LMFDB - Embedded newform 702.2.w.d.79.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [702,2,Mod(79,702)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(702, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([10, 0]))

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

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

chi := DirichletCharacter("702.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.w (of order $9$, degree $6$, 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:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			79.7
Character	$\chi$	$=$	702.79
Dual form			702.2.w.d.391.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.173648 + 0.984808i) q^{2} +(0.535231 + 1.64728i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.695265 - 0.583396i) q^{5} +(-1.71519 + 0.241052i) q^{6} +(3.66522 - 1.33403i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.42706 + 1.76335i) q^{9} +(0.453802 + 0.786008i) q^{10} +(-1.05813 - 0.887878i) q^{11} +(0.0604503 - 1.73100i) q^{12} +(0.173648 + 0.984808i) q^{13} +(0.677306 + 3.84119i) q^{14} +(1.33314 + 0.833043i) q^{15} +(0.766044 + 0.642788i) q^{16} +(3.94659 + 6.83569i) q^{17} +(-1.31511 - 2.69639i) q^{18} +(1.61897 - 2.80414i) q^{19} +(-0.852868 + 0.310419i) q^{20} +(4.15926 + 5.32363i) q^{21} +(1.05813 - 0.887878i) q^{22} +(1.95186 + 0.710417i) q^{23} +(1.69420 + 0.360116i) q^{24} +(-0.725199 + 4.11281i) q^{25} -1.00000 q^{26} +(-4.20376 - 3.05424i) q^{27} -3.90045 q^{28} +(-0.273879 + 1.55324i) q^{29} +(-1.05189 + 1.16823i) q^{30} +(7.64725 + 2.78337i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(0.896238 - 2.21826i) q^{33} +(-7.41715 + 2.69962i) q^{34} +(1.77003 - 3.06578i) q^{35} +(2.88379 - 0.826903i) q^{36} +(-4.83823 - 8.38005i) q^{37} +(2.48041 + 2.08131i) q^{38} +(-1.52931 + 0.813146i) q^{39} +(-0.157604 - 0.893815i) q^{40} +(-0.826649 - 4.68816i) q^{41} +(-5.96500 + 3.17164i) q^{42} +(6.84793 + 5.74609i) q^{43} +(0.690646 + 1.19623i) q^{44} +(-0.658715 + 2.64193i) q^{45} +(-1.03856 + 1.79884i) q^{46} +(-11.6563 + 4.24254i) q^{47} +(-0.648840 + 1.60593i) q^{48} +(6.29190 - 5.27953i) q^{49} +(-3.92440 - 1.42836i) q^{50} +(-9.14795 + 10.1598i) q^{51} +(0.173648 - 0.984808i) q^{52} -2.48261 q^{53} +(3.73782 - 3.60953i) q^{54} -1.25367 q^{55} +(0.677306 - 3.84119i) q^{56} +(5.48572 + 1.16604i) q^{57} +(-1.48209 - 0.539435i) q^{58} +(-6.54438 + 5.49138i) q^{59} +(-0.967827 - 1.23877i) q^{60} +(-2.77159 + 1.00878i) q^{61} +(-4.06902 + 7.04774i) q^{62} +(-6.54334 + 9.70083i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.695265 + 0.583396i) q^{65} +(2.02893 + 1.26782i) q^{66} +(-2.63026 - 14.9170i) q^{67} +(-1.37063 - 7.77326i) q^{68} +(-0.125563 + 3.59549i) q^{69} +(2.71184 + 2.27551i) q^{70} +(4.19449 + 7.26507i) q^{71} +(0.313577 + 2.98357i) q^{72} +(6.69446 - 11.5952i) q^{73} +(9.09289 - 3.30954i) q^{74} +(-7.16309 + 1.00670i) q^{75} +(-2.48041 + 2.08131i) q^{76} +(-5.06274 - 1.84269i) q^{77} +(-0.535231 - 1.64728i) q^{78} +(-0.509630 + 2.89025i) q^{79} +0.907603 q^{80} +(2.78120 - 8.55949i) q^{81} +4.76048 q^{82} +(1.36798 - 7.75822i) q^{83} +(-2.08764 - 6.42513i) q^{84} +(6.73183 + 2.45019i) q^{85} +(-6.84793 + 5.74609i) q^{86} +(-2.70521 + 0.380189i) q^{87} +(-1.29799 + 0.472430i) q^{88} +(3.54449 - 6.13923i) q^{89} +(-2.48741 - 1.10747i) q^{90} +(1.95022 + 3.37789i) q^{91} +(-1.59117 - 1.33515i) q^{92} +(-0.491946 + 14.0869i) q^{93} +(-2.15399 - 12.2159i) q^{94} +(-0.510312 - 2.89412i) q^{95} +(-1.46886 - 0.917849i) q^{96} +(-13.2686 - 11.1337i) q^{97} +(4.10675 + 7.11310i) q^{98} +(4.13378 + 0.289075i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 3 q^{5} + 9 q^{6} - 3 q^{7} + 33 q^{8} - 6 q^{9} - 9 q^{10} - 3 q^{11} + 3 q^{14} - 27 q^{15} + 12 q^{17} - 12 q^{18} - 21 q^{19} - 6 q^{20} - 18 q^{21} + 3 q^{22} - 3 q^{25} - 66 q^{26} + 9 q^{27}+ \cdots - 15 q^{99}+O(q^{100}) $ 66 * q + 3 * q^5 + 9 * q^6 - 3 * q^7 + 33 * q^8 - 6 * q^9 - 9 * q^10 - 3 * q^11 + 3 * q^14 - 27 * q^15 + 12 * q^17 - 12 * q^18 - 21 * q^19 - 6 * q^20 - 18 * q^21 + 3 * q^22 - 3 * q^25 - 66 * q^26 + 9 * q^27 + 18 * q^28 + 39 * q^29 + 9 * q^30 - 9 * q^31 + 15 * q^33 - 6 * q^34 - 9 * q^35 - 3 * q^36 - 21 * q^37 + 6 * q^38 - 3 * q^40 + 6 * q^41 + 9 * q^42 - 6 * q^43 + 3 * q^44 - 9 * q^45 - 9 * q^46 - 36 * q^47 + 9 * q^48 - 9 * q^49 + 3 * q^50 + 21 * q^51 - 60 * q^53 + 27 * q^54 + 84 * q^55 + 3 * q^56 + 87 * q^57 + 24 * q^58 - 30 * q^59 + 6 * q^60 - 12 * q^61 + 21 * q^62 - 60 * q^63 - 33 * q^64 + 3 * q^65 + 24 * q^66 - 3 * q^67 + 15 * q^68 - 87 * q^69 - 21 * q^70 + 3 * q^71 + 6 * q^72 - 15 * q^73 + 6 * q^74 - 117 * q^75 - 6 * q^76 + 27 * q^77 + 27 * q^79 - 18 * q^80 + 78 * q^81 + 24 * q^82 - 24 * q^83 + 33 * q^84 + 45 * q^85 + 6 * q^86 + 18 * q^87 - 6 * q^88 + 36 * q^89 - 87 * q^90 - 9 * q^91 - 63 * q^93 - 36 * q^94 + 63 * q^95 - 102 * q^97 + 72 * q^98 - 15 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$

Coefficient data

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

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

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

$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$3$	0.535231	+	1.64728i	0.309016	+	0.951057i
$3$	0.535231	+	1.64728i	0.309016	+	0.951057i
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	0.695265	−	0.583396i	0.310932	−	0.260903i	−0.473945	−	0.880554i	$-0.657171\pi$
$5$	0.695265	−	0.583396i	0.310932	−	0.260903i	0.784877	+	0.619652i	$0.212726\pi$
$6$	−1.71519	+	0.241052i	−0.700225	+	0.0984092i
$7$	3.66522	−	1.33403i	1.38532	−	0.504217i	0.461536	−	0.887121i	$-0.347298\pi$
$7$	3.66522	−	1.33403i	1.38532	−	0.504217i	0.923788	+	0.382905i	$0.125076\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−2.42706	+	1.76335i	−0.809019	+	0.587783i
$10$	0.453802	+	0.786008i	0.143505	+	0.248557i
$11$	−1.05813	−	0.887878i	−0.319039	−	0.267705i	0.469177	−	0.883104i	$-0.344551\pi$
$11$	−1.05813	−	0.887878i	−0.319039	−	0.267705i	−0.788216	+	0.615399i	$0.788995\pi$
$12$	0.0604503	−	1.73100i	0.0174505	−	0.499695i
$13$	0.173648	+	0.984808i	0.0481613	+	0.273137i
$13$	0.173648	+	0.984808i	0.0481613	+	0.273137i
$14$	0.677306	+	3.84119i	0.181018	+	1.02660i
$15$	1.33314	+	0.833043i	0.344216	+	0.215091i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	3.94659	+	6.83569i	0.957188	+	1.65790i	0.729281	+	0.684215i	$0.239855\pi$
$17$	3.94659	+	6.83569i	0.957188	+	1.65790i	0.227907	+	0.973683i	$0.426812\pi$
$18$	−1.31511	−	2.69639i	−0.309973	−	0.635544i
$19$	1.61897	−	2.80414i	0.371417	−	0.643314i	−0.618366	−	0.785890i	$-0.712205\pi$
$19$	1.61897	−	2.80414i	0.371417	−	0.643314i	0.989784	+	0.142576i	$0.0455386\pi$
$20$	−0.852868	+	0.310419i	−0.190707	+	0.0694117i
$21$	4.15926	+	5.32363i	0.907625	+	1.16171i
$22$	1.05813	−	0.887878i	0.225594	−	0.189296i
$23$	1.95186	+	0.710417i	0.406990	+	0.148132i	0.537399	−	0.843328i	$-0.319407\pi$
$23$	1.95186	+	0.710417i	0.406990	+	0.148132i	−0.130409	+	0.991460i	$0.541629\pi$
$24$	1.69420	+	0.360116i	0.345827	+	0.0735084i
$25$	−0.725199	+	4.11281i	−0.145040	+	0.822562i
$26$	−1.00000			−0.196116
$27$	−4.20376	−	3.05424i	−0.809014	−	0.587789i
$28$	−3.90045			−0.737115
$29$	−0.273879	+	1.55324i	−0.0508580	+	0.288430i	−0.999620	−	0.0275612i	$-0.991226\pi$
$29$	−0.273879	+	1.55324i	−0.0508580	+	0.288430i	0.948762	+	0.315991i	$0.102337\pi$
$30$	−1.05189	+	1.16823i	−0.192047	+	0.213289i
$31$	7.64725	+	2.78337i	1.37349	+	0.499908i	0.920197	−	0.391455i	$-0.128028\pi$
$31$	7.64725	+	2.78337i	1.37349	+	0.499908i	0.453289	+	0.891363i	$0.350250\pi$
$32$	−0.766044	+	0.642788i	−0.135419	+	0.113630i
$33$	0.896238	−	2.21826i	0.156015	−	0.386149i
$34$	−7.41715	+	2.69962i	−1.27203	+	0.462982i
$35$	1.77003	−	3.06578i	0.299190	−	0.518212i
$36$	2.88379	−	0.826903i	0.480631	−	0.137817i
$37$	−4.83823	−	8.38005i	−0.795399	−	1.37767i	−0.922585	−	0.385793i	$-0.873928\pi$
$37$	−4.83823	−	8.38005i	−0.795399	−	1.37767i	0.127186	−	0.991879i	$-0.459406\pi$
$38$	2.48041	+	2.08131i	0.402375	+	0.337633i
$39$	−1.52931	+	0.813146i	−0.244886	+	0.130208i
$40$	−0.157604	−	0.893815i	−0.0249193	−	0.141325i
$41$	−0.826649	−	4.68816i	−0.129101	−	0.732167i	−0.978787	−	0.204879i	$-0.934320\pi$
$41$	−0.826649	−	4.68816i	−0.129101	−	0.732167i	0.849687	−	0.527288i	$-0.176791\pi$
$42$	−5.96500	+	3.17164i	−0.920419	+	0.489394i
$43$	6.84793	+	5.74609i	1.04430	+	0.876271i	0.992483	−	0.122386i	$-0.0390545\pi$
$43$	6.84793	+	5.74609i	1.04430	+	0.876271i	0.0518163	+	0.998657i	$0.483499\pi$
$44$	0.690646	+	1.19623i	0.104119	+	0.180339i
$45$	−0.658715	+	2.64193i	−0.0981955	+	0.393836i
$46$	−1.03856	+	1.79884i	−0.153127	+	0.265224i
$47$	−11.6563	+	4.24254i	−1.70024	+	0.618838i	−0.995853	−	0.0909763i	$-0.971001\pi$
$47$	−11.6563	+	4.24254i	−1.70024	+	0.618838i	−0.704389	+	0.709814i	$0.748779\pi$
$48$	−0.648840	+	1.60593i	−0.0936520	+	0.231796i
$49$	6.29190	−	5.27953i	0.898843	−	0.754219i
$50$	−3.92440	−	1.42836i	−0.554994	−	0.202001i
$51$	−9.14795	+	10.1598i	−1.28097	+	1.42266i
$52$	0.173648	−	0.984808i	0.0240807	−	0.136568i
$53$	−2.48261			−0.341012			−0.170506	−	0.985357i	$-0.554540\pi$
$53$	−2.48261			−0.341012			−0.170506	+	0.985357i	$0.554540\pi$
$54$	3.73782	−	3.60953i	0.508652	−	0.491195i
$55$	−1.25367			−0.169044
$56$	0.677306	−	3.84119i	0.0905088	−	0.513301i
$57$	5.48572	+	1.16604i	0.726602	+	0.154445i
$58$	−1.48209	−	0.539435i	−0.194608	−	0.0708313i
$59$	−6.54438	+	5.49138i	−0.852005	+	0.714917i	−0.960230	−	0.279209i	$-0.909928\pi$
$59$	−6.54438	+	5.49138i	−0.852005	+	0.714917i	0.108225	+	0.994126i	$0.465483\pi$
$60$	−0.967827	−	1.23877i	−0.124946	−	0.159924i
$61$	−2.77159	+	1.00878i	−0.354866	+	0.129160i	−0.513301	−	0.858209i	$-0.671577\pi$
$61$	−2.77159	+	1.00878i	−0.354866	+	0.129160i	0.158435	+	0.987369i	$0.449355\pi$
$62$	−4.06902	+	7.04774i	−0.516766	+	0.895064i
$63$	−6.54334	+	9.70083i	−0.824383	+	1.22219i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	0.695265	+	0.583396i	0.0862370	+	0.0723614i
$66$	2.02893	+	1.26782i	0.249744	+	0.156058i
$67$	−2.63026	−	14.9170i	−0.321338	−	1.82240i	−0.534251	−	0.845326i	$-0.679406\pi$
$67$	−2.63026	−	14.9170i	−0.321338	−	1.82240i	0.212913	−	0.977071i	$-0.431705\pi$
$68$	−1.37063	−	7.77326i	−0.166214	−	0.942646i
$69$	−0.125563	+	3.59549i	−0.0151160	+	0.432846i
$70$	2.71184	+	2.27551i	0.324127	+	0.271975i
$71$	4.19449	+	7.26507i	0.497794	+	0.862205i	0.999997	−	0.00254508i	$-0.000810126\pi$
$71$	4.19449	+	7.26507i	0.497794	+	0.862205i	−0.502202	+	0.864750i	$0.667477\pi$
$72$	0.313577	+	2.98357i	0.0369553	+	0.351617i
$73$	6.69446	−	11.5952i	0.783528	−	1.35711i	−0.146347	−	0.989233i	$-0.546752\pi$
$73$	6.69446	−	11.5952i	0.783528	−	1.35711i	0.929875	−	0.367876i	$-0.119915\pi$
$74$	9.09289	−	3.30954i	1.05703	−	0.384726i
$75$	−7.16309	+	1.00670i	−0.827123	+	0.116243i
$76$	−2.48041	+	2.08131i	−0.284522	+	0.238743i
$77$	−5.06274	−	1.84269i	−0.576953	−	0.209994i
$78$	−0.535231	−	1.64728i	−0.0606029	−	0.186518i
$79$	−0.509630	+	2.89025i	−0.0573378	+	0.325179i	−0.999962	−	0.00867572i	$-0.997238\pi$
$79$	−0.509630	+	2.89025i	−0.0573378	+	0.325179i	0.942625	+	0.333855i	$0.108350\pi$
$80$	0.907603			0.101473
$81$	2.78120	−	8.55949i	0.309023	−	0.951055i
$82$	4.76048			0.525707
$83$	1.36798	−	7.75822i	0.150156	−	0.851576i	−0.812926	−	0.582367i	$-0.802127\pi$
$83$	1.36798	−	7.75822i	0.150156	−	0.851576i	0.963082	−	0.269209i	$-0.0867622\pi$
$84$	−2.08764	−	6.42513i	−0.227780	−	0.701039i
$85$	6.73183	+	2.45019i	0.730170	+	0.265760i
$86$	−6.84793	+	5.74609i	−0.738431	+	0.619617i
$87$	−2.70521	+	0.380189i	−0.290029	+	0.0407605i
$88$	−1.29799	+	0.472430i	−0.138366	+	0.0503612i
$89$	3.54449	−	6.13923i	0.375715	−	0.650757i	−0.614719	−	0.788746i	$-0.710731\pi$
$89$	3.54449	−	6.13923i	0.375715	−	0.650757i	0.990434	+	0.137989i	$0.0440639\pi$
$90$	−2.48741	−	1.10747i	−0.262196	−	0.116738i
$91$	1.95022	+	3.37789i	0.204439	+	0.354099i
$92$	−1.59117	−	1.33515i	−0.165891	−	0.139199i
$93$	−0.491946	+	14.0869i	−0.0510125	+	1.46074i
$94$	−2.15399	−	12.2159i	−0.222167	−	1.25997i
$95$	−0.510312	−	2.89412i	−0.0523569	−	0.296931i
$96$	−1.46886	−	0.917849i	−0.149915	−	0.0936776i
$97$	−13.2686	−	11.1337i	−1.34722	−	1.13045i	−0.979707	−	0.200433i	$-0.935765\pi$
$97$	−13.2686	−	11.1337i	−1.34722	−	1.13045i	−0.367512	−	0.930019i	$-0.619790\pi$
$98$	4.10675	+	7.11310i	0.414844	+	0.718531i
$99$	4.13378	+	0.289075i	0.415461	+	0.0290531i
$100$	2.08813	−	3.61674i	0.208813	−	0.361674i
$101$	1.55173	−	0.564783i	0.154403	−	0.0561980i	−0.263663	−	0.964615i	$-0.584931\pi$
$101$	1.55173	−	0.564783i	0.154403	−	0.0561980i	0.418065	+	0.908417i	$0.362708\pi$
$102$	−8.41692	−	10.7732i	−0.833399	−	1.06671i
$103$	−10.7712	+	9.03808i	−1.06131	+	0.890548i	−0.994238	−	0.107200i	$-0.965812\pi$
$103$	−10.7712	+	9.03808i	−1.06131	+	0.890548i	−0.0670765	+	0.997748i	$0.521367\pi$
$104$	0.939693	+	0.342020i	0.0921444	+	0.0335378i
$105$	5.99757	+	1.27483i	0.585303	+	0.124411i
$106$	0.431100	−	2.44489i	0.0418721	−	0.237469i
$107$	3.88681			0.375752			0.187876	−	0.982193i	$-0.439840\pi$
$107$	3.88681			0.375752			0.187876	+	0.982193i	$0.439840\pi$
$108$	2.90563	+	4.30782i	0.279595	+	0.414520i
$109$	8.19941			0.785361			0.392681	−	0.919675i	$-0.371548\pi$
$109$	8.19941			0.785361			0.392681	+	0.919675i	$0.371548\pi$
$110$	0.217697	−	1.23462i	0.0207566	−	0.117716i
$111$	11.2147	−	12.4552i	1.06445	−	1.18219i
$112$	3.66522	+	1.33403i	0.346331	+	0.126054i
$113$	0.725897	−	0.609100i	0.0682867	−	0.0572993i	−0.608005	−	0.793933i	$-0.708030\pi$
$113$	0.725897	−	0.609100i	0.0682867	−	0.0572993i	0.676292	+	0.736634i	$0.263586\pi$
$114$	−2.10091	+	5.19990i	−0.196768	+	0.487016i
$115$	1.77151	−	0.644777i	0.165194	−	0.0601258i
$116$	0.788602	−	1.36590i	0.0732198	−	0.126820i
$117$	−2.15801	−	2.08398i	−0.199508	−	0.192664i
$118$	−4.27154	−	7.39852i	−0.393227	−	0.681089i
$119$	23.5841	+	19.7894i	2.16195	+	1.81410i
$120$	1.38801	−	0.738014i	0.126707	−	0.0673712i
$121$	−1.57881	−	8.95390i	−0.143529	−	0.813991i
$122$	−0.512169	−	2.90465i	−0.0463696	−	0.262975i
$123$	7.28025	−	3.87097i	0.656438	−	0.349033i
$124$	−6.23409	−	5.23103i	−0.559838	−	0.469760i
$125$	4.16420	+	7.21261i	0.372457	+	0.645115i
$126$	−8.41722	−	8.12846i	−0.749865	−	0.724141i
$127$	3.66165	−	6.34216i	0.324919	−	0.562776i	−0.656577	−	0.754259i	$-0.727996\pi$
$127$	3.66165	−	6.34216i	0.324919	−	0.562776i	0.981496	+	0.191483i	$0.0613297\pi$
$128$	0.939693	−	0.342020i	0.0830579	−	0.0302306i
$129$	−5.80020	+	14.3559i	−0.510679	+	1.26397i
$130$	−0.695265	+	0.583396i	−0.0609787	+	0.0511672i
$131$	5.93926	+	2.16171i	0.518915	+	0.188870i	0.588182	−	0.808728i	$-0.299844\pi$
$131$	5.93926	+	2.16171i	0.518915	+	0.188870i	−0.0692670	+	0.997598i	$0.522066\pi$
$132$	−1.60088	+	1.77795i	−0.139338	+	0.154751i
$133$	2.19308	−	12.4376i	0.190164	−	1.07847i
$134$	15.1471			1.30851
$135$	−4.70456	+	0.328954i	−0.404904	+	0.0283118i
$136$	7.89317			0.676834
$137$	−3.14910	+	17.8594i	−0.269046	+	1.52583i	0.488216	+	0.872723i	$0.337648\pi$
$137$	−3.14910	+	17.8594i	−0.269046	+	1.52583i	−0.757262	+	0.653112i	$0.773463\pi$
$138$	−3.51906	−	0.748005i	−0.299562	−	0.0636744i
$139$	3.94056	+	1.43425i	0.334234	+	0.121651i	0.503685	−	0.863887i	$-0.331977\pi$
$139$	3.94056	+	1.43425i	0.334234	+	0.121651i	−0.169451	+	0.985539i	$0.554199\pi$
$140$	−2.71184	+	2.27551i	−0.229193	+	0.192315i
$141$	−13.2274	−	16.9304i	−1.11395	−	1.42580i
$142$	−7.88306	+	2.86920i	−0.661532	+	0.240778i
$143$	0.690646	−	1.19623i	0.0577547	−	0.100034i
$144$	−2.99269	−	0.209278i	−0.249391	−	0.0174399i
$145$	0.715738	+	1.23969i	0.0594388	+	0.102951i
$146$	10.2565	+	8.60624i	0.848835	+	0.712257i
$147$	12.0645	+	7.53875i	0.995062	+	0.621786i
$148$	1.68030	+	9.52944i	0.138120	+	0.783316i
$149$	−1.67714	−	9.51155i	−0.137397	−	0.779217i	−0.973161	−	0.230127i	$-0.926086\pi$
$149$	−1.67714	−	9.51155i	−0.137397	−	0.779217i	0.835764	−	0.549089i	$-0.185025\pi$
$150$	0.252456	−	7.22908i	0.0206129	−	0.590252i
$151$	14.8023	+	12.4206i	1.20459	+	1.01077i	0.999487	+	0.0320336i	$0.0101984\pi$
$151$	14.8023	+	12.4206i	1.20459	+	1.01077i	0.205106	+	0.978740i	$0.434246\pi$
$152$	−1.61897	−	2.80414i	−0.131316	−	0.227446i
$153$	−21.6323	−	9.63139i	−1.74887	−	0.778652i
$154$	2.69383	−	4.66585i	0.217075	−	0.375985i
$155$	6.94067	−	2.52620i	0.557488	−	0.202909i
$156$	1.71519	−	0.241052i	0.137326	−	0.0192996i
$157$	3.91073	−	3.28149i	0.312110	−	0.261892i	−0.473253	−	0.880926i	$-0.656920\pi$
$157$	3.91073	−	3.28149i	0.312110	−	0.261892i	0.785364	+	0.619035i	$0.212476\pi$
$158$	−2.75785	−	1.00377i	−0.219403	−	0.0798560i
$159$	−1.32877	−	4.08954i	−0.105378	−	0.324322i
$160$	−0.157604	+	0.893815i	−0.0124597	+	0.0706623i
$161$	8.10170			0.638504
$162$	7.94650	+	4.22529i	0.624336	+	0.331970i
$163$	5.56327			0.435749			0.217875	−	0.975977i	$-0.430088\pi$
$163$	5.56327			0.435749			0.217875	+	0.975977i	$0.430088\pi$
$164$	−0.826649	+	4.68816i	−0.0645504	+	0.366084i
$165$	−0.671000	−	2.06514i	−0.0522373	−	0.160771i
$166$	7.40281	+	2.69440i	0.574570	+	0.209126i
$167$	−11.0288	+	9.25423i	−0.853431	+	0.716114i	−0.960542	−	0.278133i	$-0.910284\pi$
$167$	−11.0288	+	9.25423i	−0.853431	+	0.716114i	0.107112	+	0.994247i	$0.465840\pi$
$168$	6.69003	−	0.940212i	0.516147	−	0.0725389i
$169$	−0.939693	+	0.342020i	−0.0722840	+	0.0263092i
$170$	−3.58193	+	6.20409i	−0.274722	+	0.475832i
$171$	1.01534	+	9.66062i	0.0776452	+	0.738766i
$172$	−4.46967	−	7.74169i	−0.340809	−	0.590298i
$173$	−6.39724	−	5.36792i	−0.486373	−	0.408115i	0.366351	−	0.930477i	$-0.380607\pi$
$173$	−6.39724	−	5.36792i	−0.486373	−	0.408115i	−0.852724	+	0.522361i	$0.825051\pi$
$174$	0.0953424	−	2.73013i	0.00722789	−	0.206971i
$175$	2.82860	+	16.0418i	0.213822	+	1.21265i
$176$	−0.239859	−	1.36031i	−0.0180800	−	0.102537i
$177$	−12.5486	−	7.84126i	−0.943210	−	0.589385i
$178$	5.43047	+	4.55670i	0.407031	+	0.341539i
$179$	−8.68358	−	15.0404i	−0.649041	−	1.12417i	−0.983352	−	0.181710i	$-0.941837\pi$
$179$	−8.68358	−	15.0404i	−0.649041	−	1.12417i	0.334311	−	0.942463i	$-0.391496\pi$
$180$	1.52258	−	2.25731i	0.113487	−	0.168250i
$181$	3.21094	−	5.56151i	0.238667	−	0.413384i	−0.721665	−	0.692243i	$-0.756623\pi$
$181$	3.21094	−	5.56151i	0.238667	−	0.413384i	0.960332	+	0.278859i	$0.0899561\pi$
$182$	−3.66522	+	1.33403i	−0.271684	+	0.0988850i
$183$	−3.14517	−	4.02565i	−0.232498	−	0.297585i
$184$	1.59117	−	1.33515i	0.117302	−	0.0984284i
$185$	−8.25274	−	3.00375i	−0.606753	−	0.220840i
$186$	−13.7875	−	2.93064i	−1.01095	−	0.214885i
$187$	1.89325	−	10.7371i	0.138448	−	0.785178i
$188$	12.4043			0.904680
$189$	−19.4822	−	5.58652i	−1.41712	−	0.406359i
$190$	2.93877			0.213201
$191$	−0.196912	+	1.11674i	−0.0142480	+	0.0808046i	−0.991103	−	0.133100i	$-0.957507\pi$
$191$	−0.196912	+	1.11674i	−0.0142480	+	0.0808046i	0.976855	+	0.213904i	$0.0686181\pi$
$192$	1.15897	−	1.28716i	0.0836415	−	0.0928930i
$193$	−10.1019	−	3.67678i	−0.727149	−	0.264661i	−0.0481914	−	0.998838i	$-0.515346\pi$
$193$	−10.1019	−	3.67678i	−0.727149	−	0.264661i	−0.678958	+	0.734178i	$0.737568\pi$
$194$	13.2686	−	11.1337i	0.952628	−	0.799350i
$195$	−0.588889	+	1.45755i	−0.0421712	+	0.104377i
$196$	−7.71816	+	2.80918i	−0.551297	+	0.200656i
$197$	12.3031	−	21.3097i	0.876563	−	1.51825i	0.0214739	−	0.999769i	$-0.493164\pi$
$197$	12.3031	−	21.3097i	0.876563	−	1.51825i	0.855089	−	0.518482i	$-0.173503\pi$
$198$	−1.00251	+	4.02078i	−0.0712451	+	0.285745i
$199$	−13.4852	−	23.3571i	−0.955941	−	1.65574i	−0.732201	−	0.681089i	$-0.761507\pi$
$199$	−13.4852	−	23.3571i	−0.955941	−	1.65574i	−0.223740	−	0.974649i	$-0.571827\pi$
$200$	3.19920	+	2.68445i	0.226217	+	0.189819i
$201$	23.1646	−	12.3168i	1.63391	−	0.868760i
$202$	0.286748	+	1.62623i	0.0201755	+	0.114421i
$203$	1.06825	+	6.05834i	0.0749764	+	0.425212i
$204$	12.0711	−	6.41830i	0.845147	−	0.449371i
$205$	−3.30979	−	2.77725i	−0.231166	−	0.193971i
$206$	−7.03038	−	12.1770i	−0.489829	−	0.848410i
$207$	−5.98998	+	1.71758i	−0.416332	+	0.119380i
$208$	−0.500000	+	0.866025i	−0.0346688	+	0.0600481i
$209$	−4.20282	+	1.52970i	−0.290715	+	0.105812i
$210$	−2.29693	+	5.68508i	−0.158503	+	0.392308i
$211$	7.63159	−	6.40367i	0.525381	−	0.440847i	−0.341122	−	0.940019i	$-0.610807\pi$
$211$	7.63159	−	6.40367i	0.525381	−	0.440847i	0.866503	+	0.499172i	$0.166363\pi$
$212$	2.33289	+	0.849101i	0.160223	+	0.0583165i
$213$	−9.72258	+	10.7980i	−0.666180	+	0.739865i
$214$	−0.674937	+	3.82776i	−0.0461378	+	0.261660i
$215$	8.11337			0.553327
$216$	−4.74693	+	2.11344i	−0.322988	+	0.143802i
$217$	31.7420			2.15479
$218$	−1.42381	+	8.07484i	−0.0964328	+	0.546897i
$219$	22.6835	+	4.82157i	1.53281	+	0.325811i
$220$	1.17806	+	0.428779i	0.0794248	+	0.0289083i
$221$	−6.04652	+	5.07363i	−0.406733	+	0.341289i
$222$	10.3185	+	13.2072i	0.692534	+	0.886406i
$223$	−6.68871	+	2.43449i	−0.447909	+	0.163026i	−0.556119	−	0.831102i	$-0.687710\pi$
$223$	−6.68871	+	2.43449i	−0.447909	+	0.163026i	0.108210	+	0.994128i	$0.465488\pi$
$224$	−1.95022	+	3.37789i	−0.130305	+	0.225695i
$225$	−5.49222	−	11.2608i	−0.366148	−	0.750720i
$226$	0.473796	+	0.820638i	0.0315164	+	0.0545881i
$227$	−5.88972	−	4.94206i	−0.390914	−	0.328016i	0.426055	−	0.904697i	$-0.359903\pi$
$227$	−5.88972	−	4.94206i	−0.390914	−	0.328016i	−0.816969	+	0.576681i	$0.804347\pi$
$228$	−4.75609	−	2.97194i	−0.314980	−	0.196822i
$229$	0.697540	+	3.95595i	0.0460948	+	0.261416i	0.999142	−	0.0414037i	$-0.0131830\pi$
$229$	0.697540	+	3.95595i	0.0460948	+	0.261416i	−0.953048	+	0.302820i	$0.902072\pi$
$230$	0.327362	+	1.85656i	0.0215856	+	0.122418i
$231$	0.325686	−	9.32602i	0.0214285	−	0.613607i
$232$	1.20821	+	1.01381i	0.0793227	+	0.0665597i
$233$	2.99954	+	5.19535i	0.196506	+	0.340359i	0.947393	−	0.320072i	$-0.103707\pi$
$233$	2.99954	+	5.19535i	0.196506	+	0.340359i	−0.750887	+	0.660431i	$0.770374\pi$
$234$	2.42706	−	1.76335i	0.158662	−	0.115274i
$235$	−5.62911	+	9.74991i	−0.367203	+	0.636014i
$236$	8.02786	−	2.92190i	0.522569	−	0.190200i
$237$	−5.03383	+	0.707450i	−0.326982	+	0.0459538i
$238$	−23.5841	+	19.7894i	−1.52873	+	1.28276i
$239$	−19.3315	−	7.03610i	−1.25045	−	0.455127i	−0.369897	−	0.929073i	$-0.620607\pi$
$239$	−19.3315	−	7.03610i	−1.25045	−	0.455127i	−0.880554	+	0.473945i	$0.842829\pi$
$240$	0.485777	+	1.49508i	0.0313568	+	0.0965067i
$241$	−0.926880	+	5.25660i	−0.0597056	+	0.338607i	−0.999998	−	0.00175933i	$-0.999440\pi$
$241$	−0.926880	+	5.25660i	−0.0597056	+	0.338607i	0.940293	+	0.340366i	$0.110551\pi$
$242$	9.09203			0.584458
$243$	15.5885		0.000116041i	1.00000		7.44403e-6i
$244$	2.94946			0.188820
$245$	1.29448	−	7.34134i	0.0827011	−	0.469021i
$246$	2.54795	+	7.84184i	0.162452	+	0.499977i
$247$	3.04267	+	1.10744i	0.193600	+	0.0704648i
$248$	6.23409	−	5.23103i	0.395865	−	0.332171i
$249$	13.5121	−	1.89899i	0.856297	−	0.120343i
$250$	−7.82614	+	2.84848i	−0.494968	+	0.180154i
$251$	6.32958	−	10.9632i	0.399520	−	0.691989i	−0.594147	−	0.804357i	$-0.702510\pi$
$251$	6.32958	−	10.9632i	0.399520	−	0.691989i	0.993667	+	0.112368i	$0.0358435\pi$
$252$	9.46661	−	6.87785i	0.596340	−	0.433264i
$253$	−1.43456	−	2.48472i	−0.0901898	−	0.156213i
$254$	5.60997	+	4.70732i	0.352001	+	0.295364i
$255$	−0.433058	+	12.4006i	−0.0271191	+	0.776557i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−2.55645	−	14.4983i	−0.159467	−	0.904382i	−0.954588	−	0.297931i	$-0.903704\pi$
$257$	−2.55645	−	14.4983i	−0.159467	−	0.904382i	0.795121	−	0.606451i	$-0.207408\pi$
$258$	−13.1306	−	8.20496i	−0.817478	−	0.510818i
$259$	−28.9124	−	24.2604i	−1.79653	−	1.50747i
$260$	−0.453802	−	0.786008i	−0.0281436	−	0.0487461i
$261$	−2.07419	−	4.25275i	−0.128389	−	0.263239i
$262$	−3.16021	+	5.47365i	−0.195239	+	0.338163i
$263$	−12.6892	+	4.61850i	−0.782450	+	0.284789i	−0.702194	−	0.711986i	$-0.747796\pi$
$263$	−12.6892	+	4.61850i	−0.782450	+	0.284789i	−0.0802564	+	0.996774i	$0.525574\pi$
$264$	−1.47295	−	1.88529i	−0.0906537	−	0.116032i
$265$	−1.72607	+	1.44834i	−0.106031	+	0.0889710i
$266$	11.8678	+	4.31952i	0.727660	+	0.264847i
$267$	12.0101	+	2.55285i	0.735009	+	0.156232i
$268$	−2.63026	+	14.9170i	−0.160669	+	0.911199i
$269$	−14.9762			−0.913115			−0.456557	−	0.889694i	$-0.650918\pi$
$269$	−14.9762			−0.913115			−0.456557	+	0.889694i	$0.650918\pi$
$270$	0.492982	−	4.69021i	0.0300019	−	0.285437i
$271$	2.51504			0.152778			0.0763888	−	0.997078i	$-0.475661\pi$
$271$	2.51504			0.152778			0.0763888	+	0.997078i	$0.475661\pi$
$272$	−1.37063	+	7.77326i	−0.0831069	+	0.471323i
$273$	−4.52050	+	5.02051i	−0.273593	+	0.303855i
$274$	−17.0413	−	6.20252i	−1.02950	−	0.374708i
$275$	4.41903	−	3.70801i	0.266477	−	0.223601i
$276$	1.34772	−	3.33571i	0.0811232	−	0.200786i
$277$	−25.8479	+	9.40785i	−1.55305	+	0.565263i	−0.969130	−	0.246550i	$-0.920703\pi$
$277$	−25.8479	+	9.40785i	−1.55305	+	0.565263i	−0.583917	+	0.811813i	$0.698481\pi$
$278$	−2.09673	+	3.63164i	−0.125753	+	0.217811i
$279$	−23.4684	+	6.72937i	−1.40501	+	0.402877i
$280$	−1.77003	−	3.06578i	−0.105780	−	0.183216i
$281$	−2.63370	−	2.20994i	−0.157114	−	0.131834i	0.560842	−	0.827923i	$-0.310478\pi$
$281$	−2.63370	−	2.20994i	−0.157114	−	0.131834i	−0.717956	+	0.696089i	$0.754922\pi$
$282$	18.9701	−	10.0865i	1.12965	−	0.600645i
$283$	4.54620	+	25.7828i	0.270244	+	1.53263i	0.753676	+	0.657246i	$0.228279\pi$
$283$	4.54620	+	25.7828i	0.270244	+	1.53263i	−0.483432	+	0.875382i	$0.660610\pi$
$284$	−1.45673	−	8.26153i	−0.0864411	−	0.490232i
$285$	4.49429	−	2.38965i	0.266219	−	0.141551i
$286$	1.05813	+	0.887878i	0.0625686	+	0.0525013i
$287$	−9.28400	−	16.0804i	−0.548017	−	0.949194i
$288$	0.725774	−	2.91089i	0.0427667	−	0.171526i
$289$	−22.6511	+	39.2328i	−1.33242	+	2.30781i
$290$	−1.34515	+	0.489593i	−0.0789897	+	0.0287499i
$291$	11.2385	−	27.8161i	0.658812	−	1.63061i
$292$	−10.2565	+	8.60624i	−0.600217	+	0.503642i
$293$	−12.5264	−	4.55925i	−0.731802	−	0.266354i	−0.0508746	−	0.998705i	$-0.516201\pi$
$293$	−12.5264	−	4.55925i	−0.731802	−	0.266354i	−0.680927	+	0.732351i	$0.738423\pi$
$294$	−9.51920	+	10.5721i	−0.555171	+	0.616578i
$295$	−1.34642	+	7.63593i	−0.0783916	+	0.444581i
$296$	−9.67645			−0.562432
$297$	1.73634	+	6.96422i	0.100753	+	0.404105i
$298$	9.65828			0.559489
$299$	−0.360688	+	2.04557i	−0.0208591	+	0.118298i
$300$	7.07542	+	1.50394i	0.408499	+	0.0868299i
$301$	32.7646	+	11.9254i	1.88852	+	0.687366i
$302$	−14.8023	+	12.4206i	−0.851776	+	0.714725i
$303$	1.76089	+	2.25384i	0.101160	+	0.129480i
$304$	3.04267	−	1.10744i	0.174509	−	0.0635161i
$305$	−1.33847	+	2.31830i	−0.0766406	+	0.132745i
$306$	13.2415	−	19.6312i	0.756965	−	1.12224i
$307$	7.43702	+	12.8813i	0.424453	+	0.735174i	0.996369	−	0.0851379i	$-0.0271331\pi$
$307$	7.43702	+	12.8813i	0.424453	+	0.735174i	−0.571916	+	0.820312i	$0.693800\pi$
$308$	4.12719	+	3.46312i	0.235168	+	0.197330i
$309$	−20.6533	−	12.9057i	−1.17492	−	0.734177i
$310$	1.28258	+	7.27389i	0.0728459	+	0.413129i
$311$	4.19039	+	23.7649i	0.237615	+	1.34758i	0.837035	+	0.547149i	$0.184287\pi$
$311$	4.19039	+	23.7649i	0.237615	+	1.34758i	−0.599420	+	0.800435i	$0.704602\pi$
$312$	−0.0604503	+	1.73100i	−0.00342232	+	0.0979983i
$313$	−5.44849	−	4.57182i	−0.307967	−	0.258415i	0.475684	−	0.879616i	$-0.342200\pi$
$313$	−5.44849	−	4.57182i	−0.307967	−	0.258415i	−0.783651	+	0.621201i	$0.786645\pi$
$314$	2.55255	+	4.42115i	0.144049	+	0.249500i
$315$	1.11008	+	10.5620i	0.0625459	+	0.595102i
$316$	1.46742	−	2.54165i	0.0825489	−	0.142979i
$317$	15.6197	−	5.68512i	0.877292	−	0.319308i	0.136176	−	0.990685i	$-0.456519\pi$
$317$	15.6197	−	5.68512i	0.877292	−	0.319308i	0.741116	+	0.671377i	$0.234297\pi$
$318$	4.25815	−	0.598438i	0.238785	−	0.0335587i
$319$	1.66889	−	1.40036i	0.0934398	−	0.0784053i
$320$	−0.852868	−	0.310419i	−0.0476768	−	0.0173529i
$321$	2.08034	+	6.40266i	0.116113	+	0.357362i
$322$	−1.40685	+	7.97862i	−0.0784005	+	0.444631i
$323$	25.5576			1.42206
$324$	−5.54100	+	7.09206i	−0.307833	+	0.394004i
$325$	−4.17626			−0.231657
$326$	−0.966052	+	5.47876i	−0.0535047	+	0.303440i
$327$	4.38858	+	13.5067i	0.242689	+	0.746923i
$328$	−4.47339	−	1.62818i	−0.247001	−	0.0899012i
$329$	−37.0632	+	31.0997i	−2.04336	+	1.71458i
$330$	2.15028	−	0.302199i	0.118369	−	0.0166355i
$331$	−14.3124	+	5.20930i	−0.786682	+	0.286329i	−0.703956	−	0.710244i	$-0.748585\pi$
$331$	−14.3124	+	5.20930i	−0.786682	+	0.286329i	−0.0827258	+	0.996572i	$0.526363\pi$
$332$	−3.93895	+	6.82247i	−0.216178	+	0.374432i
$333$	26.5196	+	11.8074i	1.45327	+	0.647040i
$334$	−7.19851	−	12.4682i	−0.393885	−	0.682229i
$335$	−10.5312	−	8.83675i	−0.575383	−	0.482803i
$336$	−0.235783	+	6.75166i	−0.0128630	+	0.368333i
$337$	−1.03621	−	5.87665i	−0.0564461	−	0.320122i	0.943490	−	0.331400i	$-0.107521\pi$
$337$	−1.03621	−	5.87665i	−0.0564461	−	0.320122i	−0.999936	+	0.0112784i	$0.996410\pi$
$338$	−0.173648	−	0.984808i	−0.00944522	−	0.0535665i
$339$	1.39188	+	0.869746i	0.0755966	+	0.0472381i
$340$	−5.48784	−	4.60485i	−0.297620	−	0.249733i
$341$	−5.62050	−	9.73500i	−0.304367	−	0.527180i
$342$	−9.69016	−	0.677631i	−0.523984	−	0.0366421i
$343$	2.36659	−	4.09905i	0.127784	−	0.221328i
$344$	8.40022	−	3.05743i	0.452910	−	0.164846i
$345$	2.01029	+	2.57307i	0.108231	+	0.138529i
$346$	6.39724	−	5.36792i	0.343918	−	0.288581i
$347$	31.8728	+	11.6007i	1.71102	+	0.622760i	0.997003	−	0.0773681i	$-0.0246517\pi$
$347$	31.8728	+	11.6007i	1.71102	+	0.622760i	0.714017	+	0.700128i	$0.246874\pi$
$348$	2.67210	+	0.567976i	0.143240	+	0.0304467i
$349$	−0.587042	+	3.32928i	−0.0314236	+	0.178212i	−0.996480	−	0.0838298i	$-0.973285\pi$
$349$	−0.587042	+	3.32928i	−0.0314236	+	0.178212i	0.965056	+	0.262042i	$0.0843959\pi$
$350$	−16.2893			−0.870698
$351$	2.27786	−	4.67026i	0.121583	−	0.249280i
$352$	1.38129			0.0736231
$353$	3.70275	−	20.9994i	0.197078	−	1.11768i	−0.712351	−	0.701823i	$-0.752370\pi$
$353$	3.70275	−	20.9994i	0.197078	−	1.11768i	0.909429	−	0.415860i	$-0.136519\pi$
$354$	9.90117	−	10.9963i	0.526241	−	0.584448i
$355$	7.15469	+	2.60410i	0.379732	+	0.138211i
$356$	−5.43047	+	4.55670i	−0.287814	+	0.241505i
$357$	−19.9758	+	49.4416i	−1.05723	+	2.61673i
$358$	16.3198	−	5.93992i	0.862528	−	0.313935i
$359$	10.0185	−	17.3526i	0.528758	−	0.915836i	−0.470680	−	0.882304i	$-0.655991\pi$
$359$	10.0185	−	17.3526i	0.528758	−	0.915836i	0.999438	−	0.0335316i	$-0.0106754\pi$
$360$	1.95862	+	1.89143i	0.103228	+	0.0996870i
$361$	4.25787	+	7.37484i	0.224098	+	0.388149i
$362$	4.91945	+	4.12791i	0.258560	+	0.216958i
$363$	13.9045	−	7.39315i	0.729799	−	0.388040i
$364$	−0.677306	−	3.84119i	−0.0355005	−	0.201333i
$365$	−2.11014	−	11.9672i	−0.110450	−	0.626393i
$366$	4.51065	−	2.39834i	0.235775	−	0.125363i
$367$	−7.31483	−	6.13787i	−0.381831	−	0.320394i	0.431590	−	0.902070i	$-0.357953\pi$
$367$	−7.31483	−	6.13787i	−0.381831	−	0.320394i	−0.813421	+	0.581676i	$0.802397\pi$
$368$	1.03856	+	1.79884i	0.0541387	+	0.0937710i
$369$	10.2732	+	9.92075i	0.534800	+	0.516454i
$370$	4.39119	−	7.60576i	0.228287	−	0.395405i
$371$	−9.09930	+	3.31187i	−0.472412	+	0.171944i
$372$	5.28028	−	13.0691i	0.273770	−	0.677601i
$373$	19.6601	−	16.4968i	1.01796	−	0.854170i	0.0285908	−	0.999591i	$-0.490898\pi$
$373$	19.6601	−	16.4968i	1.01796	−	0.854170i	0.989370	+	0.145421i	$0.0464536\pi$
$374$	10.2453	+	3.72897i	0.529770	+	0.192820i
$375$	−9.65237	+	10.7200i	−0.498446	+	0.553579i
$376$	−2.15399	+	12.2159i	−0.111084	+	0.629987i
$377$	−1.57720			−0.0812301
$378$	8.88469	−	18.2161i	0.456979	−	0.936936i
$379$	−13.5795			−0.697533			−0.348767	−	0.937210i	$-0.613399\pi$
$379$	−13.5795			−0.697533			−0.348767	+	0.937210i	$0.613399\pi$
$380$	−0.510312	+	2.89412i	−0.0261784	+	0.148465i
$381$	12.4071	+	2.63724i	0.635637	+	0.135110i
$382$	−1.06558	−	0.387841i	−0.0545200	−	0.0198436i
$383$	0.000239542	0	0.000200999i	1.22400e−5	0	1.02706e-5i	−0.642781	−	0.766050i	$-0.722220\pi$
$383$	0.000239542	0	0.000200999i	1.22400e−5	0	1.02706e-5i	0.642794	+	0.766039i	$0.277775\pi$
$384$	1.06635	+	1.36488i	0.0544172	+	0.0696510i
$385$	−4.59496	+	1.67243i	−0.234181	+	0.0852349i
$386$	5.37510	−	9.30994i	0.273585	−	0.473863i
$387$	−26.7527	−	1.87081i	−1.35991	−	0.0950985i
$388$	8.66045	+	15.0003i	0.439668	+	0.761527i
$389$	−24.5222	−	20.5766i	−1.24332	−	1.04327i	−0.997257	−	0.0740208i	$-0.976417\pi$
$389$	−24.5222	−	20.5766i	−1.24332	−	1.04327i	−0.246068	−	0.969253i	$-0.579139\pi$
$390$	−1.33314	−	0.833043i	−0.0675063	−	0.0421828i
$391$	2.84698	+	16.1460i	0.143978	+	0.816538i
$392$	−1.42626	−	8.08871i	−0.0720369	−	0.408542i
$393$	−0.382071	+	10.9406i	−0.0192730	+	0.551882i
$394$	18.8495	+	15.8166i	0.949625	+	0.796830i
$395$	1.33184	+	2.30681i	0.0670119	+	0.116068i
$396$	−3.78562	−	1.68548i	−0.190234	−	0.0846985i
$397$	−5.12695	+	8.88013i	−0.257314	+	0.445681i	−0.965521	−	0.260323i	$-0.916171\pi$
$397$	−5.12695	+	8.88013i	−0.257314	+	0.445681i	0.708207	+	0.706004i	$0.249504\pi$
$398$	25.3439	−	9.22442i	1.27037	−	0.462378i
$399$	21.6619	−	3.04435i	1.08445	−	0.152408i
$400$	−3.19920	+	2.68445i	−0.159960	+	0.134222i
$401$	−31.3612	−	11.4145i	−1.56610	−	0.570014i	−0.593978	−	0.804481i	$-0.702443\pi$
$401$	−31.3612	−	11.4145i	−1.56610	−	0.570014i	−0.972124	+	0.234467i	$0.924666\pi$
$402$	8.10718	+	24.9515i	0.404350	+	1.24447i
$403$	−1.41315	+	8.01440i	−0.0703942	+	0.399226i
$404$	−1.65131			−0.0821560
$405$	−3.05990	−	7.57366i	−0.152048	−	0.376338i
$406$	−6.15180			−0.305309
$407$	−2.32098	+	13.1630i	−0.115047	+	0.652463i
$408$	4.22467	+	13.0023i	0.209152	+	0.643708i
$409$	10.6516	+	3.87687i	0.526688	+	0.191699i	0.591659	−	0.806188i	$-0.298473\pi$
$409$	10.6516	+	3.87687i	0.526688	+	0.191699i	−0.0649708	+	0.997887i	$0.520695\pi$
$410$	3.30979	−	2.77725i	0.163459	−	0.137158i
$411$	−31.1050	+	4.37147i	−1.53429	+	0.215629i
$412$	13.2128	−	4.80906i	0.650947	−	0.236925i
$413$	−16.6609	+	28.8575i	−0.819830	+	1.41999i
$414$	−0.651337	−	6.19723i	−0.0320114	−	0.304577i
$415$	−3.57501	−	6.19209i	−0.175490	−	0.303958i
$416$	−0.766044	−	0.642788i	−0.0375584	−	0.0315153i
$417$	−0.253496	+	7.25886i	−0.0124137	+	0.355468i
$418$	−0.776649	−	4.40460i	−0.0379872	−	0.215436i
$419$	−5.55517	−	31.5050i	−0.271388	−	1.53912i	−0.750206	−	0.661204i	$-0.770046\pi$
$419$	−5.55517	−	31.5050i	−0.271388	−	1.53912i	0.478818	−	0.877914i	$-0.341065\pi$
$420$	−5.19986	−	3.24924i	−0.253727	−	0.158547i
$421$	14.7612	+	12.3861i	0.719418	+	0.603664i	0.927224	−	0.374506i	$-0.122188\pi$
$421$	14.7612	+	12.3861i	0.719418	+	0.603664i	−0.207806	+	0.978170i	$0.566632\pi$
$422$	4.98117	+	8.62764i	0.242480	+	0.419987i
$423$	20.8094	−	30.8509i	1.01179	−	1.50002i
$424$	−1.24130	+	2.15000i	−0.0602830	+	0.104413i
$425$	−30.9759	+	11.2743i	−1.50255	+	0.546885i
$426$	−8.94563	−	11.4499i	−0.433417	−	0.554750i
$427$	−8.81275	+	7.39477i	−0.426479	+	0.357858i
$428$	−3.65241	−	1.32937i	−0.176546	−	0.0642574i
$429$	2.34019	+	0.497426i	0.112985	+	0.0240159i
$430$	−1.40887	+	7.99011i	−0.0679418	+	0.385317i
$431$	17.1701			0.827057			0.413528	−	0.910491i	$-0.364296\pi$
$431$	17.1701			0.827057			0.413528	+	0.910491i	$0.364296\pi$
$432$	−1.25704	−	5.04181i	−0.0604794	−	0.242574i
$433$	14.1258			0.678843			0.339421	−	0.940634i	$-0.389769\pi$
$433$	14.1258			0.678843			0.339421	+	0.940634i	$0.389769\pi$
$434$	−5.51194	+	31.2597i	−0.264581	+	1.50052i
$435$	−1.65904	+	1.84254i	−0.0795447	+	0.0883431i
$436$	−7.70493	−	2.80436i	−0.368999	−	0.134305i
$437$	5.15211	−	4.32313i	0.246459	−	0.206803i
$438$	−8.68727	+	21.5017i	−0.415094	+	1.02739i
$439$	−1.38873	+	0.505455i	−0.0662803	+	0.0241241i	−0.374948	−	0.927046i	$-0.622339\pi$
$439$	−1.38873	+	0.505455i	−0.0662803	+	0.0241241i	0.308667	+	0.951170i	$0.400117\pi$
$440$	−0.626833	+	1.08571i	−0.0298831	+	0.0517590i
$441$	−5.96114	+	23.9085i	−0.283864	+	1.13850i
$442$	−3.94659	−	6.83569i	−0.187720	−	0.325140i
$443$	4.89679	+	4.10890i	0.232654	+	0.195220i	0.751660	−	0.659551i	$-0.229253\pi$
$443$	4.89679	+	4.10890i	0.232654	+	0.195220i	−0.519006	+	0.854770i	$0.673698\pi$
$444$	−14.7983	+	7.86837i	−0.702297	+	0.373416i
$445$	−1.11725	−	6.33623i	−0.0529627	−	0.300366i
$446$	−1.23602	−	7.00984i	−0.0585274	−	0.331925i
$447$	14.7705	−	7.85360i	0.698622	−	0.371462i
$448$	−2.98792	−	2.50716i	−0.141166	−	0.118452i
$449$	9.15294	+	15.8534i	0.431954	+	0.748167i	0.997042	−	0.0768645i	$-0.0244909\pi$
$449$	9.15294	+	15.8534i	0.431954	+	0.748167i	−0.565087	+	0.825031i	$0.691158\pi$
$450$	12.0434	−	3.45336i	0.567733	−	0.162793i
$451$	−3.28781	+	5.69465i	−0.154817	+	0.268151i
$452$	−0.890445	+	0.324095i	−0.0418830	+	0.0152442i
$453$	−12.5375	+	31.0314i	−0.589065	+	1.45798i
$454$	5.88972	−	4.94206i	0.276418	−	0.231942i
$455$	3.32657	+	1.21077i	0.155952	+	0.0567619i
$456$	3.75268	−	4.16776i	0.175735	−	0.195173i
$457$	−2.15606	+	12.2276i	−0.100856	+	0.571985i	0.891938	+	0.452157i	$0.149345\pi$
$457$	−2.15606	+	12.2276i	−0.100856	+	0.571985i	−0.992795	+	0.119828i	$0.961766\pi$
$458$	−4.01697			−0.187701
$459$	4.28733	−	40.7894i	0.200115	−	1.90389i
$460$	−1.88520			−0.0878980
$461$	2.72081	−	15.4305i	0.126721	−	0.718670i	−0.853550	−	0.521011i	$-0.825555\pi$
$461$	2.72081	−	15.4305i	0.126721	−	0.718670i	0.980271	−	0.197659i	$-0.0633338\pi$
$462$	9.12778	+	1.94018i	0.424663	+	0.0902655i
$463$	−19.5612	−	7.11971i	−0.909088	−	0.330881i	−0.155199	−	0.987883i	$-0.549602\pi$
$463$	−19.5612	−	7.11971i	−0.909088	−	0.330881i	−0.753889	+	0.657002i	$0.771824\pi$
$464$	−1.20821	+	1.01381i	−0.0560897	+	0.0470648i
$465$	7.87621	+	10.0811i	0.365251	+	0.467501i
$466$	−5.63728	+	2.05180i	−0.261142	+	0.0950479i
$467$	−7.44903	+	12.9021i	−0.344700	+	0.597038i	−0.985299	−	0.170838i	$-0.945353\pi$
$467$	−7.44903	+	12.9021i	−0.344700	+	0.597038i	0.640599	+	0.767875i	$0.278686\pi$
$468$	1.31511	+	2.69639i	0.0607908	+	0.124640i
$469$	−29.5402	−	51.1651i	−1.36404	−	2.36259i
$470$	−8.62430	−	7.23665i	−0.397809	−	0.333802i
$471$	7.49868	+	4.68571i	0.345521	+	0.215906i
$472$	1.48349	+	8.41329i	0.0682831	+	0.387253i
$473$	−2.14418	−	12.1602i	−0.0985894	−	0.559129i
$474$	0.177412	−	5.08020i	0.00814880	−	0.233341i
$475$	10.3588	+	8.69208i	0.475295	+	0.398820i
$476$	−15.3935	−	26.6622i	−0.705558	−	1.22206i
$477$	6.02542	−	4.37770i	0.275885	−	0.200441i
$478$	10.2861	−	17.8160i	0.470474	−	0.814886i
$479$	−36.1389	+	13.1535i	−1.65123	+	0.600998i	−0.988949	−	0.148258i	$-0.952633\pi$
$479$	−36.1389	+	13.1535i	−1.65123	+	0.600998i	−0.662280	+	0.749256i	$0.730411\pi$
$480$	−1.55672	+	0.218780i	−0.0710541	+	0.00998589i
$481$	7.41259	−	6.21990i	0.337985	−	0.283603i
$482$	−5.01578	−	1.82560i	−0.228463	−	0.0831536i
$483$	4.33628	+	13.3458i	0.197308	+	0.607253i
$484$	−1.57881	+	8.95390i	−0.0717643	+	0.406996i
$485$	−15.7205			−0.713831
$486$	−2.70702	+	15.3516i	−0.122793	+	0.696363i
$487$	−17.1846			−0.778707			−0.389354	−	0.921088i	$-0.627302\pi$
$487$	−17.1846			−0.778707			−0.389354	+	0.921088i	$0.627302\pi$
$488$	−0.512169	+	2.90465i	−0.0231848	+	0.131488i
$489$	2.97764	+	9.16427i	0.134653	+	0.414422i
$490$	7.00503	+	2.54962i	0.316455	+	0.115180i
$491$	0.215114	−	0.180502i	0.00970798	−	0.00814596i	−0.637921	−	0.770102i	$-0.720205\pi$
$491$	0.215114	−	0.180502i	0.00970798	−	0.00814596i	0.647629	+	0.761956i	$0.275761\pi$
$492$	−8.16515	+	1.14752i	−0.368113	+	0.0517344i
$493$	−11.6984	+	4.25786i	−0.526868	+	0.191764i
$494$	−1.61897	+	2.80414i	−0.0728409	+	0.126164i
$495$	3.04272	−	2.21065i	0.136760	−	0.0993613i
$496$	4.06902	+	7.04774i	0.182704	+	0.316453i
$497$	25.0656	+	21.0325i	1.12434	+	0.943437i
$498$	−0.476222	+	13.6366i	−0.0213400	+	0.611072i
$499$	1.79934	+	10.2046i	0.0805496	+	0.456820i	0.998228	+	0.0594967i	$0.0189496\pi$
$499$	1.79934	+	10.2046i	0.0805496	+	0.456820i	−0.917679	+	0.397323i	$0.869939\pi$
$500$	−1.44621	−	8.20187i	−0.0646766	−	0.366799i
$501$	−21.1472	−	13.2143i	−0.944788	−	0.590371i
$502$	9.69749	+	8.13716i	0.432820	+	0.363179i
$503$	10.8631	+	18.8155i	0.484364	+	0.838943i	0.999839	−	0.0179620i	$-0.00571780\pi$
$503$	10.8631	+	18.8155i	0.484364	+	0.838943i	−0.515475	+	0.856905i	$0.672384\pi$
$504$	5.12950	+	10.5171i	0.228486	+	0.468469i
$505$	0.749369	−	1.29795i	0.0333465	−	0.0577578i
$506$	2.69608	−	0.981294i	0.119856	−	0.0436239i
$507$	−1.06635	−	1.36488i	−0.0473585	−	0.0606163i
$508$	−5.60997	+	4.70732i	−0.248902	+	0.208854i
$509$	8.44996	+	3.07553i	0.374538	+	0.136321i	0.522428	−	0.852683i	$-0.325026\pi$
$509$	8.44996	+	3.07553i	0.374538	+	0.136321i	−0.147891	+	0.989004i	$0.547248\pi$
$510$	−12.1370	−	2.57982i	−0.537437	−	0.114237i
$511$	9.06840	−	51.4294i	0.401162	−	2.27510i
$512$	−1.00000			−0.0441942
$513$	−15.3703	+	6.84321i	−0.678615	+	0.302135i
$514$	14.7220			0.649360
$515$	−2.21603	+	12.5677i	−0.0976498	+	0.553799i
$516$	10.3604	−	11.5064i	0.456092	−	0.506540i
$517$	16.1007	+	5.86018i	0.708109	+	0.257731i
$518$	28.9124	−	24.2604i	1.27034	−	1.06594i
$519$	5.41846	−	13.4111i	0.237844	−	0.588682i
$520$	0.852868	−	0.310419i	0.0374007	−	0.0136128i
$521$	17.0738	−	29.5726i	0.748015	−	1.29560i	−0.200757	−	0.979641i	$-0.564340\pi$
$521$	17.0738	−	29.5726i	0.748015	−	1.29560i	0.948773	−	0.315960i	$-0.102326\pi$
$522$	4.54832	−	1.30420i	0.199075	−	0.0570831i
$523$	−2.47588	−	4.28836i	−0.108263	−	0.187517i	0.806804	−	0.590820i	$-0.201195\pi$
$523$	−2.47588	−	4.28836i	−0.108263	−	0.187517i	−0.915067	+	0.403303i	$0.867862\pi$
$524$	−4.84173	−	4.06269i	−0.211512	−	0.177479i
$525$	−24.9114	+	13.2456i	−1.08722	+	0.578084i
$526$	−2.34487	−	13.2984i	−0.102241	−	0.579839i
$527$	11.1543	+	63.2590i	0.485888	+	2.75561i
$528$	2.11243	−	1.12319i	0.0919316	−	0.0488807i
$529$	−14.3140	−	12.0109i	−0.622347	−	0.522211i
$530$	−1.12661	−	1.95135i	−0.0489368	−	0.0847611i
$531$	6.20034	−	24.8679i	0.269072	−	1.07918i
$532$	−6.31471	+	10.9374i	−0.273778	+	0.474197i
$533$	4.47339	−	1.62818i	0.193764	−	0.0705243i
$534$	−4.59961	+	11.3844i	−0.199045	+	0.492651i
$535$	2.70236	−	2.26755i	0.116833	−	0.0980347i
$536$	−14.2336	−	5.18061i	−0.614798	−	0.223768i
$537$	20.1280	−	22.3544i	0.868588	−	0.964662i
$538$	2.60059	−	14.7487i	0.112119	−	0.635861i
$539$	−11.3452			−0.488674
$540$	4.53335	+	1.29994i	0.195084	+	0.0559404i
$541$	10.1071			0.434537			0.217269	−	0.976112i	$-0.430285\pi$
$541$	10.1071			0.434537			0.217269	+	0.976112i	$0.430285\pi$
$542$	−0.436731	+	2.47683i	−0.0187592	+	0.106389i
$543$	10.8800	+	2.31262i	0.466904	+	0.0992442i
$544$	−7.41715	−	2.69962i	−0.318008	−	0.115745i
$545$	5.70076	−	4.78351i	0.244194	−	0.204903i
$546$	−4.15926	−	5.32363i	−0.178000	−	0.227830i
$547$	−22.3056	+	8.11857i	−0.953719	+	0.347125i	−0.771569	−	0.636146i	$-0.780528\pi$
$547$	−22.3056	+	8.11857i	−0.953719	+	0.347125i	−0.182150	+	0.983271i	$0.558306\pi$
$548$	9.06747	−	15.7053i	0.387343	−	0.670898i
$549$	4.94798	−	7.33563i	0.211175	−	0.313077i
$550$	2.88432	+	4.99578i	0.122988	+	0.213021i
$551$	3.91211	+	3.28265i	0.166661	+	0.139846i
$552$	3.05100	+	1.90648i	0.129859	+	0.0811454i
$553$	1.98778	+	11.2733i	0.0845292	+	0.479389i
$554$	−4.77649	−	27.0888i	−0.202934	−	1.15089i
$555$	0.530897	−	15.2023i	0.0225353	−	0.645300i
$556$	−3.21238	−	2.69550i	−0.136235	−	0.114315i
$557$	−12.4092	−	21.4933i	−0.525794	−	0.910702i	−0.999549	−	0.0300447i	$-0.990435\pi$
$557$	−12.4092	−	21.4933i	−0.525794	−	0.910702i	0.473755	−	0.880657i	$-0.342898\pi$
$558$	−2.55190	−	24.2804i	−0.108030	−	1.02787i
$559$	−4.46967	+	7.74169i	−0.189047	+	0.327439i
$560$	3.32657	−	1.21077i	0.140573	−	0.0511644i
$561$	18.7004	−	2.62814i	0.789531	−	0.110960i
$562$	2.63370	−	2.20994i	0.111096	−	0.0932207i
$563$	26.5186	+	9.65198i	1.11763	+	0.406783i	0.833785	−	0.552089i	$-0.186169\pi$
$563$	26.5186	+	9.65198i	1.11763	+	0.406783i	0.283841	+	0.958871i	$0.408391\pi$
$564$	6.63919	+	20.4334i	0.279560	+	0.860402i
$565$	0.149344	−	0.846971i	0.00628295	−	0.0356324i
$566$	−26.1805			−1.10045
$567$	−1.22490	−	35.0827i	−0.0514411	−	1.47333i
$568$	8.38898			0.351994
$569$	3.88329	−	22.0233i	0.162796	−	0.923263i	−0.788512	−	0.615020i	$-0.789148\pi$
$569$	3.88329	−	22.0233i	0.162796	−	0.923263i	0.951308	−	0.308243i	$-0.0997409\pi$
$570$	1.57292	+	4.84097i	0.0658823	+	0.202766i
$571$	17.0503	+	6.20580i	0.713532	+	0.259705i	0.673178	−	0.739481i	$-0.264929\pi$
$571$	17.0503	+	6.20580i	0.713532	+	0.259705i	0.0403548	+	0.999185i	$0.487151\pi$
$572$	−1.05813	+	0.887878i	−0.0442427	+	0.0371240i
$573$	−1.94498	+	0.273346i	−0.0812527	+	0.0114192i
$574$	17.4482	−	6.35063i	0.728274	−	0.265070i
$575$	−4.33730	+	7.51242i	−0.180878	+	0.313289i
$576$	2.74063	+	1.22022i	0.114193	+	0.0508424i
$577$	10.6707	+	18.4821i	0.444225	+	0.769421i	0.997998	−	0.0632472i	$-0.0201456\pi$
$577$	10.6707	+	18.4821i	0.444225	+	0.769421i	−0.553773	+	0.832668i	$0.686812\pi$
$578$	−34.7035	−	29.1197i	−1.44347	−	1.21122i
$579$	0.649852	−	18.6085i	0.0270069	−	0.773344i
$580$	−0.248573	−	1.40973i	−0.0103214	−	0.0585358i
$581$	−5.33575	−	30.2606i	−0.221364	−	1.25542i
$582$	25.4420	+	15.8980i	1.05460	+	0.658992i
$583$	2.62692	+	2.20425i	0.108796	+	0.0912907i
$584$	−6.69446	−	11.5952i	−0.277019	−	0.479811i
$585$	−2.71618	−	0.189942i	−0.112300	−	0.00785312i
$586$	6.66518	−	11.5444i	0.275336	−	0.476896i
$587$	0.286366	−	0.104229i	0.0118196	−	0.00430198i	−0.336104	−	0.941825i	$-0.609109\pi$
$587$	0.286366	−	0.104229i	0.0118196	−	0.00430198i	0.347923	+	0.937523i	$0.386887\pi$
$588$	−8.75850	−	11.2104i	−0.361195	−	0.462309i
$589$	20.1856	−	16.9378i	0.831735	−	0.697908i
$590$	−7.28612	−	2.65193i	−0.299965	−	0.109178i
$591$	41.6880	+	8.86112i	1.71481	+	0.364498i
$592$	1.68030	−	9.52944i	0.0690598	−	0.391658i
$593$	1.55378			0.0638061			0.0319030	−	0.999491i	$-0.489843\pi$
$593$	1.55378			0.0638061			0.0319030	+	0.999491i	$0.489843\pi$
$594$	−7.15993	+	0.500639i	−0.293775	+	0.0205415i
$595$	27.9423			1.14552
$596$	−1.67714	+	9.51155i	−0.0686985	+	0.389608i
$597$	31.2579	−	34.7153i	1.27930	−	1.42080i
$598$	−1.95186	−	0.710417i	−0.0798173	−	0.0290511i
$599$	17.2187	−	14.4482i	0.703537	−	0.590338i	−0.219240	−	0.975671i	$-0.570358\pi$
$599$	17.2187	−	14.4482i	0.703537	−	0.590338i	0.922778	+	0.385333i	$0.125913\pi$
$600$	−2.70972	+	6.70677i	−0.110624	+	0.273803i
$601$	0.288027	−	0.104833i	0.0117489	−	0.00427624i	−0.336139	−	0.941812i	$-0.609121\pi$
$601$	0.288027	−	0.104833i	0.0117489	−	0.00427624i	0.347888	+	0.937536i	$0.386899\pi$
$602$	−17.4337	+	30.1961i	−0.710545	+	1.23070i
$603$	32.6876	+	31.5662i	1.33114	+	1.28548i
$604$	−9.66151	−	16.7342i	−0.393121	−	0.680906i
$605$	−6.32137	−	5.30426i	−0.257000	−	0.215649i
$606$	−2.52537	+	1.34276i	−0.102586	+	0.0545459i
$607$	5.36023	+	30.3994i	0.217565	+	1.23387i	0.876400	+	0.481585i	$0.159939\pi$
$607$	5.36023	+	30.3994i	0.217565	+	1.23387i	−0.658835	+	0.752288i	$0.728950\pi$
$608$	0.562263	+	3.18875i	0.0228028	+	0.129321i
$609$	−9.40802	+	5.00231i	−0.381232	+	0.202704i
$610$	−2.05066	−	1.72071i	−0.0830287	−	0.0696693i
$611$	−6.20217	−	10.7425i	−0.250913	−	0.434594i
$612$	17.0336	+	16.4492i	0.688541	+	0.664920i
$613$	−12.4819	+	21.6193i	−0.504139	+	0.873194i	0.495850	+	0.868408i	$0.334857\pi$
$613$	−12.4819	+	21.6193i	−0.504139	+	0.873194i	−0.999989	+	0.00478551i	$0.998477\pi$
$614$	−13.9770	+	5.08722i	−0.564067	+	0.205303i
$615$	2.80340	−	6.93862i	0.113044	−	0.279792i
$616$	−4.12719	+	3.46312i	−0.166289	+	0.139533i
$617$	16.9465	+	6.16803i	0.682241	+	0.248315i	0.659810	−	0.751433i	$-0.270637\pi$
$617$	16.9465	+	6.16803i	0.682241	+	0.248315i	0.0224317	+	0.999748i	$0.492859\pi$
$618$	16.2960	−	18.0985i	0.655521	−	0.728028i
$619$	1.81217	−	10.2773i	0.0728372	−	0.413080i	−0.926487	−	0.376326i	$-0.877187\pi$
$619$	1.81217	−	10.2773i	0.0728372	−	0.413080i	0.999324	−	0.0367538i	$-0.0117017\pi$
$620$	−7.38611			−0.296633
$621$	−6.03535	−	8.94786i	−0.242190	−	0.359065i
$622$	−24.1315			−0.967586
$623$	4.80140	−	27.2301i	0.192364	−	1.09095i
$624$	−1.69420	−	0.360116i	−0.0678223	−	0.0144162i
$625$	−12.5190	−	4.55653i	−0.500758	−	0.182261i
$626$	5.44849	−	4.57182i	0.217765	−	0.182727i
$627$	−4.76932	−	6.10447i	−0.190468	−	0.243789i
$628$	−4.79722	+	1.74605i	−0.191430	+	0.0696749i
$629$	38.1889	−	66.1452i	1.52269	−	2.63738i
$630$	−10.5943	−	0.740858i	−0.422087	−	0.0295165i
$631$	−17.5101	−	30.3283i	−0.697064	−	1.20735i	−0.969480	−	0.245171i	$-0.921156\pi$
$631$	−17.5101	−	30.3283i	−0.697064	−	1.20735i	0.272415	−	0.962180i	$-0.412178\pi$
$632$	2.24822	+	1.88648i	0.0894293	+	0.0750401i
$633$	14.6333	+	9.14392i	0.581621	+	0.363438i
$634$	2.88641	+	16.3696i	0.114634	+	0.650122i
$635$	−1.15418	−	6.54567i	−0.0458022	−	0.259757i
$636$	−0.150074	+	4.29738i	−0.00595083	+	0.170402i
$637$	6.29190	+	5.27953i	0.249294	+	0.209183i
$638$	1.08929	+	1.88671i	0.0431254	+	0.0746954i
$639$	−22.9911	−	10.2364i	−0.909514	−	0.404945i
$640$	0.453802	−	0.786008i	0.0179381	−	0.0310697i
$641$	−10.9415	+	3.98238i	−0.432163	+	0.157294i	−0.548936	−	0.835864i	$-0.684967\pi$
$641$	−10.9415	+	3.98238i	−0.432163	+	0.157294i	0.116773	+	0.993159i	$0.462745\pi$
$642$	−6.66663	+	0.936924i	−0.263111	+	0.0369775i
$643$	−11.9749	+	10.0481i	−0.472245	+	0.396260i	−0.847613	−	0.530616i	$-0.821961\pi$
$643$	−11.9749	+	10.0481i	−0.472245	+	0.396260i	0.375368	+	0.926876i	$0.377516\pi$
$644$	−7.61311	−	2.77095i	−0.299999	−	0.109191i
$645$	4.34252	+	13.3650i	0.170987	+	0.526246i
$646$	−4.43804	+	25.1694i	−0.174612	+	0.990275i
$647$	−8.12231			−0.319321			−0.159661	−	0.987172i	$-0.551040\pi$
$647$	−8.12231			−0.319321			−0.159661	+	0.987172i	$0.551040\pi$
$648$	−6.02214	−	6.68834i	−0.236572	−	0.262743i
$649$	11.8005			0.463210
$650$	0.725199	−	4.11281i	0.0284447	−	0.161318i
$651$	16.9893	+	52.2879i	0.665862	+	2.04932i
$652$	−5.22777	−	1.90275i	−0.204735	−	0.0745175i
$653$	−29.8954	+	25.0852i	−1.16990	+	0.981659i	−0.999993	−	0.00380183i	$-0.998790\pi$
$653$	−29.8954	+	25.0852i	−1.16990	+	0.981659i	−0.169903	+	0.985461i	$0.554345\pi$
$654$	−14.0636	+	1.97649i	−0.549930	+	0.0772868i
$655$	5.39049	−	1.96198i	0.210624	−	0.0766608i
$656$	2.38024	−	4.12270i	0.0929327	−	0.160964i
$657$	4.19845	+	39.9468i	0.163797	+	1.55847i
$658$	−24.1913	−	41.9005i	−0.943073	−	1.63345i
$659$	10.4679	+	8.78358i	0.407770	+	0.342160i	0.823488	−	0.567334i	$-0.192025\pi$
$659$	10.4679	+	8.78358i	0.407770	+	0.342160i	−0.415718	+	0.909494i	$0.636470\pi$
$660$	−0.0757845	+	2.17009i	−0.00294991	+	0.0844706i
$661$	4.69136	+	26.6060i	0.182473	+	1.03485i	0.929160	+	0.369679i	$0.120532\pi$
$661$	4.69136	+	26.6060i	0.182473	+	1.03485i	−0.746687	+	0.665176i	$0.768357\pi$
$662$	−2.64483	−	14.9996i	−0.102794	−	0.582975i
$663$	−11.5940	−	7.24474i	−0.450273	−	0.281362i
$664$	−6.03483	−	5.06382i	−0.234197	−	0.196514i
$665$	−5.73125	−	9.92682i	−0.222249	−	0.384946i
$666$	−16.2331	+	24.0664i	−0.629019	+	0.932553i
$667$	−1.63802	+	2.83714i	−0.0634245	+	0.109854i
$668$	13.5288	−	4.92407i	0.523444	−	0.190518i
$669$	−7.59029	−	9.71516i	−0.293457	−	0.375610i
$670$	10.5312	−	8.83675i	0.406857	−	0.341393i
$671$	3.82837	+	1.39341i	0.147793	+	0.0537922i
$672$	−6.60814	−	1.40461i	−0.254915	−	0.0541842i
$673$	2.59169	−	14.6982i	0.0999023	−	0.566574i	−0.893232	−	0.449596i	$-0.851568\pi$
$673$	2.59169	−	14.6982i	0.0999023	−	0.566574i	0.993134	−	0.116978i	$-0.0373208\pi$
$674$	5.96731			0.229852
$675$	15.6101	−	15.0743i	0.600832	−	0.580212i
$676$	1.00000			0.0384615
$677$	6.95022	−	39.4166i	0.267118	−	1.51490i	−0.495816	−	0.868428i	$-0.665131\pi$
$677$	6.95022	−	39.4166i	0.267118	−	1.51490i	0.762934	−	0.646476i	$-0.223758\pi$
$678$	−1.09823	+	1.21970i	−0.0421773	+	0.0468425i
$679$	−63.4849	−	23.1066i	−2.43633	−	0.886751i
$680$	5.48784	−	4.60485i	0.210449	−	0.176588i
$681$	4.98859	−	12.3472i	0.191163	−	0.473144i
$682$	10.5631	−	3.84465i	0.404482	−	0.147219i
$683$	8.81421	−	15.2667i	0.337267	−	0.584163i	−0.646651	−	0.762786i	$-0.723831\pi$
$683$	8.81421	−	15.2667i	0.337267	−	0.584163i	0.983918	+	0.178623i	$0.0571643\pi$
$684$	2.35002	−	9.42528i	0.0898551	−	0.360384i
$685$	8.22967	+	14.2542i	0.314439	+	0.544625i
$686$	3.62583	+	3.04243i	0.138435	+	0.116160i
$687$	−6.14320	+	3.26639i	−0.234378	+	0.124620i
$688$	1.55230	+	8.80352i	0.0591808	+	0.335631i
$689$	−0.431100	−	2.44489i	−0.0164236	−	0.0931428i
$690$	−2.88306	+	1.53295i	−0.109756	+	0.0583582i
$691$	30.1662	+	25.3125i	1.14758	+	0.962932i	0.999660	−	0.0260676i	$-0.00829851\pi$
$691$	30.1662	+	25.3125i	1.14758	+	0.962932i	0.147918	+	0.989000i	$0.452743\pi$
$692$	4.17550	+	7.23218i	0.158729	+	0.274926i
$693$	15.5369	−	4.45508i	0.590197	−	0.169234i
$694$	−16.9591	+	29.3741i	−0.643760	+	1.11503i
$695$	3.57647	−	1.30173i	0.135663	−	0.0493773i
$696$	−1.02335	+	2.53288i	−0.0387901	+	0.0960084i
$697$	28.7843	−	24.1529i	1.09028	−	0.914857i
$698$	−3.17676	−	1.15625i	−0.120242	−	0.0437646i
$699$	−6.95274	+	7.72178i	−0.262977	+	0.292065i
$700$	2.82860	−	16.0418i	0.106911	−	0.606323i
$701$	−10.5323			−0.397798			−0.198899	−	0.980020i	$-0.563737\pi$
$701$	−10.5323			−0.397798			−0.198899	+	0.980020i	$0.563737\pi$
$702$	4.20376	+	3.05424i	0.158661	+	0.115275i
$703$	−31.3318			−1.18170
$704$	−0.239859	+	1.36031i	−0.00904002	+	0.0512685i
$705$	−19.0737	−	4.05427i	−0.718357	−	0.152693i
$706$	20.0374	+	7.29300i	0.754116	+	0.274476i
$707$	4.93399	−	4.14011i	0.185562	−	0.155705i
$708$	9.10995	+	11.6602i	0.342373	+	0.438219i
$709$	10.0148	−	3.64508i	0.376113	−	0.136894i	−0.147045	−	0.989130i	$-0.546976\pi$
$709$	10.0148	−	3.64508i	0.376113	−	0.136894i	0.523158	+	0.852236i	$0.324754\pi$
$710$	−3.80693	+	6.59380i	−0.142872	+	0.247461i
$711$	−3.85963	−	7.91347i	−0.144747	−	0.296778i
$712$	−3.54449	−	6.13923i	−0.132835	−	0.230077i
$713$	12.9490	+	10.8655i	0.484943	+	0.406915i
$714$	−45.2217	−	28.2577i	−1.69238	−	1.05752i
$715$	−0.217697	−	1.23462i	−0.00814140	−	0.0461722i
$716$	3.01578	+	17.1033i	0.112705	+	0.639181i
$717$	1.24359	−	35.6103i	0.0464428	−	1.32989i
$718$	15.3493	+	12.8796i	0.572830	+	0.480662i
$719$	9.35999	+	16.2120i	0.349069	+	0.604604i	0.986084	−	0.166246i	$-0.0531647\pi$
$719$	9.35999	+	16.2120i	0.349069	+	0.604604i	−0.637016	+	0.770851i	$0.719831\pi$
$720$	−2.20280	+	1.60042i	−0.0820937	+	0.0596442i
$721$	−27.4216	+	47.4956i	−1.02123	+	1.76883i
$722$	−8.00217	+	2.91255i	−0.297810	+	0.108394i
$723$	−9.15517	+	1.28666i	−0.340485	+	0.0478515i
$724$	−4.91945	+	4.12791i	−0.182830	+	0.153412i
$725$	−6.18957	−	2.25282i	−0.229875	−	0.0836676i
$726$	4.86633	+	14.9771i	0.180607	+	0.555853i
$727$	−2.74090	+	15.5444i	−0.101654	+	0.576510i	0.890850	+	0.454298i	$0.150110\pi$
$727$	−2.74090	+	15.5444i	−0.101654	+	0.576510i	−0.992504	+	0.122212i	$0.961001\pi$
$728$	3.90045			0.144560
$729$	8.34323	+	25.6786i	0.309008	+	0.951059i
$730$	12.1518			0.449760
$731$	−12.2526	+	69.4877i	−0.453177	+	2.57010i
$732$	1.57864	+	4.85859i	0.0583483	+	0.179579i
$733$	2.39134	+	0.870378i	0.0883263	+	0.0321481i	0.385805	−	0.922580i	$-0.373924\pi$
$733$	2.39134	+	0.870378i	0.0883263	+	0.0321481i	−0.297479	+	0.954728i	$0.596146\pi$
$734$	7.31483	−	6.13787i	0.269995	−	0.226553i
$735$	12.7861	−	1.79695i	0.471622	−	0.0662814i
$736$	−1.95186	+	0.710417i	−0.0719464	+	0.0261863i
$737$	−10.4613	+	18.1195i	−0.385346	+	0.667439i
$738$	−11.5540	+	8.39438i	−0.425307	+	0.309002i
$739$	5.88976	+	10.2014i	0.216658	+	0.375263i	0.953784	−	0.300492i	$-0.0971510\pi$
$739$	5.88976	+	10.2014i	0.216658	+	0.375263i	−0.737126	+	0.675755i	$0.763818\pi$
$740$	6.72769	+	5.64521i	0.247315	+	0.207522i
$741$	−0.195734	+	5.60486i	−0.00719049	+	0.205900i
$742$	−1.68148	−	9.53616i	−0.0617292	−	0.350084i
$743$	1.56781	+	8.89150i	0.0575174	+	0.326197i	0.999967	−	0.00815148i	$-0.00259473\pi$
$743$	1.56781	+	8.89150i	0.0575174	+	0.326197i	−0.942449	+	0.334349i	$0.891484\pi$
$744$	11.9536	+	7.46949i	0.438242	+	0.273845i
$745$	−6.71506	−	5.63461i	−0.246021	−	0.206436i
$746$	12.8322	+	22.2260i	0.469821	+	0.813753i
$747$	10.3603	+	21.2419i	0.379063	+	0.777200i
$748$	−5.45139	+	9.44208i	−0.199323	+	0.345237i
$749$	14.2460	−	5.18513i	0.520538	−	0.189460i
$750$	−8.88103	−	11.3672i	−0.324289	−	0.415073i
$751$	2.80987	−	2.35776i	0.102534	−	0.0860359i	−0.590080	−	0.807345i	$-0.700904\pi$
$751$	2.80987	−	2.35776i	0.102534	−	0.0860359i	0.692613	+	0.721309i	$0.256459\pi$
$752$	−11.6563	−	4.24254i	−0.425061	−	0.154709i
$753$	21.4472	+	4.55877i	0.781578	+	0.166131i
$754$	0.273879	−	1.55324i	0.00997407	−	0.0565657i
$755$	17.5376			0.638260
$756$	16.3966	+	11.9129i	0.596337	+	0.433268i
$757$	12.3875			0.450232			0.225116	−	0.974332i	$-0.427724\pi$
$757$	12.3875			0.450232			0.225116	+	0.974332i	$0.427724\pi$
$758$	2.35806	−	13.3732i	0.0856486	−	0.485737i
$759$	3.32522	−	3.69302i	0.120698	−	0.134048i
$760$	−2.76154	−	1.00512i	−0.100172	−	0.0364594i
$761$	−15.6882	+	13.1639i	−0.568696	+	0.477193i	−0.881213	−	0.472719i	$-0.843272\pi$
$761$	−15.6882	+	13.1639i	−0.568696	+	0.477193i	0.312517	+	0.949912i	$0.398828\pi$
$762$	−4.75165	+	11.7607i	−0.172134	+	0.426045i
$763$	30.0527	−	10.9383i	1.08798	−	0.395992i
$764$	0.566985	−	0.982047i	0.0205128	−	0.0355292i
$765$	−20.6591	+	5.92383i	−0.746930	+	0.214176i
$766$	0.000156350	0	0.000270806i	5.64914e−6	0	9.78460e-6i
$767$	−6.54438	−	5.49138i	−0.236304	−	0.198282i
$768$	−1.52931	+	0.813146i	−0.0551843	+	0.0293419i
$769$	−1.18864	−	6.74111i	−0.0428635	−	0.243091i	0.955847	−	0.293866i	$-0.0949419\pi$
$769$	−1.18864	−	6.74111i	−0.0428635	−	0.243091i	−0.998710	+	0.0507752i	$0.983831\pi$
$770$	−0.849115	−	4.81557i	−0.0306000	−	0.173541i
$771$	22.5145	−	11.9711i	0.810841	−	0.431130i
$772$	8.23512	+	6.91009i	0.296389	+	0.248700i
$773$	−0.743994	−	1.28864i	−0.0267596	−	0.0463490i	0.852335	−	0.522995i	$-0.175186\pi$
$773$	−0.743994	−	1.28864i	−0.0267596	−	0.0463490i	−0.879095	+	0.476646i	$0.841852\pi$
$774$	6.48794	−	26.0214i	0.233204	−	0.935319i
$775$	−16.9933	+	29.4332i	−0.610416	+	1.05727i
$776$	−16.2763	+	5.92410i	−0.584286	+	0.212663i
$777$	24.4888	−	60.6118i	0.878532	−	2.17443i
$778$	24.5222	−	20.5766i	0.879163	−	0.737706i
$779$	−14.4846	−	5.27195i	−0.518964	−	0.188887i
$780$	1.05189	−	1.16823i	0.0376635	−	0.0418295i
$781$	2.01217	−	11.4116i	0.0720012	−	0.408339i
$782$	−16.3951			−0.586287
$783$	5.89530	−	5.69297i	0.210681	−	0.203450i
$784$	8.21350			0.293339
$785$	0.804582	−	4.56301i	0.0287168	−	0.162861i
$786$	−10.7081	−	2.27609i	−0.381944	−	0.0811853i
$787$	27.2365	+	9.91329i	0.970877	+	0.353370i	0.778287	−	0.627909i	$-0.216089\pi$
$787$	27.2365	+	9.91329i	0.970877	+	0.353370i	0.192590	+	0.981279i	$0.438311\pi$
$788$	−18.8495	+	15.8166i	−0.671486	+	0.563444i
$789$	−14.3996	−	18.4307i	−0.512640	−	0.656151i
$790$	−2.50303	+	0.911029i	−0.0890539	+	0.0324130i
$791$	1.84802	−	3.20086i	0.0657079	−	0.113809i
$792$	2.31724	−	3.43542i	0.0823394	−	0.122072i
$793$	−1.47473	−	2.55431i	−0.0523692	−	0.0907062i
$794$	−7.85494	−	6.59108i	−0.278761	−	0.233909i
$795$	−3.30967	−	2.06812i	−0.117382	−	0.0733486i
$796$	4.68336	+	26.5607i	0.165997	+	0.941418i
$797$	−5.09213	−	28.8789i	−0.180373	−	1.02294i	−0.931758	−	0.363080i	$-0.881725\pi$
$797$	−5.09213	−	28.8789i	−0.180373	−	1.02294i	0.751385	−	0.659864i	$-0.229386\pi$
$798$	−0.763452	+	21.8615i	−0.0270259	+	0.773888i
$799$	−75.0031	−	62.9351i	−2.65342	−	2.22648i
$800$	−2.08813	−	3.61674i	−0.0738265	−	0.127871i
$801$	2.22294	+	21.1504i	0.0785436	+	0.747314i
$802$	16.6869	−	28.9026i	0.589236	−	1.02059i
$803$	−17.3787	+	6.32533i	−0.613281	+	0.223216i
$804$	−25.9802	+	3.65124i	−0.916251	+	0.128769i
$805$	5.63283	−	4.72650i	0.198531	−	0.166587i
$806$	−7.64725	−	2.78337i	−0.269363	−	0.0980401i
$807$	−8.01572	−	24.6700i	−0.282167	−	0.868424i
$808$	0.286748	−	1.62623i	0.0100877	−	0.0572105i
$809$	9.02720			0.317379			0.158690	−	0.987329i	$-0.449273\pi$
$809$	9.02720			0.317379			0.158690	+	0.987329i	$0.449273\pi$
$810$	7.98994	−	1.69826i	0.280738	−	0.0596709i
$811$	−13.5416			−0.475508			−0.237754	−	0.971325i	$-0.576411\pi$
$811$	−13.5416			−0.475508			−0.237754	+	0.971325i	$0.576411\pi$
$812$	1.06825	−	6.05834i	0.0374882	−	0.212606i
$813$	1.34612	+	4.14297i	0.0472106	+	0.145300i
$814$	−12.5599	−	4.57145i	−0.440226	−	0.160229i
$815$	3.86795	−	3.24559i	0.135488	−	0.113688i
$816$	−13.5383	+	1.90267i	−0.473936	+	0.0666067i
$817$	27.1994	−	9.89979i	0.951588	−	0.346350i
$818$	−5.66760	+	9.81658i	−0.198163	+	0.343229i
$819$	−10.6897	−	4.75940i	−0.373528	−	0.166307i
$820$	2.16031	+	3.74177i	0.0754414	+	0.130668i
$821$	−7.25641	−	6.08885i	−0.253250	−	0.212502i	0.507320	−	0.861758i	$-0.330636\pi$
$821$	−7.25641	−	6.08885i	−0.253250	−	0.212502i	−0.760570	+	0.649255i	$0.775081\pi$
$822$	1.09626	−	31.3915i	0.0382365	−	1.09490i
$823$	6.93645	+	39.3386i	0.241789	+	1.37126i	0.827832	+	0.560976i	$0.189574\pi$
$823$	6.93645	+	39.3386i	0.241789	+	1.37126i	−0.586043	+	0.810280i	$0.699315\pi$
$824$	2.44162	+	13.8471i	0.0850580	+	0.482388i
$825$	8.47332	+	5.29473i	0.295003	+	0.184339i
$826$	−25.5260	−	21.4189i	−0.888163	−	0.745257i
$827$	−12.3350	−	21.3649i	−0.428930	−	0.742929i	0.567848	−	0.823133i	$-0.307776\pi$
$827$	−12.3350	−	21.3649i	−0.428930	−	0.742929i	−0.996778	+	0.0802044i	$0.974443\pi$
$828$	6.21618	+	0.434697i	0.216027	+	0.0151067i
$829$	−15.1683	+	26.2723i	−0.526817	+	0.912475i	0.472694	+	0.881227i	$0.343282\pi$
$829$	−15.1683	+	26.2723i	−0.526817	+	0.912475i	−0.999512	+	0.0312481i	$0.990052\pi$
$830$	6.71882	−	2.44545i	0.233214	−	0.0848828i
$831$	−29.3319	−	37.5433i	−1.01751	−	1.30236i
$832$	0.766044	−	0.642788i	0.0265578	−	0.0222847i
$833$	60.9208	+	22.1733i	2.11078	+	0.768261i
$834$	−7.10456	−	1.51013i	−0.246011	−	0.0522916i
$835$	−2.26902	+	12.8683i	−0.0785228	+	0.445325i
$836$	4.47255			0.154686
$837$	−23.6461	−	35.0572i	−0.817330	−	1.21175i
$838$	31.9910			1.10511
$839$	3.66968	−	20.8118i	0.126691	−	0.718503i	−0.853597	−	0.520933i	$-0.825584\pi$
$839$	3.66968	−	20.8118i	0.126691	−	0.718503i	0.980289	−	0.197570i	$-0.0633049\pi$
$840$	4.10282	−	4.55663i	0.141561	−	0.157219i
$841$	24.9135	+	9.06778i	0.859087	+	0.312682i
$842$	−14.7612	+	12.3861i	−0.508706	+	0.426855i
$843$	2.23075	−	5.52127i	0.0768311	−	0.190163i
$844$	−9.36154	+	3.40732i	−0.322237	+	0.117285i
$845$	−0.453802	+	0.786008i	−0.0156113	+	0.0270395i
$846$	26.7687	+	25.8504i	0.920328	+	0.888756i
$847$	−17.7315	−	30.7119i	−0.609261	−	1.05527i
$848$	−1.90179	−	1.59579i	−0.0653076	−	0.0547996i
$849$	−40.0382	+	21.2886i	−1.37411	+	0.730623i
$850$	−5.72412	−	32.4631i	−0.196336	−	1.11348i
$851$	−3.49018	−	19.7938i	−0.119642	−	0.678523i
$852$	12.8294	−	6.82147i	0.439527	−	0.233700i
$853$	−40.4009	−	33.9004i	−1.38330	−	1.16073i	−0.967973	−	0.251054i	$-0.919223\pi$
$853$	−40.4009	−	33.9004i	−1.38330	−	1.16073i	−0.415327	−	0.909672i	$-0.636333\pi$
$854$	−5.75211	−	9.96295i	−0.196833	−	0.340925i
$855$	6.34190	+	6.12434i	0.216888	+	0.209448i
$856$	1.94340	−	3.36608i	0.0664242	−	0.115050i
$857$	−24.1118	+	8.77599i	−0.823645	+	0.299782i	−0.719248	−	0.694753i	$-0.755513\pi$
$857$	−24.1118	+	8.77599i	−0.823645	+	0.299782i	−0.104397	+	0.994536i	$0.533291\pi$
$858$	−0.896238	+	2.21826i	−0.0305971	+	0.0757301i
$859$	−13.6477	+	11.4518i	−0.465655	+	0.390731i	−0.845207	−	0.534439i	$-0.820523\pi$
$859$	−13.6477	+	11.4518i	−0.465655	+	0.390731i	0.379552	+	0.925171i	$0.376078\pi$
$860$	−7.62407	−	2.77494i	−0.259979	−	0.0946245i
$861$	21.5198	−	23.9000i	0.733391	−	0.814511i
$862$	−2.98157	+	16.9093i	−0.101553	+	0.575933i
$863$	36.3897			1.23872			0.619360	−	0.785107i	$-0.287392\pi$
$863$	36.3897			1.23872			0.619360	+	0.785107i	$0.287392\pi$
$864$	5.18350	−	0.362442i	0.176346	−	0.0123305i
$865$	−7.57939			−0.257707
$866$	−2.45292	+	13.9112i	−0.0833536	+	0.472722i
$867$	−76.7509	−	16.3140i	−2.60660	−	0.554054i
$868$	−29.8277	−	10.8564i	−1.01242	−	0.368490i
$869$	3.10545	−	2.60578i	0.105345	−	0.0883950i
$870$	−1.52646	−	1.95379i	−0.0517519	−	0.0662396i
$871$	14.2336	−	5.18061i	0.482287	−	0.175538i
$872$	4.09971	−	7.10090i	0.138834	−	0.240467i
$873$	51.8361	+	3.62489i	1.75439	+	0.122684i
$874$	3.36280	+	5.82454i	0.113748	+	0.197018i
$875$	24.8846	+	20.8806i	0.841252	+	0.705894i
$876$	−19.6665	−	12.2890i	−0.664469	−	0.415207i
$877$	3.07903	+	17.4620i	0.103971	+	0.589651i	0.991626	+	0.129142i	$0.0412221\pi$
$877$	3.07903	+	17.4620i	0.103971	+	0.589651i	−0.887655	+	0.460509i	$0.847667\pi$
$878$	−0.256626	−	1.45540i	−0.00866072	−	0.0491174i
$879$	0.805823	−	23.0748i	0.0271798	−	0.778293i
$880$	−0.960364	−	0.805841i	−0.0323739	−	0.0271649i
$881$	0.656523	+	1.13713i	0.0221188	+	0.0383109i	0.876873	−	0.480722i	$-0.159625\pi$
$881$	0.656523	+	1.13713i	0.0221188	+	0.0383109i	−0.854754	+	0.519033i	$0.826292\pi$
$882$	−22.5102	−	10.0223i	−0.757957	−	0.337467i
$883$	16.9437	−	29.3473i	0.570200	−	0.987616i	−0.426345	−	0.904561i	$-0.640199\pi$
$883$	16.9437	−	29.3473i	0.570200	−	0.987616i	0.996545	−	0.0830552i	$-0.0264678\pi$
$884$	7.41715	−	2.69962i	0.249466	−	0.0907982i
$885$	−13.2991	+	1.86905i	−0.447046	+	0.0628275i
$886$	−4.89679	+	4.10890i	−0.164511	+	0.138041i
$887$	30.6479	+	11.1549i	1.02905	+	0.374545i	0.800721	−	0.599038i	$-0.204450\pi$
$887$	30.6479	+	11.1549i	1.02905	+	0.374545i	0.228333	+	0.973583i	$0.426672\pi$
$888$	−5.17913	−	15.9398i	−0.173800	−	0.534905i
$889$	4.96011	−	28.1302i	0.166357	−	0.943456i
$890$	6.43398			0.215667
$891$	−10.5427	+	6.58770i	−0.353192	+	0.220696i
$892$	7.11798			0.238327
$893$	−6.97450	+	39.5544i	−0.233393	+	1.32364i
$894$	5.16941	+	15.9099i	0.172891	+	0.532106i
$895$	−14.8119	−	5.39109i	−0.495107	−	0.180204i
$896$	2.98792	−	2.50716i	0.0998193	−	0.0837583i
$897$	−3.56267	+	0.500695i	−0.118954	+	0.0167177i
$898$	−17.2019	+	6.26098i	−0.574035	+	0.208932i
$899$	−6.41767	+	11.1157i	−0.214041	+	0.370730i
$900$	1.30958	+	12.4601i	0.0436525	+	0.415338i
$901$	−9.79781	−	16.9703i	−0.326412	−	0.565363i
$902$	−5.03721	−	4.22672i	−0.167721	−	0.140735i
$903$	−2.10774	+	60.3553i	−0.0701413	+	2.00850i
$904$	−0.164548	−	0.933196i	−0.00547277	−	0.0310376i
$905$	−1.01211	−	5.73998i	−0.0336438	−	0.190803i
$906$	−28.3828	−	17.7356i	−0.942956	−	0.589226i
$907$	22.8585	+	19.1806i	0.759005	+	0.636881i	0.937868	−	0.346993i	$-0.112797\pi$
$907$	22.8585	+	19.1806i	0.759005	+	0.636881i	−0.178863	+	0.983874i	$0.557242\pi$
$908$	3.84424	+	6.65842i	0.127576	+	0.220967i
$909$	−2.77022	+	4.10700i	−0.0918825	+	0.136220i
$910$	−1.77003	+	3.06578i	−0.0586759	+	0.101630i
$911$	54.1023	−	19.6916i	1.79249	−	0.652413i	0.793447	−	0.608639i	$-0.208284\pi$
$911$	54.1023	−	19.6916i	1.79249	−	0.652413i	0.999041	−	0.0437738i	$-0.0139381\pi$
$912$	3.45280	+	4.41939i	0.114333	+	0.146341i
$913$	−8.33586	+	6.99462i	−0.275877	+	0.231488i
$914$	−11.6675	−	4.24662i	−0.385926	−	0.140466i
$915$	−4.53528	−	0.964010i	−0.149932	−	0.0318692i
$916$	0.697540	−	3.95595i	0.0230474	−	0.130708i
$917$	24.6525			0.814097
$918$	39.4253	+	11.3052i	1.30123	+	0.373127i
$919$	44.3239			1.46211			0.731055	−	0.682319i	$-0.239028\pi$
$919$	44.3239			1.46211			0.731055	+	0.682319i	$0.239028\pi$
$920$	0.327362	−	1.85656i	0.0107928	−	0.0612090i
$921$	−17.2386	+	19.1453i	−0.568030	+	0.630859i
$922$	14.7236	+	5.35896i	0.484896	+	0.176488i
$923$	−6.42633	+	5.39233i	−0.211525	+	0.177491i
$924$	−3.49573	+	8.65220i	−0.115001	+	0.284636i
$925$	37.9742	−	13.8215i	1.24859	−	0.454448i
$926$	10.4083	−	18.0277i	0.342039	−	0.592428i
$927$	10.2049	−	40.9292i	0.335174	−	1.34429i
$928$	−0.788602	−	1.36590i	−0.0258871	−	0.0448378i
$929$	26.6221	+	22.3386i	0.873442	+	0.732905i	0.964820	−	0.262912i	$-0.0846828\pi$
$929$	26.6221	+	22.3386i	0.873442	+	0.732905i	−0.0913782	+	0.995816i	$0.529127\pi$
$930$	−11.2957	+	6.00598i	−0.370399	+	0.196944i
$931$	−4.61814	−	26.1908i	−0.151354	−	0.858368i
$932$	−1.04173	−	5.90793i	−0.0341229	−	0.193521i
$933$	−36.9046	+	19.6225i	−1.20820	+	0.642410i
$934$	−11.4126	−	9.57629i	−0.373431	−	0.313346i
$935$	−4.94770	−	8.56967i	−0.161807	−	0.280258i
$936$	−2.88379	+	0.826903i	−0.0942595	+	0.0270282i
$937$	−1.61203	+	2.79212i	−0.0526628	+	0.0912147i	−0.891155	−	0.453699i	$-0.850104\pi$
$937$	−1.61203	+	2.79212i	−0.0526628	+	0.0912147i	0.838492	+	0.544914i	$0.183438\pi$
$938$	55.5174	−	20.2067i	1.81271	−	0.659772i
$939$	4.61487	−	11.4222i	0.150601	−	0.372748i
$940$	8.62430	−	7.23665i	0.281294	−	0.236033i
$941$	26.0615	+	9.48560i	0.849580	+	0.309222i	0.729869	−	0.683587i	$-0.239581\pi$
$941$	26.0615	+	9.48560i	0.849580	+	0.309222i	0.119711	+	0.992809i	$0.461803\pi$
$942$	−5.91666	+	6.57109i	−0.192775	+	0.214098i
$943$	1.71705	−	9.73787i	0.0559148	−	0.317109i
$944$	−8.54308			−0.278053
$945$	−16.8044	+	7.48172i	−0.546648	+	0.243380i
$946$	12.3478			0.401463
$947$	−8.81402	+	49.9868i	−0.286417	+	1.62435i	0.413762	+	0.910385i	$0.364214\pi$
$947$	−8.81402	+	49.9868i	−0.286417	+	1.62435i	−0.700179	+	0.713967i	$0.746897\pi$
$948$	4.97221	+	1.05688i	0.161490	+	0.0343260i
$949$	12.5815	+	4.57928i	0.408412	+	0.148650i
$950$	−10.3588	+	8.69208i	−0.336084	+	0.282008i
$951$	17.7251	+	22.6872i	0.574777	+	0.735683i
$952$	28.9302	−	10.5297i	0.937634	−	0.341271i
$953$	−16.2033	+	28.0649i	−0.524875	+	0.909110i	0.474705	+	0.880145i	$0.342555\pi$
$953$	−16.2033	+	28.0649i	−0.524875	+	0.909110i	−0.999580	+	0.0289656i	$0.990779\pi$
$954$	3.26489	+	6.69406i	0.105705	+	0.216728i
$955$	0.514597	+	0.891309i	0.0166520	+	0.0288421i
$956$	15.7592	+	13.2235i	0.509689	+	0.427680i
$957$	3.20003	+	1.99961i	0.103442	+	0.0646381i
$958$	−6.67820	−	37.8740i	−0.215763	−	1.22365i
$959$	12.2829	+	69.6598i	0.396636	+	2.24943i
$960$	0.0548649	−	1.57106i	0.00177076	−	0.0507057i
$961$	26.9859	+	22.6438i	0.870513	+	0.730447i
$962$	4.83823	+	8.38005i	0.155991	+	0.270184i
$963$	−9.43350	+	6.85380i	−0.303990	+	0.220861i
$964$	2.66884	−	4.62257i	0.0859577	−	0.148883i
$965$	−9.16850	+	3.33706i	−0.295144	+	0.107424i
$966$	−13.8960	+	1.95293i	−0.447097	+	0.0628346i
$967$	−10.9290	+	9.17054i	−0.351454	+	0.294905i	−0.801373	−	0.598164i	$-0.795897\pi$
$967$	−10.9290	+	9.17054i	−0.351454	+	0.294905i	0.449920	+	0.893069i	$0.351453\pi$
$968$	−8.54371	−	3.10966i	−0.274605	−	0.0999482i
$969$	13.6792	+	42.1005i	0.439440	+	1.35246i
$970$	2.72984	−	15.4817i	0.0876498	−	0.497087i
$971$	−34.0152			−1.09160			−0.545800	−	0.837916i	$-0.683774\pi$
$971$	−34.0152			−1.09160			−0.545800	+	0.837916i	$0.683774\pi$
$972$	−14.6483	−	5.33168i	−0.469845	−	0.171014i
$973$	16.3564			0.524361
$974$	2.98407	−	16.9235i	0.0956158	−	0.542264i
$975$	−2.23526	−	6.87946i	−0.0715856	−	0.220319i
$976$	−2.77159	−	1.00878i	−0.0887164	−	0.0322901i
$977$	−45.1629	+	37.8962i	−1.44489	+	1.21241i	−0.508685	+	0.860952i	$0.669868\pi$
$977$	−45.1629	+	37.8962i	−1.44489	+	1.21241i	−0.936205	+	0.351455i	$0.885687\pi$
$978$	−9.54210	+	1.34104i	−0.305123	+	0.0428817i
$979$	−9.20142	+	3.34904i	−0.294079	+	0.107036i
$980$	−3.72730	+	6.45587i	−0.119064	+	0.206225i
$981$	−19.9004	+	14.4584i	−0.635372	+	0.461622i
$982$	0.140406	+	0.243190i	0.00448053	+	0.00776051i
$983$	−3.73849	−	3.13697i	−0.119239	−	0.100054i	0.581218	−	0.813748i	$-0.302576\pi$
$983$	−3.73849	−	3.13697i	−0.119239	−	0.100054i	−0.700458	+	0.713694i	$0.747021\pi$
$984$	0.287772	−	8.24037i	0.00917385	−	0.262693i
$985$	−3.87804	−	21.9935i	−0.123565	−	0.700770i
$986$	−2.16177	−	12.2600i	−0.0688448	−	0.390438i
$987$	−71.0672	−	44.4079i	−2.26209	−	1.41352i
$988$	−2.48041	−	2.08131i	−0.0789123	−	0.0662153i
$989$	9.28404	+	16.0804i	0.295215	+	0.511328i
$990$	1.64870	+	3.38037i	0.0523992	+	0.107435i
$991$	−5.64134	+	9.77109i	−0.179203	+	0.310389i	−0.941608	−	0.336712i	$-0.890685\pi$
$991$	−5.64134	+	9.77109i	−0.179203	+	0.310389i	0.762405	+	0.647100i	$0.224019\pi$
$992$	−7.64725	+	2.78337i	−0.242800	+	0.0883721i
$993$	−16.2416	−	20.7884i	−0.515412	−	0.659699i
$994$	−25.0656	+	21.0325i	−0.795032	+	0.667111i
$995$	−23.0022	−	8.37212i	−0.729219	−	0.265414i
$996$	−13.3468	−	2.83696i	−0.422908	−	0.0898926i
$997$	−7.06191	+	40.0501i	−0.223653	+	1.26840i	0.641591	+	0.767047i	$0.278275\pi$
$997$	−7.06191	+	40.0501i	−0.223653	+	1.26840i	−0.865244	+	0.501352i	$0.832836\pi$
$998$	−10.3620			−0.328003
$999$	−5.25595	+	50.0049i	−0.166291	+	1.58208i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.w.d.79.7	✓	66
27.13	even	9	inner	702.2.w.d.391.7	yes	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
702.2.w.d.79.7	✓	66	1.1	even	1	trivial
702.2.w.d.391.7	yes	66	27.13	even	9	inner

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:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.w (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 + 0.984808i) q^{2} +(0.535231 + 1.64728i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.695265 - 0.583396i) q^{5} +(-1.71519 + 0.241052i) q^{6} +(3.66522 - 1.33403i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.42706 + 1.76335i) q^{9} +(0.453802 + 0.786008i) q^{10} +(-1.05813 - 0.887878i) q^{11} +(0.0604503 - 1.73100i) q^{12} +(0.173648 + 0.984808i) q^{13} +(0.677306 + 3.84119i) q^{14} +(1.33314 + 0.833043i) q^{15} +(0.766044 + 0.642788i) q^{16} +(3.94659 + 6.83569i) q^{17} +(-1.31511 - 2.69639i) q^{18} +(1.61897 - 2.80414i) q^{19} +(-0.852868 + 0.310419i) q^{20} +(4.15926 + 5.32363i) q^{21} +(1.05813 - 0.887878i) q^{22} +(1.95186 + 0.710417i) q^{23} +(1.69420 + 0.360116i) q^{24} +(-0.725199 + 4.11281i) q^{25} -1.00000 q^{26} +(-4.20376 - 3.05424i) q^{27} -3.90045 q^{28} +(-0.273879 + 1.55324i) q^{29} +(-1.05189 + 1.16823i) q^{30} +(7.64725 + 2.78337i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(0.896238 - 2.21826i) q^{33} +(-7.41715 + 2.69962i) q^{34} +(1.77003 - 3.06578i) q^{35} +(2.88379 - 0.826903i) q^{36} +(-4.83823 - 8.38005i) q^{37} +(2.48041 + 2.08131i) q^{38} +(-1.52931 + 0.813146i) q^{39} +(-0.157604 - 0.893815i) q^{40} +(-0.826649 - 4.68816i) q^{41} +(-5.96500 + 3.17164i) q^{42} +(6.84793 + 5.74609i) q^{43} +(0.690646 + 1.19623i) q^{44} +(-0.658715 + 2.64193i) q^{45} +(-1.03856 + 1.79884i) q^{46} +(-11.6563 + 4.24254i) q^{47} +(-0.648840 + 1.60593i) q^{48} +(6.29190 - 5.27953i) q^{49} +(-3.92440 - 1.42836i) q^{50} +(-9.14795 + 10.1598i) q^{51} +(0.173648 - 0.984808i) q^{52} -2.48261 q^{53} +(3.73782 - 3.60953i) q^{54} -1.25367 q^{55} +(0.677306 - 3.84119i) q^{56} +(5.48572 + 1.16604i) q^{57} +(-1.48209 - 0.539435i) q^{58} +(-6.54438 + 5.49138i) q^{59} +(-0.967827 - 1.23877i) q^{60} +(-2.77159 + 1.00878i) q^{61} +(-4.06902 + 7.04774i) q^{62} +(-6.54334 + 9.70083i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.695265 + 0.583396i) q^{65} +(2.02893 + 1.26782i) q^{66} +(-2.63026 - 14.9170i) q^{67} +(-1.37063 - 7.77326i) q^{68} +(-0.125563 + 3.59549i) q^{69} +(2.71184 + 2.27551i) q^{70} +(4.19449 + 7.26507i) q^{71} +(0.313577 + 2.98357i) q^{72} +(6.69446 - 11.5952i) q^{73} +(9.09289 - 3.30954i) q^{74} +(-7.16309 + 1.00670i) q^{75} +(-2.48041 + 2.08131i) q^{76} +(-5.06274 - 1.84269i) q^{77} +(-0.535231 - 1.64728i) q^{78} +(-0.509630 + 2.89025i) q^{79} +0.907603 q^{80} +(2.78120 - 8.55949i) q^{81} +4.76048 q^{82} +(1.36798 - 7.75822i) q^{83} +(-2.08764 - 6.42513i) q^{84} +(6.73183 + 2.45019i) q^{85} +(-6.84793 + 5.74609i) q^{86} +(-2.70521 + 0.380189i) q^{87} +(-1.29799 + 0.472430i) q^{88} +(3.54449 - 6.13923i) q^{89} +(-2.48741 - 1.10747i) q^{90} +(1.95022 + 3.37789i) q^{91} +(-1.59117 - 1.33515i) q^{92} +(-0.491946 + 14.0869i) q^{93} +(-2.15399 - 12.2159i) q^{94} +(-0.510312 - 2.89412i) q^{95} +(-1.46886 - 0.917849i) q^{96} +(-13.2686 - 11.1337i) q^{97} +(4.10675 + 7.11310i) q^{98} +(4.13378 + 0.289075i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 3 q^{5} + 9 q^{6} - 3 q^{7} + 33 q^{8} - 6 q^{9} - 9 q^{10} - 3 q^{11} + 3 q^{14} - 27 q^{15} + 12 q^{17} - 12 q^{18} - 21 q^{19} - 6 q^{20} - 18 q^{21} + 3 q^{22} - 3 q^{25} - 66 q^{26} + 9 q^{27}+ \cdots - 15 q^{99}+O(q^{100}) \) 66 * q + 3 * q^5 + 9 * q^6 - 3 * q^7 + 33 * q^8 - 6 * q^9 - 9 * q^10 - 3 * q^11 + 3 * q^14 - 27 * q^15 + 12 * q^17 - 12 * q^18 - 21 * q^19 - 6 * q^20 - 18 * q^21 + 3 * q^22 - 3 * q^25 - 66 * q^26 + 9 * q^27 + 18 * q^28 + 39 * q^29 + 9 * q^30 - 9 * q^31 + 15 * q^33 - 6 * q^34 - 9 * q^35 - 3 * q^36 - 21 * q^37 + 6 * q^38 - 3 * q^40 + 6 * q^41 + 9 * q^42 - 6 * q^43 + 3 * q^44 - 9 * q^45 - 9 * q^46 - 36 * q^47 + 9 * q^48 - 9 * q^49 + 3 * q^50 + 21 * q^51 - 60 * q^53 + 27 * q^54 + 84 * q^55 + 3 * q^56 + 87 * q^57 + 24 * q^58 - 30 * q^59 + 6 * q^60 - 12 * q^61 + 21 * q^62 - 60 * q^63 - 33 * q^64 + 3 * q^65 + 24 * q^66 - 3 * q^67 + 15 * q^68 - 87 * q^69 - 21 * q^70 + 3 * q^71 + 6 * q^72 - 15 * q^73 + 6 * q^74 - 117 * q^75 - 6 * q^76 + 27 * q^77 + 27 * q^79 - 18 * q^80 + 78 * q^81 + 24 * q^82 - 24 * q^83 + 33 * q^84 + 45 * q^85 + 6 * q^86 + 18 * q^87 - 6 * q^88 + 36 * q^89 - 87 * q^90 - 9 * q^91 - 63 * q^93 - 36 * q^94 + 63 * q^95 - 102 * q^97 + 72 * q^98 - 15 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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