LMFDB - Embedded newform 770.2.n.i.421.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(71,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("770.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 11 x^{10} - 21 x^{9} + 61 x^{8} - 34 x^{7} + 141 x^{6} + 192 x^{5} + 289 x^{4} + \cdots + 1 $ x^12 - 3x^11 + 11x^10 - 21x^9 + 61x^8 - 34x^7 + 141x^6 + 192x^5 + 289x^4 - 55x^3 + 222x^2 - 24*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			421.1
Root			$0.701664 + 2.15950i$ of defining polynomial
Character	$\chi$	$=$	770.421
Dual form			770.2.n.i.631.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(-0.867835 - 2.67092i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(2.27202 + 1.65072i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-3.95363 + 2.87248i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.867835 - 2.67092i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(2.27202 + 1.65072i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-3.95363 + 2.87248i) q^{9} +1.00000 q^{10} +(-1.88776 + 2.72697i) q^{11} -2.80837 q^{12} +(2.47368 - 1.79724i) q^{13} +(0.309017 + 0.951057i) q^{14} +(-0.867835 + 2.67092i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-5.61829 - 4.08193i) q^{17} +(1.51015 - 4.64777i) q^{18} +(-1.45146 - 4.46715i) q^{19} +(-0.809017 + 0.587785i) q^{20} -2.80837 q^{21} +(-0.0756411 - 3.31576i) q^{22} -1.73118 q^{23} +(2.27202 - 1.65072i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-0.944863 + 2.90799i) q^{26} +(4.28719 + 3.11483i) q^{27} +(-0.809017 - 0.587785i) q^{28} +(-2.08449 + 6.41539i) q^{29} +(-0.867835 - 2.67092i) q^{30} +(-2.70482 + 1.96516i) q^{31} +1.00000 q^{32} +(8.92178 + 2.67550i) q^{33} +6.94459 q^{34} +(-0.809017 + 0.587785i) q^{35} +(1.51015 + 4.64777i) q^{36} +(-2.26428 + 6.96873i) q^{37} +(3.79998 + 2.76085i) q^{38} +(-6.94703 - 5.04731i) q^{39} +(0.309017 - 0.951057i) q^{40} +(2.34537 + 7.21830i) q^{41} +(2.27202 - 1.65072i) q^{42} +7.27592 q^{43} +(2.01015 + 2.63805i) q^{44} +4.88695 q^{45} +(1.40055 - 1.01756i) q^{46} +(1.23778 + 3.80951i) q^{47} +(-0.867835 + 2.67092i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-0.809017 - 0.587785i) q^{50} +(-6.02676 + 18.5485i) q^{51} +(-0.944863 - 2.90799i) q^{52} +(1.37627 - 0.999919i) q^{53} -5.29926 q^{54} +(3.13010 - 1.09657i) q^{55} +1.00000 q^{56} +(-10.6718 + 7.75349i) q^{57} +(-2.08449 - 6.41539i) q^{58} +(2.36318 - 7.27312i) q^{59} +(2.27202 + 1.65072i) q^{60} +(-7.22492 - 5.24921i) q^{61} +(1.03315 - 3.17970i) q^{62} +(1.51015 + 4.64777i) q^{63} +(-0.809017 + 0.587785i) q^{64} -3.05764 q^{65} +(-8.79049 + 3.07956i) q^{66} +10.5718 q^{67} +(-5.61829 + 4.08193i) q^{68} +(1.50238 + 4.62384i) q^{69} +(0.309017 - 0.951057i) q^{70} +(1.86409 + 1.35434i) q^{71} +(-3.95363 - 2.87248i) q^{72} +(-4.05160 + 12.4695i) q^{73} +(-2.26428 - 6.96873i) q^{74} +(2.27202 - 1.65072i) q^{75} -4.69704 q^{76} +(2.01015 + 2.63805i) q^{77} +8.58700 q^{78} +(-3.44503 + 2.50296i) q^{79} +(0.309017 + 0.951057i) q^{80} +(0.0684287 - 0.210602i) q^{81} +(-6.14025 - 4.46116i) q^{82} +(-3.12339 - 2.26928i) q^{83} +(-0.867835 + 2.67092i) q^{84} +(2.14600 + 6.60470i) q^{85} +(-5.88634 + 4.27668i) q^{86} +18.9440 q^{87} +(-3.17685 - 0.952688i) q^{88} -12.3140 q^{89} +(-3.95363 + 2.87248i) q^{90} +(-0.944863 - 2.90799i) q^{91} +(-0.534964 + 1.64645i) q^{92} +(7.59613 + 5.51891i) q^{93} +(-3.24056 - 2.35440i) q^{94} +(-1.45146 + 4.46715i) q^{95} +(-0.867835 - 2.67092i) q^{96} +(5.61686 - 4.08089i) q^{97} +1.00000 q^{98} +(-0.369655 - 16.2040i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} + 2 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 3 q^{7} - 3 q^{8} - 15 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 3 * q^7 - 3 * q^8 - 15 * q^9	\( 12 q - 3 q^{2} + 2 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 3 q^{7} - 3 q^{8} - 15 q^{9} + 12 q^{10} + q^{11} + 2 q^{12} - 6 q^{13} - 3 q^{14} + 2 q^{15} - 3 q^{16} - 6 q^{17} - 13 q^{19} - 3 q^{20} + 2 q^{21} + q^{22} - 12 q^{23} - 3 q^{24} - 3 q^{25} + 4 q^{26} - 7 q^{27} - 3 q^{28} - 26 q^{29} + 2 q^{30} + 12 q^{32} - 15 q^{33} + 14 q^{34} - 3 q^{35} - 18 q^{37} + 2 q^{38} - 40 q^{39} - 3 q^{40} + 16 q^{41} - 3 q^{42} + 38 q^{43} + 6 q^{44} + 30 q^{45} + 8 q^{46} - 26 q^{47} + 2 q^{48} - 3 q^{49} - 3 q^{50} - 13 q^{51} + 4 q^{52} + 8 q^{54} + 11 q^{55} + 12 q^{56} - 41 q^{57} - 26 q^{58} + 21 q^{59} - 3 q^{60} + 4 q^{61} - 3 q^{64} + 4 q^{65} - 30 q^{66} + 10 q^{67} - 6 q^{68} + 18 q^{69} - 3 q^{70} - 4 q^{71} - 15 q^{72} - 14 q^{73} - 18 q^{74} - 3 q^{75} + 22 q^{76} + 6 q^{77} + 40 q^{78} - 2 q^{79} - 3 q^{80} + 26 q^{81} - 29 q^{82} + 35 q^{83} + 2 q^{84} - q^{85} - 37 q^{86} + 28 q^{87} - 19 q^{88} + 2 q^{89} - 15 q^{90} + 4 q^{91} - 2 q^{92} + 6 q^{93} + 4 q^{94} - 13 q^{95} + 2 q^{96} + 19 q^{97} + 12 q^{98} - 81 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 3 * q^7 - 3 * q^8 - 15 * q^9 + 12 * q^10 + q^11 + 2 * q^12 - 6 * q^13 - 3 * q^14 + 2 * q^15 - 3 * q^16 - 6 * q^17 - 13 * q^19 - 3 * q^20 + 2 * q^21 + q^22 - 12 * q^23 - 3 * q^24 - 3 * q^25 + 4 * q^26 - 7 * q^27 - 3 * q^28 - 26 * q^29 + 2 * q^30 + 12 * q^32 - 15 * q^33 + 14 * q^34 - 3 * q^35 - 18 * q^37 + 2 * q^38 - 40 * q^39 - 3 * q^40 + 16 * q^41 - 3 * q^42 + 38 * q^43 + 6 * q^44 + 30 * q^45 + 8 * q^46 - 26 * q^47 + 2 * q^48 - 3 * q^49 - 3 * q^50 - 13 * q^51 + 4 * q^52 + 8 * q^54 + 11 * q^55 + 12 * q^56 - 41 * q^57 - 26 * q^58 + 21 * q^59 - 3 * q^60 + 4 * q^61 - 3 * q^64 + 4 * q^65 - 30 * q^66 + 10 * q^67 - 6 * q^68 + 18 * q^69 - 3 * q^70 - 4 * q^71 - 15 * q^72 - 14 * q^73 - 18 * q^74 - 3 * q^75 + 22 * q^76 + 6 * q^77 + 40 * q^78 - 2 * q^79 - 3 * q^80 + 26 * q^81 - 29 * q^82 + 35 * q^83 + 2 * q^84 - q^85 - 37 * q^86 + 28 * q^87 - 19 * q^88 + 2 * q^89 - 15 * q^90 + 4 * q^91 - 2 * q^92 + 6 * q^93 + 4 * q^94 - 13 * q^95 + 2 * q^96 + 19 * q^97 + 12 * q^98 - 81 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

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 $

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$	−0.867835	−	2.67092i	−0.501045	−	1.54206i	−0.807320	−	0.590114i	$-0.799083\pi$
$3$	−0.867835	−	2.67092i	−0.501045	−	1.54206i	0.306276	−	0.951943i	$-0.400917\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$	2.27202	+	1.65072i	0.927548	+	0.673903i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	−3.95363	+	2.87248i	−1.31788	+	0.957493i
$10$	1.00000			0.316228
$11$	−1.88776	+	2.72697i	−0.569181	+	0.822212i
$11$	−1.88776	+	2.72697i	−0.569181	+	0.822212i
$12$	−2.80837			−0.810707
$13$	2.47368	−	1.79724i	0.686077	−	0.498464i	−0.189291	−	0.981921i	$-0.560619\pi$
$13$	2.47368	−	1.79724i	0.686077	−	0.498464i	0.875368	+	0.483457i	$0.160619\pi$
$14$	0.309017	+	0.951057i	0.0825883	+	0.254181i
$15$	−0.867835	+	2.67092i	−0.224074	+	0.689629i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−5.61829	−	4.08193i	−1.36264	−	0.990013i	−0.998272	−	0.0587568i	$-0.981286\pi$
$17$	−5.61829	−	4.08193i	−1.36264	−	0.990013i	−0.364364	−	0.931257i	$-0.618714\pi$
$18$	1.51015	−	4.64777i	0.355946	−	1.09549i
$19$	−1.45146	−	4.46715i	−0.332989	−	1.02483i	−0.967704	−	0.252088i	$-0.918883\pi$
$19$	−1.45146	−	4.46715i	−0.332989	−	1.02483i	0.634715	−	0.772746i	$-0.281117\pi$
$20$	−0.809017	+	0.587785i	−0.180902	+	0.131433i
$21$	−2.80837			−0.612837
$22$	−0.0756411	−	3.31576i	−0.0161267	−	0.706923i
$23$	−1.73118			−0.360976			−0.180488	−	0.983577i	$-0.557768\pi$
$23$	−1.73118			−0.360976			−0.180488	+	0.983577i	$0.557768\pi$
$24$	2.27202	−	1.65072i	0.463774	−	0.336952i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	−0.944863	+	2.90799i	−0.185303	+	0.570304i
$27$	4.28719	+	3.11483i	0.825071	+	0.599449i
$28$	−0.809017	−	0.587785i	−0.152890	−	0.111081i
$29$	−2.08449	+	6.41539i	−0.387080	+	1.19131i	0.547881	+	0.836556i	$0.315435\pi$
$29$	−2.08449	+	6.41539i	−0.387080	+	1.19131i	−0.934960	+	0.354752i	$0.884565\pi$
$30$	−0.867835	−	2.67092i	−0.158444	−	0.487641i
$31$	−2.70482	+	1.96516i	−0.485799	+	0.352954i	−0.803567	−	0.595215i	$-0.797067\pi$
$31$	−2.70482	+	1.96516i	−0.485799	+	0.352954i	0.317767	+	0.948169i	$0.397067\pi$
$32$	1.00000			0.176777
$33$	8.92178	+	2.67550i	1.55308	+	0.465745i
$34$	6.94459			1.19099
$35$	−0.809017	+	0.587785i	−0.136749	+	0.0993538i
$36$	1.51015	+	4.64777i	0.251692	+	0.774628i
$37$	−2.26428	+	6.96873i	−0.372245	+	1.14565i	0.573074	+	0.819504i	$0.305751\pi$
$37$	−2.26428	+	6.96873i	−0.372245	+	1.14565i	−0.945319	+	0.326148i	$0.894249\pi$
$38$	3.79998	+	2.76085i	0.616439	+	0.447869i
$39$	−6.94703	−	5.04731i	−1.11241	−	0.808216i
$40$	0.309017	−	0.951057i	0.0488599	−	0.150375i
$41$	2.34537	+	7.21830i	0.366285	+	1.12731i	0.949172	+	0.314756i	$0.101923\pi$
$41$	2.34537	+	7.21830i	0.366285	+	1.12731i	−0.582888	+	0.812553i	$0.698077\pi$
$42$	2.27202	−	1.65072i	0.350580	−	0.254712i
$43$	7.27592			1.10957			0.554784	−	0.831995i	$-0.312801\pi$
$43$	7.27592			1.10957			0.554784	+	0.831995i	$0.312801\pi$
$44$	2.01015	+	2.63805i	0.303042	+	0.397701i
$45$	4.88695			0.728504
$46$	1.40055	−	1.01756i	0.206500	−	0.150031i
$47$	1.23778	+	3.80951i	0.180549	+	0.555673i	0.999843	−	0.0177001i	$-0.00563440\pi$
$47$	1.23778	+	3.80951i	0.180549	+	0.555673i	−0.819294	+	0.573374i	$0.805634\pi$
$48$	−0.867835	+	2.67092i	−0.125261	+	0.385514i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	−0.809017	−	0.587785i	−0.114412	−	0.0831254i
$51$	−6.02676	+	18.5485i	−0.843915	+	2.59730i
$52$	−0.944863	−	2.90799i	−0.131029	−	0.403266i
$53$	1.37627	−	0.999919i	0.189045	−	0.137349i	−0.489237	−	0.872151i	$-0.662725\pi$
$53$	1.37627	−	0.999919i	0.189045	−	0.137349i	0.678282	+	0.734801i	$0.262725\pi$
$54$	−5.29926			−0.721138
$55$	3.13010	−	1.09657i	0.422063	−	0.147861i
$56$	1.00000			0.133631
$57$	−10.6718	+	7.75349i	−1.41351	+	1.02698i
$58$	−2.08449	−	6.41539i	−0.273707	−	0.842382i
$59$	2.36318	−	7.27312i	0.307660	−	0.946880i	−0.671011	−	0.741447i	$-0.734140\pi$
$59$	2.36318	−	7.27312i	0.307660	−	0.946880i	0.978671	−	0.205433i	$-0.0658602\pi$
$60$	2.27202	+	1.65072i	0.293317	+	0.213107i
$61$	−7.22492	−	5.24921i	−0.925057	−	0.672093i	0.0197208	−	0.999806i	$-0.493722\pi$
$61$	−7.22492	−	5.24921i	−0.925057	−	0.672093i	−0.944778	+	0.327712i	$0.893722\pi$
$62$	1.03315	−	3.17970i	0.131210	−	0.403822i
$63$	1.51015	+	4.64777i	0.190261	+	0.585564i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−3.05764			−0.379254
$66$	−8.79049	+	3.07956i	−1.08203	+	0.379068i
$67$	10.5718			1.29155			0.645773	−	0.763529i	$-0.276535\pi$
$67$	10.5718			1.29155			0.645773	+	0.763529i	$0.276535\pi$
$68$	−5.61829	+	4.08193i	−0.681318	+	0.495007i
$69$	1.50238	+	4.62384i	0.180865	+	0.556645i
$70$	0.309017	−	0.951057i	0.0369346	−	0.113673i
$71$	1.86409	+	1.35434i	0.221226	+	0.160730i	0.692879	−	0.721054i	$-0.256342\pi$
$71$	1.86409	+	1.35434i	0.221226	+	0.160730i	−0.471652	+	0.881785i	$0.656342\pi$
$72$	−3.95363	−	2.87248i	−0.465939	−	0.338525i
$73$	−4.05160	+	12.4695i	−0.474204	+	1.45945i	0.372824	+	0.927902i	$0.378389\pi$
$73$	−4.05160	+	12.4695i	−0.474204	+	1.45945i	−0.847028	+	0.531548i	$0.821611\pi$
$74$	−2.26428	−	6.96873i	−0.263217	−	0.810099i
$75$	2.27202	−	1.65072i	0.262350	−	0.190609i
$76$	−4.69704			−0.538787
$77$	2.01015	+	2.63805i	0.229078	+	0.300633i
$78$	8.58700			0.972286
$79$	−3.44503	+	2.50296i	−0.387596	+	0.281605i	−0.764470	−	0.644660i	$-0.776999\pi$
$79$	−3.44503	+	2.50296i	−0.387596	+	0.281605i	0.376874	+	0.926265i	$0.376999\pi$
$80$	0.309017	+	0.951057i	0.0345492	+	0.106331i
$81$	0.0684287	−	0.210602i	0.00760319	−	0.0234002i
$82$	−6.14025	−	4.46116i	−0.678078	−	0.492652i
$83$	−3.12339	−	2.26928i	−0.342837	−	0.249086i	0.403021	−	0.915191i	$-0.367960\pi$
$83$	−3.12339	−	2.26928i	−0.342837	−	0.249086i	−0.745858	+	0.666105i	$0.767960\pi$
$84$	−0.867835	+	2.67092i	−0.0946885	+	0.291421i
$85$	2.14600	+	6.60470i	0.232766	+	0.716380i
$86$	−5.88634	+	4.27668i	−0.634741	+	0.461166i
$87$	18.9440			2.03101
$88$	−3.17685	−	0.952688i	−0.338654	−	0.101557i
$89$	−12.3140			−1.30529			−0.652643	−	0.757665i	$-0.726340\pi$
$89$	−12.3140			−1.30529			−0.652643	+	0.757665i	$0.726340\pi$
$90$	−3.95363	+	2.87248i	−0.416749	+	0.302786i
$91$	−0.944863	−	2.90799i	−0.0990486	−	0.304840i
$92$	−0.534964	+	1.64645i	−0.0557738	+	0.171654i
$93$	7.59613	+	5.51891i	0.787682	+	0.572284i
$94$	−3.24056	−	2.35440i	−0.334238	−	0.242838i
$95$	−1.45146	+	4.46715i	−0.148917	+	0.458320i
$96$	−0.867835	−	2.67092i	−0.0885730	−	0.272600i
$97$	5.61686	−	4.08089i	0.570306	−	0.414351i	−0.264911	−	0.964273i	$-0.585342\pi$
$97$	5.61686	−	4.08089i	0.570306	−	0.414351i	0.835216	+	0.549922i	$0.185342\pi$
$98$	1.00000			0.101015
$99$	−0.369655	−	16.2040i	−0.0371517	−	1.62856i
$100$	1.00000			0.100000
$101$	−10.9957	+	7.98888i	−1.09412	+	0.794923i	−0.980090	−	0.198555i	$-0.936375\pi$
$101$	−10.9957	+	7.98888i	−1.09412	+	0.794923i	−0.114028	+	0.993478i	$0.536375\pi$
$102$	−6.02676	−	18.5485i	−0.596738	−	1.83657i
$103$	4.90072	−	15.0829i	0.482882	−	1.48616i	−0.352143	−	0.935946i	$-0.614547\pi$
$103$	4.90072	−	15.0829i	0.482882	−	1.48616i	0.835025	−	0.550212i	$-0.185453\pi$
$104$	2.47368	+	1.79724i	0.242565	+	0.176234i
$105$	2.27202	+	1.65072i	0.221726	+	0.161094i
$106$	−0.525688	+	1.61790i	−0.0510594	+	0.157145i
$107$	−1.35870	−	4.18165i	−0.131351	−	0.404256i	0.863654	−	0.504085i	$-0.168170\pi$
$107$	−1.35870	−	4.18165i	−0.131351	−	0.404256i	−0.995005	+	0.0998295i	$0.968170\pi$
$108$	4.28719	−	3.11483i	0.412535	−	0.299724i
$109$	−14.4931			−1.38819			−0.694095	−	0.719884i	$-0.744195\pi$
$109$	−14.4931			−1.38819			−0.694095	+	0.719884i	$0.744195\pi$
$110$	−1.88776	+	2.72697i	−0.179991	+	0.260006i
$111$	20.5779			1.95317
$112$	−0.809017	+	0.587785i	−0.0764449	+	0.0555405i
$113$	−5.97409	−	18.3864i	−0.561995	−	1.72964i	−0.676714	−	0.736246i	$-0.736597\pi$
$113$	−5.97409	−	18.3864i	−0.561995	−	1.72964i	0.114719	−	0.993398i	$-0.463403\pi$
$114$	4.07625	−	12.5454i	0.381776	−	1.17499i
$115$	1.40055	+	1.01756i	0.130602	+	0.0948881i
$116$	5.45726	+	3.96493i	0.506694	+	0.368135i
$117$	−4.61750	+	14.2112i	−0.426888	+	1.31383i
$118$	2.36318	+	7.27312i	0.217548	+	0.669545i
$119$	−5.61829	+	4.08193i	−0.515028	+	0.374190i
$120$	−2.80837			−0.256368
$121$	−3.87272	−	10.2957i	−0.352065	−	0.935976i
$122$	8.93050			0.808529
$123$	17.2441	−	12.5286i	1.55485	−	1.12966i
$124$	1.03315	+	3.17970i	0.0927794	+	0.285546i
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$	−3.95363	−	2.87248i	−0.352217	−	0.255901i
$127$	−17.4624	−	12.6872i	−1.54954	−	1.12581i	−0.943977	−	0.330012i	$-0.892947\pi$
$127$	−17.4624	−	12.6872i	−1.54954	−	1.12581i	−0.605565	−	0.795796i	$-0.707053\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	−6.31430	−	19.4334i	−0.555943	−	1.71102i
$130$	2.47368	−	1.79724i	0.216956	−	0.157628i
$131$	5.23468			0.457356			0.228678	−	0.973502i	$-0.426560\pi$
$131$	5.23468			0.457356			0.228678	+	0.973502i	$0.426560\pi$
$132$	5.30153	−	7.65834i	0.461439	−	0.666573i
$133$	−4.69704			−0.407285
$134$	−8.55274	+	6.21393i	−0.738844	+	0.536802i
$135$	−1.63756	−	5.03990i	−0.140939	−	0.433765i
$136$	2.14600	−	6.60470i	0.184018	−	0.566348i
$137$	−4.04540	−	2.93916i	−0.345622	−	0.251109i	0.401408	−	0.915899i	$-0.368521\pi$
$137$	−4.04540	−	2.93916i	−0.345622	−	0.251109i	−0.747030	+	0.664790i	$0.768521\pi$
$138$	−3.93327	−	2.85769i	−0.334822	−	0.243263i
$139$	−0.951845	+	2.92948i	−0.0807345	+	0.248475i	−0.983274	−	0.182131i	$-0.941700\pi$
$139$	−0.951845	+	2.92948i	−0.0807345	+	0.248475i	0.902540	+	0.430607i	$0.141700\pi$
$140$	0.309017	+	0.951057i	0.0261167	+	0.0803789i
$141$	9.10069	−	6.61204i	0.766417	−	0.556834i
$142$	−2.30414			−0.193359
$143$	0.231284	+	10.1384i	0.0193409	+	0.847817i
$144$	4.88695			0.407246
$145$	5.45726	−	3.96493i	0.453201	−	0.329270i
$146$	−4.05160	−	12.4695i	−0.335313	−	1.03199i
$147$	−0.867835	+	2.67092i	−0.0715778	+	0.220294i
$148$	5.92796	+	4.30691i	0.487275	+	0.354026i
$149$	12.8518	+	9.33741i	1.05286	+	0.764951i	0.972755	−	0.231835i	$-0.0744731\pi$
$149$	12.8518	+	9.33741i	1.05286	+	0.764951i	0.0801093	+	0.996786i	$0.474473\pi$
$150$	−0.867835	+	2.67092i	−0.0708584	+	0.218080i
$151$	−1.68697	−	5.19197i	−0.137284	−	0.422516i	0.858654	−	0.512555i	$-0.171301\pi$
$151$	−1.68697	−	5.19197i	−0.137284	−	0.422516i	−0.995938	+	0.0900386i	$0.971301\pi$
$152$	3.79998	−	2.76085i	0.308219	−	0.223934i
$153$	33.9379			2.74372
$154$	−3.17685	−	0.952688i	−0.255998	−	0.0767698i
$155$	3.34334			0.268543
$156$	−6.94703	+	5.04731i	−0.556207	+	0.404108i
$157$	2.60832	+	8.02758i	0.208166	+	0.640671i	0.999568	+	0.0293745i	$0.00935153\pi$
$157$	2.60832	+	8.02758i	0.208166	+	0.640671i	−0.791402	+	0.611296i	$0.790648\pi$
$158$	1.31588	−	4.04987i	0.104686	−	0.322191i
$159$	−3.86508	−	2.80814i	−0.306521	−	0.222700i
$160$	−0.809017	−	0.587785i	−0.0639584	−	0.0464685i
$161$	−0.534964	+	1.64645i	−0.0421610	+	0.129758i
$162$	0.0684287	+	0.210602i	0.00537627	+	0.0165465i
$163$	−7.88270	+	5.72712i	−0.617421	+	0.448582i	−0.852020	−	0.523510i	$-0.824622\pi$
$163$	−7.88270	+	5.72712i	−0.617421	+	0.448582i	0.234599	+	0.972092i	$0.424622\pi$
$164$	7.58977			0.592662
$165$	−5.64525	−	7.40862i	−0.439482	−	0.576760i
$166$	3.86073			0.299650
$167$	−16.3487	+	11.8780i	−1.26510	+	0.919147i	−0.998996	−	0.0447976i	$-0.985736\pi$
$167$	−16.3487	+	11.8780i	−1.26510	+	0.919147i	−0.266102	+	0.963945i	$0.585736\pi$
$168$	−0.867835	−	2.67092i	−0.0669549	−	0.206066i
$169$	−1.12817	+	3.47214i	−0.0867821	+	0.267088i
$170$	−5.61829	−	4.08193i	−0.430903	−	0.313070i
$171$	18.5703	+	13.4921i	1.42011	+	1.03177i
$172$	2.24838	−	6.91981i	0.171438	−	0.527631i
$173$	0.328847	+	1.01209i	0.0250017	+	0.0769474i	0.962779	−	0.270290i	$-0.0871197\pi$
$173$	0.328847	+	1.01209i	0.0250017	+	0.0769474i	−0.937777	+	0.347238i	$0.887120\pi$
$174$	−15.3260	+	11.1350i	−1.16186	+	0.844142i
$175$	1.00000			0.0755929
$176$	3.13010	−	1.09657i	0.235940	−	0.0826568i
$177$	−21.4768			−1.61429
$178$	9.96227	−	7.23802i	0.746704	−	0.542512i
$179$	−1.77308	−	5.45697i	−0.132526	−	0.407873i	0.862671	−	0.505765i	$-0.168790\pi$
$179$	−1.77308	−	5.45697i	−0.132526	−	0.407873i	−0.995197	+	0.0978925i	$0.968790\pi$
$180$	1.51015	−	4.64777i	0.112560	−	0.346424i
$181$	−3.05500	−	2.21959i	−0.227076	−	0.164981i	0.468430	−	0.883501i	$-0.344820\pi$
$181$	−3.05500	−	2.21959i	−0.227076	−	0.164981i	−0.695506	+	0.718520i	$0.744820\pi$
$182$	2.47368	+	1.79724i	0.183362	+	0.133220i
$183$	−7.75019	+	23.8526i	−0.572911	+	1.76324i
$184$	−0.534964	−	1.64645i	−0.0394380	−	0.121378i
$185$	5.92796	−	4.30691i	0.435832	−	0.316651i
$186$	−9.38933			−0.688459
$187$	21.7373	−	7.61520i	1.58959	−	0.556879i
$188$	4.00555			0.292135
$189$	4.28719	−	3.11483i	0.311847	−	0.226570i
$190$	−1.45146	−	4.46715i	−0.105300	−	0.324081i
$191$	3.62470	−	11.1557i	0.262274	−	0.807196i	−0.730035	−	0.683410i	$-0.760496\pi$
$191$	3.62470	−	11.1557i	0.262274	−	0.807196i	0.992309	−	0.123786i	$-0.0395037\pi$
$192$	2.27202	+	1.65072i	0.163969	+	0.119130i
$193$	−15.3616	−	11.1608i	−1.10575	−	0.803374i	−0.123761	−	0.992312i	$-0.539495\pi$
$193$	−15.3616	−	11.1608i	−1.10575	−	0.803374i	−0.981989	+	0.188938i	$0.939495\pi$
$194$	−2.14545	+	6.60301i	−0.154034	+	0.474069i
$195$	2.65353	+	8.16672i	0.190023	+	0.584831i
$196$	−0.809017	+	0.587785i	−0.0577869	+	0.0419847i
$197$	−3.27508			−0.233340			−0.116670	−	0.993171i	$-0.537222\pi$
$197$	−3.27508			−0.233340			−0.116670	+	0.993171i	$0.537222\pi$
$198$	9.82351	+	12.8920i	0.698126	+	0.916195i
$199$	14.7438			1.04516			0.522580	−	0.852590i	$-0.324970\pi$
$199$	14.7438			1.04516			0.522580	+	0.852590i	$0.324970\pi$
$200$	−0.809017	+	0.587785i	−0.0572061	+	0.0415627i
$201$	−9.17454	−	28.2363i	−0.647122	−	1.99164i
$202$	4.20000	−	12.9263i	0.295511	−	0.909489i
$203$	5.45726	+	3.96493i	0.383025	+	0.278284i
$204$	15.7783	+	11.4636i	1.10470	+	0.802611i
$205$	2.34537	−	7.21830i	0.163808	−	0.504148i
$206$	4.90072	+	15.0829i	0.341449	+	1.05087i
$207$	6.84443	−	4.97277i	0.475721	−	0.345632i
$208$	−3.05764			−0.212009
$209$	14.9218	+	4.47481i	1.03216	+	0.309529i
$210$	−2.80837			−0.193796
$211$	11.0600	−	8.03555i	0.761401	−	0.553190i	−0.137939	−	0.990441i	$-0.544048\pi$
$211$	11.0600	−	8.03555i	0.761401	−	0.553190i	0.899340	+	0.437251i	$0.144048\pi$
$212$	−0.525688	−	1.61790i	−0.0361044	−	0.111118i
$213$	1.99961	−	6.15417i	0.137011	−	0.421677i
$214$	3.55713	+	2.58440i	0.243160	+	0.176666i
$215$	−5.88634	−	4.27668i	−0.401445	−	0.291667i
$216$	−1.63756	+	5.03990i	−0.111422	+	0.342922i
$217$	1.03315	+	3.17970i	0.0701346	+	0.215852i
$218$	11.7252	−	8.51885i	0.794130	−	0.576969i
$219$	36.8213			2.48815
$220$	−0.0756411	−	3.31576i	−0.00509972	−	0.223549i
$221$	−21.2341			−1.42836
$222$	−16.6479	+	12.0954i	−1.11733	+	0.811791i
$223$	−1.61794	−	4.97951i	−0.108345	−	0.333453i	0.882156	−	0.470958i	$-0.156092\pi$
$223$	−1.61794	−	4.97951i	−0.108345	−	0.333453i	−0.990501	+	0.137505i	$0.956092\pi$
$224$	0.309017	−	0.951057i	0.0206471	−	0.0635451i
$225$	−3.95363	−	2.87248i	−0.263575	−	0.191499i
$226$	15.6404	+	11.3634i	1.04038	+	0.755882i
$227$	−6.96501	+	21.4361i	−0.462284	+	1.42276i	0.400082	+	0.916479i	$0.368981\pi$
$227$	−6.96501	+	21.4361i	−0.462284	+	1.42276i	−0.862366	+	0.506285i	$0.831019\pi$
$228$	4.07625	+	12.5454i	0.269956	+	0.830840i
$229$	−1.25276	+	0.910185i	−0.0827849	+	0.0601467i	−0.628408	−	0.777884i	$-0.716293\pi$
$229$	−1.25276	+	0.910185i	−0.0827849	+	0.0601467i	0.545623	+	0.838031i	$0.316293\pi$
$230$	−1.73118			−0.114151
$231$	5.30153	−	7.65834i	0.348815	−	0.503882i
$232$	−6.74554			−0.442867
$233$	5.33814	−	3.87839i	0.349713	−	0.254082i	−0.399035	−	0.916936i	$-0.630655\pi$
$233$	5.33814	−	3.87839i	0.349713	−	0.254082i	0.748749	+	0.662854i	$0.230655\pi$
$234$	−4.61750	−	14.2112i	−0.301856	−	0.929016i
$235$	1.23778	−	3.80951i	0.0807441	−	0.248505i
$236$	−6.18689	−	4.49504i	−0.402732	−	0.292602i
$237$	9.67492	+	7.02924i	0.628453	+	0.456598i
$238$	2.14600	−	6.60470i	0.139104	−	0.428119i
$239$	2.88271	+	8.87206i	0.186467	+	0.573886i	0.999971	−	0.00767368i	$-0.00244263\pi$
$239$	2.88271	+	8.87206i	0.186467	+	0.573886i	−0.813504	+	0.581560i	$0.802443\pi$
$240$	2.27202	−	1.65072i	0.146658	−	0.106553i
$241$	−4.69741			−0.302587			−0.151293	−	0.988489i	$-0.548344\pi$
$241$	−4.69741			−0.302587			−0.151293	+	0.988489i	$0.548344\pi$
$242$	9.18477	+	6.05310i	0.590419	+	0.389108i
$243$	15.2759			0.979949
$244$	−7.22492	+	5.24921i	−0.462528	+	0.336047i
$245$	0.309017	+	0.951057i	0.0197424	+	0.0607608i
$246$	−6.58667	+	20.2717i	−0.419950	+	1.29247i
$247$	−11.6190	−	8.44169i	−0.739299	−	0.537132i
$248$	−2.70482	−	1.96516i	−0.171756	−	0.124788i
$249$	−3.35047	+	10.3117i	−0.212327	+	0.653477i
$250$	0.309017	+	0.951057i	0.0195440	+	0.0601501i
$251$	−20.3133	+	14.7585i	−1.28216	+	0.931545i	−0.999616	−	0.0277087i	$-0.991179\pi$
$251$	−20.3133	+	14.7585i	−1.28216	+	0.931545i	−0.282546	+	0.959254i	$0.591179\pi$
$252$	4.88695			0.307849
$253$	3.26805	−	4.72087i	0.205461	−	0.296799i
$254$	21.5848			1.35435
$255$	15.7783	−	11.4636i	0.988073	−	0.717877i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	6.88090	−	21.1772i	0.429219	−	1.32100i	−0.469677	−	0.882838i	$-0.655630\pi$
$257$	6.88090	−	21.1772i	0.429219	−	1.32100i	0.898896	−	0.438162i	$-0.144370\pi$
$258$	16.5310	+	12.0105i	1.02918	+	0.747741i
$259$	5.92796	+	4.30691i	0.368345	+	0.267619i
$260$	−0.944863	+	2.90799i	−0.0585979	+	0.180346i
$261$	−10.1868	−	31.3517i	−0.630546	−	1.94062i
$262$	−4.23495	+	3.07687i	−0.261636	+	0.190090i
$263$	−12.5549			−0.774170			−0.387085	−	0.922044i	$-0.626518\pi$
$263$	−12.5549			−0.774170			−0.387085	+	0.922044i	$0.626518\pi$
$264$	0.212428	+	9.31189i	0.0130741	+	0.573107i
$265$	−1.70116			−0.104502
$266$	3.79998	−	2.76085i	0.232992	−	0.169279i
$267$	10.6866	+	32.8898i	0.654007	+	2.01283i
$268$	3.26685	−	10.0543i	0.199555	−	0.614167i
$269$	6.10388	+	4.43473i	0.372160	+	0.270390i	0.758106	−	0.652131i	$-0.226125\pi$
$269$	6.10388	+	4.43473i	0.372160	+	0.270390i	−0.385946	+	0.922521i	$0.626125\pi$
$270$	4.28719	+	3.11483i	0.260910	+	0.189562i
$271$	8.58535	−	26.4230i	0.521523	−	1.60508i	−0.249568	−	0.968357i	$-0.580289\pi$
$271$	8.58535	−	26.4230i	0.521523	−	1.60508i	0.771091	−	0.636725i	$-0.219711\pi$
$272$	2.14600	+	6.60470i	0.130120	+	0.400469i
$273$	−6.94703	+	5.04731i	−0.420453	+	0.305477i
$274$	5.00039			0.302085
$275$	−3.17685	−	0.952688i	−0.191571	−	0.0574492i
$276$	4.86179			0.292646
$277$	−15.2654	+	11.0910i	−0.917211	+	0.666393i	−0.942828	−	0.333279i	$-0.891845\pi$
$277$	−15.2654	+	11.0910i	−0.917211	+	0.666393i	0.0256169	+	0.999672i	$0.491845\pi$
$278$	−0.951845	−	2.92948i	−0.0570879	−	0.175698i
$279$	5.04894	−	15.5390i	0.302272	−	0.930298i
$280$	−0.809017	−	0.587785i	−0.0483480	−	0.0351269i
$281$	−5.55524	−	4.03612i	−0.331398	−	0.240774i	0.409626	−	0.912254i	$-0.365659\pi$
$281$	−5.55524	−	4.03612i	−0.331398	−	0.240774i	−0.741023	+	0.671479i	$0.765659\pi$
$282$	−3.47616	+	10.6985i	−0.207002	+	0.637087i
$283$	−7.75931	−	23.8807i	−0.461243	−	1.41956i	−0.863646	−	0.504098i	$-0.831825\pi$
$283$	−7.75931	−	23.8807i	−0.461243	−	1.41956i	0.402403	−	0.915463i	$-0.368175\pi$
$284$	1.86409	−	1.35434i	0.110613	−	0.0803652i
$285$	13.1910			0.781369
$286$	−6.14632	−	8.06620i	−0.363440	−	0.476965i
$287$	7.58977			0.448010
$288$	−3.95363	+	2.87248i	−0.232970	+	0.169262i
$289$	9.64979	+	29.6990i	0.567635	+	1.74700i
$290$	−2.08449	+	6.41539i	−0.122405	+	0.376725i
$291$	−15.7742	−	11.4606i	−0.924702	−	0.671835i
$292$	10.6072	+	7.70660i	0.620741	+	0.450995i
$293$	5.12814	−	15.7828i	0.299589	−	0.922041i	−0.682052	−	0.731304i	$-0.738912\pi$
$293$	5.12814	−	15.7828i	0.299589	−	0.922041i	0.981641	−	0.190737i	$-0.0610878\pi$
$294$	−0.867835	−	2.67092i	−0.0506131	−	0.155771i
$295$	−6.18689	+	4.49504i	−0.360215	+	0.261711i
$296$	−7.32736			−0.425894
$297$	−16.5872	+	5.81099i	−0.962489	+	0.337188i
$298$	−15.8858			−0.920237
$299$	−4.28239	+	3.11134i	−0.247657	+	0.179933i
$300$	−0.867835	−	2.67092i	−0.0501045	−	0.154206i
$301$	2.24838	−	6.91981i	0.129595	−	0.398851i
$302$	4.41655	+	3.20881i	0.254144	+	0.184646i
$303$	30.8801	+	22.4357i	1.77402	+	1.28890i
$304$	−1.45146	+	4.46715i	−0.0832472	+	0.256209i
$305$	2.75968	+	8.49341i	0.158019	+	0.486331i
$306$	−27.4563	+	19.9482i	−1.56957	+	1.14036i
$307$	−31.2886			−1.78573			−0.892867	−	0.450321i	$-0.851309\pi$
$307$	−31.2886			−1.78573			−0.892867	+	0.450321i	$0.851309\pi$
$308$	3.13010	−	1.09657i	0.178354	−	0.0624826i
$309$	−44.5381			−2.53368
$310$	−2.70482	+	1.96516i	−0.153623	+	0.111614i
$311$	−1.75895	−	5.41349i	−0.0997408	−	0.306971i	0.888719	−	0.458452i	$-0.151596\pi$
$311$	−1.75895	−	5.41349i	−0.0997408	−	0.306971i	−0.988460	+	0.151481i	$0.951596\pi$
$312$	2.65353	−	8.16672i	0.150226	−	0.462349i
$313$	−14.1028	−	10.2463i	−0.797137	−	0.579154i	0.112936	−	0.993602i	$-0.463974\pi$
$313$	−14.1028	−	10.2463i	−0.797137	−	0.579154i	−0.910073	+	0.414449i	$0.863974\pi$
$314$	−6.82867	−	4.96132i	−0.385364	−	0.279983i
$315$	1.51015	−	4.64777i	0.0850874	−	0.261872i
$316$	1.31588	+	4.04987i	0.0740242	+	0.227823i
$317$	−17.2094	+	12.5033i	−0.966575	+	0.702258i	−0.954668	−	0.297671i	$-0.903790\pi$
$317$	−17.2094	+	12.5033i	−0.966575	+	0.702258i	−0.0119067	+	0.999929i	$0.503790\pi$
$318$	4.77750			0.267909
$319$	−13.5596	−	17.7951i	−0.759190	−	0.996332i
$320$	1.00000			0.0559017
$321$	−9.98974	+	7.25797i	−0.557573	+	0.405100i
$322$	−0.534964	−	1.64645i	−0.0298124	−	0.0917530i
$323$	−10.0798	+	31.0225i	−0.560857	+	1.72614i
$324$	−0.179149	−	0.130159i	−0.00995271	−	0.00723106i
$325$	2.47368	+	1.79724i	0.137215	+	0.0996928i
$326$	3.01092	−	9.26667i	0.166760	−	0.513233i
$327$	12.5776	+	38.7100i	0.695545	+	2.14067i
$328$	−6.14025	+	4.46116i	−0.339039	+	0.246326i
$329$	4.00555			0.220833
$330$	8.92178	+	2.67550i	0.491128	+	0.147282i
$331$	0.712600			0.0391680			0.0195840	−	0.999808i	$-0.493766\pi$
$331$	0.712600			0.0391680			0.0195840	+	0.999808i	$0.493766\pi$
$332$	−3.12339	+	2.26928i	−0.171418	+	0.124543i
$333$	−11.0654	−	34.0558i	−0.606381	−	1.86625i
$334$	6.24463	−	19.2190i	0.341691	−	1.05162i
$335$	−8.55274	−	6.21393i	−0.467286	−	0.339503i
$336$	2.27202	+	1.65072i	0.123949	+	0.0900541i
$337$	8.88663	−	27.3502i	0.484086	−	1.48986i	−0.349215	−	0.937042i	$-0.613552\pi$
$337$	8.88663	−	27.3502i	0.484086	−	1.48986i	0.833301	−	0.552820i	$-0.186448\pi$
$338$	−1.12817	−	3.47214i	−0.0613642	−	0.188860i
$339$	−43.9240	+	31.9127i	−2.38562	+	1.73326i
$340$	6.94459			0.376623
$341$	−0.252894	−	11.0857i	−0.0136950	−	0.600325i
$342$	−22.9542			−1.24122
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$	2.24838	+	6.91981i	0.121225	+	0.373091i
$345$	1.50238	−	4.62384i	0.0808852	−	0.248939i
$346$	−0.860931	−	0.625503i	−0.0462840	−	0.0336273i
$347$	−27.9905	−	20.3363i	−1.50261	−	1.09171i	−0.969329	−	0.245767i	$-0.920960\pi$
$347$	−27.9905	−	20.3363i	−1.50261	−	1.09171i	−0.533278	−	0.845940i	$-0.679040\pi$
$348$	5.85402	−	18.0168i	0.313808	−	0.965802i
$349$	4.77719	+	14.7027i	0.255717	+	0.787017i	0.993688	+	0.112183i	$0.0357844\pi$
$349$	4.77719	+	14.7027i	0.255717	+	0.787017i	−0.737970	+	0.674833i	$0.764216\pi$
$350$	−0.809017	+	0.587785i	−0.0432438	+	0.0314184i
$351$	16.2032			0.864865
$352$	−1.88776	+	2.72697i	−0.100618	+	0.145348i
$353$	2.31479			0.123204			0.0616019	−	0.998101i	$-0.480379\pi$
$353$	2.31479			0.123204			0.0616019	+	0.998101i	$0.480379\pi$
$354$	17.3751	−	12.6237i	0.923475	−	0.670944i
$355$	−0.712018	−	2.19136i	−0.0377900	−	0.116306i
$356$	−3.80525	+	11.7114i	−0.201678	+	0.620701i
$357$	15.7783	+	11.4636i	0.835074	+	0.606717i
$358$	4.64197	+	3.37259i	0.245336	+	0.178247i
$359$	1.71863	−	5.28940i	0.0907059	−	0.279164i	−0.895405	−	0.445253i	$-0.853114\pi$
$359$	1.71863	−	5.28940i	0.0907059	−	0.279164i	0.986111	+	0.166089i	$0.0531138\pi$
$360$	1.51015	+	4.64777i	0.0795919	+	0.244959i
$361$	−2.47735	+	1.79990i	−0.130387	+	0.0947315i
$362$	3.77619			0.198472
$363$	−24.1382	+	19.2787i	−1.26693	+	1.01187i
$364$	−3.05764			−0.160264
$365$	10.6072	−	7.70660i	0.555208	−	0.403382i
$366$	−7.75019	−	23.8526i	−0.405109	−	1.24680i
$367$	8.06106	−	24.8094i	0.420784	−	1.29504i	−0.486190	−	0.873853i	$-0.661614\pi$
$367$	8.06106	−	24.8094i	0.420784	−	1.29504i	0.906974	−	0.421186i	$-0.138386\pi$
$368$	1.40055	+	1.01756i	0.0730089	+	0.0530440i
$369$	−30.0071	−	21.8015i	−1.56211	−	1.13494i
$370$	−2.26428	+	6.96873i	−0.117714	+	0.362287i
$371$	−0.525688	−	1.61790i	−0.0272924	−	0.0839973i
$372$	7.59613	−	5.51891i	0.393841	−	0.286142i
$373$	28.3183			1.46627			0.733134	−	0.680085i	$-0.238057\pi$
$373$	28.3183			1.46627			0.733134	+	0.680085i	$0.238057\pi$
$374$	−13.1097	+	18.9377i	−0.677888	+	0.979245i
$375$	−2.80837			−0.145024
$376$	−3.24056	+	2.35440i	−0.167119	+	0.121419i
$377$	6.37362	+	19.6160i	0.328258	+	1.01027i
$378$	−1.63756	+	5.03990i	−0.0842271	+	0.259224i
$379$	26.3455	+	19.1411i	1.35328	+	0.983213i	0.998841	+	0.0481322i	$0.0153269\pi$
$379$	26.3455	+	19.1411i	1.35328	+	0.983213i	0.354435	+	0.935081i	$0.384673\pi$
$380$	3.79998	+	2.76085i	0.194935	+	0.141629i
$381$	−18.7320	+	57.6512i	−0.959670	+	2.95356i
$382$	3.62470	+	11.1557i	0.185456	+	0.570774i
$383$	10.0272	−	7.28519i	0.512366	−	0.372256i	−0.301354	−	0.953512i	$-0.597439\pi$
$383$	10.0272	−	7.28519i	0.512366	−	0.372256i	0.813720	+	0.581257i	$0.197439\pi$
$384$	−2.80837			−0.143314
$385$	−0.0756411	−	3.31576i	−0.00385503	−	0.168987i
$386$	18.9879			0.966461
$387$	−28.7663	+	20.8999i	−1.46227	+	1.06240i
$388$	−2.14545	−	6.60301i	−0.108919	−	0.335217i
$389$	−6.14304	+	18.9063i	−0.311465	+	0.958590i	0.665721	+	0.746201i	$0.268124\pi$
$389$	−6.14304	+	18.9063i	−0.311465	+	0.958590i	−0.977185	+	0.212389i	$0.931876\pi$
$390$	−6.94703	−	5.04731i	−0.351776	−	0.255580i
$391$	9.72627	+	7.06655i	0.491879	+	0.357371i
$392$	0.309017	−	0.951057i	0.0156077	−	0.0480356i
$393$	−4.54284	−	13.9814i	−0.229156	−	0.705269i
$394$	2.64959	−	1.92504i	0.133485	−	0.0969822i
$395$	4.25829			0.214258
$396$	−15.5251	−	4.65574i	−0.780167	−	0.233960i
$397$	27.6288			1.38665			0.693325	−	0.720625i	$-0.256145\pi$
$397$	27.6288			1.38665			0.693325	+	0.720625i	$0.256145\pi$
$398$	−11.9280	+	8.66618i	−0.597896	+	0.434397i
$399$	4.07625	+	12.5454i	0.204068	+	0.628056i
$400$	0.309017	−	0.951057i	0.0154508	−	0.0475528i
$401$	−24.3969	−	17.7254i	−1.21832	−	0.885163i	−0.222363	−	0.974964i	$-0.571377\pi$
$401$	−24.3969	−	17.7254i	−1.21832	−	0.885163i	−0.995960	+	0.0898006i	$0.971377\pi$
$402$	24.0193	+	17.4510i	1.19797	+	0.870378i
$403$	−3.15900	+	9.72239i	−0.157361	+	0.484307i
$404$	4.20000	+	12.9263i	0.208958	+	0.643106i
$405$	−0.179149	+	0.130159i	−0.00890197	+	0.00646766i
$406$	−6.74554			−0.334776
$407$	−14.7291	−	19.3299i	−0.730094	−	0.958148i
$408$	−19.5030			−0.965542
$409$	−15.2701	+	11.0944i	−0.755057	+	0.548581i	−0.897390	−	0.441238i	$-0.854540\pi$
$409$	−15.2701	+	11.0944i	−0.755057	+	0.548581i	0.142333	+	0.989819i	$0.454540\pi$
$410$	2.34537	+	7.21830i	0.115829	+	0.356486i
$411$	−4.33951	+	13.3556i	−0.214052	+	0.658786i
$412$	−12.8302	−	9.32172i	−0.632101	−	0.459248i
$413$	−6.18689	−	4.49504i	−0.304437	−	0.221186i
$414$	−2.61434	+	8.04611i	−0.128488	+	0.395445i
$415$	1.19303	+	3.67177i	0.0585635	+	0.180240i
$416$	2.47368	−	1.79724i	0.121282	−	0.0881168i
$417$	8.65045			0.423614
$418$	−14.7022	+	5.15061i	−0.719109	+	0.251925i
$419$	8.51801			0.416132			0.208066	−	0.978115i	$-0.433283\pi$
$419$	8.51801			0.416132			0.208066	+	0.978115i	$0.433283\pi$
$420$	2.27202	−	1.65072i	0.110863	−	0.0805469i
$421$	−4.16347	−	12.8138i	−0.202915	−	0.624508i	−0.999793	−	0.0203674i	$-0.993516\pi$
$421$	−4.16347	−	12.8138i	−0.202915	−	0.624508i	0.796878	−	0.604141i	$-0.206484\pi$
$422$	−4.22454	+	13.0018i	−0.205647	+	0.632917i
$423$	−15.8365	−	11.5059i	−0.769995	−	0.559434i
$424$	1.37627	+	0.999919i	0.0668376	+	0.0485604i
$425$	2.14600	−	6.60470i	0.104096	−	0.320375i
$426$	1.99961	+	6.15417i	0.0968814	+	0.298170i
$427$	−7.22492	+	5.24921i	−0.349639	+	0.254027i
$428$	−4.39685			−0.212530
$429$	26.8782	−	9.41621i	1.29769	−	0.454619i
$430$	7.27592			0.350876
$431$	22.4992	−	16.3466i	1.08375	−	0.787389i	0.105415	−	0.994428i	$-0.466383\pi$
$431$	22.4992	−	16.3466i	1.08375	−	0.787389i	0.978333	+	0.207039i	$0.0663827\pi$
$432$	−1.63756	−	5.03990i	−0.0787872	−	0.242482i
$433$	−6.16730	+	18.9810i	−0.296382	+	0.912169i	0.686372	+	0.727250i	$0.259202\pi$
$433$	−6.16730	+	18.9810i	−0.296382	+	0.912169i	−0.982754	+	0.184918i	$0.940798\pi$
$434$	−2.70482	−	1.96516i	−0.129835	−	0.0943308i
$435$	−15.3260	−	11.1350i	−0.734826	−	0.533882i
$436$	−4.47862	+	13.7838i	−0.214487	+	0.660123i
$437$	2.51274	+	7.73343i	0.120201	+	0.369940i
$438$	−29.7890	+	21.6430i	−1.42338	+	1.03414i
$439$	−10.7367			−0.512436			−0.256218	−	0.966619i	$-0.582476\pi$
$439$	−10.7367			−0.512436			−0.256218	+	0.966619i	$0.582476\pi$
$440$	2.01015	+	2.63805i	0.0958302	+	0.125764i
$441$	4.88695			0.232712
$442$	17.1787	−	12.4811i	0.817109	−	0.593664i
$443$	−3.11449	−	9.58543i	−0.147974	−	0.455417i	0.849407	−	0.527738i	$-0.176960\pi$
$443$	−3.11449	−	9.58543i	−0.147974	−	0.455417i	−0.997381	+	0.0723203i	$0.976960\pi$
$444$	6.35893	−	19.5708i	0.301782	−	0.928788i
$445$	9.96227	+	7.23802i	0.472257	+	0.343115i
$446$	4.23583	+	3.07751i	0.200572	+	0.145724i
$447$	13.7862	−	42.4296i	0.652065	−	2.00685i
$448$	0.309017	+	0.951057i	0.0145997	+	0.0449332i
$449$	25.1666	−	18.2846i	1.18769	−	0.862904i	0.194668	−	0.980869i	$-0.437637\pi$
$449$	25.1666	−	18.2846i	1.18769	−	0.862904i	0.993018	+	0.117965i	$0.0376370\pi$
$450$	4.88695			0.230373
$451$	−24.1116	−	7.23068i	−1.13537	−	0.340480i
$452$	−19.3326			−0.909328
$453$	−12.4033	+	9.01154i	−0.582759	+	0.423399i
$454$	−6.96501	−	21.4361i	−0.326884	−	1.00605i
$455$	−0.944863	+	2.90799i	−0.0442959	+	0.136329i
$456$	−10.6718	−	7.75349i	−0.499751	−	0.363091i
$457$	−21.2012	−	15.4036i	−0.991752	−	0.720550i	−0.0314477	−	0.999505i	$-0.510012\pi$
$457$	−21.2012	−	15.4036i	−0.991752	−	0.720550i	−0.960304	+	0.278956i	$0.910012\pi$
$458$	0.478513	−	1.47271i	0.0223594	−	0.0688152i
$459$	−11.3722	−	35.0000i	−0.530809	−	1.63366i
$460$	1.40055	−	1.01756i	0.0653011	−	0.0474440i
$461$	−5.33572			−0.248509			−0.124255	−	0.992250i	$-0.539654\pi$
$461$	−5.33572			−0.248509			−0.124255	+	0.992250i	$0.539654\pi$
$462$	0.212428	+	9.31189i	0.00988307	+	0.433228i
$463$	28.8817			1.34224			0.671122	−	0.741347i	$-0.265813\pi$
$463$	28.8817			1.34224			0.671122	+	0.741347i	$0.265813\pi$
$464$	5.45726	−	3.96493i	0.253347	−	0.184067i
$465$	−2.90146	−	8.92978i	−0.134552	−	0.414109i
$466$	−2.03899	+	6.27536i	−0.0944544	+	0.290701i
$467$	30.4656	+	22.1345i	1.40978	+	1.02426i	0.993355	+	0.115094i	$0.0367169\pi$
$467$	30.4656	+	22.1345i	1.40978	+	1.02426i	0.416424	+	0.909170i	$0.363283\pi$
$468$	12.0888	+	8.78301i	0.558804	+	0.405995i
$469$	3.26685	−	10.0543i	0.150849	−	0.464267i
$470$	1.23778	+	3.80951i	0.0570947	+	0.175719i
$471$	19.1774	−	13.9332i	0.883649	−	0.642009i
$472$	7.64741			0.352001
$473$	−13.7352	+	19.8412i	−0.631545	+	0.912300i
$474$	−11.9589			−0.549288
$475$	3.79998	−	2.76085i	0.174355	−	0.126676i
$476$	2.14600	+	6.60470i	0.0983616	+	0.302726i
$477$	−2.56901	+	7.90661i	−0.117627	+	0.362019i
$478$	−7.54703	−	5.48324i	−0.345193	−	0.250797i
$479$	−20.6989	−	15.0386i	−0.945756	−	0.687132i	0.00404321	−	0.999992i	$-0.498713\pi$
$479$	−20.6989	−	15.0386i	−0.945756	−	0.687132i	−0.949799	+	0.312860i	$0.898713\pi$
$480$	−0.867835	+	2.67092i	−0.0396110	+	0.121910i
$481$	6.92335	+	21.3079i	0.315678	+	0.971556i
$482$	3.80028	−	2.76107i	0.173098	−	0.125763i
$483$	4.86179			0.221219
$484$	−10.9886	+	0.501616i	−0.499480	+	0.0228007i
$485$	−6.94282			−0.315257
$486$	−12.3585	+	8.97895i	−0.560591	+	0.407293i
$487$	6.24062	+	19.2066i	0.282789	+	0.870336i	0.987053	+	0.160397i	$0.0512774\pi$
$487$	6.24062	+	19.2066i	0.282789	+	0.870336i	−0.704263	+	0.709939i	$0.748723\pi$
$488$	2.75968	−	8.49341i	0.124925	−	0.384479i
$489$	22.1375	+	16.0839i	1.00109	+	0.727338i
$490$	−0.809017	−	0.587785i	−0.0365477	−	0.0265534i
$491$	5.62924	−	17.3250i	0.254044	−	0.781867i	−0.739972	−	0.672637i	$-0.765161\pi$
$491$	5.62924	−	17.3250i	0.254044	−	0.781867i	0.994017	−	0.109230i	$-0.0348385\pi$
$492$	−6.58667	−	20.2717i	−0.296950	−	0.913918i
$493$	37.8985	−	27.5348i	1.70686	−	1.24011i
$494$	14.3619			0.646171
$495$	−9.22540	+	13.3266i	−0.414651	+	0.598984i
$496$	3.34334			0.150120
$497$	1.86409	−	1.35434i	0.0836157	−	0.0607504i
$498$	−3.35047	−	10.3117i	−0.150138	−	0.462078i
$499$	−6.64037	+	20.4370i	−0.297264	+	0.914884i	0.685188	+	0.728367i	$0.259720\pi$
$499$	−6.64037	+	20.4370i	−0.297264	+	0.914884i	−0.982452	+	0.186518i	$0.940280\pi$
$500$	−0.809017	−	0.587785i	−0.0361803	−	0.0262866i
$501$	45.9131	+	33.3578i	2.05125	+	1.49032i
$502$	7.75898	−	23.8797i	0.346300	−	1.06580i
$503$	−1.72006	−	5.29380i	−0.0766937	−	0.236039i	0.905359	−	0.424648i	$-0.139602\pi$
$503$	−1.72006	−	5.29380i	−0.0766937	−	0.236039i	−0.982052	+	0.188609i	$0.939602\pi$
$504$	−3.95363	+	2.87248i	−0.176109	+	0.127950i
$505$	13.5915			0.604813
$506$	0.130948	+	5.74018i	0.00582136	+	0.255182i
$507$	10.2529			0.455346
$508$	−17.4624	+	12.6872i	−0.774771	+	0.562904i
$509$	−2.23172	−	6.86853i	−0.0989193	−	0.304442i	0.889336	−	0.457254i	$-0.151167\pi$
$509$	−2.23172	−	6.86853i	−0.0989193	−	0.304442i	−0.988255	+	0.152812i	$0.951167\pi$
$510$	−6.02676	+	18.5485i	−0.266869	+	0.821339i
$511$	10.6072	+	7.70660i	0.469236	+	0.340920i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	7.69169	−	23.6726i	0.339596	−	1.04517i
$514$	6.88090	+	21.1772i	0.303504	+	0.934088i
$515$	−12.8302	+	9.32172i	−0.565368	+	0.410764i
$516$	−20.4335			−0.899534
$517$	−12.7250	−	3.81604i	−0.559647	−	0.167829i
$518$	−7.32736			−0.321946
$519$	2.41782	−	1.75665i	0.106130	−	0.0771082i
$520$	−0.944863	−	2.90799i	−0.0414350	−	0.127524i
$521$	−2.05369	+	6.32062i	−0.0899740	+	0.276911i	−0.985911	−	0.167269i	$-0.946505\pi$
$521$	−2.05369	+	6.32062i	−0.0899740	+	0.276911i	0.895937	+	0.444181i	$0.146505\pi$
$522$	26.6694	+	19.3764i	1.16729	+	0.848083i
$523$	−20.0648	−	14.5779i	−0.877372	−	0.637448i	0.0551828	−	0.998476i	$-0.482426\pi$
$523$	−20.0648	−	14.5779i	−0.877372	−	0.637448i	−0.932555	+	0.361028i	$0.882426\pi$
$524$	1.61761	−	4.97848i	0.0706654	−	0.217486i
$525$	−0.867835	−	2.67092i	−0.0378754	−	0.116569i
$526$	10.1571	−	7.37960i	0.442873	−	0.321766i
$527$	23.2181			1.01140
$528$	−5.64525	−	7.40862i	−0.245678	−	0.322419i
$529$	−20.0030			−0.869697
$530$	1.37627	−	0.999919i	0.0597814	−	0.0434337i
$531$	11.5487	+	35.5434i	0.501173	+	1.54245i
$532$	−1.45146	+	4.46715i	−0.0629290	+	0.193675i
$533$	18.7747	+	13.6406i	0.813222	+	0.590841i
$534$	−27.9778	−	20.3270i	−1.21072	−	0.879637i
$535$	−1.35870	+	4.18165i	−0.0587418	+	0.180789i
$536$	3.26685	+	10.0543i	0.141107	+	0.434282i
$537$	−13.0364	+	9.47149i	−0.562562	+	0.408725i
$538$	−7.54481			−0.325280
$539$	3.13010	−	1.09657i	0.134823	−	0.0472324i
$540$	−5.29926			−0.228044
$541$	28.1879	−	20.4797i	1.21189	−	0.880490i	0.216490	−	0.976285i	$-0.430539\pi$
$541$	28.1879	−	20.4797i	1.21189	−	0.880490i	0.995401	+	0.0957945i	$0.0305392\pi$
$542$	8.58535	+	26.4230i	0.368772	+	1.13496i
$543$	−3.27710	+	10.0859i	−0.140634	+	0.432827i
$544$	−5.61829	−	4.08193i	−0.240882	−	0.175011i
$545$	11.7252	+	8.51885i	0.502252	+	0.364907i
$546$	2.65353	−	8.16672i	0.113560	−	0.349503i
$547$	6.96565	+	21.4381i	0.297830	+	0.916626i	0.982256	+	0.187544i	$0.0600527\pi$
$547$	6.96565	+	21.4381i	0.297830	+	0.916626i	−0.684426	+	0.729082i	$0.739947\pi$
$548$	−4.04540	+	2.93916i	−0.172811	+	0.125555i
$549$	43.6429			1.86263
$550$	3.13010	−	1.09657i	0.133468	−	0.0467577i
$551$	31.6841			1.34979
$552$	−3.93327	+	2.85769i	−0.167411	+	0.121631i
$553$	1.31588	+	4.04987i	0.0559571	+	0.172218i
$554$	5.83088	−	17.9456i	0.247730	−	0.762436i
$555$	−16.6479	−	12.0954i	−0.706664	−	0.513422i
$556$	2.49196	+	1.81052i	0.105683	+	0.0767830i
$557$	0.221345	−	0.681230i	0.00937869	−	0.0288646i	−0.946258	−	0.323414i	$-0.895169\pi$
$557$	0.221345	−	0.681230i	0.00937869	−	0.0288646i	0.955636	+	0.294549i	$0.0951694\pi$
$558$	5.04894	+	15.5390i	0.213739	+	0.657820i
$559$	17.9983	−	13.0766i	0.761248	−	0.553079i
$560$	1.00000			0.0422577
$561$	−39.2040	−	51.4498i	−1.65519	−	2.17221i
$562$	6.86665			0.289652
$563$	−36.0530	+	26.1941i	−1.51945	+	1.10395i	−0.557698	+	0.830044i	$0.688315\pi$
$563$	−36.0530	+	26.1941i	−1.51945	+	1.10395i	−0.961757	+	0.273904i	$0.911685\pi$
$564$	−3.47616	−	10.6985i	−0.146373	−	0.450488i
$565$	−5.97409	+	18.3864i	−0.251332	+	0.773520i
$566$	20.3141	+	14.7591i	0.853867	+	0.620371i
$567$	−0.179149	−	0.130159i	−0.00752354	−	0.00546617i
$568$	−0.712018	+	2.19136i	−0.0298756	+	0.0919476i
$569$	2.91551	+	8.97300i	0.122224	+	0.376168i	0.993385	−	0.114830i	$-0.0366323\pi$
$569$	2.91551	+	8.97300i	0.122224	+	0.376168i	−0.871161	+	0.490998i	$0.836632\pi$
$570$	−10.6718	+	7.75349i	−0.446991	+	0.324758i
$571$	31.2693			1.30858			0.654289	−	0.756244i	$-0.272968\pi$
$571$	31.2693			1.30858			0.654289	+	0.756244i	$0.272968\pi$
$572$	9.71368	+	2.91298i	0.406149	+	0.121798i
$573$	−32.9415			−1.37615
$574$	−6.14025	+	4.46116i	−0.256289	+	0.186205i
$575$	−0.534964	−	1.64645i	−0.0223095	−	0.0686617i
$576$	1.51015	−	4.64777i	0.0629230	−	0.193657i
$577$	−27.2994	−	19.8342i	−1.13649	−	0.825709i	−0.149864	−	0.988707i	$-0.547884\pi$
$577$	−27.2994	−	19.8342i	−1.13649	−	0.825709i	−0.986626	+	0.162998i	$0.947884\pi$
$578$	−25.2635	−	18.3550i	−1.05082	−	0.763467i
$579$	−16.4784	+	50.7153i	−0.684818	+	2.10765i
$580$	−2.08449	−	6.41539i	−0.0865536	−	0.266385i
$581$	−3.12339	+	2.26928i	−0.129580	+	0.0941455i
$582$	19.4980			0.808219
$583$	0.128678	+	5.64065i	0.00532930	+	0.233612i
$584$	−13.1113			−0.542548
$585$	12.0888	−	8.78301i	0.499809	−	0.363133i
$586$	5.12814	+	15.7828i	0.211842	+	0.651981i
$587$	8.10384	−	24.9411i	0.334481	−	1.02943i	−0.632496	−	0.774564i	$-0.717969\pi$
$587$	8.10384	−	24.9411i	0.334481	−	1.02943i	0.966977	−	0.254864i	$-0.0820307\pi$
$588$	2.27202	+	1.65072i	0.0936965	+	0.0680745i
$589$	12.7046	+	9.23045i	0.523485	+	0.380334i
$590$	2.36318	−	7.27312i	0.0972906	−	0.299430i
$591$	2.84222	+	8.74747i	0.116914	+	0.359823i
$592$	5.92796	−	4.30691i	0.243638	−	0.177013i
$593$	23.6431			0.970906			0.485453	−	0.874263i	$-0.338655\pi$
$593$	23.6431			0.970906			0.485453	+	0.874263i	$0.338655\pi$
$594$	10.0037	−	14.4509i	0.410458	−	0.592928i
$595$	6.94459			0.284701
$596$	12.8518	−	9.33741i	0.526432	−	0.382475i
$597$	−12.7952	−	39.3795i	−0.523672	−	1.61170i
$598$	1.63573	−	5.03425i	0.0668899	−	0.205866i
$599$	29.0921	+	21.1367i	1.18867	+	0.863621i	0.993123	−	0.117073i	$-0.0373510\pi$
$599$	29.0921	+	21.1367i	1.18867	+	0.863621i	0.195549	+	0.980694i	$0.437351\pi$
$600$	2.27202	+	1.65072i	0.0927548	+	0.0673903i
$601$	−9.70485	+	29.8685i	−0.395869	+	1.21836i	0.532413	+	0.846484i	$0.321285\pi$
$601$	−9.70485	+	29.8685i	−0.395869	+	1.21836i	−0.928283	+	0.371876i	$0.878715\pi$
$602$	2.24838	+	6.91981i	0.0916373	+	0.282030i
$603$	−41.7968	+	30.3672i	−1.70210	+	1.23665i
$604$	−5.45916			−0.222130
$605$	−2.91859	+	10.6057i	−0.118657	+	0.431185i
$606$	−38.1699			−1.55055
$607$	−29.0670	+	21.1184i	−1.17979	+	0.857169i	−0.992148	−	0.125068i	$-0.960085\pi$
$607$	−29.0670	+	21.1184i	−1.17979	+	0.857169i	−0.187644	+	0.982237i	$0.560085\pi$
$608$	−1.45146	−	4.46715i	−0.0588647	−	0.181167i
$609$	5.85402	−	18.0168i	0.237217	−	0.730078i
$610$	−7.22492	−	5.24921i	−0.292529	−	0.212534i
$611$	9.90847	+	7.19892i	0.400854	+	0.291237i
$612$	10.4874	−	32.2769i	0.423927	−	1.30471i
$613$	14.7119	+	45.2785i	0.594207	+	1.82878i	0.558636	+	0.829413i	$0.311325\pi$
$613$	14.7119	+	45.2785i	0.594207	+	1.82878i	0.0355702	+	0.999367i	$0.488675\pi$
$614$	25.3130	−	18.3910i	1.02155	−	0.742199i
$615$	−21.3149			−0.859500
$616$	−1.88776	+	2.72697i	−0.0760601	+	0.109873i
$617$	−5.44411			−0.219172			−0.109586	−	0.993977i	$-0.534952\pi$
$617$	−5.44411			−0.219172			−0.109586	+	0.993977i	$0.534952\pi$
$618$	36.0321	−	26.1788i	1.44942	−	1.05307i
$619$	7.62418	+	23.4648i	0.306441	+	0.943130i	0.979135	+	0.203209i	$0.0651371\pi$
$619$	7.62418	+	23.4648i	0.306441	+	0.943130i	−0.672694	+	0.739921i	$0.734863\pi$
$620$	1.03315	−	3.17970i	0.0414922	−	0.127700i
$621$	−7.42189	−	5.39232i	−0.297830	−	0.216386i
$622$	4.60499	+	3.34572i	0.184643	+	0.134151i
$623$	−3.80525	+	11.7114i	−0.152454	+	0.469206i
$624$	2.65353	+	8.16672i	0.106226	+	0.326930i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	17.4320			0.696723
$627$	−0.997785	−	43.7383i	−0.0398477	−	1.74674i
$628$	8.44070			0.336820
$629$	41.1672	−	29.9098i	1.64145	−	1.19258i
$630$	1.51015	+	4.64777i	0.0601659	+	0.185171i
$631$	−4.90582	+	15.0986i	−0.195298	+	0.601065i	0.804675	+	0.593715i	$0.202339\pi$
$631$	−4.90582	+	15.0986i	−0.195298	+	0.601065i	−0.999973	+	0.00734944i	$0.997661\pi$
$632$	−3.44503	−	2.50296i	−0.137036	−	0.0995624i
$633$	−31.0606	−	22.5668i	−1.23455	−	0.896950i
$634$	6.57340	−	20.2308i	0.261063	−	0.803469i
$635$	6.67006	+	20.5283i	0.264693	+	0.814642i
$636$	−3.86508	+	2.80814i	−0.153260	+	0.111350i
$637$	−3.05764			−0.121148
$638$	21.4296	+	6.42640i	0.848406	+	0.254424i
$639$	−11.2602			−0.445447
$640$	−0.809017	+	0.587785i	−0.0319792	+	0.0232343i
$641$	−1.04326	−	3.21082i	−0.0412062	−	0.126820i	0.928337	−	0.371739i	$-0.121238\pi$
$641$	−1.04326	−	3.21082i	−0.0412062	−	0.126820i	−0.969543	+	0.244920i	$0.921238\pi$
$642$	3.81574	−	11.7436i	0.150595	−	0.463485i
$643$	−16.7564	−	12.1742i	−0.660808	−	0.480105i	0.206128	−	0.978525i	$-0.433914\pi$
$643$	−16.7564	−	12.1742i	−0.660808	−	0.480105i	−0.866936	+	0.498420i	$0.833914\pi$
$644$	1.40055	+	1.01756i	0.0551895	+	0.0400975i
$645$	−6.31430	+	19.4334i	−0.248625	+	0.765190i
$646$	−10.0798	−	31.0225i	−0.396586	−	1.22057i
$647$	5.52423	−	4.01359i	0.217180	−	0.157791i	−0.473876	−	0.880591i	$-0.657146\pi$
$647$	5.52423	−	4.01359i	0.217180	−	0.157791i	0.691056	+	0.722801i	$0.257146\pi$
$648$	0.221440			0.00869898
$649$	15.3725	+	20.1742i	0.603422	+	0.791908i
$650$	−3.05764			−0.119931
$651$	7.59613	−	5.51891i	0.297716	−	0.216303i
$652$	3.01092	+	9.26667i	0.117917	+	0.362911i
$653$	9.55006	−	29.3921i	0.373723	−	1.15020i	−0.570614	−	0.821219i	$-0.693295\pi$
$653$	9.55006	−	29.3921i	0.373723	−	1.15020i	0.944336	−	0.328981i	$-0.106705\pi$
$654$	−32.9287	−	23.9241i	−1.28761	−	0.935506i
$655$	−4.23495	−	3.07687i	−0.165473	−	0.120223i
$656$	2.34537	−	7.21830i	0.0915712	−	0.281827i
$657$	−19.8000	−	60.9381i	−0.772471	−	2.37742i
$658$	−3.24056	+	2.35440i	−0.126330	+	0.0917842i
$659$	17.6185			0.686318			0.343159	−	0.939277i	$-0.388503\pi$
$659$	17.6185			0.686318			0.343159	+	0.939277i	$0.388503\pi$
$660$	−8.79049	+	3.07956i	−0.342169	+	0.119872i
$661$	11.7396			0.456617			0.228309	−	0.973589i	$-0.426680\pi$
$661$	11.7396			0.456617			0.228309	+	0.973589i	$0.426680\pi$
$662$	−0.576505	+	0.418856i	−0.0224065	+	0.0162793i
$663$	18.4277	+	56.7145i	0.715671	+	2.20261i
$664$	1.19303	−	3.67177i	0.0462985	−	0.142492i
$665$	3.79998	+	2.76085i	0.147357	+	0.107061i
$666$	28.9696	+	21.0477i	1.12255	+	0.815581i
$667$	3.60862	−	11.1062i	0.139726	−	0.430033i
$668$	6.24463	+	19.2190i	0.241612	+	0.743606i
$669$	−11.8958	+	8.64279i	−0.459917	+	0.334149i
$670$	10.5718			0.408423
$671$	27.9534	−	9.79288i	1.07913	−	0.378050i
$672$	−2.80837			−0.108335
$673$	−13.7542	+	9.99304i	−0.530187	+	0.385203i	−0.820428	−	0.571750i	$-0.806265\pi$
$673$	−13.7542	+	9.99304i	−0.530187	+	0.385203i	0.290241	+	0.956954i	$0.406265\pi$
$674$	8.88663	+	27.3502i	0.342300	+	1.05349i
$675$	−1.63756	+	5.03990i	−0.0630298	+	0.193986i
$676$	2.95358	+	2.14590i	0.113599	+	0.0825346i
$677$	3.11011	+	2.25963i	0.119531	+	0.0868446i	0.645945	−	0.763384i	$-0.276464\pi$
$677$	3.11011	+	2.25963i	0.119531	+	0.0868446i	−0.526413	+	0.850229i	$0.676464\pi$
$678$	16.7775	−	51.6358i	0.644335	−	1.98306i
$679$	−2.14545	−	6.60301i	−0.0823348	−	0.253400i
$680$	−5.61829	+	4.08193i	−0.215452	+	0.156535i
$681$	63.2986			2.42561
$682$	6.72061	+	8.81988i	0.257345	+	0.337731i
$683$	−2.04787			−0.0783595			−0.0391798	−	0.999232i	$-0.512474\pi$
$683$	−2.04787			−0.0783595			−0.0391798	+	0.999232i	$0.512474\pi$
$684$	18.5703	−	13.4921i	0.710055	−	0.515885i
$685$	1.54521	+	4.75566i	0.0590393	+	0.181704i
$686$	0.309017	−	0.951057i	0.0117983	−	0.0363115i
$687$	3.51822	+	2.55614i	0.134229	+	0.0975228i
$688$	−5.88634	−	4.27668i	−0.224415	−	0.163047i
$689$	1.60737	−	4.94697i	0.0612358	−	0.188464i
$690$	1.50238	+	4.62384i	0.0571945	+	0.176027i
$691$	19.4663	−	14.1431i	0.740532	−	0.538028i	−0.152346	−	0.988327i	$-0.548683\pi$
$691$	19.4663	−	14.1431i	0.740532	−	0.538028i	0.892878	+	0.450299i	$0.148683\pi$
$692$	1.06417			0.0404537
$693$	−15.5251	−	4.65574i	−0.589751	−	0.176857i
$694$	34.5981			1.31333
$695$	2.49196	−	1.81052i	0.0945255	−	0.0686768i
$696$	5.85402	+	18.0168i	0.221896	+	0.682925i
$697$	16.2876	−	50.1282i	0.616938	−	1.89874i
$698$	−12.5068	−	9.08676i	−0.473391	−	0.343939i
$699$	−14.9915	−	10.8920i	−0.567030	−	0.411972i
$700$	0.309017	−	0.951057i	0.0116797	−	0.0359466i
$701$	2.47128	+	7.60583i	0.0933391	+	0.287268i	0.986817	−	0.161838i	$-0.0517423\pi$
$701$	2.47128	+	7.60583i	0.0933391	+	0.287268i	−0.893478	+	0.449107i	$0.851742\pi$
$702$	−13.1087	+	9.52403i	−0.494756	+	0.359461i
$703$	34.4169			1.29806
$704$	−0.0756411	−	3.31576i	−0.00285083	−	0.124967i
$705$	−11.2491			−0.423665
$706$	−1.87270	+	1.36060i	−0.0704802	+	0.0512068i
$707$	4.20000	+	12.9263i	0.157957	+	0.486142i
$708$	−6.63669	+	20.4256i	−0.249422	+	0.767642i
$709$	−3.46290	−	2.51594i	−0.130052	−	0.0944882i	0.520858	−	0.853644i	$-0.325612\pi$
$709$	−3.46290	−	2.51594i	−0.130052	−	0.0944882i	−0.650909	+	0.759155i	$0.725612\pi$
$710$	1.86409	+	1.35434i	0.0699579	+	0.0508274i
$711$	6.43066	−	19.7915i	0.241169	−	0.742240i
$712$	−3.80525	−	11.7114i	−0.142608	−	0.438902i
$713$	4.68252	−	3.40205i	0.175362	−	0.127408i
$714$	−19.5030			−0.729881
$715$	5.77210	−	8.33809i	0.215864	−	0.311827i
$716$	−5.73780			−0.214432
$717$	21.1949	−	15.3990i	0.791537	−	0.575085i
$718$	1.71863	+	5.28940i	0.0641387	+	0.197399i
$719$	11.3732	−	35.0030i	0.424148	−	1.30539i	−0.479660	−	0.877454i	$-0.659240\pi$
$719$	11.3732	−	35.0030i	0.424148	−	1.30539i	0.903808	−	0.427939i	$-0.140760\pi$
$720$	−3.95363	−	2.87248i	−0.147343	−	0.107051i
$721$	−12.8302	−	9.32172i	−0.477823	−	0.347159i
$722$	0.946262	−	2.91230i	0.0352162	−	0.108384i
$723$	4.07657	+	12.5464i	0.151609	+	0.466606i
$724$	−3.05500	+	2.21959i	−0.113538	+	0.0824903i
$725$	−6.74554			−0.250523
$726$	8.19647	−	29.7849i	0.304200	−	1.10542i
$727$	−46.5408			−1.72610			−0.863051	−	0.505116i	$-0.831450\pi$
$727$	−46.5408			−1.72610			−0.863051	+	0.505116i	$0.831450\pi$
$728$	2.47368	−	1.79724i	0.0916808	−	0.0666100i
$729$	−13.4622	−	41.4325i	−0.498601	−	1.53454i
$730$	−4.05160	+	12.4695i	−0.149956	+	0.461519i
$731$	−40.8783	−	29.6998i	−1.51194	−	1.09849i
$732$	20.2903	+	14.7417i	0.749950	+	0.544871i
$733$	4.84102	−	14.8991i	0.178807	−	0.550312i	−0.820980	−	0.570958i	$-0.806572\pi$
$733$	4.84102	−	14.8991i	0.178807	−	0.550312i	0.999787	+	0.0206453i	$0.00657207\pi$
$734$	8.06106	+	24.8094i	0.297539	+	0.915731i
$735$	2.27202	−	1.65072i	0.0838047	−	0.0608877i
$736$	−1.73118			−0.0638121
$737$	−19.9570	+	28.8289i	−0.735124	+	1.06193i
$738$	37.0908			1.36533
$739$	−4.97549	+	3.61491i	−0.183026	+	0.132976i	−0.675526	−	0.737336i	$-0.736083\pi$
$739$	−4.97549	+	3.61491i	−0.183026	+	0.132976i	0.492499	+	0.870313i	$0.336083\pi$
$740$	−2.26428	−	6.96873i	−0.0832365	−	0.256176i
$741$	−12.4637	+	38.3594i	−0.457866	+	1.40917i
$742$	1.37627	+	0.999919i	0.0505245	+	0.0367082i
$743$	−22.0636	−	16.0302i	−0.809436	−	0.588090i	0.104231	−	0.994553i	$-0.466762\pi$
$743$	−22.0636	−	16.0302i	−0.809436	−	0.588090i	−0.913667	+	0.406464i	$0.866762\pi$
$744$	−2.90146	+	8.92978i	−0.106373	+	0.327382i
$745$	−4.90897	−	15.1083i	−0.179851	−	0.553524i
$746$	−22.9100	+	16.6451i	−0.838795	+	0.609420i
$747$	18.8672			0.690314
$748$	−0.525297	−	23.0266i	−0.0192068	−	0.841937i
$749$	−4.39685			−0.160657
$750$	2.27202	−	1.65072i	0.0829625	−	0.0602758i
$751$	2.45748	+	7.56335i	0.0896748	+	0.275991i	0.985829	−	0.167752i	$-0.0536506\pi$
$751$	2.45748	+	7.56335i	0.0896748	+	0.275991i	−0.896155	+	0.443742i	$0.853651\pi$
$752$	1.23778	−	3.80951i	0.0451373	−	0.138918i
$753$	57.0472	+	41.4472i	2.07892	+	1.51042i
$754$	−16.6863	−	12.1233i	−0.607681	−	0.441506i
$755$	−1.68697	+	5.19197i	−0.0613952	+	0.188955i
$756$	−1.63756	−	5.03990i	−0.0595575	−	0.183299i
$757$	−20.0935	+	14.5988i	−0.730310	+	0.530601i	−0.889662	−	0.456621i	$-0.849060\pi$
$757$	−20.0935	+	14.5988i	−0.730310	+	0.530601i	0.159351	+	0.987222i	$0.449060\pi$
$758$	−32.5648			−1.18281
$759$	−15.4452	−	4.63177i	−0.560625	−	0.168123i
$760$	−4.69704			−0.170379
$761$	−27.5610	+	20.0242i	−0.999086	+	0.725878i	−0.961892	−	0.273430i	$-0.911842\pi$
$761$	−27.5610	+	20.0242i	−0.999086	+	0.725878i	−0.0371939	+	0.999308i	$0.511842\pi$
$762$	−18.7320	−	57.6512i	−0.678589	−	2.08848i
$763$	−4.47862	+	13.7838i	−0.162137	+	0.499006i
$764$	−9.48958	−	6.89458i	−0.343321	−	0.249437i
$765$	−27.4563	−	19.9482i	−0.992686	−	0.721228i
$766$	−3.83005	+	11.7877i	−0.138385	+	0.425906i
$767$	−7.22576	−	22.2386i	−0.260907	−	0.802990i
$768$	2.27202	−	1.65072i	0.0819845	−	0.0595652i
$769$	10.7430			0.387404			0.193702	−	0.981060i	$-0.437950\pi$
$769$	10.7430			0.387404			0.193702	+	0.981060i	$0.437950\pi$
$770$	2.01015	+	2.63805i	0.0724408	+	0.0950686i
$771$	−62.5342			−2.25211
$772$	−15.3616	+	11.1608i	−0.552875	+	0.401687i
$773$	−10.9550	−	33.7160i	−0.394024	−	1.21268i	−0.929719	−	0.368270i	$-0.879950\pi$
$773$	−10.9550	−	33.7160i	−0.394024	−	1.21268i	0.535695	−	0.844412i	$-0.320050\pi$
$774$	10.9877	−	33.8168i	0.394946	−	1.21552i
$775$	−2.70482	−	1.96516i	−0.0971598	−	0.0705907i
$776$	5.61686	+	4.08089i	0.201633	+	0.146495i
$777$	6.35893	−	19.5708i	0.228125	−	0.702098i
$778$	−6.14304	−	18.9063i	−0.220239	−	0.677825i
$779$	28.8410	−	20.9542i	1.03334	−	0.750763i
$780$	8.58700			0.307464
$781$	−7.21219	+	2.52664i	−0.258072	+	0.0904102i
$782$	−12.0223			−0.429918
$783$	−28.9194	+	21.0112i	−1.03350	+	0.750879i
$784$	0.309017	+	0.951057i	0.0110363	+	0.0339663i
$785$	2.60832	−	8.02758i	0.0930949	−	0.286517i
$786$	11.8933	+	8.64099i	0.424220	+	0.308214i
$787$	18.5385	+	13.4690i	0.660825	+	0.480118i	0.866942	−	0.498410i	$-0.166082\pi$
$787$	18.5385	+	13.4690i	0.660825	+	0.480118i	−0.206116	+	0.978528i	$0.566082\pi$
$788$	−1.01205	+	3.11478i	−0.0360529	+	0.110960i
$789$	10.8956	+	33.5332i	0.387894	+	1.19381i
$790$	−3.44503	+	2.50296i	−0.122569	+	0.0890513i
$791$	−19.3326			−0.687387
$792$	15.2967	−	5.35886i	0.543543	−	0.190419i
$793$	−27.3063			−0.969674
$794$	−22.3522	+	16.2398i	−0.793249	+	0.576329i
$795$	1.47633	+	4.54367i	0.0523600	+	0.161147i
$796$	4.55608	−	14.0222i	0.161486	−	0.497003i
$797$	34.7194	+	25.2251i	1.22983	+	0.893521i	0.996877	−	0.0789684i	$-0.0251626\pi$
$797$	34.7194	+	25.2251i	1.22983	+	0.893521i	0.232949	+	0.972489i	$0.425163\pi$
$798$	−10.6718	−	7.75349i	−0.377776	−	0.274471i
$799$	8.59590	−	26.4555i	0.304101	−	0.935927i
$800$	0.309017	+	0.951057i	0.0109254	+	0.0336249i
$801$	48.6852	−	35.3718i	1.72021	−	1.24980i
$802$	30.1562			1.06485
$803$	−26.3556	−	34.5881i	−0.930069	−	1.22059i
$804$	−29.6894			−1.04707
$805$	1.40055	−	1.01756i	0.0493630	−	0.0358643i
$806$	−3.15900	−	9.72239i	−0.111271	−	0.342456i
$807$	6.54764	−	20.1516i	0.230488	−	0.709369i
$808$	−10.9957	−	7.98888i	−0.386829	−	0.281048i
$809$	−13.7512	−	9.99084i	−0.483467	−	0.351259i	0.319200	−	0.947688i	$-0.396586\pi$
$809$	−13.7512	−	9.99084i	−0.483467	−	0.351259i	−0.802666	+	0.596428i	$0.796586\pi$
$810$	0.0684287	−	0.210602i	0.00240434	−	0.00739980i
$811$	−3.30211	−	10.1629i	−0.115953	−	0.356866i	0.876192	−	0.481963i	$-0.160076\pi$
$811$	−3.30211	−	10.1629i	−0.115953	−	0.356866i	−0.992145	+	0.125097i	$0.960076\pi$
$812$	5.45726	−	3.96493i	0.191512	−	0.139142i
$813$	−78.0243			−2.73643
$814$	23.2779	+	6.98068i	0.815891	+	0.244673i
$815$	9.74355			0.341302
$816$	15.7783	−	11.4636i	0.552350	−	0.401305i
$817$	−10.5607	−	32.5026i	−0.369474	−	1.13712i
$818$	5.83265	−	17.9511i	0.203934	−	0.627644i
$819$	12.0888	+	8.78301i	0.422416	+	0.306903i
$820$	−6.14025	−	4.46116i	−0.214427	−	0.155790i
$821$	−6.28105	+	19.3311i	−0.219210	+	0.674660i	0.779618	+	0.626256i	$0.215413\pi$
$821$	−6.28105	+	19.3311i	−0.219210	+	0.674660i	−0.998828	+	0.0484038i	$0.984587\pi$
$822$	−4.33951	−	13.3556i	−0.151358	−	0.465832i
$823$	24.1536	−	17.5486i	0.841941	−	0.611706i	−0.0809713	−	0.996716i	$-0.525802\pi$
$823$	24.1536	−	17.5486i	0.841941	−	0.611706i	0.922912	+	0.385011i	$0.125802\pi$
$824$	15.8591			0.552476
$825$	0.212428	+	9.31189i	0.00739581	+	0.324198i
$826$	7.64741			0.266088
$827$	3.66922	−	2.66585i	0.127591	−	0.0927006i	−0.522159	−	0.852848i	$-0.674873\pi$
$827$	3.66922	−	2.66585i	0.127591	−	0.0927006i	0.649751	+	0.760147i	$0.274873\pi$
$828$	−2.61434	−	8.04611i	−0.0908546	−	0.279622i
$829$	−8.96845	+	27.6021i	−0.311487	+	0.958659i	0.665689	+	0.746229i	$0.268138\pi$
$829$	−8.96845	+	27.6021i	−0.311487	+	0.958659i	−0.977176	+	0.212430i	$0.931862\pi$
$830$	−3.12339	−	2.26928i	−0.108415	−	0.0787678i
$831$	42.8710	+	31.1476i	1.48718	+	1.08050i
$832$	−0.944863	+	2.90799i	−0.0327572	+	0.100816i
$833$	2.14600	+	6.60470i	0.0743544	+	0.228839i
$834$	−6.99836	+	5.08461i	−0.242333	+	0.176065i
$835$	20.2081			0.699329
$836$	8.86689	−	12.8087i	0.306668	−	0.442997i
$837$	−17.7172			−0.612396
$838$	−6.89122	+	5.00676i	−0.238053	+	0.172956i
$839$	−1.19213	−	3.66898i	−0.0411567	−	0.126667i	0.928367	−	0.371665i	$-0.121213\pi$
$839$	−1.19213	−	3.66898i	−0.0411567	−	0.126667i	−0.969524	+	0.244997i	$0.921213\pi$
$840$	−0.867835	+	2.67092i	−0.0299431	+	0.0921555i
$841$	−13.3507	−	9.69985i	−0.460369	−	0.334477i
$842$	10.9001	+	7.91939i	0.375642	+	0.272920i
$843$	−5.95912	+	18.3403i	−0.205243	+	0.631673i
$844$	−4.22454	−	13.0018i	−0.145415	−	0.447540i
$845$	2.95358	−	2.14590i	0.101606	−	0.0738212i
$846$	19.5749			0.673000
$847$	−10.9886	+	0.501616i	−0.377571	+	0.0172357i
$848$	−1.70116			−0.0584182
$849$	−57.0497	+	41.4490i	−1.95794	+	1.42253i
$850$	2.14600	+	6.60470i	0.0736071	+	0.226539i
$851$	3.91987	−	12.0641i	0.134371	−	0.413553i
$852$	−5.23505	−	3.80348i	−0.179350	−	0.130305i
$853$	12.0187	+	8.73212i	0.411513	+	0.298982i	0.774214	−	0.632924i	$-0.218145\pi$
$853$	12.0187	+	8.73212i	0.411513	+	0.298982i	−0.362701	+	0.931906i	$0.618145\pi$
$854$	2.75968	−	8.49341i	0.0944342	−	0.290638i
$855$	−7.09324	−	21.8307i	−0.242584	−	0.746596i
$856$	3.55713	−	2.58440i	0.121580	−	0.0883331i
$857$	−21.4567			−0.732948			−0.366474	−	0.930428i	$-0.619435\pi$
$857$	−21.4567			−0.732948			−0.366474	+	0.930428i	$0.619435\pi$
$858$	−16.2102	+	23.4165i	−0.553407	+	0.799425i
$859$	−50.7945			−1.73309			−0.866543	−	0.499103i	$-0.833663\pi$
$859$	−50.7945			−1.73309			−0.866543	+	0.499103i	$0.833663\pi$
$860$	−5.88634	+	4.27668i	−0.200723	+	0.145834i
$861$	−6.58667	−	20.2717i	−0.224473	−	0.690857i
$862$	−8.59393	+	26.4494i	−0.292710	+	0.900870i
$863$	11.0149	+	8.00280i	0.374952	+	0.272418i	0.759261	−	0.650786i	$-0.225560\pi$
$863$	11.0149	+	8.00280i	0.374952	+	0.272418i	−0.384310	+	0.923204i	$0.625560\pi$
$864$	4.28719	+	3.11483i	0.145853	+	0.105969i
$865$	0.328847	−	1.01209i	0.0111811	−	0.0344119i
$866$	−6.16730	−	18.9810i	−0.209573	−	0.645001i
$867$	70.9492	−	51.5476i	2.40956	−	1.75065i
$868$	3.34334			0.113480
$869$	−0.322102	−	14.1195i	−0.0109266	−	0.478970i
$870$	18.9440			0.642262
$871$	26.1512	−	19.0000i	0.886100	−	0.643789i
$872$	−4.47862	−	13.7838i	−0.151665	−	0.466778i
$873$	−10.4847	+	32.2686i	−0.354854	+	1.09213i
$874$	−6.57845	−	4.77952i	−0.222519	−	0.161670i
$875$	−0.809017	−	0.587785i	−0.0273498	−	0.0198708i
$876$	11.3784	−	35.0191i	0.384441	−	1.18319i
$877$	2.75130	+	8.46764i	0.0929049	+	0.285932i	0.986702	−	0.162540i	$-0.0519685\pi$
$877$	2.75130	+	8.46764i	0.0929049	+	0.285932i	−0.893797	+	0.448472i	$0.851969\pi$
$878$	8.68619	−	6.31089i	0.293145	−	0.212982i
$879$	−46.6050			−1.57195
$880$	−3.17685	−	0.952688i	−0.107092	−	0.0321151i
$881$	−2.11899			−0.0713904			−0.0356952	−	0.999363i	$-0.511365\pi$
$881$	−2.11899			−0.0713904			−0.0356952	+	0.999363i	$0.511365\pi$
$882$	−3.95363	+	2.87248i	−0.133126	+	0.0967214i
$883$	−3.17754	−	9.77945i	−0.106933	−	0.329105i	0.883247	−	0.468909i	$-0.155353\pi$
$883$	−3.17754	−	9.77945i	−0.106933	−	0.329105i	−0.990179	+	0.139804i	$0.955353\pi$
$884$	−6.56169	+	20.1948i	−0.220694	+	0.679225i
$885$	17.3751	+	12.6237i	0.584057	+	0.424342i
$886$	8.15385	+	5.92412i	0.273934	+	0.199025i
$887$	−1.74159	+	5.36006i	−0.0584768	+	0.179973i	−0.976028	−	0.217644i	$-0.930163\pi$
$887$	−1.74159	+	5.36006i	−0.0584768	+	0.179973i	0.917551	+	0.397617i	$0.130163\pi$
$888$	6.35893	+	19.5708i	0.213392	+	0.656753i
$889$	−17.4624	+	12.6872i	−0.585672	+	0.425515i
$890$	−12.3140			−0.412768
$891$	0.445128	+	0.584169i	0.0149123	+	0.0195704i
$892$	−5.23577			−0.175307
$893$	15.2210	−	11.0587i	0.509352	−	0.370066i
$894$	13.7862	+	42.4296i	0.461080	+	1.41906i
$895$	−1.77308	+	5.45697i	−0.0592674	+	0.182406i
$896$	−0.809017	−	0.587785i	−0.0270274	−	0.0196365i
$897$	12.0265	+	8.73779i	0.401555	+	0.291746i
$898$	−9.61279	+	29.5851i	−0.320783	+	0.987269i
$899$	−6.96914	−	21.4488i	−0.232434	−	0.715358i
$900$	−3.95363	+	2.87248i	−0.131788	+	0.0957493i
$901$	−11.8139			−0.393578
$902$	23.7568	−	8.32268i	0.791014	−	0.277115i
$903$	−20.4335			−0.679984
$904$	15.6404	−	11.3634i	0.520191	−	0.377941i
$905$	1.16691	+	3.59137i	0.0387892	+	0.119381i
$906$	4.73765	−	14.5810i	0.157398	−	0.484421i
$907$	31.6080	+	22.9646i	1.04953	+	0.762526i	0.972122	−	0.234474i	$-0.0753367\pi$
$907$	31.6080	+	22.9646i	1.04953	+	0.762526i	0.0774046	+	0.997000i	$0.475337\pi$
$908$	18.2346	+	13.2482i	0.605138	+	0.439658i
$909$	20.5252	−	63.1701i	0.680778	−	2.09522i
$910$	−0.944863	−	2.90799i	−0.0313219	−	0.0963989i
$911$	−18.4944	+	13.4370i	−0.612748	+	0.445187i	−0.850381	−	0.526168i	$-0.823628\pi$
$911$	−18.4944	+	13.4370i	−0.612748	+	0.445187i	0.237633	+	0.971355i	$0.423628\pi$
$912$	13.1910			0.436799
$913$	12.0845	−	4.23354i	0.399938	−	0.140110i
$914$	26.2062			0.866823
$915$	20.2903	−	14.7417i	0.670776	−	0.487347i
$916$	0.478513	+	1.47271i	0.0158105	+	0.0486597i
$917$	1.61761	−	4.97848i	0.0534180	−	0.164404i
$918$	29.7728	+	21.6312i	0.982649	+	0.713936i
$919$	10.5443	+	7.66090i	0.347825	+	0.252710i	0.747956	−	0.663748i	$-0.231035\pi$
$919$	10.5443	+	7.66090i	0.347825	+	0.252710i	−0.400131	+	0.916458i	$0.631035\pi$
$920$	−0.534964	+	1.64645i	−0.0176372	+	0.0542818i
$921$	27.1533	+	83.5693i	0.894732	+	2.75370i
$922$	4.31669	−	3.13626i	0.142163	−	0.103287i
$923$	7.04523			0.231896
$924$	−5.64525	−	7.40862i	−0.185715	−	0.243726i
$925$	−7.32736			−0.240922
$926$	−23.3658	+	16.9762i	−0.767846	+	0.557873i
$927$	23.9496	+	73.7092i	0.786607	+	2.42093i
$928$	−2.08449	+	6.41539i	−0.0684267	+	0.210596i
$929$	−22.1643	−	16.1033i	−0.727188	−	0.528333i	0.161485	−	0.986875i	$-0.448372\pi$
$929$	−22.1643	−	16.1033i	−0.727188	−	0.528333i	−0.888673	+	0.458542i	$0.848372\pi$
$930$	7.59613	+	5.51891i	0.249087	+	0.180972i
$931$	−1.45146	+	4.46715i	−0.0475698	+	0.146405i
$932$	−2.03899	−	6.27536i	−0.0667893	−	0.205556i
$933$	−12.9325	+	9.39602i	−0.423392	+	0.307612i
$934$	−37.6575			−1.23219
$935$	−22.0619	−	6.61603i	−0.721503	−	0.216367i
$936$	−14.9425			−0.488412
$937$	−17.9216	+	13.0208i	−0.585472	+	0.425371i	−0.840693	−	0.541512i	$-0.817852\pi$
$937$	−17.9216	+	13.0208i	−0.585472	+	0.425371i	0.255220	+	0.966883i	$0.417852\pi$
$938$	3.26685	+	10.0543i	0.106667	+	0.328286i
$939$	−15.1281	+	46.5595i	−0.493687	+	1.51941i
$940$	−3.24056	−	2.35440i	−0.105695	−	0.0767922i
$941$	9.72455	+	7.06530i	0.317011	+	0.230322i	0.734899	−	0.678176i	$-0.237229\pi$
$941$	9.72455	+	7.06530i	0.317011	+	0.230322i	−0.417888	+	0.908499i	$0.637229\pi$
$942$	−7.32513	+	22.5444i	−0.238666	+	0.734537i
$943$	−4.06025	−	12.4962i	−0.132220	−	0.406931i
$944$	−6.18689	+	4.49504i	−0.201366	+	0.146301i
$945$	−5.29926			−0.172385
$946$	−0.550359	−	24.1252i	−0.0178937	−	0.784379i
$947$	−29.5380			−0.959857			−0.479929	−	0.877307i	$-0.659337\pi$
$947$	−29.5380			−0.959857			−0.479929	+	0.877307i	$0.659337\pi$
$948$	9.67492	−	7.02924i	0.314227	−	0.228299i
$949$	12.3883	+	38.1274i	0.402143	+	1.23767i
$950$	−1.45146	+	4.46715i	−0.0470917	+	0.144933i
$951$	48.3303	+	35.1140i	1.56722	+	1.13865i
$952$	−5.61829	−	4.08193i	−0.182090	−	0.132296i
$953$	11.8349	−	36.4241i	0.383370	−	1.17989i	−0.554286	−	0.832326i	$-0.687009\pi$
$953$	11.8349	−	36.4241i	0.383370	−	1.17989i	0.937656	−	0.347565i	$-0.112991\pi$
$954$	−2.56901	−	7.90661i	−0.0831749	−	0.255986i
$955$	−9.48958	+	6.89458i	−0.307076	+	0.223104i
$956$	9.32864			0.301710
$957$	−35.7617	+	51.6597i	−1.15601	+	1.66992i
$958$	25.5852			0.826621
$959$	−4.04540	+	2.93916i	−0.130633	+	0.0949103i
$960$	−0.867835	−	2.67092i	−0.0280092	−	0.0862036i
$961$	−6.12537	+	18.8519i	−0.197593	+	0.608127i
$962$	−18.1256	−	13.1690i	−0.584392	−	0.424586i
$963$	17.3835	+	12.6299i	0.560176	+	0.406992i
$964$	−1.45158	+	4.46750i	−0.0467522	+	0.143888i
$965$	5.86760	+	18.0586i	0.188885	+	0.581327i
$966$	−3.93327	+	2.85769i	−0.126551	+	0.0919447i
$967$	2.04155			0.0656517			0.0328259	−	0.999461i	$-0.489549\pi$
$967$	2.04155			0.0656517			0.0328259	+	0.999461i	$0.489549\pi$
$968$	8.59509	−	6.86473i	0.276257	−	0.220641i
$969$	91.6063			2.94282
$970$	5.61686	−	4.08089i	0.180346	−	0.131029i
$971$	−1.55526	−	4.78660i	−0.0499107	−	0.153609i	0.922995	−	0.384812i	$-0.125734\pi$
$971$	−1.55526	−	4.78660i	−0.0499107	−	0.153609i	−0.972906	+	0.231203i	$0.925734\pi$
$972$	4.72051	−	14.5282i	0.151410	−	0.465994i
$973$	2.49196	+	1.81052i	0.0798887	+	0.0580425i
$974$	−16.3381	−	11.8704i	−0.523508	−	0.380351i
$975$	2.65353	−	8.16672i	0.0849809	−	0.261544i
$976$	2.75968	+	8.49341i	0.0883351	+	0.271867i
$977$	8.19175	−	5.95166i	0.262077	−	0.190410i	−0.448985	−	0.893539i	$-0.648214\pi$
$977$	8.19175	−	5.95166i	0.262077	−	0.190410i	0.711062	+	0.703129i	$0.248214\pi$
$978$	−27.3635			−0.874989
$979$	23.2460	−	33.5800i	0.742945	−	1.07322i
$980$	1.00000			0.0319438
$981$	57.3004	−	41.6312i	1.82946	−	1.32918i
$982$	5.62924	+	17.3250i	0.179636	+	0.552864i
$983$	10.4487	−	32.1577i	0.333261	−	1.02567i	−0.634311	−	0.773078i	$-0.718716\pi$
$983$	10.4487	−	32.1577i	0.333261	−	1.02567i	0.967572	−	0.252594i	$-0.0812838\pi$
$984$	17.2441	+	12.5286i	0.549722	+	0.399397i
$985$	2.64959	+	1.92504i	0.0844230	+	0.0613369i
$986$	−14.4759	+	44.5523i	−0.461007	+	1.41883i
$987$	−3.47616	−	10.6985i	−0.110647	−	0.340537i
$988$	−11.6190	+	8.44169i	−0.369649	+	0.268566i
$989$	−12.5959			−0.400527
$990$	−0.369655	−	16.2040i	−0.0117484	−	0.514996i
$991$	13.8867			0.441127			0.220563	−	0.975373i	$-0.429210\pi$
$991$	13.8867			0.441127			0.220563	+	0.975373i	$0.429210\pi$
$992$	−2.70482	+	1.96516i	−0.0858780	+	0.0623940i
$993$	−0.618419	−	1.90330i	−0.0196249	−	0.0603993i
$994$	−0.712018	+	2.19136i	−0.0225838	+	0.0695059i
$995$	−11.9280	−	8.66618i	−0.378142	−	0.274736i
$996$	8.77165	+	6.37297i	0.277940	+	0.201935i
$997$	1.76876	−	5.44367i	0.0560171	−	0.172403i	−0.919133	−	0.393946i	$-0.871110\pi$
$997$	1.76876	−	5.44367i	0.0560171	−	0.172403i	0.975150	+	0.221544i	$0.0711095\pi$
$998$	−6.64037	−	20.4370i	−0.210197	−	0.646921i
$999$	−31.4138	+	22.8235i	−0.993888	+	0.722102i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.n.i.421.1	✓	12
11.2	odd	10		8470.2.a.cy.1.1		6
11.4	even	5	inner	770.2.n.i.631.1	yes	12
11.9	even	5		8470.2.a.de.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.i.421.1	✓	12	1.1	even	1	trivial
770.2.n.i.631.1	yes	12	11.4	even	5	inner
8470.2.a.cy.1.1		6	11.2	odd	10
8470.2.a.de.1.1		6	11.9	even	5

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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.867835 - 2.67092i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(2.27202 + 1.65072i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-3.95363 + 2.87248i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.867835 - 2.67092i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(2.27202 + 1.65072i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-3.95363 + 2.87248i) q^{9} +1.00000 q^{10} +(-1.88776 + 2.72697i) q^{11} -2.80837 q^{12} +(2.47368 - 1.79724i) q^{13} +(0.309017 + 0.951057i) q^{14} +(-0.867835 + 2.67092i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-5.61829 - 4.08193i) q^{17} +(1.51015 - 4.64777i) q^{18} +(-1.45146 - 4.46715i) q^{19} +(-0.809017 + 0.587785i) q^{20} -2.80837 q^{21} +(-0.0756411 - 3.31576i) q^{22} -1.73118 q^{23} +(2.27202 - 1.65072i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-0.944863 + 2.90799i) q^{26} +(4.28719 + 3.11483i) q^{27} +(-0.809017 - 0.587785i) q^{28} +(-2.08449 + 6.41539i) q^{29} +(-0.867835 - 2.67092i) q^{30} +(-2.70482 + 1.96516i) q^{31} +1.00000 q^{32} +(8.92178 + 2.67550i) q^{33} +6.94459 q^{34} +(-0.809017 + 0.587785i) q^{35} +(1.51015 + 4.64777i) q^{36} +(-2.26428 + 6.96873i) q^{37} +(3.79998 + 2.76085i) q^{38} +(-6.94703 - 5.04731i) q^{39} +(0.309017 - 0.951057i) q^{40} +(2.34537 + 7.21830i) q^{41} +(2.27202 - 1.65072i) q^{42} +7.27592 q^{43} +(2.01015 + 2.63805i) q^{44} +4.88695 q^{45} +(1.40055 - 1.01756i) q^{46} +(1.23778 + 3.80951i) q^{47} +(-0.867835 + 2.67092i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-0.809017 - 0.587785i) q^{50} +(-6.02676 + 18.5485i) q^{51} +(-0.944863 - 2.90799i) q^{52} +(1.37627 - 0.999919i) q^{53} -5.29926 q^{54} +(3.13010 - 1.09657i) q^{55} +1.00000 q^{56} +(-10.6718 + 7.75349i) q^{57} +(-2.08449 - 6.41539i) q^{58} +(2.36318 - 7.27312i) q^{59} +(2.27202 + 1.65072i) q^{60} +(-7.22492 - 5.24921i) q^{61} +(1.03315 - 3.17970i) q^{62} +(1.51015 + 4.64777i) q^{63} +(-0.809017 + 0.587785i) q^{64} -3.05764 q^{65} +(-8.79049 + 3.07956i) q^{66} +10.5718 q^{67} +(-5.61829 + 4.08193i) q^{68} +(1.50238 + 4.62384i) q^{69} +(0.309017 - 0.951057i) q^{70} +(1.86409 + 1.35434i) q^{71} +(-3.95363 - 2.87248i) q^{72} +(-4.05160 + 12.4695i) q^{73} +(-2.26428 - 6.96873i) q^{74} +(2.27202 - 1.65072i) q^{75} -4.69704 q^{76} +(2.01015 + 2.63805i) q^{77} +8.58700 q^{78} +(-3.44503 + 2.50296i) q^{79} +(0.309017 + 0.951057i) q^{80} +(0.0684287 - 0.210602i) q^{81} +(-6.14025 - 4.46116i) q^{82} +(-3.12339 - 2.26928i) q^{83} +(-0.867835 + 2.67092i) q^{84} +(2.14600 + 6.60470i) q^{85} +(-5.88634 + 4.27668i) q^{86} +18.9440 q^{87} +(-3.17685 - 0.952688i) q^{88} -12.3140 q^{89} +(-3.95363 + 2.87248i) q^{90} +(-0.944863 - 2.90799i) q^{91} +(-0.534964 + 1.64645i) q^{92} +(7.59613 + 5.51891i) q^{93} +(-3.24056 - 2.35440i) q^{94} +(-1.45146 + 4.46715i) q^{95} +(-0.867835 - 2.67092i) q^{96} +(5.61686 - 4.08089i) q^{97} +1.00000 q^{98} +(-0.369655 - 16.2040i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} + 2 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 3 q^{7} - 3 q^{8} - 15 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 3 * q^7 - 3 * q^8 - 15 * q^9	\( 12 q - 3 q^{2} + 2 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 3 q^{7} - 3 q^{8} - 15 q^{9} + 12 q^{10} + q^{11} + 2 q^{12} - 6 q^{13} - 3 q^{14} + 2 q^{15} - 3 q^{16} - 6 q^{17} - 13 q^{19} - 3 q^{20} + 2 q^{21} + q^{22} - 12 q^{23} - 3 q^{24} - 3 q^{25} + 4 q^{26} - 7 q^{27} - 3 q^{28} - 26 q^{29} + 2 q^{30} + 12 q^{32} - 15 q^{33} + 14 q^{34} - 3 q^{35} - 18 q^{37} + 2 q^{38} - 40 q^{39} - 3 q^{40} + 16 q^{41} - 3 q^{42} + 38 q^{43} + 6 q^{44} + 30 q^{45} + 8 q^{46} - 26 q^{47} + 2 q^{48} - 3 q^{49} - 3 q^{50} - 13 q^{51} + 4 q^{52} + 8 q^{54} + 11 q^{55} + 12 q^{56} - 41 q^{57} - 26 q^{58} + 21 q^{59} - 3 q^{60} + 4 q^{61} - 3 q^{64} + 4 q^{65} - 30 q^{66} + 10 q^{67} - 6 q^{68} + 18 q^{69} - 3 q^{70} - 4 q^{71} - 15 q^{72} - 14 q^{73} - 18 q^{74} - 3 q^{75} + 22 q^{76} + 6 q^{77} + 40 q^{78} - 2 q^{79} - 3 q^{80} + 26 q^{81} - 29 q^{82} + 35 q^{83} + 2 q^{84} - q^{85} - 37 q^{86} + 28 q^{87} - 19 q^{88} + 2 q^{89} - 15 q^{90} + 4 q^{91} - 2 q^{92} + 6 q^{93} + 4 q^{94} - 13 q^{95} + 2 q^{96} + 19 q^{97} + 12 q^{98} - 81 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 3 * q^7 - 3 * q^8 - 15 * q^9 + 12 * q^10 + q^11 + 2 * q^12 - 6 * q^13 - 3 * q^14 + 2 * q^15 - 3 * q^16 - 6 * q^17 - 13 * q^19 - 3 * q^20 + 2 * q^21 + q^22 - 12 * q^23 - 3 * q^24 - 3 * q^25 + 4 * q^26 - 7 * q^27 - 3 * q^28 - 26 * q^29 + 2 * q^30 + 12 * q^32 - 15 * q^33 + 14 * q^34 - 3 * q^35 - 18 * q^37 + 2 * q^38 - 40 * q^39 - 3 * q^40 + 16 * q^41 - 3 * q^42 + 38 * q^43 + 6 * q^44 + 30 * q^45 + 8 * q^46 - 26 * q^47 + 2 * q^48 - 3 * q^49 - 3 * q^50 - 13 * q^51 + 4 * q^52 + 8 * q^54 + 11 * q^55 + 12 * q^56 - 41 * q^57 - 26 * q^58 + 21 * q^59 - 3 * q^60 + 4 * q^61 - 3 * q^64 + 4 * q^65 - 30 * q^66 + 10 * q^67 - 6 * q^68 + 18 * q^69 - 3 * q^70 - 4 * q^71 - 15 * q^72 - 14 * q^73 - 18 * q^74 - 3 * q^75 + 22 * q^76 + 6 * q^77 + 40 * q^78 - 2 * q^79 - 3 * q^80 + 26 * q^81 - 29 * q^82 + 35 * q^83 + 2 * q^84 - q^85 - 37 * q^86 + 28 * q^87 - 19 * q^88 + 2 * q^89 - 15 * q^90 + 4 * q^91 - 2 * q^92 + 6 * q^93 + 4 * q^94 - 13 * q^95 + 2 * q^96 + 19 * q^97 + 12 * q^98 - 81 * q^99

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