LMFDB - Embedded newform 1184.2.y.a.529.34

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1184,2,Mod(529,1184)] 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("1184.529"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1184, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1184 = 2^{5} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1184.y (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$9.45428759932$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 296)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			529.34
Character	$\chi$	$=$	1184.529
Dual form			1184.2.y.a.1137.34

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.54245 + 1.46788i) q^{3} +(-2.01329 + 3.48712i) q^{5} +(-0.477860 + 0.827678i) q^{7} +(2.80936 + 4.86595i) q^{9} +0.266146i q^{11} +(2.19590 - 3.80341i) q^{13} +(-10.2374 + 5.91054i) q^{15} +(-4.25701 + 2.45778i) q^{17} +(-0.537084 + 0.930256i) q^{19} +(-2.42987 + 1.40288i) q^{21} +4.38312i q^{23} +(-5.60666 - 9.71102i) q^{25} +7.68793i q^{27} +9.06214 q^{29} +3.47979i q^{31} +(-0.390671 + 0.676662i) q^{33} +(-1.92414 - 3.33271i) q^{35} +(-0.468706 - 6.06468i) q^{37} +(11.1659 - 6.44664i) q^{39} +(2.60116 - 4.50534i) q^{41} -2.65469 q^{43} -22.6242 q^{45} -9.88608 q^{47} +(3.04330 + 5.27115i) q^{49} -14.4309 q^{51} +(-0.693668 + 0.400490i) q^{53} +(-0.928083 - 0.535829i) q^{55} +(-2.73101 + 1.57675i) q^{57} +(6.03346 + 10.4503i) q^{59} +(2.97244 - 5.14841i) q^{61} -5.36992 q^{63} +(8.84195 + 15.3147i) q^{65} +(-11.7819 - 6.80228i) q^{67} +(-6.43390 + 11.1438i) q^{69} +(-1.67560 + 2.90222i) q^{71} -2.12560 q^{73} -32.9197i q^{75} +(-0.220283 - 0.127181i) q^{77} +(4.72714 + 2.72922i) q^{79} +(-2.85691 + 4.94831i) q^{81} +(12.7696 - 7.37255i) q^{83} -19.7929i q^{85} +(23.0400 + 13.3022i) q^{87} +(-5.07906 + 2.93240i) q^{89} +(2.09866 + 3.63499i) q^{91} +(-5.10792 + 8.84718i) q^{93} +(-2.16261 - 3.74575i) q^{95} +1.93694i q^{97} +(-1.29505 + 0.747700i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 2 q^{7} + 30 q^{9} + 6 q^{15} - 12 q^{17} - 32 q^{25} + 4 q^{33} + 6 q^{39} - 32 q^{47} - 18 q^{49} - 24 q^{55} - 6 q^{57} - 8 q^{63} + 6 q^{65} - 18 q^{71} - 64 q^{73} - 54 q^{79} - 16 q^{81} + 108 q^{87}+ \cdots - 50 q^{95}+O(q^{100}) $ 72 * q - 2 * q^7 + 30 * q^9 + 6 * q^15 - 12 * q^17 - 32 * q^25 + 4 * q^33 + 6 * q^39 - 32 * q^47 - 18 * q^49 - 24 * q^55 - 6 * q^57 - 8 * q^63 + 6 * q^65 - 18 * q^71 - 64 * q^73 - 54 * q^79 - 16 * q^81 + 108 * q^87 - 36 * q^89 - 50 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1184\mathbb{Z}\right)^\times$.

$n$	$223$	$705$	$741$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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
$3$	2.54245	+	1.46788i	1.46788	+	0.847482i	0.999353	−	0.0359656i	$-0.0114507\pi$
$3$	2.54245	+	1.46788i	1.46788	+	0.847482i	0.468529	+	0.883448i	$0.344784\pi$
$4$		0			0
$5$	−2.01329	+	3.48712i	−0.900370	+	1.55949i	−0.0733552	+	0.997306i	$0.523371\pi$
$5$	−2.01329	+	3.48712i	−0.900370	+	1.55949i	−0.827015	+	0.562180i	$0.809963\pi$
$6$		0			0
$7$	−0.477860	+	0.827678i	−0.180614	+	0.312833i	−0.942090	−	0.335361i	$-0.891142\pi$
$7$	−0.477860	+	0.827678i	−0.180614	+	0.312833i	0.761476	+	0.648193i	$0.224475\pi$
$8$		0			0
$9$	2.80936	+	4.86595i	0.936452	+	1.62198i
$10$		0			0
$11$			0.266146i			0.0802461i	0.999195	+	0.0401230i	$0.0127750\pi$
$11$			0.266146i			0.0802461i	−0.999195	+	0.0401230i	$0.987225\pi$
$12$		0			0
$13$	2.19590	−	3.80341i	0.609032	−	1.05488i	−0.382368	−	0.924010i	$-0.624891\pi$
$13$	2.19590	−	3.80341i	0.609032	−	1.05488i	0.991400	−	0.130865i	$-0.0417754\pi$
$14$		0			0
$15$	−10.2374	+	5.91054i	−2.64327	+	1.52609i
$16$		0			0
$17$	−4.25701	+	2.45778i	−1.03248	+	0.596100i	−0.917693	−	0.397291i	$-0.869950\pi$
$17$	−4.25701	+	2.45778i	−1.03248	+	0.596100i	−0.114783	+	0.993391i	$0.536617\pi$
$18$		0			0
$19$	−0.537084	+	0.930256i	−0.123215	+	0.213415i	−0.921034	−	0.389482i	$-0.872654\pi$
$19$	−0.537084	+	0.930256i	−0.123215	+	0.213415i	0.797819	+	0.602898i	$0.205987\pi$
$20$		0			0
$21$	−2.42987	+	1.40288i	−0.530240	+	0.306134i
$22$		0			0
$23$			4.38312i			0.913943i	0.889481	+	0.456972i	$0.151066\pi$
$23$			4.38312i			0.913943i	−0.889481	+	0.456972i	$0.848934\pi$
$24$		0			0
$25$	−5.60666	−	9.71102i	−1.12133	−	1.94220i
$26$		0			0
$27$			7.68793i			1.47954i
$28$		0			0
$29$	9.06214			1.68280			0.841399	−	0.540415i	$-0.181733\pi$
$29$	9.06214			1.68280			0.841399	+	0.540415i	$0.181733\pi$
$30$		0			0
$31$			3.47979i			0.624989i	0.949920	+	0.312494i	$0.101165\pi$
$31$			3.47979i			0.624989i	−0.949920	+	0.312494i	$0.898835\pi$
$32$		0			0
$33$	−0.390671	+	0.676662i	−0.0680071	+	0.117792i
$34$		0			0
$35$	−1.92414	−	3.33271i	−0.325239	−	0.563330i
$36$		0			0
$37$	−0.468706	−	6.06468i	−0.0770548	−	0.997027i
$37$	−0.468706	−	6.06468i	−0.0770548	−	0.997027i
$38$		0			0
$39$	11.1659	−	6.44664i	1.78798	−	1.03229i
$40$		0			0
$41$	2.60116	−	4.50534i	0.406233	−	0.703616i	−0.588231	−	0.808693i	$-0.700175\pi$
$41$	2.60116	−	4.50534i	0.406233	−	0.703616i	0.994464	+	0.105077i	$0.0335088\pi$
$42$		0			0
$43$	−2.65469			−0.404836			−0.202418	−	0.979299i	$-0.564880\pi$
$43$	−2.65469			−0.404836			−0.202418	+	0.979299i	$0.564880\pi$
$44$		0			0
$45$	−22.6242			−3.37261
$46$		0			0
$47$	−9.88608			−1.44203			−0.721017	−	0.692918i	$-0.756325\pi$
$47$	−9.88608			−1.44203			−0.721017	+	0.692918i	$0.756325\pi$
$48$		0			0
$49$	3.04330	+	5.27115i	0.434757	+	0.753021i
$50$		0			0
$51$	−14.4309			−2.02074
$52$		0			0
$53$	−0.693668	+	0.400490i	−0.0952827	+	0.0550115i	−0.546884	−	0.837208i	$-0.684186\pi$
$53$	−0.693668	+	0.400490i	−0.0952827	+	0.0550115i	0.451602	+	0.892220i	$0.350853\pi$
$54$		0			0
$55$	−0.928083	−	0.535829i	−0.125143	−	0.0722512i
$56$		0			0
$57$	−2.73101	+	1.57675i	−0.361732	+	0.208846i
$58$		0			0
$59$	6.03346	+	10.4503i	0.785489	+	1.36051i	0.928706	+	0.370816i	$0.120922\pi$
$59$	6.03346	+	10.4503i	0.785489	+	1.36051i	−0.143217	+	0.989691i	$0.545745\pi$
$60$		0			0
$61$	2.97244	−	5.14841i	0.380581	−	0.659186i	−0.610564	−	0.791967i	$-0.709057\pi$
$61$	2.97244	−	5.14841i	0.380581	−	0.659186i	0.991145	+	0.132781i	$0.0423906\pi$
$62$		0			0
$63$	−5.36992			−0.676546
$64$		0			0
$65$	8.84195	+	15.3147i	1.09671	+	1.89956i
$66$		0			0
$67$	−11.7819	−	6.80228i	−1.43939	−	0.831031i	−0.441581	−	0.897222i	$-0.645582\pi$
$67$	−11.7819	−	6.80228i	−1.43939	−	0.831031i	−0.997807	+	0.0661908i	$0.978915\pi$
$68$		0			0
$69$	−6.43390	+	11.1438i	−0.774551	+	1.34156i
$70$		0			0
$71$	−1.67560	+	2.90222i	−0.198857	+	0.344431i	−0.948158	−	0.317799i	$-0.897056\pi$
$71$	−1.67560	+	2.90222i	−0.198857	+	0.344431i	0.749301	+	0.662230i	$0.230390\pi$
$72$		0			0
$73$	−2.12560			−0.248782			−0.124391	−	0.992233i	$-0.539698\pi$
$73$	−2.12560			−0.248782			−0.124391	+	0.992233i	$0.539698\pi$
$74$		0			0
$75$		−	32.9197i		−	3.80123i
$76$		0			0
$77$	−0.220283	−	0.127181i	−0.0251036	−	0.0144936i
$78$		0			0
$79$	4.72714	+	2.72922i	0.531845	+	0.307061i	0.741768	−	0.670657i	$-0.233988\pi$
$79$	4.72714	+	2.72922i	0.531845	+	0.307061i	−0.209922	+	0.977718i	$0.567321\pi$
$80$		0			0
$81$	−2.85691	+	4.94831i	−0.317434	+	0.549812i
$82$		0			0
$83$	12.7696	−	7.37255i	1.40165	−	0.809243i	0.407087	−	0.913389i	$-0.366544\pi$
$83$	12.7696	−	7.37255i	1.40165	−	0.809243i	0.994562	+	0.104147i	$0.0332111\pi$
$84$		0			0
$85$		−	19.7929i		−	2.14684i
$86$		0			0
$87$	23.0400	+	13.3022i	2.47015	+	1.42614i
$88$		0			0
$89$	−5.07906	+	2.93240i	−0.538379	+	0.310833i	−0.744422	−	0.667710i	$-0.767275\pi$
$89$	−5.07906	+	2.93240i	−0.538379	+	0.310833i	0.206043	+	0.978543i	$0.433941\pi$
$90$		0			0
$91$	2.09866	+	3.63499i	0.220000	+	0.381051i
$92$		0			0
$93$	−5.10792	+	8.84718i	−0.529667	+	0.917410i
$94$		0			0
$95$	−2.16261	−	3.74575i	−0.221879	−	0.384306i
$96$		0			0
$97$			1.93694i			0.196666i	0.995154	+	0.0983332i	$0.0313511\pi$
$97$			1.93694i			0.196666i	−0.995154	+	0.0983332i	$0.968649\pi$
$98$		0			0
$99$	−1.29505	+	0.747700i	−0.130158	+	0.0751466i
$100$		0			0
$101$			4.90081i			0.487649i	0.969819	+	0.243824i	$0.0784021\pi$
$101$			4.90081i			0.487649i	−0.969819	+	0.243824i	$0.921598\pi$
$102$		0			0
$103$			6.66637i			0.656857i	0.944529	+	0.328429i	$0.106519\pi$
$103$			6.66637i			0.656857i	−0.944529	+	0.328429i	$0.893481\pi$
$104$		0			0
$105$		−	11.2976i		−	1.10254i
$106$		0			0
$107$	1.14249	+	0.659618i	0.110449	+	0.0637677i	0.554207	−	0.832379i	$-0.313022\pi$
$107$	1.14249	+	0.659618i	0.110449	+	0.0637677i	−0.443758	+	0.896147i	$0.646355\pi$
$108$		0			0
$109$	5.18058	+	8.97302i	0.496209	+	0.859460i	0.999990	−	0.00437165i	$-0.00139154\pi$
$109$	5.18058	+	8.97302i	0.496209	+	0.859460i	−0.503781	+	0.863831i	$0.668058\pi$
$110$		0			0
$111$	7.71057	−	16.1071i	0.731855	−	1.52882i
$112$		0			0
$113$	10.0582	−	5.80708i	0.946192	−	0.546284i	0.0542962	−	0.998525i	$-0.482708\pi$
$113$	10.0582	−	5.80708i	0.946192	−	0.546284i	0.891896	+	0.452241i	$0.149375\pi$
$114$		0			0
$115$	−15.2844	−	8.82448i	−1.42528	−	0.822887i
$116$		0			0
$117$	24.6762			2.28132
$118$		0			0
$119$		−	4.69790i		−	0.430656i
$120$		0			0
$121$	10.9292			0.993561
$122$		0			0
$123$	13.2266	−	7.63639i	1.19260	−	0.688551i
$124$		0			0
$125$	25.0184			2.23771
$126$		0			0
$127$	4.11358	+	7.12493i	0.365021	+	0.632235i	0.988780	−	0.149382i	$-0.0477284\pi$
$127$	4.11358	+	7.12493i	0.365021	+	0.632235i	−0.623758	+	0.781617i	$0.714395\pi$
$128$		0			0
$129$	−6.74940	−	3.89677i	−0.594251	−	0.343091i
$130$		0			0
$131$	9.07687	+	15.7216i	0.793049	+	1.37360i	0.924070	+	0.382222i	$0.124841\pi$
$131$	9.07687	+	15.7216i	0.793049	+	1.37360i	−0.131021	+	0.991380i	$0.541825\pi$
$132$		0			0
$133$	−0.513302	−	0.889064i	−0.0445089	−	0.0770917i
$134$		0			0
$135$	−26.8087	−	15.4780i	−2.30733	−	1.33214i
$136$		0			0
$137$	5.99499			0.512187			0.256093	−	0.966652i	$-0.417565\pi$
$137$	5.99499			0.512187			0.256093	+	0.966652i	$0.417565\pi$
$138$		0			0
$139$	5.97882	−	3.45187i	0.507117	−	0.292784i	−0.224531	−	0.974467i	$-0.572085\pi$
$139$	5.97882	−	3.45187i	0.507117	−	0.292784i	0.731648	+	0.681683i	$0.238752\pi$
$140$		0			0
$141$	−25.1348	−	14.5116i	−2.11674	−	1.22210i
$142$		0			0
$143$	1.01226	+	0.584430i	0.0846496	+	0.0488725i
$144$		0			0
$145$	−18.2447	+	31.6008i	−1.51514	+	2.62430i
$146$		0			0
$147$			17.8688i			1.47380i
$148$		0			0
$149$		−	10.1988i		−	0.835518i	−0.908558	−	0.417759i	$-0.862816\pi$
$149$		−	10.1988i		−	0.835518i	0.908558	−	0.417759i	$-0.137184\pi$
$150$		0			0
$151$	3.35091	−	5.80394i	0.272693	−	0.472318i	−0.696858	−	0.717210i	$-0.745419\pi$
$151$	3.35091	−	5.80394i	0.272693	−	0.472318i	0.969550	+	0.244892i	$0.0787524\pi$
$152$		0			0
$153$	−23.9189	−	13.8096i	−1.93373	−	1.11644i
$154$		0			0
$155$	−12.1344	−	7.00582i	−0.974661	−	0.562721i
$156$		0			0
$157$	4.59334	−	2.65197i	0.366588	−	0.211650i	−0.305379	−	0.952231i	$-0.598783\pi$
$157$	4.59334	−	2.65197i	0.366588	−	0.211650i	0.671967	+	0.740581i	$0.265450\pi$
$158$		0			0
$159$	−2.35149			−0.186485
$160$		0			0
$161$	−3.62781	−	2.09452i	−0.285911	−	0.165071i
$162$		0			0
$163$	6.57728	+	11.3922i	0.515173	+	0.892305i	0.999845	+	0.0176092i	$0.00560548\pi$
$163$	6.57728	+	11.3922i	0.515173	+	0.892305i	−0.484672	+	0.874696i	$0.661061\pi$
$164$		0			0
$165$	−1.57307	−	2.72463i	−0.122463	−	0.212112i
$166$		0			0
$167$	3.41713	+	1.97288i	0.264425	+	0.152666i	0.626351	−	0.779541i	$-0.284547\pi$
$167$	3.41713	+	1.97288i	0.264425	+	0.152666i	−0.361926	+	0.932207i	$0.617881\pi$
$168$		0			0
$169$	−3.14393	−	5.44545i	−0.241841	−	0.418881i
$170$		0			0
$171$	−6.03544			−0.461542
$172$		0			0
$173$	−16.4978	+	9.52503i	−1.25431	+	0.724174i	−0.971962	−	0.235139i	$-0.924446\pi$
$173$	−16.4978	+	9.52503i	−1.25431	+	0.724174i	−0.282345	+	0.959313i	$0.591112\pi$
$174$		0			0
$175$	10.7168			0.810113
$176$		0			0
$177$			35.4256i			2.66275i
$178$		0			0
$179$	10.2621			0.767027			0.383513	−	0.923535i	$-0.374714\pi$
$179$	10.2621			0.767027			0.383513	+	0.923535i	$0.374714\pi$
$180$		0			0
$181$	4.76456	+	2.75082i	0.354147	+	0.204467i	0.666510	−	0.745496i	$-0.267787\pi$
$181$	4.76456	+	2.75082i	0.354147	+	0.204467i	−0.312363	+	0.949963i	$0.601121\pi$
$182$		0			0
$183$	15.1145	−	8.72637i	1.11730	−	0.645072i
$184$		0			0
$185$	22.0919	+	10.5755i	1.62423	+	0.777527i
$186$		0			0
$187$	−0.654130	−	1.13299i	−0.0478347	−	0.0828521i
$188$		0			0
$189$	−6.36313	−	3.67375i	−0.462850	−	0.267226i
$190$		0			0
$191$			14.4151i			1.04304i	0.853239	+	0.521519i	$0.174635\pi$
$191$			14.4151i			1.04304i	−0.853239	+	0.521519i	$0.825365\pi$
$192$		0			0
$193$		−	10.7469i		−	0.773580i	−0.922168	−	0.386790i	$-0.873584\pi$
$193$		−	10.7469i		−	0.773580i	0.922168	−	0.386790i	$-0.126416\pi$
$194$		0			0
$195$			51.9158i			3.71777i
$196$		0			0
$197$	11.6291	−	6.71408i	0.828541	−	0.478359i	−0.0248115	−	0.999692i	$-0.507899\pi$
$197$	11.6291	−	6.71408i	0.828541	−	0.478359i	0.853353	+	0.521333i	$0.174565\pi$
$198$		0			0
$199$		−	7.43159i		−	0.526812i	−0.964685	−	0.263406i	$-0.915154\pi$
$199$		−	7.43159i		−	0.526812i	0.964685	−	0.263406i	$-0.0848458\pi$
$200$		0			0
$201$	−19.9699	−	34.5889i	−1.40857	−	2.43971i
$202$		0			0
$203$	−4.33043	+	7.50053i	−0.303937	+	0.526434i
$204$		0			0
$205$	10.4738	+	18.1411i	0.731520	+	1.26703i
$206$		0			0
$207$	−21.3280	+	12.3137i	−1.48240	+	0.855864i
$208$		0			0
$209$	−0.247584	−	0.142943i	−0.0171258	−	0.00988756i
$210$		0			0
$211$			12.8769i			0.886480i	0.896403	+	0.443240i	$0.146171\pi$
$211$			12.8769i			0.886480i	−0.896403	+	0.443240i	$0.853829\pi$
$212$		0			0
$213$	−8.52025	+	4.91917i	−0.583798	+	0.337056i
$214$		0			0
$215$	5.34465	−	9.25720i	0.364502	−	0.631336i
$216$		0			0
$217$	−2.88014	−	1.66285i	−0.195517	−	0.112882i
$218$		0			0
$219$	−5.40421	−	3.12012i	−0.365183	−	0.210838i
$220$		0			0
$221$			21.5882i			1.45218i
$222$		0			0
$223$	−7.72684			−0.517427			−0.258714	−	0.965954i	$-0.583299\pi$
$223$	−7.72684			−0.517427			−0.258714	+	0.965954i	$0.583299\pi$
$224$		0			0
$225$	31.5022	−	54.5634i	2.10015	−	3.63756i
$226$		0			0
$227$	−1.44010	+	2.49433i	−0.0955830	+	0.165555i	−0.909852	−	0.414933i	$-0.863805\pi$
$227$	−1.44010	+	2.49433i	−0.0955830	+	0.165555i	0.814269	+	0.580488i	$0.197138\pi$
$228$		0			0
$229$	7.32835	+	4.23103i	0.484271	+	0.279594i	0.722195	−	0.691690i	$-0.243133\pi$
$229$	7.32835	+	4.23103i	0.484271	+	0.279594i	−0.237924	+	0.971284i	$0.576467\pi$
$230$		0			0
$231$	−0.373372	−	0.646700i	−0.0245661	−	0.0425497i
$232$		0			0
$233$	−17.7454			−1.16254			−0.581269	−	0.813712i	$-0.697444\pi$
$233$	−17.7454			−1.16254			−0.581269	+	0.813712i	$0.697444\pi$
$234$		0			0
$235$	19.9035	−	34.4739i	1.29836	−	2.24883i
$236$		0			0
$237$	8.01234	+	13.8778i	0.520457	+	0.901459i
$238$		0			0
$239$	−7.09612	+	4.09695i	−0.459010	+	0.265009i	−0.711628	−	0.702557i	$-0.752042\pi$
$239$	−7.09612	+	4.09695i	−0.459010	+	0.265009i	0.252618	+	0.967566i	$0.418708\pi$
$240$		0			0
$241$	−13.6418	−	7.87612i	−0.878748	−	0.507345i	−0.00850247	−	0.999964i	$-0.502706\pi$
$241$	−13.6418	−	7.87612i	−0.878748	−	0.507345i	−0.870245	+	0.492619i	$0.836040\pi$
$242$		0			0
$243$	5.44677	−	3.14469i	0.349410	−	0.201732i
$244$		0			0
$245$	−24.5082			−1.56577
$246$		0			0
$247$	2.35876	+	4.08549i	0.150084	+	0.259954i
$248$		0			0
$249$	43.2882			2.74328
$250$		0			0
$251$	−25.5272			−1.61126			−0.805631	−	0.592417i	$-0.798174\pi$
$251$	−25.5272			−1.61126			−0.805631	+	0.592417i	$0.798174\pi$
$252$		0			0
$253$	−1.16655			−0.0733404
$254$		0			0
$255$	29.0537	−	50.3224i	1.81941	−	3.15131i
$256$		0			0
$257$	−0.160125	+	0.0924484i	−0.00998834	+	0.00576677i	−0.504986	−	0.863128i	$-0.668502\pi$
$257$	−0.160125	+	0.0924484i	−0.00998834	+	0.00576677i	0.494998	+	0.868894i	$0.335169\pi$
$258$		0			0
$259$	5.24357	+	2.51013i	0.325820	+	0.155972i
$260$		0			0
$261$	25.4588	+	44.0959i	1.57586	+	2.72947i
$262$		0			0
$263$	3.47874	−	6.02535i	0.214508	−	0.371539i	−0.738612	−	0.674131i	$-0.764519\pi$
$263$	3.47874	−	6.02535i	0.214508	−	0.371539i	0.953120	+	0.302592i	$0.0978519\pi$
$264$		0			0
$265$		−	3.22520i		−	0.198123i
$266$		0			0
$267$	−17.2176			−1.05370
$268$		0			0
$269$		−	27.7556i		−	1.69229i	−0.532955	−	0.846144i	$-0.678918\pi$
$269$		−	27.7556i		−	1.69229i	0.532955	−	0.846144i	$-0.321082\pi$
$270$		0			0
$271$	−12.2906	−	21.2880i	−0.746601	−	1.29315i	−0.949443	−	0.313940i	$-0.898351\pi$
$271$	−12.2906	−	21.2880i	−0.746601	−	1.29315i	0.202842	−	0.979212i	$-0.434982\pi$
$272$		0			0
$273$			12.3224i			0.745783i
$274$		0			0
$275$	2.58455	−	1.49219i	0.155854	−	0.0899825i
$276$		0			0
$277$	1.72174	−	2.98214i	0.103449	−	0.179179i	−0.809654	−	0.586907i	$-0.800345\pi$
$277$	1.72174	−	2.98214i	0.103449	−	0.179179i	0.913104	+	0.407728i	$0.133679\pi$
$278$		0			0
$279$	−16.9325	+	9.77597i	−1.01372	+	0.585272i
$280$		0			0
$281$	7.58117	−	4.37699i	0.452255	−	0.261109i	−0.256527	−	0.966537i	$-0.582578\pi$
$281$	7.58117	−	4.37699i	0.452255	−	0.261109i	0.708782	+	0.705428i	$0.249245\pi$
$282$		0			0
$283$	15.3095	−	26.5168i	0.910054	−	1.57626i	0.0960696	−	0.995375i	$-0.469373\pi$
$283$	15.3095	−	26.5168i	0.910054	−	1.57626i	0.813985	−	0.580886i	$-0.197294\pi$
$284$		0			0
$285$		−	12.6978i		−	0.752154i
$286$		0			0
$287$	2.48598	+	4.30584i	0.146743	+	0.254166i
$288$		0			0
$289$	3.58140	−	6.20316i	0.210670	−	0.364892i
$290$		0			0
$291$	−2.84320	+	4.92457i	−0.166671	+	0.288683i
$292$		0			0
$293$	−1.62446	−	0.937880i	−0.0949017	−	0.0547915i	0.451798	−	0.892120i	$-0.350783\pi$
$293$	−1.62446	−	0.937880i	−0.0949017	−	0.0547915i	−0.546700	+	0.837329i	$0.684116\pi$
$294$		0			0
$295$	−48.5884			−2.82892
$296$		0			0
$297$	−2.04611			−0.118728
$298$		0			0
$299$	16.6708	+	9.62488i	0.964096	+	0.556621i
$300$		0			0
$301$	1.26857	−	2.19722i	0.0731191	−	0.126646i
$302$		0			0
$303$	−7.19381	+	12.4600i	−0.413274	+	0.715811i
$304$		0			0
$305$	11.9687	+	20.7305i	0.685328	+	1.18702i
$306$		0			0
$307$		−	12.7844i		−	0.729646i	−0.931077	−	0.364823i	$-0.881129\pi$
$307$		−	12.7844i		−	0.729646i	0.931077	−	0.364823i	$-0.118871\pi$
$308$		0			0
$309$	−9.78545	+	16.9489i	−0.556675	+	0.964189i
$310$		0			0
$311$	−5.46817	+	3.15705i	−0.310071	+	0.179020i	−0.646958	−	0.762525i	$-0.723959\pi$
$311$	−5.46817	+	3.15705i	−0.310071	+	0.179020i	0.336887	+	0.941545i	$0.390626\pi$
$312$		0			0
$313$	−14.7200	+	8.49862i	−0.832026	+	0.480370i	−0.854546	−	0.519376i	$-0.826164\pi$
$313$	−14.7200	+	8.49862i	−0.832026	+	0.480370i	0.0225198	+	0.999746i	$0.492831\pi$
$314$		0			0
$315$	10.8112	−	18.7255i	0.609142	−	1.05506i
$316$		0			0
$317$	26.7726	−	15.4572i	1.50370	−	0.868160i	0.503707	−	0.863875i	$-0.331969\pi$
$317$	26.7726	−	15.4572i	1.50370	−	0.868160i	0.999991	−	0.00428585i	$-0.00136423\pi$
$318$		0			0
$319$			2.41185i			0.135038i
$320$		0			0
$321$	1.93648	+	3.35409i	0.108084	+	0.187207i
$322$		0			0
$323$		−	5.28014i		−	0.293795i
$324$		0			0
$325$	−49.2466			−2.73171
$326$		0			0
$327$			30.4179i			1.68211i
$328$		0			0
$329$	4.72416	−	8.18249i	0.260452	−	0.451115i
$330$		0			0
$331$	−1.89004	−	3.27364i	−0.103886	−	0.179936i	0.809397	−	0.587262i	$-0.199794\pi$
$331$	−1.89004	−	3.27364i	−0.103886	−	0.179936i	−0.913282	+	0.407327i	$0.866461\pi$
$332$		0			0
$333$	28.1937	−	19.3185i	1.54500	−	1.05865i
$334$		0			0
$335$	47.4407	−	27.3899i	2.59196	−	1.49647i
$336$		0			0
$337$	0.793286	−	1.37401i	0.0432131	−	0.0748472i	−0.843610	−	0.536957i	$-0.819574\pi$
$337$	0.793286	−	1.37401i	0.0432131	−	0.0748472i	0.886823	+	0.462109i	$0.152907\pi$
$338$		0			0
$339$	34.0965			1.85187
$340$		0			0
$341$	−0.926133			−0.0501529
$342$		0			0
$343$	−12.5071			−0.675321
$344$		0			0
$345$	−25.9066	−	44.8715i	−1.39476	−	2.41580i
$346$		0			0
$347$	21.3700			1.14720			0.573602	−	0.819134i	$-0.305546\pi$
$347$	21.3700			1.14720			0.573602	+	0.819134i	$0.305546\pi$
$348$		0			0
$349$	18.5185	−	10.6916i	0.991271	−	0.572311i	0.0856170	−	0.996328i	$-0.472714\pi$
$349$	18.5185	−	10.6916i	0.991271	−	0.572311i	0.905654	+	0.424018i	$0.139381\pi$
$350$		0			0
$351$	29.2403	+	16.8819i	1.56073	+	0.901090i
$352$		0			0
$353$	11.2459	−	6.49284i	0.598560	−	0.345579i	−0.169915	−	0.985459i	$-0.554349\pi$
$353$	11.2459	−	6.49284i	0.598560	−	0.345579i	0.768475	+	0.639880i	$0.221016\pi$
$354$		0			0
$355$	−6.74693	−	11.6860i	−0.358090	−	0.620230i
$356$		0			0
$357$	6.89597	−	11.9442i	0.364974	−	0.632153i
$358$		0			0
$359$	−1.40916			−0.0743727			−0.0371864	−	0.999308i	$-0.511840\pi$
$359$	−1.40916			−0.0743727			−0.0371864	+	0.999308i	$0.511840\pi$
$360$		0			0
$361$	8.92308	+	15.4552i	0.469636	+	0.813433i
$362$		0			0
$363$	27.7868	+	16.0427i	1.45843	+	0.842025i
$364$		0			0
$365$	4.27944	−	7.41220i	0.223996	−	0.387972i
$366$		0			0
$367$	−0.524345	+	0.908192i	−0.0273706	+	0.0474072i	−0.879386	−	0.476109i	$-0.842047\pi$
$367$	−0.524345	+	0.908192i	−0.0273706	+	0.0474072i	0.852016	+	0.523516i	$0.175380\pi$
$368$		0			0
$369$	29.2304			1.52167
$370$		0			0
$371$		−	0.765512i		−	0.0397434i
$372$		0			0
$373$	−8.94862	−	5.16649i	−0.463342	−	0.267510i	0.250107	−	0.968218i	$-0.419534\pi$
$373$	−8.94862	−	5.16649i	−0.463342	−	0.267510i	−0.713448	+	0.700708i	$0.752868\pi$
$374$		0			0
$375$	63.6079	+	36.7241i	3.28470	+	1.89642i
$376$		0			0
$377$	19.8995	−	34.4670i	1.02488	−	1.77514i
$378$		0			0
$379$	−9.04003	+	5.21926i	−0.464355	+	0.268096i	−0.713874	−	0.700274i	$-0.753061\pi$
$379$	−9.04003	+	5.21926i	−0.464355	+	0.268096i	0.249519	+	0.968370i	$0.419728\pi$
$380$		0			0
$381$			24.1530i			1.23740i
$382$		0			0
$383$	1.62983	+	0.940982i	0.0832804	+	0.0480819i	0.541062	−	0.840983i	$-0.318022\pi$
$383$	1.62983	+	0.940982i	0.0832804	+	0.0480819i	−0.457782	+	0.889065i	$0.651356\pi$
$384$		0			0
$385$	0.886987	−	0.512102i	0.0452051	−	0.0260992i
$386$		0			0
$387$	−7.45796	−	12.9176i	−0.379110	−	0.656637i
$388$		0			0
$389$	6.72392	−	11.6462i	0.340916	−	0.590484i	−0.643687	−	0.765289i	$-0.722596\pi$
$389$	6.72392	−	11.6462i	0.340916	−	0.590484i	0.984603	+	0.174805i	$0.0559295\pi$
$390$		0			0
$391$	−10.7728	−	18.6590i	−0.544801	−	0.943624i
$392$		0			0
$393$			53.2951i			2.68838i
$394$		0			0
$395$	−19.0342	+	10.9894i	−0.957715	+	0.552937i
$396$		0			0
$397$		−	23.3844i		−	1.17363i	−0.809721	−	0.586815i	$-0.800381\pi$
$397$		−	23.3844i		−	1.17363i	0.809721	−	0.586815i	$-0.199619\pi$
$398$		0			0
$399$		−	3.01387i		−	0.150882i
$400$		0			0
$401$			0.640444i			0.0319822i	0.999872	+	0.0159911i	$0.00509035\pi$
$401$			0.640444i			0.0319822i	−0.999872	+	0.0159911i	$0.994910\pi$
$402$		0			0
$403$	13.2351	+	7.64126i	0.659285	+	0.380638i
$404$		0			0
$405$	−11.5035	−	19.9247i	−0.571616	−	0.990068i
$406$		0			0
$407$	1.61409	−	0.124744i	0.0800075	−	0.00618335i
$408$		0			0
$409$	−2.14259	+	1.23703i	−0.105944	+	0.0611670i	−0.552036	−	0.833820i	$-0.686149\pi$
$409$	−2.14259	+	1.23703i	−0.105944	+	0.0611670i	0.446092	+	0.894987i	$0.352816\pi$
$410$		0			0
$411$	15.2420	+	8.79995i	0.751830	+	0.434069i
$412$		0			0
$413$	−11.5326			−0.567482
$414$		0			0
$415$			59.3723i			2.91447i
$416$		0			0
$417$	20.2678			0.992518
$418$		0			0
$419$	−26.1582	+	15.1024i	−1.27791	+	0.737802i	−0.976464	−	0.215682i	$-0.930803\pi$
$419$	−26.1582	+	15.1024i	−1.27791	+	0.737802i	−0.301446	+	0.953483i	$0.597469\pi$
$420$		0			0
$421$	−4.48895			−0.218778			−0.109389	−	0.993999i	$-0.534889\pi$
$421$	−4.48895			−0.218778			−0.109389	+	0.993999i	$0.534889\pi$
$422$		0			0
$423$	−27.7735	−	48.1052i	−1.35040	−	2.33895i
$424$		0			0
$425$	47.7352	+	27.5599i	2.31549	+	1.33685i
$426$		0			0
$427$	2.84082	+	4.92044i	0.137477	+	0.238117i
$428$		0			0
$429$	1.71575	+	2.97176i	0.0828371	+	0.143478i
$430$		0			0
$431$	−28.5342	−	16.4742i	−1.37444	−	0.793535i	−0.382959	−	0.923765i	$-0.625095\pi$
$431$	−28.5342	−	16.4742i	−1.37444	−	0.793535i	−0.991484	+	0.130231i	$0.958428\pi$
$432$		0			0
$433$	−37.4400			−1.79925			−0.899627	−	0.436659i	$-0.856162\pi$
$433$	−37.4400			−1.79925			−0.899627	+	0.436659i	$0.856162\pi$
$434$		0			0
$435$	−92.7724	+	53.5622i	−4.44809	+	2.56811i
$436$		0			0
$437$	−4.07742	−	2.35410i	−0.195050	−	0.112612i
$438$		0			0
$439$	6.07215	+	3.50576i	0.289808	+	0.167321i	0.637855	−	0.770156i	$-0.279822\pi$
$439$	6.07215	+	3.50576i	0.289808	+	0.167321i	−0.348047	+	0.937477i	$0.613155\pi$
$440$		0			0
$441$	−17.0994	+	29.6171i	−0.814259	+	1.41034i
$442$		0			0
$443$		−	27.9671i		−	1.32876i	−0.747396	−	0.664379i	$-0.768696\pi$
$443$		−	27.9671i		−	1.32876i	0.747396	−	0.664379i	$-0.231304\pi$
$444$		0			0
$445$		−	23.6150i		−	1.11946i
$446$		0			0
$447$	14.9706	−	25.9299i	0.708086	−	1.22644i
$448$		0			0
$449$	−16.5486	−	9.55434i	−0.780977	−	0.450897i	0.0557995	−	0.998442i	$-0.482229\pi$
$449$	−16.5486	−	9.55434i	−0.780977	−	0.450897i	−0.836776	+	0.547545i	$0.815563\pi$
$450$		0			0
$451$	1.19908	+	0.692289i	0.0564624	+	0.0325986i
$452$		0			0
$453$	17.0390	−	9.83747i	0.800562	−	0.462205i
$454$		0			0
$455$	−16.9009			−0.792324
$456$		0			0
$457$	−9.67641	−	5.58668i	−0.452643	−	0.261334i	0.256303	−	0.966597i	$-0.417496\pi$
$457$	−9.67641	−	5.58668i	−0.452643	−	0.261334i	−0.708946	+	0.705263i	$0.750829\pi$
$458$		0			0
$459$	−18.8953	−	32.7276i	−0.881956	−	1.52759i
$460$		0			0
$461$	6.92913	+	12.0016i	0.322722	+	0.558970i	0.981049	−	0.193762i	$-0.0620689\pi$
$461$	6.92913	+	12.0016i	0.322722	+	0.558970i	−0.658327	+	0.752732i	$0.728736\pi$
$462$		0			0
$463$	21.0493	+	12.1528i	0.978245	+	0.564790i	0.901740	−	0.432279i	$-0.142291\pi$
$463$	21.0493	+	12.1528i	0.978245	+	0.564790i	0.0765049	+	0.997069i	$0.475624\pi$
$464$		0			0
$465$	−20.5674	−	35.6238i	−0.953792	−	1.65202i
$466$		0			0
$467$	32.2899			1.49420			0.747100	−	0.664712i	$-0.231446\pi$
$467$	32.2899			1.49420			0.747100	+	0.664712i	$0.231446\pi$
$468$		0			0
$469$	11.2602	−	6.50107i	0.519947	−	0.300192i
$470$		0			0
$471$	15.5711			0.717478
$472$		0			0
$473$		−	0.706535i		−	0.0324865i
$474$		0			0
$475$	12.0450			0.552661
$476$		0			0
$477$	−3.89752	−	2.25024i	−0.178455	−	0.103031i
$478$		0			0
$479$	−32.9353	+	19.0152i	−1.50485	+	0.868827i	−0.504868	+	0.863197i	$0.668459\pi$
$479$	−32.9353	+	19.0152i	−1.50485	+	0.868827i	−0.999984	+	0.00563026i	$0.998208\pi$
$480$		0			0
$481$	−24.0957	−	11.5347i	−1.09867	−	0.525938i
$482$		0			0
$483$	−6.14901	−	10.6504i	−0.279789	−	0.484610i
$484$		0			0
$485$	−6.75434	−	3.89962i	−0.306699	−	0.177073i
$486$		0			0
$487$		−	10.1301i		−	0.459040i	−0.973304	−	0.229520i	$-0.926284\pi$
$487$		−	10.1301i		−	0.459040i	0.973304	−	0.229520i	$-0.0737156\pi$
$488$		0			0
$489$			38.6187i			1.74640i
$490$		0			0
$491$		−	15.2115i		−	0.686484i	−0.939247	−	0.343242i	$-0.888475\pi$
$491$		−	15.2115i		−	0.686484i	0.939247	−	0.343242i	$-0.111525\pi$
$492$		0			0
$493$	−38.5776	+	22.2728i	−1.73745	+	1.00312i
$494$		0			0
$495$		−	6.02134i		−	0.270639i
$496$		0			0
$497$	−1.60140	−	2.77371i	−0.0718328	−	0.124418i
$498$		0			0
$499$	15.7138	−	27.2170i	0.703444	−	1.21840i	−0.263806	−	0.964576i	$-0.584978\pi$
$499$	15.7138	−	27.2170i	0.703444	−	1.21840i	0.967250	−	0.253826i	$-0.0816889\pi$
$500$		0			0
$501$	5.79191	+	10.0319i	0.258763	+	0.448191i
$502$		0			0
$503$	12.5721	−	7.25849i	0.560561	−	0.323640i	−0.192809	−	0.981236i	$-0.561760\pi$
$503$	12.5721	−	7.25849i	0.560561	−	0.323640i	0.753371	+	0.657596i	$0.228427\pi$
$504$		0			0
$505$	−17.0897	−	9.86674i	−0.760482	−	0.439064i
$506$		0			0
$507$		−	18.4597i		−	0.819824i
$508$		0			0
$509$	−34.4073	+	19.8651i	−1.52508	+	0.880504i	−0.525519	+	0.850782i	$0.676129\pi$
$509$	−34.4073	+	19.8651i	−1.52508	+	0.880504i	−0.999558	+	0.0297222i	$0.990538\pi$
$510$		0			0
$511$	1.01574	−	1.75931i	0.0449336	−	0.0778272i
$512$		0			0
$513$	−7.15174	−	4.12906i	−0.315757	−	0.182303i
$514$		0			0
$515$	−23.2464	−	13.4213i	−1.02436	−	0.591414i
$516$		0			0
$517$		−	2.63114i		−	0.115718i
$518$		0			0
$519$	−55.9265			−2.45490
$520$		0			0
$521$	11.4803	−	19.8845i	0.502962	−	0.871155i	−0.497032	−	0.867732i	$-0.665577\pi$
$521$	11.4803	−	19.8845i	0.502962	−	0.871155i	0.999994	−	0.00342322i	$-0.00108965\pi$
$522$		0			0
$523$	−17.9650	+	31.1163i	−0.785555	+	1.36062i	0.143111	+	0.989707i	$0.454289\pi$
$523$	−17.9650	+	31.1163i	−0.785555	+	1.36062i	−0.928667	+	0.370915i	$0.879044\pi$
$524$		0			0
$525$	27.2469	+	15.7310i	1.18915	+	0.686557i
$526$		0			0
$527$	−8.55257	−	14.8135i	−0.372556	−	0.645285i
$528$		0			0
$529$	3.78829			0.164708
$530$		0			0
$531$	−33.9003	+	58.7170i	−1.47115	+	2.54810i
$532$		0			0
$533$	−11.4238	−	19.7865i	−0.494818	−	0.857050i
$534$		0			0
$535$	−4.60033	+	2.65600i	−0.198890	+	0.114829i
$536$		0			0
$537$	26.0909	+	15.0636i	1.12590	+	0.650042i
$538$		0			0
$539$	−1.40290	+	0.809963i	−0.0604270	+	0.0348876i
$540$		0			0
$541$	−32.0237			−1.37681			−0.688404	−	0.725328i	$-0.741688\pi$
$541$	−32.0237			−1.37681			−0.688404	+	0.725328i	$0.741688\pi$
$542$		0			0
$543$	8.07577	+	13.9876i	0.346564	+	0.600267i
$544$		0			0
$545$	−41.7200			−1.78709
$546$		0			0
$547$	−11.5140			−0.492301			−0.246151	−	0.969232i	$-0.579166\pi$
$547$	−11.5140			−0.492301			−0.246151	+	0.969232i	$0.579166\pi$
$548$		0			0
$549$	33.4025			1.42559
$550$		0			0
$551$	−4.86713	+	8.43011i	−0.207347	+	0.359135i
$552$		0			0
$553$	−4.51782	+	2.60837i	−0.192117	+	0.110919i
$554$		0			0
$555$	40.6438	+	59.3160i	1.72523	+	2.51782i
$556$		0			0
$557$	−0.263080	−	0.455668i	−0.0111470	−	0.0193073i	0.860398	−	0.509623i	$-0.170215\pi$
$557$	−0.263080	−	0.455668i	−0.0111470	−	0.0193073i	−0.871545	+	0.490315i	$0.836882\pi$
$558$		0			0
$559$	−5.82942	+	10.0969i	−0.246558	+	0.427051i
$560$		0			0
$561$		−	3.84074i		−	0.162156i
$562$		0			0
$563$	−12.9966			−0.547740			−0.273870	−	0.961767i	$-0.588304\pi$
$563$	−12.9966			−0.547740			−0.273870	+	0.961767i	$0.588304\pi$
$564$		0			0
$565$			46.7653i			1.96743i
$566$		0			0
$567$	−2.73040	−	4.72919i	−0.114666	−	0.198607i
$568$		0			0
$569$			19.0787i			0.799820i	0.916555	+	0.399910i	$0.130959\pi$
$569$			19.0787i			0.799820i	−0.916555	+	0.399910i	$0.869041\pi$
$570$		0			0
$571$	28.5852	−	16.5037i	1.19625	−	0.690658i	0.236536	−	0.971623i	$-0.423988\pi$
$571$	28.5852	−	16.5037i	1.19625	−	0.690658i	0.959718	+	0.280965i	$0.0906544\pi$
$572$		0			0
$573$	−21.1596	+	36.6496i	−0.883957	+	1.53106i
$574$		0			0
$575$	42.5645	−	24.5746i	1.77506	−	1.02483i
$576$		0			0
$577$	16.0643	−	9.27473i	0.668766	−	0.386112i	−0.126843	−	0.991923i	$-0.540484\pi$
$577$	16.0643	−	9.27473i	0.668766	−	0.386112i	0.795609	+	0.605811i	$0.207151\pi$
$578$		0			0
$579$	15.7752	−	27.3235i	0.655595	−	1.13552i
$580$		0			0
$581$			14.0922i			0.584642i
$582$		0			0
$583$	−0.106589	−	0.184617i	−0.00441445	−	0.00764606i
$584$		0			0
$585$	−49.6804	+	86.0490i	−2.05403	+	3.55769i
$586$		0			0
$587$	6.22086	−	10.7748i	0.256762	−	0.444726i	−0.708610	−	0.705600i	$-0.750678\pi$
$587$	6.22086	−	10.7748i	0.256762	−	0.444726i	0.965373	+	0.260875i	$0.0840109\pi$
$588$		0			0
$589$	−3.23710	−	1.86894i	−0.133382	−	0.0770083i
$590$		0			0
$591$	39.4219			1.62160
$592$		0			0
$593$	25.8092			1.05986			0.529928	−	0.848042i	$-0.322219\pi$
$593$	25.8092			1.05986			0.529928	+	0.848042i	$0.322219\pi$
$594$		0			0
$595$	16.3821	+	9.45824i	0.671602	+	0.387750i
$596$		0			0
$597$	10.9087	−	18.8944i	0.446464	−	0.773298i
$598$		0			0
$599$	4.13152	−	7.15600i	0.168809	−	0.292386i	−0.769192	−	0.639017i	$-0.779341\pi$
$599$	4.13152	−	7.15600i	0.168809	−	0.292386i	0.938001	+	0.346631i	$0.112674\pi$
$600$		0			0
$601$	−15.2401	−	26.3966i	−0.621657	−	1.07674i	−0.989177	−	0.146726i	$-0.953127\pi$
$601$	−15.2401	−	26.3966i	−0.621657	−	1.07674i	0.367520	−	0.930015i	$-0.380207\pi$
$602$		0			0
$603$		−	76.4401i		−	3.11288i
$604$		0			0
$605$	−22.0036	+	38.1113i	−0.894572	+	1.54944i
$606$		0			0
$607$	19.5500	−	11.2872i	0.793511	−	0.458134i	−0.0476864	−	0.998862i	$-0.515185\pi$
$607$	19.5500	−	11.2872i	0.793511	−	0.458134i	0.841197	+	0.540729i	$0.181851\pi$
$608$		0			0
$609$	−22.0198	+	12.7131i	−0.892287	+	0.515162i
$610$		0			0
$611$	−21.7088	+	37.6008i	−0.878245	+	1.52116i
$612$		0			0
$613$	8.64486	−	4.99111i	0.349163	−	0.201589i	−0.315154	−	0.949041i	$-0.602056\pi$
$613$	8.64486	−	4.99111i	0.349163	−	0.201589i	0.664316	+	0.747451i	$0.268723\pi$
$614$		0			0
$615$			61.4971i			2.47980i
$616$		0			0
$617$	−8.21863	−	14.2351i	−0.330870	−	0.573083i	0.651813	−	0.758380i	$-0.274009\pi$
$617$	−8.21863	−	14.2351i	−0.330870	−	0.573083i	−0.982683	+	0.185297i	$0.940675\pi$
$618$		0			0
$619$			4.06275i			0.163296i	0.996661	+	0.0816478i	$0.0260183\pi$
$619$			4.06275i			0.163296i	−0.996661	+	0.0816478i	$0.973982\pi$
$620$		0			0
$621$	−33.6971			−1.35222
$622$		0			0
$623$		−	5.60510i		−	0.224563i
$624$		0			0
$625$	−22.3359	+	38.6870i	−0.893438	+	1.54748i
$626$		0			0
$627$	−0.419646	−	0.726849i	−0.0167591	−	0.0290275i
$628$		0			0
$629$	16.9009	+	24.6654i	0.673885	+	0.983473i
$630$		0			0
$631$	22.2326	−	12.8360i	0.885066	−	0.510993i	0.0127409	−	0.999919i	$-0.495944\pi$
$631$	22.2326	−	12.8360i	0.885066	−	0.510993i	0.872326	+	0.488925i	$0.162611\pi$
$632$		0			0
$633$	−18.9017	+	32.7388i	−0.751276	+	1.30125i
$634$		0			0
$635$	−33.1273			−1.31462
$636$		0			0
$637$	26.7311			1.05912
$638$		0			0
$639$	−18.8294			−0.744881
$640$		0			0
$641$	4.02366	+	6.96918i	0.158925	+	0.275266i	0.934481	−	0.356012i	$-0.115864\pi$
$641$	4.02366	+	6.96918i	0.158925	+	0.275266i	−0.775556	+	0.631278i	$0.782531\pi$
$642$		0			0
$643$	−24.0799			−0.949619			−0.474810	−	0.880089i	$-0.657483\pi$
$643$	−24.0799			−0.949619			−0.474810	+	0.880089i	$0.657483\pi$
$644$		0			0
$645$	27.1770	−	15.6906i	1.07009	−	0.617818i
$646$		0			0
$647$	−5.33752	−	3.08162i	−0.209840	−	0.121151i	0.391397	−	0.920222i	$-0.371992\pi$
$647$	−5.33752	−	3.08162i	−0.209840	−	0.121151i	−0.601237	+	0.799071i	$0.705325\pi$
$648$		0			0
$649$	−2.78130	+	1.60578i	−0.109175	+	0.0630324i
$650$		0			0
$651$	−4.88174	−	8.45543i	−0.191331	−	0.331394i
$652$		0			0
$653$	7.79270	−	13.4973i	0.304952	−	0.528192i	−0.672299	−	0.740280i	$-0.734693\pi$
$653$	7.79270	−	13.4973i	0.304952	−	0.528192i	0.977251	+	0.212088i	$0.0680263\pi$
$654$		0			0
$655$	−73.0974			−2.85615
$656$		0			0
$657$	−5.97156	−	10.3430i	−0.232973	−	0.403520i
$658$		0			0
$659$	8.51965	+	4.91882i	0.331879	+	0.191610i	0.656675	−	0.754174i	$-0.271962\pi$
$659$	8.51965	+	4.91882i	0.331879	+	0.191610i	−0.324796	+	0.945784i	$0.605296\pi$
$660$		0			0
$661$	5.76154	−	9.97928i	0.224098	−	0.388149i	−0.731950	−	0.681358i	$-0.761390\pi$
$661$	5.76154	−	9.97928i	0.224098	−	0.388149i	0.956048	+	0.293209i	$0.0947231\pi$
$662$		0			0
$663$	−31.6889	+	54.8868i	−1.23069	+	2.13163i
$664$		0			0
$665$	4.13370			0.160298
$666$		0			0
$667$			39.7204i			1.53798i
$668$		0			0
$669$	−19.6451	−	11.3421i	−0.759523	−	0.438511i
$670$		0			0
$671$	1.37023	+	0.791102i	0.0528971	+	0.0305402i
$672$		0			0
$673$	−11.6027	+	20.0965i	−0.447251	+	0.774661i	−0.998206	−	0.0598736i	$-0.980930\pi$
$673$	−11.6027	+	20.0965i	−0.447251	+	0.774661i	0.550955	+	0.834535i	$0.314264\pi$
$674$		0			0
$675$	74.6576	−	43.1036i	2.87357	−	1.65906i
$676$		0			0
$677$			48.7018i			1.87176i	0.352316	+	0.935881i	$0.385394\pi$
$677$			48.7018i			1.87176i	−0.352316	+	0.935881i	$0.614606\pi$
$678$		0			0
$679$	−1.60316	−	0.925586i	−0.0615237	−	0.0355207i
$680$		0			0
$681$	−7.32277	+	4.22780i	−0.280609	+	0.162010i
$682$		0			0
$683$	−11.4575	−	19.8450i	−0.438410	−	0.759348i	0.559157	−	0.829062i	$-0.311125\pi$
$683$	−11.4575	−	19.8450i	−0.438410	−	0.759348i	−0.997567	+	0.0697136i	$0.977791\pi$
$684$		0			0
$685$	−12.0696	+	20.9052i	−0.461158	+	0.798748i
$686$		0			0
$687$	12.4213	+	21.5143i	0.473902	+	0.820823i
$688$		0			0
$689$			3.51774i			0.134015i
$690$		0			0
$691$	−34.2701	+	19.7859i	−1.30370	+	0.752690i	−0.981036	−	0.193824i	$-0.937911\pi$
$691$	−34.2701	+	19.7859i	−1.30370	+	0.752690i	−0.322661	+	0.946514i	$0.604578\pi$
$692$		0			0
$693$		−	1.42918i		−	0.0542902i
$694$		0			0
$695$			27.7985i			1.05446i
$696$		0			0
$697$			25.5724i			0.968622i
$698$		0			0
$699$	−45.1167	−	26.0481i	−1.70647	−	0.985230i
$700$		0			0
$701$	−1.68014	−	2.91009i	−0.0634580	−	0.109912i	0.832551	−	0.553948i	$-0.186880\pi$
$701$	−1.68014	−	2.91009i	−0.0634580	−	0.109912i	−0.896009	+	0.444036i	$0.853546\pi$
$702$		0			0
$703$	5.89344	+	2.82122i	0.222275	+	0.106404i
$704$		0			0
$705$	101.207	−	58.4321i	3.81169	−	2.20068i
$706$		0			0
$707$	−4.05629	−	2.34190i	−0.152553	−	0.0880762i
$708$		0			0
$709$	−8.18869			−0.307533			−0.153766	−	0.988107i	$-0.549140\pi$
$709$	−8.18869			−0.307533			−0.153766	+	0.988107i	$0.549140\pi$
$710$		0			0
$711$			30.6694i			1.15019i
$712$		0			0
$713$	−15.2523			−0.571204
$714$		0			0
$715$	−4.07595	+	2.35325i	−0.152432	+	0.0880066i
$716$		0			0
$717$	−24.0553			−0.898363
$718$		0			0
$719$	19.3258	+	33.4733i	0.720731	+	1.24834i	0.960707	+	0.277565i	$0.0895272\pi$
$719$	19.3258	+	33.4733i	0.720731	+	1.24834i	−0.239976	+	0.970779i	$0.577139\pi$
$720$		0			0
$721$	−5.51761	−	3.18559i	−0.205486	−	0.118638i
$722$		0			0
$723$	−23.1224	−	40.0492i	−0.859932	−	1.48945i
$724$		0			0
$725$	−50.8083	−	88.0026i	−1.88697	−	3.26833i
$726$		0			0
$727$	−19.0282	−	10.9859i	−0.705716	−	0.407446i	0.103757	−	0.994603i	$-0.466914\pi$
$727$	−19.0282	−	10.9859i	−0.705716	−	0.407446i	−0.809473	+	0.587157i	$0.800247\pi$
$728$		0			0
$729$	35.6056			1.31873
$730$		0			0
$731$	11.3010	−	6.52464i	0.417983	−	0.241323i
$732$		0			0
$733$	23.0327	+	13.2980i	0.850734	+	0.491171i	0.860898	−	0.508777i	$-0.169902\pi$
$733$	23.0327	+	13.2980i	0.850734	+	0.491171i	−0.0101646	+	0.999948i	$0.503236\pi$
$734$		0			0
$735$	−62.3107	−	35.9751i	−2.29836	−	1.32696i
$736$		0			0
$737$	1.81040	−	3.13571i	0.0666870	−	0.115505i
$738$		0			0
$739$			9.69260i			0.356548i	0.983981	+	0.178274i	$0.0570514\pi$
$739$			9.69260i			0.356548i	−0.983981	+	0.178274i	$0.942949\pi$
$740$		0			0
$741$			13.8495i			0.508775i
$742$		0			0
$743$	12.8024	−	22.1743i	0.469673	−	0.813497i	−0.529726	−	0.848169i	$-0.677705\pi$
$743$	12.8024	−	22.1743i	0.469673	−	0.813497i	0.999399	+	0.0346715i	$0.0110385\pi$
$744$		0			0
$745$	35.5644	+	20.5331i	1.30298	+	0.752275i
$746$		0			0
$747$	71.7489	+	41.4243i	2.62516	+	1.51563i
$748$		0			0
$749$	−1.09190	+	0.630410i	−0.0398972	+	0.0230347i
$750$		0			0
$751$	−19.2104			−0.700997			−0.350499	−	0.936563i	$-0.613988\pi$
$751$	−19.2104			−0.700997			−0.350499	+	0.936563i	$0.613988\pi$
$752$		0			0
$753$	−64.9015	−	37.4709i	−2.36514	−	1.36552i
$754$		0			0
$755$	13.4927	+	23.3700i	0.491049	+	0.850522i
$756$		0			0
$757$	8.93509	+	15.4760i	0.324751	+	0.562486i	0.981462	−	0.191657i	$-0.0613860\pi$
$757$	8.93509	+	15.4760i	0.324751	+	0.562486i	−0.656711	+	0.754143i	$0.728053\pi$
$758$		0			0
$759$	−2.96589	−	1.71236i	−0.107655	−	0.0621547i
$760$		0			0
$761$	19.3773	+	33.5625i	0.702426	+	1.21664i	0.967612	+	0.252441i	$0.0812333\pi$
$761$	19.3773	+	33.5625i	0.702426	+	1.21664i	−0.265186	+	0.964197i	$0.585433\pi$
$762$		0			0
$763$	−9.90236			−0.358490
$764$		0			0
$765$	96.3113	−	55.6053i	3.48214	−	2.01042i
$766$		0			0
$767$	52.9954			1.91355
$768$		0			0
$769$			29.7234i			1.07185i	0.844264	+	0.535927i	$0.180038\pi$
$769$			29.7234i			1.07185i	−0.844264	+	0.535927i	$0.819962\pi$
$770$		0			0
$771$	−0.542813			−0.0195489
$772$		0			0
$773$	36.9331	+	21.3233i	1.32839	+	0.766947i	0.985051	−	0.172264i	$-0.0551083\pi$
$773$	36.9331	+	21.3233i	1.32839	+	0.766947i	0.343340	+	0.939211i	$0.388442\pi$
$774$		0			0
$775$	33.7923	−	19.5100i	1.21386	−	0.700820i
$776$		0			0
$777$	9.64694	+	14.0788i	0.346082	+	0.505075i
$778$		0			0
$779$	2.79408	+	4.83949i	0.100108	+	0.173393i
$780$		0			0
$781$	−0.772416	−	0.445955i	−0.0276392	−	0.0159575i
$782$		0			0
$783$			69.6691i			2.48977i
$784$		0			0
$785$			21.3567i			0.762253i
$786$		0			0
$787$		−	31.9876i		−	1.14024i	−0.821563	−	0.570118i	$-0.806897\pi$
$787$		−	31.9876i		−	1.14024i	0.821563	−	0.570118i	$-0.193103\pi$
$788$		0			0
$789$	17.6890	−	10.2127i	0.629745	−	0.363584i
$790$		0			0
$791$			11.0999i			0.394667i
$792$		0			0
$793$	−13.0543	−	22.6108i	−0.463573	−	0.802932i
$794$		0			0
$795$	4.73422	−	8.19991i	0.167905	−	0.290821i
$796$		0			0
$797$	4.35130	+	7.53668i	0.154131	+	0.266963i	0.932742	−	0.360544i	$-0.117409\pi$
$797$	4.35130	+	7.53668i	0.154131	+	0.266963i	−0.778611	+	0.627507i	$0.784076\pi$
$798$		0			0
$799$	42.0851	−	24.2978i	1.48886	−	0.859596i
$800$		0			0
$801$	−28.5378	−	16.4763i	−1.00833	−	0.582161i
$802$		0			0
$803$		−	0.565719i		−	0.0199638i
$804$		0			0
$805$	14.6076	−	8.43373i	0.514852	−	0.297250i
$806$		0			0
$807$	40.7419	−	70.5671i	1.43418	−	2.48408i
$808$		0			0
$809$	−27.6931	−	15.9886i	−0.973639	−	0.562130i	−0.0732950	−	0.997310i	$-0.523351\pi$
$809$	−27.6931	−	15.9886i	−0.973639	−	0.562130i	−0.900344	+	0.435180i	$0.856685\pi$
$810$		0			0
$811$	−24.2042	−	13.9743i	−0.849923	−	0.490703i	0.0107017	−	0.999943i	$-0.496593\pi$
$811$	−24.2042	−	13.9743i	−0.849923	−	0.490703i	−0.860625	+	0.509239i	$0.829927\pi$
$812$		0			0
$813$		−	72.1647i		−	2.53093i
$814$		0			0
$815$	−52.9679			−1.85538
$816$		0			0
$817$	1.42579	−	2.46954i	0.0498820	−	0.0863982i
$818$		0			0
$819$	−11.7918	+	20.4240i	−0.412038	+	0.713672i
$820$		0			0
$821$	−15.4923	−	8.94446i	−0.540683	−	0.312164i	0.204672	−	0.978831i	$-0.434387\pi$
$821$	−15.4923	−	8.94446i	−0.540683	−	0.312164i	−0.745356	+	0.666667i	$0.767720\pi$
$822$		0			0
$823$	−14.5633	−	25.2243i	−0.507644	−	0.879265i	−0.999961	−	0.00884926i	$-0.997183\pi$
$823$	−14.5633	−	25.2243i	−0.507644	−	0.879265i	0.492317	−	0.870416i	$-0.336150\pi$
$824$		0			0
$825$	8.76144			0.305034
$826$		0			0
$827$	−9.77716	+	16.9345i	−0.339985	+	0.588872i	−0.984430	−	0.175780i	$-0.943755\pi$
$827$	−9.77716	+	16.9345i	−0.339985	+	0.588872i	0.644444	+	0.764651i	$0.277089\pi$
$828$		0			0
$829$	−21.8107	−	37.7773i	−0.757518	−	1.31206i	−0.944113	−	0.329623i	$-0.893078\pi$
$829$	−21.8107	−	37.7773i	−0.757518	−	1.31206i	0.186594	−	0.982437i	$-0.440255\pi$
$830$		0			0
$831$	8.75486	−	5.05462i	0.303703	−	0.175343i
$832$		0			0
$833$	−25.9107	−	14.9595i	−0.897752	−	0.518317i
$834$		0			0
$835$	−13.7593	+	7.94395i	−0.476161	+	0.274912i
$836$		0			0
$837$	−26.7524			−0.924698
$838$		0			0
$839$	−1.67977	−	2.90945i	−0.0579922	−	0.100445i	0.835572	−	0.549381i	$-0.185137\pi$
$839$	−1.67977	−	2.90945i	−0.0579922	−	0.100445i	−0.893564	+	0.448936i	$0.851803\pi$
$840$		0			0
$841$	53.1224			1.83181
$842$		0			0
$843$	25.6996			0.885142
$844$		0			0
$845$	25.3186			0.870986
$846$		0			0
$847$	−5.22261	+	9.04583i	−0.179451	+	0.310818i
$848$		0			0
$849$	77.8471	−	44.9451i	2.67171	−	1.54251i
$850$		0			0
$851$	26.5822	−	2.05439i	0.911226	−	0.0704237i
$852$		0			0
$853$	−4.24321	−	7.34946i	−0.145285	−	0.251641i	0.784194	−	0.620515i	$-0.213077\pi$
$853$	−4.24321	−	7.34946i	−0.145285	−	0.251641i	−0.929479	+	0.368875i	$0.879743\pi$
$854$		0			0
$855$	12.1511	−	21.0463i	0.415558	−	0.719768i
$856$		0			0
$857$		−	22.3887i		−	0.764783i	−0.924000	−	0.382392i	$-0.875101\pi$
$857$		−	22.3887i		−	0.764783i	0.924000	−	0.382392i	$-0.124899\pi$
$858$		0			0
$859$	24.5544			0.837784			0.418892	−	0.908036i	$-0.362419\pi$
$859$	24.5544			0.837784			0.418892	+	0.908036i	$0.362419\pi$
$860$		0			0
$861$			14.5965i			0.497448i
$862$		0			0
$863$	3.55404	+	6.15577i	0.120981	+	0.209545i	0.920155	−	0.391555i	$-0.128063\pi$
$863$	3.55404	+	6.15577i	0.120981	+	0.209545i	−0.799174	+	0.601100i	$0.794729\pi$
$864$		0			0
$865$		−	76.7065i		−	2.60810i
$866$		0			0
$867$	18.2110	−	10.5141i	0.618479	−	0.357079i
$868$		0			0
$869$	−0.726371	+	1.25811i	−0.0246404	+	0.0426785i
$870$		0			0
$871$	−51.7437	+	29.8742i	−1.75327	+	1.01225i
$872$		0			0
$873$	−9.42505	+	5.44156i	−0.318990	+	0.184169i
$874$		0			0
$875$	−11.9553	+	20.7072i	−0.404163	+	0.700030i
$876$		0			0
$877$		−	35.6827i		−	1.20492i	−0.798150	−	0.602459i	$-0.794188\pi$
$877$		−	35.6827i		−	1.20492i	0.798150	−	0.602459i	$-0.205812\pi$
$878$		0			0
$879$	−2.75339	−	4.76902i	−0.0928697	−	0.160855i
$880$		0			0
$881$	24.7405	−	42.8519i	0.833530	−	1.44372i	−0.0616913	−	0.998095i	$-0.519649\pi$
$881$	24.7405	−	42.8519i	0.833530	−	1.44372i	0.895222	−	0.445621i	$-0.147017\pi$
$882$		0			0
$883$	18.6923	−	32.3760i	0.629046	−	1.08954i	−0.358697	−	0.933454i	$-0.616779\pi$
$883$	18.6923	−	32.3760i	0.629046	−	1.08954i	0.987743	−	0.156086i	$-0.0498878\pi$
$884$		0			0
$885$	−123.533	−	71.3220i	−4.15253	−	2.39746i
$886$		0			0
$887$	54.7136			1.83710			0.918551	−	0.395303i	$-0.129360\pi$
$887$	54.7136			1.83710			0.918551	+	0.395303i	$0.129360\pi$
$888$		0			0
$889$	−7.86286			−0.263712
$890$		0			0
$891$	−1.31697	−	0.760354i	−0.0441202	−	0.0254728i
$892$		0			0
$893$	5.30965	−	9.19659i	0.177681	−	0.307752i
$894$		0			0
$895$	−20.6606	+	35.7852i	−0.690608	+	1.19617i
$896$		0			0
$897$	28.2564	+	48.9415i	0.943453	+	1.63411i
$898$		0			0
$899$			31.5343i			1.05173i
$900$		0			0
$901$	1.96863	−	3.40977i	0.0655847	−	0.113596i
$902$		0			0
$903$	6.45053	−	3.72422i	0.214660	−	0.123934i
$904$		0			0
$905$	−19.1849	+	11.0764i	−0.637727	+	0.368192i
$906$		0			0
$907$	1.07902	−	1.86892i	0.0358283	−	0.0620564i	−0.847555	−	0.530707i	$-0.821926\pi$
$907$	1.07902	−	1.86892i	0.0358283	−	0.0620564i	0.883384	+	0.468651i	$0.155260\pi$
$908$		0			0
$909$	−23.8471	+	13.7681i	−0.790958	+	0.456660i
$910$		0			0
$911$		−	49.1255i		−	1.62760i	−0.581145	−	0.813800i	$-0.697395\pi$
$911$		−	49.1255i		−	1.62760i	0.581145	−	0.813800i	$-0.302605\pi$
$912$		0			0
$913$	1.96218	+	3.39859i	0.0649386	+	0.112477i
$914$		0			0
$915$			70.2748i			2.32321i
$916$		0			0
$917$	−17.3499			−0.572944
$918$		0			0
$919$			31.9847i			1.05508i	0.849531	+	0.527539i	$0.176885\pi$
$919$			31.9847i			1.05508i	−0.849531	+	0.527539i	$0.823115\pi$
$920$		0			0
$921$	18.7660	−	32.5038i	0.618362	−	1.07104i
$922$		0			0
$923$	7.35889	+	12.7460i	0.242221	+	0.419539i
$924$		0			0
$925$	−56.2663	+	38.5542i	−1.85002	+	1.26765i
$926$		0			0
$927$	−32.4382	+	18.7282i	−1.06541	+	0.615116i
$928$		0			0
$929$	−11.5189	+	19.9513i	−0.377922	+	0.654580i	−0.990760	−	0.135629i	$-0.956695\pi$
$929$	−11.5189	+	19.9513i	−0.377922	+	0.654580i	0.612838	+	0.790209i	$0.290028\pi$
$930$		0			0
$931$	−6.53803			−0.214275
$932$		0			0
$933$	−18.5367			−0.606864
$934$		0			0
$935$	5.26781			0.172276
$936$		0			0
$937$	−15.7856	−	27.3414i	−0.515693	−	0.893206i	−0.999834	−	0.0182163i	$-0.994201\pi$
$937$	−15.7856	−	27.3414i	−0.515693	−	0.893206i	0.484141	−	0.874990i	$-0.339132\pi$
$938$		0			0
$939$	−49.8999			−1.62842
$940$		0			0
$941$	−20.3486	+	11.7483i	−0.663346	+	0.382983i	−0.793551	−	0.608504i	$-0.791770\pi$
$941$	−20.3486	+	11.7483i	−0.663346	+	0.382983i	0.130205	+	0.991487i	$0.458436\pi$
$942$		0			0
$943$	19.7474	+	11.4012i	0.643065	+	0.371274i
$944$		0			0
$945$	25.6216	−	14.7927i	0.833471	−	0.481205i
$946$		0			0
$947$	−24.9549	−	43.2231i	−0.810925	−	1.40456i	−0.912218	−	0.409706i	$-0.865631\pi$
$947$	−24.9549	−	43.2231i	−0.810925	−	1.40456i	0.101293	−	0.994857i	$-0.467702\pi$
$948$		0			0
$949$	−4.66759	+	8.08450i	−0.151516	+	0.262434i
$950$		0			0
$951$	90.7571			2.94300
$952$		0			0
$953$	−3.86548	−	6.69521i	−0.125215	−	0.216879i	0.796602	−	0.604504i	$-0.206629\pi$
$953$	−3.86548	−	6.69521i	−0.125215	−	0.216879i	−0.921817	+	0.387625i	$0.873295\pi$
$954$		0			0
$955$	−50.2671	−	29.0217i	−1.62660	−	0.939121i
$956$		0			0
$957$	−3.54032	+	6.13201i	−0.114442	+	0.198220i
$958$		0			0
$959$	−2.86477	+	4.96192i	−0.0925082	+	0.160229i
$960$		0			0
$961$	18.8911			0.609389
$962$		0			0
$963$			7.41241i			0.238862i
$964$		0			0
$965$	37.4757	+	21.6366i	1.20639	+	0.696508i
$966$		0			0
$967$	−41.0682	−	23.7107i	−1.32066	−	0.762486i	−0.336830	−	0.941565i	$-0.609355\pi$
$967$	−41.0682	−	23.7107i	−1.32066	−	0.762486i	−0.983835	+	0.179079i	$0.942688\pi$
$968$		0			0
$969$	7.75063	−	13.4245i	0.248986	−	0.431256i
$970$		0			0
$971$	−0.993477	+	0.573584i	−0.0318822	+	0.0184072i	−0.515856	−	0.856675i	$-0.672526\pi$
$971$	−0.993477	+	0.573584i	−0.0318822	+	0.0184072i	0.483974	+	0.875082i	$0.339193\pi$
$972$		0			0
$973$			6.59805i			0.211524i
$974$		0			0
$975$	−125.207	−	72.2882i	−4.00983	−	2.31508i
$976$		0			0
$977$	−7.69453	+	4.44244i	−0.246170	+	0.142126i	−0.618009	−	0.786171i	$-0.712061\pi$
$977$	−7.69453	+	4.44244i	−0.246170	+	0.142126i	0.371839	+	0.928297i	$0.378727\pi$
$978$		0			0
$979$	−0.780446	−	1.35177i	−0.0249432	−	0.0432028i
$980$		0			0
$981$	−29.1082	+	50.4169i	−0.929353	+	1.60969i
$982$		0			0
$983$	19.2704	+	33.3773i	0.614630	+	1.06457i	0.990449	+	0.137878i	$0.0440281\pi$
$983$	19.2704	+	33.3773i	0.614630	+	1.06457i	−0.375819	+	0.926693i	$0.622639\pi$
$984$		0			0
$985$			54.0695i			1.72280i
$986$		0			0
$987$	24.0219	−	13.8690i	0.764624	−	0.441456i
$988$		0			0
$989$		−	11.6358i		−	0.369997i
$990$		0			0
$991$			34.5702i			1.09816i	0.835770	+	0.549080i	$0.185022\pi$
$991$			34.5702i			1.09816i	−0.835770	+	0.549080i	$0.814978\pi$
$992$		0			0
$993$		−	11.0974i		−	0.352166i
$994$		0			0
$995$	25.9148	+	14.9619i	0.821556	+	0.474325i
$996$		0			0
$997$	16.6516	+	28.8414i	0.527360	+	0.913415i	0.999491	+	0.0318865i	$0.0101515\pi$
$997$	16.6516	+	28.8414i	0.527360	+	0.913415i	−0.472131	+	0.881528i	$0.656515\pi$
$998$		0			0
$999$	46.6248	−	3.60338i	1.47514	−	0.114006i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1184.2.y.a.529.34		72
4.3	odd	2		296.2.q.a.85.7	✓	72
8.3	odd	2		296.2.q.a.85.20	yes	72
8.5	even	2	inner	1184.2.y.a.529.3		72
37.27	even	6	inner	1184.2.y.a.1137.3		72
148.27	odd	6		296.2.q.a.101.20	yes	72
296.27	odd	6		296.2.q.a.101.7	yes	72
296.101	even	6	inner	1184.2.y.a.1137.34		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
296.2.q.a.85.7	✓	72	4.3	odd	2
296.2.q.a.85.20	yes	72	8.3	odd	2
296.2.q.a.101.7	yes	72	296.27	odd	6
296.2.q.a.101.20	yes	72	148.27	odd	6
1184.2.y.a.529.3		72	8.5	even	2	inner
1184.2.y.a.529.34		72	1.1	even	1	trivial
1184.2.y.a.1137.3		72	37.27	even	6	inner
1184.2.y.a.1137.34		72	296.101	even	6	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:	\( N \)	\(=\)	\( 1184 = 2^{5} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1184.y (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.54245 + 1.46788i) q^{3} +(-2.01329 + 3.48712i) q^{5} +(-0.477860 + 0.827678i) q^{7} +(2.80936 + 4.86595i) q^{9} +0.266146i q^{11} +(2.19590 - 3.80341i) q^{13} +(-10.2374 + 5.91054i) q^{15} +(-4.25701 + 2.45778i) q^{17} +(-0.537084 + 0.930256i) q^{19} +(-2.42987 + 1.40288i) q^{21} +4.38312i q^{23} +(-5.60666 - 9.71102i) q^{25} +7.68793i q^{27} +9.06214 q^{29} +3.47979i q^{31} +(-0.390671 + 0.676662i) q^{33} +(-1.92414 - 3.33271i) q^{35} +(-0.468706 - 6.06468i) q^{37} +(11.1659 - 6.44664i) q^{39} +(2.60116 - 4.50534i) q^{41} -2.65469 q^{43} -22.6242 q^{45} -9.88608 q^{47} +(3.04330 + 5.27115i) q^{49} -14.4309 q^{51} +(-0.693668 + 0.400490i) q^{53} +(-0.928083 - 0.535829i) q^{55} +(-2.73101 + 1.57675i) q^{57} +(6.03346 + 10.4503i) q^{59} +(2.97244 - 5.14841i) q^{61} -5.36992 q^{63} +(8.84195 + 15.3147i) q^{65} +(-11.7819 - 6.80228i) q^{67} +(-6.43390 + 11.1438i) q^{69} +(-1.67560 + 2.90222i) q^{71} -2.12560 q^{73} -32.9197i q^{75} +(-0.220283 - 0.127181i) q^{77} +(4.72714 + 2.72922i) q^{79} +(-2.85691 + 4.94831i) q^{81} +(12.7696 - 7.37255i) q^{83} -19.7929i q^{85} +(23.0400 + 13.3022i) q^{87} +(-5.07906 + 2.93240i) q^{89} +(2.09866 + 3.63499i) q^{91} +(-5.10792 + 8.84718i) q^{93} +(-2.16261 - 3.74575i) q^{95} +1.93694i q^{97} +(-1.29505 + 0.747700i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 2 q^{7} + 30 q^{9} + 6 q^{15} - 12 q^{17} - 32 q^{25} + 4 q^{33} + 6 q^{39} - 32 q^{47} - 18 q^{49} - 24 q^{55} - 6 q^{57} - 8 q^{63} + 6 q^{65} - 18 q^{71} - 64 q^{73} - 54 q^{79} - 16 q^{81} + 108 q^{87}+ \cdots - 50 q^{95}+O(q^{100}) \) 72 * q - 2 * q^7 + 30 * q^9 + 6 * q^15 - 12 * q^17 - 32 * q^25 + 4 * q^33 + 6 * q^39 - 32 * q^47 - 18 * q^49 - 24 * q^55 - 6 * q^57 - 8 * q^63 + 6 * q^65 - 18 * q^71 - 64 * q^73 - 54 * q^79 - 16 * q^81 + 108 * q^87 - 36 * q^89 - 50 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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