LMFDB - Embedded newform 222.3.r.d.61.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [222,3,Mod(13,222)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(222, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([0, 11]))

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

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

chi := DirichletCharacter("222.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 222 = 2 \cdot 3 \cdot 37 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	222.r (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.04906186880$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			61.4
Character	$\chi$	$=$	222.61
Dual form			222.3.r.d.91.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.15846 + 0.811160i) q^{2} +(1.70574 - 0.300767i) q^{3} +(0.684040 - 1.87939i) q^{4} +(0.651048 - 7.44151i) q^{5} +(-1.73205 + 1.73205i) q^{6} +(2.81141 - 2.35906i) q^{7} +(0.732051 + 2.73205i) q^{8} +(2.81908 - 1.02606i) q^{9} +O(q^{10})$	\(q+(-1.15846 + 0.811160i) q^{2} +(1.70574 - 0.300767i) q^{3} +(0.684040 - 1.87939i) q^{4} +(0.651048 - 7.44151i) q^{5} +(-1.73205 + 1.73205i) q^{6} +(2.81141 - 2.35906i) q^{7} +(0.732051 + 2.73205i) q^{8} +(2.81908 - 1.02606i) q^{9} +(5.28204 + 9.14876i) q^{10} +(-13.9337 - 8.04460i) q^{11} +(0.601535 - 3.41147i) q^{12} +(-19.7475 + 9.20839i) q^{13} +(-1.34333 + 5.01337i) q^{14} +(-1.12765 - 12.8891i) q^{15} +(-3.06418 - 2.57115i) q^{16} +(5.50944 - 11.8150i) q^{17} +(-2.43348 + 3.47537i) q^{18} +(-8.56445 - 5.99689i) q^{19} +(-13.5401 - 6.31386i) q^{20} +(4.08601 - 4.86951i) q^{21} +(22.6670 - 1.98310i) q^{22} +(3.79733 + 1.01749i) q^{23} +(2.07040 + 4.43998i) q^{24} +(-30.3320 - 5.34835i) q^{25} +(15.4071 - 26.6859i) q^{26} +(4.50000 - 2.59808i) q^{27} +(-2.51046 - 6.89742i) q^{28} +(29.9144 - 8.01553i) q^{29} +(11.7614 + 14.0167i) q^{30} +(42.3539 + 42.3539i) q^{31} +(5.63533 + 0.493027i) q^{32} +(-26.1867 - 9.53118i) q^{33} +(3.20143 + 18.1562i) q^{34} +(-15.7246 - 22.4570i) q^{35} -6.00000i q^{36} +(4.81272 - 36.6857i) q^{37} +14.7860 q^{38} +(-30.9144 + 21.6465i) q^{39} +(20.8072 - 3.66887i) q^{40} +(19.3118 - 53.0587i) q^{41} +(-0.783506 + 8.95552i) q^{42} +(25.7513 - 25.7513i) q^{43} +(-24.6501 + 20.6839i) q^{44} +(-5.80008 - 21.6462i) q^{45} +(-5.22438 + 1.90152i) q^{46} +(-13.6685 - 23.6745i) q^{47} +(-6.00000 - 3.46410i) q^{48} +(-6.16986 + 34.9910i) q^{49} +(39.4767 - 18.4083i) q^{50} +(5.84408 - 21.8104i) q^{51} +(3.79806 + 43.4120i) q^{52} +(-43.8842 - 36.8232i) q^{53} +(-3.10560 + 6.65997i) q^{54} +(-68.9355 + 98.4500i) q^{55} +(8.50316 + 5.95398i) q^{56} +(-16.4124 - 7.65321i) q^{57} +(-28.1526 + 33.5510i) q^{58} +(45.9302 - 4.01837i) q^{59} +(-24.9949 - 6.69736i) q^{60} +(-2.23345 - 4.78965i) q^{61} +(-83.4209 - 14.7094i) q^{62} +(5.50506 - 9.53504i) q^{63} +(-6.92820 + 4.00000i) q^{64} +(55.6678 + 152.946i) q^{65} +(38.0675 - 10.2001i) q^{66} +(73.8633 + 88.0269i) q^{67} +(-18.4363 - 18.4363i) q^{68} +(6.78327 + 0.593459i) q^{69} +(36.4325 + 13.2603i) q^{70} +(4.09642 + 23.2320i) q^{71} +(4.86696 + 6.95074i) q^{72} +71.5888i q^{73} +(24.1826 + 46.4026i) q^{74} -53.3470 q^{75} +(-17.1289 + 11.9938i) q^{76} +(-58.1510 + 10.2536i) q^{77} +(18.2542 - 50.1530i) q^{78} +(12.1431 - 138.796i) q^{79} +(-21.1282 + 21.1282i) q^{80} +(6.89440 - 5.78509i) q^{81} +(20.6672 + 77.1312i) q^{82} +(36.8683 - 13.4189i) q^{83} +(-6.35670 - 11.0101i) q^{84} +(-84.3347 - 48.6907i) q^{85} +(-8.94335 + 50.7202i) q^{86} +(48.6152 - 22.6697i) q^{87} +(11.7781 - 43.9565i) q^{88} +(9.62004 + 109.958i) q^{89} +(24.2777 + 20.3714i) q^{90} +(-33.7952 + 72.4740i) q^{91} +(4.50978 - 6.44063i) q^{92} +(84.9833 + 59.5059i) q^{93} +(35.0381 + 16.3385i) q^{94} +(-50.2018 + 59.8282i) q^{95} +(9.76067 - 0.853948i) q^{96} +(55.8574 + 14.9669i) q^{97} +(-21.2358 - 45.5403i) q^{98} +(-47.5343 - 8.38158i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{8}+O(q^{10}) $ 48 * q - 48 * q^8	$ 48 q - 48 q^{8} - 18 q^{11} + 12 q^{13} + 24 q^{14} + 36 q^{15} - 36 q^{17} - 150 q^{19} - 36 q^{20} - 36 q^{21} - 30 q^{22} + 90 q^{23} + 216 q^{25} + 216 q^{27} - 72 q^{28} + 210 q^{29} + 72 q^{30} - 12 q^{31} - 54 q^{34} + 180 q^{35} - 24 q^{37} - 108 q^{38} + 18 q^{39} - 438 q^{41} - 90 q^{42} - 294 q^{46} + 42 q^{47} - 288 q^{48} + 54 q^{49} + 144 q^{50} - 72 q^{51} - 120 q^{52} + 30 q^{53} - 264 q^{55} + 126 q^{57} - 102 q^{58} + 66 q^{59} + 660 q^{61} - 18 q^{62} - 36 q^{63} + 60 q^{65} + 36 q^{66} - 72 q^{67} + 12 q^{68} + 18 q^{69} + 42 q^{70} - 30 q^{71} + 282 q^{74} + 144 q^{75} - 300 q^{76} + 60 q^{77} - 108 q^{78} + 426 q^{79} + 48 q^{82} - 510 q^{83} + 72 q^{84} - 414 q^{85} + 528 q^{86} + 306 q^{87} + 24 q^{88} - 414 q^{89} - 1098 q^{91} - 132 q^{92} + 90 q^{93} + 528 q^{94} + 6 q^{95} + 966 q^{97} + 108 q^{98} - 90 q^{99}+O(q^{100}) $ 48 * q - 48 * q^8 - 18 * q^11 + 12 * q^13 + 24 * q^14 + 36 * q^15 - 36 * q^17 - 150 * q^19 - 36 * q^20 - 36 * q^21 - 30 * q^22 + 90 * q^23 + 216 * q^25 + 216 * q^27 - 72 * q^28 + 210 * q^29 + 72 * q^30 - 12 * q^31 - 54 * q^34 + 180 * q^35 - 24 * q^37 - 108 * q^38 + 18 * q^39 - 438 * q^41 - 90 * q^42 - 294 * q^46 + 42 * q^47 - 288 * q^48 + 54 * q^49 + 144 * q^50 - 72 * q^51 - 120 * q^52 + 30 * q^53 - 264 * q^55 + 126 * q^57 - 102 * q^58 + 66 * q^59 + 660 * q^61 - 18 * q^62 - 36 * q^63 + 60 * q^65 + 36 * q^66 - 72 * q^67 + 12 * q^68 + 18 * q^69 + 42 * q^70 - 30 * q^71 + 282 * q^74 + 144 * q^75 - 300 * q^76 + 60 * q^77 - 108 * q^78 + 426 * q^79 + 48 * q^82 - 510 * q^83 + 72 * q^84 - 414 * q^85 + 528 * q^86 + 306 * q^87 + 24 * q^88 - 414 * q^89 - 1098 * q^91 - 132 * q^92 + 90 * q^93 + 528 * q^94 + 6 * q^95 + 966 * q^97 + 108 * q^98 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/222\mathbb{Z}\right)^\times$.

$n$	$149$	$187$
$\chi(n)$	$1$	$e\left(\frac{29}{36}\right)$

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 $

$2$	−1.15846	+	0.811160i	−0.579228	+	0.405580i
$2$	−1.15846	+	0.811160i	−0.579228	+	0.405580i
$3$	1.70574	−	0.300767i	0.568579	−	0.100256i
$3$	1.70574	−	0.300767i	0.568579	−	0.100256i
$4$	0.684040	−	1.87939i	0.171010	−	0.469846i
$5$	0.651048	−	7.44151i	0.130210	−	1.48830i	−0.597197	−	0.802095i	$-0.703719\pi$
$5$	0.651048	−	7.44151i	0.130210	−	1.48830i	0.727406	−	0.686207i	$-0.240726\pi$
$6$	−1.73205	+	1.73205i	−0.288675	+	0.288675i
$7$	2.81141	−	2.35906i	0.401631	−	0.337008i	−0.419493	−	0.907759i	$-0.637792\pi$
$7$	2.81141	−	2.35906i	0.401631	−	0.337008i	0.821124	+	0.570751i	$0.193348\pi$
$8$	0.732051	+	2.73205i	0.0915064	+	0.341506i
$9$	2.81908	−	1.02606i	0.313231	−	0.114007i
$10$	5.28204	+	9.14876i	0.528204	+	0.914876i
$11$	−13.9337	−	8.04460i	−1.26670	−	0.731327i	−0.292335	−	0.956316i	$-0.594432\pi$
$11$	−13.9337	−	8.04460i	−1.26670	−	0.731327i	−0.974361	+	0.224989i	$0.927766\pi$
$12$	0.601535	−	3.41147i	0.0501279	−	0.284290i
$13$	−19.7475	+	9.20839i	−1.51904	+	0.708338i	−0.990105	−	0.140327i	$-0.955185\pi$
$13$	−19.7475	+	9.20839i	−1.51904	+	0.708338i	−0.528931	+	0.848665i	$0.677407\pi$
$14$	−1.34333	+	5.01337i	−0.0959520	+	0.358098i
$15$	−1.12765	−	12.8891i	−0.0751765	−	0.859271i
$16$	−3.06418	−	2.57115i	−0.191511	−	0.160697i
$17$	5.50944	−	11.8150i	0.324085	−	0.695002i	−0.674998	−	0.737819i	$-0.735856\pi$
$17$	5.50944	−	11.8150i	0.324085	−	0.695002i	0.999083	+	0.0428176i	$0.0136334\pi$
$18$	−2.43348	+	3.47537i	−0.135193	+	0.193076i
$19$	−8.56445	−	5.99689i	−0.450761	−	0.315626i	0.326059	−	0.945350i	$-0.394279\pi$
$19$	−8.56445	−	5.99689i	−0.450761	−	0.315626i	−0.776819	+	0.629724i	$0.783168\pi$
$20$	−13.5401	−	6.31386i	−0.677006	−	0.315693i
$21$	4.08601	−	4.86951i	0.194572	−	0.231882i
$22$	22.6670	−	1.98310i	1.03032	−	0.0901411i
$23$	3.79733	+	1.01749i	0.165101	+	0.0442387i	0.340423	−	0.940273i	$-0.389430\pi$
$23$	3.79733	+	1.01749i	0.165101	+	0.0442387i	−0.175322	+	0.984511i	$0.556097\pi$
$24$	2.07040	+	4.43998i	0.0862666	+	0.184999i
$25$	−30.3320	−	5.34835i	−1.21328	−	0.213934i
$26$	15.4071	−	26.6859i	0.592580	−	1.02638i
$27$	4.50000	−	2.59808i	0.166667	−	0.0962250i
$28$	−2.51046	−	6.89742i	−0.0896591	−	0.246336i
$29$	29.9144	−	8.01553i	1.03153	−	0.276398i	0.296931	−	0.954899i	$-0.404037\pi$
$29$	29.9144	−	8.01553i	1.03153	−	0.276398i	0.734599	+	0.678501i	$0.237370\pi$
$30$	11.7614	+	14.0167i	0.392047	+	0.467224i
$31$	42.3539	+	42.3539i	1.36625	+	1.36625i	0.865712	+	0.500542i	$0.166866\pi$
$31$	42.3539	+	42.3539i	1.36625	+	1.36625i	0.500542	+	0.865712i	$0.333134\pi$
$32$	5.63533	+	0.493027i	0.176104	+	0.0154071i
$33$	−26.1867	−	9.53118i	−0.793537	−	0.288824i
$34$	3.20143	+	18.1562i	0.0941598	+	0.534007i
$35$	−15.7246	−	22.4570i	−0.449274	−	0.641629i
$36$		−	6.00000i		−	0.166667i
$37$	4.81272	−	36.6857i	0.130074	−	0.991504i
$37$	4.81272	−	36.6857i	0.130074	−	0.991504i
$38$	14.7860			0.389105
$39$	−30.9144	+	21.6465i	−0.792677	+	0.555038i
$40$	20.8072	−	3.66887i	0.520180	−	0.0917217i
$41$	19.3118	−	53.0587i	0.471020	−	1.29412i	−0.445914	−	0.895076i	$-0.647121\pi$
$41$	19.3118	−	53.0587i	0.471020	−	1.29412i	0.916934	−	0.399040i	$-0.130657\pi$
$42$	−0.783506	+	8.95552i	−0.0186549	+	0.213227i
$43$	25.7513	−	25.7513i	0.598868	−	0.598868i	−0.341143	−	0.940011i	$-0.610814\pi$
$43$	25.7513	−	25.7513i	0.598868	−	0.598868i	0.940011	+	0.341143i	$0.110814\pi$
$44$	−24.6501	+	20.6839i	−0.560229	+	0.470088i
$45$	−5.80008	−	21.6462i	−0.128891	−	0.481027i
$46$	−5.22438	+	1.90152i	−0.113573	+	0.0413374i
$47$	−13.6685	−	23.6745i	−0.290818	−	0.503712i	0.683185	−	0.730245i	$-0.260594\pi$
$47$	−13.6685	−	23.6745i	−0.290818	−	0.503712i	−0.974003	+	0.226533i	$0.927261\pi$
$48$	−6.00000	−	3.46410i	−0.125000	−	0.0721688i
$49$	−6.16986	+	34.9910i	−0.125915	+	0.714102i
$50$	39.4767	−	18.4083i	0.789533	−	0.368165i
$51$	5.84408	−	21.8104i	0.114590	−	0.427655i
$52$	3.79806	+	43.4120i	0.0730396	+	0.834846i
$53$	−43.8842	−	36.8232i	−0.828004	−	0.694778i	0.126827	−	0.991925i	$-0.459521\pi$
$53$	−43.8842	−	36.8232i	−0.828004	−	0.694778i	−0.954832	+	0.297147i	$0.903965\pi$
$54$	−3.10560	+	6.65997i	−0.0575111	+	0.123333i
$55$	−68.9355	+	98.4500i	−1.25337	+	1.79000i
$56$	8.50316	+	5.95398i	0.151842	+	0.106321i
$57$	−16.4124	−	7.65321i	−0.287936	−	0.134267i
$58$	−28.1526	+	33.5510i	−0.485390	+	0.578465i
$59$	45.9302	−	4.01837i	0.778478	−	0.0681080i	0.309011	−	0.951058i	$-0.400002\pi$
$59$	45.9302	−	4.01837i	0.778478	−	0.0681080i	0.469466	+	0.882950i	$0.344446\pi$
$60$	−24.9949	−	6.69736i	−0.416581	−	0.111623i
$61$	−2.23345	−	4.78965i	−0.0366140	−	0.0785189i	0.887150	−	0.461481i	$-0.152682\pi$
$61$	−2.23345	−	4.78965i	−0.0366140	−	0.0785189i	−0.923764	+	0.382962i	$0.874904\pi$
$62$	−83.4209	−	14.7094i	−1.34550	−	0.237248i
$63$	5.50506	−	9.53504i	0.0873819	−	0.151350i
$64$	−6.92820	+	4.00000i	−0.108253	+	0.0625000i
$65$	55.6678	+	152.946i	0.856428	+	2.35302i
$66$	38.0675	−	10.2001i	0.576780	−	0.154548i
$67$	73.8633	+	88.0269i	1.10244	+	1.31383i	0.945280	+	0.326261i	$0.105789\pi$
$67$	73.8633	+	88.0269i	1.10244	+	1.31383i	0.157158	+	0.987573i	$0.449767\pi$
$68$	−18.4363	−	18.4363i	−0.271122	−	0.271122i
$69$	6.78327	+	0.593459i	0.0983082	+	0.00860085i
$70$	36.4325	+	13.2603i	0.520464	+	0.189433i
$71$	4.09642	+	23.2320i	0.0576961	+	0.327211i	0.999971	−	0.00762978i	$-0.00242866\pi$
$71$	4.09642	+	23.2320i	0.0576961	+	0.327211i	−0.942275	+	0.334841i	$0.891318\pi$
$72$	4.86696	+	6.95074i	0.0675966	+	0.0965380i
$73$			71.5888i			0.980668i	0.871534	+	0.490334i	$0.163125\pi$
$73$			71.5888i			0.980668i	−0.871534	+	0.490334i	$0.836875\pi$
$74$	24.1826	+	46.4026i	0.326792	+	0.627062i
$75$	−53.3470			−0.711294
$76$	−17.1289	+	11.9938i	−0.225380	+	0.157813i
$77$	−58.1510	+	10.2536i	−0.755207	+	0.133163i
$78$	18.2542	−	50.1530i	0.234028	−	0.642987i
$79$	12.1431	−	138.796i	0.153710	−	1.75691i	−0.392955	−	0.919558i	$-0.628547\pi$
$79$	12.1431	−	138.796i	0.153710	−	1.75691i	0.546664	−	0.837352i	$-0.315897\pi$
$80$	−21.1282	+	21.1282i	−0.264102	+	0.264102i
$81$	6.89440	−	5.78509i	0.0851160	−	0.0714208i
$82$	20.6672	+	77.1312i	0.252039	+	0.940624i
$83$	36.8683	−	13.4189i	0.444196	−	0.161674i	−0.110232	−	0.993906i	$-0.535159\pi$
$83$	36.8683	−	13.4189i	0.444196	−	0.161674i	0.554428	+	0.832232i	$0.312937\pi$
$84$	−6.35670	−	11.0101i	−0.0756750	−	0.131073i
$85$	−84.3347	−	48.6907i	−0.992173	−	0.572832i
$86$	−8.94335	+	50.7202i	−0.103992	+	0.589770i
$87$	48.6152	−	22.6697i	0.558796	−	0.260571i
$88$	11.7781	−	43.9565i	0.133842	−	0.499506i
$89$	9.62004	+	109.958i	0.108090	+	1.23548i	0.835584	+	0.549363i	$0.185130\pi$
$89$	9.62004	+	109.958i	0.108090	+	1.23548i	−0.727493	+	0.686115i	$0.759315\pi$
$90$	24.2777	+	20.3714i	0.269752	+	0.226349i
$91$	−33.7952	+	72.4740i	−0.371376	+	0.796418i
$92$	4.50978	−	6.44063i	0.0490193	−	0.0700069i
$93$	84.9833	+	59.5059i	0.913799	+	0.639849i
$94$	35.0381	+	16.3385i	0.372745	+	0.173814i
$95$	−50.2018	+	59.8282i	−0.528440	+	0.629770i
$96$	9.76067	−	0.853948i	0.101674	−	0.00889530i
$97$	55.8574	+	14.9669i	0.575850	+	0.154298i	0.534978	−	0.844866i	$-0.320320\pi$
$97$	55.8574	+	14.9669i	0.575850	+	0.154298i	0.0408716	+	0.999164i	$0.486987\pi$
$98$	−21.2358	−	45.5403i	−0.216692	−	0.464697i
$99$	−47.5343	−	8.38158i	−0.480145	−	0.0846625i
$100$	−30.7999	+	53.3470i	−0.307999	+	0.533470i
$101$	−92.9733	+	53.6782i	−0.920528	+	0.531467i	−0.883803	−	0.467858i	$-0.845026\pi$
$101$	−92.9733	+	53.6782i	−0.920528	+	0.531467i	−0.0367244	+	0.999325i	$0.511692\pi$
$102$	10.9216	+	30.0069i	0.107075	+	0.294185i
$103$	140.146	−	37.5520i	1.36064	−	0.364583i	0.496590	−	0.867985i	$-0.334585\pi$
$103$	140.146	−	37.5520i	1.36064	−	0.364583i	0.864052	+	0.503402i	$0.167919\pi$
$104$	−39.6140	−	47.2101i	−0.380903	−	0.453943i
$105$	−33.5763	−	33.5763i	−0.319775	−	0.319775i
$106$	80.7075	+	7.06099i	0.761391	+	0.0666131i
$107$	−49.7870	−	18.1210i	−0.465299	−	0.169355i	0.0987224	−	0.995115i	$-0.468524\pi$
$107$	−49.7870	−	18.1210i	−0.465299	−	0.169355i	−0.564022	+	0.825760i	$0.690747\pi$
$108$	−1.80460	−	10.2344i	−0.0167093	−	0.0947632i
$109$	−43.7568	−	62.4912i	−0.401438	−	0.573313i	0.566639	−	0.823966i	$-0.308244\pi$
$109$	−43.7568	−	62.4912i	−0.401438	−	0.573313i	−0.968077	+	0.250653i	$0.919355\pi$
$110$		−	169.968i		−	1.54516i
$111$	−2.82462	−	64.0236i	−0.0254470	−	0.576789i
$112$	−14.6802			−0.131073
$113$	11.4381	−	8.00904i	0.101222	−	0.0708765i	−0.521870	−	0.853025i	$-0.674765\pi$
$113$	11.4381	−	8.00904i	0.101222	−	0.0708765i	0.623092	+	0.782149i	$0.285876\pi$
$114$	25.2210	−	4.44714i	0.221237	−	0.0390100i
$115$	10.0439	−	27.5954i	0.0873383	−	0.239960i
$116$	5.39836	−	61.7036i	0.0465376	−	0.531927i
$117$	−46.2213	+	46.2213i	−0.395054	+	0.395054i
$118$	−49.9485	+	41.9118i	−0.423293	+	0.355185i
$119$	−12.3830	−	46.2140i	−0.104059	−	0.388353i
$120$	34.3881	−	12.5162i	0.286568	−	0.104302i
$121$	68.9313	+	119.392i	0.569680	+	0.986714i
$122$	6.47253	+	3.73692i	0.0530535	+	0.0306305i
$123$	16.9825	−	96.3126i	0.138069	−	0.783030i
$124$	108.571	−	50.6275i	0.875573	−	0.408286i
$125$	−11.2133	+	41.8488i	−0.0897068	+	0.334790i
$126$	1.35707	+	15.5114i	0.0107704	+	0.123106i
$127$	−77.9393	−	65.3989i	−0.613695	−	0.514952i	0.282119	−	0.959379i	$-0.408963\pi$
$127$	−77.9393	−	65.3989i	−0.613695	−	0.514952i	−0.895815	+	0.444428i	$0.853407\pi$
$128$	4.78138	−	10.2537i	0.0373545	−	0.0801070i
$129$	36.1799	−	51.6702i	0.280464	−	0.400544i
$130$	−188.552	−	132.026i	−1.45040	−	1.01558i
$131$	80.4539	+	37.5163i	0.614152	+	0.286384i	0.704697	−	0.709509i	$-0.251083\pi$
$131$	80.4539	+	37.5163i	0.614152	+	0.286384i	−0.0905446	+	0.995892i	$0.528861\pi$
$132$	−35.8255	+	42.6952i	−0.271406	+	0.323449i
$133$	−38.2252	+	3.34427i	−0.287408	+	0.0251449i
$134$	−156.971	−	42.0603i	−1.17143	−	0.313883i
$135$	−16.4039	−	35.1783i	−0.121510	−	0.260580i
$136$	36.3124	+	6.40286i	0.267003	+	0.0470799i
$137$	−52.4244	+	90.8017i	−0.382660	+	0.662786i	−0.991441	−	0.130552i	$-0.958325\pi$
$137$	−52.4244	+	90.8017i	−0.382660	+	0.662786i	0.608782	+	0.793338i	$0.291658\pi$
$138$	−8.33950	+	4.81482i	−0.0604312	+	0.0348900i
$139$	−51.3829	−	141.173i	−0.369661	−	1.01564i	−0.975491	−	0.220041i	$-0.929381\pi$
$139$	−51.3829	−	141.173i	−0.369661	−	1.01564i	0.605830	−	0.795594i	$-0.292841\pi$
$140$	−52.9616	+	14.1910i	−0.378297	+	0.101364i
$141$	−30.4353	−	36.2714i	−0.215853	−	0.257244i
$142$	−23.5904	−	23.5904i	−0.166129	−	0.166129i
$143$	349.232	+	30.5539i	2.44218	+	0.213663i
$144$	−11.2763	−	4.10424i	−0.0783077	−	0.0285017i
$145$	−40.1720	−	227.827i	−0.277048	−	1.57122i
$146$	−58.0699	−	82.9325i	−0.397739	−	0.568031i
$147$			61.5412i			0.418647i
$148$	−65.6544	−	34.1394i	−0.443611	−	0.230672i
$149$	159.139			1.06804			0.534022	−	0.845471i	$-0.320680\pi$
$149$	159.139			1.06804			0.534022	+	0.845471i	$0.320680\pi$
$150$	61.8002	−	43.2730i	0.412001	−	0.288486i
$151$	192.797	−	33.9953i	1.27680	−	0.225134i	0.506179	−	0.862428i	$-0.331058\pi$
$151$	192.797	−	33.9953i	1.27680	−	0.225134i	0.770621	+	0.637294i	$0.219946\pi$
$152$	10.1142	−	27.7885i	0.0665408	−	0.182819i
$153$	3.40860	−	38.9605i	0.0222784	−	0.254644i
$154$	59.0480	−	59.0480i	0.383429	−	0.383429i
$155$	342.751	−	287.602i	2.21130	−	1.85550i
$156$	19.5354	+	72.9071i	0.125227	+	0.467353i
$157$	−233.085	+	84.8360i	−1.48462	+	0.540357i	−0.952026	−	0.306016i	$-0.901004\pi$
$157$	−233.085	+	84.8360i	−1.48462	+	0.540357i	−0.532591	+	0.846373i	$0.678782\pi$
$158$	98.5184	+	170.639i	0.623534	+	1.07999i
$159$	−85.9302	−	49.6118i	−0.540441	−	0.312024i
$160$	7.33773	−	41.6144i	0.0458608	−	0.260090i
$161$	13.0762	−	6.09752i	0.0812184	−	0.0378728i
$162$	−3.29423	+	12.2942i	−0.0203347	+	0.0758903i
$163$	15.0050	+	171.508i	0.0920550	+	1.05219i	0.891974	+	0.452086i	$0.149320\pi$
$163$	15.0050	+	171.508i	0.0920550	+	1.05219i	−0.799919	+	0.600107i	$0.795124\pi$
$164$	−86.5078	−	72.5886i	−0.527486	−	0.442614i
$165$	−87.9752	+	188.663i	−0.533183	+	1.14341i
$166$	−31.8253	+	45.4513i	−0.191719	+	0.273803i
$167$	74.7148	+	52.3159i	0.447394	+	0.313269i	0.775472	−	0.631382i	$-0.217512\pi$
$167$	74.7148	+	52.3159i	0.447394	+	0.313269i	−0.328078	+	0.944651i	$0.606401\pi$
$168$	16.2949	+	7.59845i	0.0969936	+	0.0452288i
$169$	196.537	−	234.223i	1.16294	−	1.38594i
$170$	137.194	−	12.0029i	0.807023	−	0.0706054i
$171$	−30.2970	−	8.11806i	−0.177176	−	0.0474741i
$172$	−30.7817	−	66.0117i	−0.178964	−	0.383789i
$173$	−211.301	−	37.2580i	−1.22139	−	0.215364i	−0.474467	−	0.880273i	$-0.657359\pi$
$173$	−211.301	−	37.2580i	−1.22139	−	0.215364i	−0.746925	+	0.664909i	$0.768470\pi$
$174$	−37.9299	+	65.6965i	−0.217988	+	0.377566i
$175$	−97.8929	+	56.5185i	−0.559388	+	0.322963i
$176$	22.0113	+	60.4756i	0.125064	+	0.343612i
$177$	77.1362	−	20.6686i	0.435798	−	0.116772i
$178$	−100.338	−	119.578i	−0.563694	−	0.671784i
$179$	66.3028	+	66.3028i	0.370407	+	0.370407i	0.867625	−	0.497218i	$-0.165645\pi$
$179$	66.3028	+	66.3028i	0.370407	+	0.370407i	−0.497218	+	0.867625i	$0.665645\pi$
$180$	−44.6491	−	3.90629i	−0.248050	−	0.0217016i
$181$	−11.4646	−	4.17278i	−0.0633404	−	0.0230540i	0.310156	−	0.950686i	$-0.399619\pi$
$181$	−11.4646	−	4.17278i	−0.0633404	−	0.0230540i	−0.373496	+	0.927632i	$0.621841\pi$
$182$	−19.6378	−	111.371i	−0.107900	−	0.611930i
$183$	−5.25025	−	7.49814i	−0.0286899	−	0.0409734i
$184$			11.1193i			0.0604312i
$185$	−269.863	−	59.6980i	−1.45872	−	0.322692i
$186$	−146.718			−0.788807
$187$	−171.814	+	120.305i	−0.918791	+	0.643344i
$188$	−53.8432	+	9.49401i	−0.286400	+	0.0505000i
$189$	6.52235	−	17.9200i	0.0345098	−	0.0948149i
$190$	9.62638	−	110.030i	0.0506651	−	0.579105i
$191$	−60.1656	+	60.1656i	−0.315003	+	0.315003i	−0.846844	−	0.531841i	$-0.821500\pi$
$191$	−60.1656	+	60.1656i	−0.315003	+	0.315003i	0.531841	+	0.846844i	$0.321500\pi$
$192$	−10.6146	+	8.90673i	−0.0552845	+	0.0463892i
$193$	21.0307	+	78.4878i	0.108968	+	0.406672i	0.998765	−	0.0496832i	$-0.0158212\pi$
$193$	21.0307	+	78.4878i	0.108968	+	0.406672i	−0.889797	+	0.456356i	$0.849155\pi$
$194$	−76.8489	+	27.9707i	−0.396129	+	0.144179i
$195$	140.956	+	244.143i	0.722850	+	1.25201i
$196$	61.5412	+	35.5308i	0.313985	+	0.181280i
$197$	−41.4840	+	235.267i	−0.210579	+	1.19425i	0.677838	+	0.735212i	$0.262917\pi$
$197$	−41.4840	+	235.267i	−0.210579	+	1.19425i	−0.888416	+	0.459039i	$0.848194\pi$
$198$	61.8652	−	28.8482i	0.312451	−	0.145698i
$199$	21.8171	−	81.4227i	0.109634	−	0.409159i	−0.889196	−	0.457527i	$-0.848735\pi$
$199$	21.8171	−	81.4227i	0.109634	−	0.409159i	0.998830	+	0.0483678i	$0.0154020\pi$
$200$	−7.59260	−	86.7838i	−0.0379630	−	0.433919i
$201$	152.467	+	127.935i	0.758543	+	0.636493i
$202$	64.1639	−	137.600i	0.317643	−	0.681188i
$203$	65.1926	−	93.1047i	0.321146	−	0.458644i
$204$	−36.9925	−	25.9025i	−0.181336	−	0.126973i
$205$	−382.264	−	178.253i	−1.86470	−	0.869526i
$206$	−131.892	+	157.183i	−0.640254	+	0.763025i
$207$	11.7490	−	1.02790i	0.0567583	−	0.00496571i
$208$	84.1859	+	22.5575i	0.404740	+	0.108450i
$209$	71.0915	+	152.456i	0.340151	+	0.729456i
$210$	66.1325	+	11.6609i	0.314917	+	0.0555283i
$211$	−115.215	+	199.557i	−0.546040	+	0.945770i	0.452500	+	0.891764i	$0.350532\pi$
$211$	−115.215	+	199.557i	−0.546040	+	0.945770i	−0.998541	+	0.0540054i	$0.982801\pi$
$212$	−99.2236	+	57.2868i	−0.468036	+	0.270221i
$213$	13.9748	+	38.3956i	0.0656096	+	0.180261i
$214$	72.3751	−	19.3929i	0.338201	−	0.0906208i
$215$	−174.864	−	208.394i	−0.813319	−	0.969275i
$216$	10.3923	+	10.3923i	0.0481125	+	0.0481125i
$217$	218.990	+	19.1591i	1.00917	+	0.0882908i
$218$	101.381	+	36.8995i	0.465049	+	0.169264i
$219$	21.5316	+	122.112i	0.0983177	+	0.557588i
$220$	137.871	+	196.900i	0.626686	+	0.895000i
$221$			284.050i			1.28529i
$222$	55.2056	+	71.8773i	0.248674	+	0.323772i
$223$	223.775			1.00348			0.501738	−	0.865020i	$-0.332694\pi$
$223$	223.775			1.00348			0.501738	+	0.865020i	$0.332694\pi$
$224$	17.0063	−	11.9080i	0.0759211	−	0.0531605i
$225$	−90.9960	+	16.0451i	−0.404427	+	0.0713113i
$226$	−6.75392	+	18.5562i	−0.0298846	+	0.0821073i
$227$	−8.77925	+	100.347i	−0.0386751	+	0.442059i	0.952027	+	0.306013i	$0.0989950\pi$
$227$	−8.77925	+	100.347i	−0.0386751	+	0.442059i	−0.990703	+	0.136046i	$0.956561\pi$
$228$	−25.6101	+	25.6101i	−0.112325	+	0.112325i
$229$	208.617	−	175.050i	0.910989	−	0.764411i	−0.0613177	−	0.998118i	$-0.519530\pi$
$229$	208.617	−	175.050i	0.910989	−	0.764411i	0.972307	+	0.233708i	$0.0750858\pi$
$230$	10.7489	+	40.1153i	0.0467341	+	0.174414i
$231$	−96.1063	+	34.9798i	−0.416045	+	0.151428i
$232$	43.7977	+	75.8598i	0.188783	+	0.326982i
$233$	−306.462	−	176.936i	−1.31529	−	0.759380i	−0.332319	−	0.943167i	$-0.607831\pi$
$233$	−306.462	−	176.936i	−1.31529	−	0.759380i	−0.982966	+	0.183787i	$0.941164\pi$
$234$	16.0525	−	91.0381i	0.0686003	−	0.389052i
$235$	−185.072	+	86.3007i	−0.787543	+	0.367237i
$236$	23.8660	−	89.0692i	0.101127	−	0.377412i
$237$	−21.0324	−	240.401i	−0.0887443	−	1.01435i
$238$	51.8321	+	43.4923i	0.217782	+	0.182741i
$239$	61.4238	−	131.724i	0.257003	−	0.551145i	−0.734895	−	0.678181i	$-0.762769\pi$
$239$	61.4238	−	131.724i	0.257003	−	0.551145i	0.991898	+	0.127036i	$0.0405463\pi$
$240$	−29.6844	+	42.3938i	−0.123685	+	0.176641i
$241$	−80.8540	−	56.6146i	−0.335494	−	0.234915i	0.393674	−	0.919250i	$-0.371204\pi$
$241$	−80.8540	−	56.6146i	−0.335494	−	0.234915i	−0.729168	+	0.684335i	$0.760093\pi$
$242$	−176.700	−	82.3966i	−0.730166	−	0.340482i
$243$	10.0201	−	11.9415i	0.0412348	−	0.0491418i
$244$	−10.5294	+	0.921201i	−0.0431532	+	0.00377541i
$245$	256.369	+	68.6939i	1.04640	+	0.280383i
$246$	58.4514	+	125.349i	0.237607	+	0.509551i
$247$	224.348	+	39.5586i	0.908291	+	0.160156i
$248$	−84.7078	+	146.718i	−0.341564	+	0.591606i
$249$	58.8516	−	33.9780i	0.236352	−	0.136458i
$250$	−20.9559	−	57.5758i	−0.0838235	−	0.230303i
$251$	162.900	−	43.6489i	0.649003	−	0.173900i	0.0807251	−	0.996736i	$-0.474276\pi$
$251$	162.900	−	43.6489i	0.649003	−	0.173900i	0.568278	+	0.822837i	$0.307610\pi$
$252$	−14.1543	−	16.8685i	−0.0561680	−	0.0669384i
$253$	−44.7253	−	44.7253i	−0.176780	−	0.176780i
$254$	143.338	+	12.5405i	0.564324	+	0.0493719i
$255$	−158.497	−	57.6884i	−0.621559	−	0.226229i
$256$	2.77837	+	15.7569i	0.0108530	+	0.0615505i
$257$	33.2332	+	47.4619i	0.129312	+	0.184677i	0.878587	−	0.477582i	$-0.158487\pi$
$257$	33.2332	+	47.4619i	0.129312	+	0.184677i	−0.749275	+	0.662259i	$0.769598\pi$
$258$			89.2053i			0.345757i
$259$	−73.0130	−	114.492i	−0.281903	−	0.442054i
$260$	325.524			1.25201
$261$	76.1065	−	53.2904i	0.291596	−	0.204178i
$262$	−123.634	+	21.8000i	−0.471886	+	0.0832062i
$263$	−149.703	+	411.307i	−0.569215	+	1.56390i	0.236520	+	0.971627i	$0.423993\pi$
$263$	−149.703	+	411.307i	−0.569215	+	1.56390i	−0.805734	+	0.592277i	$0.798229\pi$
$264$	6.86968	−	78.5207i	0.0260215	−	0.297427i
$265$	−302.591	+	302.591i	−1.14185	+	1.14185i
$266$	41.5695	−	34.8810i	0.156276	−	0.131131i
$267$	49.4809	+	184.665i	0.185322	+	0.691630i
$268$	215.962	−	78.6037i	0.805828	−	0.293297i
$269$	−219.287	−	379.816i	−0.815193	−	1.41196i	−0.909189	−	0.416383i	$-0.863298\pi$
$269$	−219.287	−	379.816i	−0.815193	−	1.41196i	0.0939965	−	0.995573i	$-0.470036\pi$
$270$	47.5384	+	27.4463i	0.176068	+	0.101653i
$271$	90.0549	−	510.727i	0.332306	−	1.88460i	−0.120057	−	0.992767i	$-0.538308\pi$
$271$	90.0549	−	510.727i	0.332306	−	1.88460i	0.452363	−	0.891834i	$-0.350581\pi$
$272$	−47.2601	+	22.0378i	−0.173750	+	0.0810211i
$273$	−35.8479	+	133.786i	−0.131311	+	0.490059i
$274$	−12.9233	−	147.714i	−0.0471654	−	0.539103i
$275$	379.610	+	318.531i	1.38040	+	1.15829i
$276$	5.75537	−	12.3424i	0.0208528	−	0.0447189i
$277$	8.46570	−	12.0903i	0.0305621	−	0.0436472i	−0.803580	−	0.595196i	$-0.797074\pi$
$277$	8.46570	−	12.0903i	0.0305621	−	0.0436472i	0.834142	+	0.551549i	$0.185963\pi$
$278$	174.039	+	121.863i	0.626039	+	0.438357i
$279$	162.857	+	75.9413i	0.583715	+	0.272191i
$280$	49.8425	−	59.4000i	0.178009	−	0.212143i
$281$	−14.2400	+	1.24584i	−0.0506760	+	0.00443358i	−0.112466	−	0.993656i	$-0.535875\pi$
$281$	−14.2400	+	1.24584i	−0.0506760	+	0.00443358i	0.0617895	+	0.998089i	$0.480319\pi$
$282$	64.6798	+	17.3309i	0.229361	+	0.0614571i
$283$	−140.034	−	300.305i	−0.494821	−	1.06115i	−0.982180	−	0.187945i	$-0.939817\pi$
$283$	−140.034	−	300.305i	−0.494821	−	1.06115i	0.487359	−	0.873202i	$-0.337960\pi$
$284$	46.4639	+	8.19284i	0.163605	+	0.0288480i
$285$	−67.6367	+	117.150i	−0.237322	+	0.411053i
$286$	−429.354	+	247.888i	−1.50124	+	0.866741i
$287$	−70.8751	−	194.728i	−0.246952	−	0.678494i
$288$	16.3923	−	4.39230i	0.0569177	−	0.0152511i
$289$	76.5246	+	91.1985i	0.264791	+	0.315566i
$290$	231.341	+	231.341i	0.797728	+	0.797728i
$291$	99.7796	+	8.72959i	0.342885	+	0.0299986i
$292$	134.543	+	48.9696i	0.460763	+	0.167704i
$293$	−74.8660	−	424.586i	−0.255515	−	1.44910i	−0.794747	−	0.606941i	$-0.792396\pi$
$293$	−74.8660	−	424.586i	−0.255515	−	1.44910i	0.539232	−	0.842158i	$-0.318715\pi$
$294$	−49.9197	−	71.2927i	−0.169795	−	0.242492i
$295$		−	344.406i		−	1.16748i
$296$	103.750	−	13.7072i	0.350508	−	0.0463080i
$297$	−83.6020			−0.281488
$298$	−184.355	+	129.087i	−0.618641	+	0.433177i
$299$	−84.3570	+	14.8744i	−0.282130	+	0.0497472i
$300$	−36.4915	+	100.260i	−0.121638	+	0.334199i
$301$	11.6488	−	133.147i	0.0387004	−	0.442347i
$302$	−195.771	+	195.771i	−0.648248	+	0.648248i
$303$	−142.443	+	119.524i	−0.470110	+	0.394469i
$304$	10.8241	+	40.3960i	0.0356055	+	0.132882i
$305$	−37.0963	+	13.5020i	−0.121627	+	0.0442687i
$306$	27.6545	+	47.8989i	0.0903741	+	0.156532i
$307$	282.603	+	163.161i	0.920532	+	0.531469i	0.883805	−	0.467856i	$-0.154973\pi$
$307$	282.603	+	163.161i	0.920532	+	0.531469i	0.0367273	+	0.999325i	$0.488307\pi$
$308$	−20.5072	+	116.302i	−0.0665817	+	0.377604i
$309$	227.758	−	106.205i	0.737081	−	0.343706i
$310$	−163.771	+	611.201i	−0.528293	+	1.97162i
$311$	34.6841	+	396.441i	0.111524	+	1.27473i	0.821379	+	0.570382i	$0.193205\pi$
$311$	34.6841	+	396.441i	0.111524	+	1.27473i	−0.709855	+	0.704348i	$0.751240\pi$
$312$	−81.7702	−	68.6134i	−0.262084	−	0.219915i
$313$	−205.856	+	441.459i	−0.657686	+	1.41041i	0.240436	+	0.970665i	$0.422710\pi$
$313$	−205.856	+	441.459i	−0.657686	+	1.41041i	−0.898122	+	0.439747i	$0.855068\pi$
$314$	201.203	−	287.348i	0.640774	−	0.915121i
$315$	−67.3711	−	47.1737i	−0.213876	−	0.149758i
$316$	−252.545	−	117.763i	−0.799192	−	0.372669i
$317$	−350.381	+	417.568i	−1.10530	+	1.31725i	−0.161450	+	0.986881i	$0.551617\pi$
$317$	−350.381	+	417.568i	−1.10530	+	1.31725i	−0.943852	+	0.330367i	$0.892827\pi$
$318$	139.789	−	12.2300i	0.439589	−	0.0384591i
$319$	−481.298	−	128.964i	−1.50877	−	0.404274i
$320$	25.2554	+	54.1605i	0.0789233	+	0.169251i
$321$	−90.3738	−	15.9353i	−0.281538	−	0.0496428i
$322$	−10.2021	+	17.6706i	−0.0316836	+	0.0548775i
$323$	−118.039	+	68.1497i	−0.365445	+	0.210990i
$324$	−6.15636	−	16.9145i	−0.0190011	−	0.0522051i
$325$	648.230	−	173.693i	1.99455	−	0.534439i
$326$	−156.503	−	186.512i	−0.480069	−	0.572124i
$327$	−93.4329	−	93.4329i	−0.285727	−	0.285727i
$328$	159.096	+	13.9191i	0.485050	+	0.0424364i
$329$	−94.2771	−	34.3140i	−0.286556	−	0.104298i
$330$	−51.1208	−	289.920i	−0.154911	−	0.878546i
$331$	22.8048	+	32.5686i	0.0688966	+	0.0983946i	0.852122	−	0.523344i	$-0.175316\pi$
$331$	22.8048	+	32.5686i	0.0688966	+	0.0983946i	−0.783225	+	0.621738i	$0.786427\pi$
$332$		−	78.4688i		−	0.236352i
$333$	−24.0743	−	108.358i	−0.0722951	−	0.325399i
$334$	−128.990			−0.386199
$335$	703.141	−	492.345i	2.09893	−	1.46969i
$336$	−25.0405	+	4.41532i	−0.0745253	+	0.0131408i
$337$	−172.195	+	473.102i	−0.510965	+	1.40386i	0.369269	+	0.929323i	$0.379608\pi$
$337$	−172.195	+	473.102i	−0.510965	+	1.40386i	−0.880233	+	0.474541i	$0.842614\pi$
$338$	−37.6866	+	430.760i	−0.111499	+	1.27444i
$339$	17.1015	−	17.1015i	0.0504470	−	0.0504470i
$340$	−149.197	+	125.191i	−0.438814	+	0.368209i
$341$	−249.424	−	930.865i	−0.731450	−	2.72981i
$342$	41.6828	−	15.1713i	0.121880	−	0.0443605i
$343$	155.116	+	268.668i	0.452232	+	0.783290i
$344$	89.2053	+	51.5027i	0.259318	+	0.149717i
$345$	8.83246	−	50.0914i	0.0256013	−	0.145192i
$346$	275.005	−	128.237i	0.794812	−	0.370627i
$347$	92.1490	−	343.905i	0.265559	−	0.991080i	−0.696348	−	0.717704i	$-0.745193\pi$
$347$	92.1490	−	343.905i	0.265559	−	0.991080i	0.961907	−	0.273376i	$-0.0881403\pi$
$348$	−9.35024	−	106.874i	−0.0268685	−	0.307108i
$349$	−74.6336	−	62.6250i	−0.213850	−	0.179441i	0.529570	−	0.848266i	$-0.322353\pi$
$349$	−74.6336	−	62.6250i	−0.213850	−	0.179441i	−0.743420	+	0.668825i	$0.766798\pi$
$350$	67.5591	−	144.881i	0.193026	−	0.413945i
$351$	−64.9395	+	92.7432i	−0.185013	+	0.264226i
$352$	−74.5545	−	52.2036i	−0.211803	−	0.148306i
$353$	−121.765	−	56.7802i	−0.344945	−	0.160850i	0.242423	−	0.970171i	$-0.422058\pi$
$353$	−121.765	−	56.7802i	−0.344945	−	0.160850i	−0.587367	+	0.809320i	$0.699836\pi$
$354$	−72.5934	+	86.5134i	−0.205066	+	0.244388i
$355$	175.548	−	15.3584i	0.494501	−	0.0432632i
$356$	213.233	+	57.1356i	0.598969	+	0.160493i
$357$	−35.0218	−	75.1045i	−0.0981004	−	0.210377i
$358$	−130.591	−	23.0267i	−0.364780	−	0.0643205i
$359$	43.1441	−	74.7277i	0.120178	−	0.208155i	−0.799659	−	0.600454i	$-0.794987\pi$
$359$	43.1441	−	74.7277i	0.120178	−	0.208155i	0.919838	+	0.392299i	$0.128320\pi$
$360$	54.8926	−	31.6922i	0.152479	−	0.0880340i
$361$	−86.0822	−	236.509i	−0.238455	−	0.655149i
$362$	16.6660	−	4.46565i	0.0460388	−	0.0123361i
$363$	153.488	+	182.920i	0.422832	+	0.503911i
$364$	113.089	+	113.089i	0.310685	+	0.310685i
$365$	532.729	+	46.6077i	1.45953	+	0.127692i
$366$	12.1644	+	4.42747i	0.0332360	+	0.0120969i
$367$	32.7768	+	185.886i	0.0893100	+	0.506502i	0.996343	+	0.0854428i	$0.0272305\pi$
$367$	32.7768	+	185.886i	0.0893100	+	0.506502i	−0.907033	+	0.421059i	$0.861658\pi$
$368$	−9.01956	−	12.8813i	−0.0245097	−	0.0350034i
$369$		−	169.392i		−	0.459056i
$370$	361.049	−	149.745i	0.975809	−	0.404715i
$371$	−210.245			−0.566698
$372$	169.967	−	119.012i	0.456899	−	0.319924i
$373$	288.595	−	50.8872i	0.773714	−	0.136427i	0.227168	−	0.973856i	$-0.427053\pi$
$373$	288.595	−	50.8872i	0.773714	−	0.136427i	0.546546	+	0.837429i	$0.315942\pi$
$374$	101.452	−	278.737i	0.271262	−	0.745286i
$375$	−6.54027	+	74.7556i	−0.0174407	+	0.199348i
$376$	54.6738	−	54.6738i	0.145409	−	0.145409i
$377$	−516.923	+	433.750i	−1.37115	+	1.15053i
$378$	6.98014	+	26.0502i	0.0184660	+	0.0689159i
$379$	147.216	−	53.5822i	0.388432	−	0.141378i	−0.140419	−	0.990092i	$-0.544845\pi$
$379$	147.216	−	53.5822i	0.388432	−	0.141378i	0.528852	+	0.848714i	$0.322623\pi$
$380$	78.1001	+	135.273i	0.205527	+	0.355983i
$381$	−152.614	−	88.1116i	−0.400561	−	0.231264i
$382$	20.8953	−	118.503i	0.0546997	−	0.310218i
$383$	−303.275	+	141.420i	−0.791842	+	0.369242i	−0.776080	−	0.630634i	$-0.782795\pi$
$383$	−303.275	+	141.420i	−0.791842	+	0.369242i	−0.0157612	+	0.999876i	$0.505017\pi$
$384$	5.07180	−	18.9282i	0.0132078	−	0.0492922i
$385$	38.4431	+	439.406i	0.0998522	+	1.14132i
$386$	−88.0293	−	73.8653i	−0.228055	−	0.191361i
$387$	46.1726	−	99.0175i	0.119309	−	0.255859i
$388$	66.3374	−	94.7396i	0.170973	−	0.244174i
$389$	124.115	+	86.9061i	0.319061	+	0.223409i	0.722125	−	0.691763i	$-0.243166\pi$
$389$	124.115	+	86.9061i	0.319061	+	0.223409i	−0.403063	+	0.915172i	$0.632055\pi$
$390$	−361.330	−	168.491i	−0.926487	−	0.432028i
$391$	32.9428	−	39.2597i	0.0842527	−	0.100408i
$392$	−100.114	+	8.75883i	−0.255393	+	0.0223440i
$393$	148.517	+	39.7950i	0.377906	+	0.101260i
$394$	−142.782	−	306.197i	−0.362391	−	0.777150i
$395$	−1024.94	−	180.725i	−2.59480	−	0.457533i
$396$	−48.2676	+	83.6020i	−0.121888	+	0.211116i
$397$	66.3019	−	38.2794i	0.167007	−	0.0964216i	−0.414167	−	0.910201i	$-0.635927\pi$
$397$	66.3019	−	38.2794i	0.167007	−	0.0964216i	0.581174	+	0.813779i	$0.302594\pi$
$398$	40.7726	+	112.022i	0.102444	+	0.281462i
$399$	−64.1963	+	17.2014i	−0.160893	+	0.0431112i
$400$	79.1912	+	94.3764i	0.197978	+	0.235941i
$401$	380.204	+	380.204i	0.948141	+	0.948141i	0.998720	−	0.0505794i	$-0.0161068\pi$
$401$	380.204	+	380.204i	0.948141	+	0.948141i	−0.0505794	+	0.998720i	$0.516107\pi$
$402$	−280.402	−	24.5320i	−0.697518	−	0.0610249i
$403$	−1226.39	−	446.371i	−3.04316	−	1.10762i
$404$	37.2845	+	211.451i	0.0922883	+	0.523393i
$405$	−38.5612	−	55.0711i	−0.0952129	−	0.135978i
$406$			160.739i			0.395910i
$407$	−362.180	+	472.449i	−0.889878	+	1.16081i
$408$	63.8653			0.156532
$409$	588.978	−	412.407i	1.44004	−	1.00833i	0.446512	−	0.894778i	$-0.352666\pi$
$409$	588.978	−	412.407i	1.44004	−	1.00833i	0.993532	−	0.113552i	$-0.0362229\pi$
$410$	587.428	−	103.579i	1.43275	−	0.252633i
$411$	−62.1120	+	170.651i	−0.151124	+	0.415210i
$412$	25.2908	−	289.076i	0.0613855	−	0.701640i
$413$	119.649	−	119.649i	0.289707	−	0.289707i
$414$	−12.7769	+	10.7211i	−0.0308620	+	0.0258963i
$415$	−75.8542	−	283.092i	−0.182781	−	0.682149i
$416$	−115.823	+	42.1563i	−0.278422	+	0.101337i
$417$	−130.106	−	225.350i	−0.312005	−	0.540408i
$418$	−206.023	−	118.947i	−0.492877	−	0.284563i
$419$	40.6027	−	230.269i	0.0969038	−	0.549569i	−0.897244	−	0.441536i	$-0.854434\pi$
$419$	40.6027	−	230.269i	0.0969038	−	0.549569i	0.994147	−	0.108033i	$-0.0344551\pi$
$420$	−86.0704	+	40.1353i	−0.204930	+	0.0955602i
$421$	−155.776	+	581.362i	−0.370013	+	1.38091i	0.490483	+	0.871451i	$0.336820\pi$
$421$	−155.776	+	581.362i	−0.370013	+	1.38091i	−0.860496	+	0.509457i	$0.829846\pi$
$422$	−28.4020	−	324.636i	−0.0673032	−	0.769279i
$423$	−62.8239	−	52.7155i	−0.148520	−	0.124623i
$424$	68.4775	−	146.850i	0.161503	−	0.346345i
$425$	−230.303	+	328.907i	−0.541890	+	0.773899i
$426$	−47.3342	−	33.1437i	−0.111113	−	0.0778022i
$427$	−17.5782	−	8.19686i	−0.0411668	−	0.0191964i
$428$	−68.1127	+	81.1735i	−0.159142	+	0.189658i
$429$	604.888	−	52.9209i	1.41000	−	0.123359i
$430$	371.613	+	99.5733i	0.864215	+	0.231566i
$431$	−305.427	−	654.991i	−0.708648	−	1.51970i	−0.848309	−	0.529502i	$-0.822379\pi$
$431$	−305.427	−	654.991i	−0.708648	−	1.51970i	0.139661	−	0.990199i	$-0.455399\pi$
$432$	−20.4688	−	3.60921i	−0.0473816	−	0.00835465i
$433$	122.855	−	212.792i	0.283730	−	0.491436i	−0.688570	−	0.725170i	$-0.741761\pi$
$433$	122.855	−	212.792i	0.283730	−	0.491436i	0.972301	+	0.233734i	$0.0750946\pi$
$434$	−269.231	+	155.440i	−0.620347	+	0.358158i
$435$	−137.046	−	376.530i	−0.315047	−	0.865586i
$436$	−147.376	+	39.4894i	−0.338019	+	0.0905720i
$437$	−26.4202	−	31.4864i	−0.0604582	−	0.0720512i
$438$	−123.995	−	123.995i	−0.283095	−	0.283095i
$439$	−243.659	−	21.3174i	−0.555032	−	0.0485590i	−0.193810	−	0.981039i	$-0.562085\pi$
$439$	−243.659	−	21.3174i	−0.555032	−	0.0485590i	−0.361222	+	0.932480i	$0.617640\pi$
$440$	−319.435	−	116.265i	−0.725988	−	0.264238i
$441$	18.5096	+	104.973i	0.0419718	+	0.238034i
$442$	−230.410	−	329.059i	−0.521289	−	0.744478i
$443$		−	611.711i		−	1.38084i	−0.723410	−	0.690419i	$-0.757426\pi$
$443$		−	611.711i		−	1.38084i	0.723410	−	0.690419i	$-0.242574\pi$
$444$	−122.257	−	38.4862i	−0.275354	−	0.0866806i
$445$	824.513			1.85284
$446$	−259.234	+	181.517i	−0.581242	+	0.406990i
$447$	271.449	−	47.8637i	0.607267	−	0.107078i
$448$	−10.0418	+	27.5897i	−0.0224148	+	0.0615841i
$449$	−4.17558	+	47.7271i	−0.00929973	+	0.106296i	−0.999426	−	0.0338834i	$-0.989213\pi$
$449$	−4.17558	+	47.7271i	−0.00929973	+	0.106296i	0.990126	+	0.140180i	$0.0447681\pi$
$450$	92.3998	−	92.3998i	0.205333	−	0.205333i
$451$	−695.921	+	583.947i	−1.54306	+	1.29478i
$452$	−7.22796	−	26.9751i	−0.0159911	−	0.0596794i
$453$	318.636	−	115.974i	0.703390	−	0.256013i
$454$	−71.2273	−	123.369i	−0.156888	−	0.271739i
$455$	517.314	+	298.671i	1.13695	+	0.656420i
$456$	8.89428	−	50.4420i	0.0195050	−	0.110618i
$457$	437.913	−	204.202i	0.958234	−	0.446832i	0.120381	−	0.992728i	$-0.461588\pi$
$457$	437.913	−	204.202i	0.958234	−	0.446832i	0.837853	+	0.545896i	$0.183811\pi$
$458$	−99.6795	+	372.009i	−0.217641	+	0.812247i
$459$	−5.90387	−	67.4816i	−0.0128625	−	0.147019i
$460$	−44.9919	−	37.7527i	−0.0978086	−	0.0820711i
$461$	227.299	−	487.445i	0.493057	−	1.05737i	−0.489602	−	0.871946i	$-0.662858\pi$
$461$	227.299	−	487.445i	0.493057	−	1.05737i	0.982660	−	0.185419i	$-0.0593643\pi$
$462$	82.9607	−	118.480i	0.179569	−	0.256451i
$463$	414.653	+	290.343i	0.895580	+	0.627092i	0.928080	−	0.372380i	$-0.121458\pi$
$463$	414.653	+	290.343i	0.895580	+	0.627092i	−0.0325007	+	0.999472i	$0.510347\pi$
$464$	−112.272	−	52.3533i	−0.241966	−	0.112830i
$465$	498.142	−	593.663i	1.07127	−	1.27669i
$466$	498.545	−	43.6171i	1.06984	−	0.0935988i
$467$	607.085	+	162.668i	1.29997	+	0.348325i	0.841438	−	0.540354i	$-0.181710\pi$
$467$	607.085	+	162.668i	1.29997	+	0.348325i	0.458530	+	0.888679i	$0.348376\pi$
$468$	55.2504	+	118.485i	0.118056	+	0.253173i
$469$	415.321	+	73.2323i	0.885545	+	0.156146i
$470$	144.395	−	250.099i	0.307223	−	0.532125i
$471$	−372.066	+	214.812i	−0.789949	+	0.456077i
$472$	44.6016	+	122.542i	0.0944949	+	0.259623i
$473$	−565.970	+	151.651i	−1.19655	+	0.320616i
$474$	219.369	+	261.434i	0.462804	+	0.551548i
$475$	227.703	+	227.703i	0.479376	+	0.479376i
$476$	−95.3244	−	8.33980i	−0.200261	−	0.0175206i
$477$	−161.496	−	58.7797i	−0.338566	−	0.123228i
$478$	35.6922	+	202.421i	0.0746699	+	0.423474i
$479$	−228.706	−	326.627i	−0.477466	−	0.681893i	0.506093	−	0.862479i	$-0.331089\pi$
$479$	−228.706	−	326.627i	−0.477466	−	0.681893i	−0.983559	+	0.180586i	$0.942200\pi$
$480$		−	73.1901i		−	0.152479i
$481$	242.777	+	768.766i	0.504734	+	1.59827i
$482$	139.589			0.289604
$483$	20.4706	−	14.3336i	0.0423821	−	0.0296763i
$484$	271.536	−	47.8791i	0.561025	−	0.0989239i
$485$	147.743	−	405.919i	0.304624	−	0.836947i
$486$	−1.92138	+	21.9615i	−0.00395346	+	0.0451883i
$487$	−1.97637	+	1.97637i	−0.00405825	+	0.00405825i	−0.709133	−	0.705075i	$-0.750913\pi$
$487$	−1.97637	+	1.97637i	−0.00405825	+	0.00405825i	0.705075	+	0.709133i	$0.250913\pi$
$488$	11.4506	−	9.60817i	0.0234643	−	0.0196889i
$489$	77.1784	+	288.034i	0.157829	+	0.589026i
$490$	−352.714	+	128.377i	−0.719824	+	0.261995i
$491$	373.647	+	647.175i	0.760991	+	1.31808i	0.942340	+	0.334656i	$0.108620\pi$
$491$	373.647	+	647.175i	0.760991	+	1.31808i	−0.181349	+	0.983419i	$0.558046\pi$
$492$	−169.392	−	97.7984i	−0.344292	−	0.198777i
$493$	70.1076	−	397.600i	0.142206	−	0.806491i
$494$	−291.986	+	136.155i	−0.591064	+	0.275618i
$495$	−93.3187	+	348.270i	−0.188523	+	0.703576i
$496$	−20.8816	−	238.678i	−0.0421000	−	0.481206i
$497$	66.3223	+	55.6510i	0.133445	+	0.111974i
$498$	−40.6154	+	87.1000i	−0.0815570	+	0.174900i
$499$	−303.630	+	433.628i	−0.608476	+	0.868994i	−0.998660	−	0.0517425i	$-0.983522\pi$
$499$	−303.630	+	433.628i	−0.608476	+	0.868994i	0.390184	+	0.920737i	$0.372411\pi$
$500$	70.9796	+	49.7004i	0.141959	+	0.0994009i
$501$	143.179	+	66.7654i	0.285786	+	0.133264i
$502$	−153.306	+	182.703i	−0.305391	+	0.363950i
$503$	−60.5053	+	5.29353i	−0.120289	+	0.0105239i	−0.147141	−	0.989116i	$-0.547007\pi$
$503$	−60.5053	+	5.29353i	−0.120289	+	0.0105239i	0.0268523	+	0.999639i	$0.491452\pi$
$504$	30.0802	+	8.05997i	0.0596830	+	0.0159920i
$505$	338.916	+	726.809i	0.671122	+	1.43923i
$506$	88.0917	+	15.5329i	0.174094	+	0.0306975i
$507$	264.793	−	458.635i	0.522275	−	0.904606i
$508$	−176.223	+	101.743i	−0.346896	+	0.200281i
$509$	−348.132	−	956.485i	−0.683953	−	1.87915i	−0.356996	−	0.934106i	$-0.616199\pi$
$509$	−348.132	−	956.485i	−0.683953	−	1.87915i	−0.326957	−	0.945039i	$-0.606023\pi$
$510$	230.407	−	61.7373i	0.451778	−	0.121054i
$511$	168.882	+	201.266i	0.330493	+	0.393866i
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	−54.1204	−	4.73492i	−0.105498	−	0.00922987i
$514$	−76.9984	−	28.0251i	−0.149802	−	0.0545236i
$515$	−188.202	−	1067.35i	−0.365441	−	2.07252i
$516$	−72.3597	−	103.340i	−0.140232	−	0.200272i
$517$			439.829i			0.850733i
$518$	177.454	+	73.4088i	0.342575	+	0.141716i
$519$	−371.630			−0.716049
$520$	−377.105	+	264.052i	−0.725201	+	0.507791i
$521$	−179.713	+	31.6883i	−0.344939	+	0.0608221i	−0.343434	−	0.939177i	$-0.611590\pi$
$521$	−179.713	+	31.6883i	−0.344939	+	0.0608221i	−0.00150514	+	0.999999i	$0.500479\pi$
$522$	−44.9391	+	123.469i	−0.0860902	+	0.236531i
$523$	−29.5951	+	338.273i	−0.0565872	+	0.646794i	0.913947	+	0.405833i	$0.133018\pi$
$523$	−29.5951	+	338.273i	−0.0565872	+	0.646794i	−0.970535	+	0.240962i	$0.922537\pi$
$524$	125.541	−	125.541i	0.239583	−	0.239583i
$525$	−149.981	+	125.849i	−0.285677	+	0.239712i
$526$	−160.211	−	597.914i	−0.304583	−	1.13672i
$527$	733.758	−	267.066i	1.39233	−	0.506767i
$528$	55.7346	+	96.5352i	0.105558	+	0.182832i
$529$	−444.743	−	256.773i	−0.840724	−	0.485392i
$530$	105.089	−	595.988i	0.198281	−	1.12451i
$531$	125.358	−	58.4552i	0.236078	−	0.110085i
$532$	−19.8624	+	74.1275i	−0.0373354	+	0.139337i
$533$	107.227	+	1225.61i	0.201176	+	2.29945i
$534$	−207.114	−	173.790i	−0.387855	−	0.325449i
$535$	−167.261	+	358.693i	−0.312638	+	0.670454i
$536$	−186.422	+	266.239i	−0.347803	+	0.496714i
$537$	133.037	+	93.1535i	0.247741	+	0.173470i
$538$	562.126	+	262.123i	1.04484	+	0.487218i
$539$	367.457	−	437.919i	0.681739	−	0.812465i
$540$	−77.3344	+	6.76589i	−0.143212	+	0.0125294i
$541$	582.627	+	156.114i	1.07694	+	0.288566i	0.753343	−	0.657628i	$-0.228440\pi$
$541$	582.627	+	156.114i	1.07694	+	0.288566i	0.323600	+	0.946194i	$0.395107\pi$
$542$	309.956	+	664.703i	0.571875	+	1.22639i
$543$	−20.8107	−	3.66948i	−0.0383253	−	0.00675779i
$544$	36.8726	−	63.8653i	0.0677806	−	0.117399i
$545$	−493.516	+	284.932i	−0.905534	+	0.522810i
$546$	−66.9937	−	184.064i	−0.122699	−	0.337113i
$547$	−360.650	+	96.6358i	−0.659323	+	0.176665i	−0.572941	−	0.819597i	$-0.694197\pi$
$547$	−360.650	+	96.6358i	−0.659323	+	0.176665i	−0.0863826	+	0.996262i	$0.527531\pi$
$548$	134.791	+	160.638i	0.245969	+	0.293134i
$549$	−11.2107	−	11.2107i	−0.0204203	−	0.0204203i
$550$	−698.141	−	61.0795i	−1.26935	−	0.111054i
$551$	−304.268	−	110.745i	−0.552211	−	0.200988i
$552$	3.34434	+	18.9667i	0.00605858	+	0.0343599i
$553$	−293.288	−	418.859i	−0.530358	−	0.757430i
$554$			20.8731i			0.0376770i
$555$	−478.271	−	20.6630i	−0.861750	−	0.0372306i
$556$	−300.467			−0.540408
$557$	−674.873	+	472.551i	−1.21162	+	0.848386i	−0.991881	−	0.127172i	$-0.959410\pi$
$557$	−674.873	+	472.551i	−1.21162	+	0.848386i	−0.219741	+	0.975558i	$0.570521\pi$
$558$	−250.263	+	44.1281i	−0.448499	+	0.0790825i
$559$	−271.395	+	745.652i	−0.485501	+	1.33390i
$560$	−9.55749	+	109.243i	−0.0170669	+	0.195076i
$561$	−256.885	+	256.885i	−0.457906	+	0.457906i
$562$	15.4858	−	12.9941i	0.0275548	−	0.0231212i
$563$	148.147	+	552.894i	0.263139	+	0.982049i	0.963379	+	0.268142i	$0.0864096\pi$
$563$	148.147	+	552.894i	0.263139	+	0.982049i	−0.700240	+	0.713907i	$0.746924\pi$
$564$	−88.9868	+	32.3886i	−0.157778	+	0.0574265i
$565$	−52.1526	−	90.3310i	−0.0923055	−	0.159878i
$566$	405.818	+	234.299i	0.716994	+	0.413957i
$567$	5.73566	−	32.5286i	0.0101158	−	0.0573696i
$568$	−60.4721	+	28.1986i	−0.106465	+	0.0496454i
$569$	−7.07715	+	26.4123i	−0.0124379	+	0.0464188i	−0.971866	−	0.235535i	$-0.924316\pi$
$569$	−7.07715	+	26.4123i	−0.0124379	+	0.0464188i	0.959428	+	0.281954i	$0.0909825\pi$
$570$	−16.6734	−	190.578i	−0.0292515	−	0.334346i
$571$	440.591	+	369.700i	0.771614	+	0.647461i	0.941122	−	0.338068i	$-0.109773\pi$
$571$	440.591	+	369.700i	0.771614	+	0.647461i	−0.169508	+	0.985529i	$0.554218\pi$
$572$	296.311	−	635.442i	0.518027	−	1.11091i
$573$	−84.5309	+	120.723i	−0.147523	+	0.210685i
$574$	240.061	+	168.093i	0.418225	+	0.292844i
$575$	−109.739	−	51.1719i	−0.190850	−	0.0889947i
$576$	−15.4269	+	18.3851i	−0.0267828	+	0.0319185i
$577$	116.058	−	10.1538i	0.201141	−	0.0175975i	0.0138598	−	0.999904i	$-0.495588\pi$
$577$	116.058	−	10.1538i	0.201141	−	0.0175975i	0.187281	+	0.982306i	$0.440033\pi$
$578$	−162.627	−	43.5758i	−0.281362	−	0.0753906i
$579$	59.4795	+	127.554i	0.102728	+	0.220301i
$580$	−455.653	−	80.3439i	−0.785609	−	0.138524i
$581$	71.9959	−	124.701i	0.123917	−	0.214631i
$582$	−122.671	+	70.8244i	−0.210776	+	0.121691i
$583$	315.240	+	866.114i	0.540720	+	1.48562i
$584$	−195.584	+	52.4066i	−0.334905	+	0.0897374i
$585$	313.864	+	374.048i	0.536519	+	0.639399i
$586$	431.136	+	431.136i	0.735727	+	0.735727i
$587$	86.8026	+	7.59425i	0.147875	+	0.0129374i	0.160853	−	0.986978i	$-0.448576\pi$
$587$	86.8026	+	7.59425i	0.147875	+	0.0129374i	−0.0129778	+	0.999916i	$0.504131\pi$
$588$	115.660	+	42.0966i	0.196700	+	0.0715929i
$589$	−108.746	−	616.729i	−0.184628	−	1.04708i
$590$	279.368	+	398.979i	0.473505	+	0.676236i
$591$			413.781i			0.700137i
$592$	−109.071	+	100.037i	−0.184242	+	0.168982i
$593$	574.213			0.968319			0.484160	−	0.874980i	$-0.339125\pi$
$593$	574.213			0.968319			0.484160	+	0.874980i	$0.339125\pi$
$594$	96.8492	−	67.8145i	0.163046	−	0.114166i
$595$	−351.964	+	62.0607i	−0.591536	+	0.104304i
$596$	108.857	−	299.083i	0.182646	−	0.501817i
$597$	12.7250	−	145.448i	0.0213149	−	0.243631i
$598$	85.6583	−	85.6583i	0.143241	−	0.143241i
$599$	−444.536	+	373.010i	−0.742131	+	0.622722i	−0.933409	−	0.358814i	$-0.883181\pi$
$599$	−444.536	+	373.010i	−0.742131	+	0.622722i	0.191278	+	0.981536i	$0.438737\pi$
$600$	−39.0527	−	145.747i	−0.0650879	−	0.242911i
$601$	−302.193	+	109.989i	−0.502817	+	0.183011i	−0.580961	−	0.813932i	$-0.697323\pi$
$601$	−302.193	+	109.989i	−0.502817	+	0.183011i	0.0781433	+	0.996942i	$0.475101\pi$
$602$	94.5085	+	163.693i	0.156991	+	0.271916i
$603$	298.547	+	172.366i	0.495103	+	0.285848i
$604$	67.9905	−	385.593i	0.112567	−	0.638400i
$605$	933.337	−	435.222i	1.54271	−	0.719376i
$606$	68.0612	−	254.008i	0.112312	−	0.419155i
$607$	4.27852	+	48.9037i	0.00704863	+	0.0805662i	0.998904	−	0.0468014i	$-0.0149028\pi$
$607$	4.27852	+	48.9037i	0.00704863	+	0.0805662i	−0.991856	+	0.127368i	$0.959347\pi$
$608$	−45.3069	−	38.0170i	−0.0745179	−	0.0625279i
$609$	83.1986	−	178.420i	0.136615	−	0.292972i
$610$	32.0222	−	45.7325i	0.0524954	−	0.0749712i
$611$	487.921	+	341.646i	0.798561	+	0.559159i
$612$	−70.8902	−	33.0566i	−0.115834	−	0.0540141i
$613$	−53.2731	+	63.4884i	−0.0869056	+	0.103570i	−0.807745	−	0.589532i	$-0.799312\pi$
$613$	−53.2731	+	63.4884i	−0.0869056	+	0.103570i	0.720839	+	0.693102i	$0.243757\pi$
$614$	−459.733	+	40.2214i	−0.748751	+	0.0655072i
$615$	−705.655	−	189.080i	−1.14741	−	0.307447i
$616$	−70.5828	−	151.365i	−0.114582	−	0.245723i
$617$	537.252	+	94.7321i	0.870750	+	0.153537i	0.591132	−	0.806575i	$-0.298681\pi$
$617$	537.252	+	94.7321i	0.870750	+	0.153537i	0.279618	+	0.960111i	$0.409792\pi$
$618$	−177.698	+	307.782i	−0.287537	+	0.498029i
$619$	−71.1557	+	41.0817i	−0.114953	+	0.0663679i	−0.556374	−	0.830932i	$-0.687808\pi$
$619$	−71.1557	+	41.0817i	−0.114953	+	0.0663679i	0.441421	+	0.897300i	$0.354474\pi$
$620$	−306.060	−	840.893i	−0.493645	−	1.35628i
$621$	19.7315	−	5.28703i	0.0317737	−	0.00851374i
$622$	−361.757	−	431.125i	−0.581603	−	0.693127i
$623$	286.442	+	286.442i	0.459779	+	0.459779i
$624$	150.384	+	13.1569i	0.240999	+	0.0210847i
$625$	−419.444	−	152.665i	−0.671110	−	0.244264i
$626$	−119.619	−	678.392i	−0.191084	−	1.08369i
$627$	167.117	+	238.668i	0.266535	+	0.380651i
$628$			496.088i			0.789949i
$629$	−406.927	−	258.980i	−0.646942	−	0.411733i
$630$	116.312			0.184622
$631$	645.418	−	451.926i	1.02285	−	0.716207i	0.0633710	−	0.997990i	$-0.479815\pi$
$631$	645.418	−	451.926i	1.02285	−	0.716207i	0.959478	+	0.281783i	$0.0909260\pi$
$632$	388.087	−	68.4302i	0.614061	−	0.108276i
$633$	−136.505	+	375.045i	−0.215648	+	0.592489i
$634$	67.1868	−	767.949i	0.105973	−	1.21128i
$635$	−537.408	+	537.408i	−0.846312	+	0.846312i
$636$	−152.019	+	127.559i	−0.239024	+	0.200565i
$637$	−200.372	−	747.798i	−0.314556	−	1.17394i
$638$	662.173	−	241.011i	1.03789	−	0.377761i
$639$	35.3855	+	61.2895i	0.0553764	+	0.0959148i
$640$	−73.1901	−	42.2563i	−0.114360	−	0.0660255i
$641$	−10.4541	+	59.2881i	−0.0163090	+	0.0924932i	−0.991876	−	0.127210i	$-0.959398\pi$
$641$	−10.4541	+	59.2881i	−0.0163090	+	0.0924932i	0.975567	+	0.219703i	$0.0705089\pi$
$642$	117.620	−	54.8472i	0.183209	−	0.0854317i
$643$	−209.890	+	783.319i	−0.326423	+	1.21823i	0.586452	+	0.809984i	$0.300524\pi$
$643$	−209.890	+	783.319i	−0.326423	+	1.21823i	−0.912874	+	0.408241i	$0.866142\pi$
$644$	−2.51496	−	28.7461i	−0.00390522	−	0.0446368i
$645$	−360.949	−	302.872i	−0.559611	−	0.469570i
$646$	81.4624	−	174.697i	0.126103	−	0.270428i
$647$	322.901	−	461.150i	0.499074	−	0.712751i	−0.488031	−	0.872826i	$-0.662285\pi$
$647$	322.901	−	461.150i	0.499074	−	0.712751i	0.987105	+	0.160075i	$0.0511736\pi$
$648$	20.8522	+	14.6009i	0.0321793	+	0.0225322i
$649$	−672.302	−	313.499i	−1.03590	−	0.483050i
$650$	−610.053	+	727.033i	−0.938544	+	1.11851i
$651$	379.301	−	33.1845i	0.582644	−	0.0509747i
$652$	332.593	+	89.1179i	0.510112	+	0.136684i
$653$	−167.841	−	359.937i	−0.257031	−	0.551205i	0.734871	−	0.678207i	$-0.237243\pi$
$653$	−167.841	−	359.937i	−0.257031	−	0.551205i	−0.991903	+	0.127001i	$0.959465\pi$
$654$	184.027	+	32.4489i	0.281387	+	0.0496160i
$655$	331.557	−	574.274i	0.506194	−	0.876754i
$656$	−195.597	+	112.928i	−0.298166	+	0.172146i
$657$	73.4544	+	201.814i	0.111803	+	0.307176i
$658$	137.050	−	36.7224i	0.208283	−	0.0558092i
$659$	95.5864	+	113.915i	0.145048	+	0.172861i	0.833677	−	0.552253i	$-0.186232\pi$
$659$	95.5864	+	113.915i	0.145048	+	0.172861i	−0.688629	+	0.725114i	$0.741787\pi$
$660$	294.393	+	294.393i	0.446050	+	0.446050i
$661$	−555.874	−	48.6327i	−0.840960	−	0.0735744i	−0.341468	−	0.939893i	$-0.610924\pi$
$661$	−555.874	−	48.6327i	−0.840960	−	0.0735744i	−0.499491	+	0.866319i	$0.666480\pi$
$662$	−52.8367	−	19.2310i	−0.0798137	−	0.0290498i
$663$	85.4330	+	484.515i	0.128858	+	0.730791i
$664$	63.6507	+	90.9026i	0.0958595	+	0.136902i
$665$			286.631i			0.431024i
$666$	115.785	+	106.000i	0.173851	+	0.159159i
$667$	121.750			0.182534
$668$	149.430	−	104.632i	0.223697	−	0.156634i
$669$	381.702	−	67.3043i	0.570556	−	0.100604i
$670$	−415.188	+	1140.72i	−0.619684	+	1.70257i
$671$	−7.41069	+	84.7046i	−0.0110443	+	0.126236i
$672$	25.4268	−	25.4268i	0.0378375	−	0.0378375i
$673$	118.400	−	99.3494i	0.175929	−	0.147622i	−0.550571	−	0.834788i	$-0.685590\pi$
$673$	118.400	−	99.3494i	0.175929	−	0.147622i	0.726500	+	0.687166i	$0.241146\pi$
$674$	−184.281	−	687.746i	−0.273414	−	1.02039i
$675$	−150.389	+	54.7373i	−0.222799	+	0.0810923i
$676$	−305.757	−	529.587i	−0.452303	−	0.783412i
$677$	−56.4263	−	32.5778i	−0.0833476	−	0.0481208i	0.457747	−	0.889083i	$-0.348657\pi$
$677$	−56.4263	−	32.5778i	−0.0833476	−	0.0481208i	−0.541095	+	0.840962i	$0.681990\pi$
$678$	−5.93930	+	33.6834i	−0.00876003	+	0.0496806i
$679$	192.346	−	89.6925i	0.283279	−	0.132095i
$680$	71.2881	−	266.051i	0.104835	−	0.391251i
$681$	15.2061	+	173.807i	0.0223291	+	0.255223i
$682$	1044.03	+	876.043i	1.53083	+	1.28452i
$683$	122.533	−	262.773i	0.179404	−	0.384733i	−0.795955	−	0.605355i	$-0.793031\pi$
$683$	122.533	−	262.773i	0.179404	−	0.384733i	0.975359	+	0.220622i	$0.0708089\pi$
$684$	−35.9814	+	51.3867i	−0.0526043	+	0.0751268i
$685$	641.571	+	449.233i	0.936599	+	0.655814i
$686$	−397.628	−	185.417i	−0.579632	−	0.270287i
$687$	303.196	−	361.334i	0.441333	−	0.525960i
$688$	−145.117	+	12.6961i	−0.210926	+	0.0184537i
$689$	1205.69	+	323.062i	1.74991	+	0.468886i
$690$	30.4001	+	65.1932i	0.0440581	+	0.0944829i
$691$	13.3762	+	2.35859i	0.0193578	+	0.00341330i	0.183319	−	0.983054i	$-0.441316\pi$
$691$	13.3762	+	2.35859i	0.0193578	+	0.00341330i	−0.163961	+	0.986467i	$0.552427\pi$
$692$	−214.560	+	371.630i	−0.310058	+	0.537037i
$693$	−153.411	+	88.5720i	−0.221373	+	0.127810i
$694$	172.211	+	473.146i	0.248143	+	0.681767i
$695$	−1083.99	+	290.456i	−1.55970	+	0.417922i
$696$	97.5235	+	116.224i	0.140120	+	0.166988i
$697$	−520.493	−	520.493i	−0.746762	−	0.746762i
$698$	137.259	+	12.0086i	0.196646	+	0.0172043i
$699$	−575.959	−	209.632i	−0.823976	−	0.299903i
$700$	39.2573	+	222.639i	0.0560819	+	0.318056i
$701$	215.605	+	307.916i	0.307568	+	0.439252i	0.942944	−	0.332950i	$-0.108044\pi$
$701$	215.605	+	307.916i	0.307568	+	0.439252i	−0.635377	+	0.772202i	$0.719155\pi$
$702$		−	160.115i		−	0.228084i
$703$	−261.218	+	285.331i	−0.371577	+	0.405876i
$704$	128.714			0.182832
$705$	−289.729	+	202.870i	−0.410963	+	0.287759i
$706$	187.118	−	32.9939i	0.265039	−	0.0467336i
$707$	−134.757	+	370.241i	−0.190603	+	0.523679i
$708$	13.9200	−	159.107i	0.0196611	−	0.224727i
$709$	639.956	−	639.956i	0.902618	−	0.902618i	−0.0930436	−	0.995662i	$-0.529660\pi$
$709$	639.956	−	639.956i	0.902618	−	0.902618i	0.995662	+	0.0930436i	$0.0296596\pi$
$710$	−190.906	+	160.189i	−0.268882	+	0.225619i
$711$	−108.181	−	403.736i	−0.152153	−	0.567842i
$712$	−293.367	+	106.777i	−0.412033	+	0.149968i
$713$	117.737	+	203.926i	0.165129	+	0.286011i
$714$	101.493	+	58.5970i	0.142147	+	0.0820687i
$715$	454.734	−	2578.92i	0.635991	−	3.60689i
$716$	169.962	−	79.2548i	0.237378	−	0.110691i
$717$	65.1546	−	243.160i	0.0908711	−	0.339136i
$718$	10.6356	+	121.565i	0.0148128	+	0.169311i
$719$	317.688	+	266.572i	0.441847	+	0.370754i	0.836400	−	0.548119i	$-0.184656\pi$
$719$	317.688	+	266.572i	0.441847	+	0.370754i	−0.394553	+	0.918873i	$0.629100\pi$
$720$	−37.8832	+	81.2407i	−0.0526155	+	0.112834i
$721$	305.421	−	436.187i	0.423608	−	0.604975i
$722$	291.569	+	204.159i	0.403835	+	0.282768i
$723$	−154.944	−	72.2514i	−0.214306	−	0.0999327i
$724$	−15.6845	+	18.6921i	−0.0216637	+	0.0258178i
$725$	−950.233	+	83.1346i	−1.31067	+	0.114668i
$726$	−326.186	−	87.4013i	−0.449292	−	0.120388i
$727$	337.395	+	723.546i	0.464092	+	0.995248i	0.989518	+	0.144409i	$0.0461281\pi$
$727$	337.395	+	723.546i	0.464092	+	0.995248i	−0.525426	+	0.850839i	$0.676094\pi$
$728$	−222.742	−	39.2755i	−0.305965	−	0.0539499i
$729$	13.5000	−	23.3827i	0.0185185	−	0.0320750i
$730$	−654.949	+	378.135i	−0.897190	+	0.517993i
$731$	−162.377	−	446.128i	−0.222131	−	0.610299i
$732$	−17.6833	+	4.73822i	−0.0241575	+	0.00647298i
$733$	−747.963	−	891.387i	−1.02041	−	1.21608i	−0.976158	−	0.217060i	$-0.930353\pi$
$733$	−747.963	−	891.387i	−1.02041	−	1.21608i	−0.0442547	−	0.999020i	$-0.514091\pi$
$734$	−188.754	−	188.754i	−0.257158	−	0.257158i
$735$	457.959	+	40.0662i	0.623074	+	0.0545119i
$736$	20.8975	+	7.60608i	0.0283934	+	0.0103343i
$737$	−321.045	−	1820.74i	−0.435611	−	2.47047i
$738$	137.404	+	196.233i	0.186184	+	0.265898i
$739$		−	274.986i		−	0.372105i	−0.982540	−	0.186053i	$-0.940431\pi$
$739$		−	274.986i		−	0.372105i	0.982540	−	0.186053i	$-0.0595695\pi$
$740$	−296.793	+	466.341i	−0.401072	+	0.630191i
$741$	394.577			0.532492
$742$	243.559	−	170.542i	0.328247	−	0.229841i
$743$	−601.980	+	106.145i	−0.810201	+	0.142860i	−0.563377	−	0.826200i	$-0.690498\pi$
$743$	−601.980	+	106.145i	−0.810201	+	0.142860i	−0.246824	+	0.969060i	$0.579387\pi$
$744$	−100.361	+	275.740i	−0.134894	+	0.370618i
$745$	103.607	−	1184.23i	0.139070	−	1.58957i
$746$	−293.047	+	293.047i	−0.392825	+	0.392825i
$747$	90.1658	−	75.6581i	0.120704	−	0.101283i
$748$	108.573	+	405.198i	0.145150	+	0.541709i
$749$	−182.720	+	66.5048i	−0.243953	+	0.0887915i
$750$	−53.0621	−	91.9063i	−0.0707495	−	0.122542i
$751$	−115.691	−	66.7945i	−0.154050	−	0.0889407i	0.420994	−	0.907064i	$-0.361681\pi$
$751$	−115.691	−	66.7945i	−0.154050	−	0.0889407i	−0.575043	+	0.818123i	$0.695015\pi$
$752$	−18.9880	+	107.686i	−0.0252500	+	0.143200i
$753$	264.736	−	123.448i	0.351575	−	0.163942i
$754$	246.992	−	921.787i	0.327576	−	1.22253i
$755$	−127.456	−	1456.83i	−0.168816	−	1.92958i
$756$	−29.2171	−	24.5160i	−0.0386469	−	0.0324286i
$757$	476.471	−	1021.80i	0.629420	−	1.34980i	−0.290192	−	0.956968i	$-0.593719\pi$
$757$	476.471	−	1021.80i	0.629420	−	1.34980i	0.919612	−	0.392827i	$-0.128503\pi$
$758$	−127.079	+	181.488i	−0.167651	+	0.239430i
$759$	−89.7416	−	62.8377i	−0.118237	−	0.0827902i
$760$	−200.204	−	93.3566i	−0.263426	−	0.122838i
$761$	−840.822	+	1002.05i	−1.10489	+	1.31676i	−0.160831	+	0.986982i	$0.551417\pi$
$761$	−840.822	+	1002.05i	−1.10489	+	1.31676i	−0.944059	+	0.329775i	$0.893027\pi$
$762$	248.269	−	21.7207i	0.325812	−	0.0285049i
$763$	−270.439	−	72.4638i	−0.354441	−	0.0949722i
$764$	71.9187	+	154.230i	0.0941344	+	0.201872i
$765$	−287.706	−	50.7303i	−0.376086	−	0.0663141i
$766$	236.617	−	409.833i	0.308900	−	0.535030i
$767$	−870.002	+	502.296i	−1.13429	+	0.654884i
$768$	9.47834	+	26.0415i	0.0123416	+	0.0339082i
$769$	860.092	−	230.461i	1.11846	−	0.299689i	0.348197	−	0.937421i	$-0.386794\pi$
$769$	860.092	−	230.461i	1.11846	−	0.299689i	0.770258	+	0.637732i	$0.220127\pi$
$770$	−400.963	−	477.850i	−0.520732	−	0.620584i
$771$	70.9621	+	70.9621i	0.0920390	+	0.0920390i
$772$	161.895	+	14.1639i	0.209708	+	0.0183471i
$773$	−411.629	−	149.821i	−0.532509	−	0.193817i	0.0617493	−	0.998092i	$-0.480332\pi$
$773$	−411.629	−	149.821i	−0.532509	−	0.193817i	−0.594258	+	0.804274i	$0.702554\pi$
$774$	26.8300	+	152.161i	0.0346641	+	0.196590i
$775$	−1058.15	−	1511.20i	−1.36536	−	1.94994i
$776$			163.562i			0.210776i
$777$	−158.976	−	173.333i	−0.204603	−	0.223080i
$778$	−214.276			−0.275419
$779$	−483.583	+	338.608i	−0.620774	+	0.434670i
$780$	555.258	−	97.9069i	0.711869	−	0.125522i
$781$	129.814	−	356.660i	0.166215	−	0.456671i
$782$	−6.31690	+	72.2025i	−0.00807788	+	0.0923306i
$783$	113.790	−	113.790i	0.145325	−	0.145325i
$784$	108.873	−	91.3550i	0.138868	−	0.116524i
$785$	479.558	+	1789.74i	0.610902	+	2.27992i
$786$	−204.330	+	74.3702i	−0.259962	+	0.0946186i
$787$	167.343	+	289.847i	0.212635	+	0.368294i	0.952538	−	0.304419i	$-0.0984623\pi$
$787$	167.343	+	289.847i	0.212635	+	0.368294i	−0.739904	+	0.672713i	$0.765129\pi$
$788$	413.781	+	238.897i	0.525103	+	0.303168i
$789$	−131.647	+	746.607i	−0.166853	+	0.946270i
$790$	1333.95	−	622.031i	1.68855	−	0.787382i
$791$	13.2634	−	49.4999i	0.0167679	−	0.0625788i
$792$	−11.8986	−	136.002i	−0.0150235	−	0.171720i
$793$	88.2100	+	74.0170i	0.111236	+	0.0933379i
$794$	−45.7571	+	98.1264i	−0.0576286	+	0.123585i
$795$	−425.131	+	607.151i	−0.534757	+	0.763712i
$796$	−138.101	−	96.6992i	−0.173493	−	0.121481i
$797$	1249.93	+	582.853i	1.56830	+	0.731309i	0.996052	−	0.0887744i	$-0.0282950\pi$
$797$	1249.93	+	582.853i	1.56830	+	0.731309i	0.572245	+	0.820083i	$0.306073\pi$
$798$	60.4156	−	72.0005i	0.0757087	−	0.0902262i
$799$	−355.020	+	31.0602i	−0.444330	+	0.0388739i
$800$	−168.294	−	45.0942i	−0.210367	−	0.0563678i
$801$	139.943	+	300.108i	0.174710	+	0.374667i
$802$	−748.857	−	132.044i	−0.933736	−	0.164643i
$803$	575.903	−	997.494i	0.717190	−	1.24221i
$804$	344.733	−	199.032i	0.428772	−	0.247552i
$805$	−36.8615	−	101.276i	−0.0457907	−	0.125809i
$806$	1782.80	−	477.700i	2.21191	−	0.592680i
$807$	−488.282	−	581.912i	−0.605058	−	0.721080i
$808$	−214.713	−	214.713i	−0.265733	−	0.265733i
$809$	370.727	+	32.4344i	0.458253	+	0.0400920i	0.313946	−	0.949441i	$-0.398349\pi$
$809$	370.727	+	32.4344i	0.458253	+	0.0400920i	0.144307	+	0.989533i	$0.453905\pi$
$810$	89.3429	+	32.5182i	0.110300	+	0.0401459i
$811$	97.8404	+	554.880i	0.120642	+	0.684193i	0.983801	+	0.179262i	$0.0573709\pi$
$811$	97.8404	+	554.880i	0.120642	+	0.684193i	−0.863160	+	0.504931i	$0.831518\pi$
$812$	−130.385	−	186.209i	−0.160573	−	0.229322i
$813$		−	898.251i		−	1.10486i
$814$	36.3384	−	841.098i	0.0446418	−	1.03329i
$815$	1286.04			1.57797
$816$	−73.9851	+	51.8049i	−0.0906680	+	0.0634864i
$817$	−374.974	+	66.1181i	−0.458965	+	0.0809279i
$818$	−347.777	+	955.510i	−0.425156	+	1.16811i
$819$	−20.9085	+	238.986i	−0.0255294	+	0.291802i
$820$	−596.490	+	596.490i	−0.727427	+	0.727427i
$821$	900.481	−	755.593i	1.09681	−	0.920333i	0.0996032	−	0.995027i	$-0.468243\pi$
$821$	900.481	−	755.593i	1.09681	−	0.920333i	0.997206	+	0.0746946i	$0.0237982\pi$
$822$	−66.4714	−	248.075i	−0.0808655	−	0.301794i
$823$	−902.503	+	328.484i	−1.09660	+	0.399130i	−0.826062	−	0.563579i	$-0.809424\pi$
$823$	−902.503	+	328.484i	−1.09660	+	0.399130i	−0.270539	+	0.962709i	$0.587202\pi$
$824$	205.188	+	355.396i	0.249015	+	0.431306i
$825$	743.319	+	429.156i	0.900993	+	0.520189i
$826$	−41.5537	+	235.663i	−0.0503072	+	0.285306i
$827$	−171.512	+	79.9776i	−0.207391	+	0.0967081i	−0.523539	−	0.852002i	$-0.675388\pi$
$827$	−171.512	+	79.9776i	−0.207391	+	0.0967081i	0.316147	+	0.948710i	$0.397611\pi$
$828$	6.10494	−	22.7840i	0.00737312	−	0.0275168i
$829$	−6.63171	−	75.8008i	−0.00799965	−	0.0914364i	0.991145	−	0.132782i	$-0.0423911\pi$
$829$	−6.63171	−	75.8008i	−0.00799965	−	0.0914364i	−0.999145	+	0.0413457i	$0.986836\pi$
$830$	317.506	+	266.420i	0.382538	+	0.320987i
$831$	10.8039	−	23.1690i	0.0130011	−	0.0278809i
$832$	99.9809	−	142.787i	0.120169	−	0.171620i
$833$	379.427	+	265.678i	0.455495	+	0.318941i
$834$	333.517	+	155.522i	0.399901	+	0.186477i
$835$	437.952	−	521.931i	0.524493	−	0.625067i
$836$	335.154	−	29.3221i	0.400901	−	0.0350743i
$837$	300.631	+	80.5539i	0.359177	+	0.0962412i
$838$	139.749	+	299.692i	0.166765	+	0.357628i
$839$	340.677	+	60.0706i	0.406052	+	0.0715979i	0.372944	−	0.927854i	$-0.378348\pi$
$839$	340.677	+	60.0706i	0.406052	+	0.0715979i	0.0331079	+	0.999452i	$0.489460\pi$
$840$	67.1527	−	116.312i	0.0799437	−	0.138466i
$841$	102.294	−	59.0593i	0.121633	−	0.0702250i
$842$	−291.118	−	799.841i	−0.345746	−	0.949930i
$843$	−23.9149	+	6.40798i	−0.0283688	+	0.00760141i
$844$	296.234	+	353.038i	0.350988	+	0.418291i
$845$	−1615.02	−	1615.02i	−1.91127	−	1.91127i
$846$	115.539	+	10.1084i	0.136571	+	0.0119484i
$847$	475.448	+	173.049i	0.561332	+	0.204308i
$848$	39.7910	+	225.666i	0.0469233	+	0.266115i
$849$	−329.184	−	470.123i	−0.387731	−	0.553737i
$850$		−	567.837i		−	0.668043i
$851$	55.6028	−	134.410i	0.0653382	−	0.157944i
$852$	81.7194			0.0959148
$853$	−106.927	+	74.8711i	−0.125354	+	0.0877738i	−0.634572	−	0.772864i	$-0.718824\pi$
$853$	−106.927	+	74.8711i	−0.125354	+	0.0877738i	0.509218	+	0.860638i	$0.329935\pi$
$854$	27.0125	−	4.76304i	0.0316306	−	0.00557733i
$855$	−80.1355	+	220.170i	−0.0937257	+	0.257509i
$856$	13.0608	−	149.286i	0.0152580	−	0.174400i
$857$	778.847	−	778.847i	0.908806	−	0.908806i	−0.0873699	−	0.996176i	$-0.527846\pi$
$857$	778.847	−	778.847i	0.908806	−	0.908806i	0.996176	+	0.0873699i	$0.0278462\pi$
$858$	−657.809	+	551.967i	−0.766677	+	0.643319i
$859$	3.49087	+	13.0281i	0.00406388	+	0.0151666i	0.967928	−	0.251228i	$-0.0808343\pi$
$859$	3.49087	+	13.0281i	0.00406388	+	0.0151666i	−0.963864	+	0.266394i	$0.914168\pi$
$860$	−511.267	+	186.086i	−0.594496	+	0.216379i
$861$	−179.462	−	310.837i	−0.208434	−	0.361019i
$862$	885.127	+	511.028i	1.02683	+	0.592840i
$863$	−177.110	+	1004.44i	−0.205226	+	1.16389i	0.691858	+	0.722033i	$0.256792\pi$
$863$	−177.110	+	1004.44i	−0.205226	+	1.16389i	−0.897084	+	0.441860i	$0.854319\pi$
$864$	26.6399	−	12.4224i	0.0308332	−	0.0143778i
$865$	−414.823	+	1548.14i	−0.479564	+	1.78976i
$866$	30.2855	+	346.165i	0.0349717	+	0.399729i
$867$	157.960	+	132.545i	0.182192	+	0.152877i
$868$	185.805	−	398.460i	0.214061	−	0.459055i
$869$	−1285.75	+	1836.25i	−1.47958	+	2.11306i
$870$	464.187	+	325.027i	0.533548	+	0.373595i
$871$	−2269.20	−	1058.15i	−2.60528	−	1.21486i
$872$	138.697	−	165.292i	0.159056	−	0.189556i
$873$	172.823	−	15.1201i	0.197965	−	0.0173197i
$874$	56.1472	+	15.0446i	0.0642416	+	0.0172135i
$875$	67.1983	+	144.107i	0.0767980	+	0.164694i
$876$	244.223	+	43.0632i	0.278794	+	0.0491589i
$877$	−785.325	+	1360.22i	−0.895467	+	1.55099i	−0.0622417	+	0.998061i	$0.519825\pi$
$877$	−785.325	+	1360.22i	−0.895467	+	1.55099i	−0.833225	+	0.552933i	$0.813508\pi$
$878$	299.560	−	172.951i	0.341185	−	0.196983i
$879$	−255.403	−	701.715i	−0.290561	−	0.798310i
$880$	464.360	−	124.425i	0.527682	−	0.141392i
$881$	−1006.47	−	1199.47i	−1.14242	−	1.36148i	−0.922515	−	0.385962i	$-0.873870\pi$
$881$	−1006.47	−	1199.47i	−1.14242	−	1.36148i	−0.219905	−	0.975521i	$-0.570575\pi$
$882$	−106.592	−	106.592i	−0.120853	−	0.120853i
$883$	984.597	+	86.1411i	1.11506	+	0.0975550i	0.629757	−	0.776792i	$-0.283154\pi$
$883$	984.597	+	86.1411i	1.11506	+	0.0975550i	0.485301	+	0.874347i	$0.338710\pi$
$884$	533.839	+	194.302i	0.603891	+	0.219798i
$885$	−103.586	−	587.466i	−0.117046	−	0.663803i
$886$	496.195	+	708.640i	0.560040	+	0.799820i
$887$		−	853.748i		−	0.962512i	−0.876580	−	0.481256i	$-0.840181\pi$
$887$		−	853.748i		−	0.962512i	0.876580	−	0.481256i	$-0.159819\pi$
$888$	172.848	−	54.5855i	0.194649	−	0.0614702i
$889$	−373.399			−0.420022
$890$	−955.162	+	668.812i	−1.07322	+	0.751474i
$891$	−142.603	+	25.1447i	−0.160048	+	0.0282208i
$892$	153.071	−	420.560i	0.171605	−	0.471480i
$893$	−24.9104	+	284.727i	−0.0278952	+	0.318843i
$894$	−275.636	+	275.636i	−0.308318	+	0.308318i
$895$	536.560	−	450.227i	0.599508	−	0.503047i
$896$	−10.7466	−	40.1069i	−0.0119940	−	0.0447622i
$897$	−139.417	+	50.7437i	−0.155426	+	0.0565704i
$898$	−33.8771	−	58.6768i	−0.0377250	−	0.0653417i
$899$	1606.48	+	927.501i	1.78696	+	1.03170i
$900$	−32.0901	+	181.992i	−0.0356557	+	0.202213i
$901$	−676.845	+	315.618i	−0.751215	+	0.350298i
$902$	332.519	−	1240.98i	0.368647	−	1.37581i
$903$	−20.1763	−	230.617i	−0.0223437	−	0.255389i
$904$	30.2544	+	25.3864i	0.0334672	+	0.0280823i
$905$	−38.5158	+	82.5974i	−0.0425589	+	0.0912678i
$906$	−275.052	+	392.815i	−0.303590	+	0.433571i
$907$	−174.178	−	121.961i	−0.192038	−	0.134466i	0.473603	−	0.880738i	$-0.342953\pi$
$907$	−174.178	−	121.961i	−0.192038	−	0.134466i	−0.665641	+	0.746272i	$0.731842\pi$
$908$	182.586	+	85.1412i	0.201086	+	0.0937678i
$909$	−207.022	+	246.719i	−0.227747	+	0.271418i
$910$	−841.555	+	73.6265i	−0.924786	+	0.0809083i
$911$	382.226	+	102.417i	0.419568	+	0.112423i	0.462425	−	0.886658i	$-0.346979\pi$
$911$	382.226	+	102.417i	0.419568	+	0.112423i	−0.0428572	+	0.999081i	$0.513646\pi$
$912$	30.6129	+	65.6495i	0.0335667	+	0.0719841i
$913$	−621.660	−	109.615i	−0.680898	−	0.120061i
$914$	−341.662	+	591.776i	−0.373810	+	0.647458i
$915$	−59.2156	+	34.1882i	−0.0647165	+	0.0373641i
$916$	−186.284	−	511.812i	−0.203367	−	0.558747i
$917$	314.692	−	84.3216i	0.343176	−	0.0919537i
$918$	61.5777	+	73.3854i	0.0670781	+	0.0799406i
$919$	−779.058	−	779.058i	−0.847724	−	0.847724i	0.142125	−	0.989849i	$-0.454607\pi$
$919$	−779.058	−	779.058i	−0.847724	−	0.847724i	−0.989849	+	0.142125i	$0.954607\pi$
$920$	82.7447	+	7.23922i	0.0899399	+	0.00786872i
$921$	531.121	+	193.312i	0.576678	+	0.209894i
$922$	132.079	+	749.060i	0.143253	+	0.812429i
$923$	−294.823	−	421.051i	−0.319418	−	0.456177i
$924$			204.548i			0.221373i
$925$	−342.187	+	1087.01i	−0.369932	+	1.17515i
$926$	−715.873			−0.773080
$927$	356.552	−	249.660i	0.384630	−	0.269321i
$928$	172.529	−	30.4216i	0.185915	−	0.0327818i
$929$	−480.980	+	1321.48i	−0.517739	+	1.42248i	0.355265	+	0.934765i	$0.384390\pi$
$929$	−480.980	+	1321.48i	−0.517739	+	1.42248i	−0.873005	+	0.487712i	$0.837832\pi$
$930$	−95.5205	+	1091.80i	−0.102710	+	1.17398i
$931$	262.679	−	262.679i	0.282147	−	0.282147i
$932$	−542.162	+	454.928i	−0.581719	+	0.488120i
$933$	178.399	+	665.792i	0.191210	+	0.713604i
$934$	−835.231	+	303.999i	−0.894251	+	0.325481i
$935$	783.394	+	1356.88i	0.837855	+	1.45121i
$936$	−160.115	−	92.4425i	−0.171063	−	0.0987634i
$937$	−171.391	+	972.008i	−0.182915	+	1.03736i	0.745690	+	0.666293i	$0.232120\pi$
$937$	−171.391	+	972.008i	−0.182915	+	1.03736i	−0.928605	+	0.371069i	$0.878991\pi$
$938$	−540.534	+	252.055i	−0.576262	+	0.268715i
$939$	−218.359	+	814.927i	−0.232544	+	0.867867i
$940$	35.5953	+	406.856i	0.0378673	+	0.432825i
$941$	1366.68	+	1146.78i	1.45237	+	1.21868i	0.930828	+	0.365458i	$0.119088\pi$
$941$	1366.68	+	1146.78i	1.45237	+	1.21868i	0.521543	+	0.853225i	$0.325357\pi$
$942$	256.775	−	550.655i	0.272585	−	0.584560i
$943$	127.320	−	181.832i	0.135016	−	0.192823i
$944$	−151.070	−	105.780i	−0.160032	−	0.112056i
$945$	−129.106	−	60.2030i	−0.136620	−	0.0637068i
$946$	532.638	−	634.773i	0.563042	−	0.671007i
$947$	−1188.45	+	103.976i	−1.25496	+	0.109795i	−0.695174	−	0.718842i	$-0.744673\pi$
$947$	−1188.45	+	103.976i	−1.25496	+	0.109795i	−0.559787	+	0.828637i	$0.689117\pi$
$948$	−466.194	−	124.916i	−0.491766	−	0.131768i
$949$	−659.218	−	1413.70i	−0.694645	−	1.48967i
$950$	−448.488	−	79.0806i	−0.472093	−	0.0832427i
$951$	−472.067	+	817.644i	−0.496390	+	0.859773i
$952$	117.194	−	67.6620i	0.123103	−	0.0710735i
$953$	516.154	+	1418.12i	0.541610	+	1.48806i	0.844774	+	0.535123i	$0.179735\pi$
$953$	516.154	+	1418.12i	0.541610	+	1.48806i	−0.303164	+	0.952938i	$0.598043\pi$
$954$	234.766	−	62.9053i	0.246086	−	0.0659384i
$955$	408.552	+	486.894i	0.427803	+	0.509836i
$956$	−205.543	−	205.543i	−0.215003	−	0.215003i
$957$	−859.757	−	75.2190i	−0.898387	−	0.0785987i
$958$	529.892	+	192.865i	0.553124	+	0.201321i
$959$	66.8197	+	378.953i	0.0696764	+	0.395154i
$960$	59.3689	+	84.7875i	0.0618426	+	0.0883203i
$961$			2626.70i			2.73330i
$962$	−904.839	−	693.651i	−0.940581	−	0.721051i
$963$	−158.947			−0.165054
$964$	−161.708	+	113.229i	−0.167747	+	0.117458i
$965$	597.759	−	105.401i	0.619440	−	0.109224i
$966$	−12.0874	+	33.2098i	−0.0125128	+	0.0343787i
$967$	−109.799	+	1255.01i	−0.113546	+	1.29783i	0.699078	+	0.715046i	$0.253594\pi$
$967$	−109.799	+	1255.01i	−0.113546	+	1.29783i	−0.812623	+	0.582789i	$0.801961\pi$
$968$	−275.725	+	275.725i	−0.284840	+	0.284840i
$969$	−180.846	+	151.748i	−0.186631	+	0.156602i
$970$	158.112	+	590.082i	0.163002	+	0.608332i
$971$	804.123	−	292.677i	0.828139	−	0.301418i	0.107044	−	0.994254i	$-0.465861\pi$
$971$	804.123	−	292.677i	0.828139	−	0.301418i	0.721095	+	0.692836i	$0.243639\pi$
$972$	−15.5885	−	27.0000i	−0.0160375	−	0.0277778i
$973$	−477.494	−	275.681i	−0.490744	−	0.283331i
$974$	0.686385	−	3.89269i	0.000704708	−	0.00399660i
$975$	1053.47	−	491.240i	1.08048	−	0.503836i
$976$	−5.47122	+	20.4189i	−0.00560576	+	0.0209210i
$977$	11.4969	+	131.410i	0.0117675	+	0.134503i	0.999806	−	0.0197052i	$-0.00627276\pi$
$977$	11.4969	+	131.410i	0.0117675	+	0.134503i	−0.988038	+	0.154209i	$0.950717\pi$
$978$	−323.049	−	271.070i	−0.330316	−	0.277168i
$979$	750.522	−	1609.50i	0.766622	−	1.64403i
$980$	304.469	−	434.827i	0.310683	−	0.443701i
$981$	−187.473	−	131.270i	−0.191104	−	0.133813i
$982$	−957.815	−	446.637i	−0.975372	−	0.454823i
$983$	786.678	−	937.527i	0.800283	−	0.953740i	−0.199374	−	0.979923i	$-0.563891\pi$
$983$	786.678	−	937.527i	0.800283	−	0.953740i	0.999657	+	0.0261833i	$0.00833536\pi$
$984$	275.563	−	24.1086i	0.280044	−	0.0245007i
$985$	1723.74	+	461.874i	1.74999	+	0.468907i
$986$	241.301	+	517.471i	0.244727	+	0.524818i
$987$	−171.132	−	30.1753i	−0.173386	−	0.0305727i
$988$	227.809	−	394.577i	0.230576	−	0.399369i
$989$	123.988	−	71.5845i	0.125367	−	0.0723807i
$990$	−174.397	−	479.152i	−0.176159	−	0.483992i
$991$	−902.663	+	241.868i	−0.910861	+	0.244064i	−0.683675	−	0.729787i	$-0.739619\pi$
$991$	−902.663	+	241.868i	−0.910861	+	0.244064i	−0.227186	+	0.973851i	$0.572953\pi$
$992$	217.796	+	259.560i	0.219553	+	0.261653i
$993$	48.6946	+	48.6946i	0.0490378	+	0.0490378i
$994$	−121.973	−	10.6713i	−0.122709	−	0.0107357i
$995$	−591.704	−	215.363i	−0.594677	−	0.216445i
$996$	−23.6009	−	133.847i	−0.0236956	−	0.134385i
$997$	−412.796	−	589.534i	−0.414039	−	0.591308i	0.556917	−	0.830568i	$-0.311984\pi$
$997$	−412.796	−	589.534i	−0.414039	−	0.591308i	−0.970956	+	0.239260i	$0.923095\pi$
$998$		−	748.631i		−	0.750132i
$999$	−73.6549	−	177.589i	−0.0737286	−	0.177767i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	222.3.r.d.61.4	✓	48
37.17	odd	36	inner	222.3.r.d.91.4	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
222.3.r.d.61.4	✓	48	1.1	even	1	trivial
222.3.r.d.91.4	yes	48	37.17	odd	36	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 222 = 2 \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	222.r (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.15846 + 0.811160i) q^{2} +(1.70574 - 0.300767i) q^{3} +(0.684040 - 1.87939i) q^{4} +(0.651048 - 7.44151i) q^{5} +(-1.73205 + 1.73205i) q^{6} +(2.81141 - 2.35906i) q^{7} +(0.732051 + 2.73205i) q^{8} +(2.81908 - 1.02606i) q^{9} +O(q^{10})\)	\(q+(-1.15846 + 0.811160i) q^{2} +(1.70574 - 0.300767i) q^{3} +(0.684040 - 1.87939i) q^{4} +(0.651048 - 7.44151i) q^{5} +(-1.73205 + 1.73205i) q^{6} +(2.81141 - 2.35906i) q^{7} +(0.732051 + 2.73205i) q^{8} +(2.81908 - 1.02606i) q^{9} +(5.28204 + 9.14876i) q^{10} +(-13.9337 - 8.04460i) q^{11} +(0.601535 - 3.41147i) q^{12} +(-19.7475 + 9.20839i) q^{13} +(-1.34333 + 5.01337i) q^{14} +(-1.12765 - 12.8891i) q^{15} +(-3.06418 - 2.57115i) q^{16} +(5.50944 - 11.8150i) q^{17} +(-2.43348 + 3.47537i) q^{18} +(-8.56445 - 5.99689i) q^{19} +(-13.5401 - 6.31386i) q^{20} +(4.08601 - 4.86951i) q^{21} +(22.6670 - 1.98310i) q^{22} +(3.79733 + 1.01749i) q^{23} +(2.07040 + 4.43998i) q^{24} +(-30.3320 - 5.34835i) q^{25} +(15.4071 - 26.6859i) q^{26} +(4.50000 - 2.59808i) q^{27} +(-2.51046 - 6.89742i) q^{28} +(29.9144 - 8.01553i) q^{29} +(11.7614 + 14.0167i) q^{30} +(42.3539 + 42.3539i) q^{31} +(5.63533 + 0.493027i) q^{32} +(-26.1867 - 9.53118i) q^{33} +(3.20143 + 18.1562i) q^{34} +(-15.7246 - 22.4570i) q^{35} -6.00000i q^{36} +(4.81272 - 36.6857i) q^{37} +14.7860 q^{38} +(-30.9144 + 21.6465i) q^{39} +(20.8072 - 3.66887i) q^{40} +(19.3118 - 53.0587i) q^{41} +(-0.783506 + 8.95552i) q^{42} +(25.7513 - 25.7513i) q^{43} +(-24.6501 + 20.6839i) q^{44} +(-5.80008 - 21.6462i) q^{45} +(-5.22438 + 1.90152i) q^{46} +(-13.6685 - 23.6745i) q^{47} +(-6.00000 - 3.46410i) q^{48} +(-6.16986 + 34.9910i) q^{49} +(39.4767 - 18.4083i) q^{50} +(5.84408 - 21.8104i) q^{51} +(3.79806 + 43.4120i) q^{52} +(-43.8842 - 36.8232i) q^{53} +(-3.10560 + 6.65997i) q^{54} +(-68.9355 + 98.4500i) q^{55} +(8.50316 + 5.95398i) q^{56} +(-16.4124 - 7.65321i) q^{57} +(-28.1526 + 33.5510i) q^{58} +(45.9302 - 4.01837i) q^{59} +(-24.9949 - 6.69736i) q^{60} +(-2.23345 - 4.78965i) q^{61} +(-83.4209 - 14.7094i) q^{62} +(5.50506 - 9.53504i) q^{63} +(-6.92820 + 4.00000i) q^{64} +(55.6678 + 152.946i) q^{65} +(38.0675 - 10.2001i) q^{66} +(73.8633 + 88.0269i) q^{67} +(-18.4363 - 18.4363i) q^{68} +(6.78327 + 0.593459i) q^{69} +(36.4325 + 13.2603i) q^{70} +(4.09642 + 23.2320i) q^{71} +(4.86696 + 6.95074i) q^{72} +71.5888i q^{73} +(24.1826 + 46.4026i) q^{74} -53.3470 q^{75} +(-17.1289 + 11.9938i) q^{76} +(-58.1510 + 10.2536i) q^{77} +(18.2542 - 50.1530i) q^{78} +(12.1431 - 138.796i) q^{79} +(-21.1282 + 21.1282i) q^{80} +(6.89440 - 5.78509i) q^{81} +(20.6672 + 77.1312i) q^{82} +(36.8683 - 13.4189i) q^{83} +(-6.35670 - 11.0101i) q^{84} +(-84.3347 - 48.6907i) q^{85} +(-8.94335 + 50.7202i) q^{86} +(48.6152 - 22.6697i) q^{87} +(11.7781 - 43.9565i) q^{88} +(9.62004 + 109.958i) q^{89} +(24.2777 + 20.3714i) q^{90} +(-33.7952 + 72.4740i) q^{91} +(4.50978 - 6.44063i) q^{92} +(84.9833 + 59.5059i) q^{93} +(35.0381 + 16.3385i) q^{94} +(-50.2018 + 59.8282i) q^{95} +(9.76067 - 0.853948i) q^{96} +(55.8574 + 14.9669i) q^{97} +(-21.2358 - 45.5403i) q^{98} +(-47.5343 - 8.38158i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{8}+O(q^{10}) \) 48 * q - 48 * q^8	\( 48 q - 48 q^{8} - 18 q^{11} + 12 q^{13} + 24 q^{14} + 36 q^{15} - 36 q^{17} - 150 q^{19} - 36 q^{20} - 36 q^{21} - 30 q^{22} + 90 q^{23} + 216 q^{25} + 216 q^{27} - 72 q^{28} + 210 q^{29} + 72 q^{30} - 12 q^{31} - 54 q^{34} + 180 q^{35} - 24 q^{37} - 108 q^{38} + 18 q^{39} - 438 q^{41} - 90 q^{42} - 294 q^{46} + 42 q^{47} - 288 q^{48} + 54 q^{49} + 144 q^{50} - 72 q^{51} - 120 q^{52} + 30 q^{53} - 264 q^{55} + 126 q^{57} - 102 q^{58} + 66 q^{59} + 660 q^{61} - 18 q^{62} - 36 q^{63} + 60 q^{65} + 36 q^{66} - 72 q^{67} + 12 q^{68} + 18 q^{69} + 42 q^{70} - 30 q^{71} + 282 q^{74} + 144 q^{75} - 300 q^{76} + 60 q^{77} - 108 q^{78} + 426 q^{79} + 48 q^{82} - 510 q^{83} + 72 q^{84} - 414 q^{85} + 528 q^{86} + 306 q^{87} + 24 q^{88} - 414 q^{89} - 1098 q^{91} - 132 q^{92} + 90 q^{93} + 528 q^{94} + 6 q^{95} + 966 q^{97} + 108 q^{98} - 90 q^{99}+O(q^{100}) \) 48 * q - 48 * q^8 - 18 * q^11 + 12 * q^13 + 24 * q^14 + 36 * q^15 - 36 * q^17 - 150 * q^19 - 36 * q^20 - 36 * q^21 - 30 * q^22 + 90 * q^23 + 216 * q^25 + 216 * q^27 - 72 * q^28 + 210 * q^29 + 72 * q^30 - 12 * q^31 - 54 * q^34 + 180 * q^35 - 24 * q^37 - 108 * q^38 + 18 * q^39 - 438 * q^41 - 90 * q^42 - 294 * q^46 + 42 * q^47 - 288 * q^48 + 54 * q^49 + 144 * q^50 - 72 * q^51 - 120 * q^52 + 30 * q^53 - 264 * q^55 + 126 * q^57 - 102 * q^58 + 66 * q^59 + 660 * q^61 - 18 * q^62 - 36 * q^63 + 60 * q^65 + 36 * q^66 - 72 * q^67 + 12 * q^68 + 18 * q^69 + 42 * q^70 - 30 * q^71 + 282 * q^74 + 144 * q^75 - 300 * q^76 + 60 * q^77 - 108 * q^78 + 426 * q^79 + 48 * q^82 - 510 * q^83 + 72 * q^84 - 414 * q^85 + 528 * q^86 + 306 * q^87 + 24 * q^88 - 414 * q^89 - 1098 * q^91 - 132 * q^92 + 90 * q^93 + 528 * q^94 + 6 * q^95 + 966 * q^97 + 108 * q^98 - 90 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more