LMFDB - Embedded newform 855.2.i.d.286.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(286,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("855.286");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$46$
Relative dimension:	$23$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			286.4
Character	$\chi$	$=$	855.286
Dual form			855.2.i.d.571.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.04031 + 1.80187i) q^{2} +(-0.431939 + 1.67733i) q^{3} +(-1.16450 - 2.01698i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.57298 - 2.52325i) q^{6} +(1.56804 - 2.71593i) q^{7} +0.684535 q^{8} +(-2.62686 - 1.44901i) q^{9} +O(q^{10})$	\(q+(-1.04031 + 1.80187i) q^{2} +(-0.431939 + 1.67733i) q^{3} +(-1.16450 - 2.01698i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.57298 - 2.52325i) q^{6} +(1.56804 - 2.71593i) q^{7} +0.684535 q^{8} +(-2.62686 - 1.44901i) q^{9} -2.08063 q^{10} +(-1.70578 + 2.95449i) q^{11} +(3.88613 - 1.08204i) q^{12} +(-1.25747 - 2.17800i) q^{13} +(3.26251 + 5.65084i) q^{14} +(-1.66858 + 0.464594i) q^{15} +(1.61687 - 2.80051i) q^{16} -5.45624 q^{17} +(5.34368 - 3.22585i) q^{18} +1.00000 q^{19} +(1.16450 - 2.01698i) q^{20} +(3.87821 + 3.80324i) q^{21} +(-3.54908 - 6.14719i) q^{22} +(-3.03944 - 5.26446i) q^{23} +(-0.295678 + 1.14819i) q^{24} +(-0.500000 + 0.866025i) q^{25} +5.23266 q^{26} +(3.56510 - 3.78022i) q^{27} -7.30396 q^{28} +(4.50812 - 7.80830i) q^{29} +(0.898704 - 3.48989i) q^{30} +(-3.88170 - 6.72329i) q^{31} +(4.04864 + 7.01246i) q^{32} +(-4.21886 - 4.13730i) q^{33} +(5.67619 - 9.83145i) q^{34} +3.13609 q^{35} +(0.136368 + 6.98568i) q^{36} +4.69810 q^{37} +(-1.04031 + 1.80187i) q^{38} +(4.19638 - 1.16843i) q^{39} +(0.342268 + 0.592825i) q^{40} +(-1.32140 - 2.28873i) q^{41} +(-10.8875 + 3.03149i) q^{42} +(-1.87151 + 3.24155i) q^{43} +7.94552 q^{44} +(-0.0585521 - 2.99943i) q^{45} +12.6479 q^{46} +(-5.23631 + 9.06955i) q^{47} +(3.99898 + 3.92168i) q^{48} +(-1.41752 - 2.45523i) q^{49} +(-1.04031 - 1.80187i) q^{50} +(2.35676 - 9.15190i) q^{51} +(-2.92866 + 5.07258i) q^{52} -9.54211 q^{53} +(3.10266 + 10.3565i) q^{54} -3.41155 q^{55} +(1.07338 - 1.85915i) q^{56} +(-0.431939 + 1.67733i) q^{57} +(9.37971 + 16.2461i) q^{58} +(-1.95822 - 3.39174i) q^{59} +(2.88014 + 2.82446i) q^{60} +(1.66255 - 2.87963i) q^{61} +16.1527 q^{62} +(-8.05443 + 4.86226i) q^{63} -10.3799 q^{64} +(1.25747 - 2.17800i) q^{65} +(11.8438 - 3.29776i) q^{66} +(-1.16052 - 2.01008i) q^{67} +(6.35380 + 11.0051i) q^{68} +(10.1431 - 2.82421i) q^{69} +(-3.26251 + 5.65084i) q^{70} +15.4614 q^{71} +(-1.79818 - 0.991896i) q^{72} -12.5970 q^{73} +(-4.88749 + 8.46539i) q^{74} +(-1.23664 - 1.21273i) q^{75} +(-1.16450 - 2.01698i) q^{76} +(5.34946 + 9.26554i) q^{77} +(-2.26019 + 8.77688i) q^{78} +(-5.43732 + 9.41772i) q^{79} +3.23375 q^{80} +(4.80076 + 7.61267i) q^{81} +5.49868 q^{82} +(2.39979 - 4.15655i) q^{83} +(3.15487 - 12.2511i) q^{84} +(-2.72812 - 4.72524i) q^{85} +(-3.89392 - 6.74446i) q^{86} +(11.1498 + 10.9343i) q^{87} +(-1.16766 + 2.02245i) q^{88} +3.98461 q^{89} +(5.46551 + 3.01484i) q^{90} -7.88708 q^{91} +(-7.07886 + 12.2609i) q^{92} +(12.9538 - 3.60682i) q^{93} +(-10.8948 - 18.8703i) q^{94} +(0.500000 + 0.866025i) q^{95} +(-13.5110 + 3.76195i) q^{96} +(-7.72363 + 13.3777i) q^{97} +5.89868 q^{98} +(8.76190 - 5.28934i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q + 3 q^{2} + 2 q^{3} - 29 q^{4} + 23 q^{5} + 3 q^{6} - 10 q^{7} - 12 q^{8} - 8 q^{9}+O(q^{10}) $ 46 * q + 3 * q^2 + 2 * q^3 - 29 * q^4 + 23 * q^5 + 3 * q^6 - 10 * q^7 - 12 * q^8 - 8 * q^9	\( 46 q + 3 q^{2} + 2 q^{3} - 29 q^{4} + 23 q^{5} + 3 q^{6} - 10 q^{7} - 12 q^{8} - 8 q^{9} + 6 q^{10} - q^{11} + 9 q^{12} - 11 q^{13} - 3 q^{14} + q^{15} - 45 q^{16} - 30 q^{17} - 18 q^{18} + 46 q^{19} + 29 q^{20} - 2 q^{21} - 5 q^{22} + 13 q^{23} - 6 q^{24} - 23 q^{25} - 12 q^{26} + 23 q^{27} + 56 q^{28} + 2 q^{29} + 6 q^{30} - 16 q^{31} + 25 q^{32} + 19 q^{33} - 18 q^{34} - 20 q^{35} - 5 q^{36} + 58 q^{37} + 3 q^{38} + 32 q^{39} - 6 q^{40} + 14 q^{41} - 67 q^{42} - 34 q^{43} + 64 q^{44} - 7 q^{45} - 4 q^{46} + 22 q^{47} + 89 q^{48} - 61 q^{49} + 3 q^{50} - 38 q^{51} - 20 q^{52} - 70 q^{53} - 91 q^{54} - 2 q^{55} - 26 q^{56} + 2 q^{57} - 23 q^{58} - 15 q^{59} + 3 q^{60} - 32 q^{61} + 6 q^{62} - 31 q^{63} + 164 q^{64} + 11 q^{65} + 54 q^{66} - 16 q^{67} + 26 q^{68} - 19 q^{69} + 3 q^{70} + 50 q^{71} + 22 q^{72} + 82 q^{73} + 9 q^{74} - q^{75} - 29 q^{76} + 18 q^{77} - 41 q^{78} - 11 q^{79} - 90 q^{80} + 8 q^{81} + 60 q^{82} + 26 q^{83} + 123 q^{84} - 15 q^{85} - 15 q^{86} - 26 q^{87} - 22 q^{88} + 40 q^{89} - 12 q^{90} + 116 q^{91} + 2 q^{92} + 42 q^{93} - 36 q^{94} + 23 q^{95} - 48 q^{96} - 50 q^{97} - 24 q^{98} - 29 q^{99}+O(q^{100}) \) 46 * q + 3 * q^2 + 2 * q^3 - 29 * q^4 + 23 * q^5 + 3 * q^6 - 10 * q^7 - 12 * q^8 - 8 * q^9 + 6 * q^10 - q^11 + 9 * q^12 - 11 * q^13 - 3 * q^14 + q^15 - 45 * q^16 - 30 * q^17 - 18 * q^18 + 46 * q^19 + 29 * q^20 - 2 * q^21 - 5 * q^22 + 13 * q^23 - 6 * q^24 - 23 * q^25 - 12 * q^26 + 23 * q^27 + 56 * q^28 + 2 * q^29 + 6 * q^30 - 16 * q^31 + 25 * q^32 + 19 * q^33 - 18 * q^34 - 20 * q^35 - 5 * q^36 + 58 * q^37 + 3 * q^38 + 32 * q^39 - 6 * q^40 + 14 * q^41 - 67 * q^42 - 34 * q^43 + 64 * q^44 - 7 * q^45 - 4 * q^46 + 22 * q^47 + 89 * q^48 - 61 * q^49 + 3 * q^50 - 38 * q^51 - 20 * q^52 - 70 * q^53 - 91 * q^54 - 2 * q^55 - 26 * q^56 + 2 * q^57 - 23 * q^58 - 15 * q^59 + 3 * q^60 - 32 * q^61 + 6 * q^62 - 31 * q^63 + 164 * q^64 + 11 * q^65 + 54 * q^66 - 16 * q^67 + 26 * q^68 - 19 * q^69 + 3 * q^70 + 50 * q^71 + 22 * q^72 + 82 * q^73 + 9 * q^74 - q^75 - 29 * q^76 + 18 * q^77 - 41 * q^78 - 11 * q^79 - 90 * q^80 + 8 * q^81 + 60 * q^82 + 26 * q^83 + 123 * q^84 - 15 * q^85 - 15 * q^86 - 26 * q^87 - 22 * q^88 + 40 * q^89 - 12 * q^90 + 116 * q^91 + 2 * q^92 + 42 * q^93 - 36 * q^94 + 23 * q^95 - 48 * q^96 - 50 * q^97 - 24 * q^98 - 29 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.04031	+	1.80187i	−0.735612	+	1.27412i	0.218842	+	0.975760i	$0.429772\pi$
$2$	−1.04031	+	1.80187i	−0.735612	+	1.27412i	−0.954454	+	0.298358i	$0.903561\pi$
$3$	−0.431939	+	1.67733i	−0.249380	+	0.968406i
$3$	−0.431939	+	1.67733i	−0.249380	+	0.968406i
$4$	−1.16450	−	2.01698i	−0.582251	−	1.00849i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−2.57298	−	2.52325i	−1.05042	−	1.03011i
$7$	1.56804	−	2.71593i	0.592665	−	1.02653i	−0.401207	−	0.915987i	$-0.631409\pi$
$7$	1.56804	−	2.71593i	0.592665	−	1.02653i	0.993872	−	0.110538i	$-0.0352575\pi$
$8$	0.684535			0.242020
$9$	−2.62686	−	1.44901i	−0.875619	−	0.483002i
$10$	−2.08063			−0.657952
$11$	−1.70578	+	2.95449i	−0.514311	+	0.890812i	0.485552	+	0.874208i	$0.338619\pi$
$11$	−1.70578	+	2.95449i	−0.514311	+	0.890812i	−0.999862	+	0.0166040i	$0.994715\pi$
$12$	3.88613	−	1.08204i	1.12183	−	0.312358i
$13$	−1.25747	−	2.17800i	−0.348760	−	0.604070i	0.637270	−	0.770641i	$-0.280064\pi$
$13$	−1.25747	−	2.17800i	−0.348760	−	0.604070i	−0.986029	+	0.166571i	$0.946730\pi$
$14$	3.26251	+	5.65084i	0.871943	+	1.51025i
$15$	−1.66858	+	0.464594i	−0.430825	+	0.119958i
$16$	1.61687	−	2.80051i	0.404218	−	0.700127i
$17$	−5.45624			−1.32333			−0.661666	−	0.749799i	$-0.730150\pi$
$17$	−5.45624			−1.32333			−0.661666	+	0.749799i	$0.730150\pi$
$18$	5.34368	−	3.22585i	1.25952	−	0.760340i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	1.16450	−	2.01698i	0.260391	−	0.451010i
$21$	3.87821	+	3.80324i	0.846295	+	0.829935i
$22$	−3.54908	−	6.14719i	−0.756666	−	1.31058i
$23$	−3.03944	−	5.26446i	−0.633766	−	1.09772i	−0.986775	−	0.162095i	$-0.948175\pi$
$23$	−3.03944	−	5.26446i	−0.633766	−	1.09772i	0.353009	−	0.935620i	$-0.385159\pi$
$24$	−0.295678	+	1.14819i	−0.0603549	+	0.234373i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	5.23266			1.02621
$27$	3.56510	−	3.78022i	0.686104	−	0.727503i
$28$	−7.30396			−1.38032
$29$	4.50812	−	7.80830i	0.837137	−	1.44996i	−0.0551413	−	0.998479i	$-0.517561\pi$
$29$	4.50812	−	7.80830i	0.837137	−	1.44996i	0.892278	−	0.451485i	$-0.149106\pi$
$30$	0.898704	−	3.48989i	0.164080	−	0.637164i
$31$	−3.88170	−	6.72329i	−0.697173	−	1.20754i	−0.969443	−	0.245318i	$-0.921108\pi$
$31$	−3.88170	−	6.72329i	−0.697173	−	1.20754i	0.272270	−	0.962221i	$-0.412226\pi$
$32$	4.04864	+	7.01246i	0.715706	+	1.23964i
$33$	−4.21886	−	4.13730i	−0.734409	−	0.720212i
$34$	5.67619	−	9.83145i	0.973459	−	1.68608i
$35$	3.13609			0.530096
$36$	0.136368	+	6.98568i	0.0227280	+	1.16428i
$37$	4.69810			0.772363			0.386181	−	0.922423i	$-0.373794\pi$
$37$	4.69810			0.772363			0.386181	+	0.922423i	$0.373794\pi$
$38$	−1.04031	+	1.80187i	−0.168761	+	0.292303i
$39$	4.19638	−	1.16843i	0.671958	−	0.187098i
$40$	0.342268	+	0.592825i	0.0541173	+	0.0937339i
$41$	−1.32140	−	2.28873i	−0.206368	−	0.357440i	0.744200	−	0.667957i	$-0.232831\pi$
$41$	−1.32140	−	2.28873i	−0.206368	−	0.357440i	−0.950568	+	0.310517i	$0.899498\pi$
$42$	−10.8875	+	3.03149i	−1.67998	+	0.467769i
$43$	−1.87151	+	3.24155i	−0.285403	+	0.494332i	−0.972707	−	0.232038i	$-0.925461\pi$
$43$	−1.87151	+	3.24155i	−0.285403	+	0.494332i	0.687304	+	0.726370i	$0.258794\pi$
$44$	7.94552			1.19783
$45$	−0.0585521	−	2.99943i	−0.00872843	−	0.447128i
$46$	12.6479			1.86483
$47$	−5.23631	+	9.06955i	−0.763794	+	1.32293i	0.177088	+	0.984195i	$0.443332\pi$
$47$	−5.23631	+	9.06955i	−0.763794	+	1.32293i	−0.940882	+	0.338735i	$0.890001\pi$
$48$	3.99898	+	3.92168i	0.577203	+	0.566045i
$49$	−1.41752	−	2.45523i	−0.202504	−	0.350746i
$50$	−1.04031	−	1.80187i	−0.147122	−	0.254824i
$51$	2.35676	−	9.15190i	0.330013	−	1.28152i
$52$	−2.92866	+	5.07258i	−0.406132	+	0.703441i
$53$	−9.54211			−1.31071			−0.655355	−	0.755321i	$-0.727481\pi$
$53$	−9.54211			−1.31071			−0.655355	+	0.755321i	$0.727481\pi$
$54$	3.10266	+	10.3565i	0.422218	+	1.40934i
$55$	−3.41155			−0.460013
$56$	1.07338	−	1.85915i	0.143437	−	0.248440i
$57$	−0.431939	+	1.67733i	−0.0572117	+	0.222167i
$58$	9.37971	+	16.2461i	1.23162	+	2.13322i
$59$	−1.95822	−	3.39174i	−0.254939	−	0.441567i	0.709940	−	0.704262i	$-0.248722\pi$
$59$	−1.95822	−	3.39174i	−0.254939	−	0.441567i	−0.964879	+	0.262695i	$0.915389\pi$
$60$	2.88014	+	2.82446i	0.371824	+	0.364637i
$61$	1.66255	−	2.87963i	0.212868	−	0.368699i	−0.739743	−	0.672890i	$-0.765053\pi$
$61$	1.66255	−	2.87963i	0.212868	−	0.368699i	0.952611	+	0.304191i	$0.0983861\pi$
$62$	16.1527			2.05140
$63$	−8.05443	+	4.86226i	−1.01476	+	0.612587i
$64$	−10.3799			−1.29749
$65$	1.25747	−	2.17800i	0.155970	−	0.270148i
$66$	11.8438	−	3.29776i	1.45788	−	0.405926i
$67$	−1.16052	−	2.01008i	−0.141780	−	0.245570i	0.786387	−	0.617734i	$-0.211949\pi$
$67$	−1.16052	−	2.01008i	−0.141780	−	0.245570i	−0.928167	+	0.372164i	$0.878616\pi$
$68$	6.35380	+	11.0051i	0.770511	+	1.33456i
$69$	10.1431	−	2.82421i	1.22108	−	0.339995i
$70$	−3.26251	+	5.65084i	−0.389945	+	0.675404i
$71$	15.4614			1.83493			0.917465	−	0.397816i	$-0.130232\pi$
$71$	15.4614			1.83493			0.917465	+	0.397816i	$0.130232\pi$
$72$	−1.79818	−	0.991896i	−0.211917	−	0.116896i
$73$	−12.5970			−1.47436			−0.737182	−	0.675694i	$-0.763844\pi$
$73$	−12.5970			−1.47436			−0.737182	+	0.675694i	$0.763844\pi$
$74$	−4.88749	+	8.46539i	−0.568160	+	0.984081i
$75$	−1.23664	−	1.21273i	−0.142795	−	0.140034i
$76$	−1.16450	−	2.01698i	−0.133578	−	0.231363i
$77$	5.34946	+	9.26554i	0.609628	+	1.05591i
$78$	−2.26019	+	8.77688i	−0.255916	+	0.993786i
$79$	−5.43732	+	9.41772i	−0.611747	+	1.05958i	0.379199	+	0.925315i	$0.376199\pi$
$79$	−5.43732	+	9.41772i	−0.611747	+	1.05958i	−0.990946	+	0.134261i	$0.957134\pi$
$80$	3.23375			0.361544
$81$	4.80076	+	7.61267i	0.533418	+	0.845852i
$82$	5.49868			0.607228
$83$	2.39979	−	4.15655i	0.263411	−	0.456241i	−0.703735	−	0.710462i	$-0.748486\pi$
$83$	2.39979	−	4.15655i	0.263411	−	0.456241i	0.967146	+	0.254221i	$0.0818192\pi$
$84$	3.15487	−	12.2511i	0.344224	−	1.33671i
$85$	−2.72812	−	4.72524i	−0.295906	−	0.512524i
$86$	−3.89392	−	6.74446i	−0.419892	−	0.727274i
$87$	11.1498	+	10.9343i	1.19539	+	1.17228i
$88$	−1.16766	+	2.02245i	−0.124473	+	0.215594i
$89$	3.98461			0.422368			0.211184	−	0.977446i	$-0.432268\pi$
$89$	3.98461			0.422368			0.211184	+	0.977446i	$0.432268\pi$
$90$	5.46551	+	3.01484i	0.576115	+	0.317792i
$91$	−7.88708			−0.826791
$92$	−7.07886	+	12.2609i	−0.738022	+	1.27829i
$93$	12.9538	−	3.60682i	1.34325	−	0.374010i
$94$	−10.8948	−	18.8703i	−1.12371	−	1.94633i
$95$	0.500000	+	0.866025i	0.0512989	+	0.0888523i
$96$	−13.5110	+	3.76195i	−1.37896	+	0.383952i
$97$	−7.72363	+	13.3777i	−0.784216	+	1.35830i	0.145250	+	0.989395i	$0.453601\pi$
$97$	−7.72363	+	13.3777i	−0.784216	+	1.35830i	−0.929466	+	0.368907i	$0.879732\pi$
$98$	5.89868			0.595856
$99$	8.76190	−	5.28934i	0.880604	−	0.531599i
$100$	2.32900			0.232900
$101$	−2.77567	+	4.80760i	−0.276189	+	0.478374i	−0.970434	−	0.241365i	$-0.922405\pi$
$101$	−2.77567	+	4.80760i	−0.276189	+	0.478374i	0.694245	+	0.719739i	$0.255738\pi$
$102$	14.0388	+	13.7674i	1.39005	+	1.36318i
$103$	−5.69735	−	9.86809i	−0.561376	−	0.972332i	−0.997377	−	0.0723856i	$-0.976939\pi$
$103$	−5.69735	−	9.86809i	−0.561376	−	0.972332i	0.436001	−	0.899946i	$-0.356395\pi$
$104$	−0.860784	−	1.49092i	−0.0844068	−	0.146197i
$105$	−1.35460	+	5.26025i	−0.132195	+	0.513348i
$106$	9.92678	−	17.1937i	0.964174	−	1.67000i
$107$	8.62397			0.833711			0.416855	−	0.908973i	$-0.363132\pi$
$107$	8.62397			0.833711			0.416855	+	0.908973i	$0.363132\pi$
$108$	−11.7762	−	2.78866i	−1.13316	−	0.268338i
$109$	−6.00193			−0.574881			−0.287441	−	0.957798i	$-0.592804\pi$
$109$	−6.00193			−0.574881			−0.287441	+	0.957798i	$0.592804\pi$
$110$	3.54908	−	6.14719i	0.338391	−	0.586111i
$111$	−2.02929	+	7.88025i	−0.192612	+	0.747960i
$112$	−5.07066	−	8.78264i	−0.479132	−	0.829881i
$113$	−9.38548	−	16.2561i	−0.882911	−	1.52925i	−0.848089	−	0.529854i	$-0.822247\pi$
$113$	−9.38548	−	16.2561i	−0.882911	−	1.52925i	−0.0348222	−	0.999394i	$-0.511087\pi$
$114$	−2.57298	−	2.52325i	−0.240982	−	0.236324i
$115$	3.03944	−	5.26446i	0.283429	−	0.490913i
$116$	−20.9989			−1.94970
$117$	0.147255	+	7.54339i	0.0136137	+	0.697387i
$118$	8.14865			0.750144
$119$	−8.55562	+	14.8188i	−0.784292	+	1.35843i
$120$	−1.14220	+	0.318031i	−0.104268	+	0.0290321i
$121$	−0.319337	−	0.553107i	−0.0290306	−	0.0502825i
$122$	3.45915	+	5.99143i	0.313177	+	0.542439i
$123$	4.40972	−	1.22783i	0.397611	−	0.110710i
$124$	−9.04049	+	15.6586i	−0.811860	+	1.40618i
$125$	−1.00000			−0.0894427
$126$	−0.382054	−	19.5714i	−0.0340361	−	1.74355i
$127$	12.4711			1.10663			0.553314	−	0.832973i	$-0.313363\pi$
$127$	12.4711			1.10663			0.553314	+	0.832973i	$0.313363\pi$
$128$	2.70109	−	4.67843i	0.238745	−	0.413519i
$129$	−4.62877	−	4.53929i	−0.407540	−	0.399662i
$130$	2.61633	+	4.53161i	0.229467	+	0.397449i
$131$	−6.91920	−	11.9844i	−0.604533	−	1.04708i	−0.992125	−	0.125251i	$-0.960026\pi$
$131$	−6.91920	−	11.9844i	−0.604533	−	1.04708i	0.387592	−	0.921831i	$-0.373307\pi$
$132$	−3.43198	+	13.3272i	−0.298715	+	1.15999i
$133$	1.56804	−	2.71593i	0.135967	−	0.235501i
$134$	4.82922			0.417181
$135$	5.05632	+	1.19736i	0.435178	+	0.103052i
$136$	−3.73499			−0.320272
$137$	−3.98037	+	6.89420i	−0.340066	+	0.589011i	−0.984445	−	0.175695i	$-0.943783\pi$
$137$	−3.98037	+	6.89420i	−0.340066	+	0.589011i	0.644379	+	0.764706i	$0.277116\pi$
$138$	−5.46311	+	21.2146i	−0.465050	+	1.80591i
$139$	2.10243	+	3.64152i	0.178326	+	0.308870i	0.941307	−	0.337551i	$-0.109598\pi$
$139$	2.10243	+	3.64152i	0.178326	+	0.308870i	−0.762981	+	0.646421i	$0.776265\pi$
$140$	−3.65198	−	6.32542i	−0.308649	−	0.534595i
$141$	−12.9508	−	12.7005i	−1.09066	−	1.06957i
$142$	−16.0847	+	27.8595i	−1.34980	+	2.33792i
$143$	8.57985			0.717483
$144$	−8.30525	+	5.01367i	−0.692104	+	0.417806i
$145$	9.01624			0.748758
$146$	13.1048	−	22.6982i	1.08456	−	1.87851i
$147$	4.73050	−	1.31715i	0.390165	−	0.108636i
$148$	−5.47095	−	9.47596i	−0.449709	−	0.778919i
$149$	4.38896	+	7.60190i	0.359557	+	0.622772i	0.987887	−	0.155176i	$-0.0495943\pi$
$149$	4.38896	+	7.60190i	0.359557	+	0.622772i	−0.628329	+	0.777947i	$0.716261\pi$
$150$	3.47169	−	0.966646i	0.283462	−	0.0789263i
$151$	0.498340	−	0.863149i	0.0405543	−	0.0702421i	−0.845036	−	0.534710i	$-0.820421\pi$
$151$	0.498340	−	0.863149i	0.0405543	−	0.0702421i	0.885590	+	0.464468i	$0.153754\pi$
$152$	0.684535			0.0555232
$153$	14.3328	+	7.90612i	1.15873	+	0.639172i
$154$	−22.2605			−1.79380
$155$	3.88170	−	6.72329i	0.311785	−	0.540028i
$156$	−7.24338	−	7.10336i	−0.579935	−	0.568724i
$157$	−4.96639	−	8.60205i	−0.396361	−	0.686518i	0.596912	−	0.802306i	$-0.296394\pi$
$157$	−4.96639	−	8.60205i	−0.396361	−	0.686518i	−0.993274	+	0.115788i	$0.963061\pi$
$158$	−11.3130	−	19.5948i	−0.900017	−	1.55887i
$159$	4.12161	−	16.0052i	0.326865	−	1.26930i
$160$	−4.04864	+	7.01246i	−0.320073	+	0.554383i
$161$	−19.0639			−1.50244
$162$	−18.7114	+	0.730810i	−1.47010	+	0.0574179i
$163$	−15.8720			−1.24319			−0.621597	−	0.783337i	$-0.713516\pi$
$163$	−15.8720			−1.24319			−0.621597	+	0.783337i	$0.713516\pi$
$164$	−3.07755	+	5.33047i	−0.240316	+	0.416240i
$165$	1.47358	−	5.72229i	0.114718	−	0.445480i
$166$	4.99306	+	8.64823i	0.387536	+	0.671233i
$167$	0.235447	+	0.407807i	0.0182195	+	0.0315570i	0.874991	−	0.484138i	$-0.160867\pi$
$167$	0.235447	+	0.407807i	0.0182195	+	0.0315570i	−0.856772	+	0.515696i	$0.827534\pi$
$168$	2.65477	+	2.60345i	0.204820	+	0.200861i
$169$	3.33753	−	5.78077i	0.256733	−	0.444675i
$170$	11.3524			0.870688
$171$	−2.62686	−	1.44901i	−0.200881	−	0.110808i
$172$	8.71752			0.664705
$173$	6.63391	−	11.4903i	0.504367	−	0.873588i	−0.495621	−	0.868539i	$-0.665059\pi$
$173$	6.63391	−	11.4903i	0.504367	−	0.873588i	0.999987	−	0.00504940i	$-0.00160728\pi$
$174$	−31.3016	+	8.71551i	−2.37297	+	0.660721i
$175$	1.56804	+	2.71593i	0.118533	+	0.205305i
$176$	5.51604	+	9.55407i	0.415788	+	0.720165i
$177$	6.53489	−	1.81955i	0.491192	−	0.136766i
$178$	−4.14524	+	7.17977i	−0.310699	+	0.538147i
$179$	5.00218			0.373880			0.186940	−	0.982371i	$-0.440143\pi$
$179$	5.00218			0.373880			0.186940	+	0.982371i	$0.440143\pi$
$180$	−5.98159	+	3.61094i	−0.445842	+	0.269144i
$181$	15.3243			1.13905			0.569524	−	0.821975i	$-0.307128\pi$
$181$	15.3243			1.13905			0.569524	+	0.821975i	$0.307128\pi$
$182$	8.20504	−	14.2115i	0.608198	−	1.05343i
$183$	4.11196	+	4.03247i	0.303965	+	0.298089i
$184$	−2.08060	−	3.60371i	−0.153384	−	0.265669i
$185$	2.34905	+	4.06867i	0.172706	+	0.299135i
$186$	−6.97699	+	27.0934i	−0.511577	+	1.98658i
$187$	9.30711	−	16.1204i	0.680603	−	1.17884i
$188$	24.3908			1.77888
$189$	−4.67658	−	15.6101i	−0.340171	−	1.13547i
$190$	−2.08063			−0.150944
$191$	−0.134252	+	0.232532i	−0.00971415	+	0.0168254i	−0.870842	−	0.491564i	$-0.836425\pi$
$191$	−0.134252	+	0.232532i	−0.00971415	+	0.0168254i	0.861127	+	0.508389i	$0.169759\pi$
$192$	4.48350	−	17.4106i	0.323569	−	1.25650i
$193$	−3.29430	−	5.70589i	−0.237129	−	0.410719i	0.722761	−	0.691099i	$-0.242873\pi$
$193$	−3.29430	−	5.70589i	−0.237129	−	0.410719i	−0.959889	+	0.280380i	$0.909540\pi$
$194$	−16.0700	−	27.8340i	−1.15376	−	1.99837i
$195$	3.11008	+	3.04996i	0.222717	+	0.218412i
$196$	−3.30142	+	5.71823i	−0.235816	+	0.408445i
$197$	−21.7656			−1.55073			−0.775367	−	0.631511i	$-0.782435\pi$
$197$	−21.7656			−1.55073			−0.775367	+	0.631511i	$0.782435\pi$
$198$	0.415612	+	21.2904i	0.0295363	+	1.51304i
$199$	7.03747			0.498873			0.249436	−	0.968391i	$-0.419755\pi$
$199$	7.03747			0.498873			0.249436	+	0.968391i	$0.419755\pi$
$200$	−0.342268	+	0.592825i	−0.0242020	+	0.0419191i
$201$	3.87284	−	1.07834i	0.273169	−	0.0760603i
$202$	−5.77513	−	10.0028i	−0.406336	−	0.703795i
$203$	−14.1379	−	24.4875i	−0.992284	−	1.71869i
$204$	−21.2036	+	5.90387i	−1.48455	+	0.413354i
$205$	1.32140	−	2.28873i	0.0922906	−	0.159852i
$206$	23.7081			1.65182
$207$	0.355931	+	18.2331i	0.0247389	+	1.26729i
$208$	−8.13269			−0.563901
$209$	−1.70578	+	2.95449i	−0.117991	+	0.204366i
$210$	−8.06910	−	7.91312i	−0.556821	−	0.546057i
$211$	−12.8142	−	22.1948i	−0.882165	−	1.52795i	−0.848929	−	0.528507i	$-0.822752\pi$
$211$	−12.8142	−	22.1948i	−0.882165	−	1.52795i	−0.0332359	−	0.999448i	$-0.510581\pi$
$212$	11.1118	+	19.2462i	0.763162	+	1.32184i
$213$	−6.67838	+	25.9338i	−0.457595	+	1.77696i
$214$	−8.97163	+	15.5393i	−0.613288	+	1.06225i
$215$	−3.74302			−0.255272
$216$	2.44044	−	2.58769i	0.166051	−	0.176070i
$217$	−24.3467			−1.65276
$218$	6.24389	−	10.8147i	0.422890	−	0.732466i
$219$	5.44113	−	21.1293i	0.367677	−	1.42778i
$220$	3.97276	+	6.88102i	0.267843	+	0.463918i
$221$	6.86106	+	11.8837i	0.461525	+	0.799385i
$222$	−12.0881	−	11.8545i	−0.811302	−	0.795619i
$223$	−3.94901	+	6.83988i	−0.264445	+	0.458033i	−0.967418	−	0.253184i	$-0.918522\pi$
$223$	−3.94901	+	6.83988i	−0.264445	+	0.458033i	0.702973	+	0.711217i	$0.251855\pi$
$224$	25.3938			1.69670
$225$	2.56831	−	1.55042i	0.171220	−	0.103361i
$226$	39.0553			2.59792
$227$	5.32706	−	9.22675i	0.353570	−	0.612401i	−0.633302	−	0.773904i	$-0.718301\pi$
$227$	5.32706	−	9.22675i	0.353570	−	0.612401i	0.986872	+	0.161504i	$0.0516344\pi$
$228$	3.88613	−	1.08204i	0.257365	−	0.0716599i
$229$	6.77923	+	11.7420i	0.447984	+	0.775931i	0.998255	−	0.0590552i	$-0.0188088\pi$
$229$	6.77923	+	11.7420i	0.447984	+	0.775931i	−0.550271	+	0.834986i	$0.685475\pi$
$230$	6.32393	+	10.9534i	0.416988	+	0.722244i
$231$	−17.8520	+	4.97065i	−1.17457	+	0.327045i
$232$	3.08597	−	5.34505i	0.202604	−	0.350920i
$233$	−8.81116			−0.577239			−0.288619	−	0.957444i	$-0.593196\pi$
$233$	−8.81116			−0.577239			−0.288619	+	0.957444i	$0.593196\pi$
$234$	−13.7454	−	7.58215i	−0.898568	−	0.495661i
$235$	−10.4726			−0.683158
$236$	−4.56071	+	7.89937i	−0.296877	+	0.514205i
$237$	−13.4480	−	13.1881i	−0.873542	−	0.856656i
$238$	−17.8010	−	30.8323i	−1.15387	−	1.99856i
$239$	−9.52979	−	16.5061i	−0.616431	−	1.06769i	−0.990132	−	0.140140i	$-0.955245\pi$
$239$	−9.52979	−	16.5061i	−0.616431	−	1.06769i	0.373701	−	0.927549i	$-0.378089\pi$
$240$	−1.39678	+	5.42405i	−0.0901619	+	0.350121i
$241$	−2.22179	+	3.84825i	−0.143118	+	0.247887i	−0.928669	−	0.370909i	$-0.879046\pi$
$241$	−2.22179	+	3.84825i	−0.143118	+	0.247887i	0.785551	+	0.618797i	$0.212379\pi$
$242$	1.32884			0.0854211
$243$	−14.8426	+	4.76424i	−0.952152	+	0.305626i
$244$	−7.74419			−0.495771
$245$	1.41752	−	2.45523i	0.0905623	−	0.156859i
$246$	−2.37509	+	9.22309i	−0.151431	+	0.588043i
$247$	−1.25747	−	2.17800i	−0.0800110	−	0.138583i
$248$	−2.65716	−	4.60233i	−0.168730	−	0.292248i
$249$	5.93534	+	5.82060i	0.376137	+	0.368866i
$250$	1.04031	−	1.80187i	0.0657952	−	0.113961i
$251$	−22.4790			−1.41886			−0.709431	−	0.704775i	$-0.751048\pi$
$251$	−22.4790			−1.41886			−0.709431	+	0.704775i	$0.751048\pi$
$252$	19.1865	+	10.5835i	1.20863	+	0.666697i
$253$	20.7384			1.30381
$254$	−12.9738	+	22.4713i	−0.814049	+	1.40997i
$255$	9.10415	−	2.53493i	0.570124	−	0.158744i
$256$	−4.75997	−	8.24451i	−0.297498	−	0.515282i
$257$	−8.47439	−	14.6781i	−0.528618	−	0.915594i	−0.999443	−	0.0333669i	$-0.989377\pi$
$257$	−8.47439	−	14.6781i	−0.528618	−	0.915594i	0.470825	−	0.882227i	$-0.343956\pi$
$258$	12.9946	−	3.61818i	0.809009	−	0.225258i
$259$	7.36683	−	12.7597i	0.457752	−	0.792850i
$260$	−5.85731			−0.363255
$261$	−23.1565	+	13.9790i	−1.43335	+	0.865277i
$262$	28.7925			1.77881
$263$	9.55523	−	16.5501i	0.589201	−	1.02053i	−0.405137	−	0.914256i	$-0.632776\pi$
$263$	9.55523	−	16.5501i	0.589201	−	1.02053i	0.994337	−	0.106270i	$-0.0338906\pi$
$264$	−2.88796	−	2.83213i	−0.177741	−	0.174306i
$265$	−4.77106	−	8.26371i	−0.293084	−	0.507636i
$266$	3.26251	+	5.65084i	0.200038	+	0.346475i
$267$	−1.72111	+	6.68350i	−0.105330	+	0.409024i
$268$	−2.70286	+	4.68148i	−0.165103	+	0.285967i
$269$	−26.2138			−1.59828			−0.799142	−	0.601143i	$-0.794712\pi$
$269$	−26.2138			−1.59828			−0.799142	+	0.601143i	$0.794712\pi$
$270$	−7.41764	+	7.86522i	−0.451423	+	0.478662i
$271$	19.1171			1.16128			0.580640	−	0.814160i	$-0.302802\pi$
$271$	19.1171			1.16128			0.580640	+	0.814160i	$0.302802\pi$
$272$	−8.82204	+	15.2802i	−0.534915	+	0.926500i
$273$	3.40674	−	13.2292i	0.206185	−	0.800669i
$274$	−8.28166	−	14.3442i	−0.500313	−	0.866568i
$275$	−1.70578	−	2.95449i	−0.102862	−	0.178162i
$276$	−17.5080	−	17.1696i	−1.05386	−	1.03349i
$277$	−9.53168	+	16.5094i	−0.572703	+	0.991951i	0.423584	+	0.905857i	$0.360772\pi$
$277$	−9.53168	+	16.5094i	−0.572703	+	0.991951i	−0.996287	+	0.0860941i	$0.972561\pi$
$278$	−8.74876			−0.524716
$279$	0.454563	+	23.2857i	0.0272139	+	1.39408i
$280$	2.14676			0.128294
$281$	−13.3699	+	23.1574i	−0.797583	+	1.38145i	0.123603	+	0.992332i	$0.460555\pi$
$281$	−13.3699	+	23.1574i	−0.797583	+	1.38145i	−0.921186	+	0.389122i	$0.872778\pi$
$282$	36.3576	−	10.1233i	2.16507	−	0.602834i
$283$	−0.486460	−	0.842573i	−0.0289170	−	0.0500857i	0.851205	−	0.524834i	$-0.175873\pi$
$283$	−0.486460	−	0.842573i	−0.0289170	−	0.0500857i	−0.880122	+	0.474748i	$0.842539\pi$
$284$	−18.0048	−	31.1853i	−1.06839	−	1.85051i
$285$	−1.66858	+	0.464594i	−0.0988380	+	0.0275202i
$286$	−8.92573	+	15.4598i	−0.527790	+	0.914159i
$287$	−8.28806			−0.489229
$288$	−0.474113	−	24.2872i	−0.0279374	−	1.43114i
$289$	12.7705			0.751206
$290$	−9.37971	+	16.2461i	−0.550796	+	0.954006i
$291$	−19.1027	−	18.7334i	−1.11982	−	1.09817i
$292$	14.6692	+	25.4078i	0.858450	+	1.48688i
$293$	10.9954	+	19.0447i	0.642361	+	1.11260i	0.984904	+	0.173099i	$0.0553781\pi$
$293$	10.9954	+	19.0447i	0.642361	+	1.11260i	−0.342544	+	0.939502i	$0.611289\pi$
$294$	−2.54787	+	9.89402i	−0.148595	+	0.577031i
$295$	1.95822	−	3.39174i	0.114012	−	0.197475i
$296$	3.21602			0.186927
$297$	5.08735	+	16.9813i	0.295198	+	0.985352i
$298$	−18.2636			−1.05798
$299$	−7.64401	+	13.2398i	−0.442065	+	0.765678i
$300$	−1.00599	+	3.90650i	−0.0580807	+	0.225542i
$301$	5.86923	+	10.1658i	0.338297	+	0.585947i
$302$	1.03686	+	1.79589i	0.0596645	+	0.103342i
$303$	−6.86500	−	6.73229i	−0.394384	−	0.386760i
$304$	1.61687	−	2.80051i	0.0927341	−	0.160620i
$305$	3.32511			0.190395
$306$	−29.1564	+	17.6010i	−1.66676	+	1.00618i
$307$	21.1793			1.20877			0.604385	−	0.796693i	$-0.293419\pi$
$307$	21.1793			1.20877			0.604385	+	0.796693i	$0.293419\pi$
$308$	12.4589	−	21.5795i	0.709913	−	1.22961i
$309$	19.0129	−	5.29390i	1.08161	−	0.301160i
$310$	8.07636	+	13.9887i	0.458706	+	0.794502i
$311$	−11.1730	−	19.3522i	−0.633562	−	1.09736i	−0.986818	−	0.161835i	$-0.948259\pi$
$311$	−11.1730	−	19.3522i	−0.633562	−	1.09736i	0.353255	−	0.935527i	$-0.385075\pi$
$312$	2.87257	−	0.799830i	0.162627	−	0.0452814i
$313$	−2.74742	+	4.75867i	−0.155293	+	0.268976i	−0.933166	−	0.359446i	$-0.882966\pi$
$313$	−2.74742	+	4.75867i	−0.155293	+	0.268976i	0.777872	+	0.628422i	$0.216299\pi$
$314$	20.6664			1.16627
$315$	−8.23806	−	4.54421i	−0.464162	−	0.256037i
$316$	25.3271			1.42476
$317$	16.1489	−	27.9707i	0.907013	−	1.57099i	0.0888213	−	0.996048i	$-0.471690\pi$
$317$	16.1489	−	27.9707i	0.907013	−	1.57099i	0.818192	−	0.574945i	$-0.194977\pi$
$318$	24.5517	+	24.0771i	1.37679	+	1.35018i
$319$	15.3797	+	26.6384i	0.861097	+	1.49146i
$320$	−5.18997	−	8.98929i	−0.290128	−	0.502516i
$321$	−3.72503	+	14.4652i	−0.207911	+	0.807370i
$322$	19.8324	−	34.3507i	1.10522	−	1.91429i
$323$	−5.45624			−0.303593
$324$	9.76408	−	18.5480i	0.542449	−	1.03044i
$325$	2.51494			0.139504
$326$	16.5119	−	28.5994i	0.914509	−	1.58398i
$327$	2.59247	−	10.0672i	0.143364	−	0.556718i
$328$	−0.904546	−	1.56672i	−0.0499452	−	0.0865076i
$329$	16.4215	+	28.4429i	0.905348	+	1.56811i
$330$	8.77786	+	8.60818i	0.483205	+	0.473865i
$331$	3.39933	−	5.88782i	0.186844	−	0.323624i	−0.757352	−	0.653007i	$-0.773507\pi$
$331$	3.39933	−	5.88782i	0.186844	−	0.323624i	0.944196	+	0.329383i	$0.106841\pi$
$332$	−11.1782			−0.613485
$333$	−12.3412	−	6.80758i	−0.676296	−	0.373053i
$334$	−0.979755			−0.0536098
$335$	1.16052	−	2.01008i	0.0634060	−	0.109822i
$336$	16.9216	−	4.71159i	0.923148	−	0.257038i
$337$	13.6432	+	23.6307i	0.743191	+	1.28724i	0.951035	+	0.309083i	$0.100022\pi$
$337$	13.6432	+	23.6307i	0.743191	+	1.28724i	−0.207844	+	0.978162i	$0.566645\pi$
$338$	6.94415	+	12.0276i	0.377712	+	0.654217i
$339$	31.3208	−	8.72087i	1.70111	−	0.473652i
$340$	−6.35380	+	11.0051i	−0.344583	+	0.596835i
$341$	26.4852			1.43425
$342$	5.34368	−	3.22585i	0.288953	−	0.174434i
$343$	13.0617			0.705263
$344$	−1.28112	+	2.21896i	−0.0690732	+	0.119638i
$345$	7.51737	+	7.37206i	0.404722	+	0.396898i
$346$	13.8027	+	23.9069i	0.742037	+	1.28524i
$347$	14.5547	+	25.2095i	0.781338	+	1.35332i	0.931163	+	0.364604i	$0.118796\pi$
$347$	14.5547	+	25.2095i	0.781338	+	1.35332i	−0.149825	+	0.988713i	$0.547871\pi$
$348$	9.07023	−	35.2220i	0.486215	−	1.88810i
$349$	3.06897	−	5.31560i	0.164278	−	0.284538i	−0.772121	−	0.635476i	$-0.780804\pi$
$349$	3.06897	−	5.31560i	0.164278	−	0.284538i	0.936399	+	0.350938i	$0.114137\pi$
$350$	−6.52503			−0.348777
$351$	−12.7163	−	3.01129i	−0.678748	−	0.160731i
$352$	−27.6243			−1.47238
$353$	−5.41306	+	9.37570i	−0.288108	+	0.499018i	−0.973358	−	0.229290i	$-0.926360\pi$
$353$	−5.41306	+	9.37570i	−0.288108	+	0.499018i	0.685250	+	0.728308i	$0.259693\pi$
$354$	−3.51972	+	13.6680i	−0.187071	+	0.726444i
$355$	7.73070	+	13.3900i	0.410303	+	0.710665i
$356$	−4.64009	−	8.03687i	−0.245924	−	0.425953i
$357$	−21.1604	−	20.7514i	−1.11993	−	1.09828i
$358$	−5.20383	+	9.01330i	−0.275031	+	0.476368i
$359$	27.0809			1.42928			0.714639	−	0.699494i	$-0.246591\pi$
$359$	27.0809			1.42928			0.714639	+	0.699494i	$0.246591\pi$
$360$	−0.0400810	−	2.05322i	−0.00211245	−	0.108214i
$361$	1.00000			0.0526316
$362$	−15.9421	+	27.6125i	−0.837898	+	1.45128i
$363$	1.06568	−	0.296724i	0.0559335	−	0.0155740i
$364$	9.18453	+	15.9081i	0.481400	+	0.833809i
$365$	−6.29849	−	10.9093i	−0.329678	−	0.571019i
$366$	−11.5437	+	3.21420i	−0.603401	+	0.168009i
$367$	15.1229	−	26.1936i	0.789408	−	1.36729i	−0.136922	−	0.990582i	$-0.543721\pi$
$367$	15.1229	−	26.1936i	0.789408	−	1.36729i	0.926330	−	0.376713i	$-0.122946\pi$
$368$	−19.6575			−1.02472
$369$	0.154741	+	7.92689i	0.00805552	+	0.412658i
$370$	−9.77499			−0.508177
$371$	−14.9625	+	25.9157i	−0.776812	+	1.34548i
$372$	−22.3596	−	21.9274i	−1.15929	−	1.13688i
$373$	0.578594	+	1.00216i	0.0299585	+	0.0518896i	0.880616	−	0.473831i	$-0.157129\pi$
$373$	0.578594	+	1.00216i	0.0299585	+	0.0518896i	−0.850657	+	0.525720i	$0.823796\pi$
$374$	19.3646	+	33.5405i	1.00132	+	1.73434i
$375$	0.431939	−	1.67733i	0.0223052	−	0.0866168i
$376$	−3.58444	+	6.20843i	−0.184853	+	0.320175i
$377$	−22.6753			−1.16784
$378$	32.9926	+	7.81280i	1.69696	+	0.401847i
$379$	−34.9422			−1.79486			−0.897431	−	0.441156i	$-0.854569\pi$
$379$	−34.9422			−1.79486			−0.897431	+	0.441156i	$0.854569\pi$
$380$	1.16450	−	2.01698i	0.0597377	−	0.103469i
$381$	−5.38674	+	20.9181i	−0.275971	+	1.07166i
$382$	−0.279329	−	0.483812i	−0.0142917	−	0.0247540i
$383$	−0.163576	−	0.283322i	−0.00835835	−	0.0144771i	0.861816	−	0.507221i	$-0.169327\pi$
$383$	−0.163576	−	0.283322i	−0.00835835	−	0.0144771i	−0.870174	+	0.492744i	$0.835994\pi$
$384$	6.68055	+	6.55142i	0.340916	+	0.334326i
$385$	−5.34946	+	9.26554i	−0.272634	+	0.472216i
$386$	13.7084			0.697739
$387$	9.61323	−	5.80327i	0.488668	−	0.294997i
$388$	35.9768			1.82644
$389$	−7.53302	+	13.0476i	−0.381939	+	0.661538i	−0.991339	−	0.131325i	$-0.958077\pi$
$389$	−7.53302	+	13.0476i	−0.381939	+	0.661538i	0.609400	+	0.792863i	$0.291410\pi$
$390$	−8.73109	+	2.43106i	−0.442116	+	0.123101i
$391$	16.5839	+	28.7241i	0.838683	+	1.45264i
$392$	−0.970346	−	1.68069i	−0.0490099	−	0.0848876i
$393$	23.0904	−	6.42923i	1.16476	−	0.324312i
$394$	22.6430	−	39.2188i	1.14074	−	1.97582i
$395$	−10.8746			−0.547163
$396$	−20.8717	−	11.5131i	−1.04884	−	0.578555i
$397$	−12.8393			−0.644386			−0.322193	−	0.946674i	$-0.604420\pi$
$397$	−12.8393			−0.644386			−0.322193	+	0.946674i	$0.604420\pi$
$398$	−7.32117	+	12.6806i	−0.366977	+	0.635623i
$399$	3.87821	+	3.80324i	0.194153	+	0.190400i
$400$	1.61687	+	2.80051i	0.0808437	+	0.140025i
$401$	−0.892487	−	1.54583i	−0.0445687	−	0.0771952i	0.842881	−	0.538101i	$-0.180858\pi$
$401$	−0.892487	−	1.54583i	−0.0445687	−	0.0771952i	−0.887449	+	0.460906i	$0.847525\pi$
$402$	−2.08593	+	8.10018i	−0.104037	+	0.404000i
$403$	−9.76224	+	16.9087i	−0.486292	+	0.842282i
$404$	12.9291			0.643246
$405$	−4.19238	+	7.96391i	−0.208321	+	0.395730i
$406$	58.8312			2.91974
$407$	−8.01390	+	13.8805i	−0.397234	+	0.688030i
$408$	1.61329	−	6.26480i	0.0798696	−	0.310154i
$409$	−11.5353	−	19.9798i	−0.570386	−	0.987938i	−0.996526	−	0.0832805i	$-0.973460\pi$
$409$	−11.5353	−	19.9798i	−0.570386	−	0.987938i	0.426140	−	0.904657i	$-0.359873\pi$
$410$	2.74934	+	4.76200i	0.135780	+	0.235178i
$411$	−9.84456	−	9.65425i	−0.485596	−	0.476209i
$412$	−13.2691	+	22.9828i	−0.653724	+	1.13228i
$413$	−12.2823			−0.604373
$414$	−33.2241	−	18.3268i	−1.63288	−	0.900715i
$415$	4.79957			0.235602
$416$	10.1821	−	17.6359i	0.499219	−	0.864673i
$417$	−7.01615	+	1.95356i	−0.343582	+	0.0956660i
$418$	−3.54908	−	6.14719i	−0.173591	−	0.300669i
$419$	−8.45179	−	14.6389i	−0.412897	−	0.715159i	0.582308	−	0.812968i	$-0.302150\pi$
$419$	−8.45179	−	14.6389i	−0.412897	−	0.715159i	−0.995205	+	0.0978094i	$0.968816\pi$
$420$	12.1872	−	3.39338i	0.594676	−	0.165580i
$421$	−9.89128	+	17.1322i	−0.482071	+	0.834972i	−0.999788	−	0.0205800i	$-0.993449\pi$
$421$	−9.89128	+	17.1322i	−0.482071	+	0.834972i	0.517717	+	0.855552i	$0.326782\pi$
$422$	53.3231			2.59573
$423$	26.8969	−	16.2370i	1.30777	−	0.789469i
$424$	−6.53191			−0.317218
$425$	2.72812	−	4.72524i	0.132333	−	0.229208i
$426$	−39.7819	−	39.0129i	−1.92744	−	1.89018i
$427$	−5.21392	−	9.03077i	−0.252319	−	0.437030i
$428$	−10.0426	−	17.3944i	−0.485429	−	0.840788i
$429$	−3.70597	+	14.3912i	−0.178926	+	0.694815i
$430$	3.89392	−	6.74446i	0.187781	−	0.325247i
$431$	−4.14737			−0.199772			−0.0998859	−	0.994999i	$-0.531848\pi$
$431$	−4.14737			−0.199772			−0.0998859	+	0.994999i	$0.531848\pi$
$432$	−4.82221	−	16.0962i	−0.232009	−	0.774430i
$433$	25.4592			1.22349			0.611746	−	0.791055i	$-0.290468\pi$
$433$	25.4592			1.22349			0.611746	+	0.791055i	$0.290468\pi$
$434$	25.3282	−	43.8697i	1.21579	−	2.10581i
$435$	−3.89447	+	15.1232i	−0.186725	+	0.725102i
$436$	6.98927	+	12.1058i	0.334725	+	0.579761i
$437$	−3.03944	−	5.26446i	−0.145396	−	0.251833i
$438$	32.4118	+	31.7853i	1.54870	+	1.51876i
$439$	16.9396	−	29.3403i	0.808484	−	1.40033i	−0.105430	−	0.994427i	$-0.533622\pi$
$439$	16.9396	−	29.3403i	0.808484	−	1.40033i	0.913914	−	0.405908i	$-0.133045\pi$
$440$	−2.33533			−0.111332
$441$	0.165998	+	8.50353i	0.00790467	+	0.404930i
$442$	−28.5506			−1.35801
$443$	10.8308	−	18.7595i	0.514588	−	0.891292i	−0.485269	−	0.874365i	$-0.661278\pi$
$443$	10.8308	−	18.7595i	0.514588	−	0.891292i	0.999857	−	0.0169272i	$-0.00538837\pi$
$444$	18.2574	−	5.08354i	0.866458	−	0.241254i
$445$	1.99231	+	3.45077i	0.0944444	+	0.163582i
$446$	−8.21641	−	14.2312i	−0.389058	−	0.673869i
$447$	−14.6466	+	4.07817i	−0.692762	+	0.192891i
$448$	−16.2762	+	28.1912i	−0.768978	+	1.33191i
$449$	−11.3843			−0.537257			−0.268629	−	0.963244i	$-0.586570\pi$
$449$	−11.3843			−0.537257			−0.268629	+	0.963244i	$0.586570\pi$
$450$	0.121825	+	6.24069i	0.00574288	+	0.294189i
$451$	9.01605			0.424549
$452$	−21.8588	+	37.8606i	−1.02815	+	1.78081i
$453$	1.23253	+	1.20871i	0.0579094	+	0.0567900i
$454$	11.0836	+	19.1974i	0.520180	+	0.900979i
$455$	−3.94354	−	6.83041i	−0.184876	−	0.320215i
$456$	−0.295678	+	1.14819i	−0.0138464	+	0.0537689i
$457$	−3.81792	+	6.61283i	−0.178595	+	0.309335i	−0.941399	−	0.337294i	$-0.890488\pi$
$457$	−3.81792	+	6.61283i	−0.178595	+	0.309335i	0.762805	+	0.646629i	$0.223822\pi$
$458$	−28.2101			−1.31817
$459$	−19.4520	+	20.6258i	−0.907943	+	0.962728i
$460$	−14.1577			−0.660107
$461$	−11.8125	+	20.4598i	−0.550163	+	0.952910i	0.448100	+	0.893984i	$0.352101\pi$
$461$	−11.8125	+	20.4598i	−0.550163	+	0.952910i	−0.998262	+	0.0589261i	$0.981232\pi$
$462$	9.61516	−	37.3381i	0.447338	−	1.73712i
$463$	0.177678	+	0.307747i	0.00825740	+	0.0143022i	0.870125	−	0.492832i	$-0.164038\pi$
$463$	0.177678	+	0.307747i	0.00825740	+	0.0143022i	−0.861867	+	0.507134i	$0.830705\pi$
$464$	−14.5781	−	25.2501i	−0.676772	−	1.17220i
$465$	9.60051	+	9.41493i	0.445213	+	0.436607i
$466$	9.16637	−	15.8766i	0.424624	−	0.735470i
$467$	11.3685			0.526073			0.263036	−	0.964786i	$-0.415276\pi$
$467$	11.3685			0.526073			0.263036	+	0.964786i	$0.415276\pi$
$468$	15.0434	−	9.08131i	0.695380	−	0.419784i
$469$	−7.27899			−0.336112
$470$	10.8948	−	18.8703i	0.502540	−	0.870424i
$471$	16.5736	−	4.61471i	0.763673	−	0.212635i
$472$	−1.34047	−	2.32177i	−0.0617002	−	0.106868i
$473$	−6.38476	−	11.0587i	−0.293571	−	0.508481i
$474$	37.7534	−	10.5119i	1.73407	−	0.482829i
$475$	−0.500000	+	0.866025i	−0.0229416	+	0.0397360i
$476$	39.8521			1.82662
$477$	25.0658	+	13.8266i	1.14768	+	0.633076i
$478$	39.6558			1.81382
$479$	−7.04793	+	12.2074i	−0.322028	+	0.557769i	−0.980906	−	0.194481i	$-0.937698\pi$
$479$	−7.04793	+	12.2074i	−0.322028	+	0.557769i	0.658878	+	0.752250i	$0.271031\pi$
$480$	−10.0134	−	9.81986i	−0.457048	−	0.448213i
$481$	−5.90773	−	10.2325i	−0.269369	−	0.466561i
$482$	−4.62271	−	8.00676i	−0.210558	−	0.364698i
$483$	8.23444	−	31.9764i	0.374680	−	1.45498i
$484$	−0.743737	+	1.28819i	−0.0338062	+	0.0585541i
$485$	−15.4473			−0.701424
$486$	6.85636	−	31.7008i	0.311011	−	1.43798i
$487$	15.2837			0.692570			0.346285	−	0.938129i	$-0.387443\pi$
$487$	15.2837			0.692570			0.346285	+	0.938129i	$0.387443\pi$
$488$	1.13808	−	1.97121i	0.0515183	−	0.0892324i
$489$	6.85576	−	26.6226i	0.310028	−	1.20392i
$490$	2.94934	+	5.10841i	0.133238	+	0.230774i
$491$	15.5287	+	26.8965i	0.700801	+	1.21382i	0.968186	+	0.250233i	$0.0805073\pi$
$491$	15.5287	+	26.8965i	0.700801	+	1.21382i	−0.267385	+	0.963590i	$0.586159\pi$
$492$	−7.61163	−	7.46449i	−0.343159	−	0.336525i
$493$	−24.5974	+	42.6039i	−1.10781	+	1.91878i
$494$	5.23266			0.235428
$495$	8.96166	+	4.94336i	0.402796	+	0.222187i
$496$	−25.1048			−1.12724
$497$	24.2442	−	41.9921i	1.08750	−	1.88360i
$498$	−16.6626	+	4.63949i	−0.746669	+	0.207900i
$499$	−3.00112	−	5.19809i	−0.134349	−	0.232698i	0.791000	−	0.611816i	$-0.209561\pi$
$499$	−3.00112	−	5.19809i	−0.134349	−	0.232698i	−0.925348	+	0.379118i	$0.876228\pi$
$500$	1.16450	+	2.01698i	0.0520781	+	0.0902020i
$501$	−0.785724	+	0.218775i	−0.0351036	+	0.00977413i
$502$	23.3852	−	40.5044i	1.04373	−	1.80780i
$503$	−0.325249			−0.0145021			−0.00725107	−	0.999974i	$-0.502308\pi$
$503$	−0.325249			−0.0145021			−0.00725107	+	0.999974i	$0.502308\pi$
$504$	−5.51354	+	3.32839i	−0.245593	+	0.148258i
$505$	−5.55133			−0.247031
$506$	−21.5744	+	37.3680i	−0.959099	+	1.66121i
$507$	8.25464	+	8.09507i	0.366601	+	0.359515i
$508$	−14.5226	−	25.1538i	−0.644335	−	1.11602i
$509$	−10.6609	−	18.4652i	−0.472536	−	0.818456i	0.526970	−	0.849884i	$-0.323328\pi$
$509$	−10.6609	−	18.4652i	−0.472536	−	0.818456i	−0.999506	+	0.0314275i	$0.989995\pi$
$510$	−4.90354	+	19.0417i	−0.217132	+	0.843179i
$511$	−19.7526	+	34.2125i	−0.873804	+	1.51347i
$512$	30.6118			1.35286
$513$	3.56510	−	3.78022i	0.157403	−	0.166901i
$514$	35.2641			1.55543
$515$	5.69735	−	9.86809i	0.251055	−	0.434840i
$516$	−3.76544	+	14.6221i	−0.165764	+	0.643704i
$517$	−17.8639	−	30.9412i	−0.785654	−	1.36079i
$518$	15.3276	+	26.5482i	0.673457	+	1.16646i
$519$	16.4075	+	16.0903i	0.720209	+	0.706287i
$520$	0.860784	−	1.49092i	0.0377479	−	0.0653812i
$521$	−26.0297			−1.14038			−0.570191	−	0.821512i	$-0.693131\pi$
$521$	−26.0297			−1.14038			−0.570191	+	0.821512i	$0.693131\pi$
$522$	−1.09840	−	56.2676i	−0.0480758	−	2.46276i
$523$	−14.1453			−0.618533			−0.309266	−	0.950975i	$-0.600084\pi$
$523$	−14.1453			−0.618533			−0.309266	+	0.950975i	$0.600084\pi$
$524$	−16.1148	+	27.9117i	−0.703980	+	1.21933i
$525$	−5.23281	+	1.45701i	−0.228378	+	0.0635890i
$526$	19.8809	+	34.4347i	0.866847	+	1.50142i
$527$	21.1794	+	36.6839i	0.922591	+	1.59797i
$528$	−18.4079	+	5.12544i	−0.801101	+	0.223056i
$529$	−6.97635	+	12.0834i	−0.303320	+	0.525365i
$530$	19.8536			0.862384
$531$	0.229316	+	11.7471i	0.00995146	+	0.509780i
$532$	−7.30396			−0.316667
$533$	−3.32325	+	5.75603i	−0.143946	+	0.249321i
$534$	−10.2523	−	10.0542i	−0.443662	−	0.435086i
$535$	4.31199	+	7.46858i	0.186423	+	0.322895i
$536$	−0.794417	−	1.37597i	−0.0343136	−	0.0594329i
$537$	−2.16064	+	8.39029i	−0.0932383	+	0.362068i
$538$	27.2706	−	47.2340i	1.17572	−	2.03640i
$539$	9.67191			0.416599
$540$	−3.47305	−	11.5928i	−0.149456	−	0.498875i
$541$	10.1311			0.435568			0.217784	−	0.975997i	$-0.430117\pi$
$541$	10.1311			0.435568			0.217784	+	0.975997i	$0.430117\pi$
$542$	−19.8878	+	34.4466i	−0.854252	+	1.47961i
$543$	−6.61917	+	25.7039i	−0.284056	+	1.10306i
$544$	−22.0904	−	38.2616i	−0.947116	−	1.64045i
$545$	−3.00097	−	5.19783i	−0.128547	−	0.222650i
$546$	20.2933	+	19.9011i	0.868475	+	0.851686i
$547$	7.94296	−	13.7576i	0.339616	−	0.588233i	−0.644744	−	0.764398i	$-0.723036\pi$
$547$	7.94296	−	13.7576i	0.339616	−	0.588233i	0.984361	+	0.176166i	$0.0563694\pi$
$548$	18.5406			0.792015
$549$	−8.53989	+	5.15532i	−0.364474	+	0.220024i
$550$	7.09816			0.302667
$551$	4.50812	−	7.80830i	0.192052	−	0.332645i
$552$	6.94329	−	1.93327i	0.295526	−	0.0822854i
$553$	17.0519	+	29.5348i	0.725122	+	1.25595i
$554$	−19.8319	−	34.3498i	−0.842575	−	1.45938i
$555$	−7.83915	+	2.18271i	−0.332753	+	0.0926508i
$556$	4.89658	−	8.48112i	0.207661	−	0.359680i
$557$	−3.36306			−0.142498			−0.0712488	−	0.997459i	$-0.522698\pi$
$557$	−3.36306			−0.142498			−0.0712488	+	0.997459i	$0.522698\pi$
$558$	−42.4309	−	23.4054i	−1.79624	−	0.990829i
$559$	9.41349			0.398148
$560$	5.07066	−	8.78264i	0.214274	−	0.371134i
$561$	23.0191	+	22.5741i	0.971866	+	0.953079i
$562$	−27.8178	−	48.1819i	−1.17342	−	2.03243i
$563$	17.8312	+	30.8846i	0.751497	+	1.30163i	0.947097	+	0.320948i	$0.104001\pi$
$563$	17.8312	+	30.8846i	0.751497	+	1.30163i	−0.195600	+	0.980684i	$0.562665\pi$
$564$	−10.5353	+	40.9113i	−0.443617	+	1.72268i
$565$	9.38548	−	16.2561i	0.394850	−	0.683900i
$566$	2.02428			0.0850869
$567$	28.2033	−	1.10154i	1.18443	−	0.0462602i
$568$	10.5839			0.444090
$569$	−7.15055	+	12.3851i	−0.299767	+	0.519211i	−0.976082	−	0.217401i	$-0.930242\pi$
$569$	−7.15055	+	12.3851i	−0.299767	+	0.519211i	0.676316	+	0.736612i	$0.263576\pi$
$570$	0.898704	−	3.48989i	0.0376426	−	0.146175i
$571$	5.28253	+	9.14961i	0.221067	+	0.382899i	0.955132	−	0.296180i	$-0.0957128\pi$
$571$	5.28253	+	9.14961i	0.221067	+	0.382899i	−0.734065	+	0.679079i	$0.762379\pi$
$572$	−9.99126	−	17.3054i	−0.417756	−	0.723574i
$573$	−0.332043	−	0.325625i	−0.0138713	−	0.0136032i
$574$	8.62217	−	14.9340i	0.359883	−	0.623335i
$575$	6.07887			0.253507
$576$	27.2666	+	15.0406i	1.13611	+	0.626692i
$577$	−0.415085			−0.0172802			−0.00864011	−	0.999963i	$-0.502750\pi$
$577$	−0.415085			−0.0172802			−0.00864011	+	0.999963i	$0.502750\pi$
$578$	−13.2853	+	23.0109i	−0.552597	+	0.957125i
$579$	10.9936	−	3.06102i	0.456878	−	0.127212i
$580$	−10.4994	−	18.1856i	−0.435965	−	0.755114i
$581$	−7.52594	−	13.0353i	−0.312229	−	0.540796i
$582$	53.6281	−	14.9320i	2.22295	−	0.618953i
$583$	16.2767	−	28.1921i	0.674112	−	1.16760i
$584$	−8.62308			−0.356825
$585$	−6.45914	+	3.89922i	−0.267053	+	0.161213i
$586$	−45.7548			−1.89011
$587$	14.6085	−	25.3026i	0.602956	−	1.04435i	−0.389415	−	0.921063i	$-0.627323\pi$
$587$	14.6085	−	25.3026i	0.602956	−	1.04435i	0.992371	−	0.123288i	$-0.0393440\pi$
$588$	−8.16533	−	8.00749i	−0.336733	−	0.330223i
$589$	−3.88170	−	6.72329i	−0.159942	−	0.277028i
$590$	4.07433	+	7.05694i	0.167737	+	0.290530i
$591$	9.40140	−	36.5080i	0.386722	−	1.50174i
$592$	7.59623	−	13.1571i	0.312203	−	0.540752i
$593$	−26.4115			−1.08459			−0.542296	−	0.840188i	$-0.682445\pi$
$593$	−26.4115			−1.08459			−0.542296	+	0.840188i	$0.682445\pi$
$594$	−35.8905	−	8.49905i	−1.47261	−	0.348720i
$595$	−17.1112			−0.701492
$596$	10.2219	−	17.7049i	0.418705	−	0.725219i
$597$	−3.03976	+	11.8041i	−0.124409	+	0.483111i
$598$	−15.9043	−	27.5471i	−0.650376	−	1.12648i
$599$	9.10527	+	15.7708i	0.372031	+	0.644377i	0.989878	−	0.141922i	$-0.0453281\pi$
$599$	9.10527	+	15.7708i	0.372031	+	0.644377i	−0.617847	+	0.786299i	$0.711995\pi$
$600$	−0.846523	−	0.830159i	−0.0345592	−	0.0338911i
$601$	−12.9431	+	22.4180i	−0.527958	+	0.914450i	0.471511	+	0.881860i	$0.343709\pi$
$601$	−12.9431	+	22.4180i	−0.527958	+	0.914450i	−0.999469	+	0.0325899i	$0.989624\pi$
$602$	−24.4233			−0.995421
$603$	0.135902	+	6.96179i	0.00553434	+	0.283506i
$604$	−2.32127			−0.0944511
$605$	0.319337	−	0.553107i	0.0129829	−	0.0224870i
$606$	19.2725	−	5.36617i	0.782892	−	0.217986i
$607$	8.24490	+	14.2806i	0.334650	+	0.579631i	0.983418	−	0.181356i	$-0.0580485\pi$
$607$	8.24490	+	14.2806i	0.334650	+	0.579631i	−0.648767	+	0.760987i	$0.724715\pi$
$608$	4.04864	+	7.01246i	0.164194	+	0.284393i
$609$	47.1803	−	13.1367i	1.91184	−	0.532327i
$610$	−3.45915	+	5.99143i	−0.140057	+	0.242586i
$611$	26.3380			1.06552
$612$	−0.744056	−	38.1155i	−0.0300767	−	1.54073i
$613$	−42.2360			−1.70590			−0.852948	−	0.521995i	$-0.825188\pi$
$613$	−42.2360			−1.70590			−0.852948	+	0.521995i	$0.825188\pi$
$614$	−22.0332	+	38.1625i	−0.889186	+	1.54011i
$615$	3.26819	+	3.20502i	0.131786	+	0.129239i
$616$	3.66190	+	6.34259i	0.147542	+	0.255550i
$617$	3.90793	+	6.76873i	0.157327	+	0.272499i	0.933904	−	0.357524i	$-0.116379\pi$
$617$	3.90793	+	6.76873i	0.157327	+	0.272499i	−0.776577	+	0.630023i	$0.783046\pi$
$618$	−10.2404	+	39.7662i	−0.411931	+	1.59963i
$619$	−6.74258	+	11.6785i	−0.271007	+	0.469399i	−0.969120	−	0.246589i	$-0.920690\pi$
$619$	−6.74258	+	11.6785i	−0.271007	+	0.469399i	0.698113	+	0.715988i	$0.254023\pi$
$620$	−18.0810			−0.726149
$621$	−30.7367	−	7.27860i	−1.23342	−	0.292080i
$622$	46.4936			1.86423
$623$	6.24805	−	10.8219i	0.250323	−	0.433572i
$624$	3.51283	−	13.6412i	0.140626	−	0.546084i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−5.71635	−	9.90102i	−0.228471	−	0.395724i
$627$	−4.21886	−	4.13730i	−0.168485	−	0.165228i
$628$	−11.5668	+	20.0342i	−0.461564	+	0.799452i
$629$	−25.6339			−1.02209
$630$	16.7583	−	10.1165i	0.667665	−	0.403053i
$631$	21.9555			0.874035			0.437017	−	0.899453i	$-0.356035\pi$
$631$	21.9555			0.874035			0.437017	+	0.899453i	$0.356035\pi$
$632$	−3.72204	+	6.44676i	−0.148055	+	0.256438i
$633$	42.7629	−	11.9068i	1.69967	−	0.473252i
$634$	33.5998	+	58.1966i	1.33442	+	2.31128i
$635$	6.23553	+	10.8003i	0.247449	+	0.428595i
$636$	−37.0818	+	10.3250i	−1.47039	+	0.409411i
$637$	−3.56499	+	6.17475i	−0.141250	+	0.244653i
$638$	−63.9987			−2.53373
$639$	−40.6149	−	22.4037i	−1.60670	−	0.886275i
$640$	5.40219			0.213540
$641$	9.66263	−	16.7362i	0.381651	−	0.661039i	−0.609648	−	0.792673i	$-0.708689\pi$
$641$	9.66263	−	16.7362i	0.381651	−	0.661039i	0.991298	+	0.131634i	$0.0420223\pi$
$642$	−22.1893	−	21.7604i	−0.875743	−	0.858814i
$643$	−21.6103	−	37.4302i	−0.852227	−	1.47610i	−0.879194	−	0.476465i	$-0.841918\pi$
$643$	−21.6103	−	37.4302i	−0.852227	−	1.47610i	0.0269661	−	0.999636i	$-0.491415\pi$
$644$	22.1999	+	38.4514i	0.874800	+	1.51520i
$645$	1.61676	−	6.27828i	0.0636598	−	0.247207i
$646$	5.67619	−	9.83145i	0.223327	−	0.386813i
$647$	−37.9804			−1.49316			−0.746582	−	0.665294i	$-0.768306\pi$
$647$	−37.9804			−1.49316			−0.746582	+	0.665294i	$0.768306\pi$
$648$	3.28629	+	5.21114i	0.129098	+	0.204713i
$649$	13.3611			0.524471
$650$	−2.61633	+	4.53161i	−0.102621	+	0.177744i
$651$	10.5163	−	40.8374i	0.412166	−	1.60054i
$652$	18.4830	+	32.0136i	0.723852	+	1.25375i
$653$	4.75366	+	8.23359i	0.186025	+	0.322205i	0.943922	−	0.330170i	$-0.107106\pi$
$653$	4.75366	+	8.23359i	0.186025	+	0.322205i	−0.757896	+	0.652375i	$0.773773\pi$
$654$	15.4429	+	15.1444i	0.603864	+	0.592191i
$655$	6.91920	−	11.9844i	0.270355	−	0.468269i
$656$	−8.54615			−0.333671
$657$	33.0905	+	18.2531i	1.29098	+	0.712121i
$658$	−68.3341			−2.66394
$659$	11.8291	−	20.4886i	0.460796	−	0.798122i	−0.538205	−	0.842814i	$-0.680897\pi$
$659$	11.8291	−	20.4886i	0.460796	−	0.798122i	0.999001	+	0.0446920i	$0.0142306\pi$
$660$	−13.2577	+	3.69144i	−0.516056	+	0.143689i
$661$	5.92331	+	10.2595i	0.230390	+	0.399047i	0.957923	−	0.287026i	$-0.0926665\pi$
$661$	5.92331	+	10.2595i	0.230390	+	0.399047i	−0.727533	+	0.686073i	$0.759333\pi$
$662$	7.07274	+	12.2503i	0.274890	+	0.476123i
$663$	−22.8964	+	6.37521i	−0.889224	+	0.247593i
$664$	1.64274	−	2.84531i	0.0637506	−	0.110419i
$665$	3.13609			0.121612
$666$	25.1052	−	15.1554i	0.972805	−	0.587258i
$667$	−54.8086			−2.12220
$668$	0.548358	−	0.949783i	0.0212166	−	0.0367482i
$669$	−9.76700	−	9.57820i	−0.377614	−	0.370314i
$670$	2.41461	+	4.18222i	0.0932845	+	0.161573i
$671$	5.67189	+	9.82400i	0.218961	+	0.379251i
$672$	−10.9686	+	42.5937i	−0.423122	+	1.64309i
$673$	−16.7379	+	28.9909i	−0.645199	+	1.11752i	0.339057	+	0.940766i	$0.389892\pi$
$673$	−16.7379	+	28.9909i	−0.645199	+	1.11752i	−0.984256	+	0.176751i	$0.943441\pi$
$674$	−56.7727			−2.18680
$675$	1.49121	+	4.97758i	0.0573969	+	0.191587i
$676$	−15.5462			−0.597933
$677$	10.6183	−	18.3915i	0.408095	−	0.706841i	−0.586581	−	0.809890i	$-0.699527\pi$
$677$	10.6183	−	18.3915i	0.408095	−	0.706841i	0.994676	+	0.103049i	$0.0328598\pi$
$678$	−16.8695	+	65.5086i	−0.647870	+	2.51584i
$679$	24.2220	+	41.9537i	0.929555	+	1.61004i
$680$	−1.86749	−	3.23459i	−0.0716151	−	0.124041i
$681$	13.1753	+	12.9206i	0.504879	+	0.495119i
$682$	−27.5529	+	47.7230i	−1.05505	+	1.82741i
$683$	−18.7766			−0.718467			−0.359233	−	0.933248i	$-0.616962\pi$
$683$	−18.7766			−0.718467			−0.359233	+	0.933248i	$0.616962\pi$
$684$	0.136368	+	6.98568i	0.00521416	+	0.267104i
$685$	−7.96074			−0.304164
$686$	−13.5882	+	23.5355i	−0.518800	+	0.898588i
$687$	−22.6233	+	6.29918i	−0.863135	+	0.240329i
$688$	6.05200	+	10.4824i	0.230730	+	0.399636i
$689$	11.9989	+	20.7828i	0.457123	+	0.791760i
$690$	−21.1039	+	5.87612i	−0.803413	+	0.223700i
$691$	−16.0415	+	27.7846i	−0.610246	+	1.05698i	0.380953	+	0.924595i	$0.375596\pi$
$691$	−16.0415	+	27.7846i	−0.610246	+	1.05698i	−0.991199	+	0.132383i	$0.957737\pi$
$692$	−30.9008			−1.17467
$693$	−0.626444	−	32.0907i	−0.0237966	−	1.21902i
$694$	−60.5658			−2.29905
$695$	−2.10243	+	3.64152i	−0.0797499	+	0.138131i
$696$	7.63246	+	7.48492i	0.289308	+	0.283715i
$697$	7.20987	+	12.4879i	0.273093	+	0.473012i
$698$	6.38537	+	11.0598i	0.241690	+	0.418619i
$699$	3.80589	−	14.7792i	0.143952	−	0.559001i
$700$	3.65198	−	6.32542i	0.138032	−	0.239078i
$701$	−0.535633			−0.0202306			−0.0101153	−	0.999949i	$-0.503220\pi$
$701$	−0.535633			−0.0202306			−0.0101153	+	0.999949i	$0.503220\pi$
$702$	18.6549	−	19.7806i	0.704086	−	0.746570i
$703$	4.69810			0.177192
$704$	17.7058	−	30.6674i	0.667314	−	1.15582i
$705$	4.52353	−	17.5660i	0.170366	−	0.661574i
$706$	−11.2626	−	19.5073i	−0.423872	−	0.734168i
$707$	8.70474	+	15.0770i	0.327375	+	0.567031i
$708$	−11.2799	−	11.0618i	−0.423924	−	0.415730i
$709$	−4.81333	+	8.33694i	−0.180769	+	0.313100i	−0.942142	−	0.335213i	$-0.891192\pi$
$709$	−4.81333	+	8.33694i	−0.180769	+	0.313100i	0.761374	+	0.648313i	$0.224525\pi$
$710$	−32.1694			−1.20730
$711$	27.9294	−	16.8603i	1.04743	−	0.632310i
$712$	2.72761			0.102221
$713$	−23.5963	+	40.8700i	−0.883690	+	1.53060i
$714$	59.4049	−	16.5405i	2.22317	−	0.619013i
$715$	4.28993	+	7.43037i	0.160434	+	0.277880i
$716$	−5.82505	−	10.0893i	−0.217692	−	0.377054i
$717$	31.8024	−	8.85496i	1.18768	−	0.330694i
$718$	−28.1726	+	48.7965i	−1.05139	+	1.82107i
$719$	−30.8510			−1.15055			−0.575274	−	0.817961i	$-0.695105\pi$
$719$	−30.8510			−1.15055			−0.575274	+	0.817961i	$0.695105\pi$
$720$	−8.49459	−	4.68572i	−0.316575	−	0.174627i
$721$	−35.7348			−1.33083
$722$	−1.04031	+	1.80187i	−0.0387164	+	0.0670588i
$723$	−5.49510	−	5.38887i	−0.204365	−	0.200414i
$724$	−17.8452	−	30.9088i	−0.663212	−	1.14872i
$725$	4.50812	+	7.80830i	0.167427	+	0.289993i
$726$	−0.573978	+	2.22890i	−0.0213023	+	0.0827223i
$727$	3.75166	−	6.49807i	0.139142	−	0.241000i	−0.788030	−	0.615636i	$-0.788899\pi$
$727$	3.75166	−	6.49807i	0.139142	−	0.241000i	0.927172	+	0.374636i	$0.122232\pi$
$728$	−5.39899			−0.200100
$729$	−1.58010	−	26.9537i	−0.0585223	−	0.998286i
$730$	26.2096			0.970061
$731$	10.2114	−	17.6867i	0.377683	−	0.654165i
$732$	3.34502	−	12.9896i	0.123635	−	0.480108i
$733$	0.425691	+	0.737319i	0.0157233	+	0.0272335i	0.873780	−	0.486321i	$-0.161662\pi$
$733$	0.425691	+	0.737319i	0.0157233	+	0.0272335i	−0.858057	+	0.513555i	$0.828328\pi$
$734$	31.4651	+	54.4991i	1.16140	+	2.01160i
$735$	3.50593	+	3.43816i	0.129318	+	0.126818i
$736$	24.6112	−	42.6278i	0.907181	−	1.57128i
$737$	7.91834			0.291676
$738$	−14.4443	−	7.96763i	−0.531700	−	0.293292i
$739$	41.9409			1.54282			0.771411	−	0.636338i	$-0.219552\pi$
$739$	41.9409			1.54282			0.771411	+	0.636338i	$0.219552\pi$
$740$	5.47095	−	9.47596i	0.201116	−	0.348343i
$741$	4.19638	−	1.16843i	0.154158	−	0.0429232i
$742$	−31.1313	−	53.9209i	−1.14286	−	1.97950i
$743$	4.85019	+	8.40078i	0.177936	+	0.308195i	0.941174	−	0.337924i	$-0.109725\pi$
$743$	4.85019	+	8.40078i	0.177936	+	0.308195i	−0.763237	+	0.646118i	$0.776391\pi$
$744$	8.86735	−	2.46900i	0.325093	−	0.0905179i
$745$	−4.38896	+	7.60190i	−0.160799	+	0.278512i
$746$	−2.40768			−0.0881513
$747$	−12.3268	+	7.44136i	−0.451013	+	0.272265i
$748$	−43.3526			−1.58513
$749$	13.5228	−	23.4221i	0.494111	−	0.855826i
$750$	2.57298	+	2.52325i	0.0939521	+	0.0921359i
$751$	−3.61181	−	6.25584i	−0.131797	−	0.228279i	0.792572	−	0.609778i	$-0.208741\pi$
$751$	−3.61181	−	6.25584i	−0.131797	−	0.228279i	−0.924369	+	0.381499i	$0.875408\pi$
$752$	16.9329	+	29.3286i	0.617479	+	1.06951i
$753$	9.70956	−	37.7047i	0.353836	−	1.37403i
$754$	23.5894	−	40.8581i	0.859077	−	1.48797i
$755$	0.996679			0.0362729
$756$	−26.0394	+	27.6106i	−0.947043	+	1.00419i
$757$	−18.8215			−0.684077			−0.342039	−	0.939686i	$-0.611117\pi$
$757$	−18.8215			−0.684077			−0.342039	+	0.939686i	$0.611117\pi$
$758$	36.3508	−	62.9615i	1.32032	−	2.28686i
$759$	−8.95772	+	34.7851i	−0.325144	+	1.26262i
$760$	0.342268	+	0.592825i	0.0124154	+	0.0215040i
$761$	−8.97825	−	15.5508i	−0.325461	−	0.563715i	0.656144	−	0.754635i	$-0.272186\pi$
$761$	−8.97825	−	15.5508i	−0.325461	−	0.563715i	−0.981606	+	0.190920i	$0.938853\pi$
$762$	−32.0878	−	31.4675i	−1.16242	−	1.13995i
$763$	−9.41130	+	16.3008i	−0.340712	+	0.590130i
$764$	0.625348			0.0226243
$765$	0.319474	+	16.3656i	0.0115506	+	0.591699i
$766$	0.680682			0.0245940
$767$	−4.92481	+	8.53003i	−0.177825	+	0.308001i
$768$	15.8848	−	4.42291i	0.573192	−	0.159598i
$769$	1.31788	+	2.28263i	0.0475239	+	0.0823139i	0.888809	−	0.458278i	$-0.151534\pi$
$769$	1.31788	+	2.28263i	0.0475239	+	0.0823139i	−0.841285	+	0.540592i	$0.818200\pi$
$770$	−11.1302	−	19.2781i	−0.401106	−	0.694735i
$771$	28.2804	−	7.87430i	1.01849	−	0.283586i
$772$	−7.67243	+	13.2890i	−0.276137	+	0.478283i
$773$	23.8601			0.858188			0.429094	−	0.903260i	$-0.358833\pi$
$773$	23.8601			0.858188			0.429094	+	0.903260i	$0.358833\pi$
$774$	0.455994	+	23.3590i	0.0163904	+	0.839624i
$775$	7.76339			0.278869
$776$	−5.28710	+	9.15753i	−0.189796	+	0.328736i
$777$	18.2202	+	17.8680i	0.653646	+	0.641011i
$778$	−15.6734	−	27.1471i	−0.561919	−	0.973271i
$779$	−1.32140	−	2.28873i	−0.0473441	−	0.0820024i
$780$	2.53000	−	9.82464i	0.0905886	−	0.351778i
$781$	−26.3737	+	45.6805i	−0.943724	+	1.63458i
$782$	−69.0097			−2.46778
$783$	−13.4452	−	44.8790i	−0.480491	−	1.60385i
$784$	−9.16783			−0.327423
$785$	4.96639	−	8.60205i	0.177258	−	0.307020i
$786$	−12.4366	+	48.2945i	−0.443599	+	1.72261i
$787$	−10.4978	−	18.1827i	−0.374206	−	0.648143i	0.616002	−	0.787745i	$-0.288751\pi$
$787$	−10.4978	−	18.1827i	−0.374206	−	0.648143i	−0.990208	+	0.139601i	$0.955418\pi$
$788$	25.3461	+	43.9007i	0.902916	+	1.56390i
$789$	23.6327	+	23.1759i	0.841348	+	0.825084i
$790$	11.3130	−	19.5948i	0.402500	−	0.697150i
$791$	−58.8674			−2.09308
$792$	5.99783	−	3.62074i	0.213124	−	0.128657i
$793$	−8.36246			−0.296960
$794$	13.3569	−	23.1348i	0.474018	−	0.821024i
$795$	15.9218	−	4.43321i	0.564687	−	0.157230i
$796$	−8.19515	−	14.1944i	−0.290469	−	0.503108i
$797$	16.4667	+	28.5212i	0.583280	+	1.01027i	0.995087	+	0.0990002i	$0.0315644\pi$
$797$	16.4667	+	28.5212i	0.583280	+	1.01027i	−0.411807	+	0.911271i	$0.635102\pi$
$798$	−10.8875	+	3.03149i	−0.385414	+	0.107313i
$799$	28.5705	−	49.4856i	1.01075	−	1.75067i
$800$	−8.09729			−0.286282
$801$	−10.4670	−	5.77373i	−0.369833	−	0.204005i
$802$	3.71386			0.131141
$803$	21.4876	−	37.2176i	0.758281	−	1.31338i
$804$	−6.68492	−	6.55569i	−0.235759	−	0.231201i
$805$	−9.53194	−	16.5098i	−0.335957	−	0.581894i
$806$	−20.3116	−	35.1807i	−0.715445	−	1.23919i
$807$	11.3228	−	43.9691i	0.398580	−	1.54779i
$808$	−1.90004	+	3.29097i	−0.0668433	+	0.115776i
$809$	−22.6168			−0.795166			−0.397583	−	0.917566i	$-0.630151\pi$
$809$	−22.6168			−0.795166			−0.397583	+	0.917566i	$0.630151\pi$
$810$	−9.98858	−	15.8391i	−0.350963	−	0.556530i
$811$	39.8997			1.40107			0.700533	−	0.713620i	$-0.252946\pi$
$811$	39.8997			1.40107			0.700533	+	0.713620i	$0.252946\pi$
$812$	−32.9272	+	57.0315i	−1.15552	+	2.00141i
$813$	−8.25741	+	32.0656i	−0.289600	+	1.12459i
$814$	−16.6739	−	28.8801i	−0.584421	−	1.01225i
$815$	−7.93602	−	13.7456i	−0.277987	−	0.481487i
$816$	−21.8194	−	21.3976i	−0.763830	−	0.749065i
$817$	−1.87151	+	3.24155i	−0.0654759	+	0.113408i
$818$	48.0015			1.67833
$819$	20.7182	+	11.4284i	0.723954	+	0.399342i
$820$	−6.15510			−0.214945
$821$	18.3255	−	31.7407i	0.639565	−	1.10776i	−0.345963	−	0.938248i	$-0.612448\pi$
$821$	18.3255	−	31.7407i	0.639565	−	1.10776i	0.985528	−	0.169511i	$-0.0542189\pi$
$822$	27.6372	−	7.69521i	0.963957	−	0.268401i
$823$	−1.30058	−	2.25267i	−0.0453354	−	0.0785232i	0.842467	−	0.538748i	$-0.181102\pi$
$823$	−1.30058	−	2.25267i	−0.0453354	−	0.0785232i	−0.887803	+	0.460224i	$0.847769\pi$
$824$	−3.90003	−	6.75506i	−0.135864	−	0.235324i
$825$	5.69244	−	1.58498i	0.198185	−	0.0551821i
$826$	12.7774	−	22.1312i	0.444584	−	0.770042i
$827$	12.2678			0.426592			0.213296	−	0.976988i	$-0.431580\pi$
$827$	12.2678			0.426592			0.213296	+	0.976988i	$0.431580\pi$
$828$	36.3614	−	21.9504i	1.26364	−	0.762831i
$829$	27.1975			0.944610			0.472305	−	0.881435i	$-0.343422\pi$
$829$	27.1975			0.944610			0.472305	+	0.881435i	$0.343422\pi$
$830$	−4.99306	+	8.64823i	−0.173312	+	0.300184i
$831$	−23.5745	−	23.1188i	−0.817790	−	0.801982i
$832$	13.0525	+	22.6075i	0.452513	+	0.783776i
$833$	7.73435	+	13.3963i	0.267979	+	0.464154i
$834$	3.77893	−	14.6745i	0.130854	−	0.508138i
$835$	−0.235447	+	0.407807i	−0.00814799	+	0.0141127i
$836$	7.94552			0.274801
$837$	−39.2542	−	9.29557i	−1.35682	−	0.321302i
$838$	35.1700			1.21493
$839$	−17.6720	+	30.6087i	−0.610104	+	1.05673i	0.381119	+	0.924526i	$0.375539\pi$
$839$	−17.6720	+	30.6087i	−0.610104	+	1.05673i	−0.991222	+	0.132204i	$0.957794\pi$
$840$	−0.927271	+	3.60083i	−0.0319939	+	0.124240i
$841$	−26.1463	−	45.2868i	−0.901597	−	1.56161i
$842$	−20.5800	−	35.6457i	−0.709235	−	1.22843i
$843$	−33.0675	−	32.4283i	−1.13891	−	1.11689i
$844$	−29.8443	+	51.6918i	−1.02728	+	1.77931i
$845$	6.67506			0.229629
$846$	1.27583	+	65.3563i	0.0438638	+	2.24700i
$847$	−2.00294			−0.0688217
$848$	−15.4284	+	26.7227i	−0.529813	+	0.917663i
$849$	1.62339	−	0.452012i	0.0557147	−	0.0155130i
$850$	5.67619	+	9.83145i	0.194692	+	0.337216i
$851$	−14.2796	−	24.7329i	−0.489498	−	0.847835i
$852$	60.0849	−	16.7299i	2.05848	−	0.573156i
$853$	−0.0874008	+	0.151383i	−0.00299255	+	0.00518324i	−0.867518	−	0.497406i	$-0.834286\pi$
$853$	−0.0874008	+	0.151383i	−0.00299255	+	0.00518324i	0.864525	+	0.502589i	$0.167619\pi$
$854$	21.6964			0.742436
$855$	−0.0585521	−	2.99943i	−0.00200244	−	0.102578i
$856$	5.90341			0.201775
$857$	8.55110	−	14.8109i	0.292100	−	0.505932i	−0.682206	−	0.731160i	$-0.738979\pi$
$857$	8.55110	−	14.8109i	0.292100	−	0.505932i	0.974306	+	0.225228i	$0.0723127\pi$
$858$	−22.0758	−	21.6491i	−0.753656	−	0.739087i
$859$	−0.0587895	−	0.101826i	−0.00200587	−	0.00347427i	0.865021	−	0.501736i	$-0.167305\pi$
$859$	−0.0587895	−	0.101826i	−0.00200587	−	0.00347427i	−0.867027	+	0.498262i	$0.833972\pi$
$860$	4.35876	+	7.54959i	0.148632	+	0.257439i
$861$	3.57994	−	13.9018i	0.122004	−	0.473772i
$862$	4.31456	−	7.47304i	0.146955	−	0.254533i
$863$	29.5899			1.00725			0.503626	−	0.863922i	$-0.331999\pi$
$863$	29.5899			1.00725			0.503626	+	0.863922i	$0.331999\pi$
$864$	40.9425	+	9.69536i	1.39289	+	0.329843i
$865$	13.2678			0.451119
$866$	−26.4855	+	45.8743i	−0.900015	+	1.55887i
$867$	−5.51608	+	21.4203i	−0.187336	+	0.727472i
$868$	28.3518	+	49.1067i	0.962322	+	1.66679i
$869$	−18.5497	−	32.1290i	−0.629255	−	1.08990i
$870$	−23.1986	−	22.7502i	−0.786508	−	0.771304i
$871$	−2.91864	+	5.05524i	−0.0988944	+	0.171290i
$872$	−4.10854			−0.139133
$873$	39.6733	−	23.9498i	1.34274	−	0.810577i
$874$	12.6479			0.427820
$875$	−1.56804	+	2.71593i	−0.0530096	+	0.0918153i
$876$	−48.9534	+	13.6304i	−1.65398	+	0.460530i
$877$	−7.10108	−	12.2994i	−0.239786	−	0.415322i	0.720867	−	0.693074i	$-0.243744\pi$
$877$	−7.10108	−	12.2994i	−0.239786	−	0.415322i	−0.960653	+	0.277752i	$0.910411\pi$
$878$	35.2450	+	61.0461i	1.18946	+	2.06021i
$879$	−36.6935	+	10.2168i	−1.23764	+	0.344605i
$880$	−5.51604	+	9.55407i	−0.185946	+	0.322068i
$881$	38.8615			1.30928			0.654638	−	0.755942i	$-0.272821\pi$
$881$	38.8615			1.30928			0.654638	+	0.755942i	$0.272821\pi$
$882$	−15.4950	−	8.54722i	−0.521743	−	0.287800i
$883$	25.5015			0.858194			0.429097	−	0.903258i	$-0.358832\pi$
$883$	25.5015			0.858194			0.429097	+	0.903258i	$0.358832\pi$
$884$	15.9794	−	27.6772i	0.537447	−	0.930885i
$885$	4.84323	+	4.74960i	0.162803	+	0.159656i
$886$	22.5349	+	39.0316i	0.757074	+	1.31129i
$887$	−6.53241	−	11.3145i	−0.219337	−	0.379902i	0.735269	−	0.677776i	$-0.237056\pi$
$887$	−6.53241	−	11.3145i	−0.219337	−	0.379902i	−0.954605	+	0.297873i	$0.903723\pi$
$888$	−1.38912	+	5.39431i	−0.0466159	+	0.181021i
$889$	19.5552	−	33.8705i	0.655859	−	1.13598i
$890$	−8.29049			−0.277898
$891$	−30.6806	+	1.19829i	−1.02784	+	0.0401443i
$892$	18.3945			0.615894
$893$	−5.23631	+	9.06955i	−0.175226	+	0.303501i
$894$	7.88874	−	30.6340i	0.263839	−	1.02455i
$895$	2.50109	+	4.33201i	0.0836022	+	0.144803i
$896$	−8.47087	−	14.6720i	−0.282992	−	0.490156i
$897$	−18.9058	−	18.5403i	−0.631245	−	0.619043i
$898$	11.8432	−	20.5131i	0.395213	−	0.684529i
$899$	−69.9966			−2.33452
$900$	−6.11796	−	3.37474i	−0.203932	−	0.112491i
$901$	52.0640			1.73450
$902$	−9.37951	+	16.2458i	−0.312304	+	0.540926i
$903$	−19.5865	+	5.45361i	−0.651799	+	0.181485i
$904$	−6.42469	−	11.1279i	−0.213682	−	0.370108i
$905$	7.66216	+	13.2713i	0.254699	+	0.441151i
$906$	−3.46016	+	0.963436i	−0.114956	+	0.0320080i
$907$	0.202388	−	0.350546i	0.00672017	−	0.0116397i	−0.862646	−	0.505809i	$-0.831194\pi$
$907$	0.202388	−	0.350546i	0.00672017	−	0.0116397i	0.869366	+	0.494169i	$0.164528\pi$
$908$	−24.8135			−0.823465
$909$	14.2575	−	8.60691i	0.472892	−	0.285473i
$910$	16.4101			0.543989
$911$	−0.298124	+	0.516366i	−0.00987728	+	0.0171080i	−0.870922	−	0.491422i	$-0.836477\pi$
$911$	−0.298124	+	0.516366i	−0.00987728	+	0.0171080i	0.861045	+	0.508530i	$0.169811\pi$
$912$	3.99898	+	3.92168i	0.132419	+	0.129860i
$913$	8.18699	+	14.1803i	0.270950	+	0.469299i
$914$	−7.94366	−	13.7588i	−0.262753	−	0.455102i
$915$	−1.43624	+	5.57730i	−0.0474808	+	0.184380i
$916$	15.7889	−	27.3471i	0.521678	−	0.903574i
$917$	−43.3984			−1.43314
$918$	−16.9288	−	56.5074i	−0.558735	−	1.86502i
$919$	−8.55594			−0.282234			−0.141117	−	0.989993i	$-0.545069\pi$
$919$	−8.55594			−0.282234			−0.141117	+	0.989993i	$0.545069\pi$
$920$	2.08060	−	3.60371i	0.0685954	−	0.118811i
$921$	−9.14819	+	35.5247i	−0.301443	+	1.17058i
$922$	−24.5774	−	42.5693i	−0.809413	−	1.40194i
$923$	−19.4423	−	33.6750i	−0.639950	−	1.10843i
$924$	30.8144	+	30.2187i	1.01372	+	0.994123i
$925$	−2.34905	+	4.06867i	−0.0772363	+	0.133777i
$926$	−0.739363			−0.0242970
$927$	0.667183	+	34.1776i	0.0219132	+	1.12254i
$928$	73.0071			2.39658
$929$	−11.8319	+	20.4935i	−0.388192	+	0.672368i	−0.992206	−	0.124605i	$-0.960234\pi$
$929$	−11.8319	+	20.4935i	−0.388192	+	0.672368i	0.604014	+	0.796973i	$0.293567\pi$
$930$	−26.9521	+	7.50445i	−0.883793	+	0.246081i
$931$	−1.41752	−	2.45523i	−0.0464575	−	0.0804668i
$932$	10.2606	+	17.7719i	0.336098	+	0.582139i
$933$	37.2860	−	10.3818i	1.22069	−	0.339885i
$934$	−11.8268	+	20.4847i	−0.386986	+	0.670279i
$935$	18.6142			0.608750
$936$	0.100801	+	5.16372i	0.00329479	+	0.168781i
$937$	−40.2014			−1.31332			−0.656661	−	0.754186i	$-0.728032\pi$
$937$	−40.2014			−1.31332			−0.656661	+	0.754186i	$0.728032\pi$
$938$	7.57242	−	13.1158i	0.247248	−	0.428247i
$939$	−6.79514	−	6.66378i	−0.221751	−	0.217464i
$940$	12.1954	+	21.1230i	0.397770	+	0.688957i
$941$	13.0320	+	22.5721i	0.424831	+	0.735829i	0.996405	−	0.0847217i	$-0.0270001\pi$
$941$	13.0320	+	22.5721i	0.424831	+	0.735829i	−0.571574	+	0.820551i	$0.693667\pi$
$942$	−8.92663	+	34.6644i	−0.290845	+	1.12943i
$943$	−8.03263	+	13.9129i	−0.261578	+	0.453067i
$944$	−12.6648			−0.412204
$945$	11.1805	−	11.8551i	0.363701	−	0.385646i
$946$	26.5686			0.863819
$947$	24.3173	−	42.1188i	0.790206	−	1.36868i	−0.135633	−	0.990759i	$-0.543307\pi$
$947$	24.3173	−	42.1188i	0.790206	−	1.36868i	0.925839	−	0.377918i	$-0.123360\pi$
$948$	−10.9398	+	42.4819i	−0.355307	+	1.37975i
$949$	15.8403	+	27.4363i	0.514199	+	0.890619i
$950$	−1.04031	−	1.80187i	−0.0337522	−	0.0584605i
$951$	39.9407	+	39.1687i	1.29517	+	1.27013i
$952$	−5.85662	+	10.1440i	−0.189814	+	0.328768i
$953$	45.2207			1.46484			0.732421	−	0.680852i	$-0.238390\pi$
$953$	45.2207			1.46484			0.732421	+	0.680852i	$0.238390\pi$
$954$	−50.9900	+	30.7814i	−1.65086	+	0.996585i
$955$	−0.268505			−0.00868860
$956$	−22.1949	+	38.4427i	−0.717835	+	1.24333i
$957$	−51.3244	+	14.2906i	−1.65908	+	0.461950i
$958$	−14.6641	−	25.3990i	−0.473776	−	0.820604i
$959$	12.4828	+	21.6208i	0.403090	+	0.698173i
$960$	17.3197	−	4.82245i	0.558992	−	0.155644i
$961$	−14.6351	+	25.3488i	−0.472101	+	0.817702i
$962$	24.5835			0.792605
$963$	−22.6539	−	12.4962i	−0.730013	−	0.402684i
$964$	10.3491			0.333322
$965$	3.29430	−	5.70589i	0.106047	−	0.183679i
$966$	49.0511	+	48.1029i	1.57819	+	1.54768i
$967$	4.98612	+	8.63622i	0.160343	+	0.277722i	0.934992	−	0.354670i	$-0.115407\pi$
$967$	4.98612	+	8.63622i	0.160343	+	0.277722i	−0.774649	+	0.632392i	$0.782073\pi$
$968$	−0.218597	−	0.378622i	−0.00702598	−	0.0121694i
$969$	2.35676	−	9.15190i	0.0757101	−	0.294001i
$970$	16.0700	−	27.8340i	0.515976	−	0.893697i
$971$	32.0354			1.02806			0.514032	−	0.857771i	$-0.328151\pi$
$971$	32.0354			1.02806			0.514032	+	0.857771i	$0.328151\pi$
$972$	26.8936	+	24.3892i	0.862612	+	0.782283i
$973$	13.1868			0.422751
$974$	−15.8998	+	27.5393i	−0.509463	+	0.882416i
$975$	−1.08630	+	4.21838i	−0.0347895	+	0.135096i
$976$	−5.37628	−	9.31199i	−0.172091	−	0.298070i
$977$	21.5724	+	37.3645i	0.690162	+	1.19540i	0.971784	+	0.235871i	$0.0757943\pi$
$977$	21.5724	+	37.3645i	0.690162	+	1.19540i	−0.281622	+	0.959525i	$0.590872\pi$
$978$	40.8385	+	40.0491i	1.30587	+	1.28063i
$979$	−6.79685	+	11.7725i	−0.217228	+	0.376250i
$980$	−6.60284			−0.210920
$981$	15.7662	+	8.69684i	0.503377	+	0.277669i
$982$	−64.6189			−2.06207
$983$	−24.6444	+	42.6853i	−0.786034	+	1.36145i	0.142346	+	0.989817i	$0.454535\pi$
$983$	−24.6444	+	42.6853i	−0.786034	+	1.36145i	−0.928380	+	0.371633i	$0.878798\pi$
$984$	3.01861	−	0.840492i	0.0962298	−	0.0267939i
$985$	−10.8828	−	18.8495i	−0.346754	−	0.600596i
$986$	−51.1779	−	88.6428i	−1.62984	−	2.82296i
$987$	−54.8012	+	15.2587i	−1.74434	+	0.485689i
$988$	−2.92866	+	5.07258i	−0.0931730	+	0.161380i
$989$	22.7534			0.723515
$990$	−18.2302	+	11.0051i	−0.579395	+	0.349766i
$991$	−58.2484			−1.85032			−0.925161	−	0.379576i	$-0.876070\pi$
$991$	−58.2484			−1.85032			−0.925161	+	0.379576i	$0.876070\pi$
$992$	31.4312	−	54.4404i	0.997942	−	1.72849i
$993$	8.40749	+	8.24497i	0.266804	+	0.261646i
$994$	50.4430	+	87.3699i	1.59996	+	2.77120i
$995$	3.51873	+	6.09463i	0.111551	+	0.193213i
$996$	4.82831	−	18.7495i	0.152991	−	0.594102i
$997$	−10.8788	+	18.8427i	−0.344537	+	0.596755i	−0.985269	−	0.171009i	$-0.945297\pi$
$997$	−10.8788	+	18.8427i	−0.344537	+	0.596755i	0.640733	+	0.767764i	$0.278631\pi$
$998$	12.4884			0.395314
$999$	16.7492	−	17.7598i	0.529921	−	0.561897i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.i.d.286.4	✓	46
9.2	odd	6		7695.2.a.x.1.4		23
9.4	even	3	inner	855.2.i.d.571.4	yes	46
9.7	even	3		7695.2.a.w.1.20		23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
855.2.i.d.286.4	✓	46	1.1	even	1	trivial
855.2.i.d.571.4	yes	46	9.4	even	3	inner
7695.2.a.w.1.20		23	9.7	even	3
7695.2.a.x.1.4		23	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.04031 + 1.80187i) q^{2} +(-0.431939 + 1.67733i) q^{3} +(-1.16450 - 2.01698i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.57298 - 2.52325i) q^{6} +(1.56804 - 2.71593i) q^{7} +0.684535 q^{8} +(-2.62686 - 1.44901i) q^{9} +O(q^{10})\)	\(q+(-1.04031 + 1.80187i) q^{2} +(-0.431939 + 1.67733i) q^{3} +(-1.16450 - 2.01698i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.57298 - 2.52325i) q^{6} +(1.56804 - 2.71593i) q^{7} +0.684535 q^{8} +(-2.62686 - 1.44901i) q^{9} -2.08063 q^{10} +(-1.70578 + 2.95449i) q^{11} +(3.88613 - 1.08204i) q^{12} +(-1.25747 - 2.17800i) q^{13} +(3.26251 + 5.65084i) q^{14} +(-1.66858 + 0.464594i) q^{15} +(1.61687 - 2.80051i) q^{16} -5.45624 q^{17} +(5.34368 - 3.22585i) q^{18} +1.00000 q^{19} +(1.16450 - 2.01698i) q^{20} +(3.87821 + 3.80324i) q^{21} +(-3.54908 - 6.14719i) q^{22} +(-3.03944 - 5.26446i) q^{23} +(-0.295678 + 1.14819i) q^{24} +(-0.500000 + 0.866025i) q^{25} +5.23266 q^{26} +(3.56510 - 3.78022i) q^{27} -7.30396 q^{28} +(4.50812 - 7.80830i) q^{29} +(0.898704 - 3.48989i) q^{30} +(-3.88170 - 6.72329i) q^{31} +(4.04864 + 7.01246i) q^{32} +(-4.21886 - 4.13730i) q^{33} +(5.67619 - 9.83145i) q^{34} +3.13609 q^{35} +(0.136368 + 6.98568i) q^{36} +4.69810 q^{37} +(-1.04031 + 1.80187i) q^{38} +(4.19638 - 1.16843i) q^{39} +(0.342268 + 0.592825i) q^{40} +(-1.32140 - 2.28873i) q^{41} +(-10.8875 + 3.03149i) q^{42} +(-1.87151 + 3.24155i) q^{43} +7.94552 q^{44} +(-0.0585521 - 2.99943i) q^{45} +12.6479 q^{46} +(-5.23631 + 9.06955i) q^{47} +(3.99898 + 3.92168i) q^{48} +(-1.41752 - 2.45523i) q^{49} +(-1.04031 - 1.80187i) q^{50} +(2.35676 - 9.15190i) q^{51} +(-2.92866 + 5.07258i) q^{52} -9.54211 q^{53} +(3.10266 + 10.3565i) q^{54} -3.41155 q^{55} +(1.07338 - 1.85915i) q^{56} +(-0.431939 + 1.67733i) q^{57} +(9.37971 + 16.2461i) q^{58} +(-1.95822 - 3.39174i) q^{59} +(2.88014 + 2.82446i) q^{60} +(1.66255 - 2.87963i) q^{61} +16.1527 q^{62} +(-8.05443 + 4.86226i) q^{63} -10.3799 q^{64} +(1.25747 - 2.17800i) q^{65} +(11.8438 - 3.29776i) q^{66} +(-1.16052 - 2.01008i) q^{67} +(6.35380 + 11.0051i) q^{68} +(10.1431 - 2.82421i) q^{69} +(-3.26251 + 5.65084i) q^{70} +15.4614 q^{71} +(-1.79818 - 0.991896i) q^{72} -12.5970 q^{73} +(-4.88749 + 8.46539i) q^{74} +(-1.23664 - 1.21273i) q^{75} +(-1.16450 - 2.01698i) q^{76} +(5.34946 + 9.26554i) q^{77} +(-2.26019 + 8.77688i) q^{78} +(-5.43732 + 9.41772i) q^{79} +3.23375 q^{80} +(4.80076 + 7.61267i) q^{81} +5.49868 q^{82} +(2.39979 - 4.15655i) q^{83} +(3.15487 - 12.2511i) q^{84} +(-2.72812 - 4.72524i) q^{85} +(-3.89392 - 6.74446i) q^{86} +(11.1498 + 10.9343i) q^{87} +(-1.16766 + 2.02245i) q^{88} +3.98461 q^{89} +(5.46551 + 3.01484i) q^{90} -7.88708 q^{91} +(-7.07886 + 12.2609i) q^{92} +(12.9538 - 3.60682i) q^{93} +(-10.8948 - 18.8703i) q^{94} +(0.500000 + 0.866025i) q^{95} +(-13.5110 + 3.76195i) q^{96} +(-7.72363 + 13.3777i) q^{97} +5.89868 q^{98} +(8.76190 - 5.28934i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q + 3 q^{2} + 2 q^{3} - 29 q^{4} + 23 q^{5} + 3 q^{6} - 10 q^{7} - 12 q^{8} - 8 q^{9}+O(q^{10}) \) 46 * q + 3 * q^2 + 2 * q^3 - 29 * q^4 + 23 * q^5 + 3 * q^6 - 10 * q^7 - 12 * q^8 - 8 * q^9	\( 46 q + 3 q^{2} + 2 q^{3} - 29 q^{4} + 23 q^{5} + 3 q^{6} - 10 q^{7} - 12 q^{8} - 8 q^{9} + 6 q^{10} - q^{11} + 9 q^{12} - 11 q^{13} - 3 q^{14} + q^{15} - 45 q^{16} - 30 q^{17} - 18 q^{18} + 46 q^{19} + 29 q^{20} - 2 q^{21} - 5 q^{22} + 13 q^{23} - 6 q^{24} - 23 q^{25} - 12 q^{26} + 23 q^{27} + 56 q^{28} + 2 q^{29} + 6 q^{30} - 16 q^{31} + 25 q^{32} + 19 q^{33} - 18 q^{34} - 20 q^{35} - 5 q^{36} + 58 q^{37} + 3 q^{38} + 32 q^{39} - 6 q^{40} + 14 q^{41} - 67 q^{42} - 34 q^{43} + 64 q^{44} - 7 q^{45} - 4 q^{46} + 22 q^{47} + 89 q^{48} - 61 q^{49} + 3 q^{50} - 38 q^{51} - 20 q^{52} - 70 q^{53} - 91 q^{54} - 2 q^{55} - 26 q^{56} + 2 q^{57} - 23 q^{58} - 15 q^{59} + 3 q^{60} - 32 q^{61} + 6 q^{62} - 31 q^{63} + 164 q^{64} + 11 q^{65} + 54 q^{66} - 16 q^{67} + 26 q^{68} - 19 q^{69} + 3 q^{70} + 50 q^{71} + 22 q^{72} + 82 q^{73} + 9 q^{74} - q^{75} - 29 q^{76} + 18 q^{77} - 41 q^{78} - 11 q^{79} - 90 q^{80} + 8 q^{81} + 60 q^{82} + 26 q^{83} + 123 q^{84} - 15 q^{85} - 15 q^{86} - 26 q^{87} - 22 q^{88} + 40 q^{89} - 12 q^{90} + 116 q^{91} + 2 q^{92} + 42 q^{93} - 36 q^{94} + 23 q^{95} - 48 q^{96} - 50 q^{97} - 24 q^{98} - 29 q^{99}+O(q^{100}) \) 46 * q + 3 * q^2 + 2 * q^3 - 29 * q^4 + 23 * q^5 + 3 * q^6 - 10 * q^7 - 12 * q^8 - 8 * q^9 + 6 * q^10 - q^11 + 9 * q^12 - 11 * q^13 - 3 * q^14 + q^15 - 45 * q^16 - 30 * q^17 - 18 * q^18 + 46 * q^19 + 29 * q^20 - 2 * q^21 - 5 * q^22 + 13 * q^23 - 6 * q^24 - 23 * q^25 - 12 * q^26 + 23 * q^27 + 56 * q^28 + 2 * q^29 + 6 * q^30 - 16 * q^31 + 25 * q^32 + 19 * q^33 - 18 * q^34 - 20 * q^35 - 5 * q^36 + 58 * q^37 + 3 * q^38 + 32 * q^39 - 6 * q^40 + 14 * q^41 - 67 * q^42 - 34 * q^43 + 64 * q^44 - 7 * q^45 - 4 * q^46 + 22 * q^47 + 89 * q^48 - 61 * q^49 + 3 * q^50 - 38 * q^51 - 20 * q^52 - 70 * q^53 - 91 * q^54 - 2 * q^55 - 26 * q^56 + 2 * q^57 - 23 * q^58 - 15 * q^59 + 3 * q^60 - 32 * q^61 + 6 * q^62 - 31 * q^63 + 164 * q^64 + 11 * q^65 + 54 * q^66 - 16 * q^67 + 26 * q^68 - 19 * q^69 + 3 * q^70 + 50 * q^71 + 22 * q^72 + 82 * q^73 + 9 * q^74 - q^75 - 29 * q^76 + 18 * q^77 - 41 * q^78 - 11 * q^79 - 90 * q^80 + 8 * q^81 + 60 * q^82 + 26 * q^83 + 123 * q^84 - 15 * q^85 - 15 * q^86 - 26 * q^87 - 22 * q^88 + 40 * q^89 - 12 * q^90 + 116 * q^91 + 2 * q^92 + 42 * q^93 - 36 * q^94 + 23 * q^95 - 48 * q^96 - 50 * q^97 - 24 * q^98 - 29 * q^99

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