	+	0.984170i	$0.443287\pi$
$907$	−23.0000	+	39.8372i	−0.763702	+	1.32277i	−0.940930	+	0.338602i	$0.890046\pi$
$908$	−10.0000	−	17.3205i	−0.331862	−	0.574801i
$909$		0			0
$910$	3.50000	+	18.1865i	0.116024	+	0.602878i
$911$	58.0000			1.92163			0.960813	−	0.277198i	$-0.0894057\pi$
$911$	58.0000			1.92163			0.960813	+	0.277198i	$0.0894057\pi$
$912$		0			0
$913$	6.00000	−	10.3923i	0.198571	−	0.343935i
$914$	5.00000	−	8.66025i	0.165385	−	0.286456i
$915$		0			0
$916$	−22.0000			−0.726900
$917$	−32.5000	−	11.2583i	−1.07324	−	0.371783i
$918$		0			0
$919$	22.0000	+	38.1051i	0.725713	+	1.25697i	0.958680	+	0.284487i	$0.0918233\pi$
$919$	22.0000	+	38.1051i	0.725713	+	1.25697i	−0.232967	+	0.972485i	$0.574843\pi$
$920$	0.500000	−	0.866025i	0.0164845	−	0.0285520i
$921$		0			0
$922$	14.0000	+	24.2487i	0.461065	+	0.798589i
$923$	98.0000			3.22571
$924$		0			0
$925$	−3.00000			−0.0986394
$926$	16.5000	+	28.5788i	0.542224	+	0.939159i
$927$		0			0
$928$	4.00000	−	6.92820i	0.131306	−	0.227429i
$929$	15.5000	+	26.8468i	0.508539	+	0.880815i	0.999951	+	0.00988764i	$0.00314738\pi$
$929$	15.5000	+	26.8468i	0.508539	+	0.880815i	−0.491413	+	0.870927i	$0.663519\pi$
$930$		0			0
$931$	−6.50000	+	2.59808i	−0.213029	+	0.0851485i
$932$	−26.0000			−0.851658
$933$		0			0
$934$	−6.00000	+	10.3923i	−0.196326	+	0.340047i
$935$	2.00000	−	3.46410i	0.0654070	−	0.113288i
$936$		0			0
$937$	16.0000			0.522697			0.261349	−	0.965244i	$-0.415833\pi$
$937$	16.0000			0.522697			0.261349	+	0.965244i	$0.415833\pi$
$938$	−24.0000	+	20.7846i	−0.783628	+	0.678642i
$939$		0			0
$940$	1.50000	+	2.59808i	0.0489246	+	0.0847399i
$941$	−15.0000	+	25.9808i	−0.488986	+	0.846949i	−0.999920	−	0.0126715i	$-0.995966\pi$
$941$	−15.0000	+	25.9808i	−0.488986	+	0.846949i	0.510934	+	0.859620i	$0.329300\pi$
$942$		0			0
$943$	−4.50000	−	7.79423i	−0.146540	−	0.253815i
$944$	−12.0000			−0.390567
$945$		0			0
$946$	4.00000			0.130051
$947$	23.0000	+	39.8372i	0.747400	+	1.29453i	0.949065	+	0.315080i	$0.102031\pi$
$947$	23.0000	+	39.8372i	0.747400	+	1.29453i	−0.201666	+	0.979454i	$0.564635\pi$
$948$		0			0
$949$	49.0000	−	84.8705i	1.59061	−	2.75501i
$950$	0.500000	+	0.866025i	0.0162221	+	0.0280976i
$951$		0			0
$952$	−2.00000	−	10.3923i	−0.0648204	−	0.336817i
$953$	−44.0000			−1.42530			−0.712650	−	0.701520i	$-0.752505\pi$
$953$	−44.0000			−1.42530			−0.712650	+	0.701520i	$0.752505\pi$
$954$		0			0
$955$	5.00000	−	8.66025i	0.161796	−	0.280239i
$956$	−3.00000	+	5.19615i	−0.0970269	+	0.168056i
$957$		0			0
$958$	26.0000			0.840022
$959$	1.00000	+	5.19615i	0.0322917	+	0.167793i
$960$		0			0
$961$	−2.50000	−	4.33013i	−0.0806452	−	0.139682i
$962$	−10.5000	+	18.1865i	−0.338534	+	0.586357i
$963$		0			0
$964$	−3.50000	−	6.06218i	−0.112727	−	0.195250i
$965$	−26.0000			−0.836970
$966$		0			0
$967$	−20.0000			−0.643157			−0.321578	−	0.946883i	$-0.604213\pi$
$967$	−20.0000			−0.643157			−0.321578	+	0.946883i	$0.604213\pi$
$968$	−5.00000	−	8.66025i	−0.160706	−	0.278351i
$969$		0			0
$970$	8.00000	−	13.8564i	0.256865	−	0.444902i
$971$	21.5000	+	37.2391i	0.689968	+	1.19506i	0.971848	+	0.235610i	$0.0757087\pi$
$971$	21.5000	+	37.2391i	0.689968	+	1.19506i	−0.281880	+	0.959450i	$0.590958\pi$
$972$		0			0
$973$	−8.00000	+	6.92820i	−0.256468	+	0.222108i
$974$	8.00000			0.256337
$975$		0			0
$976$	2.00000	−	3.46410i	0.0640184	−	0.110883i
$977$	9.00000	−	15.5885i	0.287936	−	0.498719i	−0.685381	−	0.728184i	$-0.740364\pi$
$977$	9.00000	−	15.5885i	0.287936	−	0.498719i	0.973317	+	0.229465i	$0.0736978\pi$
$978$		0			0
$979$	2.00000			0.0639203
$980$	−1.00000	+	6.92820i	−0.0319438	+	0.221313i
$981$		0			0
$982$	6.00000	+	10.3923i	0.191468	+	0.331632i
$983$	−16.5000	+	28.5788i	−0.526268	+	0.911523i	0.473263	+	0.880921i	$0.343076\pi$
$983$	−16.5000	+	28.5788i	−0.526268	+	0.911523i	−0.999532	+	0.0306024i	$0.990257\pi$
$984$		0			0
$985$	1.50000	+	2.59808i	0.0477940	+	0.0827816i
$986$	−32.0000			−1.01909
$987$		0			0
$988$	7.00000			0.222700
$989$	−2.00000	−	3.46410i	−0.0635963	−	0.110152i
$990$		0			0
$991$	−5.00000	+	8.66025i	−0.158830	+	0.275102i	−0.934447	−	0.356102i	$-0.884106\pi$
$991$	−5.00000	+	8.66025i	−0.158830	+	0.275102i	0.775617	+	0.631204i	$0.217439\pi$
$992$	3.00000	+	5.19615i	0.0952501	+	0.164978i
$993$		0			0
$994$	35.0000	+	12.1244i	1.11013	+	0.384561i
$995$	12.0000			0.380426
$996$		0			0
$997$	−5.00000	+	8.66025i	−0.158352	+	0.274273i	−0.934274	−	0.356555i	$-0.883951\pi$
$997$	−5.00000	+	8.66025i	−0.158352	+	0.274273i	0.775923	+	0.630828i	$0.217285\pi$
$998$	12.0000	−	20.7846i	0.379853	−	0.657925i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.k.h.361.1		2
3.2	odd	2		210.2.i.a.151.1	yes	2
7.2	even	3	inner	630.2.k.h.541.1		2
7.3	odd	6		4410.2.a.q.1.1		1
7.4	even	3		4410.2.a.g.1.1		1
12.11	even	2		1680.2.bg.k.1201.1		2
15.2	even	4		1050.2.o.j.949.2		4
15.8	even	4		1050.2.o.j.949.1		4
15.14	odd	2		1050.2.i.s.151.1		2
21.2	odd	6		210.2.i.a.121.1	✓	2
21.5	even	6		1470.2.i.i.961.1		2
21.11	odd	6		1470.2.a.r.1.1		1
21.17	even	6		1470.2.a.k.1.1		1
21.20	even	2		1470.2.i.i.361.1		2
84.23	even	6		1680.2.bg.k.961.1		2
105.2	even	12		1050.2.o.j.499.1		4
105.23	even	12		1050.2.o.j.499.2		4
105.44	odd	6		1050.2.i.s.751.1		2
105.59	even	6		7350.2.a.ba.1.1		1
105.74	odd	6		7350.2.a.j.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.i.a.121.1	✓	2	21.2	odd	6
210.2.i.a.151.1	yes	2	3.2	odd	2
630.2.k.h.361.1		2	1.1	even	1	trivial
630.2.k.h.541.1		2	7.2	even	3	inner
1050.2.i.s.151.1		2	15.14	odd	2
1050.2.i.s.751.1		2	105.44	odd	6
1050.2.o.j.499.1		4	105.2	even	12
1050.2.o.j.499.2		4	105.23	even	12
1050.2.o.j.949.1		4	15.8	even	4
1050.2.o.j.949.2		4	15.2	even	4
1470.2.a.k.1.1		1	21.17	even	6
1470.2.a.r.1.1		1	21.11	odd	6
1470.2.i.i.361.1		2	21.20	even	2
1470.2.i.i.961.1		2	21.5	even	6
1680.2.bg.k.961.1		2	84.23	even	6
1680.2.bg.k.1201.1		2	12.11	even	2
4410.2.a.g.1.1		1	7.4	even	3
4410.2.a.q.1.1		1	7.3	odd	6
7350.2.a.j.1.1		1	105.74	odd	6
7350.2.a.ba.1.1		1	105.59	even	6

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.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} +(-0.500000 + 0.866025i) q^{11} +7.00000 q^{13} +(2.50000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} +(-0.500000 - 0.866025i) q^{19} -1.00000 q^{20} -1.00000 q^{22} +(0.500000 + 0.866025i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(3.50000 + 6.06218i) q^{26} +(0.500000 + 2.59808i) q^{28} +8.00000 q^{29} +(-3.00000 + 5.19615i) q^{31} +(0.500000 - 0.866025i) q^{32} -4.00000 q^{34} +(2.50000 + 0.866025i) q^{35} +(1.50000 + 2.59808i) q^{37} +(0.500000 - 0.866025i) q^{38} +(-0.500000 - 0.866025i) q^{40} -9.00000 q^{41} -4.00000 q^{43} +(-0.500000 - 0.866025i) q^{44} +(-0.500000 + 0.866025i) q^{46} +(-1.50000 - 2.59808i) q^{47} +(1.00000 - 6.92820i) q^{49} -1.00000 q^{50} +(-3.50000 + 6.06218i) q^{52} +(-0.500000 + 0.866025i) q^{53} -1.00000 q^{55} +(-2.00000 + 1.73205i) q^{56} +(4.00000 + 6.92820i) q^{58} +(6.00000 - 10.3923i) q^{59} +(2.00000 + 3.46410i) q^{61} -6.00000 q^{62} +1.00000 q^{64} +(3.50000 + 6.06218i) q^{65} +(-6.00000 + 10.3923i) q^{67} +(-2.00000 - 3.46410i) q^{68} +(0.500000 + 2.59808i) q^{70} +14.0000 q^{71} +(7.00000 - 12.1244i) q^{73} +(-1.50000 + 2.59808i) q^{74} +1.00000 q^{76} +(0.500000 + 2.59808i) q^{77} +(-2.00000 - 3.46410i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-4.50000 - 7.79423i) q^{82} -12.0000 q^{83} -4.00000 q^{85} +(-2.00000 - 3.46410i) q^{86} +(0.500000 - 0.866025i) q^{88} +(-1.00000 - 1.73205i) q^{89} +(14.0000 - 12.1244i) q^{91} -1.00000 q^{92} +(1.50000 - 2.59808i) q^{94} +(0.500000 - 0.866025i) q^{95} -16.0000 q^{97} +(6.50000 - 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} + q^{5} + 4 q^{7} - 2 q^{8}+O(q^{10}) \) 2 * q + q^2 - q^4 + q^5 + 4 * q^7 - 2 * q^8	\( 2 q + q^{2} - q^{4} + q^{5} + 4 q^{7} - 2 q^{8} - q^{10} - q^{11} + 14 q^{13} + 5 q^{14} - q^{16} - 4 q^{17} - q^{19} - 2 q^{20} - 2 q^{22} + q^{23} - q^{25} + 7 q^{26} + q^{28} + 16 q^{29} - 6 q^{31} + q^{32} - 8 q^{34} + 5 q^{35} + 3 q^{37} + q^{38} - q^{40} - 18 q^{41} - 8 q^{43} - q^{44} - q^{46} - 3 q^{47} + 2 q^{49} - 2 q^{50} - 7 q^{52} - q^{53} - 2 q^{55} - 4 q^{56} + 8 q^{58} + 12 q^{59} + 4 q^{61} - 12 q^{62} + 2 q^{64} + 7 q^{65} - 12 q^{67} - 4 q^{68} + q^{70} + 28 q^{71} + 14 q^{73} - 3 q^{74} + 2 q^{76} + q^{77} - 4 q^{79} + q^{80} - 9 q^{82} - 24 q^{83} - 8 q^{85} - 4 q^{86} + q^{88} - 2 q^{89} + 28 q^{91} - 2 q^{92} + 3 q^{94} + q^{95} - 32 q^{97} + 13 q^{98}+O(q^{100}) \) 2 * q + q^2 - q^4 + q^5 + 4 * q^7 - 2 * q^8 - q^10 - q^11 + 14 * q^13 + 5 * q^14 - q^16 - 4 * q^17 - q^19 - 2 * q^20 - 2 * q^22 + q^23 - q^25 + 7 * q^26 + q^28 + 16 * q^29 - 6 * q^31 + q^32 - 8 * q^34 + 5 * q^35 + 3 * q^37 + q^38 - q^40 - 18 * q^41 - 8 * q^43 - q^44 - q^46 - 3 * q^47 + 2 * q^49 - 2 * q^50 - 7 * q^52 - q^53 - 2 * q^55 - 4 * q^56 + 8 * q^58 + 12 * q^59 + 4 * q^61 - 12 * q^62 + 2 * q^64 + 7 * q^65 - 12 * q^67 - 4 * q^68 + q^70 + 28 * q^71 + 14 * q^73 - 3 * q^74 + 2 * q^76 + q^77 - 4 * q^79 + q^80 - 9 * q^82 - 24 * q^83 - 8 * q^85 - 4 * q^86 + q^88 - 2 * q^89 + 28 * q^91 - 2 * q^92 + 3 * q^94 + q^95 - 32 * q^97 + 13 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more