LMFDB - Embedded newform 900.3.u.b.749.4

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			749.4
Root			$-1.40126 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	900.749
Dual form			900.3.u.b.149.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

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
$3$	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	$-0.0164754\pi$
$7$	10.1723	+	5.87298i	1.45319	+	0.838998i	0.454526	+	0.890734i	$0.349809\pi$
$8$		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
$13$	15.3685	−	8.87298i	1.18219	−	0.682537i	0.225669	−	0.974204i	$-0.427543\pi$
$13$	15.3685	−	8.87298i	1.18219	−	0.682537i	0.956520	+	0.291667i	$0.0942099\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−15.1485			−0.891086			−0.445543	−	0.895261i	$-0.646989\pi$
$17$	−15.1485			−0.891086			−0.445543	+	0.895261i	$0.646989\pi$
$18$		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	−0.955189	−	0.295997i	$-0.904348\pi$
$23$	−16.8805	−	29.2379i	−0.733935	−	1.27121i	0.221254	−	0.975216i	$-0.428985\pi$
$24$		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	0.351197	−	0.936302i	$-0.385775\pi$
$29$	−8.23790	−	4.75615i	−0.284066	−	0.164005i	−0.635262	+	0.772296i	$0.719108\pi$
$30$		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
$33$	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	−0.748630	−	0.662988i	$-0.769288\pi$
$41$	−22.5000	+	12.9904i	−0.548780	+	0.316839i	0.199849	+	0.979827i	$0.435955\pi$
$42$		0			0
$43$	−17.3065	−	9.99193i	−0.402478	−	0.232371i	0.285075	−	0.958505i	$-0.407982\pi$
$43$	−17.3065	−	9.99193i	−0.402478	−	0.232371i	−0.687552	+	0.726135i	$0.741315\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−36.1531	+	62.6190i	−0.769214	+	1.33232i	0.168775	+	0.985655i	$0.446019\pi$
$47$	−36.1531	+	62.6190i	−0.769214	+	1.33232i	−0.937990	+	0.346664i	$0.887315\pi$
$48$		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	$-0.384368\pi$
$53$	37.6651			0.710663			0.355331	+	0.934740i	$0.384368\pi$
$54$		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	0.0460759	−	0.998938i	$-0.485328\pi$
$59$	55.1190	−	31.8229i	0.934219	−	0.539372i	0.888144	+	0.459566i	$0.151995\pi$
$60$		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
$63$			105.714i			1.67800i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	74.4363	−	42.9758i	1.11099	−	0.641430i	0.171904	−	0.985114i	$-0.445008\pi$
$67$	74.4363	−	42.9758i	1.11099	−	0.641430i	0.939085	+	0.343684i	$0.111675\pi$
$68$		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
$73$			60.2379i			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	−0.328887	−	0.944369i	$-0.606673\pi$
$79$	51.6190	−	89.4066i	0.653404	−	1.13173i	0.982291	−	0.187360i	$-0.0599932\pi$
$80$		0			0
$81$	−40.5000	+	70.1481i	−0.500000	+	0.866025i
$82$		0			0
$83$	−45.0333	+	78.0000i	−0.542570	+	0.939759i	0.456185	+	0.889885i	$0.349215\pi$
$83$	−45.0333	+	78.0000i	−0.542570	+	0.939759i	−0.998756	+	0.0498743i	$0.984118\pi$
$84$		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	$0.0216482\pi$
$89$			12.0964i			0.135915i	−0.997688	+	0.0679574i	$0.978352\pi$
$90$		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	$-0.505135\pi$
$97$	−86.3406	−	49.8488i	−0.890110	−	0.513905i	−0.873978	+	0.485965i	$0.838468\pi$
$98$		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
$103$	−134.852	+	77.8569i	−1.30924	+	0.755892i	−0.981970	−	0.189038i	$-0.939463\pi$
$103$	−134.852	+	77.8569i	−1.30924	+	0.755892i	−0.327273	+	0.944930i	$0.606130\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−84.8705			−0.793182			−0.396591	−	0.917995i	$-0.629807\pi$
$107$	−84.8705			−0.793182			−0.396591	+	0.917995i	$0.629807\pi$
$108$		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	$-0.176426\pi$
$113$	−3.46410	−	6.00000i	−0.0306558	−	0.0530973i	−0.880946	+	0.473216i	$0.843093\pi$
$114$		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	−0.263274	−	0.964721i	$-0.584802\pi$
$131$	57.7137	−	33.3210i	0.440563	−	0.254359i	0.703836	+	0.710362i	$0.251469\pi$
$132$		0			0
$133$	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	$-0.919433\pi$
$137$	−36.6070	+	63.4052i	−0.267205	+	0.462812i	0.700934	+	0.713226i	$0.252767\pi$
$138$		0			0
$139$	−53.3569	−	92.4168i	−0.383862	−	0.664869i	0.607748	−	0.794130i	$-0.292073\pi$
$139$	−53.3569	−	92.4168i	−0.383862	−	0.664869i	−0.991611	+	0.129261i	$0.958740\pi$
$140$		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	0.0698433	−	0.997558i	$-0.477750\pi$
$149$	144.333	−	83.3305i	0.968676	−	0.559265i	0.898832	+	0.438293i	$0.144417\pi$
$150$		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
$153$	−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	$-0.736084\pi$
$157$	−58.8338	+	33.9677i	−0.374738	+	0.216355i	0.300788	+	0.953691i	$0.402750\pi$
$158$		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	−0.882266	−	0.470752i	$-0.843983\pi$
$167$	−141.752	−	245.522i	−0.848816	−	1.47019i	0.0334495	−	0.999440i	$-0.489351\pi$
$168$		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	$-0.960906\pi$
$173$	−67.4941	+	116.903i	−0.390139	+	0.675741i	0.602328	+	0.798248i	$0.294240\pi$
$174$		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	$0.158963\pi$
$179$			171.445i			0.957794i	−0.877871	+	0.478897i	$0.841037\pi$
$180$		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	−0.291782	−	0.956485i	$-0.594248\pi$
$191$	−241.808	−	139.608i	−1.26601	−	0.730933i	−0.974231	+	0.225552i	$0.927581\pi$
$192$		0			0
$193$	91.1806	−	52.6431i	0.472438	−	0.272762i	−0.244822	−	0.969568i	$-0.578729\pi$
$193$	91.1806	−	52.6431i	0.472438	−	0.272762i	0.717260	+	0.696806i	$0.245396\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	57.9538			0.294182			0.147091	−	0.989123i	$-0.453009\pi$
$197$	57.9538			0.294182			0.147091	+	0.989123i	$0.453009\pi$
$198$		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	0.962558	−	0.271074i	$-0.0873789\pi$
$211$	52.0161	+	90.0946i	0.246522	+	0.426989i	−0.716036	+	0.698063i	$0.754046\pi$
$212$		0			0
$213$	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	$-0.146195\pi$
$223$	214.223	+	123.681i	0.960639	+	0.554625i	0.0642694	+	0.997933i	$0.479528\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−151.114	+	261.738i	−0.665702	+	1.15303i	0.313392	+	0.949624i	$0.398535\pi$
$227$	−151.114	+	261.738i	−0.665702	+	1.15303i	−0.979094	+	0.203407i	$0.934799\pi$
$228$		0			0
$229$	133.111	+	230.555i	0.581270	+	1.00679i	0.995329	+	0.0965395i	$0.0307774\pi$
$229$	133.111	+	230.555i	0.581270	+	1.00679i	−0.414059	+	0.910250i	$0.635889\pi$
$230$		0			0
$231$			533.800i			2.31082i
$232$		0			0
$233$	−176.969			−0.759526			−0.379763	−	0.925084i	$-0.623994\pi$
$233$	−176.969			−0.759526			−0.379763	+	0.925084i	$0.623994\pi$
$234$		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	−0.636009	−	0.771682i	$-0.719416\pi$
$239$	−68.2863	+	39.4251i	−0.285717	+	0.164959i	0.350292	+	0.936641i	$0.386082\pi$
$240$		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
$243$	−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	$0.186339\pi$
$251$			277.373i			1.10507i	−0.833490	+	0.552535i	$0.813661\pi$
$252$		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	$-0.262268\pi$
$257$	−76.0322	−	131.692i	−0.295845	−	0.512418i	−0.975181	+	0.221409i	$0.928935\pi$
$258$		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	$-0.836795\pi$
$263$	−2.85999	+	4.95365i	−0.0108745	+	0.0188352i	0.860537	+	0.509388i	$0.170128\pi$
$264$		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	$-0.765440\pi$
$269$		−	361.531i		−	1.34398i	0.740560	−	0.671990i	$-0.234560\pi$
$270$		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	$-0.465551\pi$
$277$	−193.606	−	111.778i	−0.698937	−	0.403532i	−0.806951	+	0.590618i	$0.798884\pi$
$278$		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
$283$	−124.736	+	72.0161i	−0.440762	+	0.254474i	−0.703921	−	0.710279i	$-0.748569\pi$
$283$	−124.736	+	72.0161i	−0.440762	+	0.254474i	0.263159	+	0.964753i	$0.415236\pi$
$284$		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	−0.963999	−	0.265905i	$-0.914329\pi$
$293$	−208.698	−	361.476i	−0.712280	−	1.23371i	0.251719	−	0.967800i	$-0.419004\pi$
$294$		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	−0.836040	−	0.548668i	$-0.815135\pi$
$311$	−242.238	+	139.856i	−0.778900	+	0.449698i	0.0571403	+	0.998366i	$0.481802\pi$
$312$		0			0
$313$	−25.2509	−	14.5786i	−0.0806738	−	0.0465771i	0.459120	−	0.888374i	$-0.348165\pi$
$313$	−25.2509	−	14.5786i	−0.0806738	−	0.0465771i	−0.539794	+	0.841797i	$0.681498\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−62.9859	+	109.095i	−0.198694	+	0.344147i	−0.948105	−	0.317957i	$-0.897003\pi$
$317$	−62.9859	+	109.095i	−0.198694	+	0.344147i	0.749411	+	0.662105i	$0.230337\pi$
$318$		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	−0.263547	−	0.964647i	$-0.584892\pi$
$331$	232.903	−	403.400i	0.703635	−	1.21873i	0.967182	−	0.254085i	$-0.0817743\pi$
$332$		0			0
$333$	−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	$-0.492768\pi$
$337$	303.259	−	175.087i	0.899878	−	0.519545i	0.877161	+	0.480197i	$0.159435\pi$
$338$		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	$-0.128914\pi$
$347$	41.0594	+	71.1169i	0.118327	+	0.204948i	−0.800778	+	0.598961i	$0.795580\pi$
$348$		0			0
$349$	22.7621	−	39.4251i	0.0652209	−	0.112966i	−0.831571	−	0.555418i	$-0.812558\pi$
$349$	22.7621	−	39.4251i	0.0652209	−	0.112966i	0.896792	+	0.442452i	$0.145891\pi$
$350$		0			0
$351$	239.571	+	414.948i	0.682537	+	1.18219i
$352$		0			0
$353$	262.046	−	453.877i	0.742340	−	1.28577i	−0.209087	−	0.977897i	$-0.567049\pi$
$353$	262.046	−	453.877i	0.742340	−	1.28577i	0.951427	−	0.307873i	$-0.0996173\pi$
$354$		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	$-0.864935\pi$
$359$		−	295.601i		−	0.823401i	0.911319	−	0.411701i	$-0.135065\pi$
$360$		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	$-0.319245\pi$
$367$	28.1249	+	16.2379i	0.0766345	+	0.0442450i	−0.461193	+	0.887300i	$0.652578\pi$
$368$		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	$-0.559025\pi$
$373$	214.334	−	123.746i	0.574623	−	0.331759i	0.758994	+	0.651098i	$0.225691\pi$
$374$		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	$-0.0773713\pi$
$383$	106.039	+	183.665i	0.276865	+	0.479544i	−0.693739	+	0.720226i	$0.744038\pi$
$384$		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	0.724734	−	0.689028i	$-0.241962\pi$
$389$	190.760	+	110.135i	0.490386	+	0.283124i	−0.234349	+	0.972153i	$0.575296\pi$
$390$		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	−0.581015	−	0.813893i	$-0.697344\pi$
$401$	−66.8347	+	38.5870i	−0.166670	+	0.0962270i	0.414345	+	0.910120i	$0.364011\pi$
$402$		0			0
$403$	−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	0.721978	−	0.691917i	$-0.243233\pi$
$409$	−97.4355	−	168.763i	−0.238229	−	0.412624i	−0.960206	+	0.279293i	$0.909900\pi$
$410$		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	−0.715786	−	0.698320i	$-0.753931\pi$
$419$	−196.476	+	113.435i	−0.468916	+	0.270729i	0.246870	+	0.969049i	$0.420598\pi$
$420$		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
$423$	−650.755			−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	$-0.693443\pi$
$431$		−	707.661i		−	1.64191i	0.570996	−	0.820953i	$-0.306557\pi$
$432$		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	−0.906377	−	0.422471i	$-0.861163\pi$
$439$	−38.3327	+	66.3941i	−0.0873181	+	0.151239i	0.819059	+	0.573710i	$0.194496\pi$
$440$		0			0
$441$	−400.355	+	693.435i	−0.907834	+	1.57241i
$442$		0			0
$443$	−340.704	+	590.117i	−0.769084	+	1.33209i	0.168976	+	0.985620i	$0.445954\pi$
$443$	−340.704	+	590.117i	−0.769084	+	1.33209i	−0.938060	+	0.346472i	$0.887379\pi$
$444$		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	$-0.752325\pi$
$449$		−	630.327i		−	1.40385i	0.712253	−	0.701923i	$-0.247675\pi$
$450$		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	$-0.117653\pi$
$457$	496.229	+	286.498i	1.08584	+	0.626910i	0.153374	+	0.988168i	$0.450986\pi$
$458$		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
$463$	−556.317	+	321.190i	−1.20155	+	0.693714i	−0.960899	−	0.276899i	$-0.910693\pi$
$463$	−556.317	+	321.190i	−1.20155	+	0.693714i	−0.240648	+	0.970612i	$0.577360\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	506.331			1.08422			0.542111	−	0.840307i	$-0.317625\pi$
$467$	506.331			1.08422			0.542111	+	0.840307i	$0.317625\pi$
$468$		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	0.987473	−	0.157789i	$-0.0504365\pi$
$479$	644.044	+	371.839i	1.34456	+	0.776282i	0.357087	+	0.934071i	$0.383770\pi$
$480$		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	−0.640490	−	0.767967i	$-0.721269\pi$
$491$	−145.167	+	83.8124i	−0.295657	+	0.170697i	0.344833	+	0.938664i	$0.387935\pi$
$492$		0			0
$493$	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	0.999987	−	0.00506391i	$-0.00161190\pi$
$499$	247.308	+	428.351i	0.495608	+	0.858418i	−0.504379	+	0.863482i	$0.668279\pi$
$500$		0			0
$501$		−	850.514i		−	1.69763i
$502$		0			0
$503$	711.349			1.41421			0.707106	−	0.707107i	$-0.250000\pi$
$503$	711.349			1.41421			0.707106	+	0.707107i	$0.250000\pi$
$504$		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	0.414654	−	0.909979i	$-0.363902\pi$
$509$	717.714	−	414.372i	1.41005	−	0.814091i	0.995392	+	0.0958882i	$0.0305691\pi$
$510$		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	$-0.796126\pi$
$521$		−	622.686i		−	1.19518i	0.801804	−	0.597588i	$-0.203874\pi$
$522$		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	$-0.632592\pi$
$547$	−765.189	−	441.782i	−1.39888	−	0.807646i	−0.994276	+	0.106845i	$0.965925\pi$
$548$		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	$-0.573940\pi$
$557$	−256.448			−0.460410			−0.230205	+	0.973142i	$0.573940\pi$
$558$		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	$-0.107564\pi$
$563$	103.937	+	180.024i	0.184613	+	0.319759i	−0.758833	+	0.651285i	$0.774230\pi$
$564$		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	0.0710034	−	0.997476i	$-0.477380\pi$
$569$	−430.923	−	248.794i	−0.757334	−	0.437247i	−0.828338	+	0.560229i	$0.810713\pi$
$570$		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
$573$	−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	0.338894	+	0.940825i	$0.389947\pi$
$587$	−378.809	+	656.117i	−0.645331	+	1.11775i	−0.984225	+	0.176921i	$0.943386\pi$
$588$		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	$-0.569981\pi$
$593$	−258.648			−0.436169			−0.218084	+	0.975930i	$0.569981\pi$
$594$		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	−0.0255038	−	0.999675i	$-0.508119\pi$
$599$	495.665	−	286.172i	0.827488	−	0.477750i	0.852992	+	0.521924i	$0.174786\pi$
$600$		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
$603$	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	$-0.661822\pi$
$607$	16.0005	−	9.23790i	0.0263600	−	0.0152189i	0.513122	+	0.858316i	$0.328489\pi$
$608$		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	$-0.0975123\pi$
$617$	132.994	+	230.353i	0.215550	+	0.373343i	−0.737893	+	0.674918i	$0.764179\pi$
$618$		0			0
$619$	416.736	−	721.808i	0.673240	−	1.16609i	−0.303739	−	0.952755i	$-0.598235\pi$
$619$	416.736	−	721.808i	0.673240	−	1.16609i	0.976980	−	0.213332i	$-0.0684315\pi$
$620$		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	0.751067	−	0.660226i	$-0.229539\pi$
$641$	355.645	+	205.332i	0.554829	+	0.320331i	−0.196239	+	0.980556i	$0.562873\pi$
$642$		0			0
$643$	191.552	−	110.593i	0.297904	−	0.171995i	−0.343597	−	0.939117i	$-0.611645\pi$
$643$	191.552	−	110.593i	0.297904	−	0.171995i	0.641501	+	0.767122i	$0.278312\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1095.26			1.69282			0.846412	−	0.532529i	$-0.178758\pi$
$647$	1095.26			1.69282			0.846412	+	0.532529i	$0.178758\pi$
$648$		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	−0.925674	−	0.378322i	$-0.876501\pi$
$653$	−516.179	−	894.048i	−0.790473	−	1.36914i	0.135201	−	0.990818i	$-0.456832\pi$
$654$		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	1.00000		0.000614829i	$0.000195706\pi$
$659$	988.851	+	570.913i	1.50053	+	0.866333i	0.500532	+	0.865718i	$0.333138\pi$
$660$		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
$663$	−806.472			−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	$-0.400013\pi$
$673$	−242.403	−	139.952i	−0.360183	−	0.207952i	−0.669161	+	0.743117i	$0.733346\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	144.060	−	249.520i	0.212792	−	0.368567i	−0.739795	−	0.672832i	$-0.765078\pi$
$677$	144.060	−	249.520i	0.212792	−	0.368567i	0.952587	+	0.304265i	$0.0984108\pi$
$678$		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	$-0.566618\pi$
$683$	−283.805			−0.415527			−0.207763	+	0.978179i	$0.566618\pi$
$684$		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	0.348800	+	0.937197i	$0.386589\pi$
$691$	−440.331	+	762.675i	−0.637237	+	1.10373i	−0.986037	+	0.166529i	$0.946744\pi$
$692$		0			0
$693$	−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	$0.161318\pi$
$701$			680.500i			0.970757i	−0.874304	+	0.485378i	$0.838682\pi$
$702$		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	−0.994733	−	0.102502i	$-0.967315\pi$
$709$	−289.696	+	501.767i	−0.408597	+	0.707711i	0.586135	+	0.810213i	$0.300649\pi$
$710$		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	$0.136349\pi$
$719$			597.306i			0.830746i	−0.909651	+	0.415373i	$0.863651\pi$
$720$		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	$-0.179956\pi$
$727$	583.537	+	336.905i	0.802664	+	0.463419i	−0.0417376	+	0.999129i	$0.513289\pi$
$728$		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	$-0.487695\pi$
$733$	676.816	−	390.760i	0.923351	−	0.533097i	0.884703	+	0.466156i	$0.154361\pi$
$734$		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	$-0.276372\pi$
$743$	−251.036	−	434.806i	−0.337868	−	0.585204i	−0.984031	+	0.177995i	$0.943039\pi$
$744$		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	−0.986429	−	0.164188i	$-0.947500\pi$
$751$	−477.190	−	826.516i	−0.635405	−	1.10055i	0.351024	−	0.936367i	$-0.385834\pi$
$752$		0			0
$753$	−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	−0.293742	−	0.955885i	$-0.594901\pi$
$761$	294.665	−	170.125i	0.387208	−	0.223555i	0.680950	+	0.732330i	$0.261567\pi$
$762$		0			0
$763$	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	0.891423	+	0.453171i	$0.149707\pi$
$769$	644.552	+	1116.40i	0.838170	+	1.45175i	−0.0532540	+	0.998581i	$0.516959\pi$
$770$		0			0
$771$		−	456.193i		−	0.591690i
$772$		0			0
$773$	919.244			1.18919			0.594595	−	0.804025i	$-0.297312\pi$
$773$	919.244			1.18919			0.594595	+	0.804025i	$0.297312\pi$
$774$		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	$-0.963359\pi$
$787$	−1094.40	+	631.855i	−1.39060	+	0.802865i	−0.397221	+	0.917723i	$0.630025\pi$
$788$		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	$-0.292299\pi$
$797$	−306.461	−	530.806i	−0.384518	−	0.666006i	−0.991702	+	0.128556i	$0.958966\pi$
$798$		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	$0.0540033\pi$
$809$			273.189i			0.337687i	−0.985643	+	0.168844i	$0.945997\pi$
$810$		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	0.628967	−	0.777432i	$-0.283478\pi$
$821$	221.813	+	128.064i	0.270174	+	0.155985i	−0.358793	+	0.933417i	$0.616812\pi$
$822$		0			0
$823$	−1065.59	+	615.218i	−1.29476	+	0.747531i	−0.979494	−	0.201473i	$-0.935427\pi$
$823$	−1065.59	+	615.218i	−1.29476	+	0.747531i	−0.315267	+	0.949003i	$0.602094\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−726.246			−0.878169			−0.439085	−	0.898446i	$-0.644697\pi$
$827$	−726.246			−0.878169			−0.439085	+	0.898446i	$0.644697\pi$
$828$		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	−0.204077	−	0.978955i	$-0.565419\pi$
$839$	−968.135	−	558.953i	−1.15392	−	0.666213i	−0.949838	+	0.312742i	$0.898753\pi$
$840$		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	$-0.467116\pi$
$853$	−602.834	−	348.046i	−0.706722	−	0.408026i	−0.809846	+	0.586642i	$0.800449\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−430.149	+	745.040i	−0.501924	+	0.869358i	0.498073	+	0.867135i	$0.334041\pi$
$857$	−430.149	+	745.040i	−0.501924	+	0.869358i	−0.999998	+	0.00222347i	$0.999292\pi$
$858$		0			0
$859$	−321.216	−	556.362i	−0.373942	−	0.647686i	0.616226	−	0.787569i	$-0.288661\pi$
$859$	−321.216	−	556.362i	−0.373942	−	0.647686i	−0.990168	+	0.139883i	$0.955327\pi$
$860$		0			0
$861$	−792.853	−	457.754i	−0.920851	−	0.531654i
$862$		0			0
$863$	1466.58			1.69940			0.849698	−	0.527269i	$-0.176784\pi$
$863$	1466.58			1.69940			0.849698	+	0.527269i	$0.176784\pi$
$864$		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	$-0.701830\pi$
$877$	−167.461	+	96.6835i	−0.190947	+	0.110243i	0.401479	+	0.915868i	$0.368496\pi$
$878$		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
$883$		−	352.460i		−	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	0.991781	+	0.127949i	$0.0408393\pi$
$887$	538.140	+	932.087i	0.606697	+	1.05083i	−0.385084	+	0.922882i	$0.625827\pi$
$888$		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	$-0.294458\pi$
$907$	191.385	+	110.496i	0.211008	+	0.121826i	−0.390772	+	0.920488i	$0.627792\pi$
$908$		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
$913$	−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	0.922441	−	0.386139i	$-0.126191\pi$
$929$	974.758	+	562.777i	1.04926	+	0.605788i	0.126814	+	0.991926i	$0.459525\pi$
$930$		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	−0.134042	−	0.990976i	$-0.542796\pi$
$941$	618.375	−	357.019i	0.657147	−	0.379404i	0.791189	+	0.611572i	$0.209462\pi$
$942$		0			0
$943$	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	$-0.709853\pi$
$947$	358.220	−	620.456i	0.378268	−	0.655180i	0.990810	+	0.135258i	$0.0431863\pi$
$948$		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	$-0.363357\pi$
$953$	793.300			0.832424			0.416212	+	0.909268i	$0.363357\pi$
$954$		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	0.656093	−	0.754680i	$-0.272208\pi$
$967$	1583.67	−	914.331i	1.63771	−	0.945533i	0.981619	−	0.190853i	$-0.0611254\pi$
$968$		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
$973$		−	1253.46i		−	1.28824i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	167.195	+	289.591i	0.171131	+	0.296408i	0.938816	−	0.344420i	$-0.111924\pi$
$977$	167.195	+	289.591i	0.171131	+	0.296408i	−0.767684	+	0.640828i	$0.778591\pi$
$978$		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	0.181825	−	0.983331i	$-0.441800\pi$
$983$	926.480	−	1604.71i	0.942502	−	1.63246i	0.760677	−	0.649131i	$-0.224867\pi$
$984$		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	$-0.537611\pi$
$997$	−1033.70	−	596.808i	−1.03681	−	0.598604i	−0.918929	+	0.394423i	$0.870944\pi$
$998$		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.749.4		8
3.2	odd	2		2700.3.u.a.2249.4		8
5.2	odd	4		900.3.p.b.101.1		4
5.3	odd	4		180.3.o.a.101.2	yes	4
5.4	even	2	inner	900.3.u.b.749.1		8
9.4	even	3		2700.3.u.a.449.1		8
9.5	odd	6	inner	900.3.u.b.149.1		8
15.2	even	4		2700.3.p.a.1601.1		4
15.8	even	4		540.3.o.a.521.1		4
15.14	odd	2		2700.3.u.a.2249.1		8
20.3	even	4		720.3.bs.a.641.2		4
45.4	even	6		2700.3.u.a.449.4		8
45.13	odd	12		540.3.o.a.341.1		4
45.14	odd	6	inner	900.3.u.b.149.4		8
45.22	odd	12		2700.3.p.a.2501.1		4
45.23	even	12		180.3.o.a.41.2	✓	4
45.32	even	12		900.3.p.b.401.1		4
45.38	even	12		1620.3.g.a.161.1		4
45.43	odd	12		1620.3.g.a.161.3		4
60.23	odd	4		2160.3.bs.a.1601.1		4
180.23	odd	12		720.3.bs.a.401.2		4
180.103	even	12		2160.3.bs.a.881.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.3.o.a.41.2	✓	4	45.23	even	12
180.3.o.a.101.2	yes	4	5.3	odd	4
540.3.o.a.341.1		4	45.13	odd	12
540.3.o.a.521.1		4	15.8	even	4
720.3.bs.a.401.2		4	180.23	odd	12
720.3.bs.a.641.2		4	20.3	even	4
900.3.p.b.101.1		4	5.2	odd	4
900.3.p.b.401.1		4	45.32	even	12
900.3.u.b.149.1		8	9.5	odd	6	inner
900.3.u.b.149.4		8	45.14	odd	6	inner
900.3.u.b.749.1		8	5.4	even	2	inner
900.3.u.b.749.4		8	1.1	even	1	trivial
1620.3.g.a.161.1		4	45.38	even	12
1620.3.g.a.161.3		4	45.43	odd	12
2160.3.bs.a.881.1		4	180.103	even	12
2160.3.bs.a.1601.1		4	60.23	odd	4
2700.3.p.a.1601.1		4	15.2	even	4
2700.3.p.a.2501.1		4	45.22	odd	12
2700.3.u.a.449.1		8	9.4	even	3
2700.3.u.a.449.4		8	45.4	even	6
2700.3.u.a.2249.1		8	15.14	odd	2
2700.3.u.a.2249.4		8	3.2	odd	2

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)

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