LMFDB - Embedded newform 65.2.m.a.36.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,2,Mod(36,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("65.36");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	65.m (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.519027613138$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			36.4
Root			$0.665665 - 1.24775i$ of defining polynomial
Character	$\chi$	$=$	65.36
Dual form			65.2.m.a.56.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.29515 - 0.747754i) q^{2} +(-0.0473938 - 0.0820885i) q^{3} +(0.118272 - 0.204852i) q^{4} +1.00000i q^{5} +(-0.122764 - 0.0708778i) q^{6} +(-4.18016 - 2.41342i) q^{7} +2.63726i q^{8} +(1.49551 - 2.59030i) q^{9} +O(q^{10})$	\(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} +(0.331331 + 3.59030i) q^{13} -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} +(3.11378 + 4.40221i) q^{26} -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} +(0.279019 - 0.197356i) q^{39} -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} +(0.774668 + 0.356756i) q^{52} +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} +(-3.59030 + 0.331331i) q^{65} +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} +(0.213797 - 0.464243i) q^{78} +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} +(7.27987 - 15.8077i) q^{91} -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} + 10 q^{26} - 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} - 6 q^{52} - 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} - 8 q^{65} + 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} - 56 q^{78} - 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} + 28 q^{91} + 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 + 10 * q^26 - 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 - 6 * q^52 - 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 - 8 * q^65 + 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 - 56 * q^78 - 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 + 28 * q^91 + 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 $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	1.29515	−	0.747754i	0.915808	−	0.528742i	0.0335125	−	0.999438i	$-0.489331\pi$
$2$	1.29515	−	0.747754i	0.915808	−	0.528742i	0.882295	+	0.470696i	$0.155997\pi$
$3$	−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	$-0.967726\pi$
$7$	−4.18016	−	2.41342i	−1.57995	−	0.912187i	−0.585089	−	0.810969i	$-0.698941\pi$
$8$			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	−0.633077	−	0.774089i	$-0.718208\pi$
$11$	−0.926118	+	0.534695i	−0.279235	+	0.161217i	0.353842	+	0.935305i	$0.384875\pi$
$12$	−0.0224214			−0.00647249
$13$	0.331331	+	3.59030i	0.0918946	+	0.995769i
$13$	0.331331	+	3.59030i	0.0918946	+	0.995769i
$14$	−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	0.946144	−	0.323747i	$-0.104943\pi$
$19$	4.96410	+	2.86603i	1.13884	+	0.657511i	0.192699	+	0.981258i	$0.438276\pi$
$20$	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
$26$	3.11378	+	4.40221i	0.610662	+	0.863344i
$27$	−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	$0.0419730\pi$
$31$			1.46410i			0.262960i	−0.991319	+	0.131480i	$0.958027\pi$
$32$	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	−0.501807	−	0.864980i	$-0.667331\pi$
$37$	−0.0219955	+	0.0126991i	−0.00361604	+	0.00208772i	0.498191	+	0.867067i	$0.333998\pi$
$38$	8.57233			1.39061
$39$	0.279019	−	0.197356i	0.0446788	−	0.0316023i
$40$	−2.63726			−0.416988
$41$	−0.232051	+	0.133975i	−0.0362402	+	0.0209233i	−0.518011	−	0.855374i	$-0.673327\pi$
$41$	−0.232051	+	0.133975i	−0.0362402	+	0.0209233i	0.481770	+	0.876297i	$0.339994\pi$
$42$	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	$0.157685\pi$
$47$			6.51793i			0.950738i	−0.879787	+	0.475369i	$0.842315\pi$
$48$	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
$52$	0.774668	+	0.356756i	0.107427	+	0.0494732i
$53$	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	−0.0801741	−	0.996781i	$-0.525548\pi$
$59$	−7.55440	−	4.36153i	−0.983499	−	0.567823i	−0.903325	+	0.428958i	$0.858881\pi$
$60$		−	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
$65$	−3.59030	+	0.331331i	−0.445321	+	0.0410965i
$66$	0.151592			0.0186597
$67$	−4.48009	+	2.58658i	−0.547330	+	0.316001i	−0.748044	−	0.663649i	$-0.769007\pi$
$67$	−4.48009	+	2.58658i	−0.547330	+	0.316001i	0.200714	+	0.979650i	$0.435674\pi$
$68$	−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	0.0447317	−	0.998999i	$-0.485757\pi$
$71$	−6.72458	−	3.88244i	−0.798061	−	0.460761i	−0.842793	+	0.538238i	$0.819090\pi$
$72$	6.83129	+	3.94405i	0.805075	+	0.464810i
$73$			10.1088i			1.18314i	0.806252	+	0.591572i	$0.201493\pi$
$73$			10.1088i			1.18314i	−0.806252	+	0.591572i	$0.798507\pi$
$74$	−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
$78$	0.213797	−	0.464243i	0.0242077	−	0.0525651i
$79$	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	$0.0126770\pi$
$83$			0.725474i			0.0796311i	−0.999207	+	0.0398155i	$0.987323\pi$
$84$	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	0.270810	−	0.962633i	$-0.412708\pi$
$89$	11.6970	−	6.75327i	1.23988	−	0.715845i	0.969070	+	0.246788i	$0.0793750\pi$
$90$	4.47309			0.471505
$91$	7.27987	−	15.8077i	0.763138	−	1.65709i
$92$	−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	0.341137	−	0.940014i	$-0.389188\pi$
$97$	−2.97800	−	1.71935i	−0.302371	−	0.174574i	−0.643507	+	0.765440i	$0.722521\pi$
$98$	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	$0.411926\pi$
$104$	−9.46855	+	0.873806i	−0.928468	+	0.0856838i
$105$	−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	$-0.770572\pi$
$109$		−	13.7804i		−	1.31993i	0.751298	−	0.659963i	$-0.229428\pi$
$110$	−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
$117$	9.79543	+	4.51107i	0.905588	+	0.417049i
$118$	−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
$130$	−4.40221	+	3.11378i	−0.386099	+	0.273097i
$131$	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	−0.244475	−	0.969656i	$-0.578616\pi$
$137$	−14.1212	−	8.15290i	−1.20646	−	0.696549i	−0.961984	+	0.273107i	$0.911949\pi$
$138$			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
$143$	−2.22656	−	3.14788i	−0.186195	−	0.263239i
$144$	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	0.169790	−	0.985480i	$-0.445691\pi$
$149$	−7.30887	−	4.21978i	−0.598766	−	0.345698i	−0.768556	+	0.639783i	$0.779024\pi$
$150$	0.122764	+	0.0708778i	0.0100236	+	0.00578715i
$151$		−	1.37017i		−	0.111503i	−0.998445	−	0.0557513i	$-0.982245\pi$
$151$		−	1.37017i		−	0.111503i	0.998445	−	0.0557513i	$-0.0177554\pi$
$152$	−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
$156$	−0.00742888	−	0.0804993i	−0.000594787	−	0.00644510i
$157$	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	$0.0118002\pi$
$163$	19.5474	+	11.2857i	1.53107	+	0.883962i	0.531754	+	0.846899i	$0.321533\pi$
$164$			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	−0.199526	−	0.979893i	$-0.563940\pi$
$167$	7.09881	−	4.09850i	0.549323	−	0.317152i	0.748849	+	0.662741i	$0.230607\pi$
$168$	−1.20661			−0.0930922
$169$	−12.7804	+	2.37915i	−0.983111	+	0.183012i
$170$	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	$0.718048\pi$
$182$	−2.39174	−	25.9168i	−0.177287	−	1.92108i
$183$	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	−0.460406	−	0.887708i	$-0.652296\pi$
$193$	1.08595	−	0.626972i	0.0781681	−	0.0451304i	0.538575	+	0.842578i	$0.318963\pi$
$194$	−5.14261			−0.369218
$195$	0.197356	+	0.279019i	0.0141330	+	0.0199810i
$196$	3.85527			0.275376
$197$	13.2346	−	7.64098i	0.942923	−	0.544397i	0.0520479	−	0.998645i	$-0.483425\pi$
$197$	13.2346	−	7.64098i	0.942923	−	0.544397i	0.890876	+	0.454247i	$0.150092\pi$
$198$	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
$208$	−13.0024	+	9.19686i	−0.901552	+	0.637688i
$209$	−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
$221$	11.6552	+	5.36754i	0.784013	+	0.361060i
$222$	0.00360034			0.000241639
$223$	−12.7420	+	7.35661i	−0.853269	+	0.492635i	−0.861753	−	0.507329i	$-0.830633\pi$
$223$	−12.7420	+	7.35661i	−0.853269	+	0.492635i	0.00848317	+	0.999964i	$0.497300\pi$
$224$	−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	0.862877	−	0.505413i	$-0.168660\pi$
$227$	12.9062	+	7.45140i	0.856615	+	0.494567i	−0.00626222	+	0.999980i	$0.501993\pi$
$228$	−0.111302	−	0.0642602i	−0.00737115	−	0.00425573i
$229$		−	19.3074i		−	1.27587i	−0.770092	−	0.637933i	$-0.779790\pi$
$229$		−	19.3074i		−	1.27587i	0.770092	−	0.637933i	$-0.220210\pi$
$230$	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	$0.255748\pi$
$234$	16.0597	−	1.48207i	1.04986	−	0.0968860i
$235$	−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	$0.160019\pi$
$239$			14.8971i			0.963612i	−0.876278	+	0.481806i	$0.839981\pi$
$240$	0.362596	+	0.209345i	0.0234055	+	0.0135131i
$241$	−8.13343	−	4.69584i	−0.523921	−	0.302486i	0.214617	−	0.976698i	$-0.431150\pi$
$241$	−8.13343	−	4.69584i	−0.523921	−	0.302486i	−0.738537	+	0.674213i	$0.764483\pi$
$242$			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
$247$	−8.64512	+	18.7722i	−0.550076	+	1.19445i
$248$	−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
$260$	−0.356756	+	0.774668i	−0.0221251	+	0.0480428i
$261$	−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	0.0809839	−	0.996715i	$-0.474194\pi$
$271$	16.2095	−	9.35856i	0.984657	−	0.568492i	0.903673	+	0.428224i	$0.140860\pi$
$272$	15.7201			0.953170
$273$	−1.64265	+	0.151592i	−0.0994176	+	0.00917476i
$274$	−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	$-0.688140\pi$
$281$		−	27.8384i		−	1.66070i	0.557241	−	0.830351i	$-0.311860\pi$
$282$	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
$286$	−5.23757	−	2.41204i	−0.309704	−	0.142627i
$287$	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	0.506889	−	0.862011i	$-0.330795\pi$
$293$	0.236400	+	0.136485i	0.0138106	+	0.00797356i	−0.493079	+	0.869985i	$0.664129\pi$
$294$		−	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
$299$	20.8579	−	14.7533i	1.20624	−	0.853204i
$300$	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	$0.0626456\pi$
$307$			6.85224i			0.391078i	−0.980696	+	0.195539i	$0.937354\pi$
$308$	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	$0.597588\pi$
$312$	0.520480	+	0.735846i	0.0294664	+	0.0416591i
$313$	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	$-0.926297\pi$
$317$		−	8.17161i		−	0.458963i	0.973313	−	0.229482i	$-0.0737031\pi$
$318$	−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
$325$	−0.331331	−	3.59030i	−0.0183789	−	0.199154i
$326$	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	0.957657	−	0.287911i	$-0.0929608\pi$
$331$	21.5983	+	12.4698i	1.18715	+	0.685400i	0.229490	+	0.973311i	$0.426294\pi$
$332$	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	$0.320690\pi$
$338$	−14.7735	+	12.6380i	−0.803575	+	0.687415i
$339$	−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	−0.982960	−	0.183822i	$-0.941153\pi$
$349$	−24.5708	+	14.1860i	−1.31525	+	0.759357i	−0.332286	+	0.943179i	$0.607820\pi$
$350$	7.21857			0.385849
$351$	−0.188154	−	2.03883i	−0.0100429	−	0.108825i
$352$	−1.42371			−0.0758840
$353$	−18.4047	+	10.6260i	−0.979586	+	0.565564i	−0.902145	−	0.431433i	$-0.858008\pi$
$353$	−18.4047	+	10.6260i	−0.979586	+	0.565564i	−0.0774407	+	0.996997i	$0.524675\pi$
$354$	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	$0.330569\pi$
$359$			32.6519i			1.72330i	−0.507502	+	0.861650i	$0.669431\pi$
$360$	−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
$364$	−2.37724	−	3.36090i	−0.124601	−	0.176159i
$365$	−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
$377$	4.33621	−	3.06710i	0.223326	−	0.157963i
$378$	4.09924			0.210842
$379$	−22.0131	+	12.7093i	−1.13074	+	0.652832i	−0.944120	−	0.329601i	$-0.893086\pi$
$379$	−22.0131	+	12.7093i	−1.13074	+	0.652832i	−0.186617	+	0.982433i	$0.559752\pi$
$380$	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	0.240937	−	0.970541i	$-0.422545\pi$
$383$	−9.37632	−	5.41342i	−0.479107	−	0.276613i	−0.720044	+	0.693928i	$0.755879\pi$
$384$	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	$0.301482\pi$
$390$	0.464243	+	0.213797i	0.0235078	+	0.0108260i
$391$	−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	−0.0339917	−	0.999422i	$-0.510822\pi$
$397$	−18.2614	−	10.5432i	−0.916512	−	0.529149i	−0.882521	+	0.470273i	$0.844155\pi$
$398$			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	−0.862434	−	0.506169i	$-0.831061\pi$
$401$	−17.1273	+	9.88845i	−0.855296	+	0.493805i	0.00713812	+	0.999975i	$0.497728\pi$
$402$	0.733324			0.0365749
$403$	−5.25656	+	0.485102i	−0.261848	+	0.0241646i
$404$	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	−0.374897	−	0.927066i	$-0.622322\pi$
$409$	−27.6096	−	15.9404i	−1.36521	−	0.788204i	−0.990312	+	0.138862i	$0.955655\pi$
$410$	−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
$416$	−2.00792	+	4.36004i	−0.0984465	+	0.213769i
$417$	−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	$-0.855618\pi$
$421$		−	17.9820i		−	0.876391i	0.898880	−	0.438195i	$-0.144382\pi$
$422$	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
$429$	−0.152879	+	0.331965i	−0.00738107	+	0.0160274i
$430$	5.32235			0.256666
$431$	−4.24308	+	2.44974i	−0.204382	+	0.118000i	−0.598698	−	0.800975i	$-0.704315\pi$
$431$	−4.24308	+	2.44974i	−0.204382	+	0.118000i	0.394316	+	0.918975i	$0.370982\pi$
$432$	−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
$442$	19.1088	−	1.76346i	0.908913	−	0.0838791i
$443$	−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	0.933973	−	0.357344i	$-0.116317\pi$
$449$	23.1283	+	13.3531i	1.09149	+	0.630173i	0.157518	+	0.987516i	$0.449651\pi$
$450$			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
$455$	15.8077	+	7.27987i	0.741075	+	0.341286i
$456$	1.43290			0.0671016
$457$	3.69903	−	2.13563i	0.173033	−	0.0999007i	−0.410982	−	0.911643i	$-0.634814\pi$
$457$	3.69903	−	2.13563i	0.173033	−	0.0999007i	0.584015	+	0.811743i	$0.301481\pi$
$458$	−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	0.854743	−	0.519051i	$-0.173715\pi$
$461$	17.8767	+	10.3211i	0.832603	+	0.480704i	−0.0221401	+	0.999755i	$0.507048\pi$
$462$	−0.633679	−	0.365855i	−0.0294814	−	0.0170211i
$463$		−	32.1040i		−	1.49200i	−0.665947	−	0.745999i	$-0.731972\pi$
$463$		−	32.1040i		−	1.49200i	0.665947	−	0.745999i	$-0.268028\pi$
$464$	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	$0.681912\pi$
$468$	2.08262	−	1.47309i	0.0962694	−	0.0680934i
$469$	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	−0.598886	−	0.800834i	$-0.704390\pi$
$479$	−4.48198	+	2.58767i	−0.204787	+	0.118234i	0.394100	+	0.919068i	$0.371057\pi$
$480$	0.126194			0.00575992
$481$	−0.0528814	−	0.0747629i	−0.00241119	−	0.00340889i
$482$	−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	−0.245391	−	0.969424i	$-0.578917\pi$
$487$	−26.6501	−	15.3865i	−1.20763	−	0.697227i	−0.962242	+	0.272197i	$0.912250\pi$
$488$	−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
$494$	2.84028	+	30.7772i	0.127790	+	1.38473i
$495$	−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	$-0.776105\pi$
$499$		−	28.8971i		−	1.29361i	0.762655	−	0.646805i	$-0.223895\pi$
$500$	−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
$507$	0.801014	+	0.936370i	0.0355743	+	0.0415856i
$508$	0.167154			0.00741625
$509$	24.2585	−	14.0057i	1.07524	−	0.620790i	0.145631	−	0.989339i	$-0.453479\pi$
$509$	24.2585	−	14.0057i	1.07524	−	0.620790i	0.929608	+	0.368549i	$0.120145\pi$
$510$	−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
$520$	−0.873806	−	9.46855i	−0.0383189	−	0.415224i
$521$	−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
$533$	−0.557894	−	0.788741i	−0.0241651	−	0.0341642i
$534$	−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	$0.139529\pi$
$541$			19.7445i			0.848882i	−0.905456	+	0.424441i	$0.860471\pi$
$542$	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
$546$	−2.01412	+	1.42463i	−0.0861963	+	0.0609685i
$547$	−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	−0.572397	−	0.819977i	$-0.693986\pi$
$557$	−3.50412	+	2.02310i	−0.148474	+	0.0857217i	0.423922	+	0.905699i	$0.360653\pi$
$558$	6.54905			0.277244
$559$	11.6552	+	5.36754i	0.492962	+	0.227023i
$560$	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	$0.711860\pi$
$572$	−0.908189	+	0.0838123i	−0.0379733	+	0.00350437i
$573$	−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	$0.201068\pi$
$577$			28.3684i			1.18099i	−0.807041	+	0.590496i	$0.798932\pi$
$578$	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
$585$	−4.51107	+	9.79543i	−0.186510	+	0.404991i
$586$	0.408230			0.0168638
$587$	29.7806	−	17.1939i	1.22918	−	0.709667i	0.262320	−	0.964981i	$-0.415512\pi$
$587$	29.7806	−	17.1939i	1.22918	−	0.709667i	0.966858	+	0.255314i	$0.0821790\pi$
$588$	−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	$-0.964134\pi$
$593$		−	5.47612i		−	0.224877i	0.993659	−	0.112439i	$-0.0358662\pi$
$594$	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
$598$	15.9823	−	34.7043i	0.653564	−	1.41916i
$599$	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
$611$	−23.4013	+	2.15959i	−0.946715	+	0.0873677i
$612$	−2.51793			−0.101781
$613$	24.9232	−	14.3894i	1.00664	−	0.581184i	0.0964341	−	0.995339i	$-0.469256\pi$
$613$	24.9232	−	14.3894i	1.00664	−	0.581184i	0.910206	+	0.414155i	$0.135923\pi$
$614$	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	0.980657	−	0.195735i	$-0.0627093\pi$
$617$	32.3279	+	18.6645i	1.30147	+	0.751406i	0.320817	+	0.947141i	$0.396043\pi$
$618$	−0.680712	−	0.393009i	−0.0273822	−	0.0158091i
$619$		−	12.7535i		−	0.512606i	−0.966597	−	0.256303i	$-0.917496\pi$
$619$		−	12.7535i		−	0.512606i	0.966597	−	0.256303i	$-0.0825045\pi$
$620$	−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
$624$	1.37119	+	0.631470i	0.0548914	+	0.0252790i
$625$	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	0.905362	−	0.424641i	$-0.139600\pi$
$631$	24.8759	+	14.3621i	0.990294	+	0.571746i	0.0849315	+	0.996387i	$0.472933\pi$
$632$			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
$637$	−47.9762	+	33.9346i	−1.90089	+	1.34454i
$638$	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	0.721976	−	0.691918i	$-0.243234\pi$
$643$	12.2665	+	7.08209i	0.483745	+	0.279290i	−0.238231	+	0.971209i	$0.576567\pi$
$644$	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
$650$	−3.11378	−	4.40221i	−0.122132	−	0.172669i
$651$	−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	−0.256326	−	0.966590i	$-0.582512\pi$
$661$	11.6364	−	6.71826i	0.452602	−	0.261310i	0.708929	+	0.705280i	$0.249179\pi$
$662$	37.2972			1.44960
$663$	−0.111771	−	1.21114i	−0.00434081	−	0.0470370i
$664$	−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
$676$	−1.02419	+	2.89949i	−0.0393919	+	0.111519i
$677$	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	0.237766	−	0.971323i	$-0.423585\pi$
$683$	−12.6631	−	7.31107i	−0.484542	−	0.279750i	−0.722307	+	0.691572i	$0.756918\pi$
$684$		−	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
$689$	0.328354	+	3.55804i	0.0125093	+	0.135550i
$690$	−1.00445			−0.0382388
$691$	−3.05231	+	1.76225i	−0.116115	+	0.0670393i	−0.556933	−	0.830558i	$-0.688022\pi$
$691$	−3.05231	+	1.76225i	−0.116115	+	0.0670393i	0.440817	+	0.897597i	$0.354689\pi$
$692$	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	$0.490774\pi$
$702$	−1.76823	−	2.49990i	−0.0667377	−	0.0943526i
$703$	−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	0.710155	−	0.704046i	$-0.248625\pi$
$709$	12.1289	+	7.00262i	0.455510	+	0.262989i	−0.254644	+	0.967035i	$0.581958\pi$
$710$		−	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
$715$	3.14788	−	2.22656i	0.117724	−	0.0832687i
$716$	−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	$0.438573\pi$
$728$	41.6890	+	19.1989i	1.54510	+	0.711560i
$729$	−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	$0.168566\pi$
$733$			27.3533i			1.01032i	−0.863026	+	0.505159i	$0.831434\pi$
$734$	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	−0.270189	−	0.962807i	$-0.587086\pi$
$739$	11.6495	−	6.72583i	0.428533	−	0.247413i	0.698721	+	0.715394i	$0.253753\pi$
$740$	−0.00600778			−0.000220851
$741$	1.95071	−	0.180021i	0.0716610	−	0.00661324i
$742$	−7.15372			−0.262621
$743$	14.1964	−	8.19632i	0.520817	−	0.300694i	−0.216452	−	0.976293i	$-0.569448\pi$
$743$	14.1964	−	8.19632i	0.520817	−	0.300694i	0.737269	+	0.675599i	$0.236115\pi$
$744$	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
$754$	3.32260	−	7.21476i	0.121002	−	0.262746i
$755$	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	0.615458	−	0.788170i	$-0.288971\pi$
$761$	6.63759	+	3.83221i	0.240612	+	0.138918i	−0.374846	+	0.927087i	$0.622304\pi$
$762$		−	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
$767$	13.1562	−	28.5676i	0.475042	−	1.03152i
$768$	0.530882			0.0191566
$769$	6.26219	−	3.61548i	0.225820	−	0.130377i	−0.382822	−	0.923822i	$-0.625048\pi$
$769$	6.26219	−	3.61548i	0.225820	−	0.130377i	0.608642	+	0.793445i	$0.291714\pi$
$770$	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	−0.124893	−	0.992170i	$-0.539859\pi$
$773$	−29.0981	−	16.7998i	−1.04658	−	0.604246i	−0.921691	+	0.387924i	$0.873192\pi$
$774$	−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
$780$	0.0804993	−	0.00742888i	0.00288234	−	0.000265997i
$781$	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	0.545167	−	0.838328i	$-0.316466\pi$
$787$	2.57355	+	1.48584i	0.0917371	+	0.0529645i	−0.453430	+	0.891292i	$0.649800\pi$
$788$		−	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
$793$	−20.7545	−	9.55802i	−0.737013	−	0.339415i
$794$	−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
$806$	−6.44528	+	4.55889i	−0.227025	+	0.160580i
$807$	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	$-0.920287\pi$
$811$		−	14.1147i		−	0.495636i	0.968807	−	0.247818i	$-0.0797135\pi$
$812$	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
$819$	−30.0594	−	42.4975i	−1.05036	−	1.48498i
$820$	−0.0633815			−0.00221338
$821$	−1.37318	+	0.792808i	−0.0479244	+	0.0276692i	−0.523771	−	0.851859i	$-0.675475\pi$
$821$	−1.37318	+	0.792808i	−0.0479244	+	0.0276692i	0.475846	+	0.879528i	$0.342142\pi$
$822$	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	$0.0500721\pi$
$827$			9.01023i			0.313316i	−0.987653	+	0.156658i	$0.949928\pi$
$828$	−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
$832$	−2.26738	−	24.5693i	−0.0786072	−	0.851787i
$833$	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	$0.0410263\pi$
$839$	46.3121	+	26.7383i	1.59887	+	0.923108i	0.607164	+	0.794576i	$0.292307\pi$
$840$		−	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
$845$	−2.37915	−	12.7804i	−0.0818453	−	0.439660i
$846$	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	$0.157736\pi$
$853$			27.7756i			0.951019i	−0.879711	+	0.475510i	$0.842264\pi$
$854$	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	$0.869426\pi$
$858$	0.0502271	+	0.544260i	0.00171472	+	0.0185807i
$859$	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	$-0.990495\pi$
$863$		−	1.75413i		−	0.0597113i	0.999554	−	0.0298557i	$-0.00950476\pi$
$864$	−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
$871$	−10.7710	−	15.2278i	−0.364961	−	0.515975i
$872$	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	0.150322	−	0.988637i	$-0.451969\pi$
$877$	−18.6777	−	10.7836i	−0.630702	−	0.364136i	−0.781024	+	0.624501i	$0.785302\pi$
$878$	−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	$0.193504\pi$
$884$	2.47803	−	1.75277i	0.0833452	−	0.0589519i
$885$	−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
$897$	−2.19961	−	1.01298i	−0.0734428	−	0.0338225i
$898$	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
$910$	25.9168	−	2.39174i	0.859134	−	0.0792853i
$911$	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
$923$	11.7110	−	25.4296i	0.385474	−	0.837026i
$924$	−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	0.179788	−	0.983705i	$-0.442459\pi$
$929$	−17.7462	−	10.2457i	−0.582232	−	0.336152i	−0.762020	+	0.647553i	$0.775792\pi$
$930$	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
$936$	−11.8969	+	25.8331i	−0.388862	+	0.844382i
$937$	−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	$-0.896391\pi$
$941$		−	19.6189i		−	0.639557i	0.947492	−	0.319779i	$-0.103609\pi$
$942$	−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	$0.713160\pi$
$947$	−49.5474	+	28.6062i	−1.61007	+	0.929576i	−0.989352	+	0.145544i	$0.953507\pi$
$948$	−0.196937			−0.00639623
$949$	−36.2936	+	3.34935i	−1.17814	+	0.108725i
$950$	−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
$962$	−0.124393	−	0.0572867i	−0.00401061	−	0.00184700i
$963$	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	$-0.946706\pi$
$967$		−	10.3643i		−	0.333293i	0.986017	−	0.166647i	$-0.0532939\pi$
$968$	−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
$975$	−0.279019	+	0.197356i	−0.00893575	+	0.00632045i
$976$	−27.9929			−0.896030
$977$	−11.9458	+	6.89691i	−0.382180	+	0.220652i	−0.678766	−	0.734354i	$-0.737485\pi$
$977$	−11.9458	+	6.89691i	−0.382180	+	0.220652i	0.296586	+	0.955006i	$0.404152\pi$
$978$	−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	$-0.792773\pi$
$983$		−	37.9997i		−	1.21200i	0.795463	−	0.606002i	$-0.207227\pi$
$984$	−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
$988$	2.82306	+	3.99119i	0.0898134	+	0.126977i
$989$	−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	65.2.m.a.36.4	✓	8
3.2	odd	2		585.2.bu.c.361.1		8
4.3	odd	2		1040.2.da.b.881.3		8
5.2	odd	4		325.2.m.b.49.4		8
5.3	odd	4		325.2.m.c.49.1		8
5.4	even	2		325.2.n.d.101.1		8
13.2	odd	12		845.2.a.l.1.4		4
13.3	even	3		845.2.c.g.506.7		8
13.4	even	6	inner	65.2.m.a.56.4	yes	8
13.5	odd	4		845.2.e.n.146.1		8
13.6	odd	12		845.2.e.n.191.1		8
13.7	odd	12		845.2.e.m.191.4		8
13.8	odd	4		845.2.e.m.146.4		8
13.9	even	3		845.2.m.g.316.1		8
13.10	even	6		845.2.c.g.506.2		8
13.11	odd	12		845.2.a.m.1.1		4
13.12	even	2		845.2.m.g.361.1		8
39.2	even	12		7605.2.a.cj.1.1		4
39.11	even	12		7605.2.a.cf.1.4		4
39.17	odd	6		585.2.bu.c.316.1		8
52.43	odd	6		1040.2.da.b.641.3		8
65.4	even	6		325.2.n.d.251.1		8
65.17	odd	12		325.2.m.c.199.1		8
65.24	odd	12		4225.2.a.bi.1.4		4
65.43	odd	12		325.2.m.b.199.4		8
65.54	odd	12		4225.2.a.bl.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.m.a.36.4	✓	8	1.1	even	1	trivial
65.2.m.a.56.4	yes	8	13.4	even	6	inner
325.2.m.b.49.4		8	5.2	odd	4
325.2.m.b.199.4		8	65.43	odd	12
325.2.m.c.49.1		8	5.3	odd	4
325.2.m.c.199.1		8	65.17	odd	12
325.2.n.d.101.1		8	5.4	even	2
325.2.n.d.251.1		8	65.4	even	6
585.2.bu.c.316.1		8	39.17	odd	6
585.2.bu.c.361.1		8	3.2	odd	2
845.2.a.l.1.4		4	13.2	odd	12
845.2.a.m.1.1		4	13.11	odd	12
845.2.c.g.506.2		8	13.10	even	6
845.2.c.g.506.7		8	13.3	even	3
845.2.e.m.146.4		8	13.8	odd	4
845.2.e.m.191.4		8	13.7	odd	12
845.2.e.n.146.1		8	13.5	odd	4
845.2.e.n.191.1		8	13.6	odd	12
845.2.m.g.316.1		8	13.9	even	3
845.2.m.g.361.1		8	13.12	even	2
1040.2.da.b.641.3		8	52.43	odd	6
1040.2.da.b.881.3		8	4.3	odd	2
4225.2.a.bi.1.4		4	65.24	odd	12
4225.2.a.bl.1.1		4	65.54	odd	12
7605.2.a.cf.1.4		4	39.11	even	12
7605.2.a.cj.1.1		4	39.2	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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	65.m (of order \(6\), degree \(2\), 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} +(0.331331 + 3.59030i) q^{13} -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} +(3.11378 + 4.40221i) q^{26} -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} +(0.279019 - 0.197356i) q^{39} -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} +(0.774668 + 0.356756i) q^{52} +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} +(-3.59030 + 0.331331i) q^{65} +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} +(0.213797 - 0.464243i) q^{78} +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} +(7.27987 - 15.8077i) q^{91} -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	\( 8 q + 2 q^{3} + 2 q^{4} - 18 q^{6} - 6 q^{7} - 4 q^{9} - 2 q^{10} + 20 q^{12} + 4 q^{14} - 6 q^{15} - 2 q^{16} - 2 q^{17} + 12 q^{19} + 12 q^{20} - 12 q^{22} - 10 q^{23} - 12 q^{24} - 8 q^{25} + 10 q^{26} - 4 q^{27} - 18 q^{28} - 8 q^{29} + 4 q^{30} + 6 q^{32} + 42 q^{33} + 10 q^{35} + 20 q^{36} + 6 q^{37} - 16 q^{38} - 12 q^{40} + 12 q^{41} + 4 q^{42} - 2 q^{43} - 42 q^{46} + 28 q^{48} + 12 q^{49} - 8 q^{51} - 6 q^{52} - 24 q^{53} + 18 q^{54} + 12 q^{56} + 36 q^{58} - 12 q^{59} - 28 q^{61} + 4 q^{62} - 24 q^{63} - 8 q^{64} - 8 q^{65} + 12 q^{66} + 6 q^{67} - 14 q^{68} - 16 q^{69} - 48 q^{72} + 10 q^{74} - 2 q^{75} + 54 q^{76} - 36 q^{77} - 56 q^{78} - 16 q^{79} + 8 q^{81} + 4 q^{82} - 30 q^{84} + 18 q^{85} + 22 q^{87} - 18 q^{88} + 24 q^{89} + 40 q^{90} + 28 q^{91} + 44 q^{92} + 32 q^{94} - 16 q^{95} - 30 q^{97} + 72 q^{98}+O(q^{100}) \) 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 + 10 * q^26 - 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 - 6 * q^52 - 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 - 8 * q^65 + 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 - 56 * q^78 - 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 + 28 * q^91 + 44 * q^92 + 32 * q^94 - 16 * q^95 - 30 * q^97 + 72 * q^98

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