LMFDB - Embedded newform 882.2.g.i.667.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [882,2,Mod(361,882)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(882, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("882.361"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$882 = 2 \cdot 3^{2} \cdot 7^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	882.g (of order $3$ , degree $2$ , not minimal)

Newform invariants

comment:select newform

sage:traces = [2,1,0,-1,-1,0,0,-2,0,1,5,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.04280545828$
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 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			667.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	882.667
Dual form			882.2.g.i.361.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{10} +(2.50000 + 4.33013i) q^{11} +(-0.500000 + 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{17} +(4.00000 - 6.92820i) q^{19} +1.00000 q^{20} +5.00000 q^{22} +(-2.00000 + 3.46410i) q^{23} +(2.00000 + 3.46410i) q^{25} +5.00000 q^{29} +(1.50000 + 2.59808i) q^{31} +(0.500000 + 0.866025i) q^{32} +4.00000 q^{34} +(2.00000 - 3.46410i) q^{37} +(-4.00000 - 6.92820i) q^{38} +(0.500000 - 0.866025i) q^{40} +2.00000 q^{43} +(2.50000 - 4.33013i) q^{44} +(2.00000 + 3.46410i) q^{46} +(3.00000 - 5.19615i) q^{47} +4.00000 q^{50} +(-4.50000 - 7.79423i) q^{53} -5.00000 q^{55} +(2.50000 - 4.33013i) q^{58} +(5.50000 + 9.52628i) q^{59} +(-3.00000 + 5.19615i) q^{61} +3.00000 q^{62} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{67} +(2.00000 - 3.46410i) q^{68} -2.00000 q^{71} +(5.00000 + 8.66025i) q^{73} +(-2.00000 - 3.46410i) q^{74} -8.00000 q^{76} +(-1.50000 + 2.59808i) q^{79} +(-0.500000 - 0.866025i) q^{80} -7.00000 q^{83} -4.00000 q^{85} +(1.00000 - 1.73205i) q^{86} +(-2.50000 - 4.33013i) q^{88} +(3.00000 - 5.19615i) q^{89} +4.00000 q^{92} +(-3.00000 - 5.19615i) q^{94} +(4.00000 + 6.92820i) q^{95} -7.00000 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$2 q + q^{2} - q^{4} - q^{5} - 2 q^{8} + q^{10} + 5 q^{11} - q^{16} + 4 q^{17} + 8 q^{19} + 2 q^{20} + 10 q^{22} - 4 q^{23} + 4 q^{25} + 10 q^{29} + 3 q^{31} + q^{32} + 8 q^{34} + 4 q^{37} - 8 q^{38}+ \cdots - 14 q^{97}+O(q^{100})$ 2 * q + q^2 - q^4 - q^5 - 2 * q^8 + q^10 + 5 * q^11 - q^16 + 4 * q^17 + 8 * q^19 + 2 * q^20 + 10 * q^22 - 4 * q^23 + 4 * q^25 + 10 * q^29 + 3 * q^31 + q^32 + 8 * q^34 + 4 * q^37 - 8 * q^38 + q^40 + 4 * q^43 + 5 * q^44 + 4 * q^46 + 6 * q^47 + 8 * q^50 - 9 * q^53 - 10 * q^55 + 5 * q^58 + 11 * q^59 - 6 * q^61 + 6 * q^62 + 2 * q^64 + 2 * q^67 + 4 * q^68 - 4 * q^71 + 10 * q^73 - 4 * q^74 - 16 * q^76 - 3 * q^79 - q^80 - 14 * q^83 - 8 * q^85 + 2 * q^86 - 5 * q^88 + 6 * q^89 + 8 * q^92 - 6 * q^94 + 8 * q^95 - 14 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$ .

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	0.500000	−	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	−0.955901	−	0.293691i	$-0.905116\pi$
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	0.732294	+	0.680989i	$0.238450\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$		0			0
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	2.50000	+	4.33013i	0.753778	+	1.30558i	0.945979	+	0.324227i	$0.105104\pi$
$11$	2.50000	+	4.33013i	0.753778	+	1.30558i	−0.192201	+	0.981356i	$0.561563\pi$
$12$		0			0
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.00000	+	3.46410i	0.485071	+	0.840168i	0.999853	−	0.0171533i	$-0.00546033\pi$
$17$	2.00000	+	3.46410i	0.485071	+	0.840168i	−0.514782	+	0.857321i	$0.672127\pi$
$18$		0			0
$19$	4.00000	−	6.92820i	0.917663	−	1.58944i	0.114708	−	0.993399i	$-0.463407\pi$
$19$	4.00000	−	6.92820i	0.917663	−	1.58944i	0.802955	−	0.596040i	$-0.203260\pi$
$20$	1.00000			0.223607
$21$		0			0
$22$	5.00000			1.06600
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	−0.995639	−	0.0932891i	$-0.970262\pi$
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	0.578610	+	0.815604i	$0.303595\pi$
$24$		0			0
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	5.00000			0.928477			0.464238	−	0.885710i	$-0.346328\pi$
$29$	5.00000			0.928477			0.464238	+	0.885710i	$0.346328\pi$
$30$		0			0
$31$	1.50000	+	2.59808i	0.269408	+	0.466628i	0.968709	−	0.248199i	$-0.0798387\pi$
$31$	1.50000	+	2.59808i	0.269408	+	0.466628i	−0.699301	+	0.714827i	$0.746505\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	4.00000			0.685994
$35$		0			0
$36$		0			0
$37$	2.00000	−	3.46410i	0.328798	−	0.569495i	−0.653476	−	0.756948i	$-0.726690\pi$
$37$	2.00000	−	3.46410i	0.328798	−	0.569495i	0.982274	+	0.187453i	$0.0600231\pi$
$38$	−4.00000	−	6.92820i	−0.648886	−	1.12390i
$39$		0			0
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$		0			0
$43$	2.00000			0.304997			0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000			0.304997			0.152499	+	0.988304i	$0.451268\pi$
$44$	2.50000	−	4.33013i	0.376889	−	0.652791i
$45$		0			0
$46$	2.00000	+	3.46410i	0.294884	+	0.510754i
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	−0.559908	−	0.828554i	$-0.689164\pi$
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	0.997503	+	0.0706177i	$0.0224970\pi$
$48$		0			0
$49$		0			0
$50$	4.00000			0.565685
$51$		0			0
$52$		0			0
$53$	−4.50000	−	7.79423i	−0.618123	−	1.07062i	−0.989828	−	0.142269i	$-0.954560\pi$
$53$	−4.50000	−	7.79423i	−0.618123	−	1.07062i	0.371706	−	0.928351i	$-0.378773\pi$
$54$		0			0
$55$	−5.00000			−0.674200
$56$		0			0
$57$		0			0
$58$	2.50000	−	4.33013i	0.328266	−	0.568574i
$59$	5.50000	+	9.52628i	0.716039	+	1.24022i	0.962557	+	0.271078i	$0.0873801\pi$
$59$	5.50000	+	9.52628i	0.716039	+	1.24022i	−0.246518	+	0.969138i	$0.579287\pi$
$60$		0			0
$61$	−3.00000	+	5.19615i	−0.384111	+	0.665299i	−0.991645	−	0.128994i	$-0.958825\pi$
$61$	−3.00000	+	5.19615i	−0.384111	+	0.665299i	0.607535	+	0.794293i	$0.292159\pi$
$62$	3.00000			0.381000
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	0.920623	−	0.390453i	$-0.127682\pi$
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	−0.798454	+	0.602056i	$0.794348\pi$
$68$	2.00000	−	3.46410i	0.242536	−	0.420084i
$69$		0			0
$70$		0			0
$71$	−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
$73$	5.00000	+	8.66025i	0.585206	+	1.01361i	0.994850	+	0.101361i	$0.0323196\pi$
$73$	5.00000	+	8.66025i	0.585206	+	1.01361i	−0.409644	+	0.912245i	$0.634347\pi$
$74$	−2.00000	−	3.46410i	−0.232495	−	0.402694i
$75$		0			0
$76$	−8.00000			−0.917663
$77$		0			0
$78$		0			0
$79$	−1.50000	+	2.59808i	−0.168763	+	0.292306i	−0.937985	−	0.346675i	$-0.887311\pi$
$79$	−1.50000	+	2.59808i	−0.168763	+	0.292306i	0.769222	+	0.638982i	$0.220644\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$		0			0
$82$		0			0
$83$	−7.00000			−0.768350			−0.384175	−	0.923260i	$-0.625514\pi$
$83$	−7.00000			−0.768350			−0.384175	+	0.923260i	$0.625514\pi$
$84$		0			0
$85$	−4.00000			−0.433861
$86$	1.00000	−	1.73205i	0.107833	−	0.186772i
$87$		0			0
$88$	−2.50000	−	4.33013i	−0.266501	−	0.461593i
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	−0.662071	−	0.749441i	$-0.730322\pi$
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	0.980071	+	0.198650i	$0.0636557\pi$
$90$		0			0
$91$		0			0
$92$	4.00000			0.417029
$93$		0			0
$94$	−3.00000	−	5.19615i	−0.309426	−	0.535942i
$95$	4.00000	+	6.92820i	0.410391	+	0.710819i
$96$		0			0
$97$	−7.00000			−0.710742			−0.355371	−	0.934725i	$-0.615646\pi$
$97$	−7.00000			−0.710742			−0.355371	+	0.934725i	$0.615646\pi$
$98$		0			0
$99$		0			0
$100$	2.00000	−	3.46410i	0.200000	−	0.346410i
$101$	−5.00000	−	8.66025i	−0.497519	−	0.861727i	0.502477	−	0.864590i	$-0.332422\pi$
$101$	−5.00000	−	8.66025i	−0.497519	−	0.861727i	−0.999996	+	0.00286291i	$0.999089\pi$
$102$		0			0
$103$	4.00000	−	6.92820i	0.394132	−	0.682656i	−0.598858	−	0.800855i	$-0.704379\pi$
$103$	4.00000	−	6.92820i	0.394132	−	0.682656i	0.992990	+	0.118199i	$0.0377120\pi$
$104$		0			0
$105$		0			0
$106$	−9.00000			−0.874157
$107$	1.50000	−	2.59808i	0.145010	−	0.251166i	−0.784366	−	0.620298i	$-0.787012\pi$
$107$	1.50000	−	2.59808i	0.145010	−	0.251166i	0.929377	+	0.369132i	$0.120345\pi$
$108$		0			0
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	0.909935	−	0.414751i	$-0.136131\pi$
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	−0.814152	+	0.580651i	$0.802798\pi$
$110$	−2.50000	+	4.33013i	−0.238366	+	0.412861i
$111$		0			0
$112$		0			0
$113$	−16.0000			−1.50515			−0.752577	−	0.658505i	$-0.771189\pi$
$113$	−16.0000			−1.50515			−0.752577	+	0.658505i	$0.771189\pi$
$114$		0			0
$115$	−2.00000	−	3.46410i	−0.186501	−	0.323029i
$116$	−2.50000	−	4.33013i	−0.232119	−	0.402042i
$117$		0			0
$118$	11.0000			1.01263
$119$		0			0
$120$		0			0
$121$	−7.00000	+	12.1244i	−0.636364	+	1.10221i
$122$	3.00000	+	5.19615i	0.271607	+	0.470438i
$123$		0			0
$124$	1.50000	−	2.59808i	0.134704	−	0.233314i
$125$	−9.00000			−0.804984
$126$		0			0
$127$	9.00000			0.798621			0.399310	−	0.916816i	$-0.369250\pi$
$127$	9.00000			0.798621			0.399310	+	0.916816i	$0.369250\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$		0			0
$131$	−0.500000	+	0.866025i	−0.0436852	+	0.0756650i	−0.887041	−	0.461690i	$-0.847243\pi$
$131$	−0.500000	+	0.866025i	−0.0436852	+	0.0756650i	0.843356	+	0.537355i	$0.180577\pi$
$132$		0			0
$133$		0			0
$134$	2.00000			0.172774
$135$		0			0
$136$	−2.00000	−	3.46410i	−0.171499	−	0.297044i
$137$	−1.00000	−	1.73205i	−0.0854358	−	0.147979i	0.820141	−	0.572161i	$-0.193895\pi$
$137$	−1.00000	−	1.73205i	−0.0854358	−	0.147979i	−0.905577	+	0.424182i	$0.860562\pi$
$138$		0			0
$139$	14.0000			1.18746			0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000			1.18746			0.593732	+	0.804663i	$0.297654\pi$
$140$		0			0
$141$		0			0
$142$	−1.00000	+	1.73205i	−0.0839181	+	0.145350i
$143$		0			0
$144$		0			0
$145$	−2.50000	+	4.33013i	−0.207614	+	0.359597i
$146$	10.0000			0.827606
$147$		0			0
$148$	−4.00000			−0.328798
$149$	−9.00000	+	15.5885i	−0.737309	+	1.27706i	0.216394	+	0.976306i	$0.430570\pi$
$149$	−9.00000	+	15.5885i	−0.737309	+	1.27706i	−0.953703	+	0.300750i	$0.902763\pi$
$150$		0			0
$151$	−9.50000	−	16.4545i	−0.773099	−	1.33905i	−0.935857	−	0.352381i	$-0.885372\pi$
$151$	−9.50000	−	16.4545i	−0.773099	−	1.33905i	0.162758	−	0.986666i	$-0.447961\pi$
$152$	−4.00000	+	6.92820i	−0.324443	+	0.561951i
$153$		0			0
$154$		0			0
$155$	−3.00000			−0.240966
$156$		0			0
$157$	−2.00000	−	3.46410i	−0.159617	−	0.276465i	0.775113	−	0.631822i	$-0.217693\pi$
$157$	−2.00000	−	3.46410i	−0.159617	−	0.276465i	−0.934731	+	0.355357i	$0.884359\pi$
$158$	1.50000	+	2.59808i	0.119334	+	0.206692i
$159$		0			0
$160$	−1.00000			−0.0790569
$161$		0			0
$162$		0			0
$163$	2.00000	−	3.46410i	0.156652	−	0.271329i	−0.777007	−	0.629492i	$-0.783263\pi$
$163$	2.00000	−	3.46410i	0.156652	−	0.271329i	0.933659	+	0.358162i	$0.116597\pi$
$164$		0			0
$165$		0			0
$166$	−3.50000	+	6.06218i	−0.271653	+	0.470516i
$167$	−14.0000			−1.08335			−0.541676	−	0.840587i	$-0.682210\pi$
$167$	−14.0000			−1.08335			−0.541676	+	0.840587i	$0.682210\pi$
$168$		0			0
$169$	−13.0000			−1.00000
$170$	−2.00000	+	3.46410i	−0.153393	+	0.265684i
$171$		0			0
$172$	−1.00000	−	1.73205i	−0.0762493	−	0.132068i
$173$	−11.0000	+	19.0526i	−0.836315	+	1.44854i	0.0566411	+	0.998395i	$0.481961\pi$
$173$	−11.0000	+	19.0526i	−0.836315	+	1.44854i	−0.892956	+	0.450145i	$0.851372\pi$
$174$		0			0
$175$		0			0
$176$	−5.00000			−0.376889
$177$		0			0
$178$	−3.00000	−	5.19615i	−0.224860	−	0.389468i
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	0.998286	−	0.0585225i	$-0.0186389\pi$
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	−0.549825	+	0.835280i	$0.685306\pi$
$180$		0			0
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$		0			0
$183$		0			0
$184$	2.00000	−	3.46410i	0.147442	−	0.255377i
$185$	2.00000	+	3.46410i	0.147043	+	0.254686i
$186$		0			0
$187$	−10.0000	+	17.3205i	−0.731272	+	1.26660i
$188$	−6.00000			−0.437595
$189$		0			0
$190$	8.00000			0.580381
$191$	12.0000	−	20.7846i	0.868290	−	1.50392i	0.00454614	−	0.999990i	$-0.498553\pi$
$191$	12.0000	−	20.7846i	0.868290	−	1.50392i	0.863743	−	0.503932i	$-0.168114\pi$
$192$		0			0
$193$	−2.50000	−	4.33013i	−0.179954	−	0.311689i	0.761911	−	0.647682i	$-0.224262\pi$
$193$	−2.50000	−	4.33013i	−0.179954	−	0.311689i	−0.941865	+	0.335993i	$0.890928\pi$
$194$	−3.50000	+	6.06218i	−0.251285	+	0.435239i
$195$		0			0
$196$		0			0
$197$	−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	$-0.211948\pi$
$199$	−2.00000	−	3.46410i	−0.141776	−	0.245564i	−0.928166	+	0.372168i	$0.878615\pi$
$200$	−2.00000	−	3.46410i	−0.141421	−	0.244949i
$201$		0			0
$202$	−10.0000			−0.703598
$203$		0			0
$204$		0			0
$205$		0			0
$206$	−4.00000	−	6.92820i	−0.278693	−	0.482711i
$207$		0			0
$208$		0			0
$209$	40.0000			2.76686
$210$		0			0
$211$	2.00000			0.137686			0.0688428	−	0.997628i	$-0.478069\pi$
$211$	2.00000			0.137686			0.0688428	+	0.997628i	$0.478069\pi$
$212$	−4.50000	+	7.79423i	−0.309061	+	0.535310i
$213$		0			0
$214$	−1.50000	−	2.59808i	−0.102538	−	0.177601i
$215$	−1.00000	+	1.73205i	−0.0681994	+	0.118125i
$216$		0			0
$217$		0			0
$218$	2.00000			0.135457
$219$		0			0
$220$	2.50000	+	4.33013i	0.168550	+	0.291937i
$221$		0			0
$222$		0			0
$223$	7.00000			0.468755			0.234377	−	0.972146i	$-0.424695\pi$
$223$	7.00000			0.468755			0.234377	+	0.972146i	$0.424695\pi$
$224$		0			0
$225$		0			0
$226$	−8.00000	+	13.8564i	−0.532152	+	0.921714i
$227$	−1.50000	−	2.59808i	−0.0995585	−	0.172440i	0.811943	−	0.583736i	$-0.198410\pi$
$227$	−1.50000	−	2.59808i	−0.0995585	−	0.172440i	−0.911502	+	0.411296i	$0.865076\pi$
$228$		0			0
$229$	−10.0000	+	17.3205i	−0.660819	+	1.14457i	0.319582	+	0.947559i	$0.396457\pi$
$229$	−10.0000	+	17.3205i	−0.660819	+	1.14457i	−0.980401	+	0.197013i	$0.936876\pi$
$230$	−4.00000			−0.263752
$231$		0			0
$232$	−5.00000			−0.328266
$233$	−2.00000	+	3.46410i	−0.131024	+	0.226941i	−0.924072	−	0.382219i	$-0.875160\pi$
$233$	−2.00000	+	3.46410i	−0.131024	+	0.226941i	0.793047	+	0.609160i	$0.208493\pi$
$234$		0			0
$235$	3.00000	+	5.19615i	0.195698	+	0.338960i
$236$	5.50000	−	9.52628i	0.358020	−	0.620108i
$237$		0			0
$238$		0			0
$239$	12.0000			0.776215			0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000			0.776215			0.388108	+	0.921614i	$0.373129\pi$
$240$		0			0
$241$	−12.5000	−	21.6506i	−0.805196	−	1.39464i	−0.916159	−	0.400815i	$-0.868727\pi$
$241$	−12.5000	−	21.6506i	−0.805196	−	1.39464i	0.110963	−	0.993825i	$-0.464606\pi$
$242$	7.00000	+	12.1244i	0.449977	+	0.779383i
$243$		0			0
$244$	6.00000			0.384111
$245$		0			0
$246$		0			0
$247$		0			0
$248$	−1.50000	−	2.59808i	−0.0952501	−	0.164978i
$249$		0			0
$250$	−4.50000	+	7.79423i	−0.284605	+	0.492950i
$251$	21.0000			1.32551			0.662754	−	0.748837i	$-0.269387\pi$
$251$	21.0000			1.32551			0.662754	+	0.748837i	$0.269387\pi$
$252$		0			0
$253$	−20.0000			−1.25739
$254$	4.50000	−	7.79423i	0.282355	−	0.489053i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	−0.757159	−	0.653231i	$-0.773413\pi$
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	0.944294	+	0.329104i	$0.106747\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$	0.500000	+	0.866025i	0.0308901	+	0.0535032i
$263$	−15.0000	−	25.9808i	−0.924940	−	1.60204i	−0.791658	−	0.610964i	$-0.790782\pi$
$263$	−15.0000	−	25.9808i	−0.924940	−	1.60204i	−0.133281	−	0.991078i	$-0.542551\pi$
$264$		0			0
$265$	9.00000			0.552866
$266$		0			0
$267$		0			0
$268$	1.00000	−	1.73205i	0.0610847	−	0.105802i
$269$	−15.5000	−	26.8468i	−0.945052	−	1.63688i	−0.755648	−	0.654978i	$-0.772678\pi$
$269$	−15.5000	−	26.8468i	−0.945052	−	1.63688i	−0.189404	−	0.981899i	$-0.560656\pi$
$270$		0			0
$271$	7.50000	−	12.9904i	0.455593	−	0.789109i	−0.543130	−	0.839649i	$-0.682761\pi$
$271$	7.50000	−	12.9904i	0.455593	−	0.789109i	0.998722	+	0.0505395i	$0.0160941\pi$
$272$	−4.00000			−0.242536
$273$		0			0
$274$	−2.00000			−0.120824
$275$	−10.0000	+	17.3205i	−0.603023	+	1.04447i
$276$		0			0
$277$	8.00000	+	13.8564i	0.480673	+	0.832551i	0.999754	−	0.0221745i	$-0.00705893\pi$
$277$	8.00000	+	13.8564i	0.480673	+	0.832551i	−0.519081	+	0.854725i	$0.673726\pi$
$278$	7.00000	−	12.1244i	0.419832	−	0.727171i
$279$		0			0
$280$		0			0
$281$	−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
$283$	5.00000	+	8.66025i	0.297219	+	0.514799i	0.975499	−	0.220005i	$-0.0706075\pi$
$283$	5.00000	+	8.66025i	0.297219	+	0.514799i	−0.678280	+	0.734804i	$0.737274\pi$
$284$	1.00000	+	1.73205i	0.0593391	+	0.102778i
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$	2.50000	+	4.33013i	0.146805	+	0.254274i
$291$		0			0
$292$	5.00000	−	8.66025i	0.292603	−	0.506803i
$293$	−21.0000			−1.22683			−0.613417	−	0.789760i	$-0.710205\pi$
$293$	−21.0000			−1.22683			−0.613417	+	0.789760i	$0.710205\pi$
$294$		0			0
$295$	−11.0000			−0.640445
$296$	−2.00000	+	3.46410i	−0.116248	+	0.201347i
$297$		0			0
$298$	9.00000	+	15.5885i	0.521356	+	0.903015i
$299$		0			0
$300$		0			0
$301$		0			0
$302$	−19.0000			−1.09333
$303$		0			0
$304$	4.00000	+	6.92820i	0.229416	+	0.397360i
$305$	−3.00000	−	5.19615i	−0.171780	−	0.297531i
$306$		0			0
$307$	−28.0000			−1.59804			−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000			−1.59804			−0.799022	+	0.601302i	$0.794649\pi$
$308$		0			0
$309$		0			0
$310$	−1.50000	+	2.59808i	−0.0851943	+	0.147561i
$311$	16.0000	+	27.7128i	0.907277	+	1.57145i	0.817832	+	0.575458i	$0.195176\pi$
$311$	16.0000	+	27.7128i	0.907277	+	1.57145i	0.0894452	+	0.995992i	$0.471491\pi$
$312$		0			0
$313$	0.500000	−	0.866025i	0.0282617	−	0.0489506i	−0.851549	−	0.524276i	$-0.824336\pi$
$313$	0.500000	−	0.866025i	0.0282617	−	0.0489506i	0.879810	+	0.475325i	$0.157669\pi$
$314$	−4.00000			−0.225733
$315$		0			0
$316$	3.00000			0.168763
$317$	1.50000	−	2.59808i	0.0842484	−	0.145922i	−0.820822	−	0.571184i	$-0.806484\pi$
$317$	1.50000	−	2.59808i	0.0842484	−	0.145922i	0.905071	+	0.425261i	$0.139818\pi$
$318$		0			0
$319$	12.5000	+	21.6506i	0.699866	+	1.21220i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$		0			0
$322$		0			0
$323$	32.0000			1.78053
$324$		0			0
$325$		0			0
$326$	−2.00000	−	3.46410i	−0.110770	−	0.191859i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	−0.805812	−	0.592172i	$-0.798271\pi$
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	0.915742	+	0.401768i	$0.131604\pi$
$332$	3.50000	+	6.06218i	0.192087	+	0.332705i
$333$		0			0
$334$	−7.00000	+	12.1244i	−0.383023	+	0.663415i
$335$	−2.00000			−0.109272
$336$		0			0
$337$	9.00000			0.490261			0.245131	−	0.969490i	$-0.421169\pi$
$337$	9.00000			0.490261			0.245131	+	0.969490i	$0.421169\pi$
$338$	−6.50000	+	11.2583i	−0.353553	+	0.612372i
$339$		0			0
$340$	2.00000	+	3.46410i	0.108465	+	0.187867i
$341$	−7.50000	+	12.9904i	−0.406148	+	0.703469i
$342$		0			0
$343$		0			0
$344$	−2.00000			−0.107833
$345$		0			0
$346$	11.0000	+	19.0526i	0.591364	+	1.02427i
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	0.980921	−	0.194409i	$-0.0622790\pi$
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	−0.658824	+	0.752297i	$0.728946\pi$
$348$		0			0
$349$	14.0000			0.749403			0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000			0.749403			0.374701	+	0.927146i	$0.377745\pi$
$350$		0			0
$351$		0			0
$352$	−2.50000	+	4.33013i	−0.133250	+	0.230797i
$353$	−12.0000	−	20.7846i	−0.638696	−	1.10625i	−0.985719	−	0.168397i	$-0.946141\pi$
$353$	−12.0000	−	20.7846i	−0.638696	−	1.10625i	0.347024	−	0.937856i	$-0.387192\pi$
$354$		0			0
$355$	1.00000	−	1.73205i	0.0530745	−	0.0919277i
$356$	−6.00000			−0.317999
$357$		0			0
$358$	12.0000			0.634220
$359$	5.00000	−	8.66025i	0.263890	−	0.457071i	−0.703382	−	0.710812i	$-0.748328\pi$
$359$	5.00000	−	8.66025i	0.263890	−	0.457071i	0.967272	+	0.253741i	$0.0816611\pi$
$360$		0			0
$361$	−22.5000	−	38.9711i	−1.18421	−	2.05111i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−10.0000			−0.523424
$366$		0			0
$367$	8.50000	+	14.7224i	0.443696	+	0.768505i	0.997960	−	0.0638362i	$-0.0203335\pi$
$367$	8.50000	+	14.7224i	0.443696	+	0.768505i	−0.554264	+	0.832341i	$0.687000\pi$
$368$	−2.00000	−	3.46410i	−0.104257	−	0.180579i
$369$		0			0
$370$	4.00000			0.207950
$371$		0			0
$372$		0			0
$373$	16.0000	−	27.7128i	0.828449	−	1.43492i	−0.0708063	−	0.997490i	$-0.522557\pi$
$373$	16.0000	−	27.7128i	0.828449	−	1.43492i	0.899255	−	0.437425i	$-0.144109\pi$
$374$	10.0000	+	17.3205i	0.517088	+	0.895622i
$375$		0			0
$376$	−3.00000	+	5.19615i	−0.154713	+	0.267971i
$377$		0			0
$378$		0			0
$379$	16.0000			0.821865			0.410932	−	0.911666i	$-0.365203\pi$
$379$	16.0000			0.821865			0.410932	+	0.911666i	$0.365203\pi$
$380$	4.00000	−	6.92820i	0.205196	−	0.355409i
$381$		0			0
$382$	−12.0000	−	20.7846i	−0.613973	−	1.06343i
$383$	17.0000	−	29.4449i	0.868659	−	1.50456i	0.00529229	−	0.999986i	$-0.498315\pi$
$383$	17.0000	−	29.4449i	0.868659	−	1.50456i	0.863367	−	0.504576i	$-0.168351\pi$
$384$		0			0
$385$		0			0
$386$	−5.00000			−0.254493
$387$		0			0
$388$	3.50000	+	6.06218i	0.177686	+	0.307760i
$389$	−1.00000	−	1.73205i	−0.0507020	−	0.0878185i	0.839561	−	0.543266i	$-0.182813\pi$
$389$	−1.00000	−	1.73205i	−0.0507020	−	0.0878185i	−0.890263	+	0.455448i	$0.849479\pi$
$390$		0			0
$391$	−16.0000			−0.809155
$392$		0			0
$393$		0			0
$394$	−1.00000	+	1.73205i	−0.0503793	+	0.0872595i
$395$	−1.50000	−	2.59808i	−0.0754732	−	0.130723i
$396$		0			0
$397$	18.0000	−	31.1769i	0.903394	−	1.56472i	0.0803356	−	0.996768i	$-0.474401\pi$
$397$	18.0000	−	31.1769i	0.903394	−	1.56472i	0.823058	−	0.567957i	$-0.192266\pi$
$398$	−4.00000			−0.200502
$399$		0			0
$400$	−4.00000			−0.200000
$401$	12.0000	−	20.7846i	0.599251	−	1.03793i	−0.393680	−	0.919247i	$-0.628798\pi$
$401$	12.0000	−	20.7846i	0.599251	−	1.03793i	0.992932	−	0.118686i	$-0.0378683\pi$
$402$		0			0
$403$		0			0
$404$	−5.00000	+	8.66025i	−0.248759	+	0.430864i
$405$		0			0
$406$		0			0
$407$	20.0000			0.991363
$408$		0			0
$409$	−12.5000	−	21.6506i	−0.618085	−	1.07056i	−0.989835	−	0.142222i	$-0.954575\pi$
$409$	−12.5000	−	21.6506i	−0.618085	−	1.07056i	0.371750	−	0.928333i	$-0.378758\pi$
$410$		0			0
$411$		0			0
$412$	−8.00000			−0.394132
$413$		0			0
$414$		0			0
$415$	3.50000	−	6.06218i	0.171808	−	0.297581i
$416$		0			0
$417$		0			0
$418$	20.0000	−	34.6410i	0.978232	−	1.69435i
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	30.0000			1.46211			0.731055	−	0.682318i	$-0.239028\pi$
$421$	30.0000			1.46211			0.731055	+	0.682318i	$0.239028\pi$
$422$	1.00000	−	1.73205i	0.0486792	−	0.0843149i
$423$		0			0
$424$	4.50000	+	7.79423i	0.218539	+	0.378521i
$425$	−8.00000	+	13.8564i	−0.388057	+	0.672134i
$426$		0			0
$427$		0			0
$428$	−3.00000			−0.145010
$429$		0			0
$430$	1.00000	+	1.73205i	0.0482243	+	0.0835269i
$431$	6.00000	+	10.3923i	0.289010	+	0.500580i	0.973574	−	0.228373i	$-0.0733406\pi$
$431$	6.00000	+	10.3923i	0.289010	+	0.500580i	−0.684564	+	0.728953i	$0.740007\pi$
$432$		0			0
$433$	−14.0000			−0.672797			−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$		0			0
$435$		0			0
$436$	1.00000	−	1.73205i	0.0478913	−	0.0829502i
$437$	16.0000	+	27.7128i	0.765384	+	1.32568i
$438$		0			0
$439$	7.50000	−	12.9904i	0.357955	−	0.619997i	−0.629664	−	0.776868i	$-0.716807\pi$
$439$	7.50000	−	12.9904i	0.357955	−	0.619997i	0.987619	+	0.156871i	$0.0501406\pi$
$440$	5.00000			0.238366
$441$		0			0
$442$		0			0
$443$	8.50000	−	14.7224i	0.403847	−	0.699484i	−0.590339	−	0.807155i	$-0.701006\pi$
$443$	8.50000	−	14.7224i	0.403847	−	0.699484i	0.994187	+	0.107671i	$0.0343394\pi$
$444$		0			0
$445$	3.00000	+	5.19615i	0.142214	+	0.246321i
$446$	3.50000	−	6.06218i	0.165730	−	0.287052i
$447$		0			0
$448$		0			0
$449$	−16.0000			−0.755087			−0.377543	−	0.925992i	$-0.623231\pi$
$449$	−16.0000			−0.755087			−0.377543	+	0.925992i	$0.623231\pi$
$450$		0			0
$451$		0			0
$452$	8.00000	+	13.8564i	0.376288	+	0.651751i
$453$		0			0
$454$	−3.00000			−0.140797
$455$		0			0
$456$		0			0
$457$	−15.5000	+	26.8468i	−0.725059	+	1.25584i	0.233890	+	0.972263i	$0.424854\pi$
$457$	−15.5000	+	26.8468i	−0.725059	+	1.25584i	−0.958950	+	0.283577i	$0.908479\pi$
$458$	10.0000	+	17.3205i	0.467269	+	0.809334i
$459$		0			0
$460$	−2.00000	+	3.46410i	−0.0932505	+	0.161515i
$461$	−14.0000			−0.652045			−0.326023	−	0.945362i	$-0.605709\pi$
$461$	−14.0000			−0.652045			−0.326023	+	0.945362i	$0.605709\pi$
$462$		0			0
$463$	16.0000			0.743583			0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000			0.743583			0.371792	+	0.928316i	$0.378744\pi$
$464$	−2.50000	+	4.33013i	−0.116060	+	0.201021i
$465$		0			0
$466$	2.00000	+	3.46410i	0.0926482	+	0.160471i
$467$	10.0000	−	17.3205i	0.462745	−	0.801498i	−0.536352	−	0.843995i	$-0.680198\pi$
$467$	10.0000	−	17.3205i	0.462745	−	0.801498i	0.999097	+	0.0424970i	$0.0135313\pi$
$468$		0			0
$469$		0			0
$470$	6.00000			0.276759
$471$		0			0
$472$	−5.50000	−	9.52628i	−0.253158	−	0.438483i
$473$	5.00000	+	8.66025i	0.229900	+	0.398199i
$474$		0			0
$475$	32.0000			1.46826
$476$		0			0
$477$		0			0
$478$	6.00000	−	10.3923i	0.274434	−	0.475333i
$479$	−19.0000	−	32.9090i	−0.868132	−	1.50365i	−0.863903	−	0.503658i	$-0.831987\pi$
$479$	−19.0000	−	32.9090i	−0.868132	−	1.50365i	−0.00422900	−	0.999991i	$-0.501346\pi$
$480$		0			0
$481$		0			0
$482$	−25.0000			−1.13872
$483$		0			0
$484$	14.0000			0.636364
$485$	3.50000	−	6.06218i	0.158927	−	0.275269i
$486$		0			0
$487$	−2.50000	−	4.33013i	−0.113286	−	0.196217i	0.803807	−	0.594890i	$-0.202804\pi$
$487$	−2.50000	−	4.33013i	−0.113286	−	0.196217i	−0.917093	+	0.398673i	$0.869471\pi$
$488$	3.00000	−	5.19615i	0.135804	−	0.235219i
$489$		0			0
$490$		0			0
$491$	−9.00000			−0.406164			−0.203082	−	0.979162i	$-0.565096\pi$
$491$	−9.00000			−0.406164			−0.203082	+	0.979162i	$0.565096\pi$
$492$		0			0
$493$	10.0000	+	17.3205i	0.450377	+	0.780076i
$494$		0			0
$495$		0			0
$496$	−3.00000			−0.134704
$497$		0			0
$498$		0			0
$499$	−5.00000	+	8.66025i	−0.223831	+	0.387686i	−0.955968	−	0.293471i	$-0.905190\pi$
$499$	−5.00000	+	8.66025i	−0.223831	+	0.387686i	0.732137	+	0.681157i	$0.238523\pi$
$500$	4.50000	+	7.79423i	0.201246	+	0.348569i
$501$		0			0
$502$	10.5000	−	18.1865i	0.468638	−	0.811705i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$	10.0000			0.444994
$506$	−10.0000	+	17.3205i	−0.444554	+	0.769991i
$507$		0			0
$508$	−4.50000	−	7.79423i	−0.199655	−	0.345813i
$509$	−7.50000	+	12.9904i	−0.332432	+	0.575789i	−0.982988	−	0.183669i	$-0.941202\pi$
$509$	−7.50000	+	12.9904i	−0.332432	+	0.575789i	0.650556	+	0.759458i	$0.274536\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−3.00000	−	5.19615i	−0.132324	−	0.229192i
$515$	4.00000	+	6.92820i	0.176261	+	0.305293i
$516$		0			0
$517$	30.0000			1.31940
$518$		0			0
$519$		0			0
$520$		0			0
$521$	9.00000	+	15.5885i	0.394297	+	0.682943i	0.993011	−	0.118020i	$-0.0376547\pi$
$521$	9.00000	+	15.5885i	0.394297	+	0.682943i	−0.598714	+	0.800963i	$0.704321\pi$
$522$		0			0
$523$	4.00000	−	6.92820i	0.174908	−	0.302949i	−0.765222	−	0.643767i	$-0.777371\pi$
$523$	4.00000	−	6.92820i	0.174908	−	0.302949i	0.940129	+	0.340818i	$0.110704\pi$
$524$	1.00000			0.0436852
$525$		0			0
$526$	−30.0000			−1.30806
$527$	−6.00000	+	10.3923i	−0.261364	+	0.452696i
$528$		0			0
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$	4.50000	−	7.79423i	0.195468	−	0.338560i
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	1.50000	+	2.59808i	0.0648507	+	0.112325i
$536$	−1.00000	−	1.73205i	−0.0431934	−	0.0748132i
$537$		0			0
$538$	−31.0000			−1.33650
$539$		0			0
$540$		0			0
$541$	9.00000	−	15.5885i	0.386940	−	0.670200i	−0.605096	−	0.796152i	$-0.706865\pi$
$541$	9.00000	−	15.5885i	0.386940	−	0.670200i	0.992036	+	0.125952i	$0.0401986\pi$
$542$	−7.50000	−	12.9904i	−0.322153	−	0.557985i
$543$		0			0
$544$	−2.00000	+	3.46410i	−0.0857493	+	0.148522i
$545$	−2.00000			−0.0856706
$546$		0			0
$547$	−12.0000			−0.513083			−0.256541	−	0.966533i	$-0.582583\pi$
$547$	−12.0000			−0.513083			−0.256541	+	0.966533i	$0.582583\pi$
$548$	−1.00000	+	1.73205i	−0.0427179	+	0.0739895i
$549$		0			0
$550$	10.0000	+	17.3205i	0.426401	+	0.738549i
$551$	20.0000	−	34.6410i	0.852029	−	1.47576i
$552$		0			0
$553$		0			0
$554$	16.0000			0.679775
$555$		0			0
$556$	−7.00000	−	12.1244i	−0.296866	−	0.514187i
$557$	−11.5000	−	19.9186i	−0.487271	−	0.843978i	0.512622	−	0.858614i	$-0.328674\pi$
$557$	−11.5000	−	19.9186i	−0.487271	−	0.843978i	−0.999893	+	0.0146368i	$0.995341\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−1.00000	+	1.73205i	−0.0421825	+	0.0730622i
$563$	−8.50000	−	14.7224i	−0.358232	−	0.620477i	0.629433	−	0.777055i	$-0.283287\pi$
$563$	−8.50000	−	14.7224i	−0.358232	−	0.620477i	−0.987666	+	0.156578i	$0.949954\pi$
$564$		0			0
$565$	8.00000	−	13.8564i	0.336563	−	0.582943i
$566$	10.0000			0.420331
$567$		0			0
$568$	2.00000			0.0839181
$569$	12.0000	−	20.7846i	0.503066	−	0.871336i	−0.496928	−	0.867792i	$-0.665539\pi$
$569$	12.0000	−	20.7846i	0.503066	−	0.871336i	0.999994	−	0.00354413i	$-0.00112814\pi$
$570$		0			0
$571$	15.0000	+	25.9808i	0.627730	+	1.08726i	0.988006	+	0.154415i	$0.0493493\pi$
$571$	15.0000	+	25.9808i	0.627730	+	1.08726i	−0.360276	+	0.932846i	$0.617317\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−16.0000			−0.667246
$576$		0			0
$577$	15.5000	+	26.8468i	0.645273	+	1.11765i	0.984238	+	0.176847i	$0.0565899\pi$
$577$	15.5000	+	26.8468i	0.645273	+	1.11765i	−0.338965	+	0.940799i	$0.610077\pi$
$578$	−0.500000	−	0.866025i	−0.0207973	−	0.0360219i
$579$		0			0
$580$	5.00000			0.207614
$581$		0			0
$582$		0			0
$583$	22.5000	−	38.9711i	0.931855	−	1.61402i
$584$	−5.00000	−	8.66025i	−0.206901	−	0.358364i
$585$		0			0
$586$	−10.5000	+	18.1865i	−0.433751	+	0.751279i
$587$	35.0000			1.44460			0.722302	−	0.691577i	$-0.243084\pi$
$587$	35.0000			1.44460			0.722302	+	0.691577i	$0.243084\pi$
$588$		0			0
$589$	24.0000			0.988903
$590$	−5.50000	+	9.52628i	−0.226431	+	0.392191i
$591$		0			0
$592$	2.00000	+	3.46410i	0.0821995	+	0.142374i
$593$	−18.0000	+	31.1769i	−0.739171	+	1.28028i	0.213697	+	0.976900i	$0.431449\pi$
$593$	−18.0000	+	31.1769i	−0.739171	+	1.28028i	−0.952869	+	0.303383i	$0.901884\pi$
$594$		0			0
$595$		0			0
$596$	18.0000			0.737309
$597$		0			0
$598$		0			0
$599$	−15.0000	−	25.9808i	−0.612883	−	1.06155i	−0.990752	−	0.135686i	$-0.956676\pi$
$599$	−15.0000	−	25.9808i	−0.612883	−	1.06155i	0.377869	−	0.925859i	$-0.376657\pi$
$600$		0			0
$601$	−35.0000			−1.42768			−0.713840	−	0.700309i	$-0.753046\pi$
$601$	−35.0000			−1.42768			−0.713840	+	0.700309i	$0.753046\pi$
$602$		0			0
$603$		0			0
$604$	−9.50000	+	16.4545i	−0.386550	+	0.669523i
$605$	−7.00000	−	12.1244i	−0.284590	−	0.492925i
$606$		0			0
$607$	−13.5000	+	23.3827i	−0.547948	+	0.949074i	0.450467	+	0.892793i	$0.351258\pi$
$607$	−13.5000	+	23.3827i	−0.547948	+	0.949074i	−0.998415	+	0.0562808i	$0.982076\pi$
$608$	8.00000			0.324443
$609$		0			0
$610$	−6.00000			−0.242933
$611$		0			0
$612$		0			0
$613$	−6.00000	−	10.3923i	−0.242338	−	0.419741i	0.719042	−	0.694967i	$-0.244581\pi$
$613$	−6.00000	−	10.3923i	−0.242338	−	0.419741i	−0.961380	+	0.275225i	$0.911248\pi$
$614$	−14.0000	+	24.2487i	−0.564994	+	0.978598i
$615$		0			0
$616$		0			0
$617$	−2.00000			−0.0805170			−0.0402585	−	0.999189i	$-0.512818\pi$
$617$	−2.00000			−0.0805170			−0.0402585	+	0.999189i	$0.512818\pi$
$618$		0			0
$619$	5.00000	+	8.66025i	0.200967	+	0.348085i	0.948840	−	0.315757i	$-0.102258\pi$
$619$	5.00000	+	8.66025i	0.200967	+	0.348085i	−0.747873	+	0.663842i	$0.768925\pi$
$620$	1.50000	+	2.59808i	0.0602414	+	0.104341i
$621$		0			0
$622$	32.0000			1.28308
$623$		0			0
$624$		0			0
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	−0.500000	−	0.866025i	−0.0199840	−	0.0346133i
$627$		0			0
$628$	−2.00000	+	3.46410i	−0.0798087	+	0.138233i
$629$	16.0000			0.637962
$630$		0			0
$631$	−19.0000			−0.756378			−0.378189	−	0.925728i	$-0.623453\pi$
$631$	−19.0000			−0.756378			−0.378189	+	0.925728i	$0.623453\pi$
$632$	1.50000	−	2.59808i	0.0596668	−	0.103346i
$633$		0			0
$634$	−1.50000	−	2.59808i	−0.0595726	−	0.103183i
$635$	−4.50000	+	7.79423i	−0.178577	+	0.309305i
$636$		0			0
$637$		0			0
$638$	25.0000			0.989759
$639$		0			0
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	13.0000	+	22.5167i	0.513469	+	0.889355i	0.999878	+	0.0156233i	$0.00497325\pi$
$641$	13.0000	+	22.5167i	0.513469	+	0.889355i	−0.486409	+	0.873731i	$0.661693\pi$
$642$		0			0
$643$	−14.0000			−0.552106			−0.276053	−	0.961142i	$-0.589027\pi$
$643$	−14.0000			−0.552106			−0.276053	+	0.961142i	$0.589027\pi$
$644$		0			0
$645$		0			0
$646$	16.0000	−	27.7128i	0.629512	−	1.09035i
$647$	9.00000	+	15.5885i	0.353827	+	0.612845i	0.986916	−	0.161233i	$-0.0515470\pi$
$647$	9.00000	+	15.5885i	0.353827	+	0.612845i	−0.633090	+	0.774078i	$0.718214\pi$
$648$		0			0
$649$	−27.5000	+	47.6314i	−1.07947	+	1.86970i
$650$		0			0
$651$		0			0
$652$	−4.00000			−0.156652
$653$	−19.5000	+	33.7750i	−0.763094	+	1.32172i	0.178154	+	0.984003i	$0.442987\pi$
$653$	−19.5000	+	33.7750i	−0.763094	+	1.32172i	−0.941248	+	0.337715i	$0.890346\pi$
$654$		0			0
$655$	−0.500000	−	0.866025i	−0.0195366	−	0.0338384i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	40.0000			1.55818			0.779089	−	0.626913i	$-0.215682\pi$
$659$	40.0000			1.55818			0.779089	+	0.626913i	$0.215682\pi$
$660$		0			0
$661$	5.00000	+	8.66025i	0.194477	+	0.336845i	0.946729	−	0.322031i	$-0.104366\pi$
$661$	5.00000	+	8.66025i	0.194477	+	0.336845i	−0.752252	+	0.658876i	$0.771032\pi$
$662$	−2.00000	−	3.46410i	−0.0777322	−	0.134636i
$663$		0			0
$664$	7.00000			0.271653
$665$		0			0
$666$		0			0
$667$	−10.0000	+	17.3205i	−0.387202	+	0.670653i
$668$	7.00000	+	12.1244i	0.270838	+	0.469105i
$669$		0			0
$670$	−1.00000	+	1.73205i	−0.0386334	+	0.0669150i
$671$	−30.0000			−1.15814
$672$		0			0
$673$	−19.0000			−0.732396			−0.366198	−	0.930537i	$-0.619341\pi$
$673$	−19.0000			−0.732396			−0.366198	+	0.930537i	$0.619341\pi$
$674$	4.50000	−	7.79423i	0.173334	−	0.300222i
$675$		0			0
$676$	6.50000	+	11.2583i	0.250000	+	0.433013i
$677$	13.5000	−	23.3827i	0.518847	−	0.898670i	−0.480913	−	0.876768i	$-0.659695\pi$
$677$	13.5000	−	23.3827i	0.518847	−	0.898670i	0.999760	−	0.0219013i	$-0.00697196\pi$
$678$		0			0
$679$		0			0
$680$	4.00000			0.153393
$681$		0			0
$682$	7.50000	+	12.9904i	0.287190	+	0.497427i
$683$	−4.50000	−	7.79423i	−0.172188	−	0.298238i	0.766997	−	0.641651i	$-0.221750\pi$
$683$	−4.50000	−	7.79423i	−0.172188	−	0.298238i	−0.939184	+	0.343413i	$0.888417\pi$
$684$		0			0
$685$	2.00000			0.0764161
$686$		0			0
$687$		0			0
$688$	−1.00000	+	1.73205i	−0.0381246	+	0.0660338i
$689$		0			0
$690$		0			0
$691$	4.00000	−	6.92820i	0.152167	−	0.263561i	−0.779857	−	0.625958i	$-0.784708\pi$
$691$	4.00000	−	6.92820i	0.152167	−	0.263561i	0.932024	+	0.362397i	$0.118041\pi$
$692$	22.0000			0.836315
$693$		0			0
$694$	12.0000			0.455514
$695$	−7.00000	+	12.1244i	−0.265525	+	0.459903i
$696$		0			0
$697$		0			0
$698$	7.00000	−	12.1244i	0.264954	−	0.458914i
$699$		0			0
$700$		0			0
$701$	5.00000			0.188847			0.0944237	−	0.995532i	$-0.469899\pi$
$701$	5.00000			0.188847			0.0944237	+	0.995532i	$0.469899\pi$
$702$		0			0
$703$	−16.0000	−	27.7128i	−0.603451	−	1.04521i
$704$	2.50000	+	4.33013i	0.0942223	+	0.163198i
$705$		0			0
$706$	−24.0000			−0.903252
$707$		0			0
$708$		0			0
$709$	−19.0000	+	32.9090i	−0.713560	+	1.23592i	0.249952	+	0.968258i	$0.419585\pi$
$709$	−19.0000	+	32.9090i	−0.713560	+	1.23592i	−0.963512	+	0.267664i	$0.913748\pi$
$710$	−1.00000	−	1.73205i	−0.0375293	−	0.0650027i
$711$		0			0
$712$	−3.00000	+	5.19615i	−0.112430	+	0.194734i
$713$	−12.0000			−0.449404
$714$		0			0
$715$		0			0
$716$	6.00000	−	10.3923i	0.224231	−	0.388379i
$717$		0			0
$718$	−5.00000	−	8.66025i	−0.186598	−	0.323198i
$719$	3.00000	−	5.19615i	0.111881	−	0.193784i	−0.804648	−	0.593753i	$-0.797646\pi$
$719$	3.00000	−	5.19615i	0.111881	−	0.193784i	0.916529	+	0.399969i	$0.130979\pi$
$720$		0			0
$721$		0			0
$722$	−45.0000			−1.67473
$723$		0			0
$724$		0			0
$725$	10.0000	+	17.3205i	0.371391	+	0.643268i
$726$		0			0
$727$	−7.00000			−0.259616			−0.129808	−	0.991539i	$-0.541436\pi$
$727$	−7.00000			−0.259616			−0.129808	+	0.991539i	$0.541436\pi$
$728$		0			0
$729$		0			0
$730$	−5.00000	+	8.66025i	−0.185058	+	0.320530i
$731$	4.00000	+	6.92820i	0.147945	+	0.256249i
$732$		0			0
$733$	−3.00000	+	5.19615i	−0.110808	+	0.191924i	−0.916096	−	0.400959i	$-0.868677\pi$
$733$	−3.00000	+	5.19615i	−0.110808	+	0.191924i	0.805289	+	0.592883i	$0.202010\pi$
$734$	17.0000			0.627481
$735$		0			0
$736$	−4.00000			−0.147442
$737$	−5.00000	+	8.66025i	−0.184177	+	0.319005i
$738$		0			0
$739$	15.0000	+	25.9808i	0.551784	+	0.955718i	0.998146	+	0.0608653i	$0.0193860\pi$
$739$	15.0000	+	25.9808i	0.551784	+	0.955718i	−0.446362	+	0.894852i	$0.647281\pi$
$740$	2.00000	−	3.46410i	0.0735215	−	0.127343i
$741$		0			0
$742$		0			0
$743$	−30.0000			−1.10059			−0.550297	−	0.834969i	$-0.685485\pi$
$743$	−30.0000			−1.10059			−0.550297	+	0.834969i	$0.685485\pi$
$744$		0			0
$745$	−9.00000	−	15.5885i	−0.329734	−	0.571117i
$746$	−16.0000	−	27.7128i	−0.585802	−	1.01464i
$747$		0			0
$748$	20.0000			0.731272
$749$		0			0
$750$		0			0
$751$	−22.5000	+	38.9711i	−0.821037	+	1.42208i	0.0838743	+	0.996476i	$0.473271\pi$
$751$	−22.5000	+	38.9711i	−0.821037	+	1.42208i	−0.904911	+	0.425601i	$0.860063\pi$
$752$	3.00000	+	5.19615i	0.109399	+	0.189484i
$753$		0			0
$754$		0			0
$755$	19.0000			0.691481
$756$		0			0
$757$	−54.0000			−1.96266			−0.981332	−	0.192323i	$-0.938398\pi$
$757$	−54.0000			−1.96266			−0.981332	+	0.192323i	$0.938398\pi$
$758$	8.00000	−	13.8564i	0.290573	−	0.503287i
$759$		0			0
$760$	−4.00000	−	6.92820i	−0.145095	−	0.251312i
$761$	−4.00000	+	6.92820i	−0.145000	+	0.251147i	−0.929373	−	0.369142i	$-0.879652\pi$
$761$	−4.00000	+	6.92820i	−0.145000	+	0.251147i	0.784373	+	0.620289i	$0.212985\pi$
$762$		0			0
$763$		0			0
$764$	−24.0000			−0.868290
$765$		0			0
$766$	−17.0000	−	29.4449i	−0.614235	−	1.06389i
$767$		0			0
$768$		0			0
$769$	35.0000			1.26213			0.631066	−	0.775729i	$-0.282618\pi$
$769$	35.0000			1.26213			0.631066	+	0.775729i	$0.282618\pi$
$770$		0			0
$771$		0			0
$772$	−2.50000	+	4.33013i	−0.0899770	+	0.155845i
$773$	−5.00000	−	8.66025i	−0.179838	−	0.311488i	0.761987	−	0.647592i	$-0.224224\pi$
$773$	−5.00000	−	8.66025i	−0.179838	−	0.311488i	−0.941825	+	0.336104i	$0.890891\pi$
$774$		0			0
$775$	−6.00000	+	10.3923i	−0.215526	+	0.373303i
$776$	7.00000			0.251285
$777$		0			0
$778$	−2.00000			−0.0717035
$779$		0			0
$780$		0			0
$781$	−5.00000	−	8.66025i	−0.178914	−	0.309888i
$782$	−8.00000	+	13.8564i	−0.286079	+	0.495504i
$783$		0			0
$784$		0			0
$785$	4.00000			0.142766
$786$		0			0
$787$	−9.00000	−	15.5885i	−0.320815	−	0.555668i	0.659841	−	0.751405i	$-0.270624\pi$
$787$	−9.00000	−	15.5885i	−0.320815	−	0.555668i	−0.980656	+	0.195737i	$0.937290\pi$
$788$	1.00000	+	1.73205i	0.0356235	+	0.0617018i
$789$		0			0
$790$	−3.00000			−0.106735
$791$		0			0
$792$		0			0
$793$		0			0
$794$	−18.0000	−	31.1769i	−0.638796	−	1.10643i
$795$		0			0
$796$	−2.00000	+	3.46410i	−0.0708881	+	0.122782i
$797$	21.0000			0.743858			0.371929	−	0.928261i	$-0.378696\pi$
$797$	21.0000			0.743858			0.371929	+	0.928261i	$0.378696\pi$
$798$		0			0
$799$	24.0000			0.849059
$800$	−2.00000	+	3.46410i	−0.0707107	+	0.122474i
$801$		0			0
$802$	−12.0000	−	20.7846i	−0.423735	−	0.733930i
$803$	−25.0000	+	43.3013i	−0.882231	+	1.52807i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	5.00000	+	8.66025i	0.175899	+	0.304667i
$809$	20.0000	+	34.6410i	0.703163	+	1.21791i	0.967351	+	0.253442i	$0.0815627\pi$
$809$	20.0000	+	34.6410i	0.703163	+	1.21791i	−0.264188	+	0.964471i	$0.585104\pi$
$810$		0			0
$811$	14.0000			0.491606			0.245803	−	0.969320i	$-0.420948\pi$
$811$	14.0000			0.491606			0.245803	+	0.969320i	$0.420948\pi$
$812$		0			0
$813$		0			0
$814$	10.0000	−	17.3205i	0.350500	−	0.607083i
$815$	2.00000	+	3.46410i	0.0700569	+	0.121342i
$816$		0			0
$817$	8.00000	−	13.8564i	0.279885	−	0.484774i
$818$	−25.0000			−0.874105
$819$		0			0
$820$		0			0
$821$	−12.5000	+	21.6506i	−0.436253	+	0.755612i	−0.997397	−	0.0721058i	$-0.977028\pi$
$821$	−12.5000	+	21.6506i	−0.436253	+	0.755612i	0.561144	+	0.827718i	$0.310361\pi$
$822$		0			0
$823$	−20.0000	−	34.6410i	−0.697156	−	1.20751i	−0.969448	−	0.245295i	$-0.921115\pi$
$823$	−20.0000	−	34.6410i	−0.697156	−	1.20751i	0.272292	−	0.962215i	$-0.412218\pi$
$824$	−4.00000	+	6.92820i	−0.139347	+	0.241355i
$825$		0			0
$826$		0			0
$827$	−9.00000			−0.312961			−0.156480	−	0.987681i	$-0.550015\pi$
$827$	−9.00000			−0.312961			−0.156480	+	0.987681i	$0.550015\pi$
$828$		0			0
$829$	−16.0000	−	27.7128i	−0.555703	−	0.962506i	−0.997848	−	0.0655624i	$-0.979116\pi$
$829$	−16.0000	−	27.7128i	−0.555703	−	0.962506i	0.442145	−	0.896943i	$-0.354217\pi$
$830$	−3.50000	−	6.06218i	−0.121487	−	0.210421i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	7.00000	−	12.1244i	0.242245	−	0.419581i
$836$	−20.0000	−	34.6410i	−0.691714	−	1.19808i
$837$		0			0
$838$		0			0
$839$	−28.0000			−0.966667			−0.483334	−	0.875436i	$-0.660574\pi$
$839$	−28.0000			−0.966667			−0.483334	+	0.875436i	$0.660574\pi$
$840$		0			0
$841$	−4.00000			−0.137931
$842$	15.0000	−	25.9808i	0.516934	−	0.895356i
$843$		0			0
$844$	−1.00000	−	1.73205i	−0.0344214	−	0.0596196i
$845$	6.50000	−	11.2583i	0.223607	−	0.387298i
$846$		0			0
$847$		0			0
$848$	9.00000			0.309061
$849$		0			0
$850$	8.00000	+	13.8564i	0.274398	+	0.475271i
$851$	8.00000	+	13.8564i	0.274236	+	0.474991i
$852$		0			0
$853$	−14.0000			−0.479351			−0.239675	−	0.970853i	$-0.577041\pi$
$853$	−14.0000			−0.479351			−0.239675	+	0.970853i	$0.577041\pi$
$854$		0			0
$855$		0			0
$856$	−1.50000	+	2.59808i	−0.0512689	+	0.0888004i
$857$	9.00000	+	15.5885i	0.307434	+	0.532492i	0.977800	−	0.209539i	$-0.0671963\pi$
$857$	9.00000	+	15.5885i	0.307434	+	0.532492i	−0.670366	+	0.742030i	$0.733863\pi$
$858$		0			0
$859$	−17.0000	+	29.4449i	−0.580033	+	1.00465i	0.415442	+	0.909620i	$0.363627\pi$
$859$	−17.0000	+	29.4449i	−0.580033	+	1.00465i	−0.995475	+	0.0950262i	$0.969707\pi$
$860$	2.00000			0.0681994
$861$		0			0
$862$	12.0000			0.408722
$863$	5.00000	−	8.66025i	0.170202	−	0.294798i	−0.768288	−	0.640104i	$-0.778891\pi$
$863$	5.00000	−	8.66025i	0.170202	−	0.294798i	0.938490	+	0.345305i	$0.112225\pi$
$864$		0			0
$865$	−11.0000	−	19.0526i	−0.374011	−	0.647806i
$866$	−7.00000	+	12.1244i	−0.237870	+	0.412002i
$867$		0			0
$868$		0			0
$869$	−15.0000			−0.508840
$870$		0			0
$871$		0			0
$872$	−1.00000	−	1.73205i	−0.0338643	−	0.0586546i
$873$		0			0
$874$	32.0000			1.08242
$875$		0			0
$876$		0			0
$877$	16.0000	−	27.7128i	0.540282	−	0.935795i	−0.458606	−	0.888640i	$-0.651651\pi$
$877$	16.0000	−	27.7128i	0.540282	−	0.935795i	0.998888	−	0.0471555i	$-0.0150156\pi$
$878$	−7.50000	−	12.9904i	−0.253113	−	0.438404i
$879$		0			0
$880$	2.50000	−	4.33013i	0.0842750	−	0.145969i
$881$	−42.0000			−1.41502			−0.707508	−	0.706705i	$-0.750181\pi$
$881$	−42.0000			−1.41502			−0.707508	+	0.706705i	$0.750181\pi$
$882$		0			0
$883$	−40.0000			−1.34611			−0.673054	−	0.739594i	$-0.735018\pi$
$883$	−40.0000			−1.34611			−0.673054	+	0.739594i	$0.735018\pi$
$884$		0			0
$885$		0			0
$886$	−8.50000	−	14.7224i	−0.285563	−	0.494610i
$887$	−18.0000	+	31.1769i	−0.604381	+	1.04682i	0.387768	+	0.921757i	$0.373246\pi$
$887$	−18.0000	+	31.1769i	−0.604381	+	1.04682i	−0.992149	+	0.125061i	$0.960087\pi$
$888$		0			0
$889$		0			0
$890$	6.00000			0.201120
$891$		0			0
$892$	−3.50000	−	6.06218i	−0.117189	−	0.202977i
$893$	−24.0000	−	41.5692i	−0.803129	−	1.39106i
$894$		0			0
$895$	−12.0000			−0.401116
$896$		0			0
$897$		0			0
$898$	−8.00000	+	13.8564i	−0.266963	+	0.462394i
$899$	7.50000	+	12.9904i	0.250139	+	0.433253i
$900$		0			0
$901$	18.0000	−	31.1769i	0.599667	−	1.03865i
$902$		0			0
$903$		0			0
$904$	16.0000			0.532152
$905$		0			0
$906$		0			0
$907$	−6.00000	−	10.3923i	−0.199227	−	0.345071i	0.749051	−	0.662512i	$-0.230510\pi$
$907$	−6.00000	−	10.3923i	−0.199227	−	0.345071i	−0.948278	+	0.317441i	$0.897176\pi$
$908$	−1.50000	+	2.59808i	−0.0497792	+	0.0862202i
$909$		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
$913$	−17.5000	−	30.3109i	−0.579165	−	1.00314i
$914$	15.5000	+	26.8468i	0.512694	+	0.888013i
$915$		0			0
$916$	20.0000			0.660819
$917$		0			0
$918$		0			0
$919$	16.0000	−	27.7128i	0.527791	−	0.914161i	−0.471684	−	0.881768i	$-0.656354\pi$
$919$	16.0000	−	27.7128i	0.527791	−	0.914161i	0.999475	−	0.0323936i	$-0.0103130\pi$
$920$	2.00000	+	3.46410i	0.0659380	+	0.114208i
$921$		0			0
$922$	−7.00000	+	12.1244i	−0.230533	+	0.399294i
$923$		0			0
$924$		0			0
$925$	16.0000			0.526077
$926$	8.00000	−	13.8564i	0.262896	−	0.455350i
$927$		0			0
$928$	2.50000	+	4.33013i	0.0820665	+	0.142143i
$929$	3.00000	−	5.19615i	0.0984268	−	0.170480i	−0.812607	−	0.582812i	$-0.801952\pi$
$929$	3.00000	−	5.19615i	0.0984268	−	0.170480i	0.911034	+	0.412332i	$0.135286\pi$
$930$		0			0
$931$		0			0
$932$	4.00000			0.131024
$933$		0			0
$934$	−10.0000	−	17.3205i	−0.327210	−	0.566744i
$935$	−10.0000	−	17.3205i	−0.327035	−	0.566441i
$936$		0			0
$937$	−35.0000			−1.14340			−0.571700	−	0.820463i	$-0.693716\pi$
$937$	−35.0000			−1.14340			−0.571700	+	0.820463i	$0.693716\pi$
$938$		0			0
$939$		0			0
$940$	3.00000	−	5.19615i	0.0978492	−	0.169480i
$941$	5.50000	+	9.52628i	0.179295	+	0.310548i	0.941639	−	0.336624i	$-0.109285\pi$
$941$	5.50000	+	9.52628i	0.179295	+	0.310548i	−0.762344	+	0.647172i	$0.775952\pi$
$942$		0			0
$943$		0			0
$944$	−11.0000			−0.358020
$945$		0			0
$946$	10.0000			0.325128
$947$	−16.0000	+	27.7128i	−0.519930	+	0.900545i	0.479801	+	0.877377i	$0.340709\pi$
$947$	−16.0000	+	27.7128i	−0.519930	+	0.900545i	−0.999732	+	0.0231683i	$0.992625\pi$
$948$		0			0
$949$		0			0
$950$	16.0000	−	27.7128i	0.519109	−	0.899122i
$951$		0			0
$952$		0			0
$953$	−2.00000			−0.0647864			−0.0323932	−	0.999475i	$-0.510313\pi$
$953$	−2.00000			−0.0647864			−0.0323932	+	0.999475i	$0.510313\pi$
$954$		0			0
$955$	12.0000	+	20.7846i	0.388311	+	0.672574i
$956$	−6.00000	−	10.3923i	−0.194054	−	0.336111i
$957$		0			0
$958$	−38.0000			−1.22772
$959$		0			0
$960$		0			0
$961$	11.0000	−	19.0526i	0.354839	−	0.614599i
$962$		0			0
$963$		0			0
$964$	−12.5000	+	21.6506i	−0.402598	+	0.697320i
$965$	5.00000			0.160956
$966$		0			0
$967$	−61.0000			−1.96163			−0.980814	−	0.194946i	$-0.937547\pi$
$967$	−61.0000			−1.96163			−0.980814	+	0.194946i	$0.937547\pi$
$968$	7.00000	−	12.1244i	0.224989	−	0.389692i
$969$		0			0
$970$	−3.50000	−	6.06218i	−0.112378	−	0.194645i
$971$	−7.50000	+	12.9904i	−0.240686	+	0.416881i	−0.960910	−	0.276861i	$-0.910706\pi$
$971$	−7.50000	+	12.9904i	−0.240686	+	0.416881i	0.720224	+	0.693742i	$0.244039\pi$
$972$		0			0
$973$		0			0
$974$	−5.00000			−0.160210
$975$		0			0
$976$	−3.00000	−	5.19615i	−0.0960277	−	0.166325i
$977$	−15.0000	−	25.9808i	−0.479893	−	0.831198i	0.519841	−	0.854263i	$-0.325991\pi$
$977$	−15.0000	−	25.9808i	−0.479893	−	0.831198i	−0.999734	+	0.0230645i	$0.992658\pi$
$978$		0			0
$979$	30.0000			0.958804
$980$		0			0
$981$		0			0
$982$	−4.50000	+	7.79423i	−0.143601	+	0.248724i
$983$	30.0000	+	51.9615i	0.956851	+	1.65732i	0.730073	+	0.683369i	$0.239486\pi$
$983$	30.0000	+	51.9615i	0.956851	+	1.65732i	0.226778	+	0.973946i	$0.427181\pi$
$984$		0			0
$985$	1.00000	−	1.73205i	0.0318626	−	0.0551877i
$986$	20.0000			0.636930
$987$		0			0
$988$		0			0
$989$	−4.00000	+	6.92820i	−0.127193	+	0.220304i
$990$		0			0
$991$	−23.5000	−	40.7032i	−0.746502	−	1.29298i	−0.949490	−	0.313798i	$-0.898398\pi$
$991$	−23.5000	−	40.7032i	−0.746502	−	1.29298i	0.202988	−	0.979181i	$-0.434935\pi$
$992$	−1.50000	+	2.59808i	−0.0476250	+	0.0824890i
$993$		0			0
$994$		0			0
$995$	4.00000			0.126809
$996$		0			0
$997$	19.0000	+	32.9090i	0.601736	+	1.04224i	0.992558	+	0.121771i	$0.0388574\pi$
$997$	19.0000	+	32.9090i	0.601736	+	1.04224i	−0.390822	+	0.920466i	$0.627809\pi$
$998$	5.00000	+	8.66025i	0.158272	+	0.274136i
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.g.i.667.1		2
3.2	odd	2		294.2.e.b.79.1		2
7.2	even	3		882.2.a.d.1.1		1
7.3	odd	6		126.2.g.c.109.1		2
7.4	even	3	inner	882.2.g.i.361.1		2
7.5	odd	6		882.2.a.c.1.1		1
7.6	odd	2		126.2.g.c.37.1		2
12.11	even	2		2352.2.q.u.961.1		2
21.2	odd	6		294.2.a.f.1.1		1
21.5	even	6		294.2.a.e.1.1		1
21.11	odd	6		294.2.e.b.67.1		2
21.17	even	6		42.2.e.a.25.1	✓	2
21.20	even	2		42.2.e.a.37.1	yes	2
28.3	even	6		1008.2.s.k.865.1		2
28.19	even	6		7056.2.a.w.1.1		1
28.23	odd	6		7056.2.a.bl.1.1		1
28.27	even	2		1008.2.s.k.289.1		2
63.13	odd	6		1134.2.h.l.541.1		2
63.20	even	6		1134.2.e.l.919.1		2
63.31	odd	6		1134.2.e.e.865.1		2
63.34	odd	6		1134.2.e.e.919.1		2
63.38	even	6		1134.2.h.e.109.1		2
63.41	even	6		1134.2.h.e.541.1		2
63.52	odd	6		1134.2.h.l.109.1		2
63.59	even	6		1134.2.e.l.865.1		2
84.11	even	6		2352.2.q.u.1537.1		2
84.23	even	6		2352.2.a.f.1.1		1
84.47	odd	6		2352.2.a.t.1.1		1
84.59	odd	6		336.2.q.b.193.1		2
84.83	odd	2		336.2.q.b.289.1		2
105.17	odd	12		1050.2.o.a.949.2		4
105.38	odd	12		1050.2.o.a.949.1		4
105.44	odd	6		7350.2.a.q.1.1		1
105.59	even	6		1050.2.i.l.151.1		2
105.62	odd	4		1050.2.o.a.499.1		4
105.83	odd	4		1050.2.o.a.499.2		4
105.89	even	6		7350.2.a.bl.1.1		1
105.104	even	2		1050.2.i.l.751.1		2
168.5	even	6		9408.2.a.ce.1.1		1
168.59	odd	6		1344.2.q.s.193.1		2
168.83	odd	2		1344.2.q.s.961.1		2
168.101	even	6		1344.2.q.g.193.1		2
168.107	even	6		9408.2.a.cr.1.1		1
168.125	even	2		1344.2.q.g.961.1		2
168.131	odd	6		9408.2.a.q.1.1		1
168.149	odd	6		9408.2.a.z.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.2.e.a.25.1	✓	2	21.17	even	6
42.2.e.a.37.1	yes	2	21.20	even	2
126.2.g.c.37.1		2	7.6	odd	2
126.2.g.c.109.1		2	7.3	odd	6
294.2.a.e.1.1		1	21.5	even	6
294.2.a.f.1.1		1	21.2	odd	6
294.2.e.b.67.1		2	21.11	odd	6
294.2.e.b.79.1		2	3.2	odd	2
336.2.q.b.193.1		2	84.59	odd	6
336.2.q.b.289.1		2	84.83	odd	2
882.2.a.c.1.1		1	7.5	odd	6
882.2.a.d.1.1		1	7.2	even	3
882.2.g.i.361.1		2	7.4	even	3	inner
882.2.g.i.667.1		2	1.1	even	1	trivial
1008.2.s.k.289.1		2	28.27	even	2
1008.2.s.k.865.1		2	28.3	even	6
1050.2.i.l.151.1		2	105.59	even	6
1050.2.i.l.751.1		2	105.104	even	2
1050.2.o.a.499.1		4	105.62	odd	4
1050.2.o.a.499.2		4	105.83	odd	4
1050.2.o.a.949.1		4	105.38	odd	12
1050.2.o.a.949.2		4	105.17	odd	12
1134.2.e.e.865.1		2	63.31	odd	6
1134.2.e.e.919.1		2	63.34	odd	6
1134.2.e.l.865.1		2	63.59	even	6
1134.2.e.l.919.1		2	63.20	even	6
1134.2.h.e.109.1		2	63.38	even	6
1134.2.h.e.541.1		2	63.41	even	6
1134.2.h.l.109.1		2	63.52	odd	6
1134.2.h.l.541.1		2	63.13	odd	6
1344.2.q.g.193.1		2	168.101	even	6
1344.2.q.g.961.1		2	168.125	even	2
1344.2.q.s.193.1		2	168.59	odd	6
1344.2.q.s.961.1		2	168.83	odd	2
2352.2.a.f.1.1		1	84.23	even	6
2352.2.a.t.1.1		1	84.47	odd	6
2352.2.q.u.961.1		2	12.11	even	2
2352.2.q.u.1537.1		2	84.11	even	6
7056.2.a.w.1.1		1	28.19	even	6
7056.2.a.bl.1.1		1	28.23	odd	6
7350.2.a.q.1.1		1	105.44	odd	6
7350.2.a.bl.1.1		1	105.89	even	6
9408.2.a.q.1.1		1	168.131	odd	6
9408.2.a.z.1.1		1	168.149	odd	6
9408.2.a.ce.1.1		1	168.5	even	6
9408.2.a.cr.1.1		1	168.107	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	882.2.g.i.667.1

Level	$882$
Weight	$2$
Character	882.667
Analytic conductor	$7.043$
Analytic rank	$0$
Dimension	$2$
Inner twists	$2$