LMFDB - Embedded newform 170.2.n.b.9.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,2,Mod(9,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1]))

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

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

chi := DirichletCharacter("170.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	170.n (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.35745683436$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{8})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 16 x^{15} + 52 x^{14} + 992 x^{13} + 6181 x^{12} + 8952 x^{11} + 6244 x^{10} - 11448 x^{9} + \cdots + 2048 $ x^20 - 16x^15 + 52x^14 + 992x^13 + 6181x^12 + 8952x^11 + 6244x^10 - 11448x^9 - 14520x^8 + 27936x^7 + 27880x^6 - 121104x^5 + 187460x^4 - 142208x^3 + 73856x^2 - 19456*x + 2048
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			9.4
Root			$0.953222 + 0.394838i$ of defining polynomial
Character	$\chi$	$=$	170.9
Dual form			170.2.n.b.19.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.394838 - 0.953222i) q^{3} +1.00000i q^{4} +(0.473610 - 2.18534i) q^{5} +(0.953222 - 0.394838i) q^{6} +(0.363965 - 0.150759i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.36858 + 1.36858i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.394838 - 0.953222i) q^{3} +1.00000i q^{4} +(0.473610 - 2.18534i) q^{5} +(0.953222 - 0.394838i) q^{6} +(0.363965 - 0.150759i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.36858 + 1.36858i) q^{9} +(1.88016 - 1.21037i) q^{10} +(2.68860 - 1.11366i) q^{11} +(0.953222 + 0.394838i) q^{12} -3.68926 q^{13} +(0.363965 + 0.150759i) q^{14} +(-1.89611 - 1.31431i) q^{15} -1.00000 q^{16} +(-2.47053 + 3.30098i) q^{17} +1.93547i q^{18} +(-1.90615 + 1.90615i) q^{19} +(2.18534 + 0.473610i) q^{20} -0.406465i q^{21} +(2.68860 + 1.11366i) q^{22} +(-0.0427996 - 0.103327i) q^{23} +(0.394838 + 0.953222i) q^{24} +(-4.55139 - 2.07000i) q^{25} +(-2.60870 - 2.60870i) q^{26} +(4.70460 - 1.94871i) q^{27} +(0.150759 + 0.363965i) q^{28} +(-1.95514 + 4.72012i) q^{29} +(-0.411397 - 2.27011i) q^{30} +(-5.35385 - 2.21764i) q^{31} +(-0.707107 - 0.707107i) q^{32} -3.00255i q^{33} +(-4.08107 + 0.587220i) q^{34} +(-0.157082 - 0.866787i) q^{35} +(-1.36858 + 1.36858i) q^{36} +(-0.770514 + 1.86018i) q^{37} -2.69570 q^{38} +(-1.45666 + 3.51668i) q^{39} +(1.21037 + 1.88016i) q^{40} +(0.671699 + 1.62163i) q^{41} +(0.287414 - 0.287414i) q^{42} +(8.76402 - 8.76402i) q^{43} +(1.11366 + 2.68860i) q^{44} +(3.63899 - 2.34264i) q^{45} +(0.0427996 - 0.103327i) q^{46} -6.55654 q^{47} +(-0.394838 + 0.953222i) q^{48} +(-4.84001 + 4.84001i) q^{49} +(-1.75461 - 4.68202i) q^{50} +(2.17111 + 3.65832i) q^{51} -3.68926i q^{52} +(4.22773 + 4.22773i) q^{53} +(4.70460 + 1.94871i) q^{54} +(-1.16036 - 6.40294i) q^{55} +(-0.150759 + 0.363965i) q^{56} +(1.06436 + 2.56960i) q^{57} +(-4.72012 + 1.95514i) q^{58} +(-0.866663 - 0.866663i) q^{59} +(1.31431 - 1.89611i) q^{60} +(-4.08798 - 9.86927i) q^{61} +(-2.21764 - 5.35385i) q^{62} +(0.704444 + 0.291790i) q^{63} -1.00000i q^{64} +(-1.74727 + 8.06226i) q^{65} +(2.12312 - 2.12312i) q^{66} -1.14194i q^{67} +(-3.30098 - 2.47053i) q^{68} -0.115393 q^{69} +(0.501837 - 0.723985i) q^{70} +(3.75506 + 1.55540i) q^{71} -1.93547 q^{72} +(12.1223 + 5.02123i) q^{73} +(-1.86018 + 0.770514i) q^{74} +(-3.77022 + 3.52117i) q^{75} +(-1.90615 - 1.90615i) q^{76} +(0.810664 - 0.810664i) q^{77} +(-3.51668 + 1.45666i) q^{78} +(12.6033 - 5.22048i) q^{79} +(-0.473610 + 2.18534i) q^{80} +0.552455i q^{81} +(-0.671699 + 1.62163i) q^{82} +(5.50188 + 5.50188i) q^{83} +0.406465 q^{84} +(6.04369 + 6.96231i) q^{85} +12.3942 q^{86} +(3.72736 + 3.72736i) q^{87} +(-1.11366 + 2.68860i) q^{88} +5.18535i q^{89} +(4.22965 + 0.916659i) q^{90} +(-1.34276 + 0.556190i) q^{91} +(0.103327 - 0.0427996i) q^{92} +(-4.22780 + 4.22780i) q^{93} +(-4.63618 - 4.63618i) q^{94} +(3.26280 + 5.06834i) q^{95} +(-0.953222 + 0.394838i) q^{96} +(-17.4345 - 7.22162i) q^{97} -6.84480 q^{98} +(5.20371 + 2.15545i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{5}+O(q^{10}) $ 20 * q - 4 * q^5	$ 20 q - 4 q^{5} + 8 q^{10} - 8 q^{11} + 24 q^{13} + 16 q^{15} - 20 q^{16} - 4 q^{20} - 8 q^{22} - 16 q^{23} + 8 q^{25} - 12 q^{26} - 24 q^{27} - 12 q^{29} + 8 q^{30} + 8 q^{31} + 8 q^{34} - 8 q^{35} + 8 q^{37} + 8 q^{38} - 4 q^{40} + 4 q^{41} - 8 q^{42} - 16 q^{43} - 8 q^{44} - 32 q^{45} + 16 q^{46} - 40 q^{47} - 56 q^{49} + 8 q^{50} - 8 q^{51} - 44 q^{53} - 24 q^{54} + 72 q^{57} + 16 q^{59} + 8 q^{60} + 8 q^{61} + 8 q^{62} + 24 q^{63} - 28 q^{65} - 8 q^{66} - 20 q^{68} - 16 q^{69} + 8 q^{71} + 28 q^{72} + 60 q^{73} + 28 q^{74} - 8 q^{78} + 56 q^{79} + 4 q^{80} - 4 q^{82} + 16 q^{84} + 84 q^{85} + 48 q^{86} + 72 q^{87} + 8 q^{88} - 12 q^{90} - 24 q^{91} + 8 q^{92} - 72 q^{93} + 32 q^{94} + 88 q^{95} - 48 q^{97} + 36 q^{98} + 72 q^{99}+O(q^{100}) $ 20 * q - 4 * q^5 + 8 * q^10 - 8 * q^11 + 24 * q^13 + 16 * q^15 - 20 * q^16 - 4 * q^20 - 8 * q^22 - 16 * q^23 + 8 * q^25 - 12 * q^26 - 24 * q^27 - 12 * q^29 + 8 * q^30 + 8 * q^31 + 8 * q^34 - 8 * q^35 + 8 * q^37 + 8 * q^38 - 4 * q^40 + 4 * q^41 - 8 * q^42 - 16 * q^43 - 8 * q^44 - 32 * q^45 + 16 * q^46 - 40 * q^47 - 56 * q^49 + 8 * q^50 - 8 * q^51 - 44 * q^53 - 24 * q^54 + 72 * q^57 + 16 * q^59 + 8 * q^60 + 8 * q^61 + 8 * q^62 + 24 * q^63 - 28 * q^65 - 8 * q^66 - 20 * q^68 - 16 * q^69 + 8 * q^71 + 28 * q^72 + 60 * q^73 + 28 * q^74 - 8 * q^78 + 56 * q^79 + 4 * q^80 - 4 * q^82 + 16 * q^84 + 84 * q^85 + 48 * q^86 + 72 * q^87 + 8 * q^88 - 12 * q^90 - 24 * q^91 + 8 * q^92 - 72 * q^93 + 32 * q^94 + 88 * q^95 - 48 * q^97 + 36 * q^98 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$.

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$-1$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	0.394838	−	0.953222i	0.227960	−	0.550343i	−0.767969	−	0.640487i	$-0.778733\pi$
$3$	0.394838	−	0.953222i	0.227960	−	0.550343i	0.995929	+	0.0901436i	$0.0287326\pi$
$4$			1.00000i			0.500000i
$5$	0.473610	−	2.18534i	0.211805	−	0.977312i
$5$	0.473610	−	2.18534i	0.211805	−	0.977312i
$6$	0.953222	−	0.394838i	0.389151	−	0.161192i
$7$	0.363965	−	0.150759i	0.137566	−	0.0569817i	−0.312838	−	0.949806i	$-0.601280\pi$
$7$	0.363965	−	0.150759i	0.137566	−	0.0569817i	0.450404	+	0.892825i	$0.351280\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	1.36858	+	1.36858i	0.456195	+	0.456195i
$10$	1.88016	−	1.21037i	0.594558	−	0.382754i
$11$	2.68860	−	1.11366i	0.810644	−	0.335780i	0.0614331	−	0.998111i	$-0.480433\pi$
$11$	2.68860	−	1.11366i	0.810644	−	0.335780i	0.749211	+	0.662331i	$0.230433\pi$
$12$	0.953222	+	0.394838i	0.275172	+	0.113980i
$13$	−3.68926			−1.02322			−0.511608	−	0.859219i	$-0.670950\pi$
$13$	−3.68926			−1.02322			−0.511608	+	0.859219i	$0.670950\pi$
$14$	0.363965	+	0.150759i	0.0972738	+	0.0402921i
$15$	−1.89611	−	1.31431i	−0.489574	−	0.339353i
$16$	−1.00000			−0.250000
$17$	−2.47053	+	3.30098i	−0.599191	+	0.800606i
$17$	−2.47053	+	3.30098i	−0.599191	+	0.800606i
$18$			1.93547i			0.456195i
$19$	−1.90615	+	1.90615i	−0.437300	+	0.437300i	−0.891102	−	0.453803i	$-0.850067\pi$
$19$	−1.90615	+	1.90615i	−0.437300	+	0.437300i	0.453803	+	0.891102i	$0.350067\pi$
$20$	2.18534	+	0.473610i	0.488656	+	0.105902i
$21$		−	0.406465i		−	0.0886980i
$22$	2.68860	+	1.11366i	0.573212	+	0.237432i
$23$	−0.0427996	−	0.103327i	−0.00892434	−	0.0215453i	0.919355	−	0.393430i	$-0.128712\pi$
$23$	−0.0427996	−	0.103327i	−0.00892434	−	0.0215453i	−0.928279	+	0.371885i	$0.878712\pi$
$24$	0.394838	+	0.953222i	0.0805959	+	0.194576i
$25$	−4.55139	−	2.07000i	−0.910277	−	0.413999i
$26$	−2.60870	−	2.60870i	−0.511608	−	0.511608i
$27$	4.70460	−	1.94871i	0.905401	−	0.375029i
$28$	0.150759	+	0.363965i	0.0284908	+	0.0687829i
$29$	−1.95514	+	4.72012i	−0.363060	+	0.876503i	0.631790	+	0.775140i	$0.282321\pi$
$29$	−1.95514	+	4.72012i	−0.363060	+	0.876503i	−0.994849	+	0.101364i	$0.967679\pi$
$30$	−0.411397	−	2.27011i	−0.0751105	−	0.414464i
$31$	−5.35385	−	2.21764i	−0.961580	−	0.398299i	−0.154009	−	0.988070i	$-0.549218\pi$
$31$	−5.35385	−	2.21764i	−0.961580	−	0.398299i	−0.807571	+	0.589770i	$0.799218\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$		−	3.00255i		−	0.522677i
$34$	−4.08107	+	0.587220i	−0.699899	+	0.100707i
$35$	−0.157082	−	0.866787i	−0.0265517	−	0.146514i
$36$	−1.36858	+	1.36858i	−0.228097	+	0.228097i
$37$	−0.770514	+	1.86018i	−0.126672	+	0.305813i	−0.974474	−	0.224500i	$-0.927925\pi$
$37$	−0.770514	+	1.86018i	−0.126672	+	0.305813i	0.847802	+	0.530312i	$0.177925\pi$
$38$	−2.69570			−0.437300
$39$	−1.45666	+	3.51668i	−0.233252	+	0.563120i
$40$	1.21037	+	1.88016i	0.191377	+	0.297279i
$41$	0.671699	+	1.62163i	0.104902	+	0.253255i	0.967611	−	0.252444i	$-0.0812344\pi$
$41$	0.671699	+	1.62163i	0.104902	+	0.253255i	−0.862710	+	0.505700i	$0.831234\pi$
$42$	0.287414	−	0.287414i	0.0443490	−	0.0443490i
$43$	8.76402	−	8.76402i	1.33650	−	1.33650i	0.437075	−	0.899425i	$-0.356015\pi$
$43$	8.76402	−	8.76402i	1.33650	−	1.33650i	0.899425	−	0.437075i	$-0.143985\pi$
$44$	1.11366	+	2.68860i	0.167890	+	0.405322i
$45$	3.63899	−	2.34264i	0.542469	−	0.349220i
$46$	0.0427996	−	0.103327i	0.00631046	−	0.0152348i
$47$	−6.55654			−0.956370			−0.478185	−	0.878259i	$-0.658705\pi$
$47$	−6.55654			−0.956370			−0.478185	+	0.878259i	$0.658705\pi$
$48$	−0.394838	+	0.953222i	−0.0569899	+	0.137586i
$49$	−4.84001	+	4.84001i	−0.691429	+	0.691429i
$50$	−1.75461	−	4.68202i	−0.248139	−	0.662138i
$51$	2.17111	+	3.65832i	0.304017	+	0.512267i
$52$		−	3.68926i		−	0.511608i
$53$	4.22773	+	4.22773i	0.580723	+	0.580723i	0.935102	−	0.354379i	$-0.115308\pi$
$53$	4.22773	+	4.22773i	0.580723	+	0.580723i	−0.354379	+	0.935102i	$0.615308\pi$
$54$	4.70460	+	1.94871i	0.640215	+	0.265186i
$55$	−1.16036	−	6.40294i	−0.156463	−	0.863372i
$56$	−0.150759	+	0.363965i	−0.0201461	+	0.0486369i
$57$	1.06436	+	2.56960i	0.140978	+	0.340352i
$58$	−4.72012	+	1.95514i	−0.619781	+	0.256722i
$59$	−0.866663	−	0.866663i	−0.112830	−	0.112830i	0.648438	−	0.761268i	$-0.275423\pi$
$59$	−0.866663	−	0.866663i	−0.112830	−	0.112830i	−0.761268	+	0.648438i	$0.775423\pi$
$60$	1.31431	−	1.89611i	0.169677	−	0.244787i
$61$	−4.08798	−	9.86927i	−0.523413	−	1.26363i	−0.935771	−	0.352609i	$-0.885295\pi$
$61$	−4.08798	−	9.86927i	−0.523413	−	1.26363i	0.412358	−	0.911022i	$-0.364705\pi$
$62$	−2.21764	−	5.35385i	−0.281640	−	0.679940i
$63$	0.704444	+	0.291790i	0.0887516	+	0.0367621i
$64$		−	1.00000i		−	0.125000i
$65$	−1.74727	+	8.06226i	−0.216722	+	1.00000i
$66$	2.12312	−	2.12312i	0.261338	−	0.261338i
$67$		−	1.14194i		−	0.139511i	−0.997564	−	0.0697553i	$-0.977778\pi$
$67$		−	1.14194i		−	0.139511i	0.997564	−	0.0697553i	$-0.0222218\pi$
$68$	−3.30098	−	2.47053i	−0.400303	−	0.299596i
$69$	−0.115393			−0.0138917
$70$	0.501837	−	0.723985i	0.0599810	−	0.0865328i
$71$	3.75506	+	1.55540i	0.445644	+	0.184592i	0.594209	−	0.804311i	$-0.297465\pi$
$71$	3.75506	+	1.55540i	0.445644	+	0.184592i	−0.148565	+	0.988903i	$0.547465\pi$
$72$	−1.93547			−0.228097
$73$	12.1223	+	5.02123i	1.41881	+	0.587691i	0.954561	−	0.298014i	$-0.0963242\pi$
$73$	12.1223	+	5.02123i	1.41881	+	0.587691i	0.464249	+	0.885705i	$0.346324\pi$
$74$	−1.86018	+	0.770514i	−0.216242	+	0.0895704i
$75$	−3.77022	+	3.52117i	−0.435348	+	0.406590i
$76$	−1.90615	−	1.90615i	−0.218650	−	0.218650i
$77$	0.810664	−	0.810664i	0.0923837	−	0.0923837i
$78$	−3.51668	+	1.45666i	−0.398186	+	0.164934i
$79$	12.6033	−	5.22048i	1.41799	−	0.587350i	0.463633	−	0.886027i	$-0.346546\pi$
$79$	12.6033	−	5.22048i	1.41799	−	0.587350i	0.954354	+	0.298678i	$0.0965455\pi$
$80$	−0.473610	+	2.18534i	−0.0529512	+	0.244328i
$81$			0.552455i			0.0613839i
$82$	−0.671699	+	1.62163i	−0.0741768	+	0.179079i
$83$	5.50188	+	5.50188i	0.603909	+	0.603909i	0.941348	−	0.337438i	$-0.109560\pi$
$83$	5.50188	+	5.50188i	0.603909	+	0.603909i	−0.337438	+	0.941348i	$0.609560\pi$
$84$	0.406465			0.0443490
$85$	6.04369	+	6.96231i	0.655530	+	0.755169i
$86$	12.3942			1.33650
$87$	3.72736	+	3.72736i	0.399615	+	0.399615i
$88$	−1.11366	+	2.68860i	−0.118716	+	0.286606i
$89$			5.18535i			0.549646i	0.961495	+	0.274823i	$0.0886193\pi$
$89$			5.18535i			0.549646i	−0.961495	+	0.274823i	$0.911381\pi$
$90$	4.22965	+	0.916659i	0.445845	+	0.0966243i
$91$	−1.34276	+	0.556190i	−0.140760	+	0.0583045i
$92$	0.103327	−	0.0427996i	0.0107726	−	0.00446217i
$93$	−4.22780	+	4.22780i	−0.438403	+	0.438403i
$94$	−4.63618	−	4.63618i	−0.478185	−	0.478185i
$95$	3.26280	+	5.06834i	0.334756	+	0.520001i
$96$	−0.953222	+	0.394838i	−0.0972879	+	0.0402980i
$97$	−17.4345	−	7.22162i	−1.77021	−	0.733245i	−0.994807	−	0.101776i	$-0.967547\pi$
$97$	−17.4345	−	7.22162i	−1.77021	−	0.733245i	−0.775402	−	0.631468i	$-0.782453\pi$
$98$	−6.84480			−0.691429
$99$	5.20371	+	2.15545i	0.522992	+	0.216631i
$100$	2.07000	−	4.55139i	0.207000	−	0.455139i
$101$	7.49145			0.745427			0.372714	−	0.927946i	$-0.378427\pi$
$101$	7.49145			0.745427			0.372714	+	0.927946i	$0.378427\pi$
$102$	−1.05161	+	4.12203i	−0.104125	+	0.408142i
$103$		−	18.6697i		−	1.83958i	−0.392416	−	0.919788i	$-0.628361\pi$
$103$		−	18.6697i		−	1.83958i	0.392416	−	0.919788i	$-0.371639\pi$
$104$	2.60870	−	2.60870i	0.255804	−	0.255804i
$105$	−0.888263	−	0.192506i	−0.0866856	−	0.0187867i
$106$			5.97891i			0.580723i
$107$	11.7227	+	4.85568i	1.13327	+	0.469417i	0.868892	−	0.495002i	$-0.164833\pi$
$107$	11.7227	+	4.85568i	1.13327	+	0.469417i	0.264380	+	0.964419i	$0.414833\pi$
$108$	1.94871	+	4.70460i	0.187515	+	0.452700i
$109$	−0.464419	−	1.12121i	−0.0444833	−	0.107392i	0.900076	−	0.435733i	$-0.143511\pi$
$109$	−0.464419	−	1.12121i	−0.0444833	−	0.107392i	−0.944559	+	0.328340i	$0.893511\pi$
$110$	3.70706	−	5.34806i	0.353454	−	0.509918i
$111$	1.46894	+	1.46894i	0.139426	+	0.139426i
$112$	−0.363965	+	0.150759i	−0.0343915	+	0.0142454i
$113$	0.668364	+	1.61357i	0.0628744	+	0.151792i	0.952194	−	0.305494i	$-0.0988216\pi$
$113$	0.668364	+	1.61357i	0.0628744	+	0.151792i	−0.889320	+	0.457286i	$0.848822\pi$
$114$	−1.06436	+	2.56960i	−0.0996867	+	0.240665i
$115$	−0.246076	+	0.0445946i	−0.0229467	+	0.00415847i
$116$	−4.72012	−	1.95514i	−0.438252	−	0.181530i
$117$	−5.04906	−	5.04906i	−0.466785	−	0.466785i
$118$		−	1.22565i		−	0.112830i
$119$	−0.401532	+	1.57390i	−0.0368084	+	0.144279i
$120$	2.27011	−	0.411397i	0.207232	−	0.0375552i
$121$	−1.78982	+	1.78982i	−0.162711	+	0.162711i
$122$	4.08798	−	9.86927i	0.370109	−	0.893522i
$123$	1.81098			0.163291
$124$	2.21764	−	5.35385i	0.199150	−	0.480790i
$125$	−6.67922	+	8.96594i	−0.597407	+	0.801938i
$126$	0.291790	+	0.704444i	0.0259947	+	0.0627568i
$127$	2.44552	−	2.44552i	0.217005	−	0.217005i	−0.590230	−	0.807235i	$-0.700963\pi$
$127$	2.44552	−	2.44552i	0.217005	−	0.217005i	0.807235	+	0.590230i	$0.200963\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−4.89369	−	11.8144i	−0.430866	−	1.04020i
$130$	−6.93639	+	4.46538i	−0.608361	+	0.391639i
$131$	4.23601	−	10.2266i	0.370102	−	0.893505i	−0.623630	−	0.781719i	$-0.714343\pi$
$131$	4.23601	−	10.2266i	0.370102	−	0.893505i	0.993732	−	0.111786i	$-0.0356571\pi$
$132$	3.00255			0.261338
$133$	−0.406401	+	0.981140i	−0.0352395	+	0.0850756i
$134$	0.807476	−	0.807476i	0.0697553	−	0.0697553i
$135$	−2.03044	−	11.2041i	−0.174752	−	0.964292i
$136$	−0.587220	−	4.08107i	−0.0503537	−	0.349949i
$137$		−	15.8536i		−	1.35447i	−0.735768	−	0.677233i	$-0.763179\pi$
$137$		−	15.8536i		−	1.35447i	0.735768	−	0.677233i	$-0.236821\pi$
$138$	−0.0815951	−	0.0815951i	−0.00694584	−	0.00694584i
$139$	−10.0949	−	4.18146i	−0.856242	−	0.354667i	−0.0890056	−	0.996031i	$-0.528369\pi$
$139$	−10.0949	−	4.18146i	−0.856242	−	0.354667i	−0.767237	+	0.641364i	$0.778369\pi$
$140$	0.866787	−	0.157082i	0.0732569	−	0.0132759i
$141$	−2.58877	+	6.24985i	−0.218014	+	0.526332i
$142$	1.55540	+	3.75506i	0.130526	+	0.315118i
$143$	−9.91894	+	4.10856i	−0.829464	+	0.343575i
$144$	−1.36858	−	1.36858i	−0.114049	−	0.114049i
$145$	9.38906	+	6.50812i	0.779719	+	0.540470i
$146$	5.02123	+	12.1223i	0.415560	+	1.00325i
$147$	2.70259	+	6.52462i	0.222905	+	0.538141i
$148$	−1.86018	−	0.770514i	−0.152906	−	0.0633358i
$149$		−	17.5137i		−	1.43478i	−0.696671	−	0.717391i	$-0.745336\pi$
$149$		−	17.5137i		−	1.43478i	0.696671	−	0.717391i	$-0.254664\pi$
$150$	−5.15580	−	0.176107i	−0.420969	−	0.0143791i
$151$	−14.6953	+	14.6953i	−1.19589	+	1.19589i	−0.220502	+	0.975386i	$0.570770\pi$
$151$	−14.6953	+	14.6953i	−1.19589	+	1.19589i	−0.975386	+	0.220502i	$0.929230\pi$
$152$		−	2.69570i		−	0.218650i
$153$	−7.89880	+	1.13655i	−0.638580	+	0.0918844i
$154$	1.14645			0.0923837
$155$	−7.38192	+	10.6497i	−0.592930	+	0.855402i
$156$	−3.51668	−	1.45666i	−0.281560	−	0.116626i
$157$	−1.96514			−0.156836			−0.0784178	−	0.996921i	$-0.524987\pi$
$157$	−1.96514			−0.156836			−0.0784178	+	0.996921i	$0.524987\pi$
$158$	12.6033	+	5.22048i	1.00267	+	0.415319i
$159$	5.69923	−	2.36070i	0.451979	−	0.187216i
$160$	−1.88016	+	1.21037i	−0.148640	+	0.0956884i
$161$	−0.0311551	−	0.0311551i	−0.00245537	−	0.00245537i
$162$	−0.390645	+	0.390645i	−0.0306920	+	0.0306920i
$163$	−1.69473	+	0.701981i	−0.132742	+	0.0549834i	−0.448066	−	0.894001i	$-0.647887\pi$
$163$	−1.69473	+	0.701981i	−0.132742	+	0.0549834i	0.315324	+	0.948984i	$0.397887\pi$
$164$	−1.62163	+	0.671699i	−0.126628	+	0.0524509i
$165$	−6.56158	−	1.42204i	−0.510818	−	0.110706i
$166$			7.78083i			0.603909i
$167$	−5.06817	+	12.2356i	−0.392186	+	0.946822i	0.597276	+	0.802035i	$0.296250\pi$
$167$	−5.06817	+	12.2356i	−0.392186	+	0.946822i	−0.989463	+	0.144786i	$0.953750\pi$
$168$	0.287414	+	0.287414i	0.0221745	+	0.0221745i
$169$	0.610609			0.0469699
$170$	−0.649566	+	9.19663i	−0.0498194	+	0.705350i
$171$	−5.21744			−0.398988
$172$	8.76402	+	8.76402i	0.668250	+	0.668250i
$173$	4.01629	−	9.69618i	0.305353	−	0.737187i	−0.694491	−	0.719502i	$-0.744370\pi$
$173$	4.01629	−	9.69618i	0.305353	−	0.737187i	0.999844	−	0.0176853i	$-0.00562970\pi$
$174$			5.27128i			0.399615i
$175$	−1.96862	−	0.0672422i	−0.148813	−	0.00508303i
$176$	−2.68860	+	1.11366i	−0.202661	+	0.0839449i
$177$	−1.16831	+	0.483932i	−0.0878159	+	0.0363745i
$178$	−3.66660	+	3.66660i	−0.274823	+	0.274823i
$179$	−2.07081	−	2.07081i	−0.154780	−	0.154780i	0.625469	−	0.780249i	$-0.284908\pi$
$179$	−2.07081	−	2.07081i	−0.154780	−	0.154780i	−0.780249	+	0.625469i	$0.784908\pi$
$180$	2.34264	+	3.63899i	0.174610	+	0.271234i
$181$	−13.9122	+	5.76264i	−1.03409	+	0.428334i	−0.834187	−	0.551482i	$-0.814063\pi$
$181$	−13.9122	+	5.76264i	−1.03409	+	0.428334i	−0.199902	+	0.979816i	$0.564063\pi$
$182$	−1.34276	−	0.556190i	−0.0995320	−	0.0412275i
$183$	−11.0217			−0.814747
$184$	0.103327	+	0.0427996i	0.00761740	+	0.00315523i
$185$	3.70021	+	2.56483i	0.272045	+	0.188570i
$186$	−5.97902			−0.438403
$187$	−2.96611	+	11.6263i	−0.216903	+	0.850203i
$188$		−	6.55654i		−	0.478185i
$189$	1.41852	−	1.41852i	0.103182	−	0.103182i
$190$	−1.27671	+	5.89100i	−0.0926222	+	0.427378i
$191$		−	8.40074i		−	0.607856i	−0.952695	−	0.303928i	$-0.901702\pi$
$191$		−	8.40074i		−	0.607856i	0.952695	−	0.303928i	$-0.0982982\pi$
$192$	−0.953222	−	0.394838i	−0.0687929	−	0.0284950i
$193$	−2.24530	−	5.42064i	−0.161621	−	0.390187i	0.822236	−	0.569147i	$-0.192727\pi$
$193$	−2.24530	−	5.42064i	−0.161621	−	0.390187i	−0.983856	+	0.178961i	$0.942727\pi$
$194$	−7.22162	−	17.4345i	−0.518482	−	1.25173i
$195$	6.99524	+	4.84882i	0.500940	+	0.347231i
$196$	−4.84001	−	4.84001i	−0.345715	−	0.345715i
$197$	5.52186	−	2.28723i	0.393416	−	0.162958i	−0.177201	−	0.984175i	$-0.556704\pi$
$197$	5.52186	−	2.28723i	0.393416	−	0.162958i	0.570617	+	0.821216i	$0.306704\pi$
$198$	2.15545	+	5.20371i	0.153181	+	0.369811i
$199$	7.72557	−	18.6512i	0.547651	−	1.32215i	−0.371570	−	0.928405i	$-0.621180\pi$
$199$	7.72557	−	18.6512i	0.547651	−	1.32215i	0.919221	−	0.393742i	$-0.128820\pi$
$200$	4.68202	−	1.75461i	0.331069	−	0.124070i
$201$	−1.08853	−	0.450882i	−0.0767787	−	0.0318028i
$202$	5.29725	+	5.29725i	0.372714	+	0.372714i
$203$			2.01271i			0.141265i
$204$	−3.65832	+	2.17111i	−0.256133	+	0.152008i
$205$	3.86192	−	0.699870i	0.269728	−	0.0488810i
$206$	13.2014	−	13.2014i	0.919788	−	0.919788i
$207$	0.0828374	−	0.199987i	0.00575760	−	0.0139001i
$208$	3.68926			0.255804
$209$	−3.00208	+	7.24766i	−0.207658	+	0.501331i
$210$	−0.491974	−	0.764219i	−0.0339495	−	0.0527361i
$211$	2.33567	+	5.63881i	0.160794	+	0.388192i	0.983658	−	0.180047i	$-0.0576250\pi$
$211$	2.33567	+	5.63881i	0.160794	+	0.388192i	−0.822864	+	0.568239i	$0.807625\pi$
$212$	−4.22773	+	4.22773i	−0.290362	+	0.290362i
$213$	2.96528	−	2.96528i	0.203178	−	0.203178i
$214$	4.85568	+	11.7227i	0.331928	+	0.801345i
$215$	−15.0016	−	23.3030i	−1.02310	−	1.58925i
$216$	−1.94871	+	4.70460i	−0.132593	+	0.320108i
$217$	−2.28294			−0.154976
$218$	0.464419	−	1.12121i	0.0314545	−	0.0759378i
$219$	9.57270	−	9.57270i	0.646863	−	0.646863i
$220$	6.40294	−	1.16036i	0.431686	−	0.0782316i
$221$	9.11441	−	12.1782i	0.613102	−	0.819192i
$222$			2.07740i			0.139426i
$223$	−17.4148	−	17.4148i	−1.16618	−	1.16618i	−0.983097	−	0.183083i	$-0.941392\pi$
$223$	−17.4148	−	17.4148i	−1.16618	−	1.16618i	−0.183083	−	0.983097i	$-0.558608\pi$
$224$	−0.363965	−	0.150759i	−0.0243184	−	0.0100730i
$225$	−3.39599	−	9.06192i	−0.226400	−	0.604128i
$226$	−0.668364	+	1.61357i	−0.0444589	+	0.107333i
$227$	4.08127	+	9.85307i	0.270884	+	0.653971i	0.999522	−	0.0309281i	$-0.00984628\pi$
$227$	4.08127	+	9.85307i	0.270884	+	0.653971i	−0.728638	+	0.684899i	$0.759846\pi$
$228$	−2.56960	+	1.06436i	−0.170176	+	0.0704891i
$229$	12.9967	+	12.9967i	0.858846	+	0.858846i	0.991202	−	0.132356i	$-0.0422543\pi$
$229$	12.9967	+	12.9967i	0.858846	+	0.858846i	−0.132356	+	0.991202i	$0.542254\pi$
$230$	−0.205535	−	0.142469i	−0.0135526	−	0.00939410i
$231$	−0.452662	−	1.09282i	−0.0297830	−	0.0719025i
$232$	−1.95514	−	4.72012i	−0.128361	−	0.309891i
$233$	20.2462	+	8.38625i	1.32637	+	0.549402i	0.929619	−	0.368523i	$-0.120136\pi$
$233$	20.2462	+	8.38625i	1.32637	+	0.549402i	0.396754	+	0.917925i	$0.370136\pi$
$234$		−	7.14044i		−	0.466785i
$235$	−3.10525	+	14.3283i	−0.202564	+	0.934672i
$236$	0.866663	−	0.866663i	0.0564150	−	0.0564150i
$237$		−	14.0750i		−	0.914272i
$238$	−1.39684	+	0.828988i	−0.0905437	+	0.0537353i
$239$	−22.6481			−1.46498			−0.732491	−	0.680777i	$-0.761642\pi$
$239$	−22.6481			−1.46498			−0.732491	+	0.680777i	$0.761642\pi$
$240$	1.89611	+	1.31431i	0.122394	+	0.0848383i
$241$	14.7905	+	6.12642i	0.952739	+	0.394638i	0.804260	−	0.594278i	$-0.202562\pi$
$241$	14.7905	+	6.12642i	0.952739	+	0.394638i	0.148480	+	0.988915i	$0.452562\pi$
$242$	−2.53119			−0.162711
$243$	14.6404	+	6.06426i	0.939183	+	0.389022i
$244$	9.86927	−	4.08798i	0.631815	−	0.261706i
$245$	8.28476	+	12.8693i	0.529294	+	0.822190i
$246$	1.28056	+	1.28056i	0.0816454	+	0.0816454i
$247$	7.03226	−	7.03226i	0.447452	−	0.447452i
$248$	5.35385	−	2.21764i	0.339970	−	0.140820i
$249$	7.41686	−	3.07216i	0.470024	−	0.194690i
$250$	−11.0628	+	1.61696i	−0.699673	+	0.102265i
$251$			6.59313i			0.416154i	0.978112	+	0.208077i	$0.0667205\pi$
$251$			6.59313i			0.416154i	−0.978112	+	0.208077i	$0.933279\pi$
$252$	−0.291790	+	0.704444i	−0.0183811	+	0.0443758i
$253$	−0.230142	−	0.230142i	−0.0144689	−	0.0144689i
$254$	3.45848			0.217005
$255$	9.02291	−	3.01200i	0.565037	−	0.188619i
$256$	1.00000			0.0625000
$257$	12.0468	+	12.0468i	0.751456	+	0.751456i	0.974751	−	0.223295i	$-0.0716812\pi$
$257$	12.0468	+	12.0468i	0.751456	+	0.751456i	−0.223295	+	0.974751i	$0.571681\pi$
$258$	4.89369	−	11.8144i	0.304668	−	0.735534i
$259$			0.793205i			0.0492873i
$260$	−8.06226	−	1.74727i	−0.500000	−	0.108361i
$261$	−9.13564	+	3.78411i	−0.565482	+	0.234230i
$262$	10.2266	−	4.23601i	0.631804	−	0.261702i
$263$	−22.7128	+	22.7128i	−1.40053	+	1.40053i	−0.602138	+	0.798392i	$0.705684\pi$
$263$	−22.7128	+	22.7128i	−1.40053	+	1.40053i	−0.798392	+	0.602138i	$0.794316\pi$
$264$	2.12312	+	2.12312i	0.130669	+	0.130669i
$265$	11.2413	−	7.23671i	0.690548	−	0.444548i
$266$	−0.981140	+	0.406401i	−0.0601575	+	0.0249181i
$267$	4.94280	+	2.04737i	0.302494	+	0.125297i
$268$	1.14194			0.0697553
$269$	18.7933	+	7.78444i	1.14585	+	0.474626i	0.873139	−	0.487471i	$-0.162081\pi$
$269$	18.7933	+	7.78444i	1.14585	+	0.474626i	0.272708	+	0.962097i	$0.412081\pi$
$270$	6.48673	−	9.35820i	0.394770	−	0.569522i
$271$	28.9091			1.75610			0.878050	−	0.478569i	$-0.158844\pi$
$271$	28.9091			1.75610			0.878050	+	0.478569i	$0.158844\pi$
$272$	2.47053	−	3.30098i	0.149798	−	0.200151i
$273$			1.49955i			0.0907571i
$274$	11.2102	−	11.2102i	0.677233	−	0.677233i
$275$	−14.5421	−	0.496717i	−0.876923	−	0.0299531i
$276$		−	0.115393i		−	0.00694584i
$277$	−12.0666	−	4.99813i	−0.725009	−	0.300309i	−0.0105100	−	0.999945i	$-0.503346\pi$
$277$	−12.0666	−	4.99813i	−0.725009	−	0.300309i	−0.714499	+	0.699636i	$0.753346\pi$
$278$	−4.18146	−	10.0949i	−0.250788	−	0.605455i
$279$	−4.29217	−	10.3622i	−0.256966	−	0.620370i
$280$	0.723985	+	0.501837i	0.0432664	+	0.0299905i
$281$	13.1272	+	13.1272i	0.783100	+	0.783100i	0.980353	−	0.197252i	$-0.0632019\pi$
$281$	13.1272	+	13.1272i	0.783100	+	0.783100i	−0.197252	+	0.980353i	$0.563202\pi$
$282$	−6.24985	+	2.58877i	−0.372173	+	0.154159i
$283$	6.83217	+	16.4943i	0.406130	+	0.980485i	0.986146	+	0.165880i	$0.0530463\pi$
$283$	6.83217	+	16.4943i	0.406130	+	0.980485i	−0.580016	+	0.814605i	$0.696954\pi$
$284$	−1.55540	+	3.75506i	−0.0922958	+	0.222822i
$285$	6.11953	−	1.10900i	0.362490	−	0.0656916i
$286$	−9.91894	−	4.10856i	−0.586519	−	0.242944i
$287$	0.488950	+	0.488950i	0.0288618	+	0.0288618i
$288$		−	1.93547i		−	0.114049i
$289$	−4.79298	−	16.3103i	−0.281940	−	0.959432i
$290$	2.03713	+	11.2410i	0.119625	+	0.660095i
$291$	−13.7676	+	13.7676i	−0.807072	+	0.807072i
$292$	−5.02123	+	12.1223i	−0.293845	+	0.709405i
$293$	6.13040			0.358142			0.179071	−	0.983836i	$-0.442691\pi$
$293$	6.13040			0.358142			0.179071	+	0.983836i	$0.442691\pi$
$294$	−2.70259	+	6.52462i	−0.157618	+	0.380523i
$295$	−2.30441	+	1.48349i	−0.134168	+	0.0863721i
$296$	−0.770514	−	1.86018i	−0.0447852	−	0.108121i
$297$	10.4786	−	10.4786i	0.608031	−	0.608031i
$298$	12.3841	−	12.3841i	0.717391	−	0.717391i
$299$	0.157899	+	0.381201i	0.00913152	+	0.0220454i
$300$	−3.52117	−	3.77022i	−0.203295	−	0.217674i
$301$	1.86854	−	4.51105i	0.107701	−	0.260013i
$302$	−20.7823			−1.19589
$303$	2.95791	−	7.14102i	0.169927	−	0.410241i
$304$	1.90615	−	1.90615i	0.109325	−	0.109325i
$305$	−23.5038	+	4.25943i	−1.34582	+	0.243894i
$306$	−6.38895	−	4.78163i	−0.365232	−	0.273348i
$307$			29.3031i			1.67241i	0.548414	+	0.836207i	$0.315232\pi$
$307$			29.3031i			1.67241i	−0.548414	+	0.836207i	$0.684768\pi$
$308$	0.810664	+	0.810664i	0.0461918	+	0.0461918i
$309$	−17.7963	−	7.37148i	−1.01240	−	0.419349i
$310$	−12.7503	+	2.31064i	−0.724166	+	0.131236i
$311$	8.59516	−	20.7505i	0.487387	−	1.17666i	−0.468644	−	0.883387i	$-0.655257\pi$
$311$	8.59516	−	20.7505i	0.487387	−	1.17666i	0.956030	−	0.293268i	$-0.0947428\pi$
$312$	−1.45666	−	3.51668i	−0.0824670	−	0.199093i
$313$	5.83076	−	2.41518i	0.329574	−	0.136514i	−0.211760	−	0.977322i	$-0.567919\pi$
$313$	5.83076	−	2.41518i	0.329574	−	0.136514i	0.541334	+	0.840808i	$0.317919\pi$
$314$	−1.38957	−	1.38957i	−0.0784178	−	0.0784178i
$315$	0.971291	−	1.40125i	0.0547261	−	0.0789516i
$316$	5.22048	+	12.6033i	0.293675	+	0.708994i
$317$	−3.97142	−	9.58786i	−0.223057	−	0.538508i	0.772245	−	0.635325i	$-0.219134\pi$
$317$	−3.97142	−	9.58786i	−0.223057	−	0.538508i	−0.995302	+	0.0968172i	$0.969134\pi$
$318$	5.69923	+	2.36070i	0.319597	+	0.132381i
$319$			14.8679i			0.832440i
$320$	−2.18534	−	0.473610i	−0.122164	−	0.0264756i
$321$	9.25710	−	9.25710i	0.516681	−	0.516681i
$322$		−	0.0440600i		−	0.00245537i
$323$	−1.58297	−	11.0013i	−0.0880786	−	0.612131i
$324$	−0.552455			−0.0306920
$325$	16.7912	+	7.63674i	0.931410	+	0.423610i
$326$	−1.69473	−	0.701981i	−0.0938626	−	0.0388792i
$327$	−1.25213			−0.0692430
$328$	−1.62163	−	0.671699i	−0.0895393	−	0.0370884i
$329$	−2.38635	+	0.988460i	−0.131564	+	0.0544956i
$330$	−3.63420	−	5.64527i	−0.200056	−	0.310762i
$331$	−5.40818	−	5.40818i	−0.297260	−	0.297260i	0.542679	−	0.839940i	$-0.317410\pi$
$331$	−5.40818	−	5.40818i	−0.297260	−	0.297260i	−0.839940	+	0.542679i	$0.817410\pi$
$332$	−5.50188	+	5.50188i	−0.301955	+	0.301955i
$333$	−3.60033	+	1.49131i	−0.197297	+	0.0817231i
$334$	−12.2356	+	5.06817i	−0.669504	+	0.277318i
$335$	−2.49553	−	0.540836i	−0.136345	−	0.0295490i
$336$			0.406465i			0.0221745i
$337$	5.05001	−	12.1918i	0.275091	−	0.664129i	−0.724595	−	0.689175i	$-0.757973\pi$
$337$	5.05001	−	12.1918i	0.275091	−	0.664129i	0.999686	+	0.0250457i	$0.00797314\pi$
$338$	0.431766	+	0.431766i	0.0234850	+	0.0234850i
$339$	1.80199			0.0978706
$340$	−6.96231	+	6.04369i	−0.377585	+	0.327765i
$341$	−16.8641			−0.913240
$342$	−3.68929	−	3.68929i	−0.199494	−	0.199494i
$343$	−2.08723	+	5.03903i	−0.112700	+	0.272082i
$344$			12.3942i			0.668250i
$345$	−0.0546513	+	0.252172i	−0.00294233	+	0.0135765i
$346$	9.69618	−	4.01629i	0.521270	−	0.215917i
$347$	−5.33087	+	2.20812i	−0.286176	+	0.118538i	−0.521154	−	0.853463i	$-0.674498\pi$
$347$	−5.33087	+	2.20812i	−0.286176	+	0.118538i	0.234978	+	0.972001i	$0.424498\pi$
$348$	−3.72736	+	3.72736i	−0.199807	+	0.199807i
$349$	9.27313	+	9.27313i	0.496379	+	0.496379i	0.910309	−	0.413929i	$-0.135844\pi$
$349$	9.27313	+	9.27313i	0.496379	+	0.496379i	−0.413929	+	0.910309i	$0.635844\pi$
$350$	−1.34448	−	1.43957i	−0.0718652	−	0.0769483i
$351$	−17.3565	+	7.18929i	−0.926420	+	0.383736i
$352$	−2.68860	−	1.11366i	−0.143303	−	0.0593580i
$353$	−23.3712			−1.24392			−0.621961	−	0.783048i	$-0.713664\pi$
$353$	−23.3712			−1.24392			−0.621961	+	0.783048i	$0.713664\pi$
$354$	−1.16831	−	0.483932i	−0.0620952	−	0.0257207i
$355$	5.17750	−	7.46942i	0.274793	−	0.396436i
$356$	−5.18535			−0.274823
$357$	1.34173	+	1.00418i	0.0710121	+	0.0531470i
$358$		−	2.92857i		−	0.154780i
$359$	−16.5678	+	16.5678i	−0.874415	+	0.874415i	−0.992950	−	0.118535i	$-0.962180\pi$
$359$	−16.5678	+	16.5678i	−0.874415	+	0.874415i	0.118535	+	0.992950i	$0.462180\pi$
$360$	−0.916659	+	4.22965i	−0.0483121	+	0.222922i
$361$			11.7332i			0.617538i
$362$	−13.9122	−	5.76264i	−0.731211	−	0.302878i
$363$	0.999409	+	2.41279i	0.0524554	+	0.126639i
$364$	−0.556190	−	1.34276i	−0.0291523	−	0.0703798i
$365$	16.7143	−	24.1132i	0.874868	−	1.26214i
$366$	−7.79352	−	7.79352i	−0.407374	−	0.407374i
$367$	−0.926723	+	0.383861i	−0.0483745	+	0.0200374i	−0.406740	−	0.913544i	$-0.633334\pi$
$367$	−0.926723	+	0.383861i	−0.0483745	+	0.0200374i	0.358365	+	0.933582i	$0.383334\pi$
$368$	0.0427996	+	0.103327i	0.00223108	+	0.00538632i
$369$	−1.30005	+	3.13861i	−0.0676781	+	0.163389i
$370$	0.802829	+	4.43005i	0.0417371	+	0.230307i
$371$	2.17612	+	0.901377i	0.112978	+	0.0467971i
$372$	−4.22780	−	4.22780i	−0.219201	−	0.219201i
$373$			18.5917i			0.962640i	0.876545	+	0.481320i	$0.159843\pi$
$373$			18.5917i			0.962640i	−0.876545	+	0.481320i	$0.840157\pi$
$374$	−10.3184	+	6.12371i	−0.533553	+	0.316650i
$375$	5.90933	+	9.90687i	0.305156	+	0.511589i
$376$	4.63618	−	4.63618i	0.239093	−	0.239093i
$377$	7.21300	−	17.4137i	0.371488	−	0.896852i
$378$	2.00610			0.103182
$379$	−12.5001	+	30.1778i	−0.642085	+	1.55013i	0.181777	+	0.983340i	$0.441815\pi$
$379$	−12.5001	+	30.1778i	−0.642085	+	1.55013i	−0.823862	+	0.566790i	$0.808185\pi$
$380$	−5.06834	+	3.26280i	−0.260000	+	0.167378i
$381$	−1.36554	−	3.29670i	−0.0699587	−	0.168895i
$382$	5.94022	−	5.94022i	0.303928	−	0.303928i
$383$	−18.9034	+	18.9034i	−0.965920	+	0.965920i	−0.999438	−	0.0335177i	$-0.989329\pi$
$383$	−18.9034	+	18.9034i	−0.965920	+	0.965920i	0.0335177	+	0.999438i	$0.489329\pi$
$384$	−0.394838	−	0.953222i	−0.0201490	−	0.0486439i
$385$	−1.38763	−	2.15551i	−0.0707204	−	0.109855i
$386$	2.24530	−	5.42064i	0.114283	−	0.275904i
$387$	23.9886			1.21941
$388$	7.22162	−	17.4345i	0.366622	−	0.885104i
$389$	−14.0519	+	14.0519i	−0.712459	+	0.712459i	−0.967049	−	0.254590i	$-0.918059\pi$
$389$	−14.0519	+	14.0519i	−0.712459	+	0.712459i	0.254590	+	0.967049i	$0.418059\pi$
$390$	1.51775	+	8.37502i	0.0768542	+	0.424086i
$391$	0.446820	+	0.113993i	0.0225967	+	0.00576485i
$392$		−	6.84480i		−	0.345715i
$393$	−8.07572	−	8.07572i	−0.407366	−	0.407366i
$394$	5.52186	+	2.28723i	0.278187	+	0.115229i
$395$	−5.43942	−	30.0150i	−0.273687	−	1.51022i
$396$	−2.15545	+	5.20371i	−0.108315	+	0.261496i
$397$	−8.19219	−	19.7777i	−0.411154	−	0.992614i	−0.984829	−	0.173530i	$-0.944483\pi$
$397$	−8.19219	−	19.7777i	−0.411154	−	0.992614i	0.573674	−	0.819083i	$-0.305517\pi$
$398$	18.6512	−	7.72557i	0.934899	−	0.387248i
$399$	0.774782	+	0.774782i	0.0387876	+	0.0387876i
$400$	4.55139	+	2.07000i	0.227569	+	0.103500i
$401$	−10.2226	−	24.6796i	−0.510494	−	1.23244i	−0.943597	−	0.331097i	$-0.892581\pi$
$401$	−10.2226	−	24.6796i	−0.510494	−	1.23244i	0.433102	−	0.901345i	$-0.357419\pi$
$402$	−0.450882	−	1.08853i	−0.0224880	−	0.0542907i
$403$	19.7517	+	8.18143i	0.983903	+	0.407546i
$404$			7.49145i			0.372714i
$405$	1.20730	+	0.261648i	0.0599912	+	0.0130014i
$406$	−1.42320	+	1.42320i	−0.0706324	+	0.0706324i
$407$			5.85938i			0.290439i
$408$	−4.12203	−	1.05161i	−0.204071	−	0.0520625i
$409$	−5.59439			−0.276625			−0.138312	−	0.990389i	$-0.544168\pi$
$409$	−5.59439			−0.276625			−0.138312	+	0.990389i	$0.544168\pi$
$410$	3.22567	+	2.23591i	0.159305	+	0.110424i
$411$	−15.1120	−	6.25961i	−0.745422	−	0.308764i
$412$	18.6697			0.919788
$413$	−0.446093	−	0.184778i	−0.0219508	−	0.00909231i
$414$	0.199987	−	0.0828374i	0.00982883	−	0.00407124i
$415$	14.6292	−	9.41770i	0.718119	−	0.462297i
$416$	2.60870	+	2.60870i	0.127902	+	0.127902i
$417$	−7.97173	+	7.97173i	−0.390377	+	0.390377i
$418$	−7.24766	+	3.00208i	−0.354494	+	0.146836i
$419$	10.9816	−	4.54871i	0.536484	−	0.222219i	−0.0979565	−	0.995191i	$-0.531231\pi$
$419$	10.9816	−	4.54871i	0.536484	−	0.222219i	0.634440	+	0.772972i	$0.281231\pi$
$420$	0.192506	−	0.888263i	0.00939334	−	0.0433428i
$421$			11.7010i			0.570272i	0.958487	+	0.285136i	$0.0920388\pi$
$421$			11.7010i			0.570272i	−0.958487	+	0.285136i	$0.907961\pi$
$422$	−2.33567	+	5.63881i	−0.113699	+	0.274493i
$423$	−8.97318	−	8.97318i	−0.436291	−	0.436291i
$424$	−5.97891			−0.290362
$425$	18.0773	−	9.91007i	0.876880	−	0.480709i
$426$	4.19354			0.203178
$427$	−2.97577	−	2.97577i	−0.144008	−	0.144008i
$428$	−4.85568	+	11.7227i	−0.234708	+	0.566636i
$429$			11.0772i			0.534811i
$430$	5.87002	−	27.0855i	0.283077	−	1.30618i
$431$	18.2947	−	7.57790i	0.881224	−	0.365015i	0.104252	−	0.994551i	$-0.466755\pi$
$431$	18.2947	−	7.57790i	0.881224	−	0.365015i	0.776971	+	0.629536i	$0.216755\pi$
$432$	−4.70460	+	1.94871i	−0.226350	+	0.0937573i
$433$	−23.2176	+	23.2176i	−1.11577	+	1.11577i	−0.123411	+	0.992356i	$0.539383\pi$
$433$	−23.2176	+	23.2176i	−1.11577	+	1.11577i	−0.992356	+	0.123411i	$0.960617\pi$
$434$	−1.61429	−	1.61429i	−0.0774882	−	0.0774882i
$435$	9.91085	−	6.38022i	0.475189	−	0.305908i
$436$	1.12121	−	0.464419i	0.0536961	−	0.0222417i
$437$	0.278539	+	0.115375i	0.0133243	+	0.00551913i
$438$	13.5378			0.646863
$439$	9.34705	+	3.87167i	0.446110	+	0.184785i	0.594418	−	0.804156i	$-0.297383\pi$
$439$	9.34705	+	3.87167i	0.446110	+	0.184785i	−0.148308	+	0.988941i	$0.547383\pi$
$440$	5.34806	+	3.70706i	0.254959	+	0.176727i
$441$	−13.2479			−0.630853
$442$	15.0561	−	2.16640i	0.716147	−	0.103045i
$443$		−	19.9465i		−	0.947686i	−0.880609	−	0.473843i	$-0.842866\pi$
$443$		−	19.9465i		−	0.947686i	0.880609	−	0.473843i	$-0.157134\pi$
$444$	−1.46894	+	1.46894i	−0.0697129	+	0.0697129i
$445$	11.3317	+	2.45584i	0.537176	+	0.116418i
$446$		−	24.6282i		−	1.16618i
$447$	−16.6945	−	6.91509i	−0.789623	−	0.327072i
$448$	−0.150759	−	0.363965i	−0.00712271	−	0.0171957i
$449$	0.748836	+	1.80785i	0.0353398	+	0.0853177i	0.940564	−	0.339616i	$-0.110297\pi$
$449$	0.748836	+	1.80785i	0.0353398	+	0.0853177i	−0.905224	+	0.424934i	$0.860297\pi$
$450$	4.00641	−	8.80907i	0.188864	−	0.415264i
$451$	3.61186	+	3.61186i	0.170076	+	0.170076i
$452$	−1.61357	+	0.668364i	−0.0758961	+	0.0314372i
$453$	8.20565	+	19.8102i	0.385535	+	0.930764i
$454$	−4.08127	+	9.85307i	−0.191544	+	0.462427i
$455$	0.579516	+	3.19780i	0.0271681	+	0.149915i
$456$	−2.56960	−	1.06436i	−0.120332	−	0.0498433i
$457$	−18.3336	−	18.3336i	−0.857610	−	0.857610i	0.133446	−	0.991056i	$-0.457396\pi$
$457$	−18.3336	−	18.3336i	−0.857610	−	0.857610i	−0.991056	+	0.133446i	$0.957396\pi$
$458$			18.3801i			0.858846i
$459$	−5.19019	+	20.3442i	−0.242258	+	0.949584i
$460$	−0.0445946	−	0.246076i	−0.00207924	−	0.0114733i
$461$	5.53188	−	5.53188i	0.257645	−	0.257645i	−0.566450	−	0.824096i	$-0.691684\pi$
$461$	5.53188	−	5.53188i	0.257645	−	0.257645i	0.824096	+	0.566450i	$0.191684\pi$
$462$	0.452662	−	1.09282i	0.0210598	−	0.0508427i
$463$	0.869987			0.0404317			0.0202159	−	0.999796i	$-0.493565\pi$
$463$	0.869987			0.0404317			0.0202159	+	0.999796i	$0.493565\pi$
$464$	1.95514	−	4.72012i	0.0907649	−	0.219126i
$465$	7.23684	+	11.2415i	0.335600	+	0.521312i
$466$	8.38625	+	20.2462i	0.388486	+	0.937887i
$467$	7.59160	−	7.59160i	0.351298	−	0.351298i	−0.509295	−	0.860592i	$-0.670094\pi$
$467$	7.59160	−	7.59160i	0.351298	−	0.351298i	0.860592	+	0.509295i	$0.170094\pi$
$468$	5.04906	−	5.04906i	0.233393	−	0.233393i
$469$	−0.172159	−	0.415627i	−0.00794954	−	0.0191919i
$470$	−12.3273	+	7.93586i	−0.568618	+	0.366054i
$471$	−0.775913	+	1.87322i	−0.0357522	+	0.0863134i
$472$	1.22565			0.0564150
$473$	13.8029	−	33.3230i	0.634656	−	1.53220i
$474$	9.95255	−	9.95255i	0.457136	−	0.457136i
$475$	12.6213	−	4.72989i	0.579106	−	0.217022i
$476$	−1.57390	−	0.401532i	−0.0721395	−	0.0184042i
$477$			11.5720i			0.529846i
$478$	−16.0146	−	16.0146i	−0.732491	−	0.732491i
$479$	20.5228	+	8.50081i	0.937709	+	0.388412i	0.798598	−	0.601865i	$-0.205575\pi$
$479$	20.5228	+	8.50081i	0.937709	+	0.388412i	0.139111	+	0.990277i	$0.455575\pi$
$480$	0.411397	+	2.27011i	0.0187776	+	0.103616i
$481$	2.84262	−	6.86270i	0.129612	−	0.312912i
$482$	6.12642	+	14.7905i	0.279051	+	0.673688i
$483$	−0.0419990	+	0.0173966i	−0.00191102	+	0.000791571i
$484$	−1.78982	−	1.78982i	−0.0813555	−	0.0813555i
$485$	−24.0388	+	34.6801i	−1.09155	+	1.57474i
$486$	6.06426	+	14.6404i	0.275080	+	0.664103i
$487$	0.274346	+	0.662330i	0.0124318	+	0.0300130i	0.929974	−	0.367626i	$-0.119829\pi$
$487$	0.274346	+	0.662330i	0.0124318	+	0.0300130i	−0.917542	+	0.397639i	$0.869829\pi$
$488$	9.86927	+	4.08798i	0.446761	+	0.185054i
$489$			1.89263i			0.0855875i
$490$	−3.24177	+	14.9582i	−0.146448	+	0.675742i
$491$	11.1861	−	11.1861i	0.504820	−	0.504820i	−0.408112	−	0.912932i	$-0.633813\pi$
$491$	11.1861	−	11.1861i	0.504820	−	0.504820i	0.912932	+	0.408112i	$0.133813\pi$
$492$			1.81098i			0.0816454i
$493$	−10.7508	−	18.1150i	−0.484192	−	0.815861i
$494$	9.94511			0.447452
$495$	7.17491	−	10.3510i	0.322488	−	0.465243i
$496$	5.35385	+	2.21764i	0.240395	+	0.0995748i
$497$	1.60120			0.0718237
$498$	7.41686	+	3.07216i	0.332357	+	0.137667i
$499$	28.4635	−	11.7900i	1.27420	−	0.527792i	0.359964	−	0.932966i	$-0.382789\pi$
$499$	28.4635	−	11.7900i	1.27420	−	0.527792i	0.914240	+	0.405174i	$0.132789\pi$
$500$	−8.96594	−	6.67922i	−0.400969	−	0.298704i
$501$	9.66218	+	9.66218i	0.431674	+	0.431674i
$502$	−4.66204	+	4.66204i	−0.208077	+	0.208077i
$503$	−31.7976	+	13.1710i	−1.41779	+	0.587266i	−0.954303	−	0.298839i	$-0.903401\pi$
$503$	−31.7976	+	13.1710i	−1.41779	+	0.587266i	−0.463483	+	0.886106i	$0.653401\pi$
$504$	−0.704444	+	0.291790i	−0.0313784	+	0.0129974i
$505$	3.54803	−	16.3713i	0.157885	−	0.728515i
$506$		−	0.325470i		−	0.0144689i
$507$	0.241091	−	0.582046i	0.0107072	−	0.0258496i
$508$	2.44552	+	2.44552i	0.108502	+	0.108502i
$509$	−11.7386			−0.520305			−0.260152	−	0.965568i	$-0.583773\pi$
$509$	−11.7386			−0.520305			−0.260152	+	0.965568i	$0.583773\pi$
$510$	8.50996	+	4.25036i	0.376828	+	0.188209i
$511$	5.16910			0.228668
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−5.25313	+	12.6822i	−0.231931	+	0.559932i
$514$			17.0367i			0.751456i
$515$	−40.7995	−	8.84214i	−1.79784	−	0.389631i
$516$	11.8144	−	4.89369i	0.520101	−	0.215433i
$517$	−17.6279	+	7.30173i	−0.775276	+	0.321130i
$518$	−0.560880	+	0.560880i	−0.0246437	+	0.0246437i
$519$	−7.65683	−	7.65683i	−0.336098	−	0.336098i
$520$	−4.46538	−	6.93639i	−0.195820	−	0.304181i
$521$	28.8194	−	11.9374i	1.26260	−	0.522986i	0.351894	−	0.936040i	$-0.385538\pi$
$521$	28.8194	−	11.9374i	1.26260	−	0.522986i	0.910707	+	0.413054i	$0.135538\pi$
$522$	−9.13564	−	3.78411i	−0.399856	−	0.165626i
$523$	19.6068			0.857346			0.428673	−	0.903460i	$-0.358981\pi$
$523$	19.6068			0.857346			0.428673	+	0.903460i	$0.358981\pi$
$524$	10.2266	+	4.23601i	0.446753	+	0.185051i
$525$	−0.841381	+	1.84998i	−0.0367209	+	0.0807398i
$526$	−32.1207			−1.40053
$527$	20.5472	−	12.1942i	0.895051	−	0.531189i
$528$			3.00255i			0.130669i
$529$	16.2546	−	16.2546i	0.706722	−	0.706722i
$530$	13.0659	+	2.83167i	0.567548	+	0.123000i
$531$		−	2.37220i		−	0.102945i
$532$	−0.981140	−	0.406401i	−0.0425378	−	0.0176197i
$533$	−2.47807	−	5.98259i	−0.107337	−	0.259135i
$534$	2.04737	+	4.94280i	0.0885985	+	0.213896i
$535$	16.1633	−	23.3182i	0.698799	−	1.00814i
$536$	0.807476	+	0.807476i	0.0348776	+	0.0348776i
$537$	−2.79158	+	1.15631i	−0.120466	+	0.0498985i
$538$	7.78444	+	18.7933i	0.335611	+	0.810237i
$539$	−7.62275	+	18.4029i	−0.328335	+	0.792671i
$540$	11.2041	−	2.03044i	0.482146	−	0.0873761i
$541$	−27.7801	−	11.5069i	−1.19436	−	0.494721i	−0.305189	−	0.952292i	$-0.598720\pi$
$541$	−27.7801	−	11.5069i	−1.19436	−	0.494721i	−0.889173	+	0.457571i	$0.848720\pi$
$542$	20.4418	+	20.4418i	0.878050	+	0.878050i
$543$			15.5368i			0.666747i
$544$	4.08107	−	0.587220i	0.174975	−	0.0251768i
$545$	−2.67017	+	0.483897i	−0.114377	+	0.0207279i
$546$	−1.06034	+	1.06034i	−0.0453786	+	0.0453786i
$547$	−8.48235	+	20.4782i	−0.362679	+	0.875585i	0.632227	+	0.774783i	$0.282141\pi$
$547$	−8.48235	+	20.4782i	−0.362679	+	0.875585i	−0.994906	+	0.100802i	$0.967859\pi$
$548$	15.8536			0.677233
$549$	7.91217	−	19.1017i	0.337683	−	0.815240i
$550$	−9.93161	−	10.6341i	−0.423485	−	0.453438i
$551$	−5.27045	−	12.7240i	−0.224529	−	0.542061i
$552$	0.0815951	−	0.0815951i	0.00347292	−	0.00347292i
$553$	3.80014	−	3.80014i	0.161599	−	0.161599i
$554$	−4.99813	−	12.0666i	−0.212350	−	0.512659i
$555$	3.90584	−	2.51443i	0.165794	−	0.106731i
$556$	4.18146	−	10.0949i	0.177334	−	0.428121i
$557$	29.1002			1.23301			0.616507	−	0.787349i	$-0.288547\pi$
$557$	29.1002			1.23301			0.616507	+	0.787349i	$0.288547\pi$
$558$	4.29217	−	10.3622i	0.181702	−	0.438668i
$559$	−32.3327	+	32.3327i	−1.36753	+	1.36753i
$560$	0.157082	+	0.866787i	0.00663793	+	0.0366284i
$561$	9.91136	+	7.41788i	0.418458	+	0.313183i
$562$			18.5646i			0.783100i
$563$	−28.3024	−	28.3024i	−1.19280	−	1.19280i	−0.976276	−	0.216528i	$-0.930527\pi$
$563$	−28.3024	−	28.3024i	−1.19280	−	1.19280i	−0.216528	−	0.976276i	$-0.569473\pi$
$564$	−6.24985	−	2.58877i	−0.263166	−	0.109007i
$565$	3.84274	−	0.696395i	0.161665	−	0.0292975i
$566$	−6.83217	+	16.4943i	−0.287177	+	0.693308i
$567$	0.0832878	+	0.201074i	0.00349776	+	0.00844433i
$568$	−3.75506	+	1.55540i	−0.157559	+	0.0652630i
$569$	9.59571	+	9.59571i	0.402273	+	0.402273i	0.879033	−	0.476760i	$-0.158189\pi$
$569$	9.59571	+	9.59571i	0.402273	+	0.402273i	−0.476760	+	0.879033i	$0.658189\pi$
$570$	5.11134	+	3.54298i	0.214091	+	0.148399i
$571$	−7.10201	−	17.1458i	−0.297210	−	0.717528i	−0.999981	−	0.00611249i	$-0.998054\pi$
$571$	−7.10201	−	17.1458i	−0.297210	−	0.717528i	0.702771	−	0.711416i	$-0.251946\pi$
$572$	−4.10856	−	9.91894i	−0.171788	−	0.414732i
$573$	−8.00777	−	3.31693i	−0.334530	−	0.138567i
$574$			0.691480i			0.0288618i
$575$	−0.0190896	+	0.558878i	−0.000796093	+	0.0233068i
$576$	1.36858	−	1.36858i	0.0570243	−	0.0570243i
$577$			14.7520i			0.614132i	0.951688	+	0.307066i	$0.0993472\pi$
$577$			14.7520i			0.614132i	−0.951688	+	0.307066i	$0.900653\pi$
$578$	8.14401	−	14.9223i	0.338746	−	0.620686i
$579$	−6.05361			−0.251579
$580$	−6.50812	+	9.38906i	−0.270235	+	0.389860i
$581$	2.83195	+	1.17303i	0.117489	+	0.0486656i
$582$	−19.4704			−0.807072
$583$	16.0749	+	6.65845i	0.665755	+	0.275765i
$584$	−12.1223	+	5.02123i	−0.501625	+	0.207780i
$585$	−13.4252	+	8.64260i	−0.555062	+	0.357328i
$586$	4.33485	+	4.33485i	0.179071	+	0.179071i
$587$	−8.87191	+	8.87191i	−0.366183	+	0.366183i	−0.866083	−	0.499900i	$-0.833370\pi$
$587$	−8.87191	+	8.87191i	−0.366183	+	0.366183i	0.499900	+	0.866083i	$0.333370\pi$
$588$	−6.52462	+	2.70259i	−0.269071	+	0.111453i
$589$	14.4324	−	5.97808i	0.594675	−	0.246322i
$590$	−2.67845	−	0.580479i	−0.110270	−	0.0238979i
$591$		−	6.16664i		−	0.253662i
$592$	0.770514	−	1.86018i	0.0316679	−	0.0764531i
$593$	24.3384	+	24.3384i	0.999457	+	0.999457i	1.00000		0.000542995i	$-0.000172841\pi$
$593$	24.3384	+	24.3384i	0.999457	+	0.999457i	−0.000542995		1.00000i	$0.500173\pi$
$594$	14.8190			0.608031
$595$	3.24933	+	1.62290i	0.133209	+	0.0665323i
$596$	17.5137			0.717391
$597$	−14.7284	−	14.7284i	−0.602792	−	0.602792i
$598$	−0.157899	+	0.381201i	−0.00645696	+	0.0155885i
$599$		−	17.4597i		−	0.713383i	−0.934222	−	0.356692i	$-0.883905\pi$
$599$		−	17.4597i		−	0.713383i	0.934222	−	0.356692i	$-0.116095\pi$
$600$	0.176107	−	5.15580i	0.00718954	−	0.210484i
$601$	−31.8764	+	13.2036i	−1.30026	+	0.538587i	−0.922028	−	0.387122i	$-0.873469\pi$
$601$	−31.8764	+	13.2036i	−1.30026	+	0.538587i	−0.378236	+	0.925709i	$0.623469\pi$
$602$	4.51105	−	1.86854i	0.183857	−	0.0761560i
$603$	1.56285	−	1.56285i	0.0636440	−	0.0636440i
$604$	−14.6953	−	14.6953i	−0.597944	−	0.597944i
$605$	3.06368	+	4.75904i	0.124556	+	0.193483i
$606$	7.14102	−	2.95791i	0.290084	−	0.120157i
$607$	10.1593	+	4.20810i	0.412352	+	0.170802i	0.579208	−	0.815179i	$-0.303362\pi$
$607$	10.1593	+	4.20810i	0.412352	+	0.170802i	−0.166857	+	0.985981i	$0.553362\pi$
$608$	2.69570			0.109325
$609$	1.91856	+	0.794695i	0.0777441	+	0.0322027i
$610$	−19.6316	−	13.6078i	−0.794858	−	0.550964i
$611$	24.1888			0.978573
$612$	−1.13655	−	7.89880i	−0.0459422	−	0.319290i
$613$			19.1671i			0.774150i	0.922048	+	0.387075i	$0.126515\pi$
$613$			19.1671i			0.774150i	−0.922048	+	0.387075i	$0.873485\pi$
$614$	−20.7204	+	20.7204i	−0.836207	+	0.836207i
$615$	0.857700	−	3.95760i	0.0345858	−	0.159586i
$616$			1.14645i			0.0461918i
$617$	−17.5554	−	7.27170i	−0.706756	−	0.292748i	0.000205623	−	1.00000i	$-0.499935\pi$
$617$	−17.5554	−	7.27170i	−0.706756	−	0.292748i	−0.706961	+	0.707252i	$0.749935\pi$
$618$	−7.37148	−	17.7963i	−0.296525	−	0.715874i
$619$	−4.37433	−	10.5606i	−0.175819	−	0.424465i	0.811263	−	0.584682i	$-0.198781\pi$
$619$	−4.37433	−	10.5606i	−0.175819	−	0.424465i	−0.987082	+	0.160217i	$0.948781\pi$
$620$	−10.6497	−	7.38192i	−0.427701	−	0.296465i
$621$	−0.402710	−	0.402710i	−0.0161602	−	0.0161602i
$622$	20.7505	−	8.59516i	0.832021	−	0.344634i
$623$	0.781740	+	1.88729i	0.0313198	+	0.0756126i
$624$	1.45666	−	3.51668i	0.0583130	−	0.140780i
$625$	16.4302	+	18.8427i	0.657210	+	0.753708i
$626$	5.83076	+	2.41518i	0.233044	+	0.0965300i
$627$	5.72329	+	5.72329i	0.228566	+	0.228566i
$628$		−	1.96514i		−	0.0784178i
$629$	−4.23686	−	7.13909i	−0.168935	−	0.284654i
$630$	1.67764	−	0.304028i	0.0668388	−	0.0121128i
$631$	−15.6208	+	15.6208i	−0.621853	+	0.621853i	−0.946005	−	0.324152i	$-0.894921\pi$
$631$	−15.6208	+	15.6208i	−0.621853	+	0.621853i	0.324152	+	0.946005i	$0.394921\pi$
$632$	−5.22048	+	12.6033i	−0.207659	+	0.501334i
$633$	6.29725			0.250293
$634$	3.97142	−	9.58786i	0.157725	−	0.380782i
$635$	−4.18605	−	6.50250i	−0.166118	−	0.258044i
$636$	2.36070	+	5.69923i	0.0936078	+	0.225989i
$637$	17.8560	−	17.8560i	0.707481	−	0.707481i
$638$	−10.5132	+	10.5132i	−0.416220	+	0.416220i
$639$	3.01042	+	7.26781i	0.119091	+	0.287510i
$640$	−1.21037	−	1.88016i	−0.0478442	−	0.0743198i
$641$	−17.8557	+	43.1074i	−0.705256	+	1.70264i	0.00627082	+	0.999980i	$0.498004\pi$
$641$	−17.8557	+	43.1074i	−0.705256	+	1.70264i	−0.711527	+	0.702659i	$0.751996\pi$
$642$	13.0915			0.516681
$643$	16.5600	−	39.9793i	0.653061	−	1.57663i	−0.155250	−	0.987875i	$-0.549618\pi$
$643$	16.5600	−	39.9793i	0.653061	−	1.57663i	0.808312	−	0.588755i	$-0.200382\pi$
$644$	0.0311551	−	0.0311551i	0.00122768	−	0.00122768i
$645$	−28.1362	+	5.09893i	−1.10786	+	0.200770i
$646$	6.65980	−	8.89845i	0.262026	−	0.350105i
$647$		−	1.65565i		−	0.0650904i	−0.999470	−	0.0325452i	$-0.989639\pi$
$647$		−	1.65565i		−	0.0650904i	0.999470	−	0.0325452i	$-0.0103613\pi$
$648$	−0.390645	−	0.390645i	−0.0153460	−	0.0153460i
$649$	−3.29528	−	1.36495i	−0.129351	−	0.0535789i
$650$	6.47320	+	17.2732i	0.253900	+	0.677510i
$651$	−0.901392	+	2.17615i	−0.0353284	+	0.0852902i
$652$	−0.701981	−	1.69473i	−0.0274917	−	0.0663709i
$653$	41.5990	−	17.2309i	1.62789	−	0.674296i	0.632901	−	0.774233i	$-0.281864\pi$
$653$	41.5990	−	17.2309i	1.62789	−	0.674296i	0.994994	+	0.0999369i	$0.0318641\pi$
$654$	−0.885390	−	0.885390i	−0.0346215	−	0.0346215i
$655$	−20.3424	−	14.1005i	−0.794844	−	0.550954i
$656$	−0.671699	−	1.62163i	−0.0262255	−	0.0633138i
$657$	9.71844	+	23.4624i	0.379153	+	0.915355i
$658$	−2.38635	−	0.988460i	−0.0930297	−	0.0385342i
$659$			8.20019i			0.319434i	0.987163	+	0.159717i	$0.0510582\pi$
$659$			8.20019i			0.319434i	−0.987163	+	0.159717i	$0.948942\pi$
$660$	1.42204	−	6.56158i	0.0553528	−	0.255409i
$661$	14.0397	−	14.0397i	0.546079	−	0.546079i	−0.379225	−	0.925304i	$-0.623809\pi$
$661$	14.0397	−	14.0397i	0.546079	−	0.546079i	0.925304	+	0.379225i	$0.123809\pi$
$662$		−	7.64832i		−	0.297260i
$663$	−8.00979	−	13.4965i	−0.311075	−	0.524159i
$664$	−7.78083			−0.301955
$665$	1.95164	+	1.35280i	0.0756815	+	0.0524594i
$666$	−3.60033	−	1.49131i	−0.139510	−	0.0577870i
$667$	0.571397			0.0221246
$668$	−12.2356	−	5.06817i	−0.473411	−	0.196093i
$669$	−23.4762	+	9.72415i	−0.907642	+	0.375957i
$670$	−1.38218	−	2.14703i	−0.0533982	−	0.0829472i
$671$	−21.9819	−	21.9819i	−0.848603	−	0.848603i
$672$	−0.287414	+	0.287414i	−0.0110872	+	0.0110872i
$673$	−41.1575	+	17.0480i	−1.58650	+	0.657152i	−0.989427	−	0.145032i	$-0.953672\pi$
$673$	−41.1575	+	17.0480i	−1.58650	+	0.657152i	−0.597077	+	0.802184i	$0.703672\pi$
$674$	12.1918	−	5.05001i	0.469610	−	0.194519i
$675$	−25.4463	−	0.869171i	−0.979428	−	0.0334544i
$676$			0.610609i			0.0234850i
$677$	−10.0478	+	24.2576i	−0.386169	+	0.932293i	0.604575	+	0.796548i	$0.293343\pi$
$677$	−10.0478	+	24.2576i	−0.386169	+	0.932293i	−0.990744	+	0.135745i	$0.956657\pi$
$678$	1.27420	+	1.27420i	0.0489353	+	0.0489353i
$679$	−7.43429			−0.285302
$680$	−9.19663	−	0.649566i	−0.352675	−	0.0249097i
$681$	11.0036			0.421659
$682$	−11.9247	−	11.9247i	−0.456620	−	0.456620i
$683$	15.2523	−	36.8224i	0.583614	−	1.40897i	−0.305901	−	0.952063i	$-0.598958\pi$
$683$	15.2523	−	36.8224i	0.583614	−	1.40897i	0.889515	−	0.456906i	$-0.151042\pi$
$684$		−	5.21744i		−	0.199494i
$685$	−34.6455	−	7.50844i	−1.32374	−	0.286883i
$686$	−5.03903	+	2.08723i	−0.192391	+	0.0796909i
$687$	17.5203	−	7.25716i	0.668442	−	0.276878i
$688$	−8.76402	+	8.76402i	−0.334125	+	0.334125i
$689$	−15.5972	−	15.5972i	−0.594205	−	0.594205i
$690$	−0.216957	+	0.139668i	−0.00825941	+	0.00531709i
$691$	−29.5061	+	12.2218i	−1.12246	+	0.464940i	−0.865213	−	0.501404i	$-0.832817\pi$
$691$	−29.5061	+	12.2218i	−1.12246	+	0.464940i	−0.257251	+	0.966344i	$0.582817\pi$
$692$	9.69618	+	4.01629i	0.368593	+	0.152676i
$693$	2.21892			0.0842899
$694$	−5.33087	−	2.20812i	−0.202357	−	0.0838191i
$695$	−13.9190	+	20.0805i	−0.527977	+	0.761696i
$696$	−5.27128			−0.199807
$697$	−7.01241	−	1.78900i	−0.265614	−	0.0677634i
$698$			13.1142i			0.496379i
$699$	15.9879	−	15.9879i	0.604719	−	0.604719i
$700$	0.0672422	−	1.96862i	0.00254152	−	0.0744067i
$701$			32.4471i			1.22551i	0.790273	+	0.612755i	$0.209939\pi$
$701$			32.4471i			1.22551i	−0.790273	+	0.612755i	$0.790061\pi$
$702$	−17.3565	−	7.18929i	−0.655078	−	0.271342i
$703$	−2.07707	−	5.01449i	−0.0783382	−	0.189125i
$704$	−1.11366	−	2.68860i	−0.0419725	−	0.101331i
$705$	12.4319	+	8.61732i	0.468214	+	0.324547i
$706$	−16.5259	−	16.5259i	−0.621961	−	0.621961i
$707$	2.72663	−	1.12941i	0.102545	−	0.0424757i
$708$	−0.483932	−	1.16831i	−0.0181873	−	0.0439079i
$709$	5.57732	−	13.4648i	0.209461	−	0.505682i	−0.783878	−	0.620915i	$-0.786761\pi$
$709$	5.57732	−	13.4648i	0.209461	−	0.505682i	0.993339	+	0.115232i	$0.0367613\pi$
$710$	8.94272	−	1.62063i	0.335614	−	0.0608212i
$711$	24.3934	+	10.1041i	0.914824	+	0.378933i
$712$	−3.66660	−	3.66660i	−0.137412	−	0.137412i
$713$			0.648114i			0.0242720i
$714$	0.238684	+	1.65881i	0.00893254	+	0.0620796i
$715$	4.28087	+	23.6221i	0.160096	+	0.883415i
$716$	2.07081	−	2.07081i	0.0773900	−	0.0773900i
$717$	−8.94231	+	21.5887i	−0.333957	+	0.806243i
$718$	−23.4304			−0.874415
$719$	6.68973	−	16.1504i	0.249485	−	0.602310i	−0.748676	−	0.662937i	$-0.769310\pi$
$719$	6.68973	−	16.1504i	0.249485	−	0.602310i	0.998161	+	0.0606266i	$0.0193099\pi$
$720$	−3.63899	+	2.34264i	−0.135617	+	0.0873051i
$721$	−2.81462	−	6.79510i	−0.104822	−	0.253063i
$722$	−8.29664	+	8.29664i	−0.308769	+	0.308769i
$723$	11.6797	−	11.6797i	0.434372	−	0.434372i
$724$	−5.76264	−	13.9122i	−0.214167	−	0.517045i
$725$	18.6692	−	17.4359i	0.693356	−	0.647555i
$726$	−0.999409	+	2.41279i	−0.0370916	+	0.0895470i
$727$	32.5886			1.20864			0.604322	−	0.796740i	$-0.293444\pi$
$727$	32.5886			1.20864			0.604322	+	0.796740i	$0.293444\pi$
$728$	0.556190	−	1.34276i	0.0206138	−	0.0497660i
$729$	10.3892	−	10.3892i	0.384787	−	0.384787i
$730$	28.8695	−	5.23182i	1.06851	−	0.193638i
$731$	7.27812	+	50.5816i	0.269191	+	1.87083i
$732$		−	11.0217i		−	0.407374i
$733$	7.51384	+	7.51384i	0.277530	+	0.277530i	0.832122	−	0.554592i	$-0.187126\pi$
$733$	7.51384	+	7.51384i	0.277530	+	0.277530i	−0.554592	+	0.832122i	$0.687126\pi$
$734$	−0.926723	−	0.383861i	−0.0342060	−	0.0141686i
$735$	15.5385	−	2.81593i	0.573145	−	0.103867i
$736$	−0.0427996	+	0.103327i	−0.00157762	+	0.00380870i
$737$	−1.27173	−	3.07023i	−0.0468448	−	0.113093i
$738$	−3.13861	+	1.30005i	−0.115534	+	0.0478556i
$739$	−31.0482	−	31.0482i	−1.14213	−	1.14213i	−0.988060	−	0.154068i	$-0.950763\pi$
$739$	−31.0482	−	31.0482i	−1.14213	−	1.14213i	−0.154068	−	0.988060i	$-0.549237\pi$
$740$	−2.56483	+	3.70021i	−0.0942852	+	0.136022i
$741$	−3.92671	−	9.47991i	−0.144251	−	0.348253i
$742$	0.901377	+	2.17612i	0.0330906	+	0.0798877i
$743$	25.2669	+	10.4659i	0.926951	+	0.383956i	0.794521	−	0.607237i	$-0.207722\pi$
$743$	25.2669	+	10.4659i	0.926951	+	0.383956i	0.132430	+	0.991192i	$0.457722\pi$
$744$		−	5.97902i		−	0.219201i
$745$	−38.2734	−	8.29469i	−1.40223	−	0.303894i
$746$	−13.1463	+	13.1463i	−0.481320	+	0.481320i
$747$			15.0596i			0.551000i
$748$	−11.6263	−	2.96611i	−0.425101	−	0.108452i
$749$	4.99868			0.182648
$750$	−2.82669	+	11.1837i	−0.103216	+	0.408372i
$751$	3.42969	+	1.42062i	0.125151	+	0.0518393i	0.444380	−	0.895838i	$-0.353424\pi$
$751$	3.42969	+	1.42062i	0.125151	+	0.0518393i	−0.319229	+	0.947678i	$0.603424\pi$
$752$	6.55654			0.239093
$753$	6.28472	+	2.60321i	0.229028	+	0.0948664i
$754$	17.4137	−	7.21300i	0.634170	−	0.262682i
$755$	25.1544	+	39.0741i	0.915461	+	1.42205i
$756$	1.41852	+	1.41852i	0.0515912	+	0.0515912i
$757$	−18.4876	+	18.4876i	−0.671943	+	0.671943i	−0.958164	−	0.286221i	$-0.907601\pi$
$757$	−18.4876	+	18.4876i	−0.671943	+	0.671943i	0.286221	+	0.958164i	$0.407601\pi$
$758$	−30.1778	+	12.5001i	−1.09611	+	0.454023i
$759$	−0.310246	+	0.128508i	−0.0112612	+	0.00466454i
$760$	−5.89100	−	1.27671i	−0.213689	−	0.0463111i
$761$		−	24.3426i		−	0.882418i	−0.897404	−	0.441209i	$-0.854550\pi$
$761$		−	24.3426i		−	0.882418i	0.897404	−	0.441209i	$-0.145450\pi$
$762$	1.36554	−	3.29670i	0.0494683	−	0.119427i
$763$	−0.338065	−	0.338065i	−0.0122388	−	0.0122388i
$764$	8.40074			0.303928
$765$	−1.25722	+	17.7998i	−0.0454547	+	0.643553i
$766$	−26.7335			−0.965920
$767$	3.19734	+	3.19734i	0.115449	+	0.115449i
$768$	0.394838	−	0.953222i	0.0142475	−	0.0343965i
$769$			1.37023i			0.0494118i	0.999695	+	0.0247059i	$0.00786493\pi$
$769$			1.37023i			0.0494118i	−0.999695	+	0.0247059i	$0.992135\pi$
$770$	0.542971	−	2.50538i	0.0195673	−	0.0902877i
$771$	16.2398	−	6.72673i	0.584861	−	0.242257i
$772$	5.42064	−	2.24530i	0.195093	−	0.0808103i
$773$	−29.1433	+	29.1433i	−1.04821	+	1.04821i	−0.0494341	+	0.998777i	$0.515742\pi$
$773$	−29.1433	+	29.1433i	−1.04821	+	1.04821i	−0.998777	+	0.0494341i	$0.984258\pi$
$774$	16.9625	+	16.9625i	0.609704	+	0.609704i
$775$	19.7769	+	21.1758i	0.710409	+	0.760656i
$776$	17.4345	−	7.22162i	0.625863	−	0.259241i
$777$	0.756100	+	0.313187i	0.0271250	+	0.0112355i
$778$	−19.8724			−0.712459
$779$	−4.37141	−	1.81070i	−0.156622	−	0.0648750i
$780$	−4.84882	+	6.99524i	−0.173616	+	0.250470i
$781$	11.8280			0.423241
$782$	0.235344	+	0.396554i	0.00841590	+	0.0141808i
$783$			26.0162i			0.929745i
$784$	4.84001	−	4.84001i	0.172857	−	0.172857i
$785$	−0.930712	+	4.29450i	−0.0332186	+	0.153277i
$786$		−	11.4208i		−	0.407366i
$787$	−24.6218	−	10.1987i	−0.877672	−	0.363544i	−0.102079	−	0.994776i	$-0.532549\pi$
$787$	−24.6218	−	10.1987i	−0.877672	−	0.363544i	−0.775594	+	0.631233i	$0.782549\pi$
$788$	2.28723	+	5.52186i	0.0814792	+	0.196708i
$789$	12.6825	+	30.6182i	0.451508	+	1.09004i
$790$	17.3776	−	25.0701i	0.618266	−	0.891953i
$791$	0.486522	+	0.486522i	0.0172987	+	0.0172987i
$792$	−5.20371	+	2.15545i	−0.184906	+	0.0765905i
$793$	15.0816	+	36.4103i	0.535564	+	1.29297i
$794$	8.19219	−	19.7777i	0.290730	−	0.701884i
$795$	−2.45971	−	13.5728i	−0.0872368	−	0.481377i
$796$	18.6512	+	7.72557i	0.661074	+	0.273826i
$797$	13.8341	+	13.8341i	0.490027	+	0.490027i	0.908315	−	0.418287i	$-0.137370\pi$
$797$	13.8341	+	13.8341i	0.490027	+	0.490027i	−0.418287	+	0.908315i	$0.637370\pi$
$798$			1.09571i			0.0387876i
$799$	16.1981	−	21.6430i	0.573049	−	0.765676i
$800$	1.75461	+	4.68202i	0.0620348	+	0.165535i
$801$	−7.09659	+	7.09659i	−0.250746	+	0.250746i
$802$	10.2226	−	24.6796i	0.360974	−	0.871468i
$803$	38.1840			1.34748
$804$	0.450882	−	1.08853i	0.0159014	−	0.0383893i
$805$	−0.0828399	+	0.0533291i	−0.00291972	+	0.00187960i
$806$	8.18143	+	19.7517i	0.288179	+	0.695725i
$807$	14.8406	−	14.8406i	0.522414	−	0.522414i
$808$	−5.29725	+	5.29725i	−0.186357	+	0.186357i
$809$	2.63652	+	6.36511i	0.0926950	+	0.223785i	0.963426	−	0.267974i	$-0.0863540\pi$
$809$	2.63652	+	6.36511i	0.0926950	+	0.223785i	−0.870731	+	0.491759i	$0.836354\pi$
$810$	0.668677	+	1.03870i	0.0234949	+	0.0364963i
$811$	2.81637	−	6.79932i	0.0988962	−	0.238757i	−0.866686	−	0.498854i	$-0.833755\pi$
$811$	2.81637	−	6.79932i	0.0988962	−	0.238757i	0.965582	+	0.260097i	$0.0837546\pi$
$812$	−2.01271			−0.0706324
$813$	11.4144	−	27.5568i	0.400320	−	0.966458i
$814$	−4.14321	+	4.14321i	−0.145219	+	0.145219i
$815$	0.731422	+	4.03603i	0.0256206	+	0.141376i
$816$	−2.17111	−	3.65832i	−0.0760042	−	0.128067i
$817$			33.4110i			1.16890i
$818$	−3.95583	−	3.95583i	−0.138312	−	0.138312i
$819$	−2.59887	−	1.07649i	−0.0908120	−	0.0376156i
$820$	0.699870	+	3.86192i	0.0244405	+	0.134864i
$821$	16.0101	−	38.6518i	0.558756	−	1.34896i	−0.351996	−	0.936002i	$-0.614497\pi$
$821$	16.0101	−	38.6518i	0.558756	−	1.34896i	0.910752	−	0.412955i	$-0.135503\pi$
$822$	−6.25961	−	15.1120i	−0.218329	−	0.527093i
$823$	−7.64393	+	3.16622i	−0.266450	+	0.110367i	−0.511909	−	0.859040i	$-0.671061\pi$
$823$	−7.64393	+	3.16622i	−0.266450	+	0.110367i	0.245458	+	0.969407i	$0.421061\pi$
$824$	13.2014	+	13.2014i	0.459894	+	0.459894i
$825$	−6.21526	+	13.6658i	−0.216388	+	0.475781i
$826$	−0.184778	−	0.446093i	−0.00642924	−	0.0155216i
$827$	−17.9548	−	43.3467i	−0.624350	−	1.50731i	−0.846548	−	0.532312i	$-0.821323\pi$
$827$	−17.9548	−	43.3467i	−0.624350	−	1.50731i	0.222199	−	0.975001i	$-0.428677\pi$
$828$	0.199987	+	0.0828374i	0.00695004	+	0.00287880i
$829$		−	32.4221i		−	1.12606i	−0.826435	−	0.563032i	$-0.809635\pi$
$829$		−	32.4221i		−	1.12606i	0.826435	−	0.563032i	$-0.190365\pi$
$830$	17.0037	+	3.68508i	0.590208	+	0.127911i
$831$	−9.52867	+	9.52867i	−0.330546	+	0.330546i
$832$			3.68926i			0.127902i
$833$	−4.01940	−	27.9341i	−0.139264	−	0.967861i
$834$	−11.2737			−0.390377
$835$	24.3386	+	16.8706i	0.842273	+	0.583830i
$836$	−7.24766	−	3.00208i	−0.250665	−	0.103829i
$837$	−29.5093			−1.01999
$838$	10.9816	+	4.54871i	0.379351	+	0.157132i
$839$	25.8063	−	10.6893i	0.890931	−	0.369036i	0.110205	−	0.993909i	$-0.464849\pi$
$839$	25.8063	−	10.6893i	0.890931	−	0.369036i	0.780726	+	0.624873i	$0.214849\pi$
$840$	0.764219	−	0.491974i	0.0263681	−	0.0169747i
$841$	2.04917	+	2.04917i	0.0706609	+	0.0706609i
$842$	−8.27386	+	8.27386i	−0.285136	+	0.285136i
$843$	17.6962	−	7.33000i	0.609489	−	0.252459i
$844$	−5.63881	+	2.33567i	−0.194096	+	0.0803971i
$845$	0.289191	−	1.33439i	0.00994846	−	0.0459043i
$846$		−	12.6900i		−	0.436291i
$847$	−0.381601	+	0.921265i	−0.0131119	+	0.0316550i
$848$	−4.22773	−	4.22773i	−0.145181	−	0.145181i
$849$	18.4203			0.632185
$850$	19.7901	+	5.77514i	0.678795	+	0.198086i
$851$	0.225186			0.00771927
$852$	2.96528	+	2.96528i	0.101589	+	0.101589i
$853$	−0.882434	+	2.13038i	−0.0302140	+	0.0729429i	−0.938266	−	0.345914i	$-0.887569\pi$
$853$	−0.882434	+	2.13038i	−0.0302140	+	0.0729429i	0.908052	+	0.418857i	$0.137569\pi$
$854$		−	4.20837i		−	0.144008i
$855$	−2.47103	+	11.4019i	−0.0845076	+	0.389935i
$856$	−11.7227	+	4.85568i	−0.400672	+	0.165964i
$857$	24.2288	−	10.0359i	0.827638	−	0.342819i	0.0716710	−	0.997428i	$-0.477167\pi$
$857$	24.2288	−	10.0359i	0.827638	−	0.342819i	0.755967	+	0.654609i	$0.227167\pi$
$858$	−7.83274	+	7.83274i	−0.267405	+	0.267405i
$859$	−14.5456	−	14.5456i	−0.496290	−	0.496290i	0.413991	−	0.910281i	$-0.364134\pi$
$859$	−14.5456	−	14.5456i	−0.496290	−	0.496290i	−0.910281	+	0.413991i	$0.864134\pi$
$860$	23.3030	−	15.0016i	0.794627	−	0.511550i
$861$	0.659134	−	0.273022i	0.0224632	−	0.00930458i
$862$	18.2947	+	7.57790i	0.623119	+	0.258104i
$863$	−20.2672			−0.689905			−0.344953	−	0.938620i	$-0.612105\pi$
$863$	−20.2672			−0.689905			−0.344953	+	0.938620i	$0.612105\pi$
$864$	−4.70460	−	1.94871i	−0.160054	−	0.0662964i
$865$	−19.2873	−	13.3692i	−0.655786	−	0.454565i
$866$	−32.8347			−1.11577
$867$	−17.4398	−	1.87116i	−0.592288	−	0.0635481i
$868$		−	2.28294i		−	0.0774882i
$869$	28.0716	−	28.0716i	0.952263	−	0.952263i
$870$	11.5195	+	2.49653i	0.390548	+	0.0846404i
$871$			4.21292i			0.142749i
$872$	1.12121	+	0.464419i	0.0379689	+	0.0157272i
$873$	−13.9772	−	33.7440i	−0.473058	−	1.14206i
$874$	0.115375	+	0.278539i	0.00390261	+	0.00942174i
$875$	−1.07930	+	4.27024i	−0.0364871	+	0.144361i
$876$	9.57270	+	9.57270i	0.323432	+	0.323432i
$877$	21.5149	−	8.91177i	0.726507	−	0.300929i	0.0113911	−	0.999935i	$-0.496374\pi$
$877$	21.5149	−	8.91177i	0.726507	−	0.300929i	0.715116	+	0.699006i	$0.246374\pi$
$878$	3.87167	+	9.34705i	0.130663	+	0.315448i
$879$	2.42051	−	5.84363i	0.0816418	−	0.197101i
$880$	1.16036	+	6.40294i	0.0391158	+	0.215843i
$881$	14.1026	+	5.84148i	0.475128	+	0.196805i	0.607380	−	0.794412i	$-0.292221\pi$
$881$	14.1026	+	5.84148i	0.475128	+	0.196805i	−0.132252	+	0.991216i	$0.542221\pi$
$882$	−9.36769	−	9.36769i	−0.315426	−	0.315426i
$883$			13.6655i			0.459881i	0.973205	+	0.229940i	$0.0738532\pi$
$883$			13.6655i			0.459881i	−0.973205	+	0.229940i	$0.926147\pi$
$884$	12.1782	+	9.11441i	0.409596	+	0.306551i
$885$	0.504227	+	2.78235i	0.0169494	+	0.0935278i
$886$	14.1043	−	14.1043i	0.473843	−	0.473843i
$887$	−4.36999	+	10.5501i	−0.146730	+	0.354238i	−0.980108	−	0.198466i	$-0.936404\pi$
$887$	−4.36999	+	10.5501i	−0.146730	+	0.354238i	0.833378	+	0.552704i	$0.186404\pi$
$888$	−2.07740			−0.0697129
$889$	0.521398	−	1.25877i	0.0174871	−	0.0422177i
$890$	6.27621	+	9.74929i	0.210379	+	0.326797i
$891$	0.615245	+	1.48533i	0.0206115	+	0.0497605i
$892$	17.4148	−	17.4148i	0.583090	−	0.583090i
$893$	12.4977	−	12.4977i	0.418220	−	0.418220i
$894$	−6.91509	−	16.6945i	−0.231275	−	0.558347i
$895$	−5.50619	+	3.54467i	−0.184051	+	0.118485i
$896$	0.150759	−	0.363965i	0.00503651	−	0.0121592i
$897$	0.425714			0.0142142
$898$	−0.748836	+	1.80785i	−0.0249890	+	0.0603287i
$899$	20.9350	−	20.9350i	0.698222	−	0.698222i
$900$	9.06192	−	3.39599i	0.302064	−	0.113200i
$901$	−24.4004	+	3.51094i	−0.812895	+	0.116966i
$902$			5.10795i			0.170076i
$903$	−3.56227	−	3.56227i	−0.118545	−	0.118545i
$904$	−1.61357	−	0.668364i	−0.0536666	−	0.0222294i
$905$	6.00432	+	33.1322i	0.199591	+	1.10135i
$906$	−8.20565	+	19.8102i	−0.272614	+	0.658149i
$907$	−9.70020	−	23.4184i	−0.322090	−	0.777594i	−0.999132	−	0.0416499i	$-0.986739\pi$
$907$	−9.70020	−	23.4184i	−0.322090	−	0.777594i	0.677042	−	0.735944i	$-0.263261\pi$
$908$	−9.85307	+	4.08127i	−0.326985	+	0.135442i
$909$	10.2527	+	10.2527i	0.340060	+	0.340060i
$910$	−1.85141	+	2.67097i	−0.0613735	+	0.0885417i
$911$	19.6184	+	47.3631i	0.649988	+	1.56921i	0.812794	+	0.582552i	$0.197946\pi$
$911$	19.6184	+	47.3631i	0.649988	+	1.56921i	−0.162806	+	0.986658i	$0.552054\pi$
$912$	−1.06436	−	2.56960i	−0.0352446	−	0.0850879i
$913$	20.9195	+	8.66516i	0.692336	+	0.286775i
$914$		−	25.9276i		−	0.857610i
$915$	−5.21999	+	24.0861i	−0.172568	+	0.796262i
$916$	−12.9967	+	12.9967i	−0.429423	+	0.429423i
$917$		−	4.36076i		−	0.144005i
$918$	−18.0555	+	10.7155i	−0.595921	+	0.353663i
$919$	41.6077			1.37251			0.686255	−	0.727361i	$-0.259253\pi$
$919$	41.6077			1.37251			0.686255	+	0.727361i	$0.259253\pi$
$920$	0.142469	−	0.205535i	0.00469705	−	0.00677628i
$921$	27.9323	+	11.5700i	0.920402	+	0.381243i
$922$	7.82326			0.257645
$923$	−13.8534	−	5.73826i	−0.455990	−	0.188877i
$924$	1.09282	−	0.452662i	0.0359512	−	0.0148915i
$925$	7.35748	−	6.87146i	0.241912	−	0.225932i
$926$	0.615174	+	0.615174i	0.0202159	+	0.0202159i
$927$	25.5510	−	25.5510i	0.839205	−	0.839205i
$928$	4.72012	−	1.95514i	0.154945	−	0.0641805i
$929$	−19.1009	+	7.91184i	−0.626679	+	0.259579i	−0.673341	−	0.739332i	$-0.735142\pi$
$929$	−19.1009	+	7.91184i	−0.626679	+	0.259579i	0.0466623	+	0.998911i	$0.485142\pi$
$930$	−2.83172	+	13.0662i	−0.0928559	+	0.428456i
$931$		−	18.4515i		−	0.604724i
$932$	−8.38625	+	20.2462i	−0.274701	+	0.663186i
$933$	−16.3862	−	16.3862i	−0.536460	−	0.536460i
$934$	10.7361			0.351298
$935$	24.0027	+	11.9883i	0.784972	+	0.392060i
$936$	7.14044			0.233393
$937$	−27.4727	−	27.4727i	−0.897494	−	0.897494i	0.0977196	−	0.995214i	$-0.468845\pi$
$937$	−27.4727	−	27.4727i	−0.897494	−	0.897494i	−0.995214	+	0.0977196i	$0.968845\pi$
$938$	0.172159	−	0.415627i	0.00562118	−	0.0135707i
$939$		−	6.51162i		−	0.212499i
$940$	−14.3283	−	3.10525i	−0.467336	−	0.101282i
$941$	−33.2690	+	13.7805i	−1.08454	+	0.449231i	−0.852100	−	0.523380i	$-0.824671\pi$
$941$	−33.2690	+	13.7805i	−1.08454	+	0.449231i	−0.232440	+	0.972611i	$0.574671\pi$
$942$	−1.87322	+	0.775913i	−0.0610328	+	0.0252806i
$943$	0.138810	−	0.138810i	0.00452027	−	0.00452027i
$944$	0.866663	+	0.866663i	0.0282075	+	0.0282075i
$945$	−2.42813	−	3.77178i	−0.0789869	−	0.122696i
$946$	33.3230	−	13.8029i	1.08343	−	0.448770i
$947$	−22.7063	−	9.40527i	−0.737857	−	0.305630i	−0.0180806	−	0.999837i	$-0.505756\pi$
$947$	−22.7063	−	9.40527i	−0.737857	−	0.305630i	−0.719776	+	0.694206i	$0.755756\pi$
$948$	14.0750			0.457136
$949$	−44.7224	−	18.5246i	−1.45175	−	0.601334i
$950$	12.2692	+	5.58008i	0.398064	+	0.181042i
$951$	−10.7074			−0.347212
$952$	−0.828988	−	1.39684i	−0.0268676	−	0.0452719i
$953$		−	23.4072i		−	0.758233i	−0.925349	−	0.379116i	$-0.876228\pi$
$953$		−	23.4072i		−	0.758233i	0.925349	−	0.379116i	$-0.123772\pi$
$954$	−8.18264	+	8.18264i	−0.264923	+	0.264923i
$955$	−18.3584	−	3.97868i	−0.594065	−	0.128747i
$956$		−	22.6481i		−	0.732491i
$957$	14.1724	+	5.87039i	0.458128	+	0.189763i
$958$	8.50081	+	20.5228i	0.274649	+	0.663060i
$959$	−2.39008	−	5.77017i	−0.0771798	−	0.186328i
$960$	−1.31431	+	1.89611i	−0.0424191	+	0.0611968i
$961$	1.82548	+	1.82548i	0.0588865	+	0.0588865i
$962$	6.86270	−	2.84262i	0.221262	−	0.0916498i
$963$	9.39803	+	22.6889i	0.302847	+	0.731138i
$964$	−6.12642	+	14.7905i	−0.197319	+	0.476370i
$965$	−12.9093	+	2.33947i	−0.415566	+	0.0753103i
$966$	−0.0419990	−	0.0173966i	−0.00135130	−	0.000559725i
$967$	−16.5916	−	16.5916i	−0.533551	−	0.533551i	0.388076	−	0.921627i	$-0.373140\pi$
$967$	−16.5916	−	16.5916i	−0.533551	−	0.533551i	−0.921627	+	0.388076i	$0.873140\pi$
$968$		−	2.53119i		−	0.0813555i
$969$	−11.1117	−	2.83482i	−0.356960	−	0.0910677i
$970$	−41.5206	+	7.52449i	−1.33314	+	0.241597i
$971$	11.9563	−	11.9563i	0.383695	−	0.383695i	−0.488737	−	0.872431i	$-0.662542\pi$
$971$	11.9563	−	11.9563i	0.383695	−	0.383695i	0.872431	+	0.488737i	$0.162542\pi$
$972$	−6.06426	+	14.6404i	−0.194511	+	0.469592i
$973$	−4.30460			−0.137999
$974$	−0.274346	+	0.662330i	−0.00879061	+	0.0212224i
$975$	13.9093	−	12.9905i	0.445455	−	0.416029i
$976$	4.08798	+	9.86927i	0.130853	+	0.315908i
$977$	−24.1459	+	24.1459i	−0.772496	+	0.772496i	−0.978542	−	0.206046i	$-0.933940\pi$
$977$	−24.1459	+	24.1459i	−0.772496	+	0.772496i	0.206046	+	0.978542i	$0.433940\pi$
$978$	−1.33829	+	1.33829i	−0.0427938	+	0.0427938i
$979$	5.77470	+	13.9414i	0.184560	+	0.445568i
$980$	−12.8693	+	8.28476i	−0.411095	+	0.264647i
$981$	0.898870	−	2.17006i	0.0286987	−	0.0692848i
$982$	15.8195			0.504820
$983$	−3.03567	+	7.32876i	−0.0968230	+	0.233751i	−0.964868	−	0.262733i	$-0.915376\pi$
$983$	−3.03567	+	7.32876i	−0.0968230	+	0.233751i	0.868046	+	0.496485i	$0.165376\pi$
$984$	−1.28056	+	1.28056i	−0.0408227	+	0.0408227i
$985$	−2.38315	−	13.1504i	−0.0759336	−	0.419006i
$986$	5.20731	−	20.4112i	0.165835	−	0.650026i
$987$			2.66501i			0.0848281i
$988$	7.03226	+	7.03226i	0.223726	+	0.223726i
$989$	−1.28066	−	0.530467i	−0.0407226	−	0.0168679i
$990$	12.3927	−	2.24585i	0.393866	−	0.0713777i
$991$	−1.15108	+	2.77894i	−0.0365651	+	0.0882761i	−0.941107	−	0.338108i	$-0.890213\pi$
$991$	−1.15108	+	2.77894i	−0.0365651	+	0.0882761i	0.904542	+	0.426384i	$0.140213\pi$
$992$	2.21764	+	5.35385i	0.0704101	+	0.169985i
$993$	−7.29055	+	3.01985i	−0.231359	+	0.0958319i
$994$	1.13222	+	1.13222i	0.0359119	+	0.0359119i
$995$	−37.1002	−	25.7164i	−1.17615	−	0.815263i
$996$	3.07216	+	7.41686i	0.0973452	+	0.235012i
$997$	−5.39844	−	13.0330i	−0.170970	−	0.412759i	0.815048	−	0.579393i	$-0.196710\pi$
$997$	−5.39844	−	13.0330i	−0.170970	−	0.412759i	−0.986019	+	0.166634i	$0.946710\pi$
$998$	28.4635	+	11.7900i	0.900998	+	0.373205i
$999$			10.2529i			0.324389i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.2.n.b.9.4	yes	20
5.2	odd	4		850.2.l.h.451.2		20
5.3	odd	4		850.2.l.i.451.4		20
5.4	even	2		170.2.n.a.9.2	✓	20
17.2	even	8		170.2.n.a.19.2	yes	20
85.2	odd	8		850.2.l.h.801.2		20
85.19	even	8	inner	170.2.n.b.19.4	yes	20
85.53	odd	8		850.2.l.i.801.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.n.a.9.2	✓	20	5.4	even	2
170.2.n.a.19.2	yes	20	17.2	even	8
170.2.n.b.9.4	yes	20	1.1	even	1	trivial
170.2.n.b.19.4	yes	20	85.19	even	8	inner
850.2.l.h.451.2		20	5.2	odd	4
850.2.l.h.801.2		20	85.2	odd	8
850.2.l.i.451.4		20	5.3	odd	4
850.2.l.i.801.4		20	85.53	odd	8

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:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	170.n (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.394838 - 0.953222i) q^{3} +1.00000i q^{4} +(0.473610 - 2.18534i) q^{5} +(0.953222 - 0.394838i) q^{6} +(0.363965 - 0.150759i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.36858 + 1.36858i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.394838 - 0.953222i) q^{3} +1.00000i q^{4} +(0.473610 - 2.18534i) q^{5} +(0.953222 - 0.394838i) q^{6} +(0.363965 - 0.150759i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.36858 + 1.36858i) q^{9} +(1.88016 - 1.21037i) q^{10} +(2.68860 - 1.11366i) q^{11} +(0.953222 + 0.394838i) q^{12} -3.68926 q^{13} +(0.363965 + 0.150759i) q^{14} +(-1.89611 - 1.31431i) q^{15} -1.00000 q^{16} +(-2.47053 + 3.30098i) q^{17} +1.93547i q^{18} +(-1.90615 + 1.90615i) q^{19} +(2.18534 + 0.473610i) q^{20} -0.406465i q^{21} +(2.68860 + 1.11366i) q^{22} +(-0.0427996 - 0.103327i) q^{23} +(0.394838 + 0.953222i) q^{24} +(-4.55139 - 2.07000i) q^{25} +(-2.60870 - 2.60870i) q^{26} +(4.70460 - 1.94871i) q^{27} +(0.150759 + 0.363965i) q^{28} +(-1.95514 + 4.72012i) q^{29} +(-0.411397 - 2.27011i) q^{30} +(-5.35385 - 2.21764i) q^{31} +(-0.707107 - 0.707107i) q^{32} -3.00255i q^{33} +(-4.08107 + 0.587220i) q^{34} +(-0.157082 - 0.866787i) q^{35} +(-1.36858 + 1.36858i) q^{36} +(-0.770514 + 1.86018i) q^{37} -2.69570 q^{38} +(-1.45666 + 3.51668i) q^{39} +(1.21037 + 1.88016i) q^{40} +(0.671699 + 1.62163i) q^{41} +(0.287414 - 0.287414i) q^{42} +(8.76402 - 8.76402i) q^{43} +(1.11366 + 2.68860i) q^{44} +(3.63899 - 2.34264i) q^{45} +(0.0427996 - 0.103327i) q^{46} -6.55654 q^{47} +(-0.394838 + 0.953222i) q^{48} +(-4.84001 + 4.84001i) q^{49} +(-1.75461 - 4.68202i) q^{50} +(2.17111 + 3.65832i) q^{51} -3.68926i q^{52} +(4.22773 + 4.22773i) q^{53} +(4.70460 + 1.94871i) q^{54} +(-1.16036 - 6.40294i) q^{55} +(-0.150759 + 0.363965i) q^{56} +(1.06436 + 2.56960i) q^{57} +(-4.72012 + 1.95514i) q^{58} +(-0.866663 - 0.866663i) q^{59} +(1.31431 - 1.89611i) q^{60} +(-4.08798 - 9.86927i) q^{61} +(-2.21764 - 5.35385i) q^{62} +(0.704444 + 0.291790i) q^{63} -1.00000i q^{64} +(-1.74727 + 8.06226i) q^{65} +(2.12312 - 2.12312i) q^{66} -1.14194i q^{67} +(-3.30098 - 2.47053i) q^{68} -0.115393 q^{69} +(0.501837 - 0.723985i) q^{70} +(3.75506 + 1.55540i) q^{71} -1.93547 q^{72} +(12.1223 + 5.02123i) q^{73} +(-1.86018 + 0.770514i) q^{74} +(-3.77022 + 3.52117i) q^{75} +(-1.90615 - 1.90615i) q^{76} +(0.810664 - 0.810664i) q^{77} +(-3.51668 + 1.45666i) q^{78} +(12.6033 - 5.22048i) q^{79} +(-0.473610 + 2.18534i) q^{80} +0.552455i q^{81} +(-0.671699 + 1.62163i) q^{82} +(5.50188 + 5.50188i) q^{83} +0.406465 q^{84} +(6.04369 + 6.96231i) q^{85} +12.3942 q^{86} +(3.72736 + 3.72736i) q^{87} +(-1.11366 + 2.68860i) q^{88} +5.18535i q^{89} +(4.22965 + 0.916659i) q^{90} +(-1.34276 + 0.556190i) q^{91} +(0.103327 - 0.0427996i) q^{92} +(-4.22780 + 4.22780i) q^{93} +(-4.63618 - 4.63618i) q^{94} +(3.26280 + 5.06834i) q^{95} +(-0.953222 + 0.394838i) q^{96} +(-17.4345 - 7.22162i) q^{97} -6.84480 q^{98} +(5.20371 + 2.15545i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{5}+O(q^{10}) \) 20 * q - 4 * q^5	\( 20 q - 4 q^{5} + 8 q^{10} - 8 q^{11} + 24 q^{13} + 16 q^{15} - 20 q^{16} - 4 q^{20} - 8 q^{22} - 16 q^{23} + 8 q^{25} - 12 q^{26} - 24 q^{27} - 12 q^{29} + 8 q^{30} + 8 q^{31} + 8 q^{34} - 8 q^{35} + 8 q^{37} + 8 q^{38} - 4 q^{40} + 4 q^{41} - 8 q^{42} - 16 q^{43} - 8 q^{44} - 32 q^{45} + 16 q^{46} - 40 q^{47} - 56 q^{49} + 8 q^{50} - 8 q^{51} - 44 q^{53} - 24 q^{54} + 72 q^{57} + 16 q^{59} + 8 q^{60} + 8 q^{61} + 8 q^{62} + 24 q^{63} - 28 q^{65} - 8 q^{66} - 20 q^{68} - 16 q^{69} + 8 q^{71} + 28 q^{72} + 60 q^{73} + 28 q^{74} - 8 q^{78} + 56 q^{79} + 4 q^{80} - 4 q^{82} + 16 q^{84} + 84 q^{85} + 48 q^{86} + 72 q^{87} + 8 q^{88} - 12 q^{90} - 24 q^{91} + 8 q^{92} - 72 q^{93} + 32 q^{94} + 88 q^{95} - 48 q^{97} + 36 q^{98} + 72 q^{99}+O(q^{100}) \) 20 * q - 4 * q^5 + 8 * q^10 - 8 * q^11 + 24 * q^13 + 16 * q^15 - 20 * q^16 - 4 * q^20 - 8 * q^22 - 16 * q^23 + 8 * q^25 - 12 * q^26 - 24 * q^27 - 12 * q^29 + 8 * q^30 + 8 * q^31 + 8 * q^34 - 8 * q^35 + 8 * q^37 + 8 * q^38 - 4 * q^40 + 4 * q^41 - 8 * q^42 - 16 * q^43 - 8 * q^44 - 32 * q^45 + 16 * q^46 - 40 * q^47 - 56 * q^49 + 8 * q^50 - 8 * q^51 - 44 * q^53 - 24 * q^54 + 72 * q^57 + 16 * q^59 + 8 * q^60 + 8 * q^61 + 8 * q^62 + 24 * q^63 - 28 * q^65 - 8 * q^66 - 20 * q^68 - 16 * q^69 + 8 * q^71 + 28 * q^72 + 60 * q^73 + 28 * q^74 - 8 * q^78 + 56 * q^79 + 4 * q^80 - 4 * q^82 + 16 * q^84 + 84 * q^85 + 48 * q^86 + 72 * q^87 + 8 * q^88 - 12 * q^90 - 24 * q^91 + 8 * q^92 - 72 * q^93 + 32 * q^94 + 88 * q^95 - 48 * q^97 + 36 * q^98 + 72 * q^99

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