LMFDB - Embedded newform 544.3.n.b.463.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [544,3,Mod(47,544)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(544, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 1]))

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

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

chi := DirichletCharacter("544.47");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 544 = 2^{5} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	544.n (of order $4$, 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:	$14.8229263812$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 136)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			463.13
Character	$\chi$	$=$	544.463
Dual form			544.3.n.b.47.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.749243 + 0.749243i) q^{3} +(3.60984 + 3.60984i) q^{5} +(3.85896 - 3.85896i) q^{7} +7.87727i q^{9} +O(q^{10})$	\(q+(-0.749243 + 0.749243i) q^{3} +(3.60984 + 3.60984i) q^{5} +(3.85896 - 3.85896i) q^{7} +7.87727i q^{9} +(2.59125 + 2.59125i) q^{11} +2.98374i q^{13} -5.40930 q^{15} +(13.0434 + 10.9027i) q^{17} -25.8973i q^{19} +5.78260i q^{21} +(-20.9457 + 20.9457i) q^{23} +1.06191i q^{25} +(-12.6452 - 12.6452i) q^{27} +(22.7491 + 22.7491i) q^{29} +(18.3612 + 18.3612i) q^{31} -3.88295 q^{33} +27.8605 q^{35} +(0.733830 + 0.733830i) q^{37} +(-2.23555 - 2.23555i) q^{39} +(-26.2827 - 26.2827i) q^{41} -10.7209i q^{43} +(-28.4357 + 28.4357i) q^{45} +84.3467i q^{47} +19.2169i q^{49} +(-17.9415 + 1.60393i) q^{51} +33.8459 q^{53} +18.7080i q^{55} +(19.4034 + 19.4034i) q^{57} +69.9591i q^{59} +(-65.8369 + 65.8369i) q^{61} +(30.3981 + 30.3981i) q^{63} +(-10.7708 + 10.7708i) q^{65} +76.0157 q^{67} -31.3868i q^{69} +(-27.4650 - 27.4650i) q^{71} +(48.3347 - 48.3347i) q^{73} +(-0.795629 - 0.795629i) q^{75} +19.9990 q^{77} +(-17.0189 + 17.0189i) q^{79} -51.9468 q^{81} +20.9027i q^{83} +(7.72772 + 86.4417i) q^{85} -34.0892 q^{87} +115.759 q^{89} +(11.5141 + 11.5141i) q^{91} -27.5140 q^{93} +(93.4853 - 93.4853i) q^{95} +(66.5506 - 66.5506i) q^{97} +(-20.4119 + 20.4119i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 8 q^{3}+O(q^{10}) $ 64 * q + 8 * q^3	$ 64 q + 8 q^{3} + 32 q^{11} - 12 q^{17} - 160 q^{27} + 128 q^{33} + 8 q^{35} - 88 q^{41} + 360 q^{51} - 24 q^{57} + 112 q^{65} + 8 q^{67} - 408 q^{73} - 32 q^{75} + 80 q^{81} - 8 q^{89} - 384 q^{91} + 112 q^{97} - 416 q^{99}+O(q^{100}) $ 64 * q + 8 * q^3 + 32 * q^11 - 12 * q^17 - 160 * q^27 + 128 * q^33 + 8 * q^35 - 88 * q^41 + 360 * q^51 - 24 * q^57 + 112 * q^65 + 8 * q^67 - 408 * q^73 - 32 * q^75 + 80 * q^81 - 8 * q^89 - 384 * q^91 + 112 * q^97 - 416 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/544\mathbb{Z}\right)^\times$.

$n$	$69$	$511$	$513$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.749243	+	0.749243i	−0.249748	+	0.249748i	−0.820867	−	0.571119i	$-0.806509\pi$
$3$	−0.749243	+	0.749243i	−0.249748	+	0.249748i	0.571119	+	0.820867i	$0.306509\pi$
$4$		0			0
$5$	3.60984	+	3.60984i	0.721968	+	0.721968i	0.969006	−	0.247038i	$-0.0794571\pi$
$5$	3.60984	+	3.60984i	0.721968	+	0.721968i	−0.247038	+	0.969006i	$0.579457\pi$
$6$		0			0
$7$	3.85896	−	3.85896i	0.551280	−	0.551280i	−0.375530	−	0.926810i	$-0.622539\pi$
$7$	3.85896	−	3.85896i	0.551280	−	0.551280i	0.926810	+	0.375530i	$0.122539\pi$
$8$		0			0
$9$			7.87727i			0.875252i
$10$		0			0
$11$	2.59125	+	2.59125i	0.235568	+	0.235568i	0.815012	−	0.579444i	$-0.196730\pi$
$11$	2.59125	+	2.59125i	0.235568	+	0.235568i	−0.579444	+	0.815012i	$0.696730\pi$
$12$		0			0
$13$			2.98374i			0.229519i	0.993393	+	0.114759i	$0.0366097\pi$
$13$			2.98374i			0.229519i	−0.993393	+	0.114759i	$0.963390\pi$
$14$		0			0
$15$	−5.40930			−0.360620
$16$		0			0
$17$	13.0434	+	10.9027i	0.767261	+	0.641335i
$17$	13.0434	+	10.9027i	0.767261	+	0.641335i
$18$		0			0
$19$		−	25.8973i		−	1.36302i	−0.731810	−	0.681509i	$-0.761324\pi$
$19$		−	25.8973i		−	1.36302i	0.731810	−	0.681509i	$-0.238676\pi$
$20$		0			0
$21$			5.78260i			0.275362i
$22$		0			0
$23$	−20.9457	+	20.9457i	−0.910682	+	0.910682i	−0.996326	−	0.0856440i	$-0.972705\pi$
$23$	−20.9457	+	20.9457i	−0.910682	+	0.910682i	0.0856440	+	0.996326i	$0.472705\pi$
$24$		0			0
$25$			1.06191i			0.0424764i
$26$		0			0
$27$	−12.6452	−	12.6452i	−0.468340	−	0.468340i
$28$		0			0
$29$	22.7491	+	22.7491i	0.784451	+	0.784451i	0.980578	−	0.196128i	$-0.0628367\pi$
$29$	22.7491	+	22.7491i	0.784451	+	0.784451i	−0.196128	+	0.980578i	$0.562837\pi$
$30$		0			0
$31$	18.3612	+	18.3612i	0.592297	+	0.592297i	0.938251	−	0.345954i	$-0.112445\pi$
$31$	18.3612	+	18.3612i	0.592297	+	0.592297i	−0.345954	+	0.938251i	$0.612445\pi$
$32$		0			0
$33$	−3.88295			−0.117665
$34$		0			0
$35$	27.8605			0.796013
$36$		0			0
$37$	0.733830	+	0.733830i	0.0198332	+	0.0198332i	0.716954	−	0.697121i	$-0.245536\pi$
$37$	0.733830	+	0.733830i	0.0198332	+	0.0198332i	−0.697121	+	0.716954i	$0.745536\pi$
$38$		0			0
$39$	−2.23555	−	2.23555i	−0.0573218	−	0.0573218i
$40$		0			0
$41$	−26.2827	−	26.2827i	−0.641042	−	0.641042i	0.309770	−	0.950812i	$-0.399748\pi$
$41$	−26.2827	−	26.2827i	−0.641042	−	0.641042i	−0.950812	+	0.309770i	$0.899748\pi$
$42$		0			0
$43$		−	10.7209i		−	0.249323i	−0.992199	−	0.124661i	$-0.960216\pi$
$43$		−	10.7209i		−	0.249323i	0.992199	−	0.124661i	$-0.0397845\pi$
$44$		0			0
$45$	−28.4357	+	28.4357i	−0.631904	+	0.631904i
$46$		0			0
$47$			84.3467i			1.79461i	0.441411	+	0.897305i	$0.354478\pi$
$47$			84.3467i			1.79461i	−0.441411	+	0.897305i	$0.645522\pi$
$48$		0			0
$49$			19.2169i			0.392181i
$50$		0			0
$51$	−17.9415	+	1.60393i	−0.351794	+	0.0314496i
$52$		0			0
$53$	33.8459			0.638602			0.319301	−	0.947653i	$-0.396552\pi$
$53$	33.8459			0.638602			0.319301	+	0.947653i	$0.396552\pi$
$54$		0			0
$55$			18.7080i			0.340145i
$56$		0			0
$57$	19.4034	+	19.4034i	0.340411	+	0.340411i
$58$		0			0
$59$			69.9591i			1.18575i	0.805296	+	0.592874i	$0.202007\pi$
$59$			69.9591i			1.18575i	−0.805296	+	0.592874i	$0.797993\pi$
$60$		0			0
$61$	−65.8369	+	65.8369i	−1.07929	+	1.07929i	−0.0827207	+	0.996573i	$0.526361\pi$
$61$	−65.8369	+	65.8369i	−1.07929	+	1.07929i	−0.996573	+	0.0827207i	$0.973639\pi$
$62$		0			0
$63$	30.3981	+	30.3981i	0.482509	+	0.482509i
$64$		0			0
$65$	−10.7708	+	10.7708i	−0.165705	+	0.165705i
$66$		0			0
$67$	76.0157			1.13456			0.567282	−	0.823524i	$-0.307995\pi$
$67$	76.0157			1.13456			0.567282	+	0.823524i	$0.307995\pi$
$68$		0			0
$69$		−	31.3868i		−	0.454882i
$70$		0			0
$71$	−27.4650	−	27.4650i	−0.386831	−	0.386831i	0.486724	−	0.873556i	$-0.338192\pi$
$71$	−27.4650	−	27.4650i	−0.386831	−	0.386831i	−0.873556	+	0.486724i	$0.838192\pi$
$72$		0			0
$73$	48.3347	−	48.3347i	0.662119	−	0.662119i	−0.293760	−	0.955879i	$-0.594907\pi$
$73$	48.3347	−	48.3347i	0.662119	−	0.662119i	0.955879	+	0.293760i	$0.0949067\pi$
$74$		0			0
$75$	−0.795629	−	0.795629i	−0.0106084	−	0.0106084i
$76$		0			0
$77$	19.9990			0.259728
$78$		0			0
$79$	−17.0189	+	17.0189i	−0.215429	+	0.215429i	−0.806569	−	0.591140i	$-0.798678\pi$
$79$	−17.0189	+	17.0189i	−0.215429	+	0.215429i	0.591140	+	0.806569i	$0.298678\pi$
$80$		0			0
$81$	−51.9468			−0.641318
$82$		0			0
$83$			20.9027i			0.251839i	0.992040	+	0.125920i	$0.0401882\pi$
$83$			20.9027i			0.251839i	−0.992040	+	0.125920i	$0.959812\pi$
$84$		0			0
$85$	7.72772	+	86.4417i	0.0909143	+	1.01696i
$86$		0			0
$87$	−34.0892			−0.391830
$88$		0			0
$89$	115.759			1.30066			0.650329	−	0.759652i	$-0.274631\pi$
$89$	115.759			1.30066			0.650329	+	0.759652i	$0.274631\pi$
$90$		0			0
$91$	11.5141	+	11.5141i	0.126529	+	0.126529i
$92$		0			0
$93$	−27.5140			−0.295850
$94$		0			0
$95$	93.4853	−	93.4853i	0.984056	−	0.984056i
$96$		0			0
$97$	66.5506	−	66.5506i	0.686088	−	0.686088i	−0.275277	−	0.961365i	$-0.588769\pi$
$97$	66.5506	−	66.5506i	0.686088	−	0.686088i	0.961365	+	0.275277i	$0.0887694\pi$
$98$		0			0
$99$	−20.4119	+	20.4119i	−0.206181	+	0.206181i
$100$		0			0
$101$			21.8709i			0.216543i	0.994121	+	0.108272i	$0.0345316\pi$
$101$			21.8709i			0.216543i	−0.994121	+	0.108272i	$0.965468\pi$
$102$		0			0
$103$		−	26.9524i		−	0.261673i	−0.991404	−	0.130837i	$-0.958234\pi$
$103$		−	26.9524i		−	0.261673i	0.991404	−	0.130837i	$-0.0417664\pi$
$104$		0			0
$105$	−20.8743	+	20.8743i	−0.198802	+	0.198802i
$106$		0			0
$107$	−69.9821	+	69.9821i	−0.654038	+	0.654038i	−0.953963	−	0.299925i	$-0.903038\pi$
$107$	−69.9821	+	69.9821i	−0.654038	+	0.654038i	0.299925	+	0.953963i	$0.403038\pi$
$108$		0			0
$109$	26.7602	−	26.7602i	0.245507	−	0.245507i	−0.573617	−	0.819124i	$-0.694460\pi$
$109$	26.7602	−	26.7602i	0.245507	−	0.245507i	0.819124	+	0.573617i	$0.194460\pi$
$110$		0			0
$111$	−1.09963			−0.00990661
$112$		0			0
$113$	−103.894	−	103.894i	−0.919414	−	0.919414i	0.0775723	−	0.996987i	$-0.475283\pi$
$113$	−103.894	−	103.894i	−0.919414	−	0.919414i	−0.996987	+	0.0775723i	$0.975283\pi$
$114$		0			0
$115$	−151.221			−1.31497
$116$		0			0
$117$	−23.5038			−0.200887
$118$		0			0
$119$	92.4071	−	8.26101i	0.776531	−	0.0694203i
$120$		0			0
$121$		−	107.571i		−	0.889016i
$122$		0			0
$123$	39.3843			0.320197
$124$		0			0
$125$	86.4127	−	86.4127i	0.691302	−	0.691302i
$126$		0			0
$127$	17.2092			0.135505			0.0677527	−	0.997702i	$-0.478417\pi$
$127$	17.2092			0.135505			0.0677527	+	0.997702i	$0.478417\pi$
$128$		0			0
$129$	8.03255	+	8.03255i	0.0622679	+	0.0622679i
$130$		0			0
$131$	112.948	−	112.948i	0.862200	−	0.862200i	−0.129393	−	0.991593i	$-0.541303\pi$
$131$	112.948	−	112.948i	0.862200	−	0.862200i	0.991593	+	0.129393i	$0.0413030\pi$
$132$		0			0
$133$	−99.9368	−	99.9368i	−0.751404	−	0.751404i
$134$		0			0
$135$		−	91.2942i		−	0.676253i
$136$		0			0
$137$	−195.481			−1.42687			−0.713436	−	0.700721i	$-0.752862\pi$
$137$	−195.481			−1.42687			−0.713436	+	0.700721i	$0.752862\pi$
$138$		0			0
$139$	4.95033	−	4.95033i	0.0356139	−	0.0356139i	−0.689076	−	0.724689i	$-0.741983\pi$
$139$	4.95033	−	4.95033i	0.0356139	−	0.0356139i	0.724689	+	0.689076i	$0.241983\pi$
$140$		0			0
$141$	−63.1962	−	63.1962i	−0.448200	−	0.448200i
$142$		0			0
$143$	−7.73162	+	7.73162i	−0.0540672	+	0.0540672i
$144$		0			0
$145$			164.241i			1.13270i
$146$		0			0
$147$	−14.3981	−	14.3981i	−0.0979463	−	0.0979463i
$148$		0			0
$149$		−	34.5639i		−	0.231973i	−0.993251	−	0.115986i	$-0.962997\pi$
$149$		−	34.5639i		−	0.231973i	0.993251	−	0.115986i	$-0.0370029\pi$
$150$		0			0
$151$	−152.346			−1.00892			−0.504458	−	0.863436i	$-0.668308\pi$
$151$	−152.346			−1.00892			−0.504458	+	0.863436i	$0.668308\pi$
$152$		0			0
$153$	−85.8835	+	102.747i	−0.561330	+	0.671547i
$154$		0			0
$155$			132.562i			0.855240i
$156$		0			0
$157$		−	287.858i		−	1.83349i	−0.399473	−	0.916745i	$-0.630807\pi$
$157$		−	287.858i		−	1.83349i	0.399473	−	0.916745i	$-0.369193\pi$
$158$		0			0
$159$	−25.3588	+	25.3588i	−0.159489	+	0.159489i
$160$		0			0
$161$			161.657i			1.00408i
$162$		0			0
$163$	−199.813	−	199.813i	−1.22584	−	1.22584i	−0.965522	−	0.260322i	$-0.916171\pi$
$163$	−199.813	−	199.813i	−1.22584	−	1.22584i	−0.260322	−	0.965522i	$-0.583829\pi$
$164$		0			0
$165$	−14.0168	−	14.0168i	−0.0849505	−	0.0849505i
$166$		0			0
$167$	−79.1049	−	79.1049i	−0.473682	−	0.473682i	0.429422	−	0.903104i	$-0.358717\pi$
$167$	−79.1049	−	79.1049i	−0.473682	−	0.473682i	−0.903104	+	0.429422i	$0.858717\pi$
$168$		0			0
$169$	160.097			0.947321
$170$		0			0
$171$	204.000			1.19298
$172$		0			0
$173$	232.520	+	232.520i	1.34404	+	1.34404i	0.891991	+	0.452052i	$0.149308\pi$
$173$	232.520	+	232.520i	1.34404	+	1.34404i	0.452052	+	0.891991i	$0.350692\pi$
$174$		0			0
$175$	4.09787	+	4.09787i	0.0234164	+	0.0234164i
$176$		0			0
$177$	−52.4164	−	52.4164i	−0.296138	−	0.296138i
$178$		0			0
$179$		−	215.338i		−	1.20301i	−0.798871	−	0.601503i	$-0.794569\pi$
$179$		−	215.338i		−	1.20301i	0.798871	−	0.601503i	$-0.205431\pi$
$180$		0			0
$181$	85.2707	−	85.2707i	0.471109	−	0.471109i	−0.431164	−	0.902273i	$-0.641897\pi$
$181$	85.2707	−	85.2707i	0.471109	−	0.471109i	0.902273	+	0.431164i	$0.141897\pi$
$182$		0			0
$183$		−	98.6557i		−	0.539102i
$184$		0			0
$185$			5.29802i			0.0286379i
$186$		0			0
$187$	5.54717	+	62.0503i	0.0296640	+	0.331820i
$188$		0			0
$189$	−97.5945			−0.516373
$190$		0			0
$191$		−	213.241i		−	1.11644i	−0.829692	−	0.558221i	$-0.811484\pi$
$191$		−	213.241i		−	1.11644i	0.829692	−	0.558221i	$-0.188516\pi$
$192$		0			0
$193$	95.8456	+	95.8456i	0.496610	+	0.496610i	0.910381	−	0.413771i	$-0.135789\pi$
$193$	95.8456	+	95.8456i	0.496610	+	0.496610i	−0.413771	+	0.910381i	$0.635789\pi$
$194$		0			0
$195$		−	16.1400i		−	0.0827690i
$196$		0			0
$197$	117.420	−	117.420i	0.596041	−	0.596041i	−0.343216	−	0.939257i	$-0.611516\pi$
$197$	117.420	−	117.420i	0.596041	−	0.596041i	0.939257	+	0.343216i	$0.111516\pi$
$198$		0			0
$199$	121.225	+	121.225i	0.609173	+	0.609173i	0.942730	−	0.333557i	$-0.108249\pi$
$199$	121.225	+	121.225i	0.609173	+	0.609173i	−0.333557	+	0.942730i	$0.608249\pi$
$200$		0			0
$201$	−56.9543	+	56.9543i	−0.283355	+	0.283355i
$202$		0			0
$203$	175.575			0.864904
$204$		0			0
$205$		−	189.753i		−	0.925624i
$206$		0			0
$207$	−164.995	−	164.995i	−0.797076	−	0.797076i
$208$		0			0
$209$	67.1064	−	67.1064i	0.321083	−	0.321083i
$210$		0			0
$211$	15.7879	+	15.7879i	0.0748241	+	0.0748241i	0.743528	−	0.668704i	$-0.233151\pi$
$211$	15.7879	+	15.7879i	0.0748241	+	0.0748241i	−0.668704	+	0.743528i	$0.733151\pi$
$212$		0			0
$213$	41.1560			0.193220
$214$		0			0
$215$	38.7007	−	38.7007i	0.180003	−	0.180003i
$216$		0			0
$217$	141.710			0.653043
$218$		0			0
$219$			72.4289i			0.330725i
$220$		0			0
$221$	−32.5309	+	38.9183i	−0.147198	+	0.176101i
$222$		0			0
$223$	−74.7498			−0.335201			−0.167600	−	0.985855i	$-0.553602\pi$
$223$	−74.7498			−0.335201			−0.167600	+	0.985855i	$0.553602\pi$
$224$		0			0
$225$	−8.36495			−0.0371775
$226$		0			0
$227$	−142.640	−	142.640i	−0.628370	−	0.628370i	0.319288	−	0.947658i	$-0.396556\pi$
$227$	−142.640	−	142.640i	−0.628370	−	0.628370i	−0.947658	+	0.319288i	$0.896556\pi$
$228$		0			0
$229$	−262.209			−1.14502			−0.572508	−	0.819899i	$-0.694029\pi$
$229$	−262.209			−1.14502			−0.572508	+	0.819899i	$0.694029\pi$
$230$		0			0
$231$	−14.9841	+	14.9841i	−0.0648664	+	0.0648664i
$232$		0			0
$233$	−60.8609	+	60.8609i	−0.261206	+	0.261206i	−0.825544	−	0.564338i	$-0.809131\pi$
$233$	−60.8609	+	60.8609i	−0.261206	+	0.261206i	0.564338	+	0.825544i	$0.309131\pi$
$234$		0			0
$235$	−304.478	+	304.478i	−1.29565	+	1.29565i
$236$		0			0
$237$		−	25.5026i		−	0.107606i
$238$		0			0
$239$			95.1858i			0.398267i	0.979972	+	0.199133i	$0.0638127\pi$
$239$			95.1858i			0.398267i	−0.979972	+	0.199133i	$0.936187\pi$
$240$		0			0
$241$	−117.983	+	117.983i	−0.489557	+	0.489557i	−0.908166	−	0.418609i	$-0.862518\pi$
$241$	−117.983	+	117.983i	−0.489557	+	0.489557i	0.418609	+	0.908166i	$0.362518\pi$
$242$		0			0
$243$	152.727	−	152.727i	0.628508	−	0.628508i
$244$		0			0
$245$	−69.3699	+	69.3699i	−0.283142	+	0.283142i
$246$		0			0
$247$	77.2710			0.312838
$248$		0			0
$249$	−15.6612	−	15.6612i	−0.0628963	−	0.0628963i
$250$		0			0
$251$	−131.822			−0.525188			−0.262594	−	0.964906i	$-0.584578\pi$
$251$	−131.822			−0.525188			−0.262594	+	0.964906i	$0.584578\pi$
$252$		0			0
$253$	−108.551			−0.429055
$254$		0			0
$255$	−70.5558	−	58.9760i	−0.276690	−	0.231278i
$256$		0			0
$257$		−	342.708i		−	1.33349i	−0.745284	−	0.666747i	$-0.767686\pi$
$257$		−	342.708i		−	1.33349i	0.745284	−	0.666747i	$-0.232314\pi$
$258$		0			0
$259$	5.66364			0.0218673
$260$		0			0
$261$	−179.201	+	179.201i	−0.686592	+	0.686592i
$262$		0			0
$263$	494.500			1.88023			0.940114	−	0.340862i	$-0.110719\pi$
$263$	494.500			1.88023			0.940114	+	0.340862i	$0.110719\pi$
$264$		0			0
$265$	122.178	+	122.178i	0.461050	+	0.461050i
$266$		0			0
$267$	−86.7314	+	86.7314i	−0.324837	+	0.324837i
$268$		0			0
$269$	116.803	+	116.803i	0.434211	+	0.434211i	0.890058	−	0.455847i	$-0.150664\pi$
$269$	116.803	+	116.803i	0.434211	+	0.434211i	−0.455847	+	0.890058i	$0.650664\pi$
$270$		0			0
$271$		−	241.196i		−	0.890021i	−0.895525	−	0.445011i	$-0.853200\pi$
$271$		−	241.196i		−	0.890021i	0.895525	−	0.445011i	$-0.146800\pi$
$272$		0			0
$273$	−17.2538			−0.0632007
$274$		0			0
$275$	−2.75167	+	2.75167i	−0.0100061	+	0.0100061i
$276$		0			0
$277$	340.749	+	340.749i	1.23014	+	1.23014i	0.963908	+	0.266234i	$0.0857794\pi$
$277$	340.749	+	340.749i	1.23014	+	1.23014i	0.266234	+	0.963908i	$0.414221\pi$
$278$		0			0
$279$	−144.636	+	144.636i	−0.518410	+	0.518410i
$280$		0			0
$281$		−	428.504i		−	1.52493i	−0.647032	−	0.762463i	$-0.723990\pi$
$281$		−	428.504i		−	1.52493i	0.647032	−	0.762463i	$-0.276010\pi$
$282$		0			0
$283$	−55.7718	−	55.7718i	−0.197073	−	0.197073i	0.601671	−	0.798744i	$-0.294502\pi$
$283$	−55.7718	−	55.7718i	−0.197073	−	0.197073i	−0.798744	+	0.601671i	$0.794502\pi$
$284$		0			0
$285$			140.086i			0.491531i
$286$		0			0
$287$	−202.848			−0.706787
$288$		0			0
$289$	51.2623	+	284.417i	0.177378	+	0.984143i
$290$		0			0
$291$			99.7252i			0.342698i
$292$		0			0
$293$		−	343.598i		−	1.17269i	−0.810062	−	0.586344i	$-0.800567\pi$
$293$		−	343.598i		−	1.17269i	0.810062	−	0.586344i	$-0.199433\pi$
$294$		0			0
$295$	−252.541	+	252.541i	−0.856072	+	0.856072i
$296$		0			0
$297$		−	65.5336i		−	0.220652i
$298$		0			0
$299$	−62.4966	−	62.4966i	−0.209019	−	0.209019i
$300$		0			0
$301$	−41.3715	−	41.3715i	−0.137447	−	0.137447i
$302$		0			0
$303$	−16.3866	−	16.3866i	−0.0540812	−	0.0540812i
$304$		0			0
$305$	−475.322			−1.55843
$306$		0			0
$307$	100.962			0.328867			0.164433	−	0.986388i	$-0.447420\pi$
$307$	100.962			0.328867			0.164433	+	0.986388i	$0.447420\pi$
$308$		0			0
$309$	20.1939	+	20.1939i	0.0653524	+	0.0653524i
$310$		0			0
$311$	36.0997	+	36.0997i	0.116076	+	0.116076i	0.762759	−	0.646683i	$-0.223844\pi$
$311$	36.0997	+	36.0997i	0.116076	+	0.116076i	−0.646683	+	0.762759i	$0.723844\pi$
$312$		0			0
$313$	−207.384	−	207.384i	−0.662568	−	0.662568i	0.293417	−	0.955985i	$-0.405208\pi$
$313$	−207.384	−	207.384i	−0.662568	−	0.662568i	−0.955985	+	0.293417i	$0.905208\pi$
$314$		0			0
$315$			219.464i			0.696712i
$316$		0			0
$317$	91.2105	−	91.2105i	0.287730	−	0.287730i	−0.548452	−	0.836182i	$-0.684783\pi$
$317$	91.2105	−	91.2105i	0.287730	−	0.287730i	0.836182	+	0.548452i	$0.184783\pi$
$318$		0			0
$319$			117.897i			0.369583i
$320$		0			0
$321$		−	104.867i		−	0.326689i
$322$		0			0
$323$	282.351	−	337.790i	0.874151	−	1.04579i
$324$		0			0
$325$	−3.16847			−0.00974913
$326$		0			0
$327$			40.0998i			0.122630i
$328$		0			0
$329$	325.490	+	325.490i	0.989332	+	0.989332i
$330$		0			0
$331$			265.861i			0.803206i	0.915814	+	0.401603i	$0.131547\pi$
$331$			265.861i			0.803206i	−0.915814	+	0.401603i	$0.868453\pi$
$332$		0			0
$333$	−5.78057	+	5.78057i	−0.0173591	+	0.0173591i
$334$		0			0
$335$	274.405	+	274.405i	0.819119	+	0.819119i
$336$		0			0
$337$	373.456	−	373.456i	1.10818	−	1.10818i	0.114787	−	0.993390i	$-0.463381\pi$
$337$	373.456	−	373.456i	1.10818	−	1.10818i	0.993390	−	0.114787i	$-0.0366186\pi$
$338$		0			0
$339$	155.684			0.459243
$340$		0			0
$341$			95.1569i			0.279052i
$342$		0			0
$343$	263.246	+	263.246i	0.767481	+	0.767481i
$344$		0			0
$345$	113.301	−	113.301i	0.328410	−	0.328410i
$346$		0			0
$347$	455.522	+	455.522i	1.31274	+	1.31274i	0.919385	+	0.393359i	$0.128687\pi$
$347$	455.522	+	455.522i	1.31274	+	1.31274i	0.393359	+	0.919385i	$0.371313\pi$
$348$		0			0
$349$	−338.237			−0.969159			−0.484580	−	0.874747i	$-0.661027\pi$
$349$	−338.237			−0.969159			−0.484580	+	0.874747i	$0.661027\pi$
$350$		0			0
$351$	37.7300	−	37.7300i	0.107493	−	0.107493i
$352$		0			0
$353$	26.2790			0.0744448			0.0372224	−	0.999307i	$-0.488149\pi$
$353$	26.2790			0.0744448			0.0372224	+	0.999307i	$0.488149\pi$
$354$		0			0
$355$		−	198.289i		−	0.558560i
$356$		0			0
$357$	−63.0459	+	75.4249i	−0.176599	+	0.211274i
$358$		0			0
$359$	562.774			1.56762			0.783808	−	0.621004i	$-0.213275\pi$
$359$	562.774			1.56762			0.783808	+	0.621004i	$0.213275\pi$
$360$		0			0
$361$	−309.672			−0.857818
$362$		0			0
$363$	80.5968	+	80.5968i	0.222030	+	0.222030i
$364$		0			0
$365$	348.961			0.956058
$366$		0			0
$367$	−294.820	+	294.820i	−0.803324	+	0.803324i	−0.983614	−	0.180290i	$-0.942297\pi$
$367$	−294.820	+	294.820i	−0.803324	+	0.803324i	0.180290	+	0.983614i	$0.442297\pi$
$368$		0			0
$369$	207.036	−	207.036i	0.561073	−	0.561073i
$370$		0			0
$371$	130.610	−	130.610i	0.352048	−	0.352048i
$372$		0			0
$373$			317.003i			0.849875i	0.905223	+	0.424937i	$0.139704\pi$
$373$			317.003i			0.849875i	−0.905223	+	0.424937i	$0.860296\pi$
$374$		0			0
$375$			129.488i			0.345302i
$376$		0			0
$377$	−67.8774	+	67.8774i	−0.180046	+	0.180046i
$378$		0			0
$379$	−315.390	+	315.390i	−0.832164	+	0.832164i	−0.987812	−	0.155649i	$-0.950253\pi$
$379$	−315.390	+	315.390i	−0.832164	+	0.832164i	0.155649	+	0.987812i	$0.450253\pi$
$380$		0			0
$381$	−12.8939	+	12.8939i	−0.0338422	+	0.0338422i
$382$		0			0
$383$	522.656			1.36464			0.682319	−	0.731055i	$-0.260972\pi$
$383$	522.656			1.36464			0.682319	+	0.731055i	$0.260972\pi$
$384$		0			0
$385$	72.1933	+	72.1933i	0.187515	+	0.187515i
$386$		0			0
$387$	84.4513			0.218220
$388$		0			0
$389$	−256.711			−0.659926			−0.329963	−	0.943994i	$-0.607036\pi$
$389$	−256.711			−0.659926			−0.329963	+	0.943994i	$0.607036\pi$
$390$		0			0
$391$	−501.568	+	44.8392i	−1.28278	+	0.114678i
$392$		0			0
$393$			169.251i			0.430665i
$394$		0			0
$395$	−122.871			−0.311066
$396$		0			0
$397$	−366.419	+	366.419i	−0.922969	+	0.922969i	−0.997238	−	0.0742691i	$-0.976338\pi$
$397$	−366.419	+	366.419i	−0.922969	+	0.922969i	0.0742691	+	0.997238i	$0.476338\pi$
$398$		0			0
$399$	149.754			0.375323
$400$		0			0
$401$	385.780	+	385.780i	0.962044	+	0.962044i	0.999306	−	0.0372612i	$-0.0118634\pi$
$401$	385.780	+	385.780i	0.962044	+	0.962044i	−0.0372612	+	0.999306i	$0.511863\pi$
$402$		0			0
$403$	−54.7852	+	54.7852i	−0.135943	+	0.135943i
$404$		0			0
$405$	−187.520	−	187.520i	−0.463012	−	0.463012i
$406$		0			0
$407$			3.80307i			0.00934414i
$408$		0			0
$409$	−270.337			−0.660970			−0.330485	−	0.943811i	$-0.607212\pi$
$409$	−270.337			−0.660970			−0.330485	+	0.943811i	$0.607212\pi$
$410$		0			0
$411$	146.463	−	146.463i	0.356358	−	0.356358i
$412$		0			0
$413$	269.969	+	269.969i	0.653678	+	0.653678i
$414$		0			0
$415$	−75.4553	+	75.4553i	−0.181820	+	0.181820i
$416$		0			0
$417$			7.41800i			0.0177890i
$418$		0			0
$419$	−252.051	−	252.051i	−0.601553	−	0.601553i	0.339172	−	0.940725i	$-0.389853\pi$
$419$	−252.051	−	252.051i	−0.601553	−	0.601553i	−0.940725	+	0.339172i	$0.889853\pi$
$420$		0			0
$421$		−	179.427i		−	0.426193i	−0.977031	−	0.213097i	$-0.931645\pi$
$421$		−	179.427i		−	0.426193i	0.977031	−	0.213097i	$-0.0683549\pi$
$422$		0			0
$423$	−664.422			−1.57074
$424$		0			0
$425$	−11.5777	+	13.8509i	−0.0272416	+	0.0325905i
$426$		0			0
$427$			508.124i			1.18999i
$428$		0			0
$429$		−	11.5857i		−	0.0270063i
$430$		0			0
$431$	−470.235	+	470.235i	−1.09103	+	1.09103i	−0.0956143	+	0.995418i	$0.530482\pi$
$431$	−470.235	+	470.235i	−1.09103	+	1.09103i	−0.995418	+	0.0956143i	$0.969518\pi$
$432$		0			0
$433$		−	261.547i		−	0.604034i	−0.953303	−	0.302017i	$-0.902340\pi$
$433$		−	261.547i		−	0.604034i	0.953303	−	0.302017i	$-0.0976600\pi$
$434$		0			0
$435$	−123.057	−	123.057i	−0.282889	−	0.282889i
$436$		0			0
$437$	542.438	+	542.438i	1.24128	+	1.24128i
$438$		0			0
$439$	−126.052	−	126.052i	−0.287134	−	0.287134i	0.548812	−	0.835946i	$-0.315080\pi$
$439$	−126.052	−	126.052i	−0.287134	−	0.287134i	−0.835946	+	0.548812i	$0.815080\pi$
$440$		0			0
$441$	−151.376			−0.343257
$442$		0			0
$443$	−69.9824			−0.157974			−0.0789869	−	0.996876i	$-0.525169\pi$
$443$	−69.9824			−0.157974			−0.0789869	+	0.996876i	$0.525169\pi$
$444$		0			0
$445$	417.870	+	417.870i	0.939034	+	0.939034i
$446$		0			0
$447$	25.8968	+	25.8968i	0.0579347	+	0.0579347i
$448$		0			0
$449$	219.719	+	219.719i	0.489352	+	0.489352i	0.908102	−	0.418749i	$-0.137531\pi$
$449$	219.719	+	219.719i	0.489352	+	0.489352i	−0.418749	+	0.908102i	$0.637531\pi$
$450$		0			0
$451$		−	136.210i		−	0.302018i
$452$		0			0
$453$	114.144	−	114.144i	0.251974	−	0.251974i
$454$		0			0
$455$			83.1285i			0.182700i
$456$		0			0
$457$			485.155i			1.06161i	0.847495	+	0.530804i	$0.178110\pi$
$457$			485.155i			1.06161i	−0.847495	+	0.530804i	$0.821890\pi$
$458$		0			0
$459$	−27.0700	−	302.803i	−0.0589760	−	0.659702i
$460$		0			0
$461$	−803.704			−1.74339			−0.871697	−	0.490046i	$-0.836980\pi$
$461$	−803.704			−1.74339			−0.871697	+	0.490046i	$0.836980\pi$
$462$		0			0
$463$		−	673.039i		−	1.45365i	−0.686824	−	0.726824i	$-0.740996\pi$
$463$		−	673.039i		−	1.45365i	0.686824	−	0.726824i	$-0.259004\pi$
$464$		0			0
$465$	−99.3213	−	99.3213i	−0.213594	−	0.213594i
$466$		0			0
$467$		−	769.187i		−	1.64708i	−0.567258	−	0.823540i	$-0.691996\pi$
$467$		−	769.187i		−	1.64708i	0.567258	−	0.823540i	$-0.308004\pi$
$468$		0			0
$469$	293.342	−	293.342i	0.625462	−	0.625462i
$470$		0			0
$471$	215.676	+	215.676i	0.457910	+	0.457910i
$472$		0			0
$473$	27.7805	−	27.7805i	0.0587325	−	0.0587325i
$474$		0			0
$475$	27.5006			0.0578961
$476$		0			0
$477$			266.613i			0.558937i
$478$		0			0
$479$	129.681	+	129.681i	0.270733	+	0.270733i	0.829395	−	0.558662i	$-0.188685\pi$
$479$	129.681	+	129.681i	0.270733	+	0.270733i	−0.558662	+	0.829395i	$0.688685\pi$
$480$		0			0
$481$	−2.18956	+	2.18956i	−0.00455210	+	0.00455210i
$482$		0			0
$483$	−121.120	−	121.120i	−0.250767	−	0.250767i
$484$		0			0
$485$	480.474			0.990668
$486$		0			0
$487$	67.2949	−	67.2949i	0.138182	−	0.138182i	−0.634632	−	0.772814i	$-0.718848\pi$
$487$	67.2949	−	67.2949i	0.138182	−	0.138182i	0.772814	+	0.634632i	$0.218848\pi$
$488$		0			0
$489$	299.416			0.612304
$490$		0			0
$491$			95.5137i			0.194529i	0.995259	+	0.0972644i	$0.0310093\pi$
$491$			95.5137i			0.194529i	−0.995259	+	0.0972644i	$0.968991\pi$
$492$		0			0
$493$	48.6997	+	544.752i	0.0987825	+	1.10497i
$494$		0			0
$495$	−147.368			−0.297713
$496$		0			0
$497$	−211.973			−0.426505
$498$		0			0
$499$	−575.936	−	575.936i	−1.15418	−	1.15418i	−0.985706	−	0.168475i	$-0.946116\pi$
$499$	−575.936	−	575.936i	−1.15418	−	1.15418i	−0.168475	−	0.985706i	$-0.553884\pi$
$500$		0			0
$501$	118.538			0.236602
$502$		0			0
$503$	401.223	−	401.223i	0.797661	−	0.797661i	−0.185065	−	0.982726i	$-0.559250\pi$
$503$	401.223	−	401.223i	0.797661	−	0.797661i	0.982726	+	0.185065i	$0.0592496\pi$
$504$		0			0
$505$	−78.9504	+	78.9504i	−0.156337	+	0.156337i
$506$		0			0
$507$	−119.952	+	119.952i	−0.236591	+	0.236591i
$508$		0			0
$509$		−	534.020i		−	1.04915i	−0.851363	−	0.524577i	$-0.824223\pi$
$509$		−	534.020i		−	1.04915i	0.851363	−	0.524577i	$-0.175777\pi$
$510$		0			0
$511$		−	373.043i		−	0.730026i
$512$		0			0
$513$	−327.477	+	327.477i	−0.638356	+	0.638356i
$514$		0			0
$515$	97.2938	−	97.2938i	0.188920	−	0.188920i
$516$		0			0
$517$	−218.563	+	218.563i	−0.422753	+	0.422753i
$518$		0			0
$519$	−348.427			−0.671344
$520$		0			0
$521$	182.296	+	182.296i	0.349897	+	0.349897i	0.860071	−	0.510174i	$-0.170419\pi$
$521$	182.296	+	182.296i	0.349897	+	0.349897i	−0.510174	+	0.860071i	$0.670419\pi$
$522$		0			0
$523$	864.350			1.65268			0.826338	−	0.563174i	$-0.190420\pi$
$523$	864.350			1.65268			0.826338	+	0.563174i	$0.190420\pi$
$524$		0			0
$525$	−6.14060			−0.0116964
$526$		0			0
$527$	39.3065	+	439.680i	0.0745854	+	0.834308i
$528$		0			0
$529$		−	348.443i		−	0.658683i
$530$		0			0
$531$	−551.086			−1.03783
$532$		0			0
$533$	78.4209	−	78.4209i	0.147131	−	0.147131i
$534$		0			0
$535$	−505.248			−0.944390
$536$		0			0
$537$	161.341	+	161.341i	0.300448	+	0.300448i
$538$		0			0
$539$	−49.7957	+	49.7957i	−0.0923853	+	0.0923853i
$540$		0			0
$541$	−671.567	−	671.567i	−1.24134	−	1.24134i	−0.959444	−	0.281899i	$-0.909036\pi$
$541$	−671.567	−	671.567i	−1.24134	−	1.24134i	−0.281899	−	0.959444i	$-0.590964\pi$
$542$		0			0
$543$			127.777i			0.235317i
$544$		0			0
$545$	193.200			0.354496
$546$		0			0
$547$	700.646	−	700.646i	1.28089	−	1.28089i	0.340725	−	0.940163i	$-0.389327\pi$
$547$	700.646	−	700.646i	1.28089	−	1.28089i	0.940163	−	0.340725i	$-0.110673\pi$
$548$		0			0
$549$	−518.615	−	518.615i	−0.944654	−	0.944654i
$550$		0			0
$551$	589.140	−	589.140i	1.06922	−	1.06922i
$552$		0			0
$553$			131.351i			0.237524i
$554$		0			0
$555$	−3.96950	−	3.96950i	−0.00715226	−	0.00715226i
$556$		0			0
$557$		−	94.2272i		−	0.169169i	−0.996416	−	0.0845845i	$-0.973044\pi$
$557$		−	94.2272i		−	0.169169i	0.996416	−	0.0845845i	$-0.0269563\pi$
$558$		0			0
$559$	31.9884			0.0572243
$560$		0			0
$561$	−50.6470	−	42.3346i	−0.0902798	−	0.0754628i
$562$		0			0
$563$			930.351i			1.65249i	0.563312	+	0.826244i	$0.309527\pi$
$563$			930.351i			1.65249i	−0.563312	+	0.826244i	$0.690473\pi$
$564$		0			0
$565$		−	750.081i		−	1.32758i
$566$		0			0
$567$	−200.461	+	200.461i	−0.353546	+	0.353546i
$568$		0			0
$569$		−	701.405i		−	1.23270i	−0.787473	−	0.616349i	$-0.788611\pi$
$569$		−	701.405i		−	1.23270i	0.787473	−	0.616349i	$-0.211389\pi$
$570$		0			0
$571$	49.4687	+	49.4687i	0.0866352	+	0.0866352i	0.749096	−	0.662461i	$-0.230488\pi$
$571$	49.4687	+	49.4687i	0.0866352	+	0.0866352i	−0.662461	+	0.749096i	$0.730488\pi$
$572$		0			0
$573$	159.769	+	159.769i	0.278829	+	0.278829i
$574$		0			0
$575$	−22.2424	−	22.2424i	−0.0386825	−	0.0386825i
$576$		0			0
$577$	−719.179			−1.24641			−0.623205	−	0.782059i	$-0.714170\pi$
$577$	−719.179			−1.24641			−0.623205	+	0.782059i	$0.714170\pi$
$578$		0			0
$579$	−143.623			−0.248054
$580$		0			0
$581$	80.6626	+	80.6626i	0.138834	+	0.138834i
$582$		0			0
$583$	87.7030	+	87.7030i	0.150434	+	0.150434i
$584$		0			0
$585$	−84.8448	−	84.8448i	−0.145034	−	0.145034i
$586$		0			0
$587$			404.505i			0.689105i	0.938767	+	0.344553i	$0.111969\pi$
$587$			404.505i			0.689105i	−0.938767	+	0.344553i	$0.888031\pi$
$588$		0			0
$589$	475.507	−	475.507i	0.807312	−	0.807312i
$590$		0			0
$591$			175.952i			0.297720i
$592$		0			0
$593$		−	70.0150i		−	0.118069i	−0.998256	−	0.0590345i	$-0.981198\pi$
$593$		−	70.0150i		−	0.118069i	0.998256	−	0.0590345i	$-0.0188022\pi$
$594$		0			0
$595$	363.396	+	303.754i	0.610750	+	0.510511i
$596$		0			0
$597$	−181.655			−0.304279
$598$		0			0
$599$		−	935.940i		−	1.56250i	−0.624216	−	0.781252i	$-0.714581\pi$
$599$		−	935.940i		−	1.56250i	0.624216	−	0.781252i	$-0.285419\pi$
$600$		0			0
$601$	264.545	+	264.545i	0.440174	+	0.440174i	0.892071	−	0.451896i	$-0.149252\pi$
$601$	264.545	+	264.545i	0.440174	+	0.440174i	−0.451896	+	0.892071i	$0.649252\pi$
$602$		0			0
$603$			598.796i			0.993029i
$604$		0			0
$605$	388.314	−	388.314i	0.641841	−	0.641841i
$606$		0			0
$607$	66.1875	+	66.1875i	0.109040	+	0.109040i	0.759522	−	0.650482i	$-0.225433\pi$
$607$	66.1875	+	66.1875i	0.109040	+	0.109040i	−0.650482	+	0.759522i	$0.725433\pi$
$608$		0			0
$609$	−131.549	+	131.549i	−0.216008	+	0.216008i
$610$		0			0
$611$	−251.669			−0.411897
$612$		0			0
$613$		−	125.163i		−	0.204181i	−0.994775	−	0.102091i	$-0.967447\pi$
$613$		−	125.163i		−	0.204181i	0.994775	−	0.102091i	$-0.0325532\pi$
$614$		0			0
$615$	142.171	+	142.171i	0.231172	+	0.231172i
$616$		0			0
$617$	−387.365	+	387.365i	−0.627819	+	0.627819i	−0.947519	−	0.319700i	$-0.896418\pi$
$617$	−387.365	+	387.365i	−0.627819	+	0.627819i	0.319700	+	0.947519i	$0.396418\pi$
$618$		0			0
$619$	83.9355	+	83.9355i	0.135599	+	0.135599i	0.771648	−	0.636050i	$-0.219433\pi$
$619$	83.9355	+	83.9355i	0.135599	+	0.135599i	−0.636050	+	0.771648i	$0.719433\pi$
$620$		0			0
$621$	529.724			0.853018
$622$		0			0
$623$	446.708	−	446.708i	0.717027	−	0.717027i
$624$		0			0
$625$	650.420			1.04067
$626$		0			0
$627$			100.558i			0.160380i
$628$		0			0
$629$	1.57094	+	17.5724i	0.00249751	+	0.0279370i
$630$		0			0
$631$	−922.673			−1.46224			−0.731120	−	0.682249i	$-0.761002\pi$
$631$	−922.673			−1.46224			−0.731120	+	0.682249i	$0.761002\pi$
$632$		0			0
$633$	−23.6579			−0.0373743
$634$		0			0
$635$	62.1224	+	62.1224i	0.0978306	+	0.0978306i
$636$		0			0
$637$	−57.3382			−0.0900129
$638$		0			0
$639$	216.349	−	216.349i	0.338575	−	0.338575i
$640$		0			0
$641$	−15.7419	+	15.7419i	−0.0245583	+	0.0245583i	−0.719279	−	0.694721i	$-0.755528\pi$
$641$	−15.7419	+	15.7419i	−0.0245583	+	0.0245583i	0.694721	+	0.719279i	$0.255528\pi$
$642$		0			0
$643$	389.434	−	389.434i	0.605651	−	0.605651i	−0.336155	−	0.941807i	$-0.609127\pi$
$643$	389.434	−	389.434i	0.605651	−	0.605651i	0.941807	+	0.336155i	$0.109127\pi$
$644$		0			0
$645$			57.9925i			0.0899108i
$646$		0			0
$647$		−	550.318i		−	0.850568i	−0.905060	−	0.425284i	$-0.860174\pi$
$647$		−	550.318i		−	0.850568i	0.905060	−	0.425284i	$-0.139826\pi$
$648$		0			0
$649$	−181.281	+	181.281i	−0.279324	+	0.279324i
$650$		0			0
$651$	−106.176	+	106.176i	−0.163096	+	0.163096i
$652$		0			0
$653$	626.017	−	626.017i	0.958678	−	0.958678i	−0.0405016	−	0.999179i	$-0.512896\pi$
$653$	626.017	−	626.017i	0.958678	−	0.958678i	0.999179	+	0.0405016i	$0.0128956\pi$
$654$		0			0
$655$	815.450			1.24496
$656$		0			0
$657$	380.745	+	380.745i	0.579521	+	0.579521i
$658$		0			0
$659$	−1139.03			−1.72841			−0.864207	−	0.503136i	$-0.832180\pi$
$659$	−1139.03			−1.72841			−0.864207	+	0.503136i	$0.832180\pi$
$660$		0			0
$661$	−1263.02			−1.91077			−0.955386	−	0.295359i	$-0.904561\pi$
$661$	−1263.02			−1.91077			−0.955386	+	0.295359i	$0.904561\pi$
$662$		0			0
$663$	−4.78572	−	53.5328i	−0.00721828	−	0.0807433i
$664$		0			0
$665$		−	721.512i		−	1.08498i
$666$		0			0
$667$	−952.989			−1.42877
$668$		0			0
$669$	56.0058	−	56.0058i	0.0837157	−	0.0837157i
$670$		0			0
$671$	−341.199			−0.508494
$672$		0			0
$673$	−700.225	−	700.225i	−1.04045	−	1.04045i	−0.999147	−	0.0413059i	$-0.986848\pi$
$673$	−700.225	−	700.225i	−1.04045	−	1.04045i	−0.0413059	−	0.999147i	$-0.513152\pi$
$674$		0			0
$675$	13.4280	−	13.4280i	0.0198934	−	0.0198934i
$676$		0			0
$677$	−378.421	−	378.421i	−0.558967	−	0.558967i	0.370046	−	0.929013i	$-0.379342\pi$
$677$	−378.421	−	378.421i	−0.558967	−	0.558967i	−0.929013	+	0.370046i	$0.879342\pi$
$678$		0			0
$679$		−	513.632i		−	0.756453i
$680$		0			0
$681$	213.744			0.313868
$682$		0			0
$683$	400.345	−	400.345i	0.586156	−	0.586156i	−0.350432	−	0.936588i	$-0.613965\pi$
$683$	400.345	−	400.345i	0.586156	−	0.586156i	0.936588	+	0.350432i	$0.113965\pi$
$684$		0			0
$685$	−705.657	−	705.657i	−1.03016	−	1.03016i
$686$		0			0
$687$	196.458	−	196.458i	0.285965	−	0.285965i
$688$		0			0
$689$			100.987i			0.146571i
$690$		0			0
$691$	665.780	+	665.780i	0.963502	+	0.963502i	0.999357	−	0.0358553i	$-0.0114155\pi$
$691$	665.780	+	665.780i	0.963502	+	0.963502i	−0.0358553	+	0.999357i	$0.511416\pi$
$692$		0			0
$693$			157.538i			0.227327i
$694$		0			0
$695$	35.7398			0.0514242
$696$		0			0
$697$	−56.2643	−	629.369i	−0.0807236	−	0.902969i
$698$		0			0
$699$		−	91.1992i		−	0.130471i
$700$		0			0
$701$		−	92.7896i		−	0.132368i	−0.997807	−	0.0661838i	$-0.978918\pi$
$701$		−	92.7896i		−	0.132368i	0.997807	−	0.0661838i	$-0.0210824\pi$
$702$		0			0
$703$	19.0042	−	19.0042i	0.0270331	−	0.0270331i
$704$		0			0
$705$		−	456.256i		−	0.647172i
$706$		0			0
$707$	84.3988	+	84.3988i	0.119376	+	0.119376i
$708$		0			0
$709$	796.746	+	796.746i	1.12376	+	1.12376i	0.991171	+	0.132590i	$0.0423293\pi$
$709$	796.746	+	796.746i	1.12376	+	1.12376i	0.132590	+	0.991171i	$0.457671\pi$
$710$		0			0
$711$	−134.063	−	134.063i	−0.188555	−	0.188555i
$712$		0			0
$713$	−769.177			−1.07879
$714$		0			0
$715$	−55.8198			−0.0780697
$716$		0			0
$717$	−71.3173	−	71.3173i	−0.0994662	−	0.0994662i
$718$		0			0
$719$	171.227	+	171.227i	0.238146	+	0.238146i	0.816082	−	0.577936i	$-0.196142\pi$
$719$	171.227	+	171.227i	0.238146	+	0.238146i	−0.577936	+	0.816082i	$0.696142\pi$
$720$		0			0
$721$	−104.008	−	104.008i	−0.144255	−	0.144255i
$722$		0			0
$723$		−	176.796i		−	0.244532i
$724$		0			0
$725$	−24.1575	+	24.1575i	−0.0333206	+	0.0333206i
$726$		0			0
$727$		−	263.954i		−	0.363073i	−0.983384	−	0.181536i	$-0.941893\pi$
$727$		−	263.954i		−	0.363073i	0.983384	−	0.181536i	$-0.0581070\pi$
$728$		0			0
$729$		−	238.661i		−	0.327382i
$730$		0			0
$731$	116.887	−	139.837i	0.159900	−	0.191296i
$732$		0			0
$733$	−61.0527			−0.0832915			−0.0416457	−	0.999132i	$-0.513260\pi$
$733$	−61.0527			−0.0832915			−0.0416457	+	0.999132i	$0.513260\pi$
$734$		0			0
$735$		−	103.950i		−	0.141428i
$736$		0			0
$737$	196.975	+	196.975i	0.267267	+	0.267267i
$738$		0			0
$739$			437.344i			0.591805i	0.955218	+	0.295903i	$0.0956204\pi$
$739$			437.344i			0.591805i	−0.955218	+	0.295903i	$0.904380\pi$
$740$		0			0
$741$	−57.8948	+	57.8948i	−0.0781306	+	0.0781306i
$742$		0			0
$743$	598.705	+	598.705i	0.805794	+	0.805794i	0.983994	−	0.178200i	$-0.0570275\pi$
$743$	598.705	+	598.705i	0.805794	+	0.805794i	−0.178200	+	0.983994i	$0.557028\pi$
$744$		0			0
$745$	124.770	−	124.770i	0.167477	−	0.167477i
$746$		0			0
$747$	−164.656			−0.220423
$748$		0			0
$749$			540.116i			0.721116i
$750$		0			0
$751$	146.723	+	146.723i	0.195370	+	0.195370i	0.798012	−	0.602642i	$-0.205885\pi$
$751$	146.723	+	146.723i	0.195370	+	0.195370i	−0.602642	+	0.798012i	$0.705885\pi$
$752$		0			0
$753$	98.7670	−	98.7670i	0.131165	−	0.131165i
$754$		0			0
$755$	−549.946	−	549.946i	−0.728405	−	0.728405i
$756$		0			0
$757$	96.4029			0.127349			0.0636743	−	0.997971i	$-0.479718\pi$
$757$	96.4029			0.127349			0.0636743	+	0.997971i	$0.479718\pi$
$758$		0			0
$759$	81.3310	−	81.3310i	0.107155	−	0.107155i
$760$		0			0
$761$	−256.811			−0.337466			−0.168733	−	0.985662i	$-0.553968\pi$
$761$	−256.811			−0.337466			−0.168733	+	0.985662i	$0.553968\pi$
$762$		0			0
$763$		−	206.533i		−	0.270686i
$764$		0			0
$765$	−680.925	+	60.8733i	−0.890098	+	0.0795730i
$766$		0			0
$767$	−208.740			−0.272151
$768$		0			0
$769$	439.409			0.571403			0.285702	−	0.958319i	$-0.407773\pi$
$769$	439.409			0.571403			0.285702	+	0.958319i	$0.407773\pi$
$770$		0			0
$771$	256.772	+	256.772i	0.333037	+	0.333037i
$772$		0			0
$773$	961.024			1.24324			0.621619	−	0.783319i	$-0.286475\pi$
$773$	961.024			1.24324			0.621619	+	0.783319i	$0.286475\pi$
$774$		0			0
$775$	−19.4980	+	19.4980i	−0.0251587	+	0.0251587i
$776$		0			0
$777$	−4.24344	+	4.24344i	−0.00546132	+	0.00546132i
$778$		0			0
$779$	−680.652	+	680.652i	−0.873751	+	0.873751i
$780$		0			0
$781$		−	142.337i		−	0.182250i
$782$		0			0
$783$		−	575.332i		−	0.734779i
$784$		0			0
$785$	1039.12	−	1039.12i	1.32372	−	1.32372i
$786$		0			0
$787$	198.734	−	198.734i	0.252521	−	0.252521i	−0.569483	−	0.822003i	$-0.692856\pi$
$787$	198.734	−	198.734i	0.252521	−	0.252521i	0.822003	+	0.569483i	$0.192856\pi$
$788$		0			0
$789$	−370.501	+	370.501i	−0.469582	+	0.469582i
$790$		0			0
$791$	−801.844			−1.01371
$792$		0			0
$793$	−196.440	−	196.440i	−0.247718	−	0.247718i
$794$		0			0
$795$	−183.082			−0.230292
$796$		0			0
$797$	−987.969			−1.23961			−0.619805	−	0.784756i	$-0.712788\pi$
$797$	−987.969			−1.23961			−0.619805	+	0.784756i	$0.712788\pi$
$798$		0			0
$799$	−919.606	+	1100.17i	−1.15095	+	1.37693i
$800$		0			0
$801$			911.862i			1.13840i
$802$		0			0
$803$	250.494			0.311948
$804$		0			0
$805$	−583.556	+	583.556i	−0.724915	+	0.724915i
$806$		0			0
$807$	−175.027			−0.216886
$808$		0			0
$809$	407.336	+	407.336i	0.503506	+	0.503506i	0.912526	−	0.409020i	$-0.134129\pi$
$809$	407.336	+	407.336i	0.503506	+	0.503506i	−0.409020	+	0.912526i	$0.634129\pi$
$810$		0			0
$811$	38.6417	−	38.6417i	0.0476469	−	0.0476469i	−0.682882	−	0.730529i	$-0.739274\pi$
$811$	38.6417	−	38.6417i	0.0476469	−	0.0476469i	0.730529	+	0.682882i	$0.239274\pi$
$812$		0			0
$813$	180.714	+	180.714i	0.222281	+	0.222281i
$814$		0			0
$815$		−	1442.58i		−	1.77004i
$816$		0			0
$817$	−277.643			−0.339832
$818$		0			0
$819$	−90.7000	+	90.7000i	−0.110745	+	0.110745i
$820$		0			0
$821$	−39.8813	−	39.8813i	−0.0485765	−	0.0485765i	0.682401	−	0.730978i	$-0.260936\pi$
$821$	−39.8813	−	39.8813i	−0.0485765	−	0.0485765i	−0.730978	+	0.682401i	$0.760936\pi$
$822$		0			0
$823$	1118.37	−	1118.37i	1.35889	−	1.35889i	0.483604	−	0.875287i	$-0.339327\pi$
$823$	1118.37	−	1118.37i	1.35889	−	1.35889i	0.875287	−	0.483604i	$-0.160673\pi$
$824$		0			0
$825$		−	4.12334i		−	0.00499799i
$826$		0			0
$827$	350.629	+	350.629i	0.423976	+	0.423976i	0.886570	−	0.462594i	$-0.153081\pi$
$827$	350.629	+	350.629i	0.423976	+	0.423976i	−0.462594	+	0.886570i	$0.653081\pi$
$828$		0			0
$829$			470.897i			0.568030i	0.958820	+	0.284015i	$0.0916665\pi$
$829$			470.897i			0.568030i	−0.958820	+	0.284015i	$0.908333\pi$
$830$		0			0
$831$	−510.608			−0.614451
$832$		0			0
$833$	−209.516	+	250.654i	−0.251520	+	0.300905i
$834$		0			0
$835$		−	571.112i		−	0.683967i
$836$		0			0
$837$		−	464.362i		−	0.554793i
$838$		0			0
$839$	−1145.65	+	1145.65i	−1.36549	+	1.36549i	−0.498747	+	0.866748i	$0.666206\pi$
$839$	−1145.65	+	1145.65i	−1.36549	+	1.36549i	−0.866748	+	0.498747i	$0.833794\pi$
$840$		0			0
$841$			194.040i			0.230726i
$842$		0			0
$843$	321.054	+	321.054i	0.380847	+	0.380847i
$844$		0			0
$845$	577.926	+	577.926i	0.683936	+	0.683936i
$846$		0			0
$847$	−415.112	−	415.112i	−0.490096	−	0.490096i
$848$		0			0
$849$	83.5732			0.0984373
$850$		0			0
$851$	−30.7411			−0.0361235
$852$		0			0
$853$	161.359	+	161.359i	0.189167	+	0.189167i	0.795336	−	0.606169i	$-0.207294\pi$
$853$	161.359	+	161.359i	0.189167	+	0.189167i	−0.606169	+	0.795336i	$0.707294\pi$
$854$		0			0
$855$	736.409	+	736.409i	0.861297	+	0.861297i
$856$		0			0
$857$	−248.656	−	248.656i	−0.290147	−	0.290147i	0.546991	−	0.837138i	$-0.315773\pi$
$857$	−248.656	−	248.656i	−0.290147	−	0.290147i	−0.837138	+	0.546991i	$0.815773\pi$
$858$		0			0
$859$		−	369.325i		−	0.429947i	−0.976620	−	0.214974i	$-0.931033\pi$
$859$		−	369.325i		−	0.429947i	0.976620	−	0.214974i	$-0.0689665\pi$
$860$		0			0
$861$	151.982	−	151.982i	0.176518	−	0.176518i
$862$		0			0
$863$			1657.91i			1.92110i	0.278107	+	0.960550i	$0.410293\pi$
$863$			1657.91i			1.92110i	−0.278107	+	0.960550i	$0.589707\pi$
$864$		0			0
$865$			1678.72i			1.94071i
$866$		0			0
$867$	−251.506	−	174.690i	−0.290087	−	0.201488i
$868$		0			0
$869$	−88.2005			−0.101497
$870$		0			0
$871$			226.811i			0.260404i
$872$		0			0
$873$	524.237	+	524.237i	0.600500	+	0.600500i
$874$		0			0
$875$		−	666.926i		−	0.762201i
$876$		0			0
$877$	262.995	−	262.995i	0.299881	−	0.299881i	−0.541086	−	0.840967i	$-0.681987\pi$
$877$	262.995	−	262.995i	0.299881	−	0.299881i	0.840967	+	0.541086i	$0.181987\pi$
$878$		0			0
$879$	257.438	+	257.438i	0.292876	+	0.292876i
$880$		0			0
$881$	−692.939	+	692.939i	−0.786537	+	0.786537i	−0.980925	−	0.194388i	$-0.937728\pi$
$881$	−692.939	+	692.939i	−0.786537	+	0.786537i	0.194388	+	0.980925i	$0.437728\pi$
$882$		0			0
$883$	654.812			0.741577			0.370788	−	0.928717i	$-0.379088\pi$
$883$	654.812			0.741577			0.370788	+	0.928717i	$0.379088\pi$
$884$		0			0
$885$		−	378.430i		−	0.427604i
$886$		0			0
$887$	1025.67	+	1025.67i	1.15634	+	1.15634i	0.985256	+	0.171085i	$0.0547273\pi$
$887$	1025.67	+	1025.67i	1.15634	+	1.15634i	0.171085	+	0.985256i	$0.445273\pi$
$888$		0			0
$889$	66.4095	−	66.4095i	0.0747014	−	0.0747014i
$890$		0			0
$891$	−134.607	−	134.607i	−0.151074	−	0.151074i
$892$		0			0
$893$	2184.36			2.44609
$894$		0			0
$895$	777.336	−	777.336i	0.868532	−	0.868532i
$896$		0			0
$897$	93.6502			0.104404
$898$		0			0
$899$			835.401i			0.929256i
$900$		0			0
$901$	441.467	+	369.011i	0.489974	+	0.409558i
$902$		0			0
$903$	61.9946			0.0686540
$904$		0			0
$905$	615.627			0.680251
$906$		0			0
$907$	63.4688	+	63.4688i	0.0699766	+	0.0699766i	0.741229	−	0.671252i	$-0.234243\pi$
$907$	63.4688	+	63.4688i	0.0699766	+	0.0699766i	−0.671252	+	0.741229i	$0.734243\pi$
$908$		0			0
$909$	−172.283			−0.189530
$910$		0			0
$911$	−949.166	+	949.166i	−1.04189	+	1.04189i	−0.0428112	+	0.999083i	$0.513631\pi$
$911$	−949.166	+	949.166i	−1.04189	+	1.04189i	−0.999083	+	0.0428112i	$0.986369\pi$
$912$		0			0
$913$	−54.1640	+	54.1640i	−0.0593253	+	0.0593253i
$914$		0			0
$915$	356.131	−	356.131i	0.389215	−	0.389215i
$916$		0			0
$917$		−	871.725i		−	0.950627i
$918$		0			0
$919$			1082.82i			1.17826i	0.808040	+	0.589128i	$0.200529\pi$
$919$			1082.82i			1.17826i	−0.808040	+	0.589128i	$0.799471\pi$
$920$		0			0
$921$	−75.6452	+	75.6452i	−0.0821338	+	0.0821338i
$922$		0			0
$923$	81.9486	−	81.9486i	0.0887850	−	0.0887850i
$924$		0			0
$925$	−0.779261	+	0.779261i	−0.000842444	+	0.000842444i
$926$		0			0
$927$	212.311			0.229030
$928$		0			0
$929$	−517.649	−	517.649i	−0.557211	−	0.557211i	0.371301	−	0.928513i	$-0.378912\pi$
$929$	−517.649	−	517.649i	−0.557211	−	0.557211i	−0.928513	+	0.371301i	$0.878912\pi$
$930$		0			0
$931$	497.666			0.534550
$932$		0			0
$933$	−54.0949			−0.0579796
$934$		0			0
$935$	−203.967	+	244.016i	−0.218147	+	0.260980i
$936$		0			0
$937$			1102.17i			1.17627i	0.808762	+	0.588137i	$0.200138\pi$
$937$			1102.17i			1.17627i	−0.808762	+	0.588137i	$0.799862\pi$
$938$		0			0
$939$	310.762			0.330950
$940$		0			0
$941$	−917.863	+	917.863i	−0.975412	+	0.975412i	−0.999705	−	0.0242925i	$-0.992267\pi$
$941$	−917.863	+	917.863i	−0.975412	+	0.975412i	0.0242925	+	0.999705i	$0.492267\pi$
$942$		0			0
$943$	1101.02			1.16757
$944$		0			0
$945$	−352.301	−	352.301i	−0.372805	−	0.372805i
$946$		0			0
$947$	356.250	−	356.250i	0.376188	−	0.376188i	−0.493537	−	0.869725i	$-0.664296\pi$
$947$	356.250	−	356.250i	0.376188	−	0.376188i	0.869725	+	0.493537i	$0.164296\pi$
$948$		0			0
$949$	144.218	+	144.218i	0.151969	+	0.151969i
$950$		0			0
$951$			136.678i			0.143720i
$952$		0			0
$953$	195.343			0.204977			0.102489	−	0.994734i	$-0.467319\pi$
$953$	195.343			0.204977			0.102489	+	0.994734i	$0.467319\pi$
$954$		0			0
$955$	769.765	−	769.765i	0.806036	−	0.806036i
$956$		0			0
$957$	−88.3334	−	88.3334i	−0.0923025	−	0.0923025i
$958$		0			0
$959$	−754.355	+	754.355i	−0.786605	+	0.786605i
$960$		0			0
$961$		−	286.731i		−	0.298367i
$962$		0			0
$963$	−551.268	−	551.268i	−0.572448	−	0.572448i
$964$		0			0
$965$			691.975i			0.717073i
$966$		0			0
$967$	−1170.65			−1.21060			−0.605299	−	0.795998i	$-0.706947\pi$
$967$	−1170.65			−1.21060			−0.605299	+	0.795998i	$0.706947\pi$
$968$		0			0
$969$	41.5376	+	464.637i	0.0428664	+	0.479501i
$970$		0			0
$971$		−	1519.02i		−	1.56438i	−0.623037	−	0.782192i	$-0.714101\pi$
$971$		−	1519.02i		−	1.56438i	0.623037	−	0.782192i	$-0.285899\pi$
$972$		0			0
$973$		−	38.2062i		−	0.0392664i
$974$		0			0
$975$	2.37395	−	2.37395i	0.00243482	−	0.00243482i
$976$		0			0
$977$		−	109.675i		−	0.112257i	−0.998424	−	0.0561283i	$-0.982124\pi$
$977$		−	109.675i		−	0.112257i	0.998424	−	0.0561283i	$-0.0178756\pi$
$978$		0			0
$979$	299.959	+	299.959i	0.306393	+	0.306393i
$980$		0			0
$981$	210.798	+	210.798i	0.214880	+	0.214880i
$982$		0			0
$983$	−176.945	−	176.945i	−0.180005	−	0.180005i	0.611353	−	0.791358i	$-0.290626\pi$
$983$	−176.945	−	176.945i	−0.180005	−	0.180005i	−0.791358	+	0.611353i	$0.790626\pi$
$984$		0			0
$985$	847.736			0.860645
$986$		0			0
$987$	−487.743			−0.494167
$988$		0			0
$989$	224.556	+	224.556i	0.227054	+	0.227054i
$990$		0			0
$991$	−478.714	−	478.714i	−0.483062	−	0.483062i	0.423046	−	0.906108i	$-0.360961\pi$
$991$	−478.714	−	478.714i	−0.483062	−	0.483062i	−0.906108	+	0.423046i	$0.860961\pi$
$992$		0			0
$993$	−199.195	−	199.195i	−0.200599	−	0.200599i
$994$		0			0
$995$			875.209i			0.879607i
$996$		0			0
$997$	−231.688	+	231.688i	−0.232385	+	0.232385i	−0.813687	−	0.581303i	$-0.802543\pi$
$997$	−231.688	+	231.688i	−0.232385	+	0.232385i	0.581303	+	0.813687i	$0.302543\pi$
$998$		0			0
$999$		−	18.5588i		−	0.0185774i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	544.3.n.b.463.13		64
4.3	odd	2		136.3.j.b.123.2	yes	64
8.3	odd	2	inner	544.3.n.b.463.14		64
8.5	even	2		136.3.j.b.123.31	yes	64
17.13	even	4	inner	544.3.n.b.47.14		64
68.47	odd	4		136.3.j.b.115.31	yes	64
136.13	even	4		136.3.j.b.115.2	✓	64
136.115	odd	4	inner	544.3.n.b.47.13		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.3.j.b.115.2	✓	64	136.13	even	4
136.3.j.b.115.31	yes	64	68.47	odd	4
136.3.j.b.123.2	yes	64	4.3	odd	2
136.3.j.b.123.31	yes	64	8.5	even	2
544.3.n.b.47.13		64	136.115	odd	4	inner
544.3.n.b.47.14		64	17.13	even	4	inner
544.3.n.b.463.13		64	1.1	even	1	trivial
544.3.n.b.463.14		64	8.3	odd	2	inner

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:	\( N \)	\(=\)	\( 544 = 2^{5} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	544.n (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.749243 + 0.749243i) q^{3} +(3.60984 + 3.60984i) q^{5} +(3.85896 - 3.85896i) q^{7} +7.87727i q^{9} +O(q^{10})\)	\(q+(-0.749243 + 0.749243i) q^{3} +(3.60984 + 3.60984i) q^{5} +(3.85896 - 3.85896i) q^{7} +7.87727i q^{9} +(2.59125 + 2.59125i) q^{11} +2.98374i q^{13} -5.40930 q^{15} +(13.0434 + 10.9027i) q^{17} -25.8973i q^{19} +5.78260i q^{21} +(-20.9457 + 20.9457i) q^{23} +1.06191i q^{25} +(-12.6452 - 12.6452i) q^{27} +(22.7491 + 22.7491i) q^{29} +(18.3612 + 18.3612i) q^{31} -3.88295 q^{33} +27.8605 q^{35} +(0.733830 + 0.733830i) q^{37} +(-2.23555 - 2.23555i) q^{39} +(-26.2827 - 26.2827i) q^{41} -10.7209i q^{43} +(-28.4357 + 28.4357i) q^{45} +84.3467i q^{47} +19.2169i q^{49} +(-17.9415 + 1.60393i) q^{51} +33.8459 q^{53} +18.7080i q^{55} +(19.4034 + 19.4034i) q^{57} +69.9591i q^{59} +(-65.8369 + 65.8369i) q^{61} +(30.3981 + 30.3981i) q^{63} +(-10.7708 + 10.7708i) q^{65} +76.0157 q^{67} -31.3868i q^{69} +(-27.4650 - 27.4650i) q^{71} +(48.3347 - 48.3347i) q^{73} +(-0.795629 - 0.795629i) q^{75} +19.9990 q^{77} +(-17.0189 + 17.0189i) q^{79} -51.9468 q^{81} +20.9027i q^{83} +(7.72772 + 86.4417i) q^{85} -34.0892 q^{87} +115.759 q^{89} +(11.5141 + 11.5141i) q^{91} -27.5140 q^{93} +(93.4853 - 93.4853i) q^{95} +(66.5506 - 66.5506i) q^{97} +(-20.4119 + 20.4119i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 8 q^{3}+O(q^{10}) \) 64 * q + 8 * q^3	\( 64 q + 8 q^{3} + 32 q^{11} - 12 q^{17} - 160 q^{27} + 128 q^{33} + 8 q^{35} - 88 q^{41} + 360 q^{51} - 24 q^{57} + 112 q^{65} + 8 q^{67} - 408 q^{73} - 32 q^{75} + 80 q^{81} - 8 q^{89} - 384 q^{91} + 112 q^{97} - 416 q^{99}+O(q^{100}) \) 64 * q + 8 * q^3 + 32 * q^11 - 12 * q^17 - 160 * q^27 + 128 * q^33 + 8 * q^35 - 88 * q^41 + 360 * q^51 - 24 * q^57 + 112 * q^65 + 8 * q^67 - 408 * q^73 - 32 * q^75 + 80 * q^81 - 8 * q^89 - 384 * q^91 + 112 * q^97 - 416 * q^99

Introduction

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