LMFDB - Embedded newform 1764.2.i.j.373.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(373,1764)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1764, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1764.373");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.i (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:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			373.11
Character	$\chi$	$=$	1764.373
Dual form			1764.2.i.j.1537.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.60601 - 0.648636i) q^{3} +(-0.0111913 - 0.0193839i) q^{5} +(2.15854 - 2.08343i) q^{9} +(0.280281 - 0.485460i) q^{11} +(2.06442 - 3.57567i) q^{13} +(-0.0305465 - 0.0238717i) q^{15} +(-1.29152 - 2.23698i) q^{17} +(-1.69669 + 2.93876i) q^{19} +(-2.24626 - 3.89064i) q^{23} +(2.49975 - 4.32969i) q^{25} +(2.11525 - 4.74613i) q^{27} +(2.57275 + 4.45613i) q^{29} +0.815136 q^{31} +(0.135247 - 0.961455i) q^{33} +(-0.235546 + 0.407978i) q^{37} +(0.996163 - 7.08162i) q^{39} +(3.02774 - 5.24420i) q^{41} +(0.811935 + 1.40631i) q^{43} +(-0.0645420 - 0.0185247i) q^{45} -12.1108 q^{47} +(-3.52519 - 2.75489i) q^{51} +(1.45922 + 2.52745i) q^{53} -0.0125468 q^{55} +(-0.818723 + 5.82022i) q^{57} +8.95882 q^{59} +2.11385 q^{61} -0.0924141 q^{65} +15.0909 q^{67} +(-6.13113 - 4.79140i) q^{69} +2.16045 q^{71} +(-3.55205 - 6.15233i) q^{73} +(1.20623 - 8.57496i) q^{75} +2.31781 q^{79} +(0.318608 - 8.99436i) q^{81} +(-3.83160 - 6.63653i) q^{83} +(-0.0289077 + 0.0500695i) q^{85} +(7.02228 + 5.48782i) q^{87} +(0.502365 - 0.870122i) q^{89} +(1.30912 - 0.528727i) q^{93} +0.0759530 q^{95} +(-7.32986 - 12.6957i) q^{97} +(-0.406427 - 1.63183i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{9} - 4 q^{11} - 28 q^{15} - 8 q^{23} - 12 q^{25} - 32 q^{29} - 12 q^{37} + 8 q^{51} - 16 q^{53} + 52 q^{57} + 72 q^{65} - 24 q^{67} + 48 q^{71} - 24 q^{79} - 8 q^{81} + 12 q^{85} - 48 q^{93}+ \cdots - 4 q^{99}+O(q^{100}) $ 24 * q - 4 * q^9 - 4 * q^11 - 28 * q^15 - 8 * q^23 - 12 * q^25 - 32 * q^29 - 12 * q^37 + 8 * q^51 - 16 * q^53 + 52 * q^57 + 72 * q^65 - 24 * q^67 + 48 * q^71 - 24 * q^79 - 8 * q^81 + 12 * q^85 - 48 * q^93 - 64 * q^95 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.60601	−	0.648636i	0.927231	−	0.374490i
$3$	1.60601	−	0.648636i	0.927231	−	0.374490i
$4$		0			0
$5$	−0.0111913	−	0.0193839i	−0.00500491	−	0.00866875i	0.863512	−	0.504328i	$-0.168260\pi$
$5$	−0.0111913	−	0.0193839i	−0.00500491	−	0.00866875i	−0.868517	+	0.495659i	$0.834926\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	2.15854	−	2.08343i	0.719514	−	0.694478i
$10$		0			0
$11$	0.280281	−	0.485460i	0.0845078	−	0.146372i	−0.820674	−	0.571397i	$-0.806402\pi$
$11$	0.280281	−	0.485460i	0.0845078	−	0.146372i	0.905181	+	0.425025i	$0.139735\pi$
$12$		0			0
$13$	2.06442	−	3.57567i	0.572566	−	0.991713i	−0.423736	−	0.905786i	$-0.639281\pi$
$13$	2.06442	−	3.57567i	0.572566	−	0.991713i	0.996301	−	0.0859272i	$-0.0273852\pi$
$14$		0			0
$15$	−0.0305465	−	0.0238717i	−0.00788707	−	0.00616365i
$16$		0			0
$17$	−1.29152	−	2.23698i	−0.313240	−	0.542548i	0.665822	−	0.746111i	$-0.268081\pi$
$17$	−1.29152	−	2.23698i	−0.313240	−	0.542548i	−0.979062	+	0.203563i	$0.934748\pi$
$18$		0			0
$19$	−1.69669	+	2.93876i	−0.389248	+	0.674198i	−0.992349	−	0.123467i	$-0.960599\pi$
$19$	−1.69669	+	2.93876i	−0.389248	+	0.674198i	0.603100	+	0.797665i	$0.293932\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.24626	−	3.89064i	−0.468378	−	0.811255i	0.530969	−	0.847391i	$-0.321828\pi$
$23$	−2.24626	−	3.89064i	−0.468378	−	0.811255i	−0.999347	+	0.0361367i	$0.988495\pi$
$24$		0			0
$25$	2.49975	−	4.32969i	0.499950	−	0.865939i
$26$		0			0
$27$	2.11525	−	4.74613i	0.407080	−	0.913392i
$28$		0			0
$29$	2.57275	+	4.45613i	0.477748	+	0.827483i	0.999675	−	0.0255069i	$-0.00811996\pi$
$29$	2.57275	+	4.45613i	0.477748	+	0.827483i	−0.521927	+	0.852990i	$0.674787\pi$
$30$		0			0
$31$	0.815136			0.146403			0.0732014	−	0.997317i	$-0.476678\pi$
$31$	0.815136			0.146403			0.0732014	+	0.997317i	$0.476678\pi$
$32$		0			0
$33$	0.135247	−	0.961455i	0.0235434	−	0.167368i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−0.235546	+	0.407978i	−0.0387236	+	0.0670712i	−0.884738	−	0.466089i	$-0.845663\pi$
$37$	−0.235546	+	0.407978i	−0.0387236	+	0.0670712i	0.846014	+	0.533161i	$0.178996\pi$
$38$		0			0
$39$	0.996163	−	7.08162i	0.159514	−	1.13397i
$40$		0			0
$41$	3.02774	−	5.24420i	0.472854	−	0.819007i	−0.526663	−	0.850074i	$-0.676557\pi$
$41$	3.02774	−	5.24420i	0.472854	−	0.819007i	0.999517	+	0.0310669i	$0.00989048\pi$
$42$		0			0
$43$	0.811935	+	1.40631i	0.123819	+	0.214461i	0.921271	−	0.388922i	$-0.127152\pi$
$43$	0.811935	+	1.40631i	0.123819	+	0.214461i	−0.797452	+	0.603383i	$0.793819\pi$
$44$		0			0
$45$	−0.0645420	−	0.0185247i	−0.00962136	−	0.00276149i
$46$		0			0
$47$	−12.1108			−1.76654			−0.883271	−	0.468863i	$-0.844664\pi$
$47$	−12.1108			−1.76654			−0.883271	+	0.468863i	$0.844664\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−3.52519	−	2.75489i	−0.493625	−	0.385762i
$52$		0			0
$53$	1.45922	+	2.52745i	0.200440	+	0.347172i	0.948670	−	0.316267i	$-0.102430\pi$
$53$	1.45922	+	2.52745i	0.200440	+	0.347172i	−0.748230	+	0.663439i	$0.769096\pi$
$54$		0			0
$55$	−0.0125468			−0.00169182
$56$		0			0
$57$	−0.818723	+	5.82022i	−0.108443	+	0.770907i
$58$		0			0
$59$	8.95882			1.16634			0.583169	−	0.812351i	$-0.301812\pi$
$59$	8.95882			1.16634			0.583169	+	0.812351i	$0.301812\pi$
$60$		0			0
$61$	2.11385			0.270650			0.135325	−	0.990801i	$-0.456792\pi$
$61$	2.11385			0.270650			0.135325	+	0.990801i	$0.456792\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.0924141			−0.0114626
$66$		0			0
$67$	15.0909			1.84364			0.921822	−	0.387614i	$-0.126701\pi$
$67$	15.0909			1.84364			0.921822	+	0.387614i	$0.126701\pi$
$68$		0			0
$69$	−6.13113	−	4.79140i	−0.738102	−	0.576817i
$70$		0			0
$71$	2.16045			0.256398			0.128199	−	0.991748i	$-0.459080\pi$
$71$	2.16045			0.256398			0.128199	+	0.991748i	$0.459080\pi$
$72$		0			0
$73$	−3.55205	−	6.15233i	−0.415736	−	0.720076i	0.579769	−	0.814781i	$-0.303143\pi$
$73$	−3.55205	−	6.15233i	−0.415736	−	0.720076i	−0.995505	+	0.0947047i	$0.969809\pi$
$74$		0			0
$75$	1.20623	−	8.57496i	0.139283	−	0.990151i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	2.31781			0.260775			0.130387	−	0.991463i	$-0.458378\pi$
$79$	2.31781			0.260775			0.130387	+	0.991463i	$0.458378\pi$
$80$		0			0
$81$	0.318608	−	8.99436i	0.0354009	−	0.999373i
$82$		0			0
$83$	−3.83160	−	6.63653i	−0.420573	−	0.728454i	0.575423	−	0.817856i	$-0.304838\pi$
$83$	−3.83160	−	6.63653i	−0.420573	−	0.728454i	−0.995996	+	0.0894025i	$0.971504\pi$
$84$		0			0
$85$	−0.0289077	+	0.0500695i	−0.00313548	+	0.00543080i
$86$		0			0
$87$	7.02228	+	5.48782i	0.752867	+	0.588356i
$88$		0			0
$89$	0.502365	−	0.870122i	0.0532506	−	0.0922327i	−0.838171	−	0.545407i	$-0.816375\pi$
$89$	0.502365	−	0.870122i	0.0532506	−	0.0922327i	0.891422	+	0.453174i	$0.149708\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	1.30912	−	0.528727i	0.135749	−	0.0548264i
$94$		0			0
$95$	0.0759530			0.00779261
$96$		0			0
$97$	−7.32986	−	12.6957i	−0.744235	−	1.28905i	−0.950551	−	0.310567i	$-0.899481\pi$
$97$	−7.32986	−	12.6957i	−0.744235	−	1.28905i	0.206316	−	0.978485i	$-0.433852\pi$
$98$		0			0
$99$	−0.406427	−	1.63183i	−0.0408474	−	0.164005i
$100$		0			0
$101$	7.57250	−	13.1160i	0.753492	−	1.30509i	−0.192629	−	0.981272i	$-0.561701\pi$
$101$	7.57250	−	13.1160i	0.753492	−	1.30509i	0.946121	−	0.323814i	$-0.104965\pi$
$102$		0			0
$103$	4.45031	+	7.70817i	0.438502	+	0.759508i	0.997574	−	0.0696109i	$-0.0221758\pi$
$103$	4.45031	+	7.70817i	0.438502	+	0.759508i	−0.559072	+	0.829119i	$0.688842\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−8.85846	+	15.3433i	−0.856380	+	1.48329i	0.0189792	+	0.999820i	$0.493958\pi$
$107$	−8.85846	+	15.3433i	−0.856380	+	1.48329i	−0.875359	+	0.483473i	$0.839375\pi$
$108$		0			0
$109$	5.97433	+	10.3478i	0.572237	+	0.991144i	0.996336	+	0.0855281i	$0.0272577\pi$
$109$	5.97433	+	10.3478i	0.572237	+	0.991144i	−0.424098	+	0.905616i	$0.639409\pi$
$110$		0			0
$111$	−0.113660	+	0.808001i	−0.0107882	+	0.0766920i
$112$		0			0
$113$	−7.50835	+	13.0048i	−0.706326	+	1.22339i	0.259884	+	0.965640i	$0.416316\pi$
$113$	−7.50835	+	13.0048i	−0.706326	+	1.22339i	−0.966211	+	0.257753i	$0.917018\pi$
$114$		0			0
$115$	−0.0502773	+	0.0870828i	−0.00468838	+	0.00812051i
$116$		0			0
$117$	−2.99355	−	12.0193i	−0.276754	−	1.11119i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	5.34289	+	9.25415i	0.485717	+	0.841286i
$122$		0			0
$123$	1.46101	−	10.3862i	0.131735	−	0.936488i
$124$		0			0
$125$	−0.223815			−0.0200186
$126$		0			0
$127$	4.17511			0.370481			0.185240	−	0.982693i	$-0.440694\pi$
$127$	4.17511			0.370481			0.185240	+	0.982693i	$0.440694\pi$
$128$		0			0
$129$	2.21616	+	1.73190i	0.195122	+	0.152485i
$130$		0			0
$131$	−3.03947	−	5.26451i	−0.265560	−	0.459963i	0.702150	−	0.712029i	$-0.252223\pi$
$131$	−3.03947	−	5.26451i	−0.265560	−	0.459963i	−0.967710	+	0.252066i	$0.918890\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−0.115671	+	0.0121135i	−0.00995537	+	0.00104256i
$136$		0			0
$137$	−8.04927	+	13.9418i	−0.687696	+	1.19112i	0.284886	+	0.958562i	$0.408044\pi$
$137$	−8.04927	+	13.9418i	−0.687696	+	1.19112i	−0.972581	+	0.232563i	$0.925289\pi$
$138$		0			0
$139$	1.83849	−	3.18435i	0.155938	−	0.270093i	−0.777462	−	0.628930i	$-0.783493\pi$
$139$	1.83849	−	3.18435i	0.155938	−	0.270093i	0.933400	+	0.358837i	$0.116827\pi$
$140$		0			0
$141$	−19.4501	+	7.85550i	−1.63799	+	0.661553i
$142$		0			0
$143$	−1.15723	−	2.00438i	−0.0967726	−	0.167615i
$144$		0			0
$145$	0.0575849	−	0.0997400i	0.00478217	−	0.00828296i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−4.57786	−	7.92909i	−0.375033	−	0.649576i	0.615299	−	0.788294i	$-0.289035\pi$
$149$	−4.57786	−	7.92909i	−0.375033	−	0.649576i	−0.990332	+	0.138718i	$0.955702\pi$
$150$		0			0
$151$	9.28603	−	16.0839i	0.755687	−	1.30889i	−0.189346	−	0.981910i	$-0.560637\pi$
$151$	9.28603	−	16.0839i	0.755687	−	1.30889i	0.945032	−	0.326977i	$-0.106030\pi$
$152$		0			0
$153$	−7.44841	−	2.13782i	−0.602168	−	0.172832i
$154$		0			0
$155$	−0.00912245	−	0.0158005i	−0.000732732	−	0.00126913i
$156$		0			0
$157$	−11.6619			−0.930721			−0.465361	−	0.885121i	$-0.654075\pi$
$157$	−11.6619			−0.930721			−0.465361	+	0.885121i	$0.654075\pi$
$158$		0			0
$159$	3.98292	+	3.11261i	0.315866	+	0.246846i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−6.53069	+	11.3115i	−0.511523	+	0.885984i	0.488388	+	0.872627i	$0.337585\pi$
$163$	−6.53069	+	11.3115i	−0.511523	+	0.885984i	−0.999911	+	0.0133569i	$0.995748\pi$
$164$		0			0
$165$	−0.0201504	+	0.00813833i	−0.00156870	+	0.000633568i
$166$		0			0
$167$	−6.86282	+	11.8867i	−0.531061	+	0.919824i	0.468282	+	0.883579i	$0.344873\pi$
$167$	−6.86282	+	11.8867i	−0.531061	+	0.919824i	−0.999343	+	0.0362450i	$0.988460\pi$
$168$		0			0
$169$	−2.02362	−	3.50502i	−0.155663	−	0.269617i
$170$		0			0
$171$	2.46033	+	9.87839i	0.188146	+	0.755419i
$172$		0			0
$173$	−24.9257			−1.89507			−0.947534	−	0.319656i	$-0.896433\pi$
$173$	−24.9257			−1.89507			−0.947534	+	0.319656i	$0.896433\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	14.3880	−	5.81101i	1.08147	−	0.436782i
$178$		0			0
$179$	4.58202	+	7.93629i	0.342476	+	0.593186i	0.984892	−	0.173170i	$-0.0554011\pi$
$179$	4.58202	+	7.93629i	0.342476	+	0.593186i	−0.642416	+	0.766356i	$0.722068\pi$
$180$		0			0
$181$	−0.882658			−0.0656075			−0.0328037	−	0.999462i	$-0.510444\pi$
$181$	−0.882658			−0.0656075			−0.0328037	+	0.999462i	$0.510444\pi$
$182$		0			0
$183$	3.39486	−	1.37112i	0.250955	−	0.101356i
$184$		0			0
$185$	0.0105443			0.000775231
$186$		0			0
$187$	−1.44795			−0.105885
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−16.6151			−1.20222			−0.601111	−	0.799165i	$-0.705275\pi$
$191$	−16.6151			−1.20222			−0.601111	+	0.799165i	$0.705275\pi$
$192$		0			0
$193$	18.5869			1.33791			0.668957	−	0.743302i	$-0.266741\pi$
$193$	18.5869			1.33791			0.668957	+	0.743302i	$0.266741\pi$
$194$		0			0
$195$	−0.148418	+	0.0599431i	−0.0106284	+	0.00429262i
$196$		0			0
$197$	23.4037			1.66744			0.833722	−	0.552184i	$-0.186205\pi$
$197$	23.4037			1.66744			0.833722	+	0.552184i	$0.186205\pi$
$198$		0			0
$199$	4.03426	+	6.98754i	0.285981	+	0.495334i	0.972847	−	0.231451i	$-0.0743472\pi$
$199$	4.03426	+	6.98754i	0.285981	+	0.495334i	−0.686865	+	0.726785i	$0.741014\pi$
$200$		0			0
$201$	24.2361	−	9.78849i	1.70948	−	0.690427i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−0.135538			−0.00946636
$206$		0			0
$207$	−12.9545	−	3.71817i	−0.900403	−	0.258431i
$208$		0			0
$209$	0.951102	+	1.64736i	0.0657891	+	0.113950i
$210$		0			0
$211$	6.94647	−	12.0316i	0.478215	−	0.828292i	−0.521473	−	0.853268i	$-0.674617\pi$
$211$	6.94647	−	12.0316i	0.478215	−	0.828292i	0.999688	+	0.0249755i	$0.00795078\pi$
$212$		0			0
$213$	3.46971	−	1.40135i	0.237740	−	0.0960187i
$214$		0			0
$215$	0.0181732	−	0.0314770i	0.00123940	−	0.00214671i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−9.69526	−	7.57672i	−0.655145	−	0.511988i
$220$		0			0
$221$	−10.6650			−0.717402
$222$		0			0
$223$	8.28588	+	14.3516i	0.554863	+	0.961052i	0.997914	+	0.0645551i	$0.0205628\pi$
$223$	8.28588	+	14.3516i	0.554863	+	0.961052i	−0.443051	+	0.896497i	$0.646104\pi$
$224$		0			0
$225$	−3.62481	−	14.5539i	−0.241654	−	0.970259i
$226$		0			0
$227$	−3.06311	+	5.30547i	−0.203306	+	0.352136i	−0.949592	−	0.313490i	$-0.898502\pi$
$227$	−3.06311	+	5.30547i	−0.203306	+	0.352136i	0.746286	+	0.665626i	$0.231835\pi$
$228$		0			0
$229$	14.4155	+	24.9683i	0.952600	+	1.64995i	0.739767	+	0.672863i	$0.234936\pi$
$229$	14.4155	+	24.9683i	0.952600	+	1.64995i	0.212833	+	0.977089i	$0.431731\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	8.44996	−	14.6358i	0.553575	−	0.958821i	−0.444438	−	0.895810i	$-0.646596\pi$
$233$	8.44996	−	14.6358i	0.553575	−	0.958821i	0.998013	−	0.0630107i	$-0.0200702\pi$
$234$		0			0
$235$	0.135536	+	0.234755i	0.00884138	+	0.0153137i
$236$		0			0
$237$	3.72244	−	1.50342i	0.241798	−	0.0976575i
$238$		0			0
$239$	−7.63989	+	13.2327i	−0.494184	+	0.855951i	−0.999978	−	0.00670310i	$-0.997866\pi$
$239$	−7.63989	+	13.2327i	−0.494184	+	0.855951i	0.505794	+	0.862654i	$0.331200\pi$
$240$		0			0
$241$	−2.09714	+	3.63236i	−0.135089	+	0.233981i	−0.925631	−	0.378426i	$-0.876465\pi$
$241$	−2.09714	+	3.63236i	−0.135089	+	0.233981i	0.790543	+	0.612407i	$0.209799\pi$
$242$		0			0
$243$	−5.32238	−	14.6517i	−0.341431	−	0.939907i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	7.00537	+	12.1336i	0.445741	+	0.772046i
$248$		0			0
$249$	−10.4583	−	8.17302i	−0.662767	−	0.517944i
$250$		0			0
$251$	19.7104			1.24411			0.622056	−	0.782973i	$-0.286298\pi$
$251$	19.7104			1.24411			0.622056	+	0.782973i	$0.286298\pi$
$252$		0			0
$253$	−2.51834			−0.158326
$254$		0			0
$255$	−0.0139491	+	0.0991628i	−0.000873527	+	0.00620981i
$256$		0			0
$257$	2.47060	+	4.27921i	0.154112	+	0.266930i	0.932735	−	0.360562i	$-0.117415\pi$
$257$	2.47060	+	4.27921i	0.154112	+	0.266930i	−0.778623	+	0.627492i	$0.784082\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	14.8375	+	4.25860i	0.918415	+	0.263601i
$262$		0			0
$263$	−13.5987	+	23.5537i	−0.838533	+	1.45238i	0.0525879	+	0.998616i	$0.483253\pi$
$263$	−13.5987	+	23.5537i	−0.838533	+	1.45238i	−0.891121	+	0.453766i	$0.850080\pi$
$264$		0			0
$265$	0.0326613	−	0.0565710i	0.00200637	−	0.00347513i
$266$		0			0
$267$	0.242411	−	1.72328i	0.0148353	−	0.105463i
$268$		0			0
$269$	−10.5884	−	18.3397i	−0.645588	−	1.11819i	−0.984165	−	0.177253i	$-0.943279\pi$
$269$	−10.5884	−	18.3397i	−0.645588	−	1.11819i	0.338578	−	0.940938i	$-0.390054\pi$
$270$		0			0
$271$	−11.7699	+	20.3860i	−0.714968	+	1.23836i	0.248003	+	0.968759i	$0.420226\pi$
$271$	−11.7699	+	20.3860i	−0.714968	+	1.23836i	−0.962972	+	0.269602i	$0.913108\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.40126	−	2.42706i	−0.0844994	−	0.146357i
$276$		0			0
$277$	−10.1560	+	17.5907i	−0.610216	+	1.05693i	0.380988	+	0.924580i	$0.375584\pi$
$277$	−10.1560	+	17.5907i	−0.610216	+	1.05693i	−0.991204	+	0.132345i	$0.957749\pi$
$278$		0			0
$279$	1.75951	−	1.69828i	0.105339	−	0.101674i
$280$		0			0
$281$	−9.63184	−	16.6828i	−0.574587	−	0.995215i	−0.996086	−	0.0883856i	$-0.971829\pi$
$281$	−9.63184	−	16.6828i	−0.574587	−	0.995215i	0.421499	−	0.906829i	$-0.361504\pi$
$282$		0			0
$283$	−17.9960			−1.06975			−0.534875	−	0.844931i	$-0.679641\pi$
$283$	−17.9960			−1.06975			−0.534875	+	0.844931i	$0.679641\pi$
$284$		0			0
$285$	0.121981	−	0.0492658i	0.00722555	−	0.00291826i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	5.16394	−	8.94421i	0.303761	−	0.526130i
$290$		0			0
$291$	−20.0067	−	15.6350i	−1.17282	−	0.916541i
$292$		0			0
$293$	−5.27396	+	9.13477i	−0.308108	+	0.533659i	−0.977949	−	0.208846i	$-0.933029\pi$
$293$	−5.27396	+	9.13477i	−0.308108	+	0.533659i	0.669840	+	0.742505i	$0.266363\pi$
$294$		0			0
$295$	−0.100261	−	0.173657i	−0.00583742	−	0.0101107i
$296$		0			0
$297$	−1.71119	−	2.35712i	−0.0992934	−	0.136774i
$298$		0			0
$299$	−18.5489			−1.07271
$300$		0			0
$301$		0			0
$302$		0			0
$303$	3.65403	−	25.9762i	0.209919	−	1.49229i
$304$		0			0
$305$	−0.0236567	−	0.0409746i	−0.00135458	−	0.00234620i
$306$		0			0
$307$	16.2337			0.926506			0.463253	−	0.886226i	$-0.346682\pi$
$307$	16.2337			0.926506			0.463253	+	0.886226i	$0.346682\pi$
$308$		0			0
$309$	12.1470	+	9.49277i	0.691021	+	0.540025i
$310$		0			0
$311$	15.7102			0.890846			0.445423	−	0.895320i	$-0.353053\pi$
$311$	15.7102			0.890846			0.445423	+	0.895320i	$0.353053\pi$
$312$		0			0
$313$	33.0387			1.86746			0.933729	−	0.357979i	$-0.116534\pi$
$313$	33.0387			1.86746			0.933729	+	0.357979i	$0.116534\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	8.26125			0.463998			0.231999	−	0.972716i	$-0.425473\pi$
$317$	8.26125			0.463998			0.231999	+	0.972716i	$0.425473\pi$
$318$		0			0
$319$	2.88437			0.161494
$320$		0			0
$321$	−4.27456	+	30.3874i	−0.238583	+	1.69606i
$322$		0			0
$323$	8.76527			0.487713
$324$		0			0
$325$	−10.3210	−	17.8766i	−0.572508	−	0.991614i
$326$		0			0
$327$	16.3068	+	12.7436i	0.901770	+	0.704722i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	18.2767			1.00458			0.502290	−	0.864699i	$-0.332491\pi$
$331$	18.2767			1.00458			0.502290	+	0.864699i	$0.332491\pi$
$332$		0			0
$333$	0.341559	+	1.37138i	0.0187173	+	0.0751513i
$334$		0			0
$335$	−0.168887	−	0.292520i	−0.00922727	−	0.0159821i
$336$		0			0
$337$	10.6530	−	18.4516i	0.580307	−	1.00512i	−0.415135	−	0.909760i	$-0.636266\pi$
$337$	10.6530	−	18.4516i	0.580307	−	1.00512i	0.995443	−	0.0953621i	$-0.0304009\pi$
$338$		0			0
$339$	−3.62308	+	25.7561i	−0.196779	+	1.39888i
$340$		0			0
$341$	0.228467	−	0.395716i	0.0123722	−	0.0214292i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−0.0242608	+	0.172468i	−0.00130616	+	0.00928534i
$346$		0			0
$347$	−21.8755			−1.17434			−0.587170	−	0.809463i	$-0.699758\pi$
$347$	−21.8755			−1.17434			−0.587170	+	0.809463i	$0.699758\pi$
$348$		0			0
$349$	2.46155	+	4.26354i	0.131764	+	0.228222i	0.924357	−	0.381530i	$-0.124603\pi$
$349$	2.46155	+	4.26354i	0.131764	+	0.228222i	−0.792593	+	0.609751i	$0.791269\pi$
$350$		0			0
$351$	−12.6038	−	17.3614i	−0.672743	−	0.926684i
$352$		0			0
$353$	−2.30915	+	3.99956i	−0.122903	+	0.212875i	−0.920911	−	0.389772i	$-0.872554\pi$
$353$	−2.30915	+	3.99956i	−0.122903	+	0.212875i	0.798008	+	0.602647i	$0.205887\pi$
$354$		0			0
$355$	−0.0241783	−	0.0418780i	−0.00128325	−	0.00222265i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−13.6695	+	23.6763i	−0.721449	+	1.24959i	0.238970	+	0.971027i	$0.423190\pi$
$359$	−13.6695	+	23.6763i	−0.721449	+	1.24959i	−0.960419	+	0.278559i	$0.910143\pi$
$360$		0			0
$361$	3.74245	+	6.48212i	0.196971	+	0.341164i
$362$		0			0
$363$	14.5833	+	11.3967i	0.765425	+	0.598170i
$364$		0			0
$365$	−0.0795042	+	0.137705i	−0.00416144	+	0.00720783i
$366$		0			0
$367$	−12.0924	+	20.9446i	−0.631217	+	1.09330i	0.356086	+	0.934453i	$0.384111\pi$
$367$	−12.0924	+	20.9446i	−0.631217	+	1.09330i	−0.987303	+	0.158847i	$0.949222\pi$
$368$		0			0
$369$	−4.39044	−	17.6279i	−0.228557	−	0.917674i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−7.11620	−	12.3256i	−0.368463	−	0.638196i	0.620863	−	0.783919i	$-0.286782\pi$
$373$	−7.11620	−	12.3256i	−0.368463	−	0.638196i	−0.989325	+	0.145723i	$0.953449\pi$
$374$		0			0
$375$	−0.359449	+	0.145175i	−0.0185619	+	0.00749678i
$376$		0			0
$377$	21.2449			1.09417
$378$		0			0
$379$	14.5071			0.745178			0.372589	−	0.927996i	$-0.378470\pi$
$379$	14.5071			0.745178			0.372589	+	0.927996i	$0.378470\pi$
$380$		0			0
$381$	6.70527	−	2.70813i	0.343521	−	0.138742i
$382$		0			0
$383$	12.4659	+	21.5916i	0.636979	+	1.10328i	0.986092	+	0.166199i	$0.0531495\pi$
$383$	12.4659	+	21.5916i	0.636979	+	1.10328i	−0.349113	+	0.937080i	$0.613517\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	4.68255	+	1.34397i	0.238028	+	0.0683179i
$388$		0			0
$389$	−15.5536	+	26.9396i	−0.788599	+	1.36589i	0.138226	+	0.990401i	$0.455860\pi$
$389$	−15.5536	+	26.9396i	−0.788599	+	1.36589i	−0.926825	+	0.375493i	$0.877473\pi$
$390$		0			0
$391$	−5.80219	+	10.0497i	−0.293430	+	0.508235i
$392$		0			0
$393$	−8.29617	−	6.48336i	−0.418487	−	0.327042i
$394$		0			0
$395$	−0.0259394	−	0.0449283i	−0.00130515	−	0.00226059i
$396$		0			0
$397$	1.52243	−	2.63693i	0.0764086	−	0.132344i	−0.825289	−	0.564710i	$-0.808988\pi$
$397$	1.52243	−	2.63693i	0.0764086	−	0.132344i	0.901698	+	0.432367i	$0.142321\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−5.73300	−	9.92985i	−0.286292	−	0.495873i	0.686629	−	0.727008i	$-0.259090\pi$
$401$	−5.73300	−	9.92985i	−0.286292	−	0.495873i	−0.972922	+	0.231135i	$0.925756\pi$
$402$		0			0
$403$	1.68278	−	2.91466i	0.0838252	−	0.145190i
$404$		0			0
$405$	−0.177912	+	0.0944828i	−0.00884050	+	0.00469489i
$406$		0			0
$407$	0.132038	+	0.228697i	0.00654489	+	0.0113361i
$408$		0			0
$409$	−5.12492			−0.253411			−0.126706	−	0.991940i	$-0.540440\pi$
$409$	−5.12492			−0.253411			−0.126706	+	0.991940i	$0.540440\pi$
$410$		0			0
$411$	−3.88410	+	27.6117i	−0.191588	+	1.36198i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−0.0857613	+	0.148543i	−0.00420986	+	0.00729169i
$416$		0			0
$417$	0.887143	−	6.30661i	0.0434436	−	0.308836i
$418$		0			0
$419$	−17.2951	+	29.9560i	−0.844921	+	1.46345i	0.0407685	+	0.999169i	$0.487019\pi$
$419$	−17.2951	+	29.9560i	−0.844921	+	1.46345i	−0.885690	+	0.464278i	$0.846314\pi$
$420$		0			0
$421$	−16.3403	−	28.3023i	−0.796379	−	1.37937i	−0.921960	−	0.387285i	$-0.873413\pi$
$421$	−16.3403	−	28.3023i	−0.796379	−	1.37937i	0.125581	−	0.992083i	$-0.459920\pi$
$422$		0			0
$423$	−26.1417	+	25.2320i	−1.27105	+	1.22682i
$424$		0			0
$425$	−12.9139			−0.626417
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−3.15864	−	2.46844i	−0.152501	−	0.119177i
$430$		0			0
$431$	−0.0725515	−	0.125663i	−0.00349468	−	0.00605297i	0.864273	−	0.503023i	$-0.167779\pi$
$431$	−0.0725515	−	0.125663i	−0.00349468	−	0.00605297i	−0.867767	+	0.496970i	$0.834446\pi$
$432$		0			0
$433$	−19.1583			−0.920690			−0.460345	−	0.887740i	$-0.652274\pi$
$433$	−19.1583			−0.920690			−0.460345	+	0.887740i	$0.652274\pi$
$434$		0			0
$435$	0.0277870	−	0.197535i	0.00133229	−	0.00947109i
$436$		0			0
$437$	15.2449			0.729262
$438$		0			0
$439$	−7.58500			−0.362012			−0.181006	−	0.983482i	$-0.557935\pi$
$439$	−7.58500			−0.362012			−0.181006	+	0.983482i	$0.557935\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−3.26484			−0.155117			−0.0775586	−	0.996988i	$-0.524712\pi$
$443$	−3.26484			−0.155117			−0.0775586	+	0.996988i	$0.524712\pi$
$444$		0			0
$445$	−0.0224885			−0.00106606
$446$		0			0
$447$	−12.4952	−	9.76483i	−0.591002	−	0.461861i
$448$		0			0
$449$	19.8316			0.935909			0.467955	−	0.883752i	$-0.344991\pi$
$449$	19.8316			0.935909			0.467955	+	0.883752i	$0.344991\pi$
$450$		0			0
$451$	−1.69724	−	2.93970i	−0.0799197	−	0.138425i
$452$		0			0
$453$	4.48088	−	31.8541i	0.210530	−	1.49664i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−4.46102			−0.208678			−0.104339	−	0.994542i	$-0.533273\pi$
$457$	−4.46102			−0.208678			−0.104339	+	0.994542i	$0.533273\pi$
$458$		0			0
$459$	−13.3489	+	1.39795i	−0.623073	+	0.0652505i
$460$		0			0
$461$	7.88515	+	13.6575i	0.367248	+	0.636092i	0.989134	−	0.147015i	$-0.0469667\pi$
$461$	7.88515	+	13.6575i	0.367248	+	0.636092i	−0.621886	+	0.783108i	$0.713633\pi$
$462$		0			0
$463$	−8.34621	+	14.4561i	−0.387881	+	0.671830i	−0.992164	−	0.124940i	$-0.960126\pi$
$463$	−8.34621	+	14.4561i	−0.387881	+	0.671830i	0.604283	+	0.796770i	$0.293460\pi$
$464$		0			0
$465$	−0.0248995	−	0.0194587i	−0.00115469	−	0.000902375i
$466$		0			0
$467$	14.6974	−	25.4566i	0.680112	−	1.17799i	−0.294834	−	0.955549i	$-0.595264\pi$
$467$	14.6974	−	25.4566i	0.680112	−	1.17799i	0.974946	−	0.222441i	$-0.0714024\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−18.7291	+	7.56433i	−0.862993	+	0.348546i
$472$		0			0
$473$	0.910278			0.0418546
$474$		0			0
$475$	8.48262	+	14.6923i	0.389209	+	0.674131i
$476$		0			0
$477$	8.41557	+	2.41541i	0.385322	+	0.110594i
$478$		0			0
$479$	−9.16675	+	15.8773i	−0.418839	+	0.725451i	−0.995823	−	0.0913046i	$-0.970896\pi$
$479$	−9.16675	+	15.8773i	−0.418839	+	0.725451i	0.576984	+	0.816756i	$0.304230\pi$
$480$		0			0
$481$	0.972530	+	1.68447i	0.0443436	+	0.0768053i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−0.164062	+	0.284163i	−0.00744965	+	0.0129032i
$486$		0			0
$487$	6.24766	+	10.8213i	0.283108	+	0.490358i	0.972149	−	0.234365i	$-0.0753010\pi$
$487$	6.24766	+	10.8213i	0.283108	+	0.490358i	−0.689040	+	0.724723i	$0.741968\pi$
$488$		0			0
$489$	−3.15132	+	22.4024i	−0.142508	+	1.01307i
$490$		0			0
$491$	−1.75354	+	3.03721i	−0.0791359	+	0.137067i	−0.902877	−	0.429898i	$-0.858549\pi$
$491$	−1.75354	+	3.03721i	−0.0791359	+	0.137067i	0.823741	+	0.566966i	$0.191883\pi$
$492$		0			0
$493$	6.64553	−	11.5104i	0.299299	−	0.518402i
$494$		0			0
$495$	−0.0270829	+	0.0261405i	−0.00121728	+	0.00117493i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	16.1819	+	28.0279i	0.724402	+	1.25470i	0.959220	+	0.282662i	$0.0912175\pi$
$499$	16.1819	+	28.0279i	0.724402	+	1.25470i	−0.234817	+	0.972040i	$0.575449\pi$
$500$		0			0
$501$	−3.31158	+	23.5417i	−0.147951	+	1.05177i
$502$		0			0
$503$	−15.3277			−0.683430			−0.341715	−	0.939804i	$-0.611008\pi$
$503$	−15.3277			−0.683430			−0.341715	+	0.939804i	$0.611008\pi$
$504$		0			0
$505$	−0.338985			−0.0150846
$506$		0			0
$507$	−5.52344	−	4.31650i	−0.245305	−	0.191702i
$508$		0			0
$509$	8.47237	+	14.6746i	0.375531	+	0.650439i	0.990406	−	0.138185i	$-0.0441269\pi$
$509$	8.47237	+	14.6746i	0.375531	+	0.650439i	−0.614875	+	0.788625i	$0.710794\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	10.3588	+	14.2689i	0.457352	+	0.629989i
$514$		0			0
$515$	0.0996097	−	0.172529i	0.00438933	−	0.00760254i
$516$		0			0
$517$	−3.39442	+	5.87931i	−0.149287	+	0.258572i
$518$		0			0
$519$	−40.0310	+	16.1677i	−1.75716	+	0.709684i
$520$		0			0
$521$	−9.36977	−	16.2289i	−0.410497	−	0.711002i	0.584447	−	0.811432i	$-0.301311\pi$
$521$	−9.36977	−	16.2289i	−0.410497	−	0.711002i	−0.994944	+	0.100430i	$0.967978\pi$
$522$		0			0
$523$	4.48382	−	7.76620i	0.196064	−	0.339592i	−0.751185	−	0.660092i	$-0.770517\pi$
$523$	4.48382	−	7.76620i	0.196064	−	0.339592i	0.947249	+	0.320499i	$0.103851\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.05277	−	1.82344i	−0.0458592	−	0.0794305i
$528$		0			0
$529$	1.40861	−	2.43978i	0.0612439	−	0.106078i
$530$		0			0
$531$	19.3380	−	18.6651i	0.839197	−	0.809996i
$532$		0			0
$533$	−12.5010	−	21.6524i	−0.541480	−	0.937871i
$534$		0			0
$535$	0.396551			0.0171444
$536$		0			0
$537$	12.5065	+	9.77370i	0.539697	+	0.421766i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−17.5759	+	30.4423i	−0.755646	+	1.30882i	0.189406	+	0.981899i	$0.439344\pi$
$541$	−17.5759	+	30.4423i	−0.755646	+	1.30882i	−0.945052	+	0.326919i	$0.893990\pi$
$542$		0			0
$543$	−1.41756	+	0.572524i	−0.0608333	+	0.0245694i
$544$		0			0
$545$	0.133721	−	0.231612i	0.00572799	−	0.00992117i
$546$		0			0
$547$	7.75354	+	13.4295i	0.331517	+	0.574205i	0.982810	−	0.184622i	$-0.0591061\pi$
$547$	7.75354	+	13.4295i	0.331517	+	0.574205i	−0.651292	+	0.758827i	$0.725773\pi$
$548$		0			0
$549$	4.56282	−	4.40406i	0.194737	−	0.187961i
$550$		0			0
$551$	−17.4607			−0.743850
$552$		0			0
$553$		0			0
$554$		0			0
$555$	0.0169342	−	0.00683940i	0.000718818	−	0.000290317i
$556$		0			0
$557$	−1.48253	−	2.56781i	−0.0628166	−	0.108802i	0.832907	−	0.553413i	$-0.186675\pi$
$557$	−1.48253	−	2.56781i	−0.0628166	−	0.108802i	−0.895723	+	0.444612i	$0.853342\pi$
$558$		0			0
$559$	6.70468			0.283578
$560$		0			0
$561$	−2.32543	+	0.939196i	−0.0981798	+	0.0396529i
$562$		0			0
$563$	−24.3713			−1.02713			−0.513564	−	0.858051i	$-0.671675\pi$
$563$	−24.3713			−1.02713			−0.513564	+	0.858051i	$0.671675\pi$
$564$		0			0
$565$	0.336113			0.0141404
$566$		0			0
$567$		0			0
$568$		0			0
$569$	44.9602			1.88483			0.942414	−	0.334448i	$-0.108550\pi$
$569$	44.9602			1.88483			0.942414	+	0.334448i	$0.108550\pi$
$570$		0			0
$571$	−15.6776			−0.656087			−0.328043	−	0.944663i	$-0.606389\pi$
$571$	−15.6776			−0.656087			−0.328043	+	0.944663i	$0.606389\pi$
$572$		0			0
$573$	−26.6840	+	10.7771i	−1.11474	+	0.450221i
$574$		0			0
$575$	−22.4604			−0.936662
$576$		0			0
$577$	13.7485	+	23.8132i	0.572360	+	0.991356i	0.996323	+	0.0856765i	$0.0273051\pi$
$577$	13.7485	+	23.8132i	0.572360	+	0.991356i	−0.423963	+	0.905679i	$0.639362\pi$
$578$		0			0
$579$	29.8507	−	12.0561i	1.24055	−	0.501035i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	1.63597			0.0677549
$584$		0			0
$585$	−0.199480	+	0.192539i	−0.00824747	+	0.00796049i
$586$		0			0
$587$	−13.3162	−	23.0644i	−0.549619	−	0.951968i	−0.998300	−	0.0582763i	$-0.981440\pi$
$587$	−13.3162	−	23.0644i	−0.549619	−	0.951968i	0.448681	−	0.893692i	$-0.351894\pi$
$588$		0			0
$589$	−1.38304	+	2.39549i	−0.0569871	+	0.0987045i
$590$		0			0
$591$	37.5866	−	15.1805i	1.54611	−	0.624442i
$592$		0			0
$593$	8.87994	−	15.3805i	0.364656	−	0.631602i	−0.624065	−	0.781372i	$-0.714520\pi$
$593$	8.87994	−	15.3805i	0.364656	−	0.631602i	0.988721	+	0.149770i	$0.0478534\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	11.0114	+	8.60531i	0.450668	+	0.352192i
$598$		0			0
$599$	16.5809			0.677475			0.338738	−	0.940881i	$-0.390000\pi$
$599$	16.5809			0.677475			0.338738	+	0.940881i	$0.390000\pi$
$600$		0			0
$601$	−12.3406	−	21.3746i	−0.503384	−	0.871886i	−0.999992	−	0.00391177i	$-0.998755\pi$
$601$	−12.3406	−	21.3746i	−0.503384	−	0.871886i	0.496608	−	0.867975i	$-0.334578\pi$
$602$		0			0
$603$	32.5743	−	31.4408i	1.32653	−	1.28037i
$604$		0			0
$605$	0.119588	−	0.207132i	0.00486194	−	0.00842112i
$606$		0			0
$607$	6.19000	+	10.7214i	0.251244	+	0.435168i	0.963869	−	0.266378i	$-0.0858269\pi$
$607$	6.19000	+	10.7214i	0.251244	+	0.435168i	−0.712624	+	0.701546i	$0.752494\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−25.0017	+	43.3042i	−1.01146	+	1.75190i
$612$		0			0
$613$	2.74800	+	4.75968i	0.110991	+	0.192242i	0.916170	−	0.400790i	$-0.131264\pi$
$613$	2.74800	+	4.75968i	0.110991	+	0.192242i	−0.805179	+	0.593032i	$0.797931\pi$
$614$		0			0
$615$	−0.217675	+	0.0879146i	−0.00877750	+	0.00354506i
$616$		0			0
$617$	−11.4573	+	19.8446i	−0.461254	+	0.798916i	−0.999024	−	0.0441763i	$-0.985934\pi$
$617$	−11.4573	+	19.8446i	−0.461254	+	0.798916i	0.537770	+	0.843092i	$0.319267\pi$
$618$		0			0
$619$	−3.49256	+	6.04930i	−0.140378	+	0.243142i	−0.927639	−	0.373478i	$-0.878165\pi$
$619$	−3.49256	+	6.04930i	−0.140378	+	0.243142i	0.787261	+	0.616620i	$0.211498\pi$
$620$		0			0
$621$	−23.2169	+	2.43136i	−0.931661	+	0.0975671i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−12.4962	−	21.6441i	−0.499850	−	0.865765i
$626$		0			0
$627$	2.59601	+	2.02875i	0.103675	+	0.0810206i
$628$		0			0
$629$	1.21685			0.0485191
$630$		0			0
$631$	−14.7028			−0.585310			−0.292655	−	0.956218i	$-0.594539\pi$
$631$	−14.7028			−0.585310			−0.292655	+	0.956218i	$0.594539\pi$
$632$		0			0
$633$	3.35195	−	23.8287i	0.133228	−	0.947105i
$634$		0			0
$635$	−0.0467249	−	0.0809300i	−0.00185422	−	0.00321161i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	4.66342	−	4.50116i	0.184482	−	0.178063i
$640$		0			0
$641$	10.8057	−	18.7161i	0.426801	−	0.739241i	−0.569786	−	0.821793i	$-0.692974\pi$
$641$	10.8057	−	18.7161i	0.426801	−	0.739241i	0.996587	+	0.0825523i	$0.0263072\pi$
$642$		0			0
$643$	−6.78105	+	11.7451i	−0.267418	+	0.463182i	−0.968194	−	0.250199i	$-0.919504\pi$
$643$	−6.78105	+	11.7451i	−0.267418	+	0.463182i	0.700776	+	0.713381i	$0.252837\pi$
$644$		0			0
$645$	0.00876931	−	0.0623401i	0.000345291	−	0.00245464i
$646$		0			0
$647$	10.2074	+	17.6798i	0.401295	+	0.695063i	0.993882	−	0.110443i	$-0.0352269\pi$
$647$	10.2074	+	17.6798i	0.401295	+	0.695063i	−0.592587	+	0.805506i	$0.701894\pi$
$648$		0			0
$649$	2.51098	−	4.34915i	0.0985647	−	0.170719i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−24.3462	−	42.1689i	−0.952741	−	1.65020i	−0.739454	−	0.673207i	$-0.764916\pi$
$653$	−24.3462	−	42.1689i	−0.952741	−	1.65020i	−0.213287	−	0.976990i	$-0.568417\pi$
$654$		0			0
$655$	−0.0680313	+	0.117834i	−0.00265820	+	0.00460414i
$656$		0			0
$657$	−20.4852	−	5.87961i	−0.799205	−	0.229385i
$658$		0			0
$659$	−7.65029	−	13.2507i	−0.298013	−	0.516174i	0.677668	−	0.735368i	$-0.262991\pi$
$659$	−7.65029	−	13.2507i	−0.298013	−	0.516174i	−0.975681	+	0.219194i	$0.929657\pi$
$660$		0			0
$661$	17.5499			0.682612			0.341306	−	0.939952i	$-0.389131\pi$
$661$	17.5499			0.682612			0.341306	+	0.939952i	$0.389131\pi$
$662$		0			0
$663$	−17.1280	+	6.91767i	−0.665197	+	0.268660i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	11.5581	−	20.0193i	0.447533	−	0.775150i
$668$		0			0
$669$	22.6162	+	17.6742i	0.874391	+	0.683326i
$670$		0			0
$671$	0.592470	−	1.02619i	0.0228721	−	0.0396156i
$672$		0			0
$673$	3.79336	+	6.57029i	0.146223	+	0.253266i	0.929829	−	0.367993i	$-0.119955\pi$
$673$	3.79336	+	6.57029i	0.146223	+	0.253266i	−0.783605	+	0.621259i	$0.786622\pi$
$674$		0			0
$675$	−15.2617	−	21.0225i	−0.587422	−	0.809157i
$676$		0			0
$677$	−11.5325			−0.443232			−0.221616	−	0.975134i	$-0.571133\pi$
$677$	−11.5325			−0.443232			−0.221616	+	0.975134i	$0.571133\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−1.47807	+	10.5075i	−0.0566399	+	0.402648i
$682$		0			0
$683$	7.47937	+	12.9546i	0.286190	+	0.495696i	0.972897	−	0.231239i	$-0.0742778\pi$
$683$	7.47937	+	12.9546i	0.286190	+	0.495696i	−0.686707	+	0.726934i	$0.740944\pi$
$684$		0			0
$685$	0.360328			0.0137674
$686$		0			0
$687$	39.3467	+	30.7490i	1.50117	+	1.17315i
$688$		0			0
$689$	12.0498			0.459060
$690$		0			0
$691$	−19.8961			−0.756882			−0.378441	−	0.925625i	$-0.623540\pi$
$691$	−19.8961			−0.756882			−0.378441	+	0.925625i	$0.623540\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−0.0823002			−0.00312183
$696$		0			0
$697$	−15.6416			−0.592467
$698$		0			0
$699$	4.07744	−	28.9861i	0.154223	−	1.09636i
$700$		0			0
$701$	34.9655			1.32063			0.660315	−	0.750989i	$-0.270423\pi$
$701$	34.9655			1.32063			0.660315	+	0.750989i	$0.270423\pi$
$702$		0			0
$703$	−0.799300	−	1.38443i	−0.0301462	−	0.0522147i
$704$		0			0
$705$	0.369942	+	0.289105i	0.0139328	+	0.0108883i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−19.3045			−0.724998			−0.362499	−	0.931984i	$-0.618076\pi$
$709$	−19.3045			−0.724998			−0.362499	+	0.931984i	$0.618076\pi$
$710$		0			0
$711$	5.00310	−	4.82901i	0.187631	−	0.181102i
$712$		0			0
$713$	−1.83101	−	3.17140i	−0.0685719	−	0.118770i
$714$		0			0
$715$	−0.0259019	+	0.0448634i	−0.000968676	+	0.00167780i
$716$		0			0
$717$	−3.68656	+	26.2074i	−0.137677	+	0.978731i
$718$		0			0
$719$	17.7284	−	30.7066i	0.661159	−	1.14516i	−0.319152	−	0.947704i	$-0.603398\pi$
$719$	17.7284	−	30.7066i	0.661159	−	1.14516i	0.980311	−	0.197458i	$-0.0632686\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−1.01196	+	7.19389i	−0.0376350	+	0.267544i
$724$		0			0
$725$	25.7249			0.955400
$726$		0			0
$727$	2.27159	+	3.93452i	0.0842487	+	0.145923i	0.905071	−	0.425261i	$-0.139818\pi$
$727$	2.27159	+	3.93452i	0.0842487	+	0.145923i	−0.820822	+	0.571184i	$0.806484\pi$
$728$		0			0
$729$	−18.0514	−	20.0785i	−0.668571	−	0.743648i
$730$		0			0
$731$	2.09726	−	3.63257i	0.0775701	−	0.134355i
$732$		0			0
$733$	−16.6444	−	28.8290i	−0.614777	−	1.06482i	−0.990424	−	0.138062i	$-0.955913\pi$
$733$	−16.6444	−	28.8290i	−0.614777	−	1.06482i	0.375647	−	0.926763i	$-0.377421\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	4.22968	−	7.32602i	0.155802	−	0.269858i
$738$		0			0
$739$	−20.6599	−	35.7841i	−0.759988	−	1.31634i	−0.942856	−	0.333200i	$-0.891871\pi$
$739$	−20.6599	−	35.7841i	−0.759988	−	1.31634i	0.182868	−	0.983137i	$-0.441462\pi$
$740$		0			0
$741$	19.1210	+	14.9428i	0.702428	+	0.548939i
$742$		0			0
$743$	−13.7638	+	23.8396i	−0.504946	+	0.874592i	0.495038	+	0.868871i	$0.335154\pi$
$743$	−13.7638	+	23.8396i	−0.504946	+	0.874592i	−0.999984	+	0.00572027i	$0.998179\pi$
$744$		0			0
$745$	−0.102465	+	0.177474i	−0.00375401	+	0.00650214i
$746$		0			0
$747$	−22.0974	−	6.34234i	−0.808503	−	0.232054i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−6.58398	−	11.4038i	−0.240253	−	0.416130i	0.720533	−	0.693420i	$-0.243897\pi$
$751$	−6.58398	−	11.4038i	−0.240253	−	0.416130i	−0.960786	+	0.277290i	$0.910564\pi$
$752$		0			0
$753$	31.6552	−	12.7849i	1.15358	−	0.465908i
$754$		0			0
$755$	−0.415692			−0.0151286
$756$		0			0
$757$	−13.7925			−0.501297			−0.250648	−	0.968078i	$-0.580644\pi$
$757$	−13.7925			−0.501297			−0.250648	+	0.968078i	$0.580644\pi$
$758$		0			0
$759$	−4.04448	+	1.63348i	−0.146805	+	0.0592917i
$760$		0			0
$761$	15.6055	+	27.0294i	0.565697	+	0.979816i	0.996984	+	0.0776016i	$0.0247262\pi$
$761$	15.6055	+	27.0294i	0.565697	+	0.979816i	−0.431287	+	0.902215i	$0.641940\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	0.0419181	+	0.168304i	0.00151555	+	0.00608506i
$766$		0			0
$767$	18.4947	−	32.0338i	0.667806	−	1.15667i
$768$		0			0
$769$	19.1337	−	33.1405i	0.689977	−	1.19508i	−0.281867	−	0.959453i	$-0.590954\pi$
$769$	19.1337	−	33.1405i	0.689977	−	1.19508i	0.971845	−	0.235622i	$-0.0757128\pi$
$770$		0			0
$771$	6.74346	+	5.26993i	0.242860	+	0.189792i
$772$		0			0
$773$	−3.73395	−	6.46739i	−0.134301	−	0.232616i	0.791029	−	0.611778i	$-0.209545\pi$
$773$	−3.73395	−	6.46739i	−0.134301	−	0.232616i	−0.925330	+	0.379162i	$0.876212\pi$
$774$		0			0
$775$	2.03764	−	3.52929i	0.0731941	−	0.126776i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	10.2743	+	17.7956i	0.368115	+	0.637594i
$780$		0			0
$781$	0.605533	−	1.04881i	0.0216677	−	0.0375295i
$782$		0			0
$783$	26.5914	−	2.78475i	0.950299	−	0.0995189i
$784$		0			0
$785$	0.130512	+	0.226053i	0.00465817	+	0.00806819i
$786$		0			0
$787$	20.6901			0.737523			0.368761	−	0.929524i	$-0.379782\pi$
$787$	20.6901			0.737523			0.368761	+	0.929524i	$0.379782\pi$
$788$		0			0
$789$	−6.56193	+	46.6481i	−0.233611	+	1.66072i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	4.36386	−	7.55842i	0.154965	−	0.268407i
$794$		0			0
$795$	0.0157604	−	0.112039i	0.000558963	−	0.00397361i
$796$		0			0
$797$	15.8354	−	27.4276i	0.560917	−	0.971537i	−0.436500	−	0.899704i	$-0.643782\pi$
$797$	15.8354	−	27.4276i	0.560917	−	0.971537i	0.997417	−	0.0718325i	$-0.0228847\pi$
$798$		0			0
$799$	15.6414	+	27.0916i	0.553352	+	0.958433i
$800$		0			0
$801$	−0.728465	−	2.92484i	−0.0257390	−	0.103344i
$802$		0			0
$803$	−3.98229			−0.140532
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−28.9009	−	22.5857i	−1.01736	−	0.795055i
$808$		0			0
$809$	−24.0430	−	41.6438i	−0.845308	−	1.46412i	−0.885353	−	0.464919i	$-0.846083\pi$
$809$	−24.0430	−	41.6438i	−0.845308	−	1.46412i	0.0400451	−	0.999198i	$-0.487250\pi$
$810$		0			0
$811$	17.6685			0.620427			0.310213	−	0.950667i	$-0.399600\pi$
$811$	17.6685			0.620427			0.310213	+	0.950667i	$0.399600\pi$
$812$		0			0
$813$	−5.67943	+	40.3745i	−0.199186	+	1.41600i
$814$		0			0
$815$	0.292348			0.0102405
$816$		0			0
$817$	−5.51042			−0.192785
$818$		0			0
$819$		0			0
$820$		0			0
$821$	28.9979			1.01203			0.506017	−	0.862523i	$-0.331117\pi$
$821$	28.9979			1.01203			0.506017	+	0.862523i	$0.331117\pi$
$822$		0			0
$823$	13.7745			0.480147			0.240074	−	0.970755i	$-0.422828\pi$
$823$	13.7745			0.480147			0.240074	+	0.970755i	$0.422828\pi$
$824$		0			0
$825$	−3.82472	−	2.98897i	−0.133160	−	0.104063i
$826$		0			0
$827$	21.4150			0.744673			0.372337	−	0.928098i	$-0.378557\pi$
$827$	21.4150			0.744673			0.372337	+	0.928098i	$0.378557\pi$
$828$		0			0
$829$	−9.40772	−	16.2947i	−0.326744	−	0.565937i	0.655120	−	0.755525i	$-0.272618\pi$
$829$	−9.40772	−	16.2947i	−0.326744	−	0.565937i	−0.981864	+	0.189588i	$0.939285\pi$
$830$		0			0
$831$	−4.90069	+	34.8385i	−0.170003	+	1.20853i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	0.307216			0.0106316
$836$		0			0
$837$	1.72422	−	3.86874i	0.0595977	−	0.133723i
$838$		0			0
$839$	−21.4124	−	37.0874i	−0.739239	−	1.28040i	−0.952839	−	0.303477i	$-0.901852\pi$
$839$	−21.4124	−	37.0874i	−0.739239	−	1.28040i	0.213600	−	0.976921i	$-0.431481\pi$
$840$		0			0
$841$	1.26191	−	2.18569i	0.0435142	−	0.0753688i
$842$		0			0
$843$	−26.2899	−	20.5453i	−0.905473	−	0.707616i
$844$		0			0
$845$	−0.0452940	+	0.0784515i	−0.00155816	+	0.00269881i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−28.9017	+	11.6728i	−0.991905	+	0.400611i
$850$		0			0
$851$	2.11639			0.0725491
$852$		0			0
$853$	−13.3281	−	23.0849i	−0.456345	−	0.790412i	0.542420	−	0.840108i	$-0.317508\pi$
$853$	−13.3281	−	23.0849i	−0.456345	−	0.790412i	−0.998764	+	0.0496954i	$0.984175\pi$
$854$		0			0
$855$	0.163948	−	0.158243i	0.00560689	−	0.00541180i
$856$		0			0
$857$	−15.5907	+	27.0040i	−0.532570	+	0.922438i	0.466707	+	0.884412i	$0.345440\pi$
$857$	−15.5907	+	27.0040i	−0.532570	+	0.922438i	−0.999277	+	0.0380257i	$0.987893\pi$
$858$		0			0
$859$	−26.9668	−	46.7078i	−0.920094	−	1.59365i	−0.799267	−	0.600976i	$-0.794779\pi$
$859$	−26.9668	−	46.7078i	−0.920094	−	1.59365i	−0.120827	−	0.992674i	$-0.538555\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	16.8755	−	29.2292i	0.574448	−	0.994974i	−0.421653	−	0.906757i	$-0.638550\pi$
$863$	16.8755	−	29.2292i	0.574448	−	0.994974i	0.996101	−	0.0882164i	$-0.0281167\pi$
$864$		0			0
$865$	0.278952	+	0.483158i	0.00948464	+	0.0164279i
$866$		0			0
$867$	2.49181	−	17.7140i	0.0846263	−	0.601600i
$868$		0			0
$869$	0.649639	−	1.12521i	0.0220375	−	0.0381700i
$870$		0			0
$871$	31.1538	−	53.9600i	1.05561	−	1.82837i
$872$		0			0
$873$	−42.2725	−	12.1329i	−1.43071	−	0.410637i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1.60808	−	2.78527i	−0.0543009	−	0.0940519i	0.837597	−	0.546288i	$-0.183960\pi$
$877$	−1.60808	−	2.78527i	−0.0543009	−	0.0940519i	−0.891898	+	0.452236i	$0.850626\pi$
$878$		0			0
$879$	−2.54490	+	18.0914i	−0.0858373	+	0.610209i
$880$		0			0
$881$	35.9141			1.20998			0.604989	−	0.796234i	$-0.293178\pi$
$881$	35.9141			1.20998			0.604989	+	0.796234i	$0.293178\pi$
$882$		0			0
$883$	4.58572			0.154322			0.0771609	−	0.997019i	$-0.475414\pi$
$883$	4.58572			0.154322			0.0771609	+	0.997019i	$0.475414\pi$
$884$		0			0
$885$	−0.273660	−	0.213862i	−0.00919899	−	0.00718890i
$886$		0			0
$887$	27.5154	+	47.6581i	0.923877	+	1.60020i	0.793357	+	0.608757i	$0.208332\pi$
$887$	27.5154	+	47.6581i	0.923877	+	1.60020i	0.130521	+	0.991446i	$0.458335\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−4.27711	−	2.67562i	−0.143288	−	0.0896366i
$892$		0			0
$893$	20.5483	−	35.5907i	0.687624	−	1.19100i
$894$		0			0
$895$	0.102558	−	0.177635i	0.00342812	−	0.00593768i
$896$		0			0
$897$	−29.7897	+	12.0315i	−0.994649	+	0.401719i
$898$		0			0
$899$	2.09714	+	3.63236i	0.0699436	+	0.121146i
$900$		0			0
$901$	3.76924	−	6.52851i	0.125572	−	0.217496i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.00987810	+	0.0171094i	0.000328359	+	0.000568735i
$906$		0			0
$907$	6.38823	−	11.0647i	0.212118	−	0.367399i	−0.740259	−	0.672321i	$-0.765297\pi$
$907$	6.38823	−	11.0647i	0.212118	−	0.367399i	0.952377	+	0.304923i	$0.0986307\pi$
$908$		0			0
$909$	−10.9807	−	44.0881i	−0.364205	−	1.46231i
$910$		0			0
$911$	−15.9053	−	27.5489i	−0.526968	−	0.912735i	−0.999506	−	0.0314246i	$-0.989996\pi$
$911$	−15.9053	−	27.5489i	−0.526968	−	0.912735i	0.472539	−	0.881310i	$-0.343338\pi$
$912$		0			0
$913$	−4.29570			−0.142167
$914$		0			0
$915$	−0.0645705	−	0.0504611i	−0.00213464	−	0.00166819i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	29.2724	−	50.7013i	0.965607	−	1.67248i	0.257631	−	0.966243i	$-0.417058\pi$
$919$	29.2724	−	50.7013i	0.965607	−	1.67248i	0.707975	−	0.706237i	$-0.249609\pi$
$920$		0			0
$921$	26.0715	−	10.5298i	0.859085	−	0.346968i
$922$		0			0
$923$	4.46007	−	7.72506i	0.146805	−	0.254274i
$924$		0			0
$925$	1.17761	+	2.03969i	0.0387197	+	0.0670644i
$926$		0			0
$927$	25.6656	+	7.36647i	0.842970	+	0.241947i
$928$		0			0
$929$	12.7327			0.417746			0.208873	−	0.977943i	$-0.433020\pi$
$929$	12.7327			0.417746			0.208873	+	0.977943i	$0.433020\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	25.2308	−	10.1902i	0.826020	−	0.333613i
$934$		0			0
$935$	0.0162045	+	0.0280670i	0.000529944	+	0.000917891i
$936$		0			0
$937$	−28.2201			−0.921911			−0.460956	−	0.887423i	$-0.652493\pi$
$937$	−28.2201			−0.921911			−0.460956	+	0.887423i	$0.652493\pi$
$938$		0			0
$939$	53.0605	−	21.4301i	1.73157	−	0.699345i
$940$		0			0
$941$	48.6046			1.58446			0.792232	−	0.610220i	$-0.208919\pi$
$941$	48.6046			1.58446			0.792232	+	0.610220i	$0.208919\pi$
$942$		0			0
$943$	−27.2044			−0.885898
$944$		0			0
$945$		0			0
$946$		0			0
$947$	12.2132			0.396875			0.198437	−	0.980114i	$-0.436413\pi$
$947$	12.2132			0.396875			0.198437	+	0.980114i	$0.436413\pi$
$948$		0			0
$949$	−29.3316			−0.952145
$950$		0			0
$951$	13.2677	−	5.35855i	0.430234	−	0.173763i
$952$		0			0
$953$	22.7206			0.735993			0.367996	−	0.929827i	$-0.380044\pi$
$953$	22.7206			0.735993			0.367996	+	0.929827i	$0.380044\pi$
$954$		0			0
$955$	0.185944	+	0.322065i	0.00601701	+	0.0104218i
$956$		0			0
$957$	4.63233	−	1.87091i	0.149742	−	0.0604778i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−30.3356			−0.978566
$962$		0			0
$963$	12.8454	+	51.5752i	0.413937	+	1.66199i
$964$		0			0
$965$	−0.208012	−	0.360287i	−0.00669613	−	0.0115980i
$966$		0			0
$967$	−26.9926	+	46.7526i	−0.868024	+	1.50346i	−0.00401026	+	0.999992i	$0.501277\pi$
$967$	−26.9926	+	46.7526i	−0.868024	+	1.50346i	−0.864013	+	0.503469i	$0.832057\pi$
$968$		0			0
$969$	14.0771	−	5.68547i	0.452222	−	0.182644i
$970$		0			0
$971$	20.3187	−	35.1930i	0.652059	−	1.12940i	−0.330564	−	0.943784i	$-0.607239\pi$
$971$	20.3187	−	35.1930i	0.652059	−	1.12940i	0.982623	−	0.185615i	$-0.0594278\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−28.1711	−	22.0154i	−0.902197	−	0.705056i
$976$		0			0
$977$	20.0440			0.641264			0.320632	−	0.947204i	$-0.396105\pi$
$977$	20.0440			0.641264			0.320632	+	0.947204i	$0.396105\pi$
$978$		0			0
$979$	−0.281607	−	0.487757i	−0.00900018	−	0.0155888i
$980$		0			0
$981$	34.4549	+	9.88914i	1.10006	+	0.315736i
$982$		0			0
$983$	4.83700	−	8.37793i	0.154276	−	0.267214i	−0.778519	−	0.627621i	$-0.784029\pi$
$983$	4.83700	−	8.37793i	0.154276	−	0.267214i	0.932795	+	0.360407i	$0.117362\pi$
$984$		0			0
$985$	−0.261918	−	0.453655i	−0.00834540	−	0.0144547i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	3.64764	−	6.31789i	0.115988	−	0.200897i
$990$		0			0
$991$	−6.46878	−	11.2043i	−0.205488	−	0.355915i	0.744800	−	0.667287i	$-0.232545\pi$
$991$	−6.46878	−	11.2043i	−0.205488	−	0.355915i	−0.950288	+	0.311372i	$0.899211\pi$
$992$		0			0
$993$	29.3526	−	11.8550i	0.931478	−	0.376206i
$994$		0			0
$995$	0.0902974	−	0.156400i	0.00286262	−	0.00495820i
$996$		0			0
$997$	−0.856372	+	1.48328i	−0.0271216	+	0.0469759i	−0.879268	−	0.476328i	$-0.841967\pi$
$997$	−0.856372	+	1.48328i	−0.0271216	+	0.0469759i	0.852146	+	0.523304i	$0.175301\pi$
$998$		0			0
$999$	1.43808	+	1.98091i	0.0454987	+	0.0626732i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.i.j.373.11		24
3.2	odd	2		5292.2.i.j.1549.7		24
7.2	even	3		1764.2.j.i.589.6	✓	24
7.3	odd	6		1764.2.l.j.949.10		24
7.4	even	3		1764.2.l.j.949.3		24
7.5	odd	6		1764.2.j.i.589.7	yes	24
7.6	odd	2	inner	1764.2.i.j.373.2		24
9.2	odd	6		5292.2.l.j.3313.6		24
9.7	even	3		1764.2.l.j.961.3		24
21.2	odd	6		5292.2.j.i.1765.7		24
21.5	even	6		5292.2.j.i.1765.6		24
21.11	odd	6		5292.2.l.j.361.6		24
21.17	even	6		5292.2.l.j.361.7		24
21.20	even	2		5292.2.i.j.1549.6		24
63.2	odd	6		5292.2.j.i.3529.7		24
63.11	odd	6		5292.2.i.j.2125.7		24
63.16	even	3		1764.2.j.i.1177.6	yes	24
63.20	even	6		5292.2.l.j.3313.7		24
63.25	even	3	inner	1764.2.i.j.1537.11		24
63.34	odd	6		1764.2.l.j.961.10		24
63.38	even	6		5292.2.i.j.2125.6		24
63.47	even	6		5292.2.j.i.3529.6		24
63.52	odd	6	inner	1764.2.i.j.1537.2		24
63.61	odd	6		1764.2.j.i.1177.7	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1764.2.i.j.373.2		24	7.6	odd	2	inner
1764.2.i.j.373.11		24	1.1	even	1	trivial
1764.2.i.j.1537.2		24	63.52	odd	6	inner
1764.2.i.j.1537.11		24	63.25	even	3	inner
1764.2.j.i.589.6	✓	24	7.2	even	3
1764.2.j.i.589.7	yes	24	7.5	odd	6
1764.2.j.i.1177.6	yes	24	63.16	even	3
1764.2.j.i.1177.7	yes	24	63.61	odd	6
1764.2.l.j.949.3		24	7.4	even	3
1764.2.l.j.949.10		24	7.3	odd	6
1764.2.l.j.961.3		24	9.7	even	3
1764.2.l.j.961.10		24	63.34	odd	6
5292.2.i.j.1549.6		24	21.20	even	2
5292.2.i.j.1549.7		24	3.2	odd	2
5292.2.i.j.2125.6		24	63.38	even	6
5292.2.i.j.2125.7		24	63.11	odd	6
5292.2.j.i.1765.6		24	21.5	even	6
5292.2.j.i.1765.7		24	21.2	odd	6
5292.2.j.i.3529.6		24	63.47	even	6
5292.2.j.i.3529.7		24	63.2	odd	6
5292.2.l.j.361.6		24	21.11	odd	6
5292.2.l.j.361.7		24	21.17	even	6
5292.2.l.j.3313.6		24	9.2	odd	6
5292.2.l.j.3313.7		24	63.20	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.60601 - 0.648636i) q^{3} +(-0.0111913 - 0.0193839i) q^{5} +(2.15854 - 2.08343i) q^{9} +(0.280281 - 0.485460i) q^{11} +(2.06442 - 3.57567i) q^{13} +(-0.0305465 - 0.0238717i) q^{15} +(-1.29152 - 2.23698i) q^{17} +(-1.69669 + 2.93876i) q^{19} +(-2.24626 - 3.89064i) q^{23} +(2.49975 - 4.32969i) q^{25} +(2.11525 - 4.74613i) q^{27} +(2.57275 + 4.45613i) q^{29} +0.815136 q^{31} +(0.135247 - 0.961455i) q^{33} +(-0.235546 + 0.407978i) q^{37} +(0.996163 - 7.08162i) q^{39} +(3.02774 - 5.24420i) q^{41} +(0.811935 + 1.40631i) q^{43} +(-0.0645420 - 0.0185247i) q^{45} -12.1108 q^{47} +(-3.52519 - 2.75489i) q^{51} +(1.45922 + 2.52745i) q^{53} -0.0125468 q^{55} +(-0.818723 + 5.82022i) q^{57} +8.95882 q^{59} +2.11385 q^{61} -0.0924141 q^{65} +15.0909 q^{67} +(-6.13113 - 4.79140i) q^{69} +2.16045 q^{71} +(-3.55205 - 6.15233i) q^{73} +(1.20623 - 8.57496i) q^{75} +2.31781 q^{79} +(0.318608 - 8.99436i) q^{81} +(-3.83160 - 6.63653i) q^{83} +(-0.0289077 + 0.0500695i) q^{85} +(7.02228 + 5.48782i) q^{87} +(0.502365 - 0.870122i) q^{89} +(1.30912 - 0.528727i) q^{93} +0.0759530 q^{95} +(-7.32986 - 12.6957i) q^{97} +(-0.406427 - 1.63183i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{9} - 4 q^{11} - 28 q^{15} - 8 q^{23} - 12 q^{25} - 32 q^{29} - 12 q^{37} + 8 q^{51} - 16 q^{53} + 52 q^{57} + 72 q^{65} - 24 q^{67} + 48 q^{71} - 24 q^{79} - 8 q^{81} + 12 q^{85} - 48 q^{93}+ \cdots - 4 q^{99}+O(q^{100}) \) 24 * q - 4 * q^9 - 4 * q^11 - 28 * q^15 - 8 * q^23 - 12 * q^25 - 32 * q^29 - 12 * q^37 + 8 * q^51 - 16 * q^53 + 52 * q^57 + 72 * q^65 - 24 * q^67 + 48 * q^71 - 24 * q^79 - 8 * q^81 + 12 * q^85 - 48 * q^93 - 64 * q^95 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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