LMFDB - Embedded newform 230.4.l.a.33.15

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			33.15
Character	$\chi$	$=$	230.33
Dual form			230.4.l.a.7.15

$q$-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 $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−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	0.908937	+	0.416934i	$0.136895\pi$
$3$	1.32678	+	6.09912i	0.255339	+	1.17378i	−0.653598	+	0.756842i	$0.726741\pi$
$4$	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	0.880366	+	0.474295i	$0.157297\pi$
$7$	14.8793	+	27.2494i	0.803406	+	1.47133i	−0.0769600	+	0.997034i	$0.524521\pi$
$8$	−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	0.907248	−	0.420597i	$-0.138179\pi$
$11$	22.6211	+	19.6013i	0.620047	+	0.537274i	−0.287201	+	0.957870i	$0.592725\pi$
$12$	1.78113	+	24.9034i	0.0428473	+	0.599084i
$13$	−2.08291	−	1.13736i	−0.0444382	−	0.0242651i	0.456876	−	0.889530i	$-0.348968\pi$
$13$	−2.08291	−	1.13736i	−0.0444382	−	0.0242651i	−0.501314	+	0.865265i	$0.667150\pi$
$14$	−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	−0.139258	−	0.990256i	$-0.544472\pi$
$17$	59.5872	−	79.5992i	0.850119	−	1.13563i	0.989377	−	0.145370i	$-0.0464372\pi$
$18$	22.4111	−	8.35890i	0.293463	−	0.109456i
$19$	11.7162	−	81.4881i	0.141468	−	0.983929i	−0.788171	−	0.615457i	$-0.788972\pi$
$19$	11.7162	−	81.4881i	0.141468	−	0.983929i	0.929639	−	0.368473i	$-0.120119\pi$
$20$	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	−0.753539	−	0.657403i	$-0.771655\pi$
$29$	−201.669	+	28.9956i	−1.29134	+	0.185667i	−0.537804	+	0.843070i	$0.680746\pi$
$30$	−80.0549	−	114.328i	−0.487199	−	0.695781i
$31$	−155.812	+	100.134i	−0.902730	+	0.580149i	−0.907599	−	0.419839i	$-0.862087\pi$
$31$	−155.812	+	100.134i	−0.902730	+	0.580149i	0.00486857	+	0.999988i	$0.498450\pi$
$32$	−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	0.601007	+	0.799244i	$0.294766\pi$
$37$	−84.7578	+	227.244i	−0.376597	+	1.00970i	−0.977604	+	0.210452i	$0.932506\pi$
$38$	−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	−0.709796	−	0.704407i	$-0.751213\pi$
$41$	75.4444	−	165.200i	0.287377	−	0.629267i	0.997173	+	0.0751400i	$0.0239404\pi$
$42$	310.272	−	232.266i	1.13990	−	0.853321i
$43$	−244.551	+	53.1987i	−0.867293	+	0.188668i	−0.624133	−	0.781318i	$-0.714548\pi$
$43$	−244.551	+	53.1987i	−0.867293	+	0.188668i	−0.243160	+	0.969986i	$0.578184\pi$
$44$	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	−0.576492	−	0.817103i	$-0.695579\pi$
$47$	77.5288	−	77.5288i	0.240611	−	0.240611i	0.817103	+	0.576492i	$0.195579\pi$
$48$	−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	−0.764763	−	0.644312i	$-0.777144\pi$
$53$	−245.473	+	134.039i	−0.636196	+	0.347389i	0.128567	+	0.991701i	$0.458962\pi$
$54$	−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	0.960952	+	0.276716i	$0.0892461\pi$
$59$	136.931	+	466.345i	0.302152	+	1.02903i	−0.658800	+	0.752318i	$0.728936\pi$
$60$	143.390	+	239.496i	0.308526	+	0.515314i
$61$	−180.929	−	281.531i	−0.379764	−	0.590925i	0.597779	−	0.801661i	$-0.296050\pi$
$61$	−180.929	−	281.531i	−0.379764	−	0.590925i	−0.977543	+	0.210737i	$0.932414\pi$
$62$	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	−0.742509	−	0.669836i	$-0.766364\pi$
$67$	48.1347	−	673.011i	0.0877699	−	1.22718i	0.830279	−	0.557348i	$-0.188181\pi$
$68$	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	0.955878	−	0.293762i	$-0.0949075\pi$
$71$	316.520	+	365.283i	0.529070	+	0.610580i	−0.426808	+	0.904342i	$0.640362\pi$
$72$	93.4902	−	20.3376i	0.153027	−	0.0332889i
$73$	644.092	−	482.161i	1.03267	−	0.773051i	0.0583724	−	0.998295i	$-0.481409\pi$
$73$	644.092	−	482.161i	1.03267	−	0.773051i	0.974302	+	0.225244i	$0.0723180\pi$
$74$	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	−0.710575	−	0.703621i	$-0.751565\pi$
$79$	−651.571	+	191.318i	−0.927942	+	0.272468i	−0.217367	+	0.976090i	$0.569747\pi$
$80$	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	0.252855	−	0.967504i	$-0.418631\pi$
$83$	−143.392	−	53.4826i	−0.189631	−	0.0707286i	−0.442486	+	0.896776i	$0.645903\pi$
$84$	−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	−0.0729428	−	0.997336i	$-0.523239\pi$
$89$	−848.401	−	545.234i	−1.01045	−	0.649379i	−0.937510	+	0.347957i	$0.886875\pi$
$90$	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	−0.383133	−	0.923693i	$-0.625155\pi$
$97$	−64.7669	+	24.1568i	−0.0677947	+	0.0252861i	0.315338	+	0.948979i	$0.397882\pi$
$98$	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	0.885351	−	0.464922i	$-0.153918\pi$
$101$	−46.4841	−	101.786i	−0.0457954	−	0.100278i	−0.931147	+	0.364644i	$0.881191\pi$
$102$	−1089.43	−	594.872i	−1.05754	−	0.577462i
$103$	−109.922	−	1536.91i	−0.105155	−	1.47026i	−0.726741	−	0.686912i	$-0.758966\pi$
$103$	−109.922	−	1536.91i	−0.105155	−	1.47026i	0.621586	−	0.783346i	$-0.286489\pi$
$104$	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	−0.339788	−	0.940502i	$-0.610355\pi$
$107$	−1150.61	−	250.300i	−1.03957	−	0.226144i	−0.699781	+	0.714358i	$0.746719\pi$
$108$	179.965	+	329.581i	0.160344	+	0.293648i
$109$	121.145	+	842.582i	0.106455	+	0.740410i	0.971212	+	0.238219i	$0.0765635\pi$
$109$	121.145	+	842.582i	0.106455	+	0.740410i	−0.864757	+	0.502191i	$0.832527\pi$
$110$	−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	0.227819	−	0.973703i	$-0.426840\pi$
$113$	378.076	+	27.0405i	0.314747	+	0.0225112i	0.0869279	+	0.996215i	$0.472295\pi$
$114$	−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	0.999487	+	0.0320403i	$0.0102005\pi$
$127$	21.0863	+	294.825i	0.0147331	+	0.205996i	−0.984753	+	0.173956i	$0.944345\pi$
$128$	−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	0.963936	−	0.266133i	$-0.0857460\pi$
$131$	2445.42	+	718.039i	1.63097	+	0.478896i	0.667033	+	0.745029i	$0.267564\pi$
$132$	−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	0.719109	−	0.694898i	$-0.244550\pi$
$137$	38.8234	+	38.8234i	0.0242110	+	0.0242110i	−0.694898	+	0.719109i	$0.744550\pi$
$138$	174.629	−	1365.87i	0.107720	−	0.842538i
$139$		−	2367.17i		−	1.44447i	−0.691649	−	0.722233i	$-0.743116\pi$
$139$		−	2367.17i		−	1.44447i	0.691649	−	0.722233i	$-0.256884\pi$
$140$	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	−0.584665	−	0.811275i	$-0.698774\pi$
$149$	548.468	−	632.965i	0.301559	−	0.348017i	0.886224	+	0.463258i	$0.153320\pi$
$150$	−1375.47	−	736.930i	−0.748709	−	0.401134i
$151$	−743.342	+	218.265i	−0.400611	+	0.117630i	−0.475831	−	0.879537i	$-0.657852\pi$
$151$	−743.342	+	218.265i	−0.400611	+	0.117630i	0.0752194	+	0.997167i	$0.476034\pi$
$152$	−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	0.171690	−	0.985151i	$-0.445077\pi$
$157$	2292.40	−	1716.07i	1.16531	−	0.872337i	0.993616	+	0.112814i	$0.0359864\pi$
$158$	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	0.730007	+	0.683440i	$0.239517\pi$
$163$	−186.947	+	2613.86i	−0.0898332	+	1.25603i	−0.819840	+	0.572593i	$0.805938\pi$
$164$	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	0.869996	−	0.493058i	$-0.164121\pi$
$167$	1385.55	+	1037.21i	0.642017	+	0.480608i	−0.227979	+	0.973666i	$0.573212\pi$
$168$	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	0.520134	−	0.854085i	$-0.325882\pi$
$173$	2631.62	−	188.217i	1.15652	−	0.0827162i	0.636389	+	0.771368i	$0.280427\pi$
$174$	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	−0.999446	−	0.0332714i	$-0.989407\pi$
$179$	−4021.18	−	1836.41i	−1.67909	−	0.766814i	−0.679643	−	0.733543i	$-0.737865\pi$
$180$	−390.002	+	366.009i	−0.161495	+	0.151559i
$181$	2159.02	−	3359.50i	0.886622	−	1.37961i	−0.0382238	−	0.999269i	$-0.512170\pi$
$181$	2159.02	−	3359.50i	0.886622	−	1.37961i	0.924846	−	0.380342i	$-0.124194\pi$
$182$	−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	0.374109	+	0.927385i	$0.377949\pi$
$191$	−1166.72	+	3973.48i	−0.441994	+	1.50529i	−0.816102	+	0.577907i	$0.803870\pi$
$192$	−84.9140	+	390.344i	−0.0319174	+	0.146722i
$193$	−493.138	+	1322.16i	−0.183922	+	0.493113i	−0.995888	−	0.0905910i	$-0.971124\pi$
$193$	−493.138	+	1322.16i	−0.183922	+	0.493113i	0.811967	+	0.583704i	$0.198397\pi$
$194$	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	−0.818280	−	0.574820i	$-0.805072\pi$
$197$	297.752	−	545.291i	0.107685	−	0.197210i	0.925965	+	0.377610i	$0.123254\pi$
$198$	670.808	+	250.199i	0.240769	+	0.0898022i
$199$	−3836.05	+	2465.28i	−1.36648	+	0.878186i	−0.998662	−	0.0517104i	$-0.983533\pi$
$199$	−3836.05	+	2465.28i	−1.36648	+	0.878186i	−0.367822	+	0.929896i	$0.619896\pi$
$200$	−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	−0.833548	−	0.552448i	$-0.813694\pi$
$211$	373.550	−	2598.10i	0.121878	−	0.847680i	0.955426	−	0.295232i	$-0.0953969\pi$
$212$	−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	−0.866217	−	0.499668i	$-0.833455\pi$
$223$	−2724.86	−	4990.21i	−0.818252	−	1.49852i	0.0479647	−	0.998849i	$-0.484726\pi$
$224$	−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	0.999975	−	0.00710376i	$-0.00226122\pi$
$227$	298.967	+	1374.33i	0.0874147	+	0.401839i	−0.912560	+	0.408943i	$0.865898\pi$
$228$	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	0.988718	+	0.149788i	$0.0478591\pi$
$233$	539.082	+	2478.12i	0.151573	+	0.696768i	−0.837145	+	0.546980i	$0.815777\pi$
$234$	−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	0.652963	−	0.757390i	$-0.273526\pi$
$239$	6107.44	−	2789.17i	1.65296	−	0.754881i	0.999997	+	0.00250874i	$0.000798558\pi$
$240$	431.385	+	1029.86i	0.116024	+	0.276989i
$241$	325.875	+	282.372i	0.0871014	+	0.0754738i	0.697323	−	0.716757i	$-0.254374\pi$
$241$	325.875	+	282.372i	0.0871014	+	0.0754738i	−0.610222	+	0.792231i	$0.708920\pi$
$242$	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	−0.153507	−	0.988148i	$-0.549057\pi$
$251$	3192.15	−	2766.02i	0.802737	−	0.695575i	0.956243	+	0.292572i	$0.0945112\pi$
$252$	−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	0.428239	−	0.903666i	$-0.359134\pi$
$257$	−2305.03	−	3079.16i	−0.559471	−	0.747365i	−0.987710	+	0.156300i	$0.950043\pi$
$258$	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	0.143060	−	0.989714i	$-0.454306\pi$
$263$	3831.45	−	7016.77i	0.898316	−	1.64514i	0.755256	−	0.655430i	$-0.227512\pi$
$264$	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	0.401902	+	0.915683i	$0.368349\pi$
$269$	−1902.67	+	6479.89i	−0.431255	+	1.46872i	−0.833157	+	0.553037i	$0.813469\pi$
$270$	−1809.58	−	1063.97i	−0.407879	−	0.239819i
$271$	1739.23	−	3808.39i	0.389856	−	0.853666i	−0.608343	−	0.793674i	$-0.708165\pi$
$271$	1739.23	−	3808.39i	0.389856	−	0.853666i	0.998199	−	0.0599913i	$-0.0191073\pi$
$272$	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	−0.989290	−	0.145964i	$-0.953372\pi$
$277$	−3887.90	+	3887.90i	−0.843326	+	0.843326i	0.145964	+	0.989290i	$0.453372\pi$
$278$	−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	0.882321	−	0.470648i	$-0.155980\pi$
$281$	5202.31	+	2375.82i	1.10443	+	0.504375i	0.222106	+	0.975023i	$0.428707\pi$
$282$	−1095.72	−	820.245i	−0.231380	−	0.173209i
$283$	−297.954	+	162.695i	−0.0625850	+	0.0341740i	−0.510237	−	0.860034i	$-0.670442\pi$
$283$	−297.954	+	162.695i	−0.0625850	+	0.0341740i	0.447652	+	0.894208i	$0.352260\pi$
$284$	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	0.915989	−	0.401203i	$-0.131408\pi$
$293$	3957.63	+	2962.64i	0.789102	+	0.590714i	−0.126887	+	0.991917i	$0.540499\pi$
$294$	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	0.708310	+	0.705902i	$0.249458\pi$
$307$	−1233.06	+	5668.31i	−0.229234	+	1.05377i	−0.937543	+	0.347868i	$0.886906\pi$
$308$	−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	−0.857008	−	0.515303i	$-0.827679\pi$
$311$	−1233.94	+	1424.04i	−0.224985	+	0.259646i	0.632023	+	0.774950i	$0.282225\pi$
$312$	−56.7929	+	104.008i	−0.0103053	+	0.0188728i
$313$	1977.14	+	737.434i	0.357043	+	0.133170i	0.521583	−	0.853200i	$-0.325342\pi$
$313$	1977.14	+	737.434i	0.357043	+	0.133170i	−0.164541	+	0.986370i	$0.552614\pi$
$314$	−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	0.896117	+	0.443818i	$0.146376\pi$
$317$	2875.72	+	7710.11i	0.509516	+	1.36607i	−0.386601	+	0.922247i	$0.626351\pi$
$318$	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	0.896801	−	0.442433i	$-0.145885\pi$
$331$	−149.631	−	327.645i	−0.0248473	−	0.0544079i	−0.921649	+	0.388025i	$0.873157\pi$
$332$	−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	0.927996	−	0.372589i	$-0.121530\pi$
$337$	10005.7	+	2176.62i	1.61735	+	0.351833i	0.689356	+	0.724423i	$0.257894\pi$
$338$	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	−0.699558	−	0.714576i	$-0.746620\pi$
$347$	−9655.05	−	690.543i	−1.49369	−	0.106831i	−0.794132	+	0.607745i	$0.792074\pi$
$348$	−1081.29	−	4970.60i	−0.166561	−	0.765667i
$349$	−9447.11	−	1358.29i	−1.44897	−	0.208331i	−0.627518	−	0.778602i	$-0.715929\pi$
$349$	−9447.11	−	1358.29i	−1.44897	−	0.208331i	−0.821456	+	0.570271i	$0.806838\pi$
$350$	−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	0.549891	−	0.835237i	$-0.314669\pi$
$353$	4663.27	+	1014.43i	0.703119	+	0.152954i	0.153228	+	0.988191i	$0.451033\pi$
$354$	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	−0.952013	−	0.306058i	$-0.900990\pi$
$359$	−3808.35	−	8339.12i	−0.559880	−	1.22597i	0.392132	−	0.919909i	$-0.371738\pi$
$360$	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	0.899349	−	0.437232i	$-0.144041\pi$
$367$	3249.01	+	3249.01i	0.462117	+	0.462117i	−0.437232	+	0.899349i	$0.644041\pi$
$368$	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	0.998695	−	0.0510783i	$-0.0162658\pi$
$373$	1516.28	+	4065.30i	0.210482	+	0.564325i	−0.788212	+	0.615404i	$0.788993\pi$
$374$	−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	−0.537924	−	0.842993i	$-0.680791\pi$
$379$	2752.44	−	3176.48i	0.373043	−	0.430514i	0.910967	+	0.412479i	$0.135337\pi$
$380$	−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	−0.962754	−	0.270377i	$-0.912852\pi$
$383$	189.760	−	872.312i	0.0253167	−	0.116379i	0.988071	+	0.153999i	$0.0492151\pi$
$384$	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	0.641733	−	0.766928i	$-0.278216\pi$
$389$	−1601.34	−	1848.04i	−0.208717	−	0.240873i	−0.850450	+	0.526056i	$0.823670\pi$
$390$	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	0.407044	−	0.913409i	$-0.366560\pi$
$397$	−2805.64	−	2100.28i	−0.354688	−	0.265516i	−0.761732	+	0.647893i	$0.775651\pi$
$398$	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	−0.929677	−	0.368377i	$-0.879914\pi$
$401$	−2784.35	−	9482.62i	−0.346742	−	1.18090i	0.582934	−	0.812519i	$-0.301905\pi$
$402$	−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	0.119555	−	0.992828i	$-0.461853\pi$
$409$	−4569.86	−	2086.98i	−0.552482	−	0.252310i	−0.672037	+	0.740518i	$0.734580\pi$
$410$	−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	−0.718287	−	0.695747i	$-0.755074\pi$
$419$	2383.48	−	5219.09i	0.277901	−	0.608519i	0.996188	+	0.0872279i	$0.0278008\pi$
$420$	−4392.60	+	7470.82i	−0.510325	+	0.867949i
$421$	−3255.29	+	11086.5i	−0.376848	+	1.28343i	0.524900	+	0.851164i	$0.324103\pi$
$421$	−3255.29	+	11086.5i	−0.376848	+	1.28343i	−0.901748	+	0.432262i	$0.857715\pi$
$422$	−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	0.0752945	−	0.997161i	$-0.476010\pi$
$431$	3833.88	−	551.228i	0.428472	−	0.0616049i	0.353177	+	0.935556i	$0.385101\pi$
$432$	524.916	+	1407.35i	0.0584607	+	0.156739i
$433$	1552.73	+	2074.20i	0.172331	+	0.230207i	0.878389	−	0.477947i	$-0.158619\pi$
$433$	1552.73	+	2074.20i	0.172331	+	0.230207i	−0.706057	+	0.708155i	$0.749528\pi$
$434$	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	−0.900211	−	0.435454i	$-0.856588\pi$
$439$	−5494.03	+	4760.61i	−0.597303	+	0.517566i	0.302908	+	0.953020i	$0.402042\pi$
$440$	−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	0.257020	+	0.966406i	$0.417259\pi$
$443$	−6924.53	+	9250.09i	−0.742651	+	0.992065i	−0.999671	+	0.0256593i	$0.991831\pi$
$444$	−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	0.449153	−	0.893455i	$-0.351726\pi$
$449$	−3532.47	−	3060.90i	−0.371286	−	0.321722i	−0.820440	+	0.571733i	$0.806271\pi$
$450$	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	0.984183	−	0.177153i	$-0.0566888\pi$
$457$	149.929	+	689.214i	0.0153466	+	0.0705472i	−0.968837	+	0.247700i	$0.920325\pi$
$458$	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	−0.870060	−	0.492945i	$-0.835920\pi$
$463$	−2823.42	−	12979.0i	−0.283402	−	1.30278i	0.586658	−	0.809835i	$-0.300443\pi$
$464$	−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	0.999945	+	0.0104830i	$0.00333690\pi$
$467$	4724.58	+	8652.42i	0.468153	+	0.857358i	−0.531792	+	0.846875i	$0.678481\pi$
$468$	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	0.744349	+	0.667790i	$0.232760\pi$
$479$	−1656.24	+	11519.4i	−0.157987	+	1.09882i	−0.902336	+	0.431033i	$0.858149\pi$
$480$	−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	0.808139	+	0.588992i	$0.200475\pi$
$487$	12311.9	+	16446.7i	1.14559	+	1.53033i	0.337454	+	0.941342i	$0.390434\pi$
$488$	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	−0.380165	−	0.924919i	$-0.624133\pi$
$491$	3299.25	−	2120.30i	0.303244	−	0.194883i	0.683409	+	0.730035i	$0.260496\pi$
$492$	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	−0.960444	−	0.278472i	$-0.910172\pi$
$499$	−21.3350	+	72.6603i	−0.00191400	+	0.00651848i	0.958530	+	0.284990i	$0.0919903\pi$
$500$	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	0.271215	−	0.962519i	$-0.412575\pi$
$503$	10353.4	−	2252.25i	0.917765	−	0.199647i	0.646550	+	0.762871i	$0.276211\pi$
$504$	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	−0.113154	−	0.993577i	$-0.536095\pi$
$509$	9619.11	−	14967.6i	0.837641	−	1.30340i	0.950796	−	0.309818i	$-0.100268\pi$
$510$	−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	0.604645	−	0.796495i	$-0.293315\pi$
$521$	−4412.55	−	6866.07i	−0.371051	−	0.577366i	−0.975696	+	0.219129i	$0.929679\pi$
$522$	−4277.24	+	2335.55i	−0.358640	+	0.195832i
$523$	8048.37	+	6024.94i	0.672908	+	0.503733i	0.880234	−	0.474539i	$-0.157385\pi$
$523$	8048.37	+	6024.94i	0.672908	+	0.503733i	−0.207326	+	0.978272i	$0.566476\pi$
$524$	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	−0.387113	−	0.922032i	$-0.626528\pi$
$541$	7306.22	−	8431.82i	0.580626	−	0.670078i	0.967739	+	0.251954i	$0.0810731\pi$
$542$	−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	0.999982	+	0.00595979i	$0.00189707\pi$
$547$	3174.63	+	8511.52i	0.248149	+	0.665313i	−0.751833	+	0.659353i	$0.770830\pi$
$548$	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	−0.199635	−	0.979870i	$-0.563976\pi$
$557$	3827.61	−	1427.63i	0.291169	−	0.108600i	0.490804	+	0.871270i	$0.336703\pi$
$558$	−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	−0.999994	−	0.00331941i	$-0.998943\pi$
$563$	−142.282	−	1989.36i	−0.0106509	−	0.148919i	0.989344	−	0.145600i	$-0.0465111\pi$
$564$	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	−0.914987	−	0.403484i	$-0.867799\pi$
$569$	−2045.93	−	14229.8i	−0.150738	−	1.04840i	0.764249	−	0.644921i	$-0.223110\pi$
$570$	−10254.4	+	5184.03i	−0.753522	+	0.380939i
$571$	−12178.0	−	1750.93i	−0.892529	−	0.128326i	−0.319235	−	0.947676i	$-0.603426\pi$
$571$	−12178.0	−	1750.93i	−0.892529	−	0.128326i	−0.573294	+	0.819349i	$0.694335\pi$
$572$	−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	−0.329834	−	0.944039i	$-0.606993\pi$
$577$	−10958.6	−	783.773i	−0.790661	−	0.0565492i	−0.460827	+	0.887490i	$0.652447\pi$
$578$	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	0.982647	+	0.185484i	$0.0593853\pi$
$587$	517.663	+	7237.88i	0.0363991	+	0.508926i	−0.946248	+	0.323441i	$0.895160\pi$
$588$	−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	−0.631971	−	0.774992i	$-0.717754\pi$
$593$	−8694.19	+	3242.76i	−0.602070	+	0.224560i	0.0299006	+	0.999553i	$0.490481\pi$
$594$	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	$-0.983709\pi$
$599$		−	1499.97i		−	0.102316i	0.998691	−	0.0511578i	$-0.0162911\pi$
$600$	−5026.36	−	3700.71i	−0.342001	−	0.251802i
$601$	−17455.2	−	11217.8i	−1.18472	−	0.761371i	−0.208468	−	0.978029i	$-0.566848\pi$
$601$	−17455.2	−	11217.8i	−1.18472	−	0.761371i	−0.976247	+	0.216658i	$0.930484\pi$
$602$	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	0.390705	−	0.920516i	$-0.372231\pi$
$607$	1243.80	+	463.914i	0.0831703	+	0.0310209i	−0.307535	+	0.951537i	$0.599504\pi$
$608$	−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	−0.757690	−	0.652615i	$-0.773672\pi$
$613$	3075.43	−	14137.5i	0.202635	−	0.931499i	0.960325	−	0.278884i	$-0.0899645\pi$
$614$	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	−0.317728	−	0.948182i	$-0.602920\pi$
$617$	7701.78	−	5765.48i	0.502532	−	0.376190i	0.820260	+	0.571991i	$0.193829\pi$
$618$	−18795.5	+	4088.71i	−1.22341	+	0.266136i
$619$	−1511.68	−	1744.57i	−0.0981573	−	0.113280i	0.704545	−	0.709659i	$-0.251151\pi$
$619$	−1511.68	−	1744.57i	−0.0981573	−	0.113280i	−0.802703	+	0.596379i	$0.796605\pi$
$620$	−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	0.995531	+	0.0944333i	$0.0301039\pi$
$631$	3314.21	+	11287.2i	0.209092	+	0.712100i	−0.786440	+	0.617667i	$0.788078\pi$
$632$	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	−0.969059	−	0.246829i	$-0.920611\pi$
$641$	−5549.84	+	8635.72i	−0.341974	+	0.532122i	0.627085	+	0.778951i	$0.284248\pi$
$642$	−1048.66	+	14662.2i	−0.0644662	+	0.901355i
$643$	−3375.34	+	3375.34i	−0.207014	+	0.207014i	−0.802997	−	0.595983i	$-0.796763\pi$
$643$	−3375.34	+	3375.34i	−0.207014	+	0.207014i	0.595983	+	0.802997i	$0.296763\pi$
$644$	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	0.557407	−	0.830239i	$-0.311796\pi$
$647$	23193.8	−	5045.49i	1.40934	−	0.306582i	0.851929	+	0.523657i	$0.175433\pi$
$648$	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	0.389250	+	0.921132i	$0.372734\pi$
$653$	−8479.14	+	22733.5i	−0.508139	+	1.36237i	−0.897389	+	0.441240i	$0.854539\pi$
$654$	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	−0.235840	−	0.971792i	$-0.575784\pi$
$659$	9307.19	−	5981.37i	0.550162	−	0.353568i	0.786002	+	0.618224i	$0.212148\pi$
$660$	−1450.81	+	8228.30i	−0.0855645	+	0.485282i
$661$	−30201.4	+	4342.31i	−1.77716	+	0.255516i	−0.951278	−	0.308333i	$-0.900229\pi$
$661$	−30201.4	+	4342.31i	−1.77716	+	0.255516i	−0.825877	+	0.563850i	$0.809320\pi$
$662$	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	0.0542842	−	0.998526i	$-0.482712\pi$
$673$	17408.0	−	23254.3i	0.997069	−	1.33193i	0.942785	−	0.333402i	$-0.108197\pi$
$674$	−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	−0.479183	−	0.877715i	$-0.659067\pi$
$677$	−26010.8	−	14203.0i	−1.47663	−	0.806301i	−0.997447	+	0.0714146i	$0.977249\pi$
$678$	−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	0.767462	−	0.641094i	$-0.221519\pi$
$683$	−3334.00	−	6105.77i	−0.186782	−	0.342066i	−0.954244	+	0.299029i	$0.903337\pi$
$684$	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	−0.974082	−	0.226196i	$-0.927371\pi$
$701$	−24807.3	−	21495.6i	−1.33660	−	1.15817i	−0.362520	−	0.931976i	$-0.618084\pi$
$702$	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	0.916050	+	0.401064i	$0.131360\pi$
$709$	−1432.63	+	9964.14i	−0.0758864	+	0.527801i	−0.991936	+	0.126737i	$0.959550\pi$
$710$	−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	−0.590722	−	0.806875i	$-0.701157\pi$
$719$	−17933.5	+	2578.45i	−0.930192	+	0.133741i	−0.339470	+	0.940617i	$0.610248\pi$
$720$	−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	0.515172	+	0.857087i	$0.327728\pi$
$727$	−8535.55	+	22884.7i	−0.435441	+	1.16746i	−0.950614	+	0.310377i	$0.899545\pi$
$728$	−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	−0.550801	−	0.834637i	$-0.685678\pi$
$733$	−13993.0	+	3043.99i	−0.705106	+	0.153386i	−0.154305	+	0.988023i	$0.549314\pi$
$734$	−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	−0.938997	−	0.343926i	$-0.888243\pi$
$739$	−4742.65	+	7379.71i	−0.236077	+	0.367344i	0.702919	+	0.711270i	$0.251879\pi$
$740$	−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	−0.242537	−	0.970142i	$-0.577980\pi$
$743$	8961.28	−	4893.23i	0.442473	−	0.241609i	0.685010	+	0.728534i	$0.259798\pi$
$744$	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	0.606750	−	0.794892i	$-0.292473\pi$
$751$	−7581.15	−	11796.5i	−0.368362	−	0.573183i	−0.975113	+	0.221709i	$0.928836\pi$
$752$	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	0.987714	+	0.156271i	$0.0499472\pi$
$757$	−253.811	+	3548.74i	−0.0121861	+	0.170384i	−0.999900	+	0.0141137i	$0.995507\pi$
$758$	−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	−0.915672	−	0.401927i	$-0.868341\pi$
$761$	−24838.9	−	28665.7i	−1.18319	−	1.36548i	−0.267522	−	0.963552i	$-0.586205\pi$
$762$	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	−0.736809	−	0.676101i	$-0.763668\pi$
$769$	−21135.7	+	6206.01i	−0.991124	+	0.291020i	−0.254315	+	0.967121i	$0.581850\pi$
$770$	−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	0.482167	−	0.876079i	$-0.339850\pi$
$773$	5864.10	+	2187.20i	0.272855	+	0.101770i	−0.209312	+	0.977849i	$0.567122\pi$
$774$	−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	−0.135950	−	0.990716i	$-0.543409\pi$
$787$	9053.95	−	3376.95i	0.410087	−	0.152954i	0.546037	+	0.837761i	$0.316136\pi$
$788$	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	−0.0406450	−	0.999174i	$-0.512941\pi$
$797$	−11085.6	−	2411.53i	−0.492689	−	0.107178i	−0.452044	+	0.891996i	$0.649305\pi$
$798$	−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	0.671636	−	0.740881i	$-0.265592\pi$
$809$	25480.2	+	3663.50i	1.10734	+	0.159211i	0.435700	+	0.900092i	$0.356501\pi$
$810$	6341.35	−	19308.4i	0.275077	−	0.837568i
$811$	3155.69	+	21948.3i	0.136635	+	0.950321i	0.936632	+	0.350316i	$0.113926\pi$
$811$	3155.69	+	21948.3i	0.136635	+	0.950321i	−0.799996	+	0.600005i	$0.795165\pi$
$812$	−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	0.344661	−	0.938727i	$-0.387994\pi$
$821$	2989.77	+	877.875i	0.127093	+	0.0373180i	−0.217567	+	0.976045i	$0.569812\pi$
$822$	410.746	−	548.693i	0.0174287	−	0.0232821i
$823$	−34604.0	+	12906.6i	−1.46564	+	0.546655i	−0.950575	−	0.310496i	$-0.899505\pi$
$823$	−34604.0	+	12906.6i	−1.46564	+	0.546655i	−0.515065	+	0.857151i	$0.672232\pi$
$824$	−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	0.283486	−	0.958976i	$-0.408509\pi$
$827$	−16064.9	−	16064.9i	−0.675490	−	0.675490i	−0.958976	+	0.283486i	$0.908509\pi$
$828$	−5276.13	+	82.5117i	−0.221447	+	0.00346314i
$829$		−	8670.64i		−	0.363261i	−0.983367	−	0.181631i	$-0.941862\pi$
$829$		−	8670.64i		−	0.363261i	0.983367	−	0.181631i	$-0.0581375\pi$
$830$	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	−0.824227	−	0.566260i	$-0.808390\pi$
$839$	−3558.58	+	4106.82i	−0.146431	+	0.168991i	0.677796	+	0.735250i	$0.262935\pi$
$840$	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	−0.999887	−	0.0150469i	$-0.995210\pi$
$853$	−200.200	+	2799.16i	−0.00803601	+	0.112358i	0.991851	+	0.127405i	$0.0406648\pi$
$854$	−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	0.520795	−	0.853682i	$-0.325636\pi$
$857$	−3802.94	−	2846.84i	−0.151582	−	0.113473i	−0.672377	+	0.740209i	$0.734727\pi$
$858$	−778.294	+	424.981i	−0.0309680	+	0.0169098i
$859$	23105.4	+	35952.7i	0.917749	+	1.42805i	0.903710	+	0.428145i	$0.140833\pi$
$859$	23105.4	+	35952.7i	0.917749	+	1.42805i	0.0140392	+	0.999901i	$0.495531\pi$
$860$	−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	0.00145011	−	0.999999i	$-0.499538\pi$
$863$	3681.15	−	263.281i	0.145200	−	0.0103849i	0.143750	+	0.989614i	$0.454084\pi$
$864$	−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	0.0761809	−	0.997094i	$-0.475727\pi$
$877$	14535.9	−	3162.10i	0.559685	−	0.121752i	0.483504	+	0.875342i	$0.339364\pi$
$878$	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	0.653922	+	0.756562i	$0.273122\pi$
$881$	−7981.36	+	27182.0i	−0.305220	+	1.03948i	−0.959143	+	0.282923i	$0.908696\pi$
$882$	−3157.01	+	14512.5i	−0.120524	+	0.554040i
$883$	−2335.40	+	6261.44i	−0.0890061	+	0.238635i	−0.973824	−	0.227302i	$-0.927010\pi$
$883$	−2335.40	+	6261.44i	−0.0890061	+	0.238635i	0.884818	+	0.465936i	$0.154282\pi$
$884$	−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	−0.971679	−	0.236306i	$-0.924063\pi$
$887$	−6539.72	+	11976.6i	−0.247556	+	0.453365i	0.724123	+	0.689671i	$0.242245\pi$
$888$	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	0.999969	+	0.00792444i	$0.00252245\pi$
$907$	42264.3	+	23078.1i	1.54726	+	0.844867i	0.547290	+	0.836943i	$0.315659\pi$
$908$	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	−0.0949736	−	0.995480i	$-0.530277\pi$
$911$	16365.0	−	7473.63i	0.595165	−	0.271803i	0.690139	+	0.723677i	$0.257549\pi$
$912$	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	−0.738267	−	0.674508i	$-0.764356\pi$
$929$	−20159.8	+	9206.65i	−0.711970	+	0.325146i	0.0262972	+	0.999654i	$0.491628\pi$
$930$	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	−0.598592	−	0.801054i	$-0.704273\pi$
$937$	9713.35	−	12975.5i	0.338657	−	0.452392i	0.937249	+	0.348662i	$0.113364\pi$
$938$	−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	−0.789763	−	0.613412i	$-0.789797\pi$
$941$	−8515.14	+	7378.41i	−0.294990	+	0.255610i	0.494773	+	0.869022i	$0.335251\pi$
$942$	−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	0.710895	−	0.703298i	$-0.248290\pi$
$947$	−4785.07	−	6392.10i	−0.164196	−	0.219341i	−0.875092	+	0.483957i	$0.839199\pi$
$948$	−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	−0.481340	−	0.876534i	$-0.659850\pi$
$953$	15188.8	−	27816.2i	0.516279	−	0.945494i	0.997619	−	0.0689607i	$-0.0219683\pi$
$954$	−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	−0.685619	−	0.727960i	$-0.740469\pi$
$967$	1273.20	−	1273.20i	0.0423407	−	0.0423407i	0.727960	+	0.685619i	$0.240469\pi$
$968$	−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	0.468462	−	0.883484i	$-0.344808\pi$
$971$	3254.06	+	1486.08i	0.107547	+	0.0491148i	−0.360915	+	0.932599i	$0.617536\pi$
$972$	−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	−0.430126	−	0.902769i	$-0.641531\pi$
$977$	−22213.3	+	1588.73i	−0.727396	+	0.0520244i	−0.297270	+	0.954793i	$0.596076\pi$
$978$	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	0.812517	−	0.582938i	$-0.198097\pi$
$983$	14858.4	+	11122.8i	0.482104	+	0.360898i	−0.330413	+	0.943837i	$0.607188\pi$
$984$	−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	0.389273	−	0.921122i	$-0.372726\pi$
$991$	−18027.8	−	20805.2i	−0.577873	−	0.666901i	−0.967146	+	0.254222i	$0.918181\pi$
$992$	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	0.745459	+	0.666552i	$0.232231\pi$
$997$	−6596.13	+	30321.9i	−0.209530	+	0.963194i	−0.954989	+	0.296642i	$0.904133\pi$
$998$	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.33.15	yes	720
5.2	odd	4	inner	230.4.l.a.217.33	yes	720
23.7	odd	22	inner	230.4.l.a.53.33	yes	720
115.7	even	44	inner	230.4.l.a.7.15	✓	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.l.a.7.15	✓	720	115.7	even	44	inner
230.4.l.a.33.15	yes	720	1.1	even	1	trivial
230.4.l.a.53.33	yes	720	23.7	odd	22	inner
230.4.l.a.217.33	yes	720	5.2	odd	4	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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