LMFDB - Embedded newform 130.2.c.b.129.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [130,2,Mod(129,130)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(130, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("130.129");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 130 = 2 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	130.c (of order $2$, degree $1$, 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:	$4$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			129.1
Root			$-1.18614 + 1.26217i$ of defining polynomial
Character	$\chi$	$=$	130.129
Dual form			130.2.c.b.129.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.52434i q^{3} +1.00000 q^{4} +(-2.18614 + 0.469882i) q^{5} -2.52434i q^{6} +2.37228 q^{7} +1.00000 q^{8} -3.37228 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.52434i q^{3} +1.00000 q^{4} +(-2.18614 + 0.469882i) q^{5} -2.52434i q^{6} +2.37228 q^{7} +1.00000 q^{8} -3.37228 q^{9} +(-2.18614 + 0.469882i) q^{10} +1.58457i q^{11} -2.52434i q^{12} +(-1.00000 - 3.46410i) q^{13} +2.37228 q^{14} +(1.18614 + 5.51856i) q^{15} +1.00000 q^{16} +5.98844i q^{17} -3.37228 q^{18} +3.46410i q^{19} +(-2.18614 + 0.469882i) q^{20} -5.98844i q^{21} +1.58457i q^{22} +6.63325i q^{23} -2.52434i q^{24} +(4.55842 - 2.05446i) q^{25} +(-1.00000 - 3.46410i) q^{26} +0.939764i q^{27} +2.37228 q^{28} +2.74456 q^{29} +(1.18614 + 5.51856i) q^{30} -3.46410i q^{31} +1.00000 q^{32} +4.00000 q^{33} +5.98844i q^{34} +(-5.18614 + 1.11469i) q^{35} -3.37228 q^{36} -9.11684 q^{37} +3.46410i q^{38} +(-8.74456 + 2.52434i) q^{39} +(-2.18614 + 0.469882i) q^{40} -10.0974i q^{41} -5.98844i q^{42} -0.644810i q^{43} +1.58457i q^{44} +(7.37228 - 1.58457i) q^{45} +6.63325i q^{46} -10.3723 q^{47} -2.52434i q^{48} -1.37228 q^{49} +(4.55842 - 2.05446i) q^{50} +15.1168 q^{51} +(-1.00000 - 3.46410i) q^{52} -5.04868i q^{53} +0.939764i q^{54} +(-0.744563 - 3.46410i) q^{55} +2.37228 q^{56} +8.74456 q^{57} +2.74456 q^{58} -6.63325i q^{59} +(1.18614 + 5.51856i) q^{60} -6.74456 q^{61} -3.46410i q^{62} -8.00000 q^{63} +1.00000 q^{64} +(3.81386 + 7.10313i) q^{65} +4.00000 q^{66} +4.00000 q^{67} +5.98844i q^{68} +16.7446 q^{69} +(-5.18614 + 1.11469i) q^{70} +12.6217i q^{71} -3.37228 q^{72} +10.0000 q^{73} -9.11684 q^{74} +(-5.18614 - 11.5070i) q^{75} +3.46410i q^{76} +3.75906i q^{77} +(-8.74456 + 2.52434i) q^{78} +4.74456 q^{79} +(-2.18614 + 0.469882i) q^{80} -7.74456 q^{81} -10.0974i q^{82} +8.74456 q^{83} -5.98844i q^{84} +(-2.81386 - 13.0916i) q^{85} -0.644810i q^{86} -6.92820i q^{87} +1.58457i q^{88} -1.87953i q^{89} +(7.37228 - 1.58457i) q^{90} +(-2.37228 - 8.21782i) q^{91} +6.63325i q^{92} -8.74456 q^{93} -10.3723 q^{94} +(-1.62772 - 7.57301i) q^{95} -2.52434i q^{96} +6.74456 q^{97} -1.37228 q^{98} -5.34363i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{4} - 3 q^{5} - 2 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^4 - 3 * q^5 - 2 * q^7 + 4 * q^8 - 2 * q^9	$ 4 q + 4 q^{2} + 4 q^{4} - 3 q^{5} - 2 q^{7} + 4 q^{8} - 2 q^{9} - 3 q^{10} - 4 q^{13} - 2 q^{14} - q^{15} + 4 q^{16} - 2 q^{18} - 3 q^{20} + q^{25} - 4 q^{26} - 2 q^{28} - 12 q^{29} - q^{30} + 4 q^{32} + 16 q^{33} - 15 q^{35} - 2 q^{36} - 2 q^{37} - 12 q^{39} - 3 q^{40} + 18 q^{45} - 30 q^{47} + 6 q^{49} + q^{50} + 26 q^{51} - 4 q^{52} + 20 q^{55} - 2 q^{56} + 12 q^{57} - 12 q^{58} - q^{60} - 4 q^{61} - 32 q^{63} + 4 q^{64} + 21 q^{65} + 16 q^{66} + 16 q^{67} + 44 q^{69} - 15 q^{70} - 2 q^{72} + 40 q^{73} - 2 q^{74} - 15 q^{75} - 12 q^{78} - 4 q^{79} - 3 q^{80} - 8 q^{81} + 12 q^{83} - 17 q^{85} + 18 q^{90} + 2 q^{91} - 12 q^{93} - 30 q^{94} - 18 q^{95} + 4 q^{97} + 6 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^4 - 3 * q^5 - 2 * q^7 + 4 * q^8 - 2 * q^9 - 3 * q^10 - 4 * q^13 - 2 * q^14 - q^15 + 4 * q^16 - 2 * q^18 - 3 * q^20 + q^25 - 4 * q^26 - 2 * q^28 - 12 * q^29 - q^30 + 4 * q^32 + 16 * q^33 - 15 * q^35 - 2 * q^36 - 2 * q^37 - 12 * q^39 - 3 * q^40 + 18 * q^45 - 30 * q^47 + 6 * q^49 + q^50 + 26 * q^51 - 4 * q^52 + 20 * q^55 - 2 * q^56 + 12 * q^57 - 12 * q^58 - q^60 - 4 * q^61 - 32 * q^63 + 4 * q^64 + 21 * q^65 + 16 * q^66 + 16 * q^67 + 44 * q^69 - 15 * q^70 - 2 * q^72 + 40 * q^73 - 2 * q^74 - 15 * q^75 - 12 * q^78 - 4 * q^79 - 3 * q^80 - 8 * q^81 + 12 * q^83 - 17 * q^85 + 18 * q^90 + 2 * q^91 - 12 * q^93 - 30 * q^94 - 18 * q^95 + 4 * q^97 + 6 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$27$	$41$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		−	2.52434i		−	1.45743i	−0.684819	−	0.728714i	$-0.740119\pi$
$3$		−	2.52434i		−	1.45743i	0.684819	−	0.728714i	$-0.259881\pi$
$4$	1.00000			0.500000
$5$	−2.18614	+	0.469882i	−0.977672	+	0.210138i
$5$	−2.18614	+	0.469882i	−0.977672	+	0.210138i
$6$		−	2.52434i		−	1.03056i
$7$	2.37228			0.896638			0.448319	−	0.893874i	$-0.352023\pi$
$7$	2.37228			0.896638			0.448319	+	0.893874i	$0.352023\pi$
$8$	1.00000			0.353553
$9$	−3.37228			−1.12409
$10$	−2.18614	+	0.469882i	−0.691318	+	0.148590i
$11$			1.58457i			0.477767i	0.971048	+	0.238884i	$0.0767814\pi$
$11$			1.58457i			0.477767i	−0.971048	+	0.238884i	$0.923219\pi$
$12$		−	2.52434i		−	0.728714i
$13$	−1.00000	−	3.46410i	−0.277350	−	0.960769i
$13$	−1.00000	−	3.46410i	−0.277350	−	0.960769i
$14$	2.37228			0.634019
$15$	1.18614	+	5.51856i	0.306260	+	1.42489i
$16$	1.00000			0.250000
$17$			5.98844i			1.45241i	0.687478	+	0.726205i	$0.258718\pi$
$17$			5.98844i			1.45241i	−0.687478	+	0.726205i	$0.741282\pi$
$18$	−3.37228			−0.794854
$19$			3.46410i			0.794719i	0.917663	+	0.397360i	$0.130073\pi$
$19$			3.46410i			0.794719i	−0.917663	+	0.397360i	$0.869927\pi$
$20$	−2.18614	+	0.469882i	−0.488836	+	0.105069i
$21$		−	5.98844i		−	1.30678i
$22$			1.58457i			0.337832i
$23$			6.63325i			1.38313i	0.722315	+	0.691564i	$0.243078\pi$
$23$			6.63325i			1.38313i	−0.722315	+	0.691564i	$0.756922\pi$
$24$		−	2.52434i		−	0.515278i
$25$	4.55842	−	2.05446i	0.911684	−	0.410891i
$26$	−1.00000	−	3.46410i	−0.196116	−	0.679366i
$27$			0.939764i			0.180858i
$28$	2.37228			0.448319
$29$	2.74456			0.509652			0.254826	−	0.966987i	$-0.417982\pi$
$29$	2.74456			0.509652			0.254826	+	0.966987i	$0.417982\pi$
$30$	1.18614	+	5.51856i	0.216559	+	1.00755i
$31$		−	3.46410i		−	0.622171i	−0.950382	−	0.311086i	$-0.899307\pi$
$31$		−	3.46410i		−	0.622171i	0.950382	−	0.311086i	$-0.100693\pi$
$32$	1.00000			0.176777
$33$	4.00000			0.696311
$34$			5.98844i			1.02701i
$35$	−5.18614	+	1.11469i	−0.876618	+	0.188417i
$36$	−3.37228			−0.562047
$37$	−9.11684			−1.49880			−0.749400	−	0.662118i	$-0.769658\pi$
$37$	−9.11684			−1.49880			−0.749400	+	0.662118i	$0.769658\pi$
$38$			3.46410i			0.561951i
$39$	−8.74456	+	2.52434i	−1.40025	+	0.404218i
$40$	−2.18614	+	0.469882i	−0.345659	+	0.0742949i
$41$		−	10.0974i		−	1.57694i	−0.615072	−	0.788471i	$-0.710873\pi$
$41$		−	10.0974i		−	1.57694i	0.615072	−	0.788471i	$-0.289127\pi$
$42$		−	5.98844i		−	0.924036i
$43$		−	0.644810i		−	0.0983326i	−0.998791	−	0.0491663i	$-0.984344\pi$
$43$		−	0.644810i		−	0.0983326i	0.998791	−	0.0491663i	$-0.0156564\pi$
$44$			1.58457i			0.238884i
$45$	7.37228	−	1.58457i	1.09899	−	0.236214i
$46$			6.63325i			0.978019i
$47$	−10.3723			−1.51295			−0.756476	−	0.654021i	$-0.773081\pi$
$47$	−10.3723			−1.51295			−0.756476	+	0.654021i	$0.773081\pi$
$48$		−	2.52434i		−	0.364357i
$49$	−1.37228			−0.196040
$50$	4.55842	−	2.05446i	0.644658	−	0.290544i
$51$	15.1168			2.11678
$52$	−1.00000	−	3.46410i	−0.138675	−	0.480384i
$53$		−	5.04868i		−	0.693489i	−0.937960	−	0.346744i	$-0.887287\pi$
$53$		−	5.04868i		−	0.693489i	0.937960	−	0.346744i	$-0.112713\pi$
$54$			0.939764i			0.127886i
$55$	−0.744563	−	3.46410i	−0.100397	−	0.467099i
$56$	2.37228			0.317009
$57$	8.74456			1.15825
$58$	2.74456			0.360379
$59$		−	6.63325i		−	0.863576i	−0.901975	−	0.431788i	$-0.857883\pi$
$59$		−	6.63325i		−	0.863576i	0.901975	−	0.431788i	$-0.142117\pi$
$60$	1.18614	+	5.51856i	0.153130	+	0.712443i
$61$	−6.74456			−0.863553			−0.431776	−	0.901981i	$-0.642113\pi$
$61$	−6.74456			−0.863553			−0.431776	+	0.901981i	$0.642113\pi$
$62$		−	3.46410i		−	0.439941i
$63$	−8.00000			−1.00791
$64$	1.00000			0.125000
$65$	3.81386	+	7.10313i	0.473051	+	0.881035i
$66$	4.00000			0.492366
$67$	4.00000			0.488678			0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000			0.488678			0.244339	+	0.969690i	$0.421429\pi$
$68$			5.98844i			0.726205i
$69$	16.7446			2.01581
$70$	−5.18614	+	1.11469i	−0.619862	+	0.133231i
$71$			12.6217i			1.49792i	0.662616	+	0.748959i	$0.269446\pi$
$71$			12.6217i			1.49792i	−0.662616	+	0.748959i	$0.730554\pi$
$72$	−3.37228			−0.397427
$73$	10.0000			1.17041			0.585206	−	0.810885i	$-0.301014\pi$
$73$	10.0000			1.17041			0.585206	+	0.810885i	$0.301014\pi$
$74$	−9.11684			−1.05981
$75$	−5.18614	−	11.5070i	−0.598844	−	1.32871i
$76$			3.46410i			0.397360i
$77$			3.75906i			0.428384i
$78$	−8.74456	+	2.52434i	−0.990127	+	0.285825i
$79$	4.74456			0.533805			0.266903	−	0.963724i	$-0.414000\pi$
$79$	4.74456			0.533805			0.266903	+	0.963724i	$0.414000\pi$
$80$	−2.18614	+	0.469882i	−0.244418	+	0.0525344i
$81$	−7.74456			−0.860507
$82$		−	10.0974i		−	1.11507i
$83$	8.74456			0.959840			0.479920	−	0.877312i	$-0.340666\pi$
$83$	8.74456			0.959840			0.479920	+	0.877312i	$0.340666\pi$
$84$		−	5.98844i		−	0.653392i
$85$	−2.81386	−	13.0916i	−0.305206	−	1.41998i
$86$		−	0.644810i		−	0.0695317i
$87$		−	6.92820i		−	0.742781i
$88$			1.58457i			0.168916i
$89$		−	1.87953i		−	0.199230i	−0.995026	−	0.0996148i	$-0.968239\pi$
$89$		−	1.87953i		−	0.199230i	0.995026	−	0.0996148i	$-0.0317610\pi$
$90$	7.37228	−	1.58457i	0.777107	−	0.167029i
$91$	−2.37228	−	8.21782i	−0.248683	−	0.861462i
$92$			6.63325i			0.691564i
$93$	−8.74456			−0.906769
$94$	−10.3723			−1.06982
$95$	−1.62772	−	7.57301i	−0.167000	−	0.776975i
$96$		−	2.52434i		−	0.257639i
$97$	6.74456			0.684807			0.342403	−	0.939553i	$-0.388759\pi$
$97$	6.74456			0.684807			0.342403	+	0.939553i	$0.388759\pi$
$98$	−1.37228			−0.138621
$99$		−	5.34363i		−	0.537055i
$100$	4.55842	−	2.05446i	0.455842	−	0.205446i
$101$	−14.7446			−1.46714			−0.733569	−	0.679615i	$-0.762147\pi$
$101$	−14.7446			−1.46714			−0.733569	+	0.679615i	$0.762147\pi$
$102$	15.1168			1.49679
$103$			10.3923i			1.02398i	0.858990	+	0.511992i	$0.171092\pi$
$103$			10.3923i			1.02398i	−0.858990	+	0.511992i	$0.828908\pi$
$104$	−1.00000	−	3.46410i	−0.0980581	−	0.339683i
$105$	2.81386	+	13.0916i	0.274605	+	1.27761i
$106$		−	5.04868i		−	0.490371i
$107$			13.5615i			1.31104i	0.755180	+	0.655518i	$0.227549\pi$
$107$			13.5615i			1.31104i	−0.755180	+	0.655518i	$0.772451\pi$
$108$			0.939764i			0.0904288i
$109$			2.81929i			0.270039i	0.990843	+	0.135020i	$0.0431097\pi$
$109$			2.81929i			0.270039i	−0.990843	+	0.135020i	$0.956890\pi$
$110$	−0.744563	−	3.46410i	−0.0709913	−	0.330289i
$111$			23.0140i			2.18439i
$112$	2.37228			0.224160
$113$		−	3.75906i		−	0.353622i	−0.984245	−	0.176811i	$-0.943422\pi$
$113$		−	3.75906i		−	0.353622i	0.984245	−	0.176811i	$-0.0565782\pi$
$114$	8.74456			0.819003
$115$	−3.11684	−	14.5012i	−0.290647	−	1.35225i
$116$	2.74456			0.254826
$117$	3.37228	+	11.6819i	0.311768	+	1.07999i
$118$		−	6.63325i		−	0.610640i
$119$			14.2063i			1.30229i
$120$	1.18614	+	5.51856i	0.108279	+	0.503773i
$121$	8.48913			0.771739
$122$	−6.74456			−0.610624
$123$	−25.4891			−2.29828
$124$		−	3.46410i		−	0.311086i
$125$	−9.00000	+	6.63325i	−0.804984	+	0.593296i
$126$	−8.00000			−0.712697
$127$		−	3.46410i		−	0.307389i	−0.988118	−	0.153695i	$-0.950883\pi$
$127$		−	3.46410i		−	0.307389i	0.988118	−	0.153695i	$-0.0491172\pi$
$128$	1.00000			0.0883883
$129$	−1.62772			−0.143313
$130$	3.81386	+	7.10313i	0.334498	+	0.622986i
$131$	−1.62772			−0.142214			−0.0711072	−	0.997469i	$-0.522653\pi$
$131$	−1.62772			−0.142214			−0.0711072	+	0.997469i	$0.522653\pi$
$132$	4.00000			0.348155
$133$			8.21782i			0.712576i
$134$	4.00000			0.345547
$135$	−0.441578	−	2.05446i	−0.0380050	−	0.176819i
$136$			5.98844i			0.513504i
$137$	−6.00000			−0.512615			−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000			−0.512615			−0.256307	+	0.966595i	$0.582506\pi$
$138$	16.7446			1.42539
$139$	6.37228			0.540490			0.270245	−	0.962792i	$-0.412895\pi$
$139$	6.37228			0.540490			0.270245	+	0.962792i	$0.412895\pi$
$140$	−5.18614	+	1.11469i	−0.438309	+	0.0942087i
$141$			26.1831i			2.20502i
$142$			12.6217i			1.05919i
$143$	5.48913	−	1.58457i	0.459024	−	0.132509i
$144$	−3.37228			−0.281023
$145$	−6.00000	+	1.28962i	−0.498273	+	0.107097i
$146$	10.0000			0.827606
$147$			3.46410i			0.285714i
$148$	−9.11684			−0.749400
$149$		−	17.0256i		−	1.39479i	−0.716688	−	0.697394i	$-0.754343\pi$
$149$		−	17.0256i		−	1.39479i	0.716688	−	0.697394i	$-0.245657\pi$
$150$	−5.18614	−	11.5070i	−0.423447	−	0.939542i
$151$		−	7.57301i		−	0.616283i	−0.951341	−	0.308142i	$-0.900293\pi$
$151$		−	7.57301i		−	0.616283i	0.951341	−	0.308142i	$-0.0997070\pi$
$152$			3.46410i			0.280976i
$153$		−	20.1947i		−	1.63264i
$154$			3.75906i			0.302913i
$155$	1.62772	+	7.57301i	0.130742	+	0.608279i
$156$	−8.74456	+	2.52434i	−0.700125	+	0.202109i
$157$		−	15.1460i		−	1.20878i	−0.796687	−	0.604392i	$-0.793416\pi$
$157$		−	15.1460i		−	1.20878i	0.796687	−	0.604392i	$-0.206584\pi$
$158$	4.74456			0.377457
$159$	−12.7446			−1.01071
$160$	−2.18614	+	0.469882i	−0.172830	+	0.0371474i
$161$			15.7359i			1.24017i
$162$	−7.74456			−0.608470
$163$	24.7446			1.93814			0.969072	−	0.246779i	$-0.0793721\pi$
$163$	24.7446			1.93814			0.969072	+	0.246779i	$0.0793721\pi$
$164$		−	10.0974i		−	0.788471i
$165$	−8.74456	+	1.87953i	−0.680763	+	0.146321i
$166$	8.74456			0.678710
$167$	17.4891			1.35335			0.676675	−	0.736282i	$-0.263420\pi$
$167$	17.4891			1.35335			0.676675	+	0.736282i	$0.263420\pi$
$168$		−	5.98844i		−	0.462018i
$169$	−11.0000	+	6.92820i	−0.846154	+	0.532939i
$170$	−2.81386	−	13.0916i	−0.215813	−	1.00408i
$171$		−	11.6819i		−	0.893339i
$172$		−	0.644810i		−	0.0491663i
$173$		−	18.9051i		−	1.43733i	−0.695358	−	0.718663i	$-0.744754\pi$
$173$		−	18.9051i		−	1.43733i	0.695358	−	0.718663i	$-0.255246\pi$
$174$		−	6.92820i		−	0.525226i
$175$	10.8139	−	4.87375i	0.817451	−	0.368421i
$176$			1.58457i			0.119442i
$177$	−16.7446			−1.25860
$178$		−	1.87953i		−	0.140877i
$179$	4.88316			0.364984			0.182492	−	0.983207i	$-0.441584\pi$
$179$	4.88316			0.364984			0.182492	+	0.983207i	$0.441584\pi$
$180$	7.37228	−	1.58457i	0.549497	−	0.118107i
$181$	−3.48913			−0.259345			−0.129672	−	0.991557i	$-0.541393\pi$
$181$	−3.48913			−0.259345			−0.129672	+	0.991557i	$0.541393\pi$
$182$	−2.37228	−	8.21782i	−0.175845	−	0.609146i
$183$			17.0256i			1.25857i
$184$			6.63325i			0.489010i
$185$	19.9307	−	4.28384i	1.46533	−	0.314954i
$186$	−8.74456			−0.641182
$187$	−9.48913			−0.693914
$188$	−10.3723			−0.756476
$189$			2.22938i			0.162164i
$190$	−1.62772	−	7.57301i	−0.118087	−	0.549404i
$191$		0			0			−	1.00000i	$-0.5\pi$
$191$		0			0				1.00000i	$0.5\pi$
$192$		−	2.52434i		−	0.182178i
$193$	−14.0000			−1.00774			−0.503871	−	0.863779i	$-0.668091\pi$
$193$	−14.0000			−1.00774			−0.503871	+	0.863779i	$0.668091\pi$
$194$	6.74456			0.484231
$195$	17.9307	−	9.62747i	1.28404	−	0.689437i
$196$	−1.37228			−0.0980201
$197$	−4.37228			−0.311512			−0.155756	−	0.987796i	$-0.549781\pi$
$197$	−4.37228			−0.311512			−0.155756	+	0.987796i	$0.549781\pi$
$198$		−	5.34363i		−	0.379755i
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$	4.55842	−	2.05446i	0.322329	−	0.145272i
$201$		−	10.0974i		−	0.712212i
$202$	−14.7446			−1.03742
$203$	6.51087			0.456974
$204$	15.1168			1.05839
$205$	4.74456	+	22.0742i	0.331375	+	1.54173i
$206$			10.3923i			0.724066i
$207$		−	22.3692i		−	1.55477i
$208$	−1.00000	−	3.46410i	−0.0693375	−	0.240192i
$209$	−5.48913			−0.379691
$210$	2.81386	+	13.0916i	0.194175	+	0.903404i
$211$	3.11684			0.214572			0.107286	−	0.994228i	$-0.465784\pi$
$211$	3.11684			0.214572			0.107286	+	0.994228i	$0.465784\pi$
$212$		−	5.04868i		−	0.346744i
$213$	31.8614			2.18311
$214$			13.5615i			0.927042i
$215$	0.302985	+	1.40965i	0.0206634	+	0.0961370i
$216$			0.939764i			0.0639428i
$217$		−	8.21782i		−	0.557862i
$218$			2.81929i			0.190947i
$219$		−	25.2434i		−	1.70579i
$220$	−0.744563	−	3.46410i	−0.0501984	−	0.233550i
$221$	20.7446	−	5.98844i	1.39543	−	0.402826i
$222$			23.0140i			1.54460i
$223$	−15.1168			−1.01230			−0.506149	−	0.862446i	$-0.668932\pi$
$223$	−15.1168			−1.01230			−0.506149	+	0.862446i	$0.668932\pi$
$224$	2.37228			0.158505
$225$	−15.3723	+	6.92820i	−1.02482	+	0.461880i
$226$		−	3.75906i		−	0.250049i
$227$	−5.48913			−0.364326			−0.182163	−	0.983268i	$-0.558310\pi$
$227$	−5.48913			−0.364326			−0.182163	+	0.983268i	$0.558310\pi$
$228$	8.74456			0.579123
$229$			24.8935i			1.64501i	0.568758	+	0.822505i	$0.307424\pi$
$229$			24.8935i			1.64501i	−0.568758	+	0.822505i	$0.692576\pi$
$230$	−3.11684	−	14.5012i	−0.205519	−	0.956182i
$231$	9.48913			0.624339
$232$	2.74456			0.180189
$233$		−	7.86797i		−	0.515448i	−0.966219	−	0.257724i	$-0.917028\pi$
$233$		−	7.86797i		−	0.515448i	0.966219	−	0.257724i	$-0.0829725\pi$
$234$	3.37228	+	11.6819i	0.220453	+	0.763671i
$235$	22.6753	−	4.87375i	1.47917	−	0.317928i
$236$		−	6.63325i		−	0.431788i
$237$		−	11.9769i		−	0.777982i
$238$			14.2063i			0.920855i
$239$		−	9.45254i		−	0.611434i	−0.952122	−	0.305717i	$-0.901104\pi$
$239$		−	9.45254i		−	0.611434i	0.952122	−	0.305717i	$-0.0988962\pi$
$240$	1.18614	+	5.51856i	0.0765651	+	0.356221i
$241$			8.21782i			0.529357i	0.964337	+	0.264678i	$0.0852658\pi$
$241$			8.21782i			0.529357i	−0.964337	+	0.264678i	$0.914734\pi$
$242$	8.48913			0.545702
$243$			22.3692i			1.43498i
$244$	−6.74456			−0.431776
$245$	3.00000	−	0.644810i	0.191663	−	0.0411954i
$246$	−25.4891			−1.62513
$247$	12.0000	−	3.46410i	0.763542	−	0.220416i
$248$		−	3.46410i		−	0.219971i
$249$		−	22.0742i		−	1.39890i
$250$	−9.00000	+	6.63325i	−0.569210	+	0.419524i
$251$	−22.9783			−1.45037			−0.725187	−	0.688552i	$-0.758247\pi$
$251$	−22.9783			−1.45037			−0.725187	+	0.688552i	$0.758247\pi$
$252$	−8.00000			−0.503953
$253$	−10.5109			−0.660813
$254$		−	3.46410i		−	0.217357i
$255$	−33.0475	+	7.10313i	−2.06952	+	0.444815i
$256$	1.00000			0.0625000
$257$			14.2063i			0.886162i	0.896481	+	0.443081i	$0.146115\pi$
$257$			14.2063i			0.886162i	−0.896481	+	0.443081i	$0.853885\pi$
$258$	−1.62772			−0.101337
$259$	−21.6277			−1.34388
$260$	3.81386	+	7.10313i	0.236526	+	0.440518i
$261$	−9.25544			−0.572897
$262$	−1.62772			−0.100561
$263$		−	18.0202i		−	1.11117i	−0.831458	−	0.555587i	$-0.812493\pi$
$263$		−	18.0202i		−	1.11117i	0.831458	−	0.555587i	$-0.187507\pi$
$264$	4.00000			0.246183
$265$	2.37228	+	11.0371i	0.145728	+	0.678005i
$266$			8.21782i			0.503867i
$267$	−4.74456			−0.290363
$268$	4.00000			0.244339
$269$	2.74456			0.167339			0.0836695	−	0.996494i	$-0.473336\pi$
$269$	2.74456			0.167339			0.0836695	+	0.996494i	$0.473336\pi$
$270$	−0.441578	−	2.05446i	−0.0268736	−	0.125030i
$271$		−	21.4294i		−	1.30174i	−0.759187	−	0.650872i	$-0.774403\pi$
$271$		−	21.4294i		−	1.30174i	0.759187	−	0.650872i	$-0.225597\pi$
$272$			5.98844i			0.363102i
$273$	−20.7446	+	5.98844i	−1.25552	+	0.362437i
$274$	−6.00000			−0.362473
$275$	3.25544	+	7.22316i	0.196310	+	0.435573i
$276$	16.7446			1.00790
$277$			23.3639i			1.40380i	0.712277	+	0.701899i	$0.247664\pi$
$277$			23.3639i			1.40380i	−0.712277	+	0.701899i	$0.752336\pi$
$278$	6.37228			0.382184
$279$			11.6819i			0.699379i
$280$	−5.18614	+	1.11469i	−0.309931	+	0.0666156i
$281$		−	1.87953i		−	0.112123i	−0.998427	−	0.0560616i	$-0.982146\pi$
$281$		−	1.87953i		−	0.112123i	0.998427	−	0.0560616i	$-0.0178543\pi$
$282$			26.1831i			1.55918i
$283$			17.3205i			1.02960i	0.857311	+	0.514799i	$0.172133\pi$
$283$			17.3205i			1.02960i	−0.857311	+	0.514799i	$0.827867\pi$
$284$			12.6217i			0.748959i
$285$	−19.1168	+	4.10891i	−1.13238	+	0.243391i
$286$	5.48913	−	1.58457i	0.324579	−	0.0936978i
$287$		−	23.9538i		−	1.41395i
$288$	−3.37228			−0.198714
$289$	−18.8614			−1.10949
$290$	−6.00000	+	1.28962i	−0.352332	+	0.0757291i
$291$		−	17.0256i		−	0.998056i
$292$	10.0000			0.585206
$293$	2.13859			0.124938			0.0624690	−	0.998047i	$-0.480103\pi$
$293$	2.13859			0.124938			0.0624690	+	0.998047i	$0.480103\pi$
$294$			3.46410i			0.202031i
$295$	3.11684	+	14.5012i	0.181470	+	0.844293i
$296$	−9.11684			−0.529906
$297$	−1.48913			−0.0864078
$298$		−	17.0256i		−	0.986264i
$299$	22.9783	−	6.63325i	1.32887	−	0.383611i
$300$	−5.18614	−	11.5070i	−0.299422	−	0.664357i
$301$		−	1.52967i		−	0.0881688i
$302$		−	7.57301i		−	0.435778i
$303$			37.2203i			2.13825i
$304$			3.46410i			0.198680i
$305$	14.7446	−	3.16915i	0.844271	−	0.181465i
$306$		−	20.1947i		−	1.15445i
$307$	18.2337			1.04065			0.520326	−	0.853968i	$-0.325811\pi$
$307$	18.2337			1.04065			0.520326	+	0.853968i	$0.325811\pi$
$308$			3.75906i			0.214192i
$309$	26.2337			1.49238
$310$	1.62772	+	7.57301i	0.0924482	+	0.430118i
$311$	3.25544			0.184599			0.0922995	−	0.995731i	$-0.470578\pi$
$311$	3.25544			0.184599			0.0922995	+	0.995731i	$0.470578\pi$
$312$	−8.74456	+	2.52434i	−0.495063	+	0.142912i
$313$			12.3267i			0.696748i	0.937356	+	0.348374i	$0.113266\pi$
$313$			12.3267i			0.696748i	−0.937356	+	0.348374i	$0.886734\pi$
$314$		−	15.1460i		−	0.854740i
$315$	17.4891	−	3.75906i	0.985401	−	0.211799i
$316$	4.74456			0.266903
$317$	16.9783			0.953594			0.476797	−	0.879014i	$-0.341798\pi$
$317$	16.9783			0.953594			0.476797	+	0.879014i	$0.341798\pi$
$318$	−12.7446			−0.714680
$319$			4.34896i			0.243495i
$320$	−2.18614	+	0.469882i	−0.122209	+	0.0262672i
$321$	34.2337			1.91074
$322$			15.7359i			0.876929i
$323$	−20.7446			−1.15426
$324$	−7.74456			−0.430253
$325$	−11.6753	−	13.7364i	−0.647627	−	0.761957i
$326$	24.7446			1.37047
$327$	7.11684			0.393562
$328$		−	10.0974i		−	0.557533i
$329$	−24.6060			−1.35657
$330$	−8.74456	+	1.87953i	−0.481372	+	0.103465i
$331$		−	10.3923i		−	0.571213i	−0.958347	−	0.285606i	$-0.907805\pi$
$331$		−	10.3923i		−	0.571213i	0.958347	−	0.285606i	$-0.0921950\pi$
$332$	8.74456			0.479920
$333$	30.7446			1.68479
$334$	17.4891			0.956962
$335$	−8.74456	+	1.87953i	−0.477766	+	0.102690i
$336$		−	5.98844i		−	0.326696i
$337$		−	1.52967i		−	0.0833265i	−0.999132	−	0.0416632i	$-0.986734\pi$
$337$		−	1.52967i		−	0.0833265i	0.999132	−	0.0416632i	$-0.0132657\pi$
$338$	−11.0000	+	6.92820i	−0.598321	+	0.376845i
$339$	−9.48913			−0.515379
$340$	−2.81386	−	13.0916i	−0.152603	−	0.709990i
$341$	5.48913			0.297253
$342$		−	11.6819i		−	0.631686i
$343$	−19.8614			−1.07242
$344$		−	0.644810i		−	0.0347658i
$345$	−36.6060	+	7.86797i	−1.97080	+	0.423597i
$346$		−	18.9051i		−	1.01634i
$347$		−	20.8395i		−	1.11872i	−0.828924	−	0.559362i	$-0.811046\pi$
$347$		−	20.8395i		−	1.11872i	0.828924	−	0.559362i	$-0.188954\pi$
$348$		−	6.92820i		−	0.371391i
$349$			27.4728i			1.47058i	0.677751	+	0.735292i	$0.262955\pi$
$349$			27.4728i			1.47058i	−0.677751	+	0.735292i	$0.737045\pi$
$350$	10.8139	−	4.87375i	0.578025	−	0.260513i
$351$	3.25544	−	0.939764i	0.173762	−	0.0501609i
$352$			1.58457i			0.0844581i
$353$	11.4891			0.611504			0.305752	−	0.952111i	$-0.401092\pi$
$353$	11.4891			0.611504			0.305752	+	0.952111i	$0.401092\pi$
$354$	−16.7446			−0.889963
$355$	−5.93070	−	27.5928i	−0.314769	−	1.46447i
$356$		−	1.87953i		−	0.0996148i
$357$	35.8614			1.89799
$358$	4.88316			0.258083
$359$			2.87419i			0.151694i	0.997119	+	0.0758471i	$0.0241661\pi$
$359$			2.87419i			0.151694i	−0.997119	+	0.0758471i	$0.975834\pi$
$360$	7.37228	−	1.58457i	0.388553	−	0.0835144i
$361$	7.00000			0.368421
$362$	−3.48913			−0.183384
$363$		−	21.4294i		−	1.12475i
$364$	−2.37228	−	8.21782i	−0.124341	−	0.430731i
$365$	−21.8614	+	4.69882i	−1.14428	+	0.245947i
$366$			17.0256i			0.889940i
$367$			4.75372i			0.248142i	0.992273	+	0.124071i	$0.0395951\pi$
$367$			4.75372i			0.248142i	−0.992273	+	0.124071i	$0.960405\pi$
$368$			6.63325i			0.345782i
$369$			34.0511i			1.77263i
$370$	19.9307	−	4.28384i	1.03615	−	0.222706i
$371$		−	11.9769i		−	0.621809i
$372$	−8.74456			−0.453384
$373$		−	9.50744i		−	0.492277i	−0.969235	−	0.246138i	$-0.920838\pi$
$373$		−	9.50744i		−	0.492277i	0.969235	−	0.246138i	$-0.0791618\pi$
$374$	−9.48913			−0.490671
$375$	16.7446	+	22.7190i	0.864685	+	1.17321i
$376$	−10.3723			−0.534910
$377$	−2.74456	−	9.50744i	−0.141352	−	0.489658i
$378$			2.22938i			0.114667i
$379$			17.3205i			0.889695i	0.895606	+	0.444847i	$0.146742\pi$
$379$			17.3205i			0.889695i	−0.895606	+	0.444847i	$0.853258\pi$
$380$	−1.62772	−	7.57301i	−0.0835002	−	0.388487i
$381$	−8.74456			−0.447998
$382$		0			0
$383$	−16.8832			−0.862689			−0.431344	−	0.902187i	$-0.641961\pi$
$383$	−16.8832			−0.862689			−0.431344	+	0.902187i	$0.641961\pi$
$384$		−	2.52434i		−	0.128820i
$385$	−1.76631	−	8.21782i	−0.0900196	−	0.418819i
$386$	−14.0000			−0.712581
$387$			2.17448i			0.110535i
$388$	6.74456			0.342403
$389$	6.00000			0.304212			0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000			0.304212			0.152106	+	0.988364i	$0.451394\pi$
$390$	17.9307	−	9.62747i	0.907956	−	0.487506i
$391$	−39.7228			−2.00887
$392$	−1.37228			−0.0693107
$393$			4.10891i			0.207267i
$394$	−4.37228			−0.220272
$395$	−10.3723	+	2.22938i	−0.521886	+	0.112172i
$396$		−	5.34363i		−	0.268527i
$397$	−8.51087			−0.427149			−0.213574	−	0.976927i	$-0.568511\pi$
$397$	−8.51087			−0.427149			−0.213574	+	0.976927i	$0.568511\pi$
$398$	8.00000			0.401004
$399$	20.7446			1.03853
$400$	4.55842	−	2.05446i	0.227921	−	0.102723i
$401$		−	32.1716i		−	1.60657i	−0.595593	−	0.803286i	$-0.703083\pi$
$401$		−	32.1716i		−	1.60657i	0.595593	−	0.803286i	$-0.296917\pi$
$402$		−	10.0974i		−	0.503610i
$403$	−12.0000	+	3.46410i	−0.597763	+	0.172559i
$404$	−14.7446			−0.733569
$405$	16.9307	−	3.63903i	0.841293	−	0.180825i
$406$	6.51087			0.323129
$407$		−	14.4463i		−	0.716077i
$408$	15.1168			0.748395
$409$			5.63858i			0.278810i	0.990235	+	0.139405i	$0.0445190\pi$
$409$			5.63858i			0.278810i	−0.990235	+	0.139405i	$0.955481\pi$
$410$	4.74456	+	22.0742i	0.234317	+	1.09017i
$411$			15.1460i			0.747098i
$412$			10.3923i			0.511992i
$413$		−	15.7359i		−	0.774315i
$414$		−	22.3692i		−	1.09939i
$415$	−19.1168	+	4.10891i	−0.938409	+	0.201699i
$416$	−1.00000	−	3.46410i	−0.0490290	−	0.169842i
$417$		−	16.0858i		−	0.787725i
$418$	−5.48913			−0.268482
$419$	19.1168			0.933919			0.466959	−	0.884279i	$-0.345349\pi$
$419$	19.1168			0.933919			0.466959	+	0.884279i	$0.345349\pi$
$420$	2.81386	+	13.0916i	0.137302	+	0.638803i
$421$		−	11.0371i		−	0.537916i	−0.963152	−	0.268958i	$-0.913321\pi$
$421$		−	11.0371i		−	0.537916i	0.963152	−	0.268958i	$-0.0866793\pi$
$422$	3.11684			0.151726
$423$	34.9783			1.70070
$424$		−	5.04868i		−	0.245185i
$425$	12.3030	+	27.2978i	0.596782	+	1.32414i
$426$	31.8614			1.54369
$427$	−16.0000			−0.774294
$428$			13.5615i			0.655518i
$429$	−4.00000	−	13.8564i	−0.193122	−	0.668994i
$430$	0.302985	+	1.40965i	0.0146112	+	0.0679792i
$431$			26.4781i			1.27540i	0.770283	+	0.637702i	$0.220115\pi$
$431$			26.4781i			1.27540i	−0.770283	+	0.637702i	$0.779885\pi$
$432$			0.939764i			0.0452144i
$433$		−	34.4010i		−	1.65320i	−0.562786	−	0.826602i	$-0.690271\pi$
$433$		−	34.4010i		−	1.65320i	0.562786	−	0.826602i	$-0.309729\pi$
$434$		−	8.21782i		−	0.394468i
$435$	3.25544	+	15.1460i	0.156086	+	0.726196i
$436$			2.81929i			0.135020i
$437$	−22.9783			−1.09920
$438$		−	25.2434i		−	1.20618i
$439$	22.2337			1.06116			0.530578	−	0.847636i	$-0.321975\pi$
$439$	22.2337			1.06116			0.530578	+	0.847636i	$0.321975\pi$
$440$	−0.744563	−	3.46410i	−0.0354956	−	0.165145i
$441$	4.62772			0.220368
$442$	20.7446	−	5.98844i	0.986718	−	0.284841i
$443$		−	4.40387i		−	0.209234i	−0.994513	−	0.104617i	$-0.966638\pi$
$443$		−	4.40387i		−	0.209234i	0.994513	−	0.104617i	$-0.0333617\pi$
$444$			23.0140i			1.09220i
$445$	0.883156	+	4.10891i	0.0418656	+	0.194781i
$446$	−15.1168			−0.715803
$447$	−42.9783			−2.03280
$448$	2.37228			0.112080
$449$		−	7.51811i		−	0.354802i	−0.984139	−	0.177401i	$-0.943231\pi$
$449$		−	7.51811i		−	0.354802i	0.984139	−	0.177401i	$-0.0567689\pi$
$450$	−15.3723	+	6.92820i	−0.724656	+	0.326599i
$451$	16.0000			0.753411
$452$		−	3.75906i		−	0.176811i
$453$	−19.1168			−0.898188
$454$	−5.48913			−0.257617
$455$	9.04755	+	16.8506i	0.424156	+	0.789970i
$456$	8.74456			0.409502
$457$	−24.9783			−1.16843			−0.584217	−	0.811598i	$-0.698598\pi$
$457$	−24.9783			−1.16843			−0.584217	+	0.811598i	$0.698598\pi$
$458$			24.8935i			1.16320i
$459$	−5.62772			−0.262679
$460$	−3.11684	−	14.5012i	−0.145324	−	0.676123i
$461$		−	1.63948i		−	0.0763580i	−0.999271	−	0.0381790i	$-0.987844\pi$
$461$		−	1.63948i		−	0.0763580i	0.999271	−	0.0381790i	$-0.0121557\pi$
$462$	9.48913			0.441474
$463$	16.0000			0.743583			0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000			0.743583			0.371792	+	0.928316i	$0.378744\pi$
$464$	2.74456			0.127413
$465$	19.1168	−	4.10891i	0.886522	−	0.190546i
$466$		−	7.86797i		−	0.364477i
$467$			27.4179i			1.26875i	0.773027	+	0.634374i	$0.218742\pi$
$467$			27.4179i			1.26875i	−0.773027	+	0.634374i	$0.781258\pi$
$468$	3.37228	+	11.6819i	0.155884	+	0.539997i
$469$	9.48913			0.438167
$470$	22.6753	−	4.87375i	1.04593	−	0.224809i
$471$	−38.2337			−1.76172
$472$		−	6.63325i		−	0.305320i
$473$	1.02175			0.0469801
$474$		−	11.9769i		−	0.550116i
$475$	7.11684	+	15.7908i	0.326543	+	0.724533i
$476$			14.2063i			0.651143i
$477$			17.0256i			0.779547i
$478$		−	9.45254i		−	0.432349i
$479$			18.2603i			0.834333i	0.908830	+	0.417167i	$0.136977\pi$
$479$			18.2603i			0.834333i	−0.908830	+	0.417167i	$0.863023\pi$
$480$	1.18614	+	5.51856i	0.0541397	+	0.251887i
$481$	9.11684	+	31.5817i	0.415692	+	1.44000i
$482$			8.21782i			0.374312i
$483$	39.7228			1.80745
$484$	8.48913			0.385869
$485$	−14.7446	+	3.16915i	−0.669516	+	0.143904i
$486$			22.3692i			1.01469i
$487$	−1.48913			−0.0674787			−0.0337394	−	0.999431i	$-0.510742\pi$
$487$	−1.48913			−0.0674787			−0.0337394	+	0.999431i	$0.510742\pi$
$488$	−6.74456			−0.305312
$489$		−	62.4636i		−	2.82470i
$490$	3.00000	−	0.644810i	0.135526	−	0.0291296i
$491$	−25.6277			−1.15656			−0.578281	−	0.815837i	$-0.696276\pi$
$491$	−25.6277			−1.15656			−0.578281	+	0.815837i	$0.696276\pi$
$492$	−25.4891			−1.14914
$493$			16.4356i			0.740224i
$494$	12.0000	−	3.46410i	0.539906	−	0.155857i
$495$	2.51087	+	11.6819i	0.112855	+	0.525063i
$496$		−	3.46410i		−	0.155543i
$497$			29.9422i			1.34309i
$498$		−	22.0742i		−	0.989170i
$499$		−	16.0309i		−	0.717641i	−0.933407	−	0.358821i	$-0.883179\pi$
$499$		−	16.0309i		−	0.717641i	0.933407	−	0.358821i	$-0.116821\pi$
$500$	−9.00000	+	6.63325i	−0.402492	+	0.296648i
$501$		−	44.1485i		−	1.97241i
$502$	−22.9783			−1.02557
$503$			6.63325i			0.295762i	0.989005	+	0.147881i	$0.0472453\pi$
$503$			6.63325i			0.295762i	−0.989005	+	0.147881i	$0.952755\pi$
$504$	−8.00000			−0.356348
$505$	32.2337	−	6.92820i	1.43438	−	0.308301i
$506$	−10.5109			−0.467265
$507$	17.4891	+	27.7677i	0.776719	+	1.23321i
$508$		−	3.46410i		−	0.153695i
$509$		−	3.16915i		−	0.140470i	−0.997530	−	0.0702350i	$-0.977625\pi$
$509$		−	3.16915i		−	0.140470i	0.997530	−	0.0702350i	$-0.0223749\pi$
$510$	−33.0475	+	7.10313i	−1.46337	+	0.314532i
$511$	23.7228			1.04944
$512$	1.00000			0.0441942
$513$	−3.25544			−0.143731
$514$			14.2063i			0.626611i
$515$	−4.88316	−	22.7190i	−0.215178	−	1.00112i
$516$	−1.62772			−0.0716563
$517$		−	16.4356i		−	0.722839i
$518$	−21.6277			−0.950267
$519$	−47.7228			−2.09480
$520$	3.81386	+	7.10313i	0.167249	+	0.311493i
$521$	18.6060			0.815142			0.407571	−	0.913173i	$-0.366376\pi$
$521$	18.6060			0.815142			0.407571	+	0.913173i	$0.366376\pi$
$522$	−9.25544			−0.405099
$523$		−	10.3923i		−	0.454424i	−0.973845	−	0.227212i	$-0.927039\pi$
$523$		−	10.3923i		−	0.454424i	0.973845	−	0.227212i	$-0.0729610\pi$
$524$	−1.62772			−0.0711072
$525$	−12.3030	−	27.2978i	−0.536946	−	1.19138i
$526$		−	18.0202i		−	0.785719i
$527$	20.7446			0.903647
$528$	4.00000			0.174078
$529$	−21.0000			−0.913043
$530$	2.37228	+	11.0371i	0.103045	+	0.479422i
$531$			22.3692i			0.970740i
$532$			8.21782i			0.356288i
$533$	−34.9783	+	10.0974i	−1.51508	+	0.437365i
$534$	−4.74456			−0.205317
$535$	−6.37228	−	29.6472i	−0.275498	−	1.28176i
$536$	4.00000			0.172774
$537$		−	12.3267i		−	0.531938i
$538$	2.74456			0.118326
$539$		−	2.17448i		−	0.0936615i
$540$	−0.441578	−	2.05446i	−0.0190025	−	0.0884097i
$541$			30.5321i			1.31268i	0.754466	+	0.656339i	$0.227896\pi$
$541$			30.5321i			1.31268i	−0.754466	+	0.656339i	$0.772104\pi$
$542$		−	21.4294i		−	0.920472i
$543$			8.80773i			0.377976i
$544$			5.98844i			0.256752i
$545$	−1.32473	−	6.16337i	−0.0567454	−	0.264010i
$546$	−20.7446	+	5.98844i	−0.887785	+	0.256282i
$547$			21.4294i			0.916256i	0.888886	+	0.458128i	$0.151480\pi$
$547$			21.4294i			0.916256i	−0.888886	+	0.458128i	$0.848520\pi$
$548$	−6.00000			−0.256307
$549$	22.7446			0.970714
$550$	3.25544	+	7.22316i	0.138812	+	0.307996i
$551$			9.50744i			0.405031i
$552$	16.7446			0.712696
$553$	11.2554			0.478630
$554$			23.3639i			0.992635i
$555$	−10.8139	−	50.3118i	−0.459023	−	2.13562i
$556$	6.37228			0.270245
$557$	−1.11684			−0.0473222			−0.0236611	−	0.999720i	$-0.507532\pi$
$557$	−1.11684			−0.0473222			−0.0236611	+	0.999720i	$0.507532\pi$
$558$			11.6819i			0.494535i
$559$	−2.23369	+	0.644810i	−0.0944749	+	0.0272726i
$560$	−5.18614	+	1.11469i	−0.219154	+	0.0471043i
$561$			23.9538i			1.01133i
$562$		−	1.87953i		−	0.0792831i
$563$		−	1.82462i		−	0.0768988i	−0.999261	−	0.0384494i	$-0.987758\pi$
$563$		−	1.82462i		−	0.0768988i	0.999261	−	0.0384494i	$-0.0122418\pi$
$564$			26.1831i			1.10251i
$565$	1.76631	+	8.21782i	0.0743093	+	0.345726i
$566$			17.3205i			0.728035i
$567$	−18.3723			−0.771563
$568$			12.6217i			0.529594i
$569$	−16.3723			−0.686362			−0.343181	−	0.939269i	$-0.611504\pi$
$569$	−16.3723			−0.686362			−0.343181	+	0.939269i	$0.611504\pi$
$570$	−19.1168	+	4.10891i	−0.800716	+	0.172103i
$571$	12.8832			0.539143			0.269572	−	0.962980i	$-0.413118\pi$
$571$	12.8832			0.539143			0.269572	+	0.962980i	$0.413118\pi$
$572$	5.48913	−	1.58457i	0.229512	−	0.0662544i
$573$		0			0
$574$		−	23.9538i		−	0.999811i
$575$	13.6277	+	30.2372i	0.568315	+	1.26098i
$576$	−3.37228			−0.140512
$577$	20.9783			0.873336			0.436668	−	0.899623i	$-0.356158\pi$
$577$	20.9783			0.873336			0.436668	+	0.899623i	$0.356158\pi$
$578$	−18.8614			−0.784531
$579$			35.3407i			1.46871i
$580$	−6.00000	+	1.28962i	−0.249136	+	0.0535486i
$581$	20.7446			0.860629
$582$		−	17.0256i		−	0.705732i
$583$	8.00000			0.331326
$584$	10.0000			0.413803
$585$	−12.8614	−	23.9538i	−0.531754	−	0.990366i
$586$	2.13859			0.0883445
$587$	19.7228			0.814048			0.407024	−	0.913418i	$-0.366567\pi$
$587$	19.7228			0.814048			0.407024	+	0.913418i	$0.366567\pi$
$588$			3.46410i			0.142857i
$589$	12.0000			0.494451
$590$	3.11684	+	14.5012i	0.128318	+	0.597006i
$591$			11.0371i			0.454006i
$592$	−9.11684			−0.374700
$593$	32.2337			1.32368			0.661839	−	0.749646i	$-0.269776\pi$
$593$	32.2337			1.32368			0.661839	+	0.749646i	$0.269776\pi$
$594$	−1.48913			−0.0610996
$595$	−6.67527	−	31.0569i	−0.273659	−	1.27321i
$596$		−	17.0256i		−	0.697394i
$597$		−	20.1947i		−	0.826514i
$598$	22.9783	−	6.63325i	0.939651	−	0.271254i
$599$	31.7228			1.29616			0.648080	−	0.761573i	$-0.275572\pi$
$599$	31.7228			1.29616			0.648080	+	0.761573i	$0.275572\pi$
$600$	−5.18614	−	11.5070i	−0.211723	−	0.469771i
$601$	−32.3723			−1.32049			−0.660246	−	0.751049i	$-0.729548\pi$
$601$	−32.3723			−1.32049			−0.660246	+	0.751049i	$0.729548\pi$
$602$		−	1.52967i		−	0.0623447i
$603$	−13.4891			−0.549320
$604$		−	7.57301i		−	0.308142i
$605$	−18.5584	+	3.98889i	−0.754507	+	0.162171i
$606$			37.2203i			1.51197i
$607$		−	3.46410i		−	0.140604i	−0.997526	−	0.0703018i	$-0.977604\pi$
$607$		−	3.46410i		−	0.140604i	0.997526	−	0.0703018i	$-0.0223962\pi$
$608$			3.46410i			0.140488i
$609$		−	16.4356i		−	0.666006i
$610$	14.7446	−	3.16915i	0.596990	−	0.128315i
$611$	10.3723	+	35.9306i	0.419618	+	1.45360i
$612$		−	20.1947i		−	0.816322i
$613$	−19.4891			−0.787158			−0.393579	−	0.919291i	$-0.628763\pi$
$613$	−19.4891			−0.787158			−0.393579	+	0.919291i	$0.628763\pi$
$614$	18.2337			0.735852
$615$	55.7228	−	11.9769i	2.24696	−	0.482954i
$616$			3.75906i			0.151457i
$617$	14.7446			0.593594			0.296797	−	0.954941i	$-0.404082\pi$
$617$	14.7446			0.593594			0.296797	+	0.954941i	$0.404082\pi$
$618$	26.2337			1.05527
$619$			9.10268i			0.365868i	0.983125	+	0.182934i	$0.0585594\pi$
$619$			9.10268i			0.365868i	−0.983125	+	0.182934i	$0.941441\pi$
$620$	1.62772	+	7.57301i	0.0653708	+	0.304140i
$621$	−6.23369			−0.250149
$622$	3.25544			0.130531
$623$		−	4.45877i		−	0.178637i
$624$	−8.74456	+	2.52434i	−0.350063	+	0.101054i
$625$	16.5584	−	18.7302i	0.662337	−	0.749206i
$626$			12.3267i			0.492675i
$627$			13.8564i			0.553372i
$628$		−	15.1460i		−	0.604392i
$629$		−	54.5957i		−	2.17687i
$630$	17.4891	−	3.75906i	0.696783	−	0.149764i
$631$		−	40.4443i		−	1.61006i	−0.593232	−	0.805031i	$-0.702148\pi$
$631$		−	40.4443i		−	1.61006i	0.593232	−	0.805031i	$-0.297852\pi$
$632$	4.74456			0.188729
$633$		−	7.86797i		−	0.312724i
$634$	16.9783			0.674292
$635$	1.62772	+	7.57301i	0.0645940	+	0.300526i
$636$	−12.7446			−0.505355
$637$	1.37228	+	4.75372i	0.0543718	+	0.188349i
$638$			4.34896i			0.172177i
$639$		−	42.5639i		−	1.68380i
$640$	−2.18614	+	0.469882i	−0.0864148	+	0.0185737i
$641$	−16.9783			−0.670601			−0.335300	−	0.942111i	$-0.608838\pi$
$641$	−16.9783			−0.670601			−0.335300	+	0.942111i	$0.608838\pi$
$642$	34.2337			1.35110
$643$	−37.4891			−1.47843			−0.739213	−	0.673471i	$-0.764803\pi$
$643$	−37.4891			−1.47843			−0.739213	+	0.673471i	$0.764803\pi$
$644$			15.7359i			0.620083i
$645$	3.55842	−	0.764836i	0.140113	−	0.0301154i
$646$	−20.7446			−0.816184
$647$		−	21.0796i		−	0.828723i	−0.910112	−	0.414362i	$-0.864005\pi$
$647$		−	21.0796i		−	0.828723i	0.910112	−	0.414362i	$-0.135995\pi$
$648$	−7.74456			−0.304235
$649$	10.5109			0.412588
$650$	−11.6753	−	13.7364i	−0.457942	−	0.538785i
$651$	−20.7446			−0.813044
$652$	24.7446			0.969072
$653$			17.0256i			0.666261i	0.942881	+	0.333131i	$0.108105\pi$
$653$			17.0256i			0.666261i	−0.942881	+	0.333131i	$0.891895\pi$
$654$	7.11684			0.278291
$655$	3.55842	−	0.764836i	0.139039	−	0.0298846i
$656$		−	10.0974i		−	0.394235i
$657$	−33.7228			−1.31565
$658$	−24.6060			−0.959241
$659$	−40.4674			−1.57639			−0.788193	−	0.615429i	$-0.788983\pi$
$659$	−40.4674			−1.57639			−0.788193	+	0.615429i	$0.788983\pi$
$660$	−8.74456	+	1.87953i	−0.340382	+	0.0731605i
$661$		−	9.50744i		−	0.369797i	−0.982758	−	0.184898i	$-0.940804\pi$
$661$		−	9.50744i		−	0.369797i	0.982758	−	0.184898i	$-0.0591956\pi$
$662$		−	10.3923i		−	0.403908i
$663$	−15.1168	−	52.3663i	−0.587090	−	2.03374i
$664$	8.74456			0.339355
$665$	−3.86141	−	17.9653i	−0.149739	−	0.696665i
$666$	30.7446			1.19133
$667$			18.2054i			0.704915i
$668$	17.4891			0.676675
$669$			38.1600i			1.47535i
$670$	−8.74456	+	1.87953i	−0.337832	+	0.0726125i
$671$		−	10.6873i		−	0.412577i
$672$		−	5.98844i		−	0.231009i
$673$			9.74749i			0.375738i	0.982194	+	0.187869i	$0.0601581\pi$
$673$			9.74749i			0.375738i	−0.982194	+	0.187869i	$0.939842\pi$
$674$		−	1.52967i		−	0.0589207i
$675$	1.93070	+	4.28384i	0.0743128	+	0.164885i
$676$	−11.0000	+	6.92820i	−0.423077	+	0.266469i
$677$			39.0998i			1.50273i	0.659889	+	0.751363i	$0.270603\pi$
$677$			39.0998i			1.50273i	−0.659889	+	0.751363i	$0.729397\pi$
$678$	−9.48913			−0.364428
$679$	16.0000			0.614024
$680$	−2.81386	−	13.0916i	−0.107907	−	0.502039i
$681$			13.8564i			0.530979i
$682$	5.48913			0.210189
$683$	−8.74456			−0.334601			−0.167301	−	0.985906i	$-0.553505\pi$
$683$	−8.74456			−0.334601			−0.167301	+	0.985906i	$0.553505\pi$
$684$		−	11.6819i		−	0.446670i
$685$	13.1168	−	2.81929i	0.501169	−	0.107720i
$686$	−19.8614			−0.758312
$687$	62.8397			2.39748
$688$		−	0.644810i		−	0.0245832i
$689$	−17.4891	+	5.04868i	−0.666283	+	0.192339i
$690$	−36.6060	+	7.86797i	−1.39357	+	0.299528i
$691$			39.3947i			1.49865i	0.662204	+	0.749323i	$0.269621\pi$
$691$			39.3947i			1.49865i	−0.662204	+	0.749323i	$0.730379\pi$
$692$		−	18.9051i		−	0.718663i
$693$		−	12.6766i		−	0.481544i
$694$		−	20.8395i		−	0.791057i
$695$	−13.9307	+	2.99422i	−0.528422	+	0.113577i
$696$		−	6.92820i		−	0.262613i
$697$	60.4674			2.29037
$698$			27.4728i			1.03986i
$699$	−19.8614			−0.751227
$700$	10.8139	−	4.87375i	0.408725	−	0.184210i
$701$	16.9783			0.641260			0.320630	−	0.947205i	$-0.396105\pi$
$701$	16.9783			0.641260			0.320630	+	0.947205i	$0.396105\pi$
$702$	3.25544	−	0.939764i	0.122869	−	0.0354691i
$703$		−	31.5817i		−	1.19113i
$704$			1.58457i			0.0597209i
$705$	−12.3030	−	57.2400i	−0.463357	−	2.15578i
$706$	11.4891			0.432399
$707$	−34.9783			−1.31549
$708$	−16.7446			−0.629299
$709$		−	20.7846i		−	0.780582i	−0.920691	−	0.390291i	$-0.872374\pi$
$709$		−	20.7846i		−	0.780582i	0.920691	−	0.390291i	$-0.127626\pi$
$710$	−5.93070	−	27.5928i	−0.222575	−	1.03554i
$711$	−16.0000			−0.600047
$712$		−	1.87953i		−	0.0704383i
$713$	22.9783			0.860542
$714$	35.8614			1.34208
$715$	−11.2554	+	6.04334i	−0.420929	+	0.226008i
$716$	4.88316			0.182492
$717$	−23.8614			−0.891121
$718$			2.87419i			0.107264i
$719$	−48.0000			−1.79010			−0.895049	−	0.445968i	$-0.852860\pi$
$719$	−48.0000			−1.79010			−0.895049	+	0.445968i	$0.852860\pi$
$720$	7.37228	−	1.58457i	0.274749	−	0.0590536i
$721$			24.6535i			0.918143i
$722$	7.00000			0.260513
$723$	20.7446			0.771499
$724$	−3.48913			−0.129672
$725$	12.5109	−	5.63858i	0.464642	−	0.209412i
$726$		−	21.4294i		−	0.795320i
$727$			2.17448i			0.0806470i	0.999187	+	0.0403235i	$0.0128389\pi$
$727$			2.17448i			0.0806470i	−0.999187	+	0.0403235i	$0.987161\pi$
$728$	−2.37228	−	8.21782i	−0.0879226	−	0.304573i
$729$	33.2337			1.23088
$730$	−21.8614	+	4.69882i	−0.809127	+	0.173911i
$731$	3.86141			0.142819
$732$			17.0256i			0.629283i
$733$	16.0951			0.594486			0.297243	−	0.954802i	$-0.403933\pi$
$733$	16.0951			0.594486			0.297243	+	0.954802i	$0.403933\pi$
$734$			4.75372i			0.175463i
$735$	−1.62772	−	7.57301i	−0.0600393	−	0.279335i
$736$			6.63325i			0.244505i
$737$			6.33830i			0.233474i
$738$			34.0511i			1.25344i
$739$			28.1176i			1.03432i	0.855888	+	0.517161i	$0.173011\pi$
$739$			28.1176i			1.03432i	−0.855888	+	0.517161i	$0.826989\pi$
$740$	19.9307	−	4.28384i	0.732667	−	0.157477i
$741$	−8.74456	−	30.2921i	−0.321240	−	1.11281i
$742$		−	11.9769i		−	0.439685i
$743$	−7.11684			−0.261092			−0.130546	−	0.991442i	$-0.541673\pi$
$743$	−7.11684			−0.261092			−0.130546	+	0.991442i	$0.541673\pi$
$744$	−8.74456			−0.320591
$745$	8.00000	+	37.2203i	0.293097	+	1.36364i
$746$		−	9.50744i		−	0.348092i
$747$	−29.4891			−1.07895
$748$	−9.48913			−0.346957
$749$			32.1716i			1.17552i
$750$	16.7446	+	22.7190i	0.611425	+	0.829582i
$751$	25.4891			0.930111			0.465056	−	0.885281i	$-0.346034\pi$
$751$	25.4891			0.930111			0.465056	+	0.885281i	$0.346034\pi$
$752$	−10.3723			−0.378238
$753$			58.0049i			2.11381i
$754$	−2.74456	−	9.50744i	−0.0999511	−	0.346241i
$755$	3.55842	+	16.5557i	0.129504	+	0.602523i
$756$			2.22938i			0.0810819i
$757$		−	45.4381i		−	1.65148i	−0.564055	−	0.825738i	$-0.690759\pi$
$757$		−	45.4381i		−	1.65148i	0.564055	−	0.825738i	$-0.309241\pi$
$758$			17.3205i			0.629109i
$759$			26.5330i			0.963087i
$760$	−1.62772	−	7.57301i	−0.0590436	−	0.274702i
$761$		−	1.87953i		−	0.0681328i	−0.999420	−	0.0340664i	$-0.989154\pi$
$761$		−	1.87953i		−	0.0681328i	0.999420	−	0.0340664i	$-0.0108458\pi$
$762$	−8.74456			−0.316782
$763$			6.68815i			0.242127i
$764$		0			0
$765$	9.48913	+	44.1485i	0.343080	+	1.59619i
$766$	−16.8832			−0.610013
$767$	−22.9783	+	6.63325i	−0.829697	+	0.239513i
$768$		−	2.52434i		−	0.0910892i
$769$			16.4356i			0.592685i	0.955082	+	0.296342i	$0.0957669\pi$
$769$			16.4356i			0.592685i	−0.955082	+	0.296342i	$0.904233\pi$
$770$	−1.76631	−	8.21782i	−0.0636535	−	0.296150i
$771$	35.8614			1.29152
$772$	−14.0000			−0.503871
$773$	30.6060			1.10082			0.550410	−	0.834894i	$-0.314471\pi$
$773$	30.6060			1.10082			0.550410	+	0.834894i	$0.314471\pi$
$774$			2.17448i			0.0781601i
$775$	−7.11684	−	15.7908i	−0.255645	−	0.567224i
$776$	6.74456			0.242116
$777$			54.5957i			1.95861i
$778$	6.00000			0.215110
$779$	34.9783			1.25323
$780$	17.9307	−	9.62747i	0.642022	−	0.344719i
$781$	−20.0000			−0.715656
$782$	−39.7228			−1.42048
$783$			2.57924i			0.0921745i
$784$	−1.37228			−0.0490100
$785$	7.11684	+	33.1113i	0.254011	+	1.18179i
$786$			4.10891i			0.146560i
$787$	−44.0000			−1.56843			−0.784215	−	0.620489i	$-0.786934\pi$
$787$	−44.0000			−1.56843			−0.784215	+	0.620489i	$0.786934\pi$
$788$	−4.37228			−0.155756
$789$	−45.4891			−1.61946
$790$	−10.3723	+	2.22938i	−0.369029	+	0.0793179i
$791$		−	8.91754i		−	0.317071i
$792$		−	5.34363i		−	0.189878i
$793$	6.74456	+	23.3639i	0.239506	+	0.829675i
$794$	−8.51087			−0.302040
$795$	27.8614	−	5.98844i	0.988142	−	0.212388i
$796$	8.00000			0.283552
$797$			25.2434i			0.894166i	0.894492	+	0.447083i	$0.147537\pi$
$797$			25.2434i			0.894166i	−0.894492	+	0.447083i	$0.852463\pi$
$798$	20.7446			0.734350
$799$		−	62.1138i		−	2.19743i
$800$	4.55842	−	2.05446i	0.161165	−	0.0726360i
$801$			6.33830i			0.223953i
$802$		−	32.1716i		−	1.13602i
$803$			15.8457i			0.559184i
$804$		−	10.0974i		−	0.356106i
$805$	−7.39403	−	34.4010i	−0.260605	−	1.21247i
$806$	−12.0000	+	3.46410i	−0.422682	+	0.122018i
$807$		−	6.92820i		−	0.243884i
$808$	−14.7446			−0.518712
$809$	39.3505			1.38349			0.691746	−	0.722141i	$-0.256842\pi$
$809$	39.3505			1.38349			0.691746	+	0.722141i	$0.256842\pi$
$810$	16.9307	−	3.63903i	0.594884	−	0.127862i
$811$			41.9740i			1.47391i	0.675944	+	0.736953i	$0.263736\pi$
$811$			41.9740i			1.47391i	−0.675944	+	0.736953i	$0.736264\pi$
$812$	6.51087			0.228487
$813$	−54.0951			−1.89720
$814$		−	14.4463i		−	0.506343i
$815$	−54.0951	+	11.6270i	−1.89487	+	0.407277i
$816$	15.1168			0.529195
$817$	2.23369			0.0781468
$818$			5.63858i			0.197148i
$819$	8.00000	+	27.7128i	0.279543	+	0.968364i
$820$	4.74456	+	22.0742i	0.165687	+	0.770866i
$821$			25.5932i			0.893210i	0.894731	+	0.446605i	$0.147367\pi$
$821$			25.5932i			0.893210i	−0.894731	+	0.446605i	$0.852633\pi$
$822$			15.1460i			0.528278i
$823$			54.5408i			1.90117i	0.310462	+	0.950586i	$0.399516\pi$
$823$			54.5408i			1.90117i	−0.310462	+	0.950586i	$0.600484\pi$
$824$			10.3923i			0.362033i
$825$	18.2337	−	8.21782i	0.634816	−	0.286108i
$826$		−	15.7359i		−	0.547523i
$827$	−15.2554			−0.530484			−0.265242	−	0.964182i	$-0.585452\pi$
$827$	−15.2554			−0.530484			−0.265242	+	0.964182i	$0.585452\pi$
$828$		−	22.3692i		−	0.777383i
$829$	−48.2337			−1.67523			−0.837613	−	0.546265i	$-0.816049\pi$
$829$	−48.2337			−1.67523			−0.837613	+	0.546265i	$0.816049\pi$
$830$	−19.1168	+	4.10891i	−0.663555	+	0.142622i
$831$	58.9783			2.04593
$832$	−1.00000	−	3.46410i	−0.0346688	−	0.120096i
$833$		−	8.21782i		−	0.284731i
$834$		−	16.0858i		−	0.557005i
$835$	−38.2337	+	8.21782i	−1.32313	+	0.284390i
$836$	−5.48913			−0.189845
$837$	3.25544			0.112524
$838$	19.1168			0.660380
$839$		−	13.5615i		−	0.468193i	−0.972213	−	0.234097i	$-0.924787\pi$
$839$		−	13.5615i		−	0.468193i	0.972213	−	0.234097i	$-0.0752132\pi$
$840$	2.81386	+	13.0916i	0.0970874	+	0.451702i
$841$	−21.4674			−0.740254
$842$		−	11.0371i		−	0.380364i
$843$	−4.74456			−0.163411
$844$	3.11684			0.107286
$845$	20.7921	−	20.3147i	0.715270	−	0.698848i
$846$	34.9783			1.20258
$847$	20.1386			0.691970
$848$		−	5.04868i		−	0.173372i
$849$	43.7228			1.50056
$850$	12.3030	+	27.2978i	0.421989	+	0.936308i
$851$		−	60.4743i		−	2.07303i
$852$	31.8614			1.09155
$853$	5.11684			0.175197			0.0875987	−	0.996156i	$-0.472081\pi$
$853$	5.11684			0.175197			0.0875987	+	0.996156i	$0.472081\pi$
$854$	−16.0000			−0.547509
$855$	5.48913	+	25.5383i	0.187724	+	0.873393i
$856$			13.5615i			0.463521i
$857$		−	22.7739i		−	0.777943i	−0.921250	−	0.388972i	$-0.872830\pi$
$857$		−	22.7739i		−	0.777943i	0.921250	−	0.388972i	$-0.127170\pi$
$858$	−4.00000	−	13.8564i	−0.136558	−	0.473050i
$859$	−32.4674			−1.10777			−0.553886	−	0.832592i	$-0.686856\pi$
$859$	−32.4674			−1.10777			−0.553886	+	0.832592i	$0.686856\pi$
$860$	0.302985	+	1.40965i	0.0103317	+	0.0480685i
$861$	−60.4674			−2.06072
$862$			26.4781i			0.901848i
$863$	−3.86141			−0.131444			−0.0657219	−	0.997838i	$-0.520935\pi$
$863$	−3.86141			−0.131444			−0.0657219	+	0.997838i	$0.520935\pi$
$864$			0.939764i			0.0319714i
$865$	8.88316	+	41.3292i	0.302036	+	1.40523i
$866$		−	34.4010i		−	1.16899i
$867$			47.6126i			1.61701i
$868$		−	8.21782i		−	0.278931i
$869$			7.51811i			0.255034i
$870$	3.25544	+	15.1460i	0.110370	+	0.513498i
$871$	−4.00000	−	13.8564i	−0.135535	−	0.469506i
$872$			2.81929i			0.0954733i
$873$	−22.7446			−0.769787
$874$	−22.9783			−0.777251
$875$	−21.3505	+	15.7359i	−0.721780	+	0.531972i
$876$		−	25.2434i		−	0.852895i
$877$	−47.3505			−1.59891			−0.799457	−	0.600723i	$-0.794879\pi$
$877$	−47.3505			−1.59891			−0.799457	+	0.600723i	$0.794879\pi$
$878$	22.2337			0.750351
$879$		−	5.39853i		−	0.182088i
$880$	−0.744563	−	3.46410i	−0.0250992	−	0.116775i
$881$	−54.6060			−1.83972			−0.919861	−	0.392245i	$-0.871699\pi$
$881$	−54.6060			−1.83972			−0.919861	+	0.392245i	$0.871699\pi$
$882$	4.62772			0.155823
$883$		−	58.6497i		−	1.97372i	−0.161581	−	0.986859i	$-0.551659\pi$
$883$		−	58.6497i		−	1.97372i	0.161581	−	0.986859i	$-0.448341\pi$
$884$	20.7446	−	5.98844i	0.697715	−	0.201413i
$885$	36.6060	−	7.86797i	1.23050	−	0.264479i
$886$		−	4.40387i		−	0.147951i
$887$		−	45.7330i		−	1.53556i	−0.640711	−	0.767782i	$-0.721360\pi$
$887$		−	45.7330i		−	1.53556i	0.640711	−	0.767782i	$-0.278640\pi$
$888$			23.0140i			0.772299i
$889$		−	8.21782i		−	0.275617i
$890$	0.883156	+	4.10891i	0.0296035	+	0.137731i
$891$		−	12.2718i		−	0.411122i
$892$	−15.1168			−0.506149
$893$		−	35.9306i		−	1.20237i
$894$	−42.9783			−1.43741
$895$	−10.6753	+	2.29451i	−0.356835	+	0.0766969i
$896$	2.37228			0.0792524
$897$	−16.7446	−	58.0049i	−0.559085	−	1.93673i
$898$		−	7.51811i		−	0.250883i
$899$		−	9.50744i		−	0.317091i
$900$	−15.3723	+	6.92820i	−0.512409	+	0.230940i
$901$	30.2337			1.00723
$902$	16.0000			0.532742
$903$	−3.86141			−0.128500
$904$		−	3.75906i		−	0.125024i
$905$	7.62772	−	1.63948i	0.253554	−	0.0544981i
$906$	−19.1168			−0.635115
$907$		−	0.644810i		−	0.0214106i	−0.999943	−	0.0107053i	$-0.996592\pi$
$907$		−	0.644810i		−	0.0214106i	0.999943	−	0.0107053i	$-0.00340766\pi$
$908$	−5.48913			−0.182163
$909$	49.7228			1.64920
$910$	9.04755	+	16.8506i	0.299923	+	0.558593i
$911$	34.9783			1.15888			0.579441	−	0.815014i	$-0.303271\pi$
$911$	34.9783			1.15888			0.579441	+	0.815014i	$0.303271\pi$
$912$	8.74456			0.289561
$913$			13.8564i			0.458580i
$914$	−24.9783			−0.826207
$915$	−8.00000	−	37.2203i	−0.264472	−	1.23046i
$916$			24.8935i			0.822505i
$917$	−3.86141			−0.127515
$918$	−5.62772			−0.185742
$919$	42.9783			1.41772			0.708861	−	0.705348i	$-0.249209\pi$
$919$	42.9783			1.41772			0.708861	+	0.705348i	$0.249209\pi$
$920$	−3.11684	−	14.5012i	−0.102759	−	0.478091i
$921$		−	46.0280i		−	1.51667i
$922$		−	1.63948i		−	0.0539933i
$923$	43.7228	−	12.6217i	1.43915	−	0.415448i
$924$	9.48913			0.312169
$925$	−41.5584	+	18.7302i	−1.36643	+	0.615844i
$926$	16.0000			0.525793
$927$		−	35.0458i		−	1.15105i
$928$	2.74456			0.0900947
$929$			47.9075i			1.57179i	0.618357	+	0.785897i	$0.287799\pi$
$929$			47.9075i			1.57179i	−0.618357	+	0.785897i	$0.712201\pi$
$930$	19.1168	−	4.10891i	0.626866	−	0.134737i
$931$		−	4.75372i		−	0.155797i
$932$		−	7.86797i		−	0.257724i
$933$		−	8.21782i		−	0.269039i
$934$			27.4179i			0.897140i
$935$	20.7446	−	4.45877i	0.678420	−	0.145817i
$936$	3.37228	+	11.6819i	0.110226	+	0.381836i
$937$			30.2921i			0.989598i	0.869007	+	0.494799i	$0.164758\pi$
$937$			30.2921i			0.989598i	−0.869007	+	0.494799i	$0.835242\pi$
$938$	9.48913			0.309831
$939$	31.1168			1.01546
$940$	22.6753	−	4.87375i	0.739586	−	0.158964i
$941$		−	40.6295i		−	1.32448i	−0.749291	−	0.662241i	$-0.769605\pi$
$941$		−	40.6295i		−	1.32448i	0.749291	−	0.662241i	$-0.230395\pi$
$942$	−38.2337			−1.24572
$943$	66.9783			2.18111
$944$		−	6.63325i		−	0.215894i
$945$	−1.04755	−	4.87375i	−0.0340767	−	0.158543i
$946$	1.02175			0.0332199
$947$	29.4891			0.958268			0.479134	−	0.877742i	$-0.340951\pi$
$947$	29.4891			0.958268			0.479134	+	0.877742i	$0.340951\pi$
$948$		−	11.9769i		−	0.388991i
$949$	−10.0000	−	34.6410i	−0.324614	−	1.12449i
$950$	7.11684	+	15.7908i	0.230901	+	0.512322i
$951$		−	42.8588i		−	1.38979i
$952$			14.2063i			0.460428i
$953$		−	16.0858i		−	0.521070i	−0.965464	−	0.260535i	$-0.916101\pi$
$953$		−	16.0858i		−	0.521070i	0.965464	−	0.260535i	$-0.0838989\pi$
$954$			17.0256i			0.551223i
$955$		0			0
$956$		−	9.45254i		−	0.305717i
$957$	10.9783			0.354876
$958$			18.2603i			0.589963i
$959$	−14.2337			−0.459630
$960$	1.18614	+	5.51856i	0.0382825	+	0.178111i
$961$	19.0000			0.612903
$962$	9.11684	+	31.5817i	0.293939	+	1.01823i
$963$		−	45.7330i		−	1.47373i
$964$			8.21782i			0.264678i
$965$	30.6060	−	6.57835i	0.985241	−	0.211764i
$966$	39.7228			1.27806
$967$	−5.35053			−0.172062			−0.0860308	−	0.996292i	$-0.527418\pi$
$967$	−5.35053			−0.172062			−0.0860308	+	0.996292i	$0.527418\pi$
$968$	8.48913			0.272851
$969$			52.3663i			1.68225i
$970$	−14.7446	+	3.16915i	−0.473419	+	0.101755i
$971$	−12.6060			−0.404545			−0.202272	−	0.979329i	$-0.564833\pi$
$971$	−12.6060			−0.404545			−0.202272	+	0.979329i	$0.564833\pi$
$972$			22.3692i			0.717492i
$973$	15.1168			0.484624
$974$	−1.48913			−0.0477147
$975$	−34.6753	+	29.4723i	−1.11050	+	0.943869i
$976$	−6.74456			−0.215888
$977$	25.7228			0.822946			0.411473	−	0.911422i	$-0.365014\pi$
$977$	25.7228			0.822946			0.411473	+	0.911422i	$0.365014\pi$
$978$		−	62.4636i		−	1.99737i
$979$	2.97825			0.0951853
$980$	3.00000	−	0.644810i	0.0958315	−	0.0205977i
$981$		−	9.50744i		−	0.303549i
$982$	−25.6277			−0.817813
$983$	−42.0951			−1.34263			−0.671313	−	0.741174i	$-0.734269\pi$
$983$	−42.0951			−1.34263			−0.671313	+	0.741174i	$0.734269\pi$
$984$	−25.4891			−0.812564
$985$	9.55842	−	2.05446i	0.304557	−	0.0654604i
$986$			16.4356i			0.523418i
$987$			62.1138i			1.97710i
$988$	12.0000	−	3.46410i	0.381771	−	0.110208i
$989$	4.27719			0.136007
$990$	2.51087	+	11.6819i	0.0798008	+	0.371276i
$991$	−1.76631			−0.0561088			−0.0280544	−	0.999606i	$-0.508931\pi$
$991$	−1.76631			−0.0561088			−0.0280544	+	0.999606i	$0.508931\pi$
$992$		−	3.46410i		−	0.109985i
$993$	−26.2337			−0.832501
$994$			29.9422i			0.949709i
$995$	−17.4891	+	3.75906i	−0.554443	+	0.119170i
$996$		−	22.0742i		−	0.699449i
$997$		−	4.34896i		−	0.137733i	−0.997626	−	0.0688665i	$-0.978062\pi$
$997$		−	4.34896i		−	0.137733i	0.997626	−	0.0688665i	$-0.0219383\pi$
$998$		−	16.0309i		−	0.507449i
$999$		−	8.56768i		−	0.271069i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	130.2.c.b.129.1	yes	4
3.2	odd	2		1170.2.f.a.649.3		4
4.3	odd	2		1040.2.f.c.129.4		4
5.2	odd	4		650.2.d.e.51.5		8
5.3	odd	4		650.2.d.e.51.4		8
5.4	even	2		130.2.c.a.129.4	yes	4
13.5	odd	4		1690.2.b.d.339.1		8
13.8	odd	4		1690.2.b.d.339.5		8
13.12	even	2		130.2.c.a.129.1	✓	4
15.14	odd	2		1170.2.f.b.649.1		4
20.19	odd	2		1040.2.f.d.129.1		4
39.38	odd	2		1170.2.f.b.649.2		4
52.51	odd	2		1040.2.f.d.129.4		4
65.8	even	4		8450.2.a.cn.1.4		4
65.12	odd	4		650.2.d.e.51.1		8
65.18	even	4		8450.2.a.cj.1.4		4
65.34	odd	4		1690.2.b.d.339.4		8
65.38	odd	4		650.2.d.e.51.8		8
65.44	odd	4		1690.2.b.d.339.8		8
65.47	even	4		8450.2.a.cj.1.1		4
65.57	even	4		8450.2.a.cn.1.1		4
65.64	even	2	inner	130.2.c.b.129.4	yes	4
195.194	odd	2		1170.2.f.a.649.4		4
260.259	odd	2		1040.2.f.c.129.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.c.a.129.1	✓	4	13.12	even	2
130.2.c.a.129.4	yes	4	5.4	even	2
130.2.c.b.129.1	yes	4	1.1	even	1	trivial
130.2.c.b.129.4	yes	4	65.64	even	2	inner
650.2.d.e.51.1		8	65.12	odd	4
650.2.d.e.51.4		8	5.3	odd	4
650.2.d.e.51.5		8	5.2	odd	4
650.2.d.e.51.8		8	65.38	odd	4
1040.2.f.c.129.1		4	260.259	odd	2
1040.2.f.c.129.4		4	4.3	odd	2
1040.2.f.d.129.1		4	20.19	odd	2
1040.2.f.d.129.4		4	52.51	odd	2
1170.2.f.a.649.3		4	3.2	odd	2
1170.2.f.a.649.4		4	195.194	odd	2
1170.2.f.b.649.1		4	15.14	odd	2
1170.2.f.b.649.2		4	39.38	odd	2
1690.2.b.d.339.1		8	13.5	odd	4
1690.2.b.d.339.4		8	65.34	odd	4
1690.2.b.d.339.5		8	13.8	odd	4
1690.2.b.d.339.8		8	65.44	odd	4
8450.2.a.cj.1.1		4	65.47	even	4
8450.2.a.cj.1.4		4	65.18	even	4
8450.2.a.cn.1.1		4	65.57	even	4
8450.2.a.cn.1.4		4	65.8	even	4

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.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.52434i q^{3} +1.00000 q^{4} +(-2.18614 + 0.469882i) q^{5} -2.52434i q^{6} +2.37228 q^{7} +1.00000 q^{8} -3.37228 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.52434i q^{3} +1.00000 q^{4} +(-2.18614 + 0.469882i) q^{5} -2.52434i q^{6} +2.37228 q^{7} +1.00000 q^{8} -3.37228 q^{9} +(-2.18614 + 0.469882i) q^{10} +1.58457i q^{11} -2.52434i q^{12} +(-1.00000 - 3.46410i) q^{13} +2.37228 q^{14} +(1.18614 + 5.51856i) q^{15} +1.00000 q^{16} +5.98844i q^{17} -3.37228 q^{18} +3.46410i q^{19} +(-2.18614 + 0.469882i) q^{20} -5.98844i q^{21} +1.58457i q^{22} +6.63325i q^{23} -2.52434i q^{24} +(4.55842 - 2.05446i) q^{25} +(-1.00000 - 3.46410i) q^{26} +0.939764i q^{27} +2.37228 q^{28} +2.74456 q^{29} +(1.18614 + 5.51856i) q^{30} -3.46410i q^{31} +1.00000 q^{32} +4.00000 q^{33} +5.98844i q^{34} +(-5.18614 + 1.11469i) q^{35} -3.37228 q^{36} -9.11684 q^{37} +3.46410i q^{38} +(-8.74456 + 2.52434i) q^{39} +(-2.18614 + 0.469882i) q^{40} -10.0974i q^{41} -5.98844i q^{42} -0.644810i q^{43} +1.58457i q^{44} +(7.37228 - 1.58457i) q^{45} +6.63325i q^{46} -10.3723 q^{47} -2.52434i q^{48} -1.37228 q^{49} +(4.55842 - 2.05446i) q^{50} +15.1168 q^{51} +(-1.00000 - 3.46410i) q^{52} -5.04868i q^{53} +0.939764i q^{54} +(-0.744563 - 3.46410i) q^{55} +2.37228 q^{56} +8.74456 q^{57} +2.74456 q^{58} -6.63325i q^{59} +(1.18614 + 5.51856i) q^{60} -6.74456 q^{61} -3.46410i q^{62} -8.00000 q^{63} +1.00000 q^{64} +(3.81386 + 7.10313i) q^{65} +4.00000 q^{66} +4.00000 q^{67} +5.98844i q^{68} +16.7446 q^{69} +(-5.18614 + 1.11469i) q^{70} +12.6217i q^{71} -3.37228 q^{72} +10.0000 q^{73} -9.11684 q^{74} +(-5.18614 - 11.5070i) q^{75} +3.46410i q^{76} +3.75906i q^{77} +(-8.74456 + 2.52434i) q^{78} +4.74456 q^{79} +(-2.18614 + 0.469882i) q^{80} -7.74456 q^{81} -10.0974i q^{82} +8.74456 q^{83} -5.98844i q^{84} +(-2.81386 - 13.0916i) q^{85} -0.644810i q^{86} -6.92820i q^{87} +1.58457i q^{88} -1.87953i q^{89} +(7.37228 - 1.58457i) q^{90} +(-2.37228 - 8.21782i) q^{91} +6.63325i q^{92} -8.74456 q^{93} -10.3723 q^{94} +(-1.62772 - 7.57301i) q^{95} -2.52434i q^{96} +6.74456 q^{97} -1.37228 q^{98} -5.34363i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{4} - 3 q^{5} - 2 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^4 - 3 * q^5 - 2 * q^7 + 4 * q^8 - 2 * q^9	\( 4 q + 4 q^{2} + 4 q^{4} - 3 q^{5} - 2 q^{7} + 4 q^{8} - 2 q^{9} - 3 q^{10} - 4 q^{13} - 2 q^{14} - q^{15} + 4 q^{16} - 2 q^{18} - 3 q^{20} + q^{25} - 4 q^{26} - 2 q^{28} - 12 q^{29} - q^{30} + 4 q^{32} + 16 q^{33} - 15 q^{35} - 2 q^{36} - 2 q^{37} - 12 q^{39} - 3 q^{40} + 18 q^{45} - 30 q^{47} + 6 q^{49} + q^{50} + 26 q^{51} - 4 q^{52} + 20 q^{55} - 2 q^{56} + 12 q^{57} - 12 q^{58} - q^{60} - 4 q^{61} - 32 q^{63} + 4 q^{64} + 21 q^{65} + 16 q^{66} + 16 q^{67} + 44 q^{69} - 15 q^{70} - 2 q^{72} + 40 q^{73} - 2 q^{74} - 15 q^{75} - 12 q^{78} - 4 q^{79} - 3 q^{80} - 8 q^{81} + 12 q^{83} - 17 q^{85} + 18 q^{90} + 2 q^{91} - 12 q^{93} - 30 q^{94} - 18 q^{95} + 4 q^{97} + 6 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^4 - 3 * q^5 - 2 * q^7 + 4 * q^8 - 2 * q^9 - 3 * q^10 - 4 * q^13 - 2 * q^14 - q^15 + 4 * q^16 - 2 * q^18 - 3 * q^20 + q^25 - 4 * q^26 - 2 * q^28 - 12 * q^29 - q^30 + 4 * q^32 + 16 * q^33 - 15 * q^35 - 2 * q^36 - 2 * q^37 - 12 * q^39 - 3 * q^40 + 18 * q^45 - 30 * q^47 + 6 * q^49 + q^50 + 26 * q^51 - 4 * q^52 + 20 * q^55 - 2 * q^56 + 12 * q^57 - 12 * q^58 - q^60 - 4 * q^61 - 32 * q^63 + 4 * q^64 + 21 * q^65 + 16 * q^66 + 16 * q^67 + 44 * q^69 - 15 * q^70 - 2 * q^72 + 40 * q^73 - 2 * q^74 - 15 * q^75 - 12 * q^78 - 4 * q^79 - 3 * q^80 - 8 * q^81 + 12 * q^83 - 17 * q^85 + 18 * q^90 + 2 * q^91 - 12 * q^93 - 30 * q^94 - 18 * q^95 + 4 * q^97 + 6 * q^98

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