LMFDB - Embedded newform 966.2.y.a.121.7

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			121.7
Character	$\chi$	$=$	966.121
Dual form			966.2.y.a.487.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.580057 - 0.814576i) q^{2} +(-0.235759 - 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(0.122200 + 2.56530i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(-0.168303 + 2.64039i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +O(q^{10})$	\(q+(-0.580057 - 0.814576i) q^{2} +(-0.235759 - 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(0.122200 + 2.56530i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(-0.168303 + 2.64039i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +(2.01875 - 1.58756i) q^{10} +(0.875190 - 1.22903i) q^{11} +(0.995472 + 0.0950560i) q^{12} +(-0.538552 - 3.74571i) q^{13} +(2.24843 - 1.39448i) q^{14} +(2.46418 - 0.723548i) q^{15} +(-0.786053 - 0.618159i) q^{16} +(1.93459 + 0.372862i) q^{17} +(0.888835 + 0.458227i) q^{18} +(-4.06838 + 0.784117i) q^{19} +(-2.46418 - 0.723548i) q^{20} +(2.60564 - 0.458937i) q^{21} -1.50880 q^{22} +(-4.12167 + 2.45191i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-1.58846 + 0.151680i) q^{25} +(-2.73878 + 2.61142i) q^{26} +(0.654861 + 0.755750i) q^{27} +(-2.44013 - 1.02263i) q^{28} +(-4.23356 + 4.88579i) q^{29} +(-2.01875 - 1.58756i) q^{30} +(6.23769 + 5.94763i) q^{31} +(-0.0475819 + 0.998867i) q^{32} +(-1.40072 - 0.560764i) q^{33} +(-0.818448 - 1.79215i) q^{34} +(-6.79396 - 0.109091i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(-3.93872 + 2.03055i) q^{37} +(2.99862 + 2.85917i) q^{38} +(-3.51316 + 1.40646i) q^{39} +(0.839978 + 2.42696i) q^{40} +(-9.30173 + 5.97786i) q^{41} +(-1.88526 - 1.85628i) q^{42} +(5.25487 + 1.54297i) q^{43} +(0.875190 + 1.22903i) q^{44} +(-1.28410 - 2.22413i) q^{45} +(4.38807 + 1.93516i) q^{46} +(-6.31820 + 10.9434i) q^{47} +(-0.415415 + 0.909632i) q^{48} +(-6.94335 - 0.888773i) q^{49} +(1.04495 + 1.20594i) q^{50} +(-0.0937456 - 1.96796i) q^{51} +(3.71585 + 0.716171i) q^{52} +(-6.25958 + 2.50596i) q^{53} +(0.235759 - 0.971812i) q^{54} +(3.25978 + 2.09494i) q^{55} +(0.582399 + 2.58085i) q^{56} +(1.72117 + 3.76884i) q^{57} +(6.43556 + 0.614521i) q^{58} +(10.4033 - 8.18122i) q^{59} +(-0.122200 + 2.56530i) q^{60} +(2.23676 - 9.22003i) q^{61} +(1.22658 - 8.53103i) q^{62} +(-1.06030 - 2.42400i) q^{63} +(0.841254 - 0.540641i) q^{64} +(9.54306 - 1.83927i) q^{65} +(0.355713 + 1.46627i) q^{66} +(-1.20025 + 0.114610i) q^{67} +(-0.985097 + 1.70624i) q^{68} +(3.35451 + 3.42742i) q^{69} +(3.85202 + 5.59748i) q^{70} +(-2.43985 + 5.34252i) q^{71} +(-0.723734 + 0.690079i) q^{72} +(2.00245 - 5.78570i) q^{73} +(3.93872 + 2.03055i) q^{74} +(0.521899 + 1.50793i) q^{75} +(0.589647 - 4.10108i) q^{76} +(3.09783 + 2.51769i) q^{77} +(3.18350 + 2.04591i) q^{78} +(-9.53834 - 3.81858i) q^{79} +(1.48971 - 2.09200i) q^{80} +(0.580057 - 0.814576i) q^{81} +(10.2650 + 4.10947i) q^{82} +(5.30696 + 3.41057i) q^{83} +(-0.418526 + 2.61244i) q^{84} +(-0.720094 + 5.00836i) q^{85} +(-1.79126 - 5.17550i) q^{86} +(5.74617 + 2.96236i) q^{87} +(0.493480 - 1.42582i) q^{88} +(-8.92818 + 8.51300i) q^{89} +(-1.06687 + 2.33612i) q^{90} +(9.98080 - 0.791574i) q^{91} +(-0.968990 - 4.69692i) q^{92} +(4.30938 - 7.46407i) q^{93} +(12.5792 - 1.20117i) q^{94} +(-2.50865 - 10.3408i) q^{95} +(0.981929 - 0.189251i) q^{96} +(-2.66682 + 1.71386i) q^{97} +(3.30356 + 6.17142i) q^{98} +(-0.214725 + 1.49344i) 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} - 2 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 - 2 * q^7 + 16 * q^8 + 8 * q^9	\( 160 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} - 16 q^{6} - 2 q^{7} + 16 q^{8} + 8 q^{9} - 2 q^{10} + 4 q^{11} - 8 q^{12} + 4 q^{13} - 9 q^{14} - 18 q^{15} + 8 q^{16} + 9 q^{17} - 8 q^{18} + 18 q^{20} + 7 q^{21} + 52 q^{22} + 22 q^{23} - 80 q^{24} + 42 q^{25} + 2 q^{26} + 16 q^{27} - 18 q^{28} - 54 q^{29} + 2 q^{30} - 15 q^{31} - 8 q^{32} + 18 q^{33} + 84 q^{34} + 82 q^{35} - 16 q^{36} + 3 q^{37} + 11 q^{38} + 2 q^{39} - 13 q^{40} + 22 q^{41} - 2 q^{42} - 96 q^{43} + 4 q^{44} - 20 q^{45} - 26 q^{47} + 16 q^{48} - 2 q^{49} - 4 q^{50} + 13 q^{51} - 2 q^{52} + 16 q^{53} + 8 q^{54} - 34 q^{55} + 2 q^{56} - 22 q^{57} - 5 q^{58} - 6 q^{59} - 2 q^{60} + 40 q^{61} - 8 q^{62} - 2 q^{63} - 16 q^{64} - 82 q^{65} + 4 q^{66} + 10 q^{67} - 46 q^{68} - 22 q^{69} + 100 q^{70} + 92 q^{71} - 8 q^{72} + 68 q^{73} - 3 q^{74} + 2 q^{75} - 7 q^{77} - 18 q^{78} - 78 q^{79} + 2 q^{80} + 8 q^{81} + 55 q^{82} - 42 q^{83} - 9 q^{84} + 50 q^{85} + 40 q^{86} + 6 q^{87} + 7 q^{88} - 80 q^{89} + 4 q^{90} - 62 q^{91} + 66 q^{92} + 26 q^{93} + 4 q^{94} - 17 q^{95} + 8 q^{96} - 8 q^{97} - 3 q^{98} + 36 q^{99}+O(q^{100}) \) 160 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 - 16 * q^6 - 2 * q^7 + 16 * q^8 + 8 * q^9 - 2 * q^10 + 4 * q^11 - 8 * q^12 + 4 * q^13 - 9 * q^14 - 18 * q^15 + 8 * q^16 + 9 * q^17 - 8 * q^18 + 18 * q^20 + 7 * q^21 + 52 * q^22 + 22 * q^23 - 80 * q^24 + 42 * q^25 + 2 * q^26 + 16 * q^27 - 18 * q^28 - 54 * q^29 + 2 * q^30 - 15 * q^31 - 8 * q^32 + 18 * q^33 + 84 * q^34 + 82 * q^35 - 16 * q^36 + 3 * q^37 + 11 * q^38 + 2 * q^39 - 13 * q^40 + 22 * q^41 - 2 * q^42 - 96 * q^43 + 4 * q^44 - 20 * q^45 - 26 * q^47 + 16 * q^48 - 2 * q^49 - 4 * q^50 + 13 * q^51 - 2 * q^52 + 16 * q^53 + 8 * q^54 - 34 * q^55 + 2 * q^56 - 22 * q^57 - 5 * q^58 - 6 * q^59 - 2 * q^60 + 40 * q^61 - 8 * q^62 - 2 * q^63 - 16 * q^64 - 82 * q^65 + 4 * q^66 + 10 * q^67 - 46 * q^68 - 22 * q^69 + 100 * q^70 + 92 * q^71 - 8 * q^72 + 68 * q^73 - 3 * q^74 + 2 * q^75 - 7 * q^77 - 18 * q^78 - 78 * q^79 + 2 * q^80 + 8 * q^81 + 55 * q^82 - 42 * q^83 - 9 * q^84 + 50 * q^85 + 40 * q^86 + 6 * q^87 + 7 * q^88 - 80 * q^89 + 4 * q^90 - 62 * q^91 + 66 * q^92 + 26 * q^93 + 4 * q^94 - 17 * q^95 + 8 * q^96 - 8 * q^97 - 3 * q^98 + 36 * 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
$5$	0.122200	+	2.56530i	0.0546496	+	1.14724i	0.845064	+	0.534664i	$0.179562\pi$
$5$	0.122200	+	2.56530i	0.0546496	+	1.14724i	−0.790415	+	0.612572i	$0.790135\pi$
$6$	−0.654861	+	0.755750i	−0.267346	+	0.308533i
$7$	−0.168303	+	2.64039i	−0.0636126	+	0.997975i
$7$	−0.168303	+	2.64039i	−0.0636126	+	0.997975i
$8$	0.959493	−	0.281733i	0.339232	−	0.0996075i
$9$	−0.888835	+	0.458227i	−0.296278	+	0.152742i
$10$	2.01875	−	1.58756i	0.638384	−	0.502031i
$11$	0.875190	−	1.22903i	0.263880	−	0.370567i	−0.661284	−	0.750136i	$-0.729988\pi$
$11$	0.875190	−	1.22903i	0.263880	−	0.370567i	0.925164	+	0.379569i	$0.123928\pi$
$12$	0.995472	+	0.0950560i	0.287368	+	0.0274403i
$13$	−0.538552	−	3.74571i	−0.149368	−	1.03887i	−0.917258	−	0.398293i	$-0.869603\pi$
$13$	−0.538552	−	3.74571i	−0.149368	−	1.03887i	0.767891	−	0.640581i	$-0.221306\pi$
$14$	2.24843	−	1.39448i	0.600917	−	0.372691i
$15$	2.46418	−	0.723548i	0.636248	−	0.186819i
$16$	−0.786053	−	0.618159i	−0.196513	−	0.154540i
$17$	1.93459	+	0.372862i	0.469207	+	0.0904322i	0.418374	−	0.908275i	$-0.362600\pi$
$17$	1.93459	+	0.372862i	0.469207	+	0.0904322i	0.0508331	+	0.998707i	$0.483812\pi$
$18$	0.888835	+	0.458227i	0.209501	+	0.108005i
$19$	−4.06838	+	0.784117i	−0.933351	+	0.179889i	−0.633187	−	0.773999i	$-0.718254\pi$
$19$	−4.06838	+	0.784117i	−0.933351	+	0.179889i	−0.300164	+	0.953888i	$0.597041\pi$
$20$	−2.46418	−	0.723548i	−0.551007	−	0.161790i
$21$	2.60564	−	0.458937i	0.568598	−	0.100148i
$22$	−1.50880			−0.321677
$23$	−4.12167	+	2.45191i	−0.859427	+	0.511258i
$23$	−4.12167	+	2.45191i	−0.859427	+	0.511258i
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−1.58846	+	0.151680i	−0.317693	+	0.0303360i
$26$	−2.73878	+	2.61142i	−0.537118	+	0.512141i
$27$	0.654861	+	0.755750i	0.126028	+	0.145444i
$28$	−2.44013	−	1.02263i	−0.461141	−	0.193260i
$29$	−4.23356	+	4.88579i	−0.786153	+	0.907269i	−0.997538	−	0.0701338i	$-0.977657\pi$
$29$	−4.23356	+	4.88579i	−0.786153	+	0.907269i	0.211384	+	0.977403i	$0.432203\pi$
$30$	−2.01875	−	1.58756i	−0.368571	−	0.289848i
$31$	6.23769	+	5.94763i	1.12032	+	1.06823i	0.997120	+	0.0758437i	$0.0241650\pi$
$31$	6.23769	+	5.94763i	1.12032	+	1.06823i	0.123203	+	0.992382i	$0.460683\pi$
$32$	−0.0475819	+	0.998867i	−0.00841137	+	0.176576i
$33$	−1.40072	−	0.560764i	−0.243834	−	0.0976165i
$34$	−0.818448	−	1.79215i	−0.140363	−	0.307351i
$35$	−6.79396	−	0.109091i	−1.14839	−	0.0184398i
$36$	−0.142315	−	0.989821i	−0.0237191	−	0.164970i
$37$	−3.93872	+	2.03055i	−0.647521	+	0.333821i	−0.750507	−	0.660862i	$-0.770191\pi$
$37$	−3.93872	+	2.03055i	−0.647521	+	0.333821i	0.102986	+	0.994683i	$0.467160\pi$
$38$	2.99862	+	2.85917i	0.486440	+	0.463819i
$39$	−3.51316	+	1.40646i	−0.562556	+	0.225213i
$40$	0.839978	+	2.42696i	0.132812	+	0.383736i
$41$	−9.30173	+	5.97786i	−1.45269	+	0.933585i	−0.453585	+	0.891213i	$0.649855\pi$
$41$	−9.30173	+	5.97786i	−1.45269	+	0.933585i	−0.999102	+	0.0423719i	$0.986509\pi$
$42$	−1.88526	−	1.85628i	−0.290902	−	0.286431i
$43$	5.25487	+	1.54297i	0.801360	+	0.235300i	0.656671	−	0.754177i	$-0.271964\pi$
$43$	5.25487	+	1.54297i	0.801360	+	0.235300i	0.144688	+	0.989477i	$0.453782\pi$
$44$	0.875190	+	1.22903i	0.131940	+	0.185284i
$45$	−1.28410	−	2.22413i	−0.191423	−	0.331554i
$46$	4.38807	+	1.93516i	0.646985	+	0.285324i
$47$	−6.31820	+	10.9434i	−0.921604	+	1.59626i	−0.124670	+	0.992198i	$0.539787\pi$
$47$	−6.31820	+	10.9434i	−0.921604	+	1.59626i	−0.796934	+	0.604067i	$0.793546\pi$
$48$	−0.415415	+	0.909632i	−0.0599600	+	0.131294i
$49$	−6.94335	−	0.888773i	−0.991907	−	0.126968i
$50$	1.04495	+	1.20594i	0.147779	+	0.170546i
$51$	−0.0937456	−	1.96796i	−0.0131270	−	0.275570i
$52$	3.71585	+	0.716171i	0.515295	+	0.0993150i
$53$	−6.25958	+	2.50596i	−0.859820	+	0.344220i	−0.759320	−	0.650717i	$-0.774468\pi$
$53$	−6.25958	+	2.50596i	−0.859820	+	0.344220i	−0.100500	+	0.994937i	$0.532044\pi$
$54$	0.235759	−	0.971812i	0.0320827	−	0.132247i
$55$	3.25978	+	2.09494i	0.439549	+	0.282481i
$56$	0.582399	+	2.58085i	0.0778263	+	0.344881i
$57$	1.72117	+	3.76884i	0.227975	+	0.499195i
$58$	6.43556	+	0.614521i	0.845030	+	0.0806906i
$59$	10.4033	−	8.18122i	1.35439	−	1.06510i	0.363333	−	0.931659i	$-0.381639\pi$
$59$	10.4033	−	8.18122i	1.35439	−	1.06510i	0.991056	−	0.133444i	$-0.0426037\pi$
$60$	−0.122200	+	2.56530i	−0.0157760	+	0.331179i
$61$	2.23676	−	9.22003i	0.286387	−	1.18050i	−0.628830	−	0.777543i	$-0.716466\pi$
$61$	2.23676	−	9.22003i	0.286387	−	1.18050i	0.915217	−	0.402961i	$-0.132019\pi$
$62$	1.22658	−	8.53103i	0.155776	−	1.08344i
$63$	−1.06030	−	2.42400i	−0.133586	−	0.305395i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	9.54306	−	1.83927i	1.18367	−	0.228134i
$66$	0.355713	+	1.46627i	0.0437853	+	0.180485i
$67$	−1.20025	+	0.114610i	−0.146634	+	0.0140018i	−0.168115	−	0.985767i	$-0.553768\pi$
$67$	−1.20025	+	0.114610i	−0.146634	+	0.0140018i	0.0214811	+	0.999769i	$0.493162\pi$
$68$	−0.985097	+	1.70624i	−0.119461	+	0.206912i
$69$	3.35451	+	3.42742i	0.403836	+	0.412613i
$70$	3.85202	+	5.59748i	0.460405	+	0.669027i
$71$	−2.43985	+	5.34252i	−0.289556	+	0.634040i	−0.997379	−	0.0723499i	$-0.976950\pi$
$71$	−2.43985	+	5.34252i	−0.289556	+	0.634040i	0.707823	+	0.706390i	$0.249677\pi$
$72$	−0.723734	+	0.690079i	−0.0852929	+	0.0813266i
$73$	2.00245	−	5.78570i	0.234369	−	0.677165i	−0.765079	−	0.643937i	$-0.777300\pi$
$73$	2.00245	−	5.78570i	0.234369	−	0.677165i	0.999448	−	0.0332281i	$-0.0105788\pi$
$74$	3.93872	+	2.03055i	0.457867	+	0.236047i
$75$	0.521899	+	1.50793i	0.0602637	+	0.174121i
$76$	0.589647	−	4.10108i	0.0676371	−	0.470427i
$77$	3.09783	+	2.51769i	0.353031	+	0.286918i
$78$	3.18350	+	2.04591i	0.360460	+	0.231654i
$79$	−9.53834	−	3.81858i	−1.07315	−	0.429623i	−0.233277	−	0.972410i	$-0.574945\pi$
$79$	−9.53834	−	3.81858i	−1.07315	−	0.429623i	−0.839870	+	0.542787i	$0.817369\pi$
$80$	1.48971	−	2.09200i	0.166554	−	0.233893i
$81$	0.580057	−	0.814576i	0.0644508	−	0.0905084i
$82$	10.2650	+	4.10947i	1.13357	+	0.453815i
$83$	5.30696	+	3.41057i	0.582514	+	0.374359i	0.798461	−	0.602046i	$-0.205648\pi$
$83$	5.30696	+	3.41057i	0.582514	+	0.374359i	−0.215947	+	0.976405i	$0.569284\pi$
$84$	−0.418526	+	2.61244i	−0.0456650	+	0.285040i
$85$	−0.720094	+	5.00836i	−0.0781052	+	0.543233i
$86$	−1.79126	−	5.17550i	−0.193156	−	0.558088i
$87$	5.74617	+	2.96236i	0.616054	+	0.317598i
$88$	0.493480	−	1.42582i	0.0526052	−	0.151993i
$89$	−8.92818	+	8.51300i	−0.946385	+	0.902377i	−0.995340	−	0.0964245i	$-0.969259\pi$
$89$	−8.92818	+	8.51300i	−0.946385	+	0.902377i	0.0489551	+	0.998801i	$0.484411\pi$
$90$	−1.06687	+	2.33612i	−0.112458	+	0.246249i
$91$	9.98080	−	0.791574i	1.04627	−	0.0829795i
$92$	−0.968990	−	4.69692i	−0.101024	−	0.489688i
$93$	4.30938	−	7.46407i	0.446862	−	0.773988i
$94$	12.5792	−	1.20117i	1.29744	−	0.123891i
$95$	−2.50865	−	10.3408i	−0.257382	−	1.06094i
$96$	0.981929	−	0.189251i	0.100218	−	0.0193154i
$97$	−2.66682	+	1.71386i	−0.270775	+	0.174016i	−0.668981	−	0.743280i	$-0.733269\pi$
$97$	−2.66682	+	1.71386i	−0.270775	+	0.174016i	0.398206	+	0.917296i	$0.369633\pi$
$98$	3.30356	+	6.17142i	0.333710	+	0.623408i
$99$	−0.214725	+	1.49344i	−0.0215806	+	0.150097i
$100$	0.376198	−	1.55071i	0.0376198	−	0.155071i
$101$	−0.660297	+	13.8613i	−0.0657020	+	1.37926i	0.689748	+	0.724049i	$0.257721\pi$
$101$	−0.660297	+	13.8613i	−0.0657020	+	1.37926i	−0.755450	+	0.655206i	$0.772582\pi$
$102$	−1.54868	+	1.21789i	−0.153342	+	0.120589i
$103$	15.5189	+	1.48187i	1.52912	+	0.146013i	0.825434	−	0.564499i	$-0.190931\pi$
$103$	15.5189	+	1.48187i	1.52912	+	0.146013i	0.703685	+	0.710512i	$0.251537\pi$
$104$	−1.57203	−	3.44226i	−0.154150	−	0.337541i
$105$	1.49572	+	6.62817i	0.145967	+	0.646843i
$106$	5.67221	+	3.64531i	0.550934	+	0.354064i
$107$	0.144809	−	0.596913i	0.0139993	−	0.0577057i	−0.964384	−	0.264508i	$-0.914790\pi$
$107$	0.144809	−	0.596913i	0.0139993	−	0.0577057i	0.978383	+	0.206802i	$0.0663056\pi$
$108$	−0.928368	+	0.371662i	−0.0893322	+	0.0357632i
$109$	−16.0693	−	3.09710i	−1.53916	−	0.296648i	−0.652038	−	0.758186i	$-0.726086\pi$
$109$	−16.0693	−	3.09710i	−1.53916	−	0.296648i	−0.887120	+	0.461538i	$0.847298\pi$
$110$	−0.184376	−	3.87052i	−0.0175795	−	0.369040i
$111$	2.90190	+	3.34897i	0.275436	+	0.317870i
$112$	1.76448	−	1.97145i	0.166727	−	0.186285i
$113$	4.58104	−	10.0311i	0.430948	−	0.943644i	−0.562224	−	0.826985i	$-0.690054\pi$
$113$	4.58104	−	10.0311i	0.430948	−	0.943644i	0.993172	−	0.116659i	$-0.0372186\pi$
$114$	2.07163	−	3.58817i	0.194026	−	0.336063i
$115$	−6.79355	−	10.2737i	−0.633501	−	0.958026i
$116$	−3.23242	−	5.59871i	−0.300122	−	0.519827i
$117$	2.19507	+	3.08254i	0.202934	+	0.284981i
$118$	−12.6987	−	3.72868i	−1.16901	−	0.343252i
$119$	−1.31010	+	5.04532i	−0.120097	+	0.462504i
$120$	2.16051	−	1.38848i	0.197227	−	0.126750i
$121$	2.85318	+	8.24374i	0.259380	+	0.749431i
$122$	−8.80786	+	3.52614i	−0.797426	+	0.319241i
$123$	8.00232	+	7.63020i	0.721545	+	0.687992i
$124$	−7.66066	+	3.94935i	−0.687948	+	0.354662i
$125$	1.24426	+	8.65398i	0.111290	+	0.774036i
$126$	−1.35949	+	2.26975i	−0.121113	+	0.202206i
$127$	0.306724	+	0.671632i	0.0272174	+	0.0595977i	0.922752	−	0.385393i	$-0.125934\pi$
$127$	0.306724	+	0.671632i	0.0272174	+	0.0595977i	−0.895535	+	0.444991i	$0.853207\pi$
$128$	−0.928368	−	0.371662i	−0.0820569	−	0.0328506i
$129$	0.260592	−	5.47051i	0.0229439	−	0.481651i
$130$	−7.03375	−	6.70667i	−0.616901	−	0.588214i
$131$	−7.60219	−	5.97843i	−0.664207	−	0.522338i	0.228174	−	0.973620i	$-0.426724\pi$
$131$	−7.60219	−	5.97843i	−0.664207	−	0.522338i	−0.892381	+	0.451282i	$0.850967\pi$
$132$	0.988054	−	1.14027i	0.0859990	−	0.0992482i
$133$	−1.38565	−	10.8741i	−0.120151	−	0.942904i
$134$	0.789570	+	0.911212i	0.0682084	+	0.0787167i
$135$	−1.85870	+	1.77227i	−0.159971	+	0.152532i
$136$	1.96127	−	0.187279i	0.168178	−	0.0160590i
$137$	−3.54342	−	6.13738i	−0.302735	−	0.524352i	0.674020	−	0.738713i	$-0.264566\pi$
$137$	−3.54342	−	6.13738i	−0.302735	−	0.524352i	−0.976754	+	0.214361i	$0.931233\pi$
$138$	0.846089	−	4.72061i	0.0720239	−	0.401845i
$139$	19.2784			1.63517			0.817586	−	0.575807i	$-0.195312\pi$
$139$	19.2784			1.63517			0.817586	+	0.575807i	$0.195312\pi$
$140$	2.32518	−	6.38462i	0.196513	−	0.539599i
$141$	12.1245	+	3.56008i	1.02107	+	0.299813i
$142$	5.76713	−	1.11152i	0.483967	−	0.0932770i
$143$	−5.07494	−	2.61631i	−0.424388	−	0.218787i
$144$	0.981929	+	0.189251i	0.0818274	+	0.0157709i
$145$	−13.0509	−	10.2633i	−1.08382	−	0.852322i
$146$	−5.87443	+	1.72489i	−0.486171	+	0.142753i
$147$	0.773236	+	6.95716i	0.0637755	+	0.573817i
$148$	−0.630643	−	4.38622i	−0.0518386	−	0.360545i
$149$	−14.8791	−	1.42079i	−1.21895	−	0.116395i	−0.534316	−	0.845285i	$-0.679431\pi$
$149$	−14.8791	−	1.42079i	−1.21895	−	0.116395i	−0.684631	+	0.728890i	$0.740037\pi$
$150$	0.925591	−	1.29981i	0.0755742	−	0.106129i
$151$	1.05212	−	0.827393i	0.0856199	−	0.0673323i	−0.574432	−	0.818553i	$-0.694777\pi$
$151$	1.05212	−	0.827393i	0.0856199	−	0.0673323i	0.660052	+	0.751220i	$0.270534\pi$
$152$	−3.68267	+	1.89855i	−0.298704	+	0.153993i
$153$	−1.89039	+	0.555068i	−0.152829	+	0.0448746i
$154$	0.253936	−	3.98382i	0.0204627	−	0.321026i
$155$	−14.4952	+	16.7283i	−1.16428	+	1.34365i
$156$	−0.180061	−	3.77995i	−0.0144164	−	0.302638i
$157$	2.40631	−	6.95257i	0.192044	−	0.554875i	−0.807335	−	0.590093i	$-0.799091\pi$
$157$	2.40631	−	6.95257i	0.192044	−	0.554875i	0.999380	+	0.0352174i	$0.0112124\pi$
$158$	2.42226	+	9.98469i	0.192705	+	0.794340i
$159$	3.91107	+	5.49233i	0.310168	+	0.435570i
$160$	−2.56821			−0.203035
$161$	−5.78031	−	11.2955i	−0.455552	−	0.890209i
$162$	−1.00000			−0.0785674
$163$	11.6407	+	16.3470i	0.911768	+	1.28040i	0.959549	+	0.281542i	$0.0908457\pi$
$163$	11.6407	+	16.3470i	0.911768	+	1.28040i	−0.0477808	+	0.998858i	$0.515215\pi$
$164$	−2.60678	−	10.7453i	−0.203556	−	0.839068i
$165$	1.26736	−	3.66179i	0.0986638	−	0.285070i
$166$	−0.300165	−	6.30125i	−0.0232973	−	0.489072i
$167$	−7.44777	+	8.59518i	−0.576326	+	0.665115i	−0.966811	−	0.255494i	$-0.917762\pi$
$167$	−7.44777	+	8.59518i	−0.576326	+	0.665115i	0.390485	+	0.920609i	$0.372307\pi$
$168$	2.37080	−	1.17444i	0.182911	−	0.0906101i
$169$	−1.26693	+	0.372003i	−0.0974558	+	0.0286156i
$170$	4.49739	−	2.31857i	0.344934	−	0.177826i
$171$	3.25682	−	2.56119i	0.249055	−	0.195859i
$172$	−3.17680	+	4.46120i	−0.242229	+	0.340163i
$173$	14.3666	+	1.37185i	1.09227	+	0.104299i	0.625610	−	0.780136i	$-0.284850\pi$
$173$	14.3666	+	1.37185i	1.09227	+	0.104299i	0.466663	+	0.884435i	$0.345456\pi$
$174$	−0.920042	−	6.39903i	−0.0697482	−	0.485109i
$175$	−0.133151	−	4.21970i	−0.0100653	−	0.318979i
$176$	−1.44768	+	0.425078i	−0.109123	+	0.0320415i
$177$	−10.4033	−	8.18122i	−0.781957	−	0.614938i
$178$	12.1133	+	2.33465i	0.907933	+	0.174990i
$179$	6.05018	+	3.11909i	0.452212	+	0.233131i	0.669258	−	0.743030i	$-0.266612\pi$
$179$	6.05018	+	3.11909i	0.452212	+	0.233131i	−0.217046	+	0.976161i	$0.569642\pi$
$180$	2.52180	−	0.486036i	0.187964	−	0.0362270i
$181$	−6.87912	−	2.01989i	−0.511321	−	0.150137i	0.0158867	−	0.999874i	$-0.494943\pi$
$181$	−6.87912	−	2.01989i	−0.511321	−	0.150137i	−0.527208	+	0.849736i	$0.676761\pi$
$182$	−6.43423	−	7.67096i	−0.476937	−	0.568609i
$183$	−9.48747			−0.701334
$184$	−3.26393	+	3.51380i	−0.240620	+	0.259041i
$185$	−5.69028	−	9.85586i	−0.418358	−	0.724617i
$186$	−8.57973	+	0.819265i	−0.629097	+	0.0600714i
$187$	2.15139	−	2.05135i	0.157325	−	0.150009i
$188$	−8.27508	−	9.54995i	−0.603522	−	0.696502i
$189$	−2.10569	+	1.60189i	−0.153166	+	0.116521i
$190$	−6.96821	+	8.04174i	−0.505527	+	0.583409i
$191$	10.0708	+	7.91975i	0.728696	+	0.573053i	0.912092	−	0.409986i	$-0.134467\pi$
$191$	10.0708	+	7.91975i	0.728696	+	0.573053i	−0.183396	+	0.983039i	$0.558709\pi$
$192$	−0.723734	−	0.690079i	−0.0522310	−	0.0498022i
$193$	0.274856	−	5.76994i	0.0197846	−	0.415330i	−0.967150	−	0.254207i	$-0.918186\pi$
$193$	0.274856	−	5.76994i	0.0197846	−	0.415330i	0.986934	−	0.161123i	$-0.0515114\pi$
$194$	2.94298	+	1.17819i	0.211294	+	0.0845892i
$195$	−4.03729	−	8.84043i	−0.289116	−	0.633077i
$196$	3.11084	−	6.27078i	0.222203	−	0.447913i
$197$	−0.441840	−	3.07306i	−0.0314798	−	0.218947i	0.968009	−	0.250915i	$-0.0807315\pi$
$197$	−0.441840	−	3.07306i	−0.0314798	−	0.218947i	−0.999489	+	0.0319684i	$0.989822\pi$
$198$	1.34107	−	0.691372i	0.0953060	−	0.0491337i
$199$	8.10196	+	7.72521i	0.574333	+	0.547625i	0.920598	−	0.390511i	$-0.127702\pi$
$199$	8.10196	+	7.72521i	0.574333	+	0.547625i	−0.346265	+	0.938137i	$0.612550\pi$
$200$	−1.48139	+	0.593058i	−0.104750	+	0.0419355i
$201$	0.394348	+	1.13939i	0.0278152	+	0.0803666i
$202$	11.6741	−	7.50251i	0.821389	−	0.527874i
$203$	−12.1879	−	12.0006i	−0.855422	−	0.842275i
$204$	1.89039	+	0.555068i	0.132354	+	0.0388625i
$205$	−16.4717	−	23.1312i	−1.15043	−	1.61555i
$206$	−7.79472	−	13.5009i	−0.543084	−	0.940649i
$207$	2.53995	−	4.06800i	0.176539	−	0.282746i
$208$	−1.89212	+	3.27724i	−0.131195	+	0.227236i
$209$	−2.59690	+	5.68642i	−0.179632	+	0.393338i
$210$	4.53155	−	5.06309i	0.312706	−	0.349387i
$211$	2.22054	+	2.56264i	0.152868	+	0.176419i	0.827018	−	0.562175i	$-0.190035\pi$
$211$	2.22054	+	2.56264i	0.152868	+	0.176419i	−0.674150	+	0.738594i	$0.735490\pi$
$212$	−0.320824	−	6.73493i	−0.0220343	−	0.462557i
$213$	5.76713	+	1.11152i	0.395158	+	0.0761604i
$214$	−0.570228	+	0.228285i	−0.0389800	+	0.0156052i
$215$	−3.31603	+	13.6689i	−0.226151	+	0.932208i
$216$	0.841254	+	0.540641i	0.0572401	+	0.0367859i
$217$	−16.7539	+	15.4689i	−1.13733	+	1.05010i
$218$	6.79828	+	14.8861i	0.460437	+	1.00822i
$219$	−6.09470	−	0.581974i	−0.411842	−	0.0393261i
$220$	−3.04589	+	2.39531i	−0.205354	+	0.161492i
$221$	0.354755	−	7.44723i	0.0238634	−	0.500955i
$222$	1.04472	−	4.30641i	0.0701173	−	0.289028i
$223$	1.12278	−	7.80908i	0.0751866	−	0.522935i	−0.917070	−	0.398727i	$-0.869452\pi$
$223$	1.12278	−	7.80908i	0.0751866	−	0.522935i	0.992256	−	0.124208i	$-0.0396388\pi$
$224$	−2.62939	−	0.293748i	−0.175684	−	0.0196268i
$225$	1.34238	−	0.862695i	0.0894920	−	0.0575130i
$226$	−10.8283	+	2.08699i	−0.720290	+	0.138825i
$227$	−0.715537	−	2.94948i	−0.0474918	−	0.195764i	0.943124	−	0.332442i	$-0.107873\pi$
$227$	−0.715537	−	2.94948i	−0.0474918	−	0.195764i	−0.990616	+	0.136678i	$0.956357\pi$
$228$	−4.12450	+	0.393842i	−0.273151	+	0.0260828i
$229$	5.24913	−	9.09176i	0.346872	−	0.600800i	−0.638820	−	0.769356i	$-0.720577\pi$
$229$	5.24913	−	9.09176i	0.346872	−	0.600800i	0.985692	+	0.168556i	$0.0539104\pi$
$230$	−4.42805	+	11.4932i	−0.291977	+	0.757838i
$231$	1.71638	−	3.60408i	0.112930	−	0.237131i
$232$	−2.68559	+	5.88062i	−0.176318	+	0.386081i
$233$	−4.86612	+	4.63984i	−0.318790	+	0.303966i	−0.832530	−	0.553980i	$-0.813108\pi$
$233$	−4.86612	+	4.63984i	−0.318790	+	0.303966i	0.513739	+	0.857946i	$0.328260\pi$
$234$	1.23770	−	3.57610i	0.0809110	−	0.233777i
$235$	−28.8453	−	14.8708i	−1.88166	−	0.970062i
$236$	4.32868	+	12.5069i	0.281773	+	0.814130i
$237$	−1.46219	+	10.1697i	−0.0949792	+	0.660595i
$238$	4.86973	−	1.85940i	0.315658	−	0.120527i
$239$	5.73370	+	3.68483i	0.370883	+	0.238352i	0.712783	−	0.701384i	$-0.247434\pi$
$239$	5.73370	+	3.68483i	0.370883	+	0.238352i	−0.341901	+	0.939736i	$0.611071\pi$
$240$	−2.38424	−	0.954506i	−0.153902	−	0.0616131i
$241$	13.9041	−	19.5255i	0.895640	−	1.25775i	−0.0699155	−	0.997553i	$-0.522273\pi$
$241$	13.9041	−	19.5255i	0.895640	−	1.25775i	0.965555	−	0.260197i	$-0.0837876\pi$
$242$	5.06014	−	7.10597i	0.325278	−	0.456789i
$243$	−0.928368	−	0.371662i	−0.0595548	−	0.0238422i
$244$	7.98137	+	5.12931i	0.510955	+	0.328371i
$245$	1.43149	−	17.9204i	0.0914545	−	1.14489i
$246$	1.57357	−	10.9444i	0.100327	−	0.697792i
$247$	5.12811	+	14.8167i	0.326294	+	0.942765i
$248$	7.66066	+	3.94935i	0.486452	+	0.250784i
$249$	2.06327	−	5.96143i	0.130755	−	0.377791i
$250$	6.32759	−	6.03334i	0.400192	−	0.381582i
$251$	11.8855	−	26.0257i	0.750209	−	1.64273i	−0.0157815	−	0.999875i	$-0.505024\pi$
$251$	11.8855	−	26.0257i	0.750209	−	1.64273i	0.765990	−	0.642852i	$-0.222249\pi$
$252$	2.63747	−	0.209177i	0.166145	−	0.0131769i
$253$	−0.593767	+	7.21155i	−0.0373298	+	0.453386i
$254$	0.369178	−	0.639435i	0.0231643	−	0.0401217i
$255$	5.03696	−	0.480971i	0.315426	−	0.0301196i
$256$	0.235759	+	0.971812i	0.0147349	+	0.0607382i
$257$	23.9862	−	4.62297i	1.49622	−	0.288373i	0.625528	−	0.780201i	$-0.284883\pi$
$257$	23.9862	−	4.62297i	1.49622	−	0.288373i	0.870692	+	0.491829i	$0.163671\pi$
$258$	−4.60730	+	2.96093i	−0.286838	+	0.184340i
$259$	−4.69855	−	10.7415i	−0.291954	−	0.667445i
$260$	−1.38311	+	9.61977i	−0.0857771	+	0.596593i
$261$	1.52414	−	6.28260i	0.0943420	−	0.388883i
$262$	−0.460181	+	9.66039i	−0.0284301	+	0.596821i
$263$	7.17207	−	5.64018i	0.442249	−	0.347788i	−0.372071	−	0.928204i	$-0.621352\pi$
$263$	7.17207	−	5.64018i	0.442249	−	0.347788i	0.814320	+	0.580416i	$0.197110\pi$
$264$	−1.50197	−	0.143421i	−0.0924397	−	0.00882692i
$265$	−7.19346	−	15.7515i	−0.441891	−	0.967605i
$266$	−8.05402	+	7.43632i	−0.493824	+	0.455950i
$267$	10.3779	+	6.66949i	0.635119	+	0.408166i
$268$	0.284256	−	1.17172i	0.0173637	−	0.0715742i
$269$	−6.26397	+	2.50771i	−0.381921	+	0.152898i	−0.554675	−	0.832067i	$-0.687158\pi$
$269$	−6.26397	+	2.50771i	−0.381921	+	0.152898i	0.172755	+	0.984965i	$0.444733\pi$
$270$	2.52180	+	0.486036i	0.153472	+	0.0295792i
$271$	−0.514158	−	10.7935i	−0.0312329	−	0.655659i	−0.959154	−	0.282883i	$-0.908709\pi$
$271$	−0.514158	−	10.7935i	−0.0312329	−	0.655659i	0.927921	−	0.372776i	$-0.121594\pi$
$272$	−1.29020	−	1.48897i	−0.0782300	−	0.0902823i
$273$	−3.12232	−	9.51283i	−0.188972	−	0.575743i
$274$	−2.94398	+	6.44642i	−0.177852	+	0.389442i
$275$	−1.20379	+	2.08502i	−0.0725912	+	0.125732i
$276$	−4.33607	+	2.04902i	−0.261001	+	0.123336i
$277$	8.25481	+	14.2977i	0.495983	+	0.859068i	0.999989	−	0.00463197i	$-0.00147441\pi$
$277$	8.25481	+	14.2977i	0.495983	+	0.859068i	−0.504006	+	0.863700i	$0.668141\pi$
$278$	−11.1826	−	15.7037i	−0.670685	−	0.941846i
$279$	−8.26964	−	2.42819i	−0.495090	−	0.145372i
$280$	−6.54949	+	1.80941i	−0.391407	+	0.108133i
$281$	0.516977	−	0.332241i	0.0308403	−	0.0198198i	−0.525130	−	0.851022i	$-0.675983\pi$
$281$	0.516977	−	0.332241i	0.0308403	−	0.0198198i	0.555970	+	0.831202i	$0.312347\pi$
$282$	−4.13296	−	11.9414i	−0.246114	−	0.711100i
$283$	−22.4933	+	9.00495i	−1.33709	+	0.535289i	−0.926418	−	0.376496i	$-0.877129\pi$
$283$	−22.4933	+	9.00495i	−1.33709	+	0.535289i	−0.410668	+	0.911785i	$0.634705\pi$
$284$	−4.25069	−	4.05302i	−0.252232	−	0.240503i
$285$	−9.45787	+	4.87587i	−0.560236	+	0.288822i
$286$	0.812568	+	5.65153i	0.0480481	+	0.334182i
$287$	−14.2184	−	25.5663i	−0.839285	−	1.50913i
$288$	−0.415415	−	0.909632i	−0.0244786	−	0.0536006i
$289$	−12.1786	−	4.87559i	−0.716391	−	0.286800i
$290$	−0.790004	+	16.5842i	−0.0463906	+	0.973859i
$291$	2.29428	+	2.18759i	0.134493	+	0.128239i
$292$	4.81255	+	3.78463i	0.281633	+	0.221479i
$293$	18.3562	−	21.1842i	1.07238	−	1.23760i	0.102317	−	0.994752i	$-0.467374\pi$
$293$	18.3562	−	21.1842i	1.07238	−	1.23760i	0.970065	−	0.242844i	$-0.0780803\pi$
$294$	5.21862	−	4.66541i	0.304356	−	0.272092i
$295$	22.2585	+	25.6877i	1.29594	+	1.49560i
$296$	−3.20710	+	3.05796i	−0.186409	+	0.177741i
$297$	1.50197	−	0.143421i	0.0871530	−	0.00832210i
$298$	7.47341	+	12.9443i	0.432923	+	0.749845i
$299$	11.4039	+	14.1181i	0.659504	+	0.816471i
$300$	−1.59569			−0.0921272
$301$	−4.95845	+	13.6152i	−0.285800	+	0.784768i
$302$	−1.28426	−	0.377093i	−0.0739009	−	0.0216993i
$303$	13.6263	−	2.62625i	0.782810	−	0.150874i
$304$	3.68267	+	1.89855i	0.211216	+	0.108889i
$305$	23.9255	+	4.61125i	1.36997	+	0.264040i
$306$	1.54868	+	1.21789i	0.0885320	+	0.0696223i
$307$	3.45815	−	1.01540i	0.197367	−	0.0579522i	−0.181555	−	0.983381i	$-0.558113\pi$
$307$	3.45815	−	1.01540i	0.197367	−	0.0579522i	0.378922	+	0.925429i	$0.376295\pi$
$308$	−3.39242	+	2.10399i	−0.193301	+	0.119886i
$309$	−2.21861	−	15.4308i	−0.126212	−	0.877826i
$310$	22.0345	+	2.10404i	1.25148	+	0.119502i
$311$	−4.36386	+	6.12818i	−0.247452	+	0.347497i	−0.919556	−	0.392959i	$-0.871451\pi$
$311$	−4.36386	+	6.12818i	−0.247452	+	0.347497i	0.672104	+	0.740457i	$0.265391\pi$
$312$	−2.97461	+	2.33926i	−0.168404	+	0.132434i
$313$	10.1605	−	5.23811i	0.574306	−	0.296075i	−0.146502	−	0.989210i	$-0.546801\pi$
$313$	10.1605	−	5.23811i	0.574306	−	0.296075i	0.720808	+	0.693135i	$0.243771\pi$
$314$	−7.05919	+	2.07277i	−0.398373	+	0.116973i
$315$	6.08870	−	3.01621i	0.343060	−	0.169944i
$316$	6.72824	−	7.76481i	0.378493	−	0.436804i
$317$	0.484379	+	10.1684i	0.0272054	+	0.571112i	0.970783	+	0.239960i	$0.0771343\pi$
$317$	0.484379	+	10.1684i	0.0272054	+	0.571112i	−0.943577	+	0.331152i	$0.892563\pi$
$318$	2.20528	−	6.37173i	0.123666	−	0.357309i
$319$	2.29963	+	9.47918i	0.128754	+	0.530732i
$320$	1.48971	+	2.09200i	0.0832771	+	0.116946i
$321$	−0.614227			−0.0342828
$322$	−5.84812	+	11.2605i	−0.325903	+	0.627525i
$323$	−8.16302			−0.454203
$324$	0.580057	+	0.814576i	0.0322254	+	0.0452542i
$325$	1.42362	+	5.86825i	0.0789683	+	0.325512i
$326$	6.56365	−	18.9644i	0.363527	−	1.05034i
$327$	0.778679	+	16.3465i	0.0430611	+	0.903963i
$328$	−7.24079	+	8.35632i	−0.399806	+	0.461400i
$329$	−27.8316	−	18.5243i	−1.53441	−	1.02128i
$330$	−3.71795	+	1.09169i	−0.204666	+	0.0600955i
$331$	−27.0169	+	13.9282i	−1.48498	+	0.765561i	−0.994385	−	0.105827i	$-0.966251\pi$
$331$	−27.0169	+	13.9282i	−1.48498	+	0.765561i	−0.490596	+	0.871387i	$0.663221\pi$
$332$	−4.95873	+	3.89959i	−0.272146	+	0.214018i
$333$	2.57042	−	3.60965i	0.140858	−	0.197808i
$334$	11.3216	+	1.08108i	0.619488	+	0.0591539i
$335$	−0.440679	−	3.06499i	−0.0240768	−	0.167458i
$336$	−2.33187	−	1.24995i	−0.127214	−	0.0681905i
$337$	9.21306	−	2.70520i	0.501867	−	0.147361i	−0.0209936	−	0.999780i	$-0.506683\pi$
$337$	9.21306	−	2.70520i	0.501867	−	0.147361i	0.522861	+	0.852418i	$0.324865\pi$
$338$	1.03791	+	0.816225i	0.0564551	+	0.0443968i
$339$	−10.8283	−	2.08699i	−0.588115	−	0.113350i
$340$	−4.49739	−	2.31857i	−0.243905	−	0.125742i
$341$	12.7690	−	2.46102i	0.691479	−	0.133272i
$342$	−3.97543	−	1.16729i	−0.214966	−	0.0631198i
$343$	3.51530	−	18.1836i	0.189808	−	0.981821i
$344$	5.47671			0.295284
$345$	−8.38245	+	9.02416i	−0.451296	+	0.485844i
$346$	−7.21598	−	12.4985i	−0.387934	−	0.671921i
$347$	32.1475	−	3.06971i	1.72577	−	0.164791i	0.815486	−	0.578777i	$-0.196470\pi$
$347$	32.1475	−	3.06971i	1.72577	−	0.164791i	0.910283	+	0.413987i	$0.135864\pi$
$348$	−4.67882	+	4.46124i	−0.250811	+	0.239148i
$349$	11.0491	+	12.7513i	0.591443	+	0.682562i	0.970025	−	0.243006i	$-0.0781336\pi$
$349$	11.0491	+	12.7513i	0.591443	+	0.682562i	−0.378582	+	0.925568i	$0.623588\pi$
$350$	−3.36003	+	2.55613i	−0.179601	+	0.136631i
$351$	2.47814	−	2.85993i	0.132274	−	0.152652i
$352$	1.18600	+	0.932678i	0.0632138	+	0.0497119i
$353$	−12.9427	−	12.3408i	−0.688870	−	0.656837i	0.262484	−	0.964936i	$-0.415458\pi$
$353$	−12.9427	−	12.3408i	−0.688870	−	0.656837i	−0.951354	+	0.308100i	$0.900307\pi$
$354$	−0.629738	+	13.2198i	−0.0334702	+	0.702625i
$355$	−14.0033	−	5.60608i	−0.743218	−	0.297540i
$356$	−5.12467	−	11.2215i	−0.271607	−	0.594737i
$357$	5.21197	+	0.0836891i	0.275847	+	0.00442930i
$358$	−0.968718	−	6.73758i	−0.0511983	−	0.356092i
$359$	−8.08094	+	4.16601i	−0.426495	+	0.219874i	−0.658091	−	0.752939i	$-0.728636\pi$
$359$	−8.08094	+	4.16601i	−0.426495	+	0.219874i	0.231595	+	0.972812i	$0.425605\pi$
$360$	−1.85870	−	1.77227i	−0.0979620	−	0.0934066i
$361$	−1.70209	+	0.681414i	−0.0895837	+	0.0358639i
$362$	2.34493	+	6.77522i	0.123247	+	0.356098i
$363$	7.33869	−	4.71629i	0.385182	−	0.247541i
$364$	−2.51636	+	9.69076i	−0.131893	+	0.507934i
$365$	15.0867	+	4.42987i	0.789676	+	0.231870i
$366$	5.50327	+	7.72826i	0.287661	+	0.403963i
$367$	15.5856	+	26.9951i	0.813564	+	1.40913i	0.910354	+	0.413829i	$0.135809\pi$
$367$	15.5856	+	26.9951i	0.813564	+	1.40913i	−0.0967905	+	0.995305i	$0.530858\pi$
$368$	4.75552	+	0.620516i	0.247899	+	0.0323466i
$369$	5.52850	−	9.57564i	0.287802	−	0.498488i
$370$	−4.72766	+	10.3521i	−0.245779	+	0.538181i
$371$	−5.56321	−	16.9495i	−0.288827	−	0.879975i
$372$	5.64409	+	6.51363i	0.292632	+	0.337716i
$373$	−0.649384	−	13.6323i	−0.0336238	−	0.705851i	−0.951253	−	0.308413i	$-0.900202\pi$
$373$	−0.649384	−	13.6323i	−0.0336238	−	0.705851i	0.917629	−	0.397439i	$-0.130101\pi$
$374$	−2.91891	−	0.562574i	−0.150933	−	0.0290900i
$375$	8.11670	−	3.24944i	0.419144	−	0.167800i
$376$	−2.97914	+	12.2802i	−0.153638	+	0.633303i
$377$	20.5808	+	13.2265i	1.05996	+	0.681198i
$378$	2.52629	+	0.786055i	0.129938	+	0.0404303i
$379$	−11.7115	−	25.6445i	−0.601578	−	1.31727i	−0.928188	−	0.372113i	$-0.878634\pi$
$379$	−11.7115	−	25.6445i	−0.601578	−	1.31727i	0.326610	−	0.945159i	$-0.394094\pi$
$380$	10.5926	+	1.01147i	0.543387	+	0.0518872i
$381$	0.580387	−	0.456422i	0.0297341	−	0.0233832i
$382$	0.609611	−	12.7973i	0.0311904	−	0.654768i
$383$	−3.34469	+	13.7870i	−0.170906	+	0.704484i	0.820275	+	0.571969i	$0.193820\pi$
$383$	−3.34469	+	13.7870i	−0.170906	+	0.704484i	−0.991181	+	0.132515i	$0.957695\pi$
$384$	−0.142315	+	0.989821i	−0.00726247	+	0.0505116i
$385$	−6.08008	+	8.25452i	−0.309870	+	0.420689i
$386$	−4.85949	+	3.12300i	−0.247341	+	0.158957i
$387$	−5.37774	+	1.03647i	−0.273366	+	0.0526870i
$388$	−0.747369	−	3.08070i	−0.0379419	−	0.156399i
$389$	2.70845	−	0.258626i	0.137324	−	0.0131128i	−0.0261677	−	0.999658i	$-0.508330\pi$
$389$	2.70845	−	0.258626i	0.137324	−	0.0131128i	0.163492	+	0.986545i	$0.447724\pi$
$390$	−4.85935	+	8.41664i	−0.246063	+	0.426193i
$391$	−8.88796	+	3.20663i	−0.449483	+	0.162166i
$392$	−6.91249	+	1.10340i	−0.349133	+	0.0557299i
$393$	−4.01762	+	8.79737i	−0.202662	+	0.443769i
$394$	−2.24695	+	2.14246i	−0.113200	+	0.107936i
$395$	8.63020	−	24.9353i	0.434232	−	1.25463i
$396$	−1.34107	−	0.691372i	−0.0673915	−	0.0347428i
$397$	1.07545	+	3.10731i	0.0539753	+	0.155951i	0.968766	−	0.247977i	$-0.0797657\pi$
$397$	1.07545	+	3.10731i	0.0539753	+	0.155951i	−0.914791	+	0.403928i	$0.867645\pi$
$398$	1.59317	−	11.0807i	0.0798583	−	0.555427i
$399$	−10.2409	+	3.91026i	−0.512686	+	0.195758i
$400$	1.34238	+	0.862695i	0.0671190	+	0.0431347i
$401$	−18.4554	−	7.38843i	−0.921619	−	0.368960i	−0.138164	−	0.990409i	$-0.544120\pi$
$401$	−18.4554	−	7.38843i	−0.921619	−	0.368960i	−0.783455	+	0.621449i	$0.786544\pi$
$402$	0.699378	−	0.982140i	0.0348818	−	0.0489847i
$403$	18.9188	−	26.5677i	0.942412	−	1.32343i
$404$	−12.8830	−	5.15758i	−0.640954	−	0.256599i
$405$	2.16051	+	1.38848i	0.107357	+	0.0689940i
$406$	−2.70570	+	16.8890i	−0.134282	+	0.838186i
$407$	−0.951515	+	6.61793i	−0.0471648	+	0.328039i
$408$	−0.644387	−	1.86183i	−0.0319019	−	0.0921746i
$409$	31.2766	+	16.1242i	1.54653	+	0.797290i	0.999214	−	0.0396380i	$-0.0126205\pi$
$409$	31.2766	+	16.1242i	1.54653	+	0.797290i	0.547313	+	0.836928i	$0.315651\pi$
$410$	−9.28763	+	26.8349i	−0.458684	+	1.32528i
$411$	−5.12899	+	4.89048i	−0.252994	+	0.241230i
$412$	−6.47609	+	14.1807i	−0.319054	+	0.698631i
$413$	19.8507	+	28.8456i	0.976790	+	1.41940i
$414$	−4.78701	+	0.290686i	−0.235269	+	0.0142864i
$415$	−8.10063	+	14.0307i	−0.397644	+	0.688740i
$416$	3.76710	−	0.359714i	0.184697	−	0.0176364i
$417$	−4.54505	−	18.7350i	−0.222572	−	0.917455i
$418$	6.13838	−	1.18307i	0.300238	−	0.0578661i
$419$	19.9703	−	12.8341i	0.975613	−	0.626988i	0.0473363	−	0.998879i	$-0.484927\pi$
$419$	19.9703	−	12.8341i	0.975613	−	0.626988i	0.928277	+	0.371891i	$0.121290\pi$
$420$	−6.75283	−	0.754405i	−0.329504	−	0.0368112i
$421$	−4.96100	+	34.5045i	−0.241784	+	1.68165i	0.401375	+	0.915914i	$0.368533\pi$
$421$	−4.96100	+	34.5045i	−0.241784	+	1.68165i	−0.643159	+	0.765733i	$0.722377\pi$
$422$	0.799425	−	3.29527i	0.0389154	−	0.160411i
$423$	0.601264	−	12.6221i	0.0292345	−	0.613707i
$424$	−5.30002	+	4.16798i	−0.257392	+	0.202415i
$425$	−3.12958	−	0.298839i	−0.151807	−	0.0144958i
$426$	−2.43985	−	5.34252i	−0.118211	−	0.258846i
$427$	23.9680	+	7.45767i	1.15990	+	0.360902i
$428$	0.516720	+	0.332076i	0.0249766	+	0.0160515i
$429$	−1.34610	+	5.54870i	−0.0649904	+	0.267894i
$430$	13.0578	−	5.22756i	0.629703	−	0.252095i
$431$	−30.3694	−	5.85322i	−1.46284	−	0.281940i	−0.605154	−	0.796108i	$-0.706888\pi$
$431$	−30.3694	−	5.85322i	−1.46284	−	0.281940i	−0.857689	+	0.514169i	$0.828101\pi$
$432$	−0.0475819	−	0.998867i	−0.00228929	−	0.0480580i
$433$	−8.10616	−	9.35500i	−0.389557	−	0.449573i	0.526767	−	0.850009i	$-0.323404\pi$
$433$	−8.10616	−	9.35500i	−0.389557	−	0.449573i	−0.916324	+	0.400437i	$0.868858\pi$
$434$	22.3188	+	4.67445i	1.07134	+	0.224381i
$435$	−6.89715	+	15.1026i	−0.330693	+	0.724117i
$436$	8.18251	−	14.1725i	0.391871	−	0.678741i
$437$	14.8459	−	13.2072i	0.710178	−	0.631785i
$438$	3.06121	+	5.30218i	0.146270	+	0.253348i
$439$	−10.4776	−	14.7138i	−0.500070	−	0.702250i	0.484979	−	0.874526i	$-0.338827\pi$
$439$	−10.4776	−	14.7138i	−0.500070	−	0.702250i	−0.985049	+	0.172276i	$0.944888\pi$
$440$	3.71795	+	1.09169i	0.177246	+	0.0520442i
$441$	6.57875	−	2.39165i	0.313274	−	0.113888i
$442$	−6.27211	+	4.03084i	−0.298334	+	0.191728i
$443$	5.40927	+	15.6290i	0.257002	+	0.742558i	0.997511	+	0.0705119i	$0.0224633\pi$
$443$	5.40927	+	15.6290i	0.257002	+	0.742558i	−0.740509	+	0.672046i	$0.765416\pi$
$444$	−4.11390	+	1.64696i	−0.195237	+	0.0781611i
$445$	−22.9294	−	21.8632i	−1.08696	−	1.03641i
$446$	−7.01236	+	3.61512i	−0.332045	+	0.171181i
$447$	2.12715	+	14.7947i	0.100611	+	0.699765i
$448$	1.28592	+	2.31223i	0.0607539	+	0.109243i
$449$	3.73830	+	8.18573i	0.176421	+	0.386308i	0.977099	−	0.212787i	$-0.0682542\pi$
$449$	3.73830	+	8.18573i	0.176421	+	0.386308i	−0.800677	+	0.599096i	$0.795527\pi$
$450$	−1.48139	−	0.593058i	−0.0698333	−	0.0279570i
$451$	−0.793799	+	16.6639i	−0.0373785	+	0.784672i
$452$	7.98107	+	7.60993i	0.375398	+	0.357941i
$453$	−1.05212	−	0.827393i	−0.0494327	−	0.0388743i
$454$	−1.98753	+	2.29373i	−0.0932792	+	0.107650i
$455$	3.25028	+	25.5070i	0.152375	+	1.19579i
$456$	2.71326	+	3.13126i	0.127060	+	0.146635i
$457$	−9.75928	+	9.30546i	−0.456520	+	0.435291i	−0.883118	−	0.469150i	$-0.844560\pi$
$457$	−9.75928	+	9.30546i	−0.456520	+	0.435291i	0.426598	+	0.904441i	$0.359712\pi$
$458$	−10.4507	+	0.997923i	−0.488330	+	0.0466299i
$459$	0.985097	+	1.70624i	0.0459804	+	0.0796404i
$460$	11.9306	−	3.05971i	0.556267	−	0.142660i
$461$	9.99456			0.465493			0.232747	−	0.972537i	$-0.425229\pi$
$461$	9.99456			0.465493			0.232747	+	0.972537i	$0.425229\pi$
$462$	−3.93139	+	0.692444i	−0.182905	+	0.0322154i
$463$	−10.4619	−	3.07190i	−0.486207	−	0.142763i	0.0294361	−	0.999567i	$-0.490629\pi$
$463$	−10.4619	−	3.07190i	−0.486207	−	0.142763i	−0.515643	+	0.856803i	$0.672447\pi$
$464$	6.34800	−	1.22348i	0.294699	−	0.0567985i
$465$	19.6742	+	10.1427i	0.912368	+	0.470358i
$466$	6.60213	+	1.27246i	0.305838	+	0.0589454i
$467$	19.3112	+	15.1865i	0.893616	+	0.702747i	0.955391	−	0.295343i	$-0.0954339\pi$
$467$	19.3112	+	15.1865i	0.893616	+	0.702747i	−0.0617757	+	0.998090i	$0.519676\pi$
$468$	−3.63094	+	1.06614i	−0.167840	+	0.0492824i
$469$	−0.100609	−	3.18841i	−0.00464570	−	0.147227i
$470$	4.61853	+	32.1226i	0.213037	+	1.48170i
$471$	−7.32389	−	0.699347i	−0.337467	−	0.0322242i
$472$	7.67694	−	10.7808i	0.353360	−	0.496225i
$473$	6.49536	−	5.10801i	0.298657	−	0.234867i
$474$	9.13217	−	4.70796i	0.419454	−	0.216244i
$475$	6.34355	−	1.86263i	0.291062	−	0.0854635i
$476$	−4.33934	−	2.88821i	−0.198893	−	0.132381i
$477$	4.41544	−	5.09569i	0.202169	−	0.233316i
$478$	−0.324303	−	6.80795i	−0.0148333	−	0.311388i
$479$	−4.25847	+	12.3040i	−0.194574	+	0.562185i	−0.999514	−	0.0311711i	$-0.990076\pi$
$479$	−4.25847	+	12.3040i	−0.194574	+	0.562185i	0.804940	+	0.593356i	$0.202198\pi$
$480$	0.605478	+	2.49581i	0.0276362	+	0.113918i
$481$	9.72707	+	13.6598i	0.443516	+	0.622831i
$482$	−23.9702			−1.09181
$483$	−9.61432	+	8.28039i	−0.437467	+	0.376771i
$484$	−8.72352			−0.396524
$485$	−4.72246	−	6.63176i	−0.214436	−	0.301133i
$486$	0.235759	+	0.971812i	0.0106942	+	0.0440823i
$487$	−4.01150	+	11.5905i	−0.181778	+	0.525214i	−0.998669	−	0.0515788i	$-0.983575\pi$
$487$	−4.01150	+	11.5905i	−0.181778	+	0.525214i	0.816891	+	0.576792i	$0.195696\pi$
$488$	−0.451432	−	9.47672i	−0.0204354	−	0.428991i
$489$	13.1419	−	15.1665i	0.594295	−	0.685853i
$490$	−15.4278	+	9.22878i	−0.696959	+	0.416914i
$491$	−21.9067	+	6.43238i	−0.988634	+	0.290289i	−0.735784	−	0.677216i	$-0.763186\pi$
$491$	−21.9067	+	6.43238i	−0.988634	+	0.290289i	−0.252850	+	0.967505i	$0.581368\pi$
$492$	−9.82785	+	5.06661i	−0.443074	+	0.228420i
$493$	−10.0119	+	7.87347i	−0.450915	+	0.354603i
$494$	9.09474	−	12.7718i	0.409192	−	0.574629i
$495$	−3.85737	−	0.368334i	−0.173376	−	0.0165554i
$496$	−1.22658	−	8.53103i	−0.0550750	−	0.383055i
$497$	−13.6957	−	7.34131i	−0.614336	−	0.329303i
$498$	−6.05286	+	1.77728i	−0.271235	+	0.0796418i
$499$	−22.3658	−	17.5886i	−1.00123	−	0.787375i	−0.0240324	−	0.999711i	$-0.507651\pi$
$499$	−22.3658	−	17.5886i	−1.00123	−	0.787375i	−0.977197	+	0.212336i	$0.931893\pi$
$500$	−8.58498	−	1.65462i	−0.383932	−	0.0739968i
$501$	10.1088	+	5.21144i	0.451627	+	0.232830i
$502$	−28.0942	+	5.41471i	−1.25391	+	0.241670i
$503$	10.8944	+	3.19889i	0.485758	+	0.142631i	0.515436	−	0.856928i	$-0.327630\pi$
$503$	10.8944	+	3.19889i	0.485758	+	0.142631i	−0.0296780	+	0.999560i	$0.509448\pi$
$504$	−1.70027	−	2.02708i	−0.0757362	−	0.0902935i
$505$	−35.6392			−1.58592
$506$	6.21877	−	3.69944i	0.276458	−	0.164460i
$507$	0.660206	+	1.14351i	0.0293208	+	0.0507851i
$508$	−0.735013	+	0.0701852i	−0.0326109	+	0.00311397i
$509$	22.0430	−	21.0179i	0.977038	−	0.931604i	−0.0206345	−	0.999787i	$-0.506569\pi$
$509$	22.0430	−	21.0179i	0.977038	−	0.931604i	0.997673	+	0.0681829i	$0.0217201\pi$
$510$	−3.31351	−	3.82399i	−0.146725	−	0.169329i
$511$	14.9395	+	6.26101i	0.660884	+	0.276971i
$512$	0.654861	−	0.755750i	0.0289410	−	0.0333997i
$513$	−3.25682	−	2.56119i	−0.143792	−	0.113079i
$514$	−17.6791	−	16.8570i	−0.779794	−	0.743532i
$515$	−1.90503	+	39.9916i	−0.0839458	+	1.76224i
$516$	5.08440	+	2.03549i	0.223828	+	0.0896074i
$517$	7.92022	+	17.3429i	0.348331	+	0.762738i
$518$	−6.02435	+	10.0580i	−0.264695	+	0.441924i
$519$	−2.05388	−	14.2851i	−0.0901555	−	0.627045i
$520$	8.63832	−	4.45336i	0.378815	−	0.195293i
$521$	−9.97048	−	9.50683i	−0.436815	−	0.416502i	0.439499	−	0.898243i	$-0.355156\pi$
$521$	−9.97048	−	9.50683i	−0.436815	−	0.416502i	−0.876314	+	0.481741i	$0.840005\pi$
$522$	−6.00174	+	2.40274i	−0.262689	+	0.105165i
$523$	11.4357	+	33.0414i	0.500050	+	1.44480i	0.859259	+	0.511541i	$0.170925\pi$
$523$	11.4357	+	33.0414i	0.500050	+	1.44480i	−0.359209	+	0.933257i	$0.616954\pi$
$524$	8.13606	−	5.22873i	0.355425	−	0.228418i
$525$	−4.06936	+	1.12423i	−0.177601	+	0.0490654i
$526$	−8.75456	−	2.57057i	−0.381717	−	0.112082i
$527$	9.84973	+	13.8320i	0.429061	+	0.602532i
$528$	0.754400	+	1.30666i	0.0328310	+	0.0568650i
$529$	10.9763	−	20.2119i	0.477230	−	0.878778i
$530$	−8.65816	+	14.9964i	−0.376086	+	0.651401i
$531$	−5.49794	+	12.0388i	−0.238590	+	0.522440i
$532$	10.7292	+	2.24713i	0.465171	+	0.0974252i
$533$	27.4008	+	31.6222i	1.18686	+	1.36971i
$534$	−0.586983	−	12.3223i	−0.0254013	−	0.533238i
$535$	1.54895	+	0.298537i	0.0669672	+	0.0129069i
$536$	−1.11934	+	0.448116i	−0.0483481	+	0.0193557i
$537$	1.60478	−	6.61499i	0.0692513	−	0.285458i
$538$	5.67618	+	3.64786i	0.244718	+	0.157270i
$539$	−7.16908	+	7.75575i	−0.308794	+	0.334064i
$540$	−1.06687	−	2.33612i	−0.0459109	−	0.100531i
$541$	−28.9136	−	2.76091i	−1.24309	−	0.118701i	−0.547295	−	0.836940i	$-0.684343\pi$
$541$	−28.9136	−	2.76091i	−1.24309	−	0.118701i	−0.695797	+	0.718239i	$0.744949\pi$
$542$	−8.49389	+	6.67967i	−0.364844	+	0.286916i
$543$	−0.341140	+	7.16142i	−0.0146397	+	0.307326i
$544$	−0.464491	+	1.91466i	−0.0199149	+	0.0820902i
$545$	5.98132	−	41.6010i	0.256211	−	1.78199i
$546$	−5.93780	+	8.06135i	−0.254114	+	0.344994i
$547$	7.00470	−	4.50165i	0.299499	−	0.192477i	−0.382257	−	0.924056i	$-0.624853\pi$
$547$	7.00470	−	4.50165i	0.299499	−	0.192477i	0.681756	+	0.731580i	$0.261217\pi$
$548$	6.95877	−	1.34119i	0.297264	−	0.0572929i
$549$	2.23676	+	9.22003i	0.0954624	+	0.393501i
$550$	2.39667	−	0.228855i	0.102195	−	0.00975840i
$551$	13.3927	−	23.1969i	0.570549	−	0.988221i
$552$	4.18425	+	2.34351i	0.178093	+	0.0997466i
$553$	11.6879	−	24.5423i	0.497019	−	1.04364i
$554$	6.85834	−	15.0177i	0.291383	−	0.638040i
$555$	−8.23650	+	7.85349i	−0.349620	+	0.333362i
$556$	−6.30534	+	18.2181i	−0.267406	+	0.772619i
$557$	4.74175	+	2.44454i	0.200914	+	0.103579i	0.555748	−	0.831351i	$-0.312432\pi$
$557$	4.74175	+	2.44454i	0.200914	+	0.103579i	−0.354833	+	0.934930i	$0.615462\pi$
$558$	2.81892	+	8.14474i	0.119334	+	0.344794i
$559$	2.94950	−	20.5142i	0.124750	−	0.867658i
$560$	5.27298	+	4.28550i	0.222824	+	0.181095i
$561$	−2.50073	−	1.60712i	−0.105581	−	0.0678528i
$562$	−0.570512	−	0.228399i	−0.0240656	−	0.00963441i
$563$	−1.09269	+	1.53447i	−0.0460513	+	0.0646700i	−0.836960	−	0.547265i	$-0.815669\pi$
$563$	−1.09269	+	1.53447i	−0.0460513	+	0.0646700i	0.790908	+	0.611935i	$0.209608\pi$
$564$	−7.32983	+	10.2933i	−0.308642	+	0.433426i
$565$	26.2925	+	10.5259i	1.10613	+	0.442829i
$566$	20.3826	+	13.0991i	0.856744	+	0.550596i
$567$	2.05318	+	1.66867i	0.0862252	+	0.0700777i
$568$	−0.835854	+	5.81349i	−0.0350716	+	0.243929i
$569$	−2.42342	−	7.00201i	−0.101595	−	0.293539i	0.882736	−	0.469869i	$-0.155699\pi$
$569$	−2.42342	−	7.00201i	−0.101595	−	0.293539i	−0.984331	+	0.176329i	$0.943578\pi$
$570$	9.45787	+	4.87587i	0.396147	+	0.204228i
$571$	−0.171487	+	0.495479i	−0.00717650	+	0.0207351i	−0.948532	−	0.316681i	$-0.897432\pi$
$571$	−0.171487	+	0.495479i	−0.00717650	+	0.0207351i	0.941356	+	0.337416i	$0.109553\pi$
$572$	4.13227	−	3.94011i	0.172779	−	0.164744i
$573$	5.32223	−	11.6541i	0.222339	−	0.486855i
$574$	−12.5782	+	26.4119i	−0.525005	+	1.10241i
$575$	6.17522	−	4.51994i	0.257524	−	0.188495i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	34.6174	−	3.30556i	1.44114	−	0.137612i	0.654985	−	0.755642i	$-0.272675\pi$
$577$	34.6174	−	3.30556i	1.44114	−	0.137612i	0.786155	+	0.618030i	$0.212069\pi$
$578$	3.09276	+	12.7486i	0.128642	+	0.530270i
$579$	−5.67210	+	1.09321i	−0.235724	+	0.0454321i
$580$	13.9674	−	8.97628i	0.579963	−	0.372720i
$581$	−9.89843	+	13.4384i	−0.410656	+	0.557520i
$582$	0.451146	−	3.13779i	0.0187006	−	0.130066i
$583$	−2.39842	+	9.88642i	−0.0993324	+	0.409454i
$584$	0.291317	−	6.11549i	0.0120548	−	0.253061i
$585$	−7.63941	+	6.00770i	−0.315851	+	0.248388i
$586$	−27.9038	−	2.66449i	−1.15270	−	0.110069i
$587$	14.5361	+	31.8296i	0.599969	+	1.31375i	0.929227	+	0.369510i	$0.120474\pi$
$587$	14.5361	+	31.8296i	0.599969	+	1.31375i	−0.329257	+	0.944240i	$0.606798\pi$
$588$	−6.82742	−	1.54476i	−0.281558	−	0.0637047i
$589$	−30.0409	−	19.3061i	−1.23782	−	0.795496i
$590$	8.01338	−	33.0316i	0.329906	−	1.35989i
$591$	−2.88227	+	1.15389i	−0.118561	+	0.0474646i
$592$	4.35125	+	0.838634i	0.178835	+	0.0344676i
$593$	0.938760	+	19.7070i	0.0385502	+	0.809269i	0.932515	+	0.361132i	$0.117609\pi$
$593$	0.938760	+	19.7070i	0.0385502	+	0.809269i	−0.893965	+	0.448137i	$0.852088\pi$
$594$	−0.988054	−	1.14027i	−0.0405403	−	0.0467860i
$595$	−13.1029	−	2.74426i	−0.537165	−	0.112503i
$596$	6.20913	−	13.5961i	0.254336	−	0.556918i
$597$	5.59733	−	9.69487i	0.229084	−	0.396785i
$598$	4.88537	−	17.4786i	0.199778	−	0.714754i
$599$	20.5841	+	35.6526i	0.841042	+	1.45673i	0.889015	+	0.457879i	$0.151391\pi$
$599$	20.5841	+	35.6526i	0.841042	+	1.45673i	−0.0479725	+	0.998849i	$0.515276\pi$
$600$	0.925591	+	1.29981i	0.0377871	+	0.0530645i
$601$	−44.9283	−	13.1921i	−1.83267	−	0.538119i	−0.832785	−	0.553597i	$-0.813255\pi$
$601$	−44.9283	−	13.1921i	−1.83267	−	0.538119i	−0.999880	+	0.0154779i	$0.995073\pi$
$602$	13.9668	−	3.85857i	0.569245	−	0.157264i
$603$	1.01430	−	0.651854i	0.0413057	−	0.0265456i
$604$	0.437773	+	1.26486i	0.0178128	+	0.0514666i
$605$	−20.7990	+	8.32666i	−0.845599	+	0.338527i
$606$	−10.0433	−	9.57627i	−0.407981	−	0.389009i
$607$	15.9296	−	8.21227i	0.646562	−	0.333326i	−0.103562	−	0.994623i	$-0.533024\pi$
$607$	15.9296	−	8.21227i	0.646562	−	0.333326i	0.750124	+	0.661297i	$0.229994\pi$
$608$	−0.589647	−	4.10108i	−0.0239133	−	0.166321i
$609$	−8.78889	+	14.6736i	−0.356144	+	0.594603i
$610$	−10.1219	−	22.1639i	−0.409824	−	0.897390i
$611$	44.3937	+	17.7725i	1.79598	+	0.719000i
$612$	0.0937456	−	1.96796i	0.00378944	−	0.0795502i
$613$	17.6037	+	16.7851i	0.711008	+	0.677944i	0.956592	−	0.291431i	$-0.0941313\pi$
$613$	17.6037	+	16.7851i	0.711008	+	0.677944i	−0.245584	+	0.969375i	$0.578980\pi$
$614$	−2.83305	−	2.22793i	−0.114333	−	0.0899121i
$615$	−18.5958	+	21.4608i	−0.749857	+	0.865381i
$616$	3.68166	+	1.54295i	0.148338	+	0.0621673i
$617$	10.6601	+	12.3024i	0.429160	+	0.495277i	0.928605	−	0.371068i	$-0.121008\pi$
$617$	10.6601	+	12.3024i	0.429160	+	0.495277i	−0.499446	+	0.866345i	$0.666463\pi$
$618$	−11.2826	+	10.7580i	−0.453853	+	0.432748i
$619$	18.5666	−	1.77290i	0.746255	−	0.0712587i	0.285002	−	0.958527i	$-0.408006\pi$
$619$	18.5666	−	1.77290i	0.746255	−	0.0712587i	0.461254	+	0.887268i	$0.347400\pi$
$620$	−11.0674	−	19.1693i	−0.444477	−	0.769856i
$621$	−4.55215	−	1.50929i	−0.182671	−	0.0605657i
$622$	7.52315			0.301651
$623$	−20.9750	−	25.0067i	−0.840347	−	1.00187i
$624$	3.63094	+	1.06614i	0.145354	+	0.0426798i
$625$	−29.8823	+	5.75934i	−1.19529	+	0.230373i
$626$	−10.1605	−	5.23811i	−0.406096	−	0.209357i
$627$	6.13838	+	1.18307i	0.245143	+	0.0472475i
$628$	5.78316	+	4.54792i	0.230773	+	0.181482i
$629$	−8.37692	+	2.45969i	−0.334010	+	0.0980741i
$630$	−5.98873	−	3.21014i	−0.238597	−	0.127895i
$631$	2.08188	+	14.4798i	0.0828783	+	0.576431i	0.988370	+	0.152067i	$0.0485931\pi$
$631$	2.08188	+	14.4798i	0.0828783	+	0.576431i	−0.905492	+	0.424364i	$0.860498\pi$
$632$	−10.2278	−	0.976635i	−0.406840	−	0.0388485i
$633$	1.96689	−	2.76211i	0.0781769	−	0.109784i
$634$	8.00193	−	6.29279i	0.317797	−	0.249919i
$635$	−1.68546	+	0.868913i	−0.0668853	+	0.0344818i
$636$	−6.46945	+	1.89960i	−0.256530	+	0.0753241i
$637$	0.410267	+	26.4864i	0.0162554	+	1.04943i
$638$	6.38760	−	7.37169i	0.252888	−	0.291848i
$639$	−0.279462	−	5.86662i	−0.0110553	−	0.232080i
$640$	0.839978	−	2.42696i	0.0332031	−	0.0959339i
$641$	−7.82571	−	32.2580i	−0.309097	−	1.27412i	−0.888425	−	0.459021i	$-0.848200\pi$
$641$	−7.82571	−	32.2580i	−0.309097	−	1.27412i	0.579328	−	0.815094i	$-0.303315\pi$
$642$	0.356286	+	0.500334i	0.0140615	+	0.0197466i
$643$	−29.8548			−1.17736			−0.588679	−	0.808367i	$-0.700352\pi$
$643$	−29.8548			−1.17736			−0.588679	+	0.808367i	$0.700352\pi$
$644$	12.5648	−	1.76801i	0.495122	−	0.0696693i
$645$	14.0653			0.553822
$646$	4.73502	+	6.64940i	0.186297	+	0.261617i
$647$	7.62123	+	31.4151i	0.299621	+	1.23506i	0.900195	+	0.435487i	$0.143424\pi$
$647$	7.62123	+	31.4151i	0.299621	+	1.23506i	−0.600574	+	0.799569i	$0.705061\pi$
$648$	0.327068	−	0.945001i	0.0128484	−	0.0371231i
$649$	−0.950148	−	19.9461i	−0.0372966	−	0.782951i
$650$	3.95435	−	4.56356i	0.155102	−	0.178998i
$651$	18.9828	+	12.6347i	0.743994	+	0.495192i
$652$	−19.2553	+	5.65386i	−0.754094	+	0.221422i
$653$	2.64405	−	1.36310i	0.103470	−	0.0533424i	−0.405715	−	0.914000i	$-0.632977\pi$
$653$	2.64405	−	1.36310i	0.103470	−	0.0533424i	0.509185	+	0.860657i	$0.329947\pi$
$654$	12.8638	−	10.1162i	0.503013	−	0.395574i
$655$	14.4075	−	20.2325i	0.562946	−	0.790548i
$656$	11.0069	+	1.05103i	0.429748	+	0.0410360i
$657$	0.871312	+	6.06011i	0.0339931	+	0.236427i
$658$	1.05443	+	33.4161i	0.0411061	+	1.30270i
$659$	19.2696	−	5.65808i	0.750639	−	0.220407i	0.116035	−	0.993245i	$-0.462981\pi$
$659$	19.2696	−	5.65808i	0.750639	−	0.220407i	0.634604	+	0.772838i	$0.281163\pi$
$660$	3.04589	+	2.39531i	0.118561	+	0.0932374i
$661$	21.8537	+	4.21196i	0.850012	+	0.163826i	0.595611	−	0.803273i	$-0.296910\pi$
$661$	21.8537	+	4.21196i	0.850012	+	0.163826i	0.254400	+	0.967099i	$0.418122\pi$
$662$	27.0169	+	13.9282i	1.05004	+	0.541333i
$663$	−7.32094	+	1.41099i	−0.284322	+	0.0547985i
$664$	6.05286	+	1.77728i	0.234896	+	0.0689718i
$665$	27.7260	−	4.88343i	1.07517	−	0.189371i
$666$	−4.43133			−0.171710
$667$	5.46983	−	30.5179i	0.211793	−	1.18166i
$668$	−5.68653	−	9.84936i	−0.220018	−	0.381083i
$669$	−7.85366	+	0.749933i	−0.303640	+	0.0289941i
$670$	−2.24105	+	2.13683i	−0.0865791	+	0.0825530i
$671$	−9.37413	−	10.8183i	−0.361884	−	0.417637i
$672$	0.334436	+	2.62453i	0.0129011	+	0.101243i
$673$	5.65305	−	6.52397i	0.217909	−	0.251481i	−0.636261	−	0.771474i	$-0.719520\pi$
$673$	5.65305	−	6.52397i	0.217909	−	0.251481i	0.854171	+	0.519993i	$0.174065\pi$
$674$	−7.54769	−	5.93557i	−0.290726	−	0.228629i
$675$	−1.15485	−	1.10115i	−0.0444504	−	0.0423834i
$676$	0.0628277	−	1.31892i	0.00241645	−	0.0507276i
$677$	16.1609	+	6.46985i	0.621114	+	0.248656i	0.660808	−	0.750555i	$-0.270214\pi$
$677$	16.1609	+	6.46985i	0.621114	+	0.248656i	−0.0396936	+	0.999212i	$0.512638\pi$
$678$	4.58104	+	10.0311i	0.175934	+	0.385241i
$679$	−4.07644	−	7.32991i	−0.156439	−	0.281296i
$680$	0.720094	+	5.00836i	0.0276143	+	0.192062i
$681$	−2.69765	+	1.39073i	−0.103374	+	0.0532930i
$682$	−9.41143	−	8.97378i	−0.360382	−	0.343624i
$683$	−23.5690	+	9.43560i	−0.901843	+	0.361043i	−0.775798	−	0.630981i	$-0.782652\pi$
$683$	−23.5690	+	9.43560i	−0.901843	+	0.361043i	−0.126045	+	0.992025i	$0.540228\pi$
$684$	1.35513	+	3.91538i	0.0518146	+	0.149708i
$685$	15.3112	−	9.83992i	0.585011	−	0.375964i
$686$	−16.8510	+	7.68404i	−0.643373	+	0.293378i
$687$	−10.0730	−	2.95770i	−0.384309	−	0.112843i
$688$	−3.17680	−	4.46120i	−0.121115	−	0.170082i
$689$	12.7577	+	22.0970i	0.486031	+	0.841830i
$690$	12.2132	+	1.59361i	0.464947	+	0.0606678i
$691$	14.7969	−	25.6290i	0.562901	−	0.974973i	−0.434340	−	0.900749i	$-0.643018\pi$
$691$	14.7969	−	25.6290i	0.562901	−	0.974973i	0.997242	−	0.0742247i	$-0.0236482\pi$
$692$	−5.99526	+	13.1278i	−0.227905	+	0.499043i
$693$	−3.90714	−	0.818308i	−0.148420	−	0.0310850i
$694$	−21.1479	−	24.4060i	−0.802763	−	0.926438i
$695$	2.35582	+	49.4548i	0.0893615	+	1.87593i
$696$	6.34800	+	1.22348i	0.240620	+	0.0463758i
$697$	−20.2240	+	8.09645i	−0.766037	+	0.306675i
$698$	3.97782	−	16.3968i	0.150563	−	0.620627i
$699$	5.65628	+	3.63507i	0.213940	+	0.137491i
$700$	4.03117	+	1.25430i	0.152364	+	0.0474081i
$701$	−13.0788	−	28.6385i	−0.493978	−	1.08166i	−0.978380	−	0.206815i	$-0.933690\pi$
$701$	−13.0788	−	28.6385i	−0.493978	−	1.08166i	0.484402	−	0.874846i	$-0.339037\pi$
$702$	−3.76710	−	0.359714i	−0.142180	−	0.0135765i
$703$	14.4320	−	11.3495i	0.544314	−	0.428054i
$704$	0.0717916	−	1.50709i	0.00270575	−	0.0568006i
$705$	−7.65106	+	31.5381i	−0.288156	+	1.18779i
$706$	−2.54505	+	17.7012i	−0.0957842	+	0.666194i
$707$	−36.4883	−	4.07635i	−1.37228	−	0.153307i
$708$	11.1338	−	7.15528i	0.418435	−	0.268912i
$709$	7.93947	−	1.53021i	0.298173	−	0.0574682i	−0.0379706	−	0.999279i	$-0.512089\pi$
$709$	7.93947	−	1.53021i	0.298173	−	0.0574682i	0.336144	+	0.941811i	$0.390877\pi$
$710$	3.55614	+	14.6586i	0.133459	+	0.550127i
$711$	10.2278	−	0.976635i	0.383572	−	0.0366267i
$712$	−6.16814	+	10.6835i	−0.231161	+	0.400382i
$713$	−40.2927	−	9.21989i	−1.50897	−	0.345288i
$714$	−2.95507	−	4.29409i	−0.110591	−	0.160702i
$715$	6.09146	−	13.3384i	0.227808	−	0.498830i
$716$	−4.92636	+	4.69727i	−0.184107	+	0.175545i
$717$	2.22919	−	6.44081i	0.0832505	−	0.240537i
$718$	8.08094	+	4.16601i	0.301578	+	0.155474i
$719$	−10.5600	−	30.5111i	−0.393822	−	1.13787i	−0.951455	−	0.307787i	$-0.900412\pi$
$719$	−10.5600	−	30.5111i	−0.393822	−	1.13787i	0.557633	−	0.830087i	$-0.311709\pi$
$720$	−0.365494	+	2.54207i	−0.0136212	+	0.0947372i
$721$	−6.52460	+	40.7265i	−0.242989	+	1.51673i
$722$	1.54237	+	0.991223i	0.0574012	+	0.0368895i
$723$	−22.2531	−	8.90882i	−0.827604	−	0.331322i
$724$	4.15874	−	5.84013i	0.154558	−	0.217047i
$725$	5.98379	−	8.40306i	0.222232	−	0.312082i
$726$	−8.09864	−	3.24221i	−0.300569	−	0.120330i
$727$	0.158573	+	0.101909i	0.00588116	+	0.00377959i	0.543578	−	0.839359i	$-0.317069\pi$
$727$	0.158573	+	0.101909i	0.00588116	+	0.00377959i	−0.537697	+	0.843138i	$0.680706\pi$
$728$	9.35349	−	3.57143i	0.346663	−	0.132366i
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$	−5.14271	−	14.8589i	−0.190340	−	0.549952i
$731$	9.59070	+	4.94435i	0.354725	+	0.182873i
$732$	3.10305	−	8.96566i	0.114692	−	0.331380i
$733$	24.0134	−	22.8967i	0.886954	−	0.845708i	−0.101870	−	0.994798i	$-0.532483\pi$
$733$	24.0134	−	22.8967i	0.886954	−	0.845708i	0.988824	+	0.149089i	$0.0476342\pi$
$734$	12.9490	−	28.3544i	0.477957	−	1.04658i
$735$	−17.7527	+	2.83375i	−0.654819	+	0.104524i
$736$	−2.25301	−	4.23367i	−0.0830472	−	0.156055i
$737$	−0.909585	+	1.57545i	−0.0335050	+	0.0580323i
$738$	−11.0069	+	1.05103i	−0.405170	+	0.0386891i
$739$	12.2750	+	50.5984i	0.451545	+	1.86129i	0.505622	+	0.862755i	$0.331263\pi$
$739$	12.2750	+	50.5984i	0.451545	+	1.86129i	−0.0540776	+	0.998537i	$0.517222\pi$
$740$	11.1749	−	2.15379i	0.410798	−	0.0791747i
$741$	13.1901	−	8.47673i	0.484549	−	0.311401i
$742$	−10.5797	+	14.3633i	−0.388393	+	0.527295i
$743$	3.67830	−	25.5831i	0.134944	−	0.938554i	−0.804036	−	0.594581i	$-0.797318\pi$
$743$	3.67830	−	25.5831i	0.134944	−	0.938554i	0.938980	−	0.343973i	$-0.111773\pi$
$744$	2.03195	−	8.37581i	0.0744949	−	0.307072i
$745$	1.82651	−	38.3431i	0.0669180	−	1.40478i
$746$	−10.7278	+	8.43645i	−0.392774	+	0.308881i
$747$	−6.27983	−	0.599651i	−0.229767	−	0.0219401i
$748$	1.23487	+	2.70400i	0.0451515	+	0.0988680i
$749$	1.55171	+	0.482816i	0.0566983	+	0.0176417i
$750$	−7.35506	−	4.72681i	−0.268569	−	0.172599i
$751$	7.73469	−	31.8828i	0.282243	−	1.16342i	−0.637359	−	0.770567i	$-0.719973\pi$
$751$	7.73469	−	31.8828i	0.282243	−	1.16342i	0.919601	−	0.392853i	$-0.128512\pi$
$752$	11.7312	−	4.69647i	0.427794	−	0.171263i
$753$	−28.0942	−	5.41471i	−1.02381	−	0.197323i
$754$	−1.16406	−	24.4367i	−0.0423927	−	0.889933i
$755$	2.25108	+	2.59788i	0.0819251	+	0.0945466i
$756$	−0.825088	−	2.51381i	−0.0300081	−	0.0914263i
$757$	−11.6419	+	25.4922i	−0.423132	+	0.926530i	0.571260	+	0.820769i	$0.306455\pi$
$757$	−11.6419	+	25.4922i	−0.423132	+	0.926530i	−0.994392	+	0.105761i	$0.966272\pi$
$758$	−14.0961	+	24.4152i	−0.511994	+	0.886799i
$759$	7.14825	−	1.12316i	0.259465	−	0.0407680i
$760$	−5.32037	−	9.21515i	−0.192990	−	0.334269i
$761$	−25.3536	−	35.6041i	−0.919067	−	1.29065i	−0.956615	−	0.291354i	$-0.905894\pi$
$761$	−25.3536	−	35.6041i	−0.919067	−	1.29065i	0.0375481	−	0.999295i	$-0.488045\pi$
$762$	−0.708448	−	0.208019i	−0.0256643	−	0.00753573i
$763$	10.8821	−	41.9080i	0.393958	−	1.51717i
$764$	−10.7780	+	6.92660i	−0.389934	+	0.250596i
$765$	−1.65492	−	4.78158i	−0.0598338	−	0.172878i
$766$	13.1707	−	5.27275i	0.475876	−	0.190512i
$767$	−36.2472	−	34.5616i	−1.30881	−	1.24795i
$768$	0.888835	−	0.458227i	0.0320731	−	0.0165348i
$769$	3.53766	+	24.6050i	0.127571	+	0.887279i	0.948619	+	0.316420i	$0.102481\pi$
$769$	3.53766	+	24.6050i	0.127571	+	0.887279i	−0.821048	+	0.570859i	$0.806610\pi$
$770$	10.2507	+	0.164597i	0.369411	+	0.00593166i
$771$	−10.1476	−	22.2202i	−0.365458	−	0.800241i
$772$	5.36270	+	2.14690i	0.193008	+	0.0772687i
$773$	0.157955	−	3.31587i	0.00568123	−	0.119264i	−0.994245	−	0.107129i	$-0.965834\pi$
$773$	0.157955	−	3.31587i	0.00568123	−	0.119264i	0.999926	−	0.0121348i	$-0.00386273\pi$
$774$	3.96368	+	3.77936i	0.142472	+	0.135846i
$775$	−10.8105	−	8.50146i	−0.388324	−	0.305381i
$776$	−2.07595	+	2.39577i	−0.0745221	+	0.0860031i
$777$	−9.33100	+	7.09852i	−0.334748	+	0.254658i
$778$	−1.78173	−	2.05622i	−0.0638780	−	0.0737191i
$779$	33.1557	−	31.6139i	1.18793	−	1.13268i
$780$	9.67469	−	0.923821i	0.346409	−	0.0330781i
$781$	4.43080	+	7.67436i	0.158546	+	0.274610i
$782$	7.76756	+	5.37989i	0.277767	+	0.192385i
$783$	−6.46483			−0.231034
$784$	4.90844	+	4.99072i	0.175301	+	0.178240i
$785$	18.1295	+	5.32329i	0.647068	+	0.189996i
$786$	9.49658	−	1.83031i	0.338732	−	0.0652852i
$787$	−37.9841	−	19.5822i	−1.35399	−	0.698029i	−0.380075	−	0.924956i	$-0.624102\pi$
$787$	−37.9841	−	19.5822i	−1.35399	−	0.698029i	−0.973912	+	0.226927i	$0.927132\pi$
$788$	3.04856	+	0.587562i	0.108600	+	0.0209310i
$789$	−7.17207	−	5.64018i	−0.255333	−	0.200796i
$790$	−25.3177	+	7.43395i	−0.900764	+	0.264488i
$791$	25.7150	+	13.7840i	0.914320	+	0.490103i
$792$	0.214725	+	1.49344i	0.00762991	+	0.0530672i
$793$	−35.7402	−	3.41278i	−1.26917	−	0.121191i
$794$	1.90732	−	2.67845i	0.0676882	−	0.0950547i
$795$	−13.6115	+	10.7042i	−0.482752	+	0.379640i
$796$	−9.95022	+	5.12969i	−0.352676	+	0.181817i
$797$	42.1082	−	12.3641i	1.49155	−	0.437958i	0.568513	−	0.822674i	$-0.307519\pi$
$797$	42.1082	−	12.3641i	1.49155	−	0.437958i	0.923035	+	0.384717i	$0.125701\pi$
$798$	9.12551	+	6.07381i	0.323039	+	0.215011i
$799$	−16.3035	+	18.8153i	−0.576777	+	0.665636i
$800$	−0.0759260	−	1.59388i	−0.00268439	−	0.0563522i
$801$	4.03480	−	11.6578i	0.142563	−	0.411908i
$802$	4.68675	+	19.3190i	0.165495	+	0.682179i
$803$	−5.35829	−	7.52466i	−0.189090	−	0.265539i
$804$	−1.20571			−0.0425220
$805$	28.2699	−	16.2085i	0.996384	−	0.571276i
$806$	−32.6154			−1.14883
$807$	3.91381	+	5.49618i	0.137773	+	0.193475i
$808$	3.27164	+	13.4859i	0.115096	+	0.474432i
$809$	−1.10059	+	3.17996i	−0.0386948	+	0.111801i	−0.962693	−	0.270595i	$-0.912780\pi$
$809$	−1.10059	+	3.17996i	−0.0386948	+	0.111801i	0.923999	+	0.382396i	$0.124901\pi$
$810$	−0.122200	−	2.56530i	−0.00429368	−	0.0901354i
$811$	−5.51315	+	6.36251i	−0.193593	+	0.223418i	−0.844244	−	0.535958i	$-0.819950\pi$
$811$	−5.51315	+	6.36251i	−0.193593	+	0.223418i	0.650652	+	0.759376i	$0.274496\pi$
$812$	15.3268	−	7.59257i	0.537866	−	0.266447i
$813$	−10.3680	+	3.04433i	−0.363623	+	0.106769i
$814$	5.94274	−	3.06370i	0.208293	−	0.107382i
$815$	−40.5126	+	31.8594i	−1.41909	+	1.11599i
$816$	−1.14282	+	1.60487i	−0.0400069	+	0.0561818i
$817$	−22.5887	−	2.15696i	−0.790278	−	0.0754624i
$818$	−5.00781	−	34.8301i	−0.175094	−	1.21781i
$819$	−8.50857	+	5.27704i	−0.297313	+	0.184395i
$820$	27.2464	−	8.00026i	0.951485	−	0.279381i
$821$	−18.7692	−	14.7602i	−0.655048	−	0.515136i	0.234418	−	0.972136i	$-0.424681\pi$
$821$	−18.7692	−	14.7602i	−0.655048	−	0.515136i	−0.889467	+	0.457000i	$0.848924\pi$
$822$	6.95877	+	1.34119i	0.242715	+	0.0467795i
$823$	21.0493	+	10.8516i	0.733731	+	0.378265i	0.784239	−	0.620459i	$-0.213054\pi$
$823$	21.0493	+	10.8516i	0.733731	+	0.378265i	−0.0505079	+	0.998724i	$0.516084\pi$
$824$	15.3077	−	2.95032i	0.533270	−	0.102779i
$825$	2.31005	+	0.678293i	0.0804257	+	0.0236151i
$826$	11.9824	−	32.9020i	0.416921	−	1.14481i
$827$	31.9260			1.11018			0.555088	−	0.831791i	$-0.312684\pi$
$827$	31.9260			1.11018			0.555088	+	0.831791i	$0.312684\pi$
$828$	3.01353	+	3.73077i	0.104727	+	0.129653i
$829$	13.4495	+	23.2953i	0.467121	+	0.809078i	0.999294	−	0.0375578i	$-0.0119578\pi$
$829$	13.4495	+	23.2953i	0.467121	+	0.809078i	−0.532173	+	0.846636i	$0.678624\pi$
$830$	16.1279	−	1.54003i	0.559807	−	0.0534551i
$831$	11.9486	−	11.3929i	0.414491	−	0.395217i
$832$	−2.47814	−	2.85993i	−0.0859142	−	0.0991503i
$833$	−13.1011	−	4.30832i	−0.453928	−	0.149274i
$834$	−12.6247	+	14.5696i	−0.437156	+	0.504505i
$835$	−22.9593	−	18.0554i	−0.794540	−	0.624833i
$836$	−4.52431	−	4.31392i	−0.156477	−	0.149200i
$837$	−0.410097	+	8.60900i	−0.0141750	+	0.297571i
$838$	−22.0383	−	8.82280i	−0.761300	−	0.304778i
$839$	−19.5644	−	42.8401i	−0.675439	−	1.47900i	−0.867405	−	0.497603i	$-0.834214\pi$
$839$	−19.5644	−	42.8401i	−0.675439	−	1.47900i	0.191966	−	0.981402i	$-0.438514\pi$
$840$	3.30251	+	5.93829i	0.113947	+	0.204890i
$841$	−1.82078	−	12.6638i	−0.0627856	−	0.436684i
$842$	30.9842	−	15.9735i	1.06779	−	0.550482i
$843$	−0.444758	−	0.424076i	−0.0153183	−	0.0146059i
$844$	−3.14796	+	1.26025i	−0.108357	+	0.0433797i
$845$	−1.10912	−	3.20458i	−0.0381548	−	0.110241i
$846$	−10.6304	+	6.83175i	−0.365481	+	0.234880i
$847$	−22.2469	+	6.14608i	−0.764413	+	0.211182i
$848$	6.46945	+	1.89960i	0.222162	+	0.0652326i
$849$	14.0541	+	19.7362i	0.482336	+	0.677346i
$850$	1.57191	+	2.72263i	0.0539160	+	0.0933853i
$851$	11.2554	−	18.0266i	0.385829	−	0.617945i
$852$	−2.93664	+	5.08640i	−0.100607	+	0.174257i
$853$	−9.33267	+	20.4357i	−0.319545	+	0.699705i	−0.999435	−	0.0336087i	$-0.989300\pi$
$853$	−9.33267	+	20.4357i	−0.319545	+	0.699705i	0.679891	+	0.733314i	$0.262027\pi$
$854$	−7.82799	−	23.8497i	−0.267868	−	0.816119i
$855$	6.96821	+	8.04174i	0.238308	+	0.275022i
$856$	−0.0292261	−	0.613531i	−0.000998927	−	0.0209701i
$857$	−19.6545	−	3.78810i	−0.671386	−	0.129399i	−0.157845	−	0.987464i	$-0.550455\pi$
$857$	−19.6545	−	3.78810i	−0.671386	−	0.129399i	−0.513541	+	0.858065i	$0.671667\pi$
$858$	5.30066	−	2.12206i	0.180961	−	0.0724460i
$859$	0.119609	−	0.493033i	0.00408099	−	0.0168221i	−0.969735	−	0.244161i	$-0.921487\pi$
$859$	0.119609	−	0.493033i	0.00408099	−	0.0168221i	0.973816	+	0.227339i	$0.0730026\pi$
$860$	−11.8325	−	7.60429i	−0.403485	−	0.259304i
$861$	−21.4935	+	19.8451i	−0.732498	+	0.676319i
$862$	12.8481	+	28.1334i	0.437608	+	0.958227i
$863$	32.8427	+	3.13610i	1.11798	+	0.106754i	0.637644	−	0.770331i	$-0.279909\pi$
$863$	32.8427	+	3.13610i	1.11798	+	0.106754i	0.480335	+	0.877085i	$0.340515\pi$
$864$	−0.786053	+	0.618159i	−0.0267421	+	0.0210302i
$865$	−1.76359	+	37.0223i	−0.0599639	+	1.25880i
$866$	−2.91833	+	12.0295i	−0.0991688	+	0.408780i
$867$	−1.86693	+	12.9848i	−0.0634044	+	0.440987i
$868$	−9.13851	−	20.8918i	−0.310181	−	0.709115i
$869$	−13.0410	+	8.38095i	−0.442386	+	0.284304i
$870$	16.3030	−	3.14214i	0.552723	−	0.106529i
$871$	1.07569	+	4.43406i	0.0364484	+	0.150242i
$872$	−16.2909	+	1.55559i	−0.551680	+	0.0526791i
$873$	1.58503	−	2.74535i	0.0536451	−	0.0929160i
$874$	−19.3697	−	4.43224i	−0.655191	−	0.149923i
$875$	−23.0593	+	1.82883i	−0.779548	+	0.0618257i
$876$	2.54335	−	5.56916i	0.0859318	−	0.188164i
$877$	5.98776	−	5.70932i	0.202192	−	0.192790i	−0.582217	−	0.813033i	$-0.697815\pi$
$877$	5.98776	−	5.70932i	0.202192	−	0.192790i	0.784410	+	0.620243i	$0.212966\pi$
$878$	−5.90786	+	17.0696i	−0.199381	+	0.576073i
$879$	−24.9147	−	12.8444i	−0.840353	−	0.433232i
$880$	−1.26736	−	3.66179i	−0.0427227	−	0.123439i
$881$	−3.85056	+	26.7812i	−0.129729	+	0.902282i	0.816168	+	0.577814i	$0.196094\pi$
$881$	−3.85056	+	26.7812i	−0.129729	+	0.902282i	−0.945897	+	0.324468i	$0.894815\pi$
$882$	−5.76423	−	3.97160i	−0.194092	−	0.133731i
$883$	27.3596	+	17.5829i	0.920723	+	0.591713i	0.912867	−	0.408256i	$-0.133863\pi$
$883$	27.3596	+	17.5829i	0.920723	+	0.591713i	0.00785588	+	0.999969i	$0.497499\pi$
$884$	6.92161	+	2.77099i	0.232799	+	0.0931986i
$885$	19.7160	−	27.6872i	0.662745	−	0.930696i
$886$	9.59336	−	13.4720i	0.322295	−	0.452600i
$887$	−25.5551	−	10.2307i	−0.858056	−	0.343514i	−0.0994338	−	0.995044i	$-0.531703\pi$
$887$	−25.5551	−	10.2307i	−0.858056	−	0.343514i	−0.758623	+	0.651530i	$0.774127\pi$
$888$	3.72787	+	2.39576i	0.125099	+	0.0803963i
$889$	−1.82500	+	0.696835i	−0.0612084	+	0.0233711i
$890$	−4.50883	+	31.3596i	−0.151136	+	1.05118i
$891$	−0.493480	−	1.42582i	−0.0165322	−	0.0477667i
$892$	7.01236	+	3.61512i	0.234791	+	0.121043i
$893$	17.1239	−	49.4763i	0.573030	−	1.65566i
$894$	10.8175	−	10.3145i	0.361792	−	0.344968i
$895$	−7.26205	+	15.9017i	−0.242744	+	0.531535i
$896$	1.13758	−	2.38870i	0.0380040	−	0.0798010i
$897$	11.0316	−	14.4109i	0.368333	−	0.481166i
$898$	4.49947	−	7.79331i	0.150149	−	0.260066i
$899$	−55.4665	+	5.29641i	−1.84991	+	0.176645i
$900$	0.376198	+	1.55071i	0.0125399	+	0.0516903i
$901$	−13.0441	+	2.51405i	−0.434562	+	0.0837550i
$902$	14.0345	−	9.01940i	0.467296	−	0.300313i
$903$	14.4004	+	1.60877i	0.479216	+	0.0535365i
$904$	1.56939	−	10.9154i	0.0521973	−	0.363040i
$905$	4.34100	−	17.8938i	0.144300	−	0.594811i
$906$	−0.0636874	+	1.33696i	−0.00211587	+	0.0444176i
$907$	32.0430	−	25.1989i	1.06397	−	0.836717i	0.0769070	−	0.997038i	$-0.475496\pi$
$907$	32.0430	−	25.1989i	1.06397	−	0.836717i	0.987065	+	0.160322i	$0.0512531\pi$
$908$	3.02129	+	0.288498i	0.100265	+	0.00957416i
$909$	−5.76474	−	12.6230i	−0.191204	−	0.418679i
$910$	18.8920	−	17.4431i	0.626265	−	0.578233i
$911$	−12.9528	−	8.32429i	−0.429147	−	0.275796i	0.308185	−	0.951326i	$-0.400278\pi$
$911$	−12.9528	−	8.32429i	−0.429147	−	0.275796i	−0.737332	+	0.675530i	$0.763915\pi$
$912$	0.976810	−	4.02647i	0.0323454	−	0.133330i
$913$	8.83630	−	3.53752i	0.292439	−	0.117075i
$914$	13.2409	+	2.55198i	0.437971	+	0.0844121i
$915$	−1.15937	−	24.3382i	−0.0383276	−	0.804596i
$916$	6.87490	+	7.93405i	0.227153	+	0.262149i
$917$	17.0649	−	19.0666i	0.563532	−	0.629634i
$918$	0.818448	−	1.79215i	0.0270128	−	0.0591498i
$919$	23.7209	−	41.0858i	0.782479	−	1.35529i	−0.148014	−	0.988985i	$-0.547288\pi$
$919$	23.7209	−	41.0858i	0.782479	−	1.35529i	0.930493	−	0.366309i	$-0.119379\pi$
$920$	−9.41279	−	7.94356i	−0.310331	−	0.261892i
$921$	−1.80207	−	3.12128i	−0.0593803	−	0.102850i
$922$	−5.79742	−	8.14133i	−0.190928	−	0.268120i
$923$	21.3255	+	6.26174i	0.701938	+	0.206108i
$924$	2.84448	+	2.80076i	0.0935766	+	0.0921383i
$925$	5.94852	−	3.82288i	0.195586	−	0.125696i
$926$	3.56622	+	10.3039i	0.117193	+	0.338608i
$927$	−14.4727	+	5.79401i	−0.475347	+	0.190300i
$928$	−4.67882	−	4.46124i	−0.153590	−	0.146448i
$929$	−30.8450	+	15.9017i	−1.01199	+	0.521718i	−0.882724	−	0.469892i	$-0.844293\pi$
$929$	−30.8450	+	15.9017i	−1.01199	+	0.521718i	−0.129267	+	0.991610i	$0.541262\pi$
$930$	−3.15011	−	21.9095i	−0.103296	−	0.718440i
$931$	28.9451	−	1.82852i	0.948637	−	0.0599275i
$932$	−2.79310	−	6.11604i	−0.0914910	−	0.200337i
$933$	6.98425	+	2.79607i	0.228654	+	0.0915393i
$934$	1.16896	−	24.5395i	0.0382495	−	0.802956i
$935$	5.52522	+	5.26829i	0.180694	+	0.172291i
$936$	2.97461	+	2.33926i	0.0972281	+	0.0764610i
$937$	−30.7033	+	35.4335i	−1.00303	+	1.15756i	−0.0155441	+	0.999879i	$0.504948\pi$
$937$	−30.7033	+	35.4335i	−1.00303	+	1.15756i	−0.987490	+	0.157684i	$0.949597\pi$
$938$	−2.53885	+	1.93141i	−0.0828962	+	0.0630629i
$939$	−7.48588	−	8.63917i	−0.244293	−	0.281929i
$940$	23.4873	−	22.3951i	0.766070	−	0.730446i
$941$	−53.7853	+	5.13587i	−1.75335	+	0.167425i	−0.921707	−	0.387886i	$-0.873205\pi$
$941$	−53.7853	+	5.13587i	−1.75335	+	0.167425i	−0.831643	+	0.555311i	$0.812599\pi$
$942$	3.67860	+	6.37153i	0.119855	+	0.207596i
$943$	23.6815	−	47.4458i	0.771175	−	1.54505i
$944$	−13.2348			−0.430756
$945$	−4.36665	−	5.20597i	−0.142047	−	0.169350i
$946$	−7.92854	−	2.32803i	−0.257779	−	0.0756908i
$947$	−6.62474	+	1.27681i	−0.215275	+	0.0414909i	−0.295748	−	0.955266i	$-0.595569\pi$
$947$	−6.62474	+	1.27681i	−0.215275	+	0.0414909i	0.0804732	+	0.996757i	$0.474357\pi$
$948$	−9.13217	−	4.70796i	−0.296599	−	0.152907i
$949$	−22.7500	−	4.38470i	−0.738496	−	0.142333i
$950$	−5.19687	−	4.08687i	−0.168609	−	0.132595i
$951$	9.76753	−	2.86801i	0.316734	−	0.0930015i
$952$	0.164401	+	5.21005i	0.00532827	+	0.168859i
$953$	3.02498	+	21.0392i	0.0979887	+	0.681526i	0.978310	+	0.207148i	$0.0664181\pi$
$953$	3.02498	+	21.0392i	0.0979887	+	0.681526i	−0.880321	+	0.474379i	$0.842673\pi$
$954$	−6.71204	−	0.640922i	−0.217310	−	0.0207506i
$955$	−19.0859	+	26.8023i	−0.617604	+	0.867304i
$956$	−5.35748	+	4.21317i	−0.173273	+	0.136264i
$957$	8.66982	−	4.46960i	0.280256	−	0.144482i
$958$	12.4927	−	3.66819i	0.403621	−	0.118514i
$959$	16.8015	−	8.32308i	0.542548	−	0.268766i
$960$	1.68182	−	1.94092i	0.0542805	−	0.0626430i
$961$	2.05949	+	43.2340i	0.0664352	+	1.39465i
$962$	5.48466	−	15.8469i	0.176832	−	0.510924i
$963$	0.144809	+	0.596913i	0.00466642	+	0.0192352i
$964$	13.9041	+	19.5255i	0.447820	+	0.628875i
$965$	14.8352			0.477562
$966$	12.3219	+	3.02850i	0.396449	+	0.0974404i
$967$	8.04121			0.258588			0.129294	−	0.991606i	$-0.458729\pi$
$967$	8.04121			0.258588			0.129294	+	0.991606i	$0.458729\pi$
$968$	5.06014	+	7.10597i	0.162639	+	0.228395i
$969$	1.92450	+	7.93292i	0.0618240	+	0.254842i
$970$	−2.66278	+	7.69360i	−0.0854967	+	0.247027i
$971$	0.782371	+	16.4240i	0.0251075	+	0.527071i	0.976029	+	0.217639i	$0.0698357\pi$
$971$	0.782371	+	16.4240i	0.0251075	+	0.527071i	−0.950922	+	0.309431i	$0.899861\pi$
$972$	0.654861	−	0.755750i	0.0210047	−	0.0242407i
$973$	−3.24461	+	50.9025i	−0.104018	+	1.63186i
$974$	11.7682	−	3.45546i	0.377078	−	0.110720i
$975$	5.36720	−	2.76698i	0.171888	−	0.0886144i
$976$	−7.45765	+	5.86476i	−0.238714	+	0.187726i
$977$	−28.1309	+	39.5044i	−0.899988	+	1.26386i	0.0640102	+	0.997949i	$0.479611\pi$
$977$	−28.1309	+	39.5044i	−0.899988	+	1.26386i	−0.963999	+	0.265908i	$0.914328\pi$
$978$	−19.9773	−	1.90760i	−0.638803	−	0.0609983i
$979$	2.64890	+	18.4235i	0.0846593	+	0.588818i
$980$	16.4666	+	7.21394i	0.526005	+	0.230441i
$981$	15.7021	−	4.61056i	0.501330	−	0.147204i
$982$	17.9468	+	14.1135i	0.572705	+	0.450380i
$983$	−10.3978	−	2.00401i	−0.331639	−	0.0639181i	0.0207139	−	0.999785i	$-0.493406\pi$
$983$	−10.3978	−	2.00401i	−0.331639	−	0.0639181i	−0.352353	+	0.935867i	$0.614618\pi$
$984$	9.82785	+	5.06661i	0.313300	+	0.161518i
$985$	7.82933	−	1.50898i	0.249463	−	0.0480801i
$986$	12.2210	+	3.58842i	0.389197	+	0.114279i
$987$	−11.4406	+	31.4144i	−0.364159	+	0.999930i
$988$	−15.6790			−0.498817
$989$	−25.4420	+	6.52485i	−0.809009	+	0.207478i
$990$	1.93746	+	3.35577i	0.0615764	+	0.106653i
$991$	−37.3756	+	3.56894i	−1.18727	+	0.113371i	−0.669942	−	0.742413i	$-0.733681\pi$
$991$	−37.3756	+	3.56894i	−1.18727	+	0.113371i	−0.517333	+	0.855784i	$0.673075\pi$
$992$	−6.23769	+	5.94763i	−0.198047	+	0.188837i
$993$	19.9050	+	22.9716i	0.631666	+	0.728982i
$994$	1.96423	+	15.4146i	0.0623017	+	0.488921i
$995$	−18.8274	+	21.7280i	−0.596869	+	0.688823i
$996$	4.95873	+	3.89959i	0.157123	+	0.123563i
$997$	−18.3680	−	17.5138i	−0.581720	−	0.554669i	0.341038	−	0.940050i	$-0.389222\pi$
$997$	−18.3680	−	17.5138i	−0.581720	−	0.554669i	−0.922758	+	0.385381i	$0.874070\pi$
$998$	−1.35386	+	28.4210i	−0.0428557	+	0.899652i
$999$	−4.11390	−	1.64696i	−0.130158	−	0.0521074i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.a.121.7	✓	160
7.4	even	3	inner	966.2.y.a.949.2	yes	160
23.4	even	11	inner	966.2.y.a.625.2	yes	160
161.4	even	33	inner	966.2.y.a.487.7	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.a.121.7	✓	160	1.1	even	1	trivial
966.2.y.a.487.7	yes	160	161.4	even	33	inner
966.2.y.a.625.2	yes	160	23.4	even	11	inner
966.2.y.a.949.2	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)

\(f(q)\)	\(=\)	\(q+(-0.580057 - 0.814576i) q^{2} +(-0.235759 - 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(0.122200 + 2.56530i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(-0.168303 + 2.64039i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +O(q^{10})\)	\(q+(-0.580057 - 0.814576i) q^{2} +(-0.235759 - 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(0.122200 + 2.56530i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(-0.168303 + 2.64039i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +(2.01875 - 1.58756i) q^{10} +(0.875190 - 1.22903i) q^{11} +(0.995472 + 0.0950560i) q^{12} +(-0.538552 - 3.74571i) q^{13} +(2.24843 - 1.39448i) q^{14} +(2.46418 - 0.723548i) q^{15} +(-0.786053 - 0.618159i) q^{16} +(1.93459 + 0.372862i) q^{17} +(0.888835 + 0.458227i) q^{18} +(-4.06838 + 0.784117i) q^{19} +(-2.46418 - 0.723548i) q^{20} +(2.60564 - 0.458937i) q^{21} -1.50880 q^{22} +(-4.12167 + 2.45191i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-1.58846 + 0.151680i) q^{25} +(-2.73878 + 2.61142i) q^{26} +(0.654861 + 0.755750i) q^{27} +(-2.44013 - 1.02263i) q^{28} +(-4.23356 + 4.88579i) q^{29} +(-2.01875 - 1.58756i) q^{30} +(6.23769 + 5.94763i) q^{31} +(-0.0475819 + 0.998867i) q^{32} +(-1.40072 - 0.560764i) q^{33} +(-0.818448 - 1.79215i) q^{34} +(-6.79396 - 0.109091i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(-3.93872 + 2.03055i) q^{37} +(2.99862 + 2.85917i) q^{38} +(-3.51316 + 1.40646i) q^{39} +(0.839978 + 2.42696i) q^{40} +(-9.30173 + 5.97786i) q^{41} +(-1.88526 - 1.85628i) q^{42} +(5.25487 + 1.54297i) q^{43} +(0.875190 + 1.22903i) q^{44} +(-1.28410 - 2.22413i) q^{45} +(4.38807 + 1.93516i) q^{46} +(-6.31820 + 10.9434i) q^{47} +(-0.415415 + 0.909632i) q^{48} +(-6.94335 - 0.888773i) q^{49} +(1.04495 + 1.20594i) q^{50} +(-0.0937456 - 1.96796i) q^{51} +(3.71585 + 0.716171i) q^{52} +(-6.25958 + 2.50596i) q^{53} +(0.235759 - 0.971812i) q^{54} +(3.25978 + 2.09494i) q^{55} +(0.582399 + 2.58085i) q^{56} +(1.72117 + 3.76884i) q^{57} +(6.43556 + 0.614521i) q^{58} +(10.4033 - 8.18122i) q^{59} +(-0.122200 + 2.56530i) q^{60} +(2.23676 - 9.22003i) q^{61} +(1.22658 - 8.53103i) q^{62} +(-1.06030 - 2.42400i) q^{63} +(0.841254 - 0.540641i) q^{64} +(9.54306 - 1.83927i) q^{65} +(0.355713 + 1.46627i) q^{66} +(-1.20025 + 0.114610i) q^{67} +(-0.985097 + 1.70624i) q^{68} +(3.35451 + 3.42742i) q^{69} +(3.85202 + 5.59748i) q^{70} +(-2.43985 + 5.34252i) q^{71} +(-0.723734 + 0.690079i) q^{72} +(2.00245 - 5.78570i) q^{73} +(3.93872 + 2.03055i) q^{74} +(0.521899 + 1.50793i) q^{75} +(0.589647 - 4.10108i) q^{76} +(3.09783 + 2.51769i) q^{77} +(3.18350 + 2.04591i) q^{78} +(-9.53834 - 3.81858i) q^{79} +(1.48971 - 2.09200i) q^{80} +(0.580057 - 0.814576i) q^{81} +(10.2650 + 4.10947i) q^{82} +(5.30696 + 3.41057i) q^{83} +(-0.418526 + 2.61244i) q^{84} +(-0.720094 + 5.00836i) q^{85} +(-1.79126 - 5.17550i) q^{86} +(5.74617 + 2.96236i) q^{87} +(0.493480 - 1.42582i) q^{88} +(-8.92818 + 8.51300i) q^{89} +(-1.06687 + 2.33612i) q^{90} +(9.98080 - 0.791574i) q^{91} +(-0.968990 - 4.69692i) q^{92} +(4.30938 - 7.46407i) q^{93} +(12.5792 - 1.20117i) q^{94} +(-2.50865 - 10.3408i) q^{95} +(0.981929 - 0.189251i) q^{96} +(-2.66682 + 1.71386i) q^{97} +(3.30356 + 6.17142i) q^{98} +(-0.214725 + 1.49344i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} - 16 q^{6} - 2 q^{7} + 16 q^{8} + 8 q^{9}+O(q^{10}) \) 160 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 - 16 * q^6 - 2 * q^7 + 16 * q^8 + 8 * q^9	\( 160 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} - 16 q^{6} - 2 q^{7} + 16 q^{8} + 8 q^{9} - 2 q^{10} + 4 q^{11} - 8 q^{12} + 4 q^{13} - 9 q^{14} - 18 q^{15} + 8 q^{16} + 9 q^{17} - 8 q^{18} + 18 q^{20} + 7 q^{21} + 52 q^{22} + 22 q^{23} - 80 q^{24} + 42 q^{25} + 2 q^{26} + 16 q^{27} - 18 q^{28} - 54 q^{29} + 2 q^{30} - 15 q^{31} - 8 q^{32} + 18 q^{33} + 84 q^{34} + 82 q^{35} - 16 q^{36} + 3 q^{37} + 11 q^{38} + 2 q^{39} - 13 q^{40} + 22 q^{41} - 2 q^{42} - 96 q^{43} + 4 q^{44} - 20 q^{45} - 26 q^{47} + 16 q^{48} - 2 q^{49} - 4 q^{50} + 13 q^{51} - 2 q^{52} + 16 q^{53} + 8 q^{54} - 34 q^{55} + 2 q^{56} - 22 q^{57} - 5 q^{58} - 6 q^{59} - 2 q^{60} + 40 q^{61} - 8 q^{62} - 2 q^{63} - 16 q^{64} - 82 q^{65} + 4 q^{66} + 10 q^{67} - 46 q^{68} - 22 q^{69} + 100 q^{70} + 92 q^{71} - 8 q^{72} + 68 q^{73} - 3 q^{74} + 2 q^{75} - 7 q^{77} - 18 q^{78} - 78 q^{79} + 2 q^{80} + 8 q^{81} + 55 q^{82} - 42 q^{83} - 9 q^{84} + 50 q^{85} + 40 q^{86} + 6 q^{87} + 7 q^{88} - 80 q^{89} + 4 q^{90} - 62 q^{91} + 66 q^{92} + 26 q^{93} + 4 q^{94} - 17 q^{95} + 8 q^{96} - 8 q^{97} - 3 q^{98} + 36 q^{99}+O(q^{100}) \) 160 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 - 16 * q^6 - 2 * q^7 + 16 * q^8 + 8 * q^9 - 2 * q^10 + 4 * q^11 - 8 * q^12 + 4 * q^13 - 9 * q^14 - 18 * q^15 + 8 * q^16 + 9 * q^17 - 8 * q^18 + 18 * q^20 + 7 * q^21 + 52 * q^22 + 22 * q^23 - 80 * q^24 + 42 * q^25 + 2 * q^26 + 16 * q^27 - 18 * q^28 - 54 * q^29 + 2 * q^30 - 15 * q^31 - 8 * q^32 + 18 * q^33 + 84 * q^34 + 82 * q^35 - 16 * q^36 + 3 * q^37 + 11 * q^38 + 2 * q^39 - 13 * q^40 + 22 * q^41 - 2 * q^42 - 96 * q^43 + 4 * q^44 - 20 * q^45 - 26 * q^47 + 16 * q^48 - 2 * q^49 - 4 * q^50 + 13 * q^51 - 2 * q^52 + 16 * q^53 + 8 * q^54 - 34 * q^55 + 2 * q^56 - 22 * q^57 - 5 * q^58 - 6 * q^59 - 2 * q^60 + 40 * q^61 - 8 * q^62 - 2 * q^63 - 16 * q^64 - 82 * q^65 + 4 * q^66 + 10 * q^67 - 46 * q^68 - 22 * q^69 + 100 * q^70 + 92 * q^71 - 8 * q^72 + 68 * q^73 - 3 * q^74 + 2 * q^75 - 7 * q^77 - 18 * q^78 - 78 * q^79 + 2 * q^80 + 8 * q^81 + 55 * q^82 - 42 * q^83 - 9 * q^84 + 50 * q^85 + 40 * q^86 + 6 * q^87 + 7 * q^88 - 80 * q^89 + 4 * q^90 - 62 * q^91 + 66 * q^92 + 26 * q^93 + 4 * q^94 - 17 * q^95 + 8 * q^96 - 8 * q^97 - 3 * q^98 + 36 * q^99

Introduction

L-functions

Modular forms

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Database

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