LMFDB - Embedded newform 220.2.g.b.219.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [220,2,Mod(219,220)] 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("220.219"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(220, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	220.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] 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:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			219.13
Character	$\chi$	$=$	220.219
Dual form			220.2.g.b.219.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.419204 - 1.35065i) q^{2} -2.05261 q^{3} +(-1.64854 - 1.13240i) q^{4} +(1.54194 - 1.61939i) q^{5} +(-0.860462 + 2.77236i) q^{6} -1.06270i q^{7} +(-2.22056 + 1.75189i) q^{8} +1.21320 q^{9} +(-1.54085 - 2.76148i) q^{10} +(-3.17551 - 0.957146i) q^{11} +(3.38380 + 2.32437i) q^{12} -4.77094 q^{13} +(-1.43534 - 0.445487i) q^{14} +(-3.16499 + 3.32398i) q^{15} +(1.43534 + 3.73361i) q^{16} +0.329831 q^{17} +(0.508578 - 1.63861i) q^{18} +0.677013 q^{19} +(-4.37574 + 0.923536i) q^{20} +2.18130i q^{21} +(-2.62396 + 3.88778i) q^{22} +4.71498 q^{23} +(4.55793 - 3.59595i) q^{24} +(-0.244866 - 4.99400i) q^{25} +(-2.00000 + 6.44389i) q^{26} +3.66760 q^{27} +(-1.20340 + 1.75189i) q^{28} -7.19190i q^{29} +(3.16277 + 5.66823i) q^{30} -9.04510i q^{31} +(5.64451 - 0.373501i) q^{32} +(6.51808 + 1.96464i) q^{33} +(0.138267 - 0.445487i) q^{34} +(-1.72092 - 1.63861i) q^{35} +(-2.00000 - 1.37383i) q^{36} -5.33925i q^{37} +(0.283807 - 0.914411i) q^{38} +9.79287 q^{39} +(-0.586950 + 6.29726i) q^{40} +5.01060i q^{41} +(2.94618 + 0.914411i) q^{42} +5.08692i q^{43} +(4.15107 + 5.17384i) q^{44} +(1.87067 - 1.96464i) q^{45} +(1.97654 - 6.36832i) q^{46} -1.61500 q^{47} +(-2.94618 - 7.66363i) q^{48} +5.87067 q^{49} +(-6.84782 - 1.76278i) q^{50} -0.677013 q^{51} +(7.86507 + 5.40262i) q^{52} +8.57804i q^{53} +(1.53748 - 4.95366i) q^{54} +(-6.44643 + 3.66654i) q^{55} +(1.86173 + 2.35978i) q^{56} -1.38964 q^{57} +(-9.71378 - 3.01488i) q^{58} +0.336403i q^{59} +(8.98167 - 1.89566i) q^{60} -13.2708i q^{61} +(-12.2168 - 3.79175i) q^{62} -1.28926i q^{63} +(1.86173 - 7.78036i) q^{64} +(-7.35649 + 7.72603i) q^{65} +(5.38596 - 7.98009i) q^{66} -4.71498 q^{67} +(-0.543738 - 0.373501i) q^{68} -9.67801 q^{69} +(-2.93462 + 1.63746i) q^{70} +3.97503i q^{71} +(-2.69397 + 2.12539i) q^{72} +11.6189 q^{73} +(-7.21148 - 2.23824i) q^{74} +(0.502613 + 10.2507i) q^{75} +(-1.11608 - 0.766650i) q^{76} +(-1.01716 + 3.37461i) q^{77} +(4.10522 - 13.2268i) q^{78} +6.35102 q^{79} +(8.25937 + 3.43261i) q^{80} -11.1677 q^{81} +(6.76759 + 2.10047i) q^{82} -12.0945i q^{83} +(2.47011 - 3.59595i) q^{84} +(0.508578 - 0.534126i) q^{85} +(6.87067 + 2.13246i) q^{86} +14.7622i q^{87} +(8.72822 - 3.43777i) q^{88} -7.95455 q^{89} +(-1.86936 - 3.35022i) q^{90} +5.07007i q^{91} +(-7.77282 - 5.33925i) q^{92} +18.5660i q^{93} +(-0.677013 + 2.18130i) q^{94} +(1.04391 - 1.09635i) q^{95} +(-11.5860 + 0.766650i) q^{96} -3.23879i q^{97} +(2.46101 - 7.92925i) q^{98} +(-3.85252 - 1.16121i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{4} - 4 q^{5} + 40 q^{9} + 12 q^{14} - 12 q^{16} - 20 q^{20} - 36 q^{25} - 48 q^{26} + 28 q^{34} - 48 q^{36} + 56 q^{44} - 48 q^{45} + 48 q^{49} + 20 q^{56} - 8 q^{60} + 20 q^{64} - 52 q^{66}+ \cdots - 16 q^{89}+O(q^{100}) $ 24 * q - 4 * q^4 - 4 * q^5 + 40 * q^9 + 12 * q^14 - 12 * q^16 - 20 * q^20 - 36 * q^25 - 48 * q^26 + 28 * q^34 - 48 * q^36 + 56 * q^44 - 48 * q^45 + 48 * q^49 + 20 * q^56 - 8 * q^60 + 20 * q^64 - 52 * q^66 - 8 * q^69 - 64 * q^70 + 64 * q^80 - 104 * q^81 + 72 * q^86 - 16 * q^89

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.419204	−	1.35065i	0.296422	−	0.955057i
$2$	0.419204	−	1.35065i	0.296422	−	0.955057i
$3$	−2.05261			−1.18507			−0.592537	−	0.805543i	$-0.701874\pi$
$3$	−2.05261			−1.18507			−0.592537	+	0.805543i	$0.701874\pi$
$4$	−1.64854	−	1.13240i	−0.824268	−	0.566200i
$5$	1.54194	−	1.61939i	0.689575	−	0.724214i
$5$	1.54194	−	1.61939i	0.689575	−	0.724214i
$6$	−0.860462	+	2.77236i	−0.351282	+	1.13181i
$7$		−	1.06270i		−	0.401662i	−0.979626	−	0.200831i	$-0.935636\pi$
$7$		−	1.06270i		−	0.401662i	0.979626	−	0.200831i	$-0.0643642\pi$
$8$	−2.22056	+	1.75189i	−0.785085	+	0.619388i
$9$	1.21320			0.404399
$10$	−1.54085	−	2.76148i	−0.487261	−	0.873257i
$11$	−3.17551	−	0.957146i	−0.957453	−	0.288590i
$11$	−3.17551	−	0.957146i	−0.957453	−	0.288590i
$12$	3.38380	+	2.32437i	0.976818	+	0.670989i
$13$	−4.77094			−1.32322			−0.661611	−	0.749848i	$-0.730127\pi$
$13$	−4.77094			−1.32322			−0.661611	+	0.749848i	$0.730127\pi$
$14$	−1.43534	−	0.445487i	−0.383610	−	0.119062i
$15$	−3.16499	+	3.32398i	−0.817197	+	0.858247i
$16$	1.43534	+	3.73361i	0.358834	+	0.933401i
$17$	0.329831			0.0799957			0.0399979	−	0.999200i	$-0.487265\pi$
$17$	0.329831			0.0799957			0.0399979	+	0.999200i	$0.487265\pi$
$18$	0.508578	−	1.63861i	0.119873	−	0.386224i
$19$	0.677013			0.155317			0.0776587	−	0.996980i	$-0.475256\pi$
$19$	0.677013			0.155317			0.0776587	+	0.996980i	$0.475256\pi$
$20$	−4.37574	+	0.923536i	−0.978445	+	0.206509i
$21$			2.18130i			0.475999i
$22$	−2.62396	+	3.88778i	−0.559430	+	0.828877i
$23$	4.71498			0.983142			0.491571	−	0.870837i	$-0.336423\pi$
$23$	4.71498			0.983142			0.491571	+	0.870837i	$0.336423\pi$
$24$	4.55793	−	3.59595i	0.930383	−	0.734021i
$25$	−0.244866	−	4.99400i	−0.0489731	−	0.998800i
$26$	−2.00000	+	6.44389i	−0.392232	+	1.26375i
$27$	3.66760			0.705831
$28$	−1.20340	+	1.75189i	−0.227421	+	0.331077i
$29$		−	7.19190i		−	1.33550i	−0.744384	−	0.667751i	$-0.767257\pi$
$29$		−	7.19190i		−	1.33550i	0.744384	−	0.667751i	$-0.232743\pi$
$30$	3.16277	+	5.66823i	0.577440	+	1.03487i
$31$		−	9.04510i		−	1.62455i	−0.583276	−	0.812274i	$-0.698230\pi$
$31$		−	9.04510i		−	1.62455i	0.583276	−	0.812274i	$-0.301770\pi$
$32$	5.64451	−	0.373501i	0.997818	−	0.0660262i
$33$	6.51808	+	1.96464i	1.13465	+	0.342001i
$34$	0.138267	−	0.445487i	0.0237125	−	0.0764005i
$35$	−1.72092	−	1.63861i	−0.290889	−	0.276976i
$36$	−2.00000	−	1.37383i	−0.333333	−	0.228971i
$37$		−	5.33925i		−	0.877768i	−0.898544	−	0.438884i	$-0.855374\pi$
$37$		−	5.33925i		−	0.877768i	0.898544	−	0.438884i	$-0.144626\pi$
$38$	0.283807	−	0.914411i	0.0460396	−	0.148337i
$39$	9.79287			1.56811
$40$	−0.586950	+	6.29726i	−0.0928050	+	0.995684i
$41$			5.01060i			0.782525i	0.920279	+	0.391262i	$0.127961\pi$
$41$			5.01060i			0.782525i	−0.920279	+	0.391262i	$0.872039\pi$
$42$	2.94618	+	0.914411i	0.454606	+	0.141097i
$43$			5.08692i			0.775748i	0.921712	+	0.387874i	$0.126790\pi$
$43$			5.08692i			0.775748i	−0.921712	+	0.387874i	$0.873210\pi$
$44$	4.15107	+	5.17384i	0.625797	+	0.779986i
$45$	1.87067	−	1.96464i	0.278864	−	0.292872i
$46$	1.97654	−	6.36832i	0.291425	−	0.938957i
$47$	−1.61500			−0.235571			−0.117786	−	0.993039i	$-0.537580\pi$
$47$	−1.61500			−0.235571			−0.117786	+	0.993039i	$0.537580\pi$
$48$	−2.94618	−	7.66363i	−0.425245	−	1.10615i
$49$	5.87067			0.838668
$50$	−6.84782	−	1.76278i	−0.968428	−	0.249294i
$51$	−0.677013			−0.0948008
$52$	7.86507	+	5.40262i	1.09069	+	0.749208i
$53$			8.57804i			1.17828i	0.808029	+	0.589142i	$0.200534\pi$
$53$			8.57804i			1.17828i	−0.808029	+	0.589142i	$0.799466\pi$
$54$	1.53748	−	4.95366i	0.209224	−	0.674108i
$55$	−6.44643	+	3.66654i	−0.869237	+	0.494397i
$56$	1.86173	+	2.35978i	0.248785	+	0.315339i
$57$	−1.38964			−0.184063
$58$	−9.71378	−	3.01488i	−1.27548	−	0.395873i
$59$			0.336403i			0.0437959i	0.999760	+	0.0218980i	$0.00697090\pi$
$59$			0.336403i			0.0437959i	−0.999760	+	0.0218980i	$0.993029\pi$
$60$	8.98167	−	1.89566i	1.15953	−	0.244728i
$61$		−	13.2708i		−	1.69915i	−0.527471	−	0.849573i	$-0.676860\pi$
$61$		−	13.2708i		−	1.69915i	0.527471	−	0.849573i	$-0.323140\pi$
$62$	−12.2168	−	3.79175i	−1.55154	−	0.481552i
$63$		−	1.28926i		−	0.162432i
$64$	1.86173	−	7.78036i	0.232717	−	0.972545i
$65$	−7.35649	+	7.72603i	−0.912460	+	0.958296i
$66$	5.38596	−	7.98009i	0.662966	−	0.982281i
$67$	−4.71498			−0.576027			−0.288014	−	0.957626i	$-0.592995\pi$
$67$	−4.71498			−0.576027			−0.288014	+	0.957626i	$0.592995\pi$
$68$	−0.543738	−	0.373501i	−0.0659379	−	0.0452936i
$69$	−9.67801			−1.16510
$70$	−2.93462	+	1.63746i	−0.350754	+	0.195714i
$71$			3.97503i			0.471749i	0.971783	+	0.235875i	$0.0757955\pi$
$71$			3.97503i			0.471749i	−0.971783	+	0.235875i	$0.924205\pi$
$72$	−2.69397	+	2.12539i	−0.317488	+	0.250480i
$73$	11.6189			1.35988			0.679942	−	0.733266i	$-0.262005\pi$
$73$	11.6189			1.35988			0.679942	+	0.733266i	$0.262005\pi$
$74$	−7.21148	−	2.23824i	−0.838318	−	0.260190i
$75$	0.502613	+	10.2507i	0.0580368	+	1.18365i
$76$	−1.11608	−	0.766650i	−0.128023	−	0.0879408i
$77$	−1.01716	+	3.37461i	−0.115916	+	0.384572i
$78$	4.10522	−	13.2268i	0.464824	−	1.49764i
$79$	6.35102			0.714546			0.357273	−	0.934000i	$-0.383707\pi$
$79$	6.35102			0.714546			0.357273	+	0.934000i	$0.383707\pi$
$80$	8.25937	+	3.43261i	0.923426	+	0.383777i
$81$	−11.1677			−1.24086
$82$	6.76759	+	2.10047i	0.747356	+	0.231958i
$83$		−	12.0945i		−	1.32754i	−0.747935	−	0.663772i	$-0.768955\pi$
$83$		−	12.0945i		−	1.32754i	0.747935	−	0.663772i	$-0.231045\pi$
$84$	2.47011	−	3.59595i	0.269511	−	0.392350i
$85$	0.508578	−	0.534126i	0.0551630	−	0.0579341i
$86$	6.87067	+	2.13246i	0.740884	+	0.229949i
$87$			14.7622i			1.58267i
$88$	8.72822	−	3.43777i	0.930431	−	0.366467i
$89$	−7.95455			−0.843180			−0.421590	−	0.906787i	$-0.638528\pi$
$89$	−7.95455			−0.843180			−0.421590	+	0.906787i	$0.638528\pi$
$90$	−1.86936	−	3.35022i	−0.197048	−	0.353144i
$91$			5.07007i			0.531487i
$92$	−7.77282	−	5.33925i	−0.810372	−	0.556656i
$93$			18.5660i			1.92521i
$94$	−0.677013	+	2.18130i	−0.0698286	+	0.224984i
$95$	1.04391	−	1.09635i	0.107103	−	0.112483i
$96$	−11.5860	+	0.766650i	−1.18249	+	0.0782459i
$97$		−	3.23879i		−	0.328849i	−0.986390	−	0.164424i	$-0.947423\pi$
$97$		−	3.23879i		−	0.328849i	0.986390	−	0.164424i	$-0.0525767\pi$
$98$	2.46101	−	7.92925i	0.248600	−	0.800975i
$99$	−3.85252	−	1.16121i	−0.387193	−	0.116706i
$100$	−5.25154	+	8.51007i	−0.525154	+	0.851007i
$101$			11.0895i			1.10344i	0.834029	+	0.551721i	$0.186029\pi$
$101$			11.0895i			1.10344i	−0.834029	+	0.551721i	$0.813971\pi$
$102$	−0.283807	+	0.914411i	−0.0281011	+	0.0905402i
$103$	3.70976			0.365533			0.182767	−	0.983156i	$-0.441495\pi$
$103$	3.70976			0.365533			0.182767	+	0.983156i	$0.441495\pi$
$104$	10.5941	−	8.35819i	1.03884	−	0.819587i
$105$	3.53238	+	3.36343i	0.344725	+	0.328237i
$106$	11.5860	+	3.59595i	1.12533	+	0.349270i
$107$		−	13.2463i		−	1.28057i	−0.768137	−	0.640285i	$-0.778816\pi$
$107$		−	13.2463i		−	1.28057i	0.768137	−	0.640285i	$-0.221184\pi$
$108$	−6.04617	−	4.15320i	−0.581793	−	0.399642i
$109$			10.4415i			1.00011i	0.865994	+	0.500055i	$0.166687\pi$
$109$			10.4415i			1.00011i	−0.865994	+	0.500055i	$0.833313\pi$
$110$	2.24986	+	10.2439i	0.214516	+	0.976721i
$111$			10.9594i			1.04022i
$112$	3.96769	−	1.52533i	0.374912	−	0.144130i
$113$			12.5363i			1.17931i	0.807654	+	0.589657i	$0.200737\pi$
$113$			12.5363i			1.17931i	−0.807654	+	0.589657i	$0.799263\pi$
$114$	−0.582544	+	1.87693i	−0.0545603	+	0.175790i
$115$	7.27021	−	7.63541i	0.677950	−	0.712006i
$116$	−8.14412	+	11.8561i	−0.756162	+	1.10081i
$117$	−5.78810			−0.535110
$118$	0.454364	+	0.141022i	0.0418276	+	0.0129821i
$119$		−	0.350510i		−	0.0321312i
$120$	1.20478	−	12.9258i	0.109981	−	1.17996i
$121$	9.16774	+	6.07885i	0.833431	+	0.552623i
$122$	−17.9242	−	5.56316i	−1.62278	−	0.503665i
$123$		−	10.2848i		−	0.927349i
$124$	−10.2427	+	14.9112i	−0.919819	+	1.33906i
$125$	−8.46482	−	7.30390i	−0.757116	−	0.653280i
$126$	−1.74135	−	0.540465i	−0.155132	−	0.0481484i
$127$		−	6.69188i		−	0.593808i	−0.954907	−	0.296904i	$-0.904046\pi$
$127$		−	6.69188i		−	0.593808i	0.954907	−	0.296904i	$-0.0959542\pi$
$128$	−9.72813	−	5.77612i	−0.859853	−	0.510542i
$129$		−	10.4415i		−	0.919319i
$130$	7.35132	+	13.1749i	0.644754	+	1.15551i
$131$	−13.9117			−1.21547			−0.607737	−	0.794138i	$-0.707922\pi$
$131$	−13.9117			−1.21547			−0.607737	+	0.794138i	$0.707922\pi$
$132$	−8.52052	−	10.6199i	−0.741616	−	0.924340i
$133$		−	0.719460i		−	0.0623851i
$134$	−1.97654	+	6.36832i	−0.170747	+	0.550139i
$135$	5.65521	−	5.93929i	0.486723	−	0.511173i
$136$	−0.732408	+	0.577829i	−0.0628034	+	0.0495484i
$137$			0.690503i			0.0589937i	0.999565	+	0.0294968i	$0.00939050\pi$
$137$			0.690503i			0.0589937i	−0.999565	+	0.0294968i	$0.990610\pi$
$138$	−4.05707	+	13.0717i	−0.345360	+	1.11273i
$139$	−16.1439			−1.36931			−0.684654	−	0.728869i	$-0.740047\pi$
$139$	−16.1439			−1.36931			−0.684654	+	0.728869i	$0.740047\pi$
$140$	0.981440	+	4.65009i	0.0829468	+	0.393004i
$141$	3.31495			0.279169
$142$	5.36889	+	1.66635i	0.450548	+	0.139837i
$143$	15.1502	+	4.56649i	1.26692	+	0.381869i
$144$	1.74135	+	4.52960i	0.145112	+	0.377467i
$145$	−11.6465	−	11.0895i	−0.967190	−	0.920929i
$146$	4.87067	−	15.6931i	0.403100	−	1.29877i
$147$	−12.0502			−0.993883
$148$	−6.04617	+	8.80195i	−0.496992	+	0.723515i
$149$			7.83990i			0.642270i	0.947033	+	0.321135i	$0.104064\pi$
$149$			7.83990i			0.642270i	−0.947033	+	0.321135i	$0.895936\pi$
$150$	14.0559	+	3.61829i	1.14766	+	0.295432i
$151$	20.9398			1.70405			0.852027	−	0.523498i	$-0.175373\pi$
$151$	20.9398			1.70405			0.852027	+	0.523498i	$0.175373\pi$
$152$	−1.50335	+	1.18606i	−0.121937	+	0.0962018i
$153$	0.400150			0.0323502
$154$	4.13153	+	2.78848i	0.332928	+	0.224702i
$155$	−14.6476	−	13.9470i	−1.17652	−	1.12025i
$156$	−16.1439	−	11.0895i	−1.29255	−	0.887867i
$157$		−	18.5660i		−	1.48173i	−0.671653	−	0.740866i	$-0.734416\pi$
$157$		−	18.5660i		−	1.48173i	0.671653	−	0.740866i	$-0.265584\pi$
$158$	2.66238	−	8.57804i	0.211807	−	0.682432i
$159$		−	17.6073i		−	1.39635i
$160$	8.09863	−	9.71659i	0.640253	−	0.768164i
$161$		−	5.01060i		−	0.394891i
$162$	−4.68157	+	15.0838i	−0.367819	+	1.18509i
$163$	4.27737			0.335030			0.167515	−	0.985870i	$-0.446426\pi$
$163$	4.27737			0.335030			0.167515	+	0.985870i	$0.446426\pi$
$164$	5.67401	−	8.26015i	0.443066	−	0.645010i
$165$	13.2320	−	7.52597i	1.03011	−	0.585896i
$166$	−16.3355	−	5.07007i	−1.26788	−	0.393514i
$167$			14.6247i			1.13169i	0.824510	+	0.565847i	$0.191451\pi$
$167$			14.6247i			1.13169i	−0.824510	+	0.565847i	$0.808549\pi$
$168$	−3.82141	−	4.84370i	−0.294828	−	0.373700i
$169$	9.76189			0.750914
$170$	−0.508221	−	0.910821i	−0.0389788	−	0.0698568i
$171$	0.821351			0.0628103
$172$	5.76043	−	8.38597i	0.439229	−	0.639424i
$173$	−6.58840			−0.500907			−0.250453	−	0.968129i	$-0.580580\pi$
$173$	−6.58840			−0.500907			−0.250453	+	0.968129i	$0.580580\pi$
$174$	19.9386	+	6.18836i	1.51154	+	0.469138i
$175$	−5.30711	+	0.260218i	−0.401180	+	0.0196706i
$176$	−0.984326	−	13.2299i	−0.0741963	−	0.997244i
$177$		−	0.690503i		−	0.0519014i
$178$	−3.33458	+	10.7438i	−0.249937	+	0.805285i
$179$			17.6215i			1.31709i	0.752542	+	0.658545i	$0.228828\pi$
$179$			17.6215i			1.31709i	−0.752542	+	0.658545i	$0.771172\pi$
$180$	−5.30864	+	1.12043i	−0.395682	+	0.0835121i
$181$	−0.231080			−0.0171760			−0.00858801	−	0.999963i	$-0.502734\pi$
$181$	−0.231080			−0.0171760			−0.00858801	+	0.999963i	$0.502734\pi$
$182$	6.84791	+	2.12539i	0.507601	+	0.157545i
$183$			27.2397i			2.01361i
$184$	−10.4699	+	8.26015i	−0.771850	+	0.608947i
$185$	−8.64635	−	8.23279i	−0.635692	−	0.605286i
$186$	25.0763	+	7.78297i	1.83868	+	0.570675i
$187$	−1.04738	−	0.315696i	−0.0765921	−	0.0230860i
$188$	2.66238	+	1.82882i	0.194174	+	0.133381i
$189$		−	3.89755i		−	0.283505i
$190$	−1.04318	−	1.86956i	−0.0756801	−	0.135632i
$191$			8.56225i			0.619542i	0.950811	+	0.309771i	$0.100252\pi$
$191$			8.56225i			0.619542i	−0.950811	+	0.309771i	$0.899748\pi$
$192$	−3.82141	+	15.9700i	−0.275786	+	1.15254i
$193$	−5.36028			−0.385842			−0.192921	−	0.981214i	$-0.561796\pi$
$193$	−5.36028			−0.385842			−0.192921	+	0.981214i	$0.561796\pi$
$194$	−4.37448	−	1.35771i	−0.314069	−	0.0974781i
$195$	15.1000	−	15.8585i	1.08133	−	1.13565i
$196$	−9.67801	−	6.64796i	−0.691287	−	0.474854i
$197$	18.1646			1.29417			0.647087	−	0.762416i	$-0.275987\pi$
$197$	18.1646			1.29417			0.647087	+	0.762416i	$0.275987\pi$
$198$	−3.18339	+	4.71665i	−0.226233	+	0.335197i
$199$			2.00012i			0.141785i	0.997484	+	0.0708923i	$0.0225847\pi$
$199$			2.00012i			0.141785i	−0.997484	+	0.0708923i	$0.977415\pi$
$200$	9.29270	+	10.6605i	0.657093	+	0.753810i
$201$	9.67801			0.682634
$202$	14.9780	+	4.64875i	1.05385	+	0.327085i
$203$	−7.64282			−0.536421
$204$	1.11608	+	0.766650i	0.0781412	+	0.0536763i
$205$	8.11413	+	7.72603i	0.566716	+	0.539609i
$206$	1.55515	−	5.01060i	0.108352	−	0.349105i
$207$	5.72021			0.397582
$208$	−6.84791	−	17.8128i	−0.474817	−	1.23510i
$209$	−2.14986	−	0.648000i	−0.148709	−	0.0448231i
$210$	6.02362	−	3.36107i	0.415669	−	0.231936i
$211$	17.3536			1.19467			0.597335	−	0.801992i	$-0.296226\pi$
$211$	17.3536			1.19467			0.597335	+	0.801992i	$0.296226\pi$
$212$	9.71378	−	14.1412i	0.667145	−	0.971221i
$213$		−	8.15918i		−	0.559058i
$214$	−17.8912	−	5.55292i	−1.22302	−	0.379590i
$215$	8.23772	+	7.84371i	0.561808	+	0.534937i
$216$	−8.14412	+	6.42525i	−0.554137	+	0.437183i
$217$	−9.61220			−0.652519
$218$	14.1028	+	4.37710i	0.955162	+	0.296455i
$219$	−23.8489			−1.61156
$220$	14.7792	+	1.25552i	0.996411	+	0.0846470i
$221$	−1.57360			−0.105852
$222$	14.8023	+	4.59422i	0.993469	+	0.308344i
$223$	−25.5854			−1.71332			−0.856662	−	0.515879i	$-0.827466\pi$
$223$	−25.5854			−1.71332			−0.856662	+	0.515879i	$0.827466\pi$
$224$	−0.396918	−	5.99841i	−0.0265202	−	0.400785i
$225$	−0.297071	−	6.05871i	−0.0198047	−	0.403914i
$226$	16.9322	+	5.25527i	1.12631	+	0.349575i
$227$		−	9.44867i		−	0.627130i	−0.949567	−	0.313565i	$-0.898477\pi$
$227$		−	9.44867i		−	0.627130i	0.949567	−	0.313565i	$-0.101523\pi$
$228$	2.29087	+	1.57363i	0.151717	+	0.104216i
$229$	23.2927			1.53922			0.769612	−	0.638512i	$-0.220450\pi$
$229$	23.2927			1.53922			0.769612	+	0.638512i	$0.220450\pi$
$230$	−7.26510	−	13.0203i	−0.479047	−	0.858535i
$231$	2.08782	−	6.92675i	0.137369	−	0.455746i
$232$	12.5995	+	15.9700i	0.827195	+	1.04848i
$233$	12.3488			0.808999			0.404499	−	0.914538i	$-0.367446\pi$
$233$	12.3488			0.808999			0.404499	+	0.914538i	$0.367446\pi$
$234$	−2.42640	+	7.81772i	−0.158618	+	0.511060i
$235$	−2.49022	+	2.61531i	−0.162444	+	0.170604i
$236$	0.380943	−	0.554572i	0.0247973	−	0.0360996i
$237$	−13.0362			−0.846789
$238$	−0.473418	−	0.146935i	−0.0306872	−	0.00952441i
$239$	19.0531			1.23244			0.616220	−	0.787574i	$-0.288663\pi$
$239$	19.0531			1.23244			0.616220	+	0.787574i	$0.288663\pi$
$240$	−16.9532	−	7.04579i	−1.09433	−	0.454804i
$241$		−	26.1213i		−	1.68262i	−0.540554	−	0.841309i	$-0.681785\pi$
$241$		−	26.1213i		−	1.68262i	0.540554	−	0.841309i	$-0.318215\pi$
$242$	12.0536	−	9.83417i	0.774834	−	0.632165i
$243$	11.9202			0.764680
$244$	−15.0278	+	21.8773i	−0.962057	+	1.40055i
$245$	9.05220	−	9.50693i	0.578324	−	0.607375i
$246$	−13.8912	−	4.31143i	−0.885671	−	0.274887i
$247$	−3.22999			−0.205519
$248$	15.8461	+	20.0851i	1.00623	+	1.27541i
$249$			24.8253i			1.57324i
$250$	−13.4135	+	8.37122i	−0.848346	+	0.529442i
$251$			5.56703i			0.351388i	0.984445	+	0.175694i	$0.0562169\pi$
$251$			5.56703i			0.351388i	−0.984445	+	0.175694i	$0.943783\pi$
$252$	−1.45996	+	2.12539i	−0.0919690	+	0.133887i
$253$	−14.9725	−	4.51293i	−0.941312	−	0.283725i
$254$	−9.03842	−	2.80527i	−0.567121	−	0.176018i
$255$	−1.04391	+	1.09635i	−0.0653723	+	0.0686561i
$256$	−11.8796	+	10.7180i	−0.742476	+	0.669873i
$257$			6.74922i			0.421004i	0.977593	+	0.210502i	$0.0675099\pi$
$257$			6.74922i			0.421004i	−0.977593	+	0.210502i	$0.932490\pi$
$258$	−14.1028	−	4.37710i	−0.878002	−	0.272507i
$259$	−5.67401			−0.352566
$260$	20.8764	−	4.40614i	1.29470	−	0.273257i
$261$		−	8.72520i		−	0.540077i
$262$	−5.83186	+	18.7899i	−0.360294	+	1.16085i
$263$			3.81948i			0.235520i	0.993042	+	0.117760i	$0.0375713\pi$
$263$			3.81948i			0.235520i	−0.993042	+	0.117760i	$0.962429\pi$
$264$	−17.9156	+	7.05638i	−1.10263	+	0.434290i
$265$	13.8912	+	13.2268i	0.853330	+	0.812515i
$266$	−0.971742	−	0.301601i	−0.0595813	−	0.0184923i
$267$	16.3276			0.999231
$268$	7.77282	+	5.33925i	0.474800	+	0.326147i
$269$	4.76189			0.290337			0.145169	−	0.989407i	$-0.453628\pi$
$269$	4.76189			0.290337			0.145169	+	0.989407i	$0.453628\pi$
$270$	−5.65124	−	10.1280i	−0.343923	−	0.616371i
$271$	−14.7899			−0.898420			−0.449210	−	0.893426i	$-0.648295\pi$
$271$	−14.7899			−0.898420			−0.449210	+	0.893426i	$0.648295\pi$
$272$	0.473418	+	1.23146i	0.0287052	+	0.0746681i
$273$		−	10.4069i		−	0.629852i
$274$	0.932631	+	0.289462i	0.0563423	+	0.0174870i
$275$	−4.00241	+	16.0929i	−0.241355	+	0.970437i
$276$	15.9545	+	10.9594i	0.960351	+	0.659678i
$277$	29.6855			1.78363			0.891813	−	0.452404i	$-0.149433\pi$
$277$	29.6855			1.78363			0.891813	+	0.452404i	$0.149433\pi$
$278$	−6.76759	+	21.8048i	−0.405893	+	1.30777i
$279$		−	10.9735i		−	0.656966i
$280$	6.69208	+	0.623750i	0.399928	+	0.0372762i
$281$		−	18.2366i		−	1.08790i	−0.839117	−	0.543951i	$-0.816928\pi$
$281$		−	18.2366i		−	1.08790i	0.839117	−	0.543951i	$-0.183072\pi$
$282$	1.38964	−	4.47735i	0.0827520	−	0.266623i
$283$		−	6.17144i		−	0.366854i	−0.983033	−	0.183427i	$-0.941281\pi$
$283$		−	6.17144i		−	0.366854i	0.983033	−	0.183427i	$-0.0587191\pi$
$284$	4.50133	−	6.55298i	0.267105	−	0.388848i
$285$	−2.14274	+	2.25038i	−0.126925	+	0.133301i
$286$	12.5188	−	18.5484i	0.740250	−	1.09679i
$287$	5.32475			0.314310
$288$	6.84791	−	0.453130i	0.403517	−	0.0267010i
$289$	−16.8912			−0.993601
$290$	−19.8603	+	11.0817i	−1.16624	+	0.650738i
$291$			6.64796i			0.389710i
$292$	−19.1541	−	13.1572i	−1.12091	−	0.769967i
$293$	−2.21761			−0.129554			−0.0647770	−	0.997900i	$-0.520634\pi$
$293$	−2.21761			−0.129554			−0.0647770	+	0.997900i	$0.520634\pi$
$294$	−5.05149	+	16.2756i	−0.294609	+	0.949215i
$295$	0.544768	+	0.518712i	0.0317176	+	0.0302006i
$296$	9.35380	+	11.8561i	0.543679	+	0.689122i
$297$	−11.6465	−	3.51043i	−0.675799	−	0.203696i
$298$	10.5890	+	3.28652i	0.613404	+	0.190383i
$299$	−22.4949			−1.30091
$300$	10.7794	−	17.4678i	0.622346	−	1.00851i
$301$	5.40586			0.311589
$302$	8.77804	−	28.2824i	0.505120	−	1.62747i
$303$		−	22.7623i		−	1.30766i
$304$	0.971742	+	2.52770i	0.0557332	+	0.144974i
$305$	−21.4906	−	20.4627i	−1.23055	−	1.17169i
$306$	0.167745	−	0.540465i	0.00958933	−	0.0308963i
$307$			14.3308i			0.817905i	0.912556	+	0.408952i	$0.134106\pi$
$307$			14.3308i			0.817905i	−0.912556	+	0.408952i	$0.865894\pi$
$308$	5.49823	−	4.41133i	0.313291	−	0.251359i
$309$	−7.61468			−0.433184
$310$	−24.9779	+	13.9372i	−1.41865	+	0.791578i
$311$		−	29.8223i		−	1.69107i	−0.533921	−	0.845535i	$-0.679282\pi$
$311$		−	29.8223i		−	1.69107i	0.533921	−	0.845535i	$-0.320718\pi$
$312$	−21.7456	+	17.1561i	−1.23110	+	0.971271i
$313$		−	17.8466i		−	1.00875i	−0.863485	−	0.504374i	$-0.831723\pi$
$313$		−	17.8466i		−	1.00875i	0.863485	−	0.504374i	$-0.168277\pi$
$314$	−25.0763	−	7.78297i	−1.41514	−	0.439218i
$315$	−2.08782	−	1.98796i	−0.117635	−	0.112009i
$316$	−10.4699	−	7.19190i	−0.588977	−	0.404576i
$317$			18.2944i			1.02752i	0.857935	+	0.513758i	$0.171747\pi$
$317$			18.2944i			1.02752i	−0.857935	+	0.513758i	$0.828253\pi$
$318$	−23.7814	−	7.38108i	−1.33360	−	0.413910i
$319$	−6.88370	+	22.8380i	−0.385413	+	1.27868i
$320$	−9.72878	−	15.0117i	−0.543855	−	0.839179i
$321$			27.1895i			1.51757i
$322$	−6.76759	−	2.10047i	−0.377143	−	0.117054i
$323$	0.223300			0.0124247
$324$	18.4104	+	12.6464i	1.02280	+	0.702576i
$325$	1.16824	+	23.8261i	0.0648023	+	1.32163i
$326$	1.79309	−	5.77725i	0.0993103	−	0.319972i
$327$		−	21.4322i		−	1.18520i
$328$	−8.77804	−	11.1263i	−0.484686	−	0.614348i
$329$			1.71625i			0.0946200i
$330$	−4.61808	−	21.0268i	−0.254217	−	1.15749i
$331$		−	21.8582i		−	1.20143i	−0.799462	−	0.600717i	$-0.794882\pi$
$331$		−	21.8582i		−	1.20143i	0.799462	−	0.600717i	$-0.205118\pi$
$332$	−13.6958	+	19.9382i	−0.751656	+	1.09425i
$333$		−	6.47757i		−	0.354969i
$334$	19.7529	+	6.13075i	1.08083	+	0.335460i
$335$	−7.27021	+	7.63541i	−0.397214	+	0.417167i
$336$	−8.14412	+	3.13090i	−0.444298	+	0.170805i
$337$	−22.1076			−1.20428			−0.602138	−	0.798392i	$-0.705684\pi$
$337$	−22.1076			−1.20428			−0.602138	+	0.798392i	$0.705684\pi$
$338$	4.09223	−	13.1849i	0.222588	−	0.717166i
$339$		−	25.7321i		−	1.39757i
$340$	−1.44325	+	0.304611i	−0.0782714	+	0.0165198i
$341$	−8.65748	+	28.7228i	−0.468829	+	1.55543i
$342$	0.344314	−	1.10936i	0.0186184	−	0.0599874i
$343$		−	13.6776i		−	0.738523i
$344$	−8.91175	−	11.2958i	−0.480489	−	0.609028i
$345$	−14.9229	+	15.6725i	−0.803421	+	0.843779i
$346$	−2.76189	+	8.89865i	−0.148480	+	0.478394i
$347$		−	5.65101i		−	0.303362i	−0.988429	−	0.151681i	$-0.951531\pi$
$347$		−	5.65101i		−	0.303362i	0.988429	−	0.151681i	$-0.0484686\pi$
$348$	16.7167	−	24.3359i	0.896108	−	1.30454i
$349$		−	1.06825i		−	0.0571822i	−0.999591	−	0.0285911i	$-0.990898\pi$
$349$		−	1.06825i		−	0.0571822i	0.999591	−	0.0285911i	$-0.00910207\pi$
$350$	−1.87330	+	7.27716i	−0.100132	+	0.388980i
$351$	−17.4979			−0.933970
$352$	−18.2817	−	4.21656i	−0.974418	−	0.224744i
$353$		−	13.9173i		−	0.740743i	−0.928884	−	0.370371i	$-0.879230\pi$
$353$		−	13.9173i		−	0.740743i	0.928884	−	0.370371i	$-0.120770\pi$
$354$	−0.932631	−	0.289462i	−0.0495688	−	0.0153847i
$355$	6.43714	+	6.12924i	0.341648	+	0.325306i
$356$	13.1134	+	9.00773i	0.695006	+	0.477409i
$357$			0.719460i			0.0380779i
$358$	23.8005	+	7.38699i	1.25790	+	0.390415i
$359$	21.1409			1.11577			0.557887	−	0.829917i	$-0.311612\pi$
$359$	21.1409			1.11577			0.557887	+	0.829917i	$0.311612\pi$
$360$	−0.712087	+	7.63982i	−0.0375303	+	0.402654i
$361$	−18.5417			−0.975876
$362$	−0.0968696	+	0.312109i	−0.00509135	+	0.0164041i
$363$	−18.8178	−	12.4775i	−0.987677	−	0.654899i
$364$	5.74135	−	8.35819i	0.300928	−	0.438088i
$365$	17.9155	−	18.8155i	0.937742	−	0.984847i
$366$	36.7914	+	11.4190i	1.92312	+	0.596880i
$367$	19.3854			1.01191			0.505955	−	0.862560i	$-0.331140\pi$
$367$	19.3854			1.01191			0.505955	+	0.862560i	$0.331140\pi$
$368$	6.76759	+	17.6039i	0.352785	+	0.917666i
$369$			6.07885i			0.316452i
$370$	−14.7442	+	8.22701i	−0.766516	+	0.427702i
$371$	9.11586			0.473272
$372$	21.0242	−	30.6068i	1.09005	−	1.58689i
$373$	−0.0979830			−0.00507337			−0.00253668	−	0.999997i	$-0.500807\pi$
$373$	−0.0979830			−0.00507337			−0.00253668	+	0.999997i	$0.500807\pi$
$374$	−0.865463	+	1.28231i	−0.0447520	+	0.0663066i
$375$	17.3749	+	14.9920i	0.897238	+	0.774185i
$376$	3.58619	−	2.82930i	0.184943	−	0.145910i
$377$			34.3122i			1.76717i
$378$	−5.26425	−	1.63387i	−0.270764	−	0.0840373i
$379$			35.5511i			1.82614i	0.407806	+	0.913069i	$0.366294\pi$
$379$			35.5511i			1.82614i	−0.407806	+	0.913069i	$0.633706\pi$
$380$	−2.96243	+	0.625246i	−0.151970	+	0.0320745i
$381$			13.7358i			0.703707i
$382$	11.5646	+	3.58933i	0.591698	+	0.183646i
$383$	−13.2697			−0.678051			−0.339026	−	0.940777i	$-0.610097\pi$
$383$	−13.2697			−0.678051			−0.339026	+	0.940777i	$0.610097\pi$
$384$	19.9680	+	11.8561i	1.01899	+	0.605029i
$385$	3.89643	+	6.85061i	0.198580	+	0.349139i
$386$	−2.24705	+	7.23989i	−0.114372	+	0.368501i
$387$			6.17144i			0.313712i
$388$	−3.66760	+	5.33925i	−0.186194	+	0.271059i
$389$	24.0135			1.21753			0.608766	−	0.793349i	$-0.291665\pi$
$389$	24.0135			1.21753			0.608766	+	0.793349i	$0.291665\pi$
$390$	−15.0894	−	27.0428i	−0.764081	−	1.36937i
$391$	1.55515			0.0786472
$392$	−13.0362	+	10.2848i	−0.658425	+	0.519461i
$393$	28.5553			1.44043
$394$	7.61468	−	24.5341i	0.383622	−	1.23601i
$395$	9.79287	−	10.2848i	0.492733	−	0.517484i
$396$	5.03607	+	6.27689i	0.253072	+	0.315426i
$397$			4.20093i			0.210839i	0.994428	+	0.105419i	$0.0336185\pi$
$397$			4.20093i			0.210839i	−0.994428	+	0.105419i	$0.966381\pi$
$398$	2.70147	+	0.838459i	0.135412	+	0.0420281i
$399$			1.47677i			0.0739310i
$400$	18.2942	−	8.08231i	0.914708	−	0.404115i
$401$	−11.5968			−0.579116			−0.289558	−	0.957160i	$-0.593508\pi$
$401$	−11.5968			−0.579116			−0.289558	+	0.957160i	$0.593508\pi$
$402$	4.05707	−	13.0717i	0.202348	−	0.651955i
$403$			43.1536i			2.14964i
$404$	12.5577	−	18.2814i	0.624769	−	0.909532i
$405$	−17.2199	+	18.0850i	−0.855666	+	0.898649i
$406$	−3.20390	+	10.3228i	−0.159007	+	0.512312i
$407$	−5.11044	+	16.9549i	−0.253315	+	0.840421i
$408$	1.50335	−	1.18606i	0.0744267	−	0.0587185i
$409$		−	24.8253i		−	1.22753i	−0.789489	−	0.613765i	$-0.789654\pi$
$409$		−	24.8253i		−	1.22753i	0.789489	−	0.613765i	$-0.210346\pi$
$410$	13.8367	−	7.72060i	0.683345	−	0.381293i
$411$		−	1.41733i		−	0.0699118i
$412$	−6.11567	−	4.20093i	−0.301297	−	0.206965i
$413$	0.357495			0.0175912
$414$	2.39794	−	7.72603i	0.117852	−	0.379714i
$415$	−19.5857	−	18.6489i	−0.961426	−	0.915441i
$416$	−26.9296	+	1.78195i	−1.32033	+	0.0873673i
$417$	33.1371			1.62273
$418$	−1.77646	+	2.63208i	−0.0868893	+	0.128739i
$419$			19.5964i			0.957345i	0.877994	+	0.478673i	$0.158882\pi$
$419$			19.5964i			0.957345i	−0.877994	+	0.478673i	$0.841118\pi$
$420$	−2.01451	−	9.54480i	−0.0982981	−	0.465739i
$421$	−8.59414			−0.418853			−0.209426	−	0.977824i	$-0.567160\pi$
$421$	−8.59414			−0.418853			−0.209426	+	0.977824i	$0.567160\pi$
$422$	7.27470	−	23.4387i	0.354127	−	1.14098i
$423$	−1.95931			−0.0952649
$424$	−15.0278	−	19.0480i	−0.729815	−	0.925053i
$425$	−0.0807642	−	1.64718i	−0.00391764	−	0.0798997i
$426$	−11.0202	−	3.42036i	−0.533932	−	0.165717i
$427$	−14.1028			−0.682482
$428$	−15.0002	+	21.8370i	−0.725060	+	1.05553i
$429$	−31.0974	−	9.37320i	−1.50140	−	0.452543i
$430$	14.0474	−	7.83820i	0.677427	−	0.377992i
$431$	−16.9652			−0.817187			−0.408594	−	0.912716i	$-0.633981\pi$
$431$	−16.9652			−0.817187			−0.408594	+	0.912716i	$0.633981\pi$
$432$	5.26425	+	13.6934i	0.253276	+	0.658823i
$433$			3.78207i			0.181755i	0.995862	+	0.0908775i	$0.0289672\pi$
$433$			3.78207i			0.181755i	−0.995862	+	0.0908775i	$0.971033\pi$
$434$	−4.02948	+	12.9828i	−0.193421	+	0.623193i
$435$	23.9057	+	22.7623i	1.14619	+	1.09137i
$436$	11.8239	−	17.2131i	0.566263	−	0.824358i
$437$	3.19211			0.152699
$438$	−9.99758	+	32.2117i	−0.477703	+	1.53913i
$439$	18.2317			0.870152			0.435076	−	0.900394i	$-0.356721\pi$
$439$	18.2317			0.870152			0.435076	+	0.900394i	$0.356721\pi$
$440$	7.89126	−	19.4352i	0.376201	−	0.926538i
$441$	7.12229			0.339157
$442$	−0.659662	+	2.12539i	−0.0313769	+	0.101095i
$443$	27.5958			1.31112			0.655559	−	0.755144i	$-0.272433\pi$
$443$	27.5958			1.31112			0.655559	+	0.755144i	$0.272433\pi$
$444$	12.4104	−	18.0669i	0.588973	−	0.857419i
$445$	−12.2654	+	12.8815i	−0.581436	+	0.610643i
$446$	−10.7255	+	34.5570i	−0.507867	+	1.63632i
$447$		−	16.0922i		−	0.761137i
$448$	−8.26816	−	1.97846i	−0.390634	−	0.0934734i
$449$	2.53081			0.119436			0.0597181	−	0.998215i	$-0.480980\pi$
$449$	2.53081			0.119436			0.0597181	+	0.998215i	$0.480980\pi$
$450$	−8.30776	−	2.13860i	−0.391632	−	0.100815i
$451$	4.79588	−	15.9112i	0.225829	−	0.749230i
$452$	14.1961	−	20.6665i	0.667728	−	0.972071i
$453$	−42.9811			−2.01943
$454$	−12.7619	−	3.96092i	−0.598945	−	0.185895i
$455$	8.21043	+	7.81772i	0.384911	+	0.366500i
$456$	3.08578	−	2.43451i	0.144505	−	0.114006i
$457$	−8.33554			−0.389920			−0.194960	−	0.980811i	$-0.562458\pi$
$457$	−8.33554			−0.389920			−0.194960	+	0.980811i	$0.562458\pi$
$458$	9.76440	−	31.4604i	0.456260	−	1.47005i
$459$	1.20969			0.0564634
$460$	−20.6315	+	4.35446i	−0.961950	+	0.203028i
$461$		−	19.3496i		−	0.901201i	−0.892726	−	0.450601i	$-0.851210\pi$
$461$		−	19.3496i		−	0.901201i	0.892726	−	0.450601i	$-0.148790\pi$
$462$	−8.48042	−	5.72365i	−0.394545	−	0.266288i
$463$	−3.57976			−0.166365			−0.0831827	−	0.996534i	$-0.526509\pi$
$463$	−3.57976			−0.166365			−0.0831827	+	0.996534i	$0.526509\pi$
$464$	26.8517	−	10.3228i	1.24656	−	0.479224i
$465$	30.0657	+	28.6276i	1.39426	+	1.32758i
$466$	5.17669	−	16.6790i	0.239805	−	0.772640i
$467$	16.8073			0.777751			0.388875	−	0.921290i	$-0.372864\pi$
$467$	16.8073			0.777751			0.388875	+	0.921290i	$0.372864\pi$
$468$	9.54188	+	6.55445i	0.441074	+	0.302979i
$469$			5.01060i			0.231368i
$470$	2.48847	+	4.45978i	0.114785	+	0.205714i
$471$			38.1088i			1.75596i
$472$	−0.589342	−	0.747001i	−0.0271267	−	0.0343835i
$473$	4.86892	−	16.1536i	0.223873	−	0.742742i
$474$	−5.46482	+	17.6073i	−0.251007	+	0.808732i
$475$	−0.165777	−	3.38100i	−0.00760638	−	0.155131i
$476$	−0.396918	+	0.577829i	−0.0181927	+	0.0264847i
$477$			10.4069i			0.476497i
$478$	7.98713	−	25.7341i	0.365323	−	1.17705i
$479$	25.2030			1.15155			0.575777	−	0.817607i	$-0.304700\pi$
$479$	25.2030			1.15155			0.575777	+	0.817607i	$0.304700\pi$
$480$	−16.6233	+	19.9444i	−0.758747	+	0.910331i
$481$			25.4733i			1.16148i
$482$	−35.2808	−	10.9501i	−1.60700	−	0.498766i
$483$			10.2848i			0.467975i
$484$	−8.22965	−	20.4028i	−0.374075	−	0.927398i
$485$	−5.24487	−	4.99400i	−0.238157	−	0.226766i
$486$	4.99700	−	16.1001i	0.226668	−	0.730313i
$487$	−20.6049			−0.933699			−0.466849	−	0.884337i	$-0.654611\pi$
$487$	−20.6049			−0.933699			−0.466849	+	0.884337i	$0.654611\pi$
$488$	23.2490	+	29.4685i	1.05243	+	1.33397i
$489$	−8.77977			−0.397035
$490$	−9.04585	−	16.2117i	−0.408650	−	0.732372i
$491$	7.22916			0.326247			0.163124	−	0.986606i	$-0.447843\pi$
$491$	7.22916			0.326247			0.163124	+	0.986606i	$0.447843\pi$
$492$	−11.6465	+	16.9549i	−0.525065	+	0.764384i
$493$		−	2.37211i		−	0.106835i
$494$	−1.35403	+	4.36260i	−0.0609205	+	0.196283i
$495$	−7.82080	+	4.44824i	−0.351519	+	0.199934i
$496$	33.7708	−	12.9828i	1.51635	−	0.582943i
$497$	4.22426			0.189484
$498$	33.5304	+	10.4069i	1.50253	+	0.466343i
$499$		−	31.4143i		−	1.40630i	−0.711042	−	0.703149i	$-0.751777\pi$
$499$		−	31.4143i		−	1.40630i	0.711042	−	0.703149i	$-0.248223\pi$
$500$	5.68361	+	21.6263i	0.254179	+	0.967157i
$501$		−	30.0188i		−	1.34114i
$502$	7.51913	+	2.33372i	0.335595	+	0.104159i
$503$			34.1581i			1.52303i	0.648145	+	0.761517i	$0.275545\pi$
$503$			34.1581i			1.52303i	−0.648145	+	0.761517i	$0.724455\pi$
$504$	2.25865	+	2.86288i	0.100608	+	0.127523i
$505$	17.9582	+	17.0992i	0.799129	+	0.760906i
$506$	−12.3719	+	18.3308i	−0.550000	+	0.814904i
$507$	−20.0373			−0.889889
$508$	−7.57789	+	11.0318i	−0.336215	+	0.489457i
$509$	−13.4604			−0.596623			−0.298312	−	0.954469i	$-0.596423\pi$
$509$	−13.4604			−0.596623			−0.298312	+	0.954469i	$0.596423\pi$
$510$	1.04318	+	1.86956i	0.0461927	+	0.0827854i
$511$		−	12.3473i		−	0.546213i
$512$	9.49628	+	20.5383i	0.419680	+	0.907672i
$513$	2.48302			0.109628
$514$	9.11586	+	2.82930i	0.402083	+	0.124795i
$515$	5.72021	−	6.00756i	0.252063	−	0.264725i
$516$	−11.8239	+	17.2131i	−0.520519	+	0.757765i
$517$	5.12844	+	1.54579i	0.225548	+	0.0679836i
$518$	−2.37857	+	7.66363i	−0.104508	+	0.336720i
$519$	13.5234			0.593611
$520$	2.80030	−	30.0439i	0.122801	−	1.31751i
$521$	7.25162			0.317699			0.158850	−	0.987303i	$-0.449222\pi$
$521$	7.25162			0.317699			0.158850	+	0.987303i	$0.449222\pi$
$522$	−11.7847	−	3.65764i	−0.515804	−	0.160091i
$523$		−	22.9670i		−	1.00428i	−0.864787	−	0.502139i	$-0.832546\pi$
$523$		−	22.9670i		−	1.00428i	0.864787	−	0.502139i	$-0.167454\pi$
$524$	22.9340	+	15.7537i	1.00188	+	0.688202i
$525$	10.8934	−	0.534126i	0.475428	−	0.0233112i
$526$	5.15880	+	1.60114i	0.224935	+	0.0698132i
$527$		−	2.98335i		−	0.129957i
$528$	2.02043	+	27.1559i	0.0879281	+	1.18181i
$529$	−0.768920			−0.0334313
$530$	23.6881	−	13.2175i	1.02894	−	0.574132i
$531$			0.408123i			0.0177110i
$532$	−0.814717	+	1.18606i	−0.0353225	+	0.0514220i
$533$		−	23.9053i		−	1.03545i
$534$	6.84459	−	22.0529i	0.296194	−	0.954322i
$535$	−21.4510	−	20.4250i	−0.927408	−	0.883049i
$536$	10.4699	−	8.26015i	0.452230	−	0.356784i
$537$		−	36.1699i		−	1.56085i
$538$	1.99620	−	6.43166i	0.0860625	−	0.277289i
$539$	−18.6424	−	5.61909i	−0.802985	−	0.242031i
$540$	−16.0485	+	3.38716i	−0.690616	+	0.145760i
$541$		−	0.465049i		−	0.0199940i	−0.999950	−	0.00999702i	$-0.996818\pi$
$541$		−	0.465049i		−	0.0199940i	0.999950	−	0.00999702i	$-0.00318220\pi$
$542$	−6.19998	+	19.9760i	−0.266312	+	0.858043i
$543$	0.474316			0.0203548
$544$	1.86173	−	0.123192i	0.0798212	−	0.00528181i
$545$	16.9088	+	16.1001i	0.724294	+	0.689651i
$546$	−14.0561	−	4.36260i	−0.601544	−	0.186702i
$547$			25.0251i			1.07000i	0.844853	+	0.534999i	$0.179688\pi$
$547$			25.0251i			1.07000i	−0.844853	+	0.534999i	$0.820312\pi$
$548$	0.781926	−	1.13832i	0.0334022	−	0.0486266i
$549$		−	16.1001i		−	0.687134i
$550$	20.0581	+	12.1521i	0.855280	+	0.518166i
$551$		−	4.86901i		−	0.207427i
$552$	21.4906	−	16.9549i	0.914699	−	0.721647i
$553$		−	6.74922i		−	0.287006i
$554$	12.4443	−	40.0948i	0.528707	−	1.70347i
$555$	17.7476	+	16.8987i	0.753342	+	0.717309i
$556$	26.6138	+	18.2814i	1.12868	+	0.775302i
$557$	−9.49923			−0.402495			−0.201248	−	0.979540i	$-0.564500\pi$
$557$	−9.49923			−0.402495			−0.201248	+	0.979540i	$0.564500\pi$
$558$	−14.8214	−	4.60014i	−0.627440	−	0.194739i
$559$		−	24.2694i		−	1.02649i
$560$	3.64782	−	8.77721i	0.154149	−	0.370905i
$561$	2.14986	+	0.648000i	0.0907673	+	0.0273586i
$562$	−24.6313	−	7.64485i	−1.03901	−	0.322478i
$563$		−	6.75919i		−	0.284866i	−0.989804	−	0.142433i	$-0.954507\pi$
$563$		−	6.75919i		−	0.284866i	0.989804	−	0.142433i	$-0.0454925\pi$
$564$	−5.46482	−	3.75385i	−0.230110	−	0.158066i
$565$	20.3012	+	19.3301i	0.854076	+	0.813225i
$566$	−8.33549	−	2.58710i	−0.350367	−	0.108744i
$567$			11.8679i			0.498406i
$568$	−6.96383	−	8.82678i	−0.292196	−	0.370363i
$569$			10.4415i			0.437729i	0.975755	+	0.218864i	$0.0702352\pi$
$569$			10.4415i			0.437729i	−0.975755	+	0.218864i	$0.929765\pi$
$570$	2.14124	+	3.83747i	0.0896865	+	0.160734i
$571$	9.93721			0.415859			0.207930	−	0.978144i	$-0.433327\pi$
$571$	9.93721			0.415859			0.207930	+	0.978144i	$0.433327\pi$
$572$	−19.8045	−	24.6841i	−0.828068	−	1.03209i
$573$		−	17.5749i		−	0.734203i
$574$	2.23216	−	7.19190i	0.0931686	−	0.300184i
$575$	−1.15454	−	23.5466i	−0.0481476	−	0.981963i
$576$	2.25865	−	9.43911i	0.0941105	−	0.393296i
$577$		−	27.4157i		−	1.14133i	−0.821182	−	0.570666i	$-0.806685\pi$
$577$		−	27.4157i		−	1.14133i	0.821182	−	0.570666i	$-0.193315\pi$
$578$	−7.08087	+	22.8142i	−0.294525	+	0.948945i
$579$	11.0026			0.457251
$580$	6.64198	+	31.4699i	0.275793	+	1.30672i
$581$	−12.8528			−0.533224
$582$	8.97909	+	2.78685i	0.372195	+	0.115519i
$583$	8.21043	−	27.2397i	0.340041	−	1.12815i
$584$	−25.8003	+	20.3550i	−1.06762	+	0.842296i
$585$	−8.92488	+	9.37320i	−0.368998	+	0.387534i
$586$	−0.929631	+	2.99522i	−0.0384027	+	0.123731i
$587$	9.60213			0.396322			0.198161	−	0.980169i	$-0.436503\pi$
$587$	9.60213			0.396322			0.198161	+	0.980169i	$0.436503\pi$
$588$	19.8652	+	13.6456i	0.819226	+	0.562737i
$589$		−	6.12365i		−	0.252321i
$590$	0.928970	−	0.518348i	0.0382451	−	0.0213400i
$591$	−37.2848			−1.53369
$592$	19.9347	−	7.66363i	0.819309	−	0.314973i
$593$	−18.8243			−0.773020			−0.386510	−	0.922285i	$-0.626319\pi$
$593$	−18.8243			−0.773020			−0.386510	+	0.922285i	$0.626319\pi$
$594$	−9.62365	+	14.2588i	−0.394863	+	0.585047i
$595$	−0.567614	−	0.540465i	−0.0232699	−	0.0221569i
$596$	8.87791	−	12.9244i	0.363653	−	0.529402i
$597$		−	4.10546i		−	0.168025i
$598$	−9.42997	+	30.3829i	−0.385620	+	1.24245i
$599$		−	28.5808i		−	1.16778i	−0.811832	−	0.583891i	$-0.801530\pi$
$599$		−	28.5808i		−	1.16778i	0.811832	−	0.583891i	$-0.198470\pi$
$600$	−19.0743	−	21.8818i	−0.778704	−	0.893320i
$601$		−	13.7358i		−	0.560295i	−0.959957	−	0.280148i	$-0.909617\pi$
$601$		−	13.7358i		−	0.560295i	0.959957	−	0.280148i	$-0.0903834\pi$
$602$	2.26616	−	7.30145i	0.0923618	−	0.297585i
$603$	−5.72021			−0.232945
$604$	−34.5199	−	23.7122i	−1.40460	−	0.964836i
$605$	23.9801	−	5.47298i	0.974931	−	0.222508i
$606$	−30.7440	−	9.54206i	−1.24889	−	0.387620i
$607$		−	17.9019i		−	0.726617i	−0.931669	−	0.363309i	$-0.881647\pi$
$607$		−	17.9019i		−	0.726617i	0.931669	−	0.363309i	$-0.118353\pi$
$608$	3.82141	−	0.252865i	0.154979	−	0.0102550i
$609$	15.6877			0.635698
$610$	−36.6469	+	20.4483i	−1.48379	+	0.827927i
$611$	7.70505			0.311713
$612$	−0.659662	−	0.453130i	−0.0266652	−	0.0183167i
$613$	−23.6932			−0.956959			−0.478479	−	0.878099i	$-0.658812\pi$
$613$	−23.6932			−0.956959			−0.478479	+	0.878099i	$0.658812\pi$
$614$	19.3560	+	6.00756i	0.781146	+	0.242445i
$615$	−16.6551	−	15.8585i	−0.671600	−	0.639477i
$616$	−3.65330	−	9.27545i	−0.147196	−	0.373719i
$617$			20.8137i			0.837929i	0.908003	+	0.418964i	$0.137607\pi$
$617$			20.8137i			0.837929i	−0.908003	+	0.418964i	$0.862393\pi$
$618$	−3.19211	+	10.2848i	−0.128405	+	0.413715i
$619$			16.6557i			0.669451i	0.942316	+	0.334726i	$0.108644\pi$
$619$			16.6557i			0.669451i	−0.942316	+	0.334726i	$0.891356\pi$
$620$	8.35348	+	39.5790i	0.335484	+	1.58953i
$621$	17.2927			0.693932
$622$	−40.2797	−	12.5017i	−1.61507	−	0.501271i
$623$			8.45328i			0.338673i
$624$	14.0561	+	36.5627i	0.562693	+	1.46368i
$625$	−24.8801	+	2.44572i	−0.995203	+	0.0978287i
$626$	−24.1046	−	7.48136i	−0.963412	−	0.299015i
$627$	4.41283	+	1.33009i	0.176231	+	0.0531187i
$628$	−21.0242	+	30.6068i	−0.838957	+	1.22134i
$629$		−	1.76105i		−	0.0702177i
$630$	−3.56027	+	1.98656i	−0.141845	+	0.0791466i
$631$			9.20565i			0.366471i	0.983069	+	0.183236i	$0.0586571\pi$
$631$			9.20565i			0.366471i	−0.983069	+	0.183236i	$0.941343\pi$
$632$	−14.1028	+	11.1263i	−0.560979	+	0.442581i
$633$	−35.6201			−1.41577
$634$	24.7094	+	7.66909i	0.981336	+	0.304579i
$635$	−10.8368	−	10.3185i	−0.430045	−	0.409475i
$636$	−19.9386	+	29.0263i	−0.790616	+	1.15097i
$637$	−28.0086			−1.10974
$638$	27.9605	+	18.8713i	1.10697	+	0.747121i
$639$			4.82250i			0.190775i
$640$	−24.3540	+	6.84725i	−0.962675	+	0.270661i
$641$	39.7780			1.57114			0.785569	−	0.618774i	$-0.212370\pi$
$641$	39.7780			1.57114			0.785569	+	0.618774i	$0.212370\pi$
$642$	36.7236	+	11.3980i	1.44937	+	0.449842i
$643$	−15.5035			−0.611398			−0.305699	−	0.952128i	$-0.598890\pi$
$643$	−15.5035			−0.611398			−0.305699	+	0.952128i	$0.598890\pi$
$644$	−5.67401	+	8.26015i	−0.223587	+	0.325496i
$645$	−16.9088	−	16.1001i	−0.665784	−	0.633939i
$646$	0.0936083	−	0.301601i	0.00368297	−	0.0118663i
$647$	1.82931			0.0719175			0.0359588	−	0.999353i	$-0.488552\pi$
$647$	1.82931			0.0719175			0.0359588	+	0.999353i	$0.488552\pi$
$648$	24.7986	−	19.5647i	0.974181	−	0.768574i
$649$	0.321987	−	1.06825i	0.0126391	−	0.0419325i
$650$	32.6705	+	8.41011i	1.28144	+	0.329872i
$651$	19.7301			0.773283
$652$	−7.05140	−	4.84370i	−0.276154	−	0.189694i
$653$			7.88753i			0.308663i	0.988019	+	0.154332i	$0.0493224\pi$
$653$			7.88753i			0.308663i	−0.988019	+	0.154332i	$0.950678\pi$
$654$	−28.9475	−	8.98448i	−1.13194	−	0.351321i
$655$	−21.4510	+	22.5286i	−0.838160	+	0.880264i
$656$	−18.7076	+	7.19190i	−0.730409	+	0.280797i
$657$	14.0960			0.549936
$658$	2.31806	+	0.719460i	0.0903675	+	0.0280475i
$659$	20.0616			0.781490			0.390745	−	0.920499i	$-0.372217\pi$
$659$	20.0616			0.781490			0.390745	+	0.920499i	$0.372217\pi$
$660$	−30.3358	−	2.57709i	−1.18082	−	0.100313i
$661$	13.9367			0.542073			0.271037	−	0.962569i	$-0.412634\pi$
$661$	13.9367			0.542073			0.271037	+	0.962569i	$0.412634\pi$
$662$	−29.5228	−	9.16304i	−1.14744	−	0.356132i
$663$	3.22999			0.125442
$664$	21.1883	+	26.8565i	0.822265	+	1.04223i
$665$	−1.16509	−	1.10936i	−0.0451802	−	0.0430192i
$666$	−8.74896	−	2.71543i	−0.339015	−	0.105221i
$667$		−	33.9097i		−	1.31299i
$668$	16.5610	−	24.1094i	0.640766	−	0.932819i
$669$	52.5167			2.03041
$670$	7.26510	+	13.0203i	0.280675	+	0.503019i
$671$	−12.7020	+	42.1414i	−0.490357	+	1.62685i
$672$	0.814717	+	12.3124i	0.0314284	+	0.474960i
$673$	21.1457			0.815109			0.407554	−	0.913181i	$-0.366382\pi$
$673$	21.1457			0.815109			0.407554	+	0.913181i	$0.366382\pi$
$674$	−9.26759	+	29.8597i	−0.356974	+	1.15015i
$675$	−0.898070	−	18.3160i	−0.0345667	−	0.704984i
$676$	−16.0928	−	11.0544i	−0.618954	−	0.425168i
$677$	23.2804			0.894737			0.447368	−	0.894350i	$-0.352361\pi$
$677$	23.2804			0.894737			0.447368	+	0.894350i	$0.352361\pi$
$678$	−34.7551	−	10.7870i	−1.33476	−	0.414272i
$679$	−3.44185			−0.132086
$680$	−0.193594	+	2.07703i	−0.00742400	+	0.0796505i
$681$			19.3944i			0.743195i
$682$	35.1653	+	23.7340i	1.34655	+	0.908821i
$683$	−37.8077			−1.44667			−0.723336	−	0.690496i	$-0.757392\pi$
$683$	−37.8077			−1.44667			−0.723336	+	0.690496i	$0.757392\pi$
$684$	−1.35403	−	0.930099i	−0.0517725	−	0.0355632i
$685$	1.11820	+	1.06471i	0.0427241	+	0.0406805i
$686$	−18.4738	−	5.73372i	−0.705331	−	0.218915i
$687$	−47.8108			−1.82409
$688$	−18.9926	+	7.30145i	−0.724084	+	0.278365i
$689$		−	40.9253i		−	1.55913i
$690$	14.9124	+	26.7256i	0.567705	+	1.01743i
$691$			28.9749i			1.10226i	0.834421	+	0.551128i	$0.185802\pi$
$691$			28.9749i			1.10226i	−0.834421	+	0.551128i	$0.814198\pi$
$692$	10.8612	+	7.46071i	0.412881	+	0.283614i
$693$	−1.23401	+	4.09407i	−0.0468762	+	0.155521i
$694$	−7.63256	−	2.36893i	−0.289728	−	0.0899233i
$695$	−24.8929	+	26.1433i	−0.944240	+	0.991672i
$696$	−25.8617	−	32.7802i	−0.980286	−	1.24253i
$697$			1.65265i			0.0625986i
$698$	−1.44284	−	0.447816i	−0.0546122	−	0.0169501i
$699$	−25.3473			−0.958723
$700$	9.04363	+	5.58080i	0.341817	+	0.210934i
$701$			23.0642i			0.871123i	0.900159	+	0.435562i	$0.143450\pi$
$701$			23.0642i			0.871123i	−0.900159	+	0.435562i	$0.856550\pi$
$702$	−7.33521	+	23.6336i	−0.276850	+	0.891994i
$703$		−	3.61474i		−	0.136333i
$704$	−13.3589	+	22.9247i	−0.503482	+	0.864006i
$705$	5.11144	−	5.36821i	0.192508	−	0.202178i
$706$	−18.7975	−	5.83419i	−0.707451	−	0.219573i
$707$	11.7847			0.443211
$708$	−0.781926	+	1.13832i	−0.0293866	+	0.0427806i
$709$	−28.0135			−1.05207			−0.526035	−	0.850463i	$-0.676322\pi$
$709$	−28.0135			−1.05207			−0.526035	+	0.850463i	$0.676322\pi$
$710$	10.9770	−	6.12494i	0.411958	−	0.229865i
$711$	7.70505			0.288962
$712$	17.6635	−	13.9355i	0.661968	−	0.522256i
$713$		−	42.6475i		−	1.59716i
$714$	0.971742	+	0.301601i	0.0363665	+	0.0112871i
$715$	30.7555	−	17.4929i	1.15019	−	0.654196i
$716$	19.9545	−	29.0496i	0.745736	−	1.08563i
$717$	−39.1085			−1.46053
$718$	8.86236	−	28.5540i	0.330740	−	1.06563i
$719$		−	2.99823i		−	0.111815i	−0.998436	−	0.0559075i	$-0.982195\pi$
$719$		−	2.99823i		−	0.111815i	0.998436	−	0.0559075i	$-0.0178052\pi$
$720$	10.0203	+	4.16443i	0.373433	+	0.155199i
$721$		−	3.94235i		−	0.146821i
$722$	−7.77274	+	25.0434i	−0.289272	+	0.932018i
$723$			53.6167i			1.99403i
$724$	0.380943	+	0.261675i	0.0141576	+	0.00972506i
$725$	−35.9164	+	1.76105i	−1.33390	+	0.0654038i
$726$	−24.7413	+	20.1857i	−0.918235	+	0.749162i
$727$	45.5805			1.69049			0.845244	−	0.534380i	$-0.179455\pi$
$727$	45.5805			1.69049			0.845244	+	0.534380i	$0.179455\pi$
$728$	−8.88222	−	11.2584i	−0.329197	−	0.417263i
$729$	9.03576			0.334658
$730$	−17.9029	−	32.0852i	−0.662618	−	1.18753i
$731$			1.67782i			0.0620565i
$732$	30.8462	−	44.9055i	1.14011	−	1.65976i
$733$	45.9346			1.69663			0.848317	−	0.529489i	$-0.177616\pi$
$733$	45.9346			1.69663			0.848317	+	0.529489i	$0.177616\pi$
$734$	8.12644	−	26.1830i	0.299953	−	0.966431i
$735$	−18.5806	+	19.5140i	−0.685357	+	0.719784i
$736$	26.6138	−	1.76105i	0.980997	−	0.0649132i
$737$	14.9725	+	4.51293i	0.551519	+	0.166236i
$738$	8.21043	+	2.54828i	0.302230	+	0.0938036i
$739$	5.52967			0.203412			0.101706	−	0.994814i	$-0.467570\pi$
$739$	5.52967			0.203412			0.101706	+	0.994814i	$0.467570\pi$
$740$	4.93099	+	23.3632i	0.181267	+	0.858847i
$741$	6.62990			0.243556
$742$	3.82141	−	12.3124i	0.140288	−	0.452002i
$743$		−	34.4520i		−	1.26392i	−0.775001	−	0.631960i	$-0.782251\pi$
$743$		−	34.4520i		−	1.26392i	0.775001	−	0.631960i	$-0.217749\pi$
$744$	−32.5257	−	41.2269i	−1.19245	−	1.51145i
$745$	12.6959	+	12.0886i	0.465141	+	0.442893i
$746$	−0.0410749	+	0.132341i	−0.00150386	+	0.00484536i
$747$		−	14.6730i		−	0.536858i
$748$	1.36915	+	1.70649i	0.0500611	+	0.0623955i
$749$	−14.0768			−0.514356
$750$	27.5327	−	17.1828i	1.00535	−	0.627428i
$751$			19.1741i			0.699674i	0.936811	+	0.349837i	$0.113763\pi$
$751$			19.1741i			0.699674i	−0.936811	+	0.349837i	$0.886237\pi$
$752$	−2.31806	−	6.02976i	−0.0845311	−	0.219883i
$753$		−	11.4269i		−	0.416420i
$754$	46.3439	+	14.3838i	1.68774	+	0.523827i
$755$	32.2878	−	33.9097i	1.17507	−	1.23410i
$756$	−4.41359	+	6.42525i	−0.160521	+	0.233684i
$757$			14.3941i			0.523161i	0.965182	+	0.261581i	$0.0842437\pi$
$757$			14.3941i			0.523161i	−0.965182	+	0.261581i	$0.915756\pi$
$758$	48.0172	+	14.9032i	1.74406	+	0.541308i
$759$	30.7326	+	9.26327i	1.11552	+	0.336235i
$760$	−0.397373	+	4.26333i	−0.0144142	+	0.154647i
$761$			9.79345i			0.355012i	0.984120	+	0.177506i	$0.0568030\pi$
$761$			9.79345i			0.355012i	−0.984120	+	0.177506i	$0.943197\pi$
$762$	18.5523	+	5.75811i	0.672080	+	0.208594i
$763$	11.0961			0.401706
$764$	9.69589	−	14.1152i	0.350785	−	0.510669i
$765$	0.617006	−	0.648000i	0.0223079	−	0.0234285i
$766$	−5.56273	+	17.9228i	−0.200990	+	0.647578i
$767$		−	1.60496i		−	0.0579517i
$768$	24.3842	−	21.9998i	0.879889	−	0.793848i
$769$			35.4945i			1.27996i	0.768390	+	0.639982i	$0.221058\pi$
$769$			35.4945i			1.27996i	−0.768390	+	0.639982i	$0.778942\pi$
$770$	10.8862	−	2.39092i	0.392311	−	0.0861628i
$771$		−	13.8535i		−	0.498921i
$772$	8.83662	+	6.06999i	0.318037	+	0.218464i
$773$		−	35.9272i		−	1.29221i	−0.763247	−	0.646107i	$-0.776396\pi$
$773$		−	35.9272i		−	1.29221i	0.763247	−	0.646107i	$-0.223604\pi$
$774$	8.33549	+	2.58710i	0.299613	+	0.0929913i
$775$	−45.1712	+	2.21483i	−1.62260	+	0.0795592i
$776$	5.67401	+	7.19190i	0.203685	+	0.258174i
$777$	11.6465			0.417816
$778$	10.0666	−	32.4339i	0.360904	−	1.16281i
$779$			3.39224i			0.121540i
$780$	−42.8510	+	9.04407i	−1.53431	+	0.323830i
$781$	3.80468	−	12.6228i	0.136142	−	0.451678i
$782$	0.651925	−	2.10047i	0.0233128	−	0.0751125i
$783$		−	26.3770i		−	0.942639i
$784$	8.42640	+	21.9188i	0.300943	+	0.782814i
$785$	−30.0657	−	28.6276i	−1.07309	−	1.02176i
$786$	11.9705	−	38.5684i	0.426974	−	1.37569i
$787$			53.0554i			1.89122i	0.325299	+	0.945611i	$0.394535\pi$
$787$			53.0554i			1.89122i	−0.325299	+	0.945611i	$0.605465\pi$
$788$	−29.9450	−	20.5696i	−1.06675	−	0.732762i
$789$		−	7.83990i		−	0.279108i
$790$	−9.78600	−	17.5382i	−0.348170	−	0.623982i
$791$	13.3223			0.473686
$792$	10.5891	−	4.17069i	0.376266	−	0.148199i
$793$			63.3140i			2.24835i
$794$	5.67401	+	1.76105i	0.201363	+	0.0624973i
$795$	−28.5132	−	27.1494i	−1.01126	−	0.962890i
$796$	2.26494	−	3.29727i	0.0802785	−	0.116869i
$797$			41.4802i			1.46930i	0.678444	+	0.734652i	$0.262655\pi$
$797$			41.4802i			1.46930i	−0.678444	+	0.734652i	$0.737345\pi$
$798$	1.99461	+	0.619068i	0.0706083	+	0.0219148i
$799$	−0.532675			−0.0188447
$800$	−3.24741	−	28.0972i	−0.114813	−	0.993387i
$801$	−9.65044			−0.340982
$802$	−4.86143	+	15.6633i	−0.171663	+	0.553089i
$803$	−36.8958	−	11.1209i	−1.30202	−	0.392449i
$804$	−15.9545	−	10.9594i	−0.562673	−	0.386508i
$805$	−8.11413	−	7.72603i	−0.285986	−	0.272307i
$806$	58.2857	+	18.0902i	2.05302	+	0.637200i
$807$	−9.77428			−0.344071
$808$	−19.4276	−	24.6248i	−0.683459	−	0.866296i
$809$		−	1.06825i		−	0.0375577i	−0.999824	−	0.0187789i	$-0.994022\pi$
$809$		−	1.06825i		−	0.0375577i	0.999824	−	0.0187789i	$-0.00597785\pi$
$810$	17.2079	+	30.8395i	0.604623	+	1.08359i
$811$	14.1129			0.495569			0.247785	−	0.968815i	$-0.420297\pi$
$811$	14.1129			0.495569			0.247785	+	0.968815i	$0.420297\pi$
$812$	12.5995	+	8.65473i	0.442154	+	0.303722i
$813$	30.3578			1.06469
$814$	20.7578	+	14.0100i	0.727562	+	0.491050i
$815$	6.59544	−	6.92675i	0.231028	−	0.242633i
$816$	−0.971742	−	2.52770i	−0.0340178	−	0.0884872i
$817$			3.44391i			0.120487i
$818$	−33.5304	−	10.4069i	−1.17236	−	0.363867i
$819$			6.15100i			0.214933i
$820$	−4.62747	−	21.9251i	−0.161598	−	0.765657i
$821$		−	29.1879i		−	1.01866i	−0.860570	−	0.509332i	$-0.829893\pi$
$821$		−	29.1879i		−	1.01866i	0.860570	−	0.509332i	$-0.170107\pi$
$822$	−1.91433	−	0.594152i	−0.0667698	−	0.0207234i
$823$	20.2606			0.706241			0.353120	−	0.935578i	$-0.385121\pi$
$823$	20.2606			0.706241			0.353120	+	0.935578i	$0.385121\pi$
$824$	−8.23772	+	6.49910i	−0.286975	+	0.226407i
$825$	8.21538	−	33.0324i	0.286023	−	1.15004i
$826$	0.149863	−	0.482852i	0.00521441	−	0.0168006i
$827$			18.5380i			0.644629i	0.946633	+	0.322315i	$0.104461\pi$
$827$			18.5380i			0.644629i	−0.946633	+	0.322315i	$0.895539\pi$
$828$	−9.42997	−	6.47757i	−0.327714	−	0.225111i
$829$	2.86630			0.0995506			0.0497753	−	0.998760i	$-0.484149\pi$
$829$	2.86630			0.0995506			0.0497753	+	0.998760i	$0.484149\pi$
$830$	−33.3987	+	18.6359i	−1.15929	+	0.646860i
$831$	−60.9326			−2.11373
$832$	−8.88222	+	37.1196i	−0.307936	+	1.28689i
$833$	1.93633			0.0670898
$834$	13.8912	−	44.7567i	0.481013	−	1.54980i
$835$	23.6832	+	22.5504i	0.819590	+	0.780388i
$836$	2.81033	+	3.50276i	0.0971973	+	0.121145i
$837$		−	33.1738i		−	1.14666i
$838$	26.4679	+	8.21488i	0.914319	+	0.283778i
$839$		−	8.40169i		−	0.290059i	−0.989427	−	0.145029i	$-0.953672\pi$
$839$		−	8.40169i		−	0.290059i	0.989427	−	0.145029i	$-0.0463276\pi$
$840$	−13.7362	−	1.28031i	−0.473945	−	0.0441751i
$841$	−22.7235			−0.783568
$842$	−3.60270	+	11.6077i	−0.124157	+	0.400028i
$843$			37.4325i			1.28924i
$844$	−28.6080	−	19.6512i	−0.984728	−	0.676423i
$845$	15.0522	−	15.8083i	0.517812	−	0.543823i
$846$	−0.821351	+	2.64635i	−0.0282386	+	0.0909834i
$847$	6.45998	−	9.74254i	0.221968	−	0.334758i
$848$	−32.0270	+	12.3124i	−1.09981	+	0.422809i
$849$			12.6676i			0.434749i
$850$	−2.25862	−	0.581419i	−0.0774701	−	0.0199425i
$851$		−	25.1745i		−	0.862970i
$852$	−9.23946	+	13.4507i	−0.316539	+	0.460813i
$853$	21.1398			0.723815			0.361907	−	0.932214i	$-0.382126\pi$
$853$	21.1398			0.723815			0.361907	+	0.932214i	$0.382126\pi$
$854$	−5.91196	+	19.0480i	−0.202303	+	0.651809i
$855$	1.26647	−	1.33009i	0.0433124	−	0.0454881i
$856$	23.2062	+	29.4142i	0.793170	+	1.00536i
$857$	−43.1494			−1.47396			−0.736978	−	0.675916i	$-0.763748\pi$
$857$	−43.1494			−1.47396			−0.736978	+	0.675916i	$0.763748\pi$
$858$	−25.6961	+	38.0725i	−0.877251	+	1.29977i
$859$		−	36.5279i		−	1.24632i	−0.782096	−	0.623158i	$-0.785849\pi$
$859$		−	36.5279i		−	1.24632i	0.782096	−	0.623158i	$-0.214151\pi$
$860$	−4.69796	−	22.2590i	−0.160199	−	0.759027i
$861$	−10.9296			−0.372481
$862$	−7.11191	+	22.9142i	−0.242232	+	0.780460i
$863$	39.7815			1.35418			0.677089	−	0.735902i	$-0.263241\pi$
$863$	39.7815			1.35418			0.677089	+	0.735902i	$0.263241\pi$
$864$	20.7018	−	1.36985i	0.704290	−	0.0466033i
$865$	−10.1589	+	10.6692i	−0.345413	+	0.362764i
$866$	5.10828	+	1.58546i	0.173586	+	0.0538762i
$867$	34.6710			1.17749
$868$	15.8461	+	10.8849i	0.537850	+	0.369456i
$869$	−20.1677	−	6.07885i	−0.684144	−	0.206211i
$870$	40.7654	−	22.7463i	1.38208	−	0.771172i
$871$	22.4949			0.762211
$872$	−18.2923	−	23.1858i	−0.619456	−	0.785171i
$873$		−	3.92929i		−	0.132986i
$874$	1.33815	−	4.31143i	0.0452634	−	0.145836i
$875$	−7.76183	+	8.99554i	−0.262398	+	0.304105i
$876$	39.3158	+	27.0066i	1.32836	+	0.912467i
$877$	8.83957			0.298491			0.149245	−	0.988800i	$-0.452316\pi$
$877$	8.83957			0.298491			0.149245	+	0.988800i	$0.452316\pi$
$878$	7.64282	−	24.6248i	0.257933	−	0.831045i
$879$	4.55188			0.153531
$880$	−22.9422	−	18.8057i	−0.773382	−	0.633940i
$881$	7.37829			0.248581			0.124290	−	0.992246i	$-0.460335\pi$
$881$	7.37829			0.248581			0.124290	+	0.992246i	$0.460335\pi$
$882$	2.98570	−	9.61975i	0.100534	−	0.323914i
$883$	51.9581			1.74853			0.874265	−	0.485449i	$-0.161344\pi$
$883$	51.9581			1.74853			0.874265	+	0.485449i	$0.161344\pi$
$884$	2.59414	+	1.78195i	0.0872504	+	0.0599335i
$885$	−1.11820	−	1.06471i	−0.0375877	−	0.0357899i
$886$	11.5683	−	37.2724i	0.388644	−	1.25219i
$887$		−	15.2608i		−	0.512406i	−0.966623	−	0.256203i	$-0.917528\pi$
$887$		−	15.2608i		−	0.512406i	0.966623	−	0.256203i	$-0.0824716\pi$
$888$	−19.1997	−	24.3359i	−0.644299	−	0.816660i
$889$	−7.11144			−0.238510
$890$	12.2568	+	21.9663i	0.410849	+	0.736313i
$891$	35.4633	+	10.6892i	1.18807	+	0.358100i
$892$	42.1784	+	28.9729i	1.41224	+	0.970084i
$893$	−1.09337			−0.0365883
$894$	−21.7351	−	6.74594i	−0.726929	−	0.225618i
$895$	28.5361	+	27.1712i	0.953855	+	0.908232i
$896$	−6.13827	+	10.3381i	−0.205065	+	0.345370i
$897$	46.1732			1.54168
$898$	1.06093	−	3.41824i	0.0354035	−	0.114068i
$899$	−65.0515			−2.16959
$900$	−6.37116	+	10.3244i	−0.212372	+	0.344147i
$901$			2.82930i			0.0942577i
$902$	−19.4801	−	13.1476i	−0.648617	−	0.437768i
$903$	−11.0961			−0.369255
$904$	−21.9622	−	27.8375i	−0.730453	−	0.925862i
$905$	−0.356310	+	0.374209i	−0.0118441	+	0.0124391i
$906$	−18.0179	+	58.0527i	−0.598604	+	1.92867i
$907$	12.1435			0.403218			0.201609	−	0.979466i	$-0.435383\pi$
$907$	12.1435			0.403218			0.201609	+	0.979466i	$0.435383\pi$
$908$	−10.6997	+	15.5765i	−0.355081	+	0.516923i
$909$			13.4537i			0.446231i
$910$	14.0009	−	7.81223i	0.464125	−	0.258973i
$911$		−	30.3628i		−	1.00596i	−0.864297	−	0.502982i	$-0.832236\pi$
$911$		−	30.3628i		−	1.00596i	0.864297	−	0.502982i	$-0.167764\pi$
$912$	−1.99461	−	5.18838i	−0.0660480	−	0.171804i
$913$	−11.5762	+	38.4062i	−0.383116	+	1.27106i
$914$	−3.49429	+	11.2584i	−0.115581	+	0.372396i
$915$	44.1117	+	42.0018i	1.45829	+	1.38854i
$916$	−38.3988	−	26.3767i	−1.26873	−	0.871509i
$917$			14.7840i			0.488209i
$918$	0.507107	−	1.63387i	0.0167370	−	0.0539258i
$919$	−30.5315			−1.00714			−0.503571	−	0.863954i	$-0.667981\pi$
$919$	−30.5315			−1.00714			−0.503571	+	0.863954i	$0.667981\pi$
$920$	−2.76746	+	29.6915i	−0.0912405	+	0.978899i
$921$		−	29.4156i		−	0.969277i
$922$	−26.1346	−	8.11144i	−0.860698	−	0.267136i
$923$		−	18.9646i		−	0.624229i
$924$	−11.2857	+	9.05473i	−0.371272	+	0.297879i
$925$	−26.6642	+	1.30740i	−0.876714	+	0.0429870i
$926$	−1.50065	+	4.83501i	−0.0493144	+	0.158888i
$927$	4.50067			0.147821
$928$	−2.68618	−	40.5948i	−0.0881782	−	1.33259i
$929$	28.4854			0.934574			0.467287	−	0.884106i	$-0.345231\pi$
$929$	28.4854			0.934574			0.467287	+	0.884106i	$0.345231\pi$
$930$	51.2697	−	28.6075i	1.68120	−	0.938078i
$931$	3.97452			0.130260
$932$	−20.3575	−	13.9838i	−0.666832	−	0.458055i
$933$			61.2135i			2.00404i
$934$	7.04571	−	22.7009i	0.230543	−	0.742796i
$935$	−2.12623	+	1.20934i	−0.0695352	+	0.0395496i
$936$	12.8528	−	10.1401i	0.420107	−	0.331441i
$937$	−20.6417			−0.674335			−0.337168	−	0.941445i	$-0.609469\pi$
$937$	−20.6417			−0.674335			−0.337168	+	0.941445i	$0.609469\pi$
$938$	6.76759	+	2.10047i	0.220970	+	0.0685827i
$939$			36.6320i			1.19544i
$940$	7.06680	−	1.49151i	0.230493	−	0.0486476i
$941$			35.0294i			1.14193i	0.820976	+	0.570963i	$0.193430\pi$
$941$			35.0294i			1.14193i	−0.820976	+	0.570963i	$0.806570\pi$
$942$	51.4718	+	15.9754i	1.67704	+	0.520506i
$943$			23.6249i			0.769333i
$944$	−1.25600	+	0.482852i	−0.0408792	+	0.0157155i
$945$	−6.31167	−	6.00978i	−0.205319	−	0.195498i
$946$	−19.7768	−	13.3479i	−0.643000	−	0.433977i
$947$	5.36691			0.174401			0.0872006	−	0.996191i	$-0.472208\pi$
$947$	5.36691			0.174401			0.0872006	+	0.996191i	$0.472208\pi$
$948$	21.4906	+	14.7622i	0.697981	+	0.479453i
$949$	−55.4329			−1.79943
$950$	−4.63606	−	1.19342i	−0.150414	−	0.0387198i
$951$		−	37.5512i		−	1.21768i
$952$	0.614057	+	0.778328i	0.0199017	+	0.0252257i
$953$	−6.71404			−0.217489			−0.108745	−	0.994070i	$-0.534683\pi$
$953$	−6.71404			−0.217489			−0.108745	+	0.994070i	$0.534683\pi$
$954$	14.0561	+	4.36260i	0.455082	+	0.141244i
$955$	13.8656	+	13.2024i	0.448682	+	0.427221i
$956$	−31.4097	−	21.5757i	−1.01586	−	0.697808i
$957$	14.1295	−	46.8774i	0.456743	−	1.51533i
$958$	10.5652	−	34.0405i	0.341346	−	1.09980i
$959$	0.733796			0.0236955
$960$	19.9694	+	30.8131i	0.644509	+	0.994489i
$961$	−50.8138			−1.63916
$962$	34.4056	+	10.6785i	1.10928	+	0.344289i
$963$		−	16.0704i		−	0.517862i
$964$	−29.5797	+	43.0618i	−0.952699	+	1.38693i
$965$	−8.26522	+	8.68041i	−0.266067	+	0.279432i
$966$	13.8912	+	4.31143i	0.446942	+	0.138718i
$967$		−	26.5818i		−	0.854813i	−0.904060	−	0.427406i	$-0.859427\pi$
$967$		−	26.5818i		−	0.854813i	0.904060	−	0.427406i	$-0.140573\pi$
$968$	−31.0070	+	2.56249i	−0.996603	+	0.0823615i
$969$	−0.458347			−0.0147242
$970$	−8.94384	+	4.99049i	−0.287169	+	0.160235i
$971$			19.4034i			0.622685i	0.950298	+	0.311342i	$0.100779\pi$
$971$			19.4034i			0.622685i	−0.950298	+	0.311342i	$0.899221\pi$
$972$	−19.6509	−	13.4984i	−0.630301	−	0.432962i
$973$			17.1561i			0.549999i
$974$	−8.63768	+	27.8301i	−0.276769	+	0.891736i
$975$	−2.39794	−	48.9056i	−0.0767955	−	1.56623i
$976$	49.5478	−	19.0480i	1.58599	−	0.609712i
$977$			27.6874i			0.885797i	0.896572	+	0.442899i	$0.146050\pi$
$977$			27.6874i			0.885797i	−0.896572	+	0.442899i	$0.853950\pi$
$978$	−3.68052	+	11.8584i	−0.117690	+	0.379191i
$979$	25.2598	+	7.61366i	0.807305	+	0.243334i
$980$	−25.6885	+	5.42178i	−0.820590	+	0.173192i
$981$			12.6676i			0.404444i
$982$	3.03049	−	9.76409i	0.0967070	−	0.311585i
$983$	−52.2271			−1.66579			−0.832893	−	0.553434i	$-0.813317\pi$
$983$	−52.2271			−1.66579			−0.832893	+	0.553434i	$0.813317\pi$
$984$	18.0179	+	22.8380i	0.574389	+	0.728048i
$985$	28.0086	−	29.4156i	0.892430	−	0.937259i
$986$	−3.20390	−	0.994400i	−0.102033	−	0.0316681i
$987$		−	3.52279i		−	0.112132i
$988$	5.32475	+	3.65764i	0.169403	+	0.116365i
$989$			23.9848i			0.762671i
$990$	2.72953	+	12.4279i	0.0867500	+	0.394985i
$991$			15.7678i			0.500880i	0.968132	+	0.250440i	$0.0805753\pi$
$991$			15.7678i			0.500880i	−0.968132	+	0.250440i	$0.919425\pi$
$992$	−3.37835	−	51.0552i	−0.107263	−	1.62100i
$993$			44.8662i			1.42379i
$994$	1.77083	−	5.70551i	0.0561672	−	0.180968i
$995$	3.23898	+	3.08406i	0.102683	+	0.0977711i
$996$	28.1121	−	40.9253i	0.890767	−	1.29677i
$997$	32.2179			1.02035			0.510176	−	0.860070i	$-0.329580\pi$
$997$	32.2179			1.02035			0.510176	+	0.860070i	$0.329580\pi$
$998$	−42.4299	−	13.1690i	−1.34309	−	0.416858i
$999$		−	19.5823i		−	0.619555i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.g.b.219.13	yes	24
4.3	odd	2	inner	220.2.g.b.219.16	yes	24
5.4	even	2	inner	220.2.g.b.219.12	yes	24
11.10	odd	2	inner	220.2.g.b.219.11	yes	24
20.19	odd	2	inner	220.2.g.b.219.9	✓	24
44.43	even	2	inner	220.2.g.b.219.10	yes	24
55.54	odd	2	inner	220.2.g.b.219.14	yes	24
220.219	even	2	inner	220.2.g.b.219.15	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.g.b.219.9	✓	24	20.19	odd	2	inner
220.2.g.b.219.10	yes	24	44.43	even	2	inner
220.2.g.b.219.11	yes	24	11.10	odd	2	inner
220.2.g.b.219.12	yes	24	5.4	even	2	inner
220.2.g.b.219.13	yes	24	1.1	even	1	trivial
220.2.g.b.219.14	yes	24	55.54	odd	2	inner
220.2.g.b.219.15	yes	24	220.219	even	2	inner
220.2.g.b.219.16	yes	24	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.419204 - 1.35065i) q^{2} -2.05261 q^{3} +(-1.64854 - 1.13240i) q^{4} +(1.54194 - 1.61939i) q^{5} +(-0.860462 + 2.77236i) q^{6} -1.06270i q^{7} +(-2.22056 + 1.75189i) q^{8} +1.21320 q^{9} +(-1.54085 - 2.76148i) q^{10} +(-3.17551 - 0.957146i) q^{11} +(3.38380 + 2.32437i) q^{12} -4.77094 q^{13} +(-1.43534 - 0.445487i) q^{14} +(-3.16499 + 3.32398i) q^{15} +(1.43534 + 3.73361i) q^{16} +0.329831 q^{17} +(0.508578 - 1.63861i) q^{18} +0.677013 q^{19} +(-4.37574 + 0.923536i) q^{20} +2.18130i q^{21} +(-2.62396 + 3.88778i) q^{22} +4.71498 q^{23} +(4.55793 - 3.59595i) q^{24} +(-0.244866 - 4.99400i) q^{25} +(-2.00000 + 6.44389i) q^{26} +3.66760 q^{27} +(-1.20340 + 1.75189i) q^{28} -7.19190i q^{29} +(3.16277 + 5.66823i) q^{30} -9.04510i q^{31} +(5.64451 - 0.373501i) q^{32} +(6.51808 + 1.96464i) q^{33} +(0.138267 - 0.445487i) q^{34} +(-1.72092 - 1.63861i) q^{35} +(-2.00000 - 1.37383i) q^{36} -5.33925i q^{37} +(0.283807 - 0.914411i) q^{38} +9.79287 q^{39} +(-0.586950 + 6.29726i) q^{40} +5.01060i q^{41} +(2.94618 + 0.914411i) q^{42} +5.08692i q^{43} +(4.15107 + 5.17384i) q^{44} +(1.87067 - 1.96464i) q^{45} +(1.97654 - 6.36832i) q^{46} -1.61500 q^{47} +(-2.94618 - 7.66363i) q^{48} +5.87067 q^{49} +(-6.84782 - 1.76278i) q^{50} -0.677013 q^{51} +(7.86507 + 5.40262i) q^{52} +8.57804i q^{53} +(1.53748 - 4.95366i) q^{54} +(-6.44643 + 3.66654i) q^{55} +(1.86173 + 2.35978i) q^{56} -1.38964 q^{57} +(-9.71378 - 3.01488i) q^{58} +0.336403i q^{59} +(8.98167 - 1.89566i) q^{60} -13.2708i q^{61} +(-12.2168 - 3.79175i) q^{62} -1.28926i q^{63} +(1.86173 - 7.78036i) q^{64} +(-7.35649 + 7.72603i) q^{65} +(5.38596 - 7.98009i) q^{66} -4.71498 q^{67} +(-0.543738 - 0.373501i) q^{68} -9.67801 q^{69} +(-2.93462 + 1.63746i) q^{70} +3.97503i q^{71} +(-2.69397 + 2.12539i) q^{72} +11.6189 q^{73} +(-7.21148 - 2.23824i) q^{74} +(0.502613 + 10.2507i) q^{75} +(-1.11608 - 0.766650i) q^{76} +(-1.01716 + 3.37461i) q^{77} +(4.10522 - 13.2268i) q^{78} +6.35102 q^{79} +(8.25937 + 3.43261i) q^{80} -11.1677 q^{81} +(6.76759 + 2.10047i) q^{82} -12.0945i q^{83} +(2.47011 - 3.59595i) q^{84} +(0.508578 - 0.534126i) q^{85} +(6.87067 + 2.13246i) q^{86} +14.7622i q^{87} +(8.72822 - 3.43777i) q^{88} -7.95455 q^{89} +(-1.86936 - 3.35022i) q^{90} +5.07007i q^{91} +(-7.77282 - 5.33925i) q^{92} +18.5660i q^{93} +(-0.677013 + 2.18130i) q^{94} +(1.04391 - 1.09635i) q^{95} +(-11.5860 + 0.766650i) q^{96} -3.23879i q^{97} +(2.46101 - 7.92925i) q^{98} +(-3.85252 - 1.16121i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{4} - 4 q^{5} + 40 q^{9} + 12 q^{14} - 12 q^{16} - 20 q^{20} - 36 q^{25} - 48 q^{26} + 28 q^{34} - 48 q^{36} + 56 q^{44} - 48 q^{45} + 48 q^{49} + 20 q^{56} - 8 q^{60} + 20 q^{64} - 52 q^{66}+ \cdots - 16 q^{89}+O(q^{100}) \) 24 * q - 4 * q^4 - 4 * q^5 + 40 * q^9 + 12 * q^14 - 12 * q^16 - 20 * q^20 - 36 * q^25 - 48 * q^26 + 28 * q^34 - 48 * q^36 + 56 * q^44 - 48 * q^45 + 48 * q^49 + 20 * q^56 - 8 * q^60 + 20 * q^64 - 52 * q^66 - 8 * q^69 - 64 * q^70 + 64 * q^80 - 104 * q^81 + 72 * q^86 - 16 * q^89

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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