LMFDB - Embedded newform 1088.2.l.b.273.14

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 = [30] 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:	$30$
Relative dimension:	$15$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 272)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			273.14
Character	$\chi$	$=$	1088.273
Dual form			1088.2.l.b.817.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.04684 + 2.04684i) q^{3} +(-0.112242 + 0.112242i) q^{5} +1.01296i q^{7} +5.37914i q^{9} +(4.56843 - 4.56843i) q^{11} +(3.07260 + 3.07260i) q^{13} -0.459483 q^{15} -1.00000 q^{17} +(2.65491 + 2.65491i) q^{19} +(-2.07337 + 2.07337i) q^{21} -5.91450i q^{23} +4.97480i q^{25} +(-4.86974 + 4.86974i) q^{27} +(-3.98716 - 3.98716i) q^{29} -4.31396 q^{31} +18.7017 q^{33} +(-0.113697 - 0.113697i) q^{35} +(-4.49312 + 4.49312i) q^{37} +12.5783i q^{39} +2.83552i q^{41} +(-3.25504 + 3.25504i) q^{43} +(-0.603764 - 0.603764i) q^{45} +0.815754 q^{47} +5.97391 q^{49} +(-2.04684 - 2.04684i) q^{51} +(-5.94015 + 5.94015i) q^{53} +1.02554i q^{55} +10.8684i q^{57} +(4.40078 - 4.40078i) q^{59} +(-9.70982 - 9.70982i) q^{61} -5.44887 q^{63} -0.689749 q^{65} +(-1.61155 - 1.61155i) q^{67} +(12.1061 - 12.1061i) q^{69} +0.780693i q^{71} -6.99816i q^{73} +(-10.1826 + 10.1826i) q^{75} +(4.62764 + 4.62764i) q^{77} +11.7856 q^{79} -3.79775 q^{81} +(-3.93699 - 3.93699i) q^{83} +(0.112242 - 0.112242i) q^{85} -16.3222i q^{87} -1.66274i q^{89} +(-3.11243 + 3.11243i) q^{91} +(-8.83001 - 8.83001i) q^{93} -0.595984 q^{95} -16.9653 q^{97} +(24.5742 + 24.5742i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 2 q^{3} - 2 q^{5} + 10 q^{11} - 6 q^{13} + 28 q^{15} - 30 q^{17} - 10 q^{19} - 4 q^{21} - 4 q^{27} - 18 q^{29} - 48 q^{31} - 12 q^{33} - 16 q^{35} + 6 q^{37} - 2 q^{43} + 42 q^{45} + 32 q^{47} - 38 q^{49}+ \cdots - 54 q^{99}+O(q^{100}) $ 30 * q + 2 * q^3 - 2 * q^5 + 10 * q^11 - 6 * q^13 + 28 * q^15 - 30 * q^17 - 10 * q^19 - 4 * q^21 - 4 * q^27 - 18 * q^29 - 48 * q^31 - 12 * q^33 - 16 * q^35 + 6 * q^37 - 2 * q^43 + 42 * q^45 + 32 * q^47 - 38 * q^49 - 2 * q^51 - 6 * q^53 + 14 * q^59 + 6 * q^61 - 84 * q^63 - 12 * q^65 - 26 * q^67 + 12 * q^69 + 26 * q^75 - 28 * q^77 + 72 * q^79 - 10 * q^81 + 34 * q^83 + 2 * q^85 - 16 * q^91 - 24 * q^93 - 76 * q^95 - 28 * q^97 - 54 * q^99

Character values

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

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

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
$3$	2.04684	+	2.04684i	1.18175	+	1.18175i	0.979292	+	0.202454i	$0.0648918\pi$
$3$	2.04684	+	2.04684i	1.18175	+	1.18175i	0.202454	+	0.979292i	$0.435108\pi$
$4$		0			0
$5$	−0.112242	+	0.112242i	−0.0501960	+	0.0501960i	−0.731759	−	0.681563i	$-0.761300\pi$
$5$	−0.112242	+	0.112242i	−0.0501960	+	0.0501960i	0.681563	+	0.731759i	$0.261300\pi$
$6$		0			0
$7$			1.01296i			0.382863i	0.981506	+	0.191432i	$0.0613131\pi$
$7$			1.01296i			0.382863i	−0.981506	+	0.191432i	$0.938687\pi$
$8$		0			0
$9$			5.37914i			1.79305i
$10$		0			0
$11$	4.56843	−	4.56843i	1.37743	−	1.37743i	0.528500	−	0.848934i	$-0.322755\pi$
$11$	4.56843	−	4.56843i	1.37743	−	1.37743i	0.848934	−	0.528500i	$-0.177245\pi$
$12$		0			0
$13$	3.07260	+	3.07260i	0.852187	+	0.852187i	0.990402	−	0.138215i	$-0.0441366\pi$
$13$	3.07260	+	3.07260i	0.852187	+	0.852187i	−0.138215	+	0.990402i	$0.544137\pi$
$14$		0			0
$15$	−0.459483			−0.118638
$16$		0			0
$17$	−1.00000			−0.242536
$17$	−1.00000			−0.242536
$18$		0			0
$19$	2.65491	+	2.65491i	0.609078	+	0.609078i	0.942705	−	0.333627i	$-0.108273\pi$
$19$	2.65491	+	2.65491i	0.609078	+	0.609078i	−0.333627	+	0.942705i	$0.608273\pi$
$20$		0			0
$21$	−2.07337	+	2.07337i	−0.452447	+	0.452447i
$22$		0			0
$23$		−	5.91450i		−	1.23326i	−0.787254	−	0.616629i	$-0.788498\pi$
$23$		−	5.91450i		−	1.23326i	0.787254	−	0.616629i	$-0.211502\pi$
$24$		0			0
$25$			4.97480i			0.994961i
$26$		0			0
$27$	−4.86974	+	4.86974i	−0.937181	+	0.937181i
$28$		0			0
$29$	−3.98716	−	3.98716i	−0.740397	−	0.740397i	0.232257	−	0.972654i	$-0.425389\pi$
$29$	−3.98716	−	3.98716i	−0.740397	−	0.740397i	−0.972654	+	0.232257i	$0.925389\pi$
$30$		0			0
$31$	−4.31396			−0.774810			−0.387405	−	0.921910i	$-0.626629\pi$
$31$	−4.31396			−0.774810			−0.387405	+	0.921910i	$0.626629\pi$
$32$		0			0
$33$	18.7017			3.25555
$34$		0			0
$35$	−0.113697	−	0.113697i	−0.0192182	−	0.0192182i
$36$		0			0
$37$	−4.49312	+	4.49312i	−0.738665	+	0.738665i	−0.972320	−	0.233655i	$-0.924931\pi$
$37$	−4.49312	+	4.49312i	−0.738665	+	0.738665i	0.233655	+	0.972320i	$0.424931\pi$
$38$		0			0
$39$			12.5783i			2.01414i
$40$		0			0
$41$			2.83552i			0.442834i	0.975179	+	0.221417i	$0.0710683\pi$
$41$			2.83552i			0.442834i	−0.975179	+	0.221417i	$0.928932\pi$
$42$		0			0
$43$	−3.25504	+	3.25504i	−0.496389	+	0.496389i	−0.910312	−	0.413923i	$-0.864158\pi$
$43$	−3.25504	+	3.25504i	−0.496389	+	0.496389i	0.413923	+	0.910312i	$0.364158\pi$
$44$		0			0
$45$	−0.603764	−	0.603764i	−0.0900039	−	0.0900039i
$46$		0			0
$47$	0.815754			0.118990			0.0594950	−	0.998229i	$-0.481051\pi$
$47$	0.815754			0.118990			0.0594950	+	0.998229i	$0.481051\pi$
$48$		0			0
$49$	5.97391			0.853416
$50$		0			0
$51$	−2.04684	−	2.04684i	−0.286616	−	0.286616i
$52$		0			0
$53$	−5.94015	+	5.94015i	−0.815942	+	0.815942i	−0.985517	−	0.169575i	$-0.945761\pi$
$53$	−5.94015	+	5.94015i	−0.815942	+	0.815942i	0.169575	+	0.985517i	$0.445761\pi$
$54$		0			0
$55$			1.02554i			0.138283i
$56$		0			0
$57$			10.8684i			1.43955i
$58$		0			0
$59$	4.40078	−	4.40078i	0.572933	−	0.572933i	−0.360014	−	0.932947i	$-0.617228\pi$
$59$	4.40078	−	4.40078i	0.572933	−	0.572933i	0.932947	+	0.360014i	$0.117228\pi$
$60$		0			0
$61$	−9.70982	−	9.70982i	−1.24321	−	1.24321i	−0.958660	−	0.284555i	$-0.908154\pi$
$61$	−9.70982	−	9.70982i	−1.24321	−	1.24321i	−0.284555	−	0.958660i	$-0.591846\pi$
$62$		0			0
$63$	−5.44887			−0.686493
$64$		0			0
$65$	−0.689749			−0.0855528
$66$		0			0
$67$	−1.61155	−	1.61155i	−0.196882	−	0.196882i	0.601780	−	0.798662i	$-0.294458\pi$
$67$	−1.61155	−	1.61155i	−0.196882	−	0.196882i	−0.798662	+	0.601780i	$0.794458\pi$
$68$		0			0
$69$	12.1061	−	12.1061i	1.45740	−	1.45740i
$70$		0			0
$71$			0.780693i			0.0926512i	0.998926	+	0.0463256i	$0.0147512\pi$
$71$			0.780693i			0.0926512i	−0.998926	+	0.0463256i	$0.985249\pi$
$72$		0			0
$73$		−	6.99816i		−	0.819072i	−0.912294	−	0.409536i	$-0.865691\pi$
$73$		−	6.99816i		−	0.819072i	0.912294	−	0.409536i	$-0.134309\pi$
$74$		0			0
$75$	−10.1826	+	10.1826i	−1.17579	+	1.17579i
$76$		0			0
$77$	4.62764	+	4.62764i	0.527369	+	0.527369i
$78$		0			0
$79$	11.7856			1.32598			0.662992	−	0.748627i	$-0.269286\pi$
$79$	11.7856			1.32598			0.662992	+	0.748627i	$0.269286\pi$
$80$		0			0
$81$	−3.79775			−0.421973
$82$		0			0
$83$	−3.93699	−	3.93699i	−0.432140	−	0.432140i	0.457216	−	0.889356i	$-0.348847\pi$
$83$	−3.93699	−	3.93699i	−0.432140	−	0.432140i	−0.889356	+	0.457216i	$0.848847\pi$
$84$		0			0
$85$	0.112242	−	0.112242i	0.0121743	−	0.0121743i
$86$		0			0
$87$		−	16.3222i		−	1.74992i
$88$		0			0
$89$		−	1.66274i		−	0.176250i	−0.996109	−	0.0881251i	$-0.971912\pi$
$89$		−	1.66274i		−	0.176250i	0.996109	−	0.0881251i	$-0.0280875\pi$
$90$		0			0
$91$	−3.11243	+	3.11243i	−0.326271	+	0.326271i
$92$		0			0
$93$	−8.83001	−	8.83001i	−0.915629	−	0.915629i
$94$		0			0
$95$	−0.595984			−0.0611466
$96$		0			0
$97$	−16.9653			−1.72257			−0.861285	−	0.508123i	$-0.830340\pi$
$97$	−16.9653			−1.72257			−0.861285	+	0.508123i	$0.830340\pi$
$98$		0			0
$99$	24.5742	+	24.5742i	2.46980	+	2.46980i
$100$		0			0
$101$	−2.09654	+	2.09654i	−0.208614	+	0.208614i	−0.803678	−	0.595064i	$-0.797127\pi$
$101$	−2.09654	+	2.09654i	−0.208614	+	0.208614i	0.595064	+	0.803678i	$0.297127\pi$
$102$		0			0
$103$		−	11.6252i		−	1.14547i	−0.819742	−	0.572733i	$-0.805883\pi$
$103$		−	11.6252i		−	1.14547i	0.819742	−	0.572733i	$-0.194117\pi$
$104$		0			0
$105$		−	0.465438i		−	0.0454221i
$106$		0			0
$107$	0.709693	−	0.709693i	0.0686086	−	0.0686086i	−0.671970	−	0.740578i	$-0.734552\pi$
$107$	0.709693	−	0.709693i	0.0686086	−	0.0686086i	0.740578	+	0.671970i	$0.234552\pi$
$108$		0			0
$109$	−1.02443	−	1.02443i	−0.0981229	−	0.0981229i	0.656341	−	0.754464i	$-0.272103\pi$
$109$	−1.02443	−	1.02443i	−0.0981229	−	0.0981229i	−0.754464	+	0.656341i	$0.772103\pi$
$110$		0			0
$111$	−18.3934			−1.74583
$112$		0			0
$113$	8.75234			0.823351			0.411675	−	0.911331i	$-0.364944\pi$
$113$	8.75234			0.823351			0.411675	+	0.911331i	$0.364944\pi$
$114$		0			0
$115$	0.663854	+	0.663854i	0.0619047	+	0.0619047i
$116$		0			0
$117$	−16.5280	+	16.5280i	−1.52801	+	1.52801i
$118$		0			0
$119$		−	1.01296i		−	0.0928580i
$120$		0			0
$121$		−	30.7411i		−	2.79464i
$122$		0			0
$123$	−5.80388	+	5.80388i	−0.523318	+	0.523318i
$124$		0			0
$125$	−1.11959	−	1.11959i	−0.100139	−	0.100139i
$126$		0			0
$127$	15.8565			1.40703			0.703517	−	0.710678i	$-0.251612\pi$
$127$	15.8565			1.40703			0.703517	+	0.710678i	$0.251612\pi$
$128$		0			0
$129$	−13.3251			−1.17321
$130$		0			0
$131$	−2.93671	−	2.93671i	−0.256582	−	0.256582i	0.567081	−	0.823662i	$-0.308073\pi$
$131$	−2.93671	−	2.93671i	−0.256582	−	0.256582i	−0.823662	+	0.567081i	$0.808073\pi$
$132$		0			0
$133$	−2.68932	+	2.68932i	−0.233194	+	0.233194i
$134$		0			0
$135$		−	1.09318i		−	0.0940855i
$136$		0			0
$137$			2.84052i			0.242682i	0.992611	+	0.121341i	$0.0387194\pi$
$137$			2.84052i			0.242682i	−0.992611	+	0.121341i	$0.961281\pi$
$138$		0			0
$139$	−0.172689	+	0.172689i	−0.0146473	+	0.0146473i	−0.714392	−	0.699745i	$-0.753297\pi$
$139$	−0.172689	+	0.172689i	−0.0146473	+	0.0146473i	0.699745	+	0.714392i	$0.253297\pi$
$140$		0			0
$141$	1.66972	+	1.66972i	0.140616	+	0.140616i
$142$		0			0
$143$	28.0739			2.34766
$144$		0			0
$145$	0.895052			0.0743300
$146$		0			0
$147$	12.2277	+	12.2277i	1.00852	+	1.00852i
$148$		0			0
$149$	−2.90961	+	2.90961i	−0.238365	+	0.238365i	−0.816173	−	0.577808i	$-0.803908\pi$
$149$	−2.90961	+	2.90961i	−0.238365	+	0.238365i	0.577808	+	0.816173i	$0.303908\pi$
$150$		0			0
$151$			12.1378i			0.987757i	0.869531	+	0.493878i	$0.164421\pi$
$151$			12.1378i			0.987757i	−0.869531	+	0.493878i	$0.835579\pi$
$152$		0			0
$153$		−	5.37914i		−	0.434878i
$154$		0			0
$155$	0.484207	−	0.484207i	0.0388924	−	0.0388924i
$156$		0			0
$157$	17.2062	+	17.2062i	1.37321	+	1.37321i	0.855646	+	0.517562i	$0.173160\pi$
$157$	17.2062	+	17.2062i	1.37321	+	1.37321i	0.517562	+	0.855646i	$0.326840\pi$
$158$		0			0
$159$	−24.3171			−1.92847
$160$		0			0
$161$	5.99116			0.472170
$162$		0			0
$163$	−6.71572	−	6.71572i	−0.526016	−	0.526016i	0.393366	−	0.919382i	$-0.371311\pi$
$163$	−6.71572	−	6.71572i	−0.526016	−	0.526016i	−0.919382	+	0.393366i	$0.871311\pi$
$164$		0			0
$165$	−2.09911	+	2.09911i	−0.163416	+	0.163416i
$166$		0			0
$167$		−	2.25312i		−	0.174352i	−0.996193	−	0.0871760i	$-0.972216\pi$
$167$		−	2.25312i		−	0.174352i	0.996193	−	0.0871760i	$-0.0277842\pi$
$168$		0			0
$169$			5.88179i			0.452445i
$170$		0			0
$171$	−14.2811	+	14.2811i	−1.09211	+	1.09211i
$172$		0			0
$173$	4.38630	+	4.38630i	0.333484	+	0.333484i	0.853908	−	0.520424i	$-0.174226\pi$
$173$	4.38630	+	4.38630i	0.333484	+	0.333484i	−0.520424	+	0.853908i	$0.674226\pi$
$174$		0			0
$175$	−5.03928			−0.380934
$176$		0			0
$177$	18.0154			1.35412
$178$		0			0
$179$	−4.10787	−	4.10787i	−0.307037	−	0.307037i	0.536722	−	0.843759i	$-0.319662\pi$
$179$	−4.10787	−	4.10787i	−0.307037	−	0.307037i	−0.843759	+	0.536722i	$0.819662\pi$
$180$		0			0
$181$	8.94790	−	8.94790i	0.665092	−	0.665092i	−0.291484	−	0.956576i	$-0.594149\pi$
$181$	8.94790	−	8.94790i	0.665092	−	0.665092i	0.956576	+	0.291484i	$0.0941489\pi$
$182$		0			0
$183$		−	39.7490i		−	2.93833i
$184$		0			0
$185$		−	1.00863i		−	0.0741561i
$186$		0			0
$187$	−4.56843	+	4.56843i	−0.334077	+	0.334077i
$188$		0			0
$189$	−4.93286	−	4.93286i	−0.358812	−	0.358812i
$190$		0			0
$191$	26.6573			1.92885			0.964427	−	0.264351i	$-0.0851576\pi$
$191$	26.6573			1.92885			0.964427	+	0.264351i	$0.0851576\pi$
$192$		0			0
$193$	13.4602			0.968888			0.484444	−	0.874822i	$-0.339022\pi$
$193$	13.4602			0.968888			0.484444	+	0.874822i	$0.339022\pi$
$194$		0			0
$195$	−1.41181	−	1.41181i	−0.101102	−	0.101102i
$196$		0			0
$197$	17.3025	−	17.3025i	1.23275	−	1.23275i	0.269847	−	0.962903i	$-0.413027\pi$
$197$	17.3025	−	17.3025i	1.23275	−	1.23275i	0.962903	−	0.269847i	$-0.0869732\pi$
$198$		0			0
$199$		−	14.3832i		−	1.01959i	−0.860295	−	0.509797i	$-0.829720\pi$
$199$		−	14.3832i		−	1.01959i	0.860295	−	0.509797i	$-0.170280\pi$
$200$		0			0
$201$		−	6.59718i		−	0.465330i
$202$		0			0
$203$	4.03884	−	4.03884i	0.283471	−	0.283471i
$204$		0			0
$205$	−0.318264	−	0.318264i	−0.0222285	−	0.0222285i
$206$		0			0
$207$	31.8149			2.21129
$208$		0			0
$209$	24.2575			1.67793
$210$		0			0
$211$	−10.4119	−	10.4119i	−0.716788	−	0.716788i	0.251158	−	0.967946i	$-0.419189\pi$
$211$	−10.4119	−	10.4119i	−0.716788	−	0.716788i	−0.967946	+	0.251158i	$0.919189\pi$
$212$		0			0
$213$	−1.59796	+	1.59796i	−0.109490	+	0.109490i
$214$		0			0
$215$		−	0.730702i		−	0.0498335i
$216$		0			0
$217$		−	4.36988i		−	0.296647i
$218$		0			0
$219$	14.3241	−	14.3241i	0.967935	−	0.967935i
$220$		0			0
$221$	−3.07260	−	3.07260i	−0.206686	−	0.206686i
$222$		0			0
$223$	−18.2677			−1.22329			−0.611647	−	0.791131i	$-0.709493\pi$
$223$	−18.2677			−1.22329			−0.611647	+	0.791131i	$0.709493\pi$
$224$		0			0
$225$	−26.7602			−1.78401
$226$		0			0
$227$	−19.9826	−	19.9826i	−1.32629	−	1.32629i	−0.908582	−	0.417707i	$-0.862834\pi$
$227$	−19.9826	−	19.9826i	−1.32629	−	1.32629i	−0.417707	−	0.908582i	$-0.637166\pi$
$228$		0			0
$229$	−6.83533	+	6.83533i	−0.451691	+	0.451691i	−0.895916	−	0.444224i	$-0.853479\pi$
$229$	−6.83533	+	6.83533i	−0.451691	+	0.451691i	0.444224	+	0.895916i	$0.353479\pi$
$230$		0			0
$231$			18.9441i			1.24643i
$232$		0			0
$233$			22.3112i			1.46166i	0.682561	+	0.730829i	$0.260866\pi$
$233$			22.3112i			1.46166i	−0.682561	+	0.730829i	$0.739134\pi$
$234$		0			0
$235$	−0.0915616	+	0.0915616i	−0.00597282	+	0.00597282i
$236$		0			0
$237$	24.1233	+	24.1233i	1.56698	+	1.56698i
$238$		0			0
$239$	3.45658			0.223587			0.111794	−	0.993731i	$-0.464340\pi$
$239$	3.45658			0.223587			0.111794	+	0.993731i	$0.464340\pi$
$240$		0			0
$241$	−3.87048			−0.249320			−0.124660	−	0.992200i	$-0.539784\pi$
$241$	−3.87048			−0.249320			−0.124660	+	0.992200i	$0.539784\pi$
$242$		0			0
$243$	6.83580	+	6.83580i	0.438517	+	0.438517i
$244$		0			0
$245$	−0.670522	+	0.670522i	−0.0428381	+	0.0428381i
$246$		0			0
$247$			16.3150i			1.03810i
$248$		0			0
$249$		−	16.1168i		−	1.02136i
$250$		0			0
$251$	−5.53871	+	5.53871i	−0.349600	+	0.349600i	−0.859961	−	0.510360i	$-0.829512\pi$
$251$	−5.53871	+	5.53871i	−0.349600	+	0.349600i	0.510360	+	0.859961i	$0.329512\pi$
$252$		0			0
$253$	−27.0200	−	27.0200i	−1.69873	−	1.69873i
$254$		0			0
$255$	0.459483			0.0287739
$256$		0			0
$257$	−25.7212			−1.60445			−0.802223	−	0.597024i	$-0.796350\pi$
$257$	−25.7212			−1.60445			−0.802223	+	0.597024i	$0.796350\pi$
$258$		0			0
$259$	−4.55136	−	4.55136i	−0.282808	−	0.282808i
$260$		0			0
$261$	21.4475	−	21.4475i	1.32757	−	1.32757i
$262$		0			0
$263$			17.3559i			1.07021i	0.844785	+	0.535105i	$0.179728\pi$
$263$			17.3559i			1.07021i	−0.844785	+	0.535105i	$0.820272\pi$
$264$		0			0
$265$		−	1.33347i		−	0.0819141i
$266$		0			0
$267$	3.40337	−	3.40337i	0.208283	−	0.208283i
$268$		0			0
$269$	−4.90641	−	4.90641i	−0.299149	−	0.299149i	0.541531	−	0.840681i	$-0.317845\pi$
$269$	−4.90641	−	4.90641i	−0.299149	−	0.299149i	−0.840681	+	0.541531i	$0.817845\pi$
$270$		0			0
$271$	−20.2369			−1.22930			−0.614652	−	0.788798i	$-0.710704\pi$
$271$	−20.2369			−1.22930			−0.614652	+	0.788798i	$0.710704\pi$
$272$		0			0
$273$	−12.7413			−0.771140
$274$		0			0
$275$	22.7270	+	22.7270i	1.37049	+	1.37049i
$276$		0			0
$277$	−7.38744	+	7.38744i	−0.443868	+	0.443868i	−0.893310	−	0.449442i	$-0.851623\pi$
$277$	−7.38744	+	7.38744i	−0.443868	+	0.443868i	0.449442	+	0.893310i	$0.351623\pi$
$278$		0			0
$279$		−	23.2054i		−	1.38927i
$280$		0			0
$281$		−	23.2693i		−	1.38813i	−0.719912	−	0.694066i	$-0.755818\pi$
$281$		−	23.2693i		−	1.38813i	0.719912	−	0.694066i	$-0.244182\pi$
$282$		0			0
$283$	−6.08235	+	6.08235i	−0.361558	+	0.361558i	−0.864386	−	0.502828i	$-0.832293\pi$
$283$	−6.08235	+	6.08235i	−0.361558	+	0.361558i	0.502828	+	0.864386i	$0.332293\pi$
$284$		0			0
$285$	−1.21989	−	1.21989i	−0.0722598	−	0.0722598i
$286$		0			0
$287$	−2.87228			−0.169545
$288$		0			0
$289$	1.00000			0.0588235
$290$		0			0
$291$	−34.7254	−	34.7254i	−2.03564	−	2.03564i
$292$		0			0
$293$	2.93453	−	2.93453i	0.171437	−	0.171437i	−0.616173	−	0.787611i	$-0.711318\pi$
$293$	2.93453	−	2.93453i	0.171437	−	0.171437i	0.787611	+	0.616173i	$0.211318\pi$
$294$		0			0
$295$			0.987903i			0.0575180i
$296$		0			0
$297$			44.4941i			2.58181i
$298$		0			0
$299$	18.1729	−	18.1729i	1.05097	−	1.05097i
$300$		0			0
$301$	−3.29723	−	3.29723i	−0.190049	−	0.190049i
$302$		0			0
$303$	−8.58259			−0.493057
$304$		0			0
$305$	2.17969			0.124809
$306$		0			0
$307$	−0.197517	−	0.197517i	−0.0112729	−	0.0112729i	0.701448	−	0.712721i	$-0.252537\pi$
$307$	−0.197517	−	0.197517i	−0.0112729	−	0.0112729i	−0.712721	+	0.701448i	$0.752537\pi$
$308$		0			0
$309$	23.7950	−	23.7950i	1.35365	−	1.35365i
$310$		0			0
$311$		−	10.3125i		−	0.584767i	−0.956301	−	0.292383i	$-0.905552\pi$
$311$		−	10.3125i		−	0.584767i	0.956301	−	0.292383i	$-0.0944484\pi$
$312$		0			0
$313$			2.95932i			0.167270i	0.996496	+	0.0836352i	$0.0266531\pi$
$313$			2.95932i			0.167270i	−0.996496	+	0.0836352i	$0.973347\pi$
$314$		0			0
$315$	0.611590	−	0.611590i	0.0344592	−	0.0344592i
$316$		0			0
$317$	−12.4351	−	12.4351i	−0.698424	−	0.698424i	0.265647	−	0.964070i	$-0.414415\pi$
$317$	−12.4351	−	12.4351i	−0.698424	−	0.698424i	−0.964070	+	0.265647i	$0.914415\pi$
$318$		0			0
$319$	−36.4301			−2.03970
$320$		0			0
$321$	2.90526			0.162156
$322$		0			0
$323$	−2.65491	−	2.65491i	−0.147723	−	0.147723i
$324$		0			0
$325$	−15.2856	+	15.2856i	−0.847893	+	0.847893i
$326$		0			0
$327$		−	4.19371i		−	0.231913i
$328$		0			0
$329$			0.826327i			0.0455569i
$330$		0			0
$331$	6.77696	−	6.77696i	0.372495	−	0.372495i	−0.495890	−	0.868385i	$-0.665158\pi$
$331$	6.77696	−	6.77696i	0.372495	−	0.372495i	0.868385	+	0.495890i	$0.165158\pi$
$332$		0			0
$333$	−24.1692	−	24.1692i	−1.32446	−	1.32446i
$334$		0			0
$335$	0.361766			0.0197654
$336$		0			0
$337$	1.53987			0.0838823			0.0419412	−	0.999120i	$-0.486646\pi$
$337$	1.53987			0.0838823			0.0419412	+	0.999120i	$0.486646\pi$
$338$		0			0
$339$	17.9147	+	17.9147i	0.972991	+	0.972991i
$340$		0			0
$341$	−19.7080	+	19.7080i	−1.06725	+	1.06725i
$342$		0			0
$343$			13.1421i			0.709605i
$344$		0			0
$345$			2.71761i			0.146311i
$346$		0			0
$347$	−18.7405	+	18.7405i	−1.00604	+	1.00604i	−0.00605993	+	0.999982i	$0.501929\pi$
$347$	−18.7405	+	18.7405i	−1.00604	+	1.00604i	−0.999982	+	0.00605993i	$0.998071\pi$
$348$		0			0
$349$	10.6170	+	10.6170i	0.568313	+	0.568313i	0.931656	−	0.363343i	$-0.118365\pi$
$349$	10.6170	+	10.6170i	0.568313	+	0.568313i	−0.363343	+	0.931656i	$0.618365\pi$
$350$		0			0
$351$	−29.9255			−1.59731
$352$		0			0
$353$	9.14327			0.486647			0.243323	−	0.969945i	$-0.421762\pi$
$353$	9.14327			0.486647			0.243323	+	0.969945i	$0.421762\pi$
$354$		0			0
$355$	−0.0876263	−	0.0876263i	−0.00465072	−	0.00465072i
$356$		0			0
$357$	2.07337	−	2.07337i	0.109735	−	0.109735i
$358$		0			0
$359$		−	14.0524i		−	0.741658i	−0.928701	−	0.370829i	$-0.879074\pi$
$359$		−	14.0524i		−	0.741658i	0.928701	−	0.370829i	$-0.120926\pi$
$360$		0			0
$361$		−	4.90289i		−	0.258047i
$362$		0			0
$363$	62.9222	−	62.9222i	3.30256	−	3.30256i
$364$		0			0
$365$	0.785485	+	0.785485i	0.0411142	+	0.0411142i
$366$		0			0
$367$	−26.4894			−1.38274			−0.691369	−	0.722502i	$-0.742992\pi$
$367$	−26.4894			−1.38274			−0.691369	+	0.722502i	$0.742992\pi$
$368$		0			0
$369$	−15.2527			−0.794023
$370$		0			0
$371$	−6.01714	−	6.01714i	−0.312395	−	0.312395i
$372$		0			0
$373$	−6.93682	+	6.93682i	−0.359175	+	0.359175i	−0.863509	−	0.504334i	$-0.831738\pi$
$373$	−6.93682	+	6.93682i	−0.359175	+	0.359175i	0.504334	+	0.863509i	$0.331738\pi$
$374$		0			0
$375$		−	4.58325i		−	0.236678i
$376$		0			0
$377$		−	24.5019i		−	1.26191i
$378$		0			0
$379$	26.0497	−	26.0497i	1.33808	−	1.33808i	0.440171	−	0.897914i	$-0.354918\pi$
$379$	26.0497	−	26.0497i	1.33808	−	1.33808i	0.897914	−	0.440171i	$-0.145082\pi$
$380$		0			0
$381$	32.4557	+	32.4557i	1.66276	+	1.66276i
$382$		0			0
$383$	21.8850			1.11827			0.559136	−	0.829076i	$-0.311133\pi$
$383$	21.8850			1.11827			0.559136	+	0.829076i	$0.311133\pi$
$384$		0			0
$385$	−1.03883			−0.0529436
$386$		0			0
$387$	−17.5093	−	17.5093i	−0.890049	−	0.890049i
$388$		0			0
$389$	11.3552	−	11.3552i	0.575732	−	0.575732i	−0.357993	−	0.933724i	$-0.616539\pi$
$389$	11.3552	−	11.3552i	0.575732	−	0.575732i	0.933724	+	0.357993i	$0.116539\pi$
$390$		0			0
$391$			5.91450i			0.299109i
$392$		0			0
$393$		−	12.0220i		−	0.606429i
$394$		0			0
$395$	−1.32284	+	1.32284i	−0.0665591	+	0.0665591i
$396$		0			0
$397$	−18.5828	−	18.5828i	−0.932642	−	0.932642i	0.0652287	−	0.997870i	$-0.479222\pi$
$397$	−18.5828	−	18.5828i	−0.932642	−	0.932642i	−0.997870	+	0.0652287i	$0.979222\pi$
$398$		0			0
$399$	−11.0093			−0.551152
$400$		0			0
$401$	15.9357			0.795792			0.397896	−	0.917431i	$-0.369741\pi$
$401$	15.9357			0.795792			0.397896	+	0.917431i	$0.369741\pi$
$402$		0			0
$403$	−13.2551	−	13.2551i	−0.660283	−	0.660283i
$404$		0			0
$405$	0.426266	−	0.426266i	0.0211814	−	0.0211814i
$406$		0			0
$407$			41.0530i			2.03492i
$408$		0			0
$409$			1.11106i			0.0549385i	0.999623	+	0.0274693i	$0.00874484\pi$
$409$			1.11106i			0.0549385i	−0.999623	+	0.0274693i	$0.991255\pi$
$410$		0			0
$411$	−5.81409	+	5.81409i	−0.286788	+	0.286788i
$412$		0			0
$413$	4.45783	+	4.45783i	0.219355	+	0.219355i
$414$		0			0
$415$	0.883788			0.0433835
$416$		0			0
$417$	−0.706934			−0.0346187
$418$		0			0
$419$	−3.75339	−	3.75339i	−0.183365	−	0.183365i	0.609455	−	0.792820i	$-0.291388\pi$
$419$	−3.75339	−	3.75339i	−0.183365	−	0.183365i	−0.792820	+	0.609455i	$0.791388\pi$
$420$		0			0
$421$	1.64504	−	1.64504i	0.0801743	−	0.0801743i	−0.665882	−	0.746057i	$-0.731945\pi$
$421$	1.64504	−	1.64504i	0.0801743	−	0.0801743i	0.746057	+	0.665882i	$0.231945\pi$
$422$		0			0
$423$			4.38806i			0.213355i
$424$		0			0
$425$		−	4.97480i		−	0.241313i
$426$		0			0
$427$	9.83567	−	9.83567i	0.475982	−	0.475982i
$428$		0			0
$429$	57.4630	+	57.4630i	2.77434	+	2.77434i
$430$		0			0
$431$	14.3879			0.693043			0.346522	−	0.938042i	$-0.387363\pi$
$431$	14.3879			0.693043			0.346522	+	0.938042i	$0.387363\pi$
$432$		0			0
$433$	27.4224			1.31783			0.658917	−	0.752215i	$-0.271015\pi$
$433$	27.4224			1.31783			0.658917	+	0.752215i	$0.271015\pi$
$434$		0			0
$435$	1.83203	+	1.83203i	0.0878392	+	0.0878392i
$436$		0			0
$437$	15.7025	−	15.7025i	0.751151	−	0.751151i
$438$		0			0
$439$			21.1786i			1.01080i	0.862885	+	0.505401i	$0.168655\pi$
$439$			21.1786i			1.01080i	−0.862885	+	0.505401i	$0.831345\pi$
$440$		0			0
$441$			32.1345i			1.53021i
$442$		0			0
$443$	−19.9521	+	19.9521i	−0.947951	+	0.947951i	−0.998711	−	0.0507595i	$-0.983836\pi$
$443$	−19.9521	+	19.9521i	−0.947951	+	0.947951i	0.0507595	+	0.998711i	$0.483836\pi$
$444$		0			0
$445$	0.186629	+	0.186629i	0.00884706	+	0.00884706i
$446$		0			0
$447$	−11.9111			−0.563374
$448$		0			0
$449$	−34.6939			−1.63730			−0.818652	−	0.574290i	$-0.805278\pi$
$449$	−34.6939			−1.63730			−0.818652	+	0.574290i	$0.805278\pi$
$450$		0			0
$451$	12.9539	+	12.9539i	0.609975	+	0.609975i
$452$		0			0
$453$	−24.8441	+	24.8441i	−1.16728	+	1.16728i
$454$		0			0
$455$		−	0.698689i		−	0.0327550i
$456$		0			0
$457$			17.8288i			0.833995i	0.908908	+	0.416998i	$0.136918\pi$
$457$			17.8288i			0.833995i	−0.908908	+	0.416998i	$0.863082\pi$
$458$		0			0
$459$	4.86974	−	4.86974i	0.227300	−	0.227300i
$460$		0			0
$461$	−23.9602	−	23.9602i	−1.11594	−	1.11594i	−0.992331	−	0.123609i	$-0.960553\pi$
$461$	−23.9602	−	23.9602i	−1.11594	−	1.11594i	−0.123609	−	0.992331i	$-0.539447\pi$
$462$		0			0
$463$	25.6632			1.19267			0.596334	−	0.802736i	$-0.296623\pi$
$463$	25.6632			1.19267			0.596334	+	0.802736i	$0.296623\pi$
$464$		0			0
$465$	1.98219			0.0919219
$466$		0			0
$467$	−9.87622	−	9.87622i	−0.457017	−	0.457017i	0.440658	−	0.897675i	$-0.354745\pi$
$467$	−9.87622	−	9.87622i	−0.457017	−	0.457017i	−0.897675	+	0.440658i	$0.854745\pi$
$468$		0			0
$469$	1.63244	−	1.63244i	0.0753790	−	0.0753790i
$470$		0			0
$471$			70.4370i			3.24557i
$472$		0			0
$473$			29.7408i			1.36748i
$474$		0			0
$475$	−13.2077	+	13.2077i	−0.606009	+	0.606009i
$476$		0			0
$477$	−31.9529	−	31.9529i	−1.46302	−	1.46302i
$478$		0			0
$479$	27.3534			1.24981			0.624905	−	0.780701i	$-0.285138\pi$
$479$	27.3534			1.24981			0.624905	+	0.780701i	$0.285138\pi$
$480$		0			0
$481$	−27.6112			−1.25896
$482$		0			0
$483$	12.2630	+	12.2630i	0.557985	+	0.557985i
$484$		0			0
$485$	1.90422	−	1.90422i	0.0864661	−	0.0864661i
$486$		0			0
$487$			24.7929i			1.12348i	0.827315	+	0.561738i	$0.189867\pi$
$487$			24.7929i			1.12348i	−0.827315	+	0.561738i	$0.810133\pi$
$488$		0			0
$489$		−	27.4921i		−	1.24323i
$490$		0			0
$491$	−17.4273	+	17.4273i	−0.786482	+	0.786482i	−0.980916	−	0.194433i	$-0.937713\pi$
$491$	−17.4273	+	17.4273i	−0.786482	+	0.786482i	0.194433	+	0.980916i	$0.437713\pi$
$492$		0			0
$493$	3.98716	+	3.98716i	0.179573	+	0.179573i
$494$		0			0
$495$	−5.51651			−0.247949
$496$		0			0
$497$	−0.790812			−0.0354728
$498$		0			0
$499$	15.0714	+	15.0714i	0.674688	+	0.674688i	0.958793	−	0.284105i	$-0.0916965\pi$
$499$	15.0714	+	15.0714i	0.674688	+	0.674688i	−0.284105	+	0.958793i	$0.591697\pi$
$500$		0			0
$501$	4.61179	−	4.61179i	0.206040	−	0.206040i
$502$		0			0
$503$		−	2.23642i		−	0.0997169i	−0.998756	−	0.0498585i	$-0.984123\pi$
$503$		−	2.23642i		−	0.0997169i	0.998756	−	0.0498585i	$-0.0158770\pi$
$504$		0			0
$505$		−	0.470639i		−	0.0209431i
$506$		0			0
$507$	−12.0391	+	12.0391i	−0.534676	+	0.534676i
$508$		0			0
$509$	−21.4598	−	21.4598i	−0.951189	−	0.951189i	0.0476743	−	0.998863i	$-0.484819\pi$
$509$	−21.4598	−	21.4598i	−0.951189	−	0.951189i	−0.998863	+	0.0476743i	$0.984819\pi$
$510$		0			0
$511$	7.08886			0.313593
$512$		0			0
$513$	−25.8574			−1.14163
$514$		0			0
$515$	1.30483	+	1.30483i	0.0574978	+	0.0574978i
$516$		0			0
$517$	3.72671	−	3.72671i	0.163901	−	0.163901i
$518$		0			0
$519$			17.9561i			0.788187i
$520$		0			0
$521$			42.7220i			1.87168i	0.352419	+	0.935842i	$0.385359\pi$
$521$			42.7220i			1.87168i	−0.352419	+	0.935842i	$0.614641\pi$
$522$		0			0
$523$	−3.20523	+	3.20523i	−0.140155	+	0.140155i	−0.773703	−	0.633548i	$-0.781598\pi$
$523$	−3.20523	+	3.20523i	−0.140155	+	0.140155i	0.633548	+	0.773703i	$0.281598\pi$
$524$		0			0
$525$	−10.3146	−	10.3146i	−0.450167	−	0.450167i
$526$		0			0
$527$	4.31396			0.187919
$528$		0			0
$529$	−11.9813			−0.520927
$530$		0			0
$531$	23.6725	+	23.6725i	1.02730	+	1.02730i
$532$		0			0
$533$	−8.71244	+	8.71244i	−0.377378	+	0.377378i
$534$		0			0
$535$			0.159314i			0.00688776i
$536$		0			0
$537$		−	16.8163i		−	0.725679i
$538$		0			0
$539$	27.2914	−	27.2914i	1.17552	−	1.17552i
$540$		0			0
$541$	27.0364	+	27.0364i	1.16239	+	1.16239i	0.983952	+	0.178436i	$0.0571038\pi$
$541$	27.0364	+	27.0364i	1.16239	+	1.16239i	0.178436	+	0.983952i	$0.442896\pi$
$542$		0			0
$543$	36.6299			1.57194
$544$		0			0
$545$	0.229968			0.00985076
$546$		0			0
$547$	−16.9275	−	16.9275i	−0.723769	−	0.723769i	0.245602	−	0.969371i	$-0.421014\pi$
$547$	−16.9275	−	16.9275i	−0.723769	−	0.723769i	−0.969371	+	0.245602i	$0.921014\pi$
$548$		0			0
$549$	52.2305	−	52.2305i	2.22914	−	2.22914i
$550$		0			0
$551$		−	21.1711i		−	0.901920i
$552$		0			0
$553$			11.9384i			0.507671i
$554$		0			0
$555$	2.06451	−	2.06451i	0.0876337	−	0.0876337i
$556$		0			0
$557$	21.7982	+	21.7982i	0.923621	+	0.923621i	0.997283	−	0.0736625i	$-0.0234688\pi$
$557$	21.7982	+	21.7982i	0.923621	+	0.923621i	−0.0736625	+	0.997283i	$0.523469\pi$
$558$		0			0
$559$	−20.0029			−0.846032
$560$		0			0
$561$	−18.7017			−0.789587
$562$		0			0
$563$	5.82606	+	5.82606i	0.245539	+	0.245539i	0.819137	−	0.573598i	$-0.194453\pi$
$563$	5.82606	+	5.82606i	0.245539	+	0.245539i	−0.573598	+	0.819137i	$0.694453\pi$
$564$		0			0
$565$	−0.982377	+	0.982377i	−0.0413289	+	0.0413289i
$566$		0			0
$567$		−	3.84698i		−	0.161558i
$568$		0			0
$569$		−	9.99322i		−	0.418938i	−0.977815	−	0.209469i	$-0.932827\pi$
$569$		−	9.99322i		−	0.418938i	0.977815	−	0.209469i	$-0.0671735\pi$
$570$		0			0
$571$	−7.14084	+	7.14084i	−0.298835	+	0.298835i	−0.840557	−	0.541723i	$-0.817772\pi$
$571$	−7.14084	+	7.14084i	−0.298835	+	0.298835i	0.541723	+	0.840557i	$0.317772\pi$
$572$		0			0
$573$	54.5633	+	54.5633i	2.27941	+	2.27941i
$574$		0			0
$575$	29.4235			1.22704
$576$		0			0
$577$	3.84281			0.159978			0.0799891	−	0.996796i	$-0.474511\pi$
$577$	3.84281			0.159978			0.0799891	+	0.996796i	$0.474511\pi$
$578$		0			0
$579$	27.5510	+	27.5510i	1.14498	+	1.14498i
$580$		0			0
$581$	3.98802	−	3.98802i	0.165451	−	0.165451i
$582$		0			0
$583$			54.2743i			2.24781i
$584$		0			0
$585$		−	3.71026i		−	0.153400i
$586$		0			0
$587$	−7.57085	+	7.57085i	−0.312482	+	0.312482i	−0.845871	−	0.533388i	$-0.820918\pi$
$587$	−7.57085	+	7.57085i	−0.312482	+	0.312482i	0.533388	+	0.845871i	$0.320918\pi$
$588$		0			0
$589$	−11.4532	−	11.4532i	−0.471920	−	0.471920i
$590$		0			0
$591$	70.8309			2.91360
$592$		0			0
$593$	−0.0598069			−0.00245597			−0.00122799	−	0.999999i	$-0.500391\pi$
$593$	−0.0598069			−0.00245597			−0.00122799	+	0.999999i	$0.500391\pi$
$594$		0			0
$595$	0.113697	+	0.113697i	0.00466110	+	0.00466110i
$596$		0			0
$597$	29.4401	−	29.4401i	1.20490	−	1.20490i
$598$		0			0
$599$		−	8.94011i		−	0.365283i	−0.983180	−	0.182641i	$-0.941535\pi$
$599$		−	8.94011i		−	0.365283i	0.983180	−	0.182641i	$-0.0584647\pi$
$600$		0			0
$601$			28.4600i			1.16091i	0.814293	+	0.580454i	$0.197125\pi$
$601$			28.4600i			1.16091i	−0.814293	+	0.580454i	$0.802875\pi$
$602$		0			0
$603$	8.66876	−	8.66876i	0.353019	−	0.353019i
$604$		0			0
$605$	3.45043	+	3.45043i	0.140280	+	0.140280i
$606$		0			0
$607$	−20.8160			−0.844896			−0.422448	−	0.906387i	$-0.638829\pi$
$607$	−20.8160			−0.844896			−0.422448	+	0.906387i	$0.638829\pi$
$608$		0			0
$609$	16.5338			0.669982
$610$		0			0
$611$	2.50649	+	2.50649i	0.101402	+	0.101402i
$612$		0			0
$613$	−30.4927	+	30.4927i	−1.23159	+	1.23159i	−0.268233	+	0.963354i	$0.586440\pi$
$613$	−30.4927	+	30.4927i	−1.23159	+	1.23159i	−0.963354	+	0.268233i	$0.913560\pi$
$614$		0			0
$615$		−	1.30287i		−	0.0525370i
$616$		0			0
$617$			24.7514i			0.996453i	0.867047	+	0.498227i	$0.166015\pi$
$617$			24.7514i			0.996453i	−0.867047	+	0.498227i	$0.833985\pi$
$618$		0			0
$619$	−13.8910	+	13.8910i	−0.558327	+	0.558327i	−0.928831	−	0.370504i	$-0.879185\pi$
$619$	−13.8910	+	13.8910i	−0.558327	+	0.558327i	0.370504	+	0.928831i	$0.379185\pi$
$620$		0			0
$621$	28.8021	+	28.8021i	1.15579	+	1.15579i
$622$		0			0
$623$	1.68429			0.0674798
$624$		0			0
$625$	−24.6227			−0.984908
$626$		0			0
$627$	49.6514	+	49.6514i	1.98289	+	1.98289i
$628$		0			0
$629$	4.49312	−	4.49312i	0.179153	−	0.179153i
$630$		0			0
$631$		−	43.5129i		−	1.73222i	−0.499854	−	0.866110i	$-0.666613\pi$
$631$		−	43.5129i		−	1.73222i	0.499854	−	0.866110i	$-0.333387\pi$
$632$		0			0
$633$		−	42.6233i		−	1.69412i
$634$		0			0
$635$	−1.77976	+	1.77976i	−0.0706275	+	0.0706275i
$636$		0			0
$637$	18.3555	+	18.3555i	0.727270	+	0.727270i
$638$		0			0
$639$	−4.19946			−0.166128
$640$		0			0
$641$	20.1009			0.793936			0.396968	−	0.917832i	$-0.370062\pi$
$641$	20.1009			0.793936			0.396968	+	0.917832i	$0.370062\pi$
$642$		0			0
$643$	−12.2175	−	12.2175i	−0.481811	−	0.481811i	0.423899	−	0.905710i	$-0.360661\pi$
$643$	−12.2175	−	12.2175i	−0.481811	−	0.481811i	−0.905710	+	0.423899i	$0.860661\pi$
$644$		0			0
$645$	1.49563	−	1.49563i	0.0588905	−	0.0588905i
$646$		0			0
$647$			16.3854i			0.644178i	0.946709	+	0.322089i	$0.104385\pi$
$647$			16.3854i			0.644178i	−0.946709	+	0.322089i	$0.895615\pi$
$648$		0			0
$649$		−	40.2093i		−	1.57835i
$650$		0			0
$651$	8.94446	−	8.94446i	0.350561	−	0.350561i
$652$		0			0
$653$	18.7699	+	18.7699i	0.734523	+	0.734523i	0.971512	−	0.236989i	$-0.0761605\pi$
$653$	18.7699	+	18.7699i	0.734523	+	0.734523i	−0.236989	+	0.971512i	$0.576161\pi$
$654$		0			0
$655$	0.659243			0.0257587
$656$		0			0
$657$	37.6441			1.46864
$658$		0			0
$659$	−28.1462	−	28.1462i	−1.09642	−	1.09642i	−0.994826	−	0.101593i	$-0.967606\pi$
$659$	−28.1462	−	28.1462i	−1.09642	−	1.09642i	−0.101593	−	0.994826i	$-0.532394\pi$
$660$		0			0
$661$	−8.99640	+	8.99640i	−0.349919	+	0.349919i	−0.860080	−	0.510160i	$-0.829586\pi$
$661$	−8.99640	+	8.99640i	−0.349919	+	0.349919i	0.510160	+	0.860080i	$0.329586\pi$
$662$		0			0
$663$		−	12.5783i		−	0.488500i
$664$		0			0
$665$		−	0.603709i		−	0.0234108i
$666$		0			0
$667$	−23.5821	+	23.5821i	−0.913102	+	0.913102i
$668$		0			0
$669$	−37.3911	−	37.3911i	−1.44562	−	1.44562i
$670$		0			0
$671$	−88.7172			−3.42489
$672$		0			0
$673$	18.4947			0.712919			0.356459	−	0.934311i	$-0.383984\pi$
$673$	18.4947			0.712919			0.356459	+	0.934311i	$0.383984\pi$
$674$		0			0
$675$	−24.2260	−	24.2260i	−0.932458	−	0.932458i
$676$		0			0
$677$	−7.27015	+	7.27015i	−0.279414	+	0.279414i	−0.832875	−	0.553461i	$-0.813307\pi$
$677$	−7.27015	+	7.27015i	−0.279414	+	0.279414i	0.553461	+	0.832875i	$0.313307\pi$
$678$		0			0
$679$		−	17.1852i		−	0.659509i
$680$		0			0
$681$		−	81.8024i		−	3.13467i
$682$		0			0
$683$	−1.07946	+	1.07946i	−0.0413043	+	0.0413043i	−0.727457	−	0.686153i	$-0.759298\pi$
$683$	−1.07946	+	1.07946i	−0.0413043	+	0.0413043i	0.686153	+	0.727457i	$0.259298\pi$
$684$		0			0
$685$	−0.318824	−	0.318824i	−0.0121817	−	0.0121817i
$686$		0			0
$687$	−27.9817			−1.06757
$688$		0			0
$689$	−36.5035			−1.39067
$690$		0			0
$691$	−15.3729	−	15.3729i	−0.584812	−	0.584812i	0.351410	−	0.936222i	$-0.385702\pi$
$691$	−15.3729	−	15.3729i	−0.584812	−	0.584812i	−0.936222	+	0.351410i	$0.885702\pi$
$692$		0			0
$693$	−24.8928	+	24.8928i	−0.945598	+	0.945598i
$694$		0			0
$695$		−	0.0387658i		−	0.00147047i
$696$		0			0
$697$		−	2.83552i		−	0.107403i
$698$		0			0
$699$	−45.6676	+	45.6676i	−1.72731	+	1.72731i
$700$		0			0
$701$	−2.22188	−	2.22188i	−0.0839191	−	0.0839191i	0.663901	−	0.747820i	$-0.268900\pi$
$701$	−2.22188	−	2.22188i	−0.0839191	−	0.0839191i	−0.747820	+	0.663901i	$0.768900\pi$
$702$		0			0
$703$	−23.8577			−0.899810
$704$		0			0
$705$	−0.374825			−0.0141167
$706$		0			0
$707$	−2.12372	−	2.12372i	−0.0798705	−	0.0798705i
$708$		0			0
$709$	−14.5326	+	14.5326i	−0.545785	+	0.545785i	−0.925219	−	0.379434i	$-0.876119\pi$
$709$	−14.5326	+	14.5326i	−0.545785	+	0.545785i	0.379434	+	0.925219i	$0.376119\pi$
$710$		0			0
$711$			63.3964i			2.37755i
$712$		0			0
$713$			25.5149i			0.955542i
$714$		0			0
$715$	−3.15107	+	3.15107i	−0.117843	+	0.117843i
$716$		0			0
$717$	7.07507	+	7.07507i	0.264223	+	0.264223i
$718$		0			0
$719$	22.0455			0.822158			0.411079	−	0.911600i	$-0.365152\pi$
$719$	22.0455			0.822158			0.411079	+	0.911600i	$0.365152\pi$
$720$		0			0
$721$	11.7759			0.438557
$722$		0			0
$723$	−7.92228	−	7.92228i	−0.294633	−	0.294633i
$724$		0			0
$725$	19.8353	−	19.8353i	0.736666	−	0.736666i
$726$		0			0
$727$		−	35.0296i		−	1.29917i	−0.760287	−	0.649587i	$-0.774942\pi$
$727$		−	35.0296i		−	1.29917i	0.760287	−	0.649587i	$-0.225058\pi$
$728$		0			0
$729$			39.3769i			1.45840i
$730$		0			0
$731$	3.25504	−	3.25504i	0.120392	−	0.120392i
$732$		0			0
$733$	33.3592	+	33.3592i	1.23215	+	1.23215i	0.963136	+	0.269015i	$0.0866983\pi$
$733$	33.3592	+	33.3592i	1.23215	+	1.23215i	0.269015	+	0.963136i	$0.413302\pi$
$734$		0			0
$735$	−2.74491			−0.101247
$736$		0			0
$737$	−14.7245			−0.542384
$738$		0			0
$739$	30.4784	+	30.4784i	1.12117	+	1.12117i	0.991566	+	0.129599i	$0.0413690\pi$
$739$	30.4784	+	30.4784i	1.12117	+	1.12117i	0.129599	+	0.991566i	$0.458631\pi$
$740$		0			0
$741$	−33.3942	+	33.3942i	−1.22677	+	1.22677i
$742$		0			0
$743$			25.9320i			0.951354i	0.879620	+	0.475677i	$0.157797\pi$
$743$			25.9320i			0.951354i	−0.879620	+	0.475677i	$0.842203\pi$
$744$		0			0
$745$		−	0.653160i		−	0.0239299i
$746$		0			0
$747$	21.1776	−	21.1776i	0.774848	−	0.774848i
$748$		0			0
$749$	0.718892	+	0.718892i	0.0262677	+	0.0262677i
$750$		0			0
$751$	−9.47512			−0.345752			−0.172876	−	0.984944i	$-0.555306\pi$
$751$	−9.47512			−0.345752			−0.172876	+	0.984944i	$0.555306\pi$
$752$		0			0
$753$	−22.6737			−0.826277
$754$		0			0
$755$	−1.36236	−	1.36236i	−0.0495815	−	0.0495815i
$756$		0			0
$757$	−11.9056	+	11.9056i	−0.432717	+	0.432717i	−0.889552	−	0.456835i	$-0.848983\pi$
$757$	−11.9056	+	11.9056i	−0.432717	+	0.432717i	0.456835	+	0.889552i	$0.348983\pi$
$758$		0			0
$759$		−	110.611i		−	4.01494i
$760$		0			0
$761$			18.8898i			0.684754i	0.939563	+	0.342377i	$0.111232\pi$
$761$			18.8898i			0.684754i	−0.939563	+	0.342377i	$0.888768\pi$
$762$		0			0
$763$	1.03771	−	1.03771i	0.0375677	−	0.0375677i
$764$		0			0
$765$	0.603764	+	0.603764i	0.0218291	+	0.0218291i
$766$		0			0
$767$	27.0437			0.976493
$768$		0			0
$769$	−13.3803			−0.482506			−0.241253	−	0.970462i	$-0.577558\pi$
$769$	−13.3803			−0.482506			−0.241253	+	0.970462i	$0.577558\pi$
$770$		0			0
$771$	−52.6474	−	52.6474i	−1.89605	−	1.89605i
$772$		0			0
$773$	4.48902	−	4.48902i	0.161459	−	0.161459i	−0.621754	−	0.783213i	$-0.713580\pi$
$773$	4.48902	−	4.48902i	0.161459	−	0.161459i	0.783213	+	0.621754i	$0.213580\pi$
$774$		0			0
$775$		−	21.4611i		−	0.770906i
$776$		0			0
$777$		−	18.6319i		−	0.668414i
$778$		0			0
$779$	−7.52806	+	7.52806i	−0.269721	+	0.269721i
$780$		0			0
$781$	3.56654	+	3.56654i	0.127621	+	0.127621i
$782$		0			0
$783$	38.8329			1.38777
$784$		0			0
$785$	−3.86252			−0.137859
$786$		0			0
$787$	−11.9747	−	11.9747i	−0.426850	−	0.426850i	0.460704	−	0.887554i	$-0.347597\pi$
$787$	−11.9747	−	11.9747i	−0.426850	−	0.426850i	−0.887554	+	0.460704i	$0.847597\pi$
$788$		0			0
$789$	−35.5248	+	35.5248i	−1.26472	+	1.26472i
$790$		0			0
$791$			8.86578i			0.315231i
$792$		0			0
$793$		−	59.6688i		−	2.11890i
$794$		0			0
$795$	2.72940	−	2.72940i	0.0968017	−	0.0968017i
$796$		0			0
$797$	3.52687	+	3.52687i	0.124928	+	0.124928i	0.766807	−	0.641878i	$-0.221845\pi$
$797$	3.52687	+	3.52687i	0.124928	+	0.124928i	−0.641878	+	0.766807i	$0.721845\pi$
$798$		0			0
$799$	−0.815754			−0.0288593
$800$		0			0
$801$	8.94412			0.316025
$802$		0			0
$803$	−31.9706	−	31.9706i	−1.12822	−	1.12822i
$804$		0			0
$805$	−0.672458	+	0.672458i	−0.0237010	+	0.0237010i
$806$		0			0
$807$		−	20.0853i		−	0.707037i
$808$		0			0
$809$			11.8721i			0.417402i	0.977980	+	0.208701i	$0.0669235\pi$
$809$			11.8721i			0.417402i	−0.977980	+	0.208701i	$0.933076\pi$
$810$		0			0
$811$	−7.06018	+	7.06018i	−0.247916	+	0.247916i	−0.820115	−	0.572199i	$-0.806091\pi$
$811$	−7.06018	+	7.06018i	−0.247916	+	0.247916i	0.572199	+	0.820115i	$0.306091\pi$
$812$		0			0
$813$	−41.4218	−	41.4218i	−1.45273	−	1.45273i
$814$		0			0
$815$	1.50757			0.0528078
$816$		0			0
$817$	−17.2837			−0.604679
$818$		0			0
$819$	−16.7422	−	16.7422i	−0.585020	−	0.585020i
$820$		0			0
$821$	−7.90352	+	7.90352i	−0.275835	+	0.275835i	−0.831444	−	0.555609i	$-0.812485\pi$
$821$	−7.90352	+	7.90352i	−0.275835	+	0.275835i	0.555609	+	0.831444i	$0.312485\pi$
$822$		0			0
$823$		−	29.3339i		−	1.02252i	−0.859427	−	0.511258i	$-0.829180\pi$
$823$		−	29.3339i		−	1.02252i	0.859427	−	0.511258i	$-0.170820\pi$
$824$		0			0
$825$			93.0374i			3.23915i
$826$		0			0
$827$	12.8238	−	12.8238i	0.445928	−	0.445928i	−0.448070	−	0.893998i	$-0.647889\pi$
$827$	12.8238	−	12.8238i	0.445928	−	0.445928i	0.893998	+	0.448070i	$0.147889\pi$
$828$		0			0
$829$	−12.8736	−	12.8736i	−0.447118	−	0.447118i	0.447277	−	0.894395i	$-0.352394\pi$
$829$	−12.8736	−	12.8736i	−0.447118	−	0.447118i	−0.894395	+	0.447277i	$0.852394\pi$
$830$		0			0
$831$	−30.2419			−1.04908
$832$		0			0
$833$	−5.97391			−0.206984
$834$		0			0
$835$	0.252894	+	0.252894i	0.00875177	+	0.00875177i
$836$		0			0
$837$	21.0079	−	21.0079i	0.726138	−	0.726138i
$838$		0			0
$839$			32.0690i			1.10714i	0.832801	+	0.553572i	$0.186736\pi$
$839$			32.0690i			1.10714i	−0.832801	+	0.553572i	$0.813264\pi$
$840$		0			0
$841$			2.79492i			0.0963766i
$842$		0			0
$843$	47.6287	−	47.6287i	1.64042	−	1.64042i
$844$		0			0
$845$	−0.660182	−	0.660182i	−0.0227110	−	0.0227110i
$846$		0			0
$847$	31.1395			1.06997
$848$		0			0
$849$	−24.8992			−0.854539
$850$		0			0
$851$	26.5746	+	26.5746i	0.910965	+	0.910965i
$852$		0			0
$853$	−27.3066	+	27.3066i	−0.934960	+	0.934960i	−0.998010	−	0.0630503i	$-0.979917\pi$
$853$	−27.3066	+	27.3066i	−0.934960	+	0.934960i	0.0630503	+	0.998010i	$0.479917\pi$
$854$		0			0
$855$		−	3.20588i		−	0.109639i
$856$		0			0
$857$		−	20.4665i		−	0.699121i	−0.936914	−	0.349560i	$-0.886331\pi$
$857$		−	20.4665i		−	0.699121i	0.936914	−	0.349560i	$-0.113669\pi$
$858$		0			0
$859$	−15.1127	+	15.1127i	−0.515638	+	0.515638i	−0.916249	−	0.400610i	$-0.868798\pi$
$859$	−15.1127	+	15.1127i	−0.515638	+	0.515638i	0.400610	+	0.916249i	$0.368798\pi$
$860$		0			0
$861$	−5.87910	−	5.87910i	−0.200359	−	0.200359i
$862$		0			0
$863$	7.40206			0.251969			0.125985	−	0.992032i	$-0.459791\pi$
$863$	7.40206			0.251969			0.125985	+	0.992032i	$0.459791\pi$
$864$		0			0
$865$	−0.984651			−0.0334791
$866$		0			0
$867$	2.04684	+	2.04684i	0.0695145	+	0.0695145i
$868$		0			0
$869$	53.8417	−	53.8417i	1.82645	−	1.82645i
$870$		0			0
$871$		−	9.90331i		−	0.335561i
$872$		0			0
$873$		−	91.2590i		−	3.08865i
$874$		0			0
$875$	1.13410	−	1.13410i	0.0383396	−	0.0383396i
$876$		0			0
$877$	−0.807629	−	0.807629i	−0.0272717	−	0.0272717i	0.693339	−	0.720611i	$-0.256139\pi$
$877$	−0.807629	−	0.807629i	−0.0272717	−	0.0272717i	−0.720611	+	0.693339i	$0.756139\pi$
$878$		0			0
$879$	12.0131			0.405191
$880$		0			0
$881$	22.8408			0.769526			0.384763	−	0.923015i	$-0.374283\pi$
$881$	22.8408			0.769526			0.384763	+	0.923015i	$0.374283\pi$
$882$		0			0
$883$	−8.29032	−	8.29032i	−0.278992	−	0.278992i	0.553715	−	0.832706i	$-0.313210\pi$
$883$	−8.29032	−	8.29032i	−0.278992	−	0.278992i	−0.832706	+	0.553715i	$0.813210\pi$
$884$		0			0
$885$	−2.02208	+	2.02208i	−0.0679716	+	0.0679716i
$886$		0			0
$887$			20.9534i			0.703546i	0.936085	+	0.351773i	$0.114421\pi$
$887$			20.9534i			0.703546i	−0.936085	+	0.351773i	$0.885579\pi$
$888$		0			0
$889$			16.0620i			0.538702i
$890$		0			0
$891$	−17.3498	+	17.3498i	−0.581239	+	0.581239i
$892$		0			0
$893$	2.16575	+	2.16575i	0.0724742	+	0.0724742i
$894$		0			0
$895$	0.922149			0.0308240
$896$		0			0
$897$	74.3943			2.48395
$898$		0			0
$899$	17.2005	+	17.2005i	0.573668	+	0.573668i
$900$		0			0
$901$	5.94015	−	5.94015i	0.197895	−	0.197895i
$902$		0			0
$903$		−	13.4978i		−	0.449180i
$904$		0			0
$905$			2.00866i			0.0667700i
$906$		0			0
$907$	24.8227	−	24.8227i	0.824223	−	0.824223i	−0.162488	−	0.986711i	$-0.551952\pi$
$907$	24.8227	−	24.8227i	0.824223	−	0.824223i	0.986711	+	0.162488i	$0.0519517\pi$
$908$		0			0
$909$	−11.2776	−	11.2776i	−0.374054	−	0.374054i
$910$		0			0
$911$	−12.4172			−0.411401			−0.205701	−	0.978615i	$-0.565947\pi$
$911$	−12.4172			−0.411401			−0.205701	+	0.978615i	$0.565947\pi$
$912$		0			0
$913$	−35.9717			−1.19049
$914$		0			0
$915$	4.46149	+	4.46149i	0.147492	+	0.147492i
$916$		0			0
$917$	2.97477	−	2.97477i	0.0982357	−	0.0982357i
$918$		0			0
$919$		−	20.5870i		−	0.679103i	−0.940587	−	0.339552i	$-0.889725\pi$
$919$		−	20.5870i		−	0.679103i	0.940587	−	0.339552i	$-0.110275\pi$
$920$		0			0
$921$		−	0.808574i		−	0.0266434i
$922$		0			0
$923$	−2.39876	+	2.39876i	−0.0789562	+	0.0789562i
$924$		0			0
$925$	−22.3524	−	22.3524i	−0.734943	−	0.734943i
$926$		0			0
$927$	62.5337			2.05388
$928$		0			0
$929$	27.0561			0.887681			0.443841	−	0.896106i	$-0.353616\pi$
$929$	27.0561			0.887681			0.443841	+	0.896106i	$0.353616\pi$
$930$		0			0
$931$	15.8602	+	15.8602i	0.519797	+	0.519797i
$932$		0			0
$933$	21.1080	−	21.1080i	0.691046	−	0.691046i
$934$		0			0
$935$		−	1.02554i		−	0.0335386i
$936$		0			0
$937$			40.2132i			1.31371i	0.754018	+	0.656854i	$0.228113\pi$
$937$			40.2132i			1.31371i	−0.754018	+	0.656854i	$0.771887\pi$
$938$		0			0
$939$	−6.05726	+	6.05726i	−0.197671	+	0.197671i
$940$		0			0
$941$	−10.2877	−	10.2877i	−0.335370	−	0.335370i	0.519252	−	0.854621i	$-0.326211\pi$
$941$	−10.2877	−	10.2877i	−0.335370	−	0.335370i	−0.854621	+	0.519252i	$0.826211\pi$
$942$		0			0
$943$	16.7707			0.546129
$944$		0			0
$945$	1.10734			0.0360219
$946$		0			0
$947$	21.5285	+	21.5285i	0.699581	+	0.699581i	0.964320	−	0.264739i	$-0.0852859\pi$
$947$	21.5285	+	21.5285i	0.699581	+	0.699581i	−0.264739	+	0.964320i	$0.585286\pi$
$948$		0			0
$949$	21.5026	−	21.5026i	0.698003	−	0.698003i
$950$		0			0
$951$		−	50.9054i		−	1.65072i
$952$		0			0
$953$			22.2373i			0.720338i	0.932887	+	0.360169i	$0.117281\pi$
$953$			22.2373i			0.720338i	−0.932887	+	0.360169i	$0.882719\pi$
$954$		0			0
$955$	−2.99206	+	2.99206i	−0.0968208	+	0.0968208i
$956$		0			0
$957$	−74.5668	−	74.5668i	−2.41040	−	2.41040i
$958$		0			0
$959$	−2.87733			−0.0929139
$960$		0			0
$961$	−12.3897			−0.399669
$962$		0			0
$963$	3.81754	+	3.81754i	0.123019	+	0.123019i
$964$		0			0
$965$	−1.51080	+	1.51080i	−0.0486343	+	0.0486343i
$966$		0			0
$967$			14.4501i			0.464683i	0.972634	+	0.232342i	$0.0746387\pi$
$967$			14.4501i			0.464683i	−0.972634	+	0.232342i	$0.925361\pi$
$968$		0			0
$969$		−	10.8684i		−	0.349143i
$970$		0			0
$971$	−6.18861	+	6.18861i	−0.198602	+	0.198602i	−0.799400	−	0.600799i	$-0.794849\pi$
$971$	−6.18861	+	6.18861i	−0.198602	+	0.198602i	0.600799	+	0.799400i	$0.294849\pi$
$972$		0			0
$973$	−0.174927	−	0.174927i	−0.00560790	−	0.00560790i
$974$		0			0
$975$	−62.5745			−2.00399
$976$		0			0
$977$	47.9589			1.53434			0.767171	−	0.641443i	$-0.221664\pi$
$977$	47.9589			1.53434			0.767171	+	0.641443i	$0.221664\pi$
$978$		0			0
$979$	−7.59611	−	7.59611i	−0.242773	−	0.242773i
$980$		0			0
$981$	5.51057	−	5.51057i	0.175939	−	0.175939i
$982$		0			0
$983$		−	32.0505i		−	1.02225i	−0.859506	−	0.511126i	$-0.829229\pi$
$983$		−	32.0505i		−	1.02225i	0.859506	−	0.511126i	$-0.170771\pi$
$984$		0			0
$985$			3.88412i			0.123758i
$986$		0			0
$987$	−1.69136	+	1.69136i	−0.0538367	+	0.0538367i
$988$		0			0
$989$	19.2519	+	19.2519i	0.612176	+	0.612176i
$990$		0			0
$991$	−37.1875			−1.18130			−0.590650	−	0.806928i	$-0.701128\pi$
$991$	−37.1875			−1.18130			−0.590650	+	0.806928i	$0.701128\pi$
$992$		0			0
$993$	27.7428			0.880390
$994$		0			0
$995$	1.61439	+	1.61439i	0.0511796	+	0.0511796i
$996$		0			0
$997$	−3.51747	+	3.51747i	−0.111399	+	0.111399i	−0.760609	−	0.649210i	$-0.775100\pi$
$997$	−3.51747	+	3.51747i	−0.111399	+	0.111399i	0.649210	+	0.760609i	$0.275100\pi$
$998$		0			0
$999$		−	43.7607i		−	1.38453i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1088.2.l.b.273.14		30
4.3	odd	2		272.2.l.b.205.6	yes	30
16.5	even	4	inner	1088.2.l.b.817.14		30
16.11	odd	4		272.2.l.b.69.6	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
272.2.l.b.69.6	✓	30	16.11	odd	4
272.2.l.b.205.6	yes	30	4.3	odd	2
1088.2.l.b.273.14		30	1.1	even	1	trivial
1088.2.l.b.817.14		30	16.5	even	4	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(2.04684 + 2.04684i) q^{3} +(-0.112242 + 0.112242i) q^{5} +1.01296i q^{7} +5.37914i q^{9} +(4.56843 - 4.56843i) q^{11} +(3.07260 + 3.07260i) q^{13} -0.459483 q^{15} -1.00000 q^{17} +(2.65491 + 2.65491i) q^{19} +(-2.07337 + 2.07337i) q^{21} -5.91450i q^{23} +4.97480i q^{25} +(-4.86974 + 4.86974i) q^{27} +(-3.98716 - 3.98716i) q^{29} -4.31396 q^{31} +18.7017 q^{33} +(-0.113697 - 0.113697i) q^{35} +(-4.49312 + 4.49312i) q^{37} +12.5783i q^{39} +2.83552i q^{41} +(-3.25504 + 3.25504i) q^{43} +(-0.603764 - 0.603764i) q^{45} +0.815754 q^{47} +5.97391 q^{49} +(-2.04684 - 2.04684i) q^{51} +(-5.94015 + 5.94015i) q^{53} +1.02554i q^{55} +10.8684i q^{57} +(4.40078 - 4.40078i) q^{59} +(-9.70982 - 9.70982i) q^{61} -5.44887 q^{63} -0.689749 q^{65} +(-1.61155 - 1.61155i) q^{67} +(12.1061 - 12.1061i) q^{69} +0.780693i q^{71} -6.99816i q^{73} +(-10.1826 + 10.1826i) q^{75} +(4.62764 + 4.62764i) q^{77} +11.7856 q^{79} -3.79775 q^{81} +(-3.93699 - 3.93699i) q^{83} +(0.112242 - 0.112242i) q^{85} -16.3222i q^{87} -1.66274i q^{89} +(-3.11243 + 3.11243i) q^{91} +(-8.83001 - 8.83001i) q^{93} -0.595984 q^{95} -16.9653 q^{97} +(24.5742 + 24.5742i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 2 q^{3} - 2 q^{5} + 10 q^{11} - 6 q^{13} + 28 q^{15} - 30 q^{17} - 10 q^{19} - 4 q^{21} - 4 q^{27} - 18 q^{29} - 48 q^{31} - 12 q^{33} - 16 q^{35} + 6 q^{37} - 2 q^{43} + 42 q^{45} + 32 q^{47} - 38 q^{49}+ \cdots - 54 q^{99}+O(q^{100}) \) 30 * q + 2 * q^3 - 2 * q^5 + 10 * q^11 - 6 * q^13 + 28 * q^15 - 30 * q^17 - 10 * q^19 - 4 * q^21 - 4 * q^27 - 18 * q^29 - 48 * q^31 - 12 * q^33 - 16 * q^35 + 6 * q^37 - 2 * q^43 + 42 * q^45 + 32 * q^47 - 38 * q^49 - 2 * q^51 - 6 * q^53 + 14 * q^59 + 6 * q^61 - 84 * q^63 - 12 * q^65 - 26 * q^67 + 12 * q^69 + 26 * q^75 - 28 * q^77 + 72 * q^79 - 10 * q^81 + 34 * q^83 + 2 * q^85 - 16 * q^91 - 24 * q^93 - 76 * q^95 - 28 * q^97 - 54 * q^99

Introduction

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