LMFDB - Embedded newform 130.2.l.b.121.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [130,2,Mod(101,130)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(130, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("130.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 130 = 2 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	130.l (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.03805522628$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.22581504.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 $ x^8 - 4x^7 + 5x^6 + 2x^5 - 11x^4 + 4x^3 + 20x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			121.2
Root			$0.665665 + 1.24775i$ of defining polynomial
Character	$\chi$	$=$	130.121
Dual form			130.2.l.b.101.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.913419 - 1.58209i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000i q^{5} +(-1.58209 + 0.913419i) q^{6} +(3.45632 - 1.99551i) q^{7} -1.00000i q^{8} +(-0.168669 - 0.292144i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.913419 - 1.58209i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000i q^{5} +(-1.58209 + 0.913419i) q^{6} +(3.45632 - 1.99551i) q^{7} -1.00000i q^{8} +(-0.168669 - 0.292144i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-4.24026 - 2.44811i) q^{11} +1.82684 q^{12} +(-2.87423 - 2.17688i) q^{13} -3.99102 q^{14} +(1.58209 + 0.913419i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.31414 + 5.74026i) q^{17} +0.337339i q^{18} +(1.81414 - 1.04739i) q^{19} +(-0.866025 + 0.500000i) q^{20} -7.29094i q^{21} +(2.44811 + 4.24026i) q^{22} +(-0.495508 + 0.858244i) q^{23} +(-1.58209 - 0.913419i) q^{24} -1.00000 q^{25} +(1.40072 + 3.32235i) q^{26} +4.86425 q^{27} +(3.45632 + 1.99551i) q^{28} +(-2.92163 + 5.06040i) q^{29} +(-0.913419 - 1.58209i) q^{30} +10.8179i q^{31} +(0.866025 - 0.500000i) q^{32} +(-7.74627 + 4.47231i) q^{33} -6.62828i q^{34} +(1.99551 + 3.45632i) q^{35} +(0.168669 - 0.292144i) q^{36} +(-2.85782 - 1.64996i) q^{37} -2.09479 q^{38} +(-6.06939 + 2.55889i) q^{39} +1.00000 q^{40} +(-4.48652 - 2.59030i) q^{41} +(-3.64547 + 6.31414i) q^{42} +(0.567874 + 0.983586i) q^{43} -4.89623i q^{44} +(0.292144 - 0.168669i) q^{45} +(0.858244 - 0.495508i) q^{46} -1.61186i q^{47} +(0.913419 + 1.58209i) q^{48} +(4.46410 - 7.73205i) q^{49} +(0.866025 + 0.500000i) q^{50} +12.1088 q^{51} +(0.448114 - 3.57760i) q^{52} -0.549905 q^{53} +(-4.21257 - 2.43213i) q^{54} +(2.44811 - 4.24026i) q^{55} +(-1.99551 - 3.45632i) q^{56} -3.82684i q^{57} +(5.06040 - 2.92163i) q^{58} +(-3.00000 + 1.73205i) q^{59} +1.82684i q^{60} +(0.685861 + 1.18795i) q^{61} +(5.40893 - 9.36854i) q^{62} +(-1.16595 - 0.673162i) q^{63} -1.00000 q^{64} +(2.17688 - 2.87423i) q^{65} +8.94462 q^{66} +(3.13575 + 1.81042i) q^{67} +(-3.31414 + 5.74026i) q^{68} +(0.905212 + 1.56787i) q^{69} -3.99102i q^{70} +(-5.19615 + 3.00000i) q^{71} +(-0.292144 + 0.168669i) q^{72} -8.94462i q^{73} +(1.64996 + 2.85782i) q^{74} +(-0.913419 + 1.58209i) q^{75} +(1.81414 + 1.04739i) q^{76} -19.5409 q^{77} +(6.53569 + 0.818632i) q^{78} +2.55231 q^{79} +(-0.866025 - 0.500000i) q^{80} +(4.94911 - 8.57211i) q^{81} +(2.59030 + 4.48652i) q^{82} -16.4207i q^{83} +(6.31414 - 3.64547i) q^{84} +(-5.74026 + 3.31414i) q^{85} -1.13575i q^{86} +(5.33734 + 9.24454i) q^{87} +(-2.44811 + 4.24026i) q^{88} +(2.98652 + 1.72427i) q^{89} -0.337339 q^{90} +(-14.2782 - 1.78843i) q^{91} -0.991015 q^{92} +(17.1148 + 9.88124i) q^{93} +(-0.805932 + 1.39592i) q^{94} +(1.04739 + 1.81414i) q^{95} -1.82684i q^{96} +(-10.0910 + 5.82606i) q^{97} +(-7.73205 + 4.46410i) q^{98} +1.65169i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} + 4 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) $ 8 * q - 2 * q^3 + 4 * q^4 - 6 * q^6 - 4 * q^9	$ 8 q - 2 q^{3} + 4 q^{4} - 6 q^{6} - 4 q^{9} + 4 q^{10} - 6 q^{11} - 4 q^{12} - 2 q^{13} + 6 q^{15} - 4 q^{16} + 6 q^{17} - 6 q^{19} + 6 q^{22} + 12 q^{23} - 6 q^{24} - 8 q^{25} + 40 q^{27} + 2 q^{30} - 42 q^{33} + 4 q^{36} - 30 q^{37} - 12 q^{38} - 40 q^{39} + 8 q^{40} + 12 q^{41} - 6 q^{42} + 4 q^{43} - 12 q^{45} - 2 q^{48} + 8 q^{49} - 10 q^{52} + 60 q^{53} + 36 q^{54} + 6 q^{55} - 24 q^{59} + 26 q^{61} + 18 q^{62} + 12 q^{63} - 8 q^{64} + 6 q^{65} - 12 q^{66} + 24 q^{67} - 6 q^{68} + 12 q^{69} + 12 q^{72} + 6 q^{74} + 2 q^{75} - 6 q^{76} - 60 q^{77} - 6 q^{78} + 20 q^{79} - 28 q^{81} + 30 q^{84} - 18 q^{85} + 48 q^{87} - 6 q^{88} - 24 q^{89} - 8 q^{90} - 66 q^{91} + 24 q^{92} + 48 q^{93} + 6 q^{95} - 6 q^{97} - 48 q^{98}+O(q^{100}) $ 8 * q - 2 * q^3 + 4 * q^4 - 6 * q^6 - 4 * q^9 + 4 * q^10 - 6 * q^11 - 4 * q^12 - 2 * q^13 + 6 * q^15 - 4 * q^16 + 6 * q^17 - 6 * q^19 + 6 * q^22 + 12 * q^23 - 6 * q^24 - 8 * q^25 + 40 * q^27 + 2 * q^30 - 42 * q^33 + 4 * q^36 - 30 * q^37 - 12 * q^38 - 40 * q^39 + 8 * q^40 + 12 * q^41 - 6 * q^42 + 4 * q^43 - 12 * q^45 - 2 * q^48 + 8 * q^49 - 10 * q^52 + 60 * q^53 + 36 * q^54 + 6 * q^55 - 24 * q^59 + 26 * q^61 + 18 * q^62 + 12 * q^63 - 8 * q^64 + 6 * q^65 - 12 * q^66 + 24 * q^67 - 6 * q^68 + 12 * q^69 + 12 * q^72 + 6 * q^74 + 2 * q^75 - 6 * q^76 - 60 * q^77 - 6 * q^78 + 20 * q^79 - 28 * q^81 + 30 * q^84 - 18 * q^85 + 48 * q^87 - 6 * q^88 - 24 * q^89 - 8 * q^90 - 66 * q^91 + 24 * q^92 + 48 * q^93 + 6 * q^95 - 6 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/130\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	0.913419	−	1.58209i	0.527363	−	0.913419i	−0.472129	−	0.881530i	$-0.656514\pi$
$3$	0.913419	−	1.58209i	0.527363	−	0.913419i	0.999491	−	0.0318895i	$-0.0101525\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−1.58209	+	0.913419i	−0.645885	+	0.372902i
$7$	3.45632	−	1.99551i	1.30637	−	0.754231i	0.324879	−	0.945756i	$-0.394677\pi$
$7$	3.45632	−	1.99551i	1.30637	−	0.754231i	0.981488	+	0.191525i	$0.0613432\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.168669	−	0.292144i	−0.0562231	−	0.0973812i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	−4.24026	−	2.44811i	−1.27849	−	0.738134i	−0.301916	−	0.953335i	$-0.597626\pi$
$11$	−4.24026	−	2.44811i	−1.27849	−	0.738134i	−0.976570	+	0.215200i	$0.930960\pi$
$12$	1.82684			0.527363
$13$	−2.87423	−	2.17688i	−0.797169	−	0.603757i
$13$	−2.87423	−	2.17688i	−0.797169	−	0.603757i
$14$	−3.99102			−1.06664
$15$	1.58209	+	0.913419i	0.408493	+	0.235844i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.31414	+	5.74026i	0.803797	+	1.39222i	0.917100	+	0.398657i	$0.130523\pi$
$17$	3.31414	+	5.74026i	0.803797	+	1.39222i	−0.113303	+	0.993560i	$0.536143\pi$
$18$			0.337339i			0.0795115i
$19$	1.81414	−	1.04739i	0.416192	−	0.240289i	−0.277255	−	0.960796i	$-0.589425\pi$
$19$	1.81414	−	1.04739i	0.416192	−	0.240289i	0.693447	+	0.720508i	$0.256091\pi$
$20$	−0.866025	+	0.500000i	−0.193649	+	0.111803i
$21$		−	7.29094i		−	1.59101i
$22$	2.44811	+	4.24026i	0.521940	+	0.904026i
$23$	−0.495508	+	0.858244i	−0.103320	+	0.178956i	−0.913051	−	0.407846i	$-0.866280\pi$
$23$	−0.495508	+	0.858244i	−0.103320	+	0.178956i	0.809730	+	0.586802i	$0.199613\pi$
$24$	−1.58209	−	0.913419i	−0.322942	−	0.186451i
$25$	−1.00000			−0.200000
$26$	1.40072	+	3.32235i	0.274704	+	0.651566i
$27$	4.86425			0.936126
$28$	3.45632	+	1.99551i	0.653183	+	0.377115i
$29$	−2.92163	+	5.06040i	−0.542532	+	0.939694i	0.456225	+	0.889864i	$0.349201\pi$
$29$	−2.92163	+	5.06040i	−0.542532	+	0.939694i	−0.998758	+	0.0498293i	$0.984132\pi$
$30$	−0.913419	−	1.58209i	−0.166767	−	0.288849i
$31$			10.8179i			1.94294i	0.237155	+	0.971472i	$0.423785\pi$
$31$			10.8179i			1.94294i	−0.237155	+	0.971472i	$0.576215\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−7.74627	+	4.47231i	−1.34845	+	0.778529i
$34$		−	6.62828i		−	1.13674i
$35$	1.99551	+	3.45632i	0.337302	+	0.584225i
$36$	0.168669	−	0.292144i	0.0281115	−	0.0486906i
$37$	−2.85782	−	1.64996i	−0.469822	−	0.271252i	0.246343	−	0.969183i	$-0.420771\pi$
$37$	−2.85782	−	1.64996i	−0.469822	−	0.271252i	−0.716165	+	0.697931i	$0.754104\pi$
$38$	−2.09479			−0.339819
$39$	−6.06939	+	2.55889i	−0.971880	+	0.409750i
$40$	1.00000			0.158114
$41$	−4.48652	−	2.59030i	−0.700677	−	0.404536i	0.106922	−	0.994267i	$-0.465900\pi$
$41$	−4.48652	−	2.59030i	−0.700677	−	0.404536i	−0.807600	+	0.589731i	$0.799234\pi$
$42$	−3.64547	+	6.31414i	−0.562508	+	0.974293i
$43$	0.567874	+	0.983586i	0.0866000	+	0.149996i	0.906072	−	0.423124i	$-0.139066\pi$
$43$	0.567874	+	0.983586i	0.0866000	+	0.149996i	−0.819472	+	0.573119i	$0.805733\pi$
$44$		−	4.89623i		−	0.738134i
$45$	0.292144	−	0.168669i	0.0435502	−	0.0251437i
$46$	0.858244	−	0.495508i	0.126541	−	0.0730586i
$47$		−	1.61186i		−	0.235115i	−0.993066	−	0.117557i	$-0.962494\pi$
$47$		−	1.61186i		−	0.235115i	0.993066	−	0.117557i	$-0.0375064\pi$
$48$	0.913419	+	1.58209i	0.131841	+	0.228355i
$49$	4.46410	−	7.73205i	0.637729	−	1.10458i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$	12.1088			1.69557
$52$	0.448114	−	3.57760i	0.0621422	−	0.496123i
$53$	−0.549905			−0.0755352			−0.0377676	−	0.999287i	$-0.512025\pi$
$53$	−0.549905			−0.0755352			−0.0377676	+	0.999287i	$0.512025\pi$
$54$	−4.21257	−	2.43213i	−0.573258	−	0.330970i
$55$	2.44811	−	4.24026i	0.330104	−	0.571756i
$56$	−1.99551	−	3.45632i	−0.266661	−	0.461870i
$57$		−	3.82684i		−	0.506877i
$58$	5.06040	−	2.92163i	0.664464	−	0.383628i
$59$	−3.00000	+	1.73205i	−0.390567	+	0.225494i	−0.682406	−	0.730974i	$-0.739066\pi$
$59$	−3.00000	+	1.73205i	−0.390567	+	0.225494i	0.291839	+	0.956467i	$0.405733\pi$
$60$			1.82684i			0.235844i
$61$	0.685861	+	1.18795i	0.0878155	+	0.152101i	0.906587	−	0.422018i	$-0.138678\pi$
$61$	0.685861	+	1.18795i	0.0878155	+	0.152101i	−0.818772	+	0.574119i	$0.805345\pi$
$62$	5.40893	−	9.36854i	0.686934	−	1.18981i
$63$	−1.16595	−	0.673162i	−0.146896	−	0.0848104i
$64$	−1.00000			−0.125000
$65$	2.17688	−	2.87423i	0.270008	−	0.356505i
$66$	8.94462			1.10101
$67$	3.13575	+	1.81042i	0.383093	+	0.221179i	0.679163	−	0.733988i	$-0.262343\pi$
$67$	3.13575	+	1.81042i	0.383093	+	0.221179i	−0.296070	+	0.955166i	$0.595676\pi$
$68$	−3.31414	+	5.74026i	−0.401898	+	0.696108i
$69$	0.905212	+	1.56787i	0.108975	+	0.188750i
$70$		−	3.99102i		−	0.477018i
$71$	−5.19615	+	3.00000i	−0.616670	+	0.356034i	−0.775571	−	0.631260i	$-0.782538\pi$
$71$	−5.19615	+	3.00000i	−0.616670	+	0.356034i	0.158901	+	0.987294i	$0.449205\pi$
$72$	−0.292144	+	0.168669i	−0.0344295	+	0.0198779i
$73$		−	8.94462i		−	1.04689i	−0.852060	−	0.523444i	$-0.824647\pi$
$73$		−	8.94462i		−	1.04689i	0.852060	−	0.523444i	$-0.175353\pi$
$74$	1.64996	+	2.85782i	0.191804	+	0.332215i
$75$	−0.913419	+	1.58209i	−0.105473	+	0.182684i
$76$	1.81414	+	1.04739i	0.208096	+	0.120144i
$77$	−19.5409			−2.22689
$78$	6.53569	+	0.818632i	0.740021	+	0.0926918i
$79$	2.55231			0.287158			0.143579	−	0.989639i	$-0.454139\pi$
$79$	2.55231			0.287158			0.143579	+	0.989639i	$0.454139\pi$
$80$	−0.866025	−	0.500000i	−0.0968246	−	0.0559017i
$81$	4.94911	−	8.57211i	0.549901	−	0.952456i
$82$	2.59030	+	4.48652i	0.286050	+	0.495454i
$83$		−	16.4207i		−	1.80241i	−0.433393	−	0.901205i	$-0.642684\pi$
$83$		−	16.4207i		−	1.80241i	0.433393	−	0.901205i	$-0.357316\pi$
$84$	6.31414	−	3.64547i	0.688929	−	0.397753i
$85$	−5.74026	+	3.31414i	−0.622618	+	0.359469i
$86$		−	1.13575i		−	0.122471i
$87$	5.33734	+	9.24454i	0.572223	+	0.991119i
$88$	−2.44811	+	4.24026i	−0.260970	+	0.452013i
$89$	2.98652	+	1.72427i	0.316571	+	0.182772i	0.649863	−	0.760051i	$-0.274826\pi$
$89$	2.98652	+	1.72427i	0.316571	+	0.182772i	−0.333292	+	0.942824i	$0.608160\pi$
$90$	−0.337339			−0.0355586
$91$	−14.2782	−	1.78843i	−1.49677	−	0.187478i
$92$	−0.991015			−0.103320
$93$	17.1148	+	9.88124i	1.77472	+	1.02464i
$94$	−0.805932	+	1.39592i	−0.0831256	+	0.143978i
$95$	1.04739	+	1.81414i	0.107460	+	0.186127i
$96$		−	1.82684i		−	0.186451i
$97$	−10.0910	+	5.82606i	−1.02459	+	0.591547i	−0.915430	−	0.402477i	$-0.868149\pi$
$97$	−10.0910	+	5.82606i	−1.02459	+	0.591547i	−0.109159	+	0.994024i	$0.534816\pi$
$98$	−7.73205	+	4.46410i	−0.781055	+	0.450942i
$99$			1.65169i			0.166001i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	1.03961	−	1.80066i	0.103445	−	0.179173i	−0.809657	−	0.586904i	$-0.800347\pi$
$101$	1.03961	−	1.80066i	0.103445	−	0.179173i	0.913102	+	0.407731i	$0.133680\pi$
$102$	−10.4865	−	6.05440i	−1.03832	−	0.599475i
$103$	−2.26795			−0.223468			−0.111734	−	0.993738i	$-0.535640\pi$
$103$	−2.26795			−0.223468			−0.111734	+	0.993738i	$0.535640\pi$
$104$	−2.17688	+	2.87423i	−0.213460	+	0.281842i
$105$	7.29094			0.711523
$106$	0.476231	+	0.274952i	0.0462557	+	0.0267057i
$107$	1.25076	−	2.16638i	0.120915	−	0.209431i	−0.799214	−	0.601047i	$-0.794750\pi$
$107$	1.25076	−	2.16638i	0.120915	−	0.209431i	0.920129	+	0.391616i	$0.128084\pi$
$108$	2.43213	+	4.21257i	0.234031	+	0.405354i
$109$			15.6357i			1.49763i	0.662780	+	0.748815i	$0.269377\pi$
$109$			15.6357i			1.49763i	−0.662780	+	0.748815i	$0.730623\pi$
$110$	−4.24026	+	2.44811i	−0.404293	+	0.233418i
$111$	−5.22077	+	3.01421i	−0.495534	+	0.286097i
$112$			3.99102i			0.377115i
$113$	−8.55889	−	14.8244i	−0.805153	−	1.39457i	−0.916188	−	0.400749i	$-0.868750\pi$
$113$	−8.55889	−	14.8244i	−0.805153	−	1.39457i	0.111035	−	0.993816i	$-0.464583\pi$
$114$	−1.91342	+	3.31414i	−0.179208	+	0.310398i
$115$	−0.858244	−	0.495508i	−0.0800317	−	0.0462063i
$116$	−5.84325			−0.542532
$117$	−0.151166	+	1.20686i	−0.0139753	+	0.111574i
$118$	3.46410			0.318896
$119$	22.9095	+	13.2268i	2.10011	+	1.21250i
$120$	0.913419	−	1.58209i	0.0833834	−	0.144424i
$121$	6.48652	+	11.2350i	0.589684	+	1.02136i
$122$		−	1.37172i		−	0.124190i
$123$	−8.19615	+	4.73205i	−0.739022	+	0.426675i
$124$	−9.36854	+	5.40893i	−0.841319	+	0.485736i
$125$		−	1.00000i		−	0.0894427i
$126$	0.673162	+	1.16595i	0.0599700	+	0.103871i
$127$	4.06218	−	7.03590i	0.360460	−	0.624335i	−0.627577	−	0.778555i	$-0.715953\pi$
$127$	4.06218	−	7.03590i	0.360460	−	0.624335i	0.988037	+	0.154220i	$0.0492864\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	2.07483			0.182678
$130$	−3.32235	+	1.40072i	−0.291389	+	0.122851i
$131$	14.1773			1.23868			0.619340	−	0.785123i	$-0.287400\pi$
$131$	14.1773			1.23868			0.619340	+	0.785123i	$0.287400\pi$
$132$	−7.74627	−	4.47231i	−0.674226	−	0.389264i
$133$	4.18016	−	7.24026i	0.362466	−	0.627810i
$134$	−1.81042	−	3.13575i	−0.156397	−	0.270887i
$135$			4.86425i			0.418648i
$136$	5.74026	−	3.31414i	0.492223	−	0.284185i
$137$	12.1386	−	7.00821i	1.03707	−	0.598752i	0.118067	−	0.993006i	$-0.462330\pi$
$137$	12.1386	−	7.00821i	1.03707	−	0.598752i	0.919001	+	0.394254i	$0.128997\pi$
$138$		−	1.81042i		−	0.154114i
$139$	−7.99473	−	13.8473i	−0.678104	−	1.17451i	−0.975551	−	0.219772i	$-0.929469\pi$
$139$	−7.99473	−	13.8473i	−0.678104	−	1.17451i	0.297447	−	0.954738i	$-0.403865\pi$
$140$	−1.99551	+	3.45632i	−0.168651	+	0.292112i
$141$	−2.55011	−	1.47231i	−0.214758	−	0.123991i
$142$	6.00000			0.503509
$143$	6.85824	+	16.2670i	0.573515	+	1.36031i
$144$	0.337339			0.0281115
$145$	−5.06040	−	2.92163i	−0.420244	−	0.242628i
$146$	−4.47231	+	7.74627i	−0.370131	+	0.641085i
$147$	−8.15519	−	14.1252i	−0.672629	−	1.16503i
$148$		−	3.29992i		−	0.271252i
$149$	6.49253	−	3.74846i	0.531889	−	0.307086i	−0.209896	−	0.977724i	$-0.567313\pi$
$149$	6.49253	−	3.74846i	0.531889	−	0.307086i	0.741785	+	0.670637i	$0.233979\pi$
$150$	1.58209	−	0.913419i	0.129177	−	0.0745804i
$151$		−	4.24913i		−	0.345789i	−0.984940	−	0.172895i	$-0.944688\pi$
$151$		−	4.24913i		−	0.345789i	0.984940	−	0.172895i	$-0.0553120\pi$
$152$	−1.04739	−	1.81414i	−0.0849549	−	0.147146i
$153$	1.11799	−	1.93641i	0.0903839	−	0.156549i
$154$	16.9229	+	9.77046i	1.36369	+	0.787326i
$155$	−10.8179			−0.868911
$156$	−5.25076	−	3.97680i	−0.420397	−	0.318399i
$157$	−22.7526			−1.81586			−0.907929	−	0.419124i	$-0.862337\pi$
$157$	−22.7526			−1.81586			−0.907929	+	0.419124i	$0.862337\pi$
$158$	−2.21037	−	1.27616i	−0.175847	−	0.101526i
$159$	−0.502293	+	0.869998i	−0.0398345	+	0.0689953i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$			3.95516i			0.311710i
$162$	−8.57211	+	4.94911i	−0.673488	+	0.388839i
$163$	4.51630	−	2.60749i	0.353744	−	0.204234i	−0.312589	−	0.949888i	$-0.601196\pi$
$163$	4.51630	−	2.60749i	0.353744	−	0.204234i	0.666333	+	0.745654i	$0.267863\pi$
$164$		−	5.18059i		−	0.404536i
$165$	−4.47231	−	7.74627i	−0.348169	−	0.603046i
$166$	−8.21037	+	14.2208i	−0.637248	+	1.10375i
$167$	−5.80624	−	3.35224i	−0.449301	−	0.259404i	0.258234	−	0.966082i	$-0.416859\pi$
$167$	−5.80624	−	3.35224i	−0.449301	−	0.259404i	−0.707535	+	0.706679i	$0.750193\pi$
$168$	−7.29094			−0.562508
$169$	3.52242	+	12.5137i	0.270955	+	0.962592i
$170$	6.62828			0.508366
$171$	−0.611979	−	0.353326i	−0.0467992	−	0.0270195i
$172$	−0.567874	+	0.983586i	−0.0433000	+	0.0749978i
$173$	9.77046	+	16.9229i	0.742834	+	1.28663i	0.951200	+	0.308576i	$0.0998523\pi$
$173$	9.77046	+	16.9229i	0.742834	+	1.28663i	−0.208365	+	0.978051i	$0.566814\pi$
$174$		−	10.6747i		−	0.809245i
$175$	−3.45632	+	1.99551i	−0.261273	+	0.150846i
$176$	4.24026	−	2.44811i	0.319621	−	0.184534i
$177$			6.32835i			0.475668i
$178$	−1.72427	−	2.98652i	−0.129239	−	0.223849i
$179$	4.48950	−	7.77604i	0.335561	−	0.581209i	−0.648031	−	0.761614i	$-0.724407\pi$
$179$	4.48950	−	7.77604i	0.335561	−	0.581209i	0.983592	+	0.180405i	$0.0577408\pi$
$180$	0.292144	+	0.168669i	0.0217751	+	0.0125719i
$181$	−5.55648			−0.413010			−0.206505	−	0.978446i	$-0.566209\pi$
$181$	−5.55648			−0.413010			−0.206505	+	0.978446i	$0.566209\pi$
$182$	11.4711	+	8.68795i	0.850295	+	0.643993i
$183$	2.50591			0.185242
$184$	0.858244	+	0.495508i	0.0632706	+	0.0365293i
$185$	1.64996	−	2.85782i	0.121308	−	0.210111i
$186$	−9.88124	−	17.1148i	−0.724527	−	1.25492i
$187$		−	32.4536i		−	2.37324i
$188$	1.39592	−	0.805932i	0.101808	−	0.0587787i
$189$	16.8124	−	9.70665i	1.22292	−	0.706055i
$190$		−	2.09479i		−	0.151972i
$191$	−5.09316	−	8.82161i	−0.368528	−	0.638309i	0.620808	−	0.783963i	$-0.286805\pi$
$191$	−5.09316	−	8.82161i	−0.368528	−	0.638309i	−0.989336	+	0.145654i	$0.953471\pi$
$192$	−0.913419	+	1.58209i	−0.0659204	+	0.114177i
$193$	7.04839	+	4.06939i	0.507354	+	0.292921i	0.731745	−	0.681578i	$-0.238706\pi$
$193$	7.04839	+	4.06939i	0.507354	+	0.292921i	−0.224391	+	0.974499i	$0.572039\pi$
$194$	11.6521			0.836574
$195$	−2.55889	−	6.06939i	−0.183246	−	0.434638i
$196$	8.92820			0.637729
$197$	12.5405	+	7.24026i	0.893473	+	0.515847i	0.875077	−	0.483984i	$-0.160811\pi$
$197$	12.5405	+	7.24026i	0.893473	+	0.515847i	0.0183962	+	0.999831i	$0.494144\pi$
$198$	0.825843	−	1.43040i	0.0586901	−	0.101654i
$199$	−5.62828	−	9.74846i	−0.398978	−	0.691050i	0.594622	−	0.804005i	$-0.297302\pi$
$199$	−5.62828	−	9.74846i	−0.398978	−	0.691050i	−0.993600	+	0.112955i	$0.963968\pi$
$200$			1.00000i			0.0707107i
$201$	5.72850	−	3.30735i	0.404058	−	0.233283i
$202$	−1.80066	+	1.03961i	−0.126694	+	0.0731469i
$203$			23.3205i			1.63678i
$204$	6.05440	+	10.4865i	0.423893	+	0.734203i
$205$	2.59030	−	4.48652i	0.180914	−	0.313352i
$206$	1.96410	+	1.13397i	0.136845	+	0.0790078i
$207$	0.334308			0.0232360
$208$	3.32235	−	1.40072i	0.230363	−	0.0971225i
$209$	−10.2566			−0.709461
$210$	−6.31414	−	3.64547i	−0.435717	−	0.251561i
$211$	−4.79257	+	8.30097i	−0.329934	+	0.571463i	−0.982498	−	0.186271i	$-0.940360\pi$
$211$	−4.79257	+	8.30097i	−0.329934	+	0.571463i	0.652564	+	0.757733i	$0.273693\pi$
$212$	−0.274952	−	0.476231i	−0.0188838	−	0.0327077i
$213$			10.9610i			0.751037i
$214$	−2.16638	+	1.25076i	−0.148090	+	0.0855000i
$215$	−0.983586	+	0.567874i	−0.0670800	+	0.0387287i
$216$		−	4.86425i		−	0.330970i
$217$	21.5871	+	37.3900i	1.46543	+	2.53820i
$218$	7.81785	−	13.5409i	0.529492	−	0.917107i
$219$	−14.1512	−	8.17018i	−0.956248	−	0.552090i
$220$	4.89623			0.330104
$221$	2.97022	−	23.7133i	0.199799	−	1.59513i
$222$	6.02843			0.404602
$223$	−23.5660	−	13.6058i	−1.57809	−	0.911113i	−0.995125	−	0.0986181i	$-0.968558\pi$
$223$	−23.5660	−	13.6058i	−1.57809	−	0.911113i	−0.582968	−	0.812495i	$-0.698109\pi$
$224$	1.99551	−	3.45632i	0.133330	−	0.230935i
$225$	0.168669	+	0.292144i	0.0112446	+	0.0194762i
$226$			17.1178i			1.13866i
$227$	5.48052	−	3.16418i	0.363755	−	0.210014i	−0.306972	−	0.951719i	$-0.599316\pi$
$227$	5.48052	−	3.16418i	0.363755	−	0.210014i	0.670726	+	0.741705i	$0.265982\pi$
$228$	3.31414	−	1.91342i	0.219484	−	0.126719i
$229$		−	2.50152i		−	0.165305i	−0.996578	−	0.0826524i	$-0.973661\pi$
$229$		−	2.50152i		−	0.165305i	0.996578	−	0.0826524i	$-0.0263391\pi$
$230$	0.495508	+	0.858244i	0.0326728	+	0.0565910i
$231$	−17.8491	+	30.9155i	−1.17438	+	2.03409i
$232$	5.06040	+	2.92163i	0.332232	+	0.191814i
$233$	9.17903			0.601339			0.300669	−	0.953728i	$-0.402790\pi$
$233$	9.17903			0.601339			0.300669	+	0.953728i	$0.402790\pi$
$234$	0.734344	−	0.969589i	0.0480056	−	0.0633840i
$235$	1.61186			0.105146
$236$	−3.00000	−	1.73205i	−0.195283	−	0.112747i
$237$	2.33133	−	4.03798i	0.151436	−	0.262295i
$238$	−13.2268	−	22.9095i	−0.857365	−	1.48500i
$239$		−	6.54030i		−	0.423057i	−0.977372	−	0.211528i	$-0.932156\pi$
$239$		−	6.54030i		−	0.423057i	0.977372	−	0.211528i	$-0.0678441\pi$
$240$	−1.58209	+	0.913419i	−0.102123	+	0.0589610i
$241$	7.86571	−	4.54127i	0.506675	−	0.292529i	−0.224791	−	0.974407i	$-0.572170\pi$
$241$	7.86571	−	4.54127i	0.506675	−	0.292529i	0.731466	+	0.681878i	$0.238837\pi$
$242$		−	12.9730i		−	0.833939i
$243$	−1.74484	−	3.02216i	−0.111932	−	0.193872i
$244$	−0.685861	+	1.18795i	−0.0439077	+	0.0760504i
$245$	7.73205	+	4.46410i	0.493983	+	0.285201i
$246$	9.46410			0.603409
$247$	−7.49430	−	0.938703i	−0.476851	−	0.0597283i
$248$	10.8179			0.686934
$249$	−25.9791	−	14.9990i	−1.64636	−	0.950524i
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	−4.81414	−	8.33833i	−0.303866	−	0.526311i	0.673142	−	0.739513i	$-0.264944\pi$
$251$	−4.81414	−	8.33833i	−0.303866	−	0.526311i	−0.977008	+	0.213202i	$0.931611\pi$
$252$		−	1.34632i		−	0.0848104i
$253$	4.20216	−	2.42612i	0.264188	−	0.152529i
$254$	−7.03590	+	4.06218i	−0.441472	+	0.254884i
$255$			12.1088i			0.758282i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−7.41113	+	12.8364i	−0.462293	+	0.800716i	−0.999075	−	0.0430058i	$-0.986307\pi$
$257$	−7.41113	+	12.8364i	−0.462293	+	0.800716i	0.536781	+	0.843721i	$0.319640\pi$
$258$	−1.79685	−	1.03741i	−0.111867	−	0.0645866i
$259$	−13.1700			−0.818347
$260$	3.57760	+	0.448114i	0.221873	+	0.0277908i
$261$	1.97115			0.122011
$262$	−12.2779	−	7.08867i	−0.758533	−	0.437939i
$263$	−5.51673	+	9.55525i	−0.340176	+	0.589202i	−0.984465	−	0.175580i	$-0.943820\pi$
$263$	−5.51673	+	9.55525i	−0.340176	+	0.589202i	0.644289	+	0.764782i	$0.277153\pi$
$264$	4.47231	+	7.74627i	0.275252	+	0.476750i
$265$		−	0.549905i		−	0.0337804i
$266$	−7.24026	+	4.18016i	−0.443929	+	0.256302i
$267$	5.45589	−	3.14996i	0.333895	−	0.192775i
$268$			3.62085i			0.221179i
$269$	1.30515	+	2.26059i	0.0795767	+	0.137831i	0.903067	−	0.429499i	$-0.141310\pi$
$269$	1.30515	+	2.26059i	0.0795767	+	0.137831i	−0.823491	+	0.567330i	$0.807976\pi$
$270$	2.43213	−	4.21257i	0.148014	−	0.256369i
$271$	24.8459	+	14.3448i	1.50928	+	0.871383i	0.999942	+	0.0108156i	$0.00344279\pi$
$271$	24.8459	+	14.3448i	1.50928	+	0.871383i	0.509337	+	0.860567i	$0.329891\pi$
$272$	−6.62828			−0.401898
$273$	−15.8715	+	20.9559i	−0.960585	+	1.26831i
$274$	−14.0164			−0.846763
$275$	4.24026	+	2.44811i	0.255697	+	0.147627i
$276$	−0.905212	+	1.56787i	−0.0544874	+	0.0943749i
$277$	2.35035	+	4.07092i	0.141219	+	0.244598i	0.927956	−	0.372690i	$-0.121565\pi$
$277$	2.35035	+	4.07092i	0.141219	+	0.244598i	−0.786737	+	0.617288i	$0.788231\pi$
$278$			15.9895i			0.958984i
$279$	3.16037	−	1.82464i	0.189206	−	0.109238i
$280$	3.45632	−	1.99551i	0.206555	−	0.119254i
$281$		−	3.32418i		−	0.198304i	−0.995072	−	0.0991521i	$-0.968387\pi$
$281$		−	3.32418i		−	0.198304i	0.995072	−	0.0991521i	$-0.0316130\pi$
$282$	1.47231	+	2.55011i	0.0876747	+	0.151857i
$283$	12.9886	−	22.4969i	0.772093	−	1.33730i	−0.164322	−	0.986407i	$-0.552543\pi$
$283$	12.9886	−	22.4969i	0.772093	−	1.33730i	0.936414	−	0.350897i	$-0.114123\pi$
$284$	−5.19615	−	3.00000i	−0.308335	−	0.178017i
$285$	3.82684			0.226682
$286$	2.19407	−	17.5167i	0.129738	−	1.03579i
$287$	−20.6758			−1.22045
$288$	−0.292144	−	0.168669i	−0.0172147	−	0.00993893i
$289$	−13.4670	+	23.3256i	−0.792179	+	1.37209i
$290$	2.92163	+	5.06040i	0.171564	+	0.297157i
$291$			21.2865i			1.24784i
$292$	7.74627	−	4.47231i	0.453316	−	0.261722i
$293$	0.824857	−	0.476231i	0.0481886	−	0.0278217i	−0.475712	−	0.879601i	$-0.657810\pi$
$293$	0.824857	−	0.476231i	0.0481886	−	0.0278217i	0.523901	+	0.851779i	$0.324476\pi$
$294$			16.3104i			0.951241i
$295$	−1.73205	−	3.00000i	−0.100844	−	0.174667i
$296$	−1.64996	+	2.85782i	−0.0959021	+	0.166107i
$297$	−20.6257	−	11.9082i	−1.19682	−	0.690986i
$298$	−7.49693			−0.434285
$299$	3.29250	−	1.38814i	0.190410	−	0.0802779i
$300$	−1.82684			−0.105473
$301$	3.92551	+	2.26639i	0.226263	+	0.130633i
$302$	−2.12456	+	3.67985i	−0.122255	+	0.211752i
$303$	−1.89920	−	3.28952i	−0.109106	−	0.188978i
$304$			2.09479i			0.120144i
$305$	−1.18795	+	0.685861i	−0.0680216	+	0.0392723i
$306$	−1.93641	+	1.11799i	−0.110697	+	0.0639111i
$307$			32.5819i			1.85955i	0.368133	+	0.929773i	$0.379997\pi$
$307$			32.5819i			1.85955i	−0.368133	+	0.929773i	$0.620003\pi$
$308$	−9.77046	−	16.9229i	−0.556724	−	0.964274i
$309$	−2.07159	+	3.58810i	−0.117849	+	0.204120i
$310$	9.36854	+	5.40893i	0.532097	+	0.307206i
$311$	18.2831			1.03674			0.518370	−	0.855157i	$-0.326539\pi$
$311$	18.2831			1.03674			0.518370	+	0.855157i	$0.326539\pi$
$312$	2.55889	+	6.06939i	0.144869	+	0.343612i
$313$	−16.0968			−0.909844			−0.454922	−	0.890531i	$-0.650333\pi$
$313$	−16.0968			−0.909844			−0.454922	+	0.890531i	$0.650333\pi$
$314$	19.7044	+	11.3763i	1.11198	+	0.642003i
$315$	0.673162	−	1.16595i	0.0379284	−	0.0656938i
$316$	1.27616	+	2.21037i	0.0717894	+	0.124343i
$317$			7.38961i			0.415042i	0.978231	+	0.207521i	$0.0665395\pi$
$317$			7.38961i			0.415042i	−0.978231	+	0.207521i	$0.933460\pi$
$318$	0.869998	−	0.502293i	0.0487870	−	0.0281672i
$319$	24.7769	−	14.3049i	1.38724	−	0.800923i
$320$		−	1.00000i		−	0.0559017i
$321$	−2.28493	−	3.95762i	−0.127532	−	0.220893i
$322$	1.97758	−	3.42527i	0.110206	−	0.190883i
$323$	12.0246	+	6.94242i	0.669068	+	0.386286i
$324$	9.89822			0.549901
$325$	2.87423	+	2.17688i	0.159434	+	0.120751i
$326$	−5.21497			−0.288831
$327$	24.7371	+	14.2820i	1.36796	+	0.789794i
$328$	−2.59030	+	4.48652i	−0.143025	+	0.247727i
$329$	−3.21649	−	5.57112i	−0.177331	−	0.307146i
$330$			8.94462i			0.492385i
$331$	−16.8848	+	9.74846i	−0.928074	+	0.535824i	−0.886202	−	0.463299i	$-0.846666\pi$
$331$	−16.8848	+	9.74846i	−0.928074	+	0.535824i	−0.0418724	+	0.999123i	$0.513332\pi$
$332$	14.2208	−	8.21037i	0.780466	−	0.450602i
$333$			1.11319i			0.0610025i
$334$	3.35224	+	5.80624i	0.183426	+	0.317704i
$335$	−1.81042	+	3.13575i	−0.0989141	+	0.171324i
$336$	6.31414	+	3.64547i	0.344465	+	0.198877i
$337$	27.8865			1.51908			0.759538	−	0.650463i	$-0.225425\pi$
$337$	27.8865			1.51908			0.759538	+	0.650463i	$0.225425\pi$
$338$	3.20634	−	12.5984i	0.174402	−	0.685262i
$339$	−31.2714			−1.69843
$340$	−5.74026	−	3.31414i	−0.311309	−	0.179734i
$341$	26.4833	−	45.8705i	1.43415	−	2.48403i
$342$	0.353326	+	0.611979i	0.0191057	+	0.0330920i
$343$		−	7.69549i		−	0.415517i
$344$	0.983586	−	0.567874i	0.0530314	−	0.0306177i
$345$	−1.56787	+	0.905212i	−0.0844115	+	0.0487350i
$346$		−	19.5409i		−	1.05053i
$347$	−10.0940	−	17.4833i	−0.541875	−	0.938555i	−0.998796	−	0.0490478i	$-0.984381\pi$
$347$	−10.0940	−	17.4833i	−0.541875	−	0.938555i	0.456922	−	0.889507i	$-0.348952\pi$
$348$	−5.33734	+	9.24454i	−0.286111	+	0.495559i
$349$	−30.8885	−	17.8335i	−1.65342	−	0.954605i	−0.975650	−	0.219335i	$-0.929611\pi$
$349$	−30.8885	−	17.8335i	−1.65342	−	0.954605i	−0.677774	−	0.735270i	$-0.737055\pi$
$350$	3.99102			0.213329
$351$	−13.9810	−	10.5889i	−0.746250	−	0.565192i
$352$	−4.89623			−0.260970
$353$	−22.1506	−	12.7886i	−1.17896	−	0.680671i	−0.223184	−	0.974776i	$-0.571645\pi$
$353$	−22.1506	−	12.7886i	−1.17896	−	0.680671i	−0.955773	+	0.294105i	$0.904978\pi$
$354$	3.16418	−	5.48052i	0.168174	−	0.291286i
$355$	−3.00000	−	5.19615i	−0.159223	−	0.275783i
$356$			3.44854i			0.182772i
$357$	41.8519	−	24.1632i	2.21504	−	1.27885i
$358$	−7.77604	+	4.48950i	−0.410977	+	0.237277i
$359$			24.2487i			1.27980i	0.768459	+	0.639899i	$0.221024\pi$
$359$			24.2487i			1.27980i	−0.768459	+	0.639899i	$0.778976\pi$
$360$	−0.168669	−	0.292144i	−0.00888965	−	0.0153973i
$361$	−7.30593	+	12.6542i	−0.384523	+	0.666013i
$362$	4.81205	+	2.77824i	0.252916	+	0.146021i
$363$	23.6997			1.24391
$364$	−5.59030	−	13.2595i	−0.293011	−	0.694988i
$365$	8.94462			0.468183
$366$	−2.17018	−	1.25296i	−0.113437	−	0.0654931i
$367$	−1.47966	+	2.56285i	−0.0772378	+	0.133780i	−0.902057	−	0.431616i	$-0.857943\pi$
$367$	−1.47966	+	2.56285i	−0.0772378	+	0.133780i	0.824819	+	0.565396i	$0.191277\pi$
$368$	−0.495508	−	0.858244i	−0.0258301	−	0.0447391i
$369$			1.74761i			0.0909771i
$370$	−2.85782	+	1.64996i	−0.148571	+	0.0857775i
$371$	−1.90065	+	1.09734i	−0.0986766	+	0.0569710i
$372$			19.7625i			1.02464i
$373$	2.91179	+	5.04337i	0.150767	+	0.261136i	0.931510	−	0.363717i	$-0.118492\pi$
$373$	2.91179	+	5.04337i	0.150767	+	0.261136i	−0.780743	+	0.624853i	$0.785159\pi$
$374$	−16.2268	+	28.1056i	−0.839067	+	1.45331i
$375$	−1.58209	−	0.913419i	−0.0816987	−	0.0471688i
$376$	−1.61186			−0.0831256
$377$	19.4133	−	8.18476i	0.999836	−	0.421537i
$378$	−19.4133			−0.998513
$379$	−0.503185	−	0.290514i	−0.0258469	−	0.0149227i	0.487021	−	0.873390i	$-0.338084\pi$
$379$	−0.503185	−	0.290514i	−0.0258469	−	0.0149227i	−0.512868	+	0.858468i	$0.671417\pi$
$380$	−1.04739	+	1.81414i	−0.0537302	+	0.0930634i
$381$	−7.42094	−	12.8534i	−0.380186	−	0.658502i
$382$			10.1863i			0.521177i
$383$	−13.2514	+	7.65070i	−0.677115	+	0.390933i	−0.798767	−	0.601640i	$-0.794514\pi$
$383$	−13.2514	+	7.65070i	−0.677115	+	0.390933i	0.121652	+	0.992573i	$0.461181\pi$
$384$	1.58209	−	0.913419i	0.0807356	−	0.0466127i
$385$		−	19.5409i		−	0.995897i
$386$	−4.06939	−	7.04839i	−0.207126	−	0.358754i
$387$	0.191566	−	0.331802i	0.00973783	−	0.0168664i
$388$	−10.0910	−	5.82606i	−0.512295	−	0.295773i
$389$	−19.7281			−1.00025			−0.500127	−	0.865952i	$-0.666713\pi$
$389$	−19.7281			−1.00025			−0.500127	+	0.865952i	$0.666713\pi$
$390$	−0.818632	+	6.53569i	−0.0414530	+	0.330948i
$391$	−6.56873			−0.332195
$392$	−7.73205	−	4.46410i	−0.390528	−	0.225471i
$393$	12.9498	−	22.4298i	0.653233	−	1.13143i
$394$	−7.24026	−	12.5405i	−0.364759	−	0.631781i
$395$			2.55231i			0.128421i
$396$	−1.43040	+	0.825843i	−0.0718804	+	0.0415002i
$397$	−0.716063	+	0.413419i	−0.0359382	+	0.0207489i	−0.517861	−	0.855465i	$-0.673272\pi$
$397$	−0.716063	+	0.413419i	−0.0359382	+	0.0207489i	0.481923	+	0.876213i	$0.339938\pi$
$398$			11.2566i			0.564240i
$399$	−7.63649	−	13.2268i	−0.382302	−	0.662167i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	27.3668	+	15.8002i	1.36663	+	0.789026i	0.990496	−	0.137538i	$-0.0439189\pi$
$401$	27.3668	+	15.8002i	1.36663	+	0.789026i	0.376137	+	0.926564i	$0.377252\pi$
$402$	−6.61471			−0.329912
$403$	23.5491	−	31.0930i	1.17307	−	1.54885i
$404$	2.07923			0.103445
$405$	8.57211	+	4.94911i	0.425951	+	0.245923i
$406$	11.6603	−	20.1962i	0.578689	−	1.00232i
$407$	8.07859	+	13.9925i	0.400441	+	0.693584i
$408$		−	12.1088i		−	0.599475i
$409$	18.9951	−	10.9668i	0.939247	−	0.542274i	0.0495227	−	0.998773i	$-0.484230\pi$
$409$	18.9951	−	10.9668i	0.939247	−	0.542274i	0.889724	+	0.456499i	$0.150897\pi$
$410$	−4.48652	+	2.59030i	−0.221574	+	0.127926i
$411$		−	25.6057i		−	1.26304i
$412$	−1.13397	−	1.96410i	−0.0558669	−	0.0967643i
$413$	−6.91264	+	11.9730i	−0.340149	+	0.589155i
$414$	−0.289519	−	0.167154i	−0.0142291	−	0.00821516i
$415$	16.4207			0.806062
$416$	−3.57760	−	0.448114i	−0.175406	−	0.0219706i
$417$	−29.2102			−1.43043
$418$	8.88244	+	5.12828i	0.434454	+	0.250832i
$419$	15.2814	−	26.4681i	0.746545	−	1.29305i	−0.202925	−	0.979194i	$-0.565045\pi$
$419$	15.2814	−	26.4681i	0.746545	−	1.29305i	0.949470	−	0.313859i	$-0.101622\pi$
$420$	3.64547	+	6.31414i	0.177881	+	0.308098i
$421$			21.4565i			1.04573i	0.852417	+	0.522863i	$0.175136\pi$
$421$			21.4565i			1.04573i	−0.852417	+	0.522863i	$0.824864\pi$
$422$	8.30097	−	4.79257i	0.404085	−	0.233299i
$423$	−0.470896	+	0.271872i	−0.0228958	+	0.0132189i
$424$			0.549905i			0.0267057i
$425$	−3.31414	−	5.74026i	−0.160759	−	0.278443i
$426$	5.48052	−	9.49253i	0.265532	−	0.459915i
$427$	4.74111	+	2.73728i	0.229438	+	0.132466i
$428$	2.50152			0.120915
$429$	32.0002	+	4.00821i	1.54499	+	0.193518i
$430$	1.13575			0.0547706
$431$	−7.93641	−	4.58209i	−0.382283	−	0.220711i	0.296528	−	0.955024i	$-0.404171\pi$
$431$	−7.93641	−	4.58209i	−0.382283	−	0.220711i	−0.678811	+	0.734313i	$0.737505\pi$
$432$	−2.43213	+	4.21257i	−0.117016	+	0.202677i
$433$	5.04839	+	8.74407i	0.242610	+	0.420213i	0.961457	−	0.274955i	$-0.0886631\pi$
$433$	5.04839	+	8.74407i	0.242610	+	0.420213i	−0.718847	+	0.695168i	$0.755330\pi$
$434$		−	43.1742i		−	2.07243i
$435$	−9.24454	+	5.33734i	−0.443242	+	0.255906i
$436$	−13.5409	+	7.81785i	−0.648492	+	0.374407i
$437$			2.07597i			0.0993069i
$438$	8.17018	+	14.1512i	0.390387	+	0.676169i
$439$	13.2648	−	22.9752i	0.633093	−	1.09655i	−0.353823	−	0.935312i	$-0.615119\pi$
$439$	13.2648	−	22.9752i	0.633093	−	1.09655i	0.986916	−	0.161236i	$-0.0515481\pi$
$440$	−4.24026	−	2.44811i	−0.202146	−	0.116709i
$441$	−3.01183			−0.143420
$442$	−14.4289	+	19.0512i	−0.686315	+	0.906174i
$443$	12.9851			0.616939			0.308469	−	0.951234i	$-0.400183\pi$
$443$	12.9851			0.616939			0.308469	+	0.951234i	$0.400183\pi$
$444$	−5.22077	−	3.01421i	−0.247767	−	0.143048i
$445$	−1.72427	+	2.98652i	−0.0817382	+	0.141575i
$446$	13.6058	+	23.5660i	0.644254	+	1.11588i
$447$		−	13.6957i		−	0.647783i
$448$	−3.45632	+	1.99551i	−0.163296	+	0.0942789i
$449$	−27.5283	+	15.8935i	−1.29914	+	0.750059i	−0.980256	−	0.197734i	$-0.936642\pi$
$449$	−27.5283	+	15.8935i	−1.29914	+	0.750059i	−0.318885	+	0.947793i	$0.603308\pi$
$450$		−	0.337339i		−	0.0159023i
$451$	12.6827	+	21.9670i	0.597204	+	1.03439i
$452$	8.55889	−	14.8244i	0.402576	−	0.697283i
$453$	−6.72250	−	3.88124i	−0.315850	−	0.182356i
$454$	−6.32835			−0.297004
$455$	1.78843	−	14.2782i	0.0838429	−	0.669374i
$456$	−3.82684			−0.179208
$457$	−6.42293	−	3.70828i	−0.300452	−	0.173466i	0.342194	−	0.939629i	$-0.388830\pi$
$457$	−6.42293	−	3.70828i	−0.300452	−	0.173466i	−0.642646	+	0.766163i	$0.722163\pi$
$458$	−1.25076	+	2.16638i	−0.0584441	+	0.101228i
$459$	16.1208	+	27.9221i	0.752455	+	1.30329i
$460$		−	0.991015i		−	0.0462063i
$461$	−34.6924	+	20.0296i	−1.61578	+	0.932873i	−0.627790	+	0.778383i	$0.716040\pi$
$461$	−34.6924	+	20.0296i	−1.61578	+	0.932873i	−0.987994	+	0.154491i	$0.950626\pi$
$462$	30.9155	−	17.8491i	1.43832	−	0.830413i
$463$			22.6119i			1.05086i	0.850836	+	0.525431i	$0.176096\pi$
$463$			22.6119i			1.05086i	−0.850836	+	0.525431i	$0.823904\pi$
$464$	−2.92163	−	5.06040i	−0.135633	−	0.234923i
$465$	−9.88124	+	17.1148i	−0.458231	+	0.793680i
$466$	−7.94928	−	4.58952i	−0.368243	−	0.212605i
$467$	−7.72244			−0.357352			−0.178676	−	0.983908i	$-0.557181\pi$
$467$	−7.72244			−0.357352			−0.178676	+	0.983908i	$0.557181\pi$
$468$	−1.12076	+	0.472517i	−0.0518069	+	0.0218421i
$469$	14.4509			0.667279
$470$	−1.39592	−	0.805932i	−0.0643888	−	0.0371749i
$471$	−20.7827	+	35.9967i	−0.957616	+	1.65864i
$472$	1.73205	+	3.00000i	0.0797241	+	0.138086i
$473$		−	5.56088i		−	0.255690i
$474$	−4.03798	+	2.33133i	−0.185471	+	0.107082i
$475$	−1.81414	+	1.04739i	−0.0832384	+	0.0480577i
$476$			26.4536i			1.21250i
$477$	0.0927520	+	0.160651i	0.00424682	+	0.00735571i
$478$	−3.27015	+	5.66406i	−0.149573	+	0.259068i
$479$	4.32100	+	2.49473i	0.197431	+	0.113987i	0.595457	−	0.803387i	$-0.296971\pi$
$479$	4.32100	+	2.49473i	0.197431	+	0.113987i	−0.398025	+	0.917374i	$0.630304\pi$
$480$	1.82684			0.0833834
$481$	4.62227	+	10.9635i	0.210757	+	0.499892i
$482$	−9.08254			−0.413699
$483$	6.25741	+	3.61272i	0.284722	+	0.164384i
$484$	−6.48652	+	11.2350i	−0.294842	+	0.510681i
$485$	−5.82606	−	10.0910i	−0.264548	−	0.458210i
$486$			3.48969i			0.158295i
$487$	22.3741	−	12.9177i	1.01387	−	0.585357i	0.101546	−	0.994831i	$-0.467621\pi$
$487$	22.3741	−	12.9177i	1.01387	−	0.585357i	0.912322	+	0.409474i	$0.134288\pi$
$488$	1.18795	−	0.685861i	0.0537758	−	0.0310475i
$489$		−	9.52691i		−	0.430822i
$490$	−4.46410	−	7.73205i	−0.201668	−	0.349298i
$491$	8.75076	−	15.1568i	0.394916	−	0.684015i	−0.598174	−	0.801366i	$-0.704107\pi$
$491$	8.75076	−	15.1568i	0.394916	−	0.684015i	0.993090	+	0.117351i	$0.0374403\pi$
$492$	−8.19615	−	4.73205i	−0.369511	−	0.213337i
$493$	−38.7307			−1.74434
$494$	6.02091	+	4.56009i	0.270893	+	0.205168i
$495$	−1.65169			−0.0742378
$496$	−9.36854	−	5.40893i	−0.420660	−	0.242868i
$497$	−11.9730	+	20.7379i	−0.537065	+	0.930223i
$498$	14.9990	+	25.9791i	0.672122	+	1.16415i
$499$			19.0519i			0.852878i	0.904516	+	0.426439i	$0.140232\pi$
$499$			19.0519i			0.852878i	−0.904516	+	0.426439i	$0.859768\pi$
$500$	0.866025	−	0.500000i	0.0387298	−	0.0223607i
$501$	−10.6071	+	6.12399i	−0.473889	+	0.273600i
$502$			9.62828i			0.429731i
$503$	1.96384	+	3.40148i	0.0875635	+	0.151664i	0.906481	−	0.422247i	$-0.138759\pi$
$503$	1.96384	+	3.40148i	0.0875635	+	0.151664i	−0.818917	+	0.573912i	$0.805425\pi$
$504$	−0.673162	+	1.16595i	−0.0299850	+	0.0519355i
$505$	1.80066	+	1.03961i	0.0801284	+	0.0462622i
$506$	−4.85224			−0.215708
$507$	23.0152	+	5.85747i	1.02214	+	0.260139i
$508$	8.12436			0.360460
$509$	−36.9221	−	21.3170i	−1.63654	−	0.944858i	−0.982011	−	0.188822i	$-0.939533\pi$
$509$	−36.9221	−	21.3170i	−1.63654	−	0.944858i	−0.654530	−	0.756036i	$-0.727134\pi$
$510$	6.05440	−	10.4865i	0.268093	−	0.464351i
$511$	−17.8491	−	30.9155i	−0.789596	−	1.36762i
$512$			1.00000i			0.0441942i
$513$	8.82443	−	5.09479i	0.389608	−	0.224940i
$514$	12.8364	−	7.41113i	0.566191	−	0.326891i
$515$		−	2.26795i		−	0.0999378i
$516$	1.03741	+	1.79685i	0.0456696	+	0.0791021i
$517$	−3.94603	+	6.83472i	−0.173546	+	0.300591i
$518$	11.4056	+	6.58502i	0.501133	+	0.289329i
$519$	35.6981			1.56697
$520$	−2.87423	−	2.17688i	−0.126043	−	0.0954623i
$521$	32.4921			1.42351			0.711753	−	0.702430i	$-0.247902\pi$
$521$	32.4921			1.42351			0.711753	+	0.702430i	$0.247902\pi$
$522$	−1.70707	−	0.985577i	−0.0747164	−	0.0431375i
$523$	−5.31194	+	9.20055i	−0.232275	+	0.402312i	−0.958477	−	0.285169i	$-0.907950\pi$
$523$	−5.31194	+	9.20055i	−0.232275	+	0.402312i	0.726202	+	0.687481i	$0.241284\pi$
$524$	7.08867	+	12.2779i	0.309670	+	0.536364i
$525$			7.29094i			0.318203i
$526$	9.55525	−	5.51673i	0.416629	−	0.240541i
$527$	−62.0973	+	35.8519i	−2.70500	+	1.56173i
$528$		−	8.94462i		−	0.389264i
$529$	11.0089	+	19.0681i	0.478650	+	0.829046i
$530$	−0.274952	+	0.476231i	−0.0119432	+	0.0206862i
$531$	1.01202	+	0.584287i	0.0439177	+	0.0253559i
$532$	8.36033			0.362466
$533$	7.25656	+	17.2117i	0.314316	+	0.745522i
$534$	−6.29992			−0.272624
$535$	2.16638	+	1.25076i	0.0936606	+	0.0540750i
$536$	1.81042	−	3.13575i	0.0781984	−	0.135444i
$537$	−8.20159	−	14.2056i	−0.353925	−	0.613016i
$538$		−	2.61031i		−	0.112538i
$539$	−37.8579	+	21.8573i	−1.63065	+	0.941459i
$540$	−4.21257	+	2.43213i	−0.181280	+	0.104662i
$541$			36.2860i			1.56006i	0.625743	+	0.780029i	$0.284796\pi$
$541$			36.2860i			1.56006i	−0.625743	+	0.780029i	$0.715204\pi$
$542$	−14.3448	−	24.8459i	−0.616161	−	1.06722i
$543$	−5.07540	+	8.79085i	−0.217806	+	0.377251i
$544$	5.74026	+	3.31414i	0.246112	+	0.142093i
$545$	−15.6357			−0.669760
$546$	24.2230	−	10.2126i	1.03665	−	0.437057i
$547$	−21.3774			−0.914030			−0.457015	−	0.889459i	$-0.651081\pi$
$547$	−21.3774			−0.914030			−0.457015	+	0.889459i	$0.651081\pi$
$548$	12.1386	+	7.00821i	0.518534	+	0.299376i
$549$	0.231367	−	0.400740i	0.00987451	−	0.0171032i
$550$	−2.44811	−	4.24026i	−0.104388	−	0.180805i
$551$			12.2404i			0.521457i
$552$	1.56787	−	0.905212i	0.0667331	−	0.0385284i
$553$	8.82161	−	5.09316i	0.375133	−	0.216583i
$554$		−	4.70070i		−	0.199714i
$555$	−3.01421	−	5.22077i	−0.127946	−	0.221609i
$556$	7.99473	−	13.8473i	0.339052	−	0.587255i
$557$	25.0600	+	14.4684i	1.06183	+	0.613045i	0.925937	−	0.377679i	$-0.123278\pi$
$557$	25.0600	+	14.4684i	1.06183	+	0.613045i	0.135889	+	0.990724i	$0.456611\pi$
$558$	−3.64928			−0.154486
$559$	0.508944	−	4.06325i	0.0215261	−	0.171857i
$560$	−3.99102			−0.168651
$561$	−51.3444	−	29.6437i	−2.16776	−	1.25156i
$562$	−1.66209	+	2.87883i	−0.0701111	+	0.121436i
$563$	−9.18717	−	15.9126i	−0.387193	−	0.670638i	0.604878	−	0.796318i	$-0.293222\pi$
$563$	−9.18717	−	15.9126i	−0.387193	−	0.670638i	−0.992071	+	0.125680i	$0.959889\pi$
$564$		−	2.94462i		−	0.123991i
$565$	14.8244	−	8.55889i	0.623668	−	0.360075i
$566$	−22.4969	+	12.9886i	−0.945616	+	0.545952i
$567$		−	39.5039i		−	1.65901i
$568$	3.00000	+	5.19615i	0.125877	+	0.218026i
$569$	−1.40280	+	2.42973i	−0.0588086	+	0.101860i	−0.893931	−	0.448205i	$-0.852064\pi$
$569$	−1.40280	+	2.42973i	−0.0588086	+	0.101860i	0.835122	+	0.550064i	$0.185397\pi$
$570$	−3.31414	−	1.91342i	−0.138814	−	0.0801443i
$571$	−0.119334			−0.00499398			−0.00249699	−	0.999997i	$-0.500795\pi$
$571$	−0.119334			−0.00499398			−0.00249699	+	0.999997i	$0.500795\pi$
$572$	−10.6585	+	14.0729i	−0.445653	+	0.588417i
$573$	−18.6088			−0.777392
$574$	17.9058	+	10.3379i	0.747373	+	0.431496i
$575$	0.495508	−	0.858244i	0.0206641	−	0.0357913i
$576$	0.168669	+	0.292144i	0.00702789	+	0.0121727i
$577$		−	27.6701i		−	1.15192i	−0.817478	−	0.575960i	$-0.804628\pi$
$577$		−	27.6701i		−	1.15192i	0.817478	−	0.575960i	$-0.195372\pi$
$578$	23.3256	−	13.4670i	0.970217	−	0.560155i
$579$	12.8763	−	7.43412i	0.535119	−	0.308951i
$580$		−	5.84325i		−	0.242628i
$581$	−32.7677	−	56.7553i	−1.35943	−	2.35461i
$582$	10.6433	−	18.4347i	0.441178	−	0.764142i
$583$	2.33174	+	1.34623i	0.0965707	+	0.0557551i
$584$	−8.94462			−0.370131
$585$	−1.20686	−	0.151166i	−0.0498976	−	0.00624995i
$586$	−0.952463			−0.0393459
$587$	15.5195	+	8.96018i	0.640558	+	0.369826i	0.784829	−	0.619712i	$-0.212751\pi$
$587$	15.5195	+	8.96018i	0.640558	+	0.369826i	−0.144272	+	0.989538i	$0.546084\pi$
$588$	8.15519	−	14.1252i	0.336314	−	0.582514i
$589$	11.3306	+	19.6251i	0.466867	+	0.808638i
$590$			3.46410i			0.142615i
$591$	22.9095	−	13.2268i	0.942369	−	0.544077i
$592$	2.85782	−	1.64996i	0.117456	−	0.0678130i
$593$		−	22.0640i		−	0.906058i	−0.891496	−	0.453029i	$-0.850343\pi$
$593$		−	22.0640i		−	0.906058i	0.891496	−	0.453029i	$-0.149657\pi$
$594$	11.9082	+	20.6257i	0.488601	+	0.846282i
$595$	−13.2268	+	22.9095i	−0.542245	+	0.939196i
$596$	6.49253	+	3.74846i	0.265944	+	0.153543i
$597$	−20.5639			−0.841625
$598$	−3.54545	−	0.444088i	−0.144984	−	0.0181601i
$599$	47.3354			1.93407			0.967035	−	0.254642i	$-0.0819577\pi$
$599$	47.3354			1.93407			0.967035	+	0.254642i	$0.0819577\pi$
$600$	1.58209	+	0.913419i	0.0645885	+	0.0372902i
$601$	13.4610	−	23.3152i	0.549087	−	0.951046i	−0.449251	−	0.893406i	$-0.648309\pi$
$601$	13.4610	−	23.3152i	0.549087	−	0.951046i	0.998337	−	0.0576406i	$-0.0183577\pi$
$602$	−2.26639	−	3.92551i	−0.0923713	−	0.159992i
$603$		−	1.22145i		−	0.0497414i
$604$	3.67985	−	2.12456i	0.149731	−	0.0864473i
$605$	−11.2350	+	6.48652i	−0.456767	+	0.263715i
$606$			3.79841i			0.154300i
$607$	−9.85548	−	17.0702i	−0.400022	−	0.692858i	0.593706	−	0.804682i	$-0.297664\pi$
$607$	−9.85548	−	17.0702i	−0.400022	−	0.692858i	−0.993728	+	0.111824i	$0.964331\pi$
$608$	1.04739	−	1.81414i	0.0424774	−	0.0735731i
$609$	36.8951	+	21.3014i	1.49507	+	0.863176i
$610$	1.37172			0.0555394
$611$	−3.50883	+	4.63287i	−0.141952	+	0.187426i
$612$	2.23597			0.0903839
$613$	12.6840	+	7.32308i	0.512300	+	0.295777i	0.733779	−	0.679389i	$-0.237755\pi$
$613$	12.6840	+	7.32308i	0.512300	+	0.295777i	−0.221479	+	0.975165i	$0.571088\pi$
$614$	16.2909	−	28.2167i	0.657449	−	1.13873i
$615$	−4.73205	−	8.19615i	−0.190815	−	0.330501i
$616$			19.5409i			0.787326i
$617$	−4.08821	+	2.36033i	−0.164585	+	0.0950233i	−0.580030	−	0.814595i	$-0.696959\pi$
$617$	−4.08821	+	2.36033i	−0.164585	+	0.0950233i	0.415445	+	0.909618i	$0.363626\pi$
$618$	3.58810	−	2.07159i	0.144334	−	0.0833315i
$619$			25.6874i			1.03246i	0.856449	+	0.516231i	$0.172665\pi$
$619$			25.6874i			1.03246i	−0.856449	+	0.516231i	$0.827335\pi$
$620$	−5.40893	−	9.36854i	−0.217228	−	0.376249i
$621$	−2.41027	+	4.17472i	−0.0967210	+	0.167526i
$622$	−15.8336	−	9.14155i	−0.634870	−	0.366543i
$623$	13.7632			0.551410
$624$	0.818632	−	6.53569i	0.0327715	−	0.261637i
$625$	1.00000			0.0400000
$626$	13.9402	+	8.04839i	0.557163	+	0.321678i
$627$	−9.36854	+	16.2268i	−0.374143	+	0.648035i
$628$	−11.3763	−	19.7044i	−0.453964	−	0.786290i
$629$		−	21.8728i		−	0.872126i
$630$	−1.16595	+	0.673162i	−0.0464526	+	0.0268194i
$631$	24.3662	−	14.0678i	0.970003	−	0.560032i	0.0707660	−	0.997493i	$-0.477456\pi$
$631$	24.3662	−	14.0678i	0.970003	−	0.560032i	0.899237	+	0.437461i	$0.144122\pi$
$632$		−	2.55231i		−	0.101526i
$633$	8.75525	+	15.1645i	0.347990	+	0.602736i
$634$	3.69481	−	6.39959i	0.146739	−	0.254160i
$635$	7.03590	+	4.06218i	0.279211	+	0.161203i
$636$	−1.00459			−0.0398345
$637$	−29.6626	+	12.5059i	−1.17527	+	0.495502i
$638$	−28.6099			−1.13268
$639$	1.75286	+	1.01202i	0.0693422	+	0.0400347i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	6.86874	+	11.8970i	0.271299	+	0.469904i	0.969195	−	0.246296i	$-0.0792134\pi$
$641$	6.86874	+	11.8970i	0.271299	+	0.469904i	−0.697896	+	0.716199i	$0.745880\pi$
$642$			4.56986i			0.180358i
$643$	10.0859	−	5.82308i	0.397748	−	0.229640i	−0.287764	−	0.957701i	$-0.592912\pi$
$643$	10.0859	−	5.82308i	0.397748	−	0.229640i	0.685512	+	0.728061i	$0.259578\pi$
$644$	−3.42527	+	1.97758i	−0.134974	+	0.0779275i
$645$			2.07483i			0.0816963i
$646$	−6.94242	−	12.0246i	−0.273146	−	0.473102i
$647$	17.2324	−	29.8473i	0.677474	−	1.17342i	−0.298265	−	0.954483i	$-0.596408\pi$
$647$	17.2324	−	29.8473i	0.677474	−	1.17342i	0.975739	−	0.218936i	$-0.0702587\pi$
$648$	−8.57211	−	4.94911i	−0.336744	−	0.194419i
$649$	16.9610			0.665779
$650$	−1.40072	−	3.32235i	−0.0549408	−	0.130313i
$651$	78.8723			3.09125
$652$	4.51630	+	2.60749i	0.176872	+	0.102117i
$653$	2.43255	−	4.21330i	0.0951931	−	0.164879i	−0.814496	−	0.580169i	$-0.802986\pi$
$653$	2.43255	−	4.21330i	0.0951931	−	0.164879i	0.909689	+	0.415290i	$0.136320\pi$
$654$	−14.2820	−	24.7371i	−0.558469	−	0.967296i
$655$			14.1773i			0.553954i
$656$	4.48652	−	2.59030i	0.175169	−	0.101134i
$657$	−2.61311	+	1.50868i	−0.101947	+	0.0588593i
$658$			6.43298i			0.250784i
$659$	8.82145	+	15.2792i	0.343635	+	0.595193i	0.985105	−	0.171955i	$-0.0550083\pi$
$659$	8.82145	+	15.2792i	0.343635	+	0.595193i	−0.641470	+	0.767148i	$0.721675\pi$
$660$	4.47231	−	7.74627i	0.174084	−	0.301523i
$661$	3.16552	+	1.82762i	0.123125	+	0.0710860i	0.560297	−	0.828292i	$-0.310687\pi$
$661$	3.16552	+	1.82762i	0.123125	+	0.0710860i	−0.437173	+	0.899378i	$0.644020\pi$
$662$	19.4969			0.757770
$663$	−34.8035	−	26.3593i	−1.35166	−	1.02371i
$664$	−16.4207			−0.637248
$665$	7.24026	+	4.18016i	0.280765	+	0.162100i
$666$	0.556596	−	0.964052i	0.0215677	−	0.0373563i
$667$	−2.89538	−	5.01494i	−0.112109	−	0.194179i
$668$		−	6.70447i		−	0.259404i
$669$	−43.0512	+	24.8556i	−1.66446	+	0.960974i
$670$	3.13575	−	1.81042i	0.121145	−	0.0699428i
$671$		−	6.71626i		−	0.259278i
$672$	−3.64547	−	6.31414i	−0.140627	−	0.243573i
$673$	15.4685	−	26.7922i	0.596267	−	1.03276i	−0.397100	−	0.917775i	$-0.629983\pi$
$673$	15.4685	−	26.7922i	0.596267	−	1.03276i	0.993367	−	0.114989i	$-0.0366833\pi$
$674$	−24.1505	−	13.9433i	−0.930241	−	0.537075i
$675$	−4.86425			−0.187225
$676$	−9.07597	+	9.30735i	−0.349076	+	0.357975i
$677$	−25.6685			−0.986522			−0.493261	−	0.869881i	$-0.664195\pi$
$677$	−25.6685			−0.986522			−0.493261	+	0.869881i	$0.664195\pi$
$678$	27.0818	+	15.6357i	1.04007	+	0.600486i
$679$	−23.2519	+	40.2735i	−0.892326	+	1.54555i
$680$	3.31414	+	5.74026i	0.127091	+	0.220129i
$681$		−	11.5609i		−	0.443014i
$682$	−45.8705	+	26.4833i	−1.75647	+	1.01410i
$683$	−26.3774	+	15.2290i	−1.00930	+	0.582721i	−0.910987	−	0.412435i	$-0.864679\pi$
$683$	−26.3774	+	15.2290i	−1.00930	+	0.582721i	−0.0983147	+	0.995155i	$0.531345\pi$
$684$		−	0.706653i		−	0.0270195i
$685$	7.00821	+	12.1386i	0.267770	+	0.463791i
$686$	−3.84774	+	6.66449i	−0.146908	+	0.254451i
$687$	−3.95762	−	2.28493i	−0.150993	−	0.0871756i
$688$	−1.13575			−0.0433000
$689$	1.58055	+	1.19707i	0.0602143	+	0.0456049i
$690$	1.81042			0.0689217
$691$	−5.41546	−	3.12662i	−0.206014	−	0.118942i	0.393444	−	0.919349i	$-0.371284\pi$
$691$	−5.41546	−	3.12662i	−0.206014	−	0.118942i	−0.599458	+	0.800407i	$0.704617\pi$
$692$	−9.77046	+	16.9229i	−0.371417	+	0.643313i
$693$	3.29595	+	5.70876i	0.125203	+	0.216858i
$694$			20.1880i			0.766327i
$695$	13.8473	−	7.99473i	0.525257	−	0.303257i
$696$	9.24454	−	5.33734i	0.350413	−	0.202311i
$697$		−	34.3384i		−	1.30066i
$698$	17.8335	+	30.8885i	0.675008	+	1.16915i
$699$	8.38431	−	14.5220i	0.317124	−	0.549274i
$700$	−3.45632	−	1.99551i	−0.130637	−	0.0754231i
$701$	9.17903			0.346687			0.173344	−	0.984861i	$-0.444543\pi$
$701$	9.17903			0.346687			0.173344	+	0.984861i	$0.444543\pi$
$702$	6.81346	+	16.1607i	0.257157	+	0.609947i
$703$	−6.91264			−0.260715
$704$	4.24026	+	2.44811i	0.159811	+	0.0922668i
$705$	1.47231	−	2.55011i	0.0554503	−	0.0960428i
$706$	12.7886	+	22.1506i	0.481307	+	0.833648i
$707$		−	8.29822i		−	0.312087i
$708$	−5.48052	+	3.16418i	−0.205970	+	0.118917i
$709$	30.0521	−	17.3506i	1.12863	−	0.651614i	0.185039	−	0.982731i	$-0.440759\pi$
$709$	30.0521	−	17.3506i	1.12863	−	0.651614i	0.943590	+	0.331117i	$0.107425\pi$
$710$			6.00000i			0.225176i
$711$	−0.430497	−	0.745642i	−0.0161449	−	0.0279638i
$712$	1.72427	−	2.98652i	0.0646197	−	0.111925i
$713$	−9.28436	−	5.36033i	−0.347702	−	0.200746i
$714$	−48.3264			−1.80857
$715$	−16.2670	+	6.85824i	−0.608350	+	0.256484i
$716$	8.97900			0.335561
$717$	−10.3473	−	5.97403i	−0.386428	−	0.223104i
$718$	12.1244	−	21.0000i	0.452477	−	0.783713i
$719$	9.12761	+	15.8095i	0.340403	+	0.589595i	0.984507	−	0.175343i	$-0.0561033\pi$
$719$	9.12761	+	15.8095i	0.340403	+	0.589595i	−0.644105	+	0.764937i	$0.722770\pi$
$720$			0.337339i			0.0125719i
$721$	−7.83876	+	4.52571i	−0.291931	+	0.168546i
$722$	12.6542	−	7.30593i	0.470942	−	0.271899i
$723$		−	16.5923i		−	0.617076i
$724$	−2.77824	−	4.81205i	−0.103253	−	0.178839i
$725$	2.92163	−	5.06040i	0.108506	−	0.187939i
$726$	−20.5245	−	11.8498i	−0.761736	−	0.439788i
$727$	4.76025			0.176548			0.0882740	−	0.996096i	$-0.471865\pi$
$727$	4.76025			0.176548			0.0882740	+	0.996096i	$0.471865\pi$
$728$	−1.78843	+	14.2782i	−0.0662836	+	0.529187i
$729$	23.3196			0.863687
$730$	−7.74627	−	4.47231i	−0.286702	−	0.165528i
$731$	−3.76403	+	6.51948i	−0.139218	+	0.241132i
$732$	1.25296	+	2.17018i	0.0463106	+	0.0802123i
$733$		−	1.44352i		−	0.0533176i	−0.999645	−	0.0266588i	$-0.991513\pi$
$733$		−	1.44352i		−	0.0533176i	0.999645	−	0.0266588i	$-0.00848676\pi$
$734$	2.56285	−	1.47966i	0.0945966	−	0.0546154i
$735$	14.1252	−	8.15519i	0.521016	−	0.300809i
$736$			0.991015i			0.0365293i
$737$	−8.86425	−	15.3533i	−0.326519	−	0.565547i
$738$	0.873806	−	1.51348i	0.0321653	−	0.0557119i
$739$	−27.0111	−	15.5949i	−0.993621	−	0.573667i	−0.0872663	−	0.996185i	$-0.527813\pi$
$739$	−27.0111	−	15.5949i	−0.993621	−	0.573667i	−0.906355	+	0.422518i	$0.861146\pi$
$740$	3.29992			0.121308
$741$	−8.33055	+	10.9992i	−0.306031	+	0.404067i
$742$	2.19468			0.0805691
$743$	−20.8591	−	12.0430i	−0.765246	−	0.441815i	0.0659301	−	0.997824i	$-0.478999\pi$
$743$	−20.8591	−	12.0430i	−0.765246	−	0.441815i	−0.831176	+	0.556009i	$0.812332\pi$
$744$	9.88124	−	17.1148i	0.362264	−	0.627459i
$745$	3.74846	+	6.49253i	0.137333	+	0.237868i
$746$		−	5.82358i		−	0.213216i
$747$	−4.79721	+	2.76967i	−0.175521	+	0.101337i
$748$	28.1056	−	16.2268i	1.02764	−	0.593310i
$749$		−	9.98359i		−	0.364792i
$750$	0.913419	+	1.58209i	0.0333534	+	0.0577697i
$751$	−0.944617	+	1.63612i	−0.0344696	+	0.0597030i	−0.882746	−	0.469851i	$-0.844308\pi$
$751$	−0.944617	+	1.63612i	−0.0344696	+	0.0597030i	0.848276	+	0.529554i	$0.177641\pi$
$752$	1.39592	+	0.805932i	0.0509038	+	0.0293893i
$753$	−17.5893			−0.640990
$754$	−20.9048	−	2.61844i	−0.761308	−	0.0953580i
$755$	4.24913			0.154642
$756$	16.8124	+	9.70665i	0.611462	+	0.353028i
$757$	11.7385	−	20.3317i	0.426642	−	0.738966i	−0.569930	−	0.821693i	$-0.693030\pi$
$757$	11.7385	−	20.3317i	0.426642	−	0.738966i	0.996572	+	0.0827270i	$0.0263629\pi$
$758$	0.290514	+	0.503185i	0.0105520	+	0.0182765i
$759$		−	8.86425i		−	0.321752i
$760$	1.81414	−	1.04739i	0.0658057	−	0.0379930i
$761$	−20.4760	+	11.8218i	−0.742253	+	0.428540i	−0.822888	−	0.568204i	$-0.807639\pi$
$761$	−20.4760	+	11.8218i	−0.742253	+	0.428540i	0.0806347	+	0.996744i	$0.474305\pi$
$762$			14.8419i			0.537665i
$763$	31.2012	+	54.0420i	1.12956	+	1.95645i
$764$	5.09316	−	8.82161i	0.184264	−	0.319155i
$765$	1.93641	+	1.11799i	0.0700111	+	0.0404209i
$766$	15.3014			0.552862
$767$	12.3932	+	1.55231i	0.447491	+	0.0560507i
$768$	−1.82684			−0.0659204
$769$	33.5563	+	19.3738i	1.21007	+	0.698636i	0.962775	−	0.270304i	$-0.0871241\pi$
$769$	33.5563	+	19.3738i	1.21007	+	0.698636i	0.247298	+	0.968940i	$0.420457\pi$
$770$	−9.77046	+	16.9229i	−0.352103	+	0.609860i
$771$	13.5389	+	23.4501i	0.487593	+	0.844535i
$772$			8.13878i			0.292921i
$773$	−6.16020	+	3.55660i	−0.221567	+	0.127922i	−0.606676	−	0.794949i	$-0.707497\pi$
$773$	−6.16020	+	3.55660i	−0.221567	+	0.127922i	0.385109	+	0.922871i	$0.374164\pi$
$774$	−0.331802	+	0.191566i	−0.0119264	+	0.00688569i
$775$		−	10.8179i		−	0.388589i
$776$	5.82606	+	10.0910i	0.209143	+	0.362247i
$777$	−12.0298	+	20.8362i	−0.431566	+	0.747494i
$778$	17.0850	+	9.86404i	0.612528	+	0.353643i
$779$	−10.8522			−0.388822
$780$	3.97680	−	5.25076i	0.142392	−	0.188007i
$781$	29.3774			1.05120
$782$	5.68868	+	3.28436i	0.203427	+	0.117449i
$783$	−14.2115	+	24.6151i	−0.507878	+	0.879671i
$784$	4.46410	+	7.73205i	0.159432	+	0.276145i
$785$		−	22.7526i		−	0.812076i
$786$	−22.4298	+	12.9498i	−0.800044	+	0.461906i
$787$	2.28033	−	1.31655i	0.0812848	−	0.0469298i	−0.458807	−	0.888536i	$-0.651723\pi$
$787$	2.28033	−	1.31655i	0.0812848	−	0.0469298i	0.540092	+	0.841606i	$0.318390\pi$
$788$			14.4805i			0.515847i
$789$	10.0782	+	17.4559i	0.358792	+	0.621446i
$790$	1.27616	−	2.21037i	0.0454036	−	0.0786413i
$791$	−59.1645	−	34.1587i	−2.10365	−	1.21454i
$792$	1.65169			0.0586901
$793$	0.614687	−	4.90747i	0.0218282	−	0.174269i
$794$	0.826838			0.0293434
$795$	−0.869998	−	0.502293i	−0.0308556	−	0.0178145i
$796$	5.62828	−	9.74846i	0.199489	−	0.345525i
$797$	−1.25953	−	2.18158i	−0.0446150	−	0.0772754i	0.842856	−	0.538140i	$-0.180873\pi$
$797$	−1.25953	−	2.18158i	−0.0446150	−	0.0772754i	−0.887471	+	0.460864i	$0.847539\pi$
$798$			15.2730i			0.540657i
$799$	9.25252	−	5.34194i	0.327331	−	0.188984i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$		−	1.16333i		−	0.0411041i
$802$	−15.8002	−	27.3668i	−0.557926	−	0.966356i
$803$	−21.8974	+	37.9275i	−0.772744	+	1.33843i
$804$	5.72850	+	3.30735i	0.202029	+	0.116641i
$805$	−3.95516			−0.139401
$806$	−35.9407	+	15.1528i	−1.26596	+	0.533734i
$807$	4.76861			0.167863
$808$	−1.80066	−	1.03961i	−0.0633471	−	0.0365735i
$809$	−4.35078	+	7.53576i	−0.152965	+	0.264943i	−0.932316	−	0.361644i	$-0.882216\pi$
$809$	−4.35078	+	7.53576i	−0.152965	+	0.264943i	0.779351	+	0.626587i	$0.215549\pi$
$810$	−4.94911	−	8.57211i	−0.173894	−	0.301193i
$811$		−	40.3063i		−	1.41535i	−0.706540	−	0.707673i	$-0.749745\pi$
$811$		−	40.3063i		−	1.41535i	0.706540	−	0.707673i	$-0.250255\pi$
$812$	−20.1962	+	11.6603i	−0.708746	+	0.409195i
$813$	45.3894	−	26.2056i	1.59188	−	0.919070i
$814$		−	16.1572i		−	0.566309i
$815$	2.60749	+	4.51630i	0.0913363	+	0.158199i
$816$	−6.05440	+	10.4865i	−0.211946	+	0.367102i
$817$	2.06040	+	1.18958i	0.0720844	+	0.0416180i
$818$	−21.9336			−0.766892
$819$	1.88582	+	4.47295i	0.0658960	+	0.156298i
$820$	5.18059			0.180914
$821$	29.2880	+	16.9095i	1.02216	+	0.590144i	0.914729	−	0.404068i	$-0.132404\pi$
$821$	29.2880	+	16.9095i	1.02216	+	0.590144i	0.107431	+	0.994213i	$0.465738\pi$
$822$	−12.8029	+	22.1752i	−0.446551	+	0.773449i
$823$	−24.1874	−	41.8938i	−0.843119	−	1.46033i	−0.887245	−	0.461299i	$-0.847383\pi$
$823$	−24.1874	−	41.8938i	−0.843119	−	1.46033i	0.0441253	−	0.999026i	$-0.485950\pi$
$824$			2.26795i			0.0790078i
$825$	7.74627	−	4.47231i	0.269690	−	0.155706i
$826$	11.9730	−	6.91264i	0.416596	−	0.240522i
$827$			15.1331i			0.526228i	0.964765	+	0.263114i	$0.0847495\pi$
$827$			15.1331i			0.526228i	−0.964765	+	0.263114i	$0.915250\pi$
$828$	0.167154	+	0.289519i	0.00580900	+	0.0100615i
$829$	−4.22458	+	7.31719i	−0.146726	+	0.254137i	−0.930015	−	0.367520i	$-0.880207\pi$
$829$	−4.22458	+	7.31719i	−0.146726	+	0.254137i	0.783290	+	0.621657i	$0.213540\pi$
$830$	−14.2208	−	8.21037i	−0.493610	−	0.284986i
$831$	8.58742			0.297894
$832$	2.87423	+	2.17688i	0.0996461	+	0.0754696i
$833$	59.1786			2.05042
$834$	25.2967	+	14.6051i	0.875954	+	0.505733i
$835$	3.35224	−	5.80624i	0.116009	−	0.200933i
$836$	−5.12828	−	8.88244i	−0.177365	−	0.307206i
$837$			52.6208i			1.81884i
$838$	−26.4681	+	15.2814i	−0.914327	+	0.527887i
$839$	−15.7792	+	9.11014i	−0.544759	+	0.314517i	−0.747006	−	0.664818i	$-0.768509\pi$
$839$	−15.7792	+	9.11014i	−0.544759	+	0.314517i	0.202246	+	0.979335i	$0.435176\pi$
$840$		−	7.29094i		−	0.251561i
$841$	−2.57180	−	4.45448i	−0.0886826	−	0.153603i
$842$	10.7282	−	18.5819i	0.369720	−	0.640373i
$843$	−5.25915	−	3.03637i	−0.181135	−	0.104578i
$844$	−9.58514			−0.329934
$845$	−12.5137	+	3.52242i	−0.430484	+	0.121175i
$846$	0.543744			0.0186943
$847$	44.8390	+	25.8878i	1.54069	+	0.889516i
$848$	0.274952	−	0.476231i	0.00944190	−	0.0163538i
$849$	−23.7281	−	41.0983i	−0.814346	−	1.41049i
$850$			6.62828i			0.227348i
$851$	2.83214	−	1.63514i	0.0970846	−	0.0560518i
$852$	−9.49253	+	5.48052i	−0.325209	+	0.187759i
$853$		−	37.4425i		−	1.28201i	−0.767539	−	0.641003i	$-0.778519\pi$
$853$		−	37.4425i		−	1.28201i	0.767539	−	0.641003i	$-0.221481\pi$
$854$	−2.73728	−	4.74111i	−0.0936678	−	0.162237i
$855$	0.353326	−	0.611979i	0.0120835	−	0.0209292i
$856$	−2.16638	−	1.25076i	−0.0740452	−	0.0427500i
$857$	−28.6086			−0.977251			−0.488626	−	0.872494i	$-0.662502\pi$
$857$	−28.6086			−0.977251			−0.488626	+	0.872494i	$0.662502\pi$
$858$	−25.7089	−	19.4713i	−0.877688	−	0.664740i
$859$	−22.4266			−0.765186			−0.382593	−	0.923917i	$-0.624969\pi$
$859$	−22.4266			−0.765186			−0.382593	+	0.923917i	$0.624969\pi$
$860$	−0.983586	−	0.567874i	−0.0335400	−	0.0193643i
$861$	−18.8857	+	32.7110i	−0.643622	+	1.11479i
$862$	4.58209	+	7.93641i	0.156067	+	0.270315i
$863$			3.08381i			0.104974i	0.998622	+	0.0524871i	$0.0167148\pi$
$863$			3.08381i			0.104974i	−0.998622	+	0.0524871i	$0.983285\pi$
$864$	4.21257	−	2.43213i	0.143314	−	0.0827426i
$865$	−16.9229	+	9.77046i	−0.575397	+	0.332206i
$866$		−	10.0968i		−	0.343102i
$867$	24.6021	+	42.6121i	0.835531	+	1.44718i
$868$	−21.5871	+	37.3900i	−0.732714	+	1.26910i
$869$	−10.8225	−	6.24835i	−0.367127	−	0.211961i
$870$	10.6747			0.361905
$871$	−5.07180	−	12.0297i	−0.171851	−	0.407611i
$872$	15.6357			0.529492
$873$	3.40409	+	1.96535i	0.115211	+	0.0665172i
$874$	1.03798	−	1.79784i	0.0351103	−	0.0608128i
$875$	−1.99551	−	3.45632i	−0.0674605	−	0.116845i
$876$		−	16.3404i		−	0.552090i
$877$	33.0587	−	19.0864i	1.11631	−	0.644503i	0.175855	−	0.984416i	$-0.443731\pi$
$877$	33.0587	−	19.0864i	1.11631	−	0.644503i	0.940457	+	0.339913i	$0.110398\pi$
$878$	−22.9752	+	13.2648i	−0.775377	+	0.447664i
$879$		−	1.74000i		−	0.0586886i
$880$	2.44811	+	4.24026i	0.0825259	+	0.142939i
$881$	−11.9835	+	20.7561i	−0.403736	+	0.699291i	−0.994173	−	0.107792i	$-0.965622\pi$
$881$	−11.9835	+	20.7561i	−0.403736	+	0.699291i	0.590438	+	0.807083i	$0.298955\pi$
$882$	2.60832	+	1.50591i	0.0878267	+	0.0507067i
$883$	19.7537			0.664765			0.332383	−	0.943145i	$-0.392147\pi$
$883$	19.7537			0.664765			0.332383	+	0.943145i	$0.392147\pi$
$884$	22.0214	−	9.28436i	0.740661	−	0.312267i
$885$	−6.32835			−0.212725
$886$	−11.2454	−	6.49253i	−0.377796	−	0.218121i
$887$	−10.0846	+	17.4670i	−0.338608	+	0.586486i	−0.984171	−	0.177221i	$-0.943289\pi$
$887$	−10.0846	+	17.4670i	−0.338608	+	0.586486i	0.645563	+	0.763707i	$0.276623\pi$
$888$	3.01421	+	5.22077i	0.101150	+	0.175198i
$889$		−	32.4244i		−	1.08748i
$890$	2.98652	−	1.72427i	0.100108	−	0.0577977i
$891$	−41.9710	+	24.2320i	−1.40608	+	0.811801i
$892$		−	27.2116i		−	0.911113i
$893$	−1.68826	−	2.92415i	−0.0564954	−	0.0978529i
$894$	−6.84784	+	11.8608i	−0.229026	+	0.396685i
$895$	7.77604	+	4.48950i	0.259924	+	0.150067i
$896$	3.99102			0.133330
$897$	0.811276	−	6.47697i	0.0270877	−	0.216260i
$898$	31.7869			1.06074
$899$	−54.7427	−	31.6057i	−1.82577	−	1.05411i
$900$	−0.168669	+	0.292144i	−0.00562231	+	0.00973812i
$901$	−1.82246	−	3.15659i	−0.0607150	−	0.105161i
$902$		−	25.3654i		−	0.844574i
$903$	7.17127	−	4.14033i	0.238645	−	0.137782i
$904$	−14.8244	+	8.55889i	−0.493053	+	0.284664i
$905$		−	5.55648i		−	0.184704i
$906$	3.88124	+	6.72250i	0.128945	+	0.223340i
$907$	−11.9528	+	20.7029i	−0.396887	+	0.687428i	−0.993340	−	0.115220i	$-0.963243\pi$
$907$	−11.9528	+	20.7029i	−0.396887	+	0.687428i	0.596453	+	0.802648i	$0.296576\pi$
$908$	5.48052	+	3.16418i	0.181877	+	0.105007i
$909$	−0.701403			−0.0232641
$910$	−8.68795	+	11.4711i	−0.288003	+	0.380263i
$911$	−26.3025			−0.871439			−0.435720	−	0.900082i	$-0.643506\pi$
$911$	−26.3025			−0.871439			−0.435720	+	0.900082i	$0.643506\pi$
$912$	3.31414	+	1.91342i	0.109742	+	0.0633596i
$913$	−40.1998	+	69.6281i	−1.33042	+	2.30436i
$914$	3.70828	+	6.42293i	0.122659	+	0.212452i
$915$			2.50591i			0.0828429i
$916$	2.16638	−	1.25076i	0.0715791	−	0.0413262i
$917$	49.0014	−	28.2910i	1.61817	−	0.934250i
$918$		−	32.2416i		−	1.06413i
$919$	−12.8564	−	22.2679i	−0.424094	−	0.734552i	0.572242	−	0.820085i	$-0.306074\pi$
$919$	−12.8564	−	22.2679i	−0.424094	−	0.734552i	−0.996335	+	0.0855332i	$0.972741\pi$
$920$	−0.495508	+	0.858244i	−0.0163364	+	0.0282955i
$921$	51.5474	+	29.7609i	1.69855	+	0.980655i
$922$	40.0593			1.31928
$923$	21.4656	+	2.68868i	0.706548	+	0.0884991i
$924$	−35.6981			−1.17438
$925$	2.85782	+	1.64996i	0.0939645	+	0.0542504i
$926$	11.3059	−	19.5824i	0.371536	−	0.643519i
$927$	0.382533	+	0.662567i	0.0125640	+	0.0217616i
$928$			5.84325i			0.191814i
$929$	22.9610	−	13.2566i	0.753327	−	0.434934i	−0.0735678	−	0.997290i	$-0.523439\pi$
$929$	22.9610	−	13.2566i	0.753327	−	0.434934i	0.826895	+	0.562357i	$0.190105\pi$
$930$	17.1148	−	9.88124i	0.561216	−	0.324018i
$931$		−	18.7027i		−	0.612956i
$932$	4.58952	+	7.94928i	0.150335	+	0.260387i
$933$	16.7001	−	28.9255i	0.546738	−	0.946977i
$934$	6.68783	+	3.86122i	0.218833	+	0.126343i
$935$	32.4536			1.06134
$936$	1.20686	+	0.151166i	0.0394475	+	0.00494102i
$937$	24.3940			0.796918			0.398459	−	0.917186i	$-0.369545\pi$
$937$	24.3940			0.796918			0.398459	+	0.917186i	$0.369545\pi$
$938$	−12.5148	−	7.22543i	−0.408623	−	0.235919i
$939$	−14.7031	+	25.4665i	−0.479818	+	0.831069i
$940$	0.805932	+	1.39592i	0.0262866	+	0.0455298i
$941$		−	3.13575i		−	0.102222i	−0.998693	−	0.0511112i	$-0.983724\pi$
$941$		−	3.13575i		−	0.102222i	0.998693	−	0.0511112i	$-0.0162763\pi$
$942$	35.9967	−	20.7827i	1.17284	−	0.677137i
$943$	4.44621	−	2.56702i	0.144789	−	0.0835937i
$944$		−	3.46410i		−	0.112747i
$945$	9.70665	+	16.8124i	0.315757	+	0.546908i
$946$	−2.78044	+	4.81586i	−0.0903999	+	0.156577i
$947$	16.2718	+	9.39450i	0.528761	+	0.305280i	0.740512	−	0.672043i	$-0.234583\pi$
$947$	16.2718	+	9.39450i	0.528761	+	0.305280i	−0.211751	+	0.977324i	$0.567916\pi$
$948$	4.66266			0.151436
$949$	−19.4713	+	25.7089i	−0.632066	+	0.834546i
$950$	2.09479			0.0679639
$951$	11.6910	+	6.74981i	0.379107	+	0.218878i
$952$	13.2268	−	22.9095i	0.428682	−	0.742500i
$953$	−3.80667	−	6.59335i	−0.123310	−	0.213579i	0.797761	−	0.602974i	$-0.206018\pi$
$953$	−3.80667	−	6.59335i	−0.123310	−	0.213579i	−0.921071	+	0.389394i	$0.872684\pi$
$954$		−	0.185504i		−	0.00600591i
$955$	8.82161	−	5.09316i	0.285461	−	0.164811i
$956$	5.66406	−	3.27015i	0.183189	−	0.105764i
$957$		−	52.2656i		−	1.68951i
$958$	−2.49473	−	4.32100i	−0.0806011	−	0.139605i
$959$	27.9699	−	48.4452i	0.903194	−	1.56438i
$960$	−1.58209	−	0.913419i	−0.0510617	−	0.0294805i
$961$	−86.0260			−2.77503
$962$	1.47874	−	11.8058i	0.0476766	−	0.380634i
$963$	−0.843858			−0.0271929
$964$	7.86571	+	4.54127i	0.253338	+	0.146265i
$965$	−4.06939	+	7.04839i	−0.130998	+	0.226896i
$966$	−3.61272	−	6.25741i	−0.116237	−	0.201329i
$967$		−	22.5849i		−	0.726282i	−0.931734	−	0.363141i	$-0.881704\pi$
$967$		−	22.5849i		−	0.726282i	0.931734	−	0.363141i	$-0.118296\pi$
$968$	11.2350	−	6.48652i	0.361106	−	0.208485i
$969$	21.9670	−	12.6827i	0.705683	−	0.407426i
$970$			11.6521i			0.374127i
$971$	16.3491	+	28.3174i	0.524666	+	0.908748i	0.999587	+	0.0287200i	$0.00914313\pi$
$971$	16.3491	+	28.3174i	0.524666	+	0.908748i	−0.474921	+	0.880028i	$0.657524\pi$
$972$	1.74484	−	3.02216i	0.0559659	−	0.0969358i
$973$	−55.2647	−	31.9071i	−1.77170	−	1.02289i
$974$	−25.8354			−0.827820
$975$	6.06939	−	2.55889i	0.194376	−	0.0819500i
$976$	−1.37172			−0.0439077
$977$	42.3066	+	24.4258i	1.35351	+	0.781449i	0.988739	−	0.149648i	$-0.0478142\pi$
$977$	42.3066	+	24.4258i	1.35351	+	0.781449i	0.364770	+	0.931098i	$0.381147\pi$
$978$	−4.76346	+	8.25055i	−0.152319	+	0.263823i
$979$	−8.44242	−	14.6227i	−0.269821	−	0.467343i
$980$			8.92820i			0.285201i
$981$	4.56787	−	2.63726i	0.145841	−	0.0842013i
$982$	−15.1568	+	8.75076i	−0.483672	+	0.279248i
$983$		−	16.3881i		−	0.522700i	−0.965244	−	0.261350i	$-0.915832\pi$
$983$		−	16.3881i		−	0.522700i	0.965244	−	0.261350i	$-0.0841677\pi$
$984$	4.73205	+	8.19615i	0.150852	+	0.261284i
$985$	−7.24026	+	12.5405i	−0.230694	+	0.399573i
$986$	33.5418	+	19.3654i	1.06819	+	0.616718i
$987$	−11.7520			−0.374071
$988$	−2.93421	−	6.95961i	−0.0933497	−	0.221415i
$989$	−1.12554			−0.0357902
$990$	1.43040	+	0.825843i	0.0454612	+	0.0262470i
$991$	21.8977	−	37.9279i	0.695603	−	1.20482i	−0.274373	−	0.961623i	$-0.588470\pi$
$991$	21.8977	−	37.9279i	0.695603	−	1.20482i	0.969977	−	0.243197i	$-0.0781962\pi$
$992$	5.40893	+	9.36854i	0.171734	+	0.297451i
$993$			35.6177i			1.13029i
$994$	20.7379	−	11.9730i	0.657767	−	0.379762i
$995$	9.74846	−	5.62828i	0.309047	−	0.178428i
$996$		−	29.9980i		−	0.950524i
$997$	22.5569	+	39.0697i	0.714384	+	1.23735i	0.963196	+	0.268798i	$0.0866265\pi$
$997$	22.5569	+	39.0697i	0.714384	+	1.23735i	−0.248812	+	0.968552i	$0.580040\pi$
$998$	9.52593	−	16.4994i	0.301538	−	0.522279i
$999$	−13.9012	−	8.02583i	−0.439813	−	0.253926i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	130.2.l.b.121.2	yes	8
3.2	odd	2		1170.2.bs.g.901.4		8
4.3	odd	2		1040.2.da.d.641.1		8
5.2	odd	4		650.2.n.e.199.2		8
5.3	odd	4		650.2.n.d.199.3		8
5.4	even	2		650.2.m.c.251.3		8
13.2	odd	12		1690.2.e.s.991.4		8
13.3	even	3		1690.2.l.j.361.4		8
13.4	even	6		1690.2.d.k.1351.1		8
13.5	odd	4		1690.2.e.s.191.4		8
13.6	odd	12		1690.2.a.u.1.1		4
13.7	odd	12		1690.2.a.t.1.1		4
13.8	odd	4		1690.2.e.t.191.4		8
13.9	even	3		1690.2.d.k.1351.5		8
13.10	even	6	inner	130.2.l.b.101.2	✓	8
13.11	odd	12		1690.2.e.t.991.4		8
13.12	even	2		1690.2.l.j.1161.4		8
39.23	odd	6		1170.2.bs.g.361.4		8
52.23	odd	6		1040.2.da.d.881.1		8
65.19	odd	12		8450.2.a.ci.1.4		4
65.23	odd	12		650.2.n.e.49.2		8
65.49	even	6		650.2.m.c.101.3		8
65.59	odd	12		8450.2.a.cm.1.4		4
65.62	odd	12		650.2.n.d.49.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.l.b.101.2	✓	8	13.10	even	6	inner
130.2.l.b.121.2	yes	8	1.1	even	1	trivial
650.2.m.c.101.3		8	65.49	even	6
650.2.m.c.251.3		8	5.4	even	2
650.2.n.d.49.3		8	65.62	odd	12
650.2.n.d.199.3		8	5.3	odd	4
650.2.n.e.49.2		8	65.23	odd	12
650.2.n.e.199.2		8	5.2	odd	4
1040.2.da.d.641.1		8	4.3	odd	2
1040.2.da.d.881.1		8	52.23	odd	6
1170.2.bs.g.361.4		8	39.23	odd	6
1170.2.bs.g.901.4		8	3.2	odd	2
1690.2.a.t.1.1		4	13.7	odd	12
1690.2.a.u.1.1		4	13.6	odd	12
1690.2.d.k.1351.1		8	13.4	even	6
1690.2.d.k.1351.5		8	13.9	even	3
1690.2.e.s.191.4		8	13.5	odd	4
1690.2.e.s.991.4		8	13.2	odd	12
1690.2.e.t.191.4		8	13.8	odd	4
1690.2.e.t.991.4		8	13.11	odd	12
1690.2.l.j.361.4		8	13.3	even	3
1690.2.l.j.1161.4		8	13.12	even	2
8450.2.a.ci.1.4		4	65.19	odd	12
8450.2.a.cm.1.4		4	65.59	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 130 = 2 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	130.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.913419 - 1.58209i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000i q^{5} +(-1.58209 + 0.913419i) q^{6} +(3.45632 - 1.99551i) q^{7} -1.00000i q^{8} +(-0.168669 - 0.292144i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.913419 - 1.58209i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000i q^{5} +(-1.58209 + 0.913419i) q^{6} +(3.45632 - 1.99551i) q^{7} -1.00000i q^{8} +(-0.168669 - 0.292144i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-4.24026 - 2.44811i) q^{11} +1.82684 q^{12} +(-2.87423 - 2.17688i) q^{13} -3.99102 q^{14} +(1.58209 + 0.913419i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.31414 + 5.74026i) q^{17} +0.337339i q^{18} +(1.81414 - 1.04739i) q^{19} +(-0.866025 + 0.500000i) q^{20} -7.29094i q^{21} +(2.44811 + 4.24026i) q^{22} +(-0.495508 + 0.858244i) q^{23} +(-1.58209 - 0.913419i) q^{24} -1.00000 q^{25} +(1.40072 + 3.32235i) q^{26} +4.86425 q^{27} +(3.45632 + 1.99551i) q^{28} +(-2.92163 + 5.06040i) q^{29} +(-0.913419 - 1.58209i) q^{30} +10.8179i q^{31} +(0.866025 - 0.500000i) q^{32} +(-7.74627 + 4.47231i) q^{33} -6.62828i q^{34} +(1.99551 + 3.45632i) q^{35} +(0.168669 - 0.292144i) q^{36} +(-2.85782 - 1.64996i) q^{37} -2.09479 q^{38} +(-6.06939 + 2.55889i) q^{39} +1.00000 q^{40} +(-4.48652 - 2.59030i) q^{41} +(-3.64547 + 6.31414i) q^{42} +(0.567874 + 0.983586i) q^{43} -4.89623i q^{44} +(0.292144 - 0.168669i) q^{45} +(0.858244 - 0.495508i) q^{46} -1.61186i q^{47} +(0.913419 + 1.58209i) q^{48} +(4.46410 - 7.73205i) q^{49} +(0.866025 + 0.500000i) q^{50} +12.1088 q^{51} +(0.448114 - 3.57760i) q^{52} -0.549905 q^{53} +(-4.21257 - 2.43213i) q^{54} +(2.44811 - 4.24026i) q^{55} +(-1.99551 - 3.45632i) q^{56} -3.82684i q^{57} +(5.06040 - 2.92163i) q^{58} +(-3.00000 + 1.73205i) q^{59} +1.82684i q^{60} +(0.685861 + 1.18795i) q^{61} +(5.40893 - 9.36854i) q^{62} +(-1.16595 - 0.673162i) q^{63} -1.00000 q^{64} +(2.17688 - 2.87423i) q^{65} +8.94462 q^{66} +(3.13575 + 1.81042i) q^{67} +(-3.31414 + 5.74026i) q^{68} +(0.905212 + 1.56787i) q^{69} -3.99102i q^{70} +(-5.19615 + 3.00000i) q^{71} +(-0.292144 + 0.168669i) q^{72} -8.94462i q^{73} +(1.64996 + 2.85782i) q^{74} +(-0.913419 + 1.58209i) q^{75} +(1.81414 + 1.04739i) q^{76} -19.5409 q^{77} +(6.53569 + 0.818632i) q^{78} +2.55231 q^{79} +(-0.866025 - 0.500000i) q^{80} +(4.94911 - 8.57211i) q^{81} +(2.59030 + 4.48652i) q^{82} -16.4207i q^{83} +(6.31414 - 3.64547i) q^{84} +(-5.74026 + 3.31414i) q^{85} -1.13575i q^{86} +(5.33734 + 9.24454i) q^{87} +(-2.44811 + 4.24026i) q^{88} +(2.98652 + 1.72427i) q^{89} -0.337339 q^{90} +(-14.2782 - 1.78843i) q^{91} -0.991015 q^{92} +(17.1148 + 9.88124i) q^{93} +(-0.805932 + 1.39592i) q^{94} +(1.04739 + 1.81414i) q^{95} -1.82684i q^{96} +(-10.0910 + 5.82606i) q^{97} +(-7.73205 + 4.46410i) q^{98} +1.65169i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} + 4 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 + 4 * q^4 - 6 * q^6 - 4 * q^9	\( 8 q - 2 q^{3} + 4 q^{4} - 6 q^{6} - 4 q^{9} + 4 q^{10} - 6 q^{11} - 4 q^{12} - 2 q^{13} + 6 q^{15} - 4 q^{16} + 6 q^{17} - 6 q^{19} + 6 q^{22} + 12 q^{23} - 6 q^{24} - 8 q^{25} + 40 q^{27} + 2 q^{30} - 42 q^{33} + 4 q^{36} - 30 q^{37} - 12 q^{38} - 40 q^{39} + 8 q^{40} + 12 q^{41} - 6 q^{42} + 4 q^{43} - 12 q^{45} - 2 q^{48} + 8 q^{49} - 10 q^{52} + 60 q^{53} + 36 q^{54} + 6 q^{55} - 24 q^{59} + 26 q^{61} + 18 q^{62} + 12 q^{63} - 8 q^{64} + 6 q^{65} - 12 q^{66} + 24 q^{67} - 6 q^{68} + 12 q^{69} + 12 q^{72} + 6 q^{74} + 2 q^{75} - 6 q^{76} - 60 q^{77} - 6 q^{78} + 20 q^{79} - 28 q^{81} + 30 q^{84} - 18 q^{85} + 48 q^{87} - 6 q^{88} - 24 q^{89} - 8 q^{90} - 66 q^{91} + 24 q^{92} + 48 q^{93} + 6 q^{95} - 6 q^{97} - 48 q^{98}+O(q^{100}) \) 8 * q - 2 * q^3 + 4 * q^4 - 6 * q^6 - 4 * q^9 + 4 * q^10 - 6 * q^11 - 4 * q^12 - 2 * q^13 + 6 * q^15 - 4 * q^16 + 6 * q^17 - 6 * q^19 + 6 * q^22 + 12 * q^23 - 6 * q^24 - 8 * q^25 + 40 * q^27 + 2 * q^30 - 42 * q^33 + 4 * q^36 - 30 * q^37 - 12 * q^38 - 40 * q^39 + 8 * q^40 + 12 * q^41 - 6 * q^42 + 4 * q^43 - 12 * q^45 - 2 * q^48 + 8 * q^49 - 10 * q^52 + 60 * q^53 + 36 * q^54 + 6 * q^55 - 24 * q^59 + 26 * q^61 + 18 * q^62 + 12 * q^63 - 8 * q^64 + 6 * q^65 - 12 * q^66 + 24 * q^67 - 6 * q^68 + 12 * q^69 + 12 * q^72 + 6 * q^74 + 2 * q^75 - 6 * q^76 - 60 * q^77 - 6 * q^78 + 20 * q^79 - 28 * q^81 + 30 * q^84 - 18 * q^85 + 48 * q^87 - 6 * q^88 - 24 * q^89 - 8 * q^90 - 66 * q^91 + 24 * q^92 + 48 * q^93 + 6 * q^95 - 6 * q^97 - 48 * q^98

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