LMFDB - Embedded newform 966.2.y.d.121.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(25,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 44, 6]))

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

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

chi := DirichletCharacter("966.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.y (of order $33$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$8$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			121.8
Character	$\chi$	$=$	966.121
Dual form			966.2.y.d.487.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.580057 + 0.814576i) q^{2} +(0.235759 + 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(0.140981 + 2.95955i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(2.61692 - 0.389498i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +O(q^{10})$	\(q+(0.580057 + 0.814576i) q^{2} +(0.235759 + 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(0.140981 + 2.95955i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(2.61692 - 0.389498i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +(-2.32900 + 1.83155i) q^{10} +(-0.318765 + 0.447643i) q^{11} +(-0.995472 - 0.0950560i) q^{12} +(0.364266 + 2.53353i) q^{13} +(1.83524 + 1.90575i) q^{14} +(-2.84289 + 0.834748i) q^{15} +(-0.786053 - 0.618159i) q^{16} +(4.61152 + 0.888798i) q^{17} +(-0.888835 - 0.458227i) q^{18} +(3.48041 - 0.670793i) q^{19} +(-2.84289 - 0.834748i) q^{20} +(0.995482 + 2.45133i) q^{21} -0.549541 q^{22} +(-4.74644 - 0.686535i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-3.76172 + 0.359201i) q^{25} +(-1.85245 + 1.76631i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(-0.487836 + 2.60039i) q^{28} +(-2.37748 + 2.74376i) q^{29} +(-2.32900 - 1.83155i) q^{30} +(-6.29436 - 6.00166i) q^{31} +(0.0475819 - 0.998867i) q^{32} +(-0.510176 - 0.204244i) q^{33} +(1.95095 + 4.27199i) q^{34} +(1.52168 + 7.69002i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(5.37589 - 2.77146i) q^{37} +(2.56525 + 2.44596i) q^{38} +(-2.37623 + 0.951299i) q^{39} +(-0.969073 - 2.79995i) q^{40} +(-6.43792 + 4.13740i) q^{41} +(-1.41936 + 2.23281i) q^{42} +(-1.58559 - 0.465571i) q^{43} +(-0.318765 - 0.447643i) q^{44} +(-1.48145 - 2.56596i) q^{45} +(-2.19397 - 4.26456i) q^{46} +(2.87817 - 4.98514i) q^{47} +(0.415415 - 0.909632i) q^{48} +(6.69658 - 2.03857i) q^{49} +(-2.47461 - 2.85585i) q^{50} +(0.223463 + 4.69107i) q^{51} +(-2.51332 - 0.484403i) q^{52} +(0.452828 - 0.181285i) q^{53} +(0.235759 - 0.971812i) q^{54} +(-1.36976 - 0.880293i) q^{55} +(-2.40119 + 1.11099i) q^{56} +(1.47242 + 3.22415i) q^{57} +(-3.61407 - 0.345102i) q^{58} +(5.57999 - 4.38815i) q^{59} +(0.140981 - 2.95955i) q^{60} +(2.17467 - 8.96409i) q^{61} +(1.23772 - 8.60854i) q^{62} +(-2.14754 + 1.54534i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-7.44675 + 1.43524i) q^{65} +(-0.129559 - 0.534050i) q^{66} +(3.69907 - 0.353218i) q^{67} +(-2.34820 + 4.06720i) q^{68} +(-0.451832 - 4.77450i) q^{69} +(-5.38144 + 5.70017i) q^{70} +(-4.57999 + 10.0288i) q^{71} +(0.723734 - 0.690079i) q^{72} +(-0.903984 + 2.61189i) q^{73} +(5.37589 + 2.77146i) q^{74} +(-1.23594 - 3.57100i) q^{75} +(-0.504429 + 3.50838i) q^{76} +(-0.659828 + 1.29560i) q^{77} +(-2.15325 - 1.38381i) q^{78} +(-13.5003 - 5.40472i) q^{79} +(1.71866 - 2.41351i) q^{80} +(0.580057 - 0.814576i) q^{81} +(-7.10459 - 2.84425i) q^{82} +(0.856613 + 0.550511i) q^{83} +(-2.64210 + 0.138979i) q^{84} +(-1.98031 + 13.7734i) q^{85} +(-0.540489 - 1.56164i) q^{86} +(-3.22693 - 1.66360i) q^{87} +(0.179737 - 0.519316i) q^{88} +(-3.26532 + 3.11348i) q^{89} +(1.23084 - 2.69516i) q^{90} +(1.94006 + 6.48816i) q^{91} +(2.20118 - 4.26084i) q^{92} +(4.34853 - 7.53187i) q^{93} +(5.73028 - 0.547176i) q^{94} +(2.47592 + 10.2059i) q^{95} +(0.981929 - 0.189251i) q^{96} +(-2.19561 + 1.41103i) q^{97} +(5.54497 + 4.27239i) q^{98} +(0.0782078 - 0.543947i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) $ 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9} - 2 q^{10} - 4 q^{11} + 8 q^{12} - 4 q^{13} + 5 q^{14} + 26 q^{15} + 8 q^{16} - 13 q^{17} + 8 q^{18} + 4 q^{19} + 26 q^{20} + 11 q^{21} - 124 q^{22} + 26 q^{23} - 80 q^{24} + 14 q^{25} + 2 q^{26} - 16 q^{27} - 22 q^{28} + 54 q^{29} - 2 q^{30} + 15 q^{31} + 8 q^{32} - 4 q^{33} + 4 q^{34} - 2 q^{35} - 16 q^{36} + 7 q^{37} - 7 q^{38} + 2 q^{39} + 9 q^{40} - 30 q^{41} + 6 q^{42} + 36 q^{43} - 4 q^{44} + 20 q^{45} + 4 q^{46} - 6 q^{47} - 16 q^{48} + 14 q^{49} - 28 q^{50} + 9 q^{51} + 2 q^{52} - 24 q^{53} + 8 q^{54} - 14 q^{55} + 6 q^{56} - 30 q^{57} - 5 q^{58} + 4 q^{59} - 2 q^{60} + 32 q^{61} - 8 q^{62} - 6 q^{63} - 16 q^{64} + 38 q^{65} - 4 q^{66} + 6 q^{67} + 42 q^{68} - 30 q^{69} - 8 q^{70} - 180 q^{71} + 8 q^{72} - 32 q^{73} + 7 q^{74} + 14 q^{75} - 8 q^{76} + 61 q^{77} + 18 q^{78} - 66 q^{79} - 2 q^{80} + 8 q^{81} - 7 q^{82} + 130 q^{83} + 5 q^{84} - 70 q^{85} - 40 q^{86} + 6 q^{87} - 15 q^{88} - 4 q^{89} + 4 q^{90} - 6 q^{91} + 58 q^{92} - 18 q^{93} + 16 q^{94} + 19 q^{95} + 8 q^{96} + 40 q^{97} + 43 q^{98} + 8 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9 - 2 * q^10 - 4 * q^11 + 8 * q^12 - 4 * q^13 + 5 * q^14 + 26 * q^15 + 8 * q^16 - 13 * q^17 + 8 * q^18 + 4 * q^19 + 26 * q^20 + 11 * q^21 - 124 * q^22 + 26 * q^23 - 80 * q^24 + 14 * q^25 + 2 * q^26 - 16 * q^27 - 22 * q^28 + 54 * q^29 - 2 * q^30 + 15 * q^31 + 8 * q^32 - 4 * q^33 + 4 * q^34 - 2 * q^35 - 16 * q^36 + 7 * q^37 - 7 * q^38 + 2 * q^39 + 9 * q^40 - 30 * q^41 + 6 * q^42 + 36 * q^43 - 4 * q^44 + 20 * q^45 + 4 * q^46 - 6 * q^47 - 16 * q^48 + 14 * q^49 - 28 * q^50 + 9 * q^51 + 2 * q^52 - 24 * q^53 + 8 * q^54 - 14 * q^55 + 6 * q^56 - 30 * q^57 - 5 * q^58 + 4 * q^59 - 2 * q^60 + 32 * q^61 - 8 * q^62 - 6 * q^63 - 16 * q^64 + 38 * q^65 - 4 * q^66 + 6 * q^67 + 42 * q^68 - 30 * q^69 - 8 * q^70 - 180 * q^71 + 8 * q^72 - 32 * q^73 + 7 * q^74 + 14 * q^75 - 8 * q^76 + 61 * q^77 + 18 * q^78 - 66 * q^79 - 2 * q^80 + 8 * q^81 - 7 * q^82 + 130 * q^83 + 5 * q^84 - 70 * q^85 - 40 * q^86 + 6 * q^87 - 15 * q^88 - 4 * q^89 + 4 * q^90 - 6 * q^91 + 58 * q^92 - 18 * q^93 + 16 * q^94 + 19 * q^95 + 8 * q^96 + 40 * q^97 + 43 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{9}{11}\right)$

Coefficient data

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

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

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

$2$	0.580057	+	0.814576i	0.410162	+	0.575992i
$2$	0.580057	+	0.814576i	0.410162	+	0.575992i
$3$	0.235759	+	0.971812i	0.136115	+	0.561076i
$3$	0.235759	+	0.971812i	0.136115	+	0.561076i
$4$	−0.327068	+	0.945001i	−0.163534	+	0.472500i
$5$	0.140981	+	2.95955i	0.0630486	+	1.32355i	0.779714	+	0.626136i	$0.215364\pi$
$5$	0.140981	+	2.95955i	0.0630486	+	1.32355i	−0.716666	+	0.697417i	$0.754333\pi$
$6$	−0.654861	+	0.755750i	−0.267346	+	0.308533i
$7$	2.61692	−	0.389498i	0.989104	−	0.147216i
$7$	2.61692	−	0.389498i	0.989104	−	0.147216i
$8$	−0.959493	+	0.281733i	−0.339232	+	0.0996075i
$9$	−0.888835	+	0.458227i	−0.296278	+	0.152742i
$10$	−2.32900	+	1.83155i	−0.736496	+	0.579187i
$11$	−0.318765	+	0.447643i	−0.0961112	+	0.134969i	−0.859831	−	0.510578i	$-0.829431\pi$
$11$	−0.318765	+	0.447643i	−0.0961112	+	0.134969i	0.763720	+	0.645548i	$0.223371\pi$
$12$	−0.995472	−	0.0950560i	−0.287368	−	0.0274403i
$13$	0.364266	+	2.53353i	0.101029	+	0.702673i	0.975884	+	0.218289i	$0.0700474\pi$
$13$	0.364266	+	2.53353i	0.101029	+	0.702673i	−0.874855	+	0.484385i	$0.839043\pi$
$14$	1.83524	+	1.90575i	0.490489	+	0.509334i
$15$	−2.84289	+	0.834748i	−0.734031	+	0.215531i
$16$	−0.786053	−	0.618159i	−0.196513	−	0.154540i
$17$	4.61152	+	0.888798i	1.11846	+	0.215565i	0.714789	−	0.699340i	$-0.246523\pi$
$17$	4.61152	+	0.888798i	1.11846	+	0.215565i	0.403669	+	0.914905i	$0.367735\pi$
$18$	−0.888835	−	0.458227i	−0.209501	−	0.108005i
$19$	3.48041	−	0.670793i	0.798460	−	0.153891i	0.226327	−	0.974051i	$-0.427328\pi$
$19$	3.48041	−	0.670793i	0.798460	−	0.153891i	0.572133	+	0.820161i	$0.306116\pi$
$20$	−2.84289	−	0.834748i	−0.635690	−	0.186655i
$21$	0.995482	+	2.45133i	0.217232	+	0.534924i
$22$	−0.549541			−0.117162
$23$	−4.74644	−	0.686535i	−0.989701	−	0.143153i
$23$	−4.74644	−	0.686535i	−0.989701	−	0.143153i
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−3.76172	+	0.359201i	−0.752345	+	0.0718402i
$26$	−1.85245	+	1.76631i	−0.363296	+	0.346402i
$27$	−0.654861	−	0.755750i	−0.126028	−	0.145444i
$28$	−0.487836	+	2.60039i	−0.0921924	+	0.491427i
$29$	−2.37748	+	2.74376i	−0.441487	+	0.509503i	−0.932262	−	0.361783i	$-0.882168\pi$
$29$	−2.37748	+	2.74376i	−0.441487	+	0.509503i	0.490775	+	0.871286i	$0.336714\pi$
$30$	−2.32900	−	1.83155i	−0.425216	−	0.334394i
$31$	−6.29436	−	6.00166i	−1.13050	−	1.07793i	−0.996209	−	0.0869876i	$-0.972276\pi$
$31$	−6.29436	−	6.00166i	−1.13050	−	1.07793i	−0.134291	−	0.990942i	$-0.542876\pi$
$32$	0.0475819	−	0.998867i	0.00841137	−	0.176576i
$33$	−0.510176	−	0.204244i	−0.0888102	−	0.0355542i
$34$	1.95095	+	4.27199i	0.334586	+	0.732640i
$35$	1.52168	+	7.69002i	0.257210	+	1.29985i
$36$	−0.142315	−	0.989821i	−0.0237191	−	0.164970i
$37$	5.37589	−	2.77146i	0.883791	−	0.455626i	0.0443117	−	0.999018i	$-0.485891\pi$
$37$	5.37589	−	2.77146i	0.883791	−	0.455626i	0.839479	+	0.543392i	$0.182860\pi$
$38$	2.56525	+	2.44596i	0.416138	+	0.396787i
$39$	−2.37623	+	0.951299i	−0.380501	+	0.152330i
$40$	−0.969073	−	2.79995i	−0.153224	−	0.442711i
$41$	−6.43792	+	4.13740i	−1.00543	+	0.646153i	−0.936208	−	0.351448i	$-0.885690\pi$
$41$	−6.43792	+	4.13740i	−1.00543	+	0.646153i	−0.0692266	+	0.997601i	$0.522053\pi$
$42$	−1.41936	+	2.23281i	−0.219012	+	0.344529i
$43$	−1.58559	−	0.465571i	−0.241800	−	0.0709990i	0.158587	−	0.987345i	$-0.449306\pi$
$43$	−1.58559	−	0.465571i	−0.241800	−	0.0709990i	−0.400387	+	0.916346i	$0.631124\pi$
$44$	−0.318765	−	0.447643i	−0.0480556	−	0.0674847i
$45$	−1.48145	−	2.56596i	−0.220842	−	0.382510i
$46$	−2.19397	−	4.26456i	−0.323483	−	0.628776i
$47$	2.87817	−	4.98514i	0.419825	−	0.727158i	−0.576097	−	0.817382i	$-0.695425\pi$
$47$	2.87817	−	4.98514i	0.419825	−	0.727158i	0.995922	+	0.0902236i	$0.0287582\pi$
$48$	0.415415	−	0.909632i	0.0599600	−	0.131294i
$49$	6.69658	−	2.03857i	0.956655	−	0.291224i
$50$	−2.47461	−	2.85585i	−0.349963	−	0.403878i
$51$	0.223463	+	4.69107i	0.0312911	+	0.656882i
$52$	−2.51332	−	0.484403i	−0.348535	−	0.0671747i
$53$	0.452828	−	0.181285i	0.0622007	−	0.0249014i	−0.340353	−	0.940298i	$-0.610547\pi$
$53$	0.452828	−	0.181285i	0.0622007	−	0.0249014i	0.402554	+	0.915396i	$0.368122\pi$
$54$	0.235759	−	0.971812i	0.0320827	−	0.132247i
$55$	−1.36976	−	0.880293i	−0.184699	−	0.118699i
$56$	−2.40119	+	1.11099i	−0.320872	+	0.148463i
$57$	1.47242	+	3.22415i	0.195027	+	0.427050i
$58$	−3.61407	−	0.345102i	−0.474551	−	0.0453141i
$59$	5.57999	−	4.38815i	0.726453	−	0.571289i	−0.184978	−	0.982743i	$-0.559221\pi$
$59$	5.57999	−	4.38815i	0.726453	−	0.571289i	0.911430	+	0.411454i	$0.134979\pi$
$60$	0.140981	−	2.95955i	0.0182006	−	0.382077i
$61$	2.17467	−	8.96409i	0.278437	−	1.14773i	−0.645061	−	0.764131i	$-0.723168\pi$
$61$	2.17467	−	8.96409i	0.278437	−	1.14773i	0.923498	−	0.383603i	$-0.125317\pi$
$62$	1.23772	−	8.60854i	0.157191	−	1.09329i
$63$	−2.14754	+	1.54534i	−0.270564	+	0.194695i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	−7.44675	+	1.43524i	−0.923656	+	0.178020i
$66$	−0.129559	−	0.534050i	−0.0159476	−	0.0657370i
$67$	3.69907	−	0.353218i	0.451913	−	0.0431524i	0.133381	−	0.991065i	$-0.457416\pi$
$67$	3.69907	−	0.353218i	0.451913	−	0.0431524i	0.318531	+	0.947912i	$0.396810\pi$
$68$	−2.34820	+	4.06720i	−0.284761	+	0.493220i
$69$	−0.451832	−	4.77450i	−0.0543942	−	0.574782i
$70$	−5.38144	+	5.70017i	−0.643206	+	0.681300i
$71$	−4.57999	+	10.0288i	−0.543545	+	1.19020i	0.416187	+	0.909279i	$0.363366\pi$
$71$	−4.57999	+	10.0288i	−0.543545	+	1.19020i	−0.959732	+	0.280918i	$0.909361\pi$
$72$	0.723734	−	0.690079i	0.0852929	−	0.0813266i
$73$	−0.903984	+	2.61189i	−0.105803	+	0.305698i	−0.985459	−	0.169912i	$-0.945652\pi$
$73$	−0.903984	+	2.61189i	−0.105803	+	0.305698i	0.879656	+	0.475611i	$0.157773\pi$
$74$	5.37589	+	2.77146i	0.624934	+	0.322176i
$75$	−1.23594	−	3.57100i	−0.142714	−	0.412344i
$76$	−0.504429	+	3.50838i	−0.0578620	+	0.402439i
$77$	−0.659828	+	1.29560i	−0.0751943	+	0.147648i
$78$	−2.15325	−	1.38381i	−0.243808	−	0.156686i
$79$	−13.5003	−	5.40472i	−1.51891	−	0.608079i	−0.545694	−	0.837985i	$-0.683734\pi$
$79$	−13.5003	−	5.40472i	−1.51891	−	0.608079i	−0.973213	+	0.229906i	$0.926158\pi$
$80$	1.71866	−	2.41351i	0.192152	−	0.269839i
$81$	0.580057	−	0.814576i	0.0644508	−	0.0905084i
$82$	−7.10459	−	2.84425i	−0.784570	−	0.314095i
$83$	0.856613	+	0.550511i	0.0940254	+	0.0604265i	0.586809	−	0.809726i	$-0.300384\pi$
$83$	0.856613	+	0.550511i	0.0940254	+	0.0604265i	−0.492783	+	0.870152i	$0.664020\pi$
$84$	−2.64210	+	0.138979i	−0.288277	+	0.0151639i
$85$	−1.98031	+	13.7734i	−0.214795	+	1.49393i
$86$	−0.540489	−	1.56164i	−0.0582825	−	0.168396i
$87$	−3.22693	−	1.66360i	−0.345963	−	0.178356i
$88$	0.179737	−	0.519316i	0.0191600	−	0.0553593i
$89$	−3.26532	+	3.11348i	−0.346123	+	0.330028i	−0.843121	−	0.537724i	$-0.819284\pi$
$89$	−3.26532	+	3.11348i	−0.346123	+	0.330028i	0.496998	+	0.867752i	$0.334436\pi$
$90$	1.23084	−	2.69516i	0.129742	−	0.284095i
$91$	1.94006	+	6.48816i	0.203373	+	0.680144i
$92$	2.20118	−	4.26084i	0.229489	−	0.444224i
$93$	4.34853	−	7.53187i	0.450922	−	0.781019i
$94$	5.73028	−	0.547176i	0.591034	−	0.0564369i
$95$	2.47592	+	10.2059i	0.254024	+	1.04710i
$96$	0.981929	−	0.189251i	0.100218	−	0.0193154i
$97$	−2.19561	+	1.41103i	−0.222930	+	0.143269i	−0.647339	−	0.762202i	$-0.724118\pi$
$97$	−2.19561	+	1.41103i	−0.222930	+	0.143269i	0.424409	+	0.905471i	$0.360482\pi$
$98$	5.54497	+	4.27239i	0.560127	+	0.431576i
$99$	0.0782078	−	0.543947i	0.00786018	−	0.0546687i
$100$	0.890894	−	3.67231i	0.0890894	−	0.367231i
$101$	0.468447	−	9.83392i	0.0466123	−	0.978512i	−0.847535	−	0.530739i	$-0.821914\pi$
$101$	0.468447	−	9.83392i	0.0466123	−	0.978512i	0.894147	−	0.447773i	$-0.147783\pi$
$102$	−3.69161	+	2.90312i	−0.365524	+	0.287451i
$103$	13.6975	+	1.30795i	1.34965	+	0.128876i	0.744708	−	0.667390i	$-0.232589\pi$
$103$	13.6975	+	1.30795i	1.34965	+	0.128876i	0.604946	+	0.796266i	$0.293195\pi$
$104$	−1.06329	−	2.32827i	−0.104264	−	0.228306i
$105$	−7.11450	+	3.29177i	−0.694304	+	0.321244i
$106$	0.410337	+	0.263707i	0.0398554	+	0.0256135i
$107$	−0.497145	+	2.04926i	−0.0480608	+	0.198109i	−0.990781	−	0.135476i	$-0.956744\pi$
$107$	−0.497145	+	2.04926i	−0.0480608	+	0.198109i	0.942720	+	0.333586i	$0.108259\pi$
$108$	0.928368	−	0.371662i	0.0893322	−	0.0357632i
$109$	11.0599	+	2.13163i	1.05935	+	0.204173i	0.689031	−	0.724732i	$-0.258036\pi$
$109$	11.0599	+	2.13163i	1.05935	+	0.204173i	0.370319	+	0.928905i	$0.379248\pi$
$110$	−0.0774747	−	1.62639i	−0.00738693	−	0.155071i
$111$	3.96075	+	4.57095i	0.375938	+	0.433856i
$112$	−2.29781	−	1.31151i	−0.217123	−	0.123926i
$113$	0.909219	−	1.99091i	0.0855321	−	0.187289i	−0.862033	−	0.506852i	$-0.830809\pi$
$113$	0.909219	−	1.99091i	0.0855321	−	0.187289i	0.947565	+	0.319563i	$0.103536\pi$
$114$	−1.77223	+	3.06959i	−0.165985	+	0.287494i
$115$	1.36268	−	14.1441i	0.127071	−	1.31895i
$116$	−1.81526	−	3.14412i	−0.168542	−	0.291924i
$117$	−1.48470	−	2.08497i	−0.137261	−	0.192756i
$118$	6.81119	+	1.99995i	0.627021	+	0.184110i
$119$	12.4142	+	0.529740i	1.13801	+	0.0485612i
$120$	2.49256	−	1.60187i	0.227538	−	0.146230i
$121$	3.49897	+	10.1096i	0.318089	+	0.919057i
$122$	8.56336	−	3.42825i	0.775291	−	0.310380i
$123$	−5.53857	−	5.28102i	−0.499396	−	0.476173i
$124$	7.73025	−	3.98522i	0.694197	−	0.357884i
$125$	0.514924	+	3.58138i	0.0460562	+	0.320328i
$126$	−2.50449	−	0.852945i	−0.223118	−	0.0759864i
$127$	5.08368	+	11.1317i	0.451104	+	0.987779i	0.989426	+	0.145040i	$0.0463312\pi$
$127$	5.08368	+	11.1317i	0.451104	+	0.987779i	−0.538322	+	0.842739i	$0.680942\pi$
$128$	0.928368	+	0.371662i	0.0820569	+	0.0328506i
$129$	0.0786305	−	1.65066i	0.00692303	−	0.145332i
$130$	−5.48865	−	5.23342i	−0.481387	−	0.459001i
$131$	7.68907	+	6.04675i	0.671797	+	0.528307i	0.894775	−	0.446516i	$-0.147336\pi$
$131$	7.68907	+	6.04675i	0.671797	+	0.528307i	−0.222979	+	0.974823i	$0.571578\pi$
$132$	0.359873	−	0.415315i	0.0313229	−	0.0361485i
$133$	8.84669	−	3.11103i	0.767105	−	0.269760i
$134$	2.43339	+	2.80828i	0.210213	+	0.242599i
$135$	2.14436	−	2.04464i	0.184557	−	0.175975i
$136$	−4.67513	+	0.446421i	−0.400889	+	0.0382802i
$137$	6.07299	+	10.5187i	0.518851	+	0.898676i	0.999760	+	0.0219055i	$0.00697330\pi$
$137$	6.07299	+	10.5187i	0.518851	+	0.898676i	−0.480909	+	0.876770i	$0.659693\pi$
$138$	3.62710	−	3.13753i	0.308760	−	0.267085i
$139$	−17.8987			−1.51814			−0.759072	−	0.651007i	$-0.774347\pi$
$139$	−17.8987			−1.51814			−0.759072	+	0.651007i	$0.774347\pi$
$140$	−7.76476	−	1.07717i	−0.656242	−	0.0910378i
$141$	5.52318	+	1.62175i	0.465135	+	0.136576i
$142$	−10.8259	+	2.08651i	−0.908486	+	0.175096i
$143$	−1.25023	−	0.644538i	−0.104549	−	0.0538990i
$144$	0.981929	+	0.189251i	0.0818274	+	0.0157709i
$145$	−8.45548	−	6.64946i	−0.702189	−	0.552208i
$146$	−2.65194	+	0.778681i	−0.219476	+	0.0644441i
$147$	3.55989	+	6.02721i	0.293614	+	0.497116i
$148$	0.860754	+	5.98668i	0.0707536	+	0.492102i
$149$	9.90240	+	0.945564i	0.811236	+	0.0774637i	0.492425	−	0.870355i	$-0.336110\pi$
$149$	9.90240	+	0.945564i	0.811236	+	0.0774637i	0.318811	+	0.947818i	$0.396717\pi$
$150$	2.19194	−	3.07815i	0.178971	−	0.251330i
$151$	18.5813	−	14.6125i	1.51213	−	1.18915i	0.586944	−	0.809628i	$-0.300331\pi$
$151$	18.5813	−	14.6125i	1.51213	−	1.18915i	0.925183	−	0.379521i	$-0.123911\pi$
$152$	−3.15044	+	1.62417i	−0.255535	+	0.131737i
$153$	−4.50616	+	1.32313i	−0.364301	+	0.106968i
$154$	−1.43811	+	0.214045i	−0.115886	+	0.0172482i
$155$	16.8748	−	19.4746i	1.35542	−	1.56424i
$156$	−0.121790	−	2.55668i	−0.00975097	−	0.204698i
$157$	−1.43400	+	4.14328i	−0.114446	+	0.330670i	−0.987648	−	0.156688i	$-0.949918\pi$
$157$	−1.43400	+	4.14328i	−0.114446	+	0.330670i	0.873202	+	0.487358i	$0.162039\pi$
$158$	−3.42841	−	14.1321i	−0.272750	−	1.12429i
$159$	0.282933	+	0.397324i	0.0224381	+	0.0315099i
$160$	2.96291			0.234239
$161$	−12.6885	+	0.0521151i	−0.999992	+	0.00410724i
$162$	1.00000			0.0785674
$163$	−7.21543	−	10.1327i	−0.565156	−	0.793651i	0.428803	−	0.903398i	$-0.358935\pi$
$163$	−7.21543	−	10.1327i	−0.565156	−	0.793651i	−0.993960	+	0.109747i	$0.964996\pi$
$164$	−1.80421	−	7.43705i	−0.140885	−	0.580736i
$165$	0.532545	−	1.53869i	0.0414586	−	0.119787i
$166$	0.0484506	+	1.01710i	0.00376050	+	0.0789426i
$167$	10.0798	−	11.6327i	0.780000	−	0.900168i	−0.217109	−	0.976147i	$-0.569663\pi$
$167$	10.0798	−	11.6327i	0.780000	−	0.900168i	0.997109	+	0.0759794i	$0.0242083\pi$
$168$	−1.64578	−	2.07157i	−0.126974	−	0.159825i
$169$	6.18735	−	1.81677i	0.475950	−	0.139751i
$170$	−12.3681	+	6.37622i	−0.948593	+	0.489033i
$171$	−2.78613	+	2.19104i	−0.213061	+	0.167553i
$172$	0.958561	−	1.34611i	0.0730896	−	0.102640i
$173$	11.1957	+	1.06906i	0.851192	+	0.0812790i	0.511527	−	0.859267i	$-0.329080\pi$
$173$	11.1957	+	1.06906i	0.851192	+	0.0812790i	0.339665	+	0.940546i	$0.389686\pi$
$174$	−0.516676	−	3.59356i	−0.0391691	−	0.272427i
$175$	−9.70423	+	2.40518i	−0.733571	+	0.181815i
$176$	0.527280	−	0.154823i	0.0397453	−	0.0116703i
$177$	5.57999	+	4.38815i	0.419418	+	0.329834i
$178$	−4.43024	−	0.853858i	−0.332060	−	0.0639994i
$179$	18.7355	+	9.65880i	1.40035	+	0.721933i	0.982444	−	0.186555i	$-0.0597324\pi$
$179$	18.7355	+	9.65880i	1.40035	+	0.721933i	0.417910	+	0.908488i	$0.362763\pi$
$180$	2.90937	−	0.560734i	0.216851	−	0.0417947i
$181$	−23.8343	−	6.99840i	−1.77159	−	0.520187i	−0.777516	−	0.628863i	$-0.783521\pi$
$181$	−23.8343	−	6.99840i	−1.77159	−	0.520187i	−0.994077	+	0.108677i	$0.965339\pi$
$182$	−4.15976	+	5.34383i	−0.308342	+	0.396111i
$183$	9.22411			0.681866
$184$	4.74759	−	0.678500i	0.349997	−	0.0500197i
$185$	8.96019	+	15.5195i	0.658767	+	1.14102i
$186$	8.65768	−	0.826708i	0.634812	−	0.0606172i
$187$	−1.86786	+	1.78100i	−0.136591	+	0.130239i
$188$	3.76961	+	4.35036i	0.274927	+	0.317282i
$189$	−2.00808	−	1.72267i	−0.146067	−	0.125306i
$190$	−6.87729	+	7.93682i	−0.498931	+	0.575797i
$191$	−2.82124	−	2.21865i	−0.204138	−	0.160536i	0.510857	−	0.859666i	$-0.329328\pi$
$191$	−2.82124	−	2.21865i	−0.204138	−	0.160536i	−0.714994	+	0.699130i	$0.753571\pi$
$192$	0.723734	+	0.690079i	0.0522310	+	0.0498022i
$193$	0.403016	−	8.46035i	0.0290097	−	0.608989i	−0.936820	−	0.349812i	$-0.886245\pi$
$193$	0.403016	−	8.46035i	0.0290097	−	0.608989i	0.965830	−	0.259178i	$-0.0834515\pi$
$194$	−2.42297	−	0.970011i	−0.173959	−	0.0696427i
$195$	−3.15042	−	6.89847i	−0.225607	−	0.494009i
$196$	−0.263786	+	6.99503i	−0.0188419	+	0.499645i
$197$	1.28220	+	8.91792i	0.0913532	+	0.635376i	0.983131	+	0.182902i	$0.0585492\pi$
$197$	1.28220	+	8.91792i	0.0913532	+	0.635376i	−0.891778	+	0.452473i	$0.850542\pi$
$198$	0.488451	−	0.251814i	0.0347127	−	0.0178956i
$199$	5.79786	+	5.52825i	0.410999	+	0.391887i	0.867176	−	0.498002i	$-0.165933\pi$
$199$	5.79786	+	5.52825i	0.410999	+	0.391887i	−0.456176	+	0.889889i	$0.650781\pi$
$200$	3.50815	−	1.40445i	0.248064	−	0.0993097i
$201$	1.21535	+	3.51152i	0.0857241	+	0.247684i
$202$	8.28220	−	5.32265i	0.582734	−	0.374500i
$203$	−5.15300	+	8.10623i	−0.361670	+	0.568946i
$204$	−4.50616	−	1.32313i	−0.315494	−	0.0926374i
$205$	−13.1525	−	18.4701i	−0.918609	−	1.29001i
$206$	6.87990	+	11.9163i	0.479345	+	0.830251i
$207$	4.53339	−	1.56473i	0.315092	−	0.108756i
$208$	1.27979	−	2.21666i	0.0887374	−	0.153698i
$209$	−0.809156	+	1.77180i	−0.0559705	+	0.122558i
$210$	−6.80821	−	3.88588i	−0.469811	−	0.268151i
$211$	−1.42941	−	1.64962i	−0.0984045	−	0.113565i	0.704411	−	0.709792i	$-0.251211\pi$
$211$	−1.42941	−	1.64962i	−0.0984045	−	0.113565i	−0.802816	+	0.596227i	$0.796666\pi$
$212$	0.0232089	+	0.487216i	0.00159400	+	0.0334621i
$213$	−10.8259	−	2.08651i	−0.741775	−	0.142965i
$214$	−1.95765	+	0.783725i	−0.133822	+	0.0535743i
$215$	1.15435	−	4.75828i	0.0787257	−	0.324512i
$216$	0.841254	+	0.540641i	0.0572401	+	0.0367859i
$217$	−18.8095	−	13.2542i	−1.27687	−	0.899757i
$218$	4.67902	+	10.2456i	0.316903	+	0.693921i
$219$	−2.75139	−	0.262726i	−0.185921	−	0.0177533i
$220$	1.27988	−	1.00651i	0.0862897	−	0.0678589i
$221$	−0.571972	+	12.0072i	−0.0384750	+	0.807690i
$222$	−1.42593	+	5.87775i	−0.0957019	+	0.394489i
$223$	2.65429	−	18.4610i	0.177745	−	1.23624i	−0.684222	−	0.729274i	$-0.739858\pi$
$223$	2.65429	−	18.4610i	0.177745	−	1.23624i	0.861966	−	0.506966i	$-0.169233\pi$
$224$	−0.264538	−	2.63249i	−0.0176752	−	0.175891i
$225$	3.17896	−	2.04299i	0.211930	−	0.136199i
$226$	2.14915	−	0.414214i	0.142959	−	0.0275531i
$227$	−3.59207	−	14.8067i	−0.238414	−	0.982757i	−0.957637	−	0.287978i	$-0.907017\pi$
$227$	−3.59207	−	14.8067i	−0.238414	−	0.982757i	0.719223	−	0.694779i	$-0.244498\pi$
$228$	−3.52841	+	0.336922i	−0.233675	+	0.0223132i
$229$	8.91326	−	15.4382i	0.589005	−	1.02019i	−0.405358	−	0.914158i	$-0.632853\pi$
$229$	8.91326	−	15.4382i	0.589005	−	1.02019i	0.994363	−	0.106028i	$-0.0338135\pi$
$230$	12.3119	−	7.09439i	0.811822	−	0.467790i
$231$	−1.41464	−	0.335778i	−0.0930767	−	0.0220926i
$232$	1.50817	−	3.30243i	0.0990162	−	0.216815i
$233$	−12.2222	+	11.6539i	−0.800705	+	0.763471i	−0.975233	−	0.221181i	$-0.929009\pi$
$233$	−12.2222	+	11.6539i	−0.800705	+	0.763471i	0.174527	+	0.984652i	$0.444160\pi$
$234$	0.837156	−	2.41880i	0.0547266	−	0.158122i
$235$	15.1596	+	7.81530i	0.988901	+	0.509814i
$236$	2.32177	+	6.70832i	0.151134	+	0.436674i
$237$	2.06954	−	14.3940i	0.134431	−	0.934990i
$238$	6.76942	+	10.4196i	0.438797	+	0.675401i
$239$	2.69179	+	1.72991i	0.174117	+	0.111898i	0.624797	−	0.780787i	$-0.285182\pi$
$239$	2.69179	+	1.72991i	0.174117	+	0.111898i	−0.450679	+	0.892686i	$0.648818\pi$
$240$	2.75067	+	1.10120i	0.177555	+	0.0710823i
$241$	−10.9955	+	15.4410i	−0.708282	+	0.994643i	0.290999	+	0.956723i	$0.406012\pi$
$241$	−10.9955	+	15.4410i	−0.708282	+	0.994643i	−0.999281	+	0.0379194i	$0.987927\pi$
$242$	−6.20545	+	8.71434i	−0.398902	+	0.560179i
$243$	0.928368	+	0.371662i	0.0595548	+	0.0238422i
$244$	7.75981	+	4.98693i	0.496771	+	0.319255i
$245$	6.97735	+	19.5315i	0.445767	+	1.24782i
$246$	1.08910	−	7.57488i	0.0694386	−	0.482956i
$247$	2.96727	+	8.57335i	0.188803	+	0.545509i
$248$	7.73025	+	3.98522i	0.490872	+	0.253062i
$249$	−0.333039	+	0.962254i	−0.0211055	+	0.0609804i
$250$	−2.61862	+	2.49685i	−0.165616	+	0.157915i
$251$	6.41622	−	14.0496i	0.404988	−	0.886800i	−0.591752	−	0.806120i	$-0.701564\pi$
$251$	6.41622	−	14.0496i	0.404988	−	0.886800i	0.996740	−	0.0806801i	$-0.0257092\pi$
$252$	−0.757960	−	2.53486i	−0.0477470	−	0.159681i
$253$	1.82032	−	1.90586i	0.114443	−	0.119821i
$254$	−6.11880	+	10.5981i	−0.383928	+	0.664982i
$255$	−13.8520	+	1.32270i	−0.867445	+	0.0828309i
$256$	0.235759	+	0.971812i	0.0147349	+	0.0607382i
$257$	14.6589	−	2.82528i	0.914399	−	0.176236i	0.289714	−	0.957113i	$-0.406440\pi$
$257$	14.6589	−	2.82528i	0.914399	−	0.176236i	0.624685	+	0.780877i	$0.285228\pi$
$258$	1.39020	−	0.893425i	0.0865498	−	0.0556222i
$259$	12.9888	−	9.34661i	0.807086	−	0.580770i
$260$	1.07929	−	7.50661i	0.0669345	−	0.465540i
$261$	0.855926	−	3.52817i	0.0529805	−	0.218388i
$262$	−0.465440	+	9.77079i	−0.0287550	+	0.603641i
$263$	9.86774	−	7.76007i	0.608471	−	0.478507i	−0.265746	−	0.964043i	$-0.585618\pi$
$263$	9.86774	−	7.76007i	0.608471	−	0.478507i	0.874216	+	0.485536i	$0.161376\pi$
$264$	0.547052	+	0.0522372i	0.0336687	+	0.00321497i
$265$	0.600363	+	1.31461i	0.0368800	+	0.0807560i
$266$	7.66575	+	5.40173i	0.470017	+	0.331201i
$267$	−3.79554	−	2.43925i	−0.232283	−	0.149280i
$268$	−0.876055	+	3.61115i	−0.0535135	+	0.220586i
$269$	−16.1815	+	6.47808i	−0.986602	+	0.394976i	−0.808152	−	0.588973i	$-0.799532\pi$
$269$	−16.1815	+	6.47808i	−0.986602	+	0.394976i	−0.178449	+	0.983949i	$0.557108\pi$
$270$	2.90937	+	0.560734i	0.177058	+	0.0341252i
$271$	0.507937	+	10.6629i	0.0308550	+	0.647726i	0.960334	+	0.278851i	$0.0899537\pi$
$271$	0.507937	+	10.6629i	0.0308550	+	0.647726i	−0.929479	+	0.368874i	$0.879743\pi$
$272$	−3.07548	−	3.54930i	−0.186479	−	0.215208i
$273$	−5.84789	+	3.41501i	−0.353930	+	0.206686i
$274$	−5.04562	+	11.0484i	−0.304817	+	0.667457i
$275$	1.03831	−	1.79841i	0.0626125	−	0.108448i
$276$	4.65969	+	1.13460i	0.280480	+	0.0682952i
$277$	−8.78653	−	15.2187i	−0.527931	−	0.914404i	−0.999470	−	0.0325586i	$-0.989634\pi$
$277$	−8.78653	−	15.2187i	−0.527931	−	0.914404i	0.471538	−	0.881846i	$-0.343699\pi$
$278$	−10.3822	−	14.5798i	−0.622685	−	0.874439i
$279$	8.34477	+	2.45024i	0.499588	+	0.146692i
$280$	−3.62656	−	6.94981i	−0.216729	−	0.415331i
$281$	−18.4411	+	11.8514i	−1.10010	+	0.706994i	−0.959115	−	0.283018i	$-0.908664\pi$
$281$	−18.4411	+	11.8514i	−1.10010	+	0.706994i	−0.140989	+	0.990011i	$0.545028\pi$
$282$	1.88272	+	5.43975i	0.112114	+	0.323933i
$283$	25.7024	−	10.2897i	1.52785	−	0.611659i	0.552734	−	0.833357i	$-0.313584\pi$
$283$	25.7024	−	10.2897i	1.52785	−	0.611659i	0.975115	+	0.221699i	$0.0711602\pi$
$284$	−7.97923	−	7.60818i	−0.473480	−	0.451463i
$285$	−9.33447	+	4.81226i	−0.552927	+	0.285053i
$286$	−0.200179	−	1.39228i	−0.0118368	−	0.0823269i
$287$	−15.2360	+	13.3348i	−0.899355	+	0.787129i
$288$	0.415415	+	0.909632i	0.0244786	+	0.0536006i
$289$	4.69393	+	1.87916i	0.276113	+	0.110539i
$290$	0.511833	−	10.7447i	0.0300559	−	0.630950i
$291$	−1.88889	−	1.80105i	−0.110729	−	0.105580i
$292$	−2.17257	−	1.70853i	−0.127140	−	0.0999842i
$293$	−1.46183	+	1.68704i	−0.0854008	+	0.0985577i	−0.796842	−	0.604188i	$-0.793497\pi$
$293$	−1.46183	+	1.68704i	−0.0854008	+	0.0985577i	0.711441	+	0.702746i	$0.248043\pi$
$294$	−2.84468	+	6.39592i	−0.165905	+	0.373018i
$295$	13.7736	+	15.8956i	0.801932	+	0.925479i
$296$	−4.37732	+	4.17376i	−0.254426	+	0.242595i
$297$	0.547052	−	0.0522372i	0.0317432	−	0.00303111i
$298$	4.97372	+	8.61474i	0.288120	+	0.499038i
$299$	0.0103892	−	12.2753i	0.000600821	−	0.709899i
$300$	3.77883			0.218171
$301$	−4.33071	−	0.600781i	−0.249618	−	0.0346284i
$302$	22.6812	+	6.65981i	1.30516	+	0.383229i
$303$	9.66716	−	1.86319i	0.555364	−	0.107038i
$304$	−3.15044	−	1.62417i	−0.180690	−	0.0931523i
$305$	26.8363	+	5.17227i	1.53664	+	0.296163i
$306$	−3.69161	−	2.90312i	−0.211036	−	0.165960i
$307$	22.2572	−	6.53531i	1.27029	−	0.372990i	0.423973	−	0.905675i	$-0.360635\pi$
$307$	22.2572	−	6.53531i	1.27029	−	0.372990i	0.846313	+	0.532685i	$0.178817\pi$
$308$	−1.00854	−	1.04729i	−0.0574668	−	0.0596748i
$309$	1.95822	+	13.6197i	0.111399	+	0.774800i
$310$	25.6519	+	2.44946i	1.45693	+	0.139120i
$311$	15.5096	−	21.7802i	0.879468	−	1.23504i	−0.0914945	−	0.995806i	$-0.529164\pi$
$311$	15.5096	−	21.7802i	0.879468	−	1.23504i	0.970962	−	0.239234i	$-0.0768962\pi$
$312$	2.01196	−	1.58223i	0.113905	−	0.0895759i
$313$	−10.3561	+	5.33894i	−0.585361	+	0.301775i	−0.725352	−	0.688378i	$-0.758323\pi$
$313$	−10.3561	+	5.33894i	−0.585361	+	0.301775i	0.139991	+	0.990153i	$0.455293\pi$
$314$	−4.20682	+	1.23523i	−0.237405	+	0.0697083i
$315$	−4.87629	−	6.13789i	−0.274748	−	0.345831i
$316$	9.52299	−	10.9901i	0.535710	−	0.618243i
$317$	0.0729609	+	1.53164i	0.00409789	+	0.0860253i	0.999990	−	0.00452511i	$-0.00144039\pi$
$317$	0.0729609	+	1.53164i	0.00409789	+	0.0860253i	−0.995892	+	0.0905504i	$0.971137\pi$
$318$	−0.159533	+	0.460941i	−0.00894618	+	0.0258483i
$319$	−0.470366	−	1.93887i	−0.0263354	−	0.108556i
$320$	1.71866	+	2.41351i	0.0960758	+	0.134920i
$321$	−2.10870			−0.117696
$322$	−7.40249	−	10.3055i	−0.412524	−	0.574303i
$323$	16.6462			0.926218
$324$	0.580057	+	0.814576i	0.0322254	+	0.0452542i
$325$	−2.28031	−	9.39957i	−0.126489	−	0.521395i
$326$	4.06846	−	11.7550i	0.225331	−	0.651051i
$327$	0.535938	+	11.2507i	0.0296374	+	0.622167i
$328$	5.01150	−	5.78358i	0.276714	−	0.319345i
$329$	5.59026	−	14.1668i	0.308201	−	0.781040i
$330$	1.56228	−	0.458728i	0.0860009	−	0.0252521i
$331$	−20.8420	+	10.7448i	−1.14558	+	0.590587i	−0.923180	−	0.384369i	$-0.874419\pi$
$331$	−20.8420	+	10.7448i	−1.14558	+	0.590587i	−0.222399	+	0.974956i	$0.571389\pi$
$332$	−0.800404	+	0.629445i	−0.0439279	+	0.0345453i
$333$	−3.50832	+	4.92675i	−0.192255	+	0.269984i
$334$	15.3226	+	1.46313i	0.838416	+	0.0800590i
$335$	1.56686	+	10.8978i	0.0856070	+	0.595410i
$336$	0.732810	−	2.54224i	0.0399781	−	0.138691i
$337$	−28.4201	+	8.34491i	−1.54814	+	0.454576i	−0.940545	−	0.339668i	$-0.889685\pi$
$337$	−28.4201	+	8.34491i	−1.54814	+	0.454576i	−0.607599	+	0.794244i	$0.707867\pi$
$338$	5.06891	+	3.98624i	0.275712	+	0.216823i
$339$	2.14915	+	0.414214i	0.116726	+	0.0224970i
$340$	−12.3681	−	6.37622i	−0.670756	−	0.345799i
$341$	4.69302	−	0.904505i	0.254141	−	0.0489817i
$342$	−3.40088	−	0.998590i	−0.183899	−	0.0539975i
$343$	16.7304	−	7.94309i	0.903358	−	0.428887i
$344$	1.65253			0.0890984
$345$	14.0667	−	2.01033i	0.757325	−	0.108233i
$346$	5.62330	+	9.73985i	0.302311	+	0.523617i
$347$	−16.3558	+	1.56179i	−0.878025	+	0.0838412i	−0.524325	−	0.851518i	$-0.675682\pi$
$347$	−16.3558	+	1.56179i	−0.878025	+	0.0838412i	−0.353699	+	0.935359i	$0.615076\pi$
$348$	2.62753	−	2.50534i	0.140850	−	0.134300i
$349$	1.34744	+	1.55503i	0.0721271	+	0.0832391i	0.790666	−	0.612247i	$-0.209734\pi$
$349$	1.34744	+	1.55503i	0.0721271	+	0.0832391i	−0.718539	+	0.695486i	$0.755189\pi$
$350$	−7.58821	−	6.50969i	−0.405607	−	0.347958i
$351$	1.67617	−	1.93440i	0.0894672	−	0.103251i
$352$	0.431968	+	0.339703i	0.0230240	+	0.0181063i
$353$	−15.1673	−	14.4620i	−0.807275	−	0.769735i	0.169151	−	0.985590i	$-0.445898\pi$
$353$	−15.1673	−	14.4620i	−0.807275	−	0.769735i	−0.976425	+	0.215855i	$0.930746\pi$
$354$	−0.337772	+	7.09070i	−0.0179524	+	0.376867i
$355$	−30.3264	−	12.1409i	−1.60956	−	0.644370i
$356$	−1.87426	−	4.10405i	−0.0993354	−	0.217514i
$357$	2.41195	+	12.1891i	0.127654	+	0.645118i
$358$	2.99981	+	20.8641i	0.158545	+	1.10270i
$359$	−27.6093	+	14.2336i	−1.45716	+	0.751219i	−0.991048	−	0.133506i	$-0.957377\pi$
$359$	−27.6093	+	14.2336i	−1.45716	+	0.751219i	−0.466114	+	0.884725i	$0.654346\pi$
$360$	2.14436	+	2.04464i	0.113018	+	0.107762i
$361$	−5.97572	+	2.39232i	−0.314512	+	0.125911i
$362$	−8.12455	−	23.4744i	−0.427017	−	1.23378i
$363$	−8.99973	+	5.78378i	−0.472364	+	0.303570i
$364$	−6.76585	−	0.288713i	−0.354627	−	0.0151327i
$365$	−7.85747	−	2.30716i	−0.411279	−	0.120762i
$366$	5.35051	+	7.51373i	0.279675	+	0.392749i
$367$	2.97726	+	5.15677i	0.155412	+	0.269181i	0.933209	−	0.359334i	$-0.116996\pi$
$367$	2.97726	+	5.15677i	0.155412	+	0.269181i	−0.777797	+	0.628515i	$0.783663\pi$
$368$	3.30656	+	3.47371i	0.172367	+	0.181079i
$369$	3.82638	−	6.62749i	0.199194	−	0.345013i
$370$	−7.44440	+	16.3010i	−0.387016	+	0.847446i
$371$	1.11441	−	0.650785i	0.0578571	−	0.0337871i
$372$	5.69536	+	6.57280i	0.295291	+	0.340784i
$373$	−0.639199	−	13.4184i	−0.0330965	−	0.694780i	−0.953061	−	0.302779i	$-0.902086\pi$
$373$	−0.639199	−	13.4184i	−0.0330965	−	0.694780i	0.919964	−	0.392002i	$-0.128217\pi$
$374$	−2.53422	−	0.488431i	−0.131041	−	0.0252561i
$375$	−3.35903	+	1.34475i	−0.173459	+	0.0694427i
$376$	−1.35711	+	5.59409i	−0.0699876	+	0.288493i
$377$	−7.81742	−	5.02395i	−0.402617	−	0.258747i
$378$	0.238445	−	2.63498i	0.0122643	−	0.135529i
$379$	10.6165	+	23.2468i	0.545331	+	1.19411i	0.958928	+	0.283649i	$0.0915449\pi$
$379$	10.6165	+	23.2468i	0.545331	+	1.19411i	−0.413597	+	0.910460i	$0.635728\pi$
$380$	−10.4544	−	0.998270i	−0.536297	−	0.0512102i
$381$	−9.61940	+	7.56478i	−0.492817	+	0.387555i
$382$	0.170777	−	3.58506i	0.00873773	−	0.183427i
$383$	−5.15147	+	21.2347i	−0.263228	+	1.08504i	0.674667	+	0.738122i	$0.264287\pi$
$383$	−5.15147	+	21.2347i	−0.263228	+	1.08504i	−0.937895	+	0.346918i	$0.887228\pi$
$384$	−0.142315	+	0.989821i	−0.00726247	+	0.0505116i
$385$	−3.92743	−	1.77014i	−0.200161	−	0.0902147i
$386$	7.12537	−	4.57920i	0.362672	−	0.233075i
$387$	1.62267	−	0.312743i	0.0824847	−	0.0158976i
$388$	−0.615313	−	2.53636i	−0.0312378	−	0.128764i
$389$	−23.7525	+	2.26809i	−1.20430	+	0.114997i	−0.677843	−	0.735206i	$-0.737085\pi$
$389$	−23.7525	+	2.26809i	−1.20430	+	0.114997i	−0.526455	+	0.850203i	$0.676479\pi$
$390$	3.79190	−	6.56776i	0.192010	−	0.332572i
$391$	−21.2781	−	7.38460i	−1.07608	−	0.373455i
$392$	−5.85099	+	3.84264i	−0.295520	+	0.194083i
$393$	−4.06353	+	8.89790i	−0.204978	+	0.448840i
$394$	−6.52057	+	6.21735i	−0.328502	+	0.313226i
$395$	14.0923	−	40.7169i	0.709059	−	2.04869i
$396$	0.488451	+	0.251814i	0.0245456	+	0.0126541i
$397$	−3.87361	−	11.1921i	−0.194411	−	0.561713i	0.805095	−	0.593146i	$-0.202114\pi$
$397$	−3.87361	−	11.1921i	−0.194411	−	0.561713i	−0.999506	+	0.0314326i	$0.989993\pi$
$398$	−1.14009	+	7.92950i	−0.0571475	+	0.397470i
$399$	5.10902	+	7.86386i	0.255771	+	0.393686i
$400$	3.17896	+	2.04299i	0.158948	+	0.102150i
$401$	18.9786	+	7.59787i	0.947744	+	0.379419i	0.793470	−	0.608609i	$-0.208272\pi$
$401$	18.9786	+	7.59787i	0.947744	+	0.379419i	0.154273	+	0.988028i	$0.450696\pi$
$402$	−2.15543	+	3.02688i	−0.107503	+	0.150967i
$403$	12.9125	−	18.1331i	0.643219	−	0.903275i
$404$	9.13985	+	3.65904i	0.454725	+	0.182044i
$405$	2.49256	+	1.60187i	0.123856	+	0.0795976i
$406$	−9.59217	+	0.504567i	−0.476052	+	0.0250412i
$407$	−0.473019	+	3.28992i	−0.0234467	+	0.163075i
$408$	−1.53604	−	4.43810i	−0.0760453	−	0.219718i
$409$	−24.8051	−	12.7879i	−1.22653	−	0.632322i	−0.281583	−	0.959537i	$-0.590859\pi$
$409$	−24.8051	−	12.7879i	−1.22653	−	0.632322i	−0.944950	+	0.327215i	$0.893890\pi$
$410$	7.41609	−	21.4274i	0.366255	−	1.05822i
$411$	−8.79046	+	8.38169i	−0.433602	+	0.413438i
$412$	−5.71603	+	12.5164i	−0.281609	+	0.616637i
$413$	12.8932	−	13.6568i	0.634434	−	0.672010i
$414$	3.90421	+	2.78516i	0.191882	+	0.136883i
$415$	−1.50850	+	2.61280i	−0.0740495	+	0.128257i
$416$	2.54799	−	0.243303i	0.124925	−	0.0119289i
$417$	−4.21977	−	17.3941i	−0.206643	−	0.851794i
$418$	−1.91262	+	0.368628i	−0.0935495	+	0.0180302i
$419$	−9.81142	+	6.30542i	−0.479319	+	0.308040i	−0.757897	−	0.652374i	$-0.773773\pi$
$419$	−9.81142	+	6.30542i	−0.479319	+	0.308040i	0.278578	+	0.960414i	$0.410137\pi$
$420$	−0.783803	−	7.79984i	−0.0382457	−	0.380593i
$421$	−2.40538	+	16.7298i	−0.117231	+	0.815358i	0.843351	+	0.537362i	$0.180579\pi$
$421$	−2.40538	+	16.7298i	−0.117231	+	0.815358i	−0.960582	+	0.277996i	$0.910330\pi$
$422$	0.514607	−	2.12124i	0.0250507	−	0.103260i
$423$	−0.273898	+	5.74983i	−0.0133174	+	0.279566i
$424$	−0.383412	+	0.301518i	−0.0186201	+	0.0146430i
$425$	−17.6665	−	1.68695i	−0.856952	−	0.0818290i
$426$	−4.57999	−	10.0288i	−0.221901	−	0.485896i
$427$	2.19944	−	24.3054i	0.106438	−	1.17622i
$428$	−1.77395	−	1.14005i	−0.0857472	−	0.0551064i
$429$	0.331617	−	1.36694i	0.0160106	−	0.0659966i
$430$	4.54556	−	1.81977i	0.219207	−	0.0877570i
$431$	−26.8347	−	5.17197i	−1.29258	−	0.249125i	−0.503813	−	0.863813i	$-0.668070\pi$
$431$	−26.8347	−	5.17197i	−1.29258	−	0.249125i	−0.788770	+	0.614688i	$0.789282\pi$
$432$	0.0475819	+	0.998867i	0.00228929	+	0.0480580i
$433$	5.83018	+	6.72838i	0.280180	+	0.323346i	0.878344	−	0.478028i	$-0.158648\pi$
$433$	5.83018	+	6.72838i	0.280180	+	0.323346i	−0.598164	+	0.801374i	$0.704103\pi$
$434$	−0.113983	−	23.0100i	−0.00547137	−	1.10451i
$435$	4.46857	−	9.78480i	0.214252	−	0.469145i
$436$	−5.63174	+	9.75446i	−0.269712	+	0.467154i
$437$	−16.9801	+	0.794457i	−0.812266	+	0.0380040i
$438$	−1.38195	−	2.39361i	−0.0660322	−	0.114371i
$439$	0.159967	+	0.224642i	0.00763480	+	0.0107216i	0.818376	−	0.574684i	$-0.194875\pi$
$439$	0.159967	+	0.224642i	0.00763480	+	0.0107216i	−0.810741	+	0.585405i	$0.800935\pi$
$440$	1.56228	+	0.458728i	0.0744790	+	0.0218690i
$441$	−5.01803	+	4.88051i	−0.238954	+	0.232405i
$442$	−10.1125	+	6.49893i	−0.481004	+	0.309122i
$443$	−7.38682	−	21.3428i	−0.350959	−	1.01403i	−0.972952	−	0.231006i	$-0.925798\pi$
$443$	−7.38682	−	21.3428i	−0.350959	−	1.01403i	0.621994	−	0.783022i	$-0.286323\pi$
$444$	−5.61499	+	2.24790i	−0.266476	+	0.106681i
$445$	−9.67485	−	9.22496i	−0.458632	−	0.437305i
$446$	16.5775	−	8.54631i	0.784969	−	0.404680i
$447$	1.41567	+	9.84619i	0.0669588	+	0.465709i
$448$	1.99092	−	1.74248i	0.0940620	−	0.0823245i
$449$	2.13385	+	4.67248i	0.100703	+	0.220508i	0.953277	−	0.302098i	$-0.0976871\pi$
$449$	2.13385	+	4.67248i	0.100703	+	0.220508i	−0.852574	+	0.522606i	$0.824960\pi$
$450$	3.50815	+	1.40445i	0.165376	+	0.0662064i
$451$	0.200106	−	4.20074i	0.00942263	−	0.197805i
$452$	1.58404	+	1.51038i	0.0745068	+	0.0710421i
$453$	18.5813	+	14.6125i	0.873027	+	0.686556i
$454$	9.97760	−	11.5148i	0.468272	−	0.540414i
$455$	−18.9286	+	6.65641i	−0.887384	+	0.312057i
$456$	−2.32113	−	2.67872i	−0.108697	−	0.125443i
$457$	−11.7203	+	11.1753i	−0.548253	+	0.522758i	−0.912789	−	0.408431i	$-0.866076\pi$
$457$	−11.7203	+	11.1753i	−0.548253	+	0.522758i	0.364536	+	0.931189i	$0.381228\pi$
$458$	17.7458	−	1.69452i	0.829207	−	0.0791797i
$459$	−2.34820	−	4.06720i	−0.109604	−	0.189840i
$460$	12.9205	+	5.91382i	0.602422	+	0.275734i
$461$	−7.42439			−0.345788			−0.172894	−	0.984940i	$-0.555312\pi$
$461$	−7.42439			−0.345788			−0.172894	+	0.984940i	$0.555312\pi$
$462$	−0.547057	−	1.34711i	−0.0254514	−	0.0626730i
$463$	−5.03494	−	1.47839i	−0.233993	−	0.0687067i	0.162634	−	0.986687i	$-0.448001\pi$
$463$	−5.03494	−	1.47839i	−0.233993	−	0.0687067i	−0.396627	+	0.917980i	$0.629819\pi$
$464$	3.56490	−	0.687079i	0.165497	−	0.0318968i
$465$	22.9040	+	11.8079i	1.06215	+	0.547576i
$466$	−16.5826	−	3.19603i	−0.768173	−	0.148053i
$467$	−8.89069	−	6.99171i	−0.411412	−	0.323538i	0.390911	−	0.920429i	$-0.372160\pi$
$467$	−8.89069	−	6.99171i	−0.411412	−	0.323538i	−0.802323	+	0.596891i	$0.796403\pi$
$468$	2.45590	−	0.721116i	0.113524	−	0.0333336i
$469$	9.54260	−	2.36512i	0.440636	−	0.109211i
$470$	2.42726	+	16.8819i	0.111961	+	0.778706i
$471$	−4.36457	−	0.416765i	−0.201109	−	0.0192035i
$472$	−4.11767	+	5.78246i	−0.189531	+	0.266159i
$473$	0.713840	−	0.561370i	0.0328224	−	0.0258118i
$474$	12.9255	−	6.66354i	0.593686	−	0.306066i
$475$	−12.8514	+	3.77350i	−0.589662	+	0.173140i
$476$	−4.56089	+	11.5582i	−0.209048	+	0.529767i
$477$	−0.319420	+	0.368631i	−0.0146252	+	0.0168784i
$478$	0.152250	+	3.19611i	0.00696374	+	0.146187i
$479$	8.85640	−	25.5889i	0.404659	−	1.16919i	−0.540151	−	0.841568i	$-0.681633\pi$
$479$	8.85640	−	25.5889i	0.404659	−	1.16919i	0.944810	−	0.327618i	$-0.106246\pi$
$480$	0.698532	+	2.87939i	0.0318835	+	0.131426i
$481$	8.97983	+	12.6104i	0.409445	+	0.574985i
$482$	−18.9559			−0.863417
$483$	−3.04207	−	12.3185i	−0.138419	−	0.560512i
$484$	−10.6980			−0.486273
$485$	−4.48556	−	6.29909i	−0.203679	−	0.286027i
$486$	0.235759	+	0.971812i	0.0106942	+	0.0440823i
$487$	−7.15943	+	20.6858i	−0.324425	+	0.937364i	0.658375	+	0.752690i	$0.271244\pi$
$487$	−7.15943	+	20.6858i	−0.324425	+	0.937364i	−0.982800	+	0.184674i	$0.940877\pi$
$488$	0.438901	+	9.21366i	0.0198681	+	0.417083i
$489$	8.14593	−	9.40090i	0.368372	−	0.425124i
$490$	−11.8626	+	17.0130i	−0.535899	+	0.768567i
$491$	16.5805	−	4.86848i	0.748269	−	0.219712i	0.114703	−	0.993400i	$-0.463408\pi$
$491$	16.5805	−	4.86848i	0.748269	−	0.219712i	0.633566	+	0.773688i	$0.281590\pi$
$492$	6.80205	−	3.50670i	0.306660	−	0.158094i
$493$	−13.4025	+	10.5398i	−0.603616	+	0.474689i
$494$	−5.26246	+	7.39010i	−0.236769	+	0.332496i
$495$	1.62087	+	0.154774i	0.0728525	+	0.00695657i
$496$	1.23772	+	8.60854i	0.0555753	+	0.386535i
$497$	−8.07930	+	28.0284i	−0.362406	+	1.25725i
$498$	−0.977011	+	0.286876i	−0.0437809	+	0.0128552i
$499$	18.0792	+	14.2176i	0.809335	+	0.636468i	0.934618	−	0.355653i	$-0.115742\pi$
$499$	18.0792	+	14.2176i	0.809335	+	0.636468i	−0.125283	+	0.992121i	$0.539984\pi$
$500$	−3.55282	−	0.684750i	−0.158887	−	0.0306229i
$501$	13.6812	+	7.05317i	0.611232	+	0.315112i
$502$	15.1662	−	2.92305i	0.676901	−	0.130462i
$503$	−19.9559	−	5.85959i	−0.889792	−	0.261266i	−0.195280	−	0.980748i	$-0.562561\pi$
$503$	−19.9559	−	5.85959i	−0.889792	−	0.261266i	−0.694512	+	0.719481i	$0.744380\pi$
$504$	1.62517	−	2.08778i	0.0723910	−	0.0929970i
$505$	29.1701			1.29805
$506$	2.60836	+	0.377279i	0.115956	+	0.0167721i
$507$	3.22428	+	5.58462i	0.143195	+	0.248022i
$508$	−12.1822	+	1.16326i	−0.540497	+	0.0516112i
$509$	31.4152	−	29.9543i	1.39245	−	1.32770i	0.507780	−	0.861487i	$-0.330466\pi$
$509$	31.4152	−	29.9543i	1.39245	−	1.32770i	0.884672	−	0.466214i	$-0.154382\pi$
$510$	−9.11238	−	10.5162i	−0.403503	−	0.465667i
$511$	−1.34833	+	7.18721i	−0.0596467	+	0.317944i
$512$	−0.654861	+	0.755750i	−0.0289410	+	0.0333997i
$513$	−2.78613	−	2.19104i	−0.123011	−	0.0967368i
$514$	10.8044	+	10.3020i	0.476562	+	0.454401i
$515$	−1.93987	+	40.7229i	−0.0854809	+	1.79446i
$516$	1.53416	+	0.614183i	0.0675374	+	0.0270379i
$517$	1.31410	+	2.87748i	0.0577941	+	0.126551i
$518$	15.1478	+	5.15881i	0.665555	+	0.226665i
$519$	1.60056	+	11.1321i	0.0702567	+	0.488646i
$520$	6.74075	−	3.47510i	0.295601	−	0.152393i
$521$	−17.8789	−	17.0475i	−0.783289	−	0.746865i	0.188663	−	0.982042i	$-0.439585\pi$
$521$	−17.8789	−	17.0475i	−0.783289	−	0.746865i	−0.971953	+	0.235177i	$0.924433\pi$
$522$	3.37045	−	1.34933i	0.147521	−	0.0590584i
$523$	3.69853	+	10.6862i	0.161725	+	0.467275i	0.996526	−	0.0832768i	$-0.0265385\pi$
$523$	3.69853	+	10.6862i	0.161725	+	0.467275i	−0.834801	+	0.550552i	$0.814417\pi$
$524$	−8.22903	+	5.28848i	−0.359487	+	0.231028i
$525$	−4.62525	−	8.86364i	−0.201862	−	0.386841i
$526$	12.0450	+	3.53674i	0.525188	+	0.154209i
$527$	−23.6923	−	33.2712i	−1.03205	−	1.44932i
$528$	0.274770	+	0.475916i	0.0119578	+	0.0207116i
$529$	22.0573	+	6.51719i	0.959015	+	0.283356i
$530$	−0.722606	+	1.25159i	−0.0313880	+	0.0543656i
$531$	−2.94892	+	6.45724i	−0.127972	+	0.280220i
$532$	0.0464535	+	9.37764i	0.00201401	+	0.406572i
$533$	−12.8273	−	14.8035i	−0.555613	−	0.641212i
$534$	−0.214679	−	4.50666i	−0.00929006	−	0.195022i
$535$	−6.13498	−	1.18242i	−0.265238	−	0.0511205i
$536$	−3.44971	+	1.38106i	−0.149005	+	0.0596526i
$537$	−4.96948	+	20.4845i	−0.214449	+	0.883971i
$538$	−14.6631	−	9.42338i	−0.632170	−	0.406271i
$539$	−1.22208	+	3.64750i	−0.0526389	+	0.157109i
$540$	1.23084	+	2.69516i	0.0529668	+	0.115981i
$541$	30.1076	+	2.87493i	1.29443	+	0.123603i	0.719437	−	0.694558i	$-0.244400\pi$
$541$	30.1076	+	2.87493i	1.29443	+	0.123603i	0.574990	+	0.818160i	$0.305006\pi$
$542$	−8.39112	+	6.59885i	−0.360429	+	0.283445i
$543$	1.18196	−	24.8124i	0.0507228	−	1.06480i
$544$	1.10722	−	4.56401i	0.0474715	−	0.195680i
$545$	−4.74943	+	33.0330i	−0.203443	+	1.41498i
$546$	−6.17389	−	2.78264i	−0.264218	−	0.119086i
$547$	4.59132	−	2.95066i	0.196310	−	0.126161i	−0.438793	−	0.898588i	$-0.644594\pi$
$547$	4.59132	−	2.95066i	0.196310	−	0.126161i	0.635103	+	0.772427i	$0.280957\pi$
$548$	−11.9265	+	2.29864i	−0.509474	+	0.0981931i
$549$	2.17467	+	8.96409i	0.0928125	+	0.382578i
$550$	2.06722	−	0.197396i	0.0881465	−	0.00841697i
$551$	−6.43410	+	11.1442i	−0.274102	+	0.474759i
$552$	1.77866	+	4.45380i	0.0757049	+	0.189566i
$553$	−37.4345	−	8.88539i	−1.59188	−	0.377845i
$554$	7.30011	−	15.9850i	0.310152	−	0.679138i
$555$	−12.9696	+	12.3665i	−0.550529	+	0.524928i
$556$	5.85408	−	16.9142i	0.248268	−	0.717324i
$557$	−22.0590	−	11.3722i	−0.934672	−	0.481857i	−0.0775603	−	0.996988i	$-0.524713\pi$
$557$	−22.0590	−	11.3722i	−0.934672	−	0.481857i	−0.857112	+	0.515131i	$0.827743\pi$
$558$	2.84453	+	8.21873i	0.120419	+	0.347927i
$559$	0.601960	−	4.18672i	0.0254602	−	0.177080i
$560$	3.55753	−	6.98540i	0.150333	−	0.295187i
$561$	−2.17116	−	1.39532i	−0.0916663	−	0.0589103i
$562$	−20.3507	−	8.14720i	−0.858444	−	0.343669i
$563$	8.19934	−	11.5144i	0.345561	−	0.485272i	−0.604819	−	0.796363i	$-0.706755\pi$
$563$	8.19934	−	11.5144i	0.345561	−	0.485272i	0.950380	+	0.311090i	$0.100694\pi$
$564$	−3.33901	+	4.68898i	−0.140598	+	0.197442i
$565$	6.02039	+	2.41020i	0.253280	+	0.101398i
$566$	23.2906	+	14.9680i	0.978977	+	0.629150i
$567$	1.20069	−	2.35761i	0.0504242	−	0.0990105i
$568$	1.56903	−	10.9129i	0.0658352	−	0.457894i
$569$	−11.4138	−	32.9780i	−0.478492	−	1.38251i	−0.883600	−	0.468242i	$-0.844888\pi$
$569$	−11.4138	−	32.9780i	−0.478492	−	1.38251i	0.405109	−	0.914269i	$-0.367234\pi$
$570$	−9.33447	−	4.81226i	−0.390978	−	0.201563i
$571$	−2.88354	+	8.33144i	−0.120672	+	0.348660i	−0.989118	−	0.147125i	$-0.952998\pi$
$571$	−2.88354	+	8.33144i	−0.120672	+	0.348660i	0.868446	+	0.495784i	$0.165119\pi$
$572$	1.01800	−	0.970660i	0.0425647	−	0.0405853i
$573$	1.49098	−	3.26478i	0.0622864	−	0.136388i
$574$	−19.7000	−	4.67596i	−0.822262	−	0.195171i
$575$	18.1014	+	0.877631i	0.754880	+	0.0365997i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	31.3399	−	2.99259i	1.30470	−	0.124583i	0.580547	−	0.814227i	$-0.302839\pi$
$577$	31.3399	−	2.99259i	1.30470	−	0.124583i	0.724149	+	0.689644i	$0.242233\pi$
$578$	1.19202	+	4.91358i	0.0495816	+	0.204378i
$579$	8.31688	−	1.60295i	0.345638	−	0.0666162i
$580$	9.04926	−	5.81561i	0.375750	−	0.241480i
$581$	2.45611	+	1.10700i	0.101897	+	0.0459260i
$582$	0.371431	−	2.58336i	0.0153963	−	0.107084i
$583$	−0.0631948	+	0.260493i	−0.00261726	+	0.0107885i
$584$	0.131512	−	2.76077i	0.00544199	−	0.114241i
$585$	5.96127	−	4.68799i	0.246468	−	0.193825i
$586$	−2.22216	−	0.212191i	−0.0917966	−	0.00876552i
$587$	11.6634	+	25.5393i	0.481400	+	1.05412i	0.982076	+	0.188484i	$0.0603573\pi$
$587$	11.6634	+	25.5393i	0.481400	+	1.05412i	−0.500677	+	0.865634i	$0.666915\pi$
$588$	−6.86004	+	1.39279i	−0.282903	+	0.0574377i
$589$	−25.9328	−	16.6660i	−1.06854	−	0.686711i
$590$	−4.95870	+	20.4400i	−0.204146	+	0.841503i
$591$	−8.36425	+	3.34854i	−0.344059	+	0.137741i
$592$	−5.93894	−	1.14464i	−0.244089	−	0.0470443i
$593$	1.20220	+	25.2373i	0.0493684	+	1.03637i	0.878628	+	0.477507i	$0.158459\pi$
$593$	1.20220	+	25.2373i	0.0493684	+	1.03637i	−0.829260	+	0.558863i	$0.811238\pi$
$594$	0.359873	+	0.415315i	0.0147657	+	0.0170406i
$595$	0.182369	+	36.8151i	0.00747640	+	1.50927i
$596$	−4.13232	+	9.04851i	−0.169266	+	0.370641i
$597$	−4.00552	+	6.93776i	−0.163935	+	0.283944i
$598$	10.0052	−	7.11191i	0.409143	−	0.290828i
$599$	−12.1220	−	20.9959i	−0.495291	−	0.857869i	0.504694	−	0.863298i	$-0.331605\pi$
$599$	−12.1220	−	20.9959i	−0.495291	−	0.857869i	−0.999985	+	0.00542880i	$0.998272\pi$
$600$	2.19194	+	3.07815i	0.0894855	+	0.125665i
$601$	−21.6074	−	6.34451i	−0.881385	−	0.258798i	−0.190434	−	0.981700i	$-0.560990\pi$
$601$	−21.6074	−	6.34451i	−0.881385	−	0.258798i	−0.690951	+	0.722902i	$0.742808\pi$
$602$	−2.02268	−	3.87618i	−0.0824381	−	0.157981i
$603$	−3.12601	+	2.00896i	−0.127301	+	0.0818113i
$604$	7.73148	+	22.3386i	0.314590	+	0.908947i
$605$	−29.4267	+	11.7807i	−1.19636	+	0.478952i
$606$	7.12522	+	6.79388i	0.289442	+	0.275982i
$607$	−37.8488	+	19.5124i	−1.53624	+	0.791985i	−0.998686	−	0.0512456i	$-0.983681\pi$
$607$	−37.8488	+	19.5124i	−1.53624	+	0.791985i	−0.537551	+	0.843231i	$0.680651\pi$
$608$	−0.504429	−	3.50838i	−0.0204573	−	0.142284i
$609$	−9.09259	−	3.09663i	−0.368450	−	0.125482i
$610$	11.3534	+	24.8604i	0.459685	+	1.00657i
$611$	13.6784	+	5.47601i	0.553369	+	0.221536i
$612$	0.223463	−	4.69107i	0.00903297	−	0.189625i
$613$	−5.02364	−	4.79004i	−0.202903	−	0.193468i	0.581814	−	0.813322i	$-0.302343\pi$
$613$	−5.02364	−	4.79004i	−0.202903	−	0.193468i	−0.784717	+	0.619854i	$0.787192\pi$
$614$	18.2339	+	14.3393i	0.735862	+	0.578688i
$615$	14.8486	−	17.1362i	0.598754	−	0.690999i
$616$	0.268086	−	1.42902i	0.0108015	−	0.0575768i
$617$	−12.0602	−	13.9182i	−0.485526	−	0.560326i	0.459139	−	0.888365i	$-0.348158\pi$
$617$	−12.0602	−	13.9182i	−0.485526	−	0.560326i	−0.944665	+	0.328038i	$0.893613\pi$
$618$	−9.95844	+	9.49535i	−0.400587	+	0.381959i
$619$	29.9740	−	2.86217i	1.20476	−	0.115040i	0.526700	−	0.850051i	$-0.323429\pi$
$619$	29.9740	−	2.86217i	1.20476	−	0.115040i	0.678055	+	0.735011i	$0.262823\pi$
$620$	12.8843	+	22.3163i	0.517446	+	0.896243i
$621$	2.58941	+	4.03670i	0.103909	+	0.161987i
$622$	26.7380			1.07210
$623$	−7.33241	+	9.41957i	−0.293767	+	0.377387i
$624$	2.45590	+	0.721116i	0.0983146	+	0.0288678i
$625$	−29.0794	+	5.60460i	−1.16318	+	0.224184i
$626$	−10.3561	−	5.33894i	−0.413913	−	0.213387i
$627$	−1.91262	−	0.368628i	−0.0763829	−	0.0147216i
$628$	−3.44639	−	2.71027i	−0.137526	−	0.108151i
$629$	27.2543	−	8.00259i	1.08670	−	0.319084i
$630$	2.17125	−	7.53243i	0.0865047	−	0.300099i
$631$	−5.36935	−	37.3446i	−0.213750	−	1.48667i	−0.760482	−	0.649359i	$-0.775037\pi$
$631$	−5.36935	−	37.3446i	−0.213750	−	1.48667i	0.546732	−	0.837308i	$-0.315872\pi$
$632$	14.4762	+	1.38231i	0.575831	+	0.0549852i
$633$	1.26613	−	1.77803i	0.0503241	−	0.0706703i
$634$	−1.20531	+	0.947869i	−0.0478691	+	0.0376447i
$635$	−32.2282	+	16.6148i	−1.27894	+	0.659338i
$636$	−0.468010	+	0.137420i	−0.0185578	+	0.00544906i
$637$	7.60411	+	16.2234i	0.301286	+	0.642794i
$638$	1.30652	−	1.50781i	0.0517257	−	0.0596946i
$639$	−0.524595	−	11.0126i	−0.0207527	−	0.435652i
$640$	−0.969073	+	2.79995i	−0.0383060	+	0.110678i
$641$	2.42623	+	10.0010i	0.0958302	+	0.395017i	0.999444	−	0.0333298i	$-0.0106112\pi$
$641$	2.42623	+	10.0010i	0.0958302	+	0.395017i	−0.903614	+	0.428347i	$0.859096\pi$
$642$	−1.22317	−	1.71770i	−0.0482745	−	0.0677921i
$643$	−20.9738			−0.827128			−0.413564	−	0.910475i	$-0.635716\pi$
$643$	−20.9738			−0.827128			−0.413564	+	0.910475i	$0.635716\pi$
$644$	4.10074	−	12.0077i	0.161592	−	0.473168i
$645$	4.89629			0.192791
$646$	9.65573	+	13.5596i	0.379900	+	0.533494i
$647$	−5.68830	−	23.4475i	−0.223630	−	0.921815i	−0.967374	−	0.253351i	$-0.918467\pi$
$647$	−5.68830	−	23.4475i	−0.223630	−	0.921815i	0.743744	−	0.668464i	$-0.233048\pi$
$648$	−0.327068	+	0.945001i	−0.0128484	+	0.0371231i
$649$	0.185619	+	3.89663i	0.00728619	+	0.152956i
$650$	6.33396	−	7.30978i	0.248438	−	0.286713i
$651$	8.44613	−	21.4041i	0.331030	−	0.838892i
$652$	11.9353	−	3.50452i	0.467423	−	0.137248i
$653$	−0.327432	+	0.168803i	−0.0128134	+	0.00660577i	−0.464621	−	0.885509i	$-0.653810\pi$
$653$	−0.327432	+	0.168803i	−0.0128134	+	0.00660577i	0.451808	+	0.892115i	$0.350779\pi$
$654$	−8.85370	+	6.96262i	−0.346207	+	0.272260i
$655$	−16.8117	+	23.6087i	−0.656886	+	0.922467i
$656$	7.61812	+	0.727442i	0.297438	+	0.0284018i
$657$	−0.393344	−	2.73577i	−0.0153458	−	0.106732i
$658$	14.7826	−	3.66385i	0.576285	−	0.142832i
$659$	−1.58138	+	0.464335i	−0.0616019	+	0.0180879i	−0.312388	−	0.949955i	$-0.601129\pi$
$659$	−1.58138	+	0.464335i	−0.0616019	+	0.0180879i	0.250786	+	0.968042i	$0.419311\pi$
$660$	1.27988	+	1.00651i	0.0498194	+	0.0391784i
$661$	18.2133	+	3.51033i	0.708417	+	0.136536i	0.530718	−	0.847549i	$-0.321922\pi$
$661$	18.2133	+	3.51033i	0.708417	+	0.136536i	0.177699	+	0.984085i	$0.443135\pi$
$662$	−20.8420	−	10.7448i	−0.810047	−	0.417608i
$663$	−11.8036	+	2.27495i	−0.458412	+	0.0883517i
$664$	−0.977011	−	0.286876i	−0.0379154	−	0.0111330i
$665$	10.4545	+	25.7437i	0.405407	+	0.998296i
$666$	−6.04824			−0.234365
$667$	13.1682	−	11.3909i	0.509877	−	0.441056i
$668$	7.69616	+	13.3301i	0.297773	+	0.515758i
$669$	18.5664	−	1.77288i	0.717818	−	0.0685433i
$670$	−7.96820	+	7.59767i	−0.307839	+	0.293523i
$671$	3.31950	+	3.83091i	0.128148	+	0.147891i
$672$	2.49592	−	0.877715i	0.0962822	−	0.0338586i
$673$	12.3388	−	14.2398i	0.475627	−	0.548903i	−0.466341	−	0.884605i	$-0.654428\pi$
$673$	12.3388	−	14.2398i	0.475627	−	0.548903i	0.941968	+	0.335702i	$0.108973\pi$
$674$	−23.2829	−	18.3098i	−0.896822	−	0.705269i
$675$	2.73487	+	2.60769i	0.105265	+	0.100370i
$676$	−0.306835	+	6.44126i	−0.0118013	+	0.247741i
$677$	−38.8158	−	15.5395i	−1.49181	−	0.597231i	−0.524633	−	0.851329i	$-0.675797\pi$
$677$	−38.8158	−	15.5395i	−1.49181	−	0.597231i	−0.967179	+	0.254098i	$0.918222\pi$
$678$	0.909219	+	1.99091i	0.0349183	+	0.0764605i
$679$	−5.19615	+	4.54775i	−0.199410	+	0.174527i
$680$	−1.98031	−	13.7734i	−0.0759414	−	0.528184i
$681$	13.5425	−	6.98164i	0.518949	−	0.267537i
$682$	3.45901	+	3.29815i	0.132452	+	0.126293i
$683$	−42.3705	+	16.9626i	−1.62126	+	0.649055i	−0.991779	−	0.127961i	$-0.959157\pi$
$683$	−42.3705	+	16.9626i	−1.62126	+	0.649055i	−0.629481	+	0.777016i	$0.716732\pi$
$684$	−1.15928	−	3.34952i	−0.0443262	−	0.128072i
$685$	−30.2746	+	19.4563i	−1.15673	+	0.743387i
$686$	16.1749	+	9.02076i	0.617559	+	0.344414i
$687$	17.1044	+	5.02231i	0.652574	+	0.191613i
$688$	0.958561	+	1.34611i	0.0365448	+	0.0513200i
$689$	0.624240	+	1.08122i	0.0237817	+	0.0411910i
$690$	9.79705	+	10.2923i	0.372967	+	0.391820i
$691$	23.8868	−	41.3732i	0.908698	−	1.57391i	0.0928235	−	0.995683i	$-0.470411\pi$
$691$	23.8868	−	41.3732i	0.908698	−	1.57391i	0.815875	−	0.578229i	$-0.196256\pi$
$692$	−4.67201	+	10.2303i	−0.177603	+	0.388897i
$693$	−0.00720225	−	1.45393i	−0.000273591	−	0.0552302i
$694$	−10.7595	−	12.4171i	−0.408424	−	0.471347i
$695$	−2.52337	−	52.9720i	−0.0957168	−	2.00934i
$696$	3.56490	+	0.687079i	0.135127	+	0.0260437i
$697$	−33.3659	+	13.3577i	−1.26382	+	0.505959i
$698$	−0.485099	+	1.99960i	−0.0183613	+	0.0756861i
$699$	−14.2069	−	9.13021i	−0.537353	−	0.345336i
$700$	0.901044	−	9.95717i	0.0340563	−	0.376346i
$701$	4.85904	+	10.6398i	0.183523	+	0.401860i	0.978924	−	0.204223i	$-0.0654669\pi$
$701$	4.85904	+	10.6398i	0.183523	+	0.401860i	−0.795401	+	0.606084i	$0.792740\pi$
$702$	2.54799	+	0.243303i	0.0961676	+	0.00918289i
$703$	16.8512	−	13.2519i	0.635555	−	0.499806i
$704$	−0.0261482	+	0.548918i	−0.000985497	+	0.0206881i
$705$	−4.02100	+	16.5748i	−0.151439	+	0.624242i
$706$	2.98250	−	20.7437i	0.112248	−	0.780700i
$707$	−2.60440	−	25.9171i	−0.0979485	−	0.974712i
$708$	−5.97184	+	3.83787i	−0.224436	+	0.144236i
$709$	26.4127	−	5.09063i	0.991950	−	0.191183i	0.332640	−	0.943054i	$-0.392061\pi$
$709$	26.4127	−	5.09063i	0.991950	−	0.191183i	0.659310	+	0.751871i	$0.270849\pi$
$710$	−7.70138	−	31.7455i	−0.289028	−	1.19139i
$711$	14.4762	−	1.38231i	0.542899	−	0.0518405i
$712$	2.25589	−	3.90731i	0.0845429	−	0.146433i
$713$	25.7554	+	32.8078i	0.964548	+	1.22866i
$714$	−8.52992	+	9.03511i	−0.319224	+	0.338131i
$715$	1.73129	−	3.79099i	0.0647464	−	0.141775i
$716$	−15.2553	+	14.5459i	−0.570119	+	0.543608i
$717$	−1.04653	+	3.02375i	−0.0390834	+	0.112924i
$718$	−27.6093	−	14.2336i	−1.03037	−	0.531192i
$719$	1.60480	+	4.63676i	0.0598488	+	0.172922i	0.970962	−	0.239235i	$-0.0768967\pi$
$719$	1.60480	+	4.63676i	0.0598488	+	0.172922i	−0.911113	+	0.412157i	$0.864776\pi$
$720$	−0.421666	+	2.93275i	−0.0157146	+	0.109297i
$721$	36.3548	−	1.91233i	1.35392	−	0.0712189i
$722$	−5.41498	−	3.48000i	−0.201525	−	0.129512i
$723$	−17.5980	−	7.04519i	−0.654478	−	0.262013i
$724$	14.4089	−	20.2345i	0.535504	−	0.752010i
$725$	7.95786	−	11.1753i	0.295548	−	0.415038i
$726$	−9.93168	−	3.97605i	−0.368599	−	0.147565i
$727$	7.05466	+	4.53375i	0.261643	+	0.168148i	0.664885	−	0.746946i	$-0.268480\pi$
$727$	7.05466	+	4.53375i	0.261643	+	0.168148i	−0.403242	+	0.915093i	$0.632117\pi$
$728$	−3.68940	−	5.67877i	−0.136738	−	0.210469i
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$	−2.67842	−	7.73879i	−0.0991328	−	0.286425i
$731$	−6.89819	−	3.55626i	−0.255139	−	0.131533i
$732$	−3.01691	+	8.71679i	−0.111508	+	0.322182i
$733$	3.61678	−	3.44860i	0.133589	−	0.127377i	−0.620339	−	0.784334i	$-0.713005\pi$
$733$	3.61678	−	3.44860i	0.133589	−	0.127377i	0.753928	+	0.656957i	$0.228157\pi$
$734$	−2.47360	+	5.41643i	−0.0913022	+	0.199924i
$735$	−17.3360	+	11.3854i	−0.639447	+	0.419957i
$736$	−0.911602	+	4.70839i	−0.0336021	+	0.173554i
$737$	−1.02102	+	1.76845i	−0.0376096	+	0.0651418i
$738$	7.61812	−	0.727442i	0.280427	−	0.0267775i
$739$	4.93470	+	20.3411i	0.181526	+	0.748260i	0.987671	+	0.156542i	$0.0500348\pi$
$739$	4.93470	+	20.3411i	0.181526	+	0.748260i	−0.806145	+	0.591718i	$0.798450\pi$
$740$	−17.5965	+	3.39146i	−0.646862	+	0.124672i
$741$	−7.63212	+	4.90487i	−0.280373	+	0.180185i
$742$	1.17653	+	0.530277i	0.0431919	+	0.0194671i
$743$	4.65720	−	32.3915i	0.170856	−	1.18833i	−0.706225	−	0.707987i	$-0.749603\pi$
$743$	4.65720	−	32.3915i	0.170856	−	1.18833i	0.877081	−	0.480342i	$-0.159487\pi$
$744$	−2.05041	+	8.45190i	−0.0751717	+	0.309862i
$745$	−1.40240	+	29.4400i	−0.0513799	+	1.07860i
$746$	10.5596	−	8.30413i	0.386613	−	0.304036i
$747$	−1.01365	−	0.0967915i	−0.0370874	−	0.00354142i
$748$	−1.07213	−	2.34763i	−0.0392009	−	0.0858379i
$749$	−0.502809	+	5.55639i	−0.0183722	+	0.203026i
$750$	−3.04383	−	1.95615i	−0.111145	−	0.0714285i
$751$	3.33326	−	13.7399i	0.121632	−	0.501375i	−0.878105	−	0.478468i	$-0.841192\pi$
$751$	3.33326	−	13.7399i	0.121632	−	0.501375i	0.999738	−	0.0229078i	$-0.00729242\pi$
$752$	−5.34401	+	2.13942i	−0.194876	+	0.0780166i
$753$	15.1662	+	2.92305i	0.552687	+	0.106522i
$754$	−0.442159	−	9.28206i	−0.0161025	−	0.338033i
$755$	45.8661	+	52.9323i	1.66924	+	1.92640i
$756$	2.28471	−	1.33421i	0.0830940	−	0.0485247i
$757$	−8.61349	+	18.8609i	−0.313062	+	0.685511i	−0.999116	−	0.0420400i	$-0.986614\pi$
$757$	−8.61349	+	18.8609i	−0.313062	+	0.685511i	0.686053	+	0.727551i	$0.259342\pi$
$758$	−12.7781	+	22.1324i	−0.464123	+	0.803885i
$759$	2.28130	+	1.31968i	0.0828059	+	0.0479015i
$760$	−5.25096	−	9.09492i	−0.190472	−	0.329908i
$761$	31.9859	+	44.9178i	1.15949	+	1.62827i	0.606531	+	0.795060i	$0.292561\pi$
$761$	31.9859	+	44.9178i	1.15949	+	1.62827i	0.552956	+	0.833211i	$0.313500\pi$
$762$	−11.7419	−	3.44773i	−0.425364	−	0.124898i
$763$	29.7733	+	1.27049i	1.07787	+	0.0459948i
$764$	3.01936	−	1.94043i	0.109237	−	0.0702021i
$765$	−4.55115	−	13.1497i	−0.164547	−	0.475427i
$766$	−20.2854	+	8.12104i	−0.732941	+	0.293425i
$767$	13.1501	+	12.5386i	0.474822	+	0.452742i
$768$	−0.888835	+	0.458227i	−0.0320731	+	0.0165348i
$769$	3.06653	+	21.3282i	0.110582	+	0.769114i	0.967356	+	0.253422i	$0.0815560\pi$
$769$	3.06653	+	21.3282i	0.110582	+	0.769114i	−0.856774	+	0.515692i	$0.827535\pi$
$770$	−0.836222	−	4.22598i	−0.0301354	−	0.152294i
$771$	6.20161	+	13.5796i	0.223346	+	0.489058i
$772$	7.86323	+	3.14796i	0.283004	+	0.113298i
$773$	0.485721	−	10.1965i	0.0174702	−	0.366744i	−0.973156	−	0.230145i	$-0.926080\pi$
$773$	0.485721	−	10.1965i	0.0174702	−	0.366744i	0.990626	−	0.136599i	$-0.0436171\pi$
$774$	1.19599	+	1.14038i	0.0429890	+	0.0409900i
$775$	25.8334	+	20.3156i	0.927964	+	0.729759i
$776$	1.70914	−	1.97245i	0.0613545	−	0.0708068i
$777$	12.1454	+	10.4191i	0.435713	+	0.373784i
$778$	−15.6253	−	18.0326i	−0.560195	−	0.646499i
$779$	−19.6312	+	18.7183i	−0.703362	+	0.670654i
$780$	7.54946	−	0.720886i	0.270314	−	0.0258119i
$781$	−3.02937	−	5.24702i	−0.108399	−	0.187753i
$782$	−6.32720	−	21.6161i	−0.226260	−	0.772991i
$783$	3.63051			0.129744
$784$	−6.52403	−	2.53713i	−0.233001	−	0.0906117i
$785$	−12.4644	−	3.65989i	−0.444874	−	0.130627i
$786$	−9.60509	+	1.85123i	−0.342602	+	0.0660312i
$787$	−18.4460	−	9.50958i	−0.657529	−	0.338980i	0.0969640	−	0.995288i	$-0.469087\pi$
$787$	−18.4460	−	9.50958i	−0.657529	−	0.338980i	−0.754493	+	0.656308i	$0.772117\pi$
$788$	−8.84681	−	1.70508i	−0.315155	−	0.0607411i
$789$	9.86774	+	7.76007i	0.351301	+	0.276266i
$790$	41.3414	−	12.1389i	1.47086	−	0.431883i
$791$	1.60390	−	5.56420i	0.0570282	−	0.197840i
$792$	0.0782078	+	0.543947i	0.00277899	+	0.0193283i
$793$	23.5029	+	2.24426i	0.834613	+	0.0796959i
$794$	6.86987	−	9.64738i	0.243802	−	0.342373i
$795$	−1.13601	+	0.893371i	−0.0402903	+	0.0316846i
$796$	−7.12049	+	3.67087i	−0.252379	+	0.130111i
$797$	−34.2922	+	10.0691i	−1.21469	+	0.356666i	−0.825453	−	0.564471i	$-0.809080\pi$
$797$	−34.2922	+	10.0691i	−1.21469	+	0.356666i	−0.389239	+	0.921137i	$0.627262\pi$
$798$	−3.44219	+	8.72317i	−0.121852	+	0.308797i
$799$	17.7036	−	20.4310i	0.626307	−	0.722796i
$800$	0.179804	+	3.77455i	0.00635704	+	0.133451i
$801$	1.47566	−	4.26363i	0.0521397	−	0.150648i
$802$	4.81960	+	19.8667i	0.170186	+	0.701517i
$803$	−0.881034	−	1.23724i	−0.0310910	−	0.0436612i
$804$	−3.71589			−0.131049
$805$	−1.94307	−	37.5449i	−0.0684842	−	1.32328i
$806$	22.2608			0.784103
$807$	−10.1104	−	14.1981i	−0.355903	−	0.499796i
$808$	2.32106	+	9.56756i	0.0816548	+	0.336585i
$809$	11.5154	−	33.2715i	0.404859	−	1.16976i	−0.539824	−	0.841778i	$-0.681509\pi$
$809$	11.5154	−	33.2715i	0.404859	−	1.16976i	0.944683	−	0.327985i	$-0.106370\pi$
$810$	0.140981	+	2.95955i	0.00495356	+	0.103988i
$811$	12.9217	−	14.9124i	0.453742	−	0.523646i	−0.482076	−	0.876129i	$-0.660117\pi$
$811$	12.9217	−	14.9124i	0.453742	−	0.523646i	0.935818	+	0.352483i	$0.114663\pi$
$812$	−5.97501	−	7.52088i	−0.209682	−	0.263931i
$813$	−10.2426	+	3.00749i	−0.359223	+	0.105477i
$814$	−2.95427	+	1.52303i	−0.103547	+	0.0533822i
$815$	28.9709	−	22.7830i	1.01481	−	0.798053i
$816$	2.72418	−	3.82557i	0.0953652	−	0.133922i
$817$	−5.83080	−	0.556774i	−0.203994	−	0.0194791i
$818$	−3.97164	−	27.6233i	−0.138865	−	0.965828i
$819$	−4.69744	−	4.87792i	−0.164142	−	0.170448i
$820$	21.7560	−	6.38813i	0.759752	−	0.223083i
$821$	−38.5199	−	30.2924i	−1.34435	−	1.05721i	−0.992640	−	0.121104i	$-0.961357\pi$
$821$	−38.5199	−	30.2924i	−1.34435	−	1.05721i	−0.351714	−	0.936108i	$-0.614401\pi$
$822$	−11.9265	−	2.29864i	−0.415984	−	0.0801744i
$823$	25.1104	+	12.9453i	0.875294	+	0.451245i	0.836478	−	0.548001i	$-0.184611\pi$
$823$	25.1104	+	12.9453i	0.875294	+	0.451245i	0.0388164	+	0.999246i	$0.487641\pi$
$824$	−13.5111	+	2.60406i	−0.470683	+	0.0907167i
$825$	1.99250	+	0.585052i	0.0693701	+	0.0203689i
$826$	18.6033	+	2.58077i	0.647293	+	0.0897963i
$827$	−48.3832			−1.68245			−0.841224	−	0.540687i	$-0.818164\pi$
$827$	−48.3832			−1.68245			−0.841224	+	0.540687i	$0.818164\pi$
$828$	−0.00405894	+	4.79583i	−0.000141058	+	0.166667i
$829$	5.17121	+	8.95680i	0.179604	+	0.311083i	0.941745	−	0.336328i	$-0.109185\pi$
$829$	5.17121	+	8.95680i	0.179604	+	0.311083i	−0.762141	+	0.647411i	$0.775852\pi$
$830$	−3.00334	+	0.286785i	−0.104248	+	0.00995444i
$831$	12.7182	−	12.1268i	0.441190	−	0.420674i
$832$	1.67617	+	1.93440i	0.0581106	+	0.0670633i
$833$	32.6933	−	3.44901i	1.13276	−	0.119501i
$834$	11.7211	−	13.5269i	0.405869	−	0.468398i
$835$	35.8488	+	28.1918i	1.24060	+	0.975617i
$836$	−1.40971	−	1.34415i	−0.0487557	−	0.0464885i
$837$	−0.413823	+	8.68721i	−0.0143038	+	0.300274i
$838$	−10.8274	−	4.33465i	−0.374027	−	0.149738i
$839$	−20.2233	−	44.2829i	−0.698187	−	1.52882i	−0.842156	−	0.539234i	$-0.818714\pi$
$839$	−20.2233	−	44.2829i	−0.698187	−	1.52882i	0.143969	−	0.989582i	$-0.454013\pi$
$840$	5.89891	−	5.16282i	0.203532	−	0.178134i
$841$	2.25133	+	15.6584i	0.0776321	+	0.539943i
$842$	−15.0229	+	7.74485i	−0.517724	+	0.266905i
$843$	−15.8650	−	15.1272i	−0.546418	−	0.521008i
$844$	2.02641	−	0.811252i	0.0697519	−	0.0279245i
$845$	6.24912	+	18.0557i	0.214976	+	0.621134i
$846$	−4.84255	+	3.11212i	−0.166490	+	0.106997i
$847$	13.0942	+	25.0933i	0.449923	+	0.862215i
$848$	−0.468010	−	0.137420i	−0.0160715	−	0.00471903i
$849$	16.0592	+	22.5520i	0.551151	+	0.773983i
$850$	−8.87344	−	15.3693i	−0.304357	−	0.527161i
$851$	−27.4190	+	9.46384i	−0.939912	+	0.324416i
$852$	5.51255	−	9.54801i	0.188857	−	0.327109i
$853$	23.8934	−	52.3192i	0.818093	−	1.79137i	0.250379	−	0.968148i	$-0.419445\pi$
$853$	23.8934	−	52.3192i	0.818093	−	1.79137i	0.567714	−	0.823226i	$-0.307828\pi$
$854$	21.0744	−	12.3069i	0.721150	−	0.421133i
$855$	−6.87729	−	7.93682i	−0.235198	−	0.271433i
$856$	−0.100336	−	2.10631i	−0.00342941	−	0.0719922i
$857$	51.1805	+	9.86423i	1.74829	+	0.336956i	0.960351	−	0.278795i	$-0.0899350\pi$
$857$	51.1805	+	9.86423i	1.74829	+	0.336956i	0.787941	+	0.615751i	$0.211147\pi$
$858$	1.30583	−	0.522777i	0.0445805	−	0.0178473i
$859$	6.81484	−	28.0912i	0.232519	−	0.958458i	−0.729174	−	0.684329i	$-0.760095\pi$
$859$	6.81484	−	28.0912i	0.232519	−	0.958458i	0.961693	−	0.274129i	$-0.0883896\pi$
$860$	4.11903	+	2.64714i	0.140458	+	0.0902666i
$861$	−16.5510	−	11.6628i	−0.564055	−	0.397466i
$862$	−11.3527	−	24.8590i	−0.386675	−	0.846699i
$863$	−4.27361	−	0.408081i	−0.145476	−	0.0138912i	0.0220642	−	0.999757i	$-0.492976\pi$
$863$	−4.27361	−	0.408081i	−0.145476	−	0.0138912i	−0.167540	+	0.985865i	$0.553582\pi$
$864$	−0.786053	+	0.618159i	−0.0267421	+	0.0210302i
$865$	−1.58556	+	33.2849i	−0.0539106	+	1.13172i
$866$	−2.09894	+	8.65197i	−0.0713250	+	0.294006i
$867$	−0.719559	+	5.00464i	−0.0244375	+	0.169967i
$868$	18.6773	−	13.4399i	0.633947	−	0.456181i
$869$	6.72282	−	4.32049i	0.228056	−	0.146563i
$870$	10.5625	−	2.03575i	0.358102	−	0.0690185i
$871$	2.24233	+	9.24301i	0.0759785	+	0.313187i
$872$	−11.2125	+	1.07066i	−0.379703	+	0.0362572i
$873$	1.30496	−	2.26026i	0.0441663	−	0.0764983i
$874$	−10.4965	−	13.3707i	−0.355051	−	0.452271i
$875$	2.74246	+	9.17163i	0.0927119	+	0.310058i
$876$	1.14817	−	2.51413i	0.0387929	−	0.0849447i
$877$	25.7009	−	24.5058i	0.867859	−	0.827502i	−0.118356	−	0.992971i	$-0.537762\pi$
$877$	25.7009	−	24.5058i	0.867859	−	0.827502i	0.986215	+	0.165469i	$0.0529138\pi$
$878$	−0.0901981	+	0.260610i	−0.00304404	+	0.00879517i
$879$	−1.98412	−	1.02289i	−0.0669227	−	0.0345011i
$880$	0.532545	+	1.53869i	0.0179521	+	0.0518691i
$881$	0.743549	−	5.17150i	0.0250508	−	0.174232i	−0.973455	−	0.228879i	$-0.926494\pi$
$881$	0.743549	−	5.17150i	0.0250508	−	0.174232i	0.998506	+	0.0546464i	$0.0174032\pi$
$882$	−6.88629	−	1.25660i	−0.231873	−	0.0423118i
$883$	44.0826	+	28.3302i	1.48350	+	0.953386i	0.996810	+	0.0798103i	$0.0254314\pi$
$883$	44.0826	+	28.3302i	1.48350	+	0.953386i	0.486688	+	0.873576i	$0.338205\pi$
$884$	−11.1597	−	4.46767i	−0.375342	−	0.150264i
$885$	−12.2003	+	17.1329i	−0.410108	+	0.575917i
$886$	13.1006	−	18.3972i	0.440122	−	0.618065i
$887$	7.55985	+	3.02651i	0.253835	+	0.101620i	0.495090	−	0.868841i	$-0.335135\pi$
$887$	7.55985	+	3.02651i	0.253835	+	0.101620i	−0.241255	+	0.970462i	$0.577559\pi$
$888$	−5.08810	−	3.26993i	−0.170746	−	0.109732i
$889$	17.6394	+	27.1508i	0.591606	+	0.910607i
$890$	1.90246	−	13.2319i	0.0637706	−	0.443534i
$891$	0.179737	+	0.519316i	0.00602142	+	0.0173978i
$892$	16.5775	+	8.54631i	0.555057	+	0.286152i
$893$	6.67322	−	19.2810i	0.223311	−	0.645214i
$894$	−7.19930	+	6.86452i	−0.240781	+	0.229584i
$895$	−25.9444	+	56.8103i	−0.867226	+	1.89896i
$896$	2.57423	+	0.611015i	0.0859990	+	0.0204126i
$897$	11.9317	−	2.88392i	0.398389	−	0.0962911i
$898$	−2.56833	+	4.44848i	−0.0857064	+	0.148448i
$899$	31.4318	−	3.00137i	1.04831	−	0.100101i
$900$	0.890894	+	3.67231i	0.0296965	+	0.122410i
$901$	2.24935	−	0.433527i	0.0749368	−	0.0144429i
$902$	3.53790	−	2.27367i	0.117799	−	0.0757049i
$903$	−0.437157	−	4.35027i	−0.0145477	−	0.144768i
$904$	−0.311484	+	2.16642i	−0.0103598	+	0.0720541i
$905$	17.3519	−	71.5257i	0.576798	−	2.37759i
$906$	−1.12478	+	23.6120i	−0.0373682	+	0.784456i
$907$	16.4346	−	12.9243i	0.545701	−	0.429144i	−0.306873	−	0.951750i	$-0.599283\pi$
$907$	16.4346	−	12.9243i	0.545701	−	0.429144i	0.852574	+	0.522607i	$0.175040\pi$
$908$	15.1672	+	1.44829i	0.503342	+	0.0480633i
$909$	4.08979	+	8.95539i	0.135650	+	0.297032i
$910$	−16.4018	−	11.5576i	−0.543714	−	0.383132i
$911$	−33.0484	−	21.2389i	−1.09494	−	0.703676i	−0.136980	−	0.990574i	$-0.543740\pi$
$911$	−33.0484	−	21.2389i	−1.09494	−	0.703676i	−0.957961	+	0.286898i	$0.907376\pi$
$912$	0.835638	−	3.44455i	0.0276707	−	0.114060i
$913$	−0.519490	+	0.207973i	−0.0171926	+	0.00688289i
$914$	−15.9016	−	3.06478i	−0.525977	−	0.101374i
$915$	1.30042	+	27.2992i	0.0429907	+	0.902485i
$916$	11.6739	+	13.4724i	0.385716	+	0.445140i
$917$	22.4769	+	12.8290i	0.742252	+	0.423651i
$918$	1.95095	−	4.27199i	0.0643910	−	0.140997i
$919$	5.78967	−	10.0280i	0.190984	−	0.330794i	−0.754593	−	0.656193i	$-0.772166\pi$
$919$	5.78967	−	10.0280i	0.190984	−	0.330794i	0.945577	+	0.325400i	$0.105499\pi$
$920$	2.67738	+	13.9551i	0.0882705	+	0.460086i
$921$	11.5984	+	20.0891i	0.382181	+	0.661957i
$922$	−4.30657	−	6.04773i	−0.141829	−	0.199171i
$923$	−27.0765	−	7.95038i	−0.891234	−	0.261690i
$924$	0.779995	−	1.22702i	0.0256599	−	0.0403659i
$925$	−19.2271	+	12.3565i	−0.632183	+	0.406279i
$926$	−1.71629	−	4.95889i	−0.0564007	−	0.162959i
$927$	−12.7742	+	5.11400i	−0.419558	+	0.167966i
$928$	2.62753	+	2.50534i	0.0862528	+	0.0822418i
$929$	−1.96509	+	1.01308i	−0.0644726	+	0.0332379i	−0.490161	−	0.871632i	$-0.663062\pi$
$929$	−1.96509	+	1.01308i	−0.0644726	+	0.0332379i	0.425689	+	0.904870i	$0.360032\pi$
$930$	3.66725	+	25.5063i	0.120254	+	0.836385i
$931$	21.9394	−	11.5871i	0.719034	−	0.379751i
$932$	−7.01542	−	15.3616i	−0.229798	−	0.503187i
$933$	24.8227	+	9.93752i	0.812660	+	0.325340i
$934$	0.538177	−	11.2977i	0.0176097	−	0.369673i
$935$	−5.53429	−	5.27693i	−0.180991	−	0.172574i
$936$	2.01196	+	1.58223i	0.0657631	+	0.0517167i
$937$	12.2232	−	14.1064i	0.399316	−	0.460835i	−0.520109	−	0.854100i	$-0.674109\pi$
$937$	12.2232	−	14.1064i	0.399316	−	0.460835i	0.919425	+	0.393264i	$0.128654\pi$
$938$	7.46182	+	6.40126i	0.243637	+	0.209009i
$939$	−7.62998	−	8.80547i	−0.248995	−	0.287356i
$940$	−12.3437	+	11.7697i	−0.402606	+	0.383884i
$941$	42.3353	−	4.04253i	1.38009	−	0.131783i	0.621533	−	0.783388i	$-0.286510\pi$
$941$	42.3353	−	4.04253i	1.38009	−	0.131783i	0.758558	+	0.651606i	$0.225904\pi$
$942$	−2.19221	−	3.79702i	−0.0714260	−	0.123714i
$943$	33.3977	−	15.2180i	1.08758	−	0.495568i
$944$	−7.09874			−0.231044
$945$	4.81524	−	6.18589i	0.156640	−	0.201227i
$946$	0.871346	+	0.255850i	0.0283299	+	0.00831841i
$947$	−55.5670	+	10.7097i	−1.80569	+	0.348018i	−0.977254	−	0.212072i	$-0.931979\pi$
$947$	−55.5670	+	10.7097i	−1.80569	+	0.348018i	−0.828432	+	0.560089i	$0.810767\pi$
$948$	12.9255	+	6.66354i	0.419799	+	0.216422i
$949$	−6.94658	−	1.33884i	−0.225495	−	0.0434607i
$950$	−10.5283	−	8.27957i	−0.341584	−	0.268625i
$951$	−1.47126	+	0.432001i	−0.0477089	+	0.0140086i
$952$	−12.0606	+	2.98920i	−0.390885	+	0.0968805i
$953$	−0.944192	−	6.56700i	−0.0305854	−	0.212726i	0.968797	−	0.247854i	$-0.0797253\pi$
$953$	−0.944192	−	6.56700i	−0.0305854	−	0.212726i	−0.999383	+	0.0351278i	$0.988816\pi$
$954$	−0.485559	−	0.0463653i	−0.0157206	−	0.00150113i
$955$	6.16847	−	8.66240i	0.199607	−	0.280309i
$956$	−2.51516	+	1.97795i	−0.0813462	+	0.0639713i
$957$	1.77333	−	0.914214i	0.0573236	−	0.0295523i
$958$	25.9813	−	7.62880i	0.839418	−	0.246475i
$959$	19.9896	+	25.1613i	0.645497	+	0.812501i
$960$	−1.94029	+	2.23922i	−0.0626227	+	0.0722704i
$961$	2.12400	+	44.5883i	0.0685162	+	1.43833i
$962$	−5.06332	+	14.6295i	−0.163248	+	0.471674i
$963$	−0.497145	−	2.04926i	−0.0160203	−	0.0660364i
$964$	−10.9955	−	15.4410i	−0.354141	−	0.497321i
$965$	25.0957			0.807859
$966$	8.26980	−	9.62343i	0.266076	−	0.309629i
$967$	−6.51818			−0.209611			−0.104805	−	0.994493i	$-0.533422\pi$
$967$	−6.51818			−0.209611			−0.104805	+	0.994493i	$0.533422\pi$
$968$	−6.20545	−	8.71434i	−0.199451	−	0.280089i
$969$	3.92448	+	16.1769i	0.126073	+	0.519678i
$970$	2.52921	−	7.30767i	0.0812080	−	0.234635i
$971$	0.00124588	+	0.0261542i	3.99822e−5	+	0.000839330i	0.998887	−	0.0471622i	$-0.0150178\pi$
$971$	0.00124588	+	0.0261542i	3.99822e−5	+	0.000839330i	−0.998847	+	0.0480016i	$0.984715\pi$
$972$	−0.654861	+	0.755750i	−0.0210047	+	0.0242407i
$973$	−46.8394	+	6.97148i	−1.50160	+	0.223495i
$974$	−21.0031	+	6.16705i	−0.672981	+	0.197605i
$975$	8.59701	−	4.43207i	0.275325	−	0.141940i
$976$	−7.25064	+	5.70196i	−0.232087	+	0.182515i
$977$	−7.32719	+	10.2896i	−0.234418	+	0.329193i	−0.914982	−	0.403495i	$-0.867795\pi$
$977$	−7.32719	+	10.2896i	−0.234418	+	0.329193i	0.680564	+	0.732688i	$0.261735\pi$
$978$	12.3829	+	1.18242i	0.395960	+	0.0378096i
$979$	−0.352856	−	2.45416i	−0.0112773	−	0.0784354i
$980$	−20.7393	+	0.205476i	−0.662494	+	0.00656368i
$981$	−10.8072	+	3.17329i	−0.345048	+	0.101315i
$982$	13.5834	+	10.6821i	0.433464	+	0.340880i
$983$	−28.9111	−	5.57217i	−0.922122	−	0.177724i	−0.293970	−	0.955815i	$-0.594976\pi$
$983$	−28.9111	−	5.57217i	−0.922122	−	0.177724i	−0.628152	+	0.778090i	$0.716189\pi$
$984$	6.80205	+	3.50670i	0.216842	+	0.111790i
$985$	−26.2123	+	5.05201i	−0.835193	+	0.160970i
$986$	−16.3597	−	4.80363i	−0.520998	−	0.152979i
$987$	15.0854	+	2.09273i	0.480174	+	0.0666125i
$988$	−9.07232			−0.288629
$989$	7.20627	+	3.29837i	0.229146	+	0.104882i
$990$	0.814120	+	1.41010i	0.0258744	+	0.0448158i
$991$	47.5162	−	4.53725i	1.50940	−	0.144130i	0.692715	−	0.721211i	$-0.256414\pi$
$991$	47.5162	−	4.53725i	1.50940	−	0.144130i	0.816687	+	0.577081i	$0.195808\pi$
$992$	−6.29436	+	6.00166i	−0.199846	+	0.190553i
$993$	−15.3556	−	17.7213i	−0.487295	−	0.562368i
$994$	−27.5177	+	9.67689i	−0.872810	+	0.306932i
$995$	−15.5438	+	17.9385i	−0.492770	+	0.568687i
$996$	−0.800404	−	0.629445i	−0.0253618	−	0.0199447i
$997$	5.45023	+	5.19678i	0.172610	+	0.164584i	0.771460	−	0.636278i	$-0.219527\pi$
$997$	5.45023	+	5.19678i	0.172610	+	0.164584i	−0.598850	+	0.800862i	$0.704375\pi$
$998$	−1.09438	+	22.9739i	−0.0346420	+	0.727225i
$999$	−5.61499	−	2.24790i	−0.177650	−	0.0711205i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.d.121.8	✓	160
7.4	even	3	inner	966.2.y.d.949.1	yes	160
23.4	even	11	inner	966.2.y.d.625.1	yes	160
161.4	even	33	inner	966.2.y.d.487.8	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.d.121.8	✓	160	1.1	even	1	trivial
966.2.y.d.487.8	yes	160	161.4	even	33	inner
966.2.y.d.625.1	yes	160	23.4	even	11	inner
966.2.y.d.949.1	yes	160	7.4	even	3	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.580057 + 0.814576i) q^{2} +(0.235759 + 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(0.140981 + 2.95955i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(2.61692 - 0.389498i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +O(q^{10})\)	\(q+(0.580057 + 0.814576i) q^{2} +(0.235759 + 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(0.140981 + 2.95955i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(2.61692 - 0.389498i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +(-2.32900 + 1.83155i) q^{10} +(-0.318765 + 0.447643i) q^{11} +(-0.995472 - 0.0950560i) q^{12} +(0.364266 + 2.53353i) q^{13} +(1.83524 + 1.90575i) q^{14} +(-2.84289 + 0.834748i) q^{15} +(-0.786053 - 0.618159i) q^{16} +(4.61152 + 0.888798i) q^{17} +(-0.888835 - 0.458227i) q^{18} +(3.48041 - 0.670793i) q^{19} +(-2.84289 - 0.834748i) q^{20} +(0.995482 + 2.45133i) q^{21} -0.549541 q^{22} +(-4.74644 - 0.686535i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-3.76172 + 0.359201i) q^{25} +(-1.85245 + 1.76631i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(-0.487836 + 2.60039i) q^{28} +(-2.37748 + 2.74376i) q^{29} +(-2.32900 - 1.83155i) q^{30} +(-6.29436 - 6.00166i) q^{31} +(0.0475819 - 0.998867i) q^{32} +(-0.510176 - 0.204244i) q^{33} +(1.95095 + 4.27199i) q^{34} +(1.52168 + 7.69002i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(5.37589 - 2.77146i) q^{37} +(2.56525 + 2.44596i) q^{38} +(-2.37623 + 0.951299i) q^{39} +(-0.969073 - 2.79995i) q^{40} +(-6.43792 + 4.13740i) q^{41} +(-1.41936 + 2.23281i) q^{42} +(-1.58559 - 0.465571i) q^{43} +(-0.318765 - 0.447643i) q^{44} +(-1.48145 - 2.56596i) q^{45} +(-2.19397 - 4.26456i) q^{46} +(2.87817 - 4.98514i) q^{47} +(0.415415 - 0.909632i) q^{48} +(6.69658 - 2.03857i) q^{49} +(-2.47461 - 2.85585i) q^{50} +(0.223463 + 4.69107i) q^{51} +(-2.51332 - 0.484403i) q^{52} +(0.452828 - 0.181285i) q^{53} +(0.235759 - 0.971812i) q^{54} +(-1.36976 - 0.880293i) q^{55} +(-2.40119 + 1.11099i) q^{56} +(1.47242 + 3.22415i) q^{57} +(-3.61407 - 0.345102i) q^{58} +(5.57999 - 4.38815i) q^{59} +(0.140981 - 2.95955i) q^{60} +(2.17467 - 8.96409i) q^{61} +(1.23772 - 8.60854i) q^{62} +(-2.14754 + 1.54534i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-7.44675 + 1.43524i) q^{65} +(-0.129559 - 0.534050i) q^{66} +(3.69907 - 0.353218i) q^{67} +(-2.34820 + 4.06720i) q^{68} +(-0.451832 - 4.77450i) q^{69} +(-5.38144 + 5.70017i) q^{70} +(-4.57999 + 10.0288i) q^{71} +(0.723734 - 0.690079i) q^{72} +(-0.903984 + 2.61189i) q^{73} +(5.37589 + 2.77146i) q^{74} +(-1.23594 - 3.57100i) q^{75} +(-0.504429 + 3.50838i) q^{76} +(-0.659828 + 1.29560i) q^{77} +(-2.15325 - 1.38381i) q^{78} +(-13.5003 - 5.40472i) q^{79} +(1.71866 - 2.41351i) q^{80} +(0.580057 - 0.814576i) q^{81} +(-7.10459 - 2.84425i) q^{82} +(0.856613 + 0.550511i) q^{83} +(-2.64210 + 0.138979i) q^{84} +(-1.98031 + 13.7734i) q^{85} +(-0.540489 - 1.56164i) q^{86} +(-3.22693 - 1.66360i) q^{87} +(0.179737 - 0.519316i) q^{88} +(-3.26532 + 3.11348i) q^{89} +(1.23084 - 2.69516i) q^{90} +(1.94006 + 6.48816i) q^{91} +(2.20118 - 4.26084i) q^{92} +(4.34853 - 7.53187i) q^{93} +(5.73028 - 0.547176i) q^{94} +(2.47592 + 10.2059i) q^{95} +(0.981929 - 0.189251i) q^{96} +(-2.19561 + 1.41103i) q^{97} +(5.54497 + 4.27239i) q^{98} +(0.0782078 - 0.543947i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) \) 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9} - 2 q^{10} - 4 q^{11} + 8 q^{12} - 4 q^{13} + 5 q^{14} + 26 q^{15} + 8 q^{16} - 13 q^{17} + 8 q^{18} + 4 q^{19} + 26 q^{20} + 11 q^{21} - 124 q^{22} + 26 q^{23} - 80 q^{24} + 14 q^{25} + 2 q^{26} - 16 q^{27} - 22 q^{28} + 54 q^{29} - 2 q^{30} + 15 q^{31} + 8 q^{32} - 4 q^{33} + 4 q^{34} - 2 q^{35} - 16 q^{36} + 7 q^{37} - 7 q^{38} + 2 q^{39} + 9 q^{40} - 30 q^{41} + 6 q^{42} + 36 q^{43} - 4 q^{44} + 20 q^{45} + 4 q^{46} - 6 q^{47} - 16 q^{48} + 14 q^{49} - 28 q^{50} + 9 q^{51} + 2 q^{52} - 24 q^{53} + 8 q^{54} - 14 q^{55} + 6 q^{56} - 30 q^{57} - 5 q^{58} + 4 q^{59} - 2 q^{60} + 32 q^{61} - 8 q^{62} - 6 q^{63} - 16 q^{64} + 38 q^{65} - 4 q^{66} + 6 q^{67} + 42 q^{68} - 30 q^{69} - 8 q^{70} - 180 q^{71} + 8 q^{72} - 32 q^{73} + 7 q^{74} + 14 q^{75} - 8 q^{76} + 61 q^{77} + 18 q^{78} - 66 q^{79} - 2 q^{80} + 8 q^{81} - 7 q^{82} + 130 q^{83} + 5 q^{84} - 70 q^{85} - 40 q^{86} + 6 q^{87} - 15 q^{88} - 4 q^{89} + 4 q^{90} - 6 q^{91} + 58 q^{92} - 18 q^{93} + 16 q^{94} + 19 q^{95} + 8 q^{96} + 40 q^{97} + 43 q^{98} + 8 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9 - 2 * q^10 - 4 * q^11 + 8 * q^12 - 4 * q^13 + 5 * q^14 + 26 * q^15 + 8 * q^16 - 13 * q^17 + 8 * q^18 + 4 * q^19 + 26 * q^20 + 11 * q^21 - 124 * q^22 + 26 * q^23 - 80 * q^24 + 14 * q^25 + 2 * q^26 - 16 * q^27 - 22 * q^28 + 54 * q^29 - 2 * q^30 + 15 * q^31 + 8 * q^32 - 4 * q^33 + 4 * q^34 - 2 * q^35 - 16 * q^36 + 7 * q^37 - 7 * q^38 + 2 * q^39 + 9 * q^40 - 30 * q^41 + 6 * q^42 + 36 * q^43 - 4 * q^44 + 20 * q^45 + 4 * q^46 - 6 * q^47 - 16 * q^48 + 14 * q^49 - 28 * q^50 + 9 * q^51 + 2 * q^52 - 24 * q^53 + 8 * q^54 - 14 * q^55 + 6 * q^56 - 30 * q^57 - 5 * q^58 + 4 * q^59 - 2 * q^60 + 32 * q^61 - 8 * q^62 - 6 * q^63 - 16 * q^64 + 38 * q^65 - 4 * q^66 + 6 * q^67 + 42 * q^68 - 30 * q^69 - 8 * q^70 - 180 * q^71 + 8 * q^72 - 32 * q^73 + 7 * q^74 + 14 * q^75 - 8 * q^76 + 61 * q^77 + 18 * q^78 - 66 * q^79 - 2 * q^80 + 8 * q^81 - 7 * q^82 + 130 * q^83 + 5 * q^84 - 70 * q^85 - 40 * q^86 + 6 * q^87 - 15 * q^88 - 4 * q^89 + 4 * q^90 - 6 * q^91 + 58 * q^92 - 18 * q^93 + 16 * q^94 + 19 * q^95 + 8 * q^96 + 40 * q^97 + 43 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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