LMFDB - Embedded newform 231.4.u.a.20.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [231,4,Mod(20,231)] 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("231.20"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(231, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 5, 6])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	231.u (of order $10$, degree $4$, 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:	$13.6294412113$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$92$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			20.2
Character	$\chi$	$=$	231.20
Dual form			231.4.u.a.104.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-5.23865 - 1.70214i) q^{2} +(5.19044 + 0.243508i) q^{3} +(18.0740 + 13.1315i) q^{4} +(3.51328 + 10.8128i) q^{5} +(-26.7764 - 10.1105i) q^{6} +(1.98968 + 18.4131i) q^{7} +(-46.4303 - 63.9058i) q^{8} +(26.8814 + 2.52783i) q^{9} -62.6244i q^{10} +(36.4742 - 0.793165i) q^{11} +(90.6144 + 72.5596i) q^{12} +(61.2668 + 19.9068i) q^{13} +(20.9184 - 99.8463i) q^{14} +(15.6025 + 56.9786i) q^{15} +(79.2260 + 243.832i) q^{16} +(-22.9593 - 70.6614i) q^{17} +(-136.519 - 58.9983i) q^{18} +(-44.9190 - 61.8257i) q^{19} +(-78.4891 + 241.565i) q^{20} +(5.84358 + 96.0565i) q^{21} +(-192.426 - 57.9291i) q^{22} +87.5177i q^{23} +(-225.432 - 343.005i) q^{24} +(-3.44574 + 2.50348i) q^{25} +(-287.071 - 208.569i) q^{26} +(138.911 + 19.6664i) q^{27} +(-205.830 + 358.925i) q^{28} +(-120.023 + 165.197i) q^{29} +(15.2495 - 325.048i) q^{30} +(-11.6382 - 3.78147i) q^{31} -780.270i q^{32} +(189.511 + 4.76490i) q^{33} +409.250i q^{34} +(-192.106 + 86.2042i) q^{35} +(452.660 + 398.682i) q^{36} +(-39.5701 - 28.7493i) q^{37} +(130.079 + 400.341i) q^{38} +(313.154 + 118.244i) q^{39} +(527.876 - 726.559i) q^{40} +(-132.224 + 96.0665i) q^{41} +(132.889 - 513.153i) q^{42} +252.173 q^{43} +(669.651 + 464.627i) q^{44} +(67.1091 + 299.543i) q^{45} +(148.967 - 458.474i) q^{46} +(-69.7013 + 50.6409i) q^{47} +(351.843 + 1284.89i) q^{48} +(-335.082 + 73.2722i) q^{49} +(22.3123 - 7.24969i) q^{50} +(-101.962 - 372.355i) q^{51} +(845.929 + 1164.32i) q^{52} +(213.123 + 69.2479i) q^{53} +(-694.230 - 339.471i) q^{54} +(136.721 + 391.601i) q^{55} +(1084.32 - 982.076i) q^{56} +(-218.094 - 331.841i) q^{57} +(909.947 - 661.115i) q^{58} +(-317.968 - 231.017i) q^{59} +(-466.216 + 1234.72i) q^{60} +(77.7467 - 25.2614i) q^{61} +(54.5317 + 39.6196i) q^{62} +(6.94020 + 499.999i) q^{63} +(-694.321 + 2136.90i) q^{64} +732.402i q^{65} +(-984.669 - 347.535i) q^{66} +80.9414 q^{67} +(512.926 - 1578.62i) q^{68} +(-21.3113 + 454.256i) q^{69} +(1153.11 - 124.602i) q^{70} +(566.163 - 183.958i) q^{71} +(-1086.57 - 1835.25i) q^{72} +(503.012 - 692.337i) q^{73} +(158.358 + 217.961i) q^{74} +(-18.4945 + 12.1551i) q^{75} -1707.29i q^{76} +(87.1766 + 670.025i) q^{77} +(-1439.24 - 1152.47i) q^{78} +(-210.755 + 648.639i) q^{79} +(-2358.16 + 1713.30i) q^{80} +(716.220 + 135.903i) q^{81} +(856.194 - 278.194i) q^{82} +(-50.3375 - 154.923i) q^{83} +(-1155.75 + 1812.86i) q^{84} +(683.383 - 496.507i) q^{85} +(-1321.05 - 429.234i) q^{86} +(-663.199 + 828.221i) q^{87} +(-1744.20 - 2294.09i) q^{88} -340.730 q^{89} +(158.304 - 1683.43i) q^{90} +(-244.644 + 1167.72i) q^{91} +(-1149.24 + 1581.79i) q^{92} +(-59.4865 - 22.4615i) q^{93} +(451.338 - 146.649i) q^{94} +(510.694 - 702.910i) q^{95} +(190.002 - 4049.95i) q^{96} +(-1508.77 - 490.228i) q^{97} +(1880.10 + 186.510i) q^{98} +(982.484 + 70.8794i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q + 340 q^{4} - 18 q^{7} + 42 q^{9} + 42 q^{15} - 1116 q^{16} - 262 q^{18} - 222 q^{21} + 696 q^{22} - 1516 q^{25} + 38 q^{28} + 624 q^{30} + 1430 q^{36} + 36 q^{37} + 390 q^{39} + 2130 q^{42} - 1376 q^{43}+ \cdots - 6218 q^{99}+O(q^{100}) $ 368 * q + 340 * q^4 - 18 * q^7 + 42 * q^9 + 42 * q^15 - 1116 * q^16 - 262 * q^18 - 222 * q^21 + 696 * q^22 - 1516 * q^25 + 38 * q^28 + 624 * q^30 + 1430 * q^36 + 36 * q^37 + 390 * q^39 + 2130 * q^42 - 1376 * q^43 + 1716 * q^46 + 474 * q^49 + 782 * q^51 + 670 * q^57 + 5576 * q^58 - 2708 * q^60 - 739 * q^63 + 5256 * q^64 - 2432 * q^67 + 2280 * q^70 - 3706 * q^72 - 10900 * q^78 + 732 * q^79 - 262 * q^81 - 510 * q^84 + 8008 * q^85 - 832 * q^88 - 5446 * q^91 + 2510 * q^93 - 6218 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−5.23865	−	1.70214i	−1.85214	−	0.601797i	−0.996438	−	0.0843295i	$-0.973125\pi$
$2$	−5.23865	−	1.70214i	−1.85214	−	0.601797i	−0.855703	−	0.517467i	$-0.826875\pi$
$3$	5.19044	+	0.243508i	0.998901	+	0.0468632i
$3$	5.19044	+	0.243508i	0.998901	+	0.0468632i
$4$	18.0740	+	13.1315i	2.25925	+	1.64144i
$5$	3.51328	+	10.8128i	0.314238	+	0.967124i	0.976067	+	0.217469i	$0.0697802\pi$
$5$	3.51328	+	10.8128i	0.314238	+	0.967124i	−0.661830	+	0.749654i	$0.730220\pi$
$6$	−26.7764	−	10.1105i	−1.82190	−	0.687933i
$7$	1.98968	+	18.4131i	0.107433	+	0.994212i
$7$	1.98968	+	18.4131i	0.107433	+	0.994212i
$8$	−46.4303	−	63.9058i	−2.05195	−	2.82426i
$9$	26.8814	+	2.52783i	0.995608	+	0.0936234i
$10$		−	62.6244i		−	1.98036i
$11$	36.4742	−	0.793165i	0.999764	−	0.0217408i
$11$	36.4742	−	0.793165i	0.999764	−	0.0217408i
$12$	90.6144	+	72.5596i	2.17984	+	1.74551i
$13$	61.2668	+	19.9068i	1.30710	+	0.424704i	0.878047	−	0.478574i	$-0.158846\pi$
$13$	61.2668	+	19.9068i	1.30710	+	0.424704i	0.429057	+	0.903278i	$0.358846\pi$
$14$	20.9184	−	99.8463i	0.399334	−	1.90607i
$15$	15.6025	+	56.9786i	0.268570	+	0.980787i
$16$	79.2260	+	243.832i	1.23791	+	3.80988i
$17$	−22.9593	−	70.6614i	−0.327555	−	1.00811i	−0.970274	−	0.242009i	$-0.922194\pi$
$17$	−22.9593	−	70.6614i	−0.327555	−	1.00811i	0.642719	−	0.766102i	$-0.277806\pi$
$18$	−136.519	−	58.9983i	−1.78766	−	0.772557i
$19$	−44.9190	−	61.8257i	−0.542375	−	0.746515i	0.446578	−	0.894745i	$-0.352642\pi$
$19$	−44.9190	−	61.8257i	−0.542375	−	0.746515i	−0.988953	+	0.148230i	$0.952642\pi$
$20$	−78.4891	+	241.565i	−0.877535	+	2.70078i
$21$	5.84358	+	96.0565i	0.0607225	+	0.998155i
$22$	−192.426	−	57.9291i	−1.86479	−	0.561388i
$23$			87.5177i			0.793422i	0.917944	+	0.396711i	$0.129848\pi$
$23$			87.5177i			0.793422i	−0.917944	+	0.396711i	$0.870152\pi$
$24$	−225.432	−	343.005i	−1.91734	−	2.91732i
$25$	−3.44574	+	2.50348i	−0.0275659	+	0.0200278i
$26$	−287.071	−	208.569i	−2.16536	−	1.57322i
$27$	138.911	+	19.6664i	0.990126	+	0.140178i
$28$	−205.830	+	358.925i	−1.38922	+	2.42252i
$29$	−120.023	+	165.197i	−0.768541	+	1.05781i	0.227914	+	0.973681i	$0.426810\pi$
$29$	−120.023	+	165.197i	−0.768541	+	1.05781i	−0.996455	+	0.0841252i	$0.973190\pi$
$30$	15.2495	−	325.048i	0.0928058	−	1.97818i
$31$	−11.6382	−	3.78147i	−0.0674283	−	0.0219088i	0.275109	−	0.961413i	$-0.411286\pi$
$31$	−11.6382	−	3.78147i	−0.0674283	−	0.0219088i	−0.342537	+	0.939504i	$0.611286\pi$
$32$		−	780.270i		−	4.31042i
$33$	189.511	+	4.76490i	0.999684	+	0.0251352i
$34$			409.250i			2.06429i
$35$	−192.106	+	86.2042i	−0.927767	+	0.416319i
$36$	452.660	+	398.682i	2.09565	+	1.84575i
$37$	−39.5701	−	28.7493i	−0.175818	−	0.127740i	0.496396	−	0.868096i	$-0.334657\pi$
$37$	−39.5701	−	28.7493i	−0.175818	−	0.127740i	−0.672214	+	0.740357i	$0.734657\pi$
$38$	130.079	+	400.341i	0.555304	+	1.70905i
$39$	313.154	+	118.244i	1.28576	+	0.485492i
$40$	527.876	−	726.559i	2.08661	−	2.87198i
$41$	−132.224	+	96.0665i	−0.503657	+	0.365929i	−0.810412	−	0.585860i	$-0.800757\pi$
$41$	−132.224	+	96.0665i	−0.503657	+	0.365929i	0.306755	+	0.951789i	$0.400757\pi$
$42$	132.889	−	513.153i	0.488220	−	1.88527i
$43$	252.173			0.894327			0.447163	−	0.894452i	$-0.352434\pi$
$43$	252.173			0.894327			0.447163	+	0.894452i	$0.352434\pi$
$44$	669.651	+	464.627i	2.29440	+	1.59193i
$45$	67.1091	+	299.543i	0.222312	+	0.992296i
$46$	148.967	−	458.474i	0.477479	−	1.46953i
$47$	−69.7013	+	50.6409i	−0.216319	+	0.157165i	−0.690668	−	0.723172i	$-0.742683\pi$
$47$	−69.7013	+	50.6409i	−0.216319	+	0.157165i	0.474349	+	0.880337i	$0.342683\pi$
$48$	351.843	+	1284.89i	1.05800	+	3.86371i
$49$	−335.082	+	73.2722i	−0.976917	+	0.213621i
$50$	22.3123	−	7.24969i	0.0631086	−	0.0205052i
$51$	−101.962	−	372.355i	−0.279952	−	1.02235i
$52$	845.929	+	1164.32i	2.25595	+	3.10504i
$53$	213.123	+	69.2479i	0.552353	+	0.179470i	0.571878	−	0.820339i	$-0.306215\pi$
$53$	213.123	+	69.2479i	0.552353	+	0.179470i	−0.0195244	+	0.999809i	$0.506215\pi$
$54$	−694.230	−	339.471i	−1.74949	−	0.855484i
$55$	136.721	+	391.601i	0.335189	+	0.960063i
$56$	1084.32	−	982.076i	2.58747	−	2.34349i
$57$	−218.094	−	331.841i	−0.506795	−	0.771112i
$58$	909.947	−	661.115i	2.06003	−	1.49670i
$59$	−317.968	−	231.017i	−0.701625	−	0.509760i	0.178836	−	0.983879i	$-0.442767\pi$
$59$	−317.968	−	231.017i	−0.701625	−	0.509760i	−0.880461	+	0.474119i	$0.842767\pi$
$60$	−466.216	+	1234.72i	−1.00314	+	2.65668i
$61$	77.7467	−	25.2614i	0.163188	−	0.0530229i	−0.226284	−	0.974061i	$-0.572658\pi$
$61$	77.7467	−	25.2614i	0.163188	−	0.0530229i	0.389471	+	0.921039i	$0.372658\pi$
$62$	54.5317	+	39.6196i	0.111702	+	0.0811563i
$63$	6.94020	+	499.999i	0.0138791	+	0.999904i
$64$	−694.321	+	2136.90i	−1.35610	+	4.17363i
$65$			732.402i			1.39759i
$66$	−984.669	−	347.535i	−1.83643	−	0.648161i
$67$	80.9414			0.147590			0.0737952	−	0.997273i	$-0.476489\pi$
$67$	80.9414			0.147590			0.0737952	+	0.997273i	$0.476489\pi$
$68$	512.926	−	1578.62i	0.914726	−	2.81524i
$69$	−21.3113	+	454.256i	−0.0371823	+	0.792550i
$70$	1153.11	−	124.602i	1.96889	−	0.212755i
$71$	566.163	−	183.958i	0.946355	−	0.307489i	0.205121	−	0.978737i	$-0.434241\pi$
$71$	566.163	−	183.958i	0.946355	−	0.307489i	0.741234	+	0.671247i	$0.234241\pi$
$72$	−1086.57	−	1835.25i	−1.77852	−	3.00397i
$73$	503.012	−	692.337i	0.806481	−	1.11003i	−0.185375	−	0.982668i	$-0.559350\pi$
$73$	503.012	−	692.337i	0.806481	−	1.11003i	0.991857	−	0.127359i	$-0.0406499\pi$
$74$	158.358	+	217.961i	0.248767	+	0.342399i
$75$	−18.4945	+	12.1551i	−0.0284742	+	0.0187140i
$76$		−	1707.29i		−	2.57684i
$77$	87.1766	+	670.025i	0.129022	+	0.991642i
$78$	−1439.24	−	1152.47i	−2.08925	−	1.67297i
$79$	−210.755	+	648.639i	−0.300150	+	0.923766i	0.681293	+	0.732011i	$0.261418\pi$
$79$	−210.755	+	648.639i	−0.300150	+	0.923766i	−0.981443	+	0.191755i	$0.938582\pi$
$80$	−2358.16	+	1713.30i	−3.29563	+	2.39442i
$81$	716.220	+	135.903i	0.982469	+	0.186424i
$82$	856.194	−	278.194i	1.15306	−	0.374652i
$83$	−50.3375	−	154.923i	−0.0665693	−	0.204879i	0.912239	−	0.409659i	$-0.134352\pi$
$83$	−50.3375	−	154.923i	−0.0665693	−	0.204879i	−0.978808	+	0.204780i	$0.934352\pi$
$84$	−1155.75	+	1812.86i	−1.50122	+	2.35475i
$85$	683.383	−	496.507i	0.872038	−	0.633573i
$86$	−1321.05	−	429.234i	−1.65642	−	0.538203i
$87$	−663.199	+	828.221i	−0.817269	+	1.02063i
$88$	−1744.20	−	2294.09i	−2.11286	−	2.77898i
$89$	−340.730			−0.405813			−0.202906	−	0.979198i	$-0.565039\pi$
$89$	−340.730			−0.405813			−0.202906	+	0.979198i	$0.565039\pi$
$90$	158.304	−	1683.43i	0.185408	−	1.97166i
$91$	−244.644	+	1167.72i	−0.281820	+	1.34517i
$92$	−1149.24	+	1581.79i	−1.30235	+	1.79254i
$93$	−59.4865	−	22.4615i	−0.0663275	−	0.0250446i
$94$	451.338	−	146.649i	0.495234	−	0.160911i
$95$	510.694	−	702.910i	0.551538	−	0.759126i
$96$	190.002	−	4049.95i	0.202000	−	4.30569i
$97$	−1508.77	−	490.228i	−1.57930	−	0.513146i	−0.617423	−	0.786631i	$-0.711823\pi$
$97$	−1508.77	−	490.228i	−1.57930	−	0.513146i	−0.961876	+	0.273486i	$0.911823\pi$
$98$	1880.10	+	186.510i	1.93794	+	0.192248i
$99$	982.484	+	70.8794i	0.997408	+	0.0719560i
$100$	−95.1527			−0.0951527
$101$	−480.399	+	1478.52i	−0.473282	+	1.45661i	0.374978	+	0.927034i	$0.377650\pi$
$101$	−480.399	+	1478.52i	−0.473282	+	1.45661i	−0.848260	+	0.529579i	$0.822350\pi$
$102$	−99.6557	+	2124.19i	−0.0967390	+	2.06202i
$103$	−234.624	+	322.932i	−0.224448	+	0.308927i	−0.906359	−	0.422509i	$-0.861149\pi$
$103$	−234.624	+	322.932i	−0.224448	+	0.308927i	0.681910	+	0.731436i	$0.261149\pi$
$104$	−1572.47	−	4839.58i	−1.48263	−	4.56307i
$105$	−1018.11	+	400.659i	−0.946258	+	0.372384i
$106$	−998.607	−	725.531i	−0.915031	−	0.664809i
$107$	−405.149	−	557.639i	−0.366049	−	0.503823i	0.585773	−	0.810475i	$-0.300791\pi$
$107$	−405.149	−	557.639i	−0.366049	−	0.503823i	−0.951822	+	0.306653i	$0.900791\pi$
$108$	2252.42	+	2179.56i	2.00685	+	1.94193i
$109$	151.796			0.133389			0.0666946	−	0.997773i	$-0.478755\pi$
$109$	151.796			0.133389			0.0666946	+	0.997773i	$0.478755\pi$
$110$	−49.6715	−	2284.18i	−0.0430544	−	1.97989i
$111$	−198.386	−	158.857i	−0.169639	−	0.135839i
$112$	−4332.07	+	1943.94i	−3.65484	+	1.64005i
$113$	179.511	+	247.076i	0.149442	+	0.205690i	0.877175	−	0.480172i	$-0.159426\pi$
$113$	179.511	+	247.076i	0.149442	+	0.205690i	−0.727732	+	0.685861i	$0.759426\pi$
$114$	577.680	+	2109.62i	0.474602	+	1.73320i
$115$	−946.309	+	307.474i	−0.767337	+	0.249323i
$116$	−4338.59	+	1409.69i	−3.47265	+	1.12833i
$117$	1596.62	+	689.995i	1.26160	+	0.545214i
$118$	1272.50	+	1751.44i	0.992735	+	1.36638i
$119$	1255.41	−	563.344i	0.967087	−	0.433963i
$120$	2916.83	−	3642.62i	2.21891	−	2.77104i
$121$	1329.74	−	57.8602i	0.999055	−	0.0434712i
$122$	−450.286			−0.334155
$123$	−709.695	+	466.430i	−0.520253	+	0.341924i
$124$	−160.692	−	221.173i	−0.116375	−	0.160177i
$125$	1110.56	+	806.870i	0.794653	+	0.577349i
$126$	814.710	−	2631.13i	0.576033	−	1.86031i
$127$	−560.260	−	1724.30i	−0.391457	−	1.20478i	−0.931686	−	0.363264i	$-0.881662\pi$
$127$	−560.260	−	1724.30i	−0.391457	−	1.20478i	0.540229	−	0.841518i	$-0.318338\pi$
$128$	3605.55	−	4962.61i	2.48975	−	3.42685i
$129$	1308.89	+	61.4062i	0.893344	+	0.0419110i
$130$	1246.65	−	3836.79i	0.841065	−	2.58853i
$131$	1191.16			0.794446			0.397223	−	0.917722i	$-0.369974\pi$
$131$	1191.16			0.794446			0.397223	+	0.917722i	$0.369974\pi$
$132$	3362.64	+	2574.68i	2.21728	+	1.69771i
$133$	1049.03	−	950.110i	0.683926	−	0.619436i
$134$	−424.023	−	137.773i	−0.273358	−	0.0888195i
$135$	275.385	+	1571.11i	0.175566	+	1.00162i
$136$	−3449.66	+	4748.06i	−2.17505	+	2.99369i
$137$	2927.97	−	951.354i	1.82593	−	0.593282i	0.826390	−	0.563097i	$-0.190390\pi$
$137$	2927.97	−	951.354i	1.82593	−	0.593282i	0.999544	−	0.0301847i	$-0.00960956\pi$
$138$	884.849	−	2343.41i	0.545821	−	1.44554i
$139$	−1239.81	+	1706.45i	−0.756541	+	1.04129i	0.240953	+	0.970537i	$0.422540\pi$
$139$	−1239.81	+	1706.45i	−0.756541	+	1.04129i	−0.997494	+	0.0707521i	$0.977460\pi$
$140$	−4604.12	−	964.590i	−2.77942	−	0.582305i
$141$	−374.112	+	245.876i	−0.223446	+	0.146855i
$142$	−3279.05			−1.93783
$143$	2250.45	+	677.490i	1.31603	+	0.396186i
$144$	1513.34	+	6754.83i	0.875774	+	3.90904i
$145$	−2207.92	−	717.395i	−1.26453	−	0.410872i
$146$	−3813.56	+	2770.71i	−2.16173	+	1.57059i
$147$	−1757.07	+	298.720i	−0.985854	+	0.167605i
$148$	−337.666	−	1039.23i	−0.187541	−	0.577191i
$149$	−1778.81	+	577.971i	−0.978027	+	0.317780i	−0.754052	−	0.656815i	$-0.771903\pi$
$149$	−1778.81	+	577.971i	−0.978027	+	0.317780i	−0.223975	+	0.974595i	$0.571903\pi$
$150$	117.576	−	32.1959i	0.0640002	−	0.0175252i
$151$	−1286.09	+	934.398i	−0.693115	+	0.503578i	−0.877683	−	0.479242i	$-0.840912\pi$
$151$	−1286.09	+	934.398i	−0.693115	+	0.503578i	0.184568	+	0.982820i	$0.440912\pi$
$152$	−1865.42	+	5741.16i	−0.995430	+	3.06362i
$153$	−438.557	−	1957.51i	−0.231734	−	1.03435i
$154$	683.788	−	3658.41i	0.357800	−	1.91431i
$155$		−	139.126i		−	0.0720961i
$156$	4107.22	+	6249.34i	2.10796	+	3.20735i
$157$	−676.942	−	931.731i	−0.344114	−	0.473632i	0.601524	−	0.798855i	$-0.294561\pi$
$157$	−676.942	−	931.731i	−0.344114	−	0.473632i	−0.945637	+	0.325223i	$0.894561\pi$
$158$	2208.15	−	3039.25i	1.11184	−	1.53032i
$159$	1089.34	+	411.325i	0.543336	+	0.205158i
$160$	8436.88	−	2741.31i	4.16871	−	1.35450i
$161$	−1611.47	+	174.132i	−0.788830	+	0.0852393i
$162$	−3520.70	−	1931.06i	−1.70748	−	0.936531i
$163$	641.676	−	1974.88i	0.308343	−	0.948983i	−0.670065	−	0.742302i	$-0.733734\pi$
$163$	641.676	−	1974.88i	0.308343	−	0.948983i	0.978408	−	0.206681i	$-0.0662662\pi$
$164$	−3651.32			−1.73854
$165$	614.283	+	2065.88i	0.289829	+	0.974717i
$166$			897.267i			0.419527i
$167$	−595.465	+	1832.65i	−0.275919	+	0.849191i	0.713056	+	0.701107i	$0.247310\pi$
$167$	−595.465	+	1832.65i	−0.275919	+	0.849191i	−0.988975	+	0.148084i	$0.952690\pi$
$168$	5867.25	−	4833.37i	2.69445	−	2.21966i
$169$	1579.93	+	1147.89i	0.719130	+	0.522479i
$170$	−4425.12	+	1437.81i	−1.99642	+	0.648676i
$171$	−1051.20	−	1775.51i	−0.470101	−	0.794015i
$172$	4557.78	+	3311.42i	2.02051	+	1.46798i
$173$	2522.87	−	1832.97i	1.10873	−	0.805540i	0.126267	−	0.991996i	$-0.459700\pi$
$173$	2522.87	−	1832.97i	1.10873	−	0.805540i	0.982463	+	0.186456i	$0.0597003\pi$
$174$	4884.01	−	3209.90i	2.12791	−	1.39852i
$175$	−52.9526	−	58.4655i	−0.0228734	−	0.0252547i
$176$	3083.11	+	8830.77i	1.32044	+	3.78207i
$177$	−1594.14	−	1276.51i	−0.676965	−	0.542080i
$178$	1784.97	+	579.971i	0.751623	+	0.244217i
$179$	−1598.22	−	2199.76i	−0.667354	−	0.918534i	0.332343	−	0.943159i	$-0.392161\pi$
$179$	−1598.22	−	2199.76i	−0.667354	−	0.918534i	−0.999697	+	0.0246249i	$0.992161\pi$
$180$	−2720.53	+	6295.19i	−1.12654	+	2.60675i
$181$	−2076.75	+	674.778i	−0.852839	+	0.277104i	−0.702634	−	0.711551i	$-0.747993\pi$
$181$	−2076.75	+	674.778i	−0.852839	+	0.277104i	−0.150204	+	0.988655i	$0.547993\pi$
$182$	3269.22	−	5700.84i	1.33149	−	2.32184i
$183$	409.691	−	112.186i	0.165493	−	0.0453171i
$184$	5592.89	−	4063.47i	2.24083	−	1.62806i
$185$	171.839	−	528.867i	0.0682912	−	0.210179i
$186$	273.396	+	218.922i	0.107776	+	0.0863019i
$187$	−893.468	−	2559.11i	−0.349395	−	1.00075i
$188$	−1924.77			−0.746694
$189$	−85.7311	+	2596.91i	−0.0329948	+	0.999456i
$190$	−3871.79	+	2813.02i	−1.47837	+	1.07410i
$191$	879.463	−	1210.48i	0.333171	−	0.458571i	−0.609260	−	0.792970i	$-0.708533\pi$
$191$	879.463	−	1210.48i	0.333171	−	0.458571i	0.942431	+	0.334399i	$0.108533\pi$
$192$	−4124.18	+	10922.4i	−1.55019	+	4.10549i
$193$	−145.310	−	447.219i	−0.0541951	−	0.166795i	0.920295	−	0.391224i	$-0.127948\pi$
$193$	−145.310	−	447.219i	−0.0541951	−	0.166795i	−0.974490	+	0.224429i	$0.927948\pi$
$194$	7069.46	+	5136.26i	2.61628	+	1.90084i
$195$	−178.346	+	3801.49i	−0.0654955	+	1.39605i
$196$	−7018.45	−	3075.82i	−2.55774	−	1.12093i
$197$			863.376i			0.312249i	0.987737	+	0.156124i	$0.0499001\pi$
$197$			863.376i			0.312249i	−0.987737	+	0.156124i	$0.950100\pi$
$198$	−5026.24	−	2043.64i	−1.80404	−	0.733510i
$199$		−	2310.73i		−	0.823131i	−0.911380	−	0.411566i	$-0.864982\pi$
$199$		−	2310.73i		−	0.823131i	0.911380	−	0.411566i	$-0.135018\pi$
$200$	319.973	+	103.966i	0.113128	+	0.0367574i
$201$	420.122	+	19.7099i	0.147428	+	0.00691656i
$202$	5033.28	−	6927.72i	1.75317	−	2.41303i
$203$	−3280.60	−	1881.30i	−1.13425	−	0.650451i
$204$	3046.72	−	8068.85i	1.04565	−	2.76928i
$205$	−1503.29	−	1092.20i	−0.512166	−	0.372111i
$206$	1778.79	−	1292.36i	0.601621	−	0.437104i
$207$	−221.230	+	2352.60i	−0.0742828	+	0.789937i
$208$			16516.0i			5.50565i
$209$	−1687.42	−	2219.42i	−0.558476	−	0.734547i
$210$	6015.48	−	365.950i	1.97670	−	0.120252i
$211$	−859.385	+	2644.91i	−0.280391	+	0.862955i	0.707351	+	0.706862i	$0.249890\pi$
$211$	−859.385	+	2644.91i	−0.280391	+	0.862955i	−0.987742	+	0.156093i	$0.950110\pi$
$212$	2942.66	+	4050.22i	0.953313	+	1.31212i
$213$	2983.43	−	816.956i	0.959725	−	0.262802i
$214$	1173.25	+	3610.89i	0.374774	+	1.15344i
$215$	885.955	+	2726.69i	0.281031	+	0.864924i
$216$	−5192.87	−	9790.32i	−1.63579	−	3.08401i
$217$	46.4723	−	221.818i	0.0145380	−	0.0693918i
$218$	−795.205	−	258.378i	−0.247055	−	0.0802732i
$219$	2779.45	−	3471.05i	0.857615	−	1.07101i
$220$	−2671.23	+	8873.14i	−0.818611	+	2.71922i
$221$		−	4786.24i		−	1.45682i
$222$	768.874	+	1169.88i	0.232448	+	0.353680i
$223$	446.121	+	614.034i	0.133966	+	0.184389i	0.870730	−	0.491762i	$-0.163647\pi$
$223$	446.121	+	614.034i	0.133966	+	0.184389i	−0.736763	+	0.676151i	$0.763647\pi$
$224$	14367.2	−	1552.49i	4.28548	−	0.463080i
$225$	−98.9547	+	58.5867i	−0.0293199	+	0.0173590i
$226$	−519.838	−	1599.90i	−0.153005	−	0.470900i
$227$	−2873.18	−	2087.49i	−0.840086	−	0.610358i	0.0823090	−	0.996607i	$-0.473771\pi$
$227$	−2873.18	−	2087.49i	−0.840086	−	0.610358i	−0.922395	+	0.386249i	$0.873771\pi$
$228$	415.740	−	8861.60i	0.120759	−	2.57401i
$229$	−4206.71	−	1366.84i	−1.21392	−	0.394426i	−0.369055	−	0.929408i	$-0.620319\pi$
$229$	−4206.71	−	1366.84i	−1.21392	−	0.394426i	−0.844864	+	0.534981i	$0.820319\pi$
$230$	5480.74			1.57126
$231$	289.329	+	3498.95i	0.0824088	+	0.996599i
$232$	16129.8			4.56453
$233$	2992.54	+	972.336i	0.841407	+	0.273390i	0.697843	−	0.716251i	$-0.254143\pi$
$233$	2992.54	+	972.336i	0.841407	+	0.273390i	0.143565	+	0.989641i	$0.454143\pi$
$234$	−7189.64	−	6332.30i	−2.00855	−	1.76904i
$235$	−792.449	−	575.748i	−0.219973	−	0.159820i
$236$	−2713.34	−	8350.80i	−0.748404	−	2.30335i
$237$	−1251.86	+	3315.40i	−0.343111	+	0.908686i
$238$	−7535.54	+	814.275i	−2.05234	+	0.221771i
$239$	−543.813	−	748.494i	−0.147181	−	0.202578i	0.729061	−	0.684449i	$-0.239957\pi$
$239$	−543.813	−	748.494i	−0.147181	−	0.202578i	−0.876242	+	0.481871i	$0.839957\pi$
$240$	−12657.1	+	8318.58i	−3.40422	+	2.23734i
$241$		−	2453.24i		−	0.655715i	−0.944727	−	0.327858i	$-0.893673\pi$
$241$		−	2453.24i		−	0.655715i	0.944727	−	0.327858i	$-0.106327\pi$
$242$	−7064.53	−	1960.30i	−1.87655	−	0.520713i
$243$	3684.41	+	879.804i	0.972653	+	0.232261i
$244$	1736.91	+	564.357i	0.455715	+	0.148071i
$245$	−1969.51	−	3365.74i	−0.513582	−	0.877671i
$246$	4511.77	−	1235.46i	1.16935	−	0.320204i
$247$	−1521.29	−	4682.05i	−0.391893	−	1.20612i
$248$	298.706	+	919.322i	0.0764832	+	0.235391i
$249$	−223.549	−	816.376i	−0.0568949	−	0.207774i
$250$	−4444.43	−	6117.23i	−1.12436	−	1.54755i
$251$	1125.11	−	3462.73i	0.282933	−	0.870778i	−0.704078	−	0.710123i	$-0.748639\pi$
$251$	1125.11	−	3462.73i	0.282933	−	0.870778i	0.987011	−	0.160655i	$-0.0513607\pi$
$252$	−6440.31	+	9128.11i	−1.60993	+	2.28181i
$253$	69.4160	+	3192.14i	0.0172496	+	0.793234i
$254$			9986.66i			2.46700i
$255$	3667.96	−	2410.68i	0.900772	−	0.592010i
$256$	−12793.2	+	9294.81i	−3.12334	+	2.26924i
$257$	−4057.52	−	2947.96i	−0.984829	−	0.715520i	−0.0260464	−	0.999661i	$-0.508292\pi$
$257$	−4057.52	−	2947.96i	−0.984829	−	0.715520i	−0.958783	+	0.284141i	$0.908292\pi$
$258$	−6752.29	−	2549.60i	−1.62938	−	0.615237i
$259$	450.632	−	785.808i	0.108112	−	0.188524i
$260$	−9617.55	+	13237.4i	−2.29406	+	3.15750i
$261$	−3643.98	+	4137.34i	−0.864201	+	0.981207i
$262$	−6240.08	−	2027.53i	−1.47143	−	0.478095i
$263$			865.568i			0.202940i	0.994839	+	0.101470i	$0.0323546\pi$
$263$			865.568i			0.202940i	−0.994839	+	0.101470i	$0.967645\pi$
$264$	−8494.53	−	12332.1i	−1.98031	−	2.87495i
$265$			2547.74i			0.590590i
$266$	−7112.69	+	3191.70i	−1.63950	+	0.735698i
$267$	−1768.54	−	82.9707i	−0.405367	−	0.0190177i
$268$	1462.93	+	1062.88i	0.333444	+	0.242261i
$269$	1651.17	+	5081.79i	0.374252	+	1.15183i	0.943982	+	0.329998i	$0.107048\pi$
$269$	1651.17	+	5081.79i	0.374252	+	1.15183i	−0.569729	+	0.821832i	$0.692952\pi$
$270$	1231.60	−	8699.21i	0.277602	−	1.96080i
$271$	551.716	−	759.372i	0.123669	−	0.170216i	−0.742693	−	0.669632i	$-0.766452\pi$
$271$	551.716	−	759.372i	0.123669	−	0.170216i	0.866363	+	0.499416i	$0.166452\pi$
$272$	15410.6	−	11196.4i	3.43530	−	2.49589i
$273$	−1554.16	+	6001.40i	−0.344549	+	1.33048i
$274$	−16957.9			−3.73892
$275$	−123.695	+	94.0454i	−0.0271240	+	0.0206224i
$276$	−6350.25	+	7930.36i	−1.38493	+	1.72954i
$277$	1242.14	−	3822.91i	0.269433	−	0.829229i	−0.721206	−	0.692720i	$-0.756412\pi$
$277$	1242.14	−	3822.91i	0.269433	−	0.829229i	0.990639	−	0.136508i	$-0.0435880\pi$
$278$	9399.53	−	6829.16i	2.02786	−	1.47333i
$279$	−303.292	−	131.071i	−0.0650810	−	0.0281254i
$280$	14428.5	+	8274.20i	3.07952	+	1.76599i
$281$	3221.71	−	1046.80i	0.683954	−	0.222230i	0.0536281	−	0.998561i	$-0.482921\pi$
$281$	3221.71	−	1046.80i	0.683954	−	0.222230i	0.630325	+	0.776331i	$0.282921\pi$
$282$	2378.35	−	651.267i	0.502230	−	0.137526i
$283$	4414.00	+	6075.36i	0.927157	+	1.27612i	0.960958	+	0.276693i	$0.0892385\pi$
$283$	4414.00	+	6075.36i	0.927157	+	1.27612i	−0.0338018	+	0.999429i	$0.510761\pi$
$284$	12648.5	+	4109.74i	2.64278	+	0.858690i
$285$	2821.89	−	3524.05i	0.586507	−	0.732446i
$286$	−10636.1	−	7379.71i	−2.19905	−	1.52577i
$287$	−2031.96	−	2243.51i	−0.417920	−	0.461430i
$288$	1972.39	−	20974.8i	0.403557	−	4.29149i
$289$	−491.199	+	356.877i	−0.0999794	+	0.0726393i
$290$	10345.4	+	7516.36i	2.09483	+	1.52199i
$291$	−7711.79	−	2911.90i	−1.55352	−	0.586593i
$292$	18182.9	−	5907.98i	3.64408	−	1.18403i
$293$	−4172.51	−	3031.51i	−0.831948	−	0.604445i	0.0881620	−	0.996106i	$-0.471901\pi$
$293$	−4172.51	−	3031.51i	−0.831948	−	0.604445i	−0.920110	+	0.391661i	$0.871901\pi$
$294$	9713.12	+	1425.89i	1.92681	+	0.282855i
$295$	1380.82	−	4249.74i	0.272524	−	0.838743i
$296$			3863.60i			0.758672i
$297$	5082.27	+	607.138i	0.992940	+	0.118619i
$298$	10302.4			2.00268
$299$	−1742.20	+	5361.93i	−0.336969	+	1.03708i
$300$	−493.885	−	23.1705i	−0.0950482	−	0.00445916i
$301$	501.743	+	4643.28i	0.0960798	+	0.889151i
$302$	8327.83	−	2705.88i	1.58680	−	0.515582i
$303$	−2853.52	+	7557.18i	−0.541024	+	1.43283i
$304$	11516.4	−	15850.9i	2.17272	−	2.99050i
$305$	546.292	+	751.906i	0.102559	+	0.141161i
$306$	−1034.51	+	11001.2i	−0.193265	+	2.05522i
$307$		−	3240.56i		−	0.602438i	−0.953555	−	0.301219i	$-0.902606\pi$
$307$		−	3240.56i		−	0.602438i	0.953555	−	0.301219i	$-0.0973936\pi$
$308$	−7222.82	+	13254.8i	−1.33623	+	2.45215i
$309$	−1296.44	+	1619.03i	−0.238679	+	0.298069i
$310$	−236.812	+	728.833i	−0.0433872	+	0.133532i
$311$	3911.78	−	2842.08i	0.713237	−	0.518197i	−0.170979	−	0.985275i	$-0.554693\pi$
$311$	3911.78	−	2842.08i	0.713237	−	0.518197i	0.884216	+	0.467078i	$0.154693\pi$
$312$	−6983.36	−	25502.5i	−1.26716	−	4.62754i
$313$	4709.16	−	1530.10i	0.850408	−	0.276314i	0.148791	−	0.988869i	$-0.452462\pi$
$313$	4709.16	−	1530.10i	0.850408	−	0.276314i	0.701617	+	0.712554i	$0.252462\pi$
$314$	1960.32	+	6033.26i	0.352317	+	1.08432i
$315$	−5381.99	+	1831.68i	−0.962669	+	0.327630i
$316$	−12326.8	+	8955.95i	−2.19442	+	1.59434i
$317$	1376.51	+	447.255i	0.243888	+	0.0792439i	0.428410	−	0.903584i	$-0.359074\pi$
$317$	1376.51	+	447.255i	0.243888	+	0.0792439i	−0.184522	+	0.982828i	$0.559074\pi$
$318$	−5006.54	−	4008.99i	−0.882871	−	0.706960i
$319$	−4246.72	+	6120.65i	−0.745362	+	1.07427i
$320$	−25545.1			−4.46255
$321$	−1967.11	−	2993.05i	−0.342036	−	0.520423i
$322$	8738.31	+	1830.73i	1.51232	+	0.316840i
$323$	−3337.38	+	4593.51i	−0.574913	+	0.791299i
$324$	11160.3	+	11861.4i	1.91364	+	2.03384i
$325$	−260.946	+	84.7863i	−0.0445374	+	0.0144711i
$326$	−6723.03	+	9253.45i	−1.14219	+	1.57209i
$327$	787.888	+	36.9636i	0.133243	+	0.00625104i
$328$	12278.4	+	3989.50i	2.06696	+	0.671595i
$329$	−1071.14	−	1182.66i	−0.179495	−	0.198182i
$330$	298.399	−	11868.0i	0.0497767	−	1.97973i
$331$	6859.03			1.13899			0.569496	−	0.821994i	$-0.307138\pi$
$331$	6859.03			1.13899			0.569496	+	0.821994i	$0.307138\pi$
$332$	1124.57	−	3461.08i	0.185901	−	0.572143i
$333$	−991.026	−	872.849i	−0.163087	−	0.143639i
$334$	6238.85	−	8587.05i	1.02208	−	1.40677i
$335$	284.370	+	875.200i	0.0463785	+	0.142738i
$336$	−22958.7	+	9035.02i	−3.72768	+	1.46697i
$337$	7636.58	+	5548.30i	1.23439	+	0.896840i	0.997212	−	0.0746249i	$-0.0237759\pi$
$337$	7636.58	+	5548.30i	1.23439	+	0.896840i	0.237183	+	0.971465i	$0.423776\pi$
$338$	−6322.83	−	8702.63i	−1.01750	−	1.40047i
$339$	871.577	+	1326.15i	0.139639	+	0.212467i
$340$	18871.3			3.01012
$341$	−427.493	−	128.695i	−0.0678887	−	0.0204377i
$342$	2484.70	+	11090.6i	0.392858	+	1.75353i
$343$	−2015.87	−	6024.11i	−0.317338	−	0.948313i
$344$	−11708.5	−	16115.3i	−1.83511	−	2.52581i
$345$	−4986.63	+	1365.49i	−0.778178	+	0.213089i
$346$	−16336.4	+	5308.02i	−2.53830	+	0.824743i
$347$	500.995	−	162.783i	0.0775067	−	0.0251834i	−0.270007	−	0.962858i	$-0.587026\pi$
$347$	500.995	−	162.783i	0.0775067	−	0.0251834i	0.347514	+	0.937675i	$0.387026\pi$
$348$	−22862.5	+	6260.45i	−3.52171	+	0.964354i
$349$	3935.20	+	5416.33i	0.603571	+	0.830744i	0.996029	−	0.0890259i	$-0.0283754\pi$
$349$	3935.20	+	5416.33i	0.603571	+	0.830744i	−0.392459	+	0.919770i	$0.628375\pi$
$350$	177.883	+	396.413i	0.0271665	+	0.0605404i
$351$	8119.13	+	3970.17i	1.23466	+	0.603737i
$352$	−618.883	−	28459.8i	−0.0937119	−	4.30941i
$353$	248.832			0.0375184			0.0187592	−	0.999824i	$-0.494028\pi$
$353$	248.832			0.0375184			0.0187592	+	0.999824i	$0.494028\pi$
$354$	6178.33	+	9400.62i	0.927612	+	1.41140i
$355$	3978.18	+	5475.50i	0.594760	+	0.818618i
$356$	−6158.36	−	4474.31i	−0.916832	−	0.666118i
$357$	6653.32	−	2618.30i	0.986361	−	0.388166i
$358$	4628.20	+	14244.1i	0.683262	+	2.10287i
$359$	4779.70	−	6578.70i	0.702683	−	0.967160i	−0.297241	−	0.954802i	$-0.596066\pi$
$359$	4779.70	−	6578.70i	0.702683	−	0.967160i	0.999924	−	0.0123572i	$-0.00393353\pi$
$360$	16026.7	−	18196.5i	2.34633	−	2.66401i
$361$	314.848	−	969.004i	0.0459030	−	0.141275i
$362$	12027.9			1.74634
$363$	6916.04	+	23.4829i	0.999994	+	0.00339541i
$364$	−19755.6	+	17892.8i	−2.84471	+	2.57647i
$365$	9253.31	+	3006.58i	1.32696	+	0.431155i
$366$	−2337.18	−	109.648i	−0.333788	−	0.0156596i
$367$	4485.03	−	6173.12i	0.637920	−	0.878022i	−0.360582	−	0.932727i	$-0.617422\pi$
$367$	4485.03	−	6173.12i	0.637920	−	0.878022i	0.998503	+	0.0547056i	$0.0174220\pi$
$368$	−21339.7	+	6933.67i	−3.02284	+	0.982181i
$369$	−3797.21	+	2248.16i	−0.535705	+	0.317167i
$370$	−1800.41	+	2478.05i	−0.252970	+	0.348183i
$371$	−851.020	+	4062.03i	−0.119091	+	0.568437i
$372$	−780.204	−	1187.12i	−0.108741	−	0.165455i
$373$	−1251.37			−0.173709			−0.0868547	−	0.996221i	$-0.527682\pi$
$373$	−1251.37			−0.173709			−0.0868547	+	0.996221i	$0.527682\pi$
$374$	324.603	+	14927.1i	0.0448791	+	2.06380i
$375$	5567.83	+	4458.44i	0.766723	+	0.613955i
$376$	6472.50	+	2103.04i	0.887749	+	0.288447i
$377$	−10642.0	+	7731.84i	−1.45382	+	1.05626i
$378$	4869.41	−	13458.3i	0.662580	−	1.83128i
$379$	−4285.81	−	13190.4i	−0.580863	−	1.78771i	−0.615284	−	0.788306i	$-0.710959\pi$
$379$	−4285.81	−	13190.4i	−0.580863	−	1.78771i	0.0344207	−	0.999407i	$-0.489041\pi$
$380$	18460.5	−	5998.20i	2.49212	−	0.809739i
$381$	−2488.12	−	9086.33i	−0.334567	−	1.22180i
$382$	−6667.60	+	4844.29i	−0.893047	+	0.648837i
$383$	2617.35	−	8055.36i	0.349191	−	1.07470i	−0.610111	−	0.792316i	$-0.708875\pi$
$383$	2617.35	−	8055.36i	0.349191	−	1.07470i	0.959302	−	0.282383i	$-0.0911248\pi$
$384$	19922.8	−	24880.2i	2.64761	−	3.30641i
$385$	−6938.55	+	3296.61i	−0.918497	+	0.436391i
$386$			2590.16i			0.341543i
$387$	6778.77	+	637.451i	0.890398	+	0.0837299i
$388$	−20832.0	−	28672.8i	−2.72573	−	3.75165i
$389$	−2552.60	+	3513.36i	−0.332705	+	0.457929i	−0.942293	−	0.334790i	$-0.891335\pi$
$389$	−2552.60	+	3513.36i	−0.332705	+	0.457929i	0.609588	+	0.792718i	$0.291335\pi$
$390$	7404.96	−	19611.1i	0.961448	−	2.54627i
$391$	6184.12	−	2009.34i	0.799858	−	0.259890i
$392$	20240.5	+	18011.7i	2.60790	+	2.32073i
$393$	6182.66	+	290.058i	0.793573	+	0.0372303i
$394$	1469.59	−	4522.92i	0.187910	−	0.578329i
$395$	−7754.02			−0.987715
$396$	16826.7	+	14182.6i	2.13528	+	1.79975i
$397$		−	5690.26i		−	0.719360i	−0.933076	−	0.359680i	$-0.882886\pi$
$397$		−	5690.26i		−	0.719360i	0.933076	−	0.359680i	$-0.117114\pi$
$398$	−3933.18	+	12105.1i	−0.495358	+	1.52456i
$399$	5676.27	−	4676.04i	0.712203	−	0.586704i
$400$	−883.421	−	641.843i	−0.110428	−	0.0802303i
$401$	−10119.3	+	3287.95i	−1.26018	+	0.409457i	−0.861558	−	0.507659i	$-0.830511\pi$
$401$	−10119.3	+	3287.95i	−1.26018	+	0.409457i	−0.398620	+	0.917116i	$0.630511\pi$
$402$	−2167.32	−	818.358i	−0.268896	−	0.101532i
$403$	−637.757	−	463.357i	−0.0788311	−	0.0572741i
$404$	−28097.9	+	20414.3i	−3.46021	+	2.51399i
$405$	1046.79	+	8221.79i	0.128433	+	1.00875i
$406$	13983.7	+	15439.5i	1.70935	+	1.88731i
$407$	−1466.09	−	1017.22i	−0.178554	−	0.123887i
$408$	−19061.5	+	23804.5i	−2.31295	+	2.88848i
$409$	−6840.67	−	2222.67i	−0.827015	−	0.268714i	−0.135228	−	0.990815i	$-0.543177\pi$
$409$	−6840.67	−	2222.67i	−0.827015	−	0.268714i	−0.691788	+	0.722101i	$0.743177\pi$
$410$	6016.11	+	8280.46i	0.724669	+	0.997421i
$411$	15429.1	−	4224.97i	1.85173	−	0.507061i
$412$	−8481.18	+	2755.70i	−1.01417	+	0.329524i
$413$	3621.08	−	6314.41i	0.431432	−	0.752329i
$414$	5163.40	−	11947.9i	0.612964	−	1.41837i
$415$	1498.29	−	1088.58i	0.177225	−	0.128762i
$416$	15532.7	−	47804.7i	1.83065	−	5.63417i
$417$	−6850.69	+	8555.33i	−0.804507	+	1.00469i
$418$	5062.06	+	14499.0i	0.592329	+	1.69657i
$419$	7454.41			0.869145			0.434572	−	0.900637i	$-0.356900\pi$
$419$	7454.41			0.869145			0.434572	+	0.900637i	$0.356900\pi$
$420$	−23662.5	−	6127.79i	−2.74908	−	0.711918i
$421$	−281.970	+	204.864i	−0.0326423	+	0.0237160i	−0.603987	−	0.796994i	$-0.706422\pi$
$421$	−281.970	+	204.864i	−0.0326423	+	0.0237160i	0.571344	+	0.820710i	$0.306422\pi$
$422$	9004.02	−	12393.0i	1.03865	−	1.42958i
$423$	−2001.68	+	1185.11i	−0.230083	+	0.136222i
$424$	−5470.02	−	16835.0i	−0.626528	−	1.92825i
$425$	256.011	+	186.003i	0.0292196	+	0.0212293i
$426$	−17019.7	−	798.476i	−1.93570	−	0.0908128i
$427$	619.831	+	1381.29i	0.0702476	+	0.156547i
$428$		−	15399.0i		−	1.73911i
$429$	11515.9	+	4064.48i	1.29602	+	0.457424i
$430$		−	15792.2i		−	1.77109i
$431$	−2205.80	−	716.707i	−0.246519	−	0.0800988i	0.183151	−	0.983085i	$-0.441370\pi$
$431$	−2205.80	−	716.707i	−0.246519	−	0.0800988i	−0.429670	+	0.902986i	$0.641370\pi$
$432$	6210.04	+	35429.1i	0.691622	+	3.94579i
$433$	−9736.49	+	13401.1i	−1.08061	+	1.48734i	−0.221772	+	0.975099i	$0.571184\pi$
$433$	−9736.49	+	13401.1i	−1.08061	+	1.48734i	−0.858843	+	0.512240i	$0.828816\pi$
$434$	−621.018	+	1082.93i	−0.0686862	+	0.119774i
$435$	−11285.4	−	4261.25i	−1.24389	−	0.469681i
$436$	2743.56	+	1993.31i	0.301359	+	0.218950i
$437$	5410.84	−	3931.21i	0.592301	−	0.430332i
$438$	−20468.7	+	13452.6i	−2.23296	+	1.46756i
$439$		−	15339.8i		−	1.66772i	−0.551977	−	0.833860i	$-0.686126\pi$
$439$		−	15339.8i		−	1.66772i	0.551977	−	0.833860i	$-0.313874\pi$
$440$	18677.6	−	26919.4i	2.02368	−	2.91666i
$441$	−9192.71	+	1122.63i	−0.992626	+	0.121221i
$442$	−8146.85	+	25073.4i	−0.876710	+	2.69824i
$443$	3289.70	+	4527.89i	0.352818	+	0.485612i	0.948130	−	0.317882i	$-0.102972\pi$
$443$	3289.70	+	4527.89i	0.352818	+	0.485612i	−0.595312	+	0.803495i	$0.702972\pi$
$444$	−1499.58	−	5476.29i	−0.160286	−	0.585345i
$445$	−1197.08	−	3684.24i	−0.127522	−	0.392471i
$446$	−1291.90	−	3976.06i	−0.137160	−	0.422135i
$447$	−9373.57	+	2566.77i	−0.991845	+	0.271598i
$448$	−40728.4	−	8532.83i	−4.29516	−	0.899863i
$449$	−8514.10	−	2766.40i	−0.894889	−	0.290767i	−0.174763	−	0.984611i	$-0.555916\pi$
$449$	−8514.10	−	2766.40i	−0.894889	−	0.290767i	−0.720126	+	0.693844i	$0.755916\pi$
$450$	618.111	−	138.480i	0.0647512	−	0.0145067i
$451$	−4746.58	+	3608.83i	−0.495583	+	0.376792i
$452$			6822.90i			0.710005i
$453$	−6902.90	+	4536.77i	−0.715953	+	0.470543i
$454$	11498.4	+	15826.1i	1.18865	+	1.63603i
$455$	−13485.8	+	1457.24i	−1.38950	+	0.150147i
$456$	−11080.4	+	29344.9i	−1.13791	+	3.01360i
$457$	−1982.78	−	6102.37i	−0.202955	−	0.624632i	−0.999791	−	0.0204364i	$-0.993494\pi$
$457$	−1982.78	−	6102.37i	−0.202955	−	0.624632i	0.796836	−	0.604196i	$-0.206506\pi$
$458$	19710.9	+	14320.8i	2.01098	+	1.46107i
$459$	−1799.64	−	10267.2i	−0.183006	−	1.04407i
$460$	−21141.2	−	6869.19i	−2.14285	−	0.696255i
$461$	−17706.2			−1.78885			−0.894426	−	0.447217i	$-0.852415\pi$
$461$	−17706.2			−1.78885			−0.894426	+	0.447217i	$0.852415\pi$
$462$	4440.02	−	18822.3i	0.447117	−	1.89543i
$463$	386.852			0.0388305			0.0194153	−	0.999812i	$-0.493820\pi$
$463$	386.852			0.0388305			0.0194153	+	0.999812i	$0.493820\pi$
$464$	−49789.4	−	16177.6i	−4.98150	−	1.61859i
$465$	33.8784	−	722.127i	0.00337865	−	0.0720169i
$466$	−14021.8	−	10187.4i	−1.39388	−	1.01271i
$467$	805.103	+	2477.85i	0.0797768	+	0.245528i	0.982988	−	0.183668i	$-0.0587971\pi$
$467$	805.103	+	2477.85i	0.0797768	+	0.245528i	−0.903212	+	0.429196i	$0.858797\pi$
$468$	19796.6	+	33437.0i	1.95533	+	3.30262i
$469$	161.047	+	1490.38i	0.0158560	+	0.146736i
$470$	3171.36	+	4365.00i	0.311242	+	0.428388i
$471$	−3286.74	−	5000.94i	−0.321540	−	0.489238i
$472$			31046.1i			3.02757i
$473$	9197.83	−	200.015i	0.894115	−	0.0194433i
$474$	12201.3	−	15237.4i	1.18233	−	1.47653i
$475$	309.558	+	100.582i	0.0299021	+	0.00971578i
$476$	30087.9	+	6303.59i	2.89722	+	0.606984i
$477$	5554.00	+	2400.22i	0.533124	+	0.230395i
$478$	1574.80	+	4846.74i	0.150690	+	0.463775i
$479$	−4302.18	−	13240.8i	−0.410380	−	1.26302i	−0.916319	−	0.400449i	$-0.868854\pi$
$479$	−4302.18	−	13240.8i	−0.410380	−	1.26302i	0.505939	−	0.862569i	$-0.331146\pi$
$480$	44458.7	−	12174.2i	4.22761	−	1.15765i
$481$	−1852.02	−	2549.09i	−0.175561	−	0.241640i
$482$	−4175.76	+	12851.7i	−0.394608	+	1.21448i
$483$	−8406.64	+	511.416i	−0.791958	+	0.0481786i
$484$	24793.5	+	16415.8i	2.32847	+	1.54168i
$485$		−	18036.3i		−	1.68863i
$486$	−17803.7	−	10880.4i	−1.66172	−	1.01552i
$487$	8902.01	−	6467.69i	0.828313	−	0.601805i	−0.0907684	−	0.995872i	$-0.528932\pi$
$487$	8902.01	−	6467.69i	0.828313	−	0.601805i	0.919082	+	0.394067i	$0.128932\pi$
$488$	−5224.15	−	3795.57i	−0.484603	−	0.352085i
$489$	3811.48	−	10094.2i	0.352477	−	0.933491i
$490$	4588.62	+	20984.3i	0.423047	+	1.93464i
$491$	9333.99	−	12847.1i	0.857917	−	1.18082i	−0.124145	−	0.992264i	$-0.539619\pi$
$491$	9333.99	−	12847.1i	0.857917	−	1.18082i	0.982062	−	0.188557i	$-0.0603812\pi$
$492$	−18952.0	−	889.126i	−1.73663	−	0.0814734i
$493$	14428.7	+	4688.17i	1.31813	+	0.428285i
$494$			27117.1i			2.46975i
$495$	2685.34	+	10872.4i	0.243833	+	0.987228i
$496$		−	3137.36i		−	0.284015i
$497$	4513.71	+	10058.8i	0.407379	+	0.907843i
$498$	−218.492	+	4657.21i	−0.0196604	+	0.419066i
$499$	2224.04	+	1615.86i	0.199522	+	0.144961i	0.683060	−	0.730362i	$-0.260649\pi$
$499$	2224.04	+	1615.86i	0.199522	+	0.144961i	−0.483538	+	0.875323i	$0.660649\pi$
$500$	9476.84	+	29166.7i	0.847634	+	2.60875i
$501$	−3536.99	+	9367.27i	−0.315411	+	0.835327i
$502$	−11788.1	+	16224.9i	−1.04806	+	1.44254i
$503$	4054.37	−	2945.67i	0.359394	−	0.261115i	−0.393405	−	0.919365i	$-0.628703\pi$
$503$	4054.37	−	2945.67i	0.359394	−	0.261115i	0.752799	+	0.658250i	$0.228703\pi$
$504$	31630.6	−	23658.6i	2.79551	−	2.09095i
$505$	−17674.6			−1.55745
$506$	5069.82	−	16840.7i	0.445417	−	1.47956i
$507$	7921.01	+	6342.76i	0.693855	+	0.555606i
$508$	12516.6	−	38522.1i	1.09318	−	3.36446i
$509$	4471.31	−	3248.60i	0.389366	−	0.282891i	−0.375830	−	0.926689i	$-0.622642\pi$
$509$	4471.31	−	3248.60i	0.389366	−	0.282891i	0.765196	+	0.643798i	$0.222642\pi$
$510$	−23318.5	+	6385.32i	−2.02463	+	0.554405i
$511$	13748.9	+	7884.47i	1.19024	+	0.682561i
$512$	36168.9	−	11752.0i	3.12198	−	1.01439i
$513$	−5023.85	−	9471.65i	−0.432375	−	0.815173i
$514$	16238.1	+	22349.8i	1.39344	+	1.91791i
$515$	−4316.09	−	1402.38i	−0.369301	−	0.119993i
$516$	22850.5	+	18297.6i	1.94949	+	1.56106i
$517$	−2502.13	+	1902.37i	−0.212851	+	0.161830i
$518$	−3698.26	+	3349.53i	−0.313691	+	0.284112i
$519$	13541.2	−	8899.61i	1.14526	−	0.752696i
$520$	46804.7	−	34005.6i	3.94716	−	2.86778i
$521$	5110.89	+	3713.28i	0.429774	+	0.312249i	0.781558	−	0.623832i	$-0.214425\pi$
$521$	5110.89	+	3713.28i	0.429774	+	0.312249i	−0.351785	+	0.936081i	$0.614425\pi$
$522$	26131.8	−	15471.5i	2.19111	−	1.29726i
$523$	−97.0733	+	31.5410i	−0.00811610	+	0.00263708i	−0.313072	−	0.949729i	$-0.601358\pi$
$523$	−97.0733	+	31.5410i	−0.00811610	+	0.00263708i	0.304956	+	0.952366i	$0.401358\pi$
$524$	21529.1	+	15641.8i	1.79485	+	1.30404i
$525$	−260.611	−	316.356i	−0.0216647	−	0.0262989i
$526$	1473.32	−	4534.40i	0.122129	−	0.375873i
$527$			909.189i			0.0751516i
$528$	13852.3	+	46586.4i	1.14175	+	3.83979i
$529$	4507.65			0.370482
$530$	4336.61	−	13346.7i	0.355415	−	1.09386i
$531$	−7963.44	−	7013.83i	−0.650817	−	0.573210i
$532$	31436.5	−	3396.96i	2.56192	−	0.276836i
$533$	−10013.3	+	3253.53i	−0.813744	+	0.264401i
$534$	9123.54	+	3444.96i	0.739352	+	0.279172i
$535$	4606.22	−	6339.92i	0.372233	−	0.512334i
$536$	−3758.13	−	5172.62i	−0.302848	−	0.416834i
$537$	−7759.80	−	11806.9i	−0.623575	−	0.948799i
$538$		−	29432.2i		−	2.35858i
$539$	−12163.8	+	2938.32i	−0.972041	+	0.234810i
$540$	−15653.7	+	32012.4i	−1.24746	+	2.55110i
$541$	−5795.14	+	17835.6i	−0.460541	+	1.41740i	0.403964	+	0.914775i	$0.367632\pi$
$541$	−5795.14	+	17835.6i	−0.460541	+	1.41740i	−0.864505	+	0.502625i	$0.832368\pi$
$542$	−4182.80	+	3038.98i	−0.331488	+	0.240840i
$543$	−10943.6	+	2996.69i	−0.864887	+	0.236833i
$544$	−55135.0	+	17914.4i	−4.34539	+	1.41190i
$545$	533.302	+	1641.33i	0.0419159	+	0.129004i
$546$	18356.9	−	28793.8i	1.43883	−	2.25689i
$547$	7417.55	−	5389.17i	0.579802	−	0.421251i	−0.258851	−	0.965917i	$-0.583344\pi$
$547$	7417.55	−	5389.17i	0.579802	−	0.421251i	0.838653	+	0.544667i	$0.183344\pi$
$548$	65412.8	+	21253.9i	5.09908	+	1.65679i
$549$	2153.80	−	482.532i	0.167435	−	0.0375118i
$550$	808.073	−	282.124i	0.0626479	−	0.0218724i
$551$	15604.7			1.20651
$552$	30019.0	−	19729.3i	2.31467	−	1.52126i
$553$	−12362.8	−	2590.07i	−0.950666	−	0.199170i
$554$	−13014.2	+	17912.6i	−0.998055	+	1.37370i
$555$	1020.70	−	2703.21i	0.0780658	−	0.206747i
$556$	−44816.6	+	14561.8i	−3.41843	+	1.11071i
$557$	−9062.90	+	12474.0i	−0.689421	+	0.948906i	−0.999999	−	0.00164167i	$-0.999477\pi$
$557$	−9062.90	+	12474.0i	−0.689421	+	0.948906i	0.310578	+	0.950548i	$0.399477\pi$
$558$	1365.74	+	1202.88i	0.103613	+	0.0912578i
$559$	15449.8	+	5019.96i	1.16898	+	0.379824i
$560$	−36239.2	−	40012.1i	−2.73462	−	3.01932i
$561$	−4014.33	−	13500.5i	−0.302113	−	1.01603i
$562$	−18659.2			−1.40052
$563$	4634.90	−	14264.8i	0.346959	−	1.06783i	−0.613568	−	0.789642i	$-0.710266\pi$
$563$	4634.90	−	14264.8i	0.346959	−	1.06783i	0.960527	−	0.278187i	$-0.0897336\pi$
$564$	−9990.42	−	468.698i	−0.745874	−	0.0349925i
$565$	−2040.90	+	2809.06i	−0.151967	+	0.209165i
$566$	−12782.3	−	39339.9i	−0.949258	−	2.92152i
$567$	−1077.35	+	13458.2i	−0.0797962	+	0.996811i
$568$	−38043.1	−	27639.9i	−2.81030	−	2.04180i
$569$	10152.4	+	13973.5i	0.747995	+	1.02953i	0.998119	+	0.0613133i	$0.0195289\pi$
$569$	10152.4	+	13973.5i	0.747995	+	1.02953i	−0.250123	+	0.968214i	$0.580471\pi$
$570$	−20781.3	+	13658.0i	−1.52708	+	1.00363i
$571$	−11829.7			−0.867002			−0.433501	−	0.901153i	$-0.642722\pi$
$571$	−11829.7			−0.867002			−0.433501	+	0.901153i	$0.642722\pi$
$572$	31778.1	+	41796.8i	2.32292	+	3.05526i
$573$	4859.57	−	6068.76i	0.354295	−	0.442454i
$574$	6825.97	+	15211.7i	0.496359	+	1.10614i
$575$	−219.098	−	301.563i	−0.0158905	−	0.0218714i
$576$	−24066.0	+	55687.7i	−1.74089	+	4.02834i
$577$	22417.3	−	7283.81i	1.61741	−	0.525527i	0.646078	−	0.763272i	$-0.276408\pi$
$577$	22417.3	−	7283.81i	1.61741	−	0.525527i	0.971328	+	0.237745i	$0.0764082\pi$
$578$	3180.67	−	1033.46i	0.228890	−	0.0743709i
$579$	−645.323	−	2356.65i	−0.0463190	−	0.169152i
$580$	−30485.4	−	41959.5i	−2.18248	−	3.00392i
$581$	2752.45	−	1235.11i	0.196542	−	0.0881948i
$582$	35442.9	+	28380.9i	2.52432	+	2.02135i
$583$	7828.43	+	2356.72i	0.556124	+	0.167419i
$584$	−67599.3			−4.78986
$585$	−1851.39	+	19688.0i	−0.130847	+	1.39145i
$586$	16698.3	+	22983.2i	1.17713	+	1.62018i
$587$	−13644.8	−	9913.50i	−0.959420	−	0.697059i	−0.00640387	−	0.999979i	$-0.502038\pi$
$587$	−13644.8	−	9913.50i	−0.959420	−	0.697059i	−0.953016	+	0.302920i	$0.902038\pi$
$588$	−35679.9	−	17673.9i	−2.50240	−	1.23956i
$589$	288.983	+	889.398i	0.0202162	+	0.0622190i
$590$	−14467.3	+	19912.5i	−1.00951	+	1.38947i
$591$	−210.239	+	4481.31i	−0.0146330	+	0.311906i
$592$	3875.04	−	11926.2i	0.269026	−	0.827977i
$593$	19664.8			1.36178			0.680890	−	0.732386i	$-0.261593\pi$
$593$	19664.8			1.36178			0.680890	+	0.732386i	$0.261593\pi$
$594$	−25590.8	−	11831.3i	−1.76768	−	0.817247i
$595$	10501.9	+	11595.3i	0.723591	+	0.798925i
$596$	−39739.9	−	12912.3i	−2.73122	−	0.887428i
$597$	562.681	−	11993.7i	0.0385746	−	0.822227i
$598$	18253.5	−	25123.8i	1.24823	−	1.71804i
$599$	1479.33	−	480.664i	0.100908	−	0.0327870i	−0.258128	−	0.966111i	$-0.583106\pi$
$599$	1479.33	−	480.664i	0.100908	−	0.0327870i	0.359036	+	0.933324i	$0.383106\pi$
$600$	1635.49	+	617.543i	0.111281	+	0.0420185i
$601$	633.065	−	871.339i	0.0429671	−	0.0591392i	−0.786993	−	0.616962i	$-0.788363\pi$
$601$	633.065	−	871.339i	0.0429671	−	0.0591392i	0.829960	+	0.557823i	$0.188363\pi$
$602$	5275.06	−	25178.5i	0.357135	−	1.70465i
$603$	2175.82	+	204.606i	0.146942	+	0.0138179i
$604$	−35514.8			−2.39251
$605$	5297.39	+	14174.9i	0.355983	+	0.952549i
$606$	27811.9	−	34732.3i	1.86433	−	2.32822i
$607$	1514.13	+	491.970i	0.101246	+	0.0328969i	0.359202	−	0.933260i	$-0.383049\pi$
$607$	1514.13	+	491.970i	0.101246	+	0.0328969i	−0.257956	+	0.966157i	$0.583049\pi$
$608$	−48240.7	+	35048.9i	−3.21780	+	2.33787i
$609$	−16569.6	−	10563.6i	−1.10252	−	0.702891i
$610$	−1581.98	−	4868.84i	−0.105004	−	0.323170i
$611$	−5278.47	+	1715.08i	−0.349499	+	0.113559i
$612$	17778.7	−	41139.0i	1.17428	−	2.71723i
$613$	−8555.02	+	6215.59i	−0.563677	+	0.409535i	−0.832803	−	0.553570i	$-0.813265\pi$
$613$	−8555.02	+	6215.59i	−0.563677	+	0.409535i	0.269126	+	0.963105i	$0.413265\pi$
$614$	−5515.88	+	16976.1i	−0.362546	+	1.11580i
$615$	−7536.76	−	6035.07i	−0.494165	−	0.395703i
$616$	38770.8	−	36680.5i	2.53591	−	2.39919i
$617$		−	5138.53i		−	0.335282i	−0.985848	−	0.167641i	$-0.946385\pi$
$617$		−	5138.53i		−	0.335282i	0.985848	−	0.167641i	$-0.0536150\pi$
$618$	9547.40	−	6274.80i	0.621444	−	0.408429i
$619$	5725.02	+	7879.81i	0.371741	+	0.511658i	0.953373	−	0.301794i	$-0.0975856\pi$
$619$	5725.02	+	7879.81i	0.371741	+	0.511658i	−0.581632	+	0.813452i	$0.697586\pi$
$620$	1826.94	−	2514.57i	0.118341	−	0.162883i
$621$	−1721.16	+	12157.2i	−0.111220	+	0.785588i
$622$	−25330.0	+	8230.23i	−1.63287	+	0.530550i
$623$	−677.944	−	6273.89i	−0.0435975	−	0.403464i
$624$	−4021.77	+	85725.2i	−0.258013	+	5.49961i
$625$	−4987.30	+	15349.3i	−0.319187	+	0.982358i
$626$	−27274.1			−1.74136
$627$	−8218.03	−	11930.7i	−0.523440	−	0.759912i
$628$		−	25729.4i		−	1.63489i
$629$	−1122.97	+	3456.14i	−0.0711854	+	0.219086i
$630$	31312.1	−	434.626i	1.98017	−	0.0274856i
$631$	−20332.3	−	14772.3i	−1.28275	−	0.931972i	−0.283117	−	0.959085i	$-0.591368\pi$
$631$	−20332.3	−	14772.3i	−1.28275	−	0.931972i	−0.999632	+	0.0271136i	$0.991368\pi$
$632$	51237.2	−	16648.0i	3.22485	−	1.04782i
$633$	−5104.65	+	13519.0i	−0.320524	+	0.848867i
$634$	−6449.75	−	4686.02i	−0.404026	−	0.293542i
$635$	16676.2	−	12115.9i	1.04216	−	0.757175i
$636$	14287.4	+	21739.0i	0.890776	+	1.35536i
$637$	−21988.0	−	2181.26i	−1.36766	−	0.135675i
$638$	32665.2	−	24835.4i	2.02701	−	1.54113i
$639$	15684.3	−	3513.87i	0.970987	−	0.217538i
$640$	66326.9	+	21550.9i	4.09656	+	1.33105i
$641$	2636.79	+	3629.23i	0.162476	+	0.223629i	0.882491	−	0.470330i	$-0.155865\pi$
$641$	2636.79	+	3629.23i	0.162476	+	0.223629i	−0.720015	+	0.693959i	$0.755865\pi$
$642$	5210.41	+	19027.8i	0.320309	+	1.16973i
$643$	−9359.19	+	3040.98i	−0.574013	+	0.186508i	−0.581617	−	0.813463i	$-0.697580\pi$
$643$	−9359.19	+	3040.98i	−0.574013	+	0.186508i	0.00760372	+	0.999971i	$0.497580\pi$
$644$	−31412.3	−	18013.8i	−1.92208	−	1.10224i
$645$	3934.53	+	14368.5i	0.240189	+	0.877144i
$646$	25302.1	−	18383.1i	1.54102	−	1.11962i
$647$	2668.48	−	8212.75i	0.162147	−	0.499036i	−0.836668	−	0.547710i	$-0.815500\pi$
$647$	2668.48	−	8212.75i	0.162147	−	0.499036i	0.998815	+	0.0486740i	$0.0154995\pi$
$648$	−24569.3	−	52080.6i	−1.48946	−	3.15728i
$649$	−11780.9	−	8173.97i	−0.712541	−	0.494386i
$650$	1511.32			0.0911982
$651$	295.227	−	1140.02i	0.0177739	−	0.0686343i
$652$	37530.8	−	27267.7i	2.25432	−	1.63786i
$653$	−6936.49	+	9547.26i	−0.415691	+	0.572149i	−0.964595	−	0.263736i	$-0.915045\pi$
$653$	−6936.49	+	9547.26i	−0.415691	+	0.572149i	0.548904	+	0.835885i	$0.315045\pi$
$654$	−4064.55	−	1534.73i	−0.243022	−	0.0917628i
$655$	4184.89	+	12879.8i	0.249645	+	0.768327i
$656$	−33899.7	−	24629.6i	−2.01763	−	1.46589i
$657$	15271.8	−	17339.5i	0.906864	−	1.02965i
$658$	3598.27	+	8018.74i	0.213184	+	0.475080i
$659$		−	7723.28i		−	0.456534i	−0.973599	−	0.228267i	$-0.926694\pi$
$659$		−	7723.28i		−	0.456534i	0.973599	−	0.228267i	$-0.0733060\pi$
$660$	−16025.6	+	45405.1i	−0.945142	+	2.67786i
$661$			7862.36i			0.462648i	0.972877	+	0.231324i	$0.0743057\pi$
$661$			7862.36i			0.462648i	−0.972877	+	0.231324i	$0.925694\pi$
$662$	−35932.0	−	11675.0i	−2.10957	−	0.685442i
$663$	1165.49	−	24842.7i	0.0682713	−	1.45522i
$664$	−7563.28	+	10410.0i	−0.442036	+	0.608411i
$665$	13958.8	+	8004.88i	0.813986	+	0.466791i
$666$	3705.92	+	6259.41i	0.215618	+	0.364185i
$667$	−14457.7	−	10504.1i	−0.839287	−	0.609778i
$668$	−34827.9	+	25304.0i	−2.01726	+	1.46563i
$669$	2166.05	+	3295.74i	0.125178	+	0.190464i
$670$		−	5068.90i		−	0.292282i
$671$	2815.72	−	983.058i	0.161996	−	0.0565581i
$672$	74950.0	−	4559.57i	4.30247	−	0.261740i
$673$	−9381.81	+	28874.2i	−0.537358	+	1.65382i	0.201140	+	0.979563i	$0.435535\pi$
$673$	−9381.81	+	28874.2i	−0.537358	+	1.65382i	−0.738498	+	0.674256i	$0.764465\pi$
$674$	−30561.4	−	42064.1i	−1.74656	−	2.40393i
$675$	−527.885	+	279.995i	−0.0301012	+	0.0159659i
$676$	13482.1	+	41493.8i	0.767077	+	2.36082i
$677$	7169.21	+	22064.6i	0.406994	+	1.25260i	0.919218	+	0.393748i	$0.128822\pi$
$677$	7169.21	+	22064.6i	0.406994	+	1.25260i	−0.512224	+	0.858852i	$0.671178\pi$
$678$	−2308.60	−	8430.75i	−0.130769	−	0.477553i
$679$	6024.64	−	28756.4i	0.340508	−	1.62529i
$680$	−63459.3	−	20619.2i	−3.57875	−	1.16281i
$681$	−14404.7	−	11534.6i	−0.810559	−	0.649056i
$682$	2020.43	+	1401.84i	0.113440	+	0.0787087i
$683$			4519.03i			0.253171i	0.991956	+	0.126586i	$0.0404018\pi$
$683$			4519.03i			0.253171i	−0.991956	+	0.126586i	$0.959598\pi$
$684$	4315.74	−	45894.4i	0.241252	−	2.56552i
$685$	20573.5	+	28317.1i	1.14755	+	1.57947i
$686$	306.568	+	34989.5i	0.0170624	+	1.94738i
$687$	−21501.9	−	8118.90i	−1.19410	−	0.450881i
$688$	19978.7	+	61488.0i	1.10709	+	3.40728i
$689$	11678.9	+	8485.20i	0.645761	+	0.469173i
$690$	28447.5	+	1334.61i	1.56953	+	0.0736341i
$691$	−12359.5	−	4015.83i	−0.680429	−	0.221085i	−0.0516457	−	0.998665i	$-0.516447\pi$
$691$	−12359.5	−	4015.83i	−0.680429	−	0.221085i	−0.628783	+	0.777581i	$0.716447\pi$
$692$	69668.1			3.82714
$693$	649.720	+	18231.6i	0.0356145	+	0.999366i
$694$	−2901.61			−0.158709
$695$	−22807.2	−	7410.52i	−1.24479	−	0.404456i
$696$	83720.6	+	3927.73i	4.55951	+	0.213908i
$697$	9823.96	+	7137.53i	0.533872	+	0.387881i
$698$	−11395.7	−	35072.5i	−0.617959	−	1.90188i
$699$	15295.8	+	5775.56i	0.827671	+	0.312520i
$700$	−189.323	−	1752.05i	−0.0102225	−	0.0946020i
$701$	−11843.1	−	16300.6i	−0.638097	−	0.878266i	0.360415	−	0.932792i	$-0.382635\pi$
$701$	−11843.1	−	16300.6i	−0.638097	−	0.878266i	−0.998512	+	0.0545265i	$0.982635\pi$
$702$	−35775.5	−	34618.2i	−1.92344	−	1.86122i
$703$			3737.84i			0.200534i
$704$	−23629.9	+	78492.5i	−1.26504	+	4.20213i
$705$	−3972.96	−	3181.35i	−0.212242	−	0.169953i
$706$	−1303.54	−	423.546i	−0.0694893	−	0.0225784i
$707$	−28179.9	−	5903.85i	−1.49903	−	0.314055i
$708$	−12049.9	−	44005.1i	−0.639639	−	2.33589i
$709$	10849.9	+	33392.5i	0.574719	+	1.76880i	0.637133	+	0.770754i	$0.280120\pi$
$709$	10849.9	+	33392.5i	0.574719	+	1.76880i	−0.0624130	+	0.998050i	$0.519880\pi$
$710$	−11520.2	−	35455.6i	−0.608939	−	1.87412i
$711$	−7305.05	+	16903.6i	−0.385318	+	0.891608i
$712$	15820.2	+	21774.6i	0.832707	+	1.14612i
$713$	330.946	−	1018.55i	0.0173829	−	0.0534991i
$714$	−39311.1	+	2391.48i	−2.06048	+	0.125349i
$715$	580.916	+	26713.8i	0.0303846	+	1.39726i
$716$		−	60745.4i		−	3.17062i
$717$	−2640.36	−	4017.44i	−0.137526	−	0.209252i
$718$	−36237.0	+	26327.7i	−1.88350	+	1.36844i
$719$	−8454.13	−	6142.28i	−0.438506	−	0.318593i	0.346535	−	0.938037i	$-0.387358\pi$
$719$	−8454.13	−	6142.28i	−0.438506	−	0.318593i	−0.785041	+	0.619444i	$0.787358\pi$
$720$	−67721.6	+	40095.0i	−3.50533	+	2.07535i
$721$	−6413.00	−	3677.62i	−0.331252	−	0.189961i
$722$	−3298.76	+	4540.35i	−0.170038	+	0.234037i
$723$	597.385	−	12733.4i	0.0307289	−	0.654995i
$724$	−46396.1	−	15075.0i	−2.38162	−	0.773837i
$725$		−	869.702i		−	0.0445516i
$726$	−36190.7	−	11895.1i	−1.85009	−	0.608082i
$727$			18994.6i			0.969012i	0.874788	+	0.484506i	$0.161001\pi$
$727$			18994.6i			0.969012i	−0.874788	+	0.484506i	$0.838999\pi$
$728$	85982.8	−	38583.3i	4.37738	−	1.96427i
$729$	18909.5	+	5463.76i	0.960700	+	0.277588i
$730$	−43357.2	−	31500.8i	−2.19825	−	1.59712i
$731$	−5789.71	−	17818.9i	−0.292941	−	0.901581i
$732$	8877.93	+	3352.22i	0.448275	+	0.169264i
$733$	18765.2	−	25828.1i	0.945578	−	1.30148i	−0.00788511	−	0.999969i	$-0.502510\pi$
$733$	18765.2	−	25828.1i	0.945578	−	1.30148i	0.953464	−	0.301508i	$-0.0974901\pi$
$734$	−34003.0	+	24704.6i	−1.70991	+	1.24232i
$735$	−9403.07	−	17949.3i	−0.471887	−	0.900775i
$736$	68287.5			3.41998
$737$	2952.28	−	64.1999i	0.147556	−	0.00320873i
$738$	23718.9	−	5313.94i	1.18307	−	0.265053i
$739$	5400.87	−	16622.2i	0.268842	−	0.827411i	−0.721941	−	0.691954i	$-0.756750\pi$
$739$	5400.87	−	16622.2i	0.268842	−	0.827411i	0.990783	−	0.135456i	$-0.0432500\pi$
$740$	10050.6	−	7302.22i	0.499282	−	0.362750i
$741$	−6756.06	−	24672.4i	−0.334939	−	1.22316i
$742$	11372.3	−	19831.0i	0.562657	−	0.981157i
$743$	26481.3	−	8604.30i	1.30754	−	0.424847i	0.429344	−	0.903141i	$-0.358745\pi$
$743$	26481.3	−	8604.30i	1.30754	−	0.424847i	0.878200	+	0.478294i	$0.158745\pi$
$744$	1326.55	+	4844.42i	0.0653680	+	0.238717i
$745$	−12498.9	−	17203.3i	−0.614665	−	0.846014i
$746$	6555.50	+	2130.01i	0.321734	+	0.104538i
$747$	−961.523	−	4291.79i	−0.0470954	−	0.210212i
$748$	17456.5	−	57985.9i	0.853304	−	2.83446i
$749$	9461.73	−	8569.55i	0.461581	−	0.418057i
$750$	−21579.0	−	32833.4i	−1.05060	−	1.59854i
$751$	10523.2	−	7645.52i	0.511312	−	0.371490i	−0.302009	−	0.953305i	$-0.597657\pi$
$751$	10523.2	−	7645.52i	0.511312	−	0.371490i	0.813321	+	0.581815i	$0.197657\pi$
$752$	−17870.1	−	12983.4i	−0.866561	−	0.629593i
$753$	6683.01	−	17699.1i	0.323429	−	0.856562i
$754$	68910.2	−	22390.3i	3.32833	−	1.08144i
$755$	−14621.8	−	10623.4i	−0.704824	−	0.512085i
$756$	−35650.8	+	45810.7i	−1.71509	+	2.20386i
$757$	−9448.20	+	29078.6i	−0.453634	+	1.39614i	0.419098	+	0.907941i	$0.362346\pi$
$757$	−9448.20	+	29078.6i	−0.453634	+	1.39614i	−0.872732	+	0.488200i	$0.837654\pi$
$758$			76394.7i			3.66066i
$759$	−417.013	+	16585.5i	−0.0199428	+	0.793171i
$760$	−68631.6			−3.27570
$761$	−12472.6	+	38386.9i	−0.594130	+	1.82854i	−0.0351213	+	0.999383i	$0.511182\pi$
$761$	−12472.6	+	38386.9i	−0.594130	+	1.82854i	−0.559009	+	0.829162i	$0.688818\pi$
$762$	−2431.83	+	51835.2i	−0.115612	+	2.46429i
$763$	302.025	+	2795.03i	0.0143303	+	0.132617i
$764$	31790.8	−	10329.5i	1.50543	−	0.489145i
$765$	19625.4	−	11619.3i	0.927525	−	0.549147i
$766$	−27422.7	+	37744.1i	−1.29350	+	1.78035i
$767$	−14882.0	−	20483.4i	−0.700599	−	0.964292i
$768$	−68665.8	+	45128.9i	−3.22625	+	2.12038i
$769$		−	7719.01i		−	0.361970i	−0.983486	−	0.180985i	$-0.942071\pi$
$769$		−	7719.01i		−	0.361970i	0.983486	−	0.180985i	$-0.0579285\pi$
$770$	41959.9	−	5459.38i	1.96380	−	0.255510i
$771$	−20342.5	−	16289.3i	−0.950215	−	0.760886i
$772$	3246.33	−	9991.17i	0.151344	−	0.465790i
$773$	10474.1	−	7609.90i	0.487359	−	0.354087i	−0.316809	−	0.948489i	$-0.602611\pi$
$773$	10474.1	−	7609.90i	0.487359	−	0.354087i	0.804168	+	0.594402i	$0.202611\pi$
$774$	−34426.5	−	14877.8i	−1.59875	−	0.690919i
$775$	49.5689	−	16.1059i	0.00229751	−	0.000746506i
$776$	38724.0	+	119180.i	1.79138	+	5.51330i
$777$	2530.33	−	3968.96i	0.116828	−	0.183251i
$778$	19352.4	−	14060.3i	0.891796	−	0.647928i
$779$	11878.8	+	3859.64i	0.546342	+	0.177517i
$780$	−53142.8	+	66366.2i	−2.43951	+	3.04653i
$781$	20504.5	−	7158.77i	0.939446	−	0.327991i
$782$	−35816.6			−1.63785
$783$	−19921.3	+	20587.3i	−0.909234	+	0.939630i
$784$	−44413.4	−	75898.9i	−2.02320	−	3.45749i
$785$	7696.30	−	10593.1i	0.349927	−	0.481633i
$786$	−31895.1	−	12043.3i	−1.44740	−	0.546526i
$787$	12689.4	−	4123.03i	0.574749	−	0.186747i	−0.00719769	−	0.999974i	$-0.502291\pi$
$787$	12689.4	−	4123.03i	0.574749	−	0.186747i	0.581947	+	0.813227i	$0.302291\pi$
$788$	−11337.4	+	15604.7i	−0.512538	+	0.705448i
$789$	−210.773	+	4492.68i	−0.00951041	+	0.202717i
$790$	40620.6	+	13198.4i	1.82939	+	0.594404i
$791$	−4192.26	+	3796.95i	−0.188444	+	0.170675i
$792$	−41087.4	−	66077.4i	−1.84341	−	2.96459i
$793$	5266.16			0.235822
$794$	−9685.61	+	29809.2i	−0.432908	+	1.33236i
$795$	−620.396	+	13223.9i	−0.0276769	+	0.589941i
$796$	30343.4	−	41764.1i	1.35112	−	1.85966i
$797$	−7633.97	−	23494.9i	−0.339284	−	1.04421i	−0.964573	−	0.263815i	$-0.915019\pi$
$797$	−7633.97	−	23494.9i	−0.339284	−	1.04421i	0.625290	−	0.780393i	$-0.284981\pi$
$798$	−37695.2	+	14834.3i	−1.67218	+	0.658057i
$799$	5178.65	+	3762.51i	0.229296	+	0.166593i
$800$	1953.39	+	2688.61i	0.0863283	+	0.118821i
$801$	−9159.31	−	861.309i	−0.404030	−	0.0379936i
$802$	58607.7			2.58044
$803$	17797.9	−	25651.4i	0.782158	−	1.12730i
$804$	7334.45	+	5873.07i	0.321724	+	0.257621i
$805$	−7544.40	−	16812.7i	−0.330317	−	0.736111i
$806$	2552.28	+	3512.92i	0.111539	+	0.153520i
$807$	7332.87	+	26778.8i	0.319863	+	1.16810i
$808$	116791.	−	37947.6i	5.08501	−	1.65222i
$809$	41167.5	−	13376.1i	1.78909	−	0.581310i	0.789611	−	0.613608i	$-0.210282\pi$
$809$	41167.5	−	13376.1i	1.78909	−	0.581310i	0.999478	+	0.0322973i	$0.0102823\pi$
$810$	8510.86	−	44852.8i	0.369187	−	1.94564i
$811$	17292.9	+	23801.6i	0.748749	+	1.03056i	0.998067	+	0.0621429i	$0.0197935\pi$
$811$	17292.9	+	23801.6i	0.748749	+	1.03056i	−0.249318	+	0.968422i	$0.580207\pi$
$812$	−34589.2	−	77081.9i	−1.49488	−	3.33133i
$813$	3048.56	−	3807.13i	0.131510	−	0.164234i
$814$	5948.88	+	7824.37i	0.256152	+	0.336909i
$815$	23608.3			1.01468
$816$	82714.1	−	54361.8i	3.54849	−	2.33216i
$817$	−11327.4	−	15590.8i	−0.485060	−	0.667628i
$818$	32052.5	+	23287.5i	1.37004	+	0.995391i
$819$	−9528.17	+	30771.5i	−0.406521	+	1.31287i
$820$	−12828.1	−	39480.9i	−0.546314	−	1.68138i
$821$	−2286.62	+	3147.27i	−0.0972030	+	0.133789i	−0.854848	−	0.518878i	$-0.826350\pi$
$821$	−2286.62	+	3147.27i	−0.0972030	+	0.133789i	0.757645	+	0.652667i	$0.226350\pi$
$822$	−88019.1	−	4129.39i	−3.73482	−	0.175218i
$823$	−4750.00	+	14619.0i	−0.201184	+	0.619181i	0.798664	+	0.601777i	$0.205540\pi$
$823$	−4750.00	+	14619.0i	−0.201184	+	0.619181i	−0.999849	+	0.0174046i	$0.994460\pi$
$824$	31530.9			1.33305
$825$	−664.933	+	458.017i	−0.0280606	+	0.0193286i
$826$	−29717.5	+	26915.4i	−1.25182	+	1.13378i
$827$	42150.0	+	13695.4i	1.77231	+	0.575858i	0.998352	−	0.0573807i	$-0.0182749\pi$
$827$	42150.0	+	13695.4i	1.77231	+	0.575858i	0.773957	+	0.633239i	$0.218275\pi$
$828$	−34891.7	+	39615.8i	−1.46446	+	1.66273i
$829$	−14855.4	+	20446.7i	−0.622374	+	0.856625i	−0.997523	−	0.0703398i	$-0.977592\pi$
$829$	−14855.4	+	20446.7i	−0.622374	+	0.856625i	0.375149	+	0.926965i	$0.377592\pi$
$830$	−9701.94	+	3152.35i	−0.405734	+	0.131831i
$831$	7378.16	−	19540.1i	0.307997	−	0.815691i
$832$	−85077.6	+	117099.i	−3.54511	+	4.87943i
$833$	12870.8	+	21995.1i	0.535348	+	0.914868i
$834$	50450.7	−	33157.5i	2.09468	−	1.37668i
$835$	−21908.1			−0.907976
$836$	−1354.16	−	62272.2i	−0.0560224	−	2.57623i
$837$	−1542.30	−	754.169i	−0.0636914	−	0.0311444i
$838$	−39051.0	−	12688.4i	−1.60978	−	0.523049i
$839$	−7939.93	+	5768.70i	−0.326719	+	0.237375i	−0.739037	−	0.673665i	$-0.764719\pi$
$839$	−7939.93	+	5768.70i	−0.326719	+	0.237375i	0.412318	+	0.911040i	$0.364719\pi$
$840$	72875.4	+	46460.2i	2.99338	+	1.90837i
$841$	−5348.06	−	16459.6i	−0.219282	−	0.674880i
$842$	1825.85	−	593.254i	0.0747303	−	0.0242813i
$843$	16977.0	−	4648.82i	0.693616	−	0.189934i
$844$	−50264.3	+	36519.1i	−2.04996	+	1.48938i
$845$	−6861.09	+	21116.3i	−0.279324	+	0.859670i
$846$	12503.3	−	2801.21i	0.508124	−	0.113839i
$847$	3711.14	+	24369.5i	0.150551	+	0.988602i
$848$			57452.6i			2.32657i
$849$	21431.2	+	32608.6i	0.866335	+	1.31817i
$850$	−1024.55	−	1410.17i	−0.0413431	−	0.0569039i
$851$	2516.08	−	3463.08i	0.101351	−	0.139498i
$852$	64650.4	+	24411.4i	2.59963	+	0.981596i
$853$	−14830.5	+	4818.71i	−0.595294	+	0.193423i	−0.591140	−	0.806569i	$-0.701322\pi$
$853$	−14830.5	+	4818.71i	−0.595294	+	0.193423i	−0.00415354	+	0.999991i	$0.501322\pi$
$854$	−895.924	−	8291.14i	−0.0358992	−	0.332221i
$855$	15505.0	−	17604.3i	0.620187	−	0.704155i
$856$	−16825.2	+	51782.7i	−0.671815	+	2.06763i
$857$	−35599.3			−1.41896			−0.709480	−	0.704726i	$-0.751070\pi$
$857$	−35599.3			−1.41896			−0.709480	+	0.704726i	$0.751070\pi$
$858$	−53409.2	−	40894.0i	−2.12513	−	1.62715i
$859$			42673.7i			1.69500i	0.530794	+	0.847501i	$0.321894\pi$
$859$			42673.7i			1.69500i	−0.530794	+	0.847501i	$0.678106\pi$
$860$	−19792.8	+	60916.1i	−0.784803	+	2.41537i
$861$	−10000.5	−	12139.6i	−0.395837	−	0.480508i
$862$	10335.5	+	7509.15i	0.408384	+	0.296708i
$863$	−38936.0	+	12651.1i	−1.53580	+	0.499012i	−0.950214	−	0.311598i	$-0.899136\pi$
$863$	−38936.0	+	12651.1i	−1.53580	+	0.499012i	−0.585587	+	0.810610i	$0.699136\pi$
$864$	15345.1	−	108388.i	0.604226	−	4.26786i
$865$	28683.1	+	20839.5i	1.12746	+	0.819149i
$866$	73816.6	−	53630.9i	2.89653	−	2.10445i
$867$	−2636.44	+	1732.74i	−0.103274	+	0.0678742i
$868$	3752.75	−	3398.89i	0.146747	−	0.132910i
$869$	−7172.67	+	23825.8i	−0.279996	+	0.930074i
$870$	51866.8	+	41532.4i	2.02121	+	1.61848i
$871$	4959.02	+	1611.28i	0.192916	+	0.0626822i
$872$	−7047.93	−	9700.64i	−0.273707	−	0.376726i
$873$	−39318.6	−	16991.9i	−1.52432	−	0.658751i
$874$	−35036.9	+	11384.2i	−1.35600	+	0.440590i
$875$	−12647.3	+	22054.3i	−0.488636	+	0.852080i
$876$	95815.9	−	26237.3i	3.69557	−	1.01196i
$877$	−2395.61	+	1740.51i	−0.0922393	+	0.0670158i	−0.632949	−	0.774193i	$-0.718156\pi$
$877$	−2395.61	+	1740.51i	−0.0922393	+	0.0670158i	0.540710	+	0.841209i	$0.318156\pi$
$878$	−26110.5	+	80359.8i	−1.00363	+	3.08885i
$879$	−20919.0	−	16750.9i	−0.802707	−	0.642769i
$880$	−84653.2	+	64361.9i	−3.24279	+	2.46550i
$881$	−15924.0			−0.608960			−0.304480	−	0.952519i	$-0.598483\pi$
$881$	−15924.0			−0.608960			−0.304480	+	0.952519i	$0.598483\pi$
$882$	50068.2	+	9766.22i	1.91143	+	0.372841i
$883$	−25727.9	+	18692.4i	−0.980534	+	0.712400i	−0.957828	−	0.287343i	$-0.907228\pi$
$883$	−25727.9	+	18692.4i	−0.980534	+	0.712400i	−0.0227060	+	0.999742i	$0.507228\pi$
$884$	62850.6	−	86506.5i	2.39128	−	3.29132i
$885$	8201.93	−	21721.8i	0.311531	−	0.825051i
$886$	−9526.49	−	29319.5i	−0.361229	−	1.11175i
$887$	13269.5	+	9640.88i	0.502308	+	0.364948i	0.809898	−	0.586571i	$-0.199522\pi$
$887$	13269.5	+	9640.88i	0.502308	+	0.364948i	−0.307590	+	0.951519i	$0.599522\pi$
$888$	−940.817	+	20053.8i	−0.0355538	+	0.757838i
$889$	30635.0	−	13746.9i	1.15575	−	0.518624i
$890$			21338.0i			0.803654i
$891$	26231.4	+	4388.89i	0.986290	+	0.165021i
$892$			16956.3i			0.636478i
$893$	6261.82	+	2034.59i	0.234652	+	0.0762429i
$894$	53473.8	+	2508.71i	2.00048	+	0.0938521i
$895$	18170.5	−	25009.5i	0.678628	−	0.934051i
$896$	98550.8	+	56515.2i	3.67450	+	2.10719i
$897$	−10348.4	+	27406.5i	−0.385200	+	1.02015i
$898$	39893.5	+	28984.3i	1.48248	+	1.07708i
$899$	2021.54	−	1468.73i	0.0749967	−	0.0544883i
$900$	−2557.84	−	240.530i	−0.0947348	−	0.00890852i
$901$		−	16649.5i		−	0.615620i
$902$	31008.4	−	10826.0i	1.14464	−	0.399631i
$903$	1473.59	+	24222.9i	0.0543058	+	0.892676i
$904$	7454.83	−	22943.6i	0.274274	−	0.844129i
$905$	−14592.4	−	20084.8i	−0.535988	−	0.737724i
$906$	43884.1	−	12016.8i	1.60922	−	0.440653i
$907$	−14049.7	−	43240.5i	−0.514347	−	1.58300i	−0.784467	−	0.620170i	$-0.787064\pi$
$907$	−14049.7	−	43240.5i	−0.514347	−	1.58300i	0.270121	−	0.962827i	$-0.412936\pi$
$908$	−24517.9	−	75458.4i	−0.896096	−	2.75790i
$909$	−16651.2	+	38530.2i	−0.607576	+	1.40590i
$910$	73127.6	+	15320.7i	2.66391	+	0.558105i
$911$	1466.35	+	476.448i	0.0533288	+	0.0173276i	0.335560	−	0.942019i	$-0.391075\pi$
$911$	1466.35	+	476.448i	0.0533288	+	0.0173276i	−0.282231	+	0.959346i	$0.591075\pi$
$912$	63634.8	−	79468.9i	2.31048	−	2.88539i
$913$	−1958.90	−	5610.77i	−0.0710078	−	0.203384i
$914$			35343.1i			1.27905i
$915$	2652.40	+	4035.75i	0.0958314	+	0.145812i
$916$	−58083.4	−	79944.9i	−2.09512	−	2.88368i
$917$	2370.03	+	21933.0i	0.0853493	+	0.789848i
$918$	−8048.47	+	56849.2i	−0.289367	+	2.04390i
$919$	−16034.6	−	49349.4i	−0.575552	−	1.77137i	−0.634293	−	0.773093i	$-0.718709\pi$
$919$	−16034.6	−	49349.4i	−0.575552	−	1.77137i	0.0587412	−	0.998273i	$-0.481291\pi$
$920$	63586.8	+	46198.5i	2.27869	+	1.65556i
$921$	789.103	−	16819.9i	0.0282322	−	0.601776i
$922$	92756.6	+	30138.4i	3.31320	+	1.07653i
$923$	38349.0			1.36758
$924$	−40717.3	+	67039.4i	−1.44968	+	2.38683i
$925$	208.321			0.00740493
$926$	−2026.58	−	658.476i	−0.0719196	−	0.0233681i
$927$	−7123.34	+	8087.78i	−0.252385	+	0.286556i
$928$	128899.	+	93650.3i	4.55960	+	3.31274i
$929$	3686.17	+	11344.9i	0.130182	+	0.400660i	0.994810	−	0.101754i	$-0.0324455\pi$
$929$	3686.17	+	11344.9i	0.130182	+	0.400660i	−0.864627	+	0.502414i	$0.832445\pi$
$930$	−1406.64	+	3725.30i	−0.0495973	+	0.131352i
$931$	19581.7	+	17425.4i	0.689326	+	0.613420i
$932$	41318.9	+	56870.6i	1.45220	+	1.99878i
$933$	20995.9	−	13799.1i	0.736738	−	0.484203i
$934$		−	14351.0i		−	0.502761i
$935$	24532.1	−	18651.7i	0.858058	−	0.652382i
$936$	−30036.7	−	134070.i	−1.04891	−	4.68184i
$937$	−10361.0	−	3366.48i	−0.361236	−	0.117373i	0.122775	−	0.992435i	$-0.460821\pi$
$937$	−10361.0	−	3366.48i	−0.361236	−	0.117373i	−0.484011	+	0.875062i	$0.660821\pi$
$938$	1693.16	−	8081.69i	0.0589379	−	0.281318i
$939$	24815.2	−	6795.18i	0.862423	−	0.236158i
$940$	−6762.27	−	20812.1i	−0.234639	−	0.722145i
$941$	−8872.26	−	27306.0i	−0.307362	−	0.945962i	−0.978785	−	0.204888i	$-0.934317\pi$
$941$	−8872.26	−	27306.0i	−0.307362	−	0.945962i	0.671424	−	0.741074i	$-0.265683\pi$
$942$	8705.80	+	31792.6i	0.301115	+	1.09964i
$943$	−8407.52	−	11572.0i	−0.290336	−	0.399613i
$944$	31138.1	−	95833.3i	1.07358	−	3.30414i
$945$	−28380.9	+	8196.67i	−0.976965	+	0.282156i
$946$	−48524.6	−	14608.2i	−1.66773	−	0.502064i
$947$			24157.4i			0.828946i	0.910062	+	0.414473i	$0.136034\pi$
$947$			24157.4i			0.828946i	−0.910062	+	0.414473i	$0.863966\pi$
$948$	−66162.4	+	43483.7i	−2.26673	+	1.48975i
$949$	44600.2	−	32403.9i	1.52559	−	1.10840i
$950$	−1450.46	−	1053.82i	−0.0495360	−	0.0359900i
$951$	7035.78	+	2656.64i	0.239906	+	0.0905862i
$952$	−94290.0	−	54071.8i	−3.21004	−	1.84084i
$953$	−28368.0	+	39045.2i	−0.964248	+	1.32717i	−0.0193491	+	0.999813i	$0.506159\pi$
$953$	−28368.0	+	39045.2i	−0.964248	+	1.32717i	−0.944899	+	0.327361i	$0.893841\pi$
$954$	−25009.9	−	22027.6i	−0.848770	−	0.747557i
$955$	16178.4	+	5256.69i	0.548190	+	0.178118i
$956$		−	20669.4i		−	0.699262i
$957$	−23532.8	+	30734.8i	−0.794887	+	1.03815i
$958$			76686.6i			2.58625i
$959$	23343.1	+	52020.0i	0.786013	+	1.75163i
$960$	−132591.	−	6220.45i	−4.45765	−	0.209129i
$961$	−23980.3	−	17422.7i	−0.804950	−	0.584831i
$962$	5363.19	+	16506.2i	0.179746	+	0.553203i
$963$	−9481.35	−	16014.3i	−0.317271	−	0.535880i
$964$	32214.8	−	44339.9i	1.07632	−	1.48142i
$965$	4325.16	−	3142.41i	0.144282	−	0.104827i
$966$	44909.9	+	11630.1i	1.49581	+	0.387364i
$967$	−19616.4			−0.652348			−0.326174	−	0.945310i	$-0.605759\pi$
$967$	−19616.4			−0.652348			−0.326174	+	0.945310i	$0.605759\pi$
$968$	−65437.9	−	82291.7i	−2.17278	−	2.73239i
$969$	−18441.0	+	23029.7i	−0.611364	+	0.763488i
$970$	−30700.2	+	94485.6i	−1.01621	+	3.12758i
$971$	−43323.0	+	31476.0i	−1.43182	+	1.04028i	−0.442150	+	0.896941i	$0.645784\pi$
$971$	−43323.0	+	31476.0i	−1.43182	+	1.04028i	−0.989674	+	0.143340i	$0.954216\pi$
$972$	55038.8	+	64283.4i	1.81622	+	2.12129i
$973$	−33887.8	−	19433.4i	−1.11654	−	0.640294i
$974$	−57643.4	+	18729.5i	−1.89632	+	0.616151i
$975$	−1375.07	+	376.536i	−0.0451666	+	0.0123680i
$976$	12319.1	+	16955.8i	0.404022	+	0.556088i
$977$	−16468.9	−	5351.08i	−0.539291	−	0.175226i	0.0266911	−	0.999644i	$-0.491503\pi$
$977$	−16468.9	−	5351.08i	−0.539291	−	0.175226i	−0.565982	+	0.824417i	$0.691503\pi$
$978$	−37148.8	+	46392.4i	−1.21461	+	1.51684i
$979$	−12427.9	+	270.256i	−0.405717	+	0.00882268i
$980$	8600.35	−	86695.1i	0.280335	−	2.82589i
$981$	4080.49	+	383.715i	0.132803	+	0.0124883i
$982$	−70765.1	+	51413.9i	−2.29960	+	1.67076i
$983$	9493.51	+	6897.44i	0.308032	+	0.223799i	0.731052	−	0.682322i	$-0.239030\pi$
$983$	9493.51	+	6897.44i	0.308032	+	0.223799i	−0.423019	+	0.906121i	$0.639030\pi$
$984$	62758.9	+	23697.2i	2.03321	+	0.767721i
$985$	−9335.49	+	3033.28i	−0.301983	+	0.0981203i
$986$	−67607.0	−	49119.3i	−2.18362	−	1.58649i
$987$	−5271.70	−	6399.34i	−0.170010	−	0.206376i
$988$	33986.7	−	104600.i	1.09439	−	3.36820i
$989$			22069.6i			0.709578i
$990$	4438.78	−	61527.4i	0.142499	−	1.97522i
$991$	29554.0			0.947339			0.473670	−	0.880703i	$-0.342929\pi$
$991$	29554.0			0.947339			0.473670	+	0.880703i	$0.342929\pi$
$992$	−2950.57	+	9080.92i	−0.0944362	+	0.290645i
$993$	35601.4	+	1670.23i	1.13774	+	0.0533768i
$994$	−6524.25	−	60377.4i	−0.208186	−	1.92661i
$995$	24985.4	−	8118.24i	0.796070	−	0.258659i
$996$	6679.84	−	17690.7i	0.212509	−	0.562803i
$997$	−8008.04	+	11022.1i	−0.254380	+	0.350124i	−0.917039	−	0.398797i	$-0.869428\pi$
$997$	−8008.04	+	11022.1i	−0.254380	+	0.350124i	0.662659	+	0.748921i	$0.269428\pi$
$998$	−8900.52	−	12250.5i	−0.282306	−	0.388561i
$999$	−4931.32	−	4771.80i	−0.156176	−	0.151124i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.4.u.a.20.2	yes	368
3.2	odd	2	inner	231.4.u.a.20.91	yes	368
7.6	odd	2	inner	231.4.u.a.20.1	✓	368
11.5	even	5	inner	231.4.u.a.104.92	yes	368
21.20	even	2	inner	231.4.u.a.20.92	yes	368
33.5	odd	10	inner	231.4.u.a.104.1	yes	368
77.27	odd	10	inner	231.4.u.a.104.91	yes	368
231.104	even	10	inner	231.4.u.a.104.2	yes	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.4.u.a.20.1	✓	368	7.6	odd	2	inner
231.4.u.a.20.2	yes	368	1.1	even	1	trivial
231.4.u.a.20.91	yes	368	3.2	odd	2	inner
231.4.u.a.20.92	yes	368	21.20	even	2	inner
231.4.u.a.104.1	yes	368	33.5	odd	10	inner
231.4.u.a.104.2	yes	368	231.104	even	10	inner
231.4.u.a.104.91	yes	368	77.27	odd	10	inner
231.4.u.a.104.92	yes	368	11.5	even	5	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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	231.u (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.23865 - 1.70214i) q^{2} +(5.19044 + 0.243508i) q^{3} +(18.0740 + 13.1315i) q^{4} +(3.51328 + 10.8128i) q^{5} +(-26.7764 - 10.1105i) q^{6} +(1.98968 + 18.4131i) q^{7} +(-46.4303 - 63.9058i) q^{8} +(26.8814 + 2.52783i) q^{9} -62.6244i q^{10} +(36.4742 - 0.793165i) q^{11} +(90.6144 + 72.5596i) q^{12} +(61.2668 + 19.9068i) q^{13} +(20.9184 - 99.8463i) q^{14} +(15.6025 + 56.9786i) q^{15} +(79.2260 + 243.832i) q^{16} +(-22.9593 - 70.6614i) q^{17} +(-136.519 - 58.9983i) q^{18} +(-44.9190 - 61.8257i) q^{19} +(-78.4891 + 241.565i) q^{20} +(5.84358 + 96.0565i) q^{21} +(-192.426 - 57.9291i) q^{22} +87.5177i q^{23} +(-225.432 - 343.005i) q^{24} +(-3.44574 + 2.50348i) q^{25} +(-287.071 - 208.569i) q^{26} +(138.911 + 19.6664i) q^{27} +(-205.830 + 358.925i) q^{28} +(-120.023 + 165.197i) q^{29} +(15.2495 - 325.048i) q^{30} +(-11.6382 - 3.78147i) q^{31} -780.270i q^{32} +(189.511 + 4.76490i) q^{33} +409.250i q^{34} +(-192.106 + 86.2042i) q^{35} +(452.660 + 398.682i) q^{36} +(-39.5701 - 28.7493i) q^{37} +(130.079 + 400.341i) q^{38} +(313.154 + 118.244i) q^{39} +(527.876 - 726.559i) q^{40} +(-132.224 + 96.0665i) q^{41} +(132.889 - 513.153i) q^{42} +252.173 q^{43} +(669.651 + 464.627i) q^{44} +(67.1091 + 299.543i) q^{45} +(148.967 - 458.474i) q^{46} +(-69.7013 + 50.6409i) q^{47} +(351.843 + 1284.89i) q^{48} +(-335.082 + 73.2722i) q^{49} +(22.3123 - 7.24969i) q^{50} +(-101.962 - 372.355i) q^{51} +(845.929 + 1164.32i) q^{52} +(213.123 + 69.2479i) q^{53} +(-694.230 - 339.471i) q^{54} +(136.721 + 391.601i) q^{55} +(1084.32 - 982.076i) q^{56} +(-218.094 - 331.841i) q^{57} +(909.947 - 661.115i) q^{58} +(-317.968 - 231.017i) q^{59} +(-466.216 + 1234.72i) q^{60} +(77.7467 - 25.2614i) q^{61} +(54.5317 + 39.6196i) q^{62} +(6.94020 + 499.999i) q^{63} +(-694.321 + 2136.90i) q^{64} +732.402i q^{65} +(-984.669 - 347.535i) q^{66} +80.9414 q^{67} +(512.926 - 1578.62i) q^{68} +(-21.3113 + 454.256i) q^{69} +(1153.11 - 124.602i) q^{70} +(566.163 - 183.958i) q^{71} +(-1086.57 - 1835.25i) q^{72} +(503.012 - 692.337i) q^{73} +(158.358 + 217.961i) q^{74} +(-18.4945 + 12.1551i) q^{75} -1707.29i q^{76} +(87.1766 + 670.025i) q^{77} +(-1439.24 - 1152.47i) q^{78} +(-210.755 + 648.639i) q^{79} +(-2358.16 + 1713.30i) q^{80} +(716.220 + 135.903i) q^{81} +(856.194 - 278.194i) q^{82} +(-50.3375 - 154.923i) q^{83} +(-1155.75 + 1812.86i) q^{84} +(683.383 - 496.507i) q^{85} +(-1321.05 - 429.234i) q^{86} +(-663.199 + 828.221i) q^{87} +(-1744.20 - 2294.09i) q^{88} -340.730 q^{89} +(158.304 - 1683.43i) q^{90} +(-244.644 + 1167.72i) q^{91} +(-1149.24 + 1581.79i) q^{92} +(-59.4865 - 22.4615i) q^{93} +(451.338 - 146.649i) q^{94} +(510.694 - 702.910i) q^{95} +(190.002 - 4049.95i) q^{96} +(-1508.77 - 490.228i) q^{97} +(1880.10 + 186.510i) q^{98} +(982.484 + 70.8794i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q + 340 q^{4} - 18 q^{7} + 42 q^{9} + 42 q^{15} - 1116 q^{16} - 262 q^{18} - 222 q^{21} + 696 q^{22} - 1516 q^{25} + 38 q^{28} + 624 q^{30} + 1430 q^{36} + 36 q^{37} + 390 q^{39} + 2130 q^{42} - 1376 q^{43}+ \cdots - 6218 q^{99}+O(q^{100}) \) 368 * q + 340 * q^4 - 18 * q^7 + 42 * q^9 + 42 * q^15 - 1116 * q^16 - 262 * q^18 - 222 * q^21 + 696 * q^22 - 1516 * q^25 + 38 * q^28 + 624 * q^30 + 1430 * q^36 + 36 * q^37 + 390 * q^39 + 2130 * q^42 - 1376 * q^43 + 1716 * q^46 + 474 * q^49 + 782 * q^51 + 670 * q^57 + 5576 * q^58 - 2708 * q^60 - 739 * q^63 + 5256 * q^64 - 2432 * q^67 + 2280 * q^70 - 3706 * q^72 - 10900 * q^78 + 732 * q^79 - 262 * q^81 - 510 * q^84 + 8008 * q^85 - 832 * q^88 - 5446 * q^91 + 2510 * q^93 - 6218 * q^99

Introduction

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