LMFDB - Embedded newform 1617.2.c.a.538.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1617,2,Mod(538,1617)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1617, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1617.538");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1617 = 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1617.c (of order $2$, degree $1$, 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:	$12.9118100068$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 231)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			538.15
Character	$\chi$	$=$	1617.538
Dual form			1617.2.c.a.538.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.416420i q^{2} -1.00000i q^{3} +1.82659 q^{4} -0.478282i q^{5} -0.416420 q^{6} -1.59347i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-0.416420i q^{2} -1.00000i q^{3} +1.82659 q^{4} -0.478282i q^{5} -0.416420 q^{6} -1.59347i q^{8} -1.00000 q^{9} -0.199166 q^{10} +(3.17784 + 0.949389i) q^{11} -1.82659i q^{12} +5.34126 q^{13} -0.478282 q^{15} +2.98963 q^{16} -0.246351 q^{17} +0.416420i q^{18} -4.04145 q^{19} -0.873627i q^{20} +(0.395345 - 1.32332i) q^{22} +1.08082 q^{23} -1.59347 q^{24} +4.77125 q^{25} -2.22421i q^{26} +1.00000i q^{27} +9.25276i q^{29} +0.199166i q^{30} -1.16123i q^{31} -4.43189i q^{32} +(0.949389 - 3.17784i) q^{33} +0.102586i q^{34} -1.82659 q^{36} +4.46928 q^{37} +1.68294i q^{38} -5.34126i q^{39} -0.762129 q^{40} -9.10753 q^{41} -2.69865i q^{43} +(5.80462 + 1.73415i) q^{44} +0.478282i q^{45} -0.450074i q^{46} -7.86658i q^{47} -2.98963i q^{48} -1.98684i q^{50} +0.246351i q^{51} +9.75630 q^{52} -0.485505 q^{53} +0.416420 q^{54} +(0.454076 - 1.51990i) q^{55} +4.04145i q^{57} +3.85304 q^{58} -1.10775i q^{59} -0.873627 q^{60} +5.33908 q^{61} -0.483558 q^{62} +4.13374 q^{64} -2.55463i q^{65} +(-1.32332 - 0.395345i) q^{66} +3.05861 q^{67} -0.449984 q^{68} -1.08082i q^{69} -11.9831 q^{71} +1.59347i q^{72} -7.88650 q^{73} -1.86110i q^{74} -4.77125i q^{75} -7.38209 q^{76} -2.22421 q^{78} -14.2786i q^{79} -1.42989i q^{80} +1.00000 q^{81} +3.79256i q^{82} +13.3453 q^{83} +0.117825i q^{85} -1.12377 q^{86} +9.25276 q^{87} +(1.51283 - 5.06380i) q^{88} -13.8401i q^{89} +0.199166 q^{90} +1.97421 q^{92} -1.16123 q^{93} -3.27580 q^{94} +1.93295i q^{95} -4.43189 q^{96} +8.20328i q^{97} +(-3.17784 - 0.949389i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 24 q^{4} - 32 q^{9}+O(q^{10}) $ 32 * q - 24 * q^4 - 32 * q^9	$ 32 q - 24 q^{4} - 32 q^{9} - 4 q^{11} + 8 q^{15} + 40 q^{16} + 8 q^{22} - 48 q^{23} + 24 q^{36} + 64 q^{37} + 56 q^{44} - 72 q^{53} - 24 q^{58} + 8 q^{64} - 40 q^{67} + 72 q^{71} - 48 q^{78} + 32 q^{81} - 128 q^{86} - 48 q^{88} - 16 q^{92} - 32 q^{93} + 4 q^{99}+O(q^{100}) $ 32 * q - 24 * q^4 - 32 * q^9 - 4 * q^11 + 8 * q^15 + 40 * q^16 + 8 * q^22 - 48 * q^23 + 24 * q^36 + 64 * q^37 + 56 * q^44 - 72 * q^53 - 24 * q^58 + 8 * q^64 - 40 * q^67 + 72 * q^71 - 48 * q^78 + 32 * q^81 - 128 * q^86 - 48 * q^88 - 16 * q^92 - 32 * q^93 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1617\mathbb{Z}\right)^\times$.

$n$	$199$	$442$	$1079$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$		−	0.416420i		−	0.294454i	−0.989103	−	0.147227i	$-0.952965\pi$
$2$		−	0.416420i		−	0.294454i	0.989103	−	0.147227i	$-0.0470347\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.82659			0.913297
$5$		−	0.478282i		−	0.213894i	−0.994265	−	0.106947i	$-0.965892\pi$
$5$		−	0.478282i		−	0.213894i	0.994265	−	0.106947i	$-0.0341076\pi$
$6$	−0.416420			−0.170003
$7$		0			0
$7$		0			0
$8$		−	1.59347i		−	0.563377i
$9$	−1.00000			−0.333333
$10$	−0.199166			−0.0629819
$11$	3.17784	+	0.949389i	0.958154	+	0.286252i
$11$	3.17784	+	0.949389i	0.958154	+	0.286252i
$12$		−	1.82659i		−	0.527292i
$13$	5.34126			1.48140			0.740699	−	0.671837i	$-0.234495\pi$
$13$	5.34126			1.48140			0.740699	+	0.671837i	$0.234495\pi$
$14$		0			0
$15$	−0.478282			−0.123492
$16$	2.98963			0.747408
$17$	−0.246351			−0.0597490			−0.0298745	−	0.999554i	$-0.509511\pi$
$17$	−0.246351			−0.0597490			−0.0298745	+	0.999554i	$0.509511\pi$
$18$			0.416420i			0.0981512i
$19$	−4.04145			−0.927173			−0.463586	−	0.886052i	$-0.653438\pi$
$19$	−4.04145			−0.927173			−0.463586	+	0.886052i	$0.653438\pi$
$20$		−	0.873627i		−	0.195349i
$21$		0			0
$22$	0.395345	−	1.32332i	0.0842879	−	0.282132i
$23$	1.08082			0.225366			0.112683	−	0.993631i	$-0.464056\pi$
$23$	1.08082			0.225366			0.112683	+	0.993631i	$0.464056\pi$
$24$	−1.59347			−0.325266
$25$	4.77125			0.954249
$26$		−	2.22421i		−	0.436203i
$27$			1.00000i			0.192450i
$28$		0			0
$29$			9.25276i			1.71819i	0.511812	+	0.859097i	$0.328974\pi$
$29$			9.25276i			1.71819i	−0.511812	+	0.859097i	$0.671026\pi$
$30$			0.199166i			0.0363626i
$31$		−	1.16123i		−	0.208562i	−0.994548	−	0.104281i	$-0.966746\pi$
$31$		−	1.16123i		−	0.208562i	0.994548	−	0.104281i	$-0.0332542\pi$
$32$		−	4.43189i		−	0.783455i
$33$	0.949389	−	3.17784i	0.165267	−	0.553191i
$34$			0.102586i			0.0175933i
$35$		0			0
$36$	−1.82659			−0.304432
$37$	4.46928			0.734745			0.367372	−	0.930074i	$-0.380258\pi$
$37$	4.46928			0.734745			0.367372	+	0.930074i	$0.380258\pi$
$38$			1.68294i			0.273009i
$39$		−	5.34126i		−	0.855285i
$40$	−0.762129			−0.120503
$41$	−9.10753			−1.42236			−0.711179	−	0.703011i	$-0.751838\pi$
$41$	−9.10753			−1.42236			−0.711179	+	0.703011i	$0.751838\pi$
$42$		0			0
$43$		−	2.69865i		−	0.411540i	−0.978600	−	0.205770i	$-0.934030\pi$
$43$		−	2.69865i		−	0.411540i	0.978600	−	0.205770i	$-0.0659699\pi$
$44$	5.80462	+	1.73415i	0.875080	+	0.261433i
$45$			0.478282i			0.0712981i
$46$		−	0.450074i		−	0.0663598i
$47$		−	7.86658i		−	1.14746i	−0.819045	−	0.573729i	$-0.805496\pi$
$47$		−	7.86658i		−	1.14746i	0.819045	−	0.573729i	$-0.194504\pi$
$48$		−	2.98963i		−	0.431516i
$49$		0			0
$50$		−	1.98684i		−	0.280982i
$51$			0.246351i			0.0344961i
$52$	9.75630			1.35296
$53$	−0.485505			−0.0666892			−0.0333446	−	0.999444i	$-0.510616\pi$
$53$	−0.485505			−0.0666892			−0.0333446	+	0.999444i	$0.510616\pi$
$54$	0.416420			0.0566676
$55$	0.454076	−	1.51990i	0.0612276	−	0.204944i
$56$		0			0
$57$			4.04145i			0.535303i
$58$	3.85304			0.505929
$59$		−	1.10775i		−	0.144216i	−0.997397	−	0.0721082i	$-0.977027\pi$
$59$		−	1.10775i		−	0.144216i	0.997397	−	0.0721082i	$-0.0229727\pi$
$60$	−0.873627			−0.112785
$61$	5.33908			0.683599			0.341799	−	0.939773i	$-0.388964\pi$
$61$	5.33908			0.683599			0.341799	+	0.939773i	$0.388964\pi$
$62$	−0.483558			−0.0614119
$63$		0			0
$64$	4.13374			0.516717
$65$		−	2.55463i		−	0.316862i
$66$	−1.32332	−	0.395345i	−0.162889	−	0.0486636i
$67$	3.05861			0.373668			0.186834	−	0.982391i	$-0.440177\pi$
$67$	3.05861			0.373668			0.186834	+	0.982391i	$0.440177\pi$
$68$	−0.449984			−0.0545685
$69$		−	1.08082i		−	0.130115i
$70$		0			0
$71$	−11.9831			−1.42213			−0.711065	−	0.703126i	$-0.751787\pi$
$71$	−11.9831			−1.42213			−0.711065	+	0.703126i	$0.751787\pi$
$72$			1.59347i			0.187792i
$73$	−7.88650			−0.923045			−0.461522	−	0.887129i	$-0.652697\pi$
$73$	−7.88650			−0.923045			−0.461522	+	0.887129i	$0.652697\pi$
$74$		−	1.86110i		−	0.216348i
$75$		−	4.77125i		−	0.550936i
$76$	−7.38209			−0.846784
$77$		0			0
$78$	−2.22421			−0.251842
$79$		−	14.2786i		−	1.60646i	−0.595666	−	0.803232i	$-0.703112\pi$
$79$		−	14.2786i		−	1.60646i	0.595666	−	0.803232i	$-0.296888\pi$
$80$		−	1.42989i		−	0.159866i
$81$	1.00000			0.111111
$82$			3.79256i			0.418818i
$83$	13.3453			1.46484			0.732419	−	0.680854i	$-0.238391\pi$
$83$	13.3453			1.46484			0.732419	+	0.680854i	$0.238391\pi$
$84$		0			0
$85$			0.117825i			0.0127800i
$86$	−1.12377			−0.121179
$87$	9.25276			0.992000
$88$	1.51283	−	5.06380i	0.161268	−	0.539803i
$89$		−	13.8401i		−	1.46705i	−0.679661	−	0.733526i	$-0.737873\pi$
$89$		−	13.8401i		−	1.46705i	0.679661	−	0.733526i	$-0.262127\pi$
$90$	0.199166			0.0209940
$91$		0			0
$92$	1.97421			0.205826
$93$	−1.16123			−0.120413
$94$	−3.27580			−0.337873
$95$			1.93295i			0.198317i
$96$	−4.43189			−0.452328
$97$			8.20328i			0.832917i	0.909155	+	0.416459i	$0.136729\pi$
$97$			8.20328i			0.832917i	−0.909155	+	0.416459i	$0.863271\pi$
$98$		0			0
$99$	−3.17784	−	0.949389i	−0.319385	−	0.0954172i
$100$	8.71513			0.871513
$101$	−10.0094			−0.995969			−0.497985	−	0.867186i	$-0.665926\pi$
$101$	−10.0094			−0.995969			−0.497985	+	0.867186i	$0.665926\pi$
$102$	0.102586			0.0101575
$103$			10.2803i			1.01295i	0.862256	+	0.506473i	$0.169051\pi$
$103$			10.2803i			1.01295i	−0.862256	+	0.506473i	$0.830949\pi$
$104$		−	8.51114i		−	0.834586i
$105$		0			0
$106$			0.202174i			0.0196369i
$107$			16.6319i			1.60787i	0.594717	+	0.803935i	$0.297264\pi$
$107$			16.6319i			1.60787i	−0.594717	+	0.803935i	$0.702736\pi$
$108$			1.82659i			0.175764i
$109$			6.33706i			0.606981i	0.952835	+	0.303490i	$0.0981520\pi$
$109$			6.33706i			0.606981i	−0.952835	+	0.303490i	$0.901848\pi$
$110$	−0.632919	−	0.189086i	−0.0603464	−	0.0180287i
$111$		−	4.46928i		−	0.424205i
$112$		0			0
$113$	−13.7254			−1.29118			−0.645590	−	0.763684i	$-0.723389\pi$
$113$	−13.7254			−1.29118			−0.645590	+	0.763684i	$0.723389\pi$
$114$	1.68294			0.157622
$115$		−	0.516935i		−	0.0482045i
$116$			16.9010i			1.56922i
$117$	−5.34126			−0.493799
$118$	−0.461289			−0.0424651
$119$		0			0
$120$			0.762129i			0.0695725i
$121$	9.19732	+	6.03401i	0.836120	+	0.548547i
$122$		−	2.22330i		−	0.201288i
$123$			9.10753i			0.821198i
$124$		−	2.12109i		−	0.190479i
$125$		−	4.67341i		−	0.418003i
$126$		0			0
$127$		−	0.464814i		−	0.0412456i	−0.999787	−	0.0206228i	$-0.993435\pi$
$127$		−	0.464814i		−	0.0412456i	0.999787	−	0.0206228i	$-0.00656490\pi$
$128$		−	10.5852i		−	0.935604i
$129$	−2.69865			−0.237603
$130$	−1.06380			−0.0933013
$131$	−14.3240			−1.25150			−0.625749	−	0.780025i	$-0.715206\pi$
$131$	−14.3240			−1.25150			−0.625749	+	0.780025i	$0.715206\pi$
$132$	1.73415	−	5.80462i	0.150938	−	0.505227i
$133$		0			0
$134$		−	1.27367i		−	0.110028i
$135$	0.478282			0.0411640
$136$			0.392554i			0.0336612i
$137$	−3.22837			−0.275818			−0.137909	−	0.990445i	$-0.544038\pi$
$137$	−3.22837			−0.275818			−0.137909	+	0.990445i	$0.544038\pi$
$138$	−0.450074			−0.0383129
$139$	6.06911			0.514775			0.257388	−	0.966308i	$-0.417138\pi$
$139$	6.06911			0.514775			0.257388	+	0.966308i	$0.417138\pi$
$140$		0			0
$141$	−7.86658			−0.662485
$142$			4.99000i			0.418751i
$143$	16.9736	+	5.07093i	1.41941	+	0.424052i
$144$	−2.98963			−0.249136
$145$	4.42543			0.367512
$146$			3.28410i			0.271794i
$147$		0			0
$148$	8.16355			0.671040
$149$		−	16.1597i		−	1.32386i	−0.749566	−	0.661929i	$-0.769738\pi$
$149$		−	16.1597i		−	1.32386i	0.749566	−	0.661929i	$-0.230262\pi$
$150$	−1.98684			−0.162225
$151$		−	10.2785i		−	0.836455i	−0.908342	−	0.418228i	$-0.862651\pi$
$151$		−	10.2785i		−	0.836455i	0.908342	−	0.418228i	$-0.137349\pi$
$152$			6.43994i			0.522348i
$153$	0.246351			0.0199163
$154$		0			0
$155$	−0.555393			−0.0446102
$156$		−	9.75630i		−	0.781130i
$157$		−	3.58113i		−	0.285805i	−0.989737	−	0.142903i	$-0.954356\pi$
$157$		−	3.58113i		−	0.285805i	0.989737	−	0.142903i	$-0.0456436\pi$
$158$	−5.94589			−0.473030
$159$			0.485505i			0.0385031i
$160$	−2.11969			−0.167576
$161$		0			0
$162$		−	0.416420i		−	0.0327171i
$163$	−15.0019			−1.17504			−0.587518	−	0.809211i	$-0.699895\pi$
$163$	−15.0019			−1.17504			−0.587518	+	0.809211i	$0.699895\pi$
$164$	−16.6358			−1.29903
$165$	−1.51990	−	0.454076i	−0.118324	−	0.0353498i
$166$		−	5.55726i		−	0.431327i
$167$	−12.7582			−0.987257			−0.493629	−	0.869673i	$-0.664330\pi$
$167$	−12.7582			−0.987257			−0.493629	+	0.869673i	$0.664330\pi$
$168$		0			0
$169$	15.5290			1.19454
$170$	0.0490649			0.00376311
$171$	4.04145			0.309058
$172$		−	4.92933i		−	0.375858i
$173$	10.0387			0.763228			0.381614	−	0.924322i	$-0.375368\pi$
$173$	10.0387			0.763228			0.381614	+	0.924322i	$0.375368\pi$
$174$		−	3.85304i		−	0.292098i
$175$		0			0
$176$	9.50057	+	2.83833i	0.716133	+	0.213947i
$177$	−1.10775			−0.0832634
$178$	−5.76332			−0.431979
$179$	19.5926			1.46442			0.732210	−	0.681079i	$-0.238489\pi$
$179$	19.5926			1.46442			0.732210	+	0.681079i	$0.238489\pi$
$180$			0.873627i			0.0651163i
$181$			20.3798i			1.51482i	0.652941	+	0.757408i	$0.273535\pi$
$181$			20.3798i			1.51482i	−0.652941	+	0.757408i	$0.726465\pi$
$182$		0			0
$183$		−	5.33908i		−	0.394676i
$184$		−	1.72225i		−	0.126966i
$185$		−	2.13757i		−	0.157158i
$186$			0.483558i			0.0354562i
$187$	−0.782865	−	0.233883i	−0.0572487	−	0.0171032i
$188$		−	14.3690i		−	1.04797i
$189$		0			0
$190$	0.804921			0.0583951
$191$	−6.49949			−0.470287			−0.235143	−	0.971961i	$-0.575556\pi$
$191$	−6.49949			−0.470287			−0.235143	+	0.971961i	$0.575556\pi$
$192$		−	4.13374i		−	0.298327i
$193$		−	13.5427i		−	0.974822i	−0.873173	−	0.487411i	$-0.837941\pi$
$193$		−	13.5427i		−	0.974822i	0.873173	−	0.487411i	$-0.162059\pi$
$194$	3.41601			0.245256
$195$	−2.55463			−0.182941
$196$		0			0
$197$		−	16.9234i		−	1.20574i	−0.797839	−	0.602871i	$-0.794023\pi$
$197$		−	16.9234i		−	1.20574i	0.797839	−	0.602871i	$-0.205977\pi$
$198$	−0.395345	+	1.32332i	−0.0280960	+	0.0940440i
$199$		−	26.2120i		−	1.85812i	−0.369930	−	0.929060i	$-0.620618\pi$
$199$		−	26.2120i		−	1.85812i	0.369930	−	0.929060i	$-0.379382\pi$
$200$		−	7.60285i		−	0.537602i
$201$		−	3.05861i		−	0.215738i
$202$			4.16811i			0.293267i
$203$		0			0
$204$			0.449984i			0.0315052i
$205$			4.35597i			0.304234i
$206$	4.28092			0.298266
$207$	−1.08082			−0.0751220
$208$	15.9684			1.10721
$209$	−12.8431	−	3.83691i	−0.888375	−	0.265405i
$210$		0			0
$211$			7.93121i			0.546007i	0.962013	+	0.273004i	$0.0880171\pi$
$211$			7.93121i			0.546007i	−0.962013	+	0.273004i	$0.911983\pi$
$212$	−0.886821			−0.0609071
$213$			11.9831i			0.821067i
$214$	6.92588			0.473443
$215$	−1.29071			−0.0880260
$216$	1.59347			0.108422
$217$		0			0
$218$	2.63888			0.178728
$219$			7.88650i			0.532920i
$220$	0.829412	−	2.77625i	0.0559190	−	0.187174i
$221$	−1.31582			−0.0885120
$222$	−1.86110			−0.124909
$223$			20.0220i			1.34077i	0.742013	+	0.670386i	$0.233871\pi$
$223$			20.0220i			1.34077i	−0.742013	+	0.670386i	$0.766129\pi$
$224$		0			0
$225$	−4.77125			−0.318083
$226$			5.71555i			0.380193i
$227$	2.56914			0.170520			0.0852600	−	0.996359i	$-0.472828\pi$
$227$	2.56914			0.170520			0.0852600	+	0.996359i	$0.472828\pi$
$228$			7.38209i			0.488891i
$229$			8.92512i			0.589788i	0.955530	+	0.294894i	$0.0952844\pi$
$229$			8.92512i			0.589788i	−0.955530	+	0.294894i	$0.904716\pi$
$230$	−0.215262			−0.0141940
$231$		0			0
$232$	14.7440			0.967992
$233$			15.5171i			1.01656i	0.861192	+	0.508280i	$0.169718\pi$
$233$			15.5171i			1.01656i	−0.861192	+	0.508280i	$0.830282\pi$
$234$			2.22421i			0.145401i
$235$	−3.76244			−0.245435
$236$		−	2.02340i		−	0.131712i
$237$	−14.2786			−0.927493
$238$		0			0
$239$		−	6.69266i		−	0.432912i	−0.976292	−	0.216456i	$-0.930550\pi$
$239$		−	6.69266i		−	0.432912i	0.976292	−	0.216456i	$-0.0694498\pi$
$240$	−1.42989			−0.0922989
$241$	11.6444			0.750079			0.375040	−	0.927009i	$-0.377629\pi$
$241$	11.6444			0.750079			0.375040	+	0.927009i	$0.377629\pi$
$242$	2.51269	−	3.82995i	0.161522	−	0.246199i
$243$		−	1.00000i		−	0.0641500i
$244$	9.75232			0.624328
$245$		0			0
$246$	3.79256			0.241805
$247$	−21.5864			−1.37351
$248$	−1.85038			−0.117499
$249$		−	13.3453i		−	0.845725i
$250$	−1.94610			−0.123082
$251$			12.4098i			0.783298i	0.920115	+	0.391649i	$0.128095\pi$
$251$			12.4098i			0.783298i	−0.920115	+	0.391649i	$0.871905\pi$
$252$		0			0
$253$	3.43466	+	1.02612i	0.215935	+	0.0645113i
$254$	−0.193558			−0.0121449
$255$	0.117825			0.00737851
$256$	3.85960			0.241225
$257$			18.5467i			1.15691i	0.815714	+	0.578455i	$0.196344\pi$
$257$			18.5467i			1.15691i	−0.815714	+	0.578455i	$0.803656\pi$
$258$			1.12377i			0.0699630i
$259$		0			0
$260$		−	4.66627i		−	0.289389i
$261$		−	9.25276i		−	0.572732i
$262$			5.96482i			0.368508i
$263$		−	1.50756i		−	0.0929602i	−0.998919	−	0.0464801i	$-0.985200\pi$
$263$		−	1.50756i		−	0.0929602i	0.998919	−	0.0464801i	$-0.0148004\pi$
$264$	−5.06380	−	1.51283i	−0.311655	−	0.0931079i
$265$			0.232208i			0.0142644i
$266$		0			0
$267$	−13.8401			−0.847003
$268$	5.58683			0.341270
$269$			18.2517i			1.11282i	0.830906	+	0.556412i	$0.187822\pi$
$269$			18.2517i			1.11282i	−0.830906	+	0.556412i	$0.812178\pi$
$270$		−	0.199166i		−	0.0121209i
$271$	1.45373			0.0883076			0.0441538	−	0.999025i	$-0.485941\pi$
$271$	1.45373			0.0883076			0.0441538	+	0.999025i	$0.485941\pi$
$272$	−0.736500			−0.0446569
$273$		0			0
$274$			1.34436i			0.0812157i
$275$	15.1623	+	4.52977i	0.914318	+	0.273155i
$276$		−	1.97421i		−	0.118834i
$277$			19.5590i			1.17519i	0.809157	+	0.587593i	$0.199924\pi$
$277$			19.5590i			1.17519i	−0.809157	+	0.587593i	$0.800076\pi$
$278$		−	2.52730i		−	0.151577i
$279$			1.16123i			0.0695207i
$280$		0			0
$281$			31.8002i			1.89704i	0.316719	+	0.948520i	$0.397419\pi$
$281$			31.8002i			1.89704i	−0.316719	+	0.948520i	$0.602581\pi$
$282$			3.27580i			0.195071i
$283$	−21.9980			−1.30764			−0.653821	−	0.756649i	$-0.726835\pi$
$283$	−21.9980			−1.30764			−0.653821	+	0.756649i	$0.726835\pi$
$284$	−21.8882			−1.29883
$285$	1.93295			0.114498
$286$	2.11164	−	7.06817i	0.124864	−	0.417950i
$287$		0			0
$288$			4.43189i			0.261152i
$289$	−16.9393			−0.996430
$290$		−	1.84284i		−	0.108215i
$291$	8.20328			0.480885
$292$	−14.4054			−0.843014
$293$	17.8824			1.04470			0.522351	−	0.852731i	$-0.325055\pi$
$293$	17.8824			1.04470			0.522351	+	0.852731i	$0.325055\pi$
$294$		0			0
$295$	−0.529816			−0.0308471
$296$		−	7.12167i		−	0.413938i
$297$	−0.949389	+	3.17784i	−0.0550892	+	0.184397i
$298$	−6.72925			−0.389815
$299$	5.77292			0.333856
$300$		−	8.71513i		−	0.503168i
$301$		0			0
$302$	−4.28019			−0.246297
$303$			10.0094i			0.575023i
$304$	−12.0825			−0.692977
$305$		−	2.55358i		−	0.146218i
$306$		−	0.102586i		−	0.00586443i
$307$	1.73541			0.0990450			0.0495225	−	0.998773i	$-0.484230\pi$
$307$	1.73541			0.0990450			0.0495225	+	0.998773i	$0.484230\pi$
$308$		0			0
$309$	10.2803			0.584825
$310$			0.231277i			0.0131357i
$311$			19.1720i			1.08714i	0.839363	+	0.543572i	$0.182929\pi$
$311$			19.1720i			1.08714i	−0.839363	+	0.543572i	$0.817071\pi$
$312$	−8.51114			−0.481848
$313$			25.3618i			1.43353i	0.697313	+	0.716767i	$0.254379\pi$
$313$			25.3618i			1.43353i	−0.697313	+	0.716767i	$0.745621\pi$
$314$	−1.49126			−0.0841565
$315$		0			0
$316$		−	26.0812i		−	1.46718i
$317$	−24.3571			−1.36803			−0.684015	−	0.729468i	$-0.739768\pi$
$317$	−24.3571			−1.36803			−0.684015	+	0.729468i	$0.739768\pi$
$318$	0.202174			0.0113374
$319$	−8.78447	+	29.4038i	−0.491836	+	1.64630i
$320$		−	1.97709i		−	0.110523i
$321$	16.6319			0.928304
$322$		0			0
$323$	0.995617			0.0553976
$324$	1.82659			0.101477
$325$	25.4844			1.41362
$326$			6.24708i			0.345994i
$327$	6.33706			0.350440
$328$			14.5126i			0.801324i
$329$		0			0
$330$	−0.189086	+	0.632919i	−0.0104089	+	0.0348410i
$331$	−5.53239			−0.304088			−0.152044	−	0.988374i	$-0.548586\pi$
$331$	−5.53239			−0.304088			−0.152044	+	0.988374i	$0.548586\pi$
$332$	24.3765			1.33783
$333$	−4.46928			−0.244915
$334$			5.31276i			0.290702i
$335$		−	1.46288i		−	0.0799255i
$336$		0			0
$337$		−	20.8649i		−	1.13658i	−0.822828	−	0.568291i	$-0.807605\pi$
$337$		−	20.8649i		−	1.13658i	0.822828	−	0.568291i	$-0.192395\pi$
$338$		−	6.46660i		−	0.351736i
$339$			13.7254i			0.745464i
$340$			0.215219i			0.0116719i
$341$	1.10245	−	3.69019i	0.0597013	−	0.199835i
$342$		−	1.68294i		−	0.0910031i
$343$		0			0
$344$	−4.30022			−0.231852
$345$	−0.516935			−0.0278309
$346$		−	4.18032i		−	0.224735i
$347$			14.1862i			0.761557i	0.924666	+	0.380778i	$0.124344\pi$
$347$			14.1862i			0.761557i	−0.924666	+	0.380778i	$0.875656\pi$
$348$	16.9010			0.905991
$349$	21.0581			1.12721			0.563606	−	0.826044i	$-0.309414\pi$
$349$	21.0581			1.12721			0.563606	+	0.826044i	$0.309414\pi$
$350$		0			0
$351$			5.34126i			0.285095i
$352$	4.20759	−	14.0838i	0.224265	−	0.750671i
$353$			1.01877i			0.0542236i	0.999632	+	0.0271118i	$0.00863101\pi$
$353$			1.01877i			0.0542236i	−0.999632	+	0.0271118i	$0.991369\pi$
$354$			0.461289i			0.0245172i
$355$			5.73129i			0.304185i
$356$		−	25.2803i		−	1.33985i
$357$		0			0
$358$		−	8.15876i		−	0.431204i
$359$			6.70666i			0.353964i	0.984214	+	0.176982i	$0.0566334\pi$
$359$			6.70666i			0.353964i	−0.984214	+	0.176982i	$0.943367\pi$
$360$	0.762129			0.0401677
$361$	−2.66667			−0.140351
$362$	8.48656			0.446043
$363$	6.03401	−	9.19732i	0.316703	−	0.482734i
$364$		0			0
$365$			3.77197i			0.197434i
$366$	−2.22330			−0.116214
$367$			5.49445i			0.286808i	0.989664	+	0.143404i	$0.0458049\pi$
$367$			5.49445i			0.286808i	−0.989664	+	0.143404i	$0.954195\pi$
$368$	3.23125			0.168440
$369$	9.10753			0.474119
$370$	−0.890130			−0.0462756
$371$		0			0
$372$	−2.12109			−0.109973
$373$			0.0504532i			0.00261237i	0.999999	+	0.00130618i	$0.000415771\pi$
$373$			0.0504532i			0.00261237i	−0.999999	+	0.00130618i	$0.999584\pi$
$374$	−0.0973938	+	0.326001i	−0.00503611	+	0.0168571i
$375$	−4.67341			−0.241334
$376$	−12.5352			−0.646452
$377$			49.4214i			2.54533i
$378$		0			0
$379$	1.32955			0.0682942			0.0341471	−	0.999417i	$-0.489129\pi$
$379$	1.32955			0.0682942			0.0341471	+	0.999417i	$0.489129\pi$
$380$			3.53072i			0.181122i
$381$	−0.464814			−0.0238131
$382$			2.70652i			0.138478i
$383$			21.8414i			1.11604i	0.829826	+	0.558022i	$0.188439\pi$
$383$			21.8414i			1.11604i	−0.829826	+	0.558022i	$0.811561\pi$
$384$	−10.5852			−0.540171
$385$		0			0
$386$	−5.63944			−0.287040
$387$			2.69865i			0.137180i
$388$			14.9841i			0.760701i
$389$	−30.7153			−1.55733			−0.778664	−	0.627442i	$-0.784102\pi$
$389$	−30.7153			−1.55733			−0.778664	+	0.627442i	$0.784102\pi$
$390$			1.06380i			0.0538675i
$391$	−0.266261			−0.0134654
$392$		0			0
$393$			14.3240i			0.722552i
$394$	−7.04725			−0.355035
$395$	−6.82918			−0.343614
$396$	−5.80462	−	1.73415i	−0.291693	−	0.0871443i
$397$			16.5074i			0.828480i	0.910168	+	0.414240i	$0.135953\pi$
$397$			16.5074i			0.828480i	−0.910168	+	0.414240i	$0.864047\pi$
$398$	−10.9152			−0.547130
$399$		0			0
$400$	14.2643			0.713214
$401$	−11.7818			−0.588357			−0.294179	−	0.955750i	$-0.595046\pi$
$401$	−11.7818			−0.588357			−0.294179	+	0.955750i	$0.595046\pi$
$402$	−1.27367			−0.0635247
$403$		−	6.20240i		−	0.308964i
$404$	−18.2831			−0.909616
$405$		−	0.478282i		−	0.0237660i
$406$		0			0
$407$	14.2026	+	4.24308i	0.703999	+	0.210322i
$408$	0.392554			0.0194343
$409$	14.5032			0.717135			0.358567	−	0.933504i	$-0.383265\pi$
$409$	14.5032			0.717135			0.358567	+	0.933504i	$0.383265\pi$
$410$	1.81391			0.0895828
$411$			3.22837i			0.159244i
$412$			18.7779i			0.925121i
$413$		0			0
$414$			0.450074i			0.0221199i
$415$		−	6.38282i		−	0.313320i
$416$		−	23.6718i		−	1.16061i
$417$		−	6.06911i		−	0.297206i
$418$	−1.59777	+	5.34812i	−0.0781494	+	0.261585i
$419$		−	26.3346i		−	1.28653i	−0.765643	−	0.643266i	$-0.777579\pi$
$419$		−	26.3346i		−	1.28653i	0.765643	−	0.643266i	$-0.222421\pi$
$420$		0			0
$421$	−31.5201			−1.53619			−0.768097	−	0.640334i	$-0.778796\pi$
$421$	−31.5201			−1.53619			−0.768097	+	0.640334i	$0.778796\pi$
$422$	3.30272			0.160774
$423$			7.86658i			0.382486i
$424$			0.773639i			0.0375712i
$425$	−1.17540			−0.0570154
$426$	4.99000			0.241766
$427$		0			0
$428$			30.3798i			1.46846i
$429$	5.07093	−	16.9736i	0.244827	−	0.819495i
$430$			0.537480i			0.0259196i
$431$		−	26.5765i		−	1.28014i	−0.768315	−	0.640072i	$-0.778905\pi$
$431$		−	26.5765i		−	1.28014i	0.768315	−	0.640072i	$-0.221095\pi$
$432$			2.98963i			0.143839i
$433$			2.09473i			0.100667i	0.998732	+	0.0503333i	$0.0160283\pi$
$433$			2.09473i			0.100667i	−0.998732	+	0.0503333i	$0.983972\pi$
$434$		0			0
$435$		−	4.42543i		−	0.212183i
$436$			11.5752i			0.554354i
$437$	−4.36807			−0.208953
$438$	3.28410			0.156920
$439$	−1.35432			−0.0646384			−0.0323192	−	0.999478i	$-0.510289\pi$
$439$	−1.35432			−0.0646384			−0.0323192	+	0.999478i	$0.510289\pi$
$440$	−2.42192	−	0.723557i	−0.115461	−	0.0344942i
$441$		0			0
$442$			0.547936i			0.0260627i
$443$	−18.2380			−0.866515			−0.433257	−	0.901270i	$-0.642636\pi$
$443$	−18.2380			−0.866515			−0.433257	+	0.901270i	$0.642636\pi$
$444$		−	8.16355i		−	0.387425i
$445$	−6.61949			−0.313794
$446$	8.33756			0.394795
$447$	−16.1597			−0.764330
$448$		0			0
$449$	9.75521			0.460377			0.230188	−	0.973146i	$-0.426066\pi$
$449$	9.75521			0.460377			0.230188	+	0.973146i	$0.426066\pi$
$450$			1.98684i			0.0936607i
$451$	−28.9423	−	8.64659i	−1.36284	−	0.407152i
$452$	−25.0708			−1.17923
$453$	−10.2785			−0.482928
$454$		−	1.06984i		−	0.0502102i
$455$		0			0
$456$	6.43994			0.301578
$457$			11.3353i			0.530244i	0.964215	+	0.265122i	$0.0854123\pi$
$457$			11.3353i			0.530244i	−0.964215	+	0.265122i	$0.914588\pi$
$458$	3.71660			0.173665
$459$		−	0.246351i		−	0.0114987i
$460$		−	0.944231i		−	0.0440250i
$461$	38.1954			1.77894			0.889468	−	0.456997i	$-0.151075\pi$
$461$	38.1954			1.77894			0.889468	+	0.456997i	$0.151075\pi$
$462$		0			0
$463$	28.5362			1.32619			0.663094	−	0.748536i	$-0.269243\pi$
$463$	28.5362			1.32619			0.663094	+	0.748536i	$0.269243\pi$
$464$			27.6624i			1.28419i
$465$			0.555393i			0.0257557i
$466$	6.46164			0.299330
$467$		−	2.62363i		−	0.121407i	−0.998156	−	0.0607034i	$-0.980666\pi$
$467$		−	2.62363i		−	0.121407i	0.998156	−	0.0607034i	$-0.0193344\pi$
$468$	−9.75630			−0.450985
$469$		0			0
$470$			1.56676i			0.0722691i
$471$	−3.58113			−0.165010
$472$	−1.76516			−0.0812483
$473$	2.56207	−	8.57587i	0.117804	−	0.394319i
$474$			5.94589i			0.273104i
$475$	−19.2828			−0.884754
$476$		0			0
$477$	0.485505			0.0222297
$478$	−2.78696			−0.127473
$479$	−17.1871			−0.785300			−0.392650	−	0.919688i	$-0.628442\pi$
$479$	−17.1871			−0.785300			−0.392650	+	0.919688i	$0.628442\pi$
$480$			2.11969i			0.0967503i
$481$	23.8715			1.08845
$482$		−	4.84895i		−	0.220864i
$483$		0			0
$484$	16.7998	+	11.0217i	0.763626	+	0.500986i
$485$	3.92348			0.178156
$486$	−0.416420			−0.0188892
$487$	2.84116			0.128745			0.0643726	−	0.997926i	$-0.479495\pi$
$487$	2.84116			0.128745			0.0643726	+	0.997926i	$0.479495\pi$
$488$		−	8.50767i		−	0.385124i
$489$			15.0019i			0.678407i
$490$		0			0
$491$		−	27.5167i		−	1.24181i	−0.783885	−	0.620906i	$-0.786765\pi$
$491$		−	27.5167i		−	1.24181i	0.783885	−	0.620906i	$-0.213235\pi$
$492$			16.6358i			0.749998i
$493$		−	2.27943i		−	0.102660i
$494$			8.98903i			0.404435i
$495$	−0.454076	+	1.51990i	−0.0204092	+	0.0683146i
$496$		−	3.47164i		−	0.155881i
$497$		0			0
$498$	−5.55726			−0.249027
$499$	16.6370			0.744775			0.372387	−	0.928077i	$-0.378539\pi$
$499$	16.6370			0.744775			0.372387	+	0.928077i	$0.378539\pi$
$500$		−	8.53643i		−	0.381761i
$501$			12.7582i			0.569993i
$502$	5.16768			0.230645
$503$	−0.132815			−0.00592194			−0.00296097	−	0.999996i	$-0.500943\pi$
$503$	−0.132815			−0.00592194			−0.00296097	+	0.999996i	$0.500943\pi$
$504$		0			0
$505$			4.78730i			0.213032i
$506$	0.427296	−	1.43026i	0.0189956	−	0.0635830i
$507$		−	15.5290i		−	0.689667i
$508$		−	0.849026i		−	0.0376695i
$509$			27.1266i			1.20237i	0.799112	+	0.601183i	$0.205304\pi$
$509$			27.1266i			1.20237i	−0.799112	+	0.601183i	$0.794696\pi$
$510$		−	0.0490649i		−	0.00217263i
$511$		0			0
$512$		−	22.7775i		−	1.00663i
$513$		−	4.04145i		−	0.178434i
$514$	7.72322			0.340657
$515$	4.91688			0.216663
$516$	−4.92933			−0.217002
$517$	7.46844	−	24.9987i	0.328462	−	1.09944i
$518$		0			0
$519$		−	10.0387i		−	0.440650i
$520$	−4.07073			−0.178513
$521$			5.89910i			0.258444i	0.991616	+	0.129222i	$0.0412480\pi$
$521$			5.89910i			0.258444i	−0.991616	+	0.129222i	$0.958752\pi$
$522$	−3.85304			−0.168643
$523$	5.49044			0.240080			0.120040	−	0.992769i	$-0.461698\pi$
$523$	5.49044			0.240080			0.120040	+	0.992769i	$0.461698\pi$
$524$	−26.1642			−1.14299
$525$		0			0
$526$	−0.627779			−0.0273725
$527$			0.286069i			0.0124614i
$528$	2.83833	−	9.50057i	0.123522	−	0.413459i
$529$	−21.8318			−0.949210
$530$	0.0966963			0.00420022
$531$			1.10775i			0.0480721i
$532$		0			0
$533$	−48.6456			−2.10708
$534$			5.76332i			0.249403i
$535$	7.95476			0.343914
$536$		−	4.87381i		−	0.210516i
$537$		−	19.5926i		−	0.845483i
$538$	7.60037			0.327675
$539$		0			0
$540$	0.873627			0.0375949
$541$			19.4959i			0.838195i	0.907941	+	0.419098i	$0.137654\pi$
$541$			19.4959i			0.838195i	−0.907941	+	0.419098i	$0.862346\pi$
$542$		−	0.605362i		−	0.0260025i
$543$	20.3798			0.874580
$544$			1.09180i			0.0468106i
$545$	3.03090			0.129830
$546$		0			0
$547$			42.3716i			1.81168i	0.423620	+	0.905840i	$0.360759\pi$
$547$			42.3716i			1.81168i	−0.423620	+	0.905840i	$0.639241\pi$
$548$	−5.89692			−0.251904
$549$	−5.33908			−0.227866
$550$	1.88629	−	6.31387i	0.0804316	−	0.269224i
$551$		−	37.3946i		−	1.59306i
$552$	−1.72225			−0.0733039
$553$		0			0
$554$	8.14476			0.346038
$555$	−2.13757			−0.0907350
$556$	11.0858			0.470143
$557$		−	2.36992i		−	0.100417i	−0.998739	−	0.0502084i	$-0.984011\pi$
$557$		−	2.36992i		−	0.100417i	0.998739	−	0.0502084i	$-0.0159886\pi$
$558$	0.483558			0.0204706
$559$		−	14.4142i		−	0.609654i
$560$		0			0
$561$	−0.233883	+	0.782865i	−0.00987456	+	0.0330526i
$562$	13.2422			0.558590
$563$	23.2570			0.980165			0.490082	−	0.871676i	$-0.336967\pi$
$563$	23.2570			0.980165			0.490082	+	0.871676i	$0.336967\pi$
$564$	−14.3690			−0.605046
$565$			6.56463i			0.276176i
$566$			9.16040i			0.385040i
$567$		0			0
$568$			19.0947i			0.801196i
$569$		−	8.35243i		−	0.350152i	−0.984555	−	0.175076i	$-0.943983\pi$
$569$		−	8.35243i		−	0.350152i	0.984555	−	0.175076i	$-0.0560172\pi$
$570$		−	0.804921i		−	0.0337144i
$571$		−	30.8938i		−	1.29287i	−0.762970	−	0.646433i	$-0.776260\pi$
$571$		−	30.8938i		−	1.29287i	0.762970	−	0.646433i	$-0.223740\pi$
$572$	31.0040	+	9.26253i	1.29634	+	0.387286i
$573$			6.49949i			0.271520i
$574$		0			0
$575$	5.15684			0.215055
$576$	−4.13374			−0.172239
$577$			18.8322i			0.783995i	0.919966	+	0.391998i	$0.128216\pi$
$577$			18.8322i			0.783995i	−0.919966	+	0.391998i	$0.871784\pi$
$578$			7.05388i			0.293403i
$579$	−13.5427			−0.562814
$580$	8.08346			0.335648
$581$		0			0
$582$		−	3.41601i		−	0.141598i
$583$	−1.54286	−	0.460933i	−0.0638986	−	0.0190899i
$584$			12.5669i			0.520022i
$585$			2.55463i			0.105621i
$586$		−	7.44660i		−	0.307616i
$587$		−	13.9495i		−	0.575758i	−0.957667	−	0.287879i	$-0.907050\pi$
$587$		−	13.9495i		−	0.575758i	0.957667	−	0.287879i	$-0.0929501\pi$
$588$		0			0
$589$			4.69303i			0.193373i
$590$			0.220626i			0.00908303i
$591$	−16.9234			−0.696135
$592$	13.3615			0.549154
$593$	−9.69556			−0.398149			−0.199074	−	0.979984i	$-0.563794\pi$
$593$	−9.69556			−0.398149			−0.199074	+	0.979984i	$0.563794\pi$
$594$	1.32332	+	0.395345i	0.0542964	+	0.0162212i
$595$		0			0
$596$		−	29.5173i		−	1.20908i
$597$	−26.2120			−1.07279
$598$		−	2.40396i		−	0.0983053i
$599$	2.26333			0.0924770			0.0462385	−	0.998930i	$-0.485277\pi$
$599$	2.26333			0.0924770			0.0462385	+	0.998930i	$0.485277\pi$
$600$	−7.60285			−0.310385
$601$	−46.5193			−1.89756			−0.948781	−	0.315935i	$-0.897682\pi$
$601$	−46.5193			−1.89756			−0.948781	+	0.315935i	$0.897682\pi$
$602$		0			0
$603$	−3.05861			−0.124556
$604$		−	18.7747i		−	0.763932i
$605$	2.88596	−	4.39891i	0.117331	−	0.178841i
$606$	4.16811			0.169318
$607$	29.5654			1.20002			0.600010	−	0.799992i	$-0.295163\pi$
$607$	29.5654			1.20002			0.600010	+	0.799992i	$0.295163\pi$
$608$			17.9113i			0.726398i
$609$		0			0
$610$	−1.06336			−0.0430544
$611$		−	42.0174i		−	1.69984i
$612$	0.449984			0.0181895
$613$			4.70088i			0.189867i	0.995484	+	0.0949333i	$0.0302638\pi$
$613$			4.70088i			0.189867i	−0.995484	+	0.0949333i	$0.969736\pi$
$614$		−	0.722659i		−	0.0291642i
$615$	4.35597			0.175650
$616$		0			0
$617$	19.2863			0.776436			0.388218	−	0.921568i	$-0.373091\pi$
$617$	19.2863			0.776436			0.388218	+	0.921568i	$0.373091\pi$
$618$		−	4.28092i		−	0.172204i
$619$		−	23.0850i		−	0.927865i	−0.885870	−	0.463933i	$-0.846438\pi$
$619$		−	23.0850i		−	0.927865i	0.885870	−	0.463933i	$-0.153562\pi$
$620$	−1.01448			−0.0407424
$621$			1.08082i			0.0433717i
$622$	7.98361			0.320114
$623$		0			0
$624$		−	15.9684i		−	0.639247i
$625$	21.6210			0.864841
$626$	10.5612			0.422109
$627$	−3.83691	+	12.8431i	−0.153231	+	0.512903i
$628$		−	6.54127i		−	0.261025i
$629$	−1.10101			−0.0439002
$630$		0			0
$631$	−5.79691			−0.230771			−0.115386	−	0.993321i	$-0.536810\pi$
$631$	−5.79691			−0.230771			−0.115386	+	0.993321i	$0.536810\pi$
$632$	−22.7525			−0.905046
$633$	7.93121			0.315237
$634$			10.1428i			0.402821i
$635$	−0.222312			−0.00882219
$636$			0.886821i			0.0351647i
$637$		0			0
$638$	12.2443	+	3.65803i	0.484758	+	0.144823i
$639$	11.9831			0.474043
$640$	−5.06269			−0.200120
$641$	32.5796			1.28682			0.643409	−	0.765523i	$-0.277520\pi$
$641$	32.5796			1.28682			0.643409	+	0.765523i	$0.277520\pi$
$642$		−	6.92588i		−	0.273343i
$643$			11.3454i			0.447418i	0.974656	+	0.223709i	$0.0718166\pi$
$643$			11.3454i			0.447418i	−0.974656	+	0.223709i	$0.928183\pi$
$644$		0			0
$645$			1.29071i			0.0508218i
$646$		−	0.414595i		−	0.0163120i
$647$		−	37.8697i		−	1.48881i	−0.667728	−	0.744405i	$-0.732733\pi$
$647$		−	37.8697i		−	1.48881i	0.667728	−	0.744405i	$-0.267267\pi$
$648$		−	1.59347i		−	0.0625975i
$649$	1.05168	−	3.52024i	0.0412822	−	0.138182i
$650$		−	10.6122i		−	0.416246i
$651$		0			0
$652$	−27.4023			−1.07316
$653$	29.4163			1.15115			0.575574	−	0.817749i	$-0.304779\pi$
$653$	29.4163			1.15115			0.575574	+	0.817749i	$0.304779\pi$
$654$		−	2.63888i		−	0.103189i
$655$			6.85093i			0.267688i
$656$	−27.2282			−1.06308
$657$	7.88650			0.307682
$658$		0			0
$659$			1.05149i			0.0409601i	0.999790	+	0.0204800i	$0.00651945\pi$
$659$			1.05149i			0.0409601i	−0.999790	+	0.0204800i	$0.993481\pi$
$660$	−2.77625	−	0.829412i	−0.108065	−	0.0322848i
$661$		−	2.04444i		−	0.0795197i	−0.999209	−	0.0397598i	$-0.987341\pi$
$661$		−	2.04444i		−	0.0795197i	0.999209	−	0.0397598i	$-0.0126593\pi$
$662$			2.30380i			0.0895398i
$663$			1.31582i			0.0511024i
$664$		−	21.2654i		−	0.825257i
$665$		0			0
$666$			1.86110i			0.0721161i
$667$			10.0005i			0.387222i
$668$	−23.3040			−0.901659
$669$	20.0220			0.774095
$670$	−0.609172			−0.0235344
$671$	16.9667	+	5.06886i	0.654993	+	0.195681i
$672$		0			0
$673$		−	35.1938i		−	1.35662i	−0.734775	−	0.678311i	$-0.762712\pi$
$673$		−	35.1938i		−	1.35662i	0.734775	−	0.678311i	$-0.237288\pi$
$674$	−8.68856			−0.334671
$675$			4.77125i			0.183645i
$676$	28.3652			1.09097
$677$	−24.2753			−0.932977			−0.466489	−	0.884527i	$-0.654481\pi$
$677$	−24.2753			−0.932977			−0.466489	+	0.884527i	$0.654481\pi$
$678$	5.71555			0.219505
$679$		0			0
$680$	0.187751			0.00719994
$681$		−	2.56914i		−	0.0984498i
$682$	−1.53667	−	0.459085i	−0.0588421	−	0.0175793i
$683$	26.0515			0.996833			0.498417	−	0.866938i	$-0.333915\pi$
$683$	26.0515			0.996833			0.498417	+	0.866938i	$0.333915\pi$
$684$	7.38209			0.282261
$685$			1.54407i			0.0589959i
$686$		0			0
$687$	8.92512			0.340514
$688$		−	8.06797i		−	0.307588i
$689$	−2.59321			−0.0987933
$690$			0.215262i			0.00819490i
$691$		−	41.8600i		−	1.59243i	−0.605015	−	0.796214i	$-0.706833\pi$
$691$		−	41.8600i		−	1.59243i	0.605015	−	0.796214i	$-0.293167\pi$
$692$	18.3366			0.697054
$693$		0			0
$694$	5.90744			0.224243
$695$		−	2.90275i		−	0.110107i
$696$		−	14.7440i		−	0.558871i
$697$	2.24365			0.0849844
$698$		−	8.76901i		−	0.331912i
$699$	15.5171			0.586911
$700$		0			0
$701$			12.0257i			0.454205i	0.973871	+	0.227103i	$0.0729253\pi$
$701$			12.0257i			0.454205i	−0.973871	+	0.227103i	$0.927075\pi$
$702$	2.22421			0.0839473
$703$	−18.0624			−0.681235
$704$	13.1364	+	3.92453i	0.495095	+	0.147911i
$705$			3.76244i			0.141702i
$706$	0.424236			0.0159663
$707$		0			0
$708$	−2.02340			−0.0760442
$709$	19.8865			0.746855			0.373427	−	0.927659i	$-0.378183\pi$
$709$	19.8865			0.746855			0.373427	+	0.927659i	$0.378183\pi$
$710$	2.38663			0.0895685
$711$			14.2786i			0.535488i
$712$	−22.0539			−0.826504
$713$		−	1.25507i		−	0.0470028i
$714$		0			0
$715$	2.42533	−	8.11819i	0.0907024	−	0.303603i
$716$	35.7877			1.33745
$717$	−6.69266			−0.249942
$718$	2.79279			0.104226
$719$		−	0.494235i		−	0.0184318i	−0.999958	−	0.00921592i	$-0.997066\pi$
$719$		−	0.494235i		−	0.0184318i	0.999958	−	0.00921592i	$-0.00293356\pi$
$720$			1.42989i			0.0532888i
$721$		0			0
$722$			1.11046i			0.0413269i
$723$		−	11.6444i		−	0.433058i
$724$			37.2256i			1.38348i
$725$			44.1472i			1.63959i
$726$	−3.82995	−	2.51269i	−0.142143	−	0.0932545i
$727$		−	46.9030i		−	1.73953i	−0.493462	−	0.869767i	$-0.664269\pi$
$727$		−	46.9030i		−	1.73953i	0.493462	−	0.869767i	$-0.335731\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	1.57073			0.0581351
$731$			0.664815i			0.0245891i
$732$		−	9.75232i		−	0.360456i
$733$	−46.0878			−1.70229			−0.851146	−	0.524928i	$-0.824092\pi$
$733$	−46.0878			−1.70229			−0.851146	+	0.524928i	$0.824092\pi$
$734$	2.28800			0.0844517
$735$		0			0
$736$		−	4.79006i		−	0.176564i
$737$	9.71976	+	2.90381i	0.358032	+	0.106963i
$738$		−	3.79256i		−	0.139606i
$739$		−	25.4491i		−	0.936161i	−0.883686	−	0.468081i	$-0.844946\pi$
$739$		−	25.4491i		−	0.936161i	0.883686	−	0.468081i	$-0.155054\pi$
$740$		−	3.90448i		−	0.143532i
$741$			21.5864i			0.792997i
$742$		0			0
$743$		−	9.19015i		−	0.337154i	−0.985688	−	0.168577i	$-0.946083\pi$
$743$		−	9.19015i		−	0.337154i	0.985688	−	0.168577i	$-0.0539172\pi$
$744$			1.85038i			0.0678382i
$745$	−7.72892			−0.283166
$746$	0.0210097			0.000769221
$747$	−13.3453			−0.488279
$748$	−1.42998	−	0.427210i	−0.0522851	−	0.0156203i
$749$		0			0
$750$			1.94610i			0.0710617i
$751$	−34.3843			−1.25470			−0.627350	−	0.778737i	$-0.715860\pi$
$751$	−34.3843			−1.25470			−0.627350	+	0.778737i	$0.715860\pi$
$752$		−	23.5182i		−	0.857620i
$753$	12.4098			0.452237
$754$	20.5801			0.749482
$755$	−4.91604			−0.178913
$756$		0			0
$757$	−25.7961			−0.937576			−0.468788	−	0.883311i	$-0.655309\pi$
$757$	−25.7961			−0.937576			−0.468788	+	0.883311i	$0.655309\pi$
$758$		−	0.553650i		−	0.0201095i
$759$	1.02612	−	3.43466i	0.0372456	−	0.124670i
$760$	3.08011			0.111727
$761$	−3.98126			−0.144321			−0.0721603	−	0.997393i	$-0.522989\pi$
$761$	−3.98126			−0.144321			−0.0721603	+	0.997393i	$0.522989\pi$
$762$			0.193558i			0.00701187i
$763$		0			0
$764$	−11.8719			−0.429511
$765$		−	0.117825i		−	0.00425999i
$766$	9.09520			0.328623
$767$		−	5.91676i		−	0.213642i
$768$		−	3.85960i		−	0.139271i
$769$	−37.7698			−1.36201			−0.681006	−	0.732277i	$-0.738457\pi$
$769$	−37.7698			−1.36201			−0.681006	+	0.732277i	$0.738457\pi$
$770$		0			0
$771$	18.5467			0.667942
$772$		−	24.7369i		−	0.890302i
$773$			42.0345i			1.51188i	0.654643	+	0.755938i	$0.272819\pi$
$773$			42.0345i			1.51188i	−0.654643	+	0.755938i	$0.727181\pi$
$774$	1.12377			0.0403932
$775$		−	5.54049i		−	0.199020i
$776$	13.0717			0.469247
$777$		0			0
$778$			12.7905i			0.458561i
$779$	36.8076			1.31877
$780$	−4.66627			−0.167079
$781$	−38.0803	−	11.3766i	−1.36262	−	0.407087i
$782$			0.110876i			0.00396493i
$783$	−9.25276			−0.330667
$784$		0			0
$785$	−1.71279			−0.0611321
$786$	5.96482			0.212758
$787$	−27.1174			−0.966632			−0.483316	−	0.875446i	$-0.660568\pi$
$787$	−27.1174			−0.966632			−0.483316	+	0.875446i	$0.660568\pi$
$788$		−	30.9122i		−	1.10120i
$789$	−1.50756			−0.0536706
$790$			2.84381i			0.101178i
$791$		0			0
$792$	−1.51283	+	5.06380i	−0.0537559	+	0.179934i
$793$	28.5174			1.01268
$794$	6.87400			0.243949
$795$	0.232208			0.00823558
$796$		−	47.8787i		−	1.69701i
$797$		−	8.03224i		−	0.284517i	−0.989830	−	0.142258i	$-0.954564\pi$
$797$		−	8.03224i		−	0.284517i	0.989830	−	0.142258i	$-0.0454364\pi$
$798$		0			0
$799$			1.93794i			0.0685594i
$800$		−	21.1456i		−	0.747611i
$801$			13.8401i			0.489017i
$802$			4.90620i			0.173244i
$803$	−25.0620	−	7.48736i	−0.884419	−	0.264223i
$804$		−	5.58683i		−	0.197032i
$805$		0			0
$806$	−2.58281			−0.0909754
$807$	18.2517			0.642489
$808$			15.9496i			0.561107i
$809$		−	43.5495i		−	1.53112i	−0.643364	−	0.765560i	$-0.722462\pi$
$809$		−	43.5495i		−	1.53112i	0.643364	−	0.765560i	$-0.277538\pi$
$810$	−0.199166			−0.00699799
$811$	−32.9735			−1.15786			−0.578929	−	0.815378i	$-0.696529\pi$
$811$	−32.9735			−1.15786			−0.578929	+	0.815378i	$0.696529\pi$
$812$		0			0
$813$		−	1.45373i		−	0.0509844i
$814$	1.76691	−	5.91427i	0.0619300	−	0.207295i
$815$			7.17512i			0.251333i
$816$			0.736500i			0.0257827i
$817$			10.9065i			0.381569i
$818$		−	6.03941i		−	0.211163i
$819$		0			0
$820$			7.95658i			0.277856i
$821$			23.4010i			0.816699i	0.912826	+	0.408349i	$0.133895\pi$
$821$			23.4010i			0.816699i	−0.912826	+	0.408349i	$0.866105\pi$
$822$	1.34436			0.0468899
$823$	27.7315			0.966661			0.483330	−	0.875438i	$-0.339427\pi$
$823$	27.7315			0.966661			0.483330	+	0.875438i	$0.339427\pi$
$824$	16.3813			0.570671
$825$	4.52977	−	15.1623i	0.157706	−	0.527882i
$826$		0			0
$827$			37.2562i			1.29553i	0.761842	+	0.647763i	$0.224295\pi$
$827$			37.2562i			1.29553i	−0.761842	+	0.647763i	$0.775705\pi$
$828$	−1.97421			−0.0686087
$829$			7.11777i			0.247210i	0.992331	+	0.123605i	$0.0394456\pi$
$829$			7.11777i			0.247210i	−0.992331	+	0.123605i	$0.960554\pi$
$830$	−2.65794			−0.0922584
$831$	19.5590			0.678494
$832$	22.0794			0.765464
$833$		0			0
$834$	−2.52730			−0.0875133
$835$			6.10201i			0.211169i
$836$	−23.4591	−	7.00848i	−0.811350	−	0.242393i
$837$	1.16123			0.0401378
$838$	−10.9663			−0.378824
$839$			49.7475i			1.71748i	0.512415	+	0.858738i	$0.328751\pi$
$839$			49.7475i			1.71748i	−0.512415	+	0.858738i	$0.671249\pi$
$840$		0			0
$841$	−56.6136			−1.95219
$842$			13.1256i			0.452338i
$843$	31.8002			1.09526
$844$			14.4871i			0.498667i
$845$		−	7.42724i		−	0.255505i
$846$	3.27580			0.112624
$847$		0			0
$848$	−1.45148			−0.0498441
$849$			21.9980i			0.754968i
$850$			0.489462i			0.0167884i
$851$	4.83047			0.165586
$852$			21.8882i			0.749878i
$853$	−23.3841			−0.800658			−0.400329	−	0.916372i	$-0.631104\pi$
$853$	−23.3841			−0.800658			−0.400329	+	0.916372i	$0.631104\pi$
$854$		0			0
$855$		−	1.93295i		−	0.0661056i
$856$	26.5025			0.905838
$857$	23.6206			0.806865			0.403432	−	0.915009i	$-0.367817\pi$
$857$	23.6206			0.806865			0.403432	+	0.915009i	$0.367817\pi$
$858$	−7.06817	−	2.11164i	−0.241303	−	0.0720902i
$859$		−	20.4436i		−	0.697526i	−0.937211	−	0.348763i	$-0.886602\pi$
$859$		−	20.4436i		−	0.697526i	0.937211	−	0.348763i	$-0.113398\pi$
$860$	−2.35761			−0.0803939
$861$		0			0
$862$	−11.0670			−0.376943
$863$	−21.1401			−0.719617			−0.359809	−	0.933026i	$-0.617158\pi$
$863$	−21.1401			−0.719617			−0.359809	+	0.933026i	$0.617158\pi$
$864$	4.43189			0.150776
$865$		−	4.80133i		−	0.163250i
$866$	0.872290			0.0296416
$867$			16.9393i			0.575289i
$868$		0			0
$869$	13.5559	−	45.3750i	0.459853	−	1.53924i
$870$	−1.84284			−0.0624781
$871$	16.3368			0.553551
$872$	10.0979			0.341959
$873$		−	8.20328i		−	0.277639i
$874$			1.81895i			0.0615270i
$875$		0			0
$876$			14.4054i			0.486714i
$877$		−	29.8809i		−	1.00901i	−0.863410	−	0.504503i	$-0.831676\pi$
$877$		−	29.8809i		−	1.00901i	0.863410	−	0.504503i	$-0.168324\pi$
$878$			0.563968i			0.0190330i
$879$		−	17.8824i		−	0.603159i
$880$	1.35752	−	4.54395i	0.0457620	−	0.153177i
$881$			4.29272i			0.144626i	0.997382	+	0.0723128i	$0.0230380\pi$
$881$			4.29272i			0.144626i	−0.997382	+	0.0723128i	$0.976962\pi$
$882$		0			0
$883$	−44.7617			−1.50635			−0.753176	−	0.657820i	$-0.771479\pi$
$883$	−44.7617			−1.50635			−0.753176	+	0.657820i	$0.771479\pi$
$884$	−2.40348			−0.0808377
$885$			0.529816i			0.0178096i
$886$			7.59469i			0.255149i
$887$	33.5103			1.12517			0.562583	−	0.826741i	$-0.309808\pi$
$887$	33.5103			1.12517			0.562583	+	0.826741i	$0.309808\pi$
$888$	−7.12167			−0.238987
$889$		0			0
$890$			2.75649i			0.0923978i
$891$	3.17784	+	0.949389i	0.106462	+	0.0318057i
$892$			36.5720i			1.22452i
$893$			31.7924i			1.06389i
$894$			6.72925i			0.225060i
$895$		−	9.37079i		−	0.313231i
$896$		0			0
$897$		−	5.77292i		−	0.192752i
$898$		−	4.06227i		−	0.135560i
$899$	10.7445			0.358350
$900$	−8.71513			−0.290504
$901$	0.119605			0.00398461
$902$	−3.60062	+	12.0521i	−0.119887	+	0.401293i
$903$		0			0
$904$			21.8711i			0.727422i
$905$	9.74728			0.324011
$906$			4.28019i			0.142200i
$907$	9.88683			0.328287			0.164143	−	0.986436i	$-0.447514\pi$
$907$	9.88683			0.328287			0.164143	+	0.986436i	$0.447514\pi$
$908$	4.69278			0.155735
$909$	10.0094			0.331990
$910$		0			0
$911$	1.59373			0.0528028			0.0264014	−	0.999651i	$-0.491595\pi$
$911$	1.59373			0.0528028			0.0264014	+	0.999651i	$0.491595\pi$
$912$			12.0825i			0.400090i
$913$	42.4092	+	12.6699i	1.40354	+	0.419312i
$914$	4.72026			0.156132
$915$	−2.55358			−0.0844189
$916$			16.3026i			0.538652i
$917$		0			0
$918$	−0.102586			−0.00338583
$919$			9.02395i			0.297673i	0.988862	+	0.148836i	$0.0475527\pi$
$919$			9.02395i			0.297673i	−0.988862	+	0.148836i	$0.952447\pi$
$920$	−0.823722			−0.0271573
$921$		−	1.73541i		−	0.0571836i
$922$		−	15.9053i		−	0.523815i
$923$	−64.0047			−2.10674
$924$		0			0
$925$	21.3240			0.701129
$926$		−	11.8831i		−	0.390501i
$927$		−	10.2803i		−	0.337649i
$928$	41.0072			1.34613
$929$		−	48.4441i		−	1.58940i	−0.607002	−	0.794700i	$-0.707628\pi$
$929$		−	48.4441i		−	1.58940i	0.607002	−	0.794700i	$-0.292372\pi$
$930$	0.231277			0.00758387
$931$		0			0
$932$			28.3435i			0.928421i
$933$	19.1720			0.627663
$934$	−1.09253			−0.0357487
$935$	−0.111862	+	0.374430i	−0.00365828	+	0.0122452i
$936$			8.51114i			0.278195i
$937$	34.8830			1.13958			0.569789	−	0.821791i	$-0.307025\pi$
$937$	34.8830			1.13958			0.569789	+	0.821791i	$0.307025\pi$
$938$		0			0
$939$	25.3618			0.827651
$940$	−6.87245			−0.224155
$941$	1.92189			0.0626519			0.0313259	−	0.999509i	$-0.490027\pi$
$941$	1.92189			0.0626519			0.0313259	+	0.999509i	$0.490027\pi$
$942$			1.49126i			0.0485878i
$943$	−9.84357			−0.320551
$944$		−	3.31176i		−	0.107789i
$945$		0			0
$946$	−3.57117	−	1.06690i	−0.116109	−	0.0346878i
$947$	13.2090			0.429234			0.214617	−	0.976698i	$-0.431150\pi$
$947$	13.2090			0.429234			0.214617	+	0.976698i	$0.431150\pi$
$948$	−26.0812			−0.847076
$949$	−42.1238			−1.36740
$950$			8.02974i			0.260519i
$951$			24.3571i			0.789832i
$952$		0			0
$953$			19.9131i			0.645050i	0.946561	+	0.322525i	$0.104532\pi$
$953$			19.9131i			0.645050i	−0.946561	+	0.322525i	$0.895468\pi$
$954$		−	0.202174i		−	0.00654563i
$955$			3.10859i			0.100592i
$956$		−	12.2248i		−	0.395377i
$957$	29.4038	+	8.78447i	0.950490	+	0.283962i
$958$			7.15707i			0.231234i
$959$		0			0
$960$	−1.97709			−0.0638104
$961$	29.6516			0.956502
$962$		−	9.94060i		−	0.320498i
$963$		−	16.6319i		−	0.535957i
$964$	21.2695			0.685045
$965$	−6.47721			−0.208509
$966$		0			0
$967$		−	10.1831i		−	0.327466i	−0.986505	−	0.163733i	$-0.947646\pi$
$967$		−	10.1831i		−	0.327466i	0.986505	−	0.163733i	$-0.0523535\pi$
$968$	9.61503	−	14.6557i	0.309039	−	0.471051i
$969$		−	0.995617i		−	0.0319838i
$970$		−	1.63382i		−	0.0524587i
$971$			5.86068i			0.188078i	0.995568	+	0.0940392i	$0.0299779\pi$
$971$			5.86068i			0.188078i	−0.995568	+	0.0940392i	$0.970022\pi$
$972$		−	1.82659i		−	0.0585880i
$973$		0			0
$974$		−	1.18312i		−	0.0379095i
$975$		−	25.4844i		−	0.816155i
$976$	15.9619			0.510927
$977$	−20.9515			−0.670298			−0.335149	−	0.942165i	$-0.608787\pi$
$977$	−20.9515			−0.670298			−0.335149	+	0.942165i	$0.608787\pi$
$978$	6.24708			0.199760
$979$	13.1397	−	43.9817i	0.419946	−	1.40566i
$980$		0			0
$981$		−	6.33706i		−	0.202327i
$982$	−11.4585			−0.365656
$983$		−	54.3627i		−	1.73390i	−0.498395	−	0.866950i	$-0.666077\pi$
$983$		−	54.3627i		−	1.73390i	0.498395	−	0.866950i	$-0.333923\pi$
$984$	14.5126			0.462645
$985$	−8.09416			−0.257901
$986$	−0.949201			−0.0302287
$987$		0			0
$988$	−39.4296			−1.25442
$989$		−	2.91674i		−	0.0927470i
$990$	0.632919	+	0.189086i	0.0201155	+	0.00600956i
$991$	−8.71977			−0.276993			−0.138496	−	0.990363i	$-0.544227\pi$
$991$	−8.71977			−0.276993			−0.138496	+	0.990363i	$0.544227\pi$
$992$	−5.14642			−0.163399
$993$			5.53239i			0.175565i
$994$		0			0
$995$	−12.5367			−0.397441
$996$		−	24.3765i		−	0.772398i
$997$	−3.89294			−0.123291			−0.0616454	−	0.998098i	$-0.519635\pi$
$997$	−3.89294			−0.123291			−0.0616454	+	0.998098i	$0.519635\pi$
$998$		−	6.92799i		−	0.219302i
$999$			4.46928i			0.141402i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.2.c.a.538.15		32
7.4	even	3		231.2.p.a.208.9	yes	32
7.5	odd	6		231.2.p.a.10.8	✓	32
7.6	odd	2	inner	1617.2.c.a.538.16		32
11.10	odd	2	inner	1617.2.c.a.538.17		32
21.5	even	6		693.2.bg.b.10.9		32
21.11	odd	6		693.2.bg.b.208.8		32
77.32	odd	6		231.2.p.a.208.8	yes	32
77.54	even	6		231.2.p.a.10.9	yes	32
77.76	even	2	inner	1617.2.c.a.538.18		32
231.32	even	6		693.2.bg.b.208.9		32
231.131	odd	6		693.2.bg.b.10.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.p.a.10.8	✓	32	7.5	odd	6
231.2.p.a.10.9	yes	32	77.54	even	6
231.2.p.a.208.8	yes	32	77.32	odd	6
231.2.p.a.208.9	yes	32	7.4	even	3
693.2.bg.b.10.8		32	231.131	odd	6
693.2.bg.b.10.9		32	21.5	even	6
693.2.bg.b.208.8		32	21.11	odd	6
693.2.bg.b.208.9		32	231.32	even	6
1617.2.c.a.538.15		32	1.1	even	1	trivial
1617.2.c.a.538.16		32	7.6	odd	2	inner
1617.2.c.a.538.17		32	11.10	odd	2	inner
1617.2.c.a.538.18		32	77.76	even	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:	\( N \)	\(=\)	\( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1617.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.416420i q^{2} -1.00000i q^{3} +1.82659 q^{4} -0.478282i q^{5} -0.416420 q^{6} -1.59347i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-0.416420i q^{2} -1.00000i q^{3} +1.82659 q^{4} -0.478282i q^{5} -0.416420 q^{6} -1.59347i q^{8} -1.00000 q^{9} -0.199166 q^{10} +(3.17784 + 0.949389i) q^{11} -1.82659i q^{12} +5.34126 q^{13} -0.478282 q^{15} +2.98963 q^{16} -0.246351 q^{17} +0.416420i q^{18} -4.04145 q^{19} -0.873627i q^{20} +(0.395345 - 1.32332i) q^{22} +1.08082 q^{23} -1.59347 q^{24} +4.77125 q^{25} -2.22421i q^{26} +1.00000i q^{27} +9.25276i q^{29} +0.199166i q^{30} -1.16123i q^{31} -4.43189i q^{32} +(0.949389 - 3.17784i) q^{33} +0.102586i q^{34} -1.82659 q^{36} +4.46928 q^{37} +1.68294i q^{38} -5.34126i q^{39} -0.762129 q^{40} -9.10753 q^{41} -2.69865i q^{43} +(5.80462 + 1.73415i) q^{44} +0.478282i q^{45} -0.450074i q^{46} -7.86658i q^{47} -2.98963i q^{48} -1.98684i q^{50} +0.246351i q^{51} +9.75630 q^{52} -0.485505 q^{53} +0.416420 q^{54} +(0.454076 - 1.51990i) q^{55} +4.04145i q^{57} +3.85304 q^{58} -1.10775i q^{59} -0.873627 q^{60} +5.33908 q^{61} -0.483558 q^{62} +4.13374 q^{64} -2.55463i q^{65} +(-1.32332 - 0.395345i) q^{66} +3.05861 q^{67} -0.449984 q^{68} -1.08082i q^{69} -11.9831 q^{71} +1.59347i q^{72} -7.88650 q^{73} -1.86110i q^{74} -4.77125i q^{75} -7.38209 q^{76} -2.22421 q^{78} -14.2786i q^{79} -1.42989i q^{80} +1.00000 q^{81} +3.79256i q^{82} +13.3453 q^{83} +0.117825i q^{85} -1.12377 q^{86} +9.25276 q^{87} +(1.51283 - 5.06380i) q^{88} -13.8401i q^{89} +0.199166 q^{90} +1.97421 q^{92} -1.16123 q^{93} -3.27580 q^{94} +1.93295i q^{95} -4.43189 q^{96} +8.20328i q^{97} +(-3.17784 - 0.949389i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 24 q^{4} - 32 q^{9}+O(q^{10}) \) 32 * q - 24 * q^4 - 32 * q^9	\( 32 q - 24 q^{4} - 32 q^{9} - 4 q^{11} + 8 q^{15} + 40 q^{16} + 8 q^{22} - 48 q^{23} + 24 q^{36} + 64 q^{37} + 56 q^{44} - 72 q^{53} - 24 q^{58} + 8 q^{64} - 40 q^{67} + 72 q^{71} - 48 q^{78} + 32 q^{81} - 128 q^{86} - 48 q^{88} - 16 q^{92} - 32 q^{93} + 4 q^{99}+O(q^{100}) \) 32 * q - 24 * q^4 - 32 * q^9 - 4 * q^11 + 8 * q^15 + 40 * q^16 + 8 * q^22 - 48 * q^23 + 24 * q^36 + 64 * q^37 + 56 * q^44 - 72 * q^53 - 24 * q^58 + 8 * q^64 - 40 * q^67 + 72 * q^71 - 48 * q^78 + 32 * q^81 - 128 * q^86 - 48 * q^88 - 16 * q^92 - 32 * q^93 + 4 * q^99

Introduction

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