LMFDB - Embedded newform 900.3.u.c.149.7

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			149.7
Character	$\chi$	$=$	900.149
Dual form			900.3.u.c.749.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.114662 + 2.99781i) q^{3} +(1.38806 - 0.801399i) q^{7} +(-8.97371 + 0.687471i) q^{9} +O(q^{10})$	\(q+(0.114662 + 2.99781i) q^{3} +(1.38806 - 0.801399i) q^{7} +(-8.97371 + 0.687471i) q^{9} +(-6.10409 + 3.52420i) q^{11} +(18.9291 + 10.9287i) q^{13} -33.1463 q^{17} +6.82330 q^{19} +(2.56160 + 4.06926i) q^{21} +(7.09299 - 12.2854i) q^{23} +(-3.08985 - 26.8226i) q^{27} +(-31.4868 + 18.1789i) q^{29} +(-17.2065 + 29.8025i) q^{31} +(-11.2648 - 17.8948i) q^{33} -43.1114i q^{37} +(-30.5917 + 57.9989i) q^{39} +(18.2263 + 10.5230i) q^{41} +(-53.1311 + 30.6752i) q^{43} +(8.44488 + 14.6270i) q^{47} +(-23.2155 + 40.2105i) q^{49} +(-3.80063 - 99.3663i) q^{51} +12.1221 q^{53} +(0.782375 + 20.4549i) q^{57} +(-54.3639 - 31.3870i) q^{59} +(3.38717 + 5.86675i) q^{61} +(-11.9051 + 8.14577i) q^{63} +(-92.5894 - 53.4565i) q^{67} +(37.6426 + 19.8547i) q^{69} -23.4326i q^{71} -69.5613i q^{73} +(-5.64858 + 9.78362i) q^{77} +(27.8659 + 48.2651i) q^{79} +(80.0548 - 12.3383i) q^{81} +(-41.3869 - 71.6843i) q^{83} +(-58.1073 - 92.3071i) q^{87} +13.5312i q^{89} +35.0331 q^{91} +(-91.3151 - 48.1645i) q^{93} +(112.060 - 64.6979i) q^{97} +(52.3535 - 35.8215i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.114662	+	2.99781i	0.0382208	+	0.999269i
$3$	0.114662	+	2.99781i	0.0382208	+	0.999269i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.38806	−	0.801399i	0.198295	−	0.114486i	−0.397565	−	0.917574i	$-0.630145\pi$
$7$	1.38806	−	0.801399i	0.198295	−	0.114486i	0.595860	+	0.803088i	$0.296811\pi$
$8$		0			0
$9$	−8.97371	+	0.687471i	−0.997078	+	0.0763857i
$10$		0			0
$11$	−6.10409	+	3.52420i	−0.554917	+	0.320382i	−0.751103	−	0.660185i	$-0.770478\pi$
$11$	−6.10409	+	3.52420i	−0.554917	+	0.320382i	0.196186	+	0.980567i	$0.437144\pi$
$12$		0			0
$13$	18.9291	+	10.9287i	1.45608	+	0.840671i	0.998815	−	0.0486581i	$-0.0154945\pi$
$13$	18.9291	+	10.9287i	1.45608	+	0.840671i	0.457269	+	0.889329i	$0.348828\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−33.1463			−1.94978			−0.974892	−	0.222679i	$-0.928520\pi$
$17$	−33.1463			−1.94978			−0.974892	+	0.222679i	$0.928520\pi$
$18$		0			0
$19$	6.82330			0.359121			0.179561	−	0.983747i	$-0.442532\pi$
$19$	6.82330			0.359121			0.179561	+	0.983747i	$0.442532\pi$
$20$		0			0
$21$	2.56160	+	4.06926i	0.121981	+	0.193774i
$22$		0			0
$23$	7.09299	−	12.2854i	0.308391	−	0.534149i	−0.669620	−	0.742704i	$-0.733543\pi$
$23$	7.09299	−	12.2854i	0.308391	−	0.534149i	0.978011	+	0.208556i	$0.0668762\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−3.08985	−	26.8226i	−0.114439	−	0.993430i
$28$		0			0
$29$	−31.4868	+	18.1789i	−1.08575	+	0.626860i	−0.932443	−	0.361318i	$-0.882327\pi$
$29$	−31.4868	+	18.1789i	−1.08575	+	0.626860i	−0.153311	+	0.988178i	$0.548994\pi$
$30$		0			0
$31$	−17.2065	+	29.8025i	−0.555048	+	0.961370i	0.442852	+	0.896595i	$0.353967\pi$
$31$	−17.2065	+	29.8025i	−0.555048	+	0.961370i	−0.997900	+	0.0647759i	$0.979367\pi$
$32$		0			0
$33$	−11.2648	−	17.8948i	−0.341357	−	0.542266i
$34$		0			0
$35$		0			0
$36$		0			0
$37$		−	43.1114i		−	1.16517i	−0.812768	−	0.582587i	$-0.802041\pi$
$37$		−	43.1114i		−	1.16517i	0.812768	−	0.582587i	$-0.197959\pi$
$38$		0			0
$39$	−30.5917	+	57.9989i	−0.784404	+	1.48715i
$40$		0			0
$41$	18.2263	+	10.5230i	0.444544	+	0.256658i	0.705523	−	0.708687i	$-0.250712\pi$
$41$	18.2263	+	10.5230i	0.444544	+	0.256658i	−0.260979	+	0.965344i	$0.584045\pi$
$42$		0			0
$43$	−53.1311	+	30.6752i	−1.23561	+	0.713378i	−0.968193	−	0.250204i	$-0.919502\pi$
$43$	−53.1311	+	30.6752i	−1.23561	+	0.713378i	−0.267414	+	0.963582i	$0.586169\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	8.44488	+	14.6270i	0.179678	+	0.311212i	0.941770	−	0.336257i	$-0.109161\pi$
$47$	8.44488	+	14.6270i	0.179678	+	0.311212i	−0.762092	+	0.647469i	$0.775828\pi$
$48$		0			0
$49$	−23.2155	+	40.2105i	−0.473786	+	0.820622i
$50$		0			0
$51$	−3.80063	−	99.3663i	−0.0745222	−	1.94836i
$52$		0			0
$53$	12.1221			0.228718			0.114359	−	0.993439i	$-0.463519\pi$
$53$	12.1221			0.228718			0.114359	+	0.993439i	$0.463519\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	0.782375	+	20.4549i	0.0137259	+	0.358859i
$58$		0			0
$59$	−54.3639	−	31.3870i	−0.921422	−	0.531983i	−0.0373338	−	0.999303i	$-0.511886\pi$
$59$	−54.3639	−	31.3870i	−0.921422	−	0.531983i	−0.884089	+	0.467319i	$0.845220\pi$
$60$		0			0
$61$	3.38717	+	5.86675i	0.0555274	+	0.0961763i	0.892453	−	0.451140i	$-0.148983\pi$
$61$	3.38717	+	5.86675i	0.0555274	+	0.0961763i	−0.836926	+	0.547317i	$0.815649\pi$
$62$		0			0
$63$	−11.9051	+	8.14577i	−0.188970	+	0.129298i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−92.5894	−	53.4565i	−1.38193	−	0.797858i	−0.389543	−	0.921008i	$-0.627367\pi$
$67$	−92.5894	−	53.4565i	−1.38193	−	0.797858i	−0.992388	+	0.123150i	$0.960700\pi$
$68$		0			0
$69$	37.6426	+	19.8547i	0.545545	+	0.287750i
$70$		0			0
$71$		−	23.4326i		−	0.330036i	−0.986291	−	0.165018i	$-0.947232\pi$
$71$		−	23.4326i		−	0.330036i	0.986291	−	0.165018i	$-0.0527683\pi$
$72$		0			0
$73$		−	69.5613i		−	0.952895i	−0.879203	−	0.476447i	$-0.841924\pi$
$73$		−	69.5613i		−	0.952895i	0.879203	−	0.476447i	$-0.158076\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−5.64858	+	9.78362i	−0.0733581	+	0.127060i
$78$		0			0
$79$	27.8659	+	48.2651i	0.352733	+	0.610951i	0.986727	−	0.162386i	$-0.0519191\pi$
$79$	27.8659	+	48.2651i	0.352733	+	0.610951i	−0.633994	+	0.773338i	$0.718586\pi$
$80$		0			0
$81$	80.0548	−	12.3383i	0.988330	−	0.152325i
$82$		0			0
$83$	−41.3869	−	71.6843i	−0.498638	−	0.863666i	0.501361	−	0.865238i	$-0.332833\pi$
$83$	−41.3869	−	71.6843i	−0.498638	−	0.863666i	−0.999999	+	0.00157207i	$0.999500\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−58.1073	−	92.3071i	−0.667900	−	1.06100i
$88$		0			0
$89$			13.5312i			0.152036i	0.997106	+	0.0760180i	$0.0242206\pi$
$89$			13.5312i			0.152036i	−0.997106	+	0.0760180i	$0.975779\pi$
$90$		0			0
$91$	35.0331			0.384979
$92$		0			0
$93$	−91.3151	−	48.1645i	−0.981882	−	0.517898i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	112.060	−	64.6979i	1.15526	−	0.666988i	0.205095	−	0.978742i	$-0.434250\pi$
$97$	112.060	−	64.6979i	1.15526	−	0.666988i	0.950163	+	0.311754i	$0.100916\pi$
$98$		0			0
$99$	52.3535	−	35.8215i	0.528823	−	0.361833i
$100$		0			0
$101$	−89.9838	+	51.9522i	−0.890929	+	0.514378i	−0.874246	−	0.485483i	$-0.838644\pi$
$101$	−89.9838	+	51.9522i	−0.890929	+	0.514378i	−0.0166826	+	0.999861i	$0.505310\pi$
$102$		0			0
$103$	6.91217	+	3.99074i	0.0671085	+	0.0387451i	0.533179	−	0.846003i	$-0.320997\pi$
$103$	6.91217	+	3.99074i	0.0671085	+	0.0387451i	−0.466070	+	0.884748i	$0.654331\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−113.941			−1.06487			−0.532433	−	0.846472i	$-0.678722\pi$
$107$	−113.941			−1.06487			−0.532433	+	0.846472i	$0.678722\pi$
$108$		0			0
$109$	−76.8649			−0.705182			−0.352591	−	0.935777i	$-0.614699\pi$
$109$	−76.8649			−0.705182			−0.352591	+	0.935777i	$0.614699\pi$
$110$		0			0
$111$	129.240	−	4.94326i	1.16432	−	0.0445338i
$112$		0			0
$113$	24.9911	−	43.2859i	0.221160	−	0.383061i	−0.734000	−	0.679149i	$-0.762349\pi$
$113$	24.9911	−	43.2859i	0.221160	−	0.383061i	0.955161	+	0.296088i	$0.0956822\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−177.377	−	85.0579i	−1.51605	−	0.726990i
$118$		0			0
$119$	−46.0092	+	26.5634i	−0.386632	+	0.223222i
$120$		0			0
$121$	−35.6601	+	61.7651i	−0.294711	+	0.510455i
$122$		0			0
$123$	−29.4560	+	55.8456i	−0.239479	+	0.454029i
$124$		0			0
$125$		0			0
$126$		0			0
$127$			53.8806i			0.424257i	0.977242	+	0.212128i	$0.0680395\pi$
$127$			53.8806i			0.424257i	−0.977242	+	0.212128i	$0.931960\pi$
$128$		0			0
$129$	−98.0506	−	155.760i	−0.760082	−	1.20744i
$130$		0			0
$131$	−221.724	−	128.012i	−1.69255	−	0.977193i	−0.952450	−	0.304694i	$-0.901446\pi$
$131$	−221.724	−	128.012i	−1.69255	−	0.977193i	−0.740098	−	0.672499i	$-0.765221\pi$
$132$		0			0
$133$	9.47118	−	5.46819i	0.0712119	−	0.0411142i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−6.53788	−	11.3239i	−0.0477217	−	0.0826565i	0.841178	−	0.540759i	$-0.181863\pi$
$137$	−6.53788	−	11.3239i	−0.0477217	−	0.0826565i	−0.888900	+	0.458102i	$0.848529\pi$
$138$		0			0
$139$	61.9474	−	107.296i	0.445664	−	0.771913i	−0.552434	−	0.833557i	$-0.686301\pi$
$139$	61.9474	−	107.296i	0.445664	−	0.771913i	0.998098	+	0.0616433i	$0.0196341\pi$
$140$		0			0
$141$	−42.8805	+	26.9933i	−0.304117	+	0.191442i
$142$		0			0
$143$	−154.060			−1.07734
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−123.205	−	64.9850i	−0.838130	−	0.442075i
$148$		0			0
$149$	54.2591	+	31.3265i	0.364155	+	0.210245i	0.670902	−	0.741546i	$-0.265907\pi$
$149$	54.2591	+	31.3265i	0.364155	+	0.210245i	−0.306747	+	0.951791i	$0.599241\pi$
$150$		0			0
$151$	122.920	+	212.903i	0.814038	+	1.40996i	0.910016	+	0.414572i	$0.136069\pi$
$151$	122.920	+	212.903i	0.814038	+	1.40996i	−0.0959781	+	0.995383i	$0.530598\pi$
$152$		0			0
$153$	297.445	−	22.7871i	1.94409	−	0.148936i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	186.757	+	107.824i	1.18953	+	0.686777i	0.958200	−	0.286098i	$-0.0923583\pi$
$157$	186.757	+	107.824i	1.18953	+	0.686777i	0.231332	+	0.972875i	$0.425692\pi$
$158$		0			0
$159$	1.38994	+	36.3396i	0.00874178	+	0.228551i
$160$		0			0
$161$		−	22.7373i		−	0.141225i
$162$		0			0
$163$		−	43.7518i		−	0.268416i	−0.990953	−	0.134208i	$-0.957151\pi$
$163$		−	43.7518i		−	0.268416i	0.990953	−	0.134208i	$-0.0428490\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−111.443	+	193.025i	−0.667325	+	1.15584i	0.311324	+	0.950304i	$0.399227\pi$
$167$	−111.443	+	193.025i	−0.667325	+	1.15584i	−0.978649	+	0.205537i	$0.934106\pi$
$168$		0			0
$169$	154.374	+	267.383i	0.913454	+	1.58215i
$170$		0			0
$171$	−61.2303	+	4.69082i	−0.358072	+	0.0274317i
$172$		0			0
$173$	149.385	+	258.742i	0.863494	+	1.49562i	0.868534	+	0.495629i	$0.165062\pi$
$173$	149.385	+	258.742i	0.863494	+	1.49562i	−0.00503988	+	0.999987i	$0.501604\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	87.8588	−	166.571i	0.496377	−	0.941082i
$178$		0			0
$179$			105.801i			0.591067i	0.955332	+	0.295533i	$0.0954973\pi$
$179$			105.801i			0.591067i	−0.955332	+	0.295533i	$0.904503\pi$
$180$		0			0
$181$	278.743			1.54002			0.770009	−	0.638033i	$-0.220252\pi$
$181$	278.743			1.54002			0.770009	+	0.638033i	$0.220252\pi$
$182$		0			0
$183$	−17.1990	+	10.8268i	−0.0939837	+	0.0591627i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	202.328	−	116.814i	1.08197	−	0.624675i
$188$		0			0
$189$	−25.7845	−	34.7553i	−0.136426	−	0.183891i
$190$		0			0
$191$	121.948	−	70.4065i	0.638470	−	0.368621i	−0.145555	−	0.989350i	$-0.546497\pi$
$191$	121.948	−	70.4065i	0.638470	−	0.368621i	0.784025	+	0.620729i	$0.213163\pi$
$192$		0			0
$193$	−134.671	−	77.7522i	−0.697776	−	0.402861i	0.108743	−	0.994070i	$-0.465318\pi$
$193$	−134.671	−	77.7522i	−0.697776	−	0.402861i	−0.806518	+	0.591209i	$0.798651\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	229.378			1.16436			0.582178	−	0.813062i	$-0.302201\pi$
$197$	229.378			1.16436			0.582178	+	0.813062i	$0.302201\pi$
$198$		0			0
$199$	−362.645			−1.82234			−0.911168	−	0.412036i	$-0.864818\pi$
$199$	−362.645			−1.82234			−0.911168	+	0.412036i	$0.864818\pi$
$200$		0			0
$201$	149.636	−	283.695i	0.744457	−	1.41142i
$202$		0			0
$203$	−29.1372	+	50.4671i	−0.143533	+	0.248606i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−55.2045	+	115.122i	−0.266689	+	0.556145i
$208$		0			0
$209$	−41.6500	+	24.0467i	−0.199282	+	0.115056i
$210$		0			0
$211$	−171.458	+	296.974i	−0.812598	+	1.40746i	0.0984416	+	0.995143i	$0.468614\pi$
$211$	−171.458	+	296.974i	−0.812598	+	1.40746i	−0.911040	+	0.412318i	$0.864719\pi$
$212$		0			0
$213$	70.2464	−	2.68683i	0.329795	−	0.0126142i
$214$		0			0
$215$		0			0
$216$		0			0
$217$			55.1570i			0.254180i
$218$		0			0
$219$	208.532	−	7.97606i	0.952199	−	0.0364204i
$220$		0			0
$221$	−627.430	−	362.247i	−2.83905	−	1.63913i
$222$		0			0
$223$	−81.7243	+	47.1836i	−0.366477	+	0.211586i	−0.671918	−	0.740625i	$-0.734529\pi$
$223$	−81.7243	+	47.1836i	−0.366477	+	0.211586i	0.305441	+	0.952211i	$0.401196\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	167.869	+	290.757i	0.739510	+	1.28087i	0.952716	+	0.303862i	$0.0982762\pi$
$227$	167.869	+	290.757i	0.739510	+	1.28087i	−0.213206	+	0.977007i	$0.568390\pi$
$228$		0			0
$229$	−108.283	+	187.552i	−0.472854	+	0.819006i	−0.999517	−	0.0310674i	$-0.990109\pi$
$229$	−108.283	+	187.552i	−0.472854	+	0.819006i	0.526664	+	0.850074i	$0.323443\pi$
$230$		0			0
$231$	−29.9771	−	15.8115i	−0.129771	−	0.0684482i
$232$		0			0
$233$	35.0415			0.150393			0.0751963	−	0.997169i	$-0.476042\pi$
$233$	35.0415			0.150393			0.0751963	+	0.997169i	$0.476042\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−141.494	+	89.0708i	−0.597023	+	0.375826i
$238$		0			0
$239$	−212.383	−	122.619i	−0.888631	−	0.513051i	−0.0151363	−	0.999885i	$-0.504818\pi$
$239$	−212.383	−	122.619i	−0.888631	−	0.513051i	−0.873494	+	0.486834i	$0.838152\pi$
$240$		0			0
$241$	0.672639	+	1.16504i	0.00279103	+	0.00483421i	0.867418	−	0.497581i	$-0.165778\pi$
$241$	0.672639	+	1.16504i	0.00279103	+	0.00483421i	−0.864627	+	0.502415i	$0.832445\pi$
$242$		0			0
$243$	46.1672	+	238.574i	0.189988	+	0.981786i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	129.159	+	74.5699i	0.522910	+	0.301902i
$248$		0			0
$249$	210.150	−	132.290i	0.843977	−	0.531284i
$250$		0			0
$251$			397.075i			1.58197i	0.611834	+	0.790986i	$0.290432\pi$
$251$			397.075i			1.58197i	−0.611834	+	0.790986i	$0.709568\pi$
$252$		0			0
$253$			99.9884i			0.395211i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−10.5655	+	18.3001i	−0.0411111	+	0.0712064i	−0.885849	−	0.463974i	$-0.846423\pi$
$257$	−10.5655	+	18.3001i	−0.0411111	+	0.0712064i	0.844738	+	0.535181i	$0.179756\pi$
$258$		0			0
$259$	−34.5495	−	59.8414i	−0.133396	−	0.231048i
$260$		0			0
$261$	270.056	−	184.779i	1.03470	−	0.707965i
$262$		0			0
$263$	−63.7204	−	110.367i	−0.242283	−	0.419646i	0.719081	−	0.694926i	$-0.244563\pi$
$263$	−63.7204	−	110.367i	−0.242283	−	0.419646i	−0.961364	+	0.275280i	$0.911230\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−40.5639	+	1.55152i	−0.151925	+	0.00581093i
$268$		0			0
$269$		−	234.170i		−	0.870520i	−0.900305	−	0.435260i	$-0.856657\pi$
$269$		−	234.170i		−	0.870520i	0.900305	−	0.435260i	$-0.143343\pi$
$270$		0			0
$271$	108.333			0.399753			0.199876	−	0.979821i	$-0.435946\pi$
$271$	108.333			0.399753			0.199876	+	0.979821i	$0.435946\pi$
$272$		0			0
$273$	4.01697	+	105.022i	0.0147142	+	0.384697i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	220.075	−	127.060i	0.794494	−	0.458701i	−0.0470483	−	0.998893i	$-0.514981\pi$
$277$	220.075	−	127.060i	0.794494	−	0.458701i	0.841542	+	0.540191i	$0.181648\pi$
$278$		0			0
$279$	133.917	−	279.268i	0.479991	−	1.00096i
$280$		0			0
$281$	−342.882	+	197.963i	−1.22022	+	0.704494i	−0.964965	−	0.262379i	$-0.915493\pi$
$281$	−342.882	+	197.963i	−1.22022	+	0.704494i	−0.255255	+	0.966874i	$0.582160\pi$
$282$		0			0
$283$	328.861	+	189.868i	1.16205	+	0.670912i	0.951795	−	0.306734i	$-0.0992361\pi$
$283$	328.861	+	189.868i	1.16205	+	0.670912i	0.210259	+	0.977646i	$0.432569\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	33.7324			0.117534
$288$		0			0
$289$	809.679			2.80166
$290$		0			0
$291$	206.801	+	328.516i	0.710656	+	1.12892i
$292$		0			0
$293$	244.975	−	424.309i	0.836092	−	1.44815i	−0.0570460	−	0.998372i	$-0.518168\pi$
$293$	244.975	−	424.309i	0.836092	−	1.44815i	0.893138	−	0.449782i	$-0.148498\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	113.389	+	152.838i	0.381781	+	0.514607i
$298$		0			0
$299$	268.528	−	155.035i	0.898086	−	0.518510i
$300$		0			0
$301$	−49.1662	+	85.1584i	−0.163343	+	0.282918i
$302$		0			0
$303$	−166.060	−	263.797i	−0.548054	−	0.870618i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			110.535i			0.360048i	0.983662	+	0.180024i	$0.0576175\pi$
$307$			110.535i			0.360048i	−0.983662	+	0.180024i	$0.942382\pi$
$308$		0			0
$309$	−11.1709	+	21.1790i	−0.0361518	+	0.0685403i
$310$		0			0
$311$	155.652	+	89.8659i	0.500490	+	0.288958i	0.728916	−	0.684603i	$-0.240025\pi$
$311$	155.652	+	89.8659i	0.500490	+	0.288958i	−0.228426	+	0.973561i	$0.573358\pi$
$312$		0			0
$313$	175.659	−	101.417i	0.561212	−	0.324016i	−0.192420	−	0.981313i	$-0.561634\pi$
$313$	175.659	−	101.417i	0.561212	−	0.324016i	0.753632	+	0.657297i	$0.228300\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	263.393	+	456.210i	0.830893	+	1.43915i	0.897331	+	0.441358i	$0.145503\pi$
$317$	263.393	+	456.210i	0.830893	+	1.43915i	−0.0664385	+	0.997791i	$0.521164\pi$
$318$		0			0
$319$	128.132	−	221.932i	0.401669	−	0.695711i
$320$		0			0
$321$	−13.0647	−	341.572i	−0.0407000	−	1.06409i
$322$		0			0
$323$	−226.167			−0.700208
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−8.81350	−	230.426i	−0.0269526	−	0.704667i
$328$		0			0
$329$	23.4441	+	13.5354i	0.0712586	+	0.0411411i
$330$		0			0
$331$	163.057	+	282.424i	0.492621	+	0.853244i	0.999964	−	0.00849989i	$-0.00270563\pi$
$331$	163.057	+	282.424i	0.492621	+	0.853244i	−0.507343	+	0.861744i	$0.669372\pi$
$332$		0			0
$333$	29.6379	+	386.869i	0.0890026	+	1.16177i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	291.165	+	168.104i	0.863991	+	0.498825i	0.865347	−	0.501174i	$-0.167098\pi$
$337$	291.165	+	168.104i	0.863991	+	0.498825i	−0.00135593	+	0.999999i	$0.500432\pi$
$338$		0			0
$339$	132.628	+	69.9553i	0.391234	+	0.206358i
$340$		0			0
$341$		−	242.556i		−	0.711308i
$342$		0			0
$343$			152.957i			0.445938i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−244.994	+	424.342i	−0.706034	+	1.22289i	0.260283	+	0.965532i	$0.416184\pi$
$347$	−244.994	+	424.342i	−0.706034	+	1.22289i	−0.966317	+	0.257355i	$0.917149\pi$
$348$		0			0
$349$	−231.672	−	401.268i	−0.663817	−	1.14976i	−0.979605	−	0.200934i	$-0.935602\pi$
$349$	−231.672	−	401.268i	−0.663817	−	1.14976i	0.315788	−	0.948830i	$-0.397731\pi$
$350$		0			0
$351$	234.649	−	541.496i	0.668515	−	1.54272i
$352$		0			0
$353$	227.910	+	394.752i	0.645639	+	1.11828i	0.984154	+	0.177318i	$0.0567421\pi$
$353$	227.910	+	394.752i	0.645639	+	1.11828i	−0.338515	+	0.940961i	$0.609925\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−84.9076	−	134.881i	−0.237836	−	0.377818i
$358$		0			0
$359$		−	479.550i		−	1.33579i	−0.744254	−	0.667896i	$-0.767195\pi$
$359$		−	479.550i		−	1.33579i	0.744254	−	0.667896i	$-0.232805\pi$
$360$		0			0
$361$	−314.443			−0.871032
$362$		0			0
$363$	−189.249	−	99.8199i	−0.521346	−	0.274986i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	221.120	−	127.663i	0.602506	−	0.347857i	−0.167521	−	0.985869i	$-0.553576\pi$
$367$	221.120	−	127.663i	0.602506	−	0.347857i	0.770027	+	0.638012i	$0.220243\pi$
$368$		0			0
$369$	−170.792	−	81.9000i	−0.462850	−	0.221951i
$370$		0			0
$371$	16.8262	−	9.71461i	0.0453536	−	0.0261849i
$372$		0			0
$373$	−29.0066	−	16.7470i	−0.0777657	−	0.0448981i	0.460613	−	0.887601i	$-0.347630\pi$
$373$	−29.0066	−	16.7470i	−0.0777657	−	0.0448981i	−0.538379	+	0.842703i	$0.680963\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−794.690			−2.10793
$378$		0			0
$379$	376.776			0.994131			0.497065	−	0.867713i	$-0.334411\pi$
$379$	376.776			0.994131			0.497065	+	0.867713i	$0.334411\pi$
$380$		0			0
$381$	−161.524	+	6.17808i	−0.423947	+	0.0162154i
$382$		0			0
$383$	118.789	−	205.748i	0.310153	−	0.537201i	−0.668242	−	0.743944i	$-0.732953\pi$
$383$	118.789	−	205.748i	0.310153	−	0.537201i	0.978395	+	0.206743i	$0.0662864\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	455.694	−	311.797i	1.17750	−	0.805676i
$388$		0			0
$389$	−355.753	+	205.394i	−0.914533	+	0.528006i	−0.881887	−	0.471461i	$-0.843727\pi$
$389$	−355.753	+	205.394i	−0.914533	+	0.528006i	−0.0326463	+	0.999467i	$0.510393\pi$
$390$		0			0
$391$	−235.107	+	407.216i	−0.601295	+	1.04147i
$392$		0			0
$393$	358.333	−	679.364i	0.911789	−	1.72866i
$394$		0			0
$395$		0			0
$396$		0			0
$397$		−	208.481i		−	0.525142i	−0.964913	−	0.262571i	$-0.915430\pi$
$397$		−	208.481i		−	0.525142i	0.964913	−	0.262571i	$-0.0845703\pi$
$398$		0			0
$399$	17.4786	+	27.7658i	0.0438059	+	0.0695884i
$400$		0			0
$401$	22.8279	+	13.1797i	0.0569274	+	0.0328671i	0.528194	−	0.849124i	$-0.322870\pi$
$401$	22.8279	+	13.1797i	0.0569274	+	0.0328671i	−0.471266	+	0.881991i	$0.656203\pi$
$402$		0			0
$403$	−651.406	+	376.089i	−1.61639	+	0.933224i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	151.933	+	263.156i	0.373300	+	0.646575i
$408$		0			0
$409$	87.1760	−	150.993i	0.213144	−	0.369177i	−0.739553	−	0.673099i	$-0.764963\pi$
$409$	87.1760	−	150.993i	0.213144	−	0.369177i	0.952697	+	0.303922i	$0.0982962\pi$
$410$		0			0
$411$	33.1973	−	20.8977i	0.0807721	−	0.0508461i
$412$		0			0
$413$	−100.614			−0.243618
$414$		0			0
$415$		0			0
$416$		0			0
$417$	328.756	+	173.403i	0.788383	+	0.415836i
$418$		0			0
$419$	227.887	+	131.571i	0.543883	+	0.314011i	0.746651	−	0.665216i	$-0.231660\pi$
$419$	227.887	+	131.571i	0.543883	+	0.314011i	−0.202768	+	0.979227i	$0.564994\pi$
$420$		0			0
$421$	188.486	+	326.467i	0.447710	+	0.775456i	0.998237	−	0.0593612i	$-0.0189064\pi$
$421$	188.486	+	326.467i	0.447710	+	0.775456i	−0.550527	+	0.834818i	$0.685573\pi$
$422$		0			0
$423$	−85.8375	−	125.452i	−0.202925	−	0.296578i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	9.40322	+	5.42895i	0.0220216	+	0.0127142i
$428$		0			0
$429$	−17.6648	−	461.842i	−0.0411768	−	1.07655i
$430$		0			0
$431$			24.6406i			0.0571707i	0.999591	+	0.0285854i	$0.00910024\pi$
$431$			24.6406i			0.0571707i	−0.999591	+	0.0285854i	$0.990900\pi$
$432$		0			0
$433$		−	149.886i		−	0.346157i	−0.984908	−	0.173079i	$-0.944629\pi$
$433$		−	149.886i		−	0.346157i	0.984908	−	0.173079i	$-0.0553715\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	48.3976	−	83.8271i	0.110750	−	0.191824i
$438$		0			0
$439$	210.058	+	363.831i	0.478492	+	0.828773i	0.999696	−	0.0246596i	$-0.00785020\pi$
$439$	210.058	+	363.831i	0.478492	+	0.828773i	−0.521204	+	0.853432i	$0.674517\pi$
$440$		0			0
$441$	180.686	−	376.797i	0.409718	−	0.854414i
$442$		0			0
$443$	96.6537	+	167.409i	0.218180	+	0.377899i	0.954252	−	0.299005i	$-0.0966547\pi$
$443$	96.6537	+	167.409i	0.218180	+	0.377899i	−0.736072	+	0.676904i	$0.763321\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−87.6893	+	166.250i	−0.196173	+	0.371924i
$448$		0			0
$449$			267.368i			0.595475i	0.954648	+	0.297738i	$0.0962320\pi$
$449$			267.368i			0.595475i	−0.954648	+	0.297738i	$0.903768\pi$
$450$		0			0
$451$	−148.340			−0.328914
$452$		0			0
$453$	−624.149	+	392.902i	−1.37781	+	0.867333i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−101.557	+	58.6341i	−0.222226	+	0.128302i	−0.606981	−	0.794717i	$-0.707619\pi$
$457$	−101.557	+	58.6341i	−0.222226	+	0.128302i	0.384755	+	0.923019i	$0.374286\pi$
$458$		0			0
$459$	102.417	+	889.071i	0.223131	+	1.93697i
$460$		0			0
$461$	576.193	−	332.665i	1.24988	−	0.721616i	0.278792	−	0.960352i	$-0.410066\pi$
$461$	576.193	−	332.665i	1.24988	−	0.721616i	0.971085	+	0.238735i	$0.0767328\pi$
$462$		0			0
$463$	−340.345	−	196.498i	−0.735087	−	0.424403i	0.0851934	−	0.996364i	$-0.472849\pi$
$463$	−340.345	−	196.498i	−0.735087	−	0.424403i	−0.820280	+	0.571962i	$0.806183\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	323.816			0.693397			0.346698	−	0.937977i	$-0.387303\pi$
$467$	323.816			0.693397			0.346698	+	0.937977i	$0.387303\pi$
$468$		0			0
$469$	−171.360			−0.365373
$470$		0			0
$471$	−301.822	+	572.224i	−0.640810	+	1.21491i
$472$		0			0
$473$	216.211	−	374.489i	0.457106	−	0.791731i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−108.780	+	8.33356i	−0.228050	+	0.0174708i
$478$		0			0
$479$	−193.983	+	111.996i	−0.404976	+	0.233813i	−0.688629	−	0.725114i	$-0.741787\pi$
$479$	−193.983	+	111.996i	−0.404976	+	0.233813i	0.283653	+	0.958927i	$0.408454\pi$
$480$		0			0
$481$	471.153	−	816.061i	0.979528	−	1.69659i
$482$		0			0
$483$	68.1619	−	2.60711i	0.141122	−	0.00539774i
$484$		0			0
$485$		0			0
$486$		0			0
$487$		−	666.654i		−	1.36890i	−0.729060	−	0.684450i	$-0.760043\pi$
$487$		−	666.654i		−	1.36890i	0.729060	−	0.684450i	$-0.239957\pi$
$488$		0			0
$489$	131.160	−	5.01668i	0.268220	−	0.0102591i
$490$		0			0
$491$	−490.592	−	283.244i	−0.999170	−	0.576871i	−0.0911673	−	0.995836i	$-0.529060\pi$
$491$	−490.592	−	283.244i	−0.999170	−	0.576871i	−0.908003	+	0.418965i	$0.862393\pi$
$492$		0			0
$493$	1043.67	−	602.565i	2.11698	−	1.22224i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−18.7789	−	32.5259i	−0.0377844	−	0.0654445i
$498$		0			0
$499$	−449.283	+	778.182i	−0.900367	+	1.55948i	−0.0733495	+	0.997306i	$0.523369\pi$
$499$	−449.283	+	778.182i	−0.900367	+	1.55948i	−0.827018	+	0.562176i	$0.809964\pi$
$500$		0			0
$501$	−591.432	−	311.953i	−1.18050	−	0.622660i
$502$		0			0
$503$	−744.710			−1.48054			−0.740268	−	0.672312i	$-0.765301\pi$
$503$	−744.710			−1.48054			−0.740268	+	0.672312i	$0.765301\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−783.862	+	493.442i	−1.54608	+	0.973257i
$508$		0			0
$509$	−461.074	−	266.201i	−0.905842	−	0.522988i	−0.0267513	−	0.999642i	$-0.508516\pi$
$509$	−461.074	−	266.201i	−0.905842	−	0.522988i	−0.879091	+	0.476654i	$0.841850\pi$
$510$		0			0
$511$	−55.7464	−	96.5556i	−0.109093	−	0.188954i
$512$		0			0
$513$	−21.0830	−	183.019i	−0.0410974	−	0.356762i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−103.097	−	59.5228i	−0.199413	−	0.115131i
$518$		0			0
$519$	−758.529	+	477.494i	−1.46152	+	0.920027i
$520$		0			0
$521$			527.079i			1.01167i	0.862631	+	0.505834i	$0.168815\pi$
$521$			527.079i			1.01167i	−0.862631	+	0.505834i	$0.831185\pi$
$522$		0			0
$523$			615.733i			1.17731i	0.808385	+	0.588655i	$0.200342\pi$
$523$			615.733i			1.17731i	−0.808385	+	0.588655i	$0.799658\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	570.331	−	987.843i	1.08222	−	1.87446i
$528$		0			0
$529$	163.879	+	283.847i	0.309790	+	0.536572i
$530$		0			0
$531$	509.423	+	244.284i	0.959366	+	0.460046i
$532$		0			0
$533$	230.005	+	398.381i	0.431529	+	0.747431i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−317.171	+	12.1314i	−0.590635	+	0.0225910i
$538$		0			0
$539$		−	327.264i		−	0.607169i
$540$		0			0
$541$	−400.878			−0.740994			−0.370497	−	0.928834i	$-0.620813\pi$
$541$	−400.878			−0.740994			−0.370497	+	0.928834i	$0.620813\pi$
$542$		0			0
$543$	31.9613	+	835.619i	0.0588607	+	1.53889i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−821.585	+	474.342i	−1.50198	+	0.867171i	−0.501986	+	0.864876i	$0.667397\pi$
$547$	−821.585	+	474.342i	−1.50198	+	0.867171i	−0.999997	+	0.00229498i	$0.999269\pi$
$548$		0			0
$549$	−34.4287	−	50.3179i	−0.0627116	−	0.0916538i
$550$		0			0
$551$	−214.844	+	124.040i	−0.389917	+	0.225119i
$552$		0			0
$553$	77.3593	+	44.6634i	0.139890	+	0.0807657i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−303.811			−0.545441			−0.272720	−	0.962093i	$-0.587923\pi$
$557$	−303.811			−0.545441			−0.272720	+	0.962093i	$0.587923\pi$
$558$		0			0
$559$	−1340.96			−2.39886
$560$		0			0
$561$	373.386	+	593.147i	0.665572	+	1.05730i
$562$		0			0
$563$	167.171	−	289.548i	0.296928	−	0.514295i	−0.678503	−	0.734597i	$-0.737371\pi$
$563$	167.171	−	289.548i	0.296928	−	0.514295i	0.975432	+	0.220302i	$0.0707044\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	101.233	−	81.2822i	0.178542	−	0.143355i
$568$		0			0
$569$	−429.145	+	247.767i	−0.754210	+	0.435443i	−0.827213	−	0.561889i	$-0.810075\pi$
$569$	−429.145	+	247.767i	−0.754210	+	0.435443i	0.0730032	+	0.997332i	$0.476742\pi$
$570$		0			0
$571$	242.752	−	420.458i	0.425134	−	0.736354i	−0.571299	−	0.820742i	$-0.693560\pi$
$571$	242.752	−	420.458i	0.425134	−	0.736354i	0.996433	+	0.0843881i	$0.0268936\pi$
$572$		0			0
$573$	225.048	+	357.503i	0.392754	+	0.623914i
$574$		0			0
$575$		0			0
$576$		0			0
$577$		−	294.155i		−	0.509800i	−0.966967	−	0.254900i	$-0.917957\pi$
$577$		−	294.155i		−	0.509800i	0.966967	−	0.254900i	$-0.0820426\pi$
$578$		0			0
$579$	217.644	−	412.632i	0.375897	−	0.712663i
$580$		0			0
$581$	−114.895	−	66.3349i	−0.197755	−	0.114174i
$582$		0			0
$583$	−73.9941	+	42.7205i	−0.126920	+	0.0732770i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−494.980	−	857.331i	−0.843237	−	1.46053i	−0.887143	−	0.461494i	$-0.847314\pi$
$587$	−494.980	−	857.331i	−0.843237	−	1.46053i	0.0439064	−	0.999036i	$-0.486020\pi$
$588$		0			0
$589$	−117.405	+	203.351i	−0.199329	+	0.345248i
$590$		0			0
$591$	26.3010	+	687.631i	0.0445025	+	1.16350i
$592$		0			0
$593$	291.067			0.490838			0.245419	−	0.969417i	$-0.421074\pi$
$593$	291.067			0.490838			0.245419	+	0.969417i	$0.421074\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−41.5817	−	1087.14i	−0.0696510	−	1.82100i
$598$		0			0
$599$	703.617	+	406.233i	1.17465	+	0.678186i	0.954771	−	0.297341i	$-0.0960998\pi$
$599$	703.617	+	406.233i	1.17465	+	0.678186i	0.219881	+	0.975527i	$0.429433\pi$
$600$		0			0
$601$	155.483	+	269.304i	0.258707	+	0.448094i	0.965896	−	0.258931i	$-0.0833703\pi$
$601$	155.483	+	269.304i	0.258707	+	0.448094i	−0.707189	+	0.707025i	$0.750037\pi$
$602$		0			0
$603$	867.620	+	416.050i	1.43884	+	0.689967i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−21.2303	−	12.2573i	−0.0349758	−	0.0201933i	0.482410	−	0.875945i	$-0.339761\pi$
$607$	−21.2303	−	12.2573i	−0.0349758	−	0.0201933i	−0.517386	+	0.855752i	$0.673095\pi$
$608$		0			0
$609$	−154.631	−	81.5610i	−0.253911	−	0.133926i
$610$		0			0
$611$			369.167i			0.604201i
$612$		0			0
$613$		−	448.122i		−	0.731031i	−0.930805	−	0.365516i	$-0.880893\pi$
$613$		−	448.122i		−	0.731031i	0.930805	−	0.365516i	$-0.119107\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	248.153	−	429.814i	0.402193	−	0.696619i	−0.591797	−	0.806087i	$-0.701581\pi$
$617$	248.153	−	429.814i	0.402193	−	0.696619i	0.993990	+	0.109468i	$0.0349148\pi$
$618$		0			0
$619$	−473.442	−	820.025i	−0.764849	−	1.32476i	−0.940326	−	0.340275i	$-0.889480\pi$
$619$	−473.442	−	820.025i	−0.764849	−	1.32476i	0.175477	−	0.984484i	$-0.443853\pi$
$620$		0			0
$621$	−351.443	−	152.292i	−0.565931	−	0.245237i
$622$		0			0
$623$	10.8439	+	18.7822i	0.0174059	+	0.0301479i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−76.8629	−	122.102i	−0.122588	−	0.194739i
$628$		0			0
$629$			1428.99i			2.27184i
$630$		0			0
$631$	158.441			0.251096			0.125548	−	0.992088i	$-0.459931\pi$
$631$	158.441			0.251096			0.125548	+	0.992088i	$0.459931\pi$
$632$		0			0
$633$	−909.932	−	479.947i	−1.43749	−	0.758210i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−878.897	+	507.432i	−1.37974	+	0.796596i
$638$		0			0
$639$	16.1092	+	210.277i	0.0252101	+	0.329072i
$640$		0			0
$641$	594.168	−	343.043i	0.926940	−	0.535169i	0.0410973	−	0.999155i	$-0.486915\pi$
$641$	594.168	−	343.043i	0.926940	−	0.535169i	0.885842	+	0.463986i	$0.153581\pi$
$642$		0			0
$643$	−761.925	−	439.898i	−1.18495	−	0.684133i	−0.227798	−	0.973708i	$-0.573153\pi$
$643$	−761.925	−	439.898i	−1.18495	−	0.684133i	−0.957155	+	0.289575i	$0.906486\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−594.407			−0.918712			−0.459356	−	0.888252i	$-0.651920\pi$
$647$	−594.407			−0.918712			−0.459356	+	0.888252i	$0.651920\pi$
$648$		0			0
$649$	442.456			0.681751
$650$		0			0
$651$	−165.350	+	6.32443i	−0.253994	+	0.00971494i
$652$		0			0
$653$	−327.215	+	566.753i	−0.501095	+	0.867921i	0.498905	+	0.866657i	$0.333736\pi$
$653$	−327.215	+	566.753i	−0.501095	+	0.867921i	−0.999999	+	0.00126434i	$0.999598\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	47.8214	+	624.223i	0.0727875	+	0.950111i
$658$		0			0
$659$	630.422	−	363.974i	0.956634	−	0.552313i	0.0614989	−	0.998107i	$-0.480412\pi$
$659$	630.422	−	363.974i	0.956634	−	0.552313i	0.895136	+	0.445794i	$0.147079\pi$
$660$		0			0
$661$	125.226	−	216.898i	0.189450	−	0.328137i	−0.755617	−	0.655014i	$-0.772663\pi$
$661$	125.226	−	216.898i	0.189450	−	0.328137i	0.945067	+	0.326877i	$0.105996\pi$
$662$		0			0
$663$	1014.00	−	1922.45i	1.52942	−	2.89962i
$664$		0			0
$665$		0			0
$666$		0			0
$667$			515.772i			0.773272i
$668$		0			0
$669$	−150.818	−	239.584i	−0.225438	−	0.358122i
$670$		0			0
$671$	−41.3512	−	23.8741i	−0.0616262	−	0.0355799i
$672$		0			0
$673$	27.5452	−	15.9032i	0.0409290	−	0.0236304i	−0.479396	−	0.877599i	$-0.659144\pi$
$673$	27.5452	−	15.9032i	0.0409290	−	0.0236304i	0.520325	+	0.853968i	$0.325811\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	9.63052	+	16.6805i	0.0142253	+	0.0246389i	0.873050	−	0.487630i	$-0.162138\pi$
$677$	9.63052	+	16.6805i	0.0142253	+	0.0246389i	−0.858825	+	0.512269i	$0.828805\pi$
$678$		0			0
$679$	103.698	−	179.610i	0.152721	−	0.264521i
$680$		0			0
$681$	−852.387	+	536.577i	−1.25167	+	0.787926i
$682$		0			0
$683$	−1241.35			−1.81750			−0.908752	−	0.417337i	$-0.862963\pi$
$683$	−1241.35			−1.81750			−0.908752	+	0.417337i	$0.862963\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−574.662	−	303.108i	−0.836481	−	0.441205i
$688$		0			0
$689$	229.460	+	132.479i	0.333033	+	0.192277i
$690$		0			0
$691$	−622.274	−	1077.81i	−0.900542	−	1.55978i	−0.826793	−	0.562507i	$-0.809837\pi$
$691$	−622.274	−	1077.81i	−0.900542	−	1.55978i	−0.0737491	−	0.997277i	$-0.523496\pi$
$692$		0			0
$693$	43.9627	−	91.6786i	0.0634382	−	0.132292i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−604.135	−	348.798i	−0.866765	−	0.500427i
$698$		0			0
$699$	4.01794	+	105.048i	0.00574812	+	0.150283i
$700$		0			0
$701$			603.491i			0.860900i	0.902614	+	0.430450i	$0.141645\pi$
$701$			603.491i			0.860900i	−0.902614	+	0.430450i	$0.858355\pi$
$702$		0			0
$703$		−	294.162i		−	0.418439i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−83.2689	+	144.226i	−0.117778	+	0.203997i
$708$		0			0
$709$	−29.6788	−	51.4053i	−0.0418601	−	0.0725039i	0.844336	−	0.535814i	$-0.179995\pi$
$709$	−29.6788	−	51.4053i	−0.0418601	−	0.0725039i	−0.886196	+	0.463310i	$0.846662\pi$
$710$		0			0
$711$	−283.241	−	413.960i	−0.398370	−	0.582223i
$712$		0			0
$713$	244.091	+	422.777i	0.342343	+	0.592956i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	343.237	−	650.742i	0.478712	−	0.907591i
$718$		0			0
$719$		−	194.207i		−	0.270108i	−0.990838	−	0.135054i	$-0.956879\pi$
$719$		−	194.207i		−	0.270108i	0.990838	−	0.135054i	$-0.0431207\pi$
$720$		0			0
$721$	12.7927			0.0177430
$722$		0			0
$723$	−3.41545	+	2.15003i	−0.00472400	+	0.00297376i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	483.552	−	279.179i	0.665134	−	0.384015i	−0.129096	−	0.991632i	$-0.541208\pi$
$727$	483.552	−	279.179i	0.665134	−	0.384015i	0.794230	+	0.607617i	$0.207874\pi$
$728$		0			0
$729$	−709.906	+	165.756i	−0.973807	+	0.227374i
$730$		0			0
$731$	1761.10	−	1016.77i	2.40917	−	1.39093i
$732$		0			0
$733$	−401.969	−	232.077i	−0.548389	−	0.316613i	0.200083	−	0.979779i	$-0.435879\pi$
$733$	−401.969	−	232.077i	−0.548389	−	0.316613i	−0.748472	+	0.663166i	$0.769212\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	753.565			1.02248
$738$		0			0
$739$	117.307			0.158738			0.0793688	−	0.996845i	$-0.474710\pi$
$739$	117.307			0.158738			0.0793688	+	0.996845i	$0.474710\pi$
$740$		0			0
$741$	−208.737	+	395.744i	−0.281696	+	0.534067i
$742$		0			0
$743$	262.194	−	454.133i	0.352885	−	0.611216i	−0.633868	−	0.773441i	$-0.718534\pi$
$743$	262.194	−	454.133i	0.352885	−	0.611216i	0.986754	+	0.162225i	$0.0518672\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	420.675	+	614.821i	0.563153	+	0.823054i
$748$		0			0
$749$	−158.157	+	91.3120i	−0.211158	+	0.121912i
$750$		0			0
$751$	218.646	−	378.706i	0.291140	−	0.504269i	−0.682940	−	0.730475i	$-0.739299\pi$
$751$	218.646	−	378.706i	0.291140	−	0.504269i	0.974080	+	0.226206i	$0.0726322\pi$
$752$		0			0
$753$	−1190.36	+	45.5295i	−1.58082	+	0.0604642i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			695.704i			0.919028i	0.888171	+	0.459514i	$0.151976\pi$
$757$			695.704i			0.919028i	−0.888171	+	0.459514i	$0.848024\pi$
$758$		0			0
$759$	−299.746	+	11.4649i	−0.394922	+	0.0151053i
$760$		0			0
$761$	102.405	+	59.1234i	0.134566	+	0.0776917i	0.565772	−	0.824562i	$-0.308578\pi$
$761$	102.405	+	59.1234i	0.134566	+	0.0776917i	−0.431206	+	0.902254i	$0.641912\pi$
$762$		0			0
$763$	−106.693	+	61.5994i	−0.139834	+	0.0807332i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−686.040	−	1188.26i	−0.894446	−	1.54923i
$768$		0			0
$769$	9.47193	−	16.4059i	0.0123172	−	0.0213340i	−0.859801	−	0.510629i	$-0.829413\pi$
$769$	9.47193	−	16.4059i	0.0123172	−	0.0213340i	0.872118	+	0.489295i	$0.162746\pi$
$770$		0			0
$771$	−56.0715	−	29.5751i	−0.0727257	−	0.0383594i
$772$		0			0
$773$	−1332.30			−1.72355			−0.861774	−	0.507292i	$-0.830646\pi$
$773$	−1332.30			−1.72355			−0.861774	+	0.507292i	$0.830646\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	175.432	−	110.434i	0.225781	−	0.142129i
$778$		0			0
$779$	124.364	+	71.8014i	0.159645	+	0.0921712i
$780$		0			0
$781$	82.5811	+	143.035i	0.105738	+	0.183143i
$782$		0			0
$783$	584.896	+	788.389i	0.746994	+	1.00688i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−195.426	−	112.829i	−0.248318	−	0.143366i	0.370676	−	0.928762i	$-0.379126\pi$
$787$	−195.426	−	112.829i	−0.248318	−	0.143366i	−0.618994	+	0.785396i	$0.712459\pi$
$788$		0			0
$789$	323.553	−	203.677i	0.410080	−	0.258145i
$790$		0			0
$791$		−	80.1115i		−	0.101279i
$792$		0			0
$793$			148.070i			0.186721i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	357.102	−	618.519i	0.448058	−	0.776059i	−0.550202	−	0.835032i	$-0.685449\pi$
$797$	357.102	−	618.519i	0.448058	−	0.776059i	0.998260	+	0.0589729i	$0.0187826\pi$
$798$		0			0
$799$	−279.917	−	484.830i	−0.350334	−	0.606796i
$800$		0			0
$801$	−9.30231	−	121.425i	−0.0116134	−	0.151592i
$802$		0			0
$803$	245.148	+	424.609i	0.305290	+	0.528778i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	701.996	−	26.8504i	0.869884	−	0.0332719i
$808$		0			0
$809$			32.6602i			0.0403710i	0.999796	+	0.0201855i	$0.00642568\pi$
$809$			32.6602i			0.0403710i	−0.999796	+	0.0201855i	$0.993574\pi$
$810$		0			0
$811$	418.250			0.515721			0.257860	−	0.966182i	$-0.416983\pi$
$811$	418.250			0.515721			0.257860	+	0.966182i	$0.416983\pi$
$812$		0			0
$813$	12.4217	+	324.761i	0.0152788	+	0.399461i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−362.529	+	209.306i	−0.443732	+	0.256189i
$818$		0			0
$819$	−314.376	+	24.0842i	−0.383854	+	0.0294068i
$820$		0			0
$821$	601.495	−	347.273i	0.732637	−	0.422988i	−0.0867493	−	0.996230i	$-0.527648\pi$
$821$	601.495	−	347.273i	0.732637	−	0.422988i	0.819386	+	0.573242i	$0.194315\pi$
$822$		0			0
$823$	866.843	+	500.472i	1.05327	+	0.608107i	0.923564	−	0.383445i	$-0.125262\pi$
$823$	866.843	+	500.472i	1.05327	+	0.608107i	0.129709	+	0.991552i	$0.458596\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	115.896			0.140140			0.0700700	−	0.997542i	$-0.477678\pi$
$827$	115.896			0.140140			0.0700700	+	0.997542i	$0.477678\pi$
$828$		0			0
$829$	1108.02			1.33657			0.668286	−	0.743904i	$-0.267028\pi$
$829$	1108.02			1.33657			0.668286	+	0.743904i	$0.267028\pi$
$830$		0			0
$831$	406.137	+	645.173i	0.488732	+	0.776381i
$832$		0			0
$833$	769.509	−	1332.83i	0.923780	−	1.60003i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	852.546	+	369.437i	1.01857	+	0.441383i
$838$		0			0
$839$	432.796	−	249.875i	0.515848	−	0.297825i	−0.219386	−	0.975638i	$-0.570406\pi$
$839$	432.796	−	249.875i	0.515848	−	0.297825i	0.735234	+	0.677813i	$0.237072\pi$
$840$		0			0
$841$	240.448	−	416.468i	0.285907	−	0.495205i
$842$		0			0
$843$	−632.770	−	1005.20i	−0.750617	−	1.19240i
$844$		0			0
$845$		0			0
$846$		0			0
$847$			114.312i			0.134961i
$848$		0			0
$849$	−531.480	+	1007.63i	−0.626007	+	1.18685i
$850$		0			0
$851$	−529.642	−	305.789i	−0.622376	−	0.359329i
$852$		0			0
$853$	−187.977	+	108.529i	−0.220372	+	0.127232i	−0.606122	−	0.795371i	$-0.707276\pi$
$853$	−187.977	+	108.529i	−0.220372	+	0.127232i	0.385751	+	0.922603i	$0.373942\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	97.2915	+	168.514i	0.113526	+	0.196632i	0.917189	−	0.398451i	$-0.130452\pi$
$857$	97.2915	+	168.514i	0.113526	+	0.196632i	−0.803664	+	0.595084i	$0.797119\pi$
$858$		0			0
$859$	−178.061	+	308.411i	−0.207289	+	0.359035i	−0.950860	−	0.309623i	$-0.899797\pi$
$859$	−178.061	+	308.411i	−0.207289	+	0.359035i	0.743571	+	0.668657i	$0.233131\pi$
$860$		0			0
$861$	3.86783	+	101.123i	0.00449226	+	0.117449i
$862$		0			0
$863$	477.201			0.552955			0.276478	−	0.961020i	$-0.410833\pi$
$863$	477.201			0.552955			0.276478	+	0.961020i	$0.410833\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	92.8396	+	2427.26i	0.107081	+	2.79961i
$868$		0			0
$869$	−340.192	−	196.410i	−0.391475	−	0.226018i
$870$		0			0
$871$	−1168.42	−	2023.77i	−1.34147	−	2.32350i
$872$		0			0
$873$	−961.115	+	657.618i	−1.10093	+	0.753285i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−190.536	−	110.006i	−0.217259	−	0.125434i	0.387422	−	0.921903i	$-0.373366\pi$
$877$	−190.536	−	110.006i	−0.217259	−	0.125434i	−0.604680	+	0.796468i	$0.706699\pi$
$878$		0			0
$879$	1300.09	+	685.736i	1.47905	+	0.780132i
$880$		0			0
$881$			1644.86i			1.86704i	0.358530	+	0.933518i	$0.383278\pi$
$881$			1644.86i			1.86704i	−0.358530	+	0.933518i	$0.616722\pi$
$882$		0			0
$883$		−	146.724i		−	0.166165i	−0.996543	−	0.0830827i	$-0.973523\pi$
$883$		−	146.724i		−	0.166165i	0.996543	−	0.0830827i	$-0.0264766\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	249.084	−	431.426i	0.280816	−	0.486388i	−0.690770	−	0.723075i	$-0.742728\pi$
$887$	249.084	−	431.426i	0.280816	−	0.486388i	0.971586	+	0.236687i	$0.0760615\pi$
$888$		0			0
$889$	43.1799	+	74.7898i	0.0485713	+	0.0841280i
$890$		0			0
$891$	−445.179	+	357.443i	−0.499639	+	0.401171i
$892$		0			0
$893$	57.6219	+	99.8041i	0.0645262	+	0.111763i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	495.554	+	787.218i	0.552457	+	0.877612i
$898$		0			0
$899$		−	1251.18i		−	1.39175i
$900$		0			0
$901$	−401.802			−0.445951
$902$		0			0
$903$	−260.926	−	137.626i	−0.288955	−	0.152410i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−35.5731	+	20.5381i	−0.0392206	+	0.0226440i	−0.519482	−	0.854481i	$-0.673875\pi$
$907$	−35.5731	+	20.5381i	−0.0392206	+	0.0226440i	0.480261	+	0.877125i	$0.340542\pi$
$908$		0			0
$909$	771.773	−	528.065i	0.849035	−	0.580929i
$910$		0			0
$911$	753.467	−	435.014i	0.827077	−	0.477513i	−0.0257741	−	0.999668i	$-0.508205\pi$
$911$	753.467	−	435.014i	0.827077	−	0.477513i	0.852851	+	0.522155i	$0.174872\pi$
$912$		0			0
$913$	505.259	+	291.712i	0.553405	+	0.319509i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−410.356			−0.447498
$918$		0			0
$919$	−1217.72			−1.32505			−0.662524	−	0.749041i	$-0.730515\pi$
$919$	−1217.72			−1.32505			−0.662524	+	0.749041i	$0.730515\pi$
$920$		0			0
$921$	−331.362	+	12.6742i	−0.359785	+	0.0137613i
$922$		0			0
$923$	256.088	−	443.558i	0.277452	−	0.480561i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−64.7713	−	31.0598i	−0.0698720	−	0.0335058i
$928$		0			0
$929$	994.384	−	574.108i	1.07038	−	0.617985i	0.142095	−	0.989853i	$-0.454616\pi$
$929$	994.384	−	574.108i	1.07038	−	0.617985i	0.928285	+	0.371868i	$0.121283\pi$
$930$		0			0
$931$	−158.406	+	274.368i	−0.170147	+	0.294702i
$932$		0			0
$933$	−251.553	+	476.920i	−0.269618	+	0.511168i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	1064.28i		−	1.13584i	−0.823084	−	0.567920i	$-0.807748\pi$
$937$		−	1064.28i		−	1.13584i	0.823084	−	0.567920i	$-0.192252\pi$
$938$		0			0
$939$	324.170	+	514.964i	0.345229	+	0.548417i
$940$		0			0
$941$	1271.42	+	734.053i	1.35113	+	0.780078i	0.988408	−	0.151818i	$-0.0485128\pi$
$941$	1271.42	+	734.053i	1.35113	+	0.780078i	0.362726	+	0.931896i	$0.381846\pi$
$942$		0			0
$943$	258.558	−	149.279i	0.274187	−	0.158302i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	878.076	+	1520.87i	0.927218	+	1.60599i	0.787954	+	0.615734i	$0.211140\pi$
$947$	878.076	+	1520.87i	0.927218	+	1.60599i	0.139264	+	0.990255i	$0.455526\pi$
$948$		0			0
$949$	760.216	−	1316.73i	0.801071	−	1.38750i
$950$		0			0
$951$	−1337.43	+	841.912i	−1.40634	+	0.885291i
$952$		0			0
$953$	860.237			0.902662			0.451331	−	0.892357i	$-0.350949\pi$
$953$	860.237			0.902662			0.451331	+	0.892357i	$0.350949\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	680.001	+	358.669i	0.710554	+	0.374785i
$958$		0			0
$959$	−18.1500	−	10.4789i	−0.0189260	−	0.0109269i
$960$		0			0
$961$	−111.625	−	193.341i	−0.116155	−	0.201187i
$962$		0			0
$963$	1022.47	−	78.3309i	1.06176	−	0.0813405i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−1584.19	−	914.632i	−1.63825	−	0.945845i	−0.981435	−	0.191795i	$-0.938569\pi$
$967$	−1584.19	−	914.632i	−1.63825	−	0.945845i	−0.656817	−	0.754050i	$-0.728097\pi$
$968$		0			0
$969$	−25.9329	−	678.006i	−0.0267625	−	0.699697i
$970$		0			0
$971$			992.165i			1.02180i	0.859641	+	0.510898i	$0.170687\pi$
$971$			992.165i			1.02180i	−0.859641	+	0.510898i	$0.829313\pi$
$972$		0			0
$973$		−	198.578i		−	0.204089i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	635.640	−	1100.96i	0.650604	−	1.12688i	−0.332372	−	0.943148i	$-0.607849\pi$
$977$	635.640	−	1100.96i	0.650604	−	1.12688i	0.982977	−	0.183731i	$-0.0588176\pi$
$978$		0			0
$979$	−47.6866	−	82.5956i	−0.0487095	−	0.0843674i
$980$		0			0
$981$	689.763	−	52.8424i	0.703122	−	0.0538658i
$982$		0			0
$983$	496.487	+	859.940i	0.505073	+	0.874812i	0.999983	+	0.00586774i	$0.00186777\pi$
$983$	496.487	+	859.940i	0.505073	+	0.874812i	−0.494910	+	0.868944i	$0.664799\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−37.8885	+	71.8328i	−0.0383875	+	0.0727789i
$988$		0			0
$989$			870.317i			0.879997i
$990$		0			0
$991$	−884.132			−0.892161			−0.446081	−	0.894993i	$-0.647181\pi$
$991$	−884.132			−0.892161			−0.446081	+	0.894993i	$0.647181\pi$
$992$		0			0
$993$	−827.956	+	521.198i	−0.833792	+	0.524873i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−734.268	+	423.930i	−0.736477	+	0.425205i	−0.820787	−	0.571234i	$-0.806465\pi$
$997$	−734.268	+	423.930i	−0.736477	+	0.425205i	0.0843097	+	0.996440i	$0.473132\pi$
$998$		0			0
$999$	−1156.36	+	133.208i	−1.15752	+	0.133341i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.u.c.149.7		24
3.2	odd	2		2700.3.u.c.449.8		24
5.2	odd	4		900.3.p.c.401.6		12
5.3	odd	4		180.3.o.b.41.1	✓	12
5.4	even	2	inner	900.3.u.c.149.6		24
9.2	odd	6	inner	900.3.u.c.749.6		24
9.7	even	3		2700.3.u.c.2249.5		24
15.2	even	4		2700.3.p.c.2501.4		12
15.8	even	4		540.3.o.b.341.2		12
15.14	odd	2		2700.3.u.c.449.5		24
20.3	even	4		720.3.bs.b.401.6		12
45.2	even	12		900.3.p.c.101.6		12
45.7	odd	12		2700.3.p.c.1601.4		12
45.13	odd	12		1620.3.g.b.161.4		12
45.23	even	12		1620.3.g.b.161.10		12
45.29	odd	6	inner	900.3.u.c.749.7		24
45.34	even	6		2700.3.u.c.2249.8		24
45.38	even	12		180.3.o.b.101.1	yes	12
45.43	odd	12		540.3.o.b.521.2		12
60.23	odd	4		2160.3.bs.b.881.2		12
180.43	even	12		2160.3.bs.b.1601.2		12
180.83	odd	12		720.3.bs.b.641.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.3.o.b.41.1	✓	12	5.3	odd	4
180.3.o.b.101.1	yes	12	45.38	even	12
540.3.o.b.341.2		12	15.8	even	4
540.3.o.b.521.2		12	45.43	odd	12
720.3.bs.b.401.6		12	20.3	even	4
720.3.bs.b.641.6		12	180.83	odd	12
900.3.p.c.101.6		12	45.2	even	12
900.3.p.c.401.6		12	5.2	odd	4
900.3.u.c.149.6		24	5.4	even	2	inner
900.3.u.c.149.7		24	1.1	even	1	trivial
900.3.u.c.749.6		24	9.2	odd	6	inner
900.3.u.c.749.7		24	45.29	odd	6	inner
1620.3.g.b.161.4		12	45.13	odd	12
1620.3.g.b.161.10		12	45.23	even	12
2160.3.bs.b.881.2		12	60.23	odd	4
2160.3.bs.b.1601.2		12	180.43	even	12
2700.3.p.c.1601.4		12	45.7	odd	12
2700.3.p.c.2501.4		12	15.2	even	4
2700.3.u.c.449.5		24	15.14	odd	2
2700.3.u.c.449.8		24	3.2	odd	2
2700.3.u.c.2249.5		24	9.7	even	3
2700.3.u.c.2249.8		24	45.34	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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.114662 + 2.99781i) q^{3} +(1.38806 - 0.801399i) q^{7} +(-8.97371 + 0.687471i) q^{9} +O(q^{10})\)	\(q+(0.114662 + 2.99781i) q^{3} +(1.38806 - 0.801399i) q^{7} +(-8.97371 + 0.687471i) q^{9} +(-6.10409 + 3.52420i) q^{11} +(18.9291 + 10.9287i) q^{13} -33.1463 q^{17} +6.82330 q^{19} +(2.56160 + 4.06926i) q^{21} +(7.09299 - 12.2854i) q^{23} +(-3.08985 - 26.8226i) q^{27} +(-31.4868 + 18.1789i) q^{29} +(-17.2065 + 29.8025i) q^{31} +(-11.2648 - 17.8948i) q^{33} -43.1114i q^{37} +(-30.5917 + 57.9989i) q^{39} +(18.2263 + 10.5230i) q^{41} +(-53.1311 + 30.6752i) q^{43} +(8.44488 + 14.6270i) q^{47} +(-23.2155 + 40.2105i) q^{49} +(-3.80063 - 99.3663i) q^{51} +12.1221 q^{53} +(0.782375 + 20.4549i) q^{57} +(-54.3639 - 31.3870i) q^{59} +(3.38717 + 5.86675i) q^{61} +(-11.9051 + 8.14577i) q^{63} +(-92.5894 - 53.4565i) q^{67} +(37.6426 + 19.8547i) q^{69} -23.4326i q^{71} -69.5613i q^{73} +(-5.64858 + 9.78362i) q^{77} +(27.8659 + 48.2651i) q^{79} +(80.0548 - 12.3383i) q^{81} +(-41.3869 - 71.6843i) q^{83} +(-58.1073 - 92.3071i) q^{87} +13.5312i q^{89} +35.0331 q^{91} +(-91.3151 - 48.1645i) q^{93} +(112.060 - 64.6979i) q^{97} +(52.3535 - 35.8215i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 52 q^{9}+O(q^{10}) \) 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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Database

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