LMFDB - Embedded newform 1088.2.l.c.817.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1088,2,Mod(273,1088)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1088.273"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1088, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1088 = 2^{6} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1088.l (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$8.68772373992$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 272)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			817.6
Character	$\chi$	$=$	1088.817
Dual form			1088.2.l.c.273.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.724061 + 0.724061i) q^{3} +(0.100057 + 0.100057i) q^{5} -2.62804i q^{7} +1.95147i q^{9} +(-1.93625 - 1.93625i) q^{11} +(1.48714 - 1.48714i) q^{13} -0.144896 q^{15} +1.00000 q^{17} +(-2.90615 + 2.90615i) q^{19} +(1.90286 + 1.90286i) q^{21} -5.35151i q^{23} -4.97998i q^{25} +(-3.58517 - 3.58517i) q^{27} +(-0.891113 + 0.891113i) q^{29} -1.44426 q^{31} +2.80393 q^{33} +(0.262955 - 0.262955i) q^{35} +(-1.18829 - 1.18829i) q^{37} +2.15356i q^{39} -4.71764i q^{41} +(-7.44242 - 7.44242i) q^{43} +(-0.195259 + 0.195259i) q^{45} +12.1594 q^{47} +0.0934039 q^{49} +(-0.724061 + 0.724061i) q^{51} +(-4.79265 - 4.79265i) q^{53} -0.387472i q^{55} -4.20846i q^{57} +(6.48840 + 6.48840i) q^{59} +(1.30973 - 1.30973i) q^{61} +5.12854 q^{63} +0.297599 q^{65} +(2.81837 - 2.81837i) q^{67} +(3.87482 + 3.87482i) q^{69} -6.09170i q^{71} -13.5126i q^{73} +(3.60581 + 3.60581i) q^{75} +(-5.08854 + 5.08854i) q^{77} +2.30465 q^{79} -0.662648 q^{81} +(-0.632423 + 0.632423i) q^{83} +(0.100057 + 0.100057i) q^{85} -1.29044i q^{87} -11.0377i q^{89} +(-3.90827 - 3.90827i) q^{91} +(1.04573 - 1.04573i) q^{93} -0.581564 q^{95} -17.9190 q^{97} +(3.77853 - 3.77853i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{11} - 24 q^{15} + 32 q^{17} - 12 q^{27} - 8 q^{29} + 24 q^{31} - 12 q^{35} - 8 q^{37} + 12 q^{43} - 40 q^{45} - 32 q^{47} - 32 q^{49} + 8 q^{53} + 12 q^{59} + 40 q^{63} - 8 q^{67} - 8 q^{75}+ \cdots + 24 q^{99}+O(q^{100}) $ 32 * q + 4 * q^11 - 24 * q^15 + 32 * q^17 - 12 * q^27 - 8 * q^29 + 24 * q^31 - 12 * q^35 - 8 * q^37 + 12 * q^43 - 40 * q^45 - 32 * q^47 - 32 * q^49 + 8 * q^53 + 12 * q^59 + 40 * q^63 - 8 * q^67 - 8 * q^75 + 56 * q^77 - 48 * q^79 - 64 * q^81 - 4 * q^83 + 28 * q^91 - 24 * q^93 + 40 * q^95 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1088\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.724061	+	0.724061i	−0.418037	+	0.418037i	−0.884527	−	0.466490i	$-0.845518\pi$
$3$	−0.724061	+	0.724061i	−0.418037	+	0.418037i	0.466490	+	0.884527i	$0.345518\pi$
$4$		0			0
$5$	0.100057	+	0.100057i	0.0447471	+	0.0447471i	0.729126	−	0.684379i	$-0.239927\pi$
$5$	0.100057	+	0.100057i	0.0447471	+	0.0447471i	−0.684379	+	0.729126i	$0.739927\pi$
$6$		0			0
$7$		−	2.62804i		−	0.993306i	−0.867949	−	0.496653i	$-0.834562\pi$
$7$		−	2.62804i		−	0.993306i	0.867949	−	0.496653i	$-0.165438\pi$
$8$		0			0
$9$			1.95147i			0.650490i
$10$		0			0
$11$	−1.93625	−	1.93625i	−0.583801	−	0.583801i	0.352145	−	0.935946i	$-0.385452\pi$
$11$	−1.93625	−	1.93625i	−0.583801	−	0.583801i	−0.935946	+	0.352145i	$0.885452\pi$
$12$		0			0
$13$	1.48714	−	1.48714i	0.412459	−	0.412459i	−0.470136	−	0.882594i	$-0.655795\pi$
$13$	1.48714	−	1.48714i	0.412459	−	0.412459i	0.882594	+	0.470136i	$0.155795\pi$
$14$		0			0
$15$	−0.144896			−0.0374119
$16$		0			0
$17$	1.00000			0.242536
$17$	1.00000			0.242536
$18$		0			0
$19$	−2.90615	+	2.90615i	−0.666716	+	0.666716i	−0.956954	−	0.290238i	$-0.906266\pi$
$19$	−2.90615	+	2.90615i	−0.666716	+	0.666716i	0.290238	+	0.956954i	$0.406266\pi$
$20$		0			0
$21$	1.90286	+	1.90286i	0.415239	+	0.415239i
$22$		0			0
$23$		−	5.35151i		−	1.11587i	−0.829886	−	0.557933i	$-0.811594\pi$
$23$		−	5.35151i		−	1.11587i	0.829886	−	0.557933i	$-0.188406\pi$
$24$		0			0
$25$		−	4.97998i		−	0.995995i
$26$		0			0
$27$	−3.58517	−	3.58517i	−0.689966	−	0.689966i
$28$		0			0
$29$	−0.891113	+	0.891113i	−0.165476	+	0.165476i	−0.784987	−	0.619512i	$-0.787331\pi$
$29$	−0.891113	+	0.891113i	−0.165476	+	0.165476i	0.619512	+	0.784987i	$0.287331\pi$
$30$		0			0
$31$	−1.44426			−0.259397			−0.129699	−	0.991553i	$-0.541401\pi$
$31$	−1.44426			−0.259397			−0.129699	+	0.991553i	$0.541401\pi$
$32$		0			0
$33$	2.80393			0.488101
$34$		0			0
$35$	0.262955	−	0.262955i	0.0444475	−	0.0444475i
$36$		0			0
$37$	−1.18829	−	1.18829i	−0.195354	−	0.195354i	0.602651	−	0.798005i	$-0.294111\pi$
$37$	−1.18829	−	1.18829i	−0.195354	−	0.195354i	−0.798005	+	0.602651i	$0.794111\pi$
$38$		0			0
$39$			2.15356i			0.344846i
$40$		0			0
$41$		−	4.71764i		−	0.736772i	−0.929673	−	0.368386i	$-0.879910\pi$
$41$		−	4.71764i		−	0.736772i	0.929673	−	0.368386i	$-0.120090\pi$
$42$		0			0
$43$	−7.44242	−	7.44242i	−1.13496	−	1.13496i	−0.989341	−	0.145617i	$-0.953483\pi$
$43$	−7.44242	−	7.44242i	−1.13496	−	1.13496i	−0.145617	−	0.989341i	$-0.546517\pi$
$44$		0			0
$45$	−0.195259	+	0.195259i	−0.0291075	+	0.0291075i
$46$		0			0
$47$	12.1594			1.77363			0.886813	−	0.462128i	$-0.152914\pi$
$47$	12.1594			1.77363			0.886813	+	0.462128i	$0.152914\pi$
$48$		0			0
$49$	0.0934039			0.0133434
$50$		0			0
$51$	−0.724061	+	0.724061i	−0.101389	+	0.101389i
$52$		0			0
$53$	−4.79265	−	4.79265i	−0.658321	−	0.658321i	0.296662	−	0.954983i	$-0.404127\pi$
$53$	−4.79265	−	4.79265i	−0.658321	−	0.658321i	−0.954983	+	0.296662i	$0.904127\pi$
$54$		0			0
$55$		−	0.387472i		−	0.0522468i
$56$		0			0
$57$		−	4.20846i		−	0.557424i
$58$		0			0
$59$	6.48840	+	6.48840i	0.844717	+	0.844717i	0.989468	−	0.144751i	$-0.0462381\pi$
$59$	6.48840	+	6.48840i	0.844717	+	0.844717i	−0.144751	+	0.989468i	$0.546238\pi$
$60$		0			0
$61$	1.30973	−	1.30973i	0.167693	−	0.167693i	−0.618271	−	0.785965i	$-0.712167\pi$
$61$	1.30973	−	1.30973i	0.167693	−	0.167693i	0.785965	+	0.618271i	$0.212167\pi$
$62$		0			0
$63$	5.12854			0.646136
$64$		0			0
$65$	0.297599			0.0369126
$66$		0			0
$67$	2.81837	−	2.81837i	0.344318	−	0.344318i	−0.513670	−	0.857988i	$-0.671714\pi$
$67$	2.81837	−	2.81837i	0.344318	−	0.344318i	0.857988	+	0.513670i	$0.171714\pi$
$68$		0			0
$69$	3.87482	+	3.87482i	0.466474	+	0.466474i
$70$		0			0
$71$		−	6.09170i		−	0.722952i	−0.932381	−	0.361476i	$-0.882273\pi$
$71$		−	6.09170i		−	0.722952i	0.932381	−	0.361476i	$-0.117727\pi$
$72$		0			0
$73$		−	13.5126i		−	1.58153i	−0.612121	−	0.790764i	$-0.709683\pi$
$73$		−	13.5126i		−	1.58153i	0.612121	−	0.790764i	$-0.290317\pi$
$74$		0			0
$75$	3.60581	+	3.60581i	0.416363	+	0.416363i
$76$		0			0
$77$	−5.08854	+	5.08854i	−0.579893	+	0.579893i
$78$		0			0
$79$	2.30465			0.259293			0.129647	−	0.991560i	$-0.458616\pi$
$79$	2.30465			0.259293			0.129647	+	0.991560i	$0.458616\pi$
$80$		0			0
$81$	−0.662648			−0.0736275
$82$		0			0
$83$	−0.632423	+	0.632423i	−0.0694175	+	0.0694175i	−0.740963	−	0.671546i	$-0.765631\pi$
$83$	−0.632423	+	0.632423i	−0.0694175	+	0.0694175i	0.671546	+	0.740963i	$0.265631\pi$
$84$		0			0
$85$	0.100057	+	0.100057i	0.0108528	+	0.0108528i
$86$		0			0
$87$		−	1.29044i		−	0.138350i
$88$		0			0
$89$		−	11.0377i		−	1.16999i	−0.811036	−	0.584996i	$-0.801096\pi$
$89$		−	11.0377i		−	1.16999i	0.811036	−	0.584996i	$-0.198904\pi$
$90$		0			0
$91$	−3.90827	−	3.90827i	−0.409698	−	0.409698i
$92$		0			0
$93$	1.04573	−	1.04573i	0.108438	−	0.108438i
$94$		0			0
$95$	−0.581564			−0.0596672
$96$		0			0
$97$	−17.9190			−1.81939			−0.909697	−	0.415272i	$-0.863686\pi$
$97$	−17.9190			−1.81939			−0.909697	+	0.415272i	$0.863686\pi$
$98$		0			0
$99$	3.77853	−	3.77853i	0.379757	−	0.379757i
$100$		0			0
$101$	8.80831	+	8.80831i	0.876460	+	0.876460i	0.993166	−	0.116707i	$-0.0372337\pi$
$101$	8.80831	+	8.80831i	0.876460	+	0.876460i	−0.116707	+	0.993166i	$0.537234\pi$
$102$		0			0
$103$		−	0.748496i		−	0.0737515i	−0.999320	−	0.0368758i	$-0.988259\pi$
$103$		−	0.748496i		−	0.0737515i	0.999320	−	0.0368758i	$-0.0117406\pi$
$104$		0			0
$105$			0.380791i			0.0371614i
$106$		0			0
$107$	−0.777335	−	0.777335i	−0.0751478	−	0.0751478i	0.668534	−	0.743682i	$-0.266922\pi$
$107$	−0.777335	−	0.777335i	−0.0751478	−	0.0751478i	−0.743682	+	0.668534i	$0.766922\pi$
$108$		0			0
$109$	0.462768	−	0.462768i	0.0443251	−	0.0443251i	−0.684597	−	0.728922i	$-0.740022\pi$
$109$	0.462768	−	0.462768i	0.0443251	−	0.0443251i	0.728922	+	0.684597i	$0.240022\pi$
$110$		0			0
$111$	1.72079			0.163330
$112$		0			0
$113$	4.80084			0.451625			0.225812	−	0.974171i	$-0.427496\pi$
$113$	4.80084			0.451625			0.225812	+	0.974171i	$0.427496\pi$
$114$		0			0
$115$	0.535458	−	0.535458i	0.0499318	−	0.0499318i
$116$		0			0
$117$	2.90211	+	2.90211i	0.268300	+	0.268300i
$118$		0			0
$119$		−	2.62804i		−	0.240912i
$120$		0			0
$121$		−	3.50188i		−	0.318353i
$122$		0			0
$123$	3.41586	+	3.41586i	0.307998	+	0.307998i
$124$		0			0
$125$	0.998571	−	0.998571i	0.0893149	−	0.0893149i
$126$		0			0
$127$	12.7782			1.13388			0.566940	−	0.823759i	$-0.308127\pi$
$127$	12.7782			1.13388			0.566940	+	0.823759i	$0.308127\pi$
$128$		0			0
$129$	10.7775			0.948909
$130$		0			0
$131$	−9.29049	+	9.29049i	−0.811714	+	0.811714i	−0.984891	−	0.173177i	$-0.944597\pi$
$131$	−9.29049	+	9.29049i	−0.811714	+	0.811714i	0.173177	+	0.984891i	$0.444597\pi$
$132$		0			0
$133$	7.63748	+	7.63748i	0.662253	+	0.662253i
$134$		0			0
$135$		−	0.717446i		−	0.0617479i
$136$		0			0
$137$			8.56962i			0.732152i	0.930585	+	0.366076i	$0.119299\pi$
$137$			8.56962i			0.732152i	−0.930585	+	0.366076i	$0.880701\pi$
$138$		0			0
$139$	−7.33080	−	7.33080i	−0.621790	−	0.621790i	0.324199	−	0.945989i	$-0.394905\pi$
$139$	−7.33080	−	7.33080i	−0.621790	−	0.621790i	−0.945989	+	0.324199i	$0.894905\pi$
$140$		0			0
$141$	−8.80413	+	8.80413i	−0.741441	+	0.741441i
$142$		0			0
$143$	−5.75895			−0.481587
$144$		0			0
$145$	−0.178325			−0.0148091
$146$		0			0
$147$	−0.0676302	+	0.0676302i	−0.00557804	+	0.00557804i
$148$		0			0
$149$	−10.3084	−	10.3084i	−0.844501	−	0.844501i	0.144940	−	0.989440i	$-0.453701\pi$
$149$	−10.3084	−	10.3084i	−0.844501	−	0.844501i	−0.989440	+	0.144940i	$0.953701\pi$
$150$		0			0
$151$			6.30991i			0.513493i	0.966479	+	0.256747i	$0.0826506\pi$
$151$			6.30991i			0.513493i	−0.966479	+	0.256747i	$0.917349\pi$
$152$		0			0
$153$			1.95147i			0.157767i
$154$		0			0
$155$	−0.144509	−	0.144509i	−0.0116073	−	0.0116073i
$156$		0			0
$157$	−9.08875	+	9.08875i	−0.725361	+	0.725361i	−0.969692	−	0.244331i	$-0.921432\pi$
$157$	−9.08875	+	9.08875i	−0.725361	+	0.725361i	0.244331	+	0.969692i	$0.421432\pi$
$158$		0			0
$159$	6.94034			0.550405
$160$		0			0
$161$	−14.0640			−1.10840
$162$		0			0
$163$	−2.71120	+	2.71120i	−0.212357	+	0.212357i	−0.805268	−	0.592911i	$-0.797979\pi$
$163$	−2.71120	+	2.71120i	−0.212357	+	0.212357i	0.592911	+	0.805268i	$0.297979\pi$
$164$		0			0
$165$	0.280554	+	0.280554i	0.0218411	+	0.0218411i
$166$		0			0
$167$			13.1921i			1.02084i	0.859927	+	0.510418i	$0.170509\pi$
$167$			13.1921i			1.02084i	−0.859927	+	0.510418i	$0.829491\pi$
$168$		0			0
$169$			8.57682i			0.659756i
$170$		0			0
$171$	−5.67127	−	5.67127i	−0.433692	−	0.433692i
$172$		0			0
$173$	12.2454	−	12.2454i	0.931000	−	0.931000i	−0.0667688	−	0.997768i	$-0.521269\pi$
$173$	12.2454	−	12.2454i	0.931000	−	0.931000i	0.997768	+	0.0667688i	$0.0212690\pi$
$174$		0			0
$175$	−13.0876			−0.989328
$176$		0			0
$177$	−9.39599			−0.706246
$178$		0			0
$179$	−16.5720	+	16.5720i	−1.23865	+	1.23865i	−0.278094	+	0.960554i	$0.589703\pi$
$179$	−16.5720	+	16.5720i	−1.23865	+	1.23865i	−0.960554	+	0.278094i	$0.910297\pi$
$180$		0			0
$181$	−7.36115	−	7.36115i	−0.547150	−	0.547150i	0.378465	−	0.925615i	$-0.376452\pi$
$181$	−7.36115	−	7.36115i	−0.547150	−	0.547150i	−0.925615	+	0.378465i	$0.876452\pi$
$182$		0			0
$183$			1.89665i			0.140204i
$184$		0			0
$185$		−	0.237795i		−	0.0174830i
$186$		0			0
$187$	−1.93625	−	1.93625i	−0.141593	−	0.141593i
$188$		0			0
$189$	−9.42197	+	9.42197i	−0.685347	+	0.685347i
$190$		0			0
$191$	15.7409			1.13897			0.569485	−	0.822002i	$-0.307143\pi$
$191$	15.7409			1.13897			0.569485	+	0.822002i	$0.307143\pi$
$192$		0			0
$193$	−17.4282			−1.25451			−0.627256	−	0.778813i	$-0.715822\pi$
$193$	−17.4282			−1.25451			−0.627256	+	0.778813i	$0.715822\pi$
$194$		0			0
$195$	−0.215480	+	0.215480i	−0.0154308	+	0.0154308i
$196$		0			0
$197$	19.1709	+	19.1709i	1.36587	+	1.36587i	0.866242	+	0.499625i	$0.166529\pi$
$197$	19.1709	+	19.1709i	1.36587	+	1.36587i	0.499625	+	0.866242i	$0.333471\pi$
$198$		0			0
$199$			20.4340i			1.44853i	0.689523	+	0.724264i	$0.257820\pi$
$199$			20.4340i			1.44853i	−0.689523	+	0.724264i	$0.742180\pi$
$200$		0			0
$201$			4.08134i			0.287876i
$202$		0			0
$203$	2.34188	+	2.34188i	0.164368	+	0.164368i
$204$		0			0
$205$	0.472036	−	0.472036i	0.0329684	−	0.0329684i
$206$		0			0
$207$	10.4433			0.725860
$208$		0			0
$209$	11.2541			0.778459
$210$		0			0
$211$	−2.87667	+	2.87667i	−0.198038	+	0.198038i	−0.799158	−	0.601121i	$-0.794721\pi$
$211$	−2.87667	+	2.87667i	−0.198038	+	0.198038i	0.601121	+	0.799158i	$0.294721\pi$
$212$		0			0
$213$	4.41076	+	4.41076i	0.302221	+	0.302221i
$214$		0			0
$215$		−	1.48934i		−	0.101572i
$216$		0			0
$217$			3.79558i			0.257661i
$218$		0			0
$219$	9.78394	+	9.78394i	0.661137	+	0.661137i
$220$		0			0
$221$	1.48714	−	1.48714i	0.100036	−	0.100036i
$222$		0			0
$223$	−7.95897			−0.532972			−0.266486	−	0.963839i	$-0.585863\pi$
$223$	−7.95897			−0.532972			−0.266486	+	0.963839i	$0.585863\pi$
$224$		0			0
$225$	9.71828			0.647885
$226$		0			0
$227$	9.46740	−	9.46740i	0.628373	−	0.628373i	−0.319285	−	0.947659i	$-0.603443\pi$
$227$	9.46740	−	9.46740i	0.628373	−	0.628373i	0.947659	+	0.319285i	$0.103443\pi$
$228$		0			0
$229$	−6.64475	−	6.64475i	−0.439097	−	0.439097i	0.452611	−	0.891708i	$-0.350493\pi$
$229$	−6.64475	−	6.64475i	−0.439097	−	0.439097i	−0.891708	+	0.452611i	$0.850493\pi$
$230$		0			0
$231$		−	7.36883i		−	0.484833i
$232$		0			0
$233$		−	9.69196i		−	0.634941i	−0.948268	−	0.317471i	$-0.897166\pi$
$233$		−	9.69196i		−	0.634941i	0.948268	−	0.317471i	$-0.102834\pi$
$234$		0			0
$235$	1.21664	+	1.21664i	0.0793646	+	0.0793646i
$236$		0			0
$237$	−1.66871	+	1.66871i	−0.108394	+	0.108394i
$238$		0			0
$239$	−24.0720			−1.55709			−0.778544	−	0.627590i	$-0.784042\pi$
$239$	−24.0720			−1.55709			−0.778544	+	0.627590i	$0.784042\pi$
$240$		0			0
$241$	16.5827			1.06819			0.534094	−	0.845425i	$-0.320653\pi$
$241$	16.5827			1.06819			0.534094	+	0.845425i	$0.320653\pi$
$242$		0			0
$243$	11.2353	−	11.2353i	0.720745	−	0.720745i
$244$		0			0
$245$	0.00934576	+	0.00934576i	0.000597079	+	0.000597079i
$246$		0			0
$247$			8.64371i			0.549986i
$248$		0			0
$249$		−	0.915826i		−	0.0580381i
$250$		0			0
$251$	8.65825	+	8.65825i	0.546504	+	0.546504i	0.925428	−	0.378924i	$-0.123706\pi$
$251$	8.65825	+	8.65825i	0.546504	+	0.546504i	−0.378924	+	0.925428i	$0.623706\pi$
$252$		0			0
$253$	−10.3618	+	10.3618i	−0.651444	+	0.651444i
$254$		0			0
$255$	−0.144896			−0.00907371
$256$		0			0
$257$	−1.98761			−0.123984			−0.0619919	−	0.998077i	$-0.519745\pi$
$257$	−1.98761			−0.123984			−0.0619919	+	0.998077i	$0.519745\pi$
$258$		0			0
$259$	−3.12287	+	3.12287i	−0.194046	+	0.194046i
$260$		0			0
$261$	−1.73898	−	1.73898i	−0.107640	−	0.107640i
$262$		0			0
$263$			12.2436i			0.754970i	0.926016	+	0.377485i	$0.123211\pi$
$263$			12.2436i			0.754970i	−0.926016	+	0.377485i	$0.876789\pi$
$264$		0			0
$265$		−	0.959081i		−	0.0589158i
$266$		0			0
$267$	7.99195	+	7.99195i	0.489100	+	0.489100i
$268$		0			0
$269$	7.98261	−	7.98261i	0.486708	−	0.486708i	−0.420558	−	0.907266i	$-0.638166\pi$
$269$	7.98261	−	7.98261i	0.486708	−	0.486708i	0.907266	+	0.420558i	$0.138166\pi$
$270$		0			0
$271$	−0.445628			−0.0270700			−0.0135350	−	0.999908i	$-0.504308\pi$
$271$	−0.445628			−0.0270700			−0.0135350	+	0.999908i	$0.504308\pi$
$272$		0			0
$273$	5.65965			0.342537
$274$		0			0
$275$	−9.64247	+	9.64247i	−0.581463	+	0.581463i
$276$		0			0
$277$	22.1926	+	22.1926i	1.33342	+	1.33342i	0.902289	+	0.431133i	$0.141886\pi$
$277$	22.1926	+	22.1926i	1.33342	+	1.33342i	0.431133	+	0.902289i	$0.358114\pi$
$278$		0			0
$279$		−	2.81844i		−	0.168735i
$280$		0			0
$281$			29.1670i			1.73996i	0.493087	+	0.869980i	$0.335868\pi$
$281$			29.1670i			1.73996i	−0.493087	+	0.869980i	$0.664132\pi$
$282$		0			0
$283$	−7.50613	−	7.50613i	−0.446193	−	0.446193i	0.447894	−	0.894087i	$-0.352174\pi$
$283$	−7.50613	−	7.50613i	−0.446193	−	0.446193i	−0.894087	+	0.447894i	$0.852174\pi$
$284$		0			0
$285$	0.421088	−	0.421088i	0.0249431	−	0.0249431i
$286$		0			0
$287$	−12.3982			−0.731840
$288$		0			0
$289$	1.00000			0.0588235
$290$		0			0
$291$	12.9744	−	12.9744i	0.760574	−	0.760574i
$292$		0			0
$293$	−6.90203	−	6.90203i	−0.403221	−	0.403221i	0.476146	−	0.879366i	$-0.342033\pi$
$293$	−6.90203	−	6.90203i	−0.403221	−	0.403221i	−0.879366	+	0.476146i	$0.842033\pi$
$294$		0			0
$295$			1.29843i			0.0755972i
$296$		0			0
$297$			13.8836i			0.805605i
$298$		0			0
$299$	−7.95845	−	7.95845i	−0.460249	−	0.460249i
$300$		0			0
$301$	−19.5590	+	19.5590i	−1.12736	+	1.12736i
$302$		0			0
$303$	−12.7555			−0.732785
$304$		0			0
$305$	0.262096			0.0150076
$306$		0			0
$307$	−3.04718	+	3.04718i	−0.173912	+	0.173912i	−0.788696	−	0.614784i	$-0.789243\pi$
$307$	−3.04718	+	3.04718i	−0.173912	+	0.173912i	0.614784	+	0.788696i	$0.289243\pi$
$308$		0			0
$309$	0.541957	+	0.541957i	0.0308309	+	0.0308309i
$310$		0			0
$311$		−	20.0156i		−	1.13498i	−0.823381	−	0.567489i	$-0.807915\pi$
$311$		−	20.0156i		−	1.13498i	0.823381	−	0.567489i	$-0.192085\pi$
$312$		0			0
$313$			27.5542i			1.55746i	0.627362	+	0.778728i	$0.284135\pi$
$313$			27.5542i			1.55746i	−0.627362	+	0.778728i	$0.715865\pi$
$314$		0			0
$315$	0.513149	+	0.513149i	0.0289127	+	0.0289127i
$316$		0			0
$317$	21.4263	−	21.4263i	1.20342	−	1.20342i	0.230302	−	0.973119i	$-0.426029\pi$
$317$	21.4263	−	21.4263i	1.20342	−	1.20342i	0.973119	−	0.230302i	$-0.0739714\pi$
$318$		0			0
$319$	3.45083			0.193210
$320$		0			0
$321$	1.12568			0.0628291
$322$		0			0
$323$	−2.90615	+	2.90615i	−0.161702	+	0.161702i
$324$		0			0
$325$	−7.40593	−	7.40593i	−0.410807	−	0.410807i
$326$		0			0
$327$			0.670145i			0.0370591i
$328$		0			0
$329$		−	31.9553i		−	1.76175i
$330$		0			0
$331$	−0.466937	−	0.466937i	−0.0256652	−	0.0256652i	0.694158	−	0.719823i	$-0.255777\pi$
$331$	−0.466937	−	0.466937i	−0.0256652	−	0.0256652i	−0.719823	+	0.694158i	$0.755777\pi$
$332$		0			0
$333$	2.31891	−	2.31891i	0.127076	−	0.127076i
$334$		0			0
$335$	0.563997			0.0308145
$336$		0			0
$337$	13.5762			0.739541			0.369770	−	0.929123i	$-0.379436\pi$
$337$	13.5762			0.739541			0.369770	+	0.929123i	$0.379436\pi$
$338$		0			0
$339$	−3.47610	+	3.47610i	−0.188796	+	0.188796i
$340$		0			0
$341$	2.79645	+	2.79645i	0.151436	+	0.151436i
$342$		0			0
$343$		−	18.6418i		−	1.00656i
$344$		0			0
$345$			0.775410i			0.0417466i
$346$		0			0
$347$	22.0844	+	22.0844i	1.18555	+	1.18555i	0.978285	+	0.207266i	$0.0664566\pi$
$347$	22.0844	+	22.0844i	1.18555	+	1.18555i	0.207266	+	0.978285i	$0.433543\pi$
$348$		0			0
$349$	1.79835	−	1.79835i	0.0962633	−	0.0962633i	−0.657335	−	0.753598i	$-0.728316\pi$
$349$	1.79835	−	1.79835i	0.0962633	−	0.0962633i	0.753598	+	0.657335i	$0.228316\pi$
$350$		0			0
$351$	−10.6633			−0.569165
$352$		0			0
$353$	−2.22119			−0.118222			−0.0591110	−	0.998251i	$-0.518827\pi$
$353$	−2.22119			−0.118222			−0.0591110	+	0.998251i	$0.518827\pi$
$354$		0			0
$355$	0.609520	−	0.609520i	0.0323500	−	0.0323500i
$356$		0			0
$357$	1.90286	+	1.90286i	0.100710	+	0.100710i
$358$		0			0
$359$		−	1.52104i		−	0.0802776i	−0.999194	−	0.0401388i	$-0.987220\pi$
$359$		−	1.52104i		−	0.0802776i	0.999194	−	0.0401388i	$-0.0127800\pi$
$360$		0			0
$361$			2.10859i			0.110978i
$362$		0			0
$363$	2.53558	+	2.53558i	0.133083	+	0.133083i
$364$		0			0
$365$	1.35204	−	1.35204i	0.0707688	−	0.0707688i
$366$		0			0
$367$	−33.3249			−1.73955			−0.869774	−	0.493451i	$-0.835735\pi$
$367$	−33.3249			−1.73955			−0.869774	+	0.493451i	$0.835735\pi$
$368$		0			0
$369$	9.20634			0.479263
$370$		0			0
$371$	−12.5953	+	12.5953i	−0.653914	+	0.653914i
$372$		0			0
$373$	−24.8863	−	24.8863i	−1.28856	−	1.28856i	−0.935659	−	0.352906i	$-0.885194\pi$
$373$	−24.8863	−	24.8863i	−1.28856	−	1.28856i	−0.352906	−	0.935659i	$-0.614806\pi$
$374$		0			0
$375$			1.44605i			0.0746739i
$376$		0			0
$377$			2.65042i			0.136504i
$378$		0			0
$379$	−12.4894	−	12.4894i	−0.641536	−	0.641536i	0.309397	−	0.950933i	$-0.399873\pi$
$379$	−12.4894	−	12.4894i	−0.641536	−	0.641536i	−0.950933	+	0.309397i	$0.899873\pi$
$380$		0			0
$381$	−9.25219	+	9.25219i	−0.474004	+	0.474004i
$382$		0			0
$383$	26.7131			1.36498			0.682488	−	0.730897i	$-0.260898\pi$
$383$	26.7131			1.36498			0.682488	+	0.730897i	$0.260898\pi$
$384$		0			0
$385$	−1.01829			−0.0518970
$386$		0			0
$387$	14.5237	−	14.5237i	0.738279	−	0.738279i
$388$		0			0
$389$	−2.66266	−	2.66266i	−0.135002	−	0.135002i	0.636376	−	0.771379i	$-0.280433\pi$
$389$	−2.66266	−	2.66266i	−0.135002	−	0.135002i	−0.771379	+	0.636376i	$0.780433\pi$
$390$		0			0
$391$		−	5.35151i		−	0.270637i
$392$		0			0
$393$		−	13.4538i		−	0.678653i
$394$		0			0
$395$	0.230597	+	0.230597i	0.0116026	+	0.0116026i
$396$		0			0
$397$	12.2181	−	12.2181i	0.613209	−	0.613209i	−0.330572	−	0.943781i	$-0.607241\pi$
$397$	12.2181	−	12.2181i	0.613209	−	0.613209i	0.943781	+	0.330572i	$0.107241\pi$
$398$		0			0
$399$	−11.0600			−0.553693
$400$		0			0
$401$	−26.8473			−1.34069			−0.670346	−	0.742049i	$-0.733854\pi$
$401$	−26.8473			−1.34069			−0.670346	+	0.742049i	$0.733854\pi$
$402$		0			0
$403$	−2.14782	+	2.14782i	−0.106991	+	0.106991i
$404$		0			0
$405$	−0.0663029	−	0.0663029i	−0.00329462	−	0.00329462i
$406$		0			0
$407$			4.60165i			0.228095i
$408$		0			0
$409$			17.8962i			0.884910i	0.896791	+	0.442455i	$0.145892\pi$
$409$			17.8962i			0.884910i	−0.896791	+	0.442455i	$0.854108\pi$
$410$		0			0
$411$	−6.20493	−	6.20493i	−0.306067	−	0.306067i
$412$		0			0
$413$	17.0518	−	17.0518i	0.839063	−	0.839063i
$414$		0			0
$415$	−0.126557			−0.00621246
$416$		0			0
$417$	10.6159			0.519862
$418$		0			0
$419$	17.1549	−	17.1549i	0.838073	−	0.838073i	−0.150533	−	0.988605i	$-0.548099\pi$
$419$	17.1549	−	17.1549i	0.838073	−	0.838073i	0.988605	+	0.150533i	$0.0480988\pi$
$420$		0			0
$421$	−28.2854	−	28.2854i	−1.37855	−	1.37855i	−0.847077	−	0.531471i	$-0.821640\pi$
$421$	−28.2854	−	28.2854i	−1.37855	−	1.37855i	−0.531471	−	0.847077i	$-0.678360\pi$
$422$		0			0
$423$			23.7287i			1.15373i
$424$		0			0
$425$		−	4.97998i		−	0.241564i
$426$		0			0
$427$	−3.44202	−	3.44202i	−0.166571	−	0.166571i
$428$		0			0
$429$	4.16983	−	4.16983i	0.201321	−	0.201321i
$430$		0			0
$431$	11.5554			0.556605			0.278303	−	0.960493i	$-0.410228\pi$
$431$	11.5554			0.556605			0.278303	+	0.960493i	$0.410228\pi$
$432$		0			0
$433$	0.357537			0.0171821			0.00859107	−	0.999963i	$-0.497265\pi$
$433$	0.357537			0.0171821			0.00859107	+	0.999963i	$0.497265\pi$
$434$		0			0
$435$	0.129118	−	0.129118i	0.00619075	−	0.00619075i
$436$		0			0
$437$	15.5523	+	15.5523i	0.743967	+	0.743967i
$438$		0			0
$439$		−	7.54117i		−	0.359920i	−0.983674	−	0.179960i	$-0.942403\pi$
$439$		−	7.54117i		−	0.359920i	0.983674	−	0.179960i	$-0.0575969\pi$
$440$		0			0
$441$			0.182275i			0.00867976i
$442$		0			0
$443$	18.1559	+	18.1559i	0.862613	+	0.862613i	0.991641	−	0.129028i	$-0.0411856\pi$
$443$	18.1559	+	18.1559i	0.862613	+	0.862613i	−0.129028	+	0.991641i	$0.541186\pi$
$444$		0			0
$445$	1.10440	−	1.10440i	0.0523537	−	0.0523537i
$446$		0			0
$447$	14.9279			0.706065
$448$		0			0
$449$	18.0732			0.852927			0.426463	−	0.904505i	$-0.359759\pi$
$449$	18.0732			0.852927			0.426463	+	0.904505i	$0.359759\pi$
$450$		0			0
$451$	−9.13453	+	9.13453i	−0.430128	+	0.430128i
$452$		0			0
$453$	−4.56876	−	4.56876i	−0.214659	−	0.214659i
$454$		0			0
$455$		−	0.782103i		−	0.0366655i
$456$		0			0
$457$			37.4375i			1.75125i	0.482991	+	0.875625i	$0.339550\pi$
$457$			37.4375i			1.75125i	−0.482991	+	0.875625i	$0.660450\pi$
$458$		0			0
$459$	−3.58517	−	3.58517i	−0.167341	−	0.167341i
$460$		0			0
$461$	14.0370	−	14.0370i	0.653770	−	0.653770i	−0.300129	−	0.953899i	$-0.597030\pi$
$461$	14.0370	−	14.0370i	0.653770	−	0.653770i	0.953899	+	0.300129i	$0.0970297\pi$
$462$		0			0
$463$	18.3120			0.851030			0.425515	−	0.904951i	$-0.360093\pi$
$463$	18.3120			0.851030			0.425515	+	0.904951i	$0.360093\pi$
$464$		0			0
$465$	0.209267			0.00970453
$466$		0			0
$467$	8.99457	−	8.99457i	0.416219	−	0.416219i	−0.467679	−	0.883898i	$-0.654910\pi$
$467$	8.99457	−	8.99457i	0.416219	−	0.416219i	0.883898	+	0.467679i	$0.154910\pi$
$468$		0			0
$469$	−7.40678	−	7.40678i	−0.342013	−	0.342013i
$470$		0			0
$471$		−	13.1616i		−	0.606456i
$472$		0			0
$473$			28.8207i			1.32518i
$474$		0			0
$475$	14.4726	+	14.4726i	0.664047	+	0.664047i
$476$		0			0
$477$	9.35271	−	9.35271i	0.428231	−	0.428231i
$478$		0			0
$479$	6.50691			0.297308			0.148654	−	0.988889i	$-0.452506\pi$
$479$	6.50691			0.297308			0.148654	+	0.988889i	$0.452506\pi$
$480$		0			0
$481$	−3.53431			−0.161151
$482$		0			0
$483$	10.1832	−	10.1832i	0.463351	−	0.463351i
$484$		0			0
$485$	−1.79293	−	1.79293i	−0.0814126	−	0.0814126i
$486$		0			0
$487$		−	19.6338i		−	0.889694i	−0.895606	−	0.444847i	$-0.853258\pi$
$487$		−	19.6338i		−	0.889694i	0.895606	−	0.444847i	$-0.146742\pi$
$488$		0			0
$489$		−	3.92615i		−	0.177546i
$490$		0			0
$491$	−7.46270	−	7.46270i	−0.336787	−	0.336787i	0.518370	−	0.855157i	$-0.326539\pi$
$491$	−7.46270	−	7.46270i	−0.336787	−	0.336787i	−0.855157	+	0.518370i	$0.826539\pi$
$492$		0			0
$493$	−0.891113	+	0.891113i	−0.0401337	+	0.0401337i
$494$		0			0
$495$	0.756141			0.0339860
$496$		0			0
$497$	−16.0092			−0.718112
$498$		0			0
$499$	29.7678	−	29.7678i	1.33259	−	1.33259i	0.429548	−	0.903044i	$-0.358673\pi$
$499$	29.7678	−	29.7678i	1.33259	−	1.33259i	0.903044	−	0.429548i	$-0.141327\pi$
$500$		0			0
$501$	−9.55189	−	9.55189i	−0.426747	−	0.426747i
$502$		0			0
$503$		−	2.48521i		−	0.110810i	−0.998464	−	0.0554051i	$-0.982355\pi$
$503$		−	2.48521i		−	0.110810i	0.998464	−	0.0554051i	$-0.0176450\pi$
$504$		0			0
$505$			1.76267i			0.0784380i
$506$		0			0
$507$	−6.21015	−	6.21015i	−0.275802	−	0.275802i
$508$		0			0
$509$	1.18351	−	1.18351i	0.0524581	−	0.0524581i	−0.680391	−	0.732849i	$-0.738190\pi$
$509$	1.18351	−	1.18351i	0.0524581	−	0.0524581i	0.732849	+	0.680391i	$0.238190\pi$
$510$		0			0
$511$	−35.5116			−1.57094
$512$		0			0
$513$	20.8381			0.920023
$514$		0			0
$515$	0.0748926	−	0.0748926i	0.00330016	−	0.00330016i
$516$		0			0
$517$	−23.5436	−	23.5436i	−1.03544	−	1.03544i
$518$		0			0
$519$			17.7328i			0.778385i
$520$		0			0
$521$			16.5566i			0.725358i	0.931914	+	0.362679i	$0.118138\pi$
$521$			16.5566i			0.725358i	−0.931914	+	0.362679i	$0.881862\pi$
$522$		0			0
$523$	−3.85369	−	3.85369i	−0.168510	−	0.168510i	0.617814	−	0.786324i	$-0.288018\pi$
$523$	−3.85369	−	3.85369i	−0.168510	−	0.168510i	−0.786324	+	0.617814i	$0.788018\pi$
$524$		0			0
$525$	9.47621	−	9.47621i	0.413576	−	0.413576i
$526$		0			0
$527$	−1.44426			−0.0629131
$528$		0			0
$529$	−5.63864			−0.245158
$530$		0			0
$531$	−12.6619	+	12.6619i	−0.549480	+	0.549480i
$532$		0			0
$533$	−7.01580	−	7.01580i	−0.303888	−	0.303888i
$534$		0			0
$535$		−	0.155556i		−	0.00672529i
$536$		0			0
$537$		−	23.9983i		−	1.03560i
$538$		0			0
$539$	−0.180853	−	0.180853i	−0.00778990	−	0.00778990i
$540$		0			0
$541$	−27.1691	+	27.1691i	−1.16809	+	1.16809i	−0.185433	+	0.982657i	$0.559369\pi$
$541$	−27.1691	+	27.1691i	−1.16809	+	1.16809i	−0.982657	+	0.185433i	$0.940631\pi$
$542$		0			0
$543$	10.6599			0.457458
$544$		0			0
$545$	0.0926068			0.00396684
$546$		0			0
$547$	1.77642	−	1.77642i	0.0759544	−	0.0759544i	−0.668109	−	0.744063i	$-0.732896\pi$
$547$	1.77642	−	1.77642i	0.0759544	−	0.0759544i	0.744063	+	0.668109i	$0.232896\pi$
$548$		0			0
$549$	2.55589	+	2.55589i	0.109083	+	0.109083i
$550$		0			0
$551$		−	5.17942i		−	0.220651i
$552$		0			0
$553$		−	6.05671i		−	0.257558i
$554$		0			0
$555$	0.172178	+	0.172178i	0.00730854	+	0.00730854i
$556$		0			0
$557$	11.1562	−	11.1562i	0.472702	−	0.472702i	−0.430086	−	0.902788i	$-0.641517\pi$
$557$	11.1562	−	11.1562i	0.472702	−	0.472702i	0.902788	+	0.430086i	$0.141517\pi$
$558$		0			0
$559$	−22.1358			−0.936246
$560$		0			0
$561$	2.80393			0.118382
$562$		0			0
$563$	5.69060	−	5.69060i	0.239830	−	0.239830i	−0.576950	−	0.816780i	$-0.695757\pi$
$563$	5.69060	−	5.69060i	0.239830	−	0.239830i	0.816780	+	0.576950i	$0.195757\pi$
$564$		0			0
$565$	0.480360	+	0.480360i	0.0202089	+	0.0202089i
$566$		0			0
$567$			1.74147i			0.0731347i
$568$		0			0
$569$		−	8.79716i		−	0.368796i	−0.982852	−	0.184398i	$-0.940966\pi$
$569$		−	8.79716i		−	0.368796i	0.982852	−	0.184398i	$-0.0590335\pi$
$570$		0			0
$571$	1.80244	+	1.80244i	0.0754297	+	0.0754297i	0.743815	−	0.668385i	$-0.233014\pi$
$571$	1.80244	+	1.80244i	0.0754297	+	0.0754297i	−0.668385	+	0.743815i	$0.733014\pi$
$572$		0			0
$573$	−11.3974	+	11.3974i	−0.476132	+	0.476132i
$574$		0			0
$575$	−26.6504			−1.11140
$576$		0			0
$577$	−28.9174			−1.20385			−0.601924	−	0.798554i	$-0.705599\pi$
$577$	−28.9174			−1.20385			−0.601924	+	0.798554i	$0.705599\pi$
$578$		0			0
$579$	12.6191	−	12.6191i	0.524432	−	0.524432i
$580$		0			0
$581$	1.66203	+	1.66203i	0.0689528	+	0.0689528i
$582$		0			0
$583$			18.5595i			0.768656i
$584$		0			0
$585$			0.580756i			0.0240113i
$586$		0			0
$587$	28.3756	+	28.3756i	1.17119	+	1.17119i	0.981927	+	0.189258i	$0.0606083\pi$
$587$	28.3756	+	28.3756i	1.17119	+	1.17119i	0.189258	+	0.981927i	$0.439392\pi$
$588$		0			0
$589$	4.19724	−	4.19724i	0.172944	−	0.172944i
$590$		0			0
$591$	−27.7617			−1.14197
$592$		0			0
$593$	−14.7813			−0.606995			−0.303498	−	0.952832i	$-0.598154\pi$
$593$	−14.7813			−0.606995			−0.303498	+	0.952832i	$0.598154\pi$
$594$		0			0
$595$	0.262955	−	0.262955i	0.0107801	−	0.0107801i
$596$		0			0
$597$	−14.7955	−	14.7955i	−0.605538	−	0.605538i
$598$		0			0
$599$		−	20.9554i		−	0.856213i	−0.903728	−	0.428106i	$-0.859181\pi$
$599$		−	20.9554i		−	0.856213i	0.903728	−	0.428106i	$-0.140819\pi$
$600$		0			0
$601$		−	43.8547i		−	1.78887i	−0.447199	−	0.894435i	$-0.647578\pi$
$601$		−	43.8547i		−	1.78887i	0.447199	−	0.894435i	$-0.352422\pi$
$602$		0			0
$603$	5.49996	+	5.49996i	0.223976	+	0.223976i
$604$		0			0
$605$	0.350390	−	0.350390i	0.0142454	−	0.0142454i
$606$		0			0
$607$	41.3621			1.67884			0.839418	−	0.543487i	$-0.182896\pi$
$607$	41.3621			1.67884			0.839418	+	0.543487i	$0.182896\pi$
$608$		0			0
$609$	−3.39133			−0.137424
$610$		0			0
$611$	18.0827	−	18.0827i	0.731548	−	0.731548i
$612$		0			0
$613$	−26.7053	−	26.7053i	−1.07862	−	1.07862i	−0.996634	−	0.0819848i	$-0.973874\pi$
$613$	−26.7053	−	26.7053i	−1.07862	−	1.07862i	−0.0819848	−	0.996634i	$-0.526126\pi$
$614$		0			0
$615$			0.683565i			0.0275640i
$616$		0			0
$617$		−	19.4571i		−	0.783314i	−0.920111	−	0.391657i	$-0.871902\pi$
$617$		−	19.4571i		−	0.783314i	0.920111	−	0.391657i	$-0.128098\pi$
$618$		0			0
$619$	−9.08683	−	9.08683i	−0.365231	−	0.365231i	0.500504	−	0.865734i	$-0.333148\pi$
$619$	−9.08683	−	9.08683i	−0.365231	−	0.365231i	−0.865734	+	0.500504i	$0.833148\pi$
$620$		0			0
$621$	−19.1861	+	19.1861i	−0.769910	+	0.769910i
$622$		0			0
$623$	−29.0075			−1.16216
$624$		0			0
$625$	−24.7001			−0.988002
$626$		0			0
$627$	−8.14863	+	8.14863i	−0.325425	+	0.325425i
$628$		0			0
$629$	−1.18829	−	1.18829i	−0.0473802	−	0.0473802i
$630$		0			0
$631$		−	17.7992i		−	0.708577i	−0.935136	−	0.354288i	$-0.884723\pi$
$631$		−	17.7992i		−	0.708577i	0.935136	−	0.354288i	$-0.115277\pi$
$632$		0			0
$633$		−	4.16577i		−	0.165574i
$634$		0			0
$635$	1.27855	+	1.27855i	0.0507378	+	0.0507378i
$636$		0			0
$637$	0.138905	−	0.138905i	0.00550361	−	0.00550361i
$638$		0			0
$639$	11.8878			0.470273
$640$		0			0
$641$	−3.54239			−0.139916			−0.0699580	−	0.997550i	$-0.522287\pi$
$641$	−3.54239			−0.139916			−0.0699580	+	0.997550i	$0.522287\pi$
$642$		0			0
$643$	6.39752	−	6.39752i	0.252294	−	0.252294i	−0.569617	−	0.821910i	$-0.692908\pi$
$643$	6.39752	−	6.39752i	0.252294	−	0.252294i	0.821910	+	0.569617i	$0.192908\pi$
$644$		0			0
$645$	1.07837	+	1.07837i	0.0424609	+	0.0424609i
$646$		0			0
$647$		−	2.11694i		−	0.0832255i	−0.999134	−	0.0416127i	$-0.986750\pi$
$647$		−	2.11694i		−	0.0832255i	0.999134	−	0.0416127i	$-0.0132496\pi$
$648$		0			0
$649$		−	25.1263i		−	0.986293i
$650$		0			0
$651$	−2.74823	−	2.74823i	−0.107712	−	0.107712i
$652$		0			0
$653$	19.0110	−	19.0110i	0.743958	−	0.743958i	−0.229379	−	0.973337i	$-0.573670\pi$
$653$	19.0110	−	19.0110i	0.743958	−	0.743958i	0.973337	+	0.229379i	$0.0736695\pi$
$654$		0			0
$655$	−1.85917			−0.0726436
$656$		0			0
$657$	26.3694			1.02877
$658$		0			0
$659$	4.51444	−	4.51444i	0.175858	−	0.175858i	−0.613690	−	0.789547i	$-0.710315\pi$
$659$	4.51444	−	4.51444i	0.175858	−	0.175858i	0.789547	+	0.613690i	$0.210315\pi$
$660$		0			0
$661$	9.76412	+	9.76412i	0.379780	+	0.379780i	0.871023	−	0.491243i	$-0.163457\pi$
$661$	9.76412	+	9.76412i	0.379780	+	0.379780i	−0.491243	+	0.871023i	$0.663457\pi$
$662$		0			0
$663$			2.15356i			0.0836374i
$664$		0			0
$665$			1.52837i			0.0592678i
$666$		0			0
$667$	4.76880	+	4.76880i	0.184649	+	0.184649i
$668$		0			0
$669$	5.76278	−	5.76278i	0.222802	−	0.222802i
$670$		0			0
$671$	−5.07192			−0.195799
$672$		0			0
$673$	21.9260			0.845186			0.422593	−	0.906319i	$-0.361120\pi$
$673$	21.9260			0.845186			0.422593	+	0.906319i	$0.361120\pi$
$674$		0			0
$675$	−17.8541	+	17.8541i	−0.687203	+	0.687203i
$676$		0			0
$677$	23.4977	+	23.4977i	0.903088	+	0.903088i	0.995702	−	0.0926137i	$-0.0295222\pi$
$677$	23.4977	+	23.4977i	0.903088	+	0.903088i	−0.0926137	+	0.995702i	$0.529522\pi$
$678$		0			0
$679$			47.0917i			1.80722i
$680$		0			0
$681$			13.7100i			0.525367i
$682$		0			0
$683$	−23.6192	−	23.6192i	−0.903765	−	0.903765i	0.0919944	−	0.995760i	$-0.470676\pi$
$683$	−23.6192	−	23.6192i	−0.903765	−	0.903765i	−0.995760	+	0.0919944i	$0.970676\pi$
$684$		0			0
$685$	−0.857455	+	0.857455i	−0.0327617	+	0.0327617i
$686$		0			0
$687$	9.62241			0.367118
$688$		0			0
$689$	−14.2547			−0.543060
$690$		0			0
$691$	26.2542	−	26.2542i	0.998755	−	0.998755i	−0.00124381	−	0.999999i	$-0.500396\pi$
$691$	26.2542	−	26.2542i	0.998755	−	0.998755i	0.999999	+	0.00124381i	$0.000395918\pi$
$692$		0			0
$693$	−9.93013	−	9.93013i	−0.377215	−	0.377215i
$694$		0			0
$695$		−	1.46700i		−	0.0556466i
$696$		0			0
$697$		−	4.71764i		−	0.178694i
$698$		0			0
$699$	7.01757	+	7.01757i	0.265429	+	0.265429i
$700$		0			0
$701$	−10.9200	+	10.9200i	−0.412444	+	0.412444i	−0.882589	−	0.470145i	$-0.844202\pi$
$701$	−10.9200	+	10.9200i	−0.412444	+	0.412444i	0.470145	+	0.882589i	$0.344202\pi$
$702$		0			0
$703$	6.90670			0.260491
$704$		0			0
$705$	−1.76184			−0.0663547
$706$		0			0
$707$	23.1486	−	23.1486i	0.870593	−	0.870593i
$708$		0			0
$709$	33.1421	+	33.1421i	1.24468	+	1.24468i	0.958039	+	0.286638i	$0.0925377\pi$
$709$	33.1421	+	33.1421i	1.24468	+	1.24468i	0.286638	+	0.958039i	$0.407462\pi$
$710$		0			0
$711$			4.49745i			0.168668i
$712$		0			0
$713$			7.72898i			0.289453i
$714$		0			0
$715$	−0.576226	−	0.576226i	−0.0215496	−	0.0215496i
$716$		0			0
$717$	17.4296	−	17.4296i	0.650921	−	0.650921i
$718$		0			0
$719$	−9.31625			−0.347437			−0.173719	−	0.984795i	$-0.555578\pi$
$719$	−9.31625			−0.347437			−0.173719	+	0.984795i	$0.555578\pi$
$720$		0			0
$721$	−1.96708			−0.0732578
$722$		0			0
$723$	−12.0069	+	12.0069i	−0.446542	+	0.446542i
$724$		0			0
$725$	4.43772	+	4.43772i	0.164813	+	0.164813i
$726$		0			0
$727$		−	50.6097i		−	1.87701i	−0.345266	−	0.938505i	$-0.612211\pi$
$727$		−	50.6097i		−	1.87701i	0.345266	−	0.938505i	$-0.387789\pi$
$728$		0			0
$729$			14.2822i			0.528969i
$730$		0			0
$731$	−7.44242	−	7.44242i	−0.275268	−	0.275268i
$732$		0			0
$733$	27.4040	−	27.4040i	1.01219	−	1.01219i	0.0122657	−	0.999925i	$-0.496096\pi$
$733$	27.4040	−	27.4040i	1.01219	−	1.01219i	0.999925	−	0.0122657i	$-0.00390438\pi$
$734$		0			0
$735$	−0.0135338			−0.000499202
$736$		0			0
$737$	−10.9141			−0.402027
$738$		0			0
$739$	13.2619	−	13.2619i	0.487848	−	0.487848i	−0.419779	−	0.907626i	$-0.637892\pi$
$739$	13.2619	−	13.2619i	0.487848	−	0.487848i	0.907626	+	0.419779i	$0.137892\pi$
$740$		0			0
$741$	−6.25857	−	6.25857i	−0.229914	−	0.229914i
$742$		0			0
$743$			23.9937i			0.880244i	0.897938	+	0.440122i	$0.145065\pi$
$743$			23.9937i			0.880244i	−0.897938	+	0.440122i	$0.854935\pi$
$744$		0			0
$745$		−	2.06287i		−	0.0755779i
$746$		0			0
$747$	−1.23416	−	1.23416i	−0.0451554	−	0.0451554i
$748$		0			0
$749$	−2.04287	+	2.04287i	−0.0746448	+	0.0746448i
$750$		0			0
$751$	−28.4233			−1.03718			−0.518590	−	0.855023i	$-0.673543\pi$
$751$	−28.4233			−1.03718			−0.518590	+	0.855023i	$0.673543\pi$
$752$		0			0
$753$	−12.5382			−0.456918
$754$		0			0
$755$	−0.631354	+	0.631354i	−0.0229773	+	0.0229773i
$756$		0			0
$757$	24.5037	+	24.5037i	0.890602	+	0.890602i	0.994580	−	0.103977i	$-0.0331570\pi$
$757$	24.5037	+	24.5037i	0.890602	+	0.890602i	−0.103977	+	0.994580i	$0.533157\pi$
$758$		0			0
$759$		−	15.0052i		−	0.544655i
$760$		0			0
$761$			9.53970i			0.345814i	0.984938	+	0.172907i	$0.0553160\pi$
$761$			9.53970i			0.345814i	−0.984938	+	0.172907i	$0.944684\pi$
$762$		0			0
$763$	−1.21617	−	1.21617i	−0.0440284	−	0.0440284i
$764$		0			0
$765$	−0.195259	+	0.195259i	−0.00705961	+	0.00705961i
$766$		0			0
$767$	19.2983			0.696822
$768$		0			0
$769$	25.2175			0.909366			0.454683	−	0.890653i	$-0.349753\pi$
$769$	25.2175			0.909366			0.454683	+	0.890653i	$0.349753\pi$
$770$		0			0
$771$	1.43915	−	1.43915i	0.0518298	−	0.0518298i
$772$		0			0
$773$	33.4601	+	33.4601i	1.20348	+	1.20348i	0.973102	+	0.230375i	$0.0739954\pi$
$773$	33.4601	+	33.4601i	1.20348	+	1.20348i	0.230375	+	0.973102i	$0.426005\pi$
$774$		0			0
$775$			7.19239i			0.258358i
$776$		0			0
$777$		−	4.52230i		−	0.162237i
$778$		0			0
$779$	13.7102	+	13.7102i	0.491218	+	0.491218i
$780$		0			0
$781$	−11.7950	+	11.7950i	−0.422060	+	0.422060i
$782$		0			0
$783$	6.38958			0.228345
$784$		0			0
$785$	−1.81880			−0.0649156
$786$		0			0
$787$	−25.7204	+	25.7204i	−0.916832	+	0.916832i	−0.996798	−	0.0799660i	$-0.974519\pi$
$787$	−25.7204	+	25.7204i	−0.916832	+	0.916832i	0.0799660	+	0.996798i	$0.474519\pi$
$788$		0			0
$789$	−8.86508	−	8.86508i	−0.315605	−	0.315605i
$790$		0			0
$791$		−	12.6168i		−	0.448601i
$792$		0			0
$793$		−	3.89550i		−	0.138333i
$794$		0			0
$795$	0.694433	+	0.694433i	0.0246290	+	0.0246290i
$796$		0			0
$797$	31.1741	−	31.1741i	1.10424	−	1.10424i	0.110352	−	0.993893i	$-0.464802\pi$
$797$	31.1741	−	31.1741i	1.10424	−	1.10424i	0.993893	−	0.110352i	$-0.0351978\pi$
$798$		0			0
$799$	12.1594			0.430168
$800$		0			0
$801$	21.5397			0.761068
$802$		0			0
$803$	−26.1637	+	26.1637i	−0.923298	+	0.923298i
$804$		0			0
$805$	−1.40721	−	1.40721i	−0.0495975	−	0.0495975i
$806$		0			0
$807$			11.5598i			0.406924i
$808$		0			0
$809$			23.8830i			0.839681i	0.907598	+	0.419840i	$0.137914\pi$
$809$			23.8830i			0.839681i	−0.907598	+	0.419840i	$0.862086\pi$
$810$		0			0
$811$	−29.5247	−	29.5247i	−1.03675	−	1.03675i	−0.999298	−	0.0374533i	$-0.988075\pi$
$811$	−29.5247	−	29.5247i	−1.03675	−	1.03675i	−0.0374533	−	0.999298i	$-0.511925\pi$
$812$		0			0
$813$	0.322662	−	0.322662i	0.0113163	−	0.0113163i
$814$		0			0
$815$	−0.542551			−0.0190047
$816$		0			0
$817$	43.2576			1.51339
$818$		0			0
$819$	7.62687	−	7.62687i	0.266504	−	0.266504i
$820$		0			0
$821$	−10.1861	−	10.1861i	−0.355496	−	0.355496i	0.506654	−	0.862150i	$-0.330882\pi$
$821$	−10.1861	−	10.1861i	−0.355496	−	0.355496i	−0.862150	+	0.506654i	$0.830882\pi$
$822$		0			0
$823$			55.6252i			1.93897i	0.245148	+	0.969486i	$0.421163\pi$
$823$			55.6252i			1.93897i	−0.245148	+	0.969486i	$0.578837\pi$
$824$		0			0
$825$		−	13.9635i		−	0.486146i
$826$		0			0
$827$	18.1650	+	18.1650i	0.631660	+	0.631660i	0.948484	−	0.316824i	$-0.102617\pi$
$827$	18.1650	+	18.1650i	0.631660	+	0.631660i	−0.316824	+	0.948484i	$0.602617\pi$
$828$		0			0
$829$	−10.1346	+	10.1346i	−0.351989	+	0.351989i	−0.860849	−	0.508860i	$-0.830067\pi$
$829$	−10.1346	+	10.1346i	−0.351989	+	0.351989i	0.508860	+	0.860849i	$0.330067\pi$
$830$		0			0
$831$	−32.1375			−1.11484
$832$		0			0
$833$	0.0934039			0.00323625
$834$		0			0
$835$	−1.31997	+	1.31997i	−0.0456794	+	0.0456794i
$836$		0			0
$837$	5.17792	+	5.17792i	0.178975	+	0.178975i
$838$		0			0
$839$		−	44.9141i		−	1.55061i	−0.631589	−	0.775303i	$-0.717597\pi$
$839$		−	44.9141i		−	1.55061i	0.631589	−	0.775303i	$-0.282403\pi$
$840$		0			0
$841$			27.4118i			0.945236i
$842$		0			0
$843$	−21.1187	−	21.1187i	−0.727367	−	0.727367i
$844$		0			0
$845$	−0.858176	+	0.858176i	−0.0295221	+	0.0295221i
$846$		0			0
$847$	−9.20309			−0.316222
$848$		0			0
$849$	10.8698			0.373050
$850$		0			0
$851$	−6.35914	+	6.35914i	−0.217989	+	0.217989i
$852$		0			0
$853$	23.6486	+	23.6486i	0.809714	+	0.809714i	0.984590	−	0.174876i	$-0.0559526\pi$
$853$	23.6486	+	23.6486i	0.809714	+	0.809714i	−0.174876	+	0.984590i	$0.555953\pi$
$854$		0			0
$855$		−	1.13491i		−	0.0388129i
$856$		0			0
$857$			33.0162i			1.12781i	0.825839	+	0.563906i	$0.190702\pi$
$857$			33.0162i			1.12781i	−0.825839	+	0.563906i	$0.809298\pi$
$858$		0			0
$859$	5.16428	+	5.16428i	0.176203	+	0.176203i	0.789698	−	0.613495i	$-0.210237\pi$
$859$	5.16428	+	5.16428i	0.176203	+	0.176203i	−0.613495	+	0.789698i	$0.710237\pi$
$860$		0			0
$861$	8.97703	−	8.97703i	0.305936	−	0.305936i
$862$		0			0
$863$	−6.25192			−0.212818			−0.106409	−	0.994322i	$-0.533935\pi$
$863$	−6.25192			−0.212818			−0.106409	+	0.994322i	$0.533935\pi$
$864$		0			0
$865$	2.45049			0.0833190
$866$		0			0
$867$	−0.724061	+	0.724061i	−0.0245904	+	0.0245904i
$868$		0			0
$869$	−4.46237	−	4.46237i	−0.151376	−	0.151376i
$870$		0			0
$871$		−	8.38261i		−	0.284034i
$872$		0			0
$873$		−	34.9683i		−	1.18350i
$874$		0			0
$875$	−2.62429	−	2.62429i	−0.0887171	−	0.0887171i
$876$		0			0
$877$	5.65049	−	5.65049i	0.190804	−	0.190804i	−0.605240	−	0.796043i	$-0.706923\pi$
$877$	5.65049	−	5.65049i	0.190804	−	0.190804i	0.796043	+	0.605240i	$0.206923\pi$
$878$		0			0
$879$	9.99498			0.337122
$880$		0			0
$881$	−4.36508			−0.147063			−0.0735316	−	0.997293i	$-0.523427\pi$
$881$	−4.36508			−0.147063			−0.0735316	+	0.997293i	$0.523427\pi$
$882$		0			0
$883$	−29.4447	+	29.4447i	−0.990893	+	0.990893i	−0.999959	−	0.00906586i	$-0.997114\pi$
$883$	−29.4447	+	29.4447i	−0.990893	+	0.990893i	0.00906586	+	0.999959i	$0.497114\pi$
$884$		0			0
$885$	−0.940140	−	0.940140i	−0.0316024	−	0.0316024i
$886$		0			0
$887$		−	44.5674i		−	1.49643i	−0.663458	−	0.748214i	$-0.730912\pi$
$887$		−	44.5674i		−	1.49643i	0.663458	−	0.748214i	$-0.269088\pi$
$888$		0			0
$889$		−	33.5816i		−	1.12629i
$890$		0			0
$891$	1.28305	+	1.28305i	0.0429838	+	0.0429838i
$892$		0			0
$893$	−35.3369	+	35.3369i	−1.18251	+	1.18251i
$894$		0			0
$895$	−3.31630			−0.110852
$896$		0			0
$897$	11.5248			0.384802
$898$		0			0
$899$	1.28700	−	1.28700i	0.0429239	−	0.0429239i
$900$		0			0
$901$	−4.79265	−	4.79265i	−0.159666	−	0.159666i
$902$		0			0
$903$		−	28.3238i		−	0.942557i
$904$		0			0
$905$		−	1.47308i		−	0.0489667i
$906$		0			0
$907$	−34.7519	−	34.7519i	−1.15392	−	1.15392i	−0.985760	−	0.168157i	$-0.946219\pi$
$907$	−34.7519	−	34.7519i	−1.15392	−	1.15392i	−0.168157	−	0.985760i	$-0.553781\pi$
$908$		0			0
$909$	−17.1892	+	17.1892i	−0.570128	+	0.570128i
$910$		0			0
$911$	40.9415			1.35645			0.678226	−	0.734853i	$-0.262749\pi$
$911$	40.9415			1.35645			0.678226	+	0.734853i	$0.262749\pi$
$912$		0			0
$913$	2.44906			0.0810520
$914$		0			0
$915$	−0.189774	+	0.189774i	−0.00627372	+	0.00627372i
$916$		0			0
$917$	24.4158	+	24.4158i	0.806280	+	0.806280i
$918$		0			0
$919$			17.6406i			0.581911i	0.956737	+	0.290956i	$0.0939732\pi$
$919$			17.6406i			0.581911i	−0.956737	+	0.290956i	$0.906027\pi$
$920$		0			0
$921$		−	4.41269i		−	0.145403i
$922$		0			0
$923$	−9.05921	−	9.05921i	−0.298188	−	0.298188i
$924$		0			0
$925$	−5.91766	+	5.91766i	−0.194571	+	0.194571i
$926$		0			0
$927$	1.46067			0.0479746
$928$		0			0
$929$	−8.34203			−0.273693			−0.136847	−	0.990592i	$-0.543697\pi$
$929$	−8.34203			−0.273693			−0.136847	+	0.990592i	$0.543697\pi$
$930$		0			0
$931$	−0.271446	+	0.271446i	−0.00889628	+	0.00889628i
$932$		0			0
$933$	14.4925	+	14.4925i	0.474463	+	0.474463i
$934$		0			0
$935$		−	0.387472i		−	0.0126717i
$936$		0			0
$937$			14.1664i			0.462796i	0.972859	+	0.231398i	$0.0743300\pi$
$937$			14.1664i			0.462796i	−0.972859	+	0.231398i	$0.925670\pi$
$938$		0			0
$939$	−19.9509	−	19.9509i	−0.651074	−	0.651074i
$940$		0			0
$941$	−22.4415	+	22.4415i	−0.731572	+	0.731572i	−0.970931	−	0.239359i	$-0.923063\pi$
$941$	−22.4415	+	22.4415i	−0.731572	+	0.731572i	0.239359	+	0.970931i	$0.423063\pi$
$942$		0			0
$943$	−25.2465			−0.822140
$944$		0			0
$945$	−1.88548			−0.0613346
$946$		0			0
$947$	−31.2571	+	31.2571i	−1.01572	+	1.01572i	−0.0158460	+	0.999874i	$0.505044\pi$
$947$	−31.2571	+	31.2571i	−1.01572	+	1.01572i	−0.999874	+	0.0158460i	$0.994956\pi$
$948$		0			0
$949$	−20.0951	−	20.0951i	−0.652315	−	0.652315i
$950$		0			0
$951$			31.0279i			1.00615i
$952$		0			0
$953$			54.5167i			1.76597i	0.469402	+	0.882985i	$0.344470\pi$
$953$			54.5167i			1.76597i	−0.469402	+	0.882985i	$0.655530\pi$
$954$		0			0
$955$	1.57499	+	1.57499i	0.0509656	+	0.0509656i
$956$		0			0
$957$	−2.49862	+	2.49862i	−0.0807688	+	0.0807688i
$958$		0			0
$959$	22.5213			0.727251
$960$		0			0
$961$	−28.9141			−0.932713
$962$		0			0
$963$	1.51695	−	1.51695i	0.0488829	−	0.0488829i
$964$		0			0
$965$	−1.74382	−	1.74382i	−0.0561357	−	0.0561357i
$966$		0			0
$967$			6.88781i			0.221497i	0.993848	+	0.110749i	$0.0353248\pi$
$967$			6.88781i			0.221497i	−0.993848	+	0.110749i	$0.964675\pi$
$968$		0			0
$969$		−	4.20846i		−	0.135195i
$970$		0			0
$971$	−25.1974	−	25.1974i	−0.808623	−	0.808623i	0.175803	−	0.984425i	$-0.443748\pi$
$971$	−25.1974	−	25.1974i	−0.808623	−	0.808623i	−0.984425	+	0.175803i	$0.943748\pi$
$972$		0			0
$973$	−19.2656	+	19.2656i	−0.617628	+	0.617628i
$974$		0			0
$975$	10.7247			0.343465
$976$		0			0
$977$	−8.31259			−0.265943			−0.132972	−	0.991120i	$-0.542452\pi$
$977$	−8.31259			−0.265943			−0.132972	+	0.991120i	$0.542452\pi$
$978$		0			0
$979$	−21.3717	+	21.3717i	−0.683042	+	0.683042i
$980$		0			0
$981$	0.903078	+	0.903078i	0.0288331	+	0.0288331i
$982$		0			0
$983$			38.9586i			1.24259i	0.783578	+	0.621293i	$0.213392\pi$
$983$			38.9586i			1.24259i	−0.783578	+	0.621293i	$0.786608\pi$
$984$		0			0
$985$			3.83637i			0.122237i
$986$		0			0
$987$	23.1376	+	23.1376i	0.736478	+	0.736478i
$988$		0			0
$989$	−39.8282	+	39.8282i	−1.26646	+	1.26646i
$990$		0			0
$991$	60.2776			1.91478			0.957391	−	0.288796i	$-0.0932550\pi$
$991$	60.2776			1.91478			0.957391	+	0.288796i	$0.0932550\pi$
$992$		0			0
$993$	0.676182			0.0214580
$994$		0			0
$995$	−2.04458	+	2.04458i	−0.0648174	+	0.0648174i
$996$		0			0
$997$	−8.55785	−	8.55785i	−0.271030	−	0.271030i	0.558485	−	0.829515i	$-0.311383\pi$
$997$	−8.55785	−	8.55785i	−0.271030	−	0.271030i	−0.829515	+	0.558485i	$0.811383\pi$
$998$		0			0
$999$			8.52044i			0.269575i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1088.2.l.c.817.6		32
4.3	odd	2		272.2.l.c.69.3	✓	32
16.3	odd	4		272.2.l.c.205.3	yes	32
16.13	even	4	inner	1088.2.l.c.273.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
272.2.l.c.69.3	✓	32	4.3	odd	2
272.2.l.c.205.3	yes	32	16.3	odd	4
1088.2.l.c.273.6		32	16.13	even	4	inner
1088.2.l.c.817.6		32	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1088 = 2^{6} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1088.l (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.724061 + 0.724061i) q^{3} +(0.100057 + 0.100057i) q^{5} -2.62804i q^{7} +1.95147i q^{9} +(-1.93625 - 1.93625i) q^{11} +(1.48714 - 1.48714i) q^{13} -0.144896 q^{15} +1.00000 q^{17} +(-2.90615 + 2.90615i) q^{19} +(1.90286 + 1.90286i) q^{21} -5.35151i q^{23} -4.97998i q^{25} +(-3.58517 - 3.58517i) q^{27} +(-0.891113 + 0.891113i) q^{29} -1.44426 q^{31} +2.80393 q^{33} +(0.262955 - 0.262955i) q^{35} +(-1.18829 - 1.18829i) q^{37} +2.15356i q^{39} -4.71764i q^{41} +(-7.44242 - 7.44242i) q^{43} +(-0.195259 + 0.195259i) q^{45} +12.1594 q^{47} +0.0934039 q^{49} +(-0.724061 + 0.724061i) q^{51} +(-4.79265 - 4.79265i) q^{53} -0.387472i q^{55} -4.20846i q^{57} +(6.48840 + 6.48840i) q^{59} +(1.30973 - 1.30973i) q^{61} +5.12854 q^{63} +0.297599 q^{65} +(2.81837 - 2.81837i) q^{67} +(3.87482 + 3.87482i) q^{69} -6.09170i q^{71} -13.5126i q^{73} +(3.60581 + 3.60581i) q^{75} +(-5.08854 + 5.08854i) q^{77} +2.30465 q^{79} -0.662648 q^{81} +(-0.632423 + 0.632423i) q^{83} +(0.100057 + 0.100057i) q^{85} -1.29044i q^{87} -11.0377i q^{89} +(-3.90827 - 3.90827i) q^{91} +(1.04573 - 1.04573i) q^{93} -0.581564 q^{95} -17.9190 q^{97} +(3.77853 - 3.77853i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{11} - 24 q^{15} + 32 q^{17} - 12 q^{27} - 8 q^{29} + 24 q^{31} - 12 q^{35} - 8 q^{37} + 12 q^{43} - 40 q^{45} - 32 q^{47} - 32 q^{49} + 8 q^{53} + 12 q^{59} + 40 q^{63} - 8 q^{67} - 8 q^{75}+ \cdots + 24 q^{99}+O(q^{100}) \) 32 * q + 4 * q^11 - 24 * q^15 + 32 * q^17 - 12 * q^27 - 8 * q^29 + 24 * q^31 - 12 * q^35 - 8 * q^37 + 12 * q^43 - 40 * q^45 - 32 * q^47 - 32 * q^49 + 8 * q^53 + 12 * q^59 + 40 * q^63 - 8 * q^67 - 8 * q^75 + 56 * q^77 - 48 * q^79 - 64 * q^81 - 4 * q^83 + 28 * q^91 - 24 * q^93 + 40 * q^95 + 24 * q^99

Introduction

L-functions

Modular forms

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Database

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