LMFDB - Embedded newform 845.2.m.g.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(316,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("845.316");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.m (of order $6$, degree $2$, not 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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.22581504.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 $ x^8 - 4x^7 + 5x^6 + 2x^5 - 11x^4 + 4x^3 + 20x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.1
Root			$0.665665 + 1.24775i$ of defining polynomial
Character	$\chi$	$=$	845.361
Dual form			845.2.m.g.316.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29515 + 0.747754i) q^{2} +(-0.0473938 - 0.0820885i) q^{3} +(0.118272 - 0.204852i) q^{4} -1.00000i q^{5} +(0.122764 + 0.0708778i) q^{6} +(4.18016 + 2.41342i) q^{7} -2.63726i q^{8} +(1.49551 - 2.59030i) q^{9} +O(q^{10})$	\(q+(-1.29515 + 0.747754i) q^{2} +(-0.0473938 - 0.0820885i) q^{3} +(0.118272 - 0.204852i) q^{4} -1.00000i q^{5} +(0.122764 + 0.0708778i) q^{6} +(4.18016 + 2.41342i) q^{7} -2.63726i q^{8} +(1.49551 - 2.59030i) q^{9} +(0.747754 + 1.29515i) q^{10} +(0.926118 - 0.534695i) q^{11} -0.0224214 q^{12} -7.21857 q^{14} +(-0.0820885 + 0.0473938i) q^{15} +(2.20857 + 3.82535i) q^{16} +(1.77944 - 3.08209i) q^{17} +4.47309i q^{18} +(-4.96410 - 2.86603i) q^{19} +(-0.204852 - 0.118272i) q^{20} -0.457524i q^{21} +(-0.799640 + 1.38502i) q^{22} +(-3.54290 - 6.13649i) q^{23} +(-0.216489 + 0.124990i) q^{24} -1.00000 q^{25} -0.567874 q^{27} +(0.988789 - 0.570878i) q^{28} +(-0.736543 - 1.27573i) q^{29} +(0.0708778 - 0.122764i) q^{30} -1.46410i q^{31} +(-1.15297 - 0.665665i) q^{32} +(-0.0877845 - 0.0506824i) q^{33} +5.32235i q^{34} +(2.41342 - 4.18016i) q^{35} +(-0.353752 - 0.612717i) q^{36} +(0.0219955 - 0.0126991i) q^{37} +8.57233 q^{38} -2.63726 q^{40} +(0.232051 - 0.133975i) q^{41} +(0.342116 + 0.592562i) q^{42} +(1.77944 - 3.08209i) q^{43} -0.252957i q^{44} +(-2.59030 - 1.49551i) q^{45} +(9.17716 + 5.29844i) q^{46} -6.51793i q^{47} +(0.209345 - 0.362596i) q^{48} +(8.14918 + 14.1148i) q^{49} +(1.29515 - 0.747754i) q^{50} -0.337339 q^{51} +0.991015 q^{53} +(0.735481 - 0.424630i) q^{54} +(-0.534695 - 0.926118i) q^{55} +(6.36482 - 11.0242i) q^{56} +0.543327i q^{57} +(1.90786 + 1.10151i) q^{58} +(7.55440 + 4.36153i) q^{59} +0.0224214i q^{60} +(-3.16867 + 5.48830i) q^{61} +(1.09479 + 1.89623i) q^{62} +(12.5029 - 7.21857i) q^{63} -6.84325 q^{64} +0.151592 q^{66} +(4.48009 - 2.58658i) q^{67} +(-0.420915 - 0.729047i) q^{68} +(-0.335823 + 0.581663i) q^{69} +7.21857i q^{70} +(6.72458 + 3.88244i) q^{71} +(-6.83129 - 3.94405i) q^{72} -10.1088i q^{73} +(-0.0189916 + 0.0328945i) q^{74} +(0.0473938 + 0.0820885i) q^{75} +(-1.17422 + 0.677939i) q^{76} +5.16177 q^{77} +8.78347 q^{79} +(3.82535 - 2.20857i) q^{80} +(-4.45961 - 7.72427i) q^{81} +(-0.200360 + 0.347034i) q^{82} -0.725474i q^{83} +(-0.0937250 - 0.0541121i) q^{84} +(-3.08209 - 1.77944i) q^{85} +5.32235i q^{86} +(-0.0698151 + 0.120923i) q^{87} +(-1.41013 - 2.44242i) q^{88} +(-11.6970 + 6.75327i) q^{89} +4.47309 q^{90} -1.67610 q^{92} +(-0.120186 + 0.0693893i) q^{93} +(4.87381 + 8.44168i) q^{94} +(-2.86603 + 4.96410i) q^{95} +0.126194i q^{96} +(2.97800 + 1.71935i) q^{97} +(-21.1088 - 12.1872i) q^{98} -3.19856i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} + 2 q^{4} + 18 q^{6} + 6 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q + 2 * q^3 + 2 * q^4 + 18 * q^6 + 6 * q^7 - 4 * q^9	$ 8 q + 2 q^{3} + 2 q^{4} + 18 q^{6} + 6 q^{7} - 4 q^{9} - 2 q^{10} + 20 q^{12} + 4 q^{14} + 6 q^{15} - 2 q^{16} - 2 q^{17} - 12 q^{19} - 12 q^{20} - 12 q^{22} - 10 q^{23} + 12 q^{24} - 8 q^{25} - 4 q^{27} + 18 q^{28} - 8 q^{29} + 4 q^{30} - 6 q^{32} - 42 q^{33} + 10 q^{35} + 20 q^{36} - 6 q^{37} - 16 q^{38} - 12 q^{40} - 12 q^{41} + 4 q^{42} - 2 q^{43} + 42 q^{46} + 28 q^{48} + 12 q^{49} - 8 q^{51} - 24 q^{53} - 18 q^{54} + 12 q^{56} - 36 q^{58} + 12 q^{59} - 28 q^{61} + 4 q^{62} + 24 q^{63} - 8 q^{64} + 12 q^{66} - 6 q^{67} - 14 q^{68} - 16 q^{69} + 48 q^{72} + 10 q^{74} - 2 q^{75} - 54 q^{76} - 36 q^{77} - 16 q^{79} + 8 q^{81} + 4 q^{82} + 30 q^{84} - 18 q^{85} + 22 q^{87} - 18 q^{88} - 24 q^{89} + 40 q^{90} + 44 q^{92} + 32 q^{94} - 16 q^{95} + 30 q^{97} - 72 q^{98}+O(q^{100}) $ 8 * q + 2 * q^3 + 2 * q^4 + 18 * q^6 + 6 * q^7 - 4 * q^9 - 2 * q^10 + 20 * q^12 + 4 * q^14 + 6 * q^15 - 2 * q^16 - 2 * q^17 - 12 * q^19 - 12 * q^20 - 12 * q^22 - 10 * q^23 + 12 * q^24 - 8 * q^25 - 4 * q^27 + 18 * q^28 - 8 * q^29 + 4 * q^30 - 6 * q^32 - 42 * q^33 + 10 * q^35 + 20 * q^36 - 6 * q^37 - 16 * q^38 - 12 * q^40 - 12 * q^41 + 4 * q^42 - 2 * q^43 + 42 * q^46 + 28 * q^48 + 12 * q^49 - 8 * q^51 - 24 * q^53 - 18 * q^54 + 12 * q^56 - 36 * q^58 + 12 * q^59 - 28 * q^61 + 4 * q^62 + 24 * q^63 - 8 * q^64 + 12 * q^66 - 6 * q^67 - 14 * q^68 - 16 * q^69 + 48 * q^72 + 10 * q^74 - 2 * q^75 - 54 * q^76 - 36 * q^77 - 16 * q^79 + 8 * q^81 + 4 * q^82 + 30 * q^84 - 18 * q^85 + 22 * q^87 - 18 * q^88 - 24 * q^89 + 40 * q^90 + 44 * q^92 + 32 * q^94 - 16 * q^95 + 30 * q^97 - 72 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.29515	+	0.747754i	−0.915808	+	0.528742i	−0.882295	−	0.470696i	$-0.844003\pi$
$2$	−1.29515	+	0.747754i	−0.915808	+	0.528742i	−0.0335125	+	0.999438i	$0.510669\pi$
$3$	−0.0473938	−	0.0820885i	−0.0273628	−	0.0473938i	0.852020	−	0.523510i	$-0.175378\pi$
$3$	−0.0473938	−	0.0820885i	−0.0273628	−	0.0473938i	−0.879383	+	0.476116i	$0.842044\pi$
$4$	0.118272	−	0.204852i	0.0591358	−	0.102426i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	0.122764	+	0.0708778i	0.0501182	+	0.0289357i
$7$	4.18016	+	2.41342i	1.57995	+	0.912187i	0.994864	+	0.101218i	$0.0322739\pi$
$7$	4.18016	+	2.41342i	1.57995	+	0.912187i	0.585089	+	0.810969i	$0.301059\pi$
$8$		−	2.63726i		−	0.932413i
$9$	1.49551	−	2.59030i	0.498503	−	0.863432i
$10$	0.747754	+	1.29515i	0.236461	+	0.409562i
$11$	0.926118	−	0.534695i	0.279235	−	0.161217i	−0.353842	−	0.935305i	$-0.615125\pi$
$11$	0.926118	−	0.534695i	0.279235	−	0.161217i	0.633077	+	0.774089i	$0.281792\pi$
$12$	−0.0224214			−0.00647249
$13$		0			0
$13$		0			0
$14$	−7.21857			−1.92924
$15$	−0.0820885	+	0.0473938i	−0.0211951	+	0.0122370i
$16$	2.20857	+	3.82535i	0.552142	+	0.956337i
$17$	1.77944	−	3.08209i	0.431579	−	0.747516i	−0.565431	−	0.824796i	$-0.691290\pi$
$17$	1.77944	−	3.08209i	0.431579	−	0.747516i	0.997009	+	0.0772795i	$0.0246234\pi$
$18$			4.47309i			1.05432i
$19$	−4.96410	−	2.86603i	−1.13884	−	0.657511i	−0.192699	−	0.981258i	$-0.561724\pi$
$19$	−4.96410	−	2.86603i	−1.13884	−	0.657511i	−0.946144	+	0.323747i	$0.895057\pi$
$20$	−0.204852	−	0.118272i	−0.0458064	−	0.0264463i
$21$		−	0.457524i		−	0.0998400i
$22$	−0.799640	+	1.38502i	−0.170484	+	0.295287i
$23$	−3.54290	−	6.13649i	−0.738746	−	1.27955i	−0.953060	−	0.302781i	$-0.902085\pi$
$23$	−3.54290	−	6.13649i	−0.738746	−	1.27955i	0.214314	−	0.976765i	$-0.431248\pi$
$24$	−0.216489	+	0.124990i	−0.0441906	+	0.0255135i
$25$	−1.00000			−0.200000
$26$		0			0
$27$	−0.567874			−0.109287
$28$	0.988789	−	0.570878i	0.186864	−	0.107886i
$29$	−0.736543	−	1.27573i	−0.136773	−	0.236897i	0.789501	−	0.613750i	$-0.210340\pi$
$29$	−0.736543	−	1.27573i	−0.136773	−	0.236897i	−0.926273	+	0.376853i	$0.877006\pi$
$30$	0.0708778	−	0.122764i	0.0129405	−	0.0224135i
$31$		−	1.46410i		−	0.262960i	−0.991319	−	0.131480i	$-0.958027\pi$
$31$		−	1.46410i		−	0.262960i	0.991319	−	0.131480i	$-0.0419730\pi$
$32$	−1.15297	−	0.665665i	−0.203818	−	0.117674i
$33$	−0.0877845	−	0.0506824i	−0.0152813	−	0.00882268i
$34$			5.32235i			0.912775i
$35$	2.41342	−	4.18016i	0.407942	−	0.706577i
$36$	−0.353752	−	0.612717i	−0.0589587	−	0.102119i
$37$	0.0219955	−	0.0126991i	0.00361604	−	0.00208772i	−0.498191	−	0.867067i	$-0.666002\pi$
$37$	0.0219955	−	0.0126991i	0.00361604	−	0.00208772i	0.501807	+	0.864980i	$0.332669\pi$
$38$	8.57233			1.39061
$39$		0			0
$40$	−2.63726			−0.416988
$41$	0.232051	−	0.133975i	0.0362402	−	0.0209233i	−0.481770	−	0.876297i	$-0.660006\pi$
$41$	0.232051	−	0.133975i	0.0362402	−	0.0209233i	0.518011	+	0.855374i	$0.326673\pi$
$42$	0.342116	+	0.592562i	0.0527896	+	0.0914342i
$43$	1.77944	−	3.08209i	0.271363	−	0.470014i	−0.697848	−	0.716246i	$-0.745859\pi$
$43$	1.77944	−	3.08209i	0.271363	−	0.470014i	0.969211	+	0.246232i	$0.0791924\pi$
$44$		−	0.252957i		−	0.0381347i
$45$	−2.59030	−	1.49551i	−0.386138	−	0.222937i
$46$	9.17716	+	5.29844i	1.35310	+	0.781212i
$47$		−	6.51793i		−	0.950738i	−0.879787	−	0.475369i	$-0.842315\pi$
$47$		−	6.51793i		−	0.950738i	0.879787	−	0.475369i	$-0.157685\pi$
$48$	0.209345	−	0.362596i	0.0302163	−	0.0523362i
$49$	8.14918	+	14.1148i	1.16417	+	2.01640i
$50$	1.29515	−	0.747754i	0.183162	−	0.105748i
$51$	−0.337339			−0.0472368
$52$		0			0
$53$	0.991015			0.136126			0.0680632	−	0.997681i	$-0.478318\pi$
$53$	0.991015			0.136126			0.0680632	+	0.997681i	$0.478318\pi$
$54$	0.735481	−	0.424630i	0.100086	−	0.0577848i
$55$	−0.534695	−	0.926118i	−0.0720982	−	0.124878i
$56$	6.36482	−	11.0242i	0.850535	−	1.47317i
$57$			0.543327i			0.0719655i
$58$	1.90786	+	1.10151i	0.250515	+	0.144635i
$59$	7.55440	+	4.36153i	0.983499	+	0.567823i	0.903325	−	0.428958i	$-0.141119\pi$
$59$	7.55440	+	4.36153i	0.983499	+	0.567823i	0.0801741	+	0.996781i	$0.474452\pi$
$60$			0.0224214i			0.00289458i
$61$	−3.16867	+	5.48830i	−0.405707	+	0.702704i	−0.994403	−	0.105650i	$-0.966308\pi$
$61$	−3.16867	+	5.48830i	−0.405707	+	0.702704i	0.588697	+	0.808354i	$0.299641\pi$
$62$	1.09479	+	1.89623i	0.139038	+	0.240821i
$63$	12.5029	−	7.21857i	1.57522	−	0.909455i
$64$	−6.84325			−0.855406
$65$		0			0
$66$	0.151592			0.0186597
$67$	4.48009	−	2.58658i	0.547330	−	0.316001i	−0.200714	−	0.979650i	$-0.564326\pi$
$67$	4.48009	−	2.58658i	0.547330	−	0.316001i	0.748044	+	0.663649i	$0.230993\pi$
$68$	−0.420915	−	0.729047i	−0.0510435	−	0.0884099i
$69$	−0.335823	+	0.581663i	−0.0404283	+	0.0700240i
$70$			7.21857i			0.862785i
$71$	6.72458	+	3.88244i	0.798061	+	0.460761i	0.842793	−	0.538238i	$-0.180910\pi$
$71$	6.72458	+	3.88244i	0.798061	+	0.460761i	−0.0447317	+	0.998999i	$0.514243\pi$
$72$	−6.83129	−	3.94405i	−0.805075	−	0.464810i
$73$		−	10.1088i		−	1.18314i	−0.806252	−	0.591572i	$-0.798507\pi$
$73$		−	10.1088i		−	1.18314i	0.806252	−	0.591572i	$-0.201493\pi$
$74$	−0.0189916	+	0.0328945i	−0.00220773	+	0.00382391i
$75$	0.0473938	+	0.0820885i	0.00547256	+	0.00947876i
$76$	−1.17422	+	0.677939i	−0.134693	+	0.0777649i
$77$	5.16177			0.588238
$78$		0			0
$79$	8.78347			0.988218			0.494109	−	0.869400i	$-0.335494\pi$
$79$	8.78347			0.988218			0.494109	+	0.869400i	$0.335494\pi$
$80$	3.82535	−	2.20857i	0.427687	−	0.246925i
$81$	−4.45961	−	7.72427i	−0.495512	−	0.858252i
$82$	−0.200360	+	0.347034i	−0.0221261	+	0.0383235i
$83$		−	0.725474i		−	0.0796311i	−0.999207	−	0.0398155i	$-0.987323\pi$
$83$		−	0.725474i		−	0.0796311i	0.999207	−	0.0398155i	$-0.0126770\pi$
$84$	−0.0937250	−	0.0541121i	−0.0102262	−	0.00590412i
$85$	−3.08209	−	1.77944i	−0.334299	−	0.193008i
$86$			5.32235i			0.573923i
$87$	−0.0698151	+	0.120923i	−0.00748497	+	0.0129643i
$88$	−1.41013	−	2.44242i	−0.150320	−	0.260363i
$89$	−11.6970	+	6.75327i	−1.23988	+	0.715845i	−0.969070	−	0.246788i	$-0.920625\pi$
$89$	−11.6970	+	6.75327i	−1.23988	+	0.715845i	−0.270810	+	0.962633i	$0.587292\pi$
$90$	4.47309			0.471505
$91$		0			0
$92$	−1.67610			−0.174745
$93$	−0.120186	+	0.0693893i	−0.0124627	+	0.00719534i
$94$	4.87381	+	8.44168i	0.502695	+	0.870693i
$95$	−2.86603	+	4.96410i	−0.294048	+	0.509306i
$96$			0.126194i			0.0128796i
$97$	2.97800	+	1.71935i	0.302371	+	0.174574i	0.643507	−	0.765440i	$-0.277479\pi$
$97$	2.97800	+	1.71935i	0.302371	+	0.174574i	−0.341137	+	0.940014i	$0.610812\pi$
$98$	−21.1088	−	12.1872i	−2.13231	−	1.23109i
$99$		−	3.19856i		−	0.321467i
$100$	−0.118272	+	0.204852i	−0.0118272	+	0.0204852i
$101$	1.42763	+	2.47273i	0.142055	+	0.246046i	0.928270	−	0.371906i	$-0.121296\pi$
$101$	1.42763	+	2.47273i	0.142055	+	0.246046i	−0.786215	+	0.617953i	$0.787962\pi$
$102$	0.436903	−	0.252246i	0.0432599	−	0.0249761i
$103$	5.54488			0.546354			0.273177	−	0.961964i	$-0.411926\pi$
$103$	5.54488			0.546354			0.273177	+	0.961964i	$0.411926\pi$
$104$		0			0
$105$	−0.457524			−0.0446498
$106$	−1.28351	+	0.741035i	−0.124666	+	0.0719757i
$107$	2.22056	+	3.84611i	0.214669	+	0.371818i	0.953170	−	0.302434i	$-0.0977993\pi$
$107$	2.22056	+	3.84611i	0.214669	+	0.371818i	−0.738501	+	0.674252i	$0.764466\pi$
$108$	−0.0671633	+	0.116330i	−0.00646280	+	0.0111939i
$109$			13.7804i			1.31993i	0.751298	+	0.659963i	$0.229428\pi$
$109$			13.7804i			1.31993i	−0.751298	+	0.659963i	$0.770572\pi$
$110$	1.38502	+	0.799640i	0.132056	+	0.0762427i
$111$	−0.00208490	−	0.00120372i	−0.000197890	−	0.000114252i
$112$			21.3208i			2.01463i
$113$	4.02200	−	6.96630i	0.378358	−	0.655334i	−0.612466	−	0.790497i	$-0.709822\pi$
$113$	4.02200	−	6.96630i	0.378358	−	0.655334i	0.990823	+	0.135163i	$0.0431557\pi$
$114$	−0.406275	−	0.703689i	−0.0380511	−	0.0659065i
$115$	−6.13649	+	3.54290i	−0.572230	+	0.330377i
$116$	−0.348448			−0.0323526
$117$		0			0
$118$	−13.0454			−1.20093
$119$	14.8767	−	8.58909i	1.36375	−	0.787361i
$120$	0.124990	+	0.216489i	0.0114100	+	0.0197626i
$121$	−4.92820	+	8.53590i	−0.448018	+	0.775991i
$122$		−	9.47754i		−	0.858056i
$123$	−0.0219955	−	0.0126991i	−0.00198327	−	0.00114504i
$124$	−0.299925	−	0.173162i	−0.0269340	−	0.0155504i
$125$			1.00000i			0.0894427i
$126$	−10.7954	+	18.6982i	−0.961734	+	1.66577i
$127$	0.353326	+	0.611979i	0.0313526	+	0.0543044i	0.881276	−	0.472602i	$-0.156685\pi$
$127$	0.353326	+	0.611979i	0.0313526	+	0.0543044i	−0.849923	+	0.526906i	$0.823352\pi$
$128$	11.1690	−	6.44840i	0.987205	−	0.569963i
$129$	−0.337339			−0.0297010
$130$		0			0
$131$	6.26554			0.547423			0.273711	−	0.961812i	$-0.411749\pi$
$131$	6.26554			0.547423			0.273711	+	0.961812i	$0.411749\pi$
$132$	−0.0207648	+	0.0119886i	−0.00180735	+	0.00104347i
$133$	−13.8338	−	23.9609i	−1.19955	−	2.07767i
$134$	−3.86825	+	6.70001i	−0.334166	+	0.578793i
$135$			0.567874i			0.0488748i
$136$	−8.12828	−	4.69286i	−0.696994	−	0.402410i
$137$	14.1212	+	8.15290i	1.20646	+	0.696549i	0.961984	−	0.273107i	$-0.0880511\pi$
$137$	14.1212	+	8.15290i	1.20646	+	0.696549i	0.244475	+	0.969656i	$0.421384\pi$
$138$		−	1.00445i		−	0.0855046i
$139$	3.41264	−	5.91087i	0.289456	−	0.501353i	−0.684224	−	0.729272i	$-0.739859\pi$
$139$	3.41264	−	5.91087i	0.289456	−	0.501353i	0.973680	+	0.227919i	$0.0731921\pi$
$140$	−0.570878	−	0.988789i	−0.0482480	−	0.0835680i
$141$	−0.535047	+	0.308909i	−0.0450591	+	0.0260149i
$142$	−11.6124			−0.974494
$143$		0			0
$144$	13.2117			1.10098
$145$	−1.27573	+	0.736543i	−0.105944	+	0.0611666i
$146$	7.55889	+	13.0924i	0.625578	+	1.08353i
$147$	0.772442	−	1.33791i	0.0637099	−	0.110349i
$148$		−	0.00600778i		−	0.000493837i
$149$	7.30887	+	4.21978i	0.598766	+	0.345698i	0.768556	−	0.639783i	$-0.220976\pi$
$149$	7.30887	+	4.21978i	0.598766	+	0.345698i	−0.169790	+	0.985480i	$0.554309\pi$
$150$	−0.122764	−	0.0708778i	−0.0100236	−	0.00578715i
$151$			1.37017i			0.111503i	0.998445	+	0.0557513i	$0.0177554\pi$
$151$			1.37017i			0.111503i	−0.998445	+	0.0557513i	$0.982245\pi$
$152$	−7.55846	+	13.0916i	−0.613072	+	1.06187i
$153$	−5.32235	−	9.21857i	−0.430286	−	0.745278i
$154$	−6.68525	+	3.85973i	−0.538713	+	0.311026i
$155$	−1.46410			−0.117599
$156$		0			0
$157$	11.9700			0.955311			0.477656	−	0.878547i	$-0.341487\pi$
$157$	11.9700			0.955311			0.477656	+	0.878547i	$0.341487\pi$
$158$	−11.3759	+	6.56787i	−0.905017	+	0.522512i
$159$	−0.0469680	−	0.0813509i	−0.00372480	−	0.00645155i
$160$	−0.665665	+	1.15297i	−0.0526255	+	0.0911500i
$161$		−	34.2020i		−	2.69550i
$162$	11.5517	+	6.66938i	0.907588	+	0.523996i
$163$	−19.5474	−	11.2857i	−1.53107	−	0.883962i	−0.999313	−	0.0370630i	$-0.988200\pi$
$163$	−19.5474	−	11.2857i	−1.53107	−	0.883962i	−0.531754	−	0.846899i	$-0.678467\pi$
$164$		−	0.0633815i		−	0.00494927i
$165$	−0.0506824	+	0.0877845i	−0.00394562	+	0.00683402i
$166$	0.542476	+	0.939595i	0.0421043	+	0.0729267i
$167$	−7.09881	+	4.09850i	−0.549323	+	0.317152i	−0.748849	−	0.662741i	$-0.769393\pi$
$167$	−7.09881	+	4.09850i	−0.549323	+	0.317152i	0.199526	+	0.979893i	$0.436060\pi$
$168$	−1.20661			−0.0930922
$169$		0			0
$170$	5.32235			0.408205
$171$	−14.8477	+	8.57233i	−1.13543	+	0.655542i
$172$	−0.420915	−	0.729047i	−0.0320945	−	0.0555893i
$173$	−4.58386	+	7.93948i	−0.348505	+	0.603628i	−0.985984	−	0.166840i	$-0.946644\pi$
$173$	−4.58386	+	7.93948i	−0.348505	+	0.603628i	0.637479	+	0.770467i	$0.279977\pi$
$174$		−	0.208818i		−	0.0158305i
$175$	−4.18016	−	2.41342i	−0.315991	−	0.182437i
$176$	4.09079	+	2.36182i	0.308355	+	0.178029i
$177$		−	0.826838i		−	0.0621490i
$178$	10.0996	−	17.4930i	0.756994	−	1.31115i
$179$	−5.01850	−	8.69229i	−0.375100	−	0.649693i	0.615242	−	0.788338i	$-0.289058\pi$
$179$	−5.01850	−	8.69229i	−0.375100	−	0.649693i	−0.990342	+	0.138646i	$0.955725\pi$
$180$	−0.612717	+	0.353752i	−0.0456692	+	0.0263671i
$181$	−17.0238			−1.26537			−0.632686	−	0.774408i	$-0.718048\pi$
$181$	−17.0238			−1.26537			−0.632686	+	0.774408i	$0.718048\pi$
$182$		0			0
$183$	0.600701			0.0444051
$184$	−16.1835	+	9.34356i	−1.19307	+	0.688817i
$185$	−0.0126991	−	0.0219955i	−0.000933659	−	0.00161714i
$186$	0.103772	−	0.179739i	0.00760895	−	0.0131791i
$187$		−	3.80584i		−	0.278310i
$188$	−1.33521	−	0.770886i	−0.0973804	−	0.0562226i
$189$	−2.37381	−	1.37052i	−0.172669	−	0.0996905i
$190$		−	8.57233i		−	0.621902i
$191$	1.93870	−	3.35793i	0.140280	−	0.242971i	−0.787322	−	0.616542i	$-0.788533\pi$
$191$	1.93870	−	3.35793i	0.140280	−	0.242971i	0.927602	+	0.373570i	$0.121867\pi$
$192$	0.324328	+	0.561752i	0.0234063	+	0.0405410i
$193$	−1.08595	+	0.626972i	−0.0781681	+	0.0451304i	−0.538575	−	0.842578i	$-0.681037\pi$
$193$	−1.08595	+	0.626972i	−0.0781681	+	0.0451304i	0.460406	+	0.887708i	$0.347704\pi$
$194$	−5.14261			−0.369218
$195$		0			0
$196$	3.85527			0.275376
$197$	−13.2346	+	7.64098i	−0.942923	+	0.544397i	−0.890876	−	0.454247i	$-0.849908\pi$
$197$	−13.2346	+	7.64098i	−0.942923	+	0.544397i	−0.0520479	+	0.998645i	$0.516575\pi$
$198$	2.39174	+	4.14261i	0.169973	+	0.294402i
$199$	−6.61480	+	11.4572i	−0.468911	+	0.812177i	−0.999368	−	0.0355340i	$-0.988687\pi$
$199$	−6.61480	+	11.4572i	−0.468911	+	0.812177i	0.530458	+	0.847711i	$0.322020\pi$
$200$			2.63726i			0.186483i
$201$	−0.424657	−	0.245176i	−0.0299530	−	0.0172934i
$202$	−3.69799	−	2.13504i	−0.260190	−	0.150221i
$203$		−	7.11035i		−	0.499049i
$204$	−0.0398976	+	0.0691046i	−0.00279339	+	0.00483829i
$205$	−0.133975	−	0.232051i	−0.00935719	−	0.0162071i
$206$	−7.18144	+	4.14621i	−0.500355	+	0.288880i
$207$	−21.1937			−1.47307
$208$		0			0
$209$	−6.12979			−0.424007
$210$	0.592562	−	0.342116i	0.0408906	−	0.0236082i
$211$	2.40521	+	4.16595i	0.165582	+	0.286796i	0.936862	−	0.349700i	$-0.113717\pi$
$211$	2.40521	+	4.16595i	0.165582	+	0.286796i	−0.771280	+	0.636496i	$0.780383\pi$
$212$	0.117209	−	0.203012i	0.00804994	−	0.0139429i
$213$		−	0.736014i		−	0.0504309i
$214$	−5.75189	−	3.32086i	−0.393191	−	0.227009i
$215$	−3.08209	−	1.77944i	−0.210197	−	0.121357i
$216$			1.49763i			0.101901i
$217$	3.53349	−	6.12019i	0.239869	−	0.415465i
$218$	−10.3044	−	17.8477i	−0.697900	−	1.20880i
$219$	−0.829815	+	0.479094i	−0.0560737	+	0.0323742i
$220$	−0.252957			−0.0170543
$221$		0			0
$222$	0.00360034			0.000241639
$223$	12.7420	−	7.35661i	0.853269	−	0.492635i	−0.00848317	−	0.999964i	$-0.502700\pi$
$223$	12.7420	−	7.35661i	0.853269	−	0.492635i	0.861753	+	0.507329i	$0.169367\pi$
$224$	−3.21306	−	5.56518i	−0.214682	−	0.371839i
$225$	−1.49551	+	2.59030i	−0.0997005	+	0.172686i
$226$			12.0299i			0.800214i
$227$	−12.9062	−	7.45140i	−0.856615	−	0.494567i	0.00626222	−	0.999980i	$-0.498007\pi$
$227$	−12.9062	−	7.45140i	−0.856615	−	0.494567i	−0.862877	+	0.505413i	$0.831340\pi$
$228$	0.111302	+	0.0642602i	0.00737115	+	0.00425573i
$229$			19.3074i			1.27587i	0.770092	+	0.637933i	$0.220210\pi$
$229$			19.3074i			1.27587i	−0.770092	+	0.637933i	$0.779790\pi$
$230$	5.29844	−	9.17716i	0.349369	−	0.605124i
$231$	−0.244636	−	0.423722i	−0.0160959	−	0.0278788i
$232$	−3.36444	+	1.94246i	−0.220886	+	0.127529i
$233$	21.1937			1.38845			0.694224	−	0.719759i	$-0.255748\pi$
$233$	21.1937			1.38845			0.694224	+	0.719759i	$0.255748\pi$
$234$		0			0
$235$	−6.51793			−0.425183
$236$	1.78694	−	1.03169i	0.116320	−	0.0671573i
$237$	−0.416282	−	0.721022i	−0.0270404	−	0.0468354i
$238$	−12.8451	+	22.2483i	−0.832621	+	1.44214i
$239$		−	14.8971i		−	0.963612i	−0.876278	−	0.481806i	$-0.839981\pi$
$239$		−	14.8971i		−	0.963612i	0.876278	−	0.481806i	$-0.160019\pi$
$240$	−0.362596	−	0.209345i	−0.0234055	−	0.0135131i
$241$	8.13343	+	4.69584i	0.523921	+	0.302486i	0.738537	−	0.674213i	$-0.235517\pi$
$241$	8.13343	+	4.69584i	0.523921	+	0.302486i	−0.214617	+	0.976698i	$0.568850\pi$
$242$		−	14.7403i		−	0.947544i
$243$	−1.27453	+	2.20754i	−0.0817609	+	0.141614i
$244$	0.749527	+	1.29822i	0.0479835	+	0.0831099i
$245$	14.1148	−	8.14918i	0.901762	−	0.520632i
$246$	0.0379833			0.00242173
$247$		0			0
$248$	−3.86122			−0.245188
$249$	−0.0595530	+	0.0343829i	−0.00377402	+	0.00217893i
$250$	−0.747754	−	1.29515i	−0.0472921	−	0.0819123i
$251$	5.65817	−	9.80024i	0.357140	−	0.618585i	−0.630341	−	0.776318i	$-0.717085\pi$
$251$	5.65817	−	9.80024i	0.357140	−	0.618585i	0.987482	+	0.157733i	$0.0504184\pi$
$252$		−	3.41501i		−	0.215125i
$253$	−6.56229	−	3.78874i	−0.412568	−	0.238196i
$254$	−0.915219	−	0.528402i	−0.0574260	−	0.0331549i
$255$			0.337339i			0.0211250i
$256$	−2.80038	+	4.85040i	−0.175024	+	0.303150i
$257$	−13.2660	−	22.9773i	−0.827508	−	1.43329i	−0.899987	−	0.435917i	$-0.856424\pi$
$257$	−13.2660	−	22.9773i	−0.827508	−	1.43329i	0.0724788	−	0.997370i	$-0.476909\pi$
$258$	0.436903	−	0.252246i	0.0272004	−	0.0157042i
$259$	0.122593			0.00761758
$260$		0			0
$261$	−4.40602			−0.272726
$262$	−8.11480	+	4.68508i	−0.501334	+	0.289445i
$263$	7.07038	+	12.2463i	0.435979	+	0.755137i	0.997375	−	0.0724100i	$-0.0230690\pi$
$263$	7.07038	+	12.2463i	0.435979	+	0.755137i	−0.561396	+	0.827547i	$0.689736\pi$
$264$	−0.133663	+	0.231511i	−0.00822638	+	0.0142485i
$265$		−	0.991015i		−	0.0608776i
$266$	35.8337	+	20.6886i	2.19711	+	1.26850i
$267$	1.10873	+	0.640126i	0.0678532	+	0.0391751i
$268$		−	1.22368i		−	0.0747479i
$269$	−12.3872	+	21.4553i	−0.755264	+	1.30815i	0.189980	+	0.981788i	$0.439158\pi$
$269$	−12.3872	+	21.4553i	−0.755264	+	1.30815i	−0.945243	+	0.326367i	$0.894176\pi$
$270$	−0.424630	−	0.735481i	−0.0258422	−	0.0447599i
$271$	−16.2095	+	9.35856i	−0.984657	+	0.568492i	−0.903673	−	0.428224i	$-0.859140\pi$
$271$	−16.2095	+	9.35856i	−0.984657	+	0.568492i	−0.0809839	+	0.996715i	$0.525806\pi$
$272$	15.7201			0.953170
$273$		0			0
$274$	−24.3854			−1.47318
$275$	−0.926118	+	0.534695i	−0.0558470	+	0.0322433i
$276$	0.0794367	+	0.137588i	0.00478152	+	0.00828184i
$277$	−11.3323	+	19.6282i	−0.680893	+	1.17934i	0.293815	+	0.955862i	$0.405075\pi$
$277$	−11.3323	+	19.6282i	−0.680893	+	1.17934i	−0.974709	+	0.223480i	$0.928258\pi$
$278$			10.2073i			0.612191i
$279$	−3.79246	−	2.18958i	−0.227048	−	0.131086i
$280$	−11.0242	−	6.36482i	−0.658822	−	0.380371i
$281$			27.8384i			1.66070i	0.557241	+	0.830351i	$0.311860\pi$
$281$			27.8384i			1.66070i	−0.557241	+	0.830351i	$0.688140\pi$
$282$	0.461976	−	0.800167i	0.0275103	−	0.0476492i
$283$	3.96004	+	6.85898i	0.235400	+	0.407724i	0.959389	−	0.282087i	$-0.0910268\pi$
$283$	3.96004	+	6.85898i	0.235400	+	0.407724i	−0.723989	+	0.689811i	$0.757693\pi$
$284$	1.59065	−	0.918364i	0.0943879	−	0.0544949i
$285$	0.543327			0.0321839
$286$		0			0
$287$	1.29335			0.0763439
$288$	−3.44854	+	1.99102i	−0.203207	+	0.117322i
$289$	2.16715	+	3.75362i	0.127480	+	0.220801i
$290$	1.10151	−	1.90786i	0.0646827	−	0.112034i
$291$		−	0.325946i		−	0.0191073i
$292$	−2.07081	−	1.19558i	−0.121185	−	0.0699662i
$293$	−0.236400	−	0.136485i	−0.0138106	−	0.00797356i	0.493079	−	0.869985i	$-0.335871\pi$
$293$	−0.236400	−	0.136485i	−0.0138106	−	0.00797356i	−0.506889	+	0.862011i	$0.669205\pi$
$294$			2.31038i			0.134744i
$295$	4.36153	−	7.55440i	0.253938	−	0.439834i
$296$	−0.0334909	−	0.0580080i	−0.00194662	−	0.00337165i
$297$	−0.525918	+	0.303639i	−0.0305169	+	0.0176189i
$298$	−12.6214			−0.731139
$299$		0			0
$300$	0.0224214			0.00129450
$301$	14.8767	−	8.58909i	0.857481	−	0.495067i
$302$	−1.02455	−	1.77457i	−0.0589560	−	0.102115i
$303$	0.135322	−	0.234385i	0.00777404	−	0.0134650i
$304$		−	25.3192i		−	1.45216i
$305$	5.48830	+	3.16867i	0.314259	+	0.181437i
$306$	13.7864	+	7.95961i	0.788119	+	0.455021i
$307$		−	6.85224i		−	0.391078i	−0.980696	−	0.195539i	$-0.937354\pi$
$307$		−	6.85224i		−	0.391078i	0.980696	−	0.195539i	$-0.0626456\pi$
$308$	0.610491	−	1.05740i	0.0347859	−	0.0602510i
$309$	−0.262793	−	0.455171i	−0.0149498	−	0.0258938i
$310$	1.89623	−	1.09479i	0.107698	−	0.0621798i
$311$	−10.6447			−0.603605			−0.301803	−	0.953370i	$-0.597588\pi$
$311$	−10.6447			−0.603605			−0.301803	+	0.953370i	$0.597588\pi$
$312$		0			0
$313$	17.8236			1.00745			0.503724	−	0.863865i	$-0.331963\pi$
$313$	17.8236			1.00745			0.503724	+	0.863865i	$0.331963\pi$
$314$	−15.5029	+	8.95062i	−0.874881	+	0.505113i
$315$	−7.21857	−	12.5029i	−0.406721	−	0.704461i
$316$	1.03883	−	1.79931i	0.0584390	−	0.101219i
$317$			8.17161i			0.458963i	0.973313	+	0.229482i	$0.0737031\pi$
$317$			8.17161i			0.458963i	−0.973313	+	0.229482i	$0.926297\pi$
$318$	0.121661	+	0.0702410i	0.00682241	+	0.00393892i
$319$	−1.36425	−	0.787651i	−0.0763835	−	0.0441000i
$320$			6.84325i			0.382549i
$321$	0.210481	−	0.364564i	0.0117479	−	0.0203480i
$322$	25.5747	+	44.2967i	1.42522	+	2.46856i
$323$	−17.6667	+	10.1999i	−0.983001	+	0.567536i
$324$	−2.10978			−0.117210
$325$		0			0
$326$	33.7556			1.86955
$327$	1.13122	−	0.653107i	0.0625563	−	0.0361169i
$328$	−0.353326	−	0.611979i	−0.0195092	−	0.0337909i
$329$	15.7305	−	27.2460i	0.867250	−	1.50212i
$330$		−	0.151592i		−	0.00834486i
$331$	−21.5983	−	12.4698i	−1.18715	−	0.685400i	−0.229490	−	0.973311i	$-0.573706\pi$
$331$	−21.5983	−	12.4698i	−1.18715	−	0.685400i	−0.957657	+	0.287911i	$0.907039\pi$
$332$	−0.148615	−	0.0858029i	−0.00815631	−	0.00470905i
$333$		−	0.0759666i		−	0.00416294i
$334$	6.12934	−	10.6163i	0.335383	−	0.580900i
$335$	−2.58658	−	4.48009i	−0.141320	−	0.244773i
$336$	1.75019	−	1.01047i	0.0954807	−	0.0551258i
$337$	19.6057			1.06799			0.533996	−	0.845487i	$-0.320690\pi$
$337$	19.6057			1.06799			0.533996	+	0.845487i	$0.320690\pi$
$338$		0			0
$339$	−0.762471			−0.0414117
$340$	−0.729047	+	0.420915i	−0.0395381	+	0.0228273i
$341$	−0.782847	−	1.35593i	−0.0423936	−	0.0734278i
$342$	12.8200	−	22.2049i	0.693225	−	1.20070i
$343$			44.8817i			2.42339i
$344$	−8.12828	−	4.69286i	−0.438247	−	0.253022i
$345$	0.581663	+	0.335823i	0.0313157	+	0.0180801i
$346$		−	13.7104i		−	0.737076i
$347$	−8.54049	+	14.7926i	−0.458478	+	0.794107i	−0.998881	−	0.0472996i	$-0.984938\pi$
$347$	−8.54049	+	14.7926i	−0.458478	+	0.794107i	0.540403	+	0.841406i	$0.318272\pi$
$348$	0.0165143	+	0.0286036i	0.000885259	+	0.00153331i
$349$	24.5708	−	14.1860i	1.31525	−	0.759357i	0.332286	−	0.943179i	$-0.392180\pi$
$349$	24.5708	−	14.1860i	1.31525	−	0.759357i	0.982960	+	0.183822i	$0.0588469\pi$
$350$	7.21857			0.385849
$351$		0			0
$352$	−1.42371			−0.0758840
$353$	18.4047	−	10.6260i	0.979586	−	0.565564i	0.0774407	−	0.996997i	$-0.475325\pi$
$353$	18.4047	−	10.6260i	0.979586	−	0.565564i	0.902145	+	0.431433i	$0.141992\pi$
$354$	0.618272	+	1.07088i	0.0328608	+	0.0569165i
$355$	3.88244	−	6.72458i	0.206058	−	0.356904i
$356$			3.19488i			0.169328i
$357$	−1.41013	−	0.814139i	−0.0746320	−	0.0430888i
$358$	12.9994	+	7.50520i	0.687039	+	0.396662i
$359$		−	32.6519i		−	1.72330i	−0.507502	−	0.861650i	$-0.669431\pi$
$359$		−	32.6519i		−	1.72330i	0.507502	−	0.861650i	$-0.330569\pi$
$360$	−3.94405	+	6.83129i	−0.207870	+	0.360041i
$361$	6.92820	+	12.0000i	0.364642	+	0.631579i
$362$	22.0484	−	12.7296i	1.15884	−	0.669055i
$363$	0.934265			0.0490362
$364$		0			0
$365$	−10.1088			−0.529118
$366$	−0.777997	+	0.449176i	−0.0406665	+	0.0234788i
$367$	2.95918	+	5.12546i	0.154468	+	0.267547i	0.932865	−	0.360226i	$-0.117300\pi$
$367$	2.95918	+	5.12546i	0.154468	+	0.267547i	−0.778397	+	0.627772i	$0.783967\pi$
$368$	15.6495	−	27.1057i	0.815785	−	1.41298i
$369$		−	0.801440i		−	0.0417213i
$370$	0.0328945	+	0.0189916i	0.00171010	+	0.000987329i
$371$	4.14261	+	2.39174i	0.215073	+	0.124173i
$372$			0.0328271i			0.00170201i
$373$	6.65926	−	11.5342i	0.344803	−	0.597217i	−0.640515	−	0.767946i	$-0.721279\pi$
$373$	6.65926	−	11.5342i	0.344803	−	0.597217i	0.985318	+	0.170729i	$0.0546123\pi$
$374$	2.84583	+	4.92912i	0.147154	+	0.254879i
$375$	0.0820885	−	0.0473938i	0.00423903	−	0.00244740i
$376$	−17.1895			−0.886480
$377$		0			0
$378$	4.09924			0.210842
$379$	22.0131	−	12.7093i	1.13074	−	0.652832i	0.186617	−	0.982433i	$-0.440248\pi$
$379$	22.0131	−	12.7093i	1.13074	−	0.652832i	0.944120	+	0.329601i	$0.106914\pi$
$380$	0.677939	+	1.17422i	0.0347775	+	0.0602364i
$381$	0.0334909	−	0.0580080i	0.00171579	−	0.00297184i
$382$			5.79869i			0.296687i
$383$	9.37632	+	5.41342i	0.479107	+	0.276613i	0.720044	−	0.693928i	$-0.244121\pi$
$383$	9.37632	+	5.41342i	0.479107	+	0.276613i	−0.240937	+	0.970541i	$0.577455\pi$
$384$	−1.05868	−	0.611228i	−0.0540254	−	0.0311916i
$385$		−	5.16177i		−	0.263068i
$386$	0.937641	−	1.62404i	0.0477247	−	0.0826615i
$387$	−5.32235	−	9.21857i	−0.270550	−	0.468606i
$388$	0.704427	−	0.406701i	0.0357618	−	0.0206471i
$389$	23.0370			1.16802			0.584011	−	0.811746i	$-0.301482\pi$
$389$	23.0370			1.16802			0.584011	+	0.811746i	$0.301482\pi$
$390$		0			0
$391$	−25.2176			−1.27531
$392$	37.2244	−	21.4915i	1.88012	−	1.08549i
$393$	−0.296948	−	0.514329i	−0.0149790	−	0.0259444i
$394$	11.4271	−	19.7924i	0.575691	−	0.997126i
$395$		−	8.78347i		−	0.441944i
$396$	−0.655233	−	0.378299i	−0.0329267	−	0.0190102i
$397$	18.2614	+	10.5432i	0.916512	+	0.529149i	0.882521	−	0.470273i	$-0.155845\pi$
$397$	18.2614	+	10.5432i	0.916512	+	0.529149i	0.0339917	+	0.999422i	$0.489178\pi$
$398$		−	19.7850i		−	0.991731i
$399$	−1.31128	+	2.27120i	−0.0656459	+	0.113702i
$400$	−2.20857	−	3.82535i	−0.110428	−	0.191267i
$401$	17.1273	−	9.88845i	0.855296	−	0.493805i	−0.00713812	−	0.999975i	$-0.502272\pi$
$401$	17.1273	−	9.88845i	0.855296	−	0.493805i	0.862434	+	0.506169i	$0.168939\pi$
$402$	0.733324			0.0365749
$403$		0			0
$404$	0.675394			0.0336021
$405$	−7.72427	+	4.45961i	−0.383822	+	0.221600i
$406$	5.31679	+	9.20895i	0.263868	+	0.457033i
$407$	0.0135803	−	0.0235218i	0.000673151	−	0.00116593i
$408$			0.889650i			0.0440443i
$409$	27.6096	+	15.9404i	1.36521	+	0.788204i	0.990312	−	0.138862i	$-0.0443446\pi$
$409$	27.6096	+	15.9404i	1.36521	+	0.788204i	0.374897	+	0.927066i	$0.377678\pi$
$410$	0.347034	+	0.200360i	0.0171388	+	0.00989508i
$411$		−	1.54559i		−	0.0762382i
$412$	0.655802	−	1.13588i	0.0323090	−	0.0559609i
$413$	21.0524	+	36.4639i	1.03592	+	1.79427i
$414$	27.4490	−	15.8477i	1.34905	−	0.778872i
$415$	−0.725474			−0.0356121
$416$		0			0
$417$	−0.646952			−0.0316814
$418$	7.93899	−	4.58358i	0.388309	−	0.224190i
$419$	−15.3648	−	26.6127i	−0.750621	−	1.30011i	−0.947522	−	0.319690i	$-0.896421\pi$
$419$	−15.3648	−	26.6127i	−0.750621	−	1.30011i	0.196902	−	0.980423i	$-0.436912\pi$
$420$	−0.0541121	+	0.0937250i	−0.00264040	+	0.00457331i
$421$			17.9820i			0.876391i	0.898880	+	0.438195i	$0.144382\pi$
$421$			17.9820i			0.876391i	−0.898880	+	0.438195i	$0.855618\pi$
$422$	−6.23021	−	3.59701i	−0.303282	−	0.175100i
$423$	−16.8834	−	9.74761i	−0.820897	−	0.473945i
$424$		−	2.61357i		−	0.126926i
$425$	−1.77944	+	3.08209i	−0.0863157	+	0.149503i
$426$	0.550357	+	0.953247i	0.0266649	+	0.0461850i
$427$	−26.4911	+	15.2947i	−1.28200	+	0.740160i
$428$	1.05051			0.0507785
$429$		0			0
$430$	5.32235			0.256666
$431$	4.24308	−	2.44974i	0.204382	−	0.118000i	−0.394316	−	0.918975i	$-0.629018\pi$
$431$	4.24308	−	2.44974i	0.204382	−	0.118000i	0.598698	+	0.800975i	$0.295685\pi$
$432$	−1.25419	−	2.17232i	−0.0603421	−	0.104516i
$433$	−9.61972	+	16.6618i	−0.462294	+	0.800717i	−0.999075	−	0.0430048i	$-0.986307\pi$
$433$	−9.61972	+	16.6618i	−0.462294	+	0.800717i	0.536781	+	0.843722i	$0.319640\pi$
$434$			10.5687i			0.507315i
$435$	0.120923	+	0.0698151i	0.00579783	+	0.00334738i
$436$	2.82296	+	1.62983i	0.135195	+	0.0780549i
$437$			40.6162i			1.94294i
$438$	0.716489	−	1.24100i	0.0342352	−	0.0592970i
$439$	−4.27987	−	7.41295i	−0.204267	−	0.353801i	0.745632	−	0.666358i	$-0.232148\pi$
$439$	−4.27987	−	7.41295i	−0.204267	−	0.353801i	−0.949899	+	0.312557i	$0.898814\pi$
$440$	−2.44242	+	1.41013i	−0.116438	+	0.0672253i
$441$	48.7487			2.32137
$442$		0			0
$443$	−37.9652			−1.80378			−0.901891	−	0.431965i	$-0.857821\pi$
$443$	−37.9652			−1.80378			−0.901891	+	0.431965i	$0.857821\pi$
$444$	−0.000493170	0	0.000284732i	−2.34048e−5	0	1.35128e-5i
$445$	6.75327	+	11.6970i	0.320136	+	0.554491i
$446$	−11.0019	+	19.0558i	−0.520954	+	0.902318i
$447$		−	0.799965i		−	0.0378370i
$448$	−28.6059	−	16.5156i	−1.35150	−	0.780290i
$449$	−23.1283	−	13.3531i	−1.09149	−	0.630173i	−0.157518	−	0.987516i	$-0.550349\pi$
$449$	−23.1283	−	13.3531i	−1.09149	−	0.630173i	−0.933973	+	0.357344i	$0.883683\pi$
$450$		−	4.47309i		−	0.210863i
$451$	0.143271	−	0.248153i	0.00674637	−	0.0116851i
$452$	−0.951375	−	1.64783i	−0.0447489	−	0.0775074i
$453$	0.112475	−	0.0649373i	0.00528453	−	0.00305102i
$454$	22.2873			1.04599
$455$		0			0
$456$	1.43290			0.0671016
$457$	−3.69903	+	2.13563i	−0.173033	+	0.0999007i	−0.584015	−	0.811743i	$-0.698519\pi$
$457$	−3.69903	+	2.13563i	−0.173033	+	0.0999007i	0.410982	+	0.911643i	$0.365186\pi$
$458$	−14.4371	−	25.0059i	−0.674604	−	1.16845i
$459$	−1.01050	+	1.75024i	−0.0471661	+	0.0816941i
$460$			1.67610i			0.0781485i
$461$	−17.8767	−	10.3211i	−0.832603	−	0.480704i	0.0221401	−	0.999755i	$-0.492952\pi$
$461$	−17.8767	−	10.3211i	−0.832603	−	0.480704i	−0.854743	+	0.519051i	$0.826285\pi$
$462$	0.633679	+	0.365855i	0.0294814	+	0.0170211i
$463$			32.1040i			1.49200i	0.665947	+	0.745999i	$0.268028\pi$
$463$			32.1040i			1.49200i	−0.665947	+	0.745999i	$0.731972\pi$
$464$	3.25341	−	5.63507i	0.151036	−	0.261602i
$465$	0.0693893	+	0.120186i	0.00321785	+	0.00557349i
$466$	−27.4490	+	15.8477i	−1.27155	+	0.734131i
$467$	−23.3774			−1.08178			−0.540888	−	0.841095i	$-0.681912\pi$
$467$	−23.3774			−1.08178			−0.540888	+	0.841095i	$0.681912\pi$
$468$		0			0
$469$	24.9700			1.15301
$470$	8.44168	−	4.87381i	0.389386	−	0.224812i
$471$	−0.567304	−	0.982600i	−0.0261400	−	0.0452758i
$472$	11.5025	−	19.9229i	0.529446	−	0.917027i
$473$		−	3.80584i		−	0.174993i
$474$	1.07829	+	0.622553i	0.0495277	+	0.0285948i
$475$	4.96410	+	2.86603i	0.227769	+	0.131502i
$476$		−	4.06338i		−	0.186245i
$477$	1.48207	−	2.56702i	0.0678594	−	0.117536i
$478$	11.1393	+	19.2939i	0.509502	+	0.882483i
$479$	4.48198	−	2.58767i	0.204787	−	0.118234i	−0.394100	−	0.919068i	$-0.628943\pi$
$479$	4.48198	−	2.58767i	0.204787	−	0.118234i	0.598886	+	0.800834i	$0.295610\pi$
$480$	0.126194			0.00575992
$481$		0			0
$482$	−14.0453			−0.639747
$483$	−2.80759	+	1.62096i	−0.127750	+	0.0737564i
$484$	1.16573	+	2.01911i	0.0529879	+	0.0917777i
$485$	1.71935	−	2.97800i	0.0780717	−	0.135224i
$486$		−	3.81213i		−	0.172922i
$487$	26.6501	+	15.3865i	1.20763	+	0.697227i	0.962242	−	0.272197i	$-0.0877502\pi$
$487$	26.6501	+	15.3865i	1.20763	+	0.697227i	0.245391	+	0.969424i	$0.421083\pi$
$488$	14.4741	+	8.35661i	0.655211	+	0.378286i
$489$			2.13948i			0.0967508i
$490$	−12.1872	+	21.1088i	−0.550560	+	0.953598i
$491$	17.8992	+	31.0023i	0.807778	+	1.39911i	0.914400	+	0.404813i	$0.132663\pi$
$491$	17.8992	+	31.0023i	0.807778	+	1.39911i	−0.106622	+	0.994300i	$0.534003\pi$
$492$	−0.00520289	+	0.00300389i	−0.000234565	+	0.000135426i
$493$	−5.24255			−0.236113
$494$		0			0
$495$	−3.19856			−0.143765
$496$	5.60070	−	3.23357i	0.251479	−	0.145191i
$497$	18.7399	+	32.4585i	0.840600	+	1.45596i
$498$	0.0514200	−	0.0890620i	0.00230418	−	0.00399096i
$499$			28.8971i			1.29361i	0.762655	+	0.646805i	$0.223895\pi$
$499$			28.8971i			1.29361i	−0.762655	+	0.646805i	$0.776105\pi$
$500$	0.204852	+	0.118272i	0.00916128	+	0.00528927i
$501$	0.672879	+	0.388487i	0.0300620	+	0.0173563i
$502$			16.9237i			0.755340i
$503$	3.93161	−	6.80974i	0.175302	−	0.303631i	−0.764964	−	0.644073i	$-0.777243\pi$
$503$	3.93161	−	6.80974i	0.175302	−	0.303631i	0.940266	+	0.340442i	$0.110577\pi$
$504$	−19.0373	−	32.9735i	−0.847988	−	1.46876i
$505$	2.47273	−	1.42763i	0.110035	−	0.0635289i
$506$	11.3322			0.503777
$507$		0			0
$508$	0.167154			0.00741625
$509$	−24.2585	+	14.0057i	−1.07524	+	0.620790i	−0.929608	−	0.368549i	$-0.879855\pi$
$509$	−24.2585	+	14.0057i	−1.07524	+	0.620790i	−0.145631	+	0.989339i	$0.546521\pi$
$510$	−0.252246	−	0.436903i	−0.0111696	−	0.0193464i
$511$	24.3968	−	42.2564i	1.07925	−	1.86931i
$512$			17.4176i			0.769757i
$513$	2.81898	+	1.62754i	0.124461	+	0.0718577i
$514$	34.3628	+	19.8394i	1.51568	+	0.875076i
$515$		−	5.54488i		−	0.244337i
$516$	−0.0398976	+	0.0691046i	−0.00175639	+	0.00304216i
$517$	−3.48510	−	6.03637i	−0.153275	−	0.265479i
$518$	−0.158776	+	0.0916696i	−0.00697623	+	0.00402773i
$519$	0.868986			0.0381443
$520$		0			0
$521$	−37.5609			−1.64557			−0.822786	−	0.568351i	$-0.807581\pi$
$521$	−37.5609			−1.64557			−0.822786	+	0.568351i	$0.807581\pi$
$522$	5.70645	−	3.29462i	0.249765	−	0.144202i
$523$	22.6553	+	39.2401i	0.990647	+	1.71585i	0.613493	+	0.789700i	$0.289764\pi$
$523$	22.6553	+	39.2401i	0.990647	+	1.71585i	0.377154	+	0.926151i	$0.376903\pi$
$524$	0.741035	−	1.28351i	0.0323723	−	0.0560704i
$525$			0.457524i			0.0199680i
$526$	−18.3144	−	10.5738i	−0.798545	−	0.461040i
$527$	−4.51249	−	2.60529i	−0.196567	−	0.113488i
$528$		−	0.447742i		−	0.0194855i
$529$	−13.6043	+	23.5633i	−0.591491	+	1.02449i
$530$	0.741035	+	1.28351i	0.0321885	+	0.0557522i
$531$	22.5953	−	13.0454i	0.980553	−	0.566123i
$532$	−6.54460			−0.283744
$533$		0			0
$534$	−1.91463			−0.0828540
$535$	3.84611	−	2.22056i	0.166282	−	0.0960030i
$536$	−6.82149	−	11.8152i	−0.294644	−	0.510338i
$537$	−0.475691	+	0.823922i	−0.0205276	+	0.0355548i
$538$		−	37.0504i		−	1.59736i
$539$	15.0942	+	8.71465i	0.650154	+	0.375367i
$540$	0.116330	+	0.0671633i	0.00500606	+	0.00289025i
$541$		−	19.7445i		−	0.848882i	−0.905456	−	0.424441i	$-0.860471\pi$
$541$		−	19.7445i		−	0.848882i	0.905456	−	0.424441i	$-0.139529\pi$
$542$	13.9958	−	24.2414i	0.601171	−	1.04126i
$543$	0.806824	+	1.39746i	0.0346242	+	0.0599708i
$544$	−4.10328	+	2.36903i	−0.175927	+	0.101571i
$545$	13.7804			0.590289
$546$		0			0
$547$	−11.8312			−0.505867			−0.252934	−	0.967484i	$-0.581395\pi$
$547$	−11.8312			−0.505867			−0.252934	+	0.967484i	$0.581395\pi$
$548$	3.34028	−	1.92851i	0.142690	−	0.0823820i
$549$	9.47754	+	16.4156i	0.404491	+	0.700600i
$550$	0.799640	−	1.38502i	0.0340968	−	0.0590573i
$551$			8.44381i			0.359718i
$552$	1.53400	+	0.885654i	0.0652913	+	0.0376959i
$553$	36.7164	+	21.1982i	1.56134	+	0.901439i
$554$		−	33.8952i		−	1.44007i
$555$	−0.00120372	+	0.00208490i	−5.10951e−5	+	8.84992e-5i
$556$	−0.807237	−	1.39818i	−0.0342345	−	0.0592958i
$557$	3.50412	−	2.02310i	0.148474	−	0.0857217i	−0.423922	−	0.905699i	$-0.639347\pi$
$557$	3.50412	−	2.02310i	0.148474	−	0.0857217i	0.572397	+	0.819977i	$0.306014\pi$
$558$	6.54905			0.277244
$559$		0			0
$560$	21.3208			0.900968
$561$	−0.312415	+	0.180373i	−0.0131902	+	0.00761536i
$562$	−20.8163	−	36.0549i	−0.878083	−	1.52088i
$563$	1.94963	−	3.37686i	0.0821671	−	0.142318i	−0.822013	−	0.569468i	$-0.807149\pi$
$563$	1.94963	−	3.37686i	0.0821671	−	0.142318i	0.904181	+	0.427151i	$0.140483\pi$
$564$			0.146141i			0.00615364i
$565$	−6.96630	−	4.02200i	−0.293074	−	0.169207i
$566$	−10.2577	−	5.92226i	−0.431162	−	0.248931i
$567$		−	43.0516i		−	1.80800i
$568$	10.2390	−	17.7345i	0.429619	−	0.744123i
$569$	−8.66778	−	15.0130i	−0.363372	−	0.629379i	0.625141	−	0.780512i	$-0.285041\pi$
$569$	−8.66778	−	15.0130i	−0.363372	−	0.629379i	−0.988514	+	0.151133i	$0.951708\pi$
$570$	−0.703689	+	0.406275i	−0.0294743	+	0.0170170i
$571$	−29.5118			−1.23503			−0.617515	−	0.786559i	$-0.711860\pi$
$571$	−29.5118			−1.23503			−0.617515	+	0.786559i	$0.711860\pi$
$572$		0			0
$573$	−0.367530			−0.0153538
$574$	−1.67508	+	0.967106i	−0.0699163	+	0.0403662i
$575$	3.54290	+	6.13649i	0.147749	+	0.255909i
$576$	−10.2341	+	17.7260i	−0.426422	+	0.738585i
$577$		−	28.3684i		−	1.18099i	−0.807041	−	0.590496i	$-0.798932\pi$
$577$		−	28.3684i		−	1.18099i	0.807041	−	0.590496i	$-0.201068\pi$
$578$	−5.61357	−	3.24100i	−0.233494	−	0.134808i
$579$	0.102934	+	0.0594291i	0.00427780	+	0.00246979i
$580$			0.348448i			0.0144685i
$581$	1.75087	−	3.03260i	0.0726384	−	0.125813i
$582$	0.243728	+	0.422149i	0.0101028	+	0.0174986i
$583$	0.917797	−	0.529891i	0.0380113	−	0.0219458i
$584$	−26.6595			−1.10318
$585$		0			0
$586$	0.408230			0.0168638
$587$	−29.7806	+	17.1939i	−1.22918	+	0.709667i	−0.966858	−	0.255314i	$-0.917821\pi$
$587$	−29.7806	+	17.1939i	−1.22918	+	0.709667i	−0.262320	+	0.964981i	$0.584488\pi$
$588$	−0.182716	−	0.316473i	−0.00753507	−	0.0130511i
$589$	−4.19615	+	7.26795i	−0.172899	+	0.299471i
$590$			13.0454i			0.537071i
$591$	1.25447	+	0.724270i	0.0516021	+	0.0297925i
$592$	0.0971572	+	0.0560937i	0.00399314	+	0.00230544i
$593$			5.47612i			0.224877i	0.993659	+	0.112439i	$0.0358662\pi$
$593$			5.47612i			0.224877i	−0.993659	+	0.112439i	$0.964134\pi$
$594$	0.454095	−	0.786515i	0.0186317	−	0.0322711i
$595$	−8.58909	−	14.8767i	−0.352118	−	0.609887i
$596$	1.72886	−	0.998159i	0.0708170	−	0.0408862i
$597$	1.25400			0.0513229
$598$		0			0
$599$	38.6039			1.57731			0.788657	−	0.614833i	$-0.210777\pi$
$599$	38.6039			1.57731			0.788657	+	0.614833i	$0.210777\pi$
$600$	0.216489	−	0.124990i	0.00883812	−	0.00510269i
$601$	−3.28948	−	5.69754i	−0.134181	−	0.232408i	0.791104	−	0.611682i	$-0.209507\pi$
$601$	−3.28948	−	5.69754i	−0.134181	−	0.232408i	−0.925284	+	0.379275i	$0.876174\pi$
$602$	−12.8451	+	22.2483i	−0.523525	+	0.906772i
$603$		−	15.4730i		−	0.630109i
$604$	0.280682	+	0.162052i	0.0114208	+	0.00659379i
$605$	8.53590	+	4.92820i	0.347034	+	0.200360i
$606$			0.404750i			0.0164418i
$607$	8.38318	−	14.5201i	0.340263	−	0.589352i	−0.644219	−	0.764841i	$-0.722817\pi$
$607$	8.38318	−	14.5201i	0.340263	−	0.589352i	0.984481	+	0.175489i	$0.0561507\pi$
$608$	3.81563	+	6.60886i	0.154744	+	0.268025i
$609$	−0.583678	+	0.336986i	−0.0236518	+	0.0136554i
$610$	−9.47754			−0.383734
$611$		0			0
$612$	−2.51793			−0.101781
$613$	−24.9232	+	14.3894i	−1.00664	+	0.581184i	−0.910206	−	0.414155i	$-0.864077\pi$
$613$	−24.9232	+	14.3894i	−1.00664	+	0.581184i	−0.0964341	+	0.995339i	$0.530744\pi$
$614$	5.12379	+	8.87466i	0.206779	+	0.358152i
$615$	−0.0126991	+	0.0219955i	−0.000512078	+	0.000886946i
$616$		−	13.6129i		−	0.548481i
$617$	−32.3279	−	18.6645i	−1.30147	−	0.751406i	−0.320817	−	0.947141i	$-0.603957\pi$
$617$	−32.3279	−	18.6645i	−1.30147	−	0.751406i	−0.980657	+	0.195735i	$0.937291\pi$
$618$	0.680712	+	0.393009i	0.0273822	+	0.0158091i
$619$			12.7535i			0.512606i	0.966597	+	0.256303i	$0.0825045\pi$
$619$			12.7535i			0.512606i	−0.966597	+	0.256303i	$0.917496\pi$
$620$	−0.173162	+	0.299925i	−0.00695434	+	0.0120453i
$621$	2.01192	+	3.48475i	0.0807356	+	0.139838i
$622$	13.7864	−	7.95961i	0.552786	−	0.319151i
$623$	−65.1939			−2.61194
$624$		0			0
$625$	1.00000			0.0400000
$626$	−23.0842	+	13.3276i	−0.922629	+	0.532680i
$627$	0.290514	+	0.503185i	0.0116020	+	0.0200953i
$628$	1.41571	−	2.45209i	0.0564931	−	0.0978489i
$629$		−	0.0903896i		−	0.00360407i
$630$	18.6982	+	10.7954i	0.744956	+	0.430100i
$631$	−24.8759	−	14.3621i	−0.990294	−	0.571746i	−0.0849315	−	0.996387i	$-0.527067\pi$
$631$	−24.8759	−	14.3621i	−0.990294	−	0.571746i	−0.905362	+	0.424641i	$0.860400\pi$
$632$		−	23.1643i		−	0.921427i
$633$	0.227984	−	0.394880i	0.00906156	−	0.0156951i
$634$	−6.11035	−	10.5834i	−0.242673	−	0.420322i
$635$	0.611979	−	0.353326i	0.0242856	−	0.0140213i
$636$	−0.0222199			−0.000881077
$637$		0			0
$638$	2.35588			0.0932701
$639$	20.1133	−	11.6124i	0.795671	−	0.459381i
$640$	−6.44840	−	11.1690i	−0.254895	−	0.441492i
$641$	−11.1985	+	19.3964i	−0.442315	+	0.766112i	−0.997861	−	0.0653739i	$-0.979176\pi$
$641$	−11.1985	+	19.3964i	−0.442315	+	0.766112i	0.555546	+	0.831486i	$0.312509\pi$
$642$			0.629552i			0.0248464i
$643$	−12.2665	−	7.08209i	−0.483745	−	0.279290i	0.238231	−	0.971209i	$-0.423433\pi$
$643$	−12.2665	−	7.08209i	−0.483745	−	0.279290i	−0.721976	+	0.691918i	$0.756766\pi$
$644$	−7.00637	−	4.04513i	−0.276090	−	0.159400i
$645$			0.337339i			0.0132827i
$646$	15.2540	−	26.4207i	0.600160	−	1.03951i
$647$	−11.8048	−	20.4466i	−0.464096	−	0.803838i	0.535064	−	0.844812i	$-0.320287\pi$
$647$	−11.8048	−	20.4466i	−0.464096	−	0.803838i	−0.999160	+	0.0409732i	$0.986954\pi$
$648$	−20.3709	+	11.7612i	−0.800246	+	0.462022i
$649$	9.32835			0.366170
$650$		0			0
$651$	−0.669862			−0.0262540
$652$	−4.62379	+	2.66955i	−0.181082	+	0.104548i
$653$	−16.6383	−	28.8183i	−0.651105	−	1.12775i	−0.982855	−	0.184380i	$-0.940972\pi$
$653$	−16.6383	−	28.8183i	−0.651105	−	1.12775i	0.331750	−	0.943367i	$-0.392361\pi$
$654$	−0.976727	+	1.69174i	−0.0381930	+	0.0661523i
$655$		−	6.26554i		−	0.244815i
$656$	1.02500	+	0.591784i	0.0400195	+	0.0231053i
$657$	−26.1848	−	15.1178i	−1.02156	−	0.589801i
$658$			47.0502i			1.83421i
$659$	−11.5454	+	19.9972i	−0.449745	+	0.778982i	−0.998369	−	0.0570875i	$-0.981819\pi$
$659$	−11.5454	+	19.9972i	−0.449745	+	0.778982i	0.548624	+	0.836069i	$0.315152\pi$
$660$	0.0119886	+	0.0207648i	0.000466655	+	0.000808270i
$661$	−11.6364	+	6.71826i	−0.452602	+	0.261310i	−0.708929	−	0.705280i	$-0.750821\pi$
$661$	−11.6364	+	6.71826i	−0.452602	+	0.261310i	0.256326	+	0.966590i	$0.417488\pi$
$662$	37.2972			1.44960
$663$		0			0
$664$	−1.91326			−0.0742491
$665$	−23.9609	+	13.8338i	−0.929164	+	0.536453i
$666$	0.0568043	+	0.0983879i	0.00220112	+	0.00381245i
$667$	−5.21900	+	9.03957i	−0.202080	+	0.350014i
$668$			1.93895i			0.0750200i
$669$	−1.20779	−	0.697316i	−0.0466957	−	0.0269598i
$670$	6.70001	+	3.86825i	0.258844	+	0.149444i
$671$			6.77708i			0.261626i
$672$	−0.304558	+	0.527510i	−0.0117486	+	0.0203491i
$673$	−0.972620	−	1.68463i	−0.0374918	−	0.0649376i	0.846671	−	0.532117i	$-0.178603\pi$
$673$	−0.972620	−	1.68463i	−0.0374918	−	0.0649376i	−0.884162	+	0.467180i	$0.845270\pi$
$674$	−25.3923	+	14.6603i	−0.978075	+	0.564692i
$675$	0.567874			0.0218575
$676$		0			0
$677$	24.8683			0.955768			0.477884	−	0.878423i	$-0.341404\pi$
$677$	24.8683			0.955768			0.477884	+	0.878423i	$0.341404\pi$
$678$	0.987512	−	0.570140i	0.0379252	−	0.0218961i
$679$	8.29903	+	14.3743i	0.318488	+	0.551637i
$680$	−4.69286	+	8.12828i	−0.179963	+	0.311705i
$681$			1.41260i			0.0541310i
$682$	2.02781	+	1.17075i	0.0776487	+	0.0448305i
$683$	12.6631	+	7.31107i	0.484542	+	0.279750i	0.722307	−	0.691572i	$-0.243082\pi$
$683$	12.6631	+	7.31107i	0.484542	+	0.279750i	−0.237766	+	0.971323i	$0.576415\pi$
$684$			4.05545i			0.155064i
$685$	8.15290	−	14.1212i	0.311506	−	0.539545i
$686$	−33.5605	−	58.1285i	−1.28135	−	2.21935i
$687$	1.58491	−	0.915049i	0.0604681	−	0.0349113i
$688$	15.7201			0.599323
$689$		0			0
$690$	−1.00445			−0.0382388
$691$	3.05231	−	1.76225i	0.116115	−	0.0670393i	−0.440817	−	0.897597i	$-0.645311\pi$
$691$	3.05231	−	1.76225i	0.116115	−	0.0670393i	0.556933	+	0.830558i	$0.311978\pi$
$692$	1.08428	+	1.87803i	0.0412182	+	0.0713920i
$693$	7.71947	−	13.3705i	0.293238	−	0.507904i
$694$		−	25.5447i		−	0.969665i
$695$	−5.91087	−	3.41264i	−0.224212	−	0.129449i
$696$	0.318907	+	0.184121i	0.0120881	+	0.00697909i
$697$		−	0.953601i		−	0.0361202i
$698$	−21.2152	+	36.7458i	−0.803008	+	1.39085i
$699$	−1.00445	−	1.73976i	−0.0379919	−	0.0658038i
$700$	−0.988789	+	0.570878i	−0.0373727	+	0.0215772i
$701$	1.53457			0.0579599			0.0289800	−	0.999580i	$-0.490774\pi$
$701$	1.53457			0.0579599			0.0289800	+	0.999580i	$0.490774\pi$
$702$		0			0
$703$	−0.145584			−0.00549081
$704$	−6.33766	+	3.65905i	−0.238860	+	0.137906i
$705$	0.308909	+	0.535047i	0.0116342	+	0.0201510i
$706$	−15.8912	+	27.5244i	−0.598075	+	1.03590i
$707$			13.7819i			0.518322i
$708$	−0.169380	−	0.0977915i	−0.00636568	−	0.00367523i
$709$	−12.1289	−	7.00262i	−0.455510	−	0.262989i	0.254644	−	0.967035i	$-0.418042\pi$
$709$	−12.1289	−	7.00262i	−0.455510	−	0.262989i	−0.710155	+	0.704046i	$0.751375\pi$
$710$			11.6124i			0.435807i
$711$	13.1357	−	22.7518i	0.492629	−	0.853259i
$712$	17.8101	+	30.8481i	0.667463	+	1.15608i
$713$	−8.98444	+	5.18717i	−0.336470	+	0.194261i
$714$	2.43510			0.0911314
$715$		0			0
$716$	−2.37418			−0.0887274
$717$	−1.22288	+	0.706029i	−0.0456692	+	0.0263671i
$718$	24.4156	+	42.2890i	0.911181	+	1.57821i
$719$	11.2381	−	19.4649i	0.419109	−	0.725918i	−0.576741	−	0.816927i	$-0.695676\pi$
$719$	11.2381	−	19.4649i	0.419109	−	0.725918i	0.995850	+	0.0910091i	$0.0290092\pi$
$720$		−	13.2117i		−	0.492372i
$721$	23.1785	+	13.3821i	0.863213	+	0.498376i
$722$	−17.9461	−	10.3612i	−0.667884	−	0.385603i
$723$		−	0.890215i		−	0.0331074i
$724$	−2.01344	+	3.48737i	−0.0748288	+	0.129607i
$725$	0.736543	+	1.27573i	0.0273545	+	0.0473794i
$726$	−1.21001	+	0.698600i	−0.0449077	+	0.0259275i
$727$	10.3421			0.383566			0.191783	−	0.981437i	$-0.438573\pi$
$727$	10.3421			0.383566			0.191783	+	0.981437i	$0.438573\pi$
$728$		0			0
$729$	−26.5160			−0.982075
$730$	13.0924	−	7.55889i	0.484571	−	0.279767i
$731$	−6.33285	−	10.9688i	−0.234229	−	0.405696i
$732$	0.0710459	−	0.123055i	0.00262593	−	0.00454824i
$733$		−	27.3533i		−	1.01032i	−0.863026	−	0.505159i	$-0.831434\pi$
$733$		−	27.3533i		−	1.01032i	0.863026	−	0.505159i	$-0.168566\pi$
$734$	−7.66516	−	4.42548i	−0.282926	−	0.163348i
$735$	−1.33791	−	0.772442i	−0.0493495	−	0.0284919i
$736$			9.43355i			0.347725i
$737$	2.76606	−	4.79096i	0.101889	−	0.176477i
$738$	0.599280	+	1.03798i	0.0220598	+	0.0382087i
$739$	−11.6495	+	6.72583i	−0.428533	+	0.247413i	−0.698721	−	0.715394i	$-0.746247\pi$
$739$	−11.6495	+	6.72583i	−0.428533	+	0.247413i	0.270189	+	0.962807i	$0.412914\pi$
$740$	−0.00600778			−0.000220851
$741$		0			0
$742$	−7.15372			−0.262621
$743$	−14.1964	+	8.19632i	−0.520817	+	0.300694i	−0.737269	−	0.675599i	$-0.763885\pi$
$743$	−14.1964	+	8.19632i	−0.520817	+	0.300694i	0.216452	+	0.976293i	$0.430552\pi$
$744$	0.182998	+	0.316962i	0.00670903	+	0.0116204i
$745$	4.21978	−	7.30887i	0.154601	−	0.267776i
$746$			19.9179i			0.729248i
$747$	−1.87919	−	1.08495i	−0.0687560	−	0.0396963i
$748$	−0.779635	−	0.450122i	−0.0285063	−	0.0164581i
$749$			21.4365i			0.783274i
$750$	−0.0708778	+	0.122764i	−0.00258809	+	0.00448270i
$751$	−13.8328	−	23.9590i	−0.504764	−	0.874277i	−0.999985	−	0.00551009i	$-0.998246\pi$
$751$	−13.8328	−	23.9590i	−0.504764	−	0.874277i	0.495221	−	0.868767i	$-0.335087\pi$
$752$	24.9334	−	14.3953i	0.909226	−	0.524942i
$753$	−1.07265			−0.0390895
$754$		0			0
$755$	1.37017			0.0498654
$756$	−0.561508	+	0.324187i	−0.0204218	+	0.0117906i
$757$	−11.4989	−	19.9167i	−0.417935	−	0.723885i	0.577797	−	0.816181i	$-0.303913\pi$
$757$	−11.4989	−	19.9167i	−0.417935	−	0.723885i	−0.995732	+	0.0922961i	$0.970579\pi$
$758$	−19.0068	+	32.9208i	−0.690359	+	1.19574i
$759$			0.718251i			0.0260709i
$760$	13.0916	+	7.55846i	0.474884	+	0.274174i
$761$	−6.63759	−	3.83221i	−0.240612	−	0.138918i	0.374846	−	0.927087i	$-0.377696\pi$
$761$	−6.63759	−	3.83221i	−0.240612	−	0.138918i	−0.615458	+	0.788170i	$0.711029\pi$
$762$			0.100172i			0.00362885i
$763$	−33.2580	+	57.6045i	−1.20402	+	2.08542i
$764$	−0.458587	−	0.794296i	−0.0165911	−	0.0287366i
$765$	−9.21857	+	5.32235i	−0.333298	+	0.192430i
$766$	−16.1916			−0.585027
$767$		0			0
$768$	0.530882			0.0191566
$769$	−6.26219	+	3.61548i	−0.225820	+	0.130377i	−0.608642	−	0.793445i	$-0.708286\pi$
$769$	−6.26219	+	3.61548i	−0.225820	+	0.130377i	0.382822	+	0.923822i	$0.374952\pi$
$770$	3.85973	+	6.68525i	0.139095	+	0.240920i
$771$	−1.25745	+	2.17797i	−0.0452859	+	0.0784375i
$772$			0.296612i			0.0106753i
$773$	29.0981	+	16.7998i	1.04658	+	0.604246i	0.921691	−	0.387924i	$-0.126808\pi$
$773$	29.0981	+	16.7998i	1.04658	+	0.604246i	0.124893	+	0.992170i	$0.460141\pi$
$774$	13.7864	+	7.95961i	0.495544	+	0.286102i
$775$			1.46410i			0.0525921i
$776$	4.53438	−	7.85378i	0.162775	−	0.281934i
$777$	−0.00581016	−	0.0100635i	−0.000208438	−	0.000361026i
$778$	−29.8363	+	17.2260i	−1.06968	+	0.617582i
$779$	−1.53590			−0.0550293
$780$		0			0
$781$	8.30368			0.297129
$782$	32.6605	−	18.8565i	1.16794	−	0.674309i
$783$	0.418264	+	0.724454i	0.0149475	+	0.0258899i
$784$	−35.9960	+	62.3470i	−1.28557	+	2.22668i
$785$		−	11.9700i		−	0.427228i
$786$	0.769182	+	0.444088i	0.0274358	+	0.0158401i
$787$	−2.57355	−	1.48584i	−0.0917371	−	0.0529645i	0.453430	−	0.891292i	$-0.350200\pi$
$787$	−2.57355	−	1.48584i	−0.0917371	−	0.0529645i	−0.545167	+	0.838328i	$0.683534\pi$
$788$			3.61484i			0.128773i
$789$	0.670185	−	1.16079i	0.0238592	−	0.0413254i
$790$	6.56787	+	11.3759i	0.233674	+	0.404736i
$791$	33.6252	−	19.4135i	1.19557	−	0.690265i
$792$	−8.43544			−0.299740
$793$		0			0
$794$	−31.5349			−1.11913
$795$	−0.0813509	+	0.0469680i	−0.00288522	+	0.00166578i
$796$	1.56469	+	2.71012i	0.0554588	+	0.0960575i
$797$	−11.2875	+	19.5506i	−0.399825	+	0.692517i	−0.993704	−	0.112037i	$-0.964262\pi$
$797$	−11.2875	+	19.5506i	−0.399825	+	0.692517i	0.593879	+	0.804554i	$0.297596\pi$
$798$		−	3.92205i		−	0.138839i
$799$	−20.0888	−	11.5983i	−0.710692	−	0.410318i
$800$	1.15297	+	0.665665i	0.0407635	+	0.0235348i
$801$			40.3983i			1.42740i
$802$	−14.7882	+	25.6140i	−0.522191	+	0.904462i
$803$	−5.40512	−	9.36194i	−0.190742	−	0.330376i
$804$	−0.100450	+	0.0579946i	−0.00354259	+	0.00204531i
$805$	−34.2020			−1.20546
$806$		0			0
$807$	2.34831			0.0826646
$808$	6.52125	−	3.76505i	0.229417	−	0.132454i
$809$	−6.82921	−	11.8285i	−0.240102	−	0.415869i	0.720641	−	0.693308i	$-0.243848\pi$
$809$	−6.82921	−	11.8285i	−0.240102	−	0.415869i	−0.960743	+	0.277439i	$0.910514\pi$
$810$	6.66938	−	11.5517i	0.234338	−	0.405886i
$811$			14.1147i			0.495636i	0.968807	+	0.247818i	$0.0797135\pi$
$811$			14.1147i			0.495636i	−0.968807	+	0.247818i	$0.920287\pi$
$812$	−1.45657	−	0.840952i	−0.0511157	−	0.0295116i
$813$	1.53646	+	0.887075i	0.0538860	+	0.0311111i
$814$			0.0406189i			0.00142369i
$815$	−11.2857	+	19.5474i	−0.395320	+	0.684714i
$816$	−0.745035	−	1.29044i	−0.0260814	−	0.0451744i
$817$	−17.6667	+	10.1999i	−0.618079	+	0.356848i
$818$	−47.6781			−1.66703
$819$		0			0
$820$	−0.0633815			−0.00221338
$821$	1.37318	−	0.792808i	0.0479244	−	0.0276692i	−0.475846	−	0.879528i	$-0.657858\pi$
$821$	1.37318	−	0.792808i	0.0479244	−	0.0276692i	0.523771	+	0.851859i	$0.324525\pi$
$822$	1.15572	+	2.00176i	0.0403103	+	0.0698195i
$823$	9.28238	−	16.0776i	0.323563	−	0.560428i	−0.657657	−	0.753317i	$-0.728452\pi$
$823$	9.28238	−	16.0776i	0.323563	−	0.560428i	0.981221	+	0.192889i	$0.0617857\pi$
$824$		−	14.6233i		−	0.509427i
$825$	0.0877845	+	0.0506824i	0.00305626	+	0.00176454i
$826$	−54.5320	−	31.4840i	−1.89741	−	1.09547i
$827$		−	9.01023i		−	0.313316i	−0.987653	−	0.156658i	$-0.949928\pi$
$827$		−	9.01023i		−	0.313316i	0.987653	−	0.156658i	$-0.0500721\pi$
$828$	−2.50662	+	4.34159i	−0.0871110	+	0.150881i
$829$	23.5588	+	40.8051i	0.818233	+	1.41722i	0.906983	+	0.421167i	$0.138379\pi$
$829$	23.5588	+	40.8051i	0.818233	+	1.41722i	−0.0887506	+	0.996054i	$0.528287\pi$
$830$	0.939595	−	0.542476i	0.0326138	−	0.0188296i
$831$	2.14833			0.0745247
$832$		0			0
$833$	58.0041			2.00972
$834$	0.837898	−	0.483761i	0.0290141	−	0.0167513i
$835$	4.09850	+	7.09881i	0.141835	+	0.245665i
$836$	−0.724980	+	1.25570i	−0.0250740	+	0.0434294i
$837$			0.831425i			0.0287383i
$838$	39.7994	+	22.9782i	1.37485	+	0.793769i
$839$	−46.3121	−	26.7383i	−1.59887	−	0.923108i	−0.991705	−	0.128531i	$-0.958974\pi$
$839$	−46.3121	−	26.7383i	−1.59887	−	0.923108i	−0.607164	−	0.794576i	$-0.707693\pi$
$840$			1.20661i			0.0416321i
$841$	13.4150	−	23.2355i	0.462586	−	0.801223i
$842$	−13.4461	−	23.2894i	−0.463384	−	0.802605i
$843$	2.28521	−	1.31937i	0.0787070	−	0.0454415i
$844$	1.13787			0.0391672
$845$		0			0
$846$	29.1553			1.00238
$847$	−41.2014	+	23.7876i	−1.41570	+	0.817353i
$848$	2.18872	+	3.79098i	0.0751611	+	0.130183i
$849$	0.375362	−	0.650146i	0.0128824	−	0.0223130i
$850$		−	5.32235i		−	0.182555i
$851$	−0.155856	−	0.0899835i	−0.00534268	−	0.00308460i
$852$	−0.150774	−	0.0870495i	−0.00516544	−	0.00298227i
$853$		−	27.7756i		−	0.951019i	−0.879711	−	0.475510i	$-0.842264\pi$
$853$		−	27.7756i		−	0.951019i	0.879711	−	0.475510i	$-0.157736\pi$
$854$	22.8733	−	39.6177i	0.782707	−	1.35569i
$855$	8.57233	+	14.8477i	0.293167	+	0.507781i
$856$	10.1432	−	5.85619i	0.346688	−	0.200160i
$857$	−53.6917			−1.83407			−0.917037	−	0.398801i	$-0.869426\pi$
$857$	−53.6917			−1.83407			−0.917037	+	0.398801i	$0.869426\pi$
$858$		0			0
$859$	2.08958			0.0712955			0.0356477	−	0.999364i	$-0.488651\pi$
$859$	2.08958			0.0712955			0.0356477	+	0.999364i	$0.488651\pi$
$860$	−0.729047	+	0.420915i	−0.0248603	+	0.0143531i
$861$	−0.0612966	−	0.106169i	−0.00208898	−	0.00361823i
$862$	−3.66361	+	6.34556i	−0.124783	+	0.216131i
$863$			1.75413i			0.0597113i	0.999554	+	0.0298557i	$0.00950476\pi$
$863$			1.75413i			0.0597113i	−0.999554	+	0.0298557i	$0.990495\pi$
$864$	0.654739	+	0.378014i	0.0222747	+	0.0128603i
$865$	7.93948	+	4.58386i	0.269950	+	0.155856i
$866$		−	28.7727i		−	0.977737i
$867$	0.205419	−	0.355797i	0.00697640	−	0.0120835i
$868$	−0.835823	−	1.44769i	−0.0283697	−	0.0491377i
$869$	8.13453	−	4.69647i	0.275945	−	0.159317i
$870$	−0.208818			−0.00707960
$871$		0			0
$872$	36.3426			1.23072
$873$	8.90726	−	5.14261i	0.301465	−	0.174051i
$874$	−30.3709	−	52.6040i	−1.02731	−	1.77936i
$875$	−2.41342	+	4.18016i	−0.0815885	+	0.141315i
$876$			0.226653i			0.00765789i
$877$	18.6777	+	10.7836i	0.630702	+	0.364136i	0.781024	−	0.624501i	$-0.214698\pi$
$877$	18.6777	+	10.7836i	0.630702	+	0.364136i	−0.150322	+	0.988637i	$0.548031\pi$
$878$	11.0861	+	6.40058i	0.374139	+	0.216009i
$879$			0.0258742i			0.000872716i
$880$	2.36182	−	4.09079i	0.0796169	−	0.137900i
$881$	12.5132	+	21.6734i	0.421579	+	0.730196i	0.996094	−	0.0882978i	$-0.0281427\pi$
$881$	12.5132	+	21.6734i	0.421579	+	0.730196i	−0.574515	+	0.818494i	$0.694809\pi$
$882$	−63.1367	+	36.4520i	−2.12592	+	1.22740i
$883$	48.7832			1.64169			0.820843	−	0.571154i	$-0.193504\pi$
$883$	48.7832			1.64169			0.820843	+	0.571154i	$0.193504\pi$
$884$		0			0
$885$	−0.826838			−0.0277939
$886$	49.1705	−	28.3886i	1.65192	−	0.953734i
$887$	16.8967	+	29.2659i	0.567334	+	0.982651i	0.996828	+	0.0795819i	$0.0253585\pi$
$887$	16.8967	+	29.2659i	0.567334	+	0.982651i	−0.429494	+	0.903070i	$0.641308\pi$
$888$	−0.00317453	+	0.00549844i	−0.000106530	+	0.000184516i
$889$			3.41090i			0.114398i
$890$	−17.4930	−	10.0996i	−0.586365	−	0.338538i
$891$	−8.26025	−	4.76906i	−0.276729	−	0.159769i
$892$		−	3.48031i		−	0.116530i
$893$	−18.6806	+	32.3557i	−0.625121	+	1.08274i
$894$	0.598177	+	1.03607i	0.0200060	+	0.0346515i
$895$	−8.69229	+	5.01850i	−0.290551	+	0.167750i
$896$	62.2508			2.07965
$897$		0			0
$898$	39.9394			1.33279
$899$	−1.86780	+	1.07837i	−0.0622946	+	0.0359658i
$900$	0.353752	+	0.612717i	0.0117917	+	0.0204239i
$901$	1.76346	−	3.05440i	0.0587493	−	0.101757i
$902$			0.428526i			0.0142683i
$903$	−1.41013	−	0.814139i	−0.0469262	−	0.0270929i
$904$	−18.3720	−	10.6071i	−0.611043	−	0.352786i
$905$			17.0238i			0.565892i
$906$	−0.0971143	+	0.168207i	−0.00322641	+	0.00558830i
$907$	−17.3135	−	29.9879i	−0.574885	−	0.995731i	−0.996054	−	0.0887485i	$-0.971713\pi$
$907$	−17.3135	−	29.9879i	−0.574885	−	0.995731i	0.421169	−	0.906982i	$-0.361620\pi$
$908$	−3.05288	+	1.76258i	−0.101313	+	0.0584932i
$909$	8.54015			0.283259
$910$		0			0
$911$	31.1865			1.03326			0.516628	−	0.856210i	$-0.327187\pi$
$911$	31.1865			1.03326			0.516628	+	0.856210i	$0.327187\pi$
$912$	−2.07842	+	1.19997i	−0.0688233	+	0.0397351i
$913$	−0.387907	−	0.671874i	−0.0128378	−	0.0222358i
$914$	3.19386	−	5.53192i	0.105643	−	0.182980i
$915$		−	0.600701i		−	0.0198586i
$916$	3.95516	+	2.28351i	0.130682	+	0.0754493i
$917$	26.1910	+	15.1214i	0.864903	+	0.499352i
$918$		−	3.02242i		−	0.0997548i
$919$	25.9610	−	44.9658i	0.856374	−	1.48328i	−0.0189904	−	0.999820i	$-0.506045\pi$
$919$	25.9610	−	44.9658i	0.856374	−	1.48328i	0.875364	−	0.483464i	$-0.160621\pi$
$920$	9.34356	+	16.1835i	0.308048	+	0.533555i
$921$	−0.562490	+	0.324753i	−0.0185347	+	0.0107010i
$922$	30.8707			1.01667
$923$		0			0
$924$	−0.115734			−0.00380736
$925$	−0.0219955	+	0.0126991i	−0.000723209	+	0.000417545i
$926$	−24.0059	−	41.5794i	−0.788882	−	1.36638i
$927$	8.29242	−	14.3629i	0.272359	−	0.471739i
$928$			1.96117i			0.0643784i
$929$	17.7462	+	10.2457i	0.582232	+	0.336152i	0.762020	−	0.647553i	$-0.224208\pi$
$929$	17.7462	+	10.2457i	0.582232	+	0.336152i	−0.179788	+	0.983705i	$0.557541\pi$
$930$	−0.179739	−	0.103772i	−0.00589387	−	0.00340283i
$931$		−	93.4231i		−	3.06182i
$932$	2.50662	−	4.34159i	0.0821070	−	0.142213i
$933$	0.504492	+	0.873806i	0.0165163	+	0.0286071i
$934$	30.2771	−	17.4805i	0.990698	−	0.571980i
$935$	−3.80584			−0.124464
$936$		0			0
$937$	−39.6806			−1.29631			−0.648154	−	0.761510i	$-0.724459\pi$
$937$	−39.6806			−1.29631			−0.648154	+	0.761510i	$0.724459\pi$
$938$	−32.3399	+	18.6714i	−1.05593	+	0.609644i
$939$	−0.844727	−	1.46311i	−0.0275666	−	0.0477468i
$940$	−0.770886	+	1.33521i	−0.0251435	+	0.0435499i
$941$			19.6189i			0.639557i	0.947492	+	0.319779i	$0.103609\pi$
$941$			19.6189i			0.639557i	−0.947492	+	0.319779i	$0.896391\pi$
$942$	1.46949	+	0.848408i	0.0478784	+	0.0276426i
$943$	−1.64427	−	0.949318i	−0.0535447	−	0.0309140i
$944$			38.5309i			1.25408i
$945$	−1.37052	+	2.37381i	−0.0445829	+	0.0772199i
$946$	2.84583	+	4.92912i	0.0925259	+	0.160260i
$947$	49.5474	−	28.6062i	1.61007	−	0.929576i	0.620721	−	0.784032i	$-0.286840\pi$
$947$	49.5474	−	28.6062i	1.61007	−	0.929576i	0.989352	−	0.145544i	$-0.0464933\pi$
$948$	−0.196937			−0.00639623
$949$		0			0
$950$	−8.57233			−0.278123
$951$	0.670795	−	0.387283i	0.0217520	−	0.0125585i
$952$	−22.6517	−	39.2339i	−0.734146	−	1.27158i
$953$	13.7385	−	23.7958i	0.445033	−	0.770820i	−0.553021	−	0.833167i	$-0.686525\pi$
$953$	13.7385	−	23.7958i	0.445033	−	0.770820i	0.998055	+	0.0623470i	$0.0198586\pi$
$954$			4.43290i			0.143520i
$955$	−3.35793	−	1.93870i	−0.108660	−	0.0627350i
$956$	−3.05170	−	1.76190i	−0.0986991	−	0.0569840i
$957$			0.149319i			0.00482680i
$958$	−3.86988	+	6.70283i	−0.125030	+	0.216559i
$959$	39.3527	+	68.1609i	1.27077	+	2.20103i
$960$	0.561752	−	0.324328i	0.0181305	−	0.0104676i
$961$	28.8564			0.930852
$962$		0			0
$963$	13.2834			0.428053
$964$	1.92391	−	1.11077i	0.0619649	−	0.0357755i
$965$	0.626972	+	1.08595i	0.0201829	+	0.0349579i
$966$	2.42416	−	4.19877i	0.0779962	−	0.135093i
$967$			10.3643i			0.333293i	0.986017	+	0.166647i	$0.0532939\pi$
$967$			10.3643i			0.333293i	−0.986017	+	0.166647i	$0.946706\pi$
$968$	22.5114	+	12.9970i	0.723544	+	0.417738i
$969$	1.67458	+	0.966821i	0.0537953	+	0.0310588i
$970$			5.14261i			0.165119i
$971$	−20.8758	+	36.1579i	−0.669935	+	1.16036i	0.307987	+	0.951391i	$0.400345\pi$
$971$	−20.8758	+	36.1579i	−0.669935	+	1.16036i	−0.977922	+	0.208971i	$0.932989\pi$
$972$	0.301481	+	0.522180i	0.00966999	+	0.0167489i
$973$	28.5308	−	16.4723i	0.914656	−	0.528077i
$974$	−46.0212			−1.47461
$975$		0			0
$976$	−27.9929			−0.896030
$977$	11.9458	−	6.89691i	0.382180	−	0.220652i	−0.296586	−	0.955006i	$-0.595848\pi$
$977$	11.9458	−	6.89691i	0.382180	−	0.220652i	0.678766	+	0.734354i	$0.262515\pi$
$978$	−1.59981	−	2.77095i	−0.0511562	−	0.0886051i
$979$	−7.22187	+	12.5087i	−0.230812	+	0.399778i
$980$		−	3.85527i		−	0.123152i
$981$	35.6954	+	20.6088i	1.13967	+	0.657987i
$982$	−46.3641	−	26.7683i	−1.47954	−	0.854212i
$983$			37.9997i			1.21200i	0.795463	+	0.606002i	$0.207227\pi$
$983$			37.9997i			1.21200i	−0.795463	+	0.606002i	$0.792773\pi$
$984$	−0.0334909	+	0.0580080i	−0.00106765	+	0.00184923i
$985$	7.64098	+	13.2346i	0.243462	+	0.421688i
$986$	6.78988	−	3.92014i	0.216234	−	0.124843i
$987$	−2.98211			−0.0949217
$988$		0			0
$989$	−25.2176			−0.801873
$990$	4.14261	−	2.39174i	0.131661	−	0.0760143i
$991$	26.2765	+	45.5122i	0.834700	+	1.44574i	0.894275	+	0.447519i	$0.147692\pi$
$991$	26.2765	+	45.5122i	0.834700	+	1.44574i	−0.0595748	+	0.998224i	$0.518974\pi$
$992$	−0.974602	+	1.68806i	−0.0309436	+	0.0535960i
$993$			2.36396i			0.0750179i
$994$	−48.5419	−	28.0257i	−1.53966	−	0.888920i
$995$	11.4572	+	6.61480i	0.363217	+	0.209703i
$996$			0.0162661i			0.000515411i
$997$	−9.29497	+	16.0994i	−0.294375	+	0.509872i	−0.974839	−	0.222909i	$-0.928445\pi$
$997$	−9.29497	+	16.0994i	−0.294375	+	0.509872i	0.680465	+	0.732781i	$0.261778\pi$
$998$	−21.6079	−	37.4260i	−0.683986	−	1.18470i
$999$	−0.0124907	+	0.00721150i	−0.000395188	+	0.000228162i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.m.g.361.1		8
13.2	odd	12		845.2.a.m.1.1		4
13.3	even	3		845.2.c.g.506.2		8
13.4	even	6	inner	845.2.m.g.316.1		8
13.5	odd	4		845.2.e.m.146.4		8
13.6	odd	12		845.2.e.m.191.4		8
13.7	odd	12		845.2.e.n.191.1		8
13.8	odd	4		845.2.e.n.146.1		8
13.9	even	3		65.2.m.a.56.4	yes	8
13.10	even	6		845.2.c.g.506.7		8
13.11	odd	12		845.2.a.l.1.4		4
13.12	even	2		65.2.m.a.36.4	✓	8
39.2	even	12		7605.2.a.cf.1.4		4
39.11	even	12		7605.2.a.cj.1.1		4
39.35	odd	6		585.2.bu.c.316.1		8
39.38	odd	2		585.2.bu.c.361.1		8
52.35	odd	6		1040.2.da.b.641.3		8
52.51	odd	2		1040.2.da.b.881.3		8
65.9	even	6		325.2.n.d.251.1		8
65.12	odd	4		325.2.m.b.49.4		8
65.22	odd	12		325.2.m.c.199.1		8
65.24	odd	12		4225.2.a.bl.1.1		4
65.38	odd	4		325.2.m.c.49.1		8
65.48	odd	12		325.2.m.b.199.4		8
65.54	odd	12		4225.2.a.bi.1.4		4
65.64	even	2		325.2.n.d.101.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.m.a.36.4	✓	8	13.12	even	2
65.2.m.a.56.4	yes	8	13.9	even	3
325.2.m.b.49.4		8	65.12	odd	4
325.2.m.b.199.4		8	65.48	odd	12
325.2.m.c.49.1		8	65.38	odd	4
325.2.m.c.199.1		8	65.22	odd	12
325.2.n.d.101.1		8	65.64	even	2
325.2.n.d.251.1		8	65.9	even	6
585.2.bu.c.316.1		8	39.35	odd	6
585.2.bu.c.361.1		8	39.38	odd	2
845.2.a.l.1.4		4	13.11	odd	12
845.2.a.m.1.1		4	13.2	odd	12
845.2.c.g.506.2		8	13.3	even	3
845.2.c.g.506.7		8	13.10	even	6
845.2.e.m.146.4		8	13.5	odd	4
845.2.e.m.191.4		8	13.6	odd	12
845.2.e.n.146.1		8	13.8	odd	4
845.2.e.n.191.1		8	13.7	odd	12
845.2.m.g.316.1		8	13.4	even	6	inner
845.2.m.g.361.1		8	1.1	even	1	trivial
1040.2.da.b.641.3		8	52.35	odd	6
1040.2.da.b.881.3		8	52.51	odd	2
4225.2.a.bi.1.4		4	65.54	odd	12
4225.2.a.bl.1.1		4	65.24	odd	12
7605.2.a.cf.1.4		4	39.2	even	12
7605.2.a.cj.1.1		4	39.11	even	12

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.29515 + 0.747754i) q^{2} +(-0.0473938 - 0.0820885i) q^{3} +(0.118272 - 0.204852i) q^{4} -1.00000i q^{5} +(0.122764 + 0.0708778i) q^{6} +(4.18016 + 2.41342i) q^{7} -2.63726i q^{8} +(1.49551 - 2.59030i) q^{9} +O(q^{10})\)	\(q+(-1.29515 + 0.747754i) q^{2} +(-0.0473938 - 0.0820885i) q^{3} +(0.118272 - 0.204852i) q^{4} -1.00000i q^{5} +(0.122764 + 0.0708778i) q^{6} +(4.18016 + 2.41342i) q^{7} -2.63726i q^{8} +(1.49551 - 2.59030i) q^{9} +(0.747754 + 1.29515i) q^{10} +(0.926118 - 0.534695i) q^{11} -0.0224214 q^{12} -7.21857 q^{14} +(-0.0820885 + 0.0473938i) q^{15} +(2.20857 + 3.82535i) q^{16} +(1.77944 - 3.08209i) q^{17} +4.47309i q^{18} +(-4.96410 - 2.86603i) q^{19} +(-0.204852 - 0.118272i) q^{20} -0.457524i q^{21} +(-0.799640 + 1.38502i) q^{22} +(-3.54290 - 6.13649i) q^{23} +(-0.216489 + 0.124990i) q^{24} -1.00000 q^{25} -0.567874 q^{27} +(0.988789 - 0.570878i) q^{28} +(-0.736543 - 1.27573i) q^{29} +(0.0708778 - 0.122764i) q^{30} -1.46410i q^{31} +(-1.15297 - 0.665665i) q^{32} +(-0.0877845 - 0.0506824i) q^{33} +5.32235i q^{34} +(2.41342 - 4.18016i) q^{35} +(-0.353752 - 0.612717i) q^{36} +(0.0219955 - 0.0126991i) q^{37} +8.57233 q^{38} -2.63726 q^{40} +(0.232051 - 0.133975i) q^{41} +(0.342116 + 0.592562i) q^{42} +(1.77944 - 3.08209i) q^{43} -0.252957i q^{44} +(-2.59030 - 1.49551i) q^{45} +(9.17716 + 5.29844i) q^{46} -6.51793i q^{47} +(0.209345 - 0.362596i) q^{48} +(8.14918 + 14.1148i) q^{49} +(1.29515 - 0.747754i) q^{50} -0.337339 q^{51} +0.991015 q^{53} +(0.735481 - 0.424630i) q^{54} +(-0.534695 - 0.926118i) q^{55} +(6.36482 - 11.0242i) q^{56} +0.543327i q^{57} +(1.90786 + 1.10151i) q^{58} +(7.55440 + 4.36153i) q^{59} +0.0224214i q^{60} +(-3.16867 + 5.48830i) q^{61} +(1.09479 + 1.89623i) q^{62} +(12.5029 - 7.21857i) q^{63} -6.84325 q^{64} +0.151592 q^{66} +(4.48009 - 2.58658i) q^{67} +(-0.420915 - 0.729047i) q^{68} +(-0.335823 + 0.581663i) q^{69} +7.21857i q^{70} +(6.72458 + 3.88244i) q^{71} +(-6.83129 - 3.94405i) q^{72} -10.1088i q^{73} +(-0.0189916 + 0.0328945i) q^{74} +(0.0473938 + 0.0820885i) q^{75} +(-1.17422 + 0.677939i) q^{76} +5.16177 q^{77} +8.78347 q^{79} +(3.82535 - 2.20857i) q^{80} +(-4.45961 - 7.72427i) q^{81} +(-0.200360 + 0.347034i) q^{82} -0.725474i q^{83} +(-0.0937250 - 0.0541121i) q^{84} +(-3.08209 - 1.77944i) q^{85} +5.32235i q^{86} +(-0.0698151 + 0.120923i) q^{87} +(-1.41013 - 2.44242i) q^{88} +(-11.6970 + 6.75327i) q^{89} +4.47309 q^{90} -1.67610 q^{92} +(-0.120186 + 0.0693893i) q^{93} +(4.87381 + 8.44168i) q^{94} +(-2.86603 + 4.96410i) q^{95} +0.126194i q^{96} +(2.97800 + 1.71935i) q^{97} +(-21.1088 - 12.1872i) q^{98} -3.19856i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} + 2 q^{4} + 18 q^{6} + 6 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q + 2 * q^3 + 2 * q^4 + 18 * q^6 + 6 * q^7 - 4 * q^9	\( 8 q + 2 q^{3} + 2 q^{4} + 18 q^{6} + 6 q^{7} - 4 q^{9} - 2 q^{10} + 20 q^{12} + 4 q^{14} + 6 q^{15} - 2 q^{16} - 2 q^{17} - 12 q^{19} - 12 q^{20} - 12 q^{22} - 10 q^{23} + 12 q^{24} - 8 q^{25} - 4 q^{27} + 18 q^{28} - 8 q^{29} + 4 q^{30} - 6 q^{32} - 42 q^{33} + 10 q^{35} + 20 q^{36} - 6 q^{37} - 16 q^{38} - 12 q^{40} - 12 q^{41} + 4 q^{42} - 2 q^{43} + 42 q^{46} + 28 q^{48} + 12 q^{49} - 8 q^{51} - 24 q^{53} - 18 q^{54} + 12 q^{56} - 36 q^{58} + 12 q^{59} - 28 q^{61} + 4 q^{62} + 24 q^{63} - 8 q^{64} + 12 q^{66} - 6 q^{67} - 14 q^{68} - 16 q^{69} + 48 q^{72} + 10 q^{74} - 2 q^{75} - 54 q^{76} - 36 q^{77} - 16 q^{79} + 8 q^{81} + 4 q^{82} + 30 q^{84} - 18 q^{85} + 22 q^{87} - 18 q^{88} - 24 q^{89} + 40 q^{90} + 44 q^{92} + 32 q^{94} - 16 q^{95} + 30 q^{97} - 72 q^{98}+O(q^{100}) \) 8 * q + 2 * q^3 + 2 * q^4 + 18 * q^6 + 6 * q^7 - 4 * q^9 - 2 * q^10 + 20 * q^12 + 4 * q^14 + 6 * q^15 - 2 * q^16 - 2 * q^17 - 12 * q^19 - 12 * q^20 - 12 * q^22 - 10 * q^23 + 12 * q^24 - 8 * q^25 - 4 * q^27 + 18 * q^28 - 8 * q^29 + 4 * q^30 - 6 * q^32 - 42 * q^33 + 10 * q^35 + 20 * q^36 - 6 * q^37 - 16 * q^38 - 12 * q^40 - 12 * q^41 + 4 * q^42 - 2 * q^43 + 42 * q^46 + 28 * q^48 + 12 * q^49 - 8 * q^51 - 24 * q^53 - 18 * q^54 + 12 * q^56 - 36 * q^58 + 12 * q^59 - 28 * q^61 + 4 * q^62 + 24 * q^63 - 8 * q^64 + 12 * q^66 - 6 * q^67 - 14 * q^68 - 16 * q^69 + 48 * q^72 + 10 * q^74 - 2 * q^75 - 54 * q^76 - 36 * q^77 - 16 * q^79 + 8 * q^81 + 4 * q^82 + 30 * q^84 - 18 * q^85 + 22 * q^87 - 18 * q^88 - 24 * q^89 + 40 * q^90 + 44 * q^92 + 32 * q^94 - 16 * q^95 + 30 * q^97 - 72 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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