LMFDB - Embedded newform 230.4.l.a.217.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,4,Mod(7,230)] 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("230.7"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([11, 38])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, 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:	$13.5704393013$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$36$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			217.5
Character	$\chi$	$=$	230.217
Dual form			230.4.l.a.53.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.142678 + 1.99490i) q^{2} +(-4.80624 + 1.04553i) q^{3} +(-3.95929 - 0.569259i) q^{4} +(2.17927 + 10.9659i) q^{5} +(-1.39999 - 9.73716i) q^{6} +(-24.2664 + 13.2505i) q^{7} +(1.70052 - 7.81717i) q^{8} +(-2.55328 + 1.16604i) q^{9} +(-22.1868 + 2.78283i) q^{10} +(29.6099 + 25.6571i) q^{11} +(19.6244 - 1.40357i) q^{12} +(-9.39512 + 17.2059i) q^{13} +(-22.9711 - 50.2997i) q^{14} +(-21.9393 - 50.4262i) q^{15} +(15.3519 + 4.50772i) q^{16} +(-27.6596 - 20.7057i) q^{17} +(-1.96185 - 5.25992i) q^{18} +(-1.40327 + 9.75994i) q^{19} +(-2.38590 - 44.6577i) q^{20} +(102.776 - 89.0562i) q^{21} +(-55.4082 + 55.4082i) q^{22} +(-80.2175 - 75.7110i) q^{23} +39.3492i q^{24} +(-115.502 + 47.7952i) q^{25} +(-32.9836 - 21.1973i) q^{26} +(117.367 - 87.8599i) q^{27} +(103.621 - 38.6485i) q^{28} +(206.180 - 29.6442i) q^{29} +(103.726 - 36.5720i) q^{30} +(0.779599 - 0.501018i) q^{31} +(-11.1829 + 29.9824i) q^{32} +(-169.137 - 92.3560i) q^{33} +(45.2524 - 52.2240i) q^{34} +(-198.186 - 237.227i) q^{35} +(10.7729 - 3.16322i) q^{36} +(128.068 + 47.7667i) q^{37} +(-19.2699 - 4.19192i) q^{38} +(27.1659 - 92.5184i) q^{39} +(89.4282 + 1.61204i) q^{40} +(96.2335 - 210.722i) q^{41} +(162.995 + 217.735i) q^{42} +(-29.1550 - 134.023i) q^{43} +(-102.628 - 118.440i) q^{44} +(-18.3510 - 25.4579i) q^{45} +(162.482 - 149.224i) q^{46} +(-367.524 - 367.524i) q^{47} +(-78.4978 - 5.61427i) q^{48} +(227.844 - 354.533i) q^{49} +(-78.8673 - 237.234i) q^{50} +(154.587 + 70.5976i) q^{51} +(46.9926 - 62.7747i) q^{52} +(135.042 + 247.310i) q^{53} +(158.526 + 246.672i) q^{54} +(-216.825 + 380.612i) q^{55} +(62.3156 + 212.228i) q^{56} +(-3.45990 - 48.3758i) q^{57} +(29.7200 + 415.539i) q^{58} +(141.602 + 482.251i) q^{59} +(58.1583 + 212.141i) q^{60} +(302.364 + 470.487i) q^{61} +(0.888251 + 1.62671i) q^{62} +(46.5083 - 62.1279i) q^{63} +(-58.2164 - 26.5866i) q^{64} +(-209.152 - 65.5297i) q^{65} +(208.374 - 324.236i) q^{66} +(-745.573 - 53.3244i) q^{67} +(97.7254 + 97.7254i) q^{68} +(464.703 + 280.015i) q^{69} +(501.521 - 361.515i) q^{70} +(-560.344 - 646.671i) q^{71} +(4.77326 + 21.9423i) q^{72} +(533.209 + 712.284i) q^{73} +(-113.562 + 248.667i) q^{74} +(505.157 - 350.476i) q^{75} +(11.1119 - 37.8436i) q^{76} +(-1058.49 - 230.261i) q^{77} +(180.689 + 67.3937i) q^{78} +(-1085.58 + 318.756i) q^{79} +(-15.9753 + 178.171i) q^{80} +(-422.604 + 487.711i) q^{81} +(406.640 + 222.042i) q^{82} +(-164.879 + 442.059i) q^{83} +(-457.617 + 294.093i) q^{84} +(166.779 - 348.436i) q^{85} +(271.523 - 39.0391i) q^{86} +(-959.957 + 358.046i) q^{87} +(250.918 - 187.835i) q^{88} +(-60.4825 - 38.8698i) q^{89} +(53.4043 - 32.9762i) q^{90} -542.015i q^{91} +(274.505 + 345.426i) q^{92} +(-3.22311 + 3.22311i) q^{93} +(785.612 - 680.737i) q^{94} +(-110.085 + 5.88143i) q^{95} +(22.3999 - 155.795i) q^{96} +(-430.997 - 1155.55i) q^{97} +(674.751 + 505.112i) q^{98} +(-105.520 - 30.9834i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q + 16 q^{3} + 16 q^{6} + 64 q^{12} - 192 q^{13} + 1152 q^{16} + 144 q^{18} + 1660 q^{23} - 880 q^{25} - 304 q^{26} - 728 q^{27} - 352 q^{28} - 608 q^{31} - 3872 q^{33} - 688 q^{35} - 2816 q^{36} - 2376 q^{37}+ \cdots + 14352 q^{98}+O(q^{100}) $ 720 * q + 16 * q^3 + 16 * q^6 + 64 * q^12 - 192 * q^13 + 1152 * q^16 + 144 * q^18 + 1660 * q^23 - 880 * q^25 - 304 * q^26 - 728 * q^27 - 352 * q^28 - 608 * q^31 - 3872 * q^33 - 688 * q^35 - 2816 * q^36 - 2376 * q^37 + 2208 * q^41 + 256 * q^46 + 3640 * q^47 - 256 * q^48 - 272 * q^50 - 768 * q^52 + 2360 * q^55 - 3872 * q^56 - 7656 * q^57 + 2112 * q^61 + 1376 * q^62 + 10912 * q^66 + 1104 * q^70 + 22752 * q^71 - 128 * q^72 + 1296 * q^73 - 5396 * q^75 + 752 * q^77 - 6000 * q^78 - 3928 * q^81 - 80 * q^82 + 3060 * q^85 - 10472 * q^86 - 6760 * q^87 - 1104 * q^92 + 5288 * q^93 + 9392 * q^95 - 256 * q^96 + 25344 * q^97 + 14352 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{22}\right)$

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 $

$2$	−0.142678	+	1.99490i	−0.0504444	+	0.705305i
$2$	−0.142678	+	1.99490i	−0.0504444	+	0.705305i
$3$	−4.80624	+	1.04553i	−0.924961	+	0.201213i	−0.649730	−	0.760165i	$-0.725118\pi$
$3$	−4.80624	+	1.04553i	−0.924961	+	0.201213i	−0.275231	+	0.961378i	$0.588754\pi$
$4$	−3.95929	−	0.569259i	−0.494911	−	0.0711574i
$5$	2.17927	+	10.9659i	0.194920	+	0.980819i
$5$	2.17927	+	10.9659i	0.194920	+	0.980819i
$6$	−1.39999	−	9.73716i	−0.0952574	−	0.662530i
$7$	−24.2664	+	13.2505i	−1.31026	+	0.715458i	−0.974051	−	0.226328i	$-0.927328\pi$
$7$	−24.2664	+	13.2505i	−1.31026	+	0.715458i	−0.336212	+	0.941786i	$0.609146\pi$
$8$	1.70052	−	7.81717i	0.0751532	−	0.345474i
$9$	−2.55328	+	1.16604i	−0.0945659	+	0.0431868i
$10$	−22.1868	+	2.78283i	−0.701609	+	0.0880009i
$11$	29.6099	+	25.6571i	0.811610	+	0.703264i	0.958252	−	0.285925i	$-0.0923009\pi$
$11$	29.6099	+	25.6571i	0.811610	+	0.703264i	−0.146642	+	0.989190i	$0.546846\pi$
$12$	19.6244	−	1.40357i	0.472091	−	0.0337646i
$13$	−9.39512	+	17.2059i	−0.200441	+	0.367081i	−0.958494	−	0.285112i	$-0.907969\pi$
$13$	−9.39512	+	17.2059i	−0.200441	+	0.367081i	0.758053	+	0.652193i	$0.226151\pi$
$14$	−22.9711	−	50.2997i	−0.438521	−	0.960227i
$15$	−21.9393	−	50.4262i	−0.377646	−	0.867999i
$16$	15.3519	+	4.50772i	0.239873	+	0.0704331i
$17$	−27.6596	−	20.7057i	−0.394614	−	0.295404i	0.383484	−	0.923548i	$-0.374724\pi$
$17$	−27.6596	−	20.7057i	−0.394614	−	0.295404i	−0.778098	+	0.628143i	$0.783815\pi$
$18$	−1.96185	−	5.25992i	−0.0256896	−	0.0688764i
$19$	−1.40327	+	9.75994i	−0.0169438	+	0.117847i	−0.996538	−	0.0831392i	$-0.973505\pi$
$19$	−1.40327	+	9.75994i	−0.0169438	+	0.117847i	0.979594	+	0.200986i	$0.0644145\pi$
$20$	−2.38590	−	44.6577i	−0.0266752	−	0.499288i
$21$	102.776	−	89.0562i	1.06798	−	0.925413i
$22$	−55.4082	+	55.4082i	−0.536957	+	0.536957i
$23$	−80.2175	−	75.7110i	−0.727239	−	0.686384i
$23$	−80.2175	−	75.7110i	−0.727239	−	0.686384i
$24$			39.3492i			0.334671i
$25$	−115.502	+	47.7952i	−0.924013	+	0.382362i
$26$	−32.9836	−	21.1973i	−0.248793	−	0.159889i
$27$	117.367	−	87.8599i	0.836567	−	0.626246i
$28$	103.621	−	38.6485i	0.699374	−	0.260853i
$29$	206.180	−	29.6442i	1.32023	−	0.189821i	0.554071	−	0.832470i	$-0.313074\pi$
$29$	206.180	−	29.6442i	1.32023	−	0.189821i	0.766161	+	0.642649i	$0.222165\pi$
$30$	103.726	−	36.5720i	0.631254	−	0.222570i
$31$	0.779599	−	0.501018i	0.00451678	−	0.00290276i	−0.538380	−	0.842702i	$-0.680964\pi$
$31$	0.779599	−	0.501018i	0.00451678	−	0.00290276i	0.542897	+	0.839799i	$0.317327\pi$
$32$	−11.1829	+	29.9824i	−0.0617771	+	0.165631i
$33$	−169.137	−	92.3560i	−0.892214	−	0.487186i
$34$	45.2524	−	52.2240i	0.228256	−	0.263422i
$35$	−198.186	−	237.227i	−0.957131	−	1.14567i
$36$	10.7729	−	3.16322i	0.0498747	−	0.0146445i
$37$	128.068	+	47.7667i	0.569032	+	0.212238i	0.617478	−	0.786588i	$-0.288154\pi$
$37$	128.068	+	47.7667i	0.569032	+	0.212238i	−0.0484466	+	0.998826i	$0.515427\pi$
$38$	−19.2699	−	4.19192i	−0.0822630	−	0.0178952i
$39$	27.1659	−	92.5184i	0.111539	−	0.379867i
$40$	89.4282	+	1.61204i	0.353496	+	0.00637214i
$41$	96.2335	−	210.722i	0.366565	−	0.802665i	−0.633028	−	0.774129i	$-0.718188\pi$
$41$	96.2335	−	210.722i	0.366565	−	0.802665i	0.999593	−	0.0285358i	$-0.00908445\pi$
$42$	162.995	+	217.735i	0.598825	+	0.799936i
$43$	−29.1550	−	134.023i	−0.103397	−	0.475310i	−0.999505	−	0.0314726i	$-0.989980\pi$
$43$	−29.1550	−	134.023i	−0.103397	−	0.475310i	0.896107	−	0.443838i	$-0.146383\pi$
$44$	−102.628	−	118.440i	−0.351632	−	0.405805i
$45$	−18.3510	−	25.4579i	−0.0607912	−	0.0843341i
$46$	162.482	−	149.224i	0.520795	−	0.478301i
$47$	−367.524	−	367.524i	−1.14061	−	1.14061i	−0.988338	−	0.152275i	$-0.951340\pi$
$47$	−367.524	−	367.524i	−1.14061	−	1.14061i	−0.152275	−	0.988338i	$-0.548660\pi$
$48$	−78.4978	−	5.61427i	−0.236045	−	0.0168823i
$49$	227.844	−	354.533i	0.664270	−	1.03362i
$50$	−78.8673	−	237.234i	−0.223070	−	0.670999i
$51$	154.587	+	70.5976i	0.424442	+	0.193836i
$52$	46.9926	−	62.7747i	0.125321	−	0.167409i
$53$	135.042	+	247.310i	0.349989	+	0.640957i	0.992071	−	0.125679i	$-0.0401110\pi$
$53$	135.042	+	247.310i	0.349989	+	0.640957i	−0.642082	+	0.766636i	$0.721929\pi$
$54$	158.526	+	246.672i	0.399495	+	0.621626i
$55$	−216.825	+	380.612i	−0.531577	+	0.933123i
$56$	62.3156	+	212.228i	0.148701	+	0.506430i
$57$	−3.45990	−	48.3758i	−0.00803992	−	0.112413i
$58$	29.7200	+	415.539i	0.0672832	+	0.940741i
$59$	141.602	+	482.251i	0.312457	+	1.06413i	0.954685	+	0.297617i	$0.0961918\pi$
$59$	141.602	+	482.251i	0.312457	+	1.06413i	−0.642228	+	0.766513i	$0.721990\pi$
$60$	58.1583	+	212.141i	0.125137	+	0.456454i
$61$	302.364	+	470.487i	0.634651	+	0.987537i	0.998428	+	0.0560505i	$0.0178508\pi$
$61$	302.364	+	470.487i	0.634651	+	0.987537i	−0.363777	+	0.931486i	$0.618513\pi$
$62$	0.888251	+	1.62671i	0.00181948	+	0.00333214i
$63$	46.5083	−	62.1279i	0.0930079	−	0.124244i
$64$	−58.2164	−	26.5866i	−0.113704	−	0.0519269i
$65$	−209.152	−	65.5297i	−0.399110	−	0.125045i
$66$	208.374	−	324.236i	0.388622	−	0.604707i
$67$	−745.573	−	53.3244i	−1.35950	−	0.0972331i	−0.627540	−	0.778584i	$-0.715938\pi$
$67$	−745.573	−	53.3244i	−1.35950	−	0.0972331i	−0.731957	+	0.681351i	$0.761393\pi$
$68$	97.7254	+	97.7254i	0.174279	+	0.174279i
$69$	464.703	+	280.015i	0.810777	+	0.488549i
$70$	501.521	−	361.515i	0.856332	−	0.617276i
$71$	−560.344	−	646.671i	−0.936628	−	1.08093i	−0.996572	−	0.0827245i	$-0.973638\pi$
$71$	−560.344	−	646.671i	−0.936628	−	1.08093i	0.0599446	−	0.998202i	$-0.480908\pi$
$72$	4.77326	+	21.9423i	0.00781297	+	0.0359157i
$73$	533.209	+	712.284i	0.854896	+	1.14201i	0.988537	+	0.150977i	$0.0482421\pi$
$73$	533.209	+	712.284i	0.854896	+	1.14201i	−0.133641	+	0.991030i	$0.542667\pi$
$74$	−113.562	+	248.667i	−0.178397	+	0.390635i
$75$	505.157	−	350.476i	0.777740	−	0.539593i
$76$	11.1119	−	37.8436i	0.0167713	−	0.0571178i
$77$	−1058.49	−	230.261i	−1.56658	−	0.340789i
$78$	180.689	+	67.3937i	0.262295	+	0.0978312i
$79$	−1085.58	+	318.756i	−1.54605	+	0.453960i	−0.939916	−	0.341405i	$-0.889097\pi$
$79$	−1085.58	+	318.756i	−1.54605	+	0.453960i	−0.606130	+	0.795365i	$0.707279\pi$
$80$	−15.9753	+	178.171i	−0.0223262	+	0.249001i
$81$	−422.604	+	487.711i	−0.579703	+	0.669013i
$82$	406.640	+	222.042i	0.547632	+	0.299030i
$83$	−164.879	+	442.059i	−0.218047	+	0.584606i	−0.999211	−	0.0397199i	$-0.987353\pi$
$83$	−164.879	+	442.059i	−0.218047	+	0.584606i	0.781164	+	0.624326i	$0.214626\pi$
$84$	−457.617	+	294.093i	−0.594406	+	0.382002i
$85$	166.779	−	348.436i	0.212820	−	0.444625i
$86$	271.523	−	39.0391i	0.340455	−	0.0489500i
$87$	−959.957	+	358.046i	−1.18297	+	0.441224i
$88$	250.918	−	187.835i	0.303954	−	0.227537i
$89$	−60.4825	−	38.8698i	−0.0720352	−	0.0462942i	0.504127	−	0.863629i	$-0.331814\pi$
$89$	−60.4825	−	38.8698i	−0.0720352	−	0.0462942i	−0.576163	+	0.817335i	$0.695451\pi$
$90$	53.4043	−	32.9762i	0.0625479	−	0.0386222i
$91$		−	542.015i		−	0.624380i
$92$	274.505	+	345.426i	0.311077	+	0.391447i
$93$	−3.22311	+	3.22311i	−0.00359377	+	0.00359377i
$94$	785.612	−	680.737i	0.862018	−	0.746943i
$95$	−110.085	+	5.88143i	−0.118889	+	0.00635181i
$96$	22.3999	−	155.795i	0.0238144	−	0.165632i
$97$	−430.997	−	1155.55i	−0.451146	−	1.20957i	−0.941192	−	0.337872i	$-0.890293\pi$
$97$	−430.997	−	1155.55i	−0.451146	−	1.20957i	0.490046	−	0.871697i	$-0.336980\pi$
$98$	674.751	+	505.112i	0.695511	+	0.520653i
$99$	−105.520	−	30.9834i	−0.107122	−	0.0314540i
$100$	484.512	−	123.485i	0.484512	−	0.123485i
$101$	209.752	+	459.292i	0.206644	+	0.452488i	0.984369	−	0.176117i	$-0.0563536\pi$
$101$	209.752	+	459.292i	0.206644	+	0.452488i	−0.777725	+	0.628605i	$0.783626\pi$
$102$	−162.892	+	298.314i	−0.158124	+	0.289583i
$103$	−1426.93	+	102.056i	−1.36505	+	0.0976302i	−0.734547	−	0.678558i	$-0.762605\pi$
$103$	−1426.93	+	102.056i	−1.36505	+	0.0976302i	−0.630502	+	0.776188i	$0.717151\pi$
$104$	118.525	+	102.702i	0.111753	+	0.0968345i
$105$	1200.56	+	932.958i	1.11583	+	0.867117i
$106$	−512.628	+	234.109i	−0.469725	+	0.214516i
$107$	−170.379	+	783.218i	−0.153936	+	0.707632i	0.833873	+	0.551957i	$0.186119\pi$
$107$	−170.379	+	783.218i	−0.153936	+	0.707632i	−0.987808	+	0.155675i	$0.950245\pi$
$108$	−514.705	+	281.050i	−0.458588	+	0.250408i
$109$	−179.851	−	1250.89i	−0.158042	−	1.09921i	−0.902236	−	0.431243i	$-0.858075\pi$
$109$	−179.851	−	1250.89i	−0.158042	−	1.09921i	0.744194	−	0.667964i	$-0.232834\pi$
$110$	−728.349	−	486.851i	−0.631321	−	0.421995i
$111$	−665.465	−	95.6794i	−0.569037	−	0.0818152i
$112$	−432.265	+	94.0334i	−0.364689	+	0.0793333i
$113$	−82.5380	+	1154.03i	−0.0687126	+	0.960728i	0.839807	+	0.542885i	$0.182668\pi$
$113$	−82.5380	+	1154.03i	−0.0687126	+	0.960728i	−0.908519	+	0.417843i	$0.862786\pi$
$114$	96.9987			0.0796909
$115$	655.424	−	1044.65i	0.531466	−	0.847080i
$116$	−833.202			−0.666904
$117$	3.92556	−	54.8865i	0.00310187	−	0.0433697i
$118$	−982.247	+	213.675i	−0.766298	+	0.166698i
$119$	945.560	+	135.951i	0.728398	+	0.104728i
$120$	−431.499	+	85.7523i	−0.328252	+	0.0652340i
$121$	29.0367	+	201.955i	0.0218157	+	0.151732i
$122$	−981.718	+	536.059i	−0.728529	+	0.397807i
$123$	−242.204	+	1113.40i	−0.177551	+	0.816191i
$124$	−3.37187	+	1.53988i	−0.00244195	+	0.00111520i
$125$	−775.826	−	1162.42i	−0.555136	−	0.831760i
$126$	117.303	+	101.644i	0.0829382	+	0.0718664i
$127$	1967.34	−	140.707i	1.37459	−	0.0983126i	0.635594	−	0.772023i	$-0.280755\pi$
$127$	1967.34	−	140.707i	1.37459	−	0.0983126i	0.738995	+	0.673711i	$0.235301\pi$
$128$	61.3439	−	112.343i	0.0423600	−	0.0775766i
$129$	280.251	+	613.665i	0.191277	+	0.418838i
$130$	160.567	−	407.889i	0.108328	−	0.275186i
$131$	957.595	+	281.175i	0.638668	+	0.187530i	0.585005	−	0.811029i	$-0.301092\pi$
$131$	957.595	+	281.175i	0.638668	+	0.187530i	0.0536623	+	0.998559i	$0.482911\pi$
$132$	617.089	+	461.947i	0.406899	+	0.304601i
$133$	−95.2715	−	255.433i	−0.0621134	−	0.166533i
$134$	212.754	−	1479.74i	0.137158	−	0.953955i
$135$	1219.24	+	1095.57i	0.777298	+	0.698454i
$136$	−208.896	+	181.009i	−0.131711	+	0.114128i
$137$	−1728.80	+	1728.80i	−1.07811	+	1.07811i	−0.0814321	+	0.996679i	$0.525949\pi$
$137$	−1728.80	+	1728.80i	−1.07811	+	1.07811i	−0.996679	+	0.0814321i	$0.974051\pi$
$138$	−624.906	+	887.085i	−0.385475	+	0.547201i
$139$		−	1224.63i		−	0.747279i	−0.927574	−	0.373640i	$-0.878110\pi$
$139$		−	1224.63i		−	0.747279i	0.927574	−	0.373640i	$-0.121890\pi$
$140$	649.632	+	1052.07i	0.392171	+	0.635114i
$141$	2150.66	+	1382.15i	1.28453	+	0.825517i
$142$	1370.00	−	1025.57i	0.809630	−	0.606082i
$143$	−719.641	+	268.412i	−0.420835	+	0.156963i
$144$	−44.4539	+	6.39150i	−0.0257256	+	0.00369879i
$145$	774.397	+	2196.35i	0.443519	+	1.25791i
$146$	−1497.02	+	962.073i	−0.848588	+	0.545355i
$147$	−724.399	+	1942.19i	−0.406445	+	1.08972i
$148$	−479.864	−	262.026i	−0.266518	−	0.145530i
$149$	1210.93	−	1397.49i	0.665794	−	0.768368i	−0.317918	−	0.948118i	$-0.602984\pi$
$149$	1210.93	−	1397.49i	0.665794	−	0.768368i	0.983712	+	0.179751i	$0.0575291\pi$
$150$	627.091	+	1057.74i	0.341345	+	0.575763i
$151$	−559.495	+	164.283i	−0.301530	+	0.0885373i	−0.428998	−	0.903305i	$-0.641133\pi$
$151$	−559.495	+	164.283i	−0.301530	+	0.0885373i	0.127468	+	0.991843i	$0.459315\pi$
$152$	73.9089	+	27.5666i	0.0394395	+	0.0147102i
$153$	94.7665	+	20.6152i	0.0500746	+	0.0108931i
$154$	610.374	−	2078.74i	0.319385	−	1.08773i
$155$	7.19306	+	7.45715i	0.00372749	+	0.00386434i
$156$	−160.224	+	350.842i	−0.0822322	+	0.180063i
$157$	−1099.30	−	1468.49i	−0.558813	−	0.746487i	0.428800	−	0.903400i	$-0.358937\pi$
$157$	−1099.30	−	1468.49i	−0.558813	−	0.746487i	−0.987612	+	0.156913i	$0.949846\pi$
$158$	−480.999	−	2211.11i	−0.242191	−	1.11333i
$159$	−907.614	−	1047.44i	−0.452695	−	0.522438i
$160$	−353.154	−	57.2904i	−0.174496	−	0.0283075i
$161$	2949.80	+	774.316i	1.44395	+	0.379035i
$162$	−912.640	−	912.640i	−0.442616	−	0.442616i
$163$	3125.79	+	223.561i	1.50203	+	0.107427i	0.797963	−	0.602706i	$-0.205911\pi$
$163$	3125.79	+	223.561i	1.50203	+	0.107427i	0.704067	+	0.710134i	$0.251366\pi$
$164$	−500.971	+	779.527i	−0.238532	+	0.371163i
$165$	644.171	−	2056.01i	0.303931	−	0.970062i
$166$	−858.340	−	391.991i	−0.401326	−	0.183280i
$167$	791.214	−	1056.94i	0.366623	−	0.489750i	−0.578858	−	0.815428i	$-0.696502\pi$
$167$	791.214	−	1056.94i	0.366623	−	0.489750i	0.945481	+	0.325678i	$0.105592\pi$
$168$	−521.395	−	954.863i	−0.239443	−	0.438508i
$169$	980.014	+	1524.93i	0.446069	+	0.694097i
$170$	671.300	+	382.423i	0.302861	+	0.172532i
$171$	−7.79758	−	26.5561i	−0.00348711	−	0.0118760i
$172$	39.1389	+	547.233i	0.0173506	+	0.242594i
$173$	60.0851	+	840.100i	0.0264057	+	0.369200i	0.993424	+	0.114493i	$0.0365244\pi$
$173$	60.0851	+	840.100i	0.0264057	+	0.369200i	−0.967018	+	0.254707i	$0.918021\pi$
$174$	−577.301	−	1966.11i	−0.251524	−	0.856611i
$175$	2169.50	−	2690.27i	0.937137	−	1.16209i
$176$	338.912	+	527.358i	0.145150	+	0.225859i
$177$	−1184.78	−	2169.76i	−0.503127	−	0.921409i
$178$	86.1710	−	115.111i	0.0362853	−	0.0484715i
$179$	−3840.21	−	1753.76i	−1.60352	−	0.732304i	−0.605542	−	0.795813i	$-0.707044\pi$
$179$	−3840.21	−	1753.76i	−1.60352	−	0.732304i	−0.997981	+	0.0635090i	$0.979771\pi$
$180$	58.1647	+	111.241i	0.0240852	+	0.0460636i
$181$	74.7139	−	116.257i	0.0306820	−	0.0477421i	−0.825574	−	0.564294i	$-0.809148\pi$
$181$	74.7139	−	116.257i	0.0306820	−	0.0477421i	0.856256	+	0.516552i	$0.172785\pi$
$182$	1081.27	+	77.3338i	0.440378	+	0.0314965i
$183$	−1945.14	−	1945.14i	−0.785733	−	0.785733i
$184$	−728.258	+	498.326i	−0.291782	+	0.199658i
$185$	−244.711	+	1508.47i	−0.0972516	+	0.599487i
$186$	−5.96992	−	6.88966i	−0.00235342	−	0.00271599i
$187$	−287.749	−	1322.76i	−0.112526	−	0.517271i
$188$	1245.91	+	1664.35i	0.483339	+	0.645665i
$189$	−1683.89	+	3687.22i	−0.648071	+	1.41908i
$190$	3.97380	−	220.447i	0.00151731	−	0.0841733i
$191$	1116.45	−	3802.29i	0.422952	−	1.44044i	−0.422487	−	0.906369i	$-0.638843\pi$
$191$	1116.45	−	3802.29i	0.422952	−	1.44044i	0.845439	−	0.534073i	$-0.179339\pi$
$192$	307.599	+	66.9141i	0.115620	+	0.0251516i
$193$	−3593.29	−	1340.23i	−1.34016	−	0.499854i	−0.425822	−	0.904807i	$-0.640015\pi$
$193$	−3593.29	−	1340.23i	−1.34016	−	0.499854i	−0.914337	+	0.404953i	$0.867288\pi$
$194$	2366.70	−	694.927i	0.875873	−	0.257179i
$195$	1073.75	+	96.2756i	0.394322	+	0.0353561i
$196$	−1103.92	+	1273.99i	−0.402304	+	0.464284i
$197$	519.427	+	283.628i	0.187856	+	0.102577i	0.570425	−	0.821350i	$-0.306779\pi$
$197$	519.427	+	283.628i	0.187856	+	0.102577i	−0.382569	+	0.923927i	$0.624960\pi$
$198$	76.8642	−	206.081i	0.0275884	−	0.0739673i
$199$	354.248	−	227.662i	0.126191	−	0.0810980i	−0.476023	−	0.879433i	$-0.657922\pi$
$199$	354.248	−	227.662i	0.126191	−	0.0810980i	0.602214	+	0.798335i	$0.294286\pi$
$200$	177.210	+	984.173i	0.0626533	+	0.347958i
$201$	3639.15	−	523.231i	1.27705	−	0.183611i
$202$	−946.172	+	352.904i	−0.329566	+	0.122922i
$203$	−4610.46	+	3451.34i	−1.59404	+	1.19329i
$204$	−571.867	−	367.516i	−0.196268	−	0.126134i
$205$	2520.47	+	596.067i	0.858719	+	0.203079i
$206$		−	2861.16i		−	0.967701i
$207$	293.100	+	99.7743i	0.0984148	+	0.0335014i
$208$	−221.792	+	221.792i	−0.0739351	+	0.0739351i
$209$	−291.962	+	252.987i	−0.0966290	+	0.0837295i
$210$	−2032.45	+	2261.89i	−0.667870	+	0.743262i
$211$	203.677	−	1416.61i	0.0664536	−	0.462195i	−0.929239	−	0.369479i	$-0.879536\pi$
$211$	203.677	−	1416.61i	0.0664536	−	0.462195i	0.995693	−	0.0927157i	$-0.0295548\pi$
$212$	−393.885	−	1056.05i	−0.127604	−	0.342121i
$213$	3369.26	+	2522.20i	1.08384	+	0.811353i
$214$	−1538.14	−	451.638i	−0.491331	−	0.144268i
$215$	1406.15	−	611.782i	0.446039	−	0.194061i
$216$	−487.231	−	1066.89i	−0.153481	−	0.336076i
$217$	−12.2794	+	22.4880i	−0.00384137	+	0.00703494i
$218$	2521.07	−	180.310i	0.783248	−	0.0560190i
$219$	−3307.45	−	2865.92i	−1.02053	−	0.884296i
$220$	1075.14	−	1383.52i	0.329482	−	0.423987i
$221$	616.125	−	281.375i	0.187534	−	0.0856440i
$222$	285.819	−	1313.89i	0.0864094	−	0.397218i
$223$	561.899	−	306.820i	0.168733	−	0.0921354i	−0.392663	−	0.919682i	$-0.628446\pi$
$223$	561.899	−	306.820i	0.168733	−	0.0921354i	0.561396	+	0.827547i	$0.310264\pi$
$224$	−125.913	−	875.743i	−0.0375576	−	0.261219i
$225$	239.177	−	256.714i	0.0708671	−	0.0760635i
$226$	−2290.41	−	329.311i	−0.674140	−	0.0969267i
$227$	−734.127	+	159.700i	−0.214651	+	0.0466944i	−0.318605	−	0.947888i	$-0.603214\pi$
$227$	−734.127	+	159.700i	−0.214651	+	0.0466944i	0.103954	+	0.994582i	$0.466851\pi$
$228$	−13.8396	+	193.503i	−0.00401996	+	0.0562064i
$229$	−2205.71			−0.636496			−0.318248	−	0.948008i	$-0.603094\pi$
$229$	−2205.71			−0.636496			−0.318248	+	0.948008i	$0.603094\pi$
$230$	1990.46	+	1456.56i	0.570640	+	0.417576i
$231$	5328.12			1.51760
$232$	118.880	−	1662.16i	0.0336416	−	0.470371i
$233$	2546.54	−	553.966i	0.716007	−	0.155758i	0.160218	−	0.987082i	$-0.448780\pi$
$233$	2546.54	−	553.966i	0.716007	−	0.155758i	0.555788	+	0.831324i	$0.312417\pi$
$234$	108.933	+	15.6622i	0.0304324	+	0.00437552i
$235$	3229.29	−	4831.16i	0.896408	−	1.34106i
$236$	−286.115	−	1989.98i	−0.0789175	−	0.548883i
$237$	4884.30	−	2667.03i	1.33869	−	0.730980i
$238$	−406.120	+	1866.91i	−0.110609	+	0.508460i
$239$	−4598.87	+	2100.23i	−1.24467	+	0.568422i	−0.925310	−	0.379211i	$-0.876195\pi$
$239$	−4598.87	+	2100.23i	−1.24467	+	0.568422i	−0.319361	+	0.947633i	$0.603468\pi$
$240$	−109.502	−	873.033i	−0.0294514	−	0.234809i
$241$	−986.021	−	854.392i	−0.263549	−	0.228366i	0.513055	−	0.858356i	$-0.328514\pi$
$241$	−986.021	−	854.392i	−0.263549	−	0.228366i	−0.776604	+	0.629990i	$0.783059\pi$
$242$	−407.024	+	29.1109i	−0.108118	+	0.00773273i
$243$	−375.873	+	688.359i	−0.0992273	+	0.181721i
$244$	−929.316	−	2034.92i	−0.243825	−	0.533903i
$245$	4384.30	+	1725.90i	1.14328	+	0.450055i
$246$	−2186.56	−	642.032i	−0.566707	−	0.166400i
$247$	−154.744	−	115.840i	−0.0398630	−	0.0298410i
$248$	−2.59082	−	6.94626i	−0.000663376	−	0.00177858i
$249$	330.263	−	2297.03i	0.0840544	−	0.584611i
$250$	2429.61	−	1381.85i	0.614648	−	0.349582i
$251$	−1363.54	+	1181.51i	−0.342892	+	0.297117i	−0.809233	−	0.587487i	$-0.800117\pi$
$251$	−1363.54	+	1181.51i	−0.342892	+	0.297117i	0.466342	+	0.884605i	$0.345572\pi$
$252$	−219.507	+	219.507i	−0.0548715	+	0.0548715i
$253$	−432.704	−	4299.94i	−0.107525	−	1.06852i
$254$			3944.72i			0.974464i
$255$	−437.279	+	1849.04i	−0.107386	+	0.454083i
$256$	215.361	+	138.404i	0.0525783	+	0.0337901i
$257$	2364.22	−	1769.83i	0.573836	−	0.429569i	−0.272547	−	0.962142i	$-0.587866\pi$
$257$	2364.22	−	1769.83i	0.573836	−	0.429569i	0.846384	+	0.532574i	$0.178775\pi$
$258$	−1264.19	+	471.518i	−0.305058	+	0.113781i
$259$	−3740.67	+	537.827i	−0.897429	+	0.129031i
$260$	790.790	+	378.512i	0.188626	+	0.0902860i
$261$	−491.869	+	316.105i	−0.116651	+	0.0749671i
$262$	−697.546	+	1870.19i	−0.164483	+	0.440996i
$263$	−3008.67	−	1642.86i	−0.705410	−	0.385183i	0.0861436	−	0.996283i	$-0.472546\pi$
$263$	−3008.67	−	1642.86i	−0.705410	−	0.385183i	−0.791554	+	0.611100i	$0.790727\pi$
$264$	−1009.59	+	1165.12i	−0.235362	+	0.271623i
$265$	−2417.69	+	2019.81i	−0.560443	+	0.468211i
$266$	523.157	−	153.613i	0.120590	−	0.0354083i
$267$	331.333	+	123.581i	0.0759447	+	0.0283259i
$268$	2921.58	+	635.551i	0.665910	+	0.144860i
$269$	−1290.58	+	4395.31i	−0.292521	+	0.996234i	0.673805	+	0.738910i	$0.264659\pi$
$269$	−1290.58	+	4395.31i	−0.292521	+	0.996234i	−0.966325	+	0.257324i	$0.917159\pi$
$270$	−2359.51	+	2275.95i	−0.531833	+	0.512999i
$271$	956.012	−	2093.37i	0.214294	−	0.469238i	−0.771707	−	0.635978i	$-0.780597\pi$
$271$	956.012	−	2093.37i	0.214294	−	0.469238i	0.986001	+	0.166740i	$0.0533242\pi$
$272$	−331.292	−	442.554i	−0.0738511	−	0.0986535i
$273$	566.694	+	2605.05i	0.125633	+	0.577527i
$274$	−3202.12	−	3695.45i	−0.706013	−	0.814782i
$275$	−4646.27	−	1548.23i	−1.01884	−	0.339497i
$276$	−1680.49	−	1373.20i	−0.366498	−	0.299481i
$277$	−3539.61	−	3539.61i	−0.767779	−	0.767779i	0.209936	−	0.977715i	$-0.432674\pi$
$277$	−3539.61	−	3539.61i	−0.767779	−	0.767779i	−0.977715	+	0.209936i	$0.932674\pi$
$278$	2443.02	+	174.728i	0.527060	+	0.0376961i
$279$	−1.40633	+	2.18829i	−0.000301773	+	0.000469567i
$280$	−2191.46	+	1145.85i	−0.467732	+	0.244562i
$281$	−3794.75	−	1733.00i	−0.805607	−	0.367908i	−0.0303382	−	0.999540i	$-0.509658\pi$
$281$	−3794.75	−	1733.00i	−0.805607	−	0.367908i	−0.775269	+	0.631631i	$0.782386\pi$
$282$	−3064.11	+	4093.17i	−0.647038	+	0.864342i
$283$	3987.38	+	7302.33i	0.837544	+	1.53385i	0.845561	+	0.533879i	$0.179266\pi$
$283$	3987.38	+	7302.33i	0.837544	+	1.53385i	−0.00801711	+	0.999968i	$0.502552\pi$
$284$	1850.44	+	2879.34i	0.386631	+	0.601610i
$285$	522.943	−	143.365i	0.108689	−	0.0297971i
$286$	−432.780	−	1473.91i	−0.0894783	−	0.304735i
$287$	456.922	+	6388.61i	0.0939765	+	1.31396i
$288$	−6.40783	−	89.5931i	−0.00131106	−	0.0183310i
$289$	−1047.83	−	3568.56i	−0.213276	−	0.726351i
$290$	−4491.99	+	1231.48i	−0.909582	+	0.249361i
$291$	3279.64	+	5103.22i	0.660673	+	1.02803i
$292$	−1705.65	−	3123.67i	−0.341835	−	0.626024i
$293$	−1339.34	+	1789.15i	−0.267048	+	0.356735i	−0.913942	−	0.405846i	$-0.866977\pi$
$293$	−1339.34	+	1789.15i	−0.267048	+	0.356735i	0.646893	+	0.762581i	$0.276068\pi$
$294$	−3771.12	−	1722.21i	−0.748083	−	0.341638i
$295$	−4979.72	+	2603.74i	−0.982816	+	0.513883i
$296$	591.182	−	919.898i	0.116087	−	0.180635i
$297$	5729.46	+	409.779i	1.11938	+	0.0800599i
$298$	2615.08	+	2615.08i	0.508348	+	0.508348i
$299$	2056.33	−	668.898i	0.397727	−	0.129376i
$300$	−2199.57	+	1100.07i	−0.423308	+	0.211708i
$301$	2483.36	+	2865.95i	0.475542	+	0.548805i
$302$	−247.900	−	1139.58i	−0.0472353	−	0.217137i
$303$	−1488.32	−	1988.17i	−0.282185	−	0.376954i
$304$	−65.5379	+	143.508i	−0.0123647	+	0.0270748i
$305$	−4500.38	+	4341.01i	−0.844889	+	0.814968i
$306$	−54.6465	+	186.109i	−0.0102089	+	0.0347684i
$307$	−10178.2	−	2214.12i	−1.89218	−	0.411618i	−0.892923	−	0.450209i	$-0.851349\pi$
$307$	−10178.2	−	2214.12i	−1.89218	−	0.411618i	−0.999255	+	0.0385911i	$0.987713\pi$
$308$	4059.80	+	1514.23i	0.751067	+	0.280134i
$309$	6751.48	−	1982.41i	1.24297	−	0.364970i
$310$	−15.9026	+	13.2855i	−0.00291357	+	0.00243408i
$311$	−3254.53	+	3755.93i	−0.593400	+	0.684820i	−0.970430	−	0.241381i	$-0.922400\pi$
$311$	−3254.53	+	3755.93i	−0.593400	+	0.684820i	0.377030	+	0.926201i	$0.376945\pi$
$312$	−677.037	−	369.690i	−0.122851	−	0.0670820i
$313$	−2546.27	+	6826.81i	−0.459820	+	1.23282i	0.475718	+	0.879598i	$0.342188\pi$
$313$	−2546.27	+	6826.81i	−0.459820	+	1.23282i	−0.935538	+	0.353227i	$0.885084\pi$
$314$	3086.35	−	1983.47i	0.554690	−	0.356478i
$315$	782.641	+	374.612i	0.139990	+	0.0670064i
$316$	4479.59	−	644.068i	0.797458	−	0.114657i
$317$	2776.35	−	1035.53i	0.491910	−	0.183473i	−0.0912535	−	0.995828i	$-0.529087\pi$
$317$	2776.35	−	1035.53i	0.491910	−	0.183473i	0.583164	+	0.812355i	$0.301815\pi$
$318$	2219.04	−	1661.16i	0.391314	−	0.292934i
$319$	6865.56	+	4412.23i	1.20501	+	0.774411i
$320$	164.676	−	696.335i	0.0287678	−	0.121645i
$321$		−	3942.47i		−	0.685506i
$322$	−1965.56	+	5774.08i	−0.340175	+	0.999308i
$323$	240.900	−	240.900i	0.0414986	−	0.0414986i
$324$	1950.84	−	1690.42i	0.334507	−	0.289852i
$325$	262.793	−	2436.35i	0.0448527	−	0.415828i
$326$	−891.966	+	6203.76i	−0.151538	+	1.05397i
$327$	2172.25	+	5824.03i	0.367357	+	0.984923i
$328$	−1483.60	−	1110.61i	−0.249751	−	0.186961i
$329$	13788.3	+	4048.62i	2.31057	+	0.678443i
$330$	4009.64	+	1578.41i	0.668858	+	0.263298i
$331$	632.944	+	1385.95i	0.105105	+	0.230148i	0.954876	−	0.297004i	$-0.0959873\pi$
$331$	632.944	+	1385.95i	0.105105	+	0.230148i	−0.849771	+	0.527151i	$0.823260\pi$
$332$	904.451	−	1656.38i	0.149513	−	0.273812i
$333$	−382.690	+	27.3706i	−0.0629769	+	0.00450420i
$334$	1995.60	+	1729.20i	0.326929	+	0.283286i
$335$	−1040.05	−	8292.08i	−0.169624	−	1.35237i
$336$	1979.25	−	903.894i	0.321360	−	0.146760i
$337$	1851.39	−	8510.69i	0.299263	−	1.37569i	−0.544405	−	0.838822i	$-0.683245\pi$
$337$	1851.39	−	8510.69i	0.299263	−	1.37569i	0.843668	−	0.536866i	$-0.180392\pi$
$338$	−3181.92	+	1737.46i	−0.512052	+	0.279602i
$339$	−809.882	−	5632.85i	−0.129754	−	0.902462i
$340$	−858.676	+	1284.62i	−0.136965	+	0.204906i
$341$	35.9385	+	5.16718i	0.00570727	+	0.000820582i
$342$	54.0895	−	11.7664i	0.00855212	−	0.00186040i
$343$	−154.705	+	2163.05i	−0.0243535	+	0.340507i
$344$	−1097.26			−0.171978
$345$	−2057.90	+	5706.11i	−0.321142	+	0.890453i
$346$	−1684.49			−0.261731
$347$	−262.488	+	3670.06i	−0.0406083	+	0.567778i	0.935896	+	0.352278i	$0.114593\pi$
$347$	−262.488	+	3670.06i	−0.0406083	+	0.567778i	−0.976504	+	0.215500i	$0.930862\pi$
$348$	4004.57	−	871.140i	0.616860	−	0.134190i
$349$	−4899.60	−	704.456i	−0.751489	−	0.108048i	−0.244082	−	0.969755i	$-0.578487\pi$
$349$	−4899.60	−	704.456i	−0.751489	−	0.108048i	−0.507407	+	0.861707i	$0.669396\pi$
$350$	5057.29	+	4711.79i	0.772353	+	0.719588i
$351$	409.029	+	2844.86i	0.0622004	+	0.432613i
$352$	−1100.38	+	600.855i	−0.166621	+	0.0909821i
$353$	−2144.07	+	9856.13i	−0.323279	+	1.48609i	0.472949	+	0.881090i	$0.343190\pi$
$353$	−2144.07	+	9856.13i	−0.323279	+	1.48609i	−0.796227	+	0.604998i	$0.793174\pi$
$354$	4497.51	−	2053.94i	0.675254	−	0.308378i
$355$	5870.19	−	7553.94i	0.877626	−	1.12936i
$356$	217.341	+	188.327i	0.0323568	+	0.0280373i
$357$	−4686.73	+	335.201i	−0.694812	+	0.0496940i
$358$	4046.51	−	7410.62i	0.597387	−	1.09403i
$359$	2082.04	+	4559.03i	0.306089	+	0.670241i	0.998695	−	0.0510749i	$-0.0162647\pi$
$359$	2082.04	+	4559.03i	0.306089	+	0.670241i	−0.692606	+	0.721316i	$0.743537\pi$
$360$	−230.215	+	100.161i	−0.0337039	+	0.0146638i
$361$	6487.88	+	1905.01i	0.945892	+	0.277739i
$362$	221.262	+	165.635i	0.0321250	+	0.0240485i
$363$	−350.708	−	940.285i	−0.0507091	−	0.135956i
$364$	−308.547	+	2145.99i	−0.0444293	+	0.309012i
$365$	−6648.82	+	7399.37i	−0.953467	+	1.06110i
$366$	4157.90	−	3602.84i	0.593817	−	0.514546i
$367$	1263.00	−	1263.00i	0.179641	−	0.179641i	−0.611559	−	0.791199i	$-0.709457\pi$
$367$	1263.00	−	1263.00i	0.179641	−	0.179641i	0.791199	+	0.611559i	$0.209457\pi$
$368$	−890.206	−	1523.90i	−0.126101	−	0.215867i
$369$			650.245i			0.0917355i
$370$	−2974.34	−	703.402i	−0.417915	−	0.0988328i
$371$	−6553.96	−	4211.97i	−0.917155	−	0.589420i
$372$	14.5960	−	10.9264i	0.00203432	−	0.00152287i
$373$	−402.953	+	150.294i	−0.0559359	+	0.0208630i	−0.377276	−	0.926101i	$-0.623139\pi$
$373$	−402.953	+	150.294i	−0.0559359	+	0.0208630i	0.321340	+	0.946964i	$0.395867\pi$
$374$	2679.83	−	385.302i	0.370510	−	0.0532714i
$375$	4944.15	+	4775.71i	0.680840	+	0.657645i
$376$	−3497.98	+	2248.01i	−0.479773	+	0.308331i
$377$	−1427.03	+	3826.02i	−0.194949	+	0.522679i
$378$	−7115.39	−	3885.29i	−0.968190	−	0.528672i
$379$	−5379.62	+	6208.42i	−0.729110	+	0.841438i	−0.992371	−	0.123287i	$-0.960657\pi$
$379$	−5379.62	+	6208.42i	−0.729110	+	0.841438i	0.263261	+	0.964725i	$0.415202\pi$
$380$	439.204	+	39.3804i	0.0592913	+	0.00531624i
$381$	−9308.37	+	2733.18i	−1.25166	+	0.367520i
$382$	7425.92	+	2769.72i	0.994615	+	0.370972i
$383$	1856.04	+	403.756i	0.247622	+	0.0538668i	0.334663	−	0.942338i	$-0.391378\pi$
$383$	1856.04	+	403.756i	0.247622	+	0.0538668i	−0.0870413	+	0.996205i	$0.527741\pi$
$384$	−177.375	+	604.084i	−0.0235720	+	0.0802787i
$385$	218.280	−	12109.1i	0.0288950	−	1.60296i
$386$	3186.31	−	6977.05i	0.420153	−	0.920006i
$387$	230.718	+	308.203i	0.0303050	+	0.0404827i
$388$	1048.63	+	4820.50i	0.137207	+	0.630731i
$389$	−3309.24	−	3819.07i	−0.431324	−	0.497775i	0.497929	−	0.867218i	$-0.334094\pi$
$389$	−3309.24	−	3819.07i	−0.431324	−	0.497775i	−0.929253	+	0.369443i	$0.879549\pi$
$390$	−345.261	+	2128.29i	−0.0448282	+	0.276334i
$391$	651.133	+	3755.10i	0.0842179	+	0.485687i
$392$	−2383.99	−	2383.99i	−0.307168	−	0.307168i
$393$	−4896.41	−	350.198i	−0.628476	−	0.0449495i
$394$	−639.922	+	995.739i	−0.0818244	+	0.127321i
$395$	−5861.22	−	11209.7i	−0.746608	−	1.42791i
$396$	400.145	+	182.740i	0.0507778	+	0.0231895i
$397$	5933.19	−	7925.81i	0.750071	−	1.00198i	−0.249366	−	0.968409i	$-0.580222\pi$
$397$	5933.19	−	7925.81i	0.750071	−	1.00198i	0.999436	−	0.0335678i	$-0.0106870\pi$
$398$	403.619	+	739.174i	0.0508332	+	0.0930941i
$399$	724.961	+	1128.06i	0.0909610	+	0.141538i
$400$	−1988.61	+	213.098i	−0.248577	+	0.0266372i
$401$	−311.979	−	1062.50i	−0.0388516	−	0.132317i	0.937784	−	0.347220i	$-0.112874\pi$
$401$	−311.979	−	1062.50i	−0.0388516	−	0.132317i	−0.976635	+	0.214904i	$0.931056\pi$
$402$	524.568	+	7334.42i	0.0650823	+	0.909969i
$403$	1.29603	+	18.1208i	0.000160198	+	0.00223986i
$404$	−569.011	−	1937.87i	−0.0700727	−	0.238646i
$405$	−6269.15	−	3571.38i	−0.769177	−	0.438180i
$406$	−6227.29	−	9689.85i	−0.761220	−	1.18448i
$407$	2566.51	+	4700.21i	0.312573	+	0.572434i
$408$	814.753	−	1088.38i	0.0988634	−	0.132066i
$409$	2741.04	+	1251.79i	0.331383	+	0.151338i	0.574157	−	0.818745i	$-0.305330\pi$
$409$	2741.04	+	1251.79i	0.331383	+	0.151338i	−0.242774	+	0.970083i	$0.578057\pi$
$410$	−1548.71	+	4943.06i	−0.186550	+	0.595415i
$411$	6501.50	−	10116.5i	0.780281	−	1.21414i
$412$	5707.74	+	408.225i	0.682524	+	0.0488151i
$413$	−9826.21	−	9826.21i	−1.17074	−	1.17074i
$414$	−240.859	+	570.471i	−0.0285932	+	0.0677225i
$415$	−5206.89	−	844.686i	−0.615894	−	0.0999133i
$416$	−410.809	−	474.099i	−0.0484172	−	0.0558765i
$417$	1280.39	+	5885.86i	0.150362	+	0.691204i
$418$	−463.028	−	618.533i	−0.0541805	−	0.0723766i
$419$	−3815.66	+	8355.13i	−0.444886	+	0.974164i	0.545790	+	0.837922i	$0.316230\pi$
$419$	−3815.66	+	8355.13i	−0.444886	+	0.974164i	−0.990676	+	0.136242i	$0.956498\pi$
$420$	−4222.26	−	4377.27i	−0.490536	−	0.508546i
$421$	−121.135	+	412.548i	−0.0140232	+	0.0477586i	−0.966207	−	0.257766i	$-0.917014\pi$
$421$	−121.135	+	412.548i	−0.0140232	+	0.0477586i	0.952184	+	0.305525i	$0.0988318\pi$
$422$	2796.93	+	608.435i	0.322636	+	0.0701852i
$423$	1366.94	+	509.842i	0.157123	+	0.0586037i
$424$	2162.91	−	635.088i	0.247736	−	0.0727420i
$425$	4184.36	+	1069.55i	0.477580	+	0.122072i
$426$	−5512.26	+	6361.49i	−0.626925	+	0.723510i
$427$	−13571.5	−	7410.58i	−1.53810	−	0.839867i
$428$	1120.43	−	3004.00i	0.126538	−	0.339261i
$429$	3178.13	−	2042.46i	0.357673	−	0.229862i
$430$	1019.82	+	2892.42i	0.114372	+	0.324383i
$431$	−10169.9	+	1462.22i	−1.13659	+	0.163416i	−0.684815	−	0.728717i	$-0.740117\pi$
$431$	−10169.9	+	1462.22i	−1.13659	+	0.163416i	−0.451772	+	0.892134i	$0.649208\pi$
$432$	2197.86	−	819.758i	0.244779	−	0.0912977i
$433$	3741.90	−	2801.15i	0.415298	−	0.310888i	−0.371118	−	0.928586i	$-0.621025\pi$
$433$	3741.90	−	2801.15i	0.415298	−	0.310888i	0.786416	+	0.617698i	$0.211934\pi$
$434$	−43.1093	−	27.7047i	−0.00476801	−	0.00306421i
$435$	−6018.29	−	9746.51i	−0.663345	−	1.07427i
$436$			5055.01i			0.555255i
$437$	851.502	−	676.675i	0.0932102	−	0.0740727i
$438$	6189.13	−	6189.13i	0.675179	−	0.675179i
$439$	4415.33	−	3825.91i	0.480028	−	0.415947i	−0.380945	−	0.924598i	$-0.624401\pi$
$439$	4415.33	−	3825.91i	0.480028	−	0.415947i	0.860973	+	0.508651i	$0.169856\pi$
$440$	2606.60	+	2342.20i	0.282420	+	0.253773i
$441$	−168.350	+	1170.90i	−0.0181784	+	0.126433i
$442$	473.408	+	1269.26i	0.0509451	+	0.136589i
$443$	−10178.2	−	7619.28i	−1.09160	−	0.817162i	−0.107400	−	0.994216i	$-0.534253\pi$
$443$	−10178.2	−	7619.28i	−1.09160	−	0.817162i	−0.984201	+	0.177054i	$0.943343\pi$
$444$	2580.30	+	757.644i	0.275801	+	0.0809824i
$445$	294.434	−	747.952i	0.0313652	−	0.0796772i
$446$	531.906	+	1164.71i	0.0564719	+	0.123656i
$447$	−4358.90	+	7982.73i	−0.461228	+	0.844676i
$448$	1764.99	−	126.235i	0.186134	−	0.0133125i
$449$	−9153.95	−	7931.94i	−0.962142	−	0.833701i	0.0239819	−	0.999712i	$-0.492366\pi$
$449$	−9153.95	−	7931.94i	−0.962142	−	0.833701i	−0.986124	+	0.166012i	$0.946911\pi$
$450$	477.995	+	513.762i	0.0500732	+	0.0538199i
$451$	8255.98	−	3770.38i	0.861993	−	0.393659i
$452$	983.735	−	4522.16i	0.102370	−	0.470585i
$453$	2517.31	−	1374.55i	0.261089	−	0.142565i
$454$	−213.841	−	1487.30i	−0.0221059	−	0.153750i
$455$	5943.67	−	1181.19i	0.612404	−	0.121704i
$456$	−384.045	−	55.2174i	−0.0394399	−	0.00567060i
$457$	−10500.9	+	2284.33i	−1.07486	+	0.233822i	−0.714958	−	0.699167i	$-0.753554\pi$
$457$	−10500.9	+	2284.33i	−1.07486	+	0.233822i	−0.359904	+	0.932989i	$0.617191\pi$
$458$	314.707	−	4400.18i	0.0321076	−	0.448924i
$459$	−5065.53			−0.515117
$460$	−3189.69	+	3762.96i	−0.323304	+	0.381411i
$461$	10450.0			1.05576			0.527879	−	0.849320i	$-0.322987\pi$
$461$	10450.0			1.05576			0.527879	+	0.849320i	$0.322987\pi$
$462$	−760.208	+	10629.1i	−0.0765542	+	1.07037i
$463$	14467.9	−	3147.30i	1.45223	−	0.315913i	0.583868	−	0.811849i	$-0.301539\pi$
$463$	14467.9	−	3147.30i	1.45223	−	0.315913i	0.868359	+	0.495936i	$0.165175\pi$
$464$	3298.88	+	474.308i	0.330058	+	0.0474552i
$465$	−42.3683	−	28.3202i	−0.00422534	−	0.00282434i
$466$	741.773	+	5159.15i	0.0737382	+	0.512860i
$467$	2758.61	−	1506.31i	0.273347	−	0.149259i	−0.336729	−	0.941602i	$-0.609321\pi$
$467$	2758.61	−	1506.31i	0.273347	−	0.149259i	0.610076	+	0.792343i	$0.291139\pi$
$468$	−46.7871	+	215.077i	−0.00462123	+	0.0212434i
$469$	18799.0	−	8585.20i	1.85086	−	0.845262i
$470$	9176.94	+	7131.43i	0.900640	+	0.699890i
$471$	6818.85	+	5908.57i	0.667083	+	0.578031i
$472$	4010.63	−	286.846i	0.391111	−	0.0279728i
$473$	2575.37	−	4716.44i	0.250350	−	0.458482i
$474$	4623.59	+	10124.2i	0.448035	+	0.981059i
$475$	−304.399	−	1194.36i	−0.0294037	−	0.115370i
$476$	−3666.35	−	1076.54i	−0.353040	−	0.103662i
$477$	−633.174	−	473.988i	−0.0607779	−	0.0454978i
$478$	−3533.61	−	9473.97i	−0.338124	−	0.906546i
$479$	−2095.70	+	14575.9i	−0.199906	+	1.39038i	0.604644	+	0.796496i	$0.293315\pi$
$479$	−2095.70	+	14575.9i	−0.199906	+	1.39038i	−0.804551	+	0.593884i	$0.797594\pi$
$480$	1757.24	−	93.8832i	0.167097	−	0.00892742i
$481$	−2025.08	+	1754.74i	−0.191966	+	0.166339i
$482$	1845.11	−	1845.11i	0.174362	−	0.174362i
$483$	−14987.0	−	637.437i	−1.41187	−	0.0600505i
$484$		−	816.127i		−	0.0766460i
$485$	11732.4	−	7244.52i	1.09843	−	0.678261i
$486$	−1319.58	−	848.044i	−0.123163	−	0.0791524i
$487$	5397.32	−	4040.38i	0.502209	−	0.375949i	−0.317929	−	0.948115i	$-0.602987\pi$
$487$	5397.32	−	4040.38i	0.502209	−	0.375949i	0.820138	+	0.572165i	$0.193896\pi$
$488$	4192.06	−	1563.56i	0.388864	−	0.145039i
$489$	−15257.0	+	2193.63i	−1.41093	+	0.202862i
$490$	−4068.54	+	8500.02i	−0.375098	+	0.783656i
$491$	−6819.97	+	4382.93i	−0.626845	+	0.402849i	−0.815140	−	0.579264i	$-0.803340\pi$
$491$	−6819.97	+	4382.93i	−0.626845	+	0.402849i	0.188295	+	0.982112i	$0.439704\pi$
$492$	1592.77	−	4270.37i	0.145950	−	0.391308i
$493$	−6316.67	−	3449.16i	−0.577056	−	0.315096i
$494$	253.169	−	292.172i	0.0230579	−	0.0266102i
$495$	109.805	−	1224.64i	0.00997042	−	0.111199i
$496$	14.2268	−	4.17736i	0.00128790	−	0.000378163i
$497$	22166.2	+	8267.58i	2.00059	+	0.746180i
$498$	4535.23	+	986.578i	0.408089	+	0.0887744i
$499$	−1853.11	+	6311.12i	−0.166246	+	0.566182i	0.833657	+	0.552282i	$0.186243\pi$
$499$	−1853.11	+	6311.12i	−0.166246	+	0.566182i	−0.999903	+	0.0138998i	$0.995575\pi$
$500$	2410.00	+	5044.00i	0.215557	+	0.451149i
$501$	−2697.70	+	5907.14i	−0.240567	+	0.526769i
$502$	−2162.46	−	2888.71i	−0.192261	−	0.256831i
$503$	−3806.06	−	17496.2i	−0.337383	−	1.55092i	−0.763229	−	0.646129i	$-0.776387\pi$
$503$	−3806.06	−	17496.2i	−0.337383	−	1.55092i	0.425846	−	0.904796i	$-0.359977\pi$
$504$	−406.576	−	469.214i	−0.0359332	−	0.0414691i
$505$	−4579.45	+	3301.04i	−0.403530	+	0.290880i
$506$	8639.71	−	249.695i	0.759055	−	0.0219373i
$507$	−6304.55	−	6304.55i	−0.552258	−	0.552258i
$508$	−7869.34	−	562.826i	−0.687295	−	0.0491563i
$509$	−11259.0	+	17519.3i	−0.980442	+	1.52560i	−0.135473	+	0.990781i	$0.543255\pi$
$509$	−11259.0	+	17519.3i	−0.980442	+	1.52560i	−0.844968	+	0.534816i	$0.820381\pi$
$510$	−3626.26	−	1136.15i	−0.314850	−	0.0986460i
$511$	−22377.2	−	10219.3i	−1.93720	−	0.884688i
$512$	−306.830	+	409.877i	−0.0264846	+	0.0353793i
$513$	692.810	+	1268.79i	0.0596264	+	0.109198i
$514$	3193.32	+	4968.91i	0.274030	+	0.426399i
$515$	−4228.81	−	15425.2i	−0.361832	−	1.31984i
$516$	−760.261	−	2589.21i	−0.0648616	−	0.220898i
$517$	−1452.74	−	20311.9i	−0.123581	−	1.72789i
$518$	−539.201	−	7539.02i	−0.0457358	−	0.639470i
$519$	−1167.14	−	3974.90i	−0.0987121	−	0.336183i
$520$	−867.925	+	1523.54i	−0.0731943	+	0.128484i
$521$	3357.97	+	5225.11i	0.282371	+	0.439379i	0.953247	−	0.302191i	$-0.0977181\pi$
$521$	3357.97	+	5225.11i	0.282371	+	0.439379i	−0.670876	+	0.741570i	$0.734082\pi$
$522$	−560.421	−	1026.33i	−0.0469903	−	0.0860563i
$523$	9598.86	−	12822.6i	0.802541	−	1.07207i	−0.193316	−	0.981137i	$-0.561924\pi$
$523$	9598.86	−	12822.6i	0.802541	−	1.07207i	0.995857	−	0.0909326i	$-0.0289848\pi$
$524$	−3631.33	−	1658.37i	−0.302739	−	0.138256i
$525$	−7614.38	+	15198.4i	−0.632988	+	1.26345i
$526$	3706.62	−	5767.62i	0.307256	−	0.478099i
$527$	−31.9374	−	2.28420i	−0.00263987	−	0.000188807i
$528$	−2180.26	−	2180.26i	−0.179704	−	0.179704i
$529$	702.686	+	12146.7i	0.0577535	+	0.998331i
$530$	−3684.37	−	5111.24i	−0.301960	−	0.418902i
$531$	−923.874	−	1066.21i	−0.0755042	−	0.0871364i
$532$	231.800	+	1065.57i	0.0188906	+	0.0868386i
$533$	2721.53	+	3635.54i	0.221168	+	0.295446i
$534$	−293.806	+	643.345i	−0.0238094	+	0.0521353i
$535$	−8959.99	−	161.513i	−0.724064	−	0.0130520i
$536$	−1684.71	+	5737.60i	−0.135762	+	0.462363i
$537$	20290.6	+	4413.94i	1.63055	+	0.354703i
$538$	−8584.09	−	3201.70i	−0.687893	−	0.256571i
$539$	15842.7	−	4651.85i	1.26604	−	0.371743i
$540$	−4203.65	−	5031.72i	−0.334993	−	0.400983i
$541$	−4119.55	+	4754.22i	−0.327381	+	0.377818i	−0.895449	−	0.445163i	$-0.853146\pi$
$541$	−4119.55	+	4754.22i	−0.327381	+	0.377818i	0.568068	+	0.822982i	$0.307691\pi$
$542$	4039.68	+	2205.83i	0.320146	+	0.174813i
$543$	−237.542	+	636.875i	−0.0187733	+	0.0503332i
$544$	930.121	−	597.752i	0.0733062	−	0.0471111i
$545$	13325.2	−	4698.25i	1.04732	−	0.369267i
$546$	−5277.68	+	758.816i	−0.413670	+	0.0594768i
$547$	−19143.4	+	7140.11i	−1.49637	+	0.558116i	−0.958544	−	0.284943i	$-0.908025\pi$
$547$	−19143.4	+	7140.11i	−1.49637	+	0.558116i	−0.537821	+	0.843059i	$0.680752\pi$
$548$	7828.94	−	5860.67i	0.610284	−	0.456853i
$549$	−1320.63	−	848.716i	−0.102665	−	0.0659788i
$550$	3751.49	−	9047.97i	0.290843	−	0.701467i
$551$			2053.91i			0.158801i
$552$	2979.16	−	3156.49i	0.229713	−	0.243386i
$553$	22119.6	−	22119.6i	1.70094	−	1.70094i
$554$	7566.22	−	6556.16i	0.580249	−	0.502788i
$555$	−401.015	−	7505.93i	−0.0306705	−	0.574070i
$556$	−697.132	+	4848.66i	−0.0531744	+	0.369836i
$557$	3643.14	+	9767.64i	0.277136	+	0.743031i	0.998714	+	0.0506974i	$0.0161444\pi$
$557$	3643.14	+	9767.64i	0.277136	+	0.743031i	−0.721578	+	0.692333i	$0.756583\pi$
$558$	−4.16477	−	3.11771i	−0.000315965	−	0.000236529i
$559$	2579.90	+	757.527i	0.195202	+	0.0573166i
$560$	−1973.18	−	4535.25i	−0.148897	−	0.342231i
$561$	2765.98	+	6056.65i	0.208163	+	0.455814i
$562$	3998.60	−	7322.89i	0.300126	−	0.549640i
$563$	14693.9	−	1050.93i	1.09995	−	0.0786701i	0.490461	−	0.871463i	$-0.336828\pi$
$563$	14693.9	−	1050.93i	1.09995	−	0.0786701i	0.609491	+	0.792793i	$0.291374\pi$
$564$	−7728.29	−	6696.60i	−0.576986	−	0.499961i
$565$	−12834.9	+	1609.84i	−0.955694	+	0.119870i
$566$	−15136.4	+	6912.55i	−1.12408	+	0.513350i
$567$	3792.69	−	17434.7i	0.280913	−	1.29134i
$568$	−6008.02	+	3280.63i	−0.443822	+	0.242345i
$569$	2675.85	+	18611.0i	0.197149	+	1.37120i	0.812507	+	0.582951i	$0.198102\pi$
$569$	2675.85	+	18611.0i	0.197149	+	1.37120i	−0.615359	+	0.788247i	$0.710989\pi$
$570$	211.386	+	1063.68i	0.0155333	+	0.0781623i
$571$	14182.9	+	2039.20i	1.03947	+	0.149453i	0.640853	−	0.767664i	$-0.278581\pi$
$571$	14182.9	+	2039.20i	1.03947	+	0.149453i	0.398618	+	0.917117i	$0.369490\pi$
$572$	3002.06	−	653.058i	0.219445	−	0.0477373i
$573$	−1390.52	+	19442.0i	−0.101378	+	1.41746i
$574$	−12809.9			−0.931486
$575$	12883.9	+	4910.73i	0.934425	+	0.356159i
$576$	179.644			0.0129951
$577$	−1260.60	+	17625.5i	−0.0909523	+	1.27168i	0.723041	+	0.690805i	$0.242744\pi$
$577$	−1260.60	+	17625.5i	−0.0909523	+	1.27168i	−0.813993	+	0.580875i	$0.802711\pi$
$578$	7268.45	−	1581.15i	0.523058	−	0.113784i
$579$	18671.5	+	2684.55i	1.34017	+	0.192688i
$580$	−1815.77	−	9136.80i	−0.129993	−	0.654112i
$581$	−1856.45	−	12911.9i	−0.132562	−	0.921991i
$582$	−10648.4	+	5814.45i	−0.758400	+	0.414118i
$583$	−2346.70	+	10787.6i	−0.166707	+	0.766342i
$584$	6474.78	−	2956.93i	0.458781	−	0.209518i
$585$	610.435	−	76.5651i	0.0431425	−	0.00541124i
$586$	−3378.09	−	2927.13i	−0.238136	−	0.206346i
$587$	27610.0	−	1974.70i	1.94137	−	0.138850i	0.954270	−	0.298947i	$-0.0966354\pi$
$587$	27610.0	−	1974.70i	1.94137	−	0.138850i	0.987101	+	0.160097i	$0.0511808\pi$
$588$	3973.71	−	7277.31i	0.278696	−	0.510393i
$589$	3.79592	+	8.31190i	0.000265549	+	0.000581470i
$590$	−4483.71	−	10305.6i	−0.312867	−	0.719107i
$591$	−2793.03	−	820.108i	−0.194399	−	0.0570808i
$592$	1750.76	+	1310.60i	0.121547	+	0.0909889i
$593$	−8023.79	−	21512.6i	−0.555645	−	1.48974i	−0.846190	−	0.532882i	$-0.821109\pi$
$593$	−8023.79	−	21512.6i	−0.555645	−	1.48974i	0.290544	−	0.956862i	$-0.406164\pi$
$594$	−1634.94	+	11371.3i	−0.112933	+	0.785468i
$595$	569.803	+	10665.2i	0.0392599	+	0.734840i
$596$	−5589.96	+	4843.73i	−0.384184	+	0.332897i
$597$	−1464.57	+	1464.57i	−0.100404	+	0.100404i
$598$	1040.99	+	4197.61i	0.0711863	+	0.287045i
$599$		−	24891.3i		−	1.69788i	−0.528490	−	0.848940i	$-0.677242\pi$
$599$		−	24891.3i		−	1.69788i	0.528490	−	0.848940i	$-0.322758\pi$
$600$	−1880.70	−	4544.89i	−0.127965	−	0.309241i
$601$	12277.5	+	7890.29i	0.833296	+	0.535527i	0.886324	−	0.463066i	$-0.153251\pi$
$601$	12277.5	+	7890.29i	0.833296	+	0.535527i	−0.0530276	+	0.998593i	$0.516887\pi$
$602$	−6071.61	+	4545.15i	−0.411064	+	0.307718i
$603$	1965.84	−	733.219i	0.132761	−	0.0495174i
$604$	2308.72	−	331.944i	0.155531	−	0.0223619i
$605$	−2151.34	+	758.528i	−0.144569	+	0.0509728i
$606$	4178.55	−	2685.39i	0.280102	−	0.180011i
$607$	−4650.83	+	12469.4i	−0.310991	+	0.833798i	0.683594	+	0.729863i	$0.260416\pi$
$607$	−4650.83	+	12469.4i	−0.310991	+	0.833798i	−0.994584	+	0.103935i	$0.966857\pi$
$608$	−276.934	−	151.217i	−0.0184723	−	0.0100866i
$609$	18550.5	−	21408.4i	1.23432	−	1.42448i
$610$	−8017.79	−	9597.20i	−0.532181	−	0.637015i
$611$	9776.49	−	2870.64i	0.647323	−	0.190071i
$612$	−363.472	−	135.568i	−0.0240073	−	0.00895428i
$613$	2119.52	+	461.073i	0.139652	+	0.0303794i	0.281848	−	0.959459i	$-0.409053\pi$
$613$	2119.52	+	461.073i	0.139652	+	0.0303794i	−0.142196	+	0.989839i	$0.545416\pi$
$614$	5869.17	−	19988.6i	0.385766	−	1.31380i
$615$	−12737.2	−	229.602i	−0.835144	−	0.0150544i
$616$	−3599.99	+	7882.87i	−0.235467	+	0.515601i
$617$	3211.27	+	4289.76i	0.209532	+	0.279901i	0.892979	−	0.450098i	$-0.148611\pi$
$617$	3211.27	+	4289.76i	0.209532	+	0.279901i	−0.683447	+	0.730000i	$0.739520\pi$
$618$	2991.44	+	13751.4i	0.194714	+	0.895085i
$619$	3297.88	+	3805.96i	0.214141	+	0.247131i	0.852650	−	0.522483i	$-0.174994\pi$
$619$	3297.88	+	3805.96i	0.214141	+	0.247131i	−0.638509	+	0.769614i	$0.720449\pi$
$620$	−24.2343	−	33.6197i	−0.00156980	−	0.00217774i
$621$	−16066.9	−	1838.08i	−1.03823	−	0.118776i
$622$	−7028.36	−	7028.36i	−0.453073	−	0.453073i
$623$	1982.74	+	141.808i	0.127507	+	0.00911946i
$624$	834.094	−	1297.88i	0.0535104	−	0.0832638i
$625$	11056.2	−	11040.8i	0.707599	−	0.706614i
$626$	−13255.5	−	6053.60i	−0.846322	−	0.386502i
$627$	1138.73	−	1521.17i	0.0725306	−	0.0968895i
$628$	3516.49	+	6439.96i	0.223444	+	0.409208i
$629$	−2553.25	−	3972.94i	−0.161852	−	0.251847i
$630$	−858.982	+	1507.85i	−0.0543217	+	0.0953556i
$631$	8021.66	+	27319.3i	0.506081	+	1.72355i	0.674903	+	0.737907i	$0.264186\pi$
$631$	8021.66	+	27319.3i	0.506081	+	1.72355i	−0.168822	+	0.985647i	$0.553996\pi$
$632$	645.713	+	9028.25i	0.0406410	+	0.568235i
$633$	502.187	+	7021.49i	0.0315326	+	0.440884i
$634$	1669.65	+	5686.31i	0.104590	+	0.356202i
$635$	5830.32	+	21267.0i	0.364361	+	1.32906i
$636$	2997.24	+	4663.79i	0.186868	+	0.290773i
$637$	3959.42	+	7251.14i	0.246276	+	0.451021i
$638$	−9781.53	+	13066.6i	−0.606982	+	0.810833i
$639$	2184.76	+	997.747i	0.135255	+	0.0617688i
$640$	1365.62	+	427.865i	0.0843454	+	0.0264263i
$641$	−13440.8	+	20914.3i	−0.828204	+	1.28871i	0.126744	+	0.991936i	$0.459547\pi$
$641$	−13440.8	+	20914.3i	−0.828204	+	1.28871i	−0.954947	+	0.296775i	$0.904089\pi$
$642$	7864.85	+	562.505i	0.483491	+	0.0345799i
$643$	−578.572	−	578.572i	−0.0354847	−	0.0354847i	0.689142	−	0.724626i	$-0.257988\pi$
$643$	−578.572	−	578.572i	−0.0354847	−	0.0354847i	−0.724626	+	0.689142i	$0.757988\pi$
$644$	−11238.3	−	4744.94i	−0.687657	−	0.290337i
$645$	−6118.64	+	4410.54i	−0.373521	+	0.269248i
$646$	446.202	+	514.945i	0.0271758	+	0.0313626i
$647$	−1965.74	−	9036.35i	−0.119445	−	0.549081i	−0.997509	−	0.0705378i	$-0.977528\pi$
$647$	−1965.74	−	9036.35i	−0.119445	−	0.549081i	0.878064	−	0.478544i	$-0.158835\pi$
$648$	3093.87	+	4132.93i	0.187560	+	0.250551i
$649$	−8180.35	+	17912.5i	−0.494772	+	1.08340i
$650$	4822.78	+	871.861i	0.291023	+	0.0526111i
$651$	35.5056	−	120.921i	0.00213760	−	0.00727998i
$652$	−12248.6	−	2664.53i	−0.735726	−	0.160047i
$653$	−8222.26	−	3066.75i	−0.492744	−	0.183784i	0.0907941	−	0.995870i	$-0.471059\pi$
$653$	−8222.26	−	3066.75i	−0.492744	−	0.183784i	−0.583538	+	0.812086i	$0.698332\pi$
$654$	−11928.3	+	3502.47i	−0.713202	+	0.209415i
$655$	−996.483	+	11113.6i	−0.0594440	+	0.662971i
$656$	2427.24	−	2801.19i	0.144463	−	0.166719i
$657$	−2191.99	−	1196.91i	−0.130164	−	0.0710747i
$658$	−10043.9	+	26928.8i	−0.595065	+	1.59543i
$659$	−17762.8	+	11415.4i	−1.04998	+	0.674783i	−0.947436	−	0.319945i	$-0.896336\pi$
$659$	−17762.8	+	11415.4i	−1.04998	+	0.674783i	−0.102547	+	0.994728i	$0.532699\pi$
$660$	−3720.86	+	7773.64i	−0.219446	+	0.458467i
$661$	−6881.71	+	989.440i	−0.404943	+	0.0582220i	−0.341777	−	0.939781i	$-0.611029\pi$
$661$	−6881.71	+	989.440i	−0.404943	+	0.0582220i	−0.0631659	+	0.998003i	$0.520120\pi$
$662$	−2855.15	+	1064.92i	−0.167626	+	0.0625214i
$663$	−2667.06	+	1996.53i	−0.156229	+	0.116952i
$664$	3175.27	+	2040.62i	0.185579	+	0.119264i
$665$	2593.43	−	1601.39i	0.151231	−	0.0933825i
$666$		−	767.336i		−	0.0446451i
$667$	−18783.7	−	13232.1i	−1.09041	−	0.768141i
$668$	−3734.31	+	3734.31i	−0.216295	+	0.216295i
$669$	−2379.83	+	2062.13i	−0.137533	+	0.119173i
$670$	16690.3	−	891.704i	0.962392	−	0.0514172i
$671$	−3118.39	+	21688.9i	−0.179410	+	1.24782i
$672$	1520.79	+	4077.38i	0.0873000	+	0.234060i
$673$	−27660.9	−	20706.7i	−1.58432	−	1.18601i	−0.878646	−	0.477474i	$-0.841552\pi$
$673$	−27660.9	−	20706.7i	−1.58432	−	1.18601i	−0.705676	−	0.708534i	$-0.749357\pi$
$674$	16713.9	+	4907.63i	0.955184	+	0.280467i
$675$	−9356.81	+	15757.5i	−0.533546	+	0.898531i
$676$	−3012.07	−	6595.52i	−0.171374	−	0.375257i
$677$	−11971.4	+	21923.9i	−0.679611	+	1.24462i	0.279108	+	0.960260i	$0.409961\pi$
$677$	−11971.4	+	21923.9i	−0.679611	+	1.24462i	−0.958719	+	0.284355i	$0.908220\pi$
$678$	11352.6	−	811.950i	0.643056	−	0.0459923i
$679$	25770.3	+	22330.1i	1.45652	+	1.26208i
$680$	−2440.17	−	1896.26i	−0.137612	−	0.106939i
$681$	3361.42	−	1535.11i	0.189148	−	0.0863810i
$682$	−15.4357	+	70.9566i	−0.000866660	+	0.00398397i
$683$	10328.0	−	5639.49i	0.578607	−	0.315943i	−0.163162	−	0.986599i	$-0.552169\pi$
$683$	10328.0	−	5639.49i	0.578607	−	0.315943i	0.741768	+	0.670656i	$0.233987\pi$
$684$	15.7555	+	109.582i	0.000880743	+	0.00612570i
$685$	−22725.3	−	15190.3i	−1.26758	−	0.847287i
$686$	−4293.01	−	617.241i	−0.238933	−	0.0343533i
$687$	10601.2	−	2306.14i	0.588733	−	0.128071i
$688$	156.555	−	2188.93i	0.00867532	−	0.121297i
$689$	−5523.92			−0.305435
$690$	−11089.5	−	4919.46i	−0.611842	−	0.271421i
$691$	30166.5			1.66076			0.830381	−	0.557196i	$-0.188123\pi$
$691$	30166.5			1.66076			0.830381	+	0.557196i	$0.188123\pi$
$692$	240.341	−	3360.40i	0.0132029	−	0.184600i
$693$	2971.13	−	646.329i	0.162863	−	0.0354286i
$694$	−7283.96	−	1047.27i	−0.398408	−	0.0572824i
$695$	13429.2	−	2668.80i	0.732946	−	0.145659i
$696$	1166.48	+	8113.02i	0.0635275	+	0.441844i
$697$	−7024.93	+	3835.90i	−0.381762	+	0.208458i
$698$	2104.39	−	9673.72i	0.114115	−	0.524579i
$699$	−11660.1	+	5324.99i	−0.630938	+	0.288140i
$700$	−10121.1	+	9416.53i	−0.546490	+	0.508445i
$701$	−13026.7	−	11287.7i	−0.701871	−	0.608174i	0.229042	−	0.973417i	$-0.426441\pi$
$701$	−13026.7	−	11287.7i	−0.701871	−	0.608174i	−0.930913	+	0.365242i	$0.880986\pi$
$702$	−5733.58	+	410.074i	−0.308262	+	0.0220473i
$703$	−645.913	+	1182.90i	−0.0346530	+	0.0634623i
$704$	−1041.65	−	2280.89i	−0.0557650	−	0.122108i
$705$	−10469.6	+	26596.0i	−0.559303	+	1.42080i
$706$	−19356.1	−	5683.47i	−1.03184	−	0.302975i
$707$	−11175.8	−	8366.07i	−0.594495	−	0.445033i
$708$	3455.72	+	9265.16i	0.183438	+	0.491816i
$709$	736.434	−	5122.01i	0.0390090	−	0.271313i	−0.960977	−	0.276629i	$-0.910783\pi$
$709$	736.434	−	5122.01i	0.0390090	−	0.271313i	0.999986	+	0.00531530i	$0.00169192\pi$
$710$	14231.8	+	12788.2i	0.752269	+	0.675964i
$711$	2400.11	−	2079.71i	0.126598	−	0.109698i
$712$	−406.704	+	406.704i	−0.0214071	+	0.0214071i
$713$	−100.470	−	18.8338i	−0.00527719	−	0.000989247i
$714$		−	9397.40i		−	0.492562i
$715$	−4511.67	−	7306.56i	−0.235982	−	0.382168i
$716$	14206.1	+	9129.73i	0.741492	+	0.476528i
$717$	19907.4	−	14902.5i	1.03690	−	0.776212i
$718$	−9391.90	+	3503.00i	−0.488165	+	0.182076i
$719$	−12312.4	+	1770.25i	−0.638628	+	0.0918209i	−0.454020	−	0.890991i	$-0.650011\pi$
$719$	−12312.4	+	1770.25i	−0.638628	+	0.0918209i	−0.184608	+	0.982812i	$0.559102\pi$
$720$	−166.965	−	473.548i	−0.00864226	−	0.0245112i
$721$	33274.3	−	21384.1i	1.71872	−	1.10456i
$722$	−4726.00	+	12670.9i	−0.243606	+	0.653132i
$723$	5632.35	+	3075.49i	0.289722	+	0.158200i
$724$	−361.994	+	417.764i	−0.0185821	+	0.0214448i
$725$	−22397.3	+	13278.4i	−1.14733	+	0.680202i
$726$	1925.82	−	565.471i	0.0984487	−	0.0289072i
$727$	22047.9	+	8223.43i	1.12477	+	0.419519i	0.841897	−	0.539638i	$-0.181439\pi$
$727$	22047.9	+	8223.43i	1.12477	+	0.419519i	0.282876	+	0.959157i	$0.408712\pi$
$728$	−4237.02	−	921.708i	−0.215707	−	0.0469241i
$729$	5995.74	−	20419.6i	0.304615	−	1.03742i
$730$	−13812.4	−	14319.5i	−0.700301	−	0.726011i
$731$	−1968.63	+	4310.70i	−0.0996067	+	0.218108i
$732$	6594.09	+	8808.67i	0.332957	+	0.444778i
$733$	4666.73	+	21452.6i	0.235156	+	1.08100i	0.931629	+	0.363412i	$0.118388\pi$
$733$	4666.73	+	21452.6i	0.235156	+	1.08100i	−0.696472	+	0.717584i	$0.745248\pi$
$734$	2339.36	+	2699.77i	0.117640	+	0.135763i
$735$	−22876.5	−	3711.13i	−1.14804	−	0.186241i
$736$	3167.06	−	1558.45i	0.158613	−	0.0780504i
$737$	−20708.2	−	20708.2i	−1.03500	−	1.03500i
$738$	−1297.18	−	92.7758i	−0.0647015	−	0.00462754i
$739$	−6291.87	+	9790.34i	−0.313194	+	0.487339i	−0.961788	−	0.273795i	$-0.911721\pi$
$739$	−6291.87	+	9790.34i	−0.313194	+	0.487339i	0.648594	+	0.761134i	$0.275357\pi$
$740$	1827.59	−	5833.16i	0.0907888	−	0.289772i
$741$	864.853	+	394.965i	0.0428761	+	0.0195809i
$742$	9337.59	−	12473.6i	0.461986	−	0.617141i
$743$	−12416.9	−	22739.8i	−0.613096	−	1.12280i	−0.981196	−	0.193016i	$-0.938173\pi$
$743$	−12416.9	−	22739.8i	−0.613096	−	1.12280i	0.368099	−	0.929786i	$-0.380009\pi$
$744$	19.7146	+	30.6766i	0.000971470	+	0.00151164i
$745$	17963.7	+	10233.4i	0.883406	+	0.503254i
$746$	−242.329	−	825.296i	−0.0118931	−	0.0405043i
$747$	−94.4767	−	1320.96i	−0.00462747	−	0.0647005i
$748$	386.286	+	5400.99i	0.0188824	+	0.264010i
$749$	−6243.53	−	21263.5i	−0.304584	−	1.03732i
$750$	−10232.5	+	9181.72i	−0.498185	+	0.447025i
$751$	−2439.70	−	3796.25i	−0.118543	−	0.184457i	0.776911	−	0.629611i	$-0.216786\pi$
$751$	−2439.70	−	3796.25i	−0.118543	−	0.184457i	−0.895454	+	0.445153i	$0.853149\pi$
$752$	−3985.49	−	7298.87i	−0.193266	−	0.353940i
$753$	5318.18	−	7104.26i	0.257378	−	0.343816i
$754$	−7428.94	−	3392.68i	−0.358814	−	0.163865i
$755$	−3020.80	−	5777.35i	−0.145613	−	0.278489i
$756$	8766.00	−	13640.2i	0.421715	−	0.656201i
$757$	−5470.59	−	391.264i	−0.262658	−	0.0187857i	−0.0606107	−	0.998161i	$-0.519305\pi$
$757$	−5470.59	−	391.264i	−0.262658	−	0.0187857i	−0.202047	+	0.979376i	$0.564759\pi$
$758$	−11617.6	−	11617.6i	−0.556691	−	0.556691i
$759$	6575.41	+	20214.1i	0.314456	+	0.966702i
$760$	−141.225	+	870.552i	−0.00674049	+	0.0415503i
$761$	−4406.05	−	5084.85i	−0.209880	−	0.242215i	0.641043	−	0.767505i	$-0.278502\pi$
$761$	−4406.05	−	5084.85i	−0.209880	−	0.242215i	−0.850923	+	0.525290i	$0.823957\pi$
$762$	−4124.34	−	18959.3i	−0.196075	−	0.901341i
$763$	20939.2	+	27971.5i	0.993513	+	1.32718i
$764$	−6584.85	+	14418.8i	−0.311821	+	0.682794i
$765$	−19.5425	+	1084.13i	−0.000923609	+	0.0512374i
$766$	−1070.27	+	3645.01i	−0.0504836	+	0.171931i
$767$	−9627.91	−	2094.42i	−0.453251	−	0.0985987i
$768$	−1179.78	−	440.036i	−0.0554319	−	0.0206750i
$769$	14267.3	−	4189.27i	0.669042	−	0.196448i	0.0704656	−	0.997514i	$-0.477551\pi$
$769$	14267.3	−	4189.27i	0.669042	−	0.196448i	0.598576	+	0.801066i	$0.295733\pi$
$770$	24125.4	+	2163.16i	1.12912	+	0.101240i
$771$	−9512.58	+	10978.1i	−0.444342	+	0.512797i
$772$	13463.9	+	7351.86i	0.627691	+	0.342745i
$773$	3318.50	−	8897.25i	0.154409	−	0.413987i	−0.836594	−	0.547823i	$-0.815457\pi$
$773$	3318.50	−	8897.25i	0.154409	−	0.413987i	0.991004	+	0.133836i	$0.0427295\pi$
$774$	−647.753	+	416.286i	−0.0300814	+	0.0193321i
$775$	−66.0987	+	95.1295i	−0.00306366	+	0.00440923i
$776$	−9766.05	+	1404.15i	−0.451779	+	0.0649560i
$777$	17416.2	−	6495.92i	0.804124	−	0.299923i
$778$	8090.83	−	6056.72i	0.372841	−	0.279105i
$779$	1921.59	+	1234.93i	0.0883802	+	0.0567985i
$780$	−4196.47	−	992.424i	−0.192638	−	0.0455570i
$781$		−	33524.7i		−	1.53599i
$782$	−7583.96	+	763.176i	−0.346806	+	0.0348991i
$783$	21594.2	−	21594.2i	0.985588	−	0.985588i
$784$	5095.98	−	4415.69i	0.232142	−	0.201152i
$785$	13707.7	−	15255.0i	0.623245	−	0.693599i
$786$	1397.22	−	9717.90i	0.0634062	−	0.441000i
$787$	6750.91	+	18099.9i	0.305774	+	0.819811i	0.995414	+	0.0956589i	$0.0304958\pi$
$787$	6750.91	+	18099.9i	0.305774	+	0.819811i	−0.689641	+	0.724152i	$0.742231\pi$
$788$	−1895.10	−	1418.65i	−0.0856728	−	0.0641338i
$789$	16178.1	+	4750.31i	0.729980	+	0.214342i
$790$	23198.6	−	10093.2i	1.04477	−	0.454556i
$791$	−13288.6	−	29097.9i	−0.597329	−	1.30797i
$792$	−421.641	+	772.177i	−0.0189171	+	0.0346441i
$793$	−10935.9	+	782.150i	−0.489716	+	0.0350252i
$794$	14964.7	+	12967.0i	0.668863	+	0.579573i
$795$	9508.21	−	12235.5i	0.424178	−	0.545845i
$796$	−1532.17	+	699.718i	−0.0682240	+	0.0311568i
$797$	2524.09	−	11603.1i	0.112181	−	0.515686i	−0.886424	−	0.462875i	$-0.846818\pi$
$797$	2524.09	−	11603.1i	0.112181	−	0.515686i	0.998604	−	0.0528118i	$-0.0168183\pi$
$798$	−2353.81	+	1285.28i	−0.104416	+	0.0570155i
$799$	2555.72	+	17775.4i	0.113160	+	0.787044i
$800$	−141.377	−	3997.50i	−0.00624804	−	0.176666i
$801$	199.753	+	28.7201i	0.00881138	+	0.00126688i
$802$	2164.11	−	470.773i	0.0952834	−	0.0207276i
$803$	−2486.89	+	34771.2i	−0.109291	+	1.52808i
$804$	−14706.3			−0.645089
$805$	−2062.67	+	34034.6i	−0.0903101	+	1.49014i
$806$	−36.3342			−0.00158786
$807$	1607.39	−	22474.3i	0.0701150	−	0.980336i
$808$	3947.06	−	858.630i	0.171853	−	0.0373843i
$809$	−6999.86	−	1006.43i	−0.304205	−	0.0437381i	−0.0114779	−	0.999934i	$-0.503654\pi$
$809$	−6999.86	−	1006.43i	−0.304205	−	0.0437381i	−0.292727	+	0.956196i	$0.594563\pi$
$810$	8019.02	−	11996.8i	0.347852	−	0.520401i
$811$	−3251.69	−	22616.0i	−0.140792	−	0.979229i	−0.930642	−	0.365930i	$-0.880751\pi$
$811$	−3251.69	−	22616.0i	−0.140792	−	0.979229i	0.789851	−	0.613299i	$-0.210158\pi$
$812$	20218.8	−	11040.3i	0.873820	−	0.477142i
$813$	−2406.13	+	11060.8i	−0.103797	+	0.477145i
$814$	−9742.65	+	4449.32i	−0.419508	+	0.191583i
$815$	4360.39	+	34764.3i	0.187408	+	1.49416i
$816$	2054.97	+	1780.64i	0.0881598	+	0.0763909i
$817$	1348.97	−	96.4803i	0.0577656	−	0.00413148i
$818$	−2888.29	+	5289.51i	−0.123456	+	0.226092i
$819$	632.013	+	1383.91i	0.0269650	+	0.0590451i
$820$	−9639.96	−	3794.80i	−0.410539	−	0.161610i
$821$	−24319.9	−	7140.95i	−1.03382	−	0.303558i	−0.279559	−	0.960129i	$-0.590188\pi$
$821$	−24319.9	−	7140.95i	−1.03382	−	0.303558i	−0.754264	+	0.656571i	$0.772006\pi$
$822$	19253.9	+	14413.3i	0.816979	+	0.611583i
$823$	6159.68	+	16514.7i	0.260891	+	0.699475i	0.999674	+	0.0255320i	$0.00812797\pi$
$823$	6159.68	+	16514.7i	0.260891	+	0.699475i	−0.738783	+	0.673943i	$0.764599\pi$
$824$	−1628.74	+	11328.1i	−0.0688591	+	0.478925i
$825$	23949.8	+	2583.31i	1.01070	+	0.109017i
$826$	21004.3	−	18200.4i	0.884787	−	0.766673i
$827$	−30117.1	+	30117.1i	−1.26635	+	1.26635i	−0.318393	+	0.947959i	$0.603143\pi$
$827$	−30117.1	+	30117.1i	−1.26635	+	1.26635i	−0.947959	+	0.318393i	$0.896857\pi$
$828$	−1103.67	−	561.885i	−0.0463227	−	0.0235832i
$829$		−	31651.2i		−	1.32605i	−0.748599	−	0.663023i	$-0.769273\pi$
$829$		−	31651.2i		−	1.32605i	0.748599	−	0.663023i	$-0.230727\pi$
$830$	2427.98	−	10266.7i	0.101538	−	0.429353i
$831$	20713.0	+	13311.4i	0.864653	+	0.555678i
$832$	1004.40	−	751.881i	0.0418523	−	0.0313303i
$833$	−13643.0	+	5088.56i	−0.567467	+	0.211654i
$834$	−11924.4	+	1714.47i	−0.495095	+	0.0711839i
$835$	13314.5	+	6373.02i	0.551819	+	0.264129i
$836$	1299.98	−	835.445i	0.0537807	−	0.0345628i
$837$	47.4799	−	127.299i	0.00196075	−	0.00525697i
$838$	−16123.3	−	8803.97i	−0.664641	−	0.362921i
$839$	25284.9	−	29180.4i	1.04044	−	1.20074i	0.0611844	−	0.998126i	$-0.480512\pi$
$839$	25284.9	−	29180.4i	1.04044	−	1.20074i	0.979260	−	0.202610i	$-0.0649423\pi$
$840$	9334.67	−	7798.46i	0.383425	−	0.320324i
$841$	18230.4	−	5352.94i	0.747486	−	0.219482i
$842$	−805.711	−	300.515i	−0.0329770	−	0.0122998i
$843$	20050.4	+	4361.69i	0.819183	+	0.178202i
$844$	−1612.83	+	5492.80i	−0.0657772	+	0.224017i
$845$	−14586.5	+	14070.0i	−0.593836	+	0.572806i
$846$	−1212.12	+	2654.17i	−0.0492594	+	0.107863i
$847$	−3380.62	−	4515.98i	−0.137142	−	0.183200i
$848$	958.339	+	4405.41i	0.0388084	+	0.178399i
$849$	−26799.1	−	30927.8i	−1.08333	−	1.25022i
$850$	−2730.66	+	8194.80i	−0.110189	+	0.330682i
$851$	−6656.79	−	13527.8i	−0.268145	−	0.544922i
$852$	−11904.1	−	11904.1i	−0.478671	−	0.478671i
$853$	−34726.6	−	2483.70i	−1.39392	−	0.0996953i	−0.645927	−	0.763399i	$-0.723529\pi$
$853$	−34726.6	−	2483.70i	−1.39392	−	0.0996953i	−0.747996	+	0.663704i	$0.768984\pi$
$854$	16719.8	−	26016.4i	0.669951	−	1.04246i
$855$	274.219	−	143.380i	0.0109685	−	0.00573509i
$856$	5832.82	+	2663.76i	0.232899	+	0.106362i
$857$	10141.0	−	13546.8i	0.404212	−	0.539964i	−0.551536	−	0.834151i	$-0.685958\pi$
$857$	10141.0	−	13546.8i	0.404212	−	0.539964i	0.955748	+	0.294187i	$0.0950490\pi$
$858$	3621.06	+	6631.48i	0.144081	+	0.263864i
$859$	12407.6	+	19306.7i	0.492833	+	0.766863i	0.995207	−	0.0977874i	$-0.0311765\pi$
$859$	12407.6	+	19306.7i	0.492833	+	0.766863i	−0.502375	+	0.864650i	$0.667540\pi$
$860$	−5915.60	+	1621.76i	−0.234559	+	0.0643041i
$861$	−8875.58	−	30227.4i	−0.351311	−	1.19646i
$862$	−1465.95	−	20496.7i	−0.0579240	−	0.809884i
$863$	1026.74	+	14355.7i	0.0404989	+	0.566249i	0.976676	+	0.214720i	$0.0688838\pi$
$863$	1026.74	+	14355.7i	0.0404989	+	0.566249i	−0.936177	+	0.351529i	$0.885662\pi$
$864$	1321.75	+	4501.47i	0.0520450	+	0.177249i
$865$	−9081.51	+	2489.69i	−0.356972	+	0.0978636i
$866$	5054.14	+	7864.39i	0.198322	+	0.308595i
$867$	8767.15	+	16055.8i	0.343423	+	0.628933i
$868$	61.4190	−	82.0461i	0.00240172	−	0.00320833i
$869$	−40322.4	−	18414.6i	−1.57404	−	0.718841i
$870$	20302.0	−	10615.3i	0.791153	−	0.413669i
$871$	7922.24	−	12327.2i	0.308192	−	0.479555i
$872$	−10084.3	−	721.241i	−0.391624	−	0.0280095i
$873$	2447.88	+	2447.88i	0.0949004	+	0.0949004i
$874$	1228.41	+	1795.21i	0.0475419	+	0.0694782i
$875$	34229.1	+	17927.7i	1.32246	+	0.692648i
$876$	11463.7	+	13229.8i	0.442148	+	0.510266i
$877$	−4526.05	−	20805.9i	−0.174269	−	0.801102i	−0.978412	−	0.206666i	$-0.933739\pi$
$877$	−4526.05	−	20805.9i	−0.174269	−	0.801102i	0.804143	−	0.594437i	$-0.202625\pi$
$878$	7002.35	+	9354.04i	0.269155	+	0.359548i
$879$	4566.58	−	9999.42i	0.175230	−	0.383700i
$880$	−5044.37	+	4865.73i	−0.193234	+	0.186391i
$881$	11188.1	−	38103.2i	0.427851	−	1.45713i	−0.410431	−	0.911892i	$-0.634622\pi$
$881$	11188.1	−	38103.2i	0.427851	−	1.45713i	0.838282	−	0.545236i	$-0.183560\pi$
$882$	−2311.81	−	502.904i	−0.0882570	−	0.0191991i
$883$	38006.5	+	14175.7i	1.44849	+	0.540260i	0.945956	−	0.324295i	$-0.105127\pi$
$883$	38006.5	+	14175.7i	1.44849	+	0.540260i	0.502538	+	0.864555i	$0.332400\pi$
$884$	−2599.59	+	763.309i	−0.0989069	+	0.0290417i
$885$	21211.4	−	17720.7i	0.805666	−	0.673077i
$886$	16651.9	−	19217.4i	0.631414	−	0.728691i
$887$	2065.03	+	1127.59i	0.0781703	+	0.0426842i	0.517859	−	0.855466i	$-0.326729\pi$
$887$	2065.03	+	1127.59i	0.0781703	+	0.0426842i	−0.439688	+	0.898150i	$0.644911\pi$
$888$	−1879.58	+	5039.35i	−0.0710299	+	0.190439i
$889$	−45875.8	+	29482.6i	−1.73074	+	1.11228i
$890$	1450.08	+	694.084i	0.0546145	+	0.0261413i
$891$	−25026.5	+	3598.27i	−0.940987	+	0.135293i
$892$	−2399.38	+	894.922i	−0.0900641	+	0.0335922i
$893$	4102.74	−	3071.27i	0.153744	−	0.115091i
$894$	−15302.9	−	9834.56i	−0.572488	−	0.367916i
$895$	10862.8	−	45933.2i	0.405700	−	1.71551i
$896$			3539.00i			0.131953i
$897$	−9183.84	+	5364.84i	−0.341850	+	0.199695i
$898$	17129.5	−	17129.5i	0.636548	−	0.636548i
$899$	145.886	−	126.411i	0.00541219	−	0.00468969i
$900$	−1093.11	+	880.252i	−0.0404854	+	0.0326019i
$901$	1385.54	−	9636.65i	0.0512309	−	0.356319i
$902$	6343.60	+	17007.8i	0.234167	+	0.627826i
$903$	−14932.0	−	11178.0i	−0.550285	−	0.411938i
$904$	8880.92	+	2607.67i	0.326742	+	0.0959401i
$905$	1437.68	+	565.950i	0.0528069	+	0.0207876i
$906$	2382.94	+	5217.90i	0.0873816	+	0.191339i
$907$	6116.76	−	11202.0i	0.223929	−	0.410095i	−0.741426	−	0.671034i	$-0.765850\pi$
$907$	6116.76	−	11202.0i	0.223929	−	0.410095i	0.965355	+	0.260939i	$0.0840321\pi$
$908$	2997.53	−	214.388i	0.109556	−	0.00783557i
$909$	−1071.11	−	928.122i	−0.0390830	−	0.0338656i
$910$	1508.34	+	12025.6i	0.0549460	+	0.438071i
$911$	−28474.5	+	13003.8i	−1.03557	+	0.472927i	−0.859330	−	0.511421i	$-0.829119\pi$
$911$	−28474.5	+	13003.8i	−1.03557	+	0.472927i	−0.176236	+	0.984348i	$0.556392\pi$
$912$	164.948	−	758.256i	0.00598902	−	0.0275311i
$913$	−16224.0	+	8858.98i	−0.588101	+	0.321128i
$914$	−3058.77	−	21274.2i	−0.110695	−	0.769901i
$915$	17091.2	−	25569.2i	0.617507	−	0.923817i
$916$	8733.04	+	1255.62i	0.315008	+	0.0452914i
$917$	−26963.1	+	5865.47i	−0.970993	+	0.211227i
$918$	722.742	−	10105.3i	0.0259848	−	0.363315i
$919$	−545.093			−0.0195658			−0.00978289	−	0.999952i	$-0.503114\pi$
$919$	−545.093			−0.0195658			−0.00978289	+	0.999952i	$0.503114\pi$
$920$	−7051.65	−	6900.01i	−0.252702	−	0.247268i
$921$	51233.6			1.83301
$922$	−1490.99	+	20846.7i	−0.0532571	+	0.744631i
$923$	16391.0	−	3565.65i	0.584526	−	0.127156i
$924$	−21095.6	−	3033.08i	−0.751075	−	0.107988i
$925$	−17075.0	+	603.881i	−0.606944	+	0.0214654i
$926$	4214.31	+	29311.2i	0.149558	+	1.04020i
$927$	3524.36	−	1924.45i	0.124871	−	0.0681846i
$928$	−1416.88	+	6513.28i	−0.0501199	+	0.230398i
$929$	−31484.3	+	14378.4i	−1.11191	+	0.507794i	−0.884751	−	0.466063i	$-0.845672\pi$
$929$	−31484.3	+	14378.4i	−1.11191	+	0.507794i	−0.227162	+	0.973857i	$0.572945\pi$
$930$	62.5412	−	80.4800i	0.00220517	−	0.00283768i
$931$	3140.49	+	2721.25i	0.110554	+	0.0957953i
$932$	−10397.8	+	743.668i	−0.365443	+	0.0261370i
$933$	11715.1	−	21454.6i	0.411077	−	0.752832i
$934$	2611.36	+	5718.08i	0.0914842	+	0.200322i
$935$	13878.2	−	6038.07i	0.485416	−	0.211193i
$936$	−422.382	−	124.023i	−0.0147500	−	0.00433099i
$937$	37498.8	+	28071.3i	1.30740	+	0.978707i	0.999629	+	0.0272459i	$0.00867371\pi$
$937$	37498.8	+	28071.3i	1.30740	+	0.978707i	0.307770	+	0.951461i	$0.400417\pi$
$938$	14444.4	+	38727.1i	0.502802	+	1.34806i
$939$	5100.32	−	35473.5i	0.177255	−	1.23284i
$940$	−15535.9	+	17289.6i	−0.539068	+	0.599921i
$941$	436.657	−	378.366i	0.0151271	−	0.0131077i	−0.647264	−	0.762266i	$-0.724087\pi$
$941$	436.657	−	378.366i	0.0151271	−	0.0131077i	0.662392	+	0.749158i	$0.269542\pi$
$942$	−12759.9	+	12759.9i	−0.441339	+	0.441339i
$943$	−23673.6	+	9617.65i	−0.817516	+	0.332125i
$944$			8041.76i			0.277264i
$945$	−44103.3	−	10430.0i	−1.51818	−	0.359034i
$946$	9041.40	+	5810.55i	0.310741	+	0.199701i
$947$	−36860.1	+	27593.1i	−1.26483	+	0.946838i	−0.999848	−	0.0174165i	$-0.994456\pi$
$947$	−36860.1	+	27593.1i	−1.26483	+	0.946838i	−0.264979	+	0.964254i	$0.585365\pi$
$948$	−20856.6	+	7779.10i	−0.714547	+	0.266512i
$949$	−17265.0	+	2482.34i	−0.590565	+	0.0849105i
$950$	2426.06	−	436.837i	0.0828546	−	0.0149188i
$951$	−12261.1	+	7879.75i	−0.418081	+	0.268684i
$952$	2670.70	−	7160.42i	0.0909221	−	0.243772i
$953$	24570.3	+	13416.4i	0.835161	+	0.456033i	0.839111	−	0.543960i	$-0.183076\pi$
$953$	24570.3	+	13416.4i	0.835161	+	0.456033i	−0.00395010	+	0.999992i	$0.501257\pi$
$954$	1035.90	−	1195.49i	0.0351557	−	0.0405718i
$955$	44128.6	+	3956.71i	1.49525	+	0.134069i
$956$	19403.8	−	5697.48i	0.656448	−	0.192751i
$957$	−37610.6	−	14028.0i	−1.27041	−	0.473837i
$958$	−28778.6	−	6260.40i	−0.970558	−	0.211132i
$959$	19044.4	−	64859.1i	0.641266	−	2.18395i
$960$	−63.4323	+	3518.92i	−0.00213257	+	0.118305i
$961$	−12375.3	+	27098.1i	−0.415403	+	0.909606i
$962$	−3211.60	−	4290.20i	−0.107636	−	0.143785i
$963$	−478.242	−	2198.44i	−0.0160033	−	0.0735658i
$964$	3417.57	+	3944.08i	0.114183	+	0.131774i
$965$	6866.06	−	42324.4i	0.229043	−	1.41189i
$966$	3409.95	−	29806.7i	0.113575	−	0.992768i
$967$	26595.0	+	26595.0i	0.884423	+	0.884423i	0.993980	−	0.109557i	$-0.0349434\pi$
$967$	26595.0	+	26595.0i	0.884423	+	0.884423i	−0.109557	+	0.993980i	$0.534943\pi$
$968$	1628.10	+	116.444i	0.0540589	+	0.00386637i
$969$	−905.956	+	1409.69i	−0.0300346	+	0.0467347i
$970$	12778.2	+	24438.6i	0.422971	+	0.808944i
$971$	−27393.8	−	12510.3i	−0.905364	−	0.413466i	−0.0923610	−	0.995726i	$-0.529441\pi$
$971$	−27393.8	−	12510.3i	−0.905364	−	0.413466i	−0.813003	+	0.582260i	$0.802169\pi$
$972$	1880.04	−	2511.44i	0.0620395	−	0.0828750i
$973$	16226.9	+	29717.4i	0.534647	+	0.979133i
$974$	7290.10	+	11343.6i	0.239825	+	0.373175i
$975$	1284.24	+	11984.4i	0.0421831	+	0.393650i
$976$	2521.03	+	8585.84i	0.0826806	+	0.281584i
$977$	2814.04	+	39345.4i	0.0921485	+	1.28841i	0.807595	+	0.589737i	$0.200769\pi$
$977$	2814.04	+	39345.4i	0.0921485	+	1.28841i	−0.715446	+	0.698668i	$0.753777\pi$
$978$	−2199.23	−	30749.3i	−0.0719057	−	1.00537i
$979$	−793.595	−	2702.73i	−0.0259074	−	0.0882327i
$980$	−16376.2	−	9329.12i	−0.533795	−	0.304090i
$981$	1917.80	+	2984.16i	0.0624166	+	0.0971221i
$982$	−7770.46	−	14230.5i	−0.252510	−	0.462438i
$983$	−6428.56	+	8587.54i	−0.208585	+	0.278637i	−0.892618	−	0.450814i	$-0.851134\pi$
$983$	−6428.56	+	8587.54i	−0.208585	+	0.278637i	0.684033	+	0.729451i	$0.260225\pi$
$984$	8291.73	+	3786.71i	0.268629	+	0.122679i
$985$	−1978.27	+	6314.08i	−0.0639928	+	0.204247i
$986$	7782.00	−	12109.0i	0.251348	−	0.391106i
$987$	−70503.0	−	5042.48i	−2.27369	−	0.162618i
$988$	546.734	+	546.734i	0.0176052	+	0.0176052i
$989$	−7808.29	+	12958.3i	−0.251051	+	0.416635i
$990$	2427.37	+	393.779i	0.0779261	+	0.0126415i
$991$	−13995.5	−	16151.7i	−0.448620	−	0.517735i	0.485722	−	0.874113i	$-0.338557\pi$
$991$	−13995.5	−	16151.7i	−0.448620	−	0.517735i	−0.934342	+	0.356379i	$0.884011\pi$
$992$	6.30357	+	28.9771i	0.000201753	+	0.000927442i
$993$	−4491.14	−	5999.46i	−0.143527	−	0.191729i
$994$	−19655.7	+	43039.9i	−0.627203	+	1.37338i
$995$	3268.51	+	3388.51i	0.104140	+	0.107963i
$996$	−2615.21	+	8906.58i	−0.0831988	+	0.283349i
$997$	39974.6	+	8695.95i	1.26982	+	0.276232i	0.796489	−	0.604653i	$-0.206688\pi$
$997$	39974.6	+	8695.95i	1.26982	+	0.276232i	0.473330	+	0.880885i	$0.343052\pi$
$998$	−12325.7	−	4597.24i	−0.390945	−	0.145815i
$999$	19227.7	−	5645.76i	0.608946	−	0.178803i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.4.l.a.217.5	yes	720
5.3	odd	4	inner	230.4.l.a.33.23	yes	720
23.7	odd	22	inner	230.4.l.a.7.23	✓	720
115.53	even	44	inner	230.4.l.a.53.5	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.l.a.7.23	✓	720	23.7	odd	22	inner
230.4.l.a.33.23	yes	720	5.3	odd	4	inner
230.4.l.a.53.5	yes	720	115.53	even	44	inner
230.4.l.a.217.5	yes	720	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142678 + 1.99490i) q^{2} +(-4.80624 + 1.04553i) q^{3} +(-3.95929 - 0.569259i) q^{4} +(2.17927 + 10.9659i) q^{5} +(-1.39999 - 9.73716i) q^{6} +(-24.2664 + 13.2505i) q^{7} +(1.70052 - 7.81717i) q^{8} +(-2.55328 + 1.16604i) q^{9} +(-22.1868 + 2.78283i) q^{10} +(29.6099 + 25.6571i) q^{11} +(19.6244 - 1.40357i) q^{12} +(-9.39512 + 17.2059i) q^{13} +(-22.9711 - 50.2997i) q^{14} +(-21.9393 - 50.4262i) q^{15} +(15.3519 + 4.50772i) q^{16} +(-27.6596 - 20.7057i) q^{17} +(-1.96185 - 5.25992i) q^{18} +(-1.40327 + 9.75994i) q^{19} +(-2.38590 - 44.6577i) q^{20} +(102.776 - 89.0562i) q^{21} +(-55.4082 + 55.4082i) q^{22} +(-80.2175 - 75.7110i) q^{23} +39.3492i q^{24} +(-115.502 + 47.7952i) q^{25} +(-32.9836 - 21.1973i) q^{26} +(117.367 - 87.8599i) q^{27} +(103.621 - 38.6485i) q^{28} +(206.180 - 29.6442i) q^{29} +(103.726 - 36.5720i) q^{30} +(0.779599 - 0.501018i) q^{31} +(-11.1829 + 29.9824i) q^{32} +(-169.137 - 92.3560i) q^{33} +(45.2524 - 52.2240i) q^{34} +(-198.186 - 237.227i) q^{35} +(10.7729 - 3.16322i) q^{36} +(128.068 + 47.7667i) q^{37} +(-19.2699 - 4.19192i) q^{38} +(27.1659 - 92.5184i) q^{39} +(89.4282 + 1.61204i) q^{40} +(96.2335 - 210.722i) q^{41} +(162.995 + 217.735i) q^{42} +(-29.1550 - 134.023i) q^{43} +(-102.628 - 118.440i) q^{44} +(-18.3510 - 25.4579i) q^{45} +(162.482 - 149.224i) q^{46} +(-367.524 - 367.524i) q^{47} +(-78.4978 - 5.61427i) q^{48} +(227.844 - 354.533i) q^{49} +(-78.8673 - 237.234i) q^{50} +(154.587 + 70.5976i) q^{51} +(46.9926 - 62.7747i) q^{52} +(135.042 + 247.310i) q^{53} +(158.526 + 246.672i) q^{54} +(-216.825 + 380.612i) q^{55} +(62.3156 + 212.228i) q^{56} +(-3.45990 - 48.3758i) q^{57} +(29.7200 + 415.539i) q^{58} +(141.602 + 482.251i) q^{59} +(58.1583 + 212.141i) q^{60} +(302.364 + 470.487i) q^{61} +(0.888251 + 1.62671i) q^{62} +(46.5083 - 62.1279i) q^{63} +(-58.2164 - 26.5866i) q^{64} +(-209.152 - 65.5297i) q^{65} +(208.374 - 324.236i) q^{66} +(-745.573 - 53.3244i) q^{67} +(97.7254 + 97.7254i) q^{68} +(464.703 + 280.015i) q^{69} +(501.521 - 361.515i) q^{70} +(-560.344 - 646.671i) q^{71} +(4.77326 + 21.9423i) q^{72} +(533.209 + 712.284i) q^{73} +(-113.562 + 248.667i) q^{74} +(505.157 - 350.476i) q^{75} +(11.1119 - 37.8436i) q^{76} +(-1058.49 - 230.261i) q^{77} +(180.689 + 67.3937i) q^{78} +(-1085.58 + 318.756i) q^{79} +(-15.9753 + 178.171i) q^{80} +(-422.604 + 487.711i) q^{81} +(406.640 + 222.042i) q^{82} +(-164.879 + 442.059i) q^{83} +(-457.617 + 294.093i) q^{84} +(166.779 - 348.436i) q^{85} +(271.523 - 39.0391i) q^{86} +(-959.957 + 358.046i) q^{87} +(250.918 - 187.835i) q^{88} +(-60.4825 - 38.8698i) q^{89} +(53.4043 - 32.9762i) q^{90} -542.015i q^{91} +(274.505 + 345.426i) q^{92} +(-3.22311 + 3.22311i) q^{93} +(785.612 - 680.737i) q^{94} +(-110.085 + 5.88143i) q^{95} +(22.3999 - 155.795i) q^{96} +(-430.997 - 1155.55i) q^{97} +(674.751 + 505.112i) q^{98} +(-105.520 - 30.9834i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q + 16 q^{3} + 16 q^{6} + 64 q^{12} - 192 q^{13} + 1152 q^{16} + 144 q^{18} + 1660 q^{23} - 880 q^{25} - 304 q^{26} - 728 q^{27} - 352 q^{28} - 608 q^{31} - 3872 q^{33} - 688 q^{35} - 2816 q^{36} - 2376 q^{37}+ \cdots + 14352 q^{98}+O(q^{100}) \) 720 * q + 16 * q^3 + 16 * q^6 + 64 * q^12 - 192 * q^13 + 1152 * q^16 + 144 * q^18 + 1660 * q^23 - 880 * q^25 - 304 * q^26 - 728 * q^27 - 352 * q^28 - 608 * q^31 - 3872 * q^33 - 688 * q^35 - 2816 * q^36 - 2376 * q^37 + 2208 * q^41 + 256 * q^46 + 3640 * q^47 - 256 * q^48 - 272 * q^50 - 768 * q^52 + 2360 * q^55 - 3872 * q^56 - 7656 * q^57 + 2112 * q^61 + 1376 * q^62 + 10912 * q^66 + 1104 * q^70 + 22752 * q^71 - 128 * q^72 + 1296 * q^73 - 5396 * q^75 + 752 * q^77 - 6000 * q^78 - 3928 * q^81 - 80 * q^82 + 3060 * q^85 - 10472 * q^86 - 6760 * q^87 - 1104 * q^92 + 5288 * q^93 + 9392 * q^95 - 256 * q^96 + 25344 * q^97 + 14352 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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