LMFDB - Embedded newform 900.3.u.b.149.1

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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.12960000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{6} + 8x^{4} - 3x^{2} + 1 $ x^8 - 3x^6 + 8x^4 - 3*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			149.1
Root			$-0.535233 + 0.309017i$ of defining polynomial
Character	$\chi$	$=$	900.149
Dual form			900.3.u.b.749.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.59808 + 1.50000i) q^{3} +(-10.1723 + 5.87298i) q^{7} +(4.50000 - 7.79423i) q^{9} +O(q^{10})$	$q+(-2.59808 + 1.50000i) q^{3} +(-10.1723 + 5.87298i) q^{7} +(4.50000 - 7.79423i) q^{9} +(13.1190 - 7.57423i) q^{11} +(-15.3685 - 8.87298i) q^{13} +15.1485 q^{17} +11.2540 q^{19} +(17.6190 - 30.5169i) q^{21} +(16.8805 - 29.2379i) q^{23} +27.0000i q^{27} +(-8.23790 + 4.75615i) q^{29} +(-28.1109 + 48.6895i) q^{31} +(-22.7227 + 39.3569i) q^{33} +14.0000i q^{37} +53.2379 q^{39} +(-22.5000 - 12.9904i) q^{41} +(17.3065 - 9.99193i) q^{43} +(36.1531 + 62.6190i) q^{47} +(44.4839 - 77.0483i) q^{49} +(-39.3569 + 22.7227i) q^{51} -37.6651 q^{53} +(-29.2388 + 16.8810i) q^{57} +(55.1190 + 31.8229i) q^{59} +(-0.618950 - 1.07205i) q^{61} +105.714i q^{63} +(-74.4363 - 42.9758i) q^{67} +101.283i q^{69} +22.1046i q^{71} +60.2379i q^{73} +(-88.9666 + 154.095i) q^{77} +(51.6190 + 89.4066i) q^{79} +(-40.5000 - 70.1481i) q^{81} +(45.0333 + 78.0000i) q^{83} +(14.2685 - 24.7137i) q^{87} -12.0964i q^{89} +208.444 q^{91} -168.665i q^{93} +(86.3406 - 49.8488i) q^{97} -136.336i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 36 q^{9}+O(q^{10}) $ 8 * q + 36 * q^9	$ 8 q + 36 q^{9} + 12 q^{11} + 152 q^{19} + 48 q^{21} + 120 q^{29} - 8 q^{31} + 240 q^{39} - 180 q^{41} + 108 q^{49} - 36 q^{51} + 348 q^{59} + 88 q^{61} + 320 q^{79} - 324 q^{81} + 800 q^{91}+O(q^{100}) $ 8 * q + 36 * q^9 + 12 * q^11 + 152 * q^19 + 48 * q^21 + 120 * q^29 - 8 * q^31 + 240 * q^39 - 180 * q^41 + 108 * q^49 - 36 * q^51 + 348 * q^59 + 88 * q^61 + 320 * q^79 - 324 * q^81 + 800 * q^91

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
$3$	−2.59808	+	1.50000i	−0.866025	+	0.500000i
$3$	−2.59808	+	1.50000i	−0.866025	+	0.500000i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−10.1723	+	5.87298i	−1.45319	+	0.838998i	−0.998661	−	0.0517360i	$-0.983525\pi$
$7$	−10.1723	+	5.87298i	−1.45319	+	0.838998i	−0.454526	+	0.890734i	$0.650191\pi$
$8$		0			0
$9$	4.50000	−	7.79423i	0.500000	−	0.866025i
$10$		0			0
$11$	13.1190	−	7.57423i	1.19263	−	0.688566i	0.233729	−	0.972302i	$-0.424907\pi$
$11$	13.1190	−	7.57423i	1.19263	−	0.688566i	0.958903	+	0.283735i	$0.0915737\pi$
$12$		0			0
$13$	−15.3685	−	8.87298i	−1.18219	−	0.682537i	−0.225669	−	0.974204i	$-0.572457\pi$
$13$	−15.3685	−	8.87298i	−1.18219	−	0.682537i	−0.956520	+	0.291667i	$0.905790\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	15.1485			0.891086			0.445543	−	0.895261i	$-0.353011\pi$
$17$	15.1485			0.891086			0.445543	+	0.895261i	$0.353011\pi$
$18$		0			0
$19$	11.2540			0.592318			0.296159	−	0.955139i	$-0.404294\pi$
$19$	11.2540			0.592318			0.296159	+	0.955139i	$0.404294\pi$
$20$		0			0
$21$	17.6190	−	30.5169i	0.838998	−	1.45319i
$22$		0			0
$23$	16.8805	−	29.2379i	0.733935	−	1.27121i	−0.221254	−	0.975216i	$-0.571015\pi$
$23$	16.8805	−	29.2379i	0.733935	−	1.27121i	0.955189	−	0.295997i	$-0.0956518\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$			27.0000i			1.00000i
$28$		0			0
$29$	−8.23790	+	4.75615i	−0.284066	+	0.164005i	−0.635262	−	0.772296i	$-0.719108\pi$
$29$	−8.23790	+	4.75615i	−0.284066	+	0.164005i	0.351197	+	0.936302i	$0.385775\pi$
$30$		0			0
$31$	−28.1109	+	48.6895i	−0.906803	+	1.57063i	−0.0883237	+	0.996092i	$0.528151\pi$
$31$	−28.1109	+	48.6895i	−0.906803	+	1.57063i	−0.818479	+	0.574537i	$0.805182\pi$
$32$		0			0
$33$	−22.7227	+	39.3569i	−0.688566	+	1.19263i
$34$		0			0
$35$		0			0
$36$		0			0
$37$			14.0000i			0.378378i	0.981941	+	0.189189i	$0.0605859\pi$
$37$			14.0000i			0.378378i	−0.981941	+	0.189189i	$0.939414\pi$
$38$		0			0
$39$	53.2379			1.36507
$40$		0			0
$41$	−22.5000	−	12.9904i	−0.548780	−	0.316839i	0.199849	−	0.979827i	$-0.435955\pi$
$41$	−22.5000	−	12.9904i	−0.548780	−	0.316839i	−0.748630	+	0.662988i	$0.769288\pi$
$42$		0			0
$43$	17.3065	−	9.99193i	0.402478	−	0.232371i	−0.285075	−	0.958505i	$-0.592018\pi$
$43$	17.3065	−	9.99193i	0.402478	−	0.232371i	0.687552	+	0.726135i	$0.258685\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	36.1531	+	62.6190i	0.769214	+	1.33232i	0.937990	+	0.346664i	$0.112685\pi$
$47$	36.1531	+	62.6190i	0.769214	+	1.33232i	−0.168775	+	0.985655i	$0.553981\pi$
$48$		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
$53$	−37.6651			−0.710663			−0.355331	−	0.934740i	$-0.615632\pi$
$53$	−37.6651			−0.710663			−0.355331	+	0.934740i	$0.615632\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−29.2388	+	16.8810i	−0.512962	+	0.296159i
$58$		0			0
$59$	55.1190	+	31.8229i	0.934219	+	0.539372i	0.888144	−	0.459566i	$-0.151995\pi$
$59$	55.1190	+	31.8229i	0.934219	+	0.539372i	0.0460759	+	0.998938i	$0.485328\pi$
$60$		0			0
$61$	−0.618950	−	1.07205i	−0.0101467	−	0.0175746i	0.860907	−	0.508762i	$-0.169897\pi$
$61$	−0.618950	−	1.07205i	−0.0101467	−	0.0175746i	−0.871054	+	0.491187i	$0.836563\pi$
$62$		0			0
$63$			105.714i			1.67800i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−74.4363	−	42.9758i	−1.11099	−	0.641430i	−0.171904	−	0.985114i	$-0.554992\pi$
$67$	−74.4363	−	42.9758i	−1.11099	−	0.641430i	−0.939085	+	0.343684i	$0.888325\pi$
$68$		0			0
$69$			101.283i			1.46787i
$70$		0			0
$71$			22.1046i			0.311332i	0.987810	+	0.155666i	$0.0497524\pi$
$71$			22.1046i			0.311332i	−0.987810	+	0.155666i	$0.950248\pi$
$72$		0			0
$73$			60.2379i			0.825177i	0.910918	+	0.412588i	$0.135375\pi$
$73$			60.2379i			0.825177i	−0.910918	+	0.412588i	$0.864625\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−88.9666	+	154.095i	−1.15541	+	2.00123i
$78$		0			0
$79$	51.6190	+	89.4066i	0.653404	+	1.13173i	0.982291	+	0.187360i	$0.0599932\pi$
$79$	51.6190	+	89.4066i	0.653404	+	1.13173i	−0.328887	+	0.944369i	$0.606673\pi$
$80$		0			0
$81$	−40.5000	−	70.1481i	−0.500000	−	0.866025i
$82$		0			0
$83$	45.0333	+	78.0000i	0.542570	+	0.939759i	0.998756	+	0.0498743i	$0.0158821\pi$
$83$	45.0333	+	78.0000i	0.542570	+	0.939759i	−0.456185	+	0.889885i	$0.650785\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	14.2685	−	24.7137i	0.164005	−	0.284066i
$88$		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
$93$		−	168.665i		−	1.81361i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	86.3406	−	49.8488i	0.890110	−	0.513905i	0.0161312	−	0.999870i	$-0.494865\pi$
$97$	86.3406	−	49.8488i	0.890110	−	0.513905i	0.873978	+	0.485965i	$0.161532\pi$
$98$		0			0
$99$		−	136.336i		−	1.37713i
$100$		0			0
$101$	−134.238	+	77.5023i	−1.32909	+	0.767349i	−0.985159	−	0.171646i	$-0.945091\pi$
$101$	−134.238	+	77.5023i	−1.32909	+	0.767349i	−0.343929	+	0.938995i	$0.611758\pi$
$102$		0			0
$103$	134.852	+	77.8569i	1.30924	+	0.755892i	0.981970	−	0.189038i	$-0.0605369\pi$
$103$	134.852	+	77.8569i	1.30924	+	0.755892i	0.327273	+	0.944930i	$0.393870\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	84.8705			0.793182			0.396591	−	0.917995i	$-0.370193\pi$
$107$	84.8705			0.793182			0.396591	+	0.917995i	$0.370193\pi$
$108$		0			0
$109$	38.0323			0.348920			0.174460	−	0.984664i	$-0.444182\pi$
$109$	38.0323			0.348920			0.174460	+	0.984664i	$0.444182\pi$
$110$		0			0
$111$	−21.0000	−	36.3731i	−0.189189	−	0.327685i
$112$		0			0
$113$	3.46410	−	6.00000i	0.0306558	−	0.0530973i	−0.850290	−	0.526314i	$-0.823574\pi$
$113$	3.46410	−	6.00000i	0.0306558	−	0.0530973i	0.880946	+	0.473216i	$0.156907\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−138.316	+	79.8569i	−1.18219	+	0.682537i
$118$		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
$123$	77.9423			0.633677
$124$		0			0
$125$		0			0
$126$		0			0
$127$			145.903i			1.14884i	0.818559	+	0.574422i	$0.194773\pi$
$127$			145.903i			1.14884i	−0.818559	+	0.574422i	$0.805227\pi$
$128$		0			0
$129$	−29.9758	+	51.9196i	−0.232371	+	0.402478i
$130$		0			0
$131$	57.7137	+	33.3210i	0.440563	+	0.254359i	0.703836	−	0.710362i	$-0.251469\pi$
$131$	57.7137	+	33.3210i	0.440563	+	0.254359i	−0.263274	+	0.964721i	$0.584802\pi$
$132$		0			0
$133$	−114.479	+	66.0948i	−0.860748	+	0.496953i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	36.6070	+	63.4052i	0.267205	+	0.462812i	0.968139	−	0.250414i	$-0.0805667\pi$
$137$	36.6070	+	63.4052i	0.267205	+	0.462812i	−0.700934	+	0.713226i	$0.747233\pi$
$138$		0			0
$139$	−53.3569	+	92.4168i	−0.383862	+	0.664869i	−0.991611	−	0.129261i	$-0.958740\pi$
$139$	−53.3569	+	92.4168i	−0.383862	+	0.664869i	0.607748	+	0.794130i	$0.292073\pi$
$140$		0			0
$141$	−187.857	−	108.459i	−1.33232	−	0.769214i
$142$		0			0
$143$	−268.824			−1.87989
$144$		0			0
$145$		0			0
$146$		0			0
$147$			266.903i			1.81567i
$148$		0			0
$149$	144.333	+	83.3305i	0.968676	+	0.559265i	0.898832	−	0.438293i	$-0.144417\pi$
$149$	144.333	+	83.3305i	0.968676	+	0.559265i	0.0698433	+	0.997558i	$0.477750\pi$
$150$		0			0
$151$	−1.71370	−	2.96822i	−0.0113490	−	0.0196571i	0.860295	−	0.509796i	$-0.170279\pi$
$151$	−1.71370	−	2.96822i	−0.0113490	−	0.0196571i	−0.871644	+	0.490139i	$0.836946\pi$
$152$		0			0
$153$	68.1681	−	118.071i	0.445543	−	0.771703i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	58.8338	+	33.9677i	0.374738	+	0.216355i	0.675526	−	0.737336i	$-0.263916\pi$
$157$	58.8338	+	33.9677i	0.374738	+	0.216355i	−0.300788	+	0.953691i	$0.597250\pi$
$158$		0			0
$159$	97.8569	−	56.4977i	0.615452	−	0.355331i
$160$		0			0
$161$			396.556i			2.46308i
$162$		0			0
$163$		−	76.4113i		−	0.468781i	−0.972143	−	0.234390i	$-0.924691\pi$
$163$		−	76.4113i		−	0.468781i	0.972143	−	0.234390i	$-0.0753094\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	141.752	−	245.522i	0.848816	−	1.47019i	−0.0334495	−	0.999440i	$-0.510649\pi$
$167$	141.752	−	245.522i	0.848816	−	1.47019i	0.882266	−	0.470752i	$-0.156017\pi$
$168$		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
$173$	67.4941	+	116.903i	0.390139	+	0.675741i	0.992468	−	0.122507i	$-0.0390935\pi$
$173$	67.4941	+	116.903i	0.390139	+	0.675741i	−0.602328	+	0.798248i	$0.705760\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−190.938			−1.07874
$178$		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
$183$	3.21616	+	1.85685i	0.0175746	+	0.0101467i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	198.732	−	114.738i	1.06274	−	0.613572i
$188$		0			0
$189$	−158.571	−	274.652i	−0.838998	−	1.45319i
$190$		0			0
$191$	−241.808	+	139.608i	−1.26601	+	0.730933i	−0.974231	−	0.225552i	$-0.927581\pi$
$191$	−241.808	+	139.608i	−1.26601	+	0.730933i	−0.291782	+	0.956485i	$0.594248\pi$
$192$		0			0
$193$	−91.1806	−	52.6431i	−0.472438	−	0.272762i	0.244822	−	0.969568i	$-0.421271\pi$
$193$	−91.1806	−	52.6431i	−0.472438	−	0.272762i	−0.717260	+	0.696806i	$0.754604\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−57.9538			−0.294182			−0.147091	−	0.989123i	$-0.546991\pi$
$197$	−57.9538			−0.294182			−0.147091	+	0.989123i	$0.546991\pi$
$198$		0			0
$199$	25.2702			0.126986			0.0634929	−	0.997982i	$-0.479776\pi$
$199$	25.2702			0.126986			0.0634929	+	0.997982i	$0.479776\pi$
$200$		0			0
$201$	257.855			1.28286
$202$		0			0
$203$	55.8656	−	96.7621i	0.275200	−	0.476661i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−151.925	−	263.141i	−0.733935	−	1.27121i
$208$		0			0
$209$	147.641	−	85.2406i	0.706417	−	0.407850i
$210$		0			0
$211$	52.0161	−	90.0946i	0.246522	−	0.426989i	−0.716036	−	0.698063i	$-0.754046\pi$
$211$	52.0161	−	90.0946i	0.246522	−	0.426989i	0.962558	+	0.271074i	$0.0873789\pi$
$212$		0			0
$213$	−33.1569	−	57.4294i	−0.155666	−	0.269622i
$214$		0			0
$215$		0			0
$216$		0			0
$217$		−	660.379i		−	3.04322i
$218$		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
$223$	−214.223	+	123.681i	−0.960639	+	0.554625i	−0.896370	−	0.443307i	$-0.853805\pi$
$223$	−214.223	+	123.681i	−0.960639	+	0.554625i	−0.0642694	+	0.997933i	$0.520472\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	151.114	+	261.738i	0.665702	+	1.15303i	0.979094	+	0.203407i	$0.0652013\pi$
$227$	151.114	+	261.738i	0.665702	+	1.15303i	−0.313392	+	0.949624i	$0.601465\pi$
$228$		0			0
$229$	133.111	−	230.555i	0.581270	−	1.00679i	−0.414059	−	0.910250i	$-0.635889\pi$
$229$	133.111	−	230.555i	0.581270	−	1.00679i	0.995329	−	0.0965395i	$-0.0307774\pi$
$230$		0			0
$231$		−	533.800i		−	2.31082i
$232$		0			0
$233$	176.969			0.759526			0.379763	−	0.925084i	$-0.376006\pi$
$233$	176.969			0.759526			0.379763	+	0.925084i	$0.376006\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−268.220	−	154.857i	−1.13173	−	0.653404i
$238$		0			0
$239$	−68.2863	−	39.4251i	−0.285717	−	0.164959i	0.350292	−	0.936641i	$-0.386082\pi$
$239$	−68.2863	−	39.4251i	−0.285717	−	0.164959i	−0.636009	+	0.771682i	$0.719416\pi$
$240$		0			0
$241$	110.246	+	190.952i	0.457452	+	0.792330i	0.998826	−	0.0484519i	$-0.0154288\pi$
$241$	110.246	+	190.952i	0.457452	+	0.792330i	−0.541373	+	0.840782i	$0.682095\pi$
$242$		0			0
$243$	210.444	+	121.500i	0.866025	+	0.500000i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−172.957	−	99.8569i	−0.700231	−	0.404279i
$248$		0			0
$249$	−234.000	−	135.100i	−0.939759	−	0.542570i
$250$		0			0
$251$		−	277.373i		−	1.10507i	−0.833490	−	0.552535i	$-0.813661\pi$
$251$		−	277.373i		−	1.10507i	0.833490	−	0.552535i	$-0.186339\pi$
$252$		0			0
$253$		−	511.427i		−	2.02145i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	76.0322	−	131.692i	0.295845	−	0.512418i	−0.679336	−	0.733827i	$-0.737732\pi$
$257$	76.0322	−	131.692i	0.295845	−	0.512418i	0.975181	+	0.221409i	$0.0710655\pi$
$258$		0			0
$259$	−82.2218	−	142.412i	−0.317459	−	0.549854i
$260$		0			0
$261$			85.6108i			0.328011i
$262$		0			0
$263$	2.85999	+	4.95365i	0.0108745	+	0.0188352i	0.871411	−	0.490553i	$-0.163205\pi$
$263$	2.85999	+	4.95365i	0.0108745	+	0.0188352i	−0.860537	+	0.509388i	$0.829872\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	18.1446	+	31.4274i	0.0679574	+	0.117706i
$268$		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
$273$	−541.552	+	312.665i	−1.98371	+	1.14529i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	193.606	−	111.778i	0.698937	−	0.403532i	−0.108014	−	0.994149i	$-0.534449\pi$
$277$	193.606	−	111.778i	0.698937	−	0.403532i	0.806951	+	0.590618i	$0.201116\pi$
$278$		0			0
$279$	252.998	+	438.205i	0.906803	+	1.57063i
$280$		0			0
$281$	−39.8105	+	22.9846i	−0.141674	+	0.0817957i	−0.569162	−	0.822226i	$-0.692732\pi$
$281$	−39.8105	+	22.9846i	−0.141674	+	0.0817957i	0.427487	+	0.904021i	$0.359399\pi$
$282$		0			0
$283$	124.736	+	72.0161i	0.440762	+	0.254474i	0.703921	−	0.710279i	$-0.251431\pi$
$283$	124.736	+	72.0161i	0.440762	+	0.254474i	−0.263159	+	0.964753i	$0.584764\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	305.169			1.06331
$288$		0			0
$289$	−59.5242			−0.205966
$290$		0			0
$291$	−149.546	+	259.022i	−0.513905	+	0.890110i
$292$		0			0
$293$	208.698	−	361.476i	0.712280	−	1.23371i	−0.251719	−	0.967800i	$-0.580996\pi$
$293$	208.698	−	361.476i	0.712280	−	1.23371i	0.963999	−	0.265905i	$-0.0856709\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	204.504	+	354.212i	0.688566	+	1.19263i
$298$		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
$303$	232.507	−	402.714i	0.767349	−	1.32909i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	310.048i		−	1.00993i	−0.863140	−	0.504965i	$-0.831505\pi$
$307$		−	310.048i		−	1.00993i	0.863140	−	0.504965i	$-0.168495\pi$
$308$		0			0
$309$	−467.141			−1.51178
$310$		0			0
$311$	−242.238	−	139.856i	−0.778900	−	0.449698i	0.0571403	−	0.998366i	$-0.481802\pi$
$311$	−242.238	−	139.856i	−0.778900	−	0.449698i	−0.836040	+	0.548668i	$0.815135\pi$
$312$		0			0
$313$	25.2509	−	14.5786i	0.0806738	−	0.0465771i	−0.459120	−	0.888374i	$-0.651835\pi$
$313$	25.2509	−	14.5786i	0.0806738	−	0.0465771i	0.539794	+	0.841797i	$0.318502\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	62.9859	+	109.095i	0.198694	+	0.344147i	0.948105	−	0.317957i	$-0.102997\pi$
$317$	62.9859	+	109.095i	0.198694	+	0.344147i	−0.749411	+	0.662105i	$0.769663\pi$
$318$		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
$323$	170.481			0.527806
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−98.8107	+	57.0484i	−0.302173	+	0.174460i
$328$		0			0
$329$	−735.520	−	424.653i	−2.23562	−	1.29074i
$330$		0			0
$331$	232.903	+	403.400i	0.703635	+	1.21873i	0.967182	+	0.254085i	$0.0817743\pi$
$331$	232.903	+	403.400i	0.703635	+	1.21873i	−0.263547	+	0.964647i	$0.584892\pi$
$332$		0			0
$333$	109.119	+	63.0000i	0.327685	+	0.189189i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−303.259	−	175.087i	−0.899878	−	0.519545i	−0.0227177	−	0.999742i	$-0.507232\pi$
$337$	−303.259	−	175.087i	−0.899878	−	0.519545i	−0.877161	+	0.480197i	$0.840565\pi$
$338$		0			0
$339$			20.7846i			0.0613115i
$340$		0			0
$341$			851.673i			2.49758i
$342$		0			0
$343$			469.460i			1.36869i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−41.0594	+	71.1169i	−0.118327	+	0.204948i	−0.919105	−	0.394013i	$-0.871086\pi$
$347$	−41.0594	+	71.1169i	−0.118327	+	0.204948i	0.800778	+	0.598961i	$0.204420\pi$
$348$		0			0
$349$	22.7621	+	39.4251i	0.0652209	+	0.112966i	0.896792	−	0.442452i	$-0.145891\pi$
$349$	22.7621	+	39.4251i	0.0652209	+	0.112966i	−0.831571	+	0.555418i	$0.812558\pi$
$350$		0			0
$351$	239.571	−	414.948i	0.682537	−	1.18219i
$352$		0			0
$353$	−262.046	−	453.877i	−0.742340	−	1.28577i	−0.951427	−	0.307873i	$-0.900383\pi$
$353$	−262.046	−	453.877i	−0.742340	−	1.28577i	0.209087	−	0.977897i	$-0.432951\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	266.900	−	462.284i	0.747619	−	1.29491i
$358$		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
$363$			325.427i			0.896494i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−28.1249	+	16.2379i	−0.0766345	+	0.0442450i	−0.537828	−	0.843055i	$-0.680755\pi$
$367$	−28.1249	+	16.2379i	−0.0766345	+	0.0442450i	0.461193	+	0.887300i	$0.347422\pi$
$368$		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
$373$	−214.334	−	123.746i	−0.574623	−	0.331759i	0.184371	−	0.982857i	$-0.440975\pi$
$373$	−214.334	−	123.746i	−0.574623	−	0.331759i	−0.758994	+	0.651098i	$0.774309\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	168.805			0.447759
$378$		0			0
$379$	−300.746			−0.793525			−0.396762	−	0.917921i	$-0.629866\pi$
$379$	−300.746			−0.793525			−0.396762	+	0.917921i	$0.629866\pi$
$380$		0			0
$381$	−218.855	−	379.068i	−0.574422	−	0.994928i
$382$		0			0
$383$	−106.039	+	183.665i	−0.276865	+	0.479544i	−0.970604	−	0.240683i	$-0.922629\pi$
$383$	−106.039	+	183.665i	−0.276865	+	0.479544i	0.693739	+	0.720226i	$0.255962\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		−	179.855i		−	0.464741i
$388$		0			0
$389$	190.760	−	110.135i	0.490386	−	0.283124i	−0.234349	−	0.972153i	$-0.575296\pi$
$389$	190.760	−	110.135i	0.490386	−	0.283124i	0.724734	+	0.689028i	$0.241962\pi$
$390$		0			0
$391$	255.714	−	442.909i	0.653999	−	1.13276i
$392$		0			0
$393$	−199.926			−0.508718
$394$		0			0
$395$		0			0
$396$		0			0
$397$		−	97.4919i		−	0.245572i	−0.992433	−	0.122786i	$-0.960817\pi$
$397$		−	97.4919i		−	0.245572i	0.992433	−	0.122786i	$-0.0391828\pi$
$398$		0			0
$399$	198.284	−	343.438i	0.496953	−	0.860748i
$400$		0			0
$401$	−66.8347	−	38.5870i	−0.166670	−	0.0962270i	0.414345	−	0.910120i	$-0.364011\pi$
$401$	−66.8347	−	38.5870i	−0.166670	−	0.0962270i	−0.581015	+	0.813893i	$0.697344\pi$
$402$		0			0
$403$	864.042	−	498.855i	2.14402	−	1.23785i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	106.039	+	183.665i	0.260539	+	0.451266i
$408$		0			0
$409$	−97.4355	+	168.763i	−0.238229	+	0.412624i	−0.960206	−	0.279293i	$-0.909900\pi$
$409$	−97.4355	+	168.763i	−0.238229	+	0.412624i	0.721978	+	0.691917i	$0.243233\pi$
$410$		0			0
$411$	−190.216	−	109.821i	−0.462812	−	0.267205i
$412$		0			0
$413$	−747.582			−1.81013
$414$		0			0
$415$		0			0
$416$		0			0
$417$		−	320.141i		−	0.767724i
$418$		0			0
$419$	−196.476	−	113.435i	−0.468916	−	0.270729i	0.246870	−	0.969049i	$-0.420598\pi$
$419$	−196.476	−	113.435i	−0.468916	−	0.270729i	−0.715786	+	0.698320i	$0.753931\pi$
$420$		0			0
$421$	150.857	+	261.292i	0.358330	+	0.620645i	0.987682	−	0.156475i	$-0.0500130\pi$
$421$	150.857	+	261.292i	0.358330	+	0.620645i	−0.629352	+	0.777120i	$0.716680\pi$
$422$		0			0
$423$	650.755			1.53843
$424$		0			0
$425$		0			0
$426$		0			0
$427$	12.5923	+	7.27017i	0.0294902	+	0.0170262i
$428$		0			0
$429$	698.425	−	403.236i	1.62803	−	0.939944i
$430$		0			0
$431$			707.661i			1.64191i	0.570996	+	0.820953i	$0.306557\pi$
$431$			707.661i			1.64191i	−0.570996	+	0.820953i	$0.693443\pi$
$432$		0			0
$433$			669.883i			1.54707i	0.633751	+	0.773537i	$0.281514\pi$
$433$			669.883i			1.54707i	−0.633751	+	0.773537i	$0.718486\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	189.974	−	329.044i	0.434723	−	0.752962i
$438$		0			0
$439$	−38.3327	−	66.3941i	−0.0873181	−	0.151239i	0.819059	−	0.573710i	$-0.194496\pi$
$439$	−38.3327	−	66.3941i	−0.0873181	−	0.151239i	−0.906377	+	0.422471i	$0.861163\pi$
$440$		0			0
$441$	−400.355	−	693.435i	−0.907834	−	1.57241i
$442$		0			0
$443$	340.704	+	590.117i	0.769084	+	1.33209i	0.938060	+	0.346472i	$0.112621\pi$
$443$	340.704	+	590.117i	0.769084	+	1.33209i	−0.168976	+	0.985620i	$0.554046\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−499.983			−1.11853
$448$		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
$453$	8.90465	+	5.14110i	0.0196571	+	0.0113490i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−496.229	+	286.498i	−1.08584	+	0.626910i	−0.932466	−	0.361258i	$-0.882347\pi$
$457$	−496.229	+	286.498i	−1.08584	+	0.626910i	−0.153374	+	0.988168i	$0.549014\pi$
$458$		0			0
$459$			409.008i			0.891086i
$460$		0			0
$461$	615.950	−	355.619i	1.33612	−	0.771407i	0.349887	−	0.936792i	$-0.386220\pi$
$461$	615.950	−	355.619i	1.33612	−	0.771407i	0.986229	+	0.165385i	$0.0528866\pi$
$462$		0			0
$463$	556.317	+	321.190i	1.20155	+	0.693714i	0.960899	−	0.276899i	$-0.0893066\pi$
$463$	556.317	+	321.190i	1.20155	+	0.693714i	0.240648	+	0.970612i	$0.422640\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−506.331			−1.08422			−0.542111	−	0.840307i	$-0.682375\pi$
$467$	−506.331			−1.08422			−0.542111	+	0.840307i	$0.682375\pi$
$468$		0			0
$469$	1009.58			2.15263
$470$		0			0
$471$	−203.806			−0.432710
$472$		0			0
$473$	151.362	−	262.167i	0.320005	−	0.554265i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−169.493	+	293.571i	−0.355331	+	0.615452i
$478$		0			0
$479$	644.044	−	371.839i	1.34456	−	0.776282i	0.357087	−	0.934071i	$-0.383770\pi$
$479$	644.044	−	371.839i	1.34456	−	0.776282i	0.987473	+	0.157789i	$0.0504365\pi$
$480$		0			0
$481$	124.222	−	215.158i	0.258257	−	0.447315i
$482$		0			0
$483$	−594.834	−	1030.28i	−1.23154	−	2.13309i
$484$		0			0
$485$		0			0
$486$		0			0
$487$			154.065i			0.316354i	0.987411	+	0.158177i	$0.0505617\pi$
$487$			154.065i			0.316354i	−0.987411	+	0.158177i	$0.949438\pi$
$488$		0			0
$489$	114.617	+	198.522i	0.234390	+	0.405976i
$490$		0			0
$491$	−145.167	−	83.8124i	−0.295657	−	0.170697i	0.344833	−	0.938664i	$-0.387935\pi$
$491$	−145.167	−	83.8124i	−0.295657	−	0.170697i	−0.640490	+	0.767967i	$0.721269\pi$
$492$		0			0
$493$	−124.791	+	72.0484i	−0.253127	+	0.146143i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−129.820	−	224.855i	−0.261207	−	0.452424i
$498$		0			0
$499$	247.308	−	428.351i	0.495608	−	0.858418i	−0.504379	−	0.863482i	$-0.668279\pi$
$499$	247.308	−	428.351i	0.495608	−	0.858418i	0.999987	+	0.00506391i	$0.00161190\pi$
$500$		0			0
$501$			850.514i			1.69763i
$502$		0			0
$503$	−711.349			−1.41421			−0.707106	−	0.707107i	$-0.750000\pi$
$503$	−711.349			−1.41421			−0.707106	+	0.707107i	$0.750000\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−379.110	−	218.879i	−0.747751	−	0.431714i
$508$		0			0
$509$	717.714	+	414.372i	1.41005	+	0.814091i	0.995392	−	0.0958882i	$-0.0305691\pi$
$509$	717.714	+	414.372i	1.41005	+	0.814091i	0.414654	+	0.909979i	$0.363902\pi$
$510$		0			0
$511$	−353.776	−	612.758i	−0.692321	−	1.19914i
$512$		0			0
$513$			303.859i			0.592318i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	948.581	+	547.663i	1.83478	+	1.05931i
$518$		0			0
$519$	−350.710	−	202.482i	−0.675741	−	0.390139i
$520$		0			0
$521$			622.686i			1.19518i	0.801804	+	0.597588i	$0.203874\pi$
$521$			622.686i			1.19518i	−0.801804	+	0.597588i	$0.796126\pi$
$522$		0			0
$523$			89.4274i			0.170989i	0.996339	+	0.0854946i	$0.0272471\pi$
$523$			89.4274i			0.170989i	−0.996339	+	0.0854946i	$0.972753\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−425.837	+	737.571i	−0.808039	+	1.39956i
$528$		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
$533$	230.527	+	399.284i	0.432508	+	0.749126i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	257.168	+	445.427i	0.478897	+	0.829474i
$538$		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
$543$	−313.833	+	181.192i	−0.577961	+	0.333686i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	765.189	−	441.782i	1.39888	−	0.807646i	0.404608	−	0.914490i	$-0.367408\pi$
$547$	765.189	−	441.782i	1.39888	−	0.807646i	0.994276	+	0.106845i	$0.0340748\pi$
$548$		0			0
$549$	−11.1411			−0.0202934
$550$		0			0
$551$	−92.7096	+	53.5259i	−0.168257	+	0.0971432i
$552$		0			0
$553$	−1050.17	−	606.314i	−1.89904	−	1.09641i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	256.448			0.460410			0.230205	−	0.973142i	$-0.426060\pi$
$557$	256.448			0.460410			0.230205	+	0.973142i	$0.426060\pi$
$558$		0			0
$559$	−354.633			−0.634406
$560$		0			0
$561$	−344.214	+	596.196i	−0.613572	+	1.06274i
$562$		0			0
$563$	−103.937	+	180.024i	−0.184613	+	0.319759i	−0.943446	−	0.331526i	$-0.892436\pi$
$563$	−103.937	+	180.024i	−0.184613	+	0.319759i	0.758833	+	0.651285i	$0.225770\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	823.957	+	475.712i	1.45319	+	0.838998i
$568$		0			0
$569$	−430.923	+	248.794i	−0.757334	+	0.437247i	−0.828338	−	0.560229i	$-0.810713\pi$
$569$	−430.923	+	248.794i	−0.757334	+	0.437247i	0.0710034	+	0.997476i	$0.477380\pi$
$570$		0			0
$571$	−453.817	+	786.033i	−0.794775	+	1.37659i	0.128207	+	0.991747i	$0.459078\pi$
$571$	−453.817	+	786.033i	−0.794775	+	1.37659i	−0.922982	+	0.384843i	$0.874256\pi$
$572$		0			0
$573$	418.825	−	725.425i	0.730933	−	1.26601i
$574$		0			0
$575$		0			0
$576$		0			0
$577$			758.810i			1.31510i	0.753413	+	0.657548i	$0.228406\pi$
$577$			758.810i			1.31510i	−0.753413	+	0.657548i	$0.771594\pi$
$578$		0			0
$579$	315.859			0.545525
$580$		0			0
$581$	−916.185	−	528.960i	−1.57691	−	0.910430i
$582$		0			0
$583$	−494.127	+	285.284i	−0.847559	+	0.489338i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	378.809	+	656.117i	0.645331	+	1.11775i	0.984225	+	0.176921i	$0.0566139\pi$
$587$	378.809	+	656.117i	0.645331	+	1.11775i	−0.338894	+	0.940825i	$0.610053\pi$
$588$		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
$593$	258.648			0.436169			0.218084	−	0.975930i	$-0.430019\pi$
$593$	258.648			0.436169			0.218084	+	0.975930i	$0.430019\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−65.6538	+	37.9052i	−0.109973	+	0.0634929i
$598$		0			0
$599$	495.665	+	286.172i	0.827488	+	0.477750i	0.852992	−	0.521924i	$-0.174786\pi$
$599$	495.665	+	286.172i	0.827488	+	0.477750i	−0.0255038	+	0.999675i	$0.508119\pi$
$600$		0			0
$601$	−68.8186	−	119.197i	−0.114507	−	0.198332i	0.803076	−	0.595877i	$-0.203195\pi$
$601$	−68.8186	−	119.197i	−0.114507	−	0.198332i	−0.917582	+	0.397545i	$0.869862\pi$
$602$		0			0
$603$	−669.926	+	386.782i	−1.11099	+	0.641430i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−16.0005	−	9.23790i	−0.0263600	−	0.0152189i	0.486762	−	0.873535i	$-0.338178\pi$
$607$	−16.0005	−	9.23790i	−0.0263600	−	0.0152189i	−0.513122	+	0.858316i	$0.671511\pi$
$608$		0			0
$609$			335.194i			0.550400i
$610$		0			0
$611$		−	1283.14i		−	2.10007i
$612$		0			0
$613$		−	392.569i		−	0.640405i	−0.947349	−	0.320203i	$-0.896249\pi$
$613$		−	392.569i		−	0.640405i	0.947349	−	0.320203i	$-0.103751\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−132.994	+	230.353i	−0.215550	+	0.373343i	−0.953443	−	0.301575i	$-0.902488\pi$
$617$	−132.994	+	230.353i	−0.215550	+	0.373343i	0.737893	+	0.674918i	$0.235821\pi$
$618$		0			0
$619$	416.736	+	721.808i	0.673240	+	1.16609i	0.976980	+	0.213332i	$0.0684315\pi$
$619$	416.736	+	721.808i	0.673240	+	1.16609i	−0.303739	+	0.952755i	$0.598235\pi$
$620$		0			0
$621$	789.423	+	455.774i	1.27121	+	0.733935i
$622$		0			0
$623$	71.0420	+	123.048i	0.114032	+	0.197509i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−255.722	+	442.923i	−0.407850	+	0.706417i
$628$		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
$633$			312.097i			0.493044i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−1367.30	+	789.409i	−2.14646	+	1.23926i
$638$		0			0
$639$	172.288	+	99.4707i	0.269622	+	0.155666i
$640$		0			0
$641$	355.645	−	205.332i	0.554829	−	0.320331i	−0.196239	−	0.980556i	$-0.562873\pi$
$641$	355.645	−	205.332i	0.554829	−	0.320331i	0.751067	+	0.660226i	$0.229539\pi$
$642$		0			0
$643$	−191.552	−	110.593i	−0.297904	−	0.171995i	0.343597	−	0.939117i	$-0.388355\pi$
$643$	−191.552	−	110.593i	−0.297904	−	0.171995i	−0.641501	+	0.767122i	$0.721688\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1095.26			−1.69282			−0.846412	−	0.532529i	$-0.821242\pi$
$647$	−1095.26			−1.69282			−0.846412	+	0.532529i	$0.821242\pi$
$648$		0			0
$649$	964.137			1.48557
$650$		0			0
$651$	990.569	+	1715.71i	1.52161	+	2.63551i
$652$		0			0
$653$	516.179	−	894.048i	0.790473	−	1.36914i	−0.135201	−	0.990818i	$-0.543168\pi$
$653$	516.179	−	894.048i	0.790473	−	1.36914i	0.925674	−	0.378322i	$-0.123499\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	469.508	+	271.071i	0.714624	+	0.412588i
$658$		0			0
$659$	988.851	−	570.913i	1.50053	−	0.866333i	0.500532	−	0.865718i	$-0.333138\pi$
$659$	988.851	−	570.913i	1.50053	−	0.866333i	1.00000		0.000614829i	$-0.000195706\pi$
$660$		0			0
$661$	513.282	−	889.031i	0.776524	−	1.34498i	−0.157410	−	0.987533i	$-0.550315\pi$
$661$	513.282	−	889.031i	0.776524	−	1.34498i	0.933934	−	0.357445i	$-0.116352\pi$
$662$		0			0
$663$	806.472			1.21640
$664$		0			0
$665$		0			0
$666$		0			0
$667$			321.145i			0.481477i
$668$		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
$673$	242.403	−	139.952i	0.360183	−	0.207952i	−0.308978	−	0.951069i	$-0.599987\pi$
$673$	242.403	−	139.952i	0.360183	−	0.207952i	0.669161	+	0.743117i	$0.266654\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−144.060	−	249.520i	−0.212792	−	0.368567i	0.739795	−	0.672832i	$-0.234922\pi$
$677$	−144.060	−	249.520i	−0.212792	−	0.368567i	−0.952587	+	0.304265i	$0.901589\pi$
$678$		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
$683$	283.805			0.415527			0.207763	−	0.978179i	$-0.433382\pi$
$683$	283.805			0.415527			0.207763	+	0.978179i	$0.433382\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$			798.665i			1.16254i
$688$		0			0
$689$	578.855	+	334.202i	0.840138	+	0.485054i
$690$		0			0
$691$	−440.331	−	762.675i	−0.637237	−	1.10373i	−0.986037	−	0.166529i	$-0.946744\pi$
$691$	−440.331	−	762.675i	−0.637237	−	1.10373i	0.348800	−	0.937197i	$-0.386589\pi$
$692$		0			0
$693$	800.700	+	1386.85i	1.15541	+	2.00123i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−340.840	−	196.784i	−0.489011	−	0.282330i
$698$		0			0
$699$	−459.780	+	265.454i	−0.657768	+	0.379763i
$700$		0			0
$701$		−	680.500i		−	0.970757i	−0.874304	−	0.485378i	$-0.838682\pi$
$701$		−	680.500i		−	0.970757i	0.874304	−	0.485378i	$-0.161318\pi$
$702$		0			0
$703$			157.556i			0.224120i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	910.339	−	1576.75i	1.28761	−	2.23020i
$708$		0			0
$709$	−289.696	−	501.767i	−0.408597	−	0.707711i	0.586135	−	0.810213i	$-0.300649\pi$
$709$	−289.696	−	501.767i	−0.408597	−	0.707711i	−0.994733	+	0.102502i	$0.967315\pi$
$710$		0			0
$711$	929.141			1.30681
$712$		0			0
$713$	949.052	+	1643.81i	1.33107	+	2.30548i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	236.551			0.329917
$718$		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
$723$	−572.855	−	330.738i	−0.792330	−	0.457452i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−583.537	+	336.905i	−0.802664	+	0.463419i	−0.844402	−	0.535710i	$-0.820044\pi$
$727$	−583.537	+	336.905i	−0.802664	+	0.463419i	0.0417376	+	0.999129i	$0.486711\pi$
$728$		0			0
$729$	−729.000			−1.00000
$730$		0			0
$731$	262.167	−	151.362i	0.358642	−	0.207062i
$732$		0			0
$733$	−676.816	−	390.760i	−0.923351	−	0.533097i	−0.0386484	−	0.999253i	$-0.512305\pi$
$733$	−676.816	−	390.760i	−0.923351	−	0.533097i	−0.884703	+	0.466156i	$0.845639\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1302.03			−1.76667
$738$		0			0
$739$	−232.335			−0.314391			−0.157195	−	0.987568i	$-0.550245\pi$
$739$	−232.335			−0.314391			−0.157195	+	0.987568i	$0.550245\pi$
$740$		0			0
$741$	599.141			0.808557
$742$		0			0
$743$	251.036	−	434.806i	0.337868	−	0.585204i	−0.646164	−	0.763199i	$-0.723628\pi$
$743$	251.036	−	434.806i	0.337868	−	0.585204i	0.984031	+	0.177995i	$0.0569611\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	810.600			1.08514
$748$		0			0
$749$	−863.329	+	498.443i	−1.15264	+	0.665478i
$750$		0			0
$751$	−477.190	+	826.516i	−0.635405	+	1.10055i	0.351024	+	0.936367i	$0.385834\pi$
$751$	−477.190	+	826.516i	−0.635405	+	1.10055i	−0.986429	+	0.164188i	$0.947500\pi$
$752$		0			0
$753$	416.059	+	720.635i	0.552535	+	0.957019i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	266.379i		−	0.351888i	−0.984400	−	0.175944i	$-0.943702\pi$
$757$		−	266.379i		−	0.351888i	0.984400	−	0.175944i	$-0.0562977\pi$
$758$		0			0
$759$	767.141	+	1328.73i	1.01073	+	1.75063i
$760$		0			0
$761$	294.665	+	170.125i	0.387208	+	0.223555i	0.680950	−	0.732330i	$-0.261567\pi$
$761$	294.665	+	170.125i	0.387208	+	0.223555i	−0.293742	+	0.955885i	$0.594901\pi$
$762$		0			0
$763$	−386.876	+	223.363i	−0.507046	+	0.292743i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−564.729	−	978.139i	−0.736283	−	1.27528i
$768$		0			0
$769$	644.552	−	1116.40i	0.838170	−	1.45175i	−0.0532540	−	0.998581i	$-0.516959\pi$
$769$	644.552	−	1116.40i	0.838170	−	1.45175i	0.891423	−	0.453171i	$-0.149707\pi$
$770$		0			0
$771$			456.193i			0.591690i
$772$		0			0
$773$	−919.244			−1.18919			−0.594595	−	0.804025i	$-0.702688\pi$
$773$	−919.244			−1.18919			−0.594595	+	0.804025i	$0.702688\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	427.237	+	246.665i	0.549854	+	0.317459i
$778$		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
$783$	−128.416	−	222.423i	−0.164005	−	0.284066i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	1094.40	+	631.855i	1.39060	+	0.802865i	0.993382	−	0.114858i	$-0.0366413\pi$
$787$	1094.40	+	631.855i	1.39060	+	0.802865i	0.397221	+	0.917723i	$0.369975\pi$
$788$		0			0
$789$	−14.8609	−	8.57997i	−0.0188352	−	0.0108745i
$790$		0			0
$791$			81.3784i			0.102880i
$792$		0			0
$793$			21.9677i			0.0277021i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	306.461	−	530.806i	0.384518	−	0.666006i	−0.607184	−	0.794561i	$-0.707701\pi$
$797$	306.461	−	530.806i	0.384518	−	0.666006i	0.991702	+	0.128556i	$0.0410342\pi$
$798$		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
$803$	456.256	+	790.258i	0.568189	+	0.984132i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−542.296	−	939.284i	−0.671990	−	1.16392i
$808$		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
$813$	−1318.34	+	761.141i	−1.62157	+	0.936213i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	194.768	−	112.450i	0.238395	−	0.137637i
$818$		0			0
$819$	937.996	−	1624.66i	1.14529	−	1.98371i
$820$		0			0
$821$	221.813	−	128.064i	0.270174	−	0.155985i	−0.358793	−	0.933417i	$-0.616812\pi$
$821$	221.813	−	128.064i	0.270174	−	0.155985i	0.628967	+	0.777432i	$0.283478\pi$
$822$		0			0
$823$	1065.59	+	615.218i	1.29476	+	0.747531i	0.979494	−	0.201473i	$-0.0645727\pi$
$823$	1065.59	+	615.218i	1.29476	+	0.747531i	0.315267	+	0.949003i	$0.397906\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	726.246			0.878169			0.439085	−	0.898446i	$-0.355303\pi$
$827$	726.246			0.878169			0.439085	+	0.898446i	$0.355303\pi$
$828$		0			0
$829$	−1439.23			−1.73610			−0.868052	−	0.496474i	$-0.834628\pi$
$829$	−1439.23			−1.73610			−0.868052	+	0.496474i	$0.834628\pi$
$830$		0			0
$831$	−335.335	+	580.817i	−0.403532	+	0.698937i
$832$		0			0
$833$	673.862	−	1167.16i	0.808958	−	1.40116i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−1314.62	−	758.994i	−1.57063	−	0.906803i
$838$		0			0
$839$	−968.135	+	558.953i	−1.15392	+	0.666213i	−0.949838	−	0.312742i	$-0.898753\pi$
$839$	−968.135	+	558.953i	−1.15392	+	0.666213i	−0.204077	+	0.978955i	$0.565419\pi$
$840$		0			0
$841$	−375.258	+	649.966i	−0.446205	+	0.772849i
$842$		0			0
$843$	68.9538	−	119.431i	0.0817957	−	0.141674i
$844$		0			0
$845$		0			0
$846$		0			0
$847$			1274.15i			1.50431i
$848$		0			0
$849$	−432.097			−0.508948
$850$		0			0
$851$	409.331	+	236.327i	0.481000	+	0.277705i
$852$		0			0
$853$	602.834	−	348.046i	0.706722	−	0.408026i	−0.103124	−	0.994669i	$-0.532884\pi$
$853$	602.834	−	348.046i	0.706722	−	0.408026i	0.809846	+	0.586642i	$0.199551\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	430.149	+	745.040i	0.501924	+	0.869358i	0.999998	+	0.00222347i	$0.000707752\pi$
$857$	430.149	+	745.040i	0.501924	+	0.869358i	−0.498073	+	0.867135i	$0.665959\pi$
$858$		0			0
$859$	−321.216	+	556.362i	−0.373942	+	0.647686i	−0.990168	−	0.139883i	$-0.955327\pi$
$859$	−321.216	+	556.362i	−0.373942	+	0.647686i	0.616226	+	0.787569i	$0.288661\pi$
$860$		0			0
$861$	−792.853	+	457.754i	−0.920851	+	0.531654i
$862$		0			0
$863$	−1466.58			−1.69940			−0.849698	−	0.527269i	$-0.823216\pi$
$863$	−1466.58			−1.69940			−0.849698	+	0.527269i	$0.823216\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	154.648	−	89.2863i	0.178372	−	0.102983i
$868$		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
$873$		−	897.278i		−	1.02781i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	167.461	+	96.6835i	0.190947	+	0.110243i	0.592426	−	0.805625i	$-0.298170\pi$
$877$	167.461	+	96.6835i	0.190947	+	0.110243i	−0.401479	+	0.915868i	$0.631504\pi$
$878$		0			0
$879$			1252.19i			1.42456i
$880$		0			0
$881$		−	554.368i		−	0.629249i	−0.949216	−	0.314624i	$-0.898121\pi$
$881$		−	554.368i		−	0.629249i	0.949216	−	0.314624i	$-0.101879\pi$
$882$		0			0
$883$		−	352.460i		−	0.399162i	−0.979881	−	0.199581i	$-0.936042\pi$
$883$		−	352.460i		−	0.399162i	0.979881	−	0.199581i	$-0.0639580\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−538.140	+	932.087i	−0.606697	+	1.05083i	0.385084	+	0.922882i	$0.374173\pi$
$887$	−538.140	+	932.087i	−0.606697	+	1.05083i	−0.991781	+	0.127949i	$0.959161\pi$
$888$		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
$893$	406.868	+	704.716i	0.455619	+	0.789155i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	898.683	−	1556.56i	1.00188	−	1.73530i
$898$		0			0
$899$		−	534.799i		−	0.594882i
$900$		0			0
$901$	−570.569			−0.633261
$902$		0			0
$903$		−	704.190i		−	0.779833i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−191.385	+	110.496i	−0.211008	+	0.121826i	−0.601780	−	0.798662i	$-0.705542\pi$
$907$	−191.385	+	110.496i	−0.211008	+	0.121826i	0.390772	+	0.920488i	$0.372208\pi$
$908$		0			0
$909$			1395.04i			1.53470i
$910$		0			0
$911$	1535.28	−	886.394i	1.68527	−	0.972991i	0.727212	−	0.686413i	$-0.240816\pi$
$911$	1535.28	−	886.394i	1.68527	−	0.972991i	0.958057	−	0.286578i	$-0.0925177\pi$
$912$		0			0
$913$	1181.58	+	682.185i	1.29417	+	0.747191i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−782.775			−0.853626
$918$		0			0
$919$	−1006.85			−1.09560			−0.547799	−	0.836610i	$-0.684534\pi$
$919$	−1006.85			−1.09560			−0.547799	+	0.836610i	$0.684534\pi$
$920$		0			0
$921$	465.073	+	805.529i	0.504965	+	0.874625i
$922$		0			0
$923$	196.134	−	339.714i	0.212496	−	0.368054i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	1213.67	−	700.712i	1.30924	−	0.755892i
$928$		0			0
$929$	974.758	−	562.777i	1.04926	−	0.605788i	0.126814	−	0.991926i	$-0.459525\pi$
$929$	974.758	−	562.777i	1.04926	−	0.605788i	0.922441	+	0.386139i	$0.126191\pi$
$930$		0			0
$931$	500.623	−	867.104i	0.537726	−	0.931369i
$932$		0			0
$933$	839.137			0.899396
$934$		0			0
$935$		0			0
$936$		0			0
$937$			1343.20i			1.43351i	0.697324	+	0.716756i	$0.254374\pi$
$937$			1343.20i			1.43351i	−0.697324	+	0.716756i	$0.745626\pi$
$938$		0			0
$939$	−43.7359	+	75.7527i	−0.0465771	+	0.0806738i
$940$		0			0
$941$	618.375	+	357.019i	0.657147	+	0.379404i	0.791189	−	0.611572i	$-0.209462\pi$
$941$	618.375	+	357.019i	0.657147	+	0.379404i	−0.134042	+	0.990976i	$0.542796\pi$
$942$		0			0
$943$	−759.623	+	438.569i	−0.805539	+	0.465078i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−358.220	−	620.456i	−0.378268	−	0.655180i	0.612542	−	0.790438i	$-0.290147\pi$
$947$	−358.220	−	620.456i	−0.378268	−	0.655180i	−0.990810	+	0.135258i	$0.956814\pi$
$948$		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
$953$	−793.300			−0.832424			−0.416212	−	0.909268i	$-0.636643\pi$
$953$	−793.300			−0.832424			−0.416212	+	0.909268i	$0.636643\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		−	432.290i		−	0.451714i
$958$		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
$963$	381.917	−	661.500i	0.396591	−	0.686916i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−1583.67	−	914.331i	−1.63771	−	0.945533i	−0.981619	−	0.190853i	$-0.938875\pi$
$967$	−1583.67	−	914.331i	−1.63771	−	0.945533i	−0.656093	−	0.754680i	$-0.727792\pi$
$968$		0			0
$969$	−442.923	+	255.722i	−0.457093	+	0.263903i
$970$		0			0
$971$			1843.33i			1.89839i	0.314691	+	0.949194i	$0.398099\pi$
$971$			1843.33i			1.89839i	−0.314691	+	0.949194i	$0.601901\pi$
$972$		0			0
$973$		−	1253.46i		−	1.28824i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−167.195	+	289.591i	−0.171131	+	0.296408i	−0.938816	−	0.344420i	$-0.888076\pi$
$977$	−167.195	+	289.591i	−0.171131	+	0.296408i	0.767684	+	0.640828i	$0.221409\pi$
$978$		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
$983$	−926.480	−	1604.71i	−0.942502	−	1.63246i	−0.760677	−	0.649131i	$-0.775133\pi$
$983$	−926.480	−	1604.71i	−0.942502	−	1.63246i	−0.181825	−	0.983331i	$-0.558200\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	2547.92			2.58148
$988$		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
$993$	−1210.20	−	698.710i	−1.21873	−	0.703635i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	1033.70	−	596.808i	1.03681	−	0.598604i	0.117884	−	0.993027i	$-0.462389\pi$
$997$	1033.70	−	596.808i	1.03681	−	0.598604i	0.918929	+	0.394423i	$0.129056\pi$
$998$		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.u.b.149.1		8
3.2	odd	2		2700.3.u.a.449.1		8
5.2	odd	4		900.3.p.b.401.1		4
5.3	odd	4		180.3.o.a.41.2	✓	4
5.4	even	2	inner	900.3.u.b.149.4		8
9.2	odd	6	inner	900.3.u.b.749.4		8
9.7	even	3		2700.3.u.a.2249.4		8
15.2	even	4		2700.3.p.a.2501.1		4
15.8	even	4		540.3.o.a.341.1		4
15.14	odd	2		2700.3.u.a.449.4		8
20.3	even	4		720.3.bs.a.401.2		4
45.2	even	12		900.3.p.b.101.1		4
45.7	odd	12		2700.3.p.a.1601.1		4
45.13	odd	12		1620.3.g.a.161.1		4
45.23	even	12		1620.3.g.a.161.3		4
45.29	odd	6	inner	900.3.u.b.749.1		8
45.34	even	6		2700.3.u.a.2249.1		8
45.38	even	12		180.3.o.a.101.2	yes	4
45.43	odd	12		540.3.o.a.521.1		4
60.23	odd	4		2160.3.bs.a.881.1		4
180.43	even	12		2160.3.bs.a.1601.1		4
180.83	odd	12		720.3.bs.a.641.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.3.o.a.41.2	✓	4	5.3	odd	4
180.3.o.a.101.2	yes	4	45.38	even	12
540.3.o.a.341.1		4	15.8	even	4
540.3.o.a.521.1		4	45.43	odd	12
720.3.bs.a.401.2		4	20.3	even	4
720.3.bs.a.641.2		4	180.83	odd	12
900.3.p.b.101.1		4	45.2	even	12
900.3.p.b.401.1		4	5.2	odd	4
900.3.u.b.149.1		8	1.1	even	1	trivial
900.3.u.b.149.4		8	5.4	even	2	inner
900.3.u.b.749.1		8	45.29	odd	6	inner
900.3.u.b.749.4		8	9.2	odd	6	inner
1620.3.g.a.161.1		4	45.13	odd	12
1620.3.g.a.161.3		4	45.23	even	12
2160.3.bs.a.881.1		4	60.23	odd	4
2160.3.bs.a.1601.1		4	180.43	even	12
2700.3.p.a.1601.1		4	45.7	odd	12
2700.3.p.a.2501.1		4	15.2	even	4
2700.3.u.a.449.1		8	3.2	odd	2
2700.3.u.a.449.4		8	15.14	odd	2
2700.3.u.a.2249.1		8	45.34	even	6
2700.3.u.a.2249.4		8	9.7	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.59808 + 1.50000i) q^{3} +(-10.1723 + 5.87298i) q^{7} +(4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(q+(-2.59808 + 1.50000i) q^{3} +(-10.1723 + 5.87298i) q^{7} +(4.50000 - 7.79423i) q^{9} +(13.1190 - 7.57423i) q^{11} +(-15.3685 - 8.87298i) q^{13} +15.1485 q^{17} +11.2540 q^{19} +(17.6190 - 30.5169i) q^{21} +(16.8805 - 29.2379i) q^{23} +27.0000i q^{27} +(-8.23790 + 4.75615i) q^{29} +(-28.1109 + 48.6895i) q^{31} +(-22.7227 + 39.3569i) q^{33} +14.0000i q^{37} +53.2379 q^{39} +(-22.5000 - 12.9904i) q^{41} +(17.3065 - 9.99193i) q^{43} +(36.1531 + 62.6190i) q^{47} +(44.4839 - 77.0483i) q^{49} +(-39.3569 + 22.7227i) q^{51} -37.6651 q^{53} +(-29.2388 + 16.8810i) q^{57} +(55.1190 + 31.8229i) q^{59} +(-0.618950 - 1.07205i) q^{61} +105.714i q^{63} +(-74.4363 - 42.9758i) q^{67} +101.283i q^{69} +22.1046i q^{71} +60.2379i q^{73} +(-88.9666 + 154.095i) q^{77} +(51.6190 + 89.4066i) q^{79} +(-40.5000 - 70.1481i) q^{81} +(45.0333 + 78.0000i) q^{83} +(14.2685 - 24.7137i) q^{87} -12.0964i q^{89} +208.444 q^{91} -168.665i q^{93} +(86.3406 - 49.8488i) q^{97} -136.336i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 36 q^{9}+O(q^{10}) \) 8 * q + 36 * q^9	\( 8 q + 36 q^{9} + 12 q^{11} + 152 q^{19} + 48 q^{21} + 120 q^{29} - 8 q^{31} + 240 q^{39} - 180 q^{41} + 108 q^{49} - 36 q^{51} + 348 q^{59} + 88 q^{61} + 320 q^{79} - 324 q^{81} + 800 q^{91}+O(q^{100}) \) 8 * q + 36 * q^9 + 12 * q^11 + 152 * q^19 + 48 * q^21 + 120 * q^29 - 8 * q^31 + 240 * q^39 - 180 * q^41 + 108 * q^49 - 36 * q^51 + 348 * q^59 + 88 * q^61 + 320 * q^79 - 324 * q^81 + 800 * q^91

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