LMFDB - Embedded newform 630.2.k.c.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.c.541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} +(-0.500000 + 0.866025i) q^{11} +1.00000 q^{13} +(0.500000 - 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.50000 + 2.59808i) q^{19} +1.00000 q^{20} +1.00000 q^{22} +(3.50000 + 6.06218i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-0.500000 - 0.866025i) q^{26} +(-2.50000 + 0.866025i) q^{28} +8.00000 q^{29} +(1.00000 - 1.73205i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.500000 - 2.59808i) q^{35} +(-5.50000 - 9.52628i) q^{37} +(1.50000 - 2.59808i) q^{38} +(-0.500000 - 0.866025i) q^{40} +11.0000 q^{41} +8.00000 q^{43} +(-0.500000 - 0.866025i) q^{44} +(3.50000 - 6.06218i) q^{46} +(-2.50000 - 4.33013i) q^{47} +(1.00000 + 6.92820i) q^{49} +1.00000 q^{50} +(-0.500000 + 0.866025i) q^{52} +(-5.50000 + 9.52628i) q^{53} +1.00000 q^{55} +(2.00000 + 1.73205i) q^{56} +(-4.00000 - 6.92820i) q^{58} +(2.00000 - 3.46410i) q^{59} -2.00000 q^{62} +1.00000 q^{64} +(-0.500000 - 0.866025i) q^{65} +(-2.50000 + 0.866025i) q^{70} +6.00000 q^{71} +(3.00000 - 5.19615i) q^{73} +(-5.50000 + 9.52628i) q^{74} -3.00000 q^{76} +(-2.50000 + 0.866025i) q^{77} +(4.00000 + 6.92820i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-5.50000 - 9.52628i) q^{82} -8.00000 q^{83} +(-4.00000 - 6.92820i) q^{86} +(-0.500000 + 0.866025i) q^{88} +(-5.00000 - 8.66025i) q^{89} +(2.00000 + 1.73205i) q^{91} -7.00000 q^{92} +(-2.50000 + 4.33013i) q^{94} +(1.50000 - 2.59808i) q^{95} -16.0000 q^{97} +(5.50000 - 4.33013i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 2 q^{13} + q^{14} - q^{16} + 3 q^{19} + 2 q^{20} + 2 q^{22} + 7 q^{23} - q^{25} - q^{26} - 5 q^{28} + 16 q^{29} + 2 q^{31} - q^{32} + q^{35} - 11 q^{37} + 3 q^{38} - q^{40} + 22 q^{41} + 16 q^{43} - q^{44} + 7 q^{46} - 5 q^{47} + 2 q^{49} + 2 q^{50} - q^{52} - 11 q^{53} + 2 q^{55} + 4 q^{56} - 8 q^{58} + 4 q^{59} - 4 q^{62} + 2 q^{64} - q^{65} - 5 q^{70} + 12 q^{71} + 6 q^{73} - 11 q^{74} - 6 q^{76} - 5 q^{77} + 8 q^{79} - q^{80} - 11 q^{82} - 16 q^{83} - 8 q^{86} - q^{88} - 10 q^{89} + 4 q^{91} - 14 q^{92} - 5 q^{94} + 3 q^{95} - 32 q^{97} + 11 q^{98}+O(q^{100}) $ 2 * q - q^2 - q^4 - q^5 + 4 * q^7 + 2 * q^8 - q^10 - q^11 + 2 * q^13 + q^14 - q^16 + 3 * q^19 + 2 * q^20 + 2 * q^22 + 7 * q^23 - q^25 - q^26 - 5 * q^28 + 16 * q^29 + 2 * q^31 - q^32 + q^35 - 11 * q^37 + 3 * q^38 - q^40 + 22 * q^41 + 16 * q^43 - q^44 + 7 * q^46 - 5 * q^47 + 2 * q^49 + 2 * q^50 - q^52 - 11 * q^53 + 2 * q^55 + 4 * q^56 - 8 * q^58 + 4 * q^59 - 4 * q^62 + 2 * q^64 - q^65 - 5 * q^70 + 12 * q^71 + 6 * q^73 - 11 * q^74 - 6 * q^76 - 5 * q^77 + 8 * q^79 - q^80 - 11 * q^82 - 16 * q^83 - 8 * q^86 - q^88 - 10 * q^89 + 4 * q^91 - 14 * q^92 - 5 * q^94 + 3 * q^95 - 32 * q^97 + 11 * 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
$13$	1.00000			0.277350			0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000			0.277350			0.138675	+	0.990338i	$0.455716\pi$
$14$	0.500000	−	2.59808i	0.133631	−	0.694365i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$		0			0
$19$	1.50000	+	2.59808i	0.344124	+	0.596040i	0.985194	−	0.171442i	$-0.0548427\pi$
$19$	1.50000	+	2.59808i	0.344124	+	0.596040i	−0.641071	+	0.767482i	$0.721509\pi$
$20$	1.00000			0.223607
$21$		0			0
$22$	1.00000			0.213201
$23$	3.50000	+	6.06218i	0.729800	+	1.26405i	0.956967	+	0.290196i	$0.0937204\pi$
$23$	3.50000	+	6.06218i	0.729800	+	1.26405i	−0.227167	+	0.973856i	$0.572946\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.500000	−	0.866025i	−0.0980581	−	0.169842i
$27$		0			0
$28$	−2.50000	+	0.866025i	−0.472456	+	0.163663i
$29$	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
$31$	1.00000	−	1.73205i	0.179605	−	0.311086i	−0.762140	−	0.647412i	$-0.775851\pi$
$31$	1.00000	−	1.73205i	0.179605	−	0.311086i	0.941745	+	0.336327i	$0.109185\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$		0			0
$35$	0.500000	−	2.59808i	0.0845154	−	0.439155i
$36$		0			0
$37$	−5.50000	−	9.52628i	−0.904194	−	1.56611i	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	−5.50000	−	9.52628i	−0.904194	−	1.56611i	−0.0821995	−	0.996616i	$-0.526194\pi$
$38$	1.50000	−	2.59808i	0.243332	−	0.421464i
$39$		0			0
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	11.0000			1.71791			0.858956	−	0.512050i	$-0.171114\pi$
$41$	11.0000			1.71791			0.858956	+	0.512050i	$0.171114\pi$
$42$		0			0
$43$	8.00000			1.21999			0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000			1.21999			0.609994	+	0.792406i	$0.291172\pi$
$44$	−0.500000	−	0.866025i	−0.0753778	−	0.130558i
$45$		0			0
$46$	3.50000	−	6.06218i	0.516047	−	0.893819i
$47$	−2.50000	−	4.33013i	−0.364662	−	0.631614i	0.624059	−	0.781377i	$-0.285482\pi$
$47$	−2.50000	−	4.33013i	−0.364662	−	0.631614i	−0.988722	+	0.149763i	$0.952149\pi$
$48$		0			0
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$	1.00000			0.141421
$51$		0			0
$52$	−0.500000	+	0.866025i	−0.0693375	+	0.120096i
$53$	−5.50000	+	9.52628i	−0.755483	+	1.30854i	0.189651	+	0.981852i	$0.439264\pi$
$53$	−5.50000	+	9.52628i	−0.755483	+	1.30854i	−0.945134	+	0.326683i	$0.894069\pi$
$54$		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
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	−0.705965	−	0.708247i	$-0.749486\pi$
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	0.966342	+	0.257260i	$0.0828195\pi$
$60$		0			0
$61$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$61$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$62$	−2.00000			−0.254000
$63$		0			0
$64$	1.00000			0.125000
$65$	−0.500000	−	0.866025i	−0.0620174	−	0.107417i
$66$		0			0
$67$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$67$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$68$		0			0
$69$		0			0
$70$	−2.50000	+	0.866025i	−0.298807	+	0.103510i
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$		0			0
$73$	3.00000	−	5.19615i	0.351123	−	0.608164i	−0.635323	−	0.772246i	$-0.719133\pi$
$73$	3.00000	−	5.19615i	0.351123	−	0.608164i	0.986447	+	0.164083i	$0.0524664\pi$
$74$	−5.50000	+	9.52628i	−0.639362	+	1.10741i
$75$		0			0
$76$	−3.00000			−0.344124
$77$	−2.50000	+	0.866025i	−0.284901	+	0.0986928i
$78$		0			0
$79$	4.00000	+	6.92820i	0.450035	+	0.779484i	0.998388	−	0.0567635i	$-0.0180781\pi$
$79$	4.00000	+	6.92820i	0.450035	+	0.779484i	−0.548352	+	0.836247i	$0.684745\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$		0			0
$82$	−5.50000	−	9.52628i	−0.607373	−	1.05200i
$83$	−8.00000			−0.878114			−0.439057	−	0.898459i	$-0.644687\pi$
$83$	−8.00000			−0.878114			−0.439057	+	0.898459i	$0.644687\pi$
$84$		0			0
$85$		0			0
$86$	−4.00000	−	6.92820i	−0.431331	−	0.747087i
$87$		0			0
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	−5.00000	−	8.66025i	−0.529999	−	0.917985i	−0.999388	−	0.0349934i	$-0.988859\pi$
$89$	−5.00000	−	8.66025i	−0.529999	−	0.917985i	0.469389	−	0.882992i	$-0.344474\pi$
$90$		0			0
$91$	2.00000	+	1.73205i	0.209657	+	0.181568i
$92$	−7.00000			−0.729800
$93$		0			0
$94$	−2.50000	+	4.33013i	−0.257855	+	0.446619i
$95$	1.50000	−	2.59808i	0.153897	−	0.266557i
$96$		0			0
$97$	−16.0000			−1.62455			−0.812277	−	0.583272i	$-0.801772\pi$
$97$	−16.0000			−1.62455			−0.812277	+	0.583272i	$0.801772\pi$
$98$	5.50000	−	4.33013i	0.555584	−	0.437409i
$99$		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	$0.122353\pi$
$103$	8.00000	+	13.8564i	0.788263	+	1.36531i	−0.138767	+	0.990325i	$0.544314\pi$
$104$	1.00000			0.0980581
$105$		0			0
$106$	11.0000			1.06841
$107$	−5.00000	−	8.66025i	−0.483368	−	0.837218i	0.516449	−	0.856318i	$-0.327253\pi$
$107$	−5.00000	−	8.66025i	−0.483368	−	0.837218i	−0.999818	+	0.0190994i	$0.993920\pi$
$108$		0			0
$109$	−3.00000	+	5.19615i	−0.287348	+	0.497701i	−0.973176	−	0.230063i	$-0.926107\pi$
$109$	−3.00000	+	5.19615i	−0.287348	+	0.497701i	0.685828	+	0.727764i	$0.259440\pi$
$110$	−0.500000	−	0.866025i	−0.0476731	−	0.0825723i
$111$		0			0
$112$	0.500000	−	2.59808i	0.0472456	−	0.245495i
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$		0			0
$115$	3.50000	−	6.06218i	0.326377	−	0.565301i
$116$	−4.00000	+	6.92820i	−0.371391	+	0.643268i
$117$		0			0
$118$	−4.00000			−0.368230
$119$		0			0
$120$		0			0
$121$	5.00000	+	8.66025i	0.454545	+	0.787296i
$122$		0			0
$123$		0			0
$124$	1.00000	+	1.73205i	0.0898027	+	0.155543i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−17.0000			−1.50851			−0.754253	−	0.656584i	$-0.772001\pi$
$127$	−17.0000			−1.50851			−0.754253	+	0.656584i	$0.772001\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−0.500000	+	0.866025i	−0.0438529	+	0.0759555i
$131$	−2.50000	−	4.33013i	−0.218426	−	0.378325i	0.735901	−	0.677089i	$-0.236759\pi$
$131$	−2.50000	−	4.33013i	−0.218426	−	0.378325i	−0.954327	+	0.298764i	$0.903426\pi$
$132$		0			0
$133$	−1.50000	+	7.79423i	−0.130066	+	0.675845i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−9.00000	+	15.5885i	−0.768922	+	1.33181i	0.169226	+	0.985577i	$0.445873\pi$
$137$	−9.00000	+	15.5885i	−0.768922	+	1.33181i	−0.938148	+	0.346235i	$0.887460\pi$
$138$		0			0
$139$	20.0000			1.69638			0.848189	−	0.529694i	$-0.177693\pi$
$139$	20.0000			1.69638			0.848189	+	0.529694i	$0.177693\pi$
$140$	2.00000	+	1.73205i	0.169031	+	0.146385i
$141$		0			0
$142$	−3.00000	−	5.19615i	−0.251754	−	0.436051i
$143$	−0.500000	+	0.866025i	−0.0418121	+	0.0724207i
$144$		0			0
$145$	−4.00000	−	6.92820i	−0.332182	−	0.575356i
$146$	−6.00000			−0.496564
$147$		0			0
$148$	11.0000			0.904194
$149$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$149$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$150$		0			0
$151$	−3.00000	+	5.19615i	−0.244137	+	0.422857i	−0.961888	−	0.273442i	$-0.911838\pi$
$151$	−3.00000	+	5.19615i	−0.244137	+	0.422857i	0.717752	+	0.696299i	$0.245171\pi$
$152$	1.50000	+	2.59808i	0.121666	+	0.210732i
$153$		0			0
$154$	2.00000	+	1.73205i	0.161165	+	0.139573i
$155$	−2.00000			−0.160644
$156$		0			0
$157$	3.50000	−	6.06218i	0.279330	−	0.483814i	−0.691888	−	0.722005i	$-0.743221\pi$
$157$	3.50000	−	6.06218i	0.279330	−	0.483814i	0.971219	+	0.238190i	$0.0765542\pi$
$158$	4.00000	−	6.92820i	0.318223	−	0.551178i
$159$		0			0
$160$	1.00000			0.0790569
$161$	−3.50000	+	18.1865i	−0.275839	+	1.43330i
$162$		0			0
$163$	−8.00000	−	13.8564i	−0.626608	−	1.08532i	−0.988227	−	0.152992i	$-0.951109\pi$
$163$	−8.00000	−	13.8564i	−0.626608	−	1.08532i	0.361619	−	0.932326i	$-0.382224\pi$
$164$	−5.50000	+	9.52628i	−0.429478	+	0.743877i
$165$		0			0
$166$	4.00000	+	6.92820i	0.310460	+	0.537733i
$167$	3.00000			0.232147			0.116073	−	0.993241i	$-0.462969\pi$
$167$	3.00000			0.232147			0.116073	+	0.993241i	$0.462969\pi$
$168$		0			0
$169$	−12.0000			−0.923077
$170$		0			0
$171$		0			0
$172$	−4.00000	+	6.92820i	−0.304997	+	0.528271i
$173$	−7.50000	−	12.9904i	−0.570214	−	0.987640i	−0.996544	−	0.0830722i	$-0.973527\pi$
$173$	−7.50000	−	12.9904i	−0.570214	−	0.987640i	0.426329	−	0.904568i	$-0.359807\pi$
$174$		0			0
$175$	−2.50000	+	0.866025i	−0.188982	+	0.0654654i
$176$	1.00000			0.0753778
$177$		0			0
$178$	−5.00000	+	8.66025i	−0.374766	+	0.649113i
$179$	−9.50000	+	16.4545i	−0.710063	+	1.22987i	0.254770	+	0.967002i	$0.418000\pi$
$179$	−9.50000	+	16.4545i	−0.710063	+	1.22987i	−0.964833	+	0.262864i	$0.915333\pi$
$180$		0			0
$181$	−24.0000			−1.78391			−0.891953	−	0.452128i	$-0.850665\pi$
$181$	−24.0000			−1.78391			−0.891953	+	0.452128i	$0.850665\pi$
$182$	0.500000	−	2.59808i	0.0370625	−	0.192582i
$183$		0			0
$184$	3.50000	+	6.06218i	0.258023	+	0.446910i
$185$	−5.50000	+	9.52628i	−0.404368	+	0.700386i
$186$		0			0
$187$		0			0
$188$	5.00000			0.364662
$189$		0			0
$190$	−3.00000			−0.217643
$191$	−3.00000	−	5.19615i	−0.217072	−	0.375980i	0.736839	−	0.676068i	$-0.236317\pi$
$191$	−3.00000	−	5.19615i	−0.217072	−	0.375980i	−0.953912	+	0.300088i	$0.902984\pi$
$192$		0			0
$193$	−11.0000	+	19.0526i	−0.791797	+	1.37143i	0.133056	+	0.991109i	$0.457521\pi$
$193$	−11.0000	+	19.0526i	−0.791797	+	1.37143i	−0.924853	+	0.380325i	$0.875812\pi$
$194$	8.00000	+	13.8564i	0.574367	+	0.994832i
$195$		0			0
$196$	−6.50000	−	2.59808i	−0.464286	−	0.185577i
$197$	1.00000			0.0712470			0.0356235	−	0.999365i	$-0.488658\pi$
$197$	1.00000			0.0712470			0.0356235	+	0.999365i	$0.488658\pi$
$198$		0			0
$199$	12.0000	−	20.7846i	0.850657	−	1.47338i	−0.0299585	−	0.999551i	$-0.509538\pi$
$199$	12.0000	−	20.7846i	0.850657	−	1.47338i	0.880616	−	0.473831i	$-0.157129\pi$
$200$	−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
$205$	−5.50000	−	9.52628i	−0.384137	−	0.665344i
$206$	8.00000	−	13.8564i	0.557386	−	0.965422i
$207$		0			0
$208$	−0.500000	−	0.866025i	−0.0346688	−	0.0600481i
$209$	−3.00000			−0.207514
$210$		0			0
$211$	5.00000			0.344214			0.172107	−	0.985078i	$-0.444942\pi$
$211$	5.00000			0.344214			0.172107	+	0.985078i	$0.444942\pi$
$212$	−5.50000	−	9.52628i	−0.377742	−	0.654268i
$213$		0			0
$214$	−5.00000	+	8.66025i	−0.341793	+	0.592003i
$215$	−4.00000	−	6.92820i	−0.272798	−	0.472500i
$216$		0			0
$217$	5.00000	−	1.73205i	0.339422	−	0.117579i
$218$	6.00000			0.406371
$219$		0			0
$220$	−0.500000	+	0.866025i	−0.0337100	+	0.0583874i
$221$		0			0
$222$		0			0
$223$	12.0000			0.803579			0.401790	−	0.915732i	$-0.368388\pi$
$223$	12.0000			0.803579			0.401790	+	0.915732i	$0.368388\pi$
$224$	−2.50000	+	0.866025i	−0.167038	+	0.0578638i
$225$		0			0
$226$	3.00000	+	5.19615i	0.199557	+	0.345643i
$227$	4.00000	−	6.92820i	0.265489	−	0.459841i	−0.702202	−	0.711977i	$-0.747800\pi$
$227$	4.00000	−	6.92820i	0.265489	−	0.459841i	0.967692	+	0.252136i	$0.0811332\pi$
$228$		0			0
$229$	−7.00000	−	12.1244i	−0.462573	−	0.801200i	0.536515	−	0.843891i	$-0.319740\pi$
$229$	−7.00000	−	12.1244i	−0.462573	−	0.801200i	−0.999088	+	0.0426906i	$0.986407\pi$
$230$	−7.00000			−0.461566
$231$		0			0
$232$	8.00000			0.525226
$233$	9.00000	+	15.5885i	0.589610	+	1.02123i	0.994283	+	0.106773i	$0.0340517\pi$
$233$	9.00000	+	15.5885i	0.589610	+	1.02123i	−0.404674	+	0.914461i	$0.632615\pi$
$234$		0			0
$235$	−2.50000	+	4.33013i	−0.163082	+	0.282466i
$236$	2.00000	+	3.46410i	0.130189	+	0.225494i
$237$		0			0
$238$		0			0
$239$	18.0000			1.16432			0.582162	−	0.813073i	$-0.302207\pi$
$239$	18.0000			1.16432			0.582162	+	0.813073i	$0.302207\pi$
$240$		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
$244$		0			0
$245$	5.50000	−	4.33013i	0.351382	−	0.276642i
$246$		0			0
$247$	1.50000	+	2.59808i	0.0954427	+	0.165312i
$248$	1.00000	−	1.73205i	0.0635001	−	0.109985i
$249$		0			0
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	−13.0000			−0.820553			−0.410276	−	0.911961i	$-0.634568\pi$
$251$	−13.0000			−0.820553			−0.410276	+	0.911961i	$0.634568\pi$
$252$		0			0
$253$	−7.00000			−0.440086
$254$	8.50000	+	14.7224i	0.533337	+	0.923768i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−10.0000	−	17.3205i	−0.623783	−	1.08042i	−0.988775	−	0.149413i	$-0.952262\pi$
$257$	−10.0000	−	17.3205i	−0.623783	−	1.08042i	0.364992	−	0.931011i	$-0.381072\pi$
$258$		0			0
$259$	5.50000	−	28.5788i	0.341753	−	1.77580i
$260$	1.00000			0.0620174
$261$		0			0
$262$	−2.50000	+	4.33013i	−0.154451	+	0.267516i
$263$	12.0000	−	20.7846i	0.739952	−	1.28163i	−0.212565	−	0.977147i	$-0.568182\pi$
$263$	12.0000	−	20.7846i	0.739952	−	1.28163i	0.952517	−	0.304487i	$-0.0984850\pi$
$264$		0			0
$265$	11.0000			0.675725
$266$	7.50000	−	2.59808i	0.459855	−	0.159298i
$267$		0			0
$268$		0			0
$269$	10.0000	−	17.3205i	0.609711	−	1.05605i	−0.381577	−	0.924337i	$-0.624619\pi$
$269$	10.0000	−	17.3205i	0.609711	−	1.05605i	0.991288	−	0.131713i	$-0.0420477\pi$
$270$		0			0
$271$	−16.0000	−	27.7128i	−0.971931	−	1.68343i	−0.689713	−	0.724083i	$-0.742263\pi$
$271$	−16.0000	−	27.7128i	−0.971931	−	1.68343i	−0.282218	−	0.959350i	$-0.591070\pi$
$272$		0			0
$273$		0			0
$274$	18.0000			1.08742
$275$	−0.500000	−	0.866025i	−0.0301511	−	0.0522233i
$276$		0			0
$277$	11.0000	−	19.0526i	0.660926	−	1.14476i	−0.319447	−	0.947604i	$-0.603497\pi$
$277$	11.0000	−	19.0526i	0.660926	−	1.14476i	0.980373	−	0.197153i	$-0.0631696\pi$
$278$	−10.0000	−	17.3205i	−0.599760	−	1.03882i
$279$		0			0
$280$	0.500000	−	2.59808i	0.0298807	−	0.155265i
$281$	1.00000			0.0596550			0.0298275	−	0.999555i	$-0.490504\pi$
$281$	1.00000			0.0596550			0.0298275	+	0.999555i	$0.490504\pi$
$282$		0			0
$283$	7.00000	−	12.1244i	0.416107	−	0.720718i	−0.579437	−	0.815017i	$-0.696728\pi$
$283$	7.00000	−	12.1244i	0.416107	−	0.720718i	0.995544	+	0.0942988i	$0.0300609\pi$
$284$	−3.00000	+	5.19615i	−0.178017	+	0.308335i
$285$		0			0
$286$	1.00000			0.0591312
$287$	22.0000	+	19.0526i	1.29862	+	1.12464i
$288$		0			0
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	−4.00000	+	6.92820i	−0.234888	+	0.406838i
$291$		0			0
$292$	3.00000	+	5.19615i	0.175562	+	0.304082i
$293$	−27.0000			−1.57736			−0.788678	−	0.614806i	$-0.789234\pi$
$293$	−27.0000			−1.57736			−0.788678	+	0.614806i	$0.789234\pi$
$294$		0			0
$295$	−4.00000			−0.232889
$296$	−5.50000	−	9.52628i	−0.319681	−	0.553704i
$297$		0			0
$298$		0			0
$299$	3.50000	+	6.06218i	0.202410	+	0.350585i
$300$		0			0
$301$	16.0000	+	13.8564i	0.922225	+	0.798670i
$302$	6.00000			0.345261
$303$		0			0
$304$	1.50000	−	2.59808i	0.0860309	−	0.149010i
$305$		0			0
$306$		0			0
$307$	20.0000			1.14146			0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000			1.14146			0.570730	+	0.821138i	$0.306660\pi$
$308$	0.500000	−	2.59808i	0.0284901	−	0.148039i
$309$		0			0
$310$	1.00000	+	1.73205i	0.0567962	+	0.0983739i
$311$	6.00000	−	10.3923i	0.340229	−	0.589294i	−0.644246	−	0.764818i	$-0.722829\pi$
$311$	6.00000	−	10.3923i	0.340229	−	0.589294i	0.984475	+	0.175525i	$0.0561621\pi$
$312$		0			0
$313$	6.00000	+	10.3923i	0.339140	+	0.587408i	0.984271	−	0.176664i	$-0.0565306\pi$
$313$	6.00000	+	10.3923i	0.339140	+	0.587408i	−0.645131	+	0.764072i	$0.723197\pi$
$314$	−7.00000			−0.395033
$315$		0			0
$316$	−8.00000			−0.450035
$317$	−9.00000	−	15.5885i	−0.505490	−	0.875535i	−0.999980	−	0.00635137i	$-0.997978\pi$
$317$	−9.00000	−	15.5885i	−0.505490	−	0.875535i	0.494489	−	0.869184i	$-0.335355\pi$
$318$		0			0
$319$	−4.00000	+	6.92820i	−0.223957	+	0.387905i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$		0			0
$322$	17.5000	−	6.06218i	0.975237	−	0.337832i
$323$		0			0
$324$		0			0
$325$	−0.500000	+	0.866025i	−0.0277350	+	0.0480384i
$326$	−8.00000	+	13.8564i	−0.443079	+	0.767435i
$327$		0			0
$328$	11.0000			0.607373
$329$	2.50000	−	12.9904i	0.137829	−	0.716183i
$330$		0			0
$331$	6.50000	+	11.2583i	0.357272	+	0.618814i	0.987504	−	0.157593i	$-0.0503735\pi$
$331$	6.50000	+	11.2583i	0.357272	+	0.618814i	−0.630232	+	0.776407i	$0.717040\pi$
$332$	4.00000	−	6.92820i	0.219529	−	0.380235i
$333$		0			0
$334$	−1.50000	−	2.59808i	−0.0820763	−	0.142160i
$335$		0			0
$336$		0			0
$337$	−12.0000			−0.653682			−0.326841	−	0.945079i	$-0.605984\pi$
$337$	−12.0000			−0.653682			−0.326841	+	0.945079i	$0.605984\pi$
$338$	6.00000	+	10.3923i	0.326357	+	0.565267i
$339$		0			0
$340$		0			0
$341$	1.00000	+	1.73205i	0.0541530	+	0.0937958i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	8.00000			0.431331
$345$		0			0
$346$	−7.50000	+	12.9904i	−0.403202	+	0.698367i
$347$	7.00000	−	12.1244i	0.375780	−	0.650870i	−0.614664	−	0.788789i	$-0.710708\pi$
$347$	7.00000	−	12.1244i	0.375780	−	0.650870i	0.990443	+	0.137920i	$0.0440416\pi$
$348$		0			0
$349$	12.0000			0.642345			0.321173	−	0.947021i	$-0.395923\pi$
$349$	12.0000			0.642345			0.321173	+	0.947021i	$0.395923\pi$
$350$	2.00000	+	1.73205i	0.106904	+	0.0925820i
$351$		0			0
$352$	−0.500000	−	0.866025i	−0.0266501	−	0.0461593i
$353$	12.0000	−	20.7846i	0.638696	−	1.10625i	−0.347024	−	0.937856i	$-0.612808\pi$
$353$	12.0000	−	20.7846i	0.638696	−	1.10625i	0.985719	−	0.168397i	$-0.0538590\pi$
$354$		0			0
$355$	−3.00000	−	5.19615i	−0.159223	−	0.275783i
$356$	10.0000			0.529999
$357$		0			0
$358$	19.0000			1.00418
$359$	2.00000	+	3.46410i	0.105556	+	0.182828i	0.913965	−	0.405793i	$-0.133004\pi$
$359$	2.00000	+	3.46410i	0.105556	+	0.182828i	−0.808409	+	0.588621i	$0.799671\pi$
$360$		0			0
$361$	5.00000	−	8.66025i	0.263158	−	0.455803i
$362$	12.0000	+	20.7846i	0.630706	+	1.09241i
$363$		0			0
$364$	−2.50000	+	0.866025i	−0.131036	+	0.0453921i
$365$	−6.00000			−0.314054
$366$		0			0
$367$	−12.5000	+	21.6506i	−0.652495	+	1.13015i	0.330021	+	0.943974i	$0.392944\pi$
$367$	−12.5000	+	21.6506i	−0.652495	+	1.13015i	−0.982516	+	0.186180i	$0.940389\pi$
$368$	3.50000	−	6.06218i	0.182450	−	0.316013i
$369$		0			0
$370$	11.0000			0.571863
$371$	−27.5000	+	9.52628i	−1.42773	+	0.494580i
$372$		0			0
$373$	−3.00000	−	5.19615i	−0.155334	−	0.269047i	0.777847	−	0.628454i	$-0.216312\pi$
$373$	−3.00000	−	5.19615i	−0.155334	−	0.269047i	−0.933181	+	0.359408i	$0.882979\pi$
$374$		0			0
$375$		0			0
$376$	−2.50000	−	4.33013i	−0.128928	−	0.223309i
$377$	8.00000			0.412021
$378$		0			0
$379$	−19.0000			−0.975964			−0.487982	−	0.872854i	$-0.662267\pi$
$379$	−19.0000			−0.975964			−0.487982	+	0.872854i	$0.662267\pi$
$380$	1.50000	+	2.59808i	0.0769484	+	0.133278i
$381$		0			0
$382$	−3.00000	+	5.19615i	−0.153493	+	0.265858i
$383$	17.5000	+	30.3109i	0.894208	+	1.54881i	0.834781	+	0.550581i	$0.185594\pi$
$383$	17.5000	+	30.3109i	0.894208	+	1.54881i	0.0594268	+	0.998233i	$0.481073\pi$
$384$		0			0
$385$	2.00000	+	1.73205i	0.101929	+	0.0882735i
$386$	22.0000			1.11977
$387$		0			0
$388$	8.00000	−	13.8564i	0.406138	−	0.703452i
$389$	5.00000	−	8.66025i	0.253510	−	0.439092i	−0.710980	−	0.703213i	$-0.751748\pi$
$389$	5.00000	−	8.66025i	0.253510	−	0.439092i	0.964490	+	0.264120i	$0.0850816\pi$
$390$		0			0
$391$		0			0
$392$	1.00000	+	6.92820i	0.0505076	+	0.349927i
$393$		0			0
$394$	−0.500000	−	0.866025i	−0.0251896	−	0.0436297i
$395$	4.00000	−	6.92820i	0.201262	−	0.348596i
$396$		0			0
$397$	−7.00000	−	12.1244i	−0.351320	−	0.608504i	0.635161	−	0.772380i	$-0.280934\pi$
$397$	−7.00000	−	12.1244i	−0.351320	−	0.608504i	−0.986481	+	0.163876i	$0.947600\pi$
$398$	−24.0000			−1.20301
$399$		0			0
$400$	1.00000			0.0500000
$401$	−2.50000	−	4.33013i	−0.124844	−	0.216236i	0.796828	−	0.604206i	$-0.206510\pi$
$401$	−2.50000	−	4.33013i	−0.124844	−	0.216236i	−0.921672	+	0.387970i	$0.873176\pi$
$402$		0			0
$403$	1.00000	−	1.73205i	0.0498135	−	0.0862796i
$404$		0			0
$405$		0			0
$406$	4.00000	−	20.7846i	0.198517	−	1.03152i
$407$	11.0000			0.545250
$408$		0			0
$409$	−1.00000	+	1.73205i	−0.0494468	+	0.0856444i	−0.889689	−	0.456566i	$-0.849079\pi$
$409$	−1.00000	+	1.73205i	−0.0494468	+	0.0856444i	0.840243	+	0.542211i	$0.182412\pi$
$410$	−5.50000	+	9.52628i	−0.271626	+	0.470469i
$411$		0			0
$412$	−16.0000			−0.788263
$413$	10.0000	−	3.46410i	0.492068	−	0.170457i
$414$		0			0
$415$	4.00000	+	6.92820i	0.196352	+	0.340092i
$416$	−0.500000	+	0.866025i	−0.0245145	+	0.0424604i
$417$		0			0
$418$	1.50000	+	2.59808i	0.0733674	+	0.127076i
$419$	5.00000			0.244266			0.122133	−	0.992514i	$-0.461027\pi$
$419$	5.00000			0.244266			0.122133	+	0.992514i	$0.461027\pi$
$420$		0			0
$421$	22.0000			1.07221			0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000			1.07221			0.536107	+	0.844150i	$0.319894\pi$
$422$	−2.50000	−	4.33013i	−0.121698	−	0.210787i
$423$		0			0
$424$	−5.50000	+	9.52628i	−0.267104	+	0.462637i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	10.0000			0.483368
$429$		0			0
$430$	−4.00000	+	6.92820i	−0.192897	+	0.334108i
$431$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$431$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$432$		0			0
$433$	−32.0000			−1.53782			−0.768911	−	0.639356i	$-0.779201\pi$
$433$	−32.0000			−1.53782			−0.768911	+	0.639356i	$0.779201\pi$
$434$	−4.00000	−	3.46410i	−0.192006	−	0.166282i
$435$		0			0
$436$	−3.00000	−	5.19615i	−0.143674	−	0.248851i
$437$	−10.5000	+	18.1865i	−0.502283	+	0.869980i
$438$		0			0
$439$	−16.0000	−	27.7128i	−0.763638	−	1.32266i	−0.940963	−	0.338508i	$-0.890078\pi$
$439$	−16.0000	−	27.7128i	−0.763638	−	1.32266i	0.177325	−	0.984152i	$-0.443256\pi$
$440$	1.00000			0.0476731
$441$		0			0
$442$		0			0
$443$	8.00000	+	13.8564i	0.380091	+	0.658338i	0.991075	−	0.133306i	$-0.0425592\pi$
$443$	8.00000	+	13.8564i	0.380091	+	0.658338i	−0.610984	+	0.791643i	$0.709226\pi$
$444$		0			0
$445$	−5.00000	+	8.66025i	−0.237023	+	0.410535i
$446$	−6.00000	−	10.3923i	−0.284108	−	0.492090i
$447$		0			0
$448$	2.00000	+	1.73205i	0.0944911	+	0.0818317i
$449$	−11.0000			−0.519122			−0.259561	−	0.965727i	$-0.583578\pi$
$449$	−11.0000			−0.519122			−0.259561	+	0.965727i	$0.583578\pi$
$450$		0			0
$451$	−5.50000	+	9.52628i	−0.258985	+	0.448575i
$452$	3.00000	−	5.19615i	0.141108	−	0.244406i
$453$		0			0
$454$	−8.00000			−0.375459
$455$	0.500000	−	2.59808i	0.0234404	−	0.121800i
$456$		0			0
$457$	9.00000	+	15.5885i	0.421002	+	0.729197i	0.996038	−	0.0889312i	$-0.0283451\pi$
$457$	9.00000	+	15.5885i	0.421002	+	0.729197i	−0.575036	+	0.818128i	$0.695012\pi$
$458$	−7.00000	+	12.1244i	−0.327089	+	0.566534i
$459$		0			0
$460$	3.50000	+	6.06218i	0.163188	+	0.282650i
$461$	12.0000			0.558896			0.279448	−	0.960161i	$-0.409849\pi$
$461$	12.0000			0.558896			0.279448	+	0.960161i	$0.409849\pi$
$462$		0			0
$463$	−13.0000			−0.604161			−0.302081	−	0.953282i	$-0.597681\pi$
$463$	−13.0000			−0.604161			−0.302081	+	0.953282i	$0.597681\pi$
$464$	−4.00000	−	6.92820i	−0.185695	−	0.321634i
$465$		0			0
$466$	9.00000	−	15.5885i	0.416917	−	0.722121i
$467$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$467$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$468$		0			0
$469$		0			0
$470$	5.00000			0.230633
$471$		0			0
$472$	2.00000	−	3.46410i	0.0920575	−	0.159448i
$473$	−4.00000	+	6.92820i	−0.183920	+	0.318559i
$474$		0			0
$475$	−3.00000			−0.137649
$476$		0			0
$477$		0			0
$478$	−9.00000	−	15.5885i	−0.411650	−	0.712999i
$479$	11.0000	−	19.0526i	0.502603	−	0.870534i	−0.497393	−	0.867526i	$-0.665709\pi$
$479$	11.0000	−	19.0526i	0.502603	−	0.870534i	0.999995	−	0.00300810i	$-0.000957509\pi$
$480$		0			0
$481$	−5.50000	−	9.52628i	−0.250778	−	0.434361i
$482$	7.00000			0.318841
$483$		0			0
$484$	−10.0000			−0.454545
$485$	8.00000	+	13.8564i	0.363261	+	0.629187i
$486$		0			0
$487$	8.00000	−	13.8564i	0.362515	−	0.627894i	−0.625859	−	0.779936i	$-0.715252\pi$
$487$	8.00000	−	13.8564i	0.362515	−	0.627894i	0.988374	+	0.152042i	$0.0485850\pi$
$488$		0			0
$489$		0			0
$490$	−6.50000	−	2.59808i	−0.293640	−	0.117369i
$491$	−20.0000			−0.902587			−0.451294	−	0.892375i	$-0.649037\pi$
$491$	−20.0000			−0.902587			−0.451294	+	0.892375i	$0.649037\pi$
$492$		0			0
$493$		0			0
$494$	1.50000	−	2.59808i	0.0674882	−	0.116893i
$495$		0			0
$496$	−2.00000			−0.0898027
$497$	12.0000	+	10.3923i	0.538274	+	0.466159i
$498$		0			0
$499$	16.0000	+	27.7128i	0.716258	+	1.24060i	0.962472	+	0.271380i	$0.0874801\pi$
$499$	16.0000	+	27.7128i	0.716258	+	1.24060i	−0.246214	+	0.969216i	$0.579187\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$		0			0
$502$	6.50000	+	11.2583i	0.290109	+	0.502484i
$503$	−36.0000			−1.60516			−0.802580	−	0.596544i	$-0.796540\pi$
$503$	−36.0000			−1.60516			−0.802580	+	0.596544i	$0.796540\pi$
$504$		0			0
$505$		0			0
$506$	3.50000	+	6.06218i	0.155594	+	0.269497i
$507$		0			0
$508$	8.50000	−	14.7224i	0.377127	−	0.653202i
$509$	−17.0000	−	29.4449i	−0.753512	−	1.30512i	−0.946111	−	0.323843i	$-0.895025\pi$
$509$	−17.0000	−	29.4449i	−0.753512	−	1.30512i	0.192599	−	0.981278i	$-0.438308\pi$
$510$		0			0
$511$	15.0000	−	5.19615i	0.663561	−	0.229864i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−10.0000	+	17.3205i	−0.441081	+	0.763975i
$515$	8.00000	−	13.8564i	0.352522	−	0.610586i
$516$		0			0
$517$	5.00000			0.219900
$518$	−27.5000	+	9.52628i	−1.20828	+	0.418561i
$519$		0			0
$520$	−0.500000	−	0.866025i	−0.0219265	−	0.0379777i
$521$	−16.5000	+	28.5788i	−0.722878	+	1.25206i	0.236963	+	0.971519i	$0.423848\pi$
$521$	−16.5000	+	28.5788i	−0.722878	+	1.25206i	−0.959841	+	0.280543i	$0.909485\pi$
$522$		0			0
$523$	−1.00000	−	1.73205i	−0.0437269	−	0.0757373i	0.843334	−	0.537390i	$-0.180590\pi$
$523$	−1.00000	−	1.73205i	−0.0437269	−	0.0757373i	−0.887061	+	0.461653i	$0.847256\pi$
$524$	5.00000			0.218426
$525$		0			0
$526$	−24.0000			−1.04645
$527$		0			0
$528$		0			0
$529$	−13.0000	+	22.5167i	−0.565217	+	0.978985i
$530$	−5.50000	−	9.52628i	−0.238905	−	0.413795i
$531$		0			0
$532$	−6.00000	−	5.19615i	−0.260133	−	0.225282i
$533$	11.0000			0.476463
$534$		0			0
$535$	−5.00000	+	8.66025i	−0.216169	+	0.374415i
$536$		0			0
$537$		0			0
$538$	−20.0000			−0.862261
$539$	−6.50000	−	2.59808i	−0.279975	−	0.111907i
$540$		0			0
$541$	5.00000	+	8.66025i	0.214967	+	0.372333i	0.953262	−	0.302144i	$-0.0977023\pi$
$541$	5.00000	+	8.66025i	0.214967	+	0.372333i	−0.738296	+	0.674477i	$0.764369\pi$
$542$	−16.0000	+	27.7128i	−0.687259	+	1.19037i
$543$		0			0
$544$		0			0
$545$	6.00000			0.257012
$546$		0			0
$547$	16.0000			0.684111			0.342055	−	0.939680i	$-0.388877\pi$
$547$	16.0000			0.684111			0.342055	+	0.939680i	$0.388877\pi$
$548$	−9.00000	−	15.5885i	−0.384461	−	0.665906i
$549$		0			0
$550$	−0.500000	+	0.866025i	−0.0213201	+	0.0369274i
$551$	12.0000	+	20.7846i	0.511217	+	0.885454i
$552$		0			0
$553$	−4.00000	+	20.7846i	−0.170097	+	0.883852i
$554$	−22.0000			−0.934690
$555$		0			0
$556$	−10.0000	+	17.3205i	−0.424094	+	0.734553i
$557$	−16.5000	+	28.5788i	−0.699127	+	1.21092i	0.269642	+	0.962961i	$0.413095\pi$
$557$	−16.5000	+	28.5788i	−0.699127	+	1.21092i	−0.968769	+	0.247964i	$0.920239\pi$
$558$		0			0
$559$	8.00000			0.338364
$560$	−2.50000	+	0.866025i	−0.105644	+	0.0365963i
$561$		0			0
$562$	−0.500000	−	0.866025i	−0.0210912	−	0.0365311i
$563$	−19.0000	+	32.9090i	−0.800755	+	1.38695i	0.118366	+	0.992970i	$0.462235\pi$
$563$	−19.0000	+	32.9090i	−0.800755	+	1.38695i	−0.919120	+	0.393977i	$0.871099\pi$
$564$		0			0
$565$	3.00000	+	5.19615i	0.126211	+	0.218604i
$566$	−14.0000			−0.588464
$567$		0			0
$568$	6.00000			0.251754
$569$	−4.50000	−	7.79423i	−0.188650	−	0.326751i	0.756151	−	0.654398i	$-0.227078\pi$
$569$	−4.50000	−	7.79423i	−0.188650	−	0.326751i	−0.944800	+	0.327647i	$0.893744\pi$
$570$		0			0
$571$	16.0000	−	27.7128i	0.669579	−	1.15975i	−0.308443	−	0.951243i	$-0.599808\pi$
$571$	16.0000	−	27.7128i	0.669579	−	1.15975i	0.978022	−	0.208502i	$-0.0668588\pi$
$572$	−0.500000	−	0.866025i	−0.0209061	−	0.0362103i
$573$		0			0
$574$	5.50000	−	28.5788i	0.229566	−	1.19286i
$575$	−7.00000			−0.291920
$576$		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	$0.0725410\pi$
$578$	8.50000	−	14.7224i	0.353553	−	0.612372i
$579$		0			0
$580$	8.00000			0.332182
$581$	−16.0000	−	13.8564i	−0.663792	−	0.574861i
$582$		0			0
$583$	−5.50000	−	9.52628i	−0.227787	−	0.394538i
$584$	3.00000	−	5.19615i	0.124141	−	0.215018i
$585$		0			0
$586$	13.5000	+	23.3827i	0.557680	+	0.965930i
$587$	18.0000			0.742940			0.371470	−	0.928445i	$-0.378854\pi$
$587$	18.0000			0.742940			0.371470	+	0.928445i	$0.378854\pi$
$588$		0			0
$589$	6.00000			0.247226
$590$	2.00000	+	3.46410i	0.0823387	+	0.142615i
$591$		0			0
$592$	−5.50000	+	9.52628i	−0.226049	+	0.391528i
$593$	8.00000	+	13.8564i	0.328521	+	0.569014i	0.982219	−	0.187741i	$-0.0601166\pi$
$593$	8.00000	+	13.8564i	0.328521	+	0.569014i	−0.653698	+	0.756756i	$0.726783\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	3.50000	−	6.06218i	0.143126	−	0.247901i
$599$	1.00000	−	1.73205i	0.0408589	−	0.0707697i	−0.844873	−	0.534967i	$-0.820324\pi$
$599$	1.00000	−	1.73205i	0.0408589	−	0.0707697i	0.885732	+	0.464198i	$0.153657\pi$
$600$		0			0
$601$	−26.0000			−1.06056			−0.530281	−	0.847822i	$-0.677914\pi$
$601$	−26.0000			−1.06056			−0.530281	+	0.847822i	$0.677914\pi$
$602$	4.00000	−	20.7846i	0.163028	−	0.847117i
$603$		0			0
$604$	−3.00000	−	5.19615i	−0.122068	−	0.211428i
$605$	5.00000	−	8.66025i	0.203279	−	0.352089i
$606$		0			0
$607$	18.5000	+	32.0429i	0.750892	+	1.30058i	0.947391	+	0.320079i	$0.103709\pi$
$607$	18.5000	+	32.0429i	0.750892	+	1.30058i	−0.196499	+	0.980504i	$0.562957\pi$
$608$	−3.00000			−0.121666
$609$		0			0
$610$		0			0
$611$	−2.50000	−	4.33013i	−0.101139	−	0.175178i
$612$		0			0
$613$	20.5000	−	35.5070i	0.827987	−	1.43412i	−0.0716275	−	0.997431i	$-0.522819\pi$
$613$	20.5000	−	35.5070i	0.827987	−	1.43412i	0.899615	−	0.436684i	$-0.143847\pi$
$614$	−10.0000	−	17.3205i	−0.403567	−	0.698999i
$615$		0			0
$616$	−2.50000	+	0.866025i	−0.100728	+	0.0348932i
$617$	−28.0000			−1.12724			−0.563619	−	0.826035i	$-0.690591\pi$
$617$	−28.0000			−1.12724			−0.563619	+	0.826035i	$0.690591\pi$
$618$		0			0
$619$	−14.5000	+	25.1147i	−0.582804	+	1.00945i	0.412341	+	0.911030i	$0.364711\pi$
$619$	−14.5000	+	25.1147i	−0.582804	+	1.00945i	−0.995145	+	0.0984169i	$0.968622\pi$
$620$	1.00000	−	1.73205i	0.0401610	−	0.0695608i
$621$		0			0
$622$	−12.0000			−0.481156
$623$	5.00000	−	25.9808i	0.200321	−	1.04090i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	6.00000	−	10.3923i	0.239808	−	0.415360i
$627$		0			0
$628$	3.50000	+	6.06218i	0.139665	+	0.241907i
$629$		0			0
$630$		0			0
$631$	−26.0000			−1.03504			−0.517522	−	0.855670i	$-0.673145\pi$
$631$	−26.0000			−1.03504			−0.517522	+	0.855670i	$0.673145\pi$
$632$	4.00000	+	6.92820i	0.159111	+	0.275589i
$633$		0			0
$634$	−9.00000	+	15.5885i	−0.357436	+	0.619097i
$635$	8.50000	+	14.7224i	0.337312	+	0.584242i
$636$		0			0
$637$	1.00000	+	6.92820i	0.0396214	+	0.274505i
$638$	8.00000			0.316723
$639$		0			0
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−1.50000	+	2.59808i	−0.0592464	+	0.102618i	−0.894127	−	0.447813i	$-0.852203\pi$
$641$	−1.50000	+	2.59808i	−0.0592464	+	0.102618i	0.834881	+	0.550431i	$0.185536\pi$
$642$		0			0
$643$	−10.0000			−0.394362			−0.197181	−	0.980367i	$-0.563179\pi$
$643$	−10.0000			−0.394362			−0.197181	+	0.980367i	$0.563179\pi$
$644$	−14.0000	−	12.1244i	−0.551677	−	0.477767i
$645$		0			0
$646$		0			0
$647$	−8.50000	+	14.7224i	−0.334169	+	0.578799i	−0.983325	−	0.181857i	$-0.941789\pi$
$647$	−8.50000	+	14.7224i	−0.334169	+	0.578799i	0.649155	+	0.760656i	$0.275122\pi$
$648$		0			0
$649$	2.00000	+	3.46410i	0.0785069	+	0.135978i
$650$	1.00000			0.0392232
$651$		0			0
$652$	16.0000			0.626608
$653$	3.50000	+	6.06218i	0.136966	+	0.237231i	0.926347	−	0.376672i	$-0.122932\pi$
$653$	3.50000	+	6.06218i	0.136966	+	0.237231i	−0.789381	+	0.613904i	$0.789598\pi$
$654$		0			0
$655$	−2.50000	+	4.33013i	−0.0976831	+	0.169192i
$656$	−5.50000	−	9.52628i	−0.214739	−	0.371939i
$657$		0			0
$658$	−12.5000	+	4.33013i	−0.487301	+	0.168806i
$659$	−36.0000			−1.40236			−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000			−1.40236			−0.701180	+	0.712984i	$0.747343\pi$
$660$		0			0
$661$	12.0000	−	20.7846i	0.466746	−	0.808428i	−0.532533	−	0.846410i	$-0.678760\pi$
$661$	12.0000	−	20.7846i	0.466746	−	0.808428i	0.999278	+	0.0379819i	$0.0120929\pi$
$662$	6.50000	−	11.2583i	0.252630	−	0.437567i
$663$		0			0
$664$	−8.00000			−0.310460
$665$	7.50000	−	2.59808i	0.290838	−	0.100749i
$666$		0			0
$667$	28.0000	+	48.4974i	1.08416	+	1.87783i
$668$	−1.50000	+	2.59808i	−0.0580367	+	0.100523i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	28.0000			1.07932			0.539660	−	0.841883i	$-0.318553\pi$
$673$	28.0000			1.07932			0.539660	+	0.841883i	$0.318553\pi$
$674$	6.00000	+	10.3923i	0.231111	+	0.400297i
$675$		0			0
$676$	6.00000	−	10.3923i	0.230769	−	0.399704i
$677$	−6.50000	−	11.2583i	−0.249815	−	0.432693i	0.713659	−	0.700493i	$-0.247037\pi$
$677$	−6.50000	−	11.2583i	−0.249815	−	0.432693i	−0.963474	+	0.267800i	$0.913703\pi$
$678$		0			0
$679$	−32.0000	−	27.7128i	−1.22805	−	1.06352i
$680$		0			0
$681$		0			0
$682$	1.00000	−	1.73205i	0.0382920	−	0.0663237i
$683$	2.00000	−	3.46410i	0.0765279	−	0.132550i	−0.825222	−	0.564809i	$-0.808950\pi$
$683$	2.00000	−	3.46410i	0.0765279	−	0.132550i	0.901750	+	0.432259i	$0.142283\pi$
$684$		0			0
$685$	18.0000			0.687745
$686$	18.5000	+	0.866025i	0.706333	+	0.0330650i
$687$		0			0
$688$	−4.00000	−	6.92820i	−0.152499	−	0.264135i
$689$	−5.50000	+	9.52628i	−0.209533	+	0.362922i
$690$		0			0
$691$	6.00000	+	10.3923i	0.228251	+	0.395342i	0.957290	−	0.289130i	$-0.0933661\pi$
$691$	6.00000	+	10.3923i	0.228251	+	0.395342i	−0.729039	+	0.684472i	$0.760033\pi$
$692$	15.0000			0.570214
$693$		0			0
$694$	−14.0000			−0.531433
$695$	−10.0000	−	17.3205i	−0.379322	−	0.657004i
$696$		0			0
$697$		0			0
$698$	−6.00000	−	10.3923i	−0.227103	−	0.393355i
$699$		0			0
$700$	0.500000	−	2.59808i	0.0188982	−	0.0981981i
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$		0			0
$703$	16.5000	−	28.5788i	0.622309	−	1.07787i
$704$	−0.500000	+	0.866025i	−0.0188445	+	0.0326396i
$705$		0			0
$706$	−24.0000			−0.903252
$707$		0			0
$708$		0			0
$709$	−22.0000	−	38.1051i	−0.826227	−	1.43107i	−0.900978	−	0.433865i	$-0.857149\pi$
$709$	−22.0000	−	38.1051i	−0.826227	−	1.43107i	0.0747503	−	0.997202i	$-0.476184\pi$
$710$	−3.00000	+	5.19615i	−0.112588	+	0.195008i
$711$		0			0
$712$	−5.00000	−	8.66025i	−0.187383	−	0.324557i
$713$	14.0000			0.524304
$714$		0			0
$715$	1.00000			0.0373979
$716$	−9.50000	−	16.4545i	−0.355032	−	0.614933i
$717$		0			0
$718$	2.00000	−	3.46410i	0.0746393	−	0.129279i
$719$	1.00000	+	1.73205i	0.0372937	+	0.0645946i	0.884070	−	0.467355i	$-0.154793\pi$
$719$	1.00000	+	1.73205i	0.0372937	+	0.0645946i	−0.846776	+	0.531949i	$0.821460\pi$
$720$		0			0
$721$	−8.00000	+	41.5692i	−0.297936	+	1.54812i
$722$	−10.0000			−0.372161
$723$		0			0
$724$	12.0000	−	20.7846i	0.445976	−	0.772454i
$725$	−4.00000	+	6.92820i	−0.148556	+	0.257307i
$726$		0			0
$727$	11.0000			0.407967			0.203984	−	0.978974i	$-0.434611\pi$
$727$	11.0000			0.407967			0.203984	+	0.978974i	$0.434611\pi$
$728$	2.00000	+	1.73205i	0.0741249	+	0.0641941i
$729$		0			0
$730$	3.00000	+	5.19615i	0.111035	+	0.192318i
$731$		0			0
$732$		0			0
$733$	−5.50000	−	9.52628i	−0.203147	−	0.351861i	0.746394	−	0.665505i	$-0.231784\pi$
$733$	−5.50000	−	9.52628i	−0.203147	−	0.351861i	−0.949541	+	0.313644i	$0.898450\pi$
$734$	25.0000			0.922767
$735$		0			0
$736$	−7.00000			−0.258023
$737$		0			0
$738$		0			0
$739$	9.50000	−	16.4545i	0.349463	−	0.605288i	−0.636691	−	0.771119i	$-0.719697\pi$
$739$	9.50000	−	16.4545i	0.349463	−	0.605288i	0.986154	+	0.165831i	$0.0530307\pi$
$740$	−5.50000	−	9.52628i	−0.202184	−	0.350193i
$741$		0			0
$742$	22.0000	+	19.0526i	0.807645	+	0.699441i
$743$	−49.0000			−1.79764			−0.898818	−	0.438322i	$-0.855573\pi$
$743$	−49.0000			−1.79764			−0.898818	+	0.438322i	$0.855573\pi$
$744$		0			0
$745$		0			0
$746$	−3.00000	+	5.19615i	−0.109838	+	0.190245i
$747$		0			0
$748$		0			0
$749$	5.00000	−	25.9808i	0.182696	−	0.949316i
$750$		0			0
$751$	−13.0000	−	22.5167i	−0.474377	−	0.821645i	0.525193	−	0.850983i	$-0.323993\pi$
$751$	−13.0000	−	22.5167i	−0.474377	−	0.821645i	−0.999570	+	0.0293387i	$0.990660\pi$
$752$	−2.50000	+	4.33013i	−0.0911656	+	0.157903i
$753$		0			0
$754$	−4.00000	−	6.92820i	−0.145671	−	0.252310i
$755$	6.00000			0.218362
$756$		0			0
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$	9.50000	+	16.4545i	0.345056	+	0.597654i
$759$		0			0
$760$	1.50000	−	2.59808i	0.0544107	−	0.0942421i
$761$	13.5000	+	23.3827i	0.489375	+	0.847622i	0.999925	−	0.0122260i	$-0.00389175\pi$
$761$	13.5000	+	23.3827i	0.489375	+	0.847622i	−0.510551	+	0.859848i	$0.670558\pi$
$762$		0			0
$763$	−15.0000	+	5.19615i	−0.543036	+	0.188113i
$764$	6.00000			0.217072
$765$		0			0
$766$	17.5000	−	30.3109i	0.632301	−	1.09518i
$767$	2.00000	−	3.46410i	0.0722158	−	0.125081i
$768$		0			0
$769$	−5.00000			−0.180305			−0.0901523	−	0.995928i	$-0.528735\pi$
$769$	−5.00000			−0.180305			−0.0901523	+	0.995928i	$0.528735\pi$
$770$	0.500000	−	2.59808i	0.0180187	−	0.0936282i
$771$		0			0
$772$	−11.0000	−	19.0526i	−0.395899	−	0.685717i
$773$	16.5000	−	28.5788i	0.593464	−	1.02791i	−0.400298	−	0.916385i	$-0.631093\pi$
$773$	16.5000	−	28.5788i	0.593464	−	1.02791i	0.993762	−	0.111524i	$-0.0355733\pi$
$774$		0			0
$775$	1.00000	+	1.73205i	0.0359211	+	0.0622171i
$776$	−16.0000			−0.574367
$777$		0			0
$778$	−10.0000			−0.358517
$779$	16.5000	+	28.5788i	0.591174	+	1.02394i
$780$		0			0
$781$	−3.00000	+	5.19615i	−0.107348	+	0.185933i
$782$		0			0
$783$		0			0
$784$	5.50000	−	4.33013i	0.196429	−	0.154647i
$785$	−7.00000			−0.249841
$786$		0			0
$787$	−11.0000	+	19.0526i	−0.392108	+	0.679150i	−0.992727	−	0.120384i	$-0.961587\pi$
$787$	−11.0000	+	19.0526i	−0.392108	+	0.679150i	0.600620	+	0.799535i	$0.294921\pi$
$788$	−0.500000	+	0.866025i	−0.0178118	+	0.0308509i
$789$		0			0
$790$	−8.00000			−0.284627
$791$	−12.0000	−	10.3923i	−0.426671	−	0.369508i
$792$		0			0
$793$		0			0
$794$	−7.00000	+	12.1244i	−0.248421	+	0.430277i
$795$		0			0
$796$	12.0000	+	20.7846i	0.425329	+	0.736691i
$797$	18.0000			0.637593			0.318796	−	0.947823i	$-0.396721\pi$
$797$	18.0000			0.637593			0.318796	+	0.947823i	$0.396721\pi$
$798$		0			0
$799$		0			0
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$		0			0
$802$	−2.50000	+	4.33013i	−0.0882781	+	0.152902i
$803$	3.00000	+	5.19615i	0.105868	+	0.183368i
$804$		0			0
$805$	17.5000	−	6.06218i	0.616794	−	0.213664i
$806$	−2.00000			−0.0704470
$807$		0			0
$808$		0			0
$809$	−19.5000	+	33.7750i	−0.685583	+	1.18747i	0.287670	+	0.957730i	$0.407120\pi$
$809$	−19.5000	+	33.7750i	−0.685583	+	1.18747i	−0.973253	+	0.229736i	$0.926214\pi$
$810$		0			0
$811$	9.00000			0.316033			0.158016	−	0.987436i	$-0.449490\pi$
$811$	9.00000			0.316033			0.158016	+	0.987436i	$0.449490\pi$
$812$	−20.0000	+	6.92820i	−0.701862	+	0.243132i
$813$		0			0
$814$	−5.50000	−	9.52628i	−0.192775	−	0.333896i
$815$	−8.00000	+	13.8564i	−0.280228	+	0.485369i
$816$		0			0
$817$	12.0000	+	20.7846i	0.419827	+	0.727161i
$818$	2.00000			0.0699284
$819$		0			0
$820$	11.0000			0.384137
$821$	21.0000	+	36.3731i	0.732905	+	1.26943i	0.955636	+	0.294549i	$0.0951694\pi$
$821$	21.0000	+	36.3731i	0.732905	+	1.26943i	−0.222731	+	0.974880i	$0.571497\pi$
$822$		0			0
$823$	12.0000	−	20.7846i	0.418294	−	0.724506i	−0.577474	−	0.816409i	$-0.695962\pi$
$823$	12.0000	−	20.7846i	0.418294	−	0.724506i	0.995768	+	0.0919029i	$0.0292950\pi$
$824$	8.00000	+	13.8564i	0.278693	+	0.482711i
$825$		0			0
$826$	−8.00000	−	6.92820i	−0.278356	−	0.241063i
$827$	10.0000			0.347734			0.173867	−	0.984769i	$-0.444374\pi$
$827$	10.0000			0.347734			0.173867	+	0.984769i	$0.444374\pi$
$828$		0			0
$829$	4.00000	−	6.92820i	0.138926	−	0.240626i	−0.788165	−	0.615465i	$-0.788968\pi$
$829$	4.00000	−	6.92820i	0.138926	−	0.240626i	0.927090	+	0.374838i	$0.122302\pi$
$830$	4.00000	−	6.92820i	0.138842	−	0.240481i
$831$		0			0
$832$	1.00000			0.0346688
$833$		0			0
$834$		0			0
$835$	−1.50000	−	2.59808i	−0.0519096	−	0.0899101i
$836$	1.50000	−	2.59808i	0.0518786	−	0.0898563i
$837$		0			0
$838$	−2.50000	−	4.33013i	−0.0863611	−	0.149582i
$839$	40.0000			1.38095			0.690477	−	0.723355i	$-0.257401\pi$
$839$	40.0000			1.38095			0.690477	+	0.723355i	$0.257401\pi$
$840$		0			0
$841$	35.0000			1.20690
$842$	−11.0000	−	19.0526i	−0.379085	−	0.656595i
$843$		0			0
$844$	−2.50000	+	4.33013i	−0.0860535	+	0.149049i
$845$	6.00000	+	10.3923i	0.206406	+	0.357506i
$846$		0			0
$847$	−5.00000	+	25.9808i	−0.171802	+	0.892710i
$848$	11.0000			0.377742
$849$		0			0
$850$		0			0
$851$	38.5000	−	66.6840i	1.31976	−	2.28590i
$852$		0			0
$853$	−41.0000			−1.40381			−0.701907	−	0.712269i	$-0.747668\pi$
$853$	−41.0000			−1.40381			−0.701907	+	0.712269i	$0.747668\pi$
$854$		0			0
$855$		0			0
$856$	−5.00000	−	8.66025i	−0.170896	−	0.296001i
$857$	−7.00000	+	12.1244i	−0.239115	+	0.414160i	−0.960461	−	0.278416i	$-0.910191\pi$
$857$	−7.00000	+	12.1244i	−0.239115	+	0.414160i	0.721345	+	0.692576i	$0.243524\pi$
$858$		0			0
$859$	−6.00000	−	10.3923i	−0.204717	−	0.354581i	0.745325	−	0.666701i	$-0.232294\pi$
$859$	−6.00000	−	10.3923i	−0.204717	−	0.354581i	−0.950043	+	0.312120i	$0.898961\pi$
$860$	8.00000			0.272798
$861$		0			0
$862$		0			0
$863$	−26.5000	−	45.8993i	−0.902070	−	1.56243i	−0.824802	−	0.565422i	$-0.808713\pi$
$863$	−26.5000	−	45.8993i	−0.902070	−	1.56243i	−0.0772684	−	0.997010i	$-0.524620\pi$
$864$		0			0
$865$	−7.50000	+	12.9904i	−0.255008	+	0.441686i
$866$	16.0000	+	27.7128i	0.543702	+	0.941720i
$867$		0			0
$868$	−1.00000	+	5.19615i	−0.0339422	+	0.176369i
$869$	−8.00000			−0.271381
$870$		0			0
$871$		0			0
$872$	−3.00000	+	5.19615i	−0.101593	+	0.175964i
$873$		0			0
$874$	21.0000			0.710336
$875$	2.00000	+	1.73205i	0.0676123	+	0.0585540i
$876$		0			0
$877$	−8.50000	−	14.7224i	−0.287025	−	0.497141i	0.686074	−	0.727532i	$-0.259333\pi$
$877$	−8.50000	−	14.7224i	−0.287025	−	0.497141i	−0.973098	+	0.230391i	$0.925999\pi$
$878$	−16.0000	+	27.7128i	−0.539974	+	0.935262i
$879$		0			0
$880$	−0.500000	−	0.866025i	−0.0168550	−	0.0291937i
$881$	53.0000			1.78562			0.892808	−	0.450438i	$-0.148732\pi$
$881$	53.0000			1.78562			0.892808	+	0.450438i	$0.148732\pi$
$882$		0			0
$883$	−42.0000			−1.41341			−0.706706	−	0.707507i	$-0.749820\pi$
$883$	−42.0000			−1.41341			−0.706706	+	0.707507i	$0.749820\pi$
$884$		0			0
$885$		0			0
$886$	8.00000	−	13.8564i	0.268765	−	0.465515i
$887$	22.0000	+	38.1051i	0.738688	+	1.27944i	0.953086	+	0.302698i	$0.0978875\pi$
$887$	22.0000	+	38.1051i	0.738688	+	1.27944i	−0.214399	+	0.976746i	$0.568779\pi$
$888$		0			0
$889$	−34.0000	−	29.4449i	−1.14032	−	0.987549i
$890$	10.0000			0.335201
$891$		0			0
$892$	−6.00000	+	10.3923i	−0.200895	+	0.347960i
$893$	7.50000	−	12.9904i	0.250978	−	0.434707i
$894$		0			0
$895$	19.0000			0.635100
$896$	0.500000	−	2.59808i	0.0167038	−	0.0867956i
$897$		0			0
$898$	5.50000	+	9.52628i	0.183537	+	0.317896i
$899$	8.00000	−	13.8564i	0.266815	−	0.462137i
$900$		0			0
$901$		0			0
$902$	11.0000			0.366260
$903$		0			0
$904$	−6.00000			−0.199557
$905$	12.0000	+	20.7846i	0.398893	+	0.690904i
$906$		0			0
$907$	5.00000	−	8.66025i	0.166022	−	0.287559i	−0.770996	−	0.636841i	$-0.780241\pi$
$907$	5.00000	−	8.66025i	0.166022	−	0.287559i	0.937018	+	0.349281i	$0.113574\pi$
$908$	4.00000	+	6.92820i	0.132745	+	0.229920i
$909$		0			0
$910$	−2.50000	+	0.866025i	−0.0828742	+	0.0287085i
$911$	2.00000			0.0662630			0.0331315	−	0.999451i	$-0.489452\pi$
$911$	2.00000			0.0662630			0.0331315	+	0.999451i	$0.489452\pi$
$912$		0			0
$913$	4.00000	−	6.92820i	0.132381	−	0.229290i
$914$	9.00000	−	15.5885i	0.297694	−	0.515620i
$915$		0			0
$916$	14.0000			0.462573
$917$	2.50000	−	12.9904i	0.0825573	−	0.428980i
$918$		0			0
$919$	18.0000	+	31.1769i	0.593765	+	1.02843i	0.993720	+	0.111897i	$0.0356925\pi$
$919$	18.0000	+	31.1769i	0.593765	+	1.02843i	−0.399955	+	0.916535i	$0.630974\pi$
$920$	3.50000	−	6.06218i	0.115392	−	0.199864i
$921$		0			0
$922$	−6.00000	−	10.3923i	−0.197599	−	0.342252i
$923$	6.00000			0.197492
$924$		0			0
$925$	11.0000			0.361678
$926$	6.50000	+	11.2583i	0.213603	+	0.369972i
$927$		0			0
$928$	−4.00000	+	6.92820i	−0.131306	+	0.227429i
$929$	−10.5000	−	18.1865i	−0.344494	−	0.596681i	0.640768	−	0.767735i	$-0.278616\pi$
$929$	−10.5000	−	18.1865i	−0.344494	−	0.596681i	−0.985262	+	0.171054i	$0.945283\pi$
$930$		0			0
$931$	−16.5000	+	12.9904i	−0.540766	+	0.425743i
$932$	−18.0000			−0.589610
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$	12.0000			0.392023			0.196011	−	0.980602i	$-0.437201\pi$
$937$	12.0000			0.392023			0.196011	+	0.980602i	$0.437201\pi$
$938$		0			0
$939$		0			0
$940$	−2.50000	−	4.33013i	−0.0815410	−	0.141233i
$941$	27.0000	−	46.7654i	0.880175	−	1.52451i	0.0290288	−	0.999579i	$-0.490759\pi$
$941$	27.0000	−	46.7654i	0.880175	−	1.52451i	0.851146	−	0.524929i	$-0.175908\pi$
$942$		0			0
$943$	38.5000	+	66.6840i	1.25373	+	2.17153i
$944$	−4.00000			−0.130189
$945$		0			0
$946$	8.00000			0.260102
$947$	11.0000	+	19.0526i	0.357452	+	0.619125i	0.987534	−	0.157403i	$-0.0503122\pi$
$947$	11.0000	+	19.0526i	0.357452	+	0.619125i	−0.630082	+	0.776528i	$0.716979\pi$
$948$		0			0
$949$	3.00000	−	5.19615i	0.0973841	−	0.168674i
$950$	1.50000	+	2.59808i	0.0486664	+	0.0842927i
$951$		0			0
$952$		0			0
$953$	20.0000			0.647864			0.323932	−	0.946080i	$-0.394995\pi$
$953$	20.0000			0.647864			0.323932	+	0.946080i	$0.394995\pi$
$954$		0			0
$955$	−3.00000	+	5.19615i	−0.0970777	+	0.168144i
$956$	−9.00000	+	15.5885i	−0.291081	+	0.504167i
$957$		0			0
$958$	−22.0000			−0.710788
$959$	−45.0000	+	15.5885i	−1.45313	+	0.503378i
$960$		0			0
$961$	13.5000	+	23.3827i	0.435484	+	0.754280i
$962$	−5.50000	+	9.52628i	−0.177327	+	0.307140i
$963$		0			0
$964$	−3.50000	−	6.06218i	−0.112727	−	0.195250i
$965$	22.0000			0.708205
$966$		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
$971$	−22.5000	−	38.9711i	−0.722059	−	1.25064i	−0.960173	−	0.279406i	$-0.909862\pi$
$971$	−22.5000	−	38.9711i	−0.722059	−	1.25064i	0.238114	−	0.971237i	$-0.423471\pi$
$972$		0			0
$973$	40.0000	+	34.6410i	1.28234	+	1.11054i
$974$	−16.0000			−0.512673
$975$		0			0
$976$		0			0
$977$	27.0000	−	46.7654i	0.863807	−	1.49616i	−0.00442082	−	0.999990i	$-0.501407\pi$
$977$	27.0000	−	46.7654i	0.863807	−	1.49616i	0.868227	−	0.496167i	$-0.165259\pi$
$978$		0			0
$979$	10.0000			0.319601
$980$	1.00000	+	6.92820i	0.0319438	+	0.221313i
$981$		0			0
$982$	10.0000	+	17.3205i	0.319113	+	0.552720i
$983$	24.5000	−	42.4352i	0.781429	−	1.35347i	−0.149681	−	0.988734i	$-0.547825\pi$
$983$	24.5000	−	42.4352i	0.781429	−	1.35347i	0.931110	−	0.364740i	$-0.118842\pi$
$984$		0			0
$985$	−0.500000	−	0.866025i	−0.0159313	−	0.0275939i
$986$		0			0
$987$		0			0
$988$	−3.00000			−0.0954427
$989$	28.0000	+	48.4974i	0.890348	+	1.54213i
$990$		0			0
$991$	−11.0000	+	19.0526i	−0.349427	+	0.605224i	−0.986148	−	0.165870i	$-0.946957\pi$
$991$	−11.0000	+	19.0526i	−0.349427	+	0.605224i	0.636721	+	0.771094i	$0.280290\pi$
$992$	1.00000	+	1.73205i	0.0317500	+	0.0549927i
$993$		0			0
$994$	3.00000	−	15.5885i	0.0951542	−	0.494436i
$995$	−24.0000			−0.760851
$996$		0			0
$997$	−7.00000	+	12.1244i	−0.221692	+	0.383982i	−0.955322	−	0.295567i	$-0.904491\pi$
$997$	−7.00000	+	12.1244i	−0.221692	+	0.383982i	0.733630	+	0.679549i	$0.237825\pi$
$998$	16.0000	−	27.7128i	0.506471	−	0.877234i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} +(-0.500000 + 0.866025i) q^{11} +1.00000 q^{13} +(0.500000 - 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.50000 + 2.59808i) q^{19} +1.00000 q^{20} +1.00000 q^{22} +(3.50000 + 6.06218i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-0.500000 - 0.866025i) q^{26} +(-2.50000 + 0.866025i) q^{28} +8.00000 q^{29} +(1.00000 - 1.73205i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.500000 - 2.59808i) q^{35} +(-5.50000 - 9.52628i) q^{37} +(1.50000 - 2.59808i) q^{38} +(-0.500000 - 0.866025i) q^{40} +11.0000 q^{41} +8.00000 q^{43} +(-0.500000 - 0.866025i) q^{44} +(3.50000 - 6.06218i) q^{46} +(-2.50000 - 4.33013i) q^{47} +(1.00000 + 6.92820i) q^{49} +1.00000 q^{50} +(-0.500000 + 0.866025i) q^{52} +(-5.50000 + 9.52628i) q^{53} +1.00000 q^{55} +(2.00000 + 1.73205i) q^{56} +(-4.00000 - 6.92820i) q^{58} +(2.00000 - 3.46410i) q^{59} -2.00000 q^{62} +1.00000 q^{64} +(-0.500000 - 0.866025i) q^{65} +(-2.50000 + 0.866025i) q^{70} +6.00000 q^{71} +(3.00000 - 5.19615i) q^{73} +(-5.50000 + 9.52628i) q^{74} -3.00000 q^{76} +(-2.50000 + 0.866025i) q^{77} +(4.00000 + 6.92820i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-5.50000 - 9.52628i) q^{82} -8.00000 q^{83} +(-4.00000 - 6.92820i) q^{86} +(-0.500000 + 0.866025i) q^{88} +(-5.00000 - 8.66025i) q^{89} +(2.00000 + 1.73205i) q^{91} -7.00000 q^{92} +(-2.50000 + 4.33013i) q^{94} +(1.50000 - 2.59808i) q^{95} -16.0000 q^{97} +(5.50000 - 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} - q^{5} + 4 q^{7} + 2 q^{8}+O(q^{10}) \) 2 * q - q^2 - q^4 - q^5 + 4 * q^7 + 2 * q^8	\( 2 q - q^{2} - q^{4} - q^{5} + 4 q^{7} + 2 q^{8} - q^{10} - q^{11} + 2 q^{13} + q^{14} - q^{16} + 3 q^{19} + 2 q^{20} + 2 q^{22} + 7 q^{23} - q^{25} - q^{26} - 5 q^{28} + 16 q^{29} + 2 q^{31} - q^{32} + q^{35} - 11 q^{37} + 3 q^{38} - q^{40} + 22 q^{41} + 16 q^{43} - q^{44} + 7 q^{46} - 5 q^{47} + 2 q^{49} + 2 q^{50} - q^{52} - 11 q^{53} + 2 q^{55} + 4 q^{56} - 8 q^{58} + 4 q^{59} - 4 q^{62} + 2 q^{64} - q^{65} - 5 q^{70} + 12 q^{71} + 6 q^{73} - 11 q^{74} - 6 q^{76} - 5 q^{77} + 8 q^{79} - q^{80} - 11 q^{82} - 16 q^{83} - 8 q^{86} - q^{88} - 10 q^{89} + 4 q^{91} - 14 q^{92} - 5 q^{94} + 3 q^{95} - 32 q^{97} + 11 q^{98}+O(q^{100}) \) 2 * q - q^2 - q^4 - q^5 + 4 * q^7 + 2 * q^8 - q^10 - q^11 + 2 * q^13 + q^14 - q^16 + 3 * q^19 + 2 * q^20 + 2 * q^22 + 7 * q^23 - q^25 - q^26 - 5 * q^28 + 16 * q^29 + 2 * q^31 - q^32 + q^35 - 11 * q^37 + 3 * q^38 - q^40 + 22 * q^41 + 16 * q^43 - q^44 + 7 * q^46 - 5 * q^47 + 2 * q^49 + 2 * q^50 - q^52 - 11 * q^53 + 2 * q^55 + 4 * q^56 - 8 * q^58 + 4 * q^59 - 4 * q^62 + 2 * q^64 - q^65 - 5 * q^70 + 12 * q^71 + 6 * q^73 - 11 * q^74 - 6 * q^76 - 5 * q^77 + 8 * q^79 - q^80 - 11 * q^82 - 16 * q^83 - 8 * q^86 - q^88 - 10 * q^89 + 4 * q^91 - 14 * q^92 - 5 * q^94 + 3 * q^95 - 32 * q^97 + 11 * q^98

Introduction

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