LMFDB - Embedded newform 38.3.f.a.21.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [38,3,Mod(3,38)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("38.3"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(38, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([13])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	38.f (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.03542500457$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			21.2
Character	$\chi$	$=$	38.21
Dual form			38.3.f.a.29.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.39273 - 0.245576i) q^{2} +(0.272417 - 0.324654i) q^{3} +(1.87939 + 0.684040i) q^{4} +(7.98876 - 2.90767i) q^{5} +(-0.459130 + 0.385256i) q^{6} +(-2.58545 - 4.47813i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(1.53164 + 8.68639i) q^{9} +(-11.8402 + 2.08775i) q^{10} +(-4.81869 + 8.34622i) q^{11} +(0.734053 - 0.423806i) q^{12} +(-8.78112 - 10.4649i) q^{13} +(2.50111 + 6.87174i) q^{14} +(1.23229 - 3.38568i) q^{15} +(3.06418 + 2.57115i) q^{16} +(-3.08077 + 17.4719i) q^{17} -12.4739i q^{18} +(-17.6183 - 7.11298i) q^{19} +17.0029 q^{20} +(-2.15816 - 0.380542i) q^{21} +(8.76075 - 10.4407i) q^{22} +(14.1083 + 5.13501i) q^{23} +(-1.12641 + 0.409981i) q^{24} +(36.2147 - 30.3877i) q^{25} +(9.65978 + 16.7312i) q^{26} +(6.54055 + 3.77619i) q^{27} +(-1.79583 - 10.1847i) q^{28} +(11.5878 - 2.04324i) q^{29} +(-2.54768 + 4.41272i) q^{30} +(-44.1349 + 25.4813i) q^{31} +(-3.63616 - 4.33340i) q^{32} +(1.39694 + 3.83806i) q^{33} +(8.58135 - 23.5771i) q^{34} +(-33.6755 - 28.2571i) q^{35} +(-3.06329 + 17.3728i) q^{36} +17.8330i q^{37} +(22.7908 + 14.2331i) q^{38} -5.78961 q^{39} +(-23.6805 - 4.17550i) q^{40} +(-15.8487 + 18.8877i) q^{41} +(2.91228 + 1.05998i) q^{42} +(14.2358 - 5.18140i) q^{43} +(-14.7653 + 12.3896i) q^{44} +(37.4931 + 64.9400i) q^{45} +(-18.3880 - 10.6163i) q^{46} +(-13.4551 - 76.3075i) q^{47} +(1.66947 - 0.294372i) q^{48} +(11.1309 - 19.2793i) q^{49} +(-57.8997 + 33.4284i) q^{50} +(4.83307 + 5.75983i) q^{51} +(-9.34467 - 25.6743i) q^{52} +(21.5316 - 59.1576i) q^{53} +(-8.18187 - 6.86541i) q^{54} +(-14.2273 + 80.6871i) q^{55} +14.6255i q^{56} +(-7.10879 + 3.78216i) q^{57} -16.6404 q^{58} +(52.2374 + 9.21086i) q^{59} +(4.63189 - 5.52007i) q^{60} +(46.5312 + 16.9360i) q^{61} +(67.7255 - 24.6501i) q^{62} +(34.9388 - 29.3171i) q^{63} +(4.00000 + 6.92820i) q^{64} +(-100.579 - 58.0692i) q^{65} +(-1.00302 - 5.68843i) q^{66} +(9.95299 - 1.75498i) q^{67} +(-17.7414 + 30.7291i) q^{68} +(5.51045 - 3.18146i) q^{69} +(39.9616 + 47.6243i) q^{70} +(38.9935 + 107.134i) q^{71} +(8.53266 - 23.4433i) q^{72} +(-85.5417 - 71.7780i) q^{73} +(4.37934 - 24.8365i) q^{74} -20.0354i q^{75} +(-28.2461 - 25.4197i) q^{76} +49.8339 q^{77} +(8.06335 + 1.42179i) q^{78} +(97.8772 - 116.645i) q^{79} +(31.9550 + 11.6307i) q^{80} +(-71.5884 + 26.0560i) q^{81} +(26.7112 - 22.4134i) q^{82} +(26.5522 + 45.9897i) q^{83} +(-3.79571 - 2.19146i) q^{84} +(26.1910 + 148.537i) q^{85} +(-21.0990 + 3.72032i) q^{86} +(2.49337 - 4.31864i) q^{87} +(23.6067 - 13.6293i) q^{88} +(-71.6292 - 85.3643i) q^{89} +(-36.2700 - 99.6511i) q^{90} +(-24.1602 + 66.3796i) q^{91} +(23.0024 + 19.3013i) q^{92} +(-3.75049 + 21.2701i) q^{93} +109.580i q^{94} +(-161.431 - 5.59555i) q^{95} -2.39741 q^{96} +(-84.8296 - 14.9577i) q^{97} +(-20.2368 + 24.1173i) q^{98} +(-79.8790 - 29.0736i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{3} + 12 q^{6} - 18 q^{7} + 6 q^{9} + 30 q^{11} - 36 q^{12} - 90 q^{13} - 48 q^{14} - 114 q^{15} + 18 q^{17} - 12 q^{19} + 24 q^{20} + 90 q^{21} + 84 q^{22} + 120 q^{23} - 24 q^{24} + 252 q^{25}+ \cdots - 204 q^{99}+O(q^{100}) $ 24 * q - 6 * q^3 + 12 * q^6 - 18 * q^7 + 6 * q^9 + 30 * q^11 - 36 * q^12 - 90 * q^13 - 48 * q^14 - 114 * q^15 + 18 * q^17 - 12 * q^19 + 24 * q^20 + 90 * q^21 + 84 * q^22 + 120 * q^23 - 24 * q^24 + 252 * q^25 + 48 * q^26 + 126 * q^27 + 72 * q^28 - 210 * q^29 - 108 * q^31 - 132 * q^33 - 24 * q^34 - 66 * q^35 - 12 * q^36 + 84 * q^38 + 120 * q^39 + 54 * q^41 + 72 * q^42 + 90 * q^43 - 48 * q^44 - 144 * q^45 - 360 * q^46 - 246 * q^47 - 48 * q^48 + 54 * q^49 - 432 * q^50 - 342 * q^51 + 36 * q^52 - 174 * q^53 - 42 * q^55 - 12 * q^57 + 48 * q^58 + 228 * q^59 + 132 * q^60 + 12 * q^61 + 204 * q^62 + 174 * q^63 + 96 * q^64 + 630 * q^65 + 696 * q^66 + 72 * q^67 - 48 * q^68 + 702 * q^69 + 528 * q^70 + 432 * q^71 + 96 * q^72 - 144 * q^74 + 72 * q^76 - 144 * q^77 - 708 * q^78 - 246 * q^79 - 642 * q^81 - 384 * q^82 - 126 * q^83 - 540 * q^84 - 684 * q^85 - 12 * q^86 - 324 * q^87 - 12 * q^89 - 336 * q^90 + 372 * q^91 - 132 * q^92 - 168 * q^93 - 570 * q^95 + 72 * q^97 + 384 * q^98 - 204 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{1}{18}\right)$

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 $

$2$	−1.39273	−	0.245576i	−0.696364	−	0.122788i
$2$	−1.39273	−	0.245576i	−0.696364	−	0.122788i
$3$	0.272417	−	0.324654i	0.0908057	−	0.108218i	−0.718728	−	0.695291i	$-0.755275\pi$
$3$	0.272417	−	0.324654i	0.0908057	−	0.108218i	0.809534	+	0.587073i	$0.199720\pi$
$4$	1.87939	+	0.684040i	0.469846	+	0.171010i
$5$	7.98876	−	2.90767i	1.59775	−	0.581534i	0.618787	−	0.785559i	$-0.287625\pi$
$5$	7.98876	−	2.90767i	1.59775	−	0.581534i	0.978966	+	0.204025i	$0.0654023\pi$
$6$	−0.459130	+	0.385256i	−0.0765217	+	0.0642093i
$7$	−2.58545	−	4.47813i	−0.369350	−	0.639733i	0.620114	−	0.784512i	$-0.287086\pi$
$7$	−2.58545	−	4.47813i	−0.369350	−	0.639733i	−0.989464	+	0.144779i	$0.953753\pi$
$8$	−2.44949	−	1.41421i	−0.306186	−	0.176777i
$9$	1.53164	+	8.68639i	0.170183	+	0.965154i
$10$	−11.8402	+	2.08775i	−1.18402	+	0.208775i
$11$	−4.81869	+	8.34622i	−0.438063	+	0.758747i	−0.997540	−	0.0700987i	$-0.977669\pi$
$11$	−4.81869	+	8.34622i	−0.438063	+	0.758747i	0.559477	+	0.828846i	$0.311002\pi$
$12$	0.734053	−	0.423806i	0.0611711	−	0.0353171i
$13$	−8.78112	−	10.4649i	−0.675471	−	0.804995i	0.314047	−	0.949407i	$-0.398315\pi$
$13$	−8.78112	−	10.4649i	−0.675471	−	0.804995i	−0.989518	+	0.144413i	$0.953871\pi$
$14$	2.50111	+	6.87174i	0.178651	+	0.490839i
$15$	1.23229	−	3.38568i	0.0821525	−	0.225712i
$16$	3.06418	+	2.57115i	0.191511	+	0.160697i
$17$	−3.08077	+	17.4719i	−0.181222	+	1.02776i	0.749493	+	0.662012i	$0.230297\pi$
$17$	−3.08077	+	17.4719i	−0.181222	+	1.02776i	−0.930715	+	0.365747i	$0.880814\pi$
$18$		−	12.4739i		−	0.692995i
$19$	−17.6183	−	7.11298i	−0.927281	−	0.374367i
$19$	−17.6183	−	7.11298i	−0.927281	−	0.374367i
$20$	17.0029			0.850146
$21$	−2.15816	−	0.380542i	−0.102770	−	0.0181211i
$22$	8.76075	−	10.4407i	0.398216	−	0.474576i
$23$	14.1083	+	5.13501i	0.613406	+	0.223261i	0.629993	−	0.776601i	$-0.283058\pi$
$23$	14.1083	+	5.13501i	0.613406	+	0.223261i	−0.0165870	+	0.999862i	$0.505280\pi$
$24$	−1.12641	+	0.409981i	−0.0469339	+	0.0170825i
$25$	36.2147	−	30.3877i	1.44859	−	1.21551i
$26$	9.65978	+	16.7312i	0.371530	+	0.643509i
$27$	6.54055	+	3.77619i	0.242243	+	0.139859i
$28$	−1.79583	−	10.1847i	−0.0641370	−	0.363739i
$29$	11.5878	−	2.04324i	0.399579	−	0.0704566i	0.0297524	−	0.999557i	$-0.490528\pi$
$29$	11.5878	−	2.04324i	0.399579	−	0.0704566i	0.369827	+	0.929101i	$0.379417\pi$
$30$	−2.54768	+	4.41272i	−0.0849227	+	0.147091i
$31$	−44.1349	+	25.4813i	−1.42371	+	0.821977i	−0.996613	−	0.0822315i	$-0.973795\pi$
$31$	−44.1349	+	25.4813i	−1.42371	+	0.821977i	−0.427092	+	0.904208i	$0.640462\pi$
$32$	−3.63616	−	4.33340i	−0.113630	−	0.135419i
$33$	1.39694	+	3.83806i	0.0423315	+	0.116305i
$34$	8.58135	−	23.5771i	0.252393	−	0.693443i
$35$	−33.6755	−	28.2571i	−0.962157	−	0.807345i
$36$	−3.06329	+	17.3728i	−0.0850914	+	0.482577i
$37$			17.8330i			0.481972i	0.970529	+	0.240986i	$0.0774708\pi$
$37$			17.8330i			0.481972i	−0.970529	+	0.240986i	$0.922529\pi$
$38$	22.7908	+	14.2331i	0.599757	+	0.374555i
$39$	−5.78961			−0.148451
$40$	−23.6805	−	4.17550i	−0.592011	−	0.104388i
$41$	−15.8487	+	18.8877i	−0.386553	+	0.460676i	−0.923871	−	0.382704i	$-0.874993\pi$
$41$	−15.8487	+	18.8877i	−0.386553	+	0.460676i	0.537318	+	0.843380i	$0.319437\pi$
$42$	2.91228	+	1.05998i	0.0693401	+	0.0252377i
$43$	14.2358	−	5.18140i	0.331065	−	0.120498i	−0.171139	−	0.985247i	$-0.554745\pi$
$43$	14.2358	−	5.18140i	0.331065	−	0.120498i	0.502204	+	0.864749i	$0.332523\pi$
$44$	−14.7653	+	12.3896i	−0.335576	+	0.281581i
$45$	37.4931	+	64.9400i	0.833180	+	1.44311i
$46$	−18.3880	−	10.6163i	−0.399740	−	0.230790i
$47$	−13.4551	−	76.3075i	−0.286278	−	1.62356i	−0.700684	−	0.713472i	$-0.747122\pi$
$47$	−13.4551	−	76.3075i	−0.286278	−	1.62356i	0.414406	−	0.910092i	$-0.363989\pi$
$48$	1.66947	−	0.294372i	0.0347806	−	0.00613276i
$49$	11.1309	−	19.2793i	0.227161	−	0.393455i
$50$	−57.8997	+	33.4284i	−1.15799	+	0.668568i
$51$	4.83307	+	5.75983i	0.0947660	+	0.112938i
$52$	−9.34467	−	25.6743i	−0.179705	−	0.493736i
$53$	21.5316	−	59.1576i	0.406257	−	1.11618i	−0.552885	−	0.833257i	$-0.686473\pi$
$53$	21.5316	−	59.1576i	0.406257	−	1.11618i	0.959142	−	0.282924i	$-0.0913045\pi$
$54$	−8.18187	−	6.86541i	−0.151516	−	0.127137i
$55$	−14.2273	+	80.6871i	−0.258678	+	1.46704i
$56$			14.6255i			0.261170i
$57$	−7.10879	+	3.78216i	−0.124716	+	0.0663538i
$58$	−16.6404			−0.286904
$59$	52.2374	+	9.21086i	0.885379	+	0.156116i	0.597805	−	0.801642i	$-0.296040\pi$
$59$	52.2374	+	9.21086i	0.885379	+	0.156116i	0.287575	+	0.957758i	$0.407151\pi$
$60$	4.63189	−	5.52007i	0.0771981	−	0.0920011i
$61$	46.5312	+	16.9360i	0.762807	+	0.277639i	0.693984	−	0.719990i	$-0.255854\pi$
$61$	46.5312	+	16.9360i	0.762807	+	0.277639i	0.0688223	+	0.997629i	$0.478076\pi$
$62$	67.7255	−	24.6501i	1.09235	−	0.397581i
$63$	34.9388	−	29.3171i	0.554584	−	0.465351i
$64$	4.00000	+	6.92820i	0.0625000	+	0.108253i
$65$	−100.579	−	58.0692i	−1.54737	−	0.893373i
$66$	−1.00302	−	5.68843i	−0.0151973	−	0.0861883i
$67$	9.95299	−	1.75498i	0.148552	−	0.0261937i	−0.0988775	−	0.995100i	$-0.531525\pi$
$67$	9.95299	−	1.75498i	0.148552	−	0.0261937i	0.247430	+	0.968906i	$0.420414\pi$
$68$	−17.7414	+	30.7291i	−0.260903	+	0.451898i
$69$	5.51045	−	3.18146i	0.0798616	−	0.0461081i
$70$	39.9616	+	47.6243i	0.570879	+	0.680347i
$71$	38.9935	+	107.134i	0.549205	+	1.50893i	0.834787	+	0.550573i	$0.185591\pi$
$71$	38.9935	+	107.134i	0.549205	+	1.50893i	−0.285582	+	0.958354i	$0.592187\pi$
$72$	8.53266	−	23.4433i	0.118509	−	0.325601i
$73$	−85.5417	−	71.7780i	−1.17180	−	0.983260i	−0.171806	−	0.985131i	$-0.554960\pi$
$73$	−85.5417	−	71.7780i	−1.17180	−	0.983260i	−0.999998	+	0.00187066i	$0.999405\pi$
$74$	4.37934	−	24.8365i	0.0591803	−	0.335628i
$75$		−	20.0354i		−	0.267138i
$76$	−28.2461	−	25.4197i	−0.371659	−	0.334469i
$77$	49.8339			0.647194
$78$	8.06335	+	1.42179i	0.103376	+	0.0182280i
$79$	97.8772	−	116.645i	1.23895	−	1.47652i	0.415043	−	0.909802i	$-0.363766\pi$
$79$	97.8772	−	116.645i	1.23895	−	1.47652i	0.823908	−	0.566723i	$-0.191789\pi$
$80$	31.9550	+	11.6307i	0.399438	+	0.145384i
$81$	−71.5884	+	26.0560i	−0.883807	+	0.321679i
$82$	26.7112	−	22.4134i	0.325747	−	0.273334i
$83$	26.5522	+	45.9897i	0.319906	+	0.554093i	0.980468	−	0.196678i	$-0.0630154\pi$
$83$	26.5522	+	45.9897i	0.319906	+	0.554093i	−0.660562	+	0.750771i	$0.729682\pi$
$84$	−3.79571	−	2.19146i	−0.0451871	−	0.0260888i
$85$	26.1910	+	148.537i	0.308130	+	1.74749i
$86$	−21.0990	+	3.72032i	−0.245337	+	0.0432596i
$87$	2.49337	−	4.31864i	0.0286594	−	0.0496395i
$88$	23.6067	−	13.6293i	0.268258	−	0.154879i
$89$	−71.6292	−	85.3643i	−0.804822	−	0.959150i	0.194943	−	0.980815i	$-0.437548\pi$
$89$	−71.6292	−	85.3643i	−0.804822	−	0.959150i	−0.999765	+	0.0216646i	$0.993103\pi$
$90$	−36.2700	−	99.6511i	−0.403000	−	1.10723i
$91$	−24.1602	+	66.3796i	−0.265497	+	0.729446i
$92$	23.0024	+	19.3013i	0.250027	+	0.209797i
$93$	−3.75049	+	21.2701i	−0.0403279	+	0.228711i
$94$			109.580i			1.16574i
$95$	−161.431	−	5.59555i	−1.69927	−	0.0589006i
$96$	−2.39741			−0.0249730
$97$	−84.8296	−	14.9577i	−0.874531	−	0.154203i	−0.281673	−	0.959510i	$-0.590889\pi$
$97$	−84.8296	−	14.9577i	−0.874531	−	0.154203i	−0.592858	+	0.805307i	$0.702001\pi$
$98$	−20.2368	+	24.1173i	−0.206498	+	0.246095i
$99$	−79.8790	−	29.0736i	−0.806859	−	0.293672i
$100$	88.8477	−	32.3379i	0.888477	−	0.323379i
$101$	−46.6818	+	39.1707i	−0.462196	+	0.387828i	−0.843938	−	0.536440i	$-0.819769\pi$
$101$	−46.6818	+	39.1707i	−0.462196	+	0.387828i	0.381742	+	0.924269i	$0.375324\pi$
$102$	−5.31668	−	9.20876i	−0.0521243	−	0.0902819i
$103$	14.3917	+	8.30906i	0.139725	+	0.0806705i	0.568233	−	0.822868i	$-0.307627\pi$
$103$	14.3917	+	8.30906i	0.139725	+	0.0806705i	−0.428508	+	0.903538i	$0.640961\pi$
$104$	6.70961	+	38.0521i	0.0645155	+	0.365886i
$105$	−18.3475	+	3.23517i	−0.174739	+	0.0308111i
$106$	−44.5154	+	77.1029i	−0.419956	+	0.727385i
$107$	27.8456	−	16.0766i	0.260239	−	0.150249i	−0.364205	−	0.931319i	$-0.618659\pi$
$107$	27.8456	−	16.0766i	0.260239	−	0.150249i	0.624444	+	0.781070i	$0.285326\pi$
$108$	9.70915	+	11.5709i	0.0898996	+	0.107138i
$109$	16.1872	+	44.4741i	0.148507	+	0.408019i	0.991533	−	0.129853i	$-0.0414505\pi$
$109$	16.1872	+	44.4741i	0.148507	+	0.408019i	−0.843026	+	0.537872i	$0.819228\pi$
$110$	39.6296	−	108.881i	0.360269	−	0.989830i
$111$	5.78954	+	4.85800i	0.0521580	+	0.0437658i
$112$	3.59167	−	20.3694i	0.0320685	−	0.181869i
$113$			45.7668i			0.405016i	0.979281	+	0.202508i	$0.0649092\pi$
$113$			45.7668i			0.405016i	−0.979281	+	0.202508i	$0.935091\pi$
$114$	10.8294	−	3.52178i	0.0949949	−	0.0308928i
$115$	127.639			1.10990
$116$	23.1756	+	4.08648i	0.199790	+	0.0352283i
$117$	77.4529	−	92.3047i	0.661990	−	0.788929i
$118$	−70.4905	−	25.6565i	−0.597377	−	0.217428i
$119$	86.2066	−	31.3767i	0.724426	−	0.263669i
$120$	−7.80655	+	6.55047i	−0.0650546	+	0.0545873i
$121$	14.0604	+	24.3534i	0.116202	+	0.201268i
$122$	−60.6463	−	35.0141i	−0.497101	−	0.287001i
$123$	1.81452	+	10.2907i	0.0147522	+	0.0836639i
$124$	−100.377	+	17.6991i	−0.809489	+	0.142735i
$125$	94.6845	−	163.998i	0.757476	−	1.31199i
$126$	−55.8598	+	32.2507i	−0.443332	+	0.255958i
$127$	38.9964	+	46.4741i	0.307058	+	0.365938i	0.897402	−	0.441214i	$-0.145452\pi$
$127$	38.9964	+	46.4741i	0.307058	+	0.365938i	−0.590343	+	0.807152i	$0.701008\pi$
$128$	−3.86952	−	10.6314i	−0.0302306	−	0.0830579i
$129$	2.19591	−	6.03320i	0.0170225	−	0.0467690i
$130$	125.819	+	105.574i	0.967836	+	0.812111i
$131$	21.6520	−	122.795i	0.165283	−	0.937364i	−0.783490	−	0.621405i	$-0.786562\pi$
$131$	21.6520	−	122.795i	0.165283	−	0.937364i	0.948773	−	0.315960i	$-0.102327\pi$
$132$			8.16875i			0.0618845i
$133$	13.6985	+	97.2874i	0.102996	+	0.731485i
$134$	−14.2928			−0.106663
$135$	63.2308	+	11.1493i	0.468377	+	0.0825874i
$136$	32.2553	−	38.4404i	0.237171	−	0.282650i
$137$	55.7673	+	20.2976i	0.407060	+	0.148158i	0.537431	−	0.843307i	$-0.319395\pi$
$137$	55.7673	+	20.2976i	0.407060	+	0.148158i	−0.130371	+	0.991465i	$0.541617\pi$
$138$	−8.45585	+	3.07768i	−0.0612743	+	0.0223020i
$139$	32.9531	−	27.6509i	0.237072	−	0.198927i	−0.516509	−	0.856282i	$-0.672769\pi$
$139$	32.9531	−	27.6509i	0.237072	−	0.198927i	0.753582	+	0.657354i	$0.228324\pi$
$140$	−43.9602	−	76.1413i	−0.314002	−	0.543867i
$141$	−28.4389	−	16.4192i	−0.201694	−	0.116448i
$142$	−27.9979	−	158.784i	−0.197169	−	1.11820i
$143$	129.656	−	22.8619i	0.906686	−	0.159873i
$144$	−17.6408	+	30.5547i	−0.122505	+	0.212186i
$145$	86.6311	−	50.0165i	0.597456	−	0.344941i
$146$	101.509	+	120.974i	0.695270	+	0.828590i
$147$	−3.22685	−	8.86569i	−0.0219513	−	0.0603108i
$148$	−12.1985	+	33.5150i	−0.0824220	+	0.226453i
$149$	−30.0869	−	25.2459i	−0.201925	−	0.169435i	0.536218	−	0.844080i	$-0.319853\pi$
$149$	−30.0869	−	25.2459i	−0.201925	−	0.169435i	−0.738143	+	0.674644i	$0.764297\pi$
$150$	−4.92019	+	27.9038i	−0.0328013	+	0.186025i
$151$		−	30.0563i		−	0.199048i	−0.995035	−	0.0995242i	$-0.968268\pi$
$151$		−	30.0563i		−	0.199048i	0.995035	−	0.0995242i	$-0.0317321\pi$
$152$	33.0967	+	42.3392i	0.217741	+	0.278548i
$153$	−156.486			−1.02279
$154$	−69.4051	−	12.2380i	−0.450683	−	0.0794675i
$155$	−278.492	+	331.894i	−1.79672	+	2.14125i
$156$	−10.8809	−	3.96032i	−0.0697494	−	0.0253867i
$157$	−217.146	+	79.0346i	−1.38309	+	0.503405i	−0.923115	−	0.384525i	$-0.874365\pi$
$157$	−217.146	+	79.0346i	−1.38309	+	0.503405i	−0.459979	+	0.887930i	$0.652143\pi$
$158$	−164.962	+	138.419i	−1.04406	+	0.876071i
$159$	−13.3402	−	23.1059i	−0.0839005	−	0.145320i
$160$	−41.6485	−	24.0458i	−0.260303	−	0.150286i
$161$	−13.4811	−	76.4553i	−0.0837337	−	0.474878i
$162$	106.102	−	18.7086i	0.654950	−	0.115485i
$163$	25.1151	−	43.5007i	0.154080	−	0.266875i	−0.778643	−	0.627467i	$-0.784092\pi$
$163$	25.1151	−	43.5007i	0.154080	−	0.266875i	0.932724	+	0.360592i	$0.117425\pi$
$164$	−42.7057	+	24.6561i	−0.260401	+	0.150342i
$165$	22.3196	+	26.5995i	0.135270	+	0.161209i
$166$	−25.6860	−	70.5718i	−0.154735	−	0.425131i
$167$	−50.6145	+	139.062i	−0.303081	+	0.832708i	0.690880	+	0.722970i	$0.257223\pi$
$167$	−50.6145	+	139.062i	−0.303081	+	0.832708i	−0.993961	+	0.109738i	$0.964999\pi$
$168$	4.74823	+	3.98424i	0.0282633	+	0.0237157i
$169$	−3.06017	+	17.3551i	−0.0181075	+	0.102693i
$170$		−	213.303i		−	1.25472i
$171$	34.8010	−	163.934i	0.203515	−	0.958679i
$172$	30.2988			0.176156
$173$	111.686	+	19.6933i	0.645584	+	0.113834i	0.486847	−	0.873487i	$-0.338147\pi$
$173$	111.686	+	19.6933i	0.645584	+	0.113834i	0.158737	+	0.987321i	$0.449258\pi$
$174$	−4.53313	+	5.40238i	−0.0260525	+	0.0310482i
$175$	−229.711	−	83.6081i	−1.31264	−	0.477760i
$176$	−36.2247	+	13.1847i	−0.205822	+	0.0749131i
$177$	17.2207	−	14.4499i	0.0972920	−	0.0816377i
$178$	78.7966	+	136.480i	0.442678	+	0.766740i
$179$	215.541	+	124.443i	1.20414	+	0.695210i	0.961473	−	0.274900i	$-0.0886448\pi$
$179$	215.541	+	124.443i	1.20414	+	0.695210i	0.242666	+	0.970110i	$0.421978\pi$
$180$	26.0424	+	147.694i	0.144680	+	0.820522i
$181$	176.042	−	31.0409i	0.972605	−	0.171497i	0.335303	−	0.942110i	$-0.391161\pi$
$181$	176.042	−	31.0409i	0.972605	−	0.171497i	0.637302	+	0.770614i	$0.280050\pi$
$182$	49.9498	−	86.5155i	0.274449	−	0.475360i
$183$	18.1742	−	10.4929i	0.0993127	−	0.0573382i
$184$	−27.2962	−	32.5304i	−0.148349	−	0.176795i
$185$	51.8524	+	142.463i	0.280283	+	0.770072i
$186$	10.4468	−	28.7024i	0.0561657	−	0.154314i
$187$	−130.979	−	109.904i	−0.700423	−	0.587724i
$188$	26.9101	−	152.615i	0.143139	−	0.811782i
$189$		−	39.0526i		−	0.206628i
$190$	223.455	+	47.4366i	1.17608	+	0.249666i
$191$	−299.431			−1.56770			−0.783850	−	0.620950i	$-0.786747\pi$
$191$	−299.431			−1.56770			−0.783850	+	0.620950i	$0.786747\pi$
$192$	3.33894	+	0.588744i	0.0173903	+	0.00306638i
$193$	2.36990	−	2.82434i	0.0122793	−	0.0146339i	−0.759870	−	0.650075i	$-0.774737\pi$
$193$	2.36990	−	2.82434i	0.0122793	−	0.0146339i	0.772149	+	0.635441i	$0.219182\pi$
$194$	114.471	+	41.6641i	0.590058	+	0.214764i
$195$	−46.2518	+	16.8343i	−0.237189	+	0.0863296i
$196$	34.1070	−	28.6192i	0.174016	−	0.146016i
$197$	−72.8974	−	126.262i	−0.370038	−	0.640924i	0.619533	−	0.784970i	$-0.287322\pi$
$197$	−72.8974	−	126.262i	−0.370038	−	0.640924i	−0.989571	+	0.144046i	$0.953989\pi$
$198$	104.110	+	60.1079i	0.525808	+	0.303575i
$199$	−8.31426	−	47.1525i	−0.0417802	−	0.236947i	0.956765	−	0.290861i	$-0.0939416\pi$
$199$	−8.31426	−	47.1525i	−0.0417802	−	0.236947i	−0.998546	+	0.0539134i	$0.982831\pi$
$200$	−131.682	+	23.2191i	−0.658411	+	0.116096i
$201$	2.14160	−	3.70936i	0.0106547	−	0.0184545i
$202$	74.6344	−	43.0902i	0.369477	−	0.213318i
$203$	−39.1096	−	46.6090i	−0.192658	−	0.229601i
$204$	5.14324	+	14.1309i	0.0252120	+	0.0692693i
$205$	−71.6920	+	196.972i	−0.349717	+	0.960839i
$206$	−18.0032	−	15.1065i	−0.0873944	−	0.0733326i
$207$	−22.9958	+	130.415i	−0.111091	+	0.630026i
$208$		−	54.6440i		−	0.262711i
$209$	144.264	−	112.771i	0.690257	−	0.539575i
$210$	26.3476			0.125465
$211$	10.7276	+	1.89157i	0.0508419	+	0.00896479i	0.199011	−	0.979997i	$-0.436227\pi$
$211$	10.7276	+	1.89157i	0.0508419	+	0.00896479i	−0.148169	+	0.988962i	$0.547338\pi$
$212$	80.9324	−	96.4515i	0.381757	−	0.454960i
$213$	45.4039	+	16.5257i	0.213164	+	0.0775853i
$214$	−42.7294	+	15.5522i	−0.199670	+	0.0726739i
$215$	98.6604	−	82.7859i	0.458886	−	0.385051i
$216$	−10.6807	−	18.4995i	−0.0494476	−	0.0856457i
$217$	228.217	+	131.761i	1.05169	+	0.607194i
$218$	−11.6227	−	65.9155i	−0.0533151	−	0.302365i
$219$	−46.6060	+	8.21790i	−0.212813	+	0.0375246i
$220$	−81.9318	+	141.910i	−0.372417	+	0.645046i
$221$	209.895	−	121.183i	0.949750	−	0.548339i
$222$	−6.87025	−	8.18764i	−0.0309471	−	0.0368813i
$223$	−104.550	−	287.248i	−0.468832	−	1.28811i	−0.918681	−	0.395001i	$-0.870744\pi$
$223$	−104.550	−	287.248i	−0.468832	−	1.28811i	0.449849	−	0.893105i	$-0.351478\pi$
$224$	−10.0044	+	27.4870i	−0.0446627	+	0.122710i
$225$	319.427	+	268.031i	1.41968	+	1.19125i
$226$	11.2392	−	63.7407i	0.0497310	−	0.282038i
$227$			227.790i			1.00348i	0.865019	+	0.501740i	$0.167306\pi$
$227$			227.790i			1.00348i	−0.865019	+	0.501740i	$0.832694\pi$
$228$	−15.9473	+	2.24545i	−0.0699443	+	0.00984845i
$229$	103.650			0.452620			0.226310	−	0.974055i	$-0.427334\pi$
$229$	103.650			0.452620			0.226310	+	0.974055i	$0.427334\pi$
$230$	−177.767	−	31.3450i	−0.772898	−	0.136283i
$231$	13.5756	−	16.1788i	0.0587689	−	0.0700380i
$232$	−31.2738	−	11.3827i	−0.134801	−	0.0490635i
$233$	−129.992	+	47.3131i	−0.557904	+	0.203060i	−0.605555	−	0.795804i	$-0.707049\pi$
$233$	−129.992	+	47.3131i	−0.557904	+	0.203060i	0.0476508	+	0.998864i	$0.484827\pi$
$234$	−130.539	+	109.535i	−0.557857	+	0.468098i
$235$	−329.366	−	570.479i	−1.40156	−	2.42757i
$236$	91.8736	+	53.0432i	0.389295	+	0.224759i
$237$	−11.2060	−	63.5524i	−0.0472827	−	0.268154i
$238$	−127.768	+	22.5289i	−0.536839	+	0.0946593i
$239$	−124.786	+	216.135i	−0.522116	+	0.904331i	0.477553	+	0.878603i	$0.341524\pi$
$239$	−124.786	+	216.135i	−0.522116	+	0.904331i	−0.999669	+	0.0257281i	$0.991810\pi$
$240$	12.4810	−	7.20593i	0.0520044	−	0.0300247i
$241$	−90.9129	−	108.346i	−0.377232	−	0.449567i	0.543707	−	0.839275i	$-0.317020\pi$
$241$	−90.9129	−	108.346i	−0.377232	−	0.449567i	−0.920939	+	0.389708i	$0.872576\pi$
$242$	−13.6018	−	37.3706i	−0.0562057	−	0.154424i
$243$	−34.2903	+	94.2118i	−0.141112	+	0.387703i
$244$	75.8652	+	63.6584i	0.310923	+	0.260895i
$245$	32.8643	−	186.383i	0.134140	−	0.760745i
$246$		−	14.7777i		−	0.0600719i
$247$	80.2719	+	246.834i	0.324987	+	0.999330i
$248$	144.144			0.581225
$249$	22.1640	+	3.90811i	0.0890121	+	0.0156952i
$250$	−172.144	+	205.153i	−0.688575	+	0.820612i
$251$	334.402	+	121.713i	1.33228	+	0.484910i	0.907373	−	0.420326i	$-0.138084\pi$
$251$	334.402	+	121.713i	1.33228	+	0.484910i	0.424907	+	0.905237i	$0.360307\pi$
$252$	85.7175	−	31.1986i	0.340149	−	0.123804i
$253$	−110.842	+	93.0072i	−0.438109	+	0.367617i
$254$	−42.8985	−	74.3024i	−0.168892	−	0.292529i
$255$	55.3579	+	31.9609i	0.217090	+	0.125337i
$256$	2.77837	+	15.7569i	0.0108530	+	0.0615505i
$257$	−500.070	+	88.1758i	−1.94580	+	0.343097i	−0.945975	+	0.324238i	$0.894892\pi$
$257$	−500.070	+	88.1758i	−1.94580	+	0.343097i	−0.999822	+	0.0188584i	$0.993997\pi$
$258$	−4.53991	+	7.86335i	−0.0175965	+	0.0304781i
$259$	79.8583	−	46.1062i	0.308333	−	0.178016i
$260$	−149.305	−	177.934i	−0.574249	−	0.684363i
$261$	35.4968	+	97.5266i	0.136003	+	0.373665i
$262$	−60.3108	+	165.703i	−0.230194	+	0.632452i
$263$	157.860	+	132.460i	0.600227	+	0.503651i	0.891519	−	0.452984i	$-0.149640\pi$
$263$	157.860	+	132.460i	0.600227	+	0.503651i	−0.291291	+	0.956634i	$0.594085\pi$
$264$	2.00605	−	11.3769i	0.00759866	−	0.0430941i
$265$		−	535.203i		−	2.01963i
$266$	4.81316	−	138.859i	0.0180946	−	0.522026i
$267$	−47.2269			−0.176880
$268$	19.9060	+	3.50996i	0.0742760	+	0.0130969i
$269$	−11.1613	+	13.3015i	−0.0414918	+	0.0494480i	−0.786391	−	0.617729i	$-0.788053\pi$
$269$	−11.1613	+	13.3015i	−0.0414918	+	0.0494480i	0.744899	+	0.667177i	$0.232497\pi$
$270$	−85.3254	−	31.0559i	−0.316020	−	0.115022i
$271$	79.0847	−	28.7845i	0.291826	−	0.106216i	−0.191959	−	0.981403i	$-0.561484\pi$
$271$	79.0847	−	28.7845i	0.291826	−	0.106216i	0.483785	+	0.875187i	$0.339262\pi$
$272$	−54.3629	+	45.6159i	−0.199864	+	0.167705i
$273$	14.9687	+	25.9266i	0.0548305	+	0.0949693i
$274$	−72.6840	−	41.9642i	−0.265270	−	0.153154i
$275$	79.1151	+	448.684i	0.287691	+	1.63158i
$276$	12.5325	−	2.20982i	0.0454076	−	0.00800659i
$277$	−87.0326	+	150.745i	−0.314197	+	0.544206i	−0.979267	−	0.202576i	$-0.935069\pi$
$277$	−87.0326	+	150.745i	−0.314197	+	0.544206i	0.665069	+	0.746782i	$0.268402\pi$
$278$	−52.6850	+	30.4177i	−0.189515	+	0.109416i
$279$	−288.939	−	344.344i	−1.03562	−	1.23421i
$280$	42.5262	+	116.840i	0.151879	+	0.417285i
$281$	15.8834	−	43.6394i	0.0565247	−	0.155300i	−0.908217	−	0.418501i	$-0.862556\pi$
$281$	15.8834	−	43.6394i	0.0565247	−	0.155300i	0.964741	+	0.263200i	$0.0847780\pi$
$282$	35.5755	+	29.8514i	0.126154	+	0.105856i
$283$	27.2953	−	154.800i	0.0964500	−	0.546995i	−0.897843	−	0.440315i	$-0.854867\pi$
$283$	27.2953	−	154.800i	0.0964500	−	0.546995i	0.994293	−	0.106680i	$-0.0340221\pi$
$284$			228.019i			0.802884i
$285$	−45.7931	+	50.8848i	−0.160678	+	0.178543i
$286$	−186.190			−0.651014
$287$	125.558	+	22.1392i	0.437483	+	0.0771400i
$288$	32.0723	−	38.2223i	0.111362	−	0.132716i
$289$	−24.2050	−	8.80992i	−0.0837545	−	0.0304841i
$290$	−132.936	+	48.3849i	−0.458401	+	0.166844i
$291$	−27.9651	+	23.4655i	−0.0961000	+	0.0806375i
$292$	−111.667	−	193.412i	−0.382420	−	0.662371i
$293$	235.642	+	136.048i	0.804238	+	0.464327i	0.844951	−	0.534844i	$-0.179630\pi$
$293$	235.642	+	136.048i	0.804238	+	0.464327i	−0.0407129	+	0.999171i	$0.512963\pi$
$294$	2.31692	+	13.1399i	0.00788070	+	0.0446936i
$295$	444.094	−	78.3058i	1.50540	−	0.265443i
$296$	25.2196	−	43.6816i	0.0852014	−	0.147573i
$297$	−63.0338	+	36.3926i	−0.212235	+	0.122534i
$298$	35.7031	+	42.5492i	0.119809	+	0.142783i
$299$	−70.1494	−	192.734i	−0.234613	−	0.644595i
$300$	13.7050	−	37.6541i	0.0456833	−	0.125514i
$301$	−60.0089	−	50.3534i	−0.199365	−	0.167287i
$302$	−7.38110	+	41.8603i	−0.0244407	+	0.138610i
$303$			25.8262i			0.0852349i
$304$	−35.6972	−	67.0948i	−0.117425	−	0.220707i
$305$	420.971			1.38023
$306$	217.943	+	38.4292i	0.712232	+	0.125586i
$307$	−170.891	+	203.660i	−0.556649	+	0.663388i	−0.968834	−	0.247712i	$-0.920321\pi$
$307$	−170.891	+	203.660i	−0.556649	+	0.663388i	0.412185	+	0.911100i	$0.364766\pi$
$308$	93.6572	+	34.0884i	0.304082	+	0.110677i
$309$	6.61812	−	2.40880i	0.0214179	−	0.00779546i
$310$	469.368	−	393.847i	1.51409	−	1.27047i
$311$	79.8596	+	138.321i	0.256783	+	0.444762i	0.965378	−	0.260854i	$-0.0840040\pi$
$311$	79.8596	+	138.321i	0.256783	+	0.444762i	−0.708595	+	0.705615i	$0.750671\pi$
$312$	14.1816	+	8.18774i	0.0454538	+	0.0262428i
$313$	−32.6715	−	185.290i	−0.104382	−	0.591979i	−0.991465	−	0.130370i	$-0.958383\pi$
$313$	−32.6715	−	185.290i	−0.104382	−	0.591979i	0.887083	−	0.461609i	$-0.152728\pi$
$314$	321.834	−	56.7480i	1.02495	−	0.180726i
$315$	193.873	−	335.798i	0.615470	−	1.06603i
$316$	263.739	−	152.270i	0.834617	−	0.481867i
$317$	109.932	+	131.012i	0.346788	+	0.413285i	0.911041	−	0.412316i	$-0.135280\pi$
$317$	109.932	+	131.012i	0.346788	+	0.413285i	−0.564253	+	0.825602i	$0.690836\pi$
$318$	12.9050	+	35.4562i	0.0405818	+	0.111498i
$319$	−38.7847	+	106.560i	−0.121582	+	0.334044i
$320$	52.1000	+	43.7171i	0.162812	+	0.136616i
$321$	2.36626	−	13.4197i	0.00737153	−	0.0418060i
$322$			109.792i			0.340969i
$323$	178.555	−	285.912i	0.552802	−	0.885177i
$324$	−152.366			−0.470264
$325$	−636.010	−	112.146i	−1.95695	−	0.345064i
$326$	−45.6612	+	54.4169i	−0.140065	+	0.166923i
$327$	18.8484	+	6.86024i	0.0576403	+	0.0209793i
$328$	65.5324	−	23.8518i	0.199794	−	0.0727190i
$329$	−306.928	+	257.543i	−0.932911	+	0.782805i
$330$	−24.5530	−	42.5270i	−0.0744030	−	0.128870i
$331$	−301.436	−	174.034i	−0.910683	−	0.525783i	−0.0300322	−	0.999549i	$-0.509561\pi$
$331$	−301.436	−	174.034i	−0.910683	−	0.525783i	−0.880651	+	0.473766i	$0.842894\pi$
$332$	18.4430	+	104.595i	0.0555511	+	0.315046i
$333$	−154.904	+	27.3138i	−0.465177	+	0.0820233i
$334$	104.643	−	181.246i	0.313301	−	0.542654i
$335$	74.4091	−	42.9601i	0.222117	−	0.128239i
$336$	−5.63456	−	6.71501i	−0.0167695	−	0.0199852i
$337$	113.696	+	312.377i	0.337377	+	0.926935i	0.986136	+	0.165941i	$0.0530662\pi$
$337$	113.696	+	312.377i	0.337377	+	0.926935i	−0.648759	+	0.760994i	$0.724712\pi$
$338$	8.52396	−	23.4194i	0.0252188	−	0.0692881i
$339$	14.8584	+	12.4676i	0.0438300	+	0.0367777i
$340$	−52.3821	+	297.073i	−0.154065	+	0.873745i
$341$		−	491.146i		−	1.44031i
$342$	−88.7266	+	219.770i	−0.259435	+	0.642601i
$343$	−368.488			−1.07431
$344$	−42.1980	−	7.44064i	−0.122669	−	0.0216298i
$345$	34.7710	−	41.4385i	0.100786	−	0.120112i
$346$	−150.712	−	54.8548i	−0.435584	−	0.158540i
$347$	−423.794	+	154.248i	−1.22131	+	0.444520i	−0.870612	−	0.491970i	$-0.836277\pi$
$347$	−423.794	+	154.248i	−1.22131	+	0.444520i	−0.350696	+	0.936489i	$0.614055\pi$
$348$	7.64012	−	6.41082i	0.0219544	−	0.0184219i
$349$	204.775	+	354.680i	0.586747	+	1.01628i	0.994655	+	0.103253i	$0.0329252\pi$
$349$	204.775	+	354.680i	0.586747	+	1.01628i	−0.407908	+	0.913023i	$0.633742\pi$
$350$	299.393	+	172.855i	0.855410	+	0.493871i
$351$	−17.9158	−	101.606i	−0.0510422	−	0.289475i
$352$	53.6890	−	9.46682i	0.152526	−	0.0268944i
$353$	32.9614	−	57.0908i	0.0933750	−	0.161730i	−0.815554	−	0.578681i	$-0.803568\pi$
$353$	32.9614	−	57.0908i	0.0933750	−	0.161730i	0.908929	+	0.416950i	$0.136901\pi$
$354$	−27.5323	+	15.8958i	−0.0777748	+	0.0449033i
$355$	623.020	+	742.486i	1.75499	+	2.09151i
$356$	−76.2262	−	209.430i	−0.214119	−	0.588286i
$357$	13.2976	−	36.5349i	0.0372482	−	0.102339i
$358$	−269.630	−	226.246i	−0.753156	−	0.631973i
$359$	−21.5577	+	122.260i	−0.0600494	+	0.340557i	−1.00000		0.000754240i	$-0.999760\pi$
$359$	−21.5577	+	122.260i	−0.0600494	+	0.340557i	0.939950	+	0.341311i	$0.110871\pi$
$360$		−	212.093i		−	0.589147i
$361$	259.811	+	250.638i	0.719698	+	0.694287i
$362$	−252.801			−0.698345
$363$	11.7367	+	2.06950i	0.0323326	+	0.00570111i
$364$	−90.8126	+	108.226i	−0.249485	+	0.297325i
$365$	−892.079	−	324.690i	−2.44405	−	0.889562i
$366$	−27.8886	+	10.1506i	−0.0761982	+	0.0277339i
$367$	245.165	−	205.718i	0.668023	−	0.560538i	−0.244456	−	0.969660i	$-0.578609\pi$
$367$	245.165	−	205.718i	0.668023	−	0.560538i	0.912480	+	0.409122i	$0.134165\pi$
$368$	30.0276	+	52.0092i	0.0815966	+	0.141329i
$369$	−188.340	−	108.738i	−0.510408	−	0.294684i
$370$	−37.2308	−	211.146i	−0.100624	−	0.570666i
$371$	−320.584	+	56.5277i	−0.864109	+	0.152366i
$372$	−21.5982	+	37.4092i	−0.0580597	+	0.100562i
$373$	−433.118	+	250.061i	−1.16117	+	0.670404i	−0.951585	−	0.307386i	$-0.900546\pi$
$373$	−433.118	+	250.061i	−1.16117	+	0.670404i	−0.209588	+	0.977790i	$0.567212\pi$
$374$	155.428	+	185.232i	0.415584	+	0.495274i
$375$	−27.4490	−	75.4156i	−0.0731974	−	0.201108i
$376$	−74.9570	+	205.943i	−0.199354	+	0.547720i
$377$	−123.136	−	103.324i	−0.326621	−	0.274068i
$378$	−9.59037	+	54.3897i	−0.0253713	+	0.143888i
$379$			715.542i			1.88797i	0.329982	+	0.943987i	$0.392957\pi$
$379$			715.542i			1.88797i	−0.329982	+	0.943987i	$0.607043\pi$
$380$	−299.563	−	120.941i	−0.788324	−	0.318267i
$381$	25.7113			0.0674837
$382$	417.026	+	73.5329i	1.09169	+	0.192495i
$383$	111.458	−	132.831i	0.291014	−	0.346817i	−0.600652	−	0.799510i	$-0.705092\pi$
$383$	111.458	−	132.831i	0.291014	−	0.346817i	0.891666	+	0.452693i	$0.149537\pi$
$384$	−4.50565	−	1.63992i	−0.0117335	−	0.00427063i
$385$	398.111	−	144.901i	1.03406	−	0.376366i
$386$	−3.99422	+	3.35155i	−0.0103477	+	0.00868278i
$387$	66.8118	+	115.721i	0.172640	+	0.299022i
$388$	−149.196	−	86.1382i	−0.384525	−	0.222006i
$389$	−37.0880	−	210.336i	−0.0953419	−	0.540711i	−0.994642	−	0.103379i	$-0.967035\pi$
$389$	−37.0880	−	210.336i	−0.0953419	−	0.540711i	0.899300	−	0.437332i	$-0.144076\pi$
$390$	68.5503	−	12.0873i	0.175770	−	0.0309930i
$391$	−133.183	+	230.680i	−0.340621	+	0.589974i
$392$	−54.5300	+	31.4829i	−0.139107	+	0.0803136i
$393$	−33.9674	−	40.4808i	−0.0864311	−	0.103005i
$394$	70.5195	+	193.751i	0.178983	+	0.491753i
$395$	442.751	−	1216.45i	1.12089	−	3.07961i
$396$	−130.236	−	109.281i	−0.328879	−	0.275962i
$397$	60.3300	−	342.149i	0.151965	−	0.861836i	−0.809544	−	0.587060i	$-0.800285\pi$
$397$	60.3300	−	342.149i	0.151965	−	0.861836i	0.961508	−	0.274776i	$-0.0886036\pi$
$398$			67.7124i			0.170132i
$399$	35.3164	+	22.0555i	0.0885124	+	0.0552769i
$400$	189.099			0.472749
$401$	98.1719	+	17.3104i	0.244818	+	0.0431680i	0.294710	−	0.955587i	$-0.404777\pi$
$401$	98.1719	+	17.3104i	0.244818	+	0.0431680i	−0.0498926	+	0.998755i	$0.515888\pi$
$402$	−3.89360	+	4.64021i	−0.00968557	+	0.0115428i
$403$	654.213	+	238.114i	1.62336	+	0.590854i
$404$	−114.527	+	41.6846i	−0.283484	+	0.103180i
$405$	−496.140	+	416.311i	−1.22504	+	1.02793i
$406$	43.0230	+	74.5180i	0.105968	+	0.183542i
$407$	−148.838	−	85.9315i	−0.365695	−	0.211134i
$408$	−3.69293	−	20.9436i	−0.00905129	−	0.0513324i
$409$	487.607	−	85.9782i	1.19219	−	0.210216i	0.457872	−	0.889018i	$-0.348612\pi$
$409$	487.607	−	85.9782i	1.19219	−	0.210216i	0.734321	+	0.678802i	$0.237501\pi$
$410$	148.219	−	256.723i	0.361510	−	0.626153i
$411$	21.7816	−	12.5756i	0.0529967	−	0.0305977i
$412$	21.3638	+	25.4604i	0.0518540	+	0.0617972i
$413$	−93.8097	−	257.740i	−0.227142	−	0.624068i
$414$	64.0537	−	175.986i	0.154719	−	0.425087i
$415$	345.842	+	290.196i	0.833354	+	0.699267i
$416$	−13.4192	+	76.1042i	−0.0322578	+	0.182943i
$417$		−	18.2309i		−	0.0437192i
$418$	−228.614	+	121.632i	−0.546924	+	0.290986i
$419$	61.5336			0.146858			0.0734291	−	0.997300i	$-0.476606\pi$
$419$	61.5336			0.146858			0.0734291	+	0.997300i	$0.476606\pi$
$420$	−36.6951	−	6.47033i	−0.0873693	−	0.0154056i
$421$	394.068	−	469.631i	0.936027	−	1.11551i	−0.0570875	−	0.998369i	$-0.518181\pi$
$421$	394.068	−	469.631i	0.936027	−	1.11551i	0.993115	−	0.117145i	$-0.0373741\pi$
$422$	−14.4762	−	5.26889i	−0.0343037	−	0.0124855i
$423$	642.228	−	233.752i	1.51827	−	0.552605i
$424$	−136.403	+	114.456i	−0.321705	+	0.269943i
$425$	419.362	+	726.356i	0.986734	+	1.70907i
$426$	−59.1770	−	34.1659i	−0.138913	−	0.0802016i
$427$	−44.4626	−	252.160i	−0.104128	−	0.590539i
$428$	63.3296	−	11.1667i	0.147966	−	0.0260905i
$429$	27.8983	−	48.3213i	0.0650310	−	0.112637i
$430$	−157.737	+	91.0697i	−0.366831	+	0.211790i
$431$	−30.0869	−	35.8562i	−0.0698073	−	0.0831931i	0.730011	−	0.683436i	$-0.239515\pi$
$431$	−30.0869	−	35.8562i	−0.0698073	−	0.0831931i	−0.799818	+	0.600243i	$0.795071\pi$
$432$	10.3323	+	28.3877i	0.0239173	+	0.0657122i
$433$	−245.011	+	673.161i	−0.565845	+	1.55465i	0.245085	+	0.969502i	$0.421184\pi$
$433$	−245.011	+	673.161i	−0.565845	+	1.55465i	−0.810930	+	0.585144i	$0.801038\pi$
$434$	−285.487	−	239.552i	−0.657804	−	0.551963i
$435$	7.36173	−	41.7504i	0.0169235	−	0.0959780i
$436$			94.6567i			0.217102i
$437$	−212.040	−	190.823i	−0.485218	−	0.436665i
$438$	66.9276			0.152803
$439$	30.4549	+	5.37002i	0.0693734	+	0.0122324i	0.208227	−	0.978080i	$-0.433231\pi$
$439$	30.4549	+	5.37002i	0.0693734	+	0.0122324i	−0.138854	+	0.990313i	$0.544342\pi$
$440$	148.958	−	177.522i	0.338542	−	0.403459i
$441$	184.516	+	67.1583i	0.418403	+	0.152286i
$442$	−322.086	+	117.230i	−0.728701	+	0.265226i
$443$	242.766	−	203.705i	0.548005	−	0.459831i	−0.326260	−	0.945280i	$-0.605788\pi$
$443$	242.766	−	203.705i	0.548005	−	0.459831i	0.874265	+	0.485449i	$0.161344\pi$
$444$	7.55771	+	13.0903i	0.0170219	+	0.0294827i
$445$	−820.440	−	473.681i	−1.84369	−	1.06445i
$446$	75.0682	+	425.733i	0.168314	+	0.954558i
$447$	−16.3923	+	2.89041i	−0.0366719	+	0.00646625i
$448$	20.6836	−	35.8250i	0.0461688	−	0.0799666i
$449$	−223.046	+	128.776i	−0.496762	+	0.286805i	−0.727375	−	0.686240i	$-0.759260\pi$
$449$	−223.046	+	128.776i	−0.496762	+	0.286805i	0.230614	+	0.973045i	$0.425927\pi$
$450$	−379.054	−	451.738i	−0.842341	−	1.00386i
$451$	−81.2710	−	223.290i	−0.180202	−	0.495101i
$452$	−31.3063	+	86.0134i	−0.0692618	+	0.190295i
$453$	−9.75790	−	8.18785i	−0.0215406	−	0.0180747i
$454$	55.9396	−	317.249i	0.123215	−	0.698787i
$455$			600.540i			1.31987i
$456$	22.7617	+	0.788971i	0.0499160	+	0.00173020i
$457$	780.810			1.70856			0.854278	−	0.519816i	$-0.174000\pi$
$457$	780.810			1.70856			0.854278	+	0.519816i	$0.174000\pi$
$458$	−144.356	−	25.4539i	−0.315189	−	0.0555762i
$459$	−86.1271	+	102.642i	−0.187641	+	0.223622i
$460$	239.883	+	87.3103i	0.521485	+	0.189805i
$461$	398.212	−	144.937i	0.863801	−	0.314398i	0.128147	−	0.991755i	$-0.459097\pi$
$461$	398.212	−	144.937i	0.863801	−	0.314398i	0.735654	+	0.677357i	$0.236875\pi$
$462$	−22.8803	+	19.1988i	−0.0495244	+	0.0415559i
$463$	−341.060	−	590.733i	−0.736630	−	1.27588i	−0.954004	−	0.299792i	$-0.903083\pi$
$463$	−341.060	−	590.733i	−0.736630	−	1.27588i	0.217374	−	0.976088i	$-0.430251\pi$
$464$	40.7605	+	23.5331i	0.0878460	+	0.0507179i
$465$	31.8847	+	180.827i	0.0685691	+	0.388875i
$466$	192.662	−	33.9715i	0.413438	−	0.0729002i
$467$	−238.816	+	413.642i	−0.511384	+	0.885743i	0.488529	+	0.872548i	$0.337534\pi$
$467$	−238.816	+	413.642i	−0.511384	+	0.885743i	−0.999913	+	0.0131953i	$0.995800\pi$
$468$	208.704	−	120.495i	0.445949	−	0.257469i
$469$	−33.5920	−	40.0334i	−0.0716247	−	0.0853590i
$470$	318.622	+	875.407i	0.677920	+	1.86257i
$471$	−33.4953	+	92.0275i	−0.0711153	+	0.195388i
$472$	−114.929	−	96.4367i	−0.243493	−	0.204315i
$473$	−25.3527	+	143.782i	−0.0535998	+	0.303980i
$474$			91.2632i			0.192538i
$475$	−854.189	+	277.787i	−1.79829	+	0.584814i
$476$	183.478			0.385459
$477$	546.845	+	96.4235i	1.14643	+	0.202146i
$478$	226.870	−	270.373i	0.474623	−	0.565634i
$479$	−566.558	−	206.210i	−1.18279	−	0.430502i	−0.325606	−	0.945505i	$-0.605568\pi$
$479$	−566.558	−	206.210i	−1.18279	−	0.430502i	−0.857188	+	0.515004i	$0.827791\pi$
$480$	−19.1523	+	6.97087i	−0.0399006	+	0.0145226i
$481$	186.621	−	156.593i	0.387985	−	0.325558i
$482$	100.010	+	173.222i	0.207489	+	0.359382i
$483$	−28.4940	−	16.4510i	−0.0589938	−	0.0340601i
$484$	9.76628	+	55.3873i	0.0201783	+	0.114437i
$485$	−721.175	+	127.163i	−1.48696	+	0.262191i
$486$	70.8932	−	122.791i	0.145871	−	0.252656i
$487$	−235.880	+	136.185i	−0.484352	+	0.279641i	−0.722229	−	0.691654i	$-0.756882\pi$
$487$	−235.880	+	136.185i	−0.484352	+	0.279641i	0.237876	+	0.971296i	$0.423549\pi$
$488$	−90.0266	−	107.290i	−0.184481	−	0.219856i
$489$	−7.28087	−	20.0040i	−0.0148893	−	0.0409080i
$490$	−91.5420	+	251.510i	−0.186820	+	0.513285i
$491$	−454.615	−	381.468i	−0.925897	−	0.776920i	0.0491792	−	0.998790i	$-0.484339\pi$
$491$	−454.615	−	381.468i	−0.925897	−	0.776920i	−0.975076	+	0.221870i	$0.928784\pi$
$492$	−3.62904	+	20.5813i	−0.00737610	+	0.0418320i
$493$			208.756i			0.423439i
$494$	−51.1804	−	363.486i	−0.103604	−	0.735802i
$495$	−722.671			−1.45994
$496$	−200.753	−	35.3982i	−0.404744	−	0.0713674i
$497$	378.944	−	451.607i	0.762462	−	0.908667i
$498$	−29.9087	−	10.8859i	−0.0600576	−	0.0218592i
$499$	219.524	−	79.9000i	0.439927	−	0.160120i	−0.112554	−	0.993646i	$-0.535903\pi$
$499$	219.524	−	79.9000i	0.439927	−	0.160120i	0.552481	+	0.833525i	$0.313681\pi$
$500$	290.130	−	243.448i	0.580260	−	0.486896i
$501$	31.3588	+	54.3151i	0.0625925	+	0.108413i
$502$	−435.842	−	251.634i	−0.868211	−	0.501262i
$503$	75.1416	+	426.149i	0.149387	+	0.847215i	0.963740	+	0.266845i	$0.0859811\pi$
$503$	75.1416	+	426.149i	0.149387	+	0.847215i	−0.814353	+	0.580370i	$0.802908\pi$
$504$	−127.043	+	22.4011i	−0.252069	+	0.0444466i
$505$	−259.034	+	448.661i	−0.512939	+	0.888437i
$506$	177.213	−	102.314i	0.350223	−	0.202201i
$507$	4.80075	+	5.72131i	0.00946893	+	0.0112846i
$508$	41.4991	+	114.018i	0.0816912	+	0.224445i
$509$	141.593	−	389.024i	0.278179	−	0.764291i	−0.719390	−	0.694606i	$-0.755579\pi$
$509$	141.593	−	389.024i	0.278179	−	0.764291i	0.997569	−	0.0696845i	$-0.0221993\pi$
$510$	−69.2497	−	58.1074i	−0.135784	−	0.113936i
$511$	−100.268	+	568.645i	−0.196218	+	1.11281i
$512$		−	22.6274i		−	0.0441942i
$513$	−88.3737	−	113.053i	−0.172268	−	0.220376i
$514$	718.116			1.39711
$515$	139.132	+	24.5327i	0.270159	+	0.0476364i
$516$	8.25391	−	9.83662i	0.0159959	−	0.0190632i
$517$	701.715	+	255.403i	1.35728	+	0.494010i
$518$	−122.544	+	44.6022i	−0.236571	+	0.0861046i
$519$	36.8187	−	30.8945i	0.0709416	−	0.0595271i
$520$	164.245	+	284.480i	0.315855	+	0.547077i
$521$	246.294	+	142.198i	0.472733	+	0.272933i	0.717383	−	0.696679i	$-0.245340\pi$
$521$	246.294	+	142.198i	0.472733	+	0.272933i	−0.244650	+	0.969611i	$0.578673\pi$
$522$	−25.4872	−	144.545i	−0.0488261	−	0.276906i
$523$	−401.387	+	70.7754i	−0.767470	+	0.135326i	−0.543658	−	0.839307i	$-0.682961\pi$
$523$	−401.387	+	70.7754i	−0.767470	+	0.135326i	−0.223812	+	0.974632i	$0.571850\pi$
$524$	124.689	−	215.968i	0.237956	−	0.412152i
$525$	−89.7209	+	51.8004i	−0.170897	+	0.0986674i
$526$	−187.327	−	223.248i	−0.356135	−	0.424425i
$527$	−309.237	−	849.622i	−0.586788	−	1.61219i
$528$	−5.58775	+	15.3522i	−0.0105829	+	0.0290762i
$529$	−232.561	−	195.142i	−0.439623	−	0.368888i
$530$	−131.433	+	745.392i	−0.247986	+	1.40640i
$531$			467.862i			0.881096i
$532$	−40.8038	+	192.211i	−0.0766989	+	0.361299i
$533$	336.827			0.631946
$534$	65.7742	+	11.5978i	0.123173	+	0.0217187i
$535$	175.706	−	209.398i	0.328423	−	0.391399i
$536$	−26.8617	−	9.77684i	−0.0501150	−	0.0182404i
$537$	99.1177	−	36.0759i	0.184577	−	0.0671804i
$538$	18.8112	−	15.7844i	0.0349650	−	0.0293391i
$539$	107.273	+	185.802i	0.199022	+	0.344716i
$540$	111.209	+	64.2063i	0.205942	+	0.118901i
$541$	−6.31951	−	35.8397i	−0.0116812	−	0.0662471i	0.978410	−	0.206673i	$-0.0662638\pi$
$541$	−6.31951	−	35.8397i	−0.0116812	−	0.0662471i	−0.990091	+	0.140426i	$0.955153\pi$
$542$	−117.212	+	20.6677i	−0.216259	+	0.0381323i
$543$	37.8792	−	65.6086i	0.0697590	−	0.120826i
$544$	86.9149	−	50.1804i	0.159770	−	0.0922433i
$545$	258.632	+	308.226i	0.474554	+	0.565552i
$546$	−14.4804	−	39.7847i	−0.0265210	−	0.0728657i
$547$	363.049	−	997.469i	0.663710	−	1.82353i	0.104458	−	0.994529i	$-0.466689\pi$
$547$	363.049	−	997.469i	0.663710	−	1.82353i	0.559252	−	0.828998i	$-0.311089\pi$
$548$	90.9238	+	76.2941i	0.165919	+	0.139223i
$549$	−75.8432	+	430.128i	−0.138148	+	0.783475i
$550$		−	644.324i		−	1.17150i
$551$	−218.691	−	46.4252i	−0.396899	−	0.0842563i
$552$	−17.9971			−0.0326034
$553$	−775.410	−	136.726i	−1.40219	−	0.247244i
$554$	158.232	−	188.574i	0.285618	−	0.340386i
$555$	60.3767	+	21.9753i	0.108787	+	0.0395952i
$556$	80.8458	−	29.4255i	0.145406	−	0.0529235i
$557$	−136.150	+	114.244i	−0.244435	+	0.205105i	−0.756771	−	0.653680i	$-0.773224\pi$
$557$	−136.150	+	114.244i	−0.244435	+	0.205105i	0.512337	+	0.858785i	$0.328780\pi$
$558$	317.851	+	550.534i	0.569626	+	0.986621i
$559$	−179.229	−	103.478i	−0.320624	−	0.185113i
$560$	−30.5344	−	173.169i	−0.0545258	−	0.309231i
$561$	−71.3618	+	12.5830i	−0.127205	+	0.0224296i
$562$	−32.8381	+	56.8772i	−0.0584308	+	0.101205i
$563$	−264.174	+	152.521i	−0.469226	+	0.270907i	−0.715915	−	0.698187i	$-0.753990\pi$
$563$	−264.174	+	152.521i	−0.469226	+	0.270907i	0.246690	+	0.969094i	$0.420657\pi$
$564$	−42.2163	−	50.3114i	−0.0748515	−	0.0892046i
$565$	133.075	+	365.620i	0.235531	+	0.647115i
$566$	−76.0300	+	208.891i	−0.134329	+	0.369065i
$567$	301.771	+	253.216i	0.532223	+	0.446588i
$568$	55.9959	−	317.568i	0.0985843	−	0.559099i
$569$		−	232.210i		−	0.408103i	−0.978960	−	0.204051i	$-0.934589\pi$
$569$		−	232.210i		−	0.408103i	0.978960	−	0.204051i	$-0.0654110\pi$
$570$	76.2735	−	59.6231i	0.133813	−	0.104602i
$571$	−153.252			−0.268392			−0.134196	−	0.990955i	$-0.542845\pi$
$571$	−153.252			−0.268392			−0.134196	+	0.990955i	$0.542845\pi$
$572$	259.312	+	45.7237i	0.453343	+	0.0799366i
$573$	−81.5700	+	97.2114i	−0.142356	+	0.169653i
$574$	−169.431	−	61.6677i	−0.295175	−	0.107435i
$575$	666.970	−	242.757i	1.15995	−	0.422186i
$576$	−54.0545	+	45.3571i	−0.0938446	+	0.0787450i
$577$	−158.150	−	273.925i	−0.274091	−	0.474739i	0.695815	−	0.718222i	$-0.255044\pi$
$577$	−158.150	−	273.925i	−0.274091	−	0.474739i	−0.969905	+	0.243482i	$0.921710\pi$
$578$	31.5476	+	18.2140i	0.0545806	+	0.0315121i
$579$	−0.271332	−	1.53880i	−0.000468621	−	0.00265768i
$580$	197.026	−	34.7411i	0.339701	−	0.0598984i
$581$	137.299	−	237.808i	0.236314	−	0.409309i
$582$	44.7103	−	25.8135i	0.0768219	−	0.0443531i
$583$	389.988	+	464.770i	0.668933	+	0.797204i
$584$	108.024	+	296.794i	0.184973	+	0.508208i
$585$	350.361	−	962.608i	0.598907	−	1.64548i
$586$	−294.775	−	247.346i	−0.503029	−	0.422091i
$587$	−41.1017	+	233.099i	−0.0700199	+	0.397103i	0.929575	+	0.368634i	$0.120174\pi$
$587$	−41.1017	+	233.099i	−0.0700199	+	0.397103i	−0.999595	+	0.0284689i	$0.990937\pi$
$588$		−	18.8693i		−	0.0320907i
$589$	958.830	−	135.007i	1.62790	−	0.229214i
$590$	−637.733			−1.08090
$591$	−60.8500	−	10.7295i	−0.102961	−	0.0181548i
$592$	−45.8512	+	54.6434i	−0.0774514	+	0.0923030i
$593$	413.201	+	150.393i	0.696797	+	0.253613i	0.666043	−	0.745913i	$-0.267987\pi$
$593$	413.201	+	150.393i	0.696797	+	0.253613i	0.0307545	+	0.999527i	$0.490209\pi$
$594$	96.7261	−	35.2054i	0.162839	−	0.0592684i
$595$	597.451	−	501.321i	1.00412	−	0.842557i
$596$	−39.2756	−	68.0273i	−0.0658987	−	0.114140i
$597$	−17.5732	−	10.1459i	−0.0294358	−	0.0169948i
$598$	50.3683	+	285.653i	0.0842280	+	0.477681i
$599$	1114.55	−	196.525i	1.86068	−	0.328089i	0.873392	−	0.487017i	$-0.161915\pi$
$599$	1114.55	−	196.525i	1.86068	−	0.328089i	0.987290	+	0.158928i	$0.0508039\pi$
$600$	−28.3343	+	49.0764i	−0.0472238	+	0.0817940i
$601$	−332.710	+	192.090i	−0.553594	+	0.319618i	−0.750570	−	0.660791i	$-0.770221\pi$
$601$	−332.710	+	192.090i	−0.553594	+	0.319618i	0.196976	+	0.980408i	$0.436888\pi$
$602$	71.2105	+	84.8654i	0.118290	+	0.140972i
$603$	30.4889	+	83.7675i	0.0505620	+	0.138918i
$604$	20.5597	−	56.4874i	0.0340393	−	0.0935222i
$605$	183.137	+	153.670i	0.302706	+	0.254001i
$606$	6.34228	−	35.9689i	0.0104658	−	0.0593545i
$607$		−	725.336i		−	1.19495i	−0.801887	−	0.597476i	$-0.796170\pi$
$607$		−	725.336i		−	1.19495i	0.801887	−	0.597476i	$-0.203830\pi$
$608$	33.2396	+	102.211i	0.0546704	+	0.168111i
$609$	−25.7859			−0.0423414
$610$	−586.298	−	103.380i	−0.961145	−	0.169476i
$611$	−680.402	+	810.872i	−1.11359	+	1.32712i
$612$	−294.098	−	107.043i	−0.480552	−	0.174907i
$613$	−323.685	+	117.812i	−0.528034	+	0.192189i	−0.592260	−	0.805747i	$-0.701764\pi$
$613$	−323.685	+	117.812i	−0.528034	+	0.192189i	0.0642263	+	0.997935i	$0.479542\pi$
$614$	288.019	−	241.677i	0.469086	−	0.393610i
$615$	44.4176	+	76.9336i	0.0722238	+	0.125095i
$616$	−122.068	−	70.4758i	−0.198162	−	0.114409i
$617$	−94.6496	−	536.785i	−0.153403	−	0.869991i	−0.960231	−	0.279206i	$-0.909929\pi$
$617$	−94.6496	−	536.785i	−0.153403	−	0.869991i	0.806828	−	0.590786i	$-0.201182\pi$
$618$	−9.80878	+	1.72955i	−0.0158718	+	0.00279863i
$619$	−492.260	+	852.619i	−0.795250	+	1.37741i	0.127431	+	0.991847i	$0.459327\pi$
$619$	−492.260	+	852.619i	−0.795250	+	1.37741i	−0.922680	+	0.385566i	$0.874006\pi$
$620$	−750.422	+	433.256i	−1.21036	+	0.698800i
$621$	72.8855	+	86.8616i	0.117368	+	0.139874i
$622$	−77.2545	−	212.255i	−0.124203	−	0.341246i
$623$	−197.079	+	541.470i	−0.316339	+	0.869134i
$624$	−17.7404	−	14.8859i	−0.0284301	−	0.0238557i
$625$	74.3286	−	421.539i	0.118926	−	0.674462i
$626$			266.081i			0.425050i
$627$	2.68828	−	77.5566i	0.00428753	−	0.123695i
$628$	−462.163			−0.735929
$629$	−311.576	−	54.9392i	−0.495351	−	0.0873437i
$630$	−352.476	+	420.065i	−0.559486	+	0.666770i
$631$	−499.596	−	181.838i	−0.791752	−	0.288174i	−0.0856881	−	0.996322i	$-0.527309\pi$
$631$	−499.596	−	181.838i	−0.791752	−	0.288174i	−0.706064	+	0.708148i	$0.749531\pi$
$632$	−404.711	+	147.303i	−0.640365	+	0.233074i
$633$	3.53650	−	2.96747i	0.00558688	−	0.00468795i
$634$	−120.932	−	209.460i	−0.190744	−	0.330379i
$635$	446.665	+	257.882i	0.703409	+	0.406113i
$636$	−9.26599	−	52.5500i	−0.0145692	−	0.0826258i
$637$	−299.498	+	52.8096i	−0.470169	+	0.0829036i
$638$	80.1851	−	138.885i	0.125682	−	0.217687i
$639$	−870.882	+	502.804i	−1.36288	+	0.786861i
$640$	−61.8253	−	73.6805i	−0.0966020	−	0.115126i
$641$	81.2045	+	223.108i	0.126684	+	0.348062i	0.986779	−	0.162073i	$-0.0518179\pi$
$641$	81.2045	+	223.108i	0.126684	+	0.348062i	−0.860095	+	0.510134i	$0.829596\pi$
$642$	−6.59111	+	18.1089i	−0.0102665	+	0.0282071i
$643$	−206.587	−	173.347i	−0.321286	−	0.269591i	0.467852	−	0.883807i	$-0.345028\pi$
$643$	−206.587	−	173.347i	−0.321286	−	0.269591i	−0.789138	+	0.614216i	$0.789472\pi$
$644$	26.9623	−	152.911i	0.0418669	−	0.237439i
$645$		−	54.5828i		−	0.0846245i
$646$	−318.892	+	354.349i	−0.493641	+	0.548529i
$647$	−172.930			−0.267280			−0.133640	−	0.991030i	$-0.542667\pi$
$647$	−172.930			−0.267280			−0.133640	+	0.991030i	$0.542667\pi$
$648$	212.204	+	37.4173i	0.327475	+	0.0577427i
$649$	−328.592	+	391.600i	−0.506305	+	0.603390i
$650$	858.249	+	312.377i	1.32038	+	0.480580i
$651$	104.947	−	38.1976i	0.161209	−	0.0586752i
$652$	76.9572	−	64.5747i	0.118032	−	0.0990410i
$653$	566.373	+	980.986i	0.867339	+	1.50228i	0.864705	+	0.502279i	$0.167505\pi$
$653$	566.373	+	980.986i	0.867339	+	1.50228i	0.00263396	+	0.999997i	$0.499162\pi$
$654$	−24.5659	−	14.1832i	−0.0375626	−	0.0216868i
$655$	−184.074	−	1043.93i	−0.281029	−	1.59379i
$656$	−97.1262	+	17.1260i	−0.148058	+	0.0261067i
$657$	492.472	−	852.987i	0.749577	−	1.29831i
$658$	490.713	−	283.313i	0.745764	−	0.430567i
$659$	−727.538	−	867.046i	−1.10400	−	1.31570i	−0.944503	−	0.328502i	$-0.893456\pi$
$659$	−727.538	−	867.046i	−1.10400	−	1.31570i	−0.159500	−	0.987198i	$-0.550988\pi$
$660$	23.7520	+	65.2582i	0.0359879	+	0.0988761i
$661$	−200.912	+	552.002i	−0.303952	+	0.835101i	0.689852	+	0.723951i	$0.257676\pi$
$661$	−200.912	+	552.002i	−0.303952	+	0.835101i	−0.993804	+	0.111150i	$0.964547\pi$
$662$	377.080	+	316.408i	0.569607	+	0.477957i
$663$	17.8364	−	101.155i	0.0269026	−	0.152572i
$664$		−	150.202i		−	0.226208i
$665$	392.314	+	737.376i	0.589946	+	1.10884i
$666$	222.447			0.334004
$667$	173.977	+	30.6768i	0.260834	+	0.0459922i
$668$	−190.248	+	226.729i	−0.284803	+	0.339415i
$669$	−121.737	−	44.3087i	−0.181969	−	0.0662312i
$670$	−114.182	+	41.5587i	−0.170420	+	0.0620280i
$671$	−365.571	+	306.750i	−0.544815	+	0.457154i
$672$	6.19837	+	10.7359i	0.00922377	+	0.0159760i
$673$	−818.808	−	472.739i	−1.21665	−	0.702435i	−0.252453	−	0.967609i	$-0.581237\pi$
$673$	−818.808	−	472.739i	−1.21665	−	0.702435i	−0.964201	+	0.265174i	$0.914571\pi$
$674$	−81.6354	−	462.978i	−0.121121	−	0.686910i
$675$	351.614	−	61.9990i	0.520909	−	0.0918503i
$676$	−17.6228	+	30.5236i	−0.0260692	+	0.0451532i
$677$	503.136	−	290.485i	0.743184	−	0.429077i	−0.0800419	−	0.996792i	$-0.525505\pi$
$677$	503.136	−	290.485i	0.743184	−	0.429077i	0.823226	+	0.567714i	$0.192172\pi$
$678$	−17.6319	−	21.0129i	−0.0260058	−	0.0309925i
$679$	152.340	+	418.550i	0.224359	+	0.616422i
$680$	145.908	−	400.879i	0.214571	−	0.589528i
$681$	73.9528	+	62.0538i	0.108594	+	0.0911216i
$682$	−120.613	+	684.032i	−0.176852	+	1.00298i
$683$		−	270.340i		−	0.395813i	−0.980221	−	0.197906i	$-0.936586\pi$
$683$		−	270.340i		−	0.395813i	0.980221	−	0.197906i	$-0.0634142\pi$
$684$	177.542	−	284.290i	0.259565	−	0.415629i
$685$	504.530			0.736540
$686$	513.203	+	90.4916i	0.748110	+	0.131912i
$687$	28.2360	−	33.6504i	0.0411005	−	0.0489816i
$688$	56.9431	+	20.7256i	0.0827661	+	0.0301244i
$689$	−808.152	+	294.143i	−1.17293	+	0.426913i
$690$	−58.6029	+	49.1737i	−0.0849318	+	0.0712662i
$691$	29.8337	+	51.6734i	0.0431746	+	0.0747806i	0.886805	−	0.462143i	$-0.152919\pi$
$691$	29.8337	+	51.6734i	0.0431746	+	0.0747806i	−0.843631	+	0.536924i	$0.819586\pi$
$692$	196.430	+	113.409i	0.283859	+	0.163886i
$693$	76.3279	+	432.877i	0.110141	+	0.624642i
$694$	628.109	−	110.753i	0.905057	−	0.159586i
$695$	182.854	−	316.713i	0.263100	−	0.455702i
$696$	−12.2149	+	7.05230i	−0.0175502	+	0.0101326i
$697$	−281.178	−	335.095i	−0.403412	−	0.480767i
$698$	−198.095	−	544.261i	−0.283804	−	0.779744i
$699$	−20.0515	+	55.0912i	−0.0286860	+	0.0788143i
$700$	−374.525	−	314.264i	−0.535035	−	0.448948i
$701$	−61.8014	+	350.493i	−0.0881618	+	0.499991i	0.908468	+	0.417955i	$0.137253\pi$
$701$	−61.8014	+	350.493i	−0.0881618	+	0.499991i	−0.996629	+	0.0820353i	$0.973858\pi$
$702$			145.909i			0.207847i
$703$	126.845	−	314.187i	0.180434	−	0.446923i
$704$	−77.0990			−0.109516
$705$	−274.933	−	48.4782i	−0.389976	−	0.0687634i
$706$	−59.9264	+	71.4175i	−0.0848815	+	0.101158i
$707$	296.105	+	107.773i	0.418819	+	0.152438i
$708$	42.2486	−	15.3772i	0.0596732	−	0.0217193i
$709$	698.190	−	585.851i	0.984754	−	0.826306i	−4.60524e−5	−	1.00000i	$-0.500015\pi$
$709$	698.190	−	585.851i	0.984754	−	0.826306i	0.984800	+	0.173694i	$0.0555702\pi$
$710$	−685.361	−	1187.08i	−0.965298	−	1.67194i
$711$	1163.14	+	671.540i	1.63592	+	0.944500i
$712$	54.7316	+	310.398i	0.0768702	+	0.435952i
$713$	−753.516	+	132.865i	−1.05682	+	0.186347i
$714$	−27.4920	+	47.6176i	−0.0385042	+	0.0666913i
$715$	969.317	−	559.635i	1.35569	−	0.782707i
$716$	319.960	+	381.314i	0.446872	+	0.532561i
$717$	36.1754	+	99.3910i	0.0504538	+	0.138621i
$718$	60.0481	−	164.981i	0.0836325	−	0.229778i
$719$	131.934	+	110.706i	0.183496	+	0.153972i	0.729909	−	0.683545i	$-0.239563\pi$
$719$	131.934	+	110.706i	0.183496	+	0.153972i	−0.546413	+	0.837516i	$0.684007\pi$
$720$	−52.0849	+	295.388i	−0.0723401	+	0.410261i
$721$		−	85.9306i		−	0.119183i
$722$	−300.296	−	412.873i	−0.415922	−	0.571847i
$723$	−59.9411			−0.0829061
$724$	352.083	+	62.0817i	0.486303	+	0.0857483i
$725$	357.559	−	426.122i	0.493184	−	0.587754i
$726$	−15.8379	−	5.76451i	−0.0218152	−	0.00794009i
$727$	−101.193	+	36.8313i	−0.139193	+	0.0506620i	−0.410677	−	0.911781i	$-0.634708\pi$
$727$	−101.193	+	36.8313i	−0.139193	+	0.0506620i	0.271485	+	0.962443i	$0.412485\pi$
$728$	153.055	−	128.428i	0.210240	−	0.176413i
$729$	−321.577	−	556.988i	−0.441121	−	0.764045i
$730$	1162.69	+	671.278i	1.59272	+	0.919559i
$731$	46.6718	+	264.689i	0.0638465	+	0.362091i
$732$	41.3339	−	7.28829i	0.0564671	−	0.00995667i
$733$	43.4420	−	75.2438i	0.0592661	−	0.102652i	−0.834870	−	0.550447i	$-0.814457\pi$
$733$	43.4420	−	75.2438i	0.0592661	−	0.102652i	0.894136	+	0.447795i	$0.147791\pi$
$734$	−391.967	+	226.302i	−0.534015	+	0.308314i
$735$	−51.5570	−	61.4433i	−0.0701456	−	0.0835963i
$736$	−29.0480	−	79.8088i	−0.0394674	−	0.108436i
$737$	−33.3129	+	91.5265i	−0.0452007	+	0.124188i
$738$	235.604	+	197.695i	0.319246	+	0.267879i
$739$	120.006	−	680.590i	0.162390	−	0.920961i	−0.789324	−	0.613977i	$-0.789569\pi$
$739$	120.006	−	680.590i	0.162390	−	0.920961i	0.951715	−	0.306984i	$-0.0993200\pi$
$740$			303.212i			0.409747i
$741$	102.003	+	41.1813i	0.137656	+	0.0555753i
$742$	460.369			0.620443
$743$	837.812	+	147.729i	1.12761	+	0.198827i	0.706178	−	0.708034i	$-0.250418\pi$
$743$	837.812	+	147.729i	1.12761	+	0.198827i	0.421428	+	0.906862i	$0.361529\pi$
$744$	39.2672	−	46.7969i	0.0527785	−	0.0628990i
$745$	−313.763	−	114.201i	−0.421159	−	0.153289i
$746$	664.624	−	241.903i	0.890917	−	0.324267i
$747$	−358.816	+	301.082i	−0.480343	+	0.403055i
$748$	−170.981	−	296.148i	−0.228584	−	0.395919i
$749$	−143.987	−	83.1308i	−0.192239	−	0.110989i
$750$	19.7088	+	111.774i	0.0262784	+	0.149032i
$751$	−1004.82	+	177.177i	−1.33797	+	0.235921i	−0.796420	−	0.604744i	$-0.793275\pi$
$751$	−1004.82	+	177.177i	−1.33797	+	0.235921i	−0.541555	+	0.840665i	$0.682164\pi$
$752$	154.969	−	268.415i	0.206076	−	0.356934i
$753$	130.611	−	75.4085i	0.173455	−	0.100144i
$754$	146.122	+	174.141i	0.193795	+	0.230956i
$755$	−87.3939	−	240.113i	−0.115753	−	0.318030i
$756$	26.7136	−	73.3949i	0.0353354	−	0.0970832i
$757$	506.858	+	425.305i	0.669562	+	0.561829i	0.912936	−	0.408103i	$-0.133810\pi$
$757$	506.858	+	425.305i	0.669562	+	0.561829i	−0.243374	+	0.969933i	$0.578254\pi$
$758$	175.720	−	996.556i	0.231820	−	1.31472i
$759$			61.3219i			0.0807930i
$760$	387.510	+	242.004i	0.509881	+	0.318426i
$761$	−723.005			−0.950072			−0.475036	−	0.879966i	$-0.657565\pi$
$761$	−723.005			−0.950072			−0.475036	+	0.879966i	$0.657565\pi$
$762$	−35.8089	−	6.31407i	−0.0469932	−	0.00828618i
$763$	157.309	−	187.474i	0.206172	−	0.245707i
$764$	−562.746	−	204.823i	−0.736578	−	0.268093i
$765$	−1250.13	+	455.011i	−1.63416	+	0.594785i
$766$	−187.851	+	157.626i	−0.245237	+	0.205778i
$767$	−362.312	−	627.542i	−0.472375	−	0.818178i
$768$	5.87242	+	3.39044i	0.00764638	+	0.00441464i
$769$	210.668	+	1194.76i	0.273951	+	1.55365i	0.742276	+	0.670095i	$0.233747\pi$
$769$	210.668	+	1194.76i	0.273951	+	1.55365i	−0.468325	+	0.883556i	$0.655142\pi$
$770$	−590.045	+	104.041i	−0.766293	+	0.135118i
$771$	−107.601	+	186.370i	−0.139560	+	0.241725i
$772$	6.38593	−	3.68692i	0.00827193	−	0.00477580i
$773$	−633.445	−	754.910i	−0.819463	−	0.976598i	0.180513	−	0.983573i	$-0.442224\pi$
$773$	−633.445	−	754.910i	−0.819463	−	0.976598i	−0.999976	+	0.00697460i	$0.997780\pi$
$774$	−64.6323	−	177.576i	−0.0835043	−	0.229426i
$775$	−824.011	+	2263.95i	−1.06324	+	2.92123i
$776$	186.636	+	156.606i	0.240510	+	0.201812i
$777$	6.78620	−	38.4864i	0.00873384	−	0.0495321i
$778$			302.049i			0.388238i
$779$	413.575	−	220.039i	0.530905	−	0.282463i
$780$	−98.4402			−0.126205
$781$	−1082.06	−	190.796i	−1.38548	−	0.244298i
$782$	242.137	−	288.568i	0.309638	−	0.369012i
$783$	83.5063	+	30.3938i	0.106649	+	0.0388171i
$784$	83.6770	−	30.4559i	0.106731	−	0.0388468i
$785$	−1504.92	+	1262.78i	−1.91709	+	1.60863i
$786$	37.3663	+	64.7203i	0.0475398	+	0.0823414i
$787$	421.297	+	243.236i	0.535320	+	0.309067i	0.743180	−	0.669091i	$-0.233316\pi$
$787$	421.297	+	243.236i	0.535320	+	0.309067i	−0.207860	+	0.978159i	$0.566650\pi$
$788$	−50.6340	−	287.160i	−0.0642564	−	0.364416i
$789$	86.0074	−	15.1654i	0.109008	−	0.0192211i
$790$	−915.361	+	1585.45i	−1.15869	+	2.00690i
$791$	204.950	−	118.328i	0.259102	−	0.149593i
$792$	154.547	+	184.181i	0.195135	+	0.232552i
$793$	−231.362	−	635.663i	−0.291756	−	0.801592i
$794$	−168.047	+	461.705i	−0.211646	+	0.581492i
$795$	−173.756	−	145.798i	−0.218561	−	0.183394i
$796$	16.6285	−	94.3050i	0.0208901	−	0.118474i
$797$		−	1186.46i		−	1.48865i	−0.667817	−	0.744326i	$-0.732771\pi$
$797$		−	1186.46i		−	1.48865i	0.667817	−	0.744326i	$-0.267229\pi$
$798$	−43.7699	−	39.3902i	−0.0548495	−	0.0493611i
$799$	1374.69			1.72051
$800$	−263.364	−	46.4382i	−0.329205	−	0.0580478i
$801$	631.797	−	752.947i	0.788761	−	0.940008i
$802$	−132.476	−	48.2173i	−0.165182	−	0.0601213i
$803$	1011.27	−	368.073i	1.25937	−	0.458373i
$804$	6.56225	−	5.50638i	0.00816200	−	0.00684873i
$805$	−330.004	−	571.584i	−0.409943	−	0.710043i
$806$	−852.666	−	492.287i	−1.05790	−	0.610778i
$807$	1.27786	+	7.24711i	0.00158347	+	0.00898031i
$808$	169.742	−	29.9301i	0.210077	−	0.0370423i
$809$	−346.462	+	600.089i	−0.428259	+	0.741766i	−0.996719	−	0.0809449i	$-0.974206\pi$
$809$	−346.462	+	600.089i	−0.428259	+	0.741766i	0.568460	+	0.822711i	$0.307540\pi$
$810$	793.224	−	457.968i	0.979289	−	0.565393i
$811$	572.213	+	681.937i	0.705565	+	0.840860i	0.993144	−	0.116897i	$-0.0372948\pi$
$811$	572.213	+	681.937i	0.705565	+	0.840860i	−0.287579	+	0.957757i	$0.592850\pi$
$812$	−41.6195	−	114.349i	−0.0512556	−	0.140824i
$813$	12.1990	−	33.5165i	0.0150050	−	0.0412258i
$814$	186.188	+	156.230i	0.228732	+	0.191929i
$815$	74.1531	−	420.543i	0.0909853	−	0.516004i
$816$			30.0757i			0.0368574i
$817$	−287.666	−	9.97114i	−0.352100	−	0.0122046i
$818$	−700.218			−0.856012
$819$	−613.603	−	108.195i	−0.749210	−	0.132106i
$820$	−269.474	+	321.146i	−0.328626	+	0.391642i
$821$	605.463	+	220.370i	0.737470	+	0.268417i	0.683323	−	0.730116i	$-0.260534\pi$
$821$	605.463	+	220.370i	0.737470	+	0.268417i	0.0541466	+	0.998533i	$0.482756\pi$
$822$	−33.4242	+	12.1654i	−0.0406620	+	0.0147998i
$823$	253.156	−	212.423i	0.307602	−	0.258109i	−0.475898	−	0.879500i	$-0.657877\pi$
$823$	253.156	−	212.423i	0.307602	−	0.258109i	0.783500	+	0.621392i	$0.213432\pi$
$824$	−23.5016	−	40.7059i	−0.0285213	−	0.0494004i
$825$	167.219	+	96.5442i	0.202690	+	0.117023i
$826$	67.3568	+	381.999i	0.0815457	+	0.462469i
$827$	641.165	−	113.055i	0.775290	−	0.136705i	0.228015	−	0.973658i	$-0.426776\pi$
$827$	641.165	−	113.055i	0.775290	−	0.136705i	0.547275	+	0.836953i	$0.315665\pi$
$828$	−132.427	+	229.371i	−0.159936	+	0.277018i
$829$	1274.18	−	735.648i	1.53701	−	0.887392i	0.537995	−	0.842948i	$-0.319182\pi$
$829$	1274.18	−	735.648i	1.53701	−	0.887392i	0.999012	−	0.0444438i	$-0.0141516\pi$
$830$	−410.399	−	489.095i	−0.494457	−	0.589271i
$831$	25.2308	+	69.3210i	0.0303619	+	0.0834187i
$832$	37.3787	−	102.697i	0.0449263	−	0.123434i
$833$	302.554	+	253.873i	0.363210	+	0.304769i
$834$	−4.47707	+	25.3907i	−0.00536819	+	0.0304445i
$835$			1258.11i			1.50671i
$836$	348.267	−	113.258i	0.416587	−	0.135476i
$837$	−384.889			−0.459843
$838$	−85.6995	−	15.1111i	−0.102267	−	0.0180324i
$839$	−397.880	+	474.175i	−0.474231	+	0.565167i	−0.949134	−	0.314871i	$-0.898039\pi$
$839$	−397.880	+	474.175i	−0.474231	+	0.565167i	0.474903	+	0.880038i	$0.342483\pi$
$840$	49.5173	+	18.0228i	0.0589492	+	0.0214558i
$841$	−660.179	+	240.286i	−0.784993	+	0.285714i
$842$	−664.159	+	557.296i	−0.788787	+	0.661871i
$843$	−9.84078	−	17.0447i	−0.0116735	−	0.0202191i
$844$	18.8674	+	10.8931i	0.0223548	+	0.0129065i
$845$	26.0159	+	147.543i	0.0307880	+	0.174608i
$846$	−951.853	+	167.837i	−1.12512	+	0.198389i
$847$	72.7051	−	125.929i	0.0858384	−	0.148677i
$848$	218.080	−	125.908i	0.257170	−	0.148477i
$849$	−42.8206	−	51.0316i	−0.0504365	−	0.0601079i
$850$	−405.682	−	1114.60i	−0.477273	−	1.31130i
$851$	−91.5725	+	251.593i	−0.107606	+	0.295644i
$852$	74.0272	+	62.1162i	0.0868864	+	0.0729064i
$853$	159.925	−	906.980i	0.187485	−	1.06328i	−0.735235	−	0.677812i	$-0.762928\pi$
$853$	159.925	−	906.980i	0.187485	−	1.06328i	0.922720	−	0.385470i	$-0.125961\pi$
$854$			362.109i			0.424016i
$855$	−198.650	−	1410.82i	−0.232339	−	1.65008i
$856$	−90.9433			−0.106242
$857$	1231.45	+	217.138i	1.43693	+	0.253370i	0.837230	−	0.546852i	$-0.184174\pi$
$857$	1231.45	+	217.138i	1.43693	+	0.253370i	0.599704	+	0.800222i	$0.295285\pi$
$858$	−50.7213	+	60.4473i	−0.0591158	+	0.0704514i
$859$	−703.340	−	255.995i	−0.818789	−	0.298015i	−0.101540	−	0.994831i	$-0.532377\pi$
$859$	−703.340	−	255.995i	−0.818789	−	0.298015i	−0.717249	+	0.696817i	$0.754599\pi$
$860$	242.050	−	88.0989i	0.281453	−	0.102441i
$861$	41.3916	−	34.7317i	0.0480738	−	0.0403387i
$862$	33.0975	+	57.3266i	0.0383962	+	0.0665042i
$863$	66.6518	+	38.4815i	0.0772327	+	0.0445903i	0.538119	−	0.842869i	$-0.319135\pi$
$863$	66.6518	+	38.4815i	0.0772327	+	0.0445903i	−0.460886	+	0.887459i	$0.652468\pi$
$864$	−7.41872	−	42.0737i	−0.00858648	−	0.0486964i
$865$	949.495	−	167.422i	1.09768	−	0.193551i
$866$	506.545	−	877.362i	0.584925	−	1.01312i
$867$	−9.45404	+	5.45829i	−0.0109043	+	0.00629561i
$868$	338.778	+	403.740i	0.390297	+	0.465138i
$869$	501.909	+	1378.98i	0.577570	+	1.58686i
$870$	−20.5058	+	56.3392i	−0.0235699	+	0.0647577i
$871$	−105.764	−	88.7466i	−0.121428	−	0.101891i
$872$	23.2454	−	131.831i	0.0266575	−	0.151182i
$873$		−	759.772i		−	0.870300i
$874$	248.453	+	317.836i	0.284271	+	0.363657i
$875$	−979.208			−1.11910
$876$	−93.2120	−	16.4358i	−0.106406	−	0.0187623i
$877$	−509.911	+	607.688i	−0.581426	+	0.692917i	−0.973934	−	0.226832i	$-0.927163\pi$
$877$	−509.911	+	607.688i	−0.581426	+	0.692917i	0.392508	+	0.919749i	$0.371608\pi$
$878$	−41.0967	−	14.9580i	−0.0468072	−	0.0170364i
$879$	108.361	−	39.4403i	0.123278	−	0.0448695i
$880$	−251.054	+	210.659i	−0.285288	+	0.239385i
$881$	−309.941	−	536.834i	−0.351806	−	0.609346i	0.634760	−	0.772710i	$-0.281099\pi$
$881$	−309.941	−	536.834i	−0.351806	−	0.609346i	−0.986566	+	0.163363i	$0.947766\pi$
$882$	−240.488	−	138.846i	−0.272662	−	0.157422i
$883$	−45.1234	−	255.907i	−0.0511024	−	0.289816i	0.948537	−	0.316666i	$-0.102563\pi$
$883$	−45.1234	−	255.907i	−0.0511024	−	0.289816i	−0.999639	+	0.0268501i	$0.991452\pi$
$884$	477.367	−	84.1727i	0.540008	−	0.0952180i
$885$	95.5565	−	165.509i	0.107973	−	0.187016i
$886$	−388.132	+	224.088i	−0.438073	+	0.252921i
$887$	75.1189	+	89.5233i	0.0846888	+	0.100928i	0.806725	−	0.590927i	$-0.201238\pi$
$887$	75.1189	+	89.5233i	0.0846888	+	0.100928i	−0.722036	+	0.691855i	$0.756794\pi$
$888$	−7.31117	−	20.0873i	−0.00823330	−	0.0226208i
$889$	107.294	−	294.788i	0.120691	−	0.331595i
$890$	1026.33	+	861.189i	1.15317	+	0.967629i
$891$	127.493	−	723.048i	0.143090	−	0.811502i
$892$		−	611.365i		−	0.685387i
$893$	−305.718	+	1440.12i	−0.342349	+	1.61267i
$894$	23.5399			0.0263310
$895$	2083.74	+	367.420i	2.32820	+	0.410525i
$896$	−37.6044	+	44.8152i	−0.0419692	+	0.0500169i
$897$	−81.6817	−	29.7297i	−0.0910610	−	0.0331435i
$898$	342.267	−	124.575i	0.381143	−	0.138725i
$899$	−459.361	+	385.450i	−0.510969	+	0.428754i
$900$	416.983	+	722.235i	0.463314	+	0.802484i
$901$	967.262	+	558.449i	1.07354	+	0.619810i
$902$	58.3538	+	330.941i	0.0646938	+	0.366897i
$903$	−32.6949	+	5.76499i	−0.0362069	+	0.00638426i
$904$	64.7240	−	112.105i	0.0715973	−	0.124010i
$905$	1316.10	−	759.849i	1.45425	−	0.839612i
$906$	11.5794	+	13.7998i	0.0127808	+	0.0152315i
$907$	191.542	+	526.257i	0.211182	+	0.580217i	0.999380	−	0.0352042i	$-0.0112082\pi$
$907$	191.542	+	526.257i	0.211182	+	0.580217i	−0.788198	+	0.615421i	$0.788986\pi$
$908$	−155.817	+	428.105i	−0.171605	+	0.471481i
$909$	−411.752	−	345.501i	−0.452972	−	0.380089i
$910$	147.478	−	836.390i	0.162064	−	0.919109i
$911$		−	749.720i		−	0.822964i	−0.911418	−	0.411482i	$-0.865011\pi$
$911$		−	749.720i		−	0.822964i	0.911418	−	0.411482i	$-0.134989\pi$
$912$	−31.5071	−	6.68854i	−0.0345473	−	0.00733392i
$913$	−511.787			−0.560555
$914$	−1087.46	−	191.748i	−1.18978	−	0.209790i
$915$	114.680	−	136.670i	0.125333	−	0.149366i
$916$	194.798	+	70.9008i	0.212662	+	0.0774026i
$917$	−605.871	+	220.519i	−0.660710	+	0.240479i
$918$	145.158	−	121.802i	0.158124	−	0.132682i
$919$	−657.952	−	1139.61i	−0.715944	−	1.24005i	−0.962594	−	0.270946i	$-0.912663\pi$
$919$	−657.952	−	1139.61i	−0.715944	−	1.24005i	0.246651	−	0.969104i	$-0.420670\pi$
$920$	−312.651	−	180.509i	−0.339838	−	0.196205i
$921$	19.5654	+	110.961i	0.0212437	+	0.120479i
$922$	−590.195	+	104.067i	−0.640125	+	0.112871i
$923$	778.741	−	1348.82i	0.843707	−	1.46134i
$924$	36.5807	−	21.1199i	0.0395895	−	0.0228570i
$925$	541.903	+	645.814i	0.585841	+	0.698178i
$926$	329.934	+	906.486i	0.356300	+	0.978927i
$927$	−50.1327	+	137.739i	−0.0540806	+	0.148585i
$928$	−50.9892	−	42.7850i	−0.0549453	−	0.0461046i
$929$	−3.86617	+	21.9261i	−0.00416164	+	0.0236019i	−0.986818	−	0.161835i	$-0.948259\pi$
$929$	−3.86617	+	21.9261i	−0.00416164	+	0.0236019i	0.982656	+	0.185437i	$0.0593699\pi$
$930$		−	259.673i		−	0.279218i
$931$	−333.241	+	260.495i	−0.357939	+	0.279801i
$932$	−276.668			−0.296854
$933$	66.6615	+	11.7542i	0.0714486	+	0.0125983i
$934$	434.187	−	517.443i	0.464868	−	0.554008i
$935$	−1365.93	−	497.156i	−1.46088	−	0.531718i
$936$	−320.259	+	116.565i	−0.342157	+	0.124535i
$937$	280.376	−	235.263i	0.299227	−	0.251081i	−0.480796	−	0.876833i	$-0.659652\pi$
$937$	280.376	−	235.263i	0.299227	−	0.251081i	0.780022	+	0.625752i	$0.215208\pi$
$938$	36.9533	+	64.0050i	0.0393958	+	0.0682356i
$939$	−69.0553	−	39.8691i	−0.0735413	−	0.0424591i
$940$	−228.776	−	1297.45i	−0.243378	−	1.38027i
$941$	1353.51	−	238.661i	1.43838	−	0.253625i	0.600563	−	0.799578i	$-0.294943\pi$
$941$	1353.51	−	238.661i	1.43838	−	0.253625i	0.837816	+	0.545953i	$0.183832\pi$
$942$	69.2496	−	119.944i	0.0735133	−	0.127329i
$943$	−320.587	+	185.091i	−0.339965	+	0.196279i
$944$	136.382	+	162.534i	0.144473	+	0.172176i
$945$	−113.552	−	311.982i	−0.120161	−	0.330140i
$946$	70.6189	−	194.024i	0.0746500	−	0.205099i
$947$	481.476	+	404.007i	0.508423	+	0.426617i	0.860574	−	0.509326i	$-0.170105\pi$
$947$	481.476	+	404.007i	0.508423	+	0.426617i	−0.352151	+	0.935943i	$0.614550\pi$
$948$	22.4120	−	127.105i	0.0236414	−	0.134077i
$949$			1525.48i			1.60746i
$950$	1257.87	−	177.113i	1.32407	−	0.186435i
$951$	72.4807			0.0762152
$952$	−255.536	−	45.0578i	−0.268420	−	0.0473296i
$953$	−1194.00	+	1422.96i	−1.25289	+	1.49314i	−0.454807	+	0.890590i	$0.650292\pi$
$953$	−1194.00	+	1422.96i	−1.25289	+	1.49314i	−0.798084	+	0.602547i	$0.794153\pi$
$954$	−737.927	−	268.583i	−0.773508	−	0.281534i
$955$	−2392.08	+	870.646i	−2.50480	+	0.911672i
$956$	−382.365	+	320.843i	−0.399964	+	0.335609i
$957$	24.0295	+	41.6203i	0.0251092	+	0.0434904i
$958$	738.422	+	426.328i	0.770795	+	0.445019i
$959$	−53.2881	−	302.212i	−0.0555663	−	0.315132i
$960$	28.3858	−	5.00519i	0.0295686	−	0.00521374i
$961$	818.091	−	1416.97i	0.851291	−	1.47448i
$962$	−298.367	+	172.262i	−0.310153	+	0.179067i
$963$	182.298	+	217.254i	0.189302	+	0.225601i
$964$	−96.7475	−	265.811i	−0.100360	−	0.275738i
$965$	10.7203	−	29.4539i	0.0111092	−	0.0305222i
$966$	35.6444	+	29.9092i	0.0368990	+	0.0309619i
$967$	−249.595	+	1415.53i	−0.258113	+	1.46383i	0.529841	+	0.848097i	$0.322252\pi$
$967$	−249.595	+	1415.53i	−0.258113	+	1.46383i	−0.787954	+	0.615735i	$0.788859\pi$
$968$		−	79.5379i		−	0.0821672i
$969$	−44.1811	−	135.856i	−0.0455945	−	0.140202i
$970$	1035.63			1.06766
$971$	−449.774	−	79.3073i	−0.463207	−	0.0816759i	−0.0628256	−	0.998025i	$-0.520011\pi$
$971$	−449.774	−	79.3073i	−0.463207	−	0.0816759i	−0.400381	+	0.916349i	$0.631122\pi$
$972$	−128.889	+	153.604i	−0.132602	+	0.158029i
$973$	−209.023	−	76.0781i	−0.214823	−	0.0781892i
$974$	361.960	−	131.743i	0.371622	−	0.135259i
$975$	−209.669	+	175.933i	−0.215045	+	0.180444i
$976$	99.0350	+	171.534i	0.101470	+	0.175752i
$977$	−13.1868	−	7.61342i	−0.0134973	−	0.00779265i	0.493236	−	0.869895i	$-0.335814\pi$
$977$	−13.1868	−	7.61342i	−0.0134973	−	0.00779265i	−0.506733	+	0.862103i	$0.669147\pi$
$978$	5.22778	+	29.6482i	0.00534537	+	0.0303151i
$979$	1057.63	−	186.488i	1.08031	−	0.190489i
$980$	189.258	−	327.804i	0.193120	−	0.334494i
$981$	−361.526	+	208.727i	−0.368528	+	0.212770i
$982$	539.477	+	642.923i	0.549365	+	0.654708i
$983$	−313.799	−	862.154i	−0.319225	−	0.877064i	−0.990703	−	0.136040i	$-0.956562\pi$
$983$	−313.799	−	862.154i	−0.319225	−	0.877064i	0.671478	−	0.741024i	$-0.265660\pi$
$984$	10.1085	−	27.7730i	0.0102729	−	0.0282246i
$985$	−949.489	−	796.716i	−0.963948	−	0.808849i
$986$	51.2653	−	290.740i	0.0519932	−	0.294868i
$987$			169.804i			0.172041i
$988$	−17.9830	+	518.806i	−0.0182014	+	0.525108i
$989$	227.450			0.229979
$990$	1006.48	+	177.470i	1.01665	+	0.179263i
$991$	−618.738	+	737.383i	−0.624357	+	0.744079i	−0.981813	−	0.189850i	$-0.939200\pi$
$991$	−618.738	+	737.383i	−0.624357	+	0.744079i	0.357456	+	0.933930i	$0.383644\pi$
$992$	270.902	+	98.6002i	0.273087	+	0.0993954i
$993$	−138.617	+	50.4525i	−0.139594	+	0.0508082i
$994$	−638.669	+	535.907i	−0.642524	+	0.539142i
$995$	−203.525	−	352.515i	−0.204547	−	0.354286i
$996$	38.9814	+	22.5059i	0.0391380	+	0.0225963i
$997$	−102.940	−	583.803i	−0.103250	−	0.585559i	−0.991905	−	0.126983i	$-0.959471\pi$
$997$	−102.940	−	583.803i	−0.103250	−	0.585559i	0.888655	−	0.458576i	$-0.151640\pi$
$998$	−325.358	+	57.3694i	−0.326010	+	0.0574844i
$999$	−67.3406	+	116.637i	−0.0674080	+	0.116754i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.3.f.a.21.2	✓	24
3.2	odd	2		342.3.z.b.325.3		24
4.3	odd	2		304.3.z.c.97.2		24
19.3	odd	18		722.3.b.f.721.20		24
19.10	odd	18	inner	38.3.f.a.29.2	yes	24
19.16	even	9		722.3.b.f.721.5		24
57.29	even	18		342.3.z.b.181.3		24
76.67	even	18		304.3.z.c.257.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.3.f.a.21.2	✓	24	1.1	even	1	trivial
38.3.f.a.29.2	yes	24	19.10	odd	18	inner
304.3.z.c.97.2		24	4.3	odd	2
304.3.z.c.257.2		24	76.67	even	18
342.3.z.b.181.3		24	57.29	even	18
342.3.z.b.325.3		24	3.2	odd	2
722.3.b.f.721.5		24	19.16	even	9
722.3.b.f.721.20		24	19.3	odd	18

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	38.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39273 - 0.245576i) q^{2} +(0.272417 - 0.324654i) q^{3} +(1.87939 + 0.684040i) q^{4} +(7.98876 - 2.90767i) q^{5} +(-0.459130 + 0.385256i) q^{6} +(-2.58545 - 4.47813i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(1.53164 + 8.68639i) q^{9} +(-11.8402 + 2.08775i) q^{10} +(-4.81869 + 8.34622i) q^{11} +(0.734053 - 0.423806i) q^{12} +(-8.78112 - 10.4649i) q^{13} +(2.50111 + 6.87174i) q^{14} +(1.23229 - 3.38568i) q^{15} +(3.06418 + 2.57115i) q^{16} +(-3.08077 + 17.4719i) q^{17} -12.4739i q^{18} +(-17.6183 - 7.11298i) q^{19} +17.0029 q^{20} +(-2.15816 - 0.380542i) q^{21} +(8.76075 - 10.4407i) q^{22} +(14.1083 + 5.13501i) q^{23} +(-1.12641 + 0.409981i) q^{24} +(36.2147 - 30.3877i) q^{25} +(9.65978 + 16.7312i) q^{26} +(6.54055 + 3.77619i) q^{27} +(-1.79583 - 10.1847i) q^{28} +(11.5878 - 2.04324i) q^{29} +(-2.54768 + 4.41272i) q^{30} +(-44.1349 + 25.4813i) q^{31} +(-3.63616 - 4.33340i) q^{32} +(1.39694 + 3.83806i) q^{33} +(8.58135 - 23.5771i) q^{34} +(-33.6755 - 28.2571i) q^{35} +(-3.06329 + 17.3728i) q^{36} +17.8330i q^{37} +(22.7908 + 14.2331i) q^{38} -5.78961 q^{39} +(-23.6805 - 4.17550i) q^{40} +(-15.8487 + 18.8877i) q^{41} +(2.91228 + 1.05998i) q^{42} +(14.2358 - 5.18140i) q^{43} +(-14.7653 + 12.3896i) q^{44} +(37.4931 + 64.9400i) q^{45} +(-18.3880 - 10.6163i) q^{46} +(-13.4551 - 76.3075i) q^{47} +(1.66947 - 0.294372i) q^{48} +(11.1309 - 19.2793i) q^{49} +(-57.8997 + 33.4284i) q^{50} +(4.83307 + 5.75983i) q^{51} +(-9.34467 - 25.6743i) q^{52} +(21.5316 - 59.1576i) q^{53} +(-8.18187 - 6.86541i) q^{54} +(-14.2273 + 80.6871i) q^{55} +14.6255i q^{56} +(-7.10879 + 3.78216i) q^{57} -16.6404 q^{58} +(52.2374 + 9.21086i) q^{59} +(4.63189 - 5.52007i) q^{60} +(46.5312 + 16.9360i) q^{61} +(67.7255 - 24.6501i) q^{62} +(34.9388 - 29.3171i) q^{63} +(4.00000 + 6.92820i) q^{64} +(-100.579 - 58.0692i) q^{65} +(-1.00302 - 5.68843i) q^{66} +(9.95299 - 1.75498i) q^{67} +(-17.7414 + 30.7291i) q^{68} +(5.51045 - 3.18146i) q^{69} +(39.9616 + 47.6243i) q^{70} +(38.9935 + 107.134i) q^{71} +(8.53266 - 23.4433i) q^{72} +(-85.5417 - 71.7780i) q^{73} +(4.37934 - 24.8365i) q^{74} -20.0354i q^{75} +(-28.2461 - 25.4197i) q^{76} +49.8339 q^{77} +(8.06335 + 1.42179i) q^{78} +(97.8772 - 116.645i) q^{79} +(31.9550 + 11.6307i) q^{80} +(-71.5884 + 26.0560i) q^{81} +(26.7112 - 22.4134i) q^{82} +(26.5522 + 45.9897i) q^{83} +(-3.79571 - 2.19146i) q^{84} +(26.1910 + 148.537i) q^{85} +(-21.0990 + 3.72032i) q^{86} +(2.49337 - 4.31864i) q^{87} +(23.6067 - 13.6293i) q^{88} +(-71.6292 - 85.3643i) q^{89} +(-36.2700 - 99.6511i) q^{90} +(-24.1602 + 66.3796i) q^{91} +(23.0024 + 19.3013i) q^{92} +(-3.75049 + 21.2701i) q^{93} +109.580i q^{94} +(-161.431 - 5.59555i) q^{95} -2.39741 q^{96} +(-84.8296 - 14.9577i) q^{97} +(-20.2368 + 24.1173i) q^{98} +(-79.8790 - 29.0736i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{3} + 12 q^{6} - 18 q^{7} + 6 q^{9} + 30 q^{11} - 36 q^{12} - 90 q^{13} - 48 q^{14} - 114 q^{15} + 18 q^{17} - 12 q^{19} + 24 q^{20} + 90 q^{21} + 84 q^{22} + 120 q^{23} - 24 q^{24} + 252 q^{25}+ \cdots - 204 q^{99}+O(q^{100}) \) 24 * q - 6 * q^3 + 12 * q^6 - 18 * q^7 + 6 * q^9 + 30 * q^11 - 36 * q^12 - 90 * q^13 - 48 * q^14 - 114 * q^15 + 18 * q^17 - 12 * q^19 + 24 * q^20 + 90 * q^21 + 84 * q^22 + 120 * q^23 - 24 * q^24 + 252 * q^25 + 48 * q^26 + 126 * q^27 + 72 * q^28 - 210 * q^29 - 108 * q^31 - 132 * q^33 - 24 * q^34 - 66 * q^35 - 12 * q^36 + 84 * q^38 + 120 * q^39 + 54 * q^41 + 72 * q^42 + 90 * q^43 - 48 * q^44 - 144 * q^45 - 360 * q^46 - 246 * q^47 - 48 * q^48 + 54 * q^49 - 432 * q^50 - 342 * q^51 + 36 * q^52 - 174 * q^53 - 42 * q^55 - 12 * q^57 + 48 * q^58 + 228 * q^59 + 132 * q^60 + 12 * q^61 + 204 * q^62 + 174 * q^63 + 96 * q^64 + 630 * q^65 + 696 * q^66 + 72 * q^67 - 48 * q^68 + 702 * q^69 + 528 * q^70 + 432 * q^71 + 96 * q^72 - 144 * q^74 + 72 * q^76 - 144 * q^77 - 708 * q^78 - 246 * q^79 - 642 * q^81 - 384 * q^82 - 126 * q^83 - 540 * q^84 - 684 * q^85 - 12 * q^86 - 324 * q^87 - 12 * q^89 - 336 * q^90 + 372 * q^91 - 132 * q^92 - 168 * q^93 - 570 * q^95 + 72 * q^97 + 384 * q^98 - 204 * q^99

Introduction

L-functions

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