LMFDB - Embedded newform 105.3.n.a.61.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(31,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("105.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.n (of order $6$, 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:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.523596960000.16
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 13x^{6} - 2x^{5} + 91x^{4} - 50x^{3} + 190x^{2} + 100x + 100 $ x^8 - 2x^7 + 13x^6 - 2x^5 + 91x^4 - 50x^3 + 190x^2 + 100*x + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			61.3
Root			$0.836732 - 1.44926i$ of defining polynomial
Character	$\chi$	$=$	105.61
Dual form			105.3.n.a.31.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.836732 - 1.44926i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(0.599760 + 1.03881i) q^{4} +(1.93649 + 1.11803i) q^{5} +2.89852i q^{6} +(4.76104 - 5.13152i) q^{7} +8.70121 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(0.836732 - 1.44926i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(0.599760 + 1.03881i) q^{4} +(1.93649 + 1.11803i) q^{5} +2.89852i q^{6} +(4.76104 - 5.13152i) q^{7} +8.70121 q^{8} +(1.50000 - 2.59808i) q^{9} +(3.24065 - 1.87099i) q^{10} +(6.91411 + 11.9756i) q^{11} +(-1.79928 - 1.03881i) q^{12} -6.12052i q^{13} +(-3.45321 - 11.1937i) q^{14} -3.87298 q^{15} +(4.88154 - 8.45507i) q^{16} +(-2.14655 + 1.23931i) q^{17} +(-2.51020 - 4.34779i) q^{18} +(-24.2290 - 13.9886i) q^{19} +2.68221i q^{20} +(-2.69753 + 11.8205i) q^{21} +23.1410 q^{22} +(-6.62020 + 11.4665i) q^{23} +(-13.0518 + 7.53547i) q^{24} +(2.50000 + 4.33013i) q^{25} +(-8.87024 - 5.12123i) q^{26} +5.19615i q^{27} +(8.18618 + 1.86816i) q^{28} -27.6516 q^{29} +(-3.24065 + 5.61297i) q^{30} +(-16.2122 + 9.36010i) q^{31} +(9.23334 + 15.9926i) q^{32} +(-20.7423 - 11.9756i) q^{33} +4.14789i q^{34} +(14.9569 - 4.61414i) q^{35} +3.59856 q^{36} +(20.5067 - 35.5187i) q^{37} +(-40.5463 + 23.4094i) q^{38} +(5.30052 + 9.18078i) q^{39} +(16.8498 + 9.72824i) q^{40} +22.5351i q^{41} +(14.8738 + 13.8000i) q^{42} +7.60485 q^{43} +(-8.29361 + 14.3650i) q^{44} +(5.80948 - 3.35410i) q^{45} +(11.0787 + 19.1888i) q^{46} +(-11.9214 - 6.88283i) q^{47} +16.9101i q^{48} +(-3.66502 - 48.8627i) q^{49} +8.36732 q^{50} +(2.14655 - 3.71794i) q^{51} +(6.35808 - 3.67084i) q^{52} +(-46.2995 - 80.1930i) q^{53} +(7.53059 + 4.34779i) q^{54} +30.9208i q^{55} +(41.4268 - 44.6504i) q^{56} +48.4579 q^{57} +(-23.1370 + 40.0744i) q^{58} +(-61.5680 + 35.5463i) q^{59} +(-2.32286 - 4.02331i) q^{60} +(-100.214 - 57.8584i) q^{61} +31.3276i q^{62} +(-6.19052 - 20.0668i) q^{63} +69.9556 q^{64} +(6.84295 - 11.8523i) q^{65} +(-34.7115 + 20.0407i) q^{66} +(5.70227 + 9.87662i) q^{67} +(-2.57483 - 1.48658i) q^{68} -22.9330i q^{69} +(5.82783 - 25.5373i) q^{70} +99.4924 q^{71} +(13.0518 - 22.6064i) q^{72} +(90.1276 - 52.0352i) q^{73} +(-34.3172 - 59.4392i) q^{74} +(-7.50000 - 4.33013i) q^{75} -33.5592i q^{76} +(94.3714 + 21.5364i) q^{77} +17.7405 q^{78} +(-64.4982 + 111.714i) q^{79} +(18.9061 - 10.9154i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(32.6592 + 18.8558i) q^{82} +30.3382i q^{83} +(-13.8971 + 4.28721i) q^{84} -5.54238 q^{85} +(6.36322 - 11.0214i) q^{86} +(41.4774 - 23.9470i) q^{87} +(60.1611 + 104.202i) q^{88} +(93.9587 + 54.2471i) q^{89} -11.2259i q^{90} +(-31.4076 - 29.1400i) q^{91} -15.8821 q^{92} +(16.2122 - 28.0803i) q^{93} +(-19.9501 + 11.5182i) q^{94} +(-31.2794 - 54.1776i) q^{95} +(-27.7000 - 15.9926i) q^{96} +153.154i q^{97} +(-73.8816 - 35.5734i) q^{98} +41.4847 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 12 q^{3} - 6 q^{4} - 16 q^{7} - 32 q^{8} + 12 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 - 12 * q^3 - 6 * q^4 - 16 * q^7 - 32 * q^8 + 12 * q^9	$ 8 q + 2 q^{2} - 12 q^{3} - 6 q^{4} - 16 q^{7} - 32 q^{8} + 12 q^{9} + 20 q^{11} + 18 q^{12} - 16 q^{14} - 2 q^{16} - 18 q^{17} - 6 q^{18} + 48 q^{21} - 16 q^{22} + 62 q^{23} + 48 q^{24} + 20 q^{25} + 120 q^{26} - 120 q^{28} - 100 q^{29} - 126 q^{31} + 36 q^{32} - 60 q^{33} - 36 q^{36} - 80 q^{37} + 114 q^{38} - 12 q^{39} + 90 q^{40} + 90 q^{42} + 352 q^{43} - 18 q^{44} - 82 q^{46} - 72 q^{47} + 38 q^{49} + 20 q^{50} + 18 q^{51} - 48 q^{52} - 76 q^{53} + 18 q^{54} + 196 q^{56} - 40 q^{58} - 54 q^{59} - 60 q^{60} - 396 q^{61} - 96 q^{63} - 4 q^{64} - 60 q^{65} + 24 q^{66} + 184 q^{67} - 312 q^{68} + 164 q^{71} - 48 q^{72} + 348 q^{73} - 140 q^{74} - 60 q^{75} + 152 q^{77} - 240 q^{78} - 206 q^{79} - 36 q^{81} + 204 q^{82} + 132 q^{84} - 60 q^{85} + 178 q^{86} + 150 q^{87} + 124 q^{88} + 282 q^{89} - 114 q^{91} - 288 q^{92} + 126 q^{93} + 30 q^{94} - 120 q^{95} - 108 q^{96} - 592 q^{98} + 120 q^{99}+O(q^{100}) $ 8 * q + 2 * q^2 - 12 * q^3 - 6 * q^4 - 16 * q^7 - 32 * q^8 + 12 * q^9 + 20 * q^11 + 18 * q^12 - 16 * q^14 - 2 * q^16 - 18 * q^17 - 6 * q^18 + 48 * q^21 - 16 * q^22 + 62 * q^23 + 48 * q^24 + 20 * q^25 + 120 * q^26 - 120 * q^28 - 100 * q^29 - 126 * q^31 + 36 * q^32 - 60 * q^33 - 36 * q^36 - 80 * q^37 + 114 * q^38 - 12 * q^39 + 90 * q^40 + 90 * q^42 + 352 * q^43 - 18 * q^44 - 82 * q^46 - 72 * q^47 + 38 * q^49 + 20 * q^50 + 18 * q^51 - 48 * q^52 - 76 * q^53 + 18 * q^54 + 196 * q^56 - 40 * q^58 - 54 * q^59 - 60 * q^60 - 396 * q^61 - 96 * q^63 - 4 * q^64 - 60 * q^65 + 24 * q^66 + 184 * q^67 - 312 * q^68 + 164 * q^71 - 48 * q^72 + 348 * q^73 - 140 * q^74 - 60 * q^75 + 152 * q^77 - 240 * q^78 - 206 * q^79 - 36 * q^81 + 204 * q^82 + 132 * q^84 - 60 * q^85 + 178 * q^86 + 150 * q^87 + 124 * q^88 + 282 * q^89 - 114 * q^91 - 288 * q^92 + 126 * q^93 + 30 * q^94 - 120 * q^95 - 108 * q^96 - 592 * q^98 + 120 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	0.836732	−	1.44926i	0.418366	−	0.724631i	−0.577409	−	0.816455i	$-0.695936\pi$
$2$	0.836732	−	1.44926i	0.418366	−	0.724631i	0.995775	+	0.0918238i	$0.0292697\pi$
$3$	−1.50000	+	0.866025i	−0.500000	+	0.288675i
$3$	−1.50000	+	0.866025i	−0.500000	+	0.288675i
$4$	0.599760	+	1.03881i	0.149940	+	0.259704i
$5$	1.93649	+	1.11803i	0.387298	+	0.223607i
$5$	1.93649	+	1.11803i	0.387298	+	0.223607i
$6$			2.89852i			0.483087i
$7$	4.76104	−	5.13152i	0.680148	−	0.733074i
$7$	4.76104	−	5.13152i	0.680148	−	0.733074i
$8$	8.70121			1.08765
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$	3.24065	−	1.87099i	0.324065	−	0.187099i
$11$	6.91411	+	11.9756i	0.628556	+	1.08869i	0.987842	+	0.155463i	$0.0496869\pi$
$11$	6.91411	+	11.9756i	0.628556	+	1.08869i	−0.359286	+	0.933227i	$0.616980\pi$
$12$	−1.79928	−	1.03881i	−0.149940	−	0.0865679i
$13$		−	6.12052i		−	0.470809i	−0.971897	−	0.235405i	$-0.924358\pi$
$13$		−	6.12052i		−	0.470809i	0.971897	−	0.235405i	$-0.0756415\pi$
$14$	−3.45321	−	11.1937i	−0.246658	−	0.799550i
$15$	−3.87298			−0.258199
$16$	4.88154	−	8.45507i	0.305096	−	0.528442i
$17$	−2.14655	+	1.23931i	−0.126268	+	0.0729008i	−0.561804	−	0.827271i	$-0.689892\pi$
$17$	−2.14655	+	1.23931i	−0.126268	+	0.0729008i	0.435536	+	0.900171i	$0.356559\pi$
$18$	−2.51020	−	4.34779i	−0.139455	−	0.241544i
$19$	−24.2290	−	13.9886i	−1.27521	−	0.736242i	−0.299245	−	0.954176i	$-0.596735\pi$
$19$	−24.2290	−	13.9886i	−1.27521	−	0.736242i	−0.975963	+	0.217935i	$0.930068\pi$
$20$			2.68221i			0.134110i
$21$	−2.69753	+	11.8205i	−0.128454	+	0.562879i
$22$	23.1410			1.05186
$23$	−6.62020	+	11.4665i	−0.287835	+	0.498544i	−0.973293	−	0.229568i	$-0.926269\pi$
$23$	−6.62020	+	11.4665i	−0.287835	+	0.498544i	0.685458	+	0.728112i	$0.259602\pi$
$24$	−13.0518	+	7.53547i	−0.543825	+	0.313978i
$25$	2.50000	+	4.33013i	0.100000	+	0.173205i
$26$	−8.87024	−	5.12123i	−0.341163	−	0.196970i
$27$			5.19615i			0.192450i
$28$	8.18618	+	1.86816i	0.292364	+	0.0667199i
$29$	−27.6516			−0.953503			−0.476751	−	0.879038i	$-0.658186\pi$
$29$	−27.6516			−0.953503			−0.476751	+	0.879038i	$0.658186\pi$
$30$	−3.24065	+	5.61297i	−0.108022	+	0.187099i
$31$	−16.2122	+	9.36010i	−0.522973	+	0.301939i	−0.738150	−	0.674636i	$-0.764300\pi$
$31$	−16.2122	+	9.36010i	−0.522973	+	0.301939i	0.215177	+	0.976575i	$0.430967\pi$
$32$	9.23334	+	15.9926i	0.288542	+	0.499769i
$33$	−20.7423	−	11.9756i	−0.628556	−	0.362897i
$34$			4.14789i			0.121997i
$35$	14.9569	−	4.61414i	0.427341	−	0.131833i
$36$	3.59856			0.0999600
$37$	20.5067	−	35.5187i	0.554235	−	0.959964i	−0.443727	−	0.896162i	$-0.646344\pi$
$37$	20.5067	−	35.5187i	0.554235	−	0.959964i	0.997963	−	0.0638017i	$-0.0203225\pi$
$38$	−40.5463	+	23.4094i	−1.06701	+	0.616037i
$39$	5.30052	+	9.18078i	0.135911	+	0.235405i
$40$	16.8498	+	9.72824i	0.421245	+	0.243206i
$41$			22.5351i			0.549636i	0.961496	+	0.274818i	$0.0886176\pi$
$41$			22.5351i			0.549636i	−0.961496	+	0.274818i	$0.911382\pi$
$42$	14.8738	+	13.8000i	0.354139	+	0.328571i
$43$	7.60485			0.176857			0.0884285	−	0.996083i	$-0.471816\pi$
$43$	7.60485			0.176857			0.0884285	+	0.996083i	$0.471816\pi$
$44$	−8.29361	+	14.3650i	−0.188491	+	0.326476i
$45$	5.80948	−	3.35410i	0.129099	−	0.0745356i
$46$	11.0787	+	19.1888i	0.240840	+	0.417148i
$47$	−11.9214	−	6.88283i	−0.253647	−	0.146443i	0.367786	−	0.929910i	$-0.380116\pi$
$47$	−11.9214	−	6.88283i	−0.253647	−	0.146443i	−0.621433	+	0.783467i	$0.713449\pi$
$48$			16.9101i			0.352295i
$49$	−3.66502	−	48.8627i	−0.0747963	−	0.997199i
$50$	8.36732			0.167346
$51$	2.14655	−	3.71794i	0.0420893	−	0.0729008i
$52$	6.35808	−	3.67084i	0.122271	−	0.0705931i
$53$	−46.2995	−	80.1930i	−0.873575	−	1.51308i	−0.858273	−	0.513193i	$-0.828463\pi$
$53$	−46.2995	−	80.1930i	−0.873575	−	1.51308i	−0.0153016	−	0.999883i	$-0.504871\pi$
$54$	7.53059	+	4.34779i	0.139455	+	0.0805146i
$55$			30.9208i			0.562197i
$56$	41.4268	−	44.6504i	0.739764	−	0.797329i
$57$	48.4579			0.850139
$58$	−23.1370	+	40.0744i	−0.398913	+	0.690938i
$59$	−61.5680	+	35.5463i	−1.04352	+	0.602479i	−0.920830	−	0.389965i	$-0.872487\pi$
$59$	−61.5680	+	35.5463i	−1.04352	+	0.602479i	−0.122695	+	0.992444i	$0.539154\pi$
$60$	−2.32286	−	4.02331i	−0.0387143	−	0.0670552i
$61$	−100.214	−	57.8584i	−1.64285	−	0.948498i	−0.979815	−	0.199906i	$-0.935936\pi$
$61$	−100.214	−	57.8584i	−1.64285	−	0.948498i	−0.663031	−	0.748592i	$-0.730730\pi$
$62$			31.3276i			0.505283i
$63$	−6.19052	−	20.0668i	−0.0982623	−	0.318521i
$64$	69.9556			1.09306
$65$	6.84295	−	11.8523i	0.105276	−	0.182344i
$66$	−34.7115	+	20.0407i	−0.525932	+	0.303647i
$67$	5.70227	+	9.87662i	0.0851085	+	0.147412i	0.905437	−	0.424480i	$-0.139543\pi$
$67$	5.70227	+	9.87662i	0.0851085	+	0.147412i	−0.820329	+	0.571892i	$0.806210\pi$
$68$	−2.57483	−	1.48658i	−0.0378652	−	0.0218615i
$69$		−	22.9330i		−	0.332363i
$70$	5.82783	−	25.5373i	0.0832547	−	0.364819i
$71$	99.4924			1.40130			0.700651	−	0.713504i	$-0.252893\pi$
$71$	99.4924			1.40130			0.700651	+	0.713504i	$0.252893\pi$
$72$	13.0518	−	22.6064i	0.181275	−	0.313978i
$73$	90.1276	−	52.0352i	1.23462	−	0.712811i	0.266634	−	0.963798i	$-0.414088\pi$
$73$	90.1276	−	52.0352i	1.23462	−	0.712811i	0.967991	+	0.250987i	$0.0807550\pi$
$74$	−34.3172	−	59.4392i	−0.463746	−	0.803232i
$75$	−7.50000	−	4.33013i	−0.100000	−	0.0577350i
$76$		−	33.5592i		−	0.441568i
$77$	94.3714	+	21.5364i	1.22560	+	0.279693i
$78$	17.7405			0.227442
$79$	−64.4982	+	111.714i	−0.816433	+	1.41410i	0.0918616	+	0.995772i	$0.470718\pi$
$79$	−64.4982	+	111.714i	−0.816433	+	1.41410i	−0.908294	+	0.418331i	$0.862615\pi$
$80$	18.9061	−	10.9154i	0.236326	−	0.136443i
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	32.6592	+	18.8558i	0.398283	+	0.229949i
$83$			30.3382i			0.365520i	0.983158	+	0.182760i	$0.0585032\pi$
$83$			30.3382i			0.365520i	−0.983158	+	0.182760i	$0.941497\pi$
$84$	−13.8971	+	4.28721i	−0.165442	+	0.0510382i
$85$	−5.54238			−0.0652045
$86$	6.36322	−	11.0214i	0.0739909	−	0.128156i
$87$	41.4774	−	23.9470i	0.476751	−	0.275253i
$88$	60.1611	+	104.202i	0.683649	+	1.18411i
$89$	93.9587	+	54.2471i	1.05572	+	0.609518i	0.924244	−	0.381802i	$-0.124696\pi$
$89$	93.9587	+	54.2471i	1.05572	+	0.609518i	0.131472	+	0.991320i	$0.458030\pi$
$90$		−	11.2259i		−	0.124733i
$91$	−31.4076	−	29.1400i	−0.345138	−	0.320220i
$92$	−15.8821			−0.172632
$93$	16.2122	−	28.0803i	0.174324	−	0.301939i
$94$	−19.9501	+	11.5182i	−0.212235	+	0.122534i
$95$	−31.2794	−	54.1776i	−0.329257	−	0.570290i
$96$	−27.7000	−	15.9926i	−0.288542	−	0.166590i
$97$			153.154i			1.57890i	0.613812	+	0.789452i	$0.289635\pi$
$97$			153.154i			1.57890i	−0.613812	+	0.789452i	$0.710365\pi$
$98$	−73.8816	−	35.5734i	−0.753893	−	0.362994i
$99$	41.4847			0.419037
$100$	−2.99880	+	5.19407i	−0.0299880	+	0.0519407i
$101$	98.9544	−	57.1314i	0.979747	−	0.565657i	0.0775531	−	0.996988i	$-0.475289\pi$
$101$	98.9544	−	57.1314i	0.979747	−	0.565657i	0.902194	+	0.431331i	$0.141956\pi$
$102$	−3.59218	−	6.22184i	−0.0352174	−	0.0609984i
$103$	−48.4794	−	27.9896i	−0.470674	−	0.271744i	0.245848	−	0.969308i	$-0.420934\pi$
$103$	−48.4794	−	27.9896i	−0.470674	−	0.271744i	−0.716522	+	0.697565i	$0.754267\pi$
$104$		−	53.2559i		−	0.512076i
$105$	−18.4394	+	19.8743i	−0.175614	+	0.189279i
$106$	−154.961			−1.46190
$107$	−49.3529	+	85.4817i	−0.461242	+	0.798895i	−0.999023	−	0.0441897i	$-0.985929\pi$
$107$	−49.3529	+	85.4817i	−0.461242	+	0.798895i	0.537781	+	0.843085i	$0.319263\pi$
$108$	−5.39784	+	3.11644i	−0.0499800	+	0.0288560i
$109$	−26.3791	−	45.6900i	−0.242010	−	0.419174i	0.719276	−	0.694724i	$-0.244473\pi$
$109$	−26.3791	−	45.6900i	−0.242010	−	0.419174i	−0.961287	+	0.275550i	$0.911140\pi$
$110$	44.8124	+	25.8725i	0.407386	+	0.235204i
$111$			71.0373i			0.639976i
$112$	−20.1462	−	65.3046i	−0.179877	−	0.583077i
$113$	106.206			0.939875			0.469937	−	0.882700i	$-0.344276\pi$
$113$	106.206			0.939875			0.469937	+	0.882700i	$0.344276\pi$
$114$	40.5463	−	70.2282i	0.355669	−	0.616037i
$115$	−25.6399	+	14.8032i	−0.222956	+	0.128724i
$116$	−16.5843	−	28.7249i	−0.142968	−	0.247628i
$117$	−15.9016	−	9.18078i	−0.135911	−	0.0784682i
$118$			118.971i			1.00823i
$119$	−3.86026	+	16.9155i	−0.0324392	+	0.142147i
$120$	−33.6996			−0.280830
$121$	−35.1099	+	60.8121i	−0.290164	+	0.502579i
$122$	−167.704	+	96.8239i	−1.37462	+	0.793638i
$123$	−19.5160	−	33.8026i	−0.158666	−	0.274818i
$124$	−19.4468	−	11.2276i	−0.156829	−	0.0905453i
$125$			11.1803i			0.0894427i
$126$	−34.2619	−	7.81886i	−0.271920	−	0.0620544i
$127$	−197.402			−1.55434			−0.777172	−	0.629288i	$-0.783347\pi$
$127$	−197.402			−1.55434			−0.777172	+	0.629288i	$0.783347\pi$
$128$	21.6007	−	37.4135i	0.168756	−	0.292293i
$129$	−11.4073	+	6.58599i	−0.0884285	+	0.0510542i
$130$	−11.4514	−	19.8344i	−0.0880879	−	0.152573i
$131$	127.379	+	73.5423i	0.972358	+	0.561391i	0.899954	−	0.435984i	$-0.143600\pi$
$131$	127.379	+	73.5423i	0.972358	+	0.561391i	0.0724040	+	0.997375i	$0.476933\pi$
$132$		−	28.7299i		−	0.217651i
$133$	−187.138	+	57.7311i	−1.40705	+	0.434069i
$134$	19.0851			0.142426
$135$	−5.80948	+	10.0623i	−0.0430331	+	0.0745356i
$136$	−18.6776	+	10.7835i	−0.137335	+	0.0792906i
$137$	−124.296	−	215.287i	−0.907270	−	1.57144i	−0.817841	−	0.575445i	$-0.804829\pi$
$137$	−124.296	−	215.287i	−0.907270	−	1.57144i	−0.0894293	−	0.995993i	$-0.528504\pi$
$138$	−33.2360	−	19.1888i	−0.240840	−	0.139049i
$139$			15.7344i			0.113197i	0.998397	+	0.0565985i	$0.0180255\pi$
$139$			15.7344i			0.113197i	−0.998397	+	0.0565985i	$0.981974\pi$
$140$	13.7638	+	12.7701i	0.0983129	+	0.0912150i
$141$	23.8428			0.169098
$142$	83.2485	−	144.191i	0.586257	−	1.01543i
$143$	73.2968	−	42.3180i	0.512565	−	0.295930i
$144$	−14.6446	−	25.3652i	−0.101699	−	0.176147i
$145$	−53.5471	−	30.9154i	−0.369290	−	0.213210i
$146$		−	174.158i		−	1.19286i
$147$	47.8139	+	70.1201i	0.325265	+	0.477008i
$148$	49.1964			0.332408
$149$	−92.1029	+	159.527i	−0.618140	+	1.07065i	0.371684	+	0.928359i	$0.378780\pi$
$149$	−92.1029	+	159.527i	−0.618140	+	1.07065i	−0.989825	+	0.142291i	$0.954553\pi$
$150$	−12.5510	+	7.24631i	−0.0836732	+	0.0483087i
$151$	131.625	+	227.982i	0.871690	+	1.50981i	0.860247	+	0.509877i	$0.170309\pi$
$151$	131.625	+	227.982i	0.871690	+	1.50981i	0.0114426	+	0.999935i	$0.496358\pi$
$152$	−210.821	−	121.718i	−1.38698	−	0.800774i
$153$			7.43588i			0.0486005i
$154$	110.175	−	118.749i	0.715424	−	0.771095i
$155$	−41.8596			−0.270062
$156$	−6.35808	+	11.0125i	−0.0407570	+	0.0705931i
$157$	187.600	−	108.311i	1.19490	−	0.689878i	0.235489	−	0.971877i	$-0.424331\pi$
$157$	187.600	−	108.311i	1.19490	−	0.689878i	0.959415	+	0.281999i	$0.0909975\pi$
$158$	107.935	+	186.950i	0.683135	+	1.18323i
$159$	138.898	+	80.1930i	0.873575	+	0.504359i
$160$			41.2928i			0.258080i
$161$	27.3217	+	88.5642i	0.169700	+	0.550088i
$162$	−15.0612			−0.0929702
$163$	86.2901	−	149.459i	0.529387	−	0.916926i	−0.470025	−	0.882653i	$-0.655755\pi$
$163$	86.2901	−	149.459i	0.529387	−	0.916926i	0.999413	−	0.0342728i	$-0.0109115\pi$
$164$	−23.4098	+	13.5156i	−0.142743	+	0.0824124i
$165$	−26.7782	−	46.3813i	−0.162292	−	0.281099i
$166$	43.9680	+	25.3849i	0.264867	+	0.152921i
$167$			156.923i			0.939658i	0.882758	+	0.469829i	$0.155684\pi$
$167$			156.923i			0.939658i	−0.882758	+	0.469829i	$0.844316\pi$
$168$	−23.4718	+	102.852i	−0.139713	+	0.612216i
$169$	131.539			0.778339
$170$	−4.63748	+	8.03236i	−0.0272793	+	0.0472492i
$171$	−72.6869	+	41.9658i	−0.425069	+	0.245414i
$172$	4.56108	+	7.90003i	0.0265179	+	0.0459304i
$173$	−41.2245	−	23.8010i	−0.238292	−	0.137578i	0.376100	−	0.926579i	$-0.377265\pi$
$173$	−41.2245	−	23.8010i	−0.238292	−	0.137578i	−0.614391	+	0.789001i	$0.710598\pi$
$174$		−	80.1488i		−	0.460625i
$175$	34.1227	+	7.78710i	0.194987	+	0.0444977i
$176$	135.006			0.767079
$177$	61.5680	−	106.639i	0.347842	−	0.602479i
$178$	157.237	−	90.7805i	0.883351	−	0.510003i
$179$	−14.7747	−	25.5905i	−0.0825402	−	0.142964i	0.821800	−	0.569776i	$-0.192970\pi$
$179$	−14.7747	−	25.5905i	−0.0825402	−	0.142964i	−0.904340	+	0.426812i	$0.859637\pi$
$180$	6.96858	+	4.02331i	0.0387143	+	0.0223517i
$181$			10.3249i			0.0570439i	0.999593	+	0.0285219i	$0.00908005\pi$
$181$			10.3249i			0.0570439i	−0.999593	+	0.0285219i	$0.990920\pi$
$182$	−68.5112	+	21.1354i	−0.376435	+	0.116129i
$183$	200.427			1.09523
$184$	−57.6037	+	99.7725i	−0.313064	+	0.542242i
$185$	79.4221	−	45.8544i	0.429309	−	0.247862i
$186$	−27.1305	−	46.9913i	−0.145863	−	0.252642i
$187$	−29.6830	−	17.1375i	−0.158733	−	0.0916444i
$188$		−	16.5122i		−	0.0878308i
$189$	26.6642	+	24.7391i	0.141080	+	0.130895i
$190$	−104.690			−0.551000
$191$	59.5045	−	103.065i	0.311542	−	0.539607i	−0.667154	−	0.744920i	$-0.732488\pi$
$191$	59.5045	−	103.065i	0.311542	−	0.539607i	0.978696	+	0.205313i	$0.0658212\pi$
$192$	−104.933	+	60.5833i	−0.546528	+	0.315538i
$193$	−4.95254	−	8.57805i	−0.0256608	−	0.0444459i	0.852910	−	0.522058i	$-0.174836\pi$
$193$	−4.95254	−	8.57805i	−0.0256608	−	0.0444459i	−0.878571	+	0.477612i	$0.841502\pi$
$194$	221.960	+	128.149i	1.14412	+	0.660560i
$195$			23.7047i			0.121562i
$196$	48.5612	−	33.1132i	0.247761	−	0.168945i
$197$	−290.342			−1.47382			−0.736908	−	0.675994i	$-0.763715\pi$
$197$	−290.342			−1.47382			−0.736908	+	0.675994i	$0.763715\pi$
$198$	34.7115	−	60.1222i	0.175311	−	0.303647i
$199$	294.002	−	169.742i	1.47740	−	0.852977i	0.477725	−	0.878509i	$-0.341461\pi$
$199$	294.002	−	169.742i	1.47740	−	0.852977i	0.999674	+	0.0255322i	$0.00812803\pi$
$200$	21.7530	+	37.6773i	0.108765	+	0.188387i
$201$	−17.1068	−	9.87662i	−0.0851085	−	0.0491374i
$202$		−	191.215i		−	0.946607i
$203$	−131.650	+	141.895i	−0.648523	+	0.698989i
$204$	5.14967			0.0252435
$205$	−25.1950	+	43.6390i	−0.122902	+	0.212873i
$206$	−81.1285	+	46.8396i	−0.393828	+	0.227377i
$207$	19.8606	+	34.3995i	0.0959449	+	0.166181i
$208$	−51.7494	−	29.8775i	−0.248795	−	0.143642i
$209$		−	386.875i		−	1.85108i
$210$	13.3742	+	43.3530i	0.0636867	+	0.206443i
$211$	11.1098			0.0526531			0.0263265	−	0.999653i	$-0.491619\pi$
$211$	11.1098			0.0526531			0.0263265	+	0.999653i	$0.491619\pi$
$212$	55.5371	−	96.1931i	0.261968	−	0.453741i
$213$	−149.239	+	86.1630i	−0.700651	+	0.404521i
$214$	82.5903	+	143.051i	0.385936	+	0.668461i
$215$	14.7267	+	8.50248i	0.0684964	+	0.0395464i
$216$			45.2128i			0.209319i
$217$	−29.1552	+	127.757i	−0.134356	+	0.588741i
$218$	−88.2890			−0.404996
$219$	−90.1276	+	156.106i	−0.411542	+	0.712811i
$220$	−32.1210	+	18.5451i	−0.146005	+	0.0842958i
$221$	7.58524	+	13.1380i	0.0343224	+	0.0594481i
$222$	102.952	+	59.4392i	0.463746	+	0.267744i
$223$		−	359.376i		−	1.61155i	−0.592220	−	0.805776i	$-0.701748\pi$
$223$		−	359.376i		−	1.61155i	0.592220	−	0.805776i	$-0.298252\pi$
$224$	126.027	+	28.7604i	0.562619	+	0.128395i
$225$	15.0000			0.0666667
$226$	88.8658	−	153.920i	0.393212	−	0.681062i
$227$	−64.3040	+	37.1259i	−0.283277	+	0.163550i	−0.634906	−	0.772589i	$-0.718961\pi$
$227$	−64.3040	+	37.1259i	−0.283277	+	0.163550i	0.351629	+	0.936140i	$0.385628\pi$
$228$	29.0631	+	50.3388i	0.127470	+	0.220784i
$229$	288.608	+	166.628i	1.26030	+	0.727633i	0.973132	−	0.230248i	$-0.0739538\pi$
$229$	288.608	+	166.628i	1.26030	+	0.727633i	0.287165	+	0.957881i	$0.407287\pi$
$230$			49.5453i			0.215414i
$231$	−160.208	+	49.4235i	−0.693541	+	0.213954i
$232$	−240.602			−1.03708
$233$	132.338	−	229.216i	0.567975	−	0.983761i	−0.428791	−	0.903404i	$-0.641060\pi$
$233$	132.338	−	229.216i	0.567975	−	0.983761i	0.996766	−	0.0803575i	$-0.0256062\pi$
$234$	−26.6107	+	15.3637i	−0.113721	+	0.0656568i
$235$	−15.3905	−	26.6571i	−0.0654914	−	0.113434i
$236$	−73.8520	−	42.6385i	−0.312932	−	0.180671i
$237$		−	223.428i		−	0.942735i
$238$	21.2850	+	19.7483i	0.0894328	+	0.0829759i
$239$	−266.197			−1.11380			−0.556898	−	0.830581i	$-0.688009\pi$
$239$	−266.197			−1.11380			−0.556898	+	0.830581i	$0.688009\pi$
$240$	−18.9061	+	32.7463i	−0.0787755	+	0.136443i
$241$	−29.4197	+	16.9855i	−0.122074	+	0.0704792i	−0.559793	−	0.828632i	$-0.689120\pi$
$241$	−29.4197	+	16.9855i	−0.122074	+	0.0704792i	0.437720	+	0.899111i	$0.355786\pi$
$242$	58.7551	+	101.767i	0.242790	+	0.420524i
$243$	13.5000	+	7.79423i	0.0555556	+	0.0320750i
$244$		−	138.805i		−	0.568871i
$245$	47.5329	−	98.7199i	0.194012	−	0.402938i
$246$	−65.3185			−0.265522
$247$	−85.6174	+	148.294i	−0.346629	+	0.600380i
$248$	−141.065	+	81.4441i	−0.568812	+	0.328404i
$249$	−26.2736	−	45.5073i	−0.105517	−	0.182760i
$250$	16.2032	+	9.35495i	0.0648130	+	0.0374198i
$251$			84.6771i			0.337359i	0.985671	+	0.168680i	$0.0539503\pi$
$251$			84.6771i			0.337359i	−0.985671	+	0.168680i	$0.946050\pi$
$252$	17.1329	−	18.4661i	0.0679876	−	0.0732781i
$253$	−183.091			−0.723680
$254$	−165.172	+	286.087i	−0.650285	+	1.12633i
$255$	8.31357	−	4.79984i	0.0326022	−	0.0188229i
$256$	103.763	+	179.723i	0.405325	+	0.702044i
$257$	27.6440	+	15.9603i	0.107564	+	0.0621022i	0.552817	−	0.833303i	$-0.313553\pi$
$257$	27.6440	+	15.9603i	0.107564	+	0.0621022i	−0.445253	+	0.895405i	$0.646886\pi$
$258$			22.0428i			0.0854374i
$259$	−84.6315	−	274.336i	−0.326763	−	1.05921i
$260$	16.4165			0.0631404
$261$	−41.4774	+	71.8409i	−0.158917	+	0.275253i
$262$	213.164	−	123.070i	0.813603	−	0.469734i
$263$	74.0405	+	128.242i	0.281523	+	0.487612i	0.971760	−	0.235971i	$-0.0758272\pi$
$263$	74.0405	+	128.242i	0.281523	+	0.487612i	−0.690237	+	0.723583i	$0.742494\pi$
$264$	−180.483	−	104.202i	−0.683649	−	0.394705i
$265$		−	207.057i		−	0.781349i
$266$	−72.9165	+	319.517i	−0.274122	+	1.20119i
$267$	−187.917			−0.703811
$268$	−6.83998	+	11.8472i	−0.0255223	+	0.0442060i
$269$	−78.8909	+	45.5477i	−0.293275	+	0.169322i	−0.639418	−	0.768859i	$-0.720825\pi$
$269$	−78.8909	+	45.5477i	−0.293275	+	0.169322i	0.346143	+	0.938182i	$0.387491\pi$
$270$	9.72194	+	16.8389i	0.0360072	+	0.0623663i
$271$	−108.045	−	62.3797i	−0.398689	−	0.230183i	0.287229	−	0.957862i	$-0.407266\pi$
$271$	−108.045	−	62.3797i	−0.398689	−	0.230183i	−0.685918	+	0.727679i	$0.740599\pi$
$272$			24.1990i			0.0889670i
$273$	72.3474	+	16.5103i	0.265009	+	0.0604772i
$274$	−416.010			−1.51828
$275$	−34.5706	+	59.8780i	−0.125711	+	0.217738i
$276$	23.8232	−	13.7543i	0.0863158	−	0.0498345i
$277$	61.9619	+	107.321i	0.223689	+	0.387441i	0.955925	−	0.293610i	$-0.0948566\pi$
$277$	61.9619	+	107.321i	0.223689	+	0.387441i	−0.732236	+	0.681051i	$0.761523\pi$
$278$	22.8033	+	13.1655i	0.0820261	+	0.0473578i
$279$			56.1606i			0.201292i
$280$	130.143	−	40.1486i	0.464798	−	0.143388i
$281$	−17.8049			−0.0633627			−0.0316814	−	0.999498i	$-0.510086\pi$
$281$	−17.8049			−0.0633627			−0.0316814	+	0.999498i	$0.510086\pi$
$282$	19.9501	−	34.5545i	0.0707449	−	0.122534i
$283$	−96.2623	+	55.5770i	−0.340149	+	0.196385i	−0.660338	−	0.750968i	$-0.729587\pi$
$283$	−96.2623	+	55.5770i	−0.340149	+	0.196385i	0.320189	+	0.947354i	$0.396254\pi$
$284$	59.6716	+	103.354i	0.210111	+	0.363923i
$285$	93.8383	+	54.1776i	0.329257	+	0.190097i
$286$		−	141.635i		−	0.495228i
$287$	115.639	+	107.290i	0.402924	+	0.373834i
$288$	55.4000			0.192361
$289$	−141.428	+	244.961i	−0.489371	+	0.847615i
$290$	−89.6091	+	51.7358i	−0.308997	+	0.178399i
$291$	−132.635	−	229.731i	−0.455791	−	0.789452i
$292$	108.110	+	62.4173i	0.370239	+	0.213758i
$293$			76.6488i			0.261600i	0.991409	+	0.130800i	$0.0417546\pi$
$293$			76.6488i			0.261600i	−0.991409	+	0.130800i	$0.958245\pi$
$294$	141.630	−	10.6231i	0.481734	−	0.0361332i
$295$	−158.968			−0.538874
$296$	178.433	−	309.055i	0.602814	−	1.04411i
$297$	−62.2270	+	35.9268i	−0.209519	+	0.120966i
$298$	154.131	+	266.963i	0.517218	+	0.895847i
$299$	70.1810	+	40.5190i	0.234719	+	0.135515i
$300$		−	10.3881i		−	0.0346272i
$301$	36.2070	−	39.0244i	0.120289	−	0.129649i
$302$	440.540			1.45874
$303$	−98.9544	+	171.394i	−0.326582	+	0.565657i
$304$	−236.549	+	136.572i	−0.778122	+	0.449249i
$305$	−129.375	−	224.084i	−0.424181	−	0.734703i
$306$	10.7765	+	6.22184i	0.0352174	+	0.0203328i
$307$			357.562i			1.16470i	0.812939	+	0.582349i	$0.197866\pi$
$307$			357.562i			1.16470i	−0.812939	+	0.582349i	$0.802134\pi$
$308$	34.2279	+	110.951i	0.111129	+	0.360230i
$309$	96.9588			0.313783
$310$	−35.0253	+	60.6656i	−0.112985	+	0.195695i
$311$	272.856	−	157.533i	0.877349	−	0.506538i	0.00756579	−	0.999971i	$-0.497592\pi$
$311$	272.856	−	157.533i	0.877349	−	0.506538i	0.869784	+	0.493434i	$0.164258\pi$
$312$	46.1210	+	79.8839i	0.147824	+	0.256038i
$313$	−227.260	−	131.209i	−0.726070	−	0.419197i	0.0909126	−	0.995859i	$-0.471022\pi$
$313$	−227.260	−	131.209i	−0.726070	−	0.419197i	−0.816983	+	0.576662i	$0.804355\pi$
$314$		−	362.508i		−	1.15449i
$315$	10.4475	−	45.7805i	0.0331666	−	0.145335i
$316$	−154.734			−0.489664
$317$	154.797	−	268.117i	0.488320	−	0.845795i	−0.511590	−	0.859230i	$-0.670943\pi$
$317$	154.797	−	268.117i	0.488320	−	0.845795i	0.999910	+	0.0134349i	$0.00427658\pi$
$318$	232.441	−	134.200i	0.730948	−	0.422013i
$319$	−191.186	−	331.144i	−0.599330	−	1.03807i
$320$	135.468	+	78.2127i	0.423339	+	0.244415i
$321$		−	170.963i		−	0.532597i
$322$	151.214	+	34.5082i	0.469607	+	0.107168i
$323$	69.3450			0.214690
$324$	5.39784	−	9.34933i	0.0166600	−	0.0288560i
$325$	26.5026	−	15.3013i	0.0815465	−	0.0470809i
$326$	−144.403	−	250.114i	−0.442955	−	0.767221i
$327$	79.1374	+	45.6900i	0.242010	+	0.139725i
$328$			196.082i			0.597812i
$329$	−92.0778	+	28.4056i	−0.279872	+	0.0863391i
$330$	−89.6248			−0.271590
$331$	43.4062	−	75.1818i	0.131137	−	0.227135i	−0.792978	−	0.609250i	$-0.791471\pi$
$331$	43.4062	−	75.1818i	0.131137	−	0.227135i	0.924115	+	0.382115i	$0.124804\pi$
$332$	−31.5157	+	18.1956i	−0.0949269	+	0.0548061i
$333$	−61.5201	−	106.556i	−0.184745	−	0.319988i
$334$	227.422	+	131.302i	0.680905	+	0.393121i
$335$			25.5013i			0.0761233i
$336$	86.7747	+	80.5098i	0.258258	+	0.239613i
$337$	373.915			1.10954			0.554770	−	0.832004i	$-0.312806\pi$
$337$	373.915			1.10954			0.554770	+	0.832004i	$0.312806\pi$
$338$	110.063	−	190.635i	0.325630	−	0.564008i
$339$	−159.309	+	91.9770i	−0.469937	+	0.271318i
$340$	−3.32410	−	5.75750i	−0.00977675	−	0.0169338i
$341$	−224.185	−	129.433i	−0.657435	−	0.379570i
$342$			140.456i			0.410691i
$343$	−268.190	−	213.830i	−0.781894	−	0.623412i
$344$	66.1714			0.192359
$345$	25.6399	−	44.4096i	0.0743186	−	0.128724i
$346$	−68.9877	+	39.8301i	−0.199386	+	0.115116i
$347$	165.439	+	286.549i	0.476770	+	0.825790i	0.999646	−	0.0266188i	$-0.00847401\pi$
$347$	165.439	+	286.549i	0.476770	+	0.825790i	−0.522875	+	0.852409i	$0.675141\pi$
$348$	49.7529	+	28.7249i	0.142968	+	0.0825427i
$349$			250.907i			0.718932i	0.933158	+	0.359466i	$0.117041\pi$
$349$			250.907i			0.718932i	−0.933158	+	0.359466i	$0.882959\pi$
$350$	39.8371	−	42.9371i	0.113820	−	0.122677i
$351$	31.8031			0.0906073
$352$	−127.681	+	221.149i	−0.362729	+	0.628265i
$353$	−108.875	+	62.8589i	−0.308427	+	0.178071i	−0.646222	−	0.763149i	$-0.723652\pi$
$353$	−108.875	+	62.8589i	−0.308427	+	0.178071i	0.337795	+	0.941220i	$0.390319\pi$
$354$	−103.032	−	178.456i	−0.291050	−	0.504114i
$355$	192.666	+	111.236i	0.542722	+	0.313341i
$356$			130.141i			0.365564i
$357$	−8.85886	−	28.7163i	−0.0248147	−	0.0804379i
$358$	−49.4498			−0.138128
$359$	178.790	−	309.674i	0.498023	−	0.862601i	−0.501975	−	0.864882i	$-0.667393\pi$
$359$	178.790	−	309.674i	0.498023	−	0.862601i	0.999997	+	0.00228149i	$0.000726221\pi$
$360$	50.5494	−	29.1847i	0.140415	−	0.0810687i
$361$	210.861	+	365.223i	0.584103	+	1.01170i
$362$	14.9636	+	8.63921i	0.0413358	+	0.0238652i
$363$		−	121.624i		−	0.335053i
$364$	11.4341	−	50.1037i	0.0314123	−	0.137647i
$365$	232.709			0.637558
$366$	167.704	−	290.472i	0.458207	−	0.793638i
$367$	603.879	−	348.650i	1.64545	−	0.949999i	0.666598	−	0.745418i	$-0.267750\pi$
$367$	603.879	−	348.650i	1.64545	−	0.949999i	0.978850	−	0.204582i	$-0.0655834\pi$
$368$	64.6334	+	111.948i	0.175634	+	0.304208i
$369$	58.5479	+	33.8026i	0.158666	+	0.0916060i
$370$		−	153.471i		−	0.414787i
$371$	−631.946	−	144.215i	−1.70336	−	0.388721i
$372$	38.8936			0.104553
$373$	72.6433	−	125.822i	0.194754	−	0.337324i	−0.752066	−	0.659088i	$-0.770942\pi$
$373$	72.6433	−	125.822i	0.194754	−	0.337324i	0.946820	+	0.321764i	$0.104276\pi$
$374$	−49.6735	+	28.6790i	−0.132817	+	0.0766818i
$375$	−9.68246	−	16.7705i	−0.0258199	−	0.0447214i
$376$	−103.731	−	59.8890i	−0.275880	−	0.159279i
$377$			169.242i			0.448918i
$378$	58.1642	−	17.9434i	0.153873	−	0.0474693i
$379$	−222.630			−0.587415			−0.293708	−	0.955895i	$-0.594889\pi$
$379$	−222.630			−0.587415			−0.293708	+	0.955895i	$0.594889\pi$
$380$	37.5203	−	64.9871i	0.0987377	−	0.171019i
$381$	296.103	−	170.955i	0.777172	−	0.448701i
$382$	−99.5787	−	172.475i	−0.260677	−	0.451506i
$383$	−30.1012	−	17.3789i	−0.0785932	−	0.0453758i	0.460188	−	0.887821i	$-0.347782\pi$
$383$	−30.1012	−	17.3789i	−0.0785932	−	0.0453758i	−0.538782	+	0.842445i	$0.681115\pi$
$384$			74.8271i			0.194862i
$385$	158.671	+	147.215i	0.412132	+	0.382378i
$386$	−16.5758			−0.0429425
$387$	11.4073	−	19.7580i	0.0294762	−	0.0510542i
$388$	−159.098	+	91.8555i	−0.410047	+	0.236741i
$389$	−276.283	−	478.537i	−0.710240	−	1.23017i	−0.964767	−	0.263105i	$-0.915253\pi$
$389$	−276.283	−	478.537i	−0.710240	−	1.23017i	0.254528	−	0.967066i	$-0.418080\pi$
$390$	34.3543	+	19.8344i	0.0880879	+	0.0508576i
$391$		−	32.8180i		−	0.0839335i
$392$	−31.8901	−	425.165i	−0.0813523	−	1.08460i
$393$	−254.758			−0.648239
$394$	−242.938	+	420.781i	−0.616594	+	1.06797i
$395$	−249.800	+	144.222i	−0.632406	+	0.365120i
$396$	24.8808	+	43.0949i	0.0628304	+	0.108825i
$397$	49.9274	+	28.8256i	0.125762	+	0.0726085i	0.561561	−	0.827435i	$-0.310201\pi$
$397$	49.9274	+	28.8256i	0.125762	+	0.0726085i	−0.435799	+	0.900044i	$0.643534\pi$
$398$		−	568.115i		−	1.42743i
$399$	230.710	−	248.663i	0.578220	−	0.623215i
$400$	48.8154			0.122038
$401$	−281.160	+	486.983i	−0.701146	+	1.21442i	0.266918	+	0.963719i	$0.413995\pi$
$401$	−281.160	+	486.983i	−0.701146	+	1.21442i	−0.968064	+	0.250701i	$0.919339\pi$
$402$	−28.6276	+	16.5282i	−0.0712130	+	0.0411148i
$403$	57.2886	+	99.2268i	0.142155	+	0.246220i
$404$	118.698	+	68.5302i	0.293806	+	0.169629i
$405$		−	20.1246i		−	0.0496904i
$406$	95.4866	+	309.524i	0.235189	+	0.762373i
$407$	567.143			1.39347
$408$	18.6776	−	32.3506i	0.0457785	−	0.0792906i
$409$	−174.709	+	100.869i	−0.427163	+	0.246622i	−0.698137	−	0.715964i	$-0.745987\pi$
$409$	−174.709	+	100.869i	−0.427163	+	0.246622i	0.270975	+	0.962587i	$0.412654\pi$
$410$	42.1629	+	73.0283i	0.102836	+	0.178118i
$411$	372.888	+	215.287i	0.907270	+	0.523813i
$412$		−	67.1482i		−	0.162981i
$413$	−110.721	+	485.175i	−0.268090	+	1.17476i
$414$	66.4719			0.160560
$415$	−33.9191	+	58.7496i	−0.0817328	+	0.141565i
$416$	97.8831	−	56.5128i	0.235296	−	0.135848i
$417$	−13.6264	−	23.6016i	−0.0326772	−	0.0565985i
$418$	−560.683	−	323.710i	−1.34135	−	0.774427i
$419$			304.381i			0.726447i	0.931702	+	0.363223i	$0.118324\pi$
$419$			304.381i			0.726447i	−0.931702	+	0.363223i	$0.881676\pi$
$420$	−31.7049	−	7.23534i	−0.0754879	−	0.0172270i
$421$	556.622			1.32214			0.661071	−	0.750323i	$-0.270102\pi$
$421$	556.622			1.32214			0.661071	+	0.750323i	$0.270102\pi$
$422$	9.29592	−	16.1010i	0.0220283	−	0.0381541i
$423$	−35.7643	+	20.6485i	−0.0845491	+	0.0488144i
$424$	−402.861	−	697.776i	−0.950144	−	1.64570i
$425$	−10.7328	−	6.19657i	−0.0252536	−	0.0145802i
$426$			288.381i			0.676951i
$427$	−774.022	+	238.782i	−1.81270	+	0.559209i
$428$	−118.400			−0.276635
$429$	−73.2968	+	126.954i	−0.170855	+	0.295930i
$430$	24.6446	−	14.2286i	0.0573131	−	0.0330897i
$431$	90.2225	+	156.270i	0.209333	+	0.362575i	0.951505	−	0.307634i	$-0.0995374\pi$
$431$	90.2225	+	156.270i	0.209333	+	0.362575i	−0.742172	+	0.670210i	$0.766204\pi$
$432$	43.9338	+	25.3652i	0.101699	+	0.0587158i
$433$			724.048i			1.67217i	0.548603	+	0.836083i	$0.315160\pi$
$433$			724.048i			1.67217i	−0.548603	+	0.836083i	$0.684840\pi$
$434$	160.758	+	149.152i	0.370410	+	0.343668i
$435$	107.094			0.246193
$436$	31.6423	−	54.8061i	0.0725741	−	0.125702i
$437$	320.801	−	185.214i	0.734098	−	0.423832i
$438$	150.825	+	261.237i	0.344350	+	0.596432i
$439$	354.272	+	204.539i	0.806997	+	0.465920i	0.845912	−	0.533322i	$-0.179057\pi$
$439$	354.272	+	204.539i	0.806997	+	0.465920i	−0.0389147	+	0.999243i	$0.512390\pi$
$440$			269.049i			0.611474i
$441$	−132.447	−	63.7721i	−0.300333	−	0.144608i
$442$	25.3873			0.0574372
$443$	199.400	−	345.370i	0.450112	−	0.779617i	−0.548280	−	0.836295i	$-0.684717\pi$
$443$	199.400	−	345.370i	0.450112	−	0.779617i	0.998393	+	0.0566775i	$0.0180507\pi$
$444$	−73.7946	+	42.6053i	−0.166204	+	0.0959579i
$445$	121.300	+	210.098i	0.272585	+	0.472131i
$446$	−520.830	−	300.702i	−1.16778	−	0.674219i
$447$		−	319.054i		−	0.713767i
$448$	333.061	−	358.979i	0.743441	−	0.801292i
$449$	−519.843			−1.15778			−0.578889	−	0.815406i	$-0.696514\pi$
$449$	−519.843			−1.15778			−0.578889	+	0.815406i	$0.696514\pi$
$450$	12.5510	−	21.7389i	0.0278911	−	0.0483087i
$451$	−269.871	+	155.810i	−0.598384	+	0.345477i
$452$	63.6980	+	110.328i	0.140925	+	0.244089i
$453$	−394.876	−	227.982i	−0.871690	−	0.503270i
$454$			124.258i			0.273695i
$455$	−28.2410	−	91.5442i	−0.0620680	−	0.201196i
$456$	421.642			0.924654
$457$	−116.891	+	202.462i	−0.255780	+	0.443024i	−0.965107	−	0.261856i	$-0.915666\pi$
$457$	−116.891	+	202.462i	−0.255780	+	0.443024i	0.709327	+	0.704880i	$0.248999\pi$
$458$	482.975	−	278.846i	1.05453	−	0.608834i
$459$	−6.43966	−	11.1538i	−0.0140298	−	0.0243003i
$460$	−30.7556	−	17.7567i	−0.0668599	−	0.0386016i
$461$			745.085i			1.61624i	0.589021	+	0.808118i	$0.299514\pi$
$461$			745.085i			1.61624i	−0.589021	+	0.808118i	$0.700486\pi$
$462$	−62.4236	+	273.538i	−0.135116	+	0.592073i
$463$	742.448			1.60356			0.801779	−	0.597620i	$-0.203887\pi$
$463$	742.448			1.60356			0.801779	+	0.597620i	$0.203887\pi$
$464$	−134.982	+	233.796i	−0.290910	+	0.503871i
$465$	62.7894	−	36.2515i	0.135031	−	0.0779602i
$466$	−221.463	−	383.585i	−0.475242	−	0.823144i
$467$	−524.404	−	302.765i	−1.12292	−	0.648318i	−0.180776	−	0.983524i	$-0.557861\pi$
$467$	−524.404	−	302.765i	−1.12292	−	0.648318i	−0.942145	+	0.335206i	$0.891194\pi$
$468$		−	22.0251i		−	0.0470621i
$469$	77.8308	+	17.7617i	0.165951	+	0.0378713i
$470$	−51.5108			−0.109598
$471$	−187.600	+	324.933i	−0.398301	+	0.689878i
$472$	−535.716	+	309.296i	−1.13499	+	0.655287i
$473$	52.5808	+	91.0726i	0.111164	+	0.192542i
$474$	−323.806	−	186.950i	−0.683135	−	0.394408i
$475$		−	139.886i		−	0.294497i
$476$	−19.8873	+	6.13515i	−0.0417801	+	0.0128890i
$477$	−277.797			−0.582383
$478$	−222.736	+	385.790i	−0.465974	+	0.807091i
$479$	260.542	−	150.424i	0.543930	−	0.314038i	−0.202740	−	0.979233i	$-0.564985\pi$
$479$	260.542	−	150.424i	0.543930	−	0.314038i	0.746670	+	0.665194i	$0.231651\pi$
$480$	−35.7606	−	61.9391i	−0.0745012	−	0.129040i
$481$	−217.393	−	125.512i	−0.451960	−	0.260939i
$482$			56.8492i			0.117944i
$483$	−117.681	−	109.185i	−0.243647	−	0.226056i
$484$	−84.2300			−0.174029
$485$	−171.231	+	296.581i	−0.353054	+	0.611507i
$486$	22.5918	−	13.0434i	0.0464851	−	0.0268382i
$487$	−295.602	−	511.998i	−0.606986	−	1.05133i	−0.991734	−	0.128309i	$-0.959045\pi$
$487$	−295.602	−	511.998i	−0.606986	−	1.05133i	0.384748	−	0.923021i	$-0.374288\pi$
$488$	−871.979	−	503.438i	−1.78684	−	1.03163i
$489$			298.918i			0.611284i
$490$	−103.299	−	151.490i	−0.210814	−	0.309163i
$491$	−308.637			−0.628589			−0.314295	−	0.949325i	$-0.601768\pi$
$491$	−308.637			−0.628589			−0.314295	+	0.949325i	$0.601768\pi$
$492$	23.4098	−	40.5469i	0.0475808	−	0.0824124i
$493$	59.3556	−	34.2690i	0.120397	−	0.0695111i
$494$	143.278	+	248.164i	0.290036	+	0.502357i
$495$	80.3347	+	46.3813i	0.162292	+	0.0936995i
$496$			182.767i			0.368481i
$497$	473.687	−	510.548i	0.953093	−	1.02726i
$498$	−87.9359			−0.176578
$499$	447.344	−	774.822i	0.896480	−	1.55275i	0.0645183	−	0.997917i	$-0.479449\pi$
$499$	447.344	−	774.822i	0.896480	−	1.55275i	0.831962	−	0.554833i	$-0.187218\pi$
$500$	−11.6143	+	6.70552i	−0.0232286	+	0.0134110i
$501$	−135.899	−	235.384i	−0.271256	−	0.469829i
$502$	122.719	+	70.8520i	0.244461	+	0.141140i
$503$			609.546i			1.21182i	0.795533	+	0.605911i	$0.207191\pi$
$503$			609.546i			1.21182i	−0.795533	+	0.605911i	$0.792809\pi$
$504$	−53.8650	−	174.606i	−0.106875	−	0.346440i
$505$	255.499			0.505939
$506$	−153.198	+	265.347i	−0.302763	+	0.524401i
$507$	−197.309	+	113.916i	−0.389169	+	0.224687i
$508$	−118.394	−	205.064i	−0.233058	−	0.403669i
$509$	205.570	+	118.686i	0.403871	+	0.233175i	0.688153	−	0.725566i	$-0.258422\pi$
$509$	205.570	+	118.686i	0.403871	+	0.233175i	−0.284282	+	0.958741i	$0.591755\pi$
$510$		−	16.0647i		−	0.0314994i
$511$	162.081	−	710.233i	0.317185	−	1.38989i
$512$	520.094			1.01581
$513$	72.6869	−	125.897i	0.141690	−	0.245414i
$514$	46.2612	−	26.7089i	0.0900023	−	0.0519629i
$515$	−62.5867	−	108.403i	−0.121527	−	0.210492i
$516$	−13.6833	−	7.90003i	−0.0265179	−	0.0153101i
$517$		−	190.355i		−	0.368191i
$518$	−468.399	−	106.893i	−0.904245	−	0.206356i
$519$	82.4490			0.158861
$520$	59.5419	−	103.130i	0.114504	−	0.198326i
$521$	−32.6670	+	18.8603i	−0.0627006	+	0.0362002i	−0.531023	−	0.847358i	$-0.678192\pi$
$521$	−32.6670	+	18.8603i	−0.0627006	+	0.0362002i	0.468322	+	0.883558i	$0.344859\pi$
$522$	69.4109	+	120.223i	0.132971	+	0.230313i
$523$	40.5068	+	23.3866i	0.0774509	+	0.0447163i	0.538225	−	0.842801i	$-0.319095\pi$
$523$	40.5068	+	23.3866i	0.0774509	+	0.0447163i	−0.460774	+	0.887517i	$0.652428\pi$
$524$			176.431i			0.336700i
$525$	−57.9279	+	17.8705i	−0.110339	+	0.0340391i
$526$	247.808			0.471118
$527$	23.2002	−	40.1839i	0.0440231	−	0.0762503i
$528$	−202.509	+	116.919i	−0.383540	+	0.221437i
$529$	176.846	+	306.306i	0.334303	+	0.579029i
$530$	−300.081	−	173.252i	−0.566190	−	0.326890i
$531$			213.278i			0.401653i
$532$	−172.210	−	159.777i	−0.323702	−	0.300332i
$533$	137.926			0.258774
$534$	−157.237	+	272.342i	−0.294450	+	0.510003i
$535$	−191.143	+	110.356i	−0.357277	+	0.206274i
$536$	49.6166	+	85.9385i	0.0925683	+	0.160333i
$537$	44.3241	+	25.5905i	0.0825402	+	0.0476546i
$538$			152.445i			0.283355i
$539$	559.820	−	381.733i	1.03863	−	0.708225i
$540$	−13.9372			−0.0258096
$541$	195.629	−	338.839i	0.361606	−	0.626320i	−0.626619	−	0.779326i	$-0.715562\pi$
$541$	195.629	−	338.839i	0.361606	−	0.626320i	0.988225	+	0.153005i	$0.0488951\pi$
$542$	−180.809	+	104.390i	−0.333596	+	0.192602i
$543$	−8.94167	−	15.4874i	−0.0164672	−	0.0285219i
$544$	−39.6397	−	22.8860i	−0.0728671	−	0.0420699i
$545$		−	117.971i		−	0.216461i
$546$	84.4631	−	91.0356i	0.154694	−	0.166732i
$547$	−389.827			−0.712664			−0.356332	−	0.934359i	$-0.615973\pi$
$547$	−389.827			−0.712664			−0.356332	+	0.934359i	$0.615973\pi$
$548$	149.096	−	258.241i	0.272072	−	0.471243i
$549$	−300.641	+	173.575i	−0.547615	+	0.316166i
$550$	57.8526	+	100.204i	0.105186	+	0.182188i
$551$	669.969	+	386.807i	1.21591	+	0.702009i
$552$		−	199.545i		−	0.361495i
$553$	266.185	+	862.849i	0.481347	+	1.56031i
$554$	207.382			0.374336
$555$	−79.4221	+	137.563i	−0.143103	+	0.247862i
$556$	−16.3451	+	9.43686i	−0.0293977	+	0.0169728i
$557$	−89.4085	−	154.860i	−0.160518	−	0.278025i	0.774537	−	0.632529i	$-0.217983\pi$
$557$	−89.4085	−	154.860i	−0.160518	−	0.278025i	−0.935055	+	0.354504i	$0.884650\pi$
$558$	81.3914	+	46.9913i	0.145863	+	0.0842139i
$559$		−	46.5456i		−	0.0832659i
$560$	33.9999	−	148.986i	0.0607141	−	0.266046i
$561$	59.3661			0.105822
$562$	−14.8979	+	25.8040i	−0.0265088	+	0.0459146i
$563$	−139.571	+	80.5815i	−0.247906	+	0.143129i	−0.618805	−	0.785545i	$-0.712383\pi$
$563$	−139.571	+	80.5815i	−0.247906	+	0.143129i	0.370899	+	0.928673i	$0.379050\pi$
$564$	14.3000	+	24.7683i	0.0253546	+	0.0439154i
$565$	205.667	+	118.742i	0.364012	+	0.210162i
$566$			186.012i			0.328644i
$567$	−61.4209	−	14.0168i	−0.108326	−	0.0247210i
$568$	865.704			1.52413
$569$	−6.24946	+	10.8244i	−0.0109832	+	0.0190235i	−0.871465	−	0.490458i	$-0.836829\pi$
$569$	−6.24946	+	10.8244i	−0.0109832	+	0.0190235i	0.860482	+	0.509482i	$0.170163\pi$
$570$	157.035	−	90.6642i	0.275500	−	0.159060i
$571$	−61.6982	−	106.864i	−0.108053	−	0.187153i	0.806929	−	0.590649i	$-0.201128\pi$
$571$	−61.6982	−	106.864i	−0.108053	−	0.187153i	−0.914981	+	0.403496i	$0.867795\pi$
$572$	87.9210	+	50.7612i	0.153708	+	0.0887434i
$573$			206.130i			0.359738i
$574$	252.251	−	77.8183i	0.439462	−	0.135572i
$575$	−66.2020			−0.115134
$576$	104.933	−	181.750i	0.182176	−	0.315538i
$577$	−143.692	+	82.9608i	−0.249033	+	0.143779i	−0.619322	−	0.785137i	$-0.712592\pi$
$577$	−143.692	+	82.9608i	−0.249033	+	0.143779i	0.370288	+	0.928917i	$0.379259\pi$
$578$	236.675	+	409.933i	0.409472	+	0.709227i
$579$	14.8576	+	8.57805i	0.0256608	+	0.0148153i
$580$		−	74.1673i		−	0.127875i
$581$	155.681	+	144.441i	0.267954	+	0.248608i
$582$	−443.920			−0.762749
$583$	640.239	−	1108.93i	1.09818	−	1.90210i
$584$	784.219	−	452.769i	1.34284	−	0.775290i
$585$	−20.5288	−	35.5570i	−0.0350920	−	0.0607812i
$586$	111.084	+	64.1345i	0.189564	+	0.109445i
$587$			186.037i			0.316929i	0.987365	+	0.158465i	$0.0506544\pi$
$587$			186.037i			0.316929i	−0.987365	+	0.158465i	$0.949346\pi$
$588$	−44.1649	+	91.7250i	−0.0751104	+	0.155995i
$589$	523.738			0.889199
$590$	−133.013	+	230.386i	−0.225446	+	0.390485i
$591$	435.512	−	251.443i	0.736908	−	0.425454i
$592$	−200.208	−	346.771i	−0.338190	−	0.585762i
$593$	494.838	+	285.695i	0.834465	+	0.481779i	0.855379	−	0.518003i	$-0.173324\pi$
$593$	494.838	+	285.695i	0.834465	+	0.481779i	−0.0209140	+	0.999781i	$0.506658\pi$
$594$			120.244i			0.202431i
$595$	−26.3875	+	28.4408i	−0.0443487	+	0.0477997i
$596$	−220.959			−0.370736
$597$	−294.002	+	509.227i	−0.492466	+	0.852977i
$598$	117.445	−	67.8071i	0.196397	−	0.113390i
$599$	−87.2619	−	151.142i	−0.145679	−	0.252324i	0.783947	−	0.620828i	$-0.213203\pi$
$599$	−87.2619	−	151.142i	−0.145679	−	0.252324i	−0.929626	+	0.368504i	$0.879870\pi$
$600$	−65.2591	−	37.6773i	−0.108765	−	0.0627956i
$601$		−	667.415i		−	1.11051i	−0.831681	−	0.555254i	$-0.812621\pi$
$601$		−	667.415i		−	1.11051i	0.831681	−	0.555254i	$-0.187379\pi$
$602$	−26.2611	−	85.1264i	−0.0436231	−	0.141406i
$603$	34.2136			0.0567390
$604$	−157.887	+	273.468i	−0.261402	+	0.452762i
$605$	−135.980	+	78.5081i	−0.224760	+	0.129765i
$606$	165.597	+	286.822i	0.273262	+	0.473303i
$607$	23.3123	+	13.4594i	0.0384057	+	0.0221736i	0.519080	−	0.854726i	$-0.326275\pi$
$607$	23.3123	+	13.4594i	0.0384057	+	0.0221736i	−0.480674	+	0.876899i	$0.659608\pi$
$608$		−	516.646i		−	0.849746i
$609$	74.5910	−	326.855i	0.122481	−	0.536707i
$610$	−433.009			−0.709852
$611$	−42.1265	+	72.9653i	−0.0689468	+	0.119419i
$612$	−7.72450	+	4.45974i	−0.0126217	+	0.00728716i
$613$	32.7197	+	56.6723i	0.0533764	+	0.0924507i	0.891479	−	0.453062i	$-0.149668\pi$
$613$	32.7197	+	56.6723i	0.0533764	+	0.0924507i	−0.838103	+	0.545513i	$0.816335\pi$
$614$	518.201	+	299.183i	0.843976	+	0.487270i
$615$		−	87.2780i		−	0.141915i
$616$	821.145	+	187.392i	1.33303	+	0.304208i
$617$	1059.51			1.71720			0.858601	−	0.512644i	$-0.171334\pi$
$617$	1059.51			1.71720			0.858601	+	0.512644i	$0.171334\pi$
$618$	81.1285	−	140.519i	0.131276	−	0.227377i
$619$	139.355	−	80.4565i	0.225129	−	0.129978i	−0.383194	−	0.923668i	$-0.625176\pi$
$619$	139.355	−	80.4565i	0.225129	−	0.129978i	0.608323	+	0.793690i	$0.291843\pi$
$620$	−25.1057	−	43.4844i	−0.0404931	−	0.0701361i
$621$	−59.5818	−	34.3995i	−0.0959449	−	0.0553938i
$622$		−	527.252i		−	0.847673i
$623$	725.711	−	223.879i	1.16487	−	0.359356i
$624$	103.499			0.165863
$625$	−12.5000	+	21.6506i	−0.0200000	+	0.0346410i
$626$	−380.311	+	219.573i	−0.607526	+	0.350755i
$627$	335.043	+	580.312i	0.534359	+	0.925538i
$628$	225.030	+	129.921i	0.358328	+	0.206881i
$629$			101.657i			0.161617i
$630$	−57.6061	−	53.4471i	−0.0914383	−	0.0848367i
$631$	−45.2151			−0.0716562			−0.0358281	−	0.999358i	$-0.511407\pi$
$631$	−45.2151			−0.0716562			−0.0358281	+	0.999358i	$0.511407\pi$
$632$	−561.212	+	972.048i	−0.887994	+	1.53805i
$633$	−16.6647	+	9.62137i	−0.0263265	+	0.0151996i
$634$	−259.048	−	448.684i	−0.408593	−	0.707703i
$635$	−382.267	−	220.702i	−0.601995	−	0.347562i
$636$			192.386i			0.302494i
$637$	−299.065	+	22.4318i	−0.469490	+	0.0352148i
$638$	−639.886			−1.00296
$639$	149.239	−	258.489i	0.233550	−	0.404521i
$640$	83.6592	−	48.3007i	0.130718	−	0.0754698i
$641$	−161.675	−	280.030i	−0.252224	−	0.436865i	0.711914	−	0.702267i	$-0.247829\pi$
$641$	−161.675	−	280.030i	−0.252224	−	0.436865i	−0.964138	+	0.265402i	$0.914495\pi$
$642$	−247.771	−	143.051i	−0.385936	−	0.222820i
$643$			363.744i			0.565698i	0.959164	+	0.282849i	$0.0912795\pi$
$643$			363.744i			0.565698i	−0.959164	+	0.282849i	$0.908720\pi$
$644$	−75.6153	+	81.4994i	−0.117415	+	0.126552i
$645$	−29.4535			−0.0456643
$646$	58.0232	−	100.499i	0.0898191	−	0.155571i
$647$	−1114.98	+	643.737i	−1.72331	+	0.994956i	−0.811503	+	0.584348i	$0.801350\pi$
$647$	−1114.98	+	643.737i	−1.72331	+	0.994956i	−0.911812	+	0.410608i	$0.865317\pi$
$648$	−39.1554	−	67.8192i	−0.0604250	−	0.104659i
$649$	−851.376	−	491.542i	−1.31183	−	0.757384i
$650$		−	51.2123i		−	0.0787882i
$651$	−66.9079	−	216.884i	−0.102777	−	0.333156i
$652$	207.013			0.317505
$653$	−308.886	+	535.007i	−0.473026	+	0.819306i	−0.999523	−	0.0308714i	$-0.990172\pi$
$653$	−308.886	+	535.007i	−0.473026	+	0.819306i	0.526497	+	0.850177i	$0.323505\pi$
$654$	132.434	−	76.4606i	0.202498	−	0.116912i
$655$	164.446	+	284.828i	0.251062	+	0.434852i
$656$	190.536	+	110.006i	0.290451	+	0.167692i
$657$		−	312.211i		−	0.475207i
$658$	−35.8773	+	157.213i	−0.0545247	+	0.238925i
$659$	−1229.62			−1.86589			−0.932945	−	0.360019i	$-0.882770\pi$
$659$	−1229.62			−1.86589			−0.932945	+	0.360019i	$0.882770\pi$
$660$	32.1210	−	55.6353i	0.0486682	−	0.0842958i
$661$	−606.437	+	350.127i	−0.917454	+	0.529692i	−0.882822	−	0.469708i	$-0.844359\pi$
$661$	−606.437	+	350.127i	−0.917454	+	0.529692i	−0.0346322	+	0.999400i	$0.511026\pi$
$662$	−72.6387	−	125.814i	−0.109726	−	0.190051i
$663$	−22.7557	−	13.1380i	−0.0343224	−	0.0198160i
$664$			263.979i			0.397558i
$665$	−426.936	−	97.4304i	−0.642009	−	0.146512i
$666$	−205.903			−0.309164
$667$	183.059	−	317.067i	0.274451	−	0.475363i
$668$	−163.014	+	94.1160i	−0.244032	+	0.140892i
$669$	311.229	+	539.064i	0.465215	+	0.805776i
$670$	36.9581	+	21.3378i	0.0551613	+	0.0318474i
$671$		−	1600.16i		−	2.38473i
$672$	−213.947	+	66.0018i	−0.318374	+	0.0982169i
$673$	−121.032			−0.179840			−0.0899201	−	0.995949i	$-0.528661\pi$
$673$	−121.032			−0.179840			−0.0899201	+	0.995949i	$0.528661\pi$
$674$	312.867	−	541.901i	0.464194	−	0.804007i
$675$	−22.5000	+	12.9904i	−0.0333333	+	0.0192450i
$676$	78.8920	+	136.645i	0.116704	+	0.202137i
$677$	−851.854	−	491.818i	−1.25828	−	0.726467i	−0.285538	−	0.958367i	$-0.592172\pi$
$677$	−851.854	−	491.818i	−1.25828	−	0.726467i	−0.972739	+	0.231901i	$0.925506\pi$
$678$			307.840i			0.454042i
$679$	785.912	+	729.171i	1.15745	+	1.07389i
$680$	−48.2254			−0.0709197
$681$	64.3040	−	111.378i	0.0944258	−	0.163550i
$682$	−375.166	+	216.602i	−0.550097	+	0.317599i
$683$	−56.5263	−	97.9064i	−0.0827618	−	0.143348i	0.821674	−	0.569958i	$-0.193041\pi$
$683$	−56.5263	−	97.9064i	−0.0827618	−	0.143348i	−0.904435	+	0.426611i	$0.859707\pi$
$684$	−87.1893	−	50.3388i	−0.127470	−	0.0735947i
$685$		−	555.869i		−	0.811487i
$686$	−534.299	+	209.758i	−0.778861	+	0.305770i
$687$	−577.216			−0.840198
$688$	37.1234	−	64.2995i	0.0539584	−	0.0934586i
$689$	−490.823	+	283.377i	−0.712370	+	0.411287i
$690$	−42.9074	−	74.3179i	−0.0621847	−	0.107707i
$691$	−771.062	−	445.173i	−1.11586	−	0.644244i	−0.175522	−	0.984475i	$-0.556161\pi$
$691$	−771.062	−	445.173i	−1.11586	−	0.644244i	−0.940342	+	0.340231i	$0.889495\pi$
$692$		−	57.0995i		−	0.0825137i
$693$	197.510	−	212.879i	0.285007	−	0.307185i
$694$	553.713			0.797858
$695$	−17.5916	+	30.4695i	−0.0253116	+	0.0438410i
$696$	360.903	−	208.368i	0.518539	−	0.299379i
$697$	−27.9280	−	48.3728i	−0.0400689	−	0.0694014i
$698$	363.630	+	209.942i	0.520960	+	0.300776i
$699$			458.433i			0.655841i
$700$	12.3761	+	40.1176i	0.0176801	+	0.0573108i
$701$	−730.892			−1.04264			−0.521321	−	0.853361i	$-0.674560\pi$
$701$	−730.892			−1.04264			−0.521321	+	0.853361i	$0.674560\pi$
$702$	26.6107	−	46.0911i	0.0379070	−	0.0656568i
$703$	−993.712	+	573.720i	−1.41353	+	0.816102i
$704$	483.681	+	837.760i	0.687047	+	1.19000i
$705$	46.1715	+	26.6571i	0.0654914	+	0.0378115i
$706$			210.384i			0.297995i
$707$	177.955	−	779.791i	0.251704	−	1.10296i
$708$	147.704			0.208621
$709$	−576.325	+	998.224i	−0.812870	+	1.40793i	0.0979765	+	0.995189i	$0.468763\pi$
$709$	−576.325	+	998.224i	−0.812870	+	1.40793i	−0.910847	+	0.412744i	$0.864570\pi$
$710$	322.420	−	186.149i	0.454113	−	0.262182i
$711$	193.495	+	335.142i	0.272144	+	0.471368i
$712$	817.554	+	472.015i	1.14825	+	0.662943i
$713$		−	247.863i		−	0.347633i
$714$	−49.0300	−	11.1891i	−0.0686695	−	0.0156710i
$715$	189.252			0.264688
$716$	17.7225	−	30.6963i	0.0247521	−	0.0428720i
$717$	399.296	−	230.534i	0.556898	−	0.321525i
$718$	−299.199	−	518.228i	−0.416712	−	0.721766i
$719$	688.275	+	397.376i	0.957267	+	0.552678i	0.895331	−	0.445402i	$-0.146939\pi$
$719$	688.275	+	397.376i	0.957267	+	0.552678i	0.0619361	+	0.998080i	$0.480273\pi$
$720$		−	65.4927i		−	0.0909621i
$721$	−374.442	+	115.514i	−0.519336	+	0.160213i
$722$	705.738			0.977476
$723$	29.4197	−	50.9565i	0.0406912	−	0.0704792i
$724$	−10.7257	+	6.19249i	−0.0148145	+	0.00855316i
$725$	−69.1290	−	119.735i	−0.0953503	−	0.165152i
$726$	−176.265	−	101.767i	−0.242790	−	0.140175i
$727$			312.108i			0.429310i	0.976690	+	0.214655i	$0.0688626\pi$
$727$			312.108i			0.429310i	−0.976690	+	0.214655i	$0.931137\pi$
$728$	−273.284	−	253.553i	−0.375390	−	0.348288i
$729$	−27.0000			−0.0370370
$730$	194.715	−	337.256i	0.266732	−	0.461994i
$731$	−16.3242	+	9.42479i	−0.0223314	+	0.0128930i
$732$	120.208	+	208.207i	0.164219	+	0.284435i
$733$	215.629	+	124.493i	0.294173	+	0.169841i	0.639822	−	0.768523i	$-0.279008\pi$
$733$	215.629	+	124.493i	0.294173	+	0.169841i	−0.345649	+	0.938364i	$0.612341\pi$
$734$		−	1166.91i		−	1.58979i
$735$	14.1946	+	189.245i	0.0193123	+	0.257476i
$736$	−244.506			−0.332209
$737$	−78.8522	+	136.576i	−0.106991	+	0.185314i
$738$	97.9777	−	56.5675i	0.132761	−	0.0766497i
$739$	−152.219	−	263.652i	−0.205980	−	0.356768i	0.744464	−	0.667662i	$-0.232705\pi$
$739$	−152.219	−	263.652i	−0.205980	−	0.356768i	−0.950445	+	0.310894i	$0.899372\pi$
$740$	95.2684	+	55.0032i	0.128741	+	0.0743287i
$741$		−	296.588i		−	0.400253i
$742$	−737.775	+	795.185i	−0.994306	+	1.07168i
$743$	−235.455			−0.316898			−0.158449	−	0.987367i	$-0.550649\pi$
$743$	−235.455			−0.316898			−0.158449	+	0.987367i	$0.550649\pi$
$744$	141.065	−	244.332i	0.189604	−	0.328404i
$745$	−356.713	+	205.948i	−0.478810	+	0.276441i
$746$	−121.566	−	210.558i	−0.162957	−	0.282250i
$747$	78.8209	+	45.5073i	0.105517	+	0.0609200i
$748$		−	41.1136i		−	0.0549646i
$749$	203.680	+	660.237i	0.271936	+	0.881492i
$750$	−32.4065			−0.0432086
$751$	387.921	−	671.900i	0.516540	−	0.894673i	−0.483276	−	0.875468i	$-0.660553\pi$
$751$	387.921	−	671.900i	0.516540	−	0.894673i	0.999816	−	0.0192050i	$-0.00611351\pi$
$752$	−116.390	+	67.1976i	−0.154774	+	0.0893585i
$753$	−73.3325	−	127.016i	−0.0973872	−	0.168680i
$754$	245.276	+	141.610i	0.325300	+	0.187812i
$755$			588.646i			0.779663i
$756$	−9.70722	+	42.5366i	−0.0128402	+	0.0562654i
$757$	−194.342			−0.256727			−0.128363	−	0.991727i	$-0.540972\pi$
$757$	−194.342			−0.256727			−0.128363	+	0.991727i	$0.540972\pi$
$758$	−186.282	+	322.650i	−0.245755	+	0.425659i
$759$	274.637	−	158.562i	0.361840	−	0.208908i
$760$	−272.169	−	471.410i	−0.358117	−	0.620277i
$761$	−441.278	−	254.772i	−0.579866	−	0.334786i	0.181214	−	0.983444i	$-0.441997\pi$
$761$	−441.278	−	254.772i	−0.579866	−	0.334786i	−0.761080	+	0.648658i	$0.775331\pi$
$762$		−	572.174i		−	0.750884i
$763$	−360.051	−	82.1668i	−0.471889	−	0.107689i
$764$	142.754			0.186850
$765$	−8.31357	+	14.3995i	−0.0108674	+	0.0188229i
$766$	−50.3732	+	29.0830i	−0.0657614	+	0.0379674i
$767$	217.562	+	376.828i	0.283653	+	0.491301i
$768$	−311.290	−	179.723i	−0.405325	−	0.234015i
$769$			1174.80i			1.52769i	0.645398	+	0.763846i	$0.276692\pi$
$769$			1174.80i			1.52769i	−0.645398	+	0.763846i	$0.723308\pi$
$770$	346.119	−	106.776i	0.449505	−	0.138670i
$771$	−55.2880			−0.0717094
$772$	5.94067	−	10.2895i	0.00769517	−	0.0133284i
$773$	996.623	−	575.401i	1.28929	−	0.744373i	0.310764	−	0.950487i	$-0.399415\pi$
$773$	996.623	−	575.401i	1.28929	−	0.744373i	0.978528	+	0.206114i	$0.0660817\pi$
$774$	−19.0897	−	33.0643i	−0.0246636	−	0.0427187i
$775$	−81.0608	−	46.8005i	−0.104595	−	0.0603877i
$776$			1332.62i			1.71730i
$777$	364.529	+	338.211i	0.469150	+	0.435278i
$778$	−924.700			−1.18856
$779$	315.234	−	546.001i	0.404665	−	0.700900i
$780$	−24.6248	+	14.2171i	−0.0315702	+	0.0182271i
$781$	687.902	+	1191.48i	0.880796	+	1.52558i
$782$	−47.5619	−	27.4599i	−0.0608208	−	0.0351149i
$783$		−	143.682i		−	0.183502i
$784$	−431.029	−	207.537i	−0.549782	−	0.264716i
$785$	484.381			0.617046
$786$	−213.164	+	369.211i	−0.271201	+	0.469734i
$787$	−199.749	+	115.325i	−0.253810	+	0.146538i	−0.621508	−	0.783408i	$-0.713480\pi$
$787$	−199.749	+	115.325i	−0.253810	+	0.146538i	0.367697	+	0.929946i	$0.380146\pi$
$788$	−174.135	−	301.611i	−0.220984	−	0.382755i
$789$	−222.121	−	128.242i	−0.281523	−	0.162537i
$790$			482.702i			0.611015i
$791$	505.650	−	544.998i	0.639254	−	0.688998i
$792$	360.967			0.455766
$793$	−354.123	+	613.359i	−0.446561	+	0.773467i
$794$	83.5517	−	48.2386i	0.105229	−	0.0607539i
$795$	179.317	+	310.586i	0.225556	+	0.390675i
$796$	352.662	+	203.609i	0.443042	+	0.255791i
$797$		−	246.018i		−	0.308680i	−0.988018	−	0.154340i	$-0.950675\pi$
$797$		−	246.018i		−	0.308680i	0.988018	−	0.154340i	$-0.0493251\pi$
$798$	−167.335	−	542.423i	−0.209693	−	0.679728i
$799$	34.1200			0.0427033
$800$	−46.1667	+	79.9631i	−0.0577084	+	0.0999538i
$801$	281.876	−	162.741i	0.351905	−	0.203173i
$802$	470.510	+	814.948i	0.586671	+	1.01614i
$803$	1246.30	+	719.554i	1.55206	+	0.896083i
$804$		−	23.6944i		−	0.0294706i
$805$	−46.1096	+	202.050i	−0.0572790	+	0.250994i
$806$	191.741			0.237892
$807$	78.8909	−	136.643i	0.0977583	−	0.169322i
$808$	861.023	−	497.112i	1.06562	−	0.615237i
$809$	−120.772	−	209.183i	−0.149285	−	0.258569i	0.781678	−	0.623682i	$-0.214364\pi$
$809$	−120.772	−	209.183i	−0.149285	−	0.258569i	−0.930963	+	0.365112i	$0.881031\pi$
$810$	−29.1658	−	16.8389i	−0.0360072	−	0.0207888i
$811$		−	626.619i		−	0.772650i	−0.922363	−	0.386325i	$-0.873744\pi$
$811$		−	626.619i		−	0.772650i	0.922363	−	0.386325i	$-0.126256\pi$
$812$	−226.361	−	51.6575i	−0.278770	−	0.0636176i
$813$	216.090			0.265793
$814$	474.546	−	821.938i	0.582981	−	1.00975i
$815$	334.200	−	192.951i	0.410062	−	0.236749i
$816$	−20.9570	−	36.2985i	−0.0256826	−	0.0444835i
$817$	−184.258	−	106.381i	−0.225529	−	0.130209i
$818$			337.600i			0.412714i
$819$	−122.819	+	37.8892i	−0.149963	+	0.0462628i
$820$	−60.4438			−0.0737119
$821$	49.3857	−	85.5386i	0.0601532	−	0.104188i	−0.834381	−	0.551189i	$-0.814174\pi$
$821$	49.3857	−	85.5386i	0.0601532	−	0.104188i	0.894534	+	0.447000i	$0.147508\pi$
$822$	624.014	−	360.275i	0.759142	−	0.438291i
$823$	−391.560	−	678.202i	−0.475772	−	0.824061i	0.523843	−	0.851815i	$-0.324498\pi$
$823$	−391.560	−	678.202i	−0.475772	−	0.824061i	−0.999615	+	0.0277542i	$0.991164\pi$
$824$	−421.829	−	243.543i	−0.511929	−	0.295562i
$825$		−	119.756i		−	0.145159i
$826$	610.501	+	566.425i	0.739106	+	0.685744i
$827$	−1131.53			−1.36823			−0.684116	−	0.729373i	$-0.739812\pi$
$827$	−1131.53			−1.36823			−0.684116	+	0.729373i	$0.739812\pi$
$828$	−23.8232	+	41.2629i	−0.0287719	+	0.0498345i
$829$	164.501	−	94.9749i	0.198434	−	0.114566i	−0.397491	−	0.917606i	$-0.630119\pi$
$829$	164.501	−	94.9749i	0.198434	−	0.114566i	0.595925	+	0.803040i	$0.296786\pi$
$830$	56.7624	+	98.3154i	0.0683884	+	0.118452i
$831$	−185.886	−	107.321i	−0.223689	−	0.129147i
$832$		−	428.165i		−	0.514621i
$833$	68.4234	+	100.344i	0.0821410	+	0.120461i
$834$	−45.6065			−0.0546841
$835$	−175.445	+	303.880i	−0.210114	+	0.363928i
$836$	401.891	−	232.032i	0.480731	−	0.277550i
$837$	−48.6365	−	84.2409i	−0.0581081	−	0.100646i
$838$	441.128	+	254.685i	0.526406	+	0.303921i
$839$		−	1431.33i		−	1.70599i	−0.521919	−	0.852995i	$-0.674784\pi$
$839$		−	1431.33i		−	1.70599i	0.521919	−	0.852995i	$-0.325216\pi$
$840$	−160.445	+	172.930i	−0.191006	+	0.205869i
$841$	−76.3899			−0.0908322
$842$	465.743	−	806.691i	0.553139	−	0.958065i
$843$	26.7074	−	15.4195i	0.0316814	−	0.0182912i
$844$	6.66321	+	11.5410i	0.00789480	+	0.0136742i
$845$	254.725	+	147.065i	0.301449	+	0.174042i
$846$			69.1090i			0.0816892i
$847$	144.899	+	469.696i	0.171073	+	0.554541i
$848$	−904.050			−1.06610
$849$	96.2623	−	166.731i	0.113383	−	0.196385i
$850$	−17.9609	+	10.3697i	−0.0211305	+	0.0121997i
$851$	271.517	+	470.281i	0.319056	+	0.552621i
$852$	−179.015	−	103.354i	−0.210111	−	0.121308i
$853$		−	1123.73i		−	1.31739i	−0.752412	−	0.658693i	$-0.771110\pi$
$853$		−	1123.73i		−	1.31739i	0.752412	−	0.658693i	$-0.228890\pi$
$854$	−301.591	+	1321.56i	−0.353151	+	1.54749i
$855$	−187.677			−0.219505
$856$	−429.430	+	743.794i	−0.501670	+	0.868919i
$857$	1300.05	−	750.584i	1.51698	−	0.875827i	0.517176	−	0.855879i	$-0.326983\pi$
$857$	1300.05	−	750.584i	1.51698	−	0.875827i	0.999801	−	0.0199480i	$-0.00635008\pi$
$858$	122.660	+	212.453i	0.142960	+	0.247614i
$859$	−1203.93	−	695.091i	−1.40155	−	0.809186i	−0.407000	−	0.913428i	$-0.633425\pi$
$859$	−1203.93	−	695.091i	−1.40155	−	0.809186i	−0.994552	+	0.104242i	$0.966758\pi$
$860$			20.3978i			0.0237184i
$861$	−266.375	−	60.7891i	−0.309379	−	0.0706029i
$862$	301.968			0.350311
$863$	−133.534	+	231.288i	−0.154732	+	0.268004i	−0.932962	−	0.359976i	$-0.882785\pi$
$863$	−133.534	+	231.288i	−0.154732	+	0.268004i	0.778229	+	0.627980i	$0.216118\pi$
$864$	−83.1001	+	47.9778i	−0.0961806	+	0.0555299i
$865$	−53.2206	−	92.1808i	−0.0615267	−	0.106567i
$866$	1049.33	+	605.834i	1.21170	+	0.699577i
$867$		−	489.922i		−	0.565077i
$868$	−150.202	+	46.3366i	−0.173044	+	0.0533832i
$869$	−1783.79			−2.05269
$870$	89.6091	−	155.207i	0.102999	−	0.178399i
$871$	60.4500	−	34.9008i	0.0694030	−	0.0400699i
$872$	−229.530	−	397.558i	−0.263223	−	0.455915i
$873$	397.905	+	229.731i	0.455791	+	0.263151i
$874$		−	619.899i		−	0.709267i
$875$	57.3722	+	53.2300i	0.0655682	+	0.0608343i
$876$	−216.220			−0.246826
$877$	499.609	−	865.348i	0.569679	−	0.986714i	−0.426918	−	0.904290i	$-0.640401\pi$
$877$	499.609	−	865.348i	0.569679	−	0.986714i	0.996597	−	0.0824232i	$-0.0262659\pi$
$878$	592.861	−	342.288i	0.675240	−	0.389850i
$879$	−66.3798	−	114.973i	−0.0755175	−	0.130800i
$880$	261.438	+	150.941i	0.297089	+	0.171524i
$881$		−	94.1956i		−	0.106919i	−0.998570	−	0.0534595i	$-0.982975\pi$
$881$		−	94.1956i		−	0.106919i	0.998570	−	0.0534595i	$-0.0170248\pi$
$882$	−203.245	+	138.590i	−0.230436	+	0.157131i
$883$	−389.465			−0.441070			−0.220535	−	0.975379i	$-0.570780\pi$
$883$	−389.465			−0.441070			−0.220535	+	0.975379i	$0.570780\pi$
$884$	−9.09865	+	15.7593i	−0.0102926	+	0.0178273i
$885$	238.452	−	137.670i	0.269437	−	0.155560i
$886$	−333.688	−	577.965i	−0.376623	−	0.652330i
$887$	638.869	+	368.851i	0.720258	+	0.415841i	0.814848	−	0.579675i	$-0.196821\pi$
$887$	638.869	+	368.851i	0.720258	+	0.415841i	−0.0945896	+	0.995516i	$0.530154\pi$
$888$			618.110i			0.696070i
$889$	−939.837	+	1012.97i	−1.05718	+	1.13945i
$890$	405.983			0.456161
$891$	62.2270	−	107.780i	0.0698395	−	0.120966i
$892$	373.325	−	215.539i	0.418526	−	0.241636i
$893$	192.562	+	333.528i	0.215635	+	0.373491i
$894$	−462.393	−	266.963i	−0.517218	−	0.298616i
$895$		−	66.0744i		−	0.0738262i
$896$	−89.1465	−	288.972i	−0.0994939	−	0.322513i
$897$	−140.362			−0.156479
$898$	−434.969	+	753.388i	−0.484375	+	0.838962i
$899$	448.292	−	258.821i	0.498656	−	0.287899i
$900$	8.99640	+	15.5822i	0.00999600	+	0.0173136i
$901$	198.769	+	114.759i	0.220609	+	0.127369i
$902$			521.485i			0.578143i
$903$	−20.5143	+	89.8928i	−0.0227180	+	0.0995491i
$904$	924.119			1.02226
$905$	−11.5436	+	19.9942i	−0.0127554	+	0.0220930i
$906$	−660.810	+	381.519i	−0.729371	+	0.421102i
$907$	−64.2146	−	111.223i	−0.0707989	−	0.122627i	0.828453	−	0.560059i	$-0.189222\pi$
$907$	−64.2146	−	111.223i	−0.0707989	−	0.122627i	−0.899252	+	0.437432i	$0.855888\pi$
$908$	−77.1339	−	44.5333i	−0.0849492	−	0.0490454i
$909$		−	342.788i		−	0.377105i
$910$	−156.302	−	35.6694i	−0.171760	−	0.0391971i
$911$	851.535			0.934725			0.467363	−	0.884066i	$-0.345204\pi$
$911$	851.535			0.934725			0.467363	+	0.884066i	$0.345204\pi$
$912$	236.549	−	409.715i	0.259374	−	0.449249i
$913$	−363.318	+	209.762i	−0.397938	+	0.229750i
$914$	195.614	+	338.813i	0.214019	+	0.370692i
$915$	388.126	+	224.084i	0.424181	+	0.244901i
$916$			399.747i			0.436405i
$917$	983.840	−	303.510i	1.07289	−	0.330982i
$918$	−21.5531			−0.0234783
$919$	755.722	−	1308.95i	0.822330	−	1.42432i	−0.0816123	−	0.996664i	$-0.526007\pi$
$919$	755.722	−	1308.95i	0.822330	−	1.42432i	0.903943	−	0.427654i	$-0.140660\pi$
$920$	−223.098	+	128.806i	−0.242498	+	0.140006i
$921$	−309.658	−	536.343i	−0.336219	−	0.582349i
$922$	1079.82	+	623.436i	1.17117	+	0.676178i
$923$		−	608.945i		−	0.659746i
$924$	−147.428	−	136.784i	−0.159554	−	0.148035i
$925$	205.067			0.221694
$926$	621.230	−	1076.00i	0.670874	−	1.16199i
$927$	−145.438	+	83.9688i	−0.156891	+	0.0905812i
$928$	−255.316	−	442.221i	−0.275126	−	0.476531i
$929$	−44.6801	−	25.7961i	−0.0480949	−	0.0277676i	0.475760	−	0.879575i	$-0.342173\pi$
$929$	−44.6801	−	25.7961i	−0.0480949	−	0.0277676i	−0.523855	+	0.851808i	$0.675506\pi$
$930$		−	121.331i		−	0.130464i
$931$	−594.721	+	1235.16i	−0.638798	+	1.32670i
$932$	317.484			0.340648
$933$	−272.856	+	472.600i	−0.292450	+	0.506538i
$934$	−877.571	+	506.666i	−0.939583	+	0.542469i
$935$	−38.3206	−	66.3733i	−0.0409846	−	0.0709875i
$936$	−138.363	−	79.8839i	−0.147824	−	0.0853460i
$937$		−	1321.41i		−	1.41026i	−0.709080	−	0.705128i	$-0.750890\pi$
$937$		−	1321.41i		−	1.41026i	0.709080	−	0.705128i	$-0.249110\pi$
$938$	90.8648	−	97.9355i	0.0968708	−	0.104409i
$939$	454.520			0.484047
$940$	18.4612	−	31.9757i	0.0196396	−	0.0340167i
$941$	708.633	−	409.129i	0.753063	−	0.434781i	−0.0737363	−	0.997278i	$-0.523492\pi$
$941$	708.633	−	409.129i	0.753063	−	0.434781i	0.826800	+	0.562496i	$0.190159\pi$
$942$	313.942	+	543.763i	0.333271	+	0.577243i
$943$	−258.399	−	149.187i	−0.274018	−	0.158204i
$944$			694.082i			0.735256i
$945$	23.9758	+	77.7185i	0.0253712	+	0.0822418i
$946$	175.984			0.186030
$947$	−716.084	+	1240.29i	−0.756160	+	1.30971i	0.188635	+	0.982047i	$0.439594\pi$
$947$	−716.084	+	1240.29i	−0.756160	+	1.30971i	−0.944796	+	0.327661i	$0.893740\pi$
$948$	232.101	−	134.003i	0.244832	−	0.141354i
$949$	−318.482	−	551.628i	−0.335598	−	0.581273i
$950$	−202.731	−	117.047i	−0.213401	−	0.123207i
$951$			536.234i			0.563863i
$952$	−33.5889	+	147.185i	−0.0352825	+	0.154606i
$953$	−864.220			−0.906841			−0.453421	−	0.891297i	$-0.649796\pi$
$953$	−864.220			−0.906841			−0.453421	+	0.891297i	$0.649796\pi$
$954$	−232.441	+	402.600i	−0.243649	+	0.422013i
$955$	230.460	−	133.056i	0.241319	−	0.139326i
$956$	−159.654	−	276.530i	−0.167003	−	0.289257i
$957$	573.558	+	331.144i	0.599330	+	0.346023i
$958$		−	503.459i		−	0.525531i
$959$	−1696.53	−	387.162i	−1.76906	−	0.403714i
$960$	−270.937			−0.282226
$961$	−305.277	+	528.756i	−0.317666	+	0.550214i
$962$	−363.799	+	210.039i	−0.378169	+	0.218336i
$963$	148.059	+	256.445i	0.153747	+	0.266298i
$964$	−35.2895	−	20.3744i	−0.0366074	−	0.0211353i
$965$		−	22.1484i		−	0.0229517i
$966$	−256.705	+	79.1925i	−0.265741	+	0.0819798i
$967$	−247.825			−0.256282			−0.128141	−	0.991756i	$-0.540901\pi$
$967$	−247.825			−0.256282			−0.128141	+	0.991756i	$0.540901\pi$
$968$	−305.498	+	529.139i	−0.315597	+	0.546631i
$969$	−104.017	+	60.0545i	−0.107345	+	0.0619758i
$970$	286.549	+	496.317i	0.295411	+	0.511667i
$971$	119.734	+	69.1286i	0.123310	+	0.0711932i	0.560386	−	0.828231i	$-0.310653\pi$
$971$	119.734	+	69.1286i	0.123310	+	0.0711932i	−0.437076	+	0.899424i	$0.643986\pi$
$972$			18.6987i			0.0192373i
$973$	80.7414	+	74.9120i	0.0829819	+	0.0769908i
$974$	−989.359			−1.01577
$975$	−26.5026	+	45.9039i	−0.0271822	+	0.0470809i
$976$	−978.393	+	564.875i	−1.00245	+	0.578766i
$977$	−89.6857	−	155.340i	−0.0917971	−	0.158997i	0.816470	−	0.577387i	$-0.195928\pi$
$977$	−89.6857	−	155.340i	−0.0917971	−	0.158997i	−0.908267	+	0.418390i	$0.862594\pi$
$978$	433.210	+	250.114i	0.442955	+	0.255740i
$979$			1500.28i			1.53246i
$980$	131.060	−	9.83034i	0.133735	−	0.0100310i
$981$	−158.275			−0.161340
$982$	−258.247	+	447.296i	−0.262980	+	0.455495i
$983$	−670.259	+	386.974i	−0.681850	+	0.393666i	−0.800552	−	0.599264i	$-0.795460\pi$
$983$	−670.259	+	386.974i	−0.681850	+	0.393666i	0.118702	+	0.992930i	$0.462127\pi$
$984$	−169.812	−	294.124i	−0.172574	−	0.298906i
$985$	−562.244	−	324.612i	−0.570806	−	0.329555i
$986$		−	114.696i		−	0.116324i
$987$	113.517	−	122.350i	0.115012	−	0.123962i
$988$	−205.400			−0.207894
$989$	−50.3456	+	87.2011i	−0.0509055	+	0.0881710i
$990$	134.437	−	77.6174i	0.135795	−	0.0784014i
$991$	314.025	+	543.907i	0.316877	+	0.548847i	0.979835	−	0.199810i	$-0.0640324\pi$
$991$	314.025	+	543.907i	0.316877	+	0.548847i	−0.662958	+	0.748657i	$0.730699\pi$
$992$	−299.385	−	172.850i	−0.301799	−	0.174244i
$993$			150.364i			0.151423i
$994$	−343.568	−	1113.69i	−0.345642	−	1.12041i
$995$	759.111			0.762926
$996$	31.5157	−	54.5869i	0.0316423	−	0.0548061i
$997$	1245.49	−	719.086i	1.24924	−	0.721250i	0.278283	−	0.960499i	$-0.410235\pi$
$997$	1245.49	−	719.086i	1.24924	−	0.721250i	0.970958	+	0.239250i	$0.0769015\pi$
$998$	−748.613	−	1296.64i	−0.750113	−	1.29923i
$999$	184.560	+	106.556i	0.184745	+	0.106663i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.n.a.61.3	yes	8
3.2	odd	2		315.3.w.a.271.2		8
5.2	odd	4		525.3.s.h.124.6		16
5.3	odd	4		525.3.s.h.124.3		16
5.4	even	2		525.3.o.l.376.2		8
7.2	even	3		735.3.h.a.391.3		8
7.3	odd	6	inner	105.3.n.a.31.3	✓	8
7.5	odd	6		735.3.h.a.391.4		8
21.17	even	6		315.3.w.a.136.2		8
35.3	even	12		525.3.s.h.199.6		16
35.17	even	12		525.3.s.h.199.3		16
35.24	odd	6		525.3.o.l.451.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.n.a.31.3	✓	8	7.3	odd	6	inner
105.3.n.a.61.3	yes	8	1.1	even	1	trivial
315.3.w.a.136.2		8	21.17	even	6
315.3.w.a.271.2		8	3.2	odd	2
525.3.o.l.376.2		8	5.4	even	2
525.3.o.l.451.2		8	35.24	odd	6
525.3.s.h.124.3		16	5.3	odd	4
525.3.s.h.124.6		16	5.2	odd	4
525.3.s.h.199.3		16	35.17	even	12
525.3.s.h.199.6		16	35.3	even	12
735.3.h.a.391.3		8	7.2	even	3
735.3.h.a.391.4		8	7.5	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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.836732 - 1.44926i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(0.599760 + 1.03881i) q^{4} +(1.93649 + 1.11803i) q^{5} +2.89852i q^{6} +(4.76104 - 5.13152i) q^{7} +8.70121 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.836732 - 1.44926i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(0.599760 + 1.03881i) q^{4} +(1.93649 + 1.11803i) q^{5} +2.89852i q^{6} +(4.76104 - 5.13152i) q^{7} +8.70121 q^{8} +(1.50000 - 2.59808i) q^{9} +(3.24065 - 1.87099i) q^{10} +(6.91411 + 11.9756i) q^{11} +(-1.79928 - 1.03881i) q^{12} -6.12052i q^{13} +(-3.45321 - 11.1937i) q^{14} -3.87298 q^{15} +(4.88154 - 8.45507i) q^{16} +(-2.14655 + 1.23931i) q^{17} +(-2.51020 - 4.34779i) q^{18} +(-24.2290 - 13.9886i) q^{19} +2.68221i q^{20} +(-2.69753 + 11.8205i) q^{21} +23.1410 q^{22} +(-6.62020 + 11.4665i) q^{23} +(-13.0518 + 7.53547i) q^{24} +(2.50000 + 4.33013i) q^{25} +(-8.87024 - 5.12123i) q^{26} +5.19615i q^{27} +(8.18618 + 1.86816i) q^{28} -27.6516 q^{29} +(-3.24065 + 5.61297i) q^{30} +(-16.2122 + 9.36010i) q^{31} +(9.23334 + 15.9926i) q^{32} +(-20.7423 - 11.9756i) q^{33} +4.14789i q^{34} +(14.9569 - 4.61414i) q^{35} +3.59856 q^{36} +(20.5067 - 35.5187i) q^{37} +(-40.5463 + 23.4094i) q^{38} +(5.30052 + 9.18078i) q^{39} +(16.8498 + 9.72824i) q^{40} +22.5351i q^{41} +(14.8738 + 13.8000i) q^{42} +7.60485 q^{43} +(-8.29361 + 14.3650i) q^{44} +(5.80948 - 3.35410i) q^{45} +(11.0787 + 19.1888i) q^{46} +(-11.9214 - 6.88283i) q^{47} +16.9101i q^{48} +(-3.66502 - 48.8627i) q^{49} +8.36732 q^{50} +(2.14655 - 3.71794i) q^{51} +(6.35808 - 3.67084i) q^{52} +(-46.2995 - 80.1930i) q^{53} +(7.53059 + 4.34779i) q^{54} +30.9208i q^{55} +(41.4268 - 44.6504i) q^{56} +48.4579 q^{57} +(-23.1370 + 40.0744i) q^{58} +(-61.5680 + 35.5463i) q^{59} +(-2.32286 - 4.02331i) q^{60} +(-100.214 - 57.8584i) q^{61} +31.3276i q^{62} +(-6.19052 - 20.0668i) q^{63} +69.9556 q^{64} +(6.84295 - 11.8523i) q^{65} +(-34.7115 + 20.0407i) q^{66} +(5.70227 + 9.87662i) q^{67} +(-2.57483 - 1.48658i) q^{68} -22.9330i q^{69} +(5.82783 - 25.5373i) q^{70} +99.4924 q^{71} +(13.0518 - 22.6064i) q^{72} +(90.1276 - 52.0352i) q^{73} +(-34.3172 - 59.4392i) q^{74} +(-7.50000 - 4.33013i) q^{75} -33.5592i q^{76} +(94.3714 + 21.5364i) q^{77} +17.7405 q^{78} +(-64.4982 + 111.714i) q^{79} +(18.9061 - 10.9154i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(32.6592 + 18.8558i) q^{82} +30.3382i q^{83} +(-13.8971 + 4.28721i) q^{84} -5.54238 q^{85} +(6.36322 - 11.0214i) q^{86} +(41.4774 - 23.9470i) q^{87} +(60.1611 + 104.202i) q^{88} +(93.9587 + 54.2471i) q^{89} -11.2259i q^{90} +(-31.4076 - 29.1400i) q^{91} -15.8821 q^{92} +(16.2122 - 28.0803i) q^{93} +(-19.9501 + 11.5182i) q^{94} +(-31.2794 - 54.1776i) q^{95} +(-27.7000 - 15.9926i) q^{96} +153.154i q^{97} +(-73.8816 - 35.5734i) q^{98} +41.4847 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 12 q^{3} - 6 q^{4} - 16 q^{7} - 32 q^{8} + 12 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 - 12 * q^3 - 6 * q^4 - 16 * q^7 - 32 * q^8 + 12 * q^9	\( 8 q + 2 q^{2} - 12 q^{3} - 6 q^{4} - 16 q^{7} - 32 q^{8} + 12 q^{9} + 20 q^{11} + 18 q^{12} - 16 q^{14} - 2 q^{16} - 18 q^{17} - 6 q^{18} + 48 q^{21} - 16 q^{22} + 62 q^{23} + 48 q^{24} + 20 q^{25} + 120 q^{26} - 120 q^{28} - 100 q^{29} - 126 q^{31} + 36 q^{32} - 60 q^{33} - 36 q^{36} - 80 q^{37} + 114 q^{38} - 12 q^{39} + 90 q^{40} + 90 q^{42} + 352 q^{43} - 18 q^{44} - 82 q^{46} - 72 q^{47} + 38 q^{49} + 20 q^{50} + 18 q^{51} - 48 q^{52} - 76 q^{53} + 18 q^{54} + 196 q^{56} - 40 q^{58} - 54 q^{59} - 60 q^{60} - 396 q^{61} - 96 q^{63} - 4 q^{64} - 60 q^{65} + 24 q^{66} + 184 q^{67} - 312 q^{68} + 164 q^{71} - 48 q^{72} + 348 q^{73} - 140 q^{74} - 60 q^{75} + 152 q^{77} - 240 q^{78} - 206 q^{79} - 36 q^{81} + 204 q^{82} + 132 q^{84} - 60 q^{85} + 178 q^{86} + 150 q^{87} + 124 q^{88} + 282 q^{89} - 114 q^{91} - 288 q^{92} + 126 q^{93} + 30 q^{94} - 120 q^{95} - 108 q^{96} - 592 q^{98} + 120 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - 12 * q^3 - 6 * q^4 - 16 * q^7 - 32 * q^8 + 12 * q^9 + 20 * q^11 + 18 * q^12 - 16 * q^14 - 2 * q^16 - 18 * q^17 - 6 * q^18 + 48 * q^21 - 16 * q^22 + 62 * q^23 + 48 * q^24 + 20 * q^25 + 120 * q^26 - 120 * q^28 - 100 * q^29 - 126 * q^31 + 36 * q^32 - 60 * q^33 - 36 * q^36 - 80 * q^37 + 114 * q^38 - 12 * q^39 + 90 * q^40 + 90 * q^42 + 352 * q^43 - 18 * q^44 - 82 * q^46 - 72 * q^47 + 38 * q^49 + 20 * q^50 + 18 * q^51 - 48 * q^52 - 76 * q^53 + 18 * q^54 + 196 * q^56 - 40 * q^58 - 54 * q^59 - 60 * q^60 - 396 * q^61 - 96 * q^63 - 4 * q^64 - 60 * q^65 + 24 * q^66 + 184 * q^67 - 312 * q^68 + 164 * q^71 - 48 * q^72 + 348 * q^73 - 140 * q^74 - 60 * q^75 + 152 * q^77 - 240 * q^78 - 206 * q^79 - 36 * q^81 + 204 * q^82 + 132 * q^84 - 60 * q^85 + 178 * q^86 + 150 * q^87 + 124 * q^88 + 282 * q^89 - 114 * q^91 - 288 * q^92 + 126 * q^93 + 30 * q^94 - 120 * q^95 - 108 * q^96 - 592 * q^98 + 120 * q^99

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