LMFDB - Embedded newform 231.4.u.a.20.91

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			20.91
Character	$\chi$	$=$	231.20
Dual form			231.4.u.a.104.91

$q$-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} +(-1.37235 + 5.01165i) q^{3} +(18.0740 + 13.1315i) q^{4} +(-3.51328 - 10.8128i) q^{5} +(-15.7198 + 23.9184i) q^{6} +(1.98968 + 18.4131i) q^{7} +(46.4303 + 63.9058i) q^{8} +(-23.2333 - 13.7554i) 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} +(59.0113 - 2.76850i) q^{15} +(79.2260 + 243.832i) q^{16} +(22.9593 + 70.6614i) q^{17} +(-98.2975 - 111.606i) q^{18} +(-44.9190 - 61.8257i) q^{19} +(78.4891 - 241.565i) q^{20} +(-95.0105 - 15.2975i) q^{21} +(-192.426 - 57.9291i) q^{22} -87.5177i q^{23} +(-383.992 + 144.992i) q^{24} +(-3.44574 + 2.50348i) q^{25} +(287.071 + 208.569i) q^{26} +(100.822 - 97.5602i) q^{27} +(-205.830 + 358.925i) q^{28} +(120.023 - 165.197i) q^{29} +(313.852 + 85.9422i) q^{30} +(-11.6382 - 3.78147i) q^{31} +780.270i q^{32} +(46.0802 - 183.885i) q^{33} +409.250i q^{34} +(192.106 - 86.2042i) q^{35} +(-239.289 - 553.705i) q^{36} +(-39.5701 - 28.7493i) q^{37} +(-130.079 - 400.341i) q^{38} +(-183.845 + 279.729i) q^{39} +(527.876 - 726.559i) q^{40} +(132.224 - 96.0665i) q^{41} +(-471.688 - 241.859i) 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} +(-1330.73 + 62.4308i) q^{48} +(-335.082 + 73.2722i) q^{49} +(-22.3123 + 7.24969i) q^{50} +(-385.638 + 18.0921i) 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} +(371.493 - 140.272i) q^{57} +(909.947 - 661.115i) q^{58} +(317.968 + 231.017i) q^{59} +(1102.92 + 724.870i) q^{60} +(77.7467 - 25.2614i) q^{61} +(-54.5317 - 39.6196i) q^{62} +(207.053 - 455.166i) q^{63} +(-694.321 + 2136.90i) q^{64} -732.402i q^{65} +(554.395 - 884.872i) q^{66} +80.9414 q^{67} +(-512.926 + 1578.62i) q^{68} +(438.608 + 120.104i) q^{69} +(1153.11 - 124.602i) q^{70} +(-566.163 + 183.958i) q^{71} +(-199.678 - 2123.41i) q^{72} +(503.012 - 692.337i) q^{73} +(-158.358 - 217.961i) q^{74} +(-7.81781 - 20.7045i) 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} +(350.576 + 639.169i) q^{81} +(856.194 - 278.194i) q^{82} +(50.3375 + 154.923i) q^{83} +(-1516.34 - 1524.12i) 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} +(-861.425 + 1454.97i) q^{90} +(-244.644 + 1167.72i) q^{91} +(1149.24 - 1581.79i) q^{92} +(34.9230 - 53.1370i) q^{93} +(451.338 - 146.649i) q^{94} +(-510.694 + 702.910i) q^{95} +(-3910.44 - 1070.80i) q^{96} +(-1508.77 - 490.228i) q^{97} +(-1880.10 - 186.510i) q^{98} +(858.329 + 483.291i) 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	$0.0268748\pi$
$2$	5.23865	+	1.70214i	1.85214	+	0.601797i	0.855703	+	0.517467i	$0.173125\pi$
$3$	−1.37235	+	5.01165i	−0.264108	+	0.964493i
$3$	−1.37235	+	5.01165i	−0.264108	+	0.964493i
$4$	18.0740	+	13.1315i	2.25925	+	1.64144i
$5$	−3.51328	−	10.8128i	−0.314238	−	0.967124i	−0.976067	−	0.217469i	$-0.930220\pi$
$5$	−3.51328	−	10.8128i	−0.314238	−	0.967124i	0.661830	−	0.749654i	$-0.269780\pi$
$6$	−15.7198	+	23.9184i	−1.06959	+	1.62744i
$7$	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
$9$	−23.2333	−	13.7554i	−0.860494	−	0.509461i
$10$		−	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
$15$	59.0113	−	2.76850i	1.01578	−	0.0476549i
$16$	79.2260	+	243.832i	1.23791	+	3.80988i
$17$	22.9593	+	70.6614i	0.327555	+	1.00811i	0.970274	+	0.242009i	$0.0778064\pi$
$17$	22.9593	+	70.6614i	0.327555	+	1.00811i	−0.642719	+	0.766102i	$0.722194\pi$
$18$	−98.2975	−	111.606i	−1.28716	−	1.46144i
$19$	−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
$21$	−95.0105	−	15.2975i	−0.987285	−	0.158961i
$22$	−192.426	−	57.9291i	−1.86479	−	0.561388i
$23$		−	87.5177i		−	0.793422i	−0.917944	−	0.396711i	$-0.870152\pi$
$23$		−	87.5177i		−	0.793422i	0.917944	−	0.396711i	$-0.129848\pi$
$24$	−383.992	+	144.992i	−3.26592	+	1.23318i
$25$	−3.44574	+	2.50348i	−0.0275659	+	0.0200278i
$26$	287.071	+	208.569i	2.16536	+	1.57322i
$27$	100.822	−	97.5602i	0.718635	−	0.695388i
$28$	−205.830	+	358.925i	−1.38922	+	2.42252i
$29$	120.023	−	165.197i	0.768541	−	1.05781i	−0.227914	−	0.973681i	$-0.573190\pi$
$29$	120.023	−	165.197i	0.768541	−	1.05781i	0.996455	−	0.0841252i	$-0.0268096\pi$
$30$	313.852	+	85.9422i	1.91004	+	0.523028i
$31$	−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
$33$	46.0802	−	183.885i	0.243077	−	0.970007i
$34$			409.250i			2.06429i
$35$	192.106	−	86.2042i	0.927767	−	0.416319i
$36$	−239.289	−	553.705i	−1.10782	−	2.56345i
$37$	−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
$39$	−183.845	+	279.729i	−0.754840	+	1.14853i
$40$	527.876	−	726.559i	2.08661	−	2.87198i
$41$	132.224	−	96.0665i	0.503657	−	0.365929i	−0.306755	−	0.951789i	$-0.599243\pi$
$41$	132.224	−	96.0665i	0.503657	−	0.365929i	0.810412	+	0.585860i	$0.199243\pi$
$42$	−471.688	−	241.859i	−1.73293	−	0.888564i
$43$	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	−0.474349	−	0.880337i	$-0.657317\pi$
$47$	69.7013	−	50.6409i	0.216319	−	0.157165i	0.690668	+	0.723172i	$0.257317\pi$
$48$	−1330.73	+	62.4308i	−4.00155	+	0.187731i
$49$	−335.082	+	73.2722i	−0.976917	+	0.213621i
$50$	−22.3123	+	7.24969i	−0.0631086	+	0.0205052i
$51$	−385.638	+	18.0921i	−1.05883	+	0.0496746i
$52$	845.929	+	1164.32i	2.25595	+	3.10504i
$53$	−213.123	−	69.2479i	−0.552353	−	0.179470i	0.0195244	−	0.999809i	$-0.493785\pi$
$53$	−213.123	−	69.2479i	−0.552353	−	0.179470i	−0.571878	+	0.820339i	$0.693785\pi$
$54$	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
$57$	371.493	−	140.272i	0.863254	−	0.325956i
$58$	909.947	−	661.115i	2.06003	−	1.49670i
$59$	317.968	+	231.017i	0.701625	+	0.509760i	0.880461	−	0.474119i	$-0.157233\pi$
$59$	317.968	+	231.017i	0.701625	+	0.509760i	−0.178836	+	0.983879i	$0.557233\pi$
$60$	1102.92	+	724.870i	2.37312	+	1.55967i
$61$	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
$63$	207.053	−	455.166i	0.414067	−	0.910246i
$64$	−694.321	+	2136.90i	−1.35610	+	4.17363i
$65$		−	732.402i		−	1.39759i
$66$	554.395	−	884.872i	1.03396	−	1.65031i
$67$	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
$69$	438.608	+	120.104i	0.765250	+	0.209549i
$70$	1153.11	−	124.602i	1.96889	−	0.212755i
$71$	−566.163	+	183.958i	−0.946355	+	0.307489i	−0.741234	−	0.671247i	$-0.765759\pi$
$71$	−566.163	+	183.958i	−0.946355	+	0.307489i	−0.205121	+	0.978737i	$0.565759\pi$
$72$	−199.678	−	2123.41i	−0.326837	−	3.47565i
$73$	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
$75$	−7.81781	−	20.7045i	−0.0120363	−	0.0318766i
$76$		−	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
$81$	350.576	+	639.169i	0.480900	+	0.876776i
$82$	856.194	−	278.194i	1.15306	−	0.374652i
$83$	50.3375	+	154.923i	0.0665693	+	0.204879i	0.978808	−	0.204780i	$-0.0656477\pi$
$83$	50.3375	+	154.923i	0.0665693	+	0.204879i	−0.912239	+	0.409659i	$0.865648\pi$
$84$	−1516.34	−	1524.12i	−1.96960	−	1.97970i
$85$	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	$-0.434961\pi$
$89$	340.730			0.405813			0.202906	+	0.979198i	$0.434961\pi$
$90$	−861.425	+	1454.97i	−1.00891	+	1.70408i
$91$	−244.644	+	1167.72i	−0.281820	+	1.34517i
$92$	1149.24	−	1581.79i	1.30235	−	1.79254i
$93$	34.9230	−	53.1370i	0.0389392	−	0.0592479i
$94$	451.338	−	146.649i	0.495234	−	0.160911i
$95$	−510.694	+	702.910i	−0.551538	+	0.759126i
$96$	−3910.44	−	1070.80i	−4.15737	−	1.13842i
$97$	−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
$99$	858.329	+	483.291i	0.871367	+	0.490632i
$100$	−95.1527			−0.0951527
$101$	480.399	−	1478.52i	0.473282	−	1.45661i	−0.374978	−	0.927034i	$-0.622350\pi$
$101$	480.399	−	1478.52i	0.473282	−	1.45661i	0.848260	−	0.529579i	$-0.177650\pi$
$102$	−2051.02	−	561.632i	−1.99099	−	0.545194i
$103$	−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
$105$	168.390	+	1081.07i	0.156507	+	1.00478i
$106$	−998.607	−	725.531i	−0.915031	−	0.664809i
$107$	405.149	+	557.639i	0.366049	+	0.503823i	0.951822	−	0.306653i	$-0.0992090\pi$
$107$	405.149	+	557.639i	0.366049	+	0.503823i	−0.585773	+	0.810475i	$0.699209\pi$
$108$	3103.36	−	439.361i	2.76501	−	0.391459i
$109$	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	0.727732	−	0.685861i	$-0.240574\pi$
$113$	−179.511	−	247.076i	−0.149442	−	0.205690i	−0.877175	+	0.480172i	$0.840574\pi$
$114$	2184.88	−	102.503i	1.79503	−	0.0842132i
$115$	−946.309	+	307.474i	−0.767337	+	0.249323i
$116$	4338.59	−	1409.69i	3.47265	−	1.12833i
$117$	−1149.61	−	1305.25i	−0.908385	−	1.03137i
$118$	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
$123$	299.995	+	794.498i	0.219916	+	0.582419i
$124$	−160.692	−	221.173i	−0.116375	−	0.160177i
$125$	−1110.56	−	806.870i	−0.794653	−	0.577349i
$126$	1859.43	−	2032.02i	1.31469	−	1.43672i
$127$	−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
$129$	−346.069	+	1263.80i	−0.236199	+	0.862572i
$130$	1246.65	−	3836.79i	0.841065	−	2.58853i
$131$	−1191.16			−0.794446			−0.397223	−	0.917722i	$-0.630026\pi$
$131$	−1191.16			−0.794446			−0.397223	+	0.917722i	$0.630026\pi$
$132$	3247.54	−	2718.43i	2.14138	−	1.79249i
$133$	1049.03	−	950.110i	0.683926	−	0.619436i
$134$	424.023	+	137.773i	0.273358	+	0.0888195i
$135$	−1409.11	−	747.405i	−0.898348	−	0.476491i
$136$	−3449.66	+	4748.06i	−2.17505	+	2.99369i
$137$	−2927.97	+	951.354i	−1.82593	+	0.593282i	−0.826390	+	0.563097i	$0.809610\pi$
$137$	−2927.97	+	951.354i	−1.82593	+	0.593282i	−0.999544	+	0.0301847i	$0.990390\pi$
$138$	2093.28	+	1375.76i	1.29124	+	0.848639i
$139$	−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
$141$	158.141	+	418.815i	0.0944528	+	0.250146i
$142$	−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
$147$	92.6340	−	1779.87i	0.0519750	−	0.998648i
$148$	−337.666	−	1039.23i	−0.187541	−	0.577191i
$149$	1778.81	−	577.971i	0.978027	−	0.317780i	0.223975	−	0.974595i	$-0.428097\pi$
$149$	1778.81	−	577.971i	0.978027	−	0.317780i	0.754052	+	0.656815i	$0.228097\pi$
$150$	−5.71283	−	121.770i	−0.00310967	−	0.0662834i
$151$	−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
$156$	−6996.08	+	2641.65i	−3.59061	+	1.35578i
$157$	−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
$159$	639.525	−	973.067i	0.318979	−	0.485341i
$160$	8436.88	−	2741.31i	4.16871	−	1.35450i
$161$	1611.47	−	174.132i	0.788830	−	0.0852393i
$162$	748.588	+	3945.11i	0.363053	+	1.91332i
$163$	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
$165$	−2150.20	+	147.785i	−1.01450	+	0.0697274i
$166$			897.267i			0.419527i
$167$	595.465	−	1832.65i	0.275919	−	0.849191i	−0.713056	−	0.701107i	$-0.752690\pi$
$167$	595.465	−	1832.65i	0.275919	−	0.849191i	0.988975	−	0.148084i	$-0.0473105\pi$
$168$	−3433.76	−	6781.98i	−1.57691	−	3.11453i
$169$	1579.93	+	1147.89i	0.719130	+	0.522479i
$170$	4425.12	−	1437.81i	1.99642	−	0.648676i
$171$	193.179	+	2054.30i	0.0863903	+	0.918690i
$172$	4557.78	+	3311.42i	2.02051	+	1.46798i
$173$	−2522.87	+	1832.97i	−1.10873	+	0.805540i	−0.982463	−	0.186456i	$-0.940300\pi$
$173$	−2522.87	+	1832.97i	−1.10873	+	0.805540i	−0.126267	+	0.991996i	$0.540300\pi$
$174$	2064.52	+	5467.61i	0.899487	+	2.38218i
$175$	−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	0.999697	−	0.0246249i	$-0.00783914\pi$
$179$	1598.22	+	2199.76i	0.667354	+	0.918534i	−0.332343	+	0.943159i	$0.607839\pi$
$180$	−5146.39	+	4532.70i	−2.13105	+	1.87693i
$181$	−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
$183$	19.9062	+	424.307i	0.00804105	+	0.171397i
$184$	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
$189$	1996.99	+	1662.32i	0.768568	+	0.639768i
$190$	−3871.79	+	2813.02i	−1.47837	+	1.07410i
$191$	−879.463	+	1210.48i	−0.333171	+	0.458571i	−0.942431	−	0.334399i	$-0.891467\pi$
$191$	−879.463	+	1210.48i	−0.333171	+	0.458571i	0.609260	+	0.792970i	$0.291467\pi$
$192$	−9756.55	−	6412.26i	−3.66728	−	2.41023i
$193$	−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
$195$	3670.54	+	1005.11i	1.34796	+	0.369114i
$196$	−7018.45	−	3075.82i	−2.55774	−	1.12093i
$197$		−	863.376i		−	0.312249i	−0.987737	−	0.156124i	$-0.950100\pi$
$197$		−	863.376i		−	0.312249i	0.987737	−	0.156124i	$-0.0499001\pi$
$198$	3673.85	+	3992.79i	1.31863	+	1.43311i
$199$		−	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
$201$	−111.079	+	405.650i	−0.0389798	+	0.142350i
$202$	5033.28	−	6927.72i	1.75317	−	2.41303i
$203$	3280.60	+	1881.30i	1.13425	+	0.650451i
$204$	−7207.60	−	4737.02i	−2.47369	−	1.62577i
$205$	−1503.29	−	1092.20i	−0.512166	−	0.372111i
$206$	−1778.79	+	1292.36i	−0.601621	+	0.437104i
$207$	−1203.84	+	2033.33i	−0.404217	+	0.682735i
$208$			16516.0i			5.50565i
$209$	1687.42	+	2219.42i	0.558476	+	0.734547i
$210$	−957.997	+	5949.97i	−0.314800	+	1.95518i
$211$	−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
$213$	−144.960	−	3089.87i	−0.0466315	−	0.993963i
$214$	1173.25	+	3610.89i	0.374774	+	1.15344i
$215$	−885.955	−	2726.69i	−0.281031	−	0.864924i
$216$	10915.8	+	1913.34i	3.43856	+	0.602714i
$217$	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
$222$	1309.67	−	494.518i	0.395942	−	0.149504i
$223$	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
$225$	114.492	−	10.7665i	0.0339237	−	0.00319006i
$226$	−519.838	−	1599.90i	−0.153005	−	0.470900i
$227$	2873.18	+	2087.49i	0.840086	+	0.610358i	0.922395	−	0.386249i	$-0.126229\pi$
$227$	2873.18	+	2087.49i	0.840086	+	0.610358i	−0.0823090	+	0.996607i	$0.526229\pi$
$228$	8556.35	+	2342.99i	2.48534	+	0.680564i
$229$	−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
$231$	3477.57	+	482.606i	0.990507	+	0.137460i
$232$	16129.8			4.56453
$233$	−2992.54	−	972.336i	−0.841407	−	0.273390i	−0.143565	−	0.989641i	$-0.545857\pi$
$233$	−2992.54	−	972.336i	−0.841407	−	0.273390i	−0.697843	+	0.716251i	$0.745857\pi$
$234$	−3800.65	−	8794.54i	−1.06178	−	2.45691i
$235$	−792.449	−	575.748i	−0.219973	−	0.159820i
$236$	2713.34	+	8350.80i	0.748404	+	2.30335i
$237$	−2961.52	−	1946.39i	−0.811694	−	0.533467i
$238$	−7535.54	+	814.275i	−2.05234	+	0.221771i
$239$	543.813	+	748.494i	0.147181	+	0.202578i	0.876242	−	0.481871i	$-0.160043\pi$
$239$	543.813	+	748.494i	0.147181	+	0.202578i	−0.729061	+	0.684449i	$0.760043\pi$
$240$	5350.28	+	14169.5i	1.43900	+	3.81100i
$241$		−	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
$246$	219.220	+	4672.73i	0.0568168	+	1.21107i
$247$	−1521.29	−	4682.05i	−0.391893	−	1.20612i
$248$	−298.706	−	919.322i	−0.0764832	−	0.235391i
$249$	−845.500	+	39.6664i	−0.215186	+	0.0100954i
$250$	−4444.43	−	6117.23i	−1.12436	−	1.54755i
$251$	−1125.11	+	3462.73i	−0.282933	+	0.870778i	0.704078	+	0.710123i	$0.251361\pi$
$251$	−1125.11	+	3462.73i	−0.282933	+	0.870778i	−0.987011	+	0.160655i	$0.948639\pi$
$252$	9719.30	−	5507.75i	2.42960	−	1.37681i
$253$	69.4160	+	3192.14i	0.0172496	+	0.793234i
$254$		−	9986.66i		−	2.46700i
$255$	1550.48	+	4106.26i	0.380764	+	1.00841i
$256$	−12793.2	+	9294.81i	−3.12334	+	2.26924i
$257$	4057.52	+	2947.96i	0.984829	+	0.715520i	0.958783	−	0.284141i	$-0.0917082\pi$
$257$	4057.52	+	2947.96i	0.984829	+	0.715520i	0.0260464	+	0.999661i	$0.491708\pi$
$258$	−3964.10	+	6031.57i	−0.956567	+	1.45546i
$259$	450.632	−	785.808i	0.108112	−	0.188524i
$260$	9617.55	−	13237.4i	2.29406	−	3.15750i
$261$	−5060.90	+	2187.12i	−1.20024	+	0.518695i
$262$	−6240.08	−	2027.53i	−1.47143	−	0.478095i
$263$		−	865.568i		−	0.202940i	−0.994839	−	0.101470i	$-0.967645\pi$
$263$		−	865.568i		−	0.202940i	0.994839	−	0.101470i	$-0.0323546\pi$
$264$	13890.8	−	5593.03i	3.23834	−	1.30389i
$265$			2547.74i			0.590590i
$266$	7112.69	−	3191.70i	1.63950	−	0.735698i
$267$	−467.600	+	1707.62i	−0.107178	+	0.391404i
$268$	1462.93	+	1062.88i	0.333444	+	0.242261i
$269$	−1651.17	−	5081.79i	−0.374252	−	1.15183i	−0.943982	−	0.329998i	$-0.892952\pi$
$269$	−1651.17	−	5081.79i	−0.374252	−	1.15183i	0.569729	−	0.821832i	$-0.307048\pi$
$270$	−6109.65	−	6313.89i	−1.37712	−	1.42315i
$271$	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
$273$	−5516.46	−	2828.58i	−1.22297	−	0.627083i
$274$	−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
$279$	218.378	+	247.944i	0.0468600	+	0.0532045i
$280$	14428.5	+	8274.20i	3.07952	+	1.76599i
$281$	−3221.71	+	1046.80i	−0.683954	+	0.222230i	−0.630325	−	0.776331i	$-0.717079\pi$
$281$	−3221.71	+	1046.80i	−0.683954	+	0.222230i	−0.0536281	+	0.998561i	$0.517079\pi$
$282$	115.560	+	2463.20i	0.0244026	+	0.520147i
$283$	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
$288$	10733.0	−	18128.3i	2.19599	−	3.70909i
$289$	−491.199	+	356.877i	−0.0999794	+	0.0726393i
$290$	−10345.4	−	7516.36i	−2.09483	−	1.52199i
$291$	4527.40	−	6888.65i	0.912031	−	1.38770i
$292$	18182.9	−	5907.98i	3.64408	−	1.18403i
$293$	4172.51	+	3031.51i	0.831948	+	0.604445i	0.920110	−	0.391661i	$-0.128099\pi$
$293$	4172.51	+	3031.51i	0.831948	+	0.604445i	−0.0881620	+	0.996106i	$0.528099\pi$
$294$	3514.86	−	9166.44i	0.697249	−	1.81836i
$295$	1380.82	−	4249.74i	0.272524	−	0.838743i
$296$		−	3863.60i		−	0.758672i
$297$	−3600.01	+	3638.40i	−0.703346	+	0.710847i
$298$	10302.4			2.00268
$299$	1742.20	−	5361.93i	0.336969	−	1.03708i
$300$	130.582	−	476.872i	0.0251306	−	0.0917741i
$301$	501.743	+	4643.28i	0.0960798	+	0.889151i
$302$	−8327.83	+	2705.88i	−1.58680	+	0.515582i
$303$	6750.54	+	4436.63i	1.27990	+	0.841181i
$304$	11516.4	−	15850.9i	2.17272	−	2.99050i
$305$	−546.292	−	751.906i	−0.102559	−	0.141161i
$306$	5629.41	−	9508.24i	1.05167	−	1.77631i
$307$		−	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	−0.884216	−	0.467078i	$-0.845307\pi$
$311$	−3911.78	+	2842.08i	−0.713237	+	0.518197i	0.170979	+	0.985275i	$0.445307\pi$
$312$	−26412.3	+	1239.12i	−4.79263	+	0.224845i
$313$	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
$315$	−5649.04	−	639.690i	−1.01044	−	0.114420i
$316$	−12326.8	+	8955.95i	−2.19442	+	1.59434i
$317$	−1376.51	−	447.255i	−0.243888	−	0.0792439i	0.184522	−	0.982828i	$-0.440926\pi$
$317$	−1376.51	−	447.255i	−0.243888	−	0.0792439i	−0.428410	+	0.903584i	$0.640926\pi$
$318$	5006.54	−	4008.99i	0.882871	−	0.706960i
$319$	−4246.72	+	6120.65i	−0.745362	+	1.07427i
$320$	25545.1			4.46255
$321$	−3350.70	+	1265.19i	−0.582610	+	0.219988i
$322$	8738.31	+	1830.73i	1.51232	+	0.316840i
$323$	3337.38	−	4593.51i	0.574913	−	0.791299i
$324$	−2056.96	+	16155.9i	−0.352702	+	2.77022i
$325$	−260.946	+	84.7863i	−0.0445374	+	0.0144711i
$326$	6723.03	−	9253.45i	1.14219	−	1.57209i
$327$	−208.316	+	760.749i	−0.0352291	+	0.128653i
$328$	12278.4	+	3989.50i	2.06696	+	0.671595i
$329$	1071.14	+	1182.66i	0.179495	+	0.198182i
$330$	−11515.7	−	2885.74i	−1.92096	−	0.481379i
$331$	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
$333$	523.885	+	1212.25i	0.0862124	+	0.199492i
$334$	6238.85	−	8587.05i	1.02208	−	1.40677i
$335$	−284.370	−	875.200i	−0.0463785	−	0.142738i
$336$	−3797.26	−	24378.6i	−0.616541	−	3.95822i
$337$	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
$339$	1484.61	−	560.574i	0.237855	−	0.0898118i
$340$	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
$345$	−242.293	−	5164.53i	−0.0378104	−	0.805939i
$346$	−16336.4	+	5308.02i	−2.53830	+	0.824743i
$347$	−500.995	+	162.783i	−0.0775067	+	0.0251834i	−0.347514	−	0.937675i	$-0.612974\pi$
$347$	−500.995	+	162.783i	−0.0775067	+	0.0251834i	0.270007	+	0.962858i	$0.412974\pi$
$348$	1110.85	+	23678.1i	0.171114	+	3.64735i
$349$	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	$-0.505972\pi$
$353$	−248.832			−0.0375184			−0.0187592	+	0.999824i	$0.505972\pi$
$354$	−10523.9	+	3973.73i	−1.58006	+	0.596614i
$355$	3978.18	+	5475.50i	0.594760	+	0.818618i
$356$	6158.36	+	4474.31i	0.916832	+	0.666118i
$357$	−1100.43	−	7064.79i	−0.163139	−	1.04736i
$358$	4628.20	+	14244.1i	0.683262	+	2.10287i
$359$	−4779.70	+	6578.70i	−0.702683	+	0.967160i	0.297241	+	0.954802i	$0.403934\pi$
$359$	−4779.70	+	6578.70i	−0.702683	+	0.967160i	−0.999924	+	0.0123572i	$0.996066\pi$
$360$	−22258.5	+	9619.22i	−3.25868	+	1.40827i
$361$	314.848	−	969.004i	0.0459030	−	0.141275i
$362$	−12027.9			−1.74634
$363$	−1534.89	+	6743.61i	−0.221931	+	0.975062i
$364$	−19755.6	+	17892.8i	−2.84471	+	2.57647i
$365$	−9253.31	−	3006.58i	−1.32696	−	0.431155i
$366$	−617.947	+	2256.68i	−0.0882531	+	0.322291i
$367$	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
$369$	−4393.45	+	413.144i	−0.619820	+	0.0582857i
$370$	−1800.41	+	2478.05i	−0.252970	+	0.348183i
$371$	851.020	−	4062.03i	0.119091	−	0.568437i
$372$	1328.97	−	501.806i	0.185225	−	0.0699393i
$373$	−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
$378$	7632.00	+	12107.5i	1.03849	+	1.64746i
$379$	−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
$381$	9410.49	−	441.490i	1.26539	−	0.0593655i
$382$	−6667.60	+	4844.29i	−0.893047	+	0.648837i
$383$	−2617.35	+	8055.36i	−0.349191	+	1.07470i	0.610111	+	0.792316i	$0.291125\pi$
$383$	−2617.35	+	8055.36i	−0.349191	+	1.07470i	−0.959302	+	0.282383i	$0.908875\pi$
$384$	−19922.8	−	24880.2i	−2.64761	−	3.30641i
$385$	−6938.55	+	3296.61i	−0.918497	+	0.436391i
$386$		−	2590.16i		−	0.341543i
$387$	−5858.82	−	3468.75i	−0.769563	−	0.455624i
$388$	−20832.0	−	28672.8i	−2.72573	−	3.75165i
$389$	2552.60	−	3513.36i	0.332705	−	0.457929i	−0.609588	−	0.792718i	$-0.708665\pi$
$389$	2552.60	−	3513.36i	0.332705	−	0.457929i	0.942293	+	0.334790i	$0.108665\pi$
$390$	17517.8	+	11513.2i	2.27449	+	1.49485i
$391$	6184.12	−	2009.34i	0.799858	−	0.259890i
$392$	−20240.5	−	18011.7i	−2.60790	−	2.32073i
$393$	1634.69	−	5969.70i	0.209819	−	0.766238i
$394$	1469.59	−	4522.92i	0.187910	−	0.578329i
$395$	7754.02			0.987715
$396$	9167.08	+	20006.2i	1.16329	+	2.53876i
$397$		−	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
$399$	3321.99	+	6561.23i	0.416811	+	0.823239i
$400$	−883.421	−	641.843i	−0.110428	−	0.0802303i
$401$	10119.3	−	3287.95i	1.26018	−	0.409457i	0.398620	−	0.917116i	$-0.369489\pi$
$401$	10119.3	−	3287.95i	1.26018	−	0.409457i	0.861558	+	0.507659i	$0.169489\pi$
$402$	−1272.38	+	1935.98i	−0.157862	+	0.240194i
$403$	−637.757	−	463.357i	−0.0788311	−	0.0572741i
$404$	28097.9	−	20414.3i	3.46021	−	2.51399i
$405$	5679.52	−	6036.28i	0.696834	−	0.740605i
$406$	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
$411$	−749.676	−	15979.5i	−0.0899727	−	1.91779i
$412$	−8481.18	+	2755.70i	−1.01417	+	0.329524i
$413$	−3621.08	+	6314.41i	−0.431432	+	0.752329i
$414$	−9767.52	+	8602.78i	−1.15953	+	1.02126i
$415$	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	$-0.643100\pi$
$419$	−7454.41			−0.869145			−0.434572	+	0.900637i	$0.643100\pi$
$420$	−11152.6	+	21750.5i	−1.29570	+	2.52694i
$421$	−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
$423$	−2315.98	+	217.787i	−0.266210	+	0.0250334i
$424$	−5470.02	−	16835.0i	−0.626528	−	1.92825i
$425$	−256.011	−	186.003i	−0.0292196	−	0.0212293i
$426$	4499.99	−	16433.5i	0.511796	−	1.86902i
$427$	619.831	+	1381.29i	0.0702476	+	0.156547i
$428$			15399.0i			1.73911i
$429$	6483.74	−	10348.7i	0.729692	−	1.16466i
$430$		−	15792.2i		−	1.77109i
$431$	2205.80	+	716.707i	0.246519	+	0.0800988i	0.429670	−	0.902986i	$-0.358630\pi$
$431$	2205.80	+	716.707i	0.246519	+	0.0800988i	−0.183151	+	0.983085i	$0.558630\pi$
$432$	31776.0	+	16854.3i	3.53895	+	1.87709i
$433$	−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
$435$	6625.36	−	10080.8i	0.730257	−	1.11112i
$436$	2743.56	+	1993.31i	0.301359	+	0.218950i
$437$	−5410.84	+	3931.21i	−0.592301	+	0.430332i
$438$	8652.33	+	22914.6i	0.943891	+	2.49978i
$439$		−	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
$441$	8792.97	+	2906.85i	0.949463	+	0.313880i
$442$	−8146.85	+	25073.4i	−0.876710	+	2.69824i
$443$	−3289.70	−	4527.89i	−0.352818	−	0.485612i	0.595312	−	0.803495i	$-0.297028\pi$
$443$	−3289.70	−	4527.89i	−0.352818	−	0.485612i	−0.948130	+	0.317882i	$0.897028\pi$
$444$	5671.66	−	266.084i	0.606227	−	0.0284410i
$445$	−1197.08	−	3684.24i	−0.127522	−	0.392471i
$446$	1291.90	+	3976.06i	0.137160	+	0.422135i
$447$	455.447	+	9707.97i	0.0481921	+	1.02723i
$448$	−40728.4	−	8532.83i	−4.29516	−	0.899863i
$449$	8514.10	+	2766.40i	0.894889	+	0.290767i	0.720126	−	0.693844i	$-0.244084\pi$
$449$	8514.10	+	2766.40i	0.894889	+	0.290767i	0.174763	+	0.984611i	$0.444084\pi$
$450$	618.111	+	138.480i	0.0647512	+	0.0145067i
$451$	−4746.58	+	3608.83i	−0.495583	+	0.376792i
$452$		−	6822.90i		−	0.710005i
$453$	−2917.92	−	7727.74i	−0.302640	−	0.801503i
$454$	11498.4	+	15826.1i	1.18865	+	1.63603i
$455$	13485.8	−	1457.24i	1.38950	−	0.150147i
$456$	26212.7	+	17227.7i	2.69194	+	1.76921i
$457$	−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
$459$	9208.53	+	4884.28i	0.936421	+	0.496686i
$460$	−21141.2	−	6869.19i	−2.14285	−	0.696255i
$461$	17706.2			1.78885			0.894426	−	0.447217i	$-0.147585\pi$
$461$	17706.2			1.78885			0.894426	+	0.447217i	$0.147585\pi$
$462$	17396.3	+	8447.51i	1.75184	+	0.850679i
$463$	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
$465$	−697.253	−	190.929i	−0.0695362	−	0.0190412i
$466$	−14021.8	−	10187.4i	−1.39388	−	1.01271i
$467$	−805.103	−	2477.85i	−0.0797768	−	0.245528i	0.903212	−	0.429196i	$-0.141203\pi$
$467$	−805.103	−	2477.85i	−0.0797768	−	0.245528i	−0.982988	+	0.183668i	$0.941203\pi$
$468$	−3638.01	−	38687.2i	−0.359331	−	3.82119i
$469$	161.047	+	1490.38i	0.0158560	+	0.146736i
$470$	−3171.36	−	4365.00i	−0.311242	−	0.428388i
$471$	5598.51	−	2113.94i	0.547698	−	0.206805i
$472$			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
$477$	3999.03	+	4540.46i	0.383863	+	0.435835i
$478$	1574.80	+	4846.74i	0.150690	+	0.463775i
$479$	4302.18	+	13240.8i	0.410380	+	1.26302i	0.916319	+	0.400449i	$0.131146\pi$
$479$	4302.18	+	13240.8i	0.410380	+	1.26302i	−0.505939	+	0.862569i	$0.668854\pi$
$480$	2160.18	+	46044.8i	0.205413	+	4.37843i
$481$	−1852.02	−	2549.09i	−0.175561	−	0.241640i
$482$	4175.76	−	12851.7i	0.394608	−	1.21448i
$483$	−1338.80	+	8315.10i	−0.126123	+	0.783333i
$484$	24793.5	+	16415.8i	2.32847	+	1.54168i
$485$			18036.3i			1.68863i
$486$	−20798.8	−	1662.39i	−1.94127	−	0.155160i
$487$	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
$489$	9016.79	+	5926.07i	0.833852	+	0.548029i
$490$	4588.62	+	20984.3i	0.423047	+	1.93464i
$491$	−9333.99	+	12847.1i	−0.857917	+	1.18082i	0.124145	+	0.992264i	$0.460381\pi$
$491$	−9333.99	+	12847.1i	−0.857917	+	1.18082i	−0.982062	+	0.188557i	$0.939619\pi$
$492$	−5010.87	+	18299.1i	−0.459162	+	1.67681i
$493$	14428.7	+	4688.17i	1.31813	+	0.428285i
$494$		−	27117.1i		−	2.46975i
$495$	2210.17	−	10978.9i	0.200686	−	0.996894i
$496$		−	3137.36i		−	0.284015i
$497$	−4513.71	−	10058.8i	−0.407379	−	0.907843i
$498$	−4496.79	−	1231.36i	−0.404631	−	0.110800i
$499$	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
$501$	8367.43	+	5499.29i	0.746166	+	0.490400i
$502$	−11788.1	+	16224.9i	−1.04806	+	1.44254i
$503$	−4054.37	+	2945.67i	−0.359394	+	0.261115i	−0.752799	−	0.658250i	$-0.771297\pi$
$503$	−4054.37	+	2945.67i	−0.359394	+	0.261115i	0.393405	+	0.919365i	$0.371297\pi$
$504$	38701.3	−	7901.60i	3.42042	−	0.698343i
$505$	−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	−0.765196	−	0.643798i	$-0.777358\pi$
$509$	−4471.31	+	3248.60i	−0.389366	+	0.282891i	0.375830	+	0.926689i	$0.377358\pi$
$510$	1133.01	+	24150.4i	0.0983733	+	2.09685i
$511$	13748.9	+	7884.47i	1.19024	+	0.682561i
$512$	−36168.9	+	11752.0i	−3.12198	+	1.01439i
$513$	−10560.5	−	1851.06i	−0.908887	−	0.159310i
$514$	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
$519$	−5723.98	−	15159.2i	−0.484113	−	1.28211i
$520$	46804.7	−	34005.6i	3.94716	−	2.86778i
$521$	−5110.89	−	3713.28i	−0.429774	−	0.312249i	0.351785	−	0.936081i	$-0.385575\pi$
$521$	−5110.89	−	3713.28i	−0.429774	−	0.312249i	−0.781558	+	0.623832i	$0.785575\pi$
$522$	−30235.0	+	2843.19i	−2.53515	+	0.238397i
$523$	−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
$525$	365.678	−	185.145i	0.0303991	−	0.0153912i
$526$	1473.32	−	4534.40i	0.122129	−	0.375873i
$527$		−	909.189i		−	0.0751516i
$528$	48487.8	−	3332.60i	3.99652	−	0.274684i
$529$	4507.65			0.370482
$530$	−4336.61	+	13346.7i	−0.355415	+	1.09386i
$531$	−4209.71	−	9741.08i	−0.344041	−	0.796096i
$532$	31436.5	−	3396.96i	2.56192	−	0.276836i
$533$	10013.3	−	3253.53i	0.813744	−	0.264401i
$534$	−5356.20	+	8149.71i	−0.434055	+	0.660435i
$535$	4606.22	−	6339.92i	0.372233	−	0.512334i
$536$	3758.13	+	5172.62i	0.302848	+	0.416834i
$537$	−13217.7	+	4990.88i	−1.06217	+	0.401066i
$538$		−	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
$543$	−531.731	−	11334.0i	−0.0420235	−	0.895742i
$544$	−55135.0	+	17914.4i	−4.34539	+	1.41190i
$545$	−533.302	−	1641.33i	−0.0419159	−	0.129004i
$546$	−24084.1	−	24207.7i	−1.88774	−	1.89743i
$547$	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
$552$	12689.3	+	33606.1i	0.978431	+	2.59125i
$553$	−12362.8	−	2590.07i	−0.950666	−	0.199170i
$554$	13014.2	−	17912.6i	0.998055	−	1.37370i
$555$	−2414.67	−	1586.99i	−0.184680	−	0.121376i
$556$	−44816.6	+	14561.8i	−3.41843	+	1.11071i
$557$	9062.90	−	12474.0i	0.689421	−	0.948906i	−0.310578	−	0.950548i	$-0.600523\pi$
$557$	9062.90	−	12474.0i	0.689421	−	0.948906i	0.999999	+	0.00164167i	$0.000522560\pi$
$558$	721.968	+	1670.60i	0.0547730	+	0.126742i
$559$	15449.8	+	5019.96i	1.16898	+	0.379824i
$560$	36239.2	+	40012.1i	2.73462	+	3.01932i
$561$	14051.5	−	965.771i	1.05750	−	0.0726825i
$562$	−18659.2			−1.40052
$563$	−4634.90	+	14264.8i	−0.346959	+	1.06783i	0.613568	+	0.789642i	$0.289734\pi$
$563$	−4634.90	+	14264.8i	−0.346959	+	1.06783i	−0.960527	+	0.278187i	$0.910266\pi$
$564$	−2641.45	+	9646.29i	−0.197208	+	0.720181i
$565$	−2040.90	+	2809.06i	−0.151967	+	0.209165i
$566$	12782.3	+	39339.9i	0.949258	+	2.92152i
$567$	−11071.5	+	7726.92i	−0.820037	+	0.572311i
$568$	−38043.1	−	27639.9i	−2.81030	−	2.04180i
$569$	−10152.4	−	13973.5i	−0.747995	−	1.02953i	−0.998119	−	0.0613133i	$-0.980471\pi$
$569$	−10152.4	−	13973.5i	−0.747995	−	1.02953i	0.250123	−	0.968214i	$-0.419529\pi$
$570$	−8784.46	−	23264.5i	−0.645510	−	1.70955i
$571$	−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
$576$	45525.4	−	40096.6i	3.29321	−	2.90051i
$577$	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
$579$	2440.72	−	114.506i	0.175186	−	0.00821882i
$580$	−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
$585$	−10074.5	+	17016.1i	−0.712017	+	1.20262i
$586$	16698.3	+	22983.2i	1.17713	+	1.62018i
$587$	13644.8	+	9913.50i	0.959420	+	0.697059i	0.953016	−	0.302920i	$-0.0979616\pi$
$587$	13644.8	+	9913.50i	0.959420	+	0.697059i	0.00640387	+	0.999979i	$0.497962\pi$
$588$	25046.7	−	30953.0i	1.75665	−	2.17088i
$589$	288.983	+	889.398i	0.0202162	+	0.0622190i
$590$	14467.3	−	19912.5i	1.00951	−	1.38947i
$591$	4326.94	+	1184.85i	0.301162	+	0.0824674i
$592$	3875.04	−	11926.2i	0.269026	−	0.827977i
$593$	−19664.8			−1.36178			−0.680890	−	0.732386i	$-0.738407\pi$
$593$	−19664.8			−1.36178			−0.680890	+	0.732386i	$0.738407\pi$
$594$	−25052.3	+	12932.6i	−1.73048	+	0.893317i
$595$	10501.9	+	11595.3i	0.723591	+	0.798925i
$596$	39739.9	+	12912.3i	2.73122	+	0.887428i
$597$	11580.6	+	3171.12i	0.793904	+	0.217396i
$598$	18253.5	−	25123.8i	1.24823	−	1.71804i
$599$	−1479.33	+	480.664i	−0.100908	+	0.0327870i	−0.359036	−	0.933324i	$-0.616894\pi$
$599$	−1479.33	+	480.664i	−0.100908	+	0.0327870i	0.258128	+	0.966111i	$0.416894\pi$
$600$	960.153	−	1460.92i	0.0653301	−	0.0994029i
$601$	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
$603$	−1880.54	−	1113.38i	−0.127001	−	0.0751915i
$604$	−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
$609$	−13930.5	+	13859.4i	−0.926920	+	0.922188i
$610$	−1581.98	−	4868.84i	−0.105004	−	0.323170i
$611$	5278.47	−	1715.08i	0.349499	−	0.113559i
$612$	33631.6	−	29621.2i	2.22137	−	1.95648i
$613$	−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	$0.0536150\pi$
$617$			5138.53i			0.335282i	−0.985848	+	0.167641i	$0.946385\pi$
$618$	−4035.77	−	10688.2i	−0.262690	−	0.695702i
$619$	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
$621$	−8538.25	−	8823.68i	−0.551736	−	0.570180i
$622$	−25330.0	+	8230.23i	−1.63287	+	0.530550i
$623$	677.944	+	6273.89i	0.0435975	+	0.403464i
$624$	−82772.3	−	22665.6i	−5.31017	−	1.45409i
$625$	−4987.30	+	15349.3i	−0.319187	+	0.982358i
$626$	27274.1			1.74136
$627$	−13438.7	+	5410.98i	−0.855963	+	0.344647i
$628$		−	25729.4i		−	1.63489i
$629$	1122.97	−	3456.14i	0.0711854	−	0.219086i
$630$	−28504.5	−	12966.6i	−1.80261	−	0.820000i
$631$	−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
$633$	−12076.0	−	7936.67i	−0.758260	−	0.498348i
$634$	−6449.75	−	4686.02i	−0.404026	−	0.293542i
$635$	−16676.2	+	12115.9i	−1.04216	+	0.757175i
$636$	24336.6	−	9189.27i	1.51731	−	0.572922i
$637$	−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	0.720015	−	0.693959i	$-0.244135\pi$
$641$	−2636.79	−	3629.23i	−0.162476	−	0.223629i	−0.882491	+	0.470330i	$0.844135\pi$
$642$	−19706.6	+	924.532i	−1.21146	+	0.0568355i
$643$	−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
$645$	14881.1	−	698.141i	0.908436	−	0.0426190i
$646$	25302.1	−	18383.1i	1.54102	−	1.11962i
$647$	−2668.48	+	8212.75i	−0.162147	+	0.499036i	−0.998815	−	0.0486740i	$-0.984500\pi$
$647$	−2668.48	+	8212.75i	−0.162147	+	0.499036i	0.836668	+	0.547710i	$0.184500\pi$
$648$	−24569.3	+	52080.6i	−1.48946	+	3.15728i
$649$	−11780.9	−	8173.97i	−0.712541	−	0.494386i
$650$	−1511.32			−0.0911982
$651$	1047.90	+	537.315i	0.0630883	+	0.0323487i
$652$	37530.8	−	27267.7i	2.25432	−	1.63786i
$653$	6936.49	−	9547.26i	0.415691	−	0.572149i	−0.548904	−	0.835885i	$-0.684955\pi$
$653$	6936.49	−	9547.26i	0.415691	−	0.572149i	0.964595	+	0.263736i	$0.0849549\pi$
$654$	−2386.20	+	3630.71i	−0.142672	+	0.217082i
$655$	4184.89	+	12879.8i	0.249645	+	0.768327i
$656$	33899.7	+	24629.6i	2.01763	+	1.46589i
$657$	−21210.1	+	9166.15i	−1.25949	+	0.544301i
$658$	3598.27	+	8018.74i	0.213184	+	0.475080i
$659$			7723.28i			0.456534i	0.973599	+	0.228267i	$0.0733060\pi$
$659$			7723.28i			0.456534i	−0.973599	+	0.228267i	$0.926694\pi$
$660$	−40803.3	−	25564.3i	−2.40646	−	1.50771i
$661$			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
$663$	−23987.0	−	6568.37i	−1.40509	−	0.384758i
$664$	−7563.28	+	10410.0i	−0.442036	+	0.608411i
$665$	−13958.8	−	8004.88i	−0.813986	−	0.466791i
$666$	681.036	+	7242.26i	0.0396240	+	0.421369i
$667$	−14457.7	−	10504.1i	−0.839287	−	0.609778i
$668$	34827.9	−	25304.0i	2.01726	−	1.46563i
$669$	−3689.56	+	1393.14i	−0.213223	+	0.0805111i
$670$		−	5068.90i		−	0.292282i
$671$	−2815.72	+	983.058i	−0.161996	+	0.0565581i
$672$	11936.2	−	74133.8i	0.685191	−	4.25562i
$673$	−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
$675$	−103.165	+	588.572i	−0.00588272	+	0.0335617i
$676$	13482.1	+	41493.8i	0.767077	+	2.36082i
$677$	−7169.21	−	22064.6i	−0.406994	−	1.25260i	−0.919218	−	0.393748i	$-0.871178\pi$
$677$	−7169.21	−	22064.6i	−0.406994	−	1.25260i	0.512224	−	0.858852i	$-0.328822\pi$
$678$	8731.52	−	409.637i	0.494590	−	0.0232036i
$679$	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	$-0.959598\pi$
$683$		−	4519.03i		−	0.253171i	0.991956	−	0.126586i	$-0.0404018\pi$
$684$	−23484.5	+	39666.1i	−1.31280	+	2.21735i
$685$	20573.5	+	28317.1i	1.14755	+	1.57947i
$686$	−306.568	−	34989.5i	−0.0170624	−	1.94738i
$687$	12623.2	−	19206.8i	0.701027	−	1.06665i
$688$	19978.7	+	61488.0i	1.10709	+	3.40728i
$689$	−11678.9	−	8485.20i	−0.645761	−	0.469173i
$690$	7521.47	−	27467.6i	0.414982	−	1.51547i
$691$	−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
$693$	−7191.08	+	16766.1i	−0.394180	+	0.919033i
$694$	−2901.61			−0.158709
$695$	22807.2	+	7410.52i	1.24479	+	0.404456i
$696$	−22135.6	+	80836.8i	−1.20553	+	4.40246i
$697$	9823.96	+	7137.53i	0.533872	+	0.387881i
$698$	11395.7	+	35072.5i	0.617959	+	1.90188i
$699$	8979.81	−	13663.2i	0.485905	−	0.739327i
$700$	−189.323	−	1752.05i	−0.0102225	−	0.0946020i
$701$	11843.1	+	16300.6i	0.638097	+	0.878266i	0.998512	−	0.0545265i	$-0.0173649\pi$
$701$	11843.1	+	16300.6i	0.638097	+	0.878266i	−0.360415	+	0.932792i	$0.617365\pi$
$702$	49291.0	−	6978.41i	2.65010	−	0.375190i
$703$			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
$708$	−45574.9	+	2138.14i	−2.41922	+	0.113497i
$709$	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
$711$	13818.9	−	12171.0i	0.728900	−	0.641981i
$712$	15820.2	+	21774.6i	0.832707	+	1.14612i
$713$	−330.946	+	1018.55i	−0.0173829	+	0.0534991i
$714$	6260.50	−	38883.0i	0.328142	−	2.03804i
$715$	580.916	+	26713.8i	0.0303846	+	1.39726i
$716$			60745.4i			3.17062i
$717$	−4497.49	+	1698.21i	−0.234256	+	0.0884529i
$718$	−36237.0	+	26327.7i	−1.88350	+	1.36844i
$719$	8454.13	+	6142.28i	0.438506	+	0.318593i	0.785041	−	0.619444i	$-0.212642\pi$
$719$	8454.13	+	6142.28i	0.438506	+	0.318593i	−0.346535	+	0.938037i	$0.612642\pi$
$720$	−78355.2	+	7368.24i	−4.05573	+	0.381386i
$721$	−6413.00	−	3677.62i	−0.331252	−	0.189961i
$722$	3298.76	−	4540.35i	0.170038	−	0.234037i
$723$	12294.8	+	3366.70i	0.632433	+	0.173180i
$724$	−46396.1	−	15075.0i	−2.38162	−	0.773837i
$725$			869.702i			0.0445516i
$726$	−19519.3	+	32714.8i	−0.997836	+	1.67240i
$727$			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
$729$	647.004	−	19672.4i	0.0328712	−	0.999460i
$730$	−43357.2	−	31500.8i	−2.19825	−	1.59712i
$731$	5789.71	+	17818.9i	0.292941	+	0.901581i
$732$	−5212.01	+	7930.32i	−0.263171	+	0.400427i
$733$	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
$735$	−19570.8	+	5251.56i	−0.982149	+	0.263547i
$736$	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
$741$	25552.6	−	1198.79i	1.26680	−	0.0594315i
$742$	11372.3	−	19831.0i	0.562657	−	0.981157i
$743$	−26481.3	+	8604.30i	−1.30754	+	0.424847i	−0.878200	−	0.478294i	$-0.841255\pi$
$743$	−26481.3	+	8604.30i	−1.30754	+	0.424847i	−0.429344	+	0.903141i	$0.641255\pi$
$744$	5017.25	−	235.383i	0.247233	−	0.0115989i
$745$	−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
$750$	36756.8	−	13879.0i	1.78956	−	0.675719i
$751$	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
$753$	−15809.9	−	10390.7i	−0.765135	−	0.502866i
$754$	68910.2	−	22390.3i	3.32833	−	1.08144i
$755$	14621.8	+	10623.4i	0.704824	+	0.512085i
$756$	14264.7	+	56268.3i	0.686245	+	2.70695i
$757$	−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
$759$	−16093.2	−	4032.83i	−0.769625	−	0.192862i
$760$	−68631.6			−3.27570
$761$	12472.6	−	38386.9i	0.594130	−	1.82854i	0.0351213	−	0.999383i	$-0.488818\pi$
$761$	12472.6	−	38386.9i	0.594130	−	1.82854i	0.559009	−	0.829162i	$-0.311182\pi$
$762$	50049.7	+	13705.1i	2.37941	+	0.651555i
$763$	302.025	+	2795.03i	0.0143303	+	0.132617i
$764$	−31790.8	+	10329.5i	−1.50543	+	0.489145i
$765$	−22706.9	+	2135.28i	−1.07316	+	0.100917i
$766$	−27422.7	+	37744.1i	−1.29350	+	1.78035i
$767$	14882.0	+	20483.4i	0.700599	+	0.964292i
$768$	−29025.7	−	76870.8i	−1.36377	−	3.61177i
$769$		−	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	−0.804168	−	0.594402i	$-0.797389\pi$
$773$	−10474.1	+	7609.90i	−0.487359	+	0.354087i	0.316809	+	0.948489i	$0.397389\pi$
$774$	−24788.0	−	28144.1i	−1.15115	−	1.30700i
$775$	49.5689	−	16.1059i	0.00229751	−	0.000746506i
$776$	−38724.0	−	119180.i	−1.79138	−	5.51330i
$777$	3319.78	+	3336.81i	0.153277	+	0.154064i
$778$	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
$783$	−4015.79	−	28364.9i	−0.183285	−	1.29461i
$784$	−44413.4	−	75898.9i	−2.02320	−	3.45749i
$785$	−7696.30	+	10593.1i	−0.349927	+	0.481633i
$786$	18724.8	−	28490.7i	0.849735	−	1.29291i
$787$	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
$789$	4337.92	+	1187.86i	0.195734	+	0.0535980i
$790$	40620.6	+	13198.4i	1.82939	+	0.594404i
$791$	4192.26	−	3796.95i	0.188444	−	0.170675i
$792$	8967.33	+	77291.5i	0.402323	+	3.46772i
$793$	5266.16			0.235822
$794$	9685.61	−	29809.2i	0.432908	−	1.33236i
$795$	−12768.4	−	3496.38i	−0.569620	−	0.155980i
$796$	30343.4	−	41764.1i	1.35112	−	1.85966i
$797$	7633.97	+	23494.9i	0.339284	+	1.04421i	0.964573	+	0.263815i	$0.0849808\pi$
$797$	7633.97	+	23494.9i	0.339284	+	1.04421i	−0.625290	+	0.780393i	$0.715019\pi$
$798$	6234.61	+	40026.5i	0.276570	+	1.77559i
$799$	5178.65	+	3762.51i	0.229296	+	0.166593i
$800$	−1953.39	−	2688.61i	−0.0863283	−	0.118821i
$801$	−7916.30	−	4686.90i	−0.349200	−	0.206746i
$802$	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
$807$	27734.2	−	1301.14i	1.20978	−	0.0567563i
$808$	116791.	−	37947.6i	5.08501	−	1.65222i
$809$	−41167.5	+	13376.1i	−1.78909	+	0.581310i	−0.999478	−	0.0322973i	$-0.989718\pi$
$809$	−41167.5	+	13376.1i	−1.78909	+	0.581310i	−0.789611	+	0.613608i	$0.789718\pi$
$810$	40027.6	−	21954.6i	1.73633	−	0.952353i
$811$	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
$816$	−34964.0	−	92597.8i	−1.49998	−	3.97251i
$817$	−11327.4	−	15590.8i	−0.485060	−	0.667628i
$818$	−32052.5	−	23287.5i	−1.37004	−	0.995391i
$819$	21746.4	−	23764.8i	0.927814	−	1.01393i
$820$	−12828.1	−	39480.9i	−0.546314	−	1.68138i
$821$	2286.62	−	3147.27i	0.0972030	−	0.133789i	−0.757645	−	0.652667i	$-0.773650\pi$
$821$	2286.62	−	3147.27i	0.0972030	−	0.133789i	0.854848	+	0.518878i	$0.173650\pi$
$822$	23272.1	−	84987.2i	0.987479	−	3.60617i
$823$	−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
$825$	301.571	+	748.980i	0.0127265	+	0.0316074i
$826$	−29717.5	+	26915.4i	−1.25182	+	1.13378i
$827$	−42150.0	−	13695.4i	−1.77231	−	0.575858i	−0.773957	−	0.633239i	$-0.781725\pi$
$827$	−42150.0	−	13695.4i	−1.77231	−	0.575858i	−0.998352	+	0.0573807i	$0.981725\pi$
$828$	−48459.0	+	20942.0i	−2.03390	+	0.878969i
$829$	−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
$831$	17454.5	+	11471.5i	0.728626	+	0.478872i
$832$	−85077.6	+	117099.i	−3.54511	+	4.87943i
$833$	−12870.8	−	21995.1i	−0.535348	−	0.914868i
$834$	−21326.0	−	56479.1i	−0.885441	−	2.34498i
$835$	−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	−0.412318	−	0.911040i	$-0.635281\pi$
$839$	7939.93	−	5768.70i	0.326719	−	0.237375i	0.739037	+	0.673665i	$0.235281\pi$
$840$	−61268.3	+	60955.5i	−2.51661	+	2.50377i
$841$	−5348.06	−	16459.6i	−0.219282	−	0.674880i
$842$	−1825.85	+	593.254i	−0.0747303	+	0.0242813i
$843$	−824.885	−	17582.6i	−0.0337017	−	0.718361i
$844$	−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
$849$	−36505.1	+	13784.0i	−1.47568	+	0.557202i
$850$	−1024.55	−	1410.17i	−0.0413431	−	0.0569039i
$851$	−2516.08	+	3463.08i	−0.101351	+	0.139498i
$852$	37954.6	−	57749.8i	1.52618	−	2.32215i
$853$	−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
$855$	21534.0	−	9306.12i	0.861340	−	0.372237i
$856$	−16825.2	+	51782.7i	−0.671815	+	2.06763i
$857$	35599.3			1.41896			0.709480	−	0.704726i	$-0.248930\pi$
$857$	35599.3			1.41896			0.709480	+	0.704726i	$0.248930\pi$
$858$	51581.0	−	43177.1i	2.05238	−	1.71800i
$859$			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
$861$	−14032.3	+	7104.62i	−0.555422	+	0.281214i
$862$	10335.5	+	7509.15i	0.408384	+	0.296708i
$863$	38936.0	−	12651.1i	1.53580	−	0.499012i	0.585587	−	0.810610i	$-0.300864\pi$
$863$	38936.0	−	12651.1i	1.53580	−	0.499012i	0.950214	+	0.311598i	$0.100864\pi$
$864$	76123.3	+	78668.1i	2.99742	+	3.09762i
$865$	28683.1	+	20839.5i	1.12746	+	0.819149i
$866$	−73816.6	+	53630.9i	−2.89653	+	2.10445i
$867$	−1114.45	−	2951.48i	−0.0436548	−	0.115614i
$868$	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
$873$	28310.4	+	32143.4i	1.09755	+	1.24615i
$874$	−35036.9	+	11384.2i	−1.35600	+	0.440590i
$875$	12647.3	−	22054.3i	0.488636	−	0.852080i
$876$	4655.54	+	99234.1i	0.179562	+	3.82741i
$877$	−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	$-0.401517\pi$
$881$	15924.0			0.608960			0.304480	+	0.952519i	$0.401517\pi$
$882$	41115.4	+	30194.8i	1.56965	+	1.15273i
$883$	−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
$885$	19403.2	+	12752.3i	0.736986	+	0.484367i
$886$	−9526.49	−	29319.5i	−0.361229	−	1.11175i
$887$	−13269.5	−	9640.88i	−0.502308	−	0.364948i	0.307590	−	0.951519i	$-0.400478\pi$
$887$	−13269.5	−	9640.88i	−0.502308	−	0.364948i	−0.809898	+	0.586571i	$0.800478\pi$
$888$	19363.0	+	5302.19i	0.731734	+	0.200371i
$889$	30635.0	−	13746.9i	1.15575	−	0.518624i
$890$		−	21338.0i		−	0.803654i
$891$	−13294.0	−	23035.2i	−0.499848	−	0.866113i
$892$			16956.3i			0.636478i
$893$	−6261.82	−	2034.59i	−0.234652	−	0.0762429i
$894$	−14138.4	+	51631.8i	−0.528924	+	1.93157i
$895$	18170.5	−	25009.5i	0.678628	−	0.934051i
$896$	−98550.8	−	56515.2i	−3.67450	−	2.10719i
$897$	24481.2	+	16089.7i	0.911265	+	0.598907i
$898$	39893.5	+	28984.3i	1.48248	+	1.07708i
$899$	−2021.54	+	1468.73i	−0.0749967	+	0.0544883i
$900$	2210.71	+	1308.87i	0.0818783	+	0.0484765i
$901$		−	16649.5i		−	0.615620i
$902$	−31008.4	+	10826.0i	−1.14464	+	0.399631i
$903$	−23959.1	−	3857.62i	−0.882955	−	0.142163i
$904$	7454.83	−	22943.6i	0.274274	−	0.844129i
$905$	14592.4	+	20084.8i	0.535988	+	0.737724i
$906$	−2132.26	−	45449.6i	−0.0781893	−	1.66663i
$907$	−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
$909$	−31498.9	+	27742.8i	−1.14934	+	1.01229i
$910$	73127.6	+	15320.7i	2.66391	+	0.558105i
$911$	−1466.35	−	476.448i	−0.0533288	−	0.0173276i	0.282231	−	0.959346i	$-0.408925\pi$
$911$	−1466.35	−	476.448i	−0.0533288	−	0.0173276i	−0.335560	+	0.942019i	$0.608925\pi$
$912$	63634.8	+	79468.9i	2.31048	+	2.88539i
$913$	−1958.90	−	5610.77i	−0.0710078	−	0.203384i
$914$		−	35343.1i		−	1.27905i
$915$	4518.00	−	1705.95i	0.163235	−	0.0616361i
$916$	−58083.4	−	79944.9i	−2.09512	−	2.88368i
$917$	−2370.03	−	21933.0i	−0.0853493	−	0.789848i
$918$	39926.5	+	41261.2i	1.43548	+	1.48347i
$919$	−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
$921$	16240.6	+	4447.17i	0.581048	+	0.159109i
$922$	92756.6	+	30138.4i	3.31320	+	1.07653i
$923$	−38349.0			−1.36758
$924$	56516.2	+	54388.4i	2.01217	+	1.93641i
$925$	208.321			0.00740493
$926$	2026.58	+	658.476i	0.0719196	+	0.0233681i
$927$	9893.17	−	4275.44i	0.350523	−	0.151482i
$928$	128899.	+	93650.3i	4.55960	+	3.31274i
$929$	−3686.17	−	11344.9i	−0.130182	−	0.400660i	0.864627	−	0.502414i	$-0.167555\pi$
$929$	−3686.17	−	11344.9i	−0.130182	−	0.400660i	−0.994810	+	0.101754i	$0.967555\pi$
$930$	−3327.67	−	2187.03i	−0.117332	−	0.0771136i
$931$	19581.7	+	17425.4i	0.689326	+	0.613420i
$932$	−41318.9	−	56870.6i	−1.45220	−	1.99878i
$933$	−8875.18	−	23504.8i	−0.311426	−	0.824772i
$934$		−	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
$939$	1205.73	+	25700.5i	0.0419037	+	0.893190i
$940$	−6762.27	−	20812.1i	−0.234639	−	0.722145i
$941$	8872.26	+	27306.0i	0.307362	+	0.945962i	0.978785	+	0.204888i	$0.0656832\pi$
$941$	8872.26	+	27306.0i	0.307362	+	0.945962i	−0.671424	+	0.741074i	$0.734317\pi$
$942$	32926.8	−	1544.75i	1.13887	−	0.0534297i
$943$	−8407.52	−	11572.0i	−0.290336	−	0.399613i
$944$	−31138.1	+	95833.3i	−1.07358	+	3.30414i
$945$	10958.3	−	27433.2i	0.377222	−	0.944339i
$946$	−48524.6	−	14608.2i	−1.66773	−	0.502064i
$947$		−	24157.4i		−	0.828946i	−0.910062	−	0.414473i	$-0.863966\pi$
$947$		−	24157.4i		−	0.828946i	0.910062	−	0.414473i	$-0.136034\pi$
$948$	−27967.5	−	74068.3i	−0.958166	−	2.53758i
$949$	44600.2	−	32403.9i	1.52559	−	1.10840i
$950$	1450.46	+	1053.82i	0.0495360	+	0.0359900i
$951$	4130.53	−	6284.80i	0.140843	−	0.214299i
$952$	−94290.0	−	54071.8i	−3.21004	−	1.84084i
$953$	28368.0	−	39045.2i	0.964248	−	1.32717i	0.0193491	−	0.999813i	$-0.493841\pi$
$953$	28368.0	−	39045.2i	0.964248	−	1.32717i	0.944899	−	0.327361i	$-0.106159\pi$
$954$	13221.0	+	30592.8i	0.448685	+	1.03824i
$955$	16178.4	+	5256.69i	0.548190	+	0.178118i
$956$			20669.4i			0.699262i
$957$	−24846.6	−	29682.7i	−0.839265	−	1.00262i
$958$			76686.6i			2.58625i
$959$	−23343.1	−	52020.0i	−0.786013	−	1.75163i
$960$	−35056.8	+	128023.i	−1.17860	+	4.30410i
$961$	−23980.3	−	17422.7i	−0.804950	−	0.584831i
$962$	−5363.19	−	16506.2i	−0.179746	−	0.553203i
$963$	−1742.38	−	18528.8i	−0.0583048	−	0.620024i
$964$	32214.8	−	44339.9i	1.07632	−	1.48142i
$965$	−4325.16	+	3142.41i	−0.144282	+	0.104827i
$966$	−21167.0	+	41281.0i	−0.705006	+	1.37494i
$967$	−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	$-0.354216\pi$
$971$	43323.0	−	31476.0i	1.43182	−	1.04028i	0.989674	−	0.143340i	$-0.0457842\pi$
$972$	−78145.1	−	32480.3i	−2.57871	−	1.07182i
$973$	−33887.8	−	19433.4i	−1.11654	−	0.640294i
$974$	57643.4	−	18729.5i	1.89632	−	0.616151i
$975$	−66.8124	−	1424.12i	−0.00219457	−	0.0467779i
$976$	12319.1	+	16955.8i	0.404022	+	0.556088i
$977$	16468.9	+	5351.08i	0.539291	+	0.175226i	0.565982	−	0.824417i	$-0.308497\pi$
$977$	16468.9	+	5351.08i	0.539291	+	0.175226i	−0.0266911	+	0.999644i	$0.508497\pi$
$978$	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
$981$	−3526.73	−	2088.02i	−0.114781	−	0.0679565i
$982$	−70765.1	+	51413.9i	−2.29960	+	1.67076i
$983$	−9493.51	−	6897.44i	−0.308032	−	0.223799i	0.423019	−	0.906121i	$-0.360970\pi$
$983$	−9493.51	−	6897.44i	−0.308032	−	0.223799i	−0.731052	+	0.682322i	$0.760970\pi$
$984$	−36844.2	+	56060.2i	−1.19365	+	1.81619i
$985$	−9335.49	+	3033.28i	−0.301983	+	0.0981203i
$986$	67607.0	+	49119.3i	2.18362	+	1.58649i
$987$	−7397.03	+	3745.16i	−0.238551	+	0.120780i
$988$	33986.7	−	104600.i	1.09439	−	3.36820i
$989$		−	22069.6i		−	0.709578i
$990$	30265.8	−	53752.3i	0.971627	−	1.72562i
$991$	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
$993$	−9412.95	+	34375.1i	−0.300817	+	1.09855i
$994$	−6524.25	−	60377.4i	−0.208186	−	1.92661i
$995$	−24985.4	+	8118.24i	−0.796070	+	0.258659i
$996$	−15802.4	−	10385.8i	−0.502730	−	0.330407i
$997$	−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
$999$	−6794.31	+	961.910i	−0.215178	+	0.0304639i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.4.u.a.20.1	✓	368	21.20	even	2	inner
231.4.u.a.20.2	yes	368	3.2	odd	2	inner
231.4.u.a.20.91	yes	368	1.1	even	1	trivial
231.4.u.a.20.92	yes	368	7.6	odd	2	inner
231.4.u.a.104.1	yes	368	11.5	even	5	inner
231.4.u.a.104.2	yes	368	77.27	odd	10	inner
231.4.u.a.104.91	yes	368	231.104	even	10	inner
231.4.u.a.104.92	yes	368	33.5	odd	10	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} +(-1.37235 + 5.01165i) q^{3} +(18.0740 + 13.1315i) q^{4} +(-3.51328 - 10.8128i) q^{5} +(-15.7198 + 23.9184i) q^{6} +(1.98968 + 18.4131i) q^{7} +(46.4303 + 63.9058i) q^{8} +(-23.2333 - 13.7554i) 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} +(59.0113 - 2.76850i) q^{15} +(79.2260 + 243.832i) q^{16} +(22.9593 + 70.6614i) q^{17} +(-98.2975 - 111.606i) q^{18} +(-44.9190 - 61.8257i) q^{19} +(78.4891 - 241.565i) q^{20} +(-95.0105 - 15.2975i) q^{21} +(-192.426 - 57.9291i) q^{22} -87.5177i q^{23} +(-383.992 + 144.992i) q^{24} +(-3.44574 + 2.50348i) q^{25} +(287.071 + 208.569i) q^{26} +(100.822 - 97.5602i) q^{27} +(-205.830 + 358.925i) q^{28} +(120.023 - 165.197i) q^{29} +(313.852 + 85.9422i) q^{30} +(-11.6382 - 3.78147i) q^{31} +780.270i q^{32} +(46.0802 - 183.885i) q^{33} +409.250i q^{34} +(192.106 - 86.2042i) q^{35} +(-239.289 - 553.705i) q^{36} +(-39.5701 - 28.7493i) q^{37} +(-130.079 - 400.341i) q^{38} +(-183.845 + 279.729i) q^{39} +(527.876 - 726.559i) q^{40} +(132.224 - 96.0665i) q^{41} +(-471.688 - 241.859i) 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} +(-1330.73 + 62.4308i) q^{48} +(-335.082 + 73.2722i) q^{49} +(-22.3123 + 7.24969i) q^{50} +(-385.638 + 18.0921i) 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} +(371.493 - 140.272i) q^{57} +(909.947 - 661.115i) q^{58} +(317.968 + 231.017i) q^{59} +(1102.92 + 724.870i) q^{60} +(77.7467 - 25.2614i) q^{61} +(-54.5317 - 39.6196i) q^{62} +(207.053 - 455.166i) q^{63} +(-694.321 + 2136.90i) q^{64} -732.402i q^{65} +(554.395 - 884.872i) q^{66} +80.9414 q^{67} +(-512.926 + 1578.62i) q^{68} +(438.608 + 120.104i) q^{69} +(1153.11 - 124.602i) q^{70} +(-566.163 + 183.958i) q^{71} +(-199.678 - 2123.41i) q^{72} +(503.012 - 692.337i) q^{73} +(-158.358 - 217.961i) q^{74} +(-7.81781 - 20.7045i) 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} +(350.576 + 639.169i) q^{81} +(856.194 - 278.194i) q^{82} +(50.3375 + 154.923i) q^{83} +(-1516.34 - 1524.12i) 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} +(-861.425 + 1454.97i) q^{90} +(-244.644 + 1167.72i) q^{91} +(1149.24 - 1581.79i) q^{92} +(34.9230 - 53.1370i) q^{93} +(451.338 - 146.649i) q^{94} +(-510.694 + 702.910i) q^{95} +(-3910.44 - 1070.80i) q^{96} +(-1508.77 - 490.228i) q^{97} +(-1880.10 - 186.510i) q^{98} +(858.329 + 483.291i) 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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