LMFDB - Embedded newform 630.2.k.f.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 70)
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.f.541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{10} +(-1.00000 + 1.73205i) q^{11} +(-2.00000 + 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} +(3.00000 + 5.19615i) q^{19} +1.00000 q^{20} -2.00000 q^{22} +(1.50000 + 2.59808i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-2.50000 - 0.866025i) q^{28} -9.00000 q^{29} +(2.00000 - 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} -4.00000 q^{34} +(2.00000 - 1.73205i) q^{35} +(2.00000 + 3.46410i) q^{37} +(-3.00000 + 5.19615i) q^{38} +(0.500000 + 0.866025i) q^{40} +7.00000 q^{41} -5.00000 q^{43} +(-1.00000 - 1.73205i) q^{44} +(-1.50000 + 2.59808i) q^{46} +(4.00000 + 6.92820i) q^{47} +(-6.50000 + 2.59808i) q^{49} -1.00000 q^{50} +(-1.00000 + 1.73205i) q^{53} +2.00000 q^{55} +(-0.500000 - 2.59808i) q^{56} +(-4.50000 - 7.79423i) q^{58} +(5.00000 - 8.66025i) q^{59} +(-0.500000 - 0.866025i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(4.50000 - 7.79423i) q^{67} +(-2.00000 - 3.46410i) q^{68} +(2.50000 + 0.866025i) q^{70} -2.00000 q^{71} +(2.00000 - 3.46410i) q^{73} +(-2.00000 + 3.46410i) q^{74} -6.00000 q^{76} +(-5.00000 - 1.73205i) q^{77} +(-5.00000 - 8.66025i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(3.50000 + 6.06218i) q^{82} +7.00000 q^{83} +4.00000 q^{85} +(-2.50000 - 4.33013i) q^{86} +(1.00000 - 1.73205i) q^{88} +(0.500000 + 0.866025i) q^{89} -3.00000 q^{92} +(-4.00000 + 6.92820i) q^{94} +(3.00000 - 5.19615i) q^{95} +14.0000 q^{97} +(-5.50000 - 4.33013i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} - q^{5} + q^{7} - 2 q^{8}+O(q^{10}) $ 2 * q + q^2 - q^4 - q^5 + q^7 - 2 * q^8	$ 2 q + q^{2} - q^{4} - q^{5} + q^{7} - 2 q^{8} + q^{10} - 2 q^{11} - 4 q^{14} - q^{16} - 4 q^{17} + 6 q^{19} + 2 q^{20} - 4 q^{22} + 3 q^{23} - q^{25} - 5 q^{28} - 18 q^{29} + 4 q^{31} + q^{32} - 8 q^{34} + 4 q^{35} + 4 q^{37} - 6 q^{38} + q^{40} + 14 q^{41} - 10 q^{43} - 2 q^{44} - 3 q^{46} + 8 q^{47} - 13 q^{49} - 2 q^{50} - 2 q^{53} + 4 q^{55} - q^{56} - 9 q^{58} + 10 q^{59} - q^{61} + 8 q^{62} + 2 q^{64} + 9 q^{67} - 4 q^{68} + 5 q^{70} - 4 q^{71} + 4 q^{73} - 4 q^{74} - 12 q^{76} - 10 q^{77} - 10 q^{79} - q^{80} + 7 q^{82} + 14 q^{83} + 8 q^{85} - 5 q^{86} + 2 q^{88} + q^{89} - 6 q^{92} - 8 q^{94} + 6 q^{95} + 28 q^{97} - 11 q^{98}+O(q^{100}) $ 2 * q + q^2 - q^4 - q^5 + q^7 - 2 * q^8 + q^10 - 2 * q^11 - 4 * q^14 - q^16 - 4 * q^17 + 6 * q^19 + 2 * q^20 - 4 * q^22 + 3 * q^23 - q^25 - 5 * q^28 - 18 * q^29 + 4 * q^31 + q^32 - 8 * q^34 + 4 * q^35 + 4 * q^37 - 6 * q^38 + q^40 + 14 * q^41 - 10 * q^43 - 2 * q^44 - 3 * q^46 + 8 * q^47 - 13 * q^49 - 2 * q^50 - 2 * q^53 + 4 * q^55 - q^56 - 9 * q^58 + 10 * q^59 - q^61 + 8 * q^62 + 2 * q^64 + 9 * q^67 - 4 * q^68 + 5 * q^70 - 4 * q^71 + 4 * q^73 - 4 * q^74 - 12 * q^76 - 10 * q^77 - 10 * q^79 - q^80 + 7 * q^82 + 14 * q^83 + 8 * q^85 - 5 * q^86 + 2 * q^88 + q^89 - 6 * q^92 - 8 * q^94 + 6 * q^95 + 28 * 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
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	−0.976478	−	0.215615i	$-0.930824\pi$
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$12$		0			0
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$	−2.00000	+	1.73205i	−0.534522	+	0.462910i
$15$		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
$19$	3.00000	+	5.19615i	0.688247	+	1.19208i	0.972404	+	0.233301i	$0.0749529\pi$
$19$	3.00000	+	5.19615i	0.688247	+	1.19208i	−0.284157	+	0.958778i	$0.591714\pi$
$20$	1.00000			0.223607
$21$		0			0
$22$	−2.00000			−0.426401
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	0.978961	−	0.204046i	$-0.0654092\pi$
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	−0.666190	+	0.745782i	$0.732076\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$		0			0
$28$	−2.50000	−	0.866025i	−0.472456	−	0.163663i
$29$	−9.00000			−1.67126			−0.835629	−	0.549294i	$-0.814897\pi$
$29$	−9.00000			−1.67126			−0.835629	+	0.549294i	$0.814897\pi$
$30$		0			0
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	0.987829	+	0.155543i	$0.0497126\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	−4.00000			−0.685994
$35$	2.00000	−	1.73205i	0.338062	−	0.292770i
$36$		0			0
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	0.982274	−	0.187453i	$-0.0600231\pi$
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	−0.653476	+	0.756948i	$0.726690\pi$
$38$	−3.00000	+	5.19615i	−0.486664	+	0.842927i
$39$		0			0
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	7.00000			1.09322			0.546608	−	0.837389i	$-0.315919\pi$
$41$	7.00000			1.09322			0.546608	+	0.837389i	$0.315919\pi$
$42$		0			0
$43$	−5.00000			−0.762493			−0.381246	−	0.924473i	$-0.624505\pi$
$43$	−5.00000			−0.762493			−0.381246	+	0.924473i	$0.624505\pi$
$44$	−1.00000	−	1.73205i	−0.150756	−	0.261116i
$45$		0			0
$46$	−1.50000	+	2.59808i	−0.221163	+	0.383065i
$47$	4.00000	+	6.92820i	0.583460	+	1.01058i	0.995066	+	0.0992202i	$0.0316348\pi$
$47$	4.00000	+	6.92820i	0.583460	+	1.01058i	−0.411606	+	0.911362i	$0.635032\pi$
$48$		0			0
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$	−1.00000			−0.141421
$51$		0			0
$52$		0			0
$53$	−1.00000	+	1.73205i	−0.137361	+	0.237915i	−0.926497	−	0.376303i	$-0.877195\pi$
$53$	−1.00000	+	1.73205i	−0.137361	+	0.237915i	0.789136	+	0.614218i	$0.210529\pi$
$54$		0			0
$55$	2.00000			0.269680
$56$	−0.500000	−	2.59808i	−0.0668153	−	0.347183i
$57$		0			0
$58$	−4.50000	−	7.79423i	−0.590879	−	1.02343i
$59$	5.00000	−	8.66025i	0.650945	−	1.12747i	−0.331949	−	0.943297i	$-0.607706\pi$
$59$	5.00000	−	8.66025i	0.650945	−	1.12747i	0.982894	−	0.184172i	$-0.0589603\pi$
$60$		0			0
$61$	−0.500000	−	0.866025i	−0.0640184	−	0.110883i	0.832240	−	0.554416i	$-0.187058\pi$
$61$	−0.500000	−	0.866025i	−0.0640184	−	0.110883i	−0.896258	+	0.443533i	$0.853725\pi$
$62$	4.00000			0.508001
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	4.50000	−	7.79423i	0.549762	−	0.952217i	−0.448528	−	0.893769i	$-0.648052\pi$
$67$	4.50000	−	7.79423i	0.549762	−	0.952217i	0.998290	−	0.0584478i	$-0.0186151\pi$
$68$	−2.00000	−	3.46410i	−0.242536	−	0.420084i
$69$		0			0
$70$	2.50000	+	0.866025i	0.298807	+	0.103510i
$71$	−2.00000			−0.237356			−0.118678	−	0.992933i	$-0.537866\pi$
$71$	−2.00000			−0.237356			−0.118678	+	0.992933i	$0.537866\pi$
$72$		0			0
$73$	2.00000	−	3.46410i	0.234082	−	0.405442i	−0.724923	−	0.688830i	$-0.758125\pi$
$73$	2.00000	−	3.46410i	0.234082	−	0.405442i	0.959006	+	0.283387i	$0.0914581\pi$
$74$	−2.00000	+	3.46410i	−0.232495	+	0.402694i
$75$		0			0
$76$	−6.00000			−0.688247
$77$	−5.00000	−	1.73205i	−0.569803	−	0.197386i
$78$		0			0
$79$	−5.00000	−	8.66025i	−0.562544	−	0.974355i	−0.997274	−	0.0737937i	$-0.976489\pi$
$79$	−5.00000	−	8.66025i	−0.562544	−	0.974355i	0.434730	−	0.900561i	$-0.356844\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$		0			0
$82$	3.50000	+	6.06218i	0.386510	+	0.669456i
$83$	7.00000			0.768350			0.384175	−	0.923260i	$-0.374486\pi$
$83$	7.00000			0.768350			0.384175	+	0.923260i	$0.374486\pi$
$84$		0			0
$85$	4.00000			0.433861
$86$	−2.50000	−	4.33013i	−0.269582	−	0.466930i
$87$		0			0
$88$	1.00000	−	1.73205i	0.106600	−	0.184637i
$89$	0.500000	+	0.866025i	0.0529999	+	0.0917985i	0.891308	−	0.453398i	$-0.149788\pi$
$89$	0.500000	+	0.866025i	0.0529999	+	0.0917985i	−0.838308	+	0.545197i	$0.816455\pi$
$90$		0			0
$91$		0			0
$92$	−3.00000			−0.312772
$93$		0			0
$94$	−4.00000	+	6.92820i	−0.412568	+	0.714590i
$95$	3.00000	−	5.19615i	0.307794	−	0.533114i
$96$		0			0
$97$	14.0000			1.42148			0.710742	−	0.703452i	$-0.248359\pi$
$97$	14.0000			1.42148			0.710742	+	0.703452i	$0.248359\pi$
$98$	−5.50000	−	4.33013i	−0.555584	−	0.437409i
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	−0.781697	−	0.623658i	$-0.785646\pi$
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	0.930953	+	0.365140i	$0.118979\pi$
$102$		0			0
$103$	−0.500000	−	0.866025i	−0.0492665	−	0.0853320i	0.840341	−	0.542059i	$-0.182355\pi$
$103$	−0.500000	−	0.866025i	−0.0492665	−	0.0853320i	−0.889607	+	0.456727i	$0.849022\pi$
$104$		0			0
$105$		0			0
$106$	−2.00000			−0.194257
$107$	1.50000	+	2.59808i	0.145010	+	0.251166i	0.929377	−	0.369132i	$-0.120345\pi$
$107$	1.50000	+	2.59808i	0.145010	+	0.251166i	−0.784366	+	0.620298i	$0.787012\pi$
$108$		0			0
$109$	4.50000	−	7.79423i	0.431022	−	0.746552i	−0.565940	−	0.824447i	$-0.691487\pi$
$109$	4.50000	−	7.79423i	0.431022	−	0.746552i	0.996962	+	0.0778949i	$0.0248199\pi$
$110$	1.00000	+	1.73205i	0.0953463	+	0.165145i
$111$		0			0
$112$	2.00000	−	1.73205i	0.188982	−	0.163663i
$113$	−2.00000			−0.188144			−0.0940721	−	0.995565i	$-0.529988\pi$
$113$	−2.00000			−0.188144			−0.0940721	+	0.995565i	$0.529988\pi$
$114$		0			0
$115$	1.50000	−	2.59808i	0.139876	−	0.242272i
$116$	4.50000	−	7.79423i	0.417815	−	0.723676i
$117$		0			0
$118$	10.0000			0.920575
$119$	−10.0000	−	3.46410i	−0.916698	−	0.317554i
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	0.500000	−	0.866025i	0.0452679	−	0.0784063i
$123$		0			0
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$	1.00000			0.0894427
$126$		0			0
$127$	16.0000			1.41977			0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000			1.41977			0.709885	+	0.704317i	$0.248747\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$		0			0
$131$	4.00000	+	6.92820i	0.349482	+	0.605320i	0.986157	−	0.165812i	$-0.0530244\pi$
$131$	4.00000	+	6.92820i	0.349482	+	0.605320i	−0.636676	+	0.771132i	$0.719691\pi$
$132$		0			0
$133$	−12.0000	+	10.3923i	−1.04053	+	0.901127i
$134$	9.00000			0.777482
$135$		0			0
$136$	2.00000	−	3.46410i	0.171499	−	0.297044i
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	−0.487278	−	0.873247i	$-0.662010\pi$
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	0.999893	−	0.0146279i	$-0.00465636\pi$
$138$		0			0
$139$	−14.0000			−1.18746			−0.593732	−	0.804663i	$-0.702346\pi$
$139$	−14.0000			−1.18746			−0.593732	+	0.804663i	$0.702346\pi$
$140$	0.500000	+	2.59808i	0.0422577	+	0.219578i
$141$		0			0
$142$	−1.00000	−	1.73205i	−0.0839181	−	0.145350i
$143$		0			0
$144$		0			0
$145$	4.50000	+	7.79423i	0.373705	+	0.647275i
$146$	4.00000			0.331042
$147$		0			0
$148$	−4.00000			−0.328798
$149$	1.50000	+	2.59808i	0.122885	+	0.212843i	0.920904	−	0.389789i	$-0.127452\pi$
$149$	1.50000	+	2.59808i	0.122885	+	0.212843i	−0.798019	+	0.602632i	$0.794119\pi$
$150$		0			0
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	−0.331842	−	0.943335i	$-0.607670\pi$
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	0.982873	−	0.184284i	$-0.0589965\pi$
$152$	−3.00000	−	5.19615i	−0.243332	−	0.421464i
$153$		0			0
$154$	−1.00000	−	5.19615i	−0.0805823	−	0.418718i
$155$	−4.00000			−0.321288
$156$		0			0
$157$	−5.00000	+	8.66025i	−0.399043	+	0.691164i	−0.993608	−	0.112884i	$-0.963991\pi$
$157$	−5.00000	+	8.66025i	−0.399043	+	0.691164i	0.594565	+	0.804048i	$0.297324\pi$
$158$	5.00000	−	8.66025i	0.397779	−	0.688973i
$159$		0			0
$160$	−1.00000			−0.0790569
$161$	−6.00000	+	5.19615i	−0.472866	+	0.409514i
$162$		0			0
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	0.933659	−	0.358162i	$-0.116597\pi$
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	−0.777007	+	0.629492i	$0.783263\pi$
$164$	−3.50000	+	6.06218i	−0.273304	+	0.473377i
$165$		0			0
$166$	3.50000	+	6.06218i	0.271653	+	0.470516i
$167$	21.0000			1.62503			0.812514	−	0.582941i	$-0.198098\pi$
$167$	21.0000			1.62503			0.812514	+	0.582941i	$0.198098\pi$
$168$		0			0
$169$	−13.0000			−1.00000
$170$	2.00000	+	3.46410i	0.153393	+	0.265684i
$171$		0			0
$172$	2.50000	−	4.33013i	0.190623	−	0.330169i
$173$	4.00000	+	6.92820i	0.304114	+	0.526742i	0.977064	−	0.212947i	$-0.0683062\pi$
$173$	4.00000	+	6.92820i	0.304114	+	0.526742i	−0.672949	+	0.739689i	$0.734973\pi$
$174$		0			0
$175$	−2.50000	−	0.866025i	−0.188982	−	0.0654654i
$176$	2.00000			0.150756
$177$		0			0
$178$	−0.500000	+	0.866025i	−0.0374766	+	0.0649113i
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	−0.549825	−	0.835280i	$-0.685306\pi$
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	0.998286	+	0.0585225i	$0.0186389\pi$
$180$		0			0
$181$	7.00000			0.520306			0.260153	−	0.965567i	$-0.416227\pi$
$181$	7.00000			0.520306			0.260153	+	0.965567i	$0.416227\pi$
$182$		0			0
$183$		0			0
$184$	−1.50000	−	2.59808i	−0.110581	−	0.191533i
$185$	2.00000	−	3.46410i	0.147043	−	0.254686i
$186$		0			0
$187$	−4.00000	−	6.92820i	−0.292509	−	0.506640i
$188$	−8.00000			−0.583460
$189$		0			0
$190$	6.00000			0.435286
$191$	−9.00000	−	15.5885i	−0.651217	−	1.12794i	−0.982828	−	0.184525i	$-0.940925\pi$
$191$	−9.00000	−	15.5885i	−0.651217	−	1.12794i	0.331611	−	0.943416i	$-0.392408\pi$
$192$		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	$0.781381\pi$
$194$	7.00000	+	12.1244i	0.502571	+	0.870478i
$195$		0			0
$196$	1.00000	−	6.92820i	0.0714286	−	0.494872i
$197$	−2.00000			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$		0			0
$199$	2.00000	−	3.46410i	0.141776	−	0.245564i	−0.786389	−	0.617731i	$-0.788052\pi$
$199$	2.00000	−	3.46410i	0.141776	−	0.245564i	0.928166	+	0.372168i	$0.121385\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$		0			0
$202$	3.00000			0.211079
$203$	−4.50000	−	23.3827i	−0.315838	−	1.64114i
$204$		0			0
$205$	−3.50000	−	6.06218i	−0.244451	−	0.423401i
$206$	0.500000	−	0.866025i	0.0348367	−	0.0603388i
$207$		0			0
$208$		0			0
$209$	−12.0000			−0.830057
$210$		0			0
$211$	−26.0000			−1.78991			−0.894957	−	0.446153i	$-0.852794\pi$
$211$	−26.0000			−1.78991			−0.894957	+	0.446153i	$0.852794\pi$
$212$	−1.00000	−	1.73205i	−0.0686803	−	0.118958i
$213$		0			0
$214$	−1.50000	+	2.59808i	−0.102538	+	0.177601i
$215$	2.50000	+	4.33013i	0.170499	+	0.295312i
$216$		0			0
$217$	10.0000	+	3.46410i	0.678844	+	0.235159i
$218$	9.00000			0.609557
$219$		0			0
$220$	−1.00000	+	1.73205i	−0.0674200	+	0.116775i
$221$		0			0
$222$		0			0
$223$	28.0000			1.87502			0.937509	−	0.347960i	$-0.113126\pi$
$223$	28.0000			1.87502			0.937509	+	0.347960i	$0.113126\pi$
$224$	2.50000	+	0.866025i	0.167038	+	0.0578638i
$225$		0			0
$226$	−1.00000	−	1.73205i	−0.0665190	−	0.115214i
$227$	−2.00000	+	3.46410i	−0.132745	+	0.229920i	−0.924734	−	0.380615i	$-0.875712\pi$
$227$	−2.00000	+	3.46410i	−0.132745	+	0.229920i	0.791989	+	0.610535i	$0.209046\pi$
$228$		0			0
$229$	−11.0000	−	19.0526i	−0.726900	−	1.25903i	−0.958187	−	0.286143i	$-0.907627\pi$
$229$	−11.0000	−	19.0526i	−0.726900	−	1.25903i	0.231287	−	0.972886i	$-0.425707\pi$
$230$	3.00000			0.197814
$231$		0			0
$232$	9.00000			0.590879
$233$	12.0000	+	20.7846i	0.786146	+	1.36165i	0.928312	+	0.371802i	$0.121260\pi$
$233$	12.0000	+	20.7846i	0.786146	+	1.36165i	−0.142166	+	0.989843i	$0.545407\pi$
$234$		0			0
$235$	4.00000	−	6.92820i	0.260931	−	0.451946i
$236$	5.00000	+	8.66025i	0.325472	+	0.563735i
$237$		0			0
$238$	−2.00000	−	10.3923i	−0.129641	−	0.673633i
$239$	−16.0000			−1.03495			−0.517477	−	0.855697i	$-0.673129\pi$
$239$	−16.0000			−1.03495			−0.517477	+	0.855697i	$0.673129\pi$
$240$		0			0
$241$	−5.00000	+	8.66025i	−0.322078	+	0.557856i	−0.980917	−	0.194429i	$-0.937715\pi$
$241$	−5.00000	+	8.66025i	−0.322078	+	0.557856i	0.658838	+	0.752285i	$0.271048\pi$
$242$	−3.50000	+	6.06218i	−0.224989	+	0.389692i
$243$		0			0
$244$	1.00000			0.0640184
$245$	5.50000	+	4.33013i	0.351382	+	0.276642i
$246$		0			0
$247$		0			0
$248$	−2.00000	+	3.46410i	−0.127000	+	0.219971i
$249$		0			0
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$	−6.00000			−0.377217
$254$	8.00000	+	13.8564i	0.501965	+	0.869428i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.00000	+	6.92820i	0.249513	+	0.432169i	0.963391	−	0.268101i	$-0.0863961\pi$
$257$	4.00000	+	6.92820i	0.249513	+	0.432169i	−0.713878	+	0.700270i	$0.753063\pi$
$258$		0			0
$259$	−8.00000	+	6.92820i	−0.497096	+	0.430498i
$260$		0			0
$261$		0			0
$262$	−4.00000	+	6.92820i	−0.247121	+	0.428026i
$263$	2.50000	−	4.33013i	0.154157	−	0.267007i	−0.778595	−	0.627527i	$-0.784067\pi$
$263$	2.50000	−	4.33013i	0.154157	−	0.267007i	0.932752	+	0.360520i	$0.117401\pi$
$264$		0			0
$265$	2.00000			0.122859
$266$	−15.0000	−	5.19615i	−0.919709	−	0.318597i
$267$		0			0
$268$	4.50000	+	7.79423i	0.274881	+	0.476108i
$269$	1.50000	−	2.59808i	0.0914566	−	0.158408i	−0.816668	−	0.577108i	$-0.804181\pi$
$269$	1.50000	−	2.59808i	0.0914566	−	0.158408i	0.908124	+	0.418701i	$0.137514\pi$
$270$		0			0
$271$	3.00000	+	5.19615i	0.182237	+	0.315644i	0.942642	−	0.333805i	$-0.108333\pi$
$271$	3.00000	+	5.19615i	0.182237	+	0.315644i	−0.760405	+	0.649449i	$0.775000\pi$
$272$	4.00000			0.242536
$273$		0			0
$274$	12.0000			0.724947
$275$	−1.00000	−	1.73205i	−0.0603023	−	0.104447i
$276$		0			0
$277$	−6.00000	+	10.3923i	−0.360505	+	0.624413i	−0.988044	−	0.154172i	$-0.950729\pi$
$277$	−6.00000	+	10.3923i	−0.360505	+	0.624413i	0.627539	+	0.778585i	$0.284062\pi$
$278$	−7.00000	−	12.1244i	−0.419832	−	0.727171i
$279$		0			0
$280$	−2.00000	+	1.73205i	−0.119523	+	0.103510i
$281$	−2.00000			−0.119310			−0.0596550	−	0.998219i	$-0.519000\pi$
$281$	−2.00000			−0.119310			−0.0596550	+	0.998219i	$0.519000\pi$
$282$		0			0
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	−0.800439	−	0.599414i	$-0.795400\pi$
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	0.919327	+	0.393494i	$0.128734\pi$
$284$	1.00000	−	1.73205i	0.0593391	−	0.102778i
$285$		0			0
$286$		0			0
$287$	3.50000	+	18.1865i	0.206598	+	1.07352i
$288$		0			0
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$	−4.50000	+	7.79423i	−0.264249	+	0.457693i
$291$		0			0
$292$	2.00000	+	3.46410i	0.117041	+	0.202721i
$293$	−28.0000			−1.63578			−0.817889	−	0.575376i	$-0.804856\pi$
$293$	−28.0000			−1.63578			−0.817889	+	0.575376i	$0.804856\pi$
$294$		0			0
$295$	−10.0000			−0.582223
$296$	−2.00000	−	3.46410i	−0.116248	−	0.201347i
$297$		0			0
$298$	−1.50000	+	2.59808i	−0.0868927	+	0.150503i
$299$		0			0
$300$		0			0
$301$	−2.50000	−	12.9904i	−0.144098	−	0.748753i
$302$	16.0000			0.920697
$303$		0			0
$304$	3.00000	−	5.19615i	0.172062	−	0.298020i
$305$	−0.500000	+	0.866025i	−0.0286299	+	0.0495885i
$306$		0			0
$307$	7.00000			0.399511			0.199756	−	0.979846i	$-0.435985\pi$
$307$	7.00000			0.399511			0.199756	+	0.979846i	$0.435985\pi$
$308$	4.00000	−	3.46410i	0.227921	−	0.197386i
$309$		0			0
$310$	−2.00000	−	3.46410i	−0.113592	−	0.196748i
$311$	−9.00000	+	15.5885i	−0.510343	+	0.883940i	0.489585	+	0.871956i	$0.337148\pi$
$311$	−9.00000	+	15.5885i	−0.510343	+	0.883940i	−0.999928	+	0.0119847i	$0.996185\pi$
$312$		0			0
$313$	−4.00000	−	6.92820i	−0.226093	−	0.391605i	0.730554	−	0.682855i	$-0.239262\pi$
$313$	−4.00000	−	6.92820i	−0.226093	−	0.391605i	−0.956647	+	0.291250i	$0.905929\pi$
$314$	−10.0000			−0.564333
$315$		0			0
$316$	10.0000			0.562544
$317$	−16.0000	−	27.7128i	−0.898650	−	1.55651i	−0.829222	−	0.558920i	$-0.811216\pi$
$317$	−16.0000	−	27.7128i	−0.898650	−	1.55651i	−0.0694277	−	0.997587i	$-0.522117\pi$
$318$		0			0
$319$	9.00000	−	15.5885i	0.503903	−	0.872786i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$		0			0
$322$	−7.50000	−	2.59808i	−0.417959	−	0.144785i
$323$	−24.0000			−1.33540
$324$		0			0
$325$		0			0
$326$	−2.00000	+	3.46410i	−0.110770	+	0.191859i
$327$		0			0
$328$	−7.00000			−0.386510
$329$	−16.0000	+	13.8564i	−0.882109	+	0.763928i
$330$		0			0
$331$	16.0000	+	27.7128i	0.879440	+	1.52323i	0.851957	+	0.523612i	$0.175416\pi$
$331$	16.0000	+	27.7128i	0.879440	+	1.52323i	0.0274825	+	0.999622i	$0.491251\pi$
$332$	−3.50000	+	6.06218i	−0.192087	+	0.332705i
$333$		0			0
$334$	10.5000	+	18.1865i	0.574534	+	0.995123i
$335$	−9.00000			−0.491723
$336$		0			0
$337$	−26.0000			−1.41631			−0.708155	−	0.706057i	$-0.750472\pi$
$337$	−26.0000			−1.41631			−0.708155	+	0.706057i	$0.750472\pi$
$338$	−6.50000	−	11.2583i	−0.353553	−	0.612372i
$339$		0			0
$340$	−2.00000	+	3.46410i	−0.108465	+	0.187867i
$341$	4.00000	+	6.92820i	0.216612	+	0.375183i
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	5.00000			0.269582
$345$		0			0
$346$	−4.00000	+	6.92820i	−0.215041	+	0.372463i
$347$	9.50000	−	16.4545i	0.509987	−	0.883323i	−0.489946	−	0.871753i	$-0.662984\pi$
$347$	9.50000	−	16.4545i	0.509987	−	0.883323i	0.999933	−	0.0115703i	$-0.00368303\pi$
$348$		0			0
$349$	−35.0000			−1.87351			−0.936754	−	0.349990i	$-0.886185\pi$
$349$	−35.0000			−1.87351			−0.936754	+	0.349990i	$0.886185\pi$
$350$	−0.500000	−	2.59808i	−0.0267261	−	0.138873i
$351$		0			0
$352$	1.00000	+	1.73205i	0.0533002	+	0.0923186i
$353$	−9.00000	+	15.5885i	−0.479022	+	0.829690i	−0.999711	−	0.0240566i	$-0.992342\pi$
$353$	−9.00000	+	15.5885i	−0.479022	+	0.829690i	0.520689	+	0.853746i	$0.325675\pi$
$354$		0			0
$355$	1.00000	+	1.73205i	0.0530745	+	0.0919277i
$356$	−1.00000			−0.0529999
$357$		0			0
$358$	12.0000			0.634220
$359$	−2.00000	−	3.46410i	−0.105556	−	0.182828i	0.808409	−	0.588621i	$-0.200329\pi$
$359$	−2.00000	−	3.46410i	−0.105556	−	0.182828i	−0.913965	+	0.405793i	$0.866996\pi$
$360$		0			0
$361$	−8.50000	+	14.7224i	−0.447368	+	0.774865i
$362$	3.50000	+	6.06218i	0.183956	+	0.318621i
$363$		0			0
$364$		0			0
$365$	−4.00000			−0.209370
$366$		0			0
$367$	5.50000	−	9.52628i	0.287098	−	0.497268i	−0.686018	−	0.727585i	$-0.740643\pi$
$367$	5.50000	−	9.52628i	0.287098	−	0.497268i	0.973116	+	0.230317i	$0.0739762\pi$
$368$	1.50000	−	2.59808i	0.0781929	−	0.135434i
$369$		0			0
$370$	4.00000			0.207950
$371$	−5.00000	−	1.73205i	−0.259587	−	0.0899236i
$372$		0			0
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	0.913147	−	0.407630i	$-0.133645\pi$
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	−0.809591	+	0.586994i	$0.800311\pi$
$374$	4.00000	−	6.92820i	0.206835	−	0.358249i
$375$		0			0
$376$	−4.00000	−	6.92820i	−0.206284	−	0.357295i
$377$		0			0
$378$		0			0
$379$	30.0000			1.54100			0.770498	−	0.637442i	$-0.220007\pi$
$379$	30.0000			1.54100			0.770498	+	0.637442i	$0.220007\pi$
$380$	3.00000	+	5.19615i	0.153897	+	0.266557i
$381$		0			0
$382$	9.00000	−	15.5885i	0.460480	−	0.797575i
$383$	7.50000	+	12.9904i	0.383232	+	0.663777i	0.991522	−	0.129937i	$-0.0414776\pi$
$383$	7.50000	+	12.9904i	0.383232	+	0.663777i	−0.608290	+	0.793715i	$0.708144\pi$
$384$		0			0
$385$	1.00000	+	5.19615i	0.0509647	+	0.264820i
$386$	−26.0000			−1.32337
$387$		0			0
$388$	−7.00000	+	12.1244i	−0.355371	+	0.615521i
$389$	13.0000	−	22.5167i	0.659126	−	1.14164i	−0.321716	−	0.946836i	$-0.604260\pi$
$389$	13.0000	−	22.5167i	0.659126	−	1.14164i	0.980842	−	0.194804i	$-0.0624070\pi$
$390$		0			0
$391$	−12.0000			−0.606866
$392$	6.50000	−	2.59808i	0.328300	−	0.131223i
$393$		0			0
$394$	−1.00000	−	1.73205i	−0.0503793	−	0.0872595i
$395$	−5.00000	+	8.66025i	−0.251577	+	0.435745i
$396$		0			0
$397$	−11.0000	−	19.0526i	−0.552074	−	0.956221i	−0.998125	−	0.0612128i	$-0.980503\pi$
$397$	−11.0000	−	19.0526i	−0.552074	−	0.956221i	0.446051	−	0.895008i	$-0.352830\pi$
$398$	4.00000			0.200502
$399$		0			0
$400$	1.00000			0.0500000
$401$	15.5000	+	26.8468i	0.774033	+	1.34066i	0.935336	+	0.353760i	$0.115097\pi$
$401$	15.5000	+	26.8468i	0.774033	+	1.34066i	−0.161303	+	0.986905i	$0.551570\pi$
$402$		0			0
$403$		0			0
$404$	1.50000	+	2.59808i	0.0746278	+	0.129259i
$405$		0			0
$406$	18.0000	−	15.5885i	0.893325	−	0.773642i
$407$	−8.00000			−0.396545
$408$		0			0
$409$	−1.50000	+	2.59808i	−0.0741702	+	0.128467i	−0.900725	−	0.434389i	$-0.856964\pi$
$409$	−1.50000	+	2.59808i	−0.0741702	+	0.128467i	0.826555	+	0.562856i	$0.190297\pi$
$410$	3.50000	−	6.06218i	0.172853	−	0.299390i
$411$		0			0
$412$	1.00000			0.0492665
$413$	25.0000	+	8.66025i	1.23017	+	0.426143i
$414$		0			0
$415$	−3.50000	−	6.06218i	−0.171808	−	0.297581i
$416$		0			0
$417$		0			0
$418$	−6.00000	−	10.3923i	−0.293470	−	0.508304i
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	−19.0000			−0.926003			−0.463002	−	0.886357i	$-0.653228\pi$
$421$	−19.0000			−0.926003			−0.463002	+	0.886357i	$0.653228\pi$
$422$	−13.0000	−	22.5167i	−0.632830	−	1.09609i
$423$		0			0
$424$	1.00000	−	1.73205i	0.0485643	−	0.0841158i
$425$	−2.00000	−	3.46410i	−0.0970143	−	0.168034i
$426$		0			0
$427$	2.00000	−	1.73205i	0.0967868	−	0.0838198i
$428$	−3.00000			−0.145010
$429$		0			0
$430$	−2.50000	+	4.33013i	−0.120561	+	0.208817i
$431$	−15.0000	+	25.9808i	−0.722525	+	1.25145i	0.237460	+	0.971397i	$0.423685\pi$
$431$	−15.0000	+	25.9808i	−0.722525	+	1.25145i	−0.959985	+	0.280052i	$0.909648\pi$
$432$		0			0
$433$	14.0000			0.672797			0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000			0.672797			0.336399	+	0.941720i	$0.390791\pi$
$434$	2.00000	+	10.3923i	0.0960031	+	0.498847i
$435$		0			0
$436$	4.50000	+	7.79423i	0.215511	+	0.373276i
$437$	−9.00000	+	15.5885i	−0.430528	+	0.745697i
$438$		0			0
$439$	10.0000	+	17.3205i	0.477274	+	0.826663i	0.999661	−	0.0260459i	$-0.00829161\pi$
$439$	10.0000	+	17.3205i	0.477274	+	0.826663i	−0.522387	+	0.852709i	$0.674958\pi$
$440$	−2.00000			−0.0953463
$441$		0			0
$442$		0			0
$443$	15.5000	+	26.8468i	0.736427	+	1.27553i	0.954094	+	0.299506i	$0.0968220\pi$
$443$	15.5000	+	26.8468i	0.736427	+	1.27553i	−0.217667	+	0.976023i	$0.569845\pi$
$444$		0			0
$445$	0.500000	−	0.866025i	0.0237023	−	0.0410535i
$446$	14.0000	+	24.2487i	0.662919	+	1.14821i
$447$		0			0
$448$	0.500000	+	2.59808i	0.0236228	+	0.122748i
$449$	33.0000			1.55737			0.778683	−	0.627417i	$-0.215888\pi$
$449$	33.0000			1.55737			0.778683	+	0.627417i	$0.215888\pi$
$450$		0			0
$451$	−7.00000	+	12.1244i	−0.329617	+	0.570914i
$452$	1.00000	−	1.73205i	0.0470360	−	0.0814688i
$453$		0			0
$454$	−4.00000			−0.187729
$455$		0			0
$456$		0			0
$457$	16.0000	+	27.7128i	0.748448	+	1.29635i	0.948566	+	0.316579i	$0.102534\pi$
$457$	16.0000	+	27.7128i	0.748448	+	1.29635i	−0.200118	+	0.979772i	$0.564132\pi$
$458$	11.0000	−	19.0526i	0.513996	−	0.890268i
$459$		0			0
$460$	1.50000	+	2.59808i	0.0699379	+	0.121136i
$461$	14.0000			0.652045			0.326023	−	0.945362i	$-0.394291\pi$
$461$	14.0000			0.652045			0.326023	+	0.945362i	$0.394291\pi$
$462$		0			0
$463$	−19.0000			−0.883005			−0.441502	−	0.897260i	$-0.645554\pi$
$463$	−19.0000			−0.883005			−0.441502	+	0.897260i	$0.645554\pi$
$464$	4.50000	+	7.79423i	0.208907	+	0.361838i
$465$		0			0
$466$	−12.0000	+	20.7846i	−0.555889	+	0.962828i
$467$	−6.50000	−	11.2583i	−0.300784	−	0.520973i	0.675530	−	0.737333i	$-0.263915\pi$
$467$	−6.50000	−	11.2583i	−0.300784	−	0.520973i	−0.976314	+	0.216359i	$0.930582\pi$
$468$		0			0
$469$	22.5000	+	7.79423i	1.03895	+	0.359904i
$470$	8.00000			0.369012
$471$		0			0
$472$	−5.00000	+	8.66025i	−0.230144	+	0.398621i
$473$	5.00000	−	8.66025i	0.229900	−	0.398199i
$474$		0			0
$475$	−6.00000			−0.275299
$476$	8.00000	−	6.92820i	0.366679	−	0.317554i
$477$		0			0
$478$	−8.00000	−	13.8564i	−0.365911	−	0.633777i
$479$	12.0000	−	20.7846i	0.548294	−	0.949673i	−0.450098	−	0.892979i	$-0.648611\pi$
$479$	12.0000	−	20.7846i	0.548294	−	0.949673i	0.998392	−	0.0566937i	$-0.0180558\pi$
$480$		0			0
$481$		0			0
$482$	−10.0000			−0.455488
$483$		0			0
$484$	−7.00000			−0.318182
$485$	−7.00000	−	12.1244i	−0.317854	−	0.550539i
$486$		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	$0.0485850\pi$
$488$	0.500000	+	0.866025i	0.0226339	+	0.0392031i
$489$		0			0
$490$	−1.00000	+	6.92820i	−0.0451754	+	0.312984i
$491$	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
$493$	18.0000	−	31.1769i	0.810679	−	1.40414i
$494$		0			0
$495$		0			0
$496$	−4.00000			−0.179605
$497$	−1.00000	−	5.19615i	−0.0448561	−	0.233079i
$498$		0			0
$499$	9.00000	+	15.5885i	0.402895	+	0.697835i	0.994074	−	0.108705i	$-0.0346705\pi$
$499$	9.00000	+	15.5885i	0.402895	+	0.697835i	−0.591179	+	0.806541i	$0.701337\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$		0			0
$502$		0			0
$503$	21.0000			0.936344			0.468172	−	0.883637i	$-0.344913\pi$
$503$	21.0000			0.936344			0.468172	+	0.883637i	$0.344913\pi$
$504$		0			0
$505$	−3.00000			−0.133498
$506$	−3.00000	−	5.19615i	−0.133366	−	0.230997i
$507$		0			0
$508$	−8.00000	+	13.8564i	−0.354943	+	0.614779i
$509$	0.500000	+	0.866025i	0.0221621	+	0.0383859i	0.876894	−	0.480684i	$-0.159612\pi$
$509$	0.500000	+	0.866025i	0.0221621	+	0.0383859i	−0.854732	+	0.519070i	$0.826278\pi$
$510$		0			0
$511$	10.0000	+	3.46410i	0.442374	+	0.153243i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−4.00000	+	6.92820i	−0.176432	+	0.305590i
$515$	−0.500000	+	0.866025i	−0.0220326	+	0.0381616i
$516$		0			0
$517$	−16.0000			−0.703679
$518$	−10.0000	−	3.46410i	−0.439375	−	0.152204i
$519$		0			0
$520$		0			0
$521$	19.0000	−	32.9090i	0.832405	−	1.44177i	−0.0637207	−	0.997968i	$-0.520297\pi$
$521$	19.0000	−	32.9090i	0.832405	−	1.44177i	0.896126	−	0.443800i	$-0.146370\pi$
$522$		0			0
$523$	10.0000	+	17.3205i	0.437269	+	0.757373i	0.997478	−	0.0709788i	$-0.0226123\pi$
$523$	10.0000	+	17.3205i	0.437269	+	0.757373i	−0.560208	+	0.828352i	$0.689279\pi$
$524$	−8.00000			−0.349482
$525$		0			0
$526$	5.00000			0.218010
$527$	8.00000	+	13.8564i	0.348485	+	0.603595i
$528$		0			0
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$	1.00000	+	1.73205i	0.0434372	+	0.0752355i
$531$		0			0
$532$	−3.00000	−	15.5885i	−0.130066	−	0.675845i
$533$		0			0
$534$		0			0
$535$	1.50000	−	2.59808i	0.0648507	−	0.112325i
$536$	−4.50000	+	7.79423i	−0.194370	+	0.336659i
$537$		0			0
$538$	3.00000			0.129339
$539$	2.00000	−	13.8564i	0.0861461	−	0.596838i
$540$		0			0
$541$	−1.50000	−	2.59808i	−0.0644900	−	0.111700i	0.831978	−	0.554809i	$-0.187209\pi$
$541$	−1.50000	−	2.59808i	−0.0644900	−	0.111700i	−0.896468	+	0.443109i	$0.853875\pi$
$542$	−3.00000	+	5.19615i	−0.128861	+	0.223194i
$543$		0			0
$544$	2.00000	+	3.46410i	0.0857493	+	0.148522i
$545$	−9.00000			−0.385518
$546$		0			0
$547$	−33.0000			−1.41098			−0.705489	−	0.708721i	$-0.749273\pi$
$547$	−33.0000			−1.41098			−0.705489	+	0.708721i	$0.749273\pi$
$548$	6.00000	+	10.3923i	0.256307	+	0.443937i
$549$		0			0
$550$	1.00000	−	1.73205i	0.0426401	−	0.0738549i
$551$	−27.0000	−	46.7654i	−1.15024	−	1.99227i
$552$		0			0
$553$	20.0000	−	17.3205i	0.850487	−	0.736543i
$554$	−12.0000			−0.509831
$555$		0			0
$556$	7.00000	−	12.1244i	0.296866	−	0.514187i
$557$	−1.00000	+	1.73205i	−0.0423714	+	0.0733893i	−0.886433	−	0.462856i	$-0.846825\pi$
$557$	−1.00000	+	1.73205i	−0.0423714	+	0.0733893i	0.844062	+	0.536246i	$0.180158\pi$
$558$		0			0
$559$		0			0
$560$	−2.50000	−	0.866025i	−0.105644	−	0.0365963i
$561$		0			0
$562$	−1.00000	−	1.73205i	−0.0421825	−	0.0730622i
$563$	8.50000	−	14.7224i	0.358232	−	0.620477i	−0.629433	−	0.777055i	$-0.716713\pi$
$563$	8.50000	−	14.7224i	0.358232	−	0.620477i	0.987666	+	0.156578i	$0.0500463\pi$
$564$		0			0
$565$	1.00000	+	1.73205i	0.0420703	+	0.0728679i
$566$	4.00000			0.168133
$567$		0			0
$568$	2.00000			0.0839181
$569$	−9.00000	−	15.5885i	−0.377300	−	0.653502i	0.613369	−	0.789797i	$-0.289814\pi$
$569$	−9.00000	−	15.5885i	−0.377300	−	0.653502i	−0.990668	+	0.136295i	$0.956481\pi$
$570$		0			0
$571$	15.0000	−	25.9808i	0.627730	−	1.08726i	−0.360276	−	0.932846i	$-0.617317\pi$
$571$	15.0000	−	25.9808i	0.627730	−	1.08726i	0.988006	−	0.154415i	$-0.0493493\pi$
$572$		0			0
$573$		0			0
$574$	−14.0000	+	12.1244i	−0.584349	+	0.506061i
$575$	−3.00000			−0.125109
$576$		0			0
$577$	−5.00000	+	8.66025i	−0.208153	+	0.360531i	−0.951133	−	0.308783i	$-0.900078\pi$
$577$	−5.00000	+	8.66025i	−0.208153	+	0.360531i	0.742980	+	0.669314i	$0.233412\pi$
$578$	−0.500000	+	0.866025i	−0.0207973	+	0.0360219i
$579$		0			0
$580$	−9.00000			−0.373705
$581$	3.50000	+	18.1865i	0.145204	+	0.754505i
$582$		0			0
$583$	−2.00000	−	3.46410i	−0.0828315	−	0.143468i
$584$	−2.00000	+	3.46410i	−0.0827606	+	0.143346i
$585$		0			0
$586$	−14.0000	−	24.2487i	−0.578335	−	1.00171i
$587$	28.0000			1.15568			0.577842	−	0.816149i	$-0.303895\pi$
$587$	28.0000			1.15568			0.577842	+	0.816149i	$0.303895\pi$
$588$		0			0
$589$	24.0000			0.988903
$590$	−5.00000	−	8.66025i	−0.205847	−	0.356537i
$591$		0			0
$592$	2.00000	−	3.46410i	0.0821995	−	0.142374i
$593$	−3.00000	−	5.19615i	−0.123195	−	0.213380i	0.797831	−	0.602881i	$-0.205981\pi$
$593$	−3.00000	−	5.19615i	−0.123195	−	0.213380i	−0.921026	+	0.389501i	$0.872647\pi$
$594$		0			0
$595$	2.00000	+	10.3923i	0.0819920	+	0.426043i
$596$	−3.00000			−0.122885
$597$		0			0
$598$		0			0
$599$	6.00000	−	10.3923i	0.245153	−	0.424618i	−0.717021	−	0.697051i	$-0.754495\pi$
$599$	6.00000	−	10.3923i	0.245153	−	0.424618i	0.962175	+	0.272433i	$0.0878284\pi$
$600$		0			0
$601$	42.0000			1.71322			0.856608	−	0.515968i	$-0.172568\pi$
$601$	42.0000			1.71322			0.856608	+	0.515968i	$0.172568\pi$
$602$	10.0000	−	8.66025i	0.407570	−	0.352966i
$603$		0			0
$604$	8.00000	+	13.8564i	0.325515	+	0.563809i
$605$	3.50000	−	6.06218i	0.142295	−	0.246463i
$606$		0			0
$607$	−0.500000	−	0.866025i	−0.0202944	−	0.0351509i	0.855700	−	0.517472i	$-0.173127\pi$
$607$	−0.500000	−	0.866025i	−0.0202944	−	0.0351509i	−0.875994	+	0.482322i	$0.839794\pi$
$608$	6.00000			0.243332
$609$		0			0
$610$	−1.00000			−0.0404888
$611$		0			0
$612$		0			0
$613$	−6.00000	+	10.3923i	−0.242338	+	0.419741i	−0.961380	−	0.275225i	$-0.911248\pi$
$613$	−6.00000	+	10.3923i	−0.242338	+	0.419741i	0.719042	+	0.694967i	$0.244581\pi$
$614$	3.50000	+	6.06218i	0.141249	+	0.244650i
$615$		0			0
$616$	5.00000	+	1.73205i	0.201456	+	0.0697863i
$617$	−44.0000			−1.77137			−0.885687	−	0.464283i	$-0.846312\pi$
$617$	−44.0000			−1.77137			−0.885687	+	0.464283i	$0.846312\pi$
$618$		0			0
$619$	23.0000	−	39.8372i	0.924448	−	1.60119i	0.132002	−	0.991250i	$-0.457860\pi$
$619$	23.0000	−	39.8372i	0.924448	−	1.60119i	0.792446	−	0.609941i	$-0.208807\pi$
$620$	2.00000	−	3.46410i	0.0803219	−	0.139122i
$621$		0			0
$622$	−18.0000			−0.721734
$623$	−2.00000	+	1.73205i	−0.0801283	+	0.0693932i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	4.00000	−	6.92820i	0.159872	−	0.276907i
$627$		0			0
$628$	−5.00000	−	8.66025i	−0.199522	−	0.345582i
$629$	−16.0000			−0.637962
$630$		0			0
$631$	2.00000			0.0796187			0.0398094	−	0.999207i	$-0.487325\pi$
$631$	2.00000			0.0796187			0.0398094	+	0.999207i	$0.487325\pi$
$632$	5.00000	+	8.66025i	0.198889	+	0.344486i
$633$		0			0
$634$	16.0000	−	27.7128i	0.635441	−	1.10062i
$635$	−8.00000	−	13.8564i	−0.317470	−	0.549875i
$636$		0			0
$637$		0			0
$638$	18.0000			0.712627
$639$		0			0
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	2.50000	−	4.33013i	0.0987441	−	0.171030i	−0.812421	−	0.583071i	$-0.801851\pi$
$641$	2.50000	−	4.33013i	0.0987441	−	0.171030i	0.911165	+	0.412042i	$0.135184\pi$
$642$		0			0
$643$	28.0000			1.10421			0.552106	−	0.833774i	$-0.313824\pi$
$643$	28.0000			1.10421			0.552106	+	0.833774i	$0.313824\pi$
$644$	−1.50000	−	7.79423i	−0.0591083	−	0.307136i
$645$		0			0
$646$	−12.0000	−	20.7846i	−0.472134	−	0.817760i
$647$	−5.50000	+	9.52628i	−0.216227	+	0.374517i	−0.953652	−	0.300913i	$-0.902709\pi$
$647$	−5.50000	+	9.52628i	−0.216227	+	0.374517i	0.737424	+	0.675430i	$0.236042\pi$
$648$		0			0
$649$	10.0000	+	17.3205i	0.392534	+	0.679889i
$650$		0			0
$651$		0			0
$652$	−4.00000			−0.156652
$653$	−2.00000	−	3.46410i	−0.0782660	−	0.135561i	0.824236	−	0.566247i	$-0.191605\pi$
$653$	−2.00000	−	3.46410i	−0.0782660	−	0.135561i	−0.902502	+	0.430686i	$0.858272\pi$
$654$		0			0
$655$	4.00000	−	6.92820i	0.156293	−	0.270707i
$656$	−3.50000	−	6.06218i	−0.136652	−	0.236688i
$657$		0			0
$658$	−20.0000	−	6.92820i	−0.779681	−	0.270089i
$659$	26.0000			1.01282			0.506408	−	0.862294i	$-0.330973\pi$
$659$	26.0000			1.01282			0.506408	+	0.862294i	$0.330973\pi$
$660$		0			0
$661$	5.50000	−	9.52628i	0.213925	−	0.370529i	−0.739014	−	0.673690i	$-0.764708\pi$
$661$	5.50000	−	9.52628i	0.213925	−	0.370529i	0.952940	+	0.303160i	$0.0980418\pi$
$662$	−16.0000	+	27.7128i	−0.621858	+	1.07709i
$663$		0			0
$664$	−7.00000			−0.271653
$665$	15.0000	+	5.19615i	0.581675	+	0.201498i
$666$		0			0
$667$	−13.5000	−	23.3827i	−0.522722	−	0.905381i
$668$	−10.5000	+	18.1865i	−0.406257	+	0.703658i
$669$		0			0
$670$	−4.50000	−	7.79423i	−0.173850	−	0.301117i
$671$	2.00000			0.0772091
$672$		0			0
$673$	16.0000			0.616755			0.308377	−	0.951264i	$-0.400214\pi$
$673$	16.0000			0.616755			0.308377	+	0.951264i	$0.400214\pi$
$674$	−13.0000	−	22.5167i	−0.500741	−	0.867309i
$675$		0			0
$676$	6.50000	−	11.2583i	0.250000	−	0.433013i
$677$	−24.0000	−	41.5692i	−0.922395	−	1.59763i	−0.795698	−	0.605693i	$-0.792896\pi$
$677$	−24.0000	−	41.5692i	−0.922395	−	1.59763i	−0.126697	−	0.991941i	$-0.540438\pi$
$678$		0			0
$679$	7.00000	+	36.3731i	0.268635	+	1.39587i
$680$	−4.00000			−0.153393
$681$		0			0
$682$	−4.00000	+	6.92820i	−0.153168	+	0.265295i
$683$	−18.5000	+	32.0429i	−0.707883	+	1.22609i	0.257758	+	0.966209i	$0.417016\pi$
$683$	−18.5000	+	32.0429i	−0.707883	+	1.22609i	−0.965641	+	0.259880i	$0.916317\pi$
$684$		0			0
$685$	−12.0000			−0.458496
$686$	8.50000	−	16.4545i	0.324532	−	0.628235i
$687$		0			0
$688$	2.50000	+	4.33013i	0.0953116	+	0.165085i
$689$		0			0
$690$		0			0
$691$	−11.0000	−	19.0526i	−0.418460	−	0.724793i	0.577325	−	0.816514i	$-0.304097\pi$
$691$	−11.0000	−	19.0526i	−0.418460	−	0.724793i	−0.995785	+	0.0917209i	$0.970763\pi$
$692$	−8.00000			−0.304114
$693$		0			0
$694$	19.0000			0.721230
$695$	7.00000	+	12.1244i	0.265525	+	0.459903i
$696$		0			0
$697$	−14.0000	+	24.2487i	−0.530288	+	0.918485i
$698$	−17.5000	−	30.3109i	−0.662385	−	1.14728i
$699$		0			0
$700$	2.00000	−	1.73205i	0.0755929	−	0.0654654i
$701$	47.0000			1.77517			0.887583	−	0.460648i	$-0.152383\pi$
$701$	47.0000			1.77517			0.887583	+	0.460648i	$0.152383\pi$
$702$		0			0
$703$	−12.0000	+	20.7846i	−0.452589	+	0.783906i
$704$	−1.00000	+	1.73205i	−0.0376889	+	0.0652791i
$705$		0			0
$706$	−18.0000			−0.677439
$707$	7.50000	+	2.59808i	0.282067	+	0.0977107i
$708$		0			0
$709$	5.50000	+	9.52628i	0.206557	+	0.357767i	0.950628	−	0.310334i	$-0.100441\pi$
$709$	5.50000	+	9.52628i	0.206557	+	0.357767i	−0.744071	+	0.668101i	$0.767108\pi$
$710$	−1.00000	+	1.73205i	−0.0375293	+	0.0650027i
$711$		0			0
$712$	−0.500000	−	0.866025i	−0.0187383	−	0.0324557i
$713$	12.0000			0.449404
$714$		0			0
$715$		0			0
$716$	6.00000	+	10.3923i	0.224231	+	0.388379i
$717$		0			0
$718$	2.00000	−	3.46410i	0.0746393	−	0.129279i
$719$	−3.00000	−	5.19615i	−0.111881	−	0.193784i	0.804648	−	0.593753i	$-0.202354\pi$
$719$	−3.00000	−	5.19615i	−0.111881	−	0.193784i	−0.916529	+	0.399969i	$0.869021\pi$
$720$		0			0
$721$	2.00000	−	1.73205i	0.0744839	−	0.0645049i
$722$	−17.0000			−0.632674
$723$		0			0
$724$	−3.50000	+	6.06218i	−0.130076	+	0.225299i
$725$	4.50000	−	7.79423i	0.167126	−	0.289470i
$726$		0			0
$727$	−21.0000			−0.778847			−0.389423	−	0.921059i	$-0.627326\pi$
$727$	−21.0000			−0.778847			−0.389423	+	0.921059i	$0.627326\pi$
$728$		0			0
$729$		0			0
$730$	−2.00000	−	3.46410i	−0.0740233	−	0.128212i
$731$	10.0000	−	17.3205i	0.369863	−	0.640622i
$732$		0			0
$733$	−11.0000	−	19.0526i	−0.406294	−	0.703722i	0.588177	−	0.808732i	$-0.299846\pi$
$733$	−11.0000	−	19.0526i	−0.406294	−	0.703722i	−0.994471	+	0.105010i	$0.966513\pi$
$734$	11.0000			0.406017
$735$		0			0
$736$	3.00000			0.110581
$737$	9.00000	+	15.5885i	0.331519	+	0.574208i
$738$		0			0
$739$	1.00000	−	1.73205i	0.0367856	−	0.0637145i	−0.847046	−	0.531519i	$-0.821621\pi$
$739$	1.00000	−	1.73205i	0.0367856	−	0.0637145i	0.883832	+	0.467804i	$0.154955\pi$
$740$	2.00000	+	3.46410i	0.0735215	+	0.127343i
$741$		0			0
$742$	−1.00000	−	5.19615i	−0.0367112	−	0.190757i
$743$	−9.00000			−0.330178			−0.165089	−	0.986279i	$-0.552791\pi$
$743$	−9.00000			−0.330178			−0.165089	+	0.986279i	$0.552791\pi$
$744$		0			0
$745$	1.50000	−	2.59808i	0.0549557	−	0.0951861i
$746$	−2.00000	+	3.46410i	−0.0732252	+	0.126830i
$747$		0			0
$748$	8.00000			0.292509
$749$	−6.00000	+	5.19615i	−0.219235	+	0.189863i
$750$		0			0
$751$	2.00000	+	3.46410i	0.0729810	+	0.126407i	0.900207	−	0.435463i	$-0.143415\pi$
$751$	2.00000	+	3.46410i	0.0729810	+	0.126407i	−0.827225	+	0.561870i	$0.810082\pi$
$752$	4.00000	−	6.92820i	0.145865	−	0.252646i
$753$		0			0
$754$		0			0
$755$	−16.0000			−0.582300
$756$		0			0
$757$	16.0000			0.581530			0.290765	−	0.956795i	$-0.406090\pi$
$757$	16.0000			0.581530			0.290765	+	0.956795i	$0.406090\pi$
$758$	15.0000	+	25.9808i	0.544825	+	0.943664i
$759$		0			0
$760$	−3.00000	+	5.19615i	−0.108821	+	0.188484i
$761$	−3.00000	−	5.19615i	−0.108750	−	0.188360i	0.806514	−	0.591215i	$-0.201351\pi$
$761$	−3.00000	−	5.19615i	−0.108750	−	0.188360i	−0.915264	+	0.402854i	$0.868018\pi$
$762$		0			0
$763$	22.5000	+	7.79423i	0.814555	+	0.282170i
$764$	18.0000			0.651217
$765$		0			0
$766$	−7.50000	+	12.9904i	−0.270986	+	0.469362i
$767$		0			0
$768$		0			0
$769$	−14.0000			−0.504853			−0.252426	−	0.967616i	$-0.581229\pi$
$769$	−14.0000			−0.504853			−0.252426	+	0.967616i	$0.581229\pi$
$770$	−4.00000	+	3.46410i	−0.144150	+	0.124838i
$771$		0			0
$772$	−13.0000	−	22.5167i	−0.467880	−	0.810392i
$773$	12.0000	−	20.7846i	0.431610	−	0.747570i	−0.565402	−	0.824815i	$-0.691279\pi$
$773$	12.0000	−	20.7846i	0.431610	−	0.747570i	0.997012	+	0.0772449i	$0.0246123\pi$
$774$		0			0
$775$	2.00000	+	3.46410i	0.0718421	+	0.124434i
$776$	−14.0000			−0.502571
$777$		0			0
$778$	26.0000			0.932145
$779$	21.0000	+	36.3731i	0.752403	+	1.30320i
$780$		0			0
$781$	2.00000	−	3.46410i	0.0715656	−	0.123955i
$782$	−6.00000	−	10.3923i	−0.214560	−	0.371628i
$783$		0			0
$784$	5.50000	+	4.33013i	0.196429	+	0.154647i
$785$	10.0000			0.356915
$786$		0			0
$787$	−15.5000	+	26.8468i	−0.552515	+	0.956985i	0.445577	+	0.895244i	$0.352999\pi$
$787$	−15.5000	+	26.8468i	−0.552515	+	0.956985i	−0.998092	+	0.0617409i	$0.980335\pi$
$788$	1.00000	−	1.73205i	0.0356235	−	0.0617018i
$789$		0			0
$790$	−10.0000			−0.355784
$791$	−1.00000	−	5.19615i	−0.0355559	−	0.184754i
$792$		0			0
$793$		0			0
$794$	11.0000	−	19.0526i	0.390375	−	0.676150i
$795$		0			0
$796$	2.00000	+	3.46410i	0.0708881	+	0.122782i
$797$		0			0			−	1.00000i	$-0.5\pi$
$797$		0			0				1.00000i	$0.5\pi$
$798$		0			0
$799$	−32.0000			−1.13208
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$		0			0
$802$	−15.5000	+	26.8468i	−0.547324	+	0.947993i
$803$	4.00000	+	6.92820i	0.141157	+	0.244491i
$804$		0			0
$805$	7.50000	+	2.59808i	0.264340	+	0.0915702i
$806$		0			0
$807$		0			0
$808$	−1.50000	+	2.59808i	−0.0527698	+	0.0914000i
$809$	−25.5000	+	44.1673i	−0.896532	+	1.55284i	−0.0646355	+	0.997909i	$0.520588\pi$
$809$	−25.5000	+	44.1673i	−0.896532	+	1.55284i	−0.831897	+	0.554930i	$0.812745\pi$
$810$		0			0
$811$	−28.0000			−0.983213			−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000			−0.983213			−0.491606	+	0.870817i	$0.663590\pi$
$812$	22.5000	+	7.79423i	0.789595	+	0.273524i
$813$		0			0
$814$	−4.00000	−	6.92820i	−0.140200	−	0.242833i
$815$	2.00000	−	3.46410i	0.0700569	−	0.121342i
$816$		0			0
$817$	−15.0000	−	25.9808i	−0.524784	−	0.908952i
$818$	−3.00000			−0.104893
$819$		0			0
$820$	7.00000			0.244451
$821$	−9.00000	−	15.5885i	−0.314102	−	0.544041i	0.665144	−	0.746715i	$-0.268370\pi$
$821$	−9.00000	−	15.5885i	−0.314102	−	0.544041i	−0.979246	+	0.202674i	$0.935037\pi$
$822$		0			0
$823$	−9.50000	+	16.4545i	−0.331149	+	0.573567i	−0.982737	−	0.185006i	$-0.940770\pi$
$823$	−9.50000	+	16.4545i	−0.331149	+	0.573567i	0.651588	+	0.758573i	$0.274103\pi$
$824$	0.500000	+	0.866025i	0.0174183	+	0.0301694i
$825$		0			0
$826$	5.00000	+	25.9808i	0.173972	+	0.903986i
$827$	19.0000			0.660695			0.330347	−	0.943859i	$-0.392834\pi$
$827$	19.0000			0.660695			0.330347	+	0.943859i	$0.392834\pi$
$828$		0			0
$829$	23.0000	−	39.8372i	0.798823	−	1.38360i	−0.121560	−	0.992584i	$-0.538790\pi$
$829$	23.0000	−	39.8372i	0.798823	−	1.38360i	0.920383	−	0.391018i	$-0.127877\pi$
$830$	3.50000	−	6.06218i	0.121487	−	0.210421i
$831$		0			0
$832$		0			0
$833$	4.00000	−	27.7128i	0.138592	−	0.960192i
$834$		0			0
$835$	−10.5000	−	18.1865i	−0.363367	−	0.629371i
$836$	6.00000	−	10.3923i	0.207514	−	0.359425i
$837$		0			0
$838$		0			0
$839$	−14.0000			−0.483334			−0.241667	−	0.970359i	$-0.577694\pi$
$839$	−14.0000			−0.483334			−0.241667	+	0.970359i	$0.577694\pi$
$840$		0			0
$841$	52.0000			1.79310
$842$	−9.50000	−	16.4545i	−0.327392	−	0.567059i
$843$		0			0
$844$	13.0000	−	22.5167i	0.447478	−	0.775055i
$845$	6.50000	+	11.2583i	0.223607	+	0.387298i
$846$		0			0
$847$	−14.0000	+	12.1244i	−0.481046	+	0.416598i
$848$	2.00000			0.0686803
$849$		0			0
$850$	2.00000	−	3.46410i	0.0685994	−	0.118818i
$851$	−6.00000	+	10.3923i	−0.205677	+	0.356244i
$852$		0			0
$853$	14.0000			0.479351			0.239675	−	0.970853i	$-0.422959\pi$
$853$	14.0000			0.479351			0.239675	+	0.970853i	$0.422959\pi$
$854$	2.50000	+	0.866025i	0.0855482	+	0.0296348i
$855$		0			0
$856$	−1.50000	−	2.59808i	−0.0512689	−	0.0888004i
$857$	−9.00000	+	15.5885i	−0.307434	+	0.532492i	−0.977800	−	0.209539i	$-0.932804\pi$
$857$	−9.00000	+	15.5885i	−0.307434	+	0.532492i	0.670366	+	0.742030i	$0.266137\pi$
$858$		0			0
$859$	24.0000	+	41.5692i	0.818869	+	1.41832i	0.906516	+	0.422172i	$0.138732\pi$
$859$	24.0000	+	41.5692i	0.818869	+	1.41832i	−0.0876464	+	0.996152i	$0.527935\pi$
$860$	−5.00000			−0.170499
$861$		0			0
$862$	−30.0000			−1.02180
$863$	−5.50000	−	9.52628i	−0.187222	−	0.324278i	0.757101	−	0.653298i	$-0.226615\pi$
$863$	−5.50000	−	9.52628i	−0.187222	−	0.324278i	−0.944323	+	0.329020i	$0.893282\pi$
$864$		0			0
$865$	4.00000	−	6.92820i	0.136004	−	0.235566i
$866$	7.00000	+	12.1244i	0.237870	+	0.412002i
$867$		0			0
$868$	−8.00000	+	6.92820i	−0.271538	+	0.235159i
$869$	20.0000			0.678454
$870$		0			0
$871$		0			0
$872$	−4.50000	+	7.79423i	−0.152389	+	0.263946i
$873$		0			0
$874$	−18.0000			−0.608859
$875$	0.500000	+	2.59808i	0.0169031	+	0.0878310i
$876$		0			0
$877$	−19.0000	−	32.9090i	−0.641584	−	1.11126i	−0.985079	−	0.172102i	$-0.944944\pi$
$877$	−19.0000	−	32.9090i	−0.641584	−	1.11126i	0.343495	−	0.939155i	$-0.388389\pi$
$878$	−10.0000	+	17.3205i	−0.337484	+	0.584539i
$879$		0			0
$880$	−1.00000	−	1.73205i	−0.0337100	−	0.0583874i
$881$	7.00000			0.235836			0.117918	−	0.993023i	$-0.462378\pi$
$881$	7.00000			0.235836			0.117918	+	0.993023i	$0.462378\pi$
$882$		0			0
$883$	−12.0000			−0.403832			−0.201916	−	0.979403i	$-0.564717\pi$
$883$	−12.0000			−0.403832			−0.201916	+	0.979403i	$0.564717\pi$
$884$		0			0
$885$		0			0
$886$	−15.5000	+	26.8468i	−0.520733	+	0.901935i
$887$	14.5000	+	25.1147i	0.486862	+	0.843270i	0.999886	−	0.0151042i	$-0.00480800\pi$
$887$	14.5000	+	25.1147i	0.486862	+	0.843270i	−0.513024	+	0.858375i	$0.671475\pi$
$888$		0			0
$889$	8.00000	+	41.5692i	0.268311	+	1.39419i
$890$	1.00000			0.0335201
$891$		0			0
$892$	−14.0000	+	24.2487i	−0.468755	+	0.811907i
$893$	−24.0000	+	41.5692i	−0.803129	+	1.39106i
$894$		0			0
$895$	−12.0000			−0.401116
$896$	−2.00000	+	1.73205i	−0.0668153	+	0.0578638i
$897$		0			0
$898$	16.5000	+	28.5788i	0.550612	+	0.953688i
$899$	−18.0000	+	31.1769i	−0.600334	+	1.03981i
$900$		0			0
$901$	−4.00000	−	6.92820i	−0.133259	−	0.230812i
$902$	−14.0000			−0.466149
$903$		0			0
$904$	2.00000			0.0665190
$905$	−3.50000	−	6.06218i	−0.116344	−	0.201514i
$906$		0			0
$907$	−2.50000	+	4.33013i	−0.0830111	+	0.143780i	−0.904542	−	0.426385i	$-0.859787\pi$
$907$	−2.50000	+	4.33013i	−0.0830111	+	0.143780i	0.821531	+	0.570164i	$0.193120\pi$
$908$	−2.00000	−	3.46410i	−0.0663723	−	0.114960i
$909$		0			0
$910$		0			0
$911$	−30.0000			−0.993944			−0.496972	−	0.867766i	$-0.665555\pi$
$911$	−30.0000			−0.993944			−0.496972	+	0.867766i	$0.665555\pi$
$912$		0			0
$913$	−7.00000	+	12.1244i	−0.231666	+	0.401258i
$914$	−16.0000	+	27.7128i	−0.529233	+	0.916658i
$915$		0			0
$916$	22.0000			0.726900
$917$	−16.0000	+	13.8564i	−0.528367	+	0.457579i
$918$		0			0
$919$	−19.0000	−	32.9090i	−0.626752	−	1.08557i	−0.988199	−	0.153174i	$-0.951051\pi$
$919$	−19.0000	−	32.9090i	−0.626752	−	1.08557i	0.361447	−	0.932393i	$-0.382283\pi$
$920$	−1.50000	+	2.59808i	−0.0494535	+	0.0856560i
$921$		0			0
$922$	7.00000	+	12.1244i	0.230533	+	0.399294i
$923$		0			0
$924$		0			0
$925$	−4.00000			−0.131519
$926$	−9.50000	−	16.4545i	−0.312189	−	0.540728i
$927$		0			0
$928$	−4.50000	+	7.79423i	−0.147720	+	0.255858i
$929$	21.5000	+	37.2391i	0.705392	+	1.22177i	0.966550	+	0.256479i	$0.0825624\pi$
$929$	21.5000	+	37.2391i	0.705392	+	1.22177i	−0.261158	+	0.965296i	$0.584104\pi$
$930$		0			0
$931$	−33.0000	−	25.9808i	−1.08153	−	0.851485i
$932$	−24.0000			−0.786146
$933$		0			0
$934$	6.50000	−	11.2583i	0.212686	−	0.368384i
$935$	−4.00000	+	6.92820i	−0.130814	+	0.226576i
$936$		0			0
$937$	−28.0000			−0.914720			−0.457360	−	0.889282i	$-0.651205\pi$
$937$	−28.0000			−0.914720			−0.457360	+	0.889282i	$0.651205\pi$
$938$	4.50000	+	23.3827i	0.146930	+	0.763472i
$939$		0			0
$940$	4.00000	+	6.92820i	0.130466	+	0.225973i
$941$	−23.0000	+	39.8372i	−0.749779	+	1.29865i	0.198150	+	0.980172i	$0.436507\pi$
$941$	−23.0000	+	39.8372i	−0.749779	+	1.29865i	−0.947929	+	0.318483i	$0.896827\pi$
$942$		0			0
$943$	10.5000	+	18.1865i	0.341927	+	0.592235i
$944$	−10.0000			−0.325472
$945$		0			0
$946$	10.0000			0.325128
$947$	−12.5000	−	21.6506i	−0.406195	−	0.703551i	0.588264	−	0.808669i	$-0.299811\pi$
$947$	−12.5000	−	21.6506i	−0.406195	−	0.703551i	−0.994460	+	0.105118i	$0.966478\pi$
$948$		0			0
$949$		0			0
$950$	−3.00000	−	5.19615i	−0.0973329	−	0.168585i
$951$		0			0
$952$	10.0000	+	3.46410i	0.324102	+	0.112272i
$953$	12.0000			0.388718			0.194359	−	0.980930i	$-0.437737\pi$
$953$	12.0000			0.388718			0.194359	+	0.980930i	$0.437737\pi$
$954$		0			0
$955$	−9.00000	+	15.5885i	−0.291233	+	0.504431i
$956$	8.00000	−	13.8564i	0.258738	−	0.448148i
$957$		0			0
$958$	24.0000			0.775405
$959$	30.0000	+	10.3923i	0.968751	+	0.335585i
$960$		0			0
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$		0			0
$963$		0			0
$964$	−5.00000	−	8.66025i	−0.161039	−	0.278928i
$965$	26.0000			0.836970
$966$		0			0
$967$	37.0000			1.18984			0.594920	−	0.803785i	$-0.297184\pi$
$967$	37.0000			1.18984			0.594920	+	0.803785i	$0.297184\pi$
$968$	−3.50000	−	6.06218i	−0.112494	−	0.194846i
$969$		0			0
$970$	7.00000	−	12.1244i	0.224756	−	0.389290i
$971$	−24.0000	−	41.5692i	−0.770197	−	1.33402i	−0.937455	−	0.348107i	$-0.886825\pi$
$971$	−24.0000	−	41.5692i	−0.770197	−	1.33402i	0.167258	−	0.985913i	$-0.446509\pi$
$972$		0			0
$973$	−7.00000	−	36.3731i	−0.224410	−	1.16607i
$974$	16.0000			0.512673
$975$		0			0
$976$	−0.500000	+	0.866025i	−0.0160046	+	0.0277208i
$977$	−15.0000	+	25.9808i	−0.479893	+	0.831198i	−0.999734	−	0.0230645i	$-0.992658\pi$
$977$	−15.0000	+	25.9808i	−0.479893	+	0.831198i	0.519841	+	0.854263i	$0.325991\pi$
$978$		0			0
$979$	−2.00000			−0.0639203
$980$	−6.50000	+	2.59808i	−0.207635	+	0.0829925i
$981$		0			0
$982$	6.00000	+	10.3923i	0.191468	+	0.331632i
$983$	8.50000	−	14.7224i	0.271108	−	0.469573i	−0.698038	−	0.716061i	$-0.745943\pi$
$983$	8.50000	−	14.7224i	0.271108	−	0.469573i	0.969146	+	0.246488i	$0.0792766\pi$
$984$		0			0
$985$	1.00000	+	1.73205i	0.0318626	+	0.0551877i
$986$	36.0000			1.14647
$987$		0			0
$988$		0			0
$989$	−7.50000	−	12.9904i	−0.238486	−	0.413070i
$990$		0			0
$991$	−20.0000	+	34.6410i	−0.635321	+	1.10041i	0.351126	+	0.936328i	$0.385799\pi$
$991$	−20.0000	+	34.6410i	−0.635321	+	1.10041i	−0.986447	+	0.164080i	$0.947534\pi$
$992$	−2.00000	−	3.46410i	−0.0635001	−	0.109985i
$993$		0			0
$994$	4.00000	−	3.46410i	0.126872	−	0.109875i
$995$	−4.00000			−0.126809
$996$		0			0
$997$	23.0000	−	39.8372i	0.728417	−	1.26166i	−0.229135	−	0.973395i	$-0.573590\pi$
$997$	23.0000	−	39.8372i	0.728417	−	1.26166i	0.957552	−	0.288261i	$-0.0930771\pi$
$998$	−9.00000	+	15.5885i	−0.284890	+	0.493444i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.k.f.361.1		2
3.2	odd	2		70.2.e.a.11.1	✓	2
7.2	even	3	inner	630.2.k.f.541.1		2
7.3	odd	6		4410.2.a.h.1.1		1
7.4	even	3		4410.2.a.r.1.1		1
12.11	even	2		560.2.q.i.81.1		2
15.2	even	4		350.2.j.f.249.2		4
15.8	even	4		350.2.j.f.249.1		4
15.14	odd	2		350.2.e.l.151.1		2
21.2	odd	6		70.2.e.a.51.1	yes	2
21.5	even	6		490.2.e.f.471.1		2
21.11	odd	6		490.2.a.k.1.1		1
21.17	even	6		490.2.a.e.1.1		1
21.20	even	2		490.2.e.f.361.1		2
84.11	even	6		3920.2.a.b.1.1		1
84.23	even	6		560.2.q.i.401.1		2
84.59	odd	6		3920.2.a.bk.1.1		1
105.2	even	12		350.2.j.f.149.1		4
105.17	odd	12		2450.2.c.a.99.2		2
105.23	even	12		350.2.j.f.149.2		4
105.32	even	12		2450.2.c.s.99.2		2
105.38	odd	12		2450.2.c.a.99.1		2
105.44	odd	6		350.2.e.l.51.1		2
105.53	even	12		2450.2.c.s.99.1		2
105.59	even	6		2450.2.a.q.1.1		1
105.74	odd	6		2450.2.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.e.a.11.1	✓	2	3.2	odd	2
70.2.e.a.51.1	yes	2	21.2	odd	6
350.2.e.l.51.1		2	105.44	odd	6
350.2.e.l.151.1		2	15.14	odd	2
350.2.j.f.149.1		4	105.2	even	12
350.2.j.f.149.2		4	105.23	even	12
350.2.j.f.249.1		4	15.8	even	4
350.2.j.f.249.2		4	15.2	even	4
490.2.a.e.1.1		1	21.17	even	6
490.2.a.k.1.1		1	21.11	odd	6
490.2.e.f.361.1		2	21.20	even	2
490.2.e.f.471.1		2	21.5	even	6
560.2.q.i.81.1		2	12.11	even	2
560.2.q.i.401.1		2	84.23	even	6
630.2.k.f.361.1		2	1.1	even	1	trivial
630.2.k.f.541.1		2	7.2	even	3	inner
2450.2.a.b.1.1		1	105.74	odd	6
2450.2.a.q.1.1		1	105.59	even	6
2450.2.c.a.99.1		2	105.38	odd	12
2450.2.c.a.99.2		2	105.17	odd	12
2450.2.c.s.99.1		2	105.53	even	12
2450.2.c.s.99.2		2	105.32	even	12
3920.2.a.b.1.1		1	84.11	even	6
3920.2.a.bk.1.1		1	84.59	odd	6
4410.2.a.h.1.1		1	7.3	odd	6
4410.2.a.r.1.1		1	7.4	even	3

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)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{10} +(-1.00000 + 1.73205i) q^{11} +(-2.00000 + 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} +(3.00000 + 5.19615i) q^{19} +1.00000 q^{20} -2.00000 q^{22} +(1.50000 + 2.59808i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-2.50000 - 0.866025i) q^{28} -9.00000 q^{29} +(2.00000 - 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} -4.00000 q^{34} +(2.00000 - 1.73205i) q^{35} +(2.00000 + 3.46410i) q^{37} +(-3.00000 + 5.19615i) q^{38} +(0.500000 + 0.866025i) q^{40} +7.00000 q^{41} -5.00000 q^{43} +(-1.00000 - 1.73205i) q^{44} +(-1.50000 + 2.59808i) q^{46} +(4.00000 + 6.92820i) q^{47} +(-6.50000 + 2.59808i) q^{49} -1.00000 q^{50} +(-1.00000 + 1.73205i) q^{53} +2.00000 q^{55} +(-0.500000 - 2.59808i) q^{56} +(-4.50000 - 7.79423i) q^{58} +(5.00000 - 8.66025i) q^{59} +(-0.500000 - 0.866025i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(4.50000 - 7.79423i) q^{67} +(-2.00000 - 3.46410i) q^{68} +(2.50000 + 0.866025i) q^{70} -2.00000 q^{71} +(2.00000 - 3.46410i) q^{73} +(-2.00000 + 3.46410i) q^{74} -6.00000 q^{76} +(-5.00000 - 1.73205i) q^{77} +(-5.00000 - 8.66025i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(3.50000 + 6.06218i) q^{82} +7.00000 q^{83} +4.00000 q^{85} +(-2.50000 - 4.33013i) q^{86} +(1.00000 - 1.73205i) q^{88} +(0.500000 + 0.866025i) q^{89} -3.00000 q^{92} +(-4.00000 + 6.92820i) q^{94} +(3.00000 - 5.19615i) q^{95} +14.0000 q^{97} +(-5.50000 - 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} - q^{5} + q^{7} - 2 q^{8}+O(q^{10}) \) 2 * q + q^2 - q^4 - q^5 + q^7 - 2 * q^8	\( 2 q + q^{2} - q^{4} - q^{5} + q^{7} - 2 q^{8} + q^{10} - 2 q^{11} - 4 q^{14} - q^{16} - 4 q^{17} + 6 q^{19} + 2 q^{20} - 4 q^{22} + 3 q^{23} - q^{25} - 5 q^{28} - 18 q^{29} + 4 q^{31} + q^{32} - 8 q^{34} + 4 q^{35} + 4 q^{37} - 6 q^{38} + q^{40} + 14 q^{41} - 10 q^{43} - 2 q^{44} - 3 q^{46} + 8 q^{47} - 13 q^{49} - 2 q^{50} - 2 q^{53} + 4 q^{55} - q^{56} - 9 q^{58} + 10 q^{59} - q^{61} + 8 q^{62} + 2 q^{64} + 9 q^{67} - 4 q^{68} + 5 q^{70} - 4 q^{71} + 4 q^{73} - 4 q^{74} - 12 q^{76} - 10 q^{77} - 10 q^{79} - q^{80} + 7 q^{82} + 14 q^{83} + 8 q^{85} - 5 q^{86} + 2 q^{88} + q^{89} - 6 q^{92} - 8 q^{94} + 6 q^{95} + 28 q^{97} - 11 q^{98}+O(q^{100}) \) 2 * q + q^2 - q^4 - q^5 + q^7 - 2 * q^8 + q^10 - 2 * q^11 - 4 * q^14 - q^16 - 4 * q^17 + 6 * q^19 + 2 * q^20 - 4 * q^22 + 3 * q^23 - q^25 - 5 * q^28 - 18 * q^29 + 4 * q^31 + q^32 - 8 * q^34 + 4 * q^35 + 4 * q^37 - 6 * q^38 + q^40 + 14 * q^41 - 10 * q^43 - 2 * q^44 - 3 * q^46 + 8 * q^47 - 13 * q^49 - 2 * q^50 - 2 * q^53 + 4 * q^55 - q^56 - 9 * q^58 + 10 * q^59 - q^61 + 8 * q^62 + 2 * q^64 + 9 * q^67 - 4 * q^68 + 5 * q^70 - 4 * q^71 + 4 * q^73 - 4 * q^74 - 12 * q^76 - 10 * q^77 - 10 * q^79 - q^80 + 7 * q^82 + 14 * q^83 + 8 * q^85 - 5 * q^86 + 2 * q^88 + q^89 - 6 * q^92 - 8 * q^94 + 6 * q^95 + 28 * q^97 - 11 * q^98

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