LMFDB - Embedded newform 414.2.m.a.223.4

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			223.4
Character	$\chi$	$=$	414.223
Dual form			414.2.m.a.13.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.327068 + 0.945001i) q^{2} +(-1.08222 - 1.35233i) q^{3} +(-0.786053 + 0.618159i) q^{4} +(0.204372 - 0.287001i) q^{5} +(0.923996 - 1.46500i) q^{6} +(-0.726527 + 2.99479i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(-0.657606 + 2.92704i) q^{9} +O(q^{10})$	\(q+(0.327068 + 0.945001i) q^{2} +(-1.08222 - 1.35233i) q^{3} +(-0.786053 + 0.618159i) q^{4} +(0.204372 - 0.287001i) q^{5} +(0.923996 - 1.46500i) q^{6} +(-0.726527 + 2.99479i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(-0.657606 + 2.92704i) q^{9} +(0.338059 + 0.0992632i) q^{10} +(4.81224 - 0.927484i) q^{11} +(1.68664 + 0.394022i) q^{12} +(-0.235775 - 0.971876i) q^{13} +(-3.06770 + 0.292930i) q^{14} +(-0.609295 + 0.0342182i) q^{15} +(0.235759 - 0.971812i) q^{16} +(-0.863401 + 6.00509i) q^{17} +(-2.98114 + 0.335902i) q^{18} +(0.209251 + 1.45537i) q^{19} +(0.0167646 + 0.351932i) q^{20} +(4.83621 - 2.25851i) q^{21} +(2.45040 + 4.24422i) q^{22} +(-1.29451 + 4.61782i) q^{23} +(0.179294 + 1.72275i) q^{24} +(1.59474 + 4.60769i) q^{25} +(0.841309 - 0.540677i) q^{26} +(4.67000 - 2.27839i) q^{27} +(-1.28017 - 2.80317i) q^{28} +(7.50349 + 5.90081i) q^{29} +(-0.231617 - 0.564593i) q^{30} +(0.0965191 - 2.02619i) q^{31} +(0.995472 - 0.0950560i) q^{32} +(-6.46216 - 5.50401i) q^{33} +(-5.95720 + 1.14816i) q^{34} +(0.711023 + 0.820565i) q^{35} +(-1.29246 - 2.70731i) q^{36} +(3.58775 - 7.85607i) q^{37} +(-1.30689 + 0.673748i) q^{38} +(-1.05914 + 1.37063i) q^{39} +(-0.327093 + 0.130948i) q^{40} +(-5.48637 + 7.70453i) q^{41} +(3.71606 + 3.83154i) q^{42} +(-0.473921 - 9.94883i) q^{43} +(-3.20935 + 3.70378i) q^{44} +(0.705665 + 0.786938i) q^{45} +(-4.78723 + 0.287026i) q^{46} +(-0.280611 + 0.486032i) q^{47} +(-1.56935 + 0.732888i) q^{48} +(-2.21906 - 1.14400i) q^{49} +(-3.83269 + 3.01406i) q^{50} +(9.05526 - 5.33121i) q^{51} +(0.786105 + 0.618200i) q^{52} +(-9.36230 + 2.74902i) q^{53} +(3.68049 + 3.66797i) q^{54} +(0.717300 - 1.57067i) q^{55} +(2.23030 - 2.12658i) q^{56} +(1.74169 - 1.85801i) q^{57} +(-3.12212 + 9.02078i) q^{58} +(-2.03035 - 8.36923i) q^{59} +(0.457786 - 0.403539i) q^{60} +(-3.86557 + 1.99284i) q^{61} +(1.94632 - 0.571490i) q^{62} +(-8.28809 - 4.09596i) q^{63} +(0.415415 + 0.909632i) q^{64} +(-0.327115 - 0.130957i) q^{65} +(3.08773 - 7.90694i) q^{66} +(-9.81171 - 1.89105i) q^{67} +(-3.03342 - 5.25404i) q^{68} +(7.64577 - 3.24688i) q^{69} +(-0.542881 + 0.940298i) q^{70} +(7.90957 - 9.12813i) q^{71} +(2.13569 - 2.10685i) q^{72} +(-0.808407 - 5.62259i) q^{73} +(8.59743 + 0.820955i) q^{74} +(4.50528 - 7.14315i) q^{75} +(-1.06413 - 1.01465i) q^{76} +(-0.718610 + 15.0855i) q^{77} +(-1.64166 - 0.552600i) q^{78} +(6.89319 - 6.57264i) q^{79} +(-0.230728 - 0.266274i) q^{80} +(-8.13511 - 3.84968i) q^{81} +(-9.07520 - 2.66472i) q^{82} +(-3.18899 - 4.47830i) q^{83} +(-2.40540 + 4.76485i) q^{84} +(1.54701 + 1.47507i) q^{85} +(9.24665 - 3.70180i) q^{86} +(-0.140560 - 16.5332i) q^{87} +(-4.54975 - 1.82145i) q^{88} +(3.18010 - 2.04373i) q^{89} +(-0.512857 + 0.924237i) q^{90} +3.08186 q^{91} +(-1.83699 - 4.43006i) q^{92} +(-2.84453 + 2.06225i) q^{93} +(-0.551080 - 0.106212i) q^{94} +(0.460458 + 0.237382i) q^{95} +(-1.20587 - 1.24334i) q^{96} +(-2.38799 - 0.228026i) q^{97} +(0.355302 - 2.47118i) q^{98} +(-0.449779 + 14.6955i) 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 $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{11}\right)$

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
$3$	−1.08222	−	1.35233i	−0.624819	−	0.780769i
$3$	−1.08222	−	1.35233i	−0.624819	−	0.780769i
$4$	−0.786053	+	0.618159i	−0.393027	+	0.309079i
$5$	0.204372	−	0.287001i	0.0913980	−	0.128351i	−0.766345	−	0.642429i	$-0.777927\pi$
$5$	0.204372	−	0.287001i	0.0913980	−	0.128351i	0.857743	+	0.514079i	$0.171866\pi$
$6$	0.923996	−	1.46500i	0.377220	−	0.598085i
$7$	−0.726527	+	2.99479i	−0.274602	+	1.13192i	0.652703	+	0.757614i	$0.273635\pi$
$7$	−0.726527	+	2.99479i	−0.274602	+	1.13192i	−0.927304	+	0.374309i	$0.877880\pi$
$8$	−0.841254	−	0.540641i	−0.297428	−	0.191145i
$9$	−0.657606	+	2.92704i	−0.219202	+	0.975680i
$10$	0.338059	+	0.0992632i	0.106904	+	0.0313898i
$11$	4.81224	−	0.927484i	1.45095	−	0.279647i	0.597937	−	0.801543i	$-0.295987\pi$
$11$	4.81224	−	0.927484i	1.45095	−	0.279647i	0.853009	+	0.521896i	$0.174775\pi$
$12$	1.68664	+	0.394022i	0.486890	+	0.113744i
$13$	−0.235775	−	0.971876i	−0.0653921	−	0.269550i	0.929725	−	0.368256i	$-0.120045\pi$
$13$	−0.235775	−	0.971876i	−0.0653921	−	0.269550i	−0.995117	+	0.0987058i	$0.968530\pi$
$14$	−3.06770	+	0.292930i	−0.819877	+	0.0782888i
$15$	−0.609295	+	0.0342182i	−0.157319	+	0.00883511i
$16$	0.235759	−	0.971812i	0.0589397	−	0.242953i
$17$	−0.863401	+	6.00509i	−0.209406	+	1.45645i	0.565698	+	0.824613i	$0.308607\pi$
$17$	−0.863401	+	6.00509i	−0.209406	+	1.45645i	−0.775103	+	0.631835i	$0.782302\pi$
$18$	−2.98114	+	0.335902i	−0.702660	+	0.0791730i
$19$	0.209251	+	1.45537i	0.0480055	+	0.333885i	0.999644	+	0.0266666i	$0.00848924\pi$
$19$	0.209251	+	1.45537i	0.0480055	+	0.333885i	−0.951639	+	0.307219i	$0.900602\pi$
$20$	0.0167646	+	0.351932i	0.00374868	+	0.0786944i
$21$	4.83621	−	2.25851i	1.05535	−	0.492847i
$22$	2.45040	+	4.24422i	0.522428	+	0.904871i
$23$	−1.29451	+	4.61782i	−0.269924	+	0.962882i
$23$	−1.29451	+	4.61782i	−0.269924	+	0.962882i
$24$	0.179294	+	1.72275i	0.0365983	+	0.351654i
$25$	1.59474	+	4.60769i	0.318948	+	0.921539i
$26$	0.841309	−	0.540677i	0.164994	−	0.106035i
$27$	4.67000	−	2.27839i	0.898742	−	0.438477i
$28$	−1.28017	−	2.80317i	−0.241928	−	0.529750i
$29$	7.50349	+	5.90081i	1.39336	+	1.09575i	0.982954	+	0.183853i	$0.0588569\pi$
$29$	7.50349	+	5.90081i	1.39336	+	1.09575i	0.410410	+	0.911901i	$0.365386\pi$
$30$	−0.231617	−	0.564593i	−0.0422873	−	0.103080i
$31$	0.0965191	−	2.02619i	0.0173353	−	0.363914i	−0.973487	−	0.228743i	$-0.926539\pi$
$31$	0.0965191	−	2.02619i	0.0173353	−	0.363914i	0.990822	−	0.135171i	$-0.0431584\pi$
$32$	0.995472	−	0.0950560i	0.175976	−	0.0168037i
$33$	−6.46216	−	5.50401i	−1.12492	−	0.958125i
$34$	−5.95720	+	1.14816i	−1.02165	+	0.196907i
$35$	0.711023	+	0.820565i	0.120185	+	0.138701i
$36$	−1.29246	−	2.70731i	−0.215410	−	0.451219i
$37$	3.58775	−	7.85607i	0.589822	−	1.29153i	−0.345727	−	0.938335i	$-0.612368\pi$
$37$	3.58775	−	7.85607i	0.589822	−	1.29153i	0.935550	−	0.353195i	$-0.114905\pi$
$38$	−1.30689	+	0.673748i	−0.212005	+	0.109296i
$39$	−1.05914	+	1.37063i	−0.169598	+	0.219476i
$40$	−0.327093	+	0.130948i	−0.0517179	+	0.0207047i
$41$	−5.48637	+	7.70453i	−0.856827	+	1.20325i	0.120753	+	0.992683i	$0.461469\pi$
$41$	−5.48637	+	7.70453i	−0.856827	+	1.20325i	−0.977580	+	0.210563i	$0.932470\pi$
$42$	3.71606	+	3.83154i	0.573401	+	0.591219i
$43$	−0.473921	−	9.94883i	−0.0722723	−	1.51718i	−0.685963	−	0.727636i	$-0.740619\pi$
$43$	−0.473921	−	9.94883i	−0.0722723	−	1.51718i	0.613691	−	0.789546i	$-0.289684\pi$
$44$	−3.20935	+	3.70378i	−0.483827	+	0.558366i
$45$	0.705665	+	0.786938i	0.105194	+	0.117310i
$46$	−4.78723	+	0.287026i	−0.705839	+	0.0423196i
$47$	−0.280611	+	0.486032i	−0.0409313	+	0.0708951i	−0.885765	−	0.464133i	$-0.846366\pi$
$47$	−0.280611	+	0.486032i	−0.0409313	+	0.0708951i	0.844834	+	0.535029i	$0.179699\pi$
$48$	−1.56935	+	0.732888i	−0.226517	+	0.105783i
$49$	−2.21906	−	1.14400i	−0.317008	−	0.163429i
$50$	−3.83269	+	3.01406i	−0.542024	+	0.426252i
$51$	9.05526	−	5.33121i	1.26799	−	0.746519i
$52$	0.786105	+	0.618200i	0.109013	+	0.0857289i
$53$	−9.36230	+	2.74902i	−1.28601	+	0.377607i	−0.852114	−	0.523356i	$-0.824680\pi$
$53$	−9.36230	+	2.74902i	−1.28601	+	0.377607i	−0.433897	+	0.900963i	$0.642862\pi$
$54$	3.68049	+	3.66797i	0.500852	+	0.499147i
$55$	0.717300	−	1.57067i	0.0967207	−	0.211789i
$56$	2.23030	−	2.12658i	0.298036	−	0.284177i
$57$	1.74169	−	1.85801i	0.230693	−	0.246099i
$58$	−3.12212	+	9.02078i	−0.409955	+	1.18449i
$59$	−2.03035	−	8.36923i	−0.264329	−	1.08958i	−0.936914	−	0.349560i	$-0.886331\pi$
$59$	−2.03035	−	8.36923i	−0.264329	−	1.08958i	0.672584	−	0.740021i	$-0.265184\pi$
$60$	0.457786	−	0.403539i	0.0591000	−	0.0520966i
$61$	−3.86557	+	1.99284i	−0.494936	+	0.255157i	−0.687576	−	0.726112i	$-0.741325\pi$
$61$	−3.86557	+	1.99284i	−0.494936	+	0.255157i	0.192640	+	0.981269i	$0.438295\pi$
$62$	1.94632	−	0.571490i	0.247182	−	0.0725793i
$63$	−8.28809	−	4.09596i	−1.04420	−	0.516043i
$64$	0.415415	+	0.909632i	0.0519269	+	0.113704i
$65$	−0.327115	−	0.130957i	−0.0405736	−	0.0162432i
$66$	3.08773	−	7.90694i	0.380073	−	0.973277i
$67$	−9.81171	−	1.89105i	−1.19869	−	0.231029i	−0.449437	−	0.893312i	$-0.648375\pi$
$67$	−9.81171	−	1.89105i	−1.19869	−	0.231029i	−0.749254	+	0.662283i	$0.769588\pi$
$68$	−3.03342	−	5.25404i	−0.367856	−	0.637146i
$69$	7.64577	−	3.24688i	0.920442	−	0.390878i
$70$	−0.542881	+	0.940298i	−0.0648867	+	0.112387i
$71$	7.90957	−	9.12813i	0.938693	−	1.08331i	−0.0576896	−	0.998335i	$-0.518373\pi$
$71$	7.90957	−	9.12813i	0.938693	−	1.08331i	0.996383	−	0.0849754i	$-0.0270812\pi$
$72$	2.13569	−	2.10685i	0.251693	−	0.248295i
$73$	−0.808407	−	5.62259i	−0.0946169	−	0.658075i	−0.980840	−	0.194816i	$-0.937589\pi$
$73$	−0.808407	−	5.62259i	−0.0946169	−	0.658075i	0.886223	−	0.463259i	$-0.153320\pi$
$74$	8.59743	+	0.820955i	0.999431	+	0.0954341i
$75$	4.50528	−	7.14315i	0.520225	−	0.824820i
$76$	−1.06413	−	1.01465i	−0.122065	−	0.116388i
$77$	−0.718610	+	15.0855i	−0.0818932	+	1.71915i
$78$	−1.64166	−	0.552600i	−0.185881	−	0.0625696i
$79$	6.89319	−	6.57264i	0.775544	−	0.739480i	−0.194896	−	0.980824i	$-0.562437\pi$
$79$	6.89319	−	6.57264i	0.775544	−	0.739480i	0.970440	+	0.241344i	$0.0775883\pi$
$80$	−0.230728	−	0.266274i	−0.0257962	−	0.0297704i
$81$	−8.13511	−	3.84968i	−0.903901	−	0.427742i
$82$	−9.07520	−	2.66472i	−1.00219	−	0.294269i
$83$	−3.18899	−	4.47830i	−0.350037	−	0.491558i	0.601594	−	0.798802i	$-0.294533\pi$
$83$	−3.18899	−	4.47830i	−0.350037	−	0.491558i	−0.951631	+	0.307244i	$0.900593\pi$
$84$	−2.40540	+	4.76485i	−0.262451	+	0.519888i
$85$	1.54701	+	1.47507i	0.167797	+	0.159994i
$86$	9.24665	−	3.70180i	0.997092	−	0.399175i
$87$	−0.140560	−	16.5332i	−0.0150696	−	1.77254i
$88$	−4.54975	−	1.82145i	−0.485005	−	0.194167i
$89$	3.18010	−	2.04373i	0.337090	−	0.216634i	−0.361134	−	0.932514i	$-0.617610\pi$
$89$	3.18010	−	2.04373i	0.337090	−	0.216634i	0.698224	+	0.715879i	$0.253974\pi$
$90$	−0.512857	+	0.924237i	−0.0540599	+	0.0974231i
$91$	3.08186			0.323067
$92$	−1.83699	−	4.43006i	−0.191520	−	0.461866i
$93$	−2.84453	+	2.06225i	−0.294964	+	0.213845i
$94$	−0.551080	−	0.106212i	−0.0568396	−	0.0109549i
$95$	0.460458	+	0.237382i	0.0472420	+	0.0243549i
$96$	−1.20587	−	1.24334i	−0.123073	−	0.126898i
$97$	−2.38799	−	0.228026i	−0.242464	−	0.0231525i	−0.0268836	−	0.999639i	$-0.508558\pi$
$97$	−2.38799	−	0.228026i	−0.242464	−	0.0231525i	−0.215581	+	0.976486i	$0.569164\pi$
$98$	0.355302	−	2.47118i	0.0358909	−	0.249627i
$99$	−0.449779	+	14.6955i	−0.0452044	+	1.47696i
$100$	−4.10184	−	2.63609i	−0.410184	−	0.263609i
$101$	4.87515	+	6.84619i	0.485096	+	0.681222i	0.982493	−	0.186301i	$-0.0596501\pi$
$101$	4.87515	+	6.84619i	0.485096	+	0.681222i	−0.497397	+	0.867523i	$0.665711\pi$
$102$	7.99969	+	6.81356i	0.792087	+	0.674643i
$103$	−3.89820	+	11.2631i	−0.384101	+	1.10979i	0.572880	+	0.819639i	$0.305826\pi$
$103$	−3.89820	+	11.2631i	−0.384101	+	1.10979i	−0.956982	+	0.290149i	$0.906295\pi$
$104$	−0.327090	+	0.945063i	−0.0320738	+	0.0926711i
$105$	0.340194	−	1.84957i	0.0331995	−	0.180500i
$106$	−5.65993	−	7.94826i	−0.549741	−	0.772004i
$107$	11.6027	+	7.45661i	1.12168	+	0.720857i	0.963807	−	0.266603i	$-0.0859012\pi$
$107$	11.6027	+	7.45661i	1.12168	+	0.720857i	0.157869	+	0.987460i	$0.449538\pi$
$108$	−2.26246	+	4.67774i	−0.217705	+	0.450116i
$109$	−1.00478	+	6.98837i	−0.0962401	+	0.669364i	0.883403	+	0.468615i	$0.155247\pi$
$109$	−1.00478	+	6.98837i	−0.0962401	+	0.669364i	−0.979643	+	0.200749i	$0.935662\pi$
$110$	1.71889	+	0.164134i	0.163890	+	0.0156496i
$111$	−14.5067	+	3.65016i	−1.37692	+	0.346458i
$112$	2.73908	+	1.41210i	0.258819	+	0.133430i
$113$	13.4539	+	2.59302i	1.26563	+	0.243931i	0.777525	−	0.628852i	$-0.216475\pi$
$113$	13.4539	+	2.59302i	1.26563	+	0.243931i	0.488109	+	0.872783i	$0.337687\pi$
$114$	2.32547	+	1.03821i	0.217800	+	0.0972368i
$115$	1.06075	+	1.31528i	0.0989158	+	0.122650i
$116$	−9.54579			−0.886304
$117$	2.99977	−	0.0510098i	0.277328	−	0.00471586i
$118$	7.24487	−	4.65599i	0.666944	−	0.428619i
$119$	−17.3567	−	6.94856i	−1.59108	−	0.636974i
$120$	0.531072	+	0.300624i	0.0484800	+	0.0274431i
$121$	12.0854	−	4.83826i	1.09867	−	0.439842i
$122$	−3.14754	−	3.00117i	−0.284965	−	0.271714i
$123$	16.3565	−	0.918588i	1.47482	−	0.0828263i
$124$	1.17664	+	1.65235i	0.105665	+	0.148386i
$125$	3.33863	+	0.980309i	0.298616	+	0.0876815i
$126$	1.15992	−	9.17191i	0.103334	−	0.817098i
$127$	2.88379	+	3.32807i	0.255895	+	0.295319i	0.869132	−	0.494581i	$-0.164678\pi$
$127$	2.88379	+	3.32807i	0.255895	+	0.295319i	−0.613237	+	0.789899i	$0.710133\pi$
$128$	−0.723734	+	0.690079i	−0.0639697	+	0.0609949i
$129$	−12.9412	+	11.4077i	−1.13941	+	1.00439i
$130$	0.0167657	−	0.351955i	0.00147045	−	0.0308685i
$131$	4.76433	+	4.54278i	0.416261	+	0.396904i	0.869059	−	0.494709i	$-0.164725\pi$
$131$	4.76433	+	4.54278i	0.416261	+	0.396904i	−0.452797	+	0.891613i	$0.649574\pi$
$132$	8.48196	+	0.331800i	0.738260	+	0.0288795i
$133$	−4.51056	−	0.430706i	−0.391115	−	0.0373469i
$134$	−1.42205	−	9.89057i	−0.122846	−	0.854415i
$135$	0.300518	−	1.80593i	0.0258645	−	0.155430i
$136$	3.97293	−	4.58501i	0.340676	−	0.393161i
$137$	5.60506	−	9.70825i	0.478873	−	0.829432i	−0.520834	−	0.853658i	$-0.674379\pi$
$137$	5.60506	−	9.70825i	0.478873	−	0.829432i	0.999707	+	0.0242262i	$0.00771219\pi$
$138$	5.56899	+	6.16331i	0.474064	+	0.524656i
$139$	−9.36306	−	16.2173i	−0.794164	−	1.37553i	−0.923368	−	0.383915i	$-0.874576\pi$
$139$	−9.36306	−	16.2173i	−0.794164	−	1.37553i	0.129204	−	0.991618i	$-0.458758\pi$
$140$	−1.06614	−	0.205482i	−0.0901054	−	0.0173664i
$141$	0.960960	−	0.146514i	0.0809274	−	0.0123387i
$142$	11.2131	+	4.48903i	0.940979	+	0.376711i
$143$	−2.03600	−	4.45823i	−0.170259	−	0.372816i
$144$	2.68949	+	1.32914i	0.224124	+	0.110762i
$145$	3.22704	−	0.947545i	0.267991	−	0.0786893i
$146$	5.04895	−	2.60292i	0.417854	−	0.215419i
$147$	0.854432	+	4.23897i	0.0704724	+	0.349624i
$148$	2.03614	+	8.39309i	0.167370	+	0.689908i
$149$	−1.42156	+	4.10732i	−0.116459	+	0.336485i	−0.988133	−	0.153600i	$-0.950913\pi$
$149$	−1.42156	+	4.10732i	−0.116459	+	0.336485i	0.871674	+	0.490085i	$0.163034\pi$
$150$	8.22381	+	1.92120i	0.671472	+	0.156865i
$151$	−4.01913	+	3.83224i	−0.327072	+	0.311863i	−0.835767	−	0.549084i	$-0.814977\pi$
$151$	−4.01913	+	3.83224i	−0.327072	+	0.311863i	0.508695	+	0.860947i	$0.330128\pi$
$152$	0.610801	−	1.33747i	0.0495425	−	0.108483i
$153$	−17.0093	−	6.47619i	−1.37512	−	0.523569i
$154$	−14.4908	+	4.25489i	−1.16770	+	0.342869i
$155$	−0.561791	−	0.441797i	−0.0451241	−	0.0354860i
$156$	−0.0147258	−	1.73210i	−0.00117901	−	0.138679i
$157$	−13.3620	+	10.5080i	−1.06641	+	0.838631i	−0.987400	−	0.158243i	$-0.949417\pi$
$157$	−13.3620	+	10.5080i	−1.06641	+	0.838631i	−0.0790057	+	0.996874i	$0.525175\pi$
$158$	8.46569	+	4.36437i	0.673494	+	0.347210i
$159$	13.8496	+	9.68590i	1.09835	+	0.768142i
$160$	0.176166	−	0.305128i	0.0139271	−	0.0241225i
$161$	−12.8889	−	7.23176i	−1.01579	−	0.569942i
$162$	0.977213	−	8.94679i	0.0767771	−	0.702926i
$163$	7.08819	−	8.18020i	0.555190	−	0.640723i	−0.406895	−	0.913475i	$-0.633388\pi$
$163$	7.08819	−	8.18020i	0.555190	−	0.640723i	0.962084	+	0.272752i	$0.0879339\pi$
$164$	−0.450045	−	9.44762i	−0.0351426	−	0.737735i
$165$	−2.90034	+	0.729778i	−0.225791	+	0.0568131i
$166$	3.18899	−	4.47830i	0.247513	−	0.347584i
$167$	−16.3158	+	6.53186i	−1.26255	+	0.505451i	−0.903790	−	0.427977i	$-0.859226\pi$
$167$	−16.3158	+	6.53186i	−1.26255	+	0.505451i	−0.358765	+	0.933428i	$0.616802\pi$
$168$	−5.28952	−	0.714675i	−0.408095	−	0.0551383i
$169$	10.6659	−	5.49866i	0.820454	−	0.422974i
$170$	−0.887965	+	1.94437i	−0.0681038	+	0.149126i
$171$	−4.39754	−	0.344576i	−0.336288	−	0.0263504i
$172$	6.52248	+	7.52735i	0.497335	+	0.573955i
$173$	18.2028	−	3.50829i	1.38393	−	0.266731i	0.557690	−	0.830049i	$-0.311688\pi$
$173$	18.2028	−	3.50829i	1.38393	−	0.266731i	0.826240	+	0.563319i	$0.190476\pi$
$174$	15.5779	−	5.54031i	1.18096	−	0.420010i
$175$	−14.9577	+	1.42829i	−1.13069	+	0.107968i
$176$	0.233190	−	4.89526i	0.0175773	−	0.368994i
$177$	−9.12070	+	11.8030i	−0.685553	+	0.887172i
$178$	2.97143	+	2.33676i	0.222718	+	0.175147i
$179$	−2.19976	−	4.81680i	−0.164418	−	0.360025i	0.809433	−	0.587212i	$-0.199774\pi$
$179$	−2.19976	−	4.81680i	−0.164418	−	0.360025i	−0.973851	+	0.227187i	$0.927047\pi$
$180$	−1.04114	−	0.182362i	−0.0776022	−	0.0135925i
$181$	−2.34127	+	1.50464i	−0.174025	+	0.111839i	−0.624754	−	0.780822i	$-0.714801\pi$
$181$	−2.34127	+	1.50464i	−0.174025	+	0.111839i	0.450729	+	0.892661i	$0.351164\pi$
$182$	1.00798	+	2.91236i	0.0747162	+	0.215878i
$183$	6.87838	+	3.07085i	0.508464	+	0.227004i
$184$	3.58559	−	3.18489i	0.264333	−	0.234793i
$185$	−1.52146	−	2.63525i	−0.111860	−	0.193747i
$186$	−2.87918	−	2.01359i	−0.211112	−	0.147644i
$187$	1.41472	+	29.6987i	0.103455	+	2.17179i
$188$	−0.0798702	−	0.555510i	−0.00582513	−	0.0405147i
$189$	3.43042	+	15.6410i	0.249526	+	1.13771i
$190$	−0.0737256	+	0.512773i	−0.00534862	+	0.0372005i
$191$	−0.978335	+	4.03275i	−0.0707898	+	0.291800i	−0.996192	−	0.0871870i	$-0.972212\pi$
$191$	−0.978335	+	4.03275i	−0.0707898	+	0.291800i	0.925402	+	0.378987i	$0.123727\pi$
$192$	0.780555	−	1.54620i	0.0563317	−	0.111587i
$193$	3.60753	−	0.344477i	0.259676	−	0.0247960i	0.0355938	−	0.999366i	$-0.488668\pi$
$193$	3.60753	−	0.344477i	0.259676	−	0.0247960i	0.224082	+	0.974570i	$0.428062\pi$
$194$	−0.565552	−	2.33124i	−0.0406043	−	0.167373i
$195$	0.176912	+	0.584092i	0.0126689	+	0.0418277i
$196$	2.45147	−	0.472483i	0.175105	−	0.0337488i
$197$	−17.1875	−	5.04671i	−1.22456	−	0.359563i	−0.395365	−	0.918524i	$-0.629382\pi$
$197$	−17.1875	−	5.04671i	−1.22456	−	0.359563i	−0.829194	+	0.558961i	$0.811200\pi$
$198$	−14.0344	+	4.38140i	−0.997382	+	0.311372i
$199$	1.17187	+	0.753116i	0.0830718	+	0.0533870i	0.581517	−	0.813534i	$-0.302459\pi$
$199$	1.17187	+	0.753116i	0.0830718	+	0.0533870i	−0.498446	+	0.866921i	$0.666096\pi$
$200$	1.14953	−	4.73842i	0.0812839	−	0.335057i
$201$	8.06108	+	15.3152i	0.568585	+	1.08025i
$202$	−4.87515	+	6.84619i	−0.343015	+	0.481696i
$203$	−23.1232	+	18.1843i	−1.62293	+	1.27629i
$204$	−3.82238	+	9.78821i	−0.267620	+	0.685312i
$205$	1.08994	+	3.14918i	0.0761249	+	0.219948i
$206$	−11.9186			−0.830411
$207$	−12.6653	−	6.82579i	−0.880296	−	0.474425i
$208$	−1.00007			−0.0693421
$209$	2.35680	+	6.80953i	0.163023	+	0.471025i
$210$	1.85911	−	0.283452i	0.128291	−	0.0195600i
$211$	17.2847	−	13.5929i	1.18993	−	0.935771i	0.190981	−	0.981594i	$-0.438833\pi$
$211$	17.2847	−	13.5929i	1.18993	−	0.935771i	0.998950	+	0.0458223i	$0.0145908\pi$
$212$	5.65993	−	7.94826i	0.388726	−	0.545889i
$213$	−20.9042	−	0.817736i	−1.43233	−	0.0560303i
$214$	−3.25163	+	13.4034i	−0.222277	+	0.916236i
$215$	−2.95218	−	1.89725i	−0.201337	−	0.129391i
$216$	−5.16045	−	0.608087i	−0.351124	−	0.0413751i
$217$	5.99787	+	1.76113i	0.407162	+	0.119554i
$218$	−6.93264	+	1.33616i	−0.469538	+	0.0904960i
$219$	−6.72874	+	7.17811i	−0.454686	+	0.485052i
$220$	0.407087	+	1.67803i	0.0274458	+	0.113133i
$221$	6.03977	−	0.576728i	0.406279	−	0.0387949i
$222$	−8.19410	−	12.5150i	−0.549952	−	0.839954i
$223$	2.70390	−	11.1456i	0.181067	−	0.746367i	−0.806769	−	0.590867i	$-0.798786\pi$
$223$	2.70390	−	11.1456i	0.181067	−	0.746367i	0.987836	−	0.155500i	$-0.0496989\pi$
$224$	−0.438565	+	3.05029i	−0.0293029	+	0.203806i
$225$	−14.5356	+	1.63781i	−0.969041	+	0.109188i
$226$	1.94992	+	13.5620i	0.129707	+	0.902132i
$227$	−0.0449630	−	0.943889i	−0.00298430	−	0.0626481i	0.996884	−	0.0788826i	$-0.0251352\pi$
$227$	−0.0449630	−	0.943889i	−0.00298430	−	0.0626481i	−0.999868	+	0.0162345i	$0.994832\pi$
$228$	−0.220518	+	2.53714i	−0.0146042	+	0.168026i
$229$	−12.9739	−	22.4714i	−0.857337	−	1.48495i	−0.874460	−	0.485098i	$-0.838784\pi$
$229$	−12.9739	−	22.4714i	−0.857337	−	1.48495i	0.0171229	−	0.999853i	$-0.494549\pi$
$230$	−0.896001	+	1.43260i	−0.0590805	+	0.0944628i
$231$	21.1783	−	15.3540i	1.39343	−	1.01022i
$232$	−3.12212	−	9.02078i	−0.204977	−	0.592243i
$233$	−2.14405	+	1.37790i	−0.140461	+	0.0902691i	−0.608984	−	0.793182i	$-0.708423\pi$
$233$	−2.14405	+	1.37790i	−0.140461	+	0.0902691i	0.468523	+	0.883451i	$0.344786\pi$
$234$	1.02933	+	2.81810i	0.0672895	+	0.184225i
$235$	0.0821425	+	0.179867i	0.00535839	+	0.0117332i
$236$	6.76948	+	5.32358i	0.440656	+	0.346535i
$237$	−16.3483	−	2.20885i	−1.06194	−	0.143480i
$238$	0.889587	−	18.6747i	0.0576633	−	1.21050i
$239$	14.0872	−	1.34516i	0.911224	−	0.0870113i	0.371096	−	0.928594i	$-0.378982\pi$
$239$	14.0872	−	1.34516i	0.911224	−	0.0870113i	0.540128	+	0.841583i	$0.318376\pi$
$240$	−0.110393	+	0.600188i	−0.00712585	+	0.0387419i
$241$	6.28416	−	1.21117i	0.404798	−	0.0780185i	0.0172119	−	0.999852i	$-0.494521\pi$
$241$	6.28416	−	1.21117i	0.404798	−	0.0780185i	0.387586	+	0.921833i	$0.373309\pi$
$242$	8.52491	+	9.83827i	0.548002	+	0.632428i
$243$	3.59792	+	15.1676i	0.230807	+	0.973000i
$244$	1.80665	−	3.95602i	0.115659	−	0.253258i
$245$	−0.781843	+	0.403068i	−0.0499501	+	0.0257511i
$246$	6.21776	+	15.1565i	0.396430	+	0.966343i
$247$	1.36511	−	0.546506i	0.0868596	−	0.0347733i
$248$	−1.17664	+	1.65235i	−0.0747165	+	0.104925i
$249$	−2.60498	+	9.15907i	−0.165084	+	0.580433i
$250$	0.165565	+	3.47563i	0.0104712	+	0.219818i
$251$	15.4279	−	17.8047i	0.973799	−	1.12382i	−0.0184836	−	0.999829i	$-0.505884\pi$
$251$	15.4279	−	17.8047i	0.973799	−	1.12382i	0.992283	−	0.123995i	$-0.0395707\pi$
$252$	9.04683	−	1.90371i	0.569897	−	0.119923i
$253$	−1.94655	+	23.4227i	−0.122379	+	1.47257i
$254$	−2.20183	+	3.81369i	−0.138155	+	0.239292i
$255$	0.320583	−	3.68842i	0.0200757	−	0.230978i
$256$	−0.888835	−	0.458227i	−0.0555522	−	0.0286392i
$257$	10.3706	−	8.15555i	0.646902	−	0.508729i	−0.239949	−	0.970786i	$-0.577131\pi$
$257$	10.3706	−	8.15555i	0.646902	−	0.508729i	0.886851	+	0.462056i	$0.152888\pi$
$258$	−15.0130	−	8.49838i	−0.934666	−	0.529086i
$259$	20.9207	+	16.4522i	1.29995	+	1.02229i
$260$	0.338082	−	0.0992697i	0.0209669	−	0.00615645i
$261$	−22.2063	+	18.0826i	−1.37453	+	1.11929i
$262$	−2.73467	+	5.98809i	−0.168948	+	0.369946i
$263$	2.30929	−	2.20190i	0.142397	−	0.135775i	−0.615533	−	0.788111i	$-0.711059\pi$
$263$	2.30929	−	2.20190i	0.142397	−	0.135775i	0.757930	+	0.652336i	$0.226211\pi$
$264$	2.46063	+	8.12398i	0.151441	+	0.499996i
$265$	−1.12442	+	3.24881i	−0.0690728	+	0.199573i
$266$	−1.06824	−	4.40335i	−0.0654981	−	0.269987i
$267$	−6.20536	−	2.08879i	−0.379762	−	0.127832i
$268$	8.88149	−	4.57873i	0.542524	−	0.279690i
$269$	−9.15874	+	2.68925i	−0.558418	+	0.163966i	−0.548750	−	0.835987i	$-0.684896\pi$
$269$	−9.15874	+	2.68925i	−0.558418	+	0.163966i	−0.00966892	+	0.999953i	$0.503078\pi$
$270$	1.80490	−	0.306673i	0.109843	−	0.0186635i
$271$	1.34694	+	2.94939i	0.0818209	+	0.179163i	0.946121	−	0.323814i	$-0.104965\pi$
$271$	1.34694	+	2.94939i	0.0818209	+	0.179163i	−0.864300	+	0.502977i	$0.832238\pi$
$272$	5.63226	+	2.25482i	0.341506	+	0.136718i
$273$	−3.33524	−	4.16770i	−0.201858	−	0.252240i
$274$	11.0075	+	2.12153i	0.664990	+	0.128166i
$275$	11.9478	+	20.6942i	0.720481	+	1.24791i
$276$	−4.00289	+	7.27852i	−0.240946	+	0.438115i
$277$	4.19601	−	7.26770i	0.252114	−	0.436674i	−0.711994	−	0.702186i	$-0.752208\pi$
$277$	4.19601	−	7.26770i	0.252114	−	0.436674i	0.964108	+	0.265512i	$0.0855409\pi$
$278$	12.2630	−	14.1523i	0.735486	−	0.848796i
$279$	5.86725	+	1.61495i	0.351263	+	0.0966844i
$280$	−0.154520	−	1.07471i	−0.00923434	−	0.0642263i
$281$	6.68210	+	0.638063i	0.398620	+	0.0380636i	0.292442	−	0.956283i	$-0.405532\pi$
$281$	6.68210	+	0.638063i	0.398620	+	0.0380636i	0.106179	+	0.994347i	$0.466138\pi$
$282$	0.452755	+	0.860188i	0.0269612	+	0.0512234i
$283$	6.85449	+	6.53574i	0.407457	+	0.388509i	0.865902	−	0.500213i	$-0.166745\pi$
$283$	6.85449	+	6.53574i	0.407457	+	0.388509i	−0.458445	+	0.888723i	$0.651594\pi$
$284$	−0.574706	+	12.0646i	−0.0341025	+	0.715900i
$285$	−0.177296	−	0.879591i	−0.0105021	−	0.0521025i
$286$	3.54712	−	3.38217i	0.209745	−	0.199992i
$287$	−19.0874	−	22.0281i	−1.12669	−	1.30028i
$288$	−0.376396	+	2.97629i	−0.0221793	+	0.175380i
$289$	−19.0042	−	5.58015i	−1.11790	−	0.328244i
$290$	1.95089	+	2.73965i	0.114560	+	0.160878i
$291$	2.27597	+	3.47614i	0.133419	+	0.203775i
$292$	4.11111	+	3.91993i	0.240584	+	0.229397i
$293$	3.31229	−	1.32604i	0.193506	−	0.0774681i	−0.272886	−	0.962047i	$-0.587978\pi$
$293$	3.31229	−	1.32604i	0.193506	−	0.0774681i	0.466392	+	0.884578i	$0.345554\pi$
$294$	−3.72637	+	2.19387i	−0.217326	+	0.127949i
$295$	−2.81692	−	1.12773i	−0.164007	−	0.0656587i
$296$	−7.26552	+	4.66927i	−0.422300	+	0.271396i
$297$	20.3600	−	15.2955i	1.18141	−	0.887537i
$298$	−4.34637			−0.251779
$299$	4.79316	+	0.169341i	0.277196	+	0.00979323i
$300$	0.874213	+	8.39987i	0.0504727	+	0.484967i
$301$	30.1389	+	5.80880i	1.73718	+	0.334814i
$302$	−4.93600	−	2.54468i	−0.284035	−	0.146430i
$303$	3.98235	−	14.0019i	0.228780	−	0.804388i
$304$	1.46368	+	0.139765i	0.0839478	+	0.00801605i
$305$	−0.218069	+	1.51670i	−0.0124866	+	0.0868461i
$306$	0.556793	−	18.1920i	0.0318297	−	1.03997i
$307$	14.2124	+	9.13373i	0.811142	+	0.521289i	0.879234	−	0.476390i	$-0.158055\pi$
$307$	14.2124	+	9.13373i	0.811142	+	0.521289i	−0.0680920	+	0.997679i	$0.521691\pi$
$308$	−8.76036	−	12.3022i	−0.499168	−	0.700983i
$309$	19.4502	−	6.91749i	1.10648	−	0.393522i
$310$	0.233755	−	0.675390i	0.0132764	−	0.0383596i
$311$	3.49200	−	10.0895i	0.198013	−	0.572121i	−0.801658	−	0.597784i	$-0.796048\pi$
$311$	3.49200	−	10.0895i	0.198013	−	0.572121i	0.999671	+	0.0256622i	$0.00816944\pi$
$312$	1.63202	−	0.580431i	0.0923951	−	0.0328605i
$313$	−2.68211	−	3.76649i	−0.151602	−	0.212895i	0.731790	−	0.681530i	$-0.238685\pi$
$313$	−2.68211	−	3.76649i	−0.151602	−	0.212895i	−0.883392	+	0.468636i	$0.844746\pi$
$314$	−14.3004	−	9.19029i	−0.807017	−	0.518638i
$315$	−2.86940	+	1.54158i	−0.161672	+	0.0868585i
$316$	−1.35547	+	9.42753i	−0.0762514	+	0.530340i
$317$	−8.39374	−	0.801505i	−0.471439	−	0.0450170i	−0.143367	−	0.989670i	$-0.545793\pi$
$317$	−8.39374	−	0.801505i	−0.471439	−	0.0450170i	−0.328072	+	0.944653i	$0.606399\pi$
$318$	−4.62341	+	16.2559i	−0.259268	+	0.911584i
$319$	41.5815	+	21.4368i	2.32812	+	1.20023i
$320$	0.345964	+	0.0666791i	0.0193400	+	0.00372748i
$321$	−2.47285	−	23.7604i	−0.138021	−	1.32618i
$322$	2.61848	−	14.5453i	0.145922	−	0.810577i
$323$	−8.92031			−0.496339
$324$	8.77434	−	2.00274i	0.487463	−	0.111263i
$325$	4.10211	−	2.63627i	0.227544	−	0.146234i
$326$	10.0486	+	4.02286i	0.556541	+	0.222806i
$327$	10.5380	−	6.20415i	0.582752	−	0.343090i
$328$	8.78081	−	3.51531i	0.484839	−	0.194100i
$329$	−1.25169	−	1.19349i	−0.0690080	−	0.0657990i
$330$	−1.63825	−	2.50214i	−0.0901826	−	0.137738i
$331$	−9.18722	−	12.9016i	−0.504975	−	0.709138i	0.480871	−	0.876791i	$-0.340321\pi$
$331$	−9.18722	−	12.9016i	−0.504975	−	0.709138i	−0.985846	+	0.167653i	$0.946381\pi$
$332$	5.27502	+	1.54888i	0.289504	+	0.0850061i
$333$	20.6357	+	15.6677i	1.13083	+	0.858583i
$334$	−11.5090	−	13.2821i	−0.629744	−	0.726763i
$335$	−2.54797	+	2.42949i	−0.139211	+	0.132737i
$336$	−1.05466	−	5.23235i	−0.0575366	−	0.285448i
$337$	1.21376	−	25.4799i	0.0661176	−	1.38798i	−0.685353	−	0.728211i	$-0.740352\pi$
$337$	1.21376	−	25.4799i	0.0661176	−	1.38798i	0.751470	−	0.659767i	$-0.229345\pi$
$338$	8.68471	+	8.28086i	0.472386	+	0.450419i
$339$	−11.0534	−	21.0003i	−0.600338	−	1.14058i
$340$	−2.12786	−	0.203186i	−0.115399	−	0.0110193i
$341$	−1.41478	−	9.84002i	−0.0766147	−	0.532867i
$342$	−1.11267	−	4.26837i	−0.0601662	−	0.230807i
$343$	−9.08812	+	10.4883i	−0.490713	+	0.566313i
$344$	−4.98005	+	8.62571i	−0.268507	+	0.465067i
$345$	0.630726	−	2.85791i	0.0339572	−	0.153865i
$346$	9.26888	+	16.0542i	0.498298	+	0.863077i
$347$	−11.8162	−	2.27738i	−0.634325	−	0.122256i	−0.138055	−	0.990425i	$-0.544085\pi$
$347$	−11.8162	−	2.27738i	−0.634325	−	0.122256i	−0.496270	+	0.868169i	$0.665297\pi$
$348$	10.3306	+	12.9091i	0.553780	+	0.691999i
$349$	−2.89416	−	1.15865i	−0.154921	−	0.0620210i	0.292906	−	0.956141i	$-0.405378\pi$
$349$	−2.89416	−	1.15865i	−0.154921	−	0.0620210i	−0.447827	+	0.894120i	$0.647802\pi$
$350$	−6.24191	−	13.6679i	−0.333644	−	0.730579i
$351$	−3.31538	−	4.00148i	−0.176962	−	0.213583i
$352$	4.70229	−	1.38072i	0.250633	−	0.0735924i
$353$	−25.1283	+	12.9545i	−1.33744	+	0.689500i	−0.970581	−	0.240774i	$-0.922599\pi$
$353$	−25.1283	+	12.9545i	−1.33744	+	0.689500i	−0.366863	+	0.930275i	$0.619568\pi$
$354$	−14.1370	−	4.75867i	−0.751372	−	0.252920i
$355$	−1.00328	−	4.13559i	−0.0532487	−	0.219494i
$356$	−1.23638	+	3.57228i	−0.0655280	+	0.189331i
$357$	9.38695	+	30.9919i	0.496810	+	1.64026i
$358$	3.83241	−	3.65420i	0.202549	−	0.193130i
$359$	−8.93968	+	19.5752i	−0.471818	+	1.03314i	0.512814	+	0.858499i	$0.328603\pi$
$359$	−8.93968	+	19.5752i	−0.471818	+	1.03314i	−0.984633	+	0.174638i	$0.944124\pi$
$360$	−0.168192	−	1.04353i	−0.00886452	−	0.0549987i
$361$	16.1560	−	4.74384i	0.850318	−	0.249676i
$362$	−2.18764	−	1.72038i	−0.114980	−	0.0904211i
$363$	−19.6220	−	11.1074i	−1.02989	−	0.582988i
$364$	−2.42250	+	1.90508i	−0.126974	+	0.0998532i
$365$	−1.77890	−	0.917088i	−0.0931120	−	0.0480026i
$366$	−0.652258	+	7.50445i	−0.0340941	+	0.392264i
$367$	−12.1107	+	20.9763i	−0.632173	+	1.09496i	0.354934	+	0.934891i	$0.384503\pi$
$367$	−12.1107	+	20.9763i	−0.632173	+	1.09496i	−0.987107	+	0.160064i	$0.948830\pi$
$368$	4.18246	+	2.34671i	0.218026	+	0.122331i
$369$	−18.9436	−	21.1254i	−0.986163	−	1.09974i
$370$	1.99269	−	2.29969i	0.103595	−	0.119555i
$371$	−1.43076	−	30.0353i	−0.0742813	−	1.55936i
$372$	0.961155	−	3.37941i	0.0498335	−	0.175214i
$373$	−19.0643	+	26.7721i	−0.987114	+	1.38621i	−0.0656064	+	0.997846i	$0.520898\pi$
$373$	−19.0643	+	26.7721i	−0.987114	+	1.38621i	−0.921507	+	0.388361i	$0.873041\pi$
$374$	−27.6026	+	11.0504i	−1.42730	+	0.571403i
$375$	−2.28742	−	5.57584i	−0.118122	−	0.287935i
$376$	0.498834	−	0.257167i	0.0257254	−	0.0132624i
$377$	3.96573	−	8.68373i	0.204245	−	0.447235i
$378$	−13.6588	+	8.35741i	−0.702531	+	0.429859i
$379$	10.3293	+	11.9207i	0.530583	+	0.612325i	0.956249	−	0.292555i	$-0.0945055\pi$
$379$	10.3293	+	11.9207i	0.530583	+	0.612325i	−0.425666	+	0.904881i	$0.639960\pi$
$380$	−0.508684	+	0.0980409i	−0.0260950	+	0.00502939i
$381$	1.37977	−	7.50154i	0.0706876	−	0.384316i
$382$	−4.13093	+	0.394456i	−0.211357	+	0.0201821i
$383$	0.788825	−	16.5595i	0.0403071	−	0.846150i	−0.884691	−	0.466178i	$-0.845631\pi$
$383$	0.788825	−	16.5595i	0.0403071	−	0.846150i	0.924998	−	0.379972i	$-0.124066\pi$
$384$	1.71645	+	0.231913i	0.0875925	+	0.0118347i
$385$	4.18268	+	3.28929i	0.213169	+	0.167638i
$386$	1.50544	+	3.29645i	0.0766248	+	0.167785i
$387$	29.4323	+	5.15522i	1.49613	+	0.262055i
$388$	2.01805	−	1.29692i	0.102451	−	0.0658411i
$389$	7.39444	+	21.3648i	0.374913	+	1.08324i	0.961843	+	0.273602i	$0.0882151\pi$
$389$	7.39444	+	21.3648i	0.374913	+	1.08324i	−0.586930	+	0.809638i	$0.699664\pi$
$390$	−0.494105	+	0.358220i	−0.0250200	+	0.0181392i
$391$	−26.6127	−	11.7607i	−1.34586	−	0.594763i
$392$	1.24830	+	2.16211i	0.0630484	+	0.109203i
$393$	0.987301	−	11.3592i	0.0498028	−	0.572998i
$394$	−0.852340	−	17.8928i	−0.0429403	−	0.901428i
$395$	−0.477576	−	3.32161i	−0.0240294	−	0.167128i
$396$	−8.73063	−	11.8295i	−0.438731	−	0.594455i
$397$	5.57856	−	38.7997i	0.279980	−	1.94730i	−0.0381943	−	0.999270i	$-0.512161\pi$
$397$	5.57856	−	38.7997i	0.279980	−	1.94730i	0.318174	−	0.948032i	$-0.396930\pi$
$398$	−0.328414	+	1.35374i	−0.0164619	+	0.0678569i
$399$	4.29895	+	6.56589i	0.215217	+	0.328706i
$400$	4.85378	−	0.463480i	0.242689	−	0.0231740i
$401$	−0.771582	−	3.18050i	−0.0385309	−	0.158827i	0.949296	−	0.314384i	$-0.101798\pi$
$401$	−0.771582	−	3.18050i	−0.0385309	−	0.158827i	−0.987827	+	0.155557i	$0.950283\pi$
$402$	−11.8364	+	12.6268i	−0.590345	+	0.629770i
$403$	−1.99196	+	0.383919i	−0.0992265	+	0.0191243i
$404$	−8.06416	−	2.36785i	−0.401207	−	0.117805i
$405$	−2.76745	+	1.54801i	−0.137516	+	0.0769214i
$406$	−24.7470	−	15.9039i	−1.22817	−	0.789299i
$407$	9.97873	−	41.1329i	0.494627	−	2.03888i
$408$	−10.5000	−	0.410744i	−0.519830	−	0.0203349i
$409$	14.9227	−	20.9559i	0.737878	−	1.03620i	−0.259634	−	0.965707i	$-0.583602\pi$
$409$	14.9227	−	20.9559i	0.737878	−	1.03620i	0.997512	−	0.0704973i	$-0.0224586\pi$
$410$	−2.61949	+	2.05999i	−0.129368	+	0.101736i
$411$	−19.1947	+	2.92654i	−0.946804	+	0.144356i
$412$	−3.89820	−	11.2631i	−0.192051	−	0.554894i
$413$	26.5392			1.30591
$414$	2.30798	−	14.2012i	0.113431	−	0.697949i
$415$	−1.93701			−0.0950843
$416$	−0.327090	−	0.945063i	−0.0160369	−	0.0463355i
$417$	−11.7983	+	30.2126i	−0.577765	+	1.47952i
$418$	−5.66417	+	4.45436i	−0.277044	+	0.217870i
$419$	1.49160	−	2.09466i	0.0728693	−	0.102331i	−0.776533	−	0.630077i	$-0.783023\pi$
$419$	1.49160	−	2.09466i	0.0728693	−	0.102331i	0.849402	+	0.527746i	$0.176963\pi$
$420$	0.875918	+	1.66415i	0.0427404	+	0.0812024i
$421$	−2.39367	+	9.86686i	−0.116661	+	0.480881i	0.883267	+	0.468870i	$0.155339\pi$
$421$	−2.39367	+	9.86686i	−0.116661	+	0.480881i	−0.999928	+	0.0120115i	$0.996177\pi$
$422$	18.4986	+	11.8883i	0.900495	+	0.578713i
$423$	−1.23810	−	1.14098i	−0.0601987	−	0.0554762i
$424$	9.36230	+	2.74902i	0.454673	+	0.133504i
$425$	−29.0465	+	5.59826i	−1.40896	+	0.271555i
$426$	−6.06432	−	20.0219i	−0.293817	−	0.970064i
$427$	−3.15969	−	13.0244i	−0.152908	−	0.630296i
$428$	−13.7297	+	1.31103i	−0.663651	+	0.0633709i
$429$	−3.82560	+	7.57813i	−0.184702	+	0.365875i
$430$	0.827339	−	3.41034i	0.0398978	−	0.164461i
$431$	−2.77087	+	19.2718i	−0.133468	+	0.928290i	0.807518	+	0.589843i	$0.200810\pi$
$431$	−2.77087	+	19.2718i	−0.133468	+	0.928290i	−0.940986	+	0.338446i	$0.890099\pi$
$432$	−1.11317	−	5.07551i	−0.0535576	−	0.244196i
$433$	−3.59241	−	24.9857i	−0.172640	−	1.20074i	−0.873279	−	0.487221i	$-0.838010\pi$
$433$	−3.59241	−	24.9857i	−0.172640	−	1.20074i	0.700638	−	0.713516i	$-0.252899\pi$
$434$	0.297439	+	6.24400i	0.0142775	+	0.299722i
$435$	−4.77376	−	3.33858i	−0.228884	−	0.160073i
$436$	−3.53012	−	6.11434i	−0.169062	−	0.292824i
$437$	−6.99152	−	0.917713i	−0.334450	−	0.0439002i
$438$	−8.98408	−	4.01094i	−0.429276	−	0.191650i
$439$	−2.09928	−	6.06546i	−0.100193	−	0.289489i	0.883753	−	0.467953i	$-0.155008\pi$
$439$	−2.09928	−	6.06546i	−0.100193	−	0.289489i	−0.983946	+	0.178464i	$0.942887\pi$
$440$	−1.45260	+	0.933528i	−0.0692499	+	0.0445042i
$441$	4.80781	−	5.74296i	0.228943	−	0.273474i
$442$	2.52042	+	5.51896i	0.119884	+	0.262510i
$443$	18.9326	+	14.8888i	0.899516	+	0.707388i	0.956731	−	0.290974i	$-0.0939794\pi$
$443$	18.9326	+	14.8888i	0.899516	+	0.707388i	−0.0572144	+	0.998362i	$0.518222\pi$
$444$	9.14670	−	11.8367i	0.434083	−	0.561745i
$445$	0.0633734	−	1.33037i	0.00300418	−	0.0630656i
$446$	11.4170	−	1.09019i	0.540610	−	0.0516220i
$447$	7.09290	−	2.52260i	0.335483	−	0.119315i
$448$	−3.02596	+	0.583207i	−0.142963	+	0.0275539i
$449$	7.83876	+	9.04641i	0.369934	+	0.426927i	0.909943	−	0.414732i	$-0.136125\pi$
$449$	7.83876	+	9.04641i	0.369934	+	0.426927i	−0.540009	+	0.841659i	$0.681579\pi$
$450$	−6.30187	−	13.2005i	−0.297073	−	0.622277i
$451$	−19.2559	+	42.1646i	−0.906726	+	1.98545i
$452$	−12.1784	+	6.27838i	−0.572822	+	0.295310i
$453$	9.53204	+	1.28789i	0.447854	+	0.0605102i
$454$	0.877270	−	0.351206i	0.0411723	−	0.0164829i
$455$	0.629846	−	0.884495i	0.0295276	−	0.0414658i
$456$	−2.46972	+	0.621426i	−0.115655	+	0.0291009i
$457$	−0.892126	−	18.7280i	−0.0417319	−	0.876060i	−0.918566	−	0.395267i	$-0.870652\pi$
$457$	−0.892126	−	18.7280i	−0.0417319	−	0.876060i	0.876834	−	0.480793i	$-0.159651\pi$
$458$	16.9921	−	19.6100i	0.793991	−	0.916314i
$459$	9.64987	+	30.0109i	0.450417	+	1.40079i
$460$	−1.64686	−	0.378164i	−0.0767853	−	0.0176320i
$461$	17.7707	−	30.7798i	0.827665	−	1.43356i	−0.0722010	−	0.997390i	$-0.523002\pi$
$461$	17.7707	−	30.7798i	0.827665	−	1.43356i	0.899866	−	0.436167i	$-0.143664\pi$
$462$	21.4363	+	14.9917i	0.997305	+	0.697477i
$463$	9.33817	+	4.81416i	0.433981	+	0.223733i	0.661353	−	0.750075i	$-0.269983\pi$
$463$	9.33817	+	4.81416i	0.433981	+	0.223733i	−0.227371	+	0.973808i	$0.573013\pi$
$464$	7.50349	−	5.90081i	0.348341	−	0.273938i
$465$	0.0105238	+	1.23785i	0.000488030	+	0.0574039i
$466$	−2.00336	−	1.57546i	−0.0928041	−	0.0729819i
$467$	−10.9147	+	3.20483i	−0.505070	+	0.148302i	−0.524334	−	0.851513i	$-0.675686\pi$
$467$	−10.9147	+	3.20483i	−0.505070	+	0.148302i	0.0192644	+	0.999814i	$0.493868\pi$
$468$	−2.32644	+	1.89443i	−0.107540	+	0.0875700i
$469$	12.7918	−	28.0101i	0.590669	−	1.29338i
$470$	−0.143108	+	0.136453i	−0.00660109	+	0.00629413i
$471$	28.6710	+	6.69793i	1.32109	+	0.308625i
$472$	−2.81671	+	8.13834i	−0.129649	+	0.374597i
$473$	−11.5080	−	47.4366i	−0.529138	−	2.18114i
$474$	−3.25965	−	16.1716i	−0.149721	−	0.742787i
$475$	−6.37221	+	3.28510i	−0.292377	+	0.150731i
$476$	17.9386	−	5.26724i	0.822214	−	0.241424i
$477$	−1.88978	−	29.2116i	−0.0865271	−	1.33751i
$478$	5.87864	+	12.8724i	0.268883	+	0.588771i
$479$	−20.2890	−	8.12249i	−0.927028	−	0.371126i	−0.141490	−	0.989940i	$-0.545189\pi$
$479$	−20.2890	−	8.12249i	−0.927028	−	0.371126i	−0.785538	+	0.618814i	$0.787614\pi$
$480$	−0.603284	+	0.0919805i	−0.0275360	+	0.00419832i
$481$	−8.48103	−	1.63458i	−0.386702	−	0.0745306i
$482$	3.19991	+	5.54240i	0.145752	+	0.252449i
$483$	4.16885	+	25.2564i	0.189689	+	1.14921i
$484$	−6.50895	+	11.2738i	−0.295861	+	0.512447i
$485$	−0.553483	+	0.638754i	−0.0251324	+	0.0290043i
$486$	−13.1566	+	8.36087i	−0.596795	+	0.379257i
$487$	2.17866	+	15.1529i	0.0987246	+	0.686645i	0.977735	+	0.209842i	$0.0672951\pi$
$487$	2.17866	+	15.1529i	0.0987246	+	0.686645i	−0.879011	+	0.476802i	$0.841796\pi$
$488$	4.32934	+	0.413402i	0.195980	+	0.0187138i
$489$	−18.7333	−	0.732816i	−0.847150	−	0.0331391i
$490$	−0.636616	−	0.607012i	−0.0287594	−	0.0274220i
$491$	1.52426	−	31.9982i	0.0687890	−	1.44406i	−0.655829	−	0.754909i	$-0.727681\pi$
$491$	1.52426	−	31.9982i	0.0687890	−	1.44406i	0.724618	−	0.689150i	$-0.242016\pi$
$492$	−12.2893	+	10.8330i	−0.554043	+	0.488389i
$493$	−41.9134	+	39.9644i	−1.88769	+	1.79990i
$494$	0.962931	+	1.11128i	0.0433243	+	0.0499989i
$495$	4.12570	+	3.13244i	0.185437	+	0.140793i
$496$	−1.94632	−	0.571490i	−0.0873922	−	0.0256607i
$497$	21.5903	+	30.3193i	0.968457	+	1.36001i
$498$	−9.50733	+	0.533935i	−0.426034	+	0.0239262i
$499$	−29.0722	−	27.7203i	−1.30145	−	1.24093i	−0.952771	−	0.303691i	$-0.901781\pi$
$499$	−29.0722	−	27.7203i	−1.30145	−	1.24093i	−0.348681	−	0.937241i	$-0.613370\pi$
$500$	−3.23033	+	1.29323i	−0.144465	+	0.0578349i
$501$	26.4905	+	14.9955i	1.18351	+	0.669949i
$502$	21.8714	+	8.75601i	0.976170	+	0.390800i
$503$	0.994853	−	0.639353i	0.0443583	−	0.0285074i	−0.518274	−	0.855215i	$-0.673425\pi$
$503$	0.994853	−	0.639353i	0.0443583	−	0.0285074i	0.562632	+	0.826707i	$0.309789\pi$
$504$	4.75794	+	7.92662i	0.211935	+	0.353080i
$505$	2.96121			0.131772
$506$	−22.7711	+	5.82132i	−1.01230	+	0.258789i
$507$	−18.9789	−	8.47310i	−0.842881	−	0.376304i
$508$	−4.32409	−	0.833400i	−0.191850	−	0.0369761i
$509$	13.7030	+	7.06439i	0.607375	+	0.313124i	0.734338	−	0.678784i	$-0.237493\pi$
$509$	13.7030	+	7.06439i	0.607375	+	0.313124i	−0.126963	+	0.991907i	$0.540523\pi$
$510$	3.59041	−	0.903412i	0.158986	−	0.0400037i
$511$	17.4258	+	1.66396i	0.770872	+	0.0736093i
$512$	0.142315	−	0.989821i	0.00628949	−	0.0437443i
$513$	4.29311	+	6.31984i	0.189546	+	0.279028i
$514$	11.0989	+	7.13283i	0.489551	+	0.314616i
$515$	2.43584	+	3.42065i	0.107336	+	0.150732i
$516$	3.12072	−	16.9668i	0.137382	−	0.746922i
$517$	−0.899581	+	2.59917i	−0.0395635	+	0.114311i
$518$	−8.70486	+	25.1510i	−0.382469	+	1.10507i
$519$	−24.4437	−	20.8194i	−1.07296	−	0.913872i
$520$	0.204386	+	0.287020i	0.00896291	+	0.0125866i
$521$	34.9155	+	22.4388i	1.52967	+	0.983062i	0.989981	+	0.141200i	$0.0450961\pi$
$521$	34.9155	+	22.4388i	1.52967	+	0.983062i	0.539693	+	0.841862i	$0.318540\pi$
$522$	−24.3510	−	15.0707i	−1.06582	−	0.659626i
$523$	0.679337	−	4.72489i	0.0297053	−	0.206605i	−0.969563	−	0.244840i	$-0.921264\pi$
$523$	0.679337	−	4.72489i	0.0297053	−	0.206605i	0.999269	+	0.0382351i	$0.0121736\pi$
$524$	−6.55317	−	0.625752i	−0.286277	−	0.0273361i
$525$	18.1190	+	18.6820i	0.790778	+	0.815351i
$526$	2.83610	+	1.46211i	0.123660	+	0.0637510i
$527$	12.0841	+	2.32902i	0.526391	+	0.101454i
$528$	−6.87237	+	4.98239i	−0.299082	+	0.216831i
$529$	−19.6485	−	11.9556i	−0.854282	−	0.519810i
$530$	−3.43789			−0.149332
$531$	25.8322	−	0.439267i	1.12102	−	0.0190626i
$532$	3.81178	−	2.44968i	0.165262	−	0.106207i
$533$	8.78139	+	3.51554i	0.380364	+	0.152275i
$534$	−0.0556626	−	6.54725i	−0.00240876	−	0.283327i
$535$	4.51132	−	1.80606i	0.195041	−	0.0780828i
$536$	7.23175	+	6.89546i	0.312364	+	0.297839i
$537$	−4.13330	+	8.18764i	−0.178365	+	0.353323i
$538$	−5.53688	−	7.77545i	−0.238712	−	0.335224i
$539$	−11.7397	−	3.44708i	−0.505664	−	0.148476i
$540$	0.880131	+	1.60533i	0.0378748	+	0.0690823i
$541$	21.7512	+	25.1023i	0.935158	+	1.07923i	0.996704	+	0.0811258i	$0.0258515\pi$
$541$	21.7512	+	25.1023i	0.935158	+	1.07923i	−0.0615457	+	0.998104i	$0.519603\pi$
$542$	−2.34664	+	2.23751i	−0.100797	+	0.0961094i
$543$	4.56854	+	1.53782i	0.196055	+	0.0659942i
$544$	−0.288672	+	6.05997i	−0.0123767	+	0.259819i
$545$	1.80032	+	1.71660i	0.0771171	+	0.0735310i
$546$	2.84763	−	4.51493i	0.121867	−	0.193221i
$547$	−10.8597	−	1.03698i	−0.464328	−	0.0443380i	−0.139729	−	0.990190i	$-0.544623\pi$
$547$	−10.8597	−	1.03698i	−0.464328	−	0.0443380i	−0.324599	+	0.945852i	$0.605229\pi$
$548$	1.59537	+	11.0960i	0.0681507	+	0.473999i
$549$	−3.29110	−	12.6252i	−0.140461	−	0.538830i
$550$	−15.6483	+	18.0591i	−0.667247	+	0.770044i
$551$	−7.01777	+	12.1551i	−0.298967	+	0.517826i
$552$	−8.18742	−	1.40217i	−0.348480	−	0.0596802i
$553$	14.6756	+	25.4188i	0.624069	+	1.08092i
$554$	8.24037	+	1.58820i	0.350100	+	0.0674762i
$555$	−1.91718	+	4.90944i	−0.0813797	+	0.208394i
$556$	17.3847	+	6.95980i	0.737277	+	0.295161i
$557$	−0.580442	−	1.27099i	−0.0245941	−	0.0538536i	0.896936	−	0.442160i	$-0.145788\pi$
$557$	−0.580442	−	1.27099i	−0.0245941	−	0.0538536i	−0.921530	+	0.388306i	$0.873060\pi$
$558$	0.392864	+	6.07276i	0.0166313	+	0.257080i
$559$	−9.55729	+	2.80627i	−0.404230	+	0.118693i
$560$	0.965064	−	0.497525i	0.0407814	−	0.0210243i
$561$	38.6315	−	34.0537i	1.63102	−	1.43775i
$562$	1.58253	+	6.52328i	0.0667550	+	0.275168i
$563$	−0.192983	+	0.557589i	−0.00813328	+	0.0234996i	−0.948994	−	0.315293i	$-0.897897\pi$
$563$	−0.192983	+	0.557589i	−0.00813328	+	0.0234996i	0.940861	+	0.338792i	$0.110018\pi$
$564$	−0.664797	+	0.709194i	−0.0279930	+	0.0298624i
$565$	3.49379	−	3.33133i	0.146985	−	0.140150i
$566$	−3.93440	+	8.61513i	−0.165375	+	0.362121i
$567$	17.4393	−	21.5660i	0.732383	−	0.905688i
$568$	−11.5890	+	3.40284i	−0.486263	+	0.142780i
$569$	23.8628	+	18.7659i	1.00038	+	0.786707i	0.977048	−	0.213020i	$-0.0683301\pi$
$569$	23.8628	+	18.7659i	1.00038	+	0.786707i	0.0233320	+	0.999728i	$0.492573\pi$
$570$	0.773227	−	0.455231i	0.0323869	−	0.0190675i
$571$	−28.9952	+	22.8021i	−1.21341	+	0.954238i	−0.999743	−	0.0226674i	$-0.992784\pi$
$571$	−28.9952	+	22.8021i	−1.21341	+	0.954238i	−0.213670	+	0.976906i	$0.568542\pi$
$572$	4.35630	+	2.24583i	0.182146	+	0.0939028i
$573$	6.51239	−	3.04128i	0.272059	−	0.127051i
$574$	14.5736	−	25.2423i	0.608292	−	1.05359i
$575$	−23.3419	+	1.39950i	−0.973424	+	0.0583631i
$576$	−2.93571	+	0.617756i	−0.122321	+	0.0257398i
$577$	3.09521	−	3.57206i	0.128855	−	0.148707i	−0.687656	−	0.726037i	$-0.741360\pi$
$577$	3.09521	−	3.57206i	0.128855	−	0.148707i	0.816511	+	0.577330i	$0.195906\pi$
$578$	−0.942433	−	19.7841i	−0.0392000	−	0.822910i
$579$	−4.36998	−	4.50578i	−0.181610	−	0.187254i
$580$	−1.95089	+	2.73965i	−0.0810064	+	0.113758i
$581$	15.7284	−	6.29672i	0.652526	−	0.261232i
$582$	−2.54056	+	3.28772i	−0.105309	+	0.136280i
$583$	−42.5040	+	21.9123i	−1.76034	+	0.907516i
$584$	−2.35973	+	5.16708i	−0.0976462	+	0.213815i
$585$	0.598429	−	0.871359i	0.0247420	−	0.0360263i
$586$	2.33645	+	2.69641i	0.0965180	+	0.111388i
$587$	−20.7769	+	4.00442i	−0.857556	+	0.165280i	−0.599032	−	0.800725i	$-0.704448\pi$
$587$	−20.7769	+	4.00442i	−0.857556	+	0.165280i	−0.258523	+	0.966005i	$0.583236\pi$
$588$	−3.29198	−	2.80388i	−0.135759	−	0.115630i
$589$	2.96905	−	0.283510i	0.122338	−	0.0116818i
$590$	0.144376	−	3.03084i	0.00594389	−	0.124778i
$591$	11.7758	+	28.7049i	0.484392	+	1.18076i
$592$	−6.78878	−	5.33875i	−0.279017	−	0.219421i
$593$	0.227442	+	0.498028i	0.00933991	+	0.0204516i	0.914244	−	0.405163i	$-0.132785\pi$
$593$	0.227442	+	0.498028i	0.00933991	+	0.0204516i	−0.904905	+	0.425615i	$0.860058\pi$
$594$	21.1134	+	14.2375i	0.866293	+	0.584174i
$595$	−5.54146	+	3.56128i	−0.227178	+	0.145998i
$596$	−1.42156	−	4.10732i	−0.0582293	−	0.168243i
$597$	−0.249758	−	2.39980i	−0.0102219	−	0.0982172i
$598$	1.40766	+	4.58493i	0.0575636	+	0.187492i
$599$	−2.78248	−	4.81940i	−0.113689	−	0.196915i	0.803566	−	0.595216i	$-0.202933\pi$
$599$	−2.78248	−	4.81940i	−0.113689	−	0.196915i	−0.917255	+	0.398301i	$0.869600\pi$
$600$	−7.65196	+	3.57346i	−0.312390	+	0.145886i
$601$	0.466768	+	9.79866i	0.0190399	+	0.399696i	0.988191	+	0.153228i	$0.0489669\pi$
$601$	0.466768	+	9.79866i	0.0190399	+	0.399696i	−0.969151	+	0.246468i	$0.920730\pi$
$602$	4.36816	+	30.3812i	0.178033	+	1.23825i
$603$	11.9874	−	27.4757i	0.488165	−	1.11890i
$604$	0.790321	−	5.49680i	0.0321577	−	0.223662i
$605$	1.08133	−	4.45732i	0.0439625	−	0.181216i
$606$	14.5343	−	0.816251i	0.590416	−	0.0331579i
$607$	28.1267	−	2.68578i	1.14163	−	0.109012i	0.492938	−	0.870065i	$-0.335923\pi$
$607$	28.1267	−	2.68578i	1.14163	−	0.109012i	0.648691	+	0.761052i	$0.275317\pi$
$608$	0.346645	+	1.42889i	0.0140583	+	0.0579492i
$609$	49.6155	+	11.5909i	2.01052	+	0.469686i
$610$	−1.50461	+	0.289990i	−0.0609198	+	0.0117413i
$611$	0.538524	+	0.158125i	0.0217864	+	0.00639705i
$612$	17.3736	−	5.42385i	0.702285	−	0.219246i
$613$	1.74233	+	1.11973i	0.0703722	+	0.0452254i	0.575354	−	0.817905i	$-0.304864\pi$
$613$	1.74233	+	1.11973i	0.0703722	+	0.0452254i	−0.504982	+	0.863130i	$0.668501\pi$
$614$	−3.98297	+	16.4180i	−0.160740	+	0.662578i
$615$	3.07918	−	4.88207i	0.124165	−	0.196864i
$616$	8.76036	−	12.3022i	0.352965	−	0.495670i
$617$	13.6605	−	10.7428i	0.549952	−	0.432487i	−0.304126	−	0.952632i	$-0.598364\pi$
$617$	13.6605	−	10.7428i	0.549952	−	0.432487i	0.854078	+	0.520144i	$0.174122\pi$
$618$	12.8986	+	16.1180i	0.518856	+	0.648359i
$619$	−11.7498	−	33.9488i	−0.472264	−	1.36452i	−0.890005	−	0.455951i	$-0.849299\pi$
$619$	−11.7498	−	33.9488i	−0.472264	−	1.36452i	0.417741	−	0.908566i	$-0.362822\pi$
$620$	0.714698			0.0287030
$621$	4.47583	+	24.5146i	0.179609	+	0.983738i
$622$	10.6767			0.428096
$623$	3.81009	+	11.0085i	0.152648	+	0.441048i
$624$	1.08229	+	1.35242i	0.0433263	+	0.0541402i
$625$	−18.1998	+	14.3125i	−0.727991	+	0.572498i
$626$	2.68211	−	3.76649i	0.107198	−	0.150539i
$627$	6.65817	−	10.5566i	0.265902	−	0.421589i
$628$	4.00764	−	16.5197i	0.159922	−	0.659208i
$629$	44.0787	+	28.3277i	1.75753	+	1.12950i
$630$	−2.39529	−	2.20738i	−0.0954305	−	0.0879441i
$631$	2.88013	+	0.845681i	0.114656	+	0.0336660i	0.338557	−	0.940946i	$-0.390061\pi$
$631$	2.88013	+	0.845681i	0.114656	+	0.0336660i	−0.223901	+	0.974612i	$0.571879\pi$
$632$	−9.35235	+	1.80252i	−0.372017	+	0.0717003i
$633$	−37.0879	−	8.66426i	−1.47411	−	0.344373i
$634$	−1.98790	−	8.19424i	−0.0789496	−	0.325435i
$635$	1.54452	−	0.147484i	0.0612926	−	0.00585273i
$636$	−16.8740	+	0.947648i	−0.669097	+	0.0375767i
$637$	−0.588632	+	2.42638i	−0.0233225	+	0.0961365i
$638$	−6.65778	+	46.3059i	−0.263584	+	1.83327i
$639$	21.5170	+	29.1543i	0.851200	+	1.15333i
$640$	0.0501420	+	0.348745i	0.00198203	+	0.0137854i
$641$	−1.09095	−	22.9019i	−0.0430900	−	0.904570i	−0.912148	−	0.409860i	$-0.865578\pi$
$641$	−1.09095	−	22.9019i	−0.0430900	−	0.904570i	0.869058	−	0.494709i	$-0.164726\pi$
$642$	21.6448	−	10.1081i	0.854252	−	0.398935i
$643$	−2.94505	−	5.10098i	−0.116142	−	0.201163i	0.802094	−	0.597198i	$-0.203719\pi$
$643$	−2.94505	−	5.10098i	−0.116142	−	0.201163i	−0.918236	+	0.396035i	$0.870386\pi$
$644$	14.6017	−	2.28283i	0.575388	−	0.0899562i
$645$	0.629189	+	6.04556i	0.0247743	+	0.238044i
$646$	−2.91755	−	8.42970i	−0.114789	−	0.331662i
$647$	16.4392	−	10.5648i	0.646290	−	0.415346i	−0.176019	−	0.984387i	$-0.556322\pi$
$647$	16.4392	−	10.5648i	0.646290	−	0.415346i	0.822309	+	0.569041i	$0.192686\pi$
$648$	4.76240	+	7.63673i	0.187085	+	0.299999i
$649$	−17.5329	−	38.3916i	−0.688226	−	1.50700i
$650$	3.83294	+	3.01426i	0.150340	+	0.118229i
$651$	−4.10937	−	10.0170i	−0.161059	−	0.392599i
$652$	−0.515025	+	10.8117i	−0.0201699	+	0.423419i
$653$	−44.5871	+	4.25755i	−1.74483	+	0.166611i	−0.918194	−	0.396130i	$-0.870353\pi$
$653$	−44.5871	+	4.25755i	−1.74483	+	0.166611i	−0.826633	+	0.562741i	$0.809747\pi$
$654$	9.30957	+	7.92922i	0.364033	+	0.310057i
$655$	2.27748	−	0.438947i	0.0889883	−	0.0171511i
$656$	6.19389	+	7.14813i	0.241831	+	0.279088i
$657$	16.9892	+	1.33121i	0.662810	+	0.0519355i
$658$	0.718457	−	1.57320i	0.0280084	−	0.0613298i
$659$	−11.6668	+	6.01465i	−0.454474	+	0.234297i	−0.670235	−	0.742149i	$-0.733807\pi$
$659$	−11.6668	+	6.01465i	−0.454474	+	0.234297i	0.215762	+	0.976446i	$0.430777\pi$
$660$	1.82870	−	2.36652i	0.0711822	−	0.0921165i
$661$	−29.7893	+	11.9258i	−1.15867	+	0.463861i	−0.869750	−	0.493493i	$-0.835720\pi$
$661$	−29.7893	+	11.9258i	−1.15867	+	0.463861i	−0.288918	+	0.957354i	$0.593296\pi$
$662$	9.18722	−	12.9016i	0.357071	−	0.501436i
$663$	−7.31628	−	7.54363i	−0.284141	−	0.292970i
$664$	0.261592	+	5.49148i	0.0101517	+	0.213111i
$665$	−1.04544	+	1.20651i	−0.0405406	+	0.0467864i
$666$	−8.05669	+	24.6252i	−0.312190	+	0.954205i
$667$	−36.9622	+	27.0111i	−1.43118	+	1.04587i
$668$	8.78736	−	15.2202i	0.339993	−	0.588885i
$669$	−17.9988	+	8.40544i	−0.695874	+	0.324973i
$670$	−3.12923	−	1.61323i	−0.120893	−	0.0623245i
$671$	−16.7537	+	13.1753i	−0.646771	+	0.508626i
$672$	4.59963	−	2.70799i	0.177434	−	0.104463i
$673$	0.952822	+	0.749307i	0.0367286	+	0.0288837i	0.636355	−	0.771397i	$-0.280442\pi$
$673$	0.952822	+	0.749307i	0.0367286	+	0.0288837i	−0.599626	+	0.800280i	$0.704684\pi$
$674$	24.4755	−	7.18666i	0.942761	−	0.276820i
$675$	17.9456	+	17.8845i	0.690725	+	0.688375i
$676$	−4.98493	+	10.9155i	−0.191728	+	0.419826i
$677$	−8.74253	+	8.33598i	−0.336003	+	0.320378i	−0.839230	−	0.543776i	$-0.816994\pi$
$677$	−8.74253	+	8.33598i	−0.336003	+	0.320378i	0.503228	+	0.864154i	$0.332146\pi$
$678$	16.2301	−	17.3140i	0.623313	−	0.664940i
$679$	2.41783	−	6.98587i	0.0927879	−	0.268093i
$680$	−0.503943	−	2.07728i	−0.0193253	−	0.0796602i
$681$	−1.22779	+	1.08230i	−0.0470491	+	0.0414738i
$682$	8.83610	−	4.55532i	0.338352	−	0.174432i
$683$	48.9576	−	14.3752i	1.87331	−	0.550053i	0.875553	−	0.483123i	$-0.160498\pi$
$683$	48.9576	−	14.3752i	1.87331	−	0.550053i	0.997758	−	0.0669306i	$-0.0213206\pi$
$684$	3.66970	−	2.44752i	0.140314	−	0.0935833i
$685$	−1.64075	−	3.59275i	−0.0626900	−	0.137272i
$686$	−12.8838	−	5.15791i	−0.491907	−	0.196930i
$687$	−16.3482	+	41.8639i	−0.623724	+	1.59721i
$688$	−9.78012	−	1.88496i	−0.372863	−	0.0718635i
$689$	4.87910	+	8.45085i	0.185879	+	0.321952i
$690$	2.90702	−	0.338694i	0.110668	−	0.0128939i
$691$	−12.9789	+	22.4802i	−0.493742	+	0.855186i	−0.999974	−	0.00721095i	$-0.997705\pi$
$691$	−12.9789	+	22.4802i	−0.493742	+	0.855186i	0.506232	+	0.862397i	$0.331038\pi$
$692$	−12.1396	+	14.0099i	−0.461480	+	0.532577i
$693$	−43.6832	−	12.0237i	−1.65939	−	0.456743i
$694$	−1.71256	−	11.9111i	−0.0650080	−	0.452141i
$695$	−6.56792	−	0.627160i	−0.249135	−	0.0237895i
$696$	−8.82027	+	13.9846i	−0.334331	+	0.530085i
$697$	−41.5294	−	39.5982i	−1.57304	−	1.49989i
$698$	0.148335	−	3.11394i	0.00561457	−	0.117864i
$699$	4.18371	+	1.40828i	0.158242	+	0.0532661i
$700$	10.8746	−	10.3689i	0.411022	−	0.391909i
$701$	−1.77743	−	2.05127i	−0.0671327	−	0.0774752i	0.721190	−	0.692738i	$-0.243596\pi$
$701$	−1.77743	−	2.05127i	−0.0671327	−	0.0774752i	−0.788322	+	0.615262i	$0.789050\pi$
$702$	2.69704	−	4.44180i	0.101793	−	0.167645i
$703$	12.1842	+	3.57762i	0.459538	+	0.134932i
$704$	2.84275	+	3.99208i	0.107140	+	0.150457i
$705$	0.154344	−	0.305739i	0.00581292	−	0.0115148i
$706$	−20.4607	−	19.5092i	−0.770049	−	0.734240i
$707$	−24.0448	+	9.62609i	−0.904299	+	0.362027i
$708$	−0.126810	−	14.9159i	−0.00476581	−	0.560572i
$709$	−23.7491	−	9.50770i	−0.891916	−	0.357069i	−0.119985	−	0.992776i	$-0.538285\pi$
$709$	−23.7491	−	9.50770i	−0.891916	−	0.357069i	−0.771931	+	0.635706i	$0.780709\pi$
$710$	3.57999	−	2.30072i	0.134355	−	0.0863445i
$711$	14.7054	+	24.4988i	0.551494	+	0.918778i
$712$	−3.78019			−0.141669
$713$	9.23161	+	3.06863i	0.345727	+	0.114921i
$714$	−26.2172	+	19.0071i	−0.981152	+	0.711323i
$715$	−1.69562	−	0.326803i	−0.0634124	−	0.0122217i
$716$	4.70668	+	2.42646i	0.175897	+	0.0906811i
$717$	−17.0645	−	17.5948i	−0.637286	−	0.657089i
$718$	−21.4224	−	2.04559i	−0.799478	−	0.0763409i
$719$	−2.57620	+	17.9179i	−0.0960760	+	0.668223i	0.883689	+	0.468074i	$0.155052\pi$
$719$	−2.57620	+	17.9179i	−0.0960760	+	0.668223i	−0.979765	+	0.200149i	$0.935857\pi$
$720$	0.931123	−	0.500246i	0.0347009	−	0.0186431i
$721$	−30.8985	−	19.8573i	−1.15072	−	0.739523i
$722$	9.76706	+	13.7159i	0.363492	+	0.510454i
$723$	−8.43874	−	7.18752i	−0.313840	−	0.267307i
$724$	0.910253	−	2.63000i	0.0338293	−	0.0977433i
$725$	−15.2230	+	43.9841i	−0.565369	+	1.63353i
$726$	4.07880	−	22.1757i	0.151378	−	0.823016i
$727$	13.7798	+	19.3510i	0.511064	+	0.717689i	0.986808	−	0.161895i	$-0.0517605\pi$
$727$	13.7798	+	19.3510i	0.511064	+	0.717689i	−0.475744	+	0.879584i	$0.657821\pi$
$728$	−2.59262	−	1.66618i	−0.0960890	−	0.0617527i
$729$	16.6178	−	21.2802i	0.615476	−	0.788156i
$730$	0.284827	−	1.98101i	0.0105419	−	0.0733206i
$731$	60.1528	+	5.74389i	2.22483	+	0.212446i
$732$	−7.30504	+	1.83808i	−0.270002	+	0.0679374i
$733$	44.0470	+	22.7078i	1.62691	+	0.838732i	0.998128	+	0.0611517i	$0.0194773\pi$
$733$	44.0470	+	22.7078i	1.62691	+	0.838732i	0.628784	+	0.777580i	$0.283553\pi$
$734$	−23.7837	−	4.58392i	−0.877871	−	0.169196i
$735$	1.39121	+	0.621104i	0.0513155	+	0.0229098i
$736$	−0.849698	+	4.71996i	−0.0313203	+	0.173980i
$737$	−48.9702			−1.80384
$738$	13.7676	−	24.8111i	0.506794	−	0.913310i
$739$	5.22981	−	3.36099i	0.192382	−	0.123636i	−0.440904	−	0.897554i	$-0.645342\pi$
$739$	5.22981	−	3.36099i	0.192382	−	0.123636i	0.633286	+	0.773918i	$0.281706\pi$
$740$	2.82495	+	1.13094i	0.103847	+	0.0415742i
$741$	−2.21640	−	1.25464i	−0.0814215	−	0.0460903i
$742$	27.9155	−	11.1757i	1.02481	−	0.410271i
$743$	−28.8403	−	27.4991i	−1.05805	−	1.00885i	−0.999945	−	0.0105344i	$-0.996647\pi$
$743$	−28.8403	−	27.4991i	−1.05805	−	1.00885i	−0.0581017	−	0.998311i	$-0.518505\pi$
$744$	3.50791	−	0.197005i	0.128606	−	0.00722256i
$745$	0.888277	+	1.24741i	0.0325440	+	0.0457016i
$746$	−31.5350	−	9.25951i	−1.15458	−	0.339015i
$747$	15.2053	−	6.38932i	0.556331	−	0.233773i
$748$	−19.4706	−	22.4702i	−0.711915	−	0.821594i
$749$	−30.7606	+	29.3302i	−1.12397	+	1.07170i
$750$	4.52103	−	3.98529i	0.165085	−	0.145522i
$751$	0.00591433	−	0.124157i	0.000215817	−	0.00453056i	−0.998757	−	0.0498471i	$-0.984127\pi$
$751$	0.00591433	−	0.124157i	0.000215817	−	0.00453056i	0.998973	+	0.0453165i	$0.0144296\pi$
$752$	0.406175	+	0.387288i	0.0148117	+	0.0141229i
$753$	−40.7742	−	1.59502i	−1.48590	−	0.0581258i
$754$	9.50319	+	0.907445i	0.346086	+	0.0330472i
$755$	0.278455	+	1.93670i	0.0101340	+	0.0704836i
$756$	−12.3651	−	10.1741i	−0.449714	−	0.370028i
$757$	7.23701	−	8.35196i	0.263034	−	0.303557i	−0.608835	−	0.793297i	$-0.708363\pi$
$757$	7.23701	−	8.35196i	0.263034	−	0.303557i	0.871869	+	0.489740i	$0.162908\pi$
$758$	−7.88668	+	13.6601i	−0.286457	+	0.496158i
$759$	33.7819	−	22.7161i	1.22620	−	0.824542i
$760$	−0.259023	−	0.448641i	−0.00939575	−	0.0162739i
$761$	28.7537	+	5.54183i	1.04232	+	0.200891i	0.681557	−	0.731765i	$-0.261303\pi$
$761$	28.7537	+	5.54183i	1.04232	+	0.200891i	0.360766	+	0.932656i	$0.382515\pi$
$762$	7.54024	−	1.14963i	0.273154	−	0.0416468i
$763$	−20.1987	−	8.08633i	−0.731241	−	0.292745i
$764$	−1.72386	−	3.77472i	−0.0623670	−	0.136565i
$765$	−5.33491	+	3.55814i	−0.192884	+	0.128645i
$766$	15.9067	−	4.67063i	0.574733	−	0.168757i
$767$	−7.65515	+	3.94650i	−0.276411	+	0.142500i
$768$	0.342240	+	1.69790i	0.0123495	+	0.0612678i
$769$	5.54738	+	22.8666i	0.200044	+	0.824591i	0.980039	+	0.198806i	$0.0637062\pi$
$769$	5.54738	+	22.8666i	0.200044	+	0.824591i	−0.779995	+	0.625785i	$0.784779\pi$
$770$	−1.74037	+	5.02846i	−0.0627184	+	0.181213i
$771$	−22.2523	−	5.19844i	−0.801397	−	0.187217i
$772$	−2.62277	+	2.50080i	−0.0943955	+	0.0900059i
$773$	−11.3421	+	24.8356i	−0.407945	+	0.893276i	0.588457	+	0.808529i	$0.299736\pi$
$773$	−11.3421	+	24.8356i	−0.407945	+	0.893276i	−0.996402	+	0.0847474i	$0.972992\pi$
$774$	4.75466	+	29.4996i	0.170903	+	1.06034i
$775$	9.48997	−	2.78651i	0.340890	−	0.100094i
$776$	1.88563	+	1.48287i	0.0676901	+	0.0532321i
$777$	−0.391899	−	46.0966i	−0.0140593	−	1.65370i
$778$	−17.7713	+	13.9755i	−0.637132	+	0.501046i
$779$	−12.3610	−	6.37253i	−0.442878	−	0.228320i
$780$	−0.500124	−	0.349767i	−0.0179073	−	0.0125237i
$781$	29.5966	−	51.2628i	1.05905	−	1.83433i
$782$	2.40969	−	28.9956i	0.0861703	−	1.03688i
$783$	48.4857	+	10.4609i	1.73274	+	0.373842i
$784$	−1.63492	+	1.88680i	−0.0583900	+	0.0673856i
$785$	0.284979	+	5.98245i	0.0101714	+	0.213523i
$786$	11.0574	−	2.78224i	0.394404	−	0.0992393i
$787$	−6.74895	+	9.47758i	−0.240574	+	0.337839i	−0.917156	−	0.398528i	$-0.869521\pi$
$787$	−6.74895	+	9.47758i	−0.240574	+	0.337839i	0.676582	+	0.736367i	$0.263460\pi$
$788$	16.6300	−	6.65763i	0.592418	−	0.237168i
$789$	−5.47686	−	0.739987i	−0.194982	−	0.0263442i
$790$	2.98273	−	1.53770i	0.106121	−	0.0547090i
$791$	−17.5402	+	38.4076i	−0.623656	+	1.36562i
$792$	8.32338	−	12.1195i	0.295759	−	0.430648i
$793$	2.84820	+	3.28700i	0.101142	+	0.116725i
$794$	38.4903	−	7.41841i	1.36597	−	0.263269i
$795$	5.61034	−	1.99533i	0.198978	−	0.0707669i
$796$	−1.38670	+	0.132414i	−0.0491503	+	0.00469328i
$797$	1.87675	−	39.3978i	0.0664779	−	1.39554i	−0.681500	−	0.731818i	$-0.738672\pi$
$797$	1.87675	−	39.3978i	0.0664779	−	1.39554i	0.747978	−	0.663724i	$-0.231025\pi$
$798$	−4.79872	+	6.21000i	−0.169873	+	0.219832i
$799$	−2.67639	−	2.10473i	−0.0946838	−	0.0744602i
$800$	2.02551	+	4.43524i	0.0716125	+	0.156809i
$801$	3.89081	+	10.6522i	0.137475	+	0.376378i
$802$	2.75322	−	1.76939i	0.0972195	−	0.0624792i
$803$	−9.10511	−	26.3075i	−0.321312	−	0.928371i
$804$	−15.8037	−	7.05555i	−0.557353	−	0.248830i
$805$	−4.70965	+	2.22115i	−0.165993	+	0.0782851i
$806$	−1.01431	−	1.75683i	−0.0357275	−	0.0618819i
$807$	13.5485	+	9.47531i	0.476931	+	0.333547i
$808$	−0.399907	−	8.39509i	−0.0140687	−	0.295338i
$809$	−1.52856	−	10.6314i	−0.0537414	−	0.373780i	−0.998889	−	0.0471348i	$-0.984991\pi$
$809$	−1.52856	−	10.6314i	−0.0537414	−	0.373780i	0.945147	−	0.326645i	$-0.105918\pi$
$810$	−2.36802	−	2.10894i	−0.0832037	−	0.0741004i
$811$	4.89102	−	34.0178i	0.171747	−	1.19453i	−0.703444	−	0.710750i	$-0.748356\pi$
$811$	4.89102	−	34.0178i	0.171747	−	1.19453i	0.875191	−	0.483777i	$-0.160735\pi$
$812$	6.93528	−	28.5876i	0.243380	−	1.00323i
$813$	2.53087	−	5.01340i	0.0887616	−	0.175828i
$814$	42.1343	−	4.02334i	1.47681	−	0.141018i
$815$	−0.899095	−	3.70612i	−0.0314939	−	0.129820i
$816$	−3.04607	−	10.0569i	−0.106634	−	0.352062i
$817$	14.3801	−	2.77153i	0.503095	−	0.0969637i
$818$	24.6841	+	7.24791i	0.863059	+	0.253417i
$819$	−2.02665	+	9.02072i	−0.0708168	+	0.315209i
$820$	−2.80345	−	1.80167i	−0.0979006	−	0.0629169i
$821$	3.73850	−	15.4103i	0.130475	−	0.537824i	−0.868628	−	0.495465i	$-0.834998\pi$
$821$	3.73850	−	15.4103i	0.130475	−	0.537824i	0.999102	−	0.0423588i	$-0.0134872\pi$
$822$	−9.04355	−	17.1818i	−0.315430	−	0.599285i
$823$	−30.8132	+	43.2711i	−1.07408	+	1.50834i	−0.229203	+	0.973379i	$0.573612\pi$
$823$	−30.8132	+	43.2711i	−1.07408	+	1.50834i	−0.844879	+	0.534958i	$0.820327\pi$
$824$	9.36868	−	7.36761i	0.326373	−	0.256663i
$825$	15.0553	−	38.5531i	0.524160	−	1.34225i
$826$	8.68011	+	25.0795i	0.302020	+	0.872629i
$827$	45.8680			1.59499			0.797493	−	0.603328i	$-0.206159\pi$
$827$	45.8680			1.59499			0.797493	+	0.603328i	$0.206159\pi$
$828$	14.1750	−	2.46371i	0.492615	−	0.0856197i
$829$	38.6908			1.34379			0.671893	−	0.740648i	$-0.265482\pi$
$829$	38.6908			1.34379			0.671893	+	0.740648i	$0.265482\pi$
$830$	−0.633536	−	1.83048i	−0.0219903	−	0.0635369i
$831$	−14.3694	+	2.19084i	−0.498467	+	0.0759995i
$832$	0.786105	−	0.618200i	0.0272533	−	0.0214322i
$833$	8.78578	−	12.3379i	0.304409	−	0.427483i
$834$	−32.4098	−	1.26782i	−1.12226	−	0.0439009i
$835$	−1.45985	+	6.01758i	−0.0505201	+	0.208247i
$836$	−6.06194	−	3.89577i	−0.209657	−	0.134738i
$837$	−4.16570	−	9.68220i	−0.143988	−	0.334666i
$838$	2.46731	+	0.724466i	0.0852316	+	0.0250263i
$839$	−50.8052	+	9.79191i	−1.75399	+	0.338054i	−0.962119	−	0.272631i	$-0.912106\pi$
$839$	−50.8052	+	9.79191i	−1.75399	+	0.338054i	−0.791873	+	0.610685i	$0.790894\pi$
$840$	−1.28614	+	1.37204i	−0.0443761	+	0.0473397i
$841$	14.6458	+	60.3709i	0.505028	+	2.08176i
$842$	−10.1071	+	0.965109i	−0.348313	+	0.0332599i
$843$	−6.36862	−	9.72694i	−0.219347	−	0.335014i
$844$	−5.18417	+	21.3694i	−0.178446	+	0.735566i
$845$	0.601697	−	4.18489i	0.0206990	−	0.143965i
$846$	0.673280	−	1.54319i	0.0231478	−	0.0530559i
$847$	5.70920	+	39.7083i	0.196170	+	1.36439i
$848$	0.464283	+	9.74650i	0.0159435	+	0.334696i
$849$	1.42044	−	16.3426i	0.0487494	−	0.560878i
$850$	−14.7905	−	25.6180i	−0.507311	−	0.878689i
$851$	31.6335	+	26.7373i	1.08438	+	0.916544i
$852$	16.9373	−	12.2793i	0.580261	−	0.420682i
$853$	14.0994	+	40.7377i	0.482756	+	1.39483i	0.879060	+	0.476712i	$0.158171\pi$
$853$	14.0994	+	40.7377i	0.482756	+	1.39483i	−0.396304	+	0.918119i	$0.629707\pi$
$854$	11.2747	−	7.24578i	0.385811	−	0.247945i
$855$	−0.997627	+	1.19167i	−0.0341181	+	0.0407544i
$856$	−5.72947	−	12.5458i	−0.195829	−	0.428806i
$857$	−29.7252	−	23.3762i	−1.01539	−	0.798515i	−0.0357709	−	0.999360i	$-0.511389\pi$
$857$	−29.7252	−	23.3762i	−1.01539	−	0.798515i	−0.979623	+	0.200845i	$0.935631\pi$
$858$	−8.41257	−	1.13663i	−0.287200	−	0.0388041i
$859$	2.51934	−	52.8875i	0.0859588	−	1.80450i	−0.385603	−	0.922665i	$-0.626006\pi$
$859$	2.51934	−	52.8875i	0.0859588	−	1.80450i	0.471561	−	0.881833i	$-0.343691\pi$
$860$	3.49337	−	0.333576i	0.119123	−	0.0113749i
$861$	−9.13250	+	49.6517i	−0.311235	+	1.69213i
$862$	−19.1181	+	3.68472i	−0.651166	+	0.125502i
$863$	−16.2312	−	18.7318i	−0.552517	−	0.637638i	0.408951	−	0.912556i	$-0.365895\pi$
$863$	−16.2312	−	18.7318i	−0.552517	−	0.637638i	−0.961468	+	0.274918i	$0.911349\pi$
$864$	4.43228	−	2.71199i	0.150789	−	0.0922637i
$865$	2.71325	−	5.94120i	0.0922534	−	0.202007i
$866$	22.4366	−	11.5669i	0.762426	−	0.393058i
$867$	13.0205	+	31.7390i	0.442200	+	1.07791i
$868$	−5.80331	+	2.32329i	−0.196977	+	0.0788577i
$869$	27.0757	−	38.0225i	0.918479	−	1.28982i
$870$	1.59362	−	5.60315i	0.0540287	−	0.189965i
$871$	0.475483	+	9.98162i	0.0161111	+	0.338214i
$872$	4.62347	−	5.33577i	0.156570	−	0.180692i
$873$	2.23780	−	6.83980i	0.0757381	−	0.231492i
$874$	−1.41946	−	6.90715i	−0.0480140	−	0.233638i
$875$	−5.36142	+	9.28625i	−0.181249	+	0.313933i
$876$	0.851936	−	9.80181i	0.0287842	−	0.331172i
$877$	−4.83307	−	2.49162i	−0.163201	−	0.0841361i	0.374691	−	0.927150i	$-0.377749\pi$
$877$	−4.83307	−	2.49162i	−0.163201	−	0.0841361i	−0.537892	+	0.843014i	$0.680779\pi$
$878$	5.04526	−	3.96764i	0.170269	−	0.133901i
$879$	−5.37787	−	3.04425i	−0.181391	−	0.102680i
$880$	−1.35728	−	1.06738i	−0.0457540	−	0.0359813i
$881$	−32.5842	+	9.56760i	−1.09779	+	0.322341i	−0.779974	−	0.625812i	$-0.784768\pi$
$881$	−32.5842	+	9.56760i	−1.09779	+	0.322341i	−0.317817	+	0.948152i	$0.602950\pi$
$882$	6.99959	+	2.66504i	0.235688	+	0.0897367i
$883$	−11.2617	+	24.6597i	−0.378986	+	0.829864i	0.619989	+	0.784610i	$0.287137\pi$
$883$	−11.2617	+	24.6597i	−0.378986	+	0.829864i	−0.998976	+	0.0452539i	$0.985590\pi$
$884$	−4.39107	+	4.18688i	−0.147688	+	0.140820i
$885$	1.52347	+	5.02986i	0.0512107	+	0.169077i
$886$	−7.87766	+	22.7610i	−0.264655	+	0.764671i
$887$	2.45098	+	10.1031i	0.0822960	+	0.339229i	0.998043	−	0.0625260i	$-0.0199156\pi$
$887$	2.45098	+	10.1031i	0.0822960	+	0.339229i	−0.915747	+	0.401755i	$0.868400\pi$
$888$	14.1773	+	4.77223i	0.475758	+	0.160146i
$889$	−12.0620	+	6.21840i	−0.404547	+	0.208559i
$890$	1.27793	−	0.375234i	0.0428363	−	0.0125779i
$891$	−42.7186	−	10.9804i	−1.43113	−	0.367857i
$892$	4.76436	+	10.4325i	0.159523	+	0.349306i
$893$	−0.766076	−	0.306691i	−0.0256358	−	0.0102630i
$894$	4.70372	+	5.87774i	0.157316	+	0.196581i
$895$	−1.83199	−	0.353088i	−0.0612368	−	0.0118024i
$896$	−1.54083	−	2.66879i	−0.0514754	−	0.0891580i
$897$	−4.95824	−	6.66521i	−0.165551	−	0.222545i
$898$	−5.98506	+	10.3664i	−0.199724	+	0.345932i
$899$	12.6804	−	14.6339i	0.422914	−	0.488069i
$900$	10.4133	−	10.2727i	0.347111	−	0.342424i
$901$	−8.42468	−	58.5949i	−0.280667	−	1.95208i
$902$	−46.1435	−	4.40617i	−1.53641	−	0.146710i
$903$	−24.7615	−	47.0443i	−0.824011	−	1.56553i
$904$	−9.91622	−	9.45510i	−0.329809	−	0.314472i
$905$	−0.0466570	+	0.979452i	−0.00155093	+	0.0325581i
$906$	1.90057	+	9.42901i	0.0631422	+	0.313258i
$907$	−22.1787	+	21.1473i	−0.736430	+	0.702185i	−0.962305	−	0.271972i	$-0.912324\pi$
$907$	−22.1787	+	21.1473i	−0.736430	+	0.702185i	0.225875	+	0.974156i	$0.427476\pi$
$908$	0.618817	+	0.714153i	0.0205362	+	0.0237000i
$909$	−23.2450	+	9.76766i	−0.770988	+	0.323973i
$910$	1.04185	+	0.305915i	0.0345370	+	0.0101410i
$911$	10.1302	+	14.2258i	0.335628	+	0.471323i	0.947556	−	0.319590i	$-0.103545\pi$
$911$	10.1302	+	14.2258i	0.335628	+	0.471323i	−0.611928	+	0.790913i	$0.709606\pi$
$912$	−1.39501	−	2.13064i	−0.0461935	−	0.0705525i
$913$	−19.4997	−	18.5929i	−0.645347	−	0.615337i
$914$	17.4062	−	6.96840i	0.575746	−	0.230494i
$915$	2.28708	−	1.34650i	0.0756087	−	0.0445140i
$916$	24.0890	+	9.64380i	0.795924	+	0.318640i
$917$	−17.0661	+	10.9677i	−0.563571	+	0.362185i
$918$	−25.2042	+	18.9347i	−0.831863	+	0.624940i
$919$	−20.3616			−0.671668			−0.335834	−	0.941921i	$-0.609018\pi$
$919$	−20.3616			−0.671668			−0.335834	+	0.941921i	$0.609018\pi$
$920$	−0.181270	−	1.67997i	−0.00597628	−	0.0553870i
$921$	−3.02904	−	29.1045i	−0.0998103	−	0.959027i
$922$	34.8991	+	6.72626i	1.14934	+	0.221518i
$923$	−10.7363	−	5.53494i	−0.353389	−	0.182185i
$924$	−7.15605	+	25.1606i	−0.235417	+	0.827723i
$925$	41.9199	+	4.00287i	1.37832	+	0.131613i
$926$	−1.49517	+	10.3991i	−0.0491343	+	0.341737i
$927$	−30.4041	−	18.8169i	−0.998602	−	0.618028i
$928$	8.03043	+	5.16084i	0.263612	+	0.169413i
$929$	−9.45414	−	13.2765i	−0.310180	−	0.435587i	0.629830	−	0.776733i	$-0.283124\pi$
$929$	−9.45414	−	13.2765i	−0.310180	−	0.435587i	−0.940010	+	0.341146i	$0.889185\pi$
$930$	−1.16633	+	0.414806i	−0.0382453	+	0.0136020i
$931$	1.20061	−	3.46894i	0.0393485	−	0.113690i
$932$	0.833578	−	2.40846i	0.0273047	−	0.0788919i
$933$	−17.4234	+	6.19667i	−0.570417	+	0.202870i
$934$	−6.59840	−	9.26616i	−0.215906	−	0.303198i
$935$	8.81268	+	5.66356i	0.288205	+	0.185218i
$936$	−2.55114	−	1.57888i	−0.0833867	−	0.0516074i
$937$	2.73846	−	19.0464i	0.0894615	−	0.622218i	−0.894927	−	0.446212i	$-0.852773\pi$
$937$	2.73846	−	19.0464i	0.0894615	−	0.622218i	0.984389	−	0.176007i	$-0.0563180\pi$
$938$	30.6533	+	2.92704i	1.00087	+	0.0955711i
$939$	−2.19092	+	7.70326i	−0.0714981	+	0.251387i
$940$	−0.175755	−	0.0906079i	−0.00573249	−	0.00295530i
$941$	8.42023	+	1.62287i	0.274491	+	0.0529039i	0.324639	−	0.945838i	$-0.394757\pi$
$941$	8.42023	+	1.62287i	0.274491	+	0.0529039i	−0.0501478	+	0.998742i	$0.515969\pi$
$942$	3.04780	+	29.2848i	0.0993027	+	0.954149i
$943$	−28.4759	−	35.3087i	−0.927304	−	1.14981i
$944$	−8.61199			−0.280296
$945$	5.19005	+	2.21205i	0.168832	+	0.0719579i
$946$	41.0637	−	26.3901i	1.33510	−	0.858015i
$947$	−32.5755	−	13.0413i	−1.05856	−	0.423785i	−0.223938	−	0.974603i	$-0.571891\pi$
$947$	−32.5755	−	13.0413i	−1.05856	−	0.423785i	−0.834625	+	0.550819i	$0.814316\pi$
$948$	14.2161	−	8.36960i	0.461717	−	0.271832i
$949$	−5.27386	+	2.11134i	−0.171197	+	0.0685369i
$950$	−5.18857	−	4.94729i	−0.168339	−	0.160511i
$951$	7.99996	+	12.2185i	0.259416	+	0.396213i
$952$	10.8447	+	15.2292i	0.351478	+	0.493582i
$953$	−4.79420	−	1.40770i	−0.155299	−	0.0456000i	0.203159	−	0.979146i	$-0.434879\pi$
$953$	−4.79420	−	1.40770i	−0.155299	−	0.0456000i	−0.358458	+	0.933546i	$0.616697\pi$
$954$	26.9869	−	11.3400i	0.873733	−	0.367147i
$955$	0.957457	+	1.10496i	0.0309826	+	0.0357558i
$956$	−10.2417	+	9.76548i	−0.331242	+	0.315838i
$957$	−16.0107	−	79.4313i	−0.517552	−	2.56765i
$958$	1.03988	−	21.8297i	0.0335969	−	0.705286i
$959$	25.0019	+	23.8393i	0.807354	+	0.769810i
$960$	−0.284236	−	0.540020i	−0.00917369	−	0.0174291i
$961$	26.7635	+	2.55561i	0.863339	+	0.0824389i
$962$	−1.22919	−	8.54920i	−0.0396306	−	0.275637i
$963$	−29.4558	+	29.0581i	−0.949199	+	0.936383i
$964$	−4.19098	+	4.83665i	−0.134983	+	0.155778i
$965$	0.638414	−	1.10576i	0.0205513	−	0.0355958i
$966$	−22.5038	+	12.2001i	−0.724048	+	0.392532i
$967$	8.47498	+	14.6791i	0.272537	+	0.472048i	0.969511	−	0.245049i	$-0.0788039\pi$
$967$	8.47498	+	14.6791i	0.272537	+	0.472048i	−0.696974	+	0.717097i	$0.745471\pi$
$968$	−12.7826	−	2.46365i	−0.410850	−	0.0791848i
$969$	9.65372	+	12.0632i	0.310122	+	0.387526i
$970$	−0.784649	−	0.314126i	−0.0251936	−	0.0100860i
$971$	20.2176	+	44.2704i	0.648814	+	1.42070i	0.892588	+	0.450873i	$0.148887\pi$
$971$	20.2176	+	44.2704i	0.648814	+	1.42070i	−0.243774	+	0.969832i	$0.578386\pi$
$972$	−12.2041	−	9.69842i	−0.391447	−	0.311077i
$973$	55.3699	−	16.2581i	1.77508	−	0.521209i
$974$	−13.6070	+	7.01488i	−0.435995	+	0.224771i
$975$	−8.00449	−	2.69440i	−0.256349	−	0.0862898i
$976$	1.02532	+	4.22644i	0.0328198	+	0.135285i
$977$	3.81762	−	11.0303i	0.122137	−	0.352890i	−0.867314	−	0.497761i	$-0.834156\pi$
$977$	3.81762	−	11.0303i	0.122137	−	0.352890i	0.989451	+	0.144871i	$0.0462767\pi$
$978$	−5.43456	−	17.9427i	−0.173778	−	0.573744i
$979$	13.4079	−	12.7844i	0.428518	−	0.408591i
$980$	0.365410	−	0.800136i	0.0116726	−	0.0255594i
$981$	−19.7945	−	7.53661i	−0.631989	−	0.240625i
$982$	30.7369	−	9.02516i	0.980853	−	0.288004i
$983$	−8.04441	−	6.32620i	−0.256577	−	0.201774i	0.481582	−	0.876401i	$-0.340062\pi$
$983$	−8.04441	−	6.32620i	−0.256577	−	0.201774i	−0.738159	+	0.674627i	$0.764305\pi$
$984$	−14.2566	−	8.07024i	−0.454484	−	0.257270i
$985$	−4.96106	+	3.90142i	−0.158072	+	0.124310i
$986$	−51.4749	−	26.5372i	−1.63929	−	0.845115i
$987$	−0.259385	+	2.98432i	−0.00825633	+	0.0949918i
$988$	−0.735218	+	1.27343i	−0.0233904	+	0.0405134i
$989$	46.5554	+	10.6904i	1.48037	+	0.339935i
$990$	−1.61078	+	4.92332i	−0.0511939	+	0.156473i
$991$	−12.3442	+	14.2460i	−0.392127	+	0.452538i	−0.917146	−	0.398552i	$-0.869513\pi$
$991$	−12.3442	+	14.2460i	−0.392127	+	0.452538i	0.525019	+	0.851091i	$0.324058\pi$
$992$	−0.0965191	−	2.02619i	−0.00306449	−	0.0643315i
$993$	−7.50473	+	26.3866i	−0.238155	+	0.837352i
$994$	−21.5903	+	30.3193i	−0.684802	+	0.961670i
$995$	0.455643	−	0.182412i	0.0144448	−	0.00578284i
$996$	−3.61411	−	8.80981i	−0.114518	−	0.279149i
$997$	54.9969	−	28.3529i	1.74177	−	0.897944i	0.779256	−	0.626706i	$-0.215597\pi$
$997$	54.9969	−	28.3529i	1.74177	−	0.897944i	0.962512	−	0.271238i	$-0.0874329\pi$
$998$	16.6871	−	36.5397i	0.528222	−	1.15664i
$999$	−1.14443	−	44.8622i	−0.0362083	−	1.41938i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.m.a.223.4	yes	240
9.4	even	3	inner	414.2.m.a.85.8	yes	240
23.13	even	11	inner	414.2.m.a.151.8	yes	240
207.13	even	33	inner	414.2.m.a.13.4	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.m.a.13.4	✓	240	207.13	even	33	inner
414.2.m.a.85.8	yes	240	9.4	even	3	inner
414.2.m.a.151.8	yes	240	23.13	even	11	inner
414.2.m.a.223.4	yes	240	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.327068 + 0.945001i) q^{2} +(-1.08222 - 1.35233i) q^{3} +(-0.786053 + 0.618159i) q^{4} +(0.204372 - 0.287001i) q^{5} +(0.923996 - 1.46500i) q^{6} +(-0.726527 + 2.99479i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(-0.657606 + 2.92704i) q^{9} +O(q^{10})\)	\(q+(0.327068 + 0.945001i) q^{2} +(-1.08222 - 1.35233i) q^{3} +(-0.786053 + 0.618159i) q^{4} +(0.204372 - 0.287001i) q^{5} +(0.923996 - 1.46500i) q^{6} +(-0.726527 + 2.99479i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(-0.657606 + 2.92704i) q^{9} +(0.338059 + 0.0992632i) q^{10} +(4.81224 - 0.927484i) q^{11} +(1.68664 + 0.394022i) q^{12} +(-0.235775 - 0.971876i) q^{13} +(-3.06770 + 0.292930i) q^{14} +(-0.609295 + 0.0342182i) q^{15} +(0.235759 - 0.971812i) q^{16} +(-0.863401 + 6.00509i) q^{17} +(-2.98114 + 0.335902i) q^{18} +(0.209251 + 1.45537i) q^{19} +(0.0167646 + 0.351932i) q^{20} +(4.83621 - 2.25851i) q^{21} +(2.45040 + 4.24422i) q^{22} +(-1.29451 + 4.61782i) q^{23} +(0.179294 + 1.72275i) q^{24} +(1.59474 + 4.60769i) q^{25} +(0.841309 - 0.540677i) q^{26} +(4.67000 - 2.27839i) q^{27} +(-1.28017 - 2.80317i) q^{28} +(7.50349 + 5.90081i) q^{29} +(-0.231617 - 0.564593i) q^{30} +(0.0965191 - 2.02619i) q^{31} +(0.995472 - 0.0950560i) q^{32} +(-6.46216 - 5.50401i) q^{33} +(-5.95720 + 1.14816i) q^{34} +(0.711023 + 0.820565i) q^{35} +(-1.29246 - 2.70731i) q^{36} +(3.58775 - 7.85607i) q^{37} +(-1.30689 + 0.673748i) q^{38} +(-1.05914 + 1.37063i) q^{39} +(-0.327093 + 0.130948i) q^{40} +(-5.48637 + 7.70453i) q^{41} +(3.71606 + 3.83154i) q^{42} +(-0.473921 - 9.94883i) q^{43} +(-3.20935 + 3.70378i) q^{44} +(0.705665 + 0.786938i) q^{45} +(-4.78723 + 0.287026i) q^{46} +(-0.280611 + 0.486032i) q^{47} +(-1.56935 + 0.732888i) q^{48} +(-2.21906 - 1.14400i) q^{49} +(-3.83269 + 3.01406i) q^{50} +(9.05526 - 5.33121i) q^{51} +(0.786105 + 0.618200i) q^{52} +(-9.36230 + 2.74902i) q^{53} +(3.68049 + 3.66797i) q^{54} +(0.717300 - 1.57067i) q^{55} +(2.23030 - 2.12658i) q^{56} +(1.74169 - 1.85801i) q^{57} +(-3.12212 + 9.02078i) q^{58} +(-2.03035 - 8.36923i) q^{59} +(0.457786 - 0.403539i) q^{60} +(-3.86557 + 1.99284i) q^{61} +(1.94632 - 0.571490i) q^{62} +(-8.28809 - 4.09596i) q^{63} +(0.415415 + 0.909632i) q^{64} +(-0.327115 - 0.130957i) q^{65} +(3.08773 - 7.90694i) q^{66} +(-9.81171 - 1.89105i) q^{67} +(-3.03342 - 5.25404i) q^{68} +(7.64577 - 3.24688i) q^{69} +(-0.542881 + 0.940298i) q^{70} +(7.90957 - 9.12813i) q^{71} +(2.13569 - 2.10685i) q^{72} +(-0.808407 - 5.62259i) q^{73} +(8.59743 + 0.820955i) q^{74} +(4.50528 - 7.14315i) q^{75} +(-1.06413 - 1.01465i) q^{76} +(-0.718610 + 15.0855i) q^{77} +(-1.64166 - 0.552600i) q^{78} +(6.89319 - 6.57264i) q^{79} +(-0.230728 - 0.266274i) q^{80} +(-8.13511 - 3.84968i) q^{81} +(-9.07520 - 2.66472i) q^{82} +(-3.18899 - 4.47830i) q^{83} +(-2.40540 + 4.76485i) q^{84} +(1.54701 + 1.47507i) q^{85} +(9.24665 - 3.70180i) q^{86} +(-0.140560 - 16.5332i) q^{87} +(-4.54975 - 1.82145i) q^{88} +(3.18010 - 2.04373i) q^{89} +(-0.512857 + 0.924237i) q^{90} +3.08186 q^{91} +(-1.83699 - 4.43006i) q^{92} +(-2.84453 + 2.06225i) q^{93} +(-0.551080 - 0.106212i) q^{94} +(0.460458 + 0.237382i) q^{95} +(-1.20587 - 1.24334i) q^{96} +(-2.38799 - 0.228026i) q^{97} +(0.355302 - 2.47118i) q^{98} +(-0.449779 + 14.6955i) 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

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Representations

Groups

Database

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