LMFDB - Embedded newform 552.2.t.a.235.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(19,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 0, 15]))

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

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

chi := DirichletCharacter("552.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.t (of order $22$, degree $10$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			235.1
Character	$\chi$	$=$	552.235
Dual form			552.2.t.a.451.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39576 - 0.227696i) q^{2} +(0.654861 - 0.755750i) q^{3} +(1.89631 + 0.635619i) q^{4} +(-0.355055 + 2.46946i) q^{5} +(-1.08611 + 0.905738i) q^{6} +(0.661764 + 1.44906i) q^{7} +(-2.50207 - 1.31896i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(-1.39576 - 0.227696i) q^{2} +(0.654861 - 0.755750i) q^{3} +(1.89631 + 0.635619i) q^{4} +(-0.355055 + 2.46946i) q^{5} +(-1.08611 + 0.905738i) q^{6} +(0.661764 + 1.44906i) q^{7} +(-2.50207 - 1.31896i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(1.05786 - 3.36594i) q^{10} +(-0.328891 - 1.12010i) q^{11} +(1.72219 - 1.01689i) q^{12} +(3.21886 + 1.47000i) q^{13} +(-0.593720 - 2.17323i) q^{14} +(1.63378 + 1.88549i) q^{15} +(3.19198 + 2.41066i) q^{16} +(-0.248908 - 0.387309i) q^{17} +(-0.0267406 + 1.41396i) q^{18} +(-3.28099 + 5.10531i) q^{19} +(-2.24293 + 4.45718i) q^{20} +(1.52849 + 0.448805i) q^{21} +(0.204012 + 1.63828i) q^{22} +(-4.16216 + 2.38252i) q^{23} +(-2.63531 + 1.02721i) q^{24} +(-1.17471 - 0.344926i) q^{25} +(-4.15805 - 2.78470i) q^{26} +(-0.841254 - 0.540641i) q^{27} +(0.333858 + 3.16850i) q^{28} +(3.40681 + 5.30111i) q^{29} +(-1.85106 - 3.00370i) q^{30} +(0.449612 - 0.389591i) q^{31} +(-3.90634 - 4.09151i) q^{32} +(-1.06189 - 0.484951i) q^{33} +(0.259228 + 0.597267i) q^{34} +(-3.81336 + 1.11970i) q^{35} +(0.359277 - 1.96747i) q^{36} +(-0.0548572 - 0.381540i) q^{37} +(5.74194 - 6.37874i) q^{38} +(3.21886 - 1.47000i) q^{39} +(4.14548 - 5.71046i) q^{40} +(-0.738033 + 5.13313i) q^{41} +(-2.03122 - 0.974457i) q^{42} +(2.16580 + 1.87668i) q^{43} +(0.0882783 - 2.33311i) q^{44} +2.49486 q^{45} +(6.35188 - 2.37772i) q^{46} +0.152392i q^{47} +(3.91216 - 0.833687i) q^{48} +(2.92218 - 3.37238i) q^{49} +(1.56108 + 0.748911i) q^{50} +(-0.455709 - 0.0655210i) q^{51} +(5.16958 + 4.83355i) q^{52} +(3.00967 + 6.59027i) q^{53} +(1.05109 + 0.946157i) q^{54} +(2.88282 - 0.414487i) q^{55} +(0.255468 - 4.49849i) q^{56} +(1.70975 + 5.82287i) q^{57} +(-3.54806 - 8.17481i) q^{58} +(0.844965 - 1.85022i) q^{59} +(1.89971 + 4.61393i) q^{60} +(6.17484 + 7.12615i) q^{61} +(-0.716261 + 0.441402i) q^{62} +(1.34013 - 0.861251i) q^{63} +(4.52071 + 6.60024i) q^{64} +(-4.77298 + 7.42691i) q^{65} +(1.37173 + 0.918665i) q^{66} +(0.430258 - 1.46532i) q^{67} +(-0.225826 - 0.892668i) q^{68} +(-0.925049 + 4.70577i) q^{69} +(5.57750 - 0.694554i) q^{70} +(0.422371 - 1.43846i) q^{71} +(-0.949449 + 2.66431i) q^{72} +(-9.07676 - 5.83328i) q^{73} +(-0.0103075 + 0.545030i) q^{74} +(-1.02995 + 0.661908i) q^{75} +(-9.46680 + 7.59579i) q^{76} +(1.40545 - 1.21783i) q^{77} +(-4.82747 + 1.31885i) q^{78} +(3.40708 - 7.46047i) q^{79} +(-7.08636 + 7.02654i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(2.19891 - 6.99659i) q^{82} +(4.37321 - 0.628773i) q^{83} +(2.61322 + 1.82261i) q^{84} +(1.04482 - 0.477153i) q^{85} +(-2.59563 - 3.11254i) q^{86} +(6.23730 + 0.896788i) q^{87} +(-0.654455 + 3.23636i) q^{88} +(-2.04054 - 1.76814i) q^{89} +(-3.48223 - 0.568069i) q^{90} +5.63711i q^{91} +(-9.40712 + 1.87244i) q^{92} -0.594922i q^{93} +(0.0346992 - 0.212704i) q^{94} +(-11.4424 - 9.91493i) q^{95} +(-5.65027 + 0.272847i) q^{96} +(10.0554 + 1.44575i) q^{97} +(-4.84655 + 4.04167i) q^{98} +(-1.06189 + 0.484951i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9}+O(q^{10}) $ 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9	$ 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9} + 4 q^{12} - 4 q^{16} + 44 q^{17} - 55 q^{20} - 24 q^{25} + 24 q^{27} + 33 q^{34} + 7 q^{36} - 132 q^{38} + 11 q^{40} - 66 q^{42} + 77 q^{44} + 37 q^{48} - 56 q^{49} - 37 q^{50} - 55 q^{52} - 11 q^{54} + 132 q^{56} + 37 q^{58} + 11 q^{60} + 51 q^{62} - 4 q^{64} - 55 q^{66} - 132 q^{70} + 144 q^{73} + 44 q^{74} + 24 q^{75} - 55 q^{76} - 198 q^{80} - 24 q^{81} - 26 q^{82} + 44 q^{84} - 110 q^{86} + 22 q^{88} - 139 q^{92} - 117 q^{94} - 209 q^{98}+O(q^{100}) $ 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9 + 4 * q^12 - 4 * q^16 + 44 * q^17 - 55 * q^20 - 24 * q^25 + 24 * q^27 + 33 * q^34 + 7 * q^36 - 132 * q^38 + 11 * q^40 - 66 * q^42 + 77 * q^44 + 37 * q^48 - 56 * q^49 - 37 * q^50 - 55 * q^52 - 11 * q^54 + 132 * q^56 + 37 * q^58 + 11 * q^60 + 51 * q^62 - 4 * q^64 - 55 * q^66 - 132 * q^70 + 144 * q^73 + 44 * q^74 + 24 * q^75 - 55 * q^76 - 198 * q^80 - 24 * q^81 - 26 * q^82 + 44 * q^84 - 110 * q^86 + 22 * q^88 - 139 * q^92 - 117 * q^94 - 209 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{1}{22}\right)$	$1$	$-1$	$-1$

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 $

$2$	−1.39576	−	0.227696i	−0.986954	−	0.161005i
$2$	−1.39576	−	0.227696i	−0.986954	−	0.161005i
$3$	0.654861	−	0.755750i	0.378084	−	0.436332i
$3$	0.654861	−	0.755750i	0.378084	−	0.436332i
$4$	1.89631	+	0.635619i	0.948155	+	0.317810i
$5$	−0.355055	+	2.46946i	−0.158785	+	1.10438i	0.742090	+	0.670300i	$0.233834\pi$
$5$	−0.355055	+	2.46946i	−0.158785	+	1.10438i	−0.900876	+	0.434077i	$0.857075\pi$
$6$	−1.08611	+	0.905738i	−0.443403	+	0.369766i
$7$	0.661764	+	1.44906i	0.250123	+	0.547693i	0.992494	−	0.122296i	$-0.0390258\pi$
$7$	0.661764	+	1.44906i	0.250123	+	0.547693i	−0.742370	+	0.669990i	$0.766299\pi$
$8$	−2.50207	−	1.31896i	−0.884615	−	0.466321i
$9$	−0.142315	−	0.989821i	−0.0474383	−	0.329940i
$10$	1.05786	−	3.36594i	0.334524	−	1.06440i
$11$	−0.328891	−	1.12010i	−0.0991645	−	0.337723i	0.894935	−	0.446197i	$-0.147222\pi$
$11$	−0.328891	−	1.12010i	−0.0991645	−	0.337723i	−0.994099	+	0.108474i	$0.965404\pi$
$12$	1.72219	−	1.01689i	0.497153	−	0.293552i
$13$	3.21886	+	1.47000i	0.892750	+	0.407705i	0.808333	−	0.588725i	$-0.200370\pi$
$13$	3.21886	+	1.47000i	0.892750	+	0.407705i	0.0844167	+	0.996431i	$0.473097\pi$
$14$	−0.593720	−	2.17323i	−0.158678	−	0.580819i
$15$	1.63378	+	1.88549i	0.421841	+	0.486830i
$16$	3.19198	+	2.41066i	0.797994	+	0.602665i
$17$	−0.248908	−	0.387309i	−0.0603691	−	0.0939362i	0.809757	−	0.586766i	$-0.199599\pi$
$17$	−0.248908	−	0.387309i	−0.0603691	−	0.0939362i	−0.870126	+	0.492829i	$0.835963\pi$
$18$	−0.0267406	+	1.41396i	−0.00630282	+	0.333274i
$19$	−3.28099	+	5.10531i	−0.752710	+	1.17124i	0.227597	+	0.973756i	$0.426913\pi$
$19$	−3.28099	+	5.10531i	−0.752710	+	1.17124i	−0.980306	+	0.197484i	$0.936723\pi$
$20$	−2.24293	+	4.45718i	−0.501535	+	0.996656i
$21$	1.52849	+	0.448805i	0.333544	+	0.0979373i
$22$	0.204012	+	1.63828i	0.0434955	+	0.349283i
$23$	−4.16216	+	2.38252i	−0.867871	+	0.496790i
$23$	−4.16216	+	2.38252i	−0.867871	+	0.496790i
$24$	−2.63531	+	1.02721i	−0.537930	+	0.209678i
$25$	−1.17471	−	0.344926i	−0.234942	−	0.0689851i
$26$	−4.15805	−	2.78470i	−0.815460	−	0.546124i
$27$	−0.841254	−	0.540641i	−0.161899	−	0.104046i
$28$	0.333858	+	3.16850i	0.0630932	+	0.598789i
$29$	3.40681	+	5.30111i	0.632629	+	0.984391i	0.998555	+	0.0537464i	$0.0171163\pi$
$29$	3.40681	+	5.30111i	0.632629	+	0.984391i	−0.365925	+	0.930644i	$0.619247\pi$
$30$	−1.85106	−	3.00370i	−0.337955	−	0.548398i
$31$	0.449612	−	0.389591i	0.0807528	−	0.0699727i	−0.613549	−	0.789657i	$-0.710259\pi$
$31$	0.449612	−	0.389591i	0.0807528	−	0.0699727i	0.694302	+	0.719684i	$0.255713\pi$
$32$	−3.90634	−	4.09151i	−0.690551	−	0.723284i
$33$	−1.06189	−	0.484951i	−0.184852	−	0.0844191i
$34$	0.259228	+	0.597267i	0.0444573	+	0.102430i
$35$	−3.81336	+	1.11970i	−0.644576	+	0.189264i
$36$	0.359277	−	1.96747i	0.0598795	−	0.327911i
$37$	−0.0548572	−	0.381540i	−0.00901847	−	0.0627248i	0.984815	−	0.173606i	$-0.0555419\pi$
$37$	−0.0548572	−	0.381540i	−0.00901847	−	0.0627248i	−0.993834	+	0.110881i	$0.964633\pi$
$38$	5.74194	−	6.37874i	0.931465	−	1.03477i
$39$	3.21886	−	1.47000i	0.515429	−	0.235389i
$40$	4.14548	−	5.71046i	0.655458	−	0.902903i
$41$	−0.738033	+	5.13313i	−0.115261	+	0.801661i	0.847400	+	0.530954i	$0.178166\pi$
$41$	−0.738033	+	5.13313i	−0.115261	+	0.801661i	−0.962662	+	0.270707i	$0.912743\pi$
$42$	−2.03122	−	0.974457i	−0.313424	−	0.150362i
$43$	2.16580	+	1.87668i	0.330281	+	0.286190i	0.804176	−	0.594391i	$-0.202607\pi$
$43$	2.16580	+	1.87668i	0.330281	+	0.286190i	−0.473895	+	0.880581i	$0.657152\pi$
$44$	0.0882783	−	2.33311i	0.0133085	−	0.351729i
$45$	2.49486			0.371911
$46$	6.35188	−	2.37772i	0.936534	−	0.350576i
$47$			0.152392i			0.0222287i	0.999938	+	0.0111144i	$0.00353788\pi$
$47$			0.152392i			0.0222287i	−0.999938	+	0.0111144i	$0.996462\pi$
$48$	3.91216	−	0.833687i	0.564671	−	0.120332i
$49$	2.92218	−	3.37238i	0.417454	−	0.481768i
$50$	1.56108	+	0.748911i	0.220770	+	0.105912i
$51$	−0.455709	−	0.0655210i	−0.0638120	−	0.00917478i
$52$	5.16958	+	4.83355i	0.716892	+	0.670292i
$53$	3.00967	+	6.59027i	0.413410	+	0.905243i	0.995733	+	0.0922845i	$0.0294169\pi$
$53$	3.00967	+	6.59027i	0.413410	+	0.905243i	−0.582322	+	0.812958i	$0.697856\pi$
$54$	1.05109	+	0.946157i	0.143035	+	0.128756i
$55$	2.88282	−	0.414487i	0.388719	−	0.0558894i
$56$	0.255468	−	4.49849i	0.0341383	−	0.601136i
$57$	1.70975	+	5.82287i	0.226462	+	0.771258i
$58$	−3.54806	−	8.17481i	−0.465884	−	1.07340i
$59$	0.844965	−	1.85022i	0.110005	−	0.240878i	−0.846621	−	0.532196i	$-0.821367\pi$
$59$	0.844965	−	1.85022i	0.110005	−	0.240878i	0.956626	+	0.291319i	$0.0940941\pi$
$60$	1.89971	+	4.61393i	0.245251	+	0.595655i
$61$	6.17484	+	7.12615i	0.790608	+	0.912410i	0.997827	−	0.0658847i	$-0.0209870\pi$
$61$	6.17484	+	7.12615i	0.790608	+	0.912410i	−0.207220	+	0.978294i	$0.566442\pi$
$62$	−0.716261	+	0.441402i	−0.0909652	+	0.0560581i
$63$	1.34013	−	0.861251i	0.168841	−	0.108507i
$64$	4.52071	+	6.60024i	0.565089	+	0.825030i
$65$	−4.77298	+	7.42691i	−0.592016	+	0.921194i
$66$	1.37173	+	0.918665i	0.168848	+	0.113080i
$67$	0.430258	−	1.46532i	0.0525643	−	0.179018i	−0.929027	−	0.370013i	$-0.879353\pi$
$67$	0.430258	−	1.46532i	0.0525643	−	0.179018i	0.981591	+	0.190995i	$0.0611715\pi$
$68$	−0.225826	−	0.892668i	−0.0273854	−	0.108252i
$69$	−0.925049	+	4.70577i	−0.111363	+	0.566508i
$70$	5.57750	−	0.694554i	0.666639	−	0.0830151i
$71$	0.422371	−	1.43846i	0.0501262	−	0.170714i	−0.930626	−	0.365973i	$-0.880736\pi$
$71$	0.422371	−	1.43846i	0.0501262	−	0.170714i	0.980752	+	0.195258i	$0.0625545\pi$
$72$	−0.949449	+	2.66431i	−0.111894	+	0.313992i
$73$	−9.07676	−	5.83328i	−1.06235	−	0.682733i	−0.111938	−	0.993715i	$-0.535706\pi$
$73$	−9.07676	−	5.83328i	−1.06235	−	0.682733i	−0.950416	+	0.310982i	$0.899342\pi$
$74$	−0.0103075	+	0.545030i	−0.00119823	+	0.0633585i
$75$	−1.02995	+	0.661908i	−0.118928	+	0.0764305i
$76$	−9.46680	+	7.59579i	−1.08592	+	0.871297i
$77$	1.40545	−	1.21783i	0.160165	−	0.138784i
$78$	−4.82747	+	1.31885i	−0.546604	+	0.149331i
$79$	3.40708	−	7.46047i	0.383327	−	0.839369i	−0.615365	−	0.788242i	$-0.710991\pi$
$79$	3.40708	−	7.46047i	0.383327	−	0.839369i	0.998692	−	0.0511267i	$-0.0162812\pi$
$80$	−7.08636	+	7.02654i	−0.792279	+	0.785591i
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$	2.19891	−	6.99659i	0.242829	−	0.772644i
$83$	4.37321	−	0.628773i	0.480022	−	0.0690168i	0.101944	−	0.994790i	$-0.467494\pi$
$83$	4.37321	−	0.628773i	0.480022	−	0.0690168i	0.378079	+	0.925773i	$0.376585\pi$
$84$	2.61322	+	1.82261i	0.285126	+	0.198863i
$85$	1.04482	−	0.477153i	0.113327	−	0.0517545i
$86$	−2.59563	−	3.11254i	−0.279894	−	0.335634i
$87$	6.23730	+	0.896788i	0.668708	+	0.0961458i
$88$	−0.654455	+	3.23636i	−0.0697651	+	0.344998i
$89$	−2.04054	−	1.76814i	−0.216297	−	0.187423i	0.539972	−	0.841683i	$-0.318435\pi$
$89$	−2.04054	−	1.76814i	−0.216297	−	0.187423i	−0.756270	+	0.654260i	$0.772980\pi$
$90$	−3.48223	−	0.568069i	−0.367059	−	0.0598797i
$91$			5.63711i			0.590930i
$92$	−9.40712	+	1.87244i	−0.980760	+	0.195215i
$93$		−	0.594922i		−	0.0616906i
$94$	0.0346992	−	0.212704i	0.00357894	−	0.0219387i
$95$	−11.4424	−	9.91493i	−1.17397	−	1.01725i
$96$	−5.65027	+	0.272847i	−0.576678	+	0.0278473i
$97$	10.0554	+	1.44575i	1.02097	+	0.146794i	0.632414	−	0.774630i	$-0.282064\pi$
$97$	10.0554	+	1.44575i	1.02097	+	0.146794i	0.388559	+	0.921424i	$0.372973\pi$
$98$	−4.84655	+	4.04167i	−0.489575	+	0.408270i
$99$	−1.06189	+	0.484951i	−0.106724	+	0.0487394i
$100$	−2.00837	−	1.40075i	−0.200837	−	0.140075i
$101$	9.63045	−	1.38465i	0.958266	−	0.137778i	0.354603	−	0.935017i	$-0.384616\pi$
$101$	9.63045	−	1.38465i	0.958266	−	0.137778i	0.603663	+	0.797239i	$0.293707\pi$
$102$	0.621142	+	0.195215i	0.0615023	+	0.0193292i
$103$	−13.5263	+	3.97169i	−1.33279	+	0.391342i	−0.869091	−	0.494652i	$-0.835296\pi$
$103$	−13.5263	+	3.97169i	−1.33279	+	0.391342i	−0.463697	+	0.885994i	$0.653477\pi$
$104$	−6.11493	−	7.92358i	−0.599619	−	0.776971i
$105$	−1.65100	+	3.61520i	−0.161122	+	0.352807i
$106$	−2.70021	−	9.88374i	−0.262268	−	0.959994i
$107$	13.4928	−	11.6916i	1.30440	−	1.13027i	0.321346	−	0.946962i	$-0.395865\pi$
$107$	13.4928	−	11.6916i	1.30440	−	1.13027i	0.983056	−	0.183308i	$-0.0586806\pi$
$108$	−1.25163	−	1.55994i	−0.120439	−	0.150105i
$109$	−14.7043	+	9.44990i	−1.40842	+	0.905136i	−0.999971	−	0.00764466i	$-0.997567\pi$
$109$	−14.7043	+	9.44990i	−1.40842	+	0.905136i	−0.408449	+	0.912781i	$0.633930\pi$
$110$	−4.11811	−	0.0778811i	−0.392646	−	0.00742567i
$111$	−0.324273	−	0.208397i	−0.0307786	−	0.0197802i
$112$	−1.38086	+	6.22065i	−0.130479	+	0.587797i
$113$	0.223923	−	0.762610i	0.0210649	−	0.0717403i	−0.948290	−	0.317406i	$-0.897188\pi$
$113$	0.223923	−	0.762610i	0.0210649	−	0.0717403i	0.969355	+	0.245665i	$0.0790065\pi$
$114$	−1.06056	−	8.51665i	−0.0993306	−	0.797658i
$115$	−4.40574	−	11.1242i	−0.410838	−	1.03734i
$116$	3.09089	+	12.2180i	0.286982	+	1.13441i
$117$	0.996949	−	3.39530i	0.0921679	−	0.313895i
$118$	−1.60066	+	2.39007i	−0.147353	+	0.220024i
$119$	0.396515	−	0.616990i	0.0363485	−	0.0565594i
$120$	−1.60097	−	6.87250i	−0.146148	−	0.627371i
$121$	8.10733	−	5.21027i	0.737030	−	0.473661i
$122$	−6.99602	−	11.3524i	−0.633390	−	1.02780i
$123$	3.39605	+	3.91926i	0.306212	+	0.353387i
$124$	1.10024	−	0.453003i	0.0988041	−	0.0406809i
$125$	−3.91313	+	8.56857i	−0.350001	+	0.766396i
$126$	−2.06661	+	0.896959i	−0.184108	+	0.0799075i
$127$	−4.87351	−	16.5976i	−0.432454	−	1.47280i	−0.831320	−	0.555794i	$-0.812415\pi$
$127$	−4.87351	−	16.5976i	−0.432454	−	1.47280i	0.398867	−	0.917009i	$-0.369404\pi$
$128$	−4.80699	−	10.2417i	−0.424882	−	0.905249i
$129$	2.83659	−	0.407841i	0.249748	−	0.0359084i
$130$	8.35303	−	9.27941i	0.732609	−	0.813858i
$131$	−1.65327	−	3.62015i	−0.144446	−	0.316294i	0.823556	−	0.567235i	$-0.191987\pi$
$131$	−1.65327	−	3.62015i	−0.144446	−	0.316294i	−0.968002	+	0.250942i	$0.919260\pi$
$132$	−1.70543	−	1.59458i	−0.148439	−	0.138790i
$133$	−9.56914	−	1.37584i	−0.829750	−	0.119300i
$134$	−0.934186	+	1.94728i	−0.0807014	+	0.168219i
$135$	1.63378	−	1.88549i	0.140614	−	0.162277i
$136$	0.111943	+	1.29737i	0.00959900	+	0.111249i
$137$		−	11.1642i		−	0.953822i	−0.878951	−	0.476911i	$-0.841756\pi$
$137$		−	11.1642i		−	0.953822i	0.878951	−	0.476911i	$-0.158244\pi$
$138$	2.36264	−	6.35751i	0.201121	−	0.541187i
$139$	17.1416			1.45393			0.726964	−	0.686676i	$-0.240931\pi$
$139$	17.1416			1.45393			0.726964	+	0.686676i	$0.240931\pi$
$140$	−7.94301	−	0.300542i	−0.671307	−	0.0254004i
$141$	0.115171	+	0.0997958i	0.00969911	+	0.00840432i
$142$	−0.917063	+	1.91158i	−0.0769582	+	0.160416i
$143$	0.587897	−	4.08891i	0.0491624	−	0.341932i
$144$	1.93186	−	3.50256i	0.160988	−	0.291880i
$145$	−14.3005	+	6.53081i	−1.18759	+	0.542354i
$146$	11.3408	+	10.2086i	0.938570	+	0.844871i
$147$	−0.635051	−	4.41687i	−0.0523781	−	0.364298i
$148$	0.138488	−	0.758386i	0.0113837	−	0.0623390i
$149$	3.16139	−	0.928269i	0.258991	−	0.0760467i	−0.149659	−	0.988738i	$-0.547818\pi$
$149$	3.16139	−	0.928269i	0.258991	−	0.0760467i	0.408651	+	0.912691i	$0.365999\pi$
$150$	1.58828	−	0.689351i	0.129682	−	0.0562853i
$151$	−8.13086	−	3.71324i	−0.661680	−	0.302179i	0.0561247	−	0.998424i	$-0.482126\pi$
$151$	−8.13086	−	3.71324i	−0.661680	−	0.302179i	−0.717804	+	0.696245i	$0.754853\pi$
$152$	14.9429	−	8.44638i	1.21203	−	0.685092i
$153$	−0.347943	+	0.301494i	−0.0281295	+	0.0243744i
$154$	−2.23896	+	1.37978i	−0.180421	+	0.111186i
$155$	0.802444	+	1.24863i	0.0644538	+	0.100292i
$156$	7.03831	−	0.741611i	0.563516	−	0.0593764i
$157$	−20.2001	−	12.9818i	−1.61214	−	1.03606i	−0.960787	−	0.277287i	$-0.910565\pi$
$157$	−20.2001	−	12.9818i	−1.61214	−	1.03606i	−0.651355	−	0.758773i	$-0.725799\pi$
$158$	−6.45420	+	9.63727i	−0.513469	+	0.766700i
$159$	6.95151	+	2.04115i	0.551290	+	0.161873i
$160$	11.4908	−	8.19385i	0.908427	−	0.647781i
$161$	−6.20678	−	4.45456i	−0.489163	−	0.351069i
$162$	1.40337	−	0.174759i	0.110259	−	0.0137304i
$163$	−12.4413	−	3.65310i	−0.974478	−	0.286133i	−0.244535	−	0.969640i	$-0.578635\pi$
$163$	−12.4413	−	3.65310i	−0.974478	−	0.286133i	−0.729943	+	0.683508i	$0.760453\pi$
$164$	−4.66226	+	9.26490i	−0.364061	+	0.723467i
$165$	1.57460	−	2.45012i	0.122582	−	0.190742i
$166$	−6.24714	−	0.118145i	−0.484872	−	0.00916982i
$167$	−13.6472	−	21.2354i	−1.05605	−	1.64325i	−0.708701	−	0.705509i	$-0.750718\pi$
$167$	−13.6472	−	21.2354i	−1.05605	−	1.64325i	−0.347349	−	0.937736i	$-0.612918\pi$
$168$	−3.23243	−	3.13895i	−0.249388	−	0.242175i
$169$	−0.313064	−	0.361296i	−0.0240819	−	0.0277920i
$170$	−1.56697	+	0.428092i	−0.120181	+	0.0328331i
$171$	5.52028	+	2.52103i	0.422146	+	0.192788i
$172$	2.91417	+	4.93538i	0.222204	+	0.376319i
$173$	2.52431	+	8.59702i	0.191920	+	0.653619i	0.998081	+	0.0619229i	$0.0197233\pi$
$173$	2.52431	+	8.59702i	0.191920	+	0.653619i	−0.806161	+	0.591696i	$0.798459\pi$
$174$	−8.50159	−	2.67191i	−0.644504	−	0.202557i
$175$	−0.277562	−	1.93048i	−0.0209817	−	0.145931i
$176$	1.65037	−	4.36818i	0.124401	−	0.329264i
$177$	−0.844965	−	1.85022i	−0.0635115	−	0.139071i
$178$	2.44552	+	2.93253i	0.183299	+	0.219803i
$179$	−1.44381	+	10.0420i	−0.107916	+	0.750571i	0.861961	+	0.506975i	$0.169236\pi$
$179$	−1.44381	+	10.0420i	−0.107916	+	0.750571i	−0.969877	+	0.243596i	$0.921673\pi$
$180$	4.73102	+	1.58578i	0.352629	+	0.118197i
$181$	−8.90279	+	10.2744i	−0.661739	+	0.763688i	−0.983060	−	0.183283i	$-0.941328\pi$
$181$	−8.90279	+	10.2744i	−0.661739	+	0.763688i	0.321321	+	0.946970i	$0.395873\pi$
$182$	1.28355	−	7.86807i	0.0951429	−	0.583220i
$183$	9.42924			0.697030
$184$	13.5565	−	0.471520i	0.999396	−	0.0347609i
$185$	0.961676			0.0707038
$186$	−0.135461	+	0.830371i	−0.00993252	+	0.0608857i
$187$	−0.351961	+	0.406185i	−0.0257379	+	0.0297032i
$188$	−0.0968636	+	0.288983i	−0.00706450	+	0.0210763i
$189$	0.226710	−	1.57680i	0.0164907	−	0.114696i
$190$	13.7133	+	16.4443i	0.994871	+	1.19299i
$191$	−5.97983	−	13.0940i	−0.432685	−	0.947449i	−0.992883	−	0.119090i	$-0.962002\pi$
$191$	−5.97983	−	13.0940i	−0.432685	−	0.947449i	0.560198	−	0.828359i	$-0.310725\pi$
$192$	7.94856	+	0.905714i	0.573638	+	0.0653643i
$193$	−1.03961	−	7.23064i	−0.0748327	−	0.520473i	−0.992416	−	0.122928i	$-0.960772\pi$
$193$	−1.03961	−	7.23064i	−0.0748327	−	0.520473i	0.917583	−	0.397544i	$-0.130138\pi$
$194$	−13.7058	−	4.30750i	−0.984018	−	0.309261i
$195$	2.48724	+	8.47077i	0.178115	+	0.606604i
$196$	7.68491	−	4.53767i	0.548922	−	0.324120i
$197$	19.0765	+	8.71195i	1.35914	+	0.620700i	0.955711	−	0.294308i	$-0.0950893\pi$
$197$	19.0765	+	8.71195i	1.35914	+	0.620700i	0.403434	+	0.915009i	$0.367817\pi$
$198$	1.59257	−	0.435087i	0.113179	−	0.0309203i
$199$	5.48953	+	6.33526i	0.389143	+	0.449095i	0.916192	−	0.400740i	$-0.131247\pi$
$199$	5.48953	+	6.33526i	0.389143	+	0.449095i	−0.527049	+	0.849835i	$0.676702\pi$
$200$	2.48426	+	2.41242i	0.175664	+	0.170584i
$201$	−0.825658	−	1.28475i	−0.0582374	−	0.0906192i
$202$	−13.7571	−	0.260172i	−0.967947	−	0.0183057i
$203$	−5.42712	+	8.44476i	−0.380909	+	0.592706i
$204$	−0.822518	−	0.413905i	−0.0575878	−	0.0289792i
$205$	−12.4140	−	3.64509i	−0.867034	−	0.254584i
$206$	19.7839	−	2.46364i	1.37841	−	0.171650i
$207$	2.95061	+	3.78073i	0.205081	+	0.262779i
$208$	6.73083	+	12.4518i	0.466699	+	0.863376i
$209$	6.79755	+	1.99594i	0.470197	+	0.138062i
$210$	3.12758	−	4.67003i	0.215823	−	0.322263i
$211$	4.16764	+	2.67838i	0.286912	+	0.184387i	0.676178	−	0.736738i	$-0.263635\pi$
$211$	4.16764	+	2.67838i	0.286912	+	0.184387i	−0.389266	+	0.921125i	$0.627271\pi$
$212$	1.51837	+	14.4102i	0.104282	+	0.989696i
$213$	−0.810524	−	1.26120i	−0.0555362	−	0.0864160i
$214$	−21.4949	+	13.2464i	−1.46936	+	0.905508i
$215$	−5.40336	+	4.68203i	−0.368506	+	0.319312i
$216$	1.39179	+	2.46230i	0.0946996	+	0.167538i
$217$	0.862078	+	0.393698i	0.0585217	+	0.0267260i
$218$	22.6755	−	9.84171i	1.53578	−	0.666564i
$219$	−10.3525	+	3.03977i	−0.699558	+	0.205409i
$220$	5.73017	+	1.04638i	0.386328	+	0.0705470i
$221$	−0.231855	−	1.61259i	−0.0155963	−	0.108474i
$222$	0.405157	+	0.364709i	0.0271923	+	0.0244777i
$223$	−0.923694	+	0.421837i	−0.0618551	+	0.0282483i	−0.446102	−	0.894982i	$-0.647188\pi$
$223$	−0.923694	+	0.421837i	−0.0618551	+	0.0282483i	0.384247	+	0.923230i	$0.374461\pi$
$224$	3.34377	−	8.36814i	0.223415	−	0.559120i
$225$	−0.174236	+	1.21184i	−0.0116158	+	0.0807893i
$226$	−0.486186	+	1.01344i	−0.0323406	+	0.0674128i
$227$	−14.9638	−	12.9662i	−0.993185	−	0.860600i	−0.00294808	−	0.999996i	$-0.500938\pi$
$227$	−14.9638	−	12.9662i	−0.993185	−	0.860600i	−0.990237	+	0.139396i	$0.955484\pi$
$228$	−0.458917	+	12.1287i	−0.0303925	+	0.803244i
$229$	3.05617			0.201957			0.100979	−	0.994889i	$-0.467803\pi$
$229$	3.05617			0.201957			0.100979	+	0.994889i	$0.467803\pi$
$230$	3.61643	+	16.5300i	0.238460	+	1.08995i
$231$		−	1.85967i		−	0.122357i
$232$	−1.53216	−	17.7572i	−0.100591	−	1.16582i
$233$	8.31228	−	9.59288i	0.544555	−	0.628450i	−0.415050	−	0.909798i	$-0.636236\pi$
$233$	8.31228	−	9.59288i	0.544555	−	0.628450i	0.959606	+	0.281348i	$0.0907815\pi$
$234$	−2.16460	+	4.51203i	−0.141504	+	0.294960i
$235$	−0.376327	−	0.0541077i	−0.0245489	−	0.00352960i
$236$	2.77835	−	2.97150i	0.180855	−	0.193428i
$237$	−3.40708	−	7.46047i	−0.221314	−	0.484610i
$238$	−0.693928	+	0.770887i	−0.0449806	+	0.0499692i
$239$	22.2208	−	3.19486i	1.43734	−	0.206658i	0.620811	−	0.783961i	$-0.286804\pi$
$239$	22.2208	−	3.19486i	1.43734	−	0.206658i	0.816531	+	0.577302i	$0.195894\pi$
$240$	0.669727	+	9.95692i	0.0432307	+	0.642717i
$241$	8.46626	+	28.8334i	0.545360	+	1.85732i	0.513955	+	0.857817i	$0.328180\pi$
$241$	8.46626	+	28.8334i	0.545360	+	1.85732i	0.0314049	+	0.999507i	$0.490002\pi$
$242$	−12.5023	+	5.42629i	−0.803676	+	0.348815i
$243$	−0.415415	+	0.909632i	−0.0266489	+	0.0583529i
$244$	7.17989	+	17.4382i	0.459645	+	1.11637i
$245$	7.29042	+	8.41359i	0.465768	+	0.537525i
$246$	−3.84769	−	6.24362i	−0.245320	−	0.398079i
$247$	−18.0658	+	11.6102i	−1.14950	+	0.738740i
$248$	−1.63882	+	0.381766i	−0.104065	+	0.0242422i
$249$	2.38865	−	3.71681i	0.151375	−	0.235543i
$250$	7.41284	−	11.0687i	0.468829	−	0.700045i
$251$	−4.99982	+	17.0278i	−0.315586	+	1.07479i	0.637088	+	0.770791i	$0.280139\pi$
$251$	−4.99982	+	17.0278i	−0.315586	+	1.07479i	−0.952673	+	0.303995i	$0.901679\pi$
$252$	3.08873	−	0.781383i	0.194572	−	0.0492225i
$253$	4.03756	+	3.87845i	0.253839	+	0.243836i
$254$	3.02304	+	24.2761i	0.189683	+	1.52322i
$255$	0.323603	−	1.10209i	0.0202648	−	0.0690156i
$256$	4.37742	+	15.3895i	0.273589	+	0.961847i
$257$	6.88489	+	4.42465i	0.429468	+	0.276002i	0.737465	−	0.675385i	$-0.236022\pi$
$257$	6.88489	+	4.42465i	0.429468	+	0.276002i	−0.307998	+	0.951387i	$0.599659\pi$
$258$	−4.05208	−	0.0766322i	−0.252271	−	0.00477091i
$259$	0.516572	−	0.331981i	0.0320982	−	0.0206283i
$260$	−13.7717	+	11.0499i	−0.854087	+	0.685286i
$261$	4.76231	−	4.12656i	0.294779	−	0.255428i
$262$	1.48327	+	5.42931i	0.0916369	+	0.335424i
$263$	−7.81443	+	17.1112i	−0.481859	+	1.05512i	0.500090	+	0.865974i	$0.333300\pi$
$263$	−7.81443	+	17.1112i	−0.481859	+	1.05512i	−0.981948	+	0.189150i	$0.939427\pi$
$264$	2.01730	+	2.61397i	0.124156	+	0.160879i
$265$	−17.3430	+	5.09237i	−1.06537	+	0.312822i
$266$	13.0430	+	4.09920i	0.799717	+	0.251338i
$267$	−2.67255	+	0.384254i	−0.163557	+	0.0235160i
$268$	1.74729	−	2.50522i	0.106733	−	0.153031i
$269$	24.1204	−	11.0154i	1.47065	−	0.671622i	0.490781	−	0.871283i	$-0.336711\pi$
$269$	24.1204	−	11.0154i	1.47065	−	0.671622i	0.979865	+	0.199661i	$0.0639841\pi$
$270$	−2.70969	+	2.25969i	−0.164907	+	0.137520i
$271$	9.68007	+	1.39178i	0.588023	+	0.0845449i	0.429903	−	0.902875i	$-0.358548\pi$
$271$	9.68007	+	1.39178i	0.588023	+	0.0845449i	0.158120	+	0.987420i	$0.449457\pi$
$272$	0.139161	−	1.83631i	0.00843789	−	0.111343i
$273$	4.26024	+	3.69152i	0.257842	+	0.223421i
$274$	−2.54205	+	15.5826i	−0.153571	+	0.941378i
$275$			1.42924i			0.0861862i
$276$	−4.74526	+	8.33562i	−0.285631	+	0.501745i
$277$		−	27.1057i		−	1.62862i	−0.580428	−	0.814312i	$-0.697115\pi$
$277$		−	27.1057i		−	1.62862i	0.580428	−	0.814312i	$-0.302885\pi$
$278$	−23.9255	−	3.90306i	−1.43496	−	0.234090i
$279$	−0.449612	−	0.389591i	−0.0269176	−	0.0233242i
$280$	11.0181	+	2.22808i	0.658459	+	0.133153i
$281$	27.6574	+	3.97653i	1.64990	+	0.237220i	0.903596	−	0.428385i	$-0.140917\pi$
$281$	27.6574	+	3.97653i	1.64990	+	0.237220i	0.746304	+	0.665605i	$0.231826\pi$
$282$	−0.138028	−	0.165515i	−0.00821943	−	0.00985629i
$283$	8.58107	−	3.91884i	0.510092	−	0.232951i	−0.143706	−	0.989620i	$-0.545902\pi$
$283$	8.58107	−	3.91884i	0.510092	−	0.232951i	0.653798	+	0.756669i	$0.273175\pi$
$284$	1.71526	−	2.45931i	0.101782	−	0.145933i
$285$	−14.9864	+	2.15472i	−0.887718	+	0.127635i
$286$	−1.75159	+	5.57329i	−0.103574	+	0.329556i
$287$	−7.92662	+	2.32747i	−0.467894	+	0.137386i
$288$	−3.49394	+	4.44887i	−0.205882	+	0.262152i
$289$	6.97400	−	15.2709i	0.410235	−	0.898290i
$290$	21.4471	−	5.85930i	1.25942	−	0.344070i
$291$	7.67752	−	6.65261i	0.450064	−	0.389983i
$292$	−13.5046	−	16.8311i	−0.790296	−	0.984963i
$293$	13.2940	−	8.54354i	0.776644	−	0.499119i	−0.0912742	−	0.995826i	$-0.529094\pi$
$293$	13.2940	−	8.54354i	0.776644	−	0.499119i	0.867918	+	0.496707i	$0.165458\pi$
$294$	−0.119324	+	6.30951i	−0.00695914	+	0.367978i
$295$	4.26903	+	2.74354i	0.248552	+	0.159735i
$296$	−0.365978	+	1.02699i	−0.0212721	+	0.0596928i
$297$	−0.328891	+	1.12010i	−0.0190842	+	0.0649948i
$298$	−4.62392	+	0.575807i	−0.267856	+	0.0333556i
$299$	−16.8997	+	1.55060i	−0.977335	+	0.0896733i
$300$	−2.37382	+	0.600526i	−0.137053	+	0.0346714i
$301$	−1.28617	+	4.38029i	−0.0741335	+	0.252476i
$302$	10.5033	+	7.03416i	0.604395	+	0.404771i
$303$	5.26016	−	8.18497i	0.302188	−	0.470214i
$304$	−22.7800	+	8.38669i	−1.30652	+	0.481010i
$305$	−19.7902	+	12.7184i	−1.13318	+	0.728251i
$306$	0.554295	−	0.341590i	0.0316870	−	0.0195274i
$307$	−10.1858	−	11.7551i	−0.581335	−	0.670897i	0.386556	−	0.922266i	$-0.373665\pi$
$307$	−10.1858	−	11.7551i	−0.581335	−	0.670897i	−0.967891	+	0.251369i	$0.919119\pi$
$308$	3.43923	−	1.41604i	0.195968	−	0.0806866i
$309$	−5.85626	+	12.8234i	−0.333151	+	0.729499i
$310$	−0.835714	−	1.92550i	−0.0474654	−	0.109361i
$311$	−4.21937	−	14.3699i	−0.239259	−	0.814840i	−0.988327	−	0.152348i	$-0.951317\pi$
$311$	−4.21937	−	14.3699i	−0.239259	−	0.814840i	0.749068	−	0.662493i	$-0.230501\pi$
$312$	−9.99267	−	0.567481i	−0.565724	−	0.0321273i
$313$	−4.90386	+	0.705069i	−0.277183	+	0.0398528i	−0.279504	−	0.960144i	$-0.590170\pi$
$313$	−4.90386	+	0.705069i	−0.277183	+	0.0398528i	0.00232165	+	0.999997i	$0.499261\pi$
$314$	25.2386	+	22.7190i	1.42430	+	1.28211i
$315$	1.65100	+	3.61520i	0.0930236	+	0.203693i
$316$	11.2029	−	11.9818i	0.630213	−	0.674026i
$317$	−20.4943	−	2.94664i	−1.15108	−	0.165500i	−0.459754	−	0.888047i	$-0.652062\pi$
$317$	−20.4943	−	2.94664i	−1.15108	−	0.165500i	−0.691322	+	0.722547i	$0.742971\pi$
$318$	−9.23790	−	4.43179i	−0.518035	−	0.248522i
$319$	4.81730	−	5.55946i	0.269717	−	0.311270i
$320$	−17.9041	+	8.82027i	−1.00087	+	0.493068i
$321$		−	17.8536i		−	0.996489i
$322$	7.64891	+	7.63077i	0.426257	+	0.425246i
$323$	2.79400			0.155462
$324$	−1.99857	−	0.0756203i	−0.111032	−	0.00420113i
$325$	−3.27418	−	2.83709i	−0.181619	−	0.157373i
$326$	16.5333	+	7.93169i	0.915696	+	0.439296i
$327$	−2.48753	+	17.3012i	−0.137561	+	0.956757i
$328$	8.61699	−	11.8700i	0.475794	−	0.655413i
$329$	−0.220826	+	0.100848i	−0.0121745	+	0.00555992i
$330$	−2.75565	+	3.06126i	−0.151693	+	0.168517i
$331$	−4.14372	−	28.8202i	−0.227759	−	1.58410i	−0.707514	−	0.706699i	$-0.750183\pi$
$331$	−4.14372	−	28.8202i	−0.227759	−	1.58410i	0.479755	−	0.877403i	$-0.340726\pi$
$332$	8.69262	+	1.58735i	0.477070	+	0.0871172i
$333$	−0.369850	+	0.108598i	−0.0202676	+	0.00595112i
$334$	14.2130	+	32.7470i	0.777701	+	1.79184i
$335$	3.46579	+	1.58277i	0.189356	+	0.0864762i
$336$	3.79699	+	5.11725i	0.207143	+	0.279169i
$337$	19.7582	−	17.1206i	1.07630	−	0.932617i	0.0783678	−	0.996925i	$-0.475029\pi$
$337$	19.7582	−	17.1206i	1.07630	−	0.932617i	0.997930	+	0.0643070i	$0.0204837\pi$
$338$	0.354698	+	0.575566i	0.0192930	+	0.0313067i
$339$	−0.429704	−	0.668633i	−0.0233383	−	0.0363152i
$340$	2.28459	−	0.240722i	0.123899	−	0.0130550i
$341$	−0.584255	−	0.375478i	−0.0316392	−	0.0203333i
$342$	−7.13098	−	4.77570i	−0.385599	−	0.258240i
$343$	17.5200	+	5.14434i	0.945991	+	0.277768i
$344$	−2.94373	−	7.55217i	−0.158715	−	0.407186i
$345$	−11.2923	−	3.95518i	−0.607956	−	0.212940i
$346$	−1.56583	−	12.5742i	−0.0841798	−	0.675992i
$347$	18.2402	+	5.35580i	0.979185	+	0.287515i	0.731888	−	0.681425i	$-0.238639\pi$
$347$	18.2402	+	5.35580i	0.979185	+	0.287515i	0.247297	+	0.968940i	$0.420458\pi$
$348$	11.2578	+	5.66513i	0.603483	+	0.303683i
$349$	−1.36890	+	2.13004i	−0.0732753	+	0.114019i	−0.875957	−	0.482389i	$-0.839769\pi$
$349$	−1.36890	+	2.13004i	−0.0732753	+	0.114019i	0.802682	+	0.596407i	$0.203406\pi$
$350$	−0.0521531	+	2.75770i	−0.00278770	+	0.147405i
$351$	−1.91313	−	2.97689i	−0.102115	−	0.158895i
$352$	−3.29814	+	5.72116i	−0.175792	+	0.304939i
$353$	−3.55220	−	4.09946i	−0.189065	−	0.218192i	0.653301	−	0.757098i	$-0.273383\pi$
$353$	−3.55220	−	4.09946i	−0.189065	−	0.218192i	−0.842366	+	0.538906i	$0.818838\pi$
$354$	0.758084	+	2.77486i	0.0402917	+	0.147482i
$355$	3.40227	+	1.55376i	0.180574	+	0.0824652i
$356$	−2.74564	−	4.64995i	−0.145519	−	0.246447i
$357$	−0.206628	−	0.703709i	−0.0109359	−	0.0372442i
$358$	4.30174	−	13.6874i	0.227354	−	0.723403i
$359$	4.82189	+	33.5370i	0.254490	+	1.77001i	0.570538	+	0.821271i	$0.306735\pi$
$359$	4.82189	+	33.5370i	0.254490	+	1.77001i	−0.316049	+	0.948743i	$0.602356\pi$
$360$	−6.24230	−	3.29060i	−0.328998	−	0.173430i
$361$	−7.40647	−	16.2179i	−0.389814	−	0.853574i
$362$	14.7656	−	12.3135i	0.776064	−	0.647181i
$363$	1.37152	−	9.53911i	0.0719860	−	0.500674i
$364$	−3.58306	+	10.6897i	−0.187803	+	0.560293i
$365$	17.6278	−	20.3436i	0.922681	−	1.06483i
$366$	−13.1610	−	2.14700i	−0.687936	−	0.112226i
$367$	0.148696			0.00776187			0.00388093	−	0.999992i	$-0.498765\pi$
$367$	0.148696			0.00776187			0.00388093	+	0.999992i	$0.498765\pi$
$368$	−19.0290	−	2.42862i	−0.991954	−	0.126601i
$369$	5.18592			0.269968
$370$	−1.34227	−	0.218970i	−0.0697814	−	0.0113837i
$371$	−7.55800	+	8.72240i	−0.392392	+	0.452844i
$372$	0.378144	−	1.12816i	0.0196059	−	0.0584922i
$373$	2.10294	−	14.6263i	0.108886	−	0.757319i	−0.860086	−	0.510149i	$-0.829590\pi$
$373$	2.10294	−	14.6263i	0.108886	−	0.757319i	0.968972	−	0.247170i	$-0.0795006\pi$
$374$	0.583741	−	0.486798i	0.0301845	−	0.0251717i
$375$	3.91313	+	8.56857i	0.202073	+	0.442479i
$376$	0.200999	−	0.381297i	0.0103657	−	0.0196639i
$377$	3.17341	+	22.0715i	0.163439	+	1.13674i
$378$	−0.675465	+	2.14922i	−0.0347422	+	0.110544i
$379$	3.30513	+	11.2562i	0.169773	+	0.578194i	0.999791	+	0.0204566i	$0.00651200\pi$
$379$	3.30513	+	11.2562i	0.169773	+	0.578194i	−0.830018	+	0.557737i	$0.811670\pi$
$380$	−15.3963	−	26.0748i	−0.789813	−	1.33761i
$381$	−15.7351	−	7.18599i	−0.806135	−	0.368150i
$382$	5.36497	+	19.6377i	0.274496	+	1.00475i
$383$	−9.84466	−	11.3613i	−0.503039	−	0.580537i	0.446264	−	0.894901i	$-0.352754\pi$
$383$	−9.84466	−	11.3613i	−0.503039	−	0.580537i	−0.949303	+	0.314364i	$0.898209\pi$
$384$	−10.8881	−	3.07402i	−0.555630	−	0.156870i
$385$	2.50836	+	3.90309i	0.127838	+	0.198920i
$386$	−0.195340	+	10.3290i	−0.00994254	+	0.525731i
$387$	1.54935	−	2.41083i	0.0787578	−	0.122550i
$388$	18.1492	+	9.13301i	0.921388	+	0.463658i
$389$	4.68156	+	1.37463i	0.237364	+	0.0696964i	0.398251	−	0.917276i	$-0.369617\pi$
$389$	4.68156	+	1.37463i	0.237364	+	0.0696964i	−0.160887	+	0.986973i	$0.551435\pi$
$390$	−1.54284	−	12.3895i	−0.0781248	−	0.627368i
$391$	1.95877	+	1.01901i	0.0990591	+	0.0515337i
$392$	−11.7595	+	4.58369i	−0.593945	+	0.231512i
$393$	−3.81858	−	1.12124i	−0.192622	−	0.0565589i
$394$	−24.6426	−	16.5035i	−1.24148	−	0.831432i
$395$	17.2136	+	11.0625i	0.866112	+	0.556617i
$396$	−2.32192	+	0.244656i	−0.116681	+	0.0122944i
$397$	−5.15396	−	8.01972i	−0.258670	−	0.402498i	0.687492	−	0.726192i	$-0.258712\pi$
$397$	−5.15396	−	8.01972i	−0.258670	−	0.402498i	−0.946162	+	0.323694i	$0.895075\pi$
$398$	−6.21957	−	10.0925i	−0.311759	−	0.505889i
$399$	−7.30624	+	6.33090i	−0.365770	+	0.316941i
$400$	−2.91814	−	3.93282i	−0.145907	−	0.196641i
$401$	−3.96461	−	1.81058i	−0.197983	−	0.0904159i	0.313956	−	0.949437i	$-0.398345\pi$
$401$	−3.96461	−	1.81058i	−0.197983	−	0.0904159i	−0.511939	+	0.859022i	$0.671073\pi$
$402$	0.859891	+	1.98120i	0.0428875	+	0.0988135i
$403$	2.01994	−	0.593107i	0.100620	−	0.0295448i
$404$	19.1424	+	3.49558i	0.952371	+	0.173912i
$405$	−0.355055	−	2.46946i	−0.0176428	−	0.122709i
$406$	9.49781	−	10.5511i	0.471368	−	0.523645i
$407$	−0.409321	+	0.186931i	−0.0202893	+	0.00926582i
$408$	1.05380	+	0.764998i	0.0521707	+	0.0378730i
$409$	−3.34599	+	23.2718i	−0.165448	+	1.15072i	0.722700	+	0.691162i	$0.242901\pi$
$409$	−3.34599	+	23.2718i	−0.165448	+	1.15072i	−0.888148	+	0.459557i	$0.848008\pi$
$410$	16.4971	+	7.91431i	0.814732	+	0.390860i
$411$	−8.43734	−	7.31100i	−0.416183	−	0.360625i
$412$	−28.1746	−	1.06605i	−1.38806	−	0.0525204i
$413$	3.24024			0.159442
$414$	−3.25749	−	5.94885i	−0.160097	−	0.292370i
$415$			11.0227i			0.541084i
$416$	−6.55943	−	18.9123i	−0.321602	−	0.927253i
$417$	11.2253	−	12.9547i	0.549707	−	0.634395i
$418$	−9.03331	−	4.33364i	−0.441833	−	0.211965i
$419$	38.5245	+	5.53898i	1.88204	+	0.270597i	0.985156	−	0.171662i	$-0.0549135\pi$
$419$	38.5245	+	5.53898i	1.88204	+	0.270597i	0.896888	+	0.442259i	$0.145823\pi$
$420$	−5.42870	+	5.80612i	−0.264894	+	0.283310i
$421$	−12.2693	−	26.8659i	−0.597967	−	1.30936i	−0.930506	−	0.366276i	$-0.880633\pi$
$421$	−12.2693	−	26.8659i	−0.597967	−	1.30936i	0.332540	−	0.943089i	$-0.392095\pi$
$422$	−5.20718	−	4.68734i	−0.253482	−	0.228176i
$423$	0.150841	−	0.0216877i	0.00733416	−	0.00105449i
$424$	1.16186	−	20.4589i	0.0564247	−	0.993574i
$425$	0.158802	+	0.540830i	0.00770303	+	0.0262341i
$426$	0.844130	+	1.94489i	0.0408982	+	0.0942302i
$427$	−6.23993	+	13.6635i	−0.301971	+	0.661225i
$428$	33.0180	−	13.5946i	1.59598	−	0.657119i
$429$	−2.70520	−	3.12197i	−0.130608	−	0.150730i
$430$	8.60788	−	5.30469i	0.415109	−	0.255815i
$431$	4.91567	−	3.15911i	0.236780	−	0.152169i	−0.416870	−	0.908966i	$-0.636873\pi$
$431$	4.91567	−	3.15911i	0.236780	−	0.152169i	0.653650	+	0.756797i	$0.273237\pi$
$432$	−1.38196	−	3.75369i	−0.0664895	−	0.180599i
$433$	−9.33229	+	14.5213i	−0.448481	+	0.697850i	−0.989720	−	0.143019i	$-0.954319\pi$
$433$	−9.33229	+	14.5213i	−0.448481	+	0.697850i	0.541239	+	0.840869i	$0.317955\pi$
$434$	−1.11361	−	0.745801i	−0.0534552	−	0.0357996i
$435$	−4.42917	+	15.0844i	−0.212362	+	0.723239i
$436$	−33.8905	+	8.57358i	−1.62306	+	0.410600i
$437$	1.49249	−	29.0662i	0.0713955	−	1.39042i
$438$	15.1418	−	1.88557i	0.723503	−	0.0900962i
$439$	−2.62016	+	8.92345i	−0.125054	+	0.425893i	−0.998091	−	0.0617598i	$-0.980329\pi$
$439$	−2.62016	+	8.92345i	−0.125054	+	0.425893i	0.873038	+	0.487653i	$0.162147\pi$
$440$	−7.75971	−	2.76524i	−0.369930	−	0.131828i
$441$	−3.75392	−	2.41250i	−0.178758	−	0.114881i
$442$	−0.0435650	+	2.30358i	−0.00207217	+	0.109570i
$443$	−3.70422	+	2.38056i	−0.175993	+	0.113104i	−0.625671	−	0.780087i	$-0.715175\pi$
$443$	−3.70422	+	2.38056i	−0.175993	+	0.113104i	0.449679	+	0.893190i	$0.351539\pi$
$444$	−0.482460	−	0.601300i	−0.0228965	−	0.0285364i
$445$	5.09086	−	4.41126i	0.241330	−	0.209114i
$446$	1.38531	−	0.378463i	0.0655963	−	0.0179207i
$447$	1.36873	−	2.99711i	0.0647389	−	0.141758i
$448$	−6.57251	+	10.9186i	−0.310522	+	0.515854i
$449$	−37.6331	+	11.0501i	−1.77602	+	0.521486i	−0.994716	−	0.102669i	$-0.967262\pi$
$449$	−37.6331	+	11.0501i	−1.77602	+	0.521486i	−0.781301	+	0.624154i	$0.785444\pi$
$450$	0.519124	−	1.65177i	0.0244717	−	0.0778651i
$451$	5.99236	−	0.861571i	0.282169	−	0.0405698i
$452$	0.909356	−	1.30382i	0.0427725	−	0.0613263i
$453$	−8.13086	+	3.71324i	−0.382021	+	0.174463i
$454$	17.9336	+	21.5050i	0.841666	+	1.00928i
$455$	−13.9206	−	2.00148i	−0.652609	−	0.0938310i
$456$	3.40220	−	16.8243i	0.159323	−	0.787871i
$457$	−6.17266	−	5.34864i	−0.288745	−	0.250199i	0.498428	−	0.866931i	$-0.333911\pi$
$457$	−6.17266	−	5.34864i	−0.288745	−	0.250199i	−0.787173	+	0.616732i	$0.788456\pi$
$458$	−4.26569	−	0.695878i	−0.199323	−	0.0325162i
$459$			0.460395i			0.0214894i
$460$	−1.28388	−	23.8953i	−0.0598610	−	1.11413i
$461$		−	10.0301i		−	0.467147i	−0.972339	−	0.233573i	$-0.924958\pi$
$461$		−	10.0301i		−	0.467147i	0.972339	−	0.233573i	$-0.0750419\pi$
$462$	−0.423440	+	2.59566i	−0.0197002	+	0.120761i
$463$	24.1947	+	20.9648i	1.12442	+	0.974318i	0.999840	−	0.0178915i	$-0.00569535\pi$
$463$	24.1947	+	20.9648i	1.12442	+	0.974318i	0.124583	+	0.992209i	$0.460241\pi$
$464$	−1.90470	+	25.1337i	−0.0884236	+	1.16680i
$465$	1.46914	+	0.211230i	0.0681296	+	0.00979556i
$466$	−13.7862	+	11.4967i	−0.638635	+	0.532575i
$467$	14.7942	−	6.75629i	0.684595	−	0.312644i	−0.0425833	−	0.999093i	$-0.513559\pi$
$467$	14.7942	−	6.75629i	0.684595	−	0.312644i	0.727178	+	0.686449i	$0.240832\pi$
$468$	4.04864	−	5.80485i	0.187148	−	0.268329i
$469$	2.40807	−	0.346228i	0.111194	−	0.0159873i
$470$	0.512943	+	0.161210i	0.0236603	+	0.00743605i
$471$	−23.0392	+	6.76493i	−1.06159	+	0.311711i
$472$	−4.55452	+	3.51490i	−0.209639	+	0.161786i
$473$	1.38975	−	3.04314i	0.0639009	−	0.139924i
$474$	3.05676	+	11.1888i	0.140402	+	0.513920i
$475$	5.61516	−	4.86556i	0.257641	−	0.223247i
$476$	1.14409	−	0.917971i	0.0524391	−	0.0420751i
$477$	6.09486	−	3.91693i	0.279065	−	0.179344i
$478$	−31.7424	−	0.600307i	−1.45186	−	0.0274574i
$479$	18.7818	+	12.0703i	0.858163	+	0.551508i	0.894111	−	0.447846i	$-0.147809\pi$
$479$	18.7818	+	12.0703i	0.858163	+	0.551508i	−0.0359476	+	0.999354i	$0.511445\pi$
$480$	1.33237	−	14.0500i	0.0608141	−	0.641292i
$481$	0.384287	−	1.30876i	0.0175220	−	0.0596745i
$482$	−5.25163	−	42.1724i	−0.239205	−	1.92090i
$483$	−7.43111	+	1.77366i	−0.338127	+	0.0807041i
$484$	18.6858	−	4.72710i	0.849352	−	0.214868i
$485$	−7.14045	+	24.3181i	−0.324231	+	1.10423i
$486$	0.786941	−	1.17504i	0.0356963	−	0.0533010i
$487$	−13.7834	+	21.4474i	−0.624586	+	0.971874i	0.374419	+	0.927260i	$0.377842\pi$
$487$	−13.7834	+	21.4474i	−0.624586	+	0.971874i	−0.999004	+	0.0446144i	$0.985794\pi$
$488$	−6.05081	−	25.9745i	−0.273907	−	1.17581i
$489$	−10.9081	+	7.01024i	−0.493283	+	0.317014i
$490$	−8.25995	−	13.4034i	−0.373147	−	0.605503i
$491$	−25.9708	−	29.9719i	−1.17204	−	1.35261i	−0.923318	−	0.384037i	$-0.874533\pi$
$491$	−25.9708	−	29.9719i	−1.17204	−	1.35261i	−0.248727	−	0.968574i	$-0.580012\pi$
$492$	3.94881	+	9.59072i	0.178026	+	0.432383i
$493$	1.20518	−	2.63898i	0.0542786	−	0.118854i
$494$	27.8592	−	12.0916i	1.25345	−	0.544026i
$495$	−0.820536	−	2.79449i	−0.0368804	−	0.125603i
$496$	2.37432	−	0.159703i	0.106610	−	0.00717088i
$497$	2.36393	−	0.339882i	0.106037	−	0.0152458i
$498$	−4.18029	+	4.64390i	−0.187323	+	0.208098i
$499$	−11.6268	−	25.4590i	−0.520485	−	1.13970i	−0.969256	−	0.246056i	$-0.920865\pi$
$499$	−11.6268	−	25.4590i	−0.520485	−	1.13970i	0.448771	−	0.893647i	$-0.351862\pi$
$500$	−12.8669	+	13.7614i	−0.575424	+	0.615428i
$501$	−24.9856	−	3.59239i	−1.11628	−	0.160496i
$502$	10.8557	−	22.6284i	0.484515	−	1.00995i
$503$	−8.02013	+	9.25572i	−0.357600	+	0.412692i	−0.905834	−	0.423633i	$-0.860755\pi$
$503$	−8.02013	+	9.25572i	−0.357600	+	0.412692i	0.548234	+	0.836325i	$0.315300\pi$
$504$	−4.48906	+	0.387334i	−0.199958	+	0.0172532i
$505$			24.2737i			1.08016i
$506$	−4.75237	−	6.33274i	−0.211269	−	0.281525i
$507$	−0.478062			−0.0212315
$508$	1.30811	−	34.5720i	0.0580378	−	1.53388i
$509$	3.99714	+	3.46354i	0.177170	+	0.153519i	0.738932	−	0.673780i	$-0.235331\pi$
$509$	3.99714	+	3.46354i	0.177170	+	0.153519i	−0.561761	+	0.827299i	$0.689876\pi$
$510$	−0.702615	+	1.46458i	−0.0311123	+	0.0648525i
$511$	2.44610	−	17.0130i	0.108209	−	0.752611i
$512$	−2.60571	−	22.4769i	−0.115157	−	0.993347i
$513$	5.52028	−	2.52103i	0.243726	−	0.111306i
$514$	−8.60220	−	7.74343i	−0.379427	−	0.341548i
$515$	−5.00534	−	34.8129i	−0.220562	−	1.53404i
$516$	5.63829	+	1.02960i	0.248212	+	0.0453257i
$517$	0.170695	−	0.0501205i	0.00750715	−	0.00220430i
$518$	−0.796603	+	0.345745i	−0.0350007	+	0.0151912i
$519$	8.15026	+	3.72210i	0.357757	+	0.163382i
$520$	21.7381	−	12.2873i	0.953279	−	0.538833i
$521$	4.39269	−	3.80629i	0.192447	−	0.166756i	−0.553308	−	0.832977i	$-0.686635\pi$
$521$	4.39269	−	3.80629i	0.192447	−	0.166756i	0.745755	+	0.666221i	$0.232089\pi$
$522$	−7.58666	+	4.67535i	−0.332059	+	0.204634i
$523$	9.34854	+	14.5466i	0.408783	+	0.636079i	0.983210	−	0.182477i	$-0.0584115\pi$
$523$	9.34854	+	14.5466i	0.408783	+	0.636079i	−0.574427	+	0.818556i	$0.694775\pi$
$524$	−0.834067	−	7.91576i	−0.0364364	−	0.345802i
$525$	−1.64073	−	1.05443i	−0.0716072	−	0.0460191i
$526$	14.8033	−	22.1039i	0.645453	−	0.963776i
$527$	−0.262804	−	0.0771663i	−0.0114479	−	0.00336142i
$528$	−2.22049	−	4.10782i	−0.0966343	−	0.178770i
$529$	11.6472	−	19.8329i	0.506400	−	0.862299i
$530$	25.3662	−	3.15880i	1.10184	−	0.137210i
$531$	−1.95163	−	0.573052i	−0.0846937	−	0.0248683i
$532$	−17.2715	−	8.69134i	−0.748816	−	0.376817i
$533$	−9.92134	+	15.4379i	−0.429741	+	0.668690i
$534$	3.81773	+	0.0722004i	0.165209	+	0.00312442i
$535$	24.0813	+	37.4712i	1.04112	+	1.62002i
$536$	−3.00923	+	3.09885i	−0.129979	+	0.133850i
$537$	6.64370	+	7.66724i	0.286697	+	0.330866i
$538$	−36.1745	+	9.88279i	−1.55959	+	0.426077i
$539$	−4.73848	−	2.16399i	−0.204101	−	0.0932097i
$540$	4.29661	−	2.53700i	0.184897	−	0.109175i
$541$	7.73400	+	26.3396i	0.332511	+	1.13243i	0.940871	+	0.338766i	$0.110010\pi$
$541$	7.73400	+	26.3396i	0.332511	+	1.13243i	−0.608360	+	0.793661i	$0.708172\pi$
$542$	−13.1942	−	4.14672i	−0.566739	−	0.178117i
$543$	1.93476	+	13.4566i	0.0830285	+	0.577476i
$544$	−0.612357	+	2.53137i	−0.0262546	+	0.108532i
$545$	−18.1153	−	39.6670i	−0.775975	−	1.69915i
$546$	−5.10575	−	6.12253i	−0.218506	−	0.262020i
$547$	−6.03953	+	42.0059i	−0.258232	+	1.79604i	0.287185	+	0.957875i	$0.407281\pi$
$547$	−6.03953	+	42.0059i	−0.258232	+	1.79604i	−0.545416	+	0.838165i	$0.683628\pi$
$548$	7.09619	−	21.1708i	0.303134	−	0.904371i
$549$	6.17484	−	7.12615i	0.263536	−	0.304137i
$550$	0.325431	−	1.99487i	0.0138764	−	0.0850617i
$551$	−38.2415			−1.62914
$552$	8.52124	−	10.5541i	0.362688	−	0.449211i
$553$	13.0654			0.555596
$554$	−6.17186	+	37.8331i	−0.262217	+	1.60738i
$555$	0.629764	−	0.726786i	0.0267320	−	0.0308504i
$556$	32.5057	+	10.8955i	1.37855	+	0.462072i
$557$	1.84560	−	12.8364i	0.0782006	−	0.543897i	−0.912630	−	0.408787i	$-0.865952\pi$
$557$	1.84560	−	12.8364i	0.0782006	−	0.543897i	0.990831	−	0.135110i	$-0.0431389\pi$
$558$	0.538844	+	0.646152i	0.0228111	+	0.0273538i
$559$	4.21268	+	9.22448i	0.178177	+	0.390154i
$560$	−14.8714	−	5.61865i	−0.628431	−	0.237431i
$561$	0.0764885	+	0.531989i	0.00322935	+	0.0224606i
$562$	−37.6977	−	11.8478i	−1.59018	−	0.499768i
$563$	−0.615411	−	2.09590i	−0.0259365	−	0.0883316i	0.945508	−	0.325600i	$-0.105566\pi$
$563$	−0.615411	−	2.09590i	−0.0259365	−	0.0883316i	−0.971444	+	0.237268i	$0.923748\pi$
$564$	0.154967	+	0.262448i	0.00652528	+	0.0110511i
$565$	1.80373	+	0.823736i	0.0758835	+	0.0346549i
$566$	−12.8694	+	3.51590i	−0.540943	+	0.147784i
$567$	−1.04320	−	1.20392i	−0.0438105	−	0.0505600i
$568$	−2.95407	+	3.04205i	−0.123950	+	0.127642i
$569$	7.37674	+	11.4784i	0.309249	+	0.481201i	0.960738	−	0.277457i	$-0.0894917\pi$
$569$	7.37674	+	11.4784i	0.309249	+	0.481201i	−0.651489	+	0.758658i	$0.725855\pi$
$570$	21.4081	+	0.404867i	0.896687	+	0.0169580i
$571$	−8.79013	+	13.6777i	−0.367856	+	0.572395i	−0.975002	−	0.222195i	$-0.928678\pi$
$571$	−8.79013	+	13.6777i	−0.367856	+	0.572395i	0.607146	+	0.794590i	$0.292314\pi$
$572$	3.71383	−	7.38017i	0.155283	−	0.308580i
$573$	−13.8117	−	4.05549i	−0.576994	−	0.169421i
$574$	11.5936	−	1.44373i	0.483909	−	0.0602602i
$575$	5.71112	−	1.36313i	0.238170	−	0.0568464i
$576$	5.88970	−	5.41401i	0.245404	−	0.225584i
$577$	16.9510	+	4.97727i	0.705680	+	0.207206i	0.614832	−	0.788658i	$-0.289224\pi$
$577$	16.9510	+	4.97727i	0.705680	+	0.207206i	0.0908485	+	0.995865i	$0.471042\pi$
$578$	−13.2112	+	19.7267i	−0.549513	+	0.820521i
$579$	−6.14535	−	3.94938i	−0.255392	−	0.164130i
$580$	−31.2692	+	3.29477i	−1.29838	+	0.136808i
$581$	3.80516	+	5.92095i	0.157865	+	0.245642i
$582$	−12.2308	+	7.53733i	−0.506982	+	0.312432i
$583$	6.39191	−	5.53862i	0.264726	−	0.229386i
$584$	15.0168	+	26.5671i	0.621401	+	1.09935i
$585$	8.03058	+	3.66744i	0.332024	+	0.151630i
$586$	−20.5006	+	8.89776i	−0.846873	+	0.367563i
$587$	−33.9337	+	9.96384i	−1.40060	+	0.411252i	−0.892888	−	0.450278i	$-0.851325\pi$
$587$	−33.9337	+	9.96384i	−1.40060	+	0.411252i	−0.507707	+	0.861530i	$0.669507\pi$
$588$	1.60320	−	8.77941i	0.0661148	−	0.362057i
$589$	0.513814	+	3.57366i	0.0211713	+	0.147250i
$590$	−5.33386	−	4.80137i	−0.219591	−	0.197669i
$591$	19.0765	−	8.71195i	0.784702	−	0.358362i
$592$	0.744661	−	1.35011i	0.0306054	−	0.0554892i
$593$	−3.63057	+	25.2512i	−0.149090	+	1.03694i	0.768624	+	0.639700i	$0.220942\pi$
$593$	−3.63057	+	25.2512i	−0.149090	+	1.03694i	−0.917714	+	0.397241i	$0.869968\pi$
$594$	0.714097	−	1.48851i	0.0292997	−	0.0610742i
$595$	1.38285	+	1.19824i	0.0566912	+	0.0491232i
$596$	6.58500	+	0.249158i	0.269732	+	0.0102059i
$597$	8.38275			0.343083
$598$	23.9411	+	1.68373i	0.979023	+	0.0688529i
$599$			23.7787i			0.971571i	0.874078	+	0.485786i	$0.161466\pi$
$599$			23.7787i			0.971571i	−0.874078	+	0.485786i	$0.838534\pi$
$600$	3.45003	−	0.297683i	0.140847	−	0.0121528i
$601$	14.8985	−	17.1938i	0.607722	−	0.701348i	−0.365605	−	0.930770i	$-0.619138\pi$
$601$	14.8985	−	17.1938i	0.607722	−	0.701348i	0.973327	+	0.229422i	$0.0736835\pi$
$602$	2.79256	−	5.82099i	0.113816	−	0.237246i
$603$	−1.51164	−	0.217341i	−0.0615587	−	0.00885081i
$604$	−13.0584	−	12.2096i	−0.531339	−	0.496801i
$605$	9.98800	+	21.8707i	0.406070	+	0.889169i
$606$	−9.20562	+	10.2266i	−0.373953	+	0.415425i
$607$	24.1431	−	3.47125i	0.979938	−	0.140894i	0.366313	−	0.930492i	$-0.380620\pi$
$607$	24.1431	−	3.47125i	0.979938	−	0.140894i	0.613625	+	0.789598i	$0.289711\pi$
$608$	33.7051	−	6.51892i	1.36692	−	0.264377i
$609$	2.82812	+	9.63168i	0.114601	+	0.390295i
$610$	30.5183	−	13.2457i	1.23565	−	0.536302i
$611$	−0.224017	+	0.490529i	−0.00906277	+	0.0198447i
$612$	−0.851444	+	0.350567i	−0.0344176	+	0.0141708i
$613$	18.9974	+	21.9241i	0.767297	+	0.885508i	0.996124	−	0.0879594i	$-0.0280346\pi$
$613$	18.9974	+	21.9241i	0.767297	+	0.885508i	−0.228827	+	0.973467i	$0.573489\pi$
$614$	11.5404	+	18.7265i	0.465733	+	0.755742i
$615$	−10.8842	+	6.99487i	−0.438895	+	0.282061i
$616$	−5.12278	+	1.19336i	−0.206403	+	0.0480820i
$617$	10.5219	−	16.3723i	0.423594	−	0.659126i	−0.562216	−	0.826991i	$-0.690051\pi$
$617$	10.5219	−	16.3723i	0.423594	−	0.659126i	0.985810	+	0.167865i	$0.0536873\pi$
$618$	11.0938	−	16.5650i	0.446258	−	0.666342i
$619$	−4.09735	+	13.9543i	−0.164686	+	0.560870i	0.835253	+	0.549866i	$0.185321\pi$
$619$	−4.09735	+	13.9543i	−0.164686	+	0.560870i	−0.999939	+	0.0110043i	$0.996497\pi$
$620$	0.728030	+	2.87783i	0.0292384	+	0.115576i
$621$	4.78952	+	0.245933i	0.192197	+	0.00986894i
$622$	2.61728	+	21.0177i	0.104944	+	0.842732i
$623$	1.21179	−	4.12696i	0.0485492	−	0.165343i
$624$	13.8182	+	3.06736i	0.553170	+	0.122793i
$625$	−24.9201	−	16.0152i	−0.996804	−	0.640607i
$626$	7.00517	+	0.132481i	0.279983	+	0.00529499i
$627$	5.95988	−	3.83018i	0.238015	−	0.152963i
$628$	−30.0541	−	37.4571i	−1.19929	−	1.49470i
$629$	−0.134119	+	0.116215i	−0.00534769	+	0.00463380i
$630$	−1.48125	−	5.42188i	−0.0590142	−	0.216013i
$631$	14.7655	−	32.3319i	0.587805	−	1.28711i	−0.348954	−	0.937140i	$-0.613463\pi$
$631$	14.7655	−	32.3319i	0.587805	−	1.28711i	0.936759	−	0.349974i	$-0.113810\pi$
$632$	−18.3648	+	14.1728i	−0.730512	+	0.563765i
$633$	4.75341	−	1.39573i	0.188931	−	0.0554751i
$634$	27.9343	+	8.77928i	1.10941	+	0.348670i
$635$	42.7176	−	6.14186i	1.69520	−	0.243732i
$636$	11.8848	+	8.28916i	0.471264	+	0.328686i
$637$	14.3635	−	6.55958i	0.569102	−	0.259900i
$638$	−7.98968	+	6.66281i	−0.316314	+	0.263783i
$639$	−1.48393	−	0.213357i	−0.0587035	−	0.00844028i
$640$	26.9983	−	8.23431i	1.06720	−	0.325489i
$641$	−0.308165	−	0.267026i	−0.0121718	−	0.0105469i	0.648754	−	0.760999i	$-0.275291\pi$
$641$	−0.308165	−	0.267026i	−0.0121718	−	0.0105469i	−0.660925	+	0.750452i	$0.729836\pi$
$642$	−4.06519	+	24.9194i	−0.160440	+	0.983489i
$643$			33.5810i			1.32431i	0.749369	+	0.662153i	$0.230357\pi$
$643$			33.5810i			1.32431i	−0.749369	+	0.662153i	$0.769643\pi$
$644$	−8.93857	−	12.3924i	−0.352229	−	0.488328i
$645$			7.14966i			0.281518i
$646$	−3.89976	−	0.636182i	−0.153434	−	0.0250302i
$647$	21.9978	+	19.0612i	0.864821	+	0.749372i	0.969489	−	0.245136i	$-0.0788325\pi$
$647$	21.9978	+	19.0612i	0.864821	+	0.749372i	−0.104668	+	0.994507i	$0.533378\pi$
$648$	2.77231	+	0.560614i	0.108907	+	0.0220230i
$649$	−2.35033	−	0.337926i	−0.0922585	−	0.0132648i
$650$	3.92398	+	4.70542i	0.153911	+	0.184562i
$651$	0.862078	−	0.393698i	0.0337875	−	0.0154302i
$652$	−21.2706	−	14.8353i	−0.833020	−	0.580997i
$653$	−32.1023	+	4.61561i	−1.25626	+	0.180623i	−0.738118	−	0.674672i	$-0.764285\pi$
$653$	−32.1023	+	4.61561i	−1.25626	+	0.180623i	−0.518142	+	0.855295i	$0.673376\pi$
$654$	7.41141	−	23.5819i	0.289809	−	0.922126i
$655$	9.52681	−	2.79732i	0.372243	−	0.109300i
$656$	−14.7300	+	14.6057i	−0.575111	+	0.570256i
$657$	−4.48215	+	9.81453i	−0.174865	+	0.382901i
$658$	0.331183	−	0.0904784i	0.0129109	−	0.00352722i
$659$	−23.7816	+	20.6068i	−0.926398	+	0.802729i	−0.980644	−	0.195799i	$-0.937270\pi$
$659$	−23.7816	+	20.6068i	−0.926398	+	0.802729i	0.0542457	+	0.998528i	$0.482725\pi$
$660$	4.54327	−	3.64534i	0.176846	−	0.141895i
$661$	8.43733	−	5.42234i	0.328174	−	0.210905i	−0.366170	−	0.930548i	$-0.619331\pi$
$661$	8.43733	−	5.42234i	0.328174	−	0.210905i	0.694344	+	0.719643i	$0.255695\pi$
$662$	−0.778595	+	41.1697i	−0.0302609	+	1.60011i
$663$	−1.37054	−	0.880795i	−0.0532275	−	0.0342073i
$664$	−11.7714	−	4.19484i	−0.456819	−	0.162791i
$665$	6.79514	−	23.1421i	0.263504	−	0.897413i
$666$	0.540950	−	0.0673633i	0.0209614	−	0.00261028i
$667$	−26.8097	−	13.9473i	−1.03808	−	0.540040i
$668$	−12.3816	−	48.9433i	−0.479059	−	1.89367i
$669$	−0.286088	+	0.974326i	−0.0110608	+	0.0376696i
$670$	−4.47703	−	2.99833i	−0.172963	−	0.115835i
$671$	5.95115	−	9.26017i	0.229742	−	0.357485i
$672$	−4.13452	−	8.00702i	−0.159492	−	0.308878i
$673$	18.9734	−	12.1935i	0.731371	−	0.470023i	−0.121205	−	0.992628i	$-0.538676\pi$
$673$	18.9734	−	12.1935i	0.731371	−	0.470023i	0.852575	+	0.522604i	$0.175039\pi$
$674$	−31.4761	+	19.3974i	−1.21241	+	0.747160i
$675$	0.801747	+	0.925266i	0.0308593	+	0.0356135i
$676$	−0.364020	−	0.884118i	−0.0140008	−	0.0340045i
$677$	3.46712	−	7.59194i	0.133252	−	0.291782i	−0.831230	−	0.555928i	$-0.812363\pi$
$677$	3.46712	−	7.59194i	0.133252	−	0.291782i	0.964483	+	0.264146i	$0.0850902\pi$
$678$	0.447520	+	1.03109i	0.0171869	+	0.0395990i
$679$	4.55933	+	15.5277i	0.174971	+	0.595897i
$680$	−3.24356	−	0.184201i	−0.124385	−	0.00706377i
$681$	−19.5985	+	2.81783i	−0.751015	+	0.107980i
$682$	0.729987	+	0.657111i	0.0279526	+	0.0251621i
$683$	−14.1890	−	31.0696i	−0.542927	−	1.18884i	−0.960007	−	0.279975i	$-0.909674\pi$
$683$	−14.1890	−	31.0696i	−0.542927	−	1.18884i	0.417080	−	0.908870i	$-0.363053\pi$
$684$	8.86575	+	8.28945i	0.338990	+	0.316955i
$685$	27.5696	+	3.96391i	1.05338	+	0.151453i
$686$	−23.2824	−	11.1695i	−0.888927	−	0.426454i
$687$	2.00137	−	2.30970i	0.0763569	−	0.0881205i
$688$	2.38915	+	11.2113i	0.0910855	+	0.427427i
$689$			25.6373i			0.976705i
$690$	14.8608	+	8.09170i	0.565740	+	0.308046i
$691$	14.1716			0.539112			0.269556	−	0.962985i	$-0.413123\pi$
$691$	14.1716			0.539112			0.269556	+	0.962985i	$0.413123\pi$
$692$	−0.677555	+	17.9071i	−0.0257568	+	0.680726i
$693$	−1.40545	−	1.21783i	−0.0533885	−	0.0462614i
$694$	−24.2395	−	11.6287i	−0.920119	−	0.441418i
$695$	−6.08619	+	42.3304i	−0.230862	+	1.60568i
$696$	−14.4233	−	10.4705i	−0.546715	−	0.396885i
$697$	2.17181	−	0.991832i	0.0822632	−	0.0375683i
$698$	2.39566	−	2.66134i	0.0906769	−	0.100733i
$699$	−1.80643	−	12.5640i	−0.0683255	−	0.475214i
$700$	0.700710	−	3.83722i	0.0264843	−	0.145033i
$701$	−24.4946	+	7.19226i	−0.925148	+	0.271648i	−0.709404	−	0.704802i	$-0.751036\pi$
$701$	−24.4946	+	7.19226i	−0.925148	+	0.271648i	−0.215744	+	0.976450i	$0.569218\pi$
$702$	1.99245	+	4.59064i	0.0752002	+	0.173263i
$703$	2.12787	+	0.971765i	0.0802541	+	0.0366508i
$704$	5.90611	−	7.23441i	0.222595	−	0.272657i
$705$	−0.287334	+	0.248976i	−0.0108216	+	0.00937698i
$706$	4.02460	+	6.53070i	0.151468	+	0.245786i
$707$	8.37953	+	13.0388i	0.315145	+	0.490374i
$708$	−0.426282	−	4.04566i	−0.0160207	−	0.152045i
$709$	−25.1352	−	16.1534i	−0.943974	−	0.606655i	−0.0244548	−	0.999701i	$-0.507785\pi$
$709$	−25.1352	−	16.1534i	−0.943974	−	0.606655i	−0.919519	+	0.393046i	$0.871421\pi$
$710$	−4.39497	−	2.94337i	−0.164940	−	0.110463i
$711$	−7.86941	−	2.31067i	−0.295126	−	0.0866568i
$712$	2.77348	+	7.11540i	0.103941	+	0.266661i
$713$	−0.943151	+	2.69275i	−0.0353213	+	0.100844i
$714$	0.128171	+	1.02926i	0.00479669	+	0.0385190i
$715$	9.88868	+	2.90358i	0.369816	+	0.108588i
$716$	−9.12078	+	18.1249i	−0.340859	+	0.677360i
$717$	12.1370	−	18.8855i	0.453264	−	0.705293i
$718$	0.906021	−	47.9076i	0.0338124	−	1.78790i
$719$	−15.7938	−	24.5757i	−0.589011	−	0.916519i	−0.999988	−	0.00487329i	$-0.998449\pi$
$719$	−15.7938	−	24.5757i	−0.589011	−	0.916519i	0.410977	−	0.911646i	$-0.365188\pi$
$720$	7.96352	+	6.01425i	0.296783	+	0.224138i
$721$	−14.7064	−	16.9721i	−0.547697	−	0.632076i
$722$	6.64492	+	24.3228i	0.247298	+	0.905200i
$723$	27.3351	+	12.4835i	1.01660	+	0.464267i
$724$	−23.4130	+	13.8246i	−0.870138	+	0.513787i
$725$	−2.17353	−	7.40235i	−0.0807228	−	0.274917i
$726$	−4.08633	+	13.0021i	−0.151658	+	0.482551i
$727$	−1.10257	−	7.66855i	−0.0408921	−	0.284411i	−0.999999	−	0.00136696i	$-0.999565\pi$
$727$	−1.10257	−	7.66855i	−0.0408921	−	0.284411i	0.959107	−	0.283044i	$-0.0913442\pi$
$728$	7.43510	−	14.1044i	0.275563	−	0.522745i
$729$	0.415415	+	0.909632i	0.0153857	+	0.0336901i
$730$	−29.2364	+	24.3810i	−1.08209	+	0.902382i
$731$	0.187768	−	1.30595i	0.00694484	−	0.0483024i
$732$	17.8808	+	5.99341i	0.660892	+	0.221523i
$733$	−0.886967	+	1.02361i	−0.0327609	+	0.0378081i	−0.771894	−	0.635752i	$-0.780690\pi$
$733$	−0.886967	+	1.02361i	−0.0327609	+	0.0378081i	0.739133	+	0.673560i	$0.235236\pi$
$734$	−0.207544	−	0.0338575i	−0.00766060	−	0.00124970i
$735$	11.1328			0.410639
$736$	26.0069	+	7.72260i	0.958629	+	0.284659i
$737$	−1.78282			−0.0656709
$738$	−7.23831	−	1.18081i	−0.266446	−	0.0434663i
$739$	−32.3937	+	37.3843i	−1.19162	+	1.37520i	−0.282184	+	0.959360i	$0.591059\pi$
$739$	−32.3937	+	37.3843i	−1.19162	+	1.37520i	−0.909436	+	0.415843i	$0.863486\pi$
$740$	1.82363	+	0.611260i	0.0670382	+	0.0224704i
$741$	−3.05620	+	21.2563i	−0.112272	+	0.780870i
$742$	12.5352	−	10.4535i	0.460183	−	0.383759i
$743$	−1.62522	−	3.55874i	−0.0596236	−	0.130557i	0.877475	−	0.479623i	$-0.159226\pi$
$743$	−1.62522	−	3.55874i	−0.0596236	−	0.130557i	−0.937098	+	0.349065i	$0.886499\pi$
$744$	−0.784676	+	1.48854i	−0.0287676	+	0.0545724i
$745$	1.16986	+	8.13652i	0.0428602	+	0.298099i
$746$	−6.26554	+	19.9360i	−0.229398	+	0.729907i
$747$	−1.24475	−	4.23922i	−0.0455429	−	0.155105i
$748$	−0.925606	+	0.546539i	−0.0338435	+	0.0199834i
$749$	25.8709	+	11.8148i	0.945302	+	0.431705i
$750$	−3.51078	−	12.8507i	−0.128196	−	0.469241i
$751$	−5.40945	−	6.24284i	−0.197394	−	0.227804i	0.648420	−	0.761283i	$-0.275430\pi$
$751$	−5.40945	−	6.24284i	−0.197394	−	0.227804i	−0.845814	+	0.533478i	$0.820885\pi$
$752$	−0.367367	+	0.486433i	−0.0133965	+	0.0177384i
$753$	9.59459	+	14.9295i	0.349646	+	0.544060i
$754$	0.596275	−	31.5292i	0.0217150	−	1.14823i
$755$	12.0566	−	18.7604i	0.438784	−	0.682762i
$756$	1.43216	−	2.84601i	0.0520871	−	0.103508i
$757$	14.4573	+	4.24506i	0.525461	+	0.154289i	0.533695	−	0.845677i	$-0.320803\pi$
$757$	14.4573	+	4.24506i	0.525461	+	0.154289i	−0.00823426	+	0.999966i	$0.502621\pi$
$758$	−2.05018	−	16.4636i	−0.0744657	−	0.597984i
$759$	5.57518	−	0.511539i	0.202366	−	0.0185677i
$760$	15.5524	+	39.8999i	0.564146	+	1.44732i
$761$	44.8587	+	13.1717i	1.62613	+	0.477474i	0.962656	−	0.270729i	$-0.0872647\pi$
$761$	44.8587	+	13.1717i	1.62613	+	0.477474i	0.663470	+	0.748203i	$0.269083\pi$
$762$	20.3263	+	13.6128i	0.736344	+	0.493139i
$763$	−23.4243	−	15.0539i	−0.848016	−	0.544986i
$764$	−3.01681	−	28.6312i	−0.109144	−	1.03584i
$765$	−0.620990	−	0.966279i	−0.0224519	−	0.0349359i
$766$	11.1539	+	18.0993i	0.403006	+	0.653955i
$767$	5.43964	−	4.71348i	0.196414	−	0.170194i
$768$	14.4972	+	6.76978i	0.523124	+	0.244283i
$769$	−21.0832	−	9.62838i	−0.760280	−	0.347208i	−0.00273933	−	0.999996i	$-0.500872\pi$
$769$	−21.0832	−	9.62838i	−0.760280	−	0.347208i	−0.757541	+	0.652788i	$0.773599\pi$
$770$	−2.61236	−	6.01893i	−0.0941430	−	0.216907i
$771$	7.85258	−	2.30572i	0.282804	−	0.0830386i
$772$	2.62451	−	14.3723i	0.0944583	−	0.517271i
$773$	−0.00105957	−	0.00736947i	−3.81101e−5	−	0.000265061i	0.989802	−	0.142447i	$-0.0454972\pi$
$773$	−0.00105957	−	0.00736947i	−3.81101e−5	−	0.000265061i	−0.989840	+	0.142182i	$0.954588\pi$
$774$	−2.71146	+	3.01217i	−0.0974614	+	0.108270i
$775$	−0.662544	+	0.302574i	−0.0237993	+	0.0108688i
$776$	−23.2525	−	16.8800i	−0.834715	−	0.605958i
$777$	0.0873885	−	0.607800i	0.00313505	−	0.0218047i
$778$	−6.22134	−	2.98463i	−0.223046	−	0.107004i
$779$	−23.7848	−	20.6096i	−0.852178	−	0.738417i
$780$	−0.667605	+	17.6441i	−0.0239041	+	0.631761i
$781$	−1.75014			−0.0626249
$782$	−2.50195	−	1.86831i	−0.0894695	−	0.0668105i
$783$		−	6.30144i		−	0.225195i
$784$	17.4572	−	3.72016i	0.623471	−	0.132863i
$785$	39.2302	−	45.2741i	1.40019	−	1.61590i
$786$	5.07453	+	2.43446i	0.181003	+	0.0868342i
$787$	4.45315	+	0.640267i	0.158738	+	0.0228230i	0.221225	−	0.975223i	$-0.428994\pi$
$787$	4.45315	+	0.640267i	0.158738	+	0.0228230i	−0.0624877	+	0.998046i	$0.519903\pi$
$788$	30.6375	+	28.6459i	1.09141	+	1.02047i
$789$	7.81443	+	17.1112i	0.278201	+	0.609176i
$790$	−21.5073	−	19.3602i	−0.765194	−	0.688804i
$791$	1.25325	−	0.180190i	0.0445605	−	0.00640683i
$792$	3.29656	+	0.187211i	0.117138	+	0.00665224i
$793$	9.40047	+	32.0151i	0.333821	+	1.13689i
$794$	5.36765	+	12.3672i	0.190491	+	0.438894i
$795$	−7.50870	+	16.4418i	−0.266306	+	0.583129i
$796$	6.38304	+	15.5029i	0.226241	+	0.549484i
$797$	−33.5215	−	38.6859i	−1.18739	−	1.37032i	−0.912616	−	0.408817i	$-0.865941\pi$
$797$	−33.5215	−	38.6859i	−1.18739	−	1.37032i	−0.274777	−	0.961508i	$-0.588604\pi$
$798$	11.6393	−	7.17283i	0.412027	−	0.253915i
$799$	0.0590229	−	0.0379317i	0.00208808	−	0.00134193i
$800$	3.17755	+	6.15374i	0.112343	+	0.217567i
$801$	−1.45975	+	2.27141i	−0.0515776	+	0.0802562i
$802$	5.12139	+	3.42986i	0.180843	+	0.121113i
$803$	−3.54859	+	12.0854i	−0.125227	+	0.426484i
$804$	−0.749092	−	2.96109i	−0.0264184	−	0.104429i
$805$	13.2041	−	13.7458i	0.465384	−	0.484476i
$806$	−2.95440	+	0.367905i	−0.104064	+	0.0129589i
$807$	7.47060	−	25.4425i	0.262978	−	0.895620i
$808$	−25.9224	−	9.23765i	−0.911946	−	0.324980i
$809$	−7.65544	−	4.91985i	−0.269151	−	0.172973i	0.399103	−	0.916906i	$-0.369322\pi$
$809$	−7.65544	−	4.91985i	−0.269151	−	0.172973i	−0.668254	+	0.743933i	$0.732958\pi$
$810$	−0.0667139	+	3.52763i	−0.00234409	+	0.123948i
$811$	7.37336	−	4.73857i	0.258914	−	0.166394i	−0.404744	−	0.914430i	$-0.632639\pi$
$811$	7.37336	−	4.73857i	0.258914	−	0.166394i	0.663658	+	0.748036i	$0.269003\pi$
$812$	−15.6591	+	12.5643i	−0.549528	+	0.440920i
$813$	7.39094	−	6.40429i	0.259212	−	0.224608i
$814$	0.613879	−	0.167710i	0.0215165	−	0.00587824i
$815$	13.4385	−	29.4263i	0.470731	−	1.03076i
$816$	−1.29666	−	1.30770i	−0.0453923	−	0.0457787i
$817$	−16.6870	+	4.89974i	−0.583803	+	0.171420i
$818$	9.96911	−	31.7201i	0.348562	−	1.10907i
$819$	5.57973	−	0.802244i	0.194972	−	0.0280327i
$820$	−21.2240	−	14.8028i	−0.741173	−	0.516937i
$821$	−32.9381	+	15.0423i	−1.14955	+	0.524981i	−0.896750	−	0.442537i	$-0.854078\pi$
$821$	−32.9381	+	15.0423i	−1.14955	+	0.524981i	−0.252799	+	0.967519i	$0.581351\pi$
$822$	10.1118	+	12.1256i	0.352691	+	0.422928i
$823$	15.3713	+	2.21005i	0.535809	+	0.0770376i	0.404907	−	0.914358i	$-0.367304\pi$
$823$	15.3713	+	2.21005i	0.535809	+	0.0770376i	0.130901	+	0.991395i	$0.458213\pi$
$824$	39.0823	+	7.90319i	1.36150	+	0.275321i
$825$	1.08014	+	0.935950i	0.0376058	+	0.0325856i
$826$	−4.52261	−	0.737790i	−0.157362	−	0.0256710i
$827$			33.0459i			1.14912i	0.818463	+	0.574559i	$0.194827\pi$
$827$			33.0459i			1.14912i	−0.818463	+	0.574559i	$0.805173\pi$
$828$	3.19216	+	9.04490i	0.110935	+	0.314332i
$829$			49.2065i			1.70901i	0.519442	+	0.854506i	$0.326140\pi$
$829$			49.2065i			1.70901i	−0.519442	+	0.854506i	$0.673860\pi$
$830$	2.50983	−	15.3851i	0.0871175	−	0.534025i
$831$	−20.4851	−	17.7505i	−0.710621	−	0.615756i
$832$	4.84914	+	27.8907i	0.168114	+	0.966935i
$833$	−2.03351	−	0.292374i	−0.0704568	−	0.0101302i
$834$	−18.6176	+	15.5258i	−0.644676	+	0.537613i
$835$	57.2855	−	26.1614i	1.98245	−	0.905353i
$836$	11.6216	+	8.10558i	0.401942	+	0.280337i
$837$	−0.588867	+	0.0846663i	−0.0203542	+	0.00292649i
$838$	−52.5098	−	16.5030i	−1.81392	−	0.570086i
$839$	6.71244	−	1.97095i	0.231739	−	0.0680447i	−0.163801	−	0.986493i	$-0.552376\pi$
$839$	6.71244	−	1.97095i	0.231739	−	0.0680447i	0.395540	+	0.918449i	$0.370557\pi$
$840$	8.89921	−	6.86787i	0.307052	−	0.236964i
$841$	−4.44831	+	9.74044i	−0.153390	+	0.335877i
$842$	11.0077	+	40.2921i	0.379351	+	1.38856i
$843$	21.1170	−	18.2980i	0.727308	−	0.630216i
$844$	6.20070	+	7.72806i	0.213437	+	0.266011i
$845$	1.00336	−	0.644820i	0.0345166	−	0.0221825i
$846$	−0.215477	−	0.00407507i	−0.00740825	−	0.000140104i
$847$	12.9151	+	8.30005i	0.443769	+	0.285193i
$848$	−6.28009	+	28.2913i	−0.215659	+	0.971526i
$849$	2.65774	−	9.05143i	0.0912134	−	0.310644i
$850$	−0.0985051	−	0.791029i	−0.00337870	−	0.0271321i
$851$	1.13735	+	1.45733i	0.0389879	+	0.0499568i
$852$	−0.735361	−	2.90681i	−0.0251931	−	0.0995857i
$853$	−4.41104	+	15.0226i	−0.151031	+	0.514365i	−0.999899	−	0.0142407i	$-0.995467\pi$
$853$	−4.41104	+	15.0226i	−0.151031	+	0.514365i	0.848867	+	0.528606i	$0.177285\pi$
$854$	11.8206	−	17.6503i	0.404493	−	0.603980i
$855$	−8.18558	+	12.7370i	−0.279941	+	0.435597i
$856$	−49.1807	+	11.4568i	−1.68096	+	0.391584i
$857$	−27.5517	+	17.7064i	−0.941147	+	0.604839i	−0.918720	−	0.394910i	$-0.870776\pi$
$857$	−27.5517	+	17.7064i	−0.941147	+	0.604839i	−0.0224274	+	0.999748i	$0.507139\pi$
$858$	3.06496	+	4.97350i	0.104636	+	0.169792i
$859$	−28.6934	−	33.1139i	−0.979005	−	1.12983i	−0.991526	−	0.129910i	$-0.958531\pi$
$859$	−28.6934	−	33.1139i	−0.979005	−	1.12983i	0.0125209	−	0.999922i	$-0.496014\pi$
$860$	−13.2224	+	5.44411i	−0.450881	+	0.185642i
$861$	−3.43185	+	7.51471i	−0.116957	+	0.256101i
$862$	−7.58043	+	3.29009i	−0.258191	+	0.112061i
$863$	−0.842832	−	2.87042i	−0.0286903	−	0.0977103i	0.943903	−	0.330222i	$-0.107124\pi$
$863$	−0.842832	−	2.87042i	−0.0286903	−	0.0977103i	−0.972594	+	0.232512i	$0.925306\pi$
$864$	1.07419	+	5.55393i	0.0365446	+	0.188948i
$865$	−22.1263	+	3.18128i	−0.752316	+	0.108167i
$866$	16.3321	−	18.1434i	0.554988	−	0.616538i
$867$	−6.97400	−	15.2709i	−0.236850	−	0.518628i
$868$	1.38452	+	1.29453i	0.0469938	+	0.0439391i
$869$	−9.47704	−	1.36259i	−0.321487	−	0.0462228i
$870$	9.61671	−	20.0457i	0.326037	−	0.679612i
$871$	3.53896	−	4.08418i	0.119913	−	0.138387i
$872$	49.2553	−	4.24995i	1.66799	−	0.143921i
$873$		−	10.1588i		−	0.343824i
$874$	−8.70141	+	40.2296i	−0.294330	+	1.36079i
$875$	−15.0059			−0.507293
$876$	−21.5637	−	0.815910i	−0.728570	−	0.0275670i
$877$	27.9210	+	24.1937i	0.942824	+	0.816962i	0.983258	−	0.182221i	$-0.0583285\pi$
$877$	27.9210	+	24.1937i	0.942824	+	0.816962i	−0.0404337	+	0.999182i	$0.512874\pi$
$878$	5.68896	−	11.8584i	0.191993	−	0.400203i
$879$	2.24895	−	15.6418i	0.0758551	−	0.527584i
$880$	10.2011	+	5.62647i	0.343878	+	0.189668i
$881$	−1.43769	+	0.656571i	−0.0484370	+	0.0221204i	−0.439486	−	0.898249i	$-0.644839\pi$
$881$	−1.43769	+	0.656571i	−0.0484370	+	0.0221204i	0.391049	+	0.920370i	$0.372112\pi$
$882$	4.69027	+	4.22203i	0.157930	+	0.142163i
$883$	0.286122	+	1.99002i	0.00962876	+	0.0669695i	0.994069	−	0.108749i	$-0.0346844\pi$
$883$	0.286122	+	1.99002i	0.00962876	+	0.0669695i	−0.984441	+	0.175718i	$0.943775\pi$
$884$	0.585323	−	3.20533i	0.0196865	−	0.107807i
$885$	4.86904	−	1.42968i	0.163671	−	0.0480582i
$886$	5.71226	−	2.47926i	0.191907	−	0.0832923i
$887$	−33.2192	−	15.1707i	−1.11539	−	0.509382i	−0.229516	−	0.973305i	$-0.573714\pi$
$887$	−33.2192	−	15.1707i	−1.11539	−	0.509382i	−0.885876	+	0.463923i	$0.846442\pi$
$888$	0.536486	+	0.949126i	0.0180033	+	0.0318506i
$889$	20.8259	−	18.0457i	0.698477	−	0.605234i
$890$	−8.11007	+	4.99790i	−0.271850	+	0.167530i
$891$	0.631138	+	0.982070i	0.0211439	+	0.0329006i
$892$	−2.01974	+	0.212815i	−0.0676258	+	0.00712559i
$893$	−0.778011	−	0.499997i	−0.0260351	−	0.0167318i
$894$	−2.59286	+	3.87160i	−0.0867181	+	0.129486i
$895$	−24.2856	−	7.13089i	−0.811777	−	0.238359i
$896$	11.6598	−	13.7432i	0.389526	−	0.459129i
$897$	−9.89509	+	13.7874i	−0.330388	+	0.460347i
$898$	55.0430	−	6.85438i	1.83681	−	0.228734i
$899$	3.59701	+	1.05618i	0.119967	+	0.0352255i
$900$	−1.10068	+	2.18728i	−0.0366892	+	0.0729092i
$901$	1.80334	−	2.80604i	0.0600778	−	0.0934829i
$902$	−8.56009	−	0.161887i	−0.285020	−	0.00539025i
$903$	2.46814	+	3.84050i	0.0821346	+	0.127804i
$904$	−1.56612	+	1.61276i	−0.0520884	+	0.0536396i
$905$	−22.2112	−	25.6331i	−0.738324	−	0.852072i
$906$	12.1942	−	3.33144i	0.405126	−	0.110680i
$907$	−10.4825	−	4.78722i	−0.348067	−	0.158957i	0.233707	−	0.972307i	$-0.424914\pi$
$907$	−10.4825	−	4.78722i	−0.348067	−	0.158957i	−0.581775	+	0.813350i	$0.697641\pi$
$908$	−20.1345	−	34.0993i	−0.668186	−	1.13163i
$909$	−2.74111	−	9.33537i	−0.0909170	−	0.309635i
$910$	18.9742	+	5.96327i	0.628987	+	0.197680i
$911$	−1.44276	−	10.0346i	−0.0478006	−	0.332461i	−0.999664	−	0.0259368i	$-0.991743\pi$
$911$	−1.44276	−	10.0346i	−0.0478006	−	0.332461i	0.951863	−	0.306524i	$-0.0991660\pi$
$912$	−8.57949	+	22.7081i	−0.284095	+	0.751940i
$913$	−2.14260	−	4.69164i	−0.0709097	−	0.155271i
$914$	7.39770	+	8.87092i	0.244694	+	0.293424i
$915$	−3.34790	+	23.2852i	−0.110678	+	0.769783i
$916$	5.79544	+	1.94256i	0.191487	+	0.0641840i
$917$	4.15174	−	4.79136i	0.137102	−	0.158225i
$918$	0.104830	−	0.642602i	0.00345991	−	0.0212090i
$919$	−37.1389			−1.22510			−0.612549	−	0.790432i	$-0.709856\pi$
$919$	−37.1389			−1.22510			−0.612549	+	0.790432i	$0.709856\pi$
$920$	−3.64889	+	33.6446i	−0.120300	+	1.10923i
$921$	−15.5542			−0.512527
$922$	−2.28381	+	13.9996i	−0.0752131	+	0.461052i
$923$	3.47410	−	4.00932i	0.114351	−	0.131968i
$924$	1.18204	−	3.52651i	0.0388863	−	0.116014i
$925$	−0.0671618	+	0.467120i	−0.00220827	+	0.0153588i
$926$	−28.9964	−	34.7710i	−0.952882	−	1.14264i
$927$	5.85626	+	12.8234i	0.192345	+	0.421176i
$928$	8.38135	−	34.6470i	0.275131	−	1.13734i
$929$	8.23560	+	57.2798i	0.270201	+	1.87929i	0.446248	+	0.894909i	$0.352760\pi$
$929$	8.23560	+	57.2798i	0.270201	+	1.87929i	−0.176047	+	0.984382i	$0.556331\pi$
$930$	−2.00247	−	0.629344i	−0.0656636	−	0.0206370i
$931$	7.62940	+	25.9834i	0.250044	+	0.851570i
$932$	21.8601	−	12.9076i	0.716050	−	0.422803i
$933$	−13.6231	−	6.22147i	−0.446001	−	0.203682i
$934$	−22.1876	+	6.06160i	−0.726000	+	0.198342i
$935$	−0.878092	−	1.01337i	−0.0287167	−	0.0331408i
$936$	−6.97268	+	7.18034i	−0.227909	+	0.234697i
$937$	−0.889974	−	1.38483i	−0.0290742	−	0.0452403i	0.826412	−	0.563066i	$-0.190378\pi$
$937$	−0.889974	−	1.38483i	−0.0290742	−	0.0452403i	−0.855486	+	0.517825i	$0.826742\pi$
$938$	−3.43993	−	0.0650554i	−0.112318	−	0.00212413i
$939$	−2.67849	+	4.16781i	−0.0874092	+	0.136011i
$940$	−0.679241	−	0.341806i	−0.0221544	−	0.0111485i
$941$	−25.1812	−	7.39388i	−0.820885	−	0.241034i	−0.155788	−	0.987791i	$-0.549792\pi$
$941$	−25.1812	−	7.39388i	−0.820885	−	0.241034i	−0.665097	+	0.746757i	$0.731610\pi$
$942$	33.6977	−	4.19630i	1.09793	−	0.136723i
$943$	−9.15797	−	23.1233i	−0.298225	−	0.752999i
$944$	7.15735	−	3.86892i	0.232952	−	0.125923i
$945$	3.81336	+	1.11970i	0.124049	+	0.0364240i
$946$	−2.63268	+	3.93106i	−0.0855957	+	0.127810i
$947$	27.0474	+	17.3823i	0.878924	+	0.564850i	0.900470	−	0.434918i	$-0.143223\pi$
$947$	27.0474	+	17.3823i	0.878924	+	0.564850i	−0.0215465	+	0.999768i	$0.506859\pi$
$948$	−1.71886	−	16.3130i	−0.0558261	−	0.529821i
$949$	−20.6418	−	32.1193i	−0.670062	−	1.04264i
$950$	−8.94530	+	5.51262i	−0.290224	+	0.178853i
$951$	−15.6478	+	13.5589i	−0.507416	+	0.439679i
$952$	−1.80589	+	1.02077i	−0.0585293	+	0.0330832i
$953$	−52.8138	−	24.1193i	−1.71081	−	0.781300i	−0.996692	−	0.0812732i	$-0.974101\pi$
$953$	−52.8138	−	24.1193i	−1.71081	−	0.781300i	−0.714117	−	0.700027i	$-0.753171\pi$
$954$	−9.39886	+	4.07933i	−0.304299	+	0.132073i
$955$	34.4583	−	10.1179i	1.11504	−	0.327407i
$956$	44.1681	+	8.06550i	1.42850	+	0.260857i
$957$	−1.04690	−	7.28135i	−0.0338415	−	0.235373i
$958$	−23.4666	−	21.1239i	−0.758171	−	0.682482i
$959$	16.1776	−	7.38806i	0.522402	−	0.238573i
$960$	−5.05880	+	19.3071i	−0.163272	+	0.623134i
$961$	−4.36139	+	30.3341i	−0.140690	+	0.978520i
$962$	−0.834374	+	1.73922i	−0.0269013	+	0.0560748i
$963$	−13.4928	−	11.6916i	−0.434800	−	0.376757i
$964$	−2.27244	+	60.0584i	−0.0731904	+	1.93435i
$965$	18.2249			0.586680
$966$	10.7759	−	0.783569i	0.346710	−	0.0252109i
$967$			45.1989i			1.45350i	0.686903	+	0.726749i	$0.258970\pi$
$967$			45.1989i			1.45350i	−0.686903	+	0.726749i	$0.741030\pi$
$968$	−27.1572	+	2.34324i	−0.872866	+	0.0753145i
$969$	1.82968	−	2.11156i	0.0587777	−	0.0678331i
$970$	15.5035	−	32.3165i	0.497788	−	1.03762i
$971$	14.0038	+	2.01344i	0.449402	+	0.0646143i	0.363300	−	0.931672i	$-0.381650\pi$
$971$	14.0038	+	2.01344i	0.449402	+	0.0646143i	0.0861018	+	0.996286i	$0.472559\pi$
$972$	−1.36593	+	1.46090i	−0.0438124	+	0.0468583i
$973$	11.3437	+	24.8391i	0.363661	+	0.796306i
$974$	24.1219	−	26.7971i	0.772914	−	0.858633i
$975$	−4.28826	+	0.616559i	−0.137334	+	0.0197457i
$976$	2.53122	+	37.6319i	0.0810223	+	1.20457i
$977$	7.88719	+	26.8613i	0.252334	+	0.859369i	0.984070	+	0.177782i	$0.0568921\pi$
$977$	7.88719	+	26.8613i	0.252334	+	0.859369i	−0.731736	+	0.681588i	$0.761290\pi$
$978$	16.8214	−	7.30089i	0.537889	−	0.233457i
$979$	−1.30938	+	2.86714i	−0.0418480	+	0.0916343i
$980$	8.47704	+	20.5887i	0.270789	+	0.657682i
$981$	11.4464	+	13.2098i	0.365454	+	0.421757i
$982$	29.4246	+	47.7471i	0.938975	+	1.52367i
$983$	6.51249	−	4.18532i	0.207716	−	0.133491i	−0.432647	−	0.901563i	$-0.642420\pi$
$983$	6.51249	−	4.18532i	0.207716	−	0.133491i	0.640363	+	0.768072i	$0.278784\pi$
$984$	−3.32784	−	14.2855i	−0.106088	−	0.455405i
$985$	−28.2870	+	44.0155i	−0.901299	+	1.40245i
$986$	−2.28303	+	3.40897i	−0.0727065	+	0.108564i
$987$	−0.0683945	+	0.232930i	−0.00217702	+	0.00741425i
$988$	−41.6381	+	10.5335i	−1.32468	+	0.335117i
$989$	−13.4856	−	2.65097i	−0.428818	−	0.0842960i
$990$	0.508980	+	4.08728i	0.0161764	+	0.129902i
$991$	14.6836	−	50.0079i	0.466441	−	1.58855i	−0.305065	−	0.952331i	$-0.598678\pi$
$991$	14.6836	−	50.0079i	0.466441	−	1.58855i	0.771507	−	0.636221i	$-0.219504\pi$
$992$	−3.35036	−	0.317717i	−0.106374	−	0.0100875i
$993$	−24.4944	−	15.7416i	−0.777307	−	0.499545i
$994$	−3.37688	−	0.0638630i	−0.107108	−	0.00202561i
$995$	−17.5938	+	11.3068i	−0.557760	+	0.358450i
$996$	6.89210	−	5.52995i	0.218384	−	0.175223i
$997$	36.7724	−	31.8635i	1.16459	−	1.00913i	0.164854	−	0.986318i	$-0.447285\pi$
$997$	36.7724	−	31.8635i	1.16459	−	1.00913i	0.999740	−	0.0228082i	$-0.00726072\pi$
$998$	10.4313	+	38.1822i	0.330196	+	1.20863i
$999$	−0.160127	+	0.350630i	−0.00506621	+	0.0110934i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.t.a.235.1	✓	240
8.3	odd	2	inner	552.2.t.a.235.4	yes	240
23.14	odd	22	inner	552.2.t.a.451.4	yes	240
184.83	even	22	inner	552.2.t.a.451.1	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.t.a.235.1	✓	240	1.1	even	1	trivial
552.2.t.a.235.4	yes	240	8.3	odd	2	inner
552.2.t.a.451.1	yes	240	184.83	even	22	inner
552.2.t.a.451.4	yes	240	23.14	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.t (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39576 - 0.227696i) q^{2} +(0.654861 - 0.755750i) q^{3} +(1.89631 + 0.635619i) q^{4} +(-0.355055 + 2.46946i) q^{5} +(-1.08611 + 0.905738i) q^{6} +(0.661764 + 1.44906i) q^{7} +(-2.50207 - 1.31896i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(-1.39576 - 0.227696i) q^{2} +(0.654861 - 0.755750i) q^{3} +(1.89631 + 0.635619i) q^{4} +(-0.355055 + 2.46946i) q^{5} +(-1.08611 + 0.905738i) q^{6} +(0.661764 + 1.44906i) q^{7} +(-2.50207 - 1.31896i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(1.05786 - 3.36594i) q^{10} +(-0.328891 - 1.12010i) q^{11} +(1.72219 - 1.01689i) q^{12} +(3.21886 + 1.47000i) q^{13} +(-0.593720 - 2.17323i) q^{14} +(1.63378 + 1.88549i) q^{15} +(3.19198 + 2.41066i) q^{16} +(-0.248908 - 0.387309i) q^{17} +(-0.0267406 + 1.41396i) q^{18} +(-3.28099 + 5.10531i) q^{19} +(-2.24293 + 4.45718i) q^{20} +(1.52849 + 0.448805i) q^{21} +(0.204012 + 1.63828i) q^{22} +(-4.16216 + 2.38252i) q^{23} +(-2.63531 + 1.02721i) q^{24} +(-1.17471 - 0.344926i) q^{25} +(-4.15805 - 2.78470i) q^{26} +(-0.841254 - 0.540641i) q^{27} +(0.333858 + 3.16850i) q^{28} +(3.40681 + 5.30111i) q^{29} +(-1.85106 - 3.00370i) q^{30} +(0.449612 - 0.389591i) q^{31} +(-3.90634 - 4.09151i) q^{32} +(-1.06189 - 0.484951i) q^{33} +(0.259228 + 0.597267i) q^{34} +(-3.81336 + 1.11970i) q^{35} +(0.359277 - 1.96747i) q^{36} +(-0.0548572 - 0.381540i) q^{37} +(5.74194 - 6.37874i) q^{38} +(3.21886 - 1.47000i) q^{39} +(4.14548 - 5.71046i) q^{40} +(-0.738033 + 5.13313i) q^{41} +(-2.03122 - 0.974457i) q^{42} +(2.16580 + 1.87668i) q^{43} +(0.0882783 - 2.33311i) q^{44} +2.49486 q^{45} +(6.35188 - 2.37772i) q^{46} +0.152392i q^{47} +(3.91216 - 0.833687i) q^{48} +(2.92218 - 3.37238i) q^{49} +(1.56108 + 0.748911i) q^{50} +(-0.455709 - 0.0655210i) q^{51} +(5.16958 + 4.83355i) q^{52} +(3.00967 + 6.59027i) q^{53} +(1.05109 + 0.946157i) q^{54} +(2.88282 - 0.414487i) q^{55} +(0.255468 - 4.49849i) q^{56} +(1.70975 + 5.82287i) q^{57} +(-3.54806 - 8.17481i) q^{58} +(0.844965 - 1.85022i) q^{59} +(1.89971 + 4.61393i) q^{60} +(6.17484 + 7.12615i) q^{61} +(-0.716261 + 0.441402i) q^{62} +(1.34013 - 0.861251i) q^{63} +(4.52071 + 6.60024i) q^{64} +(-4.77298 + 7.42691i) q^{65} +(1.37173 + 0.918665i) q^{66} +(0.430258 - 1.46532i) q^{67} +(-0.225826 - 0.892668i) q^{68} +(-0.925049 + 4.70577i) q^{69} +(5.57750 - 0.694554i) q^{70} +(0.422371 - 1.43846i) q^{71} +(-0.949449 + 2.66431i) q^{72} +(-9.07676 - 5.83328i) q^{73} +(-0.0103075 + 0.545030i) q^{74} +(-1.02995 + 0.661908i) q^{75} +(-9.46680 + 7.59579i) q^{76} +(1.40545 - 1.21783i) q^{77} +(-4.82747 + 1.31885i) q^{78} +(3.40708 - 7.46047i) q^{79} +(-7.08636 + 7.02654i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(2.19891 - 6.99659i) q^{82} +(4.37321 - 0.628773i) q^{83} +(2.61322 + 1.82261i) q^{84} +(1.04482 - 0.477153i) q^{85} +(-2.59563 - 3.11254i) q^{86} +(6.23730 + 0.896788i) q^{87} +(-0.654455 + 3.23636i) q^{88} +(-2.04054 - 1.76814i) q^{89} +(-3.48223 - 0.568069i) q^{90} +5.63711i q^{91} +(-9.40712 + 1.87244i) q^{92} -0.594922i q^{93} +(0.0346992 - 0.212704i) q^{94} +(-11.4424 - 9.91493i) q^{95} +(-5.65027 + 0.272847i) q^{96} +(10.0554 + 1.44575i) q^{97} +(-4.84655 + 4.04167i) q^{98} +(-1.06189 + 0.484951i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9}+O(q^{10}) \) 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9	\( 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9} + 4 q^{12} - 4 q^{16} + 44 q^{17} - 55 q^{20} - 24 q^{25} + 24 q^{27} + 33 q^{34} + 7 q^{36} - 132 q^{38} + 11 q^{40} - 66 q^{42} + 77 q^{44} + 37 q^{48} - 56 q^{49} - 37 q^{50} - 55 q^{52} - 11 q^{54} + 132 q^{56} + 37 q^{58} + 11 q^{60} + 51 q^{62} - 4 q^{64} - 55 q^{66} - 132 q^{70} + 144 q^{73} + 44 q^{74} + 24 q^{75} - 55 q^{76} - 198 q^{80} - 24 q^{81} - 26 q^{82} + 44 q^{84} - 110 q^{86} + 22 q^{88} - 139 q^{92} - 117 q^{94} - 209 q^{98}+O(q^{100}) \) 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9 + 4 * q^12 - 4 * q^16 + 44 * q^17 - 55 * q^20 - 24 * q^25 + 24 * q^27 + 33 * q^34 + 7 * q^36 - 132 * q^38 + 11 * q^40 - 66 * q^42 + 77 * q^44 + 37 * q^48 - 56 * q^49 - 37 * q^50 - 55 * q^52 - 11 * q^54 + 132 * q^56 + 37 * q^58 + 11 * q^60 + 51 * q^62 - 4 * q^64 - 55 * q^66 - 132 * q^70 + 144 * q^73 + 44 * q^74 + 24 * q^75 - 55 * q^76 - 198 * q^80 - 24 * q^81 - 26 * q^82 + 44 * q^84 - 110 * q^86 + 22 * q^88 - 139 * q^92 - 117 * q^94 - 209 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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