LMFDB - Embedded newform 390.2.bn.c.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(67,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("390.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.bn (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			67.1
Character	$\chi$	$=$	390.67
Dual form			390.2.bn.c.163.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.18531 + 0.473708i) q^{5} +(0.258819 + 0.965926i) q^{6} +(2.35599 + 1.36023i) q^{7} +1.00000 q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.18531 + 0.473708i) q^{5} +(0.258819 + 0.965926i) q^{6} +(2.35599 + 1.36023i) q^{7} +1.00000 q^{8} +(0.866025 + 0.500000i) q^{9} +(1.50290 + 1.65568i) q^{10} +(0.843663 - 3.14859i) q^{11} +(0.707107 - 0.707107i) q^{12} +(1.21077 - 3.39618i) q^{13} -2.72047i q^{14} +(2.23346 + 0.108035i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.25990 - 4.70202i) q^{17} -1.00000i q^{18} +(-5.26205 + 1.40996i) q^{19} +(0.682415 - 2.12939i) q^{20} +(-1.92366 - 1.92366i) q^{21} +(-3.14859 + 0.843663i) q^{22} +(1.42238 - 5.30841i) q^{23} +(-0.965926 - 0.258819i) q^{24} +(4.55120 - 2.07040i) q^{25} +(-3.54656 + 0.649535i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-2.35599 + 1.36023i) q^{28} +(-6.99208 + 4.03688i) q^{29} +(-1.02317 - 1.98825i) q^{30} +(3.70024 - 3.70024i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.62983 + 2.82295i) q^{33} +(-3.44211 + 3.44211i) q^{34} +(-5.79294 - 1.85649i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(7.40104 - 4.27299i) q^{37} +(3.85209 + 3.85209i) q^{38} +(-2.04851 + 2.96709i) q^{39} +(-2.18531 + 0.473708i) q^{40} +(7.05711 + 1.89095i) q^{41} +(-0.704109 + 2.62777i) q^{42} +(0.885982 - 0.237398i) q^{43} +(2.30493 + 2.30493i) q^{44} +(-2.12939 - 0.682415i) q^{45} +(-5.30841 + 1.42238i) q^{46} -8.15619i q^{47} +(0.258819 + 0.965926i) q^{48} +(0.200471 + 0.347226i) q^{49} +(-4.06862 - 2.90626i) q^{50} +4.86788i q^{51} +(2.33579 + 2.74665i) q^{52} +(3.97631 - 3.97631i) q^{53} +(-0.258819 + 0.965926i) q^{54} +(-0.352157 + 7.28032i) q^{55} +(2.35599 + 1.36023i) q^{56} +5.44767 q^{57} +(6.99208 + 4.03688i) q^{58} +(-0.540573 - 2.01745i) q^{59} +(-1.21029 + 1.88021i) q^{60} +(-5.12740 + 8.88092i) q^{61} +(-5.05462 - 1.35438i) q^{62} +(1.36023 + 2.35599i) q^{63} +1.00000 q^{64} +(-1.03711 + 7.99527i) q^{65} +3.25967 q^{66} +(-4.11386 - 7.12541i) q^{67} +(4.70202 + 1.25990i) q^{68} +(-2.74783 + 4.75939i) q^{69} +(1.28871 + 5.94508i) q^{70} +(-2.35918 - 8.80457i) q^{71} +(0.866025 + 0.500000i) q^{72} +3.61460 q^{73} +(-7.40104 - 4.27299i) q^{74} +(-4.93198 + 0.821916i) q^{75} +(1.40996 - 5.26205i) q^{76} +(6.27049 - 6.27049i) q^{77} +(3.59383 + 0.290516i) q^{78} -4.87099i q^{79} +(1.50290 + 1.65568i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-1.89095 - 7.05711i) q^{82} +13.6716i q^{83} +(2.62777 - 0.704109i) q^{84} +(4.98066 + 9.67856i) q^{85} +(-0.648584 - 0.648584i) q^{86} +(7.79865 - 2.08964i) q^{87} +(0.843663 - 3.14859i) q^{88} +(2.29931 + 0.616098i) q^{89} +(0.473708 + 2.18531i) q^{90} +(7.47216 - 6.35445i) q^{91} +(3.88602 + 3.88602i) q^{92} +(-4.53185 + 2.61646i) q^{93} +(-7.06347 + 4.07810i) q^{94} +(10.8313 - 5.57388i) q^{95} +(0.707107 - 0.707107i) q^{96} +(-5.57901 + 9.66313i) q^{97} +(0.200471 - 0.347226i) q^{98} +(2.30493 - 2.30493i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{2} - 16 q^{4} - 12 q^{7} + 32 q^{8}+O(q^{10}) $ 32 * q - 16 * q^2 - 16 * q^4 - 12 * q^7 + 32 * q^8	$ 32 q - 16 q^{2} - 16 q^{4} - 12 q^{7} + 32 q^{8} - 4 q^{11} + 8 q^{13} - 4 q^{15} - 16 q^{16} - 4 q^{17} + 20 q^{19} + 8 q^{21} + 8 q^{22} - 16 q^{23} - 8 q^{25} - 4 q^{26} + 12 q^{28} + 24 q^{29} + 8 q^{30} + 12 q^{31} - 16 q^{32} - 16 q^{34} + 12 q^{35} - 24 q^{37} - 4 q^{38} - 20 q^{39} - 28 q^{41} - 16 q^{42} + 4 q^{43} - 4 q^{44} - 4 q^{46} + 20 q^{49} - 8 q^{50} - 4 q^{52} - 4 q^{53} + 68 q^{55} - 12 q^{56} + 16 q^{57} - 24 q^{58} + 36 q^{59} - 4 q^{60} - 28 q^{61} - 48 q^{62} + 32 q^{64} - 28 q^{65} - 28 q^{67} + 20 q^{68} - 20 q^{69} - 24 q^{70} - 4 q^{71} - 48 q^{73} + 24 q^{74} + 24 q^{75} - 16 q^{76} + 20 q^{77} + 4 q^{78} + 16 q^{81} + 44 q^{82} + 8 q^{84} + 64 q^{85} - 8 q^{86} + 20 q^{87} - 4 q^{88} - 16 q^{89} - 40 q^{91} + 20 q^{92} - 24 q^{93} - 24 q^{94} + 68 q^{95} + 8 q^{97} + 20 q^{98} - 4 q^{99}+O(q^{100}) $ 32 * q - 16 * q^2 - 16 * q^4 - 12 * q^7 + 32 * q^8 - 4 * q^11 + 8 * q^13 - 4 * q^15 - 16 * q^16 - 4 * q^17 + 20 * q^19 + 8 * q^21 + 8 * q^22 - 16 * q^23 - 8 * q^25 - 4 * q^26 + 12 * q^28 + 24 * q^29 + 8 * q^30 + 12 * q^31 - 16 * q^32 - 16 * q^34 + 12 * q^35 - 24 * q^37 - 4 * q^38 - 20 * q^39 - 28 * q^41 - 16 * q^42 + 4 * q^43 - 4 * q^44 - 4 * q^46 + 20 * q^49 - 8 * q^50 - 4 * q^52 - 4 * q^53 + 68 * q^55 - 12 * q^56 + 16 * q^57 - 24 * q^58 + 36 * q^59 - 4 * q^60 - 28 * q^61 - 48 * q^62 + 32 * q^64 - 28 * q^65 - 28 * q^67 + 20 * q^68 - 20 * q^69 - 24 * q^70 - 4 * q^71 - 48 * q^73 + 24 * q^74 + 24 * q^75 - 16 * q^76 + 20 * q^77 + 4 * q^78 + 16 * q^81 + 44 * q^82 + 8 * q^84 + 64 * q^85 - 8 * q^86 + 20 * q^87 - 4 * q^88 - 16 * q^89 - 40 * q^91 + 20 * q^92 - 24 * q^93 - 24 * q^94 + 68 * q^95 + 8 * q^97 + 20 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{12}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−0.965926	−	0.258819i	−0.557678	−	0.149429i
$3$	−0.965926	−	0.258819i	−0.557678	−	0.149429i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−2.18531	+	0.473708i	−0.977303	+	0.211849i
$5$	−2.18531	+	0.473708i	−0.977303	+	0.211849i
$6$	0.258819	+	0.965926i	0.105662	+	0.394338i
$7$	2.35599	+	1.36023i	0.890482	+	0.514120i	0.874100	−	0.485746i	$-0.161452\pi$
$7$	2.35599	+	1.36023i	0.890482	+	0.514120i	0.0163818	+	0.999866i	$0.494785\pi$
$8$	1.00000			0.353553
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$	1.50290	+	1.65568i	0.475259	+	0.523573i
$11$	0.843663	−	3.14859i	0.254374	−	0.949337i	−0.714064	−	0.700081i	$-0.753147\pi$
$11$	0.843663	−	3.14859i	0.254374	−	0.949337i	0.968438	−	0.249256i	$-0.0801861\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	1.21077	−	3.39618i	0.335807	−	0.941931i
$13$	1.21077	−	3.39618i	0.335807	−	0.941931i
$14$		−	2.72047i		−	0.727075i
$15$	2.23346	+	0.108035i	0.576676	+	0.0278944i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.25990	−	4.70202i	−0.305571	−	1.14041i	−0.932453	−	0.361292i	$-0.882336\pi$
$17$	−1.25990	−	4.70202i	−0.305571	−	1.14041i	0.626882	−	0.779114i	$-0.284331\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−5.26205	+	1.40996i	−1.20720	+	0.323467i	−0.805662	−	0.592376i	$-0.798190\pi$
$19$	−5.26205	+	1.40996i	−1.20720	+	0.323467i	−0.401535	+	0.915843i	$0.631523\pi$
$20$	0.682415	−	2.12939i	0.152593	−	0.476147i
$21$	−1.92366	−	1.92366i	−0.419777	−	0.419777i
$22$	−3.14859	+	0.843663i	−0.671283	+	0.179870i
$23$	1.42238	−	5.30841i	0.296587	−	1.10688i	−0.643361	−	0.765563i	$-0.722461\pi$
$23$	1.42238	−	5.30841i	0.296587	−	1.10688i	0.939948	−	0.341316i	$-0.110873\pi$
$24$	−0.965926	−	0.258819i	−0.197169	−	0.0528312i
$25$	4.55120	−	2.07040i	0.910240	−	0.414080i
$26$	−3.54656	+	0.649535i	−0.695538	+	0.127384i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−2.35599	+	1.36023i	−0.445241	+	0.257060i
$29$	−6.99208	+	4.03688i	−1.29840	+	0.749630i	−0.980127	−	0.198370i	$-0.936435\pi$
$29$	−6.99208	+	4.03688i	−1.29840	+	0.749630i	−0.318270	+	0.948000i	$0.603102\pi$
$30$	−1.02317	−	1.98825i	−0.186804	−	0.363003i
$31$	3.70024	−	3.70024i	0.664583	−	0.664583i	−0.291874	−	0.956457i	$-0.594279\pi$
$31$	3.70024	−	3.70024i	0.664583	−	0.664583i	0.956457	+	0.291874i	$0.0942788\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−1.62983	+	2.82295i	−0.283717	+	0.491413i
$34$	−3.44211	+	3.44211i	−0.590318	+	0.590318i
$35$	−5.79294	−	1.85649i	−0.979186	−	0.313803i
$36$	−0.866025	+	0.500000i	−0.144338	+	0.0833333i
$37$	7.40104	−	4.27299i	1.21672	−	0.702476i	0.252508	−	0.967595i	$-0.418745\pi$
$37$	7.40104	−	4.27299i	1.21672	−	0.702476i	0.964216	+	0.265119i	$0.0854113\pi$
$38$	3.85209	+	3.85209i	0.624891	+	0.624891i
$39$	−2.04851	+	2.96709i	−0.328024	+	0.475114i
$40$	−2.18531	+	0.473708i	−0.345529	+	0.0748998i
$41$	7.05711	+	1.89095i	1.10213	+	0.295316i	0.763634	−	0.645650i	$-0.223413\pi$
$41$	7.05711	+	1.89095i	1.10213	+	0.295316i	0.338501	+	0.940966i	$0.390080\pi$
$42$	−0.704109	+	2.62777i	−0.108646	+	0.405474i
$43$	0.885982	−	0.237398i	0.135111	−	0.0362029i	−0.190630	−	0.981662i	$-0.561053\pi$
$43$	0.885982	−	0.237398i	0.135111	−	0.0362029i	0.325741	+	0.945459i	$0.394386\pi$
$44$	2.30493	+	2.30493i	0.347481	+	0.347481i
$45$	−2.12939	−	0.682415i	−0.317431	−	0.101728i
$46$	−5.30841	+	1.42238i	−0.782682	+	0.209719i
$47$		−	8.15619i		−	1.18970i	−0.803836	−	0.594852i	$-0.797211\pi$
$47$		−	8.15619i		−	1.18970i	0.803836	−	0.594852i	$-0.202789\pi$
$48$	0.258819	+	0.965926i	0.0373573	+	0.139419i
$49$	0.200471	+	0.347226i	0.0286387	+	0.0496038i
$50$	−4.06862	−	2.90626i	−0.575390	−	0.411007i
$51$			4.86788i			0.681640i
$52$	2.33579	+	2.74665i	0.323916	+	0.380891i
$53$	3.97631	−	3.97631i	0.546188	−	0.546188i	−0.379148	−	0.925336i	$-0.623783\pi$
$53$	3.97631	−	3.97631i	0.546188	−	0.546188i	0.925336	+	0.379148i	$0.123783\pi$
$54$	−0.258819	+	0.965926i	−0.0352208	+	0.131446i
$55$	−0.352157	+	7.28032i	−0.0474848	+	0.981678i
$56$	2.35599	+	1.36023i	0.314833	+	0.181769i
$57$	5.44767			0.721562
$58$	6.99208	+	4.03688i	0.918105	+	0.530068i
$59$	−0.540573	−	2.01745i	−0.0703766	−	0.262649i	0.921769	−	0.387740i	$-0.126744\pi$
$59$	−0.540573	−	2.01745i	−0.0703766	−	0.262649i	−0.992145	+	0.125091i	$0.960078\pi$
$60$	−1.21029	+	1.88021i	−0.156248	+	0.242734i
$61$	−5.12740	+	8.88092i	−0.656497	+	1.13709i	0.325020	+	0.945707i	$0.394629\pi$
$61$	−5.12740	+	8.88092i	−0.656497	+	1.13709i	−0.981516	+	0.191378i	$0.938704\pi$
$62$	−5.05462	−	1.35438i	−0.641938	−	0.172007i
$63$	1.36023	+	2.35599i	0.171373	+	0.296827i
$64$	1.00000			0.125000
$65$	−1.03711	+	7.99527i	−0.128638	+	0.991692i
$66$	3.25967			0.401237
$67$	−4.11386	−	7.12541i	−0.502588	−	0.870507i	−0.999996	−	0.00299063i	$-0.999048\pi$
$67$	−4.11386	−	7.12541i	−0.502588	−	0.870507i	0.497408	−	0.867517i	$-0.334285\pi$
$68$	4.70202	+	1.25990i	0.570203	+	0.152785i
$69$	−2.74783	+	4.75939i	−0.330800	+	0.572963i
$70$	1.28871	+	5.94508i	0.154030	+	0.710573i
$71$	−2.35918	−	8.80457i	−0.279983	−	1.04491i	−0.952428	−	0.304763i	$-0.901423\pi$
$71$	−2.35918	−	8.80457i	−0.279983	−	1.04491i	0.672445	−	0.740147i	$-0.265244\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	3.61460			0.423057			0.211529	−	0.977372i	$-0.432156\pi$
$73$	3.61460			0.423057			0.211529	+	0.977372i	$0.432156\pi$
$74$	−7.40104	−	4.27299i	−0.860353	−	0.496725i
$75$	−4.93198	+	0.821916i	−0.569496	+	0.0949067i
$76$	1.40996	−	5.26205i	0.161734	−	0.603599i
$77$	6.27049	−	6.27049i	0.714589	−	0.714589i
$78$	3.59383	+	0.290516i	0.406921	+	0.0328944i
$79$		−	4.87099i		−	0.548029i	−0.961726	−	0.274014i	$-0.911648\pi$
$79$		−	4.87099i		−	0.548029i	0.961726	−	0.274014i	$-0.0883516\pi$
$80$	1.50290	+	1.65568i	0.168029	+	0.185111i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−1.89095	−	7.05711i	−0.208820	−	0.779327i
$83$			13.6716i			1.50065i	0.661068	+	0.750326i	$0.270103\pi$
$83$			13.6716i			1.50065i	−0.661068	+	0.750326i	$0.729897\pi$
$84$	2.62777	−	0.704109i	0.286713	−	0.0768246i
$85$	4.98066	+	9.67856i	0.540229	+	1.04979i
$86$	−0.648584	−	0.648584i	−0.0699386	−	0.0699386i
$87$	7.79865	−	2.08964i	0.836104	−	0.224033i
$88$	0.843663	−	3.14859i	0.0899348	−	0.335641i
$89$	2.29931	+	0.616098i	0.243726	+	0.0653063i	0.378614	−	0.925555i	$-0.376401\pi$
$89$	2.29931	+	0.616098i	0.243726	+	0.0653063i	−0.134888	+	0.990861i	$0.543067\pi$
$90$	0.473708	+	2.18531i	0.0499332	+	0.230352i
$91$	7.47216	−	6.35445i	0.783295	−	0.666128i
$92$	3.88602	+	3.88602i	0.405146	+	0.405146i
$93$	−4.53185	+	2.61646i	−0.469931	+	0.271315i
$94$	−7.06347	+	4.07810i	−0.728541	+	0.420624i
$95$	10.8313	−	5.57388i	1.11127	−	0.571868i
$96$	0.707107	−	0.707107i	0.0721688	−	0.0721688i
$97$	−5.57901	+	9.66313i	−0.566463	+	0.981142i	0.430449	+	0.902615i	$0.358355\pi$
$97$	−5.57901	+	9.66313i	−0.566463	+	0.981142i	−0.996912	+	0.0785272i	$0.974978\pi$
$98$	0.200471	−	0.347226i	0.0202507	−	0.0350752i
$99$	2.30493	−	2.30493i	0.231654	−	0.231654i
$100$	−0.482581	+	4.97666i	−0.0482581	+	0.497666i
$101$	−12.0990	+	6.98536i	−1.20389	+	0.695069i	−0.961419	−	0.275088i	$-0.911293\pi$
$101$	−12.0990	+	6.98536i	−1.20389	+	0.695069i	−0.242476	+	0.970157i	$0.577960\pi$
$102$	4.21571	−	2.43394i	0.417418	−	0.240996i
$103$	0.725388	+	0.725388i	0.0714746	+	0.0714746i	0.741940	−	0.670466i	$-0.233906\pi$
$103$	0.725388	+	0.725388i	0.0714746	+	0.0714746i	−0.670466	+	0.741940i	$0.733906\pi$
$104$	1.21077	−	3.39618i	0.118726	−	0.333023i
$105$	5.11506	+	3.29255i	0.499179	+	0.321320i
$106$	−5.43174	−	1.45543i	−0.527577	−	0.141364i
$107$	−0.0382380	+	0.142706i	−0.00369661	+	0.0137959i	−0.967750	−	0.251914i	$-0.918940\pi$
$107$	−0.0382380	+	0.142706i	−0.00369661	+	0.0137959i	0.964053	+	0.265710i	$0.0856065\pi$
$108$	0.965926	−	0.258819i	0.0929463	−	0.0249049i
$109$	13.7212	+	13.7212i	1.31426	+	1.31426i	0.918246	+	0.396011i	$0.129606\pi$
$109$	13.7212	+	13.7212i	1.31426	+	1.31426i	0.396011	+	0.918246i	$0.370394\pi$
$110$	6.48102	−	3.33518i	0.617941	−	0.317997i
$111$	−8.25479	+	2.21186i	−0.783510	+	0.209941i
$112$		−	2.72047i		−	0.257060i
$113$	4.06783	+	15.1813i	0.382669	+	1.42814i	0.841808	+	0.539777i	$0.181491\pi$
$113$	4.06783	+	15.1813i	0.382669	+	1.42814i	−0.459139	+	0.888364i	$0.651842\pi$
$114$	−2.72384	−	4.71782i	−0.255111	−	0.441865i
$115$	−0.593722	+	12.2743i	−0.0553649	+	1.14459i
$116$		−	8.07376i		−	0.749630i
$117$	2.74665	−	2.33579i	0.253927	−	0.215944i
$118$	−1.47687	+	1.47687i	−0.135957	+	0.135957i
$119$	3.42752	−	12.7917i	0.314200	−	1.17261i
$120$	2.23346	+	0.108035i	0.203886	+	0.00986217i
$121$	0.324398	+	0.187292i	0.0294908	+	0.0170265i
$122$	10.2548			0.928427
$123$	−6.32723	−	3.65303i	−0.570507	−	0.329382i
$124$	1.35438	+	5.05462i	0.121627	+	0.453918i
$125$	−8.96504	+	6.68042i	−0.801858	+	0.597515i
$126$	1.36023	−	2.35599i	0.121179	−	0.209889i
$127$	−15.6874	−	4.20342i	−1.39203	−	0.372993i	−0.516554	−	0.856255i	$-0.672785\pi$
$127$	−15.6874	−	4.20342i	−1.39203	−	0.372993i	−0.875476	+	0.483262i	$0.839452\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−0.917236			−0.0807581
$130$	7.44267	−	3.09947i	0.652765	−	0.271842i
$131$	0.951816			0.0831605			0.0415803	−	0.999135i	$-0.486761\pi$
$131$	0.951816			0.0831605			0.0415803	+	0.999135i	$0.486761\pi$
$132$	−1.62983	−	2.82295i	−0.141859	−	0.245707i
$133$	−14.3152	−	3.83576i	−1.24129	−	0.332602i
$134$	−4.11386	+	7.12541i	−0.355383	+	0.615542i
$135$	1.88021	+	1.21029i	0.161823	+	0.104165i
$136$	−1.25990	−	4.70202i	−0.108036	−	0.403195i
$137$	13.4188	+	7.74732i	1.14644	+	0.661899i	0.948018	−	0.318218i	$-0.103084\pi$
$137$	13.4188	+	7.74732i	1.14644	+	0.661899i	0.198424	+	0.980116i	$0.436418\pi$
$138$	5.49567			0.467822
$139$	−4.37938	−	2.52843i	−0.371454	−	0.214459i	0.302640	−	0.953105i	$-0.402132\pi$
$139$	−4.37938	−	2.52843i	−0.371454	−	0.214459i	−0.674093	+	0.738646i	$0.735465\pi$
$140$	4.50424	−	4.08859i	0.380677	−	0.345549i
$141$	−2.11098	+	7.87828i	−0.177776	+	0.663471i
$142$	−6.44539	+	6.44539i	−0.540885	+	0.540885i
$143$	−9.67172	−	6.67745i	−0.808789	−	0.558396i
$144$		−	1.00000i		−	0.0833333i
$145$	13.3676	−	12.1341i	1.11012	−	1.00768i
$146$	−1.80730	−	3.13034i	−0.149573	−	0.259069i
$147$	−0.103772	−	0.387281i	−0.00855893	−	0.0319424i
$148$			8.54599i			0.702476i
$149$	4.67056	−	1.25147i	0.382627	−	0.102525i	−0.0623782	−	0.998053i	$-0.519868\pi$
$149$	4.67056	−	1.25147i	0.382627	−	0.102525i	0.445005	+	0.895528i	$0.353202\pi$
$150$	3.17779	+	3.86026i	0.259466	+	0.315189i
$151$	0.873002	+	0.873002i	0.0710439	+	0.0710439i	0.741736	−	0.670692i	$-0.234003\pi$
$151$	0.873002	+	0.873002i	0.0710439	+	0.0710439i	−0.670692	+	0.741736i	$0.734003\pi$
$152$	−5.26205	+	1.40996i	−0.426809	+	0.114363i
$153$	1.25990	−	4.70202i	0.101857	−	0.380135i
$154$	−8.56565	−	2.29516i	−0.690240	−	0.184949i
$155$	−6.33336	+	9.83902i	−0.508708	+	0.790289i
$156$	−1.54532	−	3.25760i	−0.123725	−	0.260817i
$157$	−11.0199	−	11.0199i	−0.879482	−	0.879482i	0.113999	−	0.993481i	$-0.463634\pi$
$157$	−11.0199	−	11.0199i	−0.879482	−	0.879482i	−0.993481	+	0.113999i	$0.963634\pi$
$158$	−4.21840	+	2.43549i	−0.335598	+	0.193757i
$159$	−4.86997	+	2.81168i	−0.386213	+	0.222980i
$160$	0.682415	−	2.12939i	0.0539496	−	0.168343i
$161$	10.5718	−	10.5718i	0.833175	−	0.833175i
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	10.6264	−	18.4055i	0.832326	−	1.44163i	−0.0638638	−	0.997959i	$-0.520342\pi$
$163$	10.6264	−	18.4055i	0.832326	−	1.44163i	0.896189	−	0.443672i	$-0.146324\pi$
$164$	−5.16616	+	5.16616i	−0.403409	+	0.403409i
$165$	2.22444	−	6.94111i	0.173173	−	0.540364i
$166$	11.8399	−	6.83580i	0.918958	−	0.530561i
$167$	−16.8892	+	9.75100i	−1.30693	+	0.754555i	−0.981582	−	0.191040i	$-0.938814\pi$
$167$	−16.8892	+	9.75100i	−1.30693	+	0.754555i	−0.325345	+	0.945595i	$0.605480\pi$
$168$	−1.92366	−	1.92366i	−0.148414	−	0.148414i
$169$	−10.0681	−	8.22397i	−0.774468	−	0.632613i
$170$	5.89155	−	9.15266i	0.451861	−	0.701977i
$171$	−5.26205	−	1.40996i	−0.402399	−	0.107822i
$172$	−0.237398	+	0.885982i	−0.0181014	+	0.0675555i
$173$	−5.86243	+	1.57083i	−0.445712	+	0.119428i	−0.474692	−	0.880152i	$-0.657441\pi$
$173$	−5.86243	+	1.57083i	−0.445712	+	0.119428i	0.0289802	+	0.999580i	$0.490774\pi$
$174$	−5.70901	−	5.70901i	−0.432799	−	0.432799i
$175$	13.5388	+	1.31285i	1.02344	+	0.0992419i
$176$	−3.14859	+	0.843663i	−0.237334	+	0.0635935i
$177$			2.08861i			0.156990i
$178$	−0.616098	−	2.29931i	−0.0461785	−	0.172341i
$179$	0.424199	+	0.734734i	0.0317061	+	0.0549166i	0.881443	−	0.472290i	$-0.156573\pi$
$179$	0.424199	+	0.734734i	0.0317061	+	0.0549166i	−0.849737	+	0.527207i	$0.823239\pi$
$180$	1.65568	−	1.50290i	0.123407	−	0.112020i
$181$		−	7.92591i		−	0.589128i	−0.955632	−	0.294564i	$-0.904826\pi$
$181$		−	7.92591i		−	0.589128i	0.955632	−	0.294564i	$-0.0951745\pi$
$182$	−9.23920	−	3.29385i	−0.684855	−	0.244157i
$183$	7.25124	−	7.25124i	0.536027	−	0.536027i
$184$	1.42238	−	5.30841i	0.104860	−	0.391341i
$185$	−14.1495	+	12.8438i	−1.04029	+	0.944292i
$186$	4.53185	+	2.61646i	0.332291	+	0.191849i
$187$	−15.8677			−1.16036
$188$	7.06347	+	4.07810i	0.515157	+	0.297426i
$189$	−0.704109	−	2.62777i	−0.0512164	−	0.191142i
$190$	−10.2428	−	6.59326i	−0.743090	−	0.478325i
$191$	1.46566	−	2.53860i	0.106051	−	0.183686i	−0.808116	−	0.589024i	$-0.799513\pi$
$191$	1.46566	−	2.53860i	0.106051	−	0.183686i	0.914167	+	0.405337i	$0.132846\pi$
$192$	−0.965926	−	0.258819i	−0.0697097	−	0.0186787i
$193$	−4.99068	−	8.64411i	−0.359237	−	0.622217i	0.628597	−	0.777732i	$-0.283630\pi$
$193$	−4.99068	−	8.64411i	−0.359237	−	0.622217i	−0.987834	+	0.155515i	$0.950296\pi$
$194$	11.1580			0.801099
$195$	3.07110	−	7.45442i	0.219926	−	0.533822i
$196$	−0.400942			−0.0286387
$197$	7.23766	+	12.5360i	0.515662	+	0.893153i	0.999835	+	0.0181804i	$0.00578733\pi$
$197$	7.23766	+	12.5360i	0.515662	+	0.893153i	−0.484173	+	0.874972i	$0.660879\pi$
$198$	−3.14859	−	0.843663i	−0.223761	−	0.0599565i
$199$	−5.91710	+	10.2487i	−0.419452	+	0.726513i	−0.995884	−	0.0906322i	$-0.971111\pi$
$199$	−5.91710	+	10.2487i	−0.419452	+	0.726513i	0.576432	+	0.817145i	$0.304445\pi$
$200$	4.55120	−	2.07040i	0.321819	−	0.146399i
$201$	2.12949	+	7.94736i	0.150203	+	0.560564i
$202$	12.0990	+	6.98536i	0.851282	+	0.491488i
$203$	−21.9644			−1.54160
$204$	−4.21571	−	2.43394i	−0.295159	−	0.170410i
$205$	−16.3178	−	0.789307i	−1.13968	−	0.0551276i
$206$	0.265511	−	0.990899i	0.0184990	−	0.0690392i
$207$	3.88602	−	3.88602i	0.270097	−	0.270097i
$208$	−3.54656	+	0.649535i	−0.245910	+	0.0450371i
$209$			17.7576i			1.22832i
$210$	0.293905	−	6.07605i	0.0202813	−	0.419287i
$211$	−2.35221	−	4.07414i	−0.161933	−	0.280475i	0.773629	−	0.633639i	$-0.218439\pi$
$211$	−2.35221	−	4.07414i	−0.161933	−	0.280475i	−0.935562	+	0.353163i	$0.885106\pi$
$212$	1.45543	+	5.43174i	0.0999594	+	0.373054i
$213$			9.11516i			0.624561i
$214$	0.142706	−	0.0382380i	0.00975520	−	0.00261390i
$215$	−1.82369	+	0.938486i	−0.124375	+	0.0640042i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	13.7509	−	3.68455i	0.933474	−	0.250124i
$218$	5.02232	−	18.7436i	0.340155	−	1.26947i
$219$	−3.49144	−	0.935528i	−0.235930	−	0.0632171i
$220$	−6.12886	−	3.94514i	−0.413208	−	0.265981i
$221$	−17.4943	−	1.41420i	−1.17680	−	0.0951291i
$222$	6.04292	+	6.04292i	0.405575	+	0.405575i
$223$	10.4760	−	6.04831i	0.701523	−	0.405025i	−0.106391	−	0.994324i	$-0.533930\pi$
$223$	10.4760	−	6.04831i	0.701523	−	0.405025i	0.807914	+	0.589300i	$0.200596\pi$
$224$	−2.35599	+	1.36023i	−0.157416	+	0.0908844i
$225$	4.97666	+	0.482581i	0.331777	+	0.0321721i
$226$	11.1135	−	11.1135i	0.739260	−	0.739260i
$227$	12.8448	−	22.2478i	0.852537	−	1.47664i	−0.0263751	−	0.999652i	$-0.508396\pi$
$227$	12.8448	−	22.2478i	0.852537	−	1.47664i	0.878912	−	0.476985i	$-0.158270\pi$
$228$	−2.72384	+	4.71782i	−0.180391	+	0.312446i
$229$	17.6675	−	17.6675i	1.16750	−	1.16750i	0.184710	−	0.982793i	$-0.440865\pi$
$229$	17.6675	−	17.6675i	1.16750	−	1.16750i	0.982793	−	0.184710i	$-0.0591347\pi$
$230$	10.9267	−	5.62299i	0.720488	−	0.370769i
$231$	−7.67975	+	4.43391i	−0.505291	+	0.291730i
$232$	−6.99208	+	4.03688i	−0.459053	+	0.265034i
$233$	6.87427	+	6.87427i	0.450349	+	0.450349i	0.895470	−	0.445121i	$-0.146840\pi$
$233$	6.87427	+	6.87427i	0.450349	+	0.450349i	−0.445121	+	0.895470i	$0.646840\pi$
$234$	−3.39618	−	1.21077i	−0.222015	−	0.0791504i
$235$	3.86365	+	17.8239i	0.252037	+	1.16270i
$236$	2.01745	+	0.540573i	0.131325	+	0.0351883i
$237$	−1.26070	+	4.70501i	−0.0818915	+	0.305623i
$238$	−12.7917	+	3.42752i	−0.829161	+	0.222173i
$239$	12.8512	+	12.8512i	0.831275	+	0.831275i	0.987691	−	0.156416i	$-0.0499940\pi$
$239$	12.8512	+	12.8512i	0.831275	+	0.831275i	−0.156416	+	0.987691i	$0.549994\pi$
$240$	−1.02317	−	1.98825i	−0.0660452	−	0.128341i
$241$	3.45388	−	0.925464i	0.222484	−	0.0596144i	−0.145855	−	0.989306i	$-0.546593\pi$
$241$	3.45388	−	0.925464i	0.222484	−	0.0596144i	0.368339	+	0.929692i	$0.379927\pi$
$242$		−	0.374583i		−	0.0240791i
$243$	−0.258819	−	0.965926i	−0.0166032	−	0.0619642i
$244$	−5.12740	−	8.88092i	−0.328248	−	0.568543i
$245$	−0.602577	−	0.663834i	−0.0384972	−	0.0424108i
$246$			7.30605i			0.465817i
$247$	−1.58263	+	19.5780i	−0.100701	+	1.24572i
$248$	3.70024	−	3.70024i	0.234965	−	0.234965i
$249$	3.53847	−	13.2057i	0.224241	−	0.836880i
$250$	10.2679	+	4.42375i	0.649401	+	0.279782i
$251$	−0.694692	−	0.401080i	−0.0438486	−	0.0253160i	0.477915	−	0.878406i	$-0.341393\pi$
$251$	−0.694692	−	0.401080i	−0.0438486	−	0.0253160i	−0.521764	+	0.853090i	$0.674726\pi$
$252$	−2.72047			−0.171373
$253$	−15.5140	−	8.95702i	−0.975358	−	0.563123i
$254$	4.20342	+	15.6874i	0.263746	+	0.984314i
$255$	−2.30595	−	10.6379i	−0.144404	−	0.666169i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.99322	+	1.33793i	0.311469	+	0.0834578i	0.411167	−	0.911560i	$-0.365121\pi$
$257$	4.99322	+	1.33793i	0.311469	+	0.0834578i	−0.0996987	+	0.995018i	$0.531788\pi$
$258$	0.458618	+	0.794350i	0.0285523	+	0.0494540i
$259$	23.2491			1.44463
$260$	−6.40555	−	4.89580i	−0.397256	−	0.303625i
$261$	−8.07376			−0.499753
$262$	−0.475908	−	0.824297i	−0.0294017	−	0.0509252i
$263$	−5.04602	−	1.35208i	−0.311151	−	0.0833727i	0.0998644	−	0.995001i	$-0.468159\pi$
$263$	−5.04602	−	1.35208i	−0.311151	−	0.0833727i	−0.411015	+	0.911628i	$0.634826\pi$
$264$	−1.62983	+	2.82295i	−0.100309	+	0.173741i
$265$	−6.80588	+	10.5731i	−0.418082	+	0.649500i
$266$	3.83576	+	14.3152i	0.235185	+	0.877723i
$267$	−2.06151	−	1.19021i	−0.126162	−	0.0728397i
$268$	8.22772			0.502588
$269$	−27.6490	−	15.9632i	−1.68579	−	0.973291i	−0.957682	−	0.287829i	$-0.907066\pi$
$269$	−27.6490	−	15.9632i	−1.68579	−	0.973291i	−0.728108	−	0.685462i	$-0.759600\pi$
$270$	0.108035	−	2.23346i	0.00657478	−	0.135924i
$271$	4.05016	−	15.1154i	0.246030	−	0.918196i	−0.726833	−	0.686814i	$-0.759009\pi$
$271$	4.05016	−	15.1154i	0.246030	−	0.918196i	0.972863	−	0.231382i	$-0.0743248\pi$
$272$	−3.44211	+	3.44211i	−0.208709	+	0.208709i
$273$	−8.86221	+	4.20399i	−0.536365	+	0.254437i
$274$		−	15.4946i		−	0.936066i
$275$	−2.67917	−	16.0766i	−0.161560	−	0.969456i
$276$	−2.74783	−	4.75939i	−0.165400	−	0.286481i
$277$	−5.15230	−	19.2286i	−0.309572	−	1.15534i	−0.928938	−	0.370235i	$-0.879277\pi$
$277$	−5.15230	−	19.2286i	−0.309572	−	1.15534i	0.619367	−	0.785102i	$-0.287389\pi$
$278$			5.05687i			0.303291i
$279$	5.05462	−	1.35438i	0.302612	−	0.0810847i
$280$	−5.79294	−	1.85649i	−0.346194	−	0.110946i
$281$	16.0376	+	16.0376i	0.956723	+	0.956723i	0.999102	−	0.0423787i	$-0.0134936\pi$
$281$	16.0376	+	16.0376i	0.956723	+	0.956723i	−0.0423787	+	0.999102i	$0.513494\pi$
$282$	7.87828	−	2.11098i	0.469145	−	0.125707i
$283$	1.93221	−	7.21112i	0.114858	−	0.428657i	−0.884418	−	0.466696i	$-0.845444\pi$
$283$	1.93221	−	7.21112i	0.114858	−	0.428657i	0.999276	+	0.0380388i	$0.0121111\pi$
$284$	8.80457	+	2.35918i	0.522455	+	0.139991i
$285$	−11.9049	+	2.58061i	−0.705185	+	0.152862i
$286$	−0.946983	+	11.7147i	−0.0559963	+	0.692703i
$287$	14.0544	+	14.0544i	0.829603	+	0.829603i
$288$	−0.866025	+	0.500000i	−0.0510310	+	0.0294628i
$289$	−5.79917	+	3.34815i	−0.341128	+	0.196950i
$290$	−17.1922	−	5.50965i	−1.00956	−	0.323538i
$291$	7.88991	−	7.88991i	0.462515	−	0.462515i
$292$	−1.80730	+	3.13034i	−0.105764	+	0.183189i
$293$	−3.75331	+	6.50093i	−0.219271	+	0.379788i	−0.954585	−	0.297938i	$-0.903701\pi$
$293$	−3.75331	+	6.50093i	−0.219271	+	0.379788i	0.735314	+	0.677726i	$0.237034\pi$
$294$	−0.283509	+	0.283509i	−0.0165346	+	0.0165346i
$295$	2.13700	+	4.15268i	0.124421	+	0.241778i
$296$	7.40104	−	4.27299i	0.430177	−	0.248363i
$297$	−2.82295	+	1.62983i	−0.163804	+	0.0945725i
$298$	−3.41909	−	3.41909i	−0.198062	−	0.198062i
$299$	−16.3061	−	11.2579i	−0.943008	−	0.651062i
$300$	1.75419	−	4.68218i	0.101278	−	0.270326i
$301$	2.41028	+	0.645834i	0.138926	+	0.0372252i
$302$	0.319541	−	1.19254i	0.0183875	−	0.0686231i
$303$	13.4947	−	3.61589i	0.775249	−	0.207727i
$304$	3.85209	+	3.85209i	0.220932	+	0.220932i
$305$	6.99803	−	21.8365i	0.400706	−	1.25035i
$306$	−4.70202	+	1.25990i	−0.268796	+	0.0720238i
$307$			13.4226i			0.766067i	0.923734	+	0.383034i	$0.125121\pi$
$307$			13.4226i			0.766067i	−0.923734	+	0.383034i	$0.874879\pi$
$308$	2.29516	+	8.56565i	0.130779	+	0.488073i
$309$	−0.512927	−	0.888416i	−0.0291794	−	0.0505402i
$310$	11.6875	+	0.565338i	0.663807	+	0.0321090i
$311$			21.2085i			1.20262i	0.799014	+	0.601312i	$0.205355\pi$
$311$			21.2085i			1.20262i	−0.799014	+	0.601312i	$0.794645\pi$
$312$	−2.04851	+	2.96709i	−0.115974	+	0.167978i
$313$	−9.89579	+	9.89579i	−0.559343	+	0.559343i	−0.929120	−	0.369777i	$-0.879434\pi$
$313$	−9.89579	+	9.89579i	−0.559343	+	0.559343i	0.369777	+	0.929120i	$0.379434\pi$
$314$	−4.03355	+	15.0534i	−0.227627	+	0.849514i
$315$	−4.08859	−	4.50424i	−0.230366	−	0.253785i
$316$	4.21840	+	2.43549i	0.237303	+	0.137007i
$317$	25.1436			1.41221			0.706103	−	0.708109i	$-0.250452\pi$
$317$	25.1436			1.41221			0.706103	+	0.708109i	$0.250452\pi$
$318$	4.86997	+	2.81168i	0.273094	+	0.157671i
$319$	6.81154	+	25.4210i	0.381373	+	1.42330i
$320$	−2.18531	+	0.473708i	−0.122163	+	0.0264811i
$321$	0.0738702	−	0.127947i	0.00412303	−	0.00714130i
$322$	−14.4413	−	3.86955i	−0.804785	−	0.215641i
$323$	13.2593	+	22.9658i	0.737769	+	1.27785i
$324$	−1.00000			−0.0555556
$325$	−1.52101	−	17.9635i	−0.0843703	−	0.996434i
$326$	−21.2528			−1.17709
$327$	−9.70238	−	16.8050i	−0.536543	−	0.929320i
$328$	7.05711	+	1.89095i	0.389663	+	0.104410i
$329$	11.0943	−	19.2159i	0.611650	−	1.05941i
$330$	−7.12339	+	1.54413i	−0.392130	+	0.0850015i
$331$	8.43673	+	31.4863i	0.463725	+	1.73064i	0.661083	+	0.750312i	$0.270097\pi$
$331$	8.43673	+	31.4863i	0.463725	+	1.73064i	−0.197359	+	0.980331i	$0.563236\pi$
$332$	−11.8399	−	6.83580i	−0.649801	−	0.375163i
$333$	8.54599			0.468317
$334$	16.8892	+	9.75100i	0.924137	+	0.533551i
$335$	12.3654	+	13.6225i	0.675596	+	0.744277i
$336$	−0.704109	+	2.62777i	−0.0384123	+	0.143357i
$337$	10.7771	−	10.7771i	0.587065	−	0.587065i	−0.349770	−	0.936836i	$-0.613740\pi$
$337$	10.7771	−	10.7771i	0.587065	−	0.587065i	0.936836	+	0.349770i	$0.113740\pi$
$338$	−2.08813	+	12.8312i	−0.113579	+	0.697925i
$339$		−	15.7169i		−	0.853624i
$340$	−10.8722	−	0.525900i	−0.589628	−	0.0285209i
$341$	−8.52880	−	14.7723i	−0.461860	−	0.799966i
$342$	1.40996	+	5.26205i	0.0762420	+	0.284539i
$343$		−	17.9525i		−	0.969345i
$344$	0.885982	−	0.237398i	0.0477689	−	0.0127996i
$345$	3.75032	−	11.7024i	0.201911	−	0.630038i
$346$	4.29160	+	4.29160i	0.230718	+	0.230718i
$347$	−2.06259	+	0.552670i	−0.110726	+	0.0296689i	−0.313757	−	0.949503i	$-0.601588\pi$
$347$	−2.06259	+	0.552670i	−0.110726	+	0.0296689i	0.203031	+	0.979172i	$0.434921\pi$
$348$	−2.08964	+	7.79865i	−0.112017	+	0.418052i
$349$	25.2723	+	6.77169i	1.35279	+	0.362480i	0.861165	−	0.508325i	$-0.169735\pi$
$349$	25.2723	+	6.77169i	1.35279	+	0.362480i	0.491629	+	0.870805i	$0.336402\pi$
$350$	−5.63246	−	12.3814i	−0.301068	−	0.661813i
$351$	−3.25760	+	1.54532i	−0.173878	+	0.0824831i
$352$	2.30493	+	2.30493i	0.122853	+	0.122853i
$353$	5.74611	−	3.31752i	0.305834	−	0.176574i	−0.339227	−	0.940705i	$-0.610165\pi$
$353$	5.74611	−	3.31752i	0.305834	−	0.176574i	0.645061	+	0.764131i	$0.276832\pi$
$354$	1.80879	−	1.04431i	0.0961362	−	0.0555043i
$355$	9.32634	+	18.1232i	0.494991	+	0.961879i
$356$	−1.68321	+	1.68321i	−0.0892101	+	0.0892101i
$357$	−6.62146	+	11.4687i	−0.350445	+	0.606988i
$358$	0.424199	−	0.734734i	0.0224196	−	0.0388319i
$359$	−6.44895	+	6.44895i	−0.340362	+	0.340362i	−0.856504	−	0.516141i	$-0.827368\pi$
$359$	−6.44895	+	6.44895i	−0.340362	+	0.340362i	0.516141	+	0.856504i	$0.327368\pi$
$360$	−2.12939	−	0.682415i	−0.112229	−	0.0359664i
$361$	9.24669	−	5.33858i	0.486668	−	0.280978i
$362$	−6.86404	+	3.96296i	−0.360766	+	0.208288i
$363$	−0.264870	−	0.264870i	−0.0139021	−	0.0139021i
$364$	1.76704	+	9.64831i	0.0926180	+	0.505709i
$365$	−7.89904	+	1.71226i	−0.413455	+	0.0896240i
$366$	−9.90538	−	2.65414i	−0.517763	−	0.138734i
$367$	−8.63177	+	32.2142i	−0.450575	+	1.68157i	0.250208	+	0.968192i	$0.419501\pi$
$367$	−8.63177	+	32.2142i	−0.450575	+	1.68157i	−0.700782	+	0.713375i	$0.747166\pi$
$368$	−5.30841	+	1.42238i	−0.276720	+	0.0741469i
$369$	5.16616	+	5.16616i	0.268940	+	0.268940i
$370$	18.1978	+	5.83190i	0.946056	+	0.303186i
$371$	14.7769	−	3.95945i	0.767177	−	0.205565i
$372$		−	5.23293i		−	0.271315i
$373$	1.63693	+	6.10910i	0.0847569	+	0.316317i	0.995268	−	0.0971675i	$-0.0309782\pi$
$373$	1.63693	+	6.10910i	0.0847569	+	0.316317i	−0.910511	+	0.413485i	$0.864312\pi$
$374$	7.93384	+	13.7418i	0.410249	+	0.710572i
$375$	10.3886	−	4.13246i	0.536464	−	0.213399i
$376$		−	8.15619i		−	0.420624i
$377$	5.24419	+	28.6341i	0.270089	+	1.47473i
$378$	−1.92366	+	1.92366i	−0.0989424	+	0.0989424i
$379$	2.61517	−	9.75996i	0.134332	−	0.501336i	−0.865667	−	0.500620i	$-0.833105\pi$
$379$	2.61517	−	9.75996i	0.134332	−	0.501336i	1.00000		0.000715796i	$-0.000227845\pi$
$380$	−0.588538	+	12.1671i	−0.0301913	+	0.624161i
$381$	14.0649	+	8.12038i	0.720568	+	0.416020i
$382$	−2.93132			−0.149979
$383$	−7.52449	−	4.34426i	−0.384483	−	0.221982i	0.295284	−	0.955410i	$-0.404586\pi$
$383$	−7.52449	−	4.34426i	−0.384483	−	0.221982i	−0.679767	+	0.733428i	$0.737919\pi$
$384$	0.258819	+	0.965926i	0.0132078	+	0.0492922i
$385$	−10.7326	+	16.6734i	−0.546985	+	0.849754i
$386$	−4.99068	+	8.64411i	−0.254019	+	0.439974i
$387$	0.885982	+	0.237398i	0.0450370	+	0.0120676i
$388$	−5.57901	−	9.66313i	−0.283231	−	0.490571i
$389$	23.3415			1.18346			0.591731	−	0.806136i	$-0.298445\pi$
$389$	23.3415			1.18346			0.591731	+	0.806136i	$0.298445\pi$
$390$	−7.99127	+	1.06756i	−0.404653	+	0.0540578i
$391$	−26.7523			−1.35292
$392$	0.200471	+	0.347226i	0.0101253	+	0.0175376i
$393$	−0.919384	−	0.246348i	−0.0463768	−	0.0124266i
$394$	7.23766	−	12.5360i	0.364628	−	0.631554i
$395$	2.30742	+	10.6446i	0.116099	+	0.535590i
$396$	0.843663	+	3.14859i	0.0423957	+	0.158223i
$397$	−10.9319	−	6.31152i	−0.548655	−	0.316766i	0.199924	−	0.979811i	$-0.435930\pi$
$397$	−10.9319	−	6.31152i	−0.548655	−	0.316766i	−0.748579	+	0.663045i	$0.769264\pi$
$398$	11.8342			0.593195
$399$	12.8347	+	7.41011i	0.642538	+	0.370970i
$400$	−4.06862	−	2.90626i	−0.203431	−	0.145313i
$401$	−5.12518	+	19.1274i	−0.255939	+	0.955179i	0.711626	+	0.702558i	$0.247959\pi$
$401$	−5.12518	+	19.1274i	−0.255939	+	0.955179i	−0.967566	+	0.252620i	$0.918708\pi$
$402$	5.81787	−	5.81787i	0.290169	−	0.290169i
$403$	−8.08655	−	17.0468i	−0.402820	−	0.849162i
$404$		−	13.9707i		−	0.695069i
$405$	−1.50290	−	1.65568i	−0.0746797	−	0.0822716i
$406$	10.9822	+	19.0217i	0.545038	+	0.944033i
$407$	−7.20994	−	26.9078i	−0.357383	−	1.33377i
$408$			4.86788i			0.240996i
$409$	−1.49487	+	0.400550i	−0.0739167	+	0.0198059i	−0.295588	−	0.955316i	$-0.595516\pi$
$409$	−1.49487	+	0.400550i	−0.0739167	+	0.0198059i	0.221671	+	0.975121i	$0.428849\pi$
$410$	7.47532	+	14.5262i	0.369180	+	0.717400i
$411$	−10.9564	−	10.9564i	−0.540438	−	0.540438i
$412$	−0.990899	+	0.265511i	−0.0488181	+	0.0130808i
$413$	1.47061	−	5.48839i	0.0723640	−	0.270066i
$414$	−5.30841	−	1.42238i	−0.260894	−	0.0699063i
$415$	−6.47634	−	29.8767i	−0.317911	−	1.46659i
$416$	2.33579	+	2.74665i	0.114522	+	0.134665i
$417$	3.57575	+	3.57575i	0.175105	+	0.175105i
$418$	15.3785	−	8.87880i	0.752188	−	0.434276i
$419$	22.9548	−	13.2530i	1.12142	−	0.647451i	0.179655	−	0.983730i	$-0.442502\pi$
$419$	22.9548	−	13.2530i	1.12142	−	0.647451i	0.941762	+	0.336279i	$0.109168\pi$
$420$	−5.40896	+	2.78349i	−0.263930	+	0.135821i
$421$	−19.5154	+	19.5154i	−0.951121	+	0.951121i	−0.998860	−	0.0477384i	$-0.984799\pi$
$421$	−19.5154	+	19.5154i	−0.951121	+	0.951121i	0.0477384	+	0.998860i	$0.484799\pi$
$422$	−2.35221	+	4.07414i	−0.114504	+	0.198326i
$423$	4.07810	−	7.06347i	0.198284	−	0.343438i
$424$	3.97631	−	3.97631i	0.193107	−	0.193107i
$425$	−15.4691	−	18.7913i	−0.750363	−	0.911513i
$426$	7.89396	−	4.55758i	0.382464	−	0.220815i
$427$	−24.1603	+	13.9489i	−1.16920	+	0.675036i
$428$	−0.104468	−	0.104468i	−0.00504966	−	0.00504966i
$429$	7.61391	+	8.95315i	0.367603	+	0.432262i
$430$	1.72460	+	1.11012i	0.0831675	+	0.0535348i
$431$	1.03576	+	0.277531i	0.0498907	+	0.0133682i	0.283678	−	0.958920i	$-0.408445\pi$
$431$	1.03576	+	0.277531i	0.0498907	+	0.0133682i	−0.233787	+	0.972288i	$0.575112\pi$
$432$	−0.258819	+	0.965926i	−0.0124524	+	0.0464731i
$433$	9.34471	−	2.50391i	0.449078	−	0.120330i	−0.0271899	−	0.999630i	$-0.508656\pi$
$433$	9.34471	−	2.50391i	0.449078	−	0.120330i	0.476268	+	0.879300i	$0.341989\pi$
$434$	−10.0664	−	10.0664i	−0.483202	−	0.483202i
$435$	−16.0526	+	8.26081i	−0.769665	+	0.396076i
$436$	−18.7436	+	5.02232i	−0.897654	+	0.240526i
$437$			29.9386i			1.43216i
$438$	0.935528	+	3.49144i	0.0447013	+	0.166827i
$439$	17.4946	+	30.3016i	0.834974	+	1.44622i	0.894052	+	0.447963i	$0.147850\pi$
$439$	17.4946	+	30.3016i	0.834974	+	1.44622i	−0.0590785	+	0.998253i	$0.518816\pi$
$440$	−0.352157	+	7.28032i	−0.0167884	+	0.347076i
$441$			0.400942i			0.0190925i
$442$	7.52244	+	15.8576i	0.357806	+	0.754271i
$443$	−1.29818	+	1.29818i	−0.0616784	+	0.0616784i	−0.737273	−	0.675595i	$-0.763887\pi$
$443$	−1.29818	+	1.29818i	−0.0616784	+	0.0616784i	0.675595	+	0.737273i	$0.263887\pi$
$444$	2.21186	−	8.25479i	0.104970	−	0.391755i
$445$	−5.31657	−	0.257168i	−0.252030	−	0.0121909i
$446$	−10.4760	−	6.04831i	−0.496052	−	0.286396i
$447$	−4.83532			−0.228703
$448$	2.35599	+	1.36023i	0.111310	+	0.0642650i
$449$	−4.99803	−	18.6529i	−0.235872	−	0.880285i	−0.977754	−	0.209755i	$-0.932733\pi$
$449$	−4.99803	−	18.6529i	−0.235872	−	0.880285i	0.741882	−	0.670530i	$-0.233933\pi$
$450$	−2.07040	−	4.55120i	−0.0975996	−	0.214546i
$451$	11.9076	−	20.6246i	0.560709	−	0.971177i
$452$	−15.1813	−	4.06783i	−0.714070	−	0.191335i
$453$	−0.617306	−	1.06920i	−0.0290036	−	0.0502356i
$454$	−25.6895			−1.20567
$455$	−13.3189	+	17.4261i	−0.624398	+	0.816948i
$456$	5.44767			0.255111
$457$	3.88466	+	6.72844i	0.181717	+	0.314743i	0.942465	−	0.334304i	$-0.108501\pi$
$457$	3.88466	+	6.72844i	0.181717	+	0.314743i	−0.760748	+	0.649047i	$0.775168\pi$
$458$	−24.1343	−	6.46677i	−1.12772	−	0.302172i
$459$	−2.43394	+	4.21571i	−0.113607	+	0.196773i
$460$	−10.3330	−	6.65135i	−0.481780	−	0.310121i
$461$	1.16821	+	4.35982i	0.0544090	+	0.203057i	0.987780	−	0.155857i	$-0.0498138\pi$
$461$	1.16821	+	4.35982i	0.0544090	+	0.203057i	−0.933371	+	0.358914i	$0.883147\pi$
$462$	7.67975	+	4.43391i	0.357294	+	0.206284i
$463$	−28.7621			−1.33669			−0.668345	−	0.743851i	$-0.732997\pi$
$463$	−28.7621			−1.33669			−0.668345	+	0.743851i	$0.732997\pi$
$464$	6.99208	+	4.03688i	0.324599	+	0.187407i
$465$	8.66408	−	7.86457i	0.401787	−	0.364711i
$466$	2.51616	−	9.39043i	0.116559	−	0.435003i
$467$	3.32576	−	3.32576i	0.153898	−	0.153898i	−0.625959	−	0.779856i	$-0.715292\pi$
$467$	3.32576	−	3.32576i	0.153898	−	0.153898i	0.779856	+	0.625959i	$0.215292\pi$
$468$	0.649535	+	3.54656i	0.0300248	+	0.163940i
$469$		−	22.3832i		−	1.03356i
$470$	13.5041	−	12.2579i	0.622897	−	0.565417i
$471$	7.79223	+	13.4965i	0.359047	+	0.621887i
$472$	−0.540573	−	2.01745i	−0.0248819	−	0.0928605i
$473$		−	2.98988i		−	0.137475i
$474$	4.70501	−	1.26070i	0.216108	−	0.0579060i
$475$	−21.0295	+	17.3116i	−0.964898	+	0.794310i
$476$	9.36416	+	9.36416i	0.429206	+	0.429206i
$477$	5.43174	−	1.45543i	0.248702	−	0.0666396i
$478$	4.70387	−	17.5551i	0.215150	−	0.802950i
$479$	−20.9252	−	5.60688i	−0.956095	−	0.256185i	−0.253148	−	0.967427i	$-0.581466\pi$
$479$	−20.9252	−	5.60688i	−0.956095	−	0.256185i	−0.702947	+	0.711243i	$0.748133\pi$
$480$	−1.21029	+	1.88021i	−0.0552419	+	0.0858196i
$481$	−5.55091	−	30.3089i	−0.253100	−	1.38197i
$482$	−2.52841	−	2.52841i	−0.115166	−	0.115166i
$483$	−12.9478	+	7.47539i	−0.589143	+	0.340142i
$484$	−0.324398	+	0.187292i	−0.0147454	+	0.00851325i
$485$	7.61439	−	23.7598i	0.345752	−	1.07888i
$486$	−0.707107	+	0.707107i	−0.0320750	+	0.0320750i
$487$	13.2974	−	23.0318i	0.602564	−	1.04367i	−0.389867	−	0.920871i	$-0.627479\pi$
$487$	13.2974	−	23.0318i	0.602564	−	1.04367i	0.992431	−	0.122801i	$-0.0391877\pi$
$488$	−5.12740	+	8.88092i	−0.232107	+	0.402021i
$489$	−15.0280	+	15.0280i	−0.679591	+	0.679591i
$490$	−0.273609	+	0.853764i	−0.0123604	+	0.0385691i
$491$	20.0030	−	11.5487i	0.902722	−	0.521187i	0.0246394	−	0.999696i	$-0.492156\pi$
$491$	20.0030	−	11.5487i	0.902722	−	0.521187i	0.878082	+	0.478510i	$0.158823\pi$
$492$	6.32723	−	3.65303i	0.285253	−	0.164691i
$493$	27.7908	+	27.7908i	1.25164	+	1.25164i
$494$	17.7464	−	8.41840i	0.798447	−	0.378762i
$495$	−3.94514	+	6.12886i	−0.177321	+	0.275472i
$496$	−5.05462	−	1.35438i	−0.226959	−	0.0608135i
$497$	6.41806	−	23.9525i	0.287890	−	1.07442i
$498$	−13.2057	+	3.53847i	−0.591763	+	0.158563i
$499$	2.16948	+	2.16948i	0.0971194	+	0.0971194i	0.753997	−	0.656878i	$-0.228123\pi$
$499$	2.16948	+	2.16948i	0.0971194	+	0.0971194i	−0.656878	+	0.753997i	$0.728123\pi$
$500$	−1.30289	−	11.1042i	−0.0582669	−	0.496593i
$501$	18.8375	−	5.04749i	0.841597	−	0.225505i
$502$			0.802161i			0.0358022i
$503$	−1.93899	−	7.23640i	−0.0864552	−	0.322655i	0.909131	−	0.416511i	$-0.136747\pi$
$503$	−1.93899	−	7.23640i	−0.0864552	−	0.322655i	−0.995586	+	0.0938561i	$0.970081\pi$
$504$	1.36023	+	2.35599i	0.0605896	+	0.104944i
$505$	23.1311	−	20.9966i	1.02932	−	0.934336i
$506$			17.9140i			0.796376i
$507$	7.59650	+	10.5496i	0.337372	+	0.468522i
$508$	11.4840	−	11.4840i	0.509518	−	0.509518i
$509$	−3.60812	+	13.4657i	−0.159927	+	0.596855i	0.838706	+	0.544584i	$0.183313\pi$
$509$	−3.60812	+	13.4657i	−0.159927	+	0.596855i	−0.998633	+	0.0522710i	$0.983354\pi$
$510$	−8.05968	+	7.31595i	−0.356889	+	0.323956i
$511$	8.51598	+	4.91670i	0.376725	+	0.217502i
$512$	1.00000			0.0441942
$513$	4.71782	+	2.72384i	0.208297	+	0.120260i
$514$	−1.33793	−	4.99322i	−0.0590135	−	0.220242i
$515$	−1.92882	−	1.24158i	−0.0849941	−	0.0547105i
$516$	0.458618	−	0.794350i	0.0201895	−	0.0349693i
$517$	−25.6806	−	6.88108i	−1.12943	−	0.302630i
$518$	−11.6245	−	20.1343i	−0.510753	−	0.884650i
$519$	6.06923			0.266410
$520$	−1.03711	+	7.99527i	−0.0454804	+	0.350616i
$521$	−17.5034			−0.766836			−0.383418	−	0.923575i	$-0.625253\pi$
$521$	−17.5034			−0.766836			−0.383418	+	0.923575i	$0.625253\pi$
$522$	4.03688	+	6.99208i	0.176689	+	0.306035i
$523$	−1.28354	−	0.343924i	−0.0561254	−	0.0150388i	0.230647	−	0.973037i	$-0.425916\pi$
$523$	−1.28354	−	0.343924i	−0.0561254	−	0.0150388i	−0.286773	+	0.957999i	$0.592582\pi$
$524$	−0.475908	+	0.824297i	−0.0207901	+	0.0360096i
$525$	−12.7377	−	4.77222i	−0.555920	−	0.208277i
$526$	1.35208	+	5.04602i	0.0589534	+	0.220017i
$527$	−22.0605	−	12.7366i	−0.960972	−	0.554817i
$528$	3.25967			0.141859
$529$	−6.23743	−	3.60118i	−0.271193	−	0.156573i
$530$	12.5595	+	0.607517i	0.545551	+	0.0263888i
$531$	0.540573	−	2.01745i	0.0234589	−	0.0875497i
$532$	10.4795	−	10.4795i	0.454343	−	0.454343i
$533$	14.9665	−	21.6777i	0.648271	−	0.938966i
$534$			2.38042i			0.103011i
$535$	0.0159611	−	0.329972i	0.000690058	−	0.0142659i
$536$	−4.11386	−	7.12541i	−0.177692	−	0.307771i
$537$	−0.219581	−	0.819489i	−0.00947564	−	0.0353636i
$538$			31.9263i			1.37644i
$539$	1.26241	−	0.338260i	0.0543756	−	0.0145699i
$540$	−1.98825	+	1.02317i	−0.0855605	+	0.0440301i
$541$	10.8201	+	10.8201i	0.465192	+	0.465192i	0.900353	−	0.435161i	$-0.143308\pi$
$541$	10.8201	+	10.8201i	0.465192	+	0.465192i	−0.435161	+	0.900353i	$0.643308\pi$
$542$	−15.1154	+	4.05016i	−0.649263	+	0.173969i
$543$	−2.05138	+	7.65584i	−0.0880330	+	0.328544i
$544$	4.70202	+	1.25990i	0.201597	+	0.0540178i
$545$	−36.4851	−	23.4854i	−1.56285	−	1.00600i
$546$	8.07187	+	5.57290i	0.345444	+	0.238498i
$547$	−7.31164	−	7.31164i	−0.312623	−	0.312623i	0.533302	−	0.845925i	$-0.320951\pi$
$547$	−7.31164	−	7.31164i	−0.312623	−	0.312623i	−0.845925	+	0.533302i	$0.820951\pi$
$548$	−13.4188	+	7.74732i	−0.573221	+	0.330949i
$549$	−8.88092	+	5.12740i	−0.379029	+	0.218832i
$550$	−12.5832	+	10.3585i	−0.536548	+	0.441689i
$551$	31.1008	−	31.1008i	1.32494	−	1.32494i
$552$	−2.74783	+	4.75939i	−0.116956	+	0.202573i
$553$	6.62568	−	11.4760i	0.281752	−	0.488010i
$554$	−14.0763	+	14.0763i	−0.598046	+	0.598046i
$555$	16.9915	−	8.74398i	0.721250	−	0.371161i
$556$	4.37938	−	2.52843i	0.185727	−	0.107229i
$557$	14.9775	−	8.64726i	0.634617	−	0.366396i	−0.147921	−	0.988999i	$-0.547258\pi$
$557$	14.9775	−	8.64726i	0.634617	−	0.366396i	0.782538	+	0.622603i	$0.213925\pi$
$558$	−3.70024	−	3.70024i	−0.156644	−	0.156644i
$559$	0.266471	−	3.29639i	0.0112705	−	0.139422i
$560$	1.28871	+	5.94508i	0.0544578	+	0.251225i
$561$	15.3270	+	4.10686i	0.647106	+	0.173392i
$562$	5.87017	−	21.9078i	0.247618	−	0.924123i
$563$	18.1270	−	4.85712i	0.763962	−	0.204703i	0.144260	−	0.989540i	$-0.453920\pi$
$563$	18.1270	−	4.85712i	0.763962	−	0.204703i	0.619702	+	0.784837i	$0.287253\pi$
$564$	−5.76730	−	5.76730i	−0.242847	−	0.242847i
$565$	−16.0810	−	31.2491i	−0.676533	−	1.31466i
$566$	−7.21112	+	1.93221i	−0.303106	+	0.0812170i
$567$			2.72047i			0.114249i
$568$	−2.35918	−	8.80457i	−0.0989889	−	0.369432i
$569$	−2.23653	−	3.87379i	−0.0937604	−	0.162398i	0.815330	−	0.578996i	$-0.196555\pi$
$569$	−2.23653	−	3.87379i	−0.0937604	−	0.162398i	−0.909091	+	0.416599i	$0.863222\pi$
$570$	8.18731	+	9.01963i	0.342929	+	0.377791i
$571$			12.8576i			0.538072i	0.963130	+	0.269036i	$0.0867051\pi$
$571$			12.8576i			0.538072i	−0.963130	+	0.269036i	$0.913295\pi$
$572$	10.6187	−	5.03723i	0.443990	−	0.210617i
$573$	−2.07276	+	2.07276i	−0.0865906	+	0.0865906i
$574$	5.14426	−	19.1986i	0.214717	−	0.801335i
$575$	−4.51698	−	27.1045i	−0.188371	−	1.13034i
$576$	0.866025	+	0.500000i	0.0360844	+	0.0208333i
$577$	−33.9654			−1.41400			−0.706998	−	0.707215i	$-0.749951\pi$
$577$	−33.9654			−1.41400			−0.706998	+	0.707215i	$0.749951\pi$
$578$	5.79917	+	3.34815i	0.241214	+	0.139265i
$579$	2.58337	+	9.64125i	0.107361	+	0.400677i
$580$	3.82460	+	17.6437i	0.158808	+	0.732615i
$581$	−18.5966	+	32.2102i	−0.771515	+	1.33630i
$582$	−10.7778	−	2.88791i	−0.446755	−	0.119708i
$583$	−9.16512	−	15.8745i	−0.379581	−	0.657453i
$584$	3.61460			0.149573
$585$	−4.89580	+	6.40555i	−0.202416	+	0.264837i
$586$	7.50662			0.310096
$587$	21.6991	+	37.5840i	0.895619	+	1.55126i	0.833036	+	0.553218i	$0.186600\pi$
$587$	21.6991	+	37.5840i	0.895619	+	1.55126i	0.0625828	+	0.998040i	$0.480066\pi$
$588$	0.387281	+	0.103772i	0.0159712	+	0.00427947i
$589$	−14.2537	+	24.6880i	−0.587311	+	1.01725i
$590$	2.52783	−	3.92704i	0.104069	−	0.161674i
$591$	−3.74649	−	13.9821i	−0.154110	−	0.575146i
$592$	−7.40104	−	4.27299i	−0.304181	−	0.175619i
$593$	14.3082			0.587568			0.293784	−	0.955872i	$-0.405085\pi$
$593$	14.3082			0.587568			0.293784	+	0.955872i	$0.405085\pi$
$594$	2.82295	+	1.62983i	0.115827	+	0.0668728i
$595$	−1.43069	+	29.5775i	−0.0586527	+	1.21256i
$596$	−1.25147	+	4.67056i	−0.0512623	+	0.191314i
$597$	8.36805	−	8.36805i	0.342481	−	0.342481i
$598$	−1.59658	+	19.7505i	−0.0652889	+	0.807657i
$599$		−	42.8495i		−	1.75078i	−0.483416	−	0.875391i	$-0.660604\pi$
$599$		−	42.8495i		−	1.75078i	0.483416	−	0.875391i	$-0.339396\pi$
$600$	−4.93198	+	0.821916i	−0.201347	+	0.0335546i
$601$	20.4039	+	35.3406i	0.832293	+	1.44157i	0.896216	+	0.443619i	$0.146305\pi$
$601$	20.4039	+	35.3406i	0.832293	+	1.44157i	−0.0639230	+	0.997955i	$0.520361\pi$
$602$	−0.645834	−	2.41028i	−0.0263222	−	0.0982359i
$603$		−	8.22772i		−	0.335058i
$604$	−1.19254	+	0.319541i	−0.0485239	+	0.0130019i
$605$	−0.797634	−	0.255621i	−0.0324284	−	0.0103925i
$606$	−9.87879	−	9.87879i	−0.401298	−	0.401298i
$607$	28.7782	−	7.71108i	1.16807	−	0.312983i	0.377885	−	0.925852i	$-0.376651\pi$
$607$	28.7782	−	7.71108i	1.16807	−	0.312983i	0.790184	+	0.612869i	$0.209985\pi$
$608$	1.40996	−	5.26205i	0.0571815	−	0.213404i
$609$	21.2160	+	5.68481i	0.859715	+	0.230360i
$610$	−22.4100	+	4.85778i	−0.907354	+	0.196686i
$611$	−27.6999	−	9.87526i	−1.12062	−	0.399510i
$612$	3.44211	+	3.44211i	0.139139	+	0.139139i
$613$	−21.9802	+	12.6903i	−0.887772	+	0.512555i	−0.873213	−	0.487339i	$-0.837968\pi$
$613$	−21.9802	+	12.6903i	−0.887772	+	0.512555i	−0.0145590	+	0.999894i	$0.504634\pi$
$614$	11.6243	−	6.71129i	0.469119	−	0.270846i
$615$	15.5575	+	4.98576i	0.627337	+	0.201045i
$616$	6.27049	−	6.27049i	0.252645	−	0.252645i
$617$	7.43592	−	12.8794i	0.299359	−	0.518505i	−0.676631	−	0.736323i	$-0.736561\pi$
$617$	7.43592	−	12.8794i	0.299359	−	0.518505i	0.975989	+	0.217818i	$0.0698939\pi$
$618$	−0.512927	+	0.888416i	−0.0206329	+	0.0357373i
$619$	10.7609	−	10.7609i	0.432517	−	0.432517i	−0.456967	−	0.889484i	$-0.651064\pi$
$619$	10.7609	−	10.7609i	0.432517	−	0.432517i	0.889484	+	0.456967i	$0.151064\pi$
$620$	−5.35416	−	10.4044i	−0.215028	−	0.417849i
$621$	−4.75939	+	2.74783i	−0.190988	+	0.110267i
$622$	18.3671	−	10.6043i	0.736454	−	0.425192i
$623$	4.57912	+	4.57912i	0.183459	+	0.183459i
$624$	3.59383	+	0.290516i	0.143868	+	0.0116299i
$625$	16.4269	−	18.8456i	0.657075	−	0.753825i
$626$	13.5179	+	3.62211i	0.540284	+	0.144769i
$627$	4.59600	−	17.1525i	0.183547	−	0.685006i
$628$	15.0534	−	4.03355i	0.600697	−	0.160956i
$629$	−29.4163	−	29.4163i	−1.17290	−	1.17290i
$630$	−1.85649	+	5.79294i	−0.0739642	+	0.230796i
$631$	−23.8567	+	6.39238i	−0.949720	+	0.254477i	−0.700243	−	0.713904i	$-0.746925\pi$
$631$	−23.8567	+	6.39238i	−0.949720	+	0.254477i	−0.249476	+	0.968381i	$0.580259\pi$
$632$		−	4.87099i		−	0.193757i
$633$	1.21759	+	4.54411i	0.0483949	+	0.180612i
$634$	−12.5718	−	21.7750i	−0.499290	−	0.864796i
$635$	36.2731	+	1.75457i	1.43945	+	0.0696278i
$636$		−	5.62335i		−	0.222980i
$637$	1.42197	−	0.260426i	0.0563404	−	0.0103185i
$638$	18.6095	−	18.6095i	0.736756	−	0.736756i
$639$	2.35918	−	8.80457i	0.0933276	−	0.348303i
$640$	1.50290	+	1.65568i	0.0594074	+	0.0654467i
$641$	17.7629	+	10.2554i	0.701591	+	0.405064i	0.807940	−	0.589265i	$-0.200583\pi$
$641$	17.7629	+	10.2554i	0.701591	+	0.405064i	−0.106349	+	0.994329i	$0.533916\pi$
$642$	−0.147740			−0.00583085
$643$	−5.70747	−	3.29521i	−0.225081	−	0.129950i	0.383220	−	0.923657i	$-0.374815\pi$
$643$	−5.70747	−	3.29521i	−0.225081	−	0.129950i	−0.608301	+	0.793707i	$0.708148\pi$
$644$	3.86955	+	14.4413i	0.152482	+	0.569069i
$645$	2.00445	−	0.434502i	0.0789251	−	0.0171085i
$646$	13.2593	−	22.9658i	0.521681	−	0.903578i
$647$	6.26074	+	1.67756i	0.246135	+	0.0659516i	0.379777	−	0.925078i	$-0.376001\pi$
$647$	6.26074	+	1.67756i	0.246135	+	0.0659516i	−0.133642	+	0.991030i	$0.542667\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−6.80818			−0.267244
$650$	−14.7963	+	10.2990i	−0.580360	+	0.403959i
$651$	−14.2360			−0.557953
$652$	10.6264	+	18.4055i	0.416163	+	0.720815i
$653$	−7.89693	−	2.11598i	−0.309031	−	0.0828045i	0.100971	−	0.994889i	$-0.467805\pi$
$653$	−7.89693	−	2.11598i	−0.309031	−	0.0828045i	−0.410001	+	0.912085i	$0.634472\pi$
$654$	−9.70238	+	16.8050i	−0.379393	+	0.657128i
$655$	−2.08002	+	0.450882i	−0.0812730	+	0.0176174i
$656$	−1.89095	−	7.05711i	−0.0738290	−	0.275534i
$657$	3.13034	+	1.80730i	0.122126	+	0.0705095i
$658$	−22.1887			−0.865004
$659$	14.2650	+	8.23589i	0.555684	+	0.320825i	0.751412	−	0.659834i	$-0.229373\pi$
$659$	14.2650	+	8.23589i	0.555684	+	0.320825i	−0.195727	+	0.980658i	$0.562707\pi$
$660$	4.89895	+	5.39698i	0.190691	+	0.210077i
$661$	5.53086	−	20.6415i	0.215126	−	0.802860i	−0.770997	−	0.636839i	$-0.780241\pi$
$661$	5.53086	−	20.6415i	0.215126	−	0.802860i	0.986122	−	0.166021i	$-0.0530919\pi$
$662$	23.0496	−	23.0496i	0.895847	−	0.895847i
$663$	16.5322	+	5.89388i	0.642058	+	0.228899i
$664$			13.6716i			0.530561i
$665$	33.1003	+	1.60110i	1.28358	+	0.0620879i
$666$	−4.27299	−	7.40104i	−0.165575	−	0.286784i
$667$	11.4840	+	42.8588i	0.444662	+	1.65950i
$668$		−	19.5020i		−	0.754555i
$669$	−11.6844	+	3.13083i	−0.451746	+	0.121045i
$670$	5.61471	−	17.5200i	0.216915	−	0.676858i
$671$	23.6366	+	23.6366i	0.912482	+	0.912482i
$672$	2.62777	−	0.704109i	0.101368	−	0.0271616i
$673$	−10.9464	+	40.8527i	−0.421954	+	1.57475i	0.348532	+	0.937297i	$0.386680\pi$
$673$	−10.9464	+	40.8527i	−0.421954	+	1.57475i	−0.770486	+	0.637457i	$0.779986\pi$
$674$	−14.7218	−	3.94469i	−0.567062	−	0.151944i
$675$	−4.68218	−	1.75419i	−0.180217	−	0.0675189i
$676$	12.1562	−	4.60723i	0.467547	−	0.177201i
$677$	−5.34294	−	5.34294i	−0.205346	−	0.205346i	0.596940	−	0.802286i	$-0.296383\pi$
$677$	−5.34294	−	5.34294i	−0.205346	−	0.205346i	−0.802286	+	0.596940i	$0.796383\pi$
$678$	−13.6112	+	7.85844i	−0.522736	+	0.301802i
$679$	−26.2882	+	15.1775i	−1.00885	+	0.582459i
$680$	4.98066	+	9.67856i	0.191000	+	0.371156i
$681$	−18.1652	+	18.1652i	−0.696093	+	0.696093i
$682$	−8.52880	+	14.7723i	−0.326585	+	0.565661i
$683$	0.902519	−	1.56321i	0.0345339	−	0.0598145i	−0.848242	−	0.529609i	$-0.822339\pi$
$683$	0.902519	−	1.56321i	0.0345339	−	0.0598145i	0.882776	+	0.469794i	$0.155672\pi$
$684$	3.85209	−	3.85209i	0.147288	−	0.147288i
$685$	−32.9942	−	10.5738i	−1.26064	−	0.404003i
$686$	−15.5473	+	8.97626i	−0.593600	+	0.342715i
$687$	−21.6382	+	12.4928i	−0.825550	+	0.476631i
$688$	−0.648584	−	0.648584i	−0.0247270	−	0.0247270i
$689$	−8.68988	−	18.3187i	−0.331058	−	0.697885i
$690$	−12.0098	+	2.60334i	−0.457204	+	0.0991075i
$691$	−15.7869	−	4.23010i	−0.600563	−	0.160920i	−0.0542868	−	0.998525i	$-0.517289\pi$
$691$	−15.7869	−	4.23010i	−0.600563	−	0.160920i	−0.546276	+	0.837605i	$0.683955\pi$
$692$	1.57083	−	5.86243i	0.0597141	−	0.222856i
$693$	8.56565	−	2.29516i	0.325382	−	0.0871859i
$694$	1.50992	+	1.50992i	0.0573159	+	0.0573159i
$695$	10.7681	+	3.45088i	0.408456	+	0.130899i
$696$	7.79865	−	2.08964i	0.295607	−	0.0792077i
$697$		−	35.5650i		−	1.34712i
$698$	−6.77169	−	25.2723i	−0.256312	−	0.956570i
$699$	−4.86085	−	8.41923i	−0.183854	−	0.318445i
$700$	−7.90638	+	11.0685i	−0.298833	+	0.418352i
$701$			12.7686i			0.482265i	0.970492	+	0.241133i	$0.0775189\pi$
$701$			12.7686i			0.482265i	−0.970492	+	0.241133i	$0.922481\pi$
$702$	2.96709	+	2.04851i	0.111986	+	0.0773159i
$703$	−32.9199	+	32.9199i	−1.24160	+	1.24160i
$704$	0.843663	−	3.14859i	0.0317968	−	0.118667i
$705$	0.881151	−	18.2165i	0.0331861	−	0.686073i
$706$	−5.74611	−	3.31752i	−0.216258	−	0.124856i
$707$	−38.0069			−1.42940
$708$	−1.80879	−	1.04431i	−0.0679786	−	0.0392474i
$709$	−3.23327	−	12.0667i	−0.121428	−	0.453176i	0.878259	−	0.478185i	$-0.158705\pi$
$709$	−3.23327	−	12.0667i	−0.121428	−	0.453176i	−0.999687	+	0.0250091i	$0.992039\pi$
$710$	11.0320	−	17.1384i	0.414023	−	0.643194i
$711$	2.43549	−	4.21840i	0.0913381	−	0.158202i
$712$	2.29931	+	0.616098i	0.0861703	+	0.0230893i
$713$	−14.3792	−	24.9055i	−0.538506	−	0.932720i
$714$	13.2429			0.495604
$715$	24.2989	+	10.0108i	0.908727	+	0.374381i
$716$	−0.848398			−0.0317061
$717$	−9.08717	−	15.7394i	−0.339367	−	0.587800i
$718$	8.80943	+	2.36048i	0.328765	+	0.0880923i
$719$	−15.7197	+	27.2274i	−0.586248	+	1.01541i	0.408471	+	0.912771i	$0.366062\pi$
$719$	−15.7197	+	27.2274i	−0.586248	+	1.01541i	−0.994719	+	0.102639i	$0.967271\pi$
$720$	0.473708	+	2.18531i	0.0176540	+	0.0814419i
$721$	0.722313	+	2.69571i	0.0269003	+	0.100393i
$722$	−9.24669	−	5.33858i	−0.344126	−	0.198681i
$723$	−3.57572			−0.132982
$724$	6.86404	+	3.96296i	0.255100	+	0.147282i
$725$	−23.4644	+	32.8491i	−0.871447	+	1.21998i
$726$	−0.0969492	+	0.361819i	−0.00359812	+	0.0134284i
$727$	−26.0642	+	26.0642i	−0.966669	+	0.966669i	−0.999462	−	0.0327933i	$-0.989560\pi$
$727$	−26.0642	+	26.0642i	−0.966669	+	0.966669i	0.0327933	+	0.999462i	$0.489560\pi$
$728$	7.47216	−	6.35445i	0.276937	−	0.235512i
$729$			1.00000i			0.0370370i
$730$	5.43239	+	5.98464i	0.201062	+	0.221501i
$731$	−2.23250	−	3.86680i	−0.0825720	−	0.143019i
$732$	2.65414	+	9.90538i	0.0980998	+	0.366113i
$733$		−	12.8808i		−	0.475762i	−0.971294	−	0.237881i	$-0.923547\pi$
$733$		−	12.8808i		−	0.475762i	0.971294	−	0.237881i	$-0.0764528\pi$
$734$	32.2142	−	8.63177i	1.18905	−	0.318604i
$735$	0.410231	+	0.797173i	0.0151316	+	0.0294042i
$736$	3.88602	+	3.88602i	0.143241	+	0.143241i
$737$	−25.9057	+	6.94142i	−0.954250	+	0.255691i
$738$	1.89095	−	7.05711i	0.0696067	−	0.259776i
$739$	24.3881	+	6.53477i	0.897130	+	0.240385i	0.677783	−	0.735262i	$-0.262941\pi$
$739$	24.3881	+	6.53477i	0.897130	+	0.240385i	0.219347	+	0.975647i	$0.429607\pi$
$740$	−4.04830	−	18.6757i	−0.148818	−	0.686531i
$741$	6.59587	−	18.5013i	0.242305	−	0.679662i
$742$	−10.8174	−	10.8174i	−0.397120	−	0.397120i
$743$	−24.3770	+	14.0741i	−0.894307	+	0.516328i	−0.875349	−	0.483492i	$-0.839368\pi$
$743$	−24.3770	+	14.0741i	−0.894307	+	0.516328i	−0.0189582	+	0.999820i	$0.506035\pi$
$744$	−4.53185	+	2.61646i	−0.166146	+	0.0959243i
$745$	−9.61381	+	4.94734i	−0.352223	+	0.181257i
$746$	4.47217	−	4.47217i	0.163738	−	0.163738i
$747$	−6.83580	+	11.8399i	−0.250109	+	0.433201i
$748$	7.93384	−	13.7418i	0.290090	−	0.502450i
$749$	−0.284203	+	0.284203i	−0.0103845	+	0.0103845i
$750$	−8.77311	−	6.93055i	−0.320349	−	0.253068i
$751$	31.6885	−	18.2954i	1.15633	−	0.667607i	0.205908	−	0.978571i	$-0.433985\pi$
$751$	31.6885	−	18.2954i	1.15633	−	0.667607i	0.950422	+	0.310965i	$0.100652\pi$
$752$	−7.06347	+	4.07810i	−0.257578	+	0.148713i
$753$	0.567213	+	0.567213i	0.0206704	+	0.0206704i
$754$	22.1758	−	18.8586i	0.807594	−	0.686792i
$755$	−2.32133	−	1.49424i	−0.0844819	−	0.0543808i
$756$	2.62777	+	0.704109i	0.0955711	+	0.0256082i
$757$	−3.57146	+	13.3289i	−0.129807	+	0.484446i	−0.999965	−	0.00832612i	$-0.997350\pi$
$757$	−3.57146	+	13.3289i	−0.129807	+	0.484446i	0.870158	+	0.492772i	$0.164016\pi$
$758$	−9.75996	+	2.61517i	−0.354498	+	0.0949874i
$759$	12.6671	+	12.6671i	0.459788	+	0.459788i
$760$	10.8313	−	5.57388i	0.392893	−	0.202186i
$761$	30.0292	−	8.04629i	1.08856	−	0.291678i	0.330460	−	0.943820i	$-0.392796\pi$
$761$	30.0292	−	8.04629i	1.08856	−	0.291678i	0.758097	+	0.652142i	$0.226129\pi$
$762$		−	16.2408i		−	0.588341i
$763$	13.6631	+	50.9913i	0.494636	+	1.84601i
$764$	1.46566	+	2.53860i	0.0530257	+	0.0918432i
$765$	−0.525900	+	10.8722i	−0.0190140	+	0.393086i
$766$			8.68853i			0.313929i
$767$	−7.50612	−	0.606775i	−0.271030	−	0.0219094i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$	−2.05633	+	7.67431i	−0.0741530	+	0.276743i	−0.993040	−	0.117778i	$-0.962423\pi$
$769$	−2.05633	+	7.67431i	−0.0741530	+	0.276743i	0.918887	+	0.394521i	$0.129089\pi$
$770$	19.8059	+	0.958031i	0.713754	+	0.0345250i
$771$	−4.47680	−	2.58468i	−0.161228	−	0.0930850i
$772$	9.98136			0.359237
$773$	−3.07563	−	1.77572i	−0.110623	−	0.0638680i	0.443668	−	0.896191i	$-0.353677\pi$
$773$	−3.07563	−	1.77572i	−0.110623	−	0.0638680i	−0.554291	+	0.832323i	$0.687010\pi$
$774$	−0.237398	−	0.885982i	−0.00853310	−	0.0318460i
$775$	9.17956	−	24.5015i	0.329740	−	0.880121i
$776$	−5.57901	+	9.66313i	−0.200275	+	0.346886i
$777$	−22.4569	−	6.01730i	−0.805636	−	0.215870i
$778$	−11.6708	−	20.2143i	−0.418417	−	0.724719i
$779$	−39.8010			−1.42602
$780$	4.92016	+	6.38686i	0.176170	+	0.228686i
$781$	−29.7124			−1.06319
$782$	13.3761	+	23.1682i	0.478330	+	0.828491i
$783$	7.79865	+	2.08964i	0.278701	+	0.0746778i
$784$	0.200471	−	0.347226i	0.00715969	−	0.0124009i
$785$	29.3021	+	18.8617i	1.04584	+	0.673203i
$786$	0.246348	+	0.919384i	0.00878694	+	0.0327933i
$787$	24.7242	+	14.2745i	0.881322	+	0.508831i	0.871094	−	0.491116i	$-0.163411\pi$
$787$	24.7242	+	14.2745i	0.881322	+	0.508831i	0.0102277	+	0.999948i	$0.496744\pi$
$788$	−14.4753			−0.515662
$789$	4.52414	+	2.61201i	0.161064	+	0.0929901i
$790$	8.06481	−	7.32061i	0.286933	−	0.260455i
$791$	−11.0664	+	41.3004i	−0.393476	+	1.46847i
$792$	2.30493	−	2.30493i	0.0819022	−	0.0819022i
$793$	23.9531	+	28.1663i	0.850600	+	1.00022i
$794$			12.6230i			0.447975i
$795$	9.31050	−	8.45134i	0.330209	−	0.299738i
$796$	−5.91710	−	10.2487i	−0.209726	−	0.363256i
$797$	−11.5587	−	43.1377i	−0.409430	−	1.52801i	−0.795736	−	0.605644i	$-0.792916\pi$
$797$	−11.5587	−	43.1377i	−0.409430	−	1.52801i	0.386306	−	0.922371i	$-0.373751\pi$
$798$		−	14.8202i		−	0.524630i
$799$	−38.3506	+	10.2760i	−1.35675	+	0.363539i
$800$	−0.482581	+	4.97666i	−0.0170618	+	0.175951i
$801$	1.68321	+	1.68321i	0.0594734	+	0.0594734i
$802$	19.1274	−	5.12518i	0.675413	−	0.180976i
$803$	3.04951	−	11.3809i	0.107615	−	0.401624i
$804$	−7.94736	−	2.12949i	−0.280282	−	0.0751013i
$805$	−18.0948	+	28.1107i	−0.637757	+	0.990770i
$806$	−10.7197	+	15.5266i	−0.377585	+	0.546900i
$807$	22.5753	+	22.5753i	0.794689	+	0.794689i
$808$	−12.0990	+	6.98536i	−0.425641	+	0.245744i
$809$	6.88315	−	3.97399i	0.241999	−	0.139718i	−0.374096	−	0.927390i	$-0.622047\pi$
$809$	6.88315	−	3.97399i	0.241999	−	0.139718i	0.616095	+	0.787672i	$0.288714\pi$
$810$	−0.682415	+	2.12939i	−0.0239776	+	0.0748192i
$811$	24.8844	−	24.8844i	0.873810	−	0.873810i	−0.119075	−	0.992885i	$-0.537993\pi$
$811$	24.8844	−	24.8844i	0.873810	−	0.873810i	0.992885	+	0.119075i	$0.0379928\pi$
$812$	10.9822	−	19.0217i	0.385400	−	0.667532i
$813$	−7.82432	+	13.5521i	−0.274411	+	0.475293i
$814$	−19.6979	+	19.6979i	−0.690411	+	0.690411i
$815$	−14.5033	+	45.2556i	−0.508027	+	1.58524i
$816$	4.21571	−	2.43394i	0.147579	−	0.0852050i
$817$	−4.32736	+	2.49840i	−0.151395	+	0.0874080i
$818$	1.09432	+	1.09432i	0.0382621	+	0.0382621i
$819$	9.64831	−	1.76704i	0.337139	−	0.0617453i
$820$	8.84244	−	13.7369i	0.308791	−	0.479715i
$821$	−38.1479	−	10.2217i	−1.33137	−	0.356740i	−0.478146	−	0.878281i	$-0.658691\pi$
$821$	−38.1479	−	10.2217i	−1.33137	−	0.356740i	−0.853226	+	0.521541i	$0.825358\pi$
$822$	−4.01031	+	14.9667i	−0.139876	+	0.522023i
$823$	22.1179	−	5.92648i	0.770982	−	0.206584i	0.148177	−	0.988961i	$-0.452660\pi$
$823$	22.1179	−	5.92648i	0.770982	−	0.206584i	0.622805	+	0.782377i	$0.285993\pi$
$824$	0.725388	+	0.725388i	0.0252701	+	0.0252701i
$825$	−1.57305	+	16.2222i	−0.0547667	+	0.564786i
$826$	−5.48839	+	1.47061i	−0.190966	+	0.0511691i
$827$		−	1.21655i		−	0.0423036i	−0.999776	−	0.0211518i	$-0.993267\pi$
$827$		−	1.21655i		−	0.0423036i	0.999776	−	0.0211518i	$-0.00673333\pi$
$828$	1.42238	+	5.30841i	0.0494312	+	0.184480i
$829$	18.0274	+	31.2244i	0.626118	+	1.08447i	0.988324	+	0.152370i	$0.0486905\pi$
$829$	18.0274	+	31.2244i	0.626118	+	1.08447i	−0.362206	+	0.932098i	$0.617976\pi$
$830$	−22.6358	+	20.5470i	−0.785701	+	0.713198i
$831$			19.9069i			0.690564i
$832$	1.21077	−	3.39618i	0.0419758	−	0.117741i
$833$	1.38009	−	1.38009i	0.0478173	−	0.0478173i
$834$	1.30881	−	4.88456i	0.0453205	−	0.169138i
$835$	32.2891	−	29.3096i	1.11741	−	1.01430i
$836$	−15.3785	−	8.87880i	−0.531878	−	0.307080i
$837$	−5.23293			−0.180877
$838$	−22.9548	−	13.2530i	−0.792962	−	0.457817i
$839$	−6.76489	−	25.2469i	−0.233550	−	0.871620i	−0.978797	−	0.204832i	$-0.934335\pi$
$839$	−6.76489	−	25.2469i	−0.233550	−	0.871620i	0.745247	−	0.666788i	$-0.232331\pi$
$840$	5.11506	+	3.29255i	0.176486	+	0.113604i
$841$	18.0928	−	31.3377i	0.623890	−	1.08061i
$842$	26.6585	+	7.14312i	0.918713	+	0.246168i
$843$	−11.3403	−	19.6420i	−0.390581	−	0.676505i
$844$	4.70441			0.161933
$845$	25.8977	+	13.2026i	0.890908	+	0.454185i
$846$	−8.15619			−0.280416
$847$	0.509520	+	0.882515i	0.0175073	+	0.0303236i
$848$	−5.43174	−	1.45543i	−0.186527	−	0.0499797i
$849$	−3.73275	+	6.46532i	−0.128108	+	0.221889i
$850$	−8.53920	+	22.7923i	−0.292892	+	0.781770i
$851$	−12.1557	−	45.3656i	−0.416691	−	1.55511i
$852$	−7.89396	−	4.55758i	−0.270443	−	0.156140i
$853$	23.3514			0.799537			0.399768	−	0.916616i	$-0.369091\pi$
$853$	23.3514			0.799537			0.399768	+	0.916616i	$0.369091\pi$
$854$	24.1603	+	13.9489i	0.826747	+	0.477323i
$855$	12.1671	+	0.588538i	0.416108	+	0.0201276i
$856$	−0.0382380	+	0.142706i	−0.00130695	+	0.00487760i
$857$	1.91871	−	1.91871i	0.0655420	−	0.0655420i	−0.673576	−	0.739118i	$-0.735243\pi$
$857$	1.91871	−	1.91871i	0.0655420	−	0.0655420i	0.739118	+	0.673576i	$0.235243\pi$
$858$	3.94670	−	11.0704i	0.134738	−	0.377938i
$859$			43.7604i			1.49309i	0.665337	+	0.746543i	$0.268288\pi$
$859$			43.7604i			1.49309i	−0.665337	+	0.746543i	$0.731712\pi$
$860$	0.0990932	−	2.04861i	0.00337905	−	0.0698569i
$861$	−9.93794	−	17.2130i	−0.338684	−	0.586618i
$862$	−0.277531	−	1.03576i	−0.00945273	−	0.0352781i
$863$			44.1406i			1.50256i	0.659981	+	0.751282i	$0.270564\pi$
$863$			44.1406i			1.50256i	−0.659981	+	0.751282i	$0.729436\pi$
$864$	0.965926	−	0.258819i	0.0328615	−	0.00880520i
$865$	12.0671	−	6.20984i	0.410295	−	0.211141i
$866$	−6.84080	−	6.84080i	−0.232460	−	0.232460i
$867$	6.46813	−	1.73313i	0.219669	−	0.0588602i
$868$	−3.68455	+	13.7509i	−0.125062	+	0.466737i
$869$	−15.3368	−	4.10947i	−0.520264	−	0.139404i
$870$	15.1804	+	9.77159i	0.514663	+	0.331288i
$871$	−29.1801	+	5.34419i	−0.988730	+	0.181081i
$872$	13.7212	+	13.7212i	0.464660	+	0.464660i
$873$	−9.66313	+	5.57901i	−0.327047	+	0.188821i
$874$	25.9276	−	14.9693i	0.877014	−	0.506344i
$875$	−30.2085	+	3.54447i	−1.02123	+	0.119825i
$876$	2.55591	−	2.55591i	0.0863562	−	0.0863562i
$877$	9.64408	−	16.7040i	0.325657	−	0.564055i	−0.655988	−	0.754772i	$-0.727748\pi$
$877$	9.64408	−	16.7040i	0.325657	−	0.564055i	0.981645	+	0.190716i	$0.0610811\pi$
$878$	17.4946	−	30.3016i	0.590415	−	1.02263i
$879$	5.30798	−	5.30798i	0.179034	−	0.179034i
$880$	6.48102	−	3.33518i	0.218475	−	0.112429i
$881$	−6.20854	+	3.58450i	−0.209171	+	0.120765i	−0.600926	−	0.799305i	$-0.705201\pi$
$881$	−6.20854	+	3.58450i	−0.209171	+	0.120765i	0.391755	+	0.920070i	$0.371868\pi$
$882$	0.347226	−	0.200471i	0.0116917	−	0.00675022i
$883$	35.6091	+	35.6091i	1.19834	+	1.19834i	0.974663	+	0.223680i	$0.0718071\pi$
$883$	35.6091	+	35.6091i	1.19834	+	1.19834i	0.223680	+	0.974663i	$0.428193\pi$
$884$	9.97190	−	14.4434i	0.335391	−	0.485786i
$885$	−0.989392	−	4.56428i	−0.0332581	−	0.153427i
$886$	1.77335	+	0.475167i	0.0595768	+	0.0159636i
$887$	12.7256	−	47.4925i	0.427283	−	1.59464i	−0.331604	−	0.943419i	$-0.607590\pi$
$887$	12.7256	−	47.4925i	0.427283	−	1.59464i	0.758887	−	0.651223i	$-0.225744\pi$
$888$	−8.25479	+	2.21186i	−0.277013	+	0.0742253i
$889$	−31.2417	−	31.2417i	−1.04781	−	1.04781i
$890$	2.43557	+	4.73287i	0.0816405	+	0.158646i
$891$	3.14859	−	0.843663i	0.105482	−	0.0282638i
$892$			12.0966i			0.405025i
$893$	11.4999	+	42.9183i	0.384830	+	1.43621i
$894$	2.41766	+	4.18751i	0.0808586	+	0.140051i
$895$	−1.27506	−	1.40468i	−0.0426205	−	0.0469532i
$896$		−	2.72047i		−	0.0908844i
$897$	12.8368	+	15.0947i	0.428607	+	0.503996i
$898$	−13.6549	+	13.6549i	−0.455669	+	0.455669i
$899$	−10.9350	+	40.8098i	−0.364701	+	1.36108i
$900$	−2.90626	+	4.06862i	−0.0968752	+	0.135621i
$901$	−23.7064	−	13.6869i	−0.789776	−	0.455977i
$902$	−23.8153			−0.792962
$903$	−2.16100	−	1.24766i	−0.0719136	−	0.0415194i
$904$	4.06783	+	15.1813i	0.135294	+	0.504924i
$905$	3.75457	+	17.3206i	0.124806	+	0.575757i
$906$	−0.617306	+	1.06920i	−0.0205086	+	0.0355220i
$907$	10.1294	+	2.71415i	0.336340	+	0.0901220i	0.423036	−	0.906113i	$-0.360964\pi$
$907$	10.1294	+	2.71415i	0.336340	+	0.0901220i	−0.0866963	+	0.996235i	$0.527631\pi$
$908$	12.8448	+	22.2478i	0.426268	+	0.738318i
$909$	−13.9707			−0.463379
$910$	21.7509	+	2.82143i	0.721035	+	0.0935295i
$911$	31.2425			1.03511			0.517555	−	0.855650i	$-0.326842\pi$
$911$	31.2425			1.03511			0.517555	+	0.855650i	$0.326842\pi$
$912$	−2.72384	−	4.71782i	−0.0901953	−	0.156223i
$913$	43.0463	+	11.5342i	1.42462	+	0.381727i
$914$	3.88466	−	6.72844i	0.128493	−	0.222557i
$915$	−12.4113	+	19.2812i	−0.410304	+	0.637417i
$916$	6.46677	+	24.1343i	0.213668	+	0.797420i
$917$	2.24247	+	1.29469i	0.0740530	+	0.0427545i
$918$	4.86788			0.160664
$919$	−9.89338	−	5.71194i	−0.326352	−	0.188420i	0.327868	−	0.944723i	$-0.393670\pi$
$919$	−9.89338	−	5.71194i	−0.326352	−	0.188420i	−0.654220	+	0.756304i	$0.727003\pi$
$920$	−0.593722	+	12.2743i	−0.0195744	+	0.404673i
$921$	3.47402	−	12.9652i	0.114473	−	0.427219i
$922$	3.19161	−	3.19161i	0.105110	−	0.105110i
$923$	−32.7583	−	2.64810i	−1.07825	−	0.0871631i
$924$		−	8.86781i		−	0.291730i
$925$	24.8368	−	34.7704i	0.816630	−	1.14324i
$926$	14.3811	+	24.9087i	0.472591	+	0.818552i
$927$	0.265511	+	0.990899i	0.00872051	+	0.0325454i
$928$		−	8.07376i		−	0.265034i
$929$	−24.4038	+	6.53897i	−0.800662	+	0.214537i	−0.635874	−	0.771793i	$-0.719360\pi$
$929$	−24.4038	+	6.53897i	−0.800662	+	0.214537i	−0.164787	+	0.986329i	$0.552694\pi$
$930$	−11.1430	−	3.57103i	−0.365392	−	0.117099i
$931$	−1.54447	−	1.54447i	−0.0506178	−	0.0506178i
$932$	−9.39043	+	2.51616i	−0.307594	+	0.0824195i
$933$	5.48917	−	20.4859i	0.179707	−	0.670677i
$934$	−4.54307	−	1.21731i	−0.148654	−	0.0398316i
$935$	34.6759	−	7.51664i	1.13402	−	0.245820i
$936$	2.74665	−	2.33579i	0.0897769	−	0.0763478i
$937$	26.2678	+	26.2678i	0.858133	+	0.858133i	0.991118	−	0.132985i	$-0.0424562\pi$
$937$	26.2678	+	26.2678i	0.858133	+	0.858133i	−0.132985	+	0.991118i	$0.542456\pi$
$938$	−19.3844	+	11.1916i	−0.632925	+	0.365419i
$939$	12.1198	−	6.99738i	0.395515	−	0.228351i
$940$	−17.3677	−	5.56591i	−0.566473	−	0.181540i
$941$	−3.46256	+	3.46256i	−0.112876	+	0.112876i	−0.761289	−	0.648413i	$-0.775433\pi$
$941$	−3.46256	+	3.46256i	−0.112876	+	0.112876i	0.648413	+	0.761289i	$0.275433\pi$
$942$	7.79223	−	13.4965i	0.253884	−	0.439741i
$943$	20.0758	−	34.7723i	0.653759	−	1.13234i
$944$	−1.47687	+	1.47687i	−0.0480681	+	0.0480681i
$945$	2.78349	+	5.40896i	0.0905471	+	0.175954i
$946$	−2.58931	+	1.49494i	−0.0841858	+	0.0486047i
$947$	−42.1464	+	24.3332i	−1.36957	+	0.790724i	−0.990873	−	0.134796i	$-0.956962\pi$
$947$	−42.1464	+	24.3332i	−1.36957	+	0.790724i	−0.378700	+	0.925519i	$0.623629\pi$
$948$	−3.44431	−	3.44431i	−0.111866	−	0.111866i
$949$	4.37644	−	12.2758i	0.142065	−	0.398491i
$950$	25.5070	+	9.55626i	0.827556	+	0.310046i
$951$	−24.2869	−	6.50764i	−0.787555	−	0.211025i
$952$	3.42752	−	12.7917i	0.111087	−	0.414581i
$953$	57.5032	−	15.4079i	1.86271	−	0.499112i	0.862734	−	0.505658i	$-0.168750\pi$
$953$	57.5032	−	15.4079i	1.86271	−	0.499112i	0.999979	+	0.00654619i	$0.00208373\pi$
$954$	−3.97631	−	3.97631i	−0.128738	−	0.128738i
$955$	−2.00038	+	6.24193i	−0.0647306	+	0.201984i
$956$	−17.5551	+	4.70387i	−0.567772	+	0.152134i
$957$		−	26.3178i		−	0.850732i
$958$	5.60688	+	20.9252i	0.181150	+	0.676061i
$959$	21.0763	+	36.5053i	0.680591	+	1.17882i
$960$	2.23346	+	0.108035i	0.0720845	+	0.00348680i
$961$			3.61644i			0.116659i
$962$	−23.4728	+	19.9617i	−0.756793	+	0.643590i
$963$	−0.104468	+	0.104468i	−0.00336644	+	0.00336644i
$964$	−0.925464	+	3.45388i	−0.0298072	+	0.111242i
$965$	15.0010	+	16.5260i	0.482899	+	0.531990i
$966$	12.9478	+	7.47539i	0.416587	+	0.240517i
$967$	−0.0192974			−0.000620562			−0.000310281	−	1.00000i	$-0.500099\pi$
$967$	−0.0192974			−0.000620562			−0.000310281		1.00000i	$0.500099\pi$
$968$	0.324398	+	0.187292i	0.0104266	+	0.00601978i
$969$	−6.86353	−	25.6151i	−0.220488	−	0.822874i
$970$	−24.3838	+	5.28564i	−0.782916	+	0.169712i
$971$	17.0127	−	29.4669i	0.545965	−	0.945639i	−0.452581	−	0.891723i	$-0.649497\pi$
$971$	17.0127	−	29.4669i	0.545965	−	0.945639i	0.998546	−	0.0539153i	$-0.0171701\pi$
$972$	0.965926	+	0.258819i	0.0309821	+	0.00830162i
$973$	−6.87852	−	11.9140i	−0.220515	−	0.381944i
$974$	−26.5949			−0.852155
$975$	−3.18011	+	17.7451i	−0.101845	+	0.568297i
$976$	10.2548			0.328248
$977$	29.4680	+	51.0401i	0.942766	+	1.63292i	0.760164	+	0.649731i	$0.225118\pi$
$977$	29.4680	+	51.0401i	0.942766	+	1.63292i	0.182601	+	0.983187i	$0.441548\pi$
$978$	20.5287	+	5.50064i	0.656435	+	0.175891i
$979$	3.87969	−	6.71982i	0.123995	−	0.214766i
$980$	0.876186	−	0.189930i	0.0279887	−	0.00606708i
$981$	5.02232	+	18.7436i	0.160350	+	0.598436i
$982$	−20.0030	−	11.5487i	−0.638321	−	0.368535i
$983$	50.6557			1.61566			0.807832	−	0.589412i	$-0.200641\pi$
$983$	50.6557			1.61566			0.807832	+	0.589412i	$0.200641\pi$
$984$	−6.32723	−	3.65303i	−0.201705	−	0.116454i
$985$	−21.7550	−	23.9666i	−0.693171	−	0.763638i
$986$	10.1721	−	37.9630i	0.323947	−	1.20899i
$987$	−15.6898	+	15.6898i	−0.499410	+	0.499410i
$988$	−16.1637	−	11.1596i	−0.514237	−	0.355034i
$989$		−	5.04082i		−	0.160289i
$990$	7.28032	+	0.352157i	0.231384	+	0.0111923i
$991$	−19.1464	−	33.1625i	−0.608204	−	1.05344i	−0.991536	−	0.129830i	$-0.958557\pi$
$991$	−19.1464	−	33.1625i	−0.608204	−	1.05344i	0.383332	−	0.923611i	$-0.374776\pi$
$992$	1.35438	+	5.05462i	0.0430017	+	0.160484i
$993$		−	32.5970i		−	1.03444i
$994$	−23.9525	+	6.41806i	−0.759729	+	0.203569i
$995$	8.07584	−	25.1997i	0.256021	−	0.798883i
$996$	9.66727	+	9.66727i	0.306319	+	0.306319i
$997$	48.2254	−	12.9220i	1.52731	−	0.409243i	0.605173	−	0.796094i	$-0.293104\pi$
$997$	48.2254	−	12.9220i	1.52731	−	0.409243i	0.922142	+	0.386852i	$0.126437\pi$
$998$	0.794086	−	2.96357i	0.0251364	−	0.0938102i
$999$	−8.25479	−	2.21186i	−0.261170	−	0.0699803i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.bn.c.67.1	yes	32
5.3	odd	4		390.2.bd.c.223.6	yes	32
13.7	odd	12		390.2.bd.c.7.6	✓	32
65.33	even	12	inner	390.2.bn.c.163.1	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bd.c.7.6	✓	32	13.7	odd	12
390.2.bd.c.223.6	yes	32	5.3	odd	4
390.2.bn.c.67.1	yes	32	1.1	even	1	trivial
390.2.bn.c.163.1	yes	32	65.33	even	12	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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.bn (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.18531 + 0.473708i) q^{5} +(0.258819 + 0.965926i) q^{6} +(2.35599 + 1.36023i) q^{7} +1.00000 q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.18531 + 0.473708i) q^{5} +(0.258819 + 0.965926i) q^{6} +(2.35599 + 1.36023i) q^{7} +1.00000 q^{8} +(0.866025 + 0.500000i) q^{9} +(1.50290 + 1.65568i) q^{10} +(0.843663 - 3.14859i) q^{11} +(0.707107 - 0.707107i) q^{12} +(1.21077 - 3.39618i) q^{13} -2.72047i q^{14} +(2.23346 + 0.108035i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.25990 - 4.70202i) q^{17} -1.00000i q^{18} +(-5.26205 + 1.40996i) q^{19} +(0.682415 - 2.12939i) q^{20} +(-1.92366 - 1.92366i) q^{21} +(-3.14859 + 0.843663i) q^{22} +(1.42238 - 5.30841i) q^{23} +(-0.965926 - 0.258819i) q^{24} +(4.55120 - 2.07040i) q^{25} +(-3.54656 + 0.649535i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-2.35599 + 1.36023i) q^{28} +(-6.99208 + 4.03688i) q^{29} +(-1.02317 - 1.98825i) q^{30} +(3.70024 - 3.70024i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.62983 + 2.82295i) q^{33} +(-3.44211 + 3.44211i) q^{34} +(-5.79294 - 1.85649i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(7.40104 - 4.27299i) q^{37} +(3.85209 + 3.85209i) q^{38} +(-2.04851 + 2.96709i) q^{39} +(-2.18531 + 0.473708i) q^{40} +(7.05711 + 1.89095i) q^{41} +(-0.704109 + 2.62777i) q^{42} +(0.885982 - 0.237398i) q^{43} +(2.30493 + 2.30493i) q^{44} +(-2.12939 - 0.682415i) q^{45} +(-5.30841 + 1.42238i) q^{46} -8.15619i q^{47} +(0.258819 + 0.965926i) q^{48} +(0.200471 + 0.347226i) q^{49} +(-4.06862 - 2.90626i) q^{50} +4.86788i q^{51} +(2.33579 + 2.74665i) q^{52} +(3.97631 - 3.97631i) q^{53} +(-0.258819 + 0.965926i) q^{54} +(-0.352157 + 7.28032i) q^{55} +(2.35599 + 1.36023i) q^{56} +5.44767 q^{57} +(6.99208 + 4.03688i) q^{58} +(-0.540573 - 2.01745i) q^{59} +(-1.21029 + 1.88021i) q^{60} +(-5.12740 + 8.88092i) q^{61} +(-5.05462 - 1.35438i) q^{62} +(1.36023 + 2.35599i) q^{63} +1.00000 q^{64} +(-1.03711 + 7.99527i) q^{65} +3.25967 q^{66} +(-4.11386 - 7.12541i) q^{67} +(4.70202 + 1.25990i) q^{68} +(-2.74783 + 4.75939i) q^{69} +(1.28871 + 5.94508i) q^{70} +(-2.35918 - 8.80457i) q^{71} +(0.866025 + 0.500000i) q^{72} +3.61460 q^{73} +(-7.40104 - 4.27299i) q^{74} +(-4.93198 + 0.821916i) q^{75} +(1.40996 - 5.26205i) q^{76} +(6.27049 - 6.27049i) q^{77} +(3.59383 + 0.290516i) q^{78} -4.87099i q^{79} +(1.50290 + 1.65568i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-1.89095 - 7.05711i) q^{82} +13.6716i q^{83} +(2.62777 - 0.704109i) q^{84} +(4.98066 + 9.67856i) q^{85} +(-0.648584 - 0.648584i) q^{86} +(7.79865 - 2.08964i) q^{87} +(0.843663 - 3.14859i) q^{88} +(2.29931 + 0.616098i) q^{89} +(0.473708 + 2.18531i) q^{90} +(7.47216 - 6.35445i) q^{91} +(3.88602 + 3.88602i) q^{92} +(-4.53185 + 2.61646i) q^{93} +(-7.06347 + 4.07810i) q^{94} +(10.8313 - 5.57388i) q^{95} +(0.707107 - 0.707107i) q^{96} +(-5.57901 + 9.66313i) q^{97} +(0.200471 - 0.347226i) q^{98} +(2.30493 - 2.30493i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{2} - 16 q^{4} - 12 q^{7} + 32 q^{8}+O(q^{10}) \) 32 * q - 16 * q^2 - 16 * q^4 - 12 * q^7 + 32 * q^8	\( 32 q - 16 q^{2} - 16 q^{4} - 12 q^{7} + 32 q^{8} - 4 q^{11} + 8 q^{13} - 4 q^{15} - 16 q^{16} - 4 q^{17} + 20 q^{19} + 8 q^{21} + 8 q^{22} - 16 q^{23} - 8 q^{25} - 4 q^{26} + 12 q^{28} + 24 q^{29} + 8 q^{30} + 12 q^{31} - 16 q^{32} - 16 q^{34} + 12 q^{35} - 24 q^{37} - 4 q^{38} - 20 q^{39} - 28 q^{41} - 16 q^{42} + 4 q^{43} - 4 q^{44} - 4 q^{46} + 20 q^{49} - 8 q^{50} - 4 q^{52} - 4 q^{53} + 68 q^{55} - 12 q^{56} + 16 q^{57} - 24 q^{58} + 36 q^{59} - 4 q^{60} - 28 q^{61} - 48 q^{62} + 32 q^{64} - 28 q^{65} - 28 q^{67} + 20 q^{68} - 20 q^{69} - 24 q^{70} - 4 q^{71} - 48 q^{73} + 24 q^{74} + 24 q^{75} - 16 q^{76} + 20 q^{77} + 4 q^{78} + 16 q^{81} + 44 q^{82} + 8 q^{84} + 64 q^{85} - 8 q^{86} + 20 q^{87} - 4 q^{88} - 16 q^{89} - 40 q^{91} + 20 q^{92} - 24 q^{93} - 24 q^{94} + 68 q^{95} + 8 q^{97} + 20 q^{98} - 4 q^{99}+O(q^{100}) \) 32 * q - 16 * q^2 - 16 * q^4 - 12 * q^7 + 32 * q^8 - 4 * q^11 + 8 * q^13 - 4 * q^15 - 16 * q^16 - 4 * q^17 + 20 * q^19 + 8 * q^21 + 8 * q^22 - 16 * q^23 - 8 * q^25 - 4 * q^26 + 12 * q^28 + 24 * q^29 + 8 * q^30 + 12 * q^31 - 16 * q^32 - 16 * q^34 + 12 * q^35 - 24 * q^37 - 4 * q^38 - 20 * q^39 - 28 * q^41 - 16 * q^42 + 4 * q^43 - 4 * q^44 - 4 * q^46 + 20 * q^49 - 8 * q^50 - 4 * q^52 - 4 * q^53 + 68 * q^55 - 12 * q^56 + 16 * q^57 - 24 * q^58 + 36 * q^59 - 4 * q^60 - 28 * q^61 - 48 * q^62 + 32 * q^64 - 28 * q^65 - 28 * q^67 + 20 * q^68 - 20 * q^69 - 24 * q^70 - 4 * q^71 - 48 * q^73 + 24 * q^74 + 24 * q^75 - 16 * q^76 + 20 * q^77 + 4 * q^78 + 16 * q^81 + 44 * q^82 + 8 * q^84 + 64 * q^85 - 8 * q^86 + 20 * q^87 - 4 * q^88 - 16 * q^89 - 40 * q^91 + 20 * q^92 - 24 * q^93 - 24 * q^94 + 68 * q^95 + 8 * q^97 + 20 * q^98 - 4 * q^99

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