LMFDB - Embedded newform 756.2.bt.a.103.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(103,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 14, 15]))

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

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

chi := DirichletCharacter("756.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bt (of order $18$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$840$
Relative dimension:	$140$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			103.1
Character	$\chi$	$=$	756.103
Dual form			756.2.bt.a.367.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41414 + 0.0147396i) q^{2} +(-0.326297 + 1.70104i) q^{3} +(1.99957 - 0.0416875i) q^{4} +(-1.34679 - 0.237475i) q^{5} +(0.436356 - 2.41031i) q^{6} +(1.86287 + 1.87875i) q^{7} +(-2.82704 + 0.0884245i) q^{8} +(-2.78706 - 1.11009i) q^{9} +O(q^{10})$	\(q+(-1.41414 + 0.0147396i) q^{2} +(-0.326297 + 1.70104i) q^{3} +(1.99957 - 0.0416875i) q^{4} +(-1.34679 - 0.237475i) q^{5} +(0.436356 - 2.41031i) q^{6} +(1.86287 + 1.87875i) q^{7} +(-2.82704 + 0.0884245i) q^{8} +(-2.78706 - 1.11009i) q^{9} +(1.90804 + 0.315971i) q^{10} +(0.749254 - 0.132114i) q^{11} +(-0.581540 + 3.41494i) q^{12} +(1.15190 - 1.37278i) q^{13} +(-2.66205 - 2.62936i) q^{14} +(0.843407 - 2.21345i) q^{15} +(3.99652 - 0.166714i) q^{16} +7.50794i q^{17} +(3.95765 + 1.52873i) q^{18} +0.267621 q^{19} +(-2.70289 - 0.418703i) q^{20} +(-3.80368 + 2.55578i) q^{21} +(-1.05760 + 0.197870i) q^{22} +(-4.67111 + 5.56681i) q^{23} +(0.772042 - 4.83776i) q^{24} +(-2.94102 - 1.07044i) q^{25} +(-1.60870 + 1.95827i) q^{26} +(2.79771 - 4.37868i) q^{27} +(3.80325 + 3.67903i) q^{28} +(-0.0330684 + 0.0277477i) q^{29} +(-1.16007 + 3.14255i) q^{30} +(-0.0386472 + 0.0140664i) q^{31} +(-5.64917 + 0.294663i) q^{32} +(-0.0197488 + 1.31762i) q^{33} +(-0.110664 - 10.6173i) q^{34} +(-2.06274 - 2.97267i) q^{35} +(-5.61919 - 2.10351i) q^{36} +(0.617338 + 1.06926i) q^{37} +(-0.378453 + 0.00394461i) q^{38} +(1.95928 + 2.40735i) q^{39} +(3.82843 + 0.552264i) q^{40} +(6.61046 - 7.87804i) q^{41} +(5.34125 - 3.67029i) q^{42} +(-4.04604 + 11.1164i) q^{43} +(1.49267 - 0.295404i) q^{44} +(3.48996 + 2.15691i) q^{45} +(6.52354 - 7.94109i) q^{46} +(-6.25388 - 2.27623i) q^{47} +(-1.02047 + 6.85264i) q^{48} +(-0.0594252 + 6.99975i) q^{49} +(4.17478 + 1.47040i) q^{50} +(-12.7713 - 2.44982i) q^{51} +(2.24606 - 2.79297i) q^{52} +(-2.57294 - 4.45646i) q^{53} +(-3.89180 + 6.23329i) q^{54} -1.04046 q^{55} +(-5.43255 - 5.14659i) q^{56} +(-0.0873239 + 0.455234i) q^{57} +(0.0463543 - 0.0397264i) q^{58} +(-3.49575 - 2.93328i) q^{59} +(1.59417 - 4.46110i) q^{60} +(-1.44114 + 3.95949i) q^{61} +(0.0544451 - 0.0204615i) q^{62} +(-3.10636 - 7.30415i) q^{63} +(7.98436 - 0.499960i) q^{64} +(-1.87736 + 1.57529i) q^{65} +(0.00850638 - 1.86358i) q^{66} +(1.13608 + 0.200322i) q^{67} +(0.312987 + 15.0126i) q^{68} +(-7.94519 - 9.76217i) q^{69} +(2.96081 + 4.17335i) q^{70} +(-7.23371 - 4.17638i) q^{71} +(7.97730 + 2.89182i) q^{72} +(-13.3745 - 7.72174i) q^{73} +(-0.888761 - 1.50298i) q^{74} +(2.78051 - 4.65350i) q^{75} +(0.535126 - 0.0111564i) q^{76} +(1.64397 + 1.16155i) q^{77} +(-2.80618 - 3.37544i) q^{78} +(-12.7284 + 2.24436i) q^{79} +(-5.42206 - 0.724547i) q^{80} +(6.53542 + 6.18776i) q^{81} +(-9.23197 + 11.2381i) q^{82} +(-5.39667 + 4.52834i) q^{83} +(-7.49916 + 5.26902i) q^{84} +(1.78295 - 10.1116i) q^{85} +(5.55780 - 15.7797i) q^{86} +(-0.0364097 - 0.0653046i) q^{87} +(-2.10649 + 0.439744i) q^{88} +5.06260i q^{89} +(-4.96708 - 2.99872i) q^{90} +(4.72494 - 0.393176i) q^{91} +(-9.10813 + 11.3259i) q^{92} +(-0.0113171 - 0.0703301i) q^{93} +(8.87740 + 3.12672i) q^{94} +(-0.360429 - 0.0635533i) q^{95} +(1.34207 - 9.70561i) q^{96} +(-1.46164 + 4.01581i) q^{97} +(-0.0191378 - 9.89948i) q^{98} +(-2.23487 - 0.463528i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9}+O(q^{10}) $ 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9	$ 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9} - 9 q^{12} - 21 q^{14} - 3 q^{16} - 3 q^{18} - 12 q^{21} - 12 q^{22} - 9 q^{24} - 6 q^{25} - 18 q^{26} - 12 q^{28} - 36 q^{29} - 39 q^{30} + 27 q^{32} - 18 q^{33} + 18 q^{34} + 18 q^{36} + 6 q^{37} - 99 q^{38} + 36 q^{40} + 9 q^{42} + 3 q^{44} - 18 q^{45} + 3 q^{46} - 12 q^{49} + 3 q^{50} - 9 q^{52} - 12 q^{53} - 135 q^{54} + 15 q^{56} - 42 q^{57} - 3 q^{58} - 33 q^{60} - 18 q^{61} - 99 q^{62} - 6 q^{64} + 18 q^{65} - 9 q^{66} - 54 q^{68} + 72 q^{69} - 36 q^{70} - 111 q^{72} - 18 q^{73} + 93 q^{74} - 36 q^{76} - 36 q^{77} + 6 q^{78} - 18 q^{80} - 30 q^{81} - 18 q^{82} + 84 q^{84} + 6 q^{85} + 135 q^{86} - 51 q^{88} + 81 q^{90} + 48 q^{92} - 6 q^{93} - 9 q^{94} - 9 q^{96} - 117 q^{98}+O(q^{100}) $ 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9 - 9 * q^12 - 21 * q^14 - 3 * q^16 - 3 * q^18 - 12 * q^21 - 12 * q^22 - 9 * q^24 - 6 * q^25 - 18 * q^26 - 12 * q^28 - 36 * q^29 - 39 * q^30 + 27 * q^32 - 18 * q^33 + 18 * q^34 + 18 * q^36 + 6 * q^37 - 99 * q^38 + 36 * q^40 + 9 * q^42 + 3 * q^44 - 18 * q^45 + 3 * q^46 - 12 * q^49 + 3 * q^50 - 9 * q^52 - 12 * q^53 - 135 * q^54 + 15 * q^56 - 42 * q^57 - 3 * q^58 - 33 * q^60 - 18 * q^61 - 99 * q^62 - 6 * q^64 + 18 * q^65 - 9 * q^66 - 54 * q^68 + 72 * q^69 - 36 * q^70 - 111 * q^72 - 18 * q^73 + 93 * q^74 - 36 * q^76 - 36 * q^77 + 6 * q^78 - 18 * q^80 - 30 * q^81 - 18 * q^82 + 84 * q^84 + 6 * q^85 + 135 * q^86 - 51 * q^88 + 81 * q^90 + 48 * q^92 - 6 * q^93 - 9 * q^94 - 9 * q^96 - 117 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−1.41414	+	0.0147396i	−0.999946	+	0.0104224i
$2$	−1.41414	+	0.0147396i	−0.999946	+	0.0104224i
$3$	−0.326297	+	1.70104i	−0.188388	+	0.982095i
$3$	−0.326297	+	1.70104i	−0.188388	+	0.982095i
$4$	1.99957	−	0.0416875i	0.999783	−	0.0208437i
$5$	−1.34679	−	0.237475i	−0.602302	−	0.106202i	−0.135821	−	0.990733i	$-0.543367\pi$
$5$	−1.34679	−	0.237475i	−0.602302	−	0.106202i	−0.466481	+	0.884531i	$0.654478\pi$
$6$	0.436356	−	2.41031i	0.178142	−	0.984005i
$7$	1.86287	+	1.87875i	0.704099	+	0.710102i
$7$	1.86287	+	1.87875i	0.704099	+	0.710102i
$8$	−2.82704	+	0.0884245i	−0.999511	+	0.0312628i
$9$	−2.78706	−	1.11009i	−0.929020	−	0.370029i
$10$	1.90804	+	0.315971i	0.603376	+	0.0999189i
$11$	0.749254	−	0.132114i	0.225909	−	0.0398338i	−0.0595479	−	0.998225i	$-0.518966\pi$
$11$	0.749254	−	0.132114i	0.225909	−	0.0398338i	0.285456	+	0.958392i	$0.407855\pi$
$12$	−0.581540	+	3.41494i	−0.167876	+	0.985808i
$13$	1.15190	−	1.37278i	0.319478	−	0.380739i	−0.582274	−	0.812993i	$-0.697837\pi$
$13$	1.15190	−	1.37278i	0.319478	−	0.380739i	0.901752	+	0.432253i	$0.142281\pi$
$14$	−2.66205	−	2.62936i	−0.711462	−	0.702725i
$15$	0.843407	−	2.21345i	0.217767	−	0.571510i
$16$	3.99652	−	0.166714i	0.999131	−	0.0416784i
$17$			7.50794i			1.82094i	0.413573	+	0.910471i	$0.364281\pi$
$17$			7.50794i			1.82094i	−0.413573	+	0.910471i	$0.635719\pi$
$18$	3.95765	+	1.52873i	0.932826	+	0.360326i
$19$	0.267621			0.0613965			0.0306982	−	0.999529i	$-0.490227\pi$
$19$	0.267621			0.0613965			0.0306982	+	0.999529i	$0.490227\pi$
$20$	−2.70289	−	0.418703i	−0.604385	−	0.0936248i
$21$	−3.80368	+	2.55578i	−0.830031	+	0.557718i
$22$	−1.05760	+	0.197870i	−0.225481	+	0.0421861i
$23$	−4.67111	+	5.56681i	−0.973994	+	1.16076i	0.0129853	+	0.999916i	$0.495867\pi$
$23$	−4.67111	+	5.56681i	−0.973994	+	1.16076i	−0.986980	+	0.160845i	$0.948578\pi$
$24$	0.772042	−	4.83776i	0.157592	−	0.987504i
$25$	−2.94102	−	1.07044i	−0.588204	−	0.214089i
$26$	−1.60870	+	1.95827i	−0.315493	+	0.384049i
$27$	2.79771	−	4.37868i	0.538419	−	0.842677i
$28$	3.80325	+	3.67903i	0.718747	+	0.695272i
$29$	−0.0330684	+	0.0277477i	−0.00614065	+	0.00515262i	−0.645853	−	0.763462i	$-0.723498\pi$
$29$	−0.0330684	+	0.0277477i	−0.00614065	+	0.00515262i	0.639712	+	0.768615i	$0.279054\pi$
$30$	−1.16007	+	3.14255i	−0.211798	+	0.573749i
$31$	−0.0386472	+	0.0140664i	−0.00694124	+	0.00252640i	−0.345488	−	0.938423i	$-0.612287\pi$
$31$	−0.0386472	+	0.0140664i	−0.00694124	+	0.00252640i	0.338547	+	0.940949i	$0.390065\pi$
$32$	−5.64917	+	0.294663i	−0.998642	+	0.0520895i
$33$	−0.0197488	+	1.31762i	−0.00343782	+	0.229368i
$34$	−0.110664	−	10.6173i	−0.0189787	−	1.82084i
$35$	−2.06274	−	2.97267i	−0.348666	−	0.502473i
$36$	−5.61919	−	2.10351i	−0.936531	−	0.350584i
$37$	0.617338	+	1.06926i	0.101490	+	0.175785i	0.912299	−	0.409526i	$-0.134306\pi$
$37$	0.617338	+	1.06926i	0.101490	+	0.175785i	−0.810809	+	0.585311i	$0.800972\pi$
$38$	−0.378453	+	0.00394461i	−0.0613931	+	0.000639901i
$39$	1.95928	+	2.40735i	0.313736	+	0.385485i
$40$	3.82843	+	0.552264i	0.605328	+	0.0873205i
$41$	6.61046	−	7.87804i	1.03238	−	1.23034i	0.0596943	−	0.998217i	$-0.480987\pi$
$41$	6.61046	−	7.87804i	1.03238	−	1.23034i	0.972686	−	0.232126i	$-0.0745682\pi$
$42$	5.34125	−	3.67029i	0.824173	−	0.566338i
$43$	−4.04604	+	11.1164i	−0.617015	+	1.69524i	0.0971603	+	0.995269i	$0.469024\pi$
$43$	−4.04604	+	11.1164i	−0.617015	+	1.69524i	−0.714176	+	0.699967i	$0.753198\pi$
$44$	1.49267	−	0.295404i	0.225029	−	0.0445339i
$45$	3.48996	+	2.15691i	0.520253	+	0.321533i
$46$	6.52354	−	7.94109i	0.961843	−	1.17085i
$47$	−6.25388	−	2.27623i	−0.912223	−	0.332022i	−0.157083	−	0.987585i	$-0.550209\pi$
$47$	−6.25388	−	2.27623i	−0.912223	−	0.332022i	−0.755140	+	0.655564i	$0.772431\pi$
$48$	−1.02047	+	6.85264i	−0.147292	+	0.989093i
$49$	−0.0594252	+	6.99975i	−0.00848931	+	0.999964i
$50$	4.17478	+	1.47040i	0.590403	+	0.207947i
$51$	−12.7713	−	2.44982i	−1.78834	−	0.343043i
$52$	2.24606	−	2.79297i	0.311473	−	0.387316i
$53$	−2.57294	−	4.45646i	−0.353420	−	0.612142i	0.633426	−	0.773803i	$-0.281648\pi$
$53$	−2.57294	−	4.45646i	−0.353420	−	0.612142i	−0.986846	+	0.161662i	$0.948315\pi$
$54$	−3.89180	+	6.23329i	−0.529607	+	0.848243i
$55$	−1.04046			−0.140296
$56$	−5.43255	−	5.14659i	−0.725955	−	0.687743i
$57$	−0.0873239	+	0.455234i	−0.0115663	+	0.0602972i
$58$	0.0463543	−	0.0397264i	0.00608661	−	0.00521634i
$59$	−3.49575	−	2.93328i	−0.455108	−	0.381881i	0.386219	−	0.922407i	$-0.373781\pi$
$59$	−3.49575	−	2.93328i	−0.455108	−	0.381881i	−0.841327	+	0.540526i	$0.818225\pi$
$60$	1.59417	−	4.46110i	0.205807	−	0.575925i
$61$	−1.44114	+	3.95949i	−0.184519	+	0.506961i	−0.997118	−	0.0758615i	$-0.975829\pi$
$61$	−1.44114	+	3.95949i	−0.184519	+	0.506961i	0.812600	+	0.582822i	$0.198052\pi$
$62$	0.0544451	−	0.0204615i	0.00691453	−	0.00259861i
$63$	−3.10636	−	7.30415i	−0.391364	−	0.920236i
$64$	7.98436	−	0.499960i	0.998045	−	0.0624950i
$65$	−1.87736	+	1.57529i	−0.232858	+	0.195391i
$66$	0.00850638	−	1.86358i	0.00104706	−	0.229391i
$67$	1.13608	+	0.200322i	0.138794	+	0.0244732i	0.242614	−	0.970123i	$-0.421995\pi$
$67$	1.13608	+	0.200322i	0.138794	+	0.0244732i	−0.103819	+	0.994596i	$0.533106\pi$
$68$	0.312987	+	15.0126i	0.0379552	+	1.82055i
$69$	−7.94519	−	9.76217i	−0.956489	−	1.17523i
$70$	2.96081	+	4.17335i	0.353884	+	0.498811i
$71$	−7.23371	−	4.17638i	−0.858483	−	0.495645i	0.00502099	−	0.999987i	$-0.498402\pi$
$71$	−7.23371	−	4.17638i	−0.858483	−	0.495645i	−0.863504	+	0.504342i	$0.831735\pi$
$72$	7.97730	+	2.89182i	0.940134	+	0.340804i
$73$	−13.3745	−	7.72174i	−1.56536	−	0.903762i	−0.996699	−	0.0811909i	$-0.974128\pi$
$73$	−13.3745	−	7.72174i	−1.56536	−	0.903762i	−0.568663	−	0.822571i	$-0.692539\pi$
$74$	−0.888761	−	1.50298i	−0.103316	−	0.174718i
$75$	2.78051	−	4.65350i	0.321066	−	0.537340i
$76$	0.535126	−	0.0111564i	0.0613831	−	0.00127973i
$77$	1.64397	+	1.16155i	0.187348	+	0.132371i
$78$	−2.80618	−	3.37544i	−0.317737	−	0.382194i
$79$	−12.7284	+	2.24436i	−1.43206	+	0.252510i	−0.835248	−	0.549874i	$-0.814676\pi$
$79$	−12.7284	+	2.24436i	−1.43206	+	0.252510i	−0.596808	+	0.802384i	$0.703565\pi$
$80$	−5.42206	−	0.724547i	−0.606205	−	0.0810068i
$81$	6.53542	+	6.18776i	0.726157	+	0.687529i
$82$	−9.23197	+	11.2381i	−1.01950	+	1.24104i
$83$	−5.39667	+	4.52834i	−0.592361	+	0.497050i	−0.888980	−	0.457946i	$-0.848585\pi$
$83$	−5.39667	+	4.52834i	−0.592361	+	0.497050i	0.296619	+	0.954996i	$0.404141\pi$
$84$	−7.49916	+	5.26902i	−0.818226	+	0.574897i
$85$	1.78295	−	10.1116i	0.193388	−	1.09676i
$86$	5.55780	−	15.7797i	0.599313	−	1.70157i
$87$	−0.0364097	−	0.0653046i	−0.00390353	−	0.00700139i
$88$	−2.10649	+	0.439744i	−0.224553	+	0.0468768i
$89$			5.06260i			0.536635i	0.963331	+	0.268317i	$0.0864676\pi$
$89$			5.06260i			0.536635i	−0.963331	+	0.268317i	$0.913532\pi$
$90$	−4.96708	−	2.99872i	−0.523576	−	0.316093i
$91$	4.72494	−	0.393176i	0.495308	−	0.0412161i
$92$	−9.10813	+	11.3259i	−0.949588	+	1.18081i
$93$	−0.0113171	−	0.0703301i	−0.00117353	−	0.00729290i
$94$	8.87740	+	3.12672i	0.915633	+	0.322496i
$95$	−0.360429	−	0.0635533i	−0.0369792	−	0.00652043i
$96$	1.34207	−	9.70561i	0.136975	−	0.990575i
$97$	−1.46164	+	4.01581i	−0.148407	+	0.407744i	−0.991514	−	0.130002i	$-0.958502\pi$
$97$	−1.46164	+	4.01581i	−0.148407	+	0.407744i	0.843107	+	0.537746i	$0.180724\pi$
$98$	−0.0191378	−	9.89948i	−0.00193321	−	0.999998i
$99$	−2.23487	−	0.463528i	−0.224613	−	0.0465863i
$100$	−5.92538	−	2.01782i	−0.592538	−	0.201782i
$101$	1.86876	+	2.22711i	0.185949	+	0.221605i	0.850963	−	0.525225i	$-0.176019\pi$
$101$	1.86876	+	2.22711i	0.185949	+	0.221605i	−0.665014	+	0.746831i	$0.731575\pi$
$102$	18.0965	+	3.27613i	1.79182	+	0.324385i
$103$	1.98342	−	11.2485i	0.195432	−	1.10835i	−0.716370	−	0.697720i	$-0.754198\pi$
$103$	1.98342	−	11.2485i	0.195432	−	1.10835i	0.911802	−	0.410629i	$-0.134691\pi$
$104$	−3.13507	+	3.98275i	−0.307419	+	0.390541i
$105$	5.72968	−	2.53882i	0.559160	−	0.247763i
$106$	3.70417	+	6.26412i	0.359781	+	0.608425i
$107$	9.76305	+	5.63670i	0.943830	+	0.544920i	0.891159	−	0.453692i	$-0.149893\pi$
$107$	9.76305	+	5.63670i	0.943830	+	0.544920i	0.0526709	+	0.998612i	$0.483227\pi$
$108$	5.41167	−	8.87208i	0.520738	−	0.853717i
$109$	5.94128	+	10.2906i	0.569071	+	0.985660i	0.996658	+	0.0816861i	$0.0260305\pi$
$109$	5.94128	+	10.2906i	0.569071	+	0.985660i	−0.427587	+	0.903974i	$0.640636\pi$
$110$	1.47135	−	0.0153359i	0.140288	−	0.00146222i
$111$	−2.02029	+	0.701219i	−0.191757	+	0.0665568i
$112$	7.75822	+	7.19792i	0.733083	+	0.680139i
$113$	0.683874	−	0.248910i	0.0643334	−	0.0234155i	−0.309653	−	0.950850i	$-0.600213\pi$
$113$	0.683874	−	0.248910i	0.0643334	−	0.0234155i	0.373986	+	0.927434i	$0.377991\pi$
$114$	0.116778	−	0.645050i	0.0109373	−	0.0604144i
$115$	7.61298	−	6.38805i	0.709914	−	0.595689i
$116$	−0.0649657	+	0.0568618i	−0.00603191	+	0.00527949i
$117$	−4.73430	+	2.54731i	−0.437686	+	0.235498i
$118$	4.98670	+	4.09654i	0.459063	+	0.377117i
$119$	−14.1056	+	13.9863i	−1.29305	+	1.28212i
$120$	−2.18863	+	6.33210i	−0.199793	+	0.578039i
$121$	−9.79269	+	3.56425i	−0.890245	+	0.324023i
$122$	1.97960	−	5.62050i	0.179225	−	0.508856i
$123$	11.2439	+	13.8152i	1.01383	+	1.24568i
$124$	−0.0766912	+	0.0297378i	−0.00688707	+	0.00267054i
$125$	9.62845	+	5.55899i	0.861195	+	0.497211i
$126$	4.50047	+	10.2833i	0.400934	+	0.916107i
$127$	−7.44867	+	4.30049i	−0.660963	+	0.381607i	−0.792644	−	0.609685i	$-0.791296\pi$
$127$	−7.44867	+	4.30049i	−0.660963	+	0.381607i	0.131681	+	0.991292i	$0.457963\pi$
$128$	−11.2836	+	0.824698i	−0.997340	+	0.0728937i
$129$	−17.5892	−	10.5097i	−1.54864	−	0.925329i
$130$	2.63162	−	2.25535i	0.230809	−	0.197807i
$131$	0.901652	+	0.756576i	0.0787777	+	0.0661023i	0.681326	−	0.731980i	$-0.261404\pi$
$131$	0.901652	+	0.756576i	0.0787777	+	0.0661023i	−0.602548	+	0.798082i	$0.705848\pi$
$132$	0.0154392	+	2.63549i	0.00134381	+	0.229390i
$133$	0.498543	+	0.502794i	0.0432292	+	0.0435978i
$134$	−1.60953	−	0.266537i	−0.139042	−	0.0230253i
$135$	−4.80775	+	5.23277i	−0.413785	+	0.450365i
$136$	−0.663886	−	21.2253i	−0.0569277	−	1.82005i
$137$	14.5120	+	5.28194i	1.23984	+	0.451266i	0.876958	−	0.480567i	$-0.159569\pi$
$137$	14.5120	+	5.28194i	1.23984	+	0.451266i	0.362886	+	0.931834i	$0.381791\pi$
$138$	11.3795	+	13.6879i	0.968686	+	1.16519i
$139$	−0.126973	+	0.720097i	−0.0107697	+	0.0610779i	−0.989719	−	0.143026i	$-0.954317\pi$
$139$	−0.126973	+	0.720097i	−0.0107697	+	0.0610779i	0.978949	+	0.204104i	$0.0654279\pi$
$140$	−4.24850	−	5.85805i	−0.359064	−	0.495096i
$141$	5.91257	−	9.89537i	0.497928	−	0.833340i
$142$	10.2910	+	5.79935i	0.863602	+	0.486671i
$143$	0.681700	−	1.18074i	0.0570066	−	0.0987383i
$144$	−11.3236	−	3.97185i	−0.943635	−	0.330987i
$145$	0.0511255	−	0.0295173i	0.00424574	−	0.00245128i
$146$	19.0271	+	10.7225i	1.57470	+	0.887398i
$147$	−11.8874	−	2.38508i	−0.980460	−	0.196718i
$148$	1.27898	+	2.11232i	0.105132	+	0.173632i
$149$	7.34878	−	2.67474i	0.602035	−	0.219123i	−0.0229793	−	0.999736i	$-0.507315\pi$
$149$	7.34878	−	2.67474i	0.602035	−	0.219123i	0.625015	+	0.780613i	$0.285093\pi$
$150$	−3.86343	+	6.62167i	−0.315448	+	0.540657i
$151$	0.730883	−	0.128874i	0.0594784	−	0.0104877i	−0.143830	−	0.989602i	$-0.545942\pi$
$151$	0.730883	−	0.128874i	0.0594784	−	0.0104877i	0.203308	+	0.979115i	$0.434831\pi$
$152$	−0.756577	+	0.0236643i	−0.0613665	+	0.00191942i
$153$	8.33446	−	20.9251i	0.673801	−	1.69169i
$154$	−2.34192	−	1.61836i	−0.188717	−	0.130411i
$155$	0.0553900	−	0.00976675i	0.00444903	−	0.000784484i
$156$	4.01807	+	4.73198i	0.321703	+	0.378861i
$157$	13.1572	−	15.6801i	1.05006	−	1.25141i	0.0830799	−	0.996543i	$-0.473524\pi$
$157$	13.1572	−	15.6801i	1.05006	−	1.25141i	0.966976	−	0.254866i	$-0.0820312\pi$
$158$	17.9666	−	3.36144i	1.42935	−	0.267422i
$159$	8.42015	−	2.92254i	0.667761	−	0.231772i
$160$	7.67822	+	0.944690i	0.607016	+	0.0746843i
$161$	−19.1603	+	1.59439i	−1.51005	+	0.125656i
$162$	−9.33318	−	8.65401i	−0.733284	−	0.679923i
$163$	15.1878	+	8.76866i	1.18960	+	0.686815i	0.958215	−	0.286048i	$-0.0923417\pi$
$163$	15.1878	+	8.76866i	1.18960	+	0.686815i	0.231383	+	0.972863i	$0.425675\pi$
$164$	12.8896	−	16.0282i	1.00651	−	1.25159i
$165$	0.339499	−	1.76986i	0.0264299	−	0.137784i
$166$	7.56488	−	6.48324i	0.587149	−	0.503197i
$167$	15.0919	−	5.49300i	1.16785	−	0.425061i	0.315952	−	0.948775i	$-0.397676\pi$
$167$	15.0919	−	5.49300i	1.16785	−	0.425061i	0.851894	+	0.523714i	$0.175454\pi$
$168$	10.5272	−	7.56165i	0.812189	−	0.583394i
$169$	1.69978	+	9.63991i	0.130752	+	0.741532i
$170$	−2.37229	+	14.3255i	−0.181946	+	1.09871i
$171$	−0.745876	−	0.297083i	−0.0570386	−	0.0227185i
$172$	−7.62691	+	22.3966i	−0.581546	+	1.70773i
$173$	10.3406	+	12.3235i	0.786182	+	0.936935i	0.999195	−	0.0401144i	$-0.0127722\pi$
$173$	10.3406	+	12.3235i	0.786182	+	0.936935i	−0.213013	+	0.977049i	$0.568328\pi$
$174$	0.0524509	+	0.0918130i	0.00397629	+	0.00696032i
$175$	−3.46764	−	7.51955i	−0.262129	−	0.568424i
$176$	2.97239	−	0.652906i	0.224052	−	0.0492147i
$177$	6.13028	−	4.98928i	0.460780	−	0.375017i
$178$	−0.0746205	−	7.15921i	−0.00559304	−	0.536605i
$179$		−	18.9133i		−	1.41365i	−0.707389	−	0.706824i	$-0.750127\pi$
$179$		−	18.9133i		−	1.41365i	0.707389	−	0.706824i	$-0.249873\pi$
$180$	7.06832	+	4.16739i	0.526842	+	0.310619i
$181$	3.01881	−	1.74291i	0.224387	−	0.129550i	−0.383593	−	0.923502i	$-0.625314\pi$
$181$	3.01881	−	1.74291i	0.224387	−	0.129550i	0.607980	+	0.793953i	$0.291980\pi$
$182$	−6.67591	+	0.625649i	−0.494852	+	0.0463762i
$183$	−6.26500	−	3.74340i	−0.463122	−	0.276720i
$184$	12.7132	−	16.1507i	0.937230	−	1.19064i
$185$	−0.577501	−	1.58667i	−0.0424587	−	0.116654i
$186$	0.0170405	+	0.0992896i	0.00124947	+	0.00728027i
$187$	0.991901	+	5.62535i	0.0725350	+	0.411366i
$188$	−12.5999	−	4.29076i	−0.918945	−	0.312936i
$189$	13.4382	−	2.90071i	0.977487	−	0.210996i
$190$	0.510632	+	0.0845605i	0.0370452	+	0.00613467i
$191$	−21.5958	+	3.80792i	−1.56262	+	0.275531i	−0.887016	−	0.461738i	$-0.847226\pi$
$191$	−21.5958	+	3.80792i	−1.56262	+	0.275531i	−0.675599	+	0.737269i	$0.736115\pi$
$192$	−1.75482	+	13.7448i	−0.126643	+	0.991948i
$193$	−8.75334	+	3.18596i	−0.630079	+	0.229330i	−0.637266	−	0.770644i	$-0.719935\pi$
$193$	−8.75334	+	3.18596i	−0.630079	+	0.229330i	0.00718658	+	0.999974i	$0.497712\pi$
$194$	2.00776	−	5.70045i	0.144149	−	0.409268i
$195$	−2.06705	−	3.70747i	−0.148025	−	0.265498i
$196$	0.172977	+	13.9989i	0.0123555	+	0.999924i
$197$	11.7144	+	20.2900i	0.834619	+	1.44560i	0.894340	+	0.447388i	$0.147646\pi$
$197$	11.7144	+	20.2900i	0.834619	+	1.44560i	−0.0597204	+	0.998215i	$0.519021\pi$
$198$	3.16725	+	0.622551i	0.225087	+	0.0442428i
$199$	16.6817			1.18254			0.591268	−	0.806475i	$-0.298628\pi$
$199$	16.6817			1.18254			0.591268	+	0.806475i	$0.298628\pi$
$200$	8.40905	+	2.76613i	0.594609	+	0.195595i
$201$	−0.711454	+	1.86715i	−0.0501821	+	0.131699i
$202$	−2.67551	−	3.12189i	−0.188248	−	0.219655i
$203$	−0.113733	−	0.0104370i	−0.00798251	−	0.000732534i
$204$	−25.6392	−	4.36616i	−1.79510	−	0.305693i
$205$	−10.7737	+	9.04023i	−0.752469	+	0.631397i
$206$	−2.63902	+	15.9362i	−0.183870	+	1.11033i
$207$	19.1983	−	10.3297i	1.33438	−	0.717965i
$208$	4.37472	−	5.67837i	0.303332	−	0.393724i
$209$	0.200516	−	0.0353564i	0.0138700	−	0.00244565i
$210$	−8.06514	+	3.67469i	−0.556547	+	0.253578i
$211$	1.48260	+	4.07341i	0.102066	+	0.280425i	0.980206	−	0.197979i	$-0.0634377\pi$
$211$	1.48260	+	4.07341i	0.102066	+	0.280425i	−0.878140	+	0.478404i	$0.841215\pi$
$212$	−5.33053	−	8.80372i	−0.366103	−	0.604642i
$213$	9.46452	−	10.9421i	0.648498	−	0.749738i
$214$	−13.8894	−	7.82716i	−0.949458	−	0.535054i
$215$	8.08903	−	14.0106i	0.551667	−	0.955515i
$216$	−7.52206	+	12.6261i	−0.511812	+	0.859098i
$217$	−0.0984220	−	0.0464046i	−0.00668132	−	0.00315015i
$218$	−8.55346	−	14.4647i	−0.579313	−	0.979676i
$219$	17.4990	−	20.2309i	1.18247	−	1.36708i
$220$	−2.08047	+	0.0433741i	−0.140265	+	0.00292428i
$221$	10.3067	+	8.64836i	0.693305	+	0.581752i
$222$	2.84663	−	1.02140i	0.191053	−	0.0685518i
$223$	1.22357	+	6.93923i	0.0819365	+	0.464685i	0.997976	+	0.0635963i	$0.0202570\pi$
$223$	1.22357	+	6.93923i	0.0819365	+	0.464685i	−0.916039	+	0.401089i	$0.868632\pi$
$224$	−11.0773	−	10.0645i	−0.740132	−	0.672462i
$225$	7.00851	+	6.24818i	0.467234	+	0.416545i
$226$	−0.963422	+	0.362072i	−0.0640859	+	0.0240847i
$227$	−0.773839	−	4.38866i	−0.0513615	−	0.291286i	0.948298	−	0.317382i	$-0.102804\pi$
$227$	−0.773839	−	4.38866i	−0.0513615	−	0.291286i	−0.999659	+	0.0260959i	$0.991692\pi$
$228$	−0.155632	+	0.913910i	−0.0103070	+	0.0605251i
$229$	−6.49289	−	17.8391i	−0.429062	−	1.17884i	−0.946383	−	0.323047i	$-0.895293\pi$
$229$	−6.49289	−	17.8391i	−0.429062	−	1.17884i	0.517320	−	0.855792i	$-0.326930\pi$
$230$	−10.6716	+	9.14578i	−0.703667	+	0.603055i
$231$	−2.51227	+	2.41745i	−0.165295	+	0.159056i
$232$	0.0910323	−	0.0813680i	0.00597656	−	0.00534207i
$233$	3.92479	+	6.79794i	0.257122	+	0.445348i	0.965470	−	0.260516i	$-0.0838926\pi$
$233$	3.92479	+	6.79794i	0.257122	+	0.445348i	−0.708348	+	0.705863i	$0.750559\pi$
$234$	6.65741	−	3.67202i	0.435208	−	0.240047i
$235$	7.88211	+	4.55074i	0.514172	+	0.296857i
$236$	−7.11226	−	5.71956i	−0.462969	−	0.372312i
$237$	0.335494	−	22.3838i	0.0217927	−	1.45398i
$238$	19.7410	−	19.9865i	1.27962	−	1.29553i
$239$	20.2587	+	3.57216i	1.31043	+	0.231064i	0.784852	−	0.619683i	$-0.212739\pi$
$239$	20.2587	+	3.57216i	1.31043	+	0.231064i	0.525576	+	0.850747i	$0.323850\pi$
$240$	3.00168	−	8.98672i	0.193758	−	0.580090i
$241$	−5.88412	+	16.1665i	−0.379029	+	1.04137i	0.592730	+	0.805401i	$0.298050\pi$
$241$	−5.88412	+	16.1665i	−0.379029	+	1.04137i	−0.971759	+	0.235974i	$0.924172\pi$
$242$	13.7957	−	5.18467i	0.886819	−	0.333283i
$243$	−12.6581	+	9.09794i	−0.812017	+	0.583633i
$244$	−2.71658	+	7.97733i	−0.173912	+	0.510696i
$245$	1.74230	−	9.41307i	0.111311	−	0.601379i
$246$	−16.1040	−	19.3709i	−1.02675	−	1.23504i
$247$	0.308271	−	0.367384i	0.0196148	−	0.0233761i
$248$	0.108013	−	0.0431838i	0.00685886	−	0.00274217i
$249$	−5.94197	−	10.6575i	−0.376557	−	0.675393i
$250$	−13.6979	−	7.71925i	−0.866331	−	0.488208i
$251$	6.93642	+	12.0142i	0.437823	+	0.758331i	0.997521	−	0.0703651i	$-0.0224164\pi$
$251$	6.93642	+	12.0142i	0.437823	+	0.758331i	−0.559699	+	0.828696i	$0.689083\pi$
$252$	−6.51585	−	14.4756i	−0.410460	−	0.911879i
$253$	−2.76440	+	4.78808i	−0.173796	+	0.301024i
$254$	10.4701	−	6.19127i	0.656949	−	0.388475i
$255$	16.6184	+	6.33225i	1.04069	+	0.396541i
$256$	15.9444	−	1.33255i	0.996526	−	0.0832844i
$257$	4.44837	+	12.2218i	0.277482	+	0.762375i	0.997646	+	0.0685717i	$0.0218442\pi$
$257$	4.44837	+	12.2218i	0.277482	+	0.762375i	−0.720164	+	0.693804i	$0.755934\pi$
$258$	25.0285	+	14.6029i	1.55820	+	0.909138i
$259$	−0.858856	+	3.15172i	−0.0533667	+	0.195838i
$260$	−3.68823	+	3.22816i	−0.228734	+	0.200202i
$261$	0.122966	−	0.0406257i	0.00761140	−	0.00251467i
$262$	−1.28621	−	1.05661i	−0.0794623	−	0.0652777i
$263$	−7.81328	−	9.31150i	−0.481787	−	0.574172i	0.469322	−	0.883027i	$-0.344498\pi$
$263$	−7.81328	−	9.31150i	−0.481787	−	0.574172i	−0.951109	+	0.308856i	$0.900054\pi$
$264$	−0.0606790	−	3.72671i	−0.00373453	−	0.229363i
$265$	2.40690	+	6.61291i	0.147855	+	0.406228i
$266$	−0.712420	−	0.703671i	−0.0436812	−	0.0431448i
$267$	−8.61168	−	1.65191i	−0.527026	−	0.101095i
$268$	2.28002	+	0.353196i	0.139274	+	0.0215749i
$269$	−8.84040	+	5.10401i	−0.539009	+	0.311197i	−0.744677	−	0.667425i	$-0.767396\pi$
$269$	−8.84040	+	5.10401i	−0.539009	+	0.311197i	0.205669	+	0.978622i	$0.434063\pi$
$270$	6.72168	−	7.47071i	0.409069	−	0.454653i
$271$	3.09997	−	5.36930i	0.188309	−	0.326162i	−0.756377	−	0.654136i	$-0.773033\pi$
$271$	3.09997	−	5.36930i	0.188309	−	0.326162i	0.944687	+	0.327974i	$0.106366\pi$
$272$	1.25168	+	30.0057i	0.0758940	+	1.81936i
$273$	−0.872924	+	8.16559i	−0.0528318	+	0.494204i
$274$	−20.5998	−	7.25548i	−1.24448	−	0.438320i
$275$	−2.34499	−	0.413485i	−0.141408	−	0.0249341i
$276$	−16.2939	−	19.1889i	−0.980777	−	1.15504i
$277$	9.09848	−	7.63453i	0.546675	−	0.458715i	−0.327138	−	0.944976i	$-0.606084\pi$
$277$	9.09848	−	7.63453i	0.546675	−	0.458715i	0.873813	+	0.486262i	$0.161640\pi$
$278$	0.168943	−	1.02019i	0.0101325	−	0.0611868i
$279$	0.123327	+	0.00369774i	0.00738339	+	0.000221378i
$280$	6.09430	+	8.22147i	0.364204	+	0.491327i
$281$	−12.4125	−	4.51779i	−0.740469	−	0.269509i	−0.0558796	−	0.998438i	$-0.517796\pi$
$281$	−12.4125	−	4.51779i	−0.740469	−	0.269509i	−0.684590	+	0.728929i	$0.740019\pi$
$282$	−8.21533	+	14.0806i	−0.489216	+	0.838485i
$283$	1.44402	−	8.18947i	0.0858383	−	0.486813i	−0.911334	−	0.411667i	$-0.864947\pi$
$283$	1.44402	−	8.18947i	0.0858383	−	0.486813i	0.997173	−	0.0751460i	$-0.0239423\pi$
$284$	−14.6384	−	8.04939i	−0.868628	−	0.477644i
$285$	0.225713	−	0.592366i	0.0133701	−	0.0350887i
$286$	−0.946613	+	1.67977i	−0.0559744	+	0.0993271i
$287$	27.1153	−	2.25635i	1.60057	−	0.133188i
$288$	16.0717	+	5.44983i	0.947034	+	0.321134i
$289$	−39.3691			−2.31583
$290$	−0.0718634	+	0.0424951i	−0.00421996	+	0.00249540i
$291$	−6.35412	−	3.79664i	−0.372485	−	0.222563i
$292$	−27.0650	−	14.8826i	−1.58386	−	0.870937i
$293$	25.3049	+	4.46193i	1.47833	+	0.260669i	0.853909	−	0.520422i	$-0.174225\pi$
$293$	25.3049	+	4.46193i	1.47833	+	0.260669i	0.624417	+	0.781091i	$0.285336\pi$
$294$	16.8456	+	3.19761i	0.982457	+	0.186489i
$295$	4.01145	+	4.78066i	0.233556	+	0.278341i
$296$	−1.83979	−	2.96826i	−0.106936	−	0.172527i
$297$	1.51771	−	3.65036i	0.0880665	−	0.211815i
$298$	−10.3528	+	3.89076i	−0.599719	+	0.225386i
$299$	2.26135	+	12.8248i	0.130778	+	0.741676i
$300$	5.36582	−	9.42090i	0.309796	−	0.543916i
$301$	−28.4222	+	13.1069i	−1.63823	+	0.755470i
$302$	−1.03167	+	0.193019i	−0.0593659	+	0.0111070i
$303$	−4.39816	+	2.45214i	−0.252668	+	0.140872i
$304$	1.06955	−	0.0446161i	0.0613431	−	0.00255891i
$305$	2.88118	−	4.99036i	0.164976	−	0.285747i
$306$	−11.4776	+	29.7138i	−0.656133	+	1.69862i
$307$	−2.19140	+	3.79562i	−0.125070	+	0.216628i	−0.921760	−	0.387760i	$-0.873249\pi$
$307$	−2.19140	+	3.79562i	−0.125070	+	0.216628i	0.796690	+	0.604388i	$0.206582\pi$
$308$	3.33565	+	2.25407i	0.190066	+	0.128437i
$309$	18.4870	+	7.04422i	1.05169	+	0.400732i
$310$	−0.0781851	+	0.0146279i	−0.00444061	+	0.000830811i
$311$	1.22997	−	6.97550i	0.0697452	−	0.395545i	−0.929872	−	0.367883i	$-0.880083\pi$
$311$	1.22997	−	6.97550i	0.0697452	−	0.395545i	0.999617	−	0.0276618i	$-0.00880613\pi$
$312$	−5.75185	−	6.63244i	−0.325634	−	0.375488i
$313$	0.757985	+	0.903331i	0.0428438	+	0.0510593i	0.787041	−	0.616901i	$-0.211612\pi$
$313$	0.757985	+	0.903331i	0.0428438	+	0.0510593i	−0.744197	+	0.667960i	$0.767168\pi$
$314$	−18.3749	+	22.3677i	−1.03696	+	1.26228i
$315$	2.44905	+	10.5748i	0.137988	+	0.595824i
$316$	−25.3577	+	5.01836i	−1.42648	+	0.282305i
$317$	−20.7776	−	7.56243i	−1.16699	−	0.424748i	−0.315398	−	0.948960i	$-0.602138\pi$
$317$	−20.7776	−	7.56243i	−1.16699	−	0.424748i	−0.851588	+	0.524211i	$0.824360\pi$
$318$	−11.8642	+	4.25697i	−0.665309	+	0.238719i
$319$	−0.0211108	+	0.0251588i	−0.00118198	+	0.00140862i
$320$	−10.8720	−	1.22275i	−0.607762	−	0.0683536i
$321$	−12.7739	+	14.7681i	−0.712969	+	0.824274i
$322$	27.0719	−	2.53710i	1.50866	−	0.141387i
$323$			2.00928i			0.111799i
$324$	13.3259	+	12.1004i	0.740330	+	0.672243i
$325$	−4.85723	+	2.80432i	−0.269430	+	0.155556i
$326$	−21.6068	−	12.1762i	−1.19669	−	0.674379i
$327$	−19.4433	+	6.74855i	−1.07522	+	0.373196i
$328$	−17.9914	+	22.8561i	−0.993412	+	1.26202i
$329$	−7.37371	−	15.9898i	−0.406526	−	0.881547i
$330$	−0.454011	+	2.50783i	−0.0249925	+	0.138052i
$331$	−6.96037	+	19.1235i	−0.382577	+	1.05112i	0.587691	+	0.809086i	$0.300037\pi$
$331$	−6.96037	+	19.1235i	−0.382577	+	1.05112i	−0.970267	+	0.242035i	$0.922185\pi$
$332$	−10.6022	+	9.27969i	−0.581872	+	0.509289i
$333$	−0.533587	−	3.66539i	−0.0292404	−	0.200862i
$334$	−21.2611	+	7.99031i	−1.16335	+	0.437210i
$335$	−1.48249	−	0.539581i	−0.0809969	−	0.0294805i
$336$	−14.7754	+	10.8484i	−0.806065	+	0.591827i
$337$	21.6872	+	18.1977i	1.18138	+	0.991294i	0.999969	+	0.00788686i	$0.00251049\pi$
$337$	21.6872	+	18.1977i	1.18138	+	0.991294i	0.181410	+	0.983408i	$0.441934\pi$
$338$	−2.54580	−	13.6071i	−0.138474	−	0.740129i
$339$	0.200259	+	1.24451i	0.0108766	+	0.0675927i
$340$	3.14359	−	20.2931i	0.170485	−	1.10055i
$341$	−0.0270982	+	0.0156451i	−0.00146745	+	0.000847232i
$342$	1.05915	+	0.409121i	0.0572723	+	0.0221228i
$343$	−13.2615	+	12.9280i	−0.716054	+	0.698045i
$344$	10.4554	−	31.7843i	0.563716	−	1.71370i
$345$	8.38222	+	15.0344i	0.451284	+	0.809423i
$346$	−14.8047	−	17.2746i	−0.795904	−	0.928690i
$347$	10.7755	+	29.6054i	0.578458	+	1.58930i	0.790781	+	0.612100i	$0.209675\pi$
$347$	10.7755	+	29.6054i	0.578458	+	1.58930i	−0.212323	+	0.977200i	$0.568103\pi$
$348$	−0.0755261	−	0.129063i	−0.00404862	−	0.00691850i
$349$	5.39049	+	6.42413i	0.288546	+	0.343876i	0.890773	−	0.454449i	$-0.150164\pi$
$349$	5.39049	+	6.42413i	0.288546	+	0.343876i	−0.602226	+	0.798325i	$0.705720\pi$
$350$	5.01455	+	10.5826i	0.268039	+	0.565661i
$351$	−2.78828	−	8.88441i	−0.148827	−	0.474215i
$352$	−4.19374	+	0.967110i	−0.223527	+	0.0515472i
$353$	−10.8415	+	29.7868i	−0.577035	+	1.58539i	0.216118	+	0.976367i	$0.430660\pi$
$353$	−10.8415	+	29.7868i	−0.577035	+	1.58539i	−0.793153	+	0.609023i	$0.791562\pi$
$354$	−8.59551	+	7.14589i	−0.456846	+	0.379800i
$355$	8.75048	+	7.34253i	0.464427	+	0.389701i
$356$	0.211047	+	10.1230i	0.0111855	+	0.536518i
$357$	−19.1887	−	28.5578i	−1.01557	−	1.51144i
$358$	0.278774	+	26.7460i	0.0147337	+	1.41357i
$359$		−	20.8206i		−	1.09887i	−0.835537	−	0.549434i	$-0.814843\pi$
$359$		−	20.8206i		−	1.09887i	0.835537	−	0.549434i	$-0.185157\pi$
$360$	−10.0570	−	5.78908i	−0.530051	−	0.305111i
$361$	−18.9284			−0.996230
$362$	−4.24332	+	2.50921i	−0.223024	+	0.131881i
$363$	−2.86760	−	17.8207i	−0.150510	−	0.935346i
$364$	9.43143	−	0.983153i	0.494341	−	0.0515312i
$365$	16.1788	+	13.5757i	0.846839	+	0.710582i
$366$	8.91475	+	5.20133i	0.465981	+	0.271878i
$367$	1.25046	+	7.09174i	0.0652737	+	0.370186i	0.999894	+	0.0145393i	$0.00462816\pi$
$367$	1.25046	+	7.09174i	0.0652737	+	0.370186i	−0.934621	+	0.355646i	$0.884261\pi$
$368$	−17.7401	+	23.0266i	−0.924769	+	1.20035i
$369$	−27.1691	+	14.6184i	−1.41436	+	0.761003i
$370$	0.840052	+	2.23526i	0.0436722	+	0.116205i
$371$	3.57953	−	13.1357i	0.185840	−	0.681973i
$372$	−0.0255611	−	0.140158i	−0.00132528	−	0.00726685i
$373$	0.873008	−	4.95107i	0.0452026	−	0.256357i	−0.953829	−	0.300349i	$-0.902897\pi$
$373$	0.873008	−	4.95107i	0.0452026	−	0.256357i	0.999032	+	0.0439927i	$0.0140078\pi$
$374$	−1.48560	−	7.94040i	−0.0768185	−	0.410588i
$375$	−12.5978	+	14.5645i	−0.650547	+	0.752107i
$376$	17.8813	+	5.88200i	0.922157	+	0.303341i
$377$			0.0773579i			0.00398414i
$378$	−18.9607	+	4.30007i	−0.975235	+	0.221172i
$379$		−	6.12720i		−	0.314733i	−0.987540	−	0.157367i	$-0.949700\pi$
$379$		−	6.12720i		−	0.314733i	0.987540	−	0.157367i	$-0.0503004\pi$
$380$	−0.723350	−	0.112054i	−0.0371071	−	0.00574823i
$381$	−4.88482	−	14.0737i	−0.250257	−	0.721018i
$382$	30.4832	−	5.70323i	1.55966	−	0.291803i
$383$	3.19475	−	18.1183i	0.163244	−	0.925802i	−0.787613	−	0.616171i	$-0.788683\pi$
$383$	3.19475	−	18.1183i	0.163244	−	0.925802i	0.950857	−	0.309632i	$-0.100206\pi$
$384$	2.27896	−	19.4629i	0.116298	−	0.993214i
$385$	−1.93824	−	1.95477i	−0.0987820	−	0.0996242i
$386$	12.3315	−	4.63440i	0.627655	−	0.235885i
$387$	23.6167	−	26.4906i	1.20051	−	1.34659i
$388$	−2.75523	+	8.09081i	−0.139875	+	0.410749i
$389$	−2.02188	−	11.4666i	−0.102513	−	0.581382i	−0.992184	−	0.124780i	$-0.960177\pi$
$389$	−2.02188	−	11.4666i	−0.102513	−	0.581382i	0.889671	−	0.456602i	$-0.150934\pi$
$390$	2.97774	+	5.21240i	0.150784	+	0.263940i
$391$	−41.7953	−	35.0704i	−2.11368	−	1.77359i
$392$	−0.450951	−	19.7939i	−0.0227765	−	0.999741i
$393$	−1.58117	+	1.28688i	−0.0797595	+	0.0649143i
$394$	−16.8649	−	28.5202i	−0.849641	−	1.43683i
$395$	17.6754			0.889347
$396$	−4.48810	−	0.833688i	−0.225535	−	0.0418944i
$397$		−	35.1003i		−	1.76163i	−0.473459	−	0.880816i	$-0.656995\pi$
$397$		−	35.1003i		−	1.76163i	0.473459	−	0.880816i	$-0.343005\pi$
$398$	−23.5902	+	0.245881i	−1.18247	+	0.0123249i
$399$	−1.01794	+	0.683981i	−0.0509610	+	0.0342419i
$400$	−11.9323	−	3.78775i	−0.596616	−	0.189387i
$401$	14.2965	+	11.9962i	0.713933	+	0.599061i	0.925700	−	0.378260i	$-0.123477\pi$
$401$	14.2965	+	11.9962i	0.713933	+	0.599061i	−0.211767	+	0.977320i	$0.567922\pi$
$402$	0.978572	−	2.65089i	0.0488067	−	0.132215i
$403$	−0.0252075	+	0.0692569i	−0.00125567	+	0.00344993i
$404$	3.82956	+	4.37534i	0.190528	+	0.217681i
$405$	−7.33238	−	9.88560i	−0.364349	−	0.491219i
$406$	0.160988	+	0.0130830i	0.00798971	+	0.000649297i
$407$	0.603807	+	0.719589i	0.0299296	+	0.0356687i
$408$	36.3216	+	5.79644i	1.79819	+	0.286967i
$409$	−3.50807	−	9.63834i	−0.173463	−	0.476585i	0.822245	−	0.569133i	$-0.192721\pi$
$409$	−3.50807	−	9.63834i	−0.173463	−	0.476585i	−0.995708	+	0.0925479i	$0.970499\pi$
$410$	15.1023	−	12.9429i	0.745848	−	0.639205i
$411$	−13.7200	+	22.9620i	−0.676757	+	1.13263i
$412$	3.49705	−	22.5748i	0.172287	−	1.11218i
$413$	−1.00122	−	12.0320i	−0.0492667	−	0.592055i
$414$	−26.9968	+	14.8906i	−1.32682	+	0.731833i
$415$	8.34354	−	4.81714i	0.409568	−	0.236464i
$416$	−6.10275	+	8.09447i	−0.299212	+	0.396864i
$417$	−1.18348	−	0.450951i	−0.0579554	−	0.0220831i
$418$	−0.283036	+	0.0529543i	−0.0138437	+	0.00259008i
$419$	29.7437	+	24.9580i	1.45308	+	1.21928i	0.930297	+	0.366808i	$0.119549\pi$
$419$	29.7437	+	24.9580i	1.45308	+	1.21928i	0.522780	+	0.852468i	$0.324895\pi$
$420$	11.3510	−	5.31539i	0.553874	−	0.259365i
$421$	24.4157	+	8.88659i	1.18995	+	0.433106i	0.859706	−	0.510790i	$-0.170647\pi$
$421$	24.4157	+	8.88659i	1.18995	+	0.433106i	0.330243	+	0.943896i	$0.392869\pi$
$422$	−2.15664	−	5.73851i	−0.104984	−	0.279346i
$423$	14.9031	+	13.2863i	0.724616	+	0.646004i
$424$	7.66787	+	12.3711i	0.372385	+	0.600793i
$425$	8.03682	−	22.0810i	0.389843	−	1.07109i
$426$	−13.2228	+	15.6131i	−0.640649	+	0.756456i
$427$	−10.1236	+	4.66848i	−0.489913	+	0.225923i
$428$	19.7568	+	10.8640i	0.954983	+	0.525129i
$429$	1.78604	+	1.54487i	0.0862310	+	0.0745869i
$430$	−11.2325	+	19.9321i	−0.541678	+	0.961213i
$431$	−12.2734	+	7.08604i	−0.591188	+	0.341322i	−0.765567	−	0.643356i	$-0.777541\pi$
$431$	−12.2734	+	7.08604i	−0.591188	+	0.341322i	0.174379	+	0.984679i	$0.444208\pi$
$432$	10.4511	−	17.9659i	0.502830	−	0.864385i
$433$		−	19.5794i		−	0.940927i	−0.882419	−	0.470464i	$-0.844087\pi$
$433$		−	19.5794i		−	0.940927i	0.882419	−	0.470464i	$-0.155913\pi$
$434$	0.139866	+	0.0641717i	0.00671379	+	0.00308034i
$435$	0.0335280	+	0.0965978i	0.00160754	+	0.00463151i
$436$	12.3090	+	20.3290i	0.589492	+	0.973585i
$437$	−1.25009	+	1.48980i	−0.0597998	+	0.0712666i
$438$	−24.4478	+	28.8671i	−1.16816	+	1.37933i
$439$	25.3546	+	9.22832i	1.21011	+	0.440444i	0.866741	−	0.498758i	$-0.166210\pi$
$439$	25.3546	+	9.22832i	1.21011	+	0.440444i	0.343367	+	0.939201i	$0.388432\pi$
$440$	2.94143	−	0.0920021i	0.140227	−	0.00438603i
$441$	7.93595	−	19.4428i	0.377902	−	0.925845i
$442$	−14.7026	−	12.0780i	−0.699330	−	0.574494i
$443$	6.60761	+	7.87465i	0.313937	+	0.374136i	0.899821	−	0.436259i	$-0.143697\pi$
$443$	6.60761	+	7.87465i	0.313937	+	0.374136i	−0.585884	+	0.810395i	$0.699253\pi$
$444$	−4.01047	+	1.48635i	−0.190328	+	0.0705393i
$445$	1.20224	−	6.81825i	0.0569917	−	0.323216i
$446$	−1.83258	−	9.79498i	−0.0867752	−	0.463806i
$447$	2.15195	+	13.3733i	0.101784	+	0.632536i
$448$	15.8131	+	14.0693i	0.747100	+	0.664711i
$449$	9.21455	−	15.9601i	0.434862	−	0.753202i	−0.562423	−	0.826850i	$-0.690131\pi$
$449$	9.21455	−	15.9601i	0.434862	−	0.753202i	0.997284	+	0.0736474i	$0.0234639\pi$
$450$	−10.0031	−	8.73247i	−0.471550	−	0.411653i
$451$	3.91211	−	6.77598i	0.184214	−	0.319068i
$452$	1.35707	−	0.526220i	0.0638314	−	0.0247513i
$453$	−0.0192646	+	1.28531i	−0.000905128	+	0.0603892i
$454$	1.15900	+	6.19476i	0.0543946	+	0.290734i
$455$	−6.45686	−	0.592530i	−0.302702	−	0.0277782i
$456$	0.206615	−	1.29469i	0.00967562	−	0.0606293i
$457$	3.75934	+	21.3202i	0.175854	+	0.997319i	0.937153	+	0.348918i	$0.113451\pi$
$457$	3.75934	+	21.3202i	0.175854	+	0.997319i	−0.761299	+	0.648401i	$0.775438\pi$
$458$	9.44478	+	25.1312i	0.441325	+	1.17430i
$459$	32.8748	+	21.0050i	1.53447	+	0.980430i
$460$	14.9563	−	13.0907i	0.697343	−	0.610356i
$461$	−14.5409	−	17.3292i	−0.677237	−	0.807100i	0.312513	−	0.949914i	$-0.398829\pi$
$461$	−14.5409	−	17.3292i	−0.677237	−	0.807100i	−0.989750	+	0.142814i	$0.954385\pi$
$462$	3.51706	−	3.45563i	0.163628	−	0.160771i
$463$	−10.0540	−	1.77280i	−0.467251	−	0.0823889i	−0.0649343	−	0.997890i	$-0.520684\pi$
$463$	−10.0540	−	1.77280i	−0.467251	−	0.0823889i	−0.402317	+	0.915501i	$0.631795\pi$
$464$	−0.127533	+	0.116407i	−0.00592056	+	0.00540407i
$465$	−0.00145996	+	0.0974073i	−6.77043e−5	+	0.00451716i
$466$	−5.65039	−	9.55536i	−0.261749	−	0.442644i
$467$	−24.6411			−1.14025			−0.570126	−	0.821557i	$-0.693106\pi$
$467$	−24.6411			−1.14025			−0.570126	+	0.821557i	$0.693106\pi$
$468$	−9.36036	+	5.29086i	−0.432683	+	0.244570i
$469$	1.74002	+	2.50759i	0.0803464	+	0.115790i
$470$	−11.2135	−	6.31919i	−0.517238	−	0.291482i
$471$	22.3793	+	27.4972i	1.03118	+	1.26700i
$472$	10.1420	+	7.98341i	0.466824	+	0.367466i
$473$	−1.56288	+	8.86354i	−0.0718614	+	0.407546i
$474$	−0.144507	+	31.6587i	−0.00663743	+	1.45413i
$475$	−0.787079	−	0.286473i	−0.0361136	−	0.0131443i
$476$	−27.6219	+	28.5546i	−1.26605	+	1.30880i
$477$	2.22388	+	15.2766i	0.101824	+	0.699468i
$478$	−28.7013	−	4.75292i	−1.31277	−	0.217393i
$479$	32.3119	−	27.1129i	1.47637	−	1.23882i	0.566407	−	0.824126i	$-0.308333\pi$
$479$	32.3119	−	27.1129i	1.47637	−	1.23882i	0.909961	−	0.414694i	$-0.136111\pi$
$480$	−4.11233	+	12.7527i	−0.187701	+	0.582078i
$481$	2.17896	+	0.384210i	0.0993522	+	0.0175185i
$482$	8.08266	−	22.9483i	0.368155	−	1.04527i
$483$	3.53984	−	33.1127i	0.161068	−	1.50668i
$484$	−19.4325	+	7.53518i	−0.883297	+	0.342508i
$485$	2.92217	−	5.06134i	0.132689	−	0.229824i
$486$	17.7662	−	13.0523i	0.805890	−	0.592065i
$487$	20.5770	−	11.8802i	0.932435	−	0.538341i	0.0448539	−	0.998994i	$-0.485718\pi$
$487$	20.5770	−	11.8802i	0.932435	−	0.538341i	0.887581	+	0.460652i	$0.152384\pi$
$488$	3.72404	−	11.3211i	0.168579	−	0.512481i
$489$	−19.8716	+	22.9738i	−0.898623	+	1.03891i
$490$	−2.32510	+	13.3370i	−0.105038	+	0.602506i
$491$	4.17972	+	11.4837i	0.188628	+	0.518252i	0.997573	−	0.0696333i	$-0.0221829\pi$
$491$	4.17972	+	11.4837i	0.188628	+	0.518252i	−0.808944	+	0.587885i	$0.799961\pi$
$492$	23.0588	+	27.1557i	1.03957	+	1.22427i
$493$	−0.208328	−	0.248275i	−0.00938261	−	0.0111818i
$494$	−0.430523	+	0.524074i	−0.0193701	+	0.0235792i
$495$	2.89982	+	1.15500i	0.130337	+	0.0519134i
$496$	−0.152109	+	0.0626598i	−0.00682991	+	0.00281351i
$497$	−5.62907	−	21.3704i	−0.252498	−	0.958594i
$498$	8.55984	+	14.9836i	0.383576	+	0.671432i
$499$	5.01483	+	13.7781i	0.224495	+	0.616794i	0.999892	−	0.0146794i	$-0.00467277\pi$
$499$	5.01483	+	13.7781i	0.224495	+	0.616794i	−0.775398	+	0.631473i	$0.782451\pi$
$500$	19.4845	+	10.7142i	0.871372	+	0.479153i
$501$	4.41937	+	27.4643i	0.197443	+	1.22701i
$502$	−9.98613	−	16.8875i	−0.445703	−	0.753727i
$503$	14.0350	−	24.3093i	0.625790	−	1.08390i	−0.362598	−	0.931946i	$-0.618110\pi$
$503$	14.0350	−	24.3093i	0.625790	−	1.08390i	0.988388	−	0.151954i	$-0.0485565\pi$
$504$	9.42767	+	20.3745i	0.419942	+	0.907551i
$505$	−1.98795	−	3.44322i	−0.0884624	−	0.153221i
$506$	3.83866	−	6.81174i	0.170649	−	0.302819i
$507$	−16.9525	−	0.254088i	−0.752887	−	0.0112844i
$508$	−14.7148	+	8.90963i	−0.652865	+	0.395301i
$509$	0.255818	−	0.304873i	0.0113390	−	0.0135132i	−0.760345	−	0.649519i	$-0.774970\pi$
$509$	0.255818	−	0.304873i	0.0113390	−	0.0135132i	0.771684	+	0.636006i	$0.219415\pi$
$510$	−23.5941	−	8.70971i	−1.04476	−	0.385673i
$511$	−10.4076	−	39.5119i	−0.460406	−	1.74790i
$512$	−22.5279	+	2.11942i	−0.995604	+	0.0936661i
$513$	0.748726	−	1.17183i	0.0330570	−	0.0517374i
$514$	−6.47075	−	17.2177i	−0.285413	−	0.759442i
$515$	−5.34249	+	14.6784i	−0.235418	+	0.646806i
$516$	−35.6089	−	20.2816i	−1.56759	−	0.892848i
$517$	−4.98647	−	0.879249i	−0.219305	−	0.0386693i
$518$	1.16809	−	4.46962i	0.0513227	−	0.196384i
$519$	−24.3368	+	13.5687i	−1.06827	+	0.595598i
$520$	5.16808	−	4.61942i	0.226635	−	0.202575i
$521$	−10.6512	−	6.14945i	−0.466636	−	0.269413i	0.248194	−	0.968710i	$-0.420163\pi$
$521$	−10.6512	−	6.14945i	−0.466636	−	0.269413i	−0.714831	+	0.699298i	$0.753496\pi$
$522$	−0.173292	+	0.0592627i	−0.00758478	+	0.00259386i
$523$	−18.1847	−	31.4968i	−0.795161	−	1.37726i	−0.922737	−	0.385430i	$-0.874053\pi$
$523$	−18.1847	−	31.4968i	−0.795161	−	1.37726i	0.127576	−	0.991829i	$-0.459280\pi$
$524$	1.83445	+	1.47523i	0.0801384	+	0.0644459i
$525$	13.9225	−	3.44498i	0.607628	−	0.150351i
$526$	11.1863	+	13.0526i	0.487745	+	0.569119i
$527$	−0.105610	−	0.290161i	−0.00460044	−	0.0126396i
$528$	0.140738	+	5.26918i	0.00612485	+	0.229312i
$529$	−5.17623	−	29.3559i	−0.225053	−	1.27634i
$530$	−3.50116	−	9.31609i	−0.152081	−	0.404665i
$531$	6.48667	+	12.0558i	0.281497	+	0.523178i
$532$	1.01783	+	0.984586i	0.0441285	+	0.0426872i
$533$	−3.20022	−	18.1494i	−0.138617	−	0.786136i
$534$	12.2024	+	2.20910i	0.528051	+	0.0955969i
$535$	−11.8102	−	9.90992i	−0.510599	−	0.428443i
$536$	−3.22946	−	0.465861i	−0.139492	−	0.0201221i
$537$	32.1723	+	6.17136i	1.38834	+	0.266314i
$538$	12.4263	−	7.34807i	0.535736	−	0.316798i
$539$	0.880238	+	5.25244i	0.0379145	+	0.226239i
$540$	−9.39527	+	10.6637i	−0.404308	+	0.458892i
$541$	−9.34308	+	16.1827i	−0.401690	+	0.695748i	−0.993930	−	0.110014i	$-0.964910\pi$
$541$	−9.34308	+	16.1827i	−0.401690	+	0.695748i	0.592240	+	0.805762i	$0.298244\pi$
$542$	−4.30463	+	7.63861i	−0.184900	+	0.328107i
$543$	1.97973	+	5.70382i	0.0849584	+	0.244774i
$544$	−2.21231	−	42.4136i	−0.0948520	−	1.81847i
$545$	−5.55788	−	15.2702i	−0.238074	−	0.654102i
$546$	1.11408	−	11.5601i	0.0476781	−	0.494728i
$547$	9.83022	−	1.73333i	0.420310	−	0.0741120i	0.0405067	−	0.999179i	$-0.487103\pi$
$547$	9.83022	−	1.73333i	0.420310	−	0.0741120i	0.379803	+	0.925067i	$0.375992\pi$
$548$	29.2379	+	9.95661i	1.24898	+	0.425325i
$549$	8.41191	−	9.43555i	0.359011	−	0.402699i
$550$	3.32223	+	0.550160i	0.141660	+	0.0234589i
$551$	−0.00884980	+	0.00742586i	−0.000377014	+	0.000316352i
$552$	23.3246	+	26.8956i	0.992762	+	1.14475i
$553$	−27.9279	−	19.7326i	−1.18762	−	0.839114i
$554$	−12.7540	+	10.9304i	−0.541864	+	0.464387i
$555$	2.88742	−	0.464625i	0.122564	−	0.0197222i
$556$	−0.223871	+	1.44517i	−0.00949424	+	0.0612891i
$557$	−17.2473			−0.730793			−0.365397	−	0.930852i	$-0.619067\pi$
$557$	−17.2473			−0.730793			−0.365397	+	0.930852i	$0.619067\pi$
$558$	−0.174456	−	0.00341133i	−0.00738530	−	0.000144413i
$559$	10.5997	+	18.3592i	0.448320	+	0.776513i
$560$	−8.73936	−	11.5365i	−0.369305	−	0.487504i
$561$	−9.89259	−	0.148273i	−0.417665	−	0.00626007i
$562$	17.6196	+	6.20582i	0.743238	+	0.261777i
$563$	−26.3681	+	9.59720i	−1.11128	+	0.404474i	−0.831464	−	0.555579i	$-0.812497\pi$
$563$	−26.3681	+	9.59720i	−1.11128	+	0.404474i	−0.279819	+	0.960053i	$0.590274\pi$
$564$	11.4101	−	20.0329i	0.480450	−	0.843538i
$565$	−0.980143	+	0.172826i	−0.0412349	+	0.00727083i
$566$	−1.92134	+	11.6023i	−0.0807599	+	0.487681i
$567$	0.549366	+	23.8054i	0.0230712	+	0.999734i
$568$	20.8193	+	11.1672i	0.873559	+	0.468565i
$569$	0.0652808	+	0.370226i	0.00273671	+	0.0155207i	0.986146	−	0.165882i	$-0.0530472\pi$
$569$	0.0652808	+	0.370226i	0.00273671	+	0.0155207i	−0.983409	+	0.181403i	$0.941936\pi$
$570$	−0.310458	+	0.841013i	−0.0130037	+	0.0352262i
$571$	−15.3844	−	42.2682i	−0.643815	−	1.76887i	−0.639397	−	0.768877i	$-0.720816\pi$
$571$	−15.3844	−	42.2682i	−0.643815	−	1.76887i	−0.00441851	−	0.999990i	$-0.501406\pi$
$572$	1.31388	−	2.38938i	0.0549361	−	0.0999051i
$573$	0.569220	−	37.9777i	0.0237795	−	1.58654i
$574$	−38.3115	+	3.59045i	−1.59909	+	0.149863i
$575$	19.6968	−	11.3719i	0.821413	−	0.474243i
$576$	−22.8079	−	7.46991i	−0.950329	−	0.311246i
$577$			24.3791i			1.01491i	0.861677	+	0.507457i	$0.169414\pi$
$577$			24.3791i			1.01491i	−0.861677	+	0.507457i	$0.830586\pi$
$578$	55.6733	−	0.580283i	2.31570	−	0.0241366i
$579$	−2.56324	−	15.9293i	−0.106525	−	0.662000i
$580$	0.100998	−	0.0611531i	0.00419373	−	0.00253925i
$581$	−18.5609	−	1.70329i	−0.770037	−	0.0706644i
$582$	9.04155	+	5.27532i	0.374784	+	0.218669i
$583$	−2.51654	−	2.99910i	−0.104225	−	0.124210i
$584$	38.4930	+	20.6471i	1.59285	+	0.854382i
$585$	6.98102	−	2.30640i	0.288630	−	0.0953580i
$586$	−35.8503	−	5.93680i	−1.48096	−	0.245247i
$587$	−0.415562	−	2.35677i	−0.0171521	−	0.0972742i	0.975030	−	0.222073i	$-0.0712824\pi$
$587$	−0.415562	−	2.35677i	−0.0171521	−	0.0972742i	−0.992182	+	0.124799i	$0.960171\pi$
$588$	−23.8692	−	4.27357i	−0.984347	−	0.176239i
$589$	−0.0103428	+	0.00376447i	−0.000426168	+	0.000155112i
$590$	−5.74321	−	6.70138i	−0.236444	−	0.275892i
$591$	−38.3365	+	13.3061i	−1.57695	+	0.547342i
$592$	2.64547	+	4.17041i	0.108728	+	0.171403i
$593$	−2.21911	−	1.28120i	−0.0911280	−	0.0526128i	0.453744	−	0.891132i	$-0.350088\pi$
$593$	−2.21911	−	1.28120i	−0.0911280	−	0.0526128i	−0.544871	+	0.838520i	$0.683422\pi$
$594$	−2.09245	+	5.18447i	−0.0858541	+	0.212722i
$595$	22.3186	−	15.4869i	0.914973	−	0.634900i
$596$	14.5829	−	5.65466i	0.597337	−	0.231624i
$597$	−5.44319	+	28.3762i	−0.222775	+	1.16136i
$598$	−3.38690	−	18.1027i	−0.138500	−	0.740273i
$599$	−14.2728	+	17.0097i	−0.583171	+	0.694997i	−0.974278	−	0.225349i	$-0.927648\pi$
$599$	−14.2728	+	17.0097i	−0.583171	+	0.694997i	0.391107	+	0.920345i	$0.372092\pi$
$600$	−7.44914	+	13.4015i	−0.304110	+	0.547115i
$601$	11.6927	−	2.06174i	0.476955	−	0.0841000i	0.0699975	−	0.997547i	$-0.477701\pi$
$601$	11.6927	−	2.06174i	0.476955	−	0.0841000i	0.406957	+	0.913447i	$0.366590\pi$
$602$	39.9997	−	18.9539i	1.63027	−	0.772503i
$603$	−2.94395	−	1.81946i	−0.119887	−	0.0740940i
$604$	1.45608	−	0.288162i	0.0592469	−	0.0117251i
$605$	14.0351	−	2.47477i	0.570608	−	0.100614i
$606$	6.18346	−	3.53249i	0.251186	−	0.143498i
$607$	−18.7878	+	6.83822i	−0.762575	+	0.277555i	−0.693887	−	0.720084i	$-0.744103\pi$
$607$	−18.7878	+	6.83822i	−0.762575	+	0.277555i	−0.0686877	+	0.997638i	$0.521881\pi$
$608$	−1.51184	+	0.0788580i	−0.0613131	+	0.00319811i
$609$	0.0548645	−	0.190059i	0.00222322	−	0.00770158i
$610$	−4.00083	+	7.09952i	−0.161989	+	0.287451i
$611$	−10.3286	+	5.96320i	−0.417849	+	0.241245i
$612$	15.7930	−	42.1885i	0.638394	−	1.70537i
$613$	−8.18505	+	14.1769i	−0.330591	+	0.572600i	−0.982628	−	0.185587i	$-0.940581\pi$
$613$	−8.18505	+	14.1769i	−0.330591	+	0.572600i	0.652037	+	0.758187i	$0.273915\pi$
$614$	3.04300	−	5.39983i	0.122805	−	0.217919i
$615$	−11.8623	−	21.2763i	−0.478336	−	0.857944i
$616$	−4.75029	−	3.13839i	−0.191395	−	0.126449i
$617$	1.03081	−	5.84602i	0.0414989	−	0.235352i	−0.957002	−	0.290080i	$-0.906318\pi$
$617$	1.03081	−	5.84602i	0.0414989	−	0.235352i	0.998501	+	0.0547280i	$0.0174292\pi$
$618$	−26.2469	−	9.68901i	−1.05581	−	0.389749i
$619$	−3.34311	−	1.21679i	−0.134371	−	0.0489070i	0.273959	−	0.961741i	$-0.411667\pi$
$619$	−3.34311	−	1.21679i	−0.134371	−	0.0489070i	−0.408330	+	0.912834i	$0.633889\pi$
$620$	0.110349	−	0.0218383i	0.00443171	−	0.000877048i
$621$	11.3069	+	36.0276i	0.453730	+	1.44574i
$622$	−1.63653	+	9.88245i	−0.0656189	+	0.396250i
$623$	−9.51138	+	9.43097i	−0.381065	+	0.377844i
$624$	8.23166	+	9.29439i	0.329530	+	0.372074i
$625$	0.340338	+	0.285577i	0.0136135	+	0.0114231i
$626$	−1.08521	−	1.26626i	−0.0433737	−	0.0506100i
$627$	−0.00528519	+	0.352622i	−0.000211070	+	0.0140824i
$628$	25.6550	−	31.9019i	1.02374	−	1.27302i
$629$	−8.02795	+	4.63494i	−0.320095	+	0.184807i
$630$	−3.61916	−	14.9181i	−0.144191	−	0.594353i
$631$	13.7719	+	7.95124i	0.548253	+	0.316534i	0.748417	−	0.663229i	$-0.230814\pi$
$631$	13.7719	+	7.95124i	0.548253	+	0.316534i	−0.200164	+	0.979762i	$0.564148\pi$
$632$	35.7853	−	7.47040i	1.42346	−	0.297157i
$633$	−7.41280	+	1.19282i	−0.294632	+	0.0474103i
$634$	29.4938	+	10.3881i	1.17135	+	0.412562i
$635$	11.0530	−	4.02298i	0.438627	−	0.159647i
$636$	16.7148	−	6.19482i	0.662785	−	0.245640i
$637$	9.54063	+	8.14456i	0.378014	+	0.322699i
$638$	0.0294827	−	0.0358892i	0.00116723	−	0.00142087i
$639$	15.5246	+	19.6699i	0.614145	+	0.778128i
$640$	15.3925	+	1.56888i	0.608441	+	0.0620156i
$641$	−21.8534	+	18.3371i	−0.863156	+	0.724274i	−0.962645	−	0.270765i	$-0.912723\pi$
$641$	−21.8534	+	18.3371i	−0.863156	+	0.724274i	0.0994898	+	0.995039i	$0.468279\pi$
$642$	17.8464	−	21.0724i	0.704339	−	0.831660i
$643$	−40.3119	+	14.6723i	−1.58975	+	0.578621i	−0.977294	−	0.211886i	$-0.932039\pi$
$643$	−40.3119	+	14.6723i	−1.58975	+	0.578621i	−0.612453	+	0.790507i	$0.709817\pi$
$644$	−38.2459	+	3.98684i	−1.50710	+	0.157103i
$645$	21.1931	+	18.3314i	0.834479	+	0.721796i
$646$	−0.0296159	−	2.84140i	−0.00116522	−	0.111793i
$647$	8.15199	+	14.1197i	0.320488	+	0.555101i	0.980589	−	0.196076i	$-0.0628198\pi$
$647$	8.15199	+	14.1197i	0.320488	+	0.555101i	−0.660101	+	0.751177i	$0.729486\pi$
$648$	−19.0231	−	16.9152i	−0.747296	−	0.664491i
$649$	−3.00673	−	1.73594i	−0.118025	−	0.0681415i
$650$	6.82745	−	4.03729i	0.267794	−	0.158355i
$651$	0.111051	−	0.152278i	0.00435242	−	0.00596824i
$652$	30.7345	+	16.9004i	1.20366	+	0.661870i
$653$	4.85229	−	27.5187i	0.189885	−	1.07689i	−0.729632	−	0.683840i	$-0.760309\pi$
$653$	4.85229	−	27.5187i	0.189885	−	1.07689i	0.919517	−	0.393050i	$-0.128580\pi$
$654$	27.3960	−	9.82996i	1.07127	−	0.384382i
$655$	−1.03467	−	1.23307i	−0.0404277	−	0.0481799i
$656$	25.1055	−	32.5868i	0.980204	−	1.27230i
$657$	28.7036	+	36.3678i	1.11983	+	1.41884i
$658$	10.6631	+	22.5031i	0.415691	+	0.877262i
$659$	8.06683	−	22.1634i	0.314239	−	0.863365i	−0.677549	−	0.735477i	$-0.736958\pi$
$659$	8.06683	−	22.1634i	0.314239	−	0.863365i	0.991789	−	0.127888i	$-0.0408198\pi$
$660$	0.605069	−	3.55311i	0.0235523	−	0.138305i
$661$	34.8385	+	6.14298i	1.35506	+	0.238934i	0.803552	−	0.595234i	$-0.202941\pi$
$661$	34.8385	+	6.14298i	1.35506	+	0.238934i	0.551510	+	0.834168i	$0.314052\pi$
$662$	9.56105	−	27.1458i	0.371601	−	1.05505i
$663$	−18.0742	+	14.7102i	−0.701945	+	0.571296i
$664$	14.8562	−	13.2790i	0.576533	−	0.515326i
$665$	−0.552031	−	0.795548i	−0.0214069	−	0.0308500i
$666$	0.808591	+	5.17550i	0.0313323	+	0.200547i
$667$		−	0.313698i		−	0.0121464i
$668$	29.9483	−	11.6128i	1.15873	−	0.449311i
$669$	−12.2031	−	0.182904i	−0.471801	−	0.00707146i
$670$	2.10439	+	0.741191i	0.0812998	+	0.0286347i
$671$	−0.556674	+	3.15706i	−0.0214902	+	0.121877i
$672$	20.7346	−	15.5589i	0.799853	−	0.600196i
$673$	19.7121	−	16.5404i	0.759847	−	0.637587i	−0.178240	−	0.983987i	$-0.557040\pi$
$673$	19.7121	−	16.5404i	0.759847	−	0.637587i	0.938087	+	0.346400i	$0.112596\pi$
$674$	−30.9369	−	25.4144i	−1.19165	−	0.978928i
$675$	−12.9152	+	9.88299i	−0.497108	+	0.380396i
$676$	3.80068	+	19.2048i	0.146180	+	0.738645i
$677$	35.4276	−	6.24685i	1.36160	−	0.240086i	0.555325	−	0.831633i	$-0.312594\pi$
$677$	35.4276	−	6.24685i	1.36160	−	0.240086i	0.806270	+	0.591548i	$0.201483\pi$
$678$	−0.301537	−	1.75696i	−0.0115805	−	0.0674757i
$679$	−10.2676	+	4.73488i	−0.394033	+	0.181708i
$680$	−4.14636	+	28.7436i	−0.159006	+	1.10227i
$681$	7.71778	+	0.115676i	0.295746	+	0.00443271i
$682$	0.0380899	−	0.0225238i	0.00145854	−	0.000862480i
$683$	−18.7941	−	10.8508i	−0.719136	−	0.415194i	0.0952984	−	0.995449i	$-0.469619\pi$
$683$	−18.7941	−	10.8508i	−0.719136	−	0.415194i	−0.814435	+	0.580255i	$0.802953\pi$
$684$	−1.50381	−	0.562942i	−0.0574997	−	0.0215246i
$685$	−18.2903	−	10.5599i	−0.698835	−	0.403473i
$686$	18.5630	−	18.4774i	0.708739	−	0.705470i
$687$	32.4636	−	5.22382i	1.23856	−	0.199301i
$688$	−14.3168	+	45.1015i	−0.545824	+	1.71948i
$689$	−9.08147	−	1.60131i	−0.345977	−	0.0610050i
$690$	−12.0752	−	21.1371i	−0.459695	−	0.804676i
$691$	6.13043	−	5.14404i	0.233213	−	0.195689i	−0.518691	−	0.854962i	$-0.673580\pi$
$691$	6.13043	−	5.14404i	0.233213	−	0.195689i	0.751903	+	0.659273i	$0.229136\pi$
$692$	21.1905	+	24.2105i	0.805540	+	0.920344i
$693$	−3.29243	−	5.06227i	−0.125069	−	0.192300i
$694$	−15.6744	−	41.7072i	−0.594991	−	1.58318i
$695$	0.342010	−	0.939666i	0.0129732	−	0.0356435i
$696$	0.108707	+	0.181399i	0.00412051	+	0.00687593i
$697$	59.1478	+	49.6309i	2.24038	+	1.87990i
$698$	−7.71758	−	9.00515i	−0.292115	−	0.340850i
$699$	−12.8442	+	4.45807i	−0.485812	+	0.168620i
$700$	−7.24724	−	14.8913i	−0.273920	−	0.562837i
$701$	13.8812			0.524286			0.262143	−	0.965029i	$-0.415571\pi$
$701$	13.8812			0.524286			0.262143	+	0.965029i	$0.415571\pi$
$702$	4.07395	+	12.5227i	0.153762	+	0.472638i
$703$	0.165213	+	0.286157i	0.00623111	+	0.0107926i
$704$	5.91626	−	1.42944i	0.222978	−	0.0538741i
$705$	−10.3129	+	11.9229i	−0.388406	+	0.449041i
$706$	14.8923	−	42.2824i	0.560480	−	1.59132i
$707$	−0.702916	+	7.65975i	−0.0264359	+	0.288075i
$708$	12.0499	−	10.2320i	0.452863	−	0.384540i
$709$	1.21044	+	0.440566i	0.0454592	+	0.0165458i	0.364650	−	0.931145i	$-0.381189\pi$
$709$	1.21044	+	0.440566i	0.0454592	+	0.0165458i	−0.319190	+	0.947691i	$0.603411\pi$
$710$	−12.4826	−	10.2544i	−0.468464	−	0.384839i
$711$	37.9662	+	7.87445i	1.42385	+	0.295315i
$712$	−0.447658	−	14.3122i	−0.0167767	−	0.536372i
$713$	0.102220	−	0.280848i	0.00382817	−	0.0105178i
$714$	27.5563	+	40.1018i	1.03127	+	1.50077i
$715$	−1.19850	+	1.42832i	−0.0448214	+	0.0534161i
$716$	−0.788449	−	37.8184i	−0.0294657	−	1.41334i
$717$	−12.6867	+	33.2953i	−0.473795	+	1.24344i
$718$	0.306886	+	29.4431i	0.0114529	+	1.09881i
$719$	9.98692	+	17.2979i	0.372449	+	0.645101i	0.989942	−	0.141476i	$-0.0451847\pi$
$719$	9.98692	+	17.2979i	0.372449	+	0.645101i	−0.617492	+	0.786577i	$0.711851\pi$
$720$	14.3073	+	8.03831i	0.533202	+	0.299570i
$721$	24.8280	−	17.2282i	0.924644	−	0.641611i
$722$	26.7673	−	0.278996i	0.996176	−	0.0103831i
$723$	−25.5798	−	15.2842i	−0.951324	−	0.568425i
$724$	5.96366	−	3.61091i	0.221638	−	0.134199i
$725$	0.126957	−	0.0462086i	0.00471507	−	0.00171614i
$726$	4.31784	+	25.1587i	0.160250	+	0.933727i
$727$	−26.6604	+	22.3707i	−0.988780	+	0.829685i	−0.985391	−	0.170309i	$-0.945523\pi$
$727$	−26.6604	+	22.3707i	−0.988780	+	0.829685i	−0.00338937	+	0.999994i	$0.501079\pi$
$728$	−13.3228	+	1.52933i	−0.493778	+	0.0566807i
$729$	−11.3457	−	24.5005i	−0.420209	−	0.907427i
$730$	−23.0792	−	18.9594i	−0.854199	−	0.701717i
$731$	−83.4612	−	30.3774i	−3.08693	−	1.12355i
$732$	−12.6833	−	7.22399i	−0.468790	−	0.267006i
$733$	−11.0108	+	13.1222i	−0.406694	+	0.484679i	−0.930049	−	0.367435i	$-0.880236\pi$
$733$	−11.0108	+	13.1222i	−0.406694	+	0.484679i	0.523355	+	0.852115i	$0.324680\pi$
$734$	−1.87286	−	10.0103i	−0.0691284	−	0.369485i
$735$	15.4435	+	6.03517i	0.569641	+	0.222611i
$736$	24.7476	−	32.8243i	0.912208	−	1.20992i
$737$	0.877677			0.0323297
$738$	38.2053	−	21.0729i	1.40636	−	0.775703i
$739$		−	23.1100i		−	0.850114i	−0.905167	−	0.425057i	$-0.860254\pi$
$739$		−	23.1100i		−	0.850114i	0.905167	−	0.425057i	$-0.139746\pi$
$740$	−1.22090	−	3.14858i	−0.0448810	−	0.115744i
$741$	0.524346	+	0.644258i	0.0192623	+	0.0236674i
$742$	−4.86834	+	18.6285i	−0.178722	+	0.683872i
$743$	−0.980828	+	1.16890i	−0.0359831	+	0.0428830i	−0.783736	−	0.621094i	$-0.786688\pi$
$743$	−0.980828	+	1.16890i	−0.0359831	+	0.0428830i	0.747753	+	0.663977i	$0.231133\pi$
$744$	0.0382128	+	0.197826i	0.00140095	+	0.00725264i
$745$	−10.5324	+	1.85715i	−0.385878	+	0.0680408i
$746$	−1.16158	+	7.01436i	−0.0425283	+	0.256814i
$747$	20.0677	−	6.63000i	0.734239	−	0.242579i
$748$	2.21788	+	11.2069i	0.0810936	+	0.409765i
$749$	7.59733	+	28.8428i	0.277601	+	1.05389i
$750$	17.6003	−	20.7819i	0.642673	−	0.758846i
$751$	12.1639	+	2.14482i	0.443866	+	0.0782655i	0.391114	−	0.920342i	$-0.372090\pi$
$751$	12.1639	+	2.14482i	0.443866	+	0.0782655i	0.0527516	+	0.998608i	$0.483201\pi$
$752$	−25.3733	−	8.05439i	−0.925268	−	0.293713i
$753$	−22.7000	+	7.87890i	−0.827233	+	0.287123i
$754$	−0.00114022	−	0.109395i	−4.15244e−5	−	0.00398392i
$755$	−1.01495			−0.0369378
$756$	26.7497	−	6.36036i	0.972877	−	0.231324i
$757$	37.7183			1.37090			0.685448	−	0.728122i	$-0.259607\pi$
$757$	37.7183			1.37090			0.685448	+	0.728122i	$0.259607\pi$
$758$	0.0903122	+	8.66470i	0.00328029	+	0.314716i
$759$	−7.24268	−	6.26468i	−0.262893	−	0.227393i
$760$	1.02457	+	0.147797i	0.0371650	+	0.00536117i
$761$	9.37636	+	1.65331i	0.339893	+	0.0599323i	0.340989	−	0.940067i	$-0.389238\pi$
$761$	9.37636	+	1.65331i	0.339893	+	0.0599323i	−0.00109667	+	0.999999i	$0.500349\pi$
$762$	7.11525	+	19.8301i	0.257758	+	0.718370i
$763$	−8.26565	+	30.3322i	−0.299237	+	1.09810i
$764$	−43.0234	+	8.51445i	−1.55653	+	0.308042i
$765$	−16.1939	+	26.2024i	−0.585493	+	0.947350i
$766$	−4.25075	+	25.6689i	−0.153586	+	0.927453i
$767$	−8.05348	+	1.42005i	−0.290794	+	0.0512749i
$768$	−2.93589	+	27.5569i	−0.105940	+	0.994373i
$769$	22.4621	−	26.7693i	0.810004	−	0.965325i	−0.189860	−	0.981811i	$-0.560803\pi$
$769$	22.4621	−	26.7693i	0.810004	−	0.965325i	0.999864	+	0.0164859i	$0.00524788\pi$
$770$	2.76975	+	2.73574i	0.0998149	+	0.0985892i
$771$	−22.2412	+	3.57892i	−0.800999	+	0.128892i
$772$	−17.3701	+	6.73543i	−0.625162	+	0.242413i
$773$			24.2240i			0.871276i	0.900122	+	0.435638i	$0.143477\pi$
$773$			24.2240i			0.871276i	−0.900122	+	0.435638i	$0.856523\pi$
$774$	−33.0068	+	37.8095i	−1.18641	+	1.35903i
$775$	0.128719			0.00462374
$776$	3.77701	−	11.4821i	0.135587	−	0.412184i
$777$	−5.08096	−	2.48934i	−0.182278	−	0.0893047i
$778$	3.02823	+	16.1856i	0.108567	+	0.580282i
$779$	1.76910	−	2.10833i	0.0633845	−	0.0755387i
$780$	−4.28777	−	7.32716i	−0.153527	−	0.262355i
$781$	−5.97164	−	2.17350i	−0.213682	−	0.0777739i
$782$	59.6212	+	48.9783i	2.13205	+	1.75146i
$783$	0.0289824	+	0.222426i	0.00103575	+	0.00794885i
$784$	0.929460	+	27.9846i	0.0331950	+	0.999449i
$785$	−21.4436	+	17.9933i	−0.765353	+	0.642208i
$786$	2.21702	−	1.84312i	0.0790786	−	0.0657421i
$787$	31.7698	−	11.5633i	1.13247	−	0.412186i	0.293283	−	0.956026i	$-0.405252\pi$
$787$	31.7698	−	11.5633i	1.13247	−	0.412186i	0.839189	+	0.543840i	$0.183030\pi$
$788$	24.2696	+	40.0829i	0.864570	+	1.42789i
$789$	18.3887	−	10.2524i	0.654654	−	0.364994i
$790$	−24.9955	+	0.260528i	−0.889299	+	0.00926917i
$791$	1.74161	+	0.821143i	0.0619245	+	0.0291965i
$792$	6.35907	+	1.11280i	0.225960	+	0.0395415i
$793$	3.77545	+	6.53927i	0.134070	+	0.232216i
$794$	0.517362	+	49.6366i	0.0183605	+	1.76154i
$795$	−12.0342	+	1.93646i	−0.426808	+	0.0686792i
$796$	33.3562	−	0.695419i	1.18228	−	0.0246485i
$797$	10.1284	−	12.0706i	0.358767	−	0.427562i	−0.556226	−	0.831031i	$-0.687751\pi$
$797$	10.1284	−	12.0706i	0.358767	−	0.427562i	0.914993	+	0.403469i	$0.132196\pi$
$798$	1.42943	−	0.982247i	0.0506013	−	0.0347712i
$799$	17.0898	−	46.9538i	0.604593	−	1.66110i
$800$	16.9298	+	5.18051i	0.598557	+	0.183159i
$801$	5.61993	−	14.1098i	0.198570	−	0.498544i
$802$	−20.3940	−	16.7535i	−0.720138	−	0.591587i
$803$	−11.0410	−	4.01860i	−0.389629	−	0.141813i
$804$	−1.34476	+	3.76315i	−0.0474261	+	0.132716i
$805$	26.1836	+	2.40280i	0.922849	+	0.0846875i
$806$	0.0346260	−	0.0983103i	0.00121965	−	0.00346283i
$807$	−5.79751	−	16.7033i	−0.204082	−	0.587983i
$808$	−5.48001	−	6.13088i	−0.192786	−	0.215684i
$809$	15.1476	+	26.2364i	0.532560	+	0.922421i	0.999277	+	0.0380144i	$0.0121033\pi$
$809$	15.1476	+	26.2364i	0.532560	+	0.922421i	−0.466717	+	0.884407i	$0.654563\pi$
$810$	10.5147	+	13.8715i	0.369449	+	0.487395i
$811$	39.5329			1.38819			0.694095	−	0.719884i	$-0.255805\pi$
$811$	39.5329			1.38819			0.694095	+	0.719884i	$0.255805\pi$
$812$	−0.227852	−	0.0161282i	−0.00799604	−	0.000565990i
$813$	8.12187	+	7.02514i	0.284846	+	0.246383i
$814$	−0.864472	−	1.00870i	−0.0302997	−	0.0353548i
$815$	−18.3724	−	15.4163i	−0.643556	−	0.540008i
$816$	−51.4492	−	7.66160i	−1.80108	−	0.268210i
$817$	−1.08281	+	2.97498i	−0.0378826	+	0.104081i
$818$	5.10295	+	13.5782i	0.178421	+	0.474751i
$819$	−13.6052	−	4.14928i	−0.475402	−	0.144988i
$820$	−21.1659	+	18.5257i	−0.739145	+	0.646944i
$821$	−14.8657	+	12.4738i	−0.518817	+	0.435339i	−0.864219	−	0.503116i	$-0.832187\pi$
$821$	−14.8657	+	12.4738i	−0.518817	+	0.435339i	0.345402	+	0.938455i	$0.387742\pi$
$822$	19.0635	−	32.6736i	0.664916	−	1.13962i
$823$	−22.4034	−	3.95033i	−0.780934	−	0.137700i	−0.231051	−	0.972942i	$-0.574216\pi$
$823$	−22.4034	−	3.95033i	−0.780934	−	0.137700i	−0.549883	+	0.835242i	$0.685328\pi$
$824$	−4.61256	+	31.9754i	−0.160686	+	1.11392i
$825$	1.46852	−	3.85400i	0.0511272	−	0.134179i
$826$	1.59320	+	17.0001i	0.0554347	+	0.591509i
$827$	−40.2781	−	23.2546i	−1.40061	−	0.808641i	−0.406153	−	0.913805i	$-0.633130\pi$
$827$	−40.2781	−	23.2546i	−1.40061	−	0.808641i	−0.994455	+	0.105164i	$0.966463\pi$
$828$	37.9577	−	21.4553i	1.31912	−	0.745622i
$829$	41.6045	+	24.0204i	1.44499	+	0.834263i	0.998176	−	0.0603670i	$-0.0192271\pi$
$829$	41.6045	+	24.0204i	1.44499	+	0.834263i	0.446809	+	0.894629i	$0.352560\pi$
$830$	−11.7279	+	6.93508i	−0.407081	+	0.240720i
$831$	10.0178	+	17.9680i	0.347514	+	0.623302i
$832$	8.51082	−	11.5366i	0.295060	−	0.399961i
$833$	−52.5537	−	0.446161i	−1.82088	−	0.0154585i
$834$	1.68025	+	0.620262i	0.0581824	+	0.0214779i
$835$	−21.6301	+	3.81396i	−0.748539	+	0.131988i
$836$	0.399471	−	0.0790564i	0.0138160	−	0.00273422i
$837$	−0.0465312	+	0.208577i	−0.00160835	+	0.00720949i
$838$	−42.4296	−	34.8556i	−1.46571	−	1.20407i
$839$	−17.7187	+	14.8677i	−0.611717	+	0.513292i	−0.895188	−	0.445689i	$-0.852959\pi$
$839$	−17.7187	+	14.8677i	−0.611717	+	0.513292i	0.283471	+	0.958981i	$0.408514\pi$
$840$	−15.9736	+	7.68400i	−0.551141	+	0.265123i
$841$	−5.03547	+	28.5576i	−0.173637	+	0.984744i
$842$	−34.6581	−	12.2070i	−1.19440	−	0.420680i
$843$	11.7351	−	19.6400i	0.404178	−	0.676439i
$844$	3.13437	+	8.08325i	0.107889	+	0.278237i
$845$		−	13.3866i		−	0.460512i
$846$	−21.2709	−	18.5690i	−0.731309	−	0.638416i
$847$	−24.9389	−	11.7583i	−0.856909	−	0.404020i
$848$	−11.0258	−	17.3814i	−0.378626	−	0.596880i
$849$	13.4594	+	5.12854i	0.461926	+	0.176011i
$850$	−11.0397	+	31.3440i	−0.378659	+	1.07509i
$851$	−8.83604	−	1.55803i	−0.302895	−	0.0534086i
$852$	18.4688	−	22.2739i	0.632730	−	0.763092i
$853$	17.0891	−	46.9520i	0.585120	−	1.60761i	−0.194188	−	0.980964i	$-0.562207\pi$
$853$	17.0891	−	46.9520i	0.585120	−	1.60761i	0.779308	−	0.626641i	$-0.215571\pi$
$854$	14.2473	−	6.75108i	0.487532	−	0.231017i
$855$	0.933987	+	0.577234i	0.0319417	+	0.0197410i
$856$	−28.0990	−	15.0719i	−0.960404	−	0.515147i
$857$	−30.4203	−	36.2535i	−1.03914	−	1.23839i	−0.970588	−	0.240747i	$-0.922608\pi$
$857$	−30.4203	−	36.2535i	−1.03914	−	1.23839i	−0.0685486	−	0.997648i	$-0.521837\pi$
$858$	−2.54848	−	2.15833i	−0.0870037	−	0.0736842i
$859$	−4.05815	+	23.0149i	−0.138462	+	0.785260i	0.833923	+	0.551880i	$0.186089\pi$
$859$	−4.05815	+	23.0149i	−0.138462	+	0.785260i	−0.972386	+	0.233379i	$0.925022\pi$
$860$	15.5905	−	28.3523i	0.531631	−	0.966807i
$861$	−5.00951	+	46.8604i	−0.170724	+	1.59700i
$862$	17.2518	−	10.2015i	0.587598	−	0.347465i
$863$	35.4182	+	20.4487i	1.20565	+	0.696082i	0.961806	−	0.273733i	$-0.0882585\pi$
$863$	35.4182	+	20.4487i	1.20565	+	0.696082i	0.243843	+	0.969815i	$0.421592\pi$
$864$	−14.5145	+	25.5603i	−0.493794	+	0.869579i
$865$	−11.0001	−	19.0527i	−0.374014	−	0.647812i
$866$	0.288592	+	27.6880i	0.00980675	+	0.940876i
$867$	12.8460	−	66.9684i	0.436274	−	2.27437i
$868$	−0.198736	−	0.0886860i	−0.00674553	−	0.00301020i
$869$	−9.24029	+	3.36319i	−0.313455	+	0.114088i
$870$	−0.0488370	−	0.136108i	−0.00165573	−	0.00461451i
$871$	1.58364	−	1.32883i	0.0536597	−	0.0450258i
$872$	−17.7062	−	28.5666i	−0.599608	−	0.967388i
$873$	8.53156	−	9.56977i	0.288750	−	0.323887i
$874$	1.74584	−	2.12520i	0.0590538	−	0.0718860i
$875$	7.49260	+	28.4452i	0.253296	+	0.961622i
$876$	34.1471	−	41.1824i	1.15372	−	1.39143i
$877$	23.7752	−	8.65347i	0.802832	−	0.292207i	0.0921723	−	0.995743i	$-0.470619\pi$
$877$	23.7752	−	8.65347i	0.802832	−	0.292207i	0.710659	+	0.703536i	$0.248397\pi$
$878$	−35.9909	−	12.6764i	−1.21463	−	0.427807i
$879$	−15.8468	+	41.5886i	−0.534500	+	1.40275i
$880$	−4.15822	+	0.173459i	−0.140174	+	0.00584730i
$881$	2.70531	+	1.56191i	0.0911443	+	0.0526222i	0.544879	−	0.838514i	$-0.316575\pi$
$881$	2.70531	+	1.56191i	0.0911443	+	0.0526222i	−0.453735	+	0.891137i	$0.649909\pi$
$882$	−10.9359	+	27.6117i	−0.368232	+	0.929734i
$883$	−36.2888	+	20.9513i	−1.22121	+	0.705068i	−0.965177	−	0.261598i	$-0.915750\pi$
$883$	−36.2888	+	20.9513i	−1.22121	+	0.705068i	−0.256037	+	0.966667i	$0.582417\pi$
$884$	20.9695	+	16.8633i	0.705280	+	0.567174i
$885$	−9.44101	+	5.26372i	−0.317356	+	0.176938i
$886$	−9.46014	−	11.0384i	−0.317820	−	0.370843i
$887$	−9.19927	−	7.71911i	−0.308881	−	0.259182i	0.475148	−	0.879906i	$-0.342394\pi$
$887$	−9.19927	−	7.71911i	−0.308881	−	0.259182i	−0.784029	+	0.620724i	$0.786839\pi$
$888$	5.64944	−	2.16102i	0.189583	−	0.0725191i
$889$	−21.9555	−	5.98295i	−0.736363	−	0.200662i
$890$	−1.59964	+	9.65966i	−0.0536199	+	0.323793i
$891$	5.71417	+	3.77278i	0.191432	+	0.126393i
$892$	2.73589	+	13.8244i	0.0916045	+	0.462876i
$893$	−1.67367	−	0.609166i	−0.0560073	−	0.0203850i
$894$	−3.24026	−	18.8800i	−0.108371	−	0.631441i
$895$	−4.49144	+	25.4722i	−0.150132	+	0.851443i
$896$	−22.5693	−	19.6628i	−0.753988	−	0.656888i
$897$	−22.5533	−	0.338035i	−0.753033	−	0.0112866i
$898$	−12.7954	+	22.7055i	−0.426988	+	0.757694i
$899$	0.000887690	−	0.00153752i	2.96061e−5	−	5.12793e-5i
$900$	14.2745	+	12.2015i	0.475815	+	0.406716i
$901$	33.4588	−	19.3175i	1.11467	−	0.643558i
$902$	−5.43239	+	9.63983i	−0.180879	+	0.320971i
$903$	−13.0213	−	52.6240i	−0.433321	−	1.75122i
$904$	−1.91133	+	0.764150i	−0.0635700	+	0.0254153i
$905$	−4.47960	+	1.63044i	−0.148907	+	0.0541977i
$906$	0.00829782	−	1.81789i	0.000275676	−	0.0603954i
$907$	12.6305	−	2.22709i	0.419388	−	0.0739494i	0.0400279	−	0.999199i	$-0.487255\pi$
$907$	12.6305	−	2.22709i	0.419388	−	0.0739494i	0.379360	+	0.925249i	$0.376144\pi$
$908$	−1.73029	−	8.74315i	−0.0574218	−	0.290152i
$909$	−2.73608	−	8.28157i	−0.0907499	−	0.274682i
$910$	9.13962	+	0.742747i	0.302975	+	0.0246218i
$911$	27.4263	−	4.83599i	0.908673	−	0.160223i	0.300272	−	0.953854i	$-0.402923\pi$
$911$	27.4263	−	4.83599i	0.908673	−	0.160223i	0.608401	+	0.793630i	$0.291811\pi$
$912$	−0.273098	+	1.83391i	−0.00904319	+	0.0607268i
$913$	−3.44522	+	4.10585i	−0.114020	+	0.135884i
$914$	−5.63046	−	30.0943i	−0.186239	−	0.995432i
$915$	7.54867	+	6.52934i	0.249551	+	0.215853i
$916$	−13.7266	−	35.3997i	−0.453541	−	1.16964i
$917$	0.258242	+	3.10338i	0.00852790	+	0.102483i
$918$	−46.7991	−	29.2194i	−1.54460	−	0.964384i
$919$	−31.5403	−	18.2098i	−1.04042	−	0.600686i	−0.120467	−	0.992717i	$-0.538439\pi$
$919$	−31.5403	−	18.2098i	−1.04042	−	0.600686i	−0.919952	+	0.392032i	$0.871772\pi$
$920$	−20.9574	+	18.7325i	−0.690944	+	0.617591i
$921$	−5.74145	−	4.96616i	−0.189187	−	0.163640i
$922$	20.8182	+	24.2915i	0.685612	+	0.799997i
$923$	−14.0657	+	5.11950i	−0.462978	+	0.168510i
$924$	−4.92267	+	4.93858i	−0.161944	+	0.162467i
$925$	−0.671020	−	3.80554i	−0.0220630	−	0.125125i
$926$	14.2439	+	2.35879i	0.468084	+	0.0775146i
$927$	−18.0147	+	29.1485i	−0.591681	+	0.957364i
$928$	0.178633	−	0.166496i	0.00586391	−	0.00546548i
$929$	28.9598	+	34.5129i	0.950140	+	1.13233i	0.991093	+	0.133172i	$0.0425162\pi$
$929$	28.9598	+	34.5129i	0.950140	+	1.13233i	−0.0409530	+	0.999161i	$0.513039\pi$
$930$	0.000628850	−	0.137769i	2.06208e−5	−	0.00451762i
$931$	−0.0159034	+	1.87328i	−0.000521214	+	0.0613943i
$932$	8.13127	+	13.4293i	0.266348	+	0.439892i
$933$	11.4643	+	4.36831i	0.375323	+	0.143012i
$934$	34.8458	−	0.363198i	1.14019	−	0.0118842i
$935$		−	7.81171i		−	0.255470i
$936$	13.1588	−	7.61997i	0.430110	−	0.249067i
$937$	17.9022	−	10.3358i	0.584839	−	0.337657i	−0.178215	−	0.983992i	$-0.557032\pi$
$937$	17.9022	−	10.3358i	0.584839	−	0.337657i	0.763054	+	0.646334i	$0.223699\pi$
$938$	−2.49758	−	3.52042i	−0.0815489	−	0.114946i
$939$	−1.78393	+	0.994607i	−0.0582163	+	0.0324578i
$940$	15.9505	+	8.77091i	0.520248	+	0.286076i
$941$	−7.44278	−	20.4489i	−0.242628	−	0.666614i	−0.999909	−	0.0135245i	$-0.995695\pi$
$941$	−7.44278	−	20.4489i	−0.242628	−	0.666614i	0.757281	−	0.653089i	$-0.226527\pi$
$942$	−32.0527	−	38.5550i	−1.04433	−	1.25619i
$943$	12.9774	+	73.5984i	0.422602	+	2.39669i
$944$	−14.4599	−	11.1401i	−0.470629	−	0.362581i
$945$	−18.7873	+	0.715397i	−0.611151	+	0.0232719i
$946$	2.07948	−	12.5573i	0.0676099	−	0.408273i
$947$	−0.876427	+	0.154538i	−0.0284801	+	0.00502180i	−0.187870	−	0.982194i	$-0.560158\pi$
$947$	−0.876427	+	0.154538i	−0.0284801	+	0.00502180i	0.159390	+	0.987216i	$0.449047\pi$
$948$	−0.262282	−	44.7719i	−0.00851853	−	1.45412i
$949$	−26.0062	+	9.46548i	−0.844197	+	0.307262i
$950$	1.11726	+	0.393511i	0.0362487	+	0.0127672i
$951$	19.6436	−	32.8759i	0.636989	−	1.06607i
$952$	38.6403	−	40.7872i	1.25234	−	1.32192i
$953$	1.60066	+	2.77242i	0.0518505	+	0.0898076i	0.890786	−	0.454424i	$-0.150155\pi$
$953$	1.60066	+	2.77242i	0.0518505	+	0.0898076i	−0.838935	+	0.544231i	$0.816821\pi$
$954$	−3.37004	−	21.5704i	−0.109109	−	0.698368i
$955$	29.9892			0.970428
$956$	40.6576	+	6.29823i	1.31496	+	0.203699i
$957$	−0.0359078	−	0.0441195i	−0.00116073	−	0.00142618i
$958$	−45.2938	+	38.8176i	−1.46338	+	1.25414i
$959$	17.1105	+	37.1040i	0.552528	+	1.19815i
$960$	5.62743	−	18.0947i	0.181624	−	0.584003i
$961$	−23.7461	+	19.9253i	−0.766003	+	0.642753i
$962$	−3.08702	−	0.511209i	−0.0995294	−	0.0164820i
$963$	−20.9530	−	26.5477i	−0.675201	−	0.855486i
$964$	−11.0917	+	32.5712i	−0.357241	+	1.04905i
$965$	12.5455	−	2.21211i	0.403853	−	0.0712102i
$966$	−4.51775	+	46.8781i	−0.145356	+	1.50828i
$967$	−2.38462	−	6.55168i	−0.0766841	−	0.210688i	0.895427	−	0.445208i	$-0.146870\pi$
$967$	−2.38462	−	6.55168i	−0.0766841	−	0.210688i	−0.972111	+	0.234520i	$0.924648\pi$
$968$	27.3692	−	10.9422i	0.879680	−	0.351696i
$969$	−3.41787	−	0.655622i	−0.109798	−	0.0210616i
$970$	−4.05774	+	7.20050i	−0.130286	+	0.231194i
$971$	29.8097	−	51.6319i	0.956638	−	1.65695i	0.226063	−	0.974113i	$-0.427414\pi$
$971$	29.8097	−	51.6319i	0.956638	−	1.65695i	0.730575	−	0.682833i	$-0.239252\pi$
$972$	−24.9314	+	18.7196i	−0.799676	+	0.600432i
$973$	−1.58942	+	1.10290i	−0.0509544	+	0.0353573i
$974$	−28.9236	+	17.1035i	−0.926773	+	0.548030i
$975$	−3.18536	−	9.17737i	−0.102013	−	0.293911i
$976$	−5.09943	+	16.0644i	−0.163229	+	0.514210i
$977$	21.2759	+	17.8526i	0.680676	+	0.571155i	0.916204	−	0.400713i	$-0.131238\pi$
$977$	21.2759	+	17.8526i	0.680676	+	0.571155i	−0.235528	+	0.971868i	$0.575682\pi$
$978$	27.7625	−	32.7810i	0.887746	−	1.04822i
$979$	0.668839	+	3.79317i	0.0213762	+	0.121230i
$980$	3.09143	−	18.8947i	0.0987522	−	0.603568i
$981$	−5.13525	−	35.2759i	−0.163956	−	1.12627i
$982$	−6.07996	−	16.1779i	−0.194019	−	0.516258i
$983$	3.72394	+	21.1195i	0.118775	+	0.673608i	0.984812	+	0.173627i	$0.0555486\pi$
$983$	3.72394	+	21.1195i	0.118775	+	0.673608i	−0.866036	+	0.499981i	$0.833340\pi$
$984$	−33.0085	−	38.0620i	−1.05227	−	1.21337i
$985$	−10.9585	−	30.1082i	−0.349167	−	0.959328i
$986$	0.298264	+	0.348025i	0.00949865	+	0.0110834i
$987$	29.6053	−	7.32553i	0.942347	−	0.233174i
$988$	0.601094	−	0.747459i	0.0191233	−	0.0237798i
$989$	−42.9834	−	74.4495i	−1.36679	−	2.36736i
$990$	−4.11777	−	1.59059i	−0.130871	−	0.0505522i
$991$	−42.7810	−	24.6996i	−1.35898	−	0.784610i	−0.369497	−	0.929232i	$-0.620470\pi$
$991$	−42.7810	−	24.6996i	−1.35898	−	0.784610i	−0.989487	+	0.144622i	$0.953803\pi$
$992$	0.214180	−	0.0908516i	0.00680022	−	0.00288454i
$993$	−30.2586	−	18.0798i	−0.960228	−	0.573745i
$994$	8.27526	+	30.1377i	0.262475	+	0.955910i
$995$	−22.4667	−	3.96149i	−0.712244	−	0.125588i
$996$	−12.3256	−	21.0627i	−0.390553	−	0.667397i
$997$	1.39018	−	3.81949i	0.0440274	−	0.120964i	−0.915730	−	0.401793i	$-0.868387\pi$
$997$	1.39018	−	3.81949i	0.0440274	−	0.120964i	0.959758	+	0.280829i	$0.0906093\pi$
$998$	−7.29474	−	19.4102i	−0.230911	−	0.614421i
$999$	6.40908	+	0.288356i	0.202774	+	0.00912316i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bt.a.103.1	✓	840
4.3	odd	2	inner	756.2.bt.a.103.122	yes	840
7.3	odd	6		756.2.cd.a.535.97	yes	840
27.16	even	9		756.2.cd.a.691.64	yes	840
28.3	even	6		756.2.cd.a.535.64	yes	840
108.43	odd	18		756.2.cd.a.691.97	yes	840
189.178	odd	18	inner	756.2.bt.a.367.122	yes	840
756.367	even	18	inner	756.2.bt.a.367.1	yes	840

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bt.a.103.1	✓	840	1.1	even	1	trivial
756.2.bt.a.103.122	yes	840	4.3	odd	2	inner
756.2.bt.a.367.1	yes	840	756.367	even	18	inner
756.2.bt.a.367.122	yes	840	189.178	odd	18	inner
756.2.cd.a.535.64	yes	840	28.3	even	6
756.2.cd.a.535.97	yes	840	7.3	odd	6
756.2.cd.a.691.64	yes	840	27.16	even	9
756.2.cd.a.691.97	yes	840	108.43	odd	18

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bt (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41414 + 0.0147396i) q^{2} +(-0.326297 + 1.70104i) q^{3} +(1.99957 - 0.0416875i) q^{4} +(-1.34679 - 0.237475i) q^{5} +(0.436356 - 2.41031i) q^{6} +(1.86287 + 1.87875i) q^{7} +(-2.82704 + 0.0884245i) q^{8} +(-2.78706 - 1.11009i) q^{9} +O(q^{10})\)	\(q+(-1.41414 + 0.0147396i) q^{2} +(-0.326297 + 1.70104i) q^{3} +(1.99957 - 0.0416875i) q^{4} +(-1.34679 - 0.237475i) q^{5} +(0.436356 - 2.41031i) q^{6} +(1.86287 + 1.87875i) q^{7} +(-2.82704 + 0.0884245i) q^{8} +(-2.78706 - 1.11009i) q^{9} +(1.90804 + 0.315971i) q^{10} +(0.749254 - 0.132114i) q^{11} +(-0.581540 + 3.41494i) q^{12} +(1.15190 - 1.37278i) q^{13} +(-2.66205 - 2.62936i) q^{14} +(0.843407 - 2.21345i) q^{15} +(3.99652 - 0.166714i) q^{16} +7.50794i q^{17} +(3.95765 + 1.52873i) q^{18} +0.267621 q^{19} +(-2.70289 - 0.418703i) q^{20} +(-3.80368 + 2.55578i) q^{21} +(-1.05760 + 0.197870i) q^{22} +(-4.67111 + 5.56681i) q^{23} +(0.772042 - 4.83776i) q^{24} +(-2.94102 - 1.07044i) q^{25} +(-1.60870 + 1.95827i) q^{26} +(2.79771 - 4.37868i) q^{27} +(3.80325 + 3.67903i) q^{28} +(-0.0330684 + 0.0277477i) q^{29} +(-1.16007 + 3.14255i) q^{30} +(-0.0386472 + 0.0140664i) q^{31} +(-5.64917 + 0.294663i) q^{32} +(-0.0197488 + 1.31762i) q^{33} +(-0.110664 - 10.6173i) q^{34} +(-2.06274 - 2.97267i) q^{35} +(-5.61919 - 2.10351i) q^{36} +(0.617338 + 1.06926i) q^{37} +(-0.378453 + 0.00394461i) q^{38} +(1.95928 + 2.40735i) q^{39} +(3.82843 + 0.552264i) q^{40} +(6.61046 - 7.87804i) q^{41} +(5.34125 - 3.67029i) q^{42} +(-4.04604 + 11.1164i) q^{43} +(1.49267 - 0.295404i) q^{44} +(3.48996 + 2.15691i) q^{45} +(6.52354 - 7.94109i) q^{46} +(-6.25388 - 2.27623i) q^{47} +(-1.02047 + 6.85264i) q^{48} +(-0.0594252 + 6.99975i) q^{49} +(4.17478 + 1.47040i) q^{50} +(-12.7713 - 2.44982i) q^{51} +(2.24606 - 2.79297i) q^{52} +(-2.57294 - 4.45646i) q^{53} +(-3.89180 + 6.23329i) q^{54} -1.04046 q^{55} +(-5.43255 - 5.14659i) q^{56} +(-0.0873239 + 0.455234i) q^{57} +(0.0463543 - 0.0397264i) q^{58} +(-3.49575 - 2.93328i) q^{59} +(1.59417 - 4.46110i) q^{60} +(-1.44114 + 3.95949i) q^{61} +(0.0544451 - 0.0204615i) q^{62} +(-3.10636 - 7.30415i) q^{63} +(7.98436 - 0.499960i) q^{64} +(-1.87736 + 1.57529i) q^{65} +(0.00850638 - 1.86358i) q^{66} +(1.13608 + 0.200322i) q^{67} +(0.312987 + 15.0126i) q^{68} +(-7.94519 - 9.76217i) q^{69} +(2.96081 + 4.17335i) q^{70} +(-7.23371 - 4.17638i) q^{71} +(7.97730 + 2.89182i) q^{72} +(-13.3745 - 7.72174i) q^{73} +(-0.888761 - 1.50298i) q^{74} +(2.78051 - 4.65350i) q^{75} +(0.535126 - 0.0111564i) q^{76} +(1.64397 + 1.16155i) q^{77} +(-2.80618 - 3.37544i) q^{78} +(-12.7284 + 2.24436i) q^{79} +(-5.42206 - 0.724547i) q^{80} +(6.53542 + 6.18776i) q^{81} +(-9.23197 + 11.2381i) q^{82} +(-5.39667 + 4.52834i) q^{83} +(-7.49916 + 5.26902i) q^{84} +(1.78295 - 10.1116i) q^{85} +(5.55780 - 15.7797i) q^{86} +(-0.0364097 - 0.0653046i) q^{87} +(-2.10649 + 0.439744i) q^{88} +5.06260i q^{89} +(-4.96708 - 2.99872i) q^{90} +(4.72494 - 0.393176i) q^{91} +(-9.10813 + 11.3259i) q^{92} +(-0.0113171 - 0.0703301i) q^{93} +(8.87740 + 3.12672i) q^{94} +(-0.360429 - 0.0635533i) q^{95} +(1.34207 - 9.70561i) q^{96} +(-1.46164 + 4.01581i) q^{97} +(-0.0191378 - 9.89948i) q^{98} +(-2.23487 - 0.463528i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9}+O(q^{10}) \) 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9	\( 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9} - 9 q^{12} - 21 q^{14} - 3 q^{16} - 3 q^{18} - 12 q^{21} - 12 q^{22} - 9 q^{24} - 6 q^{25} - 18 q^{26} - 12 q^{28} - 36 q^{29} - 39 q^{30} + 27 q^{32} - 18 q^{33} + 18 q^{34} + 18 q^{36} + 6 q^{37} - 99 q^{38} + 36 q^{40} + 9 q^{42} + 3 q^{44} - 18 q^{45} + 3 q^{46} - 12 q^{49} + 3 q^{50} - 9 q^{52} - 12 q^{53} - 135 q^{54} + 15 q^{56} - 42 q^{57} - 3 q^{58} - 33 q^{60} - 18 q^{61} - 99 q^{62} - 6 q^{64} + 18 q^{65} - 9 q^{66} - 54 q^{68} + 72 q^{69} - 36 q^{70} - 111 q^{72} - 18 q^{73} + 93 q^{74} - 36 q^{76} - 36 q^{77} + 6 q^{78} - 18 q^{80} - 30 q^{81} - 18 q^{82} + 84 q^{84} + 6 q^{85} + 135 q^{86} - 51 q^{88} + 81 q^{90} + 48 q^{92} - 6 q^{93} - 9 q^{94} - 9 q^{96} - 117 q^{98}+O(q^{100}) \) 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9 - 9 * q^12 - 21 * q^14 - 3 * q^16 - 3 * q^18 - 12 * q^21 - 12 * q^22 - 9 * q^24 - 6 * q^25 - 18 * q^26 - 12 * q^28 - 36 * q^29 - 39 * q^30 + 27 * q^32 - 18 * q^33 + 18 * q^34 + 18 * q^36 + 6 * q^37 - 99 * q^38 + 36 * q^40 + 9 * q^42 + 3 * q^44 - 18 * q^45 + 3 * q^46 - 12 * q^49 + 3 * q^50 - 9 * q^52 - 12 * q^53 - 135 * q^54 + 15 * q^56 - 42 * q^57 - 3 * q^58 - 33 * q^60 - 18 * q^61 - 99 * q^62 - 6 * q^64 + 18 * q^65 - 9 * q^66 - 54 * q^68 + 72 * q^69 - 36 * q^70 - 111 * q^72 - 18 * q^73 + 93 * q^74 - 36 * q^76 - 36 * q^77 + 6 * q^78 - 18 * q^80 - 30 * q^81 - 18 * q^82 + 84 * q^84 + 6 * q^85 + 135 * q^86 - 51 * q^88 + 81 * q^90 + 48 * q^92 - 6 * q^93 - 9 * q^94 - 9 * q^96 - 117 * q^98

Introduction

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