LMFDB - Embedded newform 378.3.x.a.103.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [378,3,Mod(103,378)] 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("378.103"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(378, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([14, 15])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	378.x (of order $18$, degree $6$, 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:	$10.2997539928$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$48$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			103.19
Character	$\chi$	$=$	378.103
Dual form			378.3.x.a.367.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.245576 - 1.39273i) q^{2} +(2.40164 - 1.79781i) q^{3} +(-1.87939 + 0.684040i) q^{4} +(-3.74775 - 0.660829i) q^{5} +(-3.09364 - 2.90334i) q^{6} +(6.98532 - 0.453118i) q^{7} +(1.41421 + 2.44949i) q^{8} +(2.53579 - 8.63538i) q^{9} +5.38188i q^{10} +(-1.49788 - 8.49493i) q^{11} +(-3.28384 + 5.02159i) q^{12} +(4.33681 - 5.16840i) q^{13} +(-2.34649 - 9.61738i) q^{14} +(-10.1888 + 5.15065i) q^{15} +(3.06418 - 2.57115i) q^{16} -4.56647i q^{17} +(-12.6495 - 1.41102i) q^{18} +4.66588i q^{19} +(7.49549 - 1.32166i) q^{20} +(15.9616 - 13.6465i) q^{21} +(-11.4633 + 4.17229i) q^{22} +(-21.6623 - 18.1768i) q^{23} +(7.80015 + 3.34032i) q^{24} +(-9.88340 - 3.59726i) q^{25} +(-8.26320 - 4.77076i) q^{26} +(-9.43469 - 25.2980i) q^{27} +(-12.8182 + 5.62982i) q^{28} +(-9.61554 + 8.06840i) q^{29} +(9.67557 + 12.9254i) q^{30} +(-7.47776 - 20.5450i) q^{31} +(-4.33340 - 3.63616i) q^{32} +(-18.8696 - 17.7089i) q^{33} +(-6.35985 + 1.12141i) q^{34} +(-26.4786 - 2.91793i) q^{35} +(1.14123 + 17.9638i) q^{36} +(5.70126 + 9.87487i) q^{37} +(6.49831 - 1.14583i) q^{38} +(1.12367 - 20.2094i) q^{39} +(-3.68142 - 10.1146i) q^{40} +(-29.4006 + 35.0383i) q^{41} +(-22.9256 - 18.8790i) q^{42} +(59.6536 + 21.7121i) q^{43} +(8.62597 + 14.9406i) q^{44} +(-15.2100 + 30.6875i) q^{45} +(-19.9956 + 34.6334i) q^{46} +(18.1063 - 49.7465i) q^{47} +(2.73663 - 11.6838i) q^{48} +(48.5894 - 6.33035i) q^{49} +(-2.58289 + 14.6483i) q^{50} +(-8.20962 - 10.9670i) q^{51} +(-4.61513 + 12.6800i) q^{52} +(8.57836 + 14.8582i) q^{53} +(-32.9163 + 19.3525i) q^{54} +32.8267i q^{55} +(10.9886 + 16.4697i) q^{56} +(8.38835 + 11.2058i) q^{57} +(13.5984 + 11.4104i) q^{58} +(29.4528 - 35.1004i) q^{59} +(15.6254 - 16.6496i) q^{60} +(-12.2195 + 33.5727i) q^{61} +(-26.7772 + 15.4598i) q^{62} +(13.8004 - 61.4699i) q^{63} +(-4.00000 + 6.92820i) q^{64} +(-19.6687 + 16.5040i) q^{65} +(-20.0297 + 30.6291i) q^{66} +(9.36538 - 53.1137i) q^{67} +(3.12365 + 8.58215i) q^{68} +(-84.7034 - 4.70964i) q^{69} +(2.43863 + 37.5941i) q^{70} +(-23.2236 + 40.2244i) q^{71} +(24.7384 - 6.00089i) q^{72} +(56.1148 + 32.3979i) q^{73} +(12.3529 - 10.3653i) q^{74} +(-30.2036 + 9.12909i) q^{75} +(-3.19165 - 8.76899i) q^{76} +(-14.3124 - 58.6611i) q^{77} +(-28.4222 + 3.39796i) q^{78} +(-0.801841 - 4.54747i) q^{79} +(-13.1829 + 7.61112i) q^{80} +(-68.1396 - 43.7949i) q^{81} +(56.0189 + 32.3425i) q^{82} +(9.05452 + 10.7908i) q^{83} +(-20.6633 + 36.5654i) q^{84} +(-3.01765 + 17.1140i) q^{85} +(15.5896 - 88.4133i) q^{86} +(-8.58769 + 36.6643i) q^{87} +(18.6899 - 15.6827i) q^{88} -103.731i q^{89} +(46.4746 + 13.6473i) q^{90} +(27.9521 - 38.0680i) q^{91} +(53.1454 + 19.3434i) q^{92} +(-54.8948 - 35.8981i) q^{93} +(-73.7299 - 13.0006i) q^{94} +(3.08335 - 17.4865i) q^{95} +(-16.9444 - 0.942135i) q^{96} +(-17.6131 + 48.3917i) q^{97} +(-20.7488 - 66.1172i) q^{98} +(-77.1552 - 8.60651i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 36 q^{6} - 12 q^{9} + 36 q^{11} + 36 q^{14} - 24 q^{15} + 186 q^{21} + 126 q^{23} + 36 q^{29} - 72 q^{30} + 162 q^{35} - 48 q^{36} + 246 q^{39} - 48 q^{42} + 324 q^{47} - 72 q^{49} + 288 q^{50}+ \cdots - 216 q^{99}+O(q^{100}) $ 288 * q - 36 * q^6 - 12 * q^9 + 36 * q^11 + 36 * q^14 - 24 * q^15 + 186 * q^21 + 126 * q^23 + 36 * q^29 - 72 * q^30 + 162 * q^35 - 48 * q^36 + 246 * q^39 - 48 * q^42 + 324 * q^47 - 72 * q^49 + 288 * q^50 - 198 * q^51 + 270 * q^53 + 432 * q^54 - 144 * q^56 + 354 * q^57 + 270 * q^59 + 72 * q^60 + 138 * q^63 - 1152 * q^64 - 360 * q^65 + 72 * q^69 + 180 * q^70 + 216 * q^71 - 96 * q^72 + 216 * q^74 - 1170 * q^75 + 234 * q^77 - 96 * q^78 - 36 * q^79 + 324 * q^81 - 24 * q^84 - 360 * q^85 + 144 * q^86 - 990 * q^87 - 198 * q^91 - 180 * q^92 + 168 * q^93 - 72 * q^95 + 216 * q^98 - 216 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.245576	−	1.39273i	−0.122788	−	0.696364i
$2$	−0.245576	−	1.39273i	−0.122788	−	0.696364i
$3$	2.40164	−	1.79781i	0.800548	−	0.599269i
$3$	2.40164	−	1.79781i	0.800548	−	0.599269i
$4$	−1.87939	+	0.684040i	−0.469846	+	0.171010i
$5$	−3.74775	−	0.660829i	−0.749549	−	0.132166i	−0.214192	−	0.976792i	$-0.568712\pi$
$5$	−3.74775	−	0.660829i	−0.749549	−	0.132166i	−0.535357	+	0.844626i	$0.679823\pi$
$6$	−3.09364	−	2.90334i	−0.515607	−	0.483890i
$7$	6.98532	−	0.453118i	0.997903	−	0.0647312i
$7$	6.98532	−	0.453118i	0.997903	−	0.0647312i
$8$	1.41421	+	2.44949i	0.176777	+	0.306186i
$9$	2.53579	−	8.63538i	0.281754	−	0.959487i
$10$			5.38188i			0.538188i
$11$	−1.49788	−	8.49493i	−0.136171	−	0.772266i	−0.974037	−	0.226389i	$-0.927308\pi$
$11$	−1.49788	−	8.49493i	−0.136171	−	0.772266i	0.837866	−	0.545877i	$-0.183803\pi$
$12$	−3.28384	+	5.02159i	−0.273654	+	0.418466i
$13$	4.33681	−	5.16840i	0.333600	−	0.397569i	−0.573003	−	0.819553i	$-0.694222\pi$
$13$	4.33681	−	5.16840i	0.333600	−	0.397569i	0.906603	+	0.421984i	$0.138666\pi$
$14$	−2.34649	−	9.61738i	−0.167607	−	0.686956i
$15$	−10.1888	+	5.15065i	−0.679253	+	0.343376i
$16$	3.06418	−	2.57115i	0.191511	−	0.160697i
$17$		−	4.56647i		−	0.268616i	−0.990940	−	0.134308i	$-0.957119\pi$
$17$		−	4.56647i		−	0.268616i	0.990940	−	0.134308i	$-0.0428811\pi$
$18$	−12.6495	−	1.41102i	−0.702748	−	0.0783901i
$19$			4.66588i			0.245573i	0.992433	+	0.122786i	$0.0391830\pi$
$19$			4.66588i			0.245573i	−0.992433	+	0.122786i	$0.960817\pi$
$20$	7.49549	−	1.32166i	0.374775	−	0.0660829i
$21$	15.9616	−	13.6465i	0.760078	−	0.649832i
$22$	−11.4633	+	4.17229i	−0.521058	+	0.189650i
$23$	−21.6623	−	18.1768i	−0.941838	−	0.790296i	0.0360662	−	0.999349i	$-0.488517\pi$
$23$	−21.6623	−	18.1768i	−0.941838	−	0.790296i	−0.977904	+	0.209053i	$0.932962\pi$
$24$	7.80015	+	3.34032i	0.325006	+	0.139180i
$25$	−9.88340	−	3.59726i	−0.395336	−	0.143891i
$26$	−8.26320	−	4.77076i	−0.317815	−	0.183491i
$27$	−9.43469	−	25.2980i	−0.349433	−	0.936961i
$28$	−12.8182	+	5.62982i	−0.457791	+	0.201065i
$29$	−9.61554	+	8.06840i	−0.331570	+	0.278221i	−0.793339	−	0.608780i	$-0.791659\pi$
$29$	−9.61554	+	8.06840i	−0.331570	+	0.278221i	0.461769	+	0.887000i	$0.347215\pi$
$30$	9.67557	+	12.9254i	0.322519	+	0.430845i
$31$	−7.47776	−	20.5450i	−0.241218	−	0.662741i	−0.999936	−	0.0113217i	$-0.996396\pi$
$31$	−7.47776	−	20.5450i	−0.241218	−	0.662741i	0.758718	−	0.651419i	$-0.225826\pi$
$32$	−4.33340	−	3.63616i	−0.135419	−	0.113630i
$33$	−18.8696	−	17.7089i	−0.571807	−	0.536633i
$34$	−6.35985	+	1.12141i	−0.187054	+	0.0329827i
$35$	−26.4786	−	2.91793i	−0.756533	−	0.0833694i
$36$	1.14123	+	17.9638i	0.0317008	+	0.498994i
$37$	5.70126	+	9.87487i	0.154088	+	0.266888i	0.932727	−	0.360584i	$-0.117423\pi$
$37$	5.70126	+	9.87487i	0.154088	+	0.266888i	−0.778639	+	0.627473i	$0.784089\pi$
$38$	6.49831	−	1.14583i	0.171008	−	0.0301533i
$39$	1.12367	−	20.2094i	0.0288122	−	0.518190i
$40$	−3.68142	−	10.1146i	−0.0920355	−	0.252866i
$41$	−29.4006	+	35.0383i	−0.717089	+	0.854593i	−0.994344	−	0.106203i	$-0.966131\pi$
$41$	−29.4006	+	35.0383i	−0.717089	+	0.854593i	0.277256	+	0.960796i	$0.410575\pi$
$42$	−22.9256	−	18.8790i	−0.545848	−	0.449499i
$43$	59.6536	+	21.7121i	1.38729	+	0.504933i	0.924381	−	0.381471i	$-0.124582\pi$
$43$	59.6536	+	21.7121i	1.38729	+	0.504933i	0.462912	+	0.886404i	$0.346804\pi$
$44$	8.62597	+	14.9406i	0.196045	+	0.339560i
$45$	−15.2100	+	30.6875i	−0.338000	+	0.681944i
$46$	−19.9956	+	34.6334i	−0.434688	+	0.752901i
$47$	18.1063	−	49.7465i	0.385239	−	1.05844i	−0.583879	−	0.811841i	$-0.698466\pi$
$47$	18.1063	−	49.7465i	0.385239	−	1.05844i	0.969118	−	0.246596i	$-0.0793120\pi$
$48$	2.73663	−	11.6838i	0.0570132	−	0.243412i
$49$	48.5894	−	6.33035i	0.991620	−	0.129191i
$50$	−2.58289	+	14.6483i	−0.0516578	+	0.292966i
$51$	−8.20962	−	10.9670i	−0.160973	−	0.215040i
$52$	−4.61513	+	12.6800i	−0.0887525	+	0.243846i
$53$	8.57836	+	14.8582i	0.161856	+	0.280343i	0.935534	−	0.353236i	$-0.114919\pi$
$53$	8.57836	+	14.8582i	0.161856	+	0.280343i	−0.773678	+	0.633578i	$0.781585\pi$
$54$	−32.9163	+	19.3525i	−0.609560	+	0.358380i
$55$			32.8267i			0.596849i
$56$	10.9886	+	16.4697i	0.196226	+	0.294101i
$57$	8.38835	+	11.2058i	0.147164	+	0.196593i
$58$	13.5984	+	11.4104i	0.234456	+	0.196732i
$59$	29.4528	−	35.1004i	0.499199	−	0.594922i	−0.456333	−	0.889809i	$-0.650837\pi$
$59$	29.4528	−	35.1004i	0.499199	−	0.594922i	0.955532	+	0.294887i	$0.0952819\pi$
$60$	15.6254	−	16.6496i	0.260424	−	0.277493i
$61$	−12.2195	+	33.5727i	−0.200319	+	0.550372i	−0.998655	−	0.0518395i	$-0.983492\pi$
$61$	−12.2195	+	33.5727i	−0.200319	+	0.550372i	0.798336	+	0.602212i	$0.205714\pi$
$62$	−26.7772	+	15.4598i	−0.431891	+	0.249352i
$63$	13.8004	−	61.4699i	0.219054	−	0.975713i
$64$	−4.00000	+	6.92820i	−0.0625000	+	0.108253i
$65$	−19.6687	+	16.5040i	−0.302595	+	0.253907i
$66$	−20.0297	+	30.6291i	−0.303481	+	0.464078i
$67$	9.36538	−	53.1137i	0.139782	−	0.792742i	−0.831628	−	0.555333i	$-0.812591\pi$
$67$	9.36538	−	53.1137i	0.139782	−	0.792742i	0.971410	−	0.237409i	$-0.0762981\pi$
$68$	3.12365	+	8.58215i	0.0459360	+	0.126208i
$69$	−84.7034	−	4.70964i	−1.22759	−	0.0682557i
$70$	2.43863	+	37.5941i	0.0348375	+	0.537059i
$71$	−23.2236	+	40.2244i	−0.327093	+	0.566541i	−0.981934	−	0.189225i	$-0.939402\pi$
$71$	−23.2236	+	40.2244i	−0.327093	+	0.566541i	0.654841	+	0.755767i	$0.272736\pi$
$72$	24.7384	−	6.00089i	0.343589	−	0.0833457i
$73$	56.1148	+	32.3979i	0.768696	+	0.443807i	0.832409	−	0.554162i	$-0.186961\pi$
$73$	56.1148	+	32.3979i	0.768696	+	0.443807i	−0.0637134	+	0.997968i	$0.520294\pi$
$74$	12.3529	−	10.3653i	0.166931	−	0.140072i
$75$	−30.2036	+	9.12909i	−0.402715	+	0.121721i
$76$	−3.19165	−	8.76899i	−0.0419954	−	0.115381i
$77$	−14.3124	−	58.6611i	−0.185875	−	0.761832i
$78$	−28.4222	+	3.39796i	−0.364387	+	0.0435636i
$79$	−0.801841	−	4.54747i	−0.0101499	−	0.0575629i	0.979312	−	0.202355i	$-0.0648596\pi$
$79$	−0.801841	−	4.54747i	−0.0101499	−	0.0575629i	−0.989462	+	0.144793i	$0.953749\pi$
$80$	−13.1829	+	7.61112i	−0.164786	+	0.0951391i
$81$	−68.1396	−	43.7949i	−0.841229	−	0.540678i
$82$	56.0189	+	32.3425i	0.683158	+	0.394421i
$83$	9.05452	+	10.7908i	0.109091	+	0.130009i	0.817827	−	0.575465i	$-0.195179\pi$
$83$	9.05452	+	10.7908i	0.109091	+	0.130009i	−0.708736	+	0.705474i	$0.750734\pi$
$84$	−20.6633	+	36.5654i	−0.245992	+	0.435302i
$85$	−3.01765	+	17.1140i	−0.0355018	+	0.201341i
$86$	15.5896	−	88.4133i	0.181275	−	1.02806i
$87$	−8.58769	+	36.6643i	−0.0987091	+	0.421429i
$88$	18.6899	−	15.6827i	0.212385	−	0.178212i
$89$		−	103.731i		−	1.16551i	−0.812646	−	0.582757i	$-0.801974\pi$
$89$		−	103.731i		−	1.16551i	0.812646	−	0.582757i	$-0.198026\pi$
$90$	46.4746	+	13.6473i	0.516384	+	0.151637i
$91$	27.9521	−	38.0680i	0.307166	−	0.418330i
$92$	53.1454	+	19.3434i	0.577668	+	0.210254i
$93$	−54.8948	−	35.8981i	−0.590267	−	0.386002i
$94$	−73.7299	−	13.0006i	−0.784360	−	0.138304i
$95$	3.08335	−	17.4865i	0.0324563	−	0.184069i
$96$	−16.9444	−	0.942135i	−0.176504	−	0.00981390i
$97$	−17.6131	+	48.3917i	−0.181579	+	0.498884i	−0.996770	−	0.0803083i	$-0.974410\pi$
$97$	−17.6131	+	48.3917i	−0.181579	+	0.498884i	0.815191	+	0.579192i	$0.196632\pi$
$98$	−20.7488	−	66.1172i	−0.211723	−	0.674665i
$99$	−77.1552	−	8.60651i	−0.779346	−	0.0869344i
$100$	21.0354			0.210354
$101$	3.72825	+	4.44315i	0.0369133	+	0.0439916i	0.784185	−	0.620527i	$-0.213081\pi$
$101$	3.72825	+	4.44315i	0.0369133	+	0.0439916i	−0.747272	+	0.664518i	$0.768637\pi$
$102$	−13.2580	+	14.1270i	−0.129980	+	0.138500i
$103$	74.5624	+	13.1474i	0.723907	+	0.127644i	0.523448	−	0.852058i	$-0.324646\pi$
$103$	74.5624	+	13.1474i	0.723907	+	0.127644i	0.200459	+	0.979702i	$0.435757\pi$
$104$	18.7931	+	3.31373i	0.180703	+	0.0318628i
$105$	−68.8381	+	40.5956i	−0.655601	+	0.386625i
$106$	18.5867	−	15.5961i	0.175347	−	0.147133i
$107$	11.5967	−	20.0861i	0.108380	−	0.187720i	−0.806734	−	0.590915i	$-0.798767\pi$
$107$	11.5967	−	20.0861i	0.108380	−	0.187720i	0.915114	+	0.403195i	$0.132100\pi$
$108$	35.0362	+	41.0909i	0.324410	+	0.380471i
$109$	15.3470	+	26.5819i	0.140799	+	0.243870i	0.927798	−	0.373084i	$-0.121700\pi$
$109$	15.3470	+	26.5819i	0.140799	+	0.243870i	−0.786999	+	0.616954i	$0.788366\pi$
$110$	45.7187	−	8.06143i	0.415624	−	0.0732858i
$111$	31.4455	+	13.4662i	0.283293	+	0.121317i
$112$	20.2392	−	19.3487i	0.180707	−	0.172757i
$113$	178.082	−	64.8167i	1.57595	−	0.573599i	0.601632	−	0.798773i	$-0.294517\pi$
$113$	178.082	−	64.8167i	1.57595	−	0.573599i	0.974318	+	0.225174i	$0.0722952\pi$
$114$	13.5466	−	14.4346i	0.118830	−	0.126619i
$115$	69.1730	+	82.4371i	0.601504	+	0.716845i
$116$	12.5522	−	21.7410i	0.108209	−	0.187423i
$117$	−33.6339	−	50.5559i	−0.287469	−	0.432102i
$118$	−56.1182	−	32.3999i	−0.475578	−	0.274575i
$119$	−2.06915	−	31.8982i	−0.0173878	−	0.268052i
$120$	−27.0256	−	17.6732i	−0.225213	−	0.147277i
$121$	43.7827	−	15.9356i	0.361840	−	0.131699i
$122$	49.7585	+	8.77376i	0.407856	+	0.0719161i
$123$	−7.61776	+	137.006i	−0.0619330	+	1.11387i
$124$	28.1072	+	33.4968i	0.226671	+	0.270136i
$125$	117.056	+	67.5824i	0.936449	+	0.540659i
$126$	−88.9999	−	4.12474i	−0.706349	−	0.0327360i
$127$	117.300	+	203.169i	0.923619	+	1.59975i	0.793768	+	0.608221i	$0.208116\pi$
$127$	117.300	+	203.169i	0.923619	+	1.59975i	0.129851	+	0.991534i	$0.458550\pi$
$128$	10.6314	+	3.86952i	0.0830579	+	0.0302306i
$129$	182.301	−	55.1008i	1.41319	−	0.427138i
$130$	27.8157	+	23.3402i	0.213967	+	0.179540i
$131$	120.869	−	144.047i	0.922668	−	1.09959i	−0.0720969	−	0.997398i	$-0.522969\pi$
$131$	120.869	−	144.047i	0.922668	−	1.09959i	0.994764	−	0.102195i	$-0.0325865\pi$
$132$	47.5769	+	20.3742i	0.360431	+	0.154350i
$133$	2.11420	+	32.5927i	0.0158962	+	0.245058i
$134$	−76.2729			−0.569201
$135$	18.6412	+	101.045i	0.138083	+	0.748482i
$136$	11.1855	−	6.45796i	0.0822464	−	0.0474850i
$137$	170.019	+	61.8820i	1.24102	+	0.451693i	0.877357	−	0.479838i	$-0.159305\pi$
$137$	170.019	+	61.8820i	1.24102	+	0.451693i	0.363661	+	0.931532i	$0.381527\pi$
$138$	14.2418	+	119.125i	0.103202	+	0.863228i
$139$	−90.1051	−	15.8880i	−0.648238	−	0.114302i	−0.160145	−	0.987093i	$-0.551196\pi$
$139$	−90.1051	−	15.8880i	−0.648238	−	0.114302i	−0.488093	+	0.872792i	$0.662307\pi$
$140$	51.7596	−	12.6285i	0.369711	−	0.0902039i
$141$	−45.9498	−	152.025i	−0.325885	−	1.07819i
$142$	61.7249	+	22.4660i	0.434682	+	0.158211i
$143$	−50.4012	−	29.0992i	−0.352456	−	0.203491i
$144$	−14.4328	−	32.9802i	−0.100228	−	0.229029i
$145$	41.3685	−	23.8841i	0.285300	−	0.164718i
$146$	31.3410	−	86.1088i	0.214665	−	0.589786i
$147$	105.314	−	102.558i	0.716419	−	0.697670i
$148$	−17.4697	−	14.6588i	−0.118038	−	0.0990459i
$149$	−101.811	+	37.0563i	−0.683298	+	0.248700i	−0.660263	−	0.751035i	$-0.729555\pi$
$149$	−101.811	+	37.0563i	−0.683298	+	0.248700i	−0.0230348	+	0.999735i	$0.507333\pi$
$150$	20.1316	+	39.8235i	0.134211	+	0.265490i
$151$	38.0006	+	215.512i	0.251659	+	1.42723i	0.804504	+	0.593947i	$0.202431\pi$
$151$	38.0006	+	215.512i	0.251659	+	1.42723i	−0.552845	+	0.833284i	$0.686458\pi$
$152$	−11.4290	+	6.59855i	−0.0751910	+	0.0434115i
$153$	−39.4332	−	11.5796i	−0.257733	−	0.0756836i
$154$	−78.1841	+	34.3390i	−0.507689	+	0.222981i
$155$	14.4480	+	81.9389i	0.0932131	+	0.528638i
$156$	11.7122	+	38.7499i	0.0750784	+	0.248397i
$157$	−46.8211	+	55.7992i	−0.298224	+	0.355409i	−0.894260	−	0.447549i	$-0.852297\pi$
$157$	−46.8211	+	55.7992i	−0.298224	+	0.355409i	0.596036	+	0.802958i	$0.296742\pi$
$158$	−6.13647	+	2.23349i	−0.0388384	+	0.0141360i
$159$	47.3142	+	20.2618i	0.297574	+	0.127432i
$160$	13.8376	+	16.4910i	0.0864851	+	0.103069i
$161$	−159.554	−	117.155i	−0.991020	−	0.727672i
$162$	−44.2611	+	105.655i	−0.273216	+	0.652191i
$163$	87.2406	−	151.105i	0.535219	−	0.927026i	−0.463934	−	0.885870i	$-0.653563\pi$
$163$	87.2406	−	151.105i	0.535219	−	0.927026i	0.999153	−	0.0411560i	$-0.0131041\pi$
$164$	31.2875	−	85.9617i	0.190777	−	0.524157i
$165$	59.0160	+	78.8380i	0.357673	+	0.477806i
$166$	12.8050	−	15.2604i	0.0771387	−	0.0919303i
$167$	97.2729	+	267.255i	0.582473	+	1.60033i	0.783941	+	0.620836i	$0.213207\pi$
$167$	97.2729	+	267.255i	0.582473	+	1.60033i	−0.201468	+	0.979495i	$0.564571\pi$
$168$	56.0001	+	19.7988i	0.333334	+	0.117850i
$169$	21.4420	+	121.604i	0.126876	+	0.719549i
$170$	24.5762			0.144566
$171$	40.2917	+	11.8317i	0.235624	+	0.0691911i
$172$	−126.964			−0.738163
$173$	−70.8891	−	84.4823i	−0.409764	−	0.488337i	0.521208	−	0.853430i	$-0.325482\pi$
$173$	−70.8891	−	84.4823i	−0.409764	−	0.488337i	−0.930971	+	0.365093i	$0.881037\pi$
$174$	53.1723	+	2.95647i	0.305588	+	0.0169912i
$175$	−70.6687	−	20.6497i	−0.403821	−	0.117998i
$176$	−26.4315	−	22.1787i	−0.150179	−	0.126015i
$177$	7.63126	−	137.249i	0.0431145	−	0.775418i
$178$	−144.469	+	25.4738i	−0.811623	+	0.143111i
$179$	−211.788			−1.18317			−0.591585	−	0.806242i	$-0.701498\pi$
$179$	−211.788			−1.18317			−0.591585	+	0.806242i	$0.701498\pi$
$180$	7.59395	−	68.0779i	0.0421886	−	0.378210i
$181$	192.990	−	111.423i	1.06624	−	0.615595i	0.139090	−	0.990280i	$-0.455582\pi$
$181$	192.990	−	111.423i	1.06624	−	0.615595i	0.927152	+	0.374684i	$0.122249\pi$
$182$	−59.8828	−	29.5811i	−0.329026	−	0.162533i
$183$	31.0104	+	102.598i	0.169456	+	0.560645i
$184$	13.8888	−	78.7674i	0.0754827	−	0.428084i
$185$	−14.8413	−	40.7761i	−0.0802231	−	0.220411i
$186$	−36.5155	+	85.2692i	−0.196320	+	0.458437i
$187$	−38.7918	+	6.84004i	−0.207443	+	0.0365778i
$188$			105.878i			0.563182i
$189$	−77.3673	−	172.439i	−0.409351	−	0.912377i
$190$	−25.1112			−0.132164
$191$	56.3223	+	319.419i	0.294881	+	1.67235i	0.667686	+	0.744443i	$0.267285\pi$
$191$	56.3223	+	319.419i	0.294881	+	1.67235i	−0.372805	+	0.927910i	$0.621604\pi$
$192$	2.84899	+	23.8303i	0.0148385	+	0.124116i
$193$	−181.896	+	66.2046i	−0.942464	+	0.343029i	−0.767138	−	0.641482i	$-0.778320\pi$
$193$	−181.896	+	66.2046i	−0.942464	+	0.343029i	−0.175326	+	0.984511i	$0.556098\pi$
$194$	71.7219	+	12.6465i	0.369700	+	0.0651881i
$195$	−17.5662	+	74.9972i	−0.0900831	+	0.384601i
$196$	−86.9879	+	45.1343i	−0.443816	+	0.230277i
$197$	−82.6089	−	143.083i	−0.419334	−	0.726308i	0.576538	−	0.817070i	$-0.304403\pi$
$197$	−82.6089	−	143.083i	−0.419334	−	0.726308i	−0.995873	+	0.0907617i	$0.971070\pi$
$198$	6.96091	+	109.570i	0.0351561	+	0.553383i
$199$		−	341.128i		−	1.71421i	−0.515141	−	0.857106i	$-0.672260\pi$
$199$		−	341.128i		−	1.71421i	0.515141	−	0.857106i	$-0.327740\pi$
$200$	−5.16578	−	29.2966i	−0.0258289	−	0.146483i
$201$	−72.9958	−	144.397i	−0.363163	−	0.718395i
$202$	5.27254	−	6.28356i	0.0261017	−	0.0311067i
$203$	−63.5117	+	60.7173i	−0.312866	+	0.299100i
$204$	22.9309	+	14.9956i	0.112407	+	0.0735076i
$205$	133.340	−	111.886i	0.650441	−	0.545785i
$206$		−	107.074i		−	0.519776i
$207$	−211.895	+	140.969i	−1.02365	+	0.681012i
$208$		−	26.9875i		−	0.129748i
$209$	39.6363	−	6.98895i	0.189647	−	0.0334400i
$210$	73.4437	+	85.9035i	0.349732	+	0.409064i
$211$	−120.555	+	43.8785i	−0.571351	+	0.207955i	−0.611508	−	0.791239i	$-0.709437\pi$
$211$	−120.555	+	43.8785i	−0.571351	+	0.207955i	0.0401565	+	0.999193i	$0.487214\pi$
$212$	−26.2856	−	22.0563i	−0.123989	−	0.104039i
$213$	16.5410	+	138.356i	0.0776571	+	0.649560i
$214$	−30.8223	−	11.2184i	−0.144030	−	0.0524225i
$215$	−209.219	−	120.792i	−0.973110	−	0.561825i
$216$	48.6244	−	58.8869i	0.225113	−	0.272624i
$217$	−61.5438	−	140.125i	−0.283612	−	0.645737i
$218$	33.2525	−	27.9021i	0.152534	−	0.127991i
$219$	193.013	−	23.0753i	0.881337	−	0.105367i
$220$	−22.4548	−	61.6940i	−0.102067	−	0.280427i
$221$	−23.6013	−	19.8039i	−0.106793	−	0.0896103i
$222$	11.0325	−	47.1020i	0.0496957	−	0.212171i
$223$	111.170	−	19.6023i	0.498522	−	0.0879028i	0.0812669	−	0.996692i	$-0.474103\pi$
$223$	111.170	−	19.6023i	0.498522	−	0.0879028i	0.417255	+	0.908790i	$0.362992\pi$
$224$	−31.9178	−	23.4362i	−0.142490	−	0.104626i
$225$	−56.1259	+	76.2250i	−0.249449	+	0.338778i
$226$	−134.005	−	232.103i	−0.592941	−	1.02700i
$227$	313.808	−	55.3328i	1.38241	−	0.243757i	0.567516	−	0.823362i	$-0.307904\pi$
$227$	313.808	−	55.3328i	1.38241	−	0.243757i	0.814897	+	0.579605i	$0.196793\pi$
$228$	−23.4302	−	15.3220i	−0.102764	−	0.0672018i
$229$	−137.884	−	378.832i	−0.602112	−	1.65429i	−0.746987	−	0.664839i	$-0.768500\pi$
$229$	−137.884	−	378.832i	−0.602112	−	1.65429i	0.144875	−	0.989450i	$-0.453722\pi$
$230$	97.8253	−	116.584i	0.425328	−	0.506886i
$231$	−139.835	−	115.152i	−0.605344	−	0.498494i
$232$	−33.3619	−	12.1427i	−0.143801	−	0.0523394i
$233$	46.4875	+	80.5188i	0.199517	+	0.345574i	0.948372	−	0.317160i	$-0.102729\pi$
$233$	46.4875	+	80.5188i	0.199517	+	0.345574i	−0.748855	+	0.662734i	$0.769396\pi$
$234$	−62.1510	+	59.2582i	−0.265603	+	0.253240i
$235$	−100.732	+	174.472i	−0.428645	+	0.742435i
$236$	−31.3430	+	86.1141i	−0.132809	+	0.364890i
$237$	−10.1012	−	9.47984i	−0.0426211	−	0.0399993i
$238$	−43.9174	+	10.7152i	−0.184527	+	0.0450218i
$239$	−58.5281	+	331.929i	−0.244887	+	1.38883i	0.575867	+	0.817544i	$0.304665\pi$
$239$	−58.5281	+	331.929i	−0.244887	+	1.38883i	−0.820754	+	0.571282i	$0.806446\pi$
$240$	−17.9772	+	41.9794i	−0.0749050	+	0.174914i
$241$	−66.3133	+	182.194i	−0.275159	+	0.755992i	0.722735	+	0.691125i	$0.242885\pi$
$241$	−66.3133	+	182.194i	−0.275159	+	0.755992i	−0.997894	+	0.0648673i	$0.979338\pi$
$242$	−32.9459	−	57.0640i	−0.136140	−	0.235802i
$243$	−242.382	+	17.3219i	−0.997456	+	0.0712835i
$244$		−	71.4547i		−	0.292847i
$245$	−186.284	−	8.38470i	−0.760343	−	0.0342233i
$246$	192.683	−	23.0359i	0.783265	−	0.0936419i
$247$	24.1152	+	20.2350i	0.0976322	+	0.0819232i
$248$	39.7496	−	47.3717i	0.160280	−	0.191015i
$249$	41.1454	+	9.63728i	0.165243	+	0.0387039i
$250$	65.3778	−	179.624i	0.261511	−	0.718496i
$251$	−93.3978	+	53.9233i	−0.372103	+	0.214834i	−0.674377	−	0.738387i	$-0.735588\pi$
$251$	−93.3978	+	53.9233i	−0.372103	+	0.214834i	0.302274	+	0.953221i	$0.402254\pi$
$252$	16.1116	+	124.966i	0.0639348	+	0.495895i
$253$	−121.963	+	211.246i	−0.482067	+	0.834965i
$254$	254.153	−	213.260i	1.00060	−	0.839605i
$255$	23.5203	+	46.5268i	0.0922363	+	0.182458i
$256$	2.77837	−	15.7569i	0.0108530	−	0.0615505i
$257$	−56.9096	−	156.358i	−0.221438	−	0.608396i	0.778374	−	0.627801i	$-0.216045\pi$
$257$	−56.9096	−	156.358i	−0.221438	−	0.608396i	−0.999812	+	0.0194050i	$0.993823\pi$
$258$	−121.509	−	240.364i	−0.470966	−	0.931645i
$259$	44.2996	+	66.3957i	0.171041	+	0.256354i
$260$	25.6756	−	44.4715i	0.0987525	−	0.171044i
$261$	45.2907	+	103.494i	0.173528	+	0.396527i
$262$	−230.300	−	132.964i	−0.879009	−	0.507496i
$263$	−191.127	+	160.375i	−0.726719	+	0.609790i	−0.929235	−	0.369489i	$-0.879533\pi$
$263$	−191.127	+	160.375i	−0.726719	+	0.609790i	0.202516	+	0.979279i	$0.435088\pi$
$264$	16.6921	−	71.2651i	0.0632275	−	0.269943i
$265$	−22.3308	−	61.3534i	−0.0842673	−	0.231522i
$266$	44.8735	−	10.9485i	0.168698	−	0.0411596i
$267$	−186.488	−	249.124i	−0.698456	−	0.933050i
$268$	18.7308	+	106.227i	0.0698909	+	0.396371i
$269$	−167.618	+	96.7745i	−0.623117	+	0.359757i	−0.778081	−	0.628163i	$-0.783807\pi$
$269$	−167.618	+	96.7745i	−0.623117	+	0.359757i	0.154965	+	0.987920i	$0.450474\pi$
$270$	136.151	−	50.7763i	0.504261	−	0.188060i
$271$	297.860	+	171.969i	1.09911	+	0.634573i	0.935988	−	0.352032i	$-0.114509\pi$
$271$	297.860	+	171.969i	1.09911	+	0.634573i	0.163125	+	0.986605i	$0.447843\pi$
$272$	−11.7411	−	13.9925i	−0.0431657	−	0.0514429i
$273$	−1.30803	−	141.678i	−0.00479131	−	0.518968i
$274$	44.4322	−	251.988i	0.162161	−	0.919663i
$275$	−15.7543	+	89.3471i	−0.0572884	+	0.324898i
$276$	162.412	−	49.0893i	0.588449	−	0.177860i
$277$	−76.6925	+	64.3526i	−0.276868	+	0.232320i	−0.770639	−	0.637272i	$-0.780063\pi$
$277$	−76.6925	+	64.3526i	−0.276868	+	0.232320i	0.493771	+	0.869592i	$0.335618\pi$
$278$			129.394i			0.465445i
$279$	−196.376	+	12.4756i	−0.703855	+	0.0447155i
$280$	−30.2990	−	68.9857i	−0.108211	−	0.246378i
$281$	275.913	+	100.424i	0.981895	+	0.357381i	0.782577	−	0.622554i	$-0.213905\pi$
$281$	275.913	+	100.424i	0.981895	+	0.357381i	0.199318	+	0.979935i	$0.436127\pi$
$282$	−200.445	+	101.329i	−0.710799	+	0.359324i
$283$	−454.815	−	80.1962i	−1.60712	−	0.283379i	−0.703173	−	0.711019i	$-0.748234\pi$
$283$	−454.815	−	80.1962i	−1.60712	−	0.283379i	−0.903949	+	0.427640i	$0.859345\pi$
$284$	16.1309	−	91.4831i	0.0567991	−	0.322124i
$285$	−24.0323	−	47.5397i	−0.0843239	−	0.166806i
$286$	−28.1499	+	77.3413i	−0.0984263	+	0.270424i
$287$	−189.496	+	258.076i	−0.660266	+	0.899219i
$288$	−42.3882	+	28.2001i	−0.147181	+	0.0979169i
$289$	268.147			0.927846
$290$	−43.4231	−	51.7497i	−0.149735	−	0.178447i
$291$	44.6984	+	147.885i	0.153603	+	0.508195i
$292$	−127.623	−	22.5033i	−0.437064	−	0.0770662i
$293$	−167.902	−	29.6056i	−0.573044	−	0.101043i	−0.120386	−	0.992727i	$-0.538413\pi$
$293$	−167.902	−	29.6056i	−0.573044	−	0.101043i	−0.452658	+	0.891684i	$0.649524\pi$
$294$	−168.697	−	121.488i	−0.573800	−	0.413223i
$295$	−133.577	+	112.084i	−0.452803	+	0.379947i
$296$	−16.1256	+	27.9303i	−0.0544783	+	0.0943593i
$297$	−200.772	+	118.040i	−0.676001	+	0.397442i
$298$	76.6117	+	132.695i	0.257086	+	0.445287i
$299$	−187.890	+	33.1301i	−0.628395	+	0.110803i
$300$	50.5195	−	37.8176i	0.168398	−	0.126059i
$301$	426.538	+	124.636i	1.41707	+	0.414073i
$302$	290.817	−	105.849i	0.962972	−	0.350493i
$303$	16.9418	+	3.96820i	0.0559137	+	0.0130964i
$304$	11.9967	+	14.2971i	0.0394628	+	0.0470299i
$305$	67.9813	−	117.747i	0.222890	−	0.386056i
$306$	−6.44339	+	57.7634i	−0.0210568	+	0.188769i
$307$	−178.714	−	103.181i	−0.582131	−	0.336093i	0.179849	−	0.983694i	$-0.442439\pi$
$307$	−178.714	−	103.181i	−0.582131	−	0.336093i	−0.761980	+	0.647601i	$0.775772\pi$
$308$	67.0251	+	100.456i	0.217614	+	0.326157i
$309$	202.709	−	102.473i	0.656015	−	0.331629i
$310$	110.571	−	40.2444i	0.356679	−	0.129821i
$311$	−7.06769	−	1.24622i	−0.0227257	−	0.00400715i	0.162274	−	0.986746i	$-0.448117\pi$
$311$	−7.06769	−	1.24622i	−0.0227257	−	0.00400715i	−0.184999	+	0.982739i	$0.559228\pi$
$312$	51.0918	−	25.8280i	0.163756	−	0.0827820i
$313$	−359.611	−	428.568i	−1.14892	−	1.36923i	−0.918158	−	0.396215i	$-0.870324\pi$
$313$	−359.611	−	428.568i	−1.14892	−	1.36923i	−0.230759	−	0.973011i	$-0.574121\pi$
$314$	89.2113	+	51.5062i	0.284112	+	0.164032i
$315$	−92.3416	+	221.254i	−0.293148	+	0.702393i
$316$	4.61762	+	7.99795i	0.0146127	+	0.0253100i
$317$	458.375	+	166.835i	1.44598	+	0.526293i	0.941465	−	0.337111i	$-0.109450\pi$
$317$	458.375	+	166.835i	1.44598	+	0.526293i	0.504513	+	0.863404i	$0.331672\pi$
$318$	16.5999	−	70.8717i	0.0522010	−	0.222867i
$319$	82.9434	+	69.5978i	0.260011	+	0.218175i
$320$	19.5693	−	23.3218i	0.0611542	−	0.0728807i
$321$	−8.25973	−	69.0882i	−0.0257312	−	0.215228i
$322$	−123.983	+	250.986i	−0.385040	+	0.779460i
$323$	21.3066			0.0659647
$324$	158.018	+	35.6974i	0.487710	+	0.110177i
$325$	−61.4545	+	35.4808i	−0.189091	+	0.109172i
$326$	−231.873	−	84.3947i	−0.711266	−	0.258880i
$327$	84.6472	+	36.2491i	0.258860	+	0.110854i
$328$	−127.405	−	22.4649i	−0.388429	−	0.0684905i
$329$	103.937	−	355.700i	0.315918	−	1.08115i
$330$	95.3070	−	101.554i	0.288809	−	0.307739i
$331$	314.780	+	114.570i	0.950996	+	0.346134i	0.770499	−	0.637441i	$-0.220007\pi$
$331$	314.780	+	114.570i	0.950996	+	0.346134i	0.180497	+	0.983576i	$0.442229\pi$
$332$	−24.3982	−	14.0863i	−0.0734887	−	0.0424287i
$333$	99.7304	−	24.1920i	0.299491	−	0.0726486i
$334$	348.326	−	201.106i	1.04289	−	0.602114i
$335$	−70.1981	+	192.868i	−0.209547	+	0.575725i
$336$	13.8221	−	82.8550i	0.0411373	−	0.246592i
$337$	−134.872	−	113.171i	−0.400213	−	0.335819i	0.420363	−	0.907356i	$-0.361903\pi$
$337$	−134.872	−	113.171i	−0.400213	−	0.335819i	−0.820576	+	0.571537i	$0.806347\pi$
$338$	164.095	−	59.7259i	0.485489	−	0.176704i
$339$	311.163	−	475.824i	0.917884	−	1.40361i
$340$	−6.03531	−	34.2279i	−0.0177509	−	0.100670i
$341$	−163.327	+	94.2970i	−0.478965	+	0.276531i
$342$	6.58366	−	59.0209i	0.0192505	−	0.172576i
$343$	336.544	−	66.2363i	0.981177	−	0.193109i
$344$	31.1793	+	176.827i	0.0906375	+	0.514031i
$345$	314.335	+	73.6250i	0.911115	+	0.213406i
$346$	−100.252	+	119.476i	−0.289747	+	0.345307i
$347$	−616.685	+	224.455i	−1.77719	+	0.646844i	−0.777348	+	0.629071i	$0.783435\pi$
$347$	−616.685	+	224.455i	−1.77719	+	0.646844i	−0.999842	+	0.0177728i	$0.994342\pi$
$348$	−8.94028	−	74.7807i	−0.0256905	−	0.214887i
$349$	−331.899	−	395.542i	−0.951001	−	1.13336i	−0.990960	−	0.134158i	$-0.957167\pi$
$349$	−331.899	−	395.542i	−0.951001	−	1.13336i	0.0399589	−	0.999201i	$-0.487277\pi$
$350$	−11.4049	+	103.493i	−0.0325854	+	0.295695i
$351$	−171.666	−	60.9501i	−0.489078	−	0.173647i
$352$	−24.3979	+	42.2585i	−0.0693123	+	0.120052i
$353$	−86.0300	+	236.365i	−0.243711	+	0.669590i	0.756173	+	0.654372i	$0.227067\pi$
$353$	−86.0300	+	236.365i	−0.243711	+	0.669590i	−0.999884	+	0.0152189i	$0.995155\pi$
$354$	−193.025	+	23.0767i	−0.545268	+	0.0651885i
$355$	113.618	−	135.404i	0.320050	−	0.381420i
$356$	70.9560	+	194.950i	0.199315	+	0.547613i
$357$	−62.3162	−	72.8883i	−0.174555	−	0.204169i
$358$	52.0099	+	294.963i	0.145279	+	0.823918i
$359$	−203.563			−0.567027			−0.283513	−	0.958968i	$-0.591500\pi$
$359$	−203.563			−0.567027			−0.283513	+	0.958968i	$0.591500\pi$
$360$	−96.6789	+	6.14196i	−0.268552	+	0.0170610i
$361$	339.230			0.939694
$362$	−202.575	−	241.420i	−0.559600	−	0.666905i
$363$	76.5013	−	116.984i	0.210747	−	0.322271i
$364$	−26.4926	+	90.6648i	−0.0727820	+	0.249079i
$365$	−188.895	−	158.501i	−0.517519	−	0.434250i
$366$	135.276	−	68.3847i	0.369606	−	0.186843i
$367$	471.552	−	83.1474i	1.28488	−	0.226560i	0.510831	−	0.859681i	$-0.329338\pi$
$367$	471.552	−	83.1474i	1.28488	−	0.226560i	0.774052	+	0.633122i	$0.218227\pi$
$368$	−113.112			−0.307371
$369$	228.015	+	342.735i	0.617928	+	0.928822i
$370$	−53.1453	+	30.6835i	−0.143636	+	0.0829283i
$371$	66.6551	+	99.9019i	0.179663	+	0.269277i
$372$	127.724	+	29.9162i	0.343345	+	0.0804199i
$373$	−70.8420	+	401.765i	−0.189925	+	1.07712i	0.729538	+	0.683940i	$0.239735\pi$
$373$	−70.8420	+	401.765i	−0.189925	+	1.07712i	−0.919463	+	0.393177i	$0.871376\pi$
$374$	19.0526	+	52.3467i	0.0509429	+	0.139964i
$375$	402.627	−	48.1354i	1.07367	−	0.128361i
$376$	147.460	−	26.0011i	0.392180	−	0.0691519i
$377$			84.6881i			0.224637i
$378$	−221.162	+	150.098i	−0.585084	+	0.397086i
$379$	−209.118			−0.551763			−0.275881	−	0.961192i	$-0.588970\pi$
$379$	−209.118			−0.551763			−0.275881	+	0.961192i	$0.588970\pi$
$380$	6.16670	+	34.9731i	0.0162282	+	0.0920344i
$381$	646.970	+	277.057i	1.69808	+	0.727184i
$382$	431.033	−	156.883i	1.12836	−	0.410689i
$383$	341.630	+	60.2385i	0.891984	+	0.157281i	0.600812	−	0.799390i	$-0.294844\pi$
$383$	341.630	+	60.2385i	0.891984	+	0.157281i	0.291171	+	0.956671i	$0.405955\pi$
$384$	32.4895	−	9.82001i	0.0846081	−	0.0255729i
$385$	14.8744	+	229.305i	0.0386347	+	0.595597i
$386$	136.874	+	237.073i	0.354596	+	0.614178i
$387$	338.761	−	460.074i	0.875352	−	1.18882i
$388$		−	102.995i		−	0.265450i
$389$	34.5992	+	196.222i	0.0889440	+	0.504427i	0.996436	+	0.0843565i	$0.0268835\pi$
$389$	34.5992	+	196.222i	0.0889440	+	0.504427i	−0.907492	+	0.420070i	$0.862005\pi$
$390$	108.765	+	6.04748i	0.278883	+	0.0155063i
$391$	−83.0038	+	98.9201i	−0.212286	+	0.252993i
$392$	84.2219	+	110.067i	0.214852	+	0.280782i
$393$	31.3175	−	563.248i	0.0796883	−	1.43320i
$394$	−178.989	+	150.189i	−0.454286	+	0.381191i
$395$			17.5726i			0.0444877i
$396$	150.892	−	36.6023i	0.381039	−	0.0924302i
$397$		−	114.572i		−	0.288596i	−0.989534	−	0.144298i	$-0.953908\pi$
$397$		−	114.572i		−	0.288596i	0.989534	−	0.144298i	$-0.0460923\pi$
$398$	−475.099	+	83.7727i	−1.19372	+	0.210484i
$399$	63.6729	+	74.4751i	0.159581	+	0.186654i
$400$	−39.5336	+	14.3891i	−0.0988340	+	0.0359726i
$401$	−391.014	−	328.100i	−0.975098	−	0.818204i	0.00824469	−	0.999966i	$-0.497376\pi$
$401$	−391.014	−	328.100i	−0.975098	−	0.818204i	−0.983343	+	0.181762i	$0.941820\pi$
$402$	−183.180	+	137.124i	−0.455672	+	0.341104i
$403$	−138.614	−	50.4515i	−0.343956	−	0.125190i
$404$	−10.0461	−	5.80012i	−0.0248666	−	0.0143567i
$405$	226.429	+	209.161i	0.559084	+	0.516447i
$406$	100.160	+	73.5439i	0.246699	+	0.181143i
$407$	75.3464	−	63.2232i	0.185126	−	0.155339i
$408$	15.2535	−	35.6191i	0.0373859	−	0.0873017i
$409$	−263.935	−	725.154i	−0.645317	−	1.77299i	−0.634341	−	0.773054i	$-0.718728\pi$
$409$	−263.935	−	725.154i	−0.645317	−	1.77299i	−0.0109762	−	0.999940i	$-0.503494\pi$
$410$	−188.572	−	158.231i	−0.459931	−	0.385928i
$411$	519.578	−	157.043i	1.26418	−	0.382101i
$412$	−149.125	+	26.2947i	−0.361953	+	0.0638221i
$413$	189.832	−	258.533i	0.459642	−	0.625988i
$414$	248.368	+	260.493i	0.599924	+	0.629210i
$415$	−26.8032	−	46.4245i	−0.0645860	−	0.111866i
$416$	−37.5862	+	6.62747i	−0.0903515	+	0.0159314i
$417$	−244.964	+	123.834i	−0.587443	+	0.296965i
$418$	−19.4674	−	53.4863i	−0.0465728	−	0.127958i
$419$	−270.319	+	322.153i	−0.645152	+	0.768862i	−0.985174	−	0.171555i	$-0.945121\pi$
$419$	−270.319	+	322.153i	−0.645152	+	0.768862i	0.340023	+	0.940417i	$0.389565\pi$
$420$	101.604	−	123.383i	0.241915	−	0.293769i
$421$	−435.186	−	158.395i	−1.03370	−	0.376235i	−0.231209	−	0.972904i	$-0.574268\pi$
$421$	−435.186	−	158.395i	−1.03370	−	0.376235i	−0.802487	+	0.596669i	$0.796490\pi$
$422$	90.7162	+	157.125i	0.214967	+	0.372334i
$423$	−383.667	−	282.501i	−0.907013	−	0.667851i
$424$	−24.2633	+	42.0252i	−0.0572247	+	0.0991161i
$425$	−16.4268	+	45.1322i	−0.0386513	+	0.106194i
$426$	188.631	−	57.0140i	0.442795	−	0.133836i
$427$	−70.1445	+	240.053i	−0.164273	+	0.562185i
$428$	−8.05498	+	45.6821i	−0.0188201	+	0.106734i
$429$	−173.360	+	20.7258i	−0.404104	+	0.0483119i
$430$	−116.852	+	321.048i	−0.271749	+	0.746624i
$431$	198.118	+	343.150i	0.459671	+	0.796173i	0.998943	−	0.0459584i	$-0.0146342\pi$
$431$	198.118	+	343.150i	0.459671	+	0.796173i	−0.539273	+	0.842131i	$0.681301\pi$
$432$	−93.9544	−	53.2594i	−0.217487	−	0.123286i
$433$			62.9517i			0.145385i	0.997354	+	0.0726925i	$0.0231592\pi$
$433$			62.9517i			0.145385i	−0.997354	+	0.0726925i	$0.976841\pi$
$434$	−180.042	+	120.125i	−0.414844	+	0.276786i
$435$	56.4133	−	131.734i	0.129686	−	0.302836i
$436$	−47.0261	−	39.4596i	−0.107858	−	0.0905036i
$437$	84.8108	−	101.074i	0.194075	−	0.231290i
$438$	−79.5369	−	263.148i	−0.181591	−	0.600794i
$439$	201.767	−	554.349i	0.459605	−	1.26275i	−0.466175	−	0.884693i	$-0.654368\pi$
$439$	201.767	−	554.349i	0.459605	−	1.26275i	0.925780	−	0.378062i	$-0.123409\pi$
$440$	−80.4086	+	46.4239i	−0.182747	+	0.105509i
$441$	68.5472	−	435.640i	0.155436	−	0.987846i
$442$	−21.7855	+	37.7336i	−0.0492885	+	0.0853702i
$443$	−300.654	+	252.279i	−0.678678	+	0.569478i	−0.915620	−	0.402046i	$-0.868299\pi$
$443$	−300.654	+	252.279i	−0.678678	+	0.569478i	0.236942	+	0.971524i	$0.423855\pi$
$444$	−68.3096	−	3.79812i	−0.153850	−	0.00855432i
$445$	−68.5483	+	388.757i	−0.154041	+	0.873611i
$446$	−54.6014	−	150.016i	−0.122425	−	0.336359i
$447$	−177.895	+	272.033i	−0.397974	+	0.608575i
$448$	−24.8020	+	50.2082i	−0.0553616	+	0.112072i
$449$	197.641	−	342.324i	0.440180	−	0.762414i	−0.557523	−	0.830162i	$-0.688248\pi$
$449$	197.641	−	342.324i	0.440180	−	0.762414i	0.997702	+	0.0677478i	$0.0215813\pi$
$450$	119.944	+	59.4492i	0.266542	+	0.132109i
$451$	341.687	+	197.273i	0.757620	+	0.437412i
$452$	−290.348	+	243.631i	−0.642363	+	0.539007i
$453$	478.712	+	449.265i	1.05676	+	0.991755i
$454$	−154.127	−	423.461i	−0.339487	−	0.932733i
$455$	−129.914	+	124.198i	−0.285525	+	0.272962i
$456$	−15.5855	+	36.3946i	−0.0341788	+	0.0798126i
$457$	−30.1906	−	171.219i	−0.0660625	−	0.374659i	−0.999858	−	0.0168519i	$-0.994636\pi$
$457$	−30.1906	−	171.219i	−0.0660625	−	0.374659i	0.933796	−	0.357807i	$-0.116475\pi$
$458$	−493.749	+	285.066i	−1.07806	+	0.622416i
$459$	−115.522	+	43.0832i	−0.251683	+	0.0938632i
$460$	−186.393	−	107.614i	−0.405202	−	0.233944i
$461$	108.506	+	129.312i	0.235370	+	0.280503i	0.870781	−	0.491671i	$-0.163614\pi$
$461$	108.506	+	129.312i	0.235370	+	0.280503i	−0.635411	+	0.772174i	$0.719169\pi$
$462$	−126.036	+	223.030i	−0.272804	+	0.482749i
$463$	33.2038	−	188.308i	0.0717145	−	0.406713i	−0.927726	−	0.373262i	$-0.878239\pi$
$463$	33.2038	−	188.308i	0.0717145	−	0.406713i	0.999440	−	0.0334509i	$-0.0106497\pi$
$464$	−8.71867	+	49.4460i	−0.0187902	+	0.106565i
$465$	182.009	+	170.813i	0.391418	+	0.367340i
$466$	100.725	−	84.5180i	0.216147	−	0.181369i
$467$			215.002i			0.460390i	0.973144	+	0.230195i	$0.0739364\pi$
$467$			215.002i			0.460390i	−0.973144	+	0.230195i	$0.926064\pi$
$468$	97.7934	+	72.0071i	0.208960	+	0.153861i
$469$	41.3534	−	375.260i	0.0881735	−	0.800128i
$470$	267.730	+	97.4456i	0.569638	+	0.207331i
$471$	−12.1314	+	218.185i	−0.0257568	+	0.463238i
$472$	127.631	+	22.5047i	0.270404	+	0.0476795i
$473$	95.0888	−	539.275i	0.201033	−	1.14012i
$474$	−10.7222	+	16.3962i	−0.0226208	+	0.0345912i
$475$	16.7844	−	46.1148i	0.0353356	−	0.0970838i
$476$	25.7084	+	58.5337i	0.0540093	+	0.122970i
$477$	150.059	−	36.4003i	0.314588	−	0.0763109i
$478$	476.660			0.997197
$479$	411.411	+	490.300i	0.858896	+	1.02359i	0.999438	+	0.0335172i	$0.0106709\pi$
$479$	411.411	+	490.300i	0.858896	+	1.02359i	−0.140543	+	0.990075i	$0.544885\pi$
$480$	62.8807	+	14.7282i	0.131001	+	0.0306838i
$481$	75.7625	+	13.3590i	0.157510	+	0.0277733i
$482$	270.032	+	47.6139i	0.560232	+	0.0987841i
$483$	−593.815	+	5.48232i	−1.22943	+	0.0113506i
$484$	−71.3839	+	59.8982i	−0.147487	+	0.123757i
$485$	97.9882	−	169.721i	0.202038	−	0.349939i
$486$	83.6478	+	333.318i	0.172115	+	0.685840i
$487$	228.094	+	395.070i	0.468365	+	0.811232i	0.999346	−	0.0361513i	$-0.0115098\pi$
$487$	228.094	+	395.070i	0.468365	+	0.811232i	−0.530981	+	0.847384i	$0.678176\pi$
$488$	−99.5170	+	17.5475i	−0.203928	+	0.0359581i
$489$	−62.1369	−	519.743i	−0.127069	−	1.06287i
$490$	34.0692	+	261.502i	0.0695289	+	0.533678i
$491$	771.082	−	280.651i	1.57043	−	0.571590i	0.597336	−	0.801991i	$-0.296226\pi$
$491$	771.082	−	280.651i	1.57043	−	0.571590i	0.973096	+	0.230401i	$0.0740037\pi$
$492$	−79.4010	−	262.698i	−0.161384	−	0.533939i
$493$	36.8441	+	43.9091i	0.0747345	+	0.0890651i
$494$	22.2598	−	38.5551i	0.0450603	−	0.0780467i
$495$	283.471	+	83.2414i	0.572668	+	0.168165i
$496$	−75.7374	−	43.7270i	−0.152696	−	0.0881593i
$497$	−143.998	+	291.504i	−0.289734	+	0.586526i
$498$	3.31780	−	59.6711i	0.00666226	−	0.119821i
$499$	−694.584	+	252.808i	−1.39195	+	0.506629i	−0.925779	−	0.378064i	$-0.876590\pi$
$499$	−694.584	+	252.808i	−1.39195	+	0.506629i	−0.466173	+	0.884694i	$0.654368\pi$
$500$	−266.223	−	46.9422i	−0.532445	−	0.0938845i
$501$	714.088	+	466.974i	1.42533	+	0.932084i
$502$	98.0367	+	116.836i	0.195292	+	0.232740i
$503$	283.109	+	163.453i	0.562841	+	0.324956i	0.754285	−	0.656547i	$-0.227984\pi$
$503$	283.109	+	163.453i	0.562841	+	0.324956i	−0.191444	+	0.981503i	$0.561317\pi$
$504$	170.087	−	53.1276i	0.337473	−	0.105412i
$505$	−11.0364	−	19.1155i	−0.0218542	−	0.0378525i
$506$	324.160	+	117.984i	0.640632	+	0.233171i
$507$	270.116	+	253.500i	0.532774	+	0.500001i
$508$	−359.427	−	301.595i	−0.707533	−	0.593691i
$509$	253.680	−	302.324i	0.498389	−	0.593957i	−0.456941	−	0.889497i	$-0.651055\pi$
$509$	253.680	−	302.324i	0.498389	−	0.593957i	0.955330	+	0.295540i	$0.0954995\pi$
$510$	59.0232	−	44.1832i	0.115732	−	0.0866337i
$511$	406.660	+	200.883i	0.795812	+	0.393117i
$512$	−22.6274			−0.0441942
$513$	118.037	−	44.0211i	0.230092	−	0.0858112i
$514$	−203.788	+	117.657i	−0.396476	+	0.228905i
$515$	−270.753	−	98.5459i	−0.525734	−	0.191351i
$516$	−304.923	+	228.257i	−0.590935	+	0.442358i
$517$	−449.714	−	79.2967i	−0.869853	−	0.153379i
$518$	81.5924	−	78.0025i	0.157514	−	0.150584i
$519$	−322.133	−	75.4516i	−0.620681	−	0.145379i
$520$	−68.2420	−	24.8381i	−0.131235	−	0.0477655i
$521$	199.549	+	115.210i	0.383011	+	0.221132i	0.679128	−	0.734020i	$-0.262358\pi$
$521$	199.549	+	115.210i	0.383011	+	0.221132i	−0.296116	+	0.955152i	$0.595692\pi$
$522$	133.016	−	88.4932i	0.254820	−	0.169527i
$523$	647.044	−	373.571i	1.23718	−	0.714285i	0.268662	−	0.963235i	$-0.413419\pi$
$523$	647.044	−	373.571i	1.23718	−	0.714285i	0.968516	+	0.248949i	$0.0800853\pi$
$524$	−128.627	+	353.399i	−0.245471	+	0.674425i
$525$	−206.845	+	77.4554i	−0.393991	+	0.147534i
$526$	270.295	+	226.804i	0.513868	+	0.431186i
$527$	−93.8180	+	34.1469i	−0.178023	+	0.0647950i
$528$	−103.352	−	5.74654i	−0.195743	−	0.0108836i
$529$	46.9979	+	266.539i	0.0888430	+	0.503854i
$530$	−79.9648	+	46.1677i	−0.150877	+	0.0871088i
$531$	−228.420	−	343.343i	−0.430169	−	0.646597i
$532$	−26.2681	−	59.8080i	−0.0493761	−	0.112421i
$533$	53.5873	+	303.909i	0.100539	+	0.570185i
$534$	−301.166	+	320.906i	−0.563981	+	0.600947i
$535$	−56.7350	+	67.6141i	−0.106047	+	0.126381i
$536$	143.346	−	52.1737i	0.267437	−	0.0973390i
$537$	−508.638	+	380.753i	−0.947185	+	0.709037i
$538$	175.944	+	209.681i	0.327033	+	0.389742i
$539$	−126.557	−	403.281i	−0.234800	−	0.748202i
$540$	−104.153	−	177.151i	−0.192876	−	0.328058i
$541$	−388.524	+	672.944i	−0.718160	+	1.24389i	0.243568	+	0.969884i	$0.421682\pi$
$541$	−388.524	+	672.944i	−0.718160	+	1.24389i	−0.961728	+	0.274005i	$0.911651\pi$
$542$	166.359	−	457.069i	0.306936	−	0.843301i
$543$	263.176	−	614.556i	0.484671	−	1.13178i
$544$	−16.6044	+	19.7883i	−0.0305228	+	0.0363756i
$545$	−39.9508	−	109.764i	−0.0733042	−	0.201402i
$546$	−196.998	+	36.6144i	−0.360802	+	0.0670594i
$547$	−1.31073	−	7.43351i	−0.00239621	−	0.0135896i	0.983586	−	0.180439i	$-0.0577518\pi$
$547$	−1.31073	−	7.43351i	−0.00239621	−	0.0135896i	−0.985982	+	0.166849i	$0.946641\pi$
$548$	−361.862			−0.660332
$549$	258.927	+	190.653i	0.471634	+	0.347273i
$550$	128.305			0.233282
$551$	−37.6462	−	44.8650i	−0.0683234	−	0.0814247i
$552$	−108.253	−	214.141i	−0.196110	−	0.387936i
$553$	−7.66166	−	31.4022i	−0.0138547	−	0.0567851i
$554$	108.460	+	91.0083i	0.195775	+	0.164275i
$555$	−108.951	−	71.2478i	−0.196308	−	0.128374i
$556$	180.210	−	31.7759i	0.324119	−	0.0571510i
$557$	−96.3996			−0.173069			−0.0865347	−	0.996249i	$-0.527579\pi$
$557$	−96.3996			−0.173069			−0.0865347	+	0.996249i	$0.527579\pi$
$558$	65.6002	+	270.434i	0.117563	+	0.484649i
$559$	370.923	−	214.153i	0.663548	−	0.383099i
$560$	−88.6377	+	59.1395i	−0.158282	+	0.105606i
$561$	−80.8670	+	86.1675i	−0.144148	+	0.153596i
$562$	72.1059	−	408.933i	0.128302	−	0.727639i
$563$	182.615	+	501.732i	0.324361	+	0.891175i	0.989510	+	0.144464i	$0.0461459\pi$
$563$	182.615	+	501.732i	0.324361	+	0.891175i	−0.665149	+	0.746711i	$0.731632\pi$
$564$	190.349	+	254.282i	0.337498	+	0.450854i
$565$	−710.241	+	125.235i	−1.25706	+	0.221654i
$566$			653.129i			1.15394i
$567$	−495.821	−	275.046i	−0.874464	−	0.485091i
$568$	−131.372			−0.231290
$569$	18.9804	+	107.643i	0.0333574	+	0.189179i	0.996933	−	0.0782557i	$-0.0249351\pi$
$569$	18.9804	+	107.643i	0.0333574	+	0.189179i	−0.963576	+	0.267435i	$0.913824\pi$
$570$	−60.3082	+	45.1451i	−0.105804	+	0.0792019i
$571$	59.9820	−	21.8317i	0.105047	−	0.0382341i	−0.288962	−	0.957341i	$-0.593310\pi$
$571$	59.9820	−	21.8317i	0.105047	−	0.0382341i	0.394009	+	0.919107i	$0.371088\pi$
$572$	114.628	+	20.2121i	0.200399	+	0.0353358i
$573$	709.520	+	665.875i	1.23826	+	1.16209i
$574$	405.965	+	200.540i	0.707256	+	0.349372i
$575$	148.710	+	257.574i	0.258626	+	0.447954i
$576$	49.6845	+	52.1100i	0.0862579	+	0.0904687i
$577$		−	505.705i		−	0.876439i	−0.898868	−	0.438219i	$-0.855609\pi$
$577$		−	505.705i		−	0.876439i	0.898868	−	0.438219i	$-0.144391\pi$
$578$	−65.8505	−	373.456i	−0.113928	−	0.646118i
$579$	−317.825	+	486.013i	−0.548921	+	0.839400i
$580$	−61.4096	+	73.1851i	−0.105879	+	0.126181i
$581$	68.1382	+	71.2741i	0.117277	+	0.122675i
$582$	194.986	−	98.5696i	0.335028	−	0.169364i
$583$	113.370	−	95.1283i	0.194459	−	0.163170i
$584$			183.270i			0.313819i
$585$	92.6426	+	211.697i	0.158363	+	0.361875i
$586$			241.112i			0.411454i
$587$	116.350	−	20.5156i	0.198211	−	0.0349500i	−0.0736611	−	0.997283i	$-0.523468\pi$
$587$	116.350	−	20.5156i	0.198211	−	0.0349500i	0.271872	+	0.962333i	$0.412357\pi$
$588$	−127.771	+	264.784i	−0.217298	+	0.450313i
$589$	95.8604	−	34.8903i	0.162751	−	0.0592366i
$590$	188.906	+	158.511i	0.320180	+	0.268663i
$591$	−455.632	−	195.119i	−0.770951	−	0.330151i
$592$	42.8594	+	15.5996i	0.0723977	+	0.0263506i
$593$	−100.581	−	58.0705i	−0.169614	−	0.0979267i	0.412790	−	0.910826i	$-0.364554\pi$
$593$	−100.581	−	58.0705i	−0.169614	−	0.0979267i	−0.582404	+	0.812900i	$0.697888\pi$
$594$	213.703	+	250.633i	0.359769	+	0.421942i
$595$	−13.3246	+	120.914i	−0.0223943	+	0.203217i
$596$	165.995	−	139.286i	0.278515	−	0.233702i
$597$	−613.282	−	819.268i	−1.02727	−	1.37231i
$598$	92.2825	+	253.544i	0.154319	+	0.423987i
$599$	−618.823	−	519.254i	−1.03309	−	0.866868i	−0.0418773	−	0.999123i	$-0.513334\pi$
$599$	−618.823	−	519.254i	−1.03309	−	0.866868i	−0.991216	+	0.132255i	$0.957778\pi$
$600$	−65.0760	−	61.0729i	−0.108460	−	0.101788i
$601$	−271.065	+	47.7960i	−0.451023	+	0.0795275i	−0.394546	−	0.918876i	$-0.629098\pi$
$601$	−271.065	+	47.7960i	−0.451023	+	0.0795275i	−0.0564774	+	0.998404i	$0.517987\pi$
$602$	68.8370	−	624.659i	0.114347	−	1.03764i
$603$	−434.908	−	215.559i	−0.721241	−	0.357477i
$604$	−218.836	−	379.036i	−0.362312	−	0.627543i
$605$	−174.617	+	30.7897i	−0.288623	+	0.0508921i
$606$	1.36612	−	24.5699i	0.00225433	−	0.0405443i
$607$	324.279	+	890.949i	0.534232	+	1.46779i	0.853989	+	0.520291i	$0.174176\pi$
$607$	324.279	+	890.949i	0.534232	+	1.46779i	−0.319757	+	0.947500i	$0.603601\pi$
$608$	16.9659	−	20.2191i	0.0279044	−	0.0332552i
$609$	−43.3745	+	260.003i	−0.0712225	+	0.426934i
$610$	−180.684	−	65.7637i	−0.296204	−	0.107809i
$611$	−178.587	−	309.321i	−0.292286	−	0.506254i
$612$	82.0311	−	5.21139i	0.134038	−	0.00851534i
$613$	343.442	−	594.859i	0.560264	−	0.970406i	−0.437209	−	0.899360i	$-0.644033\pi$
$613$	343.442	−	594.859i	0.560264	−	0.970406i	0.997473	−	0.0710462i	$-0.0226338\pi$
$614$	−99.8148	+	274.239i	−0.162565	+	0.446643i
$615$	119.087	−	508.430i	0.193638	−	0.826716i
$616$	123.449	−	118.017i	0.200404	−	0.191587i
$617$	134.470	−	762.616i	0.217941	−	1.23601i	−0.657788	−	0.753203i	$-0.728508\pi$
$617$	134.470	−	762.616i	0.217941	−	1.23601i	0.875729	−	0.482803i	$-0.160381\pi$
$618$	−192.498	−	257.153i	−0.311485	−	0.416105i
$619$	246.861	−	678.244i	0.398805	−	1.09571i	−0.564062	−	0.825733i	$-0.690762\pi$
$619$	246.861	−	678.244i	0.398805	−	1.09571i	0.962867	−	0.269976i	$-0.0870158\pi$
$620$	−83.2029	−	144.112i	−0.134198	−	0.232438i
$621$	−255.459	+	719.504i	−0.411368	+	1.15862i
$622$			10.1494i			0.0163174i
$623$	−47.0023	−	724.593i	−0.0754451	−	1.16307i
$624$	−48.5183	−	64.8143i	−0.0777536	−	0.103869i
$625$	−192.611	−	161.620i	−0.308177	−	0.258592i
$626$	−508.567	+	606.086i	−0.812407	+	0.968189i
$627$	82.6275	−	88.0434i	0.131782	−	0.140420i
$628$	49.8260	−	136.896i	0.0793407	−	0.217987i
$629$	45.0933	−	26.0346i	0.0716904	−	0.0413905i
$630$	330.823	+	74.2722i	0.525117	+	0.117892i
$631$	−46.7469	+	80.9680i	−0.0740838	+	0.128317i	−0.900688	−	0.434468i	$-0.856937\pi$
$631$	−46.7469	+	80.9680i	−0.0740838	+	0.128317i	0.826604	+	0.562785i	$0.190270\pi$
$632$	10.0050	−	8.39519i	0.0158307	−	0.0132835i
$633$	−210.645	+	322.115i	−0.332773	+	0.508871i
$634$	119.790	−	679.362i	0.188943	−	1.07155i
$635$	−305.349	−	838.940i	−0.480865	−	1.32117i
$636$	−102.782	−	5.71481i	−0.161606	−	0.00898556i
$637$	178.005	−	278.583i	0.279442	−	0.437336i
$638$	76.5620	−	132.609i	0.120003	−	0.207851i
$639$	288.463	+	302.545i	0.451429	+	0.473467i
$640$	−37.2867	−	21.5275i	−0.0582605	−	0.0336367i
$641$	935.999	−	785.397i	1.46022	−	1.22527i	0.535543	−	0.844508i	$-0.320107\pi$
$641$	935.999	−	785.397i	1.46022	−	1.22527i	0.924674	−	0.380760i	$-0.124338\pi$
$642$	−94.1927	+	28.4699i	−0.146718	+	0.0443457i
$643$	−332.363	−	913.160i	−0.516894	−	1.42016i	−0.873924	−	0.486063i	$-0.838433\pi$
$643$	−332.363	−	913.160i	−0.516894	−	1.42016i	0.357030	−	0.934093i	$-0.383790\pi$
$644$	380.003	+	111.038i	0.590066	+	0.172420i
$645$	−719.630	+	86.0342i	−1.11571	+	0.133386i
$646$	−5.23238	−	29.6743i	−0.00809966	−	0.0459355i
$647$	638.234	−	368.484i	0.986451	−	0.569528i	0.0822394	−	0.996613i	$-0.473793\pi$
$647$	638.234	−	368.484i	0.986451	−	0.569528i	0.904212	+	0.427085i	$0.140459\pi$
$648$	10.9114	−	228.843i	0.0168385	−	0.353152i
$649$	−342.292	−	197.623i	−0.527415	−	0.304503i
$650$	64.5068	+	76.8762i	0.0992412	+	0.118271i
$651$	−399.724	−	225.886i	−0.614015	−	0.346983i
$652$	−60.5967	+	343.661i	−0.0929397	+	0.527087i
$653$	54.9622	−	311.706i	0.0841688	−	0.477345i	−0.913364	−	0.407144i	$-0.866525\pi$
$653$	54.9622	−	311.706i	0.0841688	−	0.477345i	0.997533	−	0.0702013i	$-0.0223641\pi$
$654$	29.6979	−	126.792i	0.0454097	−	0.193872i
$655$	−548.178	+	459.976i	−0.836913	+	0.702254i
$656$			182.957i			0.278898i
$657$	422.063	−	402.418i	0.642410	−	0.612509i
$658$	−520.917	−	57.4047i	−0.791668	−	0.0872412i
$659$	458.958	+	167.047i	0.696446	+	0.253486i	0.665893	−	0.746048i	$-0.268051\pi$
$659$	458.958	+	167.047i	0.696446	+	0.253486i	0.0305533	+	0.999533i	$0.490273\pi$
$660$	−164.842	−	107.798i	−0.249761	−	0.163330i
$661$	458.835	+	80.9050i	0.694153	+	0.122398i	0.509583	−	0.860421i	$-0.329800\pi$
$661$	458.835	+	80.9050i	0.694153	+	0.122398i	0.184570	+	0.982819i	$0.440911\pi$
$662$	82.2633	−	466.538i	0.124265	−	0.704741i
$663$	−92.2856	−	5.13122i	−0.139194	−	0.00773940i
$664$	−13.6268	+	37.4394i	−0.0205223	+	0.0563846i
$665$	13.6147	−	123.546i	0.0204732	−	0.185784i
$666$	−58.1842	−	132.956i	−0.0873637	−	0.199634i
$667$	354.952			0.532162
$668$	−365.627	−	435.737i	−0.547345	−	0.652301i
$669$	231.750	−	246.940i	0.346413	−	0.369119i
$670$	285.851	+	50.4033i	0.426644	+	0.0752288i
$671$	303.501	+	53.5154i	0.452312	+	0.0797548i
$672$	−118.789	+	1.09670i	−0.176769	+	0.00163200i
$673$	−480.082	+	402.837i	−0.713346	+	0.598569i	−0.925536	−	0.378660i	$-0.876385\pi$
$673$	−480.082	+	402.837i	−0.713346	+	0.598569i	0.212190	+	0.977229i	$0.431941\pi$
$674$	−124.495	+	215.632i	−0.184711	+	0.319929i
$675$	2.24335	+	283.969i	0.00332348	+	0.420695i
$676$	−123.480	−	213.873i	−0.182662	−	0.316380i
$677$	−670.866	+	118.292i	−0.990939	+	0.174729i	−0.645540	−	0.763726i	$-0.723368\pi$
$677$	−670.866	+	118.292i	−0.990939	+	0.174729i	−0.345399	+	0.938456i	$0.612257\pi$
$678$	−739.108	−	316.514i	−1.09013	−	0.466835i
$679$	−101.106	+	346.012i	−0.148905	+	0.509591i
$680$	−46.1881	+	16.8111i	−0.0679237	+	0.0247222i
$681$	654.177	−	697.056i	0.960613	−	1.02358i
$682$	171.439	+	204.313i	0.251377	+	0.299580i
$683$	31.5159	−	54.5871i	0.0461433	−	0.0799226i	−0.842031	−	0.539429i	$-0.818640\pi$
$683$	31.5159	−	54.5871i	0.0461433	−	0.0799226i	0.888175	+	0.459506i	$0.151974\pi$
$684$	−83.8169	+	5.32484i	−0.122539	+	0.00778486i
$685$	−596.296	−	344.272i	−0.870506	−	0.502587i
$686$	−174.896	−	452.448i	−0.254951	−	0.659545i
$687$	−1012.21	−	661.932i	−1.47338	−	0.963511i
$688$	238.614	−	86.8486i	0.346823	−	0.126233i
$689$	113.996	+	20.1005i	0.165451	+	0.0291734i
$690$	25.3467	−	455.864i	0.0367344	−	0.660672i
$691$	−330.223	−	393.544i	−0.477891	−	0.569529i	0.472204	−	0.881489i	$-0.343459\pi$
$691$	−330.223	−	393.544i	−0.477891	−	0.569529i	−0.950095	+	0.311961i	$0.899014\pi$
$692$	191.017	+	110.284i	0.276037	+	0.159370i
$693$	−542.854	−	25.1588i	−0.783339	−	0.0363041i
$694$	464.047	+	803.754i	0.668656	+	1.15815i
$695$	327.192	+	119.088i	0.470780	+	0.171350i
$696$	−101.954	+	30.8157i	−0.146485	+	0.0442754i
$697$	160.001	+	134.257i	0.229557	+	0.192621i
$698$	−469.377	+	559.381i	−0.672459	+	0.801406i
$699$	256.404	+	109.802i	0.366815	+	0.157084i
$700$	146.939	−	9.53152i	0.209913	−	0.0136165i
$701$	136.333			0.194483			0.0972416	−	0.995261i	$-0.468998\pi$
$701$	136.333			0.194483			0.0972416	+	0.995261i	$0.468998\pi$
$702$	−42.7298	+	254.053i	−0.0608686	+	0.361898i
$703$	−46.0750	+	26.6014i	−0.0655405	+	0.0378398i
$704$	64.8461	+	23.6021i	0.0921110	+	0.0335256i
$705$	71.7459	+	600.116i	0.101767	+	0.851228i
$706$	350.320	+	61.7708i	0.496204	+	0.0874941i
$707$	28.0563	+	29.3475i	0.0396835	+	0.0415099i
$708$	79.5418	+	263.164i	0.112347	+	0.371700i
$709$	−1267.76	−	461.425i	−1.78809	−	0.650811i	−0.999349	−	0.0360851i	$-0.988511\pi$
$709$	−1267.76	−	461.425i	−1.78809	−	0.650811i	−0.788741	−	0.614726i	$-0.789267\pi$
$710$	−216.483	−	124.987i	−0.304906	−	0.176037i
$711$	−41.3024	−	4.60720i	−0.0580906	−	0.00647989i
$712$	254.088	−	146.697i	0.356864	−	0.206036i
$713$	−211.457	+	580.973i	−0.296573	+	0.814828i
$714$	−86.2102	+	104.689i	−0.120743	+	0.146623i
$715$	169.662	+	142.363i	0.237289	+	0.199109i
$716$	398.030	−	144.871i	0.555908	−	0.202334i
$717$	456.181	+	902.398i	0.636235	+	1.25857i
$718$	49.9900	+	283.507i	0.0696240	+	0.394857i
$719$	−64.8381	+	37.4343i	−0.0901781	+	0.0520644i	−0.544411	−	0.838819i	$-0.683247\pi$
$719$	−64.8381	+	37.4343i	−0.0901781	+	0.0520644i	0.454233	+	0.890883i	$0.349913\pi$
$720$	32.2961	+	133.139i	0.0448556	+	0.184915i
$721$	526.799	+	58.0529i	0.730651	+	0.0805172i
$722$	−83.3065	−	472.455i	−0.115383	−	0.654369i
$723$	168.289	+	556.784i	0.232765	+	0.770102i
$724$	−286.485	+	341.419i	−0.395697	+	0.471573i
$725$	124.058	−	45.1536i	0.171115	−	0.0622808i
$726$	−181.714	−	77.8170i	−0.250295	−	0.107186i
$727$	−418.905	−	499.231i	−0.576210	−	0.686701i	0.396683	−	0.917956i	$-0.370161\pi$
$727$	−418.905	−	499.231i	−0.576210	−	0.686701i	−0.972893	+	0.231255i	$0.925717\pi$
$728$	132.777	+	14.6320i	0.182387	+	0.0200989i
$729$	−550.973	+	477.357i	−0.755793	+	0.654810i
$730$	−174.361	+	302.003i	−0.238851	+	0.413703i
$731$	99.1478	−	272.406i	0.135633	−	0.372649i
$732$	−128.462	−	171.609i	−0.175494	−	0.234438i
$733$	−774.018	+	922.439i	−1.05596	+	1.25844i	−0.0910542	+	0.995846i	$0.529024\pi$
$733$	−774.018	+	922.439i	−1.05596	+	1.25844i	−0.964905	+	0.262598i	$0.915421\pi$
$734$	−231.603	−	636.325i	−0.315536	−	0.866928i
$735$	−462.462	+	314.765i	−0.629200	+	0.428252i
$736$	27.7776	+	157.535i	0.0377414	+	0.214042i
$737$	−465.225			−0.631242
$738$	421.342	−	401.731i	0.570924	−	0.544351i
$739$	−125.727			−0.170132			−0.0850659	−	0.996375i	$-0.527110\pi$
$739$	−125.727			−0.170132			−0.0850659	+	0.996375i	$0.527110\pi$
$740$	55.7849	+	66.4819i	0.0753850	+	0.0898404i
$741$	94.2947	+	5.24293i	0.127253	+	0.00707548i
$742$	122.767	−	117.366i	0.165455	−	0.158175i
$743$	−492.510	−	413.265i	−0.662866	−	0.556211i	0.248078	−	0.968740i	$-0.420201\pi$
$743$	−492.510	−	413.265i	−0.662866	−	0.556211i	−0.910944	+	0.412529i	$0.864646\pi$
$744$	10.2992	−	185.232i	0.0138430	−	0.248968i
$745$	406.051	−	71.5977i	0.545035	−	0.0961044i
$746$	576.946			0.773386
$747$	116.143	−	50.8262i	0.155479	−	0.0680404i
$748$	68.2259	−	39.3902i	0.0912111	−	0.0526607i
$749$	71.9053	−	145.562i	0.0960017	−	0.194342i
$750$	−165.915	−	548.930i	−0.221220	−	0.731906i
$751$	−162.351	+	920.736i	−0.216179	+	1.22601i	0.662669	+	0.748912i	$0.269423\pi$
$751$	−162.351	+	920.736i	−0.216179	+	1.22601i	−0.878849	+	0.477101i	$0.841688\pi$
$752$	−72.4250	−	198.986i	−0.0963099	−	0.264609i
$753$	−127.365	+	297.416i	−0.169143	+	0.394974i
$754$	117.947	−	20.7973i	0.156429	−	0.0275827i
$755$		−	832.796i		−	1.10304i
$756$	263.358	+	271.158i	0.348358	+	0.358674i
$757$	−1090.75			−1.44089			−0.720443	−	0.693515i	$-0.756061\pi$
$757$	−1090.75			−1.44089			−0.720443	+	0.693515i	$0.756061\pi$
$758$	51.3543	+	291.245i	0.0677497	+	0.384228i
$759$	86.8679	+	726.604i	0.114450	+	0.957318i
$760$	47.1936	−	17.1771i	0.0620969	−	0.0226014i
$761$	510.622	+	90.0365i	0.670989	+	0.118313i	0.498755	−	0.866743i	$-0.333791\pi$
$761$	510.622	+	90.0365i	0.670989	+	0.118313i	0.172233	+	0.985056i	$0.444902\pi$
$762$	226.985	−	969.092i	0.297881	−	1.27177i
$763$	119.249	+	178.729i	0.156289	+	0.234245i
$764$	−324.347	−	561.785i	−0.424538	−	0.735321i
$765$	140.133	+	69.4559i	0.183181	+	0.0907921i
$766$		−	490.591i		−	0.640458i
$767$	−53.6823	−	304.447i	−0.0699899	−	0.396933i
$768$	−21.6552	−	42.8375i	−0.0281969	−	0.0557780i
$769$	−69.4480	+	82.7649i	−0.0903095	+	0.107627i	−0.809307	−	0.587386i	$-0.800157\pi$
$769$	−69.4480	+	82.7649i	−0.0903095	+	0.107627i	0.718997	+	0.695013i	$0.244601\pi$
$770$	315.707	−	77.0276i	0.410009	−	0.100036i
$771$	−417.778	−	273.203i	−0.541865	−	0.354350i
$772$	296.565	−	248.848i	0.384152	−	0.322342i
$773$		−	805.881i		−	1.04254i	−0.853393	−	0.521269i	$-0.825459\pi$
$773$		−	805.881i		−	1.04254i	0.853393	−	0.521269i	$-0.174541\pi$
$774$	−723.950	−	358.820i	−0.935336	−	0.463591i
$775$			229.954i			0.296714i
$776$	−143.444	+	25.2930i	−0.184850	+	0.0325941i
$777$	225.759	+	79.8169i	0.290551	+	0.102724i
$778$	264.787	−	96.3747i	0.340343	−	0.123875i
$779$	−163.485	−	137.180i	−0.209865	−	0.176097i
$780$	−18.2874	−	152.965i	−0.0234454	−	0.196108i
$781$	376.490	+	137.031i	0.482061	+	0.175456i
$782$	158.153	+	91.3094i	0.202241	+	0.116764i
$783$	294.834	+	167.131i	0.376544	+	0.213449i
$784$	132.610	−	144.328i	0.169146	−	0.184092i
$785$	212.347	−	178.181i	0.270506	−	0.226982i
$786$	−792.143	+	94.7033i	−1.00782	+	0.120488i
$787$	−157.262	−	432.073i	−0.199824	−	0.549013i	0.798792	−	0.601608i	$-0.205473\pi$
$787$	−157.262	−	432.073i	−0.199824	−	0.549013i	−0.998616	+	0.0525950i	$0.983251\pi$
$788$	253.128	+	212.400i	0.321229	+	0.269543i
$789$	−170.697	+	728.772i	−0.216346	+	0.923666i
$790$	24.4739	−	4.31541i	0.0309796	−	0.00546255i
$791$	1214.59	−	533.458i	1.53552	−	0.674409i
$792$	−88.0324	−	201.162i	−0.111152	−	0.253993i
$793$	120.524	+	208.754i	0.151985	+	0.263245i
$794$	−159.568	+	28.1362i	−0.200968	+	0.0354360i
$795$	−163.932	−	107.203i	−0.206204	−	0.134846i
$796$	233.345	+	641.111i	0.293147	+	0.805416i
$797$	−631.459	+	752.544i	−0.792295	+	0.944221i	−0.999419	−	0.0340941i	$-0.989145\pi$
$797$	−631.459	+	752.544i	−0.792295	+	0.944221i	0.207123	+	0.978315i	$0.433590\pi$
$798$	88.0871	−	106.968i	0.110385	−	0.134045i
$799$	−227.166	−	82.6816i	−0.284313	−	0.103481i
$800$	29.7485	+	51.5260i	0.0371857	+	0.0644075i
$801$	−895.755	−	263.039i	−1.11830	−	0.328388i
$802$	−360.931	+	625.150i	−0.450038	+	0.779489i
$803$	191.164	−	525.219i	0.238063	−	0.654071i
$804$	235.961	+	221.446i	0.293484	+	0.275431i
$805$	520.549	+	544.506i	0.646645	+	0.676405i
$806$	−36.2249	+	205.442i	−0.0449441	+	0.254890i
$807$	−228.578	+	533.763i	−0.283244	+	0.661417i
$808$	−5.61091	+	15.4159i	−0.00694420	+	0.0190790i
$809$	540.170	+	935.602i	0.667701	+	1.15649i	0.978545	+	0.206031i	$0.0660547\pi$
$809$	540.170	+	935.602i	0.667701	+	1.15649i	−0.310845	+	0.950461i	$0.600612\pi$
$810$	235.699	−	366.719i	0.290986	−	0.452739i
$811$			875.717i			1.07980i	0.841730	+	0.539899i	$0.181538\pi$
$811$			875.717i			1.07980i	−0.841730	+	0.539899i	$0.818462\pi$
$812$	77.8299	−	157.556i	0.0958496	−	0.194034i
$813$	1024.52	−	122.485i	1.26017	−	0.150658i
$814$	−106.556	−	89.4111i	−0.130904	−	0.109842i
$815$	−426.810	+	508.653i	−0.523694	+	0.624114i
$816$	−53.3536	−	12.4967i	−0.0653844	−	0.0153146i
$817$	−101.306	+	278.337i	−0.123998	+	0.340681i
$818$	−945.127	+	545.669i	−1.15541	+	0.667078i
$819$	−257.851	−	337.909i	−0.314837	−	0.412587i
$820$	−174.064	+	301.487i	−0.212273	+	0.367667i
$821$	−191.643	+	160.808i	−0.233426	+	0.195868i	−0.751996	−	0.659167i	$-0.770909\pi$
$821$	−191.643	+	160.808i	−0.233426	+	0.195868i	0.518570	+	0.855035i	$0.326465\pi$
$822$	−346.315	−	685.065i	−0.421307	−	0.833412i
$823$	151.175	−	857.356i	0.183688	−	1.04175i	−0.743942	−	0.668244i	$-0.767046\pi$
$823$	151.175	−	857.356i	0.183688	−	1.04175i	0.927630	−	0.373501i	$-0.121843\pi$
$824$	73.2428	+	201.233i	0.0888869	+	0.244215i
$825$	122.792	+	242.903i	0.148839	+	0.294428i
$826$	−406.685	−	200.895i	−0.492354	−	0.243215i
$827$	433.596	−	751.010i	0.524300	−	0.908114i	−0.475300	−	0.879824i	$-0.657660\pi$
$827$	433.596	−	751.010i	0.524300	−	0.908114i	0.999600	−	0.0282901i	$-0.00900621\pi$
$828$	301.803	−	409.880i	0.364496	−	0.495025i
$829$	859.546	+	496.259i	1.03685	+	0.598624i	0.918938	−	0.394401i	$-0.129048\pi$
$829$	859.546	+	496.259i	1.03685	+	0.598624i	0.117908	+	0.993025i	$0.462381\pi$
$830$	−58.0745	+	48.7303i	−0.0699693	+	0.0587112i
$831$	−68.4944	+	292.430i	−0.0824241	+	0.351902i
$832$	18.4605	+	50.7199i	0.0221881	+	0.0609614i
$833$	−28.9073	−	221.882i	−0.0347027	−	0.266365i
$834$	232.625	+	310.758i	0.278927	+	0.372611i
$835$	−187.944	−	1065.89i	−0.225083	−	1.27651i
$836$	−69.7112	+	40.2478i	−0.0833866	+	0.0481433i
$837$	−449.196	+	383.007i	−0.536673	+	0.457595i
$838$	515.055	+	297.367i	0.614625	+	0.354854i
$839$	364.839	+	434.798i	0.434849	+	0.518233i	0.938315	−	0.345782i	$-0.112386\pi$
$839$	364.839	+	434.798i	0.434849	+	0.518233i	−0.503466	+	0.864015i	$0.667942\pi$
$840$	−196.790	−	111.207i	−0.234274	−	0.132390i
$841$	−118.679	+	673.059i	−0.141116	+	0.800308i
$842$	−113.730	+	644.994i	−0.135071	+	0.766026i
$843$	843.186	−	254.855i	1.00022	−	0.302319i
$844$	196.555	−	164.929i	0.232885	−	0.195414i
$845$		−	469.910i		−	0.556106i
$846$	−299.228	+	603.719i	−0.353697	+	0.713615i
$847$	298.615	−	131.154i	0.352556	−	0.154845i
$848$	64.4882	+	23.4718i	0.0760474	+	0.0276790i
$849$	−1236.48	+	625.067i	−1.45640	+	0.736239i
$850$	66.8910	+	11.7947i	0.0786953	+	0.0138761i
$851$	55.9913	−	317.543i	0.0657948	−	0.373141i
$852$	−125.728	−	248.710i	−0.147568	−	0.291913i
$853$	−57.5854	+	158.215i	−0.0675093	+	0.185480i	−0.968860	−	0.247610i	$-0.920355\pi$
$853$	−57.5854	+	158.215i	−0.0675093	+	0.185480i	0.901350	+	0.433091i	$0.142577\pi$
$854$	351.554	+	38.7411i	0.411656	+	0.0453642i
$855$	−143.184	−	70.9680i	−0.167467	−	0.0830035i
$856$	65.6008			0.0766365
$857$	−952.733	−	1135.42i	−1.11171	−	1.32488i	−0.940557	−	0.339637i	$-0.889696\pi$
$857$	−952.733	−	1135.42i	−1.11171	−	1.32488i	−0.171151	−	0.985245i	$-0.554749\pi$
$858$	71.4386	+	236.354i	0.0832617	+	0.275471i
$859$	711.917	+	125.530i	0.828774	+	0.146135i	0.571914	−	0.820313i	$-0.306201\pi$
$859$	711.917	+	125.530i	0.828774	+	0.146135i	0.256860	+	0.966449i	$0.417312\pi$
$860$	475.829	+	83.9015i	0.553290	+	0.0975599i
$861$	8.86754	+	960.484i	0.0102991	+	1.11554i
$862$	429.262	−	360.194i	0.497984	−	0.417858i
$863$	−241.027	+	417.471i	−0.279290	+	0.483744i	−0.971208	−	0.238231i	$-0.923432\pi$
$863$	−241.027	+	417.471i	−0.279290	+	0.483744i	0.691919	+	0.721976i	$0.256766\pi$
$864$	−51.1030	+	143.932i	−0.0591470	+	0.166588i
$865$	209.846	+	363.464i	0.242597	+	0.420190i
$866$	87.6746	−	15.4594i	0.101241	−	0.0178515i
$867$	643.994	−	482.077i	0.742785	−	0.556029i
$868$	211.516	+	221.250i	0.243682	+	0.254897i
$869$	−37.4293	+	13.6232i	−0.0430717	+	0.0156768i
$870$	−197.323	−	46.2179i	−0.226808	−	0.0531240i
$871$	−233.897	−	278.748i	−0.268539	−	0.320032i
$872$	−43.4080	+	75.1848i	−0.0497798	+	0.0862212i
$873$	373.218	+	274.807i	0.427512	+	0.314785i
$874$	−161.596	−	93.2972i	−0.184892	−	0.106747i
$875$	848.297	+	419.044i	0.969483	+	0.478908i
$876$	−346.961	+	175.396i	−0.396074	+	0.200224i
$877$	−243.652	+	88.6819i	−0.277824	+	0.101120i	−0.477174	−	0.878809i	$-0.658339\pi$
$877$	−243.652	+	88.6819i	−0.277824	+	0.101120i	0.199350	+	0.979928i	$0.436117\pi$
$878$	−821.607	−	144.871i	−0.935771	−	0.165002i
$879$	−456.466	+	230.753i	−0.519301	+	0.262517i
$880$	84.4023	+	100.587i	0.0959117	+	0.114303i
$881$	1078.80	+	622.843i	1.22451	+	0.706973i	0.965877	−	0.259002i	$-0.0833937\pi$
$881$	1078.80	+	622.843i	1.22451	+	0.706973i	0.258636	+	0.965975i	$0.416727\pi$
$882$	−623.562	+	11.5149i	−0.706986	+	0.0130554i
$883$	648.221	+	1122.75i	0.734112	+	1.27152i	0.955112	+	0.296245i	$0.0957346\pi$
$883$	648.221	+	1122.75i	0.734112	+	1.27152i	−0.221000	+	0.975274i	$0.570932\pi$
$884$	57.9027	+	21.0749i	0.0655008	+	0.0238403i
$885$	−119.298	+	509.332i	−0.134800	+	0.575516i
$886$	425.189	+	356.776i	0.479897	+	0.402682i
$887$	−795.568	+	948.121i	−0.896920	+	1.06891i	0.100342	+	0.994953i	$0.468006\pi$
$887$	−795.568	+	948.121i	−0.896920	+	1.06891i	−0.997262	+	0.0739545i	$0.976438\pi$
$888$	11.4854	+	96.0694i	0.0129340	+	0.108186i
$889$	911.434	+	1366.05i	1.02524	+	1.53661i
$890$	558.266			0.627266
$891$	−269.970	+	644.441i	−0.302996	+	0.723278i
$892$	−195.523	+	112.885i	−0.219196	+	0.126553i
$893$	232.111	+	84.4816i	0.259923	+	0.0946043i
$894$	422.555	+	180.954i	0.472656	+	0.202409i
$895$	793.726	+	139.955i	0.886845	+	0.156375i
$896$	76.0171	+	22.2125i	0.0848405	+	0.0247908i
$897$	−391.684	+	417.357i	−0.436660	+	0.465281i
$898$	−525.300	−	191.194i	−0.584967	−	0.212910i
$899$	237.668	+	137.218i	0.264369	+	0.152634i
$900$	53.3413	−	181.649i	0.0592681	−	0.201832i
$901$	67.8493	−	39.1728i	0.0753044	−	0.0434770i
$902$	190.838	−	524.322i	0.211572	−	0.581288i
$903$	1248.46	−	467.501i	1.38257	−	0.517719i
$904$	410.614	+	344.546i	0.454219	+	0.381135i
$905$	−796.909	+	290.051i	−0.880562	+	0.320498i
$906$	508.144	−	777.045i	0.560865	−	0.857665i
$907$	81.8932	+	464.439i	0.0902901	+	0.512061i	0.996089	+	0.0883533i	$0.0281604\pi$
$907$	81.8932	+	464.439i	0.0902901	+	0.512061i	−0.905799	+	0.423708i	$0.860728\pi$
$908$	−551.916	+	318.649i	−0.607837	+	0.350935i
$909$	47.8223	−	20.9279i	0.0526098	−	0.0230230i
$910$	204.877	+	150.435i	0.225140	+	0.165313i
$911$	40.1433	+	227.664i	0.0440651	+	0.249906i	0.998881	−	0.0472920i	$-0.0150591\pi$
$911$	40.1433	+	227.664i	0.0440651	+	0.249906i	−0.954816	+	0.297198i	$0.903948\pi$
$912$	54.5152	+	12.7688i	0.0597754	+	0.0140009i
$913$	78.1041	−	93.0808i	0.0855466	−	0.101950i
$914$	−231.048	+	84.0945i	−0.252787	+	0.0920071i
$915$	−48.4195	−	405.004i	−0.0529175	−	0.442627i
$916$	518.273	+	617.654i	0.565800	+	0.674294i
$917$	779.042	−	1060.98i	0.849555	−	1.15701i
$918$	88.3726	+	150.311i	0.0962665	+	0.163738i
$919$	−507.451	+	878.930i	−0.552177	+	0.956399i	0.445940	+	0.895063i	$0.352869\pi$
$919$	−507.451	+	878.930i	−0.552177	+	0.956399i	−0.998117	+	0.0613358i	$0.980464\pi$
$920$	−104.104	+	286.022i	−0.113156	+	0.310894i
$921$	−614.706	+	73.4902i	−0.667434	+	0.0797939i
$922$	153.450	−	182.875i	0.166432	−	0.198346i
$923$	107.180	+	294.474i	0.116121	+	0.319041i
$924$	341.572	+	120.763i	0.369666	+	0.130695i
$925$	−20.8253	−	118.106i	−0.0225138	−	0.127682i
$926$	−270.416			−0.292026
$927$	302.607	−	610.536i	0.326437	−	0.658614i
$928$	71.0060			0.0765151
$929$	−751.335	−	895.406i	−0.808757	−	0.963839i	0.191086	−	0.981573i	$-0.438799\pi$
$929$	−751.335	−	895.406i	−0.808757	−	0.963839i	−0.999843	+	0.0177345i	$0.994355\pi$
$930$	193.199	−	295.437i	0.207741	−	0.317674i
$931$	29.5367	+	226.712i	0.0317257	+	0.243515i
$932$	−142.446	−	119.526i	−0.152839	−	0.128247i
$933$	−19.2145	+	9.71335i	−0.0205944	+	0.0104109i
$934$	299.440	−	52.7993i	0.320599	−	0.0565303i
$935$	149.902			0.160323
$936$	76.2707	−	153.883i	0.0814858	−	0.164405i
$937$	−774.678	+	447.260i	−0.826764	+	0.477332i	−0.852743	−	0.522330i	$-0.825063\pi$
$937$	−774.678	+	447.260i	−0.826764	+	0.477332i	0.0259794	+	0.999662i	$0.491730\pi$
$938$	−532.790	+	34.5606i	−0.568007	+	0.0368450i
$939$	−1634.14	−	382.756i	−1.74030	−	0.407621i
$940$	69.9674	−	396.805i	0.0744334	−	0.422133i
$941$	18.5646	+	51.0057i	0.0197286	+	0.0542038i	0.949166	−	0.314776i	$-0.101929\pi$
$941$	18.5646	+	51.0057i	0.0197286	+	0.0542038i	−0.929437	+	0.368980i	$0.879707\pi$
$942$	306.852	−	36.6852i	0.325745	−	0.0389439i
$943$	1273.77	−	224.600i	1.35076	−	0.238176i
$944$		−	183.281i		−	0.194154i
$945$	176.000	+	697.385i	0.186243	+	0.737974i
$946$	−774.416			−0.818621
$947$	−242.134	−	1373.21i	−0.255685	−	1.45006i	−0.794308	−	0.607515i	$-0.792166\pi$
$947$	−242.134	−	1373.21i	−0.255685	−	1.45006i	0.538623	−	0.842547i	$-0.318945\pi$
$948$	25.4686	+	10.9066i	0.0268657	+	0.0115049i
$949$	410.804	−	149.521i	0.432881	−	0.157556i
$950$	−68.3472	−	12.0515i	−0.0719444	−	0.0126857i
$951$	1400.79	−	423.391i	1.47297	−	0.445207i
$952$	75.2082	−	50.1793i	0.0790002	−	0.0527093i
$953$	644.888	+	1116.98i	0.676692	+	1.17207i	0.975971	+	0.217900i	$0.0699206\pi$
$953$	644.888	+	1116.98i	0.676692	+	1.17207i	−0.299279	+	0.954166i	$0.596746\pi$
$954$	−87.5465	−	200.052i	−0.0917678	−	0.209698i
$955$		−	1234.32i		−	1.29248i
$956$	−117.056	−	663.858i	−0.122444	−	0.694413i
$957$	324.324	+	18.0329i	0.338896	+	0.0188432i
$958$	581.823	−	693.390i	0.607331	−	0.723789i
$959$	1215.68	+	355.227i	1.26765	+	0.370414i
$960$	5.07045	−	91.1926i	0.00528172	−	0.0949923i
$961$	369.990	−	310.458i	0.385005	−	0.323057i
$962$		−	108.797i		−	0.113095i
$963$	−144.044	−	151.076i	−0.149579	−	0.156880i
$964$		−	387.774i		−	0.402255i
$965$	725.448	−	127.916i	0.751760	−	0.132556i
$966$	153.462	+	825.676i	0.158863	+	0.854737i
$967$	699.304	−	254.526i	0.723169	−	0.263212i	0.0458985	−	0.998946i	$-0.485385\pi$
$967$	699.304	−	254.526i	0.723169	−	0.263212i	0.677270	+	0.735734i	$0.263163\pi$
$968$	100.952	+	84.7089i	0.104289	+	0.0875092i
$969$	51.1709	−	38.3051i	0.0528079	−	0.0395306i
$970$	−260.438	−	94.7918i	−0.268493	−	0.0977235i
$971$	−597.163	−	344.772i	−0.614997	−	0.355069i	0.159921	−	0.987130i	$-0.448876\pi$
$971$	−597.163	−	344.772i	−0.614997	−	0.355069i	−0.774919	+	0.632061i	$0.782209\pi$
$972$	443.680	−	198.353i	0.456461	−	0.204067i
$973$	−636.612	−	70.1542i	−0.654278	−	0.0721010i
$974$	494.211	−	414.692i	0.507404	−	0.425762i
$975$	−83.8043	+	195.695i	−0.0859531	+	0.200713i
$976$	48.8779	+	134.291i	0.0500798	+	0.137593i
$977$	−75.8472	−	63.6434i	−0.0776328	−	0.0651417i	0.603145	−	0.797631i	$-0.293914\pi$
$977$	−75.8472	−	63.6434i	−0.0776328	−	0.0651417i	−0.680778	+	0.732490i	$0.738358\pi$
$978$	−708.601	+	214.176i	−0.724541	+	0.218994i
$979$	−881.185	+	155.377i	−0.900087	+	0.158710i
$980$	355.835	−	111.668i	0.363097	−	0.113947i
$981$	268.461	−	65.1217i	0.273661	−	0.0663829i
$982$	−580.229	−	1004.99i	−0.590865	−	1.02341i
$983$	−1263.03	+	222.707i	−1.28487	+	0.226558i	−0.774049	−	0.633126i	$-0.781772\pi$
$983$	−1263.03	+	222.707i	−1.28487	+	0.226558i	−0.510826	+	0.859684i	$0.670660\pi$
$984$	−346.368	+	175.096i	−0.352000	+	0.177943i
$985$	215.044	+	590.828i	0.218319	+	0.599826i
$986$	52.1054	−	62.0968i	0.0528452	−	0.0629785i
$987$	−389.860	−	1041.12i	−0.394994	−	1.05484i
$988$	−59.1632	−	21.5337i	−0.0598818	−	0.0217952i
$989$	−897.575	−	1554.65i	−0.907559	−	1.57194i
$990$	46.3192	−	415.240i	0.0467871	−	0.419434i
$991$	818.130	−	1417.04i	0.825560	−	1.42991i	−0.0759303	−	0.997113i	$-0.524193\pi$
$991$	818.130	−	1417.04i	0.825560	−	1.42991i	0.901490	−	0.432799i	$-0.142474\pi$
$992$	−42.3006	+	116.220i	−0.0426417	+	0.117157i
$993$	961.964	−	290.755i	0.968745	−	0.292805i
$994$	441.348	+	128.964i	0.444012	+	0.129742i
$995$	−225.427	+	1278.46i	−0.226560	+	1.28489i
$996$	−83.9204	+	10.0330i	−0.0842574	+	0.0100733i
$997$	157.088	−	431.596i	0.157561	−	0.432895i	−0.835644	−	0.549271i	$-0.814906\pi$
$997$	157.088	−	431.596i	0.157561	−	0.432895i	0.993205	+	0.116376i	$0.0371278\pi$
$998$	522.666	+	905.284i	0.523713	+	0.907098i
$999$	196.024	−	237.396i	0.196221	−	0.237634i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.3.x.a.103.19	✓	288
7.3	odd	6		378.3.be.a.157.45	yes	288
27.16	even	9		378.3.be.a.313.45	yes	288
189.178	odd	18	inner	378.3.x.a.367.19	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.3.x.a.103.19	✓	288	1.1	even	1	trivial
378.3.x.a.367.19	yes	288	189.178	odd	18	inner
378.3.be.a.157.45	yes	288	7.3	odd	6
378.3.be.a.313.45	yes	288	27.16	even	9

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	378.x (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.245576 - 1.39273i) q^{2} +(2.40164 - 1.79781i) q^{3} +(-1.87939 + 0.684040i) q^{4} +(-3.74775 - 0.660829i) q^{5} +(-3.09364 - 2.90334i) q^{6} +(6.98532 - 0.453118i) q^{7} +(1.41421 + 2.44949i) q^{8} +(2.53579 - 8.63538i) q^{9} +5.38188i q^{10} +(-1.49788 - 8.49493i) q^{11} +(-3.28384 + 5.02159i) q^{12} +(4.33681 - 5.16840i) q^{13} +(-2.34649 - 9.61738i) q^{14} +(-10.1888 + 5.15065i) q^{15} +(3.06418 - 2.57115i) q^{16} -4.56647i q^{17} +(-12.6495 - 1.41102i) q^{18} +4.66588i q^{19} +(7.49549 - 1.32166i) q^{20} +(15.9616 - 13.6465i) q^{21} +(-11.4633 + 4.17229i) q^{22} +(-21.6623 - 18.1768i) q^{23} +(7.80015 + 3.34032i) q^{24} +(-9.88340 - 3.59726i) q^{25} +(-8.26320 - 4.77076i) q^{26} +(-9.43469 - 25.2980i) q^{27} +(-12.8182 + 5.62982i) q^{28} +(-9.61554 + 8.06840i) q^{29} +(9.67557 + 12.9254i) q^{30} +(-7.47776 - 20.5450i) q^{31} +(-4.33340 - 3.63616i) q^{32} +(-18.8696 - 17.7089i) q^{33} +(-6.35985 + 1.12141i) q^{34} +(-26.4786 - 2.91793i) q^{35} +(1.14123 + 17.9638i) q^{36} +(5.70126 + 9.87487i) q^{37} +(6.49831 - 1.14583i) q^{38} +(1.12367 - 20.2094i) q^{39} +(-3.68142 - 10.1146i) q^{40} +(-29.4006 + 35.0383i) q^{41} +(-22.9256 - 18.8790i) q^{42} +(59.6536 + 21.7121i) q^{43} +(8.62597 + 14.9406i) q^{44} +(-15.2100 + 30.6875i) q^{45} +(-19.9956 + 34.6334i) q^{46} +(18.1063 - 49.7465i) q^{47} +(2.73663 - 11.6838i) q^{48} +(48.5894 - 6.33035i) q^{49} +(-2.58289 + 14.6483i) q^{50} +(-8.20962 - 10.9670i) q^{51} +(-4.61513 + 12.6800i) q^{52} +(8.57836 + 14.8582i) q^{53} +(-32.9163 + 19.3525i) q^{54} +32.8267i q^{55} +(10.9886 + 16.4697i) q^{56} +(8.38835 + 11.2058i) q^{57} +(13.5984 + 11.4104i) q^{58} +(29.4528 - 35.1004i) q^{59} +(15.6254 - 16.6496i) q^{60} +(-12.2195 + 33.5727i) q^{61} +(-26.7772 + 15.4598i) q^{62} +(13.8004 - 61.4699i) q^{63} +(-4.00000 + 6.92820i) q^{64} +(-19.6687 + 16.5040i) q^{65} +(-20.0297 + 30.6291i) q^{66} +(9.36538 - 53.1137i) q^{67} +(3.12365 + 8.58215i) q^{68} +(-84.7034 - 4.70964i) q^{69} +(2.43863 + 37.5941i) q^{70} +(-23.2236 + 40.2244i) q^{71} +(24.7384 - 6.00089i) q^{72} +(56.1148 + 32.3979i) q^{73} +(12.3529 - 10.3653i) q^{74} +(-30.2036 + 9.12909i) q^{75} +(-3.19165 - 8.76899i) q^{76} +(-14.3124 - 58.6611i) q^{77} +(-28.4222 + 3.39796i) q^{78} +(-0.801841 - 4.54747i) q^{79} +(-13.1829 + 7.61112i) q^{80} +(-68.1396 - 43.7949i) q^{81} +(56.0189 + 32.3425i) q^{82} +(9.05452 + 10.7908i) q^{83} +(-20.6633 + 36.5654i) q^{84} +(-3.01765 + 17.1140i) q^{85} +(15.5896 - 88.4133i) q^{86} +(-8.58769 + 36.6643i) q^{87} +(18.6899 - 15.6827i) q^{88} -103.731i q^{89} +(46.4746 + 13.6473i) q^{90} +(27.9521 - 38.0680i) q^{91} +(53.1454 + 19.3434i) q^{92} +(-54.8948 - 35.8981i) q^{93} +(-73.7299 - 13.0006i) q^{94} +(3.08335 - 17.4865i) q^{95} +(-16.9444 - 0.942135i) q^{96} +(-17.6131 + 48.3917i) q^{97} +(-20.7488 - 66.1172i) q^{98} +(-77.1552 - 8.60651i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 36 q^{6} - 12 q^{9} + 36 q^{11} + 36 q^{14} - 24 q^{15} + 186 q^{21} + 126 q^{23} + 36 q^{29} - 72 q^{30} + 162 q^{35} - 48 q^{36} + 246 q^{39} - 48 q^{42} + 324 q^{47} - 72 q^{49} + 288 q^{50}+ \cdots - 216 q^{99}+O(q^{100}) \) 288 * q - 36 * q^6 - 12 * q^9 + 36 * q^11 + 36 * q^14 - 24 * q^15 + 186 * q^21 + 126 * q^23 + 36 * q^29 - 72 * q^30 + 162 * q^35 - 48 * q^36 + 246 * q^39 - 48 * q^42 + 324 * q^47 - 72 * q^49 + 288 * q^50 - 198 * q^51 + 270 * q^53 + 432 * q^54 - 144 * q^56 + 354 * q^57 + 270 * q^59 + 72 * q^60 + 138 * q^63 - 1152 * q^64 - 360 * q^65 + 72 * q^69 + 180 * q^70 + 216 * q^71 - 96 * q^72 + 216 * q^74 - 1170 * q^75 + 234 * q^77 - 96 * q^78 - 36 * q^79 + 324 * q^81 - 24 * q^84 - 360 * q^85 + 144 * q^86 - 990 * q^87 - 198 * q^91 - 180 * q^92 + 168 * q^93 - 72 * q^95 + 216 * q^98 - 216 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more