LMFDB - Embedded newform 403.2.h.b.118.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(118,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("403.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.h (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			118.16
Character	$\chi$	$=$	403.118
Dual form			403.2.h.b.222.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.53634 q^{2} +(-1.60552 - 2.78084i) q^{3} +4.43304 q^{4} +(1.34893 - 2.33641i) q^{5} +(-4.07215 - 7.05318i) q^{6} +(0.661783 + 1.14624i) q^{7} +6.17102 q^{8} +(-3.65540 + 6.33133i) q^{9} +O(q^{10})$	\(q+2.53634 q^{2} +(-1.60552 - 2.78084i) q^{3} +4.43304 q^{4} +(1.34893 - 2.33641i) q^{5} +(-4.07215 - 7.05318i) q^{6} +(0.661783 + 1.14624i) q^{7} +6.17102 q^{8} +(-3.65540 + 6.33133i) q^{9} +(3.42134 - 5.92593i) q^{10} +(-1.96273 + 3.39955i) q^{11} +(-7.11734 - 12.3276i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(1.67851 + 2.90726i) q^{14} -8.66291 q^{15} +6.78575 q^{16} +(-1.50918 - 2.61398i) q^{17} +(-9.27134 + 16.0584i) q^{18} +(2.04270 + 3.53806i) q^{19} +(5.97984 - 10.3574i) q^{20} +(2.12501 - 3.68063i) q^{21} +(-4.97816 + 8.62242i) q^{22} +6.92691 q^{23} +(-9.90771 - 17.1607i) q^{24} +(-1.13920 - 1.97315i) q^{25} +(-1.26817 + 2.19654i) q^{26} +13.8421 q^{27} +(2.93371 + 5.08134i) q^{28} -3.54948 q^{29} -21.9721 q^{30} +(-3.54638 - 4.29223i) q^{31} +4.86896 q^{32} +12.6048 q^{33} +(-3.82780 - 6.62994i) q^{34} +3.57078 q^{35} +(-16.2045 + 28.0670i) q^{36} +(-5.25632 - 9.10421i) q^{37} +(5.18099 + 8.97373i) q^{38} +3.21104 q^{39} +(8.32425 - 14.4180i) q^{40} +(-0.201439 + 0.348902i) q^{41} +(5.38977 - 9.33535i) q^{42} +(5.37367 + 9.30747i) q^{43} +(-8.70086 + 15.0703i) q^{44} +(9.86171 + 17.0810i) q^{45} +17.5690 q^{46} +3.91368 q^{47} +(-10.8947 - 18.8701i) q^{48} +(2.62409 - 4.54505i) q^{49} +(-2.88940 - 5.00458i) q^{50} +(-4.84604 + 8.39359i) q^{51} +(-2.21652 + 3.83912i) q^{52} +(-1.53201 + 2.65352i) q^{53} +35.1084 q^{54} +(5.29515 + 9.17147i) q^{55} +(4.08388 + 7.07349i) q^{56} +(6.55919 - 11.3609i) q^{57} -9.00271 q^{58} +(1.36289 + 2.36060i) q^{59} -38.4030 q^{60} -7.35204 q^{61} +(-8.99483 - 10.8866i) q^{62} -9.67632 q^{63} -1.22215 q^{64} +(1.34893 + 2.33641i) q^{65} +31.9702 q^{66} +(-6.80253 + 11.7823i) q^{67} +(-6.69025 - 11.5879i) q^{68} +(-11.1213 - 19.2627i) q^{69} +9.05674 q^{70} +(4.12093 - 7.13765i) q^{71} +(-22.5575 + 39.0708i) q^{72} +(-6.34066 + 10.9823i) q^{73} +(-13.3318 - 23.0914i) q^{74} +(-3.65801 + 6.33586i) q^{75} +(9.05537 + 15.6844i) q^{76} -5.19561 q^{77} +8.14431 q^{78} +(-3.53687 - 6.12604i) q^{79} +(9.15347 - 15.8543i) q^{80} +(-11.2577 - 19.4988i) q^{81} +(-0.510918 + 0.884936i) q^{82} +(1.35607 - 2.34878i) q^{83} +(9.42027 - 16.3164i) q^{84} -8.14308 q^{85} +(13.6295 + 23.6069i) q^{86} +(5.69877 + 9.87056i) q^{87} +(-12.1121 + 20.9787i) q^{88} +11.8364 q^{89} +(25.0127 + 43.3233i) q^{90} -1.32357 q^{91} +30.7073 q^{92} +(-6.24223 + 16.7532i) q^{93} +9.92643 q^{94} +11.0218 q^{95} +(-7.81722 - 13.5398i) q^{96} -1.84763 q^{97} +(6.65558 - 11.5278i) q^{98} +(-14.3491 - 24.8534i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9}+O(q^{10}) $ 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9} - 7 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 7 q^{14} + 8 q^{15} + 18 q^{16} - 8 q^{17} + 6 q^{18} + 3 q^{19} - 8 q^{20} + 13 q^{21} + 12 q^{22} - 14 q^{23} - 6 q^{24} - 26 q^{25} - 3 q^{26} + 28 q^{27} - 7 q^{28} - 18 q^{29} - 60 q^{30} - 9 q^{31} + 58 q^{32} - 14 q^{33} - 15 q^{34} + 50 q^{35} - 49 q^{36} - 6 q^{37} + 2 q^{38} + 4 q^{39} - 29 q^{40} - 5 q^{41} + 8 q^{42} - q^{43} - 22 q^{44} + 13 q^{45} + 34 q^{46} + 16 q^{47} - 49 q^{48} + 3 q^{49} - 35 q^{51} - 17 q^{52} + 30 q^{53} - 2 q^{54} + 21 q^{55} - 7 q^{56} + 34 q^{58} - 9 q^{59} - 38 q^{60} - 28 q^{61} - 62 q^{62} + 88 q^{63} + 56 q^{64} - 5 q^{65} + 140 q^{66} - 31 q^{67} - 39 q^{68} + 5 q^{69} + 56 q^{70} + q^{71} - 32 q^{72} - 10 q^{73} - 39 q^{74} - 2 q^{75} - 16 q^{76} + 76 q^{77} - 23 q^{79} - 22 q^{80} - 29 q^{81} - 10 q^{82} + 3 q^{83} + 52 q^{84} - 32 q^{85} + 4 q^{86} + 18 q^{87} - 10 q^{88} + 26 q^{89} + 35 q^{90} + 4 q^{91} - 94 q^{92} - 41 q^{93} + 70 q^{94} + 28 q^{95} - 23 q^{96} + 32 q^{97} - 38 q^{98} - 70 q^{99}+O(q^{100}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9 - 7 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 7 * q^14 + 8 * q^15 + 18 * q^16 - 8 * q^17 + 6 * q^18 + 3 * q^19 - 8 * q^20 + 13 * q^21 + 12 * q^22 - 14 * q^23 - 6 * q^24 - 26 * q^25 - 3 * q^26 + 28 * q^27 - 7 * q^28 - 18 * q^29 - 60 * q^30 - 9 * q^31 + 58 * q^32 - 14 * q^33 - 15 * q^34 + 50 * q^35 - 49 * q^36 - 6 * q^37 + 2 * q^38 + 4 * q^39 - 29 * q^40 - 5 * q^41 + 8 * q^42 - q^43 - 22 * q^44 + 13 * q^45 + 34 * q^46 + 16 * q^47 - 49 * q^48 + 3 * q^49 - 35 * q^51 - 17 * q^52 + 30 * q^53 - 2 * q^54 + 21 * q^55 - 7 * q^56 + 34 * q^58 - 9 * q^59 - 38 * q^60 - 28 * q^61 - 62 * q^62 + 88 * q^63 + 56 * q^64 - 5 * q^65 + 140 * q^66 - 31 * q^67 - 39 * q^68 + 5 * q^69 + 56 * q^70 + q^71 - 32 * q^72 - 10 * q^73 - 39 * q^74 - 2 * q^75 - 16 * q^76 + 76 * q^77 - 23 * q^79 - 22 * q^80 - 29 * q^81 - 10 * q^82 + 3 * q^83 + 52 * q^84 - 32 * q^85 + 4 * q^86 + 18 * q^87 - 10 * q^88 + 26 * q^89 + 35 * q^90 + 4 * q^91 - 94 * q^92 - 41 * q^93 + 70 * q^94 + 28 * q^95 - 23 * q^96 + 32 * q^97 - 38 * q^98 - 70 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	2.53634			1.79347			0.896733	−	0.442572i	$-0.145934\pi$
$2$	2.53634			1.79347			0.896733	+	0.442572i	$0.145934\pi$
$3$	−1.60552	−	2.78084i	−0.926948	−	1.60552i	−0.788398	−	0.615166i	$-0.789089\pi$
$3$	−1.60552	−	2.78084i	−0.926948	−	1.60552i	−0.138550	−	0.990355i	$-0.544244\pi$
$4$	4.43304			2.21652
$5$	1.34893	−	2.33641i	0.603258	−	1.04487i	−0.389067	−	0.921210i	$-0.627202\pi$
$5$	1.34893	−	2.33641i	0.603258	−	1.04487i	0.992324	−	0.123663i	$-0.0394642\pi$
$6$	−4.07215	−	7.05318i	−1.66245	−	2.87945i
$7$	0.661783	+	1.14624i	0.250131	+	0.433239i	0.963562	−	0.267487i	$-0.0861931\pi$
$7$	0.661783	+	1.14624i	0.250131	+	0.433239i	−0.713431	+	0.700725i	$0.752860\pi$
$8$	6.17102			2.18179
$9$	−3.65540	+	6.33133i	−1.21847	+	2.11044i
$10$	3.42134	−	5.92593i	1.08192	−	1.87394i
$11$	−1.96273	+	3.39955i	−0.591786	+	1.02500i	0.402206	+	0.915549i	$0.368243\pi$
$11$	−1.96273	+	3.39955i	−0.591786	+	1.02500i	−0.993992	+	0.109454i	$0.965090\pi$
$12$	−7.11734	−	12.3276i	−2.05460	−	3.55867i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$14$	1.67851	+	2.90726i	0.448601	+	0.776999i
$15$	−8.66291			−2.23675
$16$	6.78575			1.69644
$17$	−1.50918	−	2.61398i	−0.366030	−	0.633983i	0.622911	−	0.782293i	$-0.285950\pi$
$17$	−1.50918	−	2.61398i	−0.366030	−	0.633983i	−0.988941	+	0.148310i	$0.952617\pi$
$18$	−9.27134	+	16.0584i	−2.18528	+	3.78501i
$19$	2.04270	+	3.53806i	0.468627	+	0.811686i	0.999357	−	0.0358547i	$-0.0114154\pi$
$19$	2.04270	+	3.53806i	0.468627	+	0.811686i	−0.530730	+	0.847541i	$0.678082\pi$
$20$	5.97984	−	10.3574i	1.33713	−	2.31598i
$21$	2.12501	−	3.68063i	0.463716	−	0.803180i
$22$	−4.97816	+	8.62242i	−1.06135	+	1.83831i
$23$	6.92691			1.44436			0.722180	−	0.691705i	$-0.243140\pi$
$23$	6.92691			1.44436			0.722180	+	0.691705i	$0.243140\pi$
$24$	−9.90771	−	17.1607i	−2.02240	−	3.50290i
$25$	−1.13920	−	1.97315i	−0.227839	−	0.394630i
$26$	−1.26817	+	2.19654i	−0.248709	+	0.430777i
$27$	13.8421			2.66392
$28$	2.93371	+	5.08134i	0.554419	+	0.960282i
$29$	−3.54948			−0.659123			−0.329561	−	0.944134i	$-0.606901\pi$
$29$	−3.54948			−0.659123			−0.329561	+	0.944134i	$0.606901\pi$
$30$	−21.9721			−4.01154
$31$	−3.54638	−	4.29223i	−0.636948	−	0.770907i
$31$	−3.54638	−	4.29223i	−0.636948	−	0.770907i
$32$	4.86896			0.860719
$33$	12.6048			2.19422
$34$	−3.82780	−	6.62994i	−0.656462	−	1.13703i
$35$	3.57078			0.603573
$36$	−16.2045	+	28.0670i	−2.70075	+	4.67784i
$37$	−5.25632	−	9.10421i	−0.864133	−	1.49672i	−0.867905	−	0.496729i	$-0.834534\pi$
$37$	−5.25632	−	9.10421i	−0.864133	−	1.49672i	0.00377244	−	0.999993i	$-0.498799\pi$
$38$	5.18099	+	8.97373i	0.840467	+	1.45573i
$39$	3.21104			0.514178
$40$	8.32425	−	14.4180i	1.31618	−	2.27969i
$41$	−0.201439	+	0.348902i	−0.0314595	+	0.0544894i	−0.881326	−	0.472508i	$-0.843349\pi$
$41$	−0.201439	+	0.348902i	−0.0314595	+	0.0544894i	0.849867	+	0.526997i	$0.176682\pi$
$42$	5.38977	−	9.33535i	0.831659	−	1.44048i
$43$	5.37367	+	9.30747i	0.819477	+	1.41938i	0.906068	+	0.423131i	$0.139069\pi$
$43$	5.37367	+	9.30747i	0.819477	+	1.41938i	−0.0865916	+	0.996244i	$0.527598\pi$
$44$	−8.70086	+	15.0703i	−1.31170	+	2.27194i
$45$	9.86171	+	17.0810i	1.47010	+	2.54628i
$46$	17.5690			2.59041
$47$	3.91368			0.570869			0.285434	−	0.958398i	$-0.407862\pi$
$47$	3.91368			0.570869			0.285434	+	0.958398i	$0.407862\pi$
$48$	−10.8947	−	18.8701i	−1.57251	−	2.72367i
$49$	2.62409	−	4.54505i	0.374869	−	0.649293i
$50$	−2.88940	−	5.00458i	−0.408622	−	0.707755i
$51$	−4.84604	+	8.39359i	−0.678582	+	1.17534i
$52$	−2.21652	+	3.83912i	−0.307376	+	0.532391i
$53$	−1.53201	+	2.65352i	−0.210438	+	0.364489i	−0.951852	−	0.306559i	$-0.900822\pi$
$53$	−1.53201	+	2.65352i	−0.210438	+	0.364489i	0.741414	+	0.671048i	$0.234156\pi$
$54$	35.1084			4.77765
$55$	5.29515	+	9.17147i	0.713998	+	1.23668i
$56$	4.08388	+	7.07349i	0.545731	+	0.945234i
$57$	6.55919	−	11.3609i	0.868787	−	1.50478i
$58$	−9.00271			−1.18211
$59$	1.36289	+	2.36060i	0.177434	+	0.307324i	0.941001	−	0.338404i	$-0.109887\pi$
$59$	1.36289	+	2.36060i	0.177434	+	0.307324i	−0.763567	+	0.645728i	$0.776554\pi$
$60$	−38.4030			−4.95781
$61$	−7.35204			−0.941332			−0.470666	−	0.882312i	$-0.655986\pi$
$61$	−7.35204			−0.941332			−0.470666	+	0.882312i	$0.655986\pi$
$62$	−8.99483	−	10.8866i	−1.14234	−	1.38259i
$63$	−9.67632			−1.21910
$64$	−1.22215			−0.152769
$65$	1.34893	+	2.33641i	0.167314	+	0.289796i
$66$	31.9702			3.93525
$67$	−6.80253	+	11.7823i	−0.831061	+	1.43944i	0.0661359	+	0.997811i	$0.478933\pi$
$67$	−6.80253	+	11.7823i	−0.831061	+	1.43944i	−0.897197	+	0.441630i	$0.854400\pi$
$68$	−6.69025	−	11.5879i	−0.811313	−	1.40523i
$69$	−11.1213	−	19.2627i	−1.33885	−	2.31895i
$70$	9.05674			1.08249
$71$	4.12093	−	7.13765i	0.489064	−	0.847084i	−0.510857	−	0.859666i	$-0.670672\pi$
$71$	4.12093	−	7.13765i	0.489064	−	0.847084i	0.999921	+	0.0125822i	$0.00400515\pi$
$72$	−22.5575	+	39.0708i	−2.65843	+	4.60454i
$73$	−6.34066	+	10.9823i	−0.742118	+	1.28539i	0.209412	+	0.977828i	$0.432845\pi$
$73$	−6.34066	+	10.9823i	−0.742118	+	1.28539i	−0.951529	+	0.307558i	$0.900488\pi$
$74$	−13.3318	−	23.0914i	−1.54979	−	2.68432i
$75$	−3.65801	+	6.33586i	−0.422391	+	0.731602i
$76$	9.05537	+	15.6844i	1.03872	+	1.79912i
$77$	−5.19561			−0.592095
$78$	8.14431			0.922161
$79$	−3.53687	−	6.12604i	−0.397929	−	0.689234i	0.595541	−	0.803325i	$-0.296938\pi$
$79$	−3.53687	−	6.12604i	−0.397929	−	0.689234i	−0.993470	+	0.114091i	$0.963604\pi$
$80$	9.15347	−	15.8543i	1.02339	−	1.77256i
$81$	−11.2577	−	19.4988i	−1.25085	−	2.16654i
$82$	−0.510918	+	0.884936i	−0.0564215	+	0.0977248i
$83$	1.35607	−	2.34878i	0.148848	−	0.257812i	−0.781954	−	0.623336i	$-0.785777\pi$
$83$	1.35607	−	2.34878i	0.148848	−	0.257812i	0.930802	+	0.365524i	$0.119110\pi$
$84$	9.42027	−	16.3164i	1.02784	−	1.78026i
$85$	−8.14308			−0.883242
$86$	13.6295	+	23.6069i	1.46970	+	2.54560i
$87$	5.69877	+	9.87056i	0.610973	+	1.05824i
$88$	−12.1121	+	20.9787i	−1.29115	+	2.23634i
$89$	11.8364			1.25465			0.627326	−	0.778757i	$-0.284149\pi$
$89$	11.8364			1.25465			0.627326	+	0.778757i	$0.284149\pi$
$90$	25.0127	+	43.3233i	2.63657	+	4.56667i
$91$	−1.32357			−0.138747
$92$	30.7073			3.20145
$93$	−6.24223	+	16.7532i	−0.647289	+	1.73722i
$94$	9.92643			1.02383
$95$	11.0218			1.13081
$96$	−7.81722	−	13.5398i	−0.797842	−	1.38190i
$97$	−1.84763			−0.187598			−0.0937991	−	0.995591i	$-0.529901\pi$
$97$	−1.84763			−0.187598			−0.0937991	+	0.995591i	$0.529901\pi$
$98$	6.65558	−	11.5278i	0.672315	−	1.16448i
$99$	−14.3491	−	24.8534i	−1.44214	−	2.49786i
$100$	−5.05011	−	8.74704i	−0.505011	−	0.874704i
$101$	−18.2796			−1.81889			−0.909447	−	0.415821i	$-0.863494\pi$
$101$	−18.2796			−1.81889			−0.909447	+	0.415821i	$0.863494\pi$
$102$	−12.2912	+	21.2890i	−1.21701	+	2.10793i
$103$	5.41258	−	9.37486i	0.533317	−	0.923733i	−0.465925	−	0.884824i	$-0.654279\pi$
$103$	5.41258	−	9.37486i	0.533317	−	0.923733i	0.999243	−	0.0389087i	$-0.0123882\pi$
$104$	−3.08551	+	5.34426i	−0.302559	+	0.524048i
$105$	−5.73297	−	9.92980i	−0.559481	−	0.969049i
$106$	−3.88570	+	6.73024i	−0.377413	+	0.653699i
$107$	0.390921	+	0.677094i	0.0377917	+	0.0654572i	0.884303	−	0.466914i	$-0.154634\pi$
$107$	0.390921	+	0.677094i	0.0377917	+	0.0654572i	−0.846511	+	0.532371i	$0.821301\pi$
$108$	61.3628			5.90463
$109$	4.95286			0.474398			0.237199	−	0.971461i	$-0.423771\pi$
$109$	4.95286			0.474398			0.237199	+	0.971461i	$0.423771\pi$
$110$	13.4303	+	23.2620i	1.28053	+	2.21795i
$111$	−16.8783	+	29.2340i	−1.60201	+	2.77477i
$112$	4.49070	+	7.77812i	0.424331	+	0.734963i
$113$	−3.22750	+	5.59020i	−0.303618	+	0.525882i	−0.976953	−	0.213456i	$-0.931528\pi$
$113$	−3.22750	+	5.59020i	−0.303618	+	0.525882i	0.673335	+	0.739338i	$0.264861\pi$
$114$	16.6364	−	28.8150i	1.55814	−	2.69878i
$115$	9.34388	−	16.1841i	0.871321	−	1.50917i
$116$	−15.7350			−1.46096
$117$	−3.65540	−	6.33133i	−0.337942	−	0.585332i
$118$	3.45677	+	5.98730i	0.318221	+	0.551175i
$119$	1.99750	−	3.45977i	0.183111	−	0.317157i
$120$	−53.4590			−4.88012
$121$	−2.20462	−	3.81852i	−0.200420	−	0.347138i
$122$	−18.6473			−1.68825
$123$	1.29366			0.116645
$124$	−15.7212	−	19.0276i	−1.41181	−	1.70873i
$125$	7.34248			0.656732
$126$	−24.5425			−2.18642
$127$	2.27972	+	3.94860i	0.202293	+	0.350381i	0.949267	−	0.314472i	$-0.101827\pi$
$127$	2.27972	+	3.94860i	0.202293	+	0.350381i	−0.746974	+	0.664853i	$0.768494\pi$
$128$	−12.8377			−1.13470
$129$	17.2551	−	29.8867i	1.51922	−	2.63137i
$130$	3.42134	+	5.92593i	0.300071	+	0.519738i
$131$	−5.74729	−	9.95459i	−0.502143	−	0.869737i	−0.999997	−	0.00247595i	$-0.999212\pi$
$131$	−5.74729	−	9.95459i	−0.502143	−	0.869737i	0.497854	−	0.867261i	$-0.334121\pi$
$132$	55.8777			4.86353
$133$	−2.70365	+	4.68286i	−0.234436	+	0.406055i
$134$	−17.2536	+	29.8840i	−1.49048	+	2.58159i
$135$	18.6720	−	32.3409i	1.60703	−	2.78346i
$136$	−9.31319	−	16.1309i	−0.798599	−	1.38321i
$137$	9.17049	−	15.8838i	0.783488	−	1.35704i	−0.146410	−	0.989224i	$-0.546772\pi$
$137$	9.17049	−	15.8838i	0.783488	−	1.35704i	0.929898	−	0.367817i	$-0.119895\pi$
$138$	−28.2074	−	48.8567i	−2.40118	−	4.15896i
$139$	−2.30725			−0.195698			−0.0978492	−	0.995201i	$-0.531196\pi$
$139$	−2.30725			−0.195698			−0.0978492	+	0.995201i	$0.531196\pi$
$140$	15.8294			1.33783
$141$	−6.28349	−	10.8833i	−0.529166	−	0.916542i
$142$	10.4521	−	18.1035i	0.877119	−	1.51922i
$143$	−1.96273	−	3.39955i	−0.164132	−	0.284285i
$144$	−24.8046	+	42.9629i	−2.06705	+	3.58024i
$145$	−4.78799	+	8.29304i	−0.397621	+	0.688699i
$146$	−16.0821	+	27.8550i	−1.33096	+	2.30529i
$147$	−16.8521			−1.38994
$148$	−23.3015	−	40.3593i	−1.91537	−	3.31751i
$149$	−2.51736	−	4.36020i	−0.206230	−	0.357201i	0.744294	−	0.667852i	$-0.232786\pi$
$149$	−2.51736	−	4.36020i	−0.206230	−	0.357201i	−0.950524	+	0.310651i	$0.899453\pi$
$150$	−9.27797	+	16.0699i	−0.757543	+	1.31210i
$151$	−3.64011			−0.296228			−0.148114	−	0.988970i	$-0.547320\pi$
$151$	−3.64011			−0.296228			−0.148114	+	0.988970i	$0.547320\pi$
$152$	12.6055	+	21.8334i	1.02244	+	1.77093i
$153$	22.0666			1.78398
$154$	−13.1779			−1.06190
$155$	−14.8122	+	2.49588i	−1.18974	+	0.200474i
$156$	14.2347			1.13969
$157$	−13.0806			−1.04395			−0.521973	−	0.852962i	$-0.674804\pi$
$157$	−13.0806			−1.04395			−0.521973	+	0.852962i	$0.674804\pi$
$158$	−8.97073	−	15.5378i	−0.713673	−	1.23612i
$159$	9.83870			0.780260
$160$	6.56786	−	11.3759i	0.519235	−	0.899342i
$161$	4.58411	+	7.93992i	0.361279	+	0.625753i
$162$	−28.5533	−	49.4558i	−2.24336	−	3.88561i
$163$	8.52547			0.667766			0.333883	−	0.942615i	$-0.391641\pi$
$163$	8.52547			0.667766			0.333883	+	0.942615i	$0.391641\pi$
$164$	−0.892986	+	1.54670i	−0.0697305	+	0.120777i
$165$	17.0030	−	29.4500i	1.32368	−	2.29268i
$166$	3.43945	−	5.95730i	0.266953	−	0.462376i
$167$	7.58167	+	13.1318i	0.586687	+	1.01617i	0.994663	+	0.103179i	$0.0329015\pi$
$167$	7.58167	+	13.1318i	0.586687	+	1.01617i	−0.407976	+	0.912993i	$0.633765\pi$
$168$	13.1135	−	22.7133i	1.01173	−	1.75237i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	−20.6537			−1.58406
$171$	−29.8675			−2.28403
$172$	23.8217	+	41.2604i	1.81639	+	3.14607i
$173$	4.68020	−	8.10634i	0.355829	−	0.616314i	−0.631430	−	0.775432i	$-0.717532\pi$
$173$	4.68020	−	8.10634i	0.355829	−	0.616314i	0.987259	+	0.159119i	$0.0508652\pi$
$174$	14.4540	+	25.0351i	1.09576	+	1.89791i
$175$	1.50780	−	2.61159i	0.113979	−	0.197418i
$176$	−13.3186	+	23.0685i	−1.00393	+	1.73885i
$177$	4.37631	−	7.57999i	0.328944	−	0.569747i
$178$	30.0211			2.25017
$179$	4.96407	+	8.59803i	0.371032	+	0.642647i	0.989725	−	0.142987i	$-0.0456706\pi$
$179$	4.96407	+	8.59803i	0.371032	+	0.642647i	−0.618692	+	0.785633i	$0.712337\pi$
$180$	43.7174	+	75.7207i	3.25850	+	5.64389i
$181$	−5.86310	+	10.1552i	−0.435801	+	0.754829i	−0.997361	−	0.0726068i	$-0.976868\pi$
$181$	−5.86310	+	10.1552i	−0.435801	+	0.754829i	0.561560	+	0.827436i	$0.310202\pi$
$182$	−3.35702			−0.248839
$183$	11.8038	+	20.4449i	0.872566	+	1.51133i
$184$	42.7461			3.15128
$185$	−28.3615			−2.08518
$186$	−15.8324	+	42.4918i	−1.16089	+	3.11565i
$187$	11.8485			0.866445
$188$	17.3495			1.26534
$189$	9.16050	+	15.8664i	0.666328	+	1.15411i
$190$	27.9551			2.02807
$191$	−5.80338	+	10.0518i	−0.419918	+	0.727320i	−0.995931	−	0.0901212i	$-0.971275\pi$
$191$	−5.80338	+	10.0518i	−0.419918	+	0.727320i	0.576013	+	0.817441i	$0.304608\pi$
$192$	1.96219	+	3.39861i	0.141609	+	0.245274i
$193$	−6.13269	−	10.6221i	−0.441441	−	0.764598i	0.556356	−	0.830944i	$-0.312199\pi$
$193$	−6.13269	−	10.6221i	−0.441441	−	0.764598i	−0.997797	+	0.0663461i	$0.978866\pi$
$194$	−4.68622			−0.336451
$195$	4.33146	−	7.50230i	0.310182	−	0.537251i
$196$	11.6327	−	20.1484i	0.830905	−	1.43917i
$197$	3.20203	−	5.54608i	0.228135	−	0.395142i	−0.729120	−	0.684386i	$-0.760071\pi$
$197$	3.20203	−	5.54608i	0.228135	−	0.395142i	0.957255	+	0.289244i	$0.0934039\pi$
$198$	−36.3943	−	63.0368i	−2.58643	−	4.47983i
$199$	−5.04216	+	8.73328i	−0.357430	+	0.619086i	−0.987531	−	0.157427i	$-0.949680\pi$
$199$	−5.04216	+	8.73328i	−0.357430	+	0.619086i	0.630101	+	0.776513i	$0.283013\pi$
$200$	−7.03001	−	12.1763i	−0.497097	−	0.860997i
$201$	43.6864			3.08140
$202$	−46.3635			−3.26212
$203$	−2.34899	−	4.06857i	−0.164867	−	0.285558i
$204$	−21.4827	+	37.2091i	−1.50409	+	2.60516i
$205$	0.543452	+	0.941286i	0.0379563	+	0.0657423i
$206$	13.7282	−	23.7779i	0.956486	−	1.65668i
$207$	−25.3206	+	43.8566i	−1.75990	+	3.04824i
$208$	−3.39288	+	5.87664i	−0.235254	+	0.407471i
$209$	−16.0371			−1.10931
$210$	−14.5408	−	25.1854i	−1.00341	−	1.73796i
$211$	−3.48511	−	6.03639i	−0.239925	−	0.415562i	0.720768	−	0.693177i	$-0.243789\pi$
$211$	−3.48511	−	6.03639i	−0.239925	−	0.415562i	−0.960692	+	0.277615i	$0.910456\pi$
$212$	−6.79146	+	11.7632i	−0.466439	+	0.807897i
$213$	−26.4649			−1.81335
$214$	0.991509	+	1.71734i	0.0677782	+	0.117395i
$215$	28.9947			1.97742
$216$	85.4202			5.81211
$217$	2.57300	−	6.90553i	0.174667	−	0.468778i
$218$	12.5621			0.850816
$219$	40.7202			2.75162
$220$	23.4736	+	40.6575i	1.58259	+	2.74113i
$221$	3.01836			0.203037
$222$	−42.8091	+	74.1475i	−2.87316	+	4.97645i
$223$	−5.49100	−	9.51068i	−0.367704	−	0.636882i	0.621502	−	0.783413i	$-0.286523\pi$
$223$	−5.49100	−	9.51068i	−0.367704	−	0.636882i	−0.989206	+	0.146530i	$0.953189\pi$
$224$	3.22220	+	5.58101i	0.215292	+	0.372897i
$225$	16.6569			1.11046
$226$	−8.18606	+	14.1787i	−0.544528	+	0.943151i
$227$	−3.85780	+	6.68190i	−0.256051	+	0.443493i	−0.965180	−	0.261585i	$-0.915755\pi$
$227$	−3.85780	+	6.68190i	−0.256051	+	0.443493i	0.709129	+	0.705078i	$0.249088\pi$
$228$	29.0772	−	50.3631i	1.92568	−	3.33538i
$229$	−1.42695	−	2.47155i	−0.0942955	−	0.163325i	0.815019	−	0.579434i	$-0.196727\pi$
$229$	−1.42695	−	2.47155i	−0.0942955	−	0.163325i	−0.909314	+	0.416110i	$0.863393\pi$
$230$	23.6993	−	41.0484i	1.56268	−	2.70665i
$231$	8.34166	+	14.4482i	0.548841	+	0.950621i
$232$	−21.9039			−1.43806
$233$	4.73257			0.310041			0.155020	−	0.987911i	$-0.450456\pi$
$233$	4.73257			0.310041			0.155020	+	0.987911i	$0.450456\pi$
$234$	−9.27134	−	16.0584i	−0.606087	−	1.04977i
$235$	5.27926	−	9.14394i	0.344381	−	0.596485i
$236$	6.04176	+	10.4646i	0.393285	+	0.681190i
$237$	−11.3570	+	19.6710i	−0.737720	+	1.27777i
$238$	5.06635	−	8.77517i	0.328403	−	0.568810i
$239$	−8.08575	+	14.0049i	−0.523024	+	0.905904i	0.476617	+	0.879111i	$0.341863\pi$
$239$	−8.08575	+	14.0049i	−0.523024	+	0.905904i	−0.999641	+	0.0267928i	$0.991471\pi$
$240$	−58.7844			−3.79452
$241$	−4.69186	−	8.12654i	−0.302229	−	0.523477i	0.674411	−	0.738356i	$-0.264398\pi$
$241$	−4.69186	−	8.12654i	−0.302229	−	0.523477i	−0.976641	+	0.214879i	$0.931064\pi$
$242$	−5.59168	−	9.68508i	−0.359447	−	0.622580i
$243$	−15.3856	+	26.6487i	−0.986988	+	1.70951i
$244$	−32.5919			−2.08648
$245$	−7.07939	−	12.2619i	−0.452286	−	0.783382i
$246$	3.28116			0.209199
$247$	−4.08540			−0.259948
$248$	−21.8848	−	26.4874i	−1.38968	−	1.68195i
$249$	−8.70878			−0.551896
$250$	18.6231			1.17783
$251$	4.30920	+	7.46376i	0.271995	+	0.471108i	0.969372	−	0.245595i	$-0.0789834\pi$
$251$	4.30920	+	7.46376i	0.271995	+	0.471108i	−0.697378	+	0.716704i	$0.745650\pi$
$252$	−42.8955			−2.70216
$253$	−13.5957	+	23.5484i	−0.854752	+	1.48047i
$254$	5.78216	+	10.0150i	0.362805	+	0.628397i
$255$	13.0739	+	22.6447i	0.818719	+	1.41806i
$256$	−30.1166			−1.88229
$257$	6.23222	−	10.7945i	0.388755	−	0.673344i	−0.603527	−	0.797342i	$-0.706239\pi$
$257$	6.23222	−	10.7945i	0.388755	−	0.673344i	0.992282	+	0.123999i	$0.0395718\pi$
$258$	43.7648	−	75.8029i	2.72468	−	4.71928i
$259$	6.95708	−	12.0500i	0.432292	−	0.748752i
$260$	5.97984	+	10.3574i	0.370854	+	0.642337i
$261$	12.9748	−	22.4730i	0.803118	−	1.39104i
$262$	−14.5771	−	25.2483i	−0.900576	−	1.55984i
$263$	−25.3680			−1.56426			−0.782128	−	0.623118i	$-0.785866\pi$
$263$	−25.3680			−1.56426			−0.782128	+	0.623118i	$0.785866\pi$
$264$	77.7846			4.78731
$265$	4.13313	+	7.15880i	0.253896	+	0.439762i
$266$	−6.85738	+	11.8773i	−0.420453	+	0.728246i
$267$	−19.0035	−	32.9151i	−1.16300	−	2.01437i
$268$	−30.1559	+	52.2315i	−1.84206	+	3.19055i
$269$	8.05991	−	13.9602i	0.491422	−	0.851167i	−0.508530	−	0.861044i	$-0.669811\pi$
$269$	8.05991	−	13.9602i	0.491422	−	0.851167i	0.999951	+	0.00987735i	$0.00314411\pi$
$270$	47.3586	−	82.0276i	2.88215	−	4.99204i
$271$	−4.66859			−0.283597			−0.141798	−	0.989896i	$-0.545288\pi$
$271$	−4.66859			−0.283597			−0.141798	+	0.989896i	$0.545288\pi$
$272$	−10.2409	−	17.7378i	−0.620947	−	1.07551i
$273$	2.12501	+	3.68063i	0.128612	+	0.222762i
$274$	23.2595	−	40.2867i	1.40516	−	2.43381i
$275$	8.94375			0.539328
$276$	−49.3011	−	85.3921i	−2.96758	−	5.14000i
$277$	23.8493			1.43296			0.716482	−	0.697605i	$-0.245751\pi$
$277$	23.8493			1.43296			0.716482	+	0.697605i	$0.245751\pi$
$278$	−5.85198			−0.350978
$279$	40.1389	−	6.76350i	2.40306	−	0.404920i
$280$	22.0354			1.31687
$281$	19.8631			1.18493			0.592465	−	0.805596i	$-0.298155\pi$
$281$	19.8631			1.18493			0.592465	+	0.805596i	$0.298155\pi$
$282$	−15.9371	−	27.6039i	−0.949040	−	1.64379i
$283$	−17.2634			−1.02620			−0.513102	−	0.858328i	$-0.671504\pi$
$283$	−17.2634			−1.02620			−0.513102	+	0.858328i	$0.671504\pi$
$284$	18.2682	−	31.6415i	1.08402	−	1.87758i
$285$	−17.6957	−	30.6499i	−1.04820	−	1.81554i
$286$	−4.97816	−	8.62242i	−0.294365	−	0.509855i
$287$	−0.533235			−0.0314759
$288$	−17.7980	+	30.8270i	−1.04876	+	1.81650i
$289$	3.94475	−	6.83251i	0.232044	−	0.401912i
$290$	−12.1440	+	21.0340i	−0.713119	+	1.23516i
$291$	2.96640	+	5.13796i	0.173894	+	0.301193i
$292$	−28.1084	+	48.6851i	−1.64492	+	2.84908i
$293$	−1.05232	−	1.82267i	−0.0614772	−	0.106482i	0.833649	−	0.552295i	$-0.186248\pi$
$293$	−1.05232	−	1.82267i	−0.0614772	−	0.106482i	−0.895126	+	0.445813i	$0.852914\pi$
$294$	−42.7427			−2.49281
$295$	7.35377			0.428153
$296$	−32.4368	−	56.1823i	−1.88535	−	3.26553i
$297$	−27.1684	+	47.0570i	−1.57647	+	2.73053i
$298$	−6.38490	−	11.0590i	−0.369867	−	0.640629i
$299$	−3.46345	+	5.99888i	−0.200297	+	0.346924i
$300$	−16.2161	+	28.0871i	−0.936237	+	1.62161i
$301$	−7.11241	+	12.3191i	−0.409952	+	0.710058i
$302$	−9.23256			−0.531274
$303$	29.3484	+	50.8329i	1.68602	+	2.92027i
$304$	13.8613	+	24.0084i	0.794998	+	1.37698i
$305$	−9.91734	+	17.1773i	−0.567866	+	0.983572i
$306$	55.9685			3.19951
$307$	0.445440	+	0.771526i	0.0254226	+	0.0440333i	0.878457	−	0.477822i	$-0.158574\pi$
$307$	0.445440	+	0.771526i	0.0254226	+	0.0440333i	−0.853034	+	0.521855i	$0.825240\pi$
$308$	−23.0323			−1.31239
$309$	−34.7600			−1.97743
$310$	−37.5688	+	6.33042i	−2.13376	+	0.359544i
$311$	−12.3220			−0.698715			−0.349358	−	0.936989i	$-0.613600\pi$
$311$	−12.3220			−0.698715			−0.349358	+	0.936989i	$0.613600\pi$
$312$	19.8154			1.12183
$313$	9.81751	+	17.0044i	0.554919	+	0.961147i	0.997910	+	0.0646212i	$0.0205839\pi$
$313$	9.81751	+	17.0044i	0.554919	+	0.961147i	−0.442991	+	0.896526i	$0.646083\pi$
$314$	−33.1769			−1.87228
$315$	−13.0526	+	22.6078i	−0.735433	+	1.27381i
$316$	−15.6791	−	27.1570i	−0.882018	−	1.52770i
$317$	7.26417	+	12.5819i	0.407997	+	0.706671i	0.994665	−	0.103156i	$-0.0328942\pi$
$317$	7.26417	+	12.5819i	0.407997	+	0.706671i	−0.586669	+	0.809827i	$0.699561\pi$
$318$	24.9543			1.39937
$319$	6.96668	−	12.0666i	0.390059	−	0.675603i
$320$	−1.64859	+	2.85544i	−0.0921591	+	0.159624i
$321$	1.25526	−	2.17418i	0.0700619	−	0.121351i
$322$	11.6269	+	20.1384i	0.647941	+	1.12227i
$323$	6.16560	−	10.6791i	0.343063	−	0.594203i
$324$	−49.9057	−	86.4391i	−2.77254	−	4.80217i
$325$	2.27839			0.126383
$326$	21.6235			1.19762
$327$	−7.95192	−	13.7731i	−0.439742	−	0.761655i
$328$	−1.24308	+	2.15308i	−0.0686378	+	0.118884i
$329$	2.59001	+	4.48602i	0.142792	+	0.247322i
$330$	43.1254	−	74.6953i	2.37397	−	4.11184i
$331$	5.50182	−	9.52943i	0.302407	−	0.523785i	−0.674273	−	0.738482i	$-0.735543\pi$
$331$	5.50182	−	9.52943i	0.302407	−	0.523785i	0.976681	+	0.214697i	$0.0688764\pi$
$332$	6.01150	−	10.4122i	0.329924	−	0.571445i
$333$	76.8557			4.21167
$334$	19.2297	+	33.3068i	1.05220	+	1.82247i
$335$	18.3522	+	31.7870i	1.00269	+	1.73671i
$336$	14.4198	−	24.9759i	0.786666	−	1.36255i
$337$	−8.75126			−0.476711			−0.238356	−	0.971178i	$-0.576608\pi$
$337$	−8.75126			−0.476711			−0.238356	+	0.971178i	$0.576608\pi$
$338$	−1.26817	−	2.19654i	−0.0689795	−	0.119476i
$339$	20.7273			1.12575
$340$	−36.0986			−1.95772
$341$	21.5522	−	3.63160i	1.16712	−	0.196662i
$342$	−75.7543			−4.09632
$343$	16.2113			0.875326
$344$	33.1610	+	57.4366i	1.78792	+	3.09677i
$345$	−60.0072			−3.23068
$346$	11.8706	−	20.5605i	0.638167	−	1.10534i
$347$	6.26088	+	10.8442i	0.336102	+	0.582145i	0.983696	−	0.179840i	$-0.0575580\pi$
$347$	6.26088	+	10.8442i	0.336102	+	0.582145i	−0.647594	+	0.761986i	$0.724225\pi$
$348$	25.2629	+	43.7566i	1.35423	+	2.34560i
$349$	−21.0030			−1.12427			−0.562134	−	0.827046i	$-0.690019\pi$
$349$	−21.0030			−1.12427			−0.562134	+	0.827046i	$0.690019\pi$
$350$	3.82431	−	6.62390i	0.204418	−	0.354062i
$351$	−6.92107	+	11.9876i	−0.369419	+	0.639853i
$352$	−9.55646	+	16.5523i	−0.509361	+	0.882239i
$353$	1.69858	+	2.94203i	0.0904064	+	0.156588i	0.907682	−	0.419658i	$-0.137850\pi$
$353$	1.69858	+	2.94203i	0.0904064	+	0.156588i	−0.817276	+	0.576247i	$0.804517\pi$
$354$	11.0998	−	19.2255i	0.589949	−	1.02182i
$355$	−11.1176	−	19.2563i	−0.590063	−	1.02202i
$356$	52.4710			2.78096
$357$	−12.8281			−0.678936
$358$	12.5906	+	21.8075i	0.665434	+	1.15256i
$359$	9.00334	−	15.5942i	0.475178	−	0.823033i	−0.524418	−	0.851461i	$-0.675717\pi$
$359$	9.00334	−	15.5942i	0.475178	−	0.823033i	0.999596	+	0.0284283i	$0.00905024\pi$
$360$	60.8568	+	105.407i	3.20744	+	5.55544i
$361$	1.15476	−	2.00010i	0.0607767	−	0.105268i
$362$	−14.8708	+	25.7571i	−0.781594	+	1.35376i
$363$	−7.07914	+	12.2614i	−0.371558	+	0.643558i
$364$	−5.86742			−0.307536
$365$	17.1061	+	29.6287i	0.895376	+	1.55084i
$366$	29.9386	+	51.8552i	1.56492	+	2.71052i
$367$	15.9948	−	27.7037i	0.834919	−	1.44612i	−0.0591768	−	0.998248i	$-0.518848\pi$
$367$	15.9948	−	27.7037i	0.834919	−	1.44612i	0.894096	−	0.447875i	$-0.147819\pi$
$368$	47.0043			2.45027
$369$	−1.47268	−	2.55075i	−0.0766645	−	0.132787i
$370$	−71.9345			−3.73970
$371$	−4.05544			−0.210548
$372$	−27.6721	+	74.2675i	−1.43473	+	3.85059i
$373$	−15.7687			−0.816472			−0.408236	−	0.912877i	$-0.633856\pi$
$373$	−15.7687			−0.816472			−0.408236	+	0.912877i	$0.633856\pi$
$374$	30.0518			1.55394
$375$	−11.7885	−	20.4183i	−0.608756	−	1.05440i
$376$	24.1514			1.24551
$377$	1.77474	−	3.07394i	0.0914039	−	0.158316i
$378$	23.2342	+	40.2428i	1.19504	+	2.06986i
$379$	−11.2412	−	19.4704i	−0.577423	−	1.00013i	−0.995774	−	0.0918406i	$-0.970725\pi$
$379$	−11.2412	−	19.4704i	−0.577423	−	1.00013i	0.418351	−	0.908286i	$-0.362608\pi$
$380$	48.8600			2.50647
$381$	7.32029	−	12.6791i	0.375030	−	0.649571i
$382$	−14.7194	+	25.4947i	−0.753109	+	1.30442i
$383$	18.0275	−	31.2245i	0.921161	−	1.59550i	0.123539	−	0.992340i	$-0.460576\pi$
$383$	18.0275	−	31.2245i	0.921161	−	1.59550i	0.797622	−	0.603158i	$-0.206091\pi$
$384$	20.6112	+	35.6997i	1.05181	+	1.82179i
$385$	−7.00849	+	12.1391i	−0.357186	+	0.618664i
$386$	−15.5546	−	26.9414i	−0.791709	−	1.37128i
$387$	−78.5716			−3.99402
$388$	−8.19060			−0.415815
$389$	16.6509	+	28.8401i	0.844232	+	1.46225i	0.886286	+	0.463138i	$0.153276\pi$
$389$	16.6509	+	28.8401i	0.844232	+	1.46225i	−0.0420544	+	0.999115i	$0.513390\pi$
$390$	10.9861	−	19.0284i	0.556301	−	0.963541i
$391$	−10.4540	−	18.1068i	−0.528679	−	0.915699i
$392$	16.1933	−	28.0476i	0.817885	−	1.41662i
$393$	−18.4548	+	31.9646i	−0.930920	+	1.61240i
$394$	8.12145	−	14.0668i	0.409153	−	0.708673i
$395$	−19.0839			−0.960216
$396$	−63.6102	−	110.176i	−3.19653	−	5.53656i
$397$	−12.2408	−	21.2016i	−0.614346	−	1.06408i	−0.990499	−	0.137521i	$-0.956087\pi$
$397$	−12.2408	−	21.2016i	−0.614346	−	1.06408i	0.376153	−	0.926558i	$-0.377247\pi$
$398$	−12.7887	+	22.1506i	−0.641038	+	1.11031i
$399$	17.3631			0.869240
$400$	−7.73031	−	13.3893i	−0.386516	−	0.669465i
$401$	36.1390			1.80469			0.902347	−	0.431009i	$-0.141842\pi$
$401$	36.1390			1.80469			0.902347	+	0.431009i	$0.141842\pi$
$402$	110.804			5.52639
$403$	5.49037	−	0.925138i	0.273495	−	0.0460844i
$404$	−81.0344			−4.03161
$405$	−60.7430			−3.01834
$406$	−5.95784	−	10.3193i	−0.295683	−	0.512138i
$407$	41.2669			2.04553
$408$	−29.9050	+	51.7970i	−1.48052	+	2.56434i
$409$	1.54622	+	2.67814i	0.0764559	+	0.132425i	0.901718	−	0.432324i	$-0.142306\pi$
$409$	1.54622	+	2.67814i	0.0764559	+	0.132425i	−0.825263	+	0.564749i	$0.808973\pi$
$410$	1.37838	+	2.38742i	0.0680733	+	0.117906i
$411$	−58.8937			−2.90501
$412$	23.9942	−	41.5591i	1.18211	−	2.04747i
$413$	−1.80388	+	3.12441i	−0.0887632	+	0.153742i
$414$	−64.2217	+	111.235i	−3.15633	+	5.46692i
$415$	−3.65846	−	6.33665i	−0.179587	−	0.311054i
$416$	−2.43448	+	4.21664i	−0.119360	+	0.206738i
$417$	3.70434	+	6.41610i	0.181402	+	0.314198i
$418$	−40.6755			−1.98951
$419$	5.40393			0.263999			0.132000	−	0.991250i	$-0.457860\pi$
$419$	5.40393			0.263999			0.132000	+	0.991250i	$0.457860\pi$
$420$	−25.4145	−	44.0192i	−1.24010	−	2.14792i
$421$	10.1550	−	17.5890i	0.494926	−	0.857237i	−0.505057	−	0.863086i	$-0.668528\pi$
$421$	10.1550	−	17.5890i	0.494926	−	0.857237i	0.999983	+	0.00584889i	$0.00186177\pi$
$422$	−8.83944	−	15.3104i	−0.430297	−	0.745296i
$423$	−14.3060	+	24.7788i	−0.695584	+	1.20479i
$424$	−9.45407	+	16.3749i	−0.459130	+	0.795237i
$425$	−3.43851	+	5.95567i	−0.166792	+	0.288892i
$426$	−67.1242			−3.25218
$427$	−4.86545	−	8.42721i	−0.235456	−	0.407822i
$428$	1.73297	+	3.00159i	0.0837661	+	0.145087i
$429$	−6.30241	+	10.9161i	−0.304283	+	0.527034i
$430$	73.5405			3.54644
$431$	9.15912	+	15.8641i	0.441180	+	0.764145i	0.997777	−	0.0666368i	$-0.0212269\pi$
$431$	9.15912	+	15.8641i	0.441180	+	0.764145i	−0.556598	+	0.830782i	$0.687894\pi$
$432$	93.9294			4.51918
$433$	19.3182			0.928372			0.464186	−	0.885738i	$-0.346347\pi$
$433$	19.3182			0.928372			0.464186	+	0.885738i	$0.346347\pi$
$434$	6.52601	−	17.5148i	0.313259	−	0.840737i
$435$	30.7489			1.47430
$436$	21.9562			1.05151
$437$	14.1496	+	24.5078i	0.676867	+	1.17237i
$438$	103.281			4.93493
$439$	8.33676	−	14.4397i	0.397892	−	0.689169i	−0.595574	−	0.803301i	$-0.703075\pi$
$439$	8.33676	−	14.4397i	0.397892	−	0.689169i	0.993466	+	0.114132i	$0.0364085\pi$
$440$	32.6765	+	56.5974i	1.55779	+	2.69817i
$441$	19.1841	+	33.2279i	0.913531	+	1.58228i
$442$	7.65560			0.364140
$443$	−8.20919	+	14.2187i	−0.390030	+	0.675552i	−0.992453	−	0.122625i	$-0.960869\pi$
$443$	−8.20919	+	14.2187i	−0.390030	+	0.675552i	0.602423	+	0.798177i	$0.294202\pi$
$444$	−74.8220	+	129.595i	−3.55089	+	6.15033i
$445$	15.9664	−	27.6545i	0.756878	−	1.31095i
$446$	−13.9271	−	24.1224i	−0.659465	−	1.14223i
$447$	−8.08336	+	14.0008i	−0.382330	+	0.662214i
$448$	−0.808800	−	1.40088i	−0.0382122	−	0.0661855i
$449$	19.5215			0.921275			0.460638	−	0.887588i	$-0.347621\pi$
$449$	19.5215			0.921275			0.460638	+	0.887588i	$0.347621\pi$
$450$	42.2476			1.99157
$451$	−0.790740	−	1.36960i	−0.0372345	−	0.0644920i
$452$	−14.3076	+	24.7816i	−0.672975	+	1.16563i
$453$	5.84427	+	10.1226i	0.274588	+	0.475600i
$454$	−9.78470	+	16.9476i	−0.459219	+	0.795390i
$455$	−1.78539	+	3.09239i	−0.0837005	+	0.144973i
$456$	40.4769	−	70.1081i	1.89551	−	3.28311i
$457$	−14.4428			−0.675607			−0.337804	−	0.941217i	$-0.609684\pi$
$457$	−14.4428			−0.675607			−0.337804	+	0.941217i	$0.609684\pi$
$458$	−3.61924	−	6.26870i	−0.169116	−	0.292917i
$459$	−20.8903	−	36.1830i	−0.975075	−	1.68888i
$460$	41.4218	−	71.7446i	1.93130	−	3.34511i
$461$	−24.4176			−1.13724			−0.568620	−	0.822600i	$-0.692523\pi$
$461$	−24.4176			−1.13724			−0.568620	+	0.822600i	$0.692523\pi$
$462$	21.1573	+	36.6456i	0.984328	+	1.70491i
$463$	−40.4577			−1.88023			−0.940115	−	0.340859i	$-0.889282\pi$
$463$	−40.4577			−1.88023			−0.940115	+	0.340859i	$0.889282\pi$
$464$	−24.0859			−1.11816
$465$	30.7219	+	37.1832i	1.42470	+	1.72433i
$466$	12.0034			0.556048
$467$	40.6648			1.88174			0.940872	−	0.338763i	$-0.110008\pi$
$467$	40.6648			1.88174			0.940872	+	0.338763i	$0.110008\pi$
$468$	−16.2045	−	28.0670i	−0.749054	−	1.29740i
$469$	−18.0072			−0.831496
$470$	13.3900	−	23.1922i	0.617635	−	1.06978i
$471$	21.0012	+	36.3752i	0.967685	+	1.67608i
$472$	8.41045	+	14.5673i	0.387122	+	0.670515i
$473$	−42.1883			−1.93982
$474$	−28.8054	+	49.8924i	−1.32307	+	2.29163i
$475$	4.65408	−	8.06110i	0.213544	−	0.369868i
$476$	8.85500	−	15.3373i	0.405868	−	0.702984i
$477$	−11.2002	−	19.3993i	−0.512822	−	0.888235i
$478$	−20.5082	+	35.5213i	−0.938025	+	1.62471i
$479$	−3.09715	−	5.36442i	−0.141512	−	0.245107i	0.786554	−	0.617522i	$-0.211863\pi$
$479$	−3.09715	−	5.36442i	−0.141512	−	0.245107i	−0.928066	+	0.372415i	$0.878530\pi$
$480$	−42.1794			−1.92522
$481$	10.5126			0.479335
$482$	−11.9002	−	20.6117i	−0.542038	−	0.938837i
$483$	14.7198	−	25.4954i	0.669773	−	1.16008i
$484$	−9.77318	−	16.9276i	−0.444235	−	0.769438i
$485$	−2.49231	+	4.31681i	−0.113170	+	0.196016i
$486$	−39.0232	+	67.5902i	−1.77013	+	3.06595i
$487$	−3.19517	+	5.53419i	−0.144787	+	0.250778i	−0.929293	−	0.369342i	$-0.879583\pi$
$487$	−3.19517	+	5.53419i	−0.144787	+	0.250778i	0.784507	+	0.620121i	$0.212916\pi$
$488$	−45.3696			−2.05378
$489$	−13.6878	−	23.7080i	−0.618984	−	1.07211i
$490$	−17.9558	−	31.1003i	−0.811159	−	1.40497i
$491$	12.6940	−	21.9867i	0.572874	−	0.992246i	−0.423395	−	0.905945i	$-0.639162\pi$
$491$	12.6940	−	21.9867i	0.572874	−	0.992246i	0.996269	−	0.0863014i	$-0.0275048\pi$
$492$	5.73483			0.258546
$493$	5.35681	+	9.27827i	0.241259	+	0.417872i
$494$	−10.3620			−0.466207
$495$	−77.4235			−3.47993
$496$	−24.0648	−	29.1260i	−1.08054	−	1.30780i
$497$	10.9086			0.489319
$498$	−22.0884			−0.989807
$499$	8.73906	+	15.1365i	0.391214	+	0.677602i	0.992610	−	0.121349i	$-0.0387220\pi$
$499$	8.73906	+	15.1365i	0.391214	+	0.677602i	−0.601396	+	0.798951i	$0.705389\pi$
$500$	32.5495			1.45566
$501$	24.3451	−	42.1669i	1.08766	−	1.88388i
$502$	10.9296	+	18.9307i	0.487813	+	0.844917i
$503$	7.06495	+	12.2369i	0.315011	+	0.545615i	0.979440	−	0.201737i	$-0.0646585\pi$
$503$	7.06495	+	12.2369i	0.315011	+	0.545615i	−0.664429	+	0.747351i	$0.731325\pi$
$504$	−59.7128			−2.65982
$505$	−24.6579	+	42.7087i	−1.09726	+	1.90051i
$506$	−34.4833	+	59.7267i	−1.53297	+	2.65518i
$507$	−1.60552	+	2.78084i	−0.0713037	+	0.123502i
$508$	10.1061	+	17.5043i	0.448386	+	0.776627i
$509$	14.9241	−	25.8493i	0.661500	−	1.14575i	−0.318722	−	0.947848i	$-0.603254\pi$
$509$	14.9241	−	25.8493i	0.661500	−	1.14575i	0.980222	−	0.197903i	$-0.0634130\pi$
$510$	33.1599	+	57.4346i	1.46834	+	2.54325i
$511$	−16.7846			−0.742505
$512$	−50.7105			−2.24111
$513$	28.2753	+	48.9743i	1.24839	+	2.16227i
$514$	15.8071	−	27.3786i	0.697219	−	1.20762i
$515$	−14.6023	−	25.2920i	−0.643455	−	1.11450i
$516$	76.4924	−	132.489i	3.36739	−	5.83249i
$517$	−7.68150	+	13.3047i	−0.337832	+	0.585142i
$518$	17.6456	−	30.5630i	0.775301	−	1.34286i
$519$	−30.0566			−1.31934
$520$	8.32425	+	14.4180i	0.365042	+	0.632272i
$521$	7.41822	+	12.8487i	0.324998	+	0.562913i	0.981512	−	0.191401i	$-0.0613030\pi$
$521$	7.41822	+	12.8487i	0.324998	+	0.562913i	−0.656514	+	0.754314i	$0.727970\pi$
$522$	32.9085	−	56.9992i	1.44037	−	2.49479i
$523$	−38.6872			−1.69167			−0.845836	−	0.533443i	$-0.820898\pi$
$523$	−38.6872			−1.69167			−0.845836	+	0.533443i	$0.820898\pi$
$524$	−25.4779	−	44.1291i	−1.11301	−	1.92779i
$525$	−9.68324			−0.422611
$526$	−64.3419			−2.80544
$527$	−5.86766	+	15.7479i	−0.255599	+	0.685989i
$528$	85.5332			3.72236
$529$	24.9821			1.08618
$530$	10.4830	+	18.1572i	0.455355	+	0.788697i
$531$	−19.9277			−0.864787
$532$	−11.9854	+	20.7593i	−0.519632	+	0.900029i
$533$	−0.201439	−	0.348902i	−0.00872528	−	0.0151126i
$534$	−48.1995	−	83.4839i	−2.08579	−	3.61270i
$535$	2.10929			0.0911926
$536$	−41.9786	+	72.7090i	−1.81320	+	3.14055i
$537$	15.9398	−	27.6086i	0.687855	−	1.19140i
$538$	20.4427	−	35.4078i	0.881348	−	1.52654i
$539$	10.3007	+	17.8414i	0.443685	+	0.768484i
$540$	82.7737	−	143.368i	3.56201	−	6.16959i
$541$	−5.23022	−	9.05901i	−0.224865	−	0.389477i	0.731414	−	0.681934i	$-0.238861\pi$
$541$	−5.23022	−	9.05901i	−0.224865	−	0.389477i	−0.956279	+	0.292456i	$0.905527\pi$
$542$	−11.8412			−0.508621
$543$	37.6533			1.61586
$544$	−7.34814	−	12.7274i	−0.315049	−	0.545681i
$545$	6.68103	−	11.5719i	0.286184	−	0.495685i
$546$	5.38977	+	9.33535i	0.230661	+	0.399516i
$547$	−15.0413	+	26.0523i	−0.643120	+	1.11392i	0.341612	+	0.939841i	$0.389027\pi$
$547$	−15.0413	+	26.0523i	−0.643120	+	1.11392i	−0.984732	+	0.174075i	$0.944306\pi$
$548$	40.6531	−	70.4133i	1.73662	−	3.00791i
$549$	26.8746	−	46.5482i	1.14698	−	1.98663i
$550$	22.6844			0.967267
$551$	−7.25053	−	12.5583i	−0.308883	−	0.535001i
$552$	−68.6298	−	118.870i	−2.92108	−	5.05945i
$553$	4.68129	−	8.10823i	0.199069	−	0.344797i
$554$	60.4900			2.56997
$555$	45.5350	+	78.8689i	1.93285	+	3.34780i
$556$	−10.2281			−0.433769
$557$	2.86306			0.121312			0.0606559	−	0.998159i	$-0.480681\pi$
$557$	2.86306			0.121312			0.0606559	+	0.998159i	$0.480681\pi$
$558$	101.806	−	17.1545i	4.30980	−	0.726210i
$559$	−10.7473			−0.454564
$560$	24.2305			1.02392
$561$	−19.0230	−	32.9487i	−0.803150	−	1.39110i
$562$	50.3795			2.12513
$563$	−14.0275	+	24.2963i	−0.591187	+	1.02397i	0.402886	+	0.915250i	$0.368007\pi$
$563$	−14.0275	+	24.2963i	−0.591187	+	1.02397i	−0.994073	+	0.108716i	$0.965326\pi$
$564$	−27.8550	−	48.2462i	−1.17291	−	2.03153i
$565$	8.70732	+	15.0815i	0.366320	+	0.634484i
$566$	−43.7859			−1.84046
$567$	14.9003	−	25.8080i	0.625752	−	1.08383i
$568$	25.4303	−	44.0466i	1.06703	−	1.84815i
$569$	16.3668	−	28.3482i	0.686133	−	1.18842i	−0.286946	−	0.957947i	$-0.592640\pi$
$569$	16.3668	−	28.3482i	0.686133	−	1.18842i	0.973079	−	0.230470i	$-0.0740265\pi$
$570$	−44.8824	−	77.7387i	−1.87992	−	3.25611i
$571$	−15.5051	+	26.8557i	−0.648870	+	1.12388i	0.334523	+	0.942388i	$0.391425\pi$
$571$	−15.5051	+	26.8557i	−0.648870	+	1.12388i	−0.983393	+	0.181488i	$0.941909\pi$
$572$	−8.70086	−	15.0703i	−0.363801	−	0.630122i
$573$	37.2698			1.55697
$574$	−1.35247			−0.0564509
$575$	−7.89112	−	13.6678i	−0.329082	−	0.569987i
$576$	4.46745	−	7.73785i	0.186144	−	0.322410i
$577$	18.0839	+	31.3222i	0.752842	+	1.30396i	0.946440	+	0.322879i	$0.104651\pi$
$577$	18.0839	+	31.3222i	0.752842	+	1.30396i	−0.193599	+	0.981081i	$0.562016\pi$
$578$	10.0052	−	17.3296i	0.416163	−	0.720816i
$579$	−19.6923	+	34.1081i	−0.818386	+	1.41749i
$580$	−21.2253	+	36.7634i	−0.881334	+	1.52652i
$581$	3.58969			0.148925
$582$	7.52382	+	13.0316i	0.311872	+	0.540179i
$583$	−6.01385	−	10.4163i	−0.249068	−	0.431399i
$584$	−39.1283	+	67.7723i	−1.61914	+	2.80444i
$585$	−19.7234			−0.815463
$586$	−2.66905	−	4.62293i	−0.110257	−	0.190971i
$587$	−2.69150			−0.111090			−0.0555450	−	0.998456i	$-0.517690\pi$
$587$	−2.69150			−0.111090			−0.0555450	+	0.998456i	$0.517690\pi$
$588$	−74.7060			−3.08082
$589$	7.94197	−	21.3150i	0.327243	−	0.878270i
$590$	18.6517			0.767877
$591$	−20.5637			−0.845878
$592$	−35.6681	−	61.7789i	−1.46595	−	2.53910i
$593$	2.01622			0.0827961			0.0413980	−	0.999143i	$-0.486819\pi$
$593$	2.01622			0.0827961			0.0413980	+	0.999143i	$0.486819\pi$
$594$	−68.9084	+	119.353i	−2.82735	+	4.89711i
$595$	−5.38896	−	9.33395i	−0.220926	−	0.382655i
$596$	−11.1596	−	19.3289i	−0.457114	−	0.791744i
$597$	32.3812			1.32527
$598$	−8.78451	+	15.2152i	−0.359225	+	0.622197i
$599$	−3.62657	+	6.28140i	−0.148177	+	0.256651i	−0.930554	−	0.366155i	$-0.880674\pi$
$599$	−3.62657	+	6.28140i	−0.148177	+	0.256651i	0.782376	+	0.622806i	$0.214007\pi$
$600$	−22.5737	+	39.0987i	−0.921566	+	1.59620i
$601$	3.50141	+	6.06463i	0.142826	+	0.247381i	0.928560	−	0.371183i	$-0.121048\pi$
$601$	3.50141	+	6.06463i	0.142826	+	0.247381i	−0.785734	+	0.618565i	$0.787715\pi$
$602$	−18.0395	+	31.2453i	−0.735236	+	1.27347i
$603$	−49.7319	−	86.1382i	−2.02524	−	3.50782i
$604$	−16.1367			−0.656594
$605$	−11.8955			−0.483620
$606$	74.4375	+	128.930i	3.02382	+	5.23741i
$607$	7.48155	−	12.9584i	0.303667	−	0.525966i	−0.673297	−	0.739372i	$-0.735122\pi$
$607$	7.48155	−	12.9584i	0.303667	−	0.525966i	0.976964	+	0.213406i	$0.0684557\pi$
$608$	9.94582	+	17.2267i	0.403356	+	0.698634i
$609$	−7.54271	+	13.0643i	−0.305646	+	0.529394i
$610$	−25.1538	+	43.5676i	−1.01845	+	1.76400i
$611$	−1.95684	+	3.38934i	−0.0791652	+	0.137118i
$612$	97.8221			3.95423
$613$	−9.81686	−	17.0033i	−0.396499	−	0.686757i	0.596792	−	0.802396i	$-0.296442\pi$
$613$	−9.81686	−	17.0033i	−0.396499	−	0.686757i	−0.993291	+	0.115639i	$0.963108\pi$
$614$	1.12979	+	1.95685i	0.0455946	+	0.0789722i
$615$	1.74505	−	3.02251i	0.0703671	−	0.121879i
$616$	−32.0622			−1.29182
$617$	2.68524	+	4.65097i	0.108104	+	0.187241i	0.915002	−	0.403449i	$-0.132189\pi$
$617$	2.68524	+	4.65097i	0.108104	+	0.187241i	−0.806898	+	0.590690i	$0.798855\pi$
$618$	−88.1634			−3.54645
$619$	20.9725			0.842956			0.421478	−	0.906839i	$-0.361511\pi$
$619$	20.9725			0.842956			0.421478	+	0.906839i	$0.361511\pi$
$620$	−65.6630	+	11.0644i	−2.63709	+	0.444355i
$621$	95.8833			3.84766
$622$	−31.2528			−1.25312
$623$	7.83310	+	13.5673i	0.313827	+	0.543564i
$624$	21.7893			0.872272
$625$	15.6004	−	27.0208i	0.624018	−	1.08083i
$626$	24.9006	+	43.1291i	0.995227	+	1.72378i
$627$	25.7479	+	44.5966i	1.02827	+	1.78102i
$628$	−57.9869			−2.31393
$629$	−15.8655	+	27.4798i	−0.632597	+	1.09569i
$630$	−33.1060	+	57.3412i	−1.31897	+	2.28453i
$631$	3.53980	−	6.13111i	0.140917	−	0.244076i	−0.786925	−	0.617048i	$-0.788328\pi$
$631$	3.53980	−	6.13111i	0.140917	−	0.244076i	0.927842	+	0.372973i	$0.121662\pi$
$632$	−21.8261	−	37.8040i	−0.868196	−	1.50376i
$633$	−11.1908	+	19.3831i	−0.444796	+	0.770409i
$634$	18.4244	+	31.9121i	0.731728	+	1.26739i
$635$	12.3007			0.488139
$636$	43.6153			1.72946
$637$	2.62409	+	4.54505i	0.103970	+	0.180081i
$638$	17.6699	−	30.6052i	0.699558	−	1.21167i
$639$	30.1272	+	52.1819i	1.19182	+	2.06428i
$640$	−17.3171	+	29.9941i	−0.684519	+	1.18562i
$641$	−11.1351	+	19.2866i	−0.439810	+	0.761773i	−0.997674	−	0.0681588i	$-0.978288\pi$
$641$	−11.1351	+	19.2866i	−0.439810	+	0.761773i	0.557865	+	0.829932i	$0.311621\pi$
$642$	3.18378	−	5.51447i	0.125654	−	0.217639i
$643$	42.1022			1.66035			0.830174	−	0.557505i	$-0.188241\pi$
$643$	42.1022			1.66035			0.830174	+	0.557505i	$0.188241\pi$
$644$	20.3215	+	35.1980i	0.800781	+	1.38699i
$645$	−46.5516	−	80.6298i	−1.83297	−	3.17479i
$646$	15.6381	−	27.0860i	0.615272	−	1.06568i
$647$	42.3591			1.66531			0.832654	−	0.553793i	$-0.186820\pi$
$647$	42.3591			1.66531			0.832654	+	0.553793i	$0.186820\pi$
$648$	−69.4713	−	120.328i	−2.72909	−	4.72692i
$649$	−10.7000			−0.420011
$650$	5.77879			0.226663
$651$	−23.3342	+	3.93186i	−0.914540	+	0.154102i
$652$	37.7937			1.48012
$653$	6.20158			0.242687			0.121343	−	0.992611i	$-0.461280\pi$
$653$	6.20158			0.242687			0.121343	+	0.992611i	$0.461280\pi$
$654$	−20.1688	−	34.9334i	−0.788662	−	1.36600i
$655$	−31.0106			−1.21169
$656$	−1.36691	+	2.36756i	−0.0533690	+	0.0924379i
$657$	−46.3552	−	80.2896i	−1.80849	−	3.13240i
$658$	6.56915	+	11.3781i	0.256092	+	0.443564i
$659$	−2.77132			−0.107955			−0.0539777	−	0.998542i	$-0.517190\pi$
$659$	−2.77132			−0.107955			−0.0539777	+	0.998542i	$0.517190\pi$
$660$	75.3748	−	130.553i	2.93396	−	5.08177i
$661$	17.6335	−	30.5422i	0.685865	−	1.18795i	−0.287299	−	0.957841i	$-0.592757\pi$
$661$	17.6335	−	30.5422i	0.685865	−	1.18795i	0.973164	−	0.230112i	$-0.0739093\pi$
$662$	13.9545	−	24.1699i	0.542357	−	0.939390i
$663$	−4.84604	−	8.39359i	−0.188205	−	0.325980i
$664$	8.36832	−	14.4944i	0.324754	−	0.562490i
$665$	7.29404	+	12.6336i	0.282851	+	0.489912i
$666$	194.932			7.55348
$667$	−24.5870			−0.952011
$668$	33.6098	+	58.2139i	1.30040	+	2.25236i
$669$	−17.6318	+	30.5392i	−0.681686	+	1.18071i
$670$	46.5475	+	80.6226i	1.79829	+	3.11472i
$671$	14.4301	−	24.9936i	0.557067	−	0.964868i
$672$	10.3466	−	17.9209i	0.399129	−	0.691312i
$673$	−8.07757	+	13.9908i	−0.311368	+	0.539305i	−0.978659	−	0.205492i	$-0.934120\pi$
$673$	−8.07757	+	13.9908i	−0.311368	+	0.539305i	0.667291	+	0.744797i	$0.267454\pi$
$674$	−22.1962			−0.854965
$675$	−15.7689	−	27.3126i	−0.606946	−	1.05126i
$676$	−2.21652	−	3.83912i	−0.0852507	−	0.147659i
$677$	−5.38720	+	9.33091i	−0.207047	+	0.358616i	−0.950783	−	0.309858i	$-0.899719\pi$
$677$	−5.38720	+	9.33091i	−0.207047	+	0.358616i	0.743736	+	0.668473i	$0.233052\pi$
$678$	52.5715			2.01900
$679$	−1.22273	−	2.11783i	−0.0469240	−	0.0812748i
$680$	−50.2512			−1.92704
$681$	24.7751			0.949384
$682$	54.6638	−	9.21097i	2.09319	−	0.352706i
$683$	−19.2309			−0.735849			−0.367924	−	0.929856i	$-0.619932\pi$
$683$	−19.2309			−0.735849			−0.367924	+	0.929856i	$0.619932\pi$
$684$	−132.404			−5.06259
$685$	−24.7406	−	42.8520i	−0.945290	−	1.63729i
$686$	41.1174			1.56987
$687$	−4.58200	+	7.93625i	−0.174814	+	0.302787i
$688$	36.4644	+	63.1582i	1.39019	+	2.40788i
$689$	−1.53201	−	2.65352i	−0.0583649	−	0.101091i
$690$	−152.199			−5.79411
$691$	15.9965	−	27.7068i	0.608537	−	1.05402i	−0.382945	−	0.923771i	$-0.625090\pi$
$691$	15.9965	−	27.7068i	0.608537	−	1.05402i	0.991482	−	0.130246i	$-0.0415767\pi$
$692$	20.7475	−	35.9357i	0.788702	−	1.36607i
$693$	18.9920	−	32.8951i	0.721447	−	1.24958i
$694$	15.8798	+	27.5045i	0.602787	+	1.04406i
$695$	−3.11231	+	5.39067i	−0.118056	+	0.204480i
$696$	35.1673	+	60.9115i	1.33301	+	2.30884i
$697$	1.21603			0.0460604
$698$	−53.2709			−2.01633
$699$	−7.59824	−	13.1605i	−0.287392	−	0.497777i
$700$	6.68415	−	11.5773i	0.252637	−	0.437580i
$701$	18.9555	+	32.8319i	0.715941	+	1.24005i	0.962596	+	0.270942i	$0.0873352\pi$
$701$	18.9555	+	32.8319i	0.715941	+	1.24005i	−0.246655	+	0.969103i	$0.579331\pi$
$702$	−17.5542	+	30.4048i	−0.662541	+	1.14755i
$703$	21.4741	−	37.1943i	0.809913	−	1.40281i
$704$	2.39876	−	4.15477i	0.0904065	−	0.156589i
$705$	−33.9038			−1.27689
$706$	4.30819	+	7.46200i	0.162141	+	0.280836i
$707$	−12.0972	−	20.9529i	−0.454961	−	0.788015i
$708$	19.4003	−	33.6024i	0.729110	−	1.26286i
$709$	6.36760			0.239140			0.119570	−	0.992826i	$-0.461848\pi$
$709$	6.36760			0.239140			0.119570	+	0.992826i	$0.461848\pi$
$710$	−28.1982	−	48.8406i	−1.05826	−	1.83296i
$711$	51.7147			1.93945
$712$	73.0424			2.73738
$713$	−24.5654	−	29.7319i	−0.919982	−	1.11347i
$714$	−32.5365			−1.21765
$715$	−10.5903			−0.396055
$716$	22.0059	+	38.1154i	0.822400	+	1.42444i
$717$	51.9274			1.93926
$718$	22.8356	−	39.5524i	0.852216	−	1.47608i
$719$	−10.7247	−	18.5758i	−0.399965	−	0.692759i	0.593756	−	0.804645i	$-0.297644\pi$
$719$	−10.7247	−	18.5758i	−0.399965	−	0.692759i	−0.993721	+	0.111886i	$0.964311\pi$
$720$	66.9192	+	115.907i	2.49393	+	4.31961i
$721$	14.3278			0.533596
$722$	2.92886	−	5.07294i	0.109001	−	0.188795i
$723$	−15.0658	+	26.0947i	−0.560302	+	0.970471i
$724$	−25.9914	+	45.0184i	−0.965961	+	1.67309i
$725$	4.04356	+	7.00366i	0.150174	+	0.260109i
$726$	−17.9551	+	31.0992i	−0.666377	+	1.15420i
$727$	−2.42708	−	4.20383i	−0.0900156	−	0.155912i	0.817502	−	0.575926i	$-0.195358\pi$
$727$	−2.42708	−	4.20383i	−0.0900156	−	0.155912i	−0.907517	+	0.420014i	$0.862025\pi$
$728$	−8.16776			−0.302717
$729$	31.2618			1.15784
$730$	43.3870	+	75.1486i	1.60583	+	2.78137i
$731$	16.2197	−	28.0933i	0.599906	−	1.03907i
$732$	52.3269	+	90.6329i	1.93406	+	3.34989i
$733$	−11.1530	+	19.3175i	−0.411944	+	0.713508i	−0.995102	−	0.0988503i	$-0.968484\pi$
$733$	−11.1530	+	19.3175i	−0.411944	+	0.713508i	0.583158	+	0.812359i	$0.301817\pi$
$734$	40.5682	−	70.2662i	1.49740	−	2.59357i
$735$	−22.7322	+	39.3734i	−0.838491	+	1.45231i
$736$	33.7268			1.24319
$737$	−26.7031	−	46.2511i	−0.983620	−	1.70368i
$738$	−3.73522	−	6.46958i	−0.137495	−	0.238149i
$739$	0.152502	−	0.264141i	0.00560986	−	0.00971657i	−0.863207	−	0.504850i	$-0.831548\pi$
$739$	0.152502	−	0.264141i	0.00560986	−	0.00971657i	0.868817	+	0.495134i	$0.164881\pi$
$740$	−125.728			−4.62184
$741$	6.55919	+	11.3609i	0.240958	+	0.417352i
$742$	−10.2860			−0.377610
$743$	12.1732			0.446591			0.223296	−	0.974751i	$-0.428318\pi$
$743$	12.1732			0.446591			0.223296	+	0.974751i	$0.428318\pi$
$744$	−38.5210	+	103.384i	−1.41225	+	3.79025i
$745$	−13.5829			−0.497640
$746$	−39.9948			−1.46431
$747$	9.91392	+	17.1714i	0.362731	+	0.628269i
$748$	52.5247			1.92049
$749$	−0.517410	+	0.896180i	−0.0189057	+	0.0327457i
$750$	−29.8997	−	51.7878i	−1.09178	−	1.89102i
$751$	−4.69962	−	8.13999i	−0.171492	−	0.297032i	0.767450	−	0.641109i	$-0.221525\pi$
$751$	−4.69962	−	8.13999i	−0.171492	−	0.297032i	−0.938942	+	0.344077i	$0.888192\pi$
$752$	26.5573			0.968443
$753$	13.8370	−	23.9665i	0.504250	−	0.873386i
$754$	4.50136	−	7.79658i	0.163930	−	0.283935i
$755$	−4.91023	+	8.50477i	−0.178702	+	0.309520i
$756$	40.6088	+	70.3366i	1.47693	+	2.55812i
$757$	−15.8545	+	27.4608i	−0.576242	+	0.998080i	0.419664	+	0.907680i	$0.362148\pi$
$757$	−15.8545	+	27.4608i	−0.576242	+	0.998080i	−0.995906	+	0.0904002i	$0.971185\pi$
$758$	−28.5116	−	49.3836i	−1.03559	−	1.79369i
$759$	87.3125			3.16924
$760$	68.0157			2.46719
$761$	−4.85926	−	8.41649i	−0.176148	−	0.305097i	0.764410	−	0.644731i	$-0.223030\pi$
$761$	−4.85926	−	8.41649i	−0.176148	−	0.305097i	−0.940558	+	0.339633i	$0.889697\pi$
$762$	18.5668	−	32.1586i	0.672603	−	1.16498i
$763$	3.27772	+	5.67717i	0.118661	+	0.205527i
$764$	−25.7266	+	44.5598i	−0.930757	+	1.61212i
$765$	29.7662	−	51.5566i	1.07620	−	1.86403i
$766$	45.7239	−	79.1961i	1.65207	−	2.86147i
$767$	−2.72579			−0.0984225
$768$	48.3528	+	83.7495i	1.74478	+	3.02205i
$769$	−14.6585	−	25.3892i	−0.528598	−	0.915559i	−0.999444	−	0.0333434i	$-0.989384\pi$
$769$	−14.6585	−	25.3892i	−0.528598	−	0.915559i	0.470846	−	0.882216i	$-0.343949\pi$
$770$	−17.7759	+	30.7888i	−0.640600	+	1.10955i
$771$	−40.0238			−1.44142
$772$	−27.1865	−	47.0883i	−0.978462	−	1.69475i
$773$	14.8150			0.532857			0.266428	−	0.963855i	$-0.414156\pi$
$773$	14.8150			0.532857			0.266428	+	0.963855i	$0.414156\pi$
$774$	−199.284			−7.16313
$775$	−4.42918	+	11.8872i	−0.159101	+	0.427001i
$776$	−11.4017			−0.409299
$777$	−44.6790			−1.60285
$778$	42.2323	+	73.1485i	1.51410	+	2.62250i
$779$	−1.64592			−0.0589711
$780$	19.2015	−	33.2580i	0.687524	−	1.19083i
$781$	16.1765	+	28.0186i	0.578842	+	1.00258i
$782$	−26.5148	−	45.9250i	−0.948168	−	1.64228i
$783$	−49.1325			−1.75585
$784$	17.8064	−	30.8416i	0.635943	−	1.10149i
$785$	−17.6448	+	30.5616i	−0.629769	+	1.09079i
$786$	−46.8077	+	81.0732i	−1.66957	+	2.89179i
$787$	11.7739	+	20.3930i	0.419694	+	0.726931i	0.995908	−	0.0903674i	$-0.0288041\pi$
$787$	11.7739	+	20.3930i	0.419694	+	0.726931i	−0.576215	+	0.817298i	$0.695471\pi$
$788$	14.1947	−	24.5860i	0.505666	−	0.875839i
$789$	40.7288	+	70.5444i	1.44998	+	2.51145i
$790$	−48.4033			−1.72211
$791$	−8.54363			−0.303776
$792$	−88.5487	−	153.371i	−3.14644	−	5.44980i
$793$	3.67602	−	6.36705i	0.130539	−	0.226101i
$794$	−31.0468	−	53.7746i	−1.10181	−	1.90839i
$795$	13.2717	−	22.9872i	0.470698	−	0.815272i
$796$	−22.3521	+	38.7150i	−0.792249	+	1.37222i
$797$	17.7706	−	30.7795i	0.629466	−	1.09027i	−0.358193	−	0.933648i	$-0.616607\pi$
$797$	17.7706	−	30.7795i	0.629466	−	1.09027i	0.987659	−	0.156620i	$-0.0500597\pi$
$798$	44.0387			1.55895
$799$	−5.90645	−	10.2303i	−0.208955	−	0.361921i
$800$	−5.54671	−	9.60718i	−0.196106	−	0.339665i
$801$	−43.2666	+	74.9399i	−1.52875	+	2.64787i
$802$	91.6609			3.23666
$803$	−24.8900	−	43.1107i	−0.878349	−	1.52135i
$804$	193.664			6.82999
$805$	24.7345			0.871776
$806$	13.9255	−	2.34647i	0.490503	−	0.0826508i
$807$	−51.7614			−1.82209
$808$	−112.804			−3.96843
$809$	8.99323	+	15.5767i	0.316185	+	0.547649i	0.979689	−	0.200524i	$-0.0642646\pi$
$809$	8.99323	+	15.5767i	0.316185	+	0.547649i	−0.663503	+	0.748173i	$0.730931\pi$
$810$	−154.065			−5.41329
$811$	−8.36031	+	14.4805i	−0.293570	+	0.508479i	−0.974651	−	0.223729i	$-0.928177\pi$
$811$	−8.36031	+	14.4805i	−0.293570	+	0.508479i	0.681081	+	0.732208i	$0.261510\pi$
$812$	−10.4132	−	18.0361i	−0.365430	−	0.632944i
$813$	7.49553	+	12.9826i	0.262880	+	0.455321i
$814$	104.667			3.66858
$815$	11.5002	−	19.9190i	0.402835	−	0.697731i
$816$	−32.8841	+	56.9568i	−1.15117	+	1.99389i
$817$	−21.9536	+	38.0247i	−0.768059	+	1.33032i
$818$	3.92176	+	6.79268i	0.137121	+	0.237500i
$819$	4.83816	−	8.37994i	0.169059	−	0.292819i
$820$	2.40914	+	4.17276i	0.0841309	+	0.145719i
$821$	−22.4482			−0.783446			−0.391723	−	0.920083i	$-0.628121\pi$
$821$	−22.4482			−0.783446			−0.391723	+	0.920083i	$0.628121\pi$
$822$	−149.375			−5.21004
$823$	8.84672	+	15.3230i	0.308377	+	0.534125i	0.978008	−	0.208570i	$-0.0668808\pi$
$823$	8.84672	+	15.3230i	0.308377	+	0.534125i	−0.669630	+	0.742695i	$0.733547\pi$
$824$	33.4011	−	57.8525i	1.16358	−	2.01539i
$825$	−14.3594	−	24.8712i	−0.499929	−	0.865903i
$826$	−4.57526	+	7.92458i	−0.159194	+	0.275732i
$827$	−9.15166	+	15.8511i	−0.318234	+	0.551198i	−0.980120	−	0.198407i	$-0.936423\pi$
$827$	−9.15166	+	15.8511i	−0.318234	+	0.551198i	0.661885	+	0.749605i	$0.269757\pi$
$828$	−112.247	+	194.418i	−3.90086	+	6.75649i
$829$	10.6674			0.370496			0.185248	−	0.982692i	$-0.440691\pi$
$829$	10.6674			0.370496			0.185248	+	0.982692i	$0.440691\pi$
$830$	−9.27912	−	16.0719i	−0.322083	−	0.557864i
$831$	−38.2905	−	66.3212i	−1.32828	−	2.30066i
$832$	0.611076	−	1.05841i	0.0211852	−	0.0366939i
$833$	−15.8409			−0.548854
$834$	9.39547	+	16.2734i	0.325339	+	0.563503i
$835$	40.9084			1.41569
$836$	−71.0930			−2.45880
$837$	−49.0894	−	59.4136i	−1.69678	−	2.05364i
$838$	13.7062			0.473474
$839$	−46.0559			−1.59003			−0.795013	−	0.606593i	$-0.792536\pi$
$839$	−46.0559			−1.59003			−0.795013	+	0.606593i	$0.792536\pi$
$840$	−35.3783	−	61.2770i	−1.22067	−	2.11426i
$841$	−16.4012			−0.565557
$842$	25.7567	−	44.6118i	0.887633	−	1.53743i
$843$	−31.8906	−	55.2361i	−1.09837	−	1.90243i
$844$	−15.4496	−	26.7595i	−0.531798	−	0.921101i
$845$	−2.69785			−0.0928089
$846$	−36.2850	+	62.8475i	−1.24751	+	2.16074i
$847$	2.91797	−	5.05406i	0.100262	−	0.173660i
$848$	−10.3958	+	18.0061i	−0.356995	+	0.618333i
$849$	27.7168	+	48.0069i	0.951237	+	1.64759i
$850$	−8.72124	+	15.1056i	−0.299136	+	0.518119i
$851$	−36.4100	−	63.0640i	−1.24812	−	2.16181i
$852$	−117.320			−4.01932
$853$	−19.9002			−0.681370			−0.340685	−	0.940177i	$-0.610659\pi$
$853$	−19.9002			−0.681370			−0.340685	+	0.940177i	$0.610659\pi$
$854$	−12.3405	−	21.3743i	−0.422282	−	0.731414i
$855$	−40.2890	+	69.7826i	−1.37786	+	2.38652i
$856$	2.41238	+	4.17836i	0.0824535	+	0.142814i
$857$	0.446789	−	0.773862i	0.0152620	−	0.0264346i	−0.858294	−	0.513159i	$-0.828475\pi$
$857$	0.446789	−	0.773862i	0.0152620	−	0.0264346i	0.873556	+	0.486724i	$0.161808\pi$
$858$	−15.9851	+	27.6870i	−0.545722	+	0.945218i
$859$	−18.3051	+	31.7054i	−0.624562	+	1.08177i	0.364063	+	0.931374i	$0.381389\pi$
$859$	−18.3051	+	31.7054i	−0.624562	+	1.08177i	−0.988625	+	0.150399i	$0.951944\pi$
$860$	128.535			4.38299
$861$	0.856121	+	1.48284i	0.0291765	+	0.0505352i
$862$	23.2307	+	40.2367i	0.791240	+	1.37047i
$863$	−21.8217	+	37.7964i	−0.742821	+	1.28660i	0.208386	+	0.978047i	$0.433179\pi$
$863$	−21.8217	+	37.7964i	−0.742821	+	1.28660i	−0.951206	+	0.308556i	$0.900154\pi$
$864$	67.3968			2.29289
$865$	−12.6265	−	21.8697i	−0.429313	−	0.743592i
$866$	48.9975			1.66500
$867$	−25.3335			−0.860371
$868$	11.4062	−	30.6125i	0.387152	−	1.03906i
$869$	27.7677			0.941955
$870$	77.9897			2.64410
$871$	−6.80253	−	11.7823i	−0.230495	−	0.399229i
$872$	30.5642			1.03503
$873$	6.75381	−	11.6979i	0.228582	−	0.395915i
$874$	35.8882	+	62.1602i	1.21394	+	2.10260i
$875$	4.85913	+	8.41626i	0.164269	+	0.284522i
$876$	180.514			6.09902
$877$	25.9716	−	44.9842i	0.877000	−	1.51901i	0.0223833	−	0.999749i	$-0.492875\pi$
$877$	25.9716	−	44.9842i	0.877000	−	1.51901i	0.854617	−	0.519259i	$-0.173792\pi$
$878$	21.1449	−	36.6240i	0.713606	−	1.23600i
$879$	−3.37905	+	5.85268i	−0.113972	+	0.197406i
$880$	35.9316	+	62.2354i	1.21125	+	2.09795i
$881$	−13.6125	+	23.5775i	−0.458616	+	0.794346i	−0.998888	−	0.0471441i	$-0.984988\pi$
$881$	−13.6125	+	23.5775i	−0.458616	+	0.794346i	0.540272	+	0.841490i	$0.318321\pi$
$882$	48.6576	+	84.2774i	1.63839	+	2.83777i
$883$	43.0872			1.45000			0.725000	−	0.688749i	$-0.241840\pi$
$883$	43.0872			1.45000			0.725000	+	0.688749i	$0.241840\pi$
$884$	13.3805			0.450035
$885$	−11.8066	−	20.4497i	−0.396875	−	0.687408i
$886$	−20.8213	+	36.0636i	−0.699506	+	1.21158i
$887$	−5.27702	−	9.14007i	−0.177185	−	0.306893i	0.763730	−	0.645535i	$-0.223366\pi$
$887$	−5.27702	−	9.14007i	−0.177185	−	0.306893i	−0.940915	+	0.338642i	$0.890032\pi$
$888$	−104.156	+	180.404i	−3.49525	+	6.05395i
$889$	−3.01737	+	5.22623i	−0.101199	+	0.175282i
$890$	40.4962	−	70.1414i	1.35743	−	2.35115i
$891$	88.3830			2.96094
$892$	−24.3418	−	42.1612i	−0.815024	−	1.41166i
$893$	7.99447	+	13.8468i	0.267525	+	0.463366i
$894$	−20.5022	+	35.5108i	−0.685695	+	1.18766i
$895$	26.7846			0.895312
$896$	−8.49579	−	14.7151i	−0.283824	−	0.491598i
$897$	22.2426			0.742659
$898$	49.5132			1.65228
$899$	12.5878	+	15.2352i	0.419827	+	0.508122i
$900$	73.8406			2.46135
$901$	9.24832			0.308106
$902$	−2.00559	−	3.47378i	−0.0667788	−	0.115664i
$903$	45.6765			1.52002
$904$	−19.9170	+	34.4972i	−0.662429	+	1.14736i
$905$	15.8178	+	27.3972i	0.525801	+	0.910713i
$906$	14.8231	+	25.6743i	0.492464	+	0.852972i
$907$	18.6050			0.617770			0.308885	−	0.951099i	$-0.400044\pi$
$907$	18.6050			0.617770			0.308885	+	0.951099i	$0.400044\pi$
$908$	−17.1018	+	29.6211i	−0.567542	+	0.983011i
$909$	66.8194	−	115.735i	2.21626	−	3.83867i
$910$	−4.52837	+	7.84336i	−0.150114	+	0.260005i
$911$	−7.96555	−	13.7967i	−0.263910	−	0.457106i	0.703367	−	0.710827i	$-0.251679\pi$
$911$	−7.96555	−	13.7967i	−0.263910	−	0.457106i	−0.967278	+	0.253721i	$0.918346\pi$
$912$	44.5091	−	77.0920i	1.47384	−	2.55277i
$913$	5.32319	+	9.22003i	0.176172	+	0.305138i
$914$	−36.6320			−1.21168
$915$	63.6900			2.10553
$916$	−6.32573	−	10.9565i	−0.209008	−	0.362012i
$917$	7.60692	−	13.1756i	0.251202	−	0.435095i
$918$	−52.9849	−	91.7726i	−1.74876	−	3.02895i
$919$	16.9525	−	29.3627i	0.559213	−	0.968585i	−0.438350	−	0.898805i	$-0.644437\pi$
$919$	16.9525	−	29.3627i	0.559213	−	0.968585i	0.997562	−	0.0697804i	$-0.0222299\pi$
$920$	57.6613	−	99.8723i	1.90104	−	3.29269i
$921$	1.43033	−	2.47740i	0.0471309	−	0.0816331i
$922$	−61.9314			−2.03960
$923$	4.12093	+	7.13765i	0.135642	+	0.234939i
$924$	36.9789	+	64.0493i	1.21652	+	2.10707i
$925$	−11.9760	+	20.7430i	−0.393767	+	0.682025i
$926$	−102.615			−3.37213
$927$	39.5703	+	68.5377i	1.29966	+	2.25107i
$928$	−17.2823			−0.567319
$929$	−38.5661			−1.26531			−0.632656	−	0.774433i	$-0.718035\pi$
$929$	−38.5661			−1.26531			−0.632656	+	0.774433i	$0.718035\pi$
$930$	77.9214	+	94.3093i	2.55514	+	3.09252i
$931$	21.4409			0.702696
$932$	20.9797			0.687212
$933$	19.7832	+	34.2655i	0.647673	+	1.12180i
$934$	103.140			3.37484
$935$	15.9827	−	27.6828i	0.522690	−	0.905325i
$936$	−22.5575	−	39.0708i	−0.737316	−	1.27707i
$937$	−7.53011	−	13.0425i	−0.245998	−	0.426081i	0.716414	−	0.697676i	$-0.245782\pi$
$937$	−7.53011	−	13.0425i	−0.245998	−	0.426081i	−0.962412	+	0.271595i	$0.912449\pi$
$938$	−45.6725			−1.49126
$939$	31.5244	−	54.6019i	1.02876	−	1.78187i
$940$	23.4032	−	40.5355i	0.763327	−	1.32212i
$941$	−6.16014	+	10.6697i	−0.200815	+	0.347821i	−0.948791	−	0.315904i	$-0.897692\pi$
$941$	−6.16014	+	10.6697i	−0.200815	+	0.347821i	0.747976	+	0.663725i	$0.231026\pi$
$942$	53.2663	+	92.2599i	1.73551	+	3.00599i
$943$	−1.39535	+	2.41681i	−0.0454388	+	0.0787023i
$944$	9.24826	+	16.0185i	0.301005	+	0.521356i
$945$	49.4273			1.60787
$946$	−107.004			−3.47900
$947$	−10.3791	−	17.9771i	−0.337275	−	0.584178i	0.646644	−	0.762792i	$-0.276172\pi$
$947$	−10.3791	−	17.9771i	−0.337275	−	0.584178i	−0.983919	+	0.178614i	$0.942839\pi$
$948$	−50.3462	+	87.2022i	−1.63517	+	2.83220i
$949$	−6.34066	−	10.9823i	−0.205826	−	0.356502i
$950$	11.8043	−	20.4457i	0.382983	−	0.663346i
$951$	23.3256	−	40.4011i	0.756383	−	1.31009i
$952$	12.3266	−	21.3503i	0.399508	−	0.691968i
$953$	−2.94170			−0.0952910			−0.0476455	−	0.998864i	$-0.515172\pi$
$953$	−2.94170			−0.0952910			−0.0476455	+	0.998864i	$0.515172\pi$
$954$	−28.4076	−	49.2034i	−0.919730	−	1.59302i
$955$	15.6567	+	27.1181i	0.506638	+	0.877522i
$956$	−35.8444	+	62.0844i	−1.15929	+	2.00795i
$957$	−44.7406			−1.44626
$958$	−7.85544	−	13.6060i	−0.253798	−	0.439590i
$959$	24.2755			0.783897
$960$	10.5874			0.341707
$961$	−5.84643	+	30.4437i	−0.188594	+	0.982055i
$962$	26.6636			0.859670
$963$	−5.71588			−0.184192
$964$	−20.7992	−	36.0253i	−0.669897	−	1.16030i
$965$	−33.0902			−1.06521
$966$	37.3344	−	64.6651i	1.20122	−	2.08057i
$967$	8.44030	+	14.6190i	0.271422	+	0.470116i	0.969226	−	0.246172i	$-0.0791729\pi$
$967$	8.44030	+	14.6190i	0.271422	+	0.470116i	−0.697804	+	0.716288i	$0.745840\pi$
$968$	−13.6048	−	23.5642i	−0.437274	−	0.757381i
$969$	−39.5960			−1.27201
$970$	−6.32136	+	10.9489i	−0.202967	+	0.351548i
$971$	−13.5539	+	23.4761i	−0.434966	+	0.753383i	−0.997293	−	0.0735323i	$-0.976573\pi$
$971$	−13.5539	+	23.4761i	−0.434966	+	0.753383i	0.562327	+	0.826915i	$0.309906\pi$
$972$	−68.2050	+	118.135i	−2.18768	+	3.78917i
$973$	−1.52690	−	2.64467i	−0.0489501	−	0.0847841i
$974$	−8.10404	+	14.0366i	−0.259670	+	0.449762i
$975$	−3.65801	−	6.33586i	−0.117150	−	0.202910i
$976$	−49.8891			−1.59691
$977$	20.9524			0.670327			0.335163	−	0.942160i	$-0.391208\pi$
$977$	20.9524			0.670327			0.335163	+	0.942160i	$0.391208\pi$
$978$	−34.7170	−	60.1316i	−1.11013	−	1.92280i
$979$	−23.2316	+	40.2383i	−0.742485	+	1.28602i
$980$	−31.3832	−	54.3573i	−1.00250	−	1.73638i
$981$	−18.1047	+	31.3582i	−0.578037	+	1.00119i
$982$	32.1964	−	55.7659i	1.02743	−	1.77956i
$983$	−7.45019	+	12.9041i	−0.237624	+	0.411577i	−0.960032	−	0.279890i	$-0.909702\pi$
$983$	−7.45019	+	12.9041i	−0.237624	+	0.411577i	0.722408	+	0.691467i	$0.243035\pi$
$984$	7.98319			0.254495
$985$	−8.63860	−	14.9625i	−0.275249	−	0.476744i
$986$	13.5867	+	23.5329i	0.432689	+	0.749440i
$987$	8.31662	−	14.4048i	0.264721	−	0.458510i
$988$	−18.1107			−0.576179
$989$	37.2229	+	64.4720i	1.18362	+	2.05009i
$990$	−196.373			−6.24113
$991$	39.9563			1.26925			0.634627	−	0.772818i	$-0.281154\pi$
$991$	39.9563			1.26925			0.634627	+	0.772818i	$0.281154\pi$
$992$	−17.2672	−	20.8987i	−0.548233	−	0.663534i
$993$	−35.3332			−1.12126
$994$	27.6681			0.877577
$995$	13.6030	+	23.5611i	0.431244	+	0.746937i
$996$	−38.6063			−1.22329
$997$	−7.57465	+	13.1197i	−0.239892	+	0.415505i	−0.960683	−	0.277648i	$-0.910445\pi$
$997$	−7.57465	+	13.1197i	−0.239892	+	0.415505i	0.720791	+	0.693152i	$0.243779\pi$
$998$	22.1652	+	38.3913i	0.701629	+	1.21526i
$999$	−72.7587	−	126.022i	−2.30198	−	3.98715i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.h.b.118.16	✓	34
31.5	even	3	inner	403.2.h.b.222.16	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.h.b.118.16	✓	34	1.1	even	1	trivial
403.2.h.b.222.16	yes	34	31.5	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.53634 q^{2} +(-1.60552 - 2.78084i) q^{3} +4.43304 q^{4} +(1.34893 - 2.33641i) q^{5} +(-4.07215 - 7.05318i) q^{6} +(0.661783 + 1.14624i) q^{7} +6.17102 q^{8} +(-3.65540 + 6.33133i) q^{9} +O(q^{10})\)	\(q+2.53634 q^{2} +(-1.60552 - 2.78084i) q^{3} +4.43304 q^{4} +(1.34893 - 2.33641i) q^{5} +(-4.07215 - 7.05318i) q^{6} +(0.661783 + 1.14624i) q^{7} +6.17102 q^{8} +(-3.65540 + 6.33133i) q^{9} +(3.42134 - 5.92593i) q^{10} +(-1.96273 + 3.39955i) q^{11} +(-7.11734 - 12.3276i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(1.67851 + 2.90726i) q^{14} -8.66291 q^{15} +6.78575 q^{16} +(-1.50918 - 2.61398i) q^{17} +(-9.27134 + 16.0584i) q^{18} +(2.04270 + 3.53806i) q^{19} +(5.97984 - 10.3574i) q^{20} +(2.12501 - 3.68063i) q^{21} +(-4.97816 + 8.62242i) q^{22} +6.92691 q^{23} +(-9.90771 - 17.1607i) q^{24} +(-1.13920 - 1.97315i) q^{25} +(-1.26817 + 2.19654i) q^{26} +13.8421 q^{27} +(2.93371 + 5.08134i) q^{28} -3.54948 q^{29} -21.9721 q^{30} +(-3.54638 - 4.29223i) q^{31} +4.86896 q^{32} +12.6048 q^{33} +(-3.82780 - 6.62994i) q^{34} +3.57078 q^{35} +(-16.2045 + 28.0670i) q^{36} +(-5.25632 - 9.10421i) q^{37} +(5.18099 + 8.97373i) q^{38} +3.21104 q^{39} +(8.32425 - 14.4180i) q^{40} +(-0.201439 + 0.348902i) q^{41} +(5.38977 - 9.33535i) q^{42} +(5.37367 + 9.30747i) q^{43} +(-8.70086 + 15.0703i) q^{44} +(9.86171 + 17.0810i) q^{45} +17.5690 q^{46} +3.91368 q^{47} +(-10.8947 - 18.8701i) q^{48} +(2.62409 - 4.54505i) q^{49} +(-2.88940 - 5.00458i) q^{50} +(-4.84604 + 8.39359i) q^{51} +(-2.21652 + 3.83912i) q^{52} +(-1.53201 + 2.65352i) q^{53} +35.1084 q^{54} +(5.29515 + 9.17147i) q^{55} +(4.08388 + 7.07349i) q^{56} +(6.55919 - 11.3609i) q^{57} -9.00271 q^{58} +(1.36289 + 2.36060i) q^{59} -38.4030 q^{60} -7.35204 q^{61} +(-8.99483 - 10.8866i) q^{62} -9.67632 q^{63} -1.22215 q^{64} +(1.34893 + 2.33641i) q^{65} +31.9702 q^{66} +(-6.80253 + 11.7823i) q^{67} +(-6.69025 - 11.5879i) q^{68} +(-11.1213 - 19.2627i) q^{69} +9.05674 q^{70} +(4.12093 - 7.13765i) q^{71} +(-22.5575 + 39.0708i) q^{72} +(-6.34066 + 10.9823i) q^{73} +(-13.3318 - 23.0914i) q^{74} +(-3.65801 + 6.33586i) q^{75} +(9.05537 + 15.6844i) q^{76} -5.19561 q^{77} +8.14431 q^{78} +(-3.53687 - 6.12604i) q^{79} +(9.15347 - 15.8543i) q^{80} +(-11.2577 - 19.4988i) q^{81} +(-0.510918 + 0.884936i) q^{82} +(1.35607 - 2.34878i) q^{83} +(9.42027 - 16.3164i) q^{84} -8.14308 q^{85} +(13.6295 + 23.6069i) q^{86} +(5.69877 + 9.87056i) q^{87} +(-12.1121 + 20.9787i) q^{88} +11.8364 q^{89} +(25.0127 + 43.3233i) q^{90} -1.32357 q^{91} +30.7073 q^{92} +(-6.24223 + 16.7532i) q^{93} +9.92643 q^{94} +11.0218 q^{95} +(-7.81722 - 13.5398i) q^{96} -1.84763 q^{97} +(6.65558 - 11.5278i) q^{98} +(-14.3491 - 24.8534i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9}+O(q^{10}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9} - 7 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 7 q^{14} + 8 q^{15} + 18 q^{16} - 8 q^{17} + 6 q^{18} + 3 q^{19} - 8 q^{20} + 13 q^{21} + 12 q^{22} - 14 q^{23} - 6 q^{24} - 26 q^{25} - 3 q^{26} + 28 q^{27} - 7 q^{28} - 18 q^{29} - 60 q^{30} - 9 q^{31} + 58 q^{32} - 14 q^{33} - 15 q^{34} + 50 q^{35} - 49 q^{36} - 6 q^{37} + 2 q^{38} + 4 q^{39} - 29 q^{40} - 5 q^{41} + 8 q^{42} - q^{43} - 22 q^{44} + 13 q^{45} + 34 q^{46} + 16 q^{47} - 49 q^{48} + 3 q^{49} - 35 q^{51} - 17 q^{52} + 30 q^{53} - 2 q^{54} + 21 q^{55} - 7 q^{56} + 34 q^{58} - 9 q^{59} - 38 q^{60} - 28 q^{61} - 62 q^{62} + 88 q^{63} + 56 q^{64} - 5 q^{65} + 140 q^{66} - 31 q^{67} - 39 q^{68} + 5 q^{69} + 56 q^{70} + q^{71} - 32 q^{72} - 10 q^{73} - 39 q^{74} - 2 q^{75} - 16 q^{76} + 76 q^{77} - 23 q^{79} - 22 q^{80} - 29 q^{81} - 10 q^{82} + 3 q^{83} + 52 q^{84} - 32 q^{85} + 4 q^{86} + 18 q^{87} - 10 q^{88} + 26 q^{89} + 35 q^{90} + 4 q^{91} - 94 q^{92} - 41 q^{93} + 70 q^{94} + 28 q^{95} - 23 q^{96} + 32 q^{97} - 38 q^{98} - 70 q^{99}+O(q^{100}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9 - 7 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 7 * q^14 + 8 * q^15 + 18 * q^16 - 8 * q^17 + 6 * q^18 + 3 * q^19 - 8 * q^20 + 13 * q^21 + 12 * q^22 - 14 * q^23 - 6 * q^24 - 26 * q^25 - 3 * q^26 + 28 * q^27 - 7 * q^28 - 18 * q^29 - 60 * q^30 - 9 * q^31 + 58 * q^32 - 14 * q^33 - 15 * q^34 + 50 * q^35 - 49 * q^36 - 6 * q^37 + 2 * q^38 + 4 * q^39 - 29 * q^40 - 5 * q^41 + 8 * q^42 - q^43 - 22 * q^44 + 13 * q^45 + 34 * q^46 + 16 * q^47 - 49 * q^48 + 3 * q^49 - 35 * q^51 - 17 * q^52 + 30 * q^53 - 2 * q^54 + 21 * q^55 - 7 * q^56 + 34 * q^58 - 9 * q^59 - 38 * q^60 - 28 * q^61 - 62 * q^62 + 88 * q^63 + 56 * q^64 - 5 * q^65 + 140 * q^66 - 31 * q^67 - 39 * q^68 + 5 * q^69 + 56 * q^70 + q^71 - 32 * q^72 - 10 * q^73 - 39 * q^74 - 2 * q^75 - 16 * q^76 + 76 * q^77 - 23 * q^79 - 22 * q^80 - 29 * q^81 - 10 * q^82 + 3 * q^83 + 52 * q^84 - 32 * q^85 + 4 * q^86 + 18 * q^87 - 10 * q^88 + 26 * q^89 + 35 * q^90 + 4 * q^91 - 94 * q^92 - 41 * q^93 + 70 * q^94 + 28 * q^95 - 23 * q^96 + 32 * q^97 - 38 * q^98 - 70 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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