LMFDB - Embedded newform 845.2.e.m.191.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(146,845)]

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, 2]))

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

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

chi := DirichletCharacter("845.146");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.e (of order $3$, 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 $\Q(\zeta_{3})$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			191.4
Root			$0.665665 + 1.24775i$ of defining polynomial
Character	$\chi$	$=$	845.191
Dual form			845.2.e.m.146.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.747754	−	1.29515i	0.528742	−	0.915808i	−0.470696	−	0.882295i	$-0.655997\pi$
$2$	0.747754	−	1.29515i	0.528742	−	0.915808i	0.999438	−	0.0335125i	$-0.0106693\pi$
$3$	−0.0473938	+	0.0820885i	−0.0273628	+	0.0473938i	−0.879383	−	0.476116i	$-0.842044\pi$
$3$	−0.0473938	+	0.0820885i	−0.0273628	+	0.0473938i	0.852020	+	0.523510i	$0.175378\pi$
$4$	−0.118272	−	0.204852i	−0.0591358	−	0.102426i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	0.0708778	+	0.122764i	0.0289357	+	0.0501182i
$7$	−2.41342	−	4.18016i	−0.912187	−	1.57995i	−0.810969	−	0.585089i	$-0.801059\pi$
$7$	−2.41342	−	4.18016i	−0.912187	−	1.57995i	−0.101218	−	0.994864i	$-0.532274\pi$
$8$	2.63726			0.932413
$9$	1.49551	+	2.59030i	0.498503	+	0.863432i
$10$	−0.747754	+	1.29515i	−0.236461	+	0.409562i
$11$	0.534695	−	0.926118i	0.161217	−	0.279235i	−0.774089	−	0.633077i	$-0.781792\pi$
$11$	0.534695	−	0.926118i	0.161217	−	0.279235i	0.935305	+	0.353842i	$0.115125\pi$
$12$	0.0224214			0.00647249
$13$		0			0
$13$		0			0
$14$	−7.21857			−1.92924
$15$	0.0473938	−	0.0820885i	0.0122370	−	0.0211951i
$16$	2.20857	−	3.82535i	0.552142	−	0.956337i
$17$	−1.77944	−	3.08209i	−0.431579	−	0.747516i	0.565431	−	0.824796i	$-0.308710\pi$
$17$	−1.77944	−	3.08209i	−0.431579	−	0.747516i	−0.997009	+	0.0772795i	$0.975377\pi$
$18$	4.47309			1.05432
$19$	−2.86603	−	4.96410i	−0.657511	−	1.13884i	−0.981258	−	0.192699i	$-0.938276\pi$
$19$	−2.86603	−	4.96410i	−0.657511	−	1.13884i	0.323747	−	0.946144i	$-0.395057\pi$
$20$	0.118272	+	0.204852i	0.0264463	+	0.0458064i
$21$	0.457524			0.0998400
$22$	−0.799640	−	1.38502i	−0.170484	−	0.295287i
$23$	3.54290	−	6.13649i	0.738746	−	1.27955i	−0.214314	−	0.976765i	$-0.568752\pi$
$23$	3.54290	−	6.13649i	0.738746	−	1.27955i	0.953060	−	0.302781i	$-0.0979150\pi$
$24$	−0.124990	+	0.216489i	−0.0255135	+	0.0441906i
$25$	1.00000			0.200000
$26$		0			0
$27$	−0.567874			−0.109287
$28$	−0.570878	+	0.988789i	−0.107886	+	0.186864i
$29$	−0.736543	+	1.27573i	−0.136773	+	0.236897i	−0.926273	−	0.376853i	$-0.877006\pi$
$29$	−0.736543	+	1.27573i	−0.136773	+	0.236897i	0.789501	+	0.613750i	$0.210340\pi$
$30$	−0.0708778	−	0.122764i	−0.0129405	−	0.0224135i
$31$	−1.46410			−0.262960			−0.131480	−	0.991319i	$-0.541973\pi$
$31$	−1.46410			−0.262960			−0.131480	+	0.991319i	$0.541973\pi$
$32$	−0.665665	−	1.15297i	−0.117674	−	0.203818i
$33$	0.0506824	+	0.0877845i	0.00882268	+	0.0152813i
$34$	−5.32235			−0.912775
$35$	2.41342	+	4.18016i	0.407942	+	0.706577i
$36$	0.353752	−	0.612717i	0.0589587	−	0.102119i
$37$	0.0126991	−	0.0219955i	0.00208772	−	0.00361604i	−0.864980	−	0.501807i	$-0.832669\pi$
$37$	0.0126991	−	0.0219955i	0.00208772	−	0.00361604i	0.867067	+	0.498191i	$0.166002\pi$
$38$	−8.57233			−1.39061
$39$		0			0
$40$	−2.63726			−0.416988
$41$	−0.133975	+	0.232051i	−0.0209233	+	0.0362402i	−0.876297	−	0.481770i	$-0.839994\pi$
$41$	−0.133975	+	0.232051i	−0.0209233	+	0.0362402i	0.855374	+	0.518011i	$0.173327\pi$
$42$	0.342116	−	0.592562i	0.0527896	−	0.0914342i
$43$	−1.77944	−	3.08209i	−0.271363	−	0.470014i	0.697848	−	0.716246i	$-0.254141\pi$
$43$	−1.77944	−	3.08209i	−0.271363	−	0.470014i	−0.969211	+	0.246232i	$0.920808\pi$
$44$	−0.252957			−0.0381347
$45$	−1.49551	−	2.59030i	−0.222937	−	0.386138i
$46$	−5.29844	−	9.17716i	−0.781212	−	1.35310i
$47$	6.51793			0.950738			0.475369	−	0.879787i	$-0.342315\pi$
$47$	6.51793			0.950738			0.475369	+	0.879787i	$0.342315\pi$
$48$	0.209345	+	0.362596i	0.0302163	+	0.0523362i
$49$	−8.14918	+	14.1148i	−1.16417	+	2.01640i
$50$	0.747754	−	1.29515i	0.105748	−	0.183162i
$51$	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	$0.478318\pi$
$54$	−0.424630	+	0.735481i	−0.0577848	+	0.100086i
$55$	−0.534695	+	0.926118i	−0.0720982	+	0.124878i
$56$	−6.36482	−	11.0242i	−0.850535	−	1.47317i
$57$	0.543327			0.0719655
$58$	1.10151	+	1.90786i	0.144635	+	0.250515i
$59$	−4.36153	−	7.55440i	−0.567823	−	0.983499i	−0.996781	−	0.0801741i	$-0.974452\pi$
$59$	−4.36153	−	7.55440i	−0.567823	−	0.983499i	0.428958	−	0.903325i	$-0.358881\pi$
$60$	−0.0224214			−0.00289458
$61$	−3.16867	−	5.48830i	−0.405707	−	0.702704i	0.588697	−	0.808354i	$-0.299641\pi$
$61$	−3.16867	−	5.48830i	−0.405707	−	0.702704i	−0.994403	+	0.105650i	$0.966308\pi$
$62$	−1.09479	+	1.89623i	−0.139038	+	0.240821i
$63$	7.21857	−	12.5029i	0.909455	−	1.57522i
$64$	6.84325			0.855406
$65$		0			0
$66$	0.151592			0.0186597
$67$	−2.58658	+	4.48009i	−0.316001	+	0.547330i	−0.979650	−	0.200714i	$-0.935674\pi$
$67$	−2.58658	+	4.48009i	−0.316001	+	0.547330i	0.663649	+	0.748044i	$0.269007\pi$
$68$	−0.420915	+	0.729047i	−0.0510435	+	0.0884099i
$69$	0.335823	+	0.581663i	0.0404283	+	0.0700240i
$70$	7.21857			0.862785
$71$	3.88244	+	6.72458i	0.460761	+	0.798061i	0.998999	−	0.0447317i	$-0.0142433\pi$
$71$	3.88244	+	6.72458i	0.460761	+	0.798061i	−0.538238	+	0.842793i	$0.680910\pi$
$72$	3.94405	+	6.83129i	0.464810	+	0.805075i
$73$	10.1088			1.18314			0.591572	−	0.806252i	$-0.298507\pi$
$73$	10.1088			1.18314			0.591572	+	0.806252i	$0.298507\pi$
$74$	−0.0189916	−	0.0328945i	−0.00220773	−	0.00382391i
$75$	−0.0473938	+	0.0820885i	−0.00547256	+	0.00947876i
$76$	−0.677939	+	1.17422i	−0.0777649	+	0.134693i
$77$	−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	$0.335494\pi$
$80$	−2.20857	+	3.82535i	−0.246925	+	0.427687i
$81$	−4.45961	+	7.72427i	−0.495512	+	0.858252i
$82$	0.200360	+	0.347034i	0.0221261	+	0.0383235i
$83$	−0.725474			−0.0796311			−0.0398155	−	0.999207i	$-0.512677\pi$
$83$	−0.725474			−0.0796311			−0.0398155	+	0.999207i	$0.512677\pi$
$84$	−0.0541121	−	0.0937250i	−0.00590412	−	0.0102262i
$85$	1.77944	+	3.08209i	0.193008	+	0.334299i
$86$	−5.32235			−0.573923
$87$	−0.0698151	−	0.120923i	−0.00748497	−	0.0129643i
$88$	1.41013	−	2.44242i	0.150320	−	0.260363i
$89$	−6.75327	+	11.6970i	−0.715845	+	1.23988i	0.246788	+	0.969070i	$0.420625\pi$
$89$	−6.75327	+	11.6970i	−0.715845	+	1.23988i	−0.962633	+	0.270810i	$0.912708\pi$
$90$	−4.47309			−0.471505
$91$		0			0
$92$	−1.67610			−0.174745
$93$	0.0693893	−	0.120186i	0.00719534	−	0.0124627i
$94$	4.87381	−	8.44168i	0.502695	−	0.870693i
$95$	2.86603	+	4.96410i	0.294048	+	0.509306i
$96$	0.126194			0.0128796
$97$	1.71935	+	2.97800i	0.174574	+	0.302371i	0.940014	−	0.341137i	$-0.110812\pi$
$97$	1.71935	+	2.97800i	0.174574	+	0.302371i	−0.765440	+	0.643507i	$0.777479\pi$
$98$	12.1872	+	21.1088i	1.23109	+	2.13231i
$99$	3.19856			0.321467
$100$	−0.118272	−	0.204852i	−0.0118272	−	0.0204852i
$101$	−1.42763	+	2.47273i	−0.142055	+	0.246046i	−0.928270	−	0.371906i	$-0.878704\pi$
$101$	−1.42763	+	2.47273i	−0.142055	+	0.246046i	0.786215	+	0.617953i	$0.212038\pi$
$102$	0.252246	−	0.436903i	0.0249761	−	0.0432599i
$103$	−5.54488			−0.546354			−0.273177	−	0.961964i	$-0.588074\pi$
$103$	−5.54488			−0.546354			−0.273177	+	0.961964i	$0.588074\pi$
$104$		0			0
$105$	−0.457524			−0.0446498
$106$	0.741035	−	1.28351i	0.0719757	−	0.124666i
$107$	2.22056	−	3.84611i	0.214669	−	0.371818i	−0.738501	−	0.674252i	$-0.764466\pi$
$107$	2.22056	−	3.84611i	0.214669	−	0.371818i	0.953170	+	0.302434i	$0.0977993\pi$
$108$	0.0671633	+	0.116330i	0.00646280	+	0.0111939i
$109$	13.7804			1.31993			0.659963	−	0.751298i	$-0.270572\pi$
$109$	13.7804			1.31993			0.659963	+	0.751298i	$0.270572\pi$
$110$	0.799640	+	1.38502i	0.0762427	+	0.132056i
$111$	0.00120372	+	0.00208490i	0.000114252	+	0.000197890i
$112$	−21.3208			−2.01463
$113$	4.02200	+	6.96630i	0.378358	+	0.655334i	0.990823	−	0.135163i	$-0.0431557\pi$
$113$	4.02200	+	6.96630i	0.378358	+	0.655334i	−0.612466	+	0.790497i	$0.709822\pi$
$114$	0.406275	−	0.703689i	0.0380511	−	0.0659065i
$115$	−3.54290	+	6.13649i	−0.330377	+	0.572230i
$116$	0.348448			0.0323526
$117$		0			0
$118$	−13.0454			−1.20093
$119$	−8.58909	+	14.8767i	−0.787361	+	1.36375i
$120$	0.124990	−	0.216489i	0.0114100	−	0.0197626i
$121$	4.92820	+	8.53590i	0.448018	+	0.775991i
$122$	−9.47754			−0.858056
$123$	−0.0126991	−	0.0219955i	−0.00114504	−	0.00198327i
$124$	0.173162	+	0.299925i	0.0155504	+	0.0269340i
$125$	−1.00000			−0.0894427
$126$	−10.7954	−	18.6982i	−0.961734	−	1.66577i
$127$	−0.353326	+	0.611979i	−0.0313526	+	0.0543044i	−0.881276	−	0.472602i	$-0.843315\pi$
$127$	−0.353326	+	0.611979i	−0.0313526	+	0.0543044i	0.849923	+	0.526906i	$0.176648\pi$
$128$	6.44840	−	11.1690i	0.569963	−	0.987205i
$129$	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	$0.411749\pi$
$132$	0.0119886	−	0.0207648i	0.00104347	−	0.00180735i
$133$	−13.8338	+	23.9609i	−1.19955	+	2.07767i
$134$	3.86825	+	6.70001i	0.334166	+	0.578793i
$135$	0.567874			0.0488748
$136$	−4.69286	−	8.12828i	−0.402410	−	0.696994i
$137$	−8.15290	−	14.1212i	−0.696549	−	1.20646i	−0.969656	−	0.244475i	$-0.921384\pi$
$137$	−8.15290	−	14.1212i	−0.696549	−	1.20646i	0.273107	−	0.961984i	$-0.411949\pi$
$138$	1.00445			0.0855046
$139$	3.41264	+	5.91087i	0.289456	+	0.501353i	0.973680	−	0.227919i	$-0.0731921\pi$
$139$	3.41264	+	5.91087i	0.289456	+	0.501353i	−0.684224	+	0.729272i	$0.739859\pi$
$140$	0.570878	−	0.988789i	0.0482480	−	0.0835680i
$141$	−0.308909	+	0.535047i	−0.0260149	+	0.0450591i
$142$	11.6124			0.974494
$143$		0			0
$144$	13.2117			1.10098
$145$	0.736543	−	1.27573i	0.0611666	−	0.105944i
$146$	7.55889	−	13.0924i	0.625578	−	1.08353i
$147$	−0.772442	−	1.33791i	−0.0637099	−	0.110349i
$148$	−0.00600778			−0.000493837
$149$	4.21978	+	7.30887i	0.345698	+	0.598766i	0.985480	−	0.169790i	$-0.0543090\pi$
$149$	4.21978	+	7.30887i	0.345698	+	0.598766i	−0.639783	+	0.768556i	$0.720976\pi$
$150$	0.0708778	+	0.122764i	0.00578715	+	0.0100236i
$151$	−1.37017			−0.111503			−0.0557513	−	0.998445i	$-0.517755\pi$
$151$	−1.37017			−0.111503			−0.0557513	+	0.998445i	$0.517755\pi$
$152$	−7.55846	−	13.0916i	−0.613072	−	1.06187i
$153$	5.32235	−	9.21857i	0.430286	−	0.745278i
$154$	−3.85973	+	6.68525i	−0.311026	+	0.538713i
$155$	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	$0.341487\pi$
$158$	6.56787	−	11.3759i	0.522512	−	0.905017i
$159$	−0.0469680	+	0.0813509i	−0.00372480	+	0.00645155i
$160$	0.665665	+	1.15297i	0.0526255	+	0.0911500i
$161$	−34.2020			−2.69550
$162$	6.66938	+	11.5517i	0.523996	+	0.907588i
$163$	11.2857	+	19.5474i	0.883962	+	1.53107i	0.846899	+	0.531754i	$0.178467\pi$
$163$	11.2857	+	19.5474i	0.883962	+	1.53107i	0.0370630	+	0.999313i	$0.488200\pi$
$164$	0.0633815			0.00494927
$165$	−0.0506824	−	0.0877845i	−0.00394562	−	0.00683402i
$166$	−0.542476	+	0.939595i	−0.0421043	+	0.0729267i
$167$	−4.09850	+	7.09881i	−0.317152	+	0.549323i	−0.979893	−	0.199526i	$-0.936060\pi$
$167$	−4.09850	+	7.09881i	−0.317152	+	0.549323i	0.662741	+	0.748849i	$0.269393\pi$
$168$	1.20661			0.0930922
$169$		0			0
$170$	5.32235			0.408205
$171$	8.57233	−	14.8477i	0.655542	−	1.13543i
$172$	−0.420915	+	0.729047i	−0.0320945	+	0.0555893i
$173$	4.58386	+	7.93948i	0.348505	+	0.603628i	0.985984	−	0.166840i	$-0.0533563\pi$
$173$	4.58386	+	7.93948i	0.348505	+	0.603628i	−0.637479	+	0.770467i	$0.720023\pi$
$174$	−0.208818			−0.0158305
$175$	−2.41342	−	4.18016i	−0.182437	−	0.315991i
$176$	−2.36182	−	4.09079i	−0.178029	−	0.308355i
$177$	0.826838			0.0621490
$178$	10.0996	+	17.4930i	0.756994	+	1.31115i
$179$	5.01850	−	8.69229i	0.375100	−	0.649693i	−0.615242	−	0.788338i	$-0.710942\pi$
$179$	5.01850	−	8.69229i	0.375100	−	0.649693i	0.990342	+	0.138646i	$0.0442750\pi$
$180$	−0.353752	+	0.612717i	−0.0263671	+	0.0456692i
$181$	17.0238			1.26537			0.632686	−	0.774408i	$-0.281952\pi$
$181$	17.0238			1.26537			0.632686	+	0.774408i	$0.281952\pi$
$182$		0			0
$183$	0.600701			0.0444051
$184$	9.34356	−	16.1835i	0.688817	−	1.19307i
$185$	−0.0126991	+	0.0219955i	−0.000933659	+	0.00161714i
$186$	−0.103772	−	0.179739i	−0.00760895	−	0.0131791i
$187$	−3.80584			−0.278310
$188$	−0.770886	−	1.33521i	−0.0562226	−	0.0973804i
$189$	1.37052	+	2.37381i	0.0996905	+	0.172669i
$190$	8.57233			0.621902
$191$	1.93870	+	3.35793i	0.140280	+	0.242971i	0.927602	−	0.373570i	$-0.121867\pi$
$191$	1.93870	+	3.35793i	0.140280	+	0.242971i	−0.787322	+	0.616542i	$0.788533\pi$
$192$	−0.324328	+	0.561752i	−0.0234063	+	0.0405410i
$193$	−0.626972	+	1.08595i	−0.0451304	+	0.0781681i	−0.887708	−	0.460406i	$-0.847704\pi$
$193$	−0.626972	+	1.08595i	−0.0451304	+	0.0781681i	0.842578	+	0.538575i	$0.181037\pi$
$194$	5.14261			0.369218
$195$		0			0
$196$	3.85527			0.275376
$197$	7.64098	−	13.2346i	0.544397	−	0.942923i	−0.454247	−	0.890876i	$-0.650092\pi$
$197$	7.64098	−	13.2346i	0.544397	−	0.942923i	0.998645	−	0.0520479i	$-0.0165749\pi$
$198$	2.39174	−	4.14261i	0.169973	−	0.294402i
$199$	6.61480	+	11.4572i	0.468911	+	0.812177i	0.999368	−	0.0355340i	$-0.0113132\pi$
$199$	6.61480	+	11.4572i	0.468911	+	0.812177i	−0.530458	+	0.847711i	$0.677980\pi$
$200$	2.63726			0.186483
$201$	−0.245176	−	0.424657i	−0.0172934	−	0.0299530i
$202$	2.13504	+	3.69799i	0.150221	+	0.260190i
$203$	7.11035			0.499049
$204$	−0.0398976	−	0.0691046i	−0.00279339	−	0.00483829i
$205$	0.133975	−	0.232051i	0.00935719	−	0.0162071i
$206$	−4.14621	+	7.18144i	−0.288880	+	0.500355i
$207$	21.1937			1.47307
$208$		0			0
$209$	−6.12979			−0.424007
$210$	−0.342116	+	0.592562i	−0.0236082	+	0.0408906i
$211$	2.40521	−	4.16595i	0.165582	−	0.286796i	−0.771280	−	0.636496i	$-0.780383\pi$
$211$	2.40521	−	4.16595i	0.165582	−	0.286796i	0.936862	+	0.349700i	$0.113717\pi$
$212$	−0.117209	−	0.203012i	−0.00804994	−	0.0139429i
$213$	−0.736014			−0.0504309
$214$	−3.32086	−	5.75189i	−0.227009	−	0.393191i
$215$	1.77944	+	3.08209i	0.121357	+	0.210197i
$216$	−1.49763			−0.101901
$217$	3.53349	+	6.12019i	0.239869	+	0.415465i
$218$	10.3044	−	17.8477i	0.697900	−	1.20880i
$219$	−0.479094	+	0.829815i	−0.0323742	+	0.0560737i
$220$	0.252957			0.0170543
$221$		0			0
$222$	0.00360034			0.000241639
$223$	−7.35661	+	12.7420i	−0.492635	+	0.853269i	−0.999964	−	0.00848317i	$-0.997300\pi$
$223$	−7.35661	+	12.7420i	−0.492635	+	0.853269i	0.507329	+	0.861753i	$0.330633\pi$
$224$	−3.21306	+	5.56518i	−0.214682	+	0.371839i
$225$	1.49551	+	2.59030i	0.0997005	+	0.172686i
$226$	12.0299			0.800214
$227$	−7.45140	−	12.9062i	−0.494567	−	0.856615i	0.505413	−	0.862877i	$-0.331340\pi$
$227$	−7.45140	−	12.9062i	−0.494567	−	0.856615i	−0.999980	+	0.00626222i	$0.998007\pi$
$228$	−0.0642602	−	0.111302i	−0.00425573	−	0.00737115i
$229$	−19.3074			−1.27587			−0.637933	−	0.770092i	$-0.720210\pi$
$229$	−19.3074			−1.27587			−0.637933	+	0.770092i	$0.720210\pi$
$230$	5.29844	+	9.17716i	0.349369	+	0.605124i
$231$	0.244636	−	0.423722i	0.0160959	−	0.0278788i
$232$	−1.94246	+	3.36444i	−0.127529	+	0.220886i
$233$	−21.1937			−1.38845			−0.694224	−	0.719759i	$-0.744252\pi$
$233$	−21.1937			−1.38845			−0.694224	+	0.719759i	$0.744252\pi$
$234$		0			0
$235$	−6.51793			−0.425183
$236$	−1.03169	+	1.78694i	−0.0671573	+	0.116320i
$237$	−0.416282	+	0.721022i	−0.0270404	+	0.0468354i
$238$	12.8451	+	22.2483i	0.832621	+	1.44214i
$239$	−14.8971			−0.963612			−0.481806	−	0.876278i	$-0.660019\pi$
$239$	−14.8971			−0.963612			−0.481806	+	0.876278i	$0.660019\pi$
$240$	−0.209345	−	0.362596i	−0.0135131	−	0.0234055i
$241$	−4.69584	−	8.13343i	−0.302486	−	0.523921i	0.674213	−	0.738537i	$-0.264483\pi$
$241$	−4.69584	−	8.13343i	−0.302486	−	0.523921i	−0.976698	+	0.214617i	$0.931150\pi$
$242$	14.7403			0.947544
$243$	−1.27453	−	2.20754i	−0.0817609	−	0.141614i
$244$	−0.749527	+	1.29822i	−0.0479835	+	0.0831099i
$245$	8.14918	−	14.1148i	0.520632	−	0.901762i
$246$	−0.0379833			−0.00242173
$247$		0			0
$248$	−3.86122			−0.245188
$249$	0.0343829	−	0.0595530i	0.00217893	−	0.00377402i
$250$	−0.747754	+	1.29515i	−0.0472921	+	0.0819123i
$251$	−5.65817	−	9.80024i	−0.357140	−	0.618585i	0.630341	−	0.776318i	$-0.282915\pi$
$251$	−5.65817	−	9.80024i	−0.357140	−	0.618585i	−0.987482	+	0.157733i	$0.949582\pi$
$252$	−3.41501			−0.215125
$253$	−3.78874	−	6.56229i	−0.238196	−	0.412568i
$254$	0.528402	+	0.915219i	0.0331549	+	0.0574260i
$255$	−0.337339			−0.0211250
$256$	−2.80038	−	4.85040i	−0.175024	−	0.303150i
$257$	13.2660	−	22.9773i	0.827508	−	1.43329i	−0.0724788	−	0.997370i	$-0.523091\pi$
$257$	13.2660	−	22.9773i	0.827508	−	1.43329i	0.899987	−	0.435917i	$-0.143576\pi$
$258$	0.252246	−	0.436903i	0.0157042	−	0.0272004i
$259$	−0.122593			−0.00761758
$260$		0			0
$261$	−4.40602			−0.272726
$262$	4.68508	−	8.11480i	0.289445	−	0.501334i
$263$	7.07038	−	12.2463i	0.435979	−	0.755137i	−0.561396	−	0.827547i	$-0.689736\pi$
$263$	7.07038	−	12.2463i	0.435979	−	0.755137i	0.997375	+	0.0724100i	$0.0230690\pi$
$264$	0.133663	+	0.231511i	0.00822638	+	0.0142485i
$265$	−0.991015			−0.0608776
$266$	20.6886	+	35.8337i	1.26850	+	2.19711i
$267$	−0.640126	−	1.10873i	−0.0391751	−	0.0678532i
$268$	1.22368			0.0747479
$269$	−12.3872	−	21.4553i	−0.755264	−	1.30815i	−0.945243	−	0.326367i	$-0.894176\pi$
$269$	−12.3872	−	21.4553i	−0.755264	−	1.30815i	0.189980	−	0.981788i	$-0.439158\pi$
$270$	0.424630	−	0.735481i	0.0258422	−	0.0447599i
$271$	−9.35856	+	16.2095i	−0.568492	+	0.984657i	0.428224	+	0.903673i	$0.359140\pi$
$271$	−9.35856	+	16.2095i	−0.568492	+	0.984657i	−0.996715	+	0.0809839i	$0.974194\pi$
$272$	−15.7201			−0.953170
$273$		0			0
$274$	−24.3854			−1.47318
$275$	0.534695	−	0.926118i	0.0322433	−	0.0558470i
$276$	0.0794367	−	0.137588i	0.00478152	−	0.00828184i
$277$	11.3323	+	19.6282i	0.680893	+	1.17934i	0.974709	+	0.223480i	$0.0717417\pi$
$277$	11.3323	+	19.6282i	0.680893	+	1.17934i	−0.293815	+	0.955862i	$0.594925\pi$
$278$	10.2073			0.612191
$279$	−2.18958	−	3.79246i	−0.131086	−	0.227048i
$280$	6.36482	+	11.0242i	0.380371	+	0.658822i
$281$	−27.8384			−1.66070			−0.830351	−	0.557241i	$-0.811860\pi$
$281$	−27.8384			−1.66070			−0.830351	+	0.557241i	$0.811860\pi$
$282$	0.461976	+	0.800167i	0.0275103	+	0.0476492i
$283$	−3.96004	+	6.85898i	−0.235400	+	0.407724i	−0.959389	−	0.282087i	$-0.908973\pi$
$283$	−3.96004	+	6.85898i	−0.235400	+	0.407724i	0.723989	+	0.689811i	$0.242307\pi$
$284$	0.918364	−	1.59065i	0.0544949	−	0.0943879i
$285$	−0.543327			−0.0321839
$286$		0			0
$287$	1.29335			0.0763439
$288$	1.99102	−	3.44854i	0.117322	−	0.203207i
$289$	2.16715	−	3.75362i	0.127480	−	0.220801i
$290$	−1.10151	−	1.90786i	−0.0646827	−	0.112034i
$291$	−0.325946			−0.0191073
$292$	−1.19558	−	2.07081i	−0.0699662	−	0.121185i
$293$	0.136485	+	0.236400i	0.00797356	+	0.0138106i	0.869985	−	0.493079i	$-0.164129\pi$
$293$	0.136485	+	0.236400i	0.00797356	+	0.0138106i	−0.862011	+	0.506889i	$0.830795\pi$
$294$	−2.31038			−0.134744
$295$	4.36153	+	7.55440i	0.253938	+	0.439834i
$296$	0.0334909	−	0.0580080i	0.00194662	−	0.00337165i
$297$	−0.303639	+	0.525918i	−0.0176189	+	0.0305169i
$298$	12.6214			0.731139
$299$		0			0
$300$	0.0224214			0.00129450
$301$	−8.58909	+	14.8767i	−0.495067	+	0.857481i
$302$	−1.02455	+	1.77457i	−0.0589560	+	0.102115i
$303$	−0.135322	−	0.234385i	−0.00777404	−	0.0134650i
$304$	−25.3192			−1.45216
$305$	3.16867	+	5.48830i	0.181437	+	0.314259i
$306$	−7.95961	−	13.7864i	−0.455021	−	0.788119i
$307$	6.85224			0.391078			0.195539	−	0.980696i	$-0.437354\pi$
$307$	6.85224			0.391078			0.195539	+	0.980696i	$0.437354\pi$
$308$	0.610491	+	1.05740i	0.0347859	+	0.0602510i
$309$	0.262793	−	0.455171i	0.0149498	−	0.0258938i
$310$	1.09479	−	1.89623i	0.0621798	−	0.107698i
$311$	10.6447			0.603605			0.301803	−	0.953370i	$-0.402412\pi$
$311$	10.6447			0.603605			0.301803	+	0.953370i	$0.402412\pi$
$312$		0			0
$313$	17.8236			1.00745			0.503724	−	0.863865i	$-0.331963\pi$
$313$	17.8236			1.00745			0.503724	+	0.863865i	$0.331963\pi$
$314$	8.95062	−	15.5029i	0.505113	−	0.874881i
$315$	−7.21857	+	12.5029i	−0.406721	+	0.704461i
$316$	−1.03883	−	1.79931i	−0.0584390	−	0.101219i
$317$	8.17161			0.458963			0.229482	−	0.973313i	$-0.426297\pi$
$317$	8.17161			0.458963			0.229482	+	0.973313i	$0.426297\pi$
$318$	0.0702410	+	0.121661i	0.00393892	+	0.00682241i
$319$	0.787651	+	1.36425i	0.0441000	+	0.0763835i
$320$	−6.84325			−0.382549
$321$	0.210481	+	0.364564i	0.0117479	+	0.0203480i
$322$	−25.5747	+	44.2967i	−1.42522	+	2.46856i
$323$	−10.1999	+	17.6667i	−0.567536	+	0.983001i
$324$	2.10978			0.117210
$325$		0			0
$326$	33.7556			1.86955
$327$	−0.653107	+	1.13122i	−0.0361169	+	0.0625563i
$328$	−0.353326	+	0.611979i	−0.0195092	+	0.0337909i
$329$	−15.7305	−	27.2460i	−0.867250	−	1.50212i
$330$	−0.151592			−0.00834486
$331$	−12.4698	−	21.5983i	−0.685400	−	1.18715i	−0.973311	−	0.229490i	$-0.926294\pi$
$331$	−12.4698	−	21.5983i	−0.685400	−	1.18715i	0.287911	−	0.957657i	$-0.407039\pi$
$332$	0.0858029	+	0.148615i	0.00470905	+	0.00815631i
$333$	0.0759666			0.00416294
$334$	6.12934	+	10.6163i	0.335383	+	0.580900i
$335$	2.58658	−	4.48009i	0.141320	−	0.244773i
$336$	1.01047	−	1.75019i	0.0551258	−	0.0954807i
$337$	−19.6057			−1.06799			−0.533996	−	0.845487i	$-0.679310\pi$
$337$	−19.6057			−1.06799			−0.533996	+	0.845487i	$0.679310\pi$
$338$		0			0
$339$	−0.762471			−0.0414117
$340$	0.420915	−	0.729047i	0.0228273	−	0.0395381i
$341$	−0.782847	+	1.35593i	−0.0423936	+	0.0734278i
$342$	−12.8200	−	22.2049i	−0.693225	−	1.20070i
$343$	44.8817			2.42339
$344$	−4.69286	−	8.12828i	−0.253022	−	0.438247i
$345$	−0.335823	−	0.581663i	−0.0180801	−	0.0313157i
$346$	13.7104			0.737076
$347$	−8.54049	−	14.7926i	−0.458478	−	0.794107i	0.540403	−	0.841406i	$-0.318272\pi$
$347$	−8.54049	−	14.7926i	−0.458478	−	0.794107i	−0.998881	+	0.0472996i	$0.984938\pi$
$348$	−0.0165143	+	0.0286036i	−0.000885259	+	0.00153331i
$349$	14.1860	−	24.5708i	0.759357	−	1.31525i	−0.183822	−	0.982960i	$-0.558847\pi$
$349$	14.1860	−	24.5708i	0.759357	−	1.31525i	0.943179	−	0.332286i	$-0.107820\pi$
$350$	−7.21857			−0.385849
$351$		0			0
$352$	−1.42371			−0.0758840
$353$	−10.6260	+	18.4047i	−0.565564	+	0.979586i	0.431433	+	0.902145i	$0.358008\pi$
$353$	−10.6260	+	18.4047i	−0.565564	+	0.979586i	−0.996997	+	0.0774407i	$0.975325\pi$
$354$	0.618272	−	1.07088i	0.0328608	−	0.0569165i
$355$	−3.88244	−	6.72458i	−0.206058	−	0.356904i
$356$	3.19488			0.169328
$357$	−0.814139	−	1.41013i	−0.0430888	−	0.0746320i
$358$	−7.50520	−	12.9994i	−0.396662	−	0.687039i
$359$	32.6519			1.72330			0.861650	−	0.507502i	$-0.169431\pi$
$359$	32.6519			1.72330			0.861650	+	0.507502i	$0.169431\pi$
$360$	−3.94405	−	6.83129i	−0.207870	−	0.360041i
$361$	−6.92820	+	12.0000i	−0.364642	+	0.631579i
$362$	12.7296	−	22.0484i	0.669055	−	1.15884i
$363$	−0.934265			−0.0490362
$364$		0			0
$365$	−10.1088			−0.529118
$366$	0.449176	−	0.777997i	0.0234788	−	0.0406665i
$367$	2.95918	−	5.12546i	0.154468	−	0.267547i	−0.778397	−	0.627772i	$-0.783967\pi$
$367$	2.95918	−	5.12546i	0.154468	−	0.267547i	0.932865	+	0.360226i	$0.117300\pi$
$368$	−15.6495	−	27.1057i	−0.815785	−	1.41298i
$369$	−0.801440			−0.0417213
$370$	0.0189916	+	0.0328945i	0.000987329	+	0.00171010i
$371$	−2.39174	−	4.14261i	−0.124173	−	0.215073i
$372$	−0.0328271			−0.00170201
$373$	6.65926	+	11.5342i	0.344803	+	0.597217i	0.985318	−	0.170729i	$-0.0546123\pi$
$373$	6.65926	+	11.5342i	0.344803	+	0.597217i	−0.640515	+	0.767946i	$0.721279\pi$
$374$	−2.84583	+	4.92912i	−0.147154	+	0.254879i
$375$	0.0473938	−	0.0820885i	0.00244740	−	0.00423903i
$376$	17.1895			0.886480
$377$		0			0
$378$	4.09924			0.210842
$379$	−12.7093	+	22.0131i	−0.652832	+	1.13074i	0.329601	+	0.944120i	$0.393086\pi$
$379$	−12.7093	+	22.0131i	−0.652832	+	1.13074i	−0.982433	+	0.186617i	$0.940248\pi$
$380$	0.677939	−	1.17422i	0.0347775	−	0.0602364i
$381$	−0.0334909	−	0.0580080i	−0.00171579	−	0.00297184i
$382$	5.79869			0.296687
$383$	5.41342	+	9.37632i	0.276613	+	0.479107i	0.970541	−	0.240937i	$-0.0774547\pi$
$383$	5.41342	+	9.37632i	0.276613	+	0.479107i	−0.693928	+	0.720044i	$0.744121\pi$
$384$	0.611228	+	1.05868i	0.0311916	+	0.0540254i
$385$	5.16177			0.263068
$386$	0.937641	+	1.62404i	0.0477247	+	0.0826615i
$387$	5.32235	−	9.21857i	0.270550	−	0.468606i
$388$	0.406701	−	0.704427i	0.0206471	−	0.0357618i
$389$	−23.0370			−1.16802			−0.584011	−	0.811746i	$-0.698518\pi$
$389$	−23.0370			−1.16802			−0.584011	+	0.811746i	$0.698518\pi$
$390$		0			0
$391$	−25.2176			−1.27531
$392$	−21.4915	+	37.2244i	−1.08549	+	1.88012i
$393$	−0.296948	+	0.514329i	−0.0149790	+	0.0259444i
$394$	−11.4271	−	19.7924i	−0.575691	−	0.997126i
$395$	−8.78347			−0.441944
$396$	−0.378299	−	0.655233i	−0.0190102	−	0.0329267i
$397$	−10.5432	−	18.2614i	−0.529149	−	0.916512i	−0.999422	−	0.0339917i	$-0.989178\pi$
$397$	−10.5432	−	18.2614i	−0.529149	−	0.916512i	0.470273	−	0.882521i	$-0.344155\pi$
$398$	19.7850			0.991731
$399$	−1.31128	−	2.27120i	−0.0656459	−	0.113702i
$400$	2.20857	−	3.82535i	0.110428	−	0.191267i
$401$	9.88845	−	17.1273i	0.493805	−	0.855296i	−0.506169	−	0.862434i	$-0.668939\pi$
$401$	9.88845	−	17.1273i	0.493805	−	0.855296i	0.999975	+	0.00713812i	$0.00227215\pi$
$402$	−0.733324			−0.0365749
$403$		0			0
$404$	0.675394			0.0336021
$405$	4.45961	−	7.72427i	0.221600	−	0.383822i
$406$	5.31679	−	9.20895i	0.263868	−	0.457033i
$407$	−0.0135803	−	0.0235218i	−0.000673151	−	0.00116593i
$408$	0.889650			0.0440443
$409$	15.9404	+	27.6096i	0.788204	+	1.36521i	0.927066	+	0.374897i	$0.122322\pi$
$409$	15.9404	+	27.6096i	0.788204	+	1.36521i	−0.138862	+	0.990312i	$0.544345\pi$
$410$	−0.200360	−	0.347034i	−0.00989508	−	0.0171388i
$411$	1.54559			0.0762382
$412$	0.655802	+	1.13588i	0.0323090	+	0.0559609i
$413$	−21.0524	+	36.4639i	−1.03592	+	1.79427i
$414$	15.8477	−	27.4490i	0.778872	−	1.34905i
$415$	0.725474			0.0356121
$416$		0			0
$417$	−0.646952			−0.0316814
$418$	−4.58358	+	7.93899i	−0.224190	+	0.388309i
$419$	−15.3648	+	26.6127i	−0.750621	+	1.30011i	0.196902	+	0.980423i	$0.436912\pi$
$419$	−15.3648	+	26.6127i	−0.750621	+	1.30011i	−0.947522	+	0.319690i	$0.896421\pi$
$420$	0.0541121	+	0.0937250i	0.00264040	+	0.00457331i
$421$	17.9820			0.876391			0.438195	−	0.898880i	$-0.355618\pi$
$421$	17.9820			0.876391			0.438195	+	0.898880i	$0.355618\pi$
$422$	−3.59701	−	6.23021i	−0.175100	−	0.303282i
$423$	9.74761	+	16.8834i	0.473945	+	0.820897i
$424$	2.61357			0.126926
$425$	−1.77944	−	3.08209i	−0.0863157	−	0.149503i
$426$	−0.550357	+	0.953247i	−0.0266649	+	0.0461850i
$427$	−15.2947	+	26.4911i	−0.740160	+	1.28200i
$428$	−1.05051			−0.0507785
$429$		0			0
$430$	5.32235			0.256666
$431$	−2.44974	+	4.24308i	−0.118000	+	0.204382i	−0.918975	−	0.394316i	$-0.870982\pi$
$431$	−2.44974	+	4.24308i	−0.118000	+	0.204382i	0.800975	+	0.598698i	$0.204315\pi$
$432$	−1.25419	+	2.17232i	−0.0603421	+	0.104516i
$433$	9.61972	+	16.6618i	0.462294	+	0.800717i	0.999075	−	0.0430048i	$-0.0136931\pi$
$433$	9.61972	+	16.6618i	0.462294	+	0.800717i	−0.536781	+	0.843722i	$0.680360\pi$
$434$	10.5687			0.507315
$435$	0.0698151	+	0.120923i	0.00334738	+	0.00579783i
$436$	−1.62983	−	2.82296i	−0.0780549	−	0.135195i
$437$	−40.6162			−1.94294
$438$	0.716489	+	1.24100i	0.0342352	+	0.0592970i
$439$	4.27987	−	7.41295i	0.204267	−	0.353801i	−0.745632	−	0.666358i	$-0.767852\pi$
$439$	4.27987	−	7.41295i	0.204267	−	0.353801i	0.949899	+	0.312557i	$0.101186\pi$
$440$	−1.41013	+	2.44242i	−0.0672253	+	0.116438i
$441$	−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	$0.857821\pi$
$444$	0.000284732	0	0.000493170i	1.35128e−5	0	2.34048e-5i
$445$	6.75327	−	11.6970i	0.320136	−	0.554491i
$446$	11.0019	+	19.0558i	0.520954	+	0.902318i
$447$	−0.799965			−0.0378370
$448$	−16.5156	−	28.6059i	−0.780290	−	1.35150i
$449$	13.3531	+	23.1283i	0.630173	+	1.09149i	0.987516	+	0.157518i	$0.0503492\pi$
$449$	13.3531	+	23.1283i	0.630173	+	1.09149i	−0.357344	+	0.933973i	$0.616317\pi$
$450$	4.47309			0.210863
$451$	0.143271	+	0.248153i	0.00674637	+	0.0116851i
$452$	0.951375	−	1.64783i	0.0447489	−	0.0775074i
$453$	0.0649373	−	0.112475i	0.00305102	−	0.00528453i
$454$	−22.2873			−1.04599
$455$		0			0
$456$	1.43290			0.0671016
$457$	2.13563	−	3.69903i	0.0999007	−	0.173033i	−0.811743	−	0.584015i	$-0.801481\pi$
$457$	2.13563	−	3.69903i	0.0999007	−	0.173033i	0.911643	+	0.410982i	$0.134814\pi$
$458$	−14.4371	+	25.0059i	−0.674604	+	1.16845i
$459$	1.01050	+	1.75024i	0.0471661	+	0.0816941i
$460$	1.67610			0.0781485
$461$	−10.3211	−	17.8767i	−0.480704	−	0.832603i	0.519051	−	0.854743i	$-0.326285\pi$
$461$	−10.3211	−	17.8767i	−0.480704	−	0.832603i	−0.999755	+	0.0221401i	$0.992952\pi$
$462$	−0.365855	−	0.633679i	−0.0170211	−	0.0294814i
$463$	−32.1040			−1.49200			−0.745999	−	0.665947i	$-0.768028\pi$
$463$	−32.1040			−1.49200			−0.745999	+	0.665947i	$0.768028\pi$
$464$	3.25341	+	5.63507i	0.151036	+	0.261602i
$465$	−0.0693893	+	0.120186i	−0.00321785	+	0.00557349i
$466$	−15.8477	+	27.4490i	−0.734131	+	1.27155i
$467$	23.3774			1.08178			0.540888	−	0.841095i	$-0.318088\pi$
$467$	23.3774			1.08178			0.540888	+	0.841095i	$0.318088\pi$
$468$		0			0
$469$	24.9700			1.15301
$470$	−4.87381	+	8.44168i	−0.224812	+	0.389386i
$471$	−0.567304	+	0.982600i	−0.0261400	+	0.0452758i
$472$	−11.5025	−	19.9229i	−0.529446	−	0.917027i
$473$	−3.80584			−0.174993
$474$	0.622553	+	1.07829i	0.0285948	+	0.0495277i
$475$	−2.86603	−	4.96410i	−0.131502	−	0.227769i
$476$	4.06338			0.186245
$477$	1.48207	+	2.56702i	0.0678594	+	0.117536i
$478$	−11.1393	+	19.2939i	−0.509502	+	0.882483i
$479$	2.58767	−	4.48198i	0.118234	−	0.204787i	−0.800834	−	0.598886i	$-0.795610\pi$
$479$	2.58767	−	4.48198i	0.118234	−	0.204787i	0.919068	+	0.394100i	$0.128943\pi$
$480$	−0.126194			−0.00575992
$481$		0			0
$482$	−14.0453			−0.639747
$483$	1.62096	−	2.80759i	0.0737564	−	0.127750i
$484$	1.16573	−	2.01911i	0.0529879	−	0.0917777i
$485$	−1.71935	−	2.97800i	−0.0780717	−	0.135224i
$486$	−3.81213			−0.172922
$487$	15.3865	+	26.6501i	0.697227	+	1.20763i	0.969424	+	0.245391i	$0.0789165\pi$
$487$	15.3865	+	26.6501i	0.697227	+	1.20763i	−0.272197	+	0.962242i	$0.587750\pi$
$488$	−8.35661	−	14.4741i	−0.378286	−	0.655211i
$489$	−2.13948			−0.0967508
$490$	−12.1872	−	21.1088i	−0.550560	−	0.953598i
$491$	−17.8992	+	31.0023i	−0.807778	+	1.39911i	0.106622	+	0.994300i	$0.465997\pi$
$491$	−17.8992	+	31.0023i	−0.807778	+	1.39911i	−0.914400	+	0.404813i	$0.867337\pi$
$492$	−0.00300389	+	0.00520289i	−0.000135426	+	0.000234565i
$493$	5.24255			0.236113
$494$		0			0
$495$	−3.19856			−0.143765
$496$	−3.23357	+	5.60070i	−0.145191	+	0.251479i
$497$	18.7399	−	32.4585i	0.840600	−	1.45596i
$498$	−0.0514200	−	0.0890620i	−0.00230418	−	0.00399096i
$499$	28.8971			1.29361			0.646805	−	0.762655i	$-0.276105\pi$
$499$	28.8971			1.29361			0.646805	+	0.762655i	$0.276105\pi$
$500$	0.118272	+	0.204852i	0.00528927	+	0.00916128i
$501$	−0.388487	−	0.672879i	−0.0173563	−	0.0300620i
$502$	−16.9237			−0.755340
$503$	3.93161	+	6.80974i	0.175302	+	0.303631i	0.940266	−	0.340442i	$-0.110577\pi$
$503$	3.93161	+	6.80974i	0.175302	+	0.303631i	−0.764964	+	0.644073i	$0.777243\pi$
$504$	19.0373	−	32.9735i	0.847988	−	1.46876i
$505$	1.42763	−	2.47273i	0.0635289	−	0.110035i
$506$	−11.3322			−0.503777
$507$		0			0
$508$	0.167154			0.00741625
$509$	14.0057	−	24.2585i	0.620790	−	1.07524i	−0.368549	−	0.929608i	$-0.620145\pi$
$509$	14.0057	−	24.2585i	0.620790	−	1.07524i	0.989339	−	0.145631i	$-0.0465213\pi$
$510$	−0.252246	+	0.436903i	−0.0111696	+	0.0193464i
$511$	−24.3968	−	42.2564i	−1.07925	−	1.86931i
$512$	17.4176			0.769757
$513$	1.62754	+	2.81898i	0.0718577	+	0.124461i
$514$	−19.8394	−	34.3628i	−0.875076	−	1.51568i
$515$	5.54488			0.244337
$516$	−0.0398976	−	0.0691046i	−0.00175639	−	0.00304216i
$517$	3.48510	−	6.03637i	0.153275	−	0.265479i
$518$	−0.0916696	+	0.158776i	−0.00402773	+	0.00697623i
$519$	−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	$0.807581\pi$
$522$	−3.29462	+	5.70645i	−0.144202	+	0.249765i
$523$	22.6553	−	39.2401i	0.990647	−	1.71585i	0.377154	−	0.926151i	$-0.376903\pi$
$523$	22.6553	−	39.2401i	0.990647	−	1.71585i	0.613493	−	0.789700i	$-0.289764\pi$
$524$	−0.741035	−	1.28351i	−0.0323723	−	0.0560704i
$525$	0.457524			0.0199680
$526$	−10.5738	−	18.3144i	−0.461040	−	0.798545i
$527$	2.60529	+	4.51249i	0.113488	+	0.196567i
$528$	0.447742			0.0194855
$529$	−13.6043	−	23.5633i	−0.591491	−	1.02449i
$530$	−0.741035	+	1.28351i	−0.0321885	+	0.0557522i
$531$	13.0454	−	22.5953i	0.566123	−	0.980553i
$532$	6.54460			0.283744
$533$		0			0
$534$	−1.91463			−0.0828540
$535$	−2.22056	+	3.84611i	−0.0960030	+	0.166282i
$536$	−6.82149	+	11.8152i	−0.294644	+	0.510338i
$537$	0.475691	+	0.823922i	0.0205276	+	0.0355548i
$538$	−37.0504			−1.59736
$539$	8.71465	+	15.0942i	0.375367	+	0.650154i
$540$	−0.0671633	−	0.116330i	−0.00289025	−	0.00500606i
$541$	19.7445			0.848882			0.424441	−	0.905456i	$-0.360471\pi$
$541$	19.7445			0.848882			0.424441	+	0.905456i	$0.360471\pi$
$542$	13.9958	+	24.2414i	0.601171	+	1.04126i
$543$	−0.806824	+	1.39746i	−0.0346242	+	0.0599708i
$544$	−2.36903	+	4.10328i	−0.101571	+	0.175927i
$545$	−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	$0.581395\pi$
$548$	−1.92851	+	3.34028i	−0.0823820	+	0.142690i
$549$	9.47754	−	16.4156i	0.404491	−	0.700600i
$550$	−0.799640	−	1.38502i	−0.0340968	−	0.0590573i
$551$	8.44381			0.359718
$552$	0.885654	+	1.53400i	0.0376959	+	0.0652913i
$553$	−21.1982	−	36.7164i	−0.901439	−	1.56134i
$554$	33.8952			1.44007
$555$	−0.00120372	−	0.00208490i	−5.10951e−5	−	8.84992e-5i
$556$	0.807237	−	1.39818i	0.0342345	−	0.0592958i
$557$	2.02310	−	3.50412i	0.0857217	−	0.148474i	−0.819977	−	0.572397i	$-0.806014\pi$
$557$	2.02310	−	3.50412i	0.0857217	−	0.148474i	0.905699	+	0.423922i	$0.139347\pi$
$558$	−6.54905			−0.277244
$559$		0			0
$560$	21.3208			0.900968
$561$	0.180373	−	0.312415i	0.00761536	−	0.0131902i
$562$	−20.8163	+	36.0549i	−0.878083	+	1.52088i
$563$	−1.94963	−	3.37686i	−0.0821671	−	0.142318i	0.822013	−	0.569468i	$-0.192851\pi$
$563$	−1.94963	−	3.37686i	−0.0821671	−	0.142318i	−0.904181	+	0.427151i	$0.859517\pi$
$564$	0.146141			0.00615364
$565$	−4.02200	−	6.96630i	−0.169207	−	0.293074i
$566$	5.92226	+	10.2577i	0.248931	+	0.431162i
$567$	43.0516			1.80800
$568$	10.2390	+	17.7345i	0.429619	+	0.744123i
$569$	8.66778	−	15.0130i	0.363372	−	0.629379i	−0.625141	−	0.780512i	$-0.714959\pi$
$569$	8.66778	−	15.0130i	0.363372	−	0.629379i	0.988514	+	0.151133i	$0.0482920\pi$
$570$	−0.406275	+	0.703689i	−0.0170170	+	0.0294743i
$571$	29.5118			1.23503			0.617515	−	0.786559i	$-0.288140\pi$
$571$	29.5118			1.23503			0.617515	+	0.786559i	$0.288140\pi$
$572$		0			0
$573$	−0.367530			−0.0153538
$574$	0.967106	−	1.67508i	0.0403662	−	0.0699163i
$575$	3.54290	−	6.13649i	0.147749	−	0.255909i
$576$	10.2341	+	17.7260i	0.426422	+	0.738585i
$577$	−28.3684			−1.18099			−0.590496	−	0.807041i	$-0.701068\pi$
$577$	−28.3684			−1.18099			−0.590496	+	0.807041i	$0.701068\pi$
$578$	−3.24100	−	5.61357i	−0.134808	−	0.233494i
$579$	−0.0594291	−	0.102934i	−0.00246979	−	0.00427780i
$580$	−0.348448			−0.0144685
$581$	1.75087	+	3.03260i	0.0726384	+	0.125813i
$582$	−0.243728	+	0.422149i	−0.0101028	+	0.0174986i
$583$	0.529891	−	0.917797i	0.0219458	−	0.0380113i
$584$	26.6595			1.10318
$585$		0			0
$586$	0.408230			0.0168638
$587$	17.1939	−	29.7806i	0.709667	−	1.22918i	−0.255314	−	0.966858i	$-0.582179\pi$
$587$	17.1939	−	29.7806i	0.709667	−	1.22918i	0.964981	−	0.262320i	$-0.0844877\pi$
$588$	−0.182716	+	0.316473i	−0.00753507	+	0.0130511i
$589$	4.19615	+	7.26795i	0.172899	+	0.299471i
$590$	13.0454			0.537071
$591$	0.724270	+	1.25447i	0.0297925	+	0.0516021i
$592$	−0.0560937	−	0.0971572i	−0.00230544	−	0.00399314i
$593$	−5.47612			−0.224877			−0.112439	−	0.993659i	$-0.535866\pi$
$593$	−5.47612			−0.224877			−0.112439	+	0.993659i	$0.535866\pi$
$594$	0.454095	+	0.786515i	0.0186317	+	0.0322711i
$595$	8.58909	−	14.8767i	0.352118	−	0.609887i
$596$	0.998159	−	1.72886i	0.0408862	−	0.0708170i
$597$	−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	$0.210777\pi$
$600$	−0.124990	+	0.216489i	−0.00510269	+	0.00883812i
$601$	−3.28948	+	5.69754i	−0.134181	+	0.232408i	−0.925284	−	0.379275i	$-0.876174\pi$
$601$	−3.28948	+	5.69754i	−0.134181	+	0.232408i	0.791104	+	0.611682i	$0.209507\pi$
$602$	12.8451	+	22.2483i	0.523525	+	0.906772i
$603$	−15.4730			−0.630109
$604$	0.162052	+	0.280682i	0.00659379	+	0.0114208i
$605$	−4.92820	−	8.53590i	−0.200360	−	0.347034i
$606$	−0.404750			−0.0164418
$607$	8.38318	+	14.5201i	0.340263	+	0.589352i	0.984481	−	0.175489i	$-0.0561507\pi$
$607$	8.38318	+	14.5201i	0.340263	+	0.589352i	−0.644219	+	0.764841i	$0.722817\pi$
$608$	−3.81563	+	6.60886i	−0.154744	+	0.268025i
$609$	−0.336986	+	0.583678i	−0.0136554	+	0.0236518i
$610$	9.47754			0.383734
$611$		0			0
$612$	−2.51793			−0.101781
$613$	14.3894	−	24.9232i	0.581184	−	1.00664i	−0.414155	−	0.910206i	$-0.635923\pi$
$613$	14.3894	−	24.9232i	0.581184	−	1.00664i	0.995339	−	0.0964341i	$-0.0307437\pi$
$614$	5.12379	−	8.87466i	0.206779	−	0.358152i
$615$	0.0126991	+	0.0219955i	0.000512078	+	0.000886946i
$616$	−13.6129			−0.548481
$617$	−18.6645	−	32.3279i	−0.751406	−	1.30147i	−0.947141	−	0.320817i	$-0.896043\pi$
$617$	−18.6645	−	32.3279i	−0.751406	−	1.30147i	0.195735	−	0.980657i	$-0.437291\pi$
$618$	−0.393009	−	0.680712i	−0.0158091	−	0.0273822i
$619$	−12.7535			−0.512606			−0.256303	−	0.966597i	$-0.582504\pi$
$619$	−12.7535			−0.512606			−0.256303	+	0.966597i	$0.582504\pi$
$620$	−0.173162	−	0.299925i	−0.00695434	−	0.0120453i
$621$	−2.01192	+	3.48475i	−0.0807356	+	0.139838i
$622$	7.95961	−	13.7864i	0.319151	−	0.552786i
$623$	65.1939			2.61194
$624$		0			0
$625$	1.00000			0.0400000
$626$	13.3276	−	23.0842i	0.532680	−	0.922629i
$627$	0.290514	−	0.503185i	0.0116020	−	0.0200953i
$628$	−1.41571	−	2.45209i	−0.0564931	−	0.0978489i
$629$	−0.0903896			−0.00360407
$630$	10.7954	+	18.6982i	0.430100	+	0.744956i
$631$	14.3621	+	24.8759i	0.571746	+	0.990294i	0.996387	+	0.0849315i	$0.0270672\pi$
$631$	14.3621	+	24.8759i	0.571746	+	0.990294i	−0.424641	+	0.905362i	$0.639600\pi$
$632$	23.1643			0.921427
$633$	0.227984	+	0.394880i	0.00906156	+	0.0156951i
$634$	6.11035	−	10.5834i	0.242673	−	0.420322i
$635$	0.353326	−	0.611979i	0.0140213	−	0.0242856i
$636$	0.0222199			0.000881077
$637$		0			0
$638$	2.35588			0.0932701
$639$	−11.6124	+	20.1133i	−0.459381	+	0.795671i
$640$	−6.44840	+	11.1690i	−0.254895	+	0.441492i
$641$	11.1985	+	19.3964i	0.442315	+	0.766112i	0.997861	−	0.0653739i	$-0.0208240\pi$
$641$	11.1985	+	19.3964i	0.442315	+	0.766112i	−0.555546	+	0.831486i	$0.687491\pi$
$642$	0.629552			0.0248464
$643$	−7.08209	−	12.2665i	−0.279290	−	0.483745i	0.691918	−	0.721976i	$-0.256766\pi$
$643$	−7.08209	−	12.2665i	−0.279290	−	0.483745i	−0.971209	+	0.238231i	$0.923433\pi$
$644$	4.04513	+	7.00637i	0.159400	+	0.276090i
$645$	−0.337339			−0.0132827
$646$	15.2540	+	26.4207i	0.600160	+	1.03951i
$647$	11.8048	−	20.4466i	0.464096	−	0.803838i	−0.535064	−	0.844812i	$-0.679713\pi$
$647$	11.8048	−	20.4466i	0.464096	−	0.803838i	0.999160	+	0.0409732i	$0.0130458\pi$
$648$	−11.7612	+	20.3709i	−0.462022	+	0.800246i
$649$	−9.32835			−0.366170
$650$		0			0
$651$	−0.669862			−0.0262540
$652$	2.66955	−	4.62379i	0.104548	−	0.181082i
$653$	−16.6383	+	28.8183i	−0.651105	+	1.12775i	0.331750	+	0.943367i	$0.392361\pi$
$653$	−16.6383	+	28.8183i	−0.651105	+	1.12775i	−0.982855	+	0.184380i	$0.940972\pi$
$654$	0.976727	+	1.69174i	0.0381930	+	0.0661523i
$655$	−6.26554			−0.244815
$656$	0.591784	+	1.02500i	0.0231053	+	0.0400195i
$657$	15.1178	+	26.1848i	0.589801	+	1.02156i
$658$	−47.0502			−1.83421
$659$	−11.5454	−	19.9972i	−0.449745	−	0.778982i	0.548624	−	0.836069i	$-0.315152\pi$
$659$	−11.5454	−	19.9972i	−0.449745	−	0.778982i	−0.998369	+	0.0570875i	$0.981819\pi$
$660$	−0.0119886	+	0.0207648i	−0.000466655	+	0.000808270i
$661$	−6.71826	+	11.6364i	−0.261310	+	0.452602i	−0.966590	−	0.256326i	$-0.917488\pi$
$661$	−6.71826	+	11.6364i	−0.261310	+	0.452602i	0.705280	+	0.708929i	$0.250821\pi$
$662$	−37.2972			−1.44960
$663$		0			0
$664$	−1.91326			−0.0742491
$665$	13.8338	−	23.9609i	0.536453	−	0.929164i
$666$	0.0568043	−	0.0983879i	0.00220112	−	0.00381245i
$667$	5.21900	+	9.03957i	0.202080	+	0.350014i
$668$	1.93895			0.0750200
$669$	−0.697316	−	1.20779i	−0.0269598	−	0.0466957i
$670$	−3.86825	−	6.70001i	−0.149444	−	0.258844i
$671$	−6.77708			−0.261626
$672$	−0.304558	−	0.527510i	−0.0117486	−	0.0203491i
$673$	0.972620	−	1.68463i	0.0374918	−	0.0649376i	−0.846671	−	0.532117i	$-0.821397\pi$
$673$	0.972620	−	1.68463i	0.0374918	−	0.0649376i	0.884162	+	0.467180i	$0.154730\pi$
$674$	−14.6603	+	25.3923i	−0.564692	+	0.978075i
$675$	−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	$0.341404\pi$
$678$	−0.570140	+	0.987512i	−0.0218961	+	0.0379252i
$679$	8.29903	−	14.3743i	0.318488	−	0.551637i
$680$	4.69286	+	8.12828i	0.179963	+	0.311705i
$681$	1.41260			0.0541310
$682$	1.17075	+	2.02781i	0.0448305	+	0.0776487i
$683$	−7.31107	−	12.6631i	−0.279750	−	0.484542i	0.691572	−	0.722307i	$-0.256918\pi$
$683$	−7.31107	−	12.6631i	−0.279750	−	0.484542i	−0.971323	+	0.237766i	$0.923585\pi$
$684$	−4.05545			−0.155064
$685$	8.15290	+	14.1212i	0.311506	+	0.539545i
$686$	33.5605	−	58.1285i	1.28135	−	2.21935i
$687$	0.915049	−	1.58491i	0.0349113	−	0.0604681i
$688$	−15.7201			−0.599323
$689$		0			0
$690$	−1.00445			−0.0382388
$691$	−1.76225	+	3.05231i	−0.0670393	+	0.116115i	−0.897597	−	0.440817i	$-0.854689\pi$
$691$	−1.76225	+	3.05231i	−0.0670393	+	0.116115i	0.830558	+	0.556933i	$0.188022\pi$
$692$	1.08428	−	1.87803i	0.0412182	−	0.0713920i
$693$	−7.71947	−	13.3705i	−0.293238	−	0.507904i
$694$	−25.5447			−0.969665
$695$	−3.41264	−	5.91087i	−0.129449	−	0.224212i
$696$	−0.184121	−	0.318907i	−0.00697909	−	0.0120881i
$697$	0.953601			0.0361202
$698$	−21.2152	−	36.7458i	−0.803008	−	1.39085i
$699$	1.00445	−	1.73976i	0.0379919	−	0.0658038i
$700$	−0.570878	+	0.988789i	−0.0215772	+	0.0373727i
$701$	−1.53457			−0.0579599			−0.0289800	−	0.999580i	$-0.509226\pi$
$701$	−1.53457			−0.0579599			−0.0289800	+	0.999580i	$0.509226\pi$
$702$		0			0
$703$	−0.145584			−0.00549081
$704$	3.65905	−	6.33766i	0.137906	−	0.238860i
$705$	0.308909	−	0.535047i	0.0116342	−	0.0201510i
$706$	15.8912	+	27.5244i	0.598075	+	1.03590i
$707$	13.7819			0.518322
$708$	−0.0977915	−	0.169380i	−0.00367523	−	0.00636568i
$709$	7.00262	+	12.1289i	0.262989	+	0.455510i	0.967035	−	0.254644i	$-0.0819583\pi$
$709$	7.00262	+	12.1289i	0.262989	+	0.455510i	−0.704046	+	0.710155i	$0.748625\pi$
$710$	−11.6124			−0.435807
$711$	13.1357	+	22.7518i	0.492629	+	0.853259i
$712$	−17.8101	+	30.8481i	−0.667463	+	1.15608i
$713$	−5.18717	+	8.98444i	−0.194261	+	0.336470i
$714$	−2.43510			−0.0911314
$715$		0			0
$716$	−2.37418			−0.0887274
$717$	0.706029	−	1.22288i	0.0263671	−	0.0456692i
$718$	24.4156	−	42.2890i	0.911181	−	1.57821i
$719$	−11.2381	−	19.4649i	−0.419109	−	0.725918i	0.576741	−	0.816927i	$-0.304324\pi$
$719$	−11.2381	−	19.4649i	−0.419109	−	0.725918i	−0.995850	+	0.0910091i	$0.970991\pi$
$720$	−13.2117			−0.492372
$721$	13.3821	+	23.1785i	0.498376	+	0.863213i
$722$	10.3612	+	17.9461i	0.385603	+	0.667884i
$723$	0.890215			0.0331074
$724$	−2.01344	−	3.48737i	−0.0748288	−	0.129607i
$725$	−0.736543	+	1.27573i	−0.0273545	+	0.0473794i
$726$	−0.698600	+	1.21001i	−0.0259275	+	0.0449077i
$727$	−10.3421			−0.383566			−0.191783	−	0.981437i	$-0.561427\pi$
$727$	−10.3421			−0.383566			−0.191783	+	0.981437i	$0.561427\pi$
$728$		0			0
$729$	−26.5160			−0.982075
$730$	−7.55889	+	13.0924i	−0.279767	+	0.484571i
$731$	−6.33285	+	10.9688i	−0.234229	+	0.405696i
$732$	−0.0710459	−	0.123055i	−0.00262593	−	0.00454824i
$733$	−27.3533			−1.01032			−0.505159	−	0.863026i	$-0.668566\pi$
$733$	−27.3533			−1.01032			−0.505159	+	0.863026i	$0.668566\pi$
$734$	−4.42548	−	7.66516i	−0.163348	−	0.282926i
$735$	0.772442	+	1.33791i	0.0284919	+	0.0493495i
$736$	−9.43355			−0.347725
$737$	2.76606	+	4.79096i	0.101889	+	0.176477i
$738$	−0.599280	+	1.03798i	−0.0220598	+	0.0382087i
$739$	−6.72583	+	11.6495i	−0.247413	+	0.428533i	−0.962807	−	0.270189i	$-0.912914\pi$
$739$	−6.72583	+	11.6495i	−0.247413	+	0.428533i	0.715394	+	0.698721i	$0.246247\pi$
$740$	0.00600778			0.000220851
$741$		0			0
$742$	−7.15372			−0.262621
$743$	8.19632	−	14.1964i	0.300694	−	0.520817i	−0.675599	−	0.737269i	$-0.736115\pi$
$743$	8.19632	−	14.1964i	0.300694	−	0.520817i	0.976293	+	0.216452i	$0.0694484\pi$
$744$	0.182998	−	0.316962i	0.00670903	−	0.0116204i
$745$	−4.21978	−	7.30887i	−0.154601	−	0.267776i
$746$	19.9179			0.729248
$747$	−1.08495	−	1.87919i	−0.0396963	−	0.0687560i
$748$	0.450122	+	0.779635i	0.0164581	+	0.0285063i
$749$	−21.4365			−0.783274
$750$	−0.0708778	−	0.122764i	−0.00258809	−	0.00448270i
$751$	13.8328	−	23.9590i	0.504764	−	0.874277i	−0.495221	−	0.868767i	$-0.664913\pi$
$751$	13.8328	−	23.9590i	0.504764	−	0.874277i	0.999985	−	0.00551009i	$-0.00175392\pi$
$752$	14.3953	−	24.9334i	0.524942	−	0.909226i
$753$	1.07265			0.0390895
$754$		0			0
$755$	1.37017			0.0498654
$756$	0.324187	−	0.561508i	0.0117906	−	0.0204218i
$757$	−11.4989	+	19.9167i	−0.417935	+	0.723885i	−0.995732	−	0.0922961i	$-0.970579\pi$
$757$	−11.4989	+	19.9167i	−0.417935	+	0.723885i	0.577797	+	0.816181i	$0.303913\pi$
$758$	19.0068	+	32.9208i	0.690359	+	1.19574i
$759$	0.718251			0.0260709
$760$	7.55846	+	13.0916i	0.274174	+	0.474884i
$761$	3.83221	+	6.63759i	0.138918	+	0.240612i	0.927087	−	0.374846i	$-0.122304\pi$
$761$	3.83221	+	6.63759i	0.138918	+	0.240612i	−0.788170	+	0.615458i	$0.788971\pi$
$762$	−0.100172			−0.00362885
$763$	−33.2580	−	57.6045i	−1.20402	−	2.08542i
$764$	0.458587	−	0.794296i	0.0165911	−	0.0287366i
$765$	−5.32235	+	9.21857i	−0.192430	+	0.333298i
$766$	16.1916			0.585027
$767$		0			0
$768$	0.530882			0.0191566
$769$	3.61548	−	6.26219i	0.130377	−	0.225820i	−0.793445	−	0.608642i	$-0.791714\pi$
$769$	3.61548	−	6.26219i	0.130377	−	0.225820i	0.923822	+	0.382822i	$0.125048\pi$
$770$	3.85973	−	6.68525i	0.139095	−	0.240920i
$771$	1.25745	+	2.17797i	0.0452859	+	0.0784375i
$772$	0.296612			0.0106753
$773$	16.7998	+	29.0981i	0.604246	+	1.04658i	0.992170	+	0.124893i	$0.0398588\pi$
$773$	16.7998	+	29.0981i	0.604246	+	1.04658i	−0.387924	+	0.921691i	$0.626808\pi$
$774$	−7.95961	−	13.7864i	−0.286102	−	0.495544i
$775$	−1.46410			−0.0525921
$776$	4.53438	+	7.85378i	0.162775	+	0.281934i
$777$	0.00581016	−	0.0100635i	0.000208438	−	0.000361026i
$778$	−17.2260	+	29.8363i	−0.617582	+	1.06968i
$779$	1.53590			0.0550293
$780$		0			0
$781$	8.30368			0.297129
$782$	−18.8565	+	32.6605i	−0.674309	+	1.16794i
$783$	0.418264	−	0.724454i	0.0149475	−	0.0258899i
$784$	35.9960	+	62.3470i	1.28557	+	2.22668i
$785$	−11.9700			−0.427228
$786$	0.444088	+	0.769182i	0.0158401	+	0.0274358i
$787$	1.48584	+	2.57355i	0.0529645	+	0.0917371i	0.891292	−	0.453430i	$-0.149800\pi$
$787$	1.48584	+	2.57355i	0.0529645	+	0.0917371i	−0.838328	+	0.545167i	$0.816466\pi$
$788$	−3.61484			−0.128773
$789$	0.670185	+	1.16079i	0.0238592	+	0.0413254i
$790$	−6.56787	+	11.3759i	−0.233674	+	0.404736i
$791$	19.4135	−	33.6252i	0.690265	−	1.19557i
$792$	8.43544			0.299740
$793$		0			0
$794$	−31.5349			−1.11913
$795$	0.0469680	−	0.0813509i	0.00166578	−	0.00288522i
$796$	1.56469	−	2.71012i	0.0554588	−	0.0960575i
$797$	11.2875	+	19.5506i	0.399825	+	0.692517i	0.993704	−	0.112037i	$-0.0357375\pi$
$797$	11.2875	+	19.5506i	0.399825	+	0.692517i	−0.593879	+	0.804554i	$0.702404\pi$
$798$	−3.92205			−0.138839
$799$	−11.5983	−	20.0888i	−0.410318	−	0.710692i
$800$	−0.665665	−	1.15297i	−0.0235348	−	0.0407635i
$801$	−40.3983			−1.42740
$802$	−14.7882	−	25.6140i	−0.522191	−	0.904462i
$803$	5.40512	−	9.36194i	0.190742	−	0.330376i
$804$	−0.0579946	+	0.100450i	−0.00204531	+	0.00354259i
$805$	34.2020			1.20546
$806$		0			0
$807$	2.34831			0.0826646
$808$	−3.76505	+	6.52125i	−0.132454	+	0.229417i
$809$	−6.82921	+	11.8285i	−0.240102	+	0.415869i	−0.960743	−	0.277439i	$-0.910514\pi$
$809$	−6.82921	+	11.8285i	−0.240102	+	0.415869i	0.720641	+	0.693308i	$0.243848\pi$
$810$	−6.66938	−	11.5517i	−0.234338	−	0.405886i
$811$	14.1147			0.495636			0.247818	−	0.968807i	$-0.420287\pi$
$811$	14.1147			0.495636			0.247818	+	0.968807i	$0.420287\pi$
$812$	−0.840952	−	1.45657i	−0.0295116	−	0.0511157i
$813$	−0.887075	−	1.53646i	−0.0311111	−	0.0538860i
$814$	−0.0406189			−0.00142369
$815$	−11.2857	−	19.5474i	−0.395320	−	0.684714i
$816$	0.745035	−	1.29044i	0.0260814	−	0.0451744i
$817$	−10.1999	+	17.6667i	−0.356848	+	0.618079i
$818$	47.6781			1.66703
$819$		0			0
$820$	−0.0633815			−0.00221338
$821$	−0.792808	+	1.37318i	−0.0276692	+	0.0479244i	−0.879528	−	0.475846i	$-0.842142\pi$
$821$	−0.792808	+	1.37318i	−0.0276692	+	0.0479244i	0.851859	+	0.523771i	$0.175475\pi$
$822$	1.15572	−	2.00176i	0.0403103	−	0.0698195i
$823$	−9.28238	−	16.0776i	−0.323563	−	0.560428i	0.657657	−	0.753317i	$-0.271548\pi$
$823$	−9.28238	−	16.0776i	−0.323563	−	0.560428i	−0.981221	+	0.192889i	$0.938214\pi$
$824$	−14.6233			−0.509427
$825$	0.0506824	+	0.0877845i	0.00176454	+	0.00305626i
$826$	31.4840	+	54.5320i	1.09547	+	1.89741i
$827$	9.01023			0.313316			0.156658	−	0.987653i	$-0.449928\pi$
$827$	9.01023			0.313316			0.156658	+	0.987653i	$0.449928\pi$
$828$	−2.50662	−	4.34159i	−0.0871110	−	0.150881i
$829$	−23.5588	+	40.8051i	−0.818233	+	1.41722i	0.0887506	+	0.996054i	$0.471713\pi$
$829$	−23.5588	+	40.8051i	−0.818233	+	1.41722i	−0.906983	+	0.421167i	$0.861621\pi$
$830$	0.542476	−	0.939595i	0.0188296	−	0.0326138i
$831$	−2.14833			−0.0745247
$832$		0			0
$833$	58.0041			2.00972
$834$	−0.483761	+	0.837898i	−0.0167513	+	0.0290141i
$835$	4.09850	−	7.09881i	0.141835	−	0.245665i
$836$	0.724980	+	1.25570i	0.0250740	+	0.0434294i
$837$	0.831425			0.0287383
$838$	22.9782	+	39.7994i	0.793769	+	1.37485i
$839$	26.7383	+	46.3121i	0.923108	+	1.59887i	0.794576	+	0.607164i	$0.207693\pi$
$839$	26.7383	+	46.3121i	0.923108	+	1.59887i	0.128531	+	0.991705i	$0.458974\pi$
$840$	−1.20661			−0.0416321
$841$	13.4150	+	23.2355i	0.462586	+	0.801223i
$842$	13.4461	−	23.2894i	0.463384	−	0.802605i
$843$	1.31937	−	2.28521i	0.0454415	−	0.0787070i
$844$	−1.13787			−0.0391672
$845$		0			0
$846$	29.1553			1.00238
$847$	23.7876	−	41.2014i	0.817353	−	1.41570i
$848$	2.18872	−	3.79098i	0.0751611	−	0.130183i
$849$	−0.375362	−	0.650146i	−0.0128824	−	0.0223130i
$850$	−5.32235			−0.182555
$851$	−0.0899835	−	0.155856i	−0.00308460	−	0.00534268i
$852$	0.0870495	+	0.150774i	0.00298227	+	0.00516544i
$853$	27.7756			0.951019			0.475510	−	0.879711i	$-0.342264\pi$
$853$	27.7756			0.951019			0.475510	+	0.879711i	$0.342264\pi$
$854$	22.8733	+	39.6177i	0.782707	+	1.35569i
$855$	−8.57233	+	14.8477i	−0.293167	+	0.507781i
$856$	5.85619	−	10.1432i	0.200160	−	0.346688i
$857$	53.6917			1.83407			0.917037	−	0.398801i	$-0.130574\pi$
$857$	53.6917			1.83407			0.917037	+	0.398801i	$0.130574\pi$
$858$		0			0
$859$	2.08958			0.0712955			0.0356477	−	0.999364i	$-0.488651\pi$
$859$	2.08958			0.0712955			0.0356477	+	0.999364i	$0.488651\pi$
$860$	0.420915	−	0.729047i	0.0143531	−	0.0248603i
$861$	−0.0612966	+	0.106169i	−0.00208898	+	0.00361823i
$862$	3.66361	+	6.34556i	0.124783	+	0.216131i
$863$	1.75413			0.0597113			0.0298557	−	0.999554i	$-0.490495\pi$
$863$	1.75413			0.0597113			0.0298557	+	0.999554i	$0.490495\pi$
$864$	0.378014	+	0.654739i	0.0128603	+	0.0222747i
$865$	−4.58386	−	7.93948i	−0.155856	−	0.269950i
$866$	28.7727			0.977737
$867$	0.205419	+	0.355797i	0.00697640	+	0.0120835i
$868$	0.835823	−	1.44769i	0.0283697	−	0.0491377i
$869$	4.69647	−	8.13453i	0.159317	−	0.275945i
$870$	0.208818			0.00707960
$871$		0			0
$872$	36.3426			1.23072
$873$	−5.14261	+	8.90726i	−0.174051	+	0.301465i
$874$	−30.3709	+	52.6040i	−1.02731	+	1.77936i
$875$	2.41342	+	4.18016i	0.0815885	+	0.141315i
$876$	0.226653			0.00765789
$877$	10.7836	+	18.6777i	0.364136	+	0.630702i	0.988637	−	0.150322i	$-0.0480311\pi$
$877$	10.7836	+	18.6777i	0.364136	+	0.630702i	−0.624501	+	0.781024i	$0.714698\pi$
$878$	−6.40058	−	11.0861i	−0.216009	−	0.374139i
$879$	−0.0258742			−0.000872716
$880$	2.36182	+	4.09079i	0.0796169	+	0.137900i
$881$	−12.5132	+	21.6734i	−0.421579	+	0.730196i	−0.996094	−	0.0882978i	$-0.971857\pi$
$881$	−12.5132	+	21.6734i	−0.421579	+	0.730196i	0.574515	+	0.818494i	$0.305191\pi$
$882$	−36.4520	+	63.1367i	−1.22740	+	2.12592i
$883$	−48.7832			−1.64169			−0.820843	−	0.571154i	$-0.806496\pi$
$883$	−48.7832			−1.64169			−0.820843	+	0.571154i	$0.806496\pi$
$884$		0			0
$885$	−0.826838			−0.0277939
$886$	−28.3886	+	49.1705i	−0.953734	+	1.65192i
$887$	16.8967	−	29.2659i	0.567334	−	0.982651i	−0.429494	−	0.903070i	$-0.641308\pi$
$887$	16.8967	−	29.2659i	0.567334	−	0.982651i	0.996828	−	0.0795819i	$-0.0253585\pi$
$888$	0.00317453	+	0.00549844i	0.000106530	+	0.000184516i
$889$	3.41090			0.114398
$890$	−10.0996	−	17.4930i	−0.338538	−	0.586365i
$891$	4.76906	+	8.26025i	0.159769	+	0.276729i
$892$	3.48031			0.116530
$893$	−18.6806	−	32.3557i	−0.625121	−	1.08274i
$894$	−0.598177	+	1.03607i	−0.0200060	+	0.0346515i
$895$	−5.01850	+	8.69229i	−0.167750	+	0.290551i
$896$	−62.2508			−2.07965
$897$		0			0
$898$	39.9394			1.33279
$899$	1.07837	−	1.86780i	0.0359658	−	0.0622946i
$900$	0.353752	−	0.612717i	0.0117917	−	0.0204239i
$901$	−1.76346	−	3.05440i	−0.0587493	−	0.101757i
$902$	0.428526			0.0142683
$903$	−0.814139	−	1.41013i	−0.0270929	−	0.0469262i
$904$	10.6071	+	18.3720i	0.352786	+	0.611043i
$905$	−17.0238			−0.565892
$906$	−0.0971143	−	0.168207i	−0.00322641	−	0.00558830i
$907$	17.3135	−	29.9879i	0.574885	−	0.995731i	−0.421169	−	0.906982i	$-0.638380\pi$
$907$	17.3135	−	29.9879i	0.574885	−	0.995731i	0.996054	−	0.0887485i	$-0.0282867\pi$
$908$	−1.76258	+	3.05288i	−0.0584932	+	0.101313i
$909$	−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	$0.327187\pi$
$912$	1.19997	−	2.07842i	0.0397351	−	0.0688233i
$913$	−0.387907	+	0.671874i	−0.0128378	+	0.0222358i
$914$	−3.19386	−	5.53192i	−0.105643	−	0.182980i
$915$	−0.600701			−0.0198586
$916$	2.28351	+	3.95516i	0.0754493	+	0.130682i
$917$	−15.1214	−	26.1910i	−0.499352	−	0.864903i
$918$	3.02242			0.0997548
$919$	25.9610	+	44.9658i	0.856374	+	1.48328i	0.875364	+	0.483464i	$0.160621\pi$
$919$	25.9610	+	44.9658i	0.856374	+	1.48328i	−0.0189904	+	0.999820i	$0.506045\pi$
$920$	−9.34356	+	16.1835i	−0.308048	+	0.533555i
$921$	−0.324753	+	0.562490i	−0.0107010	+	0.0185347i
$922$	−30.8707			−1.01667
$923$		0			0
$924$	−0.115734			−0.00380736
$925$	0.0126991	−	0.0219955i	0.000417545	−	0.000723209i
$926$	−24.0059	+	41.5794i	−0.788882	+	1.36638i
$927$	−8.29242	−	14.3629i	−0.272359	−	0.471739i
$928$	1.96117			0.0643784
$929$	10.2457	+	17.7462i	0.336152	+	0.582232i	0.983705	−	0.179788i	$-0.0575411\pi$
$929$	10.2457	+	17.7462i	0.336152	+	0.582232i	−0.647553	+	0.762020i	$0.724208\pi$
$930$	0.103772	+	0.179739i	0.00340283	+	0.00589387i
$931$	93.4231			3.06182
$932$	2.50662	+	4.34159i	0.0821070	+	0.142213i
$933$	−0.504492	+	0.873806i	−0.0165163	+	0.0286071i
$934$	17.4805	−	30.2771i	0.571980	−	0.990698i
$935$	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	$0.724459\pi$
$938$	18.6714	−	32.3399i	0.609644	−	1.05593i
$939$	−0.844727	+	1.46311i	−0.0275666	+	0.0477468i
$940$	0.770886	+	1.33521i	0.0251435	+	0.0435499i
$941$	19.6189			0.639557			0.319779	−	0.947492i	$-0.396391\pi$
$941$	19.6189			0.639557			0.319779	+	0.947492i	$0.396391\pi$
$942$	0.848408	+	1.46949i	0.0276426	+	0.0478784i
$943$	0.949318	+	1.64427i	0.0309140	+	0.0535447i
$944$	−38.5309			−1.25408
$945$	−1.37052	−	2.37381i	−0.0445829	−	0.0772199i
$946$	−2.84583	+	4.92912i	−0.0925259	+	0.160260i
$947$	28.6062	−	49.5474i	0.929576	−	1.61007i	0.145544	−	0.989352i	$-0.453507\pi$
$947$	28.6062	−	49.5474i	0.929576	−	1.61007i	0.784032	−	0.620721i	$-0.213160\pi$
$948$	0.196937			0.00639623
$949$		0			0
$950$	−8.57233			−0.278123
$951$	−0.387283	+	0.670795i	−0.0125585	+	0.0217520i
$952$	−22.6517	+	39.2339i	−0.734146	+	1.27158i
$953$	−13.7385	−	23.7958i	−0.445033	−	0.770820i	0.553021	−	0.833167i	$-0.313475\pi$
$953$	−13.7385	−	23.7958i	−0.445033	−	0.770820i	−0.998055	+	0.0623470i	$0.980141\pi$
$954$	4.43290			0.143520
$955$	−1.93870	−	3.35793i	−0.0627350	−	0.108660i
$956$	1.76190	+	3.05170i	0.0569840	+	0.0986991i
$957$	−0.149319			−0.00482680
$958$	−3.86988	−	6.70283i	−0.125030	−	0.216559i
$959$	−39.3527	+	68.1609i	−1.27077	+	2.20103i
$960$	0.324328	−	0.561752i	0.0104676	−	0.0181305i
$961$	−28.8564			−0.930852
$962$		0			0
$963$	13.2834			0.428053
$964$	−1.11077	+	1.92391i	−0.0357755	+	0.0619649i
$965$	0.626972	−	1.08595i	0.0201829	−	0.0349579i
$966$	−2.42416	−	4.19877i	−0.0779962	−	0.135093i
$967$	10.3643			0.333293			0.166647	−	0.986017i	$-0.446706\pi$
$967$	10.3643			0.333293			0.166647	+	0.986017i	$0.446706\pi$
$968$	12.9970	+	22.5114i	0.417738	+	0.723544i
$969$	−0.966821	−	1.67458i	−0.0310588	−	0.0537953i
$970$	−5.14261			−0.165119
$971$	−20.8758	−	36.1579i	−0.669935	−	1.16036i	−0.977922	−	0.208971i	$-0.932989\pi$
$971$	−20.8758	−	36.1579i	−0.669935	−	1.16036i	0.307987	−	0.951391i	$-0.400345\pi$
$972$	−0.301481	+	0.522180i	−0.00966999	+	0.0167489i
$973$	16.4723	−	28.5308i	0.528077	−	0.914656i
$974$	46.0212			1.47461
$975$		0			0
$976$	−27.9929			−0.896030
$977$	−6.89691	+	11.9458i	−0.220652	+	0.382180i	−0.955006	−	0.296586i	$-0.904152\pi$
$977$	−6.89691	+	11.9458i	−0.220652	+	0.382180i	0.734354	+	0.678766i	$0.237485\pi$
$978$	−1.59981	+	2.77095i	−0.0511562	+	0.0886051i
$979$	7.22187	+	12.5087i	0.230812	+	0.399778i
$980$	−3.85527			−0.123152
$981$	20.6088	+	35.6954i	0.657987	+	1.13967i
$982$	26.7683	+	46.3641i	0.854212	+	1.47954i
$983$	−37.9997			−1.21200			−0.606002	−	0.795463i	$-0.707227\pi$
$983$	−37.9997			−1.21200			−0.606002	+	0.795463i	$0.707227\pi$
$984$	−0.0334909	−	0.0580080i	−0.00106765	−	0.00184923i
$985$	−7.64098	+	13.2346i	−0.243462	+	0.421688i
$986$	3.92014	−	6.78988i	0.124843	−	0.216234i
$987$	2.98211			0.0949217
$988$		0			0
$989$	−25.2176			−0.801873
$990$	−2.39174	+	4.14261i	−0.0760143	+	0.131661i
$991$	26.2765	−	45.5122i	0.834700	−	1.44574i	−0.0595748	−	0.998224i	$-0.518974\pi$
$991$	26.2765	−	45.5122i	0.834700	−	1.44574i	0.894275	−	0.447519i	$-0.147692\pi$
$992$	0.974602	+	1.68806i	0.0309436	+	0.0535960i
$993$	2.36396			0.0750179
$994$	−28.0257	−	48.5419i	−0.888920	−	1.53966i
$995$	−6.61480	−	11.4572i	−0.209703	−	0.363217i
$996$	−0.0162661			−0.000515411
$997$	−9.29497	−	16.0994i	−0.294375	−	0.509872i	0.680465	−	0.732781i	$-0.261778\pi$
$997$	−9.29497	−	16.0994i	−0.294375	−	0.509872i	−0.974839	+	0.222909i	$0.928445\pi$
$998$	21.6079	−	37.4260i	0.683986	−	1.18470i
$999$	−0.00721150	+	0.0124907i	−0.000228162	+	0.000395188i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.m.a.36.4	✓	8	13.2	odd	12
65.2.m.a.56.4	yes	8	13.8	odd	4
325.2.m.b.49.4		8	65.2	even	12
325.2.m.b.199.4		8	65.8	even	4
325.2.m.c.49.1		8	65.28	even	12
325.2.m.c.199.1		8	65.47	even	4
325.2.n.d.101.1		8	65.54	odd	12
325.2.n.d.251.1		8	65.34	odd	4
585.2.bu.c.316.1		8	39.8	even	4
585.2.bu.c.361.1		8	39.2	even	12
845.2.a.l.1.4		4	13.4	even	6
845.2.a.m.1.1		4	13.9	even	3
845.2.c.g.506.2		8	13.7	odd	12
845.2.c.g.506.7		8	13.6	odd	12
845.2.e.m.146.4		8	13.3	even	3	inner
845.2.e.m.191.4		8	1.1	even	1	trivial
845.2.e.n.146.1		8	13.10	even	6
845.2.e.n.191.1		8	13.12	even	2
845.2.m.g.316.1		8	13.5	odd	4
845.2.m.g.361.1		8	13.11	odd	12
1040.2.da.b.641.3		8	52.47	even	4
1040.2.da.b.881.3		8	52.15	even	12
4225.2.a.bi.1.4		4	65.9	even	6
4225.2.a.bl.1.1		4	65.4	even	6
7605.2.a.cf.1.4		4	39.35	odd	6
7605.2.a.cj.1.1		4	39.17	odd	6

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.e (of order \(3\), degree \(2\), not minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more