LMFDB - Embedded newform 1110.2.ba.a.619.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(529,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("1110.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.ba (of order $6$, degree $2$, 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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			619.9
Character	$\chi$	$=$	1110.619
Dual form			1110.2.ba.a.529.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.83047 - 1.28429i) q^{5} -1.00000i q^{6} +(-3.31268 + 1.91258i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.83047 - 1.28429i) q^{5} -1.00000i q^{6} +(-3.31268 + 1.91258i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(0.196990 + 2.22737i) q^{10} +1.67653 q^{11} +(0.866025 + 0.500000i) q^{12} +(1.56010 + 2.70218i) q^{13} -3.82515i q^{14} +(-0.943089 + 2.02746i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.75979 - 4.78010i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-1.27752 + 0.737577i) q^{19} +(-2.02746 - 0.943089i) q^{20} +(1.91258 - 3.31268i) q^{21} +(-0.838266 + 1.45192i) q^{22} -1.21394 q^{23} +(-0.866025 + 0.500000i) q^{24} +(1.70122 - 4.70168i) q^{25} -3.12020 q^{26} +1.00000i q^{27} +(3.31268 + 1.91258i) q^{28} +2.97019i q^{29} +(-1.28429 - 1.83047i) q^{30} +5.65752i q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.45192 + 0.838266i) q^{33} +(2.75979 + 4.78010i) q^{34} +(-3.60746 + 7.75534i) q^{35} -1.00000 q^{36} +(-1.06142 - 5.98944i) q^{37} -1.47515i q^{38} +(-2.70218 - 1.56010i) q^{39} +(1.83047 - 1.28429i) q^{40} +(4.89193 + 8.47308i) q^{41} +(1.91258 + 3.31268i) q^{42} +11.7908 q^{43} +(-0.838266 - 1.45192i) q^{44} +(-0.196990 - 2.22737i) q^{45} +(0.606969 - 1.05130i) q^{46} +11.2816i q^{47} -1.00000i q^{48} +(3.81590 - 6.60933i) q^{49} +(3.22117 + 3.82415i) q^{50} +5.51959i q^{51} +(1.56010 - 2.70218i) q^{52} +(2.49973 + 1.44322i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(3.06884 - 2.15315i) q^{55} +(-3.31268 + 1.91258i) q^{56} +(0.737577 - 1.27752i) q^{57} +(-2.57226 - 1.48510i) q^{58} +(5.20788 + 3.00677i) q^{59} +(2.22737 - 0.196990i) q^{60} +(-5.55247 + 3.20572i) q^{61} +(-4.89955 - 2.82876i) q^{62} +3.82515i q^{63} +1.00000 q^{64} +(6.32608 + 2.94263i) q^{65} -1.67653i q^{66} +(0.933703 - 0.539074i) q^{67} -5.51959 q^{68} +(1.05130 - 0.606969i) q^{69} +(-4.91259 - 7.00182i) q^{70} +(0.807805 + 1.39916i) q^{71} +(0.500000 - 0.866025i) q^{72} +12.7659i q^{73} +(5.71772 + 2.07550i) q^{74} +(0.877540 + 4.92239i) q^{75} +(1.27752 + 0.737577i) q^{76} +(-5.55382 + 3.20650i) q^{77} +(2.70218 - 1.56010i) q^{78} +(-1.38034 + 0.796940i) q^{79} +(0.196990 + 2.22737i) q^{80} +(-0.500000 - 0.866025i) q^{81} -9.78387 q^{82} +(3.79462 + 2.19082i) q^{83} -3.82515 q^{84} +(-1.08730 - 12.2942i) q^{85} +(-5.89540 + 10.2111i) q^{86} +(-1.48510 - 2.57226i) q^{87} +1.67653 q^{88} +(-7.36049 - 4.24958i) q^{89} +(2.02746 + 0.943089i) q^{90} +(-10.3362 - 5.96763i) q^{91} +(0.606969 + 1.05130i) q^{92} +(-2.82876 - 4.89955i) q^{93} +(-9.77017 - 5.64081i) q^{94} +(-1.39120 + 2.99081i) q^{95} +(0.866025 + 0.500000i) q^{96} +16.8340 q^{97} +(3.81590 + 6.60933i) q^{98} +(0.838266 - 1.45192i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9}+O(q^{10}) $ 36 * q - 18 * q^2 - 18 * q^4 + 2 * q^5 + 36 * q^8 + 18 * q^9	$ 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9} + 2 q^{10} + 4 q^{11} - 14 q^{13} - 2 q^{15} - 18 q^{16} + 18 q^{18} + 6 q^{19} - 4 q^{20} - 2 q^{22} - 20 q^{23} + 4 q^{25} + 28 q^{26} - 2 q^{30} - 18 q^{32} - 6 q^{33} - 40 q^{35} - 36 q^{36} + 20 q^{37} + 6 q^{39} + 2 q^{40} + 10 q^{41} - 2 q^{44} - 2 q^{45} + 10 q^{46} + 10 q^{49} - 2 q^{50} - 14 q^{52} - 12 q^{53} + 56 q^{55} + 8 q^{57} + 30 q^{58} + 18 q^{59} + 4 q^{60} - 6 q^{61} - 12 q^{62} + 36 q^{64} + 40 q^{65} + 36 q^{67} + 12 q^{69} + 20 q^{70} - 24 q^{71} + 18 q^{72} - 34 q^{74} + 8 q^{75} - 6 q^{76} - 24 q^{77} - 6 q^{78} + 2 q^{80} - 18 q^{81} - 20 q^{82} + 36 q^{83} + 26 q^{85} - 10 q^{87} + 4 q^{88} + 4 q^{90} - 36 q^{91} + 10 q^{92} + 12 q^{93} + 12 q^{94} - 30 q^{95} + 52 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) $ 36 * q - 18 * q^2 - 18 * q^4 + 2 * q^5 + 36 * q^8 + 18 * q^9 + 2 * q^10 + 4 * q^11 - 14 * q^13 - 2 * q^15 - 18 * q^16 + 18 * q^18 + 6 * q^19 - 4 * q^20 - 2 * q^22 - 20 * q^23 + 4 * q^25 + 28 * q^26 - 2 * q^30 - 18 * q^32 - 6 * q^33 - 40 * q^35 - 36 * q^36 + 20 * q^37 + 6 * q^39 + 2 * q^40 + 10 * q^41 - 2 * q^44 - 2 * q^45 + 10 * q^46 + 10 * q^49 - 2 * q^50 - 14 * q^52 - 12 * q^53 + 56 * q^55 + 8 * q^57 + 30 * q^58 + 18 * q^59 + 4 * q^60 - 6 * q^61 - 12 * q^62 + 36 * q^64 + 40 * q^65 + 36 * q^67 + 12 * q^69 + 20 * q^70 - 24 * q^71 + 18 * q^72 - 34 * q^74 + 8 * q^75 - 6 * q^76 - 24 * q^77 - 6 * q^78 + 2 * q^80 - 18 * q^81 - 20 * q^82 + 36 * q^83 + 26 * q^85 - 10 * q^87 + 4 * q^88 + 4 * q^90 - 36 * q^91 + 10 * q^92 + 12 * q^93 + 12 * q^94 - 30 * q^95 + 52 * q^97 + 10 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.83047	−	1.28429i	0.818610	−	0.574350i
$5$	1.83047	−	1.28429i	0.818610	−	0.574350i
$6$		−	1.00000i		−	0.408248i
$7$	−3.31268	+	1.91258i	−1.25208	+	0.722886i	−0.971521	−	0.236952i	$-0.923852\pi$
$7$	−3.31268	+	1.91258i	−1.25208	+	0.722886i	−0.280554	+	0.959838i	$0.590518\pi$
$8$	1.00000			0.353553
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	0.196990	+	2.22737i	0.0622936	+	0.704358i
$11$	1.67653			0.505494			0.252747	−	0.967532i	$-0.418666\pi$
$11$	1.67653			0.505494			0.252747	+	0.967532i	$0.418666\pi$
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$	1.56010	+	2.70218i	0.432694	+	0.749449i	0.997104	−	0.0760461i	$-0.0242296\pi$
$13$	1.56010	+	2.70218i	0.432694	+	0.749449i	−0.564410	+	0.825495i	$0.690896\pi$
$14$		−	3.82515i		−	1.02232i
$15$	−0.943089	+	2.02746i	−0.243505	+	0.523487i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.75979	−	4.78010i	0.669348	−	1.15935i	−0.308738	−	0.951147i	$-0.599907\pi$
$17$	2.75979	−	4.78010i	0.669348	−	1.15935i	0.978087	−	0.208199i	$-0.0667600\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	−1.27752	+	0.737577i	−0.293083	+	0.169212i	−0.639331	−	0.768931i	$-0.720789\pi$
$19$	−1.27752	+	0.737577i	−0.293083	+	0.169212i	0.346248	+	0.938143i	$0.387455\pi$
$20$	−2.02746	−	0.943089i	−0.453353	−	0.210881i
$21$	1.91258	−	3.31268i	0.417358	−	0.722886i
$22$	−0.838266	+	1.45192i	−0.178719	+	0.309550i
$23$	−1.21394			−0.253124			−0.126562	−	0.991959i	$-0.540394\pi$
$23$	−1.21394			−0.253124			−0.126562	+	0.991959i	$0.540394\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	1.70122	−	4.70168i	0.340245	−	0.940337i
$26$	−3.12020			−0.611922
$27$			1.00000i			0.192450i
$28$	3.31268	+	1.91258i	0.626038	+	0.361443i
$29$			2.97019i			0.551551i	0.961222	+	0.275775i	$0.0889346\pi$
$29$			2.97019i			0.551551i	−0.961222	+	0.275775i	$0.911065\pi$
$30$	−1.28429	−	1.83047i	−0.234477	−	0.334196i
$31$			5.65752i			1.01612i	0.861322	+	0.508060i	$0.169637\pi$
$31$			5.65752i			1.01612i	−0.861322	+	0.508060i	$0.830363\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−1.45192	+	0.838266i	−0.252747	+	0.145923i
$34$	2.75979	+	4.78010i	0.473301	+	0.819781i
$35$	−3.60746	+	7.75534i	−0.609772	+	1.31089i
$36$	−1.00000			−0.166667
$37$	−1.06142	−	5.98944i	−0.174497	−	0.984658i
$37$	−1.06142	−	5.98944i	−0.174497	−	0.984658i
$38$		−	1.47515i		−	0.239301i
$39$	−2.70218	−	1.56010i	−0.432694	−	0.249816i
$40$	1.83047	−	1.28429i	0.289422	−	0.203063i
$41$	4.89193	+	8.47308i	0.763992	+	1.32327i	0.940778	+	0.339023i	$0.110096\pi$
$41$	4.89193	+	8.47308i	0.763992	+	1.32327i	−0.176786	+	0.984249i	$0.556570\pi$
$42$	1.91258	+	3.31268i	0.295117	+	0.511158i
$43$	11.7908			1.79808			0.899040	−	0.437866i	$-0.144266\pi$
$43$	11.7908			1.79808			0.899040	+	0.437866i	$0.144266\pi$
$44$	−0.838266	−	1.45192i	−0.126373	−	0.218885i
$45$	−0.196990	−	2.22737i	−0.0293655	−	0.332037i
$46$	0.606969	−	1.05130i	0.0894927	−	0.155006i
$47$			11.2816i			1.64559i	0.568336	+	0.822796i	$0.307587\pi$
$47$			11.2816i			1.64559i	−0.568336	+	0.822796i	$0.692413\pi$
$48$		−	1.00000i		−	0.144338i
$49$	3.81590	−	6.60933i	0.545128	−	0.944190i
$50$	3.22117	+	3.82415i	0.455542	+	0.540816i
$51$			5.51959i			0.772897i
$52$	1.56010	−	2.70218i	0.216347	−	0.374724i
$53$	2.49973	+	1.44322i	0.343365	+	0.198242i	0.661759	−	0.749717i	$-0.269810\pi$
$53$	2.49973	+	1.44322i	0.343365	+	0.198242i	−0.318394	+	0.947958i	$0.603144\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$	3.06884	−	2.15315i	0.413802	−	0.290330i
$56$	−3.31268	+	1.91258i	−0.442675	+	0.255579i
$57$	0.737577	−	1.27752i	0.0976944	−	0.169212i
$58$	−2.57226	−	1.48510i	−0.337755	−	0.195003i
$59$	5.20788	+	3.00677i	0.678009	+	0.391448i	0.799104	−	0.601192i	$-0.205307\pi$
$59$	5.20788	+	3.00677i	0.678009	+	0.391448i	−0.121096	+	0.992641i	$0.538641\pi$
$60$	2.22737	−	0.196990i	0.287553	−	0.0254313i
$61$	−5.55247	+	3.20572i	−0.710921	+	0.410451i	−0.811402	−	0.584488i	$-0.801295\pi$
$61$	−5.55247	+	3.20572i	−0.710921	+	0.410451i	0.100481	+	0.994939i	$0.467962\pi$
$62$	−4.89955	−	2.82876i	−0.622244	−	0.359253i
$63$			3.82515i			0.481924i
$64$	1.00000			0.125000
$65$	6.32608	+	2.94263i	0.784653	+	0.364988i
$66$		−	1.67653i		−	0.206367i
$67$	0.933703	−	0.539074i	0.114070	−	0.0658583i	−0.441879	−	0.897074i	$-0.645688\pi$
$67$	0.933703	−	0.539074i	0.114070	−	0.0658583i	0.555949	+	0.831216i	$0.312355\pi$
$68$	−5.51959			−0.669348
$69$	1.05130	−	0.606969i	0.126562	−	0.0730705i
$70$	−4.91259	−	7.00182i	−0.587166	−	0.836877i
$71$	0.807805	+	1.39916i	0.0958689	+	0.166050i	0.909971	−	0.414672i	$-0.136104\pi$
$71$	0.807805	+	1.39916i	0.0958689	+	0.166050i	−0.814102	+	0.580722i	$0.802770\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$			12.7659i			1.49414i	0.664747	+	0.747069i	$0.268539\pi$
$73$			12.7659i			1.49414i	−0.664747	+	0.747069i	$0.731461\pi$
$74$	5.71772	+	2.07550i	0.664671	+	0.241272i
$75$	0.877540	+	4.92239i	0.101330	+	0.568389i
$76$	1.27752	+	0.737577i	0.146542	+	0.0846058i
$77$	−5.55382	+	3.20650i	−0.632916	+	0.365414i
$78$	2.70218	−	1.56010i	0.305961	−	0.176647i
$79$	−1.38034	+	0.796940i	−0.155301	+	0.0896628i	−0.575636	−	0.817706i	$-0.695246\pi$
$79$	−1.38034	+	0.796940i	−0.155301	+	0.0896628i	0.420336	+	0.907369i	$0.361912\pi$
$80$	0.196990	+	2.22737i	0.0220241	+	0.249028i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−9.78387			−1.08045
$83$	3.79462	+	2.19082i	0.416513	+	0.240474i	0.693584	−	0.720375i	$-0.256030\pi$
$83$	3.79462	+	2.19082i	0.416513	+	0.240474i	−0.277071	+	0.960849i	$0.589364\pi$
$84$	−3.82515			−0.417358
$85$	−1.08730	−	12.2942i	−0.117934	−	1.33349i
$86$	−5.89540	+	10.2111i	−0.635717	+	1.10109i
$87$	−1.48510	−	2.57226i	−0.159219	−	0.275775i
$88$	1.67653			0.178719
$89$	−7.36049	−	4.24958i	−0.780210	−	0.450454i	0.0562948	−	0.998414i	$-0.482071\pi$
$89$	−7.36049	−	4.24958i	−0.780210	−	0.450454i	−0.836505	+	0.547960i	$0.815405\pi$
$90$	2.02746	+	0.943089i	0.213713	+	0.0994103i
$91$	−10.3362	−	5.96763i	−1.08353	−	0.625577i
$92$	0.606969	+	1.05130i	0.0632809	+	0.109606i
$93$	−2.82876	−	4.89955i	−0.293329	−	0.508060i
$94$	−9.77017	−	5.64081i	−1.00772	−	0.581805i
$95$	−1.39120	+	2.99081i	−0.142734	+	0.306851i
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$	16.8340			1.70923			0.854617	−	0.519259i	$-0.173792\pi$
$97$	16.8340			1.70923			0.854617	+	0.519259i	$0.173792\pi$
$98$	3.81590	+	6.60933i	0.385464	+	0.667643i
$99$	0.838266	−	1.45192i	0.0842489	−	0.145923i
$100$	−4.92239	+	0.877540i	−0.492239	+	0.0877540i
$101$	2.23855			0.222744			0.111372	−	0.993779i	$-0.464476\pi$
$101$	2.23855			0.222744			0.111372	+	0.993779i	$0.464476\pi$
$102$	−4.78010	−	2.75979i	−0.473301	−	0.273260i
$103$	−4.22889			−0.416684			−0.208342	−	0.978056i	$-0.566807\pi$
$103$	−4.22889			−0.416684			−0.208342	+	0.978056i	$0.566807\pi$
$104$	1.56010	+	2.70218i	0.152981	+	0.264970i
$105$	−0.753516	−	8.52005i	−0.0735356	−	0.831471i
$106$	−2.49973	+	1.44322i	−0.242795	+	0.140178i
$107$	−2.24493	+	1.29611i	−0.217026	+	0.125300i	−0.604572	−	0.796550i	$-0.706656\pi$
$107$	−2.24493	+	1.29611i	−0.217026	+	0.125300i	0.387547	+	0.921850i	$0.373323\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$	12.2762	+	7.08769i	1.17585	+	0.678877i	0.955051	−	0.296442i	$-0.0958001\pi$
$109$	12.2762	+	7.08769i	1.17585	+	0.678877i	0.220799	+	0.975319i	$0.429133\pi$
$110$	0.330260	+	3.73427i	0.0314890	+	0.356048i
$111$	3.91394	+	4.65629i	0.371495	+	0.441956i
$112$		−	3.82515i		−	0.361443i
$113$	−8.59155	+	14.8810i	−0.808225	+	1.39989i	0.105868	+	0.994380i	$0.466238\pi$
$113$	−8.59155	+	14.8810i	−0.808225	+	1.39989i	−0.914092	+	0.405506i	$0.867095\pi$
$114$	0.737577	+	1.27752i	0.0690804	+	0.119651i
$115$	−2.22208	+	1.55904i	−0.207210	+	0.145382i
$116$	2.57226	−	1.48510i	0.238829	−	0.137888i
$117$	3.12020			0.288463
$118$	−5.20788	+	3.00677i	−0.479424	+	0.276796i
$119$			21.1133i			1.93545i
$120$	−0.943089	+	2.02746i	−0.0860918	+	0.185081i
$121$	−8.18924			−0.744476
$122$		−	6.41144i		−	0.580465i
$123$	−8.47308	−	4.89193i	−0.763992	−	0.441091i
$124$	4.89955	−	2.82876i	0.439993	−	0.254030i
$125$	−2.92427	−	10.7911i	−0.261555	−	0.965189i
$126$	−3.31268	−	1.91258i	−0.295117	−	0.170386i
$127$	−14.0316	−	8.10117i	−1.24511	−	0.718862i	−0.274977	−	0.961451i	$-0.588670\pi$
$127$	−14.0316	−	8.10117i	−1.24511	−	0.718862i	−0.970129	+	0.242589i	$0.922003\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−10.2111	+	5.89540i	−0.899040	+	0.519061i
$130$	−5.71143	+	4.00723i	−0.500926	+	0.351457i
$131$	15.8066	+	9.12596i	1.38103	+	0.797339i	0.992282	−	0.124004i	$-0.0395736\pi$
$131$	15.8066	+	9.12596i	1.38103	+	0.797339i	0.388750	+	0.921343i	$0.372907\pi$
$132$	1.45192	+	0.838266i	0.126373	+	0.0729617i
$133$	2.82134	−	4.88671i	0.244642	−	0.423732i
$134$			1.07815i			0.0931378i
$135$	1.28429	+	1.83047i	0.110534	+	0.157542i
$136$	2.75979	−	4.78010i	0.236650	−	0.409891i
$137$		−	2.97364i		−	0.254055i	−0.991899	−	0.127028i	$-0.959456\pi$
$137$		−	2.97364i		−	0.254055i	0.991899	−	0.127028i	$-0.0405437\pi$
$138$			1.21394i			0.103337i
$139$	−5.43980	+	9.42200i	−0.461397	+	0.799164i	−0.999031	−	0.0440148i	$-0.985985\pi$
$139$	−5.43980	+	9.42200i	−0.461397	+	0.799164i	0.537633	+	0.843179i	$0.319318\pi$
$140$	8.52005	−	0.753516i	0.720075	−	0.0636837i
$141$	−5.64081	−	9.77017i	−0.475042	−	0.822796i
$142$	−1.61561			−0.135579
$143$	2.61556	+	4.53028i	0.218724	+	0.378841i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	3.81457	+	5.43684i	0.316783	+	0.451505i
$146$	−11.0556	−	6.38296i	−0.914969	−	0.528257i
$147$			7.63180i			0.629460i
$148$	−4.65629	+	3.91394i	−0.382745	+	0.321724i
$149$	8.97575			0.735322			0.367661	−	0.929960i	$-0.380159\pi$
$149$	8.97575			0.735322			0.367661	+	0.929960i	$0.380159\pi$
$150$	−4.70168	−	1.70122i	−0.383891	−	0.138904i
$151$	−5.87683	−	10.1790i	−0.478250	−	0.828353i	0.521439	−	0.853288i	$-0.325395\pi$
$151$	−5.87683	−	10.1790i	−0.478250	−	0.828353i	−0.999689	+	0.0249354i	$0.992062\pi$
$152$	−1.27752	+	0.737577i	−0.103621	+	0.0598254i
$153$	−2.75979	−	4.78010i	−0.223116	−	0.386449i
$154$		−	6.41299i		−	0.516774i
$155$	7.26586	+	10.3559i	0.583608	+	0.831806i
$156$			3.12020i			0.249816i
$157$	−0.108243	−	0.0624939i	−0.00863870	−	0.00498755i	0.495674	−	0.868508i	$-0.334921\pi$
$157$	−0.108243	−	0.0624939i	−0.00863870	−	0.00498755i	−0.504313	+	0.863521i	$0.668254\pi$
$158$		−	1.59388i		−	0.126802i
$159$	−2.88644			−0.228910
$160$	−2.02746	−	0.943089i	−0.160285	−	0.0745577i
$161$	4.02139	−	2.32175i	0.316930	−	0.182980i
$162$	1.00000			0.0785674
$163$	8.41453	−	14.5744i	0.659077	−	1.14155i	−0.321778	−	0.946815i	$-0.604280\pi$
$163$	8.41453	−	14.5744i	0.659077	−	1.14155i	0.980855	−	0.194740i	$-0.0623862\pi$
$164$	4.89193	−	8.47308i	0.381996	−	0.661636i
$165$	−1.58112	+	3.39910i	−0.123090	+	0.264619i
$166$	−3.79462	+	2.19082i	−0.294519	+	0.170041i
$167$	−10.0346	−	17.3805i	−0.776503	−	1.34494i	−0.933946	−	0.357415i	$-0.883658\pi$
$167$	−10.0346	−	17.3805i	−0.776503	−	1.34494i	0.157443	−	0.987528i	$-0.449675\pi$
$168$	1.91258	−	3.31268i	0.147558	−	0.255579i
$169$	1.63217	−	2.82700i	0.125551	−	0.217461i
$170$	11.1907	+	5.20546i	0.858290	+	0.399241i
$171$			1.47515i			0.112808i
$172$	−5.89540	−	10.2111i	−0.449520	−	0.778592i
$173$	11.9639	+	6.90737i	0.909599	+	0.525157i	0.880302	−	0.474414i	$-0.157340\pi$
$173$	11.9639	+	6.90737i	0.909599	+	0.525157i	0.0292969	+	0.999571i	$0.490673\pi$
$174$	2.97019			0.225170
$175$	3.35672	+	18.8289i	0.253744	+	1.42333i
$176$	−0.838266	+	1.45192i	−0.0631867	+	0.109443i
$177$	−6.01354			−0.452006
$178$	7.36049	−	4.24958i	0.551692	−	0.318519i
$179$			12.8111i			0.957545i	0.877939	+	0.478773i	$0.158918\pi$
$179$			12.8111i			0.957545i	−0.877939	+	0.478773i	$0.841082\pi$
$180$	−1.83047	+	1.28429i	−0.136435	+	0.0957250i
$181$	−7.43016	−	12.8694i	−0.552280	−	0.956576i	−0.998110	−	0.0614588i	$-0.980425\pi$
$181$	−7.43016	−	12.8694i	−0.552280	−	0.956576i	0.445830	−	0.895118i	$-0.352909\pi$
$182$	10.3362	−	5.96763i	0.766173	−	0.442350i
$183$	3.20572	−	5.55247i	0.236974	−	0.410451i
$184$	−1.21394			−0.0894927
$185$	−9.63505	−	9.60030i	−0.708383	−	0.705828i
$186$	5.65752			0.414829
$187$	4.62689	−	8.01400i	0.338351	−	0.586042i
$188$	9.77017	−	5.64081i	0.712563	−	0.411398i
$189$	−1.91258	−	3.31268i	−0.139119	−	0.240962i
$190$	−1.89452	−	2.70022i	−0.137443	−	0.195895i
$191$			12.5432i			0.907597i	0.891104	+	0.453798i	$0.149931\pi$
$191$			12.5432i			0.907597i	−0.891104	+	0.453798i	$0.850069\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	26.1467			1.88208			0.941041	−	0.338292i	$-0.109849\pi$
$193$	26.1467			1.88208			0.941041	+	0.338292i	$0.109849\pi$
$194$	−8.41700	+	14.5787i	−0.604306	+	1.04669i
$195$	−6.94986	+	0.614648i	−0.497690	+	0.0440159i
$196$	−7.63180			−0.545128
$197$	−20.8765	−	12.0530i	−1.48739	−	0.858744i	−0.487492	−	0.873128i	$-0.662088\pi$
$197$	−20.8765	−	12.0530i	−1.48739	−	0.858744i	−0.999897	+	0.0143835i	$0.995421\pi$
$198$	0.838266	+	1.45192i	0.0595730	+	0.103183i
$199$		−	21.4951i		−	1.52374i	−0.647727	−	0.761872i	$-0.724280\pi$
$199$		−	21.4951i		−	1.52374i	0.647727	−	0.761872i	$-0.275720\pi$
$200$	1.70122	−	4.70168i	0.120295	−	0.332459i
$201$	−0.539074	+	0.933703i	−0.0380233	+	0.0658583i
$202$	−1.11927	+	1.93864i	−0.0787519	+	0.136402i
$203$	−5.68072	−	9.83930i	−0.398708	−	0.690583i
$204$	4.78010	−	2.75979i	0.334674	−	0.193224i
$205$	19.8364	+	9.22706i	1.38543	+	0.644446i
$206$	2.11444	−	3.66232i	0.147320	−	0.255166i
$207$	−0.606969	+	1.05130i	−0.0421873	+	0.0730705i
$208$	−3.12020			−0.216347
$209$	−2.14180	+	1.23657i	−0.148152	+	0.0855354i
$210$	7.75534	+	3.60746i	0.535169	+	0.248938i
$211$	7.62398			0.524856			0.262428	−	0.964952i	$-0.415477\pi$
$211$	7.62398			0.524856			0.262428	+	0.964952i	$0.415477\pi$
$212$		−	2.88644i		−	0.198242i
$213$	−1.39916	−	0.807805i	−0.0958689	−	0.0553499i
$214$		−	2.59222i		−	0.177201i
$215$	21.5827	−	15.1427i	1.47193	−	1.03273i
$216$			1.00000i			0.0680414i
$217$	−10.8204	−	18.7415i	−0.734539	−	1.27226i
$218$	−12.2762	+	7.08769i	−0.831452	+	0.480039i
$219$	−6.38296	−	11.0556i	−0.431320	−	0.747069i
$220$	−3.39910	−	1.58112i	−0.229167	−	0.106599i
$221$	17.2222			1.15849
$222$	−5.98944	+	1.06142i	−0.401985	+	0.0712382i
$223$		−	4.00109i		−	0.267933i	−0.990986	−	0.133966i	$-0.957229\pi$
$223$		−	4.00109i		−	0.267933i	0.990986	−	0.133966i	$-0.0427714\pi$
$224$	3.31268	+	1.91258i	0.221338	+	0.127789i
$225$	−3.22117	−	3.82415i	−0.214744	−	0.254943i
$226$	−8.59155	−	14.8810i	−0.571501	−	0.989869i
$227$	−6.44101	−	11.1562i	−0.427505	−	0.740460i	0.569146	−	0.822237i	$-0.307274\pi$
$227$	−6.44101	−	11.1562i	−0.427505	−	0.740460i	−0.996651	+	0.0817765i	$0.973941\pi$
$228$	−1.47515			−0.0976944
$229$	−7.81590	−	13.5375i	−0.516489	−	0.894586i	−0.999817	−	0.0191460i	$-0.993905\pi$
$229$	−7.81590	−	13.5375i	−0.516489	−	0.894586i	0.483327	−	0.875440i	$-0.339428\pi$
$230$	−0.239133	−	2.70389i	−0.0157680	−	0.178290i
$231$	3.20650	−	5.55382i	0.210972	−	0.365414i
$232$			2.97019i			0.195003i
$233$		−	2.50962i		−	0.164410i	−0.996615	−	0.0822052i	$-0.973804\pi$
$233$		−	2.50962i		−	0.164410i	0.996615	−	0.0822052i	$-0.0261963\pi$
$234$	−1.56010	+	2.70218i	−0.101987	+	0.176647i
$235$	14.4888	+	20.6506i	0.945146	+	1.34710i
$236$		−	6.01354i		−	0.391448i
$237$	0.796940	−	1.38034i	0.0517668	−	0.0896628i
$238$	−18.2846	−	10.5566i	−1.18522	−	0.684285i
$239$	3.69433	+	2.13292i	0.238966	+	0.137967i	0.614702	−	0.788760i	$-0.289276\pi$
$239$	3.69433	+	2.13292i	0.238966	+	0.137967i	−0.375735	+	0.926727i	$0.622610\pi$
$240$	−1.28429	−	1.83047i	−0.0829002	−	0.118156i
$241$	25.2255	−	14.5640i	1.62492	−	0.938147i	0.639341	−	0.768924i	$-0.279207\pi$
$241$	25.2255	−	14.5640i	1.62492	−	0.938147i	0.985578	−	0.169223i	$-0.0541259\pi$
$242$	4.09462	−	7.09209i	0.263212	−	0.455897i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	5.55247	+	3.20572i	0.355461	+	0.205225i
$245$	−1.50339	−	16.9989i	−0.0960478	−	1.08602i
$246$	8.47308	−	4.89193i	0.540224	−	0.311898i
$247$	−3.98612	−	2.30139i	−0.253631	−	0.146434i
$248$			5.65752i			0.359253i
$249$	−4.38165			−0.277676
$250$	10.8075	+	2.86308i	0.683528	+	0.181077i
$251$		−	13.7583i		−	0.868414i	−0.900813	−	0.434207i	$-0.857029\pi$
$251$		−	13.7583i		−	0.868414i	0.900813	−	0.434207i	$-0.142971\pi$
$252$	3.31268	−	1.91258i	0.208679	−	0.120481i
$253$	−2.03521			−0.127952
$254$	14.0316	−	8.10117i	0.880423	−	0.508312i
$255$	7.08873	+	10.1034i	0.443913	+	0.632701i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.17314	−	5.49604i	0.197935	−	0.342833i	−0.749924	−	0.661524i	$-0.769910\pi$
$257$	3.17314	−	5.49604i	0.197935	−	0.342833i	0.947859	+	0.318691i	$0.103243\pi$
$258$		−	11.7908i		−	0.734063i
$259$	14.9714	+	17.8110i	0.930279	+	1.10672i
$260$	−0.614648	−	6.94986i	−0.0381188	−	0.431012i
$261$	2.57226	+	1.48510i	0.159219	+	0.0919252i
$262$	−15.8066	+	9.12596i	−0.976537	+	0.563804i
$263$	−0.942492	+	0.544148i	−0.0581165	+	0.0335536i	−0.528777	−	0.848761i	$-0.677349\pi$
$263$	−0.942492	+	0.544148i	−0.0581165	+	0.0335536i	0.470660	+	0.882315i	$0.344016\pi$
$264$	−1.45192	+	0.838266i	−0.0893595	+	0.0515917i
$265$	6.42919	−	0.568599i	0.394942	−	0.0349288i
$266$	2.82134	+	4.88671i	0.172988	+	0.299623i
$267$	8.49916			0.520140
$268$	−0.933703	−	0.539074i	−0.0570350	−	0.0329292i
$269$	−3.18400			−0.194132			−0.0970658	−	0.995278i	$-0.530946\pi$
$269$	−3.18400			−0.194132			−0.0970658	+	0.995278i	$0.530946\pi$
$270$	−2.22737	+	0.196990i	−0.135554	+	0.0119884i
$271$	−8.94307	+	15.4898i	−0.543253	+	0.940941i	0.455462	+	0.890255i	$0.349474\pi$
$271$	−8.94307	+	15.4898i	−0.543253	+	0.940941i	−0.998715	+	0.0506859i	$0.983859\pi$
$272$	2.75979	+	4.78010i	0.167337	+	0.289836i
$273$	11.9353			0.722354
$274$	2.57525	+	1.48682i	0.155576	+	0.0898221i
$275$	2.85216	−	7.88253i	0.171992	−	0.475334i
$276$	−1.05130	−	0.606969i	−0.0632809	−	0.0365353i
$277$	9.81717	+	17.0038i	0.589857	+	1.02166i	0.994251	+	0.107077i	$0.0341491\pi$
$277$	9.81717	+	17.0038i	0.589857	+	1.02166i	−0.404394	+	0.914585i	$0.632518\pi$
$278$	−5.43980	−	9.42200i	−0.326257	−	0.565094i
$279$	4.89955	+	2.82876i	0.293329	+	0.169353i
$280$	−3.60746	+	7.75534i	−0.215587	+	0.463470i
$281$	10.2198	+	5.90041i	0.609662	+	0.351989i	0.772833	−	0.634609i	$-0.218839\pi$
$281$	10.2198	+	5.90041i	0.609662	+	0.351989i	−0.163171	+	0.986598i	$0.552172\pi$
$282$	11.2816			0.671810
$283$	−1.07987	−	1.87039i	−0.0641916	−	0.111183i	0.832144	−	0.554560i	$-0.187114\pi$
$283$	−1.07987	−	1.87039i	−0.0641916	−	0.111183i	−0.896335	+	0.443377i	$0.853780\pi$
$284$	0.807805	−	1.39916i	0.0479344	−	0.0830249i
$285$	−0.290590	−	3.28572i	−0.0172131	−	0.194629i
$286$	−5.23112			−0.309323
$287$	−32.4108	−	18.7124i	−1.91315	−	1.10456i
$288$	−1.00000			−0.0589256
$289$	−6.73293	−	11.6618i	−0.396055	−	0.685987i
$290$	−6.61573	+	0.585097i	−0.388489	+	0.0343581i
$291$	−14.5787	+	8.41700i	−0.854617	+	0.493413i
$292$	11.0556	−	6.38296i	0.646981	−	0.373534i
$293$	3.09718	−	1.78816i	0.180939	−	0.104465i	−0.406795	−	0.913520i	$-0.633354\pi$
$293$	3.09718	−	1.78816i	0.180939	−	0.104465i	0.587734	+	0.809054i	$0.300020\pi$
$294$	−6.60933	−	3.81590i	−0.385464	−	0.222548i
$295$	13.3944	−	1.18461i	0.779853	−	0.0689705i
$296$	−1.06142	−	5.98944i	−0.0616941	−	0.348129i
$297$			1.67653i			0.0972823i
$298$	−4.48787	+	7.77322i	−0.259975	+	0.450291i
$299$	−1.89387	−	3.28027i	−0.109525	−	0.189703i
$300$	3.82415	−	3.22117i	0.220787	−	0.185974i
$301$	−39.0591	+	22.5508i	−2.25133	+	1.29981i
$302$	11.7537			0.676347
$303$	−1.93864	+	1.11927i	−0.111372	+	0.0643006i
$304$		−	1.47515i		−	0.0846058i
$305$	−6.04656	+	12.9989i	−0.346225	+	0.744316i
$306$	5.51959			0.315534
$307$		−	11.3779i		−	0.649371i	−0.945822	−	0.324685i	$-0.894742\pi$
$307$		−	11.3779i		−	0.649371i	0.945822	−	0.324685i	$-0.105258\pi$
$308$	5.55382	+	3.20650i	0.316458	+	0.182707i
$309$	3.66232	−	2.11444i	0.208342	−	0.120286i
$310$	−12.6014	+	1.11447i	−0.715712	+	0.0632978i
$311$	25.0523	+	14.4639i	1.42058	+	0.820174i	0.996349	−	0.0853784i	$-0.0272099\pi$
$311$	25.0523	+	14.4639i	1.42058	+	0.820174i	0.424234	+	0.905552i	$0.360543\pi$
$312$	−2.70218	−	1.56010i	−0.152981	−	0.0883234i
$313$	−6.77595	+	11.7363i	−0.382999	+	0.663374i	−0.991489	−	0.130187i	$-0.958442\pi$
$313$	−6.77595	+	11.7363i	−0.382999	+	0.663374i	0.608490	+	0.793561i	$0.291775\pi$
$314$	0.108243	−	0.0624939i	0.00610848	−	0.00352673i
$315$	4.91259	+	7.00182i	0.276793	+	0.394508i
$316$	1.38034	+	0.796940i	0.0776503	+	0.0448314i
$317$	−0.669018	−	0.386258i	−0.0375758	−	0.0216944i	0.481094	−	0.876669i	$-0.340239\pi$
$317$	−0.669018	−	0.386258i	−0.0375758	−	0.0216944i	−0.518670	+	0.854974i	$0.673573\pi$
$318$	1.44322	−	2.49973i	0.0809318	−	0.140178i
$319$			4.97962i			0.278805i
$320$	1.83047	−	1.28429i	0.102326	−	0.0717937i
$321$	1.29611	−	2.24493i	0.0723419	−	0.125300i
$322$			4.64350i			0.258772i
$323$			8.14224i			0.453046i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	15.3589	−	2.73810i	0.851956	−	0.151883i
$326$	8.41453	+	14.5744i	0.466038	+	0.807201i
$327$	−14.1754			−0.783900
$328$	4.89193	+	8.47308i	0.270112	+	0.467847i
$329$	−21.5770	−	37.3724i	−1.18958	−	2.06041i
$330$	−2.15315	−	3.06884i	−0.118527	−	0.168934i
$331$	−6.34735	−	3.66465i	−0.348882	−	0.201427i	0.315311	−	0.948988i	$-0.397891\pi$
$331$	−6.34735	−	3.66465i	−0.348882	−	0.201427i	−0.664193	+	0.747561i	$0.731225\pi$
$332$		−	4.38165i		−	0.240474i
$333$	−5.71772	−	2.07550i	−0.313329	−	0.113737i
$334$	20.0693			1.09814
$335$	1.01679	−	2.18590i	0.0555531	−	0.119428i
$336$	1.91258	+	3.31268i	0.104340	+	0.180722i
$337$	−10.2237	+	5.90267i	−0.556922	+	0.321539i	−0.751909	−	0.659267i	$-0.770867\pi$
$337$	−10.2237	+	5.90267i	−0.556922	+	0.321539i	0.194987	+	0.980806i	$0.437533\pi$
$338$	1.63217	+	2.82700i	0.0887782	+	0.153768i
$339$		−	17.1831i		−	0.933257i
$340$	−10.1034	+	7.08873i	−0.547935	+	0.384440i
$341$			9.48501i			0.513642i
$342$	−1.27752	−	0.737577i	−0.0690804	−	0.0398836i
$343$			2.41672i			0.130491i
$344$	11.7908			0.635717
$345$	1.14485	−	2.46121i	0.0616368	−	0.132507i
$346$	−11.9639	+	6.90737i	−0.643184	+	0.371342i
$347$	10.5172			0.564593			0.282297	−	0.959327i	$-0.408904\pi$
$347$	10.5172			0.564593			0.282297	+	0.959327i	$0.408904\pi$
$348$	−1.48510	+	2.57226i	−0.0796095	+	0.137888i
$349$	−10.6455	+	18.4385i	−0.569840	+	0.986991i	0.426742	+	0.904374i	$0.359661\pi$
$349$	−10.6455	+	18.4385i	−0.569840	+	0.986991i	−0.996581	+	0.0826177i	$0.973672\pi$
$350$	−17.9847	−	6.50744i	−0.961321	−	0.347837i
$351$	−2.70218	+	1.56010i	−0.144231	+	0.0832721i
$352$	−0.838266	−	1.45192i	−0.0446797	−	0.0773876i
$353$	−1.38917	+	2.40612i	−0.0739383	+	0.128065i	−0.900624	−	0.434599i	$-0.856890\pi$
$353$	−1.38917	+	2.40612i	−0.0739383	+	0.128065i	0.826686	+	0.562664i	$0.190223\pi$
$354$	3.00677	−	5.20788i	0.159808	−	0.276796i
$355$	3.27558	+	1.52366i	0.173850	+	0.0808677i
$356$			8.49916i			0.450454i
$357$	−10.5566	−	18.2846i	−0.558716	−	0.967725i
$358$	−11.0947	−	6.40554i	−0.586374	−	0.338543i
$359$	−27.0841			−1.42945			−0.714723	−	0.699408i	$-0.753447\pi$
$359$	−27.0841			−1.42945			−0.714723	+	0.699408i	$0.753447\pi$
$360$	−0.196990	−	2.22737i	−0.0103823	−	0.117393i
$361$	−8.41196	+	14.5699i	−0.442735	+	0.766839i
$362$	14.8603			0.781041
$363$	7.09209	−	4.09462i	0.372238	−	0.214912i
$364$			11.9353i			0.625577i
$365$	16.3951	+	23.3676i	0.858158	+	1.22312i
$366$	3.20572	+	5.55247i	0.167566	+	0.290232i
$367$	0.553552	−	0.319593i	0.0288952	−	0.0166826i	−0.485483	−	0.874246i	$-0.661356\pi$
$367$	0.553552	−	0.319593i	0.0288952	−	0.0166826i	0.514378	+	0.857564i	$0.328023\pi$
$368$	0.606969	−	1.05130i	0.0316405	−	0.0548029i
$369$	9.78387			0.509328
$370$	13.1316	−	3.54405i	0.682681	−	0.184246i
$371$	−11.0411			−0.573224
$372$	−2.82876	+	4.89955i	−0.146664	+	0.254030i
$373$	−8.09384	+	4.67298i	−0.419083	+	0.241958i	−0.694685	−	0.719314i	$-0.744456\pi$
$373$	−8.09384	+	4.67298i	−0.419083	+	0.241958i	0.275602	+	0.961272i	$0.411123\pi$
$374$	4.62689	+	8.01400i	0.239251	+	0.414394i
$375$	7.92806	+	7.88326i	0.409403	+	0.407090i
$376$			11.2816i			0.581805i
$377$	−8.02598	+	4.63380i	−0.413359	+	0.238653i
$378$	3.82515			0.196745
$379$	14.4675	−	25.0584i	0.743144	−	1.28716i	−0.207913	−	0.978147i	$-0.566667\pi$
$379$	14.4675	−	25.0584i	0.743144	−	1.28716i	0.951057	−	0.309015i	$-0.0999995\pi$
$380$	3.28572	−	0.290590i	0.168554	−	0.0149070i
$381$	16.2023			0.830071
$382$	−10.8628	−	6.27162i	−0.555787	−	0.320884i
$383$	5.13077	+	8.88675i	0.262170	+	0.454092i	0.966818	−	0.255465i	$-0.0822285\pi$
$383$	5.13077	+	8.88675i	0.262170	+	0.454092i	−0.704648	+	0.709557i	$0.748895\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	−6.04802	+	13.0021i	−0.308236	+	0.662647i
$386$	−13.0734	+	22.6437i	−0.665417	+	1.15254i
$387$	5.89540	−	10.2111i	0.299680	−	0.519061i
$388$	−8.41700	−	14.5787i	−0.427309	−	0.740120i
$389$	−24.1044	+	13.9167i	−1.22214	+	0.705605i	−0.965374	−	0.260868i	$-0.915991\pi$
$389$	−24.1044	+	13.9167i	−1.22214	+	0.705605i	−0.256769	+	0.966473i	$0.582658\pi$
$390$	2.94263	−	6.32608i	0.149006	−	0.320333i
$391$	−3.35022	+	5.80275i	−0.169428	+	0.293458i
$392$	3.81590	−	6.60933i	0.192732	−	0.333822i
$393$	−18.2519			−0.920688
$394$	20.8765	−	12.0530i	1.05174	−	0.607224i
$395$	−1.50317	+	3.23152i	−0.0756327	+	0.162596i
$396$	−1.67653			−0.0842489
$397$		−	12.4253i		−	0.623610i	−0.950146	−	0.311805i	$-0.899066\pi$
$397$		−	12.4253i		−	0.623610i	0.950146	−	0.311805i	$-0.100934\pi$
$398$	18.6153	+	10.7475i	0.933099	+	0.538725i
$399$			5.64269i			0.282488i
$400$	3.22117	+	3.82415i	0.161058	+	0.191207i
$401$		−	34.4549i		−	1.72060i	−0.509790	−	0.860299i	$-0.670277\pi$
$401$		−	34.4549i		−	1.72060i	0.509790	−	0.860299i	$-0.329723\pi$
$402$	−0.539074	−	0.933703i	−0.0268866	−	0.0465689i
$403$	−15.2876	+	8.82630i	−0.761530	+	0.439669i
$404$	−1.11927	−	1.93864i	−0.0556860	−	0.0964509i
$405$	−2.02746	−	0.943089i	−0.100745	−	0.0468625i
$406$	11.3614			0.563859
$407$	−1.77951	−	10.0415i	−0.0882072	−	0.497738i
$408$			5.51959i			0.273260i
$409$	−9.78149	−	5.64735i	−0.483664	−	0.279243i	0.238278	−	0.971197i	$-0.423417\pi$
$409$	−9.78149	−	5.64735i	−0.483664	−	0.279243i	−0.721942	+	0.691954i	$0.756750\pi$
$410$	−17.9091	+	12.5653i	−0.884465	+	0.620555i
$411$	1.48682	+	2.57525i	0.0733394	+	0.127028i
$412$	2.11444	+	3.66232i	0.104171	+	0.180430i
$413$	−23.0027			−1.13189
$414$	−0.606969	−	1.05130i	−0.0298309	−	0.0516687i
$415$	9.75957	−	0.863139i	0.479078	−	0.0423698i
$416$	1.56010	−	2.70218i	0.0764903	−	0.132485i
$417$		−	10.8796i		−	0.532776i
$418$		−	2.47314i		−	0.120965i
$419$	1.76879	−	3.06364i	0.0864111	−	0.149668i	−0.819581	−	0.572964i	$-0.805793\pi$
$419$	1.76879	−	3.06364i	0.0864111	−	0.149668i	0.905992	+	0.423296i	$0.139127\pi$
$420$	−7.00182	+	4.91259i	−0.341654	+	0.239710i
$421$		−	0.321990i		−	0.0156928i	−0.999969	−	0.00784642i	$-0.997502\pi$
$421$		−	0.321990i		−	0.0156928i	0.999969	−	0.00784642i	$-0.00249762\pi$
$422$	−3.81199	+	6.60256i	−0.185565	+	0.321407i
$423$	9.77017	+	5.64081i	0.475042	+	0.274265i
$424$	2.49973	+	1.44322i	0.121398	+	0.0700890i
$425$	−17.7795	−	21.1077i	−0.862433	−	1.02387i
$426$	1.39916	−	0.807805i	0.0677895	−	0.0391383i
$427$	12.2624	−	21.2391i	0.593418	−	1.02783i
$428$	2.24493	+	1.29611i	0.108513	+	0.0626499i
$429$	−4.53028	−	2.61556i	−0.218724	−	0.126280i
$430$	2.32267	+	26.2625i	0.112009	+	1.26649i
$431$	21.4026	−	12.3568i	1.03093	−	0.595206i	0.113676	−	0.993518i	$-0.463737\pi$
$431$	21.4026	−	12.3568i	1.03093	−	0.595206i	0.917250	+	0.398312i	$0.130404\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$			2.86272i			0.137574i	0.997631	+	0.0687868i	$0.0219128\pi$
$433$			2.86272i			0.137574i	−0.997631	+	0.0687868i	$0.978087\pi$
$434$	21.6409			1.03879
$435$	−6.02194	−	2.80116i	−0.288730	−	0.134305i
$436$		−	14.1754i		−	0.678877i
$437$	1.55083	−	0.895373i	0.0741863	−	0.0428315i
$438$	12.7659			0.609979
$439$	−1.68156	+	0.970851i	−0.0802566	+	0.0463362i	−0.539591	−	0.841927i	$-0.681421\pi$
$439$	−1.68156	+	0.970851i	−0.0802566	+	0.0463362i	0.459335	+	0.888263i	$0.348088\pi$
$440$	3.06884	−	2.15315i	0.146301	−	0.102647i
$441$	−3.81590	−	6.60933i	−0.181709	−	0.314730i
$442$	−8.61112	+	14.9149i	−0.409589	+	0.709429i
$443$			19.3246i			0.918141i	0.888400	+	0.459070i	$0.151817\pi$
$443$			19.3246i			0.918141i	−0.888400	+	0.459070i	$0.848183\pi$
$444$	2.07550	−	5.71772i	0.0984988	−	0.271351i
$445$	−18.9308	+	1.67425i	−0.897406	+	0.0793669i
$446$	3.46504	+	2.00054i	0.164075	+	0.0947285i
$447$	−7.77322	+	4.48787i	−0.367661	+	0.212269i
$448$	−3.31268	+	1.91258i	−0.156509	+	0.0903608i
$449$	−19.4648	+	11.2380i	−0.918600	+	0.530354i	−0.883188	−	0.469019i	$-0.844608\pi$
$449$	−19.4648	+	11.2380i	−0.918600	+	0.530354i	−0.0354115	+	0.999373i	$0.511274\pi$
$450$	4.92239	−	0.877540i	0.232044	−	0.0413676i
$451$	8.20149	+	14.2054i	0.386193	+	0.668906i
$452$	17.1831			0.808225
$453$	10.1790	+	5.87683i	0.478250	+	0.276118i
$454$	12.8820			0.604583
$455$	−26.5843	+	2.35112i	−1.24629	+	0.110222i
$456$	0.737577	−	1.27752i	0.0345402	−	0.0598254i
$457$	−5.93888	−	10.2864i	−0.277809	−	0.481179i	0.693031	−	0.720908i	$-0.256275\pi$
$457$	−5.93888	−	10.2864i	−0.277809	−	0.481179i	−0.970840	+	0.239729i	$0.922942\pi$
$458$	15.6318			0.730426
$459$	4.78010	+	2.75979i	0.223116	+	0.128816i
$460$	2.46121	+	1.14485i	0.114754	+	0.0533790i
$461$	7.12646	+	4.11446i	0.331912	+	0.191630i	0.656690	−	0.754161i	$-0.271956\pi$
$461$	7.12646	+	4.11446i	0.331912	+	0.191630i	−0.324777	+	0.945790i	$0.605289\pi$
$462$	3.20650	+	5.55382i	0.149180	+	0.258387i
$463$	−12.3478	−	21.3871i	−0.573853	−	0.993942i	−0.996165	−	0.0874916i	$-0.972115\pi$
$463$	−12.3478	−	21.3871i	−0.573853	−	0.993942i	0.422313	−	0.906450i	$-0.361218\pi$
$464$	−2.57226	−	1.48510i	−0.119414	−	0.0689439i
$465$	−11.4704	−	5.33554i	−0.531926	−	0.247430i
$466$	2.17339	+	1.25481i	0.100680	+	0.0581279i
$467$	−14.7594			−0.682984			−0.341492	−	0.939885i	$-0.610932\pi$
$467$	−14.7594			−0.682984			−0.341492	+	0.939885i	$0.610932\pi$
$468$	−1.56010	−	2.70218i	−0.0721157	−	0.124908i
$469$	−2.06204	+	3.57156i	−0.0952161	+	0.164919i
$470$	−25.1284	+	2.22236i	−1.15909	+	0.102510i
$471$	0.124988			0.00575913
$472$	5.20788	+	3.00677i	0.239712	+	0.138398i
$473$	19.7677			0.908918
$474$	0.796940	+	1.38034i	0.0366047	+	0.0634012i
$475$	1.29451	+	7.26128i	0.0593960	+	0.333170i
$476$	18.2846	−	10.5566i	0.838075	−	0.483863i
$477$	2.49973	−	1.44322i	0.114455	−	0.0660805i
$478$	−3.69433	+	2.13292i	−0.168975	+	0.0975577i
$479$	−25.0708	−	14.4746i	−1.14551	−	0.661363i	−0.197724	−	0.980258i	$-0.563355\pi$
$479$	−25.0708	−	14.4746i	−1.14551	−	0.661363i	−0.947790	+	0.318895i	$0.896688\pi$
$480$	2.22737	−	0.196990i	0.101665	−	0.00899131i
$481$	14.5286	−	12.2123i	0.662446	−	0.556832i
$482$			29.1279i			1.32674i
$483$	−2.32175	+	4.02139i	−0.105643	+	0.182980i
$484$	4.09462	+	7.09209i	0.186119	+	0.322368i
$485$	30.8141	−	21.6197i	1.39920	−	0.981698i
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$	42.1560			1.91027			0.955135	−	0.296171i	$-0.0957098\pi$
$487$	42.1560			1.91027			0.955135	+	0.296171i	$0.0957098\pi$
$488$	−5.55247	+	3.20572i	−0.251349	+	0.145116i
$489$			16.8291i			0.761037i
$490$	15.4731	+	7.19746i	0.699005	+	0.325148i
$491$	−26.3161			−1.18763			−0.593814	−	0.804602i	$-0.702379\pi$
$491$	−26.3161			−1.18763			−0.593814	+	0.804602i	$0.702379\pi$
$492$			9.78387i			0.441091i
$493$	14.1978	+	8.19712i	0.639438	+	0.369180i
$494$	3.98612	−	2.30139i	0.179344	−	0.103544i
$495$	−0.330260	−	3.73427i	−0.0148441	−	0.167843i
$496$	−4.89955	−	2.82876i	−0.219996	−	0.127015i
$497$	−5.35200	−	3.08998i	−0.240070	−	0.138605i
$498$	2.19082	−	3.79462i	0.0981731	−	0.170041i
$499$	−17.0790	+	9.86057i	−0.764561	+	0.441420i	−0.830931	−	0.556375i	$-0.812192\pi$
$499$	−17.0790	+	9.86057i	−0.764561	+	0.441420i	0.0663697	+	0.997795i	$0.478858\pi$
$500$	−7.88326	+	7.92806i	−0.352550	+	0.354554i
$501$	17.3805	+	10.0346i	0.776503	+	0.448314i
$502$	11.9150	+	6.87914i	0.531793	+	0.307031i
$503$	9.47499	−	16.4112i	0.422469	−	0.731738i	−0.573711	−	0.819058i	$-0.694497\pi$
$503$	9.47499	−	16.4112i	0.422469	−	0.731738i	0.996180	+	0.0873197i	$0.0278302\pi$
$504$			3.82515i			0.170386i
$505$	4.09759	−	2.87493i	0.182340	−	0.127933i
$506$	1.01760	−	1.76254i	0.0452380	−	0.0783545i
$507$			3.26433i			0.144974i
$508$			16.2023i			0.718862i
$509$	12.3220	−	21.3424i	0.546164	−	0.945984i	−0.452369	−	0.891831i	$-0.649421\pi$
$509$	12.3220	−	21.3424i	0.546164	−	0.945984i	0.998533	−	0.0541528i	$-0.0172458\pi$
$510$	−12.2942	+	1.08730i	−0.544396	+	0.0481466i
$511$	−24.4158	−	42.2894i	−1.08009	−	1.87077i
$512$	1.00000			0.0441942
$513$	−0.737577	−	1.27752i	−0.0325648	−	0.0564039i
$514$	3.17314	+	5.49604i	0.139961	+	0.242420i
$515$	−7.74084	+	5.43109i	−0.341102	+	0.239323i
$516$	10.2111	+	5.89540i	0.449520	+	0.259531i
$517$			18.9140i			0.831837i
$518$	−22.9105	+	4.06011i	−1.00663	+	0.178391i
$519$	−13.8147			−0.606399
$520$	6.32608	+	2.94263i	0.277417	+	0.129043i
$521$	0.538526	+	0.932754i	0.0235933	+	0.0408647i	0.877581	−	0.479428i	$-0.159156\pi$
$521$	0.538526	+	0.932754i	0.0235933	+	0.0408647i	−0.853988	+	0.520293i	$0.825823\pi$
$522$	−2.57226	+	1.48510i	−0.112585	+	0.0650009i
$523$	−13.2793	−	23.0004i	−0.580662	−	1.00574i	−0.995401	−	0.0957956i	$-0.969460\pi$
$523$	−13.2793	−	23.0004i	−0.580662	−	1.00574i	0.414739	−	0.909940i	$-0.363873\pi$
$524$		−	18.2519i		−	0.797339i
$525$	−12.3215	−	14.6279i	−0.537752	−	0.638416i
$526$		−	1.08830i		−	0.0474519i
$527$	27.0435	+	15.6136i	1.17803	+	0.680138i
$528$		−	1.67653i		−	0.0729617i
$529$	−21.5264			−0.935928
$530$	−2.72217	+	5.85214i	−0.118244	+	0.254201i
$531$	5.20788	−	3.00677i	0.226003	−	0.130483i
$532$	−5.64269			−0.244642
$533$	−15.2638	+	26.4377i	−0.661150	+	1.14514i
$534$	−4.24958	+	7.36049i	−0.183897	+	0.318519i
$535$	−2.44470	+	5.25562i	−0.105693	+	0.227220i
$536$	0.933703	−	0.539074i	0.0403298	−	0.0232844i
$537$	−6.40554	−	11.0947i	−0.276419	−	0.478773i
$538$	1.59200	−	2.75742i	0.0686359	−	0.118881i
$539$	6.39748	−	11.0808i	0.275559	−	0.477282i
$540$	0.943089	−	2.02746i	0.0405841	−	0.0872479i
$541$		−	32.7874i		−	1.40964i	−0.709386	−	0.704821i	$-0.751027\pi$
$541$		−	32.7874i		−	1.40964i	0.709386	−	0.704821i	$-0.248973\pi$
$542$	−8.94307	−	15.4898i	−0.384138	−	0.665346i
$543$	12.8694	+	7.43016i	0.552280	+	0.318859i
$544$	−5.51959			−0.236650
$545$	31.5739	−	2.79240i	1.35248	−	0.119613i
$546$	−5.96763	+	10.3362i	−0.255391	+	0.442350i
$547$	−15.9573			−0.682284			−0.341142	−	0.940012i	$-0.610814\pi$
$547$	−15.9573			−0.682284			−0.341142	+	0.940012i	$0.610814\pi$
$548$	−2.57525	+	1.48682i	−0.110009	+	0.0635138i
$549$			6.41144i			0.273634i
$550$	5.40039	+	6.41130i	0.230273	+	0.273379i
$551$	−2.19074	−	3.79448i	−0.0933289	−	0.161650i
$552$	1.05130	−	0.606969i	0.0447464	−	0.0258343i
$553$	3.04842	−	5.28002i	0.129632	−	0.224529i
$554$	−19.6343			−0.834183
$555$	13.1443	+	3.49658i	0.557947	+	0.148422i
$556$	10.8796			0.461397
$557$	−14.2933	+	24.7567i	−0.605626	+	1.04898i	0.386326	+	0.922362i	$0.373744\pi$
$557$	−14.2933	+	24.7567i	−0.605626	+	1.04898i	−0.991952	+	0.126613i	$0.959589\pi$
$558$	−4.89955	+	2.82876i	−0.207415	+	0.119751i
$559$	18.3948	+	31.8608i	0.778019	+	1.34757i
$560$	−4.91259	−	7.00182i	−0.207595	−	0.295881i
$561$			9.25377i			0.390695i
$562$	−10.2198	+	5.90041i	−0.431096	+	0.248894i
$563$	10.1756			0.428850			0.214425	−	0.976740i	$-0.431212\pi$
$563$	10.1756			0.428850			0.214425	+	0.976740i	$0.431212\pi$
$564$	−5.64081	+	9.77017i	−0.237521	+	0.411398i
$565$	3.38489	+	38.2732i	0.142403	+	1.61016i
$566$	2.15974			0.0907806
$567$	3.31268	+	1.91258i	0.139119	+	0.0803207i
$568$	0.807805	+	1.39916i	0.0338948	+	0.0587075i
$569$		−	41.4725i		−	1.73862i	−0.494270	−	0.869308i	$-0.664565\pi$
$569$		−	41.4725i		−	1.73862i	0.494270	−	0.869308i	$-0.335435\pi$
$570$	2.99081	+	1.39120i	0.125271	+	0.0582710i
$571$	−3.26000	+	5.64649i	−0.136427	+	0.236298i	−0.926142	−	0.377176i	$-0.876895\pi$
$571$	−3.26000	+	5.64649i	−0.136427	+	0.236298i	0.789715	+	0.613474i	$0.210229\pi$
$572$	2.61556	−	4.53028i	0.109362	−	0.189421i
$573$	−6.27162	−	10.8628i	−0.262001	−	0.453798i
$574$	32.4108	−	18.7124i	1.35280	−	0.781040i
$575$	−2.06518	+	5.70756i	−0.0861240	+	0.238022i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	−17.6741	+	30.6124i	−0.735781	+	1.27441i	0.218599	+	0.975815i	$0.429851\pi$
$577$	−17.6741	+	30.6124i	−0.735781	+	1.27441i	−0.954380	+	0.298596i	$0.903482\pi$
$578$	13.4659			0.560106
$579$	−22.6437	+	13.0734i	−0.941041	+	0.543310i
$580$	2.80116	−	6.02194i	0.116312	−	0.250047i
$581$	−16.7605			−0.695341
$582$		−	16.8340i		−	0.697792i
$583$	4.19088	+	2.41961i	0.173569	+	0.100210i
$584$			12.7659i			0.528257i
$585$	5.71143	−	4.00723i	0.236139	−	0.165679i
$586$			3.57631i			0.147736i
$587$	4.39397	+	7.61058i	0.181359	+	0.314122i	0.942343	−	0.334647i	$-0.108617\pi$
$587$	4.39397	+	7.61058i	0.181359	+	0.314122i	−0.760985	+	0.648770i	$0.775284\pi$
$588$	6.60933	−	3.81590i	0.272564	−	0.157365i
$589$	−4.17285	−	7.22759i	−0.171939	−	0.297808i
$590$	−5.67131	+	12.1922i	−0.233484	+	0.501945i
$591$	24.1061			0.991592
$592$	5.71772	+	2.07550i	0.234997	+	0.0853025i
$593$			25.1637i			1.03335i	0.856182	+	0.516675i	$0.172830\pi$
$593$			25.1637i			1.03335i	−0.856182	+	0.516675i	$0.827170\pi$
$594$	−1.45192	−	0.838266i	−0.0595730	−	0.0343945i
$595$	27.1155	+	38.6472i	1.11163	+	1.58438i
$596$	−4.48787	−	7.77322i	−0.183830	−	0.318404i
$597$	10.7475	+	18.6153i	0.439867	+	0.761872i
$598$	3.78773			0.154892
$599$	14.2456	+	24.6741i	0.582060	+	1.00816i	0.995235	+	0.0975062i	$0.0310866\pi$
$599$	14.2456	+	24.6741i	0.582060	+	1.00816i	−0.413175	+	0.910652i	$0.635580\pi$
$600$	0.877540	+	4.92239i	0.0358254	+	0.200956i
$601$	11.6102	−	20.1095i	0.473591	−	0.820284i	−0.525952	−	0.850514i	$-0.676291\pi$
$601$	11.6102	−	20.1095i	0.473591	−	0.820284i	0.999543	+	0.0302304i	$0.00962411\pi$
$602$		−	45.1016i		−	1.83820i
$603$		−	1.07815i		−	0.0439056i
$604$	−5.87683	+	10.1790i	−0.239125	+	0.414177i
$605$	−14.9901	+	10.5173i	−0.609436	+	0.427590i
$606$		−	2.23855i		−	0.0909348i
$607$	−23.1472	+	40.0921i	−0.939515	+	1.62729i	−0.173138	+	0.984898i	$0.555391\pi$
$607$	−23.1472	+	40.0921i	−0.939515	+	1.62729i	−0.766377	+	0.642391i	$0.777943\pi$
$608$	1.27752	+	0.737577i	0.0518103	+	0.0299127i
$609$	9.83930	+	5.68072i	0.398708	+	0.230194i
$610$	−8.23412	−	11.7359i	−0.333390	−	0.475174i
$611$	−30.4849	+	17.6005i	−1.23329	+	0.712039i
$612$	−2.75979	+	4.78010i	−0.111558	+	0.193224i
$613$	23.1733	+	13.3791i	0.935963	+	0.540378i	0.888692	−	0.458504i	$-0.151614\pi$
$613$	23.1733	+	13.3791i	0.935963	+	0.540378i	0.0472702	+	0.998882i	$0.484948\pi$
$614$	9.85354	+	5.68895i	0.397657	+	0.229587i
$615$	−21.7923	+	1.92732i	−0.878752	+	0.0777171i
$616$	−5.55382	+	3.20650i	−0.223770	+	0.129193i
$617$	4.78348	+	2.76174i	0.192576	+	0.111184i	0.593188	−	0.805064i	$-0.297869\pi$
$617$	4.78348	+	2.76174i	0.192576	+	0.111184i	−0.400612	+	0.916248i	$0.631203\pi$
$618$			4.22889i			0.170111i
$619$	−22.2474			−0.894200			−0.447100	−	0.894484i	$-0.647543\pi$
$619$	−22.2474			−0.894200			−0.447100	+	0.894484i	$0.647543\pi$
$620$	5.33554	−	11.4704i	0.214280	−	0.460661i
$621$		−	1.21394i		−	0.0487137i
$622$	−25.0523	+	14.4639i	−1.00450	+	0.579951i
$623$	32.5106			1.30251
$624$	2.70218	−	1.56010i	0.108174	−	0.0624540i
$625$	−19.2117	−	15.9972i	−0.768467	−	0.639889i
$626$	−6.77595	−	11.7363i	−0.270821	−	0.469076i
$627$	1.23657	−	2.14180i	0.0493839	−	0.0855354i
$628$			0.124988i			0.00498755i
$629$	−31.5595	−	11.4559i	−1.25836	−	0.456777i
$630$	−8.52005	+	0.753516i	−0.339447	+	0.0300208i
$631$	−27.6705	−	15.9756i	−1.10154	−	0.635977i	−0.164918	−	0.986307i	$-0.552736\pi$
$631$	−27.6705	−	15.9756i	−1.10154	−	0.635977i	−0.936626	+	0.350330i	$0.886069\pi$
$632$	−1.38034	+	0.796940i	−0.0549070	+	0.0317006i
$633$	−6.60256	+	3.81199i	−0.262428	+	0.151513i
$634$	0.669018	−	0.386258i	0.0265701	−	0.0153403i
$635$	−36.0887	+	3.19169i	−1.43213	+	0.126658i
$636$	1.44322	+	2.49973i	0.0572274	+	0.0991208i
$637$	23.8128			0.943496
$638$	−4.31248	−	2.48981i	−0.170733	−	0.0985726i
$639$	1.61561			0.0639126
$640$	0.196990	+	2.22737i	0.00778670	+	0.0880447i
$641$	−7.48229	+	12.9597i	−0.295533	+	0.511878i	−0.975109	−	0.221727i	$-0.928830\pi$
$641$	−7.48229	+	12.9597i	−0.295533	+	0.511878i	0.679576	+	0.733605i	$0.262164\pi$
$642$	1.29611	+	2.24493i	0.0511534	+	0.0886004i
$643$	−11.0905			−0.437365			−0.218683	−	0.975796i	$-0.570176\pi$
$643$	−11.0905			−0.437365			−0.218683	+	0.975796i	$0.570176\pi$
$644$	−4.02139	−	2.32175i	−0.158465	−	0.0914898i
$645$	−11.1198	+	23.9053i	−0.437841	+	0.941272i
$646$	−7.05139	−	4.07112i	−0.277433	−	0.160176i
$647$	10.1375	+	17.5587i	0.398547	+	0.690304i	0.993547	−	0.113422i	$-0.0361812\pi$
$647$	10.1375	+	17.5587i	0.398547	+	0.690304i	−0.595000	+	0.803726i	$0.702848\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	8.73118	+	5.04095i	0.342729	+	0.197875i
$650$	−5.30816	+	14.6702i	−0.208203	+	0.575413i
$651$	18.7415	+	10.8204i	0.734539	+	0.424086i
$652$	−16.8291			−0.659077
$653$	−16.6048	−	28.7604i	−0.649797	−	1.12548i	−0.983171	−	0.182686i	$-0.941521\pi$
$653$	−16.6048	−	28.7604i	−0.649797	−	1.12548i	0.333375	−	0.942794i	$-0.391813\pi$
$654$	7.08769	−	12.2762i	0.277151	−	0.480039i
$655$	40.6539	−	3.59544i	1.58848	−	0.140486i
$656$	−9.78387			−0.381996
$657$	11.0556	+	6.38296i	0.431320	+	0.249023i
$658$	43.1539			1.68231
$659$	14.0393	+	24.3168i	0.546894	+	0.947249i	0.998485	+	0.0550236i	$0.0175234\pi$
$659$	14.0393	+	24.3168i	0.546894	+	0.947249i	−0.451591	+	0.892225i	$0.649143\pi$
$660$	3.73427	−	0.330260i	0.145356	−	0.0128553i
$661$	−15.3660	+	8.87157i	−0.597669	+	0.345064i	−0.768124	−	0.640301i	$-0.778810\pi$
$661$	−15.3660	+	8.87157i	−0.597669	+	0.345064i	0.170455	+	0.985365i	$0.445476\pi$
$662$	6.34735	−	3.66465i	0.246697	−	0.142430i
$663$	−14.9149	+	8.61112i	−0.579247	+	0.334428i
$664$	3.79462	+	2.19082i	0.147260	+	0.0850204i
$665$	−1.11155	−	12.5684i	−0.0431041	−	0.487381i
$666$	4.65629	−	3.91394i	0.180428	−	0.151662i
$667$		−	3.60563i		−	0.139611i
$668$	−10.0346	+	17.3805i	−0.388252	+	0.672471i
$669$	2.00054	+	3.46504i	0.0773455	+	0.133966i
$670$	1.38465	+	1.97351i	0.0534936	+	0.0762435i
$671$	−9.30890	+	5.37450i	−0.359366	+	0.207480i
$672$	−3.82515			−0.147558
$673$	21.5251	−	12.4275i	0.829730	−	0.479045i	−0.0240303	−	0.999711i	$-0.507650\pi$
$673$	21.5251	−	12.4275i	0.829730	−	0.479045i	0.853760	+	0.520666i	$0.174316\pi$
$674$		−	11.8053i		−	0.454725i
$675$	4.70168	+	1.70122i	0.180968	+	0.0654801i
$676$	−3.26433			−0.125551
$677$			31.6990i			1.21829i	0.793059	+	0.609145i	$0.208487\pi$
$677$			31.6990i			1.21829i	−0.793059	+	0.609145i	$0.791513\pi$
$678$	14.8810	+	8.59155i	0.571501	+	0.329956i
$679$	−55.7657	+	32.1963i	−2.14009	+	1.23558i
$680$	−1.08730	−	12.2942i	−0.0416961	−	0.471461i
$681$	11.1562	+	6.44101i	0.427505	+	0.246820i
$682$	−8.21426	−	4.74250i	−0.314540	−	0.181600i
$683$	−23.4462	+	40.6100i	−0.897144	+	1.55390i	−0.0660151	+	0.997819i	$0.521029\pi$
$683$	−23.4462	+	40.6100i	−0.897144	+	1.55390i	−0.831129	+	0.556080i	$0.812305\pi$
$684$	1.27752	−	0.737577i	0.0488472	−	0.0282019i
$685$	−3.81900	−	5.44315i	−0.145917	−	0.207972i
$686$	−2.09294	−	1.20836i	−0.0799089	−	0.0461354i
$687$	13.5375	+	7.81590i	0.516489	+	0.298195i
$688$	−5.89540	+	10.2111i	−0.224760	+	0.389296i
$689$			9.00628i			0.343112i
$690$	1.55904	+	2.22208i	0.0593518	+	0.0845930i
$691$	4.24583	−	7.35399i	0.161519	−	0.279759i	−0.773895	−	0.633314i	$-0.781694\pi$
$691$	4.24583	−	7.35399i	0.161519	−	0.279759i	0.935414	+	0.353555i	$0.115027\pi$
$692$		−	13.8147i		−	0.525157i
$693$			6.41299i			0.243609i
$694$	−5.25860	+	9.10817i	−0.199614	+	0.345741i
$695$	2.14317	+	24.2329i	0.0812950	+	0.919207i
$696$	−1.48510	−	2.57226i	−0.0562924	−	0.0975014i
$697$	54.0029			2.04551
$698$	−10.6455	−	18.4385i	−0.402938	−	0.697908i
$699$	1.25481	+	2.17339i	0.0474612	+	0.0822052i
$700$	14.6279	−	12.3215i	0.552884	−	0.465707i
$701$	10.6232	+	6.13333i	0.401234	+	0.231653i	0.687016	−	0.726642i	$-0.258920\pi$
$701$	10.6232	+	6.13333i	0.401234	+	0.231653i	−0.285782	+	0.958295i	$0.592253\pi$
$702$		−	3.12020i		−	0.117764i
$703$	5.77366	+	6.86875i	0.217758	+	0.259060i
$704$	1.67653			0.0631867
$705$	−22.8730	−	10.6396i	−0.861447	−	0.400709i
$706$	−1.38917	−	2.40612i	−0.0522823	−	0.0905555i
$707$	−7.41559	+	4.28140i	−0.278892	+	0.161018i
$708$	3.00677	+	5.20788i	0.113001	+	0.195724i
$709$			11.8142i			0.443692i	0.975082	+	0.221846i	$0.0712083\pi$
$709$			11.8142i			0.443692i	−0.975082	+	0.221846i	$0.928792\pi$
$710$	−2.95732	+	2.07491i	−0.110986	+	0.0778698i
$711$			1.59388i			0.0597752i
$712$	−7.36049	−	4.24958i	−0.275846	−	0.159260i
$713$		−	6.86788i		−	0.257204i
$714$	21.1133			0.790144
$715$	10.6059	+	4.93341i	0.396637	+	0.184499i
$716$	11.0947	−	6.40554i	0.414629	−	0.239386i
$717$	−4.26585			−0.159311
$718$	13.5421	−	23.4555i	0.505385	−	0.875353i
$719$	7.22948	−	12.5218i	0.269614	−	0.466985i	−0.699148	−	0.714977i	$-0.746437\pi$
$719$	7.22948	−	12.5218i	0.269614	−	0.466985i	0.968762	+	0.247992i	$0.0797705\pi$
$720$	2.02746	+	0.943089i	0.0755589	+	0.0351468i
$721$	14.0089	−	8.08807i	0.521720	−	0.301215i
$722$	−8.41196	−	14.5699i	−0.313061	−	0.542237i
$723$	−14.5640	+	25.2255i	−0.541639	+	0.938147i
$724$	−7.43016	+	12.8694i	−0.276140	+	0.478288i
$725$	13.9649	+	5.05296i	0.518644	+	0.187662i
$726$			8.18924i			0.303931i
$727$	15.6966	+	27.1874i	0.582156	+	1.00832i	0.995223	+	0.0976231i	$0.0311240\pi$
$727$	15.6966	+	27.1874i	0.582156	+	1.00832i	−0.413068	+	0.910700i	$0.635543\pi$
$728$	−10.3362	−	5.96763i	−0.383086	−	0.221175i
$729$	−1.00000			−0.0370370
$730$	−28.4345	+	2.51475i	−1.05241	+	0.0930752i
$731$	32.5402	−	56.3613i	1.20354	−	2.08460i
$732$	−6.41144			−0.236974
$733$	17.0623	−	9.85091i	0.630210	−	0.363852i	−0.150624	−	0.988591i	$-0.548128\pi$
$733$	17.0623	−	9.85091i	0.630210	−	0.363852i	0.780833	+	0.624739i	$0.214795\pi$
$734$			0.639187i			0.0235928i
$735$	9.80140	+	13.9698i	0.361530	+	0.515282i
$736$	0.606969	+	1.05130i	0.0223732	+	0.0387515i
$737$	1.56538	−	0.903775i	0.0576616	−	0.0332910i
$738$	−4.89193	+	8.47308i	−0.180075	+	0.311898i
$739$	20.8046			0.765309			0.382654	−	0.923892i	$-0.375010\pi$
$739$	20.8046			0.765309			0.382654	+	0.923892i	$0.375010\pi$
$740$	−3.49658	+	13.1443i	−0.128537	+	0.483196i
$741$	4.60278			0.169087
$742$	5.52054	−	9.56186i	0.202665	−	0.351027i
$743$	32.1117	−	18.5397i	1.17807	−	0.680156i	0.222499	−	0.974933i	$-0.428579\pi$
$743$	32.1117	−	18.5397i	1.17807	−	0.680156i	0.955566	+	0.294776i	$0.0952452\pi$
$744$	−2.82876	−	4.89955i	−0.103707	−	0.179626i
$745$	16.4298	−	11.5274i	0.601942	−	0.422332i
$746$		−	9.34596i		−	0.342180i
$747$	3.79462	−	2.19082i	0.138838	−	0.0801580i
$748$	−9.25377			−0.338351
$749$	4.95783	−	8.58721i	0.181155	−	0.313770i
$750$	−10.7911	+	2.92427i	−0.394037	+	0.106779i
$751$	−8.36573			−0.305270			−0.152635	−	0.988283i	$-0.548776\pi$
$751$	−8.36573			−0.305270			−0.152635	+	0.988283i	$0.548776\pi$
$752$	−9.77017	−	5.64081i	−0.356281	−	0.205699i
$753$	6.87914	+	11.9150i	0.250690	+	0.434207i
$754$		−	9.26760i		−	0.337506i
$755$	−23.8301	−	11.0848i	−0.867264	−	0.403415i
$756$	−1.91258	+	3.31268i	−0.0695597	+	0.120481i
$757$	−7.05341	+	12.2169i	−0.256361	+	0.444030i	−0.965264	−	0.261276i	$-0.915857\pi$
$757$	−7.05341	+	12.2169i	−0.256361	+	0.444030i	0.708904	+	0.705305i	$0.249190\pi$
$758$	14.4675	+	25.0584i	0.525482	+	0.910161i
$759$	1.76254	−	1.01760i	0.0639762	−	0.0369367i
$760$	−1.39120	+	2.99081i	−0.0504641	+	0.108488i
$761$	8.89832	−	15.4123i	0.322564	−	0.558697i	−0.658453	−	0.752622i	$-0.728789\pi$
$761$	8.89832	−	15.4123i	0.322564	−	0.558697i	0.981016	+	0.193926i	$0.0621220\pi$
$762$	−8.10117	+	14.0316i	−0.293474	+	0.508312i
$763$	−54.2230			−1.96300
$764$	10.8628	−	6.27162i	0.393001	−	0.226899i
$765$	−11.1907	−	5.20546i	−0.404602	−	0.188204i
$766$	−10.2615			−0.370764
$767$			18.7635i			0.677510i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$		−	21.3406i		−	0.769563i	−0.923008	−	0.384782i	$-0.874277\pi$
$769$		−	21.3406i		−	0.769563i	0.923008	−	0.384782i	$-0.125723\pi$
$770$	−8.23611	−	11.7388i	−0.296809	−	0.423036i
$771$			6.34628i			0.228556i
$772$	−13.0734	−	22.6437i	−0.470521	−	0.814966i
$773$	39.3866	−	22.7399i	1.41664	−	0.817896i	0.420636	−	0.907229i	$-0.361807\pi$
$773$	39.3866	−	22.7399i	1.41664	−	0.817896i	0.996002	+	0.0893331i	$0.0284736\pi$
$774$	5.89540	+	10.2111i	0.211906	+	0.367032i
$775$	26.5999	+	9.62470i	0.955495	+	0.345729i
$776$	16.8340			0.604306
$777$	−21.8711	−	7.93910i	−0.784623	−	0.284814i
$778$		−	27.8334i		−	0.997876i
$779$	−12.4991	−	7.21635i	−0.447826	−	0.258553i
$780$	4.00723	+	5.71143i	0.143482	+	0.204502i
$781$	1.35431	+	2.34574i	0.0484611	+	0.0839371i
$782$	−3.35022	−	5.80275i	−0.119804	−	0.207506i
$783$	−2.97019			−0.106146
$784$	3.81590	+	6.60933i	0.136282	+	0.236048i
$785$	−0.278394	+	0.0246213i	−0.00993632	+	0.000878772i
$786$	9.12596	−	15.8066i	0.325512	−	0.563804i
$787$		−	50.6502i		−	1.80549i	−0.430181	−	0.902743i	$-0.641550\pi$
$787$		−	50.6502i		−	1.80549i	0.430181	−	0.902743i	$-0.358450\pi$
$788$			24.1061i			0.858744i
$789$	0.544148	−	0.942492i	0.0193722	−	0.0335536i
$790$	−2.04700	−	2.91755i	−0.0728289	−	0.103802i
$791$		−	65.7280i		−	2.33702i
$792$	0.838266	−	1.45192i	0.0297865	−	0.0515917i
$793$	−17.3248	−	10.0025i	−0.615223	−	0.355199i
$794$	10.7607	+	6.21267i	0.381881	+	0.220479i
$795$	−5.28354	+	3.70701i	−0.187388	+	0.131474i
$796$	−18.6153	+	10.7475i	−0.659801	+	0.380936i
$797$	14.5683	−	25.2330i	0.516034	−	0.893797i	−0.483793	−	0.875183i	$-0.660741\pi$
$797$	14.5683	−	25.2330i	0.516034	−	0.893797i	0.999827	−	0.0186145i	$-0.00592551\pi$
$798$	−4.88671	−	2.82134i	−0.172988	−	0.0998745i
$799$	53.9273	+	31.1349i	1.90781	+	1.10147i
$800$	−4.92239	+	0.877540i	−0.174033	+	0.0310257i
$801$	−7.36049	+	4.24958i	−0.260070	+	0.150151i
$802$	29.8389	+	17.2275i	1.05365	+	0.608323i
$803$			21.4025i			0.755277i
$804$	1.07815			0.0380233
$805$	4.37923	−	9.41450i	0.154348	−	0.331818i
$806$		−	17.6526i		−	0.621786i
$807$	2.75742	−	1.59200i	0.0970658	−	0.0560410i
$808$	2.23855			0.0787519
$809$	11.6111	−	6.70365i	0.408223	−	0.235688i	−0.281803	−	0.959472i	$-0.590932\pi$
$809$	11.6111	−	6.70365i	0.408223	−	0.235688i	0.690026	+	0.723785i	$0.257599\pi$
$810$	1.83047	−	1.28429i	0.0643161	−	0.0451252i
$811$	−10.3926	−	18.0005i	−0.364933	−	0.632082i	0.623833	−	0.781558i	$-0.285575\pi$
$811$	−10.3926	−	18.0005i	−0.364933	−	0.632082i	−0.988765	+	0.149476i	$0.952241\pi$
$812$	−5.68072	+	9.83930i	−0.199354	+	0.345292i
$813$		−	17.8861i		−	0.627294i
$814$	9.58594	+	3.47964i	0.335987	+	0.121961i
$815$	−3.31515	−	37.4846i	−0.116125	−	1.31303i
$816$	−4.78010	−	2.75979i	−0.167337	−	0.0966121i
$817$	−15.0630	+	8.69662i	−0.526987	+	0.304256i
$818$	9.78149	−	5.64735i	0.342002	−	0.197455i
$819$	−10.3362	+	5.96763i	−0.361177	+	0.208526i
$820$	−1.92732	−	21.7923i	−0.0673050	−	0.761021i
$821$	−16.4776	−	28.5400i	−0.575072	−	0.996053i	−0.996034	−	0.0889752i	$-0.971641\pi$
$821$	−16.4776	−	28.5400i	−0.575072	−	0.996053i	0.420962	−	0.907078i	$-0.361693\pi$
$822$	−2.97364			−0.103718
$823$	−42.3090	−	24.4271i	−1.47480	−	0.851476i	−0.475203	−	0.879876i	$-0.657626\pi$
$823$	−42.3090	−	24.4271i	−1.47480	−	0.851476i	−0.999597	+	0.0283998i	$0.990959\pi$
$824$	−4.22889			−0.147320
$825$	1.47122	+	8.25255i	0.0512214	+	0.287317i
$826$	11.5014	−	19.9209i	0.400184	−	0.693138i
$827$	−4.83019	−	8.36614i	−0.167962	−	0.290919i	0.769741	−	0.638356i	$-0.220385\pi$
$827$	−4.83019	−	8.36614i	−0.167962	−	0.290919i	−0.937703	+	0.347437i	$0.887052\pi$
$828$	1.21394			0.0421873
$829$	−6.94733	−	4.01104i	−0.241291	−	0.139309i	0.374479	−	0.927235i	$-0.377822\pi$
$829$	−6.94733	−	4.01104i	−0.241291	−	0.139309i	−0.615770	+	0.787926i	$0.711155\pi$
$830$	−4.13228	+	8.88360i	−0.143434	+	0.308354i
$831$	−17.0038	−	9.81717i	−0.589857	−	0.340554i
$832$	1.56010	+	2.70218i	0.0540868	+	0.0936811i
$833$	−21.0622	−	36.4808i	−0.729762	−	1.26398i
$834$	9.42200	+	5.43980i	0.326257	+	0.188365i
$835$	−40.6896	−	18.9271i	−1.40812	−	0.654999i
$836$	2.14180	+	1.23657i	0.0740758	+	0.0427677i
$837$	−5.65752			−0.195552
$838$	1.76879	+	3.06364i	0.0611019	+	0.105832i
$839$	−6.52889	+	11.3084i	−0.225402	+	0.390408i	−0.956440	−	0.291929i	$-0.905703\pi$
$839$	−6.52889	+	11.3084i	−0.225402	+	0.390408i	0.731038	+	0.682337i	$0.239036\pi$
$840$	−0.753516	−	8.52005i	−0.0259988	−	0.293970i
$841$	20.1780			0.695792
$842$	0.278852	+	0.160995i	0.00960986	+	0.00554825i
$843$	−11.8008			−0.406442
$844$	−3.81199	−	6.60256i	−0.131214	−	0.227269i
$845$	−0.643040	−	7.27089i	−0.0221213	−	0.250126i
$846$	−9.77017	+	5.64081i	−0.335905	+	0.193935i
$847$	27.1283	−	15.6625i	0.932140	−	0.538171i
$848$	−2.49973	+	1.44322i	−0.0858411	+	0.0495604i
$849$	1.87039	+	1.07987i	0.0641916	+	0.0370610i
$850$	27.1696	−	4.84366i	0.931909	−	0.166136i
$851$	1.28850	+	7.27081i	0.0441694	+	0.249240i
$852$			1.61561i			0.0553499i
$853$	2.75064	−	4.76425i	0.0941802	−	0.163125i	−0.815086	−	0.579340i	$-0.803310\pi$
$853$	2.75064	−	4.76425i	0.0941802	−	0.163125i	0.909266	+	0.416215i	$0.136644\pi$
$854$	12.2624	+	21.2391i	0.419610	+	0.726786i
$855$	1.89452	+	2.70022i	0.0647911	+	0.0923456i
$856$	−2.24493	+	1.29611i	−0.0767302	+	0.0443002i
$857$	41.3989			1.41416			0.707080	−	0.707133i	$-0.250012\pi$
$857$	41.3989			1.41416			0.707080	+	0.707133i	$0.250012\pi$
$858$	4.53028	−	2.61556i	0.154661	−	0.0892938i
$859$			53.2983i			1.81851i	0.416234	+	0.909257i	$0.363350\pi$
$859$			53.2983i			1.81851i	−0.416234	+	0.909257i	$0.636650\pi$
$860$	−23.9053	−	11.1198i	−0.815166	−	0.379181i
$861$	37.4248			1.27543
$862$			24.7136i			0.841748i
$863$	2.65162	+	1.53092i	0.0902623	+	0.0521130i	0.544452	−	0.838792i	$-0.316738\pi$
$863$	2.65162	+	1.53092i	0.0902623	+	0.0521130i	−0.454189	+	0.890905i	$0.650071\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$	30.7706	−	2.72136i	1.04623	−	0.0925290i
$866$	−2.47919	−	1.43136i	−0.0842463	−	0.0486396i
$867$	11.6618	+	6.73293i	0.396055	+	0.228662i
$868$	−10.8204	+	18.7415i	−0.367269	+	0.636129i
$869$	−2.31419	+	1.33610i	−0.0785034	+	0.0453240i
$870$	5.43684	−	3.81457i	0.184326	−	0.129326i
$871$	2.91334	+	1.68202i	0.0987149	+	0.0569931i
$872$	12.2762	+	7.08769i	0.415726	+	0.240019i
$873$	8.41700	−	14.5787i	0.284872	−	0.493413i
$874$			1.79075i			0.0605729i
$875$	30.3260	+	30.1547i	1.02521	+	1.01941i
$876$	−6.38296	+	11.0556i	−0.215660	+	0.373534i
$877$		−	6.30833i		−	0.213017i	−0.994312	−	0.106509i	$-0.966033\pi$
$877$		−	6.30833i		−	0.213017i	0.994312	−	0.106509i	$-0.0339672\pi$
$878$		−	1.94170i		−	0.0655292i
$879$	−1.78816	+	3.09718i	−0.0603130	+	0.104465i
$880$	0.330260	+	3.73427i	0.0111331	+	0.125882i
$881$	28.6385	+	49.6034i	0.964857	+	1.67118i	0.709999	+	0.704203i	$0.248696\pi$
$881$	28.6385	+	49.6034i	0.964857	+	1.67118i	0.254858	+	0.966978i	$0.417971\pi$
$882$	7.63180			0.256976
$883$	9.87025	+	17.0958i	0.332160	+	0.575319i	0.982935	−	0.183952i	$-0.0588891\pi$
$883$	9.87025	+	17.0958i	0.332160	+	0.575319i	−0.650775	+	0.759271i	$0.725556\pi$
$884$	−8.61112	−	14.9149i	−0.289623	−	0.501642i
$885$	−11.0076	+	7.72311i	−0.370016	+	0.259609i
$886$	−16.7356	−	9.66231i	−0.562244	−	0.324612i
$887$		−	1.06021i		−	0.0355983i	−0.999842	−	0.0177992i	$-0.994334\pi$
$887$		−	1.06021i		−	0.0355983i	0.999842	−	0.0177992i	$-0.00566595\pi$
$888$	3.91394	+	4.65629i	0.131343	+	0.156255i
$889$	61.9764			2.07862
$890$	8.01546	−	17.2317i	0.268679	−	0.577607i
$891$	−0.838266	−	1.45192i	−0.0280830	−	0.0486411i
$892$	−3.46504	+	2.00054i	−0.116018	+	0.0669831i
$893$	−8.32106	−	14.4125i	−0.278453	−	0.482296i
$894$		−	8.97575i		−	0.300194i
$895$	16.4531	+	23.4503i	0.549966	+	0.783856i
$896$		−	3.82515i		−	0.127789i
$897$	3.28027	+	1.89387i	0.109525	+	0.0632344i
$898$		−	22.4760i		−	0.750033i
$899$	−16.8039			−0.560442
$900$	−1.70122	+	4.70168i	−0.0567074	+	0.156723i
$901$	13.7975	−	7.96599i	0.459661	−	0.265385i
$902$	−16.4030			−0.546159
$903$	22.5508	−	39.0591i	0.750444	−	1.29981i
$904$	−8.59155	+	14.8810i	−0.285751	+	0.494934i
$905$	−30.1287	−	14.0146i	−1.00151	−	0.465861i
$906$	−10.1790	+	5.87683i	−0.338174	+	0.195245i
$907$	−19.2578	−	33.3555i	−0.639445	−	1.10755i	−0.985555	−	0.169357i	$-0.945831\pi$
$907$	−19.2578	−	33.3555i	−0.639445	−	1.10755i	0.346110	−	0.938194i	$-0.387503\pi$
$908$	−6.44101	+	11.1562i	−0.213752	+	0.370230i
$909$	1.11927	−	1.93864i	0.0371240	−	0.0643006i
$910$	11.2560	−	24.1982i	0.373133	−	0.802163i
$911$		−	10.9579i		−	0.363052i	−0.983386	−	0.181526i	$-0.941896\pi$
$911$		−	10.9579i		−	0.363052i	0.983386	−	0.181526i	$-0.0581037\pi$
$912$	0.737577	+	1.27752i	0.0244236	+	0.0423029i
$913$	6.36180	+	3.67299i	0.210545	+	0.121558i
$914$	11.8778			0.392881
$915$	−1.26299	−	14.2807i	−0.0417531	−	0.472105i
$916$	−7.81590	+	13.5375i	−0.258245	+	0.447293i
$917$	−69.8164			−2.30554
$918$	−4.78010	+	2.75979i	−0.157767	+	0.0910868i
$919$		−	31.2290i		−	1.03015i	−0.857145	−	0.515076i	$-0.827764\pi$
$919$		−	31.2290i		−	1.03015i	0.857145	−	0.515076i	$-0.172236\pi$
$920$	−2.22208	+	1.55904i	−0.0732596	+	0.0514001i
$921$	5.68895	+	9.85354i	0.187457	+	0.324685i
$922$	−7.12646	+	4.11446i	−0.234698	+	0.135503i
$923$	−2.52052	+	4.36566i	−0.0829638	+	0.143698i
$924$	−6.41299			−0.210972
$925$	−29.9662	−	5.19889i	−0.985282	−	0.170938i
$926$	24.6957			0.811550
$927$	−2.11444	+	3.66232i	−0.0694474	+	0.120286i
$928$	2.57226	−	1.48510i	0.0844386	−	0.0487507i
$929$	−24.0026	−	41.5738i	−0.787501	−	1.36399i	−0.927493	−	0.373840i	$-0.878041\pi$
$929$	−24.0026	−	41.5738i	−0.787501	−	1.36399i	0.139992	−	0.990153i	$-0.455292\pi$
$930$	10.3559	−	7.26586i	0.339583	−	0.238257i
$931$			11.2581i			0.368968i
$932$	−2.17339	+	1.25481i	−0.0711918	+	0.0411026i
$933$	−28.9279			−0.947055
$934$	7.37971	−	12.7820i	0.241471	−	0.418241i
$935$	−1.82290	−	20.6116i	−0.0596151	−	0.674072i
$936$	3.12020			0.101987
$937$	30.9441	+	17.8656i	1.01090	+	0.583643i	0.911455	−	0.411400i	$-0.134960\pi$
$937$	30.9441	+	17.8656i	1.01090	+	0.583643i	0.0994447	+	0.995043i	$0.468293\pi$
$938$	−2.06204	−	3.57156i	−0.0673280	−	0.116615i
$939$		−	13.5519i		−	0.442249i
$940$	10.6396	−	22.8730i	0.347024	−	0.746035i
$941$	−23.9541	+	41.4898i	−0.780883	+	1.35253i	0.150545	+	0.988603i	$0.451897\pi$
$941$	−23.9541	+	41.4898i	−0.780883	+	1.35253i	−0.931428	+	0.363926i	$0.881436\pi$
$942$	−0.0624939	+	0.108243i	−0.00203616	+	0.00352673i
$943$	−5.93851	−	10.2858i	−0.193384	−	0.334952i
$944$	−5.20788	+	3.00677i	−0.169502	+	0.0978621i
$945$	−7.75534	−	3.60746i	−0.252281	−	0.117351i
$946$	−9.88383	+	17.1193i	−0.321351	+	0.556596i
$947$	−0.223569	+	0.387232i	−0.00726501	+	0.0125834i	−0.869635	−	0.493695i	$-0.835646\pi$
$947$	−0.223569	+	0.387232i	−0.00726501	+	0.0125834i	0.862370	+	0.506278i	$0.168979\pi$
$948$	−1.59388			−0.0517668
$949$	−34.4957	+	19.9161i	−1.11978	+	0.646505i
$950$	−6.93571	−	2.50957i	−0.225024	−	0.0814210i
$951$	0.772516			0.0250505
$952$			21.1133i			0.684285i
$953$	−22.5991	−	13.0476i	−0.732056	−	0.422653i	0.0871180	−	0.996198i	$-0.472234\pi$
$953$	−22.5991	−	13.0476i	−0.732056	−	0.422653i	−0.819174	+	0.573545i	$0.805568\pi$
$954$			2.88644i			0.0934520i
$955$	16.1091	+	22.9600i	0.521278	+	0.742968i
$956$		−	4.26585i		−	0.137967i
$957$	−2.48981	−	4.31248i	−0.0804842	−	0.139403i
$958$	25.0708	−	14.4746i	0.810001	−	0.467654i
$959$	5.68732	+	9.85072i	0.183653	+	0.318096i
$960$	−0.943089	+	2.02746i	−0.0304381	+	0.0654359i
$961$	−1.00749			−0.0324995
$962$	3.31186	+	18.6883i	0.106779	+	0.602534i
$963$			2.59222i			0.0835332i
$964$	−25.2255	−	14.5640i	−0.812459	−	0.469074i
$965$	47.8607	−	33.5798i	1.54069	−	1.08097i
$966$	−2.32175	−	4.02139i	−0.0747011	−	0.129386i
$967$	−18.8285	−	32.6119i	−0.605483	−	1.04873i	−0.991975	−	0.126435i	$-0.959647\pi$
$967$	−18.8285	−	32.6119i	−0.605483	−	1.04873i	0.386492	−	0.922293i	$-0.373687\pi$
$968$	−8.18924			−0.263212
$969$	−4.07112	−	7.05139i	−0.130783	−	0.226523i
$970$	3.31613	+	37.4956i	0.106474	+	1.20391i
$971$	−3.15080	+	5.45735i	−0.101114	+	0.175135i	−0.912144	−	0.409870i	$-0.865574\pi$
$971$	−3.15080	+	5.45735i	−0.101114	+	0.175135i	0.811030	+	0.585005i	$0.198907\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		−	41.6161i		−	1.33415i
$974$	−21.0780	+	36.5082i	−0.675382	+	1.16980i
$975$	−11.9321	+	10.0507i	−0.382133	+	0.321880i
$976$		−	6.41144i		−	0.205225i
$977$	−12.1860	+	21.1068i	−0.389865	+	0.675267i	−0.992431	−	0.122803i	$-0.960812\pi$
$977$	−12.1860	+	21.1068i	−0.389865	+	0.675267i	0.602566	+	0.798069i	$0.294145\pi$
$978$	−14.5744	−	8.41453i	−0.466038	−	0.269067i
$979$	−12.3401	−	7.12456i	−0.394391	−	0.227702i
$980$	−13.9698	+	9.80140i	−0.446248	+	0.313094i
$981$	12.2762	−	7.08769i	0.391950	−	0.226292i
$982$	13.1580	−	22.7904i	0.419890	−	0.727271i
$983$	21.8424	+	12.6107i	0.696664	+	0.402219i	0.806104	−	0.591774i	$-0.201572\pi$
$983$	21.8424	+	12.6107i	0.696664	+	0.402219i	−0.109440	+	0.993993i	$0.534906\pi$
$984$	−8.47308	−	4.89193i	−0.270112	−	0.155949i
$985$	−53.6933	+	4.74865i	−1.71081	+	0.151305i
$986$	−14.1978	+	8.19712i	−0.452151	+	0.261050i
$987$	37.3724	+	21.5770i	1.18958	+	0.686802i
$988$			4.60278i			0.146434i
$989$	−14.3133			−0.455137
$990$	3.39910	+	1.58112i	0.108030	+	0.0502513i
$991$			29.9420i			0.951138i	0.879678	+	0.475569i	$0.157758\pi$
$991$			29.9420i			0.951138i	−0.879678	+	0.475569i	$0.842242\pi$
$992$	4.89955	−	2.82876i	0.155561	−	0.0898132i
$993$	7.32929			0.232588
$994$	5.35200	−	3.08998i	0.169755	−	0.0980082i
$995$	−27.6058	−	39.3460i	−0.875162	−	1.24735i
$996$	2.19082	+	3.79462i	0.0694189	+	0.120237i
$997$	−1.46033	+	2.52937i	−0.0462492	+	0.0801059i	−0.888223	−	0.459412i	$-0.848060\pi$
$997$	−1.46033	+	2.52937i	−0.0462492	+	0.0801059i	0.841974	+	0.539518i	$0.181393\pi$
$998$		−	19.7211i		−	0.624262i
$999$	5.98944	−	1.06142i	0.189497	−	0.0335820i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.ba.a.619.9	yes	36
5.4	even	2		1110.2.ba.b.619.10	yes	36
37.11	even	6		1110.2.ba.b.529.10	yes	36
185.159	even	6	inner	1110.2.ba.a.529.9	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.ba.a.529.9	✓	36	185.159	even	6	inner
1110.2.ba.a.619.9	yes	36	1.1	even	1	trivial
1110.2.ba.b.529.10	yes	36	37.11	even	6
1110.2.ba.b.619.10	yes	36	5.4	even	2

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.83047 - 1.28429i) q^{5} -1.00000i q^{6} +(-3.31268 + 1.91258i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.83047 - 1.28429i) q^{5} -1.00000i q^{6} +(-3.31268 + 1.91258i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(0.196990 + 2.22737i) q^{10} +1.67653 q^{11} +(0.866025 + 0.500000i) q^{12} +(1.56010 + 2.70218i) q^{13} -3.82515i q^{14} +(-0.943089 + 2.02746i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.75979 - 4.78010i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-1.27752 + 0.737577i) q^{19} +(-2.02746 - 0.943089i) q^{20} +(1.91258 - 3.31268i) q^{21} +(-0.838266 + 1.45192i) q^{22} -1.21394 q^{23} +(-0.866025 + 0.500000i) q^{24} +(1.70122 - 4.70168i) q^{25} -3.12020 q^{26} +1.00000i q^{27} +(3.31268 + 1.91258i) q^{28} +2.97019i q^{29} +(-1.28429 - 1.83047i) q^{30} +5.65752i q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.45192 + 0.838266i) q^{33} +(2.75979 + 4.78010i) q^{34} +(-3.60746 + 7.75534i) q^{35} -1.00000 q^{36} +(-1.06142 - 5.98944i) q^{37} -1.47515i q^{38} +(-2.70218 - 1.56010i) q^{39} +(1.83047 - 1.28429i) q^{40} +(4.89193 + 8.47308i) q^{41} +(1.91258 + 3.31268i) q^{42} +11.7908 q^{43} +(-0.838266 - 1.45192i) q^{44} +(-0.196990 - 2.22737i) q^{45} +(0.606969 - 1.05130i) q^{46} +11.2816i q^{47} -1.00000i q^{48} +(3.81590 - 6.60933i) q^{49} +(3.22117 + 3.82415i) q^{50} +5.51959i q^{51} +(1.56010 - 2.70218i) q^{52} +(2.49973 + 1.44322i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(3.06884 - 2.15315i) q^{55} +(-3.31268 + 1.91258i) q^{56} +(0.737577 - 1.27752i) q^{57} +(-2.57226 - 1.48510i) q^{58} +(5.20788 + 3.00677i) q^{59} +(2.22737 - 0.196990i) q^{60} +(-5.55247 + 3.20572i) q^{61} +(-4.89955 - 2.82876i) q^{62} +3.82515i q^{63} +1.00000 q^{64} +(6.32608 + 2.94263i) q^{65} -1.67653i q^{66} +(0.933703 - 0.539074i) q^{67} -5.51959 q^{68} +(1.05130 - 0.606969i) q^{69} +(-4.91259 - 7.00182i) q^{70} +(0.807805 + 1.39916i) q^{71} +(0.500000 - 0.866025i) q^{72} +12.7659i q^{73} +(5.71772 + 2.07550i) q^{74} +(0.877540 + 4.92239i) q^{75} +(1.27752 + 0.737577i) q^{76} +(-5.55382 + 3.20650i) q^{77} +(2.70218 - 1.56010i) q^{78} +(-1.38034 + 0.796940i) q^{79} +(0.196990 + 2.22737i) q^{80} +(-0.500000 - 0.866025i) q^{81} -9.78387 q^{82} +(3.79462 + 2.19082i) q^{83} -3.82515 q^{84} +(-1.08730 - 12.2942i) q^{85} +(-5.89540 + 10.2111i) q^{86} +(-1.48510 - 2.57226i) q^{87} +1.67653 q^{88} +(-7.36049 - 4.24958i) q^{89} +(2.02746 + 0.943089i) q^{90} +(-10.3362 - 5.96763i) q^{91} +(0.606969 + 1.05130i) q^{92} +(-2.82876 - 4.89955i) q^{93} +(-9.77017 - 5.64081i) q^{94} +(-1.39120 + 2.99081i) q^{95} +(0.866025 + 0.500000i) q^{96} +16.8340 q^{97} +(3.81590 + 6.60933i) q^{98} +(0.838266 - 1.45192i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9}+O(q^{10}) \) 36 * q - 18 * q^2 - 18 * q^4 + 2 * q^5 + 36 * q^8 + 18 * q^9	\( 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9} + 2 q^{10} + 4 q^{11} - 14 q^{13} - 2 q^{15} - 18 q^{16} + 18 q^{18} + 6 q^{19} - 4 q^{20} - 2 q^{22} - 20 q^{23} + 4 q^{25} + 28 q^{26} - 2 q^{30} - 18 q^{32} - 6 q^{33} - 40 q^{35} - 36 q^{36} + 20 q^{37} + 6 q^{39} + 2 q^{40} + 10 q^{41} - 2 q^{44} - 2 q^{45} + 10 q^{46} + 10 q^{49} - 2 q^{50} - 14 q^{52} - 12 q^{53} + 56 q^{55} + 8 q^{57} + 30 q^{58} + 18 q^{59} + 4 q^{60} - 6 q^{61} - 12 q^{62} + 36 q^{64} + 40 q^{65} + 36 q^{67} + 12 q^{69} + 20 q^{70} - 24 q^{71} + 18 q^{72} - 34 q^{74} + 8 q^{75} - 6 q^{76} - 24 q^{77} - 6 q^{78} + 2 q^{80} - 18 q^{81} - 20 q^{82} + 36 q^{83} + 26 q^{85} - 10 q^{87} + 4 q^{88} + 4 q^{90} - 36 q^{91} + 10 q^{92} + 12 q^{93} + 12 q^{94} - 30 q^{95} + 52 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) \) 36 * q - 18 * q^2 - 18 * q^4 + 2 * q^5 + 36 * q^8 + 18 * q^9 + 2 * q^10 + 4 * q^11 - 14 * q^13 - 2 * q^15 - 18 * q^16 + 18 * q^18 + 6 * q^19 - 4 * q^20 - 2 * q^22 - 20 * q^23 + 4 * q^25 + 28 * q^26 - 2 * q^30 - 18 * q^32 - 6 * q^33 - 40 * q^35 - 36 * q^36 + 20 * q^37 + 6 * q^39 + 2 * q^40 + 10 * q^41 - 2 * q^44 - 2 * q^45 + 10 * q^46 + 10 * q^49 - 2 * q^50 - 14 * q^52 - 12 * q^53 + 56 * q^55 + 8 * q^57 + 30 * q^58 + 18 * q^59 + 4 * q^60 - 6 * q^61 - 12 * q^62 + 36 * q^64 + 40 * q^65 + 36 * q^67 + 12 * q^69 + 20 * q^70 - 24 * q^71 + 18 * q^72 - 34 * q^74 + 8 * q^75 - 6 * q^76 - 24 * q^77 - 6 * q^78 + 2 * q^80 - 18 * q^81 - 20 * q^82 + 36 * q^83 + 26 * q^85 - 10 * q^87 + 4 * q^88 + 4 * q^90 - 36 * q^91 + 10 * q^92 + 12 * q^93 + 12 * q^94 - 30 * q^95 + 52 * q^97 + 10 * q^98 + 2 * q^99

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