LMFDB - Embedded newform 900.3.p.b.101.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [900,3,Mod(101,900)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("900.101"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(900, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	900.p (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$24.5232237924$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-5})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 25 $ x^4 - 5*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.1
Root			$1.93649 - 1.11803i$ of defining polynomial
Character	$\chi$	$=$	900.101
Dual form			900.3.p.b.401.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 2.59808i) q^{3} +(-5.87298 + 10.1723i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(13.1190 + 7.57423i) q^{11} +(-8.87298 - 15.3685i) q^{13} -15.1485i q^{17} -11.2540 q^{19} +(17.6190 + 30.5169i) q^{21} +(-29.2379 + 16.8805i) q^{23} -27.0000 q^{27} +(8.23790 + 4.75615i) q^{29} +(-28.1109 - 48.6895i) q^{31} +(39.3569 - 22.7227i) q^{33} -14.0000 q^{37} -53.2379 q^{39} +(-22.5000 + 12.9904i) q^{41} +(-9.99193 + 17.3065i) q^{43} +(-62.6190 - 36.1531i) q^{47} +(-44.4839 - 77.0483i) q^{49} +(-39.3569 - 22.7227i) q^{51} -37.6651i q^{53} +(-16.8810 + 29.2388i) q^{57} +(-55.1190 + 31.8229i) q^{59} +(-0.618950 + 1.07205i) q^{61} +105.714 q^{63} +(42.9758 + 74.4363i) q^{67} +101.283i q^{69} -22.1046i q^{71} +60.2379 q^{73} +(-154.095 + 88.9666i) q^{77} +(-51.6190 + 89.4066i) q^{79} +(-40.5000 + 70.1481i) q^{81} +(78.0000 + 45.0333i) q^{83} +(24.7137 - 14.2685i) q^{87} -12.0964i q^{89} +208.444 q^{91} -168.665 q^{93} +(49.8488 - 86.3406i) q^{97} -136.336i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{3} - 8 q^{7} - 18 q^{9} + 6 q^{11} - 20 q^{13} - 76 q^{19} + 24 q^{21} - 24 q^{23} - 108 q^{27} - 60 q^{29} - 4 q^{31} + 18 q^{33} - 56 q^{37} - 120 q^{39} - 90 q^{41} + 22 q^{43} - 204 q^{47}+ \cdots - 2 q^{97}+O(q^{100}) $ 4 * q + 6 * q^3 - 8 * q^7 - 18 * q^9 + 6 * q^11 - 20 * q^13 - 76 * q^19 + 24 * q^21 - 24 * q^23 - 108 * q^27 - 60 * q^29 - 4 * q^31 + 18 * q^33 - 56 * q^37 - 120 * q^39 - 90 * q^41 + 22 * q^43 - 204 * q^47 - 54 * q^49 - 18 * q^51 - 114 * q^57 - 174 * q^59 + 44 * q^61 + 144 * q^63 - 14 * q^67 + 148 * q^73 - 384 * q^77 - 160 * q^79 - 162 * q^81 + 312 * q^83 - 180 * q^87 + 400 * q^91 - 24 * q^93 - 2 * q^97

Character values

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

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

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
$3$	1.50000	−	2.59808i	0.500000	−	0.866025i
$3$	1.50000	−	2.59808i	0.500000	−	0.866025i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−5.87298	+	10.1723i	−0.838998	+	1.45319i	0.0517360	+	0.998661i	$0.483525\pi$
$7$	−5.87298	+	10.1723i	−0.838998	+	1.45319i	−0.890734	+	0.454526i	$0.849809\pi$
$8$		0			0
$9$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$10$		0			0
$11$	13.1190	+	7.57423i	1.19263	+	0.688566i	0.958903	−	0.283735i	$-0.0915737\pi$
$11$	13.1190	+	7.57423i	1.19263	+	0.688566i	0.233729	+	0.972302i	$0.424907\pi$
$12$		0			0
$13$	−8.87298	−	15.3685i	−0.682537	−	1.18219i	−0.974204	−	0.225669i	$-0.927543\pi$
$13$	−8.87298	−	15.3685i	−0.682537	−	1.18219i	0.291667	−	0.956520i	$-0.405790\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	15.1485i		−	0.891086i	−0.895261	−	0.445543i	$-0.853011\pi$
$17$		−	15.1485i		−	0.891086i	0.895261	−	0.445543i	$-0.146989\pi$
$18$		0			0
$19$	−11.2540			−0.592318			−0.296159	−	0.955139i	$-0.595706\pi$
$19$	−11.2540			−0.592318			−0.296159	+	0.955139i	$0.595706\pi$
$20$		0			0
$21$	17.6190	+	30.5169i	0.838998	+	1.45319i
$22$		0			0
$23$	−29.2379	+	16.8805i	−1.27121	+	0.733935i	−0.975216	−	0.221254i	$-0.928985\pi$
$23$	−29.2379	+	16.8805i	−1.27121	+	0.733935i	−0.295997	+	0.955189i	$0.595652\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−27.0000			−1.00000
$28$		0			0
$29$	8.23790	+	4.75615i	0.284066	+	0.164005i	0.635262	−	0.772296i	$-0.280892\pi$
$29$	8.23790	+	4.75615i	0.284066	+	0.164005i	−0.351197	+	0.936302i	$0.614225\pi$
$30$		0			0
$31$	−28.1109	−	48.6895i	−0.906803	−	1.57063i	−0.818479	−	0.574537i	$-0.805182\pi$
$31$	−28.1109	−	48.6895i	−0.906803	−	1.57063i	−0.0883237	−	0.996092i	$-0.528151\pi$
$32$		0			0
$33$	39.3569	−	22.7227i	1.19263	−	0.688566i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−14.0000			−0.378378			−0.189189	−	0.981941i	$-0.560586\pi$
$37$	−14.0000			−0.378378			−0.189189	+	0.981941i	$0.560586\pi$
$38$		0			0
$39$	−53.2379			−1.36507
$40$		0			0
$41$	−22.5000	+	12.9904i	−0.548780	+	0.316839i	−0.748630	−	0.662988i	$-0.769288\pi$
$41$	−22.5000	+	12.9904i	−0.548780	+	0.316839i	0.199849	+	0.979827i	$0.435955\pi$
$42$		0			0
$43$	−9.99193	+	17.3065i	−0.232371	+	0.402478i	−0.958505	−	0.285075i	$-0.907982\pi$
$43$	−9.99193	+	17.3065i	−0.232371	+	0.402478i	0.726135	+	0.687552i	$0.241315\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−62.6190	−	36.1531i	−1.33232	−	0.769214i	−0.346664	−	0.937990i	$-0.612685\pi$
$47$	−62.6190	−	36.1531i	−1.33232	−	0.769214i	−0.985655	+	0.168775i	$0.946019\pi$
$48$		0			0
$49$	−44.4839	−	77.0483i	−0.907834	−	1.57241i
$50$		0			0
$51$	−39.3569	−	22.7227i	−0.771703	−	0.445543i
$52$		0			0
$53$		−	37.6651i		−	0.710663i	−0.934740	−	0.355331i	$-0.884368\pi$
$53$		−	37.6651i		−	0.710663i	0.934740	−	0.355331i	$-0.115632\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−16.8810	+	29.2388i	−0.296159	+	0.512962i
$58$		0			0
$59$	−55.1190	+	31.8229i	−0.934219	+	0.539372i	−0.888144	−	0.459566i	$-0.848005\pi$
$59$	−55.1190	+	31.8229i	−0.934219	+	0.539372i	−0.0460759	+	0.998938i	$0.514672\pi$
$60$		0			0
$61$	−0.618950	+	1.07205i	−0.0101467	+	0.0175746i	−0.871054	−	0.491187i	$-0.836563\pi$
$61$	−0.618950	+	1.07205i	−0.0101467	+	0.0175746i	0.860907	+	0.508762i	$0.169897\pi$
$62$		0			0
$63$	105.714			1.67800
$64$		0			0
$65$		0			0
$66$		0			0
$67$	42.9758	+	74.4363i	0.641430	+	1.11099i	0.985114	+	0.171904i	$0.0549918\pi$
$67$	42.9758	+	74.4363i	0.641430	+	1.11099i	−0.343684	+	0.939085i	$0.611675\pi$
$68$		0			0
$69$			101.283i			1.46787i
$70$		0			0
$71$		−	22.1046i		−	0.311332i	−0.987810	−	0.155666i	$-0.950248\pi$
$71$		−	22.1046i		−	0.311332i	0.987810	−	0.155666i	$-0.0497524\pi$
$72$		0			0
$73$	60.2379			0.825177			0.412588	−	0.910918i	$-0.364625\pi$
$73$	60.2379			0.825177			0.412588	+	0.910918i	$0.364625\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−154.095	+	88.9666i	−2.00123	+	1.15541i
$78$		0			0
$79$	−51.6190	+	89.4066i	−0.653404	+	1.13173i	0.328887	+	0.944369i	$0.393327\pi$
$79$	−51.6190	+	89.4066i	−0.653404	+	1.13173i	−0.982291	+	0.187360i	$0.940007\pi$
$80$		0			0
$81$	−40.5000	+	70.1481i	−0.500000	+	0.866025i
$82$		0			0
$83$	78.0000	+	45.0333i	0.939759	+	0.542570i	0.889885	−	0.456185i	$-0.150785\pi$
$83$	78.0000	+	45.0333i	0.939759	+	0.542570i	0.0498743	+	0.998756i	$0.484118\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	24.7137	−	14.2685i	0.284066	−	0.164005i
$88$		0			0
$89$		−	12.0964i		−	0.135915i	−0.997688	−	0.0679574i	$-0.978352\pi$
$89$		−	12.0964i		−	0.135915i	0.997688	−	0.0679574i	$-0.0216482\pi$
$90$		0			0
$91$	208.444			2.29059
$92$		0			0
$93$	−168.665			−1.81361
$94$		0			0
$95$		0			0
$96$		0			0
$97$	49.8488	−	86.3406i	0.513905	−	0.890110i	−0.485965	−	0.873978i	$-0.661532\pi$
$97$	49.8488	−	86.3406i	0.513905	−	0.890110i	0.999870	−	0.0161312i	$-0.00513495\pi$
$98$		0			0
$99$		−	136.336i		−	1.37713i
$100$		0			0
$101$	−134.238	−	77.5023i	−1.32909	−	0.767349i	−0.343929	−	0.938995i	$-0.611758\pi$
$101$	−134.238	−	77.5023i	−1.32909	−	0.767349i	−0.985159	+	0.171646i	$0.945091\pi$
$102$		0			0
$103$	77.8569	+	134.852i	0.755892	+	1.30924i	0.944930	+	0.327273i	$0.106130\pi$
$103$	77.8569	+	134.852i	0.755892	+	1.30924i	−0.189038	+	0.981970i	$0.560537\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	84.8705i		−	0.793182i	−0.917995	−	0.396591i	$-0.870193\pi$
$107$		−	84.8705i		−	0.793182i	0.917995	−	0.396591i	$-0.129807\pi$
$108$		0			0
$109$	−38.0323			−0.348920			−0.174460	−	0.984664i	$-0.555818\pi$
$109$	−38.0323			−0.348920			−0.174460	+	0.984664i	$0.555818\pi$
$110$		0			0
$111$	−21.0000	+	36.3731i	−0.189189	+	0.327685i
$112$		0			0
$113$	−6.00000	+	3.46410i	−0.0530973	+	0.0306558i	−0.526314	−	0.850290i	$-0.676426\pi$
$113$	−6.00000	+	3.46410i	−0.0530973	+	0.0306558i	0.473216	+	0.880946i	$0.343093\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−79.8569	+	138.316i	−0.682537	+	1.18219i
$118$		0			0
$119$	154.095	+	88.9666i	1.29491	+	0.747619i
$120$		0			0
$121$	54.2379	+	93.9428i	0.448247	+	0.776387i
$122$		0			0
$123$			77.9423i			0.633677i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−145.903			−1.14884			−0.574422	−	0.818559i	$-0.694773\pi$
$127$	−145.903			−1.14884			−0.574422	+	0.818559i	$0.694773\pi$
$128$		0			0
$129$	29.9758	+	51.9196i	0.232371	+	0.402478i
$130$		0			0
$131$	57.7137	−	33.3210i	0.440563	−	0.254359i	−0.263274	−	0.964721i	$-0.584802\pi$
$131$	57.7137	−	33.3210i	0.440563	−	0.254359i	0.703836	+	0.710362i	$0.251469\pi$
$132$		0			0
$133$	66.0948	−	114.479i	0.496953	−	0.860748i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−63.4052	−	36.6070i	−0.462812	−	0.267205i	0.250414	−	0.968139i	$-0.419433\pi$
$137$	−63.4052	−	36.6070i	−0.462812	−	0.267205i	−0.713226	+	0.700934i	$0.752767\pi$
$138$		0			0
$139$	53.3569	+	92.4168i	0.383862	+	0.664869i	0.991611	−	0.129261i	$-0.0412604\pi$
$139$	53.3569	+	92.4168i	0.383862	+	0.664869i	−0.607748	+	0.794130i	$0.707927\pi$
$140$		0			0
$141$	−187.857	+	108.459i	−1.33232	+	0.769214i
$142$		0			0
$143$		−	268.824i		−	1.87989i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−266.903			−1.81567
$148$		0			0
$149$	−144.333	+	83.3305i	−0.968676	+	0.559265i	−0.898832	−	0.438293i	$-0.855583\pi$
$149$	−144.333	+	83.3305i	−0.968676	+	0.559265i	−0.0698433	+	0.997558i	$0.522250\pi$
$150$		0			0
$151$	−1.71370	+	2.96822i	−0.0113490	+	0.0196571i	−0.871644	−	0.490139i	$-0.836946\pi$
$151$	−1.71370	+	2.96822i	−0.0113490	+	0.0196571i	0.860295	+	0.509796i	$0.170279\pi$
$152$		0			0
$153$	−118.071	+	68.1681i	−0.771703	+	0.445543i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−33.9677	−	58.8338i	−0.216355	−	0.374738i	0.737336	−	0.675526i	$-0.236084\pi$
$157$	−33.9677	−	58.8338i	−0.216355	−	0.374738i	−0.953691	+	0.300788i	$0.902750\pi$
$158$		0			0
$159$	−97.8569	−	56.4977i	−0.615452	−	0.355331i
$160$		0			0
$161$		−	396.556i		−	2.46308i
$162$		0			0
$163$	−76.4113			−0.468781			−0.234390	−	0.972143i	$-0.575309\pi$
$163$	−76.4113			−0.468781			−0.234390	+	0.972143i	$0.575309\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	245.522	−	141.752i	1.47019	−	0.848816i	0.470752	−	0.882266i	$-0.343983\pi$
$167$	245.522	−	141.752i	1.47019	−	0.848816i	0.999440	+	0.0334495i	$0.0106493\pi$
$168$		0			0
$169$	−72.9597	+	126.370i	−0.431714	+	0.747751i
$170$		0			0
$171$	50.6431	+	87.7165i	0.296159	+	0.512962i
$172$		0			0
$173$	116.903	+	67.4941i	0.675741	+	0.390139i	0.798248	−	0.602328i	$-0.205760\pi$
$173$	116.903	+	67.4941i	0.675741	+	0.390139i	−0.122507	+	0.992468i	$0.539094\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$			190.938i			1.07874i
$178$		0			0
$179$		−	171.445i		−	0.957794i	−0.877871	−	0.478897i	$-0.841037\pi$
$179$		−	171.445i		−	0.957794i	0.877871	−	0.478897i	$-0.158963\pi$
$180$		0			0
$181$	120.794			0.667372			0.333686	−	0.942684i	$-0.391707\pi$
$181$	120.794			0.667372			0.333686	+	0.942684i	$0.391707\pi$
$182$		0			0
$183$	1.85685	+	3.21616i	0.0101467	+	0.0175746i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	114.738	−	198.732i	0.613572	−	1.06274i
$188$		0			0
$189$	158.571	−	274.652i	0.838998	−	1.45319i
$190$		0			0
$191$	−241.808	−	139.608i	−1.26601	−	0.730933i	−0.291782	−	0.956485i	$-0.594248\pi$
$191$	−241.808	−	139.608i	−1.26601	−	0.730933i	−0.974231	+	0.225552i	$0.927581\pi$
$192$		0			0
$193$	−52.6431	−	91.1806i	−0.272762	−	0.472438i	0.696806	−	0.717260i	$-0.254604\pi$
$193$	−52.6431	−	91.1806i	−0.272762	−	0.472438i	−0.969568	+	0.244822i	$0.921271\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			57.9538i			0.294182i	0.989123	+	0.147091i	$0.0469910\pi$
$197$			57.9538i			0.294182i	−0.989123	+	0.147091i	$0.953009\pi$
$198$		0			0
$199$	−25.2702			−0.126986			−0.0634929	−	0.997982i	$-0.520224\pi$
$199$	−25.2702			−0.126986			−0.0634929	+	0.997982i	$0.520224\pi$
$200$		0			0
$201$	257.855			1.28286
$202$		0			0
$203$	−96.7621	+	55.8656i	−0.476661	+	0.275200i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	263.141	+	151.925i	1.27121	+	0.733935i
$208$		0			0
$209$	−147.641	−	85.2406i	−0.706417	−	0.407850i
$210$		0			0
$211$	52.0161	+	90.0946i	0.246522	+	0.426989i	0.962558	−	0.271074i	$-0.0873789\pi$
$211$	52.0161	+	90.0946i	0.246522	+	0.426989i	−0.716036	+	0.698063i	$0.754046\pi$
$212$		0			0
$213$	−57.4294	−	33.1569i	−0.269622	−	0.155666i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	660.379			3.04322
$218$		0			0
$219$	90.3569	−	156.503i	0.412588	−	0.714624i
$220$		0			0
$221$	−232.808	+	134.412i	−1.05343	+	0.608199i
$222$		0			0
$223$	123.681	−	214.223i	0.554625	−	0.960639i	−0.443307	−	0.896370i	$-0.646195\pi$
$223$	123.681	−	214.223i	0.554625	−	0.960639i	0.997933	−	0.0642694i	$-0.0204717\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−261.738	−	151.114i	−1.15303	−	0.665702i	−0.203407	−	0.979094i	$-0.565201\pi$
$227$	−261.738	−	151.114i	−1.15303	−	0.665702i	−0.949624	+	0.313392i	$0.898535\pi$
$228$		0			0
$229$	−133.111	−	230.555i	−0.581270	−	1.00679i	−0.995329	−	0.0965395i	$-0.969223\pi$
$229$	−133.111	−	230.555i	−0.581270	−	1.00679i	0.414059	−	0.910250i	$-0.364111\pi$
$230$		0			0
$231$			533.800i			2.31082i
$232$		0			0
$233$			176.969i			0.759526i	0.925084	+	0.379763i	$0.123994\pi$
$233$			176.969i			0.759526i	−0.925084	+	0.379763i	$0.876006\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	154.857	+	268.220i	0.653404	+	1.13173i
$238$		0			0
$239$	68.2863	−	39.4251i	0.285717	−	0.164959i	−0.350292	−	0.936641i	$-0.613918\pi$
$239$	68.2863	−	39.4251i	0.285717	−	0.164959i	0.636009	+	0.771682i	$0.280584\pi$
$240$		0			0
$241$	110.246	−	190.952i	0.457452	−	0.792330i	−0.541373	−	0.840782i	$-0.682095\pi$
$241$	110.246	−	190.952i	0.457452	−	0.792330i	0.998826	+	0.0484519i	$0.0154288\pi$
$242$		0			0
$243$	121.500	+	210.444i	0.500000	+	0.866025i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	99.8569	+	172.957i	0.404279	+	0.700231i
$248$		0			0
$249$	234.000	−	135.100i	0.939759	−	0.542570i
$250$		0			0
$251$			277.373i			1.10507i	0.833490	+	0.552535i	$0.186339\pi$
$251$			277.373i			1.10507i	−0.833490	+	0.552535i	$0.813661\pi$
$252$		0			0
$253$	−511.427			−2.02145
$254$		0			0
$255$		0			0
$256$		0			0
$257$	131.692	−	76.0322i	0.512418	−	0.295845i	−0.221409	−	0.975181i	$-0.571065\pi$
$257$	131.692	−	76.0322i	0.512418	−	0.295845i	0.733827	+	0.679336i	$0.237732\pi$
$258$		0			0
$259$	82.2218	−	142.412i	0.317459	−	0.549854i
$260$		0			0
$261$		−	85.6108i		−	0.328011i
$262$		0			0
$263$	4.95365	+	2.85999i	0.0188352	+	0.0108745i	0.509388	−	0.860537i	$-0.329872\pi$
$263$	4.95365	+	2.85999i	0.0188352	+	0.0108745i	−0.490553	+	0.871411i	$0.663205\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−31.4274	−	18.1446i	−0.117706	−	0.0679574i
$268$		0			0
$269$			361.531i			1.34398i	0.740560	+	0.671990i	$0.234560\pi$
$269$			361.531i			1.34398i	−0.740560	+	0.671990i	$0.765440\pi$
$270$		0			0
$271$	507.427			1.87243			0.936213	−	0.351433i	$-0.114306\pi$
$271$	507.427			1.87243			0.936213	+	0.351433i	$0.114306\pi$
$272$		0			0
$273$	312.665	−	541.552i	1.14529	−	1.98371i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	111.778	−	193.606i	0.403532	−	0.698937i	−0.590618	−	0.806951i	$-0.701116\pi$
$277$	111.778	−	193.606i	0.403532	−	0.698937i	0.994149	+	0.108014i	$0.0344492\pi$
$278$		0			0
$279$	−252.998	+	438.205i	−0.906803	+	1.57063i
$280$		0			0
$281$	−39.8105	−	22.9846i	−0.141674	−	0.0817957i	0.427487	−	0.904021i	$-0.359399\pi$
$281$	−39.8105	−	22.9846i	−0.141674	−	0.0817957i	−0.569162	+	0.822226i	$0.692732\pi$
$282$		0			0
$283$	72.0161	+	124.736i	0.254474	+	0.440762i	0.964753	−	0.263159i	$-0.0847643\pi$
$283$	72.0161	+	124.736i	0.254474	+	0.440762i	−0.710279	+	0.703921i	$0.751431\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	305.169i		−	1.06331i
$288$		0			0
$289$	59.5242			0.205966
$290$		0			0
$291$	−149.546	−	259.022i	−0.513905	−	0.890110i
$292$		0			0
$293$	−361.476	+	208.698i	−1.23371	+	0.712280i	−0.967800	−	0.251719i	$-0.919004\pi$
$293$	−361.476	+	208.698i	−1.23371	+	0.712280i	−0.265905	+	0.963999i	$0.585671\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−354.212	−	204.504i	−1.19263	−	0.688566i
$298$		0			0
$299$	518.855	+	299.561i	1.73530	+	1.00188i
$300$		0			0
$301$	−117.365	−	203.282i	−0.389917	−	0.675355i
$302$		0			0
$303$	−402.714	+	232.507i	−1.32909	+	0.767349i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	310.048			1.00993			0.504965	−	0.863140i	$-0.331505\pi$
$307$	310.048			1.00993			0.504965	+	0.863140i	$0.331505\pi$
$308$		0			0
$309$	467.141			1.51178
$310$		0			0
$311$	−242.238	+	139.856i	−0.778900	+	0.449698i	−0.836040	−	0.548668i	$-0.815135\pi$
$311$	−242.238	+	139.856i	−0.778900	+	0.449698i	0.0571403	+	0.998366i	$0.481802\pi$
$312$		0			0
$313$	−14.5786	+	25.2509i	−0.0465771	+	0.0806738i	−0.888374	−	0.459120i	$-0.848165\pi$
$313$	−14.5786	+	25.2509i	−0.0465771	+	0.0806738i	0.841797	+	0.539794i	$0.181498\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−109.095	−	62.9859i	−0.344147	−	0.198694i	0.317957	−	0.948105i	$-0.397003\pi$
$317$	−109.095	−	62.9859i	−0.344147	−	0.198694i	−0.662105	+	0.749411i	$0.730337\pi$
$318$		0			0
$319$	72.0484	+	124.791i	0.225857	+	0.391196i
$320$		0			0
$321$	−220.500	−	127.306i	−0.686916	−	0.396591i
$322$		0			0
$323$			170.481i			0.527806i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−57.0484	+	98.8107i	−0.174460	+	0.302173i
$328$		0			0
$329$	735.520	−	424.653i	2.23562	−	1.29074i
$330$		0			0
$331$	232.903	−	403.400i	0.703635	−	1.21873i	−0.263547	−	0.964647i	$-0.584892\pi$
$331$	232.903	−	403.400i	0.703635	−	1.21873i	0.967182	−	0.254085i	$-0.0817743\pi$
$332$		0			0
$333$	63.0000	+	109.119i	0.189189	+	0.327685i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	175.087	+	303.259i	0.519545	+	0.899878i	0.999742	+	0.0227177i	$0.00723189\pi$
$337$	175.087	+	303.259i	0.519545	+	0.899878i	−0.480197	+	0.877161i	$0.659435\pi$
$338$		0			0
$339$			20.7846i			0.0613115i
$340$		0			0
$341$		−	851.673i		−	2.49758i
$342$		0			0
$343$	469.460			1.36869
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−71.1169	+	41.0594i	−0.204948	+	0.118327i	−0.598961	−	0.800778i	$-0.704420\pi$
$347$	−71.1169	+	41.0594i	−0.204948	+	0.118327i	0.394013	+	0.919105i	$0.371086\pi$
$348$		0			0
$349$	−22.7621	+	39.4251i	−0.0652209	+	0.112966i	−0.896792	−	0.442452i	$-0.854109\pi$
$349$	−22.7621	+	39.4251i	−0.0652209	+	0.112966i	0.831571	+	0.555418i	$0.187442\pi$
$350$		0			0
$351$	239.571	+	414.948i	0.682537	+	1.18219i
$352$		0			0
$353$	−453.877	−	262.046i	−1.28577	−	0.742340i	−0.307873	−	0.951427i	$-0.599617\pi$
$353$	−453.877	−	262.046i	−1.28577	−	0.742340i	−0.977897	+	0.209087i	$0.932951\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	462.284	−	266.900i	1.29491	−	0.747619i
$358$		0			0
$359$			295.601i			0.823401i	0.911319	+	0.411701i	$0.135065\pi$
$359$			295.601i			0.823401i	−0.911319	+	0.411701i	$0.864935\pi$
$360$		0			0
$361$	−234.347			−0.649160
$362$		0			0
$363$	325.427			0.896494
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−16.2379	+	28.1249i	−0.0442450	+	0.0766345i	−0.887300	−	0.461193i	$-0.847422\pi$
$367$	−16.2379	+	28.1249i	−0.0442450	+	0.0766345i	0.843055	+	0.537828i	$0.180755\pi$
$368$		0			0
$369$	202.500	+	116.913i	0.548780	+	0.316839i
$370$		0			0
$371$	383.141	+	221.207i	1.03273	+	0.596244i
$372$		0			0
$373$	−123.746	−	214.334i	−0.331759	−	0.574623i	0.651098	−	0.758994i	$-0.274309\pi$
$373$	−123.746	−	214.334i	−0.331759	−	0.574623i	−0.982857	+	0.184371i	$0.940975\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	168.805i		−	0.447759i
$378$		0			0
$379$	300.746			0.793525			0.396762	−	0.917921i	$-0.370134\pi$
$379$	300.746			0.793525			0.396762	+	0.917921i	$0.370134\pi$
$380$		0			0
$381$	−218.855	+	379.068i	−0.574422	+	0.994928i
$382$		0			0
$383$	183.665	−	106.039i	0.479544	−	0.276865i	−0.240683	−	0.970604i	$-0.577371\pi$
$383$	183.665	−	106.039i	0.479544	−	0.276865i	0.720226	+	0.693739i	$0.244038\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	179.855			0.464741
$388$		0			0
$389$	−190.760	−	110.135i	−0.490386	−	0.283124i	0.234349	−	0.972153i	$-0.424704\pi$
$389$	−190.760	−	110.135i	−0.490386	−	0.283124i	−0.724734	+	0.689028i	$0.758038\pi$
$390$		0			0
$391$	255.714	+	442.909i	0.653999	+	1.13276i
$392$		0			0
$393$		−	199.926i		−	0.508718i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	97.4919			0.245572			0.122786	−	0.992433i	$-0.460817\pi$
$397$	97.4919			0.245572			0.122786	+	0.992433i	$0.460817\pi$
$398$		0			0
$399$	−198.284	−	343.438i	−0.496953	−	0.860748i
$400$		0			0
$401$	−66.8347	+	38.5870i	−0.166670	+	0.0962270i	−0.581015	−	0.813893i	$-0.697344\pi$
$401$	−66.8347	+	38.5870i	−0.166670	+	0.0962270i	0.414345	+	0.910120i	$0.364011\pi$
$402$		0			0
$403$	−498.855	+	864.042i	−1.23785	+	2.14402i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−183.665	−	106.039i	−0.451266	−	0.260539i
$408$		0			0
$409$	97.4355	+	168.763i	0.238229	+	0.412624i	0.960206	−	0.279293i	$-0.0900999\pi$
$409$	97.4355	+	168.763i	0.238229	+	0.412624i	−0.721978	+	0.691917i	$0.756767\pi$
$410$		0			0
$411$	−190.216	+	109.821i	−0.462812	+	0.267205i
$412$		0			0
$413$		−	747.582i		−	1.81013i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	320.141			0.767724
$418$		0			0
$419$	196.476	−	113.435i	0.468916	−	0.270729i	−0.246870	−	0.969049i	$-0.579402\pi$
$419$	196.476	−	113.435i	0.468916	−	0.270729i	0.715786	+	0.698320i	$0.246069\pi$
$420$		0			0
$421$	150.857	−	261.292i	0.358330	−	0.620645i	−0.629352	−	0.777120i	$-0.716680\pi$
$421$	150.857	−	261.292i	0.358330	−	0.620645i	0.987682	+	0.156475i	$0.0500130\pi$
$422$		0			0
$423$			650.755i			1.53843i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−7.27017	−	12.5923i	−0.0170262	−	0.0294902i
$428$		0			0
$429$	−698.425	−	403.236i	−1.62803	−	0.939944i
$430$		0			0
$431$		−	707.661i		−	1.64191i	−0.570996	−	0.820953i	$-0.693443\pi$
$431$		−	707.661i		−	1.64191i	0.570996	−	0.820953i	$-0.306557\pi$
$432$		0			0
$433$	669.883			1.54707			0.773537	−	0.633751i	$-0.218486\pi$
$433$	669.883			1.54707			0.773537	+	0.633751i	$0.218486\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	329.044	−	189.974i	0.752962	−	0.434723i
$438$		0			0
$439$	38.3327	−	66.3941i	0.0873181	−	0.151239i	−0.819059	−	0.573710i	$-0.805504\pi$
$439$	38.3327	−	66.3941i	0.0873181	−	0.151239i	0.906377	+	0.422471i	$0.138837\pi$
$440$		0			0
$441$	−400.355	+	693.435i	−0.907834	+	1.57241i
$442$		0			0
$443$	590.117	+	340.704i	1.33209	+	0.769084i	0.985620	−	0.168976i	$-0.0540462\pi$
$443$	590.117	+	340.704i	1.33209	+	0.769084i	0.346472	+	0.938060i	$0.387379\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$			499.983i			1.11853i
$448$		0			0
$449$			630.327i			1.40385i	0.712253	+	0.701923i	$0.247675\pi$
$449$			630.327i			1.40385i	−0.712253	+	0.701923i	$0.752325\pi$
$450$		0			0
$451$	−393.569			−0.872657
$452$		0			0
$453$	5.14110	+	8.90465i	0.0113490	+	0.0196571i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−286.498	+	496.229i	−0.626910	+	1.08584i	0.361258	+	0.932466i	$0.382347\pi$
$457$	−286.498	+	496.229i	−0.626910	+	1.08584i	−0.988168	+	0.153374i	$0.950986\pi$
$458$		0			0
$459$			409.008i			0.891086i
$460$		0			0
$461$	615.950	+	355.619i	1.33612	+	0.771407i	0.986229	−	0.165385i	$-0.0528866\pi$
$461$	615.950	+	355.619i	1.33612	+	0.771407i	0.349887	+	0.936792i	$0.386220\pi$
$462$		0			0
$463$	321.190	+	556.317i	0.693714	+	1.20155i	0.970612	+	0.240648i	$0.0773601\pi$
$463$	321.190	+	556.317i	0.693714	+	1.20155i	−0.276899	+	0.960899i	$0.589307\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			506.331i			1.08422i	0.840307	+	0.542111i	$0.182375\pi$
$467$			506.331i			1.08422i	−0.840307	+	0.542111i	$0.817625\pi$
$468$		0			0
$469$	−1009.58			−2.15263
$470$		0			0
$471$	−203.806			−0.432710
$472$		0			0
$473$	−262.167	+	151.362i	−0.554265	+	0.320005i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−293.571	+	169.493i	−0.615452	+	0.355331i
$478$		0			0
$479$	−644.044	−	371.839i	−1.34456	−	0.776282i	−0.357087	−	0.934071i	$-0.616230\pi$
$479$	−644.044	−	371.839i	−1.34456	−	0.776282i	−0.987473	+	0.157789i	$0.949563\pi$
$480$		0			0
$481$	124.222	+	215.158i	0.258257	+	0.447315i
$482$		0			0
$483$	−1030.28	−	594.834i	−2.13309	−	1.23154i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−154.065			−0.316354			−0.158177	−	0.987411i	$-0.550562\pi$
$487$	−154.065			−0.316354			−0.158177	+	0.987411i	$0.550562\pi$
$488$		0			0
$489$	−114.617	+	198.522i	−0.234390	+	0.405976i
$490$		0			0
$491$	−145.167	+	83.8124i	−0.295657	+	0.170697i	−0.640490	−	0.767967i	$-0.721269\pi$
$491$	−145.167	+	83.8124i	−0.295657	+	0.170697i	0.344833	+	0.938664i	$0.387935\pi$
$492$		0			0
$493$	72.0484	−	124.791i	0.146143	−	0.253127i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	224.855	+	129.820i	0.452424	+	0.261207i
$498$		0			0
$499$	−247.308	−	428.351i	−0.495608	−	0.858418i	0.504379	−	0.863482i	$-0.331721\pi$
$499$	−247.308	−	428.351i	−0.495608	−	0.858418i	−0.999987	+	0.00506391i	$0.998388\pi$
$500$		0			0
$501$		−	850.514i		−	1.69763i
$502$		0			0
$503$		−	711.349i		−	1.41421i	−0.707107	−	0.707106i	$-0.750000\pi$
$503$		−	711.349i		−	1.41421i	0.707107	−	0.707106i	$-0.250000\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	218.879	+	379.110i	0.431714	+	0.747751i
$508$		0			0
$509$	−717.714	+	414.372i	−1.41005	+	0.814091i	−0.995392	−	0.0958882i	$-0.969431\pi$
$509$	−717.714	+	414.372i	−1.41005	+	0.814091i	−0.414654	+	0.909979i	$0.636098\pi$
$510$		0			0
$511$	−353.776	+	612.758i	−0.692321	+	1.19914i
$512$		0			0
$513$	303.859			0.592318
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−547.663	−	948.581i	−1.05931	−	1.83478i
$518$		0			0
$519$	350.710	−	202.482i	0.675741	−	0.390139i
$520$		0			0
$521$		−	622.686i		−	1.19518i	−0.801804	−	0.597588i	$-0.796126\pi$
$521$		−	622.686i		−	1.19518i	0.801804	−	0.597588i	$-0.203874\pi$
$522$		0			0
$523$	89.4274			0.170989			0.0854946	−	0.996339i	$-0.472753\pi$
$523$	89.4274			0.170989			0.0854946	+	0.996339i	$0.472753\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−737.571	+	425.837i	−1.39956	+	0.808039i
$528$		0			0
$529$	305.403	−	528.974i	0.577322	−	0.999951i
$530$		0			0
$531$	496.071	+	286.406i	0.934219	+	0.539372i
$532$		0			0
$533$	399.284	+	230.527i	0.749126	+	0.432508i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−445.427	−	257.168i	−0.829474	−	0.478897i
$538$		0			0
$539$		−	1347.72i		−	2.50042i
$540$		0			0
$541$	834.629			1.54275			0.771376	−	0.636380i	$-0.219569\pi$
$541$	834.629			1.54275			0.771376	+	0.636380i	$0.219569\pi$
$542$		0			0
$543$	181.192	−	313.833i	0.333686	−	0.577961i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	441.782	−	765.189i	0.807646	−	1.39888i	−0.106845	−	0.994276i	$-0.534075\pi$
$547$	441.782	−	765.189i	0.807646	−	1.39888i	0.914490	−	0.404608i	$-0.132592\pi$
$548$		0			0
$549$	11.1411			0.0202934
$550$		0			0
$551$	−92.7096	−	53.5259i	−0.168257	−	0.0971432i
$552$		0			0
$553$	−606.314	−	1050.17i	−1.09641	−	1.89904i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	256.448i		−	0.460410i	−0.973142	−	0.230205i	$-0.926060\pi$
$557$		−	256.448i		−	0.460410i	0.973142	−	0.230205i	$-0.0739396\pi$
$558$		0			0
$559$	354.633			0.634406
$560$		0			0
$561$	−344.214	−	596.196i	−0.613572	−	1.06274i
$562$		0			0
$563$	180.024	−	103.937i	0.319759	−	0.184613i	−0.331526	−	0.943446i	$-0.607564\pi$
$563$	180.024	−	103.937i	0.319759	−	0.184613i	0.651285	+	0.758833i	$0.274230\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−475.712	−	823.957i	−0.838998	−	1.45319i
$568$		0			0
$569$	430.923	+	248.794i	0.757334	+	0.437247i	0.828338	−	0.560229i	$-0.189287\pi$
$569$	430.923	+	248.794i	0.757334	+	0.437247i	−0.0710034	+	0.997476i	$0.522620\pi$
$570$		0			0
$571$	−453.817	−	786.033i	−0.794775	−	1.37659i	−0.922982	−	0.384843i	$-0.874256\pi$
$571$	−453.817	−	786.033i	−0.794775	−	1.37659i	0.128207	−	0.991747i	$-0.459078\pi$
$572$		0			0
$573$	−725.425	+	418.825i	−1.26601	+	0.730933i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−758.810			−1.31510			−0.657548	−	0.753413i	$-0.728406\pi$
$577$	−758.810			−1.31510			−0.657548	+	0.753413i	$0.728406\pi$
$578$		0			0
$579$	−315.859			−0.545525
$580$		0			0
$581$	−916.185	+	528.960i	−1.57691	+	0.910430i
$582$		0			0
$583$	285.284	−	494.127i	0.489338	−	0.847559i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−656.117	−	378.809i	−1.11775	−	0.645331i	−0.176921	−	0.984225i	$-0.556614\pi$
$587$	−656.117	−	378.809i	−1.11775	−	0.645331i	−0.940825	+	0.338894i	$0.889947\pi$
$588$		0			0
$589$	316.361	+	547.953i	0.537115	+	0.930311i
$590$		0			0
$591$	150.569	+	86.9308i	0.254769	+	0.147091i
$592$		0			0
$593$			258.648i			0.436169i	0.975930	+	0.218084i	$0.0699808\pi$
$593$			258.648i			0.436169i	−0.975930	+	0.218084i	$0.930019\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−37.9052	+	65.6538i	−0.0634929	+	0.109973i
$598$		0			0
$599$	−495.665	+	286.172i	−0.827488	+	0.477750i	−0.852992	−	0.521924i	$-0.825214\pi$
$599$	−495.665	+	286.172i	−0.827488	+	0.477750i	0.0255038	+	0.999675i	$0.491881\pi$
$600$		0			0
$601$	−68.8186	+	119.197i	−0.114507	+	0.198332i	−0.917582	−	0.397545i	$-0.869862\pi$
$601$	−68.8186	+	119.197i	−0.114507	+	0.198332i	0.803076	+	0.595877i	$0.203195\pi$
$602$		0			0
$603$	386.782	−	669.926i	0.641430	−	1.11099i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	9.23790	+	16.0005i	0.0152189	+	0.0263600i	0.873535	−	0.486762i	$-0.161822\pi$
$607$	9.23790	+	16.0005i	0.0152189	+	0.0263600i	−0.858316	+	0.513122i	$0.828489\pi$
$608$		0			0
$609$			335.194i			0.550400i
$610$		0			0
$611$			1283.14i			2.10007i
$612$		0			0
$613$	−392.569			−0.640405			−0.320203	−	0.947349i	$-0.603751\pi$
$613$	−392.569			−0.640405			−0.320203	+	0.947349i	$0.603751\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−230.353	+	132.994i	−0.373343	+	0.215550i	−0.674918	−	0.737893i	$-0.735821\pi$
$617$	−230.353	+	132.994i	−0.373343	+	0.215550i	0.301575	+	0.953443i	$0.402488\pi$
$618$		0			0
$619$	−416.736	+	721.808i	−0.673240	+	1.16609i	0.303739	+	0.952755i	$0.401765\pi$
$619$	−416.736	+	721.808i	−0.673240	+	1.16609i	−0.976980	+	0.213332i	$0.931569\pi$
$620$		0			0
$621$	789.423	−	455.774i	1.27121	−	0.733935i
$622$		0			0
$623$	123.048	+	71.0420i	0.197509	+	0.114032i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−442.923	+	255.722i	−0.706417	+	0.407850i
$628$		0			0
$629$			212.078i			0.337168i
$630$		0			0
$631$	−351.875			−0.557647			−0.278823	−	0.960342i	$-0.589944\pi$
$631$	−351.875			−0.557647			−0.278823	+	0.960342i	$0.589944\pi$
$632$		0			0
$633$	312.097			0.493044
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−789.409	+	1367.30i	−1.23926	+	2.14646i
$638$		0			0
$639$	−172.288	+	99.4707i	−0.269622	+	0.155666i
$640$		0			0
$641$	355.645	+	205.332i	0.554829	+	0.320331i	0.751067	−	0.660226i	$-0.229539\pi$
$641$	355.645	+	205.332i	0.554829	+	0.320331i	−0.196239	+	0.980556i	$0.562873\pi$
$642$		0			0
$643$	−110.593	−	191.552i	−0.171995	−	0.297904i	0.767122	−	0.641501i	$-0.221688\pi$
$643$	−110.593	−	191.552i	−0.171995	−	0.297904i	−0.939117	+	0.343597i	$0.888355\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			1095.26i			1.69282i	0.532529	+	0.846412i	$0.321242\pi$
$647$			1095.26i			1.69282i	−0.532529	+	0.846412i	$0.678758\pi$
$648$		0			0
$649$	−964.137			−1.48557
$650$		0			0
$651$	990.569	−	1715.71i	1.52161	−	2.63551i
$652$		0			0
$653$	−894.048	+	516.179i	−1.36914	+	0.790473i	−0.990818	−	0.135201i	$-0.956832\pi$
$653$	−894.048	+	516.179i	−1.36914	+	0.790473i	−0.378322	+	0.925674i	$0.623499\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−271.071	−	469.508i	−0.412588	−	0.714624i
$658$		0			0
$659$	−988.851	−	570.913i	−1.50053	−	0.866333i	−1.00000		0.000614829i	$-0.999804\pi$
$659$	−988.851	−	570.913i	−1.50053	−	0.866333i	−0.500532	−	0.865718i	$-0.666862\pi$
$660$		0			0
$661$	513.282	+	889.031i	0.776524	+	1.34498i	0.933934	+	0.357445i	$0.116352\pi$
$661$	513.282	+	889.031i	0.776524	+	1.34498i	−0.157410	+	0.987533i	$0.550315\pi$
$662$		0			0
$663$			806.472i			1.21640i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−321.145			−0.481477
$668$		0			0
$669$	−371.044	−	642.668i	−0.554625	−	0.960639i
$670$		0			0
$671$	−16.2399	+	9.37614i	−0.0242026	+	0.0139734i
$672$		0			0
$673$	−139.952	+	242.403i	−0.207952	+	0.360183i	−0.951069	−	0.308978i	$-0.900013\pi$
$673$	−139.952	+	242.403i	−0.207952	+	0.360183i	0.743117	+	0.669161i	$0.233346\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	249.520	+	144.060i	0.368567	+	0.212792i	0.672832	−	0.739795i	$-0.265078\pi$
$677$	249.520	+	144.060i	0.368567	+	0.212792i	−0.304265	+	0.952587i	$0.598411\pi$
$678$		0			0
$679$	585.522	+	1014.15i	0.862330	+	1.49360i
$680$		0			0
$681$	−785.214	+	453.343i	−1.15303	+	0.665702i
$682$		0			0
$683$			283.805i			0.415527i	0.978179	+	0.207763i	$0.0666184\pi$
$683$			283.805i			0.415527i	−0.978179	+	0.207763i	$0.933382\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−798.665			−1.16254
$688$		0			0
$689$	−578.855	+	334.202i	−0.840138	+	0.485054i
$690$		0			0
$691$	−440.331	+	762.675i	−0.637237	+	1.10373i	0.348800	+	0.937197i	$0.386589\pi$
$691$	−440.331	+	762.675i	−0.637237	+	1.10373i	−0.986037	+	0.166529i	$0.946744\pi$
$692$		0			0
$693$	1386.85	+	800.700i	2.00123	+	1.15541i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	196.784	+	340.840i	0.282330	+	0.489011i
$698$		0			0
$699$	459.780	+	265.454i	0.657768	+	0.379763i
$700$		0			0
$701$			680.500i			0.970757i	0.874304	+	0.485378i	$0.161318\pi$
$701$			680.500i			0.970757i	−0.874304	+	0.485378i	$0.838682\pi$
$702$		0			0
$703$	157.556			0.224120
$704$		0			0
$705$		0			0
$706$		0			0
$707$	1576.75	−	910.339i	2.23020	−	1.28761i
$708$		0			0
$709$	289.696	−	501.767i	0.408597	−	0.707711i	−0.586135	−	0.810213i	$-0.699351\pi$
$709$	289.696	−	501.767i	0.408597	−	0.707711i	0.994733	+	0.102502i	$0.0326847\pi$
$710$		0			0
$711$	929.141			1.30681
$712$		0			0
$713$	1643.81	+	949.052i	2.30548	+	1.33107i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		−	236.551i		−	0.329917i
$718$		0			0
$719$		−	597.306i		−	0.830746i	−0.909651	−	0.415373i	$-0.863651\pi$
$719$		−	597.306i		−	0.830746i	0.909651	−	0.415373i	$-0.136349\pi$
$720$		0			0
$721$	−1829.01			−2.53677
$722$		0			0
$723$	−330.738	−	572.855i	−0.457452	−	0.792330i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−336.905	+	583.537i	−0.463419	+	0.802664i	−0.999129	−	0.0417376i	$-0.986711\pi$
$727$	−336.905	+	583.537i	−0.463419	+	0.802664i	0.535710	+	0.844402i	$0.320044\pi$
$728$		0			0
$729$	729.000			1.00000
$730$		0			0
$731$	262.167	+	151.362i	0.358642	+	0.207062i
$732$		0			0
$733$	−390.760	−	676.816i	−0.533097	−	0.923351i	−0.999253	−	0.0386484i	$-0.987695\pi$
$733$	−390.760	−	676.816i	−0.533097	−	0.923351i	0.466156	−	0.884703i	$-0.345639\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			1302.03i			1.76667i
$738$		0			0
$739$	232.335			0.314391			0.157195	−	0.987568i	$-0.449755\pi$
$739$	232.335			0.314391			0.157195	+	0.987568i	$0.449755\pi$
$740$		0			0
$741$	599.141			0.808557
$742$		0			0
$743$	−434.806	+	251.036i	−0.585204	+	0.337868i	−0.763199	−	0.646164i	$-0.776372\pi$
$743$	−434.806	+	251.036i	−0.585204	+	0.337868i	0.177995	+	0.984031i	$0.443039\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		−	810.600i		−	1.08514i
$748$		0			0
$749$	863.329	+	498.443i	1.15264	+	0.665478i
$750$		0			0
$751$	−477.190	−	826.516i	−0.635405	−	1.10055i	−0.986429	−	0.164188i	$-0.947500\pi$
$751$	−477.190	−	826.516i	−0.635405	−	1.10055i	0.351024	−	0.936367i	$-0.385834\pi$
$752$		0			0
$753$	720.635	+	416.059i	0.957019	+	0.552535i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	266.379			0.351888			0.175944	−	0.984400i	$-0.443702\pi$
$757$	266.379			0.351888			0.175944	+	0.984400i	$0.443702\pi$
$758$		0			0
$759$	−767.141	+	1328.73i	−1.01073	+	1.75063i
$760$		0			0
$761$	294.665	−	170.125i	0.387208	−	0.223555i	−0.293742	−	0.955885i	$-0.594901\pi$
$761$	294.665	−	170.125i	0.387208	−	0.223555i	0.680950	+	0.732330i	$0.261567\pi$
$762$		0			0
$763$	223.363	−	386.876i	0.292743	−	0.507046i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	978.139	+	564.729i	1.27528	+	0.736283i
$768$		0			0
$769$	−644.552	−	1116.40i	−0.838170	−	1.45175i	−0.891423	−	0.453171i	$-0.850293\pi$
$769$	−644.552	−	1116.40i	−0.838170	−	1.45175i	0.0532540	−	0.998581i	$-0.483041\pi$
$770$		0			0
$771$		−	456.193i		−	0.591690i
$772$		0			0
$773$		−	919.244i		−	1.18919i	−0.804025	−	0.594595i	$-0.797312\pi$
$773$		−	919.244i		−	1.18919i	0.804025	−	0.594595i	$-0.202688\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−246.665	−	427.237i	−0.317459	−	0.549854i
$778$		0			0
$779$	253.216	−	146.194i	0.325052	−	0.187669i
$780$		0			0
$781$	167.425	−	289.989i	0.214373	−	0.371305i
$782$		0			0
$783$	−222.423	−	128.416i	−0.284066	−	0.164005i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−631.855	−	1094.40i	−0.802865	−	1.39060i	−0.917723	−	0.397221i	$-0.869975\pi$
$787$	−631.855	−	1094.40i	−0.802865	−	1.39060i	0.114858	−	0.993382i	$-0.463359\pi$
$788$		0			0
$789$	14.8609	−	8.57997i	0.0188352	−	0.0108745i
$790$		0			0
$791$		−	81.3784i		−	0.102880i
$792$		0			0
$793$	21.9677			0.0277021
$794$		0			0
$795$		0			0
$796$		0			0
$797$	530.806	−	306.461i	0.666006	−	0.384518i	−0.128556	−	0.991702i	$-0.541034\pi$
$797$	530.806	−	306.461i	0.666006	−	0.384518i	0.794561	+	0.607184i	$0.207701\pi$
$798$		0			0
$799$	−547.663	+	948.581i	−0.685436	+	1.18721i
$800$		0			0
$801$	−94.2822	+	54.4339i	−0.117706	+	0.0679574i
$802$		0			0
$803$	790.258	+	456.256i	0.984132	+	0.568189i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	939.284	+	542.296i	1.16392	+	0.671990i
$808$		0			0
$809$		−	273.189i		−	0.337687i	−0.985643	−	0.168844i	$-0.945997\pi$
$809$		−	273.189i		−	0.337687i	0.985643	−	0.168844i	$-0.0540033\pi$
$810$		0			0
$811$	−1446.49			−1.78359			−0.891793	−	0.452444i	$-0.850552\pi$
$811$	−1446.49			−1.78359			−0.891793	+	0.452444i	$0.850552\pi$
$812$		0			0
$813$	761.141	−	1318.34i	0.936213	−	1.62157i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	112.450	−	194.768i	0.137637	−	0.238395i
$818$		0			0
$819$	−937.996	−	1624.66i	−1.14529	−	1.98371i
$820$		0			0
$821$	221.813	+	128.064i	0.270174	+	0.155985i	0.628967	−	0.777432i	$-0.283478\pi$
$821$	221.813	+	128.064i	0.270174	+	0.155985i	−0.358793	+	0.933417i	$0.616812\pi$
$822$		0			0
$823$	615.218	+	1065.59i	0.747531	+	1.29476i	0.949003	+	0.315267i	$0.102094\pi$
$823$	615.218	+	1065.59i	0.747531	+	1.29476i	−0.201473	+	0.979494i	$0.564573\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	726.246i		−	0.878169i	−0.898446	−	0.439085i	$-0.855303\pi$
$827$		−	726.246i		−	0.878169i	0.898446	−	0.439085i	$-0.144697\pi$
$828$		0			0
$829$	1439.23			1.73610			0.868052	−	0.496474i	$-0.165372\pi$
$829$	1439.23			1.73610			0.868052	+	0.496474i	$0.165372\pi$
$830$		0			0
$831$	−335.335	−	580.817i	−0.403532	−	0.698937i
$832$		0			0
$833$	−1167.16	+	673.862i	−1.40116	+	0.808958i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	758.994	+	1314.62i	0.906803	+	1.57063i
$838$		0			0
$839$	968.135	+	558.953i	1.15392	+	0.666213i	0.949838	−	0.312742i	$-0.101247\pi$
$839$	968.135	+	558.953i	1.15392	+	0.666213i	0.204077	+	0.978955i	$0.434581\pi$
$840$		0			0
$841$	−375.258	−	649.966i	−0.446205	−	0.772849i
$842$		0			0
$843$	−119.431	+	68.9538i	−0.141674	+	0.0817957i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−1274.15			−1.50431
$848$		0			0
$849$	432.097			0.508948
$850$		0			0
$851$	409.331	−	236.327i	0.481000	−	0.277705i
$852$		0			0
$853$	−348.046	+	602.834i	−0.408026	+	0.706722i	−0.994669	−	0.103124i	$-0.967116\pi$
$853$	−348.046	+	602.834i	−0.408026	+	0.706722i	0.586642	+	0.809846i	$0.300449\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−745.040	−	430.149i	−0.869358	−	0.501924i	−0.00222347	−	0.999998i	$-0.500708\pi$
$857$	−745.040	−	430.149i	−0.869358	−	0.501924i	−0.867135	+	0.498073i	$0.834041\pi$
$858$		0			0
$859$	321.216	+	556.362i	0.373942	+	0.647686i	0.990168	−	0.139883i	$-0.0446727\pi$
$859$	321.216	+	556.362i	0.373942	+	0.647686i	−0.616226	+	0.787569i	$0.711339\pi$
$860$		0			0
$861$	−792.853	−	457.754i	−0.920851	−	0.531654i
$862$		0			0
$863$		−	1466.58i		−	1.69940i	−0.527269	−	0.849698i	$-0.676784\pi$
$863$		−	1466.58i		−	1.69940i	0.527269	−	0.849698i	$-0.323216\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	89.2863	−	154.648i	0.102983	−	0.178372i
$868$		0			0
$869$	−1354.37	+	781.948i	−1.55854	+	0.899825i
$870$		0			0
$871$	762.647	−	1320.94i	0.875599	−	1.51658i
$872$		0			0
$873$	−897.278			−1.02781
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−96.6835	−	167.461i	−0.110243	−	0.190947i	0.805625	−	0.592426i	$-0.201830\pi$
$877$	−96.6835	−	167.461i	−0.110243	−	0.190947i	−0.915868	+	0.401479i	$0.868496\pi$
$878$		0			0
$879$			1252.19i			1.42456i
$880$		0			0
$881$			554.368i			0.629249i	0.949216	+	0.314624i	$0.101879\pi$
$881$			554.368i			0.629249i	−0.949216	+	0.314624i	$0.898121\pi$
$882$		0			0
$883$	−352.460			−0.399162			−0.199581	−	0.979881i	$-0.563958\pi$
$883$	−352.460			−0.399162			−0.199581	+	0.979881i	$0.563958\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−932.087	+	538.140i	−1.05083	+	0.606697i	−0.922882	−	0.385084i	$-0.874173\pi$
$887$	−932.087	+	538.140i	−1.05083	+	0.606697i	−0.127949	+	0.991781i	$0.540839\pi$
$888$		0			0
$889$	856.887	−	1484.17i	0.963877	−	1.66948i
$890$		0			0
$891$	−1062.63	+	613.513i	−1.19263	+	0.688566i
$892$		0			0
$893$	704.716	+	406.868i	0.789155	+	0.455619i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	1556.56	−	898.683i	1.73530	−	1.00188i
$898$		0			0
$899$		−	534.799i		−	0.594882i
$900$		0			0
$901$	−570.569			−0.633261
$902$		0			0
$903$	−704.190			−0.779833
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−110.496	+	191.385i	−0.121826	+	0.211008i	−0.920488	−	0.390772i	$-0.872208\pi$
$907$	−110.496	+	191.385i	−0.121826	+	0.211008i	0.798662	+	0.601780i	$0.205542\pi$
$908$		0			0
$909$			1395.04i			1.53470i
$910$		0			0
$911$	1535.28	+	886.394i	1.68527	+	0.972991i	0.958057	+	0.286578i	$0.0925177\pi$
$911$	1535.28	+	886.394i	1.68527	+	0.972991i	0.727212	+	0.686413i	$0.240816\pi$
$912$		0			0
$913$	682.185	+	1181.58i	0.747191	+	1.29417i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			782.775i			0.853626i
$918$		0			0
$919$	1006.85			1.09560			0.547799	−	0.836610i	$-0.315466\pi$
$919$	1006.85			1.09560			0.547799	+	0.836610i	$0.315466\pi$
$920$		0			0
$921$	465.073	−	805.529i	0.504965	−	0.874625i
$922$		0			0
$923$	−339.714	+	196.134i	−0.368054	+	0.212496i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	700.712	−	1213.67i	0.755892	−	1.30924i
$928$		0			0
$929$	−974.758	−	562.777i	−1.04926	−	0.605788i	−0.126814	−	0.991926i	$-0.540475\pi$
$929$	−974.758	−	562.777i	−1.04926	−	0.605788i	−0.922441	+	0.386139i	$0.873809\pi$
$930$		0			0
$931$	500.623	+	867.104i	0.537726	+	0.931369i
$932$		0			0
$933$			839.137i			0.899396i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−1343.20			−1.43351			−0.716756	−	0.697324i	$-0.754374\pi$
$937$	−1343.20			−1.43351			−0.716756	+	0.697324i	$0.754374\pi$
$938$		0			0
$939$	43.7359	+	75.7527i	0.0465771	+	0.0806738i
$940$		0			0
$941$	618.375	−	357.019i	0.657147	−	0.379404i	−0.134042	−	0.990976i	$-0.542796\pi$
$941$	618.375	−	357.019i	0.657147	−	0.379404i	0.791189	+	0.611572i	$0.209462\pi$
$942$		0			0
$943$	438.569	−	759.623i	0.465078	−	0.805539i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	620.456	+	358.220i	0.655180	+	0.378268i	0.790438	−	0.612542i	$-0.209853\pi$
$947$	620.456	+	358.220i	0.655180	+	0.378268i	−0.135258	+	0.990810i	$0.543186\pi$
$948$		0			0
$949$	−534.490	−	925.764i	−0.563214	−	0.975515i
$950$		0			0
$951$	−327.284	+	188.958i	−0.344147	+	0.198694i
$952$		0			0
$953$		−	793.300i		−	0.832424i	−0.909268	−	0.416212i	$-0.863357\pi$
$953$		−	793.300i		−	0.832424i	0.909268	−	0.416212i	$-0.136643\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	432.290			0.451714
$958$		0			0
$959$	744.756	−	429.985i	0.776596	−	0.448368i
$960$		0			0
$961$	−1099.94	+	1905.16i	−1.14458	+	1.98247i
$962$		0			0
$963$	−661.500	+	381.917i	−0.686916	+	0.396591i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	914.331	+	1583.67i	0.945533	+	1.63771i	0.754680	+	0.656093i	$0.227792\pi$
$967$	914.331	+	1583.67i	0.945533	+	1.63771i	0.190853	+	0.981619i	$0.438875\pi$
$968$		0			0
$969$	442.923	+	255.722i	0.457093	+	0.263903i
$970$		0			0
$971$		−	1843.33i		−	1.89839i	−0.314691	−	0.949194i	$-0.601901\pi$
$971$		−	1843.33i		−	1.89839i	0.314691	−	0.949194i	$-0.398099\pi$
$972$		0			0
$973$	−1253.46			−1.28824
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−289.591	+	167.195i	−0.296408	+	0.171131i	−0.640828	−	0.767684i	$-0.721409\pi$
$977$	−289.591	+	167.195i	−0.296408	+	0.171131i	0.344420	+	0.938816i	$0.388076\pi$
$978$		0			0
$979$	91.6210	−	158.692i	0.0935863	−	0.162096i
$980$		0			0
$981$	171.145	+	296.432i	0.174460	+	0.302173i
$982$		0			0
$983$	−1604.71	−	926.480i	−1.63246	−	0.942502i	−0.983331	−	0.181825i	$-0.941800\pi$
$983$	−1604.71	−	926.480i	−1.63246	−	0.942502i	−0.649131	−	0.760677i	$-0.724867\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		−	2547.92i		−	2.58148i
$988$		0			0
$989$		−	674.676i		−	0.682180i
$990$		0			0
$991$	415.419			0.419192			0.209596	−	0.977788i	$-0.432785\pi$
$991$	415.419			0.419192			0.209596	+	0.977788i	$0.432785\pi$
$992$		0			0
$993$	−698.710	−	1210.20i	−0.703635	−	1.21873i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	596.808	−	1033.70i	0.598604	−	1.03681i	−0.394423	−	0.918929i	$-0.629056\pi$
$997$	596.808	−	1033.70i	0.598604	−	1.03681i	0.993027	−	0.117884i	$-0.0376111\pi$
$998$		0			0
$999$	378.000			0.378378

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.p.b.101.1		4
3.2	odd	2		2700.3.p.a.1601.1		4
5.2	odd	4		900.3.u.b.749.1		8
5.3	odd	4		900.3.u.b.749.4		8
5.4	even	2		180.3.o.a.101.2	yes	4
9.4	even	3		2700.3.p.a.2501.1		4
9.5	odd	6	inner	900.3.p.b.401.1		4
15.2	even	4		2700.3.u.a.2249.1		8
15.8	even	4		2700.3.u.a.2249.4		8
15.14	odd	2		540.3.o.a.521.1		4
20.19	odd	2		720.3.bs.a.641.2		4
45.4	even	6		540.3.o.a.341.1		4
45.13	odd	12		2700.3.u.a.449.1		8
45.14	odd	6		180.3.o.a.41.2	✓	4
45.22	odd	12		2700.3.u.a.449.4		8
45.23	even	12		900.3.u.b.149.1		8
45.29	odd	6		1620.3.g.a.161.1		4
45.32	even	12		900.3.u.b.149.4		8
45.34	even	6		1620.3.g.a.161.3		4
60.59	even	2		2160.3.bs.a.1601.1		4
180.59	even	6		720.3.bs.a.401.2		4
180.139	odd	6		2160.3.bs.a.881.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.3.o.a.41.2	✓	4	45.14	odd	6
180.3.o.a.101.2	yes	4	5.4	even	2
540.3.o.a.341.1		4	45.4	even	6
540.3.o.a.521.1		4	15.14	odd	2
720.3.bs.a.401.2		4	180.59	even	6
720.3.bs.a.641.2		4	20.19	odd	2
900.3.p.b.101.1		4	1.1	even	1	trivial
900.3.p.b.401.1		4	9.5	odd	6	inner
900.3.u.b.149.1		8	45.23	even	12
900.3.u.b.149.4		8	45.32	even	12
900.3.u.b.749.1		8	5.2	odd	4
900.3.u.b.749.4		8	5.3	odd	4
1620.3.g.a.161.1		4	45.29	odd	6
1620.3.g.a.161.3		4	45.34	even	6
2160.3.bs.a.881.1		4	180.139	odd	6
2160.3.bs.a.1601.1		4	60.59	even	2
2700.3.p.a.1601.1		4	3.2	odd	2
2700.3.p.a.2501.1		4	9.4	even	3
2700.3.u.a.449.1		8	45.13	odd	12
2700.3.u.a.449.4		8	45.22	odd	12
2700.3.u.a.2249.1		8	15.2	even	4
2700.3.u.a.2249.4		8	15.8	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 2.59808i) q^{3} +(-5.87298 + 10.1723i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(13.1190 + 7.57423i) q^{11} +(-8.87298 - 15.3685i) q^{13} -15.1485i q^{17} -11.2540 q^{19} +(17.6190 + 30.5169i) q^{21} +(-29.2379 + 16.8805i) q^{23} -27.0000 q^{27} +(8.23790 + 4.75615i) q^{29} +(-28.1109 - 48.6895i) q^{31} +(39.3569 - 22.7227i) q^{33} -14.0000 q^{37} -53.2379 q^{39} +(-22.5000 + 12.9904i) q^{41} +(-9.99193 + 17.3065i) q^{43} +(-62.6190 - 36.1531i) q^{47} +(-44.4839 - 77.0483i) q^{49} +(-39.3569 - 22.7227i) q^{51} -37.6651i q^{53} +(-16.8810 + 29.2388i) q^{57} +(-55.1190 + 31.8229i) q^{59} +(-0.618950 + 1.07205i) q^{61} +105.714 q^{63} +(42.9758 + 74.4363i) q^{67} +101.283i q^{69} -22.1046i q^{71} +60.2379 q^{73} +(-154.095 + 88.9666i) q^{77} +(-51.6190 + 89.4066i) q^{79} +(-40.5000 + 70.1481i) q^{81} +(78.0000 + 45.0333i) q^{83} +(24.7137 - 14.2685i) q^{87} -12.0964i q^{89} +208.444 q^{91} -168.665 q^{93} +(49.8488 - 86.3406i) q^{97} -136.336i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{3} - 8 q^{7} - 18 q^{9} + 6 q^{11} - 20 q^{13} - 76 q^{19} + 24 q^{21} - 24 q^{23} - 108 q^{27} - 60 q^{29} - 4 q^{31} + 18 q^{33} - 56 q^{37} - 120 q^{39} - 90 q^{41} + 22 q^{43} - 204 q^{47}+ \cdots - 2 q^{97}+O(q^{100}) \) 4 * q + 6 * q^3 - 8 * q^7 - 18 * q^9 + 6 * q^11 - 20 * q^13 - 76 * q^19 + 24 * q^21 - 24 * q^23 - 108 * q^27 - 60 * q^29 - 4 * q^31 + 18 * q^33 - 56 * q^37 - 120 * q^39 - 90 * q^41 + 22 * q^43 - 204 * q^47 - 54 * q^49 - 18 * q^51 - 114 * q^57 - 174 * q^59 + 44 * q^61 + 144 * q^63 - 14 * q^67 + 148 * q^73 - 384 * q^77 - 160 * q^79 - 162 * q^81 + 312 * q^83 - 180 * q^87 + 400 * q^91 - 24 * q^93 - 2 * q^97

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