LMFDB - Embedded newform 230.4.l.a.7.23

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			7.23
Character	$\chi$	$=$	230.7
Dual form			230.4.l.a.33.23

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.99490 - 0.142678i) q^{2} +(-1.04553 + 4.80624i) q^{3} +(3.95929 - 0.569259i) q^{4} +(9.71458 + 5.53415i) q^{5} +(-1.39999 + 9.73716i) q^{6} +(13.2505 - 24.2664i) q^{7} +(7.81717 - 1.70052i) q^{8} +(2.55328 + 1.16604i) q^{9} +(20.1693 + 9.65404i) q^{10} +(29.6099 - 25.6571i) q^{11} +(-1.40357 + 19.6244i) q^{12} +(-17.2059 + 9.39512i) q^{13} +(22.9711 - 50.2997i) q^{14} +(-36.7554 + 40.9045i) q^{15} +(15.3519 - 4.50772i) q^{16} +(-20.7057 - 27.6596i) q^{17} +(5.25992 + 1.96185i) q^{18} +(1.40327 + 9.75994i) q^{19} +(41.6132 + 16.3812i) q^{20} +(102.776 + 89.0562i) q^{21} +(55.4082 - 55.4082i) q^{22} +(75.7110 + 80.2175i) q^{23} +39.3492i q^{24} +(63.7463 + 107.524i) q^{25} +(-32.9836 + 21.1973i) q^{26} +(-87.8599 + 117.367i) q^{27} +(38.6485 - 103.621i) q^{28} +(-206.180 - 29.6442i) q^{29} +(-67.4873 + 86.8447i) q^{30} +(0.779599 + 0.501018i) q^{31} +(29.9824 - 11.1829i) q^{32} +(92.3560 + 169.137i) q^{33} +(-45.2524 - 52.2240i) q^{34} +(263.017 - 162.408i) q^{35} +(10.7729 + 3.16322i) q^{36} +(47.7667 + 128.068i) q^{37} +(4.19192 + 19.2699i) q^{38} +(-27.1659 - 92.5184i) q^{39} +(85.3516 + 26.7416i) q^{40} +(96.2335 + 210.722i) q^{41} +(217.735 + 162.995i) q^{42} +(134.023 + 29.1550i) 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} +(5.61427 + 78.4978i) q^{48} +(-227.844 - 354.533i) q^{49} +(142.509 + 205.405i) q^{50} +(154.587 - 70.5976i) q^{51} +(-62.7747 + 46.9926i) q^{52} +(-247.310 - 135.042i) q^{53} +(-158.526 + 246.672i) q^{54} +(429.638 - 85.3825i) q^{55} +(62.3156 - 212.228i) q^{56} +(-48.3758 - 3.45990i) q^{57} +(-415.539 - 29.7200i) q^{58} +(-141.602 + 482.251i) q^{59} +(-122.240 + 182.876i) q^{60} +(302.364 - 470.487i) q^{61} +(1.62671 + 0.888251i) q^{62} +(62.1279 - 46.5083i) q^{63} +(58.2164 - 26.5866i) q^{64} +(-219.142 - 3.95027i) q^{65} +(208.374 + 324.236i) q^{66} +(-53.3244 - 745.573i) 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} +(21.9423 + 4.77326i) q^{72} +(-712.284 - 533.209i) q^{73} +(113.562 + 248.667i) q^{74} +(-583.435 + 193.960i) q^{75} +(11.1119 + 37.8436i) q^{76} +(-230.261 - 1058.49i) q^{77} +(-67.3937 - 180.689i) q^{78} +(1085.58 + 318.756i) q^{79} +(174.084 + 41.1691i) q^{80} +(-422.604 - 487.711i) q^{81} +(222.042 + 406.640i) q^{82} +(-442.059 + 164.879i) q^{83} +(457.617 + 294.093i) q^{84} +(-48.0750 - 383.290i) q^{85} +(271.523 + 39.0391i) q^{86} +(358.046 - 959.957i) q^{87} +(187.835 - 250.918i) q^{88} +(60.4825 - 38.8698i) q^{89} +(40.2408 + 48.1677i) q^{90} +542.015i q^{91} +(345.426 + 274.505i) q^{92} +(-3.22311 + 3.22311i) q^{93} +(-785.612 - 680.737i) q^{94} +(-40.3808 + 102.580i) q^{95} +(22.3999 + 155.795i) q^{96} +(-1155.55 - 430.997i) q^{97} +(-505.112 - 674.751i) 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 $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{19}{22}\right)$

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 $

$2$	1.99490	−	0.142678i	0.705305	−	0.0504444i
$2$	1.99490	−	0.142678i	0.705305	−	0.0504444i
$3$	−1.04553	+	4.80624i	−0.201213	+	0.924961i	0.760165	+	0.649730i	$0.225118\pi$
$3$	−1.04553	+	4.80624i	−0.201213	+	0.924961i	−0.961378	+	0.275231i	$0.911246\pi$
$4$	3.95929	−	0.569259i	0.494911	−	0.0711574i
$5$	9.71458	+	5.53415i	0.868899	+	0.494990i
$5$	9.71458	+	5.53415i	0.868899	+	0.494990i
$6$	−1.39999	+	9.73716i	−0.0952574	+	0.662530i
$7$	13.2505	−	24.2664i	0.715458	−	1.31026i	−0.226328	−	0.974051i	$-0.572672\pi$
$7$	13.2505	−	24.2664i	0.715458	−	1.31026i	0.941786	−	0.336212i	$-0.109146\pi$
$8$	7.81717	−	1.70052i	0.345474	−	0.0751532i
$9$	2.55328	+	1.16604i	0.0945659	+	0.0431868i
$10$	20.1693	+	9.65404i	0.637808	+	0.305288i
$11$	29.6099	−	25.6571i	0.811610	−	0.703264i	−0.146642	−	0.989190i	$-0.546846\pi$
$11$	29.6099	−	25.6571i	0.811610	−	0.703264i	0.958252	+	0.285925i	$0.0923009\pi$
$12$	−1.40357	+	19.6244i	−0.0337646	+	0.472091i
$13$	−17.2059	+	9.39512i	−0.367081	+	0.200441i	−0.652193	−	0.758053i	$-0.726151\pi$
$13$	−17.2059	+	9.39512i	−0.367081	+	0.200441i	0.285112	+	0.958494i	$0.407969\pi$
$14$	22.9711	−	50.2997i	0.438521	−	0.960227i
$15$	−36.7554	+	40.9045i	−0.632680	+	0.704099i
$16$	15.3519	−	4.50772i	0.239873	−	0.0704331i
$17$	−20.7057	−	27.6596i	−0.295404	−	0.394614i	0.628143	−	0.778098i	$-0.283815\pi$
$17$	−20.7057	−	27.6596i	−0.295404	−	0.394614i	−0.923548	+	0.383484i	$0.874724\pi$
$18$	5.25992	+	1.96185i	0.0688764	+	0.0256896i
$19$	1.40327	+	9.75994i	0.0169438	+	0.117847i	0.996538	−	0.0831392i	$-0.0264946\pi$
$19$	1.40327	+	9.75994i	0.0169438	+	0.117847i	−0.979594	+	0.200986i	$0.935586\pi$
$20$	41.6132	+	16.3812i	0.465250	+	0.183147i
$21$	102.776	+	89.0562i	1.06798	+	0.925413i
$22$	55.4082	−	55.4082i	0.536957	−	0.536957i
$23$	75.7110	+	80.2175i	0.686384	+	0.727239i
$23$	75.7110	+	80.2175i	0.686384	+	0.727239i
$24$			39.3492i			0.334671i
$25$	63.7463	+	107.524i	0.509970	+	0.860192i
$26$	−32.9836	+	21.1973i	−0.248793	+	0.159889i
$27$	−87.8599	+	117.367i	−0.626246	+	0.836567i
$28$	38.6485	−	103.621i	0.260853	−	0.699374i
$29$	−206.180	−	29.6442i	−1.32023	−	0.189821i	−0.554071	−	0.832470i	$-0.686926\pi$
$29$	−206.180	−	29.6442i	−1.32023	−	0.189821i	−0.766161	+	0.642649i	$0.777835\pi$
$30$	−67.4873	+	86.8447i	−0.410714	+	0.528520i
$31$	0.779599	+	0.501018i	0.00451678	+	0.00290276i	0.542897	−	0.839799i	$-0.317327\pi$
$31$	0.779599	+	0.501018i	0.00451678	+	0.00290276i	−0.538380	+	0.842702i	$0.680964\pi$
$32$	29.9824	−	11.1829i	0.165631	−	0.0617771i
$33$	92.3560	+	169.137i	0.487186	+	0.892214i
$34$	−45.2524	−	52.2240i	−0.228256	−	0.263422i
$35$	263.017	−	162.408i	1.27023	−	0.784342i
$36$	10.7729	+	3.16322i	0.0498747	+	0.0146445i
$37$	47.7667	+	128.068i	0.212238	+	0.569032i	0.998826	−	0.0484466i	$-0.0154271\pi$
$37$	47.7667	+	128.068i	0.212238	+	0.569032i	−0.786588	+	0.617478i	$0.788154\pi$
$38$	4.19192	+	19.2699i	0.0178952	+	0.0822630i
$39$	−27.1659	−	92.5184i	−0.111539	−	0.379867i
$40$	85.3516	+	26.7416i	0.337382	+	0.105705i
$41$	96.2335	+	210.722i	0.366565	+	0.802665i	0.999593	+	0.0285358i	$0.00908445\pi$
$41$	96.2335	+	210.722i	0.366565	+	0.802665i	−0.633028	+	0.774129i	$0.718188\pi$
$42$	217.735	+	162.995i	0.799936	+	0.598825i
$43$	134.023	+	29.1550i	0.475310	+	0.103397i	0.443838	−	0.896107i	$-0.353617\pi$
$43$	134.023	+	29.1550i	0.475310	+	0.103397i	0.0314726	+	0.999505i	$0.489980\pi$
$44$	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	$-0.548660\pi$
$48$	5.61427	+	78.4978i	0.0168823	+	0.236045i
$49$	−227.844	−	354.533i	−0.664270	−	1.03362i
$50$	142.509	+	205.405i	0.403077	+	0.580973i
$51$	154.587	−	70.5976i	0.424442	−	0.193836i
$52$	−62.7747	+	46.9926i	−0.167409	+	0.125321i
$53$	−247.310	−	135.042i	−0.640957	−	0.349989i	0.125679	−	0.992071i	$-0.459889\pi$
$53$	−247.310	−	135.042i	−0.640957	−	0.349989i	−0.766636	+	0.642082i	$0.778071\pi$
$54$	−158.526	+	246.672i	−0.399495	+	0.621626i
$55$	429.638	−	85.3825i	1.05332	−	0.209327i
$56$	62.3156	−	212.228i	0.148701	−	0.506430i
$57$	−48.3758	−	3.45990i	−0.112413	−	0.00803992i
$58$	−415.539	−	29.7200i	−0.940741	−	0.0672832i
$59$	−141.602	+	482.251i	−0.312457	+	1.06413i	0.642228	+	0.766513i	$0.278010\pi$
$59$	−141.602	+	482.251i	−0.312457	+	1.06413i	−0.954685	+	0.297617i	$0.903808\pi$
$60$	−122.240	+	182.876i	−0.263018	+	0.393486i
$61$	302.364	−	470.487i	0.634651	−	0.987537i	−0.363777	−	0.931486i	$-0.618513\pi$
$61$	302.364	−	470.487i	0.634651	−	0.987537i	0.998428	−	0.0560505i	$-0.0178508\pi$
$62$	1.62671	+	0.888251i	0.00333214	+	0.00181948i
$63$	62.1279	−	46.5083i	0.124244	−	0.0930079i
$64$	58.2164	−	26.5866i	0.113704	−	0.0519269i
$65$	−219.142	−	3.95027i	−0.418172	−	0.00753800i
$66$	208.374	+	324.236i	0.388622	+	0.604707i
$67$	−53.3244	−	745.573i	−0.0972331	−	1.35950i	−0.778584	−	0.627540i	$-0.784062\pi$
$67$	−53.3244	−	745.573i	−0.0972331	−	1.35950i	0.681351	−	0.731957i	$-0.261393\pi$
$68$	−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	0.0599446	+	0.998202i	$0.480908\pi$
$71$	−560.344	+	646.671i	−0.936628	+	1.08093i	−0.996572	+	0.0827245i	$0.973638\pi$
$72$	21.9423	+	4.77326i	0.0359157	+	0.00781297i
$73$	−712.284	−	533.209i	−1.14201	−	0.854896i	−0.150977	−	0.988537i	$-0.548242\pi$
$73$	−712.284	−	533.209i	−1.14201	−	0.854896i	−0.991030	+	0.133641i	$0.957333\pi$
$74$	113.562	+	248.667i	0.178397	+	0.390635i
$75$	−583.435	+	193.960i	−0.898257	+	0.298621i
$76$	11.1119	+	37.8436i	0.0167713	+	0.0571178i
$77$	−230.261	−	1058.49i	−0.340789	−	1.56658i
$78$	−67.3937	−	180.689i	−0.0978312	−	0.262295i
$79$	1085.58	+	318.756i	1.54605	+	0.453960i	0.939916	−	0.341405i	$-0.110903\pi$
$79$	1085.58	+	318.756i	1.54605	+	0.453960i	0.606130	+	0.795365i	$0.292721\pi$
$80$	174.084	+	41.1691i	0.243289	+	0.0575355i
$81$	−422.604	−	487.711i	−0.579703	−	0.669013i
$82$	222.042	+	406.640i	0.299030	+	0.547632i
$83$	−442.059	+	164.879i	−0.584606	+	0.218047i	−0.624326	−	0.781164i	$-0.714626\pi$
$83$	−442.059	+	164.879i	−0.584606	+	0.218047i	0.0397199	+	0.999211i	$0.487353\pi$
$84$	457.617	+	294.093i	0.594406	+	0.382002i
$85$	−48.0750	−	383.290i	−0.0613467	−	0.489102i
$86$	271.523	+	39.0391i	0.340455	+	0.0489500i
$87$	358.046	−	959.957i	0.441224	−	1.18297i
$88$	187.835	−	250.918i	0.227537	−	0.303954i
$89$	60.4825	−	38.8698i	0.0720352	−	0.0462942i	−0.504127	−	0.863629i	$-0.668186\pi$
$89$	60.4825	−	38.8698i	0.0720352	−	0.0462942i	0.576163	+	0.817335i	$0.304549\pi$
$90$	40.2408	+	48.1677i	0.0471305	+	0.0564147i
$91$			542.015i			0.624380i
$92$	345.426	+	274.505i	0.391447	+	0.311077i
$93$	−3.22311	+	3.22311i	−0.00359377	+	0.00359377i
$94$	−785.612	−	680.737i	−0.862018	−	0.746943i
$95$	−40.3808	+	102.580i	−0.0436104	+	0.110784i
$96$	22.3999	+	155.795i	0.0238144	+	0.165632i
$97$	−1155.55	−	430.997i	−1.20957	−	0.451146i	−0.337872	−	0.941192i	$-0.609707\pi$
$97$	−1155.55	−	430.997i	−1.20957	−	0.451146i	−0.871697	+	0.490046i	$0.836980\pi$
$98$	−505.112	−	674.751i	−0.520653	−	0.695511i
$99$	105.520	−	30.9834i	0.107122	−	0.0314540i
$100$	313.599	+	389.430i	0.313599	+	0.389430i
$101$	209.752	−	459.292i	0.206644	−	0.452488i	−0.777725	−	0.628605i	$-0.783626\pi$
$101$	209.752	−	459.292i	0.206644	−	0.452488i	0.984369	+	0.176117i	$0.0563536\pi$
$102$	298.314	−	162.892i	0.289583	−	0.158124i
$103$	−102.056	+	1426.93i	−0.0976302	+	1.36505i	0.678558	+	0.734547i	$0.262605\pi$
$103$	−102.056	+	1426.93i	−0.0976302	+	1.36505i	−0.776188	+	0.630502i	$0.782849\pi$
$104$	−118.525	+	102.702i	−0.111753	+	0.0968345i
$105$	505.579	+	1433.92i	0.469900	+	1.33273i
$106$	−512.628	−	234.109i	−0.469725	−	0.214516i
$107$	783.218	−	170.379i	0.707632	−	0.153936i	0.155675	−	0.987808i	$-0.450245\pi$
$107$	783.218	−	170.379i	0.707632	−	0.153936i	0.551957	+	0.833873i	$0.313881\pi$
$108$	−281.050	+	514.705i	−0.250408	+	0.458588i
$109$	179.851	−	1250.89i	0.158042	−	1.09921i	−0.744194	−	0.667964i	$-0.767166\pi$
$109$	179.851	−	1250.89i	0.158042	−	1.09921i	0.902236	−	0.431243i	$-0.141925\pi$
$110$	844.904	−	231.630i	0.732350	−	0.200773i
$111$	−665.465	+	95.6794i	−0.569037	+	0.0818152i
$112$	94.0334	−	432.265i	0.0793333	−	0.364689i
$113$	−1154.03	+	82.5380i	−0.960728	+	0.0687126i	−0.542885	−	0.839807i	$-0.682668\pi$
$113$	−1154.03	+	82.5380i	−0.960728	+	0.0687126i	−0.417843	+	0.908519i	$0.637214\pi$
$114$	−96.9987			−0.0796909
$115$	291.565	+	1198.28i	0.236423	+	0.971650i
$116$	−833.202			−0.666904
$117$	−54.8865	+	3.92556i	−0.0433697	+	0.00310187i
$118$	−213.675	+	982.247i	−0.166698	+	0.766298i
$119$	−945.560	+	135.951i	−0.728398	+	0.104728i
$120$	−217.764	+	382.261i	−0.165659	+	0.290796i
$121$	29.0367	−	201.955i	0.0218157	−	0.151732i
$122$	536.059	−	981.718i	0.397807	−	0.728529i
$123$	−1113.40	+	242.204i	−0.816191	+	0.177551i
$124$	3.37187	+	1.53988i	0.00244195	+	0.00111520i
$125$	24.2147	+	1397.33i	0.0173266	+	0.999850i
$126$	117.303	−	101.644i	0.0829382	−	0.0718664i
$127$	−140.707	+	1967.34i	−0.0983126	+	1.37459i	0.673711	+	0.738995i	$0.264699\pi$
$127$	−140.707	+	1967.34i	−0.0983126	+	1.37459i	−0.772023	+	0.635594i	$0.780755\pi$
$128$	112.343	−	61.3439i	0.0775766	−	0.0423600i
$129$	−280.251	+	613.665i	−0.191277	+	0.418838i
$130$	−437.731	+	23.3864i	−0.295319	+	0.0157779i
$131$	957.595	−	281.175i	0.638668	−	0.187530i	0.0536623	−	0.998559i	$-0.482911\pi$
$131$	957.595	−	281.175i	0.638668	−	0.187530i	0.585005	+	0.811029i	$0.301092\pi$
$132$	461.947	+	617.089i	0.304601	+	0.406899i
$133$	255.433	+	95.2715i	0.166533	+	0.0621134i
$134$	−212.754	−	1479.74i	−0.137158	−	0.953955i
$135$	−1503.05	+	653.943i	−0.958237	+	0.416907i
$136$	−208.896	−	181.009i	−0.131711	−	0.114128i
$137$	1728.80	−	1728.80i	1.07811	−	1.07811i	0.0814321	−	0.996679i	$-0.474051\pi$
$137$	1728.80	−	1728.80i	1.07811	−	1.07811i	0.996679	−	0.0814321i	$-0.0259494\pi$
$138$	−887.085	+	624.906i	−0.547201	+	0.385475i
$139$		−	1224.63i		−	0.747279i	−0.927574	−	0.373640i	$-0.878110\pi$
$139$		−	1224.63i		−	0.747279i	0.927574	−	0.373640i	$-0.121890\pi$
$140$	948.907	−	792.745i	0.572837	−	0.478565i
$141$	2150.66	−	1382.15i	1.28453	−	0.825517i
$142$	−1025.57	+	1370.00i	−0.606082	+	0.809630i
$143$	−268.412	+	719.641i	−0.156963	+	0.420835i
$144$	44.4539	+	6.39150i	0.0257256	+	0.00369879i
$145$	−1838.90	−	1429.01i	−1.05319	−	0.818436i
$146$	−1497.02	−	962.073i	−0.848588	−	0.545355i
$147$	1942.19	−	724.399i	1.08972	−	0.406445i
$148$	262.026	+	479.864i	0.145530	+	0.266518i
$149$	−1210.93	−	1397.49i	−0.665794	−	0.768368i	0.317918	−	0.948118i	$-0.397016\pi$
$149$	−1210.93	−	1397.49i	−0.665794	−	0.768368i	−0.983712	+	0.179751i	$0.942471\pi$
$150$	−1136.22	+	470.175i	−0.618481	+	0.255931i
$151$	−559.495	−	164.283i	−0.301530	−	0.0885373i	0.127468	−	0.991843i	$-0.459315\pi$
$151$	−559.495	−	164.283i	−0.301530	−	0.0885373i	−0.428998	+	0.903305i	$0.641133\pi$
$152$	27.5666	+	73.9089i	0.0147102	+	0.0394395i
$153$	−20.6152	−	94.7665i	−0.0108931	−	0.0500746i
$154$	−610.374	−	2078.74i	−0.319385	−	1.08773i
$155$	4.80077	+	9.18160i	0.00248779	+	0.00475796i
$156$	−160.224	−	350.842i	−0.0822322	−	0.180063i
$157$	−1468.49	−	1099.30i	−0.746487	−	0.558813i	0.156913	−	0.987612i	$-0.449846\pi$
$157$	−1468.49	−	1099.30i	−0.746487	−	0.558813i	−0.903400	+	0.428800i	$0.858937\pi$
$158$	2211.11	+	480.999i	1.11333	+	0.242191i
$159$	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
$163$	−223.561	−	3125.79i	−0.107427	−	1.50203i	−0.710134	−	0.704067i	$-0.751366\pi$
$163$	−223.561	−	3125.79i	−0.107427	−	1.50203i	0.602706	−	0.797963i	$-0.294089\pi$
$164$	500.971	+	779.527i	0.238532	+	0.371163i
$165$	−38.8320	+	2154.21i	−0.0183216	+	1.01640i
$166$	−858.340	+	391.991i	−0.401326	+	0.183280i
$167$	−1056.94	+	791.214i	−0.489750	+	0.366623i	−0.815428	−	0.578858i	$-0.803498\pi$
$167$	−1056.94	+	791.214i	−0.489750	+	0.366623i	0.325678	+	0.945481i	$0.394408\pi$
$168$	954.863	+	521.395i	0.438508	+	0.239443i
$169$	−980.014	+	1524.93i	−0.446069	+	0.694097i
$170$	−150.592	−	757.768i	−0.0679406	−	0.341872i
$171$	−7.79758	+	26.5561i	−0.00348711	+	0.0118760i
$172$	547.233	+	39.1389i	0.242594	+	0.0173506i
$173$	−840.100	−	60.0851i	−0.369200	−	0.0264057i	−0.114493	−	0.993424i	$-0.536524\pi$
$173$	−840.100	−	60.0851i	−0.369200	−	0.0264057i	−0.254707	+	0.967018i	$0.581979\pi$
$174$	577.301	−	1966.11i	0.251524	−	0.856611i
$175$	3453.89	−	122.152i	1.49194	−	0.0527645i
$176$	338.912	−	527.358i	0.145150	−	0.225859i
$177$	−2169.76	−	1184.78i	−0.921409	−	0.503127i
$178$	115.111	−	86.1710i	0.0484715	−	0.0362853i
$179$	3840.21	−	1753.76i	1.60352	−	0.732304i	0.605542	−	0.795813i	$-0.292956\pi$
$179$	3840.21	−	1753.76i	1.60352	−	0.732304i	0.997981	+	0.0635090i	$0.0202292\pi$
$180$	87.1489	+	90.3485i	0.0360872	+	0.0374121i
$181$	74.7139	+	116.257i	0.0306820	+	0.0477421i	0.856256	−	0.516552i	$-0.172785\pi$
$181$	74.7139	+	116.257i	0.0306820	+	0.0477421i	−0.825574	+	0.564294i	$0.809148\pi$
$182$	77.3338	+	1081.27i	0.0314965	+	0.440378i
$183$	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
$187$	−1322.76	−	287.749i	−0.517271	−	0.112526i
$188$	−1664.35	−	1245.91i	−0.645665	−	0.483339i
$189$	1683.89	+	3687.22i	0.648071	+	1.41908i
$190$	−65.9200	+	210.398i	−0.0251702	+	0.0803362i
$191$	1116.45	+	3802.29i	0.422952	+	1.44044i	0.845439	+	0.534073i	$0.179339\pi$
$191$	1116.45	+	3802.29i	0.422952	+	1.44044i	−0.422487	+	0.906369i	$0.638843\pi$
$192$	66.9141	+	307.599i	0.0251516	+	0.115620i
$193$	1340.23	+	3593.29i	0.499854	+	1.34016i	0.904807	+	0.425822i	$0.140015\pi$
$193$	1340.23	+	3593.29i	0.499854	+	1.34016i	−0.404953	+	0.914337i	$0.632712\pi$
$194$	−2366.70	−	694.927i	−0.875873	−	0.257179i
$195$	248.106	−	1049.12i	0.0911141	−	0.385276i
$196$	−1103.92	−	1273.99i	−0.402304	−	0.464284i
$197$	283.628	+	519.427i	0.102577	+	0.187856i	0.923927	−	0.382569i	$-0.124960\pi$
$197$	283.628	+	519.427i	0.102577	+	0.187856i	−0.821350	+	0.570425i	$0.806779\pi$
$198$	206.081	−	76.8642i	0.0739673	−	0.0275884i
$199$	−354.248	−	227.662i	−0.126191	−	0.0810980i	0.476023	−	0.879433i	$-0.342078\pi$
$199$	−354.248	−	227.662i	−0.126191	−	0.0810980i	−0.602214	+	0.798335i	$0.705714\pi$
$200$	681.163	+	732.132i	0.240827	+	0.258848i
$201$	3639.15	+	523.231i	1.27705	+	0.183611i
$202$	352.904	−	946.172i	0.122922	−	0.329566i
$203$	−3451.34	+	4610.46i	−1.19329	+	1.59404i
$204$	571.867	−	367.516i	0.196268	−	0.126134i
$205$	−231.299	+	2579.65i	−0.0788031	+	0.878880i
$206$			2861.16i			0.967701i
$207$	99.7743	+	293.100i	0.0335014	+	0.0984148i
$208$	−221.792	+	221.792i	−0.0739351	+	0.0739351i
$209$	291.962	+	252.987i	0.0966290	+	0.0837295i
$210$	1213.17	+	2788.41i	0.398651	+	0.916278i
$211$	203.677	+	1416.61i	0.0664536	+	0.462195i	0.995693	+	0.0927157i	$0.0295548\pi$
$211$	203.677	+	1416.61i	0.0664536	+	0.462195i	−0.929239	+	0.369479i	$0.879536\pi$
$212$	−1056.05	−	393.885i	−0.342121	−	0.127604i
$213$	−2522.20	−	3369.26i	−0.811353	−	1.08384i
$214$	1538.14	−	451.638i	0.491331	−	0.144268i
$215$	1140.63	+	1024.93i	0.361816	+	0.325116i
$216$	−487.231	+	1066.89i	−0.153481	+	0.336076i
$217$	22.4880	−	12.2794i	0.00703494	−	0.00384137i
$218$	180.310	−	2521.07i	0.0560190	−	0.783248i
$219$	3307.45	−	2865.92i	1.02053	−	0.884296i
$220$	1652.45	−	582.629i	0.506402	−	0.178549i
$221$	616.125	+	281.375i	0.187534	+	0.0856440i
$222$	−1313.89	+	285.819i	−0.397218	+	0.0864094i
$223$	306.820	−	561.899i	0.0921354	−	0.168733i	−0.827547	−	0.561396i	$-0.810264\pi$
$223$	306.820	−	561.899i	0.0921354	−	0.168733i	0.919682	+	0.392663i	$0.128446\pi$
$224$	125.913	−	875.743i	0.0375576	−	0.261219i
$225$	37.3845	+	348.870i	0.0110769	+	0.103369i
$226$	−2290.41	+	329.311i	−0.674140	+	0.0969267i
$227$	159.700	−	734.127i	0.0466944	−	0.214651i	−0.947888	−	0.318605i	$-0.896786\pi$
$227$	159.700	−	734.127i	0.0466944	−	0.214651i	0.994582	+	0.103954i	$0.0331494\pi$
$228$	−193.503	+	13.8396i	−0.0562064	+	0.00401996i
$229$	2205.71			0.636496			0.318248	−	0.948008i	$-0.396906\pi$
$229$	2205.71			0.636496			0.318248	+	0.948008i	$0.396906\pi$
$230$	752.613	+	2348.85i	0.215764	+	0.673384i
$231$	5328.12			1.51760
$232$	−1662.16	+	118.880i	−0.470371	+	0.0336416i
$233$	553.966	−	2546.54i	0.155758	−	0.716007i	−0.831324	−	0.555788i	$-0.812417\pi$
$233$	553.966	−	2546.54i	0.155758	−	0.716007i	0.987082	−	0.160218i	$-0.0512198\pi$
$234$	−108.933	+	15.6622i	−0.0304324	+	0.00437552i
$235$	−1536.41	−	5604.27i	−0.426486	−	1.55567i
$236$	−286.115	+	1989.98i	−0.0789175	+	0.548883i
$237$	−2667.03	+	4884.30i	−0.730980	+	1.33869i
$238$	−1866.91	+	406.120i	−0.508460	+	0.110609i
$239$	4598.87	+	2100.23i	1.24467	+	0.568422i	0.925310	−	0.379211i	$-0.123805\pi$
$239$	4598.87	+	2100.23i	1.24467	+	0.568422i	0.319361	+	0.947633i	$0.396532\pi$
$240$	−379.878	+	793.644i	−0.102171	+	0.213456i
$241$	−986.021	+	854.392i	−0.263549	+	0.228366i	−0.776604	−	0.629990i	$-0.783059\pi$
$241$	−986.021	+	854.392i	−0.263549	+	0.228366i	0.513055	+	0.858356i	$0.328514\pi$
$242$	29.1109	−	407.024i	0.00773273	−	0.108118i
$243$	−688.359	+	375.873i	−0.181721	+	0.0992273i
$244$	929.316	−	2034.92i	0.243825	−	0.533903i
$245$	−251.375	−	4705.07i	−0.0655501	−	1.22692i
$246$	−2186.56	+	642.032i	−0.566707	+	0.166400i
$247$	−115.840	−	154.744i	−0.0298410	−	0.0398630i
$248$	6.94626	+	2.59082i	0.00177858	+	0.000663376i
$249$	−330.263	−	2297.03i	−0.0840544	−	0.584611i
$250$	247.675	+	2784.09i	0.0626574	+	0.704325i
$251$	−1363.54	−	1181.51i	−0.342892	−	0.297117i	0.466342	−	0.884605i	$-0.345572\pi$
$251$	−1363.54	−	1181.51i	−0.342892	−	0.297117i	−0.809233	+	0.587487i	$0.800117\pi$
$252$	219.507	−	219.507i	0.0548715	−	0.0548715i
$253$	4299.94	+	432.704i	1.06852	+	0.107525i
$254$			3944.72i			0.974464i
$255$	1892.45	+	169.683i	0.464744	+	0.0416704i
$256$	215.361	−	138.404i	0.0525783	−	0.0337901i
$257$	−1769.83	+	2364.22i	−0.429569	+	0.573836i	−0.962142	−	0.272547i	$-0.912134\pi$
$257$	−1769.83	+	2364.22i	−0.429569	+	0.573836i	0.532574	+	0.846384i	$0.321225\pi$
$258$	−471.518	+	1264.19i	−0.113781	+	0.305058i
$259$	3740.67	+	537.827i	0.897429	+	0.129031i
$260$	−869.894	+	109.108i	−0.207494	+	0.0260254i
$261$	−491.869	−	316.105i	−0.116651	−	0.0749671i
$262$	1870.19	−	697.546i	0.440996	−	0.164483i
$263$	1642.86	+	3008.67i	0.385183	+	0.705410i	0.996283	−	0.0861436i	$-0.0274544\pi$
$263$	1642.86	+	3008.67i	0.385183	+	0.705410i	−0.611100	+	0.791554i	$0.709273\pi$
$264$	1009.59	+	1165.12i	0.235362	+	0.271623i
$265$	−1655.18	−	2680.53i	−0.383686	−	0.621372i
$266$	523.157	+	153.613i	0.120590	+	0.0354083i
$267$	123.581	+	331.333i	0.0283259	+	0.0759447i
$268$	−635.551	−	2921.58i	−0.144860	−	0.665910i
$269$	1290.58	+	4395.31i	0.292521	+	0.996234i	0.966325	+	0.257324i	$0.0828408\pi$
$269$	1290.58	+	4395.31i	0.292521	+	0.996234i	−0.673805	+	0.738910i	$0.735341\pi$
$270$	−2905.14	+	1519.01i	−0.654819	+	0.342384i
$271$	956.012	+	2093.37i	0.214294	+	0.469238i	0.986001	−	0.166740i	$-0.0533242\pi$
$271$	956.012	+	2093.37i	0.214294	+	0.469238i	−0.771707	+	0.635978i	$0.780597\pi$
$272$	−442.554	−	331.292i	−0.0986535	−	0.0738511i
$273$	−2605.05	−	566.694i	−0.577527	−	0.125633i
$274$	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	$0.932674\pi$
$278$	−174.728	−	2443.02i	−0.0376961	−	0.527060i
$279$	1.40633	+	2.18829i	0.000301773	+	0.000469567i
$280$	1779.87	−	1716.84i	0.379884	−	0.366431i
$281$	−3794.75	+	1733.00i	−0.805607	+	0.367908i	−0.775269	−	0.631631i	$-0.782386\pi$
$281$	−3794.75	+	1733.00i	−0.805607	+	0.367908i	−0.0303382	+	0.999540i	$0.509658\pi$
$282$	4093.17	−	3064.11i	0.864342	−	0.647038i
$283$	−7302.33	−	3987.38i	−1.53385	−	0.837544i	−0.533879	−	0.845561i	$-0.679266\pi$
$283$	−7302.33	−	3987.38i	−1.53385	−	0.837544i	−0.999968	+	0.00801711i	$0.997448\pi$
$284$	−1850.44	+	2879.34i	−0.386631	+	0.601610i
$285$	−450.803	−	301.330i	−0.0936956	−	0.0626290i
$286$	−432.780	+	1473.91i	−0.0894783	+	0.304735i
$287$	6388.61	+	456.922i	1.31396	+	0.0939765i
$288$	89.5931	+	6.40783i	0.0183310	+	0.00131106i
$289$	1047.83	−	3568.56i	0.213276	−	0.726351i
$290$	−3872.32	−	2588.38i	−0.784105	−	0.524120i
$291$	3279.64	−	5103.22i	0.660673	−	1.02803i
$292$	−3123.67	−	1705.65i	−0.626024	−	0.341835i
$293$	−1789.15	+	1339.34i	−0.356735	+	0.267048i	−0.762581	−	0.646893i	$-0.776068\pi$
$293$	−1789.15	+	1339.34i	−0.356735	+	0.267048i	0.405846	+	0.913942i	$0.366977\pi$
$294$	3771.12	−	1722.21i	0.748083	−	0.341638i
$295$	−4044.45	+	3901.22i	−0.798227	+	0.769959i
$296$	591.182	+	919.898i	0.116087	+	0.180635i
$297$	409.779	+	5729.46i	0.0800599	+	1.11938i
$298$	−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
$302$	−1139.58	−	247.900i	−0.217137	−	0.0472353i
$303$	1988.17	+	1488.32i	0.376954	+	0.282185i
$304$	65.5379	+	143.508i	0.0123647	+	0.0270748i
$305$	5541.09	−	2897.26i	1.04027	−	0.543924i
$306$	−54.6465	−	186.109i	−0.0102089	−	0.0347684i
$307$	−2214.12	−	10178.2i	−0.411618	−	1.89218i	−0.450209	−	0.892923i	$-0.648651\pi$
$307$	−2214.12	−	10178.2i	−0.411618	−	1.89218i	0.0385911	−	0.999255i	$-0.487713\pi$
$308$	−1514.23	−	4059.80i	−0.280134	−	0.751067i
$309$	−6751.48	−	1982.41i	−1.24297	−	0.364970i
$310$	10.8871	+	17.6315i	0.00199466	+	0.00323032i
$311$	−3254.53	−	3755.93i	−0.593400	−	0.684820i	0.377030	−	0.926201i	$-0.376945\pi$
$311$	−3254.53	−	3755.93i	−0.593400	−	0.684820i	−0.970430	+	0.241381i	$0.922400\pi$
$312$	−369.690	−	677.037i	−0.0670820	−	0.122851i
$313$	−6826.81	+	2546.27i	−1.23282	+	0.459820i	−0.879598	−	0.475718i	$-0.842188\pi$
$313$	−6826.81	+	2546.27i	−1.23282	+	0.459820i	−0.353227	+	0.935538i	$0.614916\pi$
$314$	−3086.35	−	1983.47i	−0.554690	−	0.356478i
$315$	860.931	−	107.984i	0.153993	−	0.0193150i
$316$	4479.59	+	644.068i	0.797458	+	0.114657i
$317$	−1035.53	+	2776.35i	−0.183473	+	0.491910i	−0.995828	−	0.0912535i	$-0.970913\pi$
$317$	−1035.53	+	2776.35i	−0.183473	+	0.491910i	0.812355	+	0.583164i	$0.198185\pi$
$318$	1661.16	−	2219.04i	0.292934	−	0.391314i
$319$	−6865.56	+	4412.23i	−1.20501	+	0.774411i
$320$	712.683	+	63.9013i	0.124501	+	0.0111631i
$321$			3942.47i			0.685506i
$322$	5774.08	−	1965.56i	0.999308	−	0.340175i
$323$	240.900	−	240.900i	0.0414986	−	0.0414986i
$324$	−1950.84	−	1690.42i	−0.334507	−	0.289852i
$325$	−2107.01	−	1251.14i	−0.359618	−	0.213541i
$326$	−891.966	−	6203.76i	−0.151538	−	1.05397i
$327$	5824.03	+	2172.25i	0.984923	+	0.367357i
$328$	1110.61	+	1483.60i	0.186961	+	0.249751i
$329$	−13788.3	+	4048.62i	−2.31057	+	0.678443i
$330$	229.893	+	4302.99i	0.0383492	+	0.717793i
$331$	632.944	−	1385.95i	0.105105	−	0.230148i	−0.849771	−	0.527151i	$-0.823260\pi$
$331$	632.944	−	1385.95i	0.105105	−	0.230148i	0.954876	+	0.297004i	$0.0959873\pi$
$332$	−1656.38	+	904.451i	−0.273812	+	0.149513i
$333$	−27.3706	+	382.690i	−0.00450420	+	0.0629769i
$334$	−1995.60	+	1729.20i	−0.326929	+	0.283286i
$335$	3608.09	−	7538.04i	0.588451	−	1.22939i
$336$	1979.25	+	903.894i	0.321360	+	0.146760i
$337$	−8510.69	+	1851.39i	−1.37569	+	0.299263i	−0.838822	−	0.544405i	$-0.816755\pi$
$337$	−8510.69	+	1851.39i	−1.37569	+	0.299263i	−0.536866	+	0.843668i	$0.680392\pi$
$338$	−1737.46	+	3181.92i	−0.279602	+	0.512052i
$339$	809.882	−	5632.85i	0.129754	−	0.902462i
$340$	−408.534	−	1490.19i	−0.0651644	−	0.237697i
$341$	35.9385	−	5.16718i	0.00570727	−	0.000820582i
$342$	−11.7664	+	54.0895i	−0.00186040	+	0.00855212i
$343$	−2163.05	+	154.705i	−0.340507	+	0.0243535i
$344$	1097.26			0.171978
$345$	−6064.04	+	148.495i	−0.946310	+	0.0231731i
$346$	−1684.49			−0.261731
$347$	3670.06	−	262.488i	0.567778	−	0.0406083i	0.215500	−	0.976504i	$-0.430862\pi$
$347$	3670.06	−	262.488i	0.567778	−	0.0406083i	0.352278	+	0.935896i	$0.385407\pi$
$348$	871.140	−	4004.57i	0.134190	−	0.616860i
$349$	4899.60	−	704.456i	0.751489	−	0.108048i	0.244082	−	0.969755i	$-0.421513\pi$
$349$	4899.60	−	704.456i	0.751489	−	0.108048i	0.507407	+	0.861707i	$0.330604\pi$
$350$	6872.75	−	736.476i	1.04961	−	0.112475i
$351$	409.029	−	2844.86i	0.0622004	−	0.432613i
$352$	600.855	−	1100.38i	0.0909821	−	0.166621i
$353$	−9856.13	+	2144.07i	−1.48609	+	0.323279i	−0.881090	−	0.472949i	$-0.843190\pi$
$353$	−9856.13	+	2144.07i	−1.48609	+	0.323279i	−0.604998	+	0.796227i	$0.706826\pi$
$354$	−4497.51	−	2053.94i	−0.675254	−	0.308378i
$355$	−9022.29	+	3181.11i	−1.34888	+	0.475594i
$356$	217.341	−	188.327i	0.0323568	−	0.0280373i
$357$	335.201	−	4686.73i	0.0496940	−	0.694812i
$358$	7410.62	−	4046.51i	1.09403	−	0.597387i
$359$	−2082.04	+	4559.03i	−0.306089	+	0.670241i	−0.998695	−	0.0510749i	$-0.983735\pi$
$359$	−2082.04	+	4559.03i	−0.306089	+	0.670241i	0.692606	+	0.721316i	$0.256463\pi$
$360$	186.745	+	167.802i	0.0273397	+	0.0245666i
$361$	6487.88	−	1905.01i	0.945892	−	0.277739i
$362$	165.635	+	221.262i	0.0240485	+	0.0321250i
$363$	940.285	+	350.708i	0.135956	+	0.0507091i
$364$	308.547	+	2145.99i	0.0444293	+	0.309012i
$365$	−3968.68	−	9121.79i	−0.569124	−	1.30810i
$366$	4157.90	+	3602.84i	0.593817	+	0.514546i
$367$	−1263.00	+	1263.00i	−0.179641	+	0.179641i	−0.791199	−	0.611559i	$-0.790543\pi$
$367$	−1263.00	+	1263.00i	−0.179641	+	0.179641i	0.611559	+	0.791199i	$0.290543\pi$
$368$	1523.90	+	890.206i	0.215867	+	0.126101i
$369$			650.245i			0.0917355i
$370$	−272.950	+	3044.17i	−0.0383513	+	0.427727i
$371$	−6553.96	+	4211.97i	−0.917155	+	0.589420i
$372$	−10.9264	+	14.5960i	−0.00152287	+	0.00203432i
$373$	−150.294	+	402.953i	−0.0208630	+	0.0559359i	−0.946964	−	0.321340i	$-0.895867\pi$
$373$	−150.294	+	402.953i	−0.0208630	+	0.0559359i	0.926101	+	0.377276i	$0.123139\pi$
$374$	−2679.83	−	385.302i	−0.370510	−	0.0532714i
$375$	−6741.23	−	1344.58i	−0.928308	−	0.185156i
$376$	−3497.98	−	2248.01i	−0.479773	−	0.308331i
$377$	3826.02	−	1427.03i	0.522679	−	0.194949i
$378$	3885.29	+	7115.39i	0.528672	+	0.968190i
$379$	5379.62	+	6208.42i	0.729110	+	0.841438i	0.992371	−	0.123287i	$-0.0393435\pi$
$379$	5379.62	+	6208.42i	0.729110	+	0.841438i	−0.263261	+	0.964725i	$0.584798\pi$
$380$	−101.485	+	429.129i	−0.0137002	+	0.0579312i
$381$	−9308.37	−	2733.18i	−1.25166	−	0.367520i
$382$	2769.72	+	7425.92i	0.370972	+	0.994615i
$383$	−403.756	−	1856.04i	−0.0538668	−	0.247622i	0.942338	−	0.334663i	$-0.108622\pi$
$383$	−403.756	−	1856.04i	−0.0538668	−	0.247622i	−0.996205	+	0.0870413i	$0.972259\pi$
$384$	177.375	+	604.084i	0.0235720	+	0.0802787i
$385$	3620.98	−	11557.1i	0.479330	−	1.52989i
$386$	3186.31	+	6977.05i	0.420153	+	0.920006i
$387$	308.203	+	230.718i	0.0404827	+	0.0303050i
$388$	−4820.50	−	1048.63i	−0.630731	−	0.137207i
$389$	3309.24	−	3819.07i	0.431324	−	0.497775i	−0.497929	−	0.867218i	$-0.665906\pi$
$389$	3309.24	−	3819.07i	0.431324	−	0.497775i	0.929253	+	0.369443i	$0.120451\pi$
$390$	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
$393$	350.198	+	4896.41i	0.0449495	+	0.628476i
$394$	639.922	+	995.739i	0.0818244	+	0.127321i
$395$	8781.95	+	9104.37i	1.11865	+	1.15972i
$396$	400.145	−	182.740i	0.0507778	−	0.0231895i
$397$	−7925.81	+	5933.19i	−1.00198	+	0.750071i	−0.968409	−	0.249366i	$-0.919778\pi$
$397$	−7925.81	+	5933.19i	−1.00198	+	0.750071i	−0.0335678	+	0.999436i	$0.510687\pi$
$398$	−739.174	−	403.619i	−0.0930941	−	0.0508332i
$399$	−724.961	+	1128.06i	−0.0909610	+	0.141538i
$400$	1463.31	+	1363.35i	0.182914	+	0.170418i
$401$	−311.979	+	1062.50i	−0.0388516	+	0.132317i	−0.976635	−	0.214904i	$-0.931056\pi$
$401$	−311.979	+	1062.50i	−0.0388516	+	0.132317i	0.937784	+	0.347220i	$0.112874\pi$
$402$	7334.42	+	524.568i	0.909969	+	0.0650823i
$403$	−18.1208	−	1.29603i	−0.00223986	−	0.000160198i
$404$	569.011	−	1937.87i	0.0700727	−	0.238646i
$405$	−1406.35	−	7076.66i	−0.172549	−	0.868252i
$406$	−6227.29	+	9689.85i	−0.761220	+	1.18448i
$407$	4700.21	+	2566.51i	0.572434	+	0.312573i
$408$	1088.38	−	814.753i	0.132066	−	0.0988634i
$409$	−2741.04	+	1251.79i	−0.331383	+	0.151338i	−0.574157	−	0.818745i	$-0.694670\pi$
$409$	−2741.04	+	1251.79i	−0.331383	+	0.151338i	0.242774	+	0.970083i	$0.421943\pi$
$410$	−93.3597	+	5179.15i	−0.0112456	+	0.623854i
$411$	6501.50	+	10116.5i	0.780281	+	1.21414i
$412$	408.225	+	5707.74i	0.0488151	+	0.682524i
$413$	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
$417$	5885.86	+	1280.39i	0.691204	+	0.150362i
$418$	618.533	+	463.028i	0.0723766	+	0.0541805i
$419$	3815.66	+	8355.13i	0.444886	+	0.974164i	0.990676	+	0.136242i	$0.0435024\pi$
$419$	3815.66	+	8355.13i	0.444886	+	0.974164i	−0.545790	+	0.837922i	$0.683770\pi$
$420$	2818.01	+	5389.51i	0.327392	+	0.626146i
$421$	−121.135	−	412.548i	−0.0140232	−	0.0477586i	0.952184	−	0.305525i	$-0.0988318\pi$
$421$	−121.135	−	412.548i	−0.0140232	−	0.0477586i	−0.966207	+	0.257766i	$0.917014\pi$
$422$	608.435	+	2796.93i	0.0701852	+	0.322636i
$423$	−509.842	−	1366.94i	−0.0586037	−	0.157123i
$424$	−2162.91	−	635.088i	−0.247736	−	0.0727420i
$425$	1654.16	−	3989.56i	0.188796	−	0.455346i
$426$	−5512.26	−	6361.49i	−0.626925	−	0.723510i
$427$	−7410.58	−	13571.5i	−0.839867	−	1.53810i
$428$	3004.00	−	1120.43i	0.339261	−	0.126538i
$429$	−3178.13	−	2042.46i	−0.357673	−	0.229862i
$430$	2421.69	+	1881.90i	0.271591	+	0.211054i
$431$	−10169.9	−	1462.22i	−1.13659	−	0.163416i	−0.451772	−	0.892134i	$-0.649208\pi$
$431$	−10169.9	−	1462.22i	−1.13659	−	0.163416i	−0.684815	+	0.728717i	$0.740117\pi$
$432$	−819.758	+	2197.86i	−0.0912977	+	0.244779i
$433$	2801.15	−	3741.90i	0.310888	−	0.415298i	−0.617698	−	0.786416i	$-0.711934\pi$
$433$	2801.15	−	3741.90i	0.310888	−	0.415298i	0.928586	+	0.371118i	$0.121025\pi$
$434$	43.1093	−	27.7047i	0.00476801	−	0.00306421i
$435$	8790.81	−	7344.11i	0.968936	−	0.809478i
$436$		−	5055.01i		−	0.555255i
$437$	−676.675	+	851.502i	−0.0740727	+	0.0932102i
$438$	6189.13	−	6189.13i	0.675179	−	0.675179i
$439$	−4415.33	−	3825.91i	−0.480028	−	0.415947i	0.380945	−	0.924598i	$-0.375599\pi$
$439$	−4415.33	−	3825.91i	−0.480028	−	0.415947i	−0.860973	+	0.508651i	$0.830144\pi$
$440$	3213.36	−	1398.06i	0.348161	−	0.151477i
$441$	−168.350	−	1170.90i	−0.0181784	−	0.126433i
$442$	1269.26	+	473.408i	0.136589	+	0.0509451i
$443$	7619.28	+	10178.2i	0.817162	+	1.09160i	0.994216	+	0.107400i	$0.0342525\pi$
$443$	7619.28	+	10178.2i	0.817162	+	1.09160i	−0.177054	+	0.984201i	$0.556657\pi$
$444$	−2580.30	+	757.644i	−0.275801	+	0.0809824i
$445$	802.674	−	42.8840i	0.0855065	−	0.00456831i
$446$	531.906	−	1164.71i	0.0564719	−	0.123656i
$447$	7982.73	−	4358.90i	0.844676	−	0.461228i
$448$	126.235	−	1764.99i	0.0133125	−	0.186134i
$449$	9153.95	−	7931.94i	0.962142	−	0.833701i	−0.0239819	−	0.999712i	$-0.507634\pi$
$449$	9153.95	−	7931.94i	0.962142	−	0.833701i	0.986124	+	0.166012i	$0.0530890\pi$
$450$	124.355	+	690.628i	0.0130270	+	0.0723478i
$451$	8255.98	+	3770.38i	0.861993	+	0.393659i
$452$	−4522.16	+	983.735i	−0.470585	+	0.102370i
$453$	1374.55	−	2517.31i	0.142565	−	0.261089i
$454$	213.841	−	1487.30i	0.0221059	−	0.153750i
$455$	−2999.59	+	5265.45i	−0.309062	+	0.542523i
$456$	−384.045	+	55.2174i	−0.0394399	+	0.00567060i
$457$	2284.33	−	10500.9i	0.233822	−	1.07486i	−0.699167	−	0.714958i	$-0.746446\pi$
$457$	2284.33	−	10500.9i	0.233822	−	1.07486i	0.932989	−	0.359904i	$-0.117191\pi$
$458$	4400.18	−	314.707i	0.448924	−	0.0321076i
$459$	5065.53			0.515117
$460$	1836.52	+	4578.34i	0.186148	+	0.464057i
$461$	10450.0			1.05576			0.527879	−	0.849320i	$-0.322987\pi$
$461$	10450.0			1.05576			0.527879	+	0.849320i	$0.322987\pi$
$462$	10629.1	−	760.208i	1.07037	−	0.0765542i
$463$	3147.30	−	14467.9i	0.315913	−	1.45223i	−0.495936	−	0.868359i	$-0.665175\pi$
$463$	3147.30	−	14467.9i	0.315913	−	1.45223i	0.811849	−	0.583868i	$-0.198461\pi$
$464$	−3298.88	+	474.308i	−0.330058	+	0.0474552i
$465$	−49.1483	+	13.4740i	−0.00490150	+	0.00134374i
$466$	741.773	−	5159.15i	0.0737382	−	0.512860i
$467$	−1506.31	+	2758.61i	−0.149259	+	0.273347i	−0.941602	−	0.336729i	$-0.890679\pi$
$467$	−1506.31	+	2758.61i	−0.149259	+	0.273347i	0.792343	+	0.610076i	$0.208861\pi$
$468$	−215.077	+	46.7871i	−0.0212434	+	0.00462123i
$469$	−18799.0	−	8585.20i	−1.85086	−	0.845262i
$470$	−3864.59	−	10960.8i	−0.379277	−	1.07571i
$471$	6818.85	−	5908.57i	0.667083	−	0.578031i
$472$	−286.846	+	4010.63i	−0.0279728	+	0.391111i
$473$	4716.44	−	2575.37i	0.458482	−	0.250350i
$474$	−4623.59	+	10124.2i	−0.448035	+	0.981059i
$475$	−959.975	+	773.045i	−0.0927298	+	0.0746731i
$476$	−3666.35	+	1076.54i	−0.353040	+	0.103662i
$477$	−473.988	−	633.174i	−0.0454978	−	0.0607779i
$478$	9473.97	+	3533.61i	0.906546	+	0.338124i
$479$	2095.70	+	14575.9i	0.199906	+	1.39038i	0.804551	+	0.593884i	$0.202406\pi$
$479$	2095.70	+	14575.9i	0.199906	+	1.39038i	−0.604644	+	0.796496i	$0.706685\pi$
$480$	−644.585	+	1637.44i	−0.0612941	+	0.155706i
$481$	−2025.08	−	1754.74i	−0.191966	−	0.166339i
$482$	−1845.11	+	1845.11i	−0.174362	+	0.174362i
$483$	637.437	+	14987.0i	0.0600505	+	1.41187i
$484$		−	816.127i		−	0.0766460i
$485$	−8840.47	−	10581.9i	−0.827680	−	0.990724i
$486$	−1319.58	+	848.044i	−0.123163	+	0.0791524i
$487$	−4040.38	+	5397.32i	−0.375949	+	0.502209i	−0.948115	−	0.317929i	$-0.897013\pi$
$487$	−4040.38	+	5397.32i	−0.375949	+	0.502209i	0.572165	+	0.820138i	$0.306104\pi$
$488$	1563.56	−	4192.06i	0.145039	−	0.388864i
$489$	15257.0	+	2193.63i	1.41093	+	0.202862i
$490$	−1172.78	−	9350.29i	−0.108124	−	0.862047i
$491$	−6819.97	−	4382.93i	−0.626845	−	0.402849i	0.188295	−	0.982112i	$-0.439704\pi$
$491$	−6819.97	−	4382.93i	−0.626845	−	0.402849i	−0.815140	+	0.579264i	$0.803340\pi$
$492$	−4270.37	+	1592.77i	−0.391308	+	0.145950i
$493$	3449.16	+	6316.67i	0.315096	+	0.577056i
$494$	−253.169	−	292.172i	−0.0230579	−	0.0266102i
$495$	1196.55	+	282.971i	0.108648	+	0.0256942i
$496$	14.2268	+	4.17736i	0.00128790	+	0.000378163i
$497$	8267.58	+	22166.2i	0.746180	+	2.00059i
$498$	−986.578	−	4535.23i	−0.0887744	−	0.408089i
$499$	1853.11	+	6311.12i	0.166246	+	0.566182i	0.999903	+	0.0138998i	$0.00442459\pi$
$499$	1853.11	+	6311.12i	0.166246	+	0.566182i	−0.833657	+	0.552282i	$0.813757\pi$
$500$	891.318	+	5518.65i	0.0797219	+	0.493604i
$501$	−2697.70	−	5907.14i	−0.240567	−	0.526769i
$502$	−2888.71	−	2162.46i	−0.256831	−	0.192261i
$503$	17496.2	+	3806.06i	1.55092	+	0.337383i	0.904796	−	0.425846i	$-0.140023\pi$
$503$	17496.2	+	3806.06i	1.55092	+	0.337383i	0.646129	+	0.763229i	$0.276387\pi$
$504$	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
$508$	562.826	+	7869.34i	0.0491563	+	0.687295i
$509$	11259.0	+	17519.3i	0.980442	+	1.52560i	0.844968	+	0.534816i	$0.179619\pi$
$509$	11259.0	+	17519.3i	0.980442	+	1.52560i	0.135473	+	0.990781i	$0.456745\pi$
$510$	3799.46	+	68.4894i	0.329888	+	0.00594659i
$511$	−22377.2	+	10219.3i	−1.93720	+	0.884688i
$512$	409.877	−	306.830i	0.0353793	−	0.0264846i
$513$	−1268.79	−	692.810i	−0.109198	−	0.0596264i
$514$	−3193.32	+	4968.91i	−0.274030	+	0.426399i
$515$	−8888.31	+	13297.3i	−0.760516	+	1.13776i
$516$	−760.261	+	2589.21i	−0.0648616	+	0.220898i
$517$	−20311.9	−	1452.74i	−1.72789	−	0.123581i
$518$	7539.02	+	539.201i	0.639470	+	0.0457358i
$519$	1167.14	−	3974.90i	0.0987121	−	0.336183i
$520$	−1719.79	+	341.776i	−0.145034	+	0.0288228i
$521$	3357.97	−	5225.11i	0.282371	−	0.439379i	−0.670876	−	0.741570i	$-0.734082\pi$
$521$	3357.97	−	5225.11i	0.282371	−	0.439379i	0.953247	+	0.302191i	$0.0977181\pi$
$522$	−1026.33	−	560.421i	−0.0860563	−	0.0469903i
$523$	12822.6	−	9598.86i	1.07207	−	0.802541i	0.0909326	−	0.995857i	$-0.471015\pi$
$523$	12822.6	−	9598.86i	1.07207	−	0.802541i	0.981137	+	0.193316i	$0.0619243\pi$
$524$	3631.33	−	1658.37i	0.302739	−	0.138256i
$525$	−3024.07	+	16727.9i	−0.251393	+	1.39060i
$526$	3706.62	+	5767.62i	0.307256	+	0.478099i
$527$	−2.28420	−	31.9374i	−0.000188807	−	0.00263987i
$528$	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
$532$	1065.57	+	231.800i	0.0868386	+	0.0188906i
$533$	−3635.54	−	2721.53i	−0.295446	−	0.221168i
$534$	293.806	+	643.345i	0.0238094	+	0.0521353i
$535$	8551.54	+	2679.29i	0.691057	+	0.216516i
$536$	−1684.71	−	5737.60i	−0.135762	−	0.462363i
$537$	4413.94	+	20290.6i	0.354703	+	1.63055i
$538$	3201.70	+	8584.09i	0.256571	+	0.687893i
$539$	−15842.7	−	4651.85i	−1.26604	−	0.371743i
$540$	−5578.74	+	3444.77i	−0.444576	+	0.274517i
$541$	−4119.55	−	4754.22i	−0.327381	−	0.377818i	0.568068	−	0.822982i	$-0.307691\pi$
$541$	−4119.55	−	4754.22i	−0.327381	−	0.377818i	−0.895449	+	0.445163i	$0.853146\pi$
$542$	2205.83	+	4039.68i	0.174813	+	0.320146i
$543$	−636.875	+	237.542i	−0.0503332	+	0.0187733i
$544$	−930.121	−	597.752i	−0.0733062	−	0.0471111i
$545$	8669.79	−	11156.6i	0.681418	−	0.876870i
$546$	−5277.68	−	758.816i	−0.413670	−	0.0594768i
$547$	7140.11	−	19143.4i	0.558116	−	1.49637i	−0.284943	−	0.958544i	$-0.591975\pi$
$547$	7140.11	−	19143.4i	0.558116	−	1.49637i	0.843059	−	0.537821i	$-0.180752\pi$
$548$	5860.67	−	7828.94i	0.456853	−	0.610284i
$549$	1320.63	−	848.716i	0.102665	−	0.0659788i
$550$	9489.77	+	2425.64i	0.735719	+	0.188054i
$551$		−	2053.91i		−	0.158801i
$552$	−3156.49	+	2979.16i	−0.243386	+	0.229713i
$553$	22119.6	−	22119.6i	1.70094	−	1.70094i
$554$	−7566.22	−	6556.16i	−0.580249	−	0.502788i
$555$	−6994.22	−	2753.30i	−0.534933	−	0.210578i
$556$	−697.132	−	4848.66i	−0.0531744	−	0.369836i
$557$	9767.64	+	3643.14i	0.743031	+	0.277136i	0.692333	−	0.721578i	$-0.256583\pi$
$557$	9767.64	+	3643.14i	0.743031	+	0.277136i	0.0506974	+	0.998714i	$0.483856\pi$
$558$	3.11771	+	4.16477i	0.000236529	+	0.000315965i
$559$	−2579.90	+	757.527i	−0.195202	+	0.0573166i
$560$	3305.72	−	3678.88i	0.249450	−	0.277609i
$561$	2765.98	−	6056.65i	0.208163	−	0.455814i
$562$	−7322.89	+	3998.60i	−0.549640	+	0.300126i
$563$	1050.93	−	14693.9i	0.0786701	−	1.09995i	−0.792793	−	0.609491i	$-0.791374\pi$
$563$	1050.93	−	14693.9i	0.0786701	−	1.09995i	0.871463	−	0.490461i	$-0.163172\pi$
$564$	7728.29	−	6696.60i	0.576986	−	0.499961i
$565$	−11667.7	−	5584.77i	−0.868787	−	0.415846i
$566$	−15136.4	−	6912.55i	−1.12408	−	0.513350i
$567$	−17434.7	+	3792.69i	−1.29134	+	0.280913i
$568$	−3280.63	+	6008.02i	−0.242345	+	0.443822i
$569$	−2675.85	+	18611.0i	−0.197149	+	1.37120i	0.615359	+	0.788247i	$0.289011\pi$
$569$	−2675.85	+	18611.0i	−0.197149	+	1.37120i	−0.812507	+	0.582951i	$0.801898\pi$
$570$	−942.302	−	536.805i	−0.0692433	−	0.0394461i
$571$	14182.9	−	2039.20i	1.03947	−	0.149453i	0.398618	−	0.917117i	$-0.369490\pi$
$571$	14182.9	−	2039.20i	1.03947	−	0.149453i	0.640853	+	0.767664i	$0.278581\pi$
$572$	−653.058	+	3002.06i	−0.0477373	+	0.219445i
$573$	−19442.0	+	1390.52i	−1.41746	+	0.101378i
$574$	12809.9			0.931486
$575$	−3799.01	+	13254.3i	−0.275530	+	0.961293i
$576$	179.644			0.0129951
$577$	17625.5	−	1260.60i	1.27168	−	0.0909523i	0.580875	−	0.813993i	$-0.302711\pi$
$577$	17625.5	−	1260.60i	1.27168	−	0.0909523i	0.690805	+	0.723041i	$0.257256\pi$
$578$	1581.15	−	7268.45i	0.113784	−	0.523058i
$579$	−18671.5	+	2684.55i	−1.34017	+	0.192688i
$580$	−8094.21	−	4611.07i	−0.579472	−	0.330110i
$581$	−1856.45	+	12911.9i	−0.132562	+	0.921991i
$582$	5814.45	−	10648.4i	0.414118	−	0.758400i
$583$	−10787.6	+	2346.70i	−0.766342	+	0.166707i
$584$	−6474.78	−	2956.93i	−0.458781	−	0.209518i
$585$	−554.924	−	265.615i	−0.0392193	−	0.0187724i
$586$	−3378.09	+	2927.13i	−0.238136	+	0.206346i
$587$	−1974.70	+	27610.0i	−0.138850	+	1.94137i	0.160097	+	0.987101i	$0.448819\pi$
$587$	−1974.70	+	27610.0i	−0.138850	+	1.94137i	−0.298947	+	0.954270i	$0.596635\pi$
$588$	7277.31	−	3973.71i	0.510393	−	0.278696i
$589$	−3.79592	+	8.31190i	−0.000265549	+	0.000581470i
$590$	−7511.67	+	8359.62i	−0.524153	+	0.583322i
$591$	−2793.03	+	820.108i	−0.194399	+	0.0570808i
$592$	1310.60	+	1750.76i	0.0909889	+	0.121547i
$593$	21512.6	+	8023.79i	1.48974	+	0.555645i	0.956862	−	0.290544i	$-0.0938364\pi$
$593$	21512.6	+	8023.79i	1.48974	+	0.555645i	0.532882	+	0.846190i	$0.321109\pi$
$594$	1634.94	+	11371.3i	0.112933	+	0.785468i
$595$	−9938.10	−	3912.17i	−0.684743	−	0.269552i
$596$	−5589.96	−	4843.73i	−0.384184	−	0.332897i
$597$	1464.57	−	1464.57i	0.100404	−	0.100404i
$598$	−4197.61	−	1040.99i	−0.287045	−	0.0711863i
$599$		−	24891.3i		−	1.69788i	−0.528490	−	0.848940i	$-0.677242\pi$
$599$		−	24891.3i		−	1.69788i	0.528490	−	0.848940i	$-0.322758\pi$
$600$	−4230.98	+	2508.36i	−0.287882	+	0.170673i
$601$	12277.5	−	7890.29i	0.833296	−	0.535527i	−0.0530276	−	0.998593i	$-0.516887\pi$
$601$	12277.5	−	7890.29i	0.833296	−	0.535527i	0.886324	+	0.463066i	$0.153251\pi$
$602$	4545.15	−	6071.61i	0.307718	−	0.411064i
$603$	733.219	−	1965.84i	0.0495174	−	0.132761i
$604$	−2308.72	−	331.944i	−0.155531	−	0.0223619i
$605$	1399.73	−	1801.22i	0.0940613	−	0.121041i
$606$	4178.55	+	2685.39i	0.280102	+	0.180011i
$607$	12469.4	−	4650.83i	0.833798	−	0.310991i	0.103935	−	0.994584i	$-0.466857\pi$
$607$	12469.4	−	4650.83i	0.833798	−	0.310991i	0.729863	+	0.683594i	$0.239584\pi$
$608$	151.217	+	276.934i	0.0100866	+	0.0184723i
$609$	−18550.5	−	21408.4i	−1.23432	−	1.42448i
$610$	10640.6	−	6570.35i	0.706269	−	0.436108i
$611$	9776.49	+	2870.64i	0.647323	+	0.190071i
$612$	−135.568	−	363.472i	−0.00895428	−	0.0240073i
$613$	−461.073	−	2119.52i	−0.0303794	−	0.139652i	0.959459	−	0.281848i	$-0.0909473\pi$
$613$	−461.073	−	2119.52i	−0.0303794	−	0.139652i	−0.989839	+	0.142196i	$0.954584\pi$
$614$	−5869.17	−	19988.6i	−0.385766	−	1.31380i
$615$	−12156.6	−	3808.79i	−0.797073	−	0.249732i
$616$	−3599.99	−	7882.87i	−0.235467	−	0.515601i
$617$	4289.76	+	3211.27i	0.279901	+	0.209532i	0.730000	−	0.683447i	$-0.239520\pi$
$617$	4289.76	+	3211.27i	0.279901	+	0.209532i	−0.450098	+	0.892979i	$0.648611\pi$
$618$	−13751.4	−	2991.44i	−0.895085	−	0.194714i
$619$	−3297.88	+	3805.96i	−0.214141	+	0.247131i	−0.852650	−	0.522483i	$-0.825006\pi$
$619$	−3297.88	+	3805.96i	−0.214141	+	0.247131i	0.638509	+	0.769614i	$0.279551\pi$
$620$	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
$623$	−141.808	−	1982.74i	−0.00911946	−	0.127507i
$624$	−834.094	−	1297.88i	−0.0535104	−	0.0832638i
$625$	−7497.82	+	13708.5i	−0.479860	+	0.877345i
$626$	−13255.5	+	6053.60i	−0.846322	+	0.386502i
$627$	−1521.17	+	1138.73i	−0.0968895	+	0.0725306i
$628$	−6439.96	−	3516.49i	−0.409208	−	0.223444i
$629$	2553.25	−	3972.94i	0.161852	−	0.251847i
$630$	1702.07	−	338.254i	0.107638	−	0.0213911i
$631$	8021.66	−	27319.3i	0.506081	−	1.72355i	−0.168822	−	0.985647i	$-0.553996\pi$
$631$	8021.66	−	27319.3i	0.506081	−	1.72355i	0.674903	−	0.737907i	$-0.264186\pi$
$632$	9028.25	+	645.713i	0.568235	+	0.0406410i
$633$	−7021.49	−	502.187i	−0.440884	−	0.0315326i
$634$	−1669.65	+	5686.31i	−0.104590	+	0.356202i
$635$	−12254.4	+	18333.2i	−0.765831	+	1.14572i
$636$	2997.24	−	4663.79i	0.186868	−	0.290773i
$637$	7251.14	+	3959.42i	0.451021	+	0.246276i
$638$	−13066.6	+	9781.53i	−0.810833	+	0.606982i
$639$	−2184.76	+	997.747i	−0.135255	+	0.0617688i
$640$	1430.85	+	25.7926i	0.0883740	+	0.00159303i
$641$	−13440.8	−	20914.3i	−0.828204	−	1.28871i	−0.954947	−	0.296775i	$-0.904089\pi$
$641$	−13440.8	−	20914.3i	−0.828204	−	1.28871i	0.126744	−	0.991936i	$-0.459547\pi$
$642$	562.505	+	7864.85i	0.0345799	+	0.483491i
$643$	578.572	+	578.572i	0.0354847	+	0.0354847i	0.724626	−	0.689142i	$-0.242012\pi$
$643$	578.572	+	578.572i	0.0354847	+	0.0354847i	−0.689142	+	0.724626i	$0.742012\pi$
$644$	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
$647$	−9036.35	−	1965.74i	−0.549081	−	0.119445i	−0.0705378	−	0.997509i	$-0.522472\pi$
$647$	−9036.35	−	1965.74i	−0.549081	−	0.119445i	−0.478544	+	0.878064i	$0.658835\pi$
$648$	−4132.93	−	3093.87i	−0.250551	−	0.187560i
$649$	8180.35	+	17912.5i	0.494772	+	1.08340i
$650$	−4381.80	−	2195.28i	−0.264413	−	0.132471i
$651$	35.5056	+	120.921i	0.00213760	+	0.00727998i
$652$	−2664.53	−	12248.6i	−0.160047	−	0.735726i
$653$	3066.75	+	8222.26i	0.183784	+	0.492744i	0.995870	−	0.0907941i	$-0.0289405\pi$
$653$	3066.75	+	8222.26i	0.183784	+	0.492744i	−0.812086	+	0.583538i	$0.801668\pi$
$654$	11928.3	+	3502.47i	0.713202	+	0.209415i
$655$	10858.7	+	2567.98i	0.647763	+	0.153190i
$656$	2427.24	+	2801.19i	0.144463	+	0.166719i
$657$	−1196.91	−	2191.99i	−0.0710747	−	0.130164i
$658$	−26928.8	+	10043.9i	−1.59543	+	0.595065i
$659$	17762.8	+	11415.4i	1.04998	+	0.674783i	0.947436	−	0.319945i	$-0.103664\pi$
$659$	17762.8	+	11415.4i	1.04998	+	0.674783i	0.102547	+	0.994728i	$0.467301\pi$
$660$	1072.56	+	8551.25i	0.0632565	+	0.504329i
$661$	−6881.71	−	989.440i	−0.404943	−	0.0582220i	−0.0631659	−	0.998003i	$-0.520120\pi$
$661$	−6881.71	−	989.440i	−0.404943	−	0.0582220i	−0.341777	+	0.939781i	$0.611029\pi$
$662$	1064.92	−	2855.15i	0.0625214	−	0.167626i
$663$	−1996.53	+	2667.06i	−0.116952	+	0.156229i
$664$	−3175.27	+	2040.62i	−0.185579	+	0.119264i
$665$	1954.18	+	2339.13i	0.113954	+	0.136402i
$666$			767.336i			0.0446451i
$667$	−13232.1	−	18783.7i	−0.768141	−	1.09041i
$668$	−3734.31	+	3734.31i	−0.216295	+	0.216295i
$669$	2379.83	+	2062.13i	0.137533	+	0.119173i
$670$	6122.28	−	15552.5i	0.353021	−	0.896782i
$671$	−3118.39	−	21688.9i	−0.179410	−	1.24782i
$672$	4077.38	+	1520.79i	0.234060	+	0.0873000i
$673$	20706.7	+	27660.9i	1.18601	+	1.58432i	0.708534	+	0.705676i	$0.249357\pi$
$673$	20706.7	+	27660.9i	1.18601	+	1.58432i	0.477474	+	0.878646i	$0.341552\pi$
$674$	−16713.9	+	4907.63i	−0.955184	+	0.280467i
$675$	−18220.5	−	1965.33i	−1.03898	−	0.112068i
$676$	−3012.07	+	6595.52i	−0.171374	+	0.375257i
$677$	21923.9	−	11971.4i	1.24462	−	0.679611i	0.284355	−	0.958719i	$-0.408220\pi$
$677$	21923.9	−	11971.4i	1.24462	−	0.679611i	0.960260	+	0.279108i	$0.0900386\pi$
$678$	811.950	−	11352.6i	0.0459923	−	0.643056i
$679$	−25770.3	+	22330.1i	−1.45652	+	1.26208i
$680$	−1027.60	−	2914.49i	−0.0579512	−	0.164361i
$681$	3361.42	+	1535.11i	0.189148	+	0.0863810i
$682$	70.9566	−	15.4357i	0.00398397	−	0.000866660i
$683$	5639.49	−	10328.0i	0.315943	−	0.578607i	−0.670656	−	0.741768i	$-0.733987\pi$
$683$	5639.49	−	10328.0i	0.315943	−	0.578607i	0.986599	+	0.163162i	$0.0521692\pi$
$684$	−15.7555	+	109.582i	−0.000880743	+	0.00612570i
$685$	26362.0	−	7227.12i	1.47042	−	0.403116i
$686$	−4293.01	+	617.241i	−0.238933	+	0.0343533i
$687$	−2306.14	+	10601.2i	−0.128071	+	0.588733i
$688$	2188.93	−	156.555i	0.121297	−	0.00867532i
$689$	5523.92			0.305435
$690$	−12076.0	+	1161.44i	−0.666268	+	0.0640801i
$691$	30166.5			1.66076			0.830381	−	0.557196i	$-0.188123\pi$
$691$	30166.5			1.66076			0.830381	+	0.557196i	$0.188123\pi$
$692$	−3360.40	+	240.341i	−0.184600	+	0.0132029i
$693$	646.329	−	2971.13i	0.0354286	−	0.162863i
$694$	7283.96	−	1047.27i	0.398408	−	0.0572824i
$695$	6777.29	−	11896.8i	0.369895	−	0.649310i
$696$	1166.48	−	8113.02i	0.0635275	−	0.441844i
$697$	3835.90	−	7024.93i	0.208458	−	0.381762i
$698$	9673.72	−	2104.39i	0.524579	−	0.114115i
$699$	11660.1	+	5324.99i	0.630938	+	0.288140i
$700$	13605.4	−	2449.79i	0.734623	−	0.132276i
$701$	−13026.7	+	11287.7i	−0.701871	+	0.608174i	−0.930913	−	0.365242i	$-0.880986\pi$
$701$	−13026.7	+	11287.7i	−0.701871	+	0.608174i	0.229042	+	0.973417i	$0.426441\pi$
$702$	410.074	−	5733.58i	0.0220473	−	0.308262i
$703$	−1182.90	+	645.913i	−0.0634623	+	0.0346530i
$704$	1041.65	−	2280.89i	0.0557650	−	0.122108i
$705$	28541.8	−	1524.89i	1.52475	−	0.0814619i
$706$	−19356.1	+	5683.47i	−1.03184	+	0.302975i
$707$	−8366.07	−	11175.8i	−0.445033	−	0.594495i
$708$	−9265.16	−	3455.72i	−0.491816	−	0.183438i
$709$	−736.434	−	5122.01i	−0.0390090	−	0.271313i	0.960977	−	0.276629i	$-0.0892172\pi$
$709$	−736.434	−	5122.01i	−0.0390090	−	0.271313i	−0.999986	+	0.00531530i	$0.998308\pi$
$710$	−17544.7	+	7633.30i	−0.927382	+	0.403483i
$711$	2400.11	+	2079.71i	0.126598	+	0.109698i
$712$	406.704	−	406.704i	0.0214071	−	0.0214071i
$713$	18.8338	+	100.470i	0.000989247	+	0.00527719i
$714$		−	9397.40i		−	0.492562i
$715$	−6590.12	+	5505.58i	−0.344694	+	0.287968i
$716$	14206.1	−	9129.73i	0.741492	−	0.476528i
$717$	−14902.5	+	19907.4i	−0.776212	+	1.03690i
$718$	−3503.00	+	9391.90i	−0.182076	+	0.488165i
$719$	12312.4	+	1770.25i	0.638628	+	0.0918209i	0.454020	−	0.890991i	$-0.349989\pi$
$719$	12312.4	+	1770.25i	0.638628	+	0.0918209i	0.184608	+	0.982812i	$0.440898\pi$
$720$	396.479	+	308.105i	0.0205221	+	0.0159478i
$721$	33274.3	+	21384.1i	1.71872	+	1.10456i
$722$	12670.9	−	4726.00i	0.653132	−	0.243606i
$723$	−3075.49	−	5632.35i	−0.158200	−	0.289722i
$724$	361.994	+	417.764i	0.0185821	+	0.0214448i
$725$	−9955.76	−	24059.0i	−0.509997	−	1.23246i
$726$	1925.82	+	565.471i	0.0984487	+	0.0289072i
$727$	8223.43	+	22047.9i	0.419519	+	1.12477i	0.959157	+	0.282876i	$0.0912883\pi$
$727$	8223.43	+	22047.9i	0.419519	+	1.12477i	−0.539638	+	0.841897i	$0.681439\pi$
$728$	921.708	+	4237.02i	0.0469241	+	0.215707i
$729$	−5995.74	−	20419.6i	−0.304615	−	1.03742i
$730$	−9218.62	−	17630.9i	−0.467392	−	0.893900i
$731$	−1968.63	−	4310.70i	−0.0996067	−	0.218108i
$732$	8808.67	+	6594.09i	0.444778	+	0.332957i
$733$	−21452.6	−	4666.73i	−1.08100	−	0.235156i	−0.363412	−	0.931629i	$-0.618388\pi$
$733$	−21452.6	−	4666.73i	−1.08100	−	0.235156i	−0.717584	+	0.696472i	$0.754752\pi$
$734$	−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
$738$	92.7758	+	1297.18i	0.00462754	+	0.0647015i
$739$	6291.87	+	9790.34i	0.313194	+	0.487339i	0.961788	−	0.273795i	$-0.0882791\pi$
$739$	6291.87	+	9790.34i	0.313194	+	0.487339i	−0.648594	+	0.761134i	$0.724643\pi$
$740$	−110.171	+	6111.77i	−0.00547294	+	0.303612i
$741$	864.853	−	394.965i	0.0428761	−	0.0195809i
$742$	−12473.6	+	9337.59i	−0.617141	+	0.461986i
$743$	22739.8	+	12416.9i	1.12280	+	0.613096i	0.929786	−	0.368099i	$-0.119991\pi$
$743$	22739.8	+	12416.9i	1.12280	+	0.613096i	0.193016	+	0.981196i	$0.438173\pi$
$744$	−19.7146	+	30.6766i	−0.000971470	+	0.00151164i
$745$	−4029.78	−	20277.5i	−0.198174	−	0.997195i
$746$	−242.329	+	825.296i	−0.0118931	+	0.0405043i
$747$	−1320.96	−	94.4767i	−0.0647005	−	0.00462747i
$748$	−5400.99	−	386.286i	−0.264010	−	0.0188824i
$749$	6243.53	−	21263.5i	0.304584	−	1.03732i
$750$	−13640.0	−	1720.47i	−0.664081	−	0.0837637i
$751$	−2439.70	+	3796.25i	−0.118543	+	0.184457i	−0.895454	−	0.445153i	$-0.853149\pi$
$751$	−2439.70	+	3796.25i	−0.118543	+	0.184457i	0.776911	+	0.629611i	$0.216786\pi$
$752$	−7298.87	−	3985.49i	−0.353940	−	0.193266i
$753$	7104.26	−	5318.18i	0.343816	−	0.257378i
$754$	7428.94	−	3392.68i	0.358814	−	0.163865i
$755$	−4526.10	−	4692.27i	−0.218174	−	0.226184i
$756$	8766.00	+	13640.2i	0.421715	+	0.656201i
$757$	−391.264	−	5470.59i	−0.0187857	−	0.262658i	−0.998161	−	0.0606107i	$-0.980695\pi$
$757$	−391.264	−	5470.59i	−0.0187857	−	0.262658i	0.979376	−	0.202047i	$-0.0647594\pi$
$758$	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	−0.850923	−	0.525290i	$-0.823957\pi$
$761$	−4406.05	+	5084.85i	−0.209880	+	0.242215i	0.641043	+	0.767505i	$0.278502\pi$
$762$	−18959.3	−	4124.34i	−0.901341	−	0.196075i
$763$	−27971.5	−	20939.2i	−1.32718	−	0.993513i
$764$	6584.85	+	14418.8i	0.311821	+	0.682794i
$765$	324.184	−	1034.70i	0.0153214	−	0.0489017i
$766$	−1070.27	−	3645.01i	−0.0504836	−	0.171931i
$767$	−2094.42	−	9627.91i	−0.0985987	−	0.453251i
$768$	440.036	+	1179.78i	0.0206750	+	0.0554319i
$769$	−14267.3	−	4189.27i	−0.669042	−	0.196448i	−0.0704656	−	0.997514i	$-0.522449\pi$
$769$	−14267.3	−	4189.27i	−0.669042	−	0.196448i	−0.598576	+	0.801066i	$0.704267\pi$
$770$	5574.55	−	23572.0i	0.260900	−	1.10322i
$771$	−9512.58	−	10978.1i	−0.444342	−	0.512797i
$772$	7351.86	+	13463.9i	0.342745	+	0.627691i
$773$	8897.25	−	3318.50i	0.413987	−	0.154409i	−0.133836	−	0.991004i	$-0.542729\pi$
$773$	8897.25	−	3318.50i	0.413987	−	0.154409i	0.547823	+	0.836594i	$0.315457\pi$
$774$	647.753	+	416.286i	0.0300814	+	0.0193321i
$775$	−4.17488	+	115.764i	−0.000193505	+	0.00536562i
$776$	−9766.05	−	1404.15i	−0.451779	−	0.0649560i
$777$	−6495.92	+	17416.2i	−0.299923	+	0.804124i
$778$	6056.72	−	8090.83i	0.279105	−	0.372841i
$779$	−1921.59	+	1234.93i	−0.0883802	+	0.0567985i
$780$	385.102	−	4294.99i	0.0176780	−	0.197161i
$781$			33524.7i			1.53599i
$782$	763.176	−	7583.96i	0.0348991	−	0.346806i
$783$	21594.2	−	21594.2i	0.985588	−	0.985588i
$784$	−5095.98	−	4415.69i	−0.232142	−	0.201152i
$785$	−8182.10	−	18806.1i	−0.372015	−	0.855055i
$786$	1397.22	+	9717.90i	0.0634062	+	0.441000i
$787$	18099.9	+	6750.91i	0.819811	+	0.305774i	0.724152	−	0.689641i	$-0.242231\pi$
$787$	18099.9	+	6750.91i	0.819811	+	0.305774i	0.0956589	+	0.995414i	$0.469504\pi$
$788$	1418.65	+	1895.10i	0.0641338	+	0.0856728i
$789$	−16178.1	+	4750.31i	−0.729980	+	0.214342i
$790$	18818.1	+	16909.3i	0.847493	+	0.761529i
$791$	−13288.6	+	29097.9i	−0.597329	+	1.30797i
$792$	772.177	−	421.641i	0.0346441	−	0.0189171i
$793$	−782.150	+	10935.9i	−0.0350252	+	0.489716i
$794$	−14964.7	+	12967.0i	−0.668863	+	0.579573i
$795$	14613.8	−	5152.59i	0.651947	−	0.229866i
$796$	−1532.17	−	699.718i	−0.0682240	−	0.0311568i
$797$	−11603.1	+	2524.09i	−0.515686	+	0.112181i	−0.462875	−	0.886424i	$-0.653182\pi$
$797$	−11603.1	+	2524.09i	−0.515686	+	0.112181i	−0.0528118	+	0.998604i	$0.516818\pi$
$798$	−1285.28	+	2353.81i	−0.0570155	+	0.104416i
$799$	−2555.72	+	17775.4i	−0.113160	+	0.787044i
$800$	3113.69	+	2510.96i	0.137607	+	0.110970i
$801$	199.753	−	28.7201i	0.00881138	−	0.00126688i
$802$	−470.773	+	2164.11i	−0.0207276	+	0.0952834i
$803$	−34771.2	+	2486.89i	−1.52808	+	0.109291i
$804$	14706.3			0.645089
$805$	32941.2	+	8802.47i	1.44227	+	0.385399i
$806$	−36.3342			−0.00158786
$807$	−22474.3	+	1607.39i	−0.980336	+	0.0701150i
$808$	858.630	−	3947.06i	0.0373843	−	0.171853i
$809$	6999.86	−	1006.43i	0.304205	−	0.0437381i	0.0114779	−	0.999934i	$-0.496346\pi$
$809$	6999.86	−	1006.43i	0.304205	−	0.0437381i	0.292727	+	0.956196i	$0.405437\pi$
$810$	−3815.23	−	13916.6i	−0.165498	−	0.603679i
$811$	−3251.69	+	22616.0i	−0.140792	+	0.979229i	0.789851	+	0.613299i	$0.210158\pi$
$811$	−3251.69	+	22616.0i	−0.140792	+	0.979229i	−0.930642	+	0.365930i	$0.880751\pi$
$812$	−11040.3	+	20218.8i	−0.477142	+	0.873820i
$813$	−11060.8	+	2406.13i	−0.477145	+	0.103797i
$814$	9742.65	+	4449.32i	0.419508	+	0.191583i
$815$	15126.8	−	31603.0i	0.650146	−	1.35829i
$816$	2054.97	−	1780.64i	0.0881598	−	0.0763909i
$817$	−96.4803	+	1348.97i	−0.00413148	+	0.0577656i
$818$	−5289.51	+	2888.29i	−0.226092	+	0.123456i
$819$	−632.013	+	1383.91i	−0.0269650	+	0.0590451i
$820$	552.709	+	10345.2i	0.0235383	+	0.440575i
$821$	−24319.9	+	7140.95i	−1.03382	+	0.303558i	−0.754264	−	0.656571i	$-0.772006\pi$
$821$	−24319.9	+	7140.95i	−1.03382	+	0.303558i	−0.279559	+	0.960129i	$0.590188\pi$
$822$	14413.3	+	19253.9i	0.611583	+	0.816979i
$823$	−16514.7	−	6159.68i	−0.699475	−	0.260891i	−0.0255320	−	0.999674i	$-0.508128\pi$
$823$	−16514.7	−	6159.68i	−0.699475	−	0.260891i	−0.673943	+	0.738783i	$0.735401\pi$
$824$	1628.74	+	11328.1i	0.0688591	+	0.478925i
$825$	−12299.0	+	20712.4i	−0.519025	+	0.874076i
$826$	21004.3	+	18200.4i	0.884787	+	0.766673i
$827$	30117.1	−	30117.1i	1.26635	−	1.26635i	0.318393	−	0.947959i	$-0.396857\pi$
$827$	30117.1	−	30117.1i	1.26635	−	1.26635i	0.947959	−	0.318393i	$-0.103143\pi$
$828$	561.885	+	1103.67i	0.0235832	+	0.0463227i
$829$		−	31651.2i		−	1.32605i	−0.748599	−	0.663023i	$-0.769273\pi$
$829$		−	31651.2i		−	1.32605i	0.748599	−	0.663023i	$-0.230727\pi$
$830$	−10507.8	−	942.158i	−0.439433	−	0.0394009i
$831$	20713.0	−	13311.4i	0.864653	−	0.555678i
$832$	−751.881	+	1004.40i	−0.0313303	+	0.0418523i
$833$	−5088.56	+	13643.0i	−0.211654	+	0.567467i
$834$	11924.4	+	1714.47i	0.495095	+	0.0711839i
$835$	−14646.4	+	1837.06i	−0.607018	+	0.0761365i
$836$	1299.98	+	835.445i	0.0537807	+	0.0345628i
$837$	−127.299	+	47.4799i	−0.00525697	+	0.00196075i
$838$	8803.97	+	16123.3i	0.362921	+	0.664641i
$839$	−25284.9	−	29180.4i	−1.04044	−	1.20074i	−0.979260	−	0.202610i	$-0.935058\pi$
$839$	−25284.9	−	29180.4i	−1.04044	−	1.20074i	−0.0611844	−	0.998126i	$-0.519488\pi$
$840$	6390.62	+	10349.5i	0.262497	+	0.425109i
$841$	18230.4	+	5352.94i	0.747486	+	0.219482i
$842$	−300.515	−	805.711i	−0.0122998	−	0.0329770i
$843$	−4361.69	−	20050.4i	−0.178202	−	0.819183i
$844$	1612.83	+	5492.80i	0.0657772	+	0.224017i
$845$	−17959.6	+	9390.53i	−0.731160	+	0.382301i
$846$	−1212.12	−	2654.17i	−0.0492594	−	0.107863i
$847$	−4515.98	−	3380.62i	−0.183200	−	0.137142i
$848$	−4405.41	−	958.339i	−0.178399	−	0.0388084i
$849$	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
$853$	2483.70	+	34726.6i	0.0996953	+	1.39392i	0.763399	+	0.645927i	$0.223529\pi$
$853$	2483.70	+	34726.6i	0.0996953	+	1.39392i	−0.663704	+	0.747996i	$0.731016\pi$
$854$	−16719.8	−	26016.4i	−0.669951	−	1.04246i
$855$	−222.716	+	214.829i	−0.00890845	+	0.00859297i
$856$	5832.82	−	2663.76i	0.232899	−	0.106362i
$857$	−13546.8	+	10141.0i	−0.539964	+	0.404212i	−0.834151	−	0.551536i	$-0.814042\pi$
$857$	−13546.8	+	10141.0i	−0.539964	+	0.404212i	0.294187	+	0.955748i	$0.404951\pi$
$858$	−6631.48	−	3621.06i	−0.263864	−	0.144081i
$859$	−12407.6	+	19306.7i	−0.492833	+	0.766863i	−0.995207	−	0.0977874i	$-0.968823\pi$
$859$	−12407.6	+	19306.7i	−0.492833	+	0.766863i	0.502375	+	0.864650i	$0.332460\pi$
$860$	5099.54	+	3408.69i	0.202201	+	0.135157i
$861$	−8875.58	+	30227.4i	−0.351311	+	1.19646i
$862$	−20496.7	−	1465.95i	−0.809884	−	0.0579240i
$863$	−14355.7	−	1026.74i	−0.566249	−	0.0404989i	−0.214720	−	0.976676i	$-0.568884\pi$
$863$	−14355.7	−	1026.74i	−0.566249	−	0.0404989i	−0.351529	+	0.936177i	$0.614338\pi$
$864$	−1321.75	+	4501.47i	−0.0520450	+	0.177249i
$865$	−7828.70	−	5232.94i	−0.307727	−	0.205694i
$866$	5054.14	−	7864.39i	0.198322	−	0.308595i
$867$	16055.8	+	8767.15i	0.628933	+	0.343423i
$868$	82.0461	−	61.4190i	0.00320833	−	0.00240172i
$869$	40322.4	−	18414.6i	1.57404	−	0.718841i
$870$	16489.0	−	15905.1i	0.642562	−	0.619807i
$871$	7922.24	+	12327.2i	0.308192	+	0.479555i
$872$	−721.241	−	10084.3i	−0.0280095	−	0.391624i
$873$	−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
$877$	−20805.9	−	4526.05i	−0.801102	−	0.174269i	−0.206666	−	0.978412i	$-0.566261\pi$
$877$	−20805.9	−	4526.05i	−0.801102	−	0.174269i	−0.594437	+	0.804143i	$0.702625\pi$
$878$	−9354.04	−	7002.35i	−0.359548	−	0.269155i
$879$	−4566.58	−	9999.42i	−0.175230	−	0.383700i
$880$	6210.87	−	3247.47i	0.237919	−	0.124400i
$881$	11188.1	+	38103.2i	0.427851	+	1.45713i	0.838282	+	0.545236i	$0.183560\pi$
$881$	11188.1	+	38103.2i	0.427851	+	1.45713i	−0.410431	+	0.911892i	$0.634622\pi$
$882$	−502.904	−	2311.81i	−0.0191991	−	0.0882570i
$883$	−14175.7	−	38006.5i	−0.540260	−	1.44849i	−0.864555	−	0.502538i	$-0.832400\pi$
$883$	−14175.7	−	38006.5i	−0.540260	−	1.44849i	0.324295	−	0.945956i	$-0.394873\pi$
$884$	2599.59	+	763.309i	0.0989069	+	0.0290417i
$885$	−14521.6	−	23517.4i	−0.551568	−	0.893254i
$886$	16651.9	+	19217.4i	0.631414	+	0.728691i
$887$	1127.59	+	2065.03i	0.0426842	+	0.0781703i	0.898150	−	0.439688i	$-0.144911\pi$
$887$	1127.59	+	2065.03i	0.0426842	+	0.0781703i	−0.855466	+	0.517859i	$0.826729\pi$
$888$	−5039.35	+	1879.58i	−0.190439	+	0.0710299i
$889$	45875.8	+	29482.6i	1.73074	+	1.11228i
$890$	1595.14	−	200.074i	0.0600777	−	0.00753538i
$891$	−25026.5	−	3598.27i	−0.940987	−	0.135293i
$892$	894.922	−	2399.38i	0.0335922	−	0.0900641i
$893$	3071.27	−	4102.74i	0.115091	−	0.153744i
$894$	15302.9	−	9834.56i	0.572488	−	0.367916i
$895$	47011.6	+	4215.21i	1.75578	+	0.157429i
$896$		−	3539.00i		−	0.131953i
$897$	5364.84	−	9183.84i	0.199695	−	0.341850i
$898$	17129.5	−	17129.5i	0.636548	−	0.636548i
$899$	−145.886	−	126.411i	−0.00541219	−	0.00468969i
$900$	346.613	+	1359.99i	0.0128375	+	0.0503701i
$901$	1385.54	+	9636.65i	0.0512309	+	0.356319i
$902$	17007.8	+	6343.60i	0.627826	+	0.234167i
$903$	11178.0	+	14932.0i	0.411938	+	0.550285i
$904$	−8880.92	+	2607.67i	−0.326742	+	0.0959401i
$905$	82.4300	+	1542.87i	0.00302770	+	0.0566704i
$906$	2382.94	−	5217.90i	0.0873816	−	0.191339i
$907$	−11202.0	+	6116.76i	−0.410095	+	0.223929i	−0.671034	−	0.741426i	$-0.734150\pi$
$907$	−11202.0	+	6116.76i	−0.410095	+	0.223929i	0.260939	+	0.965355i	$0.415968\pi$
$908$	214.388	−	2997.53i	0.00783557	−	0.109556i
$909$	1071.11	−	928.122i	0.0390830	−	0.0338656i
$910$	−5232.63	+	10932.0i	−0.190615	+	0.398235i
$911$	−28474.5	−	13003.8i	−1.03557	−	0.472927i	−0.176236	−	0.984348i	$-0.556392\pi$
$911$	−28474.5	−	13003.8i	−1.03557	−	0.472927i	−0.859330	+	0.511421i	$0.829119\pi$
$912$	−758.256	+	164.948i	−0.0275311	+	0.00598902i
$913$	−8858.98	+	16224.0i	−0.321128	+	0.588101i
$914$	3058.77	−	21274.2i	0.110695	−	0.769901i
$915$	8131.54	+	29661.0i	0.293793	+	1.07165i
$916$	8733.04	−	1255.62i	0.315008	−	0.0452914i
$917$	5865.47	−	26963.1i	0.211227	−	0.970993i
$918$	10105.3	−	722.742i	0.363315	−	0.0259848i
$919$	545.093			0.0195658			0.00978289	−	0.999952i	$-0.496886\pi$
$919$	545.093			0.0195658			0.00978289	+	0.999952i	$0.496886\pi$
$920$	4316.91	+	8871.32i	0.154700	+	0.317912i
$921$	51233.6			1.83301
$922$	20846.7	−	1490.99i	0.744631	−	0.0532571i
$923$	3565.65	−	16391.0i	0.127156	−	0.584526i
$924$	21095.6	−	3033.08i	0.751075	−	0.107988i
$925$	−10725.4	+	13299.9i	−0.381241	+	0.472755i
$926$	4214.31	−	29311.2i	0.149558	−	1.04020i
$927$	−1924.45	+	3524.36i	−0.0681846	+	0.124871i
$928$	−6513.28	+	1416.88i	−0.230398	+	0.0501199i
$929$	31484.3	+	14378.4i	1.11191	+	0.507794i	0.884751	−	0.466063i	$-0.154328\pi$
$929$	31484.3	+	14378.4i	1.11191	+	0.507794i	0.227162	+	0.973857i	$0.427055\pi$
$930$	−96.1238	+	33.8917i	−0.00338927	+	0.00119500i
$931$	3140.49	−	2721.25i	0.110554	−	0.0957953i
$932$	743.668	−	10397.8i	0.0261370	−	0.365443i
$933$	21454.6	−	11715.1i	0.752832	−	0.411077i
$934$	−2611.36	+	5718.08i	−0.0914842	+	0.200322i
$935$	−11257.6	−	10115.7i	−0.393758	−	0.353817i
$936$	−422.382	+	124.023i	−0.0147500	+	0.00433099i
$937$	28071.3	+	37498.8i	0.978707	+	1.30740i	0.951461	+	0.307770i	$0.0995828\pi$
$937$	28071.3	+	37498.8i	0.978707	+	1.30740i	0.0272459	+	0.999629i	$0.491326\pi$
$938$	−38727.1	−	14444.4i	−1.34806	−	0.502802i
$939$	−5100.32	−	35473.5i	−0.177255	−	1.23284i
$940$	−9273.36	−	21314.3i	−0.321770	−	0.739570i
$941$	436.657	+	378.366i	0.0151271	+	0.0131077i	0.662392	−	0.749158i	$-0.269542\pi$
$941$	436.657	+	378.366i	0.0151271	+	0.0131077i	−0.647264	+	0.762266i	$0.724087\pi$
$942$	12759.9	−	12759.9i	0.441339	−	0.441339i
$943$	−9617.65	+	23673.6i	−0.332125	+	0.817516i
$944$			8041.76i			0.277264i
$945$	−4047.27	+	45138.7i	−0.139320	+	1.55382i
$946$	9041.40	−	5810.55i	0.310741	−	0.199701i
$947$	27593.1	−	36860.1i	0.946838	−	1.26483i	−0.0174165	−	0.999848i	$-0.505544\pi$
$947$	27593.1	−	36860.1i	0.946838	−	1.26483i	0.964254	−	0.264979i	$-0.0853650\pi$
$948$	−7779.10	+	20856.6i	−0.266512	+	0.714547i
$949$	17265.0	+	2482.34i	0.590565	+	0.0849105i
$950$	−1804.76	+	1679.12i	−0.0616360	+	0.0573451i
$951$	−12261.1	−	7879.75i	−0.418081	−	0.268684i
$952$	−7160.42	+	2670.70i	−0.243772	+	0.0909221i
$953$	−13416.4	−	24570.3i	−0.456033	−	0.835161i	0.543960	−	0.839111i	$-0.316924\pi$
$953$	−13416.4	−	24570.3i	−0.456033	−	0.835161i	−0.999992	+	0.00395010i	$0.998743\pi$
$954$	−1035.90	−	1195.49i	−0.0351557	−	0.0405718i
$955$	−10196.6	+	43116.3i	−0.345501	+	1.46095i
$956$	19403.8	+	5697.48i	0.656448	+	0.192751i
$957$	−14028.0	−	37610.6i	−0.473837	−	1.27041i
$958$	6260.40	+	28778.6i	0.211132	+	0.970558i
$959$	−19044.4	−	64859.1i	−0.641266	−	2.18395i
$960$	−1052.26	+	3358.51i	−0.0353766	+	0.112912i
$961$	−12375.3	−	27098.1i	−0.415403	−	0.909606i
$962$	−4290.20	−	3211.60i	−0.143785	−	0.107636i
$963$	2198.44	+	478.242i	0.0735658	+	0.0160033i
$964$	−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	$0.534943\pi$
$968$	−116.444	−	1628.10i	−0.00386637	−	0.0540589i
$969$	905.956	+	1409.69i	0.0300346	+	0.0467347i
$970$	−19145.7	−	19848.6i	−0.633744	−	0.657011i
$971$	−27393.8	+	12510.3i	−0.905364	+	0.413466i	−0.813003	−	0.582260i	$-0.802169\pi$
$971$	−27393.8	+	12510.3i	−0.905364	+	0.413466i	−0.0923610	+	0.995726i	$0.529441\pi$
$972$	−2511.44	+	1880.04i	−0.0828750	+	0.0620395i
$973$	−29717.4	−	16226.9i	−0.979133	−	0.534647i
$974$	−7290.10	+	11343.6i	−0.239825	+	0.373175i
$975$	8216.23	−	8818.69i	0.269877	−	0.289666i
$976$	2521.03	−	8585.84i	0.0826806	−	0.281584i
$977$	39345.4	+	2814.04i	1.28841	+	0.0921485i	0.698668	−	0.715446i	$-0.253777\pi$
$977$	39345.4	+	2814.04i	1.28841	+	0.0921485i	0.589737	+	0.807595i	$0.299231\pi$
$978$	30749.3	+	2199.23i	1.00537	+	0.0719057i
$979$	793.595	−	2702.73i	0.0259074	−	0.0882327i
$980$	−3673.67	−	18485.6i	−0.119746	−	0.602552i
$981$	1917.80	−	2984.16i	0.0624166	−	0.0971221i
$982$	−14230.5	−	7770.46i	−0.462438	−	0.252510i
$983$	−8587.54	+	6428.56i	−0.278637	+	0.208585i	−0.729451	−	0.684033i	$-0.760225\pi$
$983$	−8587.54	+	6428.56i	−0.278637	+	0.208585i	0.450814	+	0.892618i	$0.351134\pi$
$984$	−8291.73	+	3786.71i	−0.268629	+	0.122679i
$985$	−119.254	+	6615.66i	−0.00385762	+	0.214002i
$986$	7782.00	+	12109.0i	0.251348	+	0.391106i
$987$	−5042.48	−	70503.0i	−0.162618	−	2.27369i
$988$	−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	−0.934342	−	0.356379i	$-0.884011\pi$
$991$	−13995.5	+	16151.7i	−0.448620	+	0.517735i	0.485722	+	0.874113i	$0.338557\pi$
$992$	28.9771	+	6.30357i	0.000927442	+	0.000201753i
$993$	5999.46	+	4491.14i	0.191729	+	0.143527i
$994$	19655.7	+	43039.9i	0.627203	+	1.37338i
$995$	−2181.46	−	4172.10i	−0.0695045	−	0.132929i
$996$	−2615.21	−	8906.58i	−0.0831988	−	0.283349i
$997$	8695.95	+	39974.6i	0.276232	+	1.26982i	0.880885	+	0.473330i	$0.156948\pi$
$997$	8695.95	+	39974.6i	0.276232	+	1.26982i	−0.604653	+	0.796489i	$0.706688\pi$
$998$	4597.24	+	12325.7i	0.145815	+	0.390945i
$999$	−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.7.23	✓	720
5.3	odd	4	inner	230.4.l.a.53.5	yes	720
23.10	odd	22	inner	230.4.l.a.217.5	yes	720
115.33	even	44	inner	230.4.l.a.33.23	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.l.a.7.23	✓	720	1.1	even	1	trivial
230.4.l.a.33.23	yes	720	115.33	even	44	inner
230.4.l.a.53.5	yes	720	5.3	odd	4	inner
230.4.l.a.217.5	yes	720	23.10	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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+(1.99490 - 0.142678i) q^{2} +(-1.04553 + 4.80624i) q^{3} +(3.95929 - 0.569259i) q^{4} +(9.71458 + 5.53415i) q^{5} +(-1.39999 + 9.73716i) q^{6} +(13.2505 - 24.2664i) q^{7} +(7.81717 - 1.70052i) q^{8} +(2.55328 + 1.16604i) q^{9} +(20.1693 + 9.65404i) q^{10} +(29.6099 - 25.6571i) q^{11} +(-1.40357 + 19.6244i) q^{12} +(-17.2059 + 9.39512i) q^{13} +(22.9711 - 50.2997i) q^{14} +(-36.7554 + 40.9045i) q^{15} +(15.3519 - 4.50772i) q^{16} +(-20.7057 - 27.6596i) q^{17} +(5.25992 + 1.96185i) q^{18} +(1.40327 + 9.75994i) q^{19} +(41.6132 + 16.3812i) q^{20} +(102.776 + 89.0562i) q^{21} +(55.4082 - 55.4082i) q^{22} +(75.7110 + 80.2175i) q^{23} +39.3492i q^{24} +(63.7463 + 107.524i) q^{25} +(-32.9836 + 21.1973i) q^{26} +(-87.8599 + 117.367i) q^{27} +(38.6485 - 103.621i) q^{28} +(-206.180 - 29.6442i) q^{29} +(-67.4873 + 86.8447i) q^{30} +(0.779599 + 0.501018i) q^{31} +(29.9824 - 11.1829i) q^{32} +(92.3560 + 169.137i) q^{33} +(-45.2524 - 52.2240i) q^{34} +(263.017 - 162.408i) q^{35} +(10.7729 + 3.16322i) q^{36} +(47.7667 + 128.068i) q^{37} +(4.19192 + 19.2699i) q^{38} +(-27.1659 - 92.5184i) q^{39} +(85.3516 + 26.7416i) q^{40} +(96.2335 + 210.722i) q^{41} +(217.735 + 162.995i) q^{42} +(134.023 + 29.1550i) 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} +(5.61427 + 78.4978i) q^{48} +(-227.844 - 354.533i) q^{49} +(142.509 + 205.405i) q^{50} +(154.587 - 70.5976i) q^{51} +(-62.7747 + 46.9926i) q^{52} +(-247.310 - 135.042i) q^{53} +(-158.526 + 246.672i) q^{54} +(429.638 - 85.3825i) q^{55} +(62.3156 - 212.228i) q^{56} +(-48.3758 - 3.45990i) q^{57} +(-415.539 - 29.7200i) q^{58} +(-141.602 + 482.251i) q^{59} +(-122.240 + 182.876i) q^{60} +(302.364 - 470.487i) q^{61} +(1.62671 + 0.888251i) q^{62} +(62.1279 - 46.5083i) q^{63} +(58.2164 - 26.5866i) q^{64} +(-219.142 - 3.95027i) q^{65} +(208.374 + 324.236i) q^{66} +(-53.3244 - 745.573i) 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} +(21.9423 + 4.77326i) q^{72} +(-712.284 - 533.209i) q^{73} +(113.562 + 248.667i) q^{74} +(-583.435 + 193.960i) q^{75} +(11.1119 + 37.8436i) q^{76} +(-230.261 - 1058.49i) q^{77} +(-67.3937 - 180.689i) q^{78} +(1085.58 + 318.756i) q^{79} +(174.084 + 41.1691i) q^{80} +(-422.604 - 487.711i) q^{81} +(222.042 + 406.640i) q^{82} +(-442.059 + 164.879i) q^{83} +(457.617 + 294.093i) q^{84} +(-48.0750 - 383.290i) q^{85} +(271.523 + 39.0391i) q^{86} +(358.046 - 959.957i) q^{87} +(187.835 - 250.918i) q^{88} +(60.4825 - 38.8698i) q^{89} +(40.2408 + 48.1677i) q^{90} +542.015i q^{91} +(345.426 + 274.505i) q^{92} +(-3.22311 + 3.22311i) q^{93} +(-785.612 - 680.737i) q^{94} +(-40.3808 + 102.580i) q^{95} +(22.3999 + 155.795i) q^{96} +(-1155.55 - 430.997i) q^{97} +(-505.112 - 674.751i) 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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