LMFDB - Embedded newform 536.2.c.a.269.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [536,2,Mod(269,536)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(536, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("536.269");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 536 = 2^{3} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	536.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.27998154834$
Analytic rank:	$0$
Dimension:	$66$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			269.17
Character	$\chi$	$=$	536.269
Dual form			536.2.c.a.269.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.959378 - 1.03904i) q^{2} -2.60130i q^{3} +(-0.159188 + 1.99365i) q^{4} -4.14613i q^{5} +(-2.70285 + 2.49563i) q^{6} -0.431856 q^{7} +(2.22420 - 1.74727i) q^{8} -3.76678 q^{9} +O(q^{10})$	\(q+(-0.959378 - 1.03904i) q^{2} -2.60130i q^{3} +(-0.159188 + 1.99365i) q^{4} -4.14613i q^{5} +(-2.70285 + 2.49563i) q^{6} -0.431856 q^{7} +(2.22420 - 1.74727i) q^{8} -3.76678 q^{9} +(-4.30798 + 3.97771i) q^{10} +1.51935i q^{11} +(5.18610 + 0.414097i) q^{12} -4.50121i q^{13} +(0.414313 + 0.448714i) q^{14} -10.7853 q^{15} +(-3.94932 - 0.634733i) q^{16} -1.13712 q^{17} +(3.61376 + 3.91381i) q^{18} -0.794583i q^{19} +(8.26595 + 0.660015i) q^{20} +1.12339i q^{21} +(1.57866 - 1.45763i) q^{22} +6.83181 q^{23} +(-4.54517 - 5.78582i) q^{24} -12.1904 q^{25} +(-4.67692 + 4.31836i) q^{26} +1.99462i q^{27} +(0.0687464 - 0.860972i) q^{28} +8.74093i q^{29} +(10.3472 + 11.2064i) q^{30} +7.29810 q^{31} +(3.12938 + 4.71243i) q^{32} +3.95229 q^{33} +(1.09092 + 1.18150i) q^{34} +1.79053i q^{35} +(0.599627 - 7.50965i) q^{36} -5.25163i q^{37} +(-0.825600 + 0.762306i) q^{38} -11.7090 q^{39} +(-7.24439 - 9.22182i) q^{40} +2.74971 q^{41} +(1.16724 - 1.07775i) q^{42} -1.43902i q^{43} +(-3.02906 - 0.241863i) q^{44} +15.6176i q^{45} +(-6.55429 - 7.09849i) q^{46} +6.87440 q^{47} +(-1.65113 + 10.2734i) q^{48} -6.81350 q^{49} +(11.6952 + 12.6663i) q^{50} +2.95798i q^{51} +(8.97386 + 0.716540i) q^{52} +4.26761i q^{53} +(2.07248 - 1.91359i) q^{54} +6.29943 q^{55} +(-0.960534 + 0.754567i) q^{56} -2.06695 q^{57} +(9.08213 - 8.38586i) q^{58} +5.07432i q^{59} +(1.71690 - 21.5023i) q^{60} +9.66857i q^{61} +(-7.00164 - 7.58299i) q^{62} +1.62671 q^{63} +(1.89412 - 7.77253i) q^{64} -18.6626 q^{65} +(-3.79174 - 4.10657i) q^{66} +1.00000i q^{67} +(0.181015 - 2.26702i) q^{68} -17.7716i q^{69} +(1.86043 - 1.71780i) q^{70} +13.8963 q^{71} +(-8.37806 + 6.58156i) q^{72} -7.34123 q^{73} +(-5.45663 + 5.03830i) q^{74} +31.7109i q^{75} +(1.58412 + 0.126488i) q^{76} -0.656141i q^{77} +(11.2334 + 12.1661i) q^{78} -10.9971 q^{79} +(-2.63168 + 16.3744i) q^{80} -6.11172 q^{81} +(-2.63801 - 2.85704i) q^{82} -6.32598i q^{83} +(-2.23965 - 0.178830i) q^{84} +4.71463i q^{85} +(-1.49520 + 1.38057i) q^{86} +22.7378 q^{87} +(2.65471 + 3.37934i) q^{88} -1.39591 q^{89} +(16.2272 - 14.9831i) q^{90} +1.94388i q^{91} +(-1.08754 + 13.6203i) q^{92} -18.9846i q^{93} +(-6.59515 - 7.14275i) q^{94} -3.29445 q^{95} +(12.2585 - 8.14046i) q^{96} +5.40859 q^{97} +(6.53672 + 7.07947i) q^{98} -5.72306i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q - 4 q^{4} + 2 q^{6} - 6 q^{8} - 66 q^{9}+O(q^{10}) $ 66 * q - 4 * q^4 + 2 * q^6 - 6 * q^8 - 66 * q^9	$ 66 q - 4 q^{4} + 2 q^{6} - 6 q^{8} - 66 q^{9} - 4 q^{10} + 4 q^{12} - 2 q^{14} + 8 q^{15} - 12 q^{16} - 4 q^{17} - 10 q^{18} + 22 q^{20} + 8 q^{22} - 12 q^{23} - 62 q^{25} - 24 q^{26} + 10 q^{28} + 22 q^{30} - 16 q^{31} + 10 q^{32} - 10 q^{34} + 2 q^{36} + 8 q^{38} + 8 q^{39} - 18 q^{40} + 4 q^{41} + 28 q^{42} + 34 q^{44} + 18 q^{46} + 20 q^{47} - 38 q^{48} + 66 q^{49} - 32 q^{50} - 6 q^{52} + 38 q^{54} + 16 q^{55} - 30 q^{56} + 2 q^{58} + 18 q^{60} + 22 q^{62} - 40 q^{63} + 26 q^{64} + 16 q^{65} - 34 q^{66} + 26 q^{68} - 18 q^{70} + 4 q^{71} - 2 q^{72} - 20 q^{73} - 4 q^{74} - 30 q^{76} - 36 q^{78} + 16 q^{79} - 32 q^{80} + 66 q^{81} + 16 q^{82} - 6 q^{84} + 2 q^{86} + 32 q^{87} + 22 q^{88} - 20 q^{89} - 18 q^{90} + 8 q^{92} - 16 q^{94} - 64 q^{96} + 12 q^{97} - 46 q^{98}+O(q^{100}) $ 66 * q - 4 * q^4 + 2 * q^6 - 6 * q^8 - 66 * q^9 - 4 * q^10 + 4 * q^12 - 2 * q^14 + 8 * q^15 - 12 * q^16 - 4 * q^17 - 10 * q^18 + 22 * q^20 + 8 * q^22 - 12 * q^23 - 62 * q^25 - 24 * q^26 + 10 * q^28 + 22 * q^30 - 16 * q^31 + 10 * q^32 - 10 * q^34 + 2 * q^36 + 8 * q^38 + 8 * q^39 - 18 * q^40 + 4 * q^41 + 28 * q^42 + 34 * q^44 + 18 * q^46 + 20 * q^47 - 38 * q^48 + 66 * q^49 - 32 * q^50 - 6 * q^52 + 38 * q^54 + 16 * q^55 - 30 * q^56 + 2 * q^58 + 18 * q^60 + 22 * q^62 - 40 * q^63 + 26 * q^64 + 16 * q^65 - 34 * q^66 + 26 * q^68 - 18 * q^70 + 4 * q^71 - 2 * q^72 - 20 * q^73 - 4 * q^74 - 30 * q^76 - 36 * q^78 + 16 * q^79 - 32 * q^80 + 66 * q^81 + 16 * q^82 - 6 * q^84 + 2 * q^86 + 32 * q^87 + 22 * q^88 - 20 * q^89 - 18 * q^90 + 8 * q^92 - 16 * q^94 - 64 * q^96 + 12 * q^97 - 46 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/536\mathbb{Z}\right)^\times$.

$n$	$135$	$269$	$337$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.959378	−	1.03904i	−0.678383	−	0.734709i
$2$	−0.959378	−	1.03904i	−0.678383	−	0.734709i
$3$		−	2.60130i		−	1.50186i	−0.660380	−	0.750932i	$-0.729605\pi$
$3$		−	2.60130i		−	1.50186i	0.660380	−	0.750932i	$-0.270395\pi$
$4$	−0.159188	+	1.99365i	−0.0795941	+	0.996827i
$5$		−	4.14613i		−	1.85421i	−0.374806	−	0.927103i	$-0.622291\pi$
$5$		−	4.14613i		−	1.85421i	0.374806	−	0.927103i	$-0.377709\pi$
$6$	−2.70285	+	2.49563i	−1.10343	+	1.01884i
$7$	−0.431856			−0.163226			−0.0816131	−	0.996664i	$-0.526007\pi$
$7$	−0.431856			−0.163226			−0.0816131	+	0.996664i	$0.526007\pi$
$8$	2.22420	−	1.74727i	0.786373	−	0.617752i
$9$	−3.76678			−1.25559
$10$	−4.30798	+	3.97771i	−1.36230	+	1.25786i
$11$			1.51935i			0.458102i	0.973414	+	0.229051i	$0.0735622\pi$
$11$			1.51935i			0.458102i	−0.973414	+	0.229051i	$0.926438\pi$
$12$	5.18610	+	0.414097i	1.49710	+	0.119539i
$13$		−	4.50121i		−	1.24841i	−0.781260	−	0.624206i	$-0.785423\pi$
$13$		−	4.50121i		−	1.24841i	0.781260	−	0.624206i	$-0.214577\pi$
$14$	0.414313	+	0.448714i	0.110730	+	0.119924i
$15$	−10.7853			−2.78476
$16$	−3.94932	−	0.634733i	−0.987330	−	0.158683i
$17$	−1.13712			−0.275791			−0.137895	−	0.990447i	$-0.544034\pi$
$17$	−1.13712			−0.275791			−0.137895	+	0.990447i	$0.544034\pi$
$18$	3.61376	+	3.91381i	0.851772	+	0.922495i
$19$		−	0.794583i		−	0.182290i	−0.995838	−	0.0911450i	$-0.970947\pi$
$19$		−	0.794583i		−	0.182290i	0.995838	−	0.0911450i	$-0.0290527\pi$
$20$	8.26595	+	0.660015i	1.84832	+	0.147584i
$21$			1.12339i			0.245143i
$22$	1.57866	−	1.45763i	0.336571	−	0.310768i
$23$	6.83181			1.42453			0.712266	−	0.701910i	$-0.247669\pi$
$23$	6.83181			1.42453			0.712266	+	0.701910i	$0.247669\pi$
$24$	−4.54517	−	5.78582i	−0.927779	−	1.18102i
$25$	−12.1904			−2.43808
$26$	−4.67692	+	4.31836i	−0.917219	+	0.846901i
$27$			1.99462i			0.383865i
$28$	0.0687464	−	0.860972i	0.0129918	−	0.162708i
$29$			8.74093i			1.62315i	0.584248	+	0.811575i	$0.301389\pi$
$29$			8.74093i			1.62315i	−0.584248	+	0.811575i	$0.698611\pi$
$30$	10.3472	+	11.2064i	1.88914	+	2.04599i
$31$	7.29810			1.31078			0.655389	−	0.755291i	$-0.272505\pi$
$31$	7.29810			1.31078			0.655389	+	0.755291i	$0.272505\pi$
$32$	3.12938	+	4.71243i	0.553201	+	0.833048i
$33$	3.95229			0.688006
$34$	1.09092	+	1.18150i	0.187092	+	0.202626i
$35$			1.79053i			0.302655i
$36$	0.599627	−	7.50965i	0.0999378	−	1.25161i
$37$		−	5.25163i		−	0.863363i	−0.902026	−	0.431681i	$-0.857920\pi$
$37$		−	5.25163i		−	0.863363i	0.902026	−	0.431681i	$-0.142080\pi$
$38$	−0.825600	+	0.762306i	−0.133930	+	0.123662i
$39$	−11.7090			−1.87494
$40$	−7.24439	−	9.22182i	−1.14544	−	1.45810i
$41$	2.74971			0.429432			0.214716	−	0.976677i	$-0.431117\pi$
$41$	2.74971			0.429432			0.214716	+	0.976677i	$0.431117\pi$
$42$	1.16724	−	1.07775i	0.180109	−	0.166301i
$43$		−	1.43902i		−	0.219449i	−0.993962	−	0.109725i	$-0.965003\pi$
$43$		−	1.43902i		−	0.219449i	0.993962	−	0.109725i	$-0.0349969\pi$
$44$	−3.02906	−	0.241863i	−0.456648	−	0.0364622i
$45$			15.6176i			2.32813i
$46$	−6.55429	−	7.09849i	−0.966377	−	1.04662i
$47$	6.87440			1.00273			0.501367	−	0.865235i	$-0.332831\pi$
$47$	6.87440			1.00273			0.501367	+	0.865235i	$0.332831\pi$
$48$	−1.65113	+	10.2734i	−0.238320	+	1.48283i
$49$	−6.81350			−0.973357
$50$	11.6952	+	12.6663i	1.65395	+	1.79128i
$51$			2.95798i			0.414200i
$52$	8.97386	+	0.716540i	1.24445	+	0.0993662i
$53$			4.26761i			0.586201i	0.956082	+	0.293100i	$0.0946870\pi$
$53$			4.26761i			0.586201i	−0.956082	+	0.293100i	$0.905313\pi$
$54$	2.07248	−	1.91359i	0.282029	−	0.260407i
$55$	6.29943			0.849415
$56$	−0.960534	+	0.754567i	−0.128357	+	0.100833i
$57$	−2.06695			−0.273774
$58$	9.08213	−	8.38586i	1.19254	−	1.10112i
$59$			5.07432i			0.660620i	0.943873	+	0.330310i	$0.107153\pi$
$59$			5.07432i			0.660620i	−0.943873	+	0.330310i	$0.892847\pi$
$60$	1.71690	−	21.5023i	0.221651	−	2.77593i
$61$			9.66857i			1.23793i	0.785417	+	0.618967i	$0.212448\pi$
$61$			9.66857i			1.23793i	−0.785417	+	0.618967i	$0.787552\pi$
$62$	−7.00164	−	7.58299i	−0.889209	−	0.963040i
$63$	1.62671			0.204946
$64$	1.89412	−	7.77253i	0.236765	−	0.971567i
$65$	−18.6626			−2.31481
$66$	−3.79174	−	4.10657i	−0.466731	−	0.505484i
$67$			1.00000i			0.122169i
$67$			1.00000i			0.122169i
$68$	0.181015	−	2.26702i	0.0219513	−	0.274916i
$69$		−	17.7716i		−	2.13945i
$70$	1.86043	−	1.71780i	0.222363	−	0.205316i
$71$	13.8963			1.64918			0.824592	−	0.565728i	$-0.191405\pi$
$71$	13.8963			1.64918			0.824592	+	0.565728i	$0.191405\pi$
$72$	−8.37806	+	6.58156i	−0.987364	+	0.775645i
$73$	−7.34123			−0.859226			−0.429613	−	0.903013i	$-0.641350\pi$
$73$	−7.34123			−0.859226			−0.429613	+	0.903013i	$0.641350\pi$
$74$	−5.45663	+	5.03830i	−0.634320	+	0.585690i
$75$			31.7109i			3.66166i
$76$	1.58412	+	0.126488i	0.181712	+	0.0145092i
$77$		−	0.656141i		−	0.0747742i
$78$	11.2334	+	12.1661i	1.27193	+	1.37754i
$79$	−10.9971			−1.23727			−0.618637	−	0.785677i	$-0.712315\pi$
$79$	−10.9971			−1.23727			−0.618637	+	0.785677i	$0.712315\pi$
$80$	−2.63168	+	16.3744i	−0.294231	+	1.83071i
$81$	−6.11172			−0.679080
$82$	−2.63801	−	2.85704i	−0.291319	−	0.315507i
$83$		−	6.32598i		−	0.694366i	−0.937797	−	0.347183i	$-0.887138\pi$
$83$		−	6.32598i		−	0.694366i	0.937797	−	0.347183i	$-0.112862\pi$
$84$	−2.23965	−	0.178830i	−0.244366	−	0.0195120i
$85$			4.71463i			0.511373i
$86$	−1.49520	+	1.38057i	−0.161231	+	0.148871i
$87$	22.7378			2.43775
$88$	2.65471	+	3.37934i	0.282993	+	0.360239i
$89$	−1.39591			−0.147967			−0.0739833	−	0.997259i	$-0.523571\pi$
$89$	−1.39591			−0.147967			−0.0739833	+	0.997259i	$0.523571\pi$
$90$	16.2272	−	14.9831i	1.71050	−	1.57936i
$91$			1.94388i			0.203774i
$92$	−1.08754	+	13.6203i	−0.113384	+	1.42001i
$93$		−	18.9846i		−	1.96861i
$94$	−6.59515	−	7.14275i	−0.680238	−	0.736718i
$95$	−3.29445			−0.338003
$96$	12.2585	−	8.14046i	1.25112	−	0.830833i
$97$	5.40859			0.549159			0.274580	−	0.961564i	$-0.411461\pi$
$97$	5.40859			0.549159			0.274580	+	0.961564i	$0.411461\pi$
$98$	6.53672	+	7.07947i	0.660309	+	0.715134i
$99$		−	5.72306i		−	0.575189i
$100$	1.94057	−	24.3035i	0.194057	−	2.43035i
$101$		−	15.5528i		−	1.54756i	−0.633453	−	0.773781i	$-0.718363\pi$
$101$		−	15.5528i		−	1.54756i	0.633453	−	0.773781i	$-0.281637\pi$
$102$	3.07345	−	2.83782i	0.304317	−	0.280986i
$103$	−1.82784			−0.180103			−0.0900514	−	0.995937i	$-0.528703\pi$
$103$	−1.82784			−0.180103			−0.0900514	+	0.995937i	$0.528703\pi$
$104$	−7.86482	−	10.0116i	−0.771209	−	0.981718i
$105$	4.65772			0.454546
$106$	4.43419	−	4.09425i	0.430687	−	0.397668i
$107$		−	7.11094i		−	0.687441i	−0.939072	−	0.343720i	$-0.888313\pi$
$107$		−	7.11094i		−	0.687441i	0.939072	−	0.343720i	$-0.111687\pi$
$108$	−3.97658	−	0.317520i	−0.382647	−	0.0305534i
$109$		−	17.8815i		−	1.71273i	−0.516368	−	0.856367i	$-0.672716\pi$
$109$		−	17.8815i		−	1.71273i	0.516368	−	0.856367i	$-0.327284\pi$
$110$	−6.04353	−	6.54533i	−0.576228	−	0.624073i
$111$	−13.6611			−1.29665
$112$	1.70554	+	0.274113i	0.161158	+	0.0259013i
$113$	7.21927			0.679132			0.339566	−	0.940582i	$-0.389720\pi$
$113$	7.21927			0.679132			0.339566	+	0.940582i	$0.389720\pi$
$114$	1.98299	+	2.14764i	0.185724	+	0.201145i
$115$		−	28.3256i		−	2.64138i
$116$	−17.4264	−	1.39145i	−1.61800	−	0.129193i
$117$			16.9551i			1.56750i
$118$	5.27240	−	4.86819i	0.485363	−	0.448153i
$119$	0.491070			0.0450163
$120$	−23.9888	+	18.8449i	−2.18986	+	1.72029i
$121$	8.69157			0.790143
$122$	10.0460	−	9.27581i	0.909520	−	0.839792i
$123$		−	7.15282i		−	0.644948i
$124$	−1.16177	+	14.5499i	−0.104330	+	1.30662i
$125$			29.8124i			2.66650i
$126$	−1.56063	−	1.69020i	−0.139032	−	0.150575i
$127$	−16.0285			−1.42230			−0.711149	−	0.703042i	$-0.751825\pi$
$127$	−16.0285			−1.42230			−0.711149	+	0.703042i	$0.751825\pi$
$128$	−9.89312	+	5.48874i	−0.874436	+	0.485140i
$129$	−3.74334			−0.329583
$130$	17.9045	+	19.3911i	1.57033	+	1.70071i
$131$		−	8.78056i		−	0.767161i	−0.923507	−	0.383581i	$-0.874691\pi$
$131$		−	8.78056i		−	0.767161i	0.923507	−	0.383581i	$-0.125309\pi$
$132$	−0.629158	+	7.87951i	−0.0547612	+	0.685823i
$133$			0.343146i			0.0297545i
$134$	1.03904	−	0.959378i	0.0897590	−	0.0828776i
$135$	8.26996			0.711765
$136$	−2.52917	+	1.98684i	−0.216875	+	0.170370i
$137$	−14.9248			−1.27511			−0.637557	−	0.770403i	$-0.720055\pi$
$137$	−14.9248			−1.27511			−0.637557	+	0.770403i	$0.720055\pi$
$138$	−18.4653	+	17.0497i	−1.57187	+	1.45137i
$139$			1.09409i			0.0927998i	0.998923	+	0.0463999i	$0.0147748\pi$
$139$			1.09409i			0.0927998i	−0.998923	+	0.0463999i	$0.985225\pi$
$140$	−3.56970	−	0.285032i	−0.301695	−	0.0240896i
$141$		−	17.8824i		−	1.50597i
$142$	−13.3318	−	14.4387i	−1.11878	−	1.21167i
$143$	6.83892			0.571899
$144$	14.8762	+	2.39090i	1.23968	+	0.199241i
$145$	36.2410			3.00965
$146$	7.04302	+	7.62780i	0.582884	+	0.631281i
$147$			17.7240i			1.46185i
$148$	10.4699	+	0.835998i	0.860624	+	0.0687186i
$149$		−	21.2969i		−	1.74471i	−0.488876	−	0.872353i	$-0.662593\pi$
$149$		−	21.2969i		−	1.74471i	0.488876	−	0.872353i	$-0.337407\pi$
$150$	32.9488	−	30.4228i	2.69026	−	2.48401i
$151$	−17.3984			−1.41586			−0.707932	−	0.706281i	$-0.750372\pi$
$151$	−17.3984			−1.41586			−0.707932	+	0.706281i	$0.750372\pi$
$152$	−1.38835	−	1.76731i	−0.112610	−	0.143348i
$153$	4.28326			0.346281
$154$	−0.681754	+	0.629487i	−0.0549373	+	0.0507255i
$155$		−	30.2589i		−	2.43045i
$156$	1.86394	−	23.3437i	0.149234	−	1.86900i
$157$		−	5.61395i		−	0.448042i	−0.974584	−	0.224021i	$-0.928082\pi$
$157$		−	5.61395i		−	0.448042i	0.974584	−	0.224021i	$-0.0719184\pi$
$158$	10.5504	+	11.4264i	0.839345	+	0.909036i
$159$	11.1013			0.880393
$160$	19.5383	−	12.9748i	1.54464	−	1.02575i
$161$	−2.95036			−0.232521
$162$	5.86345	+	6.35029i	0.460676	+	0.498926i
$163$			18.3341i			1.43604i	0.696024	+	0.718018i	$0.254951\pi$
$163$			18.3341i			1.43604i	−0.696024	+	0.718018i	$0.745049\pi$
$164$	−0.437721	+	5.48196i	−0.0341802	+	0.428069i
$165$		−	16.3867i		−	1.27570i
$166$	−6.57291	+	6.06900i	−0.510157	+	0.471046i
$167$	−3.75592			−0.290642			−0.145321	−	0.989385i	$-0.546422\pi$
$167$	−3.75592			−0.290642			−0.145321	+	0.989385i	$0.546422\pi$
$168$	1.96286	+	2.49864i	0.151438	+	0.192774i
$169$	−7.26092			−0.558532
$170$	4.89867	−	4.52311i	0.375711	−	0.346907i
$171$			2.99302i			0.228882i
$172$	2.86892	+	0.229076i	0.218753	+	0.0174669i
$173$		−	17.9874i		−	1.36756i	−0.729690	−	0.683778i	$-0.760336\pi$
$173$		−	17.9874i		−	1.36756i	0.729690	−	0.683778i	$-0.239664\pi$
$174$	−21.8142	−	23.6254i	−1.65373	−	1.79104i
$175$	5.26450			0.397959
$176$	0.964382	−	6.00040i	0.0726930	−	0.452297i
$177$	13.1998			0.992161
$178$	1.33921	+	1.45040i	0.100378	+	0.108712i
$179$			21.9835i			1.64312i	0.570120	+	0.821561i	$0.306897\pi$
$179$			21.9835i			1.64312i	−0.570120	+	0.821561i	$0.693103\pi$
$180$	−31.1360	−	2.48613i	−2.32074	−	0.185305i
$181$			16.8717i			1.25406i	0.778995	+	0.627031i	$0.215730\pi$
$181$			16.8717i			1.25406i	−0.778995	+	0.627031i	$0.784270\pi$
$182$	2.01976	−	1.86491i	0.149714	−	0.138236i
$183$	25.1509			1.85921
$184$	15.1953	−	11.9370i	1.12021	−	0.880007i
$185$	−21.7740			−1.60085
$186$	−19.7256	+	18.2134i	−1.44635	+	1.33547i
$187$		−	1.72768i		−	0.126340i
$188$	−1.09432	+	13.7052i	−0.0798118	+	0.999553i
$189$		−	0.861389i		−	0.0626568i
$190$	3.16062	+	3.42305i	0.229295	+	0.248334i
$191$	17.5308			1.26848			0.634242	−	0.773135i	$-0.281312\pi$
$191$	17.5308			1.26848			0.634242	+	0.773135i	$0.281312\pi$
$192$	−20.2187	−	4.92719i	−1.45916	−	0.355589i
$193$	17.2094			1.23876			0.619381	−	0.785091i	$-0.287384\pi$
$193$	17.2094			1.23876			0.619381	+	0.785091i	$0.287384\pi$
$194$	−5.18888	−	5.61972i	−0.372540	−	0.403472i
$195$			48.5471i			3.47653i
$196$	1.08463	−	13.5838i	0.0774735	−	0.970269i
$197$			9.22584i			0.657314i	0.944449	+	0.328657i	$0.106596\pi$
$197$			9.22584i			0.657314i	−0.944449	+	0.328657i	$0.893404\pi$
$198$	−5.94646	+	5.49057i	−0.422596	+	0.390198i
$199$	19.9304			1.41283			0.706414	−	0.707798i	$-0.250312\pi$
$199$	19.9304			1.41283			0.706414	+	0.707798i	$0.250312\pi$
$200$	−27.1139	+	21.2999i	−1.91724	+	1.50613i
$201$	2.60130			0.183482
$202$	−16.1599	+	14.9210i	−1.13701	+	1.04984i
$203$		−	3.77482i		−	0.264941i
$204$	−5.89719	−	0.470876i	−0.412886	−	0.0329679i
$205$		−	11.4006i		−	0.796255i
$206$	1.75359	+	1.89919i	0.122179	+	0.132323i
$207$	−25.7339			−1.78863
$208$	−2.85707	+	17.7767i	−0.198102	+	1.23259i
$209$	1.20725			0.0835073
$210$	−4.46851	−	4.83953i	−0.308356	−	0.333959i
$211$			2.54767i			0.175389i	0.996147	+	0.0876945i	$0.0279499\pi$
$211$			2.54767i			0.175389i	−0.996147	+	0.0876945i	$0.972050\pi$
$212$	−8.50813	−	0.679353i	−0.584341	−	0.0466581i
$213$		−	36.1484i		−	2.47685i
$214$	−7.38852	+	6.82208i	−0.505069	+	0.466348i
$215$	−5.96638			−0.406904
$216$	3.48513	+	4.43643i	0.237133	+	0.301861i
$217$	−3.15173			−0.213953
$218$	−18.5795	+	17.1551i	−1.25836	+	1.16189i
$219$			19.0968i			1.29044i
$220$	−1.00279	+	12.5589i	−0.0676084	+	0.846720i
$221$			5.11840i			0.344301i
$222$	13.1061	+	14.1943i	0.879627	+	0.952662i
$223$	6.85123			0.458793			0.229396	−	0.973333i	$-0.426325\pi$
$223$	6.85123			0.458793			0.229396	+	0.973333i	$0.426325\pi$
$224$	−1.35144	−	2.03509i	−0.0902970	−	0.135975i
$225$	45.9185			3.06124
$226$	−6.92601	−	7.50108i	−0.460711	−	0.498964i
$227$			13.8952i			0.922257i	0.887333	+	0.461128i	$0.152555\pi$
$227$			13.8952i			0.922257i	−0.887333	+	0.461128i	$0.847445\pi$
$228$	0.329034	−	4.12079i	0.0217908	−	0.272906i
$229$		−	3.33660i		−	0.220489i	−0.993904	−	0.110244i	$-0.964837\pi$
$229$		−	3.33660i		−	0.220489i	0.993904	−	0.110244i	$-0.0351634\pi$
$230$	−29.4313	+	27.1749i	−1.94064	+	1.79186i
$231$	−1.70682			−0.112301
$232$	15.2727	+	19.4416i	1.00270	+	1.27640i
$233$	−2.24697			−0.147204			−0.0736018	−	0.997288i	$-0.523449\pi$
$233$	−2.24697			−0.147204			−0.0736018	+	0.997288i	$0.523449\pi$
$234$	17.6169	−	16.2663i	1.15165	−	1.06336i
$235$		−	28.5022i		−	1.85928i
$236$	−10.1164	−	0.807772i	−0.658524	−	0.0525815i
$237$			28.6069i			1.85822i
$238$	−0.471122	−	0.510239i	−0.0305383	−	0.0330739i
$239$	−11.5549			−0.747422			−0.373711	−	0.927545i	$-0.621915\pi$
$239$	−11.5549			−0.747422			−0.373711	+	0.927545i	$0.621915\pi$
$240$	42.5948	+	6.84581i	2.74948	+	0.441895i
$241$	−9.34019			−0.601655			−0.300827	−	0.953679i	$-0.597263\pi$
$241$	−9.34019			−0.601655			−0.300827	+	0.953679i	$0.597263\pi$
$242$	−8.33850	−	9.03085i	−0.536019	−	0.580525i
$243$			21.8823i			1.40375i
$244$	−19.2758	−	1.53912i	−1.23401	−	0.0985322i
$245$			28.2497i			1.80480i
$246$	−7.43203	+	6.86225i	−0.473849	+	0.437521i
$247$	−3.57659			−0.227573
$248$	16.2324	−	12.7517i	1.03076	−	0.809736i
$249$	−16.4558			−1.04284
$250$	30.9761	−	28.6013i	1.95910	−	1.80891i
$251$		−	8.09818i		−	0.511153i	−0.966789	−	0.255576i	$-0.917735\pi$
$251$		−	8.09818i		−	0.511153i	0.966789	−	0.255576i	$-0.0822652\pi$
$252$	−0.258952	+	3.24309i	−0.0163125	+	0.204295i
$253$			10.3799i			0.652580i
$254$	15.3774	+	16.6541i	0.964862	+	1.04497i
$255$	12.2642			0.768013
$256$	15.1942	+	5.01352i	0.949639	+	0.313345i
$257$	−17.8009			−1.11039			−0.555196	−	0.831720i	$-0.687357\pi$
$257$	−17.8009			−1.11039			−0.555196	+	0.831720i	$0.687357\pi$
$258$	3.59128	+	3.88946i	0.223583	+	0.242147i
$259$			2.26795i			0.140923i
$260$	2.97087	−	37.2068i	0.184245	−	2.30747i
$261$		−	32.9251i		−	2.03801i
$262$	−9.12331	+	8.42388i	−0.563640	+	0.520429i
$263$	0.797438			0.0491721			0.0245861	−	0.999698i	$-0.492173\pi$
$263$	0.797438			0.0491721			0.0245861	+	0.999698i	$0.492173\pi$
$264$	8.79069	−	6.90571i	0.541029	−	0.425017i
$265$	17.6941			1.08694
$266$	0.356540	−	0.329206i	0.0218609	−	0.0201849i
$267$			3.63119i			0.222226i
$268$	−1.99365	−	0.159188i	−0.121782	−	0.00972397i
$269$			2.47425i			0.150858i	0.997151	+	0.0754288i	$0.0240326\pi$
$269$			2.47425i			0.150858i	−0.997151	+	0.0754288i	$0.975967\pi$
$270$	−7.93402	−	8.59278i	−0.482849	−	0.522940i
$271$	−18.7829			−1.14098			−0.570490	−	0.821304i	$-0.693247\pi$
$271$	−18.7829			−1.14098			−0.570490	+	0.821304i	$0.693247\pi$
$272$	4.49083	+	0.721764i	0.272297	+	0.0437634i
$273$	5.05661			0.306040
$274$	14.3185	+	15.5074i	0.865015	+	0.936837i
$275$		−	18.5215i		−	1.11689i
$276$	35.4305	+	2.82903i	2.13266	+	0.170288i
$277$		−	16.2014i		−	0.973446i	−0.873556	−	0.486723i	$-0.838192\pi$
$277$		−	16.2014i		−	0.973446i	0.873556	−	0.486723i	$-0.161808\pi$
$278$	1.13680	−	1.04965i	0.0681808	−	0.0629537i
$279$	−27.4903			−1.64580
$280$	3.12854	+	3.98250i	0.186966	+	0.238000i
$281$	26.2132			1.56375			0.781875	−	0.623435i	$-0.214263\pi$
$281$	26.2132			1.56375			0.781875	+	0.623435i	$0.214263\pi$
$282$	−18.5804	+	17.1560i	−1.10645	+	1.02162i
$283$			22.4237i			1.33295i	0.745526	+	0.666477i	$0.232198\pi$
$283$			22.4237i			1.33295i	−0.745526	+	0.666477i	$0.767802\pi$
$284$	−2.21212	+	27.7044i	−0.131265	+	1.64395i
$285$			8.56985i			0.507634i
$286$	−6.56111	−	7.10588i	−0.387967	−	0.420180i
$287$	−1.18748			−0.0700945
$288$	−11.7877	−	17.7507i	−0.694595	−	1.04597i
$289$	−15.7070			−0.923939
$290$	−34.7689	−	37.6557i	−2.04170	−	2.21122i
$291$		−	14.0694i		−	0.824762i
$292$	1.16864	−	14.6359i	0.0683893	−	0.856500i
$293$		−	11.0180i		−	0.643680i	−0.946794	−	0.321840i	$-0.895699\pi$
$293$		−	11.0180i		−	0.643680i	0.946794	−	0.321840i	$-0.104301\pi$
$294$	18.4158	−	17.0040i	1.07403	−	0.991693i
$295$	21.0388			1.22493
$296$	−9.17600	−	11.6807i	−0.533344	−	0.678925i
$297$	−3.03053			−0.175849
$298$	−22.1282	+	20.4317i	−1.28185	+	1.18358i
$299$		−	30.7514i		−	1.77840i
$300$	−63.2206	−	5.04801i	−3.65005	−	0.291447i
$301$			0.621451i			0.0358199i
$302$	16.6917	+	18.0776i	0.960497	+	1.04025i
$303$	−40.4576			−2.32423
$304$	−0.504348	+	3.13806i	−0.0289263	+	0.179980i
$305$	40.0871			2.29538
$306$	−4.10927	−	4.45046i	−0.234911	−	0.254416i
$307$			15.5032i			0.884817i	0.896814	+	0.442408i	$0.145876\pi$
$307$			15.5032i			0.884817i	−0.896814	+	0.442408i	$0.854124\pi$
$308$	1.30812	+	0.104450i	0.0745370	+	0.00595159i
$309$			4.75478i			0.270490i
$310$	−31.4401	+	29.0297i	−1.78568	+	1.64878i
$311$	27.2734			1.54653			0.773266	−	0.634082i	$-0.218622\pi$
$311$	27.2734			1.54653			0.773266	+	0.634082i	$0.218622\pi$
$312$	−26.0432	+	20.4588i	−1.47441	+	1.15825i
$313$	−17.8235			−1.00745			−0.503723	−	0.863865i	$-0.668037\pi$
$313$	−17.8235			−1.00745			−0.503723	+	0.863865i	$0.668037\pi$
$314$	−5.83309	+	5.38590i	−0.329180	+	0.303944i
$315$		−	6.74453i		−	0.380011i
$316$	1.75061	−	21.9245i	0.0984797	−	1.23335i
$317$			24.5878i			1.38099i	0.723338	+	0.690494i	$0.242607\pi$
$317$			24.5878i			1.38099i	−0.723338	+	0.690494i	$0.757393\pi$
$318$	−10.6504	−	11.5347i	−0.597244	−	0.646833i
$319$	−13.2805			−0.743568
$320$	−32.2259	−	7.85328i	−1.80149	−	0.439012i
$321$	−18.4977			−1.03244
$322$	2.83051	+	3.06553i	0.157738	+	0.170835i
$323$			0.903533i			0.0502739i
$324$	0.972914	−	12.1847i	0.0540508	−	0.676926i
$325$			54.8716i			3.04373i
$326$	19.0498	−	17.5893i	1.05507	−	0.974182i
$327$	−46.5151			−2.57229
$328$	6.11589	−	4.80447i	0.337694	−	0.265282i
$329$	−2.96875			−0.163673
$330$	−17.0264	+	15.7211i	−0.937272	+	0.865416i
$331$		−	18.7305i		−	1.02952i	−0.857334	−	0.514761i	$-0.827881\pi$
$331$		−	18.7305i		−	1.02952i	0.857334	−	0.514761i	$-0.172119\pi$
$332$	12.6118	+	1.00702i	0.692163	+	0.0552674i
$333$			19.7817i			1.08403i
$334$	3.60335	+	3.90254i	0.197167	+	0.213537i
$335$	4.14613			0.226527
$336$	0.713051	−	4.43662i	0.0389001	−	0.242037i
$337$	17.0054			0.926343			0.463172	−	0.886269i	$-0.346711\pi$
$337$	17.0054			0.926343			0.463172	+	0.886269i	$0.346711\pi$
$338$	6.96596	+	7.54435i	0.378899	+	0.410359i
$339$		−	18.7795i		−	1.01996i
$340$	−9.39934	−	0.750513i	−0.509751	−	0.0407023i
$341$			11.0884i			0.600470i
$342$	3.10985	−	2.87144i	0.168162	−	0.155269i
$343$	5.96544			0.322104
$344$	−2.51436	−	3.20068i	−0.135565	−	0.172569i
$345$	−73.6835			−3.96698
$346$	−18.6895	+	17.2567i	−1.00476	+	0.927726i
$347$		−	2.70815i		−	0.145381i	−0.997355	−	0.0726905i	$-0.976841\pi$
$347$		−	2.70815i		−	0.145381i	0.997355	−	0.0726905i	$-0.0231585\pi$
$348$	−3.61959	+	45.3313i	−0.194030	+	2.43001i
$349$			26.3491i			1.41043i	0.708991	+	0.705217i	$0.249151\pi$
$349$			26.3491i			1.41043i	−0.708991	+	0.705217i	$0.750849\pi$
$350$	−5.05064	−	5.47000i	−0.269968	−	0.292384i
$351$	8.97821			0.479222
$352$	−7.15983	+	4.75463i	−0.381620	+	0.253422i
$353$	8.87565			0.472403			0.236202	−	0.971704i	$-0.424097\pi$
$353$	8.87565			0.472403			0.236202	+	0.971704i	$0.424097\pi$
$354$	−12.6636	−	13.7151i	−0.673065	−	0.728949i
$355$		−	57.6157i		−	3.05793i
$356$	0.222213	−	2.78297i	0.0117773	−	0.147497i
$357$		−	1.27742i		−	0.0676084i
$358$	22.8416	−	21.0905i	1.20722	−	1.11467i
$359$	28.9353			1.52715			0.763573	−	0.645722i	$-0.223443\pi$
$359$	28.9353			1.52715			0.763573	+	0.645722i	$0.223443\pi$
$360$	27.2880	+	34.7365i	1.43820	+	1.83078i
$361$	18.3686			0.966770
$362$	17.5303	−	16.1863i	0.921370	−	0.850733i
$363$		−	22.6094i		−	1.18669i
$364$	−3.87542	−	0.309442i	−0.203127	−	0.0162192i
$365$			30.4377i			1.59318i
$366$	−24.1292	−	26.1326i	−1.26125	−	1.36597i
$367$	6.21853			0.324605			0.162302	−	0.986741i	$-0.448108\pi$
$367$	6.21853			0.324605			0.162302	+	0.986741i	$0.448108\pi$
$368$	−26.9810	−	4.33637i	−1.40648	−	0.226049i
$369$	−10.3575			−0.539191
$370$	20.8894	+	22.6239i	1.08599	+	1.17616i
$371$		−	1.84299i		−	0.0956834i
$372$	37.8487	+	3.02212i	1.96236	+	0.156690i
$373$		−	29.0820i		−	1.50581i	−0.658130	−	0.752904i	$-0.728652\pi$
$373$		−	29.0820i		−	1.50581i	0.658130	−	0.752904i	$-0.271348\pi$
$374$	−1.79512	+	1.65750i	−0.0928233	+	0.0857071i
$375$	77.5510			4.00471
$376$	15.2900	−	12.0114i	0.788524	−	0.619441i
$377$	39.3448			2.02636
$378$	−0.895013	+	0.826397i	−0.0460345	+	0.0425053i
$379$		−	8.43648i		−	0.433353i	−0.976243	−	0.216676i	$-0.930478\pi$
$379$		−	8.43648i		−	0.433353i	0.976243	−	0.216676i	$-0.0695216\pi$
$380$	0.524437	−	6.56799i	0.0269031	−	0.336931i
$381$			41.6949i			2.13610i
$382$	−16.8187	−	18.2151i	−0.860517	−	0.931966i
$383$	37.1670			1.89915			0.949573	−	0.313546i	$-0.101517\pi$
$383$	37.1670			1.89915			0.949573	+	0.313546i	$0.101517\pi$
$384$	14.2779	+	25.7350i	0.728615	+	1.31328i
$385$	−2.72045			−0.138647
$386$	−16.5103	−	17.8812i	−0.840354	−	0.910129i
$387$			5.42049i			0.275539i
$388$	−0.860984	+	10.7829i	−0.0437098	+	0.547417i
$389$		−	5.64588i		−	0.286257i	−0.989704	−	0.143129i	$-0.954284\pi$
$389$		−	5.64588i		−	0.286257i	0.989704	−	0.143129i	$-0.0457163\pi$
$390$	50.4422	−	46.5750i	2.55424	−	2.35842i
$391$	−7.76856			−0.392873
$392$	−15.1546	+	11.9050i	−0.765422	+	0.601293i
$393$	−22.8409			−1.15217
$394$	9.58597	−	8.85107i	0.482934	−	0.445910i
$395$			45.5955i			2.29416i
$396$	11.4098	+	0.911043i	0.573364	+	0.0457816i
$397$		−	25.8070i		−	1.29522i	−0.761973	−	0.647608i	$-0.775769\pi$
$397$		−	25.8070i		−	1.29522i	0.761973	−	0.647608i	$-0.224231\pi$
$398$	−19.1208	−	20.7084i	−0.958439	−	1.03802i
$399$	0.892626			0.0446872
$400$	48.1438	+	7.73765i	2.40719	+	0.386882i
$401$	−13.9211			−0.695188			−0.347594	−	0.937645i	$-0.613001\pi$
$401$	−13.9211			−0.695188			−0.347594	+	0.937645i	$0.613001\pi$
$402$	−2.49563	−	2.70285i	−0.124471	−	0.134806i
$403$		−	32.8503i		−	1.63639i
$404$	31.0069	+	2.47582i	1.54265	+	0.123177i
$405$			25.3400i			1.25915i
$406$	−3.92217	+	3.62148i	−0.194654	+	0.179731i
$407$	7.97907			0.395508
$408$	5.16838	+	6.57914i	0.255873	+	0.325716i
$409$	6.37706			0.315325			0.157663	−	0.987493i	$-0.449604\pi$
$409$	6.37706			0.315325			0.157663	+	0.987493i	$0.449604\pi$
$410$	−11.8457	+	10.9375i	−0.585016	+	0.540166i
$411$			38.8240i			1.91505i
$412$	0.290971	−	3.64409i	0.0143351	−	0.179531i
$413$		−	2.19137i		−	0.107831i
$414$	24.6886	+	26.7384i	1.21338	+	1.31412i
$415$	−26.2283			−1.28750
$416$	21.2116	−	14.0860i	1.03999	−	0.690623i
$417$	2.84607			0.139373
$418$	−1.15821	−	1.25438i	−0.0566499	−	0.0613536i
$419$			27.3135i			1.33435i	0.744900	+	0.667176i	$0.232497\pi$
$419$			27.3135i			1.33435i	−0.744900	+	0.667176i	$0.767503\pi$
$420$	−0.741453	+	9.28588i	−0.0361792	+	0.453104i
$421$		−	2.35367i		−	0.114711i	−0.998354	−	0.0573555i	$-0.981733\pi$
$421$		−	2.35367i		−	0.114711i	0.998354	−	0.0573555i	$-0.0182668\pi$
$422$	2.64712	−	2.44418i	0.128860	−	0.118981i
$423$	−25.8943			−1.25903
$424$	7.45664	+	9.49201i	0.362127	+	0.460973i
$425$	13.8619			0.672401
$426$	−37.5595	+	34.6800i	−1.81976	+	1.68025i
$427$		−	4.17543i		−	0.202063i
$428$	14.1768	+	1.13198i	0.685260	+	0.0547162i
$429$		−	17.7901i		−	0.858915i
$430$	5.72402	+	6.19928i	0.276037	+	0.298956i
$431$	4.45091			0.214393			0.107197	−	0.994238i	$-0.465813\pi$
$431$	4.45091			0.214393			0.107197	+	0.994238i	$0.465813\pi$
$432$	1.26605	−	7.87739i	0.0609129	−	0.379001i
$433$	32.4211			1.55806			0.779030	−	0.626987i	$-0.215712\pi$
$433$	32.4211			1.55806			0.779030	+	0.626987i	$0.215712\pi$
$434$	3.02370	+	3.27476i	0.145142	+	0.157193i
$435$		−	94.2739i		−	4.52009i
$436$	35.6495	+	2.84652i	1.70730	+	0.136323i
$437$		−	5.42844i		−	0.259678i
$438$	19.8422	−	18.3210i	0.948098	−	0.875412i
$439$	19.9977			0.954439			0.477220	−	0.878784i	$-0.341645\pi$
$439$	19.9977			0.954439			0.477220	+	0.878784i	$0.341645\pi$
$440$	14.0112	−	11.0068i	0.667957	−	0.524728i
$441$	25.6649			1.22214
$442$	5.31820	−	4.91048i	0.252961	−	0.233568i
$443$			2.04261i			0.0970475i	0.998822	+	0.0485237i	$0.0154517\pi$
$443$			2.04261i			0.0970475i	−0.998822	+	0.0485237i	$0.984548\pi$
$444$	2.17468	−	27.2355i	0.103206	−	1.29254i
$445$			5.78764i			0.274361i
$446$	−6.57292	−	7.11867i	−0.311237	−	0.337079i
$447$	−55.3996			−2.62031
$448$	−0.817988	+	3.35662i	−0.0386463	+	0.158585i
$449$	−8.15523			−0.384869			−0.192435	−	0.981310i	$-0.561638\pi$
$449$	−8.15523			−0.384869			−0.192435	+	0.981310i	$0.561638\pi$
$450$	−44.0532	−	47.7110i	−2.07669	−	2.24912i
$451$			4.17777i			0.196723i
$452$	−1.14922	+	14.3927i	−0.0540549	+	0.676978i
$453$			45.2586i			2.12643i
$454$	14.4376	−	13.3307i	0.677590	−	0.625643i
$455$	8.05956			0.377838
$456$	−4.59731	+	3.61151i	−0.215289	+	0.169125i
$457$	−10.3929			−0.486160			−0.243080	−	0.970006i	$-0.578158\pi$
$457$	−10.3929			−0.486160			−0.243080	+	0.970006i	$0.578158\pi$
$458$	−3.46685	+	3.20106i	−0.161995	+	0.149576i
$459$		−	2.26811i		−	0.105866i
$460$	56.4715	+	4.50910i	2.63300	+	0.210238i
$461$			13.5700i			0.632019i	0.948756	+	0.316010i	$0.102343\pi$
$461$			13.5700i			0.632019i	−0.948756	+	0.316010i	$0.897657\pi$
$462$	1.63749	+	1.77345i	0.0761828	+	0.0825082i
$463$	18.0351			0.838163			0.419082	−	0.907949i	$-0.362352\pi$
$463$	18.0351			0.838163			0.419082	+	0.907949i	$0.362352\pi$
$464$	5.54815	−	34.5207i	0.257567	−	1.60258i
$465$	−78.7126			−3.65021
$466$	2.15569	+	2.33468i	0.0998604	+	0.108152i
$467$			6.53721i			0.302506i	0.988495	+	0.151253i	$0.0483308\pi$
$467$			6.53721i			0.302506i	−0.988495	+	0.151253i	$0.951669\pi$
$468$	−33.8026	−	2.69905i	−1.56252	−	0.124763i
$469$		−	0.431856i		−	0.0199413i
$470$	−29.6148	+	27.3444i	−1.36603	+	1.26130i
$471$	−14.6036			−0.672897
$472$	8.86618	+	11.2863i	0.408099	+	0.519494i
$473$	2.18638			0.100530
$474$	29.7235	−	27.4448i	1.36525	−	1.26058i
$475$			9.68629i			0.444437i
$476$	−0.0781726	+	0.979024i	−0.00358303	+	0.0448735i
$477$		−	16.0751i		−	0.736029i
$478$	11.0855	+	12.0059i	0.507038	+	0.549137i
$479$	25.3964			1.16039			0.580196	−	0.814477i	$-0.302976\pi$
$479$	25.3964			1.16039			0.580196	+	0.814477i	$0.302976\pi$
$480$	−33.7514	−	50.8252i	−1.54053	−	2.31984i
$481$	−23.6387			−1.07783
$482$	8.96078	+	9.70479i	0.408152	+	0.442041i
$483$			7.67478i			0.349215i
$484$	−1.38360	+	17.3280i	−0.0628907	+	0.787636i
$485$		−	22.4247i		−	1.01825i
$486$	22.7365	−	20.9934i	1.03135	−	0.952280i
$487$	−39.3908			−1.78497			−0.892485	−	0.451078i	$-0.851040\pi$
$487$	−39.3908			−1.78497			−0.892485	+	0.451078i	$0.851040\pi$
$488$	16.8936	+	21.5048i	0.764735	+	0.973477i
$489$	47.6925			2.15673
$490$	29.3524	−	27.1021i	1.32601	−	1.22435i
$491$		−	30.9566i		−	1.39705i	−0.715585	−	0.698525i	$-0.753840\pi$
$491$		−	30.9566i		−	1.39705i	0.715585	−	0.698525i	$-0.246160\pi$
$492$	14.2602	+	1.13864i	0.642902	+	0.0513340i
$493$		−	9.93945i		−	0.447650i
$494$	3.43130	+	3.71620i	0.154381	+	0.167200i
$495$	−23.7285			−1.06652
$496$	−28.8225	−	4.63234i	−1.29417	−	0.207998i
$497$	−6.00119			−0.269190
$498$	15.7873	+	17.0981i	0.707446	+	0.766186i
$499$		−	4.33307i		−	0.193975i	−0.995286	−	0.0969874i	$-0.969079\pi$
$499$		−	4.33307i		−	0.193975i	0.995286	−	0.0969874i	$-0.0309207\pi$
$500$	−59.4355	−	4.74577i	−2.65804	−	0.212238i
$501$			9.77030i			0.436505i
$502$	−8.41430	+	7.76922i	−0.375548	+	0.346757i
$503$	−1.77626			−0.0791996			−0.0395998	−	0.999216i	$-0.512608\pi$
$503$	−1.77626			−0.0791996			−0.0395998	+	0.999216i	$0.512608\pi$
$504$	3.61812	−	2.84229i	0.161164	−	0.126606i
$505$	−64.4840			−2.86950
$506$	10.7851	−	9.95827i	0.479456	−	0.442699i
$507$			18.8879i			0.838839i
$508$	2.55154	−	31.9552i	0.113206	−	1.41778i
$509$		−	14.8803i		−	0.659558i	−0.944058	−	0.329779i	$-0.893026\pi$
$509$		−	14.8803i		−	0.659558i	0.944058	−	0.329779i	$-0.106974\pi$
$510$	−11.7660	−	12.7429i	−0.521006	−	0.564266i
$511$	3.17036			0.140248
$512$	−9.36778	−	20.5972i	−0.414001	−	0.910276i
$513$	1.58489			0.0699747
$514$	17.0778	+	18.4958i	0.753271	+	0.815815i
$515$			7.57848i			0.333948i
$516$	0.595895	−	7.46293i	0.0262328	−	0.328537i
$517$			10.4446i			0.459354i
$518$	2.35648	−	2.17582i	0.103538	−	0.0956000i
$519$	−46.7907			−2.05388
$520$	−41.5094	+	32.6086i	−1.82031	+	1.42998i
$521$	13.8852			0.608321			0.304161	−	0.952621i	$-0.401624\pi$
$521$	13.8852			0.608321			0.304161	+	0.952621i	$0.401624\pi$
$522$	−34.2104	+	31.5877i	−1.49735	+	1.38255i
$523$		−	25.8836i		−	1.13181i	−0.824470	−	0.565906i	$-0.808526\pi$
$523$		−	25.8836i		−	1.13181i	0.824470	−	0.565906i	$-0.191474\pi$
$524$	17.5054	+	1.39776i	0.764727	+	0.0610615i
$525$		−	13.6946i		−	0.597679i
$526$	−0.765045	−	0.828566i	−0.0333575	−	0.0361272i
$527$	−8.29879			−0.361501
$528$	−15.6089	−	2.50865i	−0.679289	−	0.109175i
$529$	23.6737			1.02929
$530$	−16.9753	−	18.3847i	−0.737359	−	0.798582i
$531$		−	19.1138i		−	0.829469i
$532$	−0.684114	−	0.0546247i	−0.0296601	−	0.00236828i
$533$		−	12.3770i		−	0.536108i
$534$	3.77294	−	3.48369i	0.163271	−	0.150754i
$535$	−29.4829			−1.27466
$536$	1.74727	+	2.22420i	0.0754704	+	0.0960708i
$537$	57.1857			2.46774
$538$	2.57083	−	2.37374i	0.110836	−	0.102339i
$539$		−	10.3521i		−	0.445897i
$540$	−1.31648	+	16.4874i	−0.0566523	+	0.709507i
$541$			12.3658i			0.531646i	0.964022	+	0.265823i	$0.0856437\pi$
$541$			12.3658i			0.531646i	−0.964022	+	0.265823i	$0.914356\pi$
$542$	18.0199	+	19.5161i	0.774021	+	0.838289i
$543$	43.8883			1.88343
$544$	−3.55847	−	5.35858i	−0.152568	−	0.229747i
$545$	−74.1389			−3.17576
$546$	−4.85120	−	5.25400i	−0.207612	−	0.224850i
$547$			7.48211i			0.319912i	0.987124	+	0.159956i	$0.0511352\pi$
$547$			7.48211i			0.319912i	−0.987124	+	0.159956i	$0.948865\pi$
$548$	2.37586	−	29.7549i	0.101492	−	1.27107i
$549$		−	36.4193i		−	1.55434i
$550$	−19.2445	+	17.7691i	−0.820588	+	0.757678i
$551$	6.94540			0.295884
$552$	−31.0517	−	39.5276i	−1.32165	−	1.68241i
$553$	4.74918			0.201956
$554$	−16.8338	+	15.5432i	−0.715199	+	0.660369i
$555$			56.6406i			2.40426i
$556$	−2.18124	−	0.174167i	−0.0925054	−	0.00738631i
$557$			38.5620i			1.63392i	0.576691	+	0.816962i	$0.304344\pi$
$557$			38.5620i			1.63392i	−0.576691	+	0.816962i	$0.695656\pi$
$558$	26.3736	+	28.5634i	1.11648	+	1.20919i
$559$	−6.47736			−0.273963
$560$	1.13651	−	7.07138i	0.0480263	−	0.298820i
$561$	−4.49421			−0.189746
$562$	−25.1484	−	27.2365i	−1.06082	−	1.14890i
$563$			16.3138i			0.687547i	0.939053	+	0.343773i	$0.111705\pi$
$563$			16.3138i			0.687547i	−0.939053	+	0.343773i	$0.888295\pi$
$564$	35.6513	+	2.84667i	1.50119	+	0.119866i
$565$		−	29.9321i		−	1.25925i
$566$	23.2991	−	21.5128i	0.979333	−	0.904252i
$567$	2.63938			0.110844
$568$	30.9081	−	24.2805i	1.29687	−	1.01879i
$569$	7.11115			0.298115			0.149057	−	0.988829i	$-0.452376\pi$
$569$	7.11115			0.298115			0.149057	+	0.988829i	$0.452376\pi$
$570$	8.90438	−	8.22173i	0.372963	−	0.344370i
$571$		−	19.7271i		−	0.825555i	−0.910832	−	0.412777i	$-0.864559\pi$
$571$		−	19.7271i		−	0.825555i	0.910832	−	0.412777i	$-0.135441\pi$
$572$	−1.08868	+	13.6345i	−0.0455198	+	0.570085i
$573$		−	45.6029i		−	1.90509i
$574$	1.13924	+	1.23383i	0.0475509	+	0.0514991i
$575$	−83.2826			−3.47312
$576$	−7.13474	+	29.2774i	−0.297281	+	1.21989i
$577$	29.3333			1.22116			0.610581	−	0.791954i	$-0.290936\pi$
$577$	29.3333			1.22116			0.610581	+	0.791954i	$0.290936\pi$
$578$	15.0689	+	16.3201i	0.626784	+	0.678826i
$579$		−	44.7669i		−	1.86045i
$580$	−5.76915	+	72.2521i	−0.239551	+	3.00011i
$581$			2.73191i			0.113339i
$582$	−14.6186	+	13.4979i	−0.605960	+	0.559504i
$583$	−6.48399			−0.268540
$584$	−16.3284	+	12.8271i	−0.675672	+	0.530789i
$585$	70.2979			2.90646
$586$	−11.4481	+	10.5705i	−0.472917	+	0.436661i
$587$		−	14.6822i		−	0.605999i	−0.952991	−	0.303000i	$-0.902012\pi$
$587$		−	14.6822i		−	0.605999i	0.952991	−	0.303000i	$-0.0979881\pi$
$588$	−35.3355	−	2.82145i	−1.45721	−	0.116355i
$589$		−	5.79895i		−	0.238942i
$590$	−20.1841	−	21.8600i	−0.830968	−	0.899964i
$591$	23.9992			0.987196
$592$	−3.33338	+	20.7404i	−0.137001	+	0.852424i
$593$	−13.8724			−0.569670			−0.284835	−	0.958577i	$-0.591939\pi$
$593$	−13.8724			−0.569670			−0.284835	+	0.958577i	$0.591939\pi$
$594$	2.90742	+	3.14883i	0.119293	+	0.129198i
$595$		−	2.03604i		−	0.0834695i
$596$	42.4586	+	3.39021i	1.73917	+	0.138868i
$597$		−	51.8450i		−	2.12188i
$598$	−31.9518	+	29.5023i	−1.30661	+	1.20644i
$599$	−1.99508			−0.0815166			−0.0407583	−	0.999169i	$-0.512977\pi$
$599$	−1.99508			−0.0815166			−0.0407583	+	0.999169i	$0.512977\pi$
$600$	55.4074	+	70.5314i	2.26200	+	2.87943i
$601$	−29.5830			−1.20672			−0.603358	−	0.797470i	$-0.706171\pi$
$601$	−29.5830			−1.20672			−0.603358	+	0.797470i	$0.706171\pi$
$602$	0.645710	−	0.596207i	0.0263172	−	0.0242996i
$603$		−	3.76678i		−	0.153395i
$604$	2.76962	−	34.6864i	0.112694	−	1.41137i
$605$		−	36.0364i		−	1.46509i
$606$	38.8141	+	42.0368i	1.57671	+	1.70763i
$607$	15.0777			0.611984			0.305992	−	0.952034i	$-0.401012\pi$
$607$	15.0777			0.611984			0.305992	+	0.952034i	$0.401012\pi$
$608$	3.74442	−	2.48655i	0.151856	−	0.100843i
$609$	−9.81946			−0.397905
$610$	−38.4587	−	41.6520i	−1.55715	−	1.68644i
$611$		−	30.9432i		−	1.25183i
$612$	−0.681845	+	8.53934i	−0.0275619	+	0.345182i
$613$		−	0.902610i		−	0.0364561i	−0.999834	−	0.0182280i	$-0.994198\pi$
$613$		−	0.902610i		−	0.0364561i	0.999834	−	0.0182280i	$-0.00580249\pi$
$614$	16.1084	−	14.8735i	0.650083	−	0.600244i
$615$	−29.6565			−1.19587
$616$	−1.14645	−	1.45939i	−0.0461919	−	0.0588004i
$617$	32.5165			1.30906			0.654532	−	0.756034i	$-0.272866\pi$
$617$	32.5165			1.30906			0.654532	+	0.756034i	$0.272866\pi$
$618$	4.94038	−	4.56163i	0.198731	−	0.183496i
$619$		−	24.3110i		−	0.977143i	−0.872524	−	0.488572i	$-0.837518\pi$
$619$		−	24.3110i		−	0.977143i	0.872524	−	0.488572i	$-0.162482\pi$
$620$	60.3258	+	4.81686i	2.42274	+	0.193450i
$621$			13.6269i			0.546828i
$622$	−26.1655	−	28.3380i	−1.04914	−	1.13625i
$623$	0.602834			0.0241520
$624$	46.2426	+	7.43210i	1.85119	+	0.297522i
$625$	62.6539			2.50616
$626$	17.0995	+	18.5193i	0.683434	+	0.740179i
$627$		−	3.14043i		−	0.125417i
$628$	11.1923	+	0.893674i	0.446620	+	0.0356615i
$629$			5.97171i			0.238108i
$630$	−7.00781	+	6.47056i	−0.279198	+	0.257793i
$631$	−0.184252			−0.00733496			−0.00366748	−	0.999993i	$-0.501167\pi$
$631$	−0.184252			−0.00733496			−0.00366748	+	0.999993i	$0.501167\pi$
$632$	−24.4598	+	19.2149i	−0.972959	+	0.764328i
$633$	6.62727			0.263410
$634$	25.5476	−	23.5890i	1.01462	−	0.936839i
$635$			66.4562i			2.63723i
$636$	−1.76720	+	22.1322i	−0.0700741	+	0.877600i
$637$			30.6690i			1.21515i
$638$	12.7411	+	13.7990i	0.504423	+	0.546306i
$639$	−52.3441			−2.07070
$640$	22.7570	+	41.0182i	0.899550	+	1.62139i
$641$	−16.4283			−0.648879			−0.324440	−	0.945906i	$-0.605176\pi$
$641$	−16.4283			−0.648879			−0.324440	+	0.945906i	$0.605176\pi$
$642$	17.7463	+	19.2198i	0.700391	+	0.758544i
$643$			32.8581i			1.29580i	0.761727	+	0.647898i	$0.224352\pi$
$643$			32.8581i			1.29580i	−0.761727	+	0.647898i	$0.775648\pi$
$644$	0.469662	−	5.88200i	0.0185073	−	0.231783i
$645$			15.5204i			0.611114i
$646$	0.938802	−	0.866829i	0.0369367	−	0.0341049i
$647$	−8.43010			−0.331421			−0.165711	−	0.986174i	$-0.552992\pi$
$647$	−8.43010			−0.331421			−0.165711	+	0.986174i	$0.552992\pi$
$648$	−13.5937	+	10.6788i	−0.534010	+	0.419503i
$649$	−7.70967			−0.302631
$650$	57.0135	−	52.6426i	2.23625	−	2.06481i
$651$			8.19861i			0.321329i
$652$	−36.5518	−	2.91857i	−1.43148	−	0.114300i
$653$		−	47.6601i		−	1.86509i	−0.361059	−	0.932543i	$-0.617585\pi$
$653$		−	47.6601i		−	1.86509i	0.361059	−	0.932543i	$-0.382415\pi$
$654$	44.6256	+	48.3308i	1.74500	+	1.88989i
$655$	−36.4054			−1.42248
$656$	−10.8595	−	1.74533i	−0.423991	−	0.0681436i
$657$	27.6528			1.07884
$658$	2.84816	+	3.08464i	0.111033	+	0.120252i
$659$			38.3582i			1.49423i	0.664698	+	0.747113i	$0.268560\pi$
$659$			38.3582i			1.49423i	−0.664698	+	0.747113i	$0.731440\pi$
$660$	32.6695	+	2.60857i	1.27166	+	0.101539i
$661$			41.0827i			1.59793i	0.601377	+	0.798965i	$0.294619\pi$
$661$			41.0827i			1.59793i	−0.601377	+	0.798965i	$0.705381\pi$
$662$	−19.4617	+	17.9696i	−0.756399	+	0.698410i
$663$	13.3145			0.517093
$664$	−11.0532	−	14.0702i	−0.428946	−	0.546031i
$665$	1.42273			0.0551710
$666$	20.5539	−	18.9782i	0.796448	−	0.735388i
$667$			59.7164i			2.31223i
$668$	0.597899	−	7.48802i	0.0231334	−	0.289720i
$669$		−	17.8221i		−	0.689043i
$670$	−3.97771	−	4.30798i	−0.153672	−	0.166432i
$671$	−14.6899			−0.567099
$672$	−5.29389	+	3.51551i	−0.204216	+	0.135614i
$673$	−2.68075			−0.103335			−0.0516676	−	0.998664i	$-0.516454\pi$
$673$	−2.68075			−0.103335			−0.0516676	+	0.998664i	$0.516454\pi$
$674$	−16.3146	−	17.6692i	−0.628415	−	0.680593i
$675$		−	24.3152i		−	0.935894i
$676$	1.15585	−	14.4758i	0.0444559	−	0.556760i
$677$			17.1153i			0.657795i	0.944366	+	0.328897i	$0.106677\pi$
$677$			17.1153i			0.657795i	−0.944366	+	0.328897i	$0.893323\pi$
$678$	−19.5126	+	18.0167i	−0.749376	+	0.691925i
$679$	−2.33573			−0.0896372
$680$	8.23771	+	10.4863i	0.315902	+	0.402130i
$681$	36.1456			1.38510
$682$	11.5212	−	10.6379i	0.441170	−	0.407348i
$683$		−	11.3818i		−	0.435514i	−0.976003	−	0.217757i	$-0.930126\pi$
$683$		−	11.3818i		−	0.435514i	0.976003	−	0.217757i	$-0.0698741\pi$
$684$	−5.96705	−	0.476453i	−0.228156	−	0.0182176i
$685$			61.8803i			2.36432i
$686$	−5.72311	−	6.19831i	−0.218510	−	0.236652i
$687$	−8.67952			−0.331144
$688$	−0.913396	+	5.68317i	−0.0348229	+	0.216669i
$689$	19.2094			0.731820
$690$	70.6903	+	76.5597i	2.69113	+	2.91458i
$691$		−	16.6210i		−	0.632292i	−0.948711	−	0.316146i	$-0.897611\pi$
$691$		−	16.6210i		−	0.632292i	0.948711	−	0.316146i	$-0.102389\pi$
$692$	35.8607	+	2.86338i	1.36322	+	0.108849i
$693$			2.47154i			0.0938859i
$694$	−2.81386	+	2.59814i	−0.106813	+	0.0986240i
$695$	4.53625			0.172070
$696$	50.5734	−	39.7290i	1.91698	−	1.50592i
$697$	−3.12673			−0.118433
$698$	27.3776	−	25.2787i	1.03626	−	0.956814i
$699$			5.84504i			0.221080i
$700$	−0.838046	+	10.4956i	−0.0316752	+	0.396696i
$701$			6.56740i			0.248047i	0.992279	+	0.124024i	$0.0395798\pi$
$701$			6.56740i			0.248047i	−0.992279	+	0.124024i	$0.960420\pi$
$702$	−8.61350	−	9.32868i	−0.325096	−	0.352088i
$703$	−4.17286			−0.157382
$704$	11.8092	+	2.87784i	0.445076	+	0.108463i
$705$	−74.1428			−2.79238
$706$	−8.51510	−	9.22212i	−0.320470	−	0.347079i
$707$			6.71657i			0.252603i
$708$	−2.10126	+	26.3159i	−0.0789701	+	0.989013i
$709$			33.1187i			1.24380i	0.783096	+	0.621900i	$0.213639\pi$
$709$			33.1187i			1.24380i	−0.783096	+	0.621900i	$0.786361\pi$
$710$	−59.8648	+	55.2753i	−2.24669	+	2.07444i
$711$	41.4237			1.55351
$712$	−3.10479	+	2.43903i	−0.116357	+	0.0914066i
$713$	49.8593			1.86725
$714$	−1.32729	+	1.22553i	−0.0496725	+	0.0458643i
$715$		−	28.3551i		−	1.06042i
$716$	−43.8275	−	3.49951i	−1.63791	−	0.130783i
$717$			30.0577i			1.12252i
$718$	−27.7599	−	30.0648i	−1.03599	−	1.12201i
$719$	11.0687			0.412794			0.206397	−	0.978468i	$-0.433826\pi$
$719$	11.0687			0.412794			0.206397	+	0.978468i	$0.433826\pi$
$720$	9.91297	−	61.6787i	0.369435	−	2.29863i
$721$	0.789365			0.0293975
$722$	−17.6225	−	19.0857i	−0.655840	−	0.710295i
$723$			24.2967i			0.903603i
$724$	−33.6363	−	2.68577i	−1.25008	−	0.0998159i
$725$		−	106.555i		−	3.95737i
$726$	−23.4920	+	21.6910i	−0.871869	+	0.805027i
$727$	5.11409			0.189671			0.0948356	−	0.995493i	$-0.469767\pi$
$727$	5.11409			0.189671			0.0948356	+	0.995493i	$0.469767\pi$
$728$	3.39647	+	4.32357i	0.125881	+	0.160242i
$729$	38.5873			1.42916
$730$	31.6259	−	29.2013i	1.17053	−	1.08079i
$731$			1.63634i			0.0605221i
$732$	−4.00372	+	50.1422i	−0.147982	+	1.85331i
$733$			0.670723i			0.0247737i	0.999923	+	0.0123869i	$0.00394296\pi$
$733$			0.670723i			0.0247737i	−0.999923	+	0.0123869i	$0.996057\pi$
$734$	−5.96592	−	6.46127i	−0.220206	−	0.238490i
$735$	73.4859			2.71057
$736$	21.3793	+	32.1944i	0.788053	+	1.18670i
$737$	−1.51935			−0.0559660
$738$	9.93678	+	10.7618i	0.365778	+	0.396149i
$739$			46.7577i			1.72001i	0.510286	+	0.860005i	$0.329540\pi$
$739$			46.7577i			1.72001i	−0.510286	+	0.860005i	$0.670460\pi$
$740$	3.46616	−	43.4097i	0.127418	−	1.59577i
$741$			9.30379i			0.341783i
$742$	−1.91493	+	1.76813i	−0.0702994	+	0.0649099i
$743$	−20.6101			−0.756111			−0.378055	−	0.925783i	$-0.623407\pi$
$743$	−20.6101			−0.756111			−0.378055	+	0.925783i	$0.623407\pi$
$744$	−33.1711	−	42.2255i	−1.21611	−	1.54806i
$745$	−88.2996			−3.23505
$746$	−30.2172	+	27.9006i	−1.10633	+	1.02151i
$747$			23.8285i			0.871841i
$748$	3.44439	+	0.275026i	0.125939	+	0.0100559i
$749$			3.07090i			0.112208i
$750$	−74.4007	−	80.5782i	−2.71673	−	2.94230i
$751$	−27.5799			−1.00641			−0.503203	−	0.864168i	$-0.667845\pi$
$751$	−27.5799			−1.00641			−0.503203	+	0.864168i	$0.667845\pi$
$752$	−27.1492	−	4.36341i	−0.990030	−	0.159117i
$753$	−21.0658			−0.767681
$754$	−37.7465	−	40.8806i	−1.37465	−	1.48878i
$755$			72.1361i			2.62530i
$756$	1.71731	+	0.137123i	0.0624580	+	0.00498711i
$757$		−	10.5622i		−	0.383891i	−0.981406	−	0.191945i	$-0.938520\pi$
$757$		−	10.5622i		−	0.383891i	0.981406	−	0.191945i	$-0.0614796\pi$
$758$	−8.76580	+	8.09377i	−0.318388	+	0.293979i
$759$	27.0013			0.980086
$760$	−7.32750	+	5.75627i	−0.265797	+	0.208802i
$761$	0.988268			0.0358247			0.0179123	−	0.999840i	$-0.494298\pi$
$761$	0.988268			0.0358247			0.0179123	+	0.999840i	$0.494298\pi$
$762$	43.3225	−	40.0012i	1.56941	−	1.44909i
$763$			7.72222i			0.279563i
$764$	−2.79070	+	34.9504i	−0.100964	+	1.26446i
$765$		−	17.7590i		−	0.642077i
$766$	−35.6572	−	38.6178i	−1.28835	−	1.39532i
$767$	22.8406			0.824726
$768$	13.0417	−	39.5248i	0.470601	−	1.42623i
$769$	4.72856			0.170516			0.0852582	−	0.996359i	$-0.472829\pi$
$769$	4.72856			0.170516			0.0852582	+	0.996359i	$0.472829\pi$
$770$	2.60994	+	2.82664i	0.0940556	+	0.101865i
$771$			46.3056i			1.66766i
$772$	−2.73954	+	34.3097i	−0.0985981	+	1.23483i
$773$		−	27.7634i		−	0.998580i	−0.866435	−	0.499290i	$-0.833594\pi$
$773$		−	27.7634i		−	0.998580i	0.866435	−	0.499290i	$-0.166406\pi$
$774$	5.63208	−	5.20029i	0.202441	−	0.186921i
$775$	−88.9668			−3.19578
$776$	12.0298	−	9.45025i	0.431844	−	0.339244i
$777$	5.89962			0.211648
$778$	−5.86627	+	5.41653i	−0.210316	+	0.194192i
$779$		−	2.18487i		−	0.0782811i
$780$	−96.7862	−	7.72813i	−3.46550	−	0.276711i
$781$			21.1133i			0.755494i
$782$	7.45298	+	8.07181i	0.266518	+	0.288647i
$783$	−17.4348			−0.623070
$784$	26.9087	+	4.32475i	0.961024	+	0.154455i
$785$	−23.2762			−0.830762
$786$	21.9131	+	23.7325i	0.781613	+	0.846510i
$787$		−	44.0507i		−	1.57024i	−0.619346	−	0.785118i	$-0.712602\pi$
$787$		−	44.0507i		−	1.57024i	0.619346	−	0.785118i	$-0.287398\pi$
$788$	−18.3931	−	1.46865i	−0.655229	−	0.0523183i
$789$		−	2.07438i		−	0.0738498i
$790$	47.3754	−	43.7434i	1.68554	−	1.55632i
$791$	−3.11769			−0.110852
$792$	−9.99970	−	12.7292i	−0.355324	−	0.452313i
$793$	43.5203			1.54545
$794$	−26.8144	+	24.7587i	−0.951607	+	0.878652i
$795$		−	46.0276i		−	1.63243i
$796$	−3.17269	+	39.7343i	−0.112453	+	1.40835i
$797$		−	27.7931i		−	0.984483i	−0.870459	−	0.492242i	$-0.836178\pi$
$797$		−	27.7931i		−	0.984483i	0.870459	−	0.492242i	$-0.163822\pi$
$798$	−0.856365	−	0.927469i	−0.0303150	−	0.0328321i
$799$	−7.81699			−0.276545
$800$	−38.1484	−	57.4464i	−1.34875	−	2.03104i
$801$	5.25810			0.185786
$802$	13.3556	+	14.4645i	0.471604	+	0.510761i
$803$		−	11.1539i		−	0.393613i
$804$	−0.414097	+	5.18610i	−0.0146041	+	0.182900i
$805$			12.2326i			0.431142i
$806$	−34.1326	+	31.5159i	−1.20227	+	1.11010i
$807$	6.43627			0.226568
$808$	−27.1749	−	34.5925i	−0.956009	−	1.21696i
$809$	−13.3422			−0.469087			−0.234544	−	0.972106i	$-0.575360\pi$
$809$	−13.3422			−0.469087			−0.234544	+	0.972106i	$0.575360\pi$
$810$	26.3291	−	24.3106i	0.925112	−	0.854188i
$811$			39.5426i			1.38853i	0.719720	+	0.694264i	$0.244270\pi$
$811$			39.5426i			1.38853i	−0.719720	+	0.694264i	$0.755730\pi$
$812$	7.52569	+	0.600907i	0.264100	+	0.0210877i
$813$			48.8600i			1.71360i
$814$	−7.65495	−	8.29054i	−0.268306	−	0.290583i
$815$	76.0155			2.66271
$816$	1.87753	−	11.6820i	0.0657266	−	0.408952i
$817$	−1.14342			−0.0400034
$818$	−6.11801	−	6.62599i	−0.213911	−	0.231672i
$819$		−	7.32215i		−	0.255857i
$820$	22.7289	+	1.81485i	0.793729	+	0.0633772i
$821$			21.4697i			0.749298i	0.927167	+	0.374649i	$0.122237\pi$
$821$			21.4697i			0.749298i	−0.927167	+	0.374649i	$0.877763\pi$
$822$	40.3395	−	37.2469i	1.40700	−	1.29913i
$823$	6.56227			0.228746			0.114373	−	0.993438i	$-0.463514\pi$
$823$	6.56227			0.228746			0.114373	+	0.993438i	$0.463514\pi$
$824$	−4.06549	+	3.19373i	−0.141628	+	0.111259i
$825$	−48.1800			−1.67741
$826$	−2.27692	+	2.10236i	−0.0792240	+	0.0731503i
$827$			17.1223i			0.595400i	0.954659	+	0.297700i	$0.0962195\pi$
$827$			17.1223i			0.595400i	−0.954659	+	0.297700i	$0.903781\pi$
$828$	4.09654	−	51.3046i	0.142364	−	1.78296i
$829$		−	3.99266i		−	0.138671i	−0.997593	−	0.0693355i	$-0.977912\pi$
$829$		−	3.99266i		−	0.138671i	0.997593	−	0.0693355i	$-0.0220879\pi$
$830$	25.1629	+	27.2522i	0.873416	+	0.945936i
$831$	−42.1447			−1.46198
$832$	−34.9858	−	8.52585i	−1.21292	−	0.295581i
$833$	7.74774			0.268443
$834$	−2.73045	−	2.95716i	−0.0945479	−	0.102398i
$835$			15.5726i			0.538910i
$836$	−0.192180	+	2.40684i	−0.00664669	+	0.0832424i
$837$			14.5569i			0.503162i
$838$	28.3797	−	26.2040i	0.980361	−	0.905202i
$839$	−21.9508			−0.757825			−0.378912	−	0.925433i	$-0.623702\pi$
$839$	−21.9508			−0.757825			−0.378912	+	0.925433i	$0.623702\pi$
$840$	10.3597	−	8.13827i	0.357443	−	0.280797i
$841$	−47.4039			−1.63462
$842$	−2.44555	+	2.25806i	−0.0842791	+	0.0778179i
$843$		−	68.1885i		−	2.34854i
$844$	−5.07918	−	0.405559i	−0.174833	−	0.0139599i
$845$			30.1047i			1.03563i
$846$	24.8425	+	26.9051i	0.854101	+	0.925018i
$847$	−3.75351			−0.128972
$848$	2.70879	−	16.8541i	0.0930202	−	0.578773i
$849$	58.3310			2.00191
$850$	−13.2988	−	14.4030i	−0.456145	−	0.494019i
$851$		−	35.8782i		−	1.22989i
$852$	72.0674	+	5.75440i	2.46899	+	0.197142i
$853$		−	27.1188i		−	0.928530i	−0.885696	−	0.464265i	$-0.846318\pi$
$853$		−	27.1188i		−	0.928530i	0.885696	−	0.464265i	$-0.153682\pi$
$854$	−4.33842	+	4.00581i	−0.148458	+	0.137076i
$855$	12.4094			0.424394
$856$	−12.4247	−	15.8162i	−0.424668	−	0.540585i
$857$	7.17202			0.244992			0.122496	−	0.992469i	$-0.460910\pi$
$857$	7.17202			0.244992			0.122496	+	0.992469i	$0.460910\pi$
$858$	−18.4846	+	17.0674i	−0.631052	+	0.582673i
$859$			0.0816414i			0.00278557i	0.999999	+	0.00139278i	$0.000443337\pi$
$859$			0.0816414i			0.00278557i	−0.999999	+	0.00139278i	$0.999557\pi$
$860$	0.949778	−	11.8949i	0.0323872	−	0.405613i
$861$			3.08899i			0.105272i
$862$	−4.27011	−	4.62466i	−0.145440	−	0.157516i
$863$	−27.3311			−0.930363			−0.465181	−	0.885215i	$-0.654011\pi$
$863$	−27.3311			−0.930363			−0.465181	+	0.885215i	$0.654011\pi$
$864$	−9.39951	+	6.24192i	−0.319778	+	0.212355i
$865$	−74.5781			−2.53573
$866$	−31.1041	−	33.6867i	−1.05696	−	1.14472i
$867$			40.8586i			1.38763i
$868$	0.501718	−	6.28346i	0.0170294	−	0.213275i
$869$		−	16.7085i		−	0.566797i
$870$	−97.9539	+	90.4443i	−3.32095	+	3.06635i
$871$	4.50121			0.152518
$872$	−31.2437	−	39.7719i	−1.05804	−	1.34685i
$873$	−20.3730			−0.689520
$874$	−5.64035	+	5.20793i	−0.190788	+	0.176161i
$875$		−	12.8746i		−	0.435242i
$876$	−38.0724	−	3.03998i	−1.28635	−	0.102711i
$877$			39.9918i			1.35043i	0.737622	+	0.675214i	$0.235949\pi$
$877$			39.9918i			1.35043i	−0.737622	+	0.675214i	$0.764051\pi$
$878$	−19.1854	−	20.7783i	−0.647475	−	0.701235i
$879$	−28.6612			−0.966719
$880$	−24.8785	−	3.99845i	−0.838652	−	0.134788i
$881$	−23.2657			−0.783843			−0.391921	−	0.919999i	$-0.628189\pi$
$881$	−23.2657			−0.783843			−0.391921	+	0.919999i	$0.628189\pi$
$882$	−24.6224	−	26.6668i	−0.829079	−	0.897917i
$883$			21.7460i			0.731810i	0.930652	+	0.365905i	$0.119241\pi$
$883$			21.7460i			0.731810i	−0.930652	+	0.365905i	$0.880759\pi$
$884$	−10.2043	−	0.814789i	−0.343208	−	0.0274043i
$885$		−	54.7283i		−	1.83967i
$886$	2.12235	−	1.95964i	0.0713016	−	0.0658353i
$887$	−35.1934			−1.18168			−0.590839	−	0.806789i	$-0.701203\pi$
$887$	−35.1934			−1.18168			−0.590839	+	0.806789i	$0.701203\pi$
$888$	−30.3850	+	23.8695i	−1.01965	+	0.801010i
$889$	6.92199			0.232156
$890$	6.01356	−	5.55254i	0.201575	−	0.186121i
$891$		−	9.28585i		−	0.311088i
$892$	−1.09064	+	13.6590i	−0.0365172	+	0.457337i
$893$		−	5.46229i		−	0.182788i
$894$	53.1491	+	57.5621i	1.77757	+	1.92517i
$895$	91.1464			3.04669
$896$	4.27240	−	2.37034i	0.142731	−	0.0791877i
$897$	−79.9938			−2.67092
$898$	7.82395	+	8.47357i	0.261089	+	0.282767i
$899$			63.7922i			2.12759i
$900$	−7.30969	+	91.5457i	−0.243656	+	3.05152i
$901$		−	4.85276i		−	0.161669i
$902$	4.34085	−	4.00806i	0.144534	−	0.133454i
$903$	1.61658			0.0537965
$904$	16.0571	−	12.6140i	0.534051	−	0.419535i
$905$	69.9521			2.32529
$906$	47.0252	−	43.4201i	1.56231	−	1.44254i
$907$			26.3832i			0.876040i	0.898965	+	0.438020i	$0.144320\pi$
$907$			26.3832i			0.876040i	−0.898965	+	0.438020i	$0.855680\pi$
$908$	−27.7022	−	2.21195i	−0.919331	−	0.0734062i
$909$			58.5840i			1.94311i
$910$	−7.73217	−	8.37417i	−0.256319	−	0.277601i
$911$	43.9320			1.45553			0.727766	−	0.685826i	$-0.240559\pi$
$911$	43.9320			1.45553			0.727766	+	0.685826i	$0.240559\pi$
$912$	8.16305	+	1.31196i	0.270306	+	0.0434434i
$913$	9.61138			0.318090
$914$	9.97074	+	10.7986i	0.329803	+	0.357186i
$915$		−	104.279i		−	3.44735i
$916$	6.65204	+	0.531148i	0.219789	+	0.0175496i
$917$			3.79194i			0.125221i
$918$	−2.35665	+	2.17598i	−0.0777810	+	0.0718180i
$919$	−8.06700			−0.266106			−0.133053	−	0.991109i	$-0.542478\pi$
$919$	−8.06700			−0.266106			−0.133053	+	0.991109i	$0.542478\pi$
$920$	−49.4923	−	63.0018i	−1.63171	−	2.07711i
$921$	40.3286			1.32887
$922$	14.0997	−	13.0188i	0.464350	−	0.428751i
$923$		−	62.5501i		−	2.05886i
$924$	0.271706	−	3.40281i	0.00893847	−	0.111944i
$925$			64.0195i			2.10495i
$926$	−17.3025	−	18.7391i	−0.568595	−	0.615806i
$927$	6.88508			0.226136
$928$	−41.1910	+	27.3537i	−1.35216	+	0.897929i
$929$	40.6978			1.33525			0.667626	−	0.744496i	$-0.267310\pi$
$929$	40.6978			1.33525			0.667626	+	0.744496i	$0.267310\pi$
$930$	75.5151	+	81.7851i	2.47624	+	2.68184i
$931$			5.41389i			0.177433i
$932$	0.357690	−	4.47967i	0.0117165	−	0.146737i
$933$		−	70.9463i		−	2.32268i
$934$	6.79239	−	6.27165i	0.222254	−	0.205215i
$935$	−7.16318			−0.234261
$936$	29.6250	+	37.7114i	0.968324	+	1.23264i
$937$	19.7613			0.645573			0.322787	−	0.946472i	$-0.395380\pi$
$937$	19.7613			0.645573			0.322787	+	0.946472i	$0.395380\pi$
$938$	−0.448714	+	0.414313i	−0.0146510	+	0.0135278i
$939$			46.3644i			1.51305i
$940$	56.8235	+	4.53721i	1.85338	+	0.147987i
$941$			10.0358i			0.327159i	0.986530	+	0.163579i	$0.0523040\pi$
$941$			10.0358i			0.327159i	−0.986530	+	0.163579i	$0.947696\pi$
$942$	14.0103	+	15.1736i	0.456482	+	0.494384i
$943$	18.7855			0.611739
$944$	3.22084	−	20.0401i	0.104829	−	0.652250i
$945$	−3.57143			−0.116179
$946$	−2.09757	−	2.27173i	−0.0681978	−	0.0738603i
$947$		−	0.680236i		−	0.0221047i	−0.999939	−	0.0110523i	$-0.996482\pi$
$947$		−	0.680236i		−	0.0221047i	0.999939	−	0.0110523i	$-0.00351814\pi$
$948$	−57.0322	−	4.55388i	−1.85232	−	0.147903i
$949$			33.0444i			1.07267i
$950$	10.0644	−	9.29281i	0.326532	−	0.301499i
$951$	63.9603			2.07406
$952$	1.09224	−	0.858030i	0.0353996	−	0.0278089i
$953$	7.80830			0.252936			0.126468	−	0.991971i	$-0.459636\pi$
$953$	7.80830			0.252936			0.126468	+	0.991971i	$0.459636\pi$
$954$	−16.7026	+	15.4221i	−0.540767	+	0.499310i
$955$		−	72.6850i		−	2.35203i
$956$	1.83940	−	23.0364i	0.0594904	−	0.745050i
$957$			34.5467i			1.11674i
$958$	−24.3647	−	26.3878i	−0.787189	−	0.852550i
$959$	6.44537			0.208132
$960$	−20.4288	+	83.8295i	−0.659335	+	2.70558i
$961$	22.2623			0.718140
$962$	22.6785	+	24.5615i	0.731183	+	0.791893i
$963$			26.7853i			0.863145i
$964$	1.48685	−	18.6211i	0.0478882	−	0.599746i
$965$		−	71.3526i		−	2.29692i
$966$	7.97437	−	7.36301i	0.256571	−	0.236901i
$967$	33.8138			1.08738			0.543690	−	0.839286i	$-0.317027\pi$
$967$	33.8138			1.08738			0.543690	+	0.839286i	$0.317027\pi$
$968$	19.3318	−	15.1865i	0.621347	−	0.488112i
$969$	2.35036			0.0755045
$970$	−23.3001	+	21.5138i	−0.748121	+	0.690766i
$971$			51.8499i			1.66394i	0.554819	+	0.831971i	$0.312787\pi$
$971$			51.8499i			1.66394i	−0.554819	+	0.831971i	$0.687213\pi$
$972$	−43.6257	−	3.48340i	−1.39930	−	0.111730i
$973$		−	0.472491i		−	0.0151474i
$974$	37.7907	+	40.9285i	1.21089	+	1.31143i
$975$	142.738			4.57126
$976$	6.13695	−	38.1842i	0.196439	−	1.22225i
$977$	−26.5219			−0.848510			−0.424255	−	0.905543i	$-0.639464\pi$
$977$	−26.5219			−0.848510			−0.424255	+	0.905543i	$0.639464\pi$
$978$	−45.7551	−	49.5542i	−1.46309	−	1.58457i
$979$		−	2.12088i		−	0.0677837i
$980$	−56.3201	−	4.49701i	−1.79908	−	0.143652i
$981$			67.3555i			2.15050i
$982$	−32.1650	+	29.6991i	−1.02643	+	0.947735i
$983$	37.7149			1.20292			0.601459	−	0.798903i	$-0.294586\pi$
$983$	37.7149			1.20292			0.601459	+	0.798903i	$0.294586\pi$
$984$	−12.4979	−	15.9093i	−0.398418	−	0.507170i
$985$	38.2515			1.21880
$986$	−10.3274	+	9.53569i	−0.328893	+	0.303678i
$987$			7.72262i			0.245814i
$988$	0.569351	−	7.13048i	0.0181135	−	0.226851i
$989$		−	9.83115i		−	0.312612i
$990$	22.7646	+	24.6548i	0.723508	+	0.783581i
$991$	25.6131			0.813626			0.406813	−	0.913511i	$-0.366640\pi$
$991$	25.6131			0.813626			0.406813	+	0.913511i	$0.366640\pi$
$992$	22.8385	+	34.3918i	0.725124	+	1.09194i
$993$	−48.7237			−1.54620
$994$	5.75740	+	6.23544i	0.182614	+	0.197776i
$995$		−	82.6341i		−	2.61968i
$996$	2.61957	−	32.8071i	0.0830041	−	1.03953i
$997$		−	28.1066i		−	0.890145i	−0.895495	−	0.445072i	$-0.853178\pi$
$997$		−	28.1066i		−	0.890145i	0.895495	−	0.445072i	$-0.146822\pi$
$998$	−4.50221	+	4.15705i	−0.142515	+	0.131589i
$999$	10.4750			0.331415

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	536.2.c.a.269.17	✓	66
4.3	odd	2		2144.2.c.a.1073.57		66
8.3	odd	2		2144.2.c.a.1073.10		66
8.5	even	2	inner	536.2.c.a.269.18	yes	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
536.2.c.a.269.17	✓	66	1.1	even	1	trivial
536.2.c.a.269.18	yes	66	8.5	even	2	inner
2144.2.c.a.1073.10		66	8.3	odd	2
2144.2.c.a.1073.57		66	4.3	odd	2

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:	\( N \)	\(=\)	\( 536 = 2^{3} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	536.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.959378 - 1.03904i) q^{2} -2.60130i q^{3} +(-0.159188 + 1.99365i) q^{4} -4.14613i q^{5} +(-2.70285 + 2.49563i) q^{6} -0.431856 q^{7} +(2.22420 - 1.74727i) q^{8} -3.76678 q^{9} +O(q^{10})\)	\(q+(-0.959378 - 1.03904i) q^{2} -2.60130i q^{3} +(-0.159188 + 1.99365i) q^{4} -4.14613i q^{5} +(-2.70285 + 2.49563i) q^{6} -0.431856 q^{7} +(2.22420 - 1.74727i) q^{8} -3.76678 q^{9} +(-4.30798 + 3.97771i) q^{10} +1.51935i q^{11} +(5.18610 + 0.414097i) q^{12} -4.50121i q^{13} +(0.414313 + 0.448714i) q^{14} -10.7853 q^{15} +(-3.94932 - 0.634733i) q^{16} -1.13712 q^{17} +(3.61376 + 3.91381i) q^{18} -0.794583i q^{19} +(8.26595 + 0.660015i) q^{20} +1.12339i q^{21} +(1.57866 - 1.45763i) q^{22} +6.83181 q^{23} +(-4.54517 - 5.78582i) q^{24} -12.1904 q^{25} +(-4.67692 + 4.31836i) q^{26} +1.99462i q^{27} +(0.0687464 - 0.860972i) q^{28} +8.74093i q^{29} +(10.3472 + 11.2064i) q^{30} +7.29810 q^{31} +(3.12938 + 4.71243i) q^{32} +3.95229 q^{33} +(1.09092 + 1.18150i) q^{34} +1.79053i q^{35} +(0.599627 - 7.50965i) q^{36} -5.25163i q^{37} +(-0.825600 + 0.762306i) q^{38} -11.7090 q^{39} +(-7.24439 - 9.22182i) q^{40} +2.74971 q^{41} +(1.16724 - 1.07775i) q^{42} -1.43902i q^{43} +(-3.02906 - 0.241863i) q^{44} +15.6176i q^{45} +(-6.55429 - 7.09849i) q^{46} +6.87440 q^{47} +(-1.65113 + 10.2734i) q^{48} -6.81350 q^{49} +(11.6952 + 12.6663i) q^{50} +2.95798i q^{51} +(8.97386 + 0.716540i) q^{52} +4.26761i q^{53} +(2.07248 - 1.91359i) q^{54} +6.29943 q^{55} +(-0.960534 + 0.754567i) q^{56} -2.06695 q^{57} +(9.08213 - 8.38586i) q^{58} +5.07432i q^{59} +(1.71690 - 21.5023i) q^{60} +9.66857i q^{61} +(-7.00164 - 7.58299i) q^{62} +1.62671 q^{63} +(1.89412 - 7.77253i) q^{64} -18.6626 q^{65} +(-3.79174 - 4.10657i) q^{66} +1.00000i q^{67} +(0.181015 - 2.26702i) q^{68} -17.7716i q^{69} +(1.86043 - 1.71780i) q^{70} +13.8963 q^{71} +(-8.37806 + 6.58156i) q^{72} -7.34123 q^{73} +(-5.45663 + 5.03830i) q^{74} +31.7109i q^{75} +(1.58412 + 0.126488i) q^{76} -0.656141i q^{77} +(11.2334 + 12.1661i) q^{78} -10.9971 q^{79} +(-2.63168 + 16.3744i) q^{80} -6.11172 q^{81} +(-2.63801 - 2.85704i) q^{82} -6.32598i q^{83} +(-2.23965 - 0.178830i) q^{84} +4.71463i q^{85} +(-1.49520 + 1.38057i) q^{86} +22.7378 q^{87} +(2.65471 + 3.37934i) q^{88} -1.39591 q^{89} +(16.2272 - 14.9831i) q^{90} +1.94388i q^{91} +(-1.08754 + 13.6203i) q^{92} -18.9846i q^{93} +(-6.59515 - 7.14275i) q^{94} -3.29445 q^{95} +(12.2585 - 8.14046i) q^{96} +5.40859 q^{97} +(6.53672 + 7.07947i) q^{98} -5.72306i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 4 q^{4} + 2 q^{6} - 6 q^{8} - 66 q^{9}+O(q^{10}) \) 66 * q - 4 * q^4 + 2 * q^6 - 6 * q^8 - 66 * q^9	\( 66 q - 4 q^{4} + 2 q^{6} - 6 q^{8} - 66 q^{9} - 4 q^{10} + 4 q^{12} - 2 q^{14} + 8 q^{15} - 12 q^{16} - 4 q^{17} - 10 q^{18} + 22 q^{20} + 8 q^{22} - 12 q^{23} - 62 q^{25} - 24 q^{26} + 10 q^{28} + 22 q^{30} - 16 q^{31} + 10 q^{32} - 10 q^{34} + 2 q^{36} + 8 q^{38} + 8 q^{39} - 18 q^{40} + 4 q^{41} + 28 q^{42} + 34 q^{44} + 18 q^{46} + 20 q^{47} - 38 q^{48} + 66 q^{49} - 32 q^{50} - 6 q^{52} + 38 q^{54} + 16 q^{55} - 30 q^{56} + 2 q^{58} + 18 q^{60} + 22 q^{62} - 40 q^{63} + 26 q^{64} + 16 q^{65} - 34 q^{66} + 26 q^{68} - 18 q^{70} + 4 q^{71} - 2 q^{72} - 20 q^{73} - 4 q^{74} - 30 q^{76} - 36 q^{78} + 16 q^{79} - 32 q^{80} + 66 q^{81} + 16 q^{82} - 6 q^{84} + 2 q^{86} + 32 q^{87} + 22 q^{88} - 20 q^{89} - 18 q^{90} + 8 q^{92} - 16 q^{94} - 64 q^{96} + 12 q^{97} - 46 q^{98}+O(q^{100}) \) 66 * q - 4 * q^4 + 2 * q^6 - 6 * q^8 - 66 * q^9 - 4 * q^10 + 4 * q^12 - 2 * q^14 + 8 * q^15 - 12 * q^16 - 4 * q^17 - 10 * q^18 + 22 * q^20 + 8 * q^22 - 12 * q^23 - 62 * q^25 - 24 * q^26 + 10 * q^28 + 22 * q^30 - 16 * q^31 + 10 * q^32 - 10 * q^34 + 2 * q^36 + 8 * q^38 + 8 * q^39 - 18 * q^40 + 4 * q^41 + 28 * q^42 + 34 * q^44 + 18 * q^46 + 20 * q^47 - 38 * q^48 + 66 * q^49 - 32 * q^50 - 6 * q^52 + 38 * q^54 + 16 * q^55 - 30 * q^56 + 2 * q^58 + 18 * q^60 + 22 * q^62 - 40 * q^63 + 26 * q^64 + 16 * q^65 - 34 * q^66 + 26 * q^68 - 18 * q^70 + 4 * q^71 - 2 * q^72 - 20 * q^73 - 4 * q^74 - 30 * q^76 - 36 * q^78 + 16 * q^79 - 32 * q^80 + 66 * q^81 + 16 * q^82 - 6 * q^84 + 2 * q^86 + 32 * q^87 + 22 * q^88 - 20 * q^89 - 18 * q^90 + 8 * q^92 - 16 * q^94 - 64 * q^96 + 12 * q^97 - 46 * q^98

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