LMFDB - Embedded newform 403.2.k.d.66.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(66,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("403.66");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.k (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			66.2
Character	$\chi$	$=$	403.66
Dual form			403.2.k.d.287.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.604780 - 1.86132i) q^{2} +(0.854563 - 2.63007i) q^{3} +(-1.48072 + 1.07581i) q^{4} -1.67501 q^{5} -5.41223 q^{6} +(1.22914 - 0.893026i) q^{7} +(-0.268732 - 0.195245i) q^{8} +(-3.75996 - 2.73177i) q^{9} +O(q^{10})$	\(q+(-0.604780 - 1.86132i) q^{2} +(0.854563 - 2.63007i) q^{3} +(-1.48072 + 1.07581i) q^{4} -1.67501 q^{5} -5.41223 q^{6} +(1.22914 - 0.893026i) q^{7} +(-0.268732 - 0.195245i) q^{8} +(-3.75996 - 2.73177i) q^{9} +(1.01301 + 3.11773i) q^{10} +(2.98634 - 2.16971i) q^{11} +(1.56408 + 4.81376i) q^{12} +(-0.309017 + 0.951057i) q^{13} +(-2.40557 - 1.74775i) q^{14} +(-1.43140 + 4.40540i) q^{15} +(-1.33206 + 4.09967i) q^{16} +(-5.46458 - 3.97025i) q^{17} +(-2.81075 + 8.65060i) q^{18} +(1.75464 + 5.40023i) q^{19} +(2.48023 - 1.80199i) q^{20} +(-1.29834 - 3.99589i) q^{21} +(-5.84460 - 4.24635i) q^{22} +(6.46530 + 4.69731i) q^{23} +(-0.743158 + 0.539936i) q^{24} -2.19434 q^{25} +1.95711 q^{26} +(-3.68604 + 2.67807i) q^{27} +(-0.859298 + 2.64465i) q^{28} +(-1.47816 - 4.54931i) q^{29} +9.06554 q^{30} +(4.36233 - 3.45978i) q^{31} +7.77206 q^{32} +(-3.15447 - 9.70845i) q^{33} +(-4.08504 + 12.5725i) q^{34} +(-2.05883 + 1.49583i) q^{35} +8.50631 q^{36} +7.92354 q^{37} +(8.99040 - 6.53191i) q^{38} +(2.23727 + 1.62547i) q^{39} +(0.450129 + 0.327038i) q^{40} +(2.00908 + 6.18330i) q^{41} +(-6.65241 + 4.83326i) q^{42} +(-3.15680 - 9.71565i) q^{43} +(-2.08776 + 6.42547i) q^{44} +(6.29796 + 4.57574i) q^{45} +(4.83313 - 14.8748i) q^{46} +(2.46948 - 7.60026i) q^{47} +(9.64409 + 7.00684i) q^{48} +(-1.44982 + 4.46208i) q^{49} +(1.32709 + 4.08437i) q^{50} +(-15.1119 + 10.9794i) q^{51} +(-0.565586 - 1.74069i) q^{52} +(-7.69313 - 5.58939i) q^{53} +(7.21399 + 5.24127i) q^{54} +(-5.00216 + 3.63428i) q^{55} -0.504670 q^{56} +15.7025 q^{57} +(-7.57377 + 5.50266i) q^{58} +(-1.33409 + 4.10590i) q^{59} +(-2.61986 - 8.06309i) q^{60} -0.00123644 q^{61} +(-9.07801 - 6.02729i) q^{62} -7.06107 q^{63} +(-2.03626 - 6.26696i) q^{64} +(0.517607 - 1.59303i) q^{65} +(-16.1628 + 11.7430i) q^{66} +1.97679 q^{67} +12.3627 q^{68} +(17.8793 - 12.9901i) q^{69} +(4.02935 + 2.92750i) q^{70} +(-5.04763 - 3.66732i) q^{71} +(0.477056 + 1.46823i) q^{72} +(-5.81416 + 4.22423i) q^{73} +(-4.79199 - 14.7482i) q^{74} +(-1.87520 + 5.77128i) q^{75} +(-8.40776 - 6.10859i) q^{76} +(1.73305 - 5.33376i) q^{77} +(1.67247 - 5.14734i) q^{78} +(-3.72230 - 2.70441i) q^{79} +(2.23122 - 6.86698i) q^{80} +(-0.414967 - 1.27714i) q^{81} +(10.2941 - 7.47907i) q^{82} +(1.06424 + 3.27538i) q^{83} +(6.22129 + 4.52003i) q^{84} +(9.15322 + 6.65020i) q^{85} +(-16.1748 + 11.7517i) q^{86} -13.2282 q^{87} -1.22615 q^{88} +(2.31773 - 1.68393i) q^{89} +(4.70804 - 14.4898i) q^{90} +(0.469491 + 1.44495i) q^{91} -14.6267 q^{92} +(-5.37159 - 14.4298i) q^{93} -15.6400 q^{94} +(-2.93904 - 9.04545i) q^{95} +(6.64171 - 20.4411i) q^{96} +(-0.859281 + 0.624304i) q^{97} +9.18219 q^{98} -17.1557 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9}+O(q^{10}) $ 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9	\( 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9} - 19 q^{10} - 9 q^{11} + 15 q^{12} + 12 q^{13} - 25 q^{14} - 30 q^{15} - 21 q^{16} + 11 q^{17} + 17 q^{18} + 36 q^{19} + 30 q^{20} + 11 q^{21} + 15 q^{22} - 7 q^{23} - 20 q^{24} - 16 q^{25} + 8 q^{26} - 5 q^{27} - 9 q^{28} + 12 q^{29} + 18 q^{30} + 22 q^{31} - 76 q^{32} - 49 q^{33} - 26 q^{34} + 8 q^{35} + 2 q^{36} + 64 q^{37} - 27 q^{38} - 3 q^{39} - 24 q^{40} + 46 q^{41} + 20 q^{42} - 28 q^{43} - 23 q^{45} + 34 q^{46} + 5 q^{47} - 20 q^{48} - 11 q^{49} + 9 q^{50} + 59 q^{51} + 17 q^{52} + 23 q^{53} + 41 q^{54} - 10 q^{55} - 60 q^{56} + 24 q^{57} - 37 q^{58} + 71 q^{59} - 72 q^{60} + 22 q^{61} + 43 q^{62} - 106 q^{63} - 52 q^{64} + 2 q^{65} - 21 q^{66} - 56 q^{67} - 104 q^{68} - 12 q^{69} - 32 q^{70} - 36 q^{71} + 147 q^{72} - 12 q^{73} + 10 q^{74} + 34 q^{75} - 49 q^{76} - 30 q^{77} + 5 q^{78} - 70 q^{79} + q^{81} + 130 q^{82} + 11 q^{83} + 77 q^{84} + 8 q^{85} + 11 q^{86} - 88 q^{87} + 96 q^{88} - 40 q^{89} - 48 q^{90} + 10 q^{91} + 112 q^{92} + 50 q^{93} + 78 q^{94} + 41 q^{95} - 75 q^{96} - 47 q^{97} - 46 q^{98} + 46 q^{99}+O(q^{100}) \) 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9 - 19 * q^10 - 9 * q^11 + 15 * q^12 + 12 * q^13 - 25 * q^14 - 30 * q^15 - 21 * q^16 + 11 * q^17 + 17 * q^18 + 36 * q^19 + 30 * q^20 + 11 * q^21 + 15 * q^22 - 7 * q^23 - 20 * q^24 - 16 * q^25 + 8 * q^26 - 5 * q^27 - 9 * q^28 + 12 * q^29 + 18 * q^30 + 22 * q^31 - 76 * q^32 - 49 * q^33 - 26 * q^34 + 8 * q^35 + 2 * q^36 + 64 * q^37 - 27 * q^38 - 3 * q^39 - 24 * q^40 + 46 * q^41 + 20 * q^42 - 28 * q^43 - 23 * q^45 + 34 * q^46 + 5 * q^47 - 20 * q^48 - 11 * q^49 + 9 * q^50 + 59 * q^51 + 17 * q^52 + 23 * q^53 + 41 * q^54 - 10 * q^55 - 60 * q^56 + 24 * q^57 - 37 * q^58 + 71 * q^59 - 72 * q^60 + 22 * q^61 + 43 * q^62 - 106 * q^63 - 52 * q^64 + 2 * q^65 - 21 * q^66 - 56 * q^67 - 104 * q^68 - 12 * q^69 - 32 * q^70 - 36 * q^71 + 147 * q^72 - 12 * q^73 + 10 * q^74 + 34 * q^75 - 49 * q^76 - 30 * q^77 + 5 * q^78 - 70 * q^79 + q^81 + 130 * q^82 + 11 * q^83 + 77 * q^84 + 8 * q^85 + 11 * q^86 - 88 * q^87 + 96 * q^88 - 40 * q^89 - 48 * q^90 + 10 * q^91 + 112 * q^92 + 50 * q^93 + 78 * q^94 + 41 * q^95 - 75 * q^96 - 47 * q^97 - 46 * q^98 + 46 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.604780	−	1.86132i	−0.427644	−	1.31615i	−0.900440	−	0.434981i	$-0.856755\pi$
$2$	−0.604780	−	1.86132i	−0.427644	−	1.31615i	0.472796	−	0.881172i	$-0.343245\pi$
$3$	0.854563	−	2.63007i	0.493382	−	1.51847i	−0.326081	−	0.945342i	$-0.605728\pi$
$3$	0.854563	−	2.63007i	0.493382	−	1.51847i	0.819463	−	0.573132i	$-0.194272\pi$
$4$	−1.48072	+	1.07581i	−0.740362	+	0.537904i
$5$	−1.67501			−0.749087			−0.374544	−	0.927209i	$-0.622201\pi$
$5$	−1.67501			−0.749087			−0.374544	+	0.927209i	$0.622201\pi$
$6$	−5.41223			−2.20953
$7$	1.22914	−	0.893026i	0.464573	−	0.337532i	−0.330750	−	0.943719i	$-0.607302\pi$
$7$	1.22914	−	0.893026i	0.464573	−	0.337532i	0.795322	+	0.606187i	$0.207302\pi$
$8$	−0.268732	−	0.195245i	−0.0950111	−	0.0690296i
$9$	−3.75996	−	2.73177i	−1.25332	−	0.910589i
$10$	1.01301	+	3.11773i	0.320343	+	0.985913i
$11$	2.98634	−	2.16971i	0.900417	−	0.654191i	−0.0381562	−	0.999272i	$-0.512148\pi$
$11$	2.98634	−	2.16971i	0.900417	−	0.654191i	0.938573	+	0.345081i	$0.112148\pi$
$12$	1.56408	+	4.81376i	0.451512	+	1.38961i
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i
$14$	−2.40557	−	1.74775i	−0.642915	−	0.467105i
$15$	−1.43140	+	4.40540i	−0.369586	+	1.13747i
$16$	−1.33206	+	4.09967i	−0.333016	+	1.02492i
$17$	−5.46458	−	3.97025i	−1.32535	−	0.962926i	−0.999849	−	0.0173861i	$-0.994466\pi$
$17$	−5.46458	−	3.97025i	−1.32535	−	0.962926i	−0.325505	−	0.945540i	$-0.605534\pi$
$18$	−2.81075	+	8.65060i	−0.662500	+	2.03897i
$19$	1.75464	+	5.40023i	0.402543	+	1.23890i	0.922930	+	0.384968i	$0.125788\pi$
$19$	1.75464	+	5.40023i	0.402543	+	1.23890i	−0.520387	+	0.853930i	$0.674212\pi$
$20$	2.48023	−	1.80199i	0.554595	−	0.402937i
$21$	−1.29834	−	3.99589i	−0.283321	−	0.871974i
$22$	−5.84460	−	4.24635i	−1.24607	−	0.905325i
$23$	6.46530	+	4.69731i	1.34811	+	0.979458i	0.999103	+	0.0423366i	$0.0134802\pi$
$23$	6.46530	+	4.69731i	1.34811	+	0.979458i	0.349004	+	0.937121i	$0.386520\pi$
$24$	−0.743158	+	0.539936i	−0.151696	+	0.110214i
$25$	−2.19434			−0.438868
$26$	1.95711			0.383821
$27$	−3.68604	+	2.67807i	−0.709380	+	0.515394i
$28$	−0.859298	+	2.64465i	−0.162392	+	0.499791i
$29$	−1.47816	−	4.54931i	−0.274488	−	0.844786i	−0.989355	−	0.145525i	$-0.953513\pi$
$29$	−1.47816	−	4.54931i	−0.274488	−	0.844786i	0.714867	−	0.699261i	$-0.246487\pi$
$30$	9.06554			1.65513
$31$	4.36233	−	3.45978i	0.783498	−	0.621395i
$31$	4.36233	−	3.45978i	0.783498	−	0.621395i
$32$	7.77206			1.37392
$33$	−3.15447	−	9.70845i	−0.549122	−	1.69003i
$34$	−4.08504	+	12.5725i	−0.700578	+	2.15616i
$35$	−2.05883	+	1.49583i	−0.348006	+	0.252841i
$36$	8.50631			1.41772
$37$	7.92354			1.30262			0.651311	−	0.758811i	$-0.274220\pi$
$37$	7.92354			1.30262			0.651311	+	0.758811i	$0.274220\pi$
$38$	8.99040	−	6.53191i	1.45843	−	1.05961i
$39$	2.23727	+	1.62547i	0.358251	+	0.260284i
$40$	0.450129	+	0.327038i	0.0711716	+	0.0517092i
$41$	2.00908	+	6.18330i	0.313765	+	0.965670i	0.976260	+	0.216603i	$0.0694977\pi$
$41$	2.00908	+	6.18330i	0.313765	+	0.965670i	−0.662495	+	0.749067i	$0.730502\pi$
$42$	−6.65241	+	4.83326i	−1.02649	+	0.745789i
$43$	−3.15680	−	9.71565i	−0.481408	−	1.48162i	−0.837116	−	0.547025i	$-0.815760\pi$
$43$	−3.15680	−	9.71565i	−0.481408	−	1.48162i	0.355708	−	0.934597i	$-0.384240\pi$
$44$	−2.08776	+	6.42547i	−0.314742	+	0.968676i
$45$	6.29796	+	4.57574i	0.938845	+	0.682111i
$46$	4.83313	−	14.8748i	0.712606	−	2.19317i
$47$	2.46948	−	7.60026i	0.360210	−	1.10861i	−0.592717	−	0.805411i	$-0.701945\pi$
$47$	2.46948	−	7.60026i	0.360210	−	1.10861i	0.952927	−	0.303201i	$-0.0980554\pi$
$48$	9.64409	+	7.00684i	1.39200	+	1.01135i
$49$	−1.44982	+	4.46208i	−0.207117	+	0.637440i
$50$	1.32709	+	4.08437i	0.187679	+	0.577618i
$51$	−15.1119	+	10.9794i	−2.11608	+	1.53742i
$52$	−0.565586	−	1.74069i	−0.0784327	−	0.241391i
$53$	−7.69313	−	5.58939i	−1.05673	−	0.767762i	−0.0832521	−	0.996529i	$-0.526531\pi$
$53$	−7.69313	−	5.58939i	−1.05673	−	0.767762i	−0.973481	+	0.228767i	$0.926531\pi$
$54$	7.21399	+	5.24127i	0.981700	+	0.713247i
$55$	−5.00216	+	3.63428i	−0.674491	+	0.490046i
$56$	−0.504670			−0.0674393
$57$	15.7025			2.07984
$58$	−7.57377	+	5.50266i	−0.994484	+	0.722535i
$59$	−1.33409	+	4.10590i	−0.173684	+	0.534543i	−0.999571	−	0.0292922i	$-0.990675\pi$
$59$	−1.33409	+	4.10590i	−0.173684	+	0.534543i	0.825887	+	0.563835i	$0.190675\pi$
$60$	−2.61986	−	8.06309i	−0.338222	−	1.04094i
$61$	−0.00123644			−0.000158310			−7.91552e−5	−	1.00000i	$-0.500025\pi$
$61$	−0.00123644			−0.000158310			−7.91552e−5		1.00000i	$0.500025\pi$
$62$	−9.07801	−	6.02729i	−1.15291	−	0.765467i
$63$	−7.06107			−0.889611
$64$	−2.03626	−	6.26696i	−0.254532	−	0.783370i
$65$	0.517607	−	1.59303i	0.0642012	−	0.197591i
$66$	−16.1628	+	11.7430i	−1.98950	+	1.44546i
$67$	1.97679			0.241503			0.120751	−	0.992683i	$-0.461470\pi$
$67$	1.97679			0.241503			0.120751	+	0.992683i	$0.461470\pi$
$68$	12.3627			1.49920
$69$	17.8793	−	12.9901i	2.15241	−	1.56382i
$70$	4.02935	+	2.92750i	0.481600	+	0.349903i
$71$	−5.04763	−	3.66732i	−0.599044	−	0.435231i	0.246496	−	0.969144i	$-0.420721\pi$
$71$	−5.04763	−	3.66732i	−0.599044	−	0.435231i	−0.845539	+	0.533913i	$0.820721\pi$
$72$	0.477056	+	1.46823i	0.0562216	+	0.173032i
$73$	−5.81416	+	4.22423i	−0.680496	+	0.494409i	−0.873522	−	0.486784i	$-0.838170\pi$
$73$	−5.81416	+	4.22423i	−0.680496	+	0.494409i	0.193026	+	0.981194i	$0.438170\pi$
$74$	−4.79199	−	14.7482i	−0.557058	−	1.71445i
$75$	−1.87520	+	5.77128i	−0.216530	+	0.666410i
$76$	−8.40776	−	6.10859i	−0.964436	−	0.700704i
$77$	1.73305	−	5.33376i	0.197499	−	0.607839i
$78$	1.67247	−	5.14734i	0.189370	−	0.582821i
$79$	−3.72230	−	2.70441i	−0.418792	−	0.304270i	0.358360	−	0.933584i	$-0.383336\pi$
$79$	−3.72230	−	2.70441i	−0.418792	−	0.304270i	−0.777151	+	0.629314i	$0.783336\pi$
$80$	2.23122	−	6.86698i	0.249458	−	0.767752i
$81$	−0.414967	−	1.27714i	−0.0461074	−	0.141904i
$82$	10.2941	−	7.47907i	1.13679	−	0.825925i
$83$	1.06424	+	3.27538i	0.116815	+	0.359520i	0.992321	−	0.123687i	$-0.0394719\pi$
$83$	1.06424	+	3.27538i	0.116815	+	0.359520i	−0.875506	+	0.483207i	$0.839472\pi$
$84$	6.22129	+	4.52003i	0.678799	+	0.493176i
$85$	9.15322	+	6.65020i	0.992806	+	0.721316i
$86$	−16.1748	+	11.7517i	−1.74417	+	1.26721i
$87$	−13.2282			−1.41821
$88$	−1.22615			−0.130708
$89$	2.31773	−	1.68393i	0.245679	−	0.178496i	−0.458131	−	0.888885i	$-0.651481\pi$
$89$	2.31773	−	1.68393i	0.245679	−	0.178496i	0.703810	+	0.710389i	$0.251481\pi$
$90$	4.70804	−	14.4898i	0.496271	−	1.52736i
$91$	0.469491	+	1.44495i	0.0492161	+	0.151471i
$92$	−14.6267			−1.52494
$93$	−5.37159	−	14.4298i	−0.557007	−	1.49631i
$94$	−15.6400			−1.61314
$95$	−2.93904	−	9.04545i	−0.301539	−	0.928043i
$96$	6.64171	−	20.4411i	0.677867	−	2.08626i
$97$	−0.859281	+	0.624304i	−0.0872468	+	0.0633885i	−0.630554	−	0.776146i	$-0.717172\pi$
$97$	−0.859281	+	0.624304i	−0.0872468	+	0.0633885i	0.543307	+	0.839534i	$0.317172\pi$
$98$	9.18219			0.927541
$99$	−17.1557			−1.72421
$100$	3.24921	−	2.36069i	0.324921	−	0.236069i
$101$	−3.54494	−	2.57555i	−0.352735	−	0.256277i	0.397281	−	0.917697i	$-0.369954\pi$
$101$	−3.54494	−	2.57555i	−0.352735	−	0.256277i	−0.750015	+	0.661420i	$0.769954\pi$
$102$	29.5756	+	21.4879i	2.92842	+	2.12762i
$103$	1.05641	+	3.25128i	0.104091	+	0.320358i	0.989516	−	0.144424i	$-0.0461328\pi$
$103$	1.05641	+	3.25128i	0.104091	+	0.320358i	−0.885425	+	0.464782i	$0.846133\pi$
$104$	0.268732	−	0.195245i	0.0263513	−	0.0191454i
$105$	2.17474	+	6.69315i	0.212232	+	0.653184i
$106$	−5.75100	+	17.6997i	−0.558586	+	1.71915i
$107$	8.92755	+	6.48625i	0.863059	+	0.627049i	0.928715	−	0.370793i	$-0.120914\pi$
$107$	8.92755	+	6.48625i	0.863059	+	0.627049i	−0.0656564	+	0.997842i	$0.520914\pi$
$108$	2.57692	−	7.93096i	0.247965	−	0.763157i
$109$	−1.85970	+	5.72357i	−0.178127	+	0.548218i	−0.999762	−	0.0217948i	$-0.993062\pi$
$109$	−1.85970	+	5.72357i	−0.178127	+	0.548218i	0.821635	+	0.570013i	$0.193062\pi$
$110$	9.78977	+	7.11268i	0.933418	+	0.678168i
$111$	6.77116	−	20.8395i	0.642690	−	1.97800i
$112$	2.02381	+	6.22865i	0.191232	+	0.588552i
$113$	13.2170	−	9.60270i	1.24335	−	0.903346i	0.245533	−	0.969388i	$-0.421037\pi$
$113$	13.2170	−	9.60270i	1.24335	−	0.903346i	0.997817	+	0.0660419i	$0.0210371\pi$
$114$	−9.49653	−	29.2273i	−0.889432	−	2.73739i
$115$	−10.8294	−	7.86805i	−1.00985	−	0.733699i
$116$	7.08293	+	5.14605i	0.657634	+	0.477799i
$117$	3.75996	−	2.73177i	0.347608	−	0.252552i
$118$	8.44923			0.777815
$119$	−10.2623			−0.940742
$120$	1.24480	−	0.904398i	0.113634	−	0.0825598i
$121$	0.811442	−	2.49736i	0.0737675	−	0.227033i
$122$	0.000747776		0.00230142i	6.77005e−5		0.000208361i
$123$	17.9794			1.62115
$124$	−2.73735	+	9.81601i	−0.245821	+	0.881503i
$125$	12.0506			1.07784
$126$	4.27039	+	13.1429i	0.380437	+	1.17086i
$127$	3.79696	−	11.6859i	0.336926	−	1.03695i	−0.628840	−	0.777535i	$-0.716470\pi$
$127$	3.79696	−	11.6859i	0.336926	−	1.03695i	0.965766	−	0.259416i	$-0.0835302\pi$
$128$	2.14212	−	1.55634i	0.189338	−	0.137562i
$129$	−28.2505			−2.48732
$130$	−3.27818			−0.287515
$131$	11.8278	−	8.59341i	1.03340	−	0.750810i	0.0644142	−	0.997923i	$-0.479482\pi$
$131$	11.8278	−	8.59341i	1.03340	−	0.750810i	0.968986	+	0.247114i	$0.0794821\pi$
$132$	15.1153	+	10.9819i	1.31562	+	0.955854i
$133$	6.97926	+	5.07073i	0.605178	+	0.439688i
$134$	−1.19552	−	3.67943i	−0.103277	−	0.317855i
$135$	6.17416	−	4.48579i	0.531387	−	0.386075i
$136$	0.693335	+	2.13387i	0.0594530	+	0.182977i
$137$	1.44109	−	4.43523i	0.123121	−	0.378927i	−0.870433	−	0.492287i	$-0.836161\pi$
$137$	1.44109	−	4.43523i	0.123121	−	0.378927i	0.993554	+	0.113359i	$0.0361611\pi$
$138$	−34.9917	−	25.4230i	−2.97869	−	2.16415i
$139$	−2.19671	+	6.76077i	−0.186322	+	0.573441i	−0.999969	−	0.00791923i	$-0.997479\pi$
$139$	−2.19671	+	6.76077i	−0.186322	+	0.573441i	0.813646	+	0.581360i	$0.197479\pi$
$140$	1.43933	−	4.42981i	0.121646	−	0.374387i
$141$	−17.8789	−	12.9898i	−1.50568	−	1.09394i
$142$	−3.77335	+	11.6132i	−0.316653	+	0.974557i
$143$	1.14068	+	3.51066i	0.0953886	+	0.293576i
$144$	16.2078	−	11.7757i	1.35065	−	0.981307i
$145$	2.47593	+	7.62014i	0.205615	+	0.632818i
$146$	11.3789	+	8.26729i	0.941728	+	0.684206i
$147$	10.4966	+	7.62625i	0.865748	+	0.629003i
$148$	−11.7326	+	8.52421i	−0.964411	+	0.700685i
$149$	−17.2197			−1.41069			−0.705346	−	0.708863i	$-0.749208\pi$
$149$	−17.2197			−1.41069			−0.705346	+	0.708863i	$0.749208\pi$
$150$	11.8763			0.969695
$151$	7.79189	−	5.66114i	0.634095	−	0.460697i	−0.223721	−	0.974653i	$-0.571821\pi$
$151$	7.79189	−	5.66114i	0.634095	−	0.460697i	0.857817	+	0.513956i	$0.171821\pi$
$152$	0.582841	−	1.79380i	0.0472747	−	0.145497i
$153$	9.70077	+	29.8559i	0.784261	+	2.41371i
$154$	−10.9760			−0.884468
$155$	−7.30695	+	5.79516i	−0.586908	+	0.465479i
$156$	−5.06148			−0.405243
$157$	5.31396	+	16.3547i	0.424100	+	1.30525i	0.903853	+	0.427843i	$0.140726\pi$
$157$	5.31396	+	16.3547i	0.424100	+	1.30525i	−0.479753	+	0.877404i	$0.659274\pi$
$158$	−2.78260	+	8.56397i	−0.221372	+	0.681313i
$159$	−21.2748	+	15.4570i	−1.68720	+	1.22582i
$160$	−13.0183			−1.02918
$161$	12.1416			0.956893
$162$	−2.12620	+	1.54477i	−0.167050	+	0.121369i
$163$	17.7425	+	12.8907i	1.38970	+	1.00968i	0.995898	+	0.0904844i	$0.0288415\pi$
$163$	17.7425	+	12.8907i	1.38970	+	1.00968i	0.393805	+	0.919194i	$0.371158\pi$
$164$	−9.62694	−	6.99438i	−0.751737	−	0.546169i
$165$	5.28377	+	16.2618i	0.411341	+	1.26598i
$166$	5.45290	−	3.96177i	0.423227	−	0.307493i
$167$	−2.68052	−	8.24979i	−0.207425	−	0.638388i	−0.999605	−	0.0281008i	$-0.991054\pi$
$167$	−2.68052	−	8.24979i	−0.207425	−	0.638388i	0.792180	−	0.610287i	$-0.208946\pi$
$168$	−0.431272	+	1.32732i	−0.0332733	+	0.102405i
$169$	−0.809017	−	0.587785i	−0.0622321	−	0.0452143i
$170$	6.84248	−	21.0590i	0.524794	−	1.61515i
$171$	8.15481	−	25.0979i	0.623614	−	1.91929i
$172$	15.1265	+	10.9901i	1.15339	+	0.837985i
$173$	−0.357845	+	1.10133i	−0.0272065	+	0.0837329i	−0.963738	−	0.266851i	$-0.914017\pi$
$173$	−0.357845	+	1.10133i	−0.0272065	+	0.0837329i	0.936531	+	0.350584i	$0.114017\pi$
$174$	8.00015	+	24.6219i	0.606490	+	1.86658i
$175$	−2.69716	+	1.95960i	−0.203886	+	0.148132i
$176$	4.91708	+	15.1332i	0.370638	+	1.14071i
$177$	9.65876	+	7.01750i	0.725997	+	0.527468i
$178$	−4.53605	−	3.29563i	−0.339991	−	0.247018i
$179$	−0.752006	+	0.546364i	−0.0562076	+	0.0408372i	−0.615534	−	0.788110i	$-0.711060\pi$
$179$	−0.752006	+	0.546364i	−0.0562076	+	0.0408372i	0.559327	+	0.828947i	$0.311060\pi$
$180$	−14.2482			−1.06200
$181$	0.553500			0.0411413			0.0205707	−	0.999788i	$-0.493452\pi$
$181$	0.553500			0.0411413			0.0205707	+	0.999788i	$0.493452\pi$
$182$	2.40557	−	1.74775i	0.178313	−	0.129552i
$183$	−0.00105662	+	0.00325194i	−7.81075e−5	+	0.000240390i
$184$	−0.820305	−	2.52464i	−0.0604737	−	0.186119i
$185$	−13.2720			−0.975777
$186$	−23.6099	+	18.7251i	−1.73117	+	1.37299i
$187$	−24.9334			−1.82331
$188$	4.51982	+	13.9106i	0.329642	+	1.01453i
$189$	−2.13910	+	6.58346i	−0.155596	+	0.478877i
$190$	−15.0590	+	10.9410i	−1.09249	+	0.793744i
$191$	−22.6489			−1.63881			−0.819407	−	0.573212i	$-0.805697\pi$
$191$	−22.6489			−1.63881			−0.819407	+	0.573212i	$0.805697\pi$
$192$	−18.2227			−1.31511
$193$	4.66344	−	3.38818i	0.335681	−	0.243887i	−0.407156	−	0.913359i	$-0.633479\pi$
$193$	4.66344	−	3.38818i	0.335681	−	0.243887i	0.742838	+	0.669472i	$0.233479\pi$
$194$	1.68171	+	1.22183i	0.120740	+	0.0877224i
$195$	−3.74746	−	2.72269i	−0.268361	−	0.194976i
$196$	−2.65356	−	8.16683i	−0.189540	−	0.583345i
$197$	7.30496	−	5.30737i	0.520457	−	0.378134i	−0.296319	−	0.955089i	$-0.595759\pi$
$197$	7.30496	−	5.30737i	0.520457	−	0.378134i	0.816776	+	0.576955i	$0.195759\pi$
$198$	10.3754	+	31.9322i	0.737347	+	2.26932i
$199$	1.84117	−	5.66654i	0.130517	−	0.401690i	−0.864349	−	0.502893i	$-0.832269\pi$
$199$	1.84117	−	5.66654i	0.130517	−	0.401690i	0.994866	+	0.101203i	$0.0322690\pi$
$200$	0.589690	+	0.428435i	0.0416974	+	0.0302949i
$201$	1.68929	−	5.19909i	0.119153	−	0.366716i
$202$	−2.65002	+	8.15591i	−0.186455	+	0.573848i
$203$	−5.87952	−	4.27172i	−0.412662	−	0.299816i
$204$	10.5647	−	32.5149i	0.739680	−	2.27650i
$205$	−3.36522	−	10.3571i	−0.235037	−	0.723371i
$206$	5.41279	−	3.93262i	0.377127	−	0.273999i
$207$	−11.4773	−	35.3234i	−0.797725	−	2.45515i
$208$	−3.48738	−	2.53373i	−0.241807	−	0.175683i
$209$	16.9569	+	12.3199i	1.17293	+	0.852185i
$210$	11.1429	−	8.09576i	0.768930	−	0.558661i
$211$	22.6673			1.56048			0.780241	−	0.625479i	$-0.215097\pi$
$211$	22.6673			1.56048			0.780241	+	0.625479i	$0.215097\pi$
$212$	17.4045			1.19535
$213$	−13.9588	+	10.1417i	−0.956444	+	0.694897i
$214$	6.67378	−	20.5398i	0.456210	−	1.40407i
$215$	5.28768	+	16.2738i	0.360617	+	1.10986i
$216$	1.51344			0.102976
$217$	2.27226	−	8.14824i	0.154251	−	0.553139i
$218$	11.7781			0.797714
$219$	6.14148	+	18.9015i	0.415003	+	1.27725i
$220$	3.49702	−	10.7627i	0.235769	−	0.725623i
$221$	5.46458	−	3.97025i	0.367587	−	0.267068i
$222$	−42.8840			−2.87819
$223$	6.41468			0.429559			0.214779	−	0.976663i	$-0.431097\pi$
$223$	6.41468			0.429559			0.214779	+	0.976663i	$0.431097\pi$
$224$	9.55298	−	6.94065i	0.638285	−	0.463741i
$225$	8.25063	+	5.99443i	0.550042	+	0.399629i
$226$	−25.8671	−	18.7935i	−1.72065	−	1.25013i
$227$	4.96034	+	15.2663i	0.329229	+	1.01326i	0.969495	+	0.245110i	$0.0788240\pi$
$227$	4.96034	+	15.2663i	0.329229	+	1.01326i	−0.640266	+	0.768153i	$0.721176\pi$
$228$	−23.2510	+	16.8928i	−1.53983	+	1.11876i
$229$	3.76215	+	11.5787i	0.248610	+	0.765142i	0.995022	+	0.0996581i	$0.0317749\pi$
$229$	3.76215	+	11.5787i	0.248610	+	0.765142i	−0.746412	+	0.665484i	$0.768225\pi$
$230$	−8.09554	+	24.9155i	−0.533804	+	1.64288i
$231$	−12.5472	−	9.11607i	−0.825545	−	0.599793i
$232$	−0.491002	+	1.51115i	−0.0322359	+	0.0992118i
$233$	−7.50046	+	23.0840i	−0.491371	+	1.51229i	0.331165	+	0.943573i	$0.392558\pi$
$233$	−7.50046	+	23.0840i	−0.491371	+	1.51229i	−0.822536	+	0.568713i	$0.807442\pi$
$234$	−7.35864	−	5.34637i	−0.481049	−	0.349503i
$235$	−4.13640	+	12.7305i	−0.269829	+	0.830447i
$236$	−2.44175	−	7.51493i	−0.158944	−	0.489180i
$237$	−10.2937	+	7.47884i	−0.668650	+	0.485803i
$238$	6.20642	+	19.1014i	0.402303	+	1.23816i
$239$	16.2380	+	11.7976i	1.05035	+	0.763122i	0.972279	−	0.233826i	$-0.0751244\pi$
$239$	16.2380	+	11.7976i	1.05035	+	0.763122i	0.0780693	+	0.996948i	$0.475124\pi$
$240$	−16.1539	−	11.7365i	−1.04273	−	0.757590i
$241$	23.1402	−	16.8123i	1.49059	−	1.08298i	0.516644	−	0.856200i	$-0.327181\pi$
$241$	23.1402	−	16.8123i	1.49059	−	1.08298i	0.973947	−	0.226777i	$-0.0728189\pi$
$242$	−5.13914			−0.330356
$243$	−17.3822			−1.11507
$244$	0.00183083	−	0.00133018i	0.000117207	−	8.51558e-5i
$245$	2.42846	−	7.47403i	0.155149	−	0.477498i
$246$	−10.8736	−	33.4655i	−0.693275	−	2.13368i
$247$	−5.67814			−0.361292
$248$	−1.84780	+	0.0780289i	−0.117336	+	0.00495484i
$249$	9.52394			0.603555
$250$	−7.28796	−	22.4300i	−0.460931	−	1.41860i
$251$	−7.19873	+	22.1554i	−0.454380	+	1.39844i	0.417483	+	0.908685i	$0.362912\pi$
$251$	−7.19873	+	22.1554i	−0.454380	+	1.39844i	−0.871862	+	0.489751i	$0.837088\pi$
$252$	10.4555	−	7.59635i	0.658634	−	0.478525i
$253$	29.4994			1.85461
$254$	−24.0474			−1.50887
$255$	25.3125	−	18.3906i	1.58513	−	1.15167i
$256$	−14.8543	−	10.7923i	−0.928396	−	0.674519i
$257$	14.6791	+	10.6650i	0.915659	+	0.665265i	0.942440	−	0.334376i	$-0.108525\pi$
$257$	14.6791	+	10.6650i	0.915659	+	0.665265i	−0.0267804	+	0.999641i	$0.508525\pi$
$258$	17.0854	+	52.5833i	1.06369	+	3.27370i
$259$	9.73917	−	7.07592i	0.605162	−	0.439676i
$260$	0.947362	+	2.91568i	0.0587529	+	0.180823i
$261$	−6.86984	+	21.1432i	−0.425233	+	1.30873i
$262$	−23.1483	−	16.8182i	−1.43011	−	1.03903i
$263$	3.66874	−	11.2912i	0.226224	−	0.696246i	−0.771941	−	0.635694i	$-0.780714\pi$
$263$	3.66874	−	11.2912i	0.226224	−	0.696246i	0.998165	−	0.0605517i	$-0.0192860\pi$
$264$	−1.04782	+	3.22487i	−0.0644891	+	0.198477i
$265$	12.8861	+	9.36228i	0.791585	+	0.575121i
$266$	5.21734	−	16.0573i	0.319895	−	0.984537i
$267$	−2.44821	−	7.53482i	−0.149828	−	0.461124i
$268$	−2.92707	+	2.12664i	−0.178799	+	0.129905i
$269$	3.36495	+	10.3562i	0.205164	+	0.631431i	0.999707	+	0.0242221i	$0.00771089\pi$
$269$	3.36495	+	10.3562i	0.205164	+	0.631431i	−0.794542	+	0.607209i	$0.792289\pi$
$270$	−12.0835	−	8.77918i	−0.735379	−	0.534284i
$271$	2.54257	+	1.84728i	0.154450	+	0.112214i	0.662326	−	0.749216i	$-0.269569\pi$
$271$	2.54257	+	1.84728i	0.154450	+	0.112214i	−0.507876	+	0.861430i	$0.669569\pi$
$272$	23.5558	−	17.1143i	1.42828	−	1.03771i
$273$	4.20152			0.254288
$274$	−9.12694			−0.551378
$275$	−6.55306	+	4.76108i	−0.395164	+	0.287104i
$276$	−12.4995	+	38.4694i	−0.752379	+	2.31558i
$277$	−1.21682	−	3.74500i	−0.0731118	−	0.225015i	0.907823	−	0.419355i	$-0.137744\pi$
$277$	−1.21682	−	3.74500i	−0.0731118	−	0.225015i	−0.980934	+	0.194340i	$0.937744\pi$
$278$	13.9125			0.834415
$279$	−25.8535	+	1.09174i	−1.54781	+	0.0653607i
$280$	0.845326			0.0505179
$281$	−1.78489	−	5.49332i	−0.106477	−	0.327704i	0.883597	−	0.468248i	$-0.155115\pi$
$281$	−1.78489	−	5.49332i	−0.106477	−	0.327704i	−0.990074	+	0.140544i	$0.955115\pi$
$282$	−13.3654	+	41.1344i	−0.795896	+	2.44952i
$283$	−4.46474	+	3.24382i	−0.265401	+	0.192825i	−0.712525	−	0.701647i	$-0.752448\pi$
$283$	−4.46474	+	3.24382i	−0.265401	+	0.192825i	0.447124	+	0.894472i	$0.352448\pi$
$284$	11.4195			0.677622
$285$	−26.3018			−1.55798
$286$	5.84460	−	4.24635i	0.345599	−	0.251092i
$287$	7.99129	+	5.80601i	0.471711	+	0.342718i
$288$	−29.2226	−	21.2315i	−1.72196	−	1.25108i
$289$	8.84544	+	27.2235i	0.520320	+	1.60138i
$290$	12.6861	−	9.21702i	0.744956	−	0.541242i
$291$	0.907656	+	2.79348i	0.0532078	+	0.163757i
$292$	4.06470	−	12.5098i	0.237868	−	0.732083i
$293$	1.28126	+	0.930893i	0.0748522	+	0.0543833i	0.624582	−	0.780959i	$-0.285269\pi$
$293$	1.28126	+	0.930893i	0.0748522	+	0.0543833i	−0.549730	+	0.835343i	$0.685269\pi$
$294$	7.84675	−	24.1498i	0.457632	−	1.40845i
$295$	2.23461	−	6.87743i	0.130104	−	0.400419i
$296$	−2.12931	−	1.54703i	−0.123764	−	0.0899195i
$297$	−5.19718	+	15.9953i	−0.301571	+	0.928140i
$298$	10.4141	+	32.0514i	0.603274	+	1.85669i
$299$	−6.46530	+	4.69731i	−0.373898	+	0.271653i
$300$	−3.43213	−	10.5630i	−0.198154	−	0.609856i
$301$	−12.5565	−	9.12282i	−0.723744	−	0.525831i
$302$	−15.2496	−	11.0795i	−0.877515	−	0.637552i
$303$	−9.80326	+	7.12248i	−0.563182	+	0.409176i
$304$	−24.4764			−1.40382
$305$	0.00207106			0.000118588
$306$	49.7046	−	36.1125i	2.84142	−	2.06441i
$307$	5.67778	−	17.4744i	0.324048	−	0.997318i	−0.647820	−	0.761793i	$-0.724319\pi$
$307$	5.67778	−	17.4744i	0.324048	−	0.997318i	0.971868	−	0.235525i	$-0.0756808\pi$
$308$	3.17195	+	9.76225i	0.180739	+	0.556256i
$309$	9.45387			0.537812
$310$	15.2058	+	10.0958i	0.863629	+	0.573402i
$311$	33.3780			1.89269			0.946345	−	0.323157i	$-0.104744\pi$
$311$	33.3780			1.89269			0.946345	+	0.323157i	$0.104744\pi$
$312$	−0.283861	−	0.873634i	−0.0160705	−	0.0494598i
$313$	0.535702	−	1.64872i	0.0302796	−	0.0931912i	−0.934775	−	0.355241i	$-0.884399\pi$
$313$	0.535702	−	1.64872i	0.0302796	−	0.0931912i	0.965054	+	0.262050i	$0.0843986\pi$
$314$	27.2276	−	19.7820i	1.53654	−	1.11636i
$315$	11.8274			0.666396
$316$	8.42113			0.473725
$317$	−4.58731	+	3.33287i	−0.257649	+	0.187193i	−0.709110	−	0.705098i	$-0.750903\pi$
$317$	−4.58731	+	3.33287i	−0.257649	+	0.187193i	0.451461	+	0.892291i	$0.350903\pi$
$318$	41.6370	+	30.2511i	2.33489	+	1.69640i
$319$	−14.2850	−	10.3786i	−0.799805	−	0.581092i
$320$	3.41075	+	10.4972i	0.190667	+	0.586813i
$321$	24.6885	−	17.9372i	1.37798	−	1.00116i
$322$	−7.34300	−	22.5994i	−0.409209	−	1.25942i
$323$	11.8519	−	36.4763i	0.659456	−	2.02960i
$324$	1.98840	+	1.44466i	0.110467	+	0.0802589i
$325$	0.678089	−	2.08694i	0.0376136	−	0.115763i
$326$	13.2634	−	40.8206i	0.734593	−	2.26084i
$327$	13.4642	+	9.78229i	0.744570	+	0.540962i
$328$	0.667357	−	2.05391i	0.0368486	−	0.113408i
$329$	−3.75189	−	11.5471i	−0.206848	−	0.636614i
$330$	27.0728	−	19.6696i	1.49031	−	1.08277i
$331$	−7.37592	−	22.7007i	−0.405417	−	1.24775i	−0.920546	−	0.390633i	$-0.872256\pi$
$331$	−7.37592	−	22.7007i	−0.405417	−	1.24775i	0.515129	−	0.857113i	$-0.327744\pi$
$332$	−5.09952	−	3.70502i	−0.279872	−	0.203339i
$333$	−29.7921	−	21.6453i	−1.63260	−	1.18615i
$334$	−13.7344	+	9.97861i	−0.751512	+	0.546005i
$335$	−3.31114			−0.180907
$336$	18.1113			0.988051
$337$	−8.11178	+	5.89356i	−0.441877	+	0.321042i	−0.786380	−	0.617743i	$-0.788047\pi$
$337$	−8.11178	+	5.89356i	−0.441877	+	0.321042i	0.344503	+	0.938785i	$0.388047\pi$
$338$	−0.604780	+	1.86132i	−0.0328957	+	0.101243i
$339$	−13.9611	−	42.9678i	−0.758261	−	2.33369i
$340$	−20.7077			−1.12303
$341$	5.52072	−	19.7971i	0.298964	−	1.07207i
$342$	−51.6471			−2.79276
$343$	5.48916	+	16.8939i	0.296387	+	0.912184i
$344$	−1.04860	+	3.22726i	−0.0565367	+	0.174002i
$345$	−29.9480	+	21.7585i	−1.61234	+	1.17144i
$346$	2.26635			0.121840
$347$	−31.5346			−1.69287			−0.846434	−	0.532494i	$-0.821255\pi$
$347$	−31.5346			−1.69287			−0.846434	+	0.532494i	$0.821255\pi$
$348$	19.5873	−	14.2310i	1.04999	−	0.762862i
$349$	7.79549	+	5.66375i	0.417283	+	0.303174i	0.776544	−	0.630063i	$-0.216971\pi$
$349$	7.79549	+	5.66375i	0.417283	+	0.303174i	−0.359261	+	0.933237i	$0.616971\pi$
$350$	5.27864	+	3.83516i	0.282155	+	0.204998i
$351$	−1.40794	−	4.33321i	−0.0751505	−	0.231289i
$352$	23.2100	−	16.8631i	1.23710	−	0.898805i
$353$	−0.451736	−	1.39030i	−0.0240435	−	0.0739982i	0.938315	−	0.345782i	$-0.112386\pi$
$353$	−0.451736	−	1.39030i	−0.0240435	−	0.0739982i	−0.962358	+	0.271784i	$0.912386\pi$
$354$	7.22040	−	22.2221i	0.383760	−	1.18109i
$355$	8.45484	+	6.14280i	0.448736	+	0.326026i
$356$	−1.62033	+	4.98687i	−0.0858774	+	0.264303i
$357$	−8.76976	+	26.9906i	−0.464145	+	1.42849i
$358$	1.47176	+	1.06929i	0.0777848	+	0.0565140i
$359$	−2.51244	+	7.73249i	−0.132601	+	0.408105i	−0.995209	−	0.0977681i	$-0.968830\pi$
$359$	−2.51244	+	7.73249i	−0.132601	+	0.408105i	0.862608	+	0.505873i	$0.168830\pi$
$360$	−0.799073	−	2.45930i	−0.0421149	−	0.129616i
$361$	−10.7124	+	7.78304i	−0.563812	+	0.409634i
$362$	−0.334746	−	1.03024i	−0.0175938	−	0.0541483i
$363$	−5.87482	−	4.26830i	−0.308348	−	0.224028i
$364$	−2.24967	−	1.63448i	−0.117915	−	0.0856701i
$365$	9.73878	−	7.07564i	0.509751	−	0.370356i
$366$	0.00669192			0.000349792
$367$	36.9918			1.93096			0.965479	−	0.260480i	$-0.0838809\pi$
$367$	36.9918			1.93096			0.965479	+	0.260480i	$0.0838809\pi$
$368$	−27.8696	+	20.2484i	−1.45280	+	1.05552i
$369$	9.33731	−	28.7373i	0.486081	−	1.49600i
$370$	8.02664	+	24.7035i	0.417285	+	1.28427i
$371$	−14.4474			−0.750074
$372$	23.4776	+	15.5878i	1.21726	+	0.808190i
$373$	−17.4439			−0.903211			−0.451606	−	0.892218i	$-0.649149\pi$
$373$	−17.4439			−0.903211			−0.451606	+	0.892218i	$0.649149\pi$
$374$	15.0792	+	46.4090i	0.779727	+	2.39975i
$375$	10.2980	−	31.6939i	0.531786	−	1.63667i
$376$	−2.14754	+	1.56028i	−0.110751	+	0.0804653i
$377$	4.78343			0.246359
$378$	13.5476			0.696815
$379$	−18.4259	+	13.3872i	−0.946477	+	0.687656i	−0.949971	−	0.312338i	$-0.898888\pi$
$379$	−18.4259	+	13.3872i	−0.946477	+	0.687656i	0.00349391	+	0.999994i	$0.498888\pi$
$380$	14.0831	+	10.2320i	0.722447	+	0.524888i
$381$	−27.4899	−	19.9726i	−1.40835	−	1.02323i
$382$	13.6976	+	42.1568i	0.700829	+	2.15693i
$383$	−14.8528	+	10.7912i	−0.758940	+	0.551402i	−0.898585	−	0.438799i	$-0.855404\pi$
$383$	−14.8528	+	10.7912i	−0.758940	+	0.551402i	0.139645	+	0.990202i	$0.455404\pi$
$384$	−2.26271	−	6.96391i	−0.115468	−	0.355375i
$385$	−2.90287	+	8.93411i	−0.147944	+	0.455324i
$386$	−9.12685	−	6.63105i	−0.464544	−	0.337511i
$387$	−14.6714	+	45.1541i	−0.745791	+	2.29531i
$388$	0.600726	−	1.84884i	0.0304972	−	0.0938608i
$389$	13.4488	+	9.77112i	0.681881	+	0.495416i	0.873981	−	0.485960i	$-0.161530\pi$
$389$	13.4488	+	9.77112i	0.681881	+	0.495416i	−0.192100	+	0.981375i	$0.561530\pi$
$390$	−2.80141	+	8.62184i	−0.141855	+	0.436584i
$391$	−16.6806	−	51.3377i	−0.843575	−	2.59626i
$392$	1.26081	−	0.916034i	0.0636807	−	0.0462667i
$393$	−12.4937	−	38.4516i	−0.630223	−	1.93963i
$394$	−14.2966	−	10.3871i	−0.720253	−	0.523294i
$395$	6.23489	+	4.52992i	0.313712	+	0.227925i
$396$	25.4028	−	18.4562i	1.27654	−	0.927459i
$397$	−20.8600			−1.04693			−0.523467	−	0.852046i	$-0.675362\pi$
$397$	−20.8600			−1.04693			−0.523467	+	0.852046i	$0.675362\pi$
$398$	−11.6608			−0.584501
$399$	19.3006	−	14.0227i	0.966238	−	0.702013i
$400$	2.92300	−	8.99607i	0.146150	−	0.449803i
$401$	9.03722	+	27.8137i	0.451297	+	1.38895i	0.875428	+	0.483349i	$0.160580\pi$
$401$	9.03722	+	27.8137i	0.451297	+	1.38895i	−0.424131	+	0.905601i	$0.639420\pi$
$402$	−10.6988			−0.533609
$403$	1.94241	+	5.21795i	0.0967584	+	0.259925i
$404$	8.01987			0.399004
$405$	0.695073	+	2.13922i	0.0345385	+	0.106299i
$406$	−4.39523	+	13.5271i	−0.218132	+	0.671341i
$407$	23.6624	−	17.1917i	1.17290	−	0.852163i
$408$	6.20472			0.307179
$409$	0.710473			0.0351306			0.0175653	−	0.999846i	$-0.494409\pi$
$409$	0.710473			0.0351306			0.0175653	+	0.999846i	$0.494409\pi$
$410$	−17.2427	+	12.5275i	−0.851554	+	0.618690i
$411$	−10.4335	−	7.58037i	−0.514646	−	0.373912i
$412$	−5.06200	−	3.67776i	−0.249387	−	0.181190i
$413$	2.02689	+	6.23812i	0.0997367	+	0.306958i
$414$	−58.8069	+	42.7257i	−2.89020	+	2.09986i
$415$	−1.78260	−	5.48629i	−0.0875046	−	0.269312i
$416$	−2.40170	+	7.39167i	−0.117753	+	0.362406i
$417$	15.9041	+	11.5550i	0.778827	+	0.565851i
$418$	12.6761	−	39.0130i	0.620009	−	1.90819i
$419$	−10.5034	+	32.3261i	−0.513124	+	1.57923i	0.273546	+	0.961859i	$0.411804\pi$
$419$	−10.5034	+	32.3261i	−0.513124	+	1.57923i	−0.786670	+	0.617374i	$0.788196\pi$
$420$	−10.4207	−	7.57110i	−0.508479	−	0.369432i
$421$	9.43018	−	29.0231i	0.459599	−	1.41450i	−0.406052	−	0.913850i	$-0.633095\pi$
$421$	9.43018	−	29.0231i	0.459599	−	1.41450i	0.865650	−	0.500649i	$-0.166905\pi$
$422$	−13.7087	−	42.1911i	−0.667330	−	2.05383i
$423$	−30.0473	+	21.8306i	−1.46095	+	1.06144i
$424$	0.976090	+	3.00410i	0.0474031	+	0.145892i
$425$	11.9911	+	8.71208i	0.581656	+	0.422598i
$426$	27.3190	+	19.8484i	1.32361	+	0.961658i
$427$	−0.00151977	+	0.00110418i	−7.35467e−5	+	5.34348e-5i
$428$	−20.1972			−0.976268
$429$	10.2081			0.492850
$430$	27.0929	−	19.6841i	1.30654	−	0.949253i
$431$	−3.49178	+	10.7466i	−0.168193	+	0.517645i	−0.999257	−	0.0385315i	$-0.987732\pi$
$431$	−3.49178	+	10.7466i	−0.168193	+	0.517645i	0.831064	+	0.556176i	$0.187732\pi$
$432$	−6.06914	−	18.6789i	−0.292002	−	0.898689i
$433$	−6.93116			−0.333090			−0.166545	−	0.986034i	$-0.553261\pi$
$433$	−6.93116			−0.333090			−0.166545	+	0.986034i	$0.553261\pi$
$434$	−16.5407	+	0.698480i	−0.793980	+	0.0335281i
$435$	22.1574			1.06236
$436$	−3.40376	−	10.4757i	−0.163011	−	0.501695i
$437$	−14.0223	+	43.1562i	−0.670778	+	2.06444i
$438$	31.4676	−	22.8625i	1.50358	−	1.09241i
$439$	−33.7900			−1.61271			−0.806354	−	0.591434i	$-0.798562\pi$
$439$	−33.7900			−1.61271			−0.806354	+	0.591434i	$0.798562\pi$
$440$	2.05382			0.0979118
$441$	17.6406	−	12.8167i	0.840030	−	0.610317i
$442$	−10.6948	−	7.77020i	−0.508698	−	0.369591i
$443$	−8.39706	−	6.10082i	−0.398956	−	0.289859i	0.370159	−	0.928968i	$-0.379303\pi$
$443$	−8.39706	−	6.10082i	−0.398956	−	0.289859i	−0.769116	+	0.639109i	$0.779303\pi$
$444$	12.3931	+	38.1420i	0.588149	+	1.81014i
$445$	−3.88222	+	2.82060i	−0.184035	+	0.133709i
$446$	−3.87947	−	11.9398i	−0.183698	−	0.565365i
$447$	−14.7153	+	45.2890i	−0.696010	+	2.14210i
$448$	−8.09941	−	5.88457i	−0.382661	−	0.278020i
$449$	−7.97480	+	24.5439i	−0.376354	+	1.15830i	0.566207	+	0.824263i	$0.308410\pi$
$449$	−7.97480	+	24.5439i	−0.376354	+	1.15830i	−0.942561	+	0.334035i	$0.891590\pi$
$450$	6.16775	−	18.9824i	0.290750	−	0.894838i
$451$	19.4157	+	14.1064i	0.914252	+	0.664243i
$452$	−9.24003	+	28.4379i	−0.434615	+	1.33761i
$453$	−8.23055	−	25.3310i	−0.386705	−	1.19016i
$454$	25.4157	−	18.4656i	1.19282	−	0.866631i
$455$	−0.786403	−	2.42030i	−0.0368671	−	0.113465i
$456$	−4.21975	−	3.06583i	−0.197608	−	0.143571i
$457$	0.199162	+	0.144700i	0.00931642	+	0.00676877i	0.592434	−	0.805619i	$-0.298167\pi$
$457$	0.199162	+	0.144700i	0.00931642	+	0.00676877i	−0.583117	+	0.812388i	$0.698167\pi$
$458$	19.2764	−	14.0051i	0.900728	−	0.654417i
$459$	30.7753			1.43647
$460$	24.4999			1.14231
$461$	−16.4847	+	11.9769i	−0.767770	+	0.557818i	−0.901284	−	0.433229i	$-0.857374\pi$
$461$	−16.4847	+	11.9769i	−0.767770	+	0.557818i	0.133513	+	0.991047i	$0.457374\pi$
$462$	−9.37964	+	28.8676i	−0.436381	+	1.34304i
$463$	−5.58322	−	17.1834i	−0.259474	−	0.798580i	−0.992915	−	0.118826i	$-0.962087\pi$
$463$	−5.58322	−	17.1834i	−0.259474	−	0.798580i	0.733441	−	0.679753i	$-0.237913\pi$
$464$	20.6197			0.957244
$465$	8.99746	+	24.1701i	0.417247	+	1.12086i
$466$	47.5029			2.20053
$467$	−2.21007	−	6.80190i	−0.102270	−	0.314755i	0.886810	−	0.462134i	$-0.152916\pi$
$467$	−2.21007	−	6.80190i	−0.102270	−	0.314755i	−0.989080	+	0.147380i	$0.952916\pi$
$468$	−2.62860	+	8.08998i	−0.121507	+	0.373960i
$469$	2.42976	−	1.76532i	0.112196	−	0.0815149i
$470$	26.1972			1.20839
$471$	47.5552			2.19123
$472$	1.16017	−	0.842913i	0.0534012	−	0.0387982i
$473$	−30.5074	−	22.1649i	−1.40273	−	1.01914i
$474$	20.1460	+	14.6369i	0.925335	+	0.672295i
$475$	−3.85028	−	11.8500i	−0.176663	−	0.543713i
$476$	15.1956	−	11.0403i	0.696489	−	0.506029i
$477$	13.6569	+	42.0317i	0.625308	+	1.92450i
$478$	12.1387	−	37.3590i	0.555211	−	1.70876i
$479$	−9.17778	−	6.66805i	−0.419344	−	0.304671i	0.358030	−	0.933710i	$-0.383449\pi$
$479$	−9.17778	−	6.66805i	−0.419344	−	0.304671i	−0.777374	+	0.629039i	$0.783449\pi$
$480$	−11.1249	+	34.2390i	−0.507781	+	1.56279i
$481$	−2.44851	+	7.53573i	−0.111642	+	0.343600i
$482$	−45.2879	−	32.9036i	−2.06281	−	1.49872i
$483$	10.3758	−	31.9333i	0.472113	−	1.45302i
$484$	1.48516	+	4.57086i	0.0675074	+	0.207766i
$485$	1.43930	−	1.04572i	0.0653555	−	0.0474835i
$486$	10.5124	+	32.3538i	0.476852	+	1.46760i
$487$	29.7877	+	21.6420i	1.34981	+	0.980695i	0.999021	+	0.0442403i	$0.0140867\pi$
$487$	29.7877	+	21.6420i	1.34981	+	0.980695i	0.350789	+	0.936454i	$0.385913\pi$
$488$	0.000332272	0	0.000241410i	1.50412e−5	0	1.09281e-5i
$489$	49.0656	−	35.6483i	2.21882	−	1.61207i
$490$	−15.3803			−0.694809
$491$	−15.8913			−0.717165			−0.358583	−	0.933498i	$-0.616740\pi$
$491$	−15.8913			−0.717165			−0.358583	+	0.933498i	$0.616740\pi$
$492$	−26.6225	+	19.3424i	−1.20024	+	0.872023i
$493$	−9.98437	+	30.7287i	−0.449673	+	1.38395i
$494$	3.43403	+	10.5688i	0.154504	+	0.475515i
$495$	28.7359			1.29158
$496$	8.37304	+	22.4927i	0.375961	+	1.00995i
$497$	−9.47928			−0.425204
$498$	−5.75989	−	17.7271i	−0.258107	−	0.794371i
$499$	−0.730483	+	2.24820i	−0.0327009	+	0.100643i	−0.966075	−	0.258263i	$-0.916850\pi$
$499$	−0.730483	+	2.24820i	−0.0327009	+	0.100643i	0.933374	+	0.358906i	$0.116850\pi$
$500$	−17.8436	+	12.9641i	−0.797990	+	0.579774i
$501$	−23.9882			−1.07171
$502$	45.5920			2.03487
$503$	16.6213	−	12.0761i	0.741109	−	0.538447i	−0.151949	−	0.988388i	$-0.548555\pi$
$503$	16.6213	−	12.0761i	0.741109	−	0.538447i	0.893058	+	0.449941i	$0.148555\pi$
$504$	1.89754	+	1.37864i	0.0845229	+	0.0614095i
$505$	5.93781	+	4.31407i	0.264229	+	0.191974i
$506$	−17.8406	−	54.9079i	−0.793113	−	2.44095i
$507$	−2.23727	+	1.62547i	−0.0993608	+	0.0721899i
$508$	6.94948	+	21.3883i	0.308334	+	0.948953i
$509$	−0.941285	+	2.89698i	−0.0417217	+	0.128406i	−0.969748	−	0.244109i	$-0.921505\pi$
$509$	−0.941285	+	2.89698i	−0.0417217	+	0.128406i	0.928026	+	0.372515i	$0.121505\pi$
$510$	−49.5393	−	35.9924i	−2.19364	−	1.59377i
$511$	−3.37409	+	10.3844i	−0.149261	+	0.459378i
$512$	−9.46792	+	29.1393i	−0.418427	+	1.28779i
$513$	−20.9299	−	15.2065i	−0.924077	−	0.671381i
$514$	10.9734	−	33.7726i	0.484015	−	1.48964i
$515$	−1.76949	−	5.44593i	−0.0779730	−	0.239976i
$516$	41.8312	−	30.3922i	1.84152	−	1.33794i
$517$	−9.11564	−	28.0550i	−0.400905	−	1.23386i
$518$	−19.0606	−	13.8483i	−0.837475	−	0.608461i
$519$	2.59079	+	1.88232i	0.113723	+	0.0826246i
$520$	−0.450129	+	0.327038i	−0.0197395	+	0.0143416i
$521$	−6.45038			−0.282596			−0.141298	−	0.989967i	$-0.545128\pi$
$521$	−6.45038			−0.282596			−0.141298	+	0.989967i	$0.545128\pi$
$522$	43.5090			1.90434
$523$	21.9218	−	15.9271i	0.958573	−	0.696444i	0.00575387	−	0.999983i	$-0.498168\pi$
$523$	21.9218	−	15.9271i	0.958573	−	0.696444i	0.952819	+	0.303540i	$0.0981685\pi$
$524$	−8.26885	+	25.4489i	−0.361227	+	1.11174i
$525$	2.84901	+	8.76834i	0.124341	+	0.382682i
$526$	−23.2353			−1.01311
$527$	−37.5745	+	1.58669i	−1.63677	+	0.0691174i
$528$	44.0034			1.91500
$529$	12.6279	+	38.8648i	0.549040	+	1.68977i
$530$	9.63297	−	29.6472i	0.418430	−	1.28779i
$531$	16.2325	−	11.7936i	0.704430	−	0.511798i
$532$	−15.7895			−0.684561
$533$	−6.50151			−0.281612
$534$	−12.5441	+	9.11382i	−0.542836	+	0.394393i
$535$	−14.9537	−	10.8645i	−0.646507	−	0.469714i
$536$	−0.531226	−	0.385958i	−0.0229455	−	0.0166709i
$537$	0.794342	+	2.44473i	0.0342784	+	0.105498i
$538$	17.2412	−	12.5265i	0.743322	−	0.540055i
$539$	5.35175	+	16.4710i	0.230516	+	0.709456i
$540$	−4.31637	+	13.2844i	−0.185747	+	0.571671i
$541$	4.77110	+	3.46641i	0.205126	+	0.149032i	0.685606	−	0.727973i	$-0.259538\pi$
$541$	4.77110	+	3.46641i	0.205126	+	0.149032i	−0.480480	+	0.877006i	$0.659538\pi$
$542$	1.90069	−	5.84973i	0.0816418	−	0.251268i
$543$	0.473000	−	1.45575i	0.0202984	−	0.0624720i
$544$	−42.4710	−	30.8570i	−1.82093	−	1.32298i
$545$	3.11502	−	9.58703i	0.133433	−	0.410663i
$546$	−2.54100	−	7.82038i	−0.108745	−	0.334681i
$547$	0.269332	−	0.195681i	0.0115158	−	0.00836671i	−0.582012	−	0.813180i	$-0.697735\pi$
$547$	0.269332	−	0.195681i	0.0115158	−	0.00836671i	0.593528	+	0.804813i	$0.297735\pi$
$548$	2.63760	+	8.11769i	0.112673	+	0.346771i
$549$	0.00464897	+	0.00337768i	0.000198413	+	0.000144156i
$550$	12.8251	+	9.31795i	0.546862	+	0.397319i
$551$	21.9737	−	15.9648i	0.936111	−	0.680125i
$552$	−7.34098			−0.312453
$553$	−6.99035			−0.297260
$554$	−6.23473	+	4.52980i	−0.264888	+	0.192453i
$555$	−11.3418	+	34.9063i	−0.481431	+	1.48169i
$556$	−4.02058	−	12.3741i	−0.170510	−	0.524777i
$557$	−29.7540			−1.26072			−0.630358	−	0.776305i	$-0.717092\pi$
$557$	−29.7540			−1.26072			−0.630358	+	0.776305i	$0.717092\pi$
$558$	17.6677	+	47.4614i	0.747935	+	2.00920i
$559$	10.2156			0.432075
$560$	−3.38990	−	10.4330i	−0.143250	−	0.440877i
$561$	−21.3071	+	65.5766i	−0.899588	+	2.76865i
$562$	−9.14536	+	6.64449i	−0.385774	+	0.280281i
$563$	−39.6701			−1.67189			−0.835947	−	0.548810i	$-0.815081\pi$
$563$	−39.6701			−1.67189			−0.835947	+	0.548810i	$0.815081\pi$
$564$	40.4483			1.70318
$565$	−22.1386	+	16.0846i	−0.931377	+	0.676685i
$566$	8.73797	+	6.34851i	0.367284	+	0.266848i
$567$	−1.65057	−	1.19921i	−0.0693174	−	0.0503620i
$568$	0.640434	+	1.97105i	0.0268720	+	0.0827035i
$569$	−11.0575	+	8.03373i	−0.463554	+	0.336792i	−0.794924	−	0.606709i	$-0.792489\pi$
$569$	−11.0575	+	8.03373i	−0.463554	+	0.336792i	0.331370	+	0.943501i	$0.392489\pi$
$570$	15.9068	+	48.9561i	0.666262	+	2.05054i
$571$	−4.41898	+	13.6002i	−0.184929	+	0.569152i	−0.999947	−	0.0102833i	$-0.996727\pi$
$571$	−4.41898	+	13.6002i	−0.184929	+	0.569152i	0.815019	+	0.579435i	$0.196727\pi$
$572$	−5.46583	−	3.97116i	−0.228538	−	0.166042i
$573$	−19.3549	+	59.5682i	−0.808561	+	2.48850i
$574$	5.97388	−	18.3857i	0.249345	−	0.767405i
$575$	−14.1871	−	10.3075i	−0.591642	−	0.429853i
$576$	−9.46364	+	29.1261i	−0.394318	+	1.21359i
$577$	−5.80372	−	17.8620i	−0.241612	−	0.743605i	−0.996175	−	0.0873777i	$-0.972151\pi$
$577$	−5.80372	−	17.8620i	−0.241612	−	0.743605i	0.754563	−	0.656227i	$-0.227849\pi$
$578$	45.3221	−	32.9284i	1.88515	−	1.36964i
$579$	−4.92598	−	15.1606i	−0.204717	−	0.630053i
$580$	−11.8640	−	8.61969i	−0.492625	−	0.357913i
$581$	4.23310	+	3.07552i	0.175618	+	0.127594i
$582$	4.65063	−	3.37888i	0.192775	−	0.140059i
$583$	−35.1017			−1.45376
$584$	2.38721			0.0987836
$585$	−6.29796	+	4.57574i	−0.260389	+	0.189183i
$586$	0.957807	−	2.94783i	0.0395667	−	0.121774i
$587$	2.65911	+	8.18391i	0.109753	+	0.337786i	0.990817	−	0.135212i	$-0.0431716\pi$
$587$	2.65911	+	8.18391i	0.109753	+	0.337786i	−0.881063	+	0.472998i	$0.843172\pi$
$588$	−23.7470			−0.979310
$589$	26.3379	+	17.4869i	1.08524	+	0.720537i
$590$	−14.1525			−0.582651
$591$	−7.71621	−	23.7481i	−0.317403	−	0.976865i
$592$	−10.5546	+	32.4838i	−0.433793	+	1.33508i
$593$	7.70798	−	5.60018i	0.316529	−	0.229972i	−0.418164	−	0.908372i	$-0.637326\pi$
$593$	7.70798	−	5.60018i	0.316529	−	0.229972i	0.734693	+	0.678400i	$0.237326\pi$
$594$	32.9155			1.35054
$595$	17.1894			0.704698
$596$	25.4976	−	18.5251i	1.04442	−	0.758817i
$597$	−13.3300	−	9.68482i	−0.545561	−	0.396373i
$598$	12.6533	+	9.19315i	0.517432	+	0.375936i
$599$	−2.79912	−	8.61479i	−0.114369	−	0.351991i	0.877446	−	0.479675i	$-0.159246\pi$
$599$	−2.79912	−	8.61479i	−0.114369	−	0.351991i	−0.991815	+	0.127684i	$0.959246\pi$
$600$	1.63074	−	1.18480i	0.0665747	−	0.0483694i
$601$	5.06063	+	15.5750i	0.206427	+	0.635318i	0.999652	+	0.0263888i	$0.00840079\pi$
$601$	5.06063	+	15.5750i	0.206427	+	0.635318i	−0.793224	+	0.608930i	$0.791599\pi$
$602$	−9.38659	+	28.8890i	−0.382569	+	1.17743i
$603$	−7.43263	−	5.40012i	−0.302680	−	0.219910i
$604$	−5.44733	+	16.7652i	−0.221649	+	0.682165i
$605$	−1.35917	+	4.18311i	−0.0552583	+	0.170067i
$606$	19.1860	+	13.9395i	0.779380	+	0.566252i
$607$	3.39219	−	10.4401i	0.137685	−	0.423750i	−0.858313	−	0.513126i	$-0.828487\pi$
$607$	3.39219	−	10.4401i	0.137685	−	0.423750i	0.995998	+	0.0893761i	$0.0284873\pi$
$608$	13.6372	+	41.9709i	0.553061	+	1.70215i
$609$	−16.2594	+	11.8131i	−0.658863	+	0.478692i
$610$	−0.00125253	−	0.00385490i	−5.07136e−5	−	0.000156080i
$611$	6.46517	+	4.69722i	0.261553	+	0.190029i
$612$	−46.4834	−	33.7722i	−1.87898	−	1.36516i
$613$	−22.8480	+	16.6000i	−0.922821	+	0.670468i	−0.944224	−	0.329303i	$-0.893186\pi$
$613$	−22.8480	+	16.6000i	−0.922821	+	0.670468i	0.0214039	+	0.999771i	$0.493186\pi$
$614$	−35.9593			−1.45120
$615$	−30.1157			−1.21438
$616$	−1.50712	+	1.09498i	−0.0607235	+	0.0441182i
$617$	4.96156	−	15.2701i	0.199745	−	0.614752i	−0.800143	−	0.599809i	$-0.795243\pi$
$617$	4.96156	−	15.2701i	0.199745	−	0.614752i	0.999888	−	0.0149432i	$-0.00475673\pi$
$618$	−5.71751	−	17.5967i	−0.229992	−	0.707843i
$619$	−10.8372			−0.435583			−0.217792	−	0.975995i	$-0.569885\pi$
$619$	−10.8372			−0.435583			−0.217792	+	0.975995i	$0.569885\pi$
$620$	4.58508	−	16.4419i	0.184141	−	0.660323i
$621$	−36.4111			−1.46113
$622$	−20.1863	−	62.1271i	−0.809398	−	2.49107i
$623$	1.34503	−	4.13958i	0.0538876	−	0.165849i
$624$	−9.64409	+	7.00684i	−0.386073	+	0.280498i
$625$	−9.21316			−0.368526
$626$	−3.39278			−0.135603
$627$	46.8930	−	34.0697i	1.87272	−	1.36061i
$628$	−25.4630	−	18.5000i	−1.01609	−	0.738229i
$629$	−43.2988	−	31.4584i	−1.72643	−	1.25433i
$630$	−7.15295	−	22.0145i	−0.284980	−	0.877079i
$631$	16.0393	−	11.6532i	0.638513	−	0.463907i	−0.220826	−	0.975313i	$-0.570875\pi$
$631$	16.0393	−	11.6532i	0.638513	−	0.463907i	0.859339	+	0.511406i	$0.170875\pi$
$632$	0.472278	+	1.45352i	0.0187862	+	0.0578181i
$633$	19.3706	−	59.6167i	0.769913	−	2.36955i
$634$	8.97786	+	6.52280i	0.356556	+	0.259053i
$635$	−6.35995	+	19.5739i	−0.252387	+	0.776767i
$636$	14.8732	−	45.7751i	0.589763	−	1.81510i
$637$	−3.79567	−	2.75772i	−0.150390	−	0.109265i
$638$	−10.6787	+	32.8657i	−0.422774	+	1.30117i
$639$	8.96061	+	27.5779i	0.354476	+	1.09097i
$640$	−3.58806	+	2.60688i	−0.141831	+	0.103046i
$641$	−7.35931	−	22.6496i	−0.290675	−	0.894607i	−0.984640	−	0.174598i	$-0.944138\pi$
$641$	−7.35931	−	22.6496i	−0.290675	−	0.894607i	0.693964	−	0.720009i	$-0.255862\pi$
$642$	−48.3180	−	35.1051i	−1.90696	−	1.38549i
$643$	17.3927	+	12.6365i	0.685900	+	0.498335i	0.875310	−	0.483563i	$-0.160658\pi$
$643$	17.3927	+	12.6365i	0.685900	+	0.498335i	−0.189410	+	0.981898i	$0.560658\pi$
$644$	−17.9784	+	13.0620i	−0.708447	+	0.514717i
$645$	47.3199			1.86322
$646$	−75.0620			−2.95327
$647$	5.41386	−	3.93340i	0.212841	−	0.154638i	−0.476257	−	0.879306i	$-0.658007\pi$
$647$	5.41386	−	3.93340i	0.212841	−	0.154638i	0.689098	+	0.724668i	$0.258007\pi$
$648$	−0.137840	+	0.424228i	−0.00541486	+	0.0166652i
$649$	4.92456	+	15.1562i	0.193306	+	0.594934i
$650$	−4.29456			−0.168447
$651$	−19.4887	−	12.9394i	−0.763821	−	0.507135i
$652$	−40.1397			−1.57199
$653$	−7.46511	−	22.9752i	−0.292132	−	0.899091i	−0.984170	−	0.177229i	$-0.943287\pi$
$653$	−7.46511	−	22.9752i	−0.292132	−	0.899091i	0.692037	−	0.721862i	$-0.256713\pi$
$654$	10.0651	−	30.9773i	0.393578	−	1.21131i
$655$	−19.8117	+	14.3940i	−0.774107	+	0.562422i
$656$	−28.0257			−1.09422
$657$	33.4006			1.30308
$658$	−19.2238	+	13.9669i	−0.749423	+	0.544488i
$659$	5.40796	+	3.92911i	0.210664	+	0.153056i	0.688114	−	0.725603i	$-0.258439\pi$
$659$	5.40796	+	3.92911i	0.210664	+	0.153056i	−0.477450	+	0.878659i	$0.658439\pi$
$660$	−25.3183	−	18.3948i	−0.985515	−	0.716018i
$661$	−2.08088	−	6.40429i	−0.0809369	−	0.249098i	0.902397	−	0.430905i	$-0.141806\pi$
$661$	−2.08088	−	6.40429i	−0.0809369	−	0.249098i	−0.983334	+	0.181807i	$0.941806\pi$
$662$	−37.7926	+	27.4579i	−1.46885	+	1.06718i
$663$	−5.77222	−	17.7651i	−0.224174	−	0.689938i
$664$	0.353508	−	1.08799i	0.0137188	−	0.0422221i
$665$	−11.6903	−	8.49352i	−0.453331	−	0.329364i
$666$	−22.2711	+	68.5434i	−0.862987	+	2.65600i
$667$	11.8128	−	36.3560i	0.457393	−	1.40771i
$668$	12.8443	+	9.33193i	0.496961	+	0.361063i
$669$	5.48175	−	16.8711i	0.211937	−	0.652274i
$670$	2.00251	+	6.16309i	0.0773637	+	0.238101i
$671$	−0.00369245	+	0.00268272i	−0.000142545	+	0.000103565i
$672$	−10.0908	−	31.0562i	−0.389261	−	1.19802i
$673$	13.2167	+	9.60250i	0.509467	+	0.370149i	0.812621	−	0.582792i	$-0.198040\pi$
$673$	13.2167	+	9.60250i	0.509467	+	0.370149i	−0.303154	+	0.952941i	$0.598040\pi$
$674$	15.8756	+	11.5343i	0.611507	+	0.444286i
$675$	8.08844	−	5.87660i	0.311324	−	0.226190i
$676$	1.83027			0.0703952
$677$	−5.60915			−0.215577			−0.107789	−	0.994174i	$-0.534377\pi$
$677$	−5.60915			−0.215577			−0.107789	+	0.994174i	$0.534377\pi$
$678$	−71.5334	+	51.9721i	−2.74722	+	1.99598i
$679$	−0.498661	+	1.53472i	−0.0191368	+	0.0588972i
$680$	−1.16134	−	3.57425i	−0.0445355	−	0.137066i
$681$	44.3905			1.70105
$682$	−40.1875	+	1.69704i	−1.53886	+	0.0649828i
$683$	−45.4101			−1.73757			−0.868785	−	0.495189i	$-0.835099\pi$
$683$	−45.4101			−1.73757			−0.868785	+	0.495189i	$0.835099\pi$
$684$	14.9255	+	45.9361i	0.570692	+	1.75641i
$685$	−2.41385	+	7.42906i	−0.0922284	+	0.283850i
$686$	28.1252	−	20.4342i	1.07383	−	0.780180i
$687$	33.6678			1.28451
$688$	44.0360			1.67886
$689$	7.69313	−	5.58939i	0.293085	−	0.212939i
$690$	58.6114	+	42.5837i	2.23130	+	1.62113i
$691$	0.738259	+	0.536377i	0.0280847	+	0.0204047i	0.601739	−	0.798693i	$-0.294475\pi$
$691$	0.738259	+	0.536377i	0.0280847	+	0.0204047i	−0.573654	+	0.819097i	$0.694475\pi$
$692$	−0.654955	−	2.01574i	−0.0248976	−	0.0766271i
$693$	−21.0868	+	15.3204i	−0.801021	+	0.581975i
$694$	19.0715	+	58.6961i	0.723944	+	2.22807i
$695$	3.67951	−	11.3244i	0.139572	−	0.429557i
$696$	3.55484	+	2.58274i	0.134746	+	0.0978987i
$697$	13.5705	−	41.7657i	0.514019	−	1.58199i
$698$	5.82751	−	17.9352i	0.220575	−	0.678859i
$699$	54.3031	+	39.4535i	2.05393	+	1.49227i
$700$	1.88559	−	5.80326i	0.0712687	−	0.219343i
$701$	−8.48432	−	26.1120i	−0.320448	−	0.986238i	−0.973453	−	0.228885i	$-0.926492\pi$
$701$	−8.48432	−	26.1120i	−0.320448	−	0.986238i	0.653005	−	0.757353i	$-0.273508\pi$
$702$	−7.21399	+	5.24127i	−0.272275	+	0.197819i
$703$	13.9030	+	42.7889i	0.524360	+	1.61382i
$704$	−19.6784	−	14.2972i	−0.741659	−	0.538847i
$705$	29.9474	+	21.7580i	1.12788	+	0.819455i
$706$	−2.31460	+	1.68165i	−0.0871109	+	0.0632898i
$707$	−6.65728			−0.250373
$708$	−21.8514			−0.821227
$709$	42.3678	−	30.7820i	1.59115	−	1.15604i	0.688884	−	0.724872i	$-0.258101\pi$
$709$	42.3678	−	30.7820i	1.59115	−	1.15604i	0.902271	−	0.431169i	$-0.141899\pi$
$710$	6.32040	−	19.4522i	0.237201	−	0.730028i
$711$	6.60787	+	20.3369i	0.247814	+	0.762694i
$712$	−0.951628			−0.0356638
$713$	44.4554	−	1.87726i	1.66487	−	0.0703040i
$714$	55.5419			2.07860
$715$	−1.91065	−	5.88039i	−0.0714544	−	0.219914i
$716$	0.525729	−	1.61803i	0.0196474	−	0.0604686i
$717$	44.9049	−	32.6253i	1.67700	−	1.21841i
$718$	15.9121			0.593835
$719$	−6.73668			−0.251236			−0.125618	−	0.992079i	$-0.540091\pi$
$719$	−6.73668			−0.251236			−0.125618	+	0.992079i	$0.540091\pi$
$720$	−27.1483	+	19.7244i	−1.01176	+	0.735084i
$721$	4.20195	+	3.05290i	0.156489	+	0.113696i
$722$	20.9654	+	15.2323i	0.780251	+	0.566886i
$723$	−24.4429	−	75.2276i	−0.909042	−	2.79774i
$724$	−0.819580	+	0.595460i	−0.0304595	+	0.0221301i
$725$	3.24359	+	9.98274i	0.120464	+	0.370750i
$726$	−4.39171	+	13.5163i	−0.162992	+	0.501637i
$727$	−13.4426	−	9.76661i	−0.498558	−	0.362224i	0.309908	−	0.950767i	$-0.399702\pi$
$727$	−13.4426	−	9.76661i	−0.498558	−	0.362224i	−0.808466	+	0.588543i	$0.799702\pi$
$728$	0.155951	−	0.479969i	0.00577995	−	0.0177888i
$729$	−13.6093	+	41.8850i	−0.504047	+	1.55130i
$730$	−19.0598	−	13.8478i	−0.705437	−	0.512530i
$731$	−21.3229	+	65.6252i	−0.788656	+	2.42723i
$732$	−0.00193390	−	0.00595194i	−7.14791e−5	−	0.000219990i
$733$	−1.46699	+	1.06583i	−0.0541843	+	0.0393672i	−0.614548	−	0.788880i	$-0.710661\pi$
$733$	−1.46699	+	1.06583i	−0.0541843	+	0.0393672i	0.560363	+	0.828247i	$0.310661\pi$
$734$	−22.3719	−	68.8537i	−0.825763	−	2.54144i
$735$	−17.5820	−	12.7741i	−0.648521	−	0.471178i
$736$	50.2487	+	36.5078i	1.85219	+	1.34570i
$737$	5.90336	−	4.28905i	0.217453	−	0.157989i
$738$	−59.1363			−2.17684
$739$	−44.3580			−1.63173			−0.815867	−	0.578240i	$-0.803740\pi$
$739$	−44.3580			−1.63173			−0.815867	+	0.578240i	$0.803740\pi$
$740$	19.6522	−	14.2781i	0.722428	−	0.524875i
$741$	−4.85233	+	14.9339i	−0.178255	+	0.548612i
$742$	8.73752	+	26.8913i	0.320765	+	0.987212i
$743$	34.6345			1.27062			0.635308	−	0.772259i	$-0.280873\pi$
$743$	34.6345			1.27062			0.635308	+	0.772259i	$0.280873\pi$
$744$	−1.37384	+	4.92654i	−0.0503675	+	0.180616i
$745$	28.8431			1.05673
$746$	10.5497	+	32.4687i	0.386253	+	1.18876i
$747$	4.94610	−	15.2225i	0.180968	−	0.556963i
$748$	36.9194	−	26.8235i	1.34991	−	0.980766i
$749$	16.7656			0.612603
$750$	−65.2206			−2.38152
$751$	7.50903	−	5.45563i	0.274008	−	0.199079i	−0.442291	−	0.896871i	$-0.645834\pi$
$751$	7.50903	−	5.45563i	0.274008	−	0.199079i	0.716300	+	0.697793i	$0.245834\pi$
$752$	27.8690	+	20.2480i	1.01628	+	0.738370i
$753$	52.1186	+	37.8663i	1.89931	+	1.37993i
$754$	−2.89292	−	8.90350i	−0.105354	−	0.324246i
$755$	−13.0515	+	9.48247i	−0.474993	+	0.345102i
$756$	−3.91514	−	12.0495i	−0.142392	−	0.438238i
$757$	15.2512	−	46.9385i	0.554315	−	1.70601i	−0.143429	−	0.989661i	$-0.545813\pi$
$757$	15.2512	−	46.9385i	0.554315	−	1.70601i	0.697745	−	0.716347i	$-0.254187\pi$
$758$	36.0616	+	26.2003i	1.30982	+	0.951637i
$759$	25.2091	−	77.5856i	0.915032	−	2.81618i
$760$	−0.976265	+	3.00464i	−0.0354129	+	0.108990i
$761$	5.01279	+	3.64201i	0.181714	+	0.132023i	0.674924	−	0.737888i	$-0.264177\pi$
$761$	5.01279	+	3.64201i	0.181714	+	0.132023i	−0.493210	+	0.869910i	$0.664177\pi$
$762$	−20.5500	+	63.2465i	−0.744450	+	2.29118i
$763$	2.82545	+	8.69585i	0.102288	+	0.314811i
$764$	33.5367	−	24.3658i	1.21331	−	0.881525i
$765$	−16.2489	−	50.0089i	−0.587480	−	1.80808i
$766$	29.0685	+	21.1195i	1.05029	+	0.763078i
$767$	−3.49269	−	2.53759i	−0.126114	−	0.0916270i
$768$	−41.0785	+	29.8453i	−1.48229	+	1.07695i
$769$	19.8915			0.717306			0.358653	−	0.933471i	$-0.383236\pi$
$769$	19.8915			0.717306			0.358653	+	0.933471i	$0.383236\pi$
$770$	18.3848			0.662544
$771$	40.5940	−	29.4933i	1.46196	−	1.06217i
$772$	−3.26022	+	10.0339i	−0.117338	+	0.361129i
$773$	13.5787	+	41.7911i	0.488394	+	1.50312i	0.827005	+	0.562194i	$0.190043\pi$
$773$	13.5787	+	41.7911i	0.488394	+	1.50312i	−0.338612	+	0.940926i	$0.609957\pi$
$774$	92.9192			3.33991
$775$	−9.57244	+	7.59194i	−0.343852	+	0.272710i
$776$	0.352809			0.0126651
$777$	−10.2875	−	31.6615i	−0.369060	−	1.13585i
$778$	10.0536	−	30.9419i	0.360440	−	1.10932i
$779$	−29.8661	+	21.6990i	−1.07006	+	0.777446i
$780$	8.47803			0.303562
$781$	−23.0310			−0.824113
$782$	−85.4678	+	62.0960i	−3.05632	+	2.22055i
$783$	17.6319	+	12.8103i	0.630114	+	0.457805i
$784$	−16.3618	−	11.8875i	−0.584350	−	0.424555i
$785$	−8.90094	−	27.3943i	−0.317688	−	0.977744i
$786$	−64.0149	+	46.5095i	−2.28333	+	1.65894i
$787$	10.4269	+	32.0906i	0.371678	+	1.14391i	0.945693	+	0.325062i	$0.105385\pi$
$787$	10.4269	+	32.0906i	0.371678	+	1.14391i	−0.574015	+	0.818845i	$0.694615\pi$
$788$	−5.10692	+	15.7175i	−0.181926	+	0.559912i
$789$	−26.5615	−	19.2981i	−0.945616	−	0.687030i
$790$	4.66089	−	14.3447i	0.165827	−	0.510363i
$791$	7.67012	−	23.6062i	0.272718	−	0.839340i
$792$	4.61028	+	3.34956i	0.163819	+	0.119021i
$793$	0.000382082	−	0.00117593i	1.35681e−5	−	4.17584e-5i
$794$	12.6157	+	38.8272i	0.447715	+	1.37793i
$795$	35.6354	−	25.8907i	1.26386	−	0.918247i
$796$	3.36985	+	10.3713i	0.119441	+	0.367602i
$797$	34.1382	+	24.8029i	1.20924	+	0.878563i	0.995161	−	0.0982535i	$-0.0313256\pi$
$797$	34.1382	+	24.8029i	1.20924	+	0.878563i	0.214077	+	0.976817i	$0.431326\pi$
$798$	−37.7734	−	27.4439i	−1.33716	−	0.971505i
$799$	−43.6696	+	31.7278i	−1.54492	+	1.12245i
$800$	−17.0545			−0.602969
$801$	−13.3147			−0.470451
$802$	46.3047	−	33.6423i	1.63508	−	1.18795i
$803$	−8.19774	+	25.2300i	−0.289292	+	0.890349i
$804$	3.09186	+	9.51576i	0.109041	+	0.335595i
$805$	−20.3373			−0.716796
$806$	8.53756	−	6.77116i	0.300723	−	0.238504i
$807$	30.1132			1.06004
$808$	0.449775	+	1.38427i	0.0158230	+	0.0486983i
$809$	10.9276	−	33.6317i	0.384194	−	1.18243i	−0.552870	−	0.833268i	$-0.686467\pi$
$809$	10.9276	−	33.6317i	0.384194	−	1.18243i	0.937063	−	0.349159i	$-0.113533\pi$
$810$	3.56140	−	2.58751i	0.125135	−	0.0909158i
$811$	−51.7067			−1.81567			−0.907834	−	0.419329i	$-0.862265\pi$
$811$	−51.7067			−1.81567			−0.907834	+	0.419329i	$0.862265\pi$
$812$	13.3015			0.466791
$813$	7.03127	−	5.10852i	0.246597	−	0.179164i
$814$	−46.3099	−	33.6461i	−1.62316	−	1.17930i
$815$	−29.7189	−	21.5921i	−1.04101	−	0.756337i
$816$	−24.8820	−	76.5788i	−0.871043	−	2.68080i
$817$	46.9277	−	34.0950i	1.64179	−	1.19283i
$818$	−0.429680	−	1.32242i	−0.0150234	−	0.0462372i
$819$	2.18199	−	6.71547i	0.0762449	−	0.234658i
$820$	16.1252	+	11.7157i	0.563117	+	0.409128i
$821$	6.10316	−	18.7836i	0.213002	−	0.655552i	−0.786288	−	0.617861i	$-0.788000\pi$
$821$	6.10316	−	18.7836i	0.213002	−	0.655552i	0.999289	−	0.0376915i	$-0.0120004\pi$
$822$	−7.79954	+	24.0045i	−0.272040	+	0.837253i
$823$	2.88147	+	2.09351i	0.100442	+	0.0729751i	0.636872	−	0.770969i	$-0.280228\pi$
$823$	2.88147	+	2.09351i	0.100442	+	0.0729751i	−0.536431	+	0.843944i	$0.680228\pi$
$824$	0.350907	−	1.07998i	0.0122244	−	0.0376229i
$825$	6.92198	+	21.3037i	0.240992	+	0.741698i
$826$	10.3853	−	7.54538i	0.361352	−	0.262537i
$827$	12.5282	+	38.5577i	0.435647	+	1.34078i	0.892422	+	0.451202i	$0.149005\pi$
$827$	12.5282	+	38.5577i	0.435647	+	1.34078i	−0.456775	+	0.889582i	$0.650995\pi$
$828$	54.9958	+	39.9568i	1.91124	+	1.38860i
$829$	−19.2986	−	14.0212i	−0.670267	−	0.486978i	0.199847	−	0.979827i	$-0.435955\pi$
$829$	−19.2986	−	14.0212i	−0.670267	−	0.486978i	−0.870115	+	0.492849i	$0.835955\pi$
$830$	−9.13367	+	6.63600i	−0.317034	+	0.230339i
$831$	−10.8895			−0.377751
$832$	6.58947			0.228449
$833$	25.6382	−	18.6272i	0.888311	−	0.645396i
$834$	11.8891	−	36.5908i	0.411685	−	1.26704i
$835$	4.48990	+	13.8185i	0.155379	+	0.478208i
$836$	−38.3623			−1.32679
$837$	−6.81422	+	24.4355i	−0.235534	+	0.844615i
$838$	66.5215			2.29795
$839$	−2.03735	−	6.27032i	−0.0703372	−	0.216475i	0.909709	−	0.415247i	$-0.136305\pi$
$839$	−2.03735	−	6.27032i	−0.0703372	−	0.216475i	−0.980046	+	0.198771i	$0.936305\pi$
$840$	0.722384	−	2.22327i	0.0249246	−	0.0767101i
$841$	4.95022	−	3.59654i	0.170697	−	0.124019i
$842$	−59.7245			−2.05824
$843$	−15.9731			−0.550144
$844$	−33.5640	+	24.3857i	−1.15532	+	0.839390i
$845$	1.35511	+	0.984546i	0.0466173	+	0.0338694i
$846$	58.8058	+	42.7249i	2.02178	+	1.46891i
$847$	−1.23283	−	3.79426i	−0.0423605	−	0.130372i
$848$	33.1624	−	24.0939i	1.13880	−	0.827387i
$849$	4.71609	+	14.5146i	0.161856	+	0.498141i
$850$	8.96397	−	27.5883i	0.307462	−	0.946269i
$851$	51.2280	+	37.2193i	1.75607	+	1.27586i
$852$	9.75866	−	30.0341i	0.334326	−	1.02895i
$853$	−9.17247	+	28.2300i	−0.314060	+	0.966576i	0.662080	+	0.749433i	$0.269674\pi$
$853$	−9.17247	+	28.2300i	−0.314060	+	0.966576i	−0.976140	+	0.217143i	$0.930326\pi$
$854$	0.00297435	+	0.00216099i	0.000101780	+	7.39476e-5i
$855$	−13.6594	+	42.0393i	−0.467141	+	1.43771i
$856$	−1.13271	−	3.48612i	−0.0387152	−	0.119153i
$857$	−43.0695	+	31.2919i	−1.47123	+	1.06891i	−0.490972	+	0.871175i	$0.663358\pi$
$857$	−43.0695	+	31.2919i	−1.47123	+	1.06891i	−0.980256	+	0.197734i	$0.936642\pi$
$858$	−6.17364	−	19.0005i	−0.210764	−	0.648666i
$859$	22.7087	+	16.4988i	0.774809	+	0.562932i	0.903417	−	0.428764i	$-0.141051\pi$
$859$	22.7087	+	16.4988i	0.774809	+	0.562932i	−0.128607	+	0.991696i	$0.541051\pi$
$860$	−25.3371	−	18.4085i	−0.863987	−	0.627724i
$861$	22.0993	−	16.0561i	0.753142	−	0.547190i
$862$	22.1146			0.753226
$863$	39.8576			1.35677			0.678384	−	0.734708i	$-0.262681\pi$
$863$	39.8576			1.35677			0.678384	+	0.734708i	$0.262681\pi$
$864$	−28.6481	+	20.8141i	−0.974630	+	0.708110i
$865$	0.599394	−	1.84475i	0.0203800	−	0.0627232i
$866$	4.19183	+	12.9011i	0.142444	+	0.438398i
$867$	79.1587			2.68837
$868$	5.40135	+	14.5098i	0.183334	+	0.492495i
$869$	−16.9839			−0.576138
$870$	−13.4003	−	41.2420i	−0.454314	−	1.39823i
$871$	−0.610860	+	1.88004i	−0.0206982	+	0.0637026i
$872$	1.61726	−	1.17501i	0.0547674	−	0.0397908i
$873$	4.93631			0.167069
$874$	88.8080			3.00398
$875$	14.8119	−	10.7615i	0.500734	−	0.363805i
$876$	−29.4283	−	21.3809i	−0.994289	−	0.722393i
$877$	−46.6093	−	33.8636i	−1.57388	−	1.14349i	−0.923314	−	0.384046i	$-0.874531\pi$
$877$	−46.6093	−	33.8636i	−1.57388	−	1.14349i	−0.650569	−	0.759447i	$-0.725469\pi$
$878$	20.4355	+	62.8940i	0.689665	+	2.12257i
$879$	3.54324	−	2.57431i	0.119510	−	0.0868294i
$880$	−8.23615	−	25.3483i	−0.277641	−	0.854490i
$881$	7.08391	−	21.8020i	0.238663	−	0.734529i	−0.757952	−	0.652311i	$-0.773800\pi$
$881$	7.08391	−	21.8020i	0.238663	−	0.734529i	0.996614	−	0.0822178i	$-0.0262003\pi$
$882$	−34.5246	−	25.0836i	−1.16250	−	0.844609i
$883$	7.28827	−	22.4310i	0.245270	−	0.754863i	−0.750322	−	0.661072i	$-0.770102\pi$
$883$	7.28827	−	22.4310i	0.245270	−	0.754863i	0.995592	−	0.0937904i	$-0.0298984\pi$
$884$	−3.82030	+	11.7577i	−0.128491	+	0.395453i
$885$	−16.1785	−	11.7544i	−0.543835	−	0.395119i
$886$	−6.27722	+	19.3193i	−0.210887	+	0.649044i
$887$	−2.49510	−	7.67912i	−0.0837772	−	0.257840i	0.900390	−	0.435085i	$-0.143282\pi$
$887$	−2.49510	−	7.67912i	−0.0837772	−	0.257840i	−0.984167	+	0.177245i	$0.943282\pi$
$888$	−5.88844	+	4.27820i	−0.197603	+	0.143567i
$889$	−5.76875	−	17.7544i	−0.193478	−	0.595463i
$890$	7.59793	+	5.52022i	0.254683	+	0.185038i
$891$	−4.01024	−	2.91361i	−0.134348	−	0.0976097i
$892$	−9.49837	+	6.90097i	−0.318029	+	0.231062i
$893$	45.3762			1.51846
$894$	93.1969			3.11697
$895$	1.25962	−	0.915166i	0.0421044	−	0.0305906i
$896$	1.24312	−	3.82593i	0.0415297	−	0.127815i
$897$	6.82928	+	21.0184i	0.228023	+	0.701782i
$898$	50.5071			1.68544
$899$	−22.1878	−	14.7315i	−0.740006	−	0.491323i
$900$	−18.6658			−0.622192
$901$	19.8485	+	61.0873i	0.661248	+	2.03511i
$902$	14.5142	−	44.6702i	0.483271	−	1.48735i
$903$	−34.7240	+	25.2285i	−1.15554	+	0.839551i
$904$	−5.42671			−0.180490
$905$	−0.927118			−0.0308185
$906$	−42.1715	+	30.6394i	−1.40106	+	1.01793i
$907$	−1.83970	−	1.33662i	−0.0610861	−	0.0443817i	0.556823	−	0.830631i	$-0.312020\pi$
$907$	−1.83970	−	1.33662i	−0.0610861	−	0.0443817i	−0.617909	+	0.786249i	$0.712020\pi$
$908$	−23.7685	−	17.2689i	−0.788787	−	0.573087i
$909$	6.29302	+	19.3679i	0.208726	+	0.642393i
$910$	−4.02935	+	2.92750i	−0.133572	+	0.0970455i
$911$	−9.76584	−	30.0562i	−0.323557	−	0.995805i	−0.972088	−	0.234617i	$-0.924616\pi$
$911$	−9.76584	−	30.0562i	−0.323557	−	0.995805i	0.648531	−	0.761188i	$-0.275384\pi$
$912$	−20.9167	+	64.3748i	−0.692620	+	2.13166i
$913$	10.2848	+	7.47233i	0.340377	+	0.247298i
$914$	0.148884	−	0.458217i	0.00492463	−	0.0151565i
$915$	0.00176985	−	0.00544703i	5.85093e−5	−	0.000180073i
$916$	−18.0272	−	13.0975i	−0.595634	−	0.432754i
$917$	6.86395	−	21.1251i	0.226668	−	0.697612i
$918$	−18.6123	−	57.2826i	−0.614296	−	1.89061i
$919$	20.8718	−	15.1643i	0.688498	−	0.500223i	−0.187668	−	0.982233i	$-0.560093\pi$
$919$	20.8718	−	15.1643i	0.688498	−	0.500223i	0.876166	+	0.482009i	$0.160093\pi$
$920$	1.37402	+	4.22879i	0.0453000	+	0.139419i
$921$	−41.1070	−	29.8660i	−1.35452	−	0.984117i
$922$	32.2624	+	23.4400i	1.06251	+	0.771956i
$923$	5.04763	−	3.66732i	0.166145	−	0.120711i
$924$	28.3861			0.933833
$925$	−17.3869			−0.571679
$926$	−28.6072	+	20.7843i	−0.940091	+	0.683016i
$927$	4.90971	−	15.1105i	0.161256	−	0.496295i
$928$	−11.4884	−	35.3575i	−0.377124	−	1.16067i
$929$	−16.0069			−0.525169			−0.262584	−	0.964909i	$-0.584575\pi$
$929$	−16.0069			−0.525169			−0.262584	+	0.964909i	$0.584575\pi$
$930$	39.5469	−	31.3648i	1.29679	−	1.02849i
$931$	−26.6402			−0.873097
$932$	−13.7279	−	42.2501i	−0.449672	−	1.38395i
$933$	28.5236	−	87.7865i	0.933819	−	2.87400i
$934$	−11.3239	+	8.22731i	−0.370530	+	0.269206i
$935$	41.7637			1.36582
$936$	−1.54379			−0.0504602
$937$	−37.3237	+	27.1172i	−1.21931	+	0.885881i	−0.996043	−	0.0888758i	$-0.971673\pi$
$937$	−37.3237	+	27.1172i	−1.21931	+	0.885881i	−0.223268	+	0.974757i	$0.571673\pi$
$938$	−4.75530	−	3.45492i	−0.155266	−	0.112807i
$939$	−3.87846	−	2.81787i	−0.126569	−	0.0919577i
$940$	−7.57074	−	23.3003i	−0.246930	−	0.759973i
$941$	−12.5279	+	9.10204i	−0.408397	+	0.296718i	−0.772953	−	0.634464i	$-0.781221\pi$
$941$	−12.5279	+	9.10204i	−0.408397	+	0.296718i	0.364555	+	0.931182i	$0.381221\pi$
$942$	−28.7604	−	88.5154i	−0.937064	−	2.88399i
$943$	−16.0556	+	49.4142i	−0.522843	+	1.60915i
$944$	−15.0557	−	10.9386i	−0.490023	−	0.356022i
$945$	3.58301	−	11.0274i	0.116555	−	0.358720i
$946$	−22.8058	+	70.1890i	−0.741480	+	2.28204i
$947$	33.7797	+	24.5424i	1.09769	+	0.797520i	0.980682	−	0.195611i	$-0.0626689\pi$
$947$	33.7797	+	24.5424i	1.09769	+	0.797520i	0.117010	+	0.993131i	$0.462669\pi$
$948$	7.19638	−	22.1482i	0.233728	−	0.719339i
$949$	−2.22081	−	6.83496i	−0.0720906	−	0.221872i
$950$	−19.7280	+	14.3332i	−0.640061	+	0.465031i
$951$	4.84556	+	14.9131i	0.157128	+	0.483590i
$952$	2.75780	+	2.00366i	0.0893810	+	0.0649391i
$953$	14.2237	+	10.3341i	0.460751	+	0.334755i	0.793826	−	0.608145i	$-0.208086\pi$
$953$	14.2237	+	10.3341i	0.460751	+	0.334755i	−0.333075	+	0.942900i	$0.608086\pi$
$954$	69.9751	−	50.8399i	2.26553	−	1.64600i
$955$	37.9371			1.22761
$956$	−36.7359			−1.18812
$957$	−39.5040	+	28.7013i	−1.27698	+	0.927782i
$958$	−6.86084	+	21.1155i	−0.221664	+	0.682211i
$959$	−2.18946	−	6.73847i	−0.0707014	−	0.217597i
$960$	30.5232			0.985131
$961$	7.05987	−	30.1854i	0.227738	−	0.973723i
$962$	15.5072			0.499973
$963$	−15.8483	−	48.7760i	−0.510704	−	1.57178i
$964$	−16.1774	+	49.7888i	−0.521038	+	1.60359i
$965$	−7.81130	+	5.67524i	−0.251455	+	0.182693i
$966$	−65.7132			−2.11429
$967$	−52.4395			−1.68634			−0.843170	−	0.537647i	$-0.819313\pi$
$967$	−52.4395			−1.68634			−0.843170	+	0.537647i	$0.819313\pi$
$968$	−0.705659	+	0.512691i	−0.0226807	+	0.0164785i
$969$	−85.8073	−	62.3426i	−2.75653	−	2.00273i
$970$	−2.81688	−	2.04658i	−0.0904444	−	0.0657117i
$971$	14.4536	+	44.4835i	0.463837	+	1.42754i	0.860439	+	0.509554i	$0.170190\pi$
$971$	14.4536	+	44.4835i	0.463837	+	1.42754i	−0.396601	+	0.917991i	$0.629810\pi$
$972$	25.7382	−	18.6999i	0.825553	−	0.599799i
$973$	3.33747	+	10.2717i	0.106994	+	0.329295i
$974$	22.2678	−	68.5332i	0.713506	−	2.19594i
$975$	−4.90934	−	3.56685i	−0.157225	−	0.114230i
$976$	0.00164702	−	0.00506901i	5.27198e−5	−	0.000162255i
$977$	−4.64540	+	14.2971i	−0.148619	+	0.457404i	−0.997459	−	0.0712475i	$-0.977302\pi$
$977$	−4.64540	+	14.2971i	−0.148619	+	0.457404i	0.848839	+	0.528651i	$0.177302\pi$
$978$	−96.0267	−	69.7675i	−3.07060	−	2.23092i
$979$	3.26791	−	10.0576i	0.104443	−	0.321442i
$980$	4.44475	+	13.6795i	0.141982	+	0.436976i
$981$	22.6279	−	16.4401i	0.722452	−	0.524892i
$982$	9.61075	+	29.5789i	0.306691	+	0.943899i
$983$	−10.0531	−	7.30402i	−0.320645	−	0.232962i	0.415806	−	0.909453i	$-0.363500\pi$
$983$	−10.0531	−	7.30402i	−0.320645	−	0.232962i	−0.736450	+	0.676491i	$0.763500\pi$
$984$	−4.83165	−	3.51040i	−0.154027	−	0.111907i
$985$	−12.2359	+	8.88989i	−0.389868	+	0.283255i
$986$	63.2344			2.01379
$987$	−33.5760			−1.06874
$988$	8.40776	−	6.10859i	0.267486	−	0.194340i
$989$	25.2278	−	77.6430i	0.802196	−	2.46891i
$990$	−17.3789	−	53.4867i	−0.552337	−	1.69992i
$991$	45.9695			1.46027			0.730135	−	0.683303i	$-0.239457\pi$
$991$	45.9695			1.46027			0.730135	+	0.683303i	$0.239457\pi$
$992$	33.9043	−	26.8896i	1.07646	−	0.853746i
$993$	−66.0078			−2.09469
$994$	5.73288	+	17.6440i	0.181836	+	0.559633i
$995$	−3.08398	+	9.49151i	−0.0977687	+	0.300901i
$996$	−14.1023	+	10.2459i	−0.446849	+	0.324655i
$997$	50.6814			1.60510			0.802548	−	0.596587i	$-0.203477\pi$
$997$	50.6814			1.60510			0.802548	+	0.596587i	$0.203477\pi$
$998$	4.62639			0.146446
$999$	−29.2065	+	21.2198i	−0.924053	+	0.671364i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.k.d.66.2	✓	48
31.8	even	5	inner	403.2.k.d.287.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.k.d.66.2	✓	48	1.1	even	1	trivial
403.2.k.d.287.2	yes	48	31.8	even	5	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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.604780 - 1.86132i) q^{2} +(0.854563 - 2.63007i) q^{3} +(-1.48072 + 1.07581i) q^{4} -1.67501 q^{5} -5.41223 q^{6} +(1.22914 - 0.893026i) q^{7} +(-0.268732 - 0.195245i) q^{8} +(-3.75996 - 2.73177i) q^{9} +O(q^{10})\)	\(q+(-0.604780 - 1.86132i) q^{2} +(0.854563 - 2.63007i) q^{3} +(-1.48072 + 1.07581i) q^{4} -1.67501 q^{5} -5.41223 q^{6} +(1.22914 - 0.893026i) q^{7} +(-0.268732 - 0.195245i) q^{8} +(-3.75996 - 2.73177i) q^{9} +(1.01301 + 3.11773i) q^{10} +(2.98634 - 2.16971i) q^{11} +(1.56408 + 4.81376i) q^{12} +(-0.309017 + 0.951057i) q^{13} +(-2.40557 - 1.74775i) q^{14} +(-1.43140 + 4.40540i) q^{15} +(-1.33206 + 4.09967i) q^{16} +(-5.46458 - 3.97025i) q^{17} +(-2.81075 + 8.65060i) q^{18} +(1.75464 + 5.40023i) q^{19} +(2.48023 - 1.80199i) q^{20} +(-1.29834 - 3.99589i) q^{21} +(-5.84460 - 4.24635i) q^{22} +(6.46530 + 4.69731i) q^{23} +(-0.743158 + 0.539936i) q^{24} -2.19434 q^{25} +1.95711 q^{26} +(-3.68604 + 2.67807i) q^{27} +(-0.859298 + 2.64465i) q^{28} +(-1.47816 - 4.54931i) q^{29} +9.06554 q^{30} +(4.36233 - 3.45978i) q^{31} +7.77206 q^{32} +(-3.15447 - 9.70845i) q^{33} +(-4.08504 + 12.5725i) q^{34} +(-2.05883 + 1.49583i) q^{35} +8.50631 q^{36} +7.92354 q^{37} +(8.99040 - 6.53191i) q^{38} +(2.23727 + 1.62547i) q^{39} +(0.450129 + 0.327038i) q^{40} +(2.00908 + 6.18330i) q^{41} +(-6.65241 + 4.83326i) q^{42} +(-3.15680 - 9.71565i) q^{43} +(-2.08776 + 6.42547i) q^{44} +(6.29796 + 4.57574i) q^{45} +(4.83313 - 14.8748i) q^{46} +(2.46948 - 7.60026i) q^{47} +(9.64409 + 7.00684i) q^{48} +(-1.44982 + 4.46208i) q^{49} +(1.32709 + 4.08437i) q^{50} +(-15.1119 + 10.9794i) q^{51} +(-0.565586 - 1.74069i) q^{52} +(-7.69313 - 5.58939i) q^{53} +(7.21399 + 5.24127i) q^{54} +(-5.00216 + 3.63428i) q^{55} -0.504670 q^{56} +15.7025 q^{57} +(-7.57377 + 5.50266i) q^{58} +(-1.33409 + 4.10590i) q^{59} +(-2.61986 - 8.06309i) q^{60} -0.00123644 q^{61} +(-9.07801 - 6.02729i) q^{62} -7.06107 q^{63} +(-2.03626 - 6.26696i) q^{64} +(0.517607 - 1.59303i) q^{65} +(-16.1628 + 11.7430i) q^{66} +1.97679 q^{67} +12.3627 q^{68} +(17.8793 - 12.9901i) q^{69} +(4.02935 + 2.92750i) q^{70} +(-5.04763 - 3.66732i) q^{71} +(0.477056 + 1.46823i) q^{72} +(-5.81416 + 4.22423i) q^{73} +(-4.79199 - 14.7482i) q^{74} +(-1.87520 + 5.77128i) q^{75} +(-8.40776 - 6.10859i) q^{76} +(1.73305 - 5.33376i) q^{77} +(1.67247 - 5.14734i) q^{78} +(-3.72230 - 2.70441i) q^{79} +(2.23122 - 6.86698i) q^{80} +(-0.414967 - 1.27714i) q^{81} +(10.2941 - 7.47907i) q^{82} +(1.06424 + 3.27538i) q^{83} +(6.22129 + 4.52003i) q^{84} +(9.15322 + 6.65020i) q^{85} +(-16.1748 + 11.7517i) q^{86} -13.2282 q^{87} -1.22615 q^{88} +(2.31773 - 1.68393i) q^{89} +(4.70804 - 14.4898i) q^{90} +(0.469491 + 1.44495i) q^{91} -14.6267 q^{92} +(-5.37159 - 14.4298i) q^{93} -15.6400 q^{94} +(-2.93904 - 9.04545i) q^{95} +(6.64171 - 20.4411i) q^{96} +(-0.859281 + 0.624304i) q^{97} +9.18219 q^{98} -17.1557 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9}+O(q^{10}) \) 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9	\( 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9} - 19 q^{10} - 9 q^{11} + 15 q^{12} + 12 q^{13} - 25 q^{14} - 30 q^{15} - 21 q^{16} + 11 q^{17} + 17 q^{18} + 36 q^{19} + 30 q^{20} + 11 q^{21} + 15 q^{22} - 7 q^{23} - 20 q^{24} - 16 q^{25} + 8 q^{26} - 5 q^{27} - 9 q^{28} + 12 q^{29} + 18 q^{30} + 22 q^{31} - 76 q^{32} - 49 q^{33} - 26 q^{34} + 8 q^{35} + 2 q^{36} + 64 q^{37} - 27 q^{38} - 3 q^{39} - 24 q^{40} + 46 q^{41} + 20 q^{42} - 28 q^{43} - 23 q^{45} + 34 q^{46} + 5 q^{47} - 20 q^{48} - 11 q^{49} + 9 q^{50} + 59 q^{51} + 17 q^{52} + 23 q^{53} + 41 q^{54} - 10 q^{55} - 60 q^{56} + 24 q^{57} - 37 q^{58} + 71 q^{59} - 72 q^{60} + 22 q^{61} + 43 q^{62} - 106 q^{63} - 52 q^{64} + 2 q^{65} - 21 q^{66} - 56 q^{67} - 104 q^{68} - 12 q^{69} - 32 q^{70} - 36 q^{71} + 147 q^{72} - 12 q^{73} + 10 q^{74} + 34 q^{75} - 49 q^{76} - 30 q^{77} + 5 q^{78} - 70 q^{79} + q^{81} + 130 q^{82} + 11 q^{83} + 77 q^{84} + 8 q^{85} + 11 q^{86} - 88 q^{87} + 96 q^{88} - 40 q^{89} - 48 q^{90} + 10 q^{91} + 112 q^{92} + 50 q^{93} + 78 q^{94} + 41 q^{95} - 75 q^{96} - 47 q^{97} - 46 q^{98} + 46 q^{99}+O(q^{100}) \) 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9 - 19 * q^10 - 9 * q^11 + 15 * q^12 + 12 * q^13 - 25 * q^14 - 30 * q^15 - 21 * q^16 + 11 * q^17 + 17 * q^18 + 36 * q^19 + 30 * q^20 + 11 * q^21 + 15 * q^22 - 7 * q^23 - 20 * q^24 - 16 * q^25 + 8 * q^26 - 5 * q^27 - 9 * q^28 + 12 * q^29 + 18 * q^30 + 22 * q^31 - 76 * q^32 - 49 * q^33 - 26 * q^34 + 8 * q^35 + 2 * q^36 + 64 * q^37 - 27 * q^38 - 3 * q^39 - 24 * q^40 + 46 * q^41 + 20 * q^42 - 28 * q^43 - 23 * q^45 + 34 * q^46 + 5 * q^47 - 20 * q^48 - 11 * q^49 + 9 * q^50 + 59 * q^51 + 17 * q^52 + 23 * q^53 + 41 * q^54 - 10 * q^55 - 60 * q^56 + 24 * q^57 - 37 * q^58 + 71 * q^59 - 72 * q^60 + 22 * q^61 + 43 * q^62 - 106 * q^63 - 52 * q^64 + 2 * q^65 - 21 * q^66 - 56 * q^67 - 104 * q^68 - 12 * q^69 - 32 * q^70 - 36 * q^71 + 147 * q^72 - 12 * q^73 + 10 * q^74 + 34 * q^75 - 49 * q^76 - 30 * q^77 + 5 * q^78 - 70 * q^79 + q^81 + 130 * q^82 + 11 * q^83 + 77 * q^84 + 8 * q^85 + 11 * q^86 - 88 * q^87 + 96 * q^88 - 40 * q^89 - 48 * q^90 + 10 * q^91 + 112 * q^92 + 50 * q^93 + 78 * q^94 + 41 * q^95 - 75 * q^96 - 47 * q^97 - 46 * q^98 + 46 * q^99

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