LMFDB - Embedded newform 363.3.h.q.269.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [363,3,Mod(245,363)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(363, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 8])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("363.245"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	363.h (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,-4,18,0,10,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.89103359628$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			269.4
Character	$\chi$	$=$	363.269
Dual form			363.3.h.q.251.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.647210 - 0.210291i) q^{2} +(-2.63284 + 1.43811i) q^{3} +(-2.86141 + 2.07894i) q^{4} +(-6.17237 - 2.00553i) q^{5} +(-1.40158 + 1.48442i) q^{6} +(-7.57686 + 5.50491i) q^{7} +(-3.01474 + 4.14944i) q^{8} +(4.86369 - 7.57261i) q^{9} -4.41657 q^{10} +(4.54390 - 9.58852i) q^{12} +(-1.28903 - 3.96722i) q^{13} +(-3.74618 + 5.15618i) q^{14} +(19.1350 - 3.59631i) q^{15} +(3.29326 - 10.1356i) q^{16} +(28.4618 + 9.24781i) q^{17} +(1.55538 - 5.92386i) q^{18} +(-8.32617 - 6.04932i) q^{19} +(21.8311 - 7.09334i) q^{20} +(12.0320 - 25.3899i) q^{21} +27.8850i q^{23} +(1.97000 - 15.2603i) q^{24} +(13.8506 + 10.0631i) q^{25} +(-1.66854 - 2.29655i) q^{26} +(-1.91509 + 26.9320i) q^{27} +(10.2361 - 31.5036i) q^{28} +(-9.49235 - 13.0651i) q^{29} +(11.6281 - 6.35150i) q^{30} +(-5.45778 - 16.7973i) q^{31} -27.7684i q^{32} +20.3655 q^{34} +(57.8074 - 18.7828i) q^{35} +(1.82596 + 31.7797i) q^{36} +(-11.7790 + 8.55794i) q^{37} +(-6.66090 - 2.16426i) q^{38} +(9.09910 + 8.59130i) q^{39} +(26.9299 - 19.5657i) q^{40} +(20.5756 - 28.3199i) q^{41} +(2.44796 - 18.9628i) q^{42} -64.3417 q^{43} +(-45.2076 + 36.9867i) q^{45} +(5.86397 + 18.0474i) q^{46} +(6.14617 - 8.45948i) q^{47} +(5.90548 + 31.4216i) q^{48} +(11.9629 - 36.8181i) q^{49} +(11.0804 + 3.60026i) q^{50} +(-88.2348 + 16.5832i) q^{51} +(11.9360 + 8.67204i) q^{52} +(57.4452 - 18.6651i) q^{53} +(4.42410 + 17.8334i) q^{54} -48.0356i q^{56} +(30.6211 + 3.95296i) q^{57} +(-8.89102 - 6.45971i) q^{58} +(23.9032 + 32.8999i) q^{59} +(-47.2767 + 50.0710i) q^{60} +(7.26488 - 22.3590i) q^{61} +(-7.06466 - 9.72367i) q^{62} +(4.83505 + 84.1508i) q^{63} +(7.33362 + 22.5705i) q^{64} +27.0724i q^{65} +30.8376 q^{67} +(-100.667 + 32.7086i) q^{68} +(-40.1016 - 73.4167i) q^{69} +(33.4637 - 24.3128i) q^{70} +(0.946935 + 0.307678i) q^{71} +(16.7593 + 43.0111i) q^{72} +(75.6188 - 54.9403i) q^{73} +(-5.82382 + 8.01580i) q^{74} +(-50.9383 - 6.57576i) q^{75} +36.4007 q^{76} +(7.69570 + 3.64691i) q^{78} +(-34.9425 - 107.542i) q^{79} +(-40.6545 + 55.9561i) q^{80} +(-33.6890 - 73.6617i) q^{81} +(7.36131 - 22.6558i) q^{82} +(-98.9769 - 32.1595i) q^{83} +(18.3555 + 97.6646i) q^{84} +(-157.130 - 114.162i) q^{85} +(-41.6426 + 13.5305i) q^{86} +(43.7809 + 20.7473i) q^{87} -20.3993i q^{89} +(-21.4808 + 33.4449i) q^{90} +(31.6060 + 22.9631i) q^{91} +(-57.9711 - 79.7904i) q^{92} +(38.5258 + 36.3758i) q^{93} +(2.19891 - 6.76754i) q^{94} +(39.2602 + 54.0370i) q^{95} +(39.9339 + 73.1096i) q^{96} +(58.7378 + 180.776i) q^{97} -26.3447i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{3} + 18 q^{4} + 10 q^{6} + 22 q^{9} + 72 q^{10} + 56 q^{12} + 42 q^{13} - 28 q^{15} - 30 q^{16} - 94 q^{18} - 84 q^{19} - 112 q^{21} - 48 q^{24} + 108 q^{25} + 38 q^{27} - 132 q^{28} + 148 q^{30}+ \cdots - 126 q^{97}+O(q^{100}) $ 24 * q - 4 * q^3 + 18 * q^4 + 10 * q^6 + 22 * q^9 + 72 * q^10 + 56 * q^12 + 42 * q^13 - 28 * q^15 - 30 * q^16 - 94 * q^18 - 84 * q^19 - 112 * q^21 - 48 * q^24 + 108 * q^25 + 38 * q^27 - 132 * q^28 + 148 * q^30 + 264 * q^34 - 46 * q^36 + 42 * q^37 + 82 * q^39 + 294 * q^40 + 206 * q^42 - 624 * q^43 - 472 * q^45 + 60 * q^46 + 88 * q^48 - 138 * q^49 - 182 * q^51 - 114 * q^52 + 560 * q^54 + 24 * q^57 + 54 * q^58 + 562 * q^60 - 264 * q^61 + 122 * q^63 - 294 * q^64 + 96 * q^67 - 152 * q^69 - 336 * q^70 + 306 * q^72 - 72 * q^73 - 62 * q^75 - 1632 * q^76 - 776 * q^78 + 250 * q^81 - 798 * q^82 - 328 * q^84 - 330 * q^85 + 1848 * q^87 + 230 * q^90 - 300 * q^91 + 266 * q^93 - 120 * q^94 + 386 * q^96 - 126 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.647210	−	0.210291i	0.323605	−	0.105146i	−0.142710	−	0.989765i	$-0.545582\pi$
$2$	0.647210	−	0.210291i	0.323605	−	0.105146i	0.466315	+	0.884619i	$0.345582\pi$
$3$	−2.63284	+	1.43811i	−0.877613	+	0.479369i
$3$	−2.63284	+	1.43811i	−0.877613	+	0.479369i
$4$	−2.86141	+	2.07894i	−0.715352	+	0.519734i
$5$	−6.17237	−	2.00553i	−1.23447	−	0.401105i	−0.382141	−	0.924104i	$-0.624813\pi$
$5$	−6.17237	−	2.00553i	−1.23447	−	0.401105i	−0.852333	+	0.522999i	$0.824813\pi$
$6$	−1.40158	+	1.48442i	−0.233596	+	0.247403i
$7$	−7.57686	+	5.50491i	−1.08241	+	0.786416i	−0.978101	−	0.208130i	$-0.933262\pi$
$7$	−7.57686	+	5.50491i	−1.08241	+	0.786416i	−0.104307	+	0.994545i	$0.533262\pi$
$8$	−3.01474	+	4.14944i	−0.376843	+	0.518679i
$9$	4.86369	−	7.57261i	0.540410	−	0.841402i
$10$	−4.41657			−0.441657
$11$		0			0
$11$		0			0
$12$	4.54390	−	9.58852i	0.378658	−	0.799043i
$13$	−1.28903	−	3.96722i	−0.0991561	−	0.305171i	0.889158	−	0.457599i	$-0.151291\pi$
$13$	−1.28903	−	3.96722i	−0.0991561	−	0.305171i	−0.988315	+	0.152428i	$0.951291\pi$
$14$	−3.74618	+	5.15618i	−0.267584	+	0.368298i
$15$	19.1350	−	3.59631i	1.27567	−	0.239754i
$16$	3.29326	−	10.1356i	0.205829	−	0.633477i
$17$	28.4618	+	9.24781i	1.67423	+	0.543989i	0.983777	−	0.179393i	$-0.0574135\pi$
$17$	28.4618	+	9.24781i	1.67423	+	0.543989i	0.690448	+	0.723382i	$0.257413\pi$
$18$	1.55538	−	5.92386i	0.0864097	−	0.329103i
$19$	−8.32617	−	6.04932i	−0.438220	−	0.318385i	0.346707	−	0.937973i	$-0.387300\pi$
$19$	−8.32617	−	6.04932i	−0.438220	−	0.318385i	−0.784927	+	0.619588i	$0.787300\pi$
$20$	21.8311	−	7.09334i	1.09155	−	0.354667i
$21$	12.0320	−	25.3899i	0.572952	−	1.20904i
$22$		0			0
$23$			27.8850i			1.21239i	0.795316	+	0.606195i	$0.207305\pi$
$23$			27.8850i			1.21239i	−0.795316	+	0.606195i	$0.792695\pi$
$24$	1.97000	−	15.2603i	0.0820832	−	0.635847i
$25$	13.8506	+	10.0631i	0.554026	+	0.402523i
$26$	−1.66854	−	2.29655i	−0.0641748	−	0.0883290i
$27$	−1.91509	+	26.9320i	−0.0709292	+	0.997481i
$28$	10.2361	−	31.5036i	0.365576	−	1.12513i
$29$	−9.49235	−	13.0651i	−0.327323	−	0.450521i	0.613363	−	0.789801i	$-0.289816\pi$
$29$	−9.49235	−	13.0651i	−0.327323	−	0.450521i	−0.940685	+	0.339281i	$0.889816\pi$
$30$	11.6281	−	6.35150i	0.387604	−	0.211717i
$31$	−5.45778	−	16.7973i	−0.176057	−	0.541849i	0.823623	−	0.567138i	$-0.191949\pi$
$31$	−5.45778	−	16.7973i	−0.176057	−	0.541849i	−0.999680	+	0.0252890i	$0.991949\pi$
$32$		−	27.7684i		−	0.867761i
$33$		0			0
$34$	20.3655			0.598986
$35$	57.8074	−	18.7828i	1.65164	−	0.536651i
$36$	1.82596	+	31.7797i	0.0507212	+	0.882768i
$37$	−11.7790	+	8.55794i	−0.318351	+	0.231296i	−0.735472	−	0.677556i	$-0.763039\pi$
$37$	−11.7790	+	8.55794i	−0.318351	+	0.231296i	0.417120	+	0.908851i	$0.363039\pi$
$38$	−6.66090	−	2.16426i	−0.175287	−	0.0569542i
$39$	9.09910	+	8.59130i	0.233310	+	0.220290i
$40$	26.9299	−	19.5657i	0.673248	−	0.489143i
$41$	20.5756	−	28.3199i	0.501844	−	0.690729i	−0.480673	−	0.876900i	$-0.659608\pi$
$41$	20.5756	−	28.3199i	0.501844	−	0.690729i	0.982517	+	0.186171i	$0.0596077\pi$
$42$	2.44796	−	18.9628i	0.0582848	−	0.451495i
$43$	−64.3417			−1.49632			−0.748159	−	0.663519i	$-0.769062\pi$
$43$	−64.3417			−1.49632			−0.748159	+	0.663519i	$0.769062\pi$
$44$		0			0
$45$	−45.2076	+	36.9867i	−1.00461	+	0.821928i
$46$	5.86397	+	18.0474i	0.127478	+	0.392336i
$47$	6.14617	−	8.45948i	0.130770	−	0.179989i	−0.738611	−	0.674132i	$-0.764518\pi$
$47$	6.14617	−	8.45948i	0.130770	−	0.179989i	0.869381	+	0.494143i	$0.164518\pi$
$48$	5.90548	+	31.4216i	0.123031	+	0.654616i
$49$	11.9629	−	36.8181i	0.244141	−	0.751389i
$50$	11.0804	+	3.60026i	0.221609	+	0.0720051i
$51$	−88.2348	+	16.5832i	−1.73009	+	0.325160i
$52$	11.9360	+	8.67204i	0.229539	+	0.166770i
$53$	57.4452	−	18.6651i	1.08387	−	0.352171i	0.287997	−	0.957631i	$-0.407011\pi$
$53$	57.4452	−	18.6651i	1.08387	−	0.352171i	0.795876	+	0.605460i	$0.207011\pi$
$54$	4.42410	+	17.8334i	0.0819277	+	0.330248i
$55$		0			0
$56$		−	48.0356i		−	0.857778i
$57$	30.6211	+	3.95296i	0.537212	+	0.0693501i
$58$	−8.89102	−	6.45971i	−0.153293	−	0.111374i
$59$	23.9032	+	32.8999i	0.405139	+	0.557625i	0.962024	−	0.272964i	$-0.0880039\pi$
$59$	23.9032	+	32.8999i	0.405139	+	0.557625i	−0.556886	+	0.830589i	$0.688004\pi$
$60$	−47.2767	+	50.0710i	−0.787945	+	0.834517i
$61$	7.26488	−	22.3590i	0.119096	−	0.366541i	−0.873683	−	0.486496i	$-0.838275\pi$
$61$	7.26488	−	22.3590i	0.119096	−	0.366541i	0.992779	+	0.119955i	$0.0382749\pi$
$62$	−7.06466	−	9.72367i	−0.113946	−	0.156833i
$63$	4.83505	+	84.1508i	0.0767468	+	1.33573i
$64$	7.33362	+	22.5705i	0.114588	+	0.352665i
$65$			27.0724i			0.416498i
$66$		0			0
$67$	30.8376			0.460263			0.230132	−	0.973159i	$-0.426084\pi$
$67$	30.8376			0.460263			0.230132	+	0.973159i	$0.426084\pi$
$68$	−100.667	+	32.7086i	−1.48039	+	0.481008i
$69$	−40.1016	−	73.4167i	−0.581183	−	1.06401i
$70$	33.4637	−	24.3128i	0.478053	−	0.347326i
$71$	0.946935	+	0.307678i	0.0133371	+	0.00433349i	0.315678	−	0.948866i	$-0.397768\pi$
$71$	0.946935	+	0.307678i	0.0133371	+	0.00433349i	−0.302341	+	0.953200i	$0.597768\pi$
$72$	16.7593	+	43.0111i	0.232768	+	0.597376i
$73$	75.6188	−	54.9403i	1.03587	−	0.752607i	0.0663985	−	0.997793i	$-0.478849\pi$
$73$	75.6188	−	54.9403i	1.03587	−	0.752607i	0.969476	+	0.245186i	$0.0788491\pi$
$74$	−5.82382	+	8.01580i	−0.0787003	+	0.108322i
$75$	−50.9383	−	6.57576i	−0.679177	−	0.0876769i
$76$	36.4007			0.478957
$77$		0			0
$78$	7.69570	+	3.64691i	0.0986629	+	0.0467553i
$79$	−34.9425	−	107.542i	−0.442310	−	1.36129i	−0.885407	−	0.464816i	$-0.846121\pi$
$79$	−34.9425	−	107.542i	−0.442310	−	1.36129i	0.443098	−	0.896473i	$-0.353879\pi$
$80$	−40.6545	+	55.9561i	−0.508182	+	0.699452i
$81$	−33.6890	−	73.6617i	−0.415913	−	0.909404i
$82$	7.36131	−	22.6558i	0.0897721	−	0.276290i
$83$	−98.9769	−	32.1595i	−1.19249	−	0.387464i	−0.355499	−	0.934677i	$-0.615689\pi$
$83$	−98.9769	−	32.1595i	−1.19249	−	0.387464i	−0.836994	+	0.547212i	$0.815689\pi$
$84$	18.3555	+	97.6646i	0.218517	+	1.16267i
$85$	−157.130	−	114.162i	−1.84859	−	1.34308i
$86$	−41.6426	+	13.5305i	−0.484216	+	0.157331i
$87$	43.7809	+	20.7473i	0.503228	+	0.238475i
$88$		0			0
$89$		−	20.3993i		−	0.229206i	−0.993411	−	0.114603i	$-0.963440\pi$
$89$		−	20.3993i		−	0.229206i	0.993411	−	0.114603i	$-0.0365595\pi$
$90$	−21.4808	+	33.4449i	−0.238676	+	0.371611i
$91$	31.6060	+	22.9631i	0.347319	+	0.252342i
$92$	−57.9711	−	79.7904i	−0.630121	−	0.867287i
$93$	38.5258	+	36.3758i	0.414256	+	0.391137i
$94$	2.19891	−	6.76754i	0.0233926	−	0.0719951i
$95$	39.2602	+	54.0370i	0.413265	+	0.568811i
$96$	39.9339	+	73.1096i	0.415978	+	0.761559i
$97$	58.7378	+	180.776i	0.605545	+	1.86368i	0.493002	+	0.870028i	$0.335900\pi$
$97$	58.7378	+	180.776i	0.605545	+	1.86368i	0.112543	+	0.993647i	$0.464100\pi$
$98$		−	26.3447i		−	0.268824i
$99$		0			0
$100$	−60.5528			−0.605528
$101$	−45.2739	+	14.7104i	−0.448256	+	0.145647i	−0.524442	−	0.851446i	$-0.675726\pi$
$101$	−45.2739	+	14.7104i	−0.448256	+	0.145647i	0.0761854	+	0.997094i	$0.475726\pi$
$102$	−53.6191	+	29.2878i	−0.525678	+	0.287135i
$103$	−42.6153	+	30.9619i	−0.413741	+	0.300601i	−0.775115	−	0.631821i	$-0.782308\pi$
$103$	−42.6153	+	30.9619i	−0.413741	+	0.300601i	0.361374	+	0.932421i	$0.382308\pi$
$104$	20.3478	+	6.61141i	0.195652	+	0.0635713i
$105$	−125.186	+	132.585i	−1.19225	+	1.26272i
$106$	33.2540	−	24.1605i	0.313717	−	0.227929i
$107$	40.1565	−	55.2706i	0.375294	−	0.516548i	−0.579036	−	0.815302i	$-0.696571\pi$
$107$	40.1565	−	55.2706i	0.375294	−	0.516548i	0.954330	+	0.298754i	$0.0965710\pi$
$108$	−50.5100	−	81.0448i	−0.467686	−	0.750415i
$109$	37.7254			0.346105			0.173053	−	0.984913i	$-0.444637\pi$
$109$	37.7254			0.346105			0.173053	+	0.984913i	$0.444637\pi$
$110$		0			0
$111$	18.7050	−	39.4711i	0.168513	−	0.355596i
$112$	30.8431	+	94.9253i	0.275385	+	0.847548i
$113$	100.089	−	137.760i	0.885739	−	1.21912i	−0.0890591	−	0.996026i	$-0.528386\pi$
$113$	100.089	−	137.760i	0.885739	−	1.21912i	0.974798	−	0.223089i	$-0.0716140\pi$
$114$	20.6495	−	3.88095i	0.181136	−	0.0340434i
$115$	55.9241	−	172.117i	0.486296	−	1.49667i
$116$	54.3230	+	17.6506i	0.468302	+	0.152161i
$117$	−36.3117	−	9.53404i	−0.310356	−	0.0814875i
$118$	22.3889	+	16.2665i	0.189737	+	0.137852i
$119$	−266.560	+	86.6105i	−2.24000	+	0.727819i
$120$	−42.7645	+	90.2415i	−0.356371	+	0.752013i
$121$		0			0
$122$		−	15.9987i		−	0.131137i
$123$	−13.4452	+	104.152i	−0.109311	+	0.846762i
$124$	50.5375	+	36.7176i	0.407560	+	0.296110i
$125$	30.0589	+	41.3725i	0.240471	+	0.330980i
$126$	20.8255	+	53.4465i	0.165282	+	0.424178i
$127$	44.9068	−	138.209i	0.353597	−	1.08826i	−0.603222	−	0.797573i	$-0.706117\pi$
$127$	44.9068	−	138.209i	0.353597	−	1.08826i	0.956819	−	0.290685i	$-0.0938833\pi$
$128$	74.7801	+	102.926i	0.584220	+	0.804109i
$129$	169.401	−	92.5303i	1.31319	−	0.717289i
$130$	5.69308	+	17.5215i	0.0437929	+	0.134781i
$131$			174.147i			1.32936i	0.747126	+	0.664682i	$0.231433\pi$
$131$			174.147i			1.32936i	−0.747126	+	0.664682i	$0.768567\pi$
$132$		0			0
$133$	96.3872			0.724716
$134$	19.9584	−	6.48489i	0.148944	−	0.0483947i
$135$	65.8335	−	162.394i	0.487655	−	1.20292i
$136$	−124.178	+	90.2208i	−0.913075	+	0.663388i
$137$	77.3163	+	25.1216i	0.564353	+	0.183369i	0.577279	−	0.816547i	$-0.304115\pi$
$137$	77.3163	+	25.1216i	0.564353	+	0.183369i	−0.0129260	+	0.999916i	$0.504115\pi$
$138$	−41.3931	−	39.0830i	−0.299950	−	0.283210i
$139$	0.550962	−	0.400297i	0.00396375	−	0.00287984i	−0.585802	−	0.810454i	$-0.699220\pi$
$139$	0.550962	−	0.400297i	0.00396375	−	0.00287984i	0.589765	+	0.807575i	$0.299220\pi$
$140$	−126.363	+	173.923i	−0.902590	+	1.24231i
$141$	−4.01624	+	31.1113i	−0.0284840	+	0.220648i
$142$	0.677567			0.00477160
$143$		0			0
$144$	−60.7358	−	74.2352i	−0.421776	−	0.515522i
$145$	32.3880	+	99.6799i	0.223365	+	0.687447i
$146$	37.3878	−	51.4599i	0.256081	−	0.352465i
$147$	21.4519	+	114.140i	0.145931	+	0.776463i
$148$	15.9131	−	48.9755i	0.107521	−	0.330916i
$149$	−188.245	−	61.1645i	−1.26339	−	0.410500i	−0.400688	−	0.916214i	$-0.631229\pi$
$149$	−188.245	−	61.1645i	−1.26339	−	0.410500i	−0.862701	+	0.505715i	$0.831229\pi$
$150$	−34.3506	+	6.45598i	−0.229004	+	0.0430399i
$151$	71.9338	+	52.2630i	0.476383	+	0.346112i	0.799924	−	0.600102i	$-0.204873\pi$
$151$	71.9338	+	52.2630i	0.476383	+	0.346112i	−0.323541	+	0.946214i	$0.604873\pi$
$152$	50.2025	−	16.3118i	0.330280	−	0.107314i
$153$	208.460	−	170.552i	1.36248	−	1.11472i
$154$		0			0
$155$			114.625i			0.739516i
$156$	−43.8970	−	5.66679i	−0.281391	−	0.0363256i
$157$	−53.9913	−	39.2270i	−0.343893	−	0.249853i	0.402409	−	0.915460i	$-0.368173\pi$
$157$	−53.9913	−	39.2270i	−0.343893	−	0.249853i	−0.746303	+	0.665607i	$0.768173\pi$
$158$	−45.2302	−	62.2541i	−0.286267	−	0.394013i
$159$	−124.402	+	131.755i	−0.782401	+	0.828645i
$160$	−55.6902	+	171.397i	−0.348064	+	1.07123i
$161$	−153.504	−	211.281i	−0.953443	−	1.31230i
$162$	−37.2943	−	40.5901i	−0.230212	−	0.250556i
$163$	−43.2141	−	132.999i	−0.265117	−	0.815946i	−0.991666	−	0.128832i	$-0.958877\pi$
$163$	−43.2141	−	132.999i	−0.265117	−	0.815946i	0.726549	−	0.687114i	$-0.241123\pi$
$164$			123.810i			0.754940i
$165$		0			0
$166$	−70.8217			−0.426637
$167$	130.674	−	42.4586i	0.782480	−	0.254243i	0.109581	−	0.993978i	$-0.465049\pi$
$167$	130.674	−	42.4586i	0.782480	−	0.254243i	0.672899	+	0.739735i	$0.265049\pi$
$168$	69.0803	+	126.470i	0.411192	+	0.752797i
$169$	122.647	−	89.1080i	0.725720	−	0.527266i
$170$	−125.704	−	40.8436i	−0.739433	−	0.240256i
$171$	−86.3051	+	33.6289i	−0.504708	+	0.196660i
$172$	184.108	−	133.762i	1.07040	−	0.777688i
$173$	0.622044	−	0.856170i	0.00359563	−	0.00494896i	−0.807215	−	0.590257i	$-0.799026\pi$
$173$	0.622044	−	0.856170i	0.00359563	−	0.00494896i	0.810811	+	0.585308i	$0.199026\pi$
$174$	32.6984	+	4.22112i	0.187922	+	0.0242593i
$175$	−160.341			−0.916232
$176$		0			0
$177$	−110.247	−	52.2448i	−0.622863	−	0.295168i
$178$	−4.28980	−	13.2026i	−0.0241000	−	0.0741721i
$179$	−50.9881	+	70.1791i	−0.284850	+	0.392062i	−0.927333	−	0.374238i	$-0.877904\pi$
$179$	−50.9881	+	70.1791i	−0.284850	+	0.392062i	0.642483	+	0.766300i	$0.277904\pi$
$180$	52.4644	−	199.818i	0.291469	−	1.11010i
$181$	−33.4265	+	102.876i	−0.184677	+	0.568376i	−0.999943	−	0.0107104i	$-0.996591\pi$
$181$	−33.4265	+	102.876i	−0.184677	+	0.568376i	0.815266	+	0.579087i	$0.196591\pi$
$182$	25.2847	+	8.21548i	0.138927	+	0.0451400i
$183$	13.0274	+	69.3153i	0.0711879	+	0.378772i
$184$	−115.707	−	84.0660i	−0.628842	−	0.456881i
$185$	89.8675	−	29.1997i	0.485770	−	0.157836i
$186$	32.5838	+	15.4411i	0.175182	+	0.0830168i
$187$		0			0
$188$			36.9835i			0.196721i
$189$	−133.748	−	214.602i	−0.707661	−	1.13546i
$190$	36.7731	+	26.7172i	0.193543	+	0.140617i
$191$	−16.8407	−	23.1793i	−0.0881714	−	0.121358i	0.762653	−	0.646808i	$-0.223897\pi$
$191$	−16.8407	−	23.1793i	−0.0881714	−	0.121358i	−0.850824	+	0.525451i	$0.823897\pi$
$192$	−51.7671	−	48.8781i	−0.269620	−	0.254574i
$193$	3.92289	−	12.0734i	0.0203258	−	0.0625565i	−0.940379	−	0.340128i	$-0.889530\pi$
$193$	3.92289	−	12.0734i	0.0203258	−	0.0625565i	0.960705	+	0.277572i	$0.0895296\pi$
$194$	76.0314	+	104.648i	0.391915	+	0.539424i
$195$	−38.9330	−	71.2772i	−0.199656	−	0.365524i
$196$	42.3116	+	130.222i	0.215875	+	0.664396i
$197$		−	336.692i		−	1.70910i	−0.519370	−	0.854549i	$-0.673834\pi$
$197$		−	336.692i		−	1.70910i	0.519370	−	0.854549i	$-0.326166\pi$
$198$		0			0
$199$	183.863			0.923932			0.461966	−	0.886898i	$-0.347144\pi$
$199$	183.863			0.923932			0.461966	+	0.886898i	$0.347144\pi$
$200$	−83.5122	+	27.1348i	−0.417561	+	0.135674i
$201$	−81.1906	+	44.3479i	−0.403933	+	0.220636i
$202$	−26.2082	+	19.0414i	−0.129744	+	0.0942644i
$203$	143.844	+	46.7379i	0.708593	+	0.230236i
$204$	218.001	−	230.886i	1.06863	−	1.13179i
$205$	−183.797	+	133.536i	−0.896569	+	0.651395i
$206$	−21.0701	+	29.0004i	−0.102282	+	0.140779i
$207$	211.162	+	135.624i	1.02011	+	0.655189i
$208$	−44.4554			−0.213728
$209$		0			0
$210$	−53.1401	+	112.136i	−0.253048	+	0.533981i
$211$	−55.6255	−	171.198i	−0.263628	−	0.811364i	−0.992006	−	0.126188i	$-0.959726\pi$
$211$	−55.6255	−	171.198i	−0.263628	−	0.811364i	0.728378	−	0.685175i	$-0.240274\pi$
$212$	−125.571	+	172.833i	−0.592315	+	0.815252i
$213$	−2.93560	+	0.551728i	−0.0137822	+	0.00259027i
$214$	14.3667	−	44.2162i	0.0671342	−	0.206618i
$215$	397.141	+	129.039i	1.84717	+	0.600181i
$216$	−105.979	−	89.1395i	−0.490644	−	0.412683i
$217$	133.821	+	97.2263i	0.616684	+	0.448048i
$218$	24.4163	−	7.93333i	0.112001	−	0.0363914i
$219$	−120.082	+	253.397i	−0.548321	+	1.15706i
$220$		0			0
$221$		−	124.835i		−	0.564865i
$222$	3.80560	−	29.4796i	0.0171424	−	0.132791i
$223$	−212.819	−	154.622i	−0.954344	−	0.693372i	−0.00251375	−	0.999997i	$-0.500800\pi$
$223$	−212.819	−	154.622i	−0.954344	−	0.693372i	−0.951830	+	0.306625i	$0.900800\pi$
$224$	152.862	+	210.397i	0.682421	+	0.939272i
$225$	143.569	−	55.9418i	0.638085	−	0.248630i
$226$	35.8085	−	110.207i	0.158445	−	0.487643i
$227$	5.30714	+	7.30465i	0.0233795	+	0.0321791i	0.820547	−	0.571579i	$-0.193669\pi$
$227$	5.30714	+	7.30465i	0.0233795	+	0.0321791i	−0.797167	+	0.603759i	$0.793669\pi$
$228$	−95.8373	+	52.3482i	−0.420339	+	0.229597i
$229$	−108.907	−	335.180i	−0.475575	−	1.46367i	−0.845181	−	0.534480i	$-0.820508\pi$
$229$	−108.907	−	335.180i	−0.475575	−	1.46367i	0.369607	−	0.929188i	$-0.379492\pi$
$230$		−	123.156i		−	0.535460i
$231$		0			0
$232$	82.8298			0.357025
$233$	33.6696	−	10.9399i	0.144505	−	0.0469525i	−0.235872	−	0.971784i	$-0.575794\pi$
$233$	33.6696	−	10.9399i	0.144505	−	0.0469525i	0.380376	+	0.924832i	$0.375794\pi$
$234$	−25.5062	+	1.46551i	−0.109001	+	0.00626286i
$235$	−54.9021	+	39.8887i	−0.233626	+	0.169739i
$236$	−136.794	−	44.4469i	−0.579634	−	0.188334i
$237$	246.655	+	232.889i	1.04074	+	0.982656i
$238$	−154.307	+	112.110i	−0.648347	+	0.471052i
$239$	76.8818	−	105.819i	0.321681	−	0.442756i	−0.617298	−	0.786729i	$-0.711773\pi$
$239$	76.8818	−	105.819i	0.321681	−	0.442756i	0.938980	+	0.343973i	$0.111773\pi$
$240$	26.5659	−	205.789i	0.110691	−	0.857455i
$241$	−134.526			−0.558198			−0.279099	−	0.960262i	$-0.590036\pi$
$241$	−134.526			−0.558198			−0.279099	+	0.960262i	$0.590036\pi$
$242$		0			0
$243$	194.631	+	145.491i	0.800952	+	0.598729i
$244$	25.6951	+	79.0815i	0.105308	+	0.324104i
$245$	−147.679	+	203.263i	−0.602772	+	0.829644i
$246$	13.2003	+	70.2354i	0.0536598	+	0.285510i
$247$	−13.2663	+	40.8295i	−0.0537098	+	0.165302i
$248$	86.1532	+	27.9929i	0.347392	+	0.112874i
$249$	306.839	−	57.6685i	1.23229	−	0.231600i
$250$	28.1547	+	20.4556i	0.112619	+	0.0818222i
$251$	384.764	−	125.017i	1.53292	−	0.498077i	0.583511	−	0.812105i	$-0.301679\pi$
$251$	384.764	−	125.017i	1.53292	−	0.498077i	0.949414	+	0.314028i	$0.101679\pi$
$252$	−188.779	−	230.738i	−0.749124	−	0.915628i
$253$		0			0
$254$		−	98.8936i		−	0.389345i
$255$	577.876	+	74.5996i	2.26618	+	0.292547i
$256$	−6.75577	−	4.90836i	−0.0263897	−	0.0191733i
$257$	80.7301	+	111.115i	0.314125	+	0.432356i	0.936662	−	0.350234i	$-0.113898\pi$
$257$	80.7301	+	111.115i	0.314125	+	0.432356i	−0.622537	+	0.782590i	$0.713898\pi$
$258$	90.1800	−	95.5102i	0.349535	−	0.370194i
$259$	42.1371	−	129.685i	0.162691	−	0.500713i
$260$	−56.2817	−	77.4651i	−0.216468	−	0.297943i
$261$	−145.105	+	8.33729i	−0.555957	+	0.0319436i
$262$	36.6215	+	112.710i	0.139777	+	0.430189i
$263$		−	138.001i		−	0.524720i	−0.964970	−	0.262360i	$-0.915499\pi$
$263$		−	138.001i		−	0.524720i	0.964970	−	0.262360i	$-0.0845008\pi$
$264$		0			0
$265$	−392.007			−1.47927
$266$	62.3827	−	20.2694i	0.234522	−	0.0762007i
$267$	29.3364	+	53.7081i	0.109874	+	0.201154i
$268$	−88.2391	+	64.1095i	−0.329251	+	0.239215i
$269$	−29.3816	−	9.54665i	−0.109225	−	0.0354894i	0.253895	−	0.967232i	$-0.418288\pi$
$269$	−29.3816	−	9.54665i	−0.109225	−	0.0354894i	−0.363120	+	0.931743i	$0.618288\pi$
$270$	8.45812	−	118.947i	0.0313264	−	0.440544i
$271$	−162.195	+	117.842i	−0.598507	+	0.434841i	−0.845349	−	0.534215i	$-0.820607\pi$
$271$	−162.195	+	117.842i	−0.598507	+	0.434841i	0.246842	+	0.969056i	$0.420607\pi$
$272$	187.465	−	258.023i	0.689208	−	0.948614i
$273$	−116.237	−	15.0053i	−0.425776	−	0.0549646i
$274$	55.3227			0.201908
$275$		0			0
$276$	267.376	+	126.707i	0.968753	+	0.459082i
$277$	−49.3221	−	151.798i	−0.178058	−	0.548007i	0.821702	−	0.569918i	$-0.193025\pi$
$277$	−49.3221	−	151.798i	−0.178058	−	0.548007i	−0.999760	+	0.0219109i	$0.993025\pi$
$278$	0.272409	−	0.374939i	0.000979888	−	0.00134870i
$279$	−153.745	−	40.3673i	−0.551056	−	0.144686i
$280$	−96.3366	+	296.493i	−0.344059	+	1.05891i
$281$	−377.786	−	122.750i	−1.34444	−	0.436834i	−0.453619	−	0.891196i	$-0.649867\pi$
$281$	−377.786	−	122.750i	−1.34444	−	0.436834i	−0.890817	+	0.454362i	$0.849867\pi$
$282$	3.94308	+	20.9801i	0.0139826	+	0.0743976i
$283$	−54.6819	−	39.7287i	−0.193222	−	0.140384i	0.486968	−	0.873420i	$-0.338103\pi$
$283$	−54.6819	−	39.7287i	−0.193222	−	0.140384i	−0.680190	+	0.733036i	$0.738103\pi$
$284$	−3.34921	+	1.08822i	−0.0117930	+	0.00383178i
$285$	−181.077	−	85.8104i	−0.635357	−	0.301089i
$286$		0			0
$287$			327.843i			1.14231i
$288$	−210.279	−	135.057i	−0.730136	−	0.468947i
$289$	490.748	+	356.549i	1.69809	+	1.23373i
$290$	41.9236	+	57.7029i	0.144564	+	0.198975i
$291$	−414.623	−	391.484i	−1.42482	−	1.34531i
$292$	−102.159	+	314.413i	−0.349860	+	1.07676i
$293$	−214.903	−	295.788i	−0.733457	−	1.00952i	−0.998968	−	0.0454093i	$-0.985541\pi$
$293$	−214.903	−	295.788i	−0.733457	−	1.00952i	0.265511	−	0.964108i	$-0.414459\pi$
$294$	37.8865	+	69.3614i	0.128866	+	0.235923i
$295$	−81.5577	−	251.009i	−0.276467	−	0.850878i
$296$		−	74.6761i		−	0.252284i
$297$		0			0
$298$	−134.696			−0.452001
$299$	110.626	−	35.9446i	0.369987	−	0.120216i
$300$	159.426	−	87.0815i	0.531420	−	0.290272i
$301$	487.508	−	354.195i	1.61963	−	1.17673i
$302$	57.5467	+	18.6981i	0.190552	+	0.0619141i
$303$	98.0438	−	103.839i	0.323577	−	0.342702i
$304$	−88.7339	+	64.4690i	−0.291888	+	0.212069i
$305$	−89.6831	+	123.438i	−0.294043	+	0.404715i
$306$	99.0516	−	154.220i	0.323698	−	0.503987i
$307$	484.160			1.57707			0.788534	−	0.614992i	$-0.210841\pi$
$307$	484.160			1.57707			0.788534	+	0.614992i	$0.210841\pi$
$308$		0			0
$309$	67.6729	−	142.803i	0.219006	−	0.462146i
$310$	24.1046	+	74.1865i	0.0777569	+	0.239311i
$311$	197.585	−	271.953i	0.635323	−	0.874447i	−0.363033	−	0.931776i	$-0.618259\pi$
$311$	197.585	−	271.953i	0.635323	−	0.874447i	0.998355	+	0.0573298i	$0.0182586\pi$
$312$	−63.0805	+	11.8556i	−0.202181	+	0.0379987i
$313$	−151.139	+	465.157i	−0.482871	+	1.48612i	0.352170	+	0.935936i	$0.385444\pi$
$313$	−151.139	+	465.157i	−0.482871	+	1.48612i	−0.835041	+	0.550188i	$0.814556\pi$
$314$	−43.1928	−	14.0342i	−0.137557	−	0.0446948i
$315$	138.923	−	529.107i	0.441025	−	1.67971i
$316$	323.557	+	235.078i	1.02392	+	0.743918i
$317$	148.670	−	48.3059i	0.468992	−	0.152385i	−0.0649808	−	0.997887i	$-0.520699\pi$
$317$	148.670	−	48.3059i	0.468992	−	0.152385i	0.533972	+	0.845502i	$0.320699\pi$
$318$	−52.8072	+	111.433i	−0.166060	+	0.350420i
$319$		0			0
$320$		−	154.022i		−	0.481318i
$321$	−26.2404	+	203.268i	−0.0817458	+	0.633234i
$322$	−143.780	−	104.462i	−0.446522	−	0.324417i
$323$	−181.035	−	249.174i	−0.560481	−	0.771435i
$324$	249.536	+	140.739i	0.770173	+	0.434380i
$325$	22.0686	−	67.9202i	0.0679034	−	0.208985i
$326$	−55.9371	−	76.9909i	−0.171586	−	0.236168i
$327$	−99.3251	+	54.2533i	−0.303746	+	0.165912i
$328$	55.4814	+	170.754i	0.169151	+	0.520592i
$329$			97.9303i			0.297661i
$330$		0			0
$331$	40.2792			0.121689			0.0608447	−	0.998147i	$-0.480621\pi$
$331$	40.2792			0.121689			0.0608447	+	0.998147i	$0.480621\pi$
$332$	350.071	−	113.745i	1.05443	−	0.342605i
$333$	7.51658	+	130.821i	0.0225723	+	0.392856i
$334$	75.6449	−	54.9592i	0.226482	−	0.164549i
$335$	−190.341	−	61.8457i	−0.568184	−	0.184614i
$336$	−217.718	−	205.567i	−0.647970	−	0.611808i
$337$	9.64009	−	7.00393i	0.0286056	−	0.0207832i	−0.573391	−	0.819282i	$-0.694372\pi$
$337$	9.64009	−	7.00393i	0.0286056	−	0.0207832i	0.601996	+	0.798499i	$0.294372\pi$
$338$	60.6395	−	83.4631i	0.179407	−	0.246932i
$339$	−65.4033	+	506.638i	−0.192930	+	1.49451i
$340$	686.950			2.02044
$341$		0			0
$342$	−48.7857	+	39.9142i	−0.142648	+	0.116708i
$343$	−29.7722	−	91.6294i	−0.0867994	−	0.267141i
$344$	193.974	−	266.982i	0.563877	−	0.776110i
$345$	100.283	+	533.580i	0.290676	+	1.54661i
$346$	0.222548	−	0.684932i	0.000643202	−	0.00197957i
$347$	571.856	+	185.807i	1.64800	+	0.535468i	0.978305	−	0.207168i	$-0.0664247\pi$
$347$	571.856	+	185.807i	1.64800	+	0.535468i	0.669695	+	0.742636i	$0.266425\pi$
$348$	−168.407	+	31.6511i	−0.483929	+	0.0909514i
$349$	−107.566	−	78.1511i	−0.308211	−	0.223929i	0.422917	−	0.906168i	$-0.361006\pi$
$349$	−107.566	−	78.1511i	−0.308211	−	0.223929i	−0.731129	+	0.682240i	$0.761006\pi$
$350$	−103.774	+	33.7182i	−0.296497	+	0.0963378i
$351$	109.314	−	27.1185i	0.311435	−	0.0772608i
$352$		0			0
$353$		−	172.864i		−	0.489699i	−0.969561	−	0.244850i	$-0.921261\pi$
$353$		−	172.864i		−	0.489699i	0.969561	−	0.244850i	$-0.0787386\pi$
$354$	−82.3395	−	10.6294i	−0.232597	−	0.0300266i
$355$	−5.22778	−	3.79820i	−0.0147261	−	0.0106992i
$356$	42.4089	+	58.3708i	0.119126	+	0.163963i
$357$	577.254	−	611.373i	1.61696	−	1.71253i
$358$	−18.2420	+	56.1430i	−0.0509552	+	0.156824i
$359$	354.287	+	487.634i	0.986871	+	1.35831i	0.933045	+	0.359761i	$0.117142\pi$
$359$	354.287	+	487.634i	0.986871	+	1.35831i	0.0538262	+	0.998550i	$0.482858\pi$
$360$	−17.1849	−	299.092i	−0.0477358	−	0.830810i
$361$	−78.8242	−	242.596i	−0.218350	−	0.672011i
$362$			73.6117i			0.203347i
$363$		0			0
$364$	−138.177			−0.379606
$365$	−576.932	+	187.457i	−1.58064	+	0.513580i
$366$	23.0079	+	42.1220i	0.0628630	+	0.115088i
$367$	−201.333	+	146.277i	−0.548592	+	0.398575i	−0.827266	−	0.561810i	$-0.810105\pi$
$367$	−201.333	+	146.277i	−0.548592	+	0.398575i	0.278674	+	0.960386i	$0.410105\pi$
$368$	282.632	+	91.8327i	0.768021	+	0.249545i
$369$	−114.382	−	293.550i	−0.309979	−	0.795529i
$370$	52.0227	−	37.7967i	0.140602	−	0.102153i
$371$	−332.505	+	457.654i	−0.896239	+	1.23357i
$372$	−185.861	−	23.9933i	−0.499626	−	0.0644981i
$373$	−677.639			−1.81673			−0.908364	−	0.418181i	$-0.862668\pi$
$373$	−677.639			−1.81673			−0.908364	+	0.418181i	$0.862668\pi$
$374$		0			0
$375$	−138.638	−	65.6992i	−0.369702	−	0.175198i
$376$	16.5729	+	51.0063i	0.0440770	+	0.135655i
$377$	−39.5963	+	54.4996i	−0.105030	+	0.144561i
$378$	−131.692	−	110.767i	−0.348391	−	0.293034i
$379$	−35.1742	+	108.255i	−0.0928079	+	0.285633i	−0.986676	−	0.162696i	$-0.947981\pi$
$379$	−35.1742	+	108.255i	−0.0928079	+	0.285633i	0.893868	+	0.448330i	$0.147981\pi$
$380$	−224.679	−	73.0026i	−0.591261	−	0.192112i
$381$	80.5268	+	428.463i	0.211357	+	1.12457i
$382$	−15.7739	−	11.4604i	−0.0412929	−	0.0300011i
$383$	−573.154	+	186.229i	−1.49649	+	0.486238i	−0.938991	−	0.343942i	$-0.888238\pi$
$383$	−573.154	+	186.229i	−1.49649	+	0.486238i	−0.557496	+	0.830180i	$0.688238\pi$
$384$	−344.903	−	163.446i	−0.898184	−	0.425640i
$385$		0			0
$386$		−	8.63898i		−	0.0223808i
$387$	−312.938	+	487.235i	−0.808626	+	1.25901i
$388$	−543.896	−	395.163i	−1.40179	−	1.01846i
$389$	−267.543	−	368.242i	−0.687772	−	0.946637i	0.312222	−	0.950009i	$-0.398927\pi$
$389$	−267.543	−	368.242i	−0.687772	−	0.946637i	−0.999994	+	0.00337225i	$0.998927\pi$
$390$	−40.1868	−	37.9441i	−0.103043	−	0.0972924i
$391$	−257.875	+	793.658i	−0.659527	+	2.02982i
$392$	116.709	+	160.636i	0.297727	+	0.409786i
$393$	−250.442	−	458.501i	−0.637257	−	1.16667i
$394$	−70.8035	−	217.911i	−0.179704	−	0.553073i
$395$			733.867i			1.85789i
$396$		0			0
$397$	327.783			0.825649			0.412824	−	0.910811i	$-0.364542\pi$
$397$	327.783			0.825649			0.412824	+	0.910811i	$0.364542\pi$
$398$	118.998	−	38.6647i	0.298989	−	0.0971474i
$399$	−253.772	+	138.615i	−0.636020	+	0.347406i
$400$	147.609	−	107.245i	0.369024	−	0.268111i
$401$	−239.706	−	77.8852i	−0.597770	−	0.194227i	−0.00552464	−	0.999985i	$-0.501759\pi$
$401$	−239.706	−	77.8852i	−0.597770	−	0.194227i	−0.592246	+	0.805757i	$0.701759\pi$
$402$	−43.2214	+	45.7760i	−0.107516	+	0.113871i
$403$	−59.6035	+	43.3045i	−0.147899	+	0.107455i
$404$	98.9652	−	136.214i	0.244963	−	0.337163i
$405$	60.2105	+	522.232i	0.148668	+	1.28946i
$406$	102.926			0.253513
$407$		0			0
$408$	197.194	−	416.119i	0.483319	−	1.01990i
$409$	140.226	+	431.571i	0.342851	+	1.05519i	0.962724	+	0.270485i	$0.0871840\pi$
$409$	140.226	+	431.571i	0.342851	+	1.05519i	−0.619873	+	0.784702i	$0.712816\pi$
$410$	−90.8735	+	125.077i	−0.221643	+	0.305065i
$411$	−239.689	+	45.0481i	−0.583185	+	0.109606i
$412$	57.5722	−	177.189i	0.139738	−	0.430071i
$413$	−362.222	−	117.693i	−0.877051	−	0.284971i
$414$	165.187	+	43.3716i	0.399002	+	0.104762i
$415$	546.426	+	397.001i	1.31669	+	0.956630i
$416$	−110.163	+	35.7942i	−0.264816	+	0.0860438i
$417$	−0.874924	+	1.84626i	−0.00209814	+	0.00442748i
$418$		0			0
$419$			295.753i			0.705855i	0.935651	+	0.352927i	$0.114814\pi$
$419$			295.753i			0.705855i	−0.935651	+	0.352927i	$0.885186\pi$
$420$	82.5722	−	639.635i	0.196600	−	1.52294i
$421$	−185.253	−	134.594i	−0.440030	−	0.319701i	0.345617	−	0.938376i	$-0.387670\pi$
$421$	−185.253	−	134.594i	−0.440030	−	0.319701i	−0.785647	+	0.618675i	$0.787670\pi$
$422$	−72.0028	−	99.1033i	−0.170623	−	0.234842i
$423$	−34.1673	−	87.6869i	−0.0807737	−	0.207298i
$424$	−95.7329	+	294.636i	−0.225785	+	0.694896i
$425$	301.153	+	414.502i	0.708596	+	0.975298i
$426$	−1.78393	+	0.974415i	−0.00418762	+	0.00228736i
$427$	68.0393	+	209.403i	0.159343	+	0.490406i
$428$			241.635i			0.564567i
$429$		0			0
$430$	284.169			0.660859
$431$	−531.608	+	172.730i	−1.23343	+	0.400766i	−0.851956	−	0.523614i	$-0.824583\pi$
$431$	−531.608	+	172.730i	−1.23343	+	0.400766i	−0.381474	+	0.924380i	$0.624583\pi$
$432$	266.666	+	108.105i	0.617282	+	0.250243i
$433$	−233.218	+	169.443i	−0.538609	+	0.391322i	−0.823568	−	0.567217i	$-0.808020\pi$
$433$	−233.218	+	169.443i	−0.538609	+	0.391322i	0.284959	+	0.958540i	$0.408020\pi$
$434$	107.056	+	34.7845i	0.246672	+	0.0801487i
$435$	−228.623	−	215.864i	−0.525569	−	0.496239i
$436$	−107.948	+	78.4288i	−0.247587	+	0.179883i
$437$	168.685	−	232.175i	0.386007	−	0.531294i
$438$	−24.4312	+	189.253i	−0.0557791	+	0.432085i
$439$	179.800			0.409567			0.204784	−	0.978807i	$-0.434351\pi$
$439$	179.800			0.409567			0.204784	+	0.978807i	$0.434351\pi$
$440$		0			0
$441$	−220.625	−	269.662i	−0.500284	−	0.611479i
$442$	−26.2517	−	80.7945i	−0.0593931	−	0.182793i
$443$	−165.331	+	227.558i	−0.373207	+	0.513676i	−0.953769	−	0.300541i	$-0.902833\pi$
$443$	−165.331	+	227.558i	−0.373207	+	0.513676i	0.580562	+	0.814216i	$0.302833\pi$
$444$	28.5354	+	151.830i	0.0642689	+	0.341958i
$445$	−40.9113	+	125.912i	−0.0919356	+	0.282949i
$446$	−170.254	−	55.3189i	−0.381735	−	0.124033i
$447$	583.580	−	109.680i	1.30555	−	0.245370i
$448$	−179.815	−	130.643i	−0.401372	−	0.291614i
$449$	−264.108	+	85.8140i	−0.588214	+	0.191122i	−0.587977	−	0.808878i	$-0.700075\pi$
$449$	−264.108	+	85.8140i	−0.588214	+	0.191122i	−0.000237150		1.00000i	$0.500075\pi$
$450$	81.1552	−	66.3974i	0.180345	−	0.147550i
$451$		0			0
$452$			602.265i			1.33245i
$453$	−264.550	−	34.1515i	−0.583995	−	0.0753896i
$454$	4.97093	+	3.61160i	0.0109492	+	0.00795506i
$455$	−149.031	−	205.123i	−0.327541	−	0.450821i
$456$	−108.717	+	115.143i	−0.238415	+	0.252506i
$457$	106.989	−	329.280i	0.234113	−	0.720524i	−0.763125	−	0.646251i	$-0.776336\pi$
$457$	106.989	−	329.280i	0.234113	−	0.720524i	0.997238	−	0.0742739i	$-0.0236639\pi$
$458$	−140.971	−	194.030i	−0.307797	−	0.423646i
$459$	−303.569	+	748.824i	−0.661370	+	1.63142i
$460$	197.798	+	608.759i	0.429995	+	1.32339i
$461$			67.1487i			0.145659i	0.997344	+	0.0728294i	$0.0232029\pi$
$461$			67.1487i			0.145659i	−0.997344	+	0.0728294i	$0.976797\pi$
$462$		0			0
$463$	−754.683			−1.62999			−0.814993	−	0.579471i	$-0.803259\pi$
$463$	−754.683			−1.62999			−0.814993	+	0.579471i	$0.803259\pi$
$464$	−163.684	+	53.1841i	−0.352767	+	0.114621i
$465$	−164.843	−	301.789i	−0.354501	−	0.649009i
$466$	19.4907	−	14.1609i	0.0418256	−	0.0303881i
$467$	275.211	+	89.4216i	0.589317	+	0.191481i	0.588470	−	0.808519i	$-0.299730\pi$
$467$	275.211	+	89.4216i	0.589317	+	0.191481i	0.000847110		1.00000i	$0.499730\pi$
$468$	123.723	−	48.2089i	0.264366	−	0.103010i
$469$	−233.652	+	169.758i	−0.498193	+	0.361958i
$470$	−27.1450	+	37.3618i	−0.0577552	+	0.0794933i
$471$	198.563	+	25.6330i	0.421577	+	0.0544226i
$472$	−208.578			−0.441902
$473$		0			0
$474$	208.612	+	98.8590i	0.440110	+	0.208563i
$475$	−54.4481	−	167.574i	−0.114627	−	0.352787i
$476$	582.679	−	801.988i	1.22411	−	1.68485i
$477$	138.052	−	525.792i	0.289418	−	1.10229i
$478$	27.5059	−	84.6545i	0.0575437	−	0.177101i
$479$	158.005	+	51.3391i	0.329865	+	0.107180i	0.469267	−	0.883056i	$-0.344518\pi$
$479$	158.005	+	51.3391i	0.329865	+	0.107180i	−0.139402	+	0.990236i	$0.544518\pi$
$480$	−99.8636	−	531.349i	−0.208049	−	1.10698i
$481$	49.1347	+	35.6985i	0.102151	+	0.0742172i
$482$	−87.0664	+	28.2896i	−0.180636	+	0.0586921i
$483$	707.997	+	335.512i	1.46583	+	0.694642i
$484$		0			0
$485$		−	1233.62i		−	2.54355i
$486$	156.563	+	53.2341i	0.322146	+	0.109535i
$487$	16.6332	+	12.0847i	0.0341545	+	0.0248147i	0.604732	−	0.796429i	$-0.293280\pi$
$487$	16.6332	+	12.0847i	0.0341545	+	0.0248147i	−0.570577	+	0.821244i	$0.693280\pi$
$488$	70.8755	+	97.5517i	0.145237	+	0.199901i
$489$	305.043	+	288.019i	0.623810	+	0.588996i
$490$	−52.8350	+	162.609i	−0.107827	+	0.331856i
$491$	−281.310	−	387.190i	−0.572933	−	0.788574i	0.419966	−	0.907540i	$-0.362042\pi$
$491$	−281.310	−	387.190i	−0.572933	−	0.788574i	−0.992898	+	0.118966i	$0.962042\pi$
$492$	−178.052	−	325.972i	−0.361895	−	0.662545i
$493$	−149.346	−	459.640i	−0.302933	−	0.932333i
$494$			29.2151i			0.0591398i
$495$		0			0
$496$	−188.225			−0.379486
$497$	−8.86853	+	2.88156i	−0.0178441	+	0.00579791i
$498$	186.462	−	101.849i	0.374422	−	0.204517i
$499$	206.262	−	149.858i	0.413352	−	0.300317i	−0.361606	−	0.932331i	$-0.617771\pi$
$499$	206.262	−	149.858i	0.413352	−	0.300317i	0.774957	+	0.632014i	$0.217771\pi$
$500$	−172.021	−	55.8932i	−0.344043	−	0.111786i
$501$	−282.984	+	299.710i	−0.564838	+	0.598224i
$502$	222.733	−	161.825i	0.443691	−	0.322361i
$503$	−150.204	+	206.738i	−0.298616	+	0.411010i	−0.931789	−	0.363001i	$-0.881752\pi$
$503$	−150.204	+	206.738i	−0.298616	+	0.411010i	0.633173	+	0.774011i	$0.281752\pi$
$504$	−363.755	−	233.630i	−0.721736	−	0.463552i
$505$	308.949			0.611781
$506$		0			0
$507$	−194.762	+	410.986i	−0.384146	+	0.810623i
$508$	158.831	+	488.830i	0.312659	+	0.962265i
$509$	−31.1173	+	42.8293i	−0.0611342	+	0.0841440i	−0.838489	−	0.544918i	$-0.816561\pi$
$509$	−31.1173	+	42.8293i	−0.0611342	+	0.0841440i	0.777355	+	0.629062i	$0.216561\pi$
$510$	389.695	−	73.2407i	0.764107	−	0.143609i
$511$	−270.512	+	832.550i	−0.529377	+	1.62926i
$512$	−489.392	−	159.013i	−0.955843	−	0.310572i
$513$	178.866	−	212.656i	0.348666	−	0.414533i
$514$	75.6160	+	54.9382i	0.147113	+	0.106884i
$515$	325.133	−	105.642i	0.631325	−	0.205130i
$516$	−292.362	+	616.942i	−0.566594	+	1.19562i
$517$		0			0
$518$		−	92.7942i		−	0.179139i
$519$	−0.406478	+	3.14873i	−0.000783194	+	0.00606691i
$520$	−112.335	−	81.6162i	−0.216029	−	0.156954i
$521$	512.433	+	705.303i	0.983557	+	1.35375i	0.934891	+	0.354934i	$0.115497\pi$
$521$	512.433	+	705.303i	0.983557	+	1.35375i	0.0486653	+	0.998815i	$0.484503\pi$
$522$	−92.1601	+	35.9103i	−0.176552	+	0.0687936i
$523$	219.180	−	674.565i	0.419081	−	1.28980i	−0.489467	−	0.872022i	$-0.662809\pi$
$523$	219.180	−	674.565i	0.419081	−	1.28980i	0.908549	−	0.417779i	$-0.137191\pi$
$524$	−362.040	−	498.305i	−0.690916	−	0.950964i
$525$	422.151	−	230.587i	0.804098	−	0.439214i
$526$	−29.0205	−	89.3158i	−0.0551720	−	0.169802i
$527$		−	528.555i		−	1.00295i
$528$		0			0
$529$	−248.573			−0.469892
$530$	−253.711	+	82.4356i	−0.478699	+	0.155539i
$531$	365.396	−	20.9945i	0.688128	−	0.0395377i
$532$	−275.803	+	200.383i	−0.518427	+	0.376659i
$533$	−138.874	−	45.1229i	−0.260551	−	0.0846583i
$534$	30.2812	+	28.5912i	0.0567063	+	0.0535416i
$535$	−358.707	+	260.616i	−0.670481	+	0.487133i
$536$	−92.9675	+	127.959i	−0.173447	+	0.238729i
$537$	33.3184	−	258.097i	0.0620455	−	0.480627i
$538$	−21.0236			−0.0390774
$539$		0			0
$540$	149.229	+	601.538i	0.276351	+	1.11396i
$541$	−52.7194	−	162.254i	−0.0974480	−	0.299914i	0.890436	−	0.455109i	$-0.150400\pi$
$541$	−52.7194	−	162.254i	−0.0974480	−	0.299914i	−0.987884	+	0.155195i	$0.950400\pi$
$542$	−80.1933	+	110.377i	−0.147958	+	0.203647i
$543$	−59.9404	−	318.927i	−0.110387	−	0.587343i
$544$	256.797	−	790.338i	0.472052	−	1.45283i
$545$	−232.856	−	75.6594i	−0.427258	−	0.138825i
$546$	−78.3852	+	14.7320i	−0.143563	+	0.0269817i
$547$	85.8184	+	62.3507i	0.156889	+	0.113987i	0.663460	−	0.748212i	$-0.269087\pi$
$547$	85.8184	+	62.3507i	0.156889	+	0.113987i	−0.506571	+	0.862198i	$0.669087\pi$
$548$	−273.460	+	88.8525i	−0.499014	+	0.162140i
$549$	−133.982	−	163.761i	−0.244047	−	0.298290i
$550$		0			0
$551$			166.205i			0.301642i
$552$	425.534	+	54.9333i	0.770895	+	0.0995169i
$553$	856.762	+	622.474i	1.54930	+	1.12563i
$554$	−63.8435	−	87.8731i	−0.115241	−	0.158616i
$555$	−194.614	+	206.117i	−0.350657	+	0.371383i
$556$	−0.744335	+	2.29083i	−0.00133873	+	0.00412019i
$557$	431.366	+	593.724i	0.774445	+	1.06593i	0.995873	+	0.0907553i	$0.0289281\pi$
$557$	431.366	+	593.724i	0.774445	+	1.06593i	−0.221428	+	0.975177i	$0.571072\pi$
$558$	−107.994	+	6.20500i	−0.193537	+	0.0111201i
$559$	82.9383	+	255.258i	0.148369	+	0.456633i
$560$		−	647.771i		−	1.15673i
$561$		0			0
$562$	−270.320			−0.480997
$563$	944.916	−	307.022i	1.67836	−	0.545332i	0.693767	−	0.720200i	$-0.255950\pi$
$563$	944.916	−	307.022i	1.67836	−	0.545332i	0.984592	+	0.174868i	$0.0559497\pi$
$564$	−53.1863	−	97.3717i	−0.0943019	−	0.172645i
$565$	−894.065	+	649.576i	−1.58242	+	1.14969i
$566$	−43.7452	−	14.2137i	−0.0772884	−	0.0251125i
$567$	660.758	+	372.670i	1.16536	+	0.657266i
$568$	−4.13145	+	3.00168i	−0.00727368	+	0.00528464i
$569$	626.713	−	862.596i	1.10143	−	1.51599i	0.267950	−	0.963433i	$-0.413654\pi$
$569$	626.713	−	862.596i	1.10143	−	1.51599i	0.833478	−	0.552553i	$-0.186346\pi$
$570$	−135.240	−	17.4585i	−0.237263	−	0.0306289i
$571$	−409.079			−0.716425			−0.358213	−	0.933640i	$-0.616614\pi$
$571$	−409.079			−0.716425			−0.358213	+	0.933640i	$0.616614\pi$
$572$		0			0
$573$	77.6733	+	36.8086i	0.135556	+	0.0642384i
$574$	68.9424	+	212.183i	0.120109	+	0.369657i
$575$	−280.609	+	386.225i	−0.488015	+	0.671696i
$576$	206.587	+	54.2416i	0.358657	+	0.0941694i
$577$	142.077	−	437.267i	0.246233	−	0.757828i	−0.749198	−	0.662346i	$-0.769561\pi$
$577$	142.077	−	437.267i	0.246233	−	0.757828i	0.995431	−	0.0954818i	$-0.0304392\pi$
$578$	392.596	+	127.562i	0.679232	+	0.220696i
$579$	7.03452	+	37.4289i	0.0121494	+	0.0646440i
$580$	−299.903	−	217.892i	−0.517075	−	0.375677i
$581$	926.969	−	301.191i	1.59547	−	0.518400i
$582$	−350.674	−	166.181i	−0.602533	−	0.285534i
$583$		0			0
$584$			479.406i			0.820901i
$585$	205.009	+	131.672i	0.350442	+	0.225080i
$586$	−201.289	−	146.245i	−0.343497	−	0.249565i
$587$	34.6014	+	47.6247i	0.0589461	+	0.0811324i	0.837472	−	0.546480i	$-0.184032\pi$
$587$	34.6014	+	47.6247i	0.0589461	+	0.0811324i	−0.778526	+	0.627612i	$0.784032\pi$
$588$	−298.672	−	282.004i	−0.507946	−	0.479599i
$589$	−56.1699	+	172.873i	−0.0953649	+	0.293503i
$590$	−105.570	−	145.305i	−0.178932	−	0.246279i
$591$	484.200	+	886.457i	0.819289	+	1.49993i
$592$	47.9487	+	147.571i	0.0809945	+	0.249275i
$593$		−	149.728i		−	0.252493i	−0.991999	−	0.126247i	$-0.959707\pi$
$593$		−	149.728i		−	0.252493i	0.991999	−	0.126247i	$-0.0402931\pi$
$594$		0			0
$595$	1819.01			3.05715
$596$	665.803	−	216.333i	1.11712	−	0.362974i
$597$	−484.081	+	264.414i	−0.810855	+	0.442905i
$598$	64.0394	−	46.5274i	0.107089	−	0.0778049i
$599$	421.867	+	137.073i	0.704286	+	0.228836i	0.639197	−	0.769043i	$-0.279267\pi$
$599$	421.867	+	137.073i	0.704286	+	0.228836i	0.0650891	+	0.997879i	$0.479267\pi$
$600$	180.852	−	191.541i	0.301419	−	0.319235i
$601$	334.929	−	243.340i	0.557286	−	0.404892i	−0.273178	−	0.961963i	$-0.588075\pi$
$601$	334.929	−	243.340i	0.557286	−	0.404892i	0.830465	+	0.557071i	$0.188075\pi$
$602$	241.036	−	331.757i	0.400392	−	0.551092i
$603$	149.985	−	233.522i	0.248731	−	0.387266i
$604$	−314.483			−0.520668
$605$		0			0
$606$	41.6185	−	87.8232i	0.0686774	−	0.144923i
$607$	−117.688	−	362.207i	−0.193885	−	0.596716i	−0.999988	−	0.00494086i	$-0.998427\pi$
$607$	−117.688	−	362.207i	−0.193885	−	0.596716i	0.806103	−	0.591775i	$-0.201573\pi$
$608$	−167.980	+	231.204i	−0.276282	+	0.380270i
$609$	−445.933	+	83.8104i	−0.732239	+	0.137620i
$610$	−32.0858	+	98.7500i	−0.0525997	+	0.161885i
$611$	−41.4832	−	13.4787i	−0.0678940	−	0.0220601i
$612$	−241.922	+	921.393i	−0.395297	+	1.50554i
$613$	−91.3802	−	66.3916i	−0.149071	−	0.108306i	0.510750	−	0.859729i	$-0.329368\pi$
$613$	−91.3802	−	66.3916i	−0.149071	−	0.108306i	−0.659821	+	0.751423i	$0.729368\pi$
$614$	313.353	−	101.815i	0.510347	−	0.165822i
$615$	291.868	−	615.898i	0.474582	−	1.00146i
$616$		0			0
$617$		−	378.251i		−	0.613049i	−0.951863	−	0.306524i	$-0.900834\pi$
$617$		−	378.251i		−	0.613049i	0.951863	−	0.306524i	$-0.0991661\pi$
$618$	13.7683	−	106.655i	0.0222788	−	0.172580i
$619$	23.7034	+	17.2215i	0.0382931	+	0.0278216i	0.606767	−	0.794880i	$-0.292466\pi$
$619$	23.7034	+	17.2215i	0.0382931	+	0.0278216i	−0.568474	+	0.822701i	$0.692466\pi$
$620$	−238.298	−	327.989i	−0.384352	−	0.529015i
$621$	−750.998	−	53.4022i	−1.20934	−	0.0859939i
$622$	70.6899	−	217.561i	0.113649	−	0.349777i
$623$	112.296	+	154.563i	0.180251	+	0.248094i
$624$	117.044	−	63.9317i	0.187570	−	0.102455i
$625$	−234.823	−	722.710i	−0.375716	−	1.15634i
$626$			332.837i			0.531689i
$627$		0			0
$628$	236.041			0.375862
$629$	−414.394	+	134.645i	−0.658814	+	0.214062i
$630$	−21.3543	−	371.658i	−0.0338957	−	0.589933i
$631$	787.079	−	571.847i	1.24735	−	0.906254i	0.249287	−	0.968430i	$-0.419804\pi$
$631$	787.079	−	571.847i	1.24735	−	0.906254i	0.998065	+	0.0621752i	$0.0198037\pi$
$632$	551.580	+	179.219i	0.872754	+	0.283575i
$633$	392.654	+	370.741i	0.620306	+	0.585688i
$634$	86.0626	−	62.5281i	0.135745	−	0.0986248i
$635$	−554.363	+	763.015i	−0.873012	+	1.20160i
$636$	82.0548	−	635.627i	0.129017	−	0.999414i
$637$	−161.486			−0.253510
$638$		0			0
$639$	6.93552	−	5.67432i	0.0108537	−	0.00888000i
$640$	−255.150	−	785.271i	−0.398672	−	1.22699i
$641$	−513.946	+	707.386i	−0.801788	+	1.10357i	0.190751	+	0.981639i	$0.438908\pi$
$641$	−513.946	+	707.386i	−0.801788	+	1.10357i	−0.992539	+	0.121928i	$0.961092\pi$
$642$	25.7624	+	137.075i	0.0401284	+	0.213513i
$643$	225.637	−	694.441i	0.350914	−	1.08000i	−0.607428	−	0.794375i	$-0.707798\pi$
$643$	225.637	−	694.441i	0.350914	−	1.08000i	0.958341	−	0.285626i	$-0.0922015\pi$
$644$	878.478	+	285.435i	1.36410	+	0.443222i
$645$	−1231.18	+	231.393i	−1.90881	+	0.358748i
$646$	−169.567	−	123.197i	−0.262487	−	0.190708i
$647$	−706.330	+	229.501i	−1.09170	+	0.354715i	−0.798903	−	0.601459i	$-0.794586\pi$
$647$	−706.330	+	229.501i	−1.09170	+	0.354715i	−0.292798	+	0.956174i	$0.594586\pi$
$648$	407.218	+	82.2808i	0.628423	+	0.126977i
$649$		0			0
$650$		−	48.5994i		−	0.0747684i
$651$	−492.150	−	63.5330i	−0.755991	−	0.0975929i
$652$	400.150	+	290.726i	0.613727	+	0.445899i
$653$	653.864	+	899.967i	1.00132	+	1.37820i	0.924510	+	0.381158i	$0.124475\pi$
$653$	653.864	+	899.967i	1.00132	+	1.37820i	0.0768135	+	0.997045i	$0.475525\pi$
$654$	−52.8752	+	56.0004i	−0.0808489	+	0.0856276i
$655$	349.256	−	1074.90i	0.533215	−	1.64107i
$656$	−219.279	−	301.812i	−0.334267	−	0.460079i
$657$	−48.2549	−	839.845i	−0.0734474	−	1.27830i
$658$	20.5939	+	63.3815i	0.0312977	+	0.0963244i
$659$		−	829.020i		−	1.25800i	−0.777407	−	0.628998i	$-0.783465\pi$
$659$		−	829.020i		−	1.25800i	0.777407	−	0.628998i	$-0.216535\pi$
$660$		0			0
$661$	−1040.95			−1.57480			−0.787402	−	0.616439i	$-0.788575\pi$
$661$	−1040.95			−1.57480			−0.787402	+	0.616439i	$0.788575\pi$
$662$	26.0691	−	8.47037i	0.0393793	−	0.0127951i
$663$	179.526	+	328.671i	0.270779	+	0.495733i
$664$	431.834	−	313.746i	0.650352	−	0.472508i
$665$	−594.938	−	193.307i	−0.894643	−	0.290687i
$666$	32.3753	+	83.0879i	0.0486116	+	0.124757i
$667$	364.320	−	264.694i	0.546207	−	0.396843i
$668$	−285.643	+	393.154i	−0.427610	+	0.588555i
$669$	782.681	+	101.038i	1.16993	+	0.151029i
$670$	−136.196			−0.203278
$671$		0			0
$672$	−705.035	−	334.109i	−1.04916	−	0.497186i
$673$	78.5875	+	241.868i	0.116772	+	0.359387i	0.992312	−	0.123758i	$-0.0394945\pi$
$673$	78.5875	+	241.868i	0.116772	+	0.359387i	−0.875541	+	0.483145i	$0.839495\pi$
$674$	4.76629	−	6.56024i	0.00707165	−	0.00973330i
$675$	−297.544	+	353.754i	−0.440806	+	0.524080i
$676$	−165.692	+	509.949i	−0.245107	+	0.754362i
$677$	964.286	+	313.315i	1.42435	+	0.462800i	0.916982	−	0.398929i	$-0.130618\pi$
$677$	964.286	+	313.315i	1.42435	+	0.462800i	0.507369	+	0.861729i	$0.330618\pi$
$678$	64.2119	+	341.655i	0.0947078	+	0.503916i
$679$	−1440.21	−	1046.37i	−2.12107	−	1.54105i
$680$	947.415	−	307.834i	1.39326	−	0.452697i
$681$	−24.4777	−	11.5997i	−0.0359438	−	0.0170334i
$682$		0			0
$683$			561.211i			0.821685i	0.911706	+	0.410842i	$0.134765\pi$
$683$			561.211i			0.821685i	−0.911706	+	0.410842i	$0.865235\pi$
$684$	177.042	−	275.649i	0.258833	−	0.402995i
$685$	−426.843	−	310.120i	−0.623129	−	0.452730i
$686$	−38.5377	−	53.0426i	−0.0561775	−	0.0773216i
$687$	768.758	+	725.856i	1.11901	+	1.05656i
$688$	−211.894	+	652.144i	−0.307986	+	0.947883i
$689$	−148.097	−	203.838i	−0.214945	−	0.295847i
$690$	177.111	+	324.250i	0.256683	+	0.469927i
$691$	176.558	+	543.389i	0.255510	+	0.786380i	0.993729	+	0.111818i	$0.0356674\pi$
$691$	176.558	+	543.389i	0.255510	+	0.786380i	−0.738218	+	0.674562i	$0.764333\pi$
$692$			3.74304i			0.00540902i
$693$		0			0
$694$	409.185			0.589603
$695$	−4.20355	+	1.36582i	−0.00604827	+	0.00196520i
$696$	−218.078	+	119.118i	−0.313330	+	0.171147i
$697$	847.516	−	615.757i	1.21595	−	0.883438i
$698$	−86.0521	−	27.9600i	−0.123284	−	0.0400573i
$699$	−72.9140	+	77.2236i	−0.104312	+	0.110477i
$700$	458.800	−	333.338i	0.655429	−	0.476197i
$701$	−415.641	+	572.080i	−0.592925	+	0.816092i	−0.995038	−	0.0994987i	$-0.968276\pi$
$701$	−415.641	+	572.080i	−0.592925	+	0.816092i	0.402112	+	0.915590i	$0.368276\pi$
$702$	65.0462	−	40.5391i	0.0926584	−	0.0577481i
$703$	149.844			0.213149
$704$		0			0
$705$	87.1843	−	183.976i	0.123666	−	0.260959i
$706$	−36.3517	−	111.879i	−0.0514897	−	0.158469i
$707$	262.054	−	360.687i	0.370657	−	0.510166i
$708$	424.075	−	79.7022i	0.598976	−	0.112574i
$709$	282.481	−	869.387i	0.398422	−	1.22622i	−0.527843	−	0.849342i	$-0.676999\pi$
$709$	282.481	−	869.387i	0.398422	−	1.22622i	0.926265	−	0.376874i	$-0.123001\pi$
$710$	−4.18220	−	1.35888i	−0.00589042	−	0.00191391i
$711$	−984.322	−	258.445i	−1.38442	−	0.363495i
$712$	84.6456	+	61.4986i	0.118884	+	0.0863745i
$713$	468.393	−	152.190i	0.656933	−	0.213450i
$714$	245.038	−	517.078i	0.343190	−	0.724199i
$715$		0			0
$716$		−	306.812i		−	0.428509i
$717$	−50.2388	+	389.168i	−0.0700680	+	0.542773i
$718$	331.843	+	241.098i	0.462177	+	0.335791i
$719$	−495.361	−	681.806i	−0.688958	−	0.948270i	0.311039	−	0.950397i	$-0.399323\pi$
$719$	−495.361	−	681.806i	−0.688958	−	0.948270i	−0.999998	+	0.00212717i	$0.999323\pi$
$720$	226.003	+	580.015i	0.313893	+	0.805576i
$721$	152.448	−	469.187i	0.211440	−	0.650745i
$722$	−102.032	−	140.434i	−0.141318	−	0.194508i
$723$	354.185	−	193.463i	0.489882	−	0.267583i
$724$	−118.226	−	363.862i	−0.163296	−	0.502572i
$725$		−	276.482i		−	0.381355i
$726$		0			0
$727$	958.596			1.31856			0.659282	−	0.751895i	$-0.270860\pi$
$727$	958.596			1.31856			0.659282	+	0.751895i	$0.270860\pi$
$728$	−190.568	+	61.9192i	−0.261769	+	0.0850539i
$729$	−721.665	−	103.154i	−0.989938	−	0.141501i
$730$	−333.976	+	242.647i	−0.457501	+	0.332394i
$731$	−1831.28	−	595.020i	−2.50518	−	0.813981i
$732$	−181.379	−	171.256i	−0.247785	−	0.233957i
$733$	815.585	−	592.557i	1.11267	−	0.808400i	0.129586	−	0.991568i	$-0.458635\pi$
$733$	815.585	−	592.557i	1.11267	−	0.808400i	0.983082	+	0.183168i	$0.0586352\pi$
$734$	−99.5441	+	137.011i	−0.135619	+	0.186663i
$735$	96.5016	−	747.537i	0.131295	−	1.01706i
$736$	774.320			1.05207
$737$		0			0
$738$	−135.760	−	165.935i	−0.183957	−	0.224844i
$739$	−350.139	−	1077.62i	−0.473802	−	1.45821i	−0.847567	−	0.530688i	$-0.821933\pi$
$739$	−350.139	−	1077.62i	−0.473802	−	1.45821i	0.373765	−	0.927523i	$-0.378067\pi$
$740$	−196.443	+	270.381i	−0.265464	+	0.365380i
$741$	−23.7892	−	126.576i	−0.0321041	−	0.170818i
$742$	−118.960	+	366.121i	−0.160323	+	0.493424i
$743$	−12.0434	−	3.91313i	−0.0162091	−	0.00526666i	0.300901	−	0.953655i	$-0.402713\pi$
$743$	−12.0434	−	3.91313i	−0.0162091	−	0.00526666i	−0.317110	+	0.948389i	$0.602713\pi$
$744$	−267.084	+	50.1968i	−0.358984	+	0.0674688i
$745$	1039.25	+	755.060i	1.39497	+	1.01350i
$746$	−438.575	+	142.502i	−0.587902	+	0.191021i
$747$	−724.925	+	593.100i	−0.970449	+	0.793976i
$748$		0			0
$749$			639.835i			0.854253i
$750$	−103.544	−	13.3668i	−0.138059	−	0.0178224i
$751$	155.182	+	112.746i	0.206633	+	0.150128i	0.686289	−	0.727329i	$-0.259238\pi$
$751$	155.182	+	112.746i	0.206633	+	0.150128i	−0.479656	+	0.877457i	$0.659238\pi$
$752$	−65.5011	−	90.1546i	−0.0871026	−	0.119886i
$753$	−833.234	+	882.483i	−1.10655	+	1.17196i
$754$	−14.1663	+	43.5994i	−0.0187882	+	0.0578242i
$755$	−339.188	−	466.852i	−0.449255	−	0.618346i
$756$	828.852	+	336.012i	1.09636	+	0.444460i
$757$	159.304	+	490.289i	0.210442	+	0.647673i	0.999446	+	0.0332854i	$0.0105970\pi$
$757$	159.304	+	490.289i	0.210442	+	0.647673i	−0.789004	+	0.614388i	$0.789403\pi$
$758$			77.4605i			0.102191i
$759$		0			0
$760$	−342.582			−0.450766
$761$	979.307	−	318.196i	1.28687	−	0.418129i	0.415874	−	0.909422i	$-0.363476\pi$
$761$	979.307	−	318.196i	1.28687	−	0.418129i	0.870994	+	0.491294i	$0.163476\pi$
$762$	142.220	+	260.371i	0.186640	+	0.341694i
$763$	−285.840	+	207.675i	−0.374627	+	0.272182i
$764$	96.3766	+	31.3146i	0.126147	+	0.0409877i
$765$	−1628.74	+	634.639i	−2.12907	+	0.829594i
$766$	−331.789	+	241.059i	−0.433145	+	0.314698i
$767$	99.7094	−	137.238i	0.129999	−	0.178928i
$768$	24.8456	+	3.20739i	0.0323511	+	0.00417629i
$769$	−1094.35			−1.42308			−0.711539	−	0.702647i	$-0.752001\pi$
$769$	−1094.35			−1.42308			−0.711539	+	0.702647i	$0.752001\pi$
$770$		0			0
$771$	−372.346	−	176.451i	−0.482938	−	0.228860i
$772$	13.8749	+	42.7024i	0.0179726	+	0.0553140i
$773$	303.368	−	417.550i	0.392455	−	0.540168i	−0.566376	−	0.824147i	$-0.691655\pi$
$773$	303.368	−	417.550i	0.392455	−	0.540168i	0.958830	+	0.283980i	$0.0916548\pi$
$774$	−100.076	+	381.151i	−0.129297	+	0.492444i
$775$	93.4390	−	287.576i	0.120566	−	0.371065i
$776$	−927.200	−	301.265i	−1.19485	−	0.388229i
$777$	75.5602	+	402.036i	0.0972461	+	0.517421i
$778$	−250.595	−	182.068i	−0.322101	−	0.234020i
$779$	−342.632	+	111.328i	−0.439836	+	0.142911i
$780$	259.584	+	123.014i	0.332800	+	0.157710i
$781$		0			0
$782$			567.892i			0.726205i
$783$	370.048	−	230.627i	0.472603	−	0.294543i
$784$	−333.777	−	242.503i	−0.425736	−	0.309315i
$785$	254.584	+	350.404i	0.324310	+	0.446375i
$786$	−258.507	−	244.080i	−0.328889	−	0.310535i
$787$	224.489	−	690.907i	0.285247	−	0.877900i	−0.701078	−	0.713085i	$-0.747297\pi$
$787$	224.489	−	690.907i	0.285247	−	0.877900i	0.986325	−	0.164815i	$-0.0527026\pi$
$788$	699.962	+	963.415i	0.888277	+	1.22261i
$789$	198.461	+	363.335i	0.251535	+	0.460501i
$790$	154.326	+	474.966i	0.195349	+	0.601222i
$791$			1594.77i			2.01614i
$792$		0			0
$793$	−98.0678			−0.123667
$794$	212.144	−	68.9298i	0.267184	−	0.0868134i
$795$	1032.09	−	563.748i	1.29823	−	0.709117i
$796$	−526.106	+	382.238i	−0.660937	+	0.480199i
$797$	1395.59	+	453.455i	1.75105	+	0.568952i	0.996212	−	0.0869550i	$-0.0277136\pi$
$797$	1395.59	+	453.455i	1.75105	+	0.568952i	0.754842	+	0.655907i	$0.227714\pi$
$798$	−135.094	+	143.079i	−0.169291	+	0.179297i
$799$	253.163	−	183.934i	0.316850	−	0.230205i
$800$	279.435	−	384.610i	0.349294	−	0.480762i
$801$	−154.476	−	99.2160i	−0.192854	−	0.123865i
$802$	−171.519			−0.213864
$803$		0			0
$804$	140.123	−	295.687i	0.174283	−	0.367770i
$805$	523.757	+	1611.96i	0.650630	+	2.00243i
$806$	−29.4694	+	40.5612i	−0.0365625	+	0.0503240i
$807$	91.0861	−	17.1191i	0.112870	−	0.0212132i
$808$	75.4493	−	232.209i	0.0933778	−	0.287387i
$809$	24.4139	+	7.93257i	0.0301779	+	0.00980540i	0.324067	−	0.946034i	$-0.394950\pi$
$809$	24.4139	+	7.93257i	0.0301779	+	0.00980540i	−0.293889	+	0.955840i	$0.594950\pi$
$810$	148.790	+	325.332i	0.183691	+	0.401644i
$811$	−531.579	−	386.215i	−0.655461	−	0.476221i	0.209666	−	0.977773i	$-0.432762\pi$
$811$	−531.579	−	386.215i	−0.655461	−	0.476221i	−0.865127	+	0.501553i	$0.832762\pi$
$812$	−508.763	+	165.307i	−0.626555	+	0.203580i
$813$	257.565	−	543.513i	0.316808	−	0.668528i
$814$		0			0
$815$			907.588i			1.11360i
$816$	−122.500	+	948.928i	−0.150122	+	1.16290i
$817$	535.720	+	389.224i	0.655716	+	0.476406i
$818$	181.511	+	249.829i	0.221897	+	0.305414i
$819$	327.613	−	127.655i	0.400015	−	0.155866i
$820$	248.304	−	764.203i	0.302810	−	0.931954i
$821$	−553.696	−	762.098i	−0.674417	−	0.928255i	0.325433	−	0.945565i	$-0.394490\pi$
$821$	−553.696	−	762.098i	−0.674417	−	0.928255i	−0.999850	+	0.0173098i	$0.994490\pi$
$822$	−145.656	+	79.5601i	−0.177197	+	0.0967884i
$823$	−63.1327	−	194.302i	−0.0767104	−	0.236090i	0.905347	−	0.424673i	$-0.139611\pi$
$823$	−63.1327	−	194.302i	−0.0767104	−	0.236090i	−0.982057	+	0.188582i	$0.939611\pi$
$824$		−	270.172i		−	0.327878i
$825$		0			0
$826$	−259.183			−0.313781
$827$	−110.504	+	35.9050i	−0.133620	+	0.0434159i	−0.375064	−	0.926999i	$-0.622379\pi$
$827$	−110.504	+	35.9050i	−0.133620	+	0.0434159i	0.241443	+	0.970415i	$0.422379\pi$
$828$	−886.175	+	50.9170i	−1.07026	+	0.0614939i
$829$	−1225.41	+	890.312i	−1.47818	+	1.07396i	−0.500040	+	0.866002i	$0.666681\pi$
$829$	−1225.41	+	890.312i	−1.47818	+	1.07396i	−0.978138	+	0.207957i	$0.933319\pi$
$830$	437.138	+	142.035i	0.526672	+	0.171126i
$831$	348.159	+	328.729i	0.418964	+	0.395583i
$832$	80.0892	−	58.1882i	0.0962610	−	0.0699377i
$833$	680.973	−	937.279i	0.817494	−	1.12518i
$834$	−0.178007	+	1.37891i	−0.000213437	+	0.00165337i
$835$	−891.721			−1.06793
$836$		0			0
$837$	462.837	−	114.821i	0.552972	−	0.137181i
$838$	62.1943	+	191.414i	0.0742175	+	0.228418i
$839$	494.807	−	681.043i	0.589758	−	0.811732i	−0.404965	−	0.914332i	$-0.632716\pi$
$839$	494.807	−	681.043i	0.589758	−	0.811732i	0.994723	+	0.102600i	$0.0327163\pi$
$840$	−172.751	−	919.162i	−0.205656	−	1.09424i
$841$	179.291	−	551.801i	0.213188	−	0.656125i
$842$	−148.201	−	48.1535i	−0.176011	−	0.0571894i
$843$	1171.18	−	220.116i	1.38930	−	0.261110i
$844$	515.077	+	374.225i	0.610280	+	0.443395i
$845$	−935.729	+	304.037i	−1.10737	+	0.359807i
$846$	−40.5532	−	49.5667i	−0.0479352	−	0.0585895i
$847$		0			0
$848$		−	643.713i		−	0.759095i
$849$	201.103	+	25.9609i	0.236870	+	0.0305782i
$850$	282.075	+	204.940i	0.331853	+	0.241106i
$851$	−238.638	−	328.457i	−0.280421	−	0.385966i
$852$	7.25295	−	7.68165i	0.00851285	−	0.00901602i
$853$	−111.793	+	344.062i	−0.131058	+	0.403356i	−0.994956	−	0.100311i	$-0.968016\pi$
$853$	−111.793	+	344.062i	−0.131058	+	0.403356i	0.863898	+	0.503667i	$0.168016\pi$
$854$	88.0714	+	121.220i	0.103128	+	0.141944i
$855$	600.151	−	34.4829i	0.701931	−	0.0403308i
$856$	108.281	+	333.253i	0.126496	+	0.389315i
$857$			519.778i			0.606509i	0.952910	+	0.303254i	$0.0980732\pi$
$857$			519.778i			0.606509i	−0.952910	+	0.303254i	$0.901927\pi$
$858$		0			0
$859$	−1258.77			−1.46538			−0.732692	−	0.680560i	$-0.761737\pi$
$859$	−1258.77			−1.46538			−0.732692	+	0.680560i	$0.761737\pi$
$860$	−1404.65	+	456.398i	−1.63331	+	0.530695i
$861$	−471.473	−	863.157i	−0.547588	−	1.00251i
$862$	−307.738	+	223.585i	−0.357005	+	0.259379i
$863$	1079.28	+	350.678i	1.25061	+	0.406348i	0.858139	−	0.513417i	$-0.171620\pi$
$863$	1079.28	+	350.678i	1.25061	+	0.406348i	0.392471	+	0.919765i	$0.371620\pi$
$864$	747.857	+	53.1789i	0.865576	+	0.0615496i
$865$	−5.55656	+	4.03708i	−0.00642377	+	0.00466714i
$866$	−115.309	+	158.709i	−0.133151	+	0.183266i
$867$	−1804.82	−	232.989i	−2.08168	−	0.268730i
$868$	−585.043			−0.674012
$869$		0			0
$870$	−193.361	−	91.6318i	−0.222254	−	0.105324i
$871$	−39.7506	−	122.340i	−0.0456379	−	0.140459i
$872$	−113.732	+	156.539i	−0.130427	+	0.179518i
$873$	1654.63	+	434.442i	1.89534	+	0.497643i
$874$	60.3503	−	185.739i	0.0690507	−	0.212516i
$875$	−455.503	−	148.002i	−0.520575	−	0.169145i
$876$	−183.192	−	974.716i	−0.209123	−	1.11269i
$877$	−1183.15	−	859.606i	−1.34908	−	0.980167i	−0.999057	−	0.0434275i	$-0.986172\pi$
$877$	−1183.15	−	859.606i	−1.34908	−	0.980167i	−0.350028	−	0.936739i	$-0.613828\pi$
$878$	116.368	−	37.8104i	0.132538	−	0.0430642i
$879$	991.181	+	469.710i	1.12762	+	0.534369i
$880$		0			0
$881$		−	1493.59i		−	1.69534i	−0.530526	−	0.847668i	$-0.678006\pi$
$881$		−	1493.59i		−	1.69534i	0.530526	−	0.847668i	$-0.321994\pi$
$882$	−199.498	−	128.133i	−0.226189	−	0.145275i
$883$	−1074.40	−	780.594i	−1.21676	−	0.884025i	−0.220930	−	0.975290i	$-0.570909\pi$
$883$	−1074.40	−	780.594i	−1.21676	−	0.884025i	−0.995827	+	0.0912647i	$0.970909\pi$
$884$	259.524	+	357.205i	0.293579	+	0.404078i
$885$	575.706	+	543.577i	0.650516	+	0.614212i
$886$	−59.1502	+	182.046i	−0.0667609	+	0.205469i
$887$	489.520	+	673.766i	0.551882	+	0.759601i	0.990266	−	0.139187i	$-0.0444489\pi$
$887$	489.520	+	673.766i	0.551882	+	0.759601i	−0.438384	+	0.898788i	$0.644449\pi$
$888$	107.392	+	196.610i	0.120937	+	0.221408i
$889$	420.575	+	1294.40i	0.473088	+	1.45601i
$890$			90.0949i			0.101230i
$891$		0			0
$892$	930.411			1.04306
$893$	−102.348	+	33.2549i	−0.114612	+	0.0372396i
$894$	354.634	−	193.708i	0.396682	−	0.216675i
$895$	455.464	−	330.914i	0.508898	−	0.369736i
$896$	−1133.20	−	368.198i	−1.26473	−	0.410935i
$897$	−239.568	+	253.728i	−0.267077	+	0.282863i
$898$	−152.888	+	111.079i	−0.170253	+	0.123696i
$899$	−167.652	+	230.753i	−0.186487	+	0.256677i
$900$	−294.510	+	458.543i	−0.327234	+	0.509493i
$901$	1807.61			2.00622
$902$		0			0
$903$	−774.160	+	1633.63i	−0.857320	+	1.80911i
$904$	269.885	+	830.622i	0.298546	+	0.918829i
$905$	412.641	−	567.952i	0.455957	−	0.627571i
$906$	−178.401	+	33.5294i	−0.196911	+	0.0370081i
$907$	168.952	−	519.981i	0.186276	−	0.573298i	−0.813692	−	0.581296i	$-0.802546\pi$
$907$	168.952	−	519.981i	0.186276	−	0.573298i	0.999968	+	0.00799786i	$0.00254583\pi$
$908$	−30.3718	−	9.86839i	−0.0334491	−	0.0108683i
$909$	−108.802	+	414.388i	−0.119694	+	0.455873i
$910$	−139.590	−	101.418i	−0.153396	−	0.111448i
$911$	53.0058	−	17.2226i	0.0581842	−	0.0189052i	−0.279780	−	0.960064i	$-0.590262\pi$
$911$	53.0058	−	17.2226i	0.0581842	−	0.0189052i	0.337964	+	0.941159i	$0.390262\pi$
$912$	140.909	−	297.345i	0.154505	−	0.326037i
$913$		0			0
$914$		−	235.612i		−	0.257781i
$915$	58.6038	−	453.967i	0.0640479	−	0.496139i
$916$	1008.44	+	732.677i	1.10092	+	0.799866i
$917$	−958.662	−	1319.49i	−1.04543	−	1.43892i
$918$	−39.0018	+	548.484i	−0.0424856	+	0.597477i
$919$	−330.064	+	1015.83i	−0.359156	+	1.10537i	0.594404	+	0.804166i	$0.297388\pi$
$919$	−330.064	+	1015.83i	−0.359156	+	1.10537i	−0.953560	+	0.301202i	$0.902612\pi$
$920$	545.590	+	750.940i	0.593033	+	0.816239i
$921$	−1274.71	+	696.274i	−1.38406	+	0.755997i
$922$	14.1208	+	43.4593i	0.0153154	+	0.0471359i
$923$		−	4.15331i		−	0.00449979i
$924$		0			0
$925$	−249.266			−0.269477
$926$	−488.438	+	158.703i	−0.527471	+	0.171386i
$927$	27.1943	+	473.298i	0.0293358	+	0.510570i
$928$	−362.797	+	263.587i	−0.390945	+	0.284038i
$929$	800.150	+	259.984i	0.861302	+	0.279854i	0.706172	−	0.708040i	$-0.250420\pi$
$929$	800.150	+	259.984i	0.861302	+	0.279854i	0.155130	+	0.987894i	$0.450420\pi$
$930$	−170.152	−	160.656i	−0.182959	−	0.172748i
$931$	−322.330	+	234.186i	−0.346219	+	0.251543i
$932$	−73.5992	+	101.301i	−0.0789691	+	0.108692i
$933$	−129.113	+	1000.16i	−0.138385	+	1.07198i
$934$	196.924			0.210839
$935$		0			0
$936$	149.031	−	121.930i	0.159221	−	0.130268i
$937$	−387.353	−	1192.15i	−0.413397	−	1.27231i	−0.913676	−	0.406442i	$-0.866769\pi$
$937$	−387.353	−	1192.15i	−0.413397	−	1.27231i	0.500279	−	0.865864i	$-0.333231\pi$
$938$	−115.523	+	159.004i	−0.123159	+	0.169514i
$939$	−271.022	−	1442.04i	−0.288628	−	1.53572i
$940$	74.1714	−	228.276i	0.0789057	−	0.242847i
$941$	−1298.15	−	421.795i	−1.37954	−	0.448241i	−0.477025	−	0.878890i	$-0.658285\pi$
$941$	−1298.15	−	421.795i	−1.37954	−	0.448241i	−0.902520	+	0.430649i	$0.858285\pi$
$942$	133.902	−	25.1661i	0.142147	−	0.0267156i
$943$	789.700	+	573.751i	0.837434	+	0.608431i
$944$	412.181	−	133.926i	0.436632	−	0.141870i
$945$	395.151	+	1592.84i	0.418149	+	1.68555i
$946$		0			0
$947$		−	1289.80i		−	1.36199i	−0.732289	−	0.680994i	$-0.761548\pi$
$947$		−	1289.80i		−	1.36199i	0.732289	−	0.680994i	$-0.238452\pi$
$948$	−1189.94	−	153.613i	−1.25521	−	0.162039i
$949$	−315.435	−	229.177i	−0.332387	−	0.241493i
$950$	−70.4786	−	97.0055i	−0.0741880	−	0.102111i
$951$	−321.956	+	340.986i	−0.338545	+	0.358555i
$952$	444.224	−	1367.18i	0.466622	−	1.43611i
$953$	389.907	+	536.661i	0.409137	+	0.563128i	0.963008	−	0.269474i	$-0.0868499\pi$
$953$	389.907	+	536.661i	0.409137	+	0.563128i	−0.553871	+	0.832602i	$0.686850\pi$
$954$	−21.2205	−	369.329i	−0.0222437	−	0.387137i
$955$	57.4607	+	176.846i	0.0601683	+	0.185179i
$956$			462.623i			0.483915i
$957$		0			0
$958$	113.059			0.118015
$959$	−724.107	+	235.277i	−0.755065	+	0.245335i
$960$	221.500	+	405.514i	0.230729	+	0.422411i
$961$	525.103	−	381.510i	0.546413	−	0.396992i
$962$	39.3076	+	12.7718i	0.0408602	+	0.0132763i
$963$	−223.234	−	572.909i	−0.231811	−	0.594921i
$964$	384.933	−	279.670i	0.399308	−	0.290115i
$965$	−48.4271	+	66.6541i	−0.0501835	+	0.0690716i
$966$	528.778	+	68.2614i	0.547389	+	0.0706639i
$967$	101.038			0.104486			0.0522428	−	0.998634i	$-0.483363\pi$
$967$	101.038			0.104486			0.0522428	+	0.998634i	$0.483363\pi$
$968$		0			0
$969$	834.975	+	395.686i	0.861687	+	0.408345i
$970$	−259.420	−	798.411i	−0.267443	−	0.823104i
$971$	378.084	−	520.388i	0.389376	−	0.535930i	−0.568662	−	0.822571i	$-0.692539\pi$
$971$	378.084	−	520.388i	0.389376	−	0.535930i	0.958038	+	0.286641i	$0.0925387\pi$
$972$	−859.387	−	11.6841i	−0.884143	−	0.0120206i
$973$	−1.97096	+	6.06599i	−0.00202565	+	0.00623432i
$974$	13.3065	+	4.32354i	0.0136617	+	0.00443896i
$975$	39.5734	+	210.560i	0.0405881	+	0.215959i
$976$	−202.697	−	147.268i	−0.207682	−	0.150890i
$977$	−1428.41	+	464.118i	−1.46204	+	0.475044i	−0.928691	−	0.370854i	$-0.879065\pi$
$977$	−1428.41	+	464.118i	−1.46204	+	0.475044i	−0.533345	+	0.845898i	$0.679065\pi$
$978$	257.995	+	122.261i	0.263798	+	0.125011i
$979$		0			0
$980$		−	888.634i		−	0.906769i
$981$	183.485	−	285.680i	0.187039	−	0.291213i
$982$	−263.489	−	191.436i	−0.268319	−	0.194945i
$983$	−428.555	−	589.856i	−0.435967	−	0.600057i	0.533343	−	0.845899i	$-0.320935\pi$
$983$	−428.555	−	589.856i	−0.435967	−	0.600057i	−0.969310	+	0.245842i	$0.920935\pi$
$984$	−391.637	−	369.780i	−0.398005	−	0.375793i
$985$	−675.245	+	2078.19i	−0.685528	+	2.10984i
$986$	−193.317	−	266.078i	−0.196062	−	0.269856i
$987$	−140.834	−	257.835i	−0.142689	−	0.261231i
$988$	−46.9216	−	144.410i	−0.0474915	−	0.146164i
$989$		−	1794.17i		−	1.81412i
$990$		0			0
$991$	1823.31			1.83987			0.919936	−	0.392069i	$-0.128241\pi$
$991$	1823.31			1.83987			0.919936	+	0.392069i	$0.128241\pi$
$992$	−466.434	+	151.554i	−0.470196	+	0.152776i
$993$	−106.049	+	57.9259i	−0.106796	+	0.0583342i
$994$	−5.13383	+	3.72995i	−0.00516482	+	0.00375246i
$995$	−1134.87	−	368.741i	−1.14057	−	0.370594i
$996$	−758.104	+	802.912i	−0.761148	+	0.806137i
$997$	−8.87703	+	6.44954i	−0.00890374	+	0.00646895i	−0.592228	−	0.805770i	$-0.701752\pi$
$997$	−8.87703	+	6.44954i	−0.00890374	+	0.00646895i	0.583324	+	0.812239i	$0.301752\pi$
$998$	101.981	−	140.365i	0.102186	−	0.140646i
$999$	−207.925	−	333.621i	−0.208133	−	0.333955i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.3.h.q.269.4		24
3.2	odd	2	inner	363.3.h.q.269.3		24
11.2	odd	10		363.3.h.p.251.4		24
11.3	even	5		363.3.b.j.122.3	✓	6
11.4	even	5	inner	363.3.h.q.245.4		24
11.5	even	5	inner	363.3.h.q.323.3		24
11.6	odd	10		363.3.h.p.323.4		24
11.7	odd	10		363.3.h.p.245.3		24
11.8	odd	10		363.3.b.k.122.4	yes	6
11.9	even	5	inner	363.3.h.q.251.3		24
11.10	odd	2		363.3.h.p.269.3		24
33.2	even	10		363.3.h.p.251.3		24
33.5	odd	10	inner	363.3.h.q.323.4		24
33.8	even	10		363.3.b.k.122.3	yes	6
33.14	odd	10		363.3.b.j.122.4	yes	6
33.17	even	10		363.3.h.p.323.3		24
33.20	odd	10	inner	363.3.h.q.251.4		24
33.26	odd	10	inner	363.3.h.q.245.3		24
33.29	even	10		363.3.h.p.245.4		24
33.32	even	2		363.3.h.p.269.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
363.3.b.j.122.3	✓	6	11.3	even	5
363.3.b.j.122.4	yes	6	33.14	odd	10
363.3.b.k.122.3	yes	6	33.8	even	10
363.3.b.k.122.4	yes	6	11.8	odd	10
363.3.h.p.245.3		24	11.7	odd	10
363.3.h.p.245.4		24	33.29	even	10
363.3.h.p.251.3		24	33.2	even	10
363.3.h.p.251.4		24	11.2	odd	10
363.3.h.p.269.3		24	11.10	odd	2
363.3.h.p.269.4		24	33.32	even	2
363.3.h.p.323.3		24	33.17	even	10
363.3.h.p.323.4		24	11.6	odd	10
363.3.h.q.245.3		24	33.26	odd	10	inner
363.3.h.q.245.4		24	11.4	even	5	inner
363.3.h.q.251.3		24	11.9	even	5	inner
363.3.h.q.251.4		24	33.20	odd	10	inner
363.3.h.q.269.3		24	3.2	odd	2	inner
363.3.h.q.269.4		24	1.1	even	1	trivial
363.3.h.q.323.3		24	11.5	even	5	inner
363.3.h.q.323.4		24	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:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	363.h (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.647210 - 0.210291i) q^{2} +(-2.63284 + 1.43811i) q^{3} +(-2.86141 + 2.07894i) q^{4} +(-6.17237 - 2.00553i) q^{5} +(-1.40158 + 1.48442i) q^{6} +(-7.57686 + 5.50491i) q^{7} +(-3.01474 + 4.14944i) q^{8} +(4.86369 - 7.57261i) q^{9} -4.41657 q^{10} +(4.54390 - 9.58852i) q^{12} +(-1.28903 - 3.96722i) q^{13} +(-3.74618 + 5.15618i) q^{14} +(19.1350 - 3.59631i) q^{15} +(3.29326 - 10.1356i) q^{16} +(28.4618 + 9.24781i) q^{17} +(1.55538 - 5.92386i) q^{18} +(-8.32617 - 6.04932i) q^{19} +(21.8311 - 7.09334i) q^{20} +(12.0320 - 25.3899i) q^{21} +27.8850i q^{23} +(1.97000 - 15.2603i) q^{24} +(13.8506 + 10.0631i) q^{25} +(-1.66854 - 2.29655i) q^{26} +(-1.91509 + 26.9320i) q^{27} +(10.2361 - 31.5036i) q^{28} +(-9.49235 - 13.0651i) q^{29} +(11.6281 - 6.35150i) q^{30} +(-5.45778 - 16.7973i) q^{31} -27.7684i q^{32} +20.3655 q^{34} +(57.8074 - 18.7828i) q^{35} +(1.82596 + 31.7797i) q^{36} +(-11.7790 + 8.55794i) q^{37} +(-6.66090 - 2.16426i) q^{38} +(9.09910 + 8.59130i) q^{39} +(26.9299 - 19.5657i) q^{40} +(20.5756 - 28.3199i) q^{41} +(2.44796 - 18.9628i) q^{42} -64.3417 q^{43} +(-45.2076 + 36.9867i) q^{45} +(5.86397 + 18.0474i) q^{46} +(6.14617 - 8.45948i) q^{47} +(5.90548 + 31.4216i) q^{48} +(11.9629 - 36.8181i) q^{49} +(11.0804 + 3.60026i) q^{50} +(-88.2348 + 16.5832i) q^{51} +(11.9360 + 8.67204i) q^{52} +(57.4452 - 18.6651i) q^{53} +(4.42410 + 17.8334i) q^{54} -48.0356i q^{56} +(30.6211 + 3.95296i) q^{57} +(-8.89102 - 6.45971i) q^{58} +(23.9032 + 32.8999i) q^{59} +(-47.2767 + 50.0710i) q^{60} +(7.26488 - 22.3590i) q^{61} +(-7.06466 - 9.72367i) q^{62} +(4.83505 + 84.1508i) q^{63} +(7.33362 + 22.5705i) q^{64} +27.0724i q^{65} +30.8376 q^{67} +(-100.667 + 32.7086i) q^{68} +(-40.1016 - 73.4167i) q^{69} +(33.4637 - 24.3128i) q^{70} +(0.946935 + 0.307678i) q^{71} +(16.7593 + 43.0111i) q^{72} +(75.6188 - 54.9403i) q^{73} +(-5.82382 + 8.01580i) q^{74} +(-50.9383 - 6.57576i) q^{75} +36.4007 q^{76} +(7.69570 + 3.64691i) q^{78} +(-34.9425 - 107.542i) q^{79} +(-40.6545 + 55.9561i) q^{80} +(-33.6890 - 73.6617i) q^{81} +(7.36131 - 22.6558i) q^{82} +(-98.9769 - 32.1595i) q^{83} +(18.3555 + 97.6646i) q^{84} +(-157.130 - 114.162i) q^{85} +(-41.6426 + 13.5305i) q^{86} +(43.7809 + 20.7473i) q^{87} -20.3993i q^{89} +(-21.4808 + 33.4449i) q^{90} +(31.6060 + 22.9631i) q^{91} +(-57.9711 - 79.7904i) q^{92} +(38.5258 + 36.3758i) q^{93} +(2.19891 - 6.76754i) q^{94} +(39.2602 + 54.0370i) q^{95} +(39.9339 + 73.1096i) q^{96} +(58.7378 + 180.776i) q^{97} -26.3447i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{3} + 18 q^{4} + 10 q^{6} + 22 q^{9} + 72 q^{10} + 56 q^{12} + 42 q^{13} - 28 q^{15} - 30 q^{16} - 94 q^{18} - 84 q^{19} - 112 q^{21} - 48 q^{24} + 108 q^{25} + 38 q^{27} - 132 q^{28} + 148 q^{30}+ \cdots - 126 q^{97}+O(q^{100}) \) 24 * q - 4 * q^3 + 18 * q^4 + 10 * q^6 + 22 * q^9 + 72 * q^10 + 56 * q^12 + 42 * q^13 - 28 * q^15 - 30 * q^16 - 94 * q^18 - 84 * q^19 - 112 * q^21 - 48 * q^24 + 108 * q^25 + 38 * q^27 - 132 * q^28 + 148 * q^30 + 264 * q^34 - 46 * q^36 + 42 * q^37 + 82 * q^39 + 294 * q^40 + 206 * q^42 - 624 * q^43 - 472 * q^45 + 60 * q^46 + 88 * q^48 - 138 * q^49 - 182 * q^51 - 114 * q^52 + 560 * q^54 + 24 * q^57 + 54 * q^58 + 562 * q^60 - 264 * q^61 + 122 * q^63 - 294 * q^64 + 96 * q^67 - 152 * q^69 - 336 * q^70 + 306 * q^72 - 72 * q^73 - 62 * q^75 - 1632 * q^76 - 776 * q^78 + 250 * q^81 - 798 * q^82 - 328 * q^84 - 330 * q^85 + 1848 * q^87 + 230 * q^90 - 300 * q^91 + 266 * q^93 - 120 * q^94 + 386 * q^96 - 126 * q^97

Introduction

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