LMFDB - Embedded newform 900.3.u.c.149.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(149,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("900.149");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	900.u (of order $6$, 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:	$24.5232237924$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			149.8
Character	$\chi$	$=$	900.149
Dual form			900.3.u.c.749.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.783177 + 2.89597i) q^{3} +(-4.08158 + 2.35650i) q^{7} +(-7.77327 + 4.53611i) q^{9} +O(q^{10})$	\(q+(0.783177 + 2.89597i) q^{3} +(-4.08158 + 2.35650i) q^{7} +(-7.77327 + 4.53611i) q^{9} +(16.6882 - 9.63493i) q^{11} +(8.11434 + 4.68482i) q^{13} +16.2489 q^{17} +19.0505 q^{19} +(-10.0210 - 9.97458i) q^{21} +(-8.30327 + 14.3817i) q^{23} +(-19.2243 - 18.9586i) q^{27} +(3.87581 - 2.23770i) q^{29} +(-7.19383 + 12.4601i) q^{31} +(40.9723 + 40.7826i) q^{33} +55.6092i q^{37} +(-7.21211 + 27.1679i) q^{39} +(26.7067 + 15.4191i) q^{41} +(-37.3322 + 21.5538i) q^{43} +(20.7446 + 35.9308i) q^{47} +(-13.3938 + 23.1987i) q^{49} +(12.7257 + 47.0562i) q^{51} -30.7037 q^{53} +(14.9199 + 55.1696i) q^{57} +(-74.4236 - 42.9685i) q^{59} +(-51.7462 - 89.6270i) q^{61} +(21.0379 - 36.8323i) q^{63} +(107.020 + 61.7879i) q^{67} +(-48.1518 - 12.7826i) q^{69} +111.409i q^{71} -90.5781i q^{73} +(-45.4095 + 78.6515i) q^{77} +(-41.6569 - 72.1519i) q^{79} +(39.8473 - 70.5208i) q^{81} +(17.9251 + 31.0471i) q^{83} +(9.51576 + 9.47171i) q^{87} +84.9144i q^{89} -44.1591 q^{91} +(-41.7181 - 11.0747i) q^{93} +(91.1508 - 52.6259i) q^{97} +(-86.0166 + 150.594i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 52 q^{9}+O(q^{10}) $ 24 * q - 52 * q^9	$ 24 q - 52 q^{9} + 96 q^{11} - 144 q^{19} - 256 q^{21} - 300 q^{29} - 24 q^{31} - 80 q^{39} + 180 q^{41} - 96 q^{49} - 288 q^{51} - 96 q^{59} - 156 q^{61} + 300 q^{69} - 240 q^{79} + 868 q^{81} + 240 q^{91} + 240 q^{99}+O(q^{100}) $ 24 * q - 52 * q^9 + 96 * q^11 - 144 * q^19 - 256 * q^21 - 300 * q^29 - 24 * q^31 - 80 * q^39 + 180 * q^41 - 96 * q^49 - 288 * q^51 - 96 * q^59 - 156 * q^61 + 300 * q^69 - 240 * q^79 + 868 * q^81 + 240 * q^91 + 240 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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
$3$	0.783177	+	2.89597i	0.261059	+	0.965323i
$3$	0.783177	+	2.89597i	0.261059	+	0.965323i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−4.08158	+	2.35650i	−0.583083	+	0.336643i	−0.762358	−	0.647156i	$-0.775958\pi$
$7$	−4.08158	+	2.35650i	−0.583083	+	0.336643i	0.179274	+	0.983799i	$0.442625\pi$
$8$		0			0
$9$	−7.77327	+	4.53611i	−0.863696	+	0.504013i
$10$		0			0
$11$	16.6882	−	9.63493i	1.51711	−	0.875902i	0.517310	−	0.855798i	$-0.326934\pi$
$11$	16.6882	−	9.63493i	1.51711	−	0.875902i	0.999798	−	0.0201041i	$-0.00639976\pi$
$12$		0			0
$13$	8.11434	+	4.68482i	0.624180	+	0.360370i	0.778495	−	0.627651i	$-0.215984\pi$
$13$	8.11434	+	4.68482i	0.624180	+	0.360370i	−0.154315	+	0.988022i	$0.549317\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	16.2489			0.955816			0.477908	−	0.878410i	$-0.341395\pi$
$17$	16.2489			0.955816			0.477908	+	0.878410i	$0.341395\pi$
$18$		0			0
$19$	19.0505			1.00266			0.501328	−	0.865257i	$-0.332845\pi$
$19$	19.0505			1.00266			0.501328	+	0.865257i	$0.332845\pi$
$20$		0			0
$21$	−10.0210	−	9.97458i	−0.477189	−	0.474980i
$22$		0			0
$23$	−8.30327	+	14.3817i	−0.361012	+	0.625290i	−0.988128	−	0.153635i	$-0.950902\pi$
$23$	−8.30327	+	14.3817i	−0.361012	+	0.625290i	0.627116	+	0.778926i	$0.284235\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−19.2243	−	18.9586i	−0.712011	−	0.702169i
$28$		0			0
$29$	3.87581	−	2.23770i	0.133649	−	0.0771621i	−0.431685	−	0.902024i	$-0.642081\pi$
$29$	3.87581	−	2.23770i	0.133649	−	0.0771621i	0.565334	+	0.824862i	$0.308747\pi$
$30$		0			0
$31$	−7.19383	+	12.4601i	−0.232059	+	0.401938i	−0.958414	−	0.285382i	$-0.907880\pi$
$31$	−7.19383	+	12.4601i	−0.232059	+	0.401938i	0.726355	+	0.687320i	$0.241213\pi$
$32$		0			0
$33$	40.9723	+	40.7826i	1.24158	+	1.23584i
$34$		0			0
$35$		0			0
$36$		0			0
$37$			55.6092i			1.50295i	0.659761	+	0.751476i	$0.270658\pi$
$37$			55.6092i			1.50295i	−0.659761	+	0.751476i	$0.729342\pi$
$38$		0			0
$39$	−7.21211	+	27.1679i	−0.184926	+	0.696613i
$40$		0			0
$41$	26.7067	+	15.4191i	0.651384	+	0.376077i	0.788986	−	0.614411i	$-0.210606\pi$
$41$	26.7067	+	15.4191i	0.651384	+	0.376077i	−0.137602	+	0.990488i	$0.543940\pi$
$42$		0			0
$43$	−37.3322	+	21.5538i	−0.868191	+	0.501250i	−0.866747	−	0.498749i	$-0.833793\pi$
$43$	−37.3322	+	21.5538i	−0.868191	+	0.501250i	−0.00144406	+	0.999999i	$0.500460\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	20.7446	+	35.9308i	0.441375	+	0.764484i	0.997792	−	0.0664192i	$-0.0211575\pi$
$47$	20.7446	+	35.9308i	0.441375	+	0.764484i	−0.556417	+	0.830903i	$0.687824\pi$
$48$		0			0
$49$	−13.3938	+	23.1987i	−0.273343	+	0.473443i
$50$		0			0
$51$	12.7257	+	47.0562i	0.249524	+	0.922671i
$52$		0			0
$53$	−30.7037			−0.579316			−0.289658	−	0.957130i	$-0.593542\pi$
$53$	−30.7037			−0.579316			−0.289658	+	0.957130i	$0.593542\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	14.9199	+	55.1696i	0.261753	+	0.967887i
$58$		0			0
$59$	−74.4236	−	42.9685i	−1.26142	−	0.728279i	−0.288068	−	0.957610i	$-0.593013\pi$
$59$	−74.4236	−	42.9685i	−1.26142	−	0.728279i	−0.973348	+	0.229331i	$0.926346\pi$
$60$		0			0
$61$	−51.7462	−	89.6270i	−0.848298	−	1.46930i	−0.882726	−	0.469889i	$-0.844294\pi$
$61$	−51.7462	−	89.6270i	−0.848298	−	1.46930i	0.0344274	−	0.999407i	$-0.489039\pi$
$62$		0			0
$63$	21.0379	−	36.8323i	0.333934	−	0.584639i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	107.020	+	61.7879i	1.59731	+	0.922207i	0.992003	+	0.126215i	$0.0402829\pi$
$67$	107.020	+	61.7879i	1.59731	+	0.922207i	0.605307	+	0.795992i	$0.293050\pi$
$68$		0			0
$69$	−48.1518	−	12.7826i	−0.697853	−	0.185255i
$70$		0			0
$71$			111.409i			1.56914i	0.620043	+	0.784568i	$0.287115\pi$
$71$			111.409i			1.56914i	−0.620043	+	0.784568i	$0.712885\pi$
$72$		0			0
$73$		−	90.5781i		−	1.24080i	−0.784287	−	0.620398i	$-0.786971\pi$
$73$		−	90.5781i		−	1.24080i	0.784287	−	0.620398i	$-0.213029\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−45.4095	+	78.6515i	−0.589733	+	1.02145i
$78$		0			0
$79$	−41.6569	−	72.1519i	−0.527302	−	0.913315i	−0.999494	−	0.0318185i	$-0.989870\pi$
$79$	−41.6569	−	72.1519i	−0.527302	−	0.913315i	0.472191	−	0.881496i	$-0.343463\pi$
$80$		0			0
$81$	39.8473	−	70.5208i	0.491942	−	0.870628i
$82$		0			0
$83$	17.9251	+	31.0471i	0.215965	+	0.374062i	0.953571	−	0.301170i	$-0.0973771\pi$
$83$	17.9251	+	31.0471i	0.215965	+	0.374062i	−0.737606	+	0.675231i	$0.764044\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	9.51576	+	9.47171i	0.109377	+	0.108870i
$88$		0			0
$89$			84.9144i			0.954095i	0.878878	+	0.477047i	$0.158293\pi$
$89$			84.9144i			0.954095i	−0.878878	+	0.477047i	$0.841707\pi$
$90$		0			0
$91$	−44.1591			−0.485265
$92$		0			0
$93$	−41.7181	−	11.0747i	−0.448581	−	0.119082i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	91.1508	−	52.6259i	0.939699	−	0.542535i	0.0498329	−	0.998758i	$-0.484131\pi$
$97$	91.1508	−	52.6259i	0.939699	−	0.542535i	0.889866	+	0.456222i	$0.150798\pi$
$98$		0			0
$99$	−86.0166	+	150.594i	−0.868854	+	1.52116i
$100$		0			0
$101$	69.4641	−	40.1051i	0.687763	−	0.397080i	−0.115010	−	0.993364i	$-0.536690\pi$
$101$	69.4641	−	40.1051i	0.687763	−	0.397080i	0.802773	+	0.596284i	$0.203357\pi$
$102$		0			0
$103$	112.947	+	65.2103i	1.09658	+	0.633109i	0.935320	−	0.353803i	$-0.115112\pi$
$103$	112.947	+	65.2103i	1.09658	+	0.633109i	0.161258	+	0.986912i	$0.448445\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−49.8390			−0.465785			−0.232893	−	0.972502i	$-0.574819\pi$
$107$	−49.8390			−0.465785			−0.232893	+	0.972502i	$0.574819\pi$
$108$		0			0
$109$	−121.431			−1.11404			−0.557022	−	0.830498i	$-0.688056\pi$
$109$	−121.431			−1.11404			−0.557022	+	0.830498i	$0.688056\pi$
$110$		0			0
$111$	−161.043	+	43.5519i	−1.45083	+	0.392359i
$112$		0			0
$113$	14.1371	−	24.4862i	0.125107	−	0.216692i	−0.796668	−	0.604418i	$-0.793406\pi$
$113$	14.1371	−	24.4862i	0.125107	−	0.216692i	0.921775	+	0.387725i	$0.126739\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−84.3258	+	0.391246i	−0.720733	+	0.00334398i
$118$		0			0
$119$	−66.3211	+	38.2905i	−0.557320	+	0.321769i
$120$		0			0
$121$	125.164	−	216.790i	1.03441	−	1.79165i
$122$		0			0
$123$	−23.7372	+	89.4178i	−0.192986	+	0.726974i
$124$		0			0
$125$		0			0
$126$		0			0
$127$			44.8753i			0.353349i	0.984269	+	0.176674i	$0.0565339\pi$
$127$			44.8753i			0.353349i	−0.984269	+	0.176674i	$0.943466\pi$
$128$		0			0
$129$	−91.6567	−	91.2324i	−0.710517	−	0.707228i
$130$		0			0
$131$	63.7326	+	36.7960i	0.486508	+	0.280886i	0.723125	−	0.690717i	$-0.242705\pi$
$131$	63.7326	+	36.7960i	0.486508	+	0.280886i	−0.236617	+	0.971603i	$0.576039\pi$
$132$		0			0
$133$	−77.7561	+	44.8925i	−0.584632	+	0.337538i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	109.091	+	188.952i	0.796286	+	1.37921i	0.922019	+	0.387144i	$0.126539\pi$
$137$	109.091	+	188.952i	0.796286	+	1.37921i	−0.125733	+	0.992064i	$0.540128\pi$
$138$		0			0
$139$	−33.0004	+	57.1584i	−0.237413	+	0.411212i	−0.959971	−	0.280099i	$-0.909633\pi$
$139$	−33.0004	+	57.1584i	−0.237413	+	0.411212i	0.722558	+	0.691310i	$0.242966\pi$
$140$		0			0
$141$	−87.8076	+	88.2160i	−0.622749	+	0.625645i
$142$		0			0
$143$	180.551			1.26260
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−77.6725	−	20.6193i	−0.528384	−	0.140267i
$148$		0			0
$149$	169.401	+	97.8035i	1.13692	+	0.656399i	0.945665	−	0.325142i	$-0.105412\pi$
$149$	169.401	+	97.8035i	1.13692	+	0.656399i	0.191252	+	0.981541i	$0.438745\pi$
$150$		0			0
$151$	79.5523	+	137.789i	0.526836	+	0.912507i	0.999511	+	0.0312701i	$0.00995522\pi$
$151$	79.5523	+	137.789i	0.526836	+	0.912507i	−0.472675	+	0.881237i	$0.656711\pi$
$152$		0			0
$153$	−126.307	+	73.7067i	−0.825534	+	0.481743i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−111.185	−	64.1927i	−0.708185	−	0.408871i	0.102204	−	0.994764i	$-0.467411\pi$
$157$	−111.185	−	64.1927i	−0.708185	−	0.408871i	−0.810389	+	0.585893i	$0.800744\pi$
$158$		0			0
$159$	−24.0465	−	88.9170i	−0.151236	−	0.559227i
$160$		0			0
$161$		−	78.2667i		−	0.486129i
$162$		0			0
$163$			21.6963i			0.133106i	0.997783	+	0.0665531i	$0.0212002\pi$
$163$			21.6963i			0.133106i	−0.997783	+	0.0665531i	$0.978800\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−126.957	+	219.896i	−0.760223	+	1.31674i	0.182513	+	0.983204i	$0.441577\pi$
$167$	−126.957	+	219.896i	−0.760223	+	1.31674i	−0.942736	+	0.333541i	$0.891756\pi$
$168$		0			0
$169$	−40.6050	−	70.3299i	−0.240266	−	0.416153i
$170$		0			0
$171$	−148.084	+	86.4151i	−0.865991	+	0.505352i
$172$		0			0
$173$	−29.6768	−	51.4018i	−0.171542	−	0.297120i	0.767417	−	0.641148i	$-0.221542\pi$
$173$	−29.6768	−	51.4018i	−0.171542	−	0.297120i	−0.938959	+	0.344028i	$0.888208\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	66.1485	−	249.180i	0.373720	−	1.40780i
$178$		0			0
$179$		−	5.43887i		−	0.0303848i	−0.999885	−	0.0151924i	$-0.995164\pi$
$179$		−	5.43887i		−	0.0303848i	0.999885	−	0.0151924i	$-0.00483607\pi$
$180$		0			0
$181$	45.4874			0.251312			0.125656	−	0.992074i	$-0.459896\pi$
$181$	45.4874			0.251312			0.125656	+	0.992074i	$0.459896\pi$
$182$		0			0
$183$	219.031	−	220.049i	1.19689	−	1.20245i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	271.164	−	156.557i	1.45007	−	0.837201i
$188$		0			0
$189$	123.141	+	32.0788i	0.651542	+	0.169729i
$190$		0			0
$191$	199.987	−	115.463i	1.04705	−	0.604516i	0.125230	−	0.992128i	$-0.460033\pi$
$191$	199.987	−	115.463i	1.04705	−	0.604516i	0.921823	+	0.387612i	$0.126700\pi$
$192$		0			0
$193$	−63.1231	−	36.4441i	−0.327063	−	0.188830i	0.327474	−	0.944860i	$-0.393803\pi$
$193$	−63.1231	−	36.4441i	−0.327063	−	0.188830i	−0.654536	+	0.756031i	$0.727136\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−39.2251			−0.199112			−0.0995561	−	0.995032i	$-0.531742\pi$
$197$	−39.2251			−0.199112			−0.0995561	+	0.995032i	$0.531742\pi$
$198$		0			0
$199$	268.068			1.34707			0.673537	−	0.739154i	$-0.264774\pi$
$199$	268.068			1.34707			0.673537	+	0.739154i	$0.264774\pi$
$200$		0			0
$201$	−95.1203	+	358.317i	−0.473235	+	1.78267i
$202$		0			0
$203$	−10.5463	+	18.2667i	−0.0519522	+	0.0899838i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−0.693436	−	149.457i	−0.00334993	−	0.722015i
$208$		0			0
$209$	317.918	−	183.550i	1.52114	−	0.878229i
$210$		0			0
$211$	173.445	−	300.416i	0.822015	−	1.42377i	−0.0821652	−	0.996619i	$-0.526184\pi$
$211$	173.445	−	300.416i	0.822015	−	1.42377i	0.904180	−	0.427152i	$-0.140483\pi$
$212$		0			0
$213$	−322.636	+	87.2527i	−1.51472	+	0.409637i
$214$		0			0
$215$		0			0
$216$		0			0
$217$		−	67.8092i		−	0.312485i
$218$		0			0
$219$	262.311	−	70.9387i	1.19777	−	0.323921i
$220$		0			0
$221$	131.849	+	76.1229i	0.596601	+	0.344448i
$222$		0			0
$223$	−61.2866	+	35.3838i	−0.274828	+	0.158672i	−0.631080	−	0.775718i	$-0.717388\pi$
$223$	−61.2866	+	35.3838i	−0.274828	+	0.158672i	0.356252	+	0.934390i	$0.384055\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−134.429	−	232.838i	−0.592199	−	1.02572i	−0.993936	−	0.109963i	$-0.964927\pi$
$227$	−134.429	−	232.838i	−0.592199	−	1.02572i	0.401737	−	0.915755i	$-0.368407\pi$
$228$		0			0
$229$	103.497	−	179.261i	0.451950	−	0.782801i	−0.546557	−	0.837422i	$-0.684062\pi$
$229$	103.497	−	179.261i	0.451950	−	0.782801i	0.998507	+	0.0546210i	$0.0173951\pi$
$230$		0			0
$231$	−263.336	−	69.9063i	−1.13998	−	0.302625i
$232$		0			0
$233$	−47.4893			−0.203817			−0.101908	−	0.994794i	$-0.532495\pi$
$233$	−47.4893			−0.203817			−0.101908	+	0.994794i	$0.532495\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	176.325	−	177.145i	0.743986	−	0.747446i
$238$		0			0
$239$	288.824	+	166.753i	1.20847	+	0.697710i	0.962425	−	0.271548i	$-0.0875356\pi$
$239$	288.824	+	166.753i	1.20847	+	0.697710i	0.246045	+	0.969258i	$0.420869\pi$
$240$		0			0
$241$	−213.356	−	369.544i	−0.885296	−	1.53338i	−0.845374	−	0.534176i	$-0.820622\pi$
$241$	−213.356	−	369.544i	−0.885296	−	1.53338i	−0.0399229	−	0.999203i	$-0.512711\pi$
$242$		0			0
$243$	235.434	+	60.1663i	0.968863	+	0.247598i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	154.582	+	89.2480i	0.625838	+	0.361328i
$248$		0			0
$249$	−75.8730	+	76.2258i	−0.304711	+	0.306128i
$250$		0			0
$251$			394.340i			1.57107i	0.618814	+	0.785537i	$0.287613\pi$
$251$			394.340i			1.57107i	−0.618814	+	0.785537i	$0.712387\pi$
$252$		0			0
$253$			320.005i			1.26484i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−181.057	+	313.600i	−0.704503	+	1.22023i	0.262368	+	0.964968i	$0.415497\pi$
$257$	−181.057	+	313.600i	−0.704503	+	1.22023i	−0.966871	+	0.255267i	$0.917837\pi$
$258$		0			0
$259$	−131.043	−	226.974i	−0.505959	−	0.876346i
$260$		0			0
$261$	−19.9772	+	34.9754i	−0.0765412	+	0.134005i
$262$		0			0
$263$	−169.779	−	294.065i	−0.645546	−	1.11812i	−0.984175	−	0.177198i	$-0.943297\pi$
$263$	−169.779	−	294.065i	−0.645546	−	1.11812i	0.338630	−	0.940920i	$-0.390037\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−245.910	+	66.5031i	−0.921010	+	0.249075i
$268$		0			0
$269$		−	23.2060i		−	0.0862678i	−0.999069	−	0.0431339i	$-0.986266\pi$
$269$		−	23.2060i		−	0.0862678i	0.999069	−	0.0431339i	$-0.0137342\pi$
$270$		0			0
$271$	−433.939			−1.60125			−0.800626	−	0.599165i	$-0.795499\pi$
$271$	−433.939			−1.60125			−0.800626	+	0.599165i	$0.795499\pi$
$272$		0			0
$273$	−34.5844	−	127.883i	−0.126683	−	0.468438i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	295.704	−	170.725i	1.06752	−	0.616336i	0.140021	−	0.990149i	$-0.455283\pi$
$277$	295.704	−	170.725i	1.06752	−	0.616336i	0.927504	+	0.373813i	$0.121950\pi$
$278$		0			0
$279$	−0.600783	−	129.488i	−0.00215334	−	0.464113i
$280$		0			0
$281$	175.833	−	101.517i	0.625741	−	0.361272i	−0.153360	−	0.988170i	$-0.549009\pi$
$281$	175.833	−	101.517i	0.625741	−	0.361272i	0.779101	+	0.626899i	$0.215676\pi$
$282$		0			0
$283$	−135.815	−	78.4126i	−0.479910	−	0.277076i	0.240469	−	0.970657i	$-0.422699\pi$
$283$	−135.815	−	78.4126i	−0.479910	−	0.277076i	−0.720379	+	0.693581i	$0.756032\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−145.341			−0.506415
$288$		0			0
$289$	−24.9744			−0.0864167
$290$		0			0
$291$	223.790	+	222.754i	0.769039	+	0.765479i
$292$		0			0
$293$	−31.7203	+	54.9412i	−0.108260	+	0.187513i	−0.915066	−	0.403305i	$-0.867861\pi$
$293$	−31.7203	+	54.9412i	−0.108260	+	0.187513i	0.806805	+	0.590818i	$0.201195\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−503.483	−	131.159i	−1.69523	−	0.441613i
$298$		0			0
$299$	−134.751	+	77.7986i	−0.450672	+	0.260196i
$300$		0			0
$301$	101.583	−	175.947i	0.337485	−	0.584541i
$302$		0			0
$303$	170.546	+	169.756i	0.562857	+	0.560252i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	183.760i		−	0.598568i	−0.954164	−	0.299284i	$-0.903252\pi$
$307$		−	183.760i		−	0.598568i	0.954164	−	0.299284i	$-0.0967478\pi$
$308$		0			0
$309$	−100.389	+	378.164i	−0.324883	+	1.22383i
$310$		0			0
$311$	328.599	+	189.717i	1.05659	+	0.610021i	0.924486	−	0.381215i	$-0.124494\pi$
$311$	328.599	+	189.717i	1.05659	+	0.610021i	0.132101	+	0.991236i	$0.457828\pi$
$312$		0			0
$313$	353.868	−	204.306i	1.13057	−	0.652734i	0.186491	−	0.982457i	$-0.440289\pi$
$313$	353.868	−	204.306i	1.13057	−	0.652734i	0.944078	+	0.329723i	$0.106955\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−259.421	−	449.330i	−0.818362	−	1.41744i	−0.906889	−	0.421370i	$-0.861549\pi$
$317$	−259.421	−	449.330i	−0.818362	−	1.41744i	0.0885271	−	0.996074i	$-0.471784\pi$
$318$		0			0
$319$	43.1202	−	74.6863i	0.135173	−	0.234126i
$320$		0			0
$321$	−39.0328	−	144.332i	−0.121597	−	0.449633i
$322$		0			0
$323$	309.549			0.958355
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−95.1019	−	351.660i	−0.290831	−	1.07541i
$328$		0			0
$329$	−169.342	−	97.7696i	−0.514717	−	0.297172i
$330$		0			0
$331$	−147.622	−	255.689i	−0.445988	−	0.772474i	0.552133	−	0.833756i	$-0.313814\pi$
$331$	−147.622	−	255.689i	−0.445988	−	0.772474i	−0.998120	+	0.0612827i	$0.980481\pi$
$332$		0			0
$333$	−252.250	−	432.265i	−0.757507	−	1.29809i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−93.3245	−	53.8810i	−0.276927	−	0.159884i	0.355104	−	0.934827i	$-0.384445\pi$
$337$	−93.3245	−	53.8810i	−0.276927	−	0.159884i	−0.632032	+	0.774943i	$0.717779\pi$
$338$		0			0
$339$	81.9833	+	21.7636i	0.241839	+	0.0641995i
$340$		0			0
$341$			277.248i			0.813045i
$342$		0			0
$343$		−	357.187i		−	1.04136i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	220.726	−	382.308i	0.636097	−	1.10175i	−0.350185	−	0.936681i	$-0.613881\pi$
$347$	220.726	−	382.308i	0.636097	−	1.10175i	0.986282	−	0.165071i	$-0.0527854\pi$
$348$		0			0
$349$	94.7382	+	164.091i	0.271456	+	0.470176i	0.969235	−	0.246138i	$-0.0791615\pi$
$349$	94.7382	+	164.091i	0.271456	+	0.470176i	−0.697779	+	0.716313i	$0.745828\pi$
$350$		0			0
$351$	−67.1751	−	243.898i	−0.191382	−	0.694867i
$352$		0			0
$353$	−251.430	−	435.490i	−0.712267	−	1.23368i	−0.964004	−	0.265887i	$-0.914335\pi$
$353$	−251.430	−	435.490i	−0.712267	−	1.23368i	0.251737	−	0.967796i	$-0.418998\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−162.829	−	162.076i	−0.456104	−	0.453993i
$358$		0			0
$359$			2.93084i			0.00816391i	0.999992	+	0.00408196i	$0.00129933\pi$
$359$			2.93084i			0.00816391i	−0.999992	+	0.00408196i	$0.998701\pi$
$360$		0			0
$361$	1.92045			0.00531981
$362$		0			0
$363$	725.842	+	192.685i	1.99956	+	0.530813i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−47.4055	+	27.3696i	−0.129170	+	0.0745765i	−0.563193	−	0.826326i	$-0.690427\pi$
$367$	−47.4055	+	27.3696i	−0.129170	+	0.0745765i	0.434023	+	0.900902i	$0.357094\pi$
$368$		0			0
$369$	−277.542	+	1.28771i	−0.752145	+	0.00348973i
$370$		0			0
$371$	125.320	−	72.3534i	0.337789	−	0.195023i
$372$		0			0
$373$	−586.707	−	338.735i	−1.57294	−	0.908138i	−0.995806	−	0.0914894i	$-0.970837\pi$
$373$	−586.707	−	338.735i	−1.57294	−	0.908138i	−0.577135	−	0.816649i	$-0.695829\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	41.9329			0.111228
$378$		0			0
$379$	431.714			1.13909			0.569543	−	0.821961i	$-0.307120\pi$
$379$	431.714			1.13909			0.569543	+	0.821961i	$0.307120\pi$
$380$		0			0
$381$	−129.957	+	35.1453i	−0.341095	+	0.0922449i
$382$		0			0
$383$	−292.269	+	506.226i	−0.763106	+	1.32174i	0.178137	+	0.984006i	$0.442993\pi$
$383$	−292.269	+	506.226i	−0.763106	+	1.32174i	−0.941242	+	0.337732i	$0.890340\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	192.423	−	336.886i	0.497217	−	0.870507i
$388$		0			0
$389$	49.9565	−	28.8424i	0.128423	−	0.0741450i	−0.434412	−	0.900714i	$-0.643044\pi$
$389$	49.9565	−	28.8424i	0.128423	−	0.0741450i	0.562835	+	0.826569i	$0.309711\pi$
$390$		0			0
$391$	−134.919	+	233.686i	−0.345061	+	0.597662i
$392$		0			0
$393$	−56.6462	+	213.385i	−0.144138	+	0.542965i
$394$		0			0
$395$		0			0
$396$		0			0
$397$		−	25.9853i		−	0.0654542i	−0.999464	−	0.0327271i	$-0.989581\pi$
$397$		−	25.9853i		−	0.0654542i	0.999464	−	0.0327271i	$-0.0104192\pi$
$398$		0			0
$399$	−190.904	−	190.020i	−0.478456	−	0.476242i
$400$		0			0
$401$	−229.069	−	132.253i	−0.571244	−	0.329808i	0.186402	−	0.982474i	$-0.440317\pi$
$401$	−229.069	−	132.253i	−0.571244	−	0.329808i	−0.757646	+	0.652666i	$0.773651\pi$
$402$		0			0
$403$	−116.746	+	67.4036i	−0.289693	+	0.167255i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	535.791	+	928.017i	1.31644	+	2.28014i
$408$		0			0
$409$	154.678	−	267.911i	0.378187	−	0.655039i	−0.612612	−	0.790384i	$-0.709881\pi$
$409$	154.678	−	267.911i	0.378187	−	0.655039i	0.990798	+	0.135345i	$0.0432144\pi$
$410$		0			0
$411$	−461.760	+	463.907i	−1.12350	+	1.12873i
$412$		0			0
$413$	405.021			0.980681
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−191.374	−	50.8030i	−0.458931	−	0.121830i
$418$		0			0
$419$	58.4329	+	33.7363i	0.139458	+	0.0805161i	0.568106	−	0.822956i	$-0.307676\pi$
$419$	58.4329	+	33.7363i	0.139458	+	0.0805161i	−0.428648	+	0.903472i	$0.641010\pi$
$420$		0			0
$421$	−101.577	−	175.936i	−0.241275	−	0.417901i	0.719803	−	0.694179i	$-0.244232\pi$
$421$	−101.577	−	175.936i	−0.241275	−	0.417901i	−0.961078	+	0.276278i	$0.910899\pi$
$422$		0			0
$423$	−324.240	−	185.199i	−0.766524	−	0.437824i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	422.413	+	243.880i	0.989257	+	0.571148i
$428$		0			0
$429$	141.404	+	522.871i	0.329613	+	1.21881i
$430$		0			0
$431$			319.947i			0.742337i	0.928566	+	0.371168i	$0.121043\pi$
$431$			319.947i			0.742337i	−0.928566	+	0.371168i	$0.878957\pi$
$432$		0			0
$433$		−	454.101i		−	1.04873i	−0.851493	−	0.524366i	$-0.824303\pi$
$433$		−	454.101i		−	1.04873i	0.851493	−	0.524366i	$-0.175697\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−158.181	+	273.978i	−0.361971	+	0.626951i
$438$		0			0
$439$	45.7154	+	79.1813i	0.104135	+	0.180367i	0.913385	−	0.407098i	$-0.133459\pi$
$439$	45.7154	+	79.1813i	0.104135	+	0.180367i	−0.809249	+	0.587465i	$0.800126\pi$
$440$		0			0
$441$	−1.11856	−	241.086i	−0.00253643	−	0.546679i
$442$		0			0
$443$	−108.559	−	188.030i	−0.245055	−	0.424448i	0.717092	−	0.696978i	$-0.245473\pi$
$443$	−108.559	−	188.030i	−0.245055	−	0.424448i	−0.962147	+	0.272531i	$0.912139\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−150.565	+	567.176i	−0.336835	+	1.26885i
$448$		0			0
$449$		−	832.270i		−	1.85361i	−0.375545	−	0.926804i	$-0.622544\pi$
$449$		−	832.270i		−	1.85361i	0.375545	−	0.926804i	$-0.377456\pi$
$450$		0			0
$451$	594.249			1.31763
$452$		0			0
$453$	−336.728	+	338.294i	−0.743329	+	0.746785i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−693.510	+	400.398i	−1.51753	+	0.876145i	−0.517739	+	0.855538i	$0.673226\pi$
$457$	−693.510	+	400.398i	−1.51753	+	0.876145i	−0.999788	+	0.0206062i	$0.993440\pi$
$458$		0			0
$459$	−312.373	−	308.055i	−0.680551	−	0.671144i
$460$		0			0
$461$	504.549	−	291.301i	1.09447	−	0.631890i	0.159704	−	0.987165i	$-0.448946\pi$
$461$	504.549	−	291.301i	1.09447	−	0.631890i	0.934762	+	0.355275i	$0.115613\pi$
$462$		0			0
$463$	635.871	+	367.120i	1.37337	+	0.792916i	0.991351	−	0.131237i	$-0.0418950\pi$
$463$	635.871	+	367.120i	1.37337	+	0.792916i	0.382021	+	0.924154i	$0.375228\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	670.573			1.43592			0.717958	−	0.696086i	$-0.245077\pi$
$467$	670.573			1.43592			0.717958	+	0.696086i	$0.245077\pi$
$468$		0			0
$469$	−582.413			−1.24182
$470$		0			0
$471$	98.8225	−	372.263i	0.209814	−	0.790367i
$472$		0			0
$473$	−415.338	+	719.386i	−0.878092	+	1.52090i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	238.668	−	139.276i	0.500353	−	0.291982i
$478$		0			0
$479$	−148.723	+	85.8655i	−0.310487	+	0.179260i	−0.647144	−	0.762367i	$-0.724037\pi$
$479$	−148.723	+	85.8655i	−0.310487	+	0.179260i	0.336657	+	0.941627i	$0.390704\pi$
$480$		0			0
$481$	−260.519	+	451.232i	−0.541619	+	0.938112i
$482$		0			0
$483$	226.658	−	61.2967i	0.469271	−	0.126908i
$484$		0			0
$485$		0			0
$486$		0			0
$487$		−	22.0906i		−	0.0453606i	−0.999743	−	0.0226803i	$-0.992780\pi$
$487$		−	22.0906i		−	0.0453606i	0.999743	−	0.0226803i	$-0.00721998\pi$
$488$		0			0
$489$	−62.8319	+	16.9921i	−0.128491	+	0.0347486i
$490$		0			0
$491$	−458.788	−	264.881i	−0.934395	−	0.539473i	−0.0461960	−	0.998932i	$-0.514710\pi$
$491$	−458.788	−	264.881i	−0.934395	−	0.539473i	−0.888199	+	0.459459i	$0.848043\pi$
$492$		0			0
$493$	62.9775	−	36.3601i	0.127743	−	0.0737527i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−262.535	−	454.724i	−0.528239	−	0.914937i
$498$		0			0
$499$	84.6486	−	146.616i	0.169636	−	0.293819i	−0.768656	−	0.639663i	$-0.779074\pi$
$499$	84.6486	−	146.616i	0.169636	−	0.293819i	0.938292	+	0.345844i	$0.112407\pi$
$500$		0			0
$501$	−736.243	−	195.446i	−1.46955	−	0.390112i
$502$		0			0
$503$	22.5687			0.0448682			0.0224341	−	0.999748i	$-0.492858\pi$
$503$	22.5687			0.0448682			0.0224341	+	0.999748i	$0.492858\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	171.872	−	172.672i	0.338999	−	0.340575i
$508$		0			0
$509$	654.896	+	378.104i	1.28663	+	0.742838i	0.978052	−	0.208361i	$-0.0668128\pi$
$509$	654.896	+	378.104i	1.28663	+	0.742838i	0.308580	+	0.951198i	$0.400146\pi$
$510$		0			0
$511$	213.448	+	369.702i	0.417706	+	0.723487i
$512$		0			0
$513$	−366.232	−	361.169i	−0.713902	−	0.704034i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	692.380	+	399.746i	1.33923	+	0.773203i
$518$		0			0
$519$	125.616	−	126.200i	0.242034	−	0.243160i
$520$		0			0
$521$			157.921i			0.303112i	0.988449	+	0.151556i	$0.0484283\pi$
$521$			157.921i			0.303112i	−0.988449	+	0.151556i	$0.951572\pi$
$522$		0			0
$523$			535.341i			1.02360i	0.859106	+	0.511798i	$0.171021\pi$
$523$			535.341i			1.02360i	−0.859106	+	0.511798i	$0.828979\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−116.892	+	202.462i	−0.221806	+	0.384179i
$528$		0			0
$529$	126.612	+	219.298i	0.239341	+	0.414551i
$530$		0			0
$531$	773.424	−	3.58845i	1.45654	−	0.00675791i
$532$		0			0
$533$	144.472	+	250.232i	0.271054	+	0.469479i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	15.7508	−	4.25960i	0.0293311	−	0.00793222i
$538$		0			0
$539$			516.193i			0.957686i
$540$		0			0
$541$	446.519			0.825358			0.412679	−	0.910877i	$-0.364593\pi$
$541$	446.519			0.825358			0.412679	+	0.910877i	$0.364593\pi$
$542$		0			0
$543$	35.6247	+	131.730i	0.0656072	+	0.242597i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	180.850	−	104.414i	0.330622	−	0.190885i	−0.325495	−	0.945544i	$-0.605531\pi$
$547$	180.850	−	104.414i	0.330622	−	0.190885i	0.656117	+	0.754659i	$0.272198\pi$
$548$		0			0
$549$	808.795	+	461.968i	1.47322	+	0.841472i
$550$		0			0
$551$	73.8360	−	42.6292i	0.134004	−	0.0773671i
$552$		0			0
$553$	340.052	+	196.329i	0.614923	+	0.355026i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−428.915			−0.770044			−0.385022	−	0.922907i	$-0.625806\pi$
$557$	−428.915			−0.770044			−0.385022	+	0.922907i	$0.625806\pi$
$558$		0			0
$559$	−403.901			−0.722543
$560$		0			0
$561$	665.753	+	662.671i	1.18672	+	1.18123i
$562$		0			0
$563$	394.727	−	683.687i	0.701114	−	1.21436i	−0.266962	−	0.963707i	$-0.586020\pi$
$563$	394.727	−	683.687i	0.701114	−	1.21436i	0.968076	−	0.250657i	$-0.0806468\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	3.54236	+	381.737i	0.00624756	+	0.673258i
$568$		0			0
$569$	−153.834	+	88.8163i	−0.270359	+	0.156092i	−0.629051	−	0.777364i	$-0.716556\pi$
$569$	−153.834	+	88.8163i	−0.270359	+	0.156092i	0.358692	+	0.933456i	$0.383223\pi$
$570$		0			0
$571$	−9.18137	+	15.9026i	−0.0160795	+	0.0278504i	−0.873953	−	0.486010i	$-0.838452\pi$
$571$	−9.18137	+	15.9026i	−0.0160795	+	0.0278504i	0.857874	+	0.513861i	$0.171785\pi$
$572$		0			0
$573$	491.001	+	488.729i	0.856896	+	0.852929i
$574$		0			0
$575$		0			0
$576$		0			0
$577$		−	240.588i		−	0.416963i	−0.978026	−	0.208482i	$-0.933148\pi$
$577$		−	240.588i		−	0.416963i	0.978026	−	0.208482i	$-0.0668521\pi$
$578$		0			0
$579$	56.1045	−	211.345i	0.0968989	−	0.365017i
$580$		0			0
$581$	−146.325	−	84.4809i	−0.251851	−	0.145406i
$582$		0			0
$583$	−512.389	+	295.828i	−0.878884	+	0.507424i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−82.6260	−	143.112i	−0.140760	−	0.243803i	0.787023	−	0.616923i	$-0.211621\pi$
$587$	−82.6260	−	143.112i	−0.140760	−	0.243803i	−0.927783	+	0.373120i	$0.878288\pi$
$588$		0			0
$589$	−137.046	+	237.370i	−0.232676	+	0.403006i
$590$		0			0
$591$	−30.7202	−	113.595i	−0.0519801	−	0.192208i
$592$		0			0
$593$	901.661			1.52051			0.760254	−	0.649626i	$-0.225075\pi$
$593$	901.661			1.52051			0.760254	+	0.649626i	$0.225075\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	209.945	+	776.316i	0.351666	+	1.30036i
$598$		0			0
$599$	−893.571	−	515.904i	−1.49177	−	0.861275i	−0.491817	−	0.870699i	$-0.663667\pi$
$599$	−893.571	−	515.904i	−1.49177	−	0.861275i	−0.999956	+	0.00942385i	$0.997000\pi$
$600$		0			0
$601$	−481.489	−	833.964i	−0.801147	−	1.38763i	−0.918862	−	0.394580i	$-0.870890\pi$
$601$	−481.489	−	833.964i	−0.801147	−	1.38763i	0.117715	−	0.993047i	$-0.462443\pi$
$602$		0			0
$603$	−1112.17	+	5.16013i	−1.84439	+	0.00855743i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−813.387	−	469.609i	−1.34001	−	0.773656i	−0.353202	−	0.935547i	$-0.614907\pi$
$607$	−813.387	−	469.609i	−1.34001	−	0.773656i	−0.986809	+	0.161891i	$0.948241\pi$
$608$		0			0
$609$	−61.1595	−	16.2357i	−0.100426	−	0.0266595i
$610$		0			0
$611$			388.739i			0.636234i
$612$		0			0
$613$			364.929i			0.595316i	0.954673	+	0.297658i	$0.0962055\pi$
$613$			364.929i			0.595316i	−0.954673	+	0.297658i	$0.903794\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−133.518	+	231.260i	−0.216398	+	0.374813i	−0.953704	−	0.300746i	$-0.902764\pi$
$617$	−133.518	+	231.260i	−0.216398	+	0.374813i	0.737306	+	0.675559i	$0.236098\pi$
$618$		0			0
$619$	453.122	+	784.830i	0.732022	+	1.26790i	0.956017	+	0.293310i	$0.0947567\pi$
$619$	453.122	+	784.830i	0.732022	+	1.26790i	−0.223995	+	0.974590i	$0.571910\pi$
$620$		0			0
$621$	432.280	−	119.060i	0.696103	−	0.191722i
$622$		0			0
$623$	−200.101	−	346.585i	−0.321190	−	0.556317i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	780.541	+	776.928i	1.24488	+	1.23912i
$628$		0			0
$629$			903.586i			1.43654i
$630$		0			0
$631$	597.193			0.946424			0.473212	−	0.880949i	$-0.343095\pi$
$631$	597.193			0.946424			0.473212	+	0.880949i	$0.343095\pi$
$632$		0			0
$633$	1005.83	+	267.013i	1.58899	+	0.421821i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−217.363	+	125.495i	−0.341230	+	0.197009i
$638$		0			0
$639$	−505.362	−	866.009i	−0.790864	−	1.35526i
$640$		0			0
$641$	78.1431	−	45.1160i	0.121908	−	0.0703837i	−0.437806	−	0.899070i	$-0.644244\pi$
$641$	78.1431	−	45.1160i	0.121908	−	0.0703837i	0.559714	+	0.828686i	$0.310911\pi$
$642$		0			0
$643$	336.770	+	194.434i	0.523748	+	0.302386i	0.738467	−	0.674290i	$-0.235550\pi$
$643$	336.770	+	194.434i	0.523748	+	0.302386i	−0.214719	+	0.976676i	$0.568883\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−607.624			−0.939141			−0.469570	−	0.882895i	$-0.655591\pi$
$647$	−607.624			−0.939141			−0.469570	+	0.882895i	$0.655591\pi$
$648$		0			0
$649$	−1655.99			−2.55161
$650$		0			0
$651$	196.373	−	53.1066i	0.301649	−	0.0815770i
$652$		0			0
$653$	−566.508	+	981.221i	−0.867547	+	1.50264i	−0.00305096	+	0.999995i	$0.500971\pi$
$653$	−566.508	+	981.221i	−0.867547	+	1.50264i	−0.864496	+	0.502640i	$0.832362\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	410.873	+	704.088i	0.625377	+	1.07167i
$658$		0			0
$659$	−772.309	+	445.893i	−1.17194	+	0.676621i	−0.954137	−	0.299372i	$-0.903223\pi$
$659$	−772.309	+	445.893i	−1.17194	+	0.676621i	−0.217805	+	0.975992i	$0.569890\pi$
$660$		0			0
$661$	−219.766	+	380.645i	−0.332474	+	0.575863i	−0.982996	−	0.183625i	$-0.941217\pi$
$661$	−219.766	+	380.645i	−0.332474	+	0.575863i	0.650522	+	0.759487i	$0.274550\pi$
$662$		0			0
$663$	−117.189	+	441.448i	−0.176755	+	0.665834i
$664$		0			0
$665$		0			0
$666$		0			0
$667$			74.3209i			0.111426i
$668$		0			0
$669$	−150.469	−	149.772i	−0.224916	−	0.223875i
$670$		0			0
$671$	−1727.10	−	997.142i	−2.57392	−	1.48605i
$672$		0			0
$673$	53.9165	−	31.1287i	0.0801137	−	0.0462537i	−0.459408	−	0.888225i	$-0.651938\pi$
$673$	53.9165	−	31.1287i	0.0801137	−	0.0462537i	0.539522	+	0.841972i	$0.318605\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	67.0416	+	116.119i	0.0990275	+	0.171521i	0.911282	−	0.411782i	$-0.135093\pi$
$677$	67.0416	+	116.119i	0.0990275	+	0.171521i	−0.812255	+	0.583303i	$0.801760\pi$
$678$		0			0
$679$	−248.026	+	429.594i	−0.365282	+	0.632687i
$680$		0			0
$681$	569.010	−	571.656i	0.835550	−	0.839436i
$682$		0			0
$683$	299.004			0.437780			0.218890	−	0.975750i	$-0.429756\pi$
$683$	299.004			0.437780			0.218890	+	0.975750i	$0.429756\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	600.192	+	159.329i	0.873641	+	0.231921i
$688$		0			0
$689$	−249.140	−	143.841i	−0.361597	−	0.208768i
$690$		0			0
$691$	188.288	+	326.124i	0.272486	+	0.471960i	0.969498	−	0.245100i	$-0.0788208\pi$
$691$	188.288	+	326.124i	0.272486	+	0.471960i	−0.697012	+	0.717060i	$0.745487\pi$
$692$		0			0
$693$	−3.79231	−	817.362i	−0.00547231	−	1.17945i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	433.954	+	250.544i	0.622603	+	0.359460i
$698$		0			0
$699$	−37.1925	−	137.527i	−0.0532082	−	0.196749i
$700$		0			0
$701$		−	909.992i		−	1.29813i	−0.760731	−	0.649067i	$-0.775159\pi$
$701$		−	909.992i		−	1.29813i	0.760731	−	0.649067i	$-0.224841\pi$
$702$		0			0
$703$			1059.38i			1.50694i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−189.016	+	327.385i	−0.267349	+	0.463062i
$708$		0			0
$709$	−671.694	−	1163.41i	−0.947382	−	1.64091i	−0.750911	−	0.660404i	$-0.770385\pi$
$709$	−671.694	−	1163.41i	−0.947382	−	1.64091i	−0.196471	−	0.980510i	$-0.562948\pi$
$710$		0			0
$711$	651.099	+	371.895i	0.915751	+	0.523059i
$712$		0			0
$713$	−119.465	−	206.919i	−0.167552	−	0.290209i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−256.710	+	967.023i	−0.358034	+	1.34871i
$718$		0			0
$719$		−	288.276i		−	0.400940i	−0.979700	−	0.200470i	$-0.935753\pi$
$719$		−	288.276i		−	0.400940i	0.979700	−	0.200470i	$-0.0642469\pi$
$720$		0			0
$721$	−614.673			−0.852528
$722$		0			0
$723$	903.092	−	907.292i	1.24909	−	1.25490i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−421.147	+	243.149i	−0.579294	+	0.334456i	−0.760853	−	0.648925i	$-0.775219\pi$
$727$	−421.147	+	243.149i	−0.579294	+	0.334456i	0.181559	+	0.983380i	$0.441886\pi$
$728$		0			0
$729$	10.1466	+	728.929i	0.0139185	+	0.999903i
$730$		0			0
$731$	−606.606	+	350.224i	−0.829830	+	0.479103i
$732$		0			0
$733$	−1089.83	−	629.211i	−1.48680	−	0.858406i	−0.486915	−	0.873449i	$-0.661878\pi$
$733$	−1089.83	−	629.211i	−1.48680	−	0.858406i	−0.999887	+	0.0150435i	$0.995211\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	2381.29			3.23105
$738$		0			0
$739$	1192.17			1.61322			0.806609	−	0.591086i	$-0.201300\pi$
$739$	1192.17			1.61322			0.806609	+	0.591086i	$0.201300\pi$
$740$		0			0
$741$	−137.394	+	517.562i	−0.185417	+	0.698464i
$742$		0			0
$743$	98.7194	−	170.987i	0.132866	−	0.230131i	−0.791914	−	0.610632i	$-0.790915\pi$
$743$	98.7194	−	170.987i	0.132866	−	0.230131i	0.924780	+	0.380502i	$0.124249\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−280.170	−	160.027i	−0.375060	−	0.214227i
$748$		0			0
$749$	203.422	−	117.446i	0.271592	−	0.156803i
$750$		0			0
$751$	−25.0633	+	43.4109i	−0.0333733	+	0.0578042i	−0.882230	−	0.470819i	$-0.843958\pi$
$751$	−25.0633	+	43.4109i	−0.0333733	+	0.0578042i	0.848856	+	0.528624i	$0.177292\pi$
$752$		0			0
$753$	−1142.00	+	308.838i	−1.51659	+	0.410143i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			282.361i			0.373000i	0.982455	+	0.186500i	$0.0597144\pi$
$757$			282.361i			0.373000i	−0.982455	+	0.186500i	$0.940286\pi$
$758$		0			0
$759$	−926.726	+	250.621i	−1.22098	+	0.330199i
$760$		0			0
$761$	89.9243	+	51.9178i	0.118166	+	0.0682231i	0.557918	−	0.829896i	$-0.311600\pi$
$761$	89.9243	+	51.9178i	0.118166	+	0.0682231i	−0.439752	+	0.898119i	$0.644934\pi$
$762$		0			0
$763$	495.630	−	286.152i	0.649581	−	0.375036i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−402.599	−	697.321i	−0.524900	−	0.909154i
$768$		0			0
$769$	−190.567	+	330.073i	−0.247812	+	0.429223i	−0.962918	−	0.269793i	$-0.913045\pi$
$769$	−190.567	+	330.073i	−0.247812	+	0.429223i	0.715106	+	0.699016i	$0.246378\pi$
$770$		0			0
$771$	−1049.98	−	278.731i	−1.36184	−	0.361519i
$772$		0			0
$773$	276.633			0.357870			0.178935	−	0.983861i	$-0.442735\pi$
$773$	276.633			0.357870			0.178935	+	0.983861i	$0.442735\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	554.678	−	557.258i	0.713872	−	0.717191i
$778$		0			0
$779$	508.776	+	293.742i	0.653114	+	0.377076i
$780$		0			0
$781$	1073.41	+	1859.21i	1.37441	+	2.38055i
$782$		0			0
$783$	−116.933	−	30.4616i	−0.149340	−	0.0389037i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−1153.66	−	666.067i	−1.46590	−	0.846336i	−0.466625	−	0.884455i	$-0.654530\pi$
$787$	−1153.66	−	666.067i	−1.46590	−	0.846336i	−0.999273	+	0.0381190i	$0.987863\pi$
$788$		0			0
$789$	718.636	−	721.978i	0.910819	−	0.915055i
$790$		0			0
$791$			133.257i			0.168466i
$792$		0			0
$793$		−	969.686i		−	1.22281i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	329.882	−	571.372i	0.413904	−	0.716903i	−0.581408	−	0.813612i	$-0.697498\pi$
$797$	329.882	−	571.372i	0.413904	−	0.716903i	0.995313	+	0.0967084i	$0.0308314\pi$
$798$		0			0
$799$	337.077	+	583.834i	0.421873	+	0.730706i
$800$		0			0
$801$	−385.182	−	660.063i	−0.480876	−	0.824048i
$802$		0			0
$803$	−872.713	−	1511.58i	−1.08682	−	1.88242i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	67.2039	−	18.1744i	0.0832762	−	0.0225210i
$808$		0			0
$809$		−	654.023i		−	0.808433i	−0.914663	−	0.404217i	$-0.867544\pi$
$809$		−	654.023i		−	0.808433i	0.914663	−	0.404217i	$-0.132456\pi$
$810$		0			0
$811$	−408.003			−0.503086			−0.251543	−	0.967846i	$-0.580938\pi$
$811$	−408.003			−0.503086			−0.251543	+	0.967846i	$0.580938\pi$
$812$		0			0
$813$	−339.851	−	1256.67i	−0.418021	−	1.54572i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−711.196	+	410.609i	−0.870497	+	0.502582i
$818$		0			0
$819$	343.261	−	200.311i	0.419122	−	0.244580i
$820$		0			0
$821$	762.425	−	440.186i	0.928654	−	0.536158i	0.0422680	−	0.999106i	$-0.486542\pi$
$821$	762.425	−	440.186i	0.928654	−	0.536158i	0.886385	+	0.462948i	$0.153208\pi$
$822$		0			0
$823$	−112.279	−	64.8244i	−0.136427	−	0.0787660i	0.430233	−	0.902718i	$-0.358431\pi$
$823$	−112.279	−	64.8244i	−0.136427	−	0.0787660i	−0.566660	+	0.823952i	$0.691765\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	646.300			0.781499			0.390750	−	0.920497i	$-0.372216\pi$
$827$	646.300			0.781499			0.390750	+	0.920497i	$0.372216\pi$
$828$		0			0
$829$	416.080			0.501906			0.250953	−	0.967999i	$-0.419256\pi$
$829$	416.080			0.501906			0.250953	+	0.967999i	$0.419256\pi$
$830$		0			0
$831$	726.003	+	722.642i	0.873650	+	0.869606i
$832$		0			0
$833$	−217.634	+	376.953i	−0.261265	+	0.452524i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	374.522	−	103.152i	0.447457	−	0.123240i
$838$		0			0
$839$	−240.544	+	138.878i	−0.286703	+	0.165528i	−0.636454	−	0.771315i	$-0.719600\pi$
$839$	−240.544	+	138.878i	−0.286703	+	0.165528i	0.349751	+	0.936843i	$0.386266\pi$
$840$		0			0
$841$	−410.485	+	710.982i	−0.488092	+	0.845400i
$842$		0			0
$843$	431.700	+	429.701i	0.512099	+	0.509729i
$844$		0			0
$845$		0			0
$846$		0			0
$847$			1179.79i			1.39291i
$848$		0			0
$849$	120.714	−	454.726i	0.142183	−	0.535602i
$850$		0			0
$851$	−799.754	−	461.738i	−0.939781	−	0.542583i
$852$		0			0
$853$	1139.76	−	658.042i	1.33618	−	0.771444i	0.349942	−	0.936771i	$-0.386201\pi$
$853$	1139.76	−	658.042i	1.33618	−	0.771444i	0.986239	+	0.165327i	$0.0528681\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−479.696	−	830.857i	−0.559738	−	0.969495i	−0.997518	−	0.0704129i	$-0.977568\pi$
$857$	−479.696	−	830.857i	−0.559738	−	0.969495i	0.437780	−	0.899082i	$-0.355765\pi$
$858$		0			0
$859$	−439.753	+	761.675i	−0.511936	+	0.886699i	0.487968	+	0.872861i	$0.337738\pi$
$859$	−439.753	+	761.675i	−0.511936	+	0.886699i	−0.999904	+	0.0138379i	$0.995595\pi$
$860$		0			0
$861$	−113.828	−	420.903i	−0.132204	−	0.488854i
$862$		0			0
$863$	−326.481			−0.378310			−0.189155	−	0.981947i	$-0.560575\pi$
$863$	−326.481			−0.378310			−0.189155	+	0.981947i	$0.560575\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−19.5594	−	72.3251i	−0.0225599	−	0.0834200i
$868$		0			0
$869$	−1390.36	−	802.722i	−1.59995	−	0.923731i
$870$		0			0
$871$	578.930	+	1002.74i	0.664673	+	1.15125i
$872$		0			0
$873$	−469.822	+	822.546i	−0.538170	+	0.942206i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−99.0445	−	57.1834i	−0.112936	−	0.0652034i	0.442468	−	0.896784i	$-0.354103\pi$
$877$	−99.0445	−	57.1834i	−0.112936	−	0.0652034i	−0.555404	+	0.831581i	$0.687436\pi$
$878$		0			0
$879$	−183.951	−	48.8323i	−0.209273	−	0.0555544i
$880$		0			0
$881$			429.252i			0.487233i	0.969872	+	0.243617i	$0.0783338\pi$
$881$			429.252i			0.487233i	−0.969872	+	0.243617i	$0.921666\pi$
$882$		0			0
$883$			294.993i			0.334080i	0.985950	+	0.167040i	$0.0534209\pi$
$883$			294.993i			0.334080i	−0.985950	+	0.167040i	$0.946579\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	200.830	−	347.848i	0.226415	−	0.392162i	−0.730328	−	0.683097i	$-0.760633\pi$
$887$	200.830	−	347.848i	0.226415	−	0.392162i	0.956743	+	0.290934i	$0.0939661\pi$
$888$		0			0
$889$	−105.749	−	183.162i	−0.118952	−	0.206032i
$890$		0			0
$891$	−14.4835	−	1560.79i	−0.0162553	−	1.75173i
$892$		0			0
$893$	395.195	+	684.498i	0.442548	+	0.766515i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−330.836	−	329.305i	−0.368825	−	0.367118i
$898$		0			0
$899$			64.3906i			0.0716247i
$900$		0			0
$901$	−498.901			−0.553719
$902$		0			0
$903$	589.094	+	156.383i	0.652374	+	0.173182i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−367.089	+	211.939i	−0.404729	+	0.233670i	−0.688522	−	0.725215i	$-0.741740\pi$
$907$	−367.089	+	211.939i	−0.404729	+	0.233670i	0.283794	+	0.958885i	$0.408407\pi$
$908$		0			0
$909$	−358.041	+	626.844i	−0.393885	+	0.689598i
$910$		0			0
$911$	−51.7248	+	29.8633i	−0.0567780	+	0.0327808i	−0.528120	−	0.849170i	$-0.677103\pi$
$911$	−51.7248	+	29.8633i	−0.0567780	+	0.0327808i	0.471342	+	0.881950i	$0.343770\pi$
$912$		0			0
$913$	598.273	+	345.413i	0.655283	+	0.378328i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−346.840			−0.378233
$918$		0			0
$919$	522.062			0.568077			0.284038	−	0.958813i	$-0.408326\pi$
$919$	522.062			0.568077			0.284038	+	0.958813i	$0.408326\pi$
$920$		0			0
$921$	532.164	−	143.917i	0.577811	−	0.156262i
$922$		0			0
$923$	−521.929	+	904.008i	−0.565470	+	0.979423i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−1173.77	+	5.44595i	−1.26621	+	0.00587481i
$928$		0			0
$929$	1309.83	−	756.229i	1.40993	−	0.814025i	0.414552	−	0.910026i	$-0.363938\pi$
$929$	1309.83	−	756.229i	1.40993	−	0.814025i	0.995381	+	0.0960006i	$0.0306051\pi$
$930$		0			0
$931$	−255.158	+	441.947i	−0.274069	+	0.474701i
$932$		0			0
$933$	−292.062	+	1100.19i	−0.313036	+	1.17920i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	272.803i		−	0.291145i	−0.989348	−	0.145573i	$-0.953498\pi$
$937$		−	272.803i		−	0.291145i	0.989348	−	0.145573i	$-0.0465025\pi$
$938$		0			0
$939$	868.805	+	864.783i	0.925245	+	0.920962i
$940$		0			0
$941$	−1149.68	−	663.770i	−1.22177	−	0.705388i	−0.256473	−	0.966551i	$-0.582560\pi$
$941$	−1149.68	−	663.770i	−1.22177	−	0.705388i	−0.965295	+	0.261164i	$0.915894\pi$
$942$		0			0
$943$	−443.506	+	256.059i	−0.470314	+	0.271536i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−11.3917	−	19.7310i	−0.0120292	−	0.0208352i	0.859948	−	0.510381i	$-0.170496\pi$
$947$	−11.3917	−	19.7310i	−0.0120292	−	0.0208352i	−0.871977	+	0.489546i	$0.837162\pi$
$948$		0			0
$949$	424.342	−	734.981i	0.447146	−	0.774480i
$950$		0			0
$951$	1098.07	−	1103.18i	1.15465	−	1.16002i
$952$		0			0
$953$	563.843			0.591650			0.295825	−	0.955242i	$-0.404405\pi$
$953$	563.843			0.591650			0.295825	+	0.955242i	$0.404405\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	250.060	+	66.3820i	0.261296	+	0.0693647i
$958$		0			0
$959$	−890.530	−	514.148i	−0.928603	−	0.536129i
$960$		0			0
$961$	376.998	+	652.979i	0.392297	+	0.679479i
$962$		0			0
$963$	387.412	−	226.075i	0.402297	−	0.234762i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−1103.60	−	637.165i	−1.14126	−	0.658909i	−0.194520	−	0.980899i	$-0.562315\pi$
$967$	−1103.60	−	637.165i	−1.14126	−	0.658909i	−0.946743	+	0.321990i	$0.895648\pi$
$968$		0			0
$969$	242.431	+	896.443i	0.250187	+	0.925121i
$970$		0			0
$971$			119.681i			0.123255i	0.998099	+	0.0616276i	$0.0196291\pi$
$971$			119.681i			0.123255i	−0.998099	+	0.0616276i	$0.980371\pi$
$972$		0			0
$973$		−	311.062i		−	0.319694i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	754.597	−	1307.00i	0.772361	−	1.33777i	−0.163905	−	0.986476i	$-0.552409\pi$
$977$	754.597	−	1307.00i	0.772361	−	1.33777i	0.936266	−	0.351293i	$-0.114258\pi$
$978$		0			0
$979$	818.144	+	1417.07i	0.835694	+	1.44746i
$980$		0			0
$981$	943.914	−	550.824i	0.962196	−	0.561492i
$982$		0			0
$983$	258.736	+	448.144i	0.263211	+	0.455894i	0.967093	−	0.254422i	$-0.0818852\pi$
$983$	258.736	+	448.144i	0.263211	+	0.455894i	−0.703883	+	0.710316i	$0.748552\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	150.513	−	566.980i	0.152495	−	0.574448i
$988$		0			0
$989$		−	715.866i		−	0.723828i
$990$		0			0
$991$	−201.958			−0.203793			−0.101896	−	0.994795i	$-0.532491\pi$
$991$	−201.958			−0.203793			−0.101896	+	0.994795i	$0.532491\pi$
$992$		0			0
$993$	624.852	−	627.758i	0.629257	−	0.632184i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	181.297	−	104.672i	0.181842	−	0.104987i	−0.406316	−	0.913733i	$-0.633187\pi$
$997$	181.297	−	104.672i	0.181842	−	0.104987i	0.588158	+	0.808746i	$0.299853\pi$
$998$		0			0
$999$	1054.27	−	1069.05i	1.05533	−	1.07012i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.u.c.149.8		24
3.2	odd	2		2700.3.u.c.449.3		24
5.2	odd	4		180.3.o.b.41.6	✓	12
5.3	odd	4		900.3.p.c.401.1		12
5.4	even	2	inner	900.3.u.c.149.5		24
9.2	odd	6	inner	900.3.u.c.749.5		24
9.7	even	3		2700.3.u.c.2249.10		24
15.2	even	4		540.3.o.b.341.4		12
15.8	even	4		2700.3.p.c.2501.5		12
15.14	odd	2		2700.3.u.c.449.10		24
20.7	even	4		720.3.bs.b.401.1		12
45.2	even	12		180.3.o.b.101.6	yes	12
45.7	odd	12		540.3.o.b.521.4		12
45.22	odd	12		1620.3.g.b.161.11		12
45.29	odd	6	inner	900.3.u.c.749.8		24
45.32	even	12		1620.3.g.b.161.5		12
45.34	even	6		2700.3.u.c.2249.3		24
45.38	even	12		900.3.p.c.101.1		12
45.43	odd	12		2700.3.p.c.1601.5		12
60.47	odd	4		2160.3.bs.b.881.6		12
180.7	even	12		2160.3.bs.b.1601.6		12
180.47	odd	12		720.3.bs.b.641.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.3.o.b.41.6	✓	12	5.2	odd	4
180.3.o.b.101.6	yes	12	45.2	even	12
540.3.o.b.341.4		12	15.2	even	4
540.3.o.b.521.4		12	45.7	odd	12
720.3.bs.b.401.1		12	20.7	even	4
720.3.bs.b.641.1		12	180.47	odd	12
900.3.p.c.101.1		12	45.38	even	12
900.3.p.c.401.1		12	5.3	odd	4
900.3.u.c.149.5		24	5.4	even	2	inner
900.3.u.c.149.8		24	1.1	even	1	trivial
900.3.u.c.749.5		24	9.2	odd	6	inner
900.3.u.c.749.8		24	45.29	odd	6	inner
1620.3.g.b.161.5		12	45.32	even	12
1620.3.g.b.161.11		12	45.22	odd	12
2160.3.bs.b.881.6		12	60.47	odd	4
2160.3.bs.b.1601.6		12	180.7	even	12
2700.3.p.c.1601.5		12	45.43	odd	12
2700.3.p.c.2501.5		12	15.8	even	4
2700.3.u.c.449.3		24	3.2	odd	2
2700.3.u.c.449.10		24	15.14	odd	2
2700.3.u.c.2249.3		24	45.34	even	6
2700.3.u.c.2249.10		24	9.7	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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.783177 + 2.89597i) q^{3} +(-4.08158 + 2.35650i) q^{7} +(-7.77327 + 4.53611i) q^{9} +O(q^{10})\)	\(q+(0.783177 + 2.89597i) q^{3} +(-4.08158 + 2.35650i) q^{7} +(-7.77327 + 4.53611i) q^{9} +(16.6882 - 9.63493i) q^{11} +(8.11434 + 4.68482i) q^{13} +16.2489 q^{17} +19.0505 q^{19} +(-10.0210 - 9.97458i) q^{21} +(-8.30327 + 14.3817i) q^{23} +(-19.2243 - 18.9586i) q^{27} +(3.87581 - 2.23770i) q^{29} +(-7.19383 + 12.4601i) q^{31} +(40.9723 + 40.7826i) q^{33} +55.6092i q^{37} +(-7.21211 + 27.1679i) q^{39} +(26.7067 + 15.4191i) q^{41} +(-37.3322 + 21.5538i) q^{43} +(20.7446 + 35.9308i) q^{47} +(-13.3938 + 23.1987i) q^{49} +(12.7257 + 47.0562i) q^{51} -30.7037 q^{53} +(14.9199 + 55.1696i) q^{57} +(-74.4236 - 42.9685i) q^{59} +(-51.7462 - 89.6270i) q^{61} +(21.0379 - 36.8323i) q^{63} +(107.020 + 61.7879i) q^{67} +(-48.1518 - 12.7826i) q^{69} +111.409i q^{71} -90.5781i q^{73} +(-45.4095 + 78.6515i) q^{77} +(-41.6569 - 72.1519i) q^{79} +(39.8473 - 70.5208i) q^{81} +(17.9251 + 31.0471i) q^{83} +(9.51576 + 9.47171i) q^{87} +84.9144i q^{89} -44.1591 q^{91} +(-41.7181 - 11.0747i) q^{93} +(91.1508 - 52.6259i) q^{97} +(-86.0166 + 150.594i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 52 q^{9}+O(q^{10}) \) 24 * q - 52 * q^9	\( 24 q - 52 q^{9} + 96 q^{11} - 144 q^{19} - 256 q^{21} - 300 q^{29} - 24 q^{31} - 80 q^{39} + 180 q^{41} - 96 q^{49} - 288 q^{51} - 96 q^{59} - 156 q^{61} + 300 q^{69} - 240 q^{79} + 868 q^{81} + 240 q^{91} + 240 q^{99}+O(q^{100}) \) 24 * q - 52 * q^9 + 96 * q^11 - 144 * q^19 - 256 * q^21 - 300 * q^29 - 24 * q^31 - 80 * q^39 + 180 * q^41 - 96 * q^49 - 288 * q^51 - 96 * q^59 - 156 * q^61 + 300 * q^69 - 240 * q^79 + 868 * q^81 + 240 * q^91 + 240 * q^99

Introduction

L-functions

Modular forms

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