LMFDB - Embedded newform 414.2.m.a.13.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(13,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([22, 42]))

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

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

chi := DirichletCharacter("414.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.m (of order $33$, degree $20$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			13.6
Character	$\chi$	$=$	414.13
Dual form			414.2.m.a.223.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.327068 - 0.945001i) q^{2} +(0.0157937 + 1.73198i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-1.24523 - 1.74869i) q^{5} +(1.64189 + 0.551550i) q^{6} +(-0.351646 - 1.44951i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-2.99950 + 0.0547087i) q^{9} +O(q^{10})$	\(q+(0.327068 - 0.945001i) q^{2} +(0.0157937 + 1.73198i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-1.24523 - 1.74869i) q^{5} +(1.64189 + 0.551550i) q^{6} +(-0.351646 - 1.44951i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-2.99950 + 0.0547087i) q^{9} +(-2.05979 + 0.604808i) q^{10} +(-5.44563 - 1.04956i) q^{11} +(1.05822 - 1.37119i) q^{12} +(0.622001 - 2.56392i) q^{13} +(-1.48480 - 0.141781i) q^{14} +(3.00902 - 2.18434i) q^{15} +(0.235759 + 0.971812i) q^{16} +(-0.0821263 - 0.571201i) q^{17} +(-0.929341 + 2.85242i) q^{18} +(0.860538 - 5.98517i) q^{19} +(-0.102146 + 2.14431i) q^{20} +(2.50496 - 0.631937i) q^{21} +(-2.77293 + 4.80285i) q^{22} +(3.77132 + 2.96263i) q^{23} +(-0.949665 - 1.44849i) q^{24} +(0.128041 - 0.369950i) q^{25} +(-2.21947 - 1.42637i) q^{26} +(-0.142128 - 5.19421i) q^{27} +(-0.619612 + 1.35676i) q^{28} +(-4.88858 + 3.84442i) q^{29} +(-1.08005 - 3.55796i) q^{30} +(0.352362 + 7.39699i) q^{31} +(0.995472 + 0.0950560i) q^{32} +(1.73181 - 9.44829i) q^{33} +(-0.566646 - 0.109212i) q^{34} +(-2.09685 + 2.41989i) q^{35} +(2.39159 + 1.81116i) q^{36} +(-4.83189 - 10.5804i) q^{37} +(-5.37454 - 2.77077i) q^{38} +(4.45049 + 1.03680i) q^{39} +(1.99297 + 0.797865i) q^{40} +(-3.11658 - 4.37662i) q^{41} +(0.222111 - 2.57387i) q^{42} +(-0.405752 + 8.51779i) q^{43} +(3.63176 + 4.19128i) q^{44} +(3.83075 + 5.17707i) q^{45} +(4.03316 - 2.59492i) q^{46} +(-3.55460 - 6.15675i) q^{47} +(-1.67943 + 0.423678i) q^{48} +(4.24444 - 2.18816i) q^{49} +(-0.307725 - 0.241997i) q^{50} +(0.988010 - 0.151262i) q^{51} +(-2.07384 + 1.63088i) q^{52} +(-0.595290 - 0.174793i) q^{53} +(-4.95502 - 1.56455i) q^{54} +(4.94574 + 10.8297i) q^{55} +(1.07949 + 1.02929i) q^{56} +(10.3798 + 1.39591i) q^{57} +(2.03408 + 5.87710i) q^{58} +(-1.38298 + 5.70071i) q^{59} +(-3.71552 - 0.143049i) q^{60} +(6.51652 + 3.35950i) q^{61} +(7.10541 + 2.08634i) q^{62} +(1.13406 + 4.32855i) q^{63} +(0.415415 - 0.909632i) q^{64} +(-5.25804 + 2.10500i) q^{65} +(-8.36223 - 4.72679i) q^{66} +(9.20314 - 1.77376i) q^{67} +(-0.288537 + 0.499761i) q^{68} +(-5.07165 + 6.57863i) q^{69} +(1.60099 + 2.77299i) q^{70} +(5.72012 + 6.60136i) q^{71} +(2.49376 - 1.66768i) q^{72} +(-0.717669 + 4.99150i) q^{73} +(-11.5788 + 1.10564i) q^{74} +(0.642767 + 0.215921i) q^{75} +(-4.37622 + 4.17271i) q^{76} +(0.393593 + 8.26254i) q^{77} +(2.43539 - 3.86661i) q^{78} +(-1.86726 - 1.78043i) q^{79} +(1.40582 - 1.62240i) q^{80} +(8.99401 - 0.328198i) q^{81} +(-5.15524 + 1.51372i) q^{82} +(8.58859 - 12.0610i) q^{83} +(-2.35967 - 1.05173i) q^{84} +(-0.896585 + 0.854892i) q^{85} +(7.91661 + 3.16933i) q^{86} +(-6.73566 - 8.40620i) q^{87} +(5.14859 - 2.06118i) q^{88} +(-8.39580 - 5.39565i) q^{89} +(6.14525 - 1.92681i) q^{90} -3.93515 q^{91} +(-1.13308 - 4.66006i) q^{92} +(-12.8059 + 0.727109i) q^{93} +(-6.98073 + 1.34543i) q^{94} +(-11.5378 + 5.94814i) q^{95} +(-0.148913 + 1.72564i) q^{96} +(-1.63461 + 0.156086i) q^{97} +(-0.679593 - 4.72667i) q^{98} +(16.3916 + 2.85023i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9}+O(q^{10}) $ 240 * q - 12 * q^2 + 12 * q^4 - 13 * q^7 + 24 * q^8 - 36 * q^9	\( 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9} + 2 q^{11} + 11 q^{12} + 4 q^{13} + 2 q^{14} + 6 q^{15} + 12 q^{16} - 8 q^{17} - 18 q^{18} + 12 q^{19} - 29 q^{21} + 20 q^{22} + 10 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} - 8 q^{29} - 18 q^{30} - 12 q^{32} + 50 q^{33} - 4 q^{34} - 12 q^{35} - 4 q^{36} + 92 q^{37} + 6 q^{38} + 44 q^{39} + 2 q^{41} + 42 q^{42} - 14 q^{43} - 4 q^{44} - 2 q^{45} - 44 q^{46} + 10 q^{47} - 22 q^{48} + 43 q^{49} - 43 q^{50} - 90 q^{51} - 18 q^{52} + 16 q^{53} - 29 q^{54} - 8 q^{55} + 13 q^{56} + 7 q^{57} + 8 q^{58} - 84 q^{59} + 9 q^{60} - 53 q^{61} - 66 q^{62} + 11 q^{63} - 24 q^{64} + 79 q^{65} - 110 q^{66} + 46 q^{67} - 40 q^{68} - 55 q^{69} - 6 q^{70} - 14 q^{71} - 19 q^{72} + 16 q^{73} + 46 q^{74} - 44 q^{75} - 6 q^{76} - 96 q^{77} + 20 q^{78} + 20 q^{79} - 22 q^{80} - 56 q^{81} + 26 q^{82} + 57 q^{83} + 5 q^{84} - 2 q^{85} - 8 q^{86} - 198 q^{87} - 2 q^{88} + 60 q^{89} - 22 q^{90} - 252 q^{91} - 218 q^{93} - 10 q^{94} + 6 q^{95} - q^{97} + 20 q^{98} + 84 q^{99}+O(q^{100}) \) 240 * q - 12 * q^2 + 12 * q^4 - 13 * q^7 + 24 * q^8 - 36 * q^9 + 2 * q^11 + 11 * q^12 + 4 * q^13 + 2 * q^14 + 6 * q^15 + 12 * q^16 - 8 * q^17 - 18 * q^18 + 12 * q^19 - 29 * q^21 + 20 * q^22 + 10 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 - 8 * q^29 - 18 * q^30 - 12 * q^32 + 50 * q^33 - 4 * q^34 - 12 * q^35 - 4 * q^36 + 92 * q^37 + 6 * q^38 + 44 * q^39 + 2 * q^41 + 42 * q^42 - 14 * q^43 - 4 * q^44 - 2 * q^45 - 44 * q^46 + 10 * q^47 - 22 * q^48 + 43 * q^49 - 43 * q^50 - 90 * q^51 - 18 * q^52 + 16 * q^53 - 29 * q^54 - 8 * q^55 + 13 * q^56 + 7 * q^57 + 8 * q^58 - 84 * q^59 + 9 * q^60 - 53 * q^61 - 66 * q^62 + 11 * q^63 - 24 * q^64 + 79 * q^65 - 110 * q^66 + 46 * q^67 - 40 * q^68 - 55 * q^69 - 6 * q^70 - 14 * q^71 - 19 * q^72 + 16 * q^73 + 46 * q^74 - 44 * q^75 - 6 * q^76 - 96 * q^77 + 20 * q^78 + 20 * q^79 - 22 * q^80 - 56 * q^81 + 26 * q^82 + 57 * q^83 + 5 * q^84 - 2 * q^85 - 8 * q^86 - 198 * q^87 - 2 * q^88 + 60 * q^89 - 22 * q^90 - 252 * q^91 - 218 * q^93 - 10 * q^94 + 6 * q^95 - q^97 + 20 * q^98 + 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{11}\right)$

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 $

$2$	0.327068	−	0.945001i	0.231272	−	0.668216i
$2$	0.327068	−	0.945001i	0.231272	−	0.668216i
$3$	0.0157937	+	1.73198i	0.00911850	+	0.999958i
$3$	0.0157937	+	1.73198i	0.00911850	+	0.999958i
$4$	−0.786053	−	0.618159i	−0.393027	−	0.309079i
$5$	−1.24523	−	1.74869i	−0.556886	−	0.782037i	0.436147	−	0.899876i	$-0.356343\pi$
$5$	−1.24523	−	1.74869i	−0.556886	−	0.782037i	−0.993033	+	0.117839i	$0.962403\pi$
$6$	1.64189	+	0.551550i	0.670298	+	0.225169i
$7$	−0.351646	−	1.44951i	−0.132910	−	0.547861i	−0.998860	−	0.0477317i	$-0.984801\pi$
$7$	−0.351646	−	1.44951i	−0.132910	−	0.547861i	0.865950	−	0.500130i	$-0.166714\pi$
$8$	−0.841254	+	0.540641i	−0.297428	+	0.191145i
$9$	−2.99950	+	0.0547087i	−0.999834	+	0.0182362i
$10$	−2.05979	+	0.604808i	−0.651362	+	0.191257i
$11$	−5.44563	−	1.04956i	−1.64192	−	0.316454i	−0.717132	−	0.696938i	$-0.754545\pi$
$11$	−5.44563	−	1.04956i	−1.64192	−	0.316454i	−0.924788	+	0.380483i	$0.875758\pi$
$12$	1.05822	−	1.37119i	0.305483	−	0.395829i
$13$	0.622001	−	2.56392i	0.172512	−	0.711105i	−0.818178	−	0.574966i	$-0.805015\pi$
$13$	0.622001	−	2.56392i	0.172512	−	0.711105i	0.990690	−	0.136139i	$-0.0434694\pi$
$14$	−1.48480	−	0.141781i	−0.396828	−	0.0378925i
$15$	3.00902	−	2.18434i	0.776926	−	0.563994i
$16$	0.235759	+	0.971812i	0.0589397	+	0.242953i
$17$	−0.0821263	−	0.571201i	−0.0199185	−	0.138537i	0.977435	−	0.211234i	$-0.0677483\pi$
$17$	−0.0821263	−	0.571201i	−0.0199185	−	0.138537i	−0.997354	+	0.0726977i	$0.976839\pi$
$18$	−0.929341	+	2.85242i	−0.219048	+	0.672323i
$19$	0.860538	−	5.98517i	0.197421	−	1.37309i	−0.614312	−	0.789064i	$-0.710566\pi$
$19$	0.860538	−	5.98517i	0.197421	−	1.37309i	0.811732	−	0.584029i	$-0.198525\pi$
$20$	−0.102146	+	2.14431i	−0.0228406	+	0.479483i
$21$	2.50496	−	0.631937i	0.546627	−	0.137900i
$22$	−2.77293	+	4.80285i	−0.591190	+	1.02397i
$23$	3.77132	+	2.96263i	0.786374	+	0.617751i
$23$	3.77132	+	2.96263i	0.786374	+	0.617751i
$24$	−0.949665	−	1.44849i	−0.193850	−	0.295673i
$25$	0.128041	−	0.369950i	0.0256082	−	0.0739899i
$26$	−2.21947	−	1.42637i	−0.435275	−	0.279734i
$27$	−0.142128	−	5.19421i	−0.0273525	−	0.999626i
$28$	−0.619612	+	1.35676i	−0.117096	+	0.256404i
$29$	−4.88858	+	3.84442i	−0.907786	+	0.713891i	−0.958582	−	0.284818i	$-0.908067\pi$
$29$	−4.88858	+	3.84442i	−0.907786	+	0.713891i	0.0507952	+	0.998709i	$0.483824\pi$
$30$	−1.08005	−	3.55796i	−0.197189	−	0.649591i
$31$	0.352362	+	7.39699i	0.0632861	+	1.32854i	0.777621	+	0.628734i	$0.216427\pi$
$31$	0.352362	+	7.39699i	0.0632861	+	1.32854i	−0.714334	+	0.699804i	$0.753270\pi$
$32$	0.995472	+	0.0950560i	0.175976	+	0.0168037i
$33$	1.73181	−	9.44829i	0.301469	−	1.64474i
$34$	−0.566646	−	0.109212i	−0.0971790	−	0.0187297i
$35$	−2.09685	+	2.41989i	−0.354432	+	0.409037i
$36$	2.39159	+	1.81116i	0.398598	+	0.301861i
$37$	−4.83189	−	10.5804i	−0.794357	−	1.73940i	−0.663735	−	0.747968i	$-0.731030\pi$
$37$	−4.83189	−	10.5804i	−0.794357	−	1.73940i	−0.130622	−	0.991432i	$-0.541698\pi$
$38$	−5.37454	−	2.77077i	−0.871865	−	0.449478i
$39$	4.45049	+	1.03680i	0.712648	+	0.166021i
$40$	1.99297	+	0.797865i	0.315116	+	0.126154i
$41$	−3.11658	−	4.37662i	−0.486728	−	0.683513i	0.496052	−	0.868293i	$-0.334782\pi$
$41$	−3.11658	−	4.37662i	−0.486728	−	0.683513i	−0.982780	+	0.184779i	$0.940843\pi$
$42$	0.222111	−	2.57387i	0.0342725	−	0.397157i
$43$	−0.405752	+	8.51779i	−0.0618766	+	1.29895i	0.727954	+	0.685626i	$0.240471\pi$
$43$	−0.405752	+	8.51779i	−0.0618766	+	1.29895i	−0.789831	+	0.613325i	$0.789832\pi$
$44$	3.63176	+	4.19128i	0.547509	+	0.631859i
$45$	3.83075	+	5.17707i	0.571055	+	0.771751i
$46$	4.03316	−	2.59492i	0.594658	−	0.382599i
$47$	−3.55460	−	6.15675i	−0.518492	−	0.898055i	−0.999769	−	0.0214863i	$-0.993160\pi$
$47$	−3.55460	−	6.15675i	−0.518492	−	0.898055i	0.481277	−	0.876569i	$-0.340173\pi$
$48$	−1.67943	+	0.423678i	−0.242405	+	0.0611526i
$49$	4.24444	−	2.18816i	0.606348	−	0.312594i
$50$	−0.307725	−	0.241997i	−0.0435188	−	0.0342236i
$51$	0.988010	−	0.151262i	0.138349	−	0.0211810i
$52$	−2.07384	+	1.63088i	−0.287590	+	0.226163i
$53$	−0.595290	−	0.174793i	−0.0817694	−	0.0240096i	0.240592	−	0.970626i	$-0.422658\pi$
$53$	−0.595290	−	0.174793i	−0.0817694	−	0.0240096i	−0.322361	+	0.946617i	$0.604477\pi$
$54$	−4.95502	−	1.56455i	−0.674292	−	0.212908i
$55$	4.94574	+	10.8297i	0.666883	+	1.46027i
$56$	1.07949	+	1.02929i	0.144252	+	0.137544i
$57$	10.3798	+	1.39591i	1.37484	+	0.184892i
$58$	2.03408	+	5.87710i	0.267088	+	0.771701i
$59$	−1.38298	+	5.70071i	−0.180048	+	0.742169i	0.808148	+	0.588979i	$0.200470\pi$
$59$	−1.38298	+	5.70071i	−0.180048	+	0.742169i	−0.988197	+	0.153190i	$0.951045\pi$
$60$	−3.71552	−	0.143049i	−0.479672	−	0.0184675i
$61$	6.51652	+	3.35950i	0.834355	+	0.430140i	0.821796	−	0.569781i	$-0.192972\pi$
$61$	6.51652	+	3.35950i	0.834355	+	0.430140i	0.0125584	+	0.999921i	$0.496002\pi$
$62$	7.10541	+	2.08634i	0.902388	+	0.264965i
$63$	1.13406	+	4.32855i	0.142879	+	0.545347i
$64$	0.415415	−	0.909632i	0.0519269	−	0.113704i
$65$	−5.25804	+	2.10500i	−0.652180	+	0.261093i
$66$	−8.36223	−	4.72679i	−1.02932	−	0.581828i
$67$	9.20314	−	1.77376i	1.12434	−	0.216699i	0.407006	−	0.913426i	$-0.366573\pi$
$67$	9.20314	−	1.77376i	1.12434	−	0.216699i	0.717337	+	0.696726i	$0.245361\pi$
$68$	−0.288537	+	0.499761i	−0.0349903	+	0.0606049i
$69$	−5.07165	+	6.57863i	−0.610555	+	0.791974i
$70$	1.60099	+	2.77299i	0.191355	+	0.331436i
$71$	5.72012	+	6.60136i	0.678853	+	0.783438i	0.985734	−	0.168310i	$-0.0538309\pi$
$71$	5.72012	+	6.60136i	0.678853	+	0.783438i	−0.306881	+	0.951748i	$0.599285\pi$
$72$	2.49376	−	1.66768i	0.293893	−	0.196538i
$73$	−0.717669	+	4.99150i	−0.0839968	+	0.584210i	0.903740	+	0.428082i	$0.140810\pi$
$73$	−0.717669	+	4.99150i	−0.0839968	+	0.584210i	−0.987737	+	0.156129i	$0.950099\pi$
$74$	−11.5788	+	1.10564i	−1.34601	+	0.128528i
$75$	0.642767	+	0.215921i	0.0742204	+	0.0249324i
$76$	−4.37622	+	4.17271i	−0.501987	+	0.478643i
$77$	0.393593	+	8.26254i	0.0448541	+	0.941604i
$78$	2.43539	−	3.86661i	0.275753	−	0.437807i
$79$	−1.86726	−	1.78043i	−0.210083	−	0.200314i	0.577731	−	0.816227i	$-0.303938\pi$
$79$	−1.86726	−	1.78043i	−0.210083	−	0.200314i	−0.787813	+	0.615914i	$0.788787\pi$
$80$	1.40582	−	1.62240i	0.157175	−	0.181390i
$81$	8.99401	−	0.328198i	0.999335	−	0.0364664i
$82$	−5.15524	+	1.51372i	−0.569301	+	0.167162i
$83$	8.58859	−	12.0610i	0.942721	−	1.32387i	−0.00338033	−	0.999994i	$-0.501076\pi$
$83$	8.58859	−	12.0610i	0.942721	−	1.32387i	0.946101	−	0.323872i	$-0.104985\pi$
$84$	−2.35967	−	1.05173i	−0.257461	−	0.114753i
$85$	−0.896585	+	0.854892i	−0.0972483	+	0.0927261i
$86$	7.91661	+	3.16933i	0.853670	+	0.341758i
$87$	−6.73566	−	8.40620i	−0.722139	−	0.901239i
$88$	5.14859	−	2.06118i	0.548842	−	0.219723i
$89$	−8.39580	−	5.39565i	−0.889953	−	0.571938i	0.0138418	−	0.999904i	$-0.495594\pi$
$89$	−8.39580	−	5.39565i	−0.889953	−	0.571938i	−0.903795	+	0.427966i	$0.859230\pi$
$90$	6.14525	−	1.92681i	0.647766	−	0.203104i
$91$	−3.93515			−0.412515
$92$	−1.13308	−	4.66006i	−0.118132	−	0.485845i
$93$	−12.8059	+	0.727109i	−1.32791	+	0.0753977i
$94$	−6.98073	+	1.34543i	−0.720008	+	0.138770i
$95$	−11.5378	+	5.94814i	−1.18375	+	0.610266i
$96$	−0.148913	+	1.72564i	−0.0151984	+	0.176122i
$97$	−1.63461	+	0.156086i	−0.165970	+	0.0158482i	−0.177710	−	0.984083i	$-0.556869\pi$
$97$	−1.63461	+	0.156086i	−0.165970	+	0.0158482i	0.0117404	+	0.999931i	$0.496263\pi$
$98$	−0.679593	−	4.72667i	−0.0686493	−	0.477466i
$99$	16.3916	+	2.85023i	1.64742	+	0.286459i
$100$	−0.329335	+	0.211650i	−0.0329335	+	0.0211650i
$101$	3.62581	−	5.09173i	0.360781	−	0.506647i	−0.593794	−	0.804617i	$-0.702370\pi$
$101$	3.62581	−	5.09173i	0.360781	−	0.506647i	0.954575	+	0.297971i	$0.0963098\pi$
$102$	0.180204	−	0.983144i	0.0178428	−	0.0973457i
$103$	4.42239	+	12.7777i	0.435751	+	1.25902i	0.922676	+	0.385576i	$0.125997\pi$
$103$	4.42239	+	12.7777i	0.435751	+	1.25902i	−0.486925	+	0.873444i	$0.661882\pi$
$104$	0.862901	+	2.49319i	0.0846144	+	0.244477i
$105$	−4.22432	−	3.59348i	−0.412252	−	0.350688i
$106$	−0.359880	+	0.505380i	−0.0349546	+	0.0490869i
$107$	5.36151	−	3.44563i	0.518316	−	0.333102i	−0.255189	−	0.966891i	$-0.582138\pi$
$107$	5.36151	−	3.44563i	0.518316	−	0.333102i	0.773506	+	0.633789i	$0.218501\pi$
$108$	−3.09913	+	4.17078i	−0.298214	+	0.401334i
$109$	−1.27130	−	8.84210i	−0.121769	−	0.846920i	−0.955551	−	0.294826i	$-0.904738\pi$
$109$	−1.27130	−	8.84210i	−0.121769	−	0.846920i	0.833782	−	0.552093i	$-0.186171\pi$
$110$	11.8516	−	1.13169i	1.13001	−	0.107903i
$111$	18.2486	−	8.53583i	1.73208	−	0.810185i
$112$	1.32574	−	0.683468i	0.125271	−	0.0645816i
$113$	−3.33046	+	0.641894i	−0.313304	+	0.0603843i	−0.343479	−	0.939160i	$-0.611605\pi$
$113$	−3.33046	+	0.641894i	−0.313304	+	0.0603843i	0.0301755	+	0.999545i	$0.490393\pi$
$114$	4.71403	−	9.35235i	0.441509	−	0.875928i
$115$	0.484540	−	10.2840i	0.0451836	−	0.958990i
$116$	6.21915			0.577433
$117$	−1.72542	+	7.72452i	−0.159516	+	0.714132i
$118$	4.93485	+	3.17143i	0.454290	+	0.291954i
$119$	−0.799079	+	0.319903i	−0.0732514	+	0.0293255i
$120$	−1.35041	+	3.46438i	−0.123275	+	0.316254i
$121$	18.3413	+	7.34274i	1.66739	+	0.667522i
$122$	5.30607	−	5.05933i	0.480389	−	0.458050i
$123$	7.53099	−	5.46697i	0.679047	−	0.492940i
$124$	4.29554	−	6.03224i	0.385751	−	0.541711i
$125$	−11.1053	+	3.26081i	−0.993289	+	0.291656i
$126$	4.46140	+	0.344040i	0.397453	+	0.0306496i
$127$	−3.41400	+	3.93997i	−0.302944	+	0.349616i	−0.886727	−	0.462294i	$-0.847026\pi$
$127$	−3.41400	+	3.93997i	−0.302944	+	0.349616i	0.583783	+	0.811910i	$0.301572\pi$
$128$	−0.723734	−	0.690079i	−0.0639697	−	0.0609949i
$129$	−14.7590	−	0.568227i	−1.29946	−	0.0500296i
$130$	0.269492	+	5.65733i	0.0236360	+	0.496181i
$131$	−3.30250	+	3.14892i	−0.288540	+	0.275123i	−0.820499	−	0.571647i	$-0.806305\pi$
$131$	−3.30250	+	3.14892i	−0.288540	+	0.275123i	0.531959	+	0.846770i	$0.321456\pi$
$132$	−7.20184	+	6.35633i	−0.626840	+	0.553247i
$133$	−8.97815	+	0.857309i	−0.778504	+	0.0743381i
$134$	1.33385	−	9.27712i	0.115227	−	0.801421i
$135$	−8.90607	+	6.71655i	−0.766512	+	0.578068i
$136$	0.377903	+	0.436124i	0.0324049	+	0.0373973i
$137$	−2.43280	−	4.21374i	−0.207848	−	0.360004i	0.743188	−	0.669082i	$-0.233313\pi$
$137$	−2.43280	−	4.21374i	−0.207848	−	0.360004i	−0.951036	+	0.309079i	$0.899979\pi$
$138$	4.55804	+	6.94437i	0.388006	+	0.591144i
$139$	6.98731	−	12.1024i	0.592656	−	1.02651i	−0.401217	−	0.915983i	$-0.631413\pi$
$139$	6.98731	−	12.1024i	0.592656	−	1.02651i	0.993873	−	0.110527i	$-0.0352540\pi$
$140$	3.14411	−	0.605978i	0.265726	−	0.0512145i
$141$	10.6072	−	6.25374i	0.893290	−	0.526660i
$142$	8.10916	−	3.24642i	0.680506	−	0.272433i
$143$	−6.07818	+	13.3094i	−0.508283	+	1.11298i
$144$	−0.760326	−	2.90205i	−0.0633605	−	0.241838i
$145$	12.8101	+	3.76139i	1.06382	+	0.312367i
$146$	4.48224	+	2.31076i	0.370953	+	0.191239i
$147$	3.85688	+	7.31672i	0.318110	+	0.603473i
$148$	−2.74222	+	11.3036i	−0.225409	+	0.929150i
$149$	−5.25396	−	15.1803i	−0.430421	−	1.24362i	−0.926814	−	0.375521i	$-0.877464\pi$
$149$	−5.25396	−	15.1803i	−0.430421	−	1.24362i	0.496393	−	0.868098i	$-0.334658\pi$
$150$	0.414274	−	0.536795i	0.0338253	−	0.0438291i
$151$	−13.3827	−	12.7604i	−1.08907	−	1.03842i	−0.999097	−	0.0424796i	$-0.986474\pi$
$151$	−13.3827	−	12.7604i	−1.08907	−	1.03842i	−0.0899704	−	0.995944i	$-0.528677\pi$
$152$	2.51190	+	5.50029i	0.203742	+	0.446132i
$153$	0.277587	+	1.70882i	0.0224416	+	0.138150i
$154$	7.93684	+	2.33047i	0.639569	+	0.187794i
$155$	12.4963	−	9.82716i	1.00372	−	0.789336i
$156$	−2.85741	−	3.56609i	−0.228776	−	0.285515i
$157$	−12.3270	−	9.69409i	−0.983804	−	0.773672i	−0.00974213	−	0.999953i	$-0.503101\pi$
$157$	−12.3270	−	9.69409i	−0.983804	−	0.773672i	−0.974062	+	0.226280i	$0.927343\pi$
$158$	−2.29322	+	1.18224i	−0.182439	+	0.0940539i
$159$	0.293336	−	1.03379i	0.0232630	−	0.0819849i
$160$	−1.07337	−	1.85914i	−0.0848576	−	0.146978i
$161$	2.96818	−	6.50834i	0.233925	−	0.512929i
$162$	2.63151	−	8.60669i	0.206751	−	0.676206i
$163$	−1.83703	−	2.12005i	−0.143888	−	0.166055i	0.679231	−	0.733924i	$-0.262313\pi$
$163$	−1.83703	−	2.12005i	−0.143888	−	0.166055i	−0.823119	+	0.567869i	$0.807768\pi$
$164$	−0.255652	+	5.36680i	−0.0199631	+	0.419076i
$165$	−18.6786	+	8.73695i	−1.45413	+	0.680171i
$166$	−8.58859	−	12.0610i	−0.666604	−	0.936115i
$167$	13.5680	+	5.43180i	1.04992	+	0.420326i	0.831498	−	0.555528i	$-0.187484\pi$
$167$	13.5680	+	5.43180i	1.04992	+	0.420326i	0.218425	+	0.975854i	$0.429908\pi$
$168$	−1.76565	+	1.88590i	−0.136223	+	0.145500i
$169$	5.36804	+	2.76742i	0.412926	+	0.212878i
$170$	0.514630	+	1.12688i	0.0394703	+	0.0864279i
$171$	−2.25374	+	17.9996i	−0.172348	+	1.37646i
$172$	5.58429	−	6.44461i	0.425798	−	0.491397i
$173$	−2.96907	−	0.572241i	−0.225734	−	0.0435067i	0.0751297	−	0.997174i	$-0.476063\pi$
$173$	−2.96907	−	0.572241i	−0.225734	−	0.0435067i	−0.300864	+	0.953667i	$0.597275\pi$
$174$	−10.1469	+	3.61581i	−0.769233	+	0.274114i
$175$	−0.581269	−	0.0555045i	−0.0439398	−	0.00419574i
$176$	−0.263882	−	5.53957i	−0.0198909	−	0.417561i
$177$	−9.89535	−	2.30525i	−0.743780	−	0.173273i
$178$	−7.84489	+	6.16929i	−0.588000	+	0.462408i
$179$	10.6124	−	23.2380i	0.793211	−	1.73689i	0.125986	−	0.992032i	$-0.459791\pi$
$179$	10.6124	−	23.2380i	0.793211	−	1.73689i	0.667224	−	0.744857i	$-0.267482\pi$
$180$	0.189075	−	6.43746i	0.0140928	−	0.479820i
$181$	1.59909	+	1.02767i	0.118859	+	0.0763863i	0.598720	−	0.800959i	$-0.295676\pi$
$181$	1.59909	+	1.02767i	0.118859	+	0.0763863i	−0.479860	+	0.877345i	$0.659313\pi$
$182$	−1.28706	+	3.71872i	−0.0954032	+	0.275650i
$183$	−5.71566	+	11.3395i	−0.422514	+	0.838242i
$184$	−4.77435	−	0.453395i	−0.351970	−	0.0334247i
$185$	−12.4849	+	21.6245i	−0.917909	+	1.58986i
$186$	−3.50127	+	12.3394i	−0.256725	+	0.904766i
$187$	−0.152280	+	3.19674i	−0.0111358	+	0.233769i
$188$	−1.01175	+	7.03685i	−0.0737891	+	0.513215i
$189$	−7.47905	+	2.03254i	−0.544021	+	0.147845i
$190$	1.84736	+	12.8486i	0.134021	+	0.932139i
$191$	−3.95197	−	16.2902i	−0.285954	−	1.17872i	−0.915682	−	0.401903i	$-0.868349\pi$
$191$	−3.95197	−	16.2902i	−0.285954	−	1.17872i	0.629728	−	0.776816i	$-0.283166\pi$
$192$	1.58202	+	0.705124i	0.114173	+	0.0508879i
$193$	−17.5941	−	1.68003i	−1.26645	−	0.120931i	−0.559878	−	0.828575i	$-0.689152\pi$
$193$	−17.5941	−	1.68003i	−1.26645	−	0.120931i	−0.706570	+	0.707644i	$0.749758\pi$
$194$	−0.387127	+	1.59576i	−0.0277941	+	0.114569i
$195$	−3.72886	−	9.07357i	−0.267029	−	0.649772i
$196$	−4.68898	−	0.903728i	−0.334927	−	0.0645520i
$197$	−8.37096	+	2.45794i	−0.596406	+	0.175121i	−0.565984	−	0.824416i	$-0.691504\pi$
$197$	−8.37096	+	2.45794i	−0.596406	+	0.175121i	−0.0304227	+	0.999537i	$0.509685\pi$
$198$	8.05464	−	14.5579i	0.572418	−	1.03458i
$199$	−10.2612	+	6.59449i	−0.727399	+	0.467471i	−0.851204	−	0.524836i	$-0.824127\pi$
$199$	−10.2612	+	6.59449i	−0.727399	+	0.467471i	0.123805	+	0.992307i	$0.460490\pi$
$200$	0.0922951	+	0.380446i	0.00652625	+	0.0269016i
$201$	3.21747	+	15.9116i	0.226943	+	1.12232i
$202$	−3.62581	−	5.09173i	−0.255111	−	0.358253i
$203$	7.29156	+	5.73415i	0.511767	+	0.402458i
$204$	−0.870133	−	0.491847i	−0.0609215	−	0.0344362i
$205$	−3.77247	+	10.8998i	−0.263481	+	0.761278i
$206$	13.5213			0.942074
$207$	−11.4741	−	8.68009i	−0.797508	−	0.603308i
$208$	2.63829			0.182933
$209$	−10.9680	+	31.6899i	−0.758670	+	2.19203i
$210$	−4.77748	+	2.81668i	−0.329678	+	0.194369i
$211$	−10.7455	−	8.45034i	−0.739750	−	0.581746i	0.175573	−	0.984466i	$-0.443822\pi$
$211$	−10.7455	−	8.45034i	−0.739750	−	0.581746i	−0.915323	+	0.402721i	$0.868065\pi$
$212$	0.359880	+	0.505380i	0.0247166	+	0.0347097i
$213$	−11.3431	+	10.0114i	−0.777215	+	0.685968i
$214$	−1.50255	−	6.19358i	−0.102712	−	0.423385i
$215$	15.4002	−	9.89711i	1.05029	−	0.674977i
$216$	2.92777	+	4.29281i	0.199209	+	0.292088i
$217$	10.5981	−	3.11187i	0.719444	−	0.211248i
$218$	−8.77160	−	1.69059i	−0.594087	−	0.114501i
$219$	−8.65650	−	1.16415i	−0.584952	−	0.0786662i
$220$	2.80684	−	11.5699i	0.189237	−	0.780045i
$221$	−1.51560	−	0.144722i	−0.101950	−	0.00973506i
$222$	−2.09782	−	20.0368i	−0.140796	−	1.34478i
$223$	−1.42599	−	5.87801i	−0.0954914	−	0.393621i	0.903928	−	0.427684i	$-0.140670\pi$
$223$	−1.42599	−	5.87801i	−0.0954914	−	0.393621i	−0.999420	+	0.0340632i	$0.989155\pi$
$224$	−0.212270	−	1.47637i	−0.0141829	−	0.0986440i
$225$	−0.363819	+	1.11667i	−0.0242546	+	0.0744446i
$226$	−0.482697	+	3.35723i	−0.0321086	+	0.223320i
$227$	0.0525206	−	1.10254i	0.00348591	−	0.0731783i	−0.996454	−	0.0841391i	$-0.973186\pi$
$227$	0.0525206	−	1.10254i	0.00348591	−	0.0731783i	0.999940	+	0.0109608i	$0.00348901\pi$
$228$	−7.29617	−	7.51361i	−0.483201	−	0.497601i
$229$	1.72181	−	2.98226i	0.113780	−	0.197073i	−0.803511	−	0.595290i	$-0.797037\pi$
$229$	1.72181	−	2.98226i	0.113780	−	0.197073i	0.917291	+	0.398216i	$0.130371\pi$
$230$	−9.55993	−	3.82147i	−0.630363	−	0.251980i
$231$	−14.3043	+	0.812192i	−0.941156	+	0.0534383i
$232$	2.03408	−	5.87710i	0.133544	−	0.385850i
$233$	12.2874	+	7.89663i	0.804975	+	0.517326i	0.877236	−	0.480060i	$-0.159385\pi$
$233$	12.2874	+	7.89663i	0.804975	+	0.517326i	−0.0722611	+	0.997386i	$0.523021\pi$
$234$	6.73535	+	4.15697i	0.440304	+	0.271750i
$235$	−6.33992	+	13.8825i	−0.413571	+	0.905594i
$236$	4.61104	−	3.62616i	0.300153	−	0.236043i
$237$	3.05417	−	3.26217i	0.198390	−	0.211901i
$238$	0.0409554	+	0.859760i	0.00265475	+	0.0557300i
$239$	−1.87494	−	0.179035i	−0.121279	−	0.0115808i	0.0342398	−	0.999414i	$-0.489099\pi$
$239$	−1.87494	−	0.179035i	−0.121279	−	0.0115808i	−0.155519	+	0.987833i	$0.549705\pi$
$240$	2.83217	+	2.40923i	0.182816	+	0.155515i
$241$	0.468636	+	0.0903222i	0.0301875	+	0.00581816i	0.204323	−	0.978904i	$-0.434501\pi$
$241$	0.468636	+	0.0903222i	0.0301875	+	0.00581816i	−0.174135	+	0.984722i	$0.555713\pi$
$242$	12.9377	−	14.9309i	0.831669	−	0.959798i
$243$	0.710480	+	15.5723i	0.0455773	+	0.998961i
$244$	−3.04563	−	6.66899i	−0.194976	−	0.426938i
$245$	−9.11173	−	4.69742i	−0.582127	−	0.300107i
$246$	−2.70314	−	8.90486i	−0.172346	−	0.567753i
$247$	−14.8103	−	5.92914i	−0.942355	−	0.377262i
$248$	−4.29554	−	6.03224i	−0.272767	−	0.383048i
$249$	21.0250	+	14.6848i	1.33241	+	0.930610i
$250$	−0.550720	+	11.5610i	−0.0348306	+	0.731184i
$251$	15.8248	+	18.2628i	0.998855	+	1.15274i	0.988258	+	0.152797i	$0.0488279\pi$
$251$	15.8248	+	18.2628i	0.998855	+	1.15274i	0.0105976	+	0.999944i	$0.496627\pi$
$252$	1.78430	−	4.10351i	0.112400	−	0.258497i
$253$	−17.4277	−	20.0916i	−1.09567	−	1.26315i
$254$	2.60666	+	4.51487i	0.163556	+	0.283288i
$255$	−1.49482	−	1.53936i	−0.0936090	−	0.0963987i
$256$	−0.888835	+	0.458227i	−0.0555522	+	0.0286392i
$257$	−11.6201	−	9.13819i	−0.724845	−	0.570024i	0.186111	−	0.982529i	$-0.440412\pi$
$257$	−11.6201	−	9.13819i	−0.724845	−	0.570024i	−0.910956	+	0.412504i	$0.864654\pi$
$258$	−5.36418	+	13.7614i	−0.333959	+	0.856750i
$259$	−13.6372	+	10.7244i	−0.847372	+	0.666381i
$260$	5.43433	+	1.59566i	0.337023	+	0.0989587i
$261$	14.4530	−	11.7988i	0.894617	−	0.730327i
$262$	1.89559	+	4.15077i	0.117110	+	0.256436i
$263$	5.04302	+	4.80851i	0.310966	+	0.296505i	0.829449	−	0.558583i	$-0.188655\pi$
$263$	5.04302	+	4.80851i	0.310966	+	0.296505i	−0.518483	+	0.855088i	$0.673503\pi$
$264$	3.65124	+	8.88470i	0.224719	+	0.546815i
$265$	0.435618	+	1.25863i	0.0267598	+	0.0773173i
$266$	−2.12631	+	8.76475i	−0.130372	+	0.537402i
$267$	9.21256	−	14.6266i	0.563799	−	0.895131i
$268$	−8.33062	−	4.29473i	−0.508874	−	0.262343i
$269$	15.3348	+	4.50271i	0.934980	+	0.274535i	0.713520	−	0.700635i	$-0.247100\pi$
$269$	15.3348	+	4.50271i	0.934980	+	0.274535i	0.221460	+	0.975170i	$0.428918\pi$
$270$	3.43425	+	10.6130i	0.209002	+	0.645887i
$271$	8.59909	−	18.8294i	0.522357	−	1.14380i	−0.446182	−	0.894942i	$-0.647217\pi$
$271$	8.59909	−	18.8294i	0.522357	−	1.14380i	0.968539	−	0.248861i	$-0.0800562\pi$
$272$	0.535737	−	0.214477i	0.0324839	−	0.0130046i
$273$	−0.0621505	−	6.81559i	−0.00376152	−	0.412498i
$274$	−4.77768	+	0.920822i	−0.288630	+	0.0556289i
$275$	−1.08555	+	1.88022i	−0.0654610	+	0.113382i
$276$	8.05322	−	2.03607i	0.484747	−	0.122557i
$277$	−3.70029	−	6.40909i	−0.222329	−	0.385085i	0.733186	−	0.680028i	$-0.238033\pi$
$277$	−3.70029	−	6.40909i	−0.222329	−	0.385085i	−0.955515	+	0.294943i	$0.904699\pi$
$278$	−9.15143	−	10.5613i	−0.548866	−	0.633426i
$279$	−1.46159	−	22.1680i	−0.0875031	−	1.32716i
$280$	0.455689	−	3.16939i	0.0272326	−	0.189407i
$281$	19.1673	−	1.83026i	1.14343	−	0.109184i	0.493897	−	0.869520i	$-0.335572\pi$
$281$	19.1673	−	1.83026i	1.14343	−	0.109184i	0.649530	+	0.760336i	$0.274966\pi$
$282$	−2.44050	−	12.0692i	−0.145330	−	0.718713i
$283$	10.1353	−	9.66402i	0.602483	−	0.574466i	−0.326219	−	0.945294i	$-0.605775\pi$
$283$	10.1353	−	9.66402i	0.602483	−	0.574466i	0.928702	+	0.370828i	$0.120926\pi$
$284$	−0.415621	−	8.72496i	−0.0246626	−	0.517731i
$285$	−10.4843	−	19.8892i	−0.621034	−	1.17814i
$286$	10.5894	+	10.0969i	0.626163	+	0.597045i
$287$	−5.24800	+	6.05652i	−0.309780	+	0.357505i
$288$	−2.99112	−	0.230660i	−0.176253	−	0.0135918i
$289$	15.9919	−	4.69563i	0.940697	−	0.276214i
$290$	7.74430	−	10.8753i	0.454761	−	0.638622i
$291$	−0.296155	−	2.82865i	−0.0173609	−	0.165818i
$292$	3.64966	−	3.47995i	0.213580	−	0.203648i
$293$	8.77487	+	3.51293i	0.512633	+	0.205227i	0.613533	−	0.789669i	$-0.289748\pi$
$293$	8.77487	+	3.51293i	0.512633	+	0.205227i	−0.100900	+	0.994897i	$0.532172\pi$
$294$	8.17577	−	1.25169i	0.476820	−	0.0730002i
$295$	11.6909	−	4.68033i	0.680670	−	0.272499i
$296$	9.78502	+	6.28845i	0.568742	+	0.365509i
$297$	−4.67766	+	28.4349i	−0.271425	+	1.64996i
$298$	−16.0638			−0.930551
$299$	9.94172	−	7.82661i	0.574945	−	0.452625i
$300$	−0.371776	−	0.567058i	−0.0214645	−	0.0327391i
$301$	12.4893	−	2.40711i	0.719869	−	0.138743i
$302$	−16.4356	+	8.47314i	−0.945763	+	0.487575i
$303$	8.87604	+	6.19940i	0.509915	+	0.356147i
$304$	6.01934	−	0.574777i	0.345233	−	0.0329657i
$305$	−2.23988	−	15.5787i	−0.128255	−	0.892035i
$306$	1.70563	+	0.296581i	0.0975044	+	0.0169544i
$307$	−17.4977	+	11.2451i	−0.998647	+	0.641792i	−0.934431	−	0.356144i	$-0.884091\pi$
$307$	−17.4977	+	11.2451i	−0.998647	+	0.641792i	−0.0642162	+	0.997936i	$0.520455\pi$
$308$	4.79818	−	6.73810i	0.273402	−	0.383939i
$309$	−22.0608	+	7.86129i	−1.25499	+	0.447213i
$310$	−5.19955	−	15.0231i	−0.295315	−	0.853256i
$311$	7.67304	+	22.1698i	0.435098	+	1.25713i	0.923191	+	0.384342i	$0.125572\pi$
$311$	7.67304	+	22.1698i	0.435098	+	1.25713i	−0.488093	+	0.872792i	$0.662307\pi$
$312$	−4.30452	+	1.53390i	−0.243696	+	0.0868402i
$313$	10.6935	−	15.0169i	0.604432	−	0.848806i	−0.393065	−	0.919511i	$-0.628585\pi$
$313$	10.6935	−	15.0169i	0.604432	−	0.848806i	0.997497	+	0.0707044i	$0.0225247\pi$
$314$	−13.1927	+	8.47843i	−0.744507	+	0.478466i
$315$	6.15711	−	7.37319i	0.346914	−	0.415432i
$316$	0.367177	+	2.55377i	0.0206553	+	0.143661i
$317$	−2.69873	+	0.257697i	−0.151576	+	0.0144737i	−0.170568	−	0.985346i	$-0.554560\pi$
$317$	−2.69873	+	0.257697i	−0.151576	+	0.0144737i	0.0189924	+	0.999820i	$0.493954\pi$
$318$	−0.880992	−	0.615322i	−0.0494036	−	0.0345056i
$319$	30.6563	−	15.8044i	1.71643	−	0.884879i
$320$	−2.10795	+	0.406274i	−0.117838	+	0.0227114i
$321$	6.05244	+	9.23160i	0.337814	+	0.515257i
$322$	−5.17959	−	4.93360i	−0.288647	−	0.274939i
$323$	−3.48941			−0.194156
$324$	−7.27265	−	5.30175i	−0.404036	−	0.294542i
$325$	−0.868881	−	0.558396i	−0.0481969	−	0.0309742i
$326$	−2.60429	+	1.04260i	−0.144238	+	0.0577442i
$327$	15.2943	−	2.34152i	0.845774	−	0.129486i
$328$	4.98801	+	1.99690i	0.275417	+	0.110260i
$329$	−7.67428	+	7.31742i	−0.423097	+	0.403422i
$330$	2.14725	+	20.5089i	0.118202	+	1.12898i
$331$	−19.2691	+	27.0597i	−1.05913	+	1.48733i	−0.197156	+	0.980372i	$0.563171\pi$
$331$	−19.2691	+	27.0597i	−1.05913	+	1.48733i	−0.861969	+	0.506961i	$0.830769\pi$
$332$	−14.2067	+	4.17146i	−0.779694	+	0.228939i
$333$	15.0721	+	31.4714i	0.825945	+	1.72462i
$334$	9.57071	−	11.0452i	0.523686	−	0.604366i
$335$	−14.5618	−	13.8847i	−0.795597	−	0.758601i
$336$	1.20469	+	2.28536i	0.0657212	+	0.124677i
$337$	−0.0997802	−	2.09464i	−0.00543538	−	0.114103i	−0.999954	−	0.00954705i	$-0.996961\pi$
$337$	−0.0997802	−	2.09464i	−0.00543538	−	0.114103i	0.994519	−	0.104556i	$-0.0333420\pi$
$338$	4.37092	−	4.16767i	0.237747	−	0.226691i
$339$	−1.16435	−	5.75815i	−0.0632387	−	0.312740i
$340$	1.23322	−	0.117758i	0.0668809	−	0.00638635i
$341$	5.84475	−	40.6511i	0.316511	−	2.20138i
$342$	16.2725	+	8.01689i	0.879917	+	0.433504i
$343$	−11.5016	−	13.2735i	−0.621028	−	0.716704i
$344$	−4.26372	−	7.38498i	−0.229885	−	0.398172i
$345$	17.8194	+	0.676790i	0.959362	+	0.0364371i
$346$	−1.51186	+	2.61861i	−0.0812779	+	0.140777i
$347$	−6.69947	+	1.29122i	−0.359646	+	0.0693162i	−0.365874	−	0.930664i	$-0.619230\pi$
$347$	−6.69947	+	1.29122i	−0.359646	+	0.0693162i	0.00622743	+	0.999981i	$0.498018\pi$
$348$	0.0982233	+	10.7714i	0.00526532	+	0.577409i
$349$	4.18423	−	1.67511i	0.223977	−	0.0896668i	−0.256960	−	0.966422i	$-0.582721\pi$
$349$	4.18423	−	1.67511i	0.223977	−	0.0896668i	0.480937	+	0.876755i	$0.340297\pi$
$350$	−0.242566	+	0.531146i	−0.0129657	+	0.0283909i
$351$	−13.4060	−	2.86640i	−0.715557	−	0.152997i
$352$	−5.32121	−	1.56245i	−0.283621	−	0.0832787i
$353$	−7.98124	−	4.11462i	−0.424799	−	0.218999i	0.232552	−	0.972584i	$-0.425293\pi$
$353$	−7.98124	−	4.11462i	−0.424799	−	0.218999i	−0.657350	+	0.753585i	$0.728323\pi$
$354$	−5.41492	+	8.59714i	−0.287800	+	0.456933i
$355$	4.42084	−	18.2229i	0.234634	−	0.967174i
$356$	3.26417	+	9.43121i	0.173001	+	0.499853i
$357$	−0.566686	−	1.37894i	−0.0299922	−	0.0729810i
$358$	−18.4889	−	17.6292i	−0.977170	−	0.931730i
$359$	3.71679	+	8.13863i	0.196165	+	0.429541i	0.981996	−	0.188900i	$-0.0604921\pi$
$359$	3.71679	+	8.13863i	0.196165	+	0.429541i	−0.785832	+	0.618440i	$0.787765\pi$
$360$	−6.02157	−	2.28416i	−0.317364	−	0.120386i
$361$	−16.8514	−	4.94802i	−0.886916	−	0.260422i
$362$	1.49416	−	1.17502i	0.0785315	−	0.0617578i
$363$	−12.4278	+	31.8827i	−0.652290	+	1.67341i
$364$	3.09323	+	2.43255i	0.162130	+	0.127500i
$365$	9.62223	−	4.96061i	0.503651	−	0.259650i
$366$	8.84646	+	9.11010i	0.462412	+	0.476193i
$367$	8.50848	+	14.7371i	0.444139	+	0.769272i	0.997992	−	0.0633430i	$-0.0201762\pi$
$367$	8.50848	+	14.7371i	0.444139	+	0.769272i	−0.553853	+	0.832615i	$0.686843\pi$
$368$	−1.99000	+	4.36348i	−0.103736	+	0.227462i
$369$	9.58762	+	12.9572i	0.499111	+	0.674523i
$370$	16.3518	+	18.8709i	0.850087	+	0.981053i
$371$	−0.0440318	+	0.924341i	−0.00228602	+	0.0479894i
$372$	10.5156	+	7.34451i	0.545206	+	0.380795i
$373$	0.0885419	+	0.124340i	0.00458452	+	0.00643806i	0.816862	−	0.576833i	$-0.195712\pi$
$373$	0.0885419	+	0.124340i	0.00458452	+	0.00643806i	−0.812277	+	0.583271i	$0.801772\pi$
$374$	2.97112	+	1.18946i	0.153633	+	0.0615054i
$375$	−5.82305	−	19.1827i	−0.300701	−	0.990588i
$376$	6.31892	+	3.25763i	0.325873	+	0.167999i
$377$	6.81610	+	14.9252i	0.351047	+	0.768686i
$378$	−0.525409	+	7.73249i	−0.0270241	+	0.397716i
$379$	23.7619	−	27.4227i	1.22057	−	1.40861i	0.336214	−	0.941786i	$-0.390853\pi$
$379$	23.7619	−	27.4227i	1.22057	−	1.40861i	0.884351	−	0.466822i	$-0.154601\pi$
$380$	12.7462	+	2.45663i	0.653866	+	0.126022i
$381$	−6.87786	−	5.85075i	−0.352363	−	0.299743i
$382$	−16.6868	−	1.59340i	−0.853773	−	0.0815254i
$383$	1.01159	+	21.2360i	0.0516901	+	1.08511i	0.864517	+	0.502603i	$0.167624\pi$
$383$	1.01159	+	21.2360i	0.0516901	+	1.08511i	−0.812827	+	0.582505i	$0.802073\pi$
$384$	1.18377	−	1.26439i	0.0604091	−	0.0645232i
$385$	13.9585	−	10.9771i	0.711391	−	0.559444i
$386$	−7.34208	+	16.0769i	−0.373702	+	0.818293i
$387$	0.751057	−	25.5713i	0.0381784	−	1.29986i
$388$	1.38138	+	0.887757i	0.0701288	+	0.0450690i
$389$	−8.99685	+	25.9947i	−0.456158	+	1.31798i	0.449237	+	0.893413i	$0.351696\pi$
$389$	−8.99685	+	25.9947i	−0.456158	+	1.31798i	−0.905395	+	0.424570i	$0.860425\pi$
$390$	−9.79412	+	0.556104i	−0.495945	+	0.0281594i
$391$	1.38253	−	2.39749i	0.0699176	−	0.121246i
$392$	−2.38764	+	4.13551i	−0.120594	+	0.208875i
$393$	−5.50603	−	5.67012i	−0.277742	−	0.286020i
$394$	−0.415122	+	8.71448i	−0.0209135	+	0.439029i
$395$	−0.788235	+	5.48230i	−0.0396604	+	0.275844i
$396$	−11.1228	−	12.3730i	−0.558940	−	0.621769i
$397$	3.52938	+	24.5474i	0.177134	+	1.23200i	0.863353	+	0.504601i	$0.168360\pi$
$397$	3.52938	+	24.5474i	0.177134	+	1.23200i	−0.686218	+	0.727396i	$0.740731\pi$
$398$	2.87568	+	11.8537i	0.144145	+	0.594173i
$399$	−1.62664	−	15.5364i	−0.0814338	−	0.777794i
$400$	0.389708	+	0.0372126i	0.0194854	+	0.00186063i
$401$	5.52880	−	22.7900i	0.276095	−	1.13808i	−0.649741	−	0.760155i	$-0.725123\pi$
$401$	5.52880	−	22.7900i	0.276095	−	1.13808i	0.925836	−	0.377924i	$-0.123362\pi$
$402$	16.0888	+	2.16368i	0.802438	+	0.107914i
$403$	19.1845	+	3.69751i	0.955647	+	0.184186i
$404$	−5.99758	+	1.76105i	−0.298391	+	0.0876154i
$405$	−11.7736	−	15.3190i	−0.585034	−	0.761209i
$406$	7.80361	−	5.01507i	0.387287	−	0.248894i
$407$	15.2080	+	62.6881i	0.753831	+	3.10733i
$408$	−0.749389	+	0.661409i	−0.0371003	+	0.0327446i
$409$	−0.955306	−	1.34154i	−0.0472368	−	0.0663348i	0.790282	−	0.612743i	$-0.209934\pi$
$409$	−0.955306	−	1.34154i	−0.0472368	−	0.0663348i	−0.837519	+	0.546408i	$0.815995\pi$
$410$	9.06650	+	7.12998i	0.447763	+	0.352124i
$411$	7.25968	−	4.28011i	0.358094	−	0.211122i
$412$	4.42239	−	12.7777i	0.217875	−	0.629510i
$413$	8.74953			0.430536
$414$	−11.9555	+	8.00410i	−0.587582	+	0.393380i
$415$	−31.7857			−1.56030
$416$	0.862901	−	2.49319i	0.0423072	−	0.122239i
$417$	21.0714	+	11.9107i	1.03187	+	0.583271i
$418$	26.3597	+	20.7295i	1.28929	+	1.01391i
$419$	15.7124	+	22.0650i	0.767601	+	1.07795i	0.994573	+	0.104044i	$0.0331782\pi$
$419$	15.7124	+	22.0650i	0.767601	+	1.07795i	−0.226971	+	0.973901i	$0.572882\pi$
$420$	1.09920	+	5.43597i	0.0536354	+	0.265248i
$421$	−3.00950	−	12.4053i	−0.146674	−	0.604598i	−0.996935	−	0.0782367i	$-0.975071\pi$
$421$	−3.00950	−	12.4053i	−0.146674	−	0.604598i	0.850261	−	0.526362i	$-0.176444\pi$
$422$	−11.5001	+	7.39066i	−0.559816	+	0.359772i
$423$	10.9989	+	18.2727i	0.534783	+	0.888450i
$424$	0.595290	−	0.174793i	0.0289098	−	0.00848869i
$425$	−0.221831	−	0.0427544i	−0.0107604	−	0.00207389i
$426$	5.75080	+	13.9936i	0.278627	+	0.677993i
$427$	2.57810	−	10.6271i	0.124763	−	0.514281i
$428$	−6.34438	−	0.605815i	−0.306667	−	0.0292832i
$429$	−23.1475	−	10.3171i	−1.11757	−	0.498113i
$430$	−4.31586	−	17.7902i	−0.208129	−	0.857921i
$431$	−2.15727	−	15.0042i	−0.103912	−	0.722726i	−0.973457	−	0.228871i	$-0.926497\pi$
$431$	−2.15727	−	15.0042i	−0.103912	−	0.722726i	0.869545	−	0.493855i	$-0.164412\pi$
$432$	5.01428	−	1.36270i	0.241250	−	0.0655630i
$433$	1.55232	−	10.7966i	0.0745997	−	0.518852i	−0.917920	−	0.396766i	$-0.870132\pi$
$433$	1.55232	−	10.7966i	0.0745997	−	0.518852i	0.992519	−	0.122086i	$-0.0389584\pi$
$434$	0.525565	−	11.0330i	0.0252279	−	0.529600i
$435$	−6.31233	+	22.2463i	−0.302653	+	1.06663i
$436$	−4.46651	+	7.73623i	−0.213907	+	0.370498i
$437$	20.9772	−	20.0225i	1.00348	−	0.957807i
$438$	−3.93139	+	7.79964i	−0.187849	+	0.372681i
$439$	−12.4580	+	35.9951i	−0.594590	+	1.71795i	0.0966400	+	0.995319i	$0.469190\pi$
$439$	−12.4580	+	35.9951i	−0.594590	+	1.71795i	−0.691230	+	0.722635i	$0.742931\pi$
$440$	−10.0156	−	6.43662i	−0.477474	−	0.306854i
$441$	−12.6115	+	6.79560i	−0.600547	+	0.323600i
$442$	−0.632466	+	1.38491i	−0.0300833	+	0.0658733i
$443$	6.61948	−	5.20562i	0.314501	−	0.247326i	−0.448413	−	0.893827i	$-0.648011\pi$
$443$	6.61948	−	5.20562i	0.314501	−	0.247326i	0.762914	+	0.646500i	$0.223768\pi$
$444$	−19.6209	−	4.57095i	−0.931167	−	0.216928i
$445$	1.01943	+	21.4005i	0.0483257	+	1.01448i
$446$	−6.02112	−	0.574947i	−0.285108	−	0.0272245i
$447$	26.2090	−	9.33949i	1.23964	−	0.441743i
$448$	−1.46460	−	0.282278i	−0.0691956	−	0.0133364i
$449$	9.38962	−	10.8362i	0.443123	−	0.511392i	−0.489618	−	0.871937i	$-0.662864\pi$
$449$	9.38962	−	10.8362i	0.443123	−	0.511392i	0.932742	+	0.360545i	$0.117409\pi$
$450$	0.936260	+	0.709036i	0.0441357	+	0.0334243i
$451$	12.3782	+	27.1045i	0.582867	+	1.27630i
$452$	3.01471	+	1.55419i	0.141800	+	0.0731031i
$453$	21.8893	−	23.3801i	1.02845	−	1.09849i
$454$	−1.02473	−	0.410238i	−0.0480928	−	0.0192534i
$455$	4.90018	+	6.88134i	0.229724	+	0.322602i
$456$	−9.48671	+	4.43742i	−0.444256	+	0.207801i
$457$	−1.35061	+	28.3529i	−0.0631791	+	1.32629i	0.715386	+	0.698729i	$0.246251\pi$
$457$	−1.35061	+	28.3529i	−0.0631791	+	1.32629i	−0.778565	+	0.627563i	$0.784052\pi$
$458$	−2.25509	−	2.60251i	−0.105373	−	0.121607i
$459$	−2.95526	+	0.507764i	−0.137940	+	0.0237004i
$460$	−6.73804	+	7.78427i	−0.314163	+	0.362943i
$461$	−18.7916	−	32.5480i	−0.875212	−	1.51591i	−0.856537	−	0.516086i	$-0.827388\pi$
$461$	−18.7916	−	32.5480i	−0.875212	−	1.51591i	−0.0186752	−	0.999826i	$-0.505945\pi$
$462$	−3.91097	+	13.7833i	−0.181955	+	0.641255i
$463$	−16.6811	+	8.59972i	−0.775238	+	0.399663i	−0.799977	−	0.600031i	$-0.795155\pi$
$463$	−16.6811	+	8.59972i	−0.775238	+	0.399663i	0.0247387	+	0.999694i	$0.492125\pi$
$464$	−4.88858	−	3.84442i	−0.226947	−	0.178473i
$465$	17.2178	+	21.4880i	0.798456	+	0.996484i
$466$	11.4811	−	9.02887i	0.531854	−	0.418254i
$467$	−18.1893	−	5.34085i	−0.841699	−	0.247145i	−0.167664	−	0.985844i	$-0.553622\pi$
$467$	−18.1893	−	5.34085i	−0.841699	−	0.247145i	−0.674036	+	0.738699i	$0.735441\pi$
$468$	6.13126	−	5.00530i	0.283418	−	0.231370i
$469$	−5.80732	−	12.7163i	−0.268157	−	0.587183i
$470$	11.0454	+	10.5318i	0.509486	+	0.485794i
$471$	16.5953	−	21.5033i	0.764669	−	0.990818i
$472$	−1.91860	−	5.54344i	−0.0883108	−	0.255157i
$473$	11.1495	−	45.9589i	0.512655	−	2.11319i
$474$	−2.08383	−	3.95314i	−0.0957135	−	0.181574i
$475$	−2.10403	−	1.08470i	−0.0965395	−	0.0497696i
$476$	0.825869	+	0.242497i	0.0378537	+	0.0111148i
$477$	1.79514	+	0.491724i	0.0821936	+	0.0225145i
$478$	−0.782419	+	1.71326i	−0.0357870	+	0.0783626i
$479$	−16.4505	+	6.58577i	−0.751641	+	0.300912i	−0.715668	−	0.698441i	$-0.753877\pi$
$479$	−16.4505	+	6.58577i	−0.751641	+	0.300912i	−0.0359735	+	0.999353i	$0.511453\pi$
$480$	3.20303	−	1.88842i	0.146198	−	0.0861943i
$481$	−30.1327	+	5.80760i	−1.37393	+	0.264804i
$482$	0.238630	−	0.413320i	0.0108693	−	0.0188262i
$483$	11.3192	+	5.03803i	0.515041	+	0.229238i
$484$	−9.87824	−	17.1096i	−0.449011	−	0.777709i
$485$	2.30842	+	2.66406i	0.104820	+	0.120969i
$486$	14.9482	+	4.42178i	0.678063	+	0.200576i
$487$	−4.48171	+	31.1710i	−0.203086	+	1.41249i	0.591972	+	0.805959i	$0.298350\pi$
$487$	−4.48171	+	31.1710i	−0.203086	+	1.41249i	−0.795058	+	0.606534i	$0.792559\pi$
$488$	−7.29833	+	0.696906i	−0.330380	+	0.0315474i
$489$	3.64287	−	3.21519i	0.164736	−	0.145396i
$490$	−7.41922	+	7.07422i	−0.335166	+	0.319581i
$491$	−1.82036	−	38.2141i	−0.0821518	−	1.72458i	−0.545252	−	0.838272i	$-0.683566\pi$
$491$	−1.82036	−	38.2141i	−0.0821518	−	1.72458i	0.463100	−	0.886306i	$-0.346737\pi$
$492$	−9.29921	−	0.358022i	−0.419241	−	0.0161409i
$493$	2.59742	+	2.47663i	0.116982	+	0.111542i
$494$	−10.4470	+	12.0565i	−0.470033	+	0.542447i
$495$	−15.4272	−	32.2130i	−0.693402	−	1.44787i
$496$	−7.10541	+	2.08634i	−0.319042	+	0.0936792i
$497$	7.55726	−	10.6127i	0.338989	−	0.476044i
$498$	20.7537	−	15.0658i	0.929997	−	0.675112i
$499$	−13.1773	+	12.5646i	−0.589899	+	0.562467i	−0.925121	−	0.379672i	$-0.876037\pi$
$499$	−13.1773	+	12.5646i	−0.589899	+	0.562467i	0.335222	+	0.942139i	$0.391189\pi$
$500$	10.7451	+	4.30167i	0.480534	+	0.192377i
$501$	−9.19348	+	23.5853i	−0.410734	+	1.05371i
$502$	22.4342	−	8.98130i	1.00129	−	0.400855i
$503$	2.53640	+	1.63005i	0.113092	+	0.0726801i	0.595964	−	0.803011i	$-0.296770\pi$
$503$	2.53640	+	1.63005i	0.113092	+	0.0726801i	−0.482872	+	0.875691i	$0.660406\pi$
$504$	−3.29423	−	3.02829i	−0.146737	−	0.134891i
$505$	−13.4188			−0.597130
$506$	−24.6866	+	9.89791i	−1.09746	+	0.440016i
$507$	−4.70833	+	9.34104i	−0.209104	+	0.414850i
$508$	5.11911	−	0.986628i	0.227124	−	0.0437745i
$509$	4.52899	−	2.33486i	0.200744	−	0.103491i	−0.354923	−	0.934895i	$-0.615493\pi$
$509$	4.52899	−	2.33486i	0.200744	−	0.103491i	0.555668	+	0.831405i	$0.312463\pi$
$510$	−1.94361	+	0.909125i	−0.0860644	+	0.0402567i
$511$	7.48756	−	0.714976i	0.331230	−	0.0316287i
$512$	0.142315	+	0.989821i	0.00628949	+	0.0437443i
$513$	−31.2105	−	3.61916i	−1.37798	−	0.159790i
$514$	−12.4362	+	7.99224i	−0.548536	+	0.352523i
$515$	16.8372	−	23.6446i	0.741936	−	1.04190i
$516$	11.2501	+	9.57009i	0.495259	+	0.421300i
$517$	12.8952	+	37.2582i	0.567129	+	1.63861i
$518$	5.67427	+	16.3947i	0.249313	+	0.720343i
$519$	0.944217	−	5.15141i	0.0414465	−	0.226122i
$520$	3.28530	−	4.61355i	0.144070	−	0.202318i
$521$	12.8887	−	8.28303i	0.564662	−	0.362886i	−0.226954	−	0.973906i	$-0.572877\pi$
$521$	12.8887	−	8.28303i	0.564662	−	0.362886i	0.791616	+	0.611019i	$0.209240\pi$
$522$	−6.42276	−	17.5171i	−0.281117	−	0.766702i
$523$	0.681315	+	4.73865i	0.0297918	+	0.207207i	0.999280	−	0.0379297i	$-0.0120763\pi$
$523$	0.681315	+	4.73865i	0.0297918	+	0.207207i	−0.969489	+	0.245137i	$0.921167\pi$
$524$	4.54247	−	0.433754i	0.198439	−	0.0189486i
$525$	0.0869522	−	1.00762i	0.00379490	−	0.0439762i
$526$	6.19345	−	3.19295i	0.270047	−	0.139219i
$527$	4.19623	−	0.808756i	0.182790	−	0.0352300i
$528$	9.59025	−	0.544529i	0.417362	−	0.0236976i
$529$	5.44565	+	22.3460i	0.236767	+	0.971566i
$530$	1.33189			0.0578535
$531$	3.83636	−	17.1750i	0.166484	−	0.745329i
$532$	7.58725	+	4.87603i	0.328949	+	0.211403i
$533$	−13.1598	+	5.26840i	−0.570016	+	0.228200i
$534$	−10.8090	−	13.4898i	−0.467750	−	0.583759i
$535$	−12.7017	−	5.08498i	−0.549141	−	0.219843i
$536$	−6.78321	+	6.46778i	−0.292990	+	0.279365i
$537$	40.4153	+	18.0135i	1.74405	+	0.777340i
$538$	9.27058	−	13.0187i	0.399683	−	0.561277i
$539$	−25.4102	+	7.46112i	−1.09450	+	0.321373i
$540$	11.1525	+	0.225803i	0.479929	+	0.00971701i
$541$	17.9274	−	20.6893i	0.770759	−	0.889504i	−0.225647	−	0.974209i	$-0.572450\pi$
$541$	17.9274	−	20.6893i	0.770759	−	0.889504i	0.996406	+	0.0847056i	$0.0269950\pi$
$542$	−14.9813	−	14.2846i	−0.643501	−	0.613577i
$543$	−1.75465	+	2.78582i	−0.0752993	+	0.119551i
$544$	−0.0274583	−	0.576421i	−0.00117727	−	0.0247138i
$545$	−13.8790	+	13.2336i	−0.594511	+	0.566865i
$546$	−6.46107	−	2.17043i	−0.276508	−	0.0928858i
$547$	2.70583	−	0.258375i	0.115693	−	0.0110473i	−0.0370490	−	0.999313i	$-0.511796\pi$
$547$	2.70583	−	0.258375i	0.115693	−	0.0110473i	0.152742	+	0.988266i	$0.451190\pi$
$548$	−0.692448	+	4.81608i	−0.0295799	+	0.205733i
$549$	−19.7301	−	9.72031i	−0.842060	−	0.414853i
$550$	1.42176	+	1.64080i	0.0606242	+	0.0699641i
$551$	18.8027	+	32.5673i	0.801023	+	1.38741i
$552$	0.709866	−	8.27624i	0.0302139	−	0.352260i
$553$	−1.92412	+	3.33268i	−0.0818220	+	0.141720i
$554$	−7.26684	+	1.40057i	−0.308739	+	0.0595045i
$555$	−37.6503	−	21.2821i	−1.59817	−	0.903373i
$556$	−12.9736	+	5.19384i	−0.550203	+	0.220268i
$557$	1.32277	−	2.89645i	0.0560474	−	0.122727i	−0.879536	−	0.475832i	$-0.842147\pi$
$557$	1.32277	−	2.89645i	0.0560474	−	0.122727i	0.935584	+	0.353105i	$0.114874\pi$
$558$	−21.4268	−	5.86924i	−0.907069	−	0.248465i
$559$	21.5866	+	6.33839i	0.913015	+	0.268085i
$560$	−2.84603	−	1.46723i	−0.120267	−	0.0620018i
$561$	−5.53910	−	0.213257i	−0.233861	−	0.00900371i
$562$	4.53942	−	18.7118i	0.191484	−	0.789308i
$563$	−2.02018	−	5.83692i	−0.0851404	−	0.245997i	0.894392	−	0.447284i	$-0.147609\pi$
$563$	−2.02018	−	5.83692i	−0.0851404	−	0.245997i	−0.979532	+	0.201287i	$0.935488\pi$
$564$	−12.2036	−	1.64118i	−0.513866	−	0.0691063i
$565$	5.26968	+	5.02463i	0.221697	+	0.211388i
$566$	−5.81757	−	12.7387i	−0.244530	−	0.535447i
$567$	−3.63843	−	12.9215i	−0.152800	−	0.542650i
$568$	−8.38103	−	2.46089i	−0.351660	−	0.103257i
$569$	24.7448	−	19.4596i	1.03736	−	0.815787i	0.0541970	−	0.998530i	$-0.482740\pi$
$569$	24.7448	−	19.4596i	1.03736	−	0.815787i	0.983161	+	0.182743i	$0.0584977\pi$
$570$	−22.2244	+	3.40251i	−0.930878	+	0.142515i
$571$	−21.9846	−	17.2889i	−0.920027	−	0.723517i	0.0412364	−	0.999149i	$-0.486870\pi$
$571$	−21.9846	−	17.2889i	−0.920027	−	0.723517i	−0.961263	+	0.275632i	$0.911113\pi$
$572$	13.0051	−	6.70458i	0.543769	−	0.280333i
$573$	28.1519	−	7.10200i	1.17606	−	0.296690i
$574$	4.00696	+	6.94026i	0.167247	+	0.289681i
$575$	1.57891	−	1.01586i	0.0658449	−	0.0423643i
$576$	−1.19627	+	2.75117i	−0.0498447	+	0.114632i
$577$	6.53503	+	7.54182i	0.272057	+	0.313970i	0.875294	−	0.483592i	$-0.160668\pi$
$577$	6.53503	+	7.54182i	0.272057	+	0.313970i	−0.603237	+	0.797562i	$0.706123\pi$
$578$	0.793047	−	16.6481i	0.0329864	−	0.692470i
$579$	2.63190	−	30.4991i	0.109378	−	1.26750i
$580$	−7.74430	−	10.8753i	−0.321565	−	0.451574i
$581$	−20.5026	−	8.20801i	−0.850592	−	0.340526i
$582$	−2.76994	−	0.645293i	−0.114818	−	0.0267483i
$583$	3.05827	+	1.57665i	0.126661	+	0.0652982i
$584$	−2.09486	−	4.58711i	−0.0866861	−	0.189816i
$585$	15.6563	−	6.60162i	0.647310	−	0.272943i
$586$	6.18970	−	7.14329i	0.255694	−	0.295087i
$587$	9.30608	+	1.79360i	0.384103	+	0.0740298i	0.377648	−	0.925949i	$-0.376733\pi$
$587$	9.30608	+	1.79360i	0.384103	+	0.0740298i	0.00645542	+	0.999979i	$0.497945\pi$
$588$	1.49118	−	8.13549i	0.0614953	−	0.335502i
$589$	44.5755	+	4.25644i	1.83670	+	0.175384i
$590$	−0.599197	−	12.5787i	−0.0246685	−	0.517857i
$591$	−4.38930	−	14.4595i	−0.180552	−	0.594785i
$592$	9.14295	−	7.19010i	0.375773	−	0.295511i
$593$	−15.5172	+	33.9779i	−0.637214	+	1.39530i	0.265099	+	0.964221i	$0.414595\pi$
$593$	−15.5172	+	33.9779i	−0.637214	+	1.39530i	−0.902313	+	0.431082i	$0.858132\pi$
$594$	25.3411	+	13.7205i	1.03976	+	0.562960i
$595$	1.55445	+	0.998985i	0.0637263	+	0.0409544i
$596$	−5.25396	+	15.1803i	−0.215210	+	0.621810i
$597$	−11.5836	−	17.6681i	−0.474084	−	0.723106i
$598$	−4.14453	−	11.9548i	−0.169483	−	0.488867i
$599$	18.7861	−	32.5385i	0.767580	−	1.32949i	−0.171291	−	0.985220i	$-0.554794\pi$
$599$	18.7861	−	32.5385i	0.767580	−	1.32949i	0.938871	−	0.344268i	$-0.111873\pi$
$600$	−0.657466	+	0.165862i	−0.0268409	+	0.00677128i
$601$	1.11018	−	23.3056i	0.0452852	−	0.950654i	−0.855879	−	0.517176i	$-0.826983\pi$
$601$	1.11018	−	23.3056i	0.0452852	−	0.950654i	0.901164	−	0.433478i	$-0.142714\pi$
$602$	1.81012	−	12.5896i	0.0737749	−	0.513116i
$603$	−27.5078	+	5.82389i	−1.12020	+	0.237167i
$604$	2.63157	+	18.3030i	0.107077	+	0.744737i
$605$	−9.99904	−	41.2166i	−0.406519	−	1.67569i
$606$	8.76151	−	6.36024i	0.355912	−	0.258367i
$607$	−1.18528	−	0.113181i	−0.0481091	−	0.00459386i	0.0709737	−	0.997478i	$-0.477389\pi$
$607$	−1.18528	−	0.113181i	−0.0481091	−	0.00459386i	−0.119083	+	0.992884i	$0.537995\pi$
$608$	1.42557	−	5.87627i	0.0578144	−	0.238314i
$609$	−9.81626	+	12.7194i	−0.397775	+	0.515416i
$610$	−15.4545	−	2.97861i	−0.625734	−	0.120600i
$611$	−17.9964	+	5.28423i	−0.728057	+	0.213777i
$612$	0.838126	−	1.51482i	0.0338793	−	0.0612329i
$613$	−27.9135	+	17.9389i	−1.12742	+	0.724547i	−0.965020	−	0.262178i	$-0.915559\pi$
$613$	−27.9135	+	17.9389i	−1.12742	+	0.724547i	−0.162398	+	0.986725i	$0.551923\pi$
$614$	4.90368	+	20.2133i	0.197897	+	0.815741i
$615$	−18.9379	−	6.36169i	−0.763649	−	0.256528i
$616$	−4.79818	−	6.73810i	−0.193324	−	0.271486i
$617$	6.36492	+	5.00543i	0.256242	+	0.201511i	0.738014	−	0.674786i	$-0.235764\pi$
$617$	6.36492	+	5.00543i	0.256242	+	0.201511i	−0.481771	+	0.876297i	$0.660006\pi$
$618$	0.213552	+	23.4186i	0.00859030	+	0.942035i
$619$	−2.63255	+	7.60626i	−0.105811	+	0.305722i	−0.985461	−	0.169900i	$-0.945656\pi$
$619$	−2.63255	+	7.60626i	−0.105811	+	0.305722i	0.879650	+	0.475621i	$0.157777\pi$
$620$	−15.8975			−0.638458
$621$	14.8525	−	20.0101i	0.596011	−	0.802977i
$622$	23.4601			0.940663
$623$	−4.86868	+	14.0671i	−0.195059	+	0.563587i
$624$	0.0416684	+	4.56947i	0.00166807	+	0.182925i
$625$	17.9922	+	14.1493i	0.719689	+	0.565970i
$626$	−10.6935	−	15.0169i	−0.427398	−	0.600197i
$627$	−55.0594	−	18.4958i	−2.19886	−	0.738651i
$628$	3.69722	+	15.2401i	0.147535	+	0.608148i
$629$	−5.64668	+	3.62890i	−0.225148	+	0.144694i
$630$	−4.95388	−	8.23001i	−0.197367	−	0.327892i
$631$	0.103748	−	0.0304632i	0.00413015	−	0.00121272i	−0.279667	−	0.960097i	$-0.590224\pi$
$631$	0.103748	−	0.0304632i	0.00413015	−	0.00121272i	0.283797	+	0.958884i	$0.408406\pi$
$632$	2.53341	+	0.488274i	0.100774	+	0.0194225i
$633$	14.4661	−	18.7444i	0.574976	−	0.745024i
$634$	−0.639143	+	2.63458i	−0.0253836	+	0.104633i
$635$	11.1410	+	1.06384i	0.442117	+	0.0422171i
$636$	−0.869624	+	0.631286i	−0.0344828	+	0.0250321i
$637$	−2.97023	−	12.2435i	−0.117685	−	0.485103i
$638$	−4.90850	−	34.1394i	−0.194330	−	1.35159i
$639$	−17.5186	−	19.4879i	−0.693027	−	0.770928i
$640$	−0.305514	+	2.12490i	−0.0120765	+	0.0839939i
$641$	−1.02214	+	21.4574i	−0.0403723	+	0.847518i	0.884338	+	0.466847i	$0.154610\pi$
$641$	−1.02214	+	21.4574i	−0.0403723	+	0.847518i	−0.924710	+	0.380671i	$0.875693\pi$
$642$	10.7034	−	2.70020i	0.422430	−	0.106568i
$643$	−15.1799	+	26.2924i	−0.598638	+	1.03687i	0.394384	+	0.918946i	$0.370958\pi$
$643$	−15.1799	+	26.2924i	−0.598638	+	1.03687i	−0.993022	+	0.117926i	$0.962376\pi$
$644$	−6.35633	+	3.28109i	−0.250475	+	0.129293i
$645$	17.3848	+	26.5165i	0.684526	+	1.04409i
$646$	−1.14127	+	3.29749i	−0.0449028	+	0.129738i
$647$	29.0113	+	18.6444i	1.14055	+	0.732987i	0.967736	−	0.251967i	$-0.0810775\pi$
$647$	29.0113	+	18.6444i	1.14055	+	0.732987i	0.172815	+	0.984954i	$0.444714\pi$
$648$	−7.38881	+	5.13863i	−0.290260	+	0.201864i
$649$	13.5144	−	29.5925i	0.530487	−	1.16161i
$650$	−0.811868	+	0.638460i	−0.0318441	+	0.0250425i
$651$	5.55708	+	18.3065i	0.217799	+	0.717488i
$652$	0.133478	+	2.80205i	0.00522741	+	0.109737i
$653$	−27.6103	−	2.63647i	−1.08048	−	0.103173i	−0.460397	−	0.887713i	$-0.652293\pi$
$653$	−27.6103	−	2.63647i	−1.08048	−	0.103173i	−0.620078	+	0.784540i	$0.712899\pi$
$654$	2.78952	−	15.2189i	0.109079	−	0.595107i
$655$	9.61887	+	1.85388i	0.375840	+	0.0724373i
$656$	3.51849	−	4.06055i	0.137374	−	0.158538i
$657$	1.87957	−	15.0113i	0.0733290	−	0.585645i
$658$	4.40495	+	9.64550i	0.171723	+	0.376021i
$659$	1.96044	+	1.01068i	0.0763680	+	0.0393704i	0.495987	−	0.868330i	$-0.334806\pi$
$659$	1.96044	+	1.01068i	0.0763680	+	0.0393704i	−0.419620	+	0.907700i	$0.637836\pi$
$660$	20.0832	+	4.67865i	0.781738	+	0.182116i
$661$	34.0293	+	13.6233i	1.32359	+	0.529884i	0.922444	−	0.386131i	$-0.126189\pi$
$661$	34.0293	+	13.6233i	1.32359	+	0.529884i	0.401143	+	0.916015i	$0.368613\pi$
$662$	19.2691	+	27.0597i	0.748914	+	1.05170i
$663$	0.226719	−	2.62727i	0.00880502	−	0.102035i
$664$	−0.704520	+	14.7897i	−0.0273407	+	0.573952i
$665$	12.6791	+	14.6324i	0.491673	+	0.567421i
$666$	34.6701	−	3.94983i	1.34344	−	0.153053i
$667$	−29.8260	+	0.0154779i	−1.15487	+	0.000599308i
$668$	−7.30744	−	12.6569i	−0.282733	−	0.489709i
$669$	10.1581	−	2.56262i	0.392734	−	0.0990766i
$670$	−17.8837	+	9.21970i	−0.690909	+	0.356188i
$671$	−31.9606	−	25.1341i	−1.23382	−	0.970290i
$672$	2.55369	−	0.390964i	0.0985106	−	0.0150818i
$673$	16.8202	−	13.2276i	0.648372	−	0.509886i	−0.238952	−	0.971031i	$-0.576804\pi$
$673$	16.8202	−	13.2276i	0.648372	−	0.509886i	0.887324	+	0.461146i	$0.152561\pi$
$674$	−2.01208	−	0.590799i	−0.0775023	−	0.0227567i
$675$	−1.93979	−	0.612491i	−0.0746627	−	0.0235748i
$676$	−2.50886	−	5.49364i	−0.0964946	−	0.211294i
$677$	8.12668	+	7.74878i	0.312334	+	0.297810i	0.829989	−	0.557780i	$-0.188347\pi$
$677$	8.12668	+	7.74878i	0.312334	+	0.297810i	−0.517655	+	0.855589i	$0.673195\pi$
$678$	−5.82228	−	0.782998i	−0.223603	−	0.0300709i
$679$	0.801053	+	2.31449i	0.0307416	+	0.0888220i
$680$	0.292066	−	1.20391i	0.0112002	−	0.0461679i
$681$	1.91041	+	0.0735513i	0.0732071	+	0.00281849i
$682$	−36.5037	−	18.8190i	−1.39780	−	0.720615i
$683$	−42.2342	−	12.4011i	−1.61605	−	0.474514i	−0.656094	−	0.754679i	$-0.727792\pi$
$683$	−42.2342	−	12.4011i	−1.61605	−	0.474514i	−0.959952	+	0.280165i	$0.909611\pi$
$684$	12.8982	−	12.7555i	0.493174	−	0.487718i
$685$	−4.33910	+	9.50131i	−0.165789	+	0.363026i
$686$	−16.3053	+	6.52766i	−0.622540	+	0.249227i
$687$	5.19240	+	2.93503i	0.198102	+	0.111978i
$688$	−8.37334	+	1.61383i	−0.319231	+	0.0615267i
$689$	−0.818427	+	1.41756i	−0.0311796	+	0.0540046i
$690$	6.46771	−	16.6180i	0.246222	−	0.632635i
$691$	20.2677	+	35.1046i	0.771018	+	1.33544i	0.937005	+	0.349315i	$0.113586\pi$
$691$	20.2677	+	35.1046i	0.771018	+	1.33544i	−0.165987	+	0.986128i	$0.553081\pi$
$692$	1.98011	+	2.28517i	0.0752725	+	0.0868691i
$693$	−1.63262	−	24.7620i	−0.0620180	−	0.940630i
$694$	−0.970981	+	6.75332i	−0.0368579	+	0.256353i
$695$	−29.8641	+	2.85168i	−1.13281	+	0.108170i
$696$	10.2111	+	3.43017i	0.387052	+	0.130020i
$697$	−2.24398	+	2.13963i	−0.0849966	+	0.0810441i
$698$	−0.214456	−	4.50198i	−0.00811727	−	0.170403i
$699$	−13.4827	+	21.4062i	−0.509964	+	0.809658i
$700$	0.422598	+	0.402946i	0.0159727	+	0.0152299i
$701$	−14.3452	+	16.5553i	−0.541811	+	0.625284i	−0.958955	−	0.283557i	$-0.908486\pi$
$701$	−14.3452	+	16.5553i	−0.541811	+	0.625284i	0.417144	+	0.908840i	$0.363031\pi$
$702$	−7.09341	+	11.7311i	−0.267724	+	0.442763i
$703$	−67.4833	+	19.8149i	−2.54518	+	0.747333i
$704$	−3.21691	+	4.51752i	−0.121242	+	0.170260i
$705$	−24.1443	−	10.7614i	−0.909328	−	0.405296i
$706$	−6.49872	+	6.19652i	−0.244583	+	0.233209i
$707$	−8.65550	−	3.46514i	−0.325523	−	0.130320i
$708$	6.35326	+	7.92895i	0.238770	+	0.297988i
$709$	0.799174	−	0.319941i	0.0300136	−	0.0120156i	−0.356607	−	0.934254i	$-0.616067\pi$
$709$	0.799174	−	0.319941i	0.0300136	−	0.0120156i	0.386621	+	0.922239i	$0.373642\pi$
$710$	−15.7748	−	10.1378i	−0.592017	−	0.380466i
$711$	5.69824	+	5.23823i	0.213701	+	0.196449i
$712$	9.98011			0.374020
$713$	−20.5857	+	28.9403i	−0.770939	+	1.08382i
$714$	−1.48844	+	0.0845127i	−0.0557035	+	0.00316281i
$715$	30.8427	−	5.94444i	1.15345	−	0.222309i
$716$	−22.7067	+	11.7061i	−0.848589	+	0.437478i
$717$	0.280472	−	3.25018i	0.0104744	−	0.121380i
$718$	8.90666	−	0.850483i	0.332393	−	0.0317397i
$719$	−3.32560	−	23.1301i	−0.124024	−	0.862606i	−0.952924	−	0.303209i	$-0.901942\pi$
$719$	−3.32560	−	23.1301i	−0.124024	−	0.862606i	0.828900	−	0.559397i	$-0.188967\pi$
$720$	−4.12800	+	4.94331i	−0.153841	+	0.184226i
$721$	16.9662	−	10.9035i	0.631853	−	0.406067i
$722$	−10.1874	+	14.3063i	−0.379137	+	0.532424i
$723$	−0.149035	+	0.813094i	−0.00554266	+	0.0302393i
$724$	−0.621705	−	1.79630i	−0.0231055	−	0.0667589i
$725$	0.796305	+	2.30077i	0.0295740	+	0.0854485i
$726$	26.0644	+	22.1721i	0.967341	+	0.822883i
$727$	1.67919	−	2.35810i	0.0622779	−	0.0874571i	−0.782262	−	0.622949i	$-0.785934\pi$
$727$	1.67919	−	2.35810i	0.0622779	−	0.0874571i	0.844540	+	0.535492i	$0.179874\pi$
$728$	3.31046	−	2.12750i	0.122694	−	0.0788504i
$729$	−26.9596	+	1.47648i	−0.998504	+	0.0546844i
$730$	−1.54065	−	10.7155i	−0.0570221	−	0.396597i
$731$	4.89869	−	0.467768i	0.181185	−	0.0173010i
$732$	11.5024	−	5.38029i	0.425143	−	0.198861i
$733$	−20.8106	+	10.7286i	−0.768657	+	0.396270i	−0.797504	−	0.603314i	$-0.793847\pi$
$733$	−20.8106	+	10.7286i	−0.768657	+	0.396270i	0.0288469	+	0.999584i	$0.490816\pi$
$734$	16.7094	−	3.22048i	0.616757	−	0.118870i
$735$	7.99193	−	15.8555i	0.294787	−	0.584839i
$736$	3.47262	+	3.30770i	0.128003	+	0.121923i
$737$	−51.9786			−1.91466
$738$	15.3803	−	4.82243i	0.566158	−	0.177516i
$739$	31.4916	+	20.2384i	1.15844	+	0.744483i	0.971302	−	0.237851i	$-0.0764430\pi$
$739$	31.4916	+	20.2384i	1.15844	+	0.744483i	0.187136	+	0.982334i	$0.440079\pi$
$740$	23.1812	−	9.28034i	0.852157	−	0.341152i
$741$	10.0352	−	25.7447i	0.368654	−	0.945756i
$742$	0.859102	+	0.343932i	0.0315386	+	0.0126262i
$743$	22.2162	−	21.1831i	0.815032	−	0.777131i	−0.162770	−	0.986664i	$-0.552043\pi$
$743$	22.2162	−	21.1831i	0.815032	−	0.777131i	0.977802	+	0.209533i	$0.0671943\pi$
$744$	10.3799	−	7.53506i	0.380545	−	0.276249i
$745$	−20.0032	+	28.0906i	−0.732861	+	1.02916i
$746$	0.146460	−	0.0430046i	0.00536229	−	0.00157451i
$747$	−25.1017	+	36.6468i	−0.918422	+	1.34084i
$748$	2.09580	−	2.41868i	0.0766299	−	0.0884356i
$749$	−6.87981	−	6.55989i	−0.251383	−	0.239693i
$750$	−20.0322	−	0.771244i	−0.731471	−	0.0281618i
$751$	0.911091	+	19.1262i	0.0332462	+	0.697923i	0.952551	+	0.304378i	$0.0984486\pi$
$751$	0.911091	+	19.1262i	0.0332462	+	0.697923i	−0.919305	+	0.393545i	$0.871248\pi$
$752$	5.14518	−	4.90591i	0.187625	−	0.178900i
$753$	−31.3809	+	27.6967i	−1.14358	+	1.00932i
$754$	16.3336	−	1.55967i	0.594836	−	0.0568000i
$755$	−5.64931	+	39.2918i	−0.205599	+	1.42998i
$756$	7.13536	+	3.02556i	0.259511	+	0.110039i
$757$	−32.9654	−	38.0441i	−1.19815	−	1.38274i	−0.904307	−	0.426882i	$-0.859612\pi$
$757$	−32.9654	−	38.0441i	−1.19815	−	1.38274i	−0.293841	−	0.955854i	$-0.594933\pi$
$758$	−18.1427	−	31.4241i	−0.658972	−	1.14137i
$759$	34.5230	−	30.5018i	1.25311	−	1.10715i
$760$	6.49039	−	11.2417i	0.235431	−	0.407779i
$761$	36.7964	−	7.09192i	1.33387	−	0.257082i	0.528033	−	0.849224i	$-0.322930\pi$
$761$	36.7964	−	7.09192i	1.33387	−	0.257082i	0.805834	+	0.592142i	$0.201718\pi$
$762$	−7.77849	+	4.58599i	−0.281785	+	0.166133i
$763$	−12.3696	+	4.95205i	−0.447810	+	0.179276i
$764$	−6.96349	+	15.2479i	−0.251930	+	0.551650i
$765$	2.64254	−	2.61330i	0.0955412	−	0.0944841i
$766$	20.3989	+	5.98965i	0.737042	+	0.216415i
$767$	13.7560	+	7.09170i	0.496700	+	0.256066i
$768$	−0.807677	−	1.53221i	−0.0291445	−	0.0552888i
$769$	1.13945	−	4.69687i	0.0410895	−	0.169373i	−0.947570	−	0.319549i	$-0.896469\pi$
$769$	1.13945	−	4.69687i	0.0410895	−	0.169373i	0.988659	+	0.150175i	$0.0479838\pi$
$770$	−5.80797	−	16.7810i	−0.209305	−	0.604747i
$771$	15.6436	−	20.2702i	0.563391	−	0.730013i
$772$	12.7913	+	12.1965i	0.460370	+	0.438962i
$773$	2.98161	+	6.52882i	0.107241	+	0.234826i	0.955643	−	0.294527i	$-0.0951621\pi$
$773$	2.98161	+	6.52882i	0.107241	+	0.234826i	−0.848402	+	0.529353i	$0.822435\pi$
$774$	−23.9193	−	9.07330i	−0.859760	−	0.326133i
$775$	2.78163	+	0.816760i	0.0999191	+	0.0293389i
$776$	1.29074	−	1.01505i	0.0463347	−	0.0364380i
$777$	−18.7898	−	23.4499i	−0.674080	−	0.841261i
$778$	21.6224	+	17.0041i	0.775201	+	0.609625i
$779$	−28.8768	+	14.8870i	−1.03462	+	0.533382i
$780$	−2.67782	+	9.43734i	−0.0958815	+	0.337911i
$781$	−24.2211	−	41.9522i	−0.866700	−	1.50117i
$782$	−1.81345	−	2.09064i	−0.0648487	−	0.0747610i
$783$	20.6635	+	24.8459i	0.738454	+	0.887920i
$784$	3.12714	+	3.60892i	0.111684	+	0.128890i
$785$	−1.60188	+	33.6275i	−0.0571735	+	1.20022i
$786$	−7.15911	+	3.34869i	−0.255357	+	0.119444i
$787$	−20.4855	−	28.7679i	−0.730229	−	1.02546i	−0.998076	−	0.0620017i	$-0.980252\pi$
$787$	−20.4855	−	28.7679i	−0.730229	−	1.02546i	0.267847	−	0.963461i	$-0.413688\pi$
$788$	8.09942	+	3.24252i	0.288530	+	0.115510i
$789$	−8.24858	+	8.81034i	−0.293657	+	0.313657i
$790$	4.92297	+	2.53797i	0.175151	+	0.0902968i
$791$	2.10157	+	4.60180i	0.0747234	+	0.163621i
$792$	−15.3304	+	6.46420i	−0.544743	+	0.229695i
$793$	12.6668	−	14.6182i	0.449811	−	0.519109i
$794$	24.3516	+	4.69339i	0.864207	+	0.166562i
$795$	−2.17305	+	0.774359i	−0.0770701	+	0.0274637i
$796$	12.1423	+	1.15945i	0.430373	+	0.0410956i
$797$	2.18292	+	45.8250i	0.0773228	+	1.62321i	0.620930	+	0.783866i	$0.286755\pi$
$797$	2.18292	+	45.8250i	0.0773228	+	1.62321i	−0.543607	+	0.839340i	$0.682942\pi$
$798$	−15.2139	−	3.54429i	−0.538568	−	0.125466i
$799$	−3.22482	+	2.53602i	−0.114086	+	0.0897180i
$800$	0.162627	−	0.356103i	0.00574973	−	0.0125902i
$801$	25.4784	+	15.7249i	0.900235	+	0.555614i
$802$	−19.7283	−	12.6786i	−0.696631	−	0.447697i
$803$	9.14703	−	26.4286i	0.322792	−	0.932645i
$804$	7.30682	−	14.4963i	0.257692	−	0.511245i
$805$	−15.0771	+	2.91400i	−0.531399	+	0.102705i
$806$	9.76878	−	16.9200i	0.344091	−	0.595982i
$807$	−7.55640	+	26.6307i	−0.265998	+	0.937444i
$808$	−0.297424	+	6.24370i	−0.0104633	+	0.219653i
$809$	−5.73617	+	39.8960i	−0.201673	+	1.40267i	0.597646	+	0.801760i	$0.296103\pi$
$809$	−5.73617	+	39.8960i	−0.201673	+	1.40267i	−0.799319	+	0.600907i	$0.794806\pi$
$810$	−18.3273	+	6.11567i	−0.643954	+	0.214883i
$811$	4.64382	+	32.2985i	0.163067	+	1.13415i	0.892810	+	0.450433i	$0.148730\pi$
$811$	4.64382	+	32.2985i	0.163067	+	1.13415i	−0.729744	+	0.683721i	$0.760361\pi$
$812$	−2.18694	−	9.01469i	−0.0767465	−	0.316353i
$813$	32.7479	+	14.5961i	1.14852	+	0.511906i
$814$	64.2143	+	6.13172i	2.25071	+	0.214917i
$815$	−1.41977	+	5.85236i	−0.0497323	+	0.204999i
$816$	0.379931	+	0.924498i	0.0133002	+	0.0323639i
$817$	50.6313	+	9.75838i	1.77136	+	0.341402i
$818$	−1.58021	+	0.463990i	−0.0552506	+	0.0162230i
$819$	11.8035	−	0.215287i	0.412447	−	0.00752273i
$820$	9.70320	−	6.23587i	0.338850	−	0.217766i
$821$	−3.12471	−	12.8802i	−0.109053	−	0.449523i	0.890936	−	0.454128i	$-0.150049\pi$
$821$	−3.12471	−	12.8802i	−0.109053	−	0.449523i	−0.999989	+	0.00460538i	$0.998534\pi$
$822$	−1.67030	−	8.26029i	−0.0582584	−	0.288111i
$823$	9.81356	+	13.7812i	0.342079	+	0.480383i	0.949398	−	0.314075i	$-0.101694\pi$
$823$	9.81356	+	13.7812i	0.342079	+	0.480383i	−0.607319	+	0.794458i	$0.707755\pi$
$824$	−10.6285	−	8.35832i	−0.370260	−	0.291176i
$825$	−3.27365	−	1.85045i	−0.113974	−	0.0644244i
$826$	2.86169	−	8.26831i	0.0995710	−	0.287691i
$827$	51.5563			1.79279			0.896394	−	0.443259i	$-0.146178\pi$
$827$	51.5563			1.79279			0.896394	+	0.443259i	$0.146178\pi$
$828$	3.65362	+	13.9159i	0.126972	+	0.483609i
$829$	53.9828			1.87490			0.937450	−	0.348120i	$-0.113180\pi$
$829$	53.9828			1.87490			0.937450	+	0.348120i	$0.113180\pi$
$830$	−10.3961	+	30.0375i	−0.360854	+	1.04262i
$831$	11.0420	−	6.51005i	0.383042	−	0.225831i
$832$	−2.07384	−	1.63088i	−0.0718974	−	0.0565408i
$833$	−1.59846	−	2.24472i	−0.0553833	−	0.0777749i
$834$	18.1474	−	16.0169i	0.628394	−	0.554620i
$835$	−7.39681	−	30.4900i	−0.255977	−	1.05515i
$836$	28.2108	−	18.1300i	0.975690	−	0.627038i
$837$	38.3714	−	2.88156i	1.32631	−	0.0996012i
$838$	25.9905	−	7.63149i	0.897825	−	0.263625i
$839$	−18.1181	−	3.49199i	−0.625508	−	0.120557i	−0.133359	−	0.991068i	$-0.542576\pi$
$839$	−18.1181	−	3.49199i	−0.625508	−	0.120557i	−0.492149	+	0.870511i	$0.663788\pi$
$840$	5.49651	+	0.739187i	0.189648	+	0.0255044i
$841$	2.28162	−	9.40498i	0.0786767	−	0.324310i
$842$	−12.7073	−	1.21340i	−0.437924	−	0.0418167i
$843$	3.47269	+	33.1685i	0.119606	+	1.14238i
$844$	3.22287	+	13.2848i	0.110936	+	0.457283i
$845$	−1.84512	−	12.8331i	−0.0634741	−	0.441472i
$846$	20.8651	−	4.41751i	0.717357	−	0.151877i
$847$	4.19370	−	29.1678i	0.144097	−	1.00222i
$848$	0.0295208	−	0.619719i	0.00101375	−	0.0212812i
$849$	16.8980	+	17.4016i	0.579936	+	0.597220i
$850$	−0.112957	+	0.195647i	−0.00387438	+	0.00671063i
$851$	13.1231	−	54.2170i	0.449854	−	1.85853i
$852$	15.1049	−	0.857647i	0.517485	−	0.0293825i
$853$	−5.79071	+	16.7311i	−0.198270	+	0.572864i	−0.999681	−	0.0252503i	$-0.991962\pi$
$853$	−5.79071	+	16.7311i	−0.198270	+	0.572864i	0.801411	+	0.598114i	$0.204083\pi$
$854$	−9.19939	−	5.91209i	−0.314797	−	0.202307i
$855$	34.2821	−	18.4727i	1.17242	−	0.631751i
$856$	−2.64754	+	5.79730i	−0.0904910	+	0.198148i
$857$	30.1707	−	23.7265i	1.03061	−	0.810483i	0.0485086	−	0.998823i	$-0.484553\pi$
$857$	30.1707	−	23.7265i	1.03061	−	0.810483i	0.982104	+	0.188340i	$0.0603107\pi$
$858$	−17.3205	+	18.5000i	−0.591311	+	0.631581i
$859$	1.06381	+	22.3321i	0.0362967	+	0.761962i	0.941506	+	0.336996i	$0.109411\pi$
$859$	1.06381	+	22.3321i	0.0362967	+	0.761962i	−0.905209	+	0.424966i	$0.860286\pi$
$860$	−18.2234	−	1.74012i	−0.621412	−	0.0593376i
$861$	−10.5726	−	8.99377i	−0.360315	−	0.306507i
$862$	−14.8845	−	2.86876i	−0.506969	−	0.0977103i
$863$	−1.60238	+	1.84925i	−0.0545458	+	0.0629492i	−0.782367	−	0.622818i	$-0.785988\pi$
$863$	−1.60238	+	1.84925i	−0.0545458	+	0.0629492i	0.727821	+	0.685767i	$0.240533\pi$
$864$	0.352257	−	5.18420i	0.0119840	−	0.176370i
$865$	2.69652	+	5.90455i	0.0916844	+	0.200761i
$866$	−9.69510	−	4.99817i	−0.329453	−	0.169845i
$867$	8.38531	+	27.6234i	0.284780	+	0.938140i
$868$	−10.2543	−	4.10519i	−0.348053	−	0.139339i
$869$	8.29973	+	11.6553i	0.281549	+	0.395380i
$870$	18.9582	+	13.2412i	0.642742	+	0.448919i
$871$	1.17658	−	24.6994i	0.0398669	−	0.836908i
$872$	5.84989	+	6.75113i	0.198102	+	0.228622i
$873$	4.89448	−	0.557609i	0.165653	−	0.0188722i
$874$	−12.0603	−	26.3722i	−0.407947	−	0.892053i
$875$	8.63170	+	14.9505i	0.291805	+	0.505421i
$876$	6.08484	+	6.26618i	0.205588	+	0.211715i
$877$	37.1747	−	19.1649i	1.25530	−	0.647152i	0.303196	−	0.952928i	$-0.401946\pi$
$877$	37.1747	−	19.1649i	1.25530	−	0.647152i	0.952103	+	0.305776i	$0.0989159\pi$
$878$	29.9408	+	23.5457i	1.01045	+	0.794629i
$879$	−5.94573	+	15.2534i	−0.200544	+	0.514483i
$880$	−9.35838	+	7.35951i	−0.315471	+	0.248089i
$881$	−36.3137	−	10.6627i	−1.22344	−	0.359235i	−0.394670	−	0.918823i	$-0.629141\pi$
$881$	−36.3137	−	10.6627i	−1.22344	−	0.359235i	−0.828771	+	0.559588i	$0.810959\pi$
$882$	2.29703	+	14.1405i	0.0773450	+	0.476135i
$883$	−3.55614	−	7.78686i	−0.119674	−	0.262049i	0.840309	−	0.542107i	$-0.182373\pi$
$883$	−3.55614	−	7.78686i	−0.119674	−	0.262049i	−0.959983	+	0.280059i	$0.909646\pi$
$884$	1.10188	+	1.05064i	0.0370602	+	0.0353368i
$885$	8.29087	+	20.1745i	0.278695	+	0.678157i
$886$	−2.75429	−	7.95800i	−0.0925323	−	0.267354i
$887$	−10.4762	+	43.1835i	−0.351756	+	1.44996i	0.471286	+	0.881980i	$0.343790\pi$
$887$	−10.4762	+	43.1835i	−0.351756	+	1.44996i	−0.823043	+	0.567980i	$0.807725\pi$
$888$	−10.7369	+	17.0468i	−0.360307	+	0.572052i
$889$	6.91152	+	3.56314i	0.231805	+	0.119504i
$890$	20.5569	+	6.03605i	0.689069	+	0.202329i
$891$	−49.3225	−	7.65251i	−1.65237	−	0.256369i
$892$	−2.51264	+	5.50192i	−0.0841295	+	0.184218i
$893$	−39.9081	+	15.9768i	−1.33547	+	0.534643i
$894$	−0.253707	−	27.8222i	−0.00848523	−	0.930512i
$895$	−53.8510	+	10.3789i	−1.80004	+	0.346929i
$896$	−0.745775	+	1.29172i	−0.0249146	+	0.0431533i
$897$	13.7125	+	17.0952i	0.457848	+	0.570793i
$898$	−7.16917	−	12.4174i	−0.239238	−	0.414373i
$899$	−30.1597	−	34.8061i	−1.00588	−	1.16085i
$900$	0.976260	−	0.652863i	0.0325420	−	0.0217621i
$901$	−0.0509529	+	0.354385i	−0.00169749	+	0.0118063i
$902$	29.6623	−	2.83240i	0.987646	−	0.0943088i
$903$	4.36631	+	21.5931i	0.145302	+	0.718574i
$904$	2.45473	−	2.34058i	0.0816431	−	0.0778465i
$905$	−0.194164	−	4.07600i	−0.00645423	−	0.135491i
$906$	−14.9349	−	28.3323i	−0.496178	−	0.941278i
$907$	−13.6172	−	12.9840i	−0.452152	−	0.431126i	0.429471	−	0.903081i	$-0.358700\pi$
$907$	−13.6172	−	12.9840i	−0.452152	−	0.431126i	−0.881623	+	0.471954i	$0.843549\pi$
$908$	−0.722831	+	0.834191i	−0.0239880	+	0.0276836i
$909$	−10.5971	+	15.4710i	−0.351482	+	0.513142i
$910$	8.10557	−	2.38001i	0.268697	−	0.0788965i
$911$	27.5718	−	38.7192i	0.913494	−	1.28282i	−0.0453735	−	0.998970i	$-0.514448\pi$
$911$	27.5718	−	38.7192i	0.913494	−	1.28282i	0.958868	−	0.283853i	$-0.0916128\pi$
$912$	1.09057	+	10.4163i	0.0361124	+	0.344918i
$913$	−59.4290	+	56.6655i	−1.96681	+	1.87535i
$914$	26.3518	+	10.5497i	0.871639	+	0.348952i
$915$	26.9466	−	4.12547i	0.890828	−	0.136384i
$916$	−3.19694	+	1.27986i	−0.105630	+	0.0422878i
$917$	5.72569	+	3.67968i	0.189079	+	0.121514i
$918$	−0.486734	+	2.95880i	−0.0160646	+	0.0976549i
$919$	−10.0692			−0.332152			−0.166076	−	0.986113i	$-0.553110\pi$
$919$	−10.0692			−0.332152			−0.166076	+	0.986113i	$0.553110\pi$
$920$	5.15234	+	8.91343i	0.169868	+	0.293867i
$921$	−19.7526	−	30.1281i	−0.650871	−	0.992753i
$922$	−36.9040	+	7.11267i	−1.21537	+	0.234243i
$923$	20.4833	−	10.5599i	0.674217	−	0.347583i
$924$	11.7460	+	8.20393i	0.386416	+	0.269889i
$925$	−4.53288	+	0.432837i	−0.149040	+	0.0142316i
$926$	2.67088	+	18.5764i	0.0877706	+	0.610458i
$927$	−13.9640	−	38.0846i	−0.458638	−	1.25086i
$928$	−5.23188	+	3.36232i	−0.171745	+	0.110374i
$929$	13.0009	−	18.2572i	0.426546	−	0.599000i	−0.544245	−	0.838926i	$-0.683184\pi$
$929$	13.0009	−	18.2572i	0.426546	−	0.599000i	0.970791	+	0.239926i	$0.0771233\pi$
$930$	25.9376	−	9.24278i	0.850527	−	0.303083i
$931$	−9.44402	−	27.2867i	−0.309515	−	0.894285i
$932$	−4.77718	−	13.8027i	−0.156482	−	0.452124i
$933$	−38.2764	+	13.6397i	−1.25311	+	0.446543i
$934$	−10.9962	+	15.4421i	−0.359808	+	0.505280i
$935$	5.77973	−	3.71441i	0.189017	−	0.121474i
$936$	−2.72467	−	7.43112i	−0.0890587	−	0.242894i
$937$	0.286789	+	1.99466i	0.00936900	+	0.0651628i	0.993970	−	0.109656i	$-0.0349750\pi$
$937$	0.286789	+	1.99466i	0.00936900	+	0.0651628i	−0.984601	+	0.174819i	$0.944066\pi$
$938$	−13.9163	+	1.32884i	−0.454382	+	0.0433883i
$939$	26.1779	+	18.2837i	0.854282	+	0.596667i
$940$	13.5651	−	6.99330i	0.442445	−	0.228096i
$941$	8.61716	−	1.66082i	0.280912	−	0.0541413i	−0.0468494	−	0.998902i	$-0.514918\pi$
$941$	8.61716	−	1.66082i	0.280912	−	0.0541413i	0.327761	+	0.944761i	$0.393706\pi$
$942$	−14.8928	−	22.7156i	−0.485234	−	0.740113i
$943$	1.21271	−	25.7389i	0.0394912	−	0.838173i
$944$	−5.86607			−0.190924
$945$	12.8675	+	10.5475i	0.418578	+	0.343112i
$946$	−39.7845	−	25.5680i	−1.29351	−	0.831286i
$947$	28.5700	−	11.4377i	0.928400	−	0.371675i	0.142334	−	0.989819i	$-0.454539\pi$
$947$	28.5700	−	11.4377i	0.928400	−	0.371675i	0.786065	+	0.618143i	$0.212115\pi$
$948$	−4.41728	+	0.676276i	−0.143466	+	0.0219644i
$949$	12.3514	+	4.94476i	0.400944	+	0.160514i
$950$	−1.71320	+	1.63354i	−0.0555837	+	0.0529990i
$951$	−0.488949	−	4.67007i	−0.0158552	−	0.151437i
$952$	0.499275	−	0.701134i	0.0161816	−	0.0227239i
$953$	53.4839	−	15.7043i	1.73251	−	0.508712i	0.745112	−	0.666939i	$-0.232396\pi$
$953$	53.4839	−	15.7043i	1.73251	−	0.508712i	0.987403	+	0.158227i	$0.0505777\pi$
$954$	1.05181	−	1.53558i	0.0340536	−	0.0497162i
$955$	−23.5654	+	27.1959i	−0.762558	+	0.880039i
$956$	1.36313	+	1.29974i	0.0440867	+	0.0420366i
$957$	27.8571	+	52.8465i	0.900494	+	1.70829i
$958$	0.843141	+	17.6997i	0.0272406	+	0.571851i
$959$	−5.25235	+	5.00810i	−0.169607	+	0.161720i
$960$	−0.736951	−	3.64451i	−0.0237850	−	0.117626i
$961$	−23.7317	+	2.26610i	−0.765537	+	0.0730999i
$962$	−4.36725	+	30.3749i	−0.140806	+	0.979325i
$963$	−15.8933	+	10.6285i	−0.512156	+	0.342498i
$964$	−0.312539	−	0.360690i	−0.0100662	−	0.0116170i
$965$	18.9709	+	32.8585i	0.610695	+	1.05775i
$966$	8.46309	−	9.04886i	0.272295	−	0.291142i
$967$	17.9763	−	31.1358i	0.578078	−	1.00126i	−0.417622	−	0.908621i	$-0.637136\pi$
$967$	17.9763	−	31.1358i	0.578078	−	1.00126i	0.995700	−	0.0926395i	$-0.0295304\pi$
$968$	−19.3994	+	3.73894i	−0.623522	+	0.120174i
$969$	−0.0551107	−	6.04358i	−0.00177041	−	0.194148i
$970$	3.27255	−	1.31013i	0.105075	−	0.0420658i
$971$	−9.46072	+	20.7161i	−0.303609	+	0.664811i	−0.998526	−	0.0542791i	$-0.982714\pi$
$971$	−9.46072	+	20.7161i	−0.303609	+	0.664811i	0.694917	+	0.719090i	$0.255441\pi$
$972$	9.06766	−	12.6798i	0.290845	−	0.406705i
$973$	−19.9995	−	5.87239i	−0.641155	−	0.188260i
$974$	27.9908	+	14.4303i	0.896883	+	0.462375i
$975$	0.953407	−	1.51370i	0.0305335	−	0.0484773i
$976$	−1.72847	+	7.12486i	−0.0553271	+	0.228061i
$977$	−15.8460	−	45.7841i	−0.506959	−	1.46476i	−0.850677	−	0.525689i	$-0.823808\pi$
$977$	−15.8460	−	45.7841i	−0.506959	−	1.46476i	0.343718	−	0.939073i	$-0.388314\pi$
$978$	−1.84689	−	4.49410i	−0.0590570	−	0.143705i
$979$	40.0574	+	38.1946i	1.28024	+	1.22071i
$980$	4.25855	+	9.32492i	0.136034	+	0.297874i
$981$	4.29701	+	26.4523i	0.137193	+	0.844558i
$982$	−36.7077	−	10.7784i	−1.17139	−	0.343951i
$983$	−25.6714	+	20.1882i	−0.818792	+	0.643905i	−0.937096	−	0.349072i	$-0.886497\pi$
$983$	−25.6714	+	20.1882i	−0.818792	+	0.643905i	0.118304	+	0.992977i	$0.462254\pi$
$984$	−3.37981	+	8.67067i	−0.107744	+	0.276411i
$985$	14.7220	+	11.5775i	0.469081	+	0.368890i
$986$	3.18995	−	1.64453i	0.101589	−	0.0523726i
$987$	−12.7948	−	13.1761i	−0.407263	−	0.419401i
$988$	7.97651	+	13.8157i	0.253767	+	0.439537i
$989$	−26.7653	+	30.9212i	−0.851086	+	0.983236i
$990$	−35.4871	+	4.04290i	−1.12785	+	0.128492i
$991$	−4.01937	−	4.63861i	−0.127680	−	0.147350i	0.688310	−	0.725417i	$-0.258353\pi$
$991$	−4.01937	−	4.63861i	−0.127680	−	0.147350i	−0.815990	+	0.578066i	$0.803807\pi$
$992$	−0.352362	+	7.39699i	−0.0111875	+	0.234855i
$993$	−47.1711	−	32.9463i	−1.49693	−	1.04552i
$994$	−7.55726	−	10.6127i	−0.239702	−	0.336614i
$995$	24.3093	+	9.73199i	0.770658	+	0.308525i
$996$	−7.44926	−	24.5398i	−0.236039	−	0.777574i
$997$	−40.3161	−	20.7844i	−1.27682	−	0.658248i	−0.319587	−	0.947557i	$-0.603544\pi$
$997$	−40.3161	−	20.7844i	−1.27682	−	0.658248i	−0.957236	+	0.289309i	$0.906574\pi$
$998$	7.56364	+	16.5621i	0.239423	+	0.524263i
$999$	−54.2698	+	26.6016i	−1.71702	+	0.841637i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.m.a.13.6	✓	240
9.7	even	3	inner	414.2.m.a.151.10	yes	240
23.16	even	11	inner	414.2.m.a.85.10	yes	240
207.16	even	33	inner	414.2.m.a.223.6	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.m.a.13.6	✓	240	1.1	even	1	trivial
414.2.m.a.85.10	yes	240	23.16	even	11	inner
414.2.m.a.151.10	yes	240	9.7	even	3	inner
414.2.m.a.223.6	yes	240	207.16	even	33	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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.m (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.327068 - 0.945001i) q^{2} +(0.0157937 + 1.73198i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-1.24523 - 1.74869i) q^{5} +(1.64189 + 0.551550i) q^{6} +(-0.351646 - 1.44951i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-2.99950 + 0.0547087i) q^{9} +O(q^{10})\)	\(q+(0.327068 - 0.945001i) q^{2} +(0.0157937 + 1.73198i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-1.24523 - 1.74869i) q^{5} +(1.64189 + 0.551550i) q^{6} +(-0.351646 - 1.44951i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-2.99950 + 0.0547087i) q^{9} +(-2.05979 + 0.604808i) q^{10} +(-5.44563 - 1.04956i) q^{11} +(1.05822 - 1.37119i) q^{12} +(0.622001 - 2.56392i) q^{13} +(-1.48480 - 0.141781i) q^{14} +(3.00902 - 2.18434i) q^{15} +(0.235759 + 0.971812i) q^{16} +(-0.0821263 - 0.571201i) q^{17} +(-0.929341 + 2.85242i) q^{18} +(0.860538 - 5.98517i) q^{19} +(-0.102146 + 2.14431i) q^{20} +(2.50496 - 0.631937i) q^{21} +(-2.77293 + 4.80285i) q^{22} +(3.77132 + 2.96263i) q^{23} +(-0.949665 - 1.44849i) q^{24} +(0.128041 - 0.369950i) q^{25} +(-2.21947 - 1.42637i) q^{26} +(-0.142128 - 5.19421i) q^{27} +(-0.619612 + 1.35676i) q^{28} +(-4.88858 + 3.84442i) q^{29} +(-1.08005 - 3.55796i) q^{30} +(0.352362 + 7.39699i) q^{31} +(0.995472 + 0.0950560i) q^{32} +(1.73181 - 9.44829i) q^{33} +(-0.566646 - 0.109212i) q^{34} +(-2.09685 + 2.41989i) q^{35} +(2.39159 + 1.81116i) q^{36} +(-4.83189 - 10.5804i) q^{37} +(-5.37454 - 2.77077i) q^{38} +(4.45049 + 1.03680i) q^{39} +(1.99297 + 0.797865i) q^{40} +(-3.11658 - 4.37662i) q^{41} +(0.222111 - 2.57387i) q^{42} +(-0.405752 + 8.51779i) q^{43} +(3.63176 + 4.19128i) q^{44} +(3.83075 + 5.17707i) q^{45} +(4.03316 - 2.59492i) q^{46} +(-3.55460 - 6.15675i) q^{47} +(-1.67943 + 0.423678i) q^{48} +(4.24444 - 2.18816i) q^{49} +(-0.307725 - 0.241997i) q^{50} +(0.988010 - 0.151262i) q^{51} +(-2.07384 + 1.63088i) q^{52} +(-0.595290 - 0.174793i) q^{53} +(-4.95502 - 1.56455i) q^{54} +(4.94574 + 10.8297i) q^{55} +(1.07949 + 1.02929i) q^{56} +(10.3798 + 1.39591i) q^{57} +(2.03408 + 5.87710i) q^{58} +(-1.38298 + 5.70071i) q^{59} +(-3.71552 - 0.143049i) q^{60} +(6.51652 + 3.35950i) q^{61} +(7.10541 + 2.08634i) q^{62} +(1.13406 + 4.32855i) q^{63} +(0.415415 - 0.909632i) q^{64} +(-5.25804 + 2.10500i) q^{65} +(-8.36223 - 4.72679i) q^{66} +(9.20314 - 1.77376i) q^{67} +(-0.288537 + 0.499761i) q^{68} +(-5.07165 + 6.57863i) q^{69} +(1.60099 + 2.77299i) q^{70} +(5.72012 + 6.60136i) q^{71} +(2.49376 - 1.66768i) q^{72} +(-0.717669 + 4.99150i) q^{73} +(-11.5788 + 1.10564i) q^{74} +(0.642767 + 0.215921i) q^{75} +(-4.37622 + 4.17271i) q^{76} +(0.393593 + 8.26254i) q^{77} +(2.43539 - 3.86661i) q^{78} +(-1.86726 - 1.78043i) q^{79} +(1.40582 - 1.62240i) q^{80} +(8.99401 - 0.328198i) q^{81} +(-5.15524 + 1.51372i) q^{82} +(8.58859 - 12.0610i) q^{83} +(-2.35967 - 1.05173i) q^{84} +(-0.896585 + 0.854892i) q^{85} +(7.91661 + 3.16933i) q^{86} +(-6.73566 - 8.40620i) q^{87} +(5.14859 - 2.06118i) q^{88} +(-8.39580 - 5.39565i) q^{89} +(6.14525 - 1.92681i) q^{90} -3.93515 q^{91} +(-1.13308 - 4.66006i) q^{92} +(-12.8059 + 0.727109i) q^{93} +(-6.98073 + 1.34543i) q^{94} +(-11.5378 + 5.94814i) q^{95} +(-0.148913 + 1.72564i) q^{96} +(-1.63461 + 0.156086i) q^{97} +(-0.679593 - 4.72667i) q^{98} +(16.3916 + 2.85023i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9}+O(q^{10}) \) 240 * q - 12 * q^2 + 12 * q^4 - 13 * q^7 + 24 * q^8 - 36 * q^9	\( 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9} + 2 q^{11} + 11 q^{12} + 4 q^{13} + 2 q^{14} + 6 q^{15} + 12 q^{16} - 8 q^{17} - 18 q^{18} + 12 q^{19} - 29 q^{21} + 20 q^{22} + 10 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} - 8 q^{29} - 18 q^{30} - 12 q^{32} + 50 q^{33} - 4 q^{34} - 12 q^{35} - 4 q^{36} + 92 q^{37} + 6 q^{38} + 44 q^{39} + 2 q^{41} + 42 q^{42} - 14 q^{43} - 4 q^{44} - 2 q^{45} - 44 q^{46} + 10 q^{47} - 22 q^{48} + 43 q^{49} - 43 q^{50} - 90 q^{51} - 18 q^{52} + 16 q^{53} - 29 q^{54} - 8 q^{55} + 13 q^{56} + 7 q^{57} + 8 q^{58} - 84 q^{59} + 9 q^{60} - 53 q^{61} - 66 q^{62} + 11 q^{63} - 24 q^{64} + 79 q^{65} - 110 q^{66} + 46 q^{67} - 40 q^{68} - 55 q^{69} - 6 q^{70} - 14 q^{71} - 19 q^{72} + 16 q^{73} + 46 q^{74} - 44 q^{75} - 6 q^{76} - 96 q^{77} + 20 q^{78} + 20 q^{79} - 22 q^{80} - 56 q^{81} + 26 q^{82} + 57 q^{83} + 5 q^{84} - 2 q^{85} - 8 q^{86} - 198 q^{87} - 2 q^{88} + 60 q^{89} - 22 q^{90} - 252 q^{91} - 218 q^{93} - 10 q^{94} + 6 q^{95} - q^{97} + 20 q^{98} + 84 q^{99}+O(q^{100}) \) 240 * q - 12 * q^2 + 12 * q^4 - 13 * q^7 + 24 * q^8 - 36 * q^9 + 2 * q^11 + 11 * q^12 + 4 * q^13 + 2 * q^14 + 6 * q^15 + 12 * q^16 - 8 * q^17 - 18 * q^18 + 12 * q^19 - 29 * q^21 + 20 * q^22 + 10 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 - 8 * q^29 - 18 * q^30 - 12 * q^32 + 50 * q^33 - 4 * q^34 - 12 * q^35 - 4 * q^36 + 92 * q^37 + 6 * q^38 + 44 * q^39 + 2 * q^41 + 42 * q^42 - 14 * q^43 - 4 * q^44 - 2 * q^45 - 44 * q^46 + 10 * q^47 - 22 * q^48 + 43 * q^49 - 43 * q^50 - 90 * q^51 - 18 * q^52 + 16 * q^53 - 29 * q^54 - 8 * q^55 + 13 * q^56 + 7 * q^57 + 8 * q^58 - 84 * q^59 + 9 * q^60 - 53 * q^61 - 66 * q^62 + 11 * q^63 - 24 * q^64 + 79 * q^65 - 110 * q^66 + 46 * q^67 - 40 * q^68 - 55 * q^69 - 6 * q^70 - 14 * q^71 - 19 * q^72 + 16 * q^73 + 46 * q^74 - 44 * q^75 - 6 * q^76 - 96 * q^77 + 20 * q^78 + 20 * q^79 - 22 * q^80 - 56 * q^81 + 26 * q^82 + 57 * q^83 + 5 * q^84 - 2 * q^85 - 8 * q^86 - 198 * q^87 - 2 * q^88 + 60 * q^89 - 22 * q^90 - 252 * q^91 - 218 * q^93 - 10 * q^94 + 6 * q^95 - q^97 + 20 * q^98 + 84 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more