LMFDB - Embedded newform 572.2.e.b.131.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(131,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("572.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.e (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			131.18
Character	$\chi$	$=$	572.131
Dual form			572.2.e.b.131.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.936395 + 1.05979i) q^{2} -2.78715i q^{3} +(-0.246329 - 1.98477i) q^{4} +1.09997 q^{5} +(2.95381 + 2.60987i) q^{6} -3.18482 q^{7} +(2.33411 + 1.59747i) q^{8} -4.76820 q^{9} +O(q^{10})$	\(q+(-0.936395 + 1.05979i) q^{2} -2.78715i q^{3} +(-0.246329 - 1.98477i) q^{4} +1.09997 q^{5} +(2.95381 + 2.60987i) q^{6} -3.18482 q^{7} +(2.33411 + 1.59747i) q^{8} -4.76820 q^{9} +(-1.03001 + 1.16575i) q^{10} +(-3.20589 - 0.849864i) q^{11} +(-5.53186 + 0.686556i) q^{12} -1.00000i q^{13} +(2.98224 - 3.37525i) q^{14} -3.06579i q^{15} +(-3.87864 + 0.977815i) q^{16} -0.404034i q^{17} +(4.46492 - 5.05332i) q^{18} +0.124854 q^{19} +(-0.270955 - 2.18320i) q^{20} +8.87656i q^{21} +(3.90266 - 2.60178i) q^{22} +4.72467i q^{23} +(4.45240 - 6.50552i) q^{24} -3.79006 q^{25} +(1.05979 + 0.936395i) q^{26} +4.92825i q^{27} +(0.784513 + 6.32113i) q^{28} -9.08186i q^{29} +(3.24911 + 2.87079i) q^{30} +10.4536i q^{31} +(2.59566 - 5.02619i) q^{32} +(-2.36870 + 8.93530i) q^{33} +(0.428193 + 0.378335i) q^{34} -3.50321 q^{35} +(1.17455 + 9.46380i) q^{36} +2.86681 q^{37} +(-0.116912 + 0.132319i) q^{38} -2.78715 q^{39} +(2.56746 + 1.75718i) q^{40} +3.30715i q^{41} +(-9.40733 - 8.31196i) q^{42} -7.57237 q^{43} +(-0.897081 + 6.57231i) q^{44} -5.24490 q^{45} +(-5.00718 - 4.42416i) q^{46} +4.17057i q^{47} +(2.72532 + 10.8104i) q^{48} +3.14305 q^{49} +(3.54899 - 4.01668i) q^{50} -1.12610 q^{51} +(-1.98477 + 0.246329i) q^{52} -11.5475 q^{53} +(-5.22293 - 4.61479i) q^{54} +(-3.52639 - 0.934827i) q^{55} +(-7.43372 - 5.08765i) q^{56} -0.347986i q^{57} +(9.62491 + 8.50421i) q^{58} -6.68623i q^{59} +(-6.08489 + 0.755193i) q^{60} +1.02508i q^{61} +(-11.0786 - 9.78866i) q^{62} +15.1859 q^{63} +(2.89616 + 7.45736i) q^{64} -1.09997i q^{65} +(-7.25154 - 10.8773i) q^{66} -11.3802i q^{67} +(-0.801915 + 0.0995253i) q^{68} +13.1684 q^{69} +(3.28039 - 3.71268i) q^{70} -12.4986i q^{71} +(-11.1295 - 7.61708i) q^{72} +2.91778i q^{73} +(-2.68447 + 3.03823i) q^{74} +10.5635i q^{75} +(-0.0307551 - 0.247806i) q^{76} +(10.2102 + 2.70666i) q^{77} +(2.60987 - 2.95381i) q^{78} +10.8405 q^{79} +(-4.26640 + 1.07557i) q^{80} -0.568841 q^{81} +(-3.50490 - 3.09680i) q^{82} +3.91349 q^{83} +(17.6179 - 2.18656i) q^{84} -0.444426i q^{85} +(7.09073 - 8.02516i) q^{86} -25.3125 q^{87} +(-6.12528 - 7.10500i) q^{88} -4.50758 q^{89} +(4.91129 - 5.55851i) q^{90} +3.18482i q^{91} +(9.37739 - 1.16382i) q^{92} +29.1356 q^{93} +(-4.41995 - 3.90530i) q^{94} +0.137336 q^{95} +(-14.0087 - 7.23449i) q^{96} +3.28224 q^{97} +(-2.94314 + 3.33099i) q^{98} +(15.2863 + 4.05232i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9}+O(q^{10}) $ 64 * q + 6 * q^4 + 12 * q^5 - 104 * q^9	$ 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9} - 8 q^{12} - 34 q^{14} + 26 q^{16} + 14 q^{20} - 8 q^{22} + 76 q^{25} + 2 q^{26} - 16 q^{33} + 32 q^{34} - 24 q^{36} - 32 q^{37} - 30 q^{38} + 54 q^{42} + 10 q^{44} + 12 q^{45} + 34 q^{48} - 36 q^{49} - 32 q^{53} - 36 q^{56} + 62 q^{58} + 4 q^{60} - 18 q^{64} - 30 q^{66} - 24 q^{69} - 30 q^{70} + 88 q^{77} - 10 q^{78} - 46 q^{80} + 64 q^{81} - 46 q^{82} + 98 q^{86} + 16 q^{88} + 24 q^{89} + 84 q^{92} + 8 q^{93} - 88 q^{97}+O(q^{100}) $ 64 * q + 6 * q^4 + 12 * q^5 - 104 * q^9 - 8 * q^12 - 34 * q^14 + 26 * q^16 + 14 * q^20 - 8 * q^22 + 76 * q^25 + 2 * q^26 - 16 * q^33 + 32 * q^34 - 24 * q^36 - 32 * q^37 - 30 * q^38 + 54 * q^42 + 10 * q^44 + 12 * q^45 + 34 * q^48 - 36 * q^49 - 32 * q^53 - 36 * q^56 + 62 * q^58 + 4 * q^60 - 18 * q^64 - 30 * q^66 - 24 * q^69 - 30 * q^70 + 88 * q^77 - 10 * q^78 - 46 * q^80 + 64 * q^81 - 46 * q^82 + 98 * q^86 + 16 * q^88 + 24 * q^89 + 84 * q^92 + 8 * q^93 - 88 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−0.936395	+	1.05979i	−0.662131	+	0.749388i
$2$	−0.936395	+	1.05979i	−0.662131	+	0.749388i
$3$		−	2.78715i		−	1.60916i	−0.593843	−	0.804581i	$-0.702390\pi$
$3$		−	2.78715i		−	1.60916i	0.593843	−	0.804581i	$-0.297610\pi$
$4$	−0.246329	−	1.98477i	−0.123165	−	0.992386i
$5$	1.09997			0.491923			0.245961	−	0.969280i	$-0.420896\pi$
$5$	1.09997			0.491923			0.245961	+	0.969280i	$0.420896\pi$
$6$	2.95381	+	2.60987i	1.20589	+	1.06548i
$7$	−3.18482			−1.20375			−0.601874	−	0.798591i	$-0.705579\pi$
$7$	−3.18482			−1.20375			−0.601874	+	0.798591i	$0.705579\pi$
$8$	2.33411	+	1.59747i	0.825233	+	0.564792i
$9$	−4.76820			−1.58940
$10$	−1.03001	+	1.16575i	−0.325717	+	0.368641i
$11$	−3.20589	−	0.849864i	−0.966612	−	0.256244i
$11$	−3.20589	−	0.849864i	−0.966612	−	0.256244i
$12$	−5.53186	+	0.686556i	−1.59691	+	0.198192i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	2.98224	−	3.37525i	0.797038	−	0.902074i
$15$		−	3.06579i		−	0.791583i
$16$	−3.87864	+	0.977815i	−0.969661	+	0.244454i
$17$		−	0.404034i		−	0.0979926i	−0.998799	−	0.0489963i	$-0.984398\pi$
$17$		−	0.404034i		−	0.0979926i	0.998799	−	0.0489963i	$-0.0156022\pi$
$18$	4.46492	−	5.05332i	1.05239	−	1.19108i
$19$	0.124854			0.0286434			0.0143217	−	0.999897i	$-0.495441\pi$
$19$	0.124854			0.0286434			0.0143217	+	0.999897i	$0.495441\pi$
$20$	−0.270955	−	2.18320i	−0.0605875	−	0.488177i
$21$			8.87656i			1.93702i
$22$	3.90266	−	2.60178i	0.832050	−	0.554701i
$23$			4.72467i			0.985162i	0.870267	+	0.492581i	$0.163946\pi$
$23$			4.72467i			0.985162i	−0.870267	+	0.492581i	$0.836054\pi$
$24$	4.45240	−	6.50552i	0.908841	−	1.32793i
$25$	−3.79006			−0.758012
$26$	1.05979	+	0.936395i	0.207843	+	0.183642i
$27$			4.92825i			0.948442i
$28$	0.784513	+	6.32113i	0.148259	+	1.19458i
$29$		−	9.08186i		−	1.68646i	−0.537553	−	0.843230i	$-0.680651\pi$
$29$		−	9.08186i		−	1.68646i	0.537553	−	0.843230i	$-0.319349\pi$
$30$	3.24911	+	2.87079i	0.593203	+	0.524132i
$31$			10.4536i			1.87752i	0.344578	+	0.938758i	$0.388022\pi$
$31$			10.4536i			1.87752i	−0.344578	+	0.938758i	$0.611978\pi$
$32$	2.59566	−	5.02619i	0.458852	−	0.888513i
$33$	−2.36870	+	8.93530i	−0.412337	+	1.55544i
$34$	0.428193	+	0.378335i	0.0734345	+	0.0648839i
$35$	−3.50321			−0.592151
$36$	1.17455	+	9.46380i	0.195758	+	1.57730i
$37$	2.86681			0.471301			0.235650	−	0.971838i	$-0.424278\pi$
$37$	2.86681			0.471301			0.235650	+	0.971838i	$0.424278\pi$
$38$	−0.116912	+	0.132319i	−0.0189657	+	0.0214650i
$39$	−2.78715			−0.446301
$40$	2.56746	+	1.75718i	0.405951	+	0.277834i
$41$			3.30715i			0.516490i	0.966079	+	0.258245i	$0.0831442\pi$
$41$			3.30715i			0.516490i	−0.966079	+	0.258245i	$0.916856\pi$
$42$	−9.40733	−	8.31196i	−1.45158	−	1.28256i
$43$	−7.57237			−1.15478			−0.577388	−	0.816470i	$-0.695928\pi$
$43$	−7.57237			−1.15478			−0.577388	+	0.816470i	$0.695928\pi$
$44$	−0.897081	+	6.57231i	−0.135240	+	0.990813i
$45$	−5.24490			−0.781863
$46$	−5.00718	−	4.42416i	−0.738268	−	0.652306i
$47$			4.17057i			0.608340i	0.952618	+	0.304170i	$0.0983791\pi$
$47$			4.17057i			0.608340i	−0.952618	+	0.304170i	$0.901621\pi$
$48$	2.72532	+	10.8104i	0.393366	+	1.56034i
$49$	3.14305			0.449007
$50$	3.54899	−	4.01668i	0.501903	−	0.568045i
$51$	−1.12610			−0.157686
$52$	−1.98477	+	0.246329i	−0.275238	+	0.0341597i
$53$	−11.5475			−1.58618			−0.793089	−	0.609106i	$-0.791528\pi$
$53$	−11.5475			−1.58618			−0.793089	+	0.609106i	$0.791528\pi$
$54$	−5.22293	−	4.61479i	−0.710751	−	0.627993i
$55$	−3.52639	−	0.934827i	−0.475499	−	0.126052i
$56$	−7.43372	−	5.08765i	−0.993372	−	0.679866i
$57$		−	0.347986i		−	0.0460919i
$58$	9.62491	+	8.50421i	1.26381	+	1.11666i
$59$		−	6.68623i		−	0.870473i	−0.900316	−	0.435237i	$-0.856665\pi$
$59$		−	6.68623i		−	0.870473i	0.900316	−	0.435237i	$-0.143335\pi$
$60$	−6.08489	+	0.755193i	−0.785556	+	0.0974951i
$61$			1.02508i			0.131249i	0.997844	+	0.0656243i	$0.0209039\pi$
$61$			1.02508i			0.131249i	−0.997844	+	0.0656243i	$0.979096\pi$
$62$	−11.0786	−	9.78866i	−1.40699	−	1.24316i
$63$	15.1859			1.91324
$64$	2.89616	+	7.45736i	0.362020	+	0.932170i
$65$		−	1.09997i		−	0.136435i
$66$	−7.25154	−	10.8773i	−0.892603	−	1.33890i
$67$		−	11.3802i		−	1.39032i	−0.718856	−	0.695159i	$-0.755334\pi$
$67$		−	11.3802i		−	1.39032i	0.718856	−	0.695159i	$-0.244666\pi$
$68$	−0.801915	+	0.0995253i	−0.0972465	+	0.0120692i
$69$	13.1684			1.58528
$70$	3.28039	−	3.71268i	0.392081	−	0.443751i
$71$		−	12.4986i		−	1.48331i	−0.670784	−	0.741653i	$-0.734042\pi$
$71$		−	12.4986i		−	1.48331i	0.670784	−	0.741653i	$-0.265958\pi$
$72$	−11.1295	−	7.61708i	−1.31163	−	0.897681i
$73$			2.91778i			0.341501i	0.985314	+	0.170750i	$0.0546192\pi$
$73$			2.91778i			0.341501i	−0.985314	+	0.170750i	$0.945381\pi$
$74$	−2.68447	+	3.03823i	−0.312063	+	0.353187i
$75$			10.5635i			1.21976i
$76$	−0.0307551	−	0.247806i	−0.00352785	−	0.0284253i
$77$	10.2102	+	2.70666i	1.16356	+	0.308452i
$78$	2.60987	−	2.95381i	0.295510	−	0.334453i
$79$	10.8405			1.21965			0.609824	−	0.792537i	$-0.291240\pi$
$79$	10.8405			1.21965			0.609824	+	0.792537i	$0.291240\pi$
$80$	−4.26640	+	1.07557i	−0.476998	+	0.120252i
$81$	−0.568841			−0.0632045
$82$	−3.50490	−	3.09680i	−0.387052	−	0.341984i
$83$	3.91349			0.429561			0.214781	−	0.976662i	$-0.431096\pi$
$83$	3.91349			0.429561			0.214781	+	0.976662i	$0.431096\pi$
$84$	17.6179	−	2.18656i	1.92228	−	0.238573i
$85$		−	0.444426i		−	0.0482048i
$86$	7.09073	−	8.02516i	0.764613	−	0.865375i
$87$	−25.3125			−2.71379
$88$	−6.12528	−	7.10500i	−0.652957	−	0.757395i
$89$	−4.50758			−0.477803			−0.238901	−	0.971044i	$-0.576787\pi$
$89$	−4.50758			−0.477803			−0.238901	+	0.971044i	$0.576787\pi$
$90$	4.91129	−	5.55851i	0.517696	−	0.585919i
$91$			3.18482i			0.333859i
$92$	9.37739	−	1.16382i	0.977661	−	0.121337i
$93$	29.1356			3.02123
$94$	−4.41995	−	3.90530i	−0.455883	−	0.402801i
$95$	0.137336			0.0140903
$96$	−14.0087	−	7.23449i	−1.42976	−	0.738367i
$97$	3.28224			0.333261			0.166630	−	0.986019i	$-0.446711\pi$
$97$	3.28224			0.333261			0.166630	+	0.986019i	$0.446711\pi$
$98$	−2.94314	+	3.33099i	−0.297302	+	0.336480i
$99$	15.2863	+	4.05232i	1.53633	+	0.407274i
$100$	0.933602	+	7.52241i	0.0933602	+	0.752241i
$101$		−	2.94323i		−	0.292862i	−0.989221	−	0.146431i	$-0.953221\pi$
$101$		−	2.94323i		−	0.292862i	0.989221	−	0.146431i	$-0.0467787\pi$
$102$	1.05448	−	1.19344i	0.104409	−	0.118168i
$103$		−	14.8477i		−	1.46299i	−0.681848	−	0.731494i	$-0.738823\pi$
$103$		−	14.8477i		−	1.46299i	0.681848	−	0.731494i	$-0.261177\pi$
$104$	1.59747	−	2.33411i	0.156645	−	0.228879i
$105$			9.76397i			0.952866i
$106$	10.8131	−	12.2380i	1.05026	−	1.18866i
$107$	−12.0169			−1.16172			−0.580858	−	0.814005i	$-0.697283\pi$
$107$	−12.0169			−1.16172			−0.580858	+	0.814005i	$0.697283\pi$
$108$	9.78146	−	1.21397i	0.941221	−	0.116815i
$109$		−	0.213984i		−	0.0204960i	−0.999947	−	0.0102480i	$-0.996738\pi$
$109$		−	0.213984i		−	0.0204960i	0.999947	−	0.0102480i	$-0.00326209\pi$
$110$	4.29282	−	2.86188i	0.409304	−	0.272870i
$111$		−	7.99023i		−	0.758399i
$112$	12.3528	−	3.11416i	1.16723	−	0.294260i
$113$	−13.5331			−1.27309			−0.636545	−	0.771240i	$-0.719637\pi$
$113$	−13.5331			−1.27309			−0.636545	+	0.771240i	$0.719637\pi$
$114$	0.368794	+	0.325852i	0.0345407	+	0.0305189i
$115$			5.19701i			0.484624i
$116$	−18.0254	+	2.23713i	−1.67362	+	0.207712i
$117$			4.76820i			0.440821i
$118$	7.08603	+	6.26096i	0.652322	+	0.576368i
$119$			1.28677i			0.117958i
$120$	4.89751	−	7.15590i	0.447080	−	0.653241i
$121$	9.55546	+	5.44914i	0.868679	+	0.495376i
$122$	−1.08638	−	0.959883i	−0.0983561	−	0.0869038i
$123$	9.21753			0.831116
$124$	20.7479	−	2.57502i	1.86322	−	0.231243i
$125$	−9.66883			−0.864806
$126$	−14.2200	+	16.0939i	−1.26681	+	1.43376i
$127$	−21.9470			−1.94748			−0.973741	−	0.227659i	$-0.926893\pi$
$127$	−21.9470			−1.94748			−0.973741	+	0.227659i	$0.926893\pi$
$128$	−10.6152	−	3.91370i	−0.938262	−	0.345925i
$129$			21.1053i			1.85822i
$130$	1.16575	+	1.03001i	0.102243	+	0.0903378i
$131$	0.729152			0.0637063			0.0318532	−	0.999493i	$-0.489859\pi$
$131$	0.729152			0.0637063			0.0318532	+	0.999493i	$0.489859\pi$
$132$	18.3180	+	2.50030i	1.59438	+	0.217623i
$133$	−0.397636			−0.0344794
$134$	12.0607	+	10.6564i	1.04189	+	0.920572i
$135$			5.42094i			0.466560i
$136$	0.645433	−	0.943060i	0.0553454	−	0.0808667i
$137$	−3.03978			−0.259706			−0.129853	−	0.991533i	$-0.541451\pi$
$137$	−3.03978			−0.259706			−0.129853	+	0.991533i	$0.541451\pi$
$138$	−12.3308	+	13.9558i	−1.04967	+	1.18799i
$139$	13.8449			1.17431			0.587156	−	0.809474i	$-0.300248\pi$
$139$	13.8449			1.17431			0.587156	+	0.809474i	$0.300248\pi$
$140$	0.862943	+	6.95308i	0.0729320	+	0.587642i
$141$	11.6240			0.978918
$142$	13.2459	+	11.7036i	1.11157	+	0.982143i
$143$	−0.849864	+	3.20589i	−0.0710692	+	0.268090i
$144$	18.4942	−	4.66242i	1.54118	−	0.388535i
$145$		−	9.98980i		−	0.829608i
$146$	−3.09225	−	2.73220i	−0.255917	−	0.226118i
$147$		−	8.76015i		−	0.722525i
$148$	−0.706179	−	5.68997i	−0.0580476	−	0.467712i
$149$		−	12.6321i		−	1.03487i	−0.855724	−	0.517433i	$-0.826888\pi$
$149$		−	12.6321i		−	1.03487i	0.855724	−	0.517433i	$-0.173112\pi$
$150$	−11.1951	−	9.89157i	−0.914076	−	0.807644i
$151$	8.74541			0.711691			0.355846	−	0.934545i	$-0.384193\pi$
$151$	8.74541			0.711691			0.355846	+	0.934545i	$0.384193\pi$
$152$	0.291423	+	0.199450i	0.0236375	+	0.0161776i
$153$			1.92652i			0.155750i
$154$	−12.4293	+	8.28618i	−1.00158	+	0.667719i
$155$			11.4986i			0.923593i
$156$	0.686556	+	5.53186i	0.0549685	+	0.442903i
$157$	10.8981			0.869766			0.434883	−	0.900487i	$-0.356790\pi$
$157$	10.8981			0.869766			0.434883	+	0.900487i	$0.356790\pi$
$158$	−10.1510	+	11.4887i	−0.807566	+	0.913989i
$159$			32.1848i			2.55242i
$160$	2.85515	−	5.52867i	0.225720	−	0.437080i
$161$		−	15.0472i		−	1.18589i
$162$	0.532660	−	0.602854i	0.0418497	−	0.0473647i
$163$			15.6207i			1.22350i	0.791050	+	0.611752i	$0.209535\pi$
$163$			15.6207i			1.22350i	−0.791050	+	0.611752i	$0.790465\pi$
$164$	6.56394	−	0.814648i	0.512558	−	0.0636133i
$165$	−2.60550	+	9.82858i	−0.202838	+	0.765154i
$166$	−3.66457	+	4.14750i	−0.284426	+	0.321908i
$167$	5.30031			0.410151			0.205075	−	0.978746i	$-0.434256\pi$
$167$	5.30031			0.410151			0.205075	+	0.978746i	$0.434256\pi$
$168$	−14.1801	+	20.7189i	−1.09402	+	1.59850i
$169$	−1.00000			−0.0769231
$170$	0.471000	+	0.416158i	0.0361241	+	0.0319179i
$171$	−0.595328			−0.0455259
$172$	1.86530	+	15.0294i	0.142228	+	1.14598i
$173$		−	22.9386i		−	1.74399i	−0.489514	−	0.871995i	$-0.662826\pi$
$173$		−	22.9386i		−	1.74399i	0.489514	−	0.871995i	$-0.337174\pi$
$174$	23.7025	−	26.8261i	1.79688	−	2.03368i
$175$	12.0706			0.912455
$176$	13.2655	+	0.161551i	0.999926	+	0.0121774i
$177$	−18.6355			−1.40073
$178$	4.22088	−	4.77711i	0.316368	−	0.358060i
$179$		−	15.5156i		−	1.15969i	−0.814727	−	0.579844i	$-0.803113\pi$
$179$		−	15.5156i		−	1.15969i	0.814727	−	0.579844i	$-0.196887\pi$
$180$	1.29197	+	10.4099i	0.0962978	+	0.775910i
$181$	15.2516			1.13364			0.566821	−	0.823841i	$-0.308173\pi$
$181$	15.2516			1.13364			0.566821	+	0.823841i	$0.308173\pi$
$182$	−3.37525	−	2.98224i	−0.250190	−	0.221059i
$183$	2.85706			0.211200
$184$	−7.54753	+	11.0279i	−0.556411	+	0.812988i
$185$	3.15341			0.231844
$186$	−27.2825	+	30.8778i	−2.00045	+	2.26407i
$187$	−0.343374	+	1.29529i	−0.0251100	+	0.0947208i
$188$	8.27763	−	1.02733i	0.603709	−	0.0749260i
$189$		−	15.6956i		−	1.14168i
$190$	−0.128600	+	0.145548i	−0.00932965	+	0.0105591i
$191$		−	12.5325i		−	0.906820i	−0.891302	−	0.453410i	$-0.850207\pi$
$191$		−	12.5325i		−	0.906820i	0.891302	−	0.453410i	$-0.149793\pi$
$192$	20.7848	−	8.07204i	1.50001	−	0.582549i
$193$		−	3.99734i		−	0.287735i	−0.989597	−	0.143867i	$-0.954046\pi$
$193$		−	3.99734i		−	0.287735i	0.989597	−	0.143867i	$-0.0459539\pi$
$194$	−3.07347	+	3.47850i	−0.220662	+	0.249741i
$195$	−3.06579			−0.219546
$196$	−0.774225	−	6.23824i	−0.0553018	−	0.445588i
$197$		−	4.27512i		−	0.304590i	−0.988335	−	0.152295i	$-0.951334\pi$
$197$		−	4.27512i		−	0.304590i	0.988335	−	0.152295i	$-0.0486663\pi$
$198$	−18.6087	+	12.4058i	−1.32246	+	0.881642i
$199$		−	17.2819i		−	1.22508i	−0.790440	−	0.612540i	$-0.790148\pi$
$199$		−	17.2819i		−	1.22508i	0.790440	−	0.612540i	$-0.209852\pi$
$200$	−8.84643	−	6.05452i	−0.625537	−	0.428119i
$201$	−31.7184			−2.23725
$202$	3.11922	+	2.75603i	0.219467	+	0.193913i
$203$			28.9241i			2.03007i
$204$	0.277392	+	2.23506i	0.0194213	+	0.156485i
$205$			3.63778i			0.254073i
$206$	15.7355	+	13.9033i	1.09635	+	0.968690i
$207$		−	22.5282i		−	1.56582i
$208$	0.977815	+	3.87864i	0.0677993	+	0.268936i
$209$	−0.400267	−	0.106109i	−0.0276871	−	0.00733969i
$210$	−10.3478	−	9.14293i	−0.714066	−	0.630922i
$211$	6.88191			0.473770			0.236885	−	0.971538i	$-0.423874\pi$
$211$	6.88191			0.473770			0.236885	+	0.971538i	$0.423874\pi$
$212$	2.84450	+	22.9193i	0.195361	+	1.57410i
$213$	−34.8354			−2.38688
$214$	11.2525	−	12.7354i	0.769208	−	0.870576i
$215$	−8.32941			−0.568061
$216$	−7.87274	+	11.5031i	−0.535672	+	0.782686i
$217$		−	33.2927i		−	2.26005i
$218$	0.226779	+	0.200374i	0.0153594	+	0.0135710i
$219$	8.13230			0.549530
$220$	−0.986765	+	7.22936i	−0.0665277	+	0.487403i
$221$	−0.404034			−0.0271782
$222$	8.46800	+	7.48201i	0.568335	+	0.502160i
$223$		−	6.34123i		−	0.424640i	−0.977200	−	0.212320i	$-0.931898\pi$
$223$		−	6.34123i		−	0.424640i	0.977200	−	0.212320i	$-0.0681019\pi$
$224$	−8.26670	+	16.0075i	−0.552342	+	1.06954i
$225$	18.0718			1.20479
$226$	12.6724	−	14.3423i	0.842952	−	0.954038i
$227$	−15.4340			−1.02439			−0.512197	−	0.858868i	$-0.671168\pi$
$227$	−15.4340			−1.02439			−0.512197	+	0.858868i	$0.671168\pi$
$228$	−0.690673	+	0.0857191i	−0.0457409	+	0.00567689i
$229$	14.5539			0.961751			0.480875	−	0.876789i	$-0.340319\pi$
$229$	14.5539			0.961751			0.480875	+	0.876789i	$0.340319\pi$
$230$	−5.50776	−	4.86645i	−0.363171	−	0.320884i
$231$	7.54386	−	28.4573i	0.496350	−	1.87235i
$232$	14.5080	−	21.1981i	0.952499	−	1.39172i
$233$		−	8.01550i		−	0.525113i	−0.964917	−	0.262557i	$-0.915434\pi$
$233$		−	8.01550i		−	0.525113i	0.964917	−	0.262557i	$-0.0845656\pi$
$234$	−5.05332	−	4.46492i	−0.330346	−	0.291881i
$235$			4.58751i			0.299256i
$236$	−13.2707	+	1.64701i	−0.863846	+	0.107212i
$237$		−	30.2140i		−	1.96261i
$238$	−1.36371	−	1.20493i	−0.0883965	−	0.0781039i
$239$	8.04188			0.520186			0.260093	−	0.965584i	$-0.416247\pi$
$239$	8.04188			0.520186			0.260093	+	0.965584i	$0.416247\pi$
$240$	2.99777	+	11.8911i	0.193506	+	0.767568i
$241$		−	1.69843i		−	0.109405i	−0.998503	−	0.0547026i	$-0.982579\pi$
$241$		−	1.69843i		−	0.109405i	0.998503	−	0.0547026i	$-0.0174211\pi$
$242$	−14.7227	+	5.02428i	−0.946408	+	0.322973i
$243$			16.3702i			1.05015i
$244$	2.03456	−	0.252508i	0.130249	−	0.0161652i
$245$	3.45727			0.220877
$246$	−8.63124	+	9.76868i	−0.550308	+	0.622829i
$247$		−	0.124854i		−	0.00794425i
$248$	−16.6993	+	24.3998i	−1.06041	+	1.54939i
$249$		−	10.9075i		−	0.691234i
$250$	9.05384	−	10.2470i	0.572615	−	0.648075i
$251$			9.67025i			0.610381i	0.952291	+	0.305190i	$0.0987201\pi$
$251$			9.67025i			0.610381i	−0.952291	+	0.305190i	$0.901280\pi$
$252$	−3.74072	−	30.1405i	−0.235643	−	1.89867i
$253$	4.01532	−	15.1468i	0.252441	−	0.952269i
$254$	20.5511	−	23.2593i	1.28949	−	1.45942i
$255$	−1.23868			−0.0775693
$256$	14.0878	−	7.58519i	0.880485	−	0.474074i
$257$	−15.6489			−0.976150			−0.488075	−	0.872802i	$-0.662301\pi$
$257$	−15.6489			−0.976150			−0.488075	+	0.872802i	$0.662301\pi$
$258$	−22.3673	−	19.7629i	−1.39253	−	1.23039i
$259$	−9.13026			−0.567327
$260$	−2.18320	+	0.270955i	−0.135396	+	0.0168039i
$261$			43.3042i			2.68046i
$262$	−0.682774	+	0.772751i	−0.0421819	+	0.0477407i
$263$	29.5589			1.82268			0.911341	−	0.411651i	$-0.135048\pi$
$263$	29.5589			1.82268			0.911341	+	0.411651i	$0.135048\pi$
$264$	−19.8027	+	17.0721i	−1.21877	+	1.05071i
$265$	−12.7020			−0.780277
$266$	0.372344	−	0.421412i	0.0228299	−	0.0258385i
$267$			12.5633i			0.768862i
$268$	−22.5872	+	2.80329i	−1.37973	+	0.171238i
$269$	−6.14686			−0.374781			−0.187390	−	0.982286i	$-0.560003\pi$
$269$	−6.14686			−0.374781			−0.187390	+	0.982286i	$0.560003\pi$
$270$	−5.74508	−	5.07614i	−0.349635	−	0.308924i
$271$	−22.3148			−1.35553			−0.677765	−	0.735279i	$-0.737051\pi$
$271$	−22.3148			−1.35553			−0.677765	+	0.735279i	$0.737051\pi$
$272$	0.395070	+	1.56710i	0.0239546	+	0.0950196i
$273$	8.87656			0.537234
$274$	2.84643	−	3.22154i	0.171959	−	0.194620i
$275$	12.1505	+	3.22103i	0.732704	+	0.194236i
$276$	−3.24375	−	26.1362i	−0.195251	−	1.57321i
$277$			16.8127i			1.01018i	0.863067	+	0.505090i	$0.168541\pi$
$277$			16.8127i			1.01018i	−0.863067	+	0.505090i	$0.831459\pi$
$278$	−12.9643	+	14.6728i	−0.777549	+	0.880015i
$279$		−	49.8447i		−	2.98413i
$280$	−8.17689	−	5.59628i	−0.488663	−	0.334442i
$281$			22.3218i			1.33161i	0.746127	+	0.665804i	$0.231911\pi$
$281$			22.3218i			1.33161i	−0.746127	+	0.665804i	$0.768089\pi$
$282$	−10.8847	+	12.3191i	−0.648172	+	0.733589i
$283$	−9.23091			−0.548720			−0.274360	−	0.961627i	$-0.588466\pi$
$283$	−9.23091			−0.548720			−0.274360	+	0.961627i	$0.588466\pi$
$284$	−24.8068	+	3.07876i	−1.47201	+	0.182691i
$285$		−	0.382775i		−	0.0226736i
$286$	−2.60178	−	3.90266i	−0.153846	−	0.230769i
$287$		−	10.5327i		−	0.621724i
$288$	−12.3766	+	23.9659i	−0.729300	+	1.41220i
$289$	16.8368			0.990397
$290$	10.5871	+	9.35440i	0.621698	+	0.549309i
$291$		−	9.14808i		−	0.536270i
$292$	5.79114	−	0.718736i	0.338901	−	0.0420608i
$293$			1.84539i			0.107809i	0.998546	+	0.0539045i	$0.0171667\pi$
$293$			1.84539i			0.107809i	−0.998546	+	0.0539045i	$0.982833\pi$
$294$	9.28396	+	8.20296i	0.541452	+	0.478406i
$295$		−	7.35468i		−	0.428206i
$296$	6.69146	+	4.57965i	0.388933	+	0.266187i
$297$	4.18834	−	15.7994i	0.243032	−	0.916776i
$298$	13.3875	+	11.8287i	0.775516	+	0.685217i
$299$	4.72467			0.273235
$300$	20.9661	−	2.60209i	1.21048	−	0.150232i
$301$	24.1166			1.39006
$302$	−8.18915	+	9.26833i	−0.471233	+	0.533333i
$303$	−8.20322			−0.471263
$304$	−0.484263	+	0.122084i	−0.0277744	+	0.00700199i
$305$			1.12756i			0.0645642i
$306$	−2.04171	−	1.80398i	−0.116717	−	0.103127i
$307$	−34.7935			−1.98577			−0.992885	−	0.119077i	$-0.962006\pi$
$307$	−34.7935			−1.98577			−0.992885	+	0.119077i	$0.962006\pi$
$308$	2.85704	−	20.9316i	0.162795	−	1.19269i
$309$	−41.3828			−2.35418
$310$	−12.1862	−	10.7673i	−0.692129	−	0.611539i
$311$		−	18.1045i		−	1.02661i	−0.858205	−	0.513307i	$-0.828420\pi$
$311$		−	18.1045i		−	1.02661i	0.858205	−	0.513307i	$-0.171580\pi$
$312$	−6.50552	−	4.45240i	−0.368303	−	0.252067i
$313$	−31.1943			−1.76321			−0.881604	−	0.471989i	$-0.843536\pi$
$313$	−31.1943			−1.76321			−0.881604	+	0.471989i	$0.843536\pi$
$314$	−10.2050	+	11.5498i	−0.575899	+	0.651792i
$315$	16.7040			0.941165
$316$	−2.67032	−	21.5158i	−0.150217	−	1.21036i
$317$	−21.9345			−1.23196			−0.615982	−	0.787760i	$-0.711241\pi$
$317$	−21.9345			−1.23196			−0.615982	+	0.787760i	$0.711241\pi$
$318$	−34.1092	−	30.1376i	−1.91275	−	1.69003i
$319$	−7.71834	+	29.1155i	−0.432144	+	1.63015i
$320$	3.18570	+	8.20290i	0.178086	+	0.458556i
$321$			33.4928i			1.86939i
$322$	15.9469	+	14.0901i	0.888688	+	0.785212i
$323$		−	0.0504451i		−	0.00280684i
$324$	0.140122	+	1.12902i	0.00778456	+	0.0627233i
$325$			3.79006i			0.210235i
$326$	−16.5547	−	14.6271i	−0.916879	−	0.810120i
$327$	−0.596406			−0.0329813
$328$	−5.28308	+	7.71926i	−0.291709	+	0.426225i
$329$		−	13.2825i		−	0.732288i
$330$	−7.97650	−	11.9647i	−0.439092	−	0.658637i
$331$			23.3853i			1.28537i	0.766129	+	0.642687i	$0.222180\pi$
$331$			23.3853i			1.28537i	−0.766129	+	0.642687i	$0.777820\pi$
$332$	−0.964007	−	7.76739i	−0.0529068	−	0.426291i
$333$	−13.6695			−0.749086
$334$	−4.96319	+	5.61724i	−0.271573	+	0.307362i
$335$		−	12.5180i		−	0.683929i
$336$	−8.67963	−	34.4290i	−0.473513	−	1.87826i
$337$		−	12.3138i		−	0.670778i	−0.942080	−	0.335389i	$-0.891132\pi$
$337$		−	12.3138i		−	0.670778i	0.942080	−	0.335389i	$-0.108868\pi$
$338$	0.936395	−	1.05979i	0.0509332	−	0.0576452i
$339$			37.7189i			2.04861i
$340$	−0.882085	+	0.109475i	−0.0478378	+	0.00593712i
$341$	8.88410	−	33.5130i	0.481101	−	1.81483i
$342$	0.557462	−	0.630925i	0.0301441	−	0.0341165i
$343$	12.2837			0.663256
$344$	−17.6748	−	12.0967i	−0.952960	−	0.652208i
$345$	14.4848			0.779838
$346$	24.3102	+	21.4796i	1.30693	+	1.15475i
$347$	27.3443			1.46792			0.733959	−	0.679194i	$-0.237670\pi$
$347$	27.3443			1.46792			0.733959	+	0.679194i	$0.237670\pi$
$348$	6.23521	+	50.2396i	0.334242	+	2.69312i
$349$			11.6046i			0.621182i	0.950544	+	0.310591i	$0.100527\pi$
$349$			11.6046i			0.621182i	−0.950544	+	0.310591i	$0.899473\pi$
$350$	−11.3029	+	12.7924i	−0.604165	+	0.683783i
$351$	4.92825			0.263051
$352$	−12.5930	+	13.9074i	−0.671208	+	0.741269i
$353$	29.7044			1.58101			0.790503	−	0.612458i	$-0.209819\pi$
$353$	29.7044			1.58101			0.790503	+	0.612458i	$0.209819\pi$
$354$	17.4502	−	19.7498i	0.927469	−	1.04969i
$355$		−	13.7481i		−	0.729672i
$356$	1.11035	+	8.94653i	0.0588484	+	0.474165i
$357$	3.58643			0.189814
$358$	16.4433	+	14.5287i	0.869057	+	0.767866i
$359$	2.22396			0.117376			0.0586881	−	0.998276i	$-0.481308\pi$
$359$	2.22396			0.117376			0.0586881	+	0.998276i	$0.481308\pi$
$360$	−12.2422	−	8.37858i	−0.645219	−	0.441590i
$361$	−18.9844			−0.999180
$362$	−14.2815	+	16.1635i	−0.750619	+	0.849537i
$363$	15.1876	−	26.6325i	0.797140	−	1.39784i
$364$	6.32113	−	0.784513i	0.331317	−	0.0411197i
$365$			3.20948i			0.167992i
$366$	−2.67534	+	3.02790i	−0.139842	+	0.158271i
$367$			11.3410i			0.591994i	0.955189	+	0.295997i	$0.0956518\pi$
$367$			11.3410i			0.591994i	−0.955189	+	0.295997i	$0.904348\pi$
$368$	−4.61985	−	18.3253i	−0.240826	−	0.955273i
$369$		−	15.7692i		−	0.820910i
$370$	−2.95284	+	3.34197i	−0.153511	+	0.173741i
$371$	36.7768			1.90936
$372$	−7.17696	−	57.8276i	−0.372108	−	2.99822i
$373$			28.1110i			1.45553i	0.685826	+	0.727765i	$0.259441\pi$
$373$			28.1110i			1.45553i	−0.685826	+	0.727765i	$0.740559\pi$
$374$	−1.05121	−	1.57681i	−0.0543566	−	0.0815347i
$375$			26.9485i			1.39161i
$376$	−6.66237	+	9.73458i	−0.343586	+	0.502023i
$377$	−9.08186			−0.467740
$378$	16.6341	+	14.6972i	0.855565	+	0.755945i
$379$		−	4.65148i		−	0.238930i	−0.992838	−	0.119465i	$-0.961882\pi$
$379$		−	4.65148i		−	0.238930i	0.992838	−	0.119465i	$-0.0381180\pi$
$380$	−0.0338298	−	0.272580i	−0.00173543	−	0.0139831i
$381$			61.1696i			3.13381i
$382$	13.2819	+	11.7354i	0.679560	+	0.600434i
$383$		−	1.48954i		−	0.0761119i	−0.999276	−	0.0380560i	$-0.987883\pi$
$383$		−	1.48954i		−	0.0761119i	0.999276	−	0.0380560i	$-0.0121165\pi$
$384$	−10.9081	+	29.5862i	−0.556650	+	1.50982i
$385$	11.2309	+	2.97725i	0.572380	+	0.151735i
$386$	4.23636	+	3.74309i	0.215625	+	0.190518i
$387$	36.1066			1.83540
$388$	−0.808510	−	6.51449i	−0.0410459	−	0.330723i
$389$	−2.10222			−0.106587			−0.0532934	−	0.998579i	$-0.516972\pi$
$389$	−2.10222			−0.106587			−0.0532934	+	0.998579i	$0.516972\pi$
$390$	2.87079	−	3.24911i	0.145368	−	0.164525i
$391$	1.90893			0.0965385
$392$	7.33623	+	5.02093i	0.370536	+	0.253596i
$393$		−	2.03226i		−	0.102514i
$394$	4.53075	+	4.00320i	0.228256	+	0.201678i
$395$	11.9242			0.599972
$396$	4.27747	−	31.3381i	0.214951	−	1.57480i
$397$	−10.3607			−0.519991			−0.259995	−	0.965610i	$-0.583721\pi$
$397$	−10.3607			−0.519991			−0.259995	+	0.965610i	$0.583721\pi$
$398$	18.3152	+	16.1827i	0.918060	+	0.811163i
$399$			1.10827i			0.0554829i
$400$	14.7003	−	3.70598i	0.735015	−	0.185299i
$401$	−24.2259			−1.20978			−0.604891	−	0.796308i	$-0.706783\pi$
$401$	−24.2259			−1.20978			−0.604891	+	0.796308i	$0.706783\pi$
$402$	29.7010	−	33.6150i	1.48135	−	1.67656i
$403$	10.4536			0.520729
$404$	−5.84164	+	0.725003i	−0.290633	+	0.0360703i
$405$	−0.625709			−0.0310918
$406$	−30.6536	−	27.0843i	−1.52131	−	1.34417i
$407$	−9.19068	−	2.43640i	−0.455565	−	0.120768i
$408$	−2.62845	−	1.79892i	−0.130128	−	0.0890597i
$409$			20.2912i			1.00333i	0.865061	+	0.501667i	$0.167280\pi$
$409$			20.2912i			1.00333i	−0.865061	+	0.501667i	$0.832720\pi$
$410$	−3.85530	−	3.40640i	−0.190400	−	0.168230i
$411$			8.47232i			0.417909i
$412$	−29.4693	+	3.65742i	−1.45185	+	0.180188i
$413$			21.2944i			1.04783i
$414$	23.8753	+	21.0953i	1.17340	+	1.03678i
$415$	4.30473			0.211311
$416$	−5.02619	−	2.59566i	−0.246429	−	0.127263i
$417$		−	38.5879i		−	1.88966i
$418$	0.487261	−	0.324841i	0.0238327	−	0.0158885i
$419$			9.15253i			0.447130i	0.974689	+	0.223565i	$0.0717696\pi$
$419$			9.15253i			0.447130i	−0.974689	+	0.223565i	$0.928230\pi$
$420$	19.3793	−	2.40515i	0.945611	−	0.117359i
$421$	6.93713			0.338095			0.169048	−	0.985608i	$-0.445931\pi$
$421$	6.93713			0.338095			0.169048	+	0.985608i	$0.445931\pi$
$422$	−6.44418	+	7.29341i	−0.313698	+	0.355037i
$423$		−	19.8861i		−	0.966897i
$424$	−26.9533	−	18.4469i	−1.30897	−	0.895860i
$425$			1.53131i			0.0742795i
$426$	32.6197	−	36.9183i	1.58043	−	1.78870i
$427$		−	3.26470i		−	0.157990i
$428$	2.96011	+	23.8508i	0.143082	+	1.15287i
$429$	8.93530	+	2.36870i	0.431400	+	0.114362i
$430$	7.79961	−	8.82746i	0.376131	−	0.425698i
$431$	19.6520			0.946602			0.473301	−	0.880901i	$-0.343062\pi$
$431$	19.6520			0.946602			0.473301	+	0.880901i	$0.343062\pi$
$432$	−4.81892	−	19.1149i	−0.231850	−	0.919667i
$433$	11.9743			0.575450			0.287725	−	0.957713i	$-0.407101\pi$
$433$	11.9743			0.575450			0.287725	+	0.957713i	$0.407101\pi$
$434$	35.2834	+	31.1751i	1.69366	+	1.49645i
$435$	−27.8431			−1.33497
$436$	−0.424710	+	0.0527106i	−0.0203399	+	0.00252438i
$437$			0.589892i			0.0282184i
$438$	−7.61505	+	8.61857i	−0.363861	+	0.411811i
$439$	−15.7369			−0.751080			−0.375540	−	0.926806i	$-0.622543\pi$
$439$	−15.7369			−0.751080			−0.375540	+	0.926806i	$0.622543\pi$
$440$	−6.73764	−	7.81531i	−0.321204	−	0.372580i
$441$	−14.9867			−0.713652
$442$	0.378335	−	0.428193i	0.0179956	−	0.0203671i
$443$		−	8.81640i		−	0.418880i	−0.977821	−	0.209440i	$-0.932836\pi$
$443$		−	8.81640i		−	0.418880i	0.977821	−	0.209440i	$-0.0671641\pi$
$444$	−15.8588	+	1.96823i	−0.752625	+	0.0934079i
$445$	−4.95822			−0.235042
$446$	6.72040	+	5.93790i	0.318220	+	0.281167i
$447$	−35.2077			−1.66527
$448$	−9.22375	−	23.7503i	−0.435781	−	1.12210i
$449$	7.59029			0.358208			0.179104	−	0.983830i	$-0.442680\pi$
$449$	7.59029			0.358208			0.179104	+	0.983830i	$0.442680\pi$
$450$	−16.9223	+	19.1524i	−0.797726	+	0.902852i
$451$	2.81063	−	10.6024i	0.132347	−	0.499246i
$452$	3.33360	+	26.8602i	0.156800	+	1.26340i
$453$		−	24.3748i		−	1.14523i
$454$	14.4524	−	16.3569i	0.678283	−	0.767668i
$455$			3.50321i			0.164233i
$456$	0.555898	−	0.812238i	0.0260323	−	0.0380365i
$457$			16.6392i			0.778349i	0.921164	+	0.389175i	$0.127240\pi$
$457$			16.6392i			0.778349i	−0.921164	+	0.389175i	$0.872760\pi$
$458$	−13.6282	+	15.4242i	−0.636805	+	0.720724i
$459$	1.99118			0.0929403
$460$	10.3149	−	1.28017i	0.480934	−	0.0596885i
$461$		−	19.6073i		−	0.913204i	−0.889671	−	0.456602i	$-0.849066\pi$
$461$		−	19.6073i		−	0.913204i	0.889671	−	0.456602i	$-0.150934\pi$
$462$	23.0948	+	34.6422i	1.07447	+	1.61170i
$463$			37.5026i			1.74289i	0.490489	+	0.871447i	$0.336818\pi$
$463$			37.5026i			1.74289i	−0.490489	+	0.871447i	$0.663182\pi$
$464$	8.88038	+	35.2253i	0.412261	+	1.63529i
$465$	32.0484			1.48621
$466$	8.49479	+	7.50568i	0.393513	+	0.347694i
$467$			17.4618i			0.808035i	0.914751	+	0.404017i	$0.132387\pi$
$467$			17.4618i			0.808035i	−0.914751	+	0.404017i	$0.867613\pi$
$468$	9.46380	−	1.17455i	0.437464	−	0.0542935i
$469$			36.2440i			1.67359i
$470$	−4.86182	−	4.29573i	−0.224259	−	0.198147i
$471$		−	30.3747i		−	1.39959i
$472$	10.6811	−	15.6064i	0.491636	−	0.718344i
$473$	24.2762	+	6.43548i	1.11622	+	0.295904i
$474$	32.0206	+	28.2922i	1.47076	+	1.29950i
$475$	−0.473203			−0.0217120
$476$	2.55395	−	0.316970i	0.117060	−	0.0145283i
$477$	55.0611			2.52107
$478$	−7.53037	+	8.52274i	−0.344431	+	0.389821i
$479$	−37.9234			−1.73277			−0.866383	−	0.499380i	$-0.833561\pi$
$479$	−37.9234			−1.73277			−0.866383	+	0.499380i	$0.833561\pi$
$480$	−15.4092	−	7.95774i	−0.703332	−	0.363220i
$481$		−	2.86681i		−	0.130715i
$482$	1.79998	+	1.59040i	0.0819870	+	0.0724406i
$483$	−41.9388			−1.90828
$484$	8.46151	−	20.3077i	0.384614	−	0.923077i
$485$	3.61037			0.163938
$486$	−17.3490	−	15.3290i	−0.786969	−	0.695336i
$487$			19.3802i			0.878202i	0.898438	+	0.439101i	$0.144703\pi$
$487$			19.3802i			0.878202i	−0.898438	+	0.439101i	$0.855297\pi$
$488$	−1.63754	+	2.39266i	−0.0741281	+	0.108311i
$489$	43.5371			1.96882
$490$	−3.23737	+	3.66400i	−0.146249	+	0.165522i
$491$	26.1029			1.17801			0.589004	−	0.808130i	$-0.299520\pi$
$491$	26.1029			1.17801			0.589004	+	0.808130i	$0.299520\pi$
$492$	−2.27055	−	18.2947i	−0.102364	−	0.824788i
$493$	−3.66938			−0.165261
$494$	0.132319	+	0.116912i	0.00595332	+	0.00526014i
$495$	16.8146	+	4.45745i	0.755758	+	0.200347i
$496$	−10.2216	−	40.5456i	−0.458966	−	1.82055i
$497$			39.8056i			1.78553i
$498$	11.5597	+	10.2137i	0.518002	+	0.457687i
$499$		−	7.99822i		−	0.358049i	−0.983845	−	0.179025i	$-0.942706\pi$
$499$		−	7.99822i		−	0.358049i	0.983845	−	0.179025i	$-0.0572942\pi$
$500$	2.38171	+	19.1904i	0.106514	+	0.858222i
$501$		−	14.7728i		−	0.659999i
$502$	−10.2485	−	9.05517i	−0.457412	−	0.404152i
$503$	−6.47440			−0.288679			−0.144340	−	0.989528i	$-0.546106\pi$
$503$	−6.47440			−0.288679			−0.144340	+	0.989528i	$0.546106\pi$
$504$	35.4455	+	24.2590i	1.57887	+	1.08058i
$505$		−	3.23747i		−	0.144066i
$506$	12.2925	+	18.4388i	0.546470	+	0.819704i
$507$			2.78715i			0.123782i
$508$	5.40619	+	43.5598i	0.239861	+	1.93265i
$509$	−0.678175			−0.0300596			−0.0150298	−	0.999887i	$-0.504784\pi$
$509$	−0.678175			−0.0300596			−0.0150298	+	0.999887i	$0.504784\pi$
$510$	1.15990	−	1.31275i	0.0513610	−	0.0581295i
$511$		−	9.29261i		−	0.411081i
$512$	−5.15296	+	22.0329i	−0.227731	+	0.973724i
$513$			0.615310i			0.0271666i
$514$	14.6535	−	16.5846i	0.646340	−	0.731515i
$515$		−	16.3321i		−	0.719677i
$516$	41.8893	−	5.19886i	1.84407	−	0.228867i
$517$	3.54442	−	13.3704i	0.155883	−	0.588029i
$518$	8.54953	−	9.67620i	0.375645	−	0.425148i
$519$	−63.9334			−2.80636
$520$	1.75718	−	2.56746i	0.0770573	−	0.112591i
$521$	31.0733			1.36135			0.680674	−	0.732587i	$-0.261687\pi$
$521$	31.0733			1.36135			0.680674	+	0.732587i	$0.261687\pi$
$522$	−45.8935	−	40.5498i	−2.00871	−	1.77482i
$523$	−21.7315			−0.950254			−0.475127	−	0.879917i	$-0.657598\pi$
$523$	−21.7315			−0.950254			−0.475127	+	0.879917i	$0.657598\pi$
$524$	−0.179611	−	1.44720i	−0.00784636	−	0.0632213i
$525$		−	33.6427i		−	1.46829i
$526$	−27.6788	+	31.3264i	−1.20686	+	1.36590i
$527$	4.22359			0.183983
$528$	0.450266	−	36.9730i	0.0195953	−	1.60904i
$529$	0.677499			0.0294565
$530$	11.8941	−	13.4615i	0.516646	−	0.584730i
$531$			31.8813i			1.38353i
$532$	0.0979493	+	0.789217i	0.00424664	+	0.0342169i
$533$	3.30715			0.143249
$534$	−13.3145	−	11.7642i	−0.576176	−	0.509088i
$535$	−13.2182			−0.571474
$536$	18.1796	−	26.5628i	0.785240	−	1.14734i
$537$	−43.2442			−1.86613
$538$	5.75589	−	6.51441i	0.248154	−	0.280856i
$539$	−10.0763	−	2.67116i	−0.434016	−	0.115055i
$540$	10.7593	−	1.33534i	0.463008	−	0.0574637i
$541$			7.64816i			0.328820i	0.986392	+	0.164410i	$0.0525720\pi$
$541$			7.64816i			0.328820i	−0.986392	+	0.164410i	$0.947428\pi$
$542$	20.8955	−	23.6491i	0.897539	−	1.01582i
$543$		−	42.5084i		−	1.82421i
$544$	−2.03075	−	1.04873i	−0.0870676	−	0.0449641i
$545$		−	0.235377i		−	0.0100824i
$546$	−8.31196	+	9.40733i	−0.355719	+	0.402596i
$547$	−38.7151			−1.65534			−0.827669	−	0.561216i	$-0.810334\pi$
$547$	−38.7151			−1.65534			−0.827669	+	0.561216i	$0.810334\pi$
$548$	0.748786	+	6.03327i	0.0319866	+	0.257728i
$549$		−	4.88781i		−	0.208607i
$550$	−14.7913	+	9.86089i	−0.630704	+	0.420470i
$551$		−	1.13390i		−	0.0483059i
$552$	30.7364	+	21.0361i	1.30823	+	0.895356i
$553$	−34.5249			−1.46815
$554$	−17.8180	−	15.7434i	−0.757016	−	0.668871i
$555$		−	8.78904i		−	0.373074i
$556$	−3.41041	−	27.4790i	−0.144634	−	1.16537i
$557$		−	23.1336i		−	0.980202i	−0.871666	−	0.490101i	$-0.836960\pi$
$557$		−	23.1336i		−	0.980202i	0.871666	−	0.490101i	$-0.163040\pi$
$558$	52.8252	+	46.6743i	2.23627	+	1.97588i
$559$			7.57237i			0.320277i
$560$	13.5877	−	3.42549i	0.574185	−	0.144753i
$561$	3.61016	+	0.957034i	0.152421	+	0.0404060i
$562$	−23.6565	−	20.9020i	−0.997890	−	0.881699i
$563$	1.43427			0.0604474			0.0302237	−	0.999543i	$-0.490378\pi$
$563$	1.43427			0.0604474			0.0302237	+	0.999543i	$0.490378\pi$
$564$	−2.86333	−	23.0710i	−0.120568	−	0.971465i
$565$	−14.8861			−0.626262
$566$	8.64377	−	9.78287i	0.363325	−	0.411205i
$567$	1.81165			0.0760823
$568$	19.9661	−	29.1730i	0.837759	−	1.22407i
$569$			0.761746i			0.0319341i	0.999873	+	0.0159670i	$0.00508268\pi$
$569$			0.761746i			0.0319341i	−0.999873	+	0.0159670i	$0.994917\pi$
$570$	0.405663	+	0.358429i	0.0169914	+	0.0150129i
$571$	−17.2745			−0.722916			−0.361458	−	0.932388i	$-0.617721\pi$
$571$	−17.2745			−0.722916			−0.361458	+	0.932388i	$0.617721\pi$
$572$	6.57231	+	0.897081i	0.274802	+	0.0375089i
$573$	−34.9300			−1.45922
$574$	11.1625	+	9.86274i	0.465912	+	0.411663i
$575$		−	17.9068i		−	0.746764i
$576$	−13.8095	−	35.5582i	−0.575396	−	1.48159i
$577$	34.8927			1.45260			0.726301	−	0.687377i	$-0.241238\pi$
$577$	34.8927			1.45260			0.726301	+	0.687377i	$0.241238\pi$
$578$	−15.7659	+	17.8435i	−0.655773	+	0.742192i
$579$	−11.1412			−0.463012
$580$	−19.8275	+	2.46078i	−0.823292	+	0.102178i
$581$	−12.4637			−0.517083
$582$	9.69509	+	8.56622i	0.401874	+	0.355081i
$583$	37.0202	+	9.81384i	1.53322	+	0.406448i
$584$	−4.66108	+	6.81044i	−0.192877	+	0.281818i
$585$			5.24490i			0.216850i
$586$	−1.95574	−	1.72802i	−0.0807907	−	0.0713837i
$587$			27.0974i			1.11843i	0.829023	+	0.559214i	$0.188897\pi$
$587$			27.0974i			1.11843i	−0.829023	+	0.559214i	$0.811103\pi$
$588$	−17.3869	+	2.15788i	−0.717024	+	0.0889895i
$589$			1.30517i			0.0537784i
$590$	7.79445	+	6.88688i	0.320892	+	0.283528i
$591$	−11.9154			−0.490134
$592$	−11.1193	+	2.80321i	−0.457002	+	0.115211i
$593$		−	42.5287i		−	1.74645i	−0.487321	−	0.873223i	$-0.662026\pi$
$593$		−	42.5287i		−	1.74645i	0.487321	−	0.873223i	$-0.337974\pi$
$594$	12.8222	+	19.2333i	0.526102	+	0.789151i
$595$			1.41542i			0.0580264i
$596$	−25.0719	+	3.11167i	−1.02699	+	0.127459i
$597$	−48.1672			−1.97135
$598$	−4.42416	+	5.00718i	−0.180917	+	0.204759i
$599$		−	27.8633i		−	1.13846i	−0.822177	−	0.569232i	$-0.807241\pi$
$599$		−	27.8633i		−	1.13846i	0.822177	−	0.569232i	$-0.192759\pi$
$600$	−16.8748	+	24.6563i	−0.688913	+	1.00659i
$601$		−	30.8864i		−	1.25988i	−0.776643	−	0.629940i	$-0.783079\pi$
$601$		−	30.8864i		−	1.25988i	0.776643	−	0.629940i	$-0.216921\pi$
$602$	−22.5827	+	25.5587i	−0.920401	+	1.04169i
$603$			54.2633i			2.20977i
$604$	−2.15425	−	17.3576i	−0.0876551	−	0.706272i
$605$	10.5108	+	5.99390i	0.427323	+	0.243687i
$606$	7.68146	−	8.69373i	0.312038	−	0.353159i
$607$	35.6261			1.44602			0.723010	−	0.690838i	$-0.242758\pi$
$607$	35.6261			1.44602			0.723010	+	0.690838i	$0.242758\pi$
$608$	0.324078	−	0.627538i	0.0131431	−	0.0254500i
$609$	80.6157			3.26671
$610$	−1.19499	−	1.05585i	−0.0483836	−	0.0427499i
$611$	4.17057			0.168723
$612$	3.82369	−	0.474557i	0.154564	−	0.0191828i
$613$		−	7.52250i		−	0.303831i	−0.988393	−	0.151916i	$-0.951456\pi$
$613$		−	7.52250i		−	0.303831i	0.988393	−	0.151916i	$-0.0485442\pi$
$614$	32.5805	−	36.8740i	1.31484	−	1.48811i
$615$	10.1390			0.408845
$616$	19.5079	+	22.6281i	0.785995	+	0.911713i
$617$	−32.4036			−1.30452			−0.652260	−	0.757995i	$-0.726179\pi$
$617$	−32.4036			−1.30452			−0.652260	+	0.757995i	$0.726179\pi$
$618$	38.7506	−	43.8573i	1.55878	−	1.76420i
$619$			1.89280i			0.0760782i	0.999276	+	0.0380391i	$0.0121112\pi$
$619$			1.89280i			0.0760782i	−0.999276	+	0.0380391i	$0.987889\pi$
$620$	22.8222	−	2.83245i	0.916561	−	0.113754i
$621$	−23.2844			−0.934369
$622$	19.1871	+	16.9530i	0.769332	+	0.679753i
$623$	14.3558			0.575154
$624$	10.8104	−	2.72532i	0.432761	−	0.109100i
$625$	8.31485			0.332594
$626$	29.2102	−	33.0596i	1.16748	−	1.32133i
$627$	−0.295741	+	1.11560i	−0.0118107	+	0.0445530i
$628$	−2.68453	−	21.6303i	−0.107124	−	0.863143i
$629$		−	1.15829i		−	0.0461840i
$630$	−15.6416	+	17.7028i	−0.623175	+	0.705298i
$631$			6.27266i			0.249711i	0.992175	+	0.124855i	$0.0398467\pi$
$631$			6.27266i			0.249711i	−0.992175	+	0.124855i	$0.960153\pi$
$632$	25.3029	+	17.3173i	1.00649	+	0.688847i
$633$		−	19.1809i		−	0.762372i
$634$	20.5394	−	23.2461i	0.815722	−	0.923219i
$635$	−24.1411			−0.958011
$636$	63.8794	−	7.92804i	2.53298	−	0.314367i
$637$		−	3.14305i		−	0.124532i
$638$	−23.6290	−	35.4434i	−0.935480	−	1.40322i
$639$			59.5957i			2.35757i
$640$	−11.6765	−	4.30496i	−0.461553	−	0.170168i
$641$	18.5629			0.733190			0.366595	−	0.930381i	$-0.380523\pi$
$641$	18.5629			0.733190			0.366595	+	0.930381i	$0.380523\pi$
$642$	−35.4955	−	31.3625i	−1.40090	−	1.23778i
$643$		−	40.9531i		−	1.61503i	−0.589846	−	0.807516i	$-0.700812\pi$
$643$		−	40.9531i		−	1.61503i	0.589846	−	0.807516i	$-0.299188\pi$
$644$	−29.8653	+	3.70656i	−1.17686	+	0.146059i
$645$			23.2153i			0.914102i
$646$	0.0534614	+	0.0472365i	0.00210341	+	0.00185850i
$647$			23.2745i			0.915016i	0.889206	+	0.457508i	$0.151258\pi$
$647$			23.2745i			0.915016i	−0.889206	+	0.457508i	$0.848742\pi$
$648$	−1.32774	−	0.908707i	−0.0521585	−	0.0356974i
$649$	−5.68239	+	21.4353i	−0.223053	+	0.841410i
$650$	−4.01668	−	3.54899i	−0.157547	−	0.139203i
$651$	−92.7916			−3.63679
$652$	31.0034	−	3.84782i	1.21419	−	0.150692i
$653$	28.8171			1.12770			0.563851	−	0.825877i	$-0.309319\pi$
$653$	28.8171			1.12770			0.563851	+	0.825877i	$0.309319\pi$
$654$	0.558472	−	0.632068i	0.0218380	−	0.0247158i
$655$	0.802047			0.0313386
$656$	−3.23378	−	12.8273i	−0.126258	−	0.500820i
$657$		−	13.9126i		−	0.542782i
$658$	14.0767	+	12.4377i	0.548768	+	0.484871i
$659$	20.4704			0.797413			0.398707	−	0.917079i	$-0.369459\pi$
$659$	20.4704			0.797413			0.398707	+	0.917079i	$0.369459\pi$
$660$	20.1493	+	2.75026i	0.784311	+	0.107054i
$661$	26.3215			1.02379			0.511893	−	0.859049i	$-0.328944\pi$
$661$	26.3215			1.02379			0.511893	+	0.859049i	$0.328944\pi$
$662$	−24.7836	−	21.8979i	−0.963243	−	0.851086i
$663$			1.12610i			0.0437342i
$664$	9.13453	+	6.25169i	0.354488	+	0.242613i
$665$	−0.437389			−0.0169612
$666$	12.8001	−	14.4869i	0.495993	−	0.561356i
$667$	42.9088			1.66144
$668$	−1.30562	−	10.5199i	−0.0505160	−	0.407028i
$669$	−17.6740			−0.683315
$670$	13.2665	+	11.7217i	0.512528	+	0.452851i
$671$	0.871181	−	3.28631i	0.0336316	−	0.126866i
$672$	44.6152	+	23.0405i	1.72107	+	0.888807i
$673$		−	8.62898i		−	0.332623i	−0.986073	−	0.166311i	$-0.946814\pi$
$673$		−	8.62898i		−	0.332623i	0.986073	−	0.166311i	$-0.0531857\pi$
$674$	13.0501	+	11.5306i	0.502673	+	0.444143i
$675$		−	18.6784i		−	0.718931i
$676$	0.246329	+	1.98477i	0.00947420	+	0.0763374i
$677$		−	5.05795i		−	0.194393i	−0.995265	−	0.0971965i	$-0.969012\pi$
$677$		−	5.05795i		−	0.194393i	0.995265	−	0.0971965i	$-0.0309875\pi$
$678$	−39.9742	−	35.3197i	−1.53520	−	1.35645i
$679$	−10.4533			−0.401161
$680$	0.709959	−	1.03734i	0.0272257	−	0.0397802i
$681$			43.0170i			1.64842i
$682$	27.1978	+	40.7967i	1.04146	+	1.56219i
$683$		−	30.4518i		−	1.16521i	−0.812757	−	0.582603i	$-0.802034\pi$
$683$		−	30.4518i		−	1.16521i	0.812757	−	0.582603i	$-0.197966\pi$
$684$	0.146647	+	1.18159i	0.00560717	+	0.0451792i
$685$	−3.34367			−0.127755
$686$	−11.5024	+	13.0182i	−0.439163	+	0.497036i
$687$		−	40.5640i		−	1.54761i
$688$	29.3705	−	7.40438i	1.11974	−	0.282289i
$689$			11.5475i			0.439927i
$690$	−13.5635	+	15.3510i	−0.516355	+	0.584401i
$691$			31.0783i			1.18227i	0.806571	+	0.591137i	$0.201321\pi$
$691$			31.0783i			1.18227i	−0.806571	+	0.591137i	$0.798679\pi$
$692$	−45.5279	+	5.65045i	−1.73071	+	0.214798i
$693$	−48.6842	−	12.9059i	−1.84936	−	0.490255i
$694$	−25.6051	+	28.9793i	−0.971954	+	1.10004i
$695$	15.2291			0.577671
$696$	−59.0823	−	40.4360i	−2.23951	−	1.53272i
$697$	1.33620			0.0506122
$698$	−12.2985	−	10.8665i	−0.465506	−	0.411304i
$699$	−22.3404			−0.844992
$700$	−2.97335	−	23.9575i	−0.112382	−	0.905507i
$701$			46.7314i			1.76502i	0.470292	+	0.882511i	$0.344148\pi$
$701$			46.7314i			1.76502i	−0.470292	+	0.882511i	$0.655852\pi$
$702$	−4.61479	+	5.22293i	−0.174174	+	0.197127i
$703$	0.357932			0.0134997
$704$	−2.94704	−	26.3688i	−0.111071	−	0.993812i
$705$	12.7861			0.481552
$706$	−27.8151	+	31.4806i	−1.04683	+	1.18479i
$707$			9.37364i			0.352532i
$708$	4.59048	+	36.9873i	0.172521	+	1.39007i
$709$	−11.0151			−0.413680			−0.206840	−	0.978375i	$-0.566318\pi$
$709$	−11.0151			−0.413680			−0.206840	+	0.978375i	$0.566318\pi$
$710$	14.5701	+	12.8736i	0.546808	+	0.483139i
$711$	−51.6895			−1.93851
$712$	−10.5212	−	7.20074i	−0.394299	−	0.269859i
$713$	−49.3896			−1.84966
$714$	−3.35831	+	3.80088i	−0.125682	+	0.142244i
$715$	−0.934827	+	3.52639i	−0.0349605	+	0.131880i
$716$	−30.7949	+	3.82194i	−1.15086	+	0.142833i
$717$		−	22.4139i		−	0.837063i
$718$	−2.08251	+	2.35694i	−0.0777185	+	0.0879603i
$719$			24.2300i			0.903626i	0.892113	+	0.451813i	$0.149223\pi$
$719$			24.2300i			0.903626i	−0.892113	+	0.451813i	$0.850777\pi$
$720$	20.3431	−	5.12854i	0.758142	−	0.191129i
$721$			47.2872i			1.76107i
$722$	17.7769	−	20.1196i	0.661588	−	0.748773i
$723$	−4.73377			−0.176051
$724$	−3.75691	−	30.2709i	−0.139624	−	1.12501i
$725$			34.4208i			1.27836i
$726$	14.0034	+	41.0342i	0.519716	+	1.52292i
$727$			16.8363i			0.624425i	0.950012	+	0.312212i	$0.101070\pi$
$727$			16.8363i			0.624425i	−0.950012	+	0.312212i	$0.898930\pi$
$728$	−5.08765	+	7.43372i	−0.188561	+	0.275512i
$729$	43.9197			1.62665
$730$	−3.40139	−	3.00534i	−0.125891	−	0.111233i
$731$			3.05949i			0.113159i
$732$	−0.703778	−	5.67062i	−0.0260124	−	0.209592i
$733$		−	38.8850i		−	1.43625i	−0.695913	−	0.718126i	$-0.745000\pi$
$733$		−	38.8850i		−	1.43625i	0.695913	−	0.718126i	$-0.255000\pi$
$734$	−12.0191	−	10.6196i	−0.443633	−	0.391977i
$735$		−	9.63593i		−	0.355427i
$736$	23.7471	+	12.2636i	0.875329	+	0.452043i
$737$	−9.67165	+	36.4838i	−0.356260	+	1.34390i
$738$	16.7121	+	14.7662i	0.615180	+	0.543550i
$739$	−31.7483			−1.16788			−0.583941	−	0.811796i	$-0.698490\pi$
$739$	−31.7483			−1.16788			−0.583941	+	0.811796i	$0.698490\pi$
$740$	−0.776778	−	6.25881i	−0.0285549	−	0.230078i
$741$	−0.347986			−0.0127836
$742$	−34.4376	+	38.9759i	−1.26424	+	1.43085i
$743$	9.59026			0.351832			0.175916	−	0.984405i	$-0.443711\pi$
$743$	9.59026			0.351832			0.175916	+	0.984405i	$0.443711\pi$
$744$	68.0059	+	46.5434i	2.49322	+	1.70636i
$745$		−	13.8950i		−	0.509074i
$746$	−29.7919	−	26.3230i	−1.09076	−	0.963752i
$747$	−18.6603			−0.682745
$748$	2.65543	+	0.362451i	0.0970923	+	0.0132525i
$749$	38.2715			1.39841
$750$	−28.5598	−	25.2344i	−1.04286	−	0.921430i
$751$			1.35655i			0.0495012i	0.999694	+	0.0247506i	$0.00787916\pi$
$751$			1.35655i			0.0495012i	−0.999694	+	0.0247506i	$0.992121\pi$
$752$	−4.07805	−	16.1762i	−0.148711	−	0.589884i
$753$	26.9524			0.982201
$754$	8.50421	−	9.62491i	0.309705	−	0.350519i
$755$	9.61971			0.350097
$756$	−31.1521	+	3.86628i	−1.13299	+	0.140615i
$757$	5.81206			0.211243			0.105621	−	0.994406i	$-0.466317\pi$
$757$	5.81206			0.211243			0.105621	+	0.994406i	$0.466317\pi$
$758$	4.92961	+	4.35562i	0.179052	+	0.158203i
$759$	−42.2163	−	11.1913i	−1.53236	−	0.406219i
$760$	0.320557	+	0.219390i	0.0116278	+	0.00795811i
$761$			22.1576i			0.803212i	0.915813	+	0.401606i	$0.131548\pi$
$761$			22.1576i			0.803212i	−0.915813	+	0.401606i	$0.868452\pi$
$762$	−64.8272	−	57.2789i	−2.34844	−	2.07500i
$763$			0.681500i			0.0246720i
$764$	−24.8742	+	3.08712i	−0.899916	+	0.111688i
$765$			2.11911i			0.0766168i
$766$	1.57861	+	1.39480i	0.0570373	+	0.0503961i
$767$	−6.68623			−0.241426
$768$	−21.1411	−	39.2647i	−0.762862	−	1.41684i
$769$			32.8214i			1.18357i	0.806096	+	0.591785i	$0.201577\pi$
$769$			32.8214i			1.18357i	−0.806096	+	0.591785i	$0.798423\pi$
$770$	−13.6718	+	9.11457i	−0.492699	+	0.328466i
$771$			43.6158i			1.57078i
$772$	−7.93381	+	0.984661i	−0.285544	+	0.0354387i
$773$	−48.6899			−1.75125			−0.875627	−	0.482988i	$-0.839552\pi$
$773$	−48.6899			−1.75125			−0.875627	+	0.482988i	$0.839552\pi$
$774$	−33.8101	+	38.2656i	−1.21528	+	1.37543i
$775$		−	39.6196i		−	1.42318i
$776$	7.66111	+	5.24328i	0.275018	+	0.188223i
$777$			25.4474i			0.912921i
$778$	1.96851	−	2.22792i	0.0705745	−	0.0798749i
$779$			0.412910i			0.0147940i
$780$	0.755193	+	6.08489i	0.0270403	+	0.217874i
$781$	−10.6221	+	40.0690i	−0.380088	+	1.43378i
$782$	−1.78751	+	2.02307i	−0.0639212	+	0.0723448i
$783$	44.7577			1.59951
$784$	−12.1908	+	3.07332i	−0.435385	+	0.109761i
$785$	11.9877			0.427858
$786$	2.15377	+	1.90299i	0.0768226	+	0.0678775i
$787$	19.6216			0.699434			0.349717	−	0.936855i	$-0.386278\pi$
$787$	19.6216			0.699434			0.349717	+	0.936855i	$0.386278\pi$
$788$	−8.48514	+	1.05309i	−0.302271	+	0.0375147i
$789$		−	82.3852i		−	2.93299i
$790$	−11.1658	+	12.6372i	−0.397260	+	0.449612i
$791$	43.1005			1.53248
$792$	29.2066	+	33.8781i	1.03781	+	1.20381i
$793$	1.02508			0.0364018
$794$	9.70174	−	10.9803i	0.344302	−	0.389675i
$795$			35.4024i			1.25559i
$796$	−34.3006	+	4.25703i	−1.21575	+	0.150886i
$797$	24.6757			0.874058			0.437029	−	0.899447i	$-0.356031\pi$
$797$	24.6757			0.874058			0.437029	+	0.899447i	$0.356031\pi$
$798$	−1.17454	−	1.03778i	−0.0415782	−	0.0367370i
$799$	1.68505			0.0596128
$800$	−9.83770	+	19.0495i	−0.347815	+	0.673503i
$801$	21.4931			0.759421
$802$	22.6850	−	25.6744i	0.801034	−	0.906596i
$803$	2.47972	−	9.35410i	0.0875074	−	0.330099i
$804$	7.81318	+	62.9539i	0.275549	+	2.22021i
$805$		−	16.5515i		−	0.583364i
$806$	−9.78866	+	11.0786i	−0.344791	+	0.390228i
$807$			17.1322i			0.603083i
$808$	4.70173	−	6.86983i	0.165406	−	0.241680i
$809$			28.9665i			1.01841i	0.860646	+	0.509204i	$0.170060\pi$
$809$			28.9665i			1.01841i	−0.860646	+	0.509204i	$0.829940\pi$
$810$	0.585911	−	0.663123i	0.0205868	−	0.0232998i
$811$	56.4774			1.98319			0.991595	−	0.129377i	$-0.0412977\pi$
$811$	56.4774			1.98319			0.991595	+	0.129377i	$0.0412977\pi$
$812$	57.4077	−	7.12484i	2.01461	−	0.250033i
$813$			62.1948i			2.18127i
$814$	11.1882	−	7.45880i	0.392146	−	0.261431i
$815$			17.1823i			0.601870i
$816$	4.36775	−	1.10112i	0.152902	−	0.0385469i
$817$	−0.945439			−0.0330767
$818$	−21.5045	−	19.0005i	−0.751886	−	0.664338i
$819$		−	15.1859i		−	0.530637i
$820$	7.22016	−	0.896091i	0.252139	−	0.0312928i
$821$		−	8.69317i		−	0.303394i	−0.988427	−	0.151697i	$-0.951526\pi$
$821$		−	8.69317i		−	0.303394i	0.988427	−	0.151697i	$-0.0484738\pi$
$822$	−8.97891	−	7.93343i	−0.313176	−	0.276710i
$823$		−	18.9006i		−	0.658835i	−0.944184	−	0.329418i	$-0.893148\pi$
$823$		−	18.9006i		−	0.658835i	0.944184	−	0.329418i	$-0.106852\pi$
$824$	23.7188	−	34.6562i	0.826284	−	1.20731i
$825$	8.97750	−	33.8653i	0.312557	−	1.17904i
$826$	−22.5677	−	19.9400i	−0.785231	−	0.693801i
$827$	13.0032			0.452166			0.226083	−	0.974108i	$-0.427408\pi$
$827$	13.0032			0.452166			0.226083	+	0.974108i	$0.427408\pi$
$828$	−44.7133	+	5.54935i	−1.55390	+	0.192853i
$829$	27.6999			0.962058			0.481029	−	0.876705i	$-0.340263\pi$
$829$	27.6999			0.962058			0.481029	+	0.876705i	$0.340263\pi$
$830$	−4.03093	+	4.56213i	−0.139916	+	0.158354i
$831$	46.8596			1.62554
$832$	7.45736	−	2.89616i	0.258537	−	0.100406i
$833$		−	1.26990i		−	0.0439994i
$834$	40.8953	+	36.1335i	1.41609	+	1.25120i
$835$	5.83020			0.201762
$836$	−0.112004	+	0.820577i	−0.00387374	+	0.0283802i
$837$	−51.5178			−1.78071
$838$	−9.69980	−	8.57038i	−0.335074	−	0.296059i
$839$		−	7.03051i		−	0.242720i	−0.992609	−	0.121360i	$-0.961274\pi$
$839$		−	7.03051i		−	0.242720i	0.992609	−	0.121360i	$-0.0387256\pi$
$840$	−15.5977	+	22.7902i	−0.538171	+	0.786337i
$841$	−53.4802			−1.84415
$842$	−6.49589	+	7.35193i	−0.223863	+	0.253364i
$843$	62.2142			2.14277
$844$	−1.69521	−	13.6590i	−0.0583517	−	0.470163i
$845$	−1.09997			−0.0378402
$846$	21.0752	+	18.6213i	0.724581	+	0.640213i
$847$	−30.4324	−	17.3545i	−1.04567	−	0.596308i
$848$	44.7888	−	11.2914i	1.53805	−	0.387747i
$849$			25.7279i			0.882980i
$850$	−1.62288	−	1.43391i	−0.0556642	−	0.0491828i
$851$			13.5447i			0.464307i
$852$	8.58097	+	69.1403i	0.293979	+	2.36871i
$853$			35.2284i			1.20620i	0.797666	+	0.603099i	$0.206068\pi$
$853$			35.2284i			1.20620i	−0.797666	+	0.603099i	$0.793932\pi$
$854$	3.45991	+	3.05705i	0.118396	+	0.104610i
$855$	−0.654845			−0.0223952
$856$	−28.0488	−	19.1966i	−0.958687	−	0.656128i
$857$		−	35.6180i		−	1.21669i	−0.793674	−	0.608343i	$-0.791834\pi$
$857$		−	35.6180i		−	1.21669i	0.793674	−	0.608343i	$-0.208166\pi$
$858$	−10.8773	+	7.25154i	−0.371345	+	0.247564i
$859$		−	22.6595i		−	0.773133i	−0.922262	−	0.386567i	$-0.873661\pi$
$859$		−	22.6595i		−	0.773133i	0.922262	−	0.386567i	$-0.126339\pi$
$860$	2.05178	+	16.5320i	0.0699650	+	0.563736i
$861$	−29.3561			−1.00045
$862$	−18.4020	+	20.8271i	−0.626775	+	0.709372i
$863$		−	26.4145i		−	0.899162i	−0.893240	−	0.449581i	$-0.851573\pi$
$863$		−	26.4145i		−	0.899162i	0.893240	−	0.449581i	$-0.148427\pi$
$864$	24.7703	+	12.7921i	0.842703	+	0.435195i
$865$		−	25.2319i		−	0.857909i
$866$	−11.2127	+	12.6903i	−0.381024	+	0.431235i
$867$		−	46.9266i		−	1.59371i
$868$	−66.0784	+	8.20096i	−2.24285	+	0.278359i
$869$	−34.7533	−	9.21291i	−1.17893	−	0.312527i
$870$	26.0721	−	29.5079i	0.883928	−	1.00041i
$871$	−11.3802			−0.385605
$872$	0.341834	−	0.499463i	0.0115760	−	0.0169140i
$873$	−15.6504			−0.529685
$874$	−0.625165	−	0.552372i	−0.0211465	−	0.0186843i
$875$	30.7934			1.04101
$876$	−2.00322	−	16.1408i	−0.0676827	−	0.545346i
$877$			20.8866i			0.705291i	0.935757	+	0.352645i	$0.114718\pi$
$877$			20.8866i			0.705291i	−0.935757	+	0.352645i	$0.885282\pi$
$878$	14.7359	−	16.6779i	0.497314	−	0.562851i
$879$	5.14338			0.173482
$880$	14.5917	+	0.177702i	0.491886	+	0.00599032i
$881$	21.9853			0.740704			0.370352	−	0.928891i	$-0.379237\pi$
$881$	21.9853			0.740704			0.370352	+	0.928891i	$0.379237\pi$
$882$	14.0335	−	15.8828i	0.472532	−	0.534803i
$883$		−	17.3585i		−	0.584161i	−0.956394	−	0.292080i	$-0.905653\pi$
$883$		−	17.3585i		−	0.584161i	0.956394	−	0.292080i	$-0.0943475\pi$
$884$	0.0995253	+	0.801915i	0.00334740	+	0.0269713i
$885$	−20.4986			−0.689052
$886$	9.34358	+	8.25564i	0.313904	+	0.277354i
$887$	−36.0313			−1.20981			−0.604906	−	0.796297i	$-0.706789\pi$
$887$	−36.0313			−1.20981			−0.604906	+	0.796297i	$0.706789\pi$
$888$	12.7642	−	18.6501i	0.428338	−	0.625856i
$889$	69.8972			2.34428
$890$	4.64285	−	5.25469i	0.155629	−	0.176138i
$891$	1.82364	+	0.483437i	0.0610943	+	0.0161958i
$892$	−12.5859	+	1.56203i	−0.421407	+	0.0523006i
$893$			0.520711i			0.0174249i
$894$	32.9683	−	37.3129i	1.10262	−	1.24793i
$895$		−	17.0667i		−	0.570477i
$896$	33.8075	+	12.4644i	1.12943	+	0.416406i
$897$		−	13.1684i		−	0.439679i
$898$	−7.10751	+	8.04415i	−0.237181	+	0.268437i
$899$	94.9378			3.16635
$900$	−4.45161	−	35.8684i	−0.148387	−	1.19561i
$901$			4.66560i			0.155434i
$902$	8.60447	+	12.9067i	0.286498	+	0.429746i
$903$		−	67.2166i		−	2.23683i
$904$	−31.5878	−	21.6188i	−1.05060	−	0.719030i
$905$	16.7763			0.557664
$906$	25.8322	+	22.8244i	0.858219	+	0.758290i
$907$		−	34.0513i		−	1.13065i	−0.824867	−	0.565327i	$-0.808750\pi$
$907$		−	34.0513i		−	1.13065i	0.824867	−	0.565327i	$-0.191250\pi$
$908$	3.80186	+	30.6331i	0.126169	+	1.01659i
$909$			14.0339i			0.465476i
$910$	−3.71268	−	3.28039i	−0.123074	−	0.108744i
$911$		−	46.4260i		−	1.53816i	−0.639151	−	0.769082i	$-0.720714\pi$
$911$		−	46.4260i		−	1.53816i	0.639151	−	0.769082i	$-0.279286\pi$
$912$	0.340266	+	1.34971i	0.0112673	+	0.0446935i
$913$	−12.5462	−	3.32593i	−0.415219	−	0.110072i
$914$	−17.6341	−	15.5809i	−0.583286	−	0.515369i
$915$	3.14269			0.103894
$916$	−3.58506	−	28.8862i	−0.118454	−	0.954428i
$917$	−2.32221			−0.0766863
$918$	−1.86453	+	2.11024i	−0.0615387	+	0.0696483i
$919$	26.2047			0.864415			0.432207	−	0.901774i	$-0.357735\pi$
$919$	26.2047			0.864415			0.432207	+	0.901774i	$0.357735\pi$
$920$	−8.30208	+	12.1304i	−0.273711	+	0.399928i
$921$			96.9747i			3.19543i
$922$	20.7797	+	18.3602i	0.684344	+	0.604661i
$923$	−12.4986			−0.411395
$924$	−58.3395	−	7.96300i	−1.91923	−	0.261963i
$925$	−10.8654			−0.357252
$926$	−39.7451	−	35.1173i	−1.30610	−	1.15402i
$927$			70.7969i			2.32528i
$928$	−45.6471	−	23.5734i	−1.49844	−	0.773836i
$929$	−27.2396			−0.893703			−0.446852	−	0.894608i	$-0.647455\pi$
$929$	−27.2396			−0.893703			−0.446852	+	0.894608i	$0.647455\pi$
$930$	−30.0100	+	33.9647i	−0.984066	+	1.11375i
$931$	0.392421			0.0128611
$932$	−15.9089	+	1.97445i	−0.521115	+	0.0646753i
$933$	−50.4601			−1.65199
$934$	−18.5059	−	16.3511i	−0.605532	−	0.535025i
$935$	−0.377702	+	1.42478i	−0.0123522	+	0.0465953i
$936$	−7.61708	+	11.1295i	−0.248972	+	0.363780i
$937$		−	52.1689i		−	1.70429i	−0.523310	−	0.852143i	$-0.675303\pi$
$937$		−	52.1689i		−	1.70429i	0.523310	−	0.852143i	$-0.324697\pi$
$938$	−38.4112	−	33.9387i	−1.25417	−	1.10814i
$939$			86.9433i			2.83729i
$940$	9.10517	−	1.13004i	0.296978	−	0.0368578i
$941$		−	50.2788i		−	1.63904i	−0.573050	−	0.819520i	$-0.694240\pi$
$941$		−	50.2788i		−	1.63904i	0.573050	−	0.819520i	$-0.305760\pi$
$942$	32.1910	+	28.4427i	1.04884	+	0.926715i
$943$	−15.6252			−0.508826
$944$	6.53790	+	25.9335i	0.212790	+	0.844064i
$945$		−	17.2647i		−	0.561621i
$946$	−29.5524	+	19.7016i	−0.960831	+	0.640555i
$947$			37.1438i			1.20701i	0.797359	+	0.603505i	$0.206230\pi$
$947$			37.1438i			1.20701i	−0.797359	+	0.603505i	$0.793770\pi$
$948$	−59.9679	+	7.44259i	−1.94767	+	0.241724i
$949$	2.91778			0.0947153
$950$	0.443105	−	0.501498i	0.0143762	−	0.0162707i
$951$			61.1347i			1.98243i
$952$	−2.05558	+	3.00347i	−0.0666219	+	0.0973431i
$953$		−	22.0491i		−	0.714242i	−0.934058	−	0.357121i	$-0.883758\pi$
$953$		−	22.0491i		−	0.714242i	0.934058	−	0.357121i	$-0.116242\pi$
$954$	−51.5589	+	58.3534i	−1.66928	+	1.88926i
$955$		−	13.7854i		−	0.446086i
$956$	−1.98095	−	15.9613i	−0.0640685	−	0.516225i
$957$	81.1491	+	21.5122i	2.62318	+	0.695390i
$958$	35.5113	−	40.1910i	1.14732	−	1.29851i
$959$	9.68113			0.312620
$960$	22.8627	−	8.87903i	0.737890	−	0.286569i
$961$	−78.2769			−2.52506
$962$	3.03823	+	2.68447i	0.0979565	+	0.0865507i
$963$	57.2989			1.84643
$964$	−3.37099	+	0.418372i	−0.108572	+	0.0134749i
$965$		−	4.39696i		−	0.141543i
$966$	39.2713	−	44.4465i	1.26353	−	1.43004i
$967$	15.8934			0.511098			0.255549	−	0.966796i	$-0.417744\pi$
$967$	15.8934			0.511098			0.255549	+	0.966796i	$0.417744\pi$
$968$	13.5987	+	27.9835i	0.437078	+	0.899424i
$969$	−0.140598			−0.00451666
$970$	−3.38073	+	3.82625i	−0.108549	+	0.122854i
$971$		−	35.6585i		−	1.14433i	−0.820137	−	0.572167i	$-0.806103\pi$
$971$		−	35.6585i		−	1.14433i	0.820137	−	0.572167i	$-0.193897\pi$
$972$	32.4911	−	4.03246i	1.04215	−	0.129341i
$973$	−44.0936			−1.41357
$974$	−20.5391	−	18.1476i	−0.658114	−	0.581485i
$975$	10.5635			0.338302
$976$	−1.00234	−	3.97594i	−0.0320842	−	0.127267i
$977$	−42.8948			−1.37233			−0.686163	−	0.727448i	$-0.740706\pi$
$977$	−42.8948			−1.37233			−0.686163	+	0.727448i	$0.740706\pi$
$978$	−40.7679	+	46.1404i	−1.30361	+	1.47541i
$979$	14.4508	+	3.83083i	0.461850	+	0.122434i
$980$	−0.851626	−	6.86189i	−0.0272042	−	0.219195i
$981$			1.02032i			0.0325763i
$982$	−24.4426	+	27.6637i	−0.779996	+	0.882785i
$983$		−	41.2474i		−	1.31559i	−0.753198	−	0.657794i	$-0.771490\pi$
$983$		−	41.2474i		−	1.31559i	0.753198	−	0.657794i	$-0.228510\pi$
$984$	21.5147	+	14.7247i	0.685865	+	0.469408i
$985$		−	4.70252i		−	0.149835i
$986$	3.43599	−	3.88879i	0.109424	−	0.123844i
$987$	−37.0203			−1.17837
$988$	−0.247806	+	0.0307551i	−0.00788376	+	0.000978450i
$989$		−	35.7770i		−	1.13764i
$990$	−20.4690	+	13.6460i	−0.650549	+	0.433700i
$991$			8.84218i			0.280881i	0.990089	+	0.140441i	$0.0448519\pi$
$991$			8.84218i			0.280881i	−0.990089	+	0.140441i	$0.955148\pi$
$992$	52.5416	+	27.1339i	1.66820	+	0.861502i
$993$	65.1784			2.06837
$994$	−42.1858	−	37.2738i	−1.33805	−	1.18225i
$995$		−	19.0096i		−	0.602645i
$996$	−21.6489	+	2.68683i	−0.685971	+	0.0851355i
$997$			32.0386i			1.01467i	0.861748	+	0.507336i	$0.169370\pi$
$997$			32.0386i			1.01467i	−0.861748	+	0.507336i	$0.830630\pi$
$998$	8.47647	+	7.48949i	0.268318	+	0.237076i
$999$			14.1284i			0.447002i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.e.b.131.18	yes	64
4.3	odd	2	inner	572.2.e.b.131.48	yes	64
11.10	odd	2	inner	572.2.e.b.131.47	yes	64
44.43	even	2	inner	572.2.e.b.131.17	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.e.b.131.17	✓	64	44.43	even	2	inner
572.2.e.b.131.18	yes	64	1.1	even	1	trivial
572.2.e.b.131.47	yes	64	11.10	odd	2	inner
572.2.e.b.131.48	yes	64	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.936395 + 1.05979i) q^{2} -2.78715i q^{3} +(-0.246329 - 1.98477i) q^{4} +1.09997 q^{5} +(2.95381 + 2.60987i) q^{6} -3.18482 q^{7} +(2.33411 + 1.59747i) q^{8} -4.76820 q^{9} +O(q^{10})\)	\(q+(-0.936395 + 1.05979i) q^{2} -2.78715i q^{3} +(-0.246329 - 1.98477i) q^{4} +1.09997 q^{5} +(2.95381 + 2.60987i) q^{6} -3.18482 q^{7} +(2.33411 + 1.59747i) q^{8} -4.76820 q^{9} +(-1.03001 + 1.16575i) q^{10} +(-3.20589 - 0.849864i) q^{11} +(-5.53186 + 0.686556i) q^{12} -1.00000i q^{13} +(2.98224 - 3.37525i) q^{14} -3.06579i q^{15} +(-3.87864 + 0.977815i) q^{16} -0.404034i q^{17} +(4.46492 - 5.05332i) q^{18} +0.124854 q^{19} +(-0.270955 - 2.18320i) q^{20} +8.87656i q^{21} +(3.90266 - 2.60178i) q^{22} +4.72467i q^{23} +(4.45240 - 6.50552i) q^{24} -3.79006 q^{25} +(1.05979 + 0.936395i) q^{26} +4.92825i q^{27} +(0.784513 + 6.32113i) q^{28} -9.08186i q^{29} +(3.24911 + 2.87079i) q^{30} +10.4536i q^{31} +(2.59566 - 5.02619i) q^{32} +(-2.36870 + 8.93530i) q^{33} +(0.428193 + 0.378335i) q^{34} -3.50321 q^{35} +(1.17455 + 9.46380i) q^{36} +2.86681 q^{37} +(-0.116912 + 0.132319i) q^{38} -2.78715 q^{39} +(2.56746 + 1.75718i) q^{40} +3.30715i q^{41} +(-9.40733 - 8.31196i) q^{42} -7.57237 q^{43} +(-0.897081 + 6.57231i) q^{44} -5.24490 q^{45} +(-5.00718 - 4.42416i) q^{46} +4.17057i q^{47} +(2.72532 + 10.8104i) q^{48} +3.14305 q^{49} +(3.54899 - 4.01668i) q^{50} -1.12610 q^{51} +(-1.98477 + 0.246329i) q^{52} -11.5475 q^{53} +(-5.22293 - 4.61479i) q^{54} +(-3.52639 - 0.934827i) q^{55} +(-7.43372 - 5.08765i) q^{56} -0.347986i q^{57} +(9.62491 + 8.50421i) q^{58} -6.68623i q^{59} +(-6.08489 + 0.755193i) q^{60} +1.02508i q^{61} +(-11.0786 - 9.78866i) q^{62} +15.1859 q^{63} +(2.89616 + 7.45736i) q^{64} -1.09997i q^{65} +(-7.25154 - 10.8773i) q^{66} -11.3802i q^{67} +(-0.801915 + 0.0995253i) q^{68} +13.1684 q^{69} +(3.28039 - 3.71268i) q^{70} -12.4986i q^{71} +(-11.1295 - 7.61708i) q^{72} +2.91778i q^{73} +(-2.68447 + 3.03823i) q^{74} +10.5635i q^{75} +(-0.0307551 - 0.247806i) q^{76} +(10.2102 + 2.70666i) q^{77} +(2.60987 - 2.95381i) q^{78} +10.8405 q^{79} +(-4.26640 + 1.07557i) q^{80} -0.568841 q^{81} +(-3.50490 - 3.09680i) q^{82} +3.91349 q^{83} +(17.6179 - 2.18656i) q^{84} -0.444426i q^{85} +(7.09073 - 8.02516i) q^{86} -25.3125 q^{87} +(-6.12528 - 7.10500i) q^{88} -4.50758 q^{89} +(4.91129 - 5.55851i) q^{90} +3.18482i q^{91} +(9.37739 - 1.16382i) q^{92} +29.1356 q^{93} +(-4.41995 - 3.90530i) q^{94} +0.137336 q^{95} +(-14.0087 - 7.23449i) q^{96} +3.28224 q^{97} +(-2.94314 + 3.33099i) q^{98} +(15.2863 + 4.05232i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9}+O(q^{10}) \) 64 * q + 6 * q^4 + 12 * q^5 - 104 * q^9	\( 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9} - 8 q^{12} - 34 q^{14} + 26 q^{16} + 14 q^{20} - 8 q^{22} + 76 q^{25} + 2 q^{26} - 16 q^{33} + 32 q^{34} - 24 q^{36} - 32 q^{37} - 30 q^{38} + 54 q^{42} + 10 q^{44} + 12 q^{45} + 34 q^{48} - 36 q^{49} - 32 q^{53} - 36 q^{56} + 62 q^{58} + 4 q^{60} - 18 q^{64} - 30 q^{66} - 24 q^{69} - 30 q^{70} + 88 q^{77} - 10 q^{78} - 46 q^{80} + 64 q^{81} - 46 q^{82} + 98 q^{86} + 16 q^{88} + 24 q^{89} + 84 q^{92} + 8 q^{93} - 88 q^{97}+O(q^{100}) \) 64 * q + 6 * q^4 + 12 * q^5 - 104 * q^9 - 8 * q^12 - 34 * q^14 + 26 * q^16 + 14 * q^20 - 8 * q^22 + 76 * q^25 + 2 * q^26 - 16 * q^33 + 32 * q^34 - 24 * q^36 - 32 * q^37 - 30 * q^38 + 54 * q^42 + 10 * q^44 + 12 * q^45 + 34 * q^48 - 36 * q^49 - 32 * q^53 - 36 * q^56 + 62 * q^58 + 4 * q^60 - 18 * q^64 - 30 * q^66 - 24 * q^69 - 30 * q^70 + 88 * q^77 - 10 * q^78 - 46 * q^80 + 64 * q^81 - 46 * q^82 + 98 * q^86 + 16 * q^88 + 24 * q^89 + 84 * q^92 + 8 * q^93 - 88 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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