LMFDB - Embedded newform 845.2.e.n.146.1

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			146.1
Root			$0.665665 - 1.24775i$ of defining polynomial
Character	$\chi$	$=$	845.146
Dual form			845.2.e.n.191.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.747754 - 1.29515i) q^{2} +(-0.0473938 - 0.0820885i) q^{3} +(-0.118272 + 0.204852i) q^{4} +1.00000 q^{5} +(-0.0708778 + 0.122764i) q^{6} +(2.41342 - 4.18016i) q^{7} -2.63726 q^{8} +(1.49551 - 2.59030i) q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

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

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	−0.999438	−	0.0335125i	$-0.989331\pi$
$2$	−0.747754	−	1.29515i	−0.528742	−	0.915808i	0.470696	−	0.882295i	$-0.344003\pi$
$3$	−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
$5$	1.00000			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	0.101218	−	0.994864i	$-0.467726\pi$
$7$	2.41342	−	4.18016i	0.912187	−	1.57995i	0.810969	−	0.585089i	$-0.198941\pi$
$8$	−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	$-0.218208\pi$
$11$	−0.534695	−	0.926118i	−0.161217	−	0.279235i	−0.935305	+	0.353842i	$0.884875\pi$
$12$	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	−0.997009	−	0.0772795i	$-0.975377\pi$
$17$	−1.77944	+	3.08209i	−0.431579	+	0.747516i	0.565431	+	0.824796i	$0.308710\pi$
$18$	−4.47309			−1.05432
$19$	2.86603	−	4.96410i	0.657511	−	1.13884i	−0.323747	−	0.946144i	$-0.604943\pi$
$19$	2.86603	−	4.96410i	0.657511	−	1.13884i	0.981258	−	0.192699i	$-0.0617242\pi$
$20$	−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	0.953060	+	0.302781i	$0.0979150\pi$
$23$	3.54290	+	6.13649i	0.738746	+	1.27955i	−0.214314	+	0.976765i	$0.568752\pi$
$24$	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	0.789501	−	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
$31$	1.46410			0.262960			0.131480	−	0.991319i	$-0.458027\pi$
$31$	1.46410			0.262960			0.131480	+	0.991319i	$0.458027\pi$
$32$	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	$-0.167331\pi$
$37$	−0.0126991	−	0.0219955i	−0.00208772	−	0.00361604i	−0.867067	+	0.498191i	$0.833998\pi$
$38$	−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	$-0.160006\pi$
$41$	0.133975	+	0.232051i	0.0209233	+	0.0362402i	−0.855374	+	0.518011i	$0.826673\pi$
$42$	0.342116	+	0.592562i	0.0527896	+	0.0914342i
$43$	−1.77944	+	3.08209i	−0.271363	+	0.470014i	−0.969211	−	0.246232i	$-0.920808\pi$
$43$	−1.77944	+	3.08209i	−0.271363	+	0.470014i	0.697848	+	0.716246i	$0.254141\pi$
$44$	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	$-0.657685\pi$
$47$	−6.51793			−0.950738			−0.475369	+	0.879787i	$0.657685\pi$
$48$	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	−0.428958	−	0.903325i	$-0.641119\pi$
$59$	4.36153	−	7.55440i	0.567823	−	0.983499i	0.996781	−	0.0801741i	$-0.0255476\pi$
$60$	0.0224214			0.00289458
$61$	−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
$63$	−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	$-0.0643263\pi$
$67$	2.58658	+	4.48009i	0.316001	+	0.547330i	−0.663649	+	0.748044i	$0.730993\pi$
$68$	−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	$-0.985757\pi$
$71$	−3.88244	+	6.72458i	−0.460761	+	0.798061i	0.538238	+	0.842793i	$0.319090\pi$
$72$	−3.94405	+	6.83129i	−0.464810	+	0.805075i
$73$	−10.1088			−1.18314			−0.591572	−	0.806252i	$-0.701493\pi$
$73$	−10.1088			−1.18314			−0.591572	+	0.806252i	$0.701493\pi$
$74$	−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	$-0.487323\pi$
$83$	0.725474			0.0796311			0.0398155	+	0.999207i	$0.487323\pi$
$84$	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	0.962633	+	0.270810i	$0.0872916\pi$
$89$	6.75327	+	11.6970i	0.715845	+	1.23988i	−0.246788	+	0.969070i	$0.579375\pi$
$90$	−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	$-0.889188\pi$
$97$	−1.71935	+	2.97800i	−0.174574	+	0.302371i	0.765440	+	0.643507i	$0.222521\pi$
$98$	−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	0.786215	−	0.617953i	$-0.212038\pi$
$101$	−1.42763	−	2.47273i	−0.142055	−	0.246046i	−0.928270	+	0.371906i	$0.878704\pi$
$102$	−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	0.953170	−	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
$109$	−13.7804			−1.31993			−0.659963	−	0.751298i	$-0.729428\pi$
$109$	−13.7804			−1.31993			−0.659963	+	0.751298i	$0.729428\pi$
$110$	−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	−0.612466	−	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
$115$	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	0.849923	−	0.526906i	$-0.176648\pi$
$127$	−0.353326	−	0.611979i	−0.0313526	−	0.0543044i	−0.881276	+	0.472602i	$0.843315\pi$
$128$	−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	−0.273107	−	0.961984i	$-0.588051\pi$
$137$	8.15290	−	14.1212i	0.696549	−	1.20646i	0.969656	−	0.244475i	$-0.0786155\pi$
$138$	−1.00445			−0.0855046
$139$	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
$141$	0.308909	+	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	$-0.945691\pi$
$149$	−4.21978	+	7.30887i	−0.345698	+	0.598766i	0.639783	+	0.768556i	$0.279024\pi$
$150$	−0.0708778	+	0.122764i	−0.00578715	+	0.0100236i
$151$	1.37017			0.111503			0.0557513	−	0.998445i	$-0.482245\pi$
$151$	1.37017			0.111503			0.0557513	+	0.998445i	$0.482245\pi$
$152$	−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	−0.0370630	+	0.999313i	$0.511800\pi$
$163$	−11.2857	+	19.5474i	−0.883962	+	1.53107i	−0.846899	+	0.531754i	$0.821533\pi$
$164$	−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	$-0.0639403\pi$
$167$	4.09850	+	7.09881i	0.317152	+	0.549323i	−0.662741	+	0.748849i	$0.730607\pi$
$168$	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	−0.637479	−	0.770467i	$-0.720023\pi$
$173$	4.58386	−	7.93948i	0.348505	−	0.603628i	0.985984	+	0.166840i	$0.0533563\pi$
$174$	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	0.990342	−	0.138646i	$-0.0442750\pi$
$179$	5.01850	+	8.69229i	0.375100	+	0.649693i	−0.615242	+	0.788338i	$0.710942\pi$
$180$	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	−0.787322	−	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
$193$	0.626972	+	1.08595i	0.0451304	+	0.0781681i	0.887708	−	0.460406i	$-0.152296\pi$
$193$	0.626972	+	1.08595i	0.0451304	+	0.0781681i	−0.842578	+	0.538575i	$0.818963\pi$
$194$	5.14261			0.369218
$195$		0			0
$196$	3.85527			0.275376
$197$	−7.64098	−	13.2346i	−0.544397	−	0.942923i	−0.998645	−	0.0520479i	$-0.983425\pi$
$197$	−7.64098	−	13.2346i	−0.544397	−	0.942923i	0.454247	−	0.890876i	$-0.349908\pi$
$198$	2.39174	+	4.14261i	0.169973	+	0.294402i
$199$	6.61480	−	11.4572i	0.468911	−	0.812177i	−0.530458	−	0.847711i	$-0.677980\pi$
$199$	6.61480	−	11.4572i	0.468911	−	0.812177i	0.999368	+	0.0355340i	$0.0113132\pi$
$200$	−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	0.936862	−	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
$213$	0.736014			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	$-0.00270031\pi$
$223$	7.35661	+	12.7420i	0.492635	+	0.853269i	−0.507329	+	0.861753i	$0.669367\pi$
$224$	−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	$-0.668660\pi$
$227$	7.45140	−	12.9062i	0.494567	−	0.856615i	0.999980	+	0.00626222i	$0.00199334\pi$
$228$	0.0642602	−	0.111302i	0.00425573	−	0.00737115i
$229$	19.3074			1.27587			0.637933	−	0.770092i	$-0.279790\pi$
$229$	19.3074			1.27587			0.637933	+	0.770092i	$0.279790\pi$
$230$	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	$-0.339981\pi$
$239$	14.8971			0.963612			0.481806	+	0.876278i	$0.339981\pi$
$240$	0.209345	−	0.362596i	0.0135131	−	0.0234055i
$241$	4.69584	−	8.13343i	0.302486	−	0.523921i	−0.674213	−	0.738537i	$-0.735517\pi$
$241$	4.69584	−	8.13343i	0.302486	−	0.523921i	0.976698	+	0.214617i	$0.0688502\pi$
$242$	−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	−0.987482	−	0.157733i	$-0.949582\pi$
$251$	−5.65817	+	9.80024i	−0.357140	+	0.618585i	0.630341	+	0.776318i	$0.282915\pi$
$252$	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	0.899987	+	0.435917i	$0.143576\pi$
$257$	13.2660	+	22.9773i	0.827508	+	1.43329i	−0.0724788	+	0.997370i	$0.523091\pi$
$258$	−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	0.997375	−	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
$265$	0.991015			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	0.189980	+	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
$271$	9.35856	+	16.2095i	0.568492	+	0.984657i	0.996715	+	0.0809839i	$0.0258062\pi$
$271$	9.35856	+	16.2095i	0.568492	+	0.984657i	−0.428224	+	0.903673i	$0.640860\pi$
$272$	−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	−0.293815	−	0.955862i	$-0.594925\pi$
$277$	11.3323	−	19.6282i	0.680893	−	1.17934i	0.974709	−	0.223480i	$-0.0717417\pi$
$278$	−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	$-0.188140\pi$
$281$	27.8384			1.66070			0.830351	+	0.557241i	$0.188140\pi$
$282$	0.461976	−	0.800167i	0.0275103	−	0.0476492i
$283$	−3.96004	−	6.85898i	−0.235400	−	0.407724i	0.723989	−	0.689811i	$-0.242307\pi$
$283$	−3.96004	−	6.85898i	−0.235400	−	0.407724i	−0.959389	+	0.282087i	$0.908973\pi$
$284$	−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	$-0.835871\pi$
$293$	−0.136485	+	0.236400i	−0.00797356	+	0.0138106i	0.862011	+	0.506889i	$0.169205\pi$
$294$	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	$-0.562646\pi$
$307$	−6.85224			−0.391078			−0.195539	+	0.980696i	$0.562646\pi$
$308$	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	$-0.573703\pi$
$317$	−8.17161			−0.458963			−0.229482	+	0.973313i	$0.573703\pi$
$318$	−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	−0.287911	−	0.957657i	$-0.592961\pi$
$331$	12.4698	−	21.5983i	0.685400	−	1.18715i	0.973311	−	0.229490i	$-0.0737059\pi$
$332$	−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	−0.998881	−	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
$349$	−14.1860	−	24.5708i	−0.759357	−	1.31525i	−0.943179	−	0.332286i	$-0.892180\pi$
$349$	−14.1860	−	24.5708i	−0.759357	−	1.31525i	0.183822	−	0.982960i	$-0.441153\pi$
$350$	−7.21857			−0.385849
$351$		0			0
$352$	−1.42371			−0.0758840
$353$	10.6260	+	18.4047i	0.565564	+	0.979586i	0.996997	+	0.0774407i	$0.0246749\pi$
$353$	10.6260	+	18.4047i	0.565564	+	0.979586i	−0.431433	+	0.902145i	$0.641992\pi$
$354$	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	$-0.830569\pi$
$359$	−32.6519			−1.72330			−0.861650	+	0.507502i	$0.830569\pi$
$360$	−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	0.932865	−	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
$369$	0.801440			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	−0.640515	−	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
$375$	−0.0473938	−	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	0.982433	+	0.186617i	$0.0597525\pi$
$379$	12.7093	+	22.0131i	0.652832	+	1.13074i	−0.329601	+	0.944120i	$0.606914\pi$
$380$	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	$-0.922545\pi$
$383$	−5.41342	+	9.37632i	−0.276613	+	0.479107i	0.693928	+	0.720044i	$0.255879\pi$
$384$	−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	−0.470273	−	0.882521i	$-0.655845\pi$
$397$	10.5432	−	18.2614i	0.529149	−	0.916512i	0.999422	−	0.0339917i	$-0.0108220\pi$
$398$	−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	$-0.331061\pi$
$401$	−9.88845	−	17.1273i	−0.493805	−	0.855296i	−0.999975	+	0.00713812i	$0.997728\pi$
$402$	−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	0.138862	+	0.990312i	$0.455655\pi$
$409$	−15.9404	+	27.6096i	−0.788204	+	1.36521i	−0.927066	+	0.374897i	$0.877678\pi$
$410$	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	−0.947522	−	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
$421$	−17.9820			−0.876391			−0.438195	−	0.898880i	$-0.644382\pi$
$421$	−17.9820			−0.876391			−0.438195	+	0.898880i	$0.644382\pi$
$422$	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	$-0.129018\pi$
$431$	2.44974	+	4.24308i	0.118000	+	0.204382i	−0.800975	+	0.598698i	$0.795685\pi$
$432$	−1.25419	−	2.17232i	−0.0603421	−	0.104516i
$433$	9.61972	−	16.6618i	0.462294	−	0.800717i	−0.536781	−	0.843722i	$-0.680360\pi$
$433$	9.61972	−	16.6618i	0.462294	−	0.800717i	0.999075	+	0.0430048i	$0.0136931\pi$
$434$	−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	0.949899	−	0.312557i	$-0.101186\pi$
$439$	4.27987	+	7.41295i	0.204267	+	0.353801i	−0.745632	+	0.666358i	$0.767852\pi$
$440$	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	0.357344	+	0.933973i	$0.383683\pi$
$449$	−13.3531	+	23.1283i	−0.630173	+	1.09149i	−0.987516	+	0.157518i	$0.949651\pi$
$450$	−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	$-0.198519\pi$
$457$	−2.13563	−	3.69903i	−0.0999007	−	0.173033i	−0.911643	+	0.410982i	$0.865186\pi$
$458$	−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	$-0.673715\pi$
$461$	10.3211	−	17.8767i	0.480704	−	0.832603i	0.999755	+	0.0221401i	$0.00704800\pi$
$462$	0.365855	−	0.633679i	0.0170211	−	0.0294814i
$463$	32.1040			1.49200			0.745999	−	0.665947i	$-0.231972\pi$
$463$	32.1040			1.49200			0.745999	+	0.665947i	$0.231972\pi$
$464$	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	$-0.204390\pi$
$479$	−2.58767	−	4.48198i	−0.118234	−	0.204787i	−0.919068	+	0.394100i	$0.871057\pi$
$480$	−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	0.272197	+	0.962242i	$0.412250\pi$
$487$	−15.3865	+	26.6501i	−0.697227	+	1.20763i	−0.969424	+	0.245391i	$0.921083\pi$
$488$	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	−0.914400	−	0.404813i	$-0.867337\pi$
$491$	−17.8992	−	31.0023i	−0.807778	−	1.39911i	0.106622	−	0.994300i	$-0.465997\pi$
$492$	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	$-0.723895\pi$
$499$	−28.8971			−1.29361			−0.646805	+	0.762655i	$0.723895\pi$
$500$	−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	−0.764964	−	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
$505$	−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	−0.989339	−	0.145631i	$-0.953479\pi$
$509$	−14.0057	−	24.2585i	−0.620790	−	1.07524i	0.368549	−	0.929608i	$-0.379855\pi$
$510$	−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	0.613493	+	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
$525$	−0.457524			−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	$-0.639529\pi$
$541$	−19.7445			−0.848882			−0.424441	+	0.905456i	$0.639529\pi$
$542$	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	$-0.193986\pi$
$557$	−2.02310	−	3.50412i	−0.0857217	−	0.148474i	−0.905699	+	0.423922i	$0.860653\pi$
$558$	−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	−0.904181	−	0.427151i	$-0.859517\pi$
$563$	−1.94963	+	3.37686i	−0.0821671	+	0.142318i	0.822013	+	0.569468i	$0.192851\pi$
$564$	−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	0.988514	−	0.151133i	$-0.0482920\pi$
$569$	8.66778	+	15.0130i	0.363372	+	0.629379i	−0.625141	+	0.780512i	$0.714959\pi$
$570$	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	$-0.298932\pi$
$577$	28.3684			1.18099			0.590496	+	0.807041i	$0.298932\pi$
$578$	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	−0.964981	−	0.262320i	$-0.915512\pi$
$587$	−17.1939	−	29.7806i	−0.709667	−	1.22918i	0.255314	−	0.966858i	$-0.417821\pi$
$588$	−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	$-0.464134\pi$
$593$	5.47612			0.224877			0.112439	+	0.993659i	$0.464134\pi$
$594$	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	0.791104	−	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
$603$	15.4730			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	−0.644219	−	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
$609$	0.336986	+	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	−0.995339	−	0.0964341i	$-0.969256\pi$
$613$	−14.3894	−	24.9232i	−0.581184	−	1.00664i	0.414155	−	0.910206i	$-0.364077\pi$
$614$	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	−0.195735	−	0.980657i	$-0.562709\pi$
$617$	18.6645	−	32.3279i	0.751406	−	1.30147i	0.947141	−	0.320817i	$-0.103957\pi$
$618$	0.393009	−	0.680712i	0.0158091	−	0.0273822i
$619$	12.7535			0.512606			0.256303	−	0.966597i	$-0.417496\pi$
$619$	12.7535			0.512606			0.256303	+	0.966597i	$0.417496\pi$
$620$	−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	0.424641	+	0.905362i	$0.360400\pi$
$631$	−14.3621	+	24.8759i	−0.571746	+	0.990294i	−0.996387	+	0.0849315i	$0.972933\pi$
$632$	−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	−0.555546	−	0.831486i	$-0.687491\pi$
$641$	11.1985	−	19.3964i	0.442315	−	0.766112i	0.997861	+	0.0653739i	$0.0208240\pi$
$642$	−0.629552			−0.0248464
$643$	7.08209	−	12.2665i	0.279290	−	0.483745i	−0.691918	−	0.721976i	$-0.743234\pi$
$643$	7.08209	−	12.2665i	0.279290	−	0.483745i	0.971209	+	0.238231i	$0.0765675\pi$
$644$	−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	0.999160	−	0.0409732i	$-0.0130458\pi$
$647$	11.8048	+	20.4466i	0.464096	+	0.803838i	−0.535064	+	0.844812i	$0.679713\pi$
$648$	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	−0.982855	−	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
$655$	6.26554			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	−0.998369	−	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
$661$	6.71826	+	11.6364i	0.261310	+	0.452602i	0.966590	−	0.256326i	$-0.0825121\pi$
$661$	6.71826	+	11.6364i	0.261310	+	0.452602i	−0.705280	+	0.708929i	$0.749179\pi$
$662$	−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	0.884162	−	0.467180i	$-0.154730\pi$
$673$	0.972620	+	1.68463i	0.0374918	+	0.0649376i	−0.846671	+	0.532117i	$0.821397\pi$
$674$	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	$-0.743082\pi$
$683$	7.31107	−	12.6631i	0.279750	−	0.484542i	0.971323	+	0.237766i	$0.0764150\pi$
$684$	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	$-0.145311\pi$
$691$	1.76225	+	3.05231i	0.0670393	+	0.116115i	−0.830558	+	0.556933i	$0.811978\pi$
$692$	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	$-0.918042\pi$
$709$	−7.00262	+	12.1289i	−0.262989	+	0.455510i	0.704046	+	0.710155i	$0.251375\pi$
$710$	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	−0.995850	−	0.0910091i	$-0.970991\pi$
$719$	−11.2381	+	19.4649i	−0.419109	+	0.725918i	0.576741	+	0.816927i	$0.304324\pi$
$720$	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	$-0.331434\pi$
$733$	27.3533			1.01032			0.505159	+	0.863026i	$0.331434\pi$
$734$	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	$-0.0870861\pi$
$739$	6.72583	+	11.6495i	0.247413	+	0.428533i	−0.715394	+	0.698721i	$0.753753\pi$
$740$	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	$-0.263885\pi$
$743$	−8.19632	−	14.1964i	−0.300694	−	0.520817i	−0.976293	+	0.216452i	$0.930552\pi$
$744$	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	0.999985	+	0.00551009i	$0.00175392\pi$
$751$	13.8328	+	23.9590i	0.504764	+	0.874277i	−0.495221	+	0.868767i	$0.664913\pi$
$752$	−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	0.577797	−	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
$759$	−0.718251			−0.0260709
$760$	−7.55846	+	13.0916i	−0.274174	+	0.474884i
$761$	−3.83221	+	6.63759i	−0.138918	+	0.240612i	−0.927087	−	0.374846i	$-0.877696\pi$
$761$	−3.83221	+	6.63759i	−0.138918	+	0.240612i	0.788170	+	0.615458i	$0.211029\pi$
$762$	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	$-0.208286\pi$
$769$	−3.61548	−	6.26219i	−0.130377	−	0.225820i	−0.923822	+	0.382822i	$0.874952\pi$
$770$	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	0.387924	+	0.921691i	$0.373192\pi$
$773$	−16.7998	+	29.0981i	−0.604246	+	1.04658i	−0.992170	+	0.124893i	$0.960141\pi$
$774$	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	$-0.850200\pi$
$787$	−1.48584	+	2.57355i	−0.0529645	+	0.0917371i	0.838328	+	0.545167i	$0.183534\pi$
$788$	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	−0.593879	−	0.804554i	$-0.702404\pi$
$797$	11.2875	−	19.5506i	0.399825	−	0.692517i	0.993704	+	0.112037i	$0.0357375\pi$
$798$	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	0.720641	−	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
$811$	−14.1147			−0.495636			−0.247818	−	0.968807i	$-0.579713\pi$
$811$	−14.1147			−0.495636			−0.247818	+	0.968807i	$0.579713\pi$
$812$	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	$-0.157858\pi$
$821$	0.792808	+	1.37318i	0.0276692	+	0.0479244i	−0.851859	+	0.523771i	$0.824525\pi$
$822$	1.15572	+	2.00176i	0.0403103	+	0.0698195i
$823$	−9.28238	+	16.0776i	−0.323563	+	0.560428i	−0.981221	−	0.192889i	$-0.938214\pi$
$823$	−9.28238	+	16.0776i	−0.323563	+	0.560428i	0.657657	+	0.753317i	$0.271548\pi$
$824$	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	$-0.550072\pi$
$827$	−9.01023			−0.313316			−0.156658	+	0.987653i	$0.550072\pi$
$828$	−2.50662	+	4.34159i	−0.0871110	+	0.150881i
$829$	−23.5588	−	40.8051i	−0.818233	−	1.41722i	−0.906983	−	0.421167i	$-0.861621\pi$
$829$	−23.5588	−	40.8051i	−0.818233	−	1.41722i	0.0887506	−	0.996054i	$-0.471713\pi$
$830$	−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	−0.128531	+	0.991705i	$0.541026\pi$
$839$	−26.7383	+	46.3121i	−0.923108	+	1.59887i	−0.794576	+	0.607164i	$0.792307\pi$
$840$	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	$-0.657736\pi$
$853$	−27.7756			−0.951019			−0.475510	+	0.879711i	$0.657736\pi$
$854$	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	$-0.509505\pi$
$863$	−1.75413			−0.0597113			−0.0298557	+	0.999554i	$0.509505\pi$
$864$	−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	$-0.951969\pi$
$877$	−10.7836	+	18.6777i	−0.364136	+	0.630702i	0.624501	+	0.781024i	$0.285302\pi$
$878$	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	0.574515	−	0.818494i	$-0.305191\pi$
$881$	−12.5132	−	21.6734i	−0.421579	−	0.730196i	−0.996094	+	0.0882978i	$0.971857\pi$
$882$	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	0.996828	+	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
$889$	−3.41090			−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	0.996054	+	0.0887485i	$0.0282867\pi$
$907$	17.3135	+	29.9879i	0.574885	+	0.995731i	−0.421169	+	0.906982i	$0.638380\pi$
$908$	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	−0.0189904	−	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
$921$	0.324753	+	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	$-0.942459\pi$
$929$	−10.2457	+	17.7462i	−0.336152	+	0.582232i	0.647553	+	0.762020i	$0.275792\pi$
$930$	−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	$-0.603609\pi$
$941$	−19.6189			−0.639557			−0.319779	+	0.947492i	$0.603609\pi$
$942$	−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	−0.784032	−	0.620721i	$-0.786840\pi$
$947$	−28.6062	−	49.5474i	−0.929576	−	1.61007i	−0.145544	−	0.989352i	$-0.546493\pi$
$948$	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	−0.998055	−	0.0623470i	$-0.980141\pi$
$953$	−13.7385	+	23.7958i	−0.445033	+	0.770820i	0.553021	+	0.833167i	$0.313475\pi$
$954$	−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	$-0.553294\pi$
$967$	−10.3643			−0.333293			−0.166647	+	0.986017i	$0.553294\pi$
$968$	−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	0.307987	+	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
$973$	−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	$-0.0958482\pi$
$977$	6.89691	+	11.9458i	0.220652	+	0.382180i	−0.734354	+	0.678766i	$0.762515\pi$
$978$	−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	$-0.292773\pi$
$983$	37.9997			1.21200			0.606002	+	0.795463i	$0.292773\pi$
$984$	−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	0.894275	+	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
$993$	−2.36396			−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	−0.974839	−	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
$999$	0.00721150	+	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.n.146.1		8
13.2	odd	12		845.2.c.g.506.2		8
13.3	even	3		845.2.a.l.1.4		4
13.4	even	6		845.2.e.m.191.4		8
13.5	odd	4		845.2.m.g.361.1		8
13.6	odd	12		65.2.m.a.56.4	yes	8
13.7	odd	12		845.2.m.g.316.1		8
13.8	odd	4		65.2.m.a.36.4	✓	8
13.9	even	3	inner	845.2.e.n.191.1		8
13.10	even	6		845.2.a.m.1.1		4
13.11	odd	12		845.2.c.g.506.7		8
13.12	even	2		845.2.e.m.146.4		8
39.8	even	4		585.2.bu.c.361.1		8
39.23	odd	6		7605.2.a.cf.1.4		4
39.29	odd	6		7605.2.a.cj.1.1		4
39.32	even	12		585.2.bu.c.316.1		8
52.19	even	12		1040.2.da.b.641.3		8
52.47	even	4		1040.2.da.b.881.3		8
65.8	even	4		325.2.m.c.49.1		8
65.19	odd	12		325.2.n.d.251.1		8
65.29	even	6		4225.2.a.bl.1.1		4
65.32	even	12		325.2.m.c.199.1		8
65.34	odd	4		325.2.n.d.101.1		8
65.47	even	4		325.2.m.b.49.4		8
65.49	even	6		4225.2.a.bi.1.4		4
65.58	even	12		325.2.m.b.199.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.m.a.36.4	✓	8	13.8	odd	4
65.2.m.a.56.4	yes	8	13.6	odd	12
325.2.m.b.49.4		8	65.47	even	4
325.2.m.b.199.4		8	65.58	even	12
325.2.m.c.49.1		8	65.8	even	4
325.2.m.c.199.1		8	65.32	even	12
325.2.n.d.101.1		8	65.34	odd	4
325.2.n.d.251.1		8	65.19	odd	12
585.2.bu.c.316.1		8	39.32	even	12
585.2.bu.c.361.1		8	39.8	even	4
845.2.a.l.1.4		4	13.3	even	3
845.2.a.m.1.1		4	13.10	even	6
845.2.c.g.506.2		8	13.2	odd	12
845.2.c.g.506.7		8	13.11	odd	12
845.2.e.m.146.4		8	13.12	even	2
845.2.e.m.191.4		8	13.4	even	6
845.2.e.n.146.1		8	1.1	even	1	trivial
845.2.e.n.191.1		8	13.9	even	3	inner
845.2.m.g.316.1		8	13.7	odd	12
845.2.m.g.361.1		8	13.5	odd	4
1040.2.da.b.641.3		8	52.19	even	12
1040.2.da.b.881.3		8	52.47	even	4
4225.2.a.bi.1.4		4	65.49	even	6
4225.2.a.bl.1.1		4	65.29	even	6
7605.2.a.cf.1.4		4	39.23	odd	6
7605.2.a.cj.1.1		4	39.29	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

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