LMFDB - Embedded newform 230.4.l.a.7.15

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			7.15
Character	$\chi$	$=$	230.7
Dual form			230.4.l.a.33.15

$q$-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} +(1.32678 - 6.09912i) q^{3} +(3.95929 - 0.569259i) q^{4} +(9.97777 + 5.04421i) q^{5} +(-1.77659 + 12.3565i) q^{6} +(14.8793 - 27.2494i) q^{7} +(-7.81717 + 1.70052i) q^{8} +(-10.8788 - 4.96819i) q^{9} +(-20.6244 - 8.63909i) q^{10} +(22.6211 - 19.6013i) q^{11} +(1.78113 - 24.9034i) q^{12} +(-2.08291 + 1.13736i) q^{13} +(-25.7949 + 56.4829i) q^{14} +(44.0035 - 54.1631i) q^{15} +(15.3519 - 4.50772i) q^{16} +(59.5872 + 79.5992i) q^{17} +(22.4111 + 8.35890i) q^{18} +(11.7162 + 81.4881i) q^{19} +(42.3763 + 14.2915i) q^{20} +(-146.456 - 126.905i) q^{21} +(-42.3302 + 42.3302i) q^{22} +(106.309 - 29.4175i) q^{23} +49.9341i q^{24} +(74.1120 + 100.660i) q^{25} +(3.99294 - 2.56610i) q^{26} +(56.2594 - 75.1537i) q^{27} +(43.3994 - 116.358i) q^{28} +(-201.669 - 28.9956i) q^{29} +(-80.0549 + 114.328i) q^{30} +(-155.812 - 100.134i) q^{31} +(-29.9824 + 11.1829i) q^{32} +(-89.5373 - 163.975i) q^{33} +(-130.228 - 150.291i) q^{34} +(285.914 - 196.834i) q^{35} +(-45.9006 - 13.4776i) q^{36} +(-84.7578 - 227.244i) q^{37} +(-34.9993 - 160.889i) q^{38} +(4.17330 + 14.2130i) q^{39} +(-86.5758 - 22.4640i) q^{40} +(75.4444 + 165.200i) q^{41} +(310.272 + 232.266i) q^{42} +(-244.551 - 53.1987i) q^{43} +(78.4052 - 90.4844i) q^{44} +(-83.4859 - 104.447i) q^{45} +(-207.879 + 73.8531i) q^{46} +(77.5288 + 77.5288i) q^{47} +(-7.12452 - 99.6137i) q^{48} +(-335.696 - 522.353i) q^{49} +(-162.208 - 190.233i) q^{50} +(564.544 - 257.819i) q^{51} +(-7.59940 + 5.68884i) q^{52} +(-245.473 - 134.039i) q^{53} +(-101.509 + 157.951i) q^{54} +(324.581 - 81.4718i) q^{55} +(-69.9758 + 238.316i) q^{56} +(512.551 + 36.6583i) q^{57} +(406.447 + 29.0697i) q^{58} +(136.931 - 466.345i) q^{59} +(143.390 - 239.496i) q^{60} +(-180.929 + 281.531i) q^{61} +(325.117 + 177.527i) q^{62} +(-297.250 + 222.518i) q^{63} +(58.2164 - 26.5866i) q^{64} +(-26.5199 + 0.841646i) q^{65} +(202.014 + 314.340i) q^{66} +(48.1347 + 673.011i) q^{67} +(281.235 + 281.235i) q^{68} +(-38.3721 - 687.422i) q^{69} +(-542.287 + 433.459i) q^{70} +(316.520 - 365.283i) q^{71} +(93.4902 + 20.3376i) q^{72} +(644.092 + 482.161i) q^{73} +(201.507 + 441.238i) q^{74} +(712.267 - 318.464i) q^{75} +(92.7758 + 315.965i) q^{76} +(-197.537 - 908.064i) q^{77} +(-10.3532 - 27.7580i) q^{78} +(-651.571 - 191.318i) q^{79} +(175.916 + 32.4611i) q^{80} +(-595.188 - 686.884i) q^{81} +(-174.075 - 318.794i) q^{82} +(-143.392 + 53.4826i) q^{83} +(-652.101 - 419.080i) q^{84} +(193.033 + 1094.79i) q^{85} +(495.445 + 71.2343i) q^{86} +(-444.418 + 1191.53i) q^{87} +(-143.501 + 191.694i) q^{88} +(-848.401 + 545.234i) q^{89} +(181.449 + 196.449i) q^{90} +73.6812i q^{91} +(404.162 - 176.990i) q^{92} +(-817.459 + 817.459i) q^{93} +(-165.724 - 143.601i) q^{94} +(-294.141 + 872.169i) q^{95} +(28.4255 + 197.703i) q^{96} +(-64.7669 - 24.1568i) q^{97} +(744.210 + 994.148i) q^{98} +(-343.474 + 100.853i) 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
$3$	1.32678	−	6.09912i	0.255339	−	1.17378i	−0.653598	−	0.756842i	$-0.726741\pi$
$3$	1.32678	−	6.09912i	0.255339	−	1.17378i	0.908937	−	0.416934i	$-0.136895\pi$
$4$	3.95929	−	0.569259i	0.494911	−	0.0711574i
$5$	9.97777	+	5.04421i	0.892439	+	0.451167i
$5$	9.97777	+	5.04421i	0.892439	+	0.451167i
$6$	−1.77659	+	12.3565i	−0.120882	+	0.840751i
$7$	14.8793	−	27.2494i	0.803406	−	1.47133i	−0.0769600	−	0.997034i	$-0.524521\pi$
$7$	14.8793	−	27.2494i	0.803406	−	1.47133i	0.880366	−	0.474295i	$-0.157297\pi$
$8$	−7.81717	+	1.70052i	−0.345474	+	0.0751532i
$9$	−10.8788	−	4.96819i	−0.402920	−	0.184007i
$10$	−20.6244	−	8.63909i	−0.652201	−	0.273192i
$11$	22.6211	−	19.6013i	0.620047	−	0.537274i	−0.287201	−	0.957870i	$-0.592725\pi$
$11$	22.6211	−	19.6013i	0.620047	−	0.537274i	0.907248	+	0.420597i	$0.138179\pi$
$12$	1.78113	−	24.9034i	0.0428473	−	0.599084i
$13$	−2.08291	+	1.13736i	−0.0444382	+	0.0242651i	−0.501314	−	0.865265i	$-0.667150\pi$
$13$	−2.08291	+	1.13736i	−0.0444382	+	0.0242651i	0.456876	+	0.889530i	$0.348968\pi$
$14$	−25.7949	+	56.4829i	−0.492426	+	1.07826i
$15$	44.0035	−	54.1631i	0.757444	−	0.932323i
$16$	15.3519	−	4.50772i	0.239873	−	0.0704331i
$17$	59.5872	+	79.5992i	0.850119	+	1.13563i	0.989377	+	0.145370i	$0.0464372\pi$
$17$	59.5872	+	79.5992i	0.850119	+	1.13563i	−0.139258	+	0.990256i	$0.544472\pi$
$18$	22.4111	+	8.35890i	0.293463	+	0.109456i
$19$	11.7162	+	81.4881i	0.141468	+	0.983929i	0.929639	+	0.368473i	$0.120119\pi$
$19$	11.7162	+	81.4881i	0.141468	+	0.983929i	−0.788171	+	0.615457i	$0.788972\pi$
$20$	42.3763	+	14.2915i	0.473782	+	0.159784i
$21$	−146.456	−	126.905i	−1.52187	−	1.31871i
$22$	−42.3302	+	42.3302i	−0.410220	+	0.410220i
$23$	106.309	−	29.4175i	0.963781	−	0.266695i
$23$	106.309	−	29.4175i	0.963781	−	0.266695i
$24$			49.9341i			0.424698i
$25$	74.1120	+	100.660i	0.592896	+	0.805279i
$26$	3.99294	−	2.56610i	0.0301184	−	0.0193559i
$27$	56.2594	−	75.1537i	0.401004	−	0.535679i
$28$	43.3994	−	116.358i	0.292918	−	0.785345i
$29$	−201.669	−	28.9956i	−1.29134	−	0.185667i	−0.537804	−	0.843070i	$-0.680746\pi$
$29$	−201.669	−	28.9956i	−1.29134	−	0.185667i	−0.753539	+	0.657403i	$0.771655\pi$
$30$	−80.0549	+	114.328i	−0.487199	+	0.695781i
$31$	−155.812	−	100.134i	−0.902730	−	0.580149i	0.00486857	−	0.999988i	$-0.498450\pi$
$31$	−155.812	−	100.134i	−0.902730	−	0.580149i	−0.907599	+	0.419839i	$0.862087\pi$
$32$	−29.9824	+	11.1829i	−0.165631	+	0.0617771i
$33$	−89.5373	−	163.975i	−0.472317	−	0.864983i
$34$	−130.228	−	150.291i	−0.656879	−	0.758079i
$35$	285.914	−	196.834i	1.38081	−	0.950601i
$36$	−45.9006	−	13.4776i	−0.212503	−	0.0623964i
$37$	−84.7578	−	227.244i	−0.376597	−	1.00970i	−0.977604	−	0.210452i	$-0.932506\pi$
$37$	−84.7578	−	227.244i	−0.376597	−	1.00970i	0.601007	−	0.799244i	$-0.294766\pi$
$38$	−34.9993	−	160.889i	−0.149412	−	0.686834i
$39$	4.17330	+	14.2130i	0.0171349	+	0.0583563i
$40$	−86.5758	−	22.4640i	−0.342221	−	0.0887968i
$41$	75.4444	+	165.200i	0.287377	+	0.629267i	0.997173	−	0.0751400i	$-0.0239404\pi$
$41$	75.4444	+	165.200i	0.287377	+	0.629267i	−0.709796	+	0.704407i	$0.751213\pi$
$42$	310.272	+	232.266i	1.13990	+	0.853321i
$43$	−244.551	−	53.1987i	−0.867293	−	0.188668i	−0.243160	−	0.969986i	$-0.578184\pi$
$43$	−244.551	−	53.1987i	−0.867293	−	0.188668i	−0.624133	+	0.781318i	$0.714548\pi$
$44$	78.4052	−	90.4844i	0.268637	−	0.310023i
$45$	−83.4859	−	104.447i	−0.276563	−	0.345999i
$46$	−207.879	+	73.8531i	−0.666306	+	0.236719i
$47$	77.5288	+	77.5288i	0.240611	+	0.240611i	0.817103	−	0.576492i	$-0.195579\pi$
$47$	77.5288	+	77.5288i	0.240611	+	0.240611i	−0.576492	+	0.817103i	$0.695579\pi$
$48$	−7.12452	−	99.6137i	−0.0214237	−	0.299542i
$49$	−335.696	−	522.353i	−0.978706	−	1.52290i
$50$	−162.208	−	190.233i	−0.458794	−	0.538059i
$51$	564.544	−	257.819i	1.55004	−	0.707879i
$52$	−7.59940	+	5.68884i	−0.0202663	+	0.0151711i
$53$	−245.473	−	134.039i	−0.636196	−	0.347389i	0.128567	−	0.991701i	$-0.458962\pi$
$53$	−245.473	−	134.039i	−0.636196	−	0.347389i	−0.764763	+	0.644312i	$0.777144\pi$
$54$	−101.509	+	157.951i	−0.255808	+	0.398046i
$55$	324.581	−	81.4718i	0.795755	−	0.199739i
$56$	−69.9758	+	238.316i	−0.166981	+	0.568684i
$57$	512.551	+	36.6583i	1.19103	+	0.0851845i
$58$	406.447	+	29.0697i	0.920157	+	0.0658109i
$59$	136.931	−	466.345i	0.302152	−	1.02903i	−0.658800	−	0.752318i	$-0.728936\pi$
$59$	136.931	−	466.345i	0.302152	−	1.02903i	0.960952	−	0.276716i	$-0.0892461\pi$
$60$	143.390	−	239.496i	0.308526	−	0.515314i
$61$	−180.929	+	281.531i	−0.379764	+	0.590925i	−0.977543	−	0.210737i	$-0.932414\pi$
$61$	−180.929	+	281.531i	−0.379764	+	0.590925i	0.597779	+	0.801661i	$0.296050\pi$
$62$	325.117	+	177.527i	0.665966	+	0.363645i
$63$	−297.250	+	222.518i	−0.594443	+	0.444995i
$64$	58.2164	−	26.5866i	0.113704	−	0.0519269i
$65$	−26.5199	+	0.841646i	−0.0506060	+	0.00160605i
$66$	202.014	+	314.340i	0.376761	+	0.586251i
$67$	48.1347	+	673.011i	0.0877699	+	1.22718i	0.830279	+	0.557348i	$0.188181\pi$
$67$	48.1347	+	673.011i	0.0877699	+	1.22718i	−0.742509	+	0.669836i	$0.766364\pi$
$68$	281.235	+	281.235i	0.501541	+	0.501541i
$69$	−38.3721	−	687.422i	−0.0669486	−	1.19936i
$70$	−542.287	+	433.459i	−0.925938	+	0.740118i
$71$	316.520	−	365.283i	0.529070	−	0.610580i	−0.426808	−	0.904342i	$-0.640362\pi$
$71$	316.520	−	365.283i	0.529070	−	0.610580i	0.955878	+	0.293762i	$0.0949075\pi$
$72$	93.4902	+	20.3376i	0.153027	+	0.0332889i
$73$	644.092	+	482.161i	1.03267	+	0.773051i	0.974302	−	0.225244i	$-0.0723180\pi$
$73$	644.092	+	482.161i	1.03267	+	0.773051i	0.0583724	+	0.998295i	$0.481409\pi$
$74$	201.507	+	441.238i	0.316549	+	0.693147i
$75$	712.267	−	318.464i	1.09661	−	0.490307i
$76$	92.7758	+	315.965i	0.140028	+	0.476891i
$77$	−197.537	−	908.064i	−0.292357	−	1.34394i
$78$	−10.3532	−	27.7580i	−0.0150291	−	0.0402946i
$79$	−651.571	−	191.318i	−0.927942	−	0.272468i	−0.217367	−	0.976090i	$-0.569747\pi$
$79$	−651.571	−	191.318i	−0.927942	−	0.272468i	−0.710575	+	0.703621i	$0.751565\pi$
$80$	175.916	+	32.4611i	0.245849	+	0.0453657i
$81$	−595.188	−	686.884i	−0.816444	−	0.942227i
$82$	−174.075	−	318.794i	−0.234431	−	0.429329i
$83$	−143.392	+	53.4826i	−0.189631	+	0.0707286i	−0.442486	−	0.896776i	$-0.645903\pi$
$83$	−143.392	+	53.4826i	−0.189631	+	0.0707286i	0.252855	+	0.967504i	$0.418631\pi$
$84$	−652.101	−	419.080i	−0.847025	−	0.544350i
$85$	193.033	+	1094.79i	0.246322	+	1.39702i
$86$	495.445	+	71.2343i	0.621224	+	0.0893185i
$87$	−444.418	+	1191.53i	−0.547662	+	1.46834i
$88$	−143.501	+	191.694i	−0.173832	+	0.232212i
$89$	−848.401	+	545.234i	−1.01045	+	0.649379i	−0.937510	−	0.347957i	$-0.886875\pi$
$89$	−848.401	+	545.234i	−1.01045	+	0.649379i	−0.0729428	+	0.997336i	$0.523239\pi$
$90$	181.449	+	196.449i	0.212515	+	0.230084i
$91$			73.6812i			0.0848778i
$92$	404.162	−	176.990i	0.458008	−	0.200570i
$93$	−817.459	+	817.459i	−0.911468	+	0.911468i
$94$	−165.724	−	143.601i	−0.181842	−	0.157567i
$95$	−294.141	+	872.169i	−0.317666	+	0.941923i
$96$	28.4255	+	197.703i	0.0302204	+	0.210188i
$97$	−64.7669	−	24.1568i	−0.0677947	−	0.0252861i	0.315338	−	0.948979i	$-0.397882\pi$
$97$	−64.7669	−	24.1568i	−0.0677947	−	0.0252861i	−0.383133	+	0.923693i	$0.625155\pi$
$98$	744.210	+	994.148i	0.767108	+	1.02474i
$99$	−343.474	+	100.853i	−0.348691	+	0.102385i
$100$	350.732	+	356.352i	0.350732	+	0.356352i
$101$	−46.4841	+	101.786i	−0.0457954	+	0.100278i	−0.931147	−	0.364644i	$-0.881191\pi$
$101$	−46.4841	+	101.786i	−0.0457954	+	0.100278i	0.885351	+	0.464922i	$0.153918\pi$
$102$	−1089.43	+	594.872i	−1.05754	+	0.577462i
$103$	−109.922	+	1536.91i	−0.105155	+	1.47026i	0.621586	+	0.783346i	$0.286489\pi$
$103$	−109.922	+	1536.91i	−0.105155	+	1.47026i	−0.726741	+	0.686912i	$0.758966\pi$
$104$	14.3484	−	12.4330i	0.0135286	−	0.0117226i
$105$	−821.169	−	2004.98i	−0.763218	−	1.86348i
$106$	508.820	+	232.370i	0.466236	+	0.212923i
$107$	−1150.61	+	250.300i	−1.03957	+	0.226144i	−0.699781	−	0.714358i	$-0.746719\pi$
$107$	−1150.61	+	250.300i	−1.03957	+	0.226144i	−0.339788	+	0.940502i	$0.610355\pi$
$108$	179.965	−	329.581i	0.160344	−	0.293648i
$109$	121.145	−	842.582i	0.106455	−	0.740410i	−0.864757	−	0.502191i	$-0.832527\pi$
$109$	121.145	−	842.582i	0.106455	−	0.740410i	0.971212	−	0.238219i	$-0.0765635\pi$
$110$	−635.884	+	208.839i	−0.551174	+	0.181018i
$111$	−1498.45	+	215.444i	−1.28132	+	0.184226i
$112$	105.593	−	485.401i	0.0890854	−	0.409519i
$113$	378.076	−	27.0405i	0.314747	−	0.0225112i	0.0869279	−	0.996215i	$-0.472295\pi$
$113$	378.076	−	27.0405i	0.314747	−	0.0225112i	0.227819	+	0.973703i	$0.426840\pi$
$114$	−1027.72			−0.844340
$115$	1209.12	+	242.723i	0.980440	+	0.196818i
$116$	−814.970			−0.652311
$117$	28.3103	−	2.02479i	0.0223700	−	0.00159993i
$118$	−206.628	+	949.851i	−0.161200	+	0.741025i
$119$	3055.65	−	439.335i	2.35387	−	0.338435i
$120$	−251.878	+	498.231i	−0.191610	+	0.379017i
$121$	−61.9177	+	430.647i	−0.0465197	+	0.323552i
$122$	320.768	−	587.443i	0.238041	−	0.435939i
$123$	1107.67	−	240.960i	0.811997	−	0.176639i
$124$	−673.906	−	307.763i	−0.488053	−	0.222886i
$125$	231.723	+	1378.20i	0.165808	+	0.986158i
$126$	561.236	−	486.314i	0.396816	−	0.343843i
$127$	21.0863	−	294.825i	0.0147331	−	0.205996i	−0.984753	−	0.173956i	$-0.944345\pi$
$127$	21.0863	−	294.825i	0.0147331	−	0.205996i	0.999487	−	0.0320403i	$-0.0102005\pi$
$128$	−112.343	+	61.3439i	−0.0775766	+	0.0423600i
$129$	−648.930	+	1420.96i	−0.442908	+	0.969833i
$130$	52.7846	−	5.46282i	0.0356116	−	0.00368554i
$131$	2445.42	−	718.039i	1.63097	−	0.478896i	0.667033	−	0.745029i	$-0.267564\pi$
$131$	2445.42	−	718.039i	1.63097	−	0.478896i	0.963936	+	0.266133i	$0.0857460\pi$
$132$	−447.848	−	598.255i	−0.295304	−	0.394481i
$133$	2394.83	+	893.226i	1.56134	+	0.582350i
$134$	−192.048	−	1335.72i	−0.123809	−	0.861112i
$135$	940.434	−	466.083i	0.599553	−	0.297141i
$136$	−601.164	−	520.912i	−0.379040	−	0.328440i
$137$	38.8234	−	38.8234i	0.0242110	−	0.0242110i	−0.694898	−	0.719109i	$-0.744550\pi$
$137$	38.8234	−	38.8234i	0.0242110	−	0.0242110i	0.719109	+	0.694898i	$0.244550\pi$
$138$	174.629	+	1365.87i	0.107720	+	0.842538i
$139$			2367.17i			1.44447i	0.691649	+	0.722233i	$0.256884\pi$
$139$			2367.17i			1.44447i	−0.691649	+	0.722233i	$0.743116\pi$
$140$	1019.96	−	942.081i	0.615734	−	0.568717i
$141$	575.721	−	369.994i	0.343861	−	0.220986i
$142$	−579.309	+	773.866i	−0.342356	+	0.457334i
$143$	−24.8241	+	66.5560i	−0.0145168	+	0.0389209i
$144$	−189.406	−	27.2324i	−0.109610	−	0.0157595i
$145$	−1865.95	−	1306.57i	−1.06868	−	0.748309i
$146$	−1353.70	−	869.967i	−0.767347	−	0.493144i
$147$	−3631.29	+	1354.40i	−2.03744	+	0.759926i
$148$	−464.941	−	851.476i	−0.258229	−	0.472912i
$149$	548.468	+	632.965i	0.301559	+	0.348017i	0.886224	−	0.463258i	$-0.153320\pi$
$149$	548.468	+	632.965i	0.301559	+	0.348017i	−0.584665	+	0.811275i	$0.698774\pi$
$150$	−1375.47	+	736.930i	−0.748709	+	0.401134i
$151$	−743.342	−	218.265i	−0.400611	−	0.117630i	0.0752194	−	0.997167i	$-0.476034\pi$
$151$	−743.342	−	218.265i	−0.400611	−	0.117630i	−0.475831	+	0.879537i	$0.657852\pi$
$152$	−230.160	−	617.083i	−0.122819	−	0.329290i
$153$	−252.775	−	1161.99i	−0.133566	−	0.613994i
$154$	523.629	+	1783.32i	0.273995	+	0.933141i
$155$	−1049.56	−	1785.06i	−0.543887	−	0.925031i
$156$	24.6141	+	53.8975i	0.0126327	+	0.0276619i
$157$	2292.40	+	1716.07i	1.16531	+	0.872337i	0.993616	−	0.112814i	$-0.0359864\pi$
$157$	2292.40	+	1716.07i	1.16531	+	0.872337i	0.171690	+	0.985151i	$0.445077\pi$
$158$	1327.12	+	288.697i	0.668227	+	0.145364i
$159$	−1143.21	+	1319.33i	−0.570203	+	0.658049i
$160$	−355.566	−	39.6573i	−0.175687	−	0.0195949i
$161$	780.193	−	3334.57i	0.381912	−	1.63230i
$162$	1285.35	+	1285.35i	0.623373	+	0.623373i
$163$	−186.947	−	2613.86i	−0.0898332	−	1.25603i	−0.819840	−	0.572593i	$-0.805938\pi$
$163$	−186.947	−	2613.86i	−0.0898332	−	1.25603i	0.730007	−	0.683440i	$-0.239517\pi$
$164$	392.748	+	611.128i	0.187003	+	0.290982i
$165$	−66.2578	−	2087.75i	−0.0312616	−	0.985039i
$166$	278.423	−	127.152i	0.130180	−	0.0594511i
$167$	1385.55	−	1037.21i	0.642017	−	0.480608i	−0.227979	−	0.973666i	$-0.573212\pi$
$167$	1385.55	−	1037.21i	0.642017	−	0.480608i	0.869996	+	0.493058i	$0.164121\pi$
$168$	1360.67	+	742.984i	0.624871	+	0.341205i
$169$	−1184.74	+	1843.50i	−0.539255	+	0.839097i
$170$	−541.286	−	2156.47i	−0.244204	−	0.972902i
$171$	277.390	−	944.704i	0.124050	−	0.422475i
$172$	−998.529	−	71.4162i	−0.442658	−	0.0316595i
$173$	2631.62	+	188.217i	1.15652	+	0.0827162i	0.636389	−	0.771368i	$-0.280427\pi$
$173$	2631.62	+	188.217i	1.15652	+	0.0827162i	0.520134	+	0.854085i	$0.325882\pi$
$174$	716.566	−	2440.40i	0.312199	−	1.06325i
$175$	3845.65	−	521.758i	1.66117	−	0.225378i
$176$	258.919	−	402.886i	0.110891	−	0.172549i
$177$	−2662.62	−	1453.90i	−1.13070	−	0.617411i
$178$	1614.69	−	1208.74i	0.679920	−	0.508982i
$179$	−4021.18	+	1836.41i	−1.67909	+	0.766814i	−0.679643	+	0.733543i	$0.737865\pi$
$179$	−4021.18	+	1836.41i	−1.67909	+	0.766814i	−0.999446	+	0.0332714i	$0.989407\pi$
$180$	−390.002	−	366.009i	−0.161495	−	0.151559i
$181$	2159.02	+	3359.50i	0.886622	+	1.37961i	0.924846	+	0.380342i	$0.124194\pi$
$181$	2159.02	+	3359.50i	0.886622	+	1.37961i	−0.0382238	+	0.999269i	$0.512170\pi$
$182$	−10.5127	−	146.987i	−0.00428161	−	0.0598648i
$183$	1477.04	+	1477.04i	0.596644	+	0.596644i
$184$	−781.011	+	410.743i	−0.312918	+	0.164567i
$185$	300.573	−	2694.93i	0.119452	−	1.07100i
$186$	1514.12	−	1747.39i	0.596885	−	0.688841i
$187$	2908.17	+	632.635i	1.13726	+	0.247395i
$188$	351.093	+	262.825i	0.136202	+	0.101960i
$189$	−1210.79	−	2651.27i	−0.465991	−	1.02038i
$190$	462.343	−	1781.86i	0.176536	−	0.680367i
$191$	−1166.72	−	3973.48i	−0.441994	−	1.50529i	−0.816102	−	0.577907i	$-0.803870\pi$
$191$	−1166.72	−	3973.48i	−0.441994	−	1.50529i	0.374109	−	0.927385i	$-0.377949\pi$
$192$	−84.9140	−	390.344i	−0.0319174	−	0.146722i
$193$	−493.138	−	1322.16i	−0.183922	−	0.493113i	0.811967	−	0.583704i	$-0.198397\pi$
$193$	−493.138	−	1322.16i	−0.183922	−	0.493113i	−0.995888	+	0.0905910i	$0.971124\pi$
$194$	132.650	+	38.9497i	0.0490915	+	0.0144146i
$195$	−30.0528	+	162.865i	−0.0110365	+	0.0598101i
$196$	−1626.47	−	1877.05i	−0.592737	−	0.684055i
$197$	297.752	+	545.291i	0.107685	+	0.197210i	0.925965	−	0.377610i	$-0.123254\pi$
$197$	297.752	+	545.291i	0.107685	+	0.197210i	−0.818280	+	0.574820i	$0.805072\pi$
$198$	670.808	−	250.199i	0.240769	−	0.0898022i
$199$	−3836.05	−	2465.28i	−1.36648	−	0.878186i	−0.367822	−	0.929896i	$-0.619896\pi$
$199$	−3836.05	−	2465.28i	−1.36648	−	0.878186i	−0.998662	+	0.0517104i	$0.983533\pi$
$200$	−750.521	−	660.847i	−0.265349	−	0.233645i
$201$	4168.64	+	599.359i	1.46285	+	0.210326i
$202$	78.2086	−	209.685i	0.0272413	−	0.0730367i
$203$	−3790.80	+	5063.92i	−1.31065	+	1.75082i
$204$	2088.43	−	1342.15i	0.716760	−	0.460634i
$205$	−80.5365	+	2028.89i	−0.0274386	+	0.691237i
$206$		−	3081.68i		−	1.04228i
$207$	−1302.67	−	208.136i	−0.437400	−	0.0698861i
$208$	−26.8498	+	26.8498i	−0.00895046	+	0.00895046i
$209$	1862.31	+	1613.70i	0.616356	+	0.534075i
$210$	1924.22	+	3882.58i	0.632304	+	1.27582i
$211$	373.550	+	2598.10i	0.121878	+	0.847680i	0.955426	+	0.295232i	$0.0953969\pi$
$211$	373.550	+	2598.10i	0.121878	+	0.847680i	−0.833548	+	0.552448i	$0.813694\pi$
$212$	−1048.20	−	390.959i	−0.339579	−	0.126657i
$213$	−1807.95	−	2415.14i	−0.581591	−	0.776915i
$214$	2259.65	−	663.493i	0.721806	−	0.211941i
$215$	−2171.72	−	1764.37i	−0.688886	−	0.559669i
$216$	−311.989	+	683.160i	−0.0982785	+	0.215200i
$217$	−5046.97	+	2755.85i	−1.57885	+	0.862117i
$218$	−121.454	+	1698.15i	−0.0377336	+	0.527585i
$219$	3795.33	−	3288.67i	1.17107	−	1.01474i
$220$	1238.73	−	507.341i	0.379615	−	0.155477i
$221$	−214.648	−	98.0263i	−0.0653338	−	0.0298369i
$222$	2958.52	−	643.586i	0.894426	−	0.194571i
$223$	−2724.86	+	4990.21i	−0.818252	+	1.49852i	0.0479647	+	0.998849i	$0.484726\pi$
$223$	−2724.86	+	4990.21i	−0.818252	+	1.49852i	−0.866217	+	0.499668i	$0.833455\pi$
$224$	−141.391	+	983.395i	−0.0421744	+	0.293330i
$225$	−306.154	−	1463.26i	−0.0907122	−	0.433560i
$226$	−750.368	+	107.887i	−0.220857	+	0.0317545i
$227$	298.967	−	1374.33i	0.0874147	−	0.401839i	−0.912560	−	0.408943i	$-0.865898\pi$
$227$	298.967	−	1374.33i	0.0874147	−	0.401839i	0.999975	+	0.00710376i	$0.00226122\pi$
$228$	2050.20	−	146.633i	0.595517	−	0.0425922i
$229$	−4042.53			−1.16654			−0.583270	−	0.812278i	$-0.698227\pi$
$229$	−4042.53			−1.16654			−0.583270	+	0.812278i	$0.698227\pi$
$230$	−2446.70	−	311.695i	−0.701438	−	0.0893589i
$231$	−5800.48			−1.65214
$232$	1625.79	−	116.279i	0.460078	−	0.0329055i
$233$	539.082	−	2478.12i	0.151573	−	0.696768i	−0.837145	−	0.546980i	$-0.815777\pi$
$233$	539.082	−	2478.12i	0.151573	−	0.696768i	0.988718	−	0.149788i	$-0.0478591\pi$
$234$	−56.1874	+	8.07852i	−0.0156969	+	0.00225688i
$235$	382.494	+	1164.64i	0.106175	+	0.323287i
$236$	276.679	−	1924.34i	0.0763147	−	0.530780i
$237$	−2031.37	+	3720.17i	−0.556757	+	1.01962i
$238$	−6033.04	+	1312.41i	−1.64312	+	0.357440i
$239$	6107.44	+	2789.17i	1.65296	+	0.754881i	0.999997	−	0.00250874i	$-0.000798558\pi$
$239$	6107.44	+	2789.17i	1.65296	+	0.754881i	0.652963	+	0.757390i	$0.273526\pi$
$240$	431.385	−	1029.86i	0.116024	−	0.276989i
$241$	325.875	−	282.372i	0.0871014	−	0.0754738i	−0.610222	−	0.792231i	$-0.708920\pi$
$241$	325.875	−	282.372i	0.0871014	−	0.0754738i	0.697323	+	0.716757i	$0.254374\pi$
$242$	62.0759	−	867.934i	0.0164892	−	0.230549i
$243$	−2754.40	+	1504.01i	−0.727138	+	0.397047i
$244$	−556.086	+	1217.66i	−0.145901	+	0.319478i
$245$	−714.642	−	6905.24i	−0.186354	−	1.80065i
$246$	−2175.32	+	638.733i	−0.563795	+	0.165545i
$247$	−117.085	−	156.407i	−0.0301617	−	0.0402913i
$248$	1388.29	+	517.805i	0.355470	+	0.132583i
$249$	135.946	+	945.527i	0.0345994	+	0.240644i
$250$	−658.905	−	2716.31i	−0.166691	−	0.687178i
$251$	3192.15	+	2766.02i	0.802737	+	0.695575i	0.956243	−	0.292572i	$-0.0945112\pi$
$251$	3192.15	+	2766.02i	0.802737	+	0.695575i	−0.153507	+	0.988148i	$0.549057\pi$
$252$	−1050.23	+	1050.23i	−0.262532	+	0.262532i
$253$	1828.20	−	2749.25i	0.454301	−	0.683177i
$254$			591.157i			0.146033i
$255$	6933.39	+	275.220i	1.70269	+	0.0675880i
$256$	215.361	−	138.404i	0.0525783	−	0.0337901i
$257$	−2305.03	+	3079.16i	−0.559471	+	0.747365i	−0.987710	−	0.156300i	$-0.950043\pi$
$257$	−2305.03	+	3079.16i	−0.559471	+	0.747365i	0.428239	+	0.903666i	$0.359134\pi$
$258$	1091.81	−	2927.27i	0.263463	−	0.706371i
$259$	−7453.41	−	1071.64i	−1.78816	−	0.257098i
$260$	−104.521	+	18.4290i	−0.0249312	+	0.00439584i
$261$	2049.86	+	1317.37i	0.486143	+	0.312425i
$262$	−4775.92	+	1781.33i	−1.12617	+	0.420041i
$263$	3831.45	+	7016.77i	0.898316	+	1.64514i	0.755256	+	0.655430i	$0.227512\pi$
$263$	3831.45	+	7016.77i	0.898316	+	1.64514i	0.143060	+	0.989714i	$0.454306\pi$
$264$	978.773	+	1129.56i	0.228179	+	0.263333i
$265$	−1773.16	−	2575.63i	−0.411035	−	0.597054i
$266$	−4904.90	−	1440.21i	−1.13060	−	0.331973i
$267$	2199.80	+	5897.91i	0.504217	+	1.35186i
$268$	573.697	+	2637.24i	0.130762	+	0.601101i
$269$	−1902.67	−	6479.89i	−0.431255	−	1.46872i	−0.833157	−	0.553037i	$-0.813469\pi$
$269$	−1902.67	−	6479.89i	−0.431255	−	1.46872i	0.401902	−	0.915683i	$-0.368349\pi$
$270$	−1809.58	+	1063.97i	−0.407879	+	0.239819i
$271$	1739.23	+	3808.39i	0.389856	+	0.853666i	0.998199	+	0.0599913i	$0.0191073\pi$
$271$	1739.23	+	3808.39i	0.389856	+	0.853666i	−0.608343	+	0.793674i	$0.708165\pi$
$272$	1273.59	+	953.395i	0.283907	+	0.212530i
$273$	449.390	+	97.7588i	0.0996276	+	0.0216726i
$274$	−71.9097	+	82.9882i	−0.0158548	+	0.0182974i
$275$	3649.56	+	824.347i	0.800279	+	0.180764i
$276$	−543.247	−	2699.86i	−0.118477	−	0.588813i
$277$	−3887.90	−	3887.90i	−0.843326	−	0.843326i	0.145964	−	0.989290i	$-0.453372\pi$
$277$	−3887.90	−	3887.90i	−0.843326	−	0.843326i	−0.989290	+	0.145964i	$0.953372\pi$
$278$	−337.744	−	4722.28i	−0.0728653	−	1.01879i
$279$	1197.56	+	1863.45i	0.256976	+	0.399862i
$280$	−1900.32	+	2024.89i	−0.405592	+	0.432180i
$281$	5202.31	−	2375.82i	1.10443	−	0.504375i	0.222106	−	0.975023i	$-0.428707\pi$
$281$	5202.31	−	2375.82i	1.10443	−	0.504375i	0.882321	+	0.470648i	$0.155980\pi$
$282$	−1095.72	+	820.245i	−0.231380	+	0.173209i
$283$	−297.954	−	162.695i	−0.0625850	−	0.0341740i	0.447652	−	0.894208i	$-0.352260\pi$
$283$	−297.954	−	162.695i	−0.0625850	−	0.0341740i	−0.510237	+	0.860034i	$0.670442\pi$
$284$	1045.25	−	1626.44i	0.218395	−	0.339830i
$285$	4929.20	+	2951.18i	1.02449	+	0.613378i
$286$	40.0256	−	136.315i	0.00827540	−	0.0281834i
$287$	5624.17	+	402.248i	1.15674	+	0.0827316i
$288$	381.732	+	27.3020i	0.0781034	+	0.00558606i
$289$	−1401.24	+	4772.20i	−0.285212	+	0.971342i
$290$	3908.80	+	2340.25i	0.791492	+	0.473877i
$291$	−233.267	+	362.970i	−0.0469909	+	0.0731192i
$292$	2824.62	+	1542.36i	0.566090	+	0.309109i
$293$	3957.63	−	2962.64i	0.789102	−	0.590714i	−0.126887	−	0.991917i	$-0.540499\pi$
$293$	3957.63	−	2962.64i	0.789102	−	0.590714i	0.915989	+	0.401203i	$0.131408\pi$
$294$	7050.83	−	3220.01i	1.39868	−	0.638757i
$295$	3718.61	−	3962.38i	0.733919	−	0.782029i
$296$	1049.00	+	1632.28i	0.205986	+	0.320521i
$297$	−200.461	−	2802.82i	−0.0391648	−	0.547595i
$298$	−1184.45	−	1184.45i	−0.230246	−	0.230246i
$299$	−187.974	+	182.185i	−0.0363573	+	0.0352376i
$300$	2638.78	−	1666.35i	0.507833	−	0.320690i
$301$	−5088.37	+	5872.29i	−0.974382	+	1.12450i
$302$	1514.04	+	329.359i	0.288487	+	0.0627565i
$303$	559.130	+	418.559i	0.106010	+	0.0793584i
$304$	547.192	+	1198.18i	0.103236	+	0.226054i
$305$	−3225.37	+	1896.41i	−0.605522	+	0.356027i
$306$	670.052	+	2281.99i	0.125178	+	0.426315i
$307$	−1233.06	−	5668.31i	−0.229234	−	1.05377i	−0.937543	−	0.347868i	$-0.886906\pi$
$307$	−1233.06	−	5668.31i	−0.229234	−	1.05377i	0.708310	−	0.705902i	$-0.249458\pi$
$308$	−1299.03	−	3482.84i	−0.240322	−	0.644328i
$309$	9227.97	+	2709.58i	1.69890	+	0.498843i
$310$	2348.46	+	3411.28i	0.430269	+	0.624993i
$311$	−1233.94	−	1424.04i	−0.224985	−	0.259646i	0.632023	−	0.774950i	$-0.282225\pi$
$311$	−1233.94	−	1424.04i	−0.224985	−	0.259646i	−0.857008	+	0.515303i	$0.827679\pi$
$312$	−56.7929	−	104.008i	−0.0103053	−	0.0188728i
$313$	1977.14	−	737.434i	0.357043	−	0.133170i	−0.164541	−	0.986370i	$-0.552614\pi$
$313$	1977.14	−	737.434i	0.357043	−	0.133170i	0.521583	+	0.853200i	$0.325342\pi$
$314$	−4817.95	−	3096.31i	−0.865901	−	0.556481i
$315$	−4088.32	+	720.849i	−0.731272	+	0.128937i
$316$	−2688.66	−	386.572i	−0.478637	−	0.0688176i
$317$	2875.72	−	7710.11i	0.509516	−	1.36607i	−0.386601	−	0.922247i	$-0.626351\pi$
$317$	2875.72	−	7710.11i	0.509516	−	1.36607i	0.896117	−	0.443818i	$-0.146376\pi$
$318$	2092.35	−	2795.05i	0.368972	−	0.492889i
$319$	−5130.32	+	3297.06i	−0.900447	+	0.578682i
$320$	714.979	+	28.3810i	0.124902	+	0.00495796i
$321$			7349.81i			1.27796i
$322$	−1080.64	+	6763.46i	−0.187024	+	1.17054i
$323$	−5788.25	+	5788.25i	−0.997111	+	0.997111i
$324$	−2747.53	−	2380.75i	−0.471114	−	0.408222i
$325$	−268.855	−	125.374i	−0.0458874	−	0.0213985i
$326$	745.883	+	5187.73i	0.126720	+	0.881355i
$327$	−4978.27	−	1856.80i	−0.841893	−	0.314010i
$328$	−870.689	−	1163.10i	−0.146572	−	0.195798i
$329$	3266.19	−	959.039i	0.547327	−	0.160710i
$330$	430.055	+	4155.42i	0.0717387	+	0.693176i
$331$	−149.631	+	327.645i	−0.0248473	+	0.0544079i	−0.921649	−	0.388025i	$-0.873157\pi$
$331$	−149.631	+	327.645i	−0.0248473	+	0.0544079i	0.896801	+	0.442433i	$0.145885\pi$
$332$	−537.286	+	293.380i	−0.0888175	+	0.0484980i
$333$	−206.929	+	2893.25i	−0.0340530	+	0.476123i
$334$	−2616.05	+	2266.82i	−0.428574	+	0.371361i
$335$	−2914.53	+	6957.95i	−0.475336	+	1.13479i
$336$	−2820.42	−	1288.04i	−0.457936	−	0.209133i
$337$	10005.7	−	2176.62i	1.61735	−	0.351833i	0.689356	−	0.724423i	$-0.257894\pi$
$337$	10005.7	−	2176.62i	1.61735	−	0.351833i	0.927996	+	0.372589i	$0.121530\pi$
$338$	2100.42	−	3846.64i	0.338011	−	0.619022i
$339$	336.701	−	2341.81i	0.0539442	−	0.375190i
$340$	1387.49	+	4224.71i	0.221316	+	0.673874i
$341$	−5487.39	+	788.968i	−0.871434	+	0.125293i
$342$	−418.578	+	1924.17i	−0.0661816	+	0.304232i
$343$	−8606.70	+	615.564i	−1.35486	+	0.0969018i
$344$	2002.16			0.313806
$345$	3084.63	−	7052.50i	0.481365	−	1.10056i
$346$	−5276.69			−0.819874
$347$	−9655.05	+	690.543i	−1.49369	+	0.106831i	−0.794132	−	0.607745i	$-0.792074\pi$
$347$	−9655.05	+	690.543i	−1.49369	+	0.106831i	−0.699558	+	0.714576i	$0.746620\pi$
$348$	−1081.29	+	4970.60i	−0.166561	+	0.765667i
$349$	−9447.11	+	1358.29i	−1.44897	+	0.208331i	−0.821456	−	0.570271i	$-0.806838\pi$
$349$	−9447.11	+	1358.29i	−1.44897	+	0.208331i	−0.627518	+	0.778602i	$0.715929\pi$
$350$	−7597.27	+	1589.55i	−1.16026	+	0.242757i
$351$	−31.7068	+	220.526i	−0.00482161	+	0.0335350i
$352$	−459.036	+	840.662i	−0.0695077	+	0.127294i
$353$	4663.27	−	1014.43i	0.703119	−	0.152954i	0.153228	−	0.988191i	$-0.451033\pi$
$353$	4663.27	−	1014.43i	0.703119	−	0.152954i	0.549891	+	0.835237i	$0.314669\pi$
$354$	5519.11	+	2520.49i	0.828636	+	0.378425i
$355$	5000.73	−	2048.12i	0.747637	−	0.306206i
$356$	−3048.68	+	2641.70i	−0.453876	+	0.393286i
$357$	1374.62	−	19219.6i	0.203788	−	2.84933i
$358$	7759.85	−	4237.20i	1.14559	−	0.625539i
$359$	−3808.35	+	8339.12i	−0.559880	+	1.22597i	0.392132	+	0.919909i	$0.371738\pi$
$359$	−3808.35	+	8339.12i	−0.559880	+	1.22597i	−0.952013	+	0.306058i	$0.900990\pi$
$360$	830.238	+	674.508i	0.121548	+	0.0987491i
$361$	78.1182	−	22.9376i	0.0113891	−	0.00334416i
$362$	−4786.36	−	6393.83i	−0.694933	−	0.928322i
$363$	2544.42	+	949.019i	0.367899	+	0.137219i
$364$	41.9437	+	291.725i	0.00603969	+	0.0420070i
$365$	3994.48	+	8059.83i	0.572824	+	1.15581i
$366$	−3157.29	−	2735.81i	−0.450914	−	0.390719i
$367$	3249.01	−	3249.01i	0.462117	−	0.462117i	−0.437232	−	0.899349i	$-0.644041\pi$
$367$	3249.01	−	3249.01i	0.462117	−	0.462117i	0.899349	+	0.437232i	$0.144041\pi$
$368$	1499.44	−	930.826i	0.212401	−	0.131855i
$369$		−	2172.01i		−	0.306423i
$370$	−215.107	+	5419.01i	−0.0302240	+	0.761408i
$371$	−7304.94	+	4694.60i	−1.02225	+	0.656958i
$372$	−2771.21	+	3701.90i	−0.386238	+	0.515953i
$373$	1516.28	−	4065.30i	0.210482	−	0.564325i	−0.788212	−	0.615404i	$-0.788993\pi$
$373$	1516.28	−	4065.30i	0.210482	−	0.564325i	0.998695	+	0.0510783i	$0.0162658\pi$
$374$	−5891.79	−	847.112i	−0.814592	−	0.117121i
$375$	8713.24	+	415.259i	1.19987	+	0.0571837i
$376$	−737.896	−	474.217i	−0.101208	−	0.0650422i
$377$	453.037	−	168.974i	0.0618901	−	0.0230838i
$378$	2793.70	+	5116.27i	0.380138	+	0.696171i
$379$	2752.44	+	3176.48i	0.373043	+	0.430514i	0.910967	−	0.412479i	$-0.135337\pi$
$379$	2752.44	+	3176.48i	0.373043	+	0.430514i	−0.537924	+	0.842993i	$0.680791\pi$
$380$	−668.098	+	3620.61i	−0.0901913	+	0.488772i
$381$	−1770.20	−	519.777i	−0.238031	−	0.0698923i
$382$	2894.42	+	7760.24i	0.387674	+	1.03939i
$383$	189.760	+	872.312i	0.0253167	+	0.116379i	0.988071	−	0.153999i	$-0.0492151\pi$
$383$	189.760	+	872.312i	0.0253167	+	0.116379i	−0.962754	+	0.270377i	$0.912852\pi$
$384$	225.089	+	766.583i	0.0299128	+	0.101874i
$385$	2609.48	−	10056.9i	0.345432	−	1.33129i
$386$	1172.41	+	2567.21i	0.154596	+	0.338517i
$387$	2396.12	+	1793.71i	0.314733	+	0.235606i
$388$	−270.182	−	58.7745i	−0.0353516	−	0.00769027i
$389$	−1601.34	+	1848.04i	−0.208717	+	0.240873i	−0.850450	−	0.526056i	$-0.823670\pi$
$389$	−1601.34	+	1848.04i	−0.208717	+	0.240873i	0.641733	+	0.766928i	$0.278216\pi$
$390$	36.7152	−	329.187i	0.00476705	−	0.0427411i
$391$	8676.27	+	6709.21i	1.12219	+	0.867773i
$392$	3512.47	+	3512.47i	0.452567	+	0.452567i
$393$	−1134.87	−	15867.6i	−0.145666	−	2.03667i
$394$	−671.787	−	1045.32i	−0.0858989	−	0.133661i
$395$	−5536.18	−	5195.59i	−0.705203	−	0.661819i
$396$	−1302.50	+	594.832i	−0.165286	+	0.0754834i
$397$	−2805.64	+	2100.28i	−0.354688	+	0.265516i	−0.761732	−	0.647893i	$-0.775651\pi$
$397$	−2805.64	+	2100.28i	−0.354688	+	0.265516i	0.407044	+	0.913409i	$0.366560\pi$
$398$	8004.29	+	4370.67i	1.00809	+	0.550458i
$399$	8625.31	−	13421.2i	1.08222	−	1.68397i
$400$	1591.51	+	1211.24i	0.198938	+	0.151405i
$401$	−2784.35	+	9482.62i	−0.346742	+	1.18090i	0.582934	+	0.812519i	$0.301905\pi$
$401$	−2784.35	+	9482.62i	−0.346742	+	1.18090i	−0.929677	+	0.368377i	$0.879914\pi$
$402$	−8401.54	−	600.890i	−1.04237	−	0.0745515i
$403$	438.431	+	31.3572i	0.0541930	+	0.00387596i
$404$	−126.101	+	429.461i	−0.0155291	+	0.0528873i
$405$	−2473.87	−	9855.82i	−0.303525	−	1.20923i
$406$	6839.77	−	10642.9i	0.836089	−	1.30098i
$407$	−6371.60	−	3479.16i	−0.775991	−	0.423723i
$408$	−3974.71	+	2975.43i	−0.482298	+	0.361044i
$409$	−4569.86	+	2086.98i	−0.552482	+	0.252310i	−0.672037	−	0.740518i	$-0.734580\pi$
$409$	−4569.86	+	2086.98i	−0.552482	+	0.252310i	0.119555	+	0.992828i	$0.461853\pi$
$410$	−128.816	−	4058.93i	−0.0155165	−	0.488917i
$411$	−185.278	−	288.299i	−0.0222363	−	0.0346003i
$412$	439.689	+	6147.65i	0.0525774	+	0.735129i
$413$	−10670.2	−	10670.2i	−1.27130	−	1.27130i
$414$	2628.40	+	229.348i	0.312026	+	0.0272267i
$415$	−1700.51	−	189.663i	−0.201144	−	0.0224342i
$416$	49.7318	−	57.3936i	0.00586130	−	0.00676431i
$417$	14437.7	+	3140.72i	1.69548	+	0.368829i
$418$	−3945.36	−	2953.46i	−0.461660	−	0.345594i
$419$	2383.48	+	5219.09i	0.277901	+	0.608519i	0.996188	−	0.0872279i	$-0.0278008\pi$
$419$	2383.48	+	5219.09i	0.277901	+	0.608519i	−0.718287	+	0.695747i	$0.755074\pi$
$420$	−4392.60	−	7470.82i	−0.510325	−	0.867949i
$421$	−3255.29	−	11086.5i	−0.376848	−	1.28343i	−0.901748	−	0.432262i	$-0.857715\pi$
$421$	−3255.29	−	11086.5i	−0.376848	−	1.28343i	0.524900	−	0.851164i	$-0.324103\pi$
$422$	−1115.89	−	5129.66i	−0.128722	−	0.591725i
$423$	−458.244	−	1228.60i	−0.0526728	−	0.141221i
$424$	2146.84	+	630.370i	0.245896	+	0.0722016i
$425$	−3596.32	+	11897.3i	−0.410464	+	1.35789i
$426$	3951.28	+	4560.02i	0.449390	+	0.518624i
$427$	4979.46	+	9119.20i	0.564339	+	1.03351i
$428$	−4413.12	+	1646.01i	−0.498402	+	0.185894i
$429$	372.997	+	239.711i	0.0419778	+	0.0269775i
$430$	4584.12	+	3209.89i	0.514107	+	0.359987i
$431$	3833.88	+	551.228i	0.428472	+	0.0616049i	0.353177	−	0.935556i	$-0.385101\pi$
$431$	3833.88	+	551.228i	0.428472	+	0.0616049i	0.0752945	+	0.997161i	$0.476010\pi$
$432$	524.916	−	1407.35i	0.0584607	−	0.156739i
$433$	1552.73	−	2074.20i	0.172331	−	0.230207i	−0.706057	−	0.708155i	$-0.749528\pi$
$433$	1552.73	−	2074.20i	0.172331	−	0.230207i	0.878389	+	0.477947i	$0.158619\pi$
$434$	9675.01	−	6217.75i	1.07008	−	0.687700i
$435$	−10444.6	+	9647.09i	−1.15122	+	1.06332i
$436$		−	3404.98i		−	0.374012i
$437$	3642.72	+	8318.26i	0.398753	+	0.910564i
$438$	−7102.09	+	7102.09i	−0.774774	+	0.774774i
$439$	−5494.03	−	4760.61i	−0.597303	−	0.517566i	0.302908	−	0.953020i	$-0.402042\pi$
$439$	−5494.03	−	4760.61i	−0.597303	−	0.517566i	−0.900211	+	0.435454i	$0.856588\pi$
$440$	−2398.76	+	1188.84i	−0.259901	+	0.128808i
$441$	1056.83	+	7350.40i	0.114116	+	0.793694i
$442$	442.188	+	164.927i	0.0475853	+	0.0177484i
$443$	−6924.53	−	9250.09i	−0.742651	−	0.992065i	−0.999671	−	0.0256593i	$-0.991831\pi$
$443$	−6924.53	−	9250.09i	−0.742651	−	0.992065i	0.257020	−	0.966406i	$-0.417259\pi$
$444$	−5810.13	+	1706.01i	−0.621028	+	0.182350i
$445$	−11215.4	+	1160.72i	−1.19475	+	0.123648i
$446$	4723.84	−	10343.8i	0.501526	−	1.09819i
$447$	4588.23	−	2505.36i	0.485494	−	0.265100i
$448$	141.752	−	1981.95i	0.0149490	−	0.209014i
$449$	−3532.47	+	3060.90i	−0.371286	+	0.321722i	−0.820440	−	0.571733i	$-0.806271\pi$
$449$	−3532.47	+	3060.90i	−0.371286	+	0.321722i	0.449153	+	0.893455i	$0.351726\pi$
$450$	819.523	+	2875.39i	0.0858504	+	0.301216i
$451$	4944.77	+	2258.20i	0.516276	+	0.235775i
$452$	1481.52	−	322.285i	0.154170	−	0.0335376i
$453$	−2317.48	+	4244.14i	−0.240363	+	0.440192i
$454$	−400.324	+	2784.31i	−0.0413835	+	0.287829i
$455$	−371.663	+	735.174i	−0.0382941	+	0.0757483i
$456$	−4069.04	+	585.039i	−0.417873	+	0.0600811i
$457$	149.929	−	689.214i	0.0153466	−	0.0705472i	−0.968837	−	0.247700i	$-0.920325\pi$
$457$	149.929	−	689.214i	0.0153466	−	0.0705472i	0.984183	+	0.177153i	$0.0566888\pi$
$458$	8064.45	−	576.781i	0.822767	−	0.0588454i
$459$	9334.52			0.949233
$460$	4925.41	+	272.710i	0.499235	+	0.0276417i
$461$	8359.09			0.844516			0.422258	−	0.906476i	$-0.361238\pi$
$461$	8359.09			0.844516			0.422258	+	0.906476i	$0.361238\pi$
$462$	11571.4	−	827.603i	1.16526	−	0.0833411i
$463$	−2823.42	+	12979.0i	−0.283402	+	1.30278i	0.586658	+	0.809835i	$0.300443\pi$
$463$	−2823.42	+	12979.0i	−0.283402	+	1.30278i	−0.870060	+	0.492945i	$0.835920\pi$
$464$	−3226.70	+	463.929i	−0.322836	+	0.0464168i
$465$	−12279.8	+	4032.99i	−1.22465	+	0.402205i
$466$	−721.843	+	5020.53i	−0.0717569	+	0.499080i
$467$	4724.58	−	8652.42i	0.468153	−	0.857358i	−0.531792	−	0.846875i	$-0.678481\pi$
$467$	4724.58	−	8652.42i	0.468153	−	0.857358i	0.999945	−	0.0104830i	$-0.00333690\pi$
$468$	110.936	−	24.1326i	0.0109573	−	0.00238361i
$469$	19055.3	+	8702.28i	1.87611	+	0.856789i
$470$	−929.207	−	2268.76i	−0.0911939	−	0.222660i
$471$	13508.0	−	11704.7i	1.32148	−	1.14507i
$472$	−277.386	+	3878.36i	−0.0270502	+	0.378212i
$473$	−6574.76	+	3590.09i	−0.639129	+	0.348991i
$474$	3521.59	−	7711.21i	0.341249	−	0.747232i
$475$	−7334.27	+	7218.60i	−0.708462	+	0.697289i
$476$	11848.1	−	3478.91i	1.14087	−	0.334991i
$477$	2004.53	+	2677.74i	0.192414	+	0.257034i
$478$	−12581.7	−	4692.73i	−1.20392	−	0.449039i
$479$	−1656.24	−	11519.4i	−0.157987	−	1.09882i	−0.902336	−	0.431033i	$-0.858149\pi$
$479$	−1656.24	−	11519.4i	−0.157987	−	1.09882i	0.744349	−	0.667790i	$-0.232760\pi$
$480$	−713.634	+	2116.02i	−0.0678599	+	0.201214i
$481$	435.001	+	376.930i	0.0412356	+	0.0357309i
$482$	−609.801	+	609.801i	−0.0576258	+	0.0576258i
$483$	−19302.8	−	9182.74i	−1.81844	−	0.865070i
$484$			1740.30i			0.163439i
$485$	−524.378	−	567.729i	−0.0490944	−	0.0531531i
$486$	5280.16	−	3393.36i	0.492825	−	0.316720i
$487$	12311.9	−	16446.7i	1.14559	−	1.53033i	0.337454	−	0.941342i	$-0.390434\pi$
$487$	12311.9	−	16446.7i	1.14559	−	1.53033i	0.808139	−	0.588992i	$-0.200475\pi$
$488$	935.605	−	2508.45i	0.0867886	−	0.232689i
$489$	−16190.3	−	2327.81i	−1.49724	−	0.215270i
$490$	2410.87	+	13673.3i	0.222270	+	1.26061i
$491$	3299.25	+	2120.30i	0.303244	+	0.194883i	0.683409	−	0.730035i	$-0.260496\pi$
$491$	3299.25	+	2120.30i	0.303244	+	0.194883i	−0.380165	+	0.924919i	$0.624133\pi$
$492$	4248.43	−	1584.58i	0.389297	−	0.145200i
$493$	−9708.86	−	17780.4i	−0.886947	−	1.62432i
$494$	255.889	+	295.312i	0.0233057	+	0.0268962i
$495$	−3935.83	−	726.264i	−0.357379	−	0.0659458i
$496$	−2843.38	−	834.893i	−0.257403	−	0.0755802i
$497$	−5244.16	−	14060.1i	−0.473305	−	1.26898i
$498$	−406.106	−	1866.84i	−0.0365423	−	0.167982i
$499$	−21.3350	−	72.6603i	−0.00191400	−	0.00651848i	0.958530	−	0.284990i	$-0.0919903\pi$
$499$	−21.3350	−	72.6603i	−0.00191400	−	0.00651848i	−0.960444	+	0.278472i	$0.910172\pi$
$500$	1702.01	+	5324.77i	0.152233	+	0.476262i
$501$	−4487.73	−	9826.76i	−0.400194	−	0.876302i
$502$	−6762.69	−	5062.49i	−0.601262	−	0.450099i
$503$	10353.4	+	2252.25i	0.917765	+	0.199647i	0.646550	−	0.762871i	$-0.276211\pi$
$503$	10353.4	+	2252.25i	0.917765	+	0.199647i	0.271215	+	0.962519i	$0.412575\pi$
$504$	1945.25	−	2244.94i	0.171922	−	0.198408i
$505$	−977.236	+	781.121i	−0.0861118	+	0.0688306i
$506$	−3254.84	+	5745.34i	−0.285959	+	0.504766i
$507$	9671.80	+	9671.80i	0.847219	+	0.847219i
$508$	−84.3453	−	1179.30i	−0.00736657	−	0.102998i
$509$	9619.11	+	14967.6i	0.837641	+	1.30340i	0.950796	+	0.309818i	$0.100268\pi$
$509$	9619.11	+	14967.6i	0.837641	+	1.30340i	−0.113154	+	0.993577i	$0.536095\pi$
$510$	−13870.7	+	440.206i	−1.20432	+	0.0382209i
$511$	22722.2	−	10376.9i	1.96707	−	0.898330i
$512$	−409.877	+	306.830i	−0.0353793	+	0.0264846i
$513$	6783.28	+	3703.95i	0.583800	+	0.318779i
$514$	4158.99	−	6471.51i	0.356897	−	0.555343i
$515$	−8849.28	+	14780.5i	−0.757177	+	1.26467i
$516$	−1760.41	+	5995.39i	−0.150189	+	0.511497i
$517$	3273.45	+	234.122i	0.278465	+	0.0199162i
$518$	15021.7	+	1074.38i	1.27416	+	0.0911300i
$519$	4639.55	−	15800.8i	0.392396	−	1.33638i
$520$	205.879	−	51.6770i	0.0173623	−	0.00435805i
$521$	−4412.55	+	6866.07i	−0.371051	+	0.577366i	−0.975696	−	0.219129i	$-0.929679\pi$
$521$	−4412.55	+	6866.07i	−0.371051	+	0.577366i	0.604645	+	0.796495i	$0.293315\pi$
$522$	−4277.24	−	2335.55i	−0.358640	−	0.195832i
$523$	8048.37	−	6024.94i	0.672908	−	0.503733i	−0.207326	−	0.978272i	$-0.566476\pi$
$523$	8048.37	−	6024.94i	0.672908	−	0.503733i	0.880234	+	0.474539i	$0.157385\pi$
$524$	9273.35	−	4235.00i	0.773107	−	0.353066i
$525$	1920.08	−	24147.4i	0.159617	−	2.00739i
$526$	−8644.51	−	13451.1i	−0.716576	−	1.11501i
$527$	−1313.79	−	18369.2i	−0.108595	−	1.51836i
$528$	−2113.72	−	2113.72i	−0.174220	−	0.174220i
$529$	10436.2	−	6254.70i	0.857748	−	0.514071i
$530$	3904.77	+	4885.14i	0.320023	+	0.400371i
$531$	−3806.55	+	4392.99i	−0.311092	+	0.359020i
$532$	9990.30	+	2173.26i	0.814162	+	0.177110i
$533$	−345.036	−	258.290i	−0.0280397	−	0.0209902i
$534$	−5229.90	−	11451.9i	−0.423820	−	0.928037i
$535$	−12743.1	−	3306.48i	−1.02978	−	0.267200i
$536$	−1520.75	−	5179.19i	−0.122549	−	0.417363i
$537$	5865.26	+	26962.2i	0.471331	+	2.16667i
$538$	4720.18	+	12655.3i	0.378255	+	1.01414i
$539$	−17832.6	−	5236.13i	−1.42506	−	0.418434i
$540$	3458.13	−	2380.71i	0.275582	−	0.189721i
$541$	7306.22	+	8431.82i	0.580626	+	0.670078i	0.967739	−	0.251954i	$-0.0810731\pi$
$541$	7306.22	+	8431.82i	0.580626	+	0.670078i	−0.387113	+	0.922032i	$0.626528\pi$
$542$	−4012.98	−	7349.23i	−0.318030	−	0.582429i
$543$	23354.5	−	8710.79i	1.84574	−	0.688427i
$544$	−2676.71	−	1720.22i	−0.210962	−	0.135577i
$545$	5458.91	−	7796.01i	0.429053	−	0.612742i
$546$	−910.438	−	130.901i	−0.0713611	−	0.0102602i
$547$	3174.63	−	8511.52i	0.248149	−	0.665313i	−0.751833	−	0.659353i	$-0.770830\pi$
$547$	3174.63	−	8511.52i	0.248149	−	0.665313i	0.999982	−	0.00595979i	$-0.00189707\pi$
$548$	131.612	−	175.813i	0.0102595	−	0.0137051i
$549$	3367.00	−	2163.84i	0.261749	−	0.168216i
$550$	−7398.13	−	1123.78i	−0.573559	−	0.0871238i
$551$		−	16773.3i		−	1.29686i
$552$	1468.94	+	5308.45i	0.113265	+	0.409316i
$553$	−14908.2	+	14908.2i	−1.14641	+	1.14641i
$554$	8310.71	+	7201.27i	0.637343	+	0.552261i
$555$	−16037.9	−	5408.82i	−1.22661	−	0.413678i
$556$	1347.53	+	9372.31i	0.102785	+	0.714882i
$557$	3827.61	+	1427.63i	0.291169	+	0.108600i	0.490804	−	0.871270i	$-0.336703\pi$
$557$	3827.61	+	1427.63i	0.291169	+	0.108600i	−0.199635	+	0.979870i	$0.563976\pi$
$558$	−2654.90	−	3546.53i	−0.201417	−	0.269062i
$559$	569.883	−	167.333i	0.0431190	−	0.0126609i
$560$	3502.04	−	4310.59i	0.264265	−	0.325278i
$561$	7717.03	−	16897.9i	0.580772	−	1.27171i
$562$	−10039.1	+	5481.78i	−0.753515	+	0.411450i
$563$	−142.282	+	1989.36i	−0.0106509	+	0.148919i	0.989344	+	0.145600i	$0.0465111\pi$
$563$	−142.282	+	1989.36i	−0.0106509	+	0.148919i	−0.999994	+	0.00331941i	$0.998943\pi$
$564$	2068.82	−	1792.64i	0.154456	−	0.133837i
$565$	3908.76	+	1637.29i	0.291049	+	0.121914i
$566$	617.603	+	282.050i	0.0458654	+	0.0209460i
$567$	−27573.1	+	5998.17i	−2.04226	+	0.444267i
$568$	−1853.12	+	3393.73i	−0.136893	+	0.250700i
$569$	−2045.93	+	14229.8i	−0.150738	+	1.04840i	0.764249	+	0.644921i	$0.223110\pi$
$569$	−2045.93	+	14229.8i	−0.150738	+	1.04840i	−0.914987	+	0.403484i	$0.867799\pi$
$570$	−10254.4	−	5184.03i	−0.753522	−	0.380939i
$571$	−12178.0	+	1750.93i	−0.892529	+	0.128326i	−0.573294	−	0.819349i	$-0.694335\pi$
$571$	−12178.0	+	1750.93i	−0.892529	+	0.128326i	−0.319235	+	0.947676i	$0.603426\pi$
$572$	−60.3981	+	277.646i	−0.00441499	+	0.0202954i
$573$	−25782.7	+	1844.01i	−1.87973	+	0.134441i
$574$	−11277.1			−0.820027
$575$	10839.9	+	8520.86i	0.786185	+	0.617991i
$576$	−765.414			−0.0553685
$577$	−10958.6	+	783.773i	−0.790661	+	0.0565492i	−0.460827	−	0.887490i	$-0.652447\pi$
$577$	−10958.6	+	783.773i	−0.790661	+	0.0565492i	−0.329834	+	0.944039i	$0.606993\pi$
$578$	2114.46	−	9720.01i	0.152162	−	0.699480i
$579$	−8718.27	+	1253.50i	−0.625767	+	0.0899717i
$580$	−8131.59	−	4110.88i	−0.582148	−	0.294302i
$581$	−676.209	+	4703.14i	−0.0482855	+	0.335833i
$582$	413.557	−	757.373i	0.0294544	−	0.0539418i
$583$	−8180.21	+	1779.50i	−0.581114	+	0.126414i
$584$	−5854.90	−	2673.85i	−0.414859	−	0.189460i
$585$	292.687	+	122.600i	0.0206857	+	0.00866475i
$586$	−7472.38	+	6474.85i	−0.526760	+	0.456440i
$587$	517.663	−	7237.88i	0.0363991	−	0.508926i	−0.946248	−	0.323441i	$-0.895160\pi$
$587$	517.663	−	7237.88i	0.0363991	−	0.508926i	0.982647	−	0.185484i	$-0.0593853\pi$
$588$	−13606.3	+	7429.61i	−0.954277	+	0.521075i
$589$	6334.22	−	13870.0i	0.443119	−	0.970295i
$590$	−6852.93	+	8435.13i	−0.478188	+	0.588591i
$591$	3720.85	−	1092.54i	0.258977	−	0.0760424i
$592$	−2325.55	−	3106.57i	−0.161452	−	0.215674i
$593$	−8694.19	−	3242.76i	−0.602070	−	0.224560i	0.0299006	−	0.999553i	$-0.490481\pi$
$593$	−8694.19	−	3242.76i	−0.602070	−	0.224560i	−0.631971	+	0.774992i	$0.717754\pi$
$594$	799.802	+	5562.75i	0.0552463	+	0.384246i
$595$	32704.6	+	11029.7i	2.25338	+	0.759957i
$596$	2531.86	+	2193.87i	0.174009	+	0.150779i
$597$	−20125.6	+	20125.6i	−1.37971	+	1.37971i
$598$	348.997	−	390.262i	0.0238654	−	0.0266873i
$599$			1499.97i			0.102316i	0.998691	+	0.0511578i	$0.0162911\pi$
$599$			1499.97i			0.102316i	−0.998691	+	0.0511578i	$0.983709\pi$
$600$	−5026.36	+	3700.71i	−0.342001	+	0.251802i
$601$	−17455.2	+	11217.8i	−1.18472	+	0.761371i	−0.976247	−	0.216658i	$-0.930484\pi$
$601$	−17455.2	+	11217.8i	−1.18472	+	0.761371i	−0.208468	+	0.978029i	$0.566848\pi$
$602$	9312.96	−	12440.7i	0.630512	−	0.842265i
$603$	2820.00	−	7560.71i	0.190447	−	0.510607i
$604$	−3067.35	−	441.019i	−0.206637	−	0.0297099i
$605$	−2790.07	+	3984.58i	−0.187492	+	0.267762i
$606$	−1175.13	−	755.210i	−0.0787729	−	0.0506243i
$607$	1243.80	−	463.914i	0.0831703	−	0.0310209i	−0.307535	−	0.951537i	$-0.599504\pi$
$607$	1243.80	−	463.914i	0.0831703	−	0.0310209i	0.390705	+	0.920516i	$0.372231\pi$
$608$	−1262.55	−	2312.19i	−0.0842157	−	0.154230i
$609$	25855.9	+	29839.3i	1.72041	+	1.98546i
$610$	6163.73	−	4243.35i	0.409119	−	0.281653i
$611$	−249.664	−	73.3079i	−0.0165308	−	0.00485388i
$612$	−1662.28	−	4456.74i	−0.109794	−	0.294368i
$613$	3075.43	+	14137.5i	0.202635	+	0.931499i	0.960325	+	0.278884i	$0.0899645\pi$
$613$	3075.43	+	14137.5i	0.202635	+	0.931499i	−0.757690	+	0.652615i	$0.773672\pi$
$614$	3268.59	+	11131.8i	0.214837	+	0.731666i
$615$	12267.6	+	3183.09i	0.804352	+	0.208707i
$616$	3088.37	+	6762.58i	0.202003	+	0.442325i
$617$	7701.78	+	5765.48i	0.502532	+	0.376190i	0.820260	−	0.571991i	$-0.193829\pi$
$617$	7701.78	+	5765.48i	0.502532	+	0.376190i	−0.317728	+	0.948182i	$0.602920\pi$
$618$	−18795.5	−	4088.71i	−1.22341	−	0.266136i
$619$	−1511.68	+	1744.57i	−0.0981573	+	0.113280i	−0.802703	−	0.596379i	$-0.796605\pi$
$619$	−1511.68	+	1744.57i	−0.0981573	+	0.113280i	0.704545	+	0.709659i	$0.251151\pi$
$620$	−5171.66	−	6470.11i	−0.334998	−	0.419106i
$621$	3770.04	−	9644.53i	0.243618	−	0.623223i
$622$	2664.77	+	2664.77i	0.171781	+	0.171781i
$623$	2233.69	+	31231.1i	0.143645	+	2.00842i
$624$	128.136	+	199.384i	0.00822043	+	0.0127912i
$625$	−4639.83	+	14920.2i	−0.296949	+	0.954893i
$626$	−3838.98	+	1753.20i	−0.245106	+	0.111936i
$627$	12313.0	−	9217.40i	0.784265	−	0.587093i
$628$	10053.1	+	5489.43i	0.638796	+	0.348809i
$629$	13038.0	−	20287.5i	0.826485	−	1.28604i
$630$	8052.95	−	2021.34i	0.509265	−	0.127829i
$631$	3314.21	−	11287.2i	0.209092	−	0.712100i	−0.786440	−	0.617667i	$-0.788078\pi$
$631$	3314.21	−	11287.2i	0.209092	−	0.712100i	0.995531	−	0.0944333i	$-0.0301039\pi$
$632$	5418.78	+	387.559i	0.341056	+	0.0243928i
$633$	16341.7	+	1168.78i	1.02611	+	0.0733885i
$634$	−4636.72	+	15791.2i	−0.290454	+	0.989195i
$635$	1697.55	−	2835.34i	0.106087	−	0.177192i
$636$	−3775.24	+	5874.39i	−0.235374	+	0.366250i
$637$	1293.33	+	706.210i	0.0804451	+	0.0439263i
$638$	9764.08	−	7309.30i	0.605899	−	0.453570i
$639$	−5258.16	+	2401.32i	−0.325524	+	0.148662i
$640$	−1430.36	+	45.3946i	−0.0883439	+	0.00280372i
$641$	−5549.84	−	8635.72i	−0.341974	−	0.532122i	0.627085	−	0.778951i	$-0.284248\pi$
$641$	−5549.84	−	8635.72i	−0.341974	−	0.532122i	−0.969059	+	0.246829i	$0.920611\pi$
$642$	−1048.66	−	14662.2i	−0.0644662	−	0.901355i
$643$	−3375.34	−	3375.34i	−0.207014	−	0.207014i	0.595983	−	0.802997i	$-0.296763\pi$
$643$	−3375.34	−	3375.34i	−0.207014	−	0.207014i	−0.802997	+	0.595983i	$0.796763\pi$
$644$	1190.77	−	13646.6i	0.0728619	−	0.835020i
$645$	−13642.5	+	10904.7i	−0.832826	+	0.665692i
$646$	10721.2	−	12372.9i	0.652969	−	0.753567i
$647$	23193.8	+	5045.49i	1.40934	+	0.306582i	0.851929	−	0.523657i	$-0.175433\pi$
$647$	23193.8	+	5045.49i	1.40934	+	0.306582i	0.557407	+	0.830239i	$0.311796\pi$
$648$	5820.75	+	4357.36i	0.352871	+	0.264156i
$649$	−6043.43	−	13233.3i	−0.365525	−	0.800387i
$650$	554.228	+	211.749i	0.0334440	+	0.0127777i
$651$	10112.0	+	34438.5i	0.608790	+	2.07335i
$652$	−2228.14	−	10242.6i	−0.133835	−	0.615232i
$653$	−8479.14	−	22733.5i	−0.508139	−	1.36237i	−0.897389	−	0.441240i	$-0.854539\pi$
$653$	−8479.14	−	22733.5i	−0.508139	−	1.36237i	0.389250	−	0.921132i	$-0.372734\pi$
$654$	10196.1	+	2993.85i	0.609632	+	0.179004i
$655$	28021.7	+	5170.75i	1.67160	+	0.308455i
$656$	1902.89	+	2196.05i	0.113255	+	0.130703i
$657$	−4611.50	−	8445.32i	−0.273838	−	0.501497i
$658$	−6378.90	+	2379.20i	−0.377926	+	0.140959i
$659$	9307.19	+	5981.37i	0.550162	+	0.353568i	0.786002	−	0.618224i	$-0.212148\pi$
$659$	9307.19	+	5981.37i	0.550162	+	0.353568i	−0.235840	+	0.971792i	$0.575784\pi$
$660$	−1450.81	−	8228.30i	−0.0855645	−	0.485282i
$661$	−30201.4	−	4342.31i	−1.77716	−	0.255516i	−0.825877	−	0.563850i	$-0.809320\pi$
$661$	−30201.4	−	4342.31i	−1.77716	−	0.255516i	−0.951278	+	0.308333i	$0.900229\pi$
$662$	251.751	−	674.970i	0.0147803	−	0.0396276i
$663$	−882.665	+	1179.10i	−0.0517041	+	0.0690687i
$664$	1029.97	−	661.925i	0.0601970	−	0.0386862i
$665$	19389.5	+	20992.4i	1.13066	+	1.22414i
$666$		−	5801.27i		−	0.337530i
$667$	−22292.2	+	2850.10i	−1.29409	+	0.165452i
$668$	4895.34	−	4895.34i	0.283542	−	0.283542i
$669$	26820.6	+	23240.2i	1.54999	+	1.34308i
$670$	4821.45	−	14296.3i	0.278013	−	0.824349i
$671$	1425.56	+	9914.99i	0.0820166	+	0.570438i
$672$	5810.25	+	2167.11i	0.333534	+	0.124402i
$673$	17408.0	+	23254.3i	0.997069	+	1.33193i	0.942785	+	0.333402i	$0.108197\pi$
$673$	17408.0	+	23254.3i	0.997069	+	1.33193i	0.0542842	+	0.998526i	$0.482712\pi$
$674$	−19649.9	+	5769.75i	−1.12298	+	0.329736i
$675$	11734.5	+	93.2713i	0.669125	+	0.00531854i
$676$	−3641.31	+	7973.35i	−0.207175	+	0.453650i
$677$	−26010.8	+	14203.0i	−1.47663	+	0.806301i	−0.997447	−	0.0714146i	$-0.977249\pi$
$677$	−26010.8	+	14203.0i	−1.47663	+	0.806301i	−0.479183	+	0.877715i	$0.659067\pi$
$678$	−337.561	+	4719.72i	−0.0191209	+	0.267345i
$679$	−1621.94	+	1405.42i	−0.0916708	+	0.0794332i
$680$	−3370.69	−	8229.93i	−0.190089	−	0.464123i
$681$	−7985.53	−	3646.87i	−0.449348	−	0.205211i
$682$	10834.3	−	2356.85i	0.608307	−	0.132329i
$683$	−3334.00	+	6105.77i	−0.186782	+	0.342066i	−0.954244	−	0.299029i	$-0.903337\pi$
$683$	−3334.00	+	6105.77i	−0.186782	+	0.342066i	0.767462	+	0.641094i	$0.221519\pi$
$684$	560.485	−	3898.26i	0.0313314	−	0.217915i
$685$	583.204	−	191.538i	0.0325301	−	0.0106836i
$686$	17081.7	−	2455.98i	0.950704	−	0.136691i
$687$	−5363.55	+	24655.8i	−0.297863	+	1.36926i
$688$	−3994.12	+	285.665i	−0.221329	+	0.0158298i
$689$	663.749			0.0367008
$690$	−5147.30	+	14509.2i	−0.283992	+	0.800514i
$691$	−34.8587			−0.00191908			−0.000959542	−	1.00000i	$-0.500305\pi$
$691$	−34.8587			−0.00191908			−0.000959542		1.00000i	$0.500305\pi$
$692$	10526.5	−	752.869i	0.578262	−	0.0413581i
$693$	−2362.47	+	10860.1i	−0.129499	+	0.595296i
$694$	19162.4	−	2755.13i	1.04812	−	0.150697i
$695$	−11940.5	+	23619.1i	−0.651696	+	1.28910i
$696$	1447.87	−	10070.1i	0.0788525	−	0.548431i
$697$	−8654.28	+	15849.1i	−0.470308	+	0.861304i
$698$	18652.3	−	4057.55i	1.01146	−	0.220030i
$699$	−14399.1	−	6575.85i	−0.779148	−	0.355825i
$700$	14929.0	−	4254.96i	0.806092	−	0.229746i
$701$	−24807.3	+	21495.6i	−1.33660	+	1.15817i	−0.362520	+	0.931976i	$0.618084\pi$
$701$	−24807.3	+	21495.6i	−1.33660	+	1.15817i	−0.974082	+	0.226196i	$0.927371\pi$
$702$	31.7878	−	444.451i	0.00170905	−	0.0238956i
$703$	17524.7	−	9569.20i	0.940193	−	0.513384i
$704$	795.789	−	1742.53i	0.0426029	−	0.0932873i
$705$	7610.74	−	787.656i	0.406577	−	0.0420778i
$706$	−9158.04	+	2689.04i	−0.488198	+	0.143348i
$707$	2081.95	+	2781.16i	0.110750	+	0.147944i
$708$	−11369.7	−	4240.68i	−0.603531	−	0.225105i
$709$	−1432.63	−	9964.14i	−0.0758864	−	0.527801i	−0.991936	−	0.126737i	$-0.959550\pi$
$709$	−1432.63	−	9964.14i	−0.0758864	−	0.527801i	0.916050	−	0.401064i	$-0.131360\pi$
$710$	−9683.75	+	4799.31i	−0.511866	+	0.253683i
$711$	6137.82	+	5318.45i	0.323750	+	0.280531i
$712$	5704.92	−	5704.92i	0.300282	−	0.300282i
$713$	−19509.9	−	6061.57i	−1.02476	−	0.318384i
$714$			38537.5i			2.01993i
$715$	−583.412	+	538.863i	−0.0305152	+	0.0281851i
$716$	−14875.6	+	9559.97i	−0.776435	+	0.498984i
$717$	25114.7	−	33549.4i	1.30813	−	1.74745i
$718$	6407.48	−	17179.1i	0.333043	−	0.892924i
$719$	−17933.5	−	2578.45i	−0.930192	−	0.133741i	−0.339470	−	0.940617i	$-0.610248\pi$
$719$	−17933.5	−	2578.45i	−0.930192	−	0.133741i	−0.590722	+	0.806875i	$0.701157\pi$
$720$	−1752.48	−	1227.12i	−0.0907099	−	0.0635168i
$721$	40244.4	+	25863.5i	2.07875	+	1.33593i
$722$	−152.566	+	56.9040i	−0.00786413	+	0.00293317i
$723$	−1289.86	−	2362.20i	−0.0663489	−	0.121509i
$724$	10460.6	+	12072.2i	0.536968	+	0.619695i
$725$	−12027.4	−	22448.9i	−0.616118	−	1.14997i
$726$	−5211.27	−	1530.17i	−0.266403	−	0.0782229i
$727$	−8535.55	−	22884.7i	−0.435441	−	1.16746i	−0.950614	−	0.310377i	$-0.899545\pi$
$727$	−8535.55	−	22884.7i	−0.435441	−	1.16746i	0.515172	−	0.857087i	$-0.327728\pi$
$728$	−125.296	−	575.978i	−0.00637884	−	0.0293231i
$729$	−1394.95	−	4750.77i	−0.0708709	−	0.241364i
$730$	−9118.58	−	15508.7i	−0.462320	−	0.786303i
$731$	−10337.5	−	22636.0i	−0.523046	−	1.14531i
$732$	6688.84	+	5007.20i	0.337741	+	0.252830i
$733$	−13993.0	−	3043.99i	−0.705106	−	0.153386i	−0.154305	−	0.988023i	$-0.549314\pi$
$733$	−13993.0	−	3043.99i	−0.705106	−	0.153386i	−0.550801	+	0.834637i	$0.685678\pi$
$734$	−6017.90	+	6945.03i	−0.302622	+	0.349245i
$735$	−43064.1	−	4803.06i	−2.16115	−	0.241039i
$736$	−2858.43	+	2070.85i	−0.143156	+	0.103713i
$737$	14280.7	+	14280.7i	0.713755	+	0.713755i
$738$	309.899	+	4332.95i	0.0154573	+	0.216122i
$739$	−4742.65	−	7379.71i	−0.236077	−	0.367344i	0.702919	−	0.711270i	$-0.251879\pi$
$739$	−4742.65	−	7379.71i	−0.236077	−	0.367344i	−0.938997	+	0.343926i	$0.888243\pi$
$740$	−344.058	−	10841.1i	−0.0170916	−	0.538550i
$741$	−1109.29	+	506.597i	−0.0549944	+	0.0251151i
$742$	13902.8	−	10407.5i	0.687856	−	0.514923i
$743$	8961.28	+	4893.23i	0.442473	+	0.241609i	0.685010	−	0.728534i	$-0.259798\pi$
$743$	8961.28	+	4893.23i	0.442473	+	0.241609i	−0.242537	+	0.970142i	$0.577980\pi$
$744$	5000.11	−	7780.32i	0.246388	−	0.383388i
$745$	2279.68	+	9082.17i	0.112109	+	0.446638i
$746$	−2444.80	+	8326.23i	−0.119987	+	0.408639i
$747$	1825.65	+	130.573i	0.0894206	+	0.00639548i
$748$	11874.4	+	849.276i	0.580444	+	0.0415142i
$749$	−10299.8	+	35077.8i	−0.502463	+	1.71123i
$750$	−17441.3	+	414.788i	−0.849156	+	0.0201946i
$751$	−7581.15	+	11796.5i	−0.368362	+	0.573183i	−0.975113	−	0.221709i	$-0.928836\pi$
$751$	−7581.15	+	11796.5i	−0.368362	+	0.573183i	0.606750	+	0.794892i	$0.292473\pi$
$752$	1539.69	+	840.735i	0.0746633	+	0.0407692i
$753$	21105.5	−	15799.4i	1.02142	−	0.764625i
$754$	−879.656	+	401.725i	−0.0424870	+	0.0194032i
$755$	−6315.93	−	5927.37i	−0.304450	−	0.285720i
$756$	−6303.14	−	9807.87i	−0.303231	−	0.471837i
$757$	−253.811	−	3548.74i	−0.0121861	−	0.170384i	−0.999900	−	0.0141137i	$-0.995507\pi$
$757$	−253.811	−	3548.74i	−0.0121861	−	0.170384i	0.987714	−	0.156271i	$-0.0499472\pi$
$758$	−5944.07	−	5944.07i	−0.284826	−	0.284826i
$759$	−14342.4	−	14798.1i	−0.685896	−	0.707690i
$760$	816.209	−	7318.09i	0.0389566	−	0.349283i
$761$	−24838.9	+	28665.7i	−1.18319	+	1.36548i	−0.267522	+	0.963552i	$0.586205\pi$
$761$	−24838.9	+	28665.7i	−1.18319	+	1.36548i	−0.915672	+	0.401927i	$0.868341\pi$
$762$	3605.54	+	784.336i	0.171411	+	0.0372881i
$763$	−21157.3	−	15838.1i	−1.00386	−	0.751480i
$764$	−6881.31	−	15068.0i	−0.325860	−	0.713534i
$765$	3339.17	−	12869.1i	0.157814	−	0.608213i
$766$	−503.013	−	1713.11i	−0.0237266	−	0.0808055i
$767$	245.185	+	1127.10i	0.0115425	+	0.0530601i
$768$	−558.406	−	1497.14i	−0.0262366	−	0.0703431i
$769$	−21135.7	−	6206.01i	−0.991124	−	0.291020i	−0.254315	−	0.967121i	$-0.581850\pi$
$769$	−21135.7	−	6206.01i	−0.991124	−	0.291020i	−0.736809	+	0.676101i	$0.763668\pi$
$770$	−3770.76	+	20434.8i	−0.176479	+	0.956390i
$771$	15721.9	+	18144.0i	0.734384	+	0.847525i
$772$	−2705.13	−	4954.07i	−0.126113	−	0.230960i
$773$	5864.10	−	2187.20i	0.272855	−	0.101770i	−0.209312	−	0.977849i	$-0.567122\pi$
$773$	5864.10	−	2187.20i	0.272855	−	0.101770i	0.482167	+	0.876079i	$0.339850\pi$
$774$	−5035.96	−	3236.41i	−0.233868	−	0.150298i
$775$	−1468.03	−	23105.1i	−0.0680427	−	1.07092i
$776$	547.373	+	78.7004i	0.0253216	+	0.00364070i
$777$	−16425.1	+	44037.4i	−0.758362	+	2.03325i
$778$	2930.84	−	3915.14i	0.135059	−	0.180417i
$779$	−12577.9	+	8083.35i	−0.578500	+	0.371779i
$780$	−26.2755	+	661.936i	−0.00120617	+	0.0303860i
$781$		−	14467.3i		−	0.662844i
$782$	−18265.6	−	12146.3i	−0.835264	−	0.555436i
$783$	−13524.9	+	13524.9i	−0.617292	+	0.617292i
$784$	−7508.19	−	6505.88i	−0.342028	−	0.296369i
$785$	14216.8	+	28685.8i	0.646395	+	1.30426i
$786$	4527.91	+	31492.3i	0.205478	+	1.42913i
$787$	9053.95	+	3376.95i	0.410087	+	0.152954i	0.546037	−	0.837761i	$-0.316136\pi$
$787$	9053.95	+	3376.95i	0.410087	+	0.152954i	−0.135950	+	0.990716i	$0.543409\pi$
$788$	1489.30	+	1989.47i	0.0673274	+	0.0899389i
$789$	47879.6	−	14058.7i	2.16041	−	0.634352i
$790$	11785.4	+	9574.81i	0.530769	+	0.431211i
$791$	4888.67	−	10704.7i	0.219748	−	0.481182i
$792$	2513.49	−	1372.47i	0.112769	−	0.0615766i
$793$	56.6583	−	792.186i	0.00253719	−	0.0354746i
$794$	5297.32	−	4590.15i	0.236769	−	0.205162i
$795$	−18061.6	+	7397.42i	−0.805762	+	0.330012i
$796$	−16591.4	−	7577.04i	−0.738777	−	0.337388i
$797$	−11085.6	+	2411.53i	−0.492689	+	0.107178i	−0.452044	−	0.891996i	$-0.649305\pi$
$797$	−11085.6	+	2411.53i	−0.492689	+	0.107178i	−0.0406450	+	0.999174i	$0.512941\pi$
$798$	−15291.7	+	28004.7i	−0.678348	+	1.24230i
$799$	−1551.51	+	10791.0i	−0.0686963	+	0.477793i
$800$	−3347.72	−	2189.24i	−0.147950	−	0.0967517i
$801$	11938.4	−	1716.49i	0.526622	−	0.0757168i
$802$	4201.54	−	19314.2i	0.184990	−	0.850384i
$803$	24021.0	−	1718.02i	1.05565	−	0.0755013i
$804$	16846.0			0.738946
$805$	24604.8	−	29336.1i	1.07728	−	1.28442i
$806$	−879.101			−0.0384181
$807$	−42046.0	+	3007.19i	−1.83406	+	0.131175i
$808$	190.285	−	874.725i	0.00828490	−	0.0380851i
$809$	25480.2	−	3663.50i	1.10734	−	0.159211i	0.435700	−	0.900092i	$-0.356501\pi$
$809$	25480.2	−	3663.50i	1.10734	−	0.159211i	0.671636	+	0.740881i	$0.265592\pi$
$810$	6341.35	+	19308.4i	0.275077	+	0.837568i
$811$	3155.69	−	21948.3i	0.136635	−	0.950321i	−0.799996	−	0.600005i	$-0.795165\pi$
$811$	3155.69	−	21948.3i	0.136635	−	0.950321i	0.936632	−	0.350316i	$-0.113926\pi$
$812$	−12126.2	+	22207.4i	−0.524071	+	0.959764i
$813$	25535.4	−	5554.89i	1.10156	−	0.239629i
$814$	13207.1	+	6031.49i	0.568685	+	0.259710i
$815$	11319.5	−	27023.5i	0.486510	−	1.16146i
$816$	7504.64	−	6502.81i	0.321955	−	0.278975i
$817$	1469.85	−	20551.3i	0.0629421	−	0.880046i
$818$	8818.66	−	4815.36i	0.376941	−	0.205825i
$819$	366.062	−	801.565i	0.0156181	−	0.0341989i
$820$	836.096	+	8078.79i	0.0356070	+	0.344053i
$821$	2989.77	−	877.875i	0.127093	−	0.0373180i	−0.217567	−	0.976045i	$-0.569812\pi$
$821$	2989.77	−	877.875i	0.127093	−	0.0373180i	0.344661	+	0.938727i	$0.387994\pi$
$822$	410.746	+	548.693i	0.0174287	+	0.0232821i
$823$	−34604.0	−	12906.6i	−1.46564	−	0.546655i	−0.515065	−	0.857151i	$-0.672232\pi$
$823$	−34604.0	−	12906.6i	−1.46564	−	0.546655i	−0.950575	+	0.310496i	$0.899505\pi$
$824$	−1754.27	−	12201.2i	−0.0741663	−	0.515838i
$825$	9869.95	−	21165.4i	0.416518	−	0.893192i
$826$	22808.4	+	19763.6i	0.960782	+	0.832522i
$827$	−16064.9	+	16064.9i	−0.675490	+	0.675490i	−0.958976	−	0.283486i	$-0.908509\pi$
$827$	−16064.9	+	16064.9i	−0.675490	+	0.675490i	0.283486	+	0.958976i	$0.408509\pi$
$828$	−5276.13	−	82.5117i	−0.221447	−	0.00346314i
$829$			8670.64i			0.363261i	0.983367	+	0.181631i	$0.0581375\pi$
$829$			8670.64i			0.363261i	−0.983367	+	0.181631i	$0.941862\pi$
$830$	3419.42	+	135.734i	0.143000	+	0.00567637i
$831$	−28871.2	+	18554.4i	−1.20521	+	0.774541i
$832$	−91.0214	+	121.590i	−0.00379279	+	0.00506657i
$833$	21575.7	−	57846.7i	0.897424	−	2.40609i
$834$	−29249.9	−	4205.49i	−1.21444	−	0.174610i
$835$	19056.6	−	3360.04i	0.789796	−	0.139256i
$836$	8292.01	+	5328.95i	0.343045	+	0.220461i
$837$	−16291.3	+	6076.35i	−0.672773	+	0.250931i
$838$	−5499.47	−	10071.5i	−0.226702	−	0.415173i
$839$	−3558.58	−	4106.82i	−0.146431	−	0.168991i	0.677796	−	0.735250i	$-0.262935\pi$
$839$	−3558.58	−	4106.82i	−0.146431	−	0.168991i	−0.824227	+	0.566260i	$0.808390\pi$
$840$	9828.73	+	14276.8i	0.403718	+	0.586426i
$841$	16428.5	+	4823.84i	0.673602	+	0.197787i
$842$	8075.79	+	21652.0i	0.330535	+	0.886197i
$843$	−7588.05	−	34881.7i	−0.310019	−	1.42514i
$844$	2957.98	+	10074.0i	0.120637	+	0.410853i
$845$	−21120.1	+	12417.9i	−0.859825	+	0.505549i
$846$	1089.45	+	2385.56i	0.0442742	+	0.0969471i
$847$	10813.6	+	8094.95i	0.438677	+	0.328389i
$848$	−4372.69	−	951.220i	−0.177074	−	0.0385201i
$849$	−1387.62	+	1601.40i	−0.0560930	+	0.0647348i
$850$	5476.83	−	24247.1i	0.221004	−	0.978433i
$851$	−15695.5	−	21664.8i	−0.632238	−	0.872689i
$852$	−8533.05	−	8533.05i	−0.343119	−	0.343119i
$853$	−200.200	−	2799.16i	−0.00803601	−	0.112358i	0.991851	−	0.127405i	$-0.0406648\pi$
$853$	−200.200	−	2799.16i	−0.00803601	−	0.112358i	−0.999887	+	0.0150469i	$0.995210\pi$
$854$	−11234.7	−	17481.5i	−0.450166	−	0.700472i
$855$	7533.02	−	8026.83i	0.301314	−	0.321066i
$856$	8568.90	−	3913.28i	0.342148	−	0.156254i
$857$	−3802.94	+	2846.84i	−0.151582	+	0.113473i	−0.672377	−	0.740209i	$-0.734727\pi$
$857$	−3802.94	+	2846.84i	−0.151582	+	0.113473i	0.520795	+	0.853682i	$0.325636\pi$
$858$	−778.294	−	424.981i	−0.0309680	−	0.0169098i
$859$	23105.4	−	35952.7i	0.917749	−	1.42805i	0.0140392	−	0.999901i	$-0.495531\pi$
$859$	23105.4	−	35952.7i	0.917749	−	1.42805i	0.903710	−	0.428145i	$-0.140833\pi$
$860$	−9602.86	−	5749.36i	−0.380762	−	0.227967i
$861$	9915.40	−	33768.8i	0.392469	−	1.33663i
$862$	−7726.87	−	552.636i	−0.305311	−	0.0218363i
$863$	3681.15	+	263.281i	0.145200	+	0.0103849i	0.143750	−	0.989614i	$-0.454084\pi$
$863$	3681.15	+	263.281i	0.145200	+	0.0103849i	0.00145011	+	0.999999i	$0.499538\pi$
$864$	−846.357	+	2882.43i	−0.0333260	+	0.113498i
$865$	25308.3	+	15152.4i	0.994808	+	0.595605i
$866$	−2801.60	+	4359.38i	−0.109933	+	0.171060i
$867$	27247.1	+	14878.0i	1.06731	+	0.582796i
$868$	−18413.6	+	13784.2i	−0.720044	+	0.539018i
$869$	−18489.3	+	8443.79i	−0.721758	+	0.329616i
$870$	19459.6	−	20735.2i	0.758325	−	0.808035i
$871$	−865.713	−	1347.08i	−0.0336780	−	0.0524041i
$872$	485.818	+	6792.62i	0.0188668	+	0.263792i
$873$	584.572	+	584.572i	0.0226630	+	0.0226630i
$874$	−8453.71	−	16074.4i	−0.327175	−	0.622110i
$875$	41002.9	+	14192.3i	1.58417	+	0.548328i
$876$	13154.7	−	15181.3i	0.507369	−	0.585535i
$877$	14535.9	+	3162.10i	0.559685	+	0.121752i	0.483504	−	0.875342i	$-0.339364\pi$
$877$	14535.9	+	3162.10i	0.559685	+	0.121752i	0.0761809	+	0.997094i	$0.475727\pi$
$878$	11639.3	+	8713.07i	0.447389	+	0.334911i
$879$	−12818.6	−	28068.8i	−0.491878	−	1.07706i
$880$	4615.68	−	2713.87i	0.176812	−	0.103960i
$881$	−7981.36	−	27182.0i	−0.305220	−	1.03948i	−0.959143	−	0.282923i	$-0.908696\pi$
$881$	−7981.36	−	27182.0i	−0.305220	−	1.03948i	0.653922	−	0.756562i	$-0.273122\pi$
$882$	−3157.01	−	14512.5i	−0.120524	−	0.554040i
$883$	−2335.40	−	6261.44i	−0.0890061	−	0.238635i	0.884818	−	0.465936i	$-0.154282\pi$
$883$	−2335.40	−	6261.44i	−0.0890061	−	0.238635i	−0.973824	+	0.227302i	$0.927010\pi$
$884$	−905.654	−	265.924i	−0.0344575	−	0.0101176i
$885$	−19233.2	−	27937.5i	−0.730529	−	1.06114i
$886$	15133.6	+	17465.1i	0.573840	+	0.662246i
$887$	−6539.72	−	11976.6i	−0.247556	−	0.453365i	0.724123	−	0.689671i	$-0.242245\pi$
$887$	−6539.72	−	11976.6i	−0.247556	−	0.453365i	−0.971679	+	0.236306i	$0.924063\pi$
$888$	11347.2	−	4232.30i	0.428816	−	0.159940i
$889$	−7720.06	−	4961.38i	−0.291252	−	0.187176i
$890$	22208.1	−	3915.71i	0.836424	−	0.147478i
$891$	−26927.6	−	3871.60i	−1.01247	−	0.145571i
$892$	−7947.78	+	21308.8i	−0.298331	+	0.799857i
$893$	−5409.33	+	7226.02i	−0.202706	+	0.270783i
$894$	−8795.61	+	5652.60i	−0.329048	+	0.211467i
$895$	−49385.6	−	1960.36i	−1.84445	−	0.0732152i
$896$			3974.03i			0.148173i
$897$	861.769	+	1388.20i	0.0320776	+	0.0516729i
$898$	6610.22	−	6610.22i	0.245641	−	0.245641i
$899$	28518.9	+	24711.8i	1.05802	+	0.916779i
$900$	−2045.13	−	5619.20i	−0.0757454	−	0.208119i
$901$	−3957.71	−	27526.5i	−0.146338	−	1.01780i
$902$	−10186.5	−	3799.38i	−0.376025	−	0.140250i
$903$	29064.7	+	38825.8i	1.07111	+	1.43083i
$904$	−2909.50	+	854.308i	−0.107045	+	0.0314313i
$905$	4596.20	+	44410.9i	0.168821	+	1.63123i
$906$	4017.60	−	8797.31i	0.147324	−	0.322595i
$907$	42264.3	−	23078.1i	1.54726	−	0.844867i	0.547290	−	0.836943i	$-0.315659\pi$
$907$	42264.3	−	23078.1i	1.54726	−	0.844867i	0.999969	−	0.00792444i	$-0.00252245\pi$
$908$	401.346	−	5611.55i	0.0146687	−	0.205095i
$909$	1011.38	−	876.369i	0.0369037	−	0.0319773i
$910$	636.538	−	1519.63i	0.0231880	−	0.0553574i
$911$	16365.0	+	7473.63i	0.595165	+	0.271803i	0.690139	−	0.723677i	$-0.257549\pi$
$911$	16365.0	+	7473.63i	0.595165	+	0.271803i	−0.0949736	+	0.995480i	$0.530277\pi$
$912$	8033.86	−	1747.66i	0.291697	−	0.0634548i
$913$	−2195.36	+	4020.51i	−0.0795794	+	0.145739i
$914$	−200.759	+	1396.31i	−0.00726533	+	0.0505315i
$915$	7287.08	+	22188.1i	0.263282	+	0.801655i
$916$	−16005.5	+	2301.25i	−0.577333	+	0.0830080i
$917$	16819.9	−	77320.0i	0.605718	−	2.78444i
$918$	−18621.5	+	1331.83i	−0.669499	+	0.0478835i
$919$	−50913.0			−1.82749			−0.913746	−	0.406286i	$-0.866824\pi$
$919$	−50913.0			−1.82749			−0.913746	+	0.406286i	$0.866824\pi$
$920$	−9864.62	+	158.719i	−0.353508	+	0.00568784i
$921$	−36207.7			−1.29542
$922$	−16675.6	+	1192.66i	−0.595641	+	0.0426011i
$923$	−243.826	+	1120.85i	−0.00869515	+	0.0399710i
$924$	−22965.8	+	3301.98i	−0.817660	+	0.117562i
$925$	16592.8	−	25373.2i	0.589804	−	0.901910i
$926$	3780.62	−	26294.8i	0.134167	−	0.933153i
$927$	8831.51	−	16173.7i	0.312907	−	0.573046i
$928$	6370.77	−	1385.88i	0.225356	−	0.0490233i
$929$	−20159.8	−	9206.65i	−0.711970	−	0.325146i	0.0262972	−	0.999654i	$-0.491628\pi$
$929$	−20159.8	−	9206.65i	−0.711970	−	0.325146i	−0.738267	+	0.674508i	$0.764356\pi$
$930$	23921.7	−	9797.50i	0.843466	−	0.345454i
$931$	38632.5	−	33475.3i	1.35997	−	1.17842i
$932$	723.687	−	10118.5i	0.0254347	−	0.355624i
$933$	−10322.6	+	5636.55i	−0.362214	+	0.197784i
$934$	−8190.57	+	17934.8i	−0.286942	+	0.628315i
$935$	25826.0	+	20981.7i	0.903315	+	0.733878i
$936$	−217.863	+	63.9704i	−0.00760799	+	0.00223391i
$937$	9713.35	+	12975.5i	0.338657	+	0.452392i	0.937249	−	0.348662i	$-0.113364\pi$
$937$	9713.35	+	12975.5i	0.338657	+	0.452392i	−0.598592	+	0.801054i	$0.704273\pi$
$938$	−39255.2	−	14641.4i	−1.36645	−	0.509659i
$939$	−1874.47	−	13037.2i	−0.0651447	−	0.453092i
$940$	2177.38	+	4393.39i	0.0755515	+	0.152443i
$941$	−8515.14	−	7378.41i	−0.294990	−	0.255610i	0.494773	−	0.869022i	$-0.335251\pi$
$941$	−8515.14	−	7378.41i	−0.294990	−	0.255610i	−0.789763	+	0.613412i	$0.789797\pi$
$942$	−25277.1	+	25277.1i	−0.874282	+	0.874282i
$943$	12880.2	+	15342.9i	0.444790	+	0.529834i
$944$		−	7776.53i		−	0.268119i
$945$	1292.52	−	32561.2i	0.0444926	−	1.12086i
$946$	12603.8	−	8099.97i	0.433176	−	0.278385i
$947$	−4785.07	+	6392.10i	−0.164196	+	0.219341i	−0.875092	−	0.483957i	$-0.839199\pi$
$947$	−4785.07	+	6392.10i	−0.164196	+	0.219341i	0.710895	+	0.703298i	$0.248290\pi$
$948$	−5925.02	+	15885.6i	−0.202991	+	0.544240i
$949$	−1889.98	−	271.738i	−0.0646483	−	0.00929502i
$950$	13601.2	−	15446.9i	0.464508	−	0.527539i
$951$	−43209.4	−	27769.0i	−1.47335	−	0.946868i
$952$	−23139.4	+	8630.56i	−0.787765	+	0.293821i
$953$	15188.8	+	27816.2i	0.516279	+	0.945494i	0.997619	+	0.0689607i	$0.0219683\pi$
$953$	15188.8	+	27816.2i	0.516279	+	0.945494i	−0.481340	+	0.876534i	$0.659850\pi$
$954$	−4380.91	−	5055.84i	−0.148676	−	0.171582i
$955$	8401.79	−	45531.6i	0.284686	−	1.54279i
$956$	25768.9	+	7566.42i	0.871783	+	0.255979i
$957$	13302.3	+	35664.9i	0.449324	+	1.20468i
$958$	4947.62	+	22743.8i	0.166858	+	0.767036i
$959$	−480.249	−	1635.58i	−0.0161711	−	0.0550736i
$960$	1121.72	−	4323.08i	0.0377118	−	0.145341i
$961$	1874.85	+	4105.34i	0.0629334	+	0.137805i
$962$	−921.565	−	689.875i	−0.0308861	−	0.0231211i
$963$	13760.9	+	2993.49i	0.460475	+	0.100170i
$964$	1129.49	−	1303.50i	0.0377369	−	0.0435507i
$965$	1748.80	−	15679.7i	0.0583376	−	0.523053i
$966$	39817.4	+	15564.6i	1.32619	+	0.518408i
$967$	1273.20	+	1273.20i	0.0423407	+	0.0423407i	0.727960	−	0.685619i	$-0.240469\pi$
$967$	1273.20	+	1273.20i	0.0423407	+	0.0423407i	−0.685619	+	0.727960i	$0.740469\pi$
$968$	−248.304	−	3471.74i	−0.00824461	−	0.115275i
$969$	27623.5	+	42983.0i	0.915784	+	1.42499i
$970$	1127.09	+	1057.75i	0.0373078	+	0.0350126i
$971$	3254.06	−	1486.08i	0.107547	−	0.0491148i	−0.360915	−	0.932599i	$-0.617536\pi$
$971$	3254.06	−	1486.08i	0.107547	−	0.0491148i	0.468462	+	0.883484i	$0.344808\pi$
$972$	−10049.3	+	7522.78i	−0.331616	+	0.248244i
$973$	64504.0	+	35221.8i	2.12529	+	1.16049i
$974$	−22214.4	+	34566.3i	−0.730796	+	1.13714i
$975$	−1121.38	+	1473.43i	−0.0368338	+	0.0483976i
$976$	−1508.54	+	5137.62i	−0.0494746	+	0.168495i
$977$	−22213.3	−	1588.73i	−0.727396	−	0.0520244i	−0.297270	−	0.954793i	$-0.596076\pi$
$977$	−22213.3	−	1588.73i	−0.727396	−	0.0520244i	−0.430126	+	0.902769i	$0.641531\pi$
$978$	32630.2	+	2333.76i	1.06687	+	0.0763040i
$979$	−8504.46	+	28963.5i	−0.277634	+	0.945535i
$980$	−6760.35	−	26933.0i	−0.220359	−	0.877902i
$981$	−5504.02	+	8564.43i	−0.179134	+	0.278737i
$982$	−6884.20	−	3759.06i	−0.223711	−	0.122155i
$983$	14858.4	−	11122.8i	0.482104	−	0.360898i	−0.330413	−	0.943837i	$-0.607188\pi$
$983$	14858.4	−	11122.8i	0.482104	−	0.360898i	0.812517	+	0.582938i	$0.198097\pi$
$984$	−8249.12	+	3767.25i	−0.267248	+	0.122048i
$985$	220.337	+	6942.72i	0.00712743	+	0.224582i
$986$	21905.1	+	34085.0i	0.707506	+	1.10090i
$987$	−1515.77	−	21193.3i	−0.0488831	−	0.683475i
$988$	−552.609	−	552.609i	−0.0177944	−	0.0177944i
$989$	−27562.9	+	1538.57i	−0.886198	+	0.0494678i
$990$	7955.23	+	887.270i	0.255388	+	0.0284841i
$991$	−18027.8	+	20805.2i	−0.577873	+	0.666901i	−0.967146	−	0.254222i	$-0.918181\pi$
$991$	−18027.8	+	20805.2i	−0.577873	+	0.666901i	0.389273	+	0.921122i	$0.372726\pi$
$992$	5791.40	+	1259.84i	0.185360	+	0.0403226i
$993$	1799.82	+	1347.33i	0.0575182	+	0.0430576i
$994$	12467.7	+	27300.4i	0.397837	+	0.871143i
$995$	−25839.9	−	43947.8i	−0.823295	−	1.40024i
$996$	1076.50	+	3666.22i	0.0342472	+	0.116635i
$997$	−6596.13	−	30321.9i	−0.209530	−	0.963194i	−0.954989	−	0.296642i	$-0.904133\pi$
$997$	−6596.13	−	30321.9i	−0.209530	−	0.963194i	0.745459	−	0.666552i	$-0.232231\pi$
$998$	52.9283	+	141.906i	0.00167877	+	0.00450097i
$999$	−21846.7	−	6414.77i	−0.691890	−	0.203157i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.4.l.a.7.15	✓	720
5.3	odd	4	inner	230.4.l.a.53.33	yes	720
23.10	odd	22	inner	230.4.l.a.217.33	yes	720
115.33	even	44	inner	230.4.l.a.33.15	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.l.a.7.15	✓	720	1.1	even	1	trivial
230.4.l.a.33.15	yes	720	115.33	even	44	inner
230.4.l.a.53.33	yes	720	5.3	odd	4	inner
230.4.l.a.217.33	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} +(1.32678 - 6.09912i) q^{3} +(3.95929 - 0.569259i) q^{4} +(9.97777 + 5.04421i) q^{5} +(-1.77659 + 12.3565i) q^{6} +(14.8793 - 27.2494i) q^{7} +(-7.81717 + 1.70052i) q^{8} +(-10.8788 - 4.96819i) q^{9} +(-20.6244 - 8.63909i) q^{10} +(22.6211 - 19.6013i) q^{11} +(1.78113 - 24.9034i) q^{12} +(-2.08291 + 1.13736i) q^{13} +(-25.7949 + 56.4829i) q^{14} +(44.0035 - 54.1631i) q^{15} +(15.3519 - 4.50772i) q^{16} +(59.5872 + 79.5992i) q^{17} +(22.4111 + 8.35890i) q^{18} +(11.7162 + 81.4881i) q^{19} +(42.3763 + 14.2915i) q^{20} +(-146.456 - 126.905i) q^{21} +(-42.3302 + 42.3302i) q^{22} +(106.309 - 29.4175i) q^{23} +49.9341i q^{24} +(74.1120 + 100.660i) q^{25} +(3.99294 - 2.56610i) q^{26} +(56.2594 - 75.1537i) q^{27} +(43.3994 - 116.358i) q^{28} +(-201.669 - 28.9956i) q^{29} +(-80.0549 + 114.328i) q^{30} +(-155.812 - 100.134i) q^{31} +(-29.9824 + 11.1829i) q^{32} +(-89.5373 - 163.975i) q^{33} +(-130.228 - 150.291i) q^{34} +(285.914 - 196.834i) q^{35} +(-45.9006 - 13.4776i) q^{36} +(-84.7578 - 227.244i) q^{37} +(-34.9993 - 160.889i) q^{38} +(4.17330 + 14.2130i) q^{39} +(-86.5758 - 22.4640i) q^{40} +(75.4444 + 165.200i) q^{41} +(310.272 + 232.266i) q^{42} +(-244.551 - 53.1987i) q^{43} +(78.4052 - 90.4844i) q^{44} +(-83.4859 - 104.447i) q^{45} +(-207.879 + 73.8531i) q^{46} +(77.5288 + 77.5288i) q^{47} +(-7.12452 - 99.6137i) q^{48} +(-335.696 - 522.353i) q^{49} +(-162.208 - 190.233i) q^{50} +(564.544 - 257.819i) q^{51} +(-7.59940 + 5.68884i) q^{52} +(-245.473 - 134.039i) q^{53} +(-101.509 + 157.951i) q^{54} +(324.581 - 81.4718i) q^{55} +(-69.9758 + 238.316i) q^{56} +(512.551 + 36.6583i) q^{57} +(406.447 + 29.0697i) q^{58} +(136.931 - 466.345i) q^{59} +(143.390 - 239.496i) q^{60} +(-180.929 + 281.531i) q^{61} +(325.117 + 177.527i) q^{62} +(-297.250 + 222.518i) q^{63} +(58.2164 - 26.5866i) q^{64} +(-26.5199 + 0.841646i) q^{65} +(202.014 + 314.340i) q^{66} +(48.1347 + 673.011i) q^{67} +(281.235 + 281.235i) q^{68} +(-38.3721 - 687.422i) q^{69} +(-542.287 + 433.459i) q^{70} +(316.520 - 365.283i) q^{71} +(93.4902 + 20.3376i) q^{72} +(644.092 + 482.161i) q^{73} +(201.507 + 441.238i) q^{74} +(712.267 - 318.464i) q^{75} +(92.7758 + 315.965i) q^{76} +(-197.537 - 908.064i) q^{77} +(-10.3532 - 27.7580i) q^{78} +(-651.571 - 191.318i) q^{79} +(175.916 + 32.4611i) q^{80} +(-595.188 - 686.884i) q^{81} +(-174.075 - 318.794i) q^{82} +(-143.392 + 53.4826i) q^{83} +(-652.101 - 419.080i) q^{84} +(193.033 + 1094.79i) q^{85} +(495.445 + 71.2343i) q^{86} +(-444.418 + 1191.53i) q^{87} +(-143.501 + 191.694i) q^{88} +(-848.401 + 545.234i) q^{89} +(181.449 + 196.449i) q^{90} +73.6812i q^{91} +(404.162 - 176.990i) q^{92} +(-817.459 + 817.459i) q^{93} +(-165.724 - 143.601i) q^{94} +(-294.141 + 872.169i) q^{95} +(28.4255 + 197.703i) q^{96} +(-64.7669 - 24.1568i) q^{97} +(744.210 + 994.148i) q^{98} +(-343.474 + 100.853i) 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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