LMFDB - Embedded newform 387.2.f.d.130.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,2,Mod(130,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("387.130");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	387.f (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:	$3.09021055822$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			130.1
Character	$\chi$	$=$	387.130
Dual form			387.2.f.d.259.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31834 - 2.28344i) q^{2} +(1.31217 - 1.13058i) q^{3} +(-2.47606 + 4.28866i) q^{4} +(1.39983 - 2.42457i) q^{5} +(-4.31150 - 1.50576i) q^{6} +(1.99111 + 3.44870i) q^{7} +7.78382 q^{8} +(0.443574 - 2.96703i) q^{9} +O(q^{10})$	\(q+(-1.31834 - 2.28344i) q^{2} +(1.31217 - 1.13058i) q^{3} +(-2.47606 + 4.28866i) q^{4} +(1.39983 - 2.42457i) q^{5} +(-4.31150 - 1.50576i) q^{6} +(1.99111 + 3.44870i) q^{7} +7.78382 q^{8} +(0.443574 - 2.96703i) q^{9} -7.38182 q^{10} +(-2.07235 - 3.58941i) q^{11} +(1.59967 + 8.42684i) q^{12} +(1.53392 - 2.65683i) q^{13} +(5.24992 - 9.09313i) q^{14} +(-0.904366 - 4.76407i) q^{15} +(-5.30963 - 9.19655i) q^{16} -5.89483 q^{17} +(-7.35980 + 2.89869i) q^{18} -0.423608 q^{19} +(6.93212 + 12.0068i) q^{20} +(6.51170 + 2.27417i) q^{21} +(-5.46414 + 9.46416i) q^{22} +(0.535334 - 0.927226i) q^{23} +(10.2137 - 8.80024i) q^{24} +(-1.41904 - 2.45784i) q^{25} -8.08895 q^{26} +(-2.77242 - 4.39473i) q^{27} -19.7204 q^{28} +(2.91479 + 5.04856i) q^{29} +(-9.68619 + 8.34574i) q^{30} +(4.87493 - 8.44362i) q^{31} +(-6.21601 + 10.7665i) q^{32} +(-6.77739 - 2.36696i) q^{33} +(7.77142 + 13.4605i) q^{34} +11.1488 q^{35} +(11.6263 + 9.24887i) q^{36} +3.05211 q^{37} +(0.558461 + 0.967284i) q^{38} +(-0.990998 - 5.22044i) q^{39} +(10.8960 - 18.8724i) q^{40} +(-5.02745 + 8.70780i) q^{41} +(-3.39174 - 17.8672i) q^{42} +(0.500000 + 0.866025i) q^{43} +20.5250 q^{44} +(-6.57284 - 5.22880i) q^{45} -2.82302 q^{46} +(4.13133 + 7.15568i) q^{47} +(-17.3646 - 6.06446i) q^{48} +(-4.42900 + 7.67126i) q^{49} +(-3.74156 + 6.48057i) q^{50} +(-7.73502 + 6.66459i) q^{51} +(7.59617 + 13.1570i) q^{52} -4.04613 q^{53} +(-6.38010 + 12.1244i) q^{54} -11.6037 q^{55} +(15.4984 + 26.8440i) q^{56} +(-0.555846 + 0.478924i) q^{57} +(7.68539 - 13.3115i) q^{58} +(1.40350 - 2.43093i) q^{59} +(22.6707 + 7.91760i) q^{60} +(6.49271 + 11.2457i) q^{61} -25.7073 q^{62} +(11.1156 - 4.37791i) q^{63} +11.5409 q^{64} +(-4.29446 - 7.43822i) q^{65} +(3.53013 + 18.5962i) q^{66} +(-0.766282 + 1.32724i) q^{67} +(14.5960 - 25.2810i) q^{68} +(-0.345855 - 1.82191i) q^{69} +(-14.6980 - 25.4576i) q^{70} +3.85095 q^{71} +(3.45270 - 23.0948i) q^{72} +4.68286 q^{73} +(-4.02373 - 6.96931i) q^{74} +(-4.64081 - 1.62077i) q^{75} +(1.04888 - 1.81671i) q^{76} +(8.25253 - 14.2938i) q^{77} +(-10.6141 + 9.14521i) q^{78} +(-5.77387 - 10.0006i) q^{79} -29.7303 q^{80} +(-8.60648 - 2.63219i) q^{81} +26.5116 q^{82} +(0.655725 + 1.13575i) q^{83} +(-25.8765 + 22.2955i) q^{84} +(-8.25175 + 14.2925i) q^{85} +(1.31834 - 2.28344i) q^{86} +(9.53251 + 3.32916i) q^{87} +(-16.1308 - 27.9393i) q^{88} -0.630048 q^{89} +(-3.27438 + 21.9020i) q^{90} +12.2168 q^{91} +(2.65104 + 4.59173i) q^{92} +(-3.14947 - 16.5910i) q^{93} +(10.8930 - 18.8673i) q^{94} +(-0.592979 + 1.02707i) q^{95} +(4.01589 + 21.1551i) q^{96} +(-2.05730 - 3.56335i) q^{97} +23.3558 q^{98} +(-11.5691 + 4.55654i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 6 q^{2} + 2 q^{3} - 22 q^{4} + 17 q^{5} - 6 q^{6} - 3 q^{7} - 30 q^{8}+O(q^{10}) $ 40 * q + 6 * q^2 + 2 * q^3 - 22 * q^4 + 17 * q^5 - 6 * q^6 - 3 * q^7 - 30 * q^8	\( 40 q + 6 q^{2} + 2 q^{3} - 22 q^{4} + 17 q^{5} - 6 q^{6} - 3 q^{7} - 30 q^{8} - 4 q^{10} + 10 q^{11} - 17 q^{12} + q^{13} + 10 q^{14} + 7 q^{15} - 22 q^{16} - 40 q^{17} + 3 q^{18} + 16 q^{19} + 30 q^{20} + 6 q^{21} - 15 q^{22} + 19 q^{23} + 33 q^{24} - 19 q^{25} - 50 q^{26} + 8 q^{27} - 6 q^{28} + 25 q^{29} - 54 q^{30} + 11 q^{31} + 36 q^{32} - 6 q^{33} - 9 q^{34} + 44 q^{36} + 18 q^{37} + 28 q^{38} - 35 q^{39} - 12 q^{40} + 12 q^{41} + 37 q^{42} + 20 q^{43} - 10 q^{44} - 25 q^{45} + 8 q^{46} + 38 q^{47} - 7 q^{48} - 37 q^{49} + 36 q^{50} - 4 q^{51} + 8 q^{52} - 138 q^{53} + 33 q^{54} - 18 q^{55} + 30 q^{56} - 53 q^{57} + 27 q^{58} + 31 q^{59} + 38 q^{60} - 19 q^{61} - 64 q^{62} - 35 q^{63} + 22 q^{64} + 47 q^{65} - 33 q^{66} - 9 q^{67} + 68 q^{68} + 26 q^{69} + 6 q^{70} - 42 q^{71} + 6 q^{72} - 4 q^{73} - 16 q^{74} - 56 q^{75} - 37 q^{76} + 85 q^{77} + 43 q^{78} + 4 q^{79} - 122 q^{80} - 36 q^{81} + 2 q^{82} + 19 q^{83} - 83 q^{84} + 6 q^{85} - 6 q^{86} + 49 q^{87} - 60 q^{88} - 108 q^{89} + 3 q^{90} - 6 q^{91} + 85 q^{92} - 10 q^{93} + 19 q^{94} - 11 q^{95} + 93 q^{96} - 2 q^{97} - 10 q^{98} + 19 q^{99}+O(q^{100}) \) 40 * q + 6 * q^2 + 2 * q^3 - 22 * q^4 + 17 * q^5 - 6 * q^6 - 3 * q^7 - 30 * q^8 - 4 * q^10 + 10 * q^11 - 17 * q^12 + q^13 + 10 * q^14 + 7 * q^15 - 22 * q^16 - 40 * q^17 + 3 * q^18 + 16 * q^19 + 30 * q^20 + 6 * q^21 - 15 * q^22 + 19 * q^23 + 33 * q^24 - 19 * q^25 - 50 * q^26 + 8 * q^27 - 6 * q^28 + 25 * q^29 - 54 * q^30 + 11 * q^31 + 36 * q^32 - 6 * q^33 - 9 * q^34 + 44 * q^36 + 18 * q^37 + 28 * q^38 - 35 * q^39 - 12 * q^40 + 12 * q^41 + 37 * q^42 + 20 * q^43 - 10 * q^44 - 25 * q^45 + 8 * q^46 + 38 * q^47 - 7 * q^48 - 37 * q^49 + 36 * q^50 - 4 * q^51 + 8 * q^52 - 138 * q^53 + 33 * q^54 - 18 * q^55 + 30 * q^56 - 53 * q^57 + 27 * q^58 + 31 * q^59 + 38 * q^60 - 19 * q^61 - 64 * q^62 - 35 * q^63 + 22 * q^64 + 47 * q^65 - 33 * q^66 - 9 * q^67 + 68 * q^68 + 26 * q^69 + 6 * q^70 - 42 * q^71 + 6 * q^72 - 4 * q^73 - 16 * q^74 - 56 * q^75 - 37 * q^76 + 85 * q^77 + 43 * q^78 + 4 * q^79 - 122 * q^80 - 36 * q^81 + 2 * q^82 + 19 * q^83 - 83 * q^84 + 6 * q^85 - 6 * q^86 + 49 * q^87 - 60 * q^88 - 108 * q^89 + 3 * q^90 - 6 * q^91 + 85 * q^92 - 10 * q^93 + 19 * q^94 - 11 * q^95 + 93 * q^96 - 2 * q^97 - 10 * q^98 + 19 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/387\mathbb{Z}\right)^\times$.

$n$	$46$	$173$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.31834	−	2.28344i	−0.932210	−	1.61463i	−0.779535	−	0.626358i	$-0.784545\pi$
$2$	−1.31834	−	2.28344i	−0.932210	−	1.61463i	−0.152674	−	0.988277i	$-0.548789\pi$
$3$	1.31217	−	1.13058i	0.757581	−	0.652741i
$3$	1.31217	−	1.13058i	0.757581	−	0.652741i
$4$	−2.47606	+	4.28866i	−1.23803	+	2.14433i
$5$	1.39983	−	2.42457i	0.626022	−	1.08430i	−0.362320	−	0.932054i	$-0.618015\pi$
$5$	1.39983	−	2.42457i	0.626022	−	1.08430i	0.988342	−	0.152248i	$-0.0486514\pi$
$6$	−4.31150	−	1.50576i	−1.76016	−	0.614725i
$7$	1.99111	+	3.44870i	0.752567	+	1.30348i	0.946575	+	0.322484i	$0.104518\pi$
$7$	1.99111	+	3.44870i	0.752567	+	1.30348i	−0.194008	+	0.981000i	$0.562149\pi$
$8$	7.78382			2.75200
$9$	0.443574	−	2.96703i	0.147858	−	0.989009i
$10$	−7.38182			−2.33434
$11$	−2.07235	−	3.58941i	−0.624837	−	1.08225i	−0.988572	−	0.150747i	$-0.951832\pi$
$11$	−2.07235	−	3.58941i	−0.624837	−	1.08225i	0.363736	−	0.931502i	$-0.381501\pi$
$12$	1.59967	+	8.42684i	0.461785	+	2.43262i
$13$	1.53392	−	2.65683i	0.425434	−	0.736873i	−0.571027	−	0.820931i	$-0.693455\pi$
$13$	1.53392	−	2.65683i	0.425434	−	0.736873i	0.996461	+	0.0840584i	$0.0267882\pi$
$14$	5.24992	−	9.09313i	1.40310	−	2.43024i
$15$	−0.904366	−	4.76407i	−0.233506	−	1.23008i
$16$	−5.30963	−	9.19655i	−1.32741	−	2.29914i
$17$	−5.89483			−1.42971			−0.714854	−	0.699274i	$-0.753507\pi$
$17$	−5.89483			−1.42971			−0.714854	+	0.699274i	$0.753507\pi$
$18$	−7.35980	+	2.89869i	−1.73472	+	0.683227i
$19$	−0.423608			−0.0971824			−0.0485912	−	0.998819i	$-0.515473\pi$
$19$	−0.423608			−0.0971824			−0.0485912	+	0.998819i	$0.515473\pi$
$20$	6.93212	+	12.0068i	1.55007	+	2.68480i
$21$	6.51170	+	2.27417i	1.42097	+	0.496263i
$22$	−5.46414	+	9.46416i	−1.16496	+	2.01777i
$23$	0.535334	−	0.927226i	0.111625	−	0.193340i	−0.804801	−	0.593545i	$-0.797728\pi$
$23$	0.535334	−	0.927226i	0.111625	−	0.193340i	0.916426	+	0.400205i	$0.131061\pi$
$24$	10.2137	−	8.80024i	2.08486	−	1.79634i
$25$	−1.41904	−	2.45784i	−0.283807	−	0.491569i
$26$	−8.08895			−1.58637
$27$	−2.77242	−	4.39473i	−0.533552	−	0.845767i
$28$	−19.7204			−3.72680
$29$	2.91479	+	5.04856i	0.541263	+	0.937495i	0.998832	+	0.0483207i	$0.0153870\pi$
$29$	2.91479	+	5.04856i	0.541263	+	0.937495i	−0.457569	+	0.889174i	$0.651280\pi$
$30$	−9.68619	+	8.34574i	−1.76845	+	1.52372i
$31$	4.87493	−	8.44362i	0.875563	−	1.51652i	0.0194008	−	0.999812i	$-0.493824\pi$
$31$	4.87493	−	8.44362i	0.875563	−	1.51652i	0.856162	−	0.516707i	$-0.172843\pi$
$32$	−6.21601	+	10.7665i	−1.09885	+	1.90326i
$33$	−6.77739	−	2.36696i	−1.17979	−	0.412035i
$34$	7.77142	+	13.4605i	1.33279	+	2.30846i
$35$	11.1488			1.88449
$36$	11.6263	+	9.24887i	1.93771	+	1.54148i
$37$	3.05211			0.501764			0.250882	−	0.968018i	$-0.419279\pi$
$37$	3.05211			0.501764			0.250882	+	0.968018i	$0.419279\pi$
$38$	0.558461	+	0.967284i	0.0905944	+	0.156914i
$39$	−0.990998	−	5.22044i	−0.158687	−	0.835939i
$40$	10.8960	−	18.8724i	1.72281	−	2.98400i
$41$	−5.02745	+	8.70780i	−0.785156	+	1.35993i	0.143750	+	0.989614i	$0.454084\pi$
$41$	−5.02745	+	8.70780i	−0.785156	+	1.35993i	−0.928906	+	0.370316i	$0.879250\pi$
$42$	−3.39174	−	17.8672i	−0.523356	−	2.75697i
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i
$44$	20.5250			3.09427
$45$	−6.57284	−	5.22880i	−0.979822	−	0.779464i
$46$	−2.82302			−0.416231
$47$	4.13133	+	7.15568i	0.602617	+	1.04376i	0.992423	+	0.122866i	$0.0392086\pi$
$47$	4.13133	+	7.15568i	0.602617	+	1.04376i	−0.389806	+	0.920897i	$0.627458\pi$
$48$	−17.3646	−	6.06446i	−2.50636	−	0.875329i
$49$	−4.42900	+	7.67126i	−0.632714	+	1.09589i
$50$	−3.74156	+	6.48057i	−0.529136	+	0.916491i
$51$	−7.73502	+	6.66459i	−1.08312	+	0.933229i
$52$	7.59617	+	13.1570i	1.05340	+	1.82454i
$53$	−4.04613			−0.555778			−0.277889	−	0.960613i	$-0.589635\pi$
$53$	−4.04613			−0.555778			−0.277889	+	0.960613i	$0.589635\pi$
$54$	−6.38010	+	12.1244i	−0.868222	+	1.64992i
$55$	−11.6037			−1.56465
$56$	15.4984	+	26.8440i	2.07106	+	3.58718i
$57$	−0.555846	+	0.478924i	−0.0736236	+	0.0634350i
$58$	7.68539	−	13.3115i	1.00914	−	1.74788i
$59$	1.40350	−	2.43093i	0.182720	−	0.316481i	−0.760086	−	0.649823i	$-0.774843\pi$
$59$	1.40350	−	2.43093i	0.182720	−	0.316481i	0.942806	+	0.333342i	$0.108176\pi$
$60$	22.6707	+	7.91760i	2.92678	+	1.02216i
$61$	6.49271	+	11.2457i	0.831307	+	1.43987i	0.897002	+	0.442026i	$0.145740\pi$
$61$	6.49271	+	11.2457i	0.831307	+	1.43987i	−0.0656957	+	0.997840i	$0.520927\pi$
$62$	−25.7073			−3.26483
$63$	11.1156	−	4.37791i	1.40043	−	0.551565i
$64$	11.5409			1.44261
$65$	−4.29446	−	7.43822i	−0.532662	−	0.922597i
$66$	3.53013	+	18.5962i	0.434529	+	2.28904i
$67$	−0.766282	+	1.32724i	−0.0936162	+	0.162148i	−0.909030	−	0.416730i	$-0.863176\pi$
$67$	−0.766282	+	1.32724i	−0.0936162	+	0.162148i	0.815414	+	0.578878i	$0.196509\pi$
$68$	14.5960	−	25.2810i	1.77002	−	3.06577i
$69$	−0.345855	−	1.82191i	−0.0416361	−	0.219333i
$70$	−14.6980	−	25.4576i	−1.75674	−	3.04277i
$71$	3.85095			0.457024			0.228512	−	0.973541i	$-0.426614\pi$
$71$	3.85095			0.457024			0.228512	+	0.973541i	$0.426614\pi$
$72$	3.45270	−	23.0948i	0.406904	−	2.72175i
$73$	4.68286			0.548087			0.274043	−	0.961717i	$-0.411639\pi$
$73$	4.68286			0.548087			0.274043	+	0.961717i	$0.411639\pi$
$74$	−4.02373	−	6.96931i	−0.467749	−	0.810165i
$75$	−4.64081	−	1.62077i	−0.535874	−	0.187150i
$76$	1.04888	−	1.81671i	0.120315	−	0.208391i
$77$	8.25253	−	14.2938i	0.940463	−	1.62893i
$78$	−10.6141	+	9.14521i	−1.20181	+	1.03549i
$79$	−5.77387	−	10.0006i	−0.649611	−	1.12516i	−0.983216	−	0.182446i	$-0.941599\pi$
$79$	−5.77387	−	10.0006i	−0.649611	−	1.12516i	0.333605	−	0.942713i	$-0.391735\pi$
$80$	−29.7303			−3.32395
$81$	−8.60648	−	2.63219i	−0.956276	−	0.292465i
$82$	26.5116			2.92772
$83$	0.655725	+	1.13575i	0.0719752	+	0.124665i	0.899767	−	0.436371i	$-0.143736\pi$
$83$	0.655725	+	1.13575i	0.0719752	+	0.124665i	−0.827792	+	0.561036i	$0.810403\pi$
$84$	−25.8765	+	22.2955i	−2.82336	+	2.43264i
$85$	−8.25175	+	14.2925i	−0.895028	+	1.55023i
$86$	1.31834	−	2.28344i	0.142161	−	0.246229i
$87$	9.53251	+	3.32916i	1.02199	+	0.356924i
$88$	−16.1308	−	27.9393i	−1.71955	−	2.97834i
$89$	−0.630048			−0.0667850			−0.0333925	−	0.999442i	$-0.510631\pi$
$89$	−0.630048			−0.0667850			−0.0333925	+	0.999442i	$0.510631\pi$
$90$	−3.27438	+	21.9020i	−0.345150	+	2.30868i
$91$	12.2168			1.28067
$92$	2.65104	+	4.59173i	0.276390	+	0.478721i
$93$	−3.14947	−	16.5910i	−0.326585	−	1.72040i
$94$	10.8930	−	18.8673i	1.12353	−	1.94601i
$95$	−0.592979	+	1.02707i	−0.0608384	+	0.105375i
$96$	4.01589	+	21.1551i	0.409870	+	2.15913i
$97$	−2.05730	−	3.56335i	−0.208887	−	0.361803i	0.742477	−	0.669871i	$-0.233651\pi$
$97$	−2.05730	−	3.56335i	−0.208887	−	0.361803i	−0.951364	+	0.308068i	$0.900317\pi$
$98$	23.3558			2.35929
$99$	−11.5691	+	4.55654i	−1.16274	+	0.457950i
$100$	14.0545			1.40545
$101$	2.28610	+	3.95965i	0.227476	+	0.394000i	0.957059	−	0.289892i	$-0.0936194\pi$
$101$	2.28610	+	3.95965i	0.227476	+	0.394000i	−0.729583	+	0.683892i	$0.760286\pi$
$102$	25.4156	+	8.87622i	2.51652	+	0.878877i
$103$	−0.111247	+	0.192685i	−0.0109615	+	0.0189858i	−0.871454	−	0.490477i	$-0.836823\pi$
$103$	−0.111247	+	0.192685i	−0.0109615	+	0.0189858i	0.860493	+	0.509463i	$0.170156\pi$
$104$	11.9398	−	20.6803i	1.17079	−	2.02787i
$105$	14.6291	−	12.6046i	1.42766	−	1.23009i
$106$	5.33419	+	9.23908i	0.518102	+	0.897379i
$107$	2.94239			0.284452			0.142226	−	0.989834i	$-0.454574\pi$
$107$	2.94239			0.284452			0.142226	+	0.989834i	$0.454574\pi$
$108$	25.7122	−	1.00834i	2.47416	−	0.0970278i
$109$	7.54440			0.722622			0.361311	−	0.932445i	$-0.382329\pi$
$109$	7.54440			0.722622			0.361311	+	0.932445i	$0.382329\pi$
$110$	15.2977	+	26.4964i	1.45858	+	2.52633i
$111$	4.00488	−	3.45066i	0.380127	−	0.327522i
$112$	21.1441	−	36.6226i	1.99793	−	3.46051i
$113$	4.88746	−	8.46533i	0.459773	−	0.796351i	−0.539175	−	0.842194i	$-0.681264\pi$
$113$	4.88746	−	8.46533i	0.459773	−	0.796351i	0.998949	+	0.0458427i	$0.0145973\pi$
$114$	1.82639	+	0.637854i	0.171057	+	0.0597405i
$115$	−1.49875	−	2.59591i	−0.139759	−	0.242070i
$116$	−28.8688			−2.68040
$117$	−7.20248	−	5.72969i	−0.665870	−	0.529710i
$118$	−7.40118			−0.681334
$119$	−11.7372	−	20.3295i	−1.07595	−	1.86360i
$120$	−7.03942	−	37.0826i	−0.642608	−	3.38517i
$121$	−3.08926	+	5.35076i	−0.280842	+	0.486432i
$122$	17.1193	−	29.6514i	1.54990	−	2.68451i
$123$	3.24801	+	17.1100i	0.292863	+	1.54276i
$124$	24.1412	+	41.8138i	2.16795	+	3.75499i
$125$	6.05265			0.541365
$126$	−24.6508	−	19.6101i	−2.19607	−	1.74701i
$127$	−3.17610			−0.281833			−0.140916	−	0.990021i	$-0.545005\pi$
$127$	−3.17610			−0.281833			−0.140916	+	0.990021i	$0.545005\pi$
$128$	−2.78278	−	4.81992i	−0.245966	−	0.426025i
$129$	1.63520	+	0.571081i	0.143971	+	0.0502809i
$130$	−11.3231	+	19.6123i	−0.993105	+	1.72011i
$131$	−2.33983	+	4.05271i	−0.204432	+	0.354087i	−0.949952	−	0.312397i	$-0.898868\pi$
$131$	−2.33983	+	4.05271i	−0.204432	+	0.354087i	0.745520	+	0.666484i	$0.232201\pi$
$132$	26.9323	−	23.2052i	2.34416	−	2.01976i
$133$	−0.843449	−	1.46090i	−0.0731363	−	0.126676i
$134$	4.04089			0.349080
$135$	−14.5363	+	0.570061i	−1.25108	+	0.0490630i
$136$	−45.8843			−3.93455
$137$	9.95621	+	17.2447i	0.850617	+	1.47331i	0.880653	+	0.473762i	$0.157104\pi$
$137$	9.95621	+	17.2447i	0.850617	+	1.47331i	−0.0300362	+	0.999549i	$0.509562\pi$
$138$	−3.70427	+	3.19165i	−0.315329	+	0.271691i
$139$	−1.81702	+	3.14717i	−0.154118	+	0.266940i	−0.932737	−	0.360556i	$-0.882587\pi$
$139$	−1.81702	+	3.14717i	−0.154118	+	0.266940i	0.778620	+	0.627496i	$0.215920\pi$
$140$	−27.6052	+	47.8135i	−2.33306	+	4.04098i
$141$	13.5111	+	4.71865i	1.13784	+	0.397382i
$142$	−5.07688	−	8.79342i	−0.426042	−	0.737927i
$143$	−12.7153			−1.06331
$144$	−29.6416	+	11.6745i	−2.47013	+	0.972872i
$145$	16.3208			1.35537
$146$	−6.17361	−	10.6930i	−0.510932	−	0.884960i
$147$	2.86138	+	15.0733i	0.236002	+	1.24323i
$148$	−7.55721	+	13.0895i	−0.621199	+	1.07595i
$149$	−3.53945	+	6.13050i	−0.289963	+	0.502230i	−0.973801	−	0.227404i	$-0.926976\pi$
$149$	−3.53945	+	6.13050i	−0.289963	+	0.502230i	0.683838	+	0.729634i	$0.260310\pi$
$150$	2.41725	+	12.7337i	0.197368	+	1.03970i
$151$	3.99720	+	6.92336i	0.325288	+	0.563415i	0.981571	−	0.191100i	$-0.0612055\pi$
$151$	3.99720	+	6.92336i	0.325288	+	0.563415i	−0.656283	+	0.754515i	$0.727872\pi$
$152$	−3.29729			−0.267446
$153$	−2.61479	+	17.4901i	−0.211394	+	1.41399i
$154$	−43.5187			−3.50684
$155$	−13.6481	−	23.6392i	−1.09624	−	1.89875i
$156$	24.8425	+	8.67606i	1.98899	+	0.694641i
$157$	−7.54081	+	13.0611i	−0.601822	+	1.04239i	0.390723	+	0.920508i	$0.372225\pi$
$157$	−7.54081	+	13.0611i	−0.601822	+	1.04239i	−0.992545	+	0.121878i	$0.961108\pi$
$158$	−15.2239	+	26.3685i	−1.21115	+	2.09777i
$159$	−5.30920	+	4.57447i	−0.421047	+	0.362779i
$160$	17.4027	+	30.1424i	1.37580	+	2.38296i
$161$	4.26363			0.336021
$162$	5.33586	+	23.1225i	0.419225	+	1.81668i
$163$	−4.92573			−0.385813			−0.192906	−	0.981217i	$-0.561791\pi$
$163$	−4.92573			−0.385813			−0.192906	+	0.981217i	$0.561791\pi$
$164$	−24.8965	−	43.1221i	−1.94409	−	3.36727i
$165$	−15.2260	+	13.1190i	−1.18535	+	1.02131i
$166$	1.72894	−	2.99462i	0.134192	−	0.232427i
$167$	9.20065	−	15.9360i	0.711968	−	1.23316i	−0.252150	−	0.967688i	$-0.581138\pi$
$167$	9.20065	−	15.9360i	0.711968	−	1.23316i	0.964117	−	0.265476i	$-0.0855292\pi$
$168$	50.6859	+	17.7017i	3.91050	+	1.36572i
$169$	1.79416	+	3.10758i	0.138012	+	0.239044i
$170$	43.5146			3.33742
$171$	−0.187902	+	1.25686i	−0.0143692	+	0.0961143i
$172$	−4.95212			−0.377596
$173$	−2.50951	−	4.34660i	−0.190795	−	0.330466i	0.754719	−	0.656048i	$-0.227773\pi$
$173$	−2.50951	−	4.34660i	−0.190795	−	0.330466i	−0.945514	+	0.325582i	$0.894440\pi$
$174$	−4.96518	−	26.1559i	−0.376410	−	1.98287i
$175$	5.65090	−	9.78765i	0.427168	−	0.739877i
$176$	−22.0068	+	38.1169i	−1.65883	+	2.87317i
$177$	−0.906738	−	4.77656i	−0.0681546	−	0.359029i
$178$	0.830620	+	1.43868i	0.0622576	+	0.107833i
$179$	−12.5210			−0.935862			−0.467931	−	0.883765i	$-0.655000\pi$
$179$	−12.5210			−0.935862			−0.467931	+	0.883765i	$0.655000\pi$
$180$	38.6993	−	15.2419i	2.88448	−	1.13606i
$181$	18.7634			1.39467			0.697337	−	0.716744i	$-0.254368\pi$
$181$	18.7634			1.39467			0.697337	+	0.716744i	$0.254368\pi$
$182$	−16.1060	−	27.8963i	−1.19385	−	2.06781i
$183$	21.2337	+	7.41573i	1.56964	+	0.548187i
$184$	4.16694	−	7.21736i	0.307191	−	0.532071i
$185$	4.27243	−	7.40006i	0.314115	−	0.544064i
$186$	−33.7323	+	29.0642i	−2.47338	+	2.13109i
$187$	12.2162	+	21.1590i	0.893334	+	1.54730i
$188$	−40.9177			−2.98423
$189$	9.63592	−	18.3116i	0.700910	−	1.33197i
$190$	3.12700			0.226856
$191$	4.45605	+	7.71810i	0.322428	+	0.558462i	0.980988	−	0.194066i	$-0.0621676\pi$
$191$	4.45605	+	7.71810i	0.322428	+	0.558462i	−0.658560	+	0.752528i	$0.728834\pi$
$192$	15.1435	−	13.0479i	1.09289	−	0.941649i
$193$	2.75595	−	4.77344i	0.198378	−	0.343600i	−0.749625	−	0.661863i	$-0.769766\pi$
$193$	2.75595	−	4.77344i	0.198378	−	0.343600i	0.948003	+	0.318263i	$0.103099\pi$
$194$	−5.42445	+	9.39543i	−0.389453	+	0.674553i
$195$	−14.0446	−	4.90497i	−1.00575	−	0.351252i
$196$	−21.9329	−	37.9890i	−1.56664	−	2.71350i
$197$	−5.01927			−0.357608			−0.178804	−	0.983885i	$-0.557223\pi$
$197$	−5.01927			−0.357608			−0.178804	+	0.983885i	$0.557223\pi$
$198$	25.6567	+	20.4103i	1.82334	+	1.45050i
$199$	0.286051			0.0202776			0.0101388	−	0.999949i	$-0.496773\pi$
$199$	0.286051			0.0202776			0.0101388	+	0.999949i	$0.496773\pi$
$200$	−11.0455	−	19.1314i	−0.781037	−	1.35280i
$201$	0.495060	+	2.60791i	0.0349189	+	0.183947i
$202$	6.02774	−	10.4404i	0.424111	−	0.734581i
$203$	−11.6073	+	20.1044i	−0.814673	+	1.41106i
$204$	−9.42979	−	49.6748i	−0.660218	−	3.47793i
$205$	14.0751	+	24.3788i	0.983050	+	1.70269i
$206$	0.586646			0.0408735
$207$	−2.51364	−	1.99964i	−0.174710	−	0.138985i
$208$	−32.5782			−2.25890
$209$	0.877864	+	1.52051i	0.0607232	+	0.105176i
$210$	−48.0682	−	16.7875i	−3.31702	−	1.15845i
$211$	−8.78760	+	15.2206i	−0.604963	+	1.04783i	0.387094	+	0.922040i	$0.373479\pi$
$211$	−8.78760	+	15.2206i	−0.604963	+	1.04783i	−0.992057	+	0.125787i	$0.959854\pi$
$212$	10.0185	−	17.3525i	0.688070	−	1.19177i
$213$	5.05310	−	4.35381i	0.346233	−	0.298318i
$214$	−3.87908	−	6.71877i	−0.265169	−	0.459285i
$215$	2.79966			0.190935
$216$	−21.5800	−	34.2078i	−1.46833	−	2.32755i
$217$	38.8260			2.63568
$218$	−9.94611	−	17.2272i	−0.673635	−	1.16677i
$219$	6.14470	−	5.29435i	0.415220	−	0.357759i
$220$	28.7315	−	49.7645i	1.93708	−	3.35512i
$221$	−9.04222	+	15.6616i	−0.608246	+	1.05351i
$222$	−13.1592	−	4.59575i	−0.883186	−	0.308447i
$223$	−5.44391	−	9.42913i	−0.364551	−	0.631421i	0.624153	−	0.781302i	$-0.285444\pi$
$223$	−5.44391	−	9.42913i	−0.364551	−	0.631421i	−0.988704	+	0.149881i	$0.952111\pi$
$224$	−49.5070			−3.30782
$225$	−7.92194	+	3.12008i	−0.528129	+	0.208006i
$226$	−25.7734			−1.71442
$227$	5.22224	+	9.04519i	0.346612	+	0.600350i	0.985645	−	0.168829i	$-0.0539986\pi$
$227$	5.22224	+	9.04519i	0.346612	+	0.600350i	−0.639033	+	0.769179i	$0.720665\pi$
$228$	−0.677634	−	3.56968i	−0.0448774	−	0.236408i
$229$	−7.64089	+	13.2344i	−0.504925	+	0.874555i	0.495059	+	0.868859i	$0.335146\pi$
$229$	−7.64089	+	13.2344i	−0.504925	+	0.874555i	−0.999984	+	0.00569574i	$0.998187\pi$
$230$	−3.95174	+	6.84461i	−0.260570	+	0.451320i
$231$	−5.33159	−	28.0860i	−0.350793	−	1.84793i
$232$	22.6882	+	39.2971i	1.48955	+	2.57998i
$233$	21.3798			1.40064			0.700319	−	0.713830i	$-0.253041\pi$
$233$	21.3798			1.40064			0.700319	+	0.713830i	$0.253041\pi$
$234$	−3.58805	+	24.0001i	−0.234558	+	1.56894i
$235$	23.1326			1.50901
$236$	6.95030	+	12.0383i	0.452426	+	0.783625i
$237$	−18.8828	−	6.59469i	−1.22657	−	0.428371i
$238$	−30.9474	+	53.6025i	−2.00602	+	3.47453i
$239$	0.604130	−	1.04638i	0.0390779	−	0.0676850i	−0.845825	−	0.533461i	$-0.820891\pi$
$239$	0.604130	−	1.04638i	0.0390779	−	0.0676850i	0.884903	+	0.465776i	$0.154225\pi$
$240$	−39.0111	+	33.6125i	−2.51816	+	2.16968i
$241$	−14.1265	−	24.4678i	−0.909968	−	1.57611i	−0.814106	−	0.580716i	$-0.802773\pi$
$241$	−14.1265	−	24.4678i	−0.909968	−	1.57611i	−0.0958618	−	0.995395i	$-0.530561\pi$
$242$	16.2908			1.04721
$243$	−14.2691	+	6.27645i	−0.915361	+	0.402635i
$244$	−64.3054			−4.11673
$245$	12.3997	+	21.4769i	0.792187	+	1.37211i
$246$	34.7877	−	29.9735i	2.21798	−	1.91104i
$247$	−0.649783	+	1.12546i	−0.0413447	+	0.0716111i
$248$	37.9456	−	65.7236i	2.40955	−	4.17345i
$249$	2.14448	+	0.748944i	0.135901	+	0.0474624i
$250$	−7.97947	−	13.8208i	−0.504666	−	0.874107i
$251$	15.9212			1.00494			0.502469	−	0.864595i	$-0.332425\pi$
$251$	15.9212			1.00494			0.502469	+	0.864595i	$0.332425\pi$
$252$	−8.74745	+	58.5109i	−0.551037	+	3.68584i
$253$	−4.43760			−0.278989
$254$	4.18719	+	7.25242i	0.262727	+	0.455057i
$255$	5.33109	+	28.0834i	0.333846	+	1.75865i
$256$	4.20352	−	7.28071i	0.262720	−	0.455045i
$257$	9.27207	−	16.0597i	0.578376	−	1.00178i	−0.417290	−	0.908773i	$-0.637020\pi$
$257$	9.27207	−	16.0597i	0.578376	−	1.00178i	0.995666	−	0.0930031i	$-0.0296466\pi$
$258$	−0.851722	−	4.48675i	−0.0530259	−	0.279333i
$259$	6.07707	+	10.5258i	0.377611	+	0.654041i
$260$	42.5333			2.63781
$261$	16.2721	−	6.40885i	1.00722	−	0.396698i
$262$	12.3388			0.762294
$263$	−0.781763	−	1.35405i	−0.0482056	−	0.0834945i	0.840916	−	0.541166i	$-0.182017\pi$
$263$	−0.781763	−	1.35405i	−0.0482056	−	0.0834945i	−0.889121	+	0.457671i	$0.848684\pi$
$264$	−52.7540	−	18.4240i	−3.24679	−	1.13392i
$265$	−5.66388	+	9.81013i	−0.347930	+	0.602632i
$266$	−2.22391	+	3.85193i	−0.136357	+	0.236177i
$267$	−0.826729	+	0.712320i	−0.0505950	+	0.0435933i
$268$	−3.79472	−	6.57265i	−0.231799	−	0.401488i
$269$	−16.6610			−1.01584			−0.507919	−	0.861405i	$-0.669585\pi$
$269$	−16.6610			−1.01584			−0.507919	+	0.861405i	$0.669585\pi$
$270$	20.4655	+	32.4411i	1.24549	+	1.97430i
$271$	−23.5537			−1.43078			−0.715392	−	0.698724i	$-0.753752\pi$
$271$	−23.5537			−1.43078			−0.715392	+	0.698724i	$0.753752\pi$
$272$	31.2994	+	54.2121i	1.89780	+	3.28709i
$273$	16.0305	−	13.8121i	0.970211	−	0.835946i
$274$	26.2514	−	45.4688i	1.58591	−	2.74687i
$275$	−5.88148	+	10.1870i	−0.354667	+	0.614301i
$276$	8.66994	+	3.02792i	0.521869	+	0.182259i
$277$	−10.7167	−	18.5619i	−0.643904	−	1.11528i	−0.984553	−	0.175085i	$-0.943980\pi$
$277$	−10.7167	−	18.5619i	−0.643904	−	1.11528i	0.340649	−	0.940191i	$-0.389353\pi$
$278$	9.58183			0.574680
$279$	−22.8901	−	18.2094i	−1.37039	−	1.09017i
$280$	86.7804			5.18612
$281$	1.04696	+	1.81339i	0.0624566	+	0.108178i	0.895563	−	0.444935i	$-0.146773\pi$
$281$	1.04696	+	1.81339i	0.0624566	+	0.108178i	−0.833106	+	0.553113i	$0.813440\pi$
$282$	−7.03750	−	37.0725i	−0.419077	−	2.20764i
$283$	5.02403	−	8.70187i	0.298647	−	0.517272i	−0.677179	−	0.735818i	$-0.736798\pi$
$283$	5.02403	−	8.70187i	0.298647	−	0.517272i	0.975827	+	0.218546i	$0.0701312\pi$
$284$	−9.53519	+	16.5154i	−0.565810	+	0.980011i
$285$	0.383097	+	2.01810i	0.0226927	+	0.119542i
$286$	16.7631	+	29.0346i	0.991225	+	1.71685i
$287$	−40.0407			−2.36353
$288$	29.1871	+	23.2188i	1.71987	+	1.36818i
$289$	17.7491			1.04406
$290$	−21.5165	−	37.2676i	−1.26349	−	2.18843i
$291$	−6.72817	−	2.34977i	−0.394413	−	0.137746i
$292$	−11.5950	+	20.0832i	−0.678548	+	1.17528i
$293$	−13.4087	+	23.2246i	−0.783346	+	1.35679i	0.146637	+	0.989190i	$0.453155\pi$
$293$	−13.4087	+	23.2246i	−0.783346	+	1.35679i	−0.929982	+	0.367604i	$0.880178\pi$
$294$	30.6467	−	26.4056i	1.78735	−	1.54001i
$295$	−3.92932	−	6.80578i	−0.228774	−	0.396248i
$296$	23.7571			1.38085
$297$	−10.0291	+	19.0588i	−0.581947	+	1.10590i
$298$	18.6648			1.08122
$299$	−1.64232	−	2.84459i	−0.0949779	−	0.164507i
$300$	18.4419	−	15.8897i	1.06474	−	0.917394i
$301$	−1.99111	+	3.44870i	−0.114765	+	0.198780i
$302$	10.5394	−	18.2547i	0.606473	−	1.05044i
$303$	7.47646	+	2.61110i	0.429511	+	0.150004i
$304$	2.24920	+	3.89574i	0.129001	+	0.223436i
$305$	36.3547			2.08167
$306$	43.3848	−	17.0873i	2.48015	−	0.976815i
$307$	−1.57624			−0.0899608			−0.0449804	−	0.998988i	$-0.514323\pi$
$307$	−1.57624			−0.0899608			−0.0449804	+	0.998988i	$0.514323\pi$
$308$	40.8675	+	70.7846i	2.32864	+	4.03333i
$309$	0.0718715	+	0.378609i	0.00408863	+	0.0215383i
$310$	−35.9858	+	62.3293i	−2.04386	+	3.54007i
$311$	−15.6121	+	27.0410i	−0.885281	+	1.53335i	−0.0398905	+	0.999204i	$0.512701\pi$
$311$	−15.6121	+	27.0410i	−0.885281	+	1.53335i	−0.845391	+	0.534148i	$0.820632\pi$
$312$	−7.71375	−	40.6349i	−0.436705	−	2.30050i
$313$	−13.2903	−	23.0195i	−0.751213	−	1.30114i	−0.947235	−	0.320539i	$-0.896136\pi$
$313$	−13.2903	−	23.0195i	−0.751213	−	1.30114i	0.196023	−	0.980599i	$-0.437197\pi$
$314$	39.7655			2.24410
$315$	4.94532	−	33.0788i	0.278637	−	1.86378i
$316$	57.1858			3.21695
$317$	14.6177	+	25.3186i	0.821013	+	1.42204i	0.904929	+	0.425563i	$0.139924\pi$
$317$	14.6177	+	25.3186i	0.821013	+	1.42204i	−0.0839155	+	0.996473i	$0.526743\pi$
$318$	17.4449	+	6.09251i	0.978261	+	0.341651i
$319$	12.0809	−	20.9248i	0.676402	−	1.17156i
$320$	16.1552	−	27.9816i	0.903104	−	1.56422i
$321$	3.86091	−	3.32661i	0.215495	−	0.185673i
$322$	−5.62092	−	9.73573i	−0.313242	−	0.542551i
$323$	2.49710			0.138942
$324$	32.5987	−	30.3928i	1.81104	−	1.68849i
$325$	−8.70677			−0.482965
$326$	6.49380	+	11.2476i	0.359659	+	0.622947i
$327$	9.89952	−	8.52955i	0.547445	−	0.471685i
$328$	−39.1328	+	67.7799i	−2.16075	+	3.74252i
$329$	−16.4518	+	28.4954i	−0.907019	+	1.57100i
$330$	50.0295	+	17.4725i	2.75403	+	0.961827i
$331$	−0.816193	−	1.41369i	−0.0448620	−	0.0777033i	0.842722	−	0.538348i	$-0.180951\pi$
$331$	−0.816193	−	1.41369i	−0.0448620	−	0.0777033i	−0.887584	+	0.460645i	$0.847618\pi$
$332$	−6.49446			−0.356430
$333$	1.35384	−	9.05569i	0.0741897	−	0.496249i
$334$	−48.5185			−2.65481
$335$	2.14533	+	3.71581i	0.117212	+	0.203017i
$336$	−13.6602	−	71.9601i	−0.745226	−	3.92575i
$337$	−10.5307	+	18.2397i	−0.573644	+	0.993580i	0.422544	+	0.906342i	$0.361137\pi$
$337$	−10.5307	+	18.2397i	−0.573644	+	0.993580i	−0.996188	+	0.0872375i	$0.972196\pi$
$338$	4.73064	−	8.19371i	0.257313	−	0.445679i
$339$	−3.15757	−	16.6336i	−0.171495	−	0.903413i
$340$	−40.8637	−	70.7780i	−2.21614	−	3.83848i
$341$	−40.4102			−2.18834
$342$	3.11767	−	1.22791i	0.168585	−	0.0663977i
$343$	−7.39896			−0.399506
$344$	3.89191	+	6.74099i	0.209838	+	0.363450i
$345$	−4.90150	−	1.71182i	−0.263888	−	0.0921611i
$346$	−6.61680	+	11.4606i	−0.355721	+	0.616127i
$347$	1.11639	−	1.93365i	0.0599312	−	0.103804i	−0.834503	−	0.551003i	$-0.814245\pi$
$347$	1.11639	−	1.93365i	0.0599312	−	0.103804i	0.894434	+	0.447199i	$0.147579\pi$
$348$	−37.8807	+	32.6385i	−2.03062	+	1.74961i
$349$	16.2649	+	28.1717i	0.870642	+	1.50800i	0.861333	+	0.508040i	$0.169630\pi$
$349$	16.2649	+	28.1717i	0.870642	+	1.50800i	0.00930889	+	0.999957i	$0.497037\pi$
$350$	−29.7993			−1.59284
$351$	−15.9288	+	0.624669i	−0.850214	+	0.0333424i
$352$	51.5270			2.74640
$353$	−12.0631	−	20.8939i	−0.642054	−	1.11207i	−0.984973	−	0.172706i	$-0.944749\pi$
$353$	−12.0631	−	20.8939i	−0.642054	−	1.11207i	0.342919	−	0.939365i	$-0.388584\pi$
$354$	−9.71160	+	8.36763i	−0.516166	+	0.444735i
$355$	5.39067	−	9.33692i	0.286107	−	0.495552i
$356$	1.56004	−	2.70206i	0.0826818	−	0.143209i
$357$	−38.3854	−	13.4058i	−2.03157	−	0.709512i
$358$	16.5070	+	28.5909i	0.872420	+	1.51108i
$359$	−11.7399			−0.619610			−0.309805	−	0.950800i	$-0.600264\pi$
$359$	−11.7399			−0.619610			−0.309805	+	0.950800i	$0.600264\pi$
$360$	−51.1618	−	40.7001i	−2.69647	−	2.14508i
$361$	−18.8206			−0.990556
$362$	−24.7366	−	42.8451i	−1.30013	−	2.25189i
$363$	1.99583	+	10.5138i	0.104754	+	0.551829i
$364$	−30.2496	+	52.3938i	−1.58551	+	2.74618i
$365$	6.55519	−	11.3539i	0.343114	−	0.594292i
$366$	−11.0600	−	58.2624i	−0.578114	−	3.04542i
$367$	−11.7190	−	20.2978i	−0.611725	−	1.05954i	−0.990950	−	0.134234i	$-0.957143\pi$
$367$	−11.7190	−	20.2978i	−0.611725	−	1.05954i	0.379225	−	0.925304i	$-0.376191\pi$
$368$	−11.3697			−0.592687
$369$	23.6062	+	18.7791i	1.22889	+	0.977602i
$370$	−22.5301			−1.17129
$371$	−8.05627	−	13.9539i	−0.418261	−	0.724448i
$372$	78.9513	+	27.5732i	4.09343	+	1.42960i
$373$	14.8316	−	25.6890i	0.767950	−	1.33013i	−0.170723	−	0.985319i	$-0.554610\pi$
$373$	14.8316	−	25.6890i	0.767950	−	1.33013i	0.938673	−	0.344809i	$-0.112056\pi$
$374$	32.2102	−	55.7897i	1.66555	−	2.88482i
$375$	7.94210	−	6.84301i	0.410128	−	0.353371i
$376$	32.1576	+	55.6985i	1.65840	+	2.87243i
$377$	17.8843			0.921086
$378$	−54.5169	+	2.13796i	−2.80405	+	0.109965i
$379$	6.39478			0.328478			0.164239	−	0.986421i	$-0.447483\pi$
$379$	6.39478			0.328478			0.164239	+	0.986421i	$0.447483\pi$
$380$	−2.93650	−	5.08617i	−0.150639	−	0.260915i
$381$	−4.16757	+	3.59083i	−0.213511	+	0.183964i
$382$	11.7492	−	20.3502i	0.601141	−	1.04121i
$383$	18.2711	−	31.6465i	0.933610	−	1.61706i	0.156517	−	0.987675i	$-0.449973\pi$
$383$	18.2711	−	31.6465i	0.933610	−	1.61706i	0.777093	−	0.629385i	$-0.216693\pi$
$384$	−9.10079	−	3.17839i	−0.464423	−	0.162197i
$385$	−23.1042	−	40.0177i	−1.17750	−	2.03949i
$386$	−14.5332			−0.739718
$387$	2.79131	−	1.09937i	0.141890	−	0.0558840i
$388$	20.3760			1.03443
$389$	10.6761	+	18.4916i	0.541300	+	0.937559i	0.998830	+	0.0483649i	$0.0154010\pi$
$389$	10.6761	+	18.4916i	0.541300	+	0.937559i	−0.457530	+	0.889194i	$0.651266\pi$
$390$	7.31537	+	38.5363i	0.370428	+	1.95136i
$391$	−3.15571	+	5.46584i	−0.159591	+	0.276420i
$392$	−34.4745	+	59.7117i	−1.74123	+	3.01589i
$393$	1.51166	+	7.96320i	0.0762531	+	0.401690i
$394$	6.61713	+	11.4612i	0.333366	+	0.577407i
$395$	−32.3297			−1.62668
$396$	9.10437	−	60.8983i	0.457512	−	3.06026i
$397$	1.77261			0.0889646			0.0444823	−	0.999010i	$-0.485836\pi$
$397$	1.77261			0.0889646			0.0444823	+	0.999010i	$0.485836\pi$
$398$	−0.377114	−	0.653181i	−0.0189030	−	0.0327410i
$399$	−2.75841	−	0.963355i	−0.138093	−	0.0482281i
$400$	−15.0691	+	26.1005i	−0.753456	+	1.30502i
$401$	−4.64888	+	8.05210i	−0.232154	+	0.402103i	−0.958442	−	0.285288i	$-0.907911\pi$
$401$	−4.64888	+	8.05210i	−0.232154	+	0.402103i	0.726288	+	0.687391i	$0.241244\pi$
$402$	5.30233	−	4.56856i	0.264456	−	0.227859i
$403$	−14.9555	−	25.9037i	−0.744988	−	1.29036i
$404$	−22.6421			−1.12649
$405$	−18.4295	+	17.1824i	−0.915771	+	0.853802i
$406$	61.2097			3.03779
$407$	−6.32504	−	10.9553i	−0.313520	−	0.543033i
$408$	−60.2080	+	51.8759i	−2.98074	+	2.56824i
$409$	−10.3979	+	18.0097i	−0.514144	+	0.890523i	0.485722	+	0.874113i	$0.338557\pi$
$409$	−10.3979	+	18.0097i	−0.514144	+	0.890523i	−0.999865	+	0.0164093i	$0.994777\pi$
$410$	37.1117	−	64.2794i	1.83282	−	3.17453i
$411$	32.5607	+	11.3716i	1.60610	+	0.560920i
$412$	−0.550907	−	0.954199i	−0.0271412	−	0.0470100i
$413$	11.1781			0.550037
$414$	−1.25222	+	8.37596i	−0.0615431	+	0.411656i
$415$	3.67161			0.180232
$416$	19.0698	+	33.0298i	0.934972	+	1.61942i
$417$	1.17390	+	6.18391i	0.0574859	+	0.302827i
$418$	2.31465	−	4.00910i	0.113213	−	0.196091i
$419$	17.0187	−	29.4772i	0.831417	−	1.44006i	−0.0654984	−	0.997853i	$-0.520864\pi$
$419$	17.0187	−	29.4772i	0.831417	−	1.44006i	0.896915	−	0.442203i	$-0.145803\pi$
$420$	17.8344	+	93.9493i	0.870232	+	4.58426i
$421$	−11.1239	−	19.2671i	−0.542145	−	0.939022i	−0.998781	−	0.0493685i	$-0.984279\pi$
$421$	−11.1239	−	19.2671i	−0.542145	−	0.939022i	0.456636	−	0.889654i	$-0.349054\pi$
$422$	46.3403			2.25581
$423$	23.0636	−	9.08370i	1.12139	−	0.441665i
$424$	−31.4943			−1.52950
$425$	8.36499	+	14.4886i	0.405762	+	0.702800i
$426$	−16.6034	−	5.79862i	−0.804437	−	0.280944i
$427$	−25.8554	+	44.7828i	−1.25123	+	2.16719i
$428$	−7.28554	+	12.6189i	−0.352160	+	0.609958i
$429$	−16.6846	+	14.3757i	−0.805541	+	0.694064i
$430$	−3.69091	−	6.39284i	−0.177991	−	0.308290i
$431$	13.1389			0.632879			0.316439	−	0.948613i	$-0.397513\pi$
$431$	13.1389			0.632879			0.316439	+	0.948613i	$0.397513\pi$
$432$	−25.6959	+	48.8311i	−1.23629	+	2.34939i
$433$	4.43558			0.213160			0.106580	−	0.994304i	$-0.466010\pi$
$433$	4.43558			0.213160			0.106580	+	0.994304i	$0.466010\pi$
$434$	−51.1860	−	88.6567i	−2.45701	−	4.25566i
$435$	21.4157	−	18.4520i	1.02680	−	0.884706i
$436$	−18.6804	+	32.3554i	−0.894628	+	1.54954i
$437$	−0.226772	+	0.392781i	−0.0108480	+	0.0187892i
$438$	−20.1901	−	7.05127i	−0.964722	−	0.336923i
$439$	−5.27411	−	9.13503i	−0.251720	−	0.435991i	0.712280	−	0.701896i	$-0.247663\pi$
$439$	−5.27411	−	9.13503i	−0.251720	−	0.435991i	−0.963999	+	0.265905i	$0.914329\pi$
$440$	−90.3213			−4.30590
$441$	20.7962	+	16.5437i	0.990296	+	0.787797i
$442$	47.6830			2.26805
$443$	−14.0548	−	24.3437i	−0.667766	−	1.15660i	−0.978527	−	0.206116i	$-0.933917\pi$
$443$	−14.0548	−	24.3437i	−0.667766	−	1.15660i	0.310762	−	0.950488i	$-0.399416\pi$
$444$	4.88237	+	25.7196i	0.231707	+	1.22060i
$445$	−0.881959	+	1.52760i	−0.0418089	+	0.0724151i
$446$	−14.3539	+	24.8617i	−0.679677	+	1.17723i
$447$	2.28668	+	12.0459i	0.108156	+	0.569751i
$448$	22.9791	+	39.8009i	1.08566	+	1.88042i
$449$	−29.5048			−1.39242			−0.696208	−	0.717840i	$-0.745131\pi$
$449$	−29.5048			−1.39242			−0.696208	+	0.717840i	$0.745131\pi$
$450$	17.5684	+	13.9759i	0.828180	+	0.658831i
$451$	41.6745			1.96238
$452$	24.2033	+	41.9213i	1.13843	+	1.97181i
$453$	13.0724	+	4.56546i	0.614196	+	0.214504i
$454$	13.7694	−	23.8493i	0.646231	−	1.11930i
$455$	17.1014	−	29.6205i	0.801727	−	1.38863i
$456$	−4.32660	+	3.72785i	−0.202612	+	0.174573i
$457$	18.2519	+	31.6132i	0.853789	+	1.47881i	0.877764	+	0.479093i	$0.159034\pi$
$457$	18.2519	+	31.6132i	0.853789	+	1.47881i	−0.0239758	+	0.999713i	$0.507632\pi$
$458$	40.2933			1.88278
$459$	16.3430	+	25.9062i	0.762824	+	1.20920i
$460$	14.8440			0.692105
$461$	10.1261	+	17.5389i	0.471619	+	0.816869i	0.999473	−	0.0324669i	$-0.0103363\pi$
$461$	10.1261	+	17.5389i	0.471619	+	0.816869i	−0.527854	+	0.849335i	$0.677003\pi$
$462$	−57.1039	+	49.2014i	−2.65671	+	2.28906i
$463$	10.9574	−	18.9788i	0.509233	−	0.882017i	−0.490710	−	0.871323i	$-0.663262\pi$
$463$	10.9574	−	18.9788i	0.509233	−	0.882017i	0.999943	−	0.0106943i	$-0.00340417\pi$
$464$	30.9529	−	53.6120i	1.43695	−	2.48888i
$465$	−44.6347	−	15.5884i	−2.06988	−	0.722893i
$466$	−28.1859	−	48.8195i	−1.30569	−	2.26152i
$467$	−1.61995			−0.0749623			−0.0374812	−	0.999297i	$-0.511933\pi$
$467$	−1.61995			−0.0749623			−0.0374812	+	0.999297i	$0.511933\pi$
$468$	42.4065	−	16.7020i	1.96024	−	0.772048i
$469$	−6.10299			−0.281810
$470$	−30.4968	−	52.8219i	−1.40671	−	2.43649i
$471$	4.87178	+	25.6638i	0.224480	+	1.18253i
$472$	10.9246	−	18.9219i	0.502845	−	0.870953i
$473$	2.07235	−	3.58941i	0.0952867	−	0.165041i
$474$	9.83546	+	51.8118i	0.451758	+	2.37979i
$475$	0.601116	+	1.04116i	0.0275811	+	0.0477719i
$476$	116.248			5.32824
$477$	−1.79476	+	12.0050i	−0.0821762	+	0.549670i
$478$	−3.18580			−0.145715
$479$	3.62256	+	6.27445i	0.165519	+	0.286687i	0.936839	−	0.349760i	$-0.113737\pi$
$479$	3.62256	+	6.27445i	0.165519	+	0.286687i	−0.771321	+	0.636447i	$0.780403\pi$
$480$	56.9137	+	19.8767i	2.59774	+	0.907243i
$481$	4.68170	−	8.10894i	0.213467	−	0.369736i
$482$	−37.2472	+	64.5140i	−1.69656	+	2.93853i
$483$	5.59460	−	4.82037i	0.254563	−	0.219335i
$484$	−15.2984	−	26.4976i	−0.695381	−	1.20444i
$485$	−11.5195			−0.523072
$486$	33.1434	+	24.3080i	1.50342	+	1.10263i
$487$	−29.5624			−1.33960			−0.669800	−	0.742542i	$-0.733620\pi$
$487$	−29.5624			−1.33960			−0.669800	+	0.742542i	$0.733620\pi$
$488$	50.5381	+	87.5346i	2.28775	+	3.96250i
$489$	−6.46339	+	5.56894i	−0.292284	+	0.251836i
$490$	32.6941	−	56.6278i	1.47697	−	2.55818i
$491$	5.75467	−	9.96738i	0.259705	−	0.449822i	−0.706458	−	0.707755i	$-0.749708\pi$
$491$	5.75467	−	9.96738i	0.259705	−	0.449822i	0.966163	+	0.257933i	$0.0830415\pi$
$492$	−81.4214	−	28.4359i	−3.67076	−	1.28199i
$493$	−17.1822	−	29.7605i	−0.773848	−	1.34034i
$494$	3.42655			0.154168
$495$	−5.14711	+	34.4286i	−0.231345	+	1.54745i
$496$	−103.536			−4.64891
$497$	7.66765	+	13.2808i	0.343941	+	0.595724i
$498$	−1.11699	−	5.88415i	−0.0500536	−	0.263675i
$499$	−15.5985	+	27.0174i	−0.698286	+	1.20947i	0.270775	+	0.962643i	$0.412720\pi$
$499$	−15.5985	+	27.0174i	−0.698286	+	1.20947i	−0.969060	+	0.246824i	$0.920613\pi$
$500$	−14.9867	+	25.9578i	−0.670227	+	1.16087i
$501$	−5.94413	−	31.3128i	−0.265564	−	1.39895i
$502$	−20.9896	−	36.3551i	−0.936813	−	1.62261i
$503$	−17.1085			−0.762831			−0.381416	−	0.924404i	$-0.624563\pi$
$503$	−17.1085			−0.762831			−0.381416	+	0.924404i	$0.624563\pi$
$504$	86.5216	−	34.0769i	3.85398	−	1.51790i
$505$	12.8006			0.569620
$506$	5.85028	+	10.1330i	0.260076	+	0.450466i
$507$	5.86761	+	2.04922i	0.260590	+	0.0910092i
$508$	7.86421	−	13.6212i	0.348918	−	0.604343i
$509$	−14.5671	+	25.2309i	−0.645674	+	1.11834i	0.338472	+	0.940977i	$0.390090\pi$
$509$	−14.5671	+	25.2309i	−0.645674	+	1.11834i	−0.984145	+	0.177363i	$0.943243\pi$
$510$	57.0985	−	49.1968i	2.52836	−	2.17847i
$511$	9.32406	+	16.1497i	0.412472	+	0.714423i
$512$	−33.2979			−1.47157
$513$	1.17442	+	1.86165i	0.0518519	+	0.0821937i
$514$	−48.8951			−2.15667
$515$	0.311453	+	0.539452i	0.0137242	+	0.0237711i
$516$	−6.49802	+	5.59877i	−0.286059	+	0.246472i
$517$	17.1231	−	29.6581i	0.753074	−	1.30436i
$518$	16.0233	−	27.7532i	0.704025	−	1.21941i
$519$	−8.20709	−	2.86627i	−0.360251	−	0.125815i
$520$	−33.4273	−	57.8977i	−1.46588	−	2.53898i
$521$	−32.9618			−1.44408			−0.722042	−	0.691850i	$-0.756796\pi$
$521$	−32.9618			−1.44408			−0.722042	+	0.691850i	$0.756796\pi$
$522$	−36.0865	−	28.7074i	−1.57946	−	1.25649i
$523$	9.33844			0.408342			0.204171	−	0.978935i	$-0.434550\pi$
$523$	9.33844			0.408342			0.204171	+	0.978935i	$0.434550\pi$
$524$	−11.5871	−	20.0695i	−0.506186	−	0.876740i
$525$	−3.65079	−	19.2319i	−0.159334	−	0.839347i
$526$	−2.06126	+	3.57021i	−0.0898754	+	0.155669i
$527$	−28.7369	+	49.7738i	−1.25180	+	2.16818i
$528$	14.2176	+	74.8963i	0.618742	+	3.25944i
$529$	10.9268	+	18.9258i	0.475080	+	0.822862i
$530$	29.8678			1.29737
$531$	−6.59009	−	5.24252i	−0.285985	−	0.227506i
$532$	8.35372			0.362180
$533$	15.4234	+	26.7142i	0.668063	+	1.15712i
$534$	2.71645	+	0.948703i	0.117552	+	0.0410544i
$535$	4.11884	−	7.13404i	0.178073	−	0.308431i
$536$	−5.96460	+	10.3310i	−0.257632	+	0.446231i
$537$	−16.4296	+	14.1560i	−0.708991	+	0.610876i
$538$	21.9649	+	38.0444i	0.946975	+	1.64021i
$539$	36.7137			1.58137
$540$	33.5479	−	63.7526i	1.44367	−	2.74348i
$541$	−13.4426			−0.577943			−0.288972	−	0.957338i	$-0.593313\pi$
$541$	−13.4426			−0.577943			−0.288972	+	0.957338i	$0.593313\pi$
$542$	31.0518	+	53.7833i	1.33379	+	2.31019i
$543$	24.6208	−	21.2136i	1.05658	−	0.910361i
$544$	36.6424	−	63.4665i	1.57103	−	2.72110i
$545$	10.5609	−	18.2919i	0.452377	−	0.783541i
$546$	−52.6728	−	18.3956i	−2.25419	−	0.787259i
$547$	15.0500	+	26.0674i	0.643493	+	1.11456i	0.984647	+	0.174556i	$0.0558489\pi$
$547$	15.0500	+	26.0674i	0.643493	+	1.11456i	−0.341154	+	0.940007i	$0.610818\pi$
$548$	−98.6087			−4.21236
$549$	36.2463	−	14.2757i	1.54695	−	0.609274i
$550$	31.0152			1.32249
$551$	−1.23473	−	2.13861i	−0.0526012	−	0.0911080i
$552$	−2.69207	−	14.1815i	−0.114582	−	0.603603i
$553$	22.9927	−	39.8246i	0.977751	−	1.69351i
$554$	−28.2566	+	48.9419i	−1.20051	+	2.07934i
$555$	−2.76022	−	14.5405i	−0.117165	−	0.617208i
$556$	−8.99811	−	15.5852i	−0.381605	−	0.660959i
$557$	−24.0468			−1.01890			−0.509448	−	0.860502i	$-0.670150\pi$
$557$	−24.0468			−1.01890			−0.509448	+	0.860502i	$0.670150\pi$
$558$	−11.4031	+	76.2743i	−0.482731	+	3.22895i
$559$	3.06785			0.129756
$560$	−59.1961	−	102.531i	−2.50149	−	4.33271i
$561$	39.9516	+	13.9528i	1.68676	+	0.589089i
$562$	2.76052	−	4.78135i	0.116445	−	0.201689i
$563$	14.1990	−	24.5934i	0.598418	−	1.03649i	−0.394637	−	0.918837i	$-0.629130\pi$
$563$	14.1990	−	24.5934i	0.598418	−	1.03649i	0.993055	−	0.117653i	$-0.0375371\pi$
$564$	−53.6910	+	46.2608i	−2.26080	+	1.94793i
$565$	−13.6832	−	23.7000i	−0.575657	−	0.997067i
$566$	−26.4936			−1.11361
$567$	−8.05880	−	34.9221i	−0.338438	−	1.46659i
$568$	29.9751			1.25773
$569$	−3.78124	−	6.54930i	−0.158518	−	0.274561i	0.775817	−	0.630958i	$-0.217338\pi$
$569$	−3.78124	−	6.54930i	−0.158518	−	0.274561i	−0.934334	+	0.356398i	$0.884005\pi$
$570$	4.10315	−	3.53533i	0.171862	−	0.148079i
$571$	−0.371104	+	0.642771i	−0.0155302	+	0.0268991i	−0.873686	−	0.486490i	$-0.838277\pi$
$571$	−0.371104	+	0.642771i	−0.0155302	+	0.0268991i	0.858156	+	0.513389i	$0.171610\pi$
$572$	31.4838	−	54.5316i	1.31641	−	2.28008i
$573$	14.5730	+	5.08953i	0.608797	+	0.212618i
$574$	52.7874	+	91.4305i	2.20331	+	3.81624i
$575$	−3.03864			−0.126720
$576$	5.11922	−	34.2420i	0.213301	−	1.42675i
$577$	−35.8196			−1.49119			−0.745596	−	0.666399i	$-0.767835\pi$
$577$	−35.8196			−1.49119			−0.745596	+	0.666399i	$0.767835\pi$
$578$	−23.3994	−	40.5289i	−0.973286	−	1.68578i
$579$	−1.78049	−	9.37939i	−0.0739948	−	0.389794i
$580$	−40.4113	+	69.9945i	−1.67799	+	2.90636i
$581$	−2.61124	+	4.52279i	−0.108332	+	0.187637i
$582$	3.50449	+	18.4612i	0.145266	+	0.765240i
$583$	8.38499	+	14.5232i	0.347271	+	0.601491i
$584$	36.4505			1.50833
$585$	−23.9743	+	9.44237i	−0.991215	+	0.390394i
$586$	70.7092			2.92097
$587$	−14.5053	−	25.1240i	−0.598699	−	1.03698i	−0.993013	−	0.118002i	$-0.962351\pi$
$587$	−14.5053	−	25.1240i	−0.598699	−	1.03698i	0.394314	−	0.918976i	$-0.370982\pi$
$588$	−71.7294	−	25.0510i	−2.95807	−	1.03309i
$589$	−2.06506	+	3.57679i	−0.0850893	+	0.147379i
$590$	−10.3604	+	17.9447i	−0.426530	+	0.738772i
$591$	−6.58613	+	5.67470i	−0.270917	+	0.233426i
$592$	−16.2056	−	28.0689i	−0.666045	−	1.15362i
$593$	−37.8607			−1.55475			−0.777376	−	0.629036i	$-0.783450\pi$
$593$	−37.8607			−1.55475			−0.777376	+	0.629036i	$0.783450\pi$
$594$	56.7414	−	2.22520i	2.32813	−	0.0913009i
$595$	−65.7205			−2.69428
$596$	−17.5278	−	30.3590i	−0.717965	−	1.24355i
$597$	0.375348	−	0.323404i	0.0153620	−	0.0132361i
$598$	−4.33029	+	7.50028i	−0.177079	+	0.306709i
$599$	−12.6312	+	21.8779i	−0.516098	+	0.893908i	0.483728	+	0.875219i	$0.339283\pi$
$599$	−12.6312	+	21.8779i	−0.516098	+	0.893908i	−0.999825	+	0.0186890i	$0.994051\pi$
$600$	−36.1232	−	12.6158i	−1.47472	−	0.515037i
$601$	13.2093	+	22.8791i	0.538818	+	0.933260i	0.998968	+	0.0454186i	$0.0144622\pi$
$601$	13.2093	+	22.8791i	0.538818	+	0.933260i	−0.460150	+	0.887841i	$0.652204\pi$
$602$	10.4998			0.427942
$603$	3.59805	+	2.86231i	0.146524	+	0.116562i
$604$	−39.5893			−1.61086
$605$	8.64887	+	14.9803i	0.351626	+	0.609035i
$606$	−3.89425	−	20.5144i	−0.158193	−	0.833339i
$607$	−1.46630	+	2.53971i	−0.0595153	+	0.103084i	−0.894248	−	0.447572i	$-0.852289\pi$
$607$	−1.46630	+	2.53971i	−0.0595153	+	0.103084i	0.834733	+	0.550655i	$0.185622\pi$
$608$	2.63316	−	4.56076i	0.106789	−	0.184963i
$609$	7.49896	+	39.5034i	0.303873	+	1.60076i
$610$	−47.9280	−	83.0138i	−1.94055	−	3.36113i
$611$	25.3486			1.02549
$612$	−68.5349	−	54.5206i	−2.77036	−	2.20386i
$613$	−17.6161			−0.711506			−0.355753	−	0.934580i	$-0.615776\pi$
$613$	−17.6161			−0.711506			−0.355753	+	0.934580i	$0.615776\pi$
$614$	2.07803	+	3.59925i	0.0838624	+	0.145254i
$615$	46.0312	+	16.0761i	1.85616	+	0.648250i
$616$	64.2362	−	111.260i	2.58815	−	4.48281i
$617$	3.48648	−	6.03877i	0.140361	−	0.243112i	−0.787272	−	0.616606i	$-0.788507\pi$
$617$	3.48648	−	6.03877i	0.140361	−	0.243112i	0.927632	+	0.373494i	$0.121840\pi$
$618$	0.769778	−	0.663250i	0.0309650	−	0.0266798i
$619$	−17.8000	−	30.8305i	−0.715443	−	1.23918i	−0.962788	−	0.270256i	$-0.912892\pi$
$619$	−17.8000	−	30.8305i	−0.715443	−	1.23918i	0.247345	−	0.968927i	$-0.420442\pi$
$620$	135.174			5.42873
$621$	−5.55908	+	0.218007i	−0.223078	+	0.00874834i
$622$	82.3285			3.30107
$623$	−1.25449	−	2.17284i	−0.0502602	−	0.0870532i
$624$	−42.7482	+	36.8323i	−1.71130	+	1.47447i
$625$	15.5679	−	26.9643i	0.622714	−	1.07857i
$626$	−35.0424	+	60.6952i	−1.40058	+	2.42587i
$627$	2.87096	+	1.00266i	0.114655	+	0.0400425i
$628$	−37.3430	−	64.6800i	−1.49015	−	2.58101i
$629$	−17.9917			−0.717375
$630$	−82.0531	+	32.3169i	−3.26907	+	1.28754i
$631$	−31.8092			−1.26630			−0.633151	−	0.774028i	$-0.718239\pi$
$631$	−31.8092			−1.26630			−0.633151	+	0.774028i	$0.718239\pi$
$632$	−44.9427	−	77.8431i	−1.78773	−	3.09643i
$633$	5.67727	+	29.9070i	0.225651	+	1.18870i
$634$	38.5424	−	66.7573i	1.53071	−	2.65127i
$635$	−4.44599	+	7.70068i	−0.176434	+	0.305592i
$636$	−6.47247	−	34.0961i	−0.256650	−	1.35200i
$637$	13.5875	+	23.5342i	0.538356	+	0.932460i
$638$	−63.7072			−2.52219
$639$	1.70818	−	11.4259i	0.0675746	−	0.452001i
$640$	−15.5817			−0.615920
$641$	17.5758	+	30.4421i	0.694201	+	1.20239i	0.970449	+	0.241305i	$0.0775753\pi$
$641$	17.5758	+	30.4421i	0.694201	+	1.20239i	−0.276249	+	0.961086i	$0.589091\pi$
$642$	−12.6861	−	4.43054i	−0.500681	−	0.174859i
$643$	0.964272	−	1.67017i	0.0380272	−	0.0658650i	−0.846385	−	0.532571i	$-0.821226\pi$
$643$	0.964272	−	1.67017i	0.0380272	−	0.0658650i	0.884413	+	0.466706i	$0.154559\pi$
$644$	−10.5570	+	18.2853i	−0.416004	+	0.720540i
$645$	3.67362	−	3.16524i	0.144649	−	0.124631i
$646$	−3.29204	−	5.70198i	−0.129524	−	0.224341i
$647$	−23.8139			−0.936221			−0.468111	−	0.883670i	$-0.655065\pi$
$647$	−23.8139			−0.936221			−0.468111	+	0.883670i	$0.655065\pi$
$648$	−66.9913	−	20.4885i	−2.63167	−	0.804864i
$649$	−11.6342			−0.456681
$650$	11.4785	+	19.8814i	0.450225	+	0.779812i
$651$	50.9462	−	43.8959i	1.99674	−	1.72042i
$652$	12.1964	−	21.1248i	0.477648	−	0.827311i
$653$	−0.767582	+	1.32949i	−0.0300378	+	0.0520270i	−0.880654	−	0.473761i	$-0.842896\pi$
$653$	−0.767582	+	1.32949i	−0.0300378	+	0.0520270i	0.850616	+	0.525788i	$0.176229\pi$
$654$	−32.5277	−	11.3601i	−1.27193	−	0.444214i
$655$	6.55072	+	11.3462i	0.255958	+	0.443332i
$656$	106.776			4.16889
$657$	2.07719	−	13.8942i	0.0810390	−	0.542063i
$658$	86.7567			3.38213
$659$	4.91274	+	8.50911i	0.191373	+	0.331468i	0.945705	−	0.325025i	$-0.105373\pi$
$659$	4.91274	+	8.50911i	0.191373	+	0.331468i	−0.754332	+	0.656493i	$0.772039\pi$
$660$	−18.5621	−	97.7827i	−0.722531	−	3.80619i
$661$	−1.49661	+	2.59220i	−0.0582113	+	0.100825i	−0.893663	−	0.448740i	$-0.851873\pi$
$661$	−1.49661	+	2.59220i	−0.0582113	+	0.100825i	0.835451	+	0.549565i	$0.185206\pi$
$662$	−2.15204	+	3.72745i	−0.0836416	+	0.144871i
$663$	5.84177	+	30.7736i	0.226876	+	1.19515i
$664$	5.10405	+	8.84047i	0.198075	+	0.343077i
$665$	−4.72273			−0.183140
$666$	−22.4629	+	8.84711i	−0.870421	+	0.342819i
$667$	6.24154			0.241674
$668$	45.5627	+	78.9170i	1.76288	+	3.05339i
$669$	−17.8037	−	6.21783i	−0.688332	−	0.240395i
$670$	5.65655	−	9.79744i	0.218532	−	0.378508i
$671$	26.9103	−	46.6101i	1.03886	−	1.79936i
$672$	−64.9615	+	55.9716i	−2.50594	+	2.15915i
$673$	−6.80885	−	11.7933i	−0.262462	−	0.454598i	0.704434	−	0.709770i	$-0.251201\pi$
$673$	−6.80885	−	11.7933i	−0.262462	−	0.454598i	−0.966896	+	0.255172i	$0.917868\pi$
$674$	55.5323			2.13903
$675$	−6.86741	+	13.0505i	−0.264327	+	0.502313i
$676$	−17.7698			−0.683454
$677$	12.8430	+	22.2447i	0.493595	+	0.854932i	0.999973	−	0.00738021i	$-0.00234921\pi$
$677$	12.8430	+	22.2447i	0.493595	+	0.854932i	−0.506378	+	0.862312i	$0.669016\pi$
$678$	−33.8190	+	29.1389i	−1.29881	+	1.11907i
$679$	8.19260	−	14.1900i	0.314403	−	0.544562i
$680$	−64.2302	+	111.250i	−2.46311	+	4.26624i
$681$	17.0788	+	5.96465i	0.654460	+	0.228566i
$682$	53.2745	+	92.2742i	2.03999	+	3.53336i
$683$	−19.3240			−0.739413			−0.369707	−	0.929149i	$-0.620542\pi$
$683$	−19.3240			−0.739413			−0.369707	+	0.929149i	$0.620542\pi$
$684$	−4.92498	−	3.91790i	−0.188311	−	0.149805i
$685$	55.7479			2.13002
$686$	9.75437	+	16.8951i	0.372424	+	0.645057i
$687$	4.93644	+	26.0044i	0.188337	+	0.992131i
$688$	5.30963	−	9.19655i	0.202428	−	0.350615i
$689$	−6.20645	+	10.7499i	−0.236447	+	0.409538i
$690$	2.55304	+	13.4490i	0.0971925	+	0.511996i
$691$	19.9695	+	34.5883i	0.759677	+	1.31580i	0.943015	+	0.332750i	$0.107976\pi$
$691$	19.9695	+	34.5883i	0.759677	+	1.31580i	−0.183338	+	0.983050i	$0.558690\pi$
$692$	24.8548			0.944838
$693$	−38.7495	−	30.8258i	−1.47197	−	1.17098i
$694$	−5.88716			−0.223474
$695$	5.08703	+	8.81100i	0.192962	+	0.334220i
$696$	74.1993	+	25.9136i	2.81252	+	0.982253i
$697$	29.6360	−	51.3310i	1.12254	−	1.94430i
$698$	42.8856	−	74.2800i	1.62324	−	2.81154i
$699$	28.0539	−	24.1716i	1.06110	−	0.914254i
$700$	27.9840	+	48.4696i	1.05769	+	1.83198i
$701$	−1.68883			−0.0637864			−0.0318932	−	0.999491i	$-0.510154\pi$
$701$	−1.68883			−0.0637864			−0.0318932	+	0.999491i	$0.510154\pi$
$702$	22.4260	+	35.5488i	0.846413	+	1.34170i
$703$	−1.29290			−0.0487626
$704$	−23.9167	−	41.4249i	−0.901394	−	1.56126i
$705$	30.3539	−	26.1533i	1.14319	−	0.984991i
$706$	−31.8066	+	55.0907i	−1.19706	+	2.07337i
$707$	−9.10375	+	15.7682i	−0.342382	+	0.593023i
$708$	22.7302	+	7.93837i	0.854254	+	0.298342i
$709$	−12.9666	−	22.4587i	−0.486969	−	0.843455i	0.512919	−	0.858437i	$-0.328564\pi$
$709$	−12.9666	−	22.4587i	−0.486969	−	0.843455i	−0.999888	+	0.0149821i	$0.995231\pi$
$710$	−28.4270			−1.06685
$711$	−32.2333	+	12.6952i	−1.20884	+	0.476107i
$712$	−4.90418			−0.183792
$713$	−5.21943	−	9.04032i	−0.195469	−	0.338562i
$714$	19.9937	+	105.324i	0.748247	+	3.94166i
$715$	−17.7992	+	30.8292i	−0.665653	+	1.15295i
$716$	31.0027	−	53.6983i	1.15863	−	2.00680i
$717$	−0.390301	−	2.05605i	−0.0145761	−	0.0767846i
$718$	15.4773	+	26.8074i	0.577606	+	1.00044i
$719$	−18.4698			−0.688808			−0.344404	−	0.938822i	$-0.611919\pi$
$719$	−18.4698			−0.688808			−0.344404	+	0.938822i	$0.611919\pi$
$720$	−13.1876	+	88.2105i	−0.491472	+	3.28741i
$721$	−0.886016			−0.0329969
$722$	24.8120	+	42.9756i	0.923406	+	1.59939i
$723$	−46.1992	−	16.1348i	−1.71817	−	0.600058i
$724$	−46.4593	+	80.4699i	−1.72665	+	2.99064i
$725$	8.27239	−	14.3282i	0.307229	−	0.532136i
$726$	21.3763	−	18.4181i	0.793349	−	0.683560i
$727$	−0.496885	−	0.860630i	−0.0184284	−	0.0319190i	0.856664	−	0.515875i	$-0.172533\pi$
$727$	−0.496885	−	0.860630i	−0.0184284	−	0.0319190i	−0.875093	+	0.483956i	$0.839200\pi$
$728$	95.0934			3.52440
$729$	−11.6274	+	24.3681i	−0.430644	+	0.902522i
$730$	−34.5680			−1.27942
$731$	−2.94742	−	5.10508i	−0.109014	−	0.188818i
$732$	−84.3795	+	72.7025i	−3.11876	+	2.68716i
$733$	−13.3517	+	23.1259i	−0.493157	+	0.854173i	−0.999969	−	0.00788351i	$-0.997491\pi$
$733$	−13.3517	+	23.1259i	−0.493157	+	0.854173i	0.506812	+	0.862057i	$0.330824\pi$
$734$	−30.8992	+	53.5190i	−1.14051	+	1.97542i
$735$	40.5518	+	14.1624i	1.49578	+	0.522390i
$736$	6.65529	+	11.5273i	0.245317	+	0.424902i
$737$	6.35201			0.233979
$738$	11.7599	−	78.6607i	0.432886	−	2.89554i
$739$	9.66176			0.355413			0.177707	−	0.984083i	$-0.443132\pi$
$739$	9.66176			0.355413			0.177707	+	0.984083i	$0.443132\pi$
$740$	21.1576	+	36.6460i	0.777768	+	1.34713i
$741$	0.419795	+	2.21142i	0.0154216	+	0.0812386i
$742$	−21.2419	+	36.7920i	−0.779813	+	1.35068i
$743$	10.7735	−	18.6602i	0.395241	−	0.684578i	−0.597891	−	0.801578i	$-0.703994\pi$
$743$	10.7735	−	18.6602i	0.395241	−	0.684578i	0.993132	+	0.117000i	$0.0373277\pi$
$744$	−24.5149	−	129.141i	−0.898760	−	4.73454i
$745$	9.90923	+	17.1633i	0.363046	+	0.628814i
$746$	−78.2124			−2.86356
$747$	3.66066	−	1.44176i	0.133937	−	0.0527514i
$748$	−120.992			−4.42390
$749$	5.85861	+	10.1474i	0.214069	+	0.370778i
$750$	−26.0960	−	9.11385i	−0.952891	−	0.332791i
$751$	1.77478	−	3.07401i	0.0647626	−	0.112172i	−0.831826	−	0.555036i	$-0.812704\pi$
$751$	1.77478	−	3.07401i	0.0647626	−	0.112172i	0.896589	+	0.442864i	$0.146038\pi$
$752$	43.8717	−	75.9880i	1.59984	−	2.77100i
$753$	20.8913	−	18.0002i	0.761322	−	0.655965i
$754$	−23.5776	−	40.8376i	−0.858645	−	1.48722i
$755$	22.3816			0.814550
$756$	54.6732	+	86.6659i	1.98844	+	3.15201i
$757$	21.5297			0.782509			0.391255	−	0.920282i	$-0.372041\pi$
$757$	21.5297			0.782509			0.391255	+	0.920282i	$0.372041\pi$
$758$	−8.43051	−	14.6021i	−0.306210	−	0.530371i
$759$	−5.82287	+	5.01706i	−0.211357	+	0.182108i
$760$	−4.61564	+	7.99453i	−0.167427	+	0.289992i
$761$	7.00704	−	12.1366i	0.254005	−	0.439950i	−0.710620	−	0.703576i	$-0.751585\pi$
$761$	7.00704	−	12.1366i	0.254005	−	0.439950i	0.964625	+	0.263627i	$0.0849186\pi$
$762$	13.6937	+	4.78245i	0.496072	+	0.173250i
$763$	15.0217	+	26.0183i	0.543822	+	0.941927i
$764$	−44.1338			−1.59670
$765$	38.7458	+	30.8229i	1.40086	+	1.11441i
$766$	−96.3504			−3.48128
$767$	−4.30572	−	7.45773i	−0.155471	−	0.269283i
$768$	−2.71571	−	14.3059i	−0.0979946	−	0.516221i
$769$	14.9750	−	25.9375i	0.540014	−	0.935332i	−0.458889	−	0.888494i	$-0.651752\pi$
$769$	14.9750	−	25.9375i	0.540014	−	0.935332i	0.998903	−	0.0468377i	$-0.0149144\pi$
$770$	−60.9187	+	105.514i	−2.19536	+	3.80247i
$771$	−5.99027	−	31.5559i	−0.215734	−	1.13646i
$772$	13.6478	+	23.6387i	0.491195	+	0.850775i
$773$	−13.9807			−0.502851			−0.251425	−	0.967877i	$-0.580899\pi$
$773$	−13.9807			−0.502851			−0.251425	+	0.967877i	$0.580899\pi$
$774$	−6.19024	−	4.92443i	−0.222504	−	0.177005i
$775$	−27.6708			−0.993965
$776$	−16.0136	−	27.7364i	−0.574856	−	0.995680i
$777$	19.8744	+	6.94100i	0.712991	+	0.249007i
$778$	28.1496	−	48.7565i	1.00921	−	1.74800i
$779$	2.12967	−	3.68870i	0.0763033	−	0.132161i
$780$	55.8109	−	48.0874i	1.99835	−	1.72180i
$781$	−7.98052	−	13.8227i	−0.285565	−	0.494614i
$782$	16.6412			0.595089
$783$	14.1061	−	26.8065i	0.504110	−	0.957985i
$784$	94.0654			3.35948
$785$	21.1117	+	36.5665i	0.753508	+	1.30511i
$786$	16.1906	−	13.9500i	0.577499	−	0.497581i
$787$	3.83330	−	6.63948i	0.136643	−	0.236672i	−0.789581	−	0.613646i	$-0.789702\pi$
$787$	3.83330	−	6.63948i	0.136643	−	0.236672i	0.926224	+	0.376974i	$0.123036\pi$
$788$	12.4280	−	21.5260i	0.442730	−	0.766831i
$789$	−2.55667	−	0.892900i	−0.0910199	−	0.0317881i
$790$	42.6216	+	73.8228i	1.51641	+	2.62650i
$791$	38.9258			1.38404
$792$	−90.0520	+	35.4673i	−3.19986	+	1.26028i
$793$	39.8373			1.41466
$794$	−2.33690	−	4.04764i	−0.0829336	−	0.143645i
$795$	3.65918	+	19.2760i	0.129778	+	0.683650i
$796$	−0.708280	+	1.22678i	−0.0251043	+	0.0434820i
$797$	5.90468	−	10.2272i	0.209154	−	0.362266i	−0.742294	−	0.670074i	$-0.766262\pi$
$797$	5.90468	−	10.2272i	0.209154	−	0.362266i	0.951448	+	0.307808i	$0.0995955\pi$
$798$	1.43677	+	7.56869i	0.0508611	+	0.267929i
$799$	−24.3535	−	42.1816i	−0.861566	−	1.49228i
$800$	35.2830			1.24744
$801$	−0.279473	+	1.86937i	−0.00987468	+	0.0660509i
$802$	24.5153			0.865665
$803$	−9.70451	−	16.8087i	−0.342465	−	0.593166i
$804$	−12.4102	−	4.33419i	−0.437675	−	0.152855i
$805$	5.96834	−	10.3375i	0.210356	−	0.364348i
$806$	−39.4330	+	68.3000i	−1.38897	+	2.40577i
$807$	−21.8620	+	18.8366i	−0.769580	+	0.663080i
$808$	17.7946	+	30.8212i	0.626013	+	1.08429i
$809$	29.3361			1.03140			0.515701	−	0.856769i	$-0.327532\pi$
$809$	29.3361			1.03140			0.515701	+	0.856769i	$0.327532\pi$
$810$	63.5315	+	19.4303i	2.23227	+	0.682713i
$811$	−20.2768			−0.712016			−0.356008	−	0.934483i	$-0.615862\pi$
$811$	−20.2768			−0.712016			−0.356008	+	0.934483i	$0.615862\pi$
$812$	−57.4808	−	99.5597i	−2.01718	−	3.49386i
$813$	−30.9064	+	26.6293i	−1.08393	+	0.933931i
$814$	−16.6771	+	28.8857i	−0.584534	+	1.01244i
$815$	−6.89517	+	11.9428i	−0.241527	+	0.418338i
$816$	102.361	+	35.7490i	3.58336	+	1.25146i
$817$	−0.211804	−	0.366856i	−0.00741009	−	0.0128347i
$818$	54.8321			1.91716
$819$	5.41905	−	36.2476i	0.189357	−	1.26659i
$820$	−139.403			−4.86818
$821$	−8.16015	−	14.1338i	−0.284791	−	0.493273i	0.687767	−	0.725931i	$-0.258591\pi$
$821$	−8.16015	−	14.1338i	−0.284791	−	0.493273i	−0.972559	+	0.232658i	$0.925258\pi$
$822$	−16.9599	−	89.3421i	−0.591543	−	3.11616i
$823$	−9.24734	+	16.0169i	−0.322342	+	0.558312i	−0.980971	−	0.194155i	$-0.937803\pi$
$823$	−9.24734	+	16.0169i	−0.322342	+	0.558312i	0.658629	+	0.752468i	$0.271137\pi$
$824$	−0.865924	+	1.49983i	−0.0301659	+	0.0522489i
$825$	3.79976	+	20.0166i	0.132291	+	0.696888i
$826$	−14.7365	−	25.5244i	−0.512750	−	0.888108i
$827$	12.6473			0.439789			0.219894	−	0.975524i	$-0.429429\pi$
$827$	12.6473			0.439789			0.219894	+	0.975524i	$0.429429\pi$
$828$	14.7997	−	5.82893i	0.514326	−	0.202569i
$829$	36.0863			1.25333			0.626665	−	0.779289i	$-0.284419\pi$
$829$	36.0863			1.25333			0.626665	+	0.779289i	$0.284419\pi$
$830$	−4.84044	−	8.38389i	−0.168014	−	0.291009i
$831$	−35.0478	−	12.2402i	−1.21580	−	0.424608i
$832$	17.7028	−	30.6621i	0.613733	−	1.06302i
$833$	26.1082	−	45.2208i	0.904597	−	1.56681i
$834$	12.5730	−	10.8330i	0.435367	−	0.375117i
$835$	−25.7587	−	44.6153i	−0.891415	−	1.54398i
$836$	−8.69458			−0.300708
$837$	−50.6228	+	1.98525i	−1.74978	+	0.0686202i
$838$	−89.7458			−3.10022
$839$	−22.3275	−	38.6723i	−0.770830	−	1.33512i	−0.937109	−	0.349038i	$-0.886508\pi$
$839$	−22.3275	−	38.6723i	−0.770830	−	1.33512i	0.166279	−	0.986079i	$-0.446825\pi$
$840$	113.871	−	98.1123i	3.92891	−	3.38520i
$841$	−2.49200	+	4.31627i	−0.0859311	+	0.148837i
$842$	−29.3302	+	50.8014i	−1.01079	+	1.75073i
$843$	3.42398	+	1.19580i	0.117928	+	0.0411856i
$844$	−43.5173	−	75.3741i	−1.49793	−	2.59448i
$845$	10.0461			0.345595
$846$	−51.1479	−	40.6890i	−1.75850	−	1.39892i
$847$	−24.6042			−0.845409
$848$	21.4834	+	37.2104i	0.737744	+	1.27781i
$849$	−3.24580	−	17.0984i	−0.111395	−	0.586815i
$850$	22.0559	−	38.2019i	0.756510	−	1.31031i
$851$	1.63390	−	2.82999i	0.0560093	−	0.0970110i
$852$	6.16026	+	32.4514i	0.211047	+	1.11177i
$853$	23.5820	+	40.8451i	0.807431	+	1.39851i	0.914638	+	0.404275i	$0.132476\pi$
$853$	23.5820	+	40.8451i	0.807431	+	1.39851i	−0.107207	+	0.994237i	$0.534191\pi$
$854$	136.345			4.66563
$855$	2.78431	+	2.21496i	0.0952215	+	0.0757502i
$856$	22.9030			0.782810
$857$	−18.7348	−	32.4497i	−0.639969	−	1.10846i	−0.985439	−	0.170030i	$-0.945614\pi$
$857$	−18.7348	−	32.4497i	−0.639969	−	1.10846i	0.345470	−	0.938430i	$-0.387720\pi$
$858$	54.8220	+	19.1462i	1.87159	+	0.653641i
$859$	−15.2219	+	26.3652i	−0.519366	+	0.899568i	0.480381	+	0.877060i	$0.340499\pi$
$859$	−15.2219	+	26.3652i	−0.519366	+	0.899568i	−0.999747	+	0.0225082i	$0.992835\pi$
$860$	−6.93212	+	12.0068i	−0.236383	+	0.409428i
$861$	−52.5402	+	45.2693i	−1.79057	+	1.54277i
$862$	−17.3216	−	30.0019i	−0.589976	−	1.02187i
$863$	−18.3473			−0.624549			−0.312275	−	0.949992i	$-0.601091\pi$
$863$	−18.3473			−0.624549			−0.312275	+	0.949992i	$0.601091\pi$
$864$	64.5491	−	2.53139i	2.19600	−	0.0861195i
$865$	−14.0515			−0.477767
$866$	−5.84761	−	10.1284i	−0.198710	−	0.344176i
$867$	23.2898	−	20.0668i	0.790963	−	0.681503i
$868$	−96.1355	+	166.512i	−3.26305	+	5.65177i
$869$	−23.9309	+	41.4496i	−0.811801	+	1.40608i
$870$	−70.3672	−	24.5753i	−2.38567	−	0.833180i
$871$	2.35084	+	4.07177i	0.0796550	+	0.137967i
$872$	58.7242			1.98865
$873$	−11.4851	+	4.52345i	−0.388712	+	0.153096i
$874$	1.19585			0.0404504
$875$	12.0515	+	20.8737i	0.407414	+	0.705661i
$876$	7.49103	+	39.4617i	0.253098	+	1.33329i
$877$	6.23156	−	10.7934i	0.210425	−	0.364466i	−0.741423	−	0.671038i	$-0.765849\pi$
$877$	6.23156	−	10.7934i	0.210425	−	0.364466i	0.951848	+	0.306572i	$0.0991820\pi$
$878$	−13.9062	+	24.0862i	−0.469311	+	0.812870i
$879$	8.66277	+	45.6342i	0.292188	+	1.53920i
$880$	61.6115	+	106.714i	2.07692	+	3.59734i
$881$	31.5694			1.06360			0.531800	−	0.846870i	$-0.321516\pi$
$881$	31.5694			1.06360			0.531800	+	0.846870i	$0.321516\pi$
$882$	10.3600	−	69.2972i	0.348840	−	2.33336i
$883$	−3.34872			−0.112693			−0.0563466	−	0.998411i	$-0.517945\pi$
$883$	−3.34872			−0.112693			−0.0563466	+	0.998411i	$0.517945\pi$
$884$	−44.7782	−	77.5581i	−1.50605	−	2.60856i
$885$	−12.8504	−	4.48792i	−0.431962	−	0.150860i
$886$	−37.0582	+	64.1867i	−1.24500	+	2.15640i
$887$	22.4045	−	38.8057i	0.752270	−	1.30297i	−0.194451	−	0.980912i	$-0.562292\pi$
$887$	22.4045	−	38.8057i	0.752270	−	1.30297i	0.946720	−	0.322057i	$-0.104374\pi$
$888$	31.1733	−	26.8593i	1.04611	−	0.901339i
$889$	−6.32394	−	10.9534i	−0.212098	−	0.367365i
$890$	4.65090			0.155899
$891$	8.38762	+	36.3470i	0.280996	+	1.21767i
$892$	53.9178			1.80530
$893$	−1.75007	−	3.03121i	−0.0585638	−	0.101435i
$894$	24.4914	−	21.1021i	0.819115	−	0.705760i
$895$	−17.5272	+	30.3580i	−0.585870	+	1.01476i
$896$	11.0816	−	19.1939i	0.370211	−	0.641225i
$897$	−5.37104	−	1.87580i	−0.179334	−	0.0626311i
$898$	38.8975	+	67.3724i	1.29802	+	2.24824i
$899$	56.8376			1.89564
$900$	6.23420	−	41.7000i	0.207807	−	1.39000i
$901$	23.8513			0.794600
$902$	−54.9413	−	95.1612i	−1.82935	−	3.16852i
$903$	1.28636	+	6.77638i	0.0428075	+	0.225504i
$904$	38.0431	−	65.8926i	1.26529	−	2.19155i
$905$	26.2656	−	45.4933i	0.873096	−	1.51225i
$906$	−6.80902	−	35.8689i	−0.226214	−	1.19167i
$907$	15.4188	+	26.7062i	0.511974	+	0.886765i	0.999904	+	0.0138819i	$0.00441889\pi$
$907$	15.4188	+	26.7062i	0.511974	+	0.886765i	−0.487930	+	0.872883i	$0.662248\pi$
$908$	−51.7223			−1.71647
$909$	12.7624	−	5.02654i	0.423303	−	0.166720i
$910$	−90.1823			−2.98951
$911$	20.3087	+	35.1756i	0.672856	+	1.16542i	0.977091	+	0.212824i	$0.0682660\pi$
$911$	20.3087	+	35.1756i	0.672856	+	1.16542i	−0.304234	+	0.952597i	$0.598401\pi$
$912$	7.35578	+	2.56896i	0.243574	+	0.0850666i
$913$	2.71778	−	4.70734i	0.0899455	−	0.155790i
$914$	48.1246	−	83.3542i	1.59182	−	2.75711i
$915$	47.7035	−	41.1020i	1.57703	−	1.35879i
$916$	−37.8386	−	65.5384i	−1.25022	−	2.16545i
$917$	−18.6354			−0.615395
$918$	37.6097	−	71.4714i	1.24130	−	2.35891i
$919$	15.3680			0.506944			0.253472	−	0.967343i	$-0.418427\pi$
$919$	15.3680			0.506944			0.253472	+	0.967343i	$0.418427\pi$
$920$	−11.6660	−	20.2061i	−0.384617	−	0.666176i
$921$	−2.06829	+	1.78207i	−0.0681526	+	0.0587211i
$922$	26.6993	−	46.2446i	0.879296	−	1.52299i
$923$	5.90707	−	10.2313i	0.194433	−	0.336769i
$924$	133.653	+	46.6773i	4.39686	+	1.53557i
$925$	−4.33106	−	7.50161i	−0.142404	−	0.246651i
$926$	−57.7824			−1.89885
$927$	0.522355	+	0.415542i	0.0171564	+	0.0136482i
$928$	−72.4735			−2.37906
$929$	22.6444	+	39.2212i	0.742937	+	1.28680i	0.951152	+	0.308722i	$0.0999012\pi$
$929$	22.6444	+	39.2212i	0.742937	+	1.28680i	−0.208215	+	0.978083i	$0.566765\pi$
$930$	23.2488	+	122.471i	0.762359	+	4.01600i
$931$	1.87616	−	3.24961i	0.0614887	−	0.106502i
$932$	−52.9377	+	91.6908i	−1.73403	+	3.00343i
$933$	10.0863	+	53.1331i	0.330210	+	1.73950i
$934$	2.13565	+	3.69905i	0.0698806	+	0.121037i
$935$	68.4021			2.23699
$936$	−56.0628	−	44.5989i	−1.83247	−	1.45776i
$937$	2.74160			0.0895642			0.0447821	−	0.998997i	$-0.485741\pi$
$937$	2.74160			0.0895642			0.0447821	+	0.998997i	$0.485741\pi$
$938$	8.04584	+	13.9358i	0.262706	+	0.455020i
$939$	−43.4645	−	15.1797i	−1.41841	−	0.495370i
$940$	−57.2778	+	99.2080i	−1.86820	+	3.23581i
$941$	22.2355	−	38.5130i	0.724857	−	1.25549i	−0.234176	−	0.972194i	$-0.575239\pi$
$941$	22.2355	−	38.5130i	0.724857	−	1.25549i	0.959033	−	0.283295i	$-0.0914274\pi$
$942$	52.1791	−	44.9581i	1.70009	−	1.46482i
$943$	5.38273	+	9.32316i	0.175286	+	0.303604i
$944$	−29.8083			−0.970176
$945$	−30.9092	−	48.9961i	−1.00548	−	1.59384i
$946$	−10.9283			−0.355309
$947$	−16.9679	−	29.3893i	−0.551383	−	0.955024i	−0.998175	−	0.0603861i	$-0.980767\pi$
$947$	−16.9679	−	29.3893i	−0.551383	−	0.955024i	0.446792	−	0.894638i	$-0.352567\pi$
$948$	75.0374	−	64.6531i	2.43710	−	2.09984i
$949$	7.18314	−	12.4416i	0.233175	−	0.403870i
$950$	1.58496	−	2.74522i	0.0514227	−	0.0890668i
$951$	47.8057	+	16.6958i	1.55021	+	0.541399i
$952$	−91.3605	−	158.241i	−2.96101	−	5.12862i
$953$	7.93119			0.256916			0.128458	−	0.991715i	$-0.458997\pi$
$953$	7.93119			0.256916			0.128458	+	0.991715i	$0.458997\pi$
$954$	29.7787	−	11.7285i	0.964121	−	0.379723i
$955$	24.9508			0.807389
$956$	2.99173	+	5.18182i	0.0967593	+	0.167592i
$957$	−7.80494	−	41.1153i	−0.252298	−	1.32907i
$958$	9.55155	−	16.5438i	0.308597	−	0.534505i
$959$	−39.6477	+	68.6719i	−1.28029	+	2.21753i
$960$	−10.4372	−	54.9814i	−0.336858	−	1.77452i
$961$	−32.0298	−	55.4773i	−1.03322	−	1.78959i
$962$	−24.6884			−0.795985
$963$	1.30517	−	8.73015i	0.0420584	−	0.281325i
$964$	139.912			4.50627
$965$	−7.71571	−	13.3640i	−0.248378	−	0.430202i
$966$	−18.3826	−	6.42001i	−0.591451	−	0.206560i
$967$	−23.5991	+	40.8749i	−0.758897	+	1.31445i	0.184516	+	0.982829i	$0.440928\pi$
$967$	−23.5991	+	40.8749i	−0.758897	+	1.31445i	−0.943413	+	0.331619i	$0.892405\pi$
$968$	−24.0462	+	41.6493i	−0.772876	+	1.33866i
$969$	3.27662	−	2.82318i	0.105260	−	0.0906935i
$970$	15.1866	+	26.3040i	0.487613	+	0.844570i
$971$	36.8198			1.18160			0.590801	−	0.806817i	$-0.298812\pi$
$971$	36.8198			1.18160			0.590801	+	0.806817i	$0.298812\pi$
$972$	8.41348	−	76.7361i	0.269863	−	2.46131i
$973$	−14.4715			−0.463936
$974$	38.9734	+	67.5039i	1.24879	+	2.16296i
$975$	−11.4248	+	9.84371i	−0.365885	+	0.315251i
$976$	68.9478	−	119.421i	2.20697	−	3.82258i
$977$	−2.41808	+	4.18824i	−0.0773613	+	0.133994i	−0.902111	−	0.431505i	$-0.857983\pi$
$977$	−2.41808	+	4.18824i	−0.0773613	+	0.133994i	0.824749	+	0.565498i	$0.191316\pi$
$978$	21.2373	+	7.41698i	0.679094	+	0.237169i
$979$	1.30568	+	2.26150i	0.0417297	+	0.0722780i
$980$	−122.809			−3.92300
$981$	3.34650	−	22.3844i	0.106845	−	0.714679i
$982$	−30.3465			−0.968397
$983$	−14.9629	−	25.9165i	−0.477242	−	0.826607i	0.522418	−	0.852689i	$-0.325030\pi$
$983$	−14.9629	−	25.9165i	−0.477242	−	0.826607i	−0.999660	+	0.0260827i	$0.991697\pi$
$984$	25.2819	+	133.181i	0.805958	+	4.24567i
$985$	−7.02612	+	12.1696i	−0.223871	+	0.387756i
$986$	−45.3041	+	78.4690i	−1.44278	+	2.49896i
$987$	10.6288	+	55.9909i	0.338318	+	1.78221i
$988$	−3.21780	−	5.57340i	−0.102372	−	0.177313i
$989$	1.07067			0.0340453
$990$	85.4012	−	33.6356i	2.71423	−	1.06901i
$991$	−45.3361			−1.44015			−0.720074	−	0.693897i	$-0.755892\pi$
$991$	−45.3361			−1.44015			−0.720074	+	0.693897i	$0.755892\pi$
$992$	60.6052	+	104.971i	1.92422	+	3.33284i
$993$	−2.66927	−	0.932224i	−0.0847067	−	0.0295832i
$994$	20.2172	−	35.0172i	0.641251	−	1.11068i
$995$	0.400423	−	0.693552i	0.0126943	−	0.0219871i
$996$	−8.52183	+	7.34251i	−0.270024	+	0.232656i
$997$	19.9559	+	34.5647i	0.632011	+	1.09468i	0.987140	+	0.159858i	$0.0511037\pi$
$997$	19.9559	+	34.5647i	0.632011	+	1.09468i	−0.355129	+	0.934817i	$0.615563\pi$
$998$	82.2569			2.60380
$999$	−8.46173	−	13.4132i	−0.267717	−	0.424375i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.2.f.d.130.1	✓	40
3.2	odd	2		1161.2.f.d.388.20		40
9.2	odd	6		1161.2.f.d.775.20		40
9.4	even	3		3483.2.a.t.1.20		20
9.5	odd	6		3483.2.a.u.1.1		20
9.7	even	3	inner	387.2.f.d.259.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
387.2.f.d.130.1	✓	40	1.1	even	1	trivial
387.2.f.d.259.1	yes	40	9.7	even	3	inner
1161.2.f.d.388.20		40	3.2	odd	2
1161.2.f.d.775.20		40	9.2	odd	6
3483.2.a.t.1.20		20	9.4	even	3
3483.2.a.u.1.1		20	9.5	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:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	387.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31834 - 2.28344i) q^{2} +(1.31217 - 1.13058i) q^{3} +(-2.47606 + 4.28866i) q^{4} +(1.39983 - 2.42457i) q^{5} +(-4.31150 - 1.50576i) q^{6} +(1.99111 + 3.44870i) q^{7} +7.78382 q^{8} +(0.443574 - 2.96703i) q^{9} +O(q^{10})\)	\(q+(-1.31834 - 2.28344i) q^{2} +(1.31217 - 1.13058i) q^{3} +(-2.47606 + 4.28866i) q^{4} +(1.39983 - 2.42457i) q^{5} +(-4.31150 - 1.50576i) q^{6} +(1.99111 + 3.44870i) q^{7} +7.78382 q^{8} +(0.443574 - 2.96703i) q^{9} -7.38182 q^{10} +(-2.07235 - 3.58941i) q^{11} +(1.59967 + 8.42684i) q^{12} +(1.53392 - 2.65683i) q^{13} +(5.24992 - 9.09313i) q^{14} +(-0.904366 - 4.76407i) q^{15} +(-5.30963 - 9.19655i) q^{16} -5.89483 q^{17} +(-7.35980 + 2.89869i) q^{18} -0.423608 q^{19} +(6.93212 + 12.0068i) q^{20} +(6.51170 + 2.27417i) q^{21} +(-5.46414 + 9.46416i) q^{22} +(0.535334 - 0.927226i) q^{23} +(10.2137 - 8.80024i) q^{24} +(-1.41904 - 2.45784i) q^{25} -8.08895 q^{26} +(-2.77242 - 4.39473i) q^{27} -19.7204 q^{28} +(2.91479 + 5.04856i) q^{29} +(-9.68619 + 8.34574i) q^{30} +(4.87493 - 8.44362i) q^{31} +(-6.21601 + 10.7665i) q^{32} +(-6.77739 - 2.36696i) q^{33} +(7.77142 + 13.4605i) q^{34} +11.1488 q^{35} +(11.6263 + 9.24887i) q^{36} +3.05211 q^{37} +(0.558461 + 0.967284i) q^{38} +(-0.990998 - 5.22044i) q^{39} +(10.8960 - 18.8724i) q^{40} +(-5.02745 + 8.70780i) q^{41} +(-3.39174 - 17.8672i) q^{42} +(0.500000 + 0.866025i) q^{43} +20.5250 q^{44} +(-6.57284 - 5.22880i) q^{45} -2.82302 q^{46} +(4.13133 + 7.15568i) q^{47} +(-17.3646 - 6.06446i) q^{48} +(-4.42900 + 7.67126i) q^{49} +(-3.74156 + 6.48057i) q^{50} +(-7.73502 + 6.66459i) q^{51} +(7.59617 + 13.1570i) q^{52} -4.04613 q^{53} +(-6.38010 + 12.1244i) q^{54} -11.6037 q^{55} +(15.4984 + 26.8440i) q^{56} +(-0.555846 + 0.478924i) q^{57} +(7.68539 - 13.3115i) q^{58} +(1.40350 - 2.43093i) q^{59} +(22.6707 + 7.91760i) q^{60} +(6.49271 + 11.2457i) q^{61} -25.7073 q^{62} +(11.1156 - 4.37791i) q^{63} +11.5409 q^{64} +(-4.29446 - 7.43822i) q^{65} +(3.53013 + 18.5962i) q^{66} +(-0.766282 + 1.32724i) q^{67} +(14.5960 - 25.2810i) q^{68} +(-0.345855 - 1.82191i) q^{69} +(-14.6980 - 25.4576i) q^{70} +3.85095 q^{71} +(3.45270 - 23.0948i) q^{72} +4.68286 q^{73} +(-4.02373 - 6.96931i) q^{74} +(-4.64081 - 1.62077i) q^{75} +(1.04888 - 1.81671i) q^{76} +(8.25253 - 14.2938i) q^{77} +(-10.6141 + 9.14521i) q^{78} +(-5.77387 - 10.0006i) q^{79} -29.7303 q^{80} +(-8.60648 - 2.63219i) q^{81} +26.5116 q^{82} +(0.655725 + 1.13575i) q^{83} +(-25.8765 + 22.2955i) q^{84} +(-8.25175 + 14.2925i) q^{85} +(1.31834 - 2.28344i) q^{86} +(9.53251 + 3.32916i) q^{87} +(-16.1308 - 27.9393i) q^{88} -0.630048 q^{89} +(-3.27438 + 21.9020i) q^{90} +12.2168 q^{91} +(2.65104 + 4.59173i) q^{92} +(-3.14947 - 16.5910i) q^{93} +(10.8930 - 18.8673i) q^{94} +(-0.592979 + 1.02707i) q^{95} +(4.01589 + 21.1551i) q^{96} +(-2.05730 - 3.56335i) q^{97} +23.3558 q^{98} +(-11.5691 + 4.55654i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 6 q^{2} + 2 q^{3} - 22 q^{4} + 17 q^{5} - 6 q^{6} - 3 q^{7} - 30 q^{8}+O(q^{10}) \) 40 * q + 6 * q^2 + 2 * q^3 - 22 * q^4 + 17 * q^5 - 6 * q^6 - 3 * q^7 - 30 * q^8	\( 40 q + 6 q^{2} + 2 q^{3} - 22 q^{4} + 17 q^{5} - 6 q^{6} - 3 q^{7} - 30 q^{8} - 4 q^{10} + 10 q^{11} - 17 q^{12} + q^{13} + 10 q^{14} + 7 q^{15} - 22 q^{16} - 40 q^{17} + 3 q^{18} + 16 q^{19} + 30 q^{20} + 6 q^{21} - 15 q^{22} + 19 q^{23} + 33 q^{24} - 19 q^{25} - 50 q^{26} + 8 q^{27} - 6 q^{28} + 25 q^{29} - 54 q^{30} + 11 q^{31} + 36 q^{32} - 6 q^{33} - 9 q^{34} + 44 q^{36} + 18 q^{37} + 28 q^{38} - 35 q^{39} - 12 q^{40} + 12 q^{41} + 37 q^{42} + 20 q^{43} - 10 q^{44} - 25 q^{45} + 8 q^{46} + 38 q^{47} - 7 q^{48} - 37 q^{49} + 36 q^{50} - 4 q^{51} + 8 q^{52} - 138 q^{53} + 33 q^{54} - 18 q^{55} + 30 q^{56} - 53 q^{57} + 27 q^{58} + 31 q^{59} + 38 q^{60} - 19 q^{61} - 64 q^{62} - 35 q^{63} + 22 q^{64} + 47 q^{65} - 33 q^{66} - 9 q^{67} + 68 q^{68} + 26 q^{69} + 6 q^{70} - 42 q^{71} + 6 q^{72} - 4 q^{73} - 16 q^{74} - 56 q^{75} - 37 q^{76} + 85 q^{77} + 43 q^{78} + 4 q^{79} - 122 q^{80} - 36 q^{81} + 2 q^{82} + 19 q^{83} - 83 q^{84} + 6 q^{85} - 6 q^{86} + 49 q^{87} - 60 q^{88} - 108 q^{89} + 3 q^{90} - 6 q^{91} + 85 q^{92} - 10 q^{93} + 19 q^{94} - 11 q^{95} + 93 q^{96} - 2 q^{97} - 10 q^{98} + 19 q^{99}+O(q^{100}) \) 40 * q + 6 * q^2 + 2 * q^3 - 22 * q^4 + 17 * q^5 - 6 * q^6 - 3 * q^7 - 30 * q^8 - 4 * q^10 + 10 * q^11 - 17 * q^12 + q^13 + 10 * q^14 + 7 * q^15 - 22 * q^16 - 40 * q^17 + 3 * q^18 + 16 * q^19 + 30 * q^20 + 6 * q^21 - 15 * q^22 + 19 * q^23 + 33 * q^24 - 19 * q^25 - 50 * q^26 + 8 * q^27 - 6 * q^28 + 25 * q^29 - 54 * q^30 + 11 * q^31 + 36 * q^32 - 6 * q^33 - 9 * q^34 + 44 * q^36 + 18 * q^37 + 28 * q^38 - 35 * q^39 - 12 * q^40 + 12 * q^41 + 37 * q^42 + 20 * q^43 - 10 * q^44 - 25 * q^45 + 8 * q^46 + 38 * q^47 - 7 * q^48 - 37 * q^49 + 36 * q^50 - 4 * q^51 + 8 * q^52 - 138 * q^53 + 33 * q^54 - 18 * q^55 + 30 * q^56 - 53 * q^57 + 27 * q^58 + 31 * q^59 + 38 * q^60 - 19 * q^61 - 64 * q^62 - 35 * q^63 + 22 * q^64 + 47 * q^65 - 33 * q^66 - 9 * q^67 + 68 * q^68 + 26 * q^69 + 6 * q^70 - 42 * q^71 + 6 * q^72 - 4 * q^73 - 16 * q^74 - 56 * q^75 - 37 * q^76 + 85 * q^77 + 43 * q^78 + 4 * q^79 - 122 * q^80 - 36 * q^81 + 2 * q^82 + 19 * q^83 - 83 * q^84 + 6 * q^85 - 6 * q^86 + 49 * q^87 - 60 * q^88 - 108 * q^89 + 3 * q^90 - 6 * q^91 + 85 * q^92 - 10 * q^93 + 19 * q^94 - 11 * q^95 + 93 * q^96 - 2 * q^97 - 10 * q^98 + 19 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more