LMFDB - Embedded newform 170.2.n.a.9.2

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			9.2
Root			$0.953222 - 0.394838i$ of defining polynomial
Character	$\chi$	$=$	170.9
Dual form			170.2.n.a.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-0.394838 + 0.953222i) q^{3} +1.00000i q^{4} +(1.21037 - 1.88016i) q^{5} +(0.953222 - 0.394838i) q^{6} +(-0.363965 + 0.150759i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.36858 + 1.36858i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.394838 + 0.953222i) q^{3} +1.00000i q^{4} +(1.21037 - 1.88016i) 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} +(-2.18534 + 0.473610i) q^{10} +(2.68860 - 1.11366i) q^{11} +(-0.953222 - 0.394838i) q^{12} +3.68926 q^{13} +(0.363965 + 0.150759i) q^{14} +(1.31431 + 1.89611i) q^{15} -1.00000 q^{16} +(2.47053 - 3.30098i) q^{17} -1.93547i q^{18} +(-1.90615 + 1.90615i) q^{19} +(1.88016 + 1.21037i) q^{20} -0.406465i q^{21} +(-2.68860 - 1.11366i) q^{22} +(0.0427996 + 0.103327i) q^{23} +(0.394838 + 0.953222i) q^{24} +(-2.07000 - 4.55139i) 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} +(-0.473610 - 2.18534i) 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} +(4.22965 - 0.916659i) 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} +(-1.89611 + 1.31431i) q^{60} +(-4.08798 - 9.86927i) q^{61} +(2.21764 + 5.35385i) q^{62} +(-0.704444 - 0.291790i) q^{63} -1.00000i q^{64} +(4.46538 - 6.93639i) q^{65} +(2.12312 - 2.12312i) q^{66} +1.14194i q^{67} +(3.30098 + 2.47053i) q^{68} -0.115393 q^{69} +(0.723985 - 0.501837i) q^{70} +(3.75506 + 1.55540i) q^{71} +1.93547 q^{72} +(-12.1223 - 5.02123i) q^{73} +(-1.86018 + 0.770514i) q^{74} +(5.15580 - 0.176107i) 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} +(-1.21037 + 1.88016i) q^{80} +0.552455i q^{81} +(0.671699 - 1.62163i) q^{82} +(-5.50188 - 5.50188i) q^{83} +0.406465 q^{84} +(-3.21611 - 8.64041i) q^{85} +12.3942 q^{86} +(-3.72736 - 3.72736i) q^{87} +(1.11366 - 2.68860i) q^{88} +5.18535i q^{89} +(-3.63899 - 2.34264i) 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} +(1.27671 + 5.89100i) 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} + 4 q^{10} - 8 q^{11} - 24 q^{13} + 8 q^{15} - 20 q^{16} + 8 q^{20} + 8 q^{22} + 16 q^{23} - 12 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} - 12 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} + 16 q^{60} + 8 q^{61} - 8 q^{62} - 24 q^{63} - 8 q^{65} - 8 q^{66} + 20 q^{68} - 16 q^{69} - 16 q^{70} + 8 q^{71} - 28 q^{72} - 60 q^{73} + 28 q^{74} + 64 q^{75} + 8 q^{78} + 56 q^{79} + 4 q^{80} + 4 q^{82} + 16 q^{84} - 16 q^{85} + 48 q^{86} - 72 q^{87} - 8 q^{88} + 32 q^{90} - 24 q^{91} - 8 q^{92} + 72 q^{93} + 32 q^{94} + 8 q^{95} + 48 q^{97} - 36 q^{98} + 72 q^{99}+O(q^{100}) $ 20 * q - 4 * q^5 + 4 * q^10 - 8 * q^11 - 24 * q^13 + 8 * q^15 - 20 * q^16 + 8 * q^20 + 8 * q^22 + 16 * q^23 - 12 * 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 - 12 * 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 + 16 * q^60 + 8 * q^61 - 8 * q^62 - 24 * q^63 - 8 * q^65 - 8 * q^66 + 20 * q^68 - 16 * q^69 - 16 * q^70 + 8 * q^71 - 28 * q^72 - 60 * q^73 + 28 * q^74 + 64 * q^75 + 8 * q^78 + 56 * q^79 + 4 * q^80 + 4 * q^82 + 16 * q^84 - 16 * q^85 + 48 * q^86 - 72 * q^87 - 8 * q^88 + 32 * q^90 - 24 * q^91 - 8 * q^92 + 72 * q^93 + 32 * q^94 + 8 * 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	−0.995929	−	0.0901436i	$-0.971267\pi$
$3$	−0.394838	+	0.953222i	−0.227960	+	0.550343i	0.767969	+	0.640487i	$0.221267\pi$
$4$			1.00000i			0.500000i
$5$	1.21037	−	1.88016i	0.541295	−	0.840833i
$5$	1.21037	−	1.88016i	0.541295	−	0.840833i
$6$	0.953222	−	0.394838i	0.389151	−	0.161192i
$7$	−0.363965	+	0.150759i	−0.137566	+	0.0569817i	−0.450404	−	0.892825i	$-0.648720\pi$
$7$	−0.363965	+	0.150759i	−0.137566	+	0.0569817i	0.312838	+	0.949806i	$0.398720\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	1.36858	+	1.36858i	0.456195	+	0.456195i
$10$	−2.18534	+	0.473610i	−0.691064	+	0.149769i
$11$	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	$-0.329050\pi$
$13$	3.68926			1.02322			0.511608	+	0.859219i	$0.329050\pi$
$14$	0.363965	+	0.150759i	0.0972738	+	0.0402921i
$15$	1.31431	+	1.89611i	0.339353	+	0.489574i
$16$	−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	$0.350067\pi$
$20$	1.88016	+	1.21037i	0.420416	+	0.270648i
$21$		−	0.406465i		−	0.0886980i
$22$	−2.68860	−	1.11366i	−0.573212	−	0.237432i
$23$	0.0427996	+	0.103327i	0.00892434	+	0.0215453i	0.928279	−	0.371885i	$-0.121288\pi$
$23$	0.0427996	+	0.103327i	0.00892434	+	0.0215453i	−0.919355	+	0.393430i	$0.871288\pi$
$24$	0.394838	+	0.953222i	0.0805959	+	0.194576i
$25$	−2.07000	−	4.55139i	−0.413999	−	0.910277i
$26$	−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	−0.847802	−	0.530312i	$-0.822075\pi$
$37$	0.770514	−	1.86018i	0.126672	−	0.305813i	0.974474	+	0.224500i	$0.0720747\pi$
$38$	2.69570			0.437300
$39$	−1.45666	+	3.51668i	−0.233252	+	0.563120i
$40$	−0.473610	−	2.18534i	−0.0748844	−	0.345532i
$41$	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	$0.643985\pi$
$43$	−8.76402	+	8.76402i	−1.33650	+	1.33650i	−0.899425	+	0.437075i	$0.856015\pi$
$44$	1.11366	+	2.68860i	0.167890	+	0.405322i
$45$	4.22965	−	0.916659i	0.630519	−	0.136647i
$46$	0.0427996	−	0.103327i	0.00631046	−	0.0152348i
$47$	6.55654			0.956370			0.478185	−	0.878259i	$-0.341295\pi$
$47$	6.55654			0.956370			0.478185	+	0.878259i	$0.341295\pi$
$48$	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	0.354379	−	0.935102i	$-0.384692\pi$
$53$	−4.22773	−	4.22773i	−0.580723	−	0.580723i	−0.935102	+	0.354379i	$0.884692\pi$
$54$	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	$0.775423\pi$
$60$	−1.89611	+	1.31431i	−0.244787	+	0.169677i
$61$	−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
$65$	4.46538	−	6.93639i	0.553862	−	0.860353i
$66$	2.12312	−	2.12312i	0.261338	−	0.261338i
$67$			1.14194i			0.139511i	0.997564	+	0.0697553i	$0.0222218\pi$
$67$			1.14194i			0.139511i	−0.997564	+	0.0697553i	$0.977778\pi$
$68$	3.30098	+	2.47053i	0.400303	+	0.299596i
$69$	−0.115393			−0.0138917
$70$	0.723985	−	0.501837i	0.0865328	−	0.0599810i
$71$	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	−0.464249	−	0.885705i	$-0.653676\pi$
$73$	−12.1223	−	5.02123i	−1.41881	−	0.587691i	−0.954561	+	0.298014i	$0.903676\pi$
$74$	−1.86018	+	0.770514i	−0.216242	+	0.0895704i
$75$	5.15580	−	0.176107i	0.595340	−	0.0203351i
$76$	−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	$0.0965455\pi$
$80$	−1.21037	+	1.88016i	−0.135324	+	0.210208i
$81$			0.552455i			0.0613839i
$82$	0.671699	−	1.62163i	0.0741768	−	0.179079i
$83$	−5.50188	−	5.50188i	−0.603909	−	0.603909i	0.337438	−	0.941348i	$-0.390440\pi$
$83$	−5.50188	−	5.50188i	−0.603909	−	0.603909i	−0.941348	+	0.337438i	$0.890440\pi$
$84$	0.406465			0.0443490
$85$	−3.21611	−	8.64041i	−0.348836	−	0.937184i
$86$	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	$0.911381\pi$
$90$	−3.63899	−	2.34264i	−0.383583	−	0.246936i
$91$	−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
$95$	1.27671	+	5.89100i	0.130988	+	0.604404i
$96$	−0.953222	+	0.394838i	−0.0972879	+	0.0402980i
$97$	17.4345	+	7.22162i	1.77021	+	0.733245i	0.994807	+	0.101776i	$0.0324526\pi$
$97$	17.4345	+	7.22162i	1.77021	+	0.733245i	0.775402	+	0.631468i	$0.217547\pi$
$98$	6.84480			0.691429
$99$	5.20371	+	2.15545i	0.522992	+	0.216631i
$100$	4.55139	−	2.07000i	0.455139	−	0.207000i
$101$	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	$0.371639\pi$
$103$			18.6697i			1.83958i	−0.392416	+	0.919788i	$0.628361\pi$
$104$	2.60870	−	2.60870i	0.255804	−	0.255804i
$105$	−0.764219	−	0.491974i	−0.0745802	−	0.0480118i
$106$			5.97891i			0.580723i
$107$	−11.7227	−	4.85568i	−1.13327	−	0.469417i	−0.264380	−	0.964419i	$-0.585167\pi$
$107$	−11.7227	−	4.85568i	−1.13327	−	0.469417i	−0.868892	+	0.495002i	$0.835167\pi$
$108$	−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	$0.893511\pi$
$110$	−5.34806	+	3.70706i	−0.509918	+	0.353454i
$111$	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	0.889320	−	0.457286i	$-0.151178\pi$
$113$	−0.668364	−	1.61357i	−0.0628744	−	0.151792i	−0.952194	+	0.305494i	$0.901178\pi$
$114$	−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
$125$	−11.0628	−	1.61696i	−0.989487	−	0.144625i
$126$	0.291790	+	0.704444i	0.0259947	+	0.0627568i
$127$	−2.44552	+	2.44552i	−0.217005	+	0.217005i	−0.807235	−	0.590230i	$-0.799037\pi$
$127$	−2.44552	+	2.44552i	−0.217005	+	0.217005i	0.590230	+	0.807235i	$0.299037\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−4.89369	−	11.8144i	−0.430866	−	1.04020i
$130$	−8.06226	+	1.74727i	−0.707107	+	0.153246i
$131$	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	$0.236821\pi$
$137$			15.8536i			1.35447i	−0.735768	+	0.677233i	$0.763179\pi$
$138$	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
$145$	6.50812	+	9.38906i	0.540470	+	0.779719i
$146$	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	$-0.254664\pi$
$150$	−3.77022	−	3.52117i	−0.307838	−	0.287502i
$151$	−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
$155$	−10.6497	+	7.38192i	−0.855402	+	0.592930i
$156$	−3.51668	−	1.45666i	−0.281560	−	0.116626i
$157$	1.96514			0.156836			0.0784178	−	0.996921i	$-0.475013\pi$
$157$	1.96514			0.156836			0.0784178	+	0.996921i	$0.475013\pi$
$158$	−12.6033	−	5.22048i	−1.00267	−	0.415319i
$159$	5.69923	−	2.36070i	0.451979	−	0.187216i
$160$	2.18534	−	0.473610i	0.172766	−	0.0374422i
$161$	−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	−0.315324	−	0.948984i	$-0.602113\pi$
$163$	1.69473	−	0.701981i	0.132742	−	0.0549834i	0.448066	+	0.894001i	$0.352113\pi$
$164$	−1.62163	+	0.671699i	−0.126628	+	0.0524509i
$165$	5.64527	+	3.63420i	0.439484	+	0.282922i
$166$			7.78083i			0.603909i
$167$	5.06817	−	12.2356i	0.392186	−	0.946822i	−0.597276	−	0.802035i	$-0.703750\pi$
$167$	5.06817	−	12.2356i	0.392186	−	0.946822i	0.989463	−	0.144786i	$-0.0462495\pi$
$168$	−0.287414	−	0.287414i	−0.0221745	−	0.0221745i
$169$	0.610609			0.0469699
$170$	−3.83556	+	8.38382i	−0.294174	+	0.643010i
$171$	−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	$0.255630\pi$
$173$	−4.01629	+	9.69618i	−0.305353	+	0.737187i	−0.999844	+	0.0176853i	$0.994370\pi$
$174$			5.27128i			0.399615i
$175$	1.43957	+	1.34448i	0.108821	+	0.101633i
$176$	−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	$0.784908\pi$
$180$	0.916659	+	4.22965i	0.0683237	+	0.315260i
$181$	−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
$185$	−2.56483	−	3.70021i	−0.188570	−	0.272045i
$186$	−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
$190$	3.26280	−	5.06834i	0.236708	−	0.367696i
$191$		−	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	0.983856	−	0.178961i	$-0.0572735\pi$
$193$	2.24530	+	5.42064i	0.161621	+	0.390187i	−0.822236	+	0.569147i	$0.807273\pi$
$194$	−7.22162	−	17.4345i	−0.518482	−	1.25173i
$195$	4.84882	+	6.99524i	0.347231	+	0.500940i
$196$	−4.84001	−	4.84001i	−0.345715	−	0.345715i
$197$	−5.52186	+	2.28723i	−0.393416	+	0.162958i	−0.570617	−	0.821216i	$-0.693296\pi$
$197$	−5.52186	+	2.28723i	−0.393416	+	0.162958i	0.177201	+	0.984175i	$0.443296\pi$
$198$	−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
$210$	0.192506	+	0.888263i	0.0132842	+	0.0612960i
$211$	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
$215$	5.87002	+	27.0855i	0.400332	+	1.84721i
$216$	−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	$0.0586077\pi$
$223$	17.4148	+	17.4148i	1.16618	+	1.16618i	0.183083	+	0.983097i	$0.441392\pi$
$224$	−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	0.728638	−	0.684899i	$-0.240154\pi$
$227$	−4.08127	−	9.85307i	−0.270884	−	0.653971i	−0.999522	+	0.0309281i	$0.990154\pi$
$228$	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	$0.542254\pi$
$230$	−0.142469	−	0.205535i	−0.00939410	−	0.0135526i
$231$	−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	−0.396754	−	0.917925i	$-0.629864\pi$
$233$	−20.2462	−	8.38625i	−1.32637	−	0.549402i	−0.929619	+	0.368523i	$0.879864\pi$
$234$		−	7.14044i		−	0.466785i
$235$	7.93586	−	12.3273i	0.517679	−	0.804147i
$236$	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	$0.761642\pi$
$240$	−1.31431	−	1.89611i	−0.0848383	−	0.122394i
$241$	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
$245$	3.24177	+	14.9582i	0.207109	+	0.955644i
$246$	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
$250$	6.67922	+	8.96594i	0.422431	+	0.567056i
$251$			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
$255$	9.50607	+	0.345888i	0.595293	+	0.0216603i
$256$	1.00000			0.0625000
$257$	−12.0468	−	12.0468i	−0.751456	−	0.751456i	0.223295	−	0.974751i	$-0.428319\pi$
$257$	−12.0468	−	12.0468i	−0.751456	−	0.751456i	−0.974751	+	0.223295i	$0.928319\pi$
$258$	−4.89369	+	11.8144i	−0.304668	+	0.735534i
$259$			0.793205i			0.0492873i
$260$	6.93639	+	4.46538i	0.430176	+	0.276931i
$261$	−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	$-0.294316\pi$
$263$	22.7128	−	22.7128i	1.40053	−	1.40053i	0.798392	−	0.602138i	$-0.205684\pi$
$264$	2.12312	+	2.12312i	0.130669	+	0.130669i
$265$	−13.0659	+	2.83167i	−0.802634	+	0.173948i
$266$	−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	$0.412081\pi$
$270$	9.35820	−	6.48673i	0.569522	−	0.394770i
$271$	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
$275$	−10.6341	−	9.93161i	−0.641259	−	0.598898i
$276$		−	0.115393i		−	0.00694584i
$277$	12.0666	+	4.99813i	0.725009	+	0.300309i	0.714499	−	0.699636i	$-0.246654\pi$
$277$	12.0666	+	4.99813i	0.725009	+	0.300309i	0.0105100	+	0.999945i	$0.496654\pi$
$278$	4.18146	+	10.0949i	0.250788	+	0.605455i
$279$	−4.29217	−	10.3622i	−0.256966	−	0.620370i
$280$	0.501837	+	0.723985i	0.0299905	+	0.0432664i
$281$	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	$-0.946954\pi$
$283$	−6.83217	−	16.4943i	−0.406130	−	0.980485i	0.580016	−	0.814605i	$-0.303046\pi$
$284$	−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	$-0.557309\pi$
$293$	−6.13040			−0.358142			−0.179071	+	0.983836i	$0.557309\pi$
$294$	−2.70259	+	6.52462i	−0.157618	+	0.380523i
$295$	−2.67845	+	0.580479i	−0.155945	+	0.0337968i
$296$	−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
$300$	0.176107	+	5.15580i	0.0101675	+	0.297670i
$301$	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	$-0.684768\pi$
$307$		−	29.3031i		−	1.67241i	0.548414	−	0.836207i	$-0.315232\pi$
$308$	−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	−0.541334	−	0.840808i	$-0.682081\pi$
$313$	−5.83076	+	2.41518i	−0.329574	+	0.136514i	0.211760	+	0.977322i	$0.432081\pi$
$314$	−1.38957	−	1.38957i	−0.0784178	−	0.0784178i
$315$	−1.40125	+	0.971291i	−0.0789516	+	0.0547261i
$316$	5.22048	+	12.6033i	0.293675	+	0.708994i
$317$	3.97142	+	9.58786i	0.223057	+	0.538508i	0.995302	−	0.0968172i	$-0.0308662\pi$
$317$	3.97142	+	9.58786i	0.223057	+	0.538508i	−0.772245	+	0.635325i	$0.780866\pi$
$318$	−5.69923	−	2.36070i	−0.319597	−	0.132381i
$319$			14.8679i			0.832440i
$320$	−1.88016	−	1.21037i	−0.105104	−	0.0676619i
$321$	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
$325$	−7.63674	−	16.7912i	−0.423610	−	0.931410i
$326$	−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
$330$	−1.42204	−	6.56158i	−0.0782806	−	0.361203i
$331$	−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
$335$	2.14703	+	1.38218i	0.117305	+	0.0755164i
$336$			0.406465i			0.0221745i
$337$	−5.05001	+	12.1918i	−0.275091	+	0.664129i	−0.999686	−	0.0250457i	$-0.992027\pi$
$337$	−5.05001	+	12.1918i	−0.275091	+	0.664129i	0.724595	+	0.689175i	$0.242027\pi$
$338$	−0.431766	−	0.431766i	−0.0234850	−	0.0234850i
$339$	1.80199			0.0978706
$340$	8.64041	−	3.21611i	0.468592	−	0.174418i
$341$	−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
$345$	−0.139668	+	0.216957i	−0.00751950	+	0.0116806i
$346$	9.69618	−	4.01629i	0.521270	−	0.215917i
$347$	5.33087	−	2.20812i	0.286176	−	0.118538i	−0.234978	−	0.972001i	$-0.575502\pi$
$347$	5.33087	−	2.20812i	0.286176	−	0.118538i	0.521154	+	0.853463i	$0.325502\pi$
$348$	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	$0.635844\pi$
$350$	−0.0672422	−	1.96862i	−0.00359425	−	0.105227i
$351$	−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	$-0.286336\pi$
$353$	23.3712			1.24392			0.621961	+	0.783048i	$0.286336\pi$
$354$	−1.16831	−	0.483932i	−0.0620952	−	0.0257207i
$355$	7.46942	−	5.17750i	0.396436	−	0.274793i
$356$	−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	$0.462180\pi$
$360$	2.34264	−	3.63899i	0.123468	−	0.191792i
$361$			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
$365$	−24.1132	+	16.7143i	−1.26214	+	0.874868i
$366$	−7.79352	−	7.79352i	−0.407374	−	0.407374i
$367$	0.926723	−	0.383861i	0.0483745	−	0.0200374i	−0.358365	−	0.933582i	$-0.616666\pi$
$367$	0.926723	−	0.383861i	0.0483745	−	0.0200374i	0.406740	+	0.913544i	$0.366666\pi$
$368$	−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	$-0.840157\pi$
$373$		−	18.5917i		−	0.962640i	0.876545	−	0.481320i	$-0.159843\pi$
$374$	−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	$0.808185\pi$
$380$	−5.89100	+	1.27671i	−0.302202	+	0.0654938i
$381$	−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	−0.0335177	−	0.999438i	$-0.510671\pi$
$383$	18.9034	−	18.9034i	0.965920	−	0.965920i	0.999438	+	0.0335177i	$0.0106710\pi$
$384$	−0.394838	−	0.953222i	−0.0201490	−	0.0486439i
$385$	0.542971	+	2.50538i	0.0276724	+	0.127686i
$386$	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	$0.0555175\pi$
$397$	8.19219	+	19.7777i	0.411154	+	0.992614i	−0.573674	+	0.819083i	$0.694483\pi$
$398$	−18.6512	+	7.72557i	−0.934899	+	0.387248i
$399$	0.774782	+	0.774782i	0.0387876	+	0.0387876i
$400$	2.07000	+	4.55139i	0.103500	+	0.227569i
$401$	−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
$405$	1.03870	+	0.668677i	0.0516136	+	0.0332268i
$406$	−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	$0.544168\pi$
$410$	−2.23591	−	3.22567i	−0.110424	−	0.159305i
$411$	−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
$415$	−17.0037	+	3.68508i	−0.834680	+	0.180893i
$416$	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	$0.281231\pi$
$420$	0.491974	−	0.764219i	0.0240059	−	0.0372901i
$421$			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
$425$	−20.1380	−	4.41131i	−0.976838	−	0.213980i
$426$	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
$430$	15.0016	−	23.3030i	0.723441	−	1.12377i
$431$	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	$-0.460617\pi$
$433$	23.2176	−	23.2176i	1.11577	−	1.11577i	0.992356	−	0.123411i	$-0.0393835\pi$
$434$	−1.61429	−	1.61429i	−0.0774882	−	0.0774882i
$435$	−11.5195	+	2.49653i	−0.552319	+	0.119700i
$436$	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	$0.547383\pi$
$440$	−3.70706	−	5.34806i	−0.176727	−	0.254959i
$441$	−13.2479			−0.630853
$442$	−15.0561	+	2.16640i	−0.716147	+	0.103045i
$443$			19.9465i			0.947686i	0.880609	+	0.473843i	$0.157134\pi$
$443$			19.9465i			0.947686i	−0.880609	+	0.473843i	$0.842866\pi$
$444$	−1.46894	+	1.46894i	−0.0697129	+	0.0697129i
$445$	9.74929	+	6.27621i	0.462161	+	0.297521i
$446$		−	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	$0.860297\pi$
$450$	−8.80907	+	4.00641i	−0.415264	+	0.188864i
$451$	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	0.991056	−	0.133446i	$-0.0426044\pi$
$457$	18.3336	+	18.3336i	0.857610	+	0.857610i	−0.133446	+	0.991056i	$0.542604\pi$
$458$		−	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	$-0.506435\pi$
$463$	−0.869987			−0.0404317			−0.0202159	+	0.999796i	$0.506435\pi$
$464$	1.95514	−	4.72012i	0.0907649	−	0.219126i
$465$	−2.83172	−	13.0662i	−0.131318	−	0.605929i
$466$	8.38625	+	20.2462i	0.388486	+	0.937887i
$467$	−7.59160	+	7.59160i	−0.351298	+	0.351298i	−0.860592	−	0.509295i	$-0.829906\pi$
$467$	−7.59160	+	7.59160i	−0.351298	+	0.351298i	0.509295	+	0.860592i	$0.329906\pi$
$468$	−5.04906	+	5.04906i	−0.233393	+	0.233393i
$469$	−0.172159	−	0.415627i	−0.00794954	−	0.0191919i
$470$	−14.3283	+	3.10525i	−0.660913	+	0.143234i
$471$	−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
$485$	34.6801	−	24.0388i	1.57474	−	1.09155i
$486$	6.06426	+	14.6404i	0.275080	+	0.664103i
$487$	−0.274346	−	0.662330i	−0.0124318	−	0.0300130i	0.917542	−	0.397639i	$-0.130171\pi$
$487$	−0.274346	−	0.662330i	−0.0124318	−	0.0300130i	−0.929974	+	0.367626i	$0.880171\pi$
$488$	−9.86927	−	4.08798i	−0.446761	−	0.185054i
$489$			1.89263i			0.0855875i
$490$	8.28476	−	12.8693i	0.374267	−	0.581376i
$491$	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
$495$	10.3510	−	7.17491i	0.465243	−	0.322488i
$496$	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	$0.132789\pi$
$500$	1.61696	−	11.0628i	0.0723124	−	0.494743i
$501$	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	0.463483	−	0.886106i	$-0.346599\pi$
$503$	31.7976	−	13.1710i	1.41779	−	0.587266i	0.954303	+	0.298839i	$0.0965994\pi$
$504$	−0.704444	+	0.291790i	−0.0313784	+	0.0129974i
$505$	9.06745	−	14.0851i	0.403496	−	0.626779i
$506$		−	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	$0.583773\pi$
$510$	−6.47723	−	6.96639i	−0.286816	−	0.308477i
$511$	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
$515$	35.1019	+	22.5972i	1.54678	+	0.995754i
$516$	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
$520$	−1.74727	−	8.06226i	−0.0766228	−	0.353554i
$521$	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	$-0.641019\pi$
$523$	−19.6068			−0.857346			−0.428673	+	0.903460i	$0.641019\pi$
$524$	10.2266	+	4.23601i	0.446753	+	0.185051i
$525$	−1.84998	+	0.841381i	−0.0807398	+	0.0367209i
$526$	−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
$530$	11.2413	+	7.23671i	0.488291	+	0.314343i
$531$		−	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
$535$	−23.3182	+	16.1633i	−1.00814	+	0.698799i
$536$	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	$-0.717859\pi$
$547$	8.48235	−	20.4782i	0.362679	−	0.875585i	0.994906	−	0.100802i	$-0.0321409\pi$
$548$	−15.8536			−0.677233
$549$	7.91217	−	19.1017i	0.337683	−	0.815240i
$550$	0.496717	+	14.5421i	0.0211801	+	0.620078i
$551$	−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
$555$	4.53981	−	0.983877i	0.192704	−	0.0417633i
$556$	4.18146	−	10.0949i	0.177334	−	0.428121i
$557$	−29.1002			−1.23301			−0.616507	−	0.787349i	$-0.711453\pi$
$557$	−29.1002			−1.23301			−0.616507	+	0.787349i	$0.711453\pi$
$558$	−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	$0.0694733\pi$
$563$	28.3024	+	28.3024i	1.19280	+	1.19280i	0.216528	+	0.976276i	$0.430527\pi$
$564$	−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	$0.658189\pi$
$570$	3.54298	+	5.11134i	0.148399	+	0.214091i
$571$	−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
$575$	0.381688	−	0.408685i	0.0159175	−	0.0170433i
$576$	1.36858	−	1.36858i	0.0570243	−	0.0570243i
$577$		−	14.7520i		−	0.614132i	−0.951688	−	0.307066i	$-0.900653\pi$
$577$		−	14.7520i		−	0.614132i	0.951688	−	0.307066i	$-0.0993472\pi$
$578$	−8.14401	+	14.9223i	−0.338746	+	0.620686i
$579$	−6.05361			−0.251579
$580$	−9.38906	+	6.50812i	−0.389860	+	0.270235i
$581$	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
$585$	15.6043	−	3.38179i	0.645157	−	0.139820i
$586$	4.33485	+	4.33485i	0.179071	+	0.179071i
$587$	8.87191	−	8.87191i	0.366183	−	0.366183i	−0.499900	−	0.866083i	$-0.666630\pi$
$587$	8.87191	−	8.87191i	0.366183	−	0.366183i	0.866083	+	0.499900i	$0.166630\pi$
$588$	6.52462	−	2.70259i	0.269071	−	0.111453i
$589$	14.4324	−	5.97808i	0.594675	−	0.246322i
$590$	2.30441	+	1.48349i	0.0948711	+	0.0610743i
$591$		−	6.16664i		−	0.253662i
$592$	−0.770514	+	1.86018i	−0.0316679	+	0.0764531i
$593$	−24.3384	−	24.3384i	−0.999457	−	0.999457i	0.000542995	−	1.00000i	$-0.499827\pi$
$593$	−24.3384	−	24.3384i	−0.999457	−	0.999457i	−1.00000		0.000542995i	$0.999827\pi$
$594$	14.8190			0.608031
$595$	2.47317	+	2.65995i	0.101390	+	0.109047i
$596$	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	$-0.116095\pi$
$600$	3.52117	−	3.77022i	0.143751	−	0.153919i
$601$	−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
$605$	1.19880	+	5.53150i	0.0487381	+	0.224888i
$606$	7.14102	−	2.95791i	0.290084	−	0.120157i
$607$	−10.1593	−	4.20810i	−0.412352	−	0.170802i	0.166857	−	0.985981i	$-0.446638\pi$
$607$	−10.1593	−	4.20810i	−0.412352	−	0.170802i	−0.579208	+	0.815179i	$0.696638\pi$
$608$	−2.69570			−0.109325
$609$	1.91856	+	0.794695i	0.0777441	+	0.0322027i
$610$	13.6078	+	19.6316i	0.550964	+	0.794858i
$611$	24.1888			0.978573
$612$	1.13655	+	7.89880i	0.0459422	+	0.319290i
$613$		−	19.1671i		−	0.774150i	−0.922048	−	0.387075i	$-0.873485\pi$
$613$		−	19.1671i		−	0.774150i	0.922048	−	0.387075i	$-0.126515\pi$
$614$	−20.7204	+	20.7204i	−0.836207	+	0.836207i
$615$	−2.19196	+	3.40493i	−0.0883885	+	0.137300i
$616$			1.14645i			0.0461918i
$617$	17.5554	+	7.27170i	0.706756	+	0.292748i	0.706961	−	0.707252i	$-0.250065\pi$
$617$	17.5554	+	7.27170i	0.706756	+	0.292748i	−0.000205623		1.00000i	$0.500065\pi$
$618$	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	$0.948781\pi$
$620$	−7.38192	−	10.6497i	−0.296465	−	0.427701i
$621$	−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
$635$	1.63797	+	7.55795i	0.0650010	+	0.299928i
$636$	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
$640$	0.473610	+	2.18534i	0.0187211	+	0.0863830i
$641$	−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	$0.450382\pi$
$643$	−16.5600	+	39.9793i	−0.653061	+	1.57663i	−0.808312	+	0.588755i	$0.799618\pi$
$644$	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	$0.0103613\pi$
$647$			1.65565i			0.0650904i	−0.999470	+	0.0325452i	$0.989639\pi$
$648$	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	−0.994994	−	0.0999369i	$-0.968136\pi$
$653$	−41.5990	+	17.2309i	−1.62789	+	0.674296i	−0.632901	+	0.774233i	$0.718136\pi$
$654$	−0.885390	−	0.885390i	−0.0346215	−	0.0346215i
$655$	−14.1005	−	20.3424i	−0.550954	−	0.794844i
$656$	−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	$0.948942\pi$
$660$	−3.63420	+	5.64527i	−0.141461	+	0.219742i
$661$	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
$665$	−1.35280	−	1.95164i	−0.0524594	−	0.0756815i
$666$	−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
$670$	−0.540836	−	2.49553i	−0.0208943	−	0.0964107i
$671$	−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	0.597077	−	0.802184i	$-0.296328\pi$
$673$	41.1575	−	17.0480i	1.58650	−	0.657152i	0.989427	+	0.145032i	$0.0463285\pi$
$674$	12.1918	−	5.05001i	0.469610	−	0.194519i
$675$	18.6078	+	17.3786i	0.716216	+	0.668904i
$676$			0.610609i			0.0234850i
$677$	10.0478	−	24.2576i	0.386169	−	0.932293i	−0.604575	−	0.796548i	$-0.706657\pi$
$677$	10.0478	−	24.2576i	0.386169	−	0.932293i	0.990744	−	0.135745i	$-0.0433429\pi$
$678$	−1.27420	−	1.27420i	−0.0489353	−	0.0489353i
$679$	−7.43429			−0.285302
$680$	−8.38382	−	3.83556i	−0.321505	−	0.147087i
$681$	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	$0.401042\pi$
$683$	−15.2523	+	36.8224i	−0.583614	+	1.40897i	−0.889515	+	0.456906i	$0.848958\pi$
$684$		−	5.21744i		−	0.199494i
$685$	29.8073	+	19.1888i	1.13888	+	0.733166i
$686$	−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
$690$	0.252172	−	0.0546513i	0.00960004	−	0.00208054i
$691$	−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
$695$	−20.0805	+	13.9190i	−0.761696	+	0.527977i
$696$	−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
$700$	−1.34448	+	1.43957i	−0.0508164	+	0.0544106i
$701$			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
$705$	8.61732	+	12.4319i	0.324547	+	0.468214i
$706$	−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	$0.0193099\pi$
$720$	−4.22965	+	0.916659i	−0.157630	+	0.0341618i
$721$	−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
$725$	25.5302	−	0.872037i	0.948167	−	0.0323866i
$726$	−0.999409	+	2.41279i	−0.0370916	+	0.0895470i
$727$	−32.5886			−1.20864			−0.604322	−	0.796740i	$-0.706556\pi$
$727$	−32.5886			−1.20864			−0.604322	+	0.796740i	$0.706556\pi$
$728$	−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	0.554592	−	0.832122i	$-0.312874\pi$
$733$	−7.51384	−	7.51384i	−0.277530	−	0.277530i	−0.832122	+	0.554592i	$0.812874\pi$
$734$	−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	$-0.549237\pi$
$740$	3.70021	−	2.56483i	0.136022	−	0.0942852i
$741$	−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	−0.132430	−	0.991192i	$-0.542278\pi$
$743$	−25.2669	−	10.4659i	−0.926951	−	0.383956i	−0.794521	+	0.607237i	$0.792278\pi$
$744$		−	5.97902i		−	0.219201i
$745$	−32.9286	−	21.1982i	−1.20641	−	0.776641i
$746$	−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
$750$	−11.1837	+	2.82669i	−0.408372	+	0.103216i
$751$	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
$755$	9.84273	+	45.4164i	0.358213	+	1.65287i
$756$	1.41852	+	1.41852i	0.0515912	+	0.0515912i
$757$	18.4876	−	18.4876i	0.671943	−	0.671943i	−0.286221	−	0.958164i	$-0.592399\pi$
$757$	18.4876	−	18.4876i	0.671943	−	0.671943i	0.958164	+	0.286221i	$0.0923990\pi$
$758$	30.1778	−	12.5001i	1.09611	−	0.454023i
$759$	−0.310246	+	0.128508i	−0.0112612	+	0.00466454i
$760$	5.06834	+	3.26280i	0.183848	+	0.118354i
$761$		−	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
$765$	7.42360	−	16.2266i	0.268401	−	0.586675i
$766$	−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	$0.992135\pi$
$770$	1.38763	−	2.15551i	0.0500068	−	0.0776792i
$771$	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	$-0.484258\pi$
$773$	29.1433	−	29.1433i	1.04821	−	1.04821i	0.998777	−	0.0494341i	$-0.0157418\pi$
$774$	16.9625	+	16.9625i	0.609704	+	0.609704i
$775$	0.989119	+	28.9579i	0.0355302	+	1.04020i
$776$	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
$780$	−6.99524	+	4.84882i	−0.250470	+	0.173616i
$781$	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
$785$	2.37856	−	3.69478i	0.0848943	−	0.131872i
$786$		−	11.4208i		−	0.407366i
$787$	24.6218	+	10.1987i	0.877672	+	0.363544i	0.775594	−	0.631233i	$-0.217451\pi$
$787$	24.6218	+	10.1987i	0.877672	+	0.363544i	0.102079	+	0.994776i	$0.467451\pi$
$788$	−2.28723	−	5.52186i	−0.0814792	−	0.196708i
$789$	12.6825	+	30.6182i	0.451508	+	1.09004i
$790$	−25.0701	+	17.3776i	−0.891953	+	0.618266i
$791$	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	0.418287	−	0.908315i	$-0.362630\pi$
$797$	−13.8341	−	13.8341i	−0.490027	−	0.490027i	−0.908315	+	0.418287i	$0.862630\pi$
$798$		−	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
$805$	−0.0962860	+	0.0208673i	−0.00339363	+	0.000735475i
$806$	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	$0.836354\pi$
$810$	−0.261648	−	1.20730i	−0.00919339	−	0.0424202i
$811$	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	−0.245458	−	0.969407i	$-0.578939\pi$
$823$	7.64393	−	3.16622i	0.266450	−	0.110367i	0.511909	+	0.859040i	$0.328939\pi$
$824$	13.2014	+	13.2014i	0.459894	+	0.459894i
$825$	13.6658	−	6.21526i	0.475781	−	0.216388i
$826$	−0.184778	−	0.446093i	−0.00642924	−	0.0155216i
$827$	17.9548	+	43.3467i	0.624350	+	1.50731i	0.846548	+	0.532312i	$0.178677\pi$
$827$	17.9548	+	43.3467i	0.624350	+	1.50731i	−0.222199	+	0.975001i	$0.571323\pi$
$828$	−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	$-0.190365\pi$
$830$	14.6292	+	9.41770i	0.507787	+	0.326893i
$831$	−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
$835$	−16.8706	−	24.3386i	−0.583830	−	0.842273i
$836$	−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	$0.214849\pi$
$840$	−0.888263	+	0.192506i	−0.0306480	+	0.00664209i
$841$	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
$845$	0.739064	−	1.14804i	0.0254246	−	0.0394938i
$846$		−	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
$850$	11.1205	+	17.3590i	0.381429	+	0.595409i
$851$	0.225186			0.00771927
$852$	−2.96528	−	2.96528i	−0.101589	−	0.101589i
$853$	0.882434	−	2.13038i	0.0302140	−	0.0729429i	−0.908052	−	0.418857i	$-0.862431\pi$
$853$	0.882434	−	2.13038i	0.0302140	−	0.0729429i	0.938266	+	0.345914i	$0.112431\pi$
$854$		−	4.20837i		−	0.144008i
$855$	−6.31505	+	9.80962i	−0.215970	+	0.335482i
$856$	−11.7227	+	4.85568i	−0.400672	+	0.165964i
$857$	−24.2288	+	10.0359i	−0.827638	+	0.342819i	−0.755967	−	0.654609i	$-0.772833\pi$
$857$	−24.2288	+	10.0359i	−0.827638	+	0.342819i	−0.0716710	+	0.997428i	$0.522833\pi$
$858$	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	$0.864134\pi$
$860$	−27.0855	+	5.87002i	−0.923607	+	0.200166i
$861$	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	$-0.387895\pi$
$863$	20.2672			0.689905			0.344953	+	0.938620i	$0.387895\pi$
$864$	−4.70460	−	1.94871i	−0.160054	−	0.0662964i
$865$	13.3692	+	19.2873i	0.454565	+	0.655786i
$866$	−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
$870$	9.91085	+	6.38022i	0.336009	+	0.216310i
$871$			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
$875$	4.27024	−	1.07930i	0.144361	−	0.0364871i
$876$	9.57270	+	9.57270i	0.323432	+	0.323432i
$877$	−21.5149	+	8.91177i	−0.726507	+	0.300929i	−0.715116	−	0.699006i	$-0.753626\pi$
$877$	−21.5149	+	8.91177i	−0.726507	+	0.300929i	−0.0113911	+	0.999935i	$0.503626\pi$
$878$	−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	$-0.926147\pi$
$883$		−	13.6655i		−	0.459881i	0.973205	−	0.229940i	$-0.0738532\pi$
$884$	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	−0.833378	−	0.552704i	$-0.813596\pi$
$887$	4.36999	−	10.5501i	0.146730	−	0.354238i	0.980108	+	0.198466i	$0.0635961\pi$
$888$	2.07740			0.0697129
$889$	0.521398	−	1.25877i	0.0174871	−	0.0422177i
$890$	−2.45584	−	11.3317i	−0.0823198	−	0.379841i
$891$	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
$895$	−6.39992	+	1.38700i	−0.213926	+	0.0463624i
$896$	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	$0.0132614\pi$
$907$	9.70020	+	23.4184i	0.322090	+	0.777594i	−0.677042	+	0.735944i	$0.736739\pi$
$908$	9.85307	−	4.08127i	0.326985	−	0.135442i
$909$	10.2527	+	10.2527i	0.340060	+	0.340060i
$910$	2.67097	−	1.85141i	0.0885417	−	0.0613735i
$911$	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
$915$	13.3404	−	20.7225i	0.441019	−	0.685066i
$916$	−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	$0.259253\pi$
$920$	0.205535	−	0.142469i	0.00677628	−	0.00469705i
$921$	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
$925$	−10.0614	+	0.343667i	−0.330816	+	0.0112997i
$926$	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	$0.485142\pi$
$930$	−7.23684	+	11.2415i	−0.237305	+	0.368623i
$931$		−	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
$935$	−18.2693	−	19.6490i	−0.597469	−	0.642590i
$936$	7.14044			0.233393
$937$	27.4727	+	27.4727i	0.897494	+	0.897494i	0.995214	−	0.0977196i	$-0.0311548\pi$
$937$	27.4727	+	27.4727i	0.897494	+	0.897494i	−0.0977196	+	0.995214i	$0.531155\pi$
$938$	−0.172159	+	0.415627i	−0.00562118	+	0.0135707i
$939$		−	6.51162i		−	0.212499i
$940$	12.3273	+	7.93586i	0.402074	+	0.258839i
$941$	−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
$945$	−0.950108	−	4.38400i	−0.0309070	−	0.142611i
$946$	33.3230	−	13.8029i	1.08343	−	0.448770i
$947$	22.7063	+	9.40527i	0.737857	+	0.305630i	0.719776	−	0.694206i	$-0.244244\pi$
$947$	22.7063	+	9.40527i	0.737857	+	0.305630i	0.0180806	+	0.999837i	$0.494244\pi$
$948$	−14.0750			−0.457136
$949$	−44.7224	−	18.5246i	−1.45175	−	0.601334i
$950$	−5.58008	−	12.2692i	−0.181042	−	0.398064i
$951$	−10.7074			−0.347212
$952$	0.828988	+	1.39684i	0.0268676	+	0.0452719i
$953$			23.4072i			0.758233i	0.925349	+	0.379116i	$0.123772\pi$
$953$			23.4072i			0.758233i	−0.925349	+	0.379116i	$0.876228\pi$
$954$	−8.18264	+	8.18264i	−0.264923	+	0.264923i
$955$	−15.7947	−	10.1680i	−0.511105	−	0.329030i
$956$		−	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
$960$	1.89611	−	1.31431i	0.0611968	−	0.0424191i
$961$	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	0.921627	−	0.388076i	$-0.126860\pi$
$967$	16.5916	+	16.5916i	0.533551	+	0.533551i	−0.388076	+	0.921627i	$0.626860\pi$
$968$			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
$975$	19.0211	−	0.649704i	0.609161	−	0.0208072i
$976$	4.08798	+	9.86927i	0.130853	+	0.315908i
$977$	24.1459	−	24.1459i	0.772496	−	0.772496i	−0.206046	−	0.978542i	$-0.566060\pi$
$977$	24.1459	−	24.1459i	0.772496	−	0.772496i	0.978542	+	0.206046i	$0.0660597\pi$
$978$	1.33829	−	1.33829i	0.0427938	−	0.0427938i
$979$	5.77470	+	13.9414i	0.184560	+	0.445568i
$980$	−14.9582	+	3.24177i	−0.477822	+	0.103554i
$981$	0.898870	−	2.17006i	0.0286987	−	0.0692848i
$982$	−15.8195			−0.504820
$983$	3.03567	−	7.32876i	0.0968230	−	0.233751i	−0.868046	−	0.496485i	$-0.834624\pi$
$983$	3.03567	−	7.32876i	0.0968230	−	0.233751i	0.964868	+	0.262733i	$0.0846239\pi$
$984$	−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
$995$	−25.7164	−	37.1002i	−0.815263	−	1.17615i
$996$	3.07216	+	7.41686i	0.0973452	+	0.235012i
$997$	5.39844	+	13.0330i	0.170970	+	0.412759i	0.986019	−	0.166634i	$-0.0532897\pi$
$997$	5.39844	+	13.0330i	0.170970	+	0.412759i	−0.815048	+	0.579393i	$0.803290\pi$
$998$	−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.a.9.2	✓	20
5.2	odd	4		850.2.l.i.451.4		20
5.3	odd	4		850.2.l.h.451.2		20
5.4	even	2		170.2.n.b.9.4	yes	20
17.2	even	8		170.2.n.b.19.4	yes	20
85.2	odd	8		850.2.l.i.801.4		20
85.19	even	8	inner	170.2.n.a.19.2	yes	20
85.53	odd	8		850.2.l.h.801.2		20

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

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.394838 + 0.953222i) q^{3} +1.00000i q^{4} +(1.21037 - 1.88016i) q^{5} +(0.953222 - 0.394838i) q^{6} +(-0.363965 + 0.150759i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.36858 + 1.36858i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.394838 + 0.953222i) q^{3} +1.00000i q^{4} +(1.21037 - 1.88016i) 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} +(-2.18534 + 0.473610i) q^{10} +(2.68860 - 1.11366i) q^{11} +(-0.953222 - 0.394838i) q^{12} +3.68926 q^{13} +(0.363965 + 0.150759i) q^{14} +(1.31431 + 1.89611i) q^{15} -1.00000 q^{16} +(2.47053 - 3.30098i) q^{17} -1.93547i q^{18} +(-1.90615 + 1.90615i) q^{19} +(1.88016 + 1.21037i) q^{20} -0.406465i q^{21} +(-2.68860 - 1.11366i) q^{22} +(0.0427996 + 0.103327i) q^{23} +(0.394838 + 0.953222i) q^{24} +(-2.07000 - 4.55139i) 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} +(-0.473610 - 2.18534i) 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} +(4.22965 - 0.916659i) 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} +(-1.89611 + 1.31431i) q^{60} +(-4.08798 - 9.86927i) q^{61} +(2.21764 + 5.35385i) q^{62} +(-0.704444 - 0.291790i) q^{63} -1.00000i q^{64} +(4.46538 - 6.93639i) q^{65} +(2.12312 - 2.12312i) q^{66} +1.14194i q^{67} +(3.30098 + 2.47053i) q^{68} -0.115393 q^{69} +(0.723985 - 0.501837i) q^{70} +(3.75506 + 1.55540i) q^{71} +1.93547 q^{72} +(-12.1223 - 5.02123i) q^{73} +(-1.86018 + 0.770514i) q^{74} +(5.15580 - 0.176107i) 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} +(-1.21037 + 1.88016i) q^{80} +0.552455i q^{81} +(0.671699 - 1.62163i) q^{82} +(-5.50188 - 5.50188i) q^{83} +0.406465 q^{84} +(-3.21611 - 8.64041i) q^{85} +12.3942 q^{86} +(-3.72736 - 3.72736i) q^{87} +(1.11366 - 2.68860i) q^{88} +5.18535i q^{89} +(-3.63899 - 2.34264i) 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} +(1.27671 + 5.89100i) 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	\( 20 q - 4 q^{5} + 4 q^{10} - 8 q^{11} - 24 q^{13} + 8 q^{15} - 20 q^{16} + 8 q^{20} + 8 q^{22} + 16 q^{23} - 12 q^{25} - 12 q^{26} + 24 q^{27} - 12 q^{29} - 8 q^{30} + 8 q^{31} + 8 q^{34} - 8 q^{35} - 8 q^{37} - 8 q^{38} + 4 q^{40} + 4 q^{41} + 8 q^{42} + 16 q^{43} - 8 q^{44} - 12 q^{45} + 16 q^{46} + 40 q^{47} - 56 q^{49} + 8 q^{50} - 8 q^{51} + 44 q^{53} - 24 q^{54} - 72 q^{57} + 16 q^{59} + 16 q^{60} + 8 q^{61} - 8 q^{62} - 24 q^{63} - 8 q^{65} - 8 q^{66} + 20 q^{68} - 16 q^{69} - 16 q^{70} + 8 q^{71} - 28 q^{72} - 60 q^{73} + 28 q^{74} + 64 q^{75} + 8 q^{78} + 56 q^{79} + 4 q^{80} + 4 q^{82} + 16 q^{84} - 16 q^{85} + 48 q^{86} - 72 q^{87} - 8 q^{88} + 32 q^{90} - 24 q^{91} - 8 q^{92} + 72 q^{93} + 32 q^{94} + 8 q^{95} + 48 q^{97} - 36 q^{98} + 72 q^{99}+O(q^{100}) \) 20 * q - 4 * q^5 + 4 * q^10 - 8 * q^11 - 24 * q^13 + 8 * q^15 - 20 * q^16 + 8 * q^20 + 8 * q^22 + 16 * q^23 - 12 * 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 - 12 * 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 + 16 * q^60 + 8 * q^61 - 8 * q^62 - 24 * q^63 - 8 * q^65 - 8 * q^66 + 20 * q^68 - 16 * q^69 - 16 * q^70 + 8 * q^71 - 28 * q^72 - 60 * q^73 + 28 * q^74 + 64 * q^75 + 8 * q^78 + 56 * q^79 + 4 * q^80 + 4 * q^82 + 16 * q^84 - 16 * q^85 + 48 * q^86 - 72 * q^87 - 8 * q^88 + 32 * q^90 - 24 * q^91 - 8 * q^92 + 72 * q^93 + 32 * q^94 + 8 * q^95 + 48 * q^97 - 36 * q^98 + 72 * q^99

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