LMFDB - Embedded newform 156.2.w.c.7.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [156,2,Mod(7,156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(156, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 11]))

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

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

chi := DirichletCharacter("156.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 156 = 2^{2} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	156.w (of order $12$, degree $4$, 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:	$1.24566627153$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			7.5
Character	$\chi$	$=$	156.7
Dual form			156.2.w.c.67.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.806088 + 1.16199i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.700446 + 1.87333i) q^{4} +(-0.922964 - 0.922964i) q^{5} +(0.117097 + 1.40936i) q^{6} +(-0.757268 + 2.82616i) q^{7} +(-2.74142 + 0.696159i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.806088 + 1.16199i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.700446 + 1.87333i) q^{4} +(-0.922964 - 0.922964i) q^{5} +(0.117097 + 1.40936i) q^{6} +(-0.757268 + 2.82616i) q^{7} +(-2.74142 + 0.696159i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.328486 - 1.81647i) q^{10} +(6.23908 - 1.67176i) q^{11} +(-1.54327 + 1.27213i) q^{12} +(-1.11510 - 3.42878i) q^{13} +(-3.89440 + 1.39820i) q^{14} +(-0.337828 - 1.26079i) q^{15} +(-3.01875 - 2.62434i) q^{16} +(4.26744 - 2.46381i) q^{17} +(-0.603270 + 1.27909i) q^{18} +(-5.87432 - 1.57402i) q^{19} +(2.37551 - 1.08253i) q^{20} +(-2.06889 + 2.06889i) q^{21} +(6.97182 + 5.90218i) q^{22} +(-1.59497 + 2.76257i) q^{23} +(-2.72222 - 0.767817i) q^{24} -3.29627i q^{25} +(3.08535 - 4.05963i) q^{26} +1.00000i q^{27} +(-4.76392 - 3.39819i) q^{28} +(1.83272 - 3.17437i) q^{29} +(1.19271 - 1.40886i) q^{30} +(-1.77808 + 1.77808i) q^{31} +(0.616076 - 5.62321i) q^{32} +(6.23908 + 1.67176i) q^{33} +(6.30285 + 2.97268i) q^{34} +(3.30738 - 1.90952i) q^{35} +(-1.97258 + 0.330063i) q^{36} +(1.65532 + 6.17774i) q^{37} +(-2.90622 - 8.09471i) q^{38} +(0.748687 - 3.52696i) q^{39} +(3.17276 + 1.88770i) q^{40} +(-8.16771 + 2.18853i) q^{41} +(-4.07175 - 0.736326i) q^{42} +(0.803327 + 1.39140i) q^{43} +(-1.23838 + 12.8589i) q^{44} +(0.337828 - 1.26079i) q^{45} +(-4.49577 + 0.373532i) q^{46} +(-1.94917 - 1.94917i) q^{47} +(-1.30215 - 3.78212i) q^{48} +(-1.35156 - 0.780323i) q^{49} +(3.83024 - 2.65709i) q^{50} +4.92762 q^{51} +(7.20432 + 0.312724i) q^{52} +2.19902 q^{53} +(-1.16199 + 0.806088i) q^{54} +(-7.30143 - 4.21548i) q^{55} +(0.108529 - 8.27487i) q^{56} +(-4.30030 - 4.30030i) q^{57} +(5.16592 - 0.429212i) q^{58} +(0.998196 - 3.72532i) q^{59} +(2.59851 + 0.250252i) q^{60} +(1.35734 + 2.35098i) q^{61} +(-3.49941 - 0.632826i) q^{62} +(-2.82616 + 0.757268i) q^{63} +(7.03073 - 3.81692i) q^{64} +(-2.13545 + 4.19384i) q^{65} +(3.08668 + 8.59734i) q^{66} +(1.55464 + 5.80201i) q^{67} +(1.62642 + 9.72010i) q^{68} +(-2.76257 + 1.59497i) q^{69} +(4.88488 + 2.30391i) q^{70} +(-6.51621 - 1.74601i) q^{71} +(-1.97360 - 2.02606i) q^{72} +(-7.04372 + 7.04372i) q^{73} +(-5.84414 + 6.90326i) q^{74} +(1.64814 - 2.85466i) q^{75} +(7.06331 - 9.90205i) q^{76} +18.8986i q^{77} +(4.70181 - 1.97307i) q^{78} +3.26039i q^{79} +(0.364032 + 5.20837i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-9.12695 - 7.72666i) q^{82} +(-1.56980 + 1.56980i) q^{83} +(-2.42658 - 5.32488i) q^{84} +(-6.21270 - 1.66469i) q^{85} +(-0.969246 + 2.05505i) q^{86} +(3.17437 - 1.83272i) q^{87} +(-15.9401 + 8.92638i) q^{88} +(-2.53716 - 9.46880i) q^{89} +(1.73735 - 0.623756i) q^{90} +(10.5347 - 0.554944i) q^{91} +(-4.05802 - 4.92294i) q^{92} +(-2.42891 + 0.650824i) q^{93} +(0.693718 - 3.83613i) q^{94} +(3.96903 + 6.87456i) q^{95} +(3.34514 - 4.56180i) q^{96} +(-1.76604 + 6.59095i) q^{97} +(-0.182747 - 2.19951i) q^{98} +(4.56733 + 4.56733i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 12 q^{9}+O(q^{10}) $ 24 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 12 * q^9	\( 24 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 12 q^{9} + 12 q^{10} + 4 q^{11} - 4 q^{12} - 22 q^{14} - 4 q^{15} + 12 q^{16} - 2 q^{18} - 22 q^{19} - 4 q^{20} + 10 q^{21} - 34 q^{22} + 2 q^{24} - 4 q^{26} - 14 q^{28} + 8 q^{29} - 16 q^{30} - 2 q^{31} - 34 q^{32} + 4 q^{33} + 20 q^{34} + 24 q^{35} - 4 q^{36} - 12 q^{37} - 12 q^{38} - 6 q^{39} + 28 q^{40} - 36 q^{41} + 6 q^{42} + 10 q^{43} + 20 q^{44} + 4 q^{45} - 2 q^{46} + 20 q^{47} + 32 q^{48} - 54 q^{49} - 24 q^{50} + 36 q^{51} + 4 q^{52} - 36 q^{53} - 4 q^{54} - 24 q^{55} + 70 q^{56} - 32 q^{57} + 48 q^{58} - 36 q^{59} - 28 q^{60} - 2 q^{61} + 64 q^{62} + 8 q^{63} - 8 q^{64} + 16 q^{65} + 20 q^{66} - 16 q^{67} - 10 q^{68} + 12 q^{69} + 36 q^{71} - 2 q^{72} - 40 q^{73} - 30 q^{74} - 8 q^{75} + 58 q^{76} + 24 q^{78} - 48 q^{80} - 12 q^{81} - 30 q^{82} - 24 q^{83} - 26 q^{84} + 18 q^{85} + 30 q^{86} + 6 q^{87} - 78 q^{88} + 66 q^{89} + 12 q^{90} + 42 q^{91} + 36 q^{92} - 10 q^{93} + 6 q^{94} - 28 q^{95} + 8 q^{96} + 4 q^{97} + 44 q^{98} - 4 q^{99}+O(q^{100}) \) 24 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 12 * q^9 + 12 * q^10 + 4 * q^11 - 4 * q^12 - 22 * q^14 - 4 * q^15 + 12 * q^16 - 2 * q^18 - 22 * q^19 - 4 * q^20 + 10 * q^21 - 34 * q^22 + 2 * q^24 - 4 * q^26 - 14 * q^28 + 8 * q^29 - 16 * q^30 - 2 * q^31 - 34 * q^32 + 4 * q^33 + 20 * q^34 + 24 * q^35 - 4 * q^36 - 12 * q^37 - 12 * q^38 - 6 * q^39 + 28 * q^40 - 36 * q^41 + 6 * q^42 + 10 * q^43 + 20 * q^44 + 4 * q^45 - 2 * q^46 + 20 * q^47 + 32 * q^48 - 54 * q^49 - 24 * q^50 + 36 * q^51 + 4 * q^52 - 36 * q^53 - 4 * q^54 - 24 * q^55 + 70 * q^56 - 32 * q^57 + 48 * q^58 - 36 * q^59 - 28 * q^60 - 2 * q^61 + 64 * q^62 + 8 * q^63 - 8 * q^64 + 16 * q^65 + 20 * q^66 - 16 * q^67 - 10 * q^68 + 12 * q^69 + 36 * q^71 - 2 * q^72 - 40 * q^73 - 30 * q^74 - 8 * q^75 + 58 * q^76 + 24 * q^78 - 48 * q^80 - 12 * q^81 - 30 * q^82 - 24 * q^83 - 26 * q^84 + 18 * q^85 + 30 * q^86 + 6 * q^87 - 78 * q^88 + 66 * q^89 + 12 * q^90 + 42 * q^91 + 36 * q^92 - 10 * q^93 + 6 * q^94 - 28 * q^95 + 8 * q^96 + 4 * q^97 + 44 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/156\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{12}\right)$

Coefficient data

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

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

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

$2$	0.806088	+	1.16199i	0.569990	+	0.821652i
$2$	0.806088	+	1.16199i	0.569990	+	0.821652i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	−0.700446	+	1.87333i	−0.350223	+	0.936666i
$5$	−0.922964	−	0.922964i	−0.412762	−	0.412762i	0.469937	−	0.882700i	$-0.344276\pi$
$5$	−0.922964	−	0.922964i	−0.412762	−	0.412762i	−0.882700	+	0.469937i	$0.844276\pi$
$6$	0.117097	+	1.40936i	0.0478046	+	0.575368i
$7$	−0.757268	+	2.82616i	−0.286220	+	1.06819i	0.661723	+	0.749749i	$0.269826\pi$
$7$	−0.757268	+	2.82616i	−0.286220	+	1.06819i	−0.947943	+	0.318440i	$0.896841\pi$
$8$	−2.74142	+	0.696159i	−0.969237	+	0.246129i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	0.328486	−	1.81647i	0.103876	−	0.574417i
$11$	6.23908	−	1.67176i	1.88115	−	0.504054i	0.881673	−	0.471860i	$-0.156417\pi$
$11$	6.23908	−	1.67176i	1.88115	−	0.504054i	0.999482	−	0.0321934i	$-0.0102493\pi$
$12$	−1.54327	+	1.27213i	−0.445504	+	0.367233i
$13$	−1.11510	−	3.42878i	−0.309273	−	0.950973i
$13$	−1.11510	−	3.42878i	−0.309273	−	0.950973i
$14$	−3.89440	+	1.39820i	−1.04082	+	0.373684i
$15$	−0.337828	−	1.26079i	−0.0872269	−	0.325535i
$16$	−3.01875	−	2.62434i	−0.754688	−	0.656084i
$17$	4.26744	−	2.46381i	1.03501	−	0.597561i	0.116591	−	0.993180i	$-0.462803\pi$
$17$	4.26744	−	2.46381i	1.03501	−	0.597561i	0.918415	+	0.395619i	$0.129470\pi$
$18$	−0.603270	+	1.27909i	−0.142192	+	0.301484i
$19$	−5.87432	−	1.57402i	−1.34766	−	0.361105i	−0.488391	−	0.872625i	$-0.662416\pi$
$19$	−5.87432	−	1.57402i	−1.34766	−	0.361105i	−0.859271	+	0.511520i	$0.829083\pi$
$20$	2.37551	−	1.08253i	0.531179	−	0.242062i
$21$	−2.06889	+	2.06889i	−0.451470	+	0.451470i
$22$	6.97182	+	5.90218i	1.48640	+	1.25835i
$23$	−1.59497	+	2.76257i	−0.332574	+	0.576036i	−0.983016	−	0.183521i	$-0.941251\pi$
$23$	−1.59497	+	2.76257i	−0.332574	+	0.576036i	0.650442	+	0.759556i	$0.274584\pi$
$24$	−2.72222	−	0.767817i	−0.555670	−	0.156730i
$25$		−	3.29627i		−	0.659255i
$26$	3.08535	−	4.05963i	0.605086	−	0.796160i
$27$			1.00000i			0.192450i
$28$	−4.76392	−	3.39819i	−0.900296	−	0.642197i
$29$	1.83272	−	3.17437i	0.340328	−	0.589465i	−0.644166	−	0.764886i	$-0.722795\pi$
$29$	1.83272	−	3.17437i	0.340328	−	0.589465i	0.984494	+	0.175421i	$0.0561286\pi$
$30$	1.19271	−	1.40886i	0.217758	−	0.257222i
$31$	−1.77808	+	1.77808i	−0.319353	+	0.319353i	−0.848519	−	0.529165i	$-0.822505\pi$
$31$	−1.77808	+	1.77808i	−0.319353	+	0.319353i	0.529165	+	0.848519i	$0.322505\pi$
$32$	0.616076	−	5.62321i	0.108908	−	0.994052i
$33$	6.23908	+	1.67176i	1.08609	+	0.291016i
$34$	6.30285	+	2.97268i	1.08093	+	0.509811i
$35$	3.30738	−	1.90952i	0.559049	−	0.322767i
$36$	−1.97258	+	0.330063i	−0.328763	+	0.0550104i
$37$	1.65532	+	6.17774i	0.272133	+	1.01561i	0.957738	+	0.287640i	$0.0928708\pi$
$37$	1.65532	+	6.17774i	0.272133	+	1.01561i	−0.685606	+	0.727973i	$0.740463\pi$
$38$	−2.90622	−	8.09471i	−0.471451	−	1.31314i
$39$	0.748687	−	3.52696i	0.119886	−	0.564766i
$40$	3.17276	+	1.88770i	0.501657	+	0.298472i
$41$	−8.16771	+	2.18853i	−1.27558	+	0.341791i	−0.832167	−	0.554525i	$-0.812900\pi$
$41$	−8.16771	+	2.18853i	−1.27558	+	0.341791i	−0.443415	+	0.896316i	$0.646233\pi$
$42$	−4.07175	−	0.736326i	−0.628284	−	0.113618i
$43$	0.803327	+	1.39140i	0.122506	+	0.212187i	0.920755	−	0.390140i	$-0.127574\pi$
$43$	0.803327	+	1.39140i	0.122506	+	0.212187i	−0.798249	+	0.602327i	$0.794240\pi$
$44$	−1.23838	+	12.8589i	−0.186693	+	1.93855i
$45$	0.337828	−	1.26079i	0.0503605	−	0.187948i
$46$	−4.49577	+	0.373532i	−0.662865	+	0.0550743i
$47$	−1.94917	−	1.94917i	−0.284316	−	0.284316i	0.550511	−	0.834828i	$-0.314433\pi$
$47$	−1.94917	−	1.94917i	−0.284316	−	0.284316i	−0.834828	+	0.550511i	$0.814433\pi$
$48$	−1.30215	−	3.78212i	−0.187949	−	0.545902i
$49$	−1.35156	−	0.780323i	−0.193080	−	0.111475i
$50$	3.83024	−	2.65709i	0.541678	−	0.375769i
$51$	4.92762			0.690004
$52$	7.20432	+	0.312724i	0.999059	+	0.0433670i
$53$	2.19902			0.302059			0.151029	−	0.988529i	$-0.451741\pi$
$53$	2.19902			0.302059			0.151029	+	0.988529i	$0.451741\pi$
$54$	−1.16199	+	0.806088i	−0.158127	+	0.109695i
$55$	−7.30143	−	4.21548i	−0.984524	−	0.568415i
$56$	0.108529	−	8.27487i	0.0145028	−	1.10578i
$57$	−4.30030	−	4.30030i	−0.569589	−	0.569589i
$58$	5.16592	−	0.429212i	0.678319	−	0.0563583i
$59$	0.998196	−	3.72532i	0.129954	−	0.484995i	−0.870014	−	0.493028i	$-0.835890\pi$
$59$	0.998196	−	3.72532i	0.129954	−	0.484995i	0.999968	+	0.00803240i	$0.00255682\pi$
$60$	2.59851	+	0.250252i	0.335467	+	0.0323074i
$61$	1.35734	+	2.35098i	0.173789	+	0.301012i	0.939742	−	0.341886i	$-0.111066\pi$
$61$	1.35734	+	2.35098i	0.173789	+	0.301012i	−0.765952	+	0.642897i	$0.777732\pi$
$62$	−3.49941	−	0.632826i	−0.444425	−	0.0803690i
$63$	−2.82616	+	0.757268i	−0.356063	+	0.0954068i
$64$	7.03073	−	3.81692i	0.878841	−	0.477115i
$65$	−2.13545	+	4.19384i	−0.264870	+	0.520182i
$66$	3.08668	+	8.59734i	0.379944	+	1.05826i
$67$	1.55464	+	5.80201i	0.189930	+	0.708829i	0.993521	+	0.113647i	$0.0362533\pi$
$67$	1.55464	+	5.80201i	0.189930	+	0.708829i	−0.803591	+	0.595182i	$0.797080\pi$
$68$	1.62642	+	9.72010i	0.197233	+	1.17874i
$69$	−2.76257	+	1.59497i	−0.332574	+	0.192012i
$70$	4.88488	+	2.30391i	0.583854	+	0.275369i
$71$	−6.51621	−	1.74601i	−0.773332	−	0.207214i	−0.149489	−	0.988763i	$-0.547763\pi$
$71$	−6.51621	−	1.74601i	−0.773332	−	0.207214i	−0.623843	+	0.781550i	$0.714430\pi$
$72$	−1.97360	−	2.02606i	−0.232591	−	0.238773i
$73$	−7.04372	+	7.04372i	−0.824405	+	0.824405i	−0.986736	−	0.162332i	$-0.948099\pi$
$73$	−7.04372	+	7.04372i	−0.824405	+	0.824405i	0.162332	+	0.986736i	$0.448099\pi$
$74$	−5.84414	+	6.90326i	−0.679367	+	0.802488i
$75$	1.64814	−	2.85466i	0.190310	−	0.329627i
$76$	7.06331	−	9.90205i	0.810217	−	1.13584i
$77$			18.8986i			2.15370i
$78$	4.70181	−	1.97307i	0.532375	−	0.223407i
$79$			3.26039i			0.366822i	0.983036	+	0.183411i	$0.0587139\pi$
$79$			3.26039i			0.366822i	−0.983036	+	0.183411i	$0.941286\pi$
$80$	0.364032	+	5.20837i	0.0407000	+	0.582313i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−9.12695	−	7.72666i	−1.00790	−	0.853267i
$83$	−1.56980	+	1.56980i	−0.172308	+	0.172308i	−0.787993	−	0.615684i	$-0.788880\pi$
$83$	−1.56980	+	1.56980i	−0.172308	+	0.172308i	0.615684	+	0.787993i	$0.288880\pi$
$84$	−2.42658	−	5.32488i	−0.264762	−	0.580992i
$85$	−6.21270	−	1.66469i	−0.673862	−	0.180561i
$86$	−0.969246	+	2.05505i	−0.104516	+	0.221602i
$87$	3.17437	−	1.83272i	0.340328	−	0.196488i
$88$	−15.9401	+	8.92638i	−1.69922	+	0.951555i
$89$	−2.53716	−	9.46880i	−0.268938	−	1.00369i	−0.959796	−	0.280700i	$-0.909434\pi$
$89$	−2.53716	−	9.46880i	−0.268938	−	1.00369i	0.690858	−	0.722991i	$-0.257233\pi$
$90$	1.73735	−	0.623756i	0.183133	−	0.0657496i
$91$	10.5347	−	0.554944i	1.10434	−	0.0581740i
$92$	−4.05802	−	4.92294i	−0.423078	−	0.513252i
$93$	−2.42891	+	0.650824i	−0.251866	+	0.0674873i
$94$	0.693718	−	3.83613i	0.0715515	−	0.395666i
$95$	3.96903	+	6.87456i	0.407214	+	0.705315i
$96$	3.34514	−	4.56180i	0.341412	−	0.465587i
$97$	−1.76604	+	6.59095i	−0.179314	+	0.669209i	0.816462	+	0.577399i	$0.195932\pi$
$97$	−1.76604	+	6.59095i	−0.179314	+	0.669209i	−0.995776	+	0.0918106i	$0.970735\pi$
$98$	−0.182747	−	2.19951i	−0.0184602	−	0.222184i
$99$	4.56733	+	4.56733i	0.459034	+	0.459034i
$100$	6.17502	+	2.30886i	0.617502	+	0.230886i
$101$	6.90398	+	3.98602i	0.686972	+	0.396623i	0.802477	−	0.596683i	$-0.203515\pi$
$101$	6.90398	+	3.98602i	0.686972	+	0.396623i	−0.115505	+	0.993307i	$0.536849\pi$
$102$	3.97209	+	5.72584i	0.393295	+	0.566943i
$103$	−13.6446			−1.34444			−0.672220	−	0.740352i	$-0.734659\pi$
$103$	−13.6446			−1.34444			−0.672220	+	0.740352i	$0.734659\pi$
$104$	5.44393	+	8.62344i	0.533821	+	0.845597i
$105$	3.81903			0.372699
$106$	1.77260	+	2.55524i	0.172170	+	0.248187i
$107$	−1.28577	−	0.742339i	−0.124300	−	0.0717646i	0.436561	−	0.899675i	$-0.356196\pi$
$107$	−1.28577	−	0.742339i	−0.124300	−	0.0717646i	−0.560861	+	0.827910i	$0.689530\pi$
$108$	−1.87333	−	0.700446i	−0.180262	−	0.0674004i
$109$	−11.4283	−	11.4283i	−1.09463	−	1.09463i	−0.995027	−	0.0996053i	$-0.968242\pi$
$109$	−11.4283	−	11.4283i	−1.09463	−	1.09463i	−0.0996053	−	0.995027i	$-0.531758\pi$
$110$	−0.987239	−	11.8822i	−0.0941295	−	1.13293i
$111$	−1.65532	+	6.17774i	−0.157116	+	0.586365i
$112$	9.70280	−	6.54416i	0.916829	−	0.618365i
$113$	0.511720	+	0.886326i	0.0481386	+	0.0833785i	0.889091	−	0.457731i	$-0.151338\pi$
$113$	0.511720	+	0.886326i	0.0481386	+	0.0833785i	−0.840952	+	0.541110i	$0.818004\pi$
$114$	1.53049	−	8.46333i	0.143344	−	0.792664i
$115$	4.02185	−	1.07765i	0.375040	−	0.100492i
$116$	4.66293	+	5.65677i	0.432942	+	0.525218i
$117$	2.41186	−	2.68010i	0.222977	−	0.247775i
$118$	5.13342	−	1.84304i	0.472570	−	0.169665i
$119$	3.73152	+	13.9262i	0.342068	+	1.27662i
$120$	1.80384	+	3.22118i	0.164667	+	0.294052i
$121$	26.6051	−	15.3605i	2.41865	−	1.39641i
$122$	−1.63768	+	3.47231i	−0.148269	+	0.314368i
$123$	−8.16771	−	2.18853i	−0.736458	−	0.197333i
$124$	−2.08549	−	4.57640i	−0.187283	−	0.410972i
$125$	−7.65716	+	7.65716i	−0.684878	+	0.684878i
$126$	−3.15807	−	2.67355i	−0.281343	−	0.238179i
$127$	4.05853	−	7.02958i	0.360136	−	0.623774i	−0.627847	−	0.778337i	$-0.716064\pi$
$127$	4.05853	−	7.02958i	0.360136	−	0.623774i	0.987983	+	0.154563i	$0.0493968\pi$
$128$	10.1026	+	5.09287i	0.892953	+	0.450150i
$129$			1.60665i			0.141458i
$130$	−6.59456	+	0.899233i	−0.578381	+	0.0788679i
$131$		−	6.93662i		−	0.606055i	−0.952982	−	0.303028i	$-0.902003\pi$
$131$		−	6.93662i		−	0.606055i	0.952982	−	0.303028i	$-0.0979974\pi$
$132$	−7.50190	+	10.5169i	−0.652956	+	0.915379i
$133$	8.89687	−	15.4098i	0.771457	−	1.33620i
$134$	−5.48871	+	6.48341i	−0.474152	+	0.560082i
$135$	0.922964	−	0.922964i	0.0794361	−	0.0794361i
$136$	−9.98363	+	9.72514i	−0.856089	+	0.833924i
$137$	8.03913	+	2.15408i	0.686829	+	0.184035i	0.585324	−	0.810800i	$-0.300967\pi$
$137$	8.03913	+	2.15408i	0.686829	+	0.184035i	0.101505	+	0.994835i	$0.467634\pi$
$138$	−4.08021	−	1.92439i	−0.347331	−	0.163815i
$139$	9.25550	−	5.34366i	0.785041	−	0.453244i	−0.0531727	−	0.998585i	$-0.516933\pi$
$139$	9.25550	−	5.34366i	0.785041	−	0.453244i	0.838214	+	0.545342i	$0.183600\pi$
$140$	1.26052	+	7.53333i	0.106533	+	0.636683i
$141$	−0.713447	−	2.66262i	−0.0600831	−	0.224233i
$142$	−3.22378	−	8.97922i	−0.270534	−	0.753519i
$143$	−12.6893	−	19.5283i	−1.06113	−	1.63304i
$144$	0.763366	−	3.92648i	0.0636138	−	0.327207i
$145$	−4.62137	+	1.23829i	−0.383784	+	0.102835i
$146$	−13.8626	−	2.50688i	−1.14728	−	0.207471i
$147$	−0.780323	−	1.35156i	−0.0643600	−	0.111475i
$148$	−12.7324	−	1.22620i	−1.04660	−	0.100793i
$149$	4.08855	−	15.2587i	0.334947	−	1.25004i	−0.568980	−	0.822351i	$-0.692662\pi$
$149$	4.08855	−	15.2587i	0.334947	−	1.25004i	0.903927	−	0.427687i	$-0.140672\pi$
$150$	4.64563	−	0.385983i	0.379314	−	0.0315154i
$151$	−1.19577	−	1.19577i	−0.0973104	−	0.0973104i	0.656776	−	0.754086i	$-0.271920\pi$
$151$	−1.19577	−	1.19577i	−0.0973104	−	0.0973104i	−0.754086	+	0.656776i	$0.771920\pi$
$152$	17.1997	+	0.225583i	1.39508	+	0.0182972i
$153$	4.26744	+	2.46381i	0.345002	+	0.199187i
$154$	−21.9600	+	15.2340i	−1.76959	+	1.22759i
$155$	3.28222			0.263634
$156$	6.08276	+	3.87299i	0.487011	+	0.310087i
$157$	6.37074			0.508440			0.254220	−	0.967146i	$-0.418181\pi$
$157$	6.37074			0.508440			0.254220	+	0.967146i	$0.418181\pi$
$158$	−3.78854	+	2.62816i	−0.301400	+	0.209085i
$159$	1.90441	+	1.09951i	0.151029	+	0.0871969i
$160$	−5.75864	+	4.62140i	−0.455260	+	0.365354i
$161$	−6.59965	−	6.59965i	−0.520125	−	0.520125i
$162$	−1.40936	+	0.117097i	−0.110730	+	0.00920000i
$163$	−2.76497	+	10.3190i	−0.216569	+	0.808246i	0.769040	+	0.639201i	$0.220735\pi$
$163$	−2.76497	+	10.3190i	−0.216569	+	0.808246i	−0.985608	+	0.169045i	$0.945932\pi$
$164$	1.62119	−	16.8338i	0.126594	−	1.31450i
$165$	−4.21548	−	7.30143i	−0.328175	−	0.568415i
$166$	−3.08950	−	0.558699i	−0.239792	−	0.0433634i
$167$	−7.08854	+	1.89937i	−0.548528	+	0.146978i	−0.522431	−	0.852682i	$-0.674975\pi$
$167$	−7.08854	+	1.89937i	−0.548528	+	0.146978i	−0.0260972	+	0.999659i	$0.508308\pi$
$168$	4.23142	−	7.11198i	0.326461	−	0.548701i
$169$	−10.5131	+	7.64687i	−0.808701	+	0.588221i
$170$	−3.07363	−	8.56099i	−0.235737	−	0.656598i
$171$	−1.57402	−	5.87432i	−0.120368	−	0.449221i
$172$	−3.16925	+	0.530296i	−0.241653	+	0.0404347i
$173$	11.6048	−	6.70004i	0.882297	−	0.509394i	0.0108819	−	0.999941i	$-0.496536\pi$
$173$	11.6048	−	6.70004i	0.882297	−	0.509394i	0.871415	+	0.490546i	$0.163203\pi$
$174$	4.68843	+	2.21125i	0.355429	+	0.167635i
$175$	9.31580	+	2.49616i	0.704209	+	0.188692i
$176$	−23.2215	−	11.3268i	−1.75039	−	0.853792i
$177$	2.72712	−	2.72712i	0.204983	−	0.204983i
$178$	8.95749	−	10.5808i	0.671392	−	0.793067i
$179$	−10.1189	+	17.5265i	−0.756326	+	1.30999i	0.188387	+	0.982095i	$0.439674\pi$
$179$	−10.1189	+	17.5265i	−0.756326	+	1.30999i	−0.944713	+	0.327899i	$0.893659\pi$
$180$	2.12525	+	1.51598i	0.158407	+	0.112995i
$181$			7.21615i			0.536372i	0.963367	+	0.268186i	$0.0864242\pi$
$181$			7.21615i			0.536372i	−0.963367	+	0.268186i	$0.913576\pi$
$182$	9.13675	+	11.7939i	0.677261	+	0.874224i
$183$			2.71468i			0.200675i
$184$	2.44929	−	8.68371i	0.180564	−	0.640171i
$185$	4.17403	−	7.22963i	0.306881	−	0.531533i
$186$	−2.71416	−	2.29775i	−0.199012	−	0.168479i
$187$	22.5060	−	22.5060i	1.64580	−	1.64580i
$188$	5.01674	−	2.28616i	0.365884	−	0.166735i
$189$	−2.82616	−	0.757268i	−0.205573	−	0.0550831i
$190$	−4.78879	+	10.1535i	−0.347415	+	0.736610i
$191$	−1.27416	+	0.735635i	−0.0921947	+	0.0532287i	−0.545389	−	0.838183i	$-0.683618\pi$
$191$	−1.27416	+	0.735635i	−0.0921947	+	0.0532287i	0.453194	+	0.891412i	$0.350285\pi$
$192$	7.99725	+	0.209812i	0.577152	+	0.0151419i
$193$	5.87057	+	21.9093i	0.422573	+	1.57706i	0.769166	+	0.639049i	$0.220672\pi$
$193$	5.87057	+	21.9093i	0.422573	+	1.57706i	−0.346593	+	0.938016i	$0.612662\pi$
$194$	−9.08220	+	3.26076i	−0.652064	+	0.234109i
$195$	−3.94627	+	2.56425i	−0.282598	+	0.183630i
$196$	2.40850	−	1.98535i	0.172036	−	0.141810i
$197$	25.9643	−	6.95710i	1.84988	−	0.495673i	0.850343	−	0.526228i	$-0.176394\pi$
$197$	25.9643	−	6.95710i	1.84988	−	0.495673i	0.999533	+	0.0305553i	$0.00972758\pi$
$198$	−1.62553	+	8.98886i	−0.115521	+	0.638810i
$199$	−9.25911	−	16.0373i	−0.656361	−	1.13685i	−0.981551	−	0.191202i	$-0.938762\pi$
$199$	−9.25911	−	16.0373i	−0.656361	−	1.13685i	0.325190	−	0.945649i	$-0.394572\pi$
$200$	2.29473	+	9.03646i	0.162262	+	0.638974i
$201$	−1.55464	+	5.80201i	−0.109656	+	0.409242i
$202$	0.933500	+	11.2354i	0.0656808	+	0.790523i
$203$	7.58342	+	7.58342i	0.532252	+	0.532252i
$204$	−3.45153	+	9.23106i	−0.241655	+	0.646304i
$205$	9.55845	+	5.51857i	0.667591	+	0.385434i
$206$	−10.9987	−	15.8549i	−0.766317	−	1.10466i
$207$	−3.18994			−0.221716
$208$	−5.63207	+	13.2770i	−0.390514	+	0.920597i
$209$	−39.2818			−2.71718
$210$	3.07847	+	4.43768i	0.212435	+	0.306229i
$211$	13.7143	+	7.91795i	0.944130	+	0.545094i	0.891253	−	0.453507i	$-0.149827\pi$
$211$	13.7143	+	7.91795i	0.944130	+	0.545094i	0.0528778	+	0.998601i	$0.483161\pi$
$212$	−1.54029	+	4.11950i	−0.105788	+	0.282928i
$213$	−4.77020	−	4.77020i	−0.326848	−	0.326848i
$214$	−0.173851	−	2.09244i	−0.0118842	−	0.143036i
$215$	0.542773	−	2.02566i	0.0370168	−	0.138149i
$216$	−0.696159	−	2.74142i	−0.0473676	−	0.186530i
$217$	−3.67867	−	6.37164i	−0.249724	−	0.432535i
$218$	4.06737	−	22.4918i	0.275477	−	1.52334i
$219$	−9.62189	+	2.57818i	−0.650187	+	0.174217i
$220$	13.0112	−	10.7253i	0.877218	−	0.723099i
$221$	−13.2065	−	11.8847i	−0.888364	−	0.799454i
$222$	−8.51280	+	3.05633i	−0.571342	+	0.205127i
$223$	3.04406	+	11.3606i	0.203845	+	0.760761i	0.989798	+	0.142475i	$0.0455060\pi$
$223$	3.04406	+	11.3606i	0.203845	+	0.760761i	−0.785953	+	0.618286i	$0.787827\pi$
$224$	15.4256	+	5.99940i	1.03066	+	0.400852i
$225$	2.85466	−	1.64814i	0.190310	−	0.109876i
$226$	−0.617411	+	1.30907i	−0.0410696	+	0.0870781i
$227$	19.7539	+	5.29304i	1.31111	+	0.351312i	0.845641	−	0.533751i	$-0.179218\pi$
$227$	19.7539	+	5.29304i	1.31111	+	0.351312i	0.465471	+	0.885063i	$0.345885\pi$
$228$	11.0680	−	5.04377i	0.732998	−	0.334032i
$229$	−2.34169	+	2.34169i	−0.154743	+	0.154743i	−0.780233	−	0.625489i	$-0.784899\pi$
$229$	−2.34169	+	2.34169i	−0.154743	+	0.154743i	0.625489	+	0.780233i	$0.284899\pi$
$230$	4.49419	+	3.80468i	0.296338	+	0.250873i
$231$	−9.44932	+	16.3667i	−0.621719	+	1.07685i
$232$	−2.81439	+	9.97813i	−0.184774	+	0.655096i
$233$			4.82769i			0.316272i	0.987417	+	0.158136i	$0.0505485\pi$
$233$			4.82769i			0.316272i	−0.987417	+	0.158136i	$0.949451\pi$
$234$	5.05842	+	0.642172i	0.330679	+	0.0419801i
$235$			3.59804i			0.234710i
$236$	6.27958	+	4.47934i	0.408766	+	0.291580i
$237$	−1.63019	+	2.82358i	−0.105892	+	0.183411i
$238$	−13.1742	+	15.5618i	−0.853958	+	1.00872i
$239$	−5.85402	+	5.85402i	−0.378665	+	0.378665i	−0.870620	−	0.491955i	$-0.836282\pi$
$239$	−5.85402	+	5.85402i	−0.378665	+	0.378665i	0.491955	+	0.870620i	$0.336282\pi$
$240$	−2.28892	+	4.69260i	−0.147749	+	0.302906i
$241$	8.36500	+	2.24139i	0.538837	+	0.144381i	0.517966	−	0.855401i	$-0.326689\pi$
$241$	8.36500	+	2.24139i	0.538837	+	0.144381i	0.0208710	+	0.999782i	$0.493356\pi$
$242$	39.2948	+	18.5330i	2.52597	+	1.19135i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−5.35491	+	0.896013i	−0.342813	+	0.0573613i
$245$	0.527231	+	1.96765i	0.0336835	+	0.125709i
$246$	−4.04084	−	11.2550i	−0.257634	−	0.717590i
$247$	1.15348	+	21.8970i	0.0733942	+	1.39327i
$248$	3.63664	−	6.11230i	0.230927	−	0.388131i
$249$	−2.14439	+	0.574588i	−0.135895	+	0.0364131i
$250$	−15.0699	−	2.72521i	−0.953104	−	0.172357i
$251$	−1.00373	−	1.73851i	−0.0633547	−	0.109734i	0.832608	−	0.553862i	$-0.186847\pi$
$251$	−1.00373	−	1.73851i	−0.0633547	−	0.109734i	−0.895963	+	0.444129i	$0.853513\pi$
$252$	0.560958	−	5.82477i	0.0353371	−	0.366926i
$253$	−5.33281	+	19.9023i	−0.335271	+	1.25125i
$254$	11.4398	−	0.950482i	0.717799	−	0.0596386i
$255$	−4.54801	−	4.54801i	−0.284808	−	0.284808i
$256$	2.22572	+	15.8444i	0.139108	+	0.990277i
$257$	−8.98006	−	5.18464i	−0.560161	−	0.323409i	0.193049	−	0.981189i	$-0.438162\pi$
$257$	−8.98006	−	5.18464i	−0.560161	−	0.323409i	−0.753210	+	0.657780i	$0.771496\pi$
$258$	−1.86692	+	1.29510i	−0.116229	+	0.0806296i
$259$	−18.7128			−1.16276
$260$	−6.36070	−	6.93796i	−0.394474	−	0.430274i
$261$	3.66545			0.226885
$262$	8.06029	−	5.59152i	0.497966	−	0.345445i
$263$	11.7530	+	6.78557i	0.724718	+	0.418416i	0.816487	−	0.577364i	$-0.195919\pi$
$263$	11.7530	+	6.78557i	0.724718	+	0.418416i	−0.0917686	+	0.995780i	$0.529252\pi$
$264$	−18.2677	−	0.239591i	−1.12430	−	0.0147458i
$265$	−2.02962	−	2.02962i	−0.124678	−	0.124678i
$266$	25.0777	−	2.08359i	1.53762	−	0.127753i
$267$	2.53716	−	9.46880i	0.155271	−	0.579481i
$268$	−11.9580	−	1.15163i	−0.730454	−	0.0703469i
$269$	4.29489	+	7.43897i	0.261864	+	0.453562i	0.966737	−	0.255771i	$-0.0823294\pi$
$269$	4.29489	+	7.43897i	0.261864	+	0.453562i	−0.704873	+	0.709333i	$0.748996\pi$
$270$	1.81647	+	0.328486i	0.110547	+	0.0199910i
$271$	20.1056	−	5.38729i	1.22133	−	0.327254i	0.410132	−	0.912026i	$-0.365483\pi$
$271$	20.1056	−	5.38729i	1.22133	−	0.327254i	0.811198	+	0.584772i	$0.198816\pi$
$272$	−19.3482	−	3.76157i	−1.17316	−	0.228079i
$273$	9.40081	+	4.78677i	0.568963	+	0.289708i
$274$	3.97722	+	11.0778i	0.240273	+	0.669233i
$275$	−5.51057	−	20.5657i	−0.332300	−	1.24016i
$276$	−1.05288	−	6.29240i	−0.0633759	−	0.378758i
$277$	−25.0962	+	14.4893i	−1.50788	+	0.870576i	−0.507924	+	0.861402i	$0.669587\pi$
$277$	−25.0962	+	14.4893i	−1.50788	+	0.870576i	−0.999958	+	0.00917370i	$0.997080\pi$
$278$	13.6700	+	6.44734i	0.819874	+	0.386686i
$279$	−2.42891	−	0.650824i	−0.145415	−	0.0389638i
$280$	−7.73757	+	7.53724i	−0.462408	+	0.450436i
$281$	−10.6557	+	10.6557i	−0.635668	+	0.635668i	−0.949484	−	0.313816i	$-0.898393\pi$
$281$	−10.6557	+	10.6557i	−0.635668	+	0.635668i	0.313816	+	0.949484i	$0.398393\pi$
$282$	2.51884	−	2.97533i	0.149995	−	0.177178i
$283$	5.56627	−	9.64106i	0.330880	−	0.573101i	−0.651804	−	0.758387i	$-0.725988\pi$
$283$	5.56627	−	9.64106i	0.330880	−	0.573101i	0.982685	+	0.185286i	$0.0593210\pi$
$284$	7.83512	−	10.9840i	0.464929	−	0.651783i
$285$			7.93805i			0.470210i
$286$	12.4630	−	30.4864i	0.736954	−	1.80270i
$287$		−	24.7406i		−	1.46039i
$288$	5.17788	−	2.27807i	0.305109	−	0.134236i
$289$	3.64070	−	6.30587i	0.214159	−	0.370934i
$290$	−5.16411	−	4.37181i	−0.303247	−	0.256722i
$291$	−4.82491	+	4.82491i	−0.282841	+	0.282841i
$292$	−8.26148	−	18.1290i	−0.483467	−	1.06092i
$293$	13.1230	+	3.51630i	0.766655	+	0.205425i	0.620893	−	0.783895i	$-0.286770\pi$
$293$	13.1230	+	3.51630i	0.766655	+	0.205425i	0.145762	+	0.989320i	$0.453437\pi$
$294$	0.941491	−	1.99620i	0.0549089	−	0.116421i
$295$	−4.35964	+	2.51704i	−0.253828	+	0.146548i
$296$	−8.83860	−	15.7834i	−0.513733	−	0.917390i
$297$	1.67176	+	6.23908i	0.0970052	+	0.362028i
$298$	21.0262	−	7.54897i	1.21801	−	0.437300i
$299$	11.2508	+	2.38827i	0.650651	+	0.138117i
$300$	4.19329	+	5.08704i	0.242100	+	0.293700i
$301$	−4.54066	+	1.21667i	−0.261720	+	0.0701275i
$302$	0.425579	−	2.35337i	0.0244893	−	0.135421i
$303$	3.98602	+	6.90398i	0.228991	+	0.396623i
$304$	13.6024	+	20.1678i	0.780149	+	1.15670i
$305$	0.917094	−	3.42264i	0.0525127	−	0.195980i
$306$	0.577008	+	6.94477i	0.0329854	+	0.397006i
$307$	−20.1672	−	20.1672i	−1.15100	−	1.15100i	−0.986352	−	0.164650i	$-0.947350\pi$
$307$	−20.1672	−	20.1672i	−1.15100	−	1.15100i	−0.164650	−	0.986352i	$-0.552650\pi$
$308$	−35.4034	−	13.2375i	−2.01730	−	0.754275i
$309$	−11.8165	−	6.82229i	−0.672220	−	0.388106i
$310$	2.64575	+	3.81391i	0.150269	+	0.216615i
$311$	−10.4030			−0.589902			−0.294951	−	0.955512i	$-0.595303\pi$
$311$	−10.4030			−0.589902			−0.294951	+	0.955512i	$0.595303\pi$
$312$	0.402863	+	10.1901i	0.0228076	+	0.576900i
$313$	12.5246			0.707932			0.353966	−	0.935258i	$-0.384833\pi$
$313$	12.5246			0.707932			0.353966	+	0.935258i	$0.384833\pi$
$314$	5.13537	+	7.40274i	0.289806	+	0.417761i
$315$	3.30738	+	1.90952i	0.186350	+	0.107589i
$316$	−6.10779	−	2.28372i	−0.343590	−	0.128470i
$317$	5.42429	+	5.42429i	0.304658	+	0.304658i	0.842833	−	0.538175i	$-0.180886\pi$
$317$	5.42429	+	5.42429i	0.304658	+	0.304658i	−0.538175	+	0.842833i	$0.680886\pi$
$318$	0.257498	+	3.09921i	0.0144398	+	0.173795i
$319$	6.12774	−	22.8690i	0.343087	−	1.28042i
$320$	−10.0120	−	2.96623i	−0.559687	−	0.165817i
$321$	−0.742339	−	1.28577i	−0.0414333	−	0.0717646i
$322$	2.34884	−	12.9886i	0.130896	−	0.723828i
$323$	−28.9464	+	7.75617i	−1.61062	+	0.431565i
$324$	−1.27213	−	1.54327i	−0.0706739	−	0.0857372i
$325$	−11.3022	+	3.67567i	−0.626934	+	0.203890i
$326$	−14.2194	+	5.10515i	−0.787538	+	0.282748i
$327$	−4.18305	−	15.6113i	−0.231323	−	0.863309i
$328$	20.8675	−	11.6857i	1.15222	−	0.645235i
$329$	6.98473	−	4.03264i	0.385081	−	0.222326i
$330$	5.08614	−	10.7839i	0.279983	−	0.593636i
$331$	−28.1779	−	7.55024i	−1.54880	−	0.414999i	−0.619701	−	0.784838i	$-0.712746\pi$
$331$	−28.1779	−	7.55024i	−1.54880	−	0.414999i	−0.929096	+	0.369840i	$0.879413\pi$
$332$	−1.84120	−	4.04033i	−0.101049	−	0.221742i
$333$	−4.52242	+	4.52242i	−0.247827	+	0.247827i
$334$	−7.92103	−	6.70576i	−0.433420	−	0.366923i
$335$	3.92017	−	6.78993i	0.214182	−	0.370974i
$336$	11.6750	−	0.816004i	0.636921	−	0.0445167i
$337$		−	7.53714i		−	0.410574i	−0.978702	−	0.205287i	$-0.934187\pi$
$337$		−	7.53714i		−	0.410574i	0.978702	−	0.205287i	$-0.0658128\pi$
$338$	−17.3601	−	6.05209i	−0.944264	−	0.329190i
$339$			1.02344i			0.0555857i
$340$	7.47018	−	10.4724i	0.405127	−	0.567947i
$341$	−8.12109	+	14.0661i	−0.439782	+	0.761725i
$342$	5.55711	−	6.56422i	0.300494	−	0.354952i
$343$	−11.2534	+	11.2534i	−0.607629	+	0.607629i
$344$	−3.17089	−	3.25517i	−0.170963	−	0.175507i
$345$	4.02185	+	1.07765i	0.216529	+	0.0580189i
$346$	17.1399	+	8.08386i	0.921445	+	0.434591i
$347$	−4.13498	+	2.38733i	−0.221977	+	0.128159i	−0.606866	−	0.794805i	$-0.707573\pi$
$347$	−4.13498	+	2.38733i	−0.221977	+	0.128159i	0.384888	+	0.922963i	$0.374240\pi$
$348$	1.20983	+	7.23037i	0.0648535	+	0.387589i
$349$	−7.81771	−	29.1761i	−0.418472	−	1.56176i	−0.777778	−	0.628539i	$-0.783653\pi$
$349$	−7.81771	−	29.1761i	−0.418472	−	1.56176i	0.359305	−	0.933220i	$-0.383014\pi$
$350$	4.60884	+	12.8370i	0.246353	+	0.686167i
$351$	3.42878	−	1.11510i	0.183015	−	0.0595196i
$352$	−5.55689	−	36.1136i	−0.296183	−	1.92486i
$353$	1.57297	−	0.421477i	0.0837209	−	0.0224330i	−0.216715	−	0.976235i	$-0.569534\pi$
$353$	1.57297	−	0.421477i	0.0837209	−	0.0224330i	0.300436	+	0.953802i	$0.402868\pi$
$354$	5.36719	+	0.970592i	0.285263	+	0.0515864i
$355$	4.40272	+	7.62574i	0.233672	+	0.404732i
$356$	19.5153	+	1.87944i	1.03431	+	0.0996101i
$357$	−3.73152	+	13.9262i	−0.197493	+	0.737055i
$358$	−28.5224	+	2.36979i	−1.50746	+	0.125247i
$359$	−7.48936	−	7.48936i	−0.395273	−	0.395273i	0.481289	−	0.876562i	$-0.340169\pi$
$359$	−7.48936	−	7.48936i	−0.395273	−	0.395273i	−0.876562	+	0.481289i	$0.840169\pi$
$360$	−0.0484164	+	3.69154i	−0.00255177	+	0.194561i
$361$	15.5757	+	8.99261i	0.819771	+	0.473295i
$362$	−8.38510	+	5.81685i	−0.440711	+	0.305727i
$363$	30.7210			1.61243
$364$	−6.33941	+	20.1238i	−0.332275	+	1.05477i
$365$	13.0022			0.680566
$366$	−3.15443	+	2.18827i	−0.164885	+	0.114382i
$367$	7.58760	+	4.38070i	0.396070	+	0.228671i	0.684787	−	0.728744i	$-0.259895\pi$
$367$	7.58760	+	4.38070i	0.396070	+	0.228671i	−0.288717	+	0.957414i	$0.593229\pi$
$368$	12.0647	−	4.15377i	0.628917	−	0.216530i
$369$	−5.97918	−	5.97918i	−0.311264	−	0.311264i
$370$	11.7654	−	0.977531i	0.611654	−	0.0508194i
$371$	−1.66525	+	6.21479i	−0.0864554	+	0.322656i
$372$	0.482108	−	5.00602i	0.0249962	−	0.259550i
$373$	−13.0127	−	22.5387i	−0.673774	−	1.16701i	−0.976826	−	0.214036i	$-0.931339\pi$
$373$	−13.0127	−	22.5387i	−0.673774	−	1.16701i	0.303052	−	0.952974i	$-0.401994\pi$
$374$	44.2936	+	8.00997i	2.29037	+	0.414186i
$375$	−10.4599	+	2.80272i	−0.540146	+	0.144732i
$376$	6.70043	+	3.98656i	0.345548	+	0.205591i
$377$	−12.9279	−	2.74427i	−0.665820	−	0.141337i
$378$	−1.39820	−	3.89440i	−0.0719154	−	0.200306i
$379$	2.74154	+	10.2316i	0.140824	+	0.525561i	0.999906	+	0.0137231i	$0.00436832\pi$
$379$	2.74154	+	10.2316i	0.140824	+	0.525561i	−0.859082	+	0.511837i	$0.828965\pi$
$380$	−15.6584	+	2.62005i	−0.803260	+	0.134406i
$381$	7.02958	−	4.05853i	0.360136	−	0.207925i
$382$	−1.88188	−	0.887572i	−0.0962855	−	0.0454122i
$383$	23.6735	+	6.34330i	1.20966	+	0.324127i	0.806629	−	0.591059i	$-0.201290\pi$
$383$	23.6735	+	6.34330i	1.20966	+	0.324127i	0.403032	+	0.915186i	$0.367956\pi$
$384$	6.20268	+	9.46186i	0.316529	+	0.482848i
$385$	17.4428	−	17.4428i	0.888966	−	0.888966i
$386$	−20.7262	+	24.4823i	−1.05493	+	1.24612i
$387$	−0.803327	+	1.39140i	−0.0408354	+	0.0707290i
$388$	−11.1100	−	7.92498i	−0.564026	−	0.402330i
$389$			10.7574i			0.545424i	0.962096	+	0.272712i	$0.0879206\pi$
$389$			10.7574i			0.545424i	−0.962096	+	0.272712i	$0.912079\pi$
$390$	−6.16068	−	2.51852i	−0.311958	−	0.127530i
$391$			15.7188i			0.794934i
$392$	4.24842	+	1.19829i	0.214577	+	0.0605228i
$393$	3.46831	−	6.00729i	0.174953	−	0.303028i
$394$	29.0135	+	24.5622i	1.46168	+	1.23743i
$395$	3.00922	−	3.00922i	0.151410	−	0.151410i
$396$	−11.7553	+	5.35696i	−0.590725	+	0.269197i
$397$	26.5578	+	7.11615i	1.33290	+	0.357149i	0.853795	−	0.520609i	$-0.174295\pi$
$397$	26.5578	+	7.11615i	1.33290	+	0.357149i	0.479104	+	0.877758i	$0.340962\pi$
$398$	11.1715	−	23.6864i	0.559976	−	1.18729i
$399$	15.4098	−	8.89687i	0.771457	−	0.445401i
$400$	−8.65053	+	9.95063i	−0.432526	+	0.497532i
$401$	2.35576	+	8.79182i	0.117641	+	0.439043i	0.999471	−	0.0325252i	$-0.0103549\pi$
$401$	2.35576	+	8.79182i	0.117641	+	0.439043i	−0.881830	+	0.471568i	$0.843688\pi$
$402$	−7.99507	+	2.87045i	−0.398758	+	0.143165i
$403$	8.07941	+	4.11393i	0.402464	+	0.204929i
$404$	−12.3030	+	10.1415i	−0.612097	+	0.504557i
$405$	1.26079	−	0.337828i	0.0626493	−	0.0167868i
$406$	−2.69896	+	14.9248i	−0.133947	+	0.740703i
$407$	20.6554	+	35.7761i	1.02385	+	1.77336i
$408$	−13.5086	+	3.43040i	−0.668778	+	0.169830i
$409$	0.509778	−	1.90252i	0.0252069	−	0.0940733i	−0.952176	−	0.305549i	$-0.901160\pi$
$409$	0.509778	−	1.90252i	0.0252069	−	0.0940733i	0.977383	+	0.211475i	$0.0678268\pi$
$410$	1.29241	+	15.5553i	0.0638278	+	0.768220i
$411$	5.88505	+	5.88505i	0.290288	+	0.290288i
$412$	9.55728	−	25.5608i	0.470853	−	1.25929i
$413$	9.77245	+	5.64213i	0.480871	+	0.277631i
$414$	−2.57137	−	3.70668i	−0.126376	−	0.182173i
$415$	2.89775			0.142245
$416$	−19.9677	+	4.15804i	−0.978999	+	0.203865i
$417$	10.6873			0.523361
$418$	−31.6646	−	45.6451i	−1.54876	−	2.23257i
$419$	−13.5703	−	7.83484i	−0.662954	−	0.382757i	0.130447	−	0.991455i	$-0.458359\pi$
$419$	−13.5703	−	7.83484i	−0.662954	−	0.382757i	−0.793402	+	0.608698i	$0.791692\pi$
$420$	−2.67502	+	7.15432i	−0.130528	+	0.349095i
$421$	−1.01880	−	1.01880i	−0.0496532	−	0.0496532i	0.681844	−	0.731497i	$-0.261178\pi$
$421$	−1.01880	−	1.01880i	−0.0496532	−	0.0496532i	−0.731497	+	0.681844i	$0.761178\pi$
$422$	1.85433	+	22.3184i	0.0902675	+	1.08644i
$423$	0.713447	−	2.66262i	0.0346890	−	0.129461i
$424$	−6.02843	+	1.53087i	−0.292767	+	0.0743455i
$425$	−8.12138	−	14.0666i	−0.393945	−	0.682333i
$426$	1.69773	−	9.38812i	0.0822552	−	0.454856i
$427$	−7.67211	+	2.05574i	−0.371280	+	0.0994841i
$428$	2.29126	−	1.88870i	0.110752	−	0.0912940i
$429$	−1.22510	−	23.2566i	−0.0591486	−	1.12284i
$430$	2.79132	−	1.00216i	0.134609	−	0.0483284i
$431$	−4.35540	−	16.2546i	−0.209792	−	0.782955i	−0.987935	−	0.154868i	$-0.950505\pi$
$431$	−4.35540	−	16.2546i	−0.209792	−	0.782955i	0.778143	−	0.628087i	$-0.216162\pi$
$432$	2.62434	−	3.01875i	0.126263	−	0.145240i
$433$	−8.76783	+	5.06211i	−0.421355	+	0.243269i	−0.695657	−	0.718374i	$-0.744887\pi$
$433$	−8.76783	+	5.06211i	−0.421355	+	0.243269i	0.274302	+	0.961644i	$0.411553\pi$
$434$	4.43846	−	9.41068i	0.213053	−	0.451727i
$435$	−4.62137	−	1.23829i	−0.221578	−	0.0593715i
$436$	29.4139	−	13.4041i	1.40867	−	0.641940i
$437$	13.7177	−	13.7177i	0.656207	−	0.656207i
$438$	−10.7519	−	9.10232i	−0.513746	−	0.434925i
$439$	2.77803	−	4.81169i	0.132588	−	0.229650i	−0.792085	−	0.610410i	$-0.791005\pi$
$439$	2.77803	−	4.81169i	0.132588	−	0.229650i	0.924674	+	0.380761i	$0.124338\pi$
$440$	22.9509	+	6.47343i	1.09414	+	0.308609i
$441$		−	1.56065i		−	0.0743165i
$442$	3.16437	−	24.9259i	0.150514	−	1.18561i
$443$			20.6130i			0.979354i	0.871904	+	0.489677i	$0.162885\pi$
$443$			20.6130i			0.979354i	−0.871904	+	0.489677i	$0.837115\pi$
$444$	−10.4135	−	7.42813i	−0.494203	−	0.352524i
$445$	−6.39766	+	11.0811i	−0.303278	+	0.525293i
$446$	−10.7471	+	12.6948i	−0.508891	+	0.601116i
$447$	11.1701	−	11.1701i	0.528329	−	0.528329i
$448$	5.46310	+	22.7604i	0.258107	+	1.07533i
$449$	−31.8553	−	8.53560i	−1.50334	−	0.402820i	−0.589125	−	0.808042i	$-0.700528\pi$
$449$	−31.8553	−	8.53560i	−1.50334	−	0.402820i	−0.914218	+	0.405222i	$0.867194\pi$
$450$	4.21622	+	1.98854i	0.198755	+	0.0937408i
$451$	−47.3004	+	27.3089i	−2.22729	+	1.28592i
$452$	−2.01882	+	0.337800i	−0.0949571	+	0.0158888i
$453$	−0.437682	−	1.63345i	−0.0205641	−	0.0767463i
$454$	9.77291	+	27.2205i	0.458665	+	1.27752i
$455$	−10.2354	−	9.21098i	−0.479842	−	0.431818i
$456$	14.7826	+	8.79523i	0.692259	+	0.411874i
$457$	−12.5118	+	3.35252i	−0.585276	+	0.156824i	−0.539294	−	0.842118i	$-0.681309\pi$
$457$	−12.5118	+	3.35252i	−0.585276	+	0.156824i	−0.0459830	+	0.998942i	$0.514642\pi$
$458$	−4.60863	−	0.833416i	−0.215347	−	0.0389430i
$459$	2.46381	+	4.26744i	0.115001	+	0.199187i
$460$	−0.798289	+	8.28911i	−0.0372204	+	0.386482i
$461$	−7.85478	+	29.3145i	−0.365834	+	1.36531i	0.500453	+	0.865764i	$0.333167\pi$
$461$	−7.85478	+	29.3145i	−0.365834	+	1.36531i	−0.866287	+	0.499547i	$0.833500\pi$
$462$	−26.6349	+	2.21297i	−1.23917	+	0.102957i
$463$	−5.53376	−	5.53376i	−0.257175	−	0.257175i	0.566729	−	0.823904i	$-0.308209\pi$
$463$	−5.53376	−	5.53376i	−0.257175	−	0.257175i	−0.823904	+	0.566729i	$0.808209\pi$
$464$	−13.8631	+	4.77295i	−0.643580	+	0.221579i
$465$	2.84248	+	1.64111i	0.131817	+	0.0761046i
$466$	−5.60973	+	3.89154i	−0.259866	+	0.180272i
$467$	−6.57406			−0.304211			−0.152106	−	0.988364i	$-0.548605\pi$
$467$	−6.57406			−0.304211			−0.152106	+	0.988364i	$0.548605\pi$
$468$	3.33133	+	6.39548i	0.153991	+	0.295631i
$469$	−17.5747			−0.811525
$470$	−4.18089	+	2.90033i	−0.192850	+	0.133782i
$471$	5.51722	+	3.18537i	0.254220	+	0.146774i
$472$	−0.143058	+	10.9076i	−0.00658478	+	0.502061i
$473$	7.33811	+	7.33811i	0.337407	+	0.337407i
$474$	−4.59505	+	0.381781i	−0.211058	+	0.0175358i
$475$	−5.18840	+	19.3634i	−0.238060	+	0.888453i
$476$	−28.7022	−	2.76419i	−1.31556	−	0.126696i
$477$	1.09951	+	1.90441i	0.0503431	+	0.0871969i
$478$	−11.5212	−	2.08347i	−0.526966	−	0.0952955i
$479$	36.2433	−	9.71135i	1.65600	−	0.443723i	0.694714	−	0.719287i	$-0.255531\pi$
$479$	36.2433	−	9.71135i	1.65600	−	0.443723i	0.961283	+	0.275564i	$0.0888645\pi$
$480$	−7.29783	+	1.12293i	−0.333099	+	0.0512547i
$481$	19.3363	−	12.5645i	0.881658	−	0.572893i
$482$	4.13844	+	11.5268i	0.188501	+	0.525032i
$483$	−2.41564	−	9.01529i	−0.109915	−	0.410210i
$484$	10.1398	+	60.5994i	0.460902	+	2.75452i
$485$	7.71320	−	4.45322i	0.350238	−	0.202210i
$486$	−1.27909	−	0.603270i	−0.0580206	−	0.0273649i
$487$	41.0959	+	11.0116i	1.86223	+	0.498984i	0.999972	−	0.00748077i	$-0.00238123\pi$
$487$	41.0959	+	11.0116i	1.86223	+	0.498984i	0.862261	+	0.506465i	$0.169048\pi$
$488$	−5.35768	−	5.50009i	−0.242531	−	0.248977i
$489$	−7.55403	+	7.55403i	−0.341605	+	0.341605i
$490$	−1.86140	+	2.19874i	−0.0840895	+	0.0993288i
$491$	8.72998	−	15.1208i	0.393979	−	0.682391i	−0.598992	−	0.800755i	$-0.704432\pi$
$491$	8.72998	−	15.1208i	0.393979	−	0.682391i	0.992970	+	0.118364i	$0.0377651\pi$
$492$	9.82089	−	13.7679i	0.442760	−	0.620705i
$493$		−	18.0619i		−	0.813467i
$494$	−24.5143	+	18.9912i	−1.10295	+	0.854455i
$495$		−	8.43096i		−	0.378943i
$496$	10.0339	−	0.701305i	0.450535	−	0.0314895i
$497$	9.86903	−	17.0937i	0.442687	−	0.766756i
$498$	−2.39624	−	2.02860i	−0.107378	−	0.0909036i
$499$	25.7413	−	25.7413i	1.15234	−	1.15234i	0.166254	−	0.986083i	$-0.446833\pi$
$499$	25.7413	−	25.7413i	1.15234	−	1.15234i	0.986083	−	0.166254i	$-0.0531673\pi$
$500$	−8.98099	−	19.7078i	−0.401642	−	0.881362i
$501$	−7.08854	−	1.89937i	−0.316693	−	0.0848575i
$502$	1.21104	−	2.56771i	0.0540512	−	0.114603i
$503$	−0.245467	+	0.141721i	−0.0109448	+	0.00631901i	−0.505462	−	0.862849i	$-0.668678\pi$
$503$	−0.245467	+	0.141721i	−0.0109448	+	0.00631901i	0.494518	+	0.869168i	$0.335345\pi$
$504$	7.22051	−	4.04344i	0.321627	−	0.180109i
$505$	−2.69318	−	10.0511i	−0.119845	−	0.447267i
$506$	−27.4250	+	9.84633i	−1.21919	+	0.437723i
$507$	−12.9281	+	1.36583i	−0.574155	+	0.0606586i
$508$	10.3260	+	12.5268i	0.458141	+	0.555788i
$509$	13.2375	−	3.54698i	0.586742	−	0.157217i	0.0467780	−	0.998905i	$-0.485105\pi$
$509$	13.2375	−	3.54698i	0.586742	−	0.157217i	0.539964	+	0.841688i	$0.318438\pi$
$510$	1.61865	−	8.95085i	0.0716752	−	0.396350i
$511$	−14.5727	−	25.2407i	−0.644658	−	1.11658i
$512$	−16.6170	+	15.3583i	−0.734373	+	0.678746i
$513$	1.57402	−	5.87432i	0.0694947	−	0.259358i
$514$	−1.21421	−	14.6140i	−0.0535565	−	0.644597i
$515$	12.5935	+	12.5935i	0.554934	+	0.554934i
$516$	−3.00980	−	1.12537i	−0.132499	−	0.0495418i
$517$	−15.4196	−	8.90252i	−0.678154	−	0.391532i
$518$	−15.0842	−	21.7441i	−0.662760	−	0.955381i
$519$	13.4001			0.588198
$520$	2.93457	−	12.9837i	0.128689	−	0.569372i
$521$	30.0491			1.31647			0.658237	−	0.752810i	$-0.271302\pi$
$521$	30.0491			1.31647			0.658237	+	0.752810i	$0.271302\pi$
$522$	2.95467	+	4.25921i	0.129322	+	0.186421i
$523$	−15.8089	−	9.12729i	−0.691276	−	0.399109i	0.112814	−	0.993616i	$-0.464014\pi$
$523$	−15.8089	−	9.12729i	−0.691276	−	0.399109i	−0.804090	+	0.594508i	$0.797347\pi$
$524$	12.9946	+	4.85872i	0.567671	+	0.212254i
$525$	6.81964	+	6.81964i	0.297634	+	0.297634i
$526$	1.58914	+	19.1266i	0.0692897	+	0.833959i
$527$	−3.20701	+	11.9687i	−0.139700	+	0.521366i
$528$	−14.4470	−	21.4201i	−0.628725	−	0.932189i
$529$	6.41214	+	11.1062i	0.278789	+	0.482876i
$530$	0.722348	−	3.99445i	0.0313768	−	0.173508i
$531$	3.72532	−	0.998196i	0.161665	−	0.0433180i
$532$	22.6360	+	27.4606i	0.981394	+	1.19057i
$533$	16.6118	+	25.5649i	0.719538	+	1.10734i
$534$	13.0478	−	4.68453i	0.564635	−	0.202719i
$535$	0.501566	+	1.87187i	0.0216846	+	0.0809280i
$536$	−8.30105	−	14.8235i	−0.358551	−	0.640276i
$537$	−17.5265	+	10.1189i	−0.756326	+	0.436665i
$538$	−5.18196	+	10.9871i	−0.223410	+	0.473687i
$539$	−9.73701	−	2.60902i	−0.419403	−	0.112379i
$540$	1.08253	+	2.37551i	0.0465848	+	0.102225i
$541$	11.4509	−	11.4509i	0.492314	−	0.492314i	−0.416720	−	0.909035i	$-0.636821\pi$
$541$	11.4509	−	11.4509i	0.492314	−	0.492314i	0.909035	+	0.416720i	$0.136821\pi$
$542$	22.4669	+	19.0199i	0.965035	+	0.816976i
$543$	−3.60807	+	6.24937i	−0.154837	+	0.268186i
$544$	−11.2254	−	25.5146i	−0.481286	−	1.09393i
$545$			21.0958i			0.903646i
$546$	2.01570	+	14.7822i	0.0862639	+	0.632620i
$547$			46.6062i			1.99274i	0.0851464	+	0.996368i	$0.472864\pi$
$547$			46.6062i			1.99274i	−0.0851464	+	0.996368i	$0.527136\pi$
$548$	−9.66628	+	13.5512i	−0.412923	+	0.578876i
$549$	−1.35734	+	2.35098i	−0.0579298	+	0.100337i
$550$	19.4552	−	22.9810i	0.829572	−	0.979914i
$551$	−15.7625	+	15.7625i	−0.671506	+	0.671506i
$552$	6.46300	−	6.29566i	0.275084	−	0.267961i
$553$	−9.21438	−	2.46899i	−0.391835	−	0.104992i
$554$	−37.0661	−	17.4819i	−1.57479	−	0.742734i
$555$	7.22963	−	4.17403i	0.306881	−	0.177178i
$556$	3.52749	+	21.0816i	0.149599	+	0.894058i
$557$	−9.72648	−	36.2997i	−0.412124	−	1.53807i	−0.790527	−	0.612427i	$-0.790193\pi$
$557$	−9.72648	−	36.2997i	−0.412124	−	1.53807i	0.378403	−	0.925641i	$-0.376473\pi$
$558$	−1.20166	−	3.34699i	−0.0508704	−	0.141689i
$559$	3.87503	−	4.30599i	0.163896	−	0.182124i
$560$	−14.9954	−	2.91532i	−0.633670	−	0.123195i
$561$	30.7438	−	8.23778i	1.29800	−	0.347799i
$562$	−20.9713	−	3.79241i	−0.884622	−	0.159973i
$563$	−13.4868	−	23.3598i	−0.568401	−	0.984499i	−0.996724	−	0.0808737i	$-0.974229\pi$
$563$	−13.4868	−	23.3598i	−0.568401	−	0.984499i	0.428324	−	0.903625i	$-0.359104\pi$
$564$	5.48771	+	0.528498i	0.231074	+	0.0222538i
$565$	0.345747	−	1.29035i	0.0145457	−	0.0542853i
$566$	15.6897	−	1.30358i	0.659488	−	0.0547938i
$567$	−2.06889	−	2.06889i	−0.0868854	−	0.0868854i
$568$	19.0791	+	0.250233i	0.800543	+	0.0104995i
$569$	0.207790	+	0.119968i	0.00871103	+	0.00502931i	0.504349	−	0.863500i	$-0.331732\pi$
$569$	0.207790	+	0.119968i	0.00871103	+	0.00502931i	−0.495638	+	0.868529i	$0.665066\pi$
$570$	−9.22395	+	6.39877i	−0.386349	+	0.268015i
$571$	−20.0858			−0.840566			−0.420283	−	0.907393i	$-0.638069\pi$
$571$	−20.0858			−0.840566			−0.420283	+	0.907393i	$0.638069\pi$
$572$	45.4712	−	10.0928i	1.90124	−	0.422000i
$573$	−1.47127			−0.0614632
$574$	28.7483	−	19.9431i	1.19993	−	0.832408i
$575$	9.10618	+	5.25746i	0.379754	+	0.219251i
$576$	6.82091	+	4.18033i	0.284205	+	0.174180i
$577$	3.70927	+	3.70927i	0.154419	+	0.154419i	0.780088	−	0.625669i	$-0.215174\pi$
$577$	3.70927	+	3.70927i	0.154419	+	0.154419i	−0.625669	+	0.780088i	$0.715174\pi$
$578$	10.2621	−	0.852628i	0.426846	−	0.0354646i
$579$	−5.87057	+	21.9093i	−0.243973	+	0.910518i
$580$	0.917284	−	9.52471i	0.0380882	−	0.395492i
$581$	−3.24776	−	5.62529i	−0.134740	−	0.233376i
$582$	−9.49580	−	1.71720i	−0.393613	−	0.0711803i
$583$	13.7199	−	3.67623i	0.568219	−	0.152254i
$584$	14.4062	−	24.2133i	0.596133	−	1.00195i
$585$	−4.69970	+	0.247569i	−0.194309	+	0.0102357i
$586$	6.49239	+	18.0833i	0.268198	+	0.747014i
$587$	−8.29145	−	30.9441i	−0.342225	−	1.27720i	−0.895821	−	0.444415i	$-0.853411\pi$
$587$	−8.29145	−	30.9441i	−0.342225	−	1.27720i	0.553596	−	0.832785i	$-0.313255\pi$
$588$	3.07850	−	0.515111i	0.126955	−	0.0212428i
$589$	13.2438	−	7.64630i	0.545701	−	0.315060i
$590$	−6.43902	−	3.03691i	−0.265090	−	0.125027i
$591$	25.9643	+	6.95710i	1.06803	+	0.286177i
$592$	11.2155	−	22.9932i	0.460952	−	0.945013i
$593$	11.3544	−	11.3544i	0.466270	−	0.466270i	−0.434434	−	0.900704i	$-0.643051\pi$
$593$	11.3544	−	11.3544i	0.466270	−	0.466270i	0.900704	+	0.434434i	$0.143051\pi$
$594$	−5.90218	+	6.97182i	−0.242169	+	0.286057i
$595$	9.40936	−	16.2975i	0.385746	−	0.668132i
$596$	25.7208	+	18.3471i	1.05356	+	0.751526i
$597$		−	18.5182i		−	0.757900i
$598$	6.29399	+	14.9985i	0.257380	+	0.613334i
$599$		−	21.1939i		−	0.865959i	−0.901404	−	0.432979i	$-0.857462\pi$
$599$		−	21.1939i		−	0.865959i	0.901404	−	0.432979i	$-0.142538\pi$
$600$	−2.53093	+	8.97317i	−0.103325	+	0.366328i
$601$	−19.0073	+	32.9217i	−0.775326	+	1.34290i	0.159285	+	0.987233i	$0.449081\pi$
$601$	−19.0073	+	32.9217i	−0.775326	+	1.34290i	−0.934611	+	0.355671i	$0.884252\pi$
$602$	−5.07393	−	4.29547i	−0.206798	−	0.175070i
$603$	−4.24737	+	4.24737i	−0.172966	+	0.172966i
$604$	3.07765	−	1.40250i	0.125228	−	0.0570670i
$605$	−38.7328	−	10.3784i	−1.57471	−	0.421942i
$606$	−4.80929	+	10.1969i	−0.195364	+	0.414222i
$607$	−38.9901	+	22.5109i	−1.58256	+	0.913690i	−0.588074	+	0.808807i	$0.700113\pi$
$607$	−38.9901	+	22.5109i	−1.58256	+	0.913690i	−0.994485	+	0.104883i	$0.966553\pi$
$608$	−12.4701	+	32.0628i	−0.505728	+	1.30032i
$609$	2.77572	+	10.3591i	0.112478	+	0.419774i
$610$	4.71634	−	1.69329i	0.190959	−	0.0685595i
$611$	−4.50977	+	8.85682i	−0.182446	+	0.358309i
$612$	−7.60464	+	6.26857i	−0.307399	+	0.253392i
$613$	−4.06482	+	1.08917i	−0.164177	+	0.0439910i	−0.339971	−	0.940436i	$-0.610417\pi$
$613$	−4.06482	+	1.08917i	−0.164177	+	0.0439910i	0.175794	+	0.984427i	$0.443751\pi$
$614$	7.17757	−	39.6906i	0.289663	−	1.60178i
$615$	5.51857	+	9.55845i	0.222530	+	0.385434i
$616$	−13.1564	−	51.8090i	−0.530088	−	2.08744i
$617$	5.97214	−	22.2883i	0.240429	−	0.897295i	−0.735196	−	0.677854i	$-0.762910\pi$
$617$	5.97214	−	22.2883i	0.240429	−	0.897295i	0.975626	−	0.219441i	$-0.0704233\pi$
$618$	−1.59774	−	19.2301i	−0.0642704	−	0.773547i
$619$	−4.58670	−	4.58670i	−0.184355	−	0.184355i	0.608895	−	0.793251i	$-0.291613\pi$
$619$	−4.58670	−	4.58670i	−0.184355	−	0.184355i	−0.793251	+	0.608895i	$0.791613\pi$
$620$	−2.29901	+	6.14869i	−0.0923307	+	0.246937i
$621$	−2.76257	−	1.59497i	−0.110858	−	0.0640040i
$622$	−8.38576	−	12.0882i	−0.336238	−	0.484694i
$623$	28.6817			1.14911
$624$	−11.5160	+	8.68222i	−0.461010	+	0.347567i
$625$	−2.34679			−0.0938715
$626$	10.0959	+	14.5535i	0.403514	+	0.581674i
$627$	−34.0190	−	19.6409i	−1.35859	−	0.784382i
$628$	−4.46236	+	11.9345i	−0.178067	+	0.476239i
$629$	22.2847	+	22.2847i	0.888550	+	0.888550i
$630$	0.447197	+	5.38238i	0.0178167	+	0.214439i
$631$	2.41432	−	9.01037i	0.0961126	−	0.358697i	−0.901073	−	0.433667i	$-0.857219\pi$
$631$	2.41432	−	9.01037i	0.0961126	−	0.358697i	0.997186	+	0.0749700i	$0.0238861\pi$
$632$	−2.26975	−	8.93808i	−0.0902857	−	0.355538i
$633$	7.91795	+	13.7143i	0.314710	+	0.545094i
$634$	−1.93052	+	10.6754i	−0.0766708	+	0.423975i
$635$	−10.2339	+	2.74217i	−0.406121	+	0.108820i
$636$	−3.39368	+	2.79744i	−0.134568	+	0.110926i
$637$	−1.16844	+	5.50434i	−0.0462951	+	0.218090i
$638$	31.5131	−	11.3141i	1.24762	−	0.447928i
$639$	−1.74601	−	6.51621i	−0.0690712	−	0.257777i
$640$	−4.62381	−	14.0249i	−0.182772	−	0.554382i
$641$	−37.5688	+	21.6904i	−1.48388	+	0.856719i	−0.999832	−	0.0183230i	$-0.994167\pi$
$641$	−37.5688	+	21.6904i	−1.48388	+	0.856719i	−0.484048	+	0.875042i	$0.660834\pi$
$642$	0.895661	−	1.89903i	0.0353489	−	0.0749489i
$643$	−28.1799	−	7.55079i	−1.11131	−	0.297774i	−0.343947	−	0.938989i	$-0.611764\pi$
$643$	−28.1799	−	7.55079i	−1.11131	−	0.297774i	−0.767361	+	0.641215i	$0.778431\pi$
$644$	16.9860	−	7.74064i	0.669344	−	0.305024i
$645$	1.48288	−	1.48288i	0.0583885	−	0.0583885i
$646$	−32.3459	−	27.3833i	−1.27263	−	1.07738i
$647$	3.93858	−	6.82182i	0.154842	−	0.268194i	−0.778160	−	0.628066i	$-0.783847\pi$
$647$	3.93858	−	6.82182i	0.154842	−	0.268194i	0.933001	+	0.359873i	$0.117180\pi$
$648$	0.767817	−	2.72222i	0.0301627	−	0.106939i
$649$		−	24.9113i		−	0.977855i
$650$	−13.3817	−	10.1701i	−0.524872	−	0.398906i
$651$		−	7.35734i		−	0.288357i
$652$	−17.3942	−	12.4076i	−0.681209	−	0.485919i
$653$	−20.5890	+	35.6613i	−0.805712	+	1.39553i	0.110098	+	0.993921i	$0.464884\pi$
$653$	−20.5890	+	35.6613i	−0.805712	+	1.39553i	−0.915810	+	0.401613i	$0.868450\pi$
$654$	14.7683	−	17.4448i	0.577488	−	0.682145i
$655$	−6.40225	+	6.40225i	−0.250157	+	0.250157i
$656$	30.3997	+	14.8282i	1.18691	+	0.578944i
$657$	−9.62189	−	2.57818i	−0.375386	−	0.100584i
$658$	10.3162	+	4.86553i	0.402167	+	0.189678i
$659$	9.52527	−	5.49942i	0.371052	−	0.214227i	−0.302866	−	0.953033i	$-0.597943\pi$
$659$	9.52527	−	5.49942i	0.371052	−	0.214227i	0.673918	+	0.738806i	$0.264610\pi$
$660$	16.6307	−	2.78274i	0.647350	−	0.108318i
$661$	10.4604	+	39.0388i	0.406863	+	1.51843i	0.800593	+	0.599208i	$0.204518\pi$
$661$	10.4604	+	39.0388i	0.406863	+	1.51843i	−0.393730	+	0.919226i	$0.628816\pi$
$662$	−13.9405	−	38.8286i	−0.541814	−	1.50912i
$663$	−5.49478	−	16.8957i	−0.213400	−	0.656176i
$664$	3.21065	−	5.39632i	0.124598	−	0.209418i
$665$	−22.4342	+	6.01123i	−0.869962	+	0.233106i
$666$	−8.90047	−	1.60954i	−0.344886	−	0.0623685i
$667$	5.84628	+	10.1260i	0.226369	+	0.392082i
$668$	1.40699	−	14.6096i	0.0544380	−	0.565262i
$669$	−3.04406	+	11.3606i	−0.117690	+	0.439225i
$670$	11.0498	−	0.918079i	0.426893	−	0.0354685i
$671$	12.3988	+	12.3988i	0.478651	+	0.478651i
$672$	10.3592	+	12.9084i	0.399616	+	0.497953i
$673$	24.9962	+	14.4316i	0.963534	+	0.556297i	0.897259	−	0.441505i	$-0.145555\pi$
$673$	24.9962	+	14.4316i	0.963534	+	0.556297i	0.0662751	+	0.997801i	$0.478888\pi$
$674$	8.75809	−	6.07559i	0.337349	−	0.234023i
$675$	3.29627			0.126874
$676$	−6.96127	−	25.0508i	−0.267741	−	0.963491i
$677$	−1.10159			−0.0423376			−0.0211688	−	0.999776i	$-0.506739\pi$
$677$	−1.10159			−0.0423376			−0.0211688	+	0.999776i	$0.506739\pi$
$678$	−1.18923	+	0.824983i	−0.0456721	+	0.0316833i
$679$	−17.2897	−	9.98222i	−0.663518	−	0.383083i
$680$	18.1905	+	0.238577i	0.697573	+	0.00914902i
$681$	14.4609	+	14.4609i	0.554141	+	0.554141i
$682$	−22.8910	+	1.90191i	−0.876543	+	0.0728279i
$683$	6.23217	−	23.2588i	0.238467	−	0.889973i	−0.738088	−	0.674705i	$-0.764271\pi$
$683$	6.23217	−	23.2588i	0.238467	−	0.889973i	0.976555	−	0.215268i	$-0.0690624\pi$
$684$	12.1071	+	1.16598i	0.462926	+	0.0445824i
$685$	−5.43169	−	9.40797i	−0.207534	−	0.359460i
$686$	−22.1477	−	4.00514i	−0.845602	−	0.152917i
$687$	−3.19881	+	0.857118i	−0.122042	+	0.0327011i
$688$	1.22646	−	6.30850i	0.0467585	−	0.240509i
$689$	−2.45213	−	7.53997i	−0.0934186	−	0.287250i
$690$	1.98974	+	5.54204i	0.0757483	+	0.210982i
$691$	5.93120	+	22.1355i	0.225633	+	0.842075i	0.982150	+	0.188101i	$0.0602331\pi$
$691$	5.93120	+	22.1355i	0.225633	+	0.842075i	−0.756516	+	0.653975i	$0.773100\pi$
$692$	4.42286	+	26.4327i	0.168132	+	1.00482i
$693$	−16.3667	+	9.44932i	−0.621719	+	0.358950i
$694$	−6.10722	−	2.88041i	−0.231827	−	0.109339i
$695$	−13.4745	−	3.61048i	−0.511117	−	0.136953i
$696$	−7.42640	+	7.23412i	−0.281497	+	0.274209i
$697$	−29.4631	+	29.4631i	−1.11599	+	1.11599i
$698$	27.6006	−	32.6026i	1.04470	−	1.23403i
$699$	−2.41384	+	4.18090i	−0.0913000	+	0.158136i
$700$	−11.2014	+	15.7032i	−0.423371	+	0.593524i
$701$		−	50.0647i		−	1.89092i	−0.325741	−	0.945459i	$-0.605614\pi$
$701$		−	50.0647i		−	1.89092i	0.325741	−	0.945459i	$-0.394386\pi$
$702$	4.05963	+	3.08535i	0.153221	+	0.116449i
$703$		−	38.8955i		−	1.46697i
$704$	37.4843	−	35.5678i	1.41274	−	1.34051i
$705$	−1.79902	+	3.11599i	−0.0677549	+	0.117355i
$706$	1.75771	+	1.48803i	0.0661522	+	0.0560029i
$707$	−16.4933	+	16.4933i	−0.620294	+	0.620294i
$708$	3.19861	+	7.01901i	0.120211	+	0.263791i
$709$	15.0600	+	4.03531i	0.565590	+	0.151549i	0.530273	−	0.847827i	$-0.322089\pi$
$709$	15.0600	+	4.03531i	0.565590	+	0.151549i	0.0353166	+	0.999376i	$0.488756\pi$
$710$	−5.31206	+	11.2629i	−0.199358	+	0.422690i
$711$	−2.82358	+	1.63019i	−0.105892	+	0.0611370i
$712$	13.5472	+	24.1917i	0.507702	+	0.906620i
$713$	−2.07609	−	7.74807i	−0.0777502	−	0.290168i
$714$	−19.1901	+	6.88977i	−0.718171	+	0.257843i
$715$	−6.31215	+	29.7357i	−0.236061	+	1.11205i
$716$	−25.7453	−	31.2325i	−0.962145	−	1.16721i
$717$	−7.99674	+	2.14272i	−0.298644	+	0.0800213i
$718$	2.66549	−	14.7396i	0.0994751	−	0.550078i
$719$	17.7882	+	30.8101i	0.663389	+	1.14902i	0.979719	+	0.200374i	$0.0642159\pi$
$719$	17.7882	+	30.8101i	0.663389	+	1.14902i	−0.316330	+	0.948649i	$0.602451\pi$
$720$	−4.32856	+	2.91944i	−0.161316	+	0.108801i
$721$	10.3326	−	38.5618i	0.384806	−	1.43612i
$722$	2.10601	+	25.3476i	0.0783776	+	0.943340i
$723$	6.12360	+	6.12360i	0.227739	+	0.227739i
$724$	−13.5182	−	5.05452i	−0.502402	−	0.187850i
$725$	−10.4636	−	6.04115i	−0.388608	−	0.224363i
$726$	24.7638	+	35.6975i	0.919070	+	1.32486i
$727$	−9.90883			−0.367498			−0.183749	−	0.982973i	$-0.558823\pi$
$727$	−9.90883			−0.367498			−0.183749	+	0.982973i	$0.558823\pi$
$728$	−28.4937	+	8.85517i	−1.05605	+	0.328195i
$729$	−1.00000			−0.0370370
$730$	10.4809	+	15.1084i	0.387916	+	0.559188i
$731$	6.85630	+	3.95849i	0.253589	+	0.146410i
$732$	−5.08549	−	1.90148i	−0.187965	−	0.0702808i
$733$	25.2750	+	25.2750i	0.933552	+	0.933552i	0.997926	−	0.0643735i	$-0.0205049\pi$
$733$	25.2750	+	25.2750i	0.933552	+	0.933552i	−0.0643735	+	0.997926i	$0.520505\pi$
$734$	1.02593	+	12.3480i	0.0378679	+	0.455771i
$735$	−0.527231	+	1.96765i	−0.0194472	+	0.0725779i
$736$	14.5519	+	10.6708i	0.536389	+	0.393331i
$737$	19.3991	+	33.6003i	0.714576	+	1.23768i
$738$	2.12801	−	11.7675i	0.0783332	−	0.433168i
$739$	8.85522	−	2.37275i	0.325745	−	0.0872830i	−0.0922408	−	0.995737i	$-0.529403\pi$
$739$	8.85522	−	2.37275i	0.325745	−	0.0872830i	0.417985	+	0.908454i	$0.362736\pi$
$740$	10.6198	+	12.8833i	0.390392	+	0.473600i
$741$	−9.94954	+	19.5401i	−0.365506	+	0.717822i
$742$	−8.56387	+	3.07466i	−0.314389	+	0.112874i
$743$	2.25636	+	8.42086i	0.0827779	+	0.308931i	0.994884	−	0.101023i	$-0.0322114\pi$
$743$	2.25636	+	8.42086i	0.0827779	+	0.308931i	−0.912106	+	0.409954i	$0.865545\pi$
$744$	6.20557	−	3.47509i	0.227507	−	0.127403i
$745$	−17.8568	+	10.3096i	−0.654222	+	0.377715i
$746$	15.7004	−	33.2889i	0.574832	−	1.21879i
$747$	−2.14439	−	0.574588i	−0.0784592	−	0.0210231i
$748$	26.3970	+	57.9255i	0.965171	+	2.11797i
$749$	3.07164	−	3.07164i	0.112235	−	0.112235i
$750$	−11.6883	−	9.89505i	−0.426797	−	0.361316i
$751$	26.0718	−	45.1577i	0.951375	−	1.64783i	0.208920	−	0.977933i	$-0.433005\pi$
$751$	26.0718	−	45.1577i	0.951375	−	1.64783i	0.742454	−	0.669897i	$-0.233662\pi$
$752$	0.768785	+	10.9994i	0.0280347	+	0.401105i
$753$		−	2.00745i		−	0.0731557i
$754$	−7.23219	−	17.2342i	−0.263381	−	0.627633i
$755$			2.20731i			0.0803321i
$756$	3.39819	−	4.76392i	0.123591	−	0.173262i
$757$	−1.74267	+	3.01839i	−0.0633384	+	0.109705i	−0.895956	−	0.444143i	$-0.853508\pi$
$757$	−1.74267	+	3.01839i	−0.0633384	+	0.109705i	0.832617	+	0.553849i	$0.186841\pi$
$758$	−9.67907	+	11.4332i	−0.351560	+	0.415272i
$759$	−14.5695	+	14.5695i	−0.528839	+	0.528839i
$760$	−15.6665	−	16.0829i	−0.568285	−	0.583390i
$761$	10.1797	+	2.72765i	0.369015	+	0.0988772i	0.438561	−	0.898702i	$-0.355488\pi$
$761$	10.1797	+	2.72765i	0.369015	+	0.0988772i	−0.0695460	+	0.997579i	$0.522155\pi$
$762$	10.3824	+	4.89678i	0.376116	+	0.177392i
$763$	40.9525	−	23.6439i	1.48258	−	0.855968i
$764$	−0.485611	−	2.90219i	−0.0175688	−	0.104998i
$765$	−1.66469	−	6.21270i	−0.0601869	−	0.224621i
$766$	11.7121	+	32.6217i	0.423174	+	1.17867i
$767$	−13.8864	+	0.731502i	−0.501409	+	0.0264130i
$768$	−5.99469	+	14.8345i	−0.216315	+	0.535296i
$769$	−25.9859	+	6.96289i	−0.937074	+	0.251088i	−0.694869	−	0.719137i	$-0.744537\pi$
$769$	−25.9859	+	6.96289i	−0.937074	+	0.251088i	−0.242205	+	0.970225i	$0.577871\pi$
$770$	34.3287	+	6.20794i	1.23712	+	0.223719i
$771$	−5.18464	−	8.98006i	−0.186720	−	0.323409i
$772$	−45.1554	−	4.34872i	−1.62518	−	0.156514i
$773$	2.60534	−	9.72325i	0.0937075	−	0.349721i	−0.903113	−	0.429403i	$-0.858724\pi$
$773$	2.60534	−	9.72325i	0.0937075	−	0.349721i	0.996820	+	0.0796823i	$0.0253906\pi$
$774$	−2.26435	+	0.188134i	−0.0813904	+	0.00676234i
$775$	5.86105	+	5.86105i	0.210535	+	0.210535i
$776$	0.253103	−	19.2980i	0.00908585	−	0.692757i
$777$	−16.2058	−	9.35640i	−0.581378	−	0.335659i
$778$	−12.5001	+	8.67144i	−0.448149	+	0.310886i
$779$	51.4246			1.84248
$780$	−2.03954	−	9.18880i	−0.0730274	−	0.329012i
$781$	−43.5741			−1.55920
$782$	−18.2651	+	12.6707i	−0.653159	+	0.453104i
$783$	3.17437	+	1.83272i	0.113443	+	0.0654962i
$784$	2.03219	+	5.90255i	0.0725783	+	0.210805i
$785$	−5.87996	−	5.87996i	−0.209865	−	0.209865i
$786$	9.77617	−	0.812256i	0.348705	−	0.0289722i
$787$	7.18044	−	26.7978i	0.255955	−	0.955238i	−0.711601	−	0.702583i	$-0.752030\pi$
$787$	7.18044	−	26.7978i	0.255955	−	0.955238i	0.967557	−	0.252654i	$-0.0813036\pi$
$788$	−5.15358	+	53.5128i	−0.183589	+	1.90631i
$789$	6.78557	+	11.7530i	0.241573	+	0.418416i
$790$	5.92238	+	1.07099i	0.210709	+	0.0381042i
$791$	−2.89241	+	0.775019i	−0.102842	+	0.0275565i
$792$	−15.7005	−	9.34136i	−0.557894	−	0.331931i
$793$	6.54743	−	7.27559i	0.232506	−	0.258364i
$794$	13.1390	+	36.5962i	0.466287	+	1.29875i
$795$	−0.742892	−	2.77251i	−0.0263477	−	0.0983308i
$796$	36.5286	−	6.11217i	1.29472	−	0.216640i
$797$	−21.1621	+	12.2179i	−0.749598	+	0.432781i	−0.825549	−	0.564331i	$-0.809134\pi$
$797$	−21.1621	+	12.2179i	−0.749598	+	0.432781i	0.0759503	+	0.997112i	$0.475801\pi$
$798$	22.7598	+	10.7344i	0.805687	+	0.379995i
$799$	−13.1204	−	3.51559i	−0.464165	−	0.124373i
$800$	−18.5356	−	2.03076i	−0.655333	−	0.0717981i
$801$	6.93164	−	6.93164i	0.244917	−	0.244917i
$802$	−8.31707	+	9.82435i	−0.293686	+	0.346910i
$803$	−32.1710	+	55.7217i	−1.13529	+	1.96638i
$804$	−9.78016	−	6.97636i	−0.344920	−	0.246037i
$805$			12.1825i			0.429376i
$806$	1.73237	+	12.7044i	0.0610200	+	0.447493i
$807$			8.58978i			0.302375i
$808$	−21.7016	−	6.12106i	−0.763459	−	0.215338i
$809$	8.82801	−	15.2906i	0.310376	−	0.537587i	−0.668068	−	0.744101i	$-0.732878\pi$
$809$	8.82801	−	15.2906i	0.310376	−	0.537587i	0.978444	+	0.206513i	$0.0662117\pi$
$810$	1.40886	+	1.19271i	0.0495024	+	0.0419076i
$811$	6.14447	−	6.14447i	0.215762	−	0.215762i	−0.590948	−	0.806710i	$-0.701246\pi$
$811$	6.14447	−	6.14447i	0.215762	−	0.215762i	0.806710	+	0.590948i	$0.201246\pi$
$812$	−19.5180	+	8.89449i	−0.684949	+	0.312136i
$813$	20.1056	+	5.38729i	0.705135	+	0.188940i
$814$	−24.9215	+	52.8400i	−0.873498	+	1.85204i
$815$	12.0760	−	6.97210i	0.423005	−	0.244222i
$816$	−14.8752	−	12.9317i	−0.520738	−	0.452701i
$817$	−2.52891	−	9.43800i	−0.0884752	−	0.330194i
$818$	2.62163	−	0.941237i	0.0916632	−	0.0329096i
$819$	5.74796	+	8.84587i	0.200850	+	0.309100i
$820$	−17.0333	+	14.0407i	−0.594828	+	0.490322i
$821$	36.7362	−	9.84343i	1.28210	−	0.343538i	0.447447	−	0.894311i	$-0.352333\pi$
$821$	36.7362	−	9.84343i	1.28210	−	0.343538i	0.834655	+	0.550772i	$0.185667\pi$
$822$	−2.09451	+	11.5822i	−0.0730544	+	0.403977i
$823$	10.5068	+	18.1983i	0.366243	+	0.634352i	0.988975	−	0.148084i	$-0.0473105\pi$
$823$	10.5068	+	18.1983i	0.366243	+	0.634352i	−0.622732	+	0.782435i	$0.713977\pi$
$824$	37.4055	−	9.49879i	1.30308	−	0.330906i
$825$	5.51057	−	20.5657i	0.191853	−	0.716007i
$826$	1.32135	+	15.9036i	0.0459757	+	0.553355i
$827$	−21.3446	−	21.3446i	−0.742225	−	0.742225i	0.230781	−	0.973006i	$-0.425872\pi$
$827$	−21.3446	−	21.3446i	−0.742225	−	0.742225i	−0.973006	+	0.230781i	$0.925872\pi$
$828$	2.23438	−	5.97582i	0.0776501	−	0.207674i
$829$	5.48391	+	3.16614i	0.190464	+	0.109964i	0.592200	−	0.805791i	$-0.298260\pi$
$829$	5.48391	+	3.16614i	0.190464	+	0.109964i	−0.401736	+	0.915756i	$0.631593\pi$
$830$	2.33584	+	3.36716i	0.0810781	+	0.116876i
$831$	−28.9785			−1.00525
$832$	−20.9274	−	19.8506i	−0.725525	−	0.688195i
$833$	−7.69027			−0.266452
$834$	8.61492	+	12.4186i	0.298310	+	0.430020i
$835$	8.29552	+	4.78942i	0.287078	+	0.165745i
$836$	27.5148	−	73.5879i	0.951618	−	2.54509i
$837$	−1.77808	−	1.77808i	−0.0614596	−	0.0614596i
$838$	−1.83487	−	22.0842i	−0.0633845	−	0.762885i
$839$	0.162969	−	0.608210i	0.00562633	−	0.0209977i	−0.963056	−	0.269303i	$-0.913207\pi$
$839$	0.162969	−	0.608210i	0.00562633	−	0.0209977i	0.968682	+	0.248305i	$0.0798735\pi$
$840$	−10.4696	+	2.65865i	−0.361234	+	0.0917322i
$841$	7.78226	+	13.4793i	0.268354	+	0.464802i
$842$	0.362594	−	2.00507i	0.0124958	−	0.0690994i
$843$	−14.5560	+	3.90027i	−0.501336	+	0.134332i
$844$	−24.4391	+	20.1453i	−0.841227	+	0.693431i
$845$	16.7610	+	2.64544i	0.576596	+	0.0910058i
$846$	3.66904	−	1.31729i	0.126144	−	0.0452893i
$847$	23.2640	+	86.8224i	0.799360	+	2.98325i
$848$	−6.63830	−	5.77097i	−0.227960	−	0.198176i
$849$	9.64106	−	5.56627i	0.330880	−	0.191034i
$850$	9.79877	−	20.7759i	0.336095	−	0.712608i
$851$	−19.7066	−	5.28037i	−0.675534	−	0.181009i
$852$	12.2774	−	5.59490i	0.420618	−	0.191678i
$853$	30.6514	−	30.6514i	1.04948	−	1.04948i	0.0507738	−	0.998710i	$-0.483831\pi$
$853$	30.6514	−	30.6514i	1.04948	−	1.04948i	0.998710	−	0.0507738i	$-0.0161688\pi$
$854$	−8.57314	−	7.25782i	−0.293367	−	0.248358i
$855$	−3.96903	+	6.87456i	−0.135738	+	0.235105i
$856$	4.04161	+	1.13996i	0.138139	+	0.0389631i
$857$		−	1.01692i		−	0.0347372i	−0.999849	−	0.0173686i	$-0.994471\pi$
$857$		−	1.01692i		−	0.0347372i	0.999849	−	0.0173686i	$-0.00552887\pi$
$858$	26.0365	−	20.1705i	0.888870	−	0.688608i
$859$		−	8.96260i		−	0.305800i	−0.988242	−	0.152900i	$-0.951139\pi$
$859$		−	8.96260i		−	0.305800i	0.988242	−	0.152900i	$-0.0488612\pi$
$860$	3.41455	+	2.43566i	0.116435	+	0.0830553i
$861$	12.3703	−	21.4260i	0.421578	−	0.730195i
$862$	15.3768	−	18.1635i	0.523737	−	0.618652i
$863$	2.15959	−	2.15959i	0.0735132	−	0.0735132i	−0.669394	−	0.742907i	$-0.733446\pi$
$863$	2.15959	−	2.15959i	0.0735132	−	0.0735132i	0.742907	+	0.669394i	$0.233446\pi$
$864$	5.62321	+	0.616076i	0.191305	+	0.0209593i
$865$	−16.8947	−	4.52693i	−0.574438	−	0.153920i
$866$	−12.9498	−	6.10764i	−0.440051	−	0.207546i
$867$	6.30587	−	3.64070i	0.214159	−	0.123645i
$868$	14.5129	−	2.42838i	0.492600	−	0.0824247i
$869$	5.45058	+	20.3418i	0.184898	+	0.690049i
$870$	−2.28634	−	6.36816i	−0.0775143	−	0.215901i
$871$	18.1603	−	11.8004i	0.615337	−	0.399840i
$872$	39.2856	+	23.3738i	1.33038	+	0.791537i
$873$	−6.59095	+	1.76604i	−0.223070	+	0.0597713i
$874$	26.9975	+	4.88218i	0.913205	+	0.165142i
$875$	−15.8419	−	27.4389i	−0.535553	−	0.927605i
$876$	1.90983	−	19.8309i	0.0645271	−	0.670023i
$877$	9.35760	−	34.9230i	0.315984	−	1.17927i	−0.607087	−	0.794636i	$-0.707662\pi$
$877$	9.35760	−	34.9230i	0.315984	−	1.17927i	0.923070	−	0.384631i	$-0.125671\pi$
$878$	7.83048	−	0.650598i	0.264266	−	0.0219566i
$879$	9.60672	+	9.60672i	0.324027	+	0.324027i
$880$	10.9784	+	31.8869i	0.370080	+	1.07491i
$881$	−43.9972	−	25.4018i	−1.48230	−	0.855808i	−0.482504	−	0.875894i	$-0.660273\pi$
$881$	−43.9972	−	25.4018i	−1.48230	−	0.855808i	−0.999798	+	0.0200857i	$0.993606\pi$
$882$	1.81346	−	1.25802i	0.0610623	−	0.0423597i
$883$	24.2471			0.815980			0.407990	−	0.912986i	$-0.366230\pi$
$883$	24.2471			0.815980			0.407990	+	0.912986i	$0.366230\pi$
$884$	31.5145	−	16.4155i	1.05995	−	0.552114i
$885$	−5.03407			−0.169219
$886$	−23.9521	+	16.6159i	−0.804688	+	0.558222i
$887$	−15.7955	−	9.11956i	−0.530362	−	0.306205i	0.210802	−	0.977529i	$-0.432393\pi$
$887$	−15.7955	−	9.11956i	−0.530362	−	0.306205i	−0.741164	+	0.671324i	$0.765726\pi$
$888$	0.237235	−	18.0881i	0.00796107	−	0.606997i
$889$	16.7933	+	16.7933i	0.563231	+	0.563231i
$890$	−18.0332	+	1.49829i	−0.604473	+	0.0502228i
$891$	−1.67176	+	6.23908i	−0.0560060	+	0.209017i
$892$	−23.4143	−	2.25494i	−0.783970	−	0.0755008i
$893$	8.38204	+	14.5181i	0.280494	+	0.485830i
$894$	21.9837	+	3.97548i	0.735244	+	0.132960i
$895$	25.5158	−	6.83694i	0.852899	−	0.228534i
$896$	−22.0436	+	24.6949i	−0.736427	+	0.825000i
$897$	8.54935	+	7.69370i	0.285454	+	0.256885i
$898$	−15.7599	−	43.8960i	−0.525913	−	1.46483i
$899$	2.38556	+	8.90303i	0.0795629	+	0.296933i
$900$	1.08798	+	6.50215i	0.0362659	+	0.216738i
$901$	9.38419	−	5.41796i	0.312633	−	0.180499i
$902$	−69.8609	−	32.9492i	−2.32611	−	1.09709i
$903$	−4.54066	−	1.21667i	−0.151104	−	0.0404882i
$904$	−2.01986	−	2.07355i	−0.0671796	−	0.0689652i
$905$	6.66025	−	6.66025i	0.221394	−	0.221394i
$906$	1.54525	−	1.82529i	0.0513374	−	0.0606411i
$907$	11.0452	−	19.1309i	0.366750	−	0.635230i	−0.622305	−	0.782775i	$-0.713804\pi$
$907$	11.0452	−	19.1309i	0.366750	−	0.635230i	0.989055	+	0.147545i	$0.0471371\pi$
$908$	−23.7522	+	33.2982i	−0.788243	+	1.10504i
$909$			7.97203i			0.264416i
$910$	2.45247	−	19.3183i	0.0812987	−	0.640394i
$911$		−	33.4829i		−	1.10934i	−0.832071	−	0.554670i	$-0.812845\pi$
$911$		−	33.4829i		−	1.10934i	0.832071	−	0.554670i	$-0.187155\pi$
$912$	1.69611	+	24.2670i	0.0561637	+	0.803560i
$913$	−7.16981	+	12.4185i	−0.237286	+	0.410992i
$914$	−13.9812	−	11.8362i	−0.462457	−	0.391505i
$915$	2.50555	−	2.50555i	0.0828309	−	0.0828309i
$916$	−2.74654	−	6.02699i	−0.0907482	−	0.199137i
$917$	19.6040	+	5.25288i	0.647381	+	0.173465i
$918$	−2.97268	+	6.30285i	−0.0981131	+	0.208025i
$919$	10.1236	−	5.84487i	0.333947	−	0.192804i	−0.323645	−	0.946179i	$-0.604908\pi$
$919$	10.1236	−	5.84487i	0.333947	−	0.192804i	0.657592	+	0.753374i	$0.271575\pi$
$920$	−10.2754	+	5.75414i	−0.338769	+	0.189708i
$921$	−7.38170	−	27.5489i	−0.243235	−	0.907767i
$922$	−40.3948	+	14.5028i	−1.33033	+	0.477625i
$923$	1.27952	+	24.2896i	0.0421159	+	0.799504i
$924$	−24.0415	−	29.1657i	−0.790908	−	0.959481i
$925$	20.3635	−	5.45639i	0.669548	−	0.179405i
$926$	1.96948	−	10.8909i	0.0647212	−	0.357896i
$927$	−6.82229	−	11.8165i	−0.224073	−	0.388106i
$928$	−16.7210	−	12.2614i	−0.548895	−	0.402501i
$929$	1.33569	−	4.98484i	0.0438224	−	0.163547i	−0.940547	−	0.339664i	$-0.889687\pi$
$929$	1.33569	−	4.98484i	0.0438224	−	0.163547i	0.984369	+	0.176116i	$0.0563534\pi$
$930$	0.384337	+	4.62582i	0.0126029	+	0.151687i
$931$	6.71125	+	6.71125i	0.219952	+	0.219952i
$932$	−9.04387	−	3.38153i	−0.296242	−	0.110766i
$933$	−9.00930	−	5.20152i	−0.294951	−	0.170290i
$934$	−5.29927	−	7.63900i	−0.173397	−	0.249956i
$935$	−41.5445			−1.35865
$936$	−4.74615	+	9.02630i	−0.155133	+	0.295034i
$937$	29.5884			0.966611			0.483305	−	0.875452i	$-0.339436\pi$
$937$	29.5884			0.966611			0.483305	+	0.875452i	$0.339436\pi$
$938$	−14.1668	−	20.4217i	−0.462561	−	0.666791i
$939$	10.8466	+	6.26230i	0.353966	+	0.204362i
$940$	−6.74032	−	2.52023i	−0.219845	−	0.0822008i
$941$	−29.9139	−	29.9139i	−0.975164	−	0.975164i	0.0245352	−	0.999699i	$-0.492189\pi$
$941$	−29.9139	−	29.9139i	−0.975164	−	0.975164i	−0.999699	+	0.0245352i	$0.992189\pi$
$942$	0.745993	+	8.97865i	0.0243058	+	0.292540i
$943$	6.98129	−	26.0545i	0.227342	−	0.848452i
$944$	−12.7898	+	8.62621i	−0.416272	+	0.280759i
$945$	1.90952	+	3.30738i	0.0621165	+	0.107589i
$946$	−2.61166	+	14.4420i	−0.0849124	+	0.469549i
$947$	−21.3180	+	5.71214i	−0.692742	+	0.185620i	−0.587977	−	0.808877i	$-0.700076\pi$
$947$	−21.3180	+	5.71214i	−0.692742	+	0.185620i	−0.104765	+	0.994497i	$0.533409\pi$
$948$	−4.14764	−	5.03166i	−0.134709	−	0.163421i
$949$	32.0058	+	16.2969i	1.03895	+	0.529021i
$950$	−26.6824	+	9.57970i	−0.865690	+	0.310807i
$951$	1.98543	+	7.40971i	0.0643819	+	0.240276i
$952$	−19.9245	−	35.5799i	−0.645758	−	1.15315i
$953$	−11.1981	+	6.46521i	−0.362741	+	0.209429i	−0.670282	−	0.742106i	$-0.733827\pi$
$953$	−11.1981	+	6.46521i	−0.362741	+	0.209429i	0.307542	+	0.951535i	$0.400494\pi$
$954$	−1.32660	+	2.81274i	−0.0429504	+	0.0910659i
$955$	1.85497	+	0.497037i	0.0600253	+	0.0160837i
$956$	−6.86610	−	15.0669i	−0.222066	−	0.487300i
$957$	16.7413	−	16.7413i	0.541169	−	0.541169i
$958$	40.4997	+	34.2861i	1.30849	+	1.10773i
$959$	−12.1755	+	21.0887i	−0.393169	+	0.680989i
$960$	−7.18753	−	7.57482i	−0.231976	−	0.244476i
$961$			24.6768i			0.796027i
$962$	30.1866	+	12.3405i	0.973255	+	0.397873i
$963$		−	1.48468i		−	0.0478431i
$964$	−10.0581	+	14.1004i	−0.323950	+	0.454145i
$965$	14.8032	−	25.6398i	0.476530	−	0.825375i
$966$	8.52847	−	10.0741i	0.274399	−	0.324128i
$967$	−22.6838	+	22.6838i	−0.729461	+	0.729461i	−0.970512	−	0.241051i	$-0.922508\pi$
$967$	−22.6838	+	22.6838i	−0.729461	+	0.729461i	0.241051	+	0.970512i	$0.422508\pi$
$968$	−62.2424	+	60.6309i	−2.00055	+	1.94875i
$969$	−28.9464	−	7.75617i	−0.929892	−	0.249164i
$970$	11.3921	+	5.37298i	0.365779	+	0.172516i
$971$	13.9027	−	8.02675i	0.446160	−	0.257591i	−0.260047	−	0.965596i	$-0.583738\pi$
$971$	13.9027	−	8.02675i	0.446160	−	0.257591i	0.706207	+	0.708005i	$0.250405\pi$
$972$	−0.330063	−	1.97258i	−0.0105868	−	0.0632704i
$973$	8.09317	+	30.2041i	0.259455	+	0.968300i
$974$	20.3315	+	56.6294i	0.651463	+	1.81452i
$975$	−11.6258	−	2.46788i	−0.372325	−	0.0790353i
$976$	2.07229	−	10.6591i	0.0663324	−	0.341190i
$977$	−3.17539	+	0.850843i	−0.101590	+	0.0272209i	−0.309256	−	0.950979i	$-0.600080\pi$
$977$	−3.17539	+	0.850843i	−0.101590	+	0.0272209i	0.207666	+	0.978200i	$0.433413\pi$
$978$	−14.8669	−	2.68850i	−0.475392	−	0.0859688i
$979$	−31.6591	−	54.8351i	−1.01183	−	1.75254i
$980$	−4.05536	−	0.390555i	−0.129544	−	0.0124758i
$981$	4.18305	−	15.6113i	0.133554	−	0.498432i
$982$	24.6073	−	2.04451i	0.785251	−	0.0652428i
$983$	9.37699	+	9.37699i	0.299080	+	0.299080i	0.840653	−	0.541574i	$-0.182171\pi$
$983$	9.37699	+	9.37699i	0.299080	+	0.299080i	−0.541574	+	0.840653i	$0.682171\pi$
$984$	23.9147	+	0.313653i	0.762372	+	0.00999889i
$985$	−30.3852	−	17.5429i	−0.968154	−	0.558964i
$986$	20.9878	−	14.5595i	0.668387	−	0.463668i
$987$	8.06527			0.256720
$988$	−41.8283	−	13.1768i	−1.33073	−	0.419209i
$989$	−5.12513			−0.162970
$990$	9.79670	−	6.79609i	0.311360	−	0.215994i
$991$	35.8971	+	20.7252i	1.14031	+	0.658357i	0.946507	−	0.322684i	$-0.104585\pi$
$991$	35.8971	+	20.7252i	1.14031	+	0.658357i	0.193801	+	0.981041i	$0.437918\pi$
$992$	8.90310	+	11.0940i	0.282674	+	0.352234i
$993$	−20.6276	−	20.6276i	−0.654598	−	0.654598i
$994$	27.8180	−	2.31127i	0.882333	−	0.0733089i
$995$	−6.25598	+	23.3476i	−0.198328	+	0.740170i
$996$	0.425636	−	4.41963i	0.0134868	−	0.140041i
$997$	−23.0706	−	39.9595i	−0.730654	−	1.26553i	−0.956604	−	0.291392i	$-0.905882\pi$
$997$	−23.0706	−	39.9595i	−0.730654	−	1.26553i	0.225949	−	0.974139i	$-0.427452\pi$
$998$	50.6608	+	9.16140i	1.60364	+	0.289999i
$999$	−6.17774	+	1.65532i	−0.195455	+	0.0523720i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.2.w.c.7.5	✓	24
3.2	odd	2		468.2.cb.h.163.2		24
4.3	odd	2		156.2.w.d.7.4	yes	24
12.11	even	2		468.2.cb.g.163.3		24
13.2	odd	12		156.2.w.d.67.4	yes	24
39.2	even	12		468.2.cb.g.379.3		24
52.15	even	12	inner	156.2.w.c.67.5	yes	24
156.119	odd	12		468.2.cb.h.379.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.2.w.c.7.5	✓	24	1.1	even	1	trivial
156.2.w.c.67.5	yes	24	52.15	even	12	inner
156.2.w.d.7.4	yes	24	4.3	odd	2
156.2.w.d.67.4	yes	24	13.2	odd	12
468.2.cb.g.163.3		24	12.11	even	2
468.2.cb.g.379.3		24	39.2	even	12
468.2.cb.h.163.2		24	3.2	odd	2
468.2.cb.h.379.2		24	156.119	odd	12

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:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	156.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.806088 + 1.16199i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.700446 + 1.87333i) q^{4} +(-0.922964 - 0.922964i) q^{5} +(0.117097 + 1.40936i) q^{6} +(-0.757268 + 2.82616i) q^{7} +(-2.74142 + 0.696159i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.806088 + 1.16199i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.700446 + 1.87333i) q^{4} +(-0.922964 - 0.922964i) q^{5} +(0.117097 + 1.40936i) q^{6} +(-0.757268 + 2.82616i) q^{7} +(-2.74142 + 0.696159i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.328486 - 1.81647i) q^{10} +(6.23908 - 1.67176i) q^{11} +(-1.54327 + 1.27213i) q^{12} +(-1.11510 - 3.42878i) q^{13} +(-3.89440 + 1.39820i) q^{14} +(-0.337828 - 1.26079i) q^{15} +(-3.01875 - 2.62434i) q^{16} +(4.26744 - 2.46381i) q^{17} +(-0.603270 + 1.27909i) q^{18} +(-5.87432 - 1.57402i) q^{19} +(2.37551 - 1.08253i) q^{20} +(-2.06889 + 2.06889i) q^{21} +(6.97182 + 5.90218i) q^{22} +(-1.59497 + 2.76257i) q^{23} +(-2.72222 - 0.767817i) q^{24} -3.29627i q^{25} +(3.08535 - 4.05963i) q^{26} +1.00000i q^{27} +(-4.76392 - 3.39819i) q^{28} +(1.83272 - 3.17437i) q^{29} +(1.19271 - 1.40886i) q^{30} +(-1.77808 + 1.77808i) q^{31} +(0.616076 - 5.62321i) q^{32} +(6.23908 + 1.67176i) q^{33} +(6.30285 + 2.97268i) q^{34} +(3.30738 - 1.90952i) q^{35} +(-1.97258 + 0.330063i) q^{36} +(1.65532 + 6.17774i) q^{37} +(-2.90622 - 8.09471i) q^{38} +(0.748687 - 3.52696i) q^{39} +(3.17276 + 1.88770i) q^{40} +(-8.16771 + 2.18853i) q^{41} +(-4.07175 - 0.736326i) q^{42} +(0.803327 + 1.39140i) q^{43} +(-1.23838 + 12.8589i) q^{44} +(0.337828 - 1.26079i) q^{45} +(-4.49577 + 0.373532i) q^{46} +(-1.94917 - 1.94917i) q^{47} +(-1.30215 - 3.78212i) q^{48} +(-1.35156 - 0.780323i) q^{49} +(3.83024 - 2.65709i) q^{50} +4.92762 q^{51} +(7.20432 + 0.312724i) q^{52} +2.19902 q^{53} +(-1.16199 + 0.806088i) q^{54} +(-7.30143 - 4.21548i) q^{55} +(0.108529 - 8.27487i) q^{56} +(-4.30030 - 4.30030i) q^{57} +(5.16592 - 0.429212i) q^{58} +(0.998196 - 3.72532i) q^{59} +(2.59851 + 0.250252i) q^{60} +(1.35734 + 2.35098i) q^{61} +(-3.49941 - 0.632826i) q^{62} +(-2.82616 + 0.757268i) q^{63} +(7.03073 - 3.81692i) q^{64} +(-2.13545 + 4.19384i) q^{65} +(3.08668 + 8.59734i) q^{66} +(1.55464 + 5.80201i) q^{67} +(1.62642 + 9.72010i) q^{68} +(-2.76257 + 1.59497i) q^{69} +(4.88488 + 2.30391i) q^{70} +(-6.51621 - 1.74601i) q^{71} +(-1.97360 - 2.02606i) q^{72} +(-7.04372 + 7.04372i) q^{73} +(-5.84414 + 6.90326i) q^{74} +(1.64814 - 2.85466i) q^{75} +(7.06331 - 9.90205i) q^{76} +18.8986i q^{77} +(4.70181 - 1.97307i) q^{78} +3.26039i q^{79} +(0.364032 + 5.20837i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-9.12695 - 7.72666i) q^{82} +(-1.56980 + 1.56980i) q^{83} +(-2.42658 - 5.32488i) q^{84} +(-6.21270 - 1.66469i) q^{85} +(-0.969246 + 2.05505i) q^{86} +(3.17437 - 1.83272i) q^{87} +(-15.9401 + 8.92638i) q^{88} +(-2.53716 - 9.46880i) q^{89} +(1.73735 - 0.623756i) q^{90} +(10.5347 - 0.554944i) q^{91} +(-4.05802 - 4.92294i) q^{92} +(-2.42891 + 0.650824i) q^{93} +(0.693718 - 3.83613i) q^{94} +(3.96903 + 6.87456i) q^{95} +(3.34514 - 4.56180i) q^{96} +(-1.76604 + 6.59095i) q^{97} +(-0.182747 - 2.19951i) q^{98} +(4.56733 + 4.56733i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 12 q^{9}+O(q^{10}) \) 24 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 12 * q^9	\( 24 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 12 q^{9} + 12 q^{10} + 4 q^{11} - 4 q^{12} - 22 q^{14} - 4 q^{15} + 12 q^{16} - 2 q^{18} - 22 q^{19} - 4 q^{20} + 10 q^{21} - 34 q^{22} + 2 q^{24} - 4 q^{26} - 14 q^{28} + 8 q^{29} - 16 q^{30} - 2 q^{31} - 34 q^{32} + 4 q^{33} + 20 q^{34} + 24 q^{35} - 4 q^{36} - 12 q^{37} - 12 q^{38} - 6 q^{39} + 28 q^{40} - 36 q^{41} + 6 q^{42} + 10 q^{43} + 20 q^{44} + 4 q^{45} - 2 q^{46} + 20 q^{47} + 32 q^{48} - 54 q^{49} - 24 q^{50} + 36 q^{51} + 4 q^{52} - 36 q^{53} - 4 q^{54} - 24 q^{55} + 70 q^{56} - 32 q^{57} + 48 q^{58} - 36 q^{59} - 28 q^{60} - 2 q^{61} + 64 q^{62} + 8 q^{63} - 8 q^{64} + 16 q^{65} + 20 q^{66} - 16 q^{67} - 10 q^{68} + 12 q^{69} + 36 q^{71} - 2 q^{72} - 40 q^{73} - 30 q^{74} - 8 q^{75} + 58 q^{76} + 24 q^{78} - 48 q^{80} - 12 q^{81} - 30 q^{82} - 24 q^{83} - 26 q^{84} + 18 q^{85} + 30 q^{86} + 6 q^{87} - 78 q^{88} + 66 q^{89} + 12 q^{90} + 42 q^{91} + 36 q^{92} - 10 q^{93} + 6 q^{94} - 28 q^{95} + 8 q^{96} + 4 q^{97} + 44 q^{98} - 4 q^{99}+O(q^{100}) \) 24 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 12 * q^9 + 12 * q^10 + 4 * q^11 - 4 * q^12 - 22 * q^14 - 4 * q^15 + 12 * q^16 - 2 * q^18 - 22 * q^19 - 4 * q^20 + 10 * q^21 - 34 * q^22 + 2 * q^24 - 4 * q^26 - 14 * q^28 + 8 * q^29 - 16 * q^30 - 2 * q^31 - 34 * q^32 + 4 * q^33 + 20 * q^34 + 24 * q^35 - 4 * q^36 - 12 * q^37 - 12 * q^38 - 6 * q^39 + 28 * q^40 - 36 * q^41 + 6 * q^42 + 10 * q^43 + 20 * q^44 + 4 * q^45 - 2 * q^46 + 20 * q^47 + 32 * q^48 - 54 * q^49 - 24 * q^50 + 36 * q^51 + 4 * q^52 - 36 * q^53 - 4 * q^54 - 24 * q^55 + 70 * q^56 - 32 * q^57 + 48 * q^58 - 36 * q^59 - 28 * q^60 - 2 * q^61 + 64 * q^62 + 8 * q^63 - 8 * q^64 + 16 * q^65 + 20 * q^66 - 16 * q^67 - 10 * q^68 + 12 * q^69 + 36 * q^71 - 2 * q^72 - 40 * q^73 - 30 * q^74 - 8 * q^75 + 58 * q^76 + 24 * q^78 - 48 * q^80 - 12 * q^81 - 30 * q^82 - 24 * q^83 - 26 * q^84 + 18 * q^85 + 30 * q^86 + 6 * q^87 - 78 * q^88 + 66 * q^89 + 12 * q^90 + 42 * q^91 + 36 * q^92 - 10 * q^93 + 6 * q^94 - 28 * q^95 + 8 * q^96 + 4 * q^97 + 44 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

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