LMFDB - Embedded newform 230.4.l.a.53.27

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			53.27
Character	$\chi$	$=$	230.53
Dual form			230.4.l.a.217.27

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.142678 + 1.99490i) q^{2} +(-0.661230 - 0.143842i) q^{3} +(-3.95929 + 0.569259i) q^{4} +(9.60780 - 5.71754i) q^{5} +(0.192607 - 1.33961i) q^{6} +(13.1154 + 7.16158i) q^{7} +(-1.70052 - 7.81717i) q^{8} +(-24.1435 - 11.0260i) q^{9} +(12.7768 + 18.3509i) q^{10} +(24.5384 - 21.2626i) q^{11} +(2.69988 + 0.193099i) q^{12} +(-20.0292 - 36.6808i) q^{13} +(-12.4154 + 27.1859i) q^{14} +(-7.17538 + 2.39861i) q^{15} +(15.3519 - 4.50772i) q^{16} +(12.6720 - 9.48612i) q^{17} +(18.5510 - 49.7372i) q^{18} +(-8.10752 - 56.3890i) q^{19} +(-34.7852 + 28.1067i) q^{20} +(-7.64219 - 6.62200i) q^{21} +(45.9180 + 45.9180i) q^{22} +(109.810 - 10.4325i) q^{23} +5.41355i q^{24} +(59.6195 - 109.866i) q^{25} +(70.3169 - 45.1899i) q^{26} +(29.0049 + 21.7128i) q^{27} +(-56.0046 - 20.8886i) q^{28} +(-34.0703 - 4.89857i) q^{29} +(-5.80876 - 13.9720i) q^{30} +(79.8548 + 51.3195i) q^{31} +(11.1829 + 29.9824i) q^{32} +(-19.2840 + 10.5298i) q^{33} +(20.7319 + 23.9259i) q^{34} +(166.957 - 6.18115i) q^{35} +(101.868 + 29.9111i) q^{36} +(399.487 - 149.001i) q^{37} +(111.334 - 24.2192i) q^{38} +(7.96769 + 27.1355i) q^{39} +(-61.0333 - 65.3830i) q^{40} +(101.452 + 222.149i) q^{41} +(12.1199 - 16.1903i) q^{42} +(-2.13596 + 9.81886i) q^{43} +(-85.0506 + 98.1536i) q^{44} +(-295.008 + 32.1063i) q^{45} +(36.4793 + 217.571i) q^{46} +(180.757 - 180.757i) q^{47} +(-10.7995 + 0.772397i) q^{48} +(-64.7130 - 100.695i) q^{49} +(227.678 + 103.260i) q^{50} +(-9.74359 + 4.44975i) q^{51} +(100.182 + 133.828i) q^{52} +(-334.679 + 612.918i) q^{53} +(-39.1766 + 60.9600i) q^{54} +(114.190 - 344.586i) q^{55} +(33.6802 - 114.704i) q^{56} +(-2.75016 + 38.4523i) q^{57} +(4.91108 - 68.6659i) q^{58} +(-21.1230 + 71.9384i) q^{59} +(27.0440 - 13.5814i) q^{60} +(69.9852 - 108.899i) q^{61} +(-90.9840 + 166.625i) q^{62} +(-237.690 - 317.516i) q^{63} +(-58.2164 + 26.5866i) q^{64} +(-402.161 - 237.904i) q^{65} +(-23.7574 - 36.9673i) q^{66} +(-916.306 + 65.5355i) q^{67} +(-44.7719 + 44.7719i) q^{68} +(-74.1100 - 8.89694i) q^{69} +(36.1520 + 332.182i) q^{70} +(372.219 - 429.563i) q^{71} +(-45.1354 + 207.484i) q^{72} +(327.177 - 437.058i) q^{73} +(354.240 + 775.678i) q^{74} +(-55.2255 + 64.0708i) q^{75} +(64.1999 + 218.645i) q^{76} +(474.106 - 103.135i) q^{77} +(-52.9958 + 19.7664i) q^{78} +(307.002 + 90.1439i) q^{79} +(121.725 - 131.084i) q^{80} +(453.241 + 523.068i) q^{81} +(-428.691 + 234.083i) q^{82} +(-475.186 - 1274.02i) q^{83} +(34.0272 + 21.8680i) q^{84} +(67.5125 - 163.593i) q^{85} +(-19.8924 - 2.86010i) q^{86} +(21.8237 + 8.13981i) q^{87} +(-207.942 - 155.663i) q^{88} +(-211.363 + 135.834i) q^{89} +(-106.140 - 583.931i) q^{90} -624.526i q^{91} +(-428.829 + 103.815i) q^{92} +(-45.4204 - 45.4204i) q^{93} +(386.383 + 334.803i) q^{94} +(-400.302 - 495.419i) q^{95} +(-3.08172 - 21.4338i) q^{96} +(-225.689 + 605.095i) q^{97} +(191.645 - 143.463i) q^{98} +(-826.885 + 242.795i) 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 $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{19}{22}\right)$

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 $

$2$	0.142678	+	1.99490i	0.0504444	+	0.705305i
$2$	0.142678	+	1.99490i	0.0504444	+	0.705305i
$3$	−0.661230	−	0.143842i	−0.127254	−	0.0276824i	0.148487	−	0.988914i	$-0.452560\pi$
$3$	−0.661230	−	0.143842i	−0.127254	−	0.0276824i	−0.275741	+	0.961232i	$0.588923\pi$
$4$	−3.95929	+	0.569259i	−0.494911	+	0.0711574i
$5$	9.60780	−	5.71754i	0.859347	−	0.511392i
$5$	9.60780	−	5.71754i	0.859347	−	0.511392i
$6$	0.192607	−	1.33961i	0.0131053	−	0.0911491i
$7$	13.1154	+	7.16158i	0.708168	+	0.386689i	0.792601	−	0.609740i	$-0.208726\pi$
$7$	13.1154	+	7.16158i	0.708168	+	0.386689i	−0.0844336	+	0.996429i	$0.526908\pi$
$8$	−1.70052	−	7.81717i	−0.0751532	−	0.345474i
$9$	−24.1435	−	11.0260i	−0.894205	−	0.408370i
$10$	12.7768	+	18.3509i	0.404037	+	0.580305i
$11$	24.5384	−	21.2626i	0.672601	−	0.582812i	−0.250151	−	0.968207i	$-0.580480\pi$
$11$	24.5384	−	21.2626i	0.672601	−	0.582812i	0.922752	+	0.385395i	$0.125935\pi$
$12$	2.69988	+	0.193099i	0.0649490	+	0.00464525i
$13$	−20.0292	−	36.6808i	−0.427316	−	0.782571i	0.571973	−	0.820272i	$-0.306178\pi$
$13$	−20.0292	−	36.6808i	−0.427316	−	0.782571i	−0.999289	+	0.0377015i	$0.987996\pi$
$14$	−12.4154	+	27.1859i	−0.237010	+	0.518981i
$15$	−7.17538	+	2.39861i	−0.123512	+	0.0412878i
$16$	15.3519	−	4.50772i	0.239873	−	0.0704331i
$17$	12.6720	−	9.48612i	0.180789	−	0.135337i	−0.505051	−	0.863090i	$-0.668526\pi$
$17$	12.6720	−	9.48612i	0.180789	−	0.135337i	0.685839	+	0.727753i	$0.259435\pi$
$18$	18.5510	−	49.7372i	0.242918	−	0.651287i
$19$	−8.10752	−	56.3890i	−0.0978943	−	0.680870i	−0.978383	−	0.206802i	$-0.933694\pi$
$19$	−8.10752	−	56.3890i	−0.0978943	−	0.680870i	0.880488	−	0.474068i	$-0.157215\pi$
$20$	−34.7852	+	28.1067i	−0.388911	+	0.314243i
$21$	−7.64219	−	6.62200i	−0.0794125	−	0.0688113i
$22$	45.9180	+	45.9180i	0.444989	+	0.444989i
$23$	109.810	−	10.4325i	0.995517	−	0.0945793i
$23$	109.810	−	10.4325i	0.995517	−	0.0945793i
$24$			5.41355i			0.0460432i
$25$	59.6195	−	109.866i	0.476956	−	0.878927i
$26$	70.3169	−	45.1899i	0.530396	−	0.340865i
$27$	29.0049	+	21.7128i	0.206741	+	0.154764i
$28$	−56.0046	−	20.8886i	−0.377996	−	0.140985i
$29$	−34.0703	−	4.89857i	−0.218162	−	0.0313670i	0.0323670	−	0.999476i	$-0.489695\pi$
$29$	−34.0703	−	4.89857i	−0.218162	−	0.0313670i	−0.250529	+	0.968109i	$0.580605\pi$
$30$	−5.80876	−	13.9720i	−0.0353510	−	0.0850307i
$31$	79.8548	+	51.3195i	0.462656	+	0.297331i	0.751127	−	0.660158i	$-0.229511\pi$
$31$	79.8548	+	51.3195i	0.462656	+	0.297331i	−0.288471	+	0.957489i	$0.593147\pi$
$32$	11.1829	+	29.9824i	0.0617771	+	0.165631i
$33$	−19.2840	+	10.5298i	−0.101725	+	0.0555458i
$34$	20.7319	+	23.9259i	0.104573	+	0.120684i
$35$	166.957	−	6.18115i	0.806312	−	0.0298516i
$36$	101.868	+	29.9111i	0.471610	+	0.138477i
$37$	399.487	−	149.001i	1.77501	−	0.662043i	0.775476	−	0.631378i	$-0.217510\pi$
$37$	399.487	−	149.001i	1.77501	−	0.662043i	0.999530	−	0.0306652i	$-0.00976258\pi$
$38$	111.334	−	24.2192i	0.475283	−	0.103391i
$39$	7.96769	+	27.1355i	0.0327142	+	0.111414i
$40$	−61.0333	−	65.3830i	−0.241255	−	0.258449i
$41$	101.452	+	222.149i	0.386443	+	0.846192i	0.998467	+	0.0553530i	$0.0176284\pi$
$41$	101.452	+	222.149i	0.386443	+	0.846192i	−0.612024	+	0.790839i	$0.709644\pi$
$42$	12.1199	−	16.1903i	0.0445271	−	0.0594812i
$43$	−2.13596	+	9.81886i	−0.00757514	+	0.0348224i	−0.980779	−	0.195120i	$-0.937490\pi$
$43$	−2.13596	+	9.81886i	−0.00757514	+	0.0348224i	0.973204	+	0.229943i	$0.0738539\pi$
$44$	−85.0506	+	98.1536i	−0.291406	+	0.336300i
$45$	−295.008	+	32.1063i	−0.977270	+	0.106358i
$46$	36.4793	+	217.571i	0.116926	+	0.697373i
$47$	180.757	−	180.757i	0.560982	−	0.560982i	−0.368604	−	0.929586i	$-0.620164\pi$
$47$	180.757	−	180.757i	0.560982	−	0.560982i	0.929586	+	0.368604i	$0.120164\pi$
$48$	−10.7995	+	0.772397i	−0.0324745	+	0.00232262i
$49$	−64.7130	−	100.695i	−0.188668	−	0.293573i
$50$	227.678	+	103.260i	0.643972	+	0.292062i
$51$	−9.74359	+	4.44975i	−0.0267524	+	0.0122174i
$52$	100.182	+	133.828i	0.267169	+	0.356896i
$53$	−334.679	+	612.918i	−0.867390	+	1.58851i	−0.0602212	+	0.998185i	$0.519181\pi$
$53$	−334.679	+	612.918i	−0.867390	+	1.58851i	−0.807169	+	0.590321i	$0.799001\pi$
$54$	−39.1766	+	60.9600i	−0.0987270	+	0.153622i
$55$	114.190	−	344.586i	0.279952	−	0.844800i
$56$	33.6802	−	114.704i	0.0803697	−	0.273714i
$57$	−2.75016	+	38.4523i	−0.00639066	+	0.0893532i
$58$	4.91108	−	68.6659i	0.0111182	−	0.155453i
$59$	−21.1230	+	71.9384i	−0.0466099	+	0.158739i	−0.979510	−	0.201398i	$-0.935452\pi$
$59$	−21.1230	+	71.9384i	−0.0466099	+	0.158739i	0.932900	+	0.360136i	$0.117270\pi$
$60$	27.0440	−	13.5814i	0.0581893	−	0.0292226i
$61$	69.9852	−	108.899i	0.146896	−	0.228575i	−0.760006	−	0.649916i	$-0.774804\pi$
$61$	69.9852	−	108.899i	0.146896	−	0.228575i	0.906902	+	0.421341i	$0.138440\pi$
$62$	−90.9840	+	166.625i	−0.186371	+	0.341312i
$63$	−237.690	−	317.516i	−0.475335	−	0.634973i
$64$	−58.2164	+	26.5866i	−0.113704	+	0.0519269i
$65$	−402.161	−	237.904i	−0.767414	−	0.453974i
$66$	−23.7574	−	36.9673i	−0.0443082	−	0.0689448i
$67$	−916.306	+	65.5355i	−1.67081	+	0.119499i	−0.874385	−	0.485232i	$-0.838735\pi$
$67$	−916.306	+	65.5355i	−1.67081	+	0.119499i	−0.796430	+	0.604731i	$0.793280\pi$
$68$	−44.7719	+	44.7719i	−0.0798440	+	0.0798440i
$69$	−74.1100	−	8.89694i	−0.129301	−	0.0155227i
$70$	36.1520	+	332.182i	0.0617284	+	0.567190i
$71$	372.219	−	429.563i	0.622173	−	0.718025i	−0.353945	−	0.935266i	$-0.615160\pi$
$71$	372.219	−	429.563i	0.622173	−	0.718025i	0.976118	+	0.217241i	$0.0697056\pi$
$72$	−45.1354	+	207.484i	−0.0738786	+	0.339614i
$73$	327.177	−	437.058i	0.524565	−	0.700736i	−0.457515	−	0.889202i	$-0.651260\pi$
$73$	327.177	−	437.058i	0.524565	−	0.700736i	0.982080	+	0.188466i	$0.0603514\pi$
$74$	354.240	+	775.678i	0.556481	+	1.21852i
$75$	−55.2255	+	64.0708i	−0.0850252	+	0.0986435i
$76$	64.1999	+	218.645i	0.0968979	+	0.330004i
$77$	474.106	−	103.135i	0.701681	−	0.152641i
$78$	−52.9958	+	19.7664i	−0.0769307	+	0.0286937i
$79$	307.002	+	90.1439i	0.437221	+	0.128380i	0.492933	−	0.870067i	$-0.335925\pi$
$79$	307.002	+	90.1439i	0.437221	+	0.128380i	−0.0557123	+	0.998447i	$0.517743\pi$
$80$	121.725	−	131.084i	0.170115	−	0.183196i
$81$	453.241	+	523.068i	0.621730	+	0.717515i
$82$	−428.691	+	234.083i	−0.577330	+	0.315246i
$83$	−475.186	−	1274.02i	−0.628414	−	1.68484i	−0.724329	−	0.689454i	$-0.757850\pi$
$83$	−475.186	−	1274.02i	−0.628414	−	1.68484i	0.0959149	−	0.995390i	$-0.469422\pi$
$84$	34.0272	+	21.8680i	0.0441985	+	0.0284047i
$85$	67.5125	−	163.593i	0.0861500	−	0.208755i
$86$	−19.8924	−	2.86010i	−0.0249425	−	0.00358619i
$87$	21.8237	+	8.13981i	0.0268936	+	0.0100308i
$88$	−207.942	−	155.663i	−0.251894	−	0.188566i
$89$	−211.363	+	135.834i	−0.251735	+	0.161780i	−0.660423	−	0.750894i	$-0.729623\pi$
$89$	−211.363	+	135.834i	−0.251735	+	0.161780i	0.408688	+	0.912674i	$0.365986\pi$
$90$	−106.140	−	583.931i	−0.124313	−	0.683908i
$91$		−	624.526i		−	0.719430i
$92$	−428.829	+	103.815i	−0.485962	+	0.117647i
$93$	−45.4204	−	45.4204i	−0.0506439	−	0.0506439i
$94$	386.383	+	334.803i	0.423962	+	0.367365i
$95$	−400.302	−	495.419i	−0.432317	−	0.535041i
$96$	−3.08172	−	21.4338i	−0.00327632	−	0.0227873i
$97$	−225.689	+	605.095i	−0.236239	+	0.633382i	−0.999926	−	0.0122057i	$-0.996115\pi$
$97$	−225.689	+	605.095i	−0.236239	+	0.633382i	0.763686	+	0.645588i	$0.223387\pi$
$98$	191.645	−	143.463i	0.197541	−	0.147877i
$99$	−826.885	+	242.795i	−0.839445	+	0.246483i
$100$	−173.508	+	468.930i	−0.173508	+	0.468930i
$101$	−100.502	+	220.070i	−0.0990136	+	0.216810i	−0.952656	−	0.304050i	$-0.901661\pi$
$101$	−100.502	+	220.070i	−0.0990136	+	0.216810i	0.853643	+	0.520859i	$0.174388\pi$
$102$	−10.2670	−	18.8026i	−0.00996653	−	0.0182523i
$103$	−1256.45	−	89.8632i	−1.20196	−	0.0859659i	−0.544044	−	0.839057i	$-0.683107\pi$
$103$	−1256.45	−	89.8632i	−1.20196	−	0.0859659i	−0.657916	+	0.753091i	$0.728562\pi$
$104$	−252.680	+	218.948i	−0.238243	+	0.206439i
$105$	−111.286	−	19.9282i	−0.103433	−	0.0185219i
$106$	−1270.46	−	580.202i	−1.16414	−	0.531643i
$107$	−102.428	−	470.856i	−0.0925433	−	0.425415i	−0.999986	−	0.00523946i	$-0.998332\pi$
$107$	−102.428	−	470.856i	−0.0925433	−	0.425415i	0.907443	−	0.420175i	$-0.138031\pi$
$108$	−127.199	−	69.4559i	−0.113331	−	0.0618833i
$109$	−308.099	+	2142.88i	−0.270739	+	1.88303i	0.170073	+	0.985431i	$0.445600\pi$
$109$	−308.099	+	2142.88i	−0.270739	+	1.88303i	−0.440812	+	0.897599i	$0.645309\pi$
$110$	703.709	+	178.633i	0.609964	+	0.154836i
$111$	−285.585	+	41.0609i	−0.244203	+	0.0351111i
$112$	233.629	+	50.8229i	0.197106	+	0.0428778i
$113$	−72.2648	−	1010.39i	−0.0601602	−	0.841150i	−0.934529	−	0.355887i	$-0.884179\pi$
$113$	−72.2648	−	1010.39i	−0.0601602	−	0.841150i	0.874369	−	0.485262i	$-0.161276\pi$
$114$	−77.1010			−0.0633436
$115$	995.381	−	728.074i	0.807128	−	0.590376i
$116$	137.683			0.110203
$117$	79.1346	+	1106.45i	0.0625299	+	0.874282i
$118$	−146.524	−	31.8744i	−0.114310	−	0.0248667i
$119$	234.134	−	33.6634i	0.180362	−	0.0259321i
$120$	30.9522	+	52.0123i	0.0235461	+	0.0395671i
$121$	−39.3880	+	273.950i	−0.0295928	+	0.205823i
$122$	227.229	+	124.076i	0.168626	+	0.0920765i
$123$	−35.1289	−	161.485i	−0.0257517	−	0.118379i
$124$	−345.382	−	157.731i	−0.250131	−	0.114231i
$125$	−55.3513	−	1396.45i	−0.0396062	−	0.999215i
$126$	599.502	−	519.471i	0.423872	−	0.367287i
$127$	−644.164	−	46.0715i	−0.450081	−	0.0321905i	−0.155541	−	0.987829i	$-0.549712\pi$
$127$	−644.164	−	46.0715i	−0.450081	−	0.0321905i	−0.294541	+	0.955639i	$0.595167\pi$
$128$	−61.3439	−	112.343i	−0.0423600	−	0.0775766i
$129$	2.82472	−	6.18528i	0.00192793	−	0.00422158i
$130$	417.215	−	836.216i	0.281478	−	0.564161i
$131$	−1475.80	+	433.333i	−0.984282	+	0.289011i	−0.733991	−	0.679159i	$-0.762345\pi$
$131$	−1475.80	+	433.333i	−0.984282	+	0.289011i	−0.250291	+	0.968171i	$0.580526\pi$
$132$	70.3565	−	52.6683i	0.0463921	−	0.0347287i
$133$	297.500	−	797.630i	0.193959	−	0.520025i
$134$	−261.474	−	1818.59i	−0.168567	−	1.17241i
$135$	402.817	+	42.7754i	0.256807	+	0.0272705i
$136$	−95.7036	−	82.9277i	−0.0603421	−	0.0522867i
$137$	−1045.74	−	1045.74i	−0.652144	−	0.652144i	0.301365	−	0.953509i	$-0.402558\pi$
$137$	−1045.74	−	1045.74i	−0.652144	−	0.652144i	−0.953509	+	0.301365i	$0.902558\pi$
$138$	7.17464	−	149.112i	0.00442570	−	0.0919800i
$139$			2871.98i			1.75250i	0.481853	+	0.876252i	$0.339964\pi$
$139$			2871.98i			1.75250i	−0.481853	+	0.876252i	$0.660036\pi$
$140$	−657.512	+	119.515i	−0.396928	+	0.0721489i
$141$	−145.522	+	93.5216i	−0.0869163	+	0.0558577i
$142$	910.046	+	681.252i	0.537812	+	0.402601i
$143$	−1271.42	−	474.214i	−0.743504	−	0.277313i
$144$	−420.351	−	60.4373i	−0.243259	−	0.0349753i
$145$	−355.348	+	147.734i	−0.203518	+	0.0846113i
$146$	918.569	+	590.329i	0.520694	+	0.334630i
$147$	28.3060	+	75.8912i	0.0158819	+	0.0425810i
$148$	−1496.86	+	817.348i	−0.831360	+	0.453957i
$149$	559.309	+	645.477i	0.307519	+	0.354896i	0.888382	−	0.459106i	$-0.151830\pi$
$149$	559.309	+	645.477i	0.307519	+	0.354896i	−0.580863	+	0.814002i	$0.697285\pi$
$150$	−135.695	−	101.028i	−0.0738628	−	0.0549927i
$151$	1013.24	+	297.515i	0.546070	+	0.160341i	0.543120	−	0.839655i	$-0.317243\pi$
$151$	1013.24	+	297.515i	0.546070	+	0.160341i	0.00294993	+	0.999996i	$0.499061\pi$
$152$	−427.016	+	159.269i	−0.227865	+	0.0849894i
$153$	−410.540	+	89.3075i	−0.216929	+	0.0471901i
$154$	273.390	+	931.081i	0.143055	+	0.487199i
$155$	1060.65	+	36.4948i	0.549635	+	0.0189118i
$156$	−46.9935	−	102.901i	−0.0241185	−	0.0528122i
$157$	−377.548	+	504.345i	−0.191921	+	0.256377i	−0.886172	−	0.463356i	$-0.846645\pi$
$157$	−377.548	+	504.345i	−0.191921	+	0.256377i	0.694251	+	0.719733i	$0.255736\pi$
$158$	−136.026	+	625.301i	−0.0684914	+	0.314850i
$159$	309.463	−	357.139i	0.154352	−	0.178132i
$160$	278.868	+	224.126i	0.137790	+	0.110742i
$161$	1514.92	+	649.584i	0.741566	+	0.317977i
$162$	−978.803	+	978.803i	−0.474704	+	0.474704i
$163$	−395.670	+	28.2989i	−0.190131	+	0.0135984i	−0.166080	−	0.986112i	$-0.553111\pi$
$163$	−395.670	+	28.2989i	−0.190131	+	0.0135984i	−0.0240508	+	0.999711i	$0.507656\pi$
$164$	−528.139	−	821.800i	−0.251468	−	0.391291i
$165$	−125.072	+	211.426i	−0.0590110	+	0.0997543i
$166$	2473.75	−	1129.72i	1.15663	−	0.528215i
$167$	1103.60	+	1474.24i	0.511373	+	0.683115i	0.979707	−	0.200437i	$-0.0642363\pi$
$167$	1103.60	+	1474.24i	0.511373	+	0.683115i	−0.468333	+	0.883552i	$0.655145\pi$
$168$	−38.7696	+	71.0012i	−0.0178044	+	0.0326063i
$169$	243.477	−	378.858i	0.110823	−	0.172443i
$170$	335.985	+	111.340i	0.151582	+	0.0502315i
$171$	−426.000	+	1450.82i	−0.190509	+	0.648814i
$172$	2.86741	−	40.0916i	0.00127115	−	0.0177730i
$173$	−165.049	+	2307.69i	−0.0725343	+	1.01416i	0.822674	+	0.568514i	$0.192481\pi$
$173$	−165.049	+	2307.69i	−0.0725343	+	1.01416i	−0.895208	+	0.445649i	$0.852973\pi$
$174$	−13.1244	+	44.6975i	−0.00571814	+	0.0194742i
$175$	1568.75	−	1013.97i	0.677636	−	0.437994i
$176$	280.865	−	437.034i	0.120290	−	0.187174i
$177$	24.3149	−	44.5295i	0.0103255	−	0.0189098i
$178$	−301.134	−	402.267i	−0.126803	−	0.169389i
$179$	678.099	−	309.677i	0.283148	−	0.129309i	−0.268779	−	0.963202i	$-0.586620\pi$
$179$	678.099	−	309.677i	0.283148	−	0.129309i	0.551927	+	0.833893i	$0.313893\pi$
$180$	1149.74	−	295.054i	0.476093	−	0.122178i
$181$	2272.18	+	3535.59i	0.933095	+	1.45192i	0.891620	+	0.452784i	$0.149569\pi$
$181$	2272.18	+	3535.59i	0.933095	+	1.45192i	0.0414743	+	0.999140i	$0.486795\pi$
$182$	1245.87	−	89.1063i	0.507417	−	0.0362912i
$183$	−61.9405	+	61.9405i	−0.0250206	+	0.0250206i
$184$	−268.286	−	840.661i	−0.107491	−	0.336817i
$185$	2986.27	−	3715.65i	1.18678	−	1.47665i
$186$	84.1289	−	97.0900i	0.0331647	−	0.0382741i
$187$	109.250	−	502.214i	0.0427227	−	0.196393i
$188$	−612.772	+	818.567i	−0.237718	+	0.317554i
$189$	224.914	+	492.494i	0.0865615	+	0.189543i
$190$	931.199	−	869.249i	0.355559	−	0.331905i
$191$	43.2655	+	147.349i	0.0163905	+	0.0558208i	0.967282	−	0.253703i	$-0.0816486\pi$
$191$	43.2655	+	147.349i	0.0163905	+	0.0558208i	−0.950892	+	0.309524i	$0.899830\pi$
$192$	42.3187	−	9.20587i	0.0159067	−	0.00346029i
$193$	3995.63	−	1490.29i	1.49022	−	0.555822i	0.533234	−	0.845968i	$-0.320977\pi$
$193$	3995.63	−	1490.29i	1.49022	−	0.555822i	0.956982	+	0.290146i	$0.0937039\pi$
$194$	−1239.31	−	363.893i	−0.458644	−	0.134670i
$195$	231.700	+	215.156i	0.0850892	+	0.0790137i
$196$	313.539	+	361.843i	0.114264	+	0.131867i
$197$	−713.688	+	389.703i	−0.258113	+	0.140940i	−0.603096	−	0.797669i	$-0.706066\pi$
$197$	−713.688	+	389.703i	−0.258113	+	0.140940i	0.344983	+	0.938609i	$0.387885\pi$
$198$	−602.332	−	1614.91i	−0.216191	−	0.579631i
$199$	3618.29	+	2325.33i	1.28891	+	0.828334i	0.991959	−	0.126558i	$-0.0403930\pi$
$199$	3618.29	+	2325.33i	1.28891	+	0.828334i	0.296954	+	0.954892i	$0.404029\pi$
$200$	−960.225	−	279.226i	−0.339491	−	0.0987214i
$201$	615.315	+	88.4690i	0.215925	+	0.0310454i
$202$	−453.358	−	169.094i	−0.157912	−	0.0588980i
$203$	−411.766	−	308.244i	−0.142366	−	0.106574i
$204$	36.0446	−	23.1644i	0.0123707	−	0.00795017i
$205$	2244.88	+	1554.31i	0.764825	+	0.529549i
$206$		−	2519.32i		−	0.852085i
$207$	−2766.22	−	958.882i	−0.928820	−	0.321966i
$208$	−472.833	−	472.833i	−0.157621	−	0.157621i
$209$	−1397.92	−	1211.31i	−0.462663	−	0.400899i
$210$	23.8768	−	224.848i	0.00784598	−	0.0738858i
$211$	−457.118	−	3179.33i	−0.149144	−	1.03732i	−0.917626	−	0.397445i	$-0.869897\pi$
$211$	−457.118	−	3179.33i	−0.149144	−	1.03732i	0.768482	−	0.639871i	$-0.221012\pi$
$212$	976.179	−	2617.24i	0.316247	−	0.847890i
$213$	−307.911	+	230.500i	−0.0990504	+	0.0741482i
$214$	924.699	−	271.516i	0.295379	−	0.0867311i
$215$	35.6178	+	106.550i	0.0112982	+	0.0337984i
$216$	120.409	−	263.660i	0.0379297	−	0.0830544i
$217$	679.802	+	1244.96i	0.212663	+	0.389464i
$218$	−4318.79	−	308.886i	−1.34177	−	0.0959652i
$219$	−279.207	+	241.934i	−0.0861508	+	0.0746501i
$220$	−255.951	+	1429.32i	−0.0784374	+	0.438021i
$221$	−601.768	−	274.818i	−0.183164	−	0.0836484i
$222$	−122.659	−	563.856i	−0.0370827	−	0.170466i
$223$	1206.88	+	659.008i	0.362416	+	0.197894i	0.650131	−	0.759822i	$-0.274714\pi$
$223$	1206.88	+	659.008i	0.362416	+	0.197894i	−0.287715	+	0.957716i	$0.592896\pi$
$224$	−68.0530	+	473.319i	−0.0202990	+	0.141183i
$225$	−2650.80	+	1995.19i	−0.785423	+	0.591167i
$226$	2005.33	−	288.323i	0.590232	−	0.0848626i
$227$	−15.7523	−	3.42671i	−0.00460581	−	0.00100193i	0.210262	−	0.977645i	$-0.432568\pi$
$227$	−15.7523	−	3.42671i	−0.00460581	−	0.00100193i	−0.214868	+	0.976643i	$0.568932\pi$
$228$	−11.0006	−	153.809i	−0.00319533	−	0.0446766i
$229$	3602.64			1.03960			0.519802	−	0.854287i	$-0.326006\pi$
$229$	3602.64			1.03960			0.519802	+	0.854287i	$0.326006\pi$
$230$	1594.46	+	1881.81i	0.457111	+	0.539490i
$231$	−328.328			−0.0935169
$232$	19.6443	+	274.664i	0.00555911	+	0.0777265i
$233$	−5122.94	−	1114.43i	−1.44041	−	0.313342i	−0.576544	−	0.817066i	$-0.695599\pi$
$233$	−5122.94	−	1114.43i	−1.44041	−	0.313342i	−0.863864	+	0.503724i	$0.831963\pi$
$234$	−2195.96	+	315.732i	−0.613481	+	0.0882053i
$235$	703.192	−	2770.16i	0.195196	−	0.768960i
$236$	42.6805	−	296.849i	0.0117723	−	0.0818781i
$237$	−190.032	−	103.766i	−0.0520841	−	0.0284401i
$238$	100.561	+	462.272i	0.0273883	+	0.125902i
$239$	236.564	+	108.035i	0.0640253	+	0.0292394i	0.447170	−	0.894449i	$-0.352432\pi$
$239$	236.564	+	108.035i	0.0640253	+	0.0292394i	−0.383145	+	0.923688i	$0.625159\pi$
$240$	−99.3434	+	69.1677i	−0.0267191	+	0.0186032i
$241$	−1240.47	+	1074.88i	−0.331560	+	0.287298i	−0.804691	−	0.593694i	$-0.797669\pi$
$241$	−1240.47	+	1074.88i	−0.331560	+	0.287298i	0.473131	+	0.880992i	$0.343124\pi$
$242$	−552.124	−	39.4887i	−0.146661	−	0.0104894i
$243$	−693.285	−	1269.66i	−0.183022	−	0.335179i
$244$	−215.100	+	471.002i	−0.0564358	+	0.123577i
$245$	−1197.48	−	597.462i	−0.312262	−	0.155798i
$246$	317.134	−	93.1191i	0.0821941	−	0.0241344i
$247$	−1906.01	+	1426.82i	−0.490997	+	0.367556i
$248$	265.379	−	711.509i	0.0679499	−	0.182181i
$249$	130.949	+	910.772i	0.0333276	+	0.231799i
$250$	2777.88	−	309.663i	0.702754	−	0.0783393i
$251$	−3925.57	−	3401.52i	−0.987170	−	0.855387i	0.00231906	−	0.999997i	$-0.499262\pi$
$251$	−3925.57	−	3401.52i	−0.987170	−	0.855387i	−0.989489	+	0.144610i	$0.953807\pi$
$252$	1121.83	+	1121.83i	0.280431	+	0.280431i
$253$	2472.73	−	2590.84i	0.614464	−	0.643813i
$254$		−	1291.62i		−	0.319069i
$255$	−68.1728	+	98.4616i	−0.0167417	+	0.0241800i
$256$	215.361	−	138.404i	0.0525783	−	0.0337901i
$257$	2190.31	+	1639.64i	0.531625	+	0.397969i	0.831090	−	0.556138i	$-0.187717\pi$
$257$	2190.31	+	1639.64i	0.531625	+	0.397969i	−0.299465	+	0.954107i	$0.596808\pi$
$258$	12.7421	+	4.75254i	0.00307475	+	0.00114682i
$259$	6306.53	+	906.742i	1.51301	+	0.217537i
$260$	1727.70	+	712.995i	0.412105	+	0.170069i
$261$	768.566	+	493.927i	0.182272	+	0.117139i
$262$	−1075.02	−	2882.25i	−0.253493	−	0.679640i
$263$	2755.68	−	1504.72i	0.646094	−	0.352794i	−0.122558	−	0.992461i	$-0.539110\pi$
$263$	2755.68	−	1504.72i	0.646094	−	0.352794i	0.768652	+	0.639667i	$0.220928\pi$
$264$	115.106	+	132.840i	0.0268345	+	0.0309687i
$265$	288.861	+	7802.33i	0.0669607	+	1.80865i
$266$	1633.64	+	479.680i	0.376560	+	0.110568i
$267$	159.298	−	59.4150i	0.0365126	−	0.0136185i
$268$	3590.61	−	781.090i	0.818401	−	0.178032i
$269$	−69.2585	−	235.873i	−0.0156980	−	0.0534625i	0.951272	−	0.308354i	$-0.0997783\pi$
$269$	−69.2585	−	235.873i	−0.0156980	−	0.0534625i	−0.966970	+	0.254892i	$0.917960\pi$
$270$	−27.8596	+	809.685i	−0.00627955	+	0.182503i
$271$	−2075.58	−	4544.88i	−0.465248	−	1.01875i	−0.986260	−	0.165202i	$-0.947172\pi$
$271$	−2075.58	−	4544.88i	−0.465248	−	1.01875i	0.521011	−	0.853550i	$-0.325555\pi$
$272$	151.778	−	202.752i	0.0338342	−	0.0451971i
$273$	−89.8329	+	412.955i	−0.0199155	+	0.0915501i
$274$	1936.95	−	2235.36i	0.427063	−	0.492857i
$275$	−873.074	−	3963.60i	−0.191448	−	0.869142i
$276$	298.487	−	6.96231i	0.0650972	−	0.00151841i
$277$	−1953.96	+	1953.96i	−0.423834	+	0.423834i	−0.886521	−	0.462688i	$-0.846885\pi$
$277$	−1953.96	+	1953.96i	−0.423834	+	0.423834i	0.462688	+	0.886521i	$0.346885\pi$
$278$	−5729.32	+	409.769i	−1.23605	+	0.0884041i
$279$	−1362.13	−	2119.51i	−0.292288	−	0.454809i
$280$	−332.233	−	1294.62i	−0.0709098	−	0.276316i
$281$	−2719.48	+	1241.94i	−0.577333	+	0.263659i	−0.682609	−	0.730784i	$-0.739155\pi$
$281$	−2719.48	+	1241.94i	−0.577333	+	0.263659i	0.105276	+	0.994443i	$0.466427\pi$
$282$	−207.330	−	276.960i	−0.0437812	−	0.0584848i
$283$	838.114	−	1534.89i	0.176045	−	0.322402i	−0.774726	−	0.632297i	$-0.782112\pi$
$283$	838.114	−	1534.89i	0.176045	−	0.322402i	0.950771	+	0.309895i	$0.100294\pi$
$284$	−1229.19	+	1912.65i	−0.256827	+	0.399631i
$285$	193.430	+	385.166i	0.0402027	+	0.0800535i
$286$	764.607	−	2604.01i	0.158085	−	0.538386i
$287$	−260.348	+	3640.14i	−0.0535466	+	0.748679i
$288$	60.5917	−	847.183i	0.0123972	−	0.173336i
$289$	−1313.56	+	4473.57i	−0.267364	+	0.910558i
$290$	−345.416	−	687.807i	−0.0699431	−	0.139274i
$291$	236.270	−	367.643i	0.0475958	−	0.0740605i
$292$	−1046.59	+	1916.69i	−0.209750	+	0.384129i
$293$	4171.02	+	5571.83i	0.831651	+	1.11096i	0.992289	+	0.123942i	$0.0395537\pi$
$293$	4171.02	+	5571.83i	0.831651	+	1.11096i	−0.160639	+	0.987013i	$0.551355\pi$
$294$	−147.357	+	67.2957i	−0.0292314	+	0.0133495i
$295$	208.365	+	811.942i	0.0411237	+	0.160248i
$296$	−1844.10	−	2869.48i	−0.362116	−	0.563463i
$297$	1173.41	−	83.9236i	0.229252	−	0.0163964i
$298$	−1207.86	+	1207.86i	−0.234797	+	0.234797i
$299$	−2582.07	−	3818.95i	−0.499416	−	0.738648i
$300$	182.180	−	285.112i	0.0350606	−	0.0548699i
$301$	−98.3326	+	113.482i	−0.0188299	+	0.0217308i
$302$	−448.946	+	2063.77i	−0.0855429	+	0.393234i
$303$	98.1105	−	131.060i	0.0186016	−	0.0248489i
$304$	−378.652	−	829.131i	−0.0714380	−	0.156427i
$305$	49.7684	−	1446.42i	0.00934339	−	0.271547i
$306$	−236.735	−	806.246i	−0.0442263	−	0.150621i
$307$	630.598	−	137.178i	0.117232	−	0.0255022i	−0.153567	−	0.988138i	$-0.549076\pi$
$307$	630.598	−	137.178i	0.117232	−	0.0255022i	0.270798	+	0.962636i	$0.412712\pi$
$308$	−1818.41	+	678.232i	−0.336408	+	0.125474i
$309$	817.877	+	240.150i	0.150574	+	0.0442126i
$310$	78.5282	+	2121.10i	0.0143874	+	0.388614i
$311$	1851.15	+	2136.34i	0.337520	+	0.389519i	0.898984	−	0.437982i	$-0.144307\pi$
$311$	1851.15	+	2136.34i	0.337520	+	0.389519i	−0.561463	+	0.827502i	$0.689761\pi$
$312$	198.573	−	108.429i	0.0360321	−	0.0196750i
$313$	2076.92	+	5568.43i	0.375062	+	1.00558i	0.978149	+	0.207904i	$0.0666643\pi$
$313$	2076.92	+	5568.43i	0.375062	+	1.00558i	−0.603087	+	0.797675i	$0.706063\pi$
$314$	−1059.99	−	681.214i	−0.190505	−	0.122430i
$315$	−4099.09	−	1691.63i	−0.733198	−	0.302580i
$316$	−1266.82	−	182.142i	−0.225520	−	0.0324249i
$317$	−6105.42	−	2277.20i	−1.08175	−	0.403471i	−0.255519	−	0.966804i	$-0.582246\pi$
$317$	−6105.42	−	2277.20i	−1.08175	−	0.403471i	−0.826230	+	0.563333i	$0.809519\pi$
$318$	756.612	+	566.393i	0.133424	+	0.0998796i
$319$	−940.187	+	604.222i	−0.165017	+	0.106050i
$320$	−407.322	+	588.293i	−0.0711562	+	0.102771i
$321$			326.078i			0.0566974i
$322$	−1079.71	+	3114.79i	−0.186863	+	0.539070i
$323$	−637.651	−	637.651i	−0.109845	−	0.109845i
$324$	−2092.27	−	1812.97i	−0.358757	−	0.310865i
$325$	−5224.10	+	13.6407i	−0.891634	+	0.00232815i
$326$	−112.907	−	785.286i	−0.0191820	−	0.133414i
$327$	511.959	−	1372.62i	0.0865793	−	0.232128i
$328$	1564.06	−	1170.84i	0.263295	−	0.197100i
$329$	3665.22	−	1076.21i	0.614195	−	0.180344i
$330$	−439.619	−	219.340i	−0.0733340	−	0.0365887i
$331$	−4643.72	+	10168.3i	−0.771124	+	1.68853i	−0.0469625	+	0.998897i	$0.514954\pi$
$331$	−4643.72	+	10168.3i	−0.771124	+	1.68853i	−0.724162	+	0.689630i	$0.757773\pi$
$332$	2606.64	+	4773.71i	0.430898	+	0.789131i
$333$	−11287.9	−	807.326i	−1.85758	−	0.132856i
$334$	−2783.51	+	2411.92i	−0.456008	+	0.395133i
$335$	−8428.98	+	5868.67i	−1.37470	+	0.957133i
$336$	−147.172	−	67.2113i	−0.0238955	−	0.0109127i
$337$	920.725	+	4232.51i	0.148828	+	0.684152i	0.989728	+	0.142962i	$0.0456626\pi$
$337$	920.725	+	4232.51i	0.148828	+	0.684152i	−0.840900	+	0.541191i	$0.817974\pi$
$338$	790.524	+	431.659i	0.127216	+	0.0694650i
$339$	−97.5532	+	678.497i	−0.0156294	+	0.108705i
$340$	−174.174	+	686.144i	−0.0277821	+	0.109445i
$341$	3050.70	−	438.624i	0.484471	−	0.0696564i
$342$	−2955.03	−	642.828i	−0.467222	−	0.101638i
$343$	−493.256	−	6896.62i	−0.0776481	−	1.08566i
$344$	80.3880			0.0125995
$345$	−762.903	+	338.247i	−0.119053	+	0.0527844i
$346$	−4627.16			−0.718953
$347$	−608.375	−	8506.19i	−0.0941189	−	1.31595i	−0.796710	−	0.604361i	$-0.793428\pi$
$347$	−608.375	−	8506.19i	−0.0941189	−	1.31595i	0.702592	−	0.711593i	$-0.252026\pi$
$348$	−91.0399	−	19.8045i	−0.0140237	−	0.00305067i
$349$	488.218	−	70.1952i	0.0748818	−	0.0107664i	−0.104772	−	0.994496i	$-0.533411\pi$
$349$	488.218	−	70.1952i	0.0748818	−	0.0107664i	0.179654	+	0.983730i	$0.442502\pi$
$350$	2246.60	+	2984.83i	0.343103	+	0.455846i
$351$	215.497	−	1498.81i	0.0327703	−	0.227922i
$352$	911.914	+	497.943i	0.138083	+	0.0753990i
$353$	992.594	+	4562.88i	0.149661	+	0.687982i	0.989427	+	0.145033i	$0.0463287\pi$
$353$	992.594	+	4562.88i	0.149661	+	0.687982i	−0.839766	+	0.542949i	$0.817308\pi$
$354$	92.3012	+	42.1526i	0.0138581	+	0.00632876i
$355$	1120.16	−	6255.33i	0.167470	−	0.935208i
$356$	759.520	−	658.127i	0.113074	−	0.0979794i
$357$	−159.659	−	11.4190i	−0.0236696	−	0.00169288i
$358$	714.527	+	1308.56i	0.105486	+	0.193183i
$359$	−491.867	+	1077.04i	−0.0723112	+	0.158340i	−0.942336	−	0.334669i	$-0.891376\pi$
$359$	−491.867	+	1077.04i	−0.0723112	+	0.158340i	0.870025	+	0.493008i	$0.164103\pi$
$360$	752.647	+	2251.53i	0.110189	+	0.329628i
$361$	3467.17	−	1018.05i	0.505493	−	0.148426i
$362$	−6728.97	+	5037.24i	−0.976980	+	0.731358i
$363$	65.4500	−	175.478i	0.00946345	−	0.0253725i
$364$	355.517	+	2472.68i	0.0511928	+	0.356053i
$365$	644.557	−	6069.81i	0.0924320	−	0.870434i
$366$	−132.403	−	114.728i	−0.0189093	−	0.0163850i
$367$	−3064.09	−	3064.09i	−0.435816	−	0.435816i	0.454785	−	0.890601i	$-0.349716\pi$
$367$	−3064.09	−	3064.09i	−0.435816	−	0.435816i	−0.890601	+	0.454785i	$0.849716\pi$
$368$	1638.76	−	655.150i	0.232136	−	0.0928045i
$369$		−	6482.08i		−	0.914481i
$370$	7838.44	+	5427.17i	1.10135	+	0.762555i
$371$	−8778.92	+	5641.87i	−1.22851	+	0.789519i
$372$	205.689	+	153.977i	0.0286679	+	0.0214605i
$373$	1742.83	+	650.043i	0.241932	+	0.0902358i	0.467505	−	0.883990i	$-0.345153\pi$
$373$	1742.83	+	650.043i	0.241932	+	0.0902358i	−0.225574	+	0.974226i	$0.572426\pi$
$374$	1017.46	+	146.288i	0.140672	+	0.0202256i
$375$	−164.267	+	931.333i	−0.0226206	+	0.128250i
$376$	−1720.39	−	1105.63i	−0.235964	−	0.151645i
$377$	502.719	+	1347.84i	0.0686772	+	0.184131i
$378$	−950.388	+	518.951i	−0.129319	+	0.0706137i
$379$	−6925.27	−	7992.19i	−0.938595	−	1.08320i	−0.996392	−	0.0848677i	$-0.972953\pi$
$379$	−6925.27	−	7992.19i	−0.938595	−	1.08320i	0.0577976	−	0.998328i	$-0.481592\pi$
$380$	1866.93	+	1733.63i	0.252030	+	0.234035i
$381$	419.314	+	123.122i	0.0563834	+	0.0165557i
$382$	−287.774	+	107.334i	−0.0385439	+	0.0143761i
$383$	6171.39	−	1342.50i	0.823351	−	0.179109i	0.218896	−	0.975748i	$-0.429755\pi$
$383$	6171.39	−	1342.50i	0.823351	−	0.179109i	0.604455	+	0.796639i	$0.293391\pi$
$384$	24.4028	+	83.1083i	0.00324297	+	0.0110445i
$385$	3965.43	−	3701.63i	0.524928	−	0.490006i
$386$	3543.08	+	7758.27i	0.467197	+	1.02302i
$387$	159.832	−	213.511i	0.0209941	−	0.0280449i
$388$	549.110	−	2524.22i	0.0718475	−	0.330278i
$389$	−2532.56	+	2922.73i	−0.330092	+	0.380946i	−0.896399	−	0.443248i	$-0.853826\pi$
$389$	−2532.56	+	2922.73i	−0.330092	+	0.380946i	0.566307	+	0.824194i	$0.308372\pi$
$390$	−396.158	+	492.918i	−0.0514365	+	0.0639996i
$391$	1292.54	−	1173.87i	0.167178	−	0.151829i
$392$	−677.108	+	677.108i	−0.0872426	+	0.0872426i
$393$	1038.17	−	74.2515i	0.133254	−	0.00953052i
$394$	−879.249	−	1368.14i	−0.112426	−	0.174939i
$395$	3465.01	−	889.212i	0.441377	−	0.113269i
$396$	3135.66	−	1432.01i	0.397911	−	0.181720i
$397$	−4700.17	−	6278.70i	−0.594194	−	0.793750i	0.398142	−	0.917324i	$-0.369655\pi$
$397$	−4700.17	−	6278.70i	−0.594194	−	0.793750i	−0.992335	+	0.123574i	$0.960564\pi$
$398$	−4122.56	+	7549.91i	−0.519210	+	0.950862i
$399$	−311.449	+	484.623i	−0.0390775	+	0.0608058i
$400$	420.026	−	1955.40i	0.0525033	−	0.244425i
$401$	328.991	−	1120.44i	0.0409701	−	0.139531i	−0.936468	−	0.350753i	$-0.885926\pi$
$401$	328.991	−	1120.44i	0.0409701	−	0.139531i	0.977438	+	0.211221i	$0.0677440\pi$
$402$	−88.6950	+	1240.12i	−0.0110042	+	0.153859i
$403$	283.012	−	3957.03i	0.0349822	−	0.489115i
$404$	272.641	−	928.531i	0.0335753	−	0.114347i
$405$	7345.31	+	2434.11i	0.901214	+	0.298646i
$406$	556.167	−	865.413i	0.0679855	−	0.105788i
$407$	6634.61	−	12150.4i	0.808023	−	1.47978i
$408$	51.3536	+	68.6004i	0.00623133	+	0.00832409i
$409$	1944.06	−	887.825i	0.235031	−	0.107335i	−0.294418	−	0.955677i	$-0.595126\pi$
$409$	1944.06	−	887.825i	0.235031	−	0.107335i	0.529449	+	0.848342i	$0.322399\pi$
$410$	−2780.40	+	4700.08i	−0.334913	+	0.566148i
$411$	541.054	+	841.896i	0.0649348	+	0.101041i
$412$	5025.81	−	359.453i	0.600980	−	0.0429829i
$413$	−792.231	+	792.231i	−0.0943901	+	0.0943901i
$414$	1518.20	−	5655.16i	0.180230	−	0.671343i
$415$	−11849.8	−	9523.65i	−1.40164	−	1.12650i
$416$	875.794	−	1010.72i	0.103220	−	0.119122i
$417$	413.110	−	1899.04i	0.0485134	−	0.223013i
$418$	2216.99	−	2961.55i	0.259418	−	0.346541i
$419$	6191.15	+	13556.7i	0.721855	+	1.58064i	0.811286	+	0.584649i	$0.198768\pi$
$419$	6191.15	+	13556.7i	0.721855	+	1.58064i	−0.0894308	+	0.995993i	$0.528505\pi$
$420$	451.958	+	15.5509i	0.0525078	+	0.00180669i
$421$	3222.72	+	10975.6i	0.373078	+	1.27059i	0.905587	+	0.424161i	$0.139431\pi$
$421$	3222.72	+	10975.6i	0.373078	+	1.27059i	−0.532509	+	0.846424i	$0.678751\pi$
$422$	6277.23	−	1365.53i	0.724101	−	0.157519i
$423$	−6357.14	+	2371.09i	−0.730721	+	0.272545i
$424$	5360.42	+	1573.96i	0.613974	+	0.180279i
$425$	−286.705	−	1957.78i	−0.0327229	−	0.223450i
$426$	−503.757	−	581.366i	−0.0572937	−	0.0661204i
$427$	1697.78	−	927.056i	0.192415	−	0.105066i
$428$	673.583	+	1805.95i	0.0760721	+	0.203957i
$429$	772.486	+	496.447i	0.0869370	+	0.0558710i
$430$	−207.475	+	86.2565i	−0.0232682	+	0.00967363i
$431$	−6549.77	−	941.715i	−0.731998	−	0.105245i	−0.233771	−	0.972292i	$-0.575107\pi$
$431$	−6549.77	−	941.715i	−0.731998	−	0.105245i	−0.498228	+	0.867046i	$0.666016\pi$
$432$	543.155	+	202.586i	0.0604921	+	0.0225624i
$433$	13235.3	+	9907.80i	1.46893	+	1.09963i	0.972874	+	0.231337i	$0.0743101\pi$
$433$	13235.3	+	9907.80i	1.46893	+	1.09963i	0.496057	+	0.868290i	$0.334781\pi$
$434$	−2386.59	+	1533.77i	−0.263963	+	0.169639i
$435$	256.217	−	46.5721i	0.0282406	−	0.00513325i
$436$		−	8659.65i		−	0.951197i
$437$	−1478.56	−	6107.48i	−0.161852	−	0.668559i
$438$	−522.472	−	522.472i	−0.0569969	−	0.0569969i
$439$	4026.76	+	3489.21i	0.437783	+	0.379341i	0.845683	−	0.533685i	$-0.179193\pi$
$439$	4026.76	+	3489.21i	0.437783	+	0.379341i	−0.407900	+	0.913027i	$0.633739\pi$
$440$	−2887.87	−	306.665i	−0.312896	−	0.0332266i
$441$	452.135	+	3144.67i	0.0488214	+	0.339560i
$442$	462.377	−	1239.68i	0.0497580	−	0.133406i
$443$	13644.4	−	10214.0i	1.46335	−	1.09545i	0.488502	−	0.872563i	$-0.337543\pi$
$443$	13644.4	−	10214.0i	1.46335	−	1.09545i	0.974845	−	0.222885i	$-0.0715475\pi$
$444$	1107.34	−	325.144i	0.118360	−	0.0347537i
$445$	−1254.09	+	2513.54i	−0.133594	+	0.267760i
$446$	−1142.46	+	2501.64i	−0.121294	+	0.265597i
$447$	−276.985	−	507.260i	−0.0293086	−	0.0536747i
$448$	−953.936	−	68.2269i	−0.100601	−	0.00719513i
$449$	2225.45	−	1928.37i	0.233910	−	0.202684i	−0.530017	−	0.847987i	$-0.677814\pi$
$449$	2225.45	−	1928.37i	0.233910	−	0.202684i	0.763927	+	0.645303i	$0.223269\pi$
$450$	−4358.42	−	5003.43i	−0.456573	−	0.524142i
$451$	7212.95	+	3294.05i	0.753093	+	0.343926i
$452$	861.294	+	3959.30i	0.0896280	+	0.412013i
$453$	−627.192	−	342.472i	−0.0650508	−	0.0355204i
$454$	4.58845	−	31.9133i	0.000474331	−	0.00329905i
$455$	−3570.75	−	6000.32i	−0.367911	−	0.618240i
$456$	305.265	−	43.8905i	0.0313494	−	0.00450737i
$457$	239.911	+	52.1893i	0.0245570	+	0.00534205i	0.224827	−	0.974399i	$-0.427818\pi$
$457$	239.911	+	52.1893i	0.0245570	+	0.00534205i	−0.200270	+	0.979741i	$0.564182\pi$
$458$	514.019	+	7186.93i	0.0524422	+	0.733238i
$459$	573.520			0.0583216
$460$	−3526.53	+	3449.28i	−0.357447	+	0.349617i
$461$	−14889.0			−1.50423			−0.752117	−	0.659030i	$-0.770967\pi$
$461$	−14889.0			−1.50423			−0.752117	+	0.659030i	$0.770967\pi$
$462$	−46.8453	−	654.983i	−0.00471741	−	0.0659580i
$463$	9461.65	+	2058.26i	0.949720	+	0.206599i	0.660637	−	0.750705i	$-0.270286\pi$
$463$	9461.65	+	2058.26i	0.949720	+	0.206599i	0.289083	+	0.957304i	$0.406650\pi$
$464$	−545.125	+	78.3771i	−0.0545405	+	0.00784174i
$465$	−696.084	−	176.697i	−0.0694196	−	0.0176218i
$466$	1492.24	−	10378.8i	0.148341	−	1.03173i
$467$	−899.976	−	491.424i	−0.0891776	−	0.0486947i	0.434041	−	0.900893i	$-0.357087\pi$
$467$	−899.976	−	491.424i	−0.0891776	−	0.0486947i	−0.523219	+	0.852198i	$0.675269\pi$
$468$	−943.171	−	4335.69i	−0.0931583	−	0.428242i
$469$	−12487.1	−	5702.67i	−1.22943	−	0.561460i
$470$	5626.54	+	1007.56i	0.552198	+	0.0988833i
$471$	322.192	−	279.181i	0.0315198	−	0.0273121i
$472$	598.275	+	42.7895i	0.0583429	+	0.00417277i
$473$	156.362	+	286.355i	0.0151998	+	0.0278364i
$474$	179.889	−	393.902i	0.0174316	−	0.0381698i
$475$	−6678.60	−	2471.14i	−0.645126	−	0.238703i
$476$	−907.841	+	266.566i	−0.0874177	+	0.0256682i
$477$	14838.4	−	11107.9i	1.42432	−	1.06623i
$478$	−181.767	+	487.337i	−0.0173930	+	0.0466324i
$479$	−2289.45	−	15923.5i	−0.218388	−	1.51892i	−0.743991	−	0.668189i	$-0.767070\pi$
$479$	−2289.45	−	15923.5i	−0.218388	−	1.51892i	0.525604	−	0.850730i	$-0.323839\pi$
$480$	−152.157	−	188.312i	−0.0144687	−	0.0179067i
$481$	−13466.9	−	11669.1i	−1.27658	−	1.10617i
$482$	−2321.26	−	2321.26i	−0.219358	−	0.219358i
$483$	−908.270	−	647.432i	−0.0855647	−	0.0609921i
$484$		−	1107.07i		−	0.103970i
$485$	1291.28	+	7104.01i	0.120895	+	0.665106i
$486$	2433.93	−	1564.19i	0.227171	−	0.145994i
$487$	9722.96	+	7278.52i	0.904701	+	0.677251i	0.946786	−	0.321863i	$-0.104309\pi$
$487$	9722.96	+	7278.52i	0.904701	+	0.677251i	−0.0420849	+	0.999114i	$0.513400\pi$
$488$	−970.295	−	361.901i	−0.0900065	−	0.0335707i
$489$	265.699	+	38.2018i	0.0245713	+	0.00353281i
$490$	1021.02	−	2474.10i	0.0941330	−	0.228099i
$491$	17388.8	+	11175.1i	1.59826	+	1.02714i	0.968062	+	0.250711i	$0.0806644\pi$
$491$	17388.8	+	11175.1i	1.59826	+	1.02714i	0.630202	+	0.776431i	$0.282972\pi$
$492$	231.012	+	619.367i	0.0211683	+	0.0567545i
$493$	−478.207	+	261.121i	−0.0436863	+	0.0238545i
$494$	−3118.31	−	3598.72i	−0.284007	−	0.327762i
$495$	−6556.35	+	7060.48i	−0.595325	+	0.641101i
$496$	1457.26	+	427.889i	0.131921	+	0.0387354i
$497$	7958.17	−	2968.24i	0.718255	−	0.267895i
$498$	−1798.22	+	391.179i	−0.161808	+	0.0351991i
$499$	1385.10	+	4717.21i	0.124260	+	0.423189i	0.998001	−	0.0632020i	$-0.0201312\pi$
$499$	1385.10	+	4717.21i	0.124260	+	0.423189i	−0.873741	+	0.486391i	$0.838313\pi$
$500$	1014.09	+	5497.42i	0.0907031	+	0.491704i
$501$	−517.677	−	1133.56i	−0.0461639	−	0.101085i
$502$	6225.62	−	8316.45i	0.553512	−	0.739405i
$503$	−1833.10	+	8426.61i	−0.162492	+	0.746966i	0.821708	+	0.569909i	$0.193021\pi$
$503$	−1833.10	+	8426.61i	−0.162492	+	0.746966i	−0.984201	+	0.177057i	$0.943342\pi$
$504$	−2077.88	+	2398.01i	−0.183644	+	0.211936i
$505$	292.650	+	2689.01i	0.0257877	+	0.236949i
$506$	5521.28	+	4563.20i	0.485081	+	0.400908i
$507$	−215.490	+	215.490i	−0.0188762	+	0.0188762i
$508$	2576.66	−	184.286i	0.225041	−	0.0160952i
$509$	−7591.12	−	11812.0i	−0.661042	−	1.02860i	−0.996255	−	0.0864594i	$-0.972445\pi$
$509$	−7591.12	−	11812.0i	−0.661042	−	1.02860i	0.335213	−	0.942142i	$-0.391192\pi$
$510$	−206.148	−	121.950i	−0.0178988	−	0.0105883i
$511$	7421.10	−	3389.10i	0.642446	−	0.293395i
$512$	306.830	+	409.877i	0.0264846	+	0.0353793i
$513$	989.206	−	1811.59i	0.0851355	−	0.155914i
$514$	−2958.42	+	4603.40i	−0.253872	+	0.395033i
$515$	−12585.5	+	6320.43i	−1.07686	+	0.540799i
$516$	−7.66285	+	26.0973i	−0.000653756	+	0.00222649i
$517$	592.116	−	8278.87i	0.0503699	−	0.704263i
$518$	−909.058	+	12710.3i	−0.0771075	+	1.07810i
$519$	441.077	−	1502.17i	0.0373047	−	0.127048i
$520$	−1175.85	+	3548.32i	−0.0991625	+	0.299239i
$521$	−1767.26	+	2749.91i	−0.148609	+	0.231239i	−0.907575	−	0.419891i	$-0.862068\pi$
$521$	−1767.26	+	2749.91i	−0.148609	+	0.231239i	0.758966	+	0.651130i	$0.225705\pi$
$522$	−875.680	+	1603.69i	−0.0734243	+	0.134467i
$523$	7974.03	+	10652.1i	0.666692	+	0.890596i	0.998610	−	0.0527120i	$-0.0167865\pi$
$523$	7974.03	+	10652.1i	0.666692	+	0.890596i	−0.331918	+	0.943308i	$0.607696\pi$
$524$	5596.42	−	2555.80i	0.466567	−	0.213074i
$525$	−1183.15	+	444.816i	−0.0983564	+	0.0369779i
$526$	3394.94	+	5282.64i	0.281419	+	0.437897i
$527$	1498.74	−	107.192i	0.123883	−	0.00886026i
$528$	−248.580	+	248.580i	−0.0204887	+	0.0204887i
$529$	11949.3	−	2291.18i	0.982110	−	0.188311i
$530$	−15523.7	+	1689.47i	−1.27228	+	0.138464i
$531$	1303.18	−	1503.95i	0.106503	−	0.122911i
$532$	−723.831	+	3327.40i	−0.0589888	+	0.271167i
$533$	6116.60	−	8170.82i	0.497072	−	0.664011i
$534$	141.256	+	309.307i	0.0114471	+	0.0250656i
$535$	−3676.25	−	3938.25i	−0.297081	−	0.318253i
$536$	2070.50	+	7051.48i	0.166851	+	0.568242i
$537$	−492.924	+	107.229i	−0.0396112	+	0.00861689i
$538$	460.662	−	171.818i	0.0369155	−	0.0137688i
$539$	−3729.00	−	1094.93i	−0.297995	−	0.0874994i
$540$	−1619.22	+	59.9473i	−0.129037	+	0.00477726i
$541$	4106.59	+	4739.26i	0.326352	+	0.376630i	0.895088	−	0.445890i	$-0.147113\pi$
$541$	4106.59	+	4739.26i	0.326352	+	0.376630i	−0.568736	+	0.822520i	$0.692567\pi$
$542$	8770.46	−	4789.03i	0.695062	−	0.379532i
$543$	−993.871	−	2664.67i	−0.0785471	−	0.210593i
$544$	426.125	+	273.854i	0.0335845	+	0.0215835i
$545$	9291.83	+	22349.9i	0.730309	+	1.75663i
$546$	−836.623	−	120.288i	−0.0655754	−	0.00942832i
$547$	16932.6	+	6315.52i	1.32355	+	0.493660i	0.909164	−	0.416439i	$-0.136722\pi$
$547$	16932.6	+	6315.52i	1.32355	+	0.493660i	0.414391	+	0.910099i	$0.363995\pi$
$548$	4735.68	+	3545.09i	0.369158	+	0.276348i
$549$	−2890.41	+	1857.55i	−0.224699	+	0.144405i
$550$	7782.44	−	2307.22i	0.603353	−	0.178873i
$551$			1960.91i			0.151611i
$552$	56.4768	+	594.461i	0.00435474	+	0.0458368i
$553$	3380.90	+	3380.90i	0.259983	+	0.259983i
$554$	−4176.75	−	3619.17i	−0.320312	−	0.277552i
$555$	−2509.07	+	2027.35i	−0.191900	+	0.155056i
$556$	−1634.90	−	11371.0i	−0.124704	−	0.867333i
$557$	6779.16	−	18175.6i	0.515695	−	1.38263i	−0.374573	−	0.927197i	$-0.622211\pi$
$557$	6779.16	−	18175.6i	0.515695	−	1.38263i	0.890269	−	0.455435i	$-0.150516\pi$
$558$	4033.88	−	3019.72i	0.306035	−	0.229095i
$559$	402.945	−	118.315i	0.0304879	−	0.00895207i
$560$	2535.24	−	847.488i	0.191310	−	0.0639517i
$561$	−144.479	+	316.364i	−0.0108732	+	0.0238091i
$562$	−2865.57	−	5247.90i	−0.215083	−	0.393896i
$563$	−17483.2	−	1250.42i	−1.30875	−	0.0936039i	−0.600536	−	0.799598i	$-0.705046\pi$
$563$	−17483.2	−	1250.42i	−1.30875	−	0.0936039i	−0.708218	+	0.705994i	$0.750500\pi$
$564$	522.927	−	453.119i	0.0390411	−	0.0338293i
$565$	−6471.28	−	9294.49i	−0.481856	−	0.692074i
$566$	3181.54	+	1452.96i	0.236272	+	0.107902i
$567$	2198.47	+	10106.2i	0.162834	+	0.748537i
$568$	−3990.94	−	2179.22i	−0.294817	−	0.160982i
$569$	−765.661	+	5325.29i	−0.0564116	+	0.392351i	0.941981	+	0.335667i	$0.108962\pi$
$569$	−765.661	+	5325.29i	−0.0564116	+	0.392351i	−0.998392	+	0.0566837i	$0.981947\pi$
$570$	−740.771	+	440.828i	−0.0544342	+	0.0323934i
$571$	6182.46	−	888.903i	0.453114	−	0.0651479i	0.0880200	−	0.996119i	$-0.471946\pi$
$571$	6182.46	−	888.903i	0.453114	−	0.0651479i	0.365094	+	0.930971i	$0.381037\pi$
$572$	5303.85	+	1153.78i	0.387701	+	0.0843392i
$573$	−7.41353	−	103.655i	−0.000540497	−	0.00755714i
$574$	−7298.89			−0.530748
$575$	5400.62	−	12686.3i	0.391689	−	0.920098i
$576$	1698.69			0.122880
$577$	1645.91	+	23012.8i	0.118752	+	1.66037i	0.612280	+	0.790641i	$0.290253\pi$
$577$	1645.91	+	23012.8i	0.118752	+	1.66037i	−0.493528	+	0.869730i	$0.664293\pi$
$578$	−9111.77	−	1982.14i	−0.655709	−	0.142641i
$579$	−2856.40	+	410.688i	−0.205022	+	0.0294777i
$580$	1322.83	−	787.206i	0.0947024	−	0.0563568i
$581$	2891.73	−	20112.4i	0.206488	−	1.43615i
$582$	767.123	+	418.881i	0.0546362	+	0.0298336i
$583$	4819.78	+	22156.2i	0.342393	+	1.57395i
$584$	−3972.93	−	1814.38i	−0.281509	−	0.128561i
$585$	7086.46	+	10178.0i	0.500836	+	0.719334i
$586$	−10520.2	+	9115.77i	−0.741610	+	0.642609i
$587$	−9785.57	−	699.878i	−0.688064	−	0.0492113i	−0.277071	−	0.960850i	$-0.589364\pi$
$587$	−9785.57	−	699.878i	−0.688064	−	0.0492113i	−0.410994	+	0.911638i	$0.634818\pi$
$588$	−155.273	−	284.362i	−0.0108901	−	0.0199437i
$589$	2246.43	−	4919.00i	0.157152	−	0.344116i
$590$	−1590.02	+	531.515i	−0.110949	+	0.0370884i
$591$	527.967	−	155.025i	0.0367473	−	0.0107900i
$592$	5461.22	−	4088.22i	0.379147	−	0.283826i
$593$	906.323	−	2429.95i	0.0627626	−	0.168273i	−0.901783	−	0.432189i	$-0.857741\pi$
$593$	906.323	−	2429.95i	0.0627626	−	0.168273i	0.964546	+	0.263916i	$0.0850141\pi$
$594$	334.839	+	2328.86i	0.0231290	+	0.160866i
$595$	2057.04	−	1662.10i	0.141732	−	0.114520i
$596$	−2581.91	−	2237.23i	−0.177448	−	0.153760i
$597$	−2058.04	−	2058.04i	−0.141089	−	0.141089i
$598$	7250.04	−	5695.87i	0.495779	−	0.389501i
$599$		−	1041.02i		−	0.0710100i	−0.999369	−	0.0355050i	$-0.988696\pi$
$599$		−	1041.02i		−	0.0710100i	0.999369	−	0.0355050i	$-0.0113040\pi$
$600$	594.765	+	322.753i	0.0404686	+	0.0219606i
$601$	−21925.9	+	14090.9i	−1.48814	+	0.956372i	−0.491821	+	0.870696i	$0.663669\pi$
$601$	−21925.9	+	14090.9i	−1.48814	+	0.956372i	−0.996323	+	0.0856760i	$0.972695\pi$
$602$	−240.415	−	179.973i	−0.0162767	−	0.0121846i
$603$	22845.5	+	8520.91i	1.54285	+	0.575453i
$604$	−4181.08	−	601.149i	−0.281665	−	0.0404974i
$605$	1187.89	+	2857.26i	0.0798256	+	0.192007i
$606$	275.451	+	177.021i	0.0184644	+	0.0118663i
$607$	−4373.67	−	11726.3i	−0.292458	−	0.784109i	−0.997209	−	0.0746552i	$-0.976214\pi$
$607$	−4373.67	−	11726.3i	−0.292458	−	0.784109i	0.704752	−	0.709454i	$-0.251058\pi$
$608$	1600.01	−	873.673i	0.106725	−	0.0582765i
$609$	227.933	+	263.049i	0.0151664	+	0.0175029i
$610$	2892.58	−	107.090i	0.191995	−	0.00710811i
$611$	−10250.7	−	3009.89i	−0.678725	−	0.199292i
$612$	1574.61	−	587.298i	0.104003	−	0.0387910i
$613$	−8352.97	+	1817.08i	−0.550364	+	0.119724i	−0.479144	−	0.877736i	$-0.659053\pi$
$613$	−8352.97	+	1817.08i	−0.550364	+	0.119724i	−0.0712201	+	0.997461i	$0.522689\pi$
$614$	363.630	+	1238.41i	0.0239005	+	0.0813977i
$615$	−1260.81	−	1350.66i	−0.0826677	−	0.0885592i
$616$	−1612.46	−	3530.79i	−0.105467	−	0.230941i
$617$	−15438.8	+	20623.8i	−1.00736	+	1.34568i	−0.0699148	+	0.997553i	$0.522273\pi$
$617$	−15438.8	+	20623.8i	−1.00736	+	1.34568i	−0.937448	+	0.348126i	$0.886818\pi$
$618$	−362.384	+	1665.85i	−0.0235877	+	0.108431i
$619$	−11241.2	+	12973.0i	−0.729921	+	0.842373i	−0.992463	−	0.122547i	$-0.960894\pi$
$619$	−11241.2	+	12973.0i	−0.729921	+	0.842373i	0.262542	+	0.964921i	$0.415439\pi$
$620$	−4220.19	+	459.292i	−0.273366	+	0.0297510i
$621$	3411.54	+	2081.68i	0.220451	+	0.134517i
$622$	−3997.67	+	3997.67i	−0.257704	+	0.257704i
$623$	−3744.90	+	267.841i	−0.240829	+	0.0172244i
$624$	244.638	+	380.665i	0.0156945	+	0.0244211i
$625$	−8516.04	−	13100.3i	−0.545027	−	0.838419i
$626$	−10812.2	+	4937.75i	−0.690321	+	0.315259i
$627$	750.113	+	1002.03i	0.0477777	+	0.0638235i
$628$	1207.72	−	2211.77i	0.0767408	−	0.140540i
$629$	3648.84	−	5677.71i	0.231302	−	0.359913i
$630$	2789.79	−	8418.65i	0.176425	−	0.532392i
$631$	−6939.05	+	23632.2i	−0.437780	+	1.49094i	0.385179	+	0.922842i	$0.374140\pi$
$631$	−6939.05	+	23632.2i	−0.437780	+	1.49094i	−0.822959	+	0.568100i	$0.807679\pi$
$632$	182.607	−	2553.18i	0.0114932	−	0.160696i
$633$	−155.060	+	2168.02i	−0.00973628	+	0.136131i
$634$	3671.69	−	12504.6i	0.230002	−	0.783316i
$635$	−6452.41	+	3240.39i	−0.403238	+	0.202505i
$636$	−1021.95	+	1590.18i	−0.0637151	+	0.0991427i
$637$	−2397.44	+	4390.58i	−0.149121	+	0.273094i
$638$	−1339.51	−	1789.37i	−0.0831217	−	0.111038i
$639$	−13723.0	+	6267.10i	−0.849570	+	0.387985i
$640$	−1231.70	−	728.632i	−0.0760741	−	0.0450026i
$641$	−2188.59	−	3405.51i	−0.134858	−	0.209844i	0.767256	−	0.641341i	$-0.221622\pi$
$641$	−2188.59	−	3405.51i	−0.134858	−	0.209844i	−0.902114	+	0.431498i	$0.857985\pi$
$642$	−650.493	+	46.5242i	−0.0399890	+	0.00286007i
$643$	16590.8	−	16590.8i	1.01754	−	1.01754i	0.0176956	−	0.999843i	$-0.494367\pi$
$643$	16590.8	−	16590.8i	1.01754	−	1.01754i	0.999843	−	0.0176956i	$-0.00563299\pi$
$644$	−6367.77	−	1709.51i	−0.389635	−	0.104602i
$645$	−8.22523	−	75.5774i	−0.000502121	−	0.00461373i
$646$	1181.07	−	1363.03i	0.0719330	−	0.0830151i
$647$	−1335.55	+	6139.44i	−0.0811530	+	0.373054i	−0.999755	−	0.0221294i	$-0.992955\pi$
$647$	−1335.55	+	6139.44i	−0.0811530	+	0.373054i	0.918602	+	0.395184i	$0.129319\pi$
$648$	3318.17	−	4432.56i	0.201157	−	0.268715i
$649$	1011.28	+	2214.39i	0.0611649	+	0.133933i
$650$	−772.578	−	10419.6i	−0.0466200	−	0.628756i
$651$	−270.427	−	920.991i	−0.0162809	−	0.0554478i
$652$	1550.46	−	337.282i	0.0931300	−	0.0202592i
$653$	7984.86	−	2978.20i	0.478517	−	0.178478i	−0.0986196	−	0.995125i	$-0.531443\pi$
$653$	7984.86	−	2978.20i	0.478517	−	0.178478i	0.577137	+	0.816648i	$0.304170\pi$
$654$	2811.28	+	825.467i	0.168089	+	0.0493552i
$655$	−11701.6	+	12601.3i	−0.698042	+	0.751716i
$656$	2558.87	+	2953.09i	0.152297	+	0.175760i
$657$	−12718.2	+	6944.67i	−0.755228	+	0.412385i
$658$	2669.87	+	7158.21i	0.158180	+	0.424097i
$659$	4505.31	+	2895.39i	0.266316	+	0.171151i	0.666983	−	0.745073i	$-0.267585\pi$
$659$	4505.31	+	2895.39i	0.266316	+	0.171151i	−0.400667	+	0.916224i	$0.631222\pi$
$660$	374.838	−	908.292i	0.0221069	−	0.0535685i
$661$	−3601.01	−	517.746i	−0.211895	−	0.0304660i	0.0355495	−	0.999368i	$-0.488682\pi$
$661$	−3601.01	−	517.746i	−0.211895	−	0.0304660i	−0.247445	+	0.968902i	$0.579591\pi$
$662$	−20947.4	−	7812.98i	−1.22983	−	0.458701i
$663$	358.377	+	268.277i	0.0209928	+	0.0157150i
$664$	−9151.19	+	5881.11i	−0.534842	+	0.343722i
$665$	−1702.16	−	9364.43i	−0.0992583	−	0.546071i
$666$		−	22633.5i		−	1.31686i
$667$	−3792.35	−	182.472i	−0.220151	−	0.0105927i
$668$	−5208.70	−	5208.70i	−0.301693	−	0.301693i
$669$	−703.234	−	609.356i	−0.0406407	−	0.0352153i
$670$	−12910.1	−	15977.7i	−0.744417	−	0.921300i
$671$	−598.158	−	4160.28i	−0.0344138	−	0.239353i
$672$	113.082	−	303.184i	0.00649140	−	0.0174041i
$673$	20761.1	−	15541.6i	1.18913	−	0.890169i	0.193273	−	0.981145i	$-0.438090\pi$
$673$	20761.1	−	15541.6i	1.18913	−	0.890169i	0.995853	+	0.0909765i	$0.0289988\pi$
$674$	−8312.08	+	2440.65i	−0.475029	+	0.139481i
$675$	4114.75	−	1892.15i	0.234633	−	0.107894i
$676$	−748.328	+	1638.61i	−0.0425767	+	0.0932299i
$677$	−12750.7	−	23351.1i	−0.723853	−	1.32564i	−0.937245	−	0.348671i	$-0.886633\pi$
$677$	−12750.7	−	23351.1i	−0.723853	−	1.32564i	0.213392	−	0.976967i	$-0.431549\pi$
$678$	−1367.46	−	97.8024i	−0.0774585	−	0.00553994i
$679$	−7293.44	+	6319.80i	−0.412219	+	0.357189i
$680$	−1393.64	−	249.563i	−0.0785938	−	0.0140740i
$681$	9.92302	+	4.53169i	0.000558371	+	0.000255000i
$682$	1310.28	+	6023.27i	0.0735678	+	0.338186i
$683$	−10431.5	−	5696.04i	−0.584409	−	0.319111i	0.159705	−	0.987165i	$-0.448946\pi$
$683$	−10431.5	−	5696.04i	−0.584409	−	0.319111i	−0.744113	+	0.668054i	$0.767128\pi$
$684$	860.761	−	5986.73i	0.0481170	−	0.334661i
$685$	−16026.3	−	4068.20i	−0.893919	−	0.226917i
$686$	13687.7	−	1968.00i	0.761806	−	0.109531i
$687$	−2382.17	−	518.210i	−0.132293	−	0.0287787i
$688$	11.4696	+	160.366i	0.000635575	+	0.00888649i
$689$	29185.7			1.61377
$690$	−783.620	−	1473.66i	−0.0432347	−	0.0813060i
$691$	−16912.4			−0.931083			−0.465541	−	0.885026i	$-0.654140\pi$
$691$	−16912.4			−0.931083			−0.465541	+	0.885026i	$0.654140\pi$
$692$	−660.196	−	9230.74i	−0.0362672	−	0.507081i
$693$	−12583.8	−	2737.43i	−0.689780	−	0.150053i
$694$	16882.2	−	2427.30i	0.923402	−	0.132765i
$695$	16420.7	+	27593.4i	0.896217	+	1.50601i
$696$	26.5187	−	184.441i	0.00144424	−	0.0100449i
$697$	3392.93	+	1852.68i	0.184385	+	0.100682i
$698$	209.691	+	963.934i	0.0113709	+	0.0522714i
$699$	3227.14	+	1473.79i	0.174623	+	0.0797478i
$700$	−5633.91	+	4907.63i	−0.304203	+	0.264987i
$701$	−2077.36	+	1800.04i	−0.111927	+	0.0969853i	−0.709026	−	0.705182i	$-0.750865\pi$
$701$	−2077.36	+	1800.04i	−0.111927	+	0.0969853i	0.597099	+	0.802167i	$0.296320\pi$
$702$	3020.74	+	216.047i	0.162408	+	0.0116156i
$703$	−11640.9	−	21318.6i	−0.624528	−	1.14374i
$704$	−863.238	+	1890.23i	−0.0462138	+	0.101194i
$705$	−863.436	+	1730.57i	−0.0461261	+	0.0924495i
$706$	−8960.88	+	2631.15i	−0.477687	+	0.140262i
$707$	−2894.18	+	2166.56i	−0.153956	+	0.115250i
$708$	−70.9209	+	190.146i	−0.00376465	+	0.0100934i
$709$	2224.70	+	15473.1i	0.117842	+	0.819611i	0.959924	+	0.280261i	$0.0904210\pi$
$709$	2224.70	+	15473.1i	0.117842	+	0.819611i	−0.842082	+	0.539350i	$0.818670\pi$
$710$	12638.6	+	1342.10i	0.668055	+	0.0709412i
$711$	−6418.19	−	5561.39i	−0.338538	−	0.293345i
$712$	1421.27	+	1421.27i	0.0748094	+	0.0748094i
$713$	9304.21	+	4802.30i	0.488703	+	0.252240i
$714$		−	320.133i		−	0.0167797i
$715$	−14926.8	+	2713.22i	−0.780744	+	0.141914i
$716$	−2508.50	+	1612.12i	−0.130932	+	0.0841447i
$717$	−140.883	−	105.464i	−0.00733804	−	0.00549319i
$718$	−2218.77	−	827.557i	−0.115325	−	0.0430141i
$719$	16111.5	+	2316.49i	0.835687	+	0.120154i	0.546856	−	0.837226i	$-0.315824\pi$
$719$	16111.5	+	2316.49i	0.835687	+	0.120154i	0.288831	+	0.957380i	$0.406733\pi$
$720$	−4384.20	+	1822.70i	−0.226930	+	0.0943446i
$721$	−15835.4	−	10176.8i	−0.817947	−	0.525663i
$722$	2525.61	+	6771.43i	0.130185	+	0.349039i
$723$	974.849	−	532.308i	0.0501453	−	0.0273814i
$724$	−11008.9	−	12704.9i	−0.565114	−	0.652176i
$725$	−2569.44	+	3451.12i	−0.131623	+	0.176788i
$726$	359.400	+	105.529i	0.0183727	+	0.00539472i
$727$	30883.4	−	11518.9i	1.57552	−	0.587637i	0.598560	−	0.801078i	$-0.295740\pi$
$727$	30883.4	−	11518.9i	1.57552	−	0.587637i	0.976956	+	0.213441i	$0.0684670\pi$
$728$	−4882.03	+	1062.02i	−0.248544	+	0.0540674i
$729$	−4989.00	−	16991.0i	−0.253468	−	0.863231i
$730$	12200.7	+	419.799i	0.618584	+	0.0212842i
$731$	66.0760	+	144.686i	0.00334324	+	0.00732068i
$732$	209.980	−	280.500i	0.0106026	−	0.0141634i
$733$	−5508.97	+	25324.3i	−0.277597	+	1.27609i	0.601279	+	0.799039i	$0.294658\pi$
$733$	−5508.97	+	25324.3i	−0.277597	+	1.27609i	−0.878875	+	0.477051i	$0.841706\pi$
$734$	5675.39	−	6549.75i	0.285399	−	0.329367i
$735$	705.869	+	567.307i	0.0354236	+	0.0284700i
$736$	1540.78	+	3175.69i	0.0771655	+	0.159046i
$737$	−21091.2	+	21091.2i	−1.05415	+	1.05415i
$738$	12931.1	−	924.852i	0.644988	−	0.0461305i
$739$	3240.02	+	5041.57i	0.161280	+	0.250957i	0.912483	−	0.409114i	$-0.134162\pi$
$739$	3240.02	+	5041.57i	0.161280	+	0.250957i	−0.751203	+	0.660072i	$0.770526\pi$
$740$	−9708.32	+	16411.3i	−0.482277	+	0.815258i
$741$	1465.54	−	669.292i	0.0726560	−	0.0331809i
$742$	−12507.6	−	16708.1i	−0.618823	−	0.826651i
$743$	−14910.6	+	27306.7i	−0.736228	+	1.34830i	0.193884	+	0.981024i	$0.437891\pi$
$743$	−14910.6	+	27306.7i	−0.736228	+	1.34830i	−0.930112	+	0.367276i	$0.880291\pi$
$744$	−277.821	+	432.298i	−0.0136901	+	0.0213022i
$745$	9064.26	+	3003.74i	0.445757	+	0.147716i
$746$	−1048.11	+	3569.53i	−0.0514397	+	0.175187i
$747$	−2574.68	+	35998.8i	−0.126108	+	1.76322i
$748$	−146.662	+	2050.60i	−0.00716910	+	0.100237i
$749$	2028.68	−	6909.04i	0.0989669	−	0.337050i
$750$	−1881.36	−	194.816i	−0.0915967	−	0.00948491i
$751$	19854.4	−	30894.1i	0.964712	−	1.50112i	0.102401	−	0.994743i	$-0.467348\pi$
$751$	19854.4	−	30894.1i	0.964712	−	1.50112i	0.862311	−	0.506378i	$-0.169016\pi$
$752$	1960.16	−	3589.77i	0.0950528	−	0.174076i
$753$	2106.42	+	2813.85i	0.101942	+	0.136178i
$754$	−2617.09	+	1195.18i	−0.126404	+	0.0577268i
$755$	11436.1	−	2934.80i	0.551261	−	0.141468i
$756$	−1170.86	−	1821.89i	−0.0563276	−	0.0876475i
$757$	14489.7	−	1036.32i	0.695688	−	0.0497566i	0.280983	−	0.959713i	$-0.409339\pi$
$757$	14489.7	−	1036.32i	0.695688	−	0.0497566i	0.414705	+	0.909956i	$0.363885\pi$
$758$	14955.6	−	14955.6i	0.716637	−	0.716637i
$759$	−2007.71	+	1357.46i	−0.0960150	+	0.0649178i
$760$	−3192.05	+	3971.70i	−0.152353	+	0.189564i
$761$	−9830.74	+	11345.3i	−0.468284	+	0.540428i	−0.939933	−	0.341358i	$-0.889113\pi$
$761$	−9830.74	+	11345.3i	−0.468284	+	0.540428i	0.471650	+	0.881786i	$0.343659\pi$
$762$	−185.789	+	854.057i	−0.00883257	+	0.0406027i
$763$	−19387.2	+	25898.3i	−0.919875	+	1.22881i
$764$	−255.180	−	558.767i	−0.0120839	−	0.0264600i
$765$	−3433.76	+	3205.33i	−0.162285	+	0.151489i
$766$	3558.69	+	12119.8i	0.167860	+	0.571679i
$767$	3061.84	−	666.062i	0.144141	−	0.0313561i
$768$	−162.311	+	60.5390i	−0.00762618	+	0.00284442i
$769$	−18988.0	−	5575.38i	−0.890409	−	0.261448i	−0.195636	−	0.980677i	$-0.562677\pi$
$769$	−18988.0	−	5575.38i	−0.890409	−	0.261448i	−0.694773	+	0.719229i	$0.744495\pi$
$770$	7950.17	+	7382.52i	0.372083	+	0.345516i
$771$	−1212.45	−	1399.24i	−0.0566345	−	0.0653597i
$772$	−14971.5	+	8175.04i	−0.697973	+	0.381122i
$773$	−2809.07	−	7531.40i	−0.130705	−	0.350434i	0.855068	−	0.518516i	$-0.173515\pi$
$773$	−2809.07	−	7531.40i	−0.130705	−	0.350434i	−0.985773	+	0.168082i	$0.946243\pi$
$774$	448.738	+	288.386i	0.0208392	+	0.0133926i
$775$	10399.2	−	5713.67i	0.481999	−	0.264827i
$776$	5113.92	+	735.270i	0.236571	+	0.0340138i
$777$	−4039.64	−	1506.71i	−0.186514	−	0.0695660i
$778$	−6191.90	−	4635.20i	−0.285335	−	0.213599i
$779$	11704.3	−	7521.87i	0.538316	−	0.345955i
$780$	−1039.85	−	719.968i	−0.0477340	−	0.0330500i
$781$		−	18455.2i		−	0.845554i
$782$	2526.17	+	2411.01i	0.115519	+	0.110253i
$783$	−881.844	−	881.844i	−0.0402485	−	0.0402485i
$784$	−1447.37	−	1254.16i	−0.0659336	−	0.0571318i
$785$	−743.791	+	7004.30i	−0.0338179	+	0.318464i
$786$	296.249	+	2060.46i	0.0134439	+	0.0935040i
$787$	12249.8	−	32842.9i	0.554838	−	1.48758i	−0.292365	−	0.956307i	$-0.594442\pi$
$787$	12249.8	−	32842.9i	0.554838	−	1.48758i	0.847202	−	0.531270i	$-0.178285\pi$
$788$	2603.85	−	1949.22i	0.117714	−	0.0881194i
$789$	−2038.58	+	598.581i	−0.0919840	+	0.0270090i
$790$	2268.28	+	6785.50i	0.102154	+	0.305592i
$791$	6288.23	−	13769.3i	0.282660	−	0.618938i
$792$	3304.11	+	6051.03i	0.148240	+	0.271482i
$793$	−5396.25	−	385.948i	−0.241648	−	0.0172830i
$794$	11854.8	−	10272.2i	0.529862	−	0.459128i
$795$	931.298	−	5200.69i	0.0415468	−	0.232012i
$796$	−15649.6	−	7146.91i	−0.696839	−	0.318236i
$797$	−1615.52	−	7426.42i	−0.0718000	−	0.330059i	0.927210	−	0.374541i	$-0.122200\pi$
$797$	−1615.52	−	7426.42i	−0.0718000	−	0.330059i	−0.999010	+	0.0444821i	$0.985836\pi$
$798$	−1011.21	−	552.165i	−0.0448579	−	0.0244943i
$799$	575.866	−	4005.24i	0.0254977	−	0.177340i
$800$	3960.76	+	558.919i	0.175042	+	0.0247010i
$801$	6600.74	−	949.044i	0.291168	−	0.0418637i
$802$	2282.11	+	496.443i	0.100479	+	0.0218579i
$803$	−1264.60	−	17681.4i	−0.0555748	−	0.777038i
$804$	−2486.57			−0.109073
$805$	18269.0	−	2420.53i	0.799874	−	0.105978i
$806$	7934.27			0.346740
$807$	11.8674	+	165.928i	0.000517662	+	0.00723786i
$808$	1891.23	+	411.412i	0.0823431	+	0.0179127i
$809$	15558.0	−	2236.90i	0.676130	−	0.0972128i	0.204308	−	0.978907i	$-0.434506\pi$
$809$	15558.0	−	2236.90i	0.676130	−	0.0972128i	0.471822	+	0.881694i	$0.343597\pi$
$810$	−3807.79	+	15000.5i	−0.165176	+	0.650696i
$811$	−2517.36	+	17508.6i	−0.108997	+	0.758089i	0.859871	+	0.510511i	$0.170544\pi$
$811$	−2517.36	+	17508.6i	−0.108997	+	0.758089i	−0.968868	+	0.247578i	$0.920365\pi$
$812$	1805.77	+	986.025i	0.0780420	+	0.0426141i
$813$	718.690	+	3303.76i	0.0310031	+	0.142519i
$814$	25185.5	+	11501.8i	1.08446	+	0.495256i
$815$	−3639.72	+	2534.15i	−0.156434	+	0.108917i
$816$	−129.524	+	112.233i	−0.00555668	+	0.00481489i
$817$	570.993	+	40.8382i	0.0244511	+	0.00174877i
$818$	2048.50	+	3751.55i	0.0875601	+	0.160354i
$819$	−6886.01	+	15078.3i	−0.293793	+	0.643317i
$820$	−9772.92	−	4876.03i	−0.416202	−	0.207657i
$821$	32772.3	−	9622.80i	1.39313	−	0.409060i	0.502811	−	0.864397i	$-0.332299\pi$
$821$	32772.3	−	9622.80i	1.39313	−	0.409060i	0.890319	+	0.455337i	$0.150481\pi$
$822$	−1602.31	+	1199.47i	−0.0679888	+	0.0508958i
$823$	7196.20	−	19293.8i	0.304792	−	0.817179i	−0.690770	−	0.723074i	$-0.742729\pi$
$823$	7196.20	−	19293.8i	0.304792	−	0.817179i	0.995562	−	0.0941045i	$-0.0299988\pi$
$824$	1434.15	+	9974.72i	0.0606322	+	0.421706i
$825$	7.17122	+	2746.44i	0.000302630	+	0.115901i
$826$	−1693.46	−	1467.39i	−0.0713353	−	0.0618124i
$827$	−5953.70	−	5953.70i	−0.250339	−	0.250339i	0.570770	−	0.821110i	$-0.306645\pi$
$827$	−5953.70	−	5953.70i	−0.250339	−	0.250339i	−0.821110	+	0.570770i	$0.806645\pi$
$828$	11498.1	+	2221.79i	0.482593	+	0.0932519i
$829$		−	41515.5i		−	1.73932i	−0.493655	−	0.869658i	$-0.664339\pi$
$829$		−	41515.5i		−	1.73932i	0.493655	−	0.869658i	$-0.335661\pi$
$830$	17308.1	−	24997.9i	0.723821	−	1.04541i
$831$	1573.08	−	1010.95i	0.0656671	−	0.0422017i
$832$	2141.25	+	1602.92i	0.0892240	+	0.0667923i
$833$	−1775.25	−	662.134i	−0.0738401	−	0.0275409i
$834$	3847.34	+	553.164i	0.159739	+	0.0229670i
$835$	19032.2	+	7854.31i	0.788787	+	0.325520i
$836$	6224.33	+	4000.14i	0.257504	+	0.165488i
$837$	1201.89	+	3222.39i	0.0496336	+	0.133073i
$838$	−26161.0	+	14285.0i	−1.07842	+	0.588863i
$839$	8329.87	+	9613.18i	0.342764	+	0.395571i	0.900792	−	0.434252i	$-0.142987\pi$
$839$	8329.87	+	9613.18i	0.342764	+	0.395571i	−0.558028	+	0.829822i	$0.688442\pi$
$840$	33.4620	+	903.832i	0.00137446	+	0.0371252i
$841$	−22264.3	−	6537.38i	−0.912882	−	0.268046i
$842$	−21435.4	+	7994.99i	−0.877331	+	0.327228i
$843$	1976.84	−	430.036i	0.0807664	−	0.0175697i
$844$	3619.72	+	12327.6i	0.147626	+	0.502766i
$845$	173.144	−	5032.08i	0.00704890	−	0.204863i
$846$	−5637.13	−	12343.6i	−0.229088	−	0.501633i
$847$	−2478.51	+	3310.90i	−0.100546	+	0.134314i
$848$	−2375.09	+	10918.1i	−0.0961802	+	0.442133i
$849$	−774.967	+	894.360i	−0.0313272	+	0.0361535i
$850$	3864.67	−	851.282i	0.155949	−	0.0343514i
$851$	42313.0	−	20529.4i	1.70443	−	0.826954i
$852$	1087.89	−	1087.89i	0.0437449	−	0.0437449i
$853$	−17556.8	+	1255.68i	−0.704727	+	0.0504030i	−0.419103	−	0.907939i	$-0.637655\pi$
$853$	−17556.8	+	1255.68i	−0.704727	+	0.0504030i	−0.285624	+	0.958342i	$0.592201\pi$
$854$	2091.62	+	3254.63i	0.0838102	+	0.130411i
$855$	4202.22	+	16374.9i	0.168085	+	0.654982i
$856$	−3506.58	+	1601.40i	−0.140015	+	0.0639425i
$857$	−13099.0	−	17498.3i	−0.522117	−	0.697467i	0.459532	−	0.888161i	$-0.348017\pi$
$857$	−13099.0	−	17498.3i	−0.522117	−	0.697467i	−0.981649	+	0.190694i	$0.938926\pi$
$858$	−880.147	+	1611.87i	−0.0350206	+	0.0641355i
$859$	−9482.79	+	14755.5i	−0.376657	+	0.586090i	−0.976892	−	0.213734i	$-0.931438\pi$
$859$	−9482.79	+	14755.5i	−0.376657	+	0.586090i	0.600235	+	0.799824i	$0.295074\pi$
$860$	−201.676	−	401.586i	−0.00799661	−	0.0159232i
$861$	695.755	−	2369.52i	0.0275392	−	0.0937899i
$862$	944.120	−	13200.5i	0.0373050	−	0.521591i
$863$	−1718.91	+	24033.5i	−0.0678010	+	0.947982i	0.843734	+	0.536761i	$0.180352\pi$
$863$	−1718.91	+	24033.5i	−0.0678010	+	0.947982i	−0.911535	+	0.411221i	$0.865102\pi$
$864$	−326.644	+	1112.45i	−0.0128619	+	0.0438035i
$865$	11608.5	+	23115.4i	0.456303	+	0.908611i
$866$	−17876.7	+	27816.7i	−0.701474	+	1.09151i
$867$	1512.05	−	2769.11i	0.0592295	−	0.108471i
$868$	−3400.24	−	4542.19i	−0.132963	−	0.177617i
$869$	9450.04	−	4315.69i	0.368896	−	0.168469i
$870$	129.464	+	504.484i	0.00504509	+	0.0196593i
$871$	20756.8	+	32298.2i	0.807482	+	1.25647i
$872$	17275.2	−	1235.54i	0.670884	−	0.0479826i
$873$	12120.7	−	12120.7i	0.469900	−	0.469900i
$874$	11972.9	−	3820.99i	0.463374	−	0.147880i
$875$	9274.80	−	18711.4i	0.358338	−	0.722927i
$876$	967.735	−	1116.83i	0.0373251	−	0.0430754i
$877$	−3464.14	+	15924.4i	−0.133382	+	0.613146i	0.861118	+	0.508405i	$0.169765\pi$
$877$	−3464.14	+	15924.4i	−0.133382	+	0.613146i	−0.994500	+	0.104741i	$0.966599\pi$
$878$	−6386.11	+	8530.84i	−0.245468	+	0.327907i
$879$	−1956.54	−	4284.23i	−0.0750768	−	0.164395i
$880$	199.731	−	5804.79i	0.00765105	−	0.222363i
$881$	12035.0	+	40987.6i	0.460239	+	1.56743i	0.783669	+	0.621179i	$0.213346\pi$
$881$	12035.0	+	40987.6i	0.460239	+	1.56743i	−0.323430	+	0.946252i	$0.604836\pi$
$882$	−6208.80	+	1350.64i	−0.237031	+	0.0515629i
$883$	−21610.9	+	8060.46i	−0.823631	+	0.307198i	−0.725714	−	0.687996i	$-0.758491\pi$
$883$	−21610.9	+	8060.46i	−0.823631	+	0.307198i	−0.0979165	+	0.995195i	$0.531218\pi$
$884$	2539.02	+	745.522i	0.0966022	+	0.0283650i
$885$	−20.9862	−	566.851i	−0.000797110	−	0.0215305i
$886$	22322.8	+	25761.9i	0.846443	+	0.976847i
$887$	4986.84	−	2723.02i	0.188773	−	0.103078i	−0.382083	−	0.924128i	$-0.624793\pi$
$887$	4986.84	−	2723.02i	0.188773	−	0.103078i	0.570856	+	0.821050i	$0.306611\pi$
$888$	806.624	+	2162.64i	0.0304826	+	0.0817269i
$889$	−8118.56	−	5217.48i	−0.306285	−	0.196838i
$890$	−5193.21	−	2143.16i	−0.195592	−	0.0807178i
$891$	22243.6	+	3198.15i	0.836352	+	0.120249i
$892$	−5153.54	−	1922.17i	−0.193445	−	0.0721514i
$893$	−11658.2	−	8727.23i	−0.436873	−	0.327039i
$894$	972.416	−	624.934i	0.0363786	−	0.0233791i
$895$	4744.44	−	6852.38i	0.177195	−	0.255921i
$896$		−	1912.75i		−	0.0713174i
$897$	1158.02	+	2896.61i	0.0431050	+	0.107821i
$898$	4164.43	+	4164.43i	0.154754	+	0.154754i
$899$	−2469.28	−	2139.65i	−0.0916076	−	0.0793784i
$900$	9359.51	−	9408.51i	0.346649	−	0.348464i
$901$	1573.18	+	10941.7i	0.0581689	+	0.404573i
$902$	−5542.17	+	14859.1i	−0.204583	+	0.548509i
$903$	81.3438	−	60.8932i	0.00299773	−	0.00224408i
$904$	−7775.54	+	2283.11i	−0.286074	+	0.0839988i
$905$	42045.5	+	20977.9i	1.54435	+	0.770529i
$906$	593.713	−	1300.05i	0.0217713	−	0.0476725i
$907$	595.295	+	1090.20i	0.0217932	+	0.0399113i	0.888349	−	0.459169i	$-0.151853\pi$
$907$	595.295	+	1090.20i	0.0217932	+	0.0399113i	−0.866555	+	0.499081i	$0.833671\pi$
$908$	64.3187	+	4.60017i	0.00235076	+	0.000168130i
$909$	4852.97	−	4205.12i	0.177077	−	0.153438i
$910$	11460.6	−	7979.42i	0.417489	−	0.290676i
$911$	18704.1	+	8541.86i	0.680234	+	0.310652i	0.725401	−	0.688327i	$-0.241655\pi$
$911$	18704.1	+	8541.86i	0.680234	+	0.310652i	−0.0451665	+	0.998979i	$0.514382\pi$
$912$	131.112	+	602.712i	0.00476047	+	0.0218835i
$913$	−38749.4	−	21158.8i	−1.40462	−	0.766980i
$914$	−69.8827	+	486.045i	−0.00252901	+	0.0175896i
$915$	−240.964	+	949.259i	−0.00870605	+	0.0342968i
$916$	−14263.9	+	2050.84i	−0.514511	+	0.0739755i
$917$	−22459.1	−	4885.68i	−0.808794	−	0.175942i
$918$	81.8289	+	1144.12i	0.00294200	+	0.0411345i
$919$	−27142.2			−0.974254			−0.487127	−	0.873331i	$-0.661955\pi$
$919$	−27142.2			−0.974254			−0.487127	+	0.873331i	$0.661955\pi$
$920$	−7384.15	−	6542.96i	−0.264618	−	0.234473i
$921$	−436.702			−0.0156241
$922$	−2124.34	−	29702.2i	−0.0758802	−	1.06094i
$923$	−23212.0	−	5049.46i	−0.827770	−	0.180070i
$924$	1299.95	−	186.904i	0.0462825	−	0.00665442i
$925$	7447.06	−	52773.3i	0.264711	−	1.87587i
$926$	−2756.05	+	19168.8i	−0.0978072	+	0.680264i
$927$	29344.4	+	16023.2i	1.03969	+	0.567715i
$928$	−234.132	−	1076.29i	−0.00828208	−	0.0380721i
$929$	32544.8	+	14862.7i	1.14937	+	0.524897i	0.896692	−	0.442654i	$-0.145963\pi$
$929$	32544.8	+	14862.7i	1.14937	+	0.524897i	0.252673	+	0.967552i	$0.418690\pi$
$930$	253.178	−	1413.83i	0.00892691	−	0.0498509i
$931$	−5153.45	+	4465.49i	−0.181415	+	0.157197i
$932$	20917.6	+	1496.06i	0.735170	+	0.0525804i
$933$	−916.738	−	1678.88i	−0.0321679	−	0.0589111i
$934$	851.937	−	1865.48i	0.0298461	−	0.0653538i
$935$	−1821.78	−	5449.81i	−0.0637203	−	0.190618i
$936$	8514.71	−	2500.14i	0.297342	−	0.0873074i
$937$	−17748.8	+	13286.6i	−0.618814	+	0.463238i	−0.862115	−	0.506713i	$-0.830861\pi$
$937$	−17748.8	+	13286.6i	−0.618814	+	0.463238i	0.243301	+	0.969951i	$0.421770\pi$
$938$	9594.64	−	25724.2i	0.333983	−	0.895443i
$939$	−572.347	−	3980.76i	−0.0198912	−	0.138346i
$940$	−1207.19	+	11368.2i	−0.0418876	+	0.394456i
$941$	−38048.8	−	32969.5i	−1.31813	−	1.14216i	−0.979545	−	0.201225i	$-0.935508\pi$
$941$	−38048.8	−	32969.5i	−1.31813	−	1.14216i	−0.338580	−	0.940937i	$-0.609947\pi$
$942$	602.909	+	602.909i	0.0208533	+	0.0208533i
$943$	13458.0	+	23335.7i	0.464743	+	0.805850i
$944$			1199.61i			0.0413601i
$945$	4976.79	+	3445.82i	0.171317	+	0.118617i
$946$	−548.942	+	352.783i	−0.0188664	+	0.0121247i
$947$	−24384.9	−	18254.3i	−0.836750	−	0.626383i	0.0925505	−	0.995708i	$-0.470498\pi$
$947$	−24384.9	−	18254.3i	−0.836750	−	0.626383i	−0.929300	+	0.369325i	$0.879589\pi$
$948$	811.462	+	302.660i	0.0278007	+	0.0103691i
$949$	−22584.7	−	3247.19i	−0.772531	−	0.111073i
$950$	3976.80	−	13675.7i	0.135815	−	0.467052i
$951$	3709.53	+	2383.97i	0.126488	+	0.0812886i
$952$	−661.303	−	1773.02i	−0.0225136	−	0.0603613i
$953$	28813.9	−	15733.6i	0.979406	−	0.534796i	0.0919869	−	0.995760i	$-0.470678\pi$
$953$	28813.9	−	15733.6i	0.979406	−	0.534796i	0.887419	+	0.460964i	$0.152496\pi$
$954$	24276.2	+	28016.2i	0.823869	+	0.950796i
$955$	1258.16	+	1168.32i	0.0426315	+	0.0395875i
$956$	−998.124	−	293.076i	−0.0337674	−	0.00991501i
$957$	708.592	−	264.291i	0.0239347	−	0.00892719i
$958$	31439.2	−	6839.17i	1.06028	−	0.230651i
$959$	−6226.21	−	21204.5i	−0.209650	−	0.714004i
$960$	353.954	−	330.407i	0.0118998	−	0.0111082i
$961$	−8632.54	−	18902.6i	−0.289770	−	0.634508i
$962$	21357.3	−	28530.1i	0.715788	−	0.956181i
$963$	−2718.67	+	12497.5i	−0.0909738	+	0.418200i
$964$	4299.50	−	4961.89i	0.143649	−	0.165780i
$965$	29868.4	−	37163.6i	0.996370	−	1.23973i
$966$	1161.97	−	1904.29i	0.0387018	−	0.0634259i
$967$	−16350.2	+	16350.2i	−0.543729	+	0.543729i	−0.924620	−	0.380891i	$-0.875617\pi$
$967$	−16350.2	+	16350.2i	−0.543729	+	0.543729i	0.380891	+	0.924620i	$0.375617\pi$
$968$	2208.49	−	157.955i	0.0733303	−	0.00524468i
$969$	329.913	+	513.355i	0.0109374	+	0.0170189i
$970$	−13987.6	+	3589.57i	−0.463004	+	0.118819i
$971$	49595.1	−	22649.3i	1.63912	−	0.748559i	0.639323	−	0.768938i	$-0.279215\pi$
$971$	49595.1	−	22649.3i	1.63912	−	0.748559i	0.999792	+	0.0203791i	$0.00648732\pi$
$972$	3467.68	+	4632.27i	0.114430	+	0.152860i
$973$	−20567.9	+	37667.3i	−0.677674	+	1.24107i
$974$	−13132.7	+	20434.9i	−0.432031	+	0.672254i
$975$	3456.29	+	742.424i	0.113528	+	0.0243863i
$976$	583.518	−	1987.28i	0.0191373	−	0.0651755i
$977$	−235.716	+	3295.74i	−0.00771874	+	0.107922i	−0.999851	−	0.0172736i	$-0.994501\pi$
$977$	−235.716	+	3295.74i	−0.00771874	+	0.107922i	0.992132	+	0.125196i	$0.0399559\pi$
$978$	−38.2994	+	535.495i	−0.00125223	+	0.0175084i
$979$	−2298.30	+	7827.29i	−0.0750296	+	0.255527i
$980$	5081.27	+	1683.84i	0.165628	+	0.0548862i
$981$	31065.9	−	48339.5i	1.01107	−	1.57325i
$982$	−19812.3	+	36283.5i	−0.643825	+	1.17908i
$983$	−29033.8	−	38784.6i	−0.942049	−	1.25843i	−0.965953	−	0.258717i	$-0.916700\pi$
$983$	−29033.8	−	38784.6i	−0.942049	−	1.25843i	0.0239038	−	0.999714i	$-0.492390\pi$
$984$	−1202.62	+	549.217i	−0.0389614	+	0.0177931i
$985$	−4628.83	+	7824.73i	−0.149733	+	0.253113i
$986$	−589.140	−	916.720i	−0.0190284	−	0.0296088i
$987$	−2578.35	+	184.408i	−0.0831509	+	0.00594707i
$988$	6734.19	−	6734.19i	0.216845	−	0.216845i
$989$	−132.114	+	1100.49i	−0.00424771	+	0.0353827i
$990$	−15020.4	−	12071.9i	−0.482202	−	0.387546i
$991$	−26283.4	+	30332.6i	−0.842502	+	0.972299i	−0.999884	−	0.0152387i	$-0.995149\pi$
$991$	−26283.4	+	30332.6i	−0.842502	+	0.972299i	0.157382	+	0.987538i	$0.449695\pi$
$992$	−645.678	+	2968.14i	−0.0206656	+	0.0949984i
$993$	4533.20	−	6055.65i	0.144871	−	0.193525i
$994$	7056.82	+	15452.3i	0.225180	+	0.493075i
$995$	48059.0	+	1653.61i	1.53123	+	0.0526864i
$996$	−1036.93	−	3531.46i	−0.0329884	−	0.112348i
$997$	−22282.7	+	4847.32i	−0.707825	+	0.153978i	−0.552046	−	0.833814i	$-0.686153\pi$
$997$	−22282.7	+	4847.32i	−0.707825	+	0.153978i	−0.155780	+	0.987792i	$0.549789\pi$
$998$	−9212.76	+	3436.18i	−0.292209	+	0.108988i
$999$	14822.3	+	4352.22i	0.469426	+	0.137836i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.4.l.a.53.27	yes	720
5.2	odd	4	inner	230.4.l.a.7.9	✓	720
23.10	odd	22	inner	230.4.l.a.33.9	yes	720
115.102	even	44	inner	230.4.l.a.217.27	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.l.a.7.9	✓	720	5.2	odd	4	inner
230.4.l.a.33.9	yes	720	23.10	odd	22	inner
230.4.l.a.53.27	yes	720	1.1	even	1	trivial
230.4.l.a.217.27	yes	720	115.102	even	44	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+(0.142678 + 1.99490i) q^{2} +(-0.661230 - 0.143842i) q^{3} +(-3.95929 + 0.569259i) q^{4} +(9.60780 - 5.71754i) q^{5} +(0.192607 - 1.33961i) q^{6} +(13.1154 + 7.16158i) q^{7} +(-1.70052 - 7.81717i) q^{8} +(-24.1435 - 11.0260i) q^{9} +(12.7768 + 18.3509i) q^{10} +(24.5384 - 21.2626i) q^{11} +(2.69988 + 0.193099i) q^{12} +(-20.0292 - 36.6808i) q^{13} +(-12.4154 + 27.1859i) q^{14} +(-7.17538 + 2.39861i) q^{15} +(15.3519 - 4.50772i) q^{16} +(12.6720 - 9.48612i) q^{17} +(18.5510 - 49.7372i) q^{18} +(-8.10752 - 56.3890i) q^{19} +(-34.7852 + 28.1067i) q^{20} +(-7.64219 - 6.62200i) q^{21} +(45.9180 + 45.9180i) q^{22} +(109.810 - 10.4325i) q^{23} +5.41355i q^{24} +(59.6195 - 109.866i) q^{25} +(70.3169 - 45.1899i) q^{26} +(29.0049 + 21.7128i) q^{27} +(-56.0046 - 20.8886i) q^{28} +(-34.0703 - 4.89857i) q^{29} +(-5.80876 - 13.9720i) q^{30} +(79.8548 + 51.3195i) q^{31} +(11.1829 + 29.9824i) q^{32} +(-19.2840 + 10.5298i) q^{33} +(20.7319 + 23.9259i) q^{34} +(166.957 - 6.18115i) q^{35} +(101.868 + 29.9111i) q^{36} +(399.487 - 149.001i) q^{37} +(111.334 - 24.2192i) q^{38} +(7.96769 + 27.1355i) q^{39} +(-61.0333 - 65.3830i) q^{40} +(101.452 + 222.149i) q^{41} +(12.1199 - 16.1903i) q^{42} +(-2.13596 + 9.81886i) q^{43} +(-85.0506 + 98.1536i) q^{44} +(-295.008 + 32.1063i) q^{45} +(36.4793 + 217.571i) q^{46} +(180.757 - 180.757i) q^{47} +(-10.7995 + 0.772397i) q^{48} +(-64.7130 - 100.695i) q^{49} +(227.678 + 103.260i) q^{50} +(-9.74359 + 4.44975i) q^{51} +(100.182 + 133.828i) q^{52} +(-334.679 + 612.918i) q^{53} +(-39.1766 + 60.9600i) q^{54} +(114.190 - 344.586i) q^{55} +(33.6802 - 114.704i) q^{56} +(-2.75016 + 38.4523i) q^{57} +(4.91108 - 68.6659i) q^{58} +(-21.1230 + 71.9384i) q^{59} +(27.0440 - 13.5814i) q^{60} +(69.9852 - 108.899i) q^{61} +(-90.9840 + 166.625i) q^{62} +(-237.690 - 317.516i) q^{63} +(-58.2164 + 26.5866i) q^{64} +(-402.161 - 237.904i) q^{65} +(-23.7574 - 36.9673i) q^{66} +(-916.306 + 65.5355i) q^{67} +(-44.7719 + 44.7719i) q^{68} +(-74.1100 - 8.89694i) q^{69} +(36.1520 + 332.182i) q^{70} +(372.219 - 429.563i) q^{71} +(-45.1354 + 207.484i) q^{72} +(327.177 - 437.058i) q^{73} +(354.240 + 775.678i) q^{74} +(-55.2255 + 64.0708i) q^{75} +(64.1999 + 218.645i) q^{76} +(474.106 - 103.135i) q^{77} +(-52.9958 + 19.7664i) q^{78} +(307.002 + 90.1439i) q^{79} +(121.725 - 131.084i) q^{80} +(453.241 + 523.068i) q^{81} +(-428.691 + 234.083i) q^{82} +(-475.186 - 1274.02i) q^{83} +(34.0272 + 21.8680i) q^{84} +(67.5125 - 163.593i) q^{85} +(-19.8924 - 2.86010i) q^{86} +(21.8237 + 8.13981i) q^{87} +(-207.942 - 155.663i) q^{88} +(-211.363 + 135.834i) q^{89} +(-106.140 - 583.931i) q^{90} -624.526i q^{91} +(-428.829 + 103.815i) q^{92} +(-45.4204 - 45.4204i) q^{93} +(386.383 + 334.803i) q^{94} +(-400.302 - 495.419i) q^{95} +(-3.08172 - 21.4338i) q^{96} +(-225.689 + 605.095i) q^{97} +(191.645 - 143.463i) q^{98} +(-826.885 + 242.795i) 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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