LMFDB - Embedded newform 624.2.q.g.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,2,Mod(289,624)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(624, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("624.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	624.q (of order $3$, degree $2$, not 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:	$4.98266508613$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	624.289
Dual form			624.2.q.g.529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{3} +3.00000 q^{5} +(1.00000 - 1.73205i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(3.00000 + 5.19615i) q^{11} +(-3.50000 + 0.866025i) q^{13} +(1.50000 + 2.59808i) q^{15} +(1.50000 - 2.59808i) q^{17} +(1.00000 - 1.73205i) q^{19} +2.00000 q^{21} +(-3.00000 - 5.19615i) q^{23} +4.00000 q^{25} -1.00000 q^{27} +(-1.50000 - 2.59808i) q^{29} +4.00000 q^{31} +(-3.00000 + 5.19615i) q^{33} +(3.00000 - 5.19615i) q^{35} +(3.50000 + 6.06218i) q^{37} +(-2.50000 - 2.59808i) q^{39} +(1.50000 + 2.59808i) q^{41} +(-5.00000 + 8.66025i) q^{43} +(-1.50000 + 2.59808i) q^{45} -6.00000 q^{47} +(1.50000 + 2.59808i) q^{49} +3.00000 q^{51} +3.00000 q^{53} +(9.00000 + 15.5885i) q^{55} +2.00000 q^{57} +(3.50000 - 6.06218i) q^{61} +(1.00000 + 1.73205i) q^{63} +(-10.5000 + 2.59808i) q^{65} +(-5.00000 - 8.66025i) q^{67} +(3.00000 - 5.19615i) q^{69} +(3.00000 - 5.19615i) q^{71} -13.0000 q^{73} +(2.00000 + 3.46410i) q^{75} +12.0000 q^{77} +4.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +6.00000 q^{83} +(4.50000 - 7.79423i) q^{85} +(1.50000 - 2.59808i) q^{87} +(-9.00000 - 15.5885i) q^{89} +(-2.00000 + 6.92820i) q^{91} +(2.00000 + 3.46410i) q^{93} +(3.00000 - 5.19615i) q^{95} +(-7.00000 + 12.1244i) q^{97} -6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{3} + 6 q^{5} + 2 q^{7} - q^{9} + 6 q^{11} - 7 q^{13} + 3 q^{15} + 3 q^{17} + 2 q^{19} + 4 q^{21} - 6 q^{23} + 8 q^{25} - 2 q^{27} - 3 q^{29} + 8 q^{31} - 6 q^{33} + 6 q^{35} + 7 q^{37} - 5 q^{39}+ \cdots - 12 q^{99}+O(q^{100}) $ 2 * q + q^3 + 6 * q^5 + 2 * q^7 - q^9 + 6 * q^11 - 7 * q^13 + 3 * q^15 + 3 * q^17 + 2 * q^19 + 4 * q^21 - 6 * q^23 + 8 * q^25 - 2 * q^27 - 3 * q^29 + 8 * q^31 - 6 * q^33 + 6 * q^35 + 7 * q^37 - 5 * q^39 + 3 * q^41 - 10 * q^43 - 3 * q^45 - 12 * q^47 + 3 * q^49 + 6 * q^51 + 6 * q^53 + 18 * q^55 + 4 * q^57 + 7 * q^61 + 2 * q^63 - 21 * q^65 - 10 * q^67 + 6 * q^69 + 6 * q^71 - 26 * q^73 + 4 * q^75 + 24 * q^77 + 8 * q^79 - q^81 + 12 * q^83 + 9 * q^85 + 3 * q^87 - 18 * q^89 - 4 * q^91 + 4 * q^93 + 6 * q^95 - 14 * q^97 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$		0			0
$2$		0			0
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$		0			0
$5$	3.00000			1.34164			0.670820	−	0.741620i	$-0.265942\pi$
$5$	3.00000			1.34164			0.670820	+	0.741620i	$0.265942\pi$
$6$		0			0
$7$	1.00000	−	1.73205i	0.377964	−	0.654654i	−0.612801	−	0.790237i	$-0.709957\pi$
$7$	1.00000	−	1.73205i	0.377964	−	0.654654i	0.990766	+	0.135583i	$0.0432908\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	3.00000	+	5.19615i	0.904534	+	1.56670i	0.821541	+	0.570149i	$0.193114\pi$
$11$	3.00000	+	5.19615i	0.904534	+	1.56670i	0.0829925	+	0.996550i	$0.473552\pi$
$12$		0			0
$13$	−3.50000	+	0.866025i	−0.970725	+	0.240192i
$13$	−3.50000	+	0.866025i	−0.970725	+	0.240192i
$14$		0			0
$15$	1.50000	+	2.59808i	0.387298	+	0.670820i
$16$		0			0
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$		0			0
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	−0.728219	−	0.685344i	$-0.759652\pi$
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	0.957635	+	0.287984i	$0.0929851\pi$
$20$		0			0
$21$	2.00000			0.436436
$22$		0			0
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	−0.988436	−	0.151642i	$-0.951544\pi$
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	0.362892	−	0.931831i	$-0.381789\pi$
$24$		0			0
$25$	4.00000			0.800000
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	0.692480	−	0.721437i	$-0.256518\pi$
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	−0.971023	+	0.238987i	$0.923185\pi$
$30$		0			0
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$		0			0
$33$	−3.00000	+	5.19615i	−0.522233	+	0.904534i
$34$		0			0
$35$	3.00000	−	5.19615i	0.507093	−	0.878310i
$36$		0			0
$37$	3.50000	+	6.06218i	0.575396	+	0.996616i	0.995998	+	0.0893706i	$0.0284856\pi$
$37$	3.50000	+	6.06218i	0.575396	+	0.996616i	−0.420602	+	0.907245i	$0.638181\pi$
$38$		0			0
$39$	−2.50000	−	2.59808i	−0.400320	−	0.416025i
$40$		0			0
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	0.959058	−	0.283211i	$-0.0913998\pi$
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	−0.724797	+	0.688963i	$0.758066\pi$
$42$		0			0
$43$	−5.00000	+	8.66025i	−0.762493	+	1.32068i	0.179069	+	0.983836i	$0.442691\pi$
$43$	−5.00000	+	8.66025i	−0.762493	+	1.32068i	−0.941562	+	0.336840i	$0.890642\pi$
$44$		0			0
$45$	−1.50000	+	2.59808i	−0.223607	+	0.387298i
$46$		0			0
$47$	−6.00000			−0.875190			−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000			−0.875190			−0.437595	+	0.899172i	$0.644170\pi$
$48$		0			0
$49$	1.50000	+	2.59808i	0.214286	+	0.371154i
$50$		0			0
$51$	3.00000			0.420084
$52$		0			0
$53$	3.00000			0.412082			0.206041	−	0.978543i	$-0.433942\pi$
$53$	3.00000			0.412082			0.206041	+	0.978543i	$0.433942\pi$
$54$		0			0
$55$	9.00000	+	15.5885i	1.21356	+	2.10195i
$56$		0			0
$57$	2.00000			0.264906
$58$		0			0
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$		0			0
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	−0.550135	−	0.835076i	$-0.685424\pi$
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	0.998264	+	0.0588933i	$0.0187572\pi$
$62$		0			0
$63$	1.00000	+	1.73205i	0.125988	+	0.218218i
$64$		0			0
$65$	−10.5000	+	2.59808i	−1.30236	+	0.322252i
$66$		0			0
$67$	−5.00000	−	8.66025i	−0.610847	−	1.05802i	−0.991098	−	0.133135i	$-0.957496\pi$
$67$	−5.00000	−	8.66025i	−0.610847	−	1.05802i	0.380251	−	0.924883i	$-0.375838\pi$
$68$		0			0
$69$	3.00000	−	5.19615i	0.361158	−	0.625543i
$70$		0			0
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	−0.631260	−	0.775571i	$-0.717462\pi$
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	0.987294	+	0.158901i	$0.0507952\pi$
$72$		0			0
$73$	−13.0000			−1.52153			−0.760767	−	0.649025i	$-0.775177\pi$
$73$	−13.0000			−1.52153			−0.760767	+	0.649025i	$0.775177\pi$
$74$		0			0
$75$	2.00000	+	3.46410i	0.230940	+	0.400000i
$76$		0			0
$77$	12.0000			1.36753
$78$		0			0
$79$	4.00000			0.450035			0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000			0.450035			0.225018	+	0.974355i	$0.427756\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$		0			0
$85$	4.50000	−	7.79423i	0.488094	−	0.845403i
$86$		0			0
$87$	1.50000	−	2.59808i	0.160817	−	0.278543i
$88$		0			0
$89$	−9.00000	−	15.5885i	−0.953998	−	1.65237i	−0.736644	−	0.676280i	$-0.763591\pi$
$89$	−9.00000	−	15.5885i	−0.953998	−	1.65237i	−0.217354	−	0.976093i	$-0.569742\pi$
$90$		0			0
$91$	−2.00000	+	6.92820i	−0.209657	+	0.726273i
$92$		0			0
$93$	2.00000	+	3.46410i	0.207390	+	0.359211i
$94$		0			0
$95$	3.00000	−	5.19615i	0.307794	−	0.533114i
$96$		0			0
$97$	−7.00000	+	12.1244i	−0.710742	+	1.23104i	0.253837	+	0.967247i	$0.418307\pi$
$97$	−7.00000	+	12.1244i	−0.710742	+	1.23104i	−0.964579	+	0.263795i	$0.915026\pi$
$98$		0			0
$99$	−6.00000			−0.603023
$100$		0			0
$101$	−7.50000	−	12.9904i	−0.746278	−	1.29259i	−0.949595	−	0.313478i	$-0.898506\pi$
$101$	−7.50000	−	12.9904i	−0.746278	−	1.29259i	0.203317	−	0.979113i	$-0.434828\pi$
$102$		0			0
$103$	−14.0000			−1.37946			−0.689730	−	0.724066i	$-0.742271\pi$
$103$	−14.0000			−1.37946			−0.689730	+	0.724066i	$0.742271\pi$
$104$		0			0
$105$	6.00000			0.585540
$106$		0			0
$107$	−3.00000	−	5.19615i	−0.290021	−	0.502331i	0.683793	−	0.729676i	$-0.260329\pi$
$107$	−3.00000	−	5.19615i	−0.290021	−	0.502331i	−0.973814	+	0.227345i	$0.926996\pi$
$108$		0			0
$109$	14.0000			1.34096			0.670478	−	0.741929i	$-0.266089\pi$
$109$	14.0000			1.34096			0.670478	+	0.741929i	$0.266089\pi$
$110$		0			0
$111$	−3.50000	+	6.06218i	−0.332205	+	0.575396i
$112$		0			0
$113$	1.50000	−	2.59808i	0.141108	−	0.244406i	−0.786806	−	0.617200i	$-0.788267\pi$
$113$	1.50000	−	2.59808i	0.141108	−	0.244406i	0.927914	+	0.372794i	$0.121600\pi$
$114$		0			0
$115$	−9.00000	−	15.5885i	−0.839254	−	1.45363i
$116$		0			0
$117$	1.00000	−	3.46410i	0.0924500	−	0.320256i
$118$		0			0
$119$	−3.00000	−	5.19615i	−0.275010	−	0.476331i
$120$		0			0
$121$	−12.5000	+	21.6506i	−1.13636	+	1.96824i
$122$		0			0
$123$	−1.50000	+	2.59808i	−0.135250	+	0.234261i
$124$		0			0
$125$	−3.00000			−0.268328
$126$		0			0
$127$	−2.00000	−	3.46410i	−0.177471	−	0.307389i	0.763542	−	0.645758i	$-0.223458\pi$
$127$	−2.00000	−	3.46410i	−0.177471	−	0.307389i	−0.941014	+	0.338368i	$0.890125\pi$
$128$		0			0
$129$	−10.0000			−0.880451
$130$		0			0
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$		0			0
$133$	−2.00000	−	3.46410i	−0.173422	−	0.300376i
$134$		0			0
$135$	−3.00000			−0.258199
$136$		0			0
$137$	−4.50000	+	7.79423i	−0.384461	+	0.665906i	−0.991694	−	0.128618i	$-0.958946\pi$
$137$	−4.50000	+	7.79423i	−0.384461	+	0.665906i	0.607233	+	0.794524i	$0.292279\pi$
$138$		0			0
$139$	−2.00000	+	3.46410i	−0.169638	+	0.293821i	−0.938293	−	0.345843i	$-0.887593\pi$
$139$	−2.00000	+	3.46410i	−0.169638	+	0.293821i	0.768655	+	0.639664i	$0.220926\pi$
$140$		0			0
$141$	−3.00000	−	5.19615i	−0.252646	−	0.437595i
$142$		0			0
$143$	−15.0000	−	15.5885i	−1.25436	−	1.30357i
$144$		0			0
$145$	−4.50000	−	7.79423i	−0.373705	−	0.647275i
$146$		0			0
$147$	−1.50000	+	2.59808i	−0.123718	+	0.214286i
$148$		0			0
$149$	4.50000	−	7.79423i	0.368654	−	0.638528i	−0.620701	−	0.784047i	$-0.713152\pi$
$149$	4.50000	−	7.79423i	0.368654	−	0.638528i	0.989355	+	0.145519i	$0.0464853\pi$
$150$		0			0
$151$	10.0000			0.813788			0.406894	−	0.913475i	$-0.366612\pi$
$151$	10.0000			0.813788			0.406894	+	0.913475i	$0.366612\pi$
$152$		0			0
$153$	1.50000	+	2.59808i	0.121268	+	0.210042i
$154$		0			0
$155$	12.0000			0.963863
$156$		0			0
$157$	5.00000			0.399043			0.199522	−	0.979893i	$-0.436061\pi$
$157$	5.00000			0.399043			0.199522	+	0.979893i	$0.436061\pi$
$158$		0			0
$159$	1.50000	+	2.59808i	0.118958	+	0.206041i
$160$		0			0
$161$	−12.0000			−0.945732
$162$		0			0
$163$	−2.00000	+	3.46410i	−0.156652	+	0.271329i	−0.933659	−	0.358162i	$-0.883403\pi$
$163$	−2.00000	+	3.46410i	−0.156652	+	0.271329i	0.777007	+	0.629492i	$0.216737\pi$
$164$		0			0
$165$	−9.00000	+	15.5885i	−0.700649	+	1.21356i
$166$		0			0
$167$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$167$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$168$		0			0
$169$	11.5000	−	6.06218i	0.884615	−	0.466321i
$170$		0			0
$171$	1.00000	+	1.73205i	0.0764719	+	0.132453i
$172$		0			0
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	−0.729155	−	0.684349i	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$		0			0
$175$	4.00000	−	6.92820i	0.302372	−	0.523723i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	3.00000	+	5.19615i	0.224231	+	0.388379i	0.956088	−	0.293079i	$-0.0946798\pi$
$179$	3.00000	+	5.19615i	0.224231	+	0.388379i	−0.731858	+	0.681457i	$0.761346\pi$
$180$		0			0
$181$	−7.00000			−0.520306			−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000			−0.520306			−0.260153	+	0.965567i	$0.583773\pi$
$182$		0			0
$183$	7.00000			0.517455
$184$		0			0
$185$	10.5000	+	18.1865i	0.771975	+	1.33710i
$186$		0			0
$187$	18.0000			1.31629
$188$		0			0
$189$	−1.00000	+	1.73205i	−0.0727393	+	0.125988i
$190$		0			0
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	−0.997225	−	0.0744412i	$-0.976283\pi$
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	0.563081	+	0.826402i	$0.309616\pi$
$192$		0			0
$193$	−11.5000	−	19.9186i	−0.827788	−	1.43377i	−0.899770	−	0.436365i	$-0.856266\pi$
$193$	−11.5000	−	19.9186i	−0.827788	−	1.43377i	0.0719816	−	0.997406i	$-0.477068\pi$
$194$		0			0
$195$	−7.50000	−	7.79423i	−0.537086	−	0.558156i
$196$		0			0
$197$	−3.00000	−	5.19615i	−0.213741	−	0.370211i	0.739141	−	0.673550i	$-0.235232\pi$
$197$	−3.00000	−	5.19615i	−0.213741	−	0.370211i	−0.952882	+	0.303340i	$0.901898\pi$
$198$		0			0
$199$	−5.00000	+	8.66025i	−0.354441	+	0.613909i	−0.987022	−	0.160585i	$-0.948662\pi$
$199$	−5.00000	+	8.66025i	−0.354441	+	0.613909i	0.632581	+	0.774494i	$0.281995\pi$
$200$		0			0
$201$	5.00000	−	8.66025i	0.352673	−	0.610847i
$202$		0			0
$203$	−6.00000			−0.421117
$204$		0			0
$205$	4.50000	+	7.79423i	0.314294	+	0.544373i
$206$		0			0
$207$	6.00000			0.417029
$208$		0			0
$209$	12.0000			0.830057
$210$		0			0
$211$	−8.00000	−	13.8564i	−0.550743	−	0.953914i	−0.998221	−	0.0596196i	$-0.981011\pi$
$211$	−8.00000	−	13.8564i	−0.550743	−	0.953914i	0.447478	−	0.894295i	$-0.352322\pi$
$212$		0			0
$213$	6.00000			0.411113
$214$		0			0
$215$	−15.0000	+	25.9808i	−1.02299	+	1.77187i
$216$		0			0
$217$	4.00000	−	6.92820i	0.271538	−	0.470317i
$218$		0			0
$219$	−6.50000	−	11.2583i	−0.439229	−	0.760767i
$220$		0			0
$221$	−3.00000	+	10.3923i	−0.201802	+	0.699062i
$222$		0			0
$223$	4.00000	+	6.92820i	0.267860	+	0.463947i	0.968309	−	0.249756i	$-0.0803503\pi$
$223$	4.00000	+	6.92820i	0.267860	+	0.463947i	−0.700449	+	0.713702i	$0.747017\pi$
$224$		0			0
$225$	−2.00000	+	3.46410i	−0.133333	+	0.230940i
$226$		0			0
$227$	9.00000	−	15.5885i	0.597351	−	1.03464i	−0.395860	−	0.918311i	$-0.629553\pi$
$227$	9.00000	−	15.5885i	0.597351	−	1.03464i	0.993210	−	0.116331i	$-0.0371134\pi$
$228$		0			0
$229$	−22.0000			−1.45380			−0.726900	−	0.686743i	$-0.759040\pi$
$229$	−22.0000			−1.45380			−0.726900	+	0.686743i	$0.759040\pi$
$230$		0			0
$231$	6.00000	+	10.3923i	0.394771	+	0.683763i
$232$		0			0
$233$	−6.00000			−0.393073			−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000			−0.393073			−0.196537	+	0.980497i	$0.562969\pi$
$234$		0			0
$235$	−18.0000			−1.17419
$236$		0			0
$237$	2.00000	+	3.46410i	0.129914	+	0.225018i
$238$		0			0
$239$	−6.00000			−0.388108			−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000			−0.388108			−0.194054	+	0.980991i	$0.562164\pi$
$240$		0			0
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	−0.849472	−	0.527633i	$-0.823079\pi$
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	0.881680	+	0.471848i	$0.156413\pi$
$242$		0			0
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$		0			0
$245$	4.50000	+	7.79423i	0.287494	+	0.497955i
$246$		0			0
$247$	−2.00000	+	6.92820i	−0.127257	+	0.440831i
$248$		0			0
$249$	3.00000	+	5.19615i	0.190117	+	0.329293i
$250$		0			0
$251$	−6.00000	+	10.3923i	−0.378717	+	0.655956i	−0.990876	−	0.134778i	$-0.956968\pi$
$251$	−6.00000	+	10.3923i	−0.378717	+	0.655956i	0.612159	+	0.790735i	$0.290301\pi$
$252$		0			0
$253$	18.0000	−	31.1769i	1.13165	−	1.96008i
$254$		0			0
$255$	9.00000			0.563602
$256$		0			0
$257$	1.50000	+	2.59808i	0.0935674	+	0.162064i	0.909010	−	0.416775i	$-0.136840\pi$
$257$	1.50000	+	2.59808i	0.0935674	+	0.162064i	−0.815442	+	0.578838i	$0.803506\pi$
$258$		0			0
$259$	14.0000			0.869918
$260$		0			0
$261$	3.00000			0.185695
$262$		0			0
$263$	−3.00000	−	5.19615i	−0.184988	−	0.320408i	0.758585	−	0.651575i	$-0.225891\pi$
$263$	−3.00000	−	5.19615i	−0.184988	−	0.320408i	−0.943572	+	0.331166i	$0.892558\pi$
$264$		0			0
$265$	9.00000			0.552866
$266$		0			0
$267$	9.00000	−	15.5885i	0.550791	−	0.953998i
$268$		0			0
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	0.449622	+	0.893219i	$0.351559\pi$
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	−0.998361	+	0.0572259i	$0.981774\pi$
$270$		0			0
$271$	−8.00000	−	13.8564i	−0.485965	−	0.841717i	0.513905	−	0.857847i	$-0.328199\pi$
$271$	−8.00000	−	13.8564i	−0.485965	−	0.841717i	−0.999870	+	0.0161307i	$0.994865\pi$
$272$		0			0
$273$	−7.00000	+	1.73205i	−0.423659	+	0.104828i
$274$		0			0
$275$	12.0000	+	20.7846i	0.723627	+	1.25336i
$276$		0			0
$277$	−8.50000	+	14.7224i	−0.510716	+	0.884585i	0.489207	+	0.872167i	$0.337286\pi$
$277$	−8.50000	+	14.7224i	−0.510716	+	0.884585i	−0.999923	+	0.0124177i	$0.996047\pi$
$278$		0			0
$279$	−2.00000	+	3.46410i	−0.119737	+	0.207390i
$280$		0			0
$281$	9.00000			0.536895			0.268447	−	0.963294i	$-0.413489\pi$
$281$	9.00000			0.536895			0.268447	+	0.963294i	$0.413489\pi$
$282$		0			0
$283$	7.00000	+	12.1244i	0.416107	+	0.720718i	0.995544	−	0.0942988i	$-0.0300609\pi$
$283$	7.00000	+	12.1244i	0.416107	+	0.720718i	−0.579437	+	0.815017i	$0.696728\pi$
$284$		0			0
$285$	6.00000			0.355409
$286$		0			0
$287$	6.00000			0.354169
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$	−14.0000			−0.820695
$292$		0			0
$293$	10.5000	−	18.1865i	0.613417	−	1.06247i	−0.377244	−	0.926114i	$-0.623128\pi$
$293$	10.5000	−	18.1865i	0.613417	−	1.06247i	0.990660	−	0.136355i	$-0.0435386\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−3.00000	−	5.19615i	−0.174078	−	0.301511i
$298$		0			0
$299$	15.0000	+	15.5885i	0.867472	+	0.901504i
$300$		0			0
$301$	10.0000	+	17.3205i	0.576390	+	0.998337i
$302$		0			0
$303$	7.50000	−	12.9904i	0.430864	−	0.746278i
$304$		0			0
$305$	10.5000	−	18.1865i	0.601228	−	1.04136i
$306$		0			0
$307$	10.0000			0.570730			0.285365	−	0.958419i	$-0.407885\pi$
$307$	10.0000			0.570730			0.285365	+	0.958419i	$0.407885\pi$
$308$		0			0
$309$	−7.00000	−	12.1244i	−0.398216	−	0.689730i
$310$		0			0
$311$	30.0000			1.70114			0.850572	−	0.525859i	$-0.176256\pi$
$311$	30.0000			1.70114			0.850572	+	0.525859i	$0.176256\pi$
$312$		0			0
$313$	−10.0000			−0.565233			−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000			−0.565233			−0.282617	+	0.959233i	$0.591202\pi$
$314$		0			0
$315$	3.00000	+	5.19615i	0.169031	+	0.292770i
$316$		0			0
$317$	3.00000			0.168497			0.0842484	−	0.996445i	$-0.473151\pi$
$317$	3.00000			0.168497			0.0842484	+	0.996445i	$0.473151\pi$
$318$		0			0
$319$	9.00000	−	15.5885i	0.503903	−	0.872786i
$320$		0			0
$321$	3.00000	−	5.19615i	0.167444	−	0.290021i
$322$		0			0
$323$	−3.00000	−	5.19615i	−0.166924	−	0.289122i
$324$		0			0
$325$	−14.0000	+	3.46410i	−0.776580	+	0.192154i
$326$		0			0
$327$	7.00000	+	12.1244i	0.387101	+	0.670478i
$328$		0			0
$329$	−6.00000	+	10.3923i	−0.330791	+	0.572946i
$330$		0			0
$331$	−2.00000	+	3.46410i	−0.109930	+	0.190404i	−0.915742	−	0.401768i	$-0.868396\pi$
$331$	−2.00000	+	3.46410i	−0.109930	+	0.190404i	0.805812	+	0.592172i	$0.201729\pi$
$332$		0			0
$333$	−7.00000			−0.383598
$334$		0			0
$335$	−15.0000	−	25.9808i	−0.819538	−	1.41948i
$336$		0			0
$337$	23.0000			1.25289			0.626445	−	0.779466i	$-0.284509\pi$
$337$	23.0000			1.25289			0.626445	+	0.779466i	$0.284509\pi$
$338$		0			0
$339$	3.00000			0.162938
$340$		0			0
$341$	12.0000	+	20.7846i	0.649836	+	1.12555i
$342$		0			0
$343$	20.0000			1.07990
$344$		0			0
$345$	9.00000	−	15.5885i	0.484544	−	0.839254i
$346$		0			0
$347$	−15.0000	+	25.9808i	−0.805242	+	1.39472i	0.110885	+	0.993833i	$0.464631\pi$
$347$	−15.0000	+	25.9808i	−0.805242	+	1.39472i	−0.916127	+	0.400887i	$0.868702\pi$
$348$		0			0
$349$	5.00000	+	8.66025i	0.267644	+	0.463573i	0.968253	−	0.249973i	$-0.0804216\pi$
$349$	5.00000	+	8.66025i	0.267644	+	0.463573i	−0.700609	+	0.713545i	$0.747088\pi$
$350$		0			0
$351$	3.50000	−	0.866025i	0.186816	−	0.0462250i
$352$		0			0
$353$	7.50000	+	12.9904i	0.399185	+	0.691408i	0.993626	−	0.112731i	$-0.0359599\pi$
$353$	7.50000	+	12.9904i	0.399185	+	0.691408i	−0.594441	+	0.804139i	$0.702627\pi$
$354$		0			0
$355$	9.00000	−	15.5885i	0.477670	−	0.827349i
$356$		0			0
$357$	3.00000	−	5.19615i	0.158777	−	0.275010i
$358$		0			0
$359$	−6.00000			−0.316668			−0.158334	−	0.987386i	$-0.550612\pi$
$359$	−6.00000			−0.316668			−0.158334	+	0.987386i	$0.550612\pi$
$360$		0			0
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$		0			0
$363$	−25.0000			−1.31216
$364$		0			0
$365$	−39.0000			−2.04135
$366$		0			0
$367$	1.00000	+	1.73205i	0.0521996	+	0.0904123i	0.890945	−	0.454112i	$-0.150043\pi$
$367$	1.00000	+	1.73205i	0.0521996	+	0.0904123i	−0.838745	+	0.544524i	$0.816710\pi$
$368$		0			0
$369$	−3.00000			−0.156174
$370$		0			0
$371$	3.00000	−	5.19615i	0.155752	−	0.269771i
$372$		0			0
$373$	−14.5000	+	25.1147i	−0.750782	+	1.30039i	0.196663	+	0.980471i	$0.436990\pi$
$373$	−14.5000	+	25.1147i	−0.750782	+	1.30039i	−0.947444	+	0.319921i	$0.896344\pi$
$374$		0			0
$375$	−1.50000	−	2.59808i	−0.0774597	−	0.134164i
$376$		0			0
$377$	7.50000	+	7.79423i	0.386270	+	0.401423i
$378$		0			0
$379$	10.0000	+	17.3205i	0.513665	+	0.889695i	0.999874	+	0.0158521i	$0.00504609\pi$
$379$	10.0000	+	17.3205i	0.513665	+	0.889695i	−0.486209	+	0.873843i	$0.661621\pi$
$380$		0			0
$381$	2.00000	−	3.46410i	0.102463	−	0.177471i
$382$		0			0
$383$	12.0000	−	20.7846i	0.613171	−	1.06204i	−0.377531	−	0.925997i	$-0.623227\pi$
$383$	12.0000	−	20.7846i	0.613171	−	1.06204i	0.990702	−	0.136047i	$-0.0434398\pi$
$384$		0			0
$385$	36.0000			1.83473
$386$		0			0
$387$	−5.00000	−	8.66025i	−0.254164	−	0.440225i
$388$		0			0
$389$	39.0000			1.97738			0.988689	−	0.149979i	$-0.0479205\pi$
$389$	39.0000			1.97738			0.988689	+	0.149979i	$0.0479205\pi$
$390$		0			0
$391$	−18.0000			−0.910299
$392$		0			0
$393$		0			0
$394$		0			0
$395$	12.0000			0.603786
$396$		0			0
$397$	−7.00000	+	12.1244i	−0.351320	+	0.608504i	−0.986481	−	0.163876i	$-0.947600\pi$
$397$	−7.00000	+	12.1244i	−0.351320	+	0.608504i	0.635161	+	0.772380i	$0.280934\pi$
$398$		0			0
$399$	2.00000	−	3.46410i	0.100125	−	0.173422i
$400$		0			0
$401$	1.50000	+	2.59808i	0.0749064	+	0.129742i	0.901046	−	0.433724i	$-0.142801\pi$
$401$	1.50000	+	2.59808i	0.0749064	+	0.129742i	−0.826139	+	0.563466i	$0.809468\pi$
$402$		0			0
$403$	−14.0000	+	3.46410i	−0.697390	+	0.172559i
$404$		0			0
$405$	−1.50000	−	2.59808i	−0.0745356	−	0.129099i
$406$		0			0
$407$	−21.0000	+	36.3731i	−1.04093	+	1.80295i
$408$		0			0
$409$	0.500000	−	0.866025i	0.0247234	−	0.0428222i	−0.853399	−	0.521258i	$-0.825463\pi$
$409$	0.500000	−	0.866025i	0.0247234	−	0.0428222i	0.878122	+	0.478436i	$0.158796\pi$
$410$		0			0
$411$	−9.00000			−0.443937
$412$		0			0
$413$		0			0
$414$		0			0
$415$	18.0000			0.883585
$416$		0			0
$417$	−4.00000			−0.195881
$418$		0			0
$419$	12.0000	+	20.7846i	0.586238	+	1.01539i	0.994720	+	0.102628i	$0.0327251\pi$
$419$	12.0000	+	20.7846i	0.586238	+	1.01539i	−0.408481	+	0.912767i	$0.633942\pi$
$420$		0			0
$421$	29.0000			1.41337			0.706687	−	0.707527i	$-0.250189\pi$
$421$	29.0000			1.41337			0.706687	+	0.707527i	$0.250189\pi$
$422$		0			0
$423$	3.00000	−	5.19615i	0.145865	−	0.252646i
$424$		0			0
$425$	6.00000	−	10.3923i	0.291043	−	0.504101i
$426$		0			0
$427$	−7.00000	−	12.1244i	−0.338754	−	0.586739i
$428$		0			0
$429$	6.00000	−	20.7846i	0.289683	−	1.00349i
$430$		0			0
$431$	−3.00000	−	5.19615i	−0.144505	−	0.250290i	0.784683	−	0.619897i	$-0.212826\pi$
$431$	−3.00000	−	5.19615i	−0.144505	−	0.250290i	−0.929188	+	0.369607i	$0.879492\pi$
$432$		0			0
$433$	6.50000	−	11.2583i	0.312370	−	0.541041i	−0.666505	−	0.745501i	$-0.732210\pi$
$433$	6.50000	−	11.2583i	0.312370	−	0.541041i	0.978875	+	0.204460i	$0.0655438\pi$
$434$		0			0
$435$	4.50000	−	7.79423i	0.215758	−	0.373705i
$436$		0			0
$437$	−12.0000			−0.574038
$438$		0			0
$439$	7.00000	+	12.1244i	0.334092	+	0.578664i	0.983310	−	0.181938i	$-0.0582371\pi$
$439$	7.00000	+	12.1244i	0.334092	+	0.578664i	−0.649218	+	0.760602i	$0.724904\pi$
$440$		0			0
$441$	−3.00000			−0.142857
$442$		0			0
$443$	36.0000			1.71041			0.855206	−	0.518289i	$-0.173431\pi$
$443$	36.0000			1.71041			0.855206	+	0.518289i	$0.173431\pi$
$444$		0			0
$445$	−27.0000	−	46.7654i	−1.27992	−	2.21689i
$446$		0			0
$447$	9.00000			0.425685
$448$		0			0
$449$	−9.00000	+	15.5885i	−0.424736	+	0.735665i	−0.996396	−	0.0848262i	$-0.972967\pi$
$449$	−9.00000	+	15.5885i	−0.424736	+	0.735665i	0.571660	+	0.820491i	$0.306300\pi$
$450$		0			0
$451$	−9.00000	+	15.5885i	−0.423793	+	0.734032i
$452$		0			0
$453$	5.00000	+	8.66025i	0.234920	+	0.406894i
$454$		0			0
$455$	−6.00000	+	20.7846i	−0.281284	+	0.974398i
$456$		0			0
$457$	−5.50000	−	9.52628i	−0.257279	−	0.445621i	0.708233	−	0.705979i	$-0.249493\pi$
$457$	−5.50000	−	9.52628i	−0.257279	−	0.445621i	−0.965512	+	0.260358i	$0.916159\pi$
$458$		0			0
$459$	−1.50000	+	2.59808i	−0.0700140	+	0.121268i
$460$		0			0
$461$	−7.50000	+	12.9904i	−0.349310	+	0.605022i	−0.986127	−	0.165992i	$-0.946917\pi$
$461$	−7.50000	+	12.9904i	−0.349310	+	0.605022i	0.636817	+	0.771015i	$0.280251\pi$
$462$		0			0
$463$	−38.0000			−1.76601			−0.883005	−	0.469364i	$-0.844483\pi$
$463$	−38.0000			−1.76601			−0.883005	+	0.469364i	$0.844483\pi$
$464$		0			0
$465$	6.00000	+	10.3923i	0.278243	+	0.481932i
$466$		0			0
$467$	18.0000			0.832941			0.416470	−	0.909149i	$-0.363267\pi$
$467$	18.0000			0.832941			0.416470	+	0.909149i	$0.363267\pi$
$468$		0			0
$469$	−20.0000			−0.923514
$470$		0			0
$471$	2.50000	+	4.33013i	0.115194	+	0.199522i
$472$		0			0
$473$	−60.0000			−2.75880
$474$		0			0
$475$	4.00000	−	6.92820i	0.183533	−	0.317888i
$476$		0			0
$477$	−1.50000	+	2.59808i	−0.0686803	+	0.118958i
$478$		0			0
$479$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$479$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$480$		0			0
$481$	−17.5000	−	18.1865i	−0.797931	−	0.829235i
$482$		0			0
$483$	−6.00000	−	10.3923i	−0.273009	−	0.472866i
$484$		0			0
$485$	−21.0000	+	36.3731i	−0.953561	+	1.65162i
$486$		0			0
$487$	1.00000	−	1.73205i	0.0453143	−	0.0784867i	−0.842479	−	0.538730i	$-0.818904\pi$
$487$	1.00000	−	1.73205i	0.0453143	−	0.0784867i	0.887793	+	0.460243i	$0.152238\pi$
$488$		0			0
$489$	−4.00000			−0.180886
$490$		0			0
$491$	−9.00000	−	15.5885i	−0.406164	−	0.703497i	0.588292	−	0.808649i	$-0.299801\pi$
$491$	−9.00000	−	15.5885i	−0.406164	−	0.703497i	−0.994456	+	0.105151i	$0.966467\pi$
$492$		0			0
$493$	−9.00000			−0.405340
$494$		0			0
$495$	−18.0000			−0.809040
$496$		0			0
$497$	−6.00000	−	10.3923i	−0.269137	−	0.466159i
$498$		0			0
$499$	−32.0000			−1.43252			−0.716258	−	0.697835i	$-0.754147\pi$
$499$	−32.0000			−1.43252			−0.716258	+	0.697835i	$0.754147\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	3.00000	−	5.19615i	0.133763	−	0.231685i	−0.791361	−	0.611349i	$-0.790627\pi$
$503$	3.00000	−	5.19615i	0.133763	−	0.231685i	0.925124	+	0.379664i	$0.123960\pi$
$504$		0			0
$505$	−22.5000	−	38.9711i	−1.00124	−	1.73419i
$506$		0			0
$507$	11.0000	+	6.92820i	0.488527	+	0.307692i
$508$		0			0
$509$	−1.50000	−	2.59808i	−0.0664863	−	0.115158i	0.830866	−	0.556473i	$-0.187846\pi$
$509$	−1.50000	−	2.59808i	−0.0664863	−	0.115158i	−0.897352	+	0.441315i	$0.854512\pi$
$510$		0			0
$511$	−13.0000	+	22.5167i	−0.575086	+	0.996078i
$512$		0			0
$513$	−1.00000	+	1.73205i	−0.0441511	+	0.0764719i
$514$		0			0
$515$	−42.0000			−1.85074
$516$		0			0
$517$	−18.0000	−	31.1769i	−0.791639	−	1.37116i
$518$		0			0
$519$	6.00000			0.263371
$520$		0			0
$521$	33.0000			1.44576			0.722878	−	0.690976i	$-0.242819\pi$
$521$	33.0000			1.44576			0.722878	+	0.690976i	$0.242819\pi$
$522$		0			0
$523$	−17.0000	−	29.4449i	−0.743358	−	1.28753i	−0.950958	−	0.309320i	$-0.899899\pi$
$523$	−17.0000	−	29.4449i	−0.743358	−	1.28753i	0.207600	−	0.978214i	$-0.433435\pi$
$524$		0			0
$525$	8.00000			0.349149
$526$		0			0
$527$	6.00000	−	10.3923i	0.261364	−	0.452696i
$528$		0			0
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−7.50000	−	7.79423i	−0.324861	−	0.337606i
$534$		0			0
$535$	−9.00000	−	15.5885i	−0.389104	−	0.673948i
$536$		0			0
$537$	−3.00000	+	5.19615i	−0.129460	+	0.224231i
$538$		0			0
$539$	−9.00000	+	15.5885i	−0.387657	+	0.671442i
$540$		0			0
$541$	29.0000			1.24681			0.623404	−	0.781900i	$-0.285749\pi$
$541$	29.0000			1.24681			0.623404	+	0.781900i	$0.285749\pi$
$542$		0			0
$543$	−3.50000	−	6.06218i	−0.150199	−	0.260153i
$544$		0			0
$545$	42.0000			1.79908
$546$		0			0
$547$	34.0000			1.45374			0.726868	−	0.686778i	$-0.240975\pi$
$547$	34.0000			1.45374			0.726868	+	0.686778i	$0.240975\pi$
$548$		0			0
$549$	3.50000	+	6.06218i	0.149376	+	0.258727i
$550$		0			0
$551$	−6.00000			−0.255609
$552$		0			0
$553$	4.00000	−	6.92820i	0.170097	−	0.294617i
$554$		0			0
$555$	−10.5000	+	18.1865i	−0.445700	+	0.771975i
$556$		0			0
$557$	−1.50000	−	2.59808i	−0.0635570	−	0.110084i	0.832496	−	0.554031i	$-0.186911\pi$
$557$	−1.50000	−	2.59808i	−0.0635570	−	0.110084i	−0.896053	+	0.443947i	$0.853578\pi$
$558$		0			0
$559$	10.0000	−	34.6410i	0.422955	−	1.46516i
$560$		0			0
$561$	9.00000	+	15.5885i	0.379980	+	0.658145i
$562$		0			0
$563$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$563$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$564$		0			0
$565$	4.50000	−	7.79423i	0.189316	−	0.327906i
$566$		0			0
$567$	−2.00000			−0.0839921
$568$		0			0
$569$	−3.00000	−	5.19615i	−0.125767	−	0.217834i	0.796266	−	0.604947i	$-0.206806\pi$
$569$	−3.00000	−	5.19615i	−0.125767	−	0.217834i	−0.922032	+	0.387113i	$0.873472\pi$
$570$		0			0
$571$	22.0000			0.920671			0.460336	−	0.887745i	$-0.347729\pi$
$571$	22.0000			0.920671			0.460336	+	0.887745i	$0.347729\pi$
$572$		0			0
$573$	−12.0000			−0.501307
$574$		0			0
$575$	−12.0000	−	20.7846i	−0.500435	−	0.866778i
$576$		0			0
$577$	11.0000			0.457936			0.228968	−	0.973434i	$-0.426465\pi$
$577$	11.0000			0.457936			0.228968	+	0.973434i	$0.426465\pi$
$578$		0			0
$579$	11.5000	−	19.9186i	0.477924	−	0.827788i
$580$		0			0
$581$	6.00000	−	10.3923i	0.248922	−	0.431145i
$582$		0			0
$583$	9.00000	+	15.5885i	0.372742	+	0.645608i
$584$		0			0
$585$	3.00000	−	10.3923i	0.124035	−	0.429669i
$586$		0			0
$587$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$587$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$588$		0			0
$589$	4.00000	−	6.92820i	0.164817	−	0.285472i
$590$		0			0
$591$	3.00000	−	5.19615i	0.123404	−	0.213741i
$592$		0			0
$593$	9.00000			0.369586			0.184793	−	0.982777i	$-0.440839\pi$
$593$	9.00000			0.369586			0.184793	+	0.982777i	$0.440839\pi$
$594$		0			0
$595$	−9.00000	−	15.5885i	−0.368964	−	0.639064i
$596$		0			0
$597$	−10.0000			−0.409273
$598$		0			0
$599$	−24.0000			−0.980613			−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000			−0.980613			−0.490307	+	0.871550i	$0.663115\pi$
$600$		0			0
$601$	18.5000	+	32.0429i	0.754631	+	1.30706i	0.945558	+	0.325455i	$0.105517\pi$
$601$	18.5000	+	32.0429i	0.754631	+	1.30706i	−0.190927	+	0.981604i	$0.561149\pi$
$602$		0			0
$603$	10.0000			0.407231
$604$		0			0
$605$	−37.5000	+	64.9519i	−1.52459	+	2.64067i
$606$		0			0
$607$	16.0000	−	27.7128i	0.649420	−	1.12483i	−0.333842	−	0.942629i	$-0.608345\pi$
$607$	16.0000	−	27.7128i	0.649420	−	1.12483i	0.983262	−	0.182199i	$-0.0583216\pi$
$608$		0			0
$609$	−3.00000	−	5.19615i	−0.121566	−	0.210559i
$610$		0			0
$611$	21.0000	−	5.19615i	0.849569	−	0.210214i
$612$		0			0
$613$	15.5000	+	26.8468i	0.626039	+	1.08433i	0.988339	+	0.152270i	$0.0486583\pi$
$613$	15.5000	+	26.8468i	0.626039	+	1.08433i	−0.362300	+	0.932062i	$0.618008\pi$
$614$		0			0
$615$	−4.50000	+	7.79423i	−0.181458	+	0.314294i
$616$		0			0
$617$	7.50000	−	12.9904i	0.301939	−	0.522973i	−0.674636	−	0.738150i	$-0.735700\pi$
$617$	7.50000	−	12.9904i	0.301939	−	0.522973i	0.976575	+	0.215177i	$0.0690329\pi$
$618$		0			0
$619$	−8.00000			−0.321547			−0.160774	−	0.986991i	$-0.551399\pi$
$619$	−8.00000			−0.321547			−0.160774	+	0.986991i	$0.551399\pi$
$620$		0			0
$621$	3.00000	+	5.19615i	0.120386	+	0.208514i
$622$		0			0
$623$	−36.0000			−1.44231
$624$		0			0
$625$	−29.0000			−1.16000
$626$		0			0
$627$	6.00000	+	10.3923i	0.239617	+	0.415029i
$628$		0			0
$629$	21.0000			0.837325
$630$		0			0
$631$	10.0000	−	17.3205i	0.398094	−	0.689519i	−0.595397	−	0.803432i	$-0.703005\pi$
$631$	10.0000	−	17.3205i	0.398094	−	0.689519i	0.993491	+	0.113913i	$0.0363385\pi$
$632$		0			0
$633$	8.00000	−	13.8564i	0.317971	−	0.550743i
$634$		0			0
$635$	−6.00000	−	10.3923i	−0.238103	−	0.412406i
$636$		0			0
$637$	−7.50000	−	7.79423i	−0.297161	−	0.308819i
$638$		0			0
$639$	3.00000	+	5.19615i	0.118678	+	0.205557i
$640$		0			0
$641$	1.50000	−	2.59808i	0.0592464	−	0.102618i	−0.834881	−	0.550431i	$-0.814464\pi$
$641$	1.50000	−	2.59808i	0.0592464	−	0.102618i	0.894127	+	0.447813i	$0.147797\pi$
$642$		0			0
$643$	−8.00000	+	13.8564i	−0.315489	+	0.546443i	−0.979541	−	0.201243i	$-0.935502\pi$
$643$	−8.00000	+	13.8564i	−0.315489	+	0.546443i	0.664052	+	0.747686i	$0.268835\pi$
$644$		0			0
$645$	−30.0000			−1.18125
$646$		0			0
$647$	12.0000	+	20.7846i	0.471769	+	0.817127i	0.999478	−	0.0322975i	$-0.0102824\pi$
$647$	12.0000	+	20.7846i	0.471769	+	0.817127i	−0.527710	+	0.849425i	$0.676949\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	8.00000			0.313545
$652$		0			0
$653$	−21.0000	−	36.3731i	−0.821794	−	1.42339i	−0.904345	−	0.426801i	$-0.859640\pi$
$653$	−21.0000	−	36.3731i	−0.821794	−	1.42339i	0.0825519	−	0.996587i	$-0.473693\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	6.50000	−	11.2583i	0.253589	−	0.439229i
$658$		0			0
$659$	12.0000	−	20.7846i	0.467454	−	0.809653i	−0.531855	−	0.846836i	$-0.678505\pi$
$659$	12.0000	−	20.7846i	0.467454	−	0.809653i	0.999309	+	0.0371821i	$0.0118382\pi$
$660$		0			0
$661$	−2.50000	−	4.33013i	−0.0972387	−	0.168422i	0.813302	−	0.581842i	$-0.197668\pi$
$661$	−2.50000	−	4.33013i	−0.0972387	−	0.168422i	−0.910541	+	0.413419i	$0.864334\pi$
$662$		0			0
$663$	−10.5000	+	2.59808i	−0.407786	+	0.100901i
$664$		0			0
$665$	−6.00000	−	10.3923i	−0.232670	−	0.402996i
$666$		0			0
$667$	−9.00000	+	15.5885i	−0.348481	+	0.603587i
$668$		0			0
$669$	−4.00000	+	6.92820i	−0.154649	+	0.267860i
$670$		0			0
$671$	42.0000			1.62139
$672$		0			0
$673$	6.50000	+	11.2583i	0.250557	+	0.433977i	0.963679	−	0.267063i	$-0.0860531\pi$
$673$	6.50000	+	11.2583i	0.250557	+	0.433977i	−0.713123	+	0.701039i	$0.752720\pi$
$674$		0			0
$675$	−4.00000			−0.153960
$676$		0			0
$677$	18.0000			0.691796			0.345898	−	0.938272i	$-0.387574\pi$
$677$	18.0000			0.691796			0.345898	+	0.938272i	$0.387574\pi$
$678$		0			0
$679$	14.0000	+	24.2487i	0.537271	+	0.930580i
$680$		0			0
$681$	18.0000			0.689761
$682$		0			0
$683$	−24.0000	+	41.5692i	−0.918334	+	1.59060i	−0.116390	+	0.993204i	$0.537132\pi$
$683$	−24.0000	+	41.5692i	−0.918334	+	1.59060i	−0.801945	+	0.597398i	$0.796201\pi$
$684$		0			0
$685$	−13.5000	+	23.3827i	−0.515808	+	0.893407i
$686$		0			0
$687$	−11.0000	−	19.0526i	−0.419676	−	0.726900i
$688$		0			0
$689$	−10.5000	+	2.59808i	−0.400018	+	0.0989788i
$690$		0			0
$691$	13.0000	+	22.5167i	0.494543	+	0.856574i	0.999980	−	0.00628943i	$-0.00200200\pi$
$691$	13.0000	+	22.5167i	0.494543	+	0.856574i	−0.505437	+	0.862864i	$0.668669\pi$
$692$		0			0
$693$	−6.00000	+	10.3923i	−0.227921	+	0.394771i
$694$		0			0
$695$	−6.00000	+	10.3923i	−0.227593	+	0.394203i
$696$		0			0
$697$	9.00000			0.340899
$698$		0			0
$699$	−3.00000	−	5.19615i	−0.113470	−	0.196537i
$700$		0			0
$701$	−30.0000			−1.13308			−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000			−1.13308			−0.566542	+	0.824033i	$0.691719\pi$
$702$		0			0
$703$	14.0000			0.528020
$704$		0			0
$705$	−9.00000	−	15.5885i	−0.338960	−	0.587095i
$706$		0			0
$707$	−30.0000			−1.12827
$708$		0			0
$709$	−2.50000	+	4.33013i	−0.0938895	+	0.162621i	−0.909145	−	0.416481i	$-0.863263\pi$
$709$	−2.50000	+	4.33013i	−0.0938895	+	0.162621i	0.815255	+	0.579102i	$0.196597\pi$
$710$		0			0
$711$	−2.00000	+	3.46410i	−0.0750059	+	0.129914i
$712$		0			0
$713$	−12.0000	−	20.7846i	−0.449404	−	0.778390i
$714$		0			0
$715$	−45.0000	−	46.7654i	−1.68290	−	1.74893i
$716$		0			0
$717$	−3.00000	−	5.19615i	−0.112037	−	0.194054i
$718$		0			0
$719$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$719$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$720$		0			0
$721$	−14.0000	+	24.2487i	−0.521387	+	0.903069i
$722$		0			0
$723$	1.00000			0.0371904
$724$		0			0
$725$	−6.00000	−	10.3923i	−0.222834	−	0.385961i
$726$		0			0
$727$	−14.0000			−0.519231			−0.259616	−	0.965712i	$-0.583596\pi$
$727$	−14.0000			−0.519231			−0.259616	+	0.965712i	$0.583596\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	15.0000	+	25.9808i	0.554795	+	0.960933i
$732$		0			0
$733$	−31.0000			−1.14501			−0.572506	−	0.819901i	$-0.694029\pi$
$733$	−31.0000			−1.14501			−0.572506	+	0.819901i	$0.694029\pi$
$734$		0			0
$735$	−4.50000	+	7.79423i	−0.165985	+	0.287494i
$736$		0			0
$737$	30.0000	−	51.9615i	1.10506	−	1.91403i
$738$		0			0
$739$	−8.00000	−	13.8564i	−0.294285	−	0.509716i	0.680534	−	0.732717i	$-0.261748\pi$
$739$	−8.00000	−	13.8564i	−0.294285	−	0.509716i	−0.974818	+	0.223001i	$0.928415\pi$
$740$		0			0
$741$	−7.00000	+	1.73205i	−0.257151	+	0.0636285i
$742$		0			0
$743$	−18.0000	−	31.1769i	−0.660356	−	1.14377i	−0.980522	−	0.196409i	$-0.937072\pi$
$743$	−18.0000	−	31.1769i	−0.660356	−	1.14377i	0.320166	−	0.947361i	$-0.396261\pi$
$744$		0			0
$745$	13.5000	−	23.3827i	0.494602	−	0.856675i
$746$		0			0
$747$	−3.00000	+	5.19615i	−0.109764	+	0.190117i
$748$		0			0
$749$	−12.0000			−0.438470
$750$		0			0
$751$	7.00000	+	12.1244i	0.255434	+	0.442424i	0.965013	−	0.262201i	$-0.0844484\pi$
$751$	7.00000	+	12.1244i	0.255434	+	0.442424i	−0.709580	+	0.704625i	$0.751115\pi$
$752$		0			0
$753$	−12.0000			−0.437304
$754$		0			0
$755$	30.0000			1.09181
$756$		0			0
$757$	17.0000	+	29.4449i	0.617876	+	1.07019i	0.989873	+	0.141958i	$0.0453398\pi$
$757$	17.0000	+	29.4449i	0.617876	+	1.07019i	−0.371997	+	0.928234i	$0.621327\pi$
$758$		0			0
$759$	36.0000			1.30672
$760$		0			0
$761$	15.0000	−	25.9808i	0.543750	−	0.941802i	−0.454935	−	0.890525i	$-0.650337\pi$
$761$	15.0000	−	25.9808i	0.543750	−	0.941802i	0.998684	−	0.0512772i	$-0.0163292\pi$
$762$		0			0
$763$	14.0000	−	24.2487i	0.506834	−	0.877862i
$764$		0			0
$765$	4.50000	+	7.79423i	0.162698	+	0.281801i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−7.00000	−	12.1244i	−0.252426	−	0.437215i	0.711767	−	0.702416i	$-0.247895\pi$
$769$	−7.00000	−	12.1244i	−0.252426	−	0.437215i	−0.964193	+	0.265200i	$0.914562\pi$
$770$		0			0
$771$	−1.50000	+	2.59808i	−0.0540212	+	0.0935674i
$772$		0			0
$773$	15.0000	−	25.9808i	0.539513	−	0.934463i	−0.459418	−	0.888220i	$-0.651942\pi$
$773$	15.0000	−	25.9808i	0.539513	−	0.934463i	0.998930	−	0.0462427i	$-0.0147248\pi$
$774$		0			0
$775$	16.0000			0.574737
$776$		0			0
$777$	7.00000	+	12.1244i	0.251124	+	0.434959i
$778$		0			0
$779$	6.00000			0.214972
$780$		0			0
$781$	36.0000			1.28818
$782$		0			0
$783$	1.50000	+	2.59808i	0.0536056	+	0.0928477i
$784$		0			0
$785$	15.0000			0.535373
$786$		0			0
$787$	−14.0000	+	24.2487i	−0.499046	+	0.864373i	−0.999999	−	0.00110111i	$-0.999650\pi$
$787$	−14.0000	+	24.2487i	−0.499046	+	0.864373i	0.500953	+	0.865474i	$0.332983\pi$
$788$		0			0
$789$	3.00000	−	5.19615i	0.106803	−	0.184988i
$790$		0			0
$791$	−3.00000	−	5.19615i	−0.106668	−	0.184754i
$792$		0			0
$793$	−7.00000	+	24.2487i	−0.248577	+	0.861097i
$794$		0			0
$795$	4.50000	+	7.79423i	0.159599	+	0.276433i
$796$		0			0
$797$	−15.0000	+	25.9808i	−0.531327	+	0.920286i	0.468004	+	0.883726i	$0.344973\pi$
$797$	−15.0000	+	25.9808i	−0.531327	+	0.920286i	−0.999331	+	0.0365596i	$0.988360\pi$
$798$		0			0
$799$	−9.00000	+	15.5885i	−0.318397	+	0.551480i
$800$		0			0
$801$	18.0000			0.635999
$802$		0			0
$803$	−39.0000	−	67.5500i	−1.37628	−	2.38379i
$804$		0			0
$805$	−36.0000			−1.26883
$806$		0			0
$807$	−18.0000			−0.633630
$808$		0			0
$809$	25.5000	+	44.1673i	0.896532	+	1.55284i	0.831897	+	0.554930i	$0.187255\pi$
$809$	25.5000	+	44.1673i	0.896532	+	1.55284i	0.0646355	+	0.997909i	$0.479412\pi$
$810$		0			0
$811$	4.00000			0.140459			0.0702295	−	0.997531i	$-0.477627\pi$
$811$	4.00000			0.140459			0.0702295	+	0.997531i	$0.477627\pi$
$812$		0			0
$813$	8.00000	−	13.8564i	0.280572	−	0.485965i
$814$		0			0
$815$	−6.00000	+	10.3923i	−0.210171	+	0.364027i
$816$		0			0
$817$	10.0000	+	17.3205i	0.349856	+	0.605968i
$818$		0			0
$819$	−5.00000	−	5.19615i	−0.174714	−	0.181568i
$820$		0			0
$821$	−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
$823$	−20.0000	+	34.6410i	−0.697156	+	1.20751i	0.272292	+	0.962215i	$0.412218\pi$
$823$	−20.0000	+	34.6410i	−0.697156	+	1.20751i	−0.969448	+	0.245295i	$0.921115\pi$
$824$		0			0
$825$	−12.0000	+	20.7846i	−0.417786	+	0.723627i
$826$		0			0
$827$	48.0000			1.66912			0.834562	−	0.550914i	$-0.185721\pi$
$827$	48.0000			1.66912			0.834562	+	0.550914i	$0.185721\pi$
$828$		0			0
$829$	−8.50000	−	14.7224i	−0.295217	−	0.511331i	0.679818	−	0.733381i	$-0.262059\pi$
$829$	−8.50000	−	14.7224i	−0.295217	−	0.511331i	−0.975035	+	0.222049i	$0.928725\pi$
$830$		0			0
$831$	−17.0000			−0.589723
$832$		0			0
$833$	9.00000			0.311832
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−4.00000			−0.138260
$838$		0			0
$839$	−6.00000	+	10.3923i	−0.207143	+	0.358782i	−0.950813	−	0.309764i	$-0.899750\pi$
$839$	−6.00000	+	10.3923i	−0.207143	+	0.358782i	0.743670	+	0.668546i	$0.233083\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$		0			0
$843$	4.50000	+	7.79423i	0.154988	+	0.268447i
$844$		0			0
$845$	34.5000	−	18.1865i	1.18684	−	0.625636i
$846$		0			0
$847$	25.0000	+	43.3013i	0.859010	+	1.48785i
$848$		0			0
$849$	−7.00000	+	12.1244i	−0.240239	+	0.416107i
$850$		0			0
$851$	21.0000	−	36.3731i	0.719871	−	1.24685i
$852$		0			0
$853$	−19.0000			−0.650548			−0.325274	−	0.945620i	$-0.605456\pi$
$853$	−19.0000			−0.650548			−0.325274	+	0.945620i	$0.605456\pi$
$854$		0			0
$855$	3.00000	+	5.19615i	0.102598	+	0.177705i
$856$		0			0
$857$	21.0000			0.717346			0.358673	−	0.933463i	$-0.383229\pi$
$857$	21.0000			0.717346			0.358673	+	0.933463i	$0.383229\pi$
$858$		0			0
$859$	−26.0000			−0.887109			−0.443554	−	0.896248i	$-0.646283\pi$
$859$	−26.0000			−0.887109			−0.443554	+	0.896248i	$0.646283\pi$
$860$		0			0
$861$	3.00000	+	5.19615i	0.102240	+	0.177084i
$862$		0			0
$863$	−18.0000			−0.612727			−0.306364	−	0.951915i	$-0.599112\pi$
$863$	−18.0000			−0.612727			−0.306364	+	0.951915i	$0.599112\pi$
$864$		0			0
$865$	9.00000	−	15.5885i	0.306009	−	0.530023i
$866$		0			0
$867$	−4.00000	+	6.92820i	−0.135847	+	0.235294i
$868$		0			0
$869$	12.0000	+	20.7846i	0.407072	+	0.705070i
$870$		0			0
$871$	25.0000	+	25.9808i	0.847093	+	0.880325i
$872$		0			0
$873$	−7.00000	−	12.1244i	−0.236914	−	0.410347i
$874$		0			0
$875$	−3.00000	+	5.19615i	−0.101419	+	0.175662i
$876$		0			0
$877$	−20.5000	+	35.5070i	−0.692236	+	1.19899i	0.278868	+	0.960329i	$0.410041\pi$
$877$	−20.5000	+	35.5070i	−0.692236	+	1.19899i	−0.971104	+	0.238658i	$0.923292\pi$
$878$		0			0
$879$	21.0000			0.708312
$880$		0			0
$881$	−16.5000	−	28.5788i	−0.555899	−	0.962846i	−0.997833	−	0.0657979i	$-0.979041\pi$
$881$	−16.5000	−	28.5788i	−0.555899	−	0.962846i	0.441934	−	0.897048i	$-0.354293\pi$
$882$		0			0
$883$	−8.00000			−0.269221			−0.134611	−	0.990899i	$-0.542978\pi$
$883$	−8.00000			−0.269221			−0.134611	+	0.990899i	$0.542978\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−24.0000	−	41.5692i	−0.805841	−	1.39576i	−0.915722	−	0.401813i	$-0.868380\pi$
$887$	−24.0000	−	41.5692i	−0.805841	−	1.39576i	0.109881	−	0.993945i	$-0.464953\pi$
$888$		0			0
$889$	−8.00000			−0.268311
$890$		0			0
$891$	3.00000	−	5.19615i	0.100504	−	0.174078i
$892$		0			0
$893$	−6.00000	+	10.3923i	−0.200782	+	0.347765i
$894$		0			0
$895$	9.00000	+	15.5885i	0.300837	+	0.521065i
$896$		0			0
$897$	−6.00000	+	20.7846i	−0.200334	+	0.693978i
$898$		0			0
$899$	−6.00000	−	10.3923i	−0.200111	−	0.346603i
$900$		0			0
$901$	4.50000	−	7.79423i	0.149917	−	0.259663i
$902$		0			0
$903$	−10.0000	+	17.3205i	−0.332779	+	0.576390i
$904$		0			0
$905$	−21.0000			−0.698064
$906$		0			0
$907$	22.0000	+	38.1051i	0.730498	+	1.26526i	0.956671	+	0.291172i	$0.0940453\pi$
$907$	22.0000	+	38.1051i	0.730498	+	1.26526i	−0.226173	+	0.974087i	$0.572621\pi$
$908$		0			0
$909$	15.0000			0.497519
$910$		0			0
$911$	24.0000			0.795155			0.397578	−	0.917568i	$-0.369851\pi$
$911$	24.0000			0.795155			0.397578	+	0.917568i	$0.369851\pi$
$912$		0			0
$913$	18.0000	+	31.1769i	0.595713	+	1.03181i
$914$		0			0
$915$	21.0000			0.694239
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−8.00000	+	13.8564i	−0.263896	+	0.457081i	−0.967274	−	0.253735i	$-0.918341\pi$
$919$	−8.00000	+	13.8564i	−0.263896	+	0.457081i	0.703378	+	0.710816i	$0.251674\pi$
$920$		0			0
$921$	5.00000	+	8.66025i	0.164756	+	0.285365i
$922$		0			0
$923$	−6.00000	+	20.7846i	−0.197492	+	0.684134i
$924$		0			0
$925$	14.0000	+	24.2487i	0.460317	+	0.797293i
$926$		0			0
$927$	7.00000	−	12.1244i	0.229910	−	0.398216i
$928$		0			0
$929$	−16.5000	+	28.5788i	−0.541347	+	0.937641i	0.457480	+	0.889220i	$0.348752\pi$
$929$	−16.5000	+	28.5788i	−0.541347	+	0.937641i	−0.998827	+	0.0484211i	$0.984581\pi$
$930$		0			0
$931$	6.00000			0.196642
$932$		0			0
$933$	15.0000	+	25.9808i	0.491078	+	0.850572i
$934$		0			0
$935$	54.0000			1.76599
$936$		0			0
$937$	47.0000			1.53542			0.767712	−	0.640796i	$-0.221395\pi$
$937$	47.0000			1.53542			0.767712	+	0.640796i	$0.221395\pi$
$938$		0			0
$939$	−5.00000	−	8.66025i	−0.163169	−	0.282617i
$940$		0			0
$941$	42.0000			1.36916			0.684580	−	0.728937i	$-0.259985\pi$
$941$	42.0000			1.36916			0.684580	+	0.728937i	$0.259985\pi$
$942$		0			0
$943$	9.00000	−	15.5885i	0.293080	−	0.507630i
$944$		0			0
$945$	−3.00000	+	5.19615i	−0.0975900	+	0.169031i
$946$		0			0
$947$	12.0000	+	20.7846i	0.389948	+	0.675409i	0.992442	−	0.122714i	$-0.0391598\pi$
$947$	12.0000	+	20.7846i	0.389948	+	0.675409i	−0.602494	+	0.798123i	$0.705826\pi$
$948$		0			0
$949$	45.5000	−	11.2583i	1.47699	−	0.365461i
$950$		0			0
$951$	1.50000	+	2.59808i	0.0486408	+	0.0842484i
$952$		0			0
$953$	−27.0000	+	46.7654i	−0.874616	+	1.51488i	−0.0174443	+	0.999848i	$0.505553\pi$
$953$	−27.0000	+	46.7654i	−0.874616	+	1.51488i	−0.857171	+	0.515031i	$0.827780\pi$
$954$		0			0
$955$	−18.0000	+	31.1769i	−0.582466	+	1.00886i
$956$		0			0
$957$	18.0000			0.581857
$958$		0			0
$959$	9.00000	+	15.5885i	0.290625	+	0.503378i
$960$		0			0
$961$	−15.0000			−0.483871
$962$		0			0
$963$	6.00000			0.193347
$964$		0			0
$965$	−34.5000	−	59.7558i	−1.11059	−	1.92361i
$966$		0			0
$967$	22.0000			0.707472			0.353736	−	0.935345i	$-0.384911\pi$
$967$	22.0000			0.707472			0.353736	+	0.935345i	$0.384911\pi$
$968$		0			0
$969$	3.00000	−	5.19615i	0.0963739	−	0.166924i
$970$		0			0
$971$	30.0000	−	51.9615i	0.962746	−	1.66752i	0.247193	−	0.968966i	$-0.420492\pi$
$971$	30.0000	−	51.9615i	0.962746	−	1.66752i	0.715553	−	0.698558i	$-0.246175\pi$
$972$		0			0
$973$	4.00000	+	6.92820i	0.128234	+	0.222108i
$974$		0			0
$975$	−10.0000	−	10.3923i	−0.320256	−	0.332820i
$976$		0			0
$977$	1.50000	+	2.59808i	0.0479893	+	0.0831198i	0.889022	−	0.457864i	$-0.151385\pi$
$977$	1.50000	+	2.59808i	0.0479893	+	0.0831198i	−0.841033	+	0.540984i	$0.818052\pi$
$978$		0			0
$979$	54.0000	−	93.5307i	1.72585	−	2.98926i
$980$		0			0
$981$	−7.00000	+	12.1244i	−0.223493	+	0.387101i
$982$		0			0
$983$	36.0000			1.14822			0.574111	−	0.818778i	$-0.305348\pi$
$983$	36.0000			1.14822			0.574111	+	0.818778i	$0.305348\pi$
$984$		0			0
$985$	−9.00000	−	15.5885i	−0.286764	−	0.496690i
$986$		0			0
$987$	−12.0000			−0.381964
$988$		0			0
$989$	60.0000			1.90789
$990$		0			0
$991$	19.0000	+	32.9090i	0.603555	+	1.04539i	0.992278	+	0.124033i	$0.0395829\pi$
$991$	19.0000	+	32.9090i	0.603555	+	1.04539i	−0.388723	+	0.921355i	$0.627084\pi$
$992$		0			0
$993$	−4.00000			−0.126936
$994$		0			0
$995$	−15.0000	+	25.9808i	−0.475532	+	0.823646i
$996$		0			0
$997$	−2.50000	+	4.33013i	−0.0791758	+	0.137136i	−0.902895	−	0.429862i	$-0.858562\pi$
$997$	−2.50000	+	4.33013i	−0.0791758	+	0.137136i	0.823719	+	0.566999i	$0.191896\pi$
$998$		0			0
$999$	−3.50000	−	6.06218i	−0.110735	−	0.191799i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.2.q.g.289.1		2
3.2	odd	2		1872.2.t.c.289.1		2
4.3	odd	2		78.2.e.a.55.1	✓	2
12.11	even	2		234.2.h.a.55.1		2
13.3	even	3		8112.2.a.m.1.1		1
13.9	even	3	inner	624.2.q.g.529.1		2
13.10	even	6		8112.2.a.c.1.1		1
20.3	even	4		1950.2.z.g.1849.2		4
20.7	even	4		1950.2.z.g.1849.1		4
20.19	odd	2		1950.2.i.m.601.1		2
39.35	odd	6		1872.2.t.c.1153.1		2
52.3	odd	6		1014.2.a.c.1.1		1
52.7	even	12		1014.2.i.b.823.2		4
52.11	even	12		1014.2.b.c.337.1		2
52.15	even	12		1014.2.b.c.337.2		2
52.19	even	12		1014.2.i.b.823.1		4
52.23	odd	6		1014.2.a.f.1.1		1
52.31	even	4		1014.2.i.b.361.2		4
52.35	odd	6		78.2.e.a.61.1	yes	2
52.43	odd	6		1014.2.e.a.529.1		2
52.47	even	4		1014.2.i.b.361.1		4
52.51	odd	2		1014.2.e.a.991.1		2
156.11	odd	12		3042.2.b.h.1351.2		2
156.23	even	6		3042.2.a.h.1.1		1
156.35	even	6		234.2.h.a.217.1		2
156.107	even	6		3042.2.a.i.1.1		1
156.119	odd	12		3042.2.b.h.1351.1		2
260.87	even	12		1950.2.z.g.1699.2		4
260.139	odd	6		1950.2.i.m.451.1		2
260.243	even	12		1950.2.z.g.1699.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.e.a.55.1	✓	2	4.3	odd	2
78.2.e.a.61.1	yes	2	52.35	odd	6
234.2.h.a.55.1		2	12.11	even	2
234.2.h.a.217.1		2	156.35	even	6
624.2.q.g.289.1		2	1.1	even	1	trivial
624.2.q.g.529.1		2	13.9	even	3	inner
1014.2.a.c.1.1		1	52.3	odd	6
1014.2.a.f.1.1		1	52.23	odd	6
1014.2.b.c.337.1		2	52.11	even	12
1014.2.b.c.337.2		2	52.15	even	12
1014.2.e.a.529.1		2	52.43	odd	6
1014.2.e.a.991.1		2	52.51	odd	2
1014.2.i.b.361.1		4	52.47	even	4
1014.2.i.b.361.2		4	52.31	even	4
1014.2.i.b.823.1		4	52.19	even	12
1014.2.i.b.823.2		4	52.7	even	12
1872.2.t.c.289.1		2	3.2	odd	2
1872.2.t.c.1153.1		2	39.35	odd	6
1950.2.i.m.451.1		2	260.139	odd	6
1950.2.i.m.601.1		2	20.19	odd	2
1950.2.z.g.1699.1		4	260.243	even	12
1950.2.z.g.1699.2		4	260.87	even	12
1950.2.z.g.1849.1		4	20.7	even	4
1950.2.z.g.1849.2		4	20.3	even	4
3042.2.a.h.1.1		1	156.23	even	6
3042.2.a.i.1.1		1	156.107	even	6
3042.2.b.h.1351.1		2	156.119	odd	12
3042.2.b.h.1351.2		2	156.11	odd	12
8112.2.a.c.1.1		1	13.10	even	6
8112.2.a.m.1.1		1	13.3	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:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} +3.00000 q^{5} +(1.00000 - 1.73205i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(3.00000 + 5.19615i) q^{11} +(-3.50000 + 0.866025i) q^{13} +(1.50000 + 2.59808i) q^{15} +(1.50000 - 2.59808i) q^{17} +(1.00000 - 1.73205i) q^{19} +2.00000 q^{21} +(-3.00000 - 5.19615i) q^{23} +4.00000 q^{25} -1.00000 q^{27} +(-1.50000 - 2.59808i) q^{29} +4.00000 q^{31} +(-3.00000 + 5.19615i) q^{33} +(3.00000 - 5.19615i) q^{35} +(3.50000 + 6.06218i) q^{37} +(-2.50000 - 2.59808i) q^{39} +(1.50000 + 2.59808i) q^{41} +(-5.00000 + 8.66025i) q^{43} +(-1.50000 + 2.59808i) q^{45} -6.00000 q^{47} +(1.50000 + 2.59808i) q^{49} +3.00000 q^{51} +3.00000 q^{53} +(9.00000 + 15.5885i) q^{55} +2.00000 q^{57} +(3.50000 - 6.06218i) q^{61} +(1.00000 + 1.73205i) q^{63} +(-10.5000 + 2.59808i) q^{65} +(-5.00000 - 8.66025i) q^{67} +(3.00000 - 5.19615i) q^{69} +(3.00000 - 5.19615i) q^{71} -13.0000 q^{73} +(2.00000 + 3.46410i) q^{75} +12.0000 q^{77} +4.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +6.00000 q^{83} +(4.50000 - 7.79423i) q^{85} +(1.50000 - 2.59808i) q^{87} +(-9.00000 - 15.5885i) q^{89} +(-2.00000 + 6.92820i) q^{91} +(2.00000 + 3.46410i) q^{93} +(3.00000 - 5.19615i) q^{95} +(-7.00000 + 12.1244i) q^{97} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{3} + 6 q^{5} + 2 q^{7} - q^{9} + 6 q^{11} - 7 q^{13} + 3 q^{15} + 3 q^{17} + 2 q^{19} + 4 q^{21} - 6 q^{23} + 8 q^{25} - 2 q^{27} - 3 q^{29} + 8 q^{31} - 6 q^{33} + 6 q^{35} + 7 q^{37} - 5 q^{39}+ \cdots - 12 q^{99}+O(q^{100}) \) 2 * q + q^3 + 6 * q^5 + 2 * q^7 - q^9 + 6 * q^11 - 7 * q^13 + 3 * q^15 + 3 * q^17 + 2 * q^19 + 4 * q^21 - 6 * q^23 + 8 * q^25 - 2 * q^27 - 3 * q^29 + 8 * q^31 - 6 * q^33 + 6 * q^35 + 7 * q^37 - 5 * q^39 + 3 * q^41 - 10 * q^43 - 3 * q^45 - 12 * q^47 + 3 * q^49 + 6 * q^51 + 6 * q^53 + 18 * q^55 + 4 * q^57 + 7 * q^61 + 2 * q^63 - 21 * q^65 - 10 * q^67 + 6 * q^69 + 6 * q^71 - 26 * q^73 + 4 * q^75 + 24 * q^77 + 8 * q^79 - q^81 + 12 * q^83 + 9 * q^85 + 3 * q^87 - 18 * q^89 - 4 * q^91 + 4 * q^93 + 6 * q^95 - 14 * q^97 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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