LMFDB - Embedded newform 363.3.h.q.269.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,3,Mod(245,363)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			269.3
Character	$\chi$	$=$	363.269
Dual form			363.3.h.q.251.3

$q$-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} +(0.554129 - 2.94838i) q^{3} +(-2.86141 + 2.07894i) q^{4} +(6.17237 + 2.00553i) q^{5} +(0.261380 + 2.02475i) q^{6} +(-7.57686 + 5.50491i) q^{7} +(3.01474 - 4.14944i) q^{8} +(-8.38588 - 3.26757i) q^{9} -4.41657 q^{10} +(4.54390 + 9.58852i) q^{12} +(-1.28903 - 3.96722i) q^{13} +(3.74618 - 5.15618i) q^{14} +(9.33334 - 17.0872i) q^{15} +(3.29326 - 10.1356i) q^{16} +(-28.4618 - 9.24781i) q^{17} +(6.11457 + 0.351324i) q^{18} +(-8.32617 - 6.04932i) q^{19} +(-21.8311 + 7.09334i) q^{20} +(12.0320 + 25.3899i) q^{21} -27.8850i q^{23} +(-10.5636 - 11.1879i) q^{24} +(13.8506 + 10.0631i) q^{25} +(1.66854 + 2.29655i) q^{26} +(-14.2809 + 22.9141i) q^{27} +(10.2361 - 31.5036i) q^{28} +(9.49235 + 13.0651i) q^{29} +(-2.44735 + 13.0217i) q^{30} +(-5.45778 - 16.7973i) q^{31} +27.7684i q^{32} +20.3655 q^{34} +(-57.8074 + 18.7828i) q^{35} +(30.7885 - 8.08386i) q^{36} +(-11.7790 + 8.55794i) q^{37} +(6.66090 + 2.16426i) q^{38} +(-12.4112 + 1.60219i) q^{39} +(26.9299 - 19.5657i) q^{40} +(-20.5756 + 28.3199i) q^{41} +(-13.1265 - 13.9024i) q^{42} -64.3417 q^{43} +(-45.2076 - 36.9867i) q^{45} +(5.86397 + 18.0474i) q^{46} +(-6.14617 + 8.45948i) q^{47} +(-28.0588 - 15.3262i) q^{48} +(11.9629 - 36.8181i) q^{49} +(-11.0804 - 3.60026i) q^{50} +(-43.0376 + 78.7918i) q^{51} +(11.9360 + 8.67204i) q^{52} +(-57.4452 + 18.6651i) q^{53} +(4.42410 - 17.8334i) q^{54} +48.0356i q^{56} +(-22.4495 + 21.1966i) q^{57} +(-8.89102 - 6.45971i) q^{58} +(-23.9032 - 32.8999i) q^{59} +(8.81663 + 68.2968i) q^{60} +(7.26488 - 22.3590i) q^{61} +(7.06466 + 9.72367i) q^{62} +(81.5263 - 21.4056i) q^{63} +(7.33362 + 22.5705i) q^{64} -27.0724i q^{65} +30.8376 q^{67} +(100.667 - 32.7086i) q^{68} +(-82.2155 - 15.4519i) q^{69} +(33.4637 - 24.3128i) q^{70} +(-0.946935 - 0.307678i) q^{71} +(-38.8398 + 24.9458i) q^{72} +(75.6188 - 54.9403i) q^{73} +(5.82382 - 8.01580i) q^{74} +(37.3448 - 35.2607i) q^{75} +36.4007 q^{76} +(7.69570 - 3.64691i) q^{78} +(-34.9425 - 107.542i) q^{79} +(40.6545 - 55.9561i) q^{80} +(59.6460 + 54.8029i) q^{81} +(7.36131 - 22.6558i) q^{82} +(98.9769 + 32.1595i) q^{83} +(-87.2124 - 47.6371i) q^{84} +(-157.130 - 114.162i) q^{85} +(41.6426 - 13.5305i) q^{86} +(43.7809 - 20.7473i) q^{87} +20.3993i q^{89} +(37.0368 + 14.4314i) q^{90} +(31.6060 + 22.9631i) q^{91} +(57.9711 + 79.7904i) q^{92} +(-52.5492 + 6.78372i) q^{93} +(2.19891 - 6.76754i) q^{94} +(-39.2602 - 54.0370i) q^{95} +(81.8717 + 15.3873i) 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	−0.466315	−	0.884619i	$-0.654418\pi$
$2$	−0.647210	+	0.210291i	−0.323605	+	0.105146i	0.142710	+	0.989765i	$0.454418\pi$
$3$	0.554129	−	2.94838i	0.184710	−	0.982793i
$3$	0.554129	−	2.94838i	0.184710	−	0.982793i
$4$	−2.86141	+	2.07894i	−0.715352	+	0.519734i
$5$	6.17237	+	2.00553i	1.23447	+	0.401105i	0.852333	−	0.522999i	$-0.175187\pi$
$5$	6.17237	+	2.00553i	1.23447	+	0.401105i	0.382141	+	0.924104i	$0.375187\pi$
$6$	0.261380	+	2.02475i	0.0435634	+	0.337458i
$7$	−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
$9$	−8.38588	−	3.26757i	−0.931765	−	0.363063i
$10$	−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
$15$	9.33334	−	17.0872i	0.622223	−	1.13915i
$16$	3.29326	−	10.1356i	0.205829	−	0.633477i
$17$	−28.4618	−	9.24781i	−1.67423	−	0.543989i	−0.690448	−	0.723382i	$-0.742587\pi$
$17$	−28.4618	−	9.24781i	−1.67423	−	0.543989i	−0.983777	+	0.179393i	$0.942587\pi$
$18$	6.11457	+	0.351324i	0.339698	+	0.0195180i
$19$	−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	$-0.792695\pi$
$23$		−	27.8850i		−	1.21239i	0.795316	−	0.606195i	$-0.207305\pi$
$24$	−10.5636	−	11.1879i	−0.440148	−	0.466164i
$25$	13.8506	+	10.0631i	0.554026	+	0.402523i
$26$	1.66854	+	2.29655i	0.0641748	+	0.0883290i
$27$	−14.2809	+	22.9141i	−0.528922	+	0.848671i
$28$	10.2361	−	31.5036i	0.365576	−	1.12513i
$29$	9.49235	+	13.0651i	0.327323	+	0.450521i	0.940685	−	0.339281i	$-0.110184\pi$
$29$	9.49235	+	13.0651i	0.327323	+	0.450521i	−0.613363	+	0.789801i	$0.710184\pi$
$30$	−2.44735	+	13.0217i	−0.0815783	+	0.434057i
$31$	−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
$36$	30.7885	−	8.08386i	0.855236	−	0.224552i
$37$	−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
$39$	−12.4112	+	1.60219i	−0.318235	+	0.0410818i
$40$	26.9299	−	19.5657i	0.673248	−	0.489143i
$41$	−20.5756	+	28.3199i	−0.501844	+	0.690729i	−0.982517	−	0.186171i	$-0.940392\pi$
$41$	−20.5756	+	28.3199i	−0.501844	+	0.690729i	0.480673	+	0.876900i	$0.340392\pi$
$42$	−13.1265	−	13.9024i	−0.312536	−	0.331009i
$43$	−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	−0.869381	−	0.494143i	$-0.835482\pi$
$47$	−6.14617	+	8.45948i	−0.130770	+	0.179989i	0.738611	+	0.674132i	$0.235482\pi$
$48$	−28.0588	−	15.3262i	−0.584558	−	0.319297i
$49$	11.9629	−	36.8181i	0.244141	−	0.751389i
$50$	−11.0804	−	3.60026i	−0.221609	−	0.0720051i
$51$	−43.0376	+	78.7918i	−0.843874	+	1.54494i
$52$	11.9360	+	8.67204i	0.229539	+	0.166770i
$53$	−57.4452	+	18.6651i	−1.08387	+	0.352171i	−0.795876	−	0.605460i	$-0.792989\pi$
$53$	−57.4452	+	18.6651i	−1.08387	+	0.352171i	−0.287997	+	0.957631i	$0.592989\pi$
$54$	4.42410	−	17.8334i	0.0819277	−	0.330248i
$55$		0			0
$56$			48.0356i			0.857778i
$57$	−22.4495	+	21.1966i	−0.393850	+	0.371870i
$58$	−8.89102	−	6.45971i	−0.153293	−	0.111374i
$59$	−23.9032	−	32.8999i	−0.405139	−	0.557625i	0.556886	−	0.830589i	$-0.311996\pi$
$59$	−23.9032	−	32.8999i	−0.405139	−	0.557625i	−0.962024	+	0.272964i	$0.911996\pi$
$60$	8.81663	+	68.2968i	0.146944	+	1.13828i
$61$	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
$63$	81.5263	−	21.4056i	1.29407	−	0.339772i
$64$	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
$69$	−82.2155	−	15.4519i	−1.19153	−	0.223940i
$70$	33.4637	−	24.3128i	0.478053	−	0.347326i
$71$	−0.946935	−	0.307678i	−0.0133371	−	0.00433349i	0.302341	−	0.953200i	$-0.402232\pi$
$71$	−0.946935	−	0.307678i	−0.0133371	−	0.00433349i	−0.315678	+	0.948866i	$0.602232\pi$
$72$	−38.8398	+	24.9458i	−0.539442	+	0.346469i
$73$	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
$75$	37.3448	−	35.2607i	0.497931	−	0.470143i
$76$	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
$81$	59.6460	+	54.8029i	0.736370	+	0.676579i
$82$	7.36131	−	22.6558i	0.0897721	−	0.276290i
$83$	98.9769	+	32.1595i	1.19249	+	0.387464i	0.836994	−	0.547212i	$-0.184311\pi$
$83$	98.9769	+	32.1595i	1.19249	+	0.387464i	0.355499	+	0.934677i	$0.384311\pi$
$84$	−87.2124	−	47.6371i	−1.03824	−	0.567108i
$85$	−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	$0.0365595\pi$
$89$			20.3993i			0.229206i	−0.993411	+	0.114603i	$0.963440\pi$
$90$	37.0368	+	14.4314i	0.411520	+	0.160349i
$91$	31.6060	+	22.9631i	0.347319	+	0.252342i
$92$	57.9711	+	79.7904i	0.630121	+	0.867287i
$93$	−52.5492	+	6.78372i	−0.565045	+	0.0729432i
$94$	2.19891	−	6.76754i	0.0233926	−	0.0719951i
$95$	−39.2602	−	54.0370i	−0.413265	−	0.568811i
$96$	81.8717	+	15.3873i	0.852830	+	0.160284i
$97$	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	−0.0761854	−	0.997094i	$-0.524274\pi$
$101$	45.2739	−	14.7104i	0.448256	−	0.145647i	0.524442	+	0.851446i	$0.324274\pi$
$102$	11.2851	−	60.0453i	0.110639	−	0.588679i
$103$	−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
$105$	23.3459	+	180.846i	0.222342	+	1.72235i
$106$	33.2540	−	24.1605i	0.313717	−	0.227929i
$107$	−40.1565	+	55.2706i	−0.375294	+	0.516548i	−0.954330	−	0.298754i	$-0.903429\pi$
$107$	−40.1565	+	55.2706i	−0.375294	+	0.516548i	0.579036	+	0.815302i	$0.303429\pi$
$108$	−6.77347	−	95.2557i	−0.0627173	−	0.881997i
$109$	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	$0.471614\pi$
$113$	−100.089	+	137.760i	−0.885739	+	1.21912i	−0.974798	+	0.223089i	$0.928386\pi$
$114$	10.0721	−	18.4396i	0.0883514	−	0.161751i
$115$	55.9241	−	172.117i	0.486296	−	1.49667i
$116$	−54.3230	−	17.6506i	−0.468302	−	0.152161i
$117$	−2.15352	+	37.4807i	−0.0184062	+	0.320347i
$118$	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
$123$	72.0962	+	76.3576i	0.586148	+	0.620793i
$124$	50.5375	+	36.7176i	0.407560	+	0.296110i
$125$	−30.0589	−	41.3725i	−0.240471	−	0.330980i
$126$	−48.2632	+	30.9982i	−0.383041	+	0.246017i
$127$	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
$129$	−35.6536	+	189.704i	−0.276385	+	1.47057i
$130$	5.69308	+	17.5215i	0.0437929	+	0.134781i
$131$		−	174.147i		−	1.32936i	−0.747126	−	0.664682i	$-0.768567\pi$
$131$		−	174.147i		−	1.32936i	0.747126	−	0.664682i	$-0.231433\pi$
$132$		0			0
$133$	96.3872			0.724716
$134$	−19.9584	+	6.48489i	−0.148944	+	0.0483947i
$135$	−134.102	+	112.794i	−0.993347	+	0.835509i
$136$	−124.178	+	90.2208i	−0.913075	+	0.663388i
$137$	−77.3163	−	25.1216i	−0.564353	−	0.183369i	0.0129260	−	0.999916i	$-0.495885\pi$
$137$	−77.3163	−	25.1216i	−0.564353	−	0.183369i	−0.577279	+	0.816547i	$0.695885\pi$
$138$	56.4601	−	7.28859i	0.409131	−	0.0528159i
$139$	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
$141$	21.5360	+	22.8089i	0.152737	+	0.161765i
$142$	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
$147$	−101.925	−	55.6732i	−0.693365	−	0.378729i
$148$	15.9131	−	48.9755i	0.107521	−	0.330916i
$149$	188.245	+	61.1645i	1.26339	+	0.410500i	0.862701	−	0.505715i	$-0.168771\pi$
$149$	188.245	+	61.1645i	1.26339	+	0.410500i	0.400688	+	0.916214i	$0.368771\pi$
$150$	−16.7549	+	30.6744i	−0.111699	+	0.204496i
$151$	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
$156$	32.1826	−	30.3866i	0.206299	−	0.194786i
$157$	−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
$159$	23.1997	+	179.713i	0.145910	+	1.13027i
$160$	−55.6902	+	171.397i	−0.348064	+	1.07123i
$161$	153.504	+	211.281i	0.953443	+	1.31230i
$162$	−50.1280	−	22.9259i	−0.309432	−	0.141518i
$163$	−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	−0.672899	−	0.739735i	$-0.734951\pi$
$167$	−130.674	+	42.4586i	−0.782480	+	0.254243i	−0.109581	+	0.993978i	$0.534951\pi$
$168$	141.627	+	26.6179i	0.843018	+	0.158440i
$169$	122.647	−	89.1080i	0.725720	−	0.527266i
$170$	125.704	+	40.8436i	0.739433	+	0.240256i
$171$	50.0557	+	77.9352i	0.292724	+	0.455761i
$172$	184.108	−	133.762i	1.07040	−	0.777688i
$173$	−0.622044	+	0.856170i	−0.00359563	+	0.00494896i	−0.810811	−	0.585308i	$-0.800974\pi$
$173$	−0.622044	+	0.856170i	−0.00359563	+	0.00494896i	0.807215	+	0.590257i	$0.200974\pi$
$174$	−23.9724	+	22.6346i	−0.137773	+	0.130084i
$175$	−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	−0.642483	−	0.766300i	$-0.722096\pi$
$179$	50.9881	−	70.1791i	0.284850	−	0.392062i	0.927333	+	0.374238i	$0.122096\pi$
$180$	206.251	+	11.8505i	1.14584	+	0.0658363i
$181$	−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
$183$	−61.8971	−	33.8094i	−0.338236	−	0.184751i
$184$	−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
$189$	−17.9358	−	252.232i	−0.0948984	−	1.33456i
$190$	36.7731	+	26.7172i	0.193543	+	0.140617i
$191$	16.8407	+	23.1793i	0.0881714	+	0.121358i	0.850824	−	0.525451i	$-0.176103\pi$
$191$	16.8407	+	23.1793i	0.0881714	+	0.121358i	−0.762653	+	0.646808i	$0.776103\pi$
$192$	70.6103	−	9.11528i	0.367762	−	0.0474754i
$193$	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
$195$	−79.8196	−	15.0016i	−0.409331	−	0.0769313i
$196$	42.3116	+	130.222i	0.215875	+	0.664396i
$197$			336.692i			1.70910i	0.519370	+	0.854549i	$0.326166\pi$
$197$			336.692i			1.70910i	−0.519370	+	0.854549i	$0.673834\pi$
$198$		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
$201$	17.0880	−	90.9211i	0.0850152	−	0.452344i
$202$	−26.2082	+	19.0414i	−0.129744	+	0.0942644i
$203$	−143.844	−	46.7379i	−0.708593	−	0.230236i
$204$	−40.6549	−	314.928i	−0.199289	−	1.54376i
$205$	−183.797	+	133.536i	−0.896569	+	0.651395i
$206$	21.0701	−	29.0004i	0.102282	−	0.140779i
$207$	−91.1161	+	233.840i	−0.440174	+	1.12966i
$208$	−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
$213$	−1.43187	+	2.62143i	−0.00672242	+	0.0123072i
$214$	14.3667	−	44.2162i	0.0671342	−	0.206618i
$215$	−397.141	−	129.039i	−1.84717	−	0.600181i
$216$	52.0274	+	128.338i	0.240868	+	0.594156i
$217$	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
$222$	−20.4065	−	21.6126i	−0.0919211	−	0.0973542i
$223$	−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
$225$	−83.2680	−	129.646i	−0.370080	−	0.576203i
$226$	35.8085	−	110.207i	0.158445	−	0.487643i
$227$	−5.30714	−	7.30465i	−0.0233795	−	0.0321791i	0.797167	−	0.603759i	$-0.206331\pi$
$227$	−5.30714	−	7.30465i	−0.0233795	−	0.0321791i	−0.820547	+	0.571579i	$0.806331\pi$
$228$	20.1707	−	107.323i	0.0884681	−	0.470716i
$229$	−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	−0.380376	−	0.924832i	$-0.624206\pi$
$233$	−33.6696	+	10.9399i	−0.144505	+	0.0469525i	0.235872	+	0.971784i	$0.424206\pi$
$234$	−6.48807	−	24.7107i	−0.0277268	−	0.105601i
$235$	−54.9021	+	39.8887i	−0.233626	+	0.169739i
$236$	136.794	+	44.4469i	0.579634	+	0.188334i
$237$	−336.437	+	43.4315i	−1.41956	+	0.183255i
$238$	−154.307	+	112.110i	−0.648347	+	0.471052i
$239$	−76.8818	+	105.819i	−0.321681	+	0.442756i	−0.938980	−	0.343973i	$-0.888227\pi$
$239$	−76.8818	+	105.819i	−0.321681	+	0.442756i	0.617298	+	0.786729i	$0.288227\pi$
$240$	−142.452	−	150.872i	−0.593550	−	0.628633i
$241$	−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
$246$	−62.7187	−	34.2582i	−0.254954	−	0.139261i
$247$	−13.2663	+	40.8295i	−0.0537098	+	0.165302i
$248$	−86.1532	−	27.9929i	−0.347392	−	0.112874i
$249$	149.665	−	274.001i	0.601062	−	1.10041i
$250$	28.1547	+	20.4556i	0.112619	+	0.0818222i
$251$	−384.764	+	125.017i	−1.53292	+	0.498077i	−0.949414	−	0.314028i	$-0.898321\pi$
$251$	−384.764	+	125.017i	−1.53292	+	0.498077i	−0.583511	+	0.812105i	$0.698321\pi$
$252$	−188.779	+	230.738i	−0.749124	+	0.915628i
$253$		0			0
$254$			98.8936i			0.389345i
$255$	−423.663	+	400.019i	−1.66142	+	1.56870i
$256$	−6.75577	−	4.90836i	−0.0263897	−	0.0191733i
$257$	−80.7301	−	111.115i	−0.314125	−	0.432356i	0.622537	−	0.782590i	$-0.286102\pi$
$257$	−80.7301	−	111.115i	−0.314125	−	0.432356i	−0.936662	+	0.350234i	$0.886102\pi$
$258$	−16.8177	−	130.276i	−0.0651847	−	0.504945i
$259$	42.1371	−	129.685i	0.162691	−	0.500713i
$260$	56.2817	+	77.4651i	0.216468	+	0.297943i
$261$	−36.9106	−	140.579i	−0.141420	−	0.538618i
$262$	36.6215	+	112.710i	0.139777	+	0.430189i
$263$			138.001i			0.524720i	0.964970	+	0.262360i	$0.0845008\pi$
$263$			138.001i			0.524720i	−0.964970	+	0.262360i	$0.915499\pi$
$264$		0			0
$265$	−392.007			−1.47927
$266$	−62.3827	+	20.2694i	−0.234522	+	0.0762007i
$267$	60.1449	+	11.3039i	0.225262	+	0.0423365i
$268$	−88.2391	+	64.1095i	−0.329251	+	0.239215i
$269$	29.3816	+	9.54665i	0.109225	+	0.0354894i	0.363120	−	0.931743i	$-0.381712\pi$
$269$	29.3816	+	9.54665i	0.109225	+	0.0354894i	−0.253895	+	0.967232i	$0.581712\pi$
$270$	63.0725	−	101.202i	0.233602	−	0.374821i
$271$	−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
$273$	85.2177	−	80.4619i	0.312153	−	0.294732i
$274$	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
$279$	−9.11807	+	158.694i	−0.0326813	+	0.568796i
$280$	−96.3366	+	296.493i	−0.344059	+	1.05891i
$281$	377.786	+	122.750i	1.34444	+	0.436834i	0.890817	−	0.454362i	$-0.150133\pi$
$281$	377.786	+	122.750i	1.34444	+	0.436834i	0.453619	+	0.891196i	$0.350133\pi$
$282$	−18.7348	−	10.2333i	−0.0664355	−	0.0362883i
$283$	−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
$288$	90.7350	−	232.862i	0.315052	−	0.808549i
$289$	490.748	+	356.549i	1.69809	+	1.23373i
$290$	−41.9236	−	57.7029i	−0.144564	−	0.198975i
$291$	565.546	−	73.0079i	1.94346	−	0.250886i
$292$	−102.159	+	314.413i	−0.349860	+	1.07676i
$293$	214.903	+	295.788i	0.733457	+	1.00952i	0.998968	+	0.0454093i	$0.0144592\pi$
$293$	214.903	+	295.788i	0.733457	+	1.00952i	−0.265511	+	0.964108i	$0.585541\pi$
$294$	77.6742	+	14.5984i	0.264198	+	0.0496543i
$295$	−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
$300$	−33.5541	+	178.533i	−0.111847	+	0.595109i
$301$	487.508	−	354.195i	1.61963	−	1.17673i
$302$	−57.5467	−	18.6981i	−0.190552	−	0.0619141i
$303$	−18.2842	−	141.636i	−0.0603438	−	0.467446i
$304$	−88.7339	+	64.4690i	−0.291888	+	0.212069i
$305$	89.6831	−	123.438i	0.294043	−	0.404715i
$306$	−170.783	−	66.5457i	−0.558114	−	0.217470i
$307$	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	−0.998355	−	0.0573298i	$-0.981741\pi$
$311$	−197.585	+	271.953i	−0.635323	+	0.874447i	0.363033	+	0.931776i	$0.381741\pi$
$312$	−30.7683	+	56.3295i	−0.0986163	+	0.180543i
$313$	−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
$315$	546.140	+	31.3796i	1.73378	+	0.0996177i
$316$	323.557	+	235.078i	1.02392	+	0.743918i
$317$	−148.670	+	48.3059i	−0.468992	+	0.152385i	−0.533972	−	0.845502i	$-0.679301\pi$
$317$	−148.670	+	48.3059i	−0.468992	+	0.152385i	0.0649808	+	0.997887i	$0.479301\pi$
$318$	−52.8072	−	111.433i	−0.166060	−	0.350420i
$319$		0			0
$320$			154.022i			0.481318i
$321$	140.707	+	149.024i	0.438339	+	0.464248i
$322$	−143.780	−	104.462i	−0.446522	−	0.324417i
$323$	181.035	+	249.174i	0.560481	+	0.771435i
$324$	−284.603	−	32.8132i	−0.878405	−	0.101275i
$325$	22.0686	−	67.9202i	0.0679034	−	0.208985i
$326$	55.9371	+	76.9909i	0.171586	+	0.236168i
$327$	20.9048	−	111.229i	0.0639290	−	0.340150i
$328$	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
$333$	126.741	−	33.2772i	0.380603	−	0.0999316i
$334$	75.6449	−	54.9592i	0.226482	−	0.164549i
$335$	190.341	+	61.8457i	0.568184	+	0.184614i
$336$	296.967	−	38.3363i	0.883830	−	0.114096i
$337$	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
$339$	350.707	+	371.436i	1.03453	+	1.09568i
$340$	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
$345$	−476.476	−	260.260i	−1.38109	−	0.754377i
$346$	0.222548	−	0.684932i	0.000643202	−	0.00197957i
$347$	−571.856	−	185.807i	−1.64800	−	0.535468i	−0.669695	−	0.742636i	$-0.733575\pi$
$347$	−571.856	−	185.807i	−1.64800	−	0.535468i	−0.978305	+	0.207168i	$0.933575\pi$
$348$	−82.1427	+	150.384i	−0.236042	+	0.432138i
$349$	−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	$0.0787386\pi$
$353$			172.864i			0.489699i	−0.969561	+	0.244850i	$0.921261\pi$
$354$	60.3662	−	56.9973i	0.170526	−	0.161009i
$355$	−5.22778	−	3.79820i	−0.0147261	−	0.0106992i
$356$	−42.4089	−	58.3708i	−0.119126	−	0.163963i
$357$	−107.652	−	833.912i	−0.301546	−	2.33589i
$358$	−18.2420	+	56.1430i	−0.0509552	+	0.156824i
$359$	−354.287	−	487.634i	−0.986871	−	1.35831i	−0.933045	−	0.359761i	$-0.882858\pi$
$359$	−354.287	−	487.634i	−0.986871	−	1.35831i	−0.0538262	−	0.998550i	$-0.517142\pi$
$360$	−289.763	+	76.0806i	−0.804898	+	0.211335i
$361$	−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
$366$	47.1702	+	8.86535i	0.128880	+	0.0242223i
$367$	−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
$369$	265.082	−	170.255i	0.718379	−	0.461396i
$370$	52.0227	−	37.7967i	0.140602	−	0.102153i
$371$	332.505	−	457.654i	0.896239	−	1.23357i
$372$	136.262	−	128.657i	0.366295	−	0.345853i
$373$	−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
$378$	64.6504	+	159.475i	0.171033	+	0.421892i
$379$	−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
$381$	−382.608	−	208.988i	−1.00422	−	0.548524i
$382$	−15.7739	−	11.4604i	−0.0412929	−	0.0300011i
$383$	573.154	−	186.229i	1.49649	−	0.486238i	0.557496	−	0.830180i	$-0.311762\pi$
$383$	573.154	−	186.229i	1.49649	−	0.486238i	0.938991	+	0.343942i	$0.111762\pi$
$384$	−344.903	+	163.446i	−0.898184	+	0.425640i
$385$		0			0
$386$			8.63898i			0.0223808i
$387$	539.562	+	210.241i	1.39422	+	0.543258i
$388$	−543.896	−	395.163i	−1.40179	−	1.01846i
$389$	267.543	+	368.242i	0.687772	+	0.946637i	0.999994	−	0.00337225i	$-0.00107342\pi$
$389$	267.543	+	368.242i	0.687772	+	0.946637i	−0.312222	+	0.950009i	$0.601073\pi$
$390$	54.8147	−	7.07618i	0.140551	−	0.0181441i
$391$	−257.875	+	793.658i	−0.659527	+	2.02982i
$392$	−116.709	−	160.636i	−0.297727	−	0.409786i
$393$	−513.451	−	96.4998i	−1.30649	−	0.245547i
$394$	−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
$399$	53.4110	−	284.186i	0.133862	−	0.712246i
$400$	147.609	−	107.245i	0.369024	−	0.268111i
$401$	239.706	+	77.8852i	0.597770	+	0.194227i	0.592246	−	0.805757i	$-0.298241\pi$
$401$	239.706	+	77.8852i	0.597770	+	0.194227i	0.00552464	+	0.999985i	$0.498241\pi$
$402$	8.06035	+	62.4385i	0.0200506	+	0.155320i
$403$	−59.6035	+	43.3045i	−0.147899	+	0.107455i
$404$	−98.9652	+	136.214i	−0.244963	+	0.337163i
$405$	258.249	+	457.885i	0.637652	+	1.13058i
$406$	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
$411$	−116.911	+	214.037i	−0.284456	+	0.520772i
$412$	57.5722	−	177.189i	0.139738	−	0.430071i
$413$	362.222	+	117.693i	0.877051	+	0.284971i
$414$	9.79668	−	170.505i	0.0236635	−	0.411847i
$415$	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	$-0.885186\pi$
$419$		−	295.753i		−	0.705855i	0.935651	−	0.352927i	$-0.114814\pi$
$420$	−442.770	−	468.941i	−1.05421	−	1.11653i
$421$	−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
$423$	79.1829	−	50.8571i	0.187194	−	0.120230i
$424$	−95.7329	+	294.636i	−0.225785	+	0.694896i
$425$	−301.153	−	414.502i	−0.708596	−	0.975298i
$426$	0.375460	−	1.99773i	0.000881361	−	0.00468950i
$427$	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	0.381474	−	0.924380i	$-0.375417\pi$
$431$	531.608	−	172.730i	1.23343	−	0.400766i	0.851956	+	0.523614i	$0.175417\pi$
$432$	185.218	+	220.208i	0.428745	+	0.509741i
$433$	−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
$435$	311.841	−	40.2564i	0.716876	−	0.0925435i
$436$	−107.948	+	78.4288i	−0.247587	+	0.179883i
$437$	−168.685	+	232.175i	−0.386007	+	0.531294i
$438$	131.006	+	138.749i	0.299099	+	0.316778i
$439$	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	−0.580562	−	0.814216i	$-0.697167\pi$
$443$	165.331	−	227.558i	0.373207	−	0.513676i	0.953769	+	0.300541i	$0.0971671\pi$
$444$	−135.581	−	74.0567i	−0.305362	−	0.166794i
$445$	−40.9113	+	125.912i	−0.0919356	+	0.282949i
$446$	170.254	+	55.3189i	0.381735	+	0.124033i
$447$	284.648	−	521.125i	0.636797	−	1.16583i
$448$	−179.815	−	130.643i	−0.401372	−	0.291614i
$449$	264.108	−	85.8140i	0.588214	−	0.191122i	0.000237150	−	1.00000i	$-0.499925\pi$
$449$	264.108	−	85.8140i	0.588214	−	0.191122i	0.587977	+	0.808878i	$0.299925\pi$
$450$	81.1552	+	66.3974i	0.180345	+	0.147550i
$451$		0			0
$452$		−	602.265i		−	1.33245i
$453$	193.952	−	183.128i	0.428149	−	0.404255i
$454$	4.97093	+	3.61160i	0.0109492	+	0.00795506i
$455$	149.031	+	205.123i	0.327541	+	0.450821i
$456$	20.2746	+	157.055i	0.0444619	+	0.344419i
$457$	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
$459$	618.366	−	520.110i	1.34720	−	1.13314i
$460$	197.798	+	608.759i	0.429995	+	1.32339i
$461$		−	67.1487i		−	0.145659i	−0.997344	−	0.0728294i	$-0.976797\pi$
$461$		−	67.1487i		−	0.145659i	0.997344	−	0.0728294i	$-0.0232029\pi$
$462$		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
$465$	−337.958	−	63.5171i	−0.726792	−	0.136596i
$466$	19.4907	−	14.1609i	0.0418256	−	0.0303881i
$467$	−275.211	−	89.4216i	−0.589317	−	0.191481i	−0.000847110	−	1.00000i	$-0.500270\pi$
$467$	−275.211	−	89.4216i	−0.589317	−	0.191481i	−0.588470	+	0.808519i	$0.700270\pi$
$468$	−71.7578	−	111.725i	−0.153329	−	0.238728i
$469$	−233.652	+	169.758i	−0.498193	+	0.361958i
$470$	27.1450	−	37.3618i	0.0577552	−	0.0794933i
$471$	−145.574	+	137.450i	−0.309075	+	0.291826i
$472$	−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
$477$	542.718	+	31.1829i	1.13777	+	0.0653731i
$478$	27.5059	−	84.6545i	0.0575437	−	0.177101i
$479$	−158.005	−	51.3391i	−0.329865	−	0.107180i	0.139402	−	0.990236i	$-0.455482\pi$
$479$	−158.005	−	51.3391i	−0.329865	−	0.107180i	−0.469267	+	0.883056i	$0.655482\pi$
$480$	474.483	+	259.172i	0.988506	+	0.539941i
$481$	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
$486$	−95.3717	+	135.093i	−0.196238	+	0.277968i
$487$	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
$489$	−416.078	+	53.7127i	−0.850876	+	0.109842i
$490$	−52.8350	+	162.609i	−0.107827	+	0.331856i
$491$	281.310	+	387.190i	0.572933	+	0.788574i	0.992898	−	0.118966i	$-0.0379579\pi$
$491$	281.310	+	387.190i	0.572933	+	0.788574i	−0.419966	+	0.907540i	$0.637958\pi$
$492$	−365.039	−	68.6068i	−0.741950	−	0.139445i
$493$	−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
$498$	−39.2444	+	208.809i	−0.0788040	+	0.419296i
$499$	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
$501$	52.7737	+	408.804i	0.105337	+	0.815977i
$502$	222.733	−	161.825i	0.443691	−	0.322361i
$503$	150.204	−	206.738i	0.298616	−	0.411010i	−0.633173	−	0.774011i	$-0.718248\pi$
$503$	150.204	−	206.738i	0.298616	−	0.411010i	0.931789	+	0.363001i	$0.118248\pi$
$504$	156.959	−	402.821i	0.311427	−	0.799247i
$505$	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	−0.777355	−	0.629062i	$-0.783439\pi$
$509$	31.1173	−	42.8293i	0.0611342	−	0.0841440i	0.838489	+	0.544918i	$0.183439\pi$
$510$	190.078	−	347.989i	0.372703	−	0.682332i
$511$	−270.512	+	832.550i	−0.529377	+	1.62926i
$512$	489.392	+	159.013i	0.955843	+	0.310572i
$513$	257.520	−	104.397i	0.501988	−	0.203503i
$514$	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
$519$	2.17962	+	2.30845i	0.00419966	+	0.00444788i
$520$	−112.335	−	81.6162i	−0.216029	−	0.156954i
$521$	−512.433	−	705.303i	−0.983557	−	1.35375i	−0.934891	−	0.354934i	$-0.884503\pi$
$521$	−512.433	−	705.303i	−0.983557	−	1.35375i	−0.0486653	−	0.998815i	$-0.515497\pi$
$522$	53.4515	+	83.2223i	0.102398	+	0.159430i
$523$	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
$525$	−88.8495	+	472.745i	−0.169237	+	0.900467i
$526$	−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
$531$	92.9466	+	354.000i	0.175041	+	0.666666i
$532$	−275.803	+	200.383i	−0.518427	+	0.376659i
$533$	138.874	+	45.1229i	0.260551	+	0.0846583i
$534$	−41.3035	+	5.33198i	−0.0773473	+	0.00998498i
$535$	−358.707	+	260.616i	−0.670481	+	0.487133i
$536$	92.9675	−	127.959i	0.173447	−	0.238729i
$537$	−178.661	−	189.221i	−0.332702	−	0.352366i
$538$	−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
$543$	284.795	+	155.561i	0.524485	+	0.286484i
$544$	256.797	−	790.338i	0.472052	−	1.45283i
$545$	232.856	+	75.6594i	0.427258	+	0.138825i
$546$	−38.2333	+	69.9963i	−0.0700244	+	0.128198i
$547$	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
$552$	−311.975	+	294.565i	−0.565172	+	0.533631i
$553$	856.762	+	622.474i	1.54930	+	1.12563i
$554$	63.8435	+	87.8731i	0.115241	+	0.158616i
$555$	36.2936	+	281.144i	0.0653939	+	0.506566i
$556$	−0.744335	+	2.29083i	−0.00133873	+	0.00412019i
$557$	−431.366	−	593.724i	−0.774445	−	1.06593i	−0.995873	−	0.0907553i	$-0.971072\pi$
$557$	−431.366	−	593.724i	−0.774445	−	1.06593i	0.221428	−	0.975177i	$-0.428928\pi$
$558$	−27.4706	−	104.626i	−0.0492305	−	0.187501i
$559$	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	−0.984592	−	0.174868i	$-0.944050\pi$
$563$	−944.916	+	307.022i	−1.67836	+	0.545332i	−0.693767	+	0.720200i	$0.744050\pi$
$564$	−109.041	−	20.4937i	−0.193336	−	0.0363363i
$565$	−894.065	+	649.576i	−1.58242	+	1.14969i
$566$	43.7452	+	14.2137i	0.0772884	+	0.0251125i
$567$	−753.614	−	86.8876i	−1.32913	−	0.153241i
$568$	−4.13145	+	3.00168i	−0.00727368	+	0.00528464i
$569$	−626.713	+	862.596i	−1.10143	+	1.51599i	−0.267950	+	0.963433i	$0.586346\pi$
$569$	−626.713	+	862.596i	−1.10143	+	1.51599i	−0.833478	+	0.552553i	$0.813654\pi$
$570$	99.1495	−	93.6162i	0.173947	−	0.164239i
$571$	−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
$576$	12.2520	−	213.237i	0.0212708	−	0.370203i
$577$	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
$579$	−33.4232	−	18.2564i	−0.0577257	−	0.0315309i
$580$	−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
$585$	−88.4608	+	227.026i	−0.151215	+	0.388078i
$586$	−201.289	−	146.245i	−0.343497	−	0.249565i
$587$	−34.6014	−	47.6247i	−0.0589461	−	0.0811324i	0.778526	−	0.627612i	$-0.215968\pi$
$587$	−34.6014	−	47.6247i	−0.0589461	−	0.0811324i	−0.837472	+	0.546480i	$0.815968\pi$
$588$	407.389	−	52.5910i	0.692838	−	0.0894404i
$589$	−56.1699	+	172.873i	−0.0953649	+	0.293503i
$590$	105.570	+	145.305i	0.178932	+	0.246279i
$591$	992.697	+	186.571i	1.67969	+	0.315687i
$592$	47.9487	+	147.571i	0.0809945	+	0.249275i
$593$			149.728i			0.252493i	0.991999	+	0.126247i	$0.0402931\pi$
$593$			149.728i			0.252493i	−0.991999	+	0.126247i	$0.959707\pi$
$594$		0			0
$595$	1819.01			3.05715
$596$	−665.803	+	216.333i	−1.11712	+	0.362974i
$597$	101.884	−	542.096i	0.170659	−	0.908034i
$598$	64.0394	−	46.5274i	0.107089	−	0.0778049i
$599$	−421.867	−	137.073i	−0.704286	−	0.228836i	−0.0650891	−	0.997879i	$-0.520733\pi$
$599$	−421.867	−	137.073i	−0.704286	−	0.228836i	−0.639197	+	0.769043i	$0.720733\pi$
$600$	−33.7270	−	261.262i	−0.0562117	−	0.435436i
$601$	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
$603$	−258.601	−	100.764i	−0.428857	−	0.167105i
$604$	−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
$609$	−217.509	+	398.209i	−0.357158	+	0.653874i
$610$	−32.0858	+	98.7500i	−0.0525997	+	0.161885i
$611$	41.4832	+	13.4787i	0.0678940	+	0.0220601i
$612$	−951.055	−	54.6448i	−1.55401	−	0.0892888i
$613$	−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	$0.0991661\pi$
$617$			378.251i			0.613049i	−0.951863	+	0.306524i	$0.900834\pi$
$618$	−73.8288	−	78.1925i	−0.119464	−	0.126525i
$619$	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
$621$	638.960	+	398.223i	1.02892	+	0.641260i
$622$	70.6899	−	217.561i	0.113649	−	0.349777i
$623$	−112.296	−	154.563i	−0.180251	−	0.248094i
$624$	−24.6340	+	131.071i	−0.0394776	+	0.210050i
$625$	−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
$630$	−360.066	+	94.5393i	−0.571534	+	0.150062i
$631$	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
$633$	−535.580	+	69.1394i	−0.846097	+	0.109225i
$634$	86.0626	−	62.5281i	0.135745	−	0.0986248i
$635$	554.363	−	763.015i	0.873012	−	1.20160i
$636$	−439.996	−	466.003i	−0.691818	−	0.732708i
$637$	−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	$-0.561092\pi$
$641$	513.946	−	707.386i	0.801788	−	1.10357i	0.992539	−	0.121928i	$-0.0389078\pi$
$642$	−122.405	−	66.8601i	−0.190662	−	0.104143i
$643$	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
$645$	−600.523	+	1099.42i	−0.931044	+	1.70452i
$646$	−169.567	−	123.197i	−0.262487	−	0.190708i
$647$	706.330	−	229.501i	1.09170	−	0.354715i	0.292798	−	0.956174i	$-0.405414\pi$
$647$	706.330	−	229.501i	1.09170	−	0.354715i	0.798903	+	0.601459i	$0.205414\pi$
$648$	407.218	−	82.2808i	0.628423	−	0.126977i
$649$		0			0
$650$			48.5994i			0.0747684i
$651$	360.814	−	340.678i	0.554246	−	0.523314i
$652$	400.150	+	290.726i	0.613727	+	0.445899i
$653$	−653.864	−	899.967i	−1.00132	−	1.37820i	−0.924510	−	0.381158i	$-0.875525\pi$
$653$	−653.864	−	899.967i	−1.00132	−	1.37820i	−0.0768135	−	0.997045i	$-0.524475\pi$
$654$	9.86069	+	76.3846i	0.0150775	+	0.116796i
$655$	349.256	−	1074.90i	0.533215	−	1.64107i
$656$	219.279	+	301.812i	0.334267	+	0.460079i
$657$	−813.652	+	213.633i	−1.23843	+	0.325165i
$658$	20.5939	+	63.3815i	0.0312977	+	0.0963244i
$659$			829.020i			1.25800i	0.777407	+	0.628998i	$0.216535\pi$
$659$			829.020i			1.25800i	−0.777407	+	0.628998i	$0.783465\pi$
$660$		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
$663$	368.061	+	69.1748i	0.555145	+	0.104336i
$664$	431.834	−	313.746i	0.650352	−	0.472508i
$665$	594.938	+	193.307i	0.894643	+	0.290687i
$666$	−75.0300	+	48.1898i	−0.112658	+	0.0723571i
$667$	364.320	−	264.694i	0.546207	−	0.396843i
$668$	285.643	−	393.154i	0.427610	−	0.588555i
$669$	−573.813	+	541.790i	−0.857717	+	0.809850i
$670$	−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
$675$	−428.386	+	173.665i	−0.634646	+	0.257282i
$676$	−165.692	+	509.949i	−0.245107	+	0.754362i
$677$	−964.286	−	313.315i	−1.42435	−	0.462800i	−0.507369	−	0.861729i	$-0.669382\pi$
$677$	−964.286	−	313.315i	−1.42435	−	0.462800i	−0.916982	+	0.398929i	$0.869382\pi$
$678$	−305.091	−	166.646i	−0.449986	−	0.245791i
$679$	−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	$-0.865235\pi$
$683$		−	561.211i		−	0.821685i	0.911706	−	0.410842i	$-0.134765\pi$
$684$	−305.252	−	118.942i	−0.446275	−	0.173892i
$685$	−426.843	−	310.120i	−0.623129	−	0.452730i
$686$	38.5377	+	53.0426i	0.0561775	+	0.0773216i
$687$	−1048.59	+	135.365i	−1.52633	+	0.197038i
$688$	−211.894	+	652.144i	−0.307986	+	0.947883i
$689$	148.097	+	203.838i	0.214945	+	0.295847i
$690$	363.110	+	68.2443i	0.526247	+	0.0989048i
$691$	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
$696$	45.8984	−	244.214i	0.0659460	−	0.350882i
$697$	847.516	−	615.757i	1.21595	−	0.883438i
$698$	86.0521	+	27.9600i	0.123284	+	0.0400573i
$699$	13.5977	+	105.333i	0.0194531	+	0.150691i
$700$	458.800	−	333.338i	0.655429	−	0.476197i
$701$	415.641	−	572.080i	0.592925	−	0.816092i	−0.402112	−	0.915590i	$-0.631724\pi$
$701$	415.641	−	572.080i	0.592925	−	0.816092i	0.995038	+	0.0994987i	$0.0317239\pi$
$702$	−76.4518	+	5.43636i	−0.108906	+	0.00774410i
$703$	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
$708$	206.848	−	378.690i	0.292158	−	0.534873i
$709$	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
$711$	−58.3769	+	1016.01i	−0.0821053	+	1.42899i
$712$	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
$717$	269.391	+	285.314i	0.375720	+	0.397927i
$718$	331.843	+	241.098i	0.462177	+	0.335791i
$719$	495.361	+	681.806i	0.688958	+	0.948270i	0.999998	−	0.00212717i	$-0.000677098\pi$
$719$	495.361	+	681.806i	0.688958	+	0.948270i	−0.311039	+	0.950397i	$0.600677\pi$
$720$	−523.764	+	336.400i	−0.727451	+	0.467223i
$721$	152.448	−	469.187i	0.211440	−	0.650745i
$722$	102.032	+	140.434i	0.141318	+	0.194508i
$723$	−74.5447	+	396.633i	−0.103105	+	0.548593i
$724$	−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
$729$	−321.112	−	654.468i	−0.440483	−	0.897761i
$730$	−333.976	+	242.647i	−0.457501	+	0.332394i
$731$	1831.28	+	595.020i	2.50518	+	0.813981i
$732$	247.401	−	31.9376i	0.337979	−	0.0436306i
$733$	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
$735$	−517.463	−	548.048i	−0.704031	−	0.745644i
$736$	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
$741$	113.030	+	61.7390i	0.152537	+	0.0833185i
$742$	−118.960	+	366.121i	−0.160323	+	0.493424i
$743$	12.0434	+	3.91313i	0.0162091	+	0.00526666i	0.317110	−	0.948389i	$-0.397287\pi$
$743$	12.0434	+	3.91313i	0.0162091	+	0.00526666i	−0.300901	+	0.953655i	$0.597287\pi$
$744$	−130.274	+	238.501i	−0.175099	+	0.320565i
$745$	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
$750$	75.9121	−	71.6756i	0.101216	−	0.0955675i
$751$	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
$753$	155.390	+	1203.71i	0.206361	+	1.59855i
$754$	−14.1663	+	43.5994i	−0.0187882	+	0.0578242i
$755$	339.188	+	466.852i	0.449255	+	0.618346i
$756$	575.696	+	684.452i	0.761502	+	0.905359i
$757$	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	−0.870994	−	0.491294i	$-0.836524\pi$
$761$	−979.307	+	318.196i	−1.28687	+	0.418129i	−0.415874	+	0.909422i	$0.636524\pi$
$762$	291.576	+	54.7999i	0.382646	+	0.0719158i
$763$	−285.840	+	207.675i	−0.374627	+	0.272182i
$764$	−96.3766	−	31.3146i	−0.126147	−	0.0409877i
$765$	944.645	+	1470.78i	1.23483	+	1.92259i
$766$	−331.789	+	241.059i	−0.433145	+	0.314698i
$767$	−99.7094	+	137.238i	−0.129999	+	0.178928i
$768$	−18.2153	+	17.1987i	−0.0237178	+	0.0223942i
$769$	−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	−0.958830	−	0.283980i	$-0.908345\pi$
$773$	−303.368	+	417.550i	−0.392455	+	0.540168i	0.566376	+	0.824147i	$0.308345\pi$
$774$	−393.422	−	22.6048i	−0.508297	−	0.0292052i
$775$	93.4390	−	287.576i	0.120566	−	0.371065i
$776$	927.200	+	301.265i	1.19485	+	0.388229i
$777$	−359.010	−	196.098i	−0.462046	−	0.252379i
$778$	−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
$783$	−434.934	+	30.9275i	−0.555472	+	0.0394987i
$784$	−333.777	−	242.503i	−0.425736	−	0.309315i
$785$	−254.584	−	350.404i	−0.324310	−	0.446375i
$786$	352.603	−	45.5185i	0.448605	−	0.0579116i
$787$	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
$789$	406.880	+	76.4706i	0.515691	+	0.0969209i
$790$	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
$795$	−217.222	+	1155.78i	−0.273236	+	1.45382i
$796$	−526.106	+	382.238i	−0.660937	+	0.480199i
$797$	−1395.59	−	453.455i	−1.75105	−	0.568952i	−0.754842	−	0.655907i	$-0.772286\pi$
$797$	−1395.59	−	453.455i	−1.75105	−	0.568952i	−0.996212	+	0.0869550i	$0.972286\pi$
$798$	25.1937	+	195.160i	0.0315711	+	0.244561i
$799$	253.163	−	183.934i	0.316850	−	0.230205i
$800$	−279.435	+	384.610i	−0.349294	+	0.480762i
$801$	66.6561	−	171.066i	0.0832161	−	0.213566i
$802$	−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
$807$	44.4283	−	81.3379i	0.0550537	−	0.100791i
$808$	75.4493	−	232.209i	0.0933778	−	0.287387i
$809$	−24.4139	−	7.93257i	−0.0301779	−	0.00980540i	0.293889	−	0.955840i	$-0.405050\pi$
$809$	−24.4139	−	7.93257i	−0.0301779	−	0.00980540i	−0.324067	+	0.946034i	$0.605050\pi$
$810$	−263.431	−	242.040i	−0.325223	−	0.298815i
$811$	−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
$816$	656.870	+	695.695i	0.804988	+	0.852568i
$817$	535.720	+	389.224i	0.655716	+	0.476406i
$818$	−181.511	−	249.829i	−0.221897	−	0.305414i
$819$	−190.011	−	295.841i	−0.232003	−	0.361222i
$820$	248.304	−	764.203i	0.302810	−	0.931954i
$821$	553.696	+	762.098i	0.674417	+	0.928255i	0.999850	−	0.0173098i	$-0.00551014\pi$
$821$	553.696	+	762.098i	0.674417	+	0.928255i	−0.325433	+	0.945565i	$0.605510\pi$
$822$	30.6560	−	163.112i	0.0372944	−	0.198434i
$823$	−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	−0.241443	−	0.970415i	$-0.577621\pi$
$827$	110.504	−	35.9050i	0.133620	−	0.0434159i	0.375064	+	0.926999i	$0.377621\pi$
$828$	−225.418	−	858.537i	−0.272244	−	1.03688i
$829$	−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
$831$	−474.889	+	61.3047i	−0.571466	+	0.0737722i
$832$	80.0892	−	58.1882i	0.0962610	−	0.0699377i
$833$	−680.973	+	937.279i	−0.817494	+	1.12518i
$834$	0.954512	+	1.01093i	0.00114450	+	0.00121215i
$835$	−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	−0.994723	−	0.102600i	$-0.967284\pi$
$839$	−494.807	+	681.043i	−0.589758	+	0.811732i	0.404965	+	0.914332i	$0.367284\pi$
$840$	820.792	+	448.332i	0.977134	+	0.533729i
$841$	179.291	−	551.801i	0.213188	−	0.656125i
$842$	148.201	+	48.1535i	0.176011	+	0.0571894i
$843$	571.257	−	1045.84i	0.677647	−	1.24061i
$844$	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
$849$	−147.436	+	139.208i	−0.173659	+	0.163967i
$850$	282.075	+	204.940i	0.331853	+	0.241106i
$851$	238.638	+	328.457i	0.280421	+	0.385966i
$852$	−1.35260	−	10.4778i	−0.00158756	−	0.0122978i
$853$	−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
$855$	152.662	+	581.433i	0.178552	+	0.680039i
$856$	108.281	+	333.253i	0.126496	+	0.389315i
$857$		−	519.778i		−	0.606509i	−0.952910	−	0.303254i	$-0.901927\pi$
$857$		−	519.778i		−	0.606509i	0.952910	−	0.303254i	$-0.0980732\pi$
$858$		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
$861$	−966.604	−	181.667i	−1.12265	−	0.210996i
$862$	−307.738	+	223.585i	−0.357005	+	0.259379i
$863$	−1079.28	−	350.678i	−1.25061	−	0.406348i	−0.392471	−	0.919765i	$-0.628380\pi$
$863$	−1079.28	−	350.678i	−1.25061	−	0.406348i	−0.858139	+	0.513417i	$0.828380\pi$
$864$	−636.287	−	396.557i	−0.736443	−	0.458978i
$865$	−5.55656	+	4.03708i	−0.00642377	+	0.00466714i
$866$	115.309	−	158.709i	0.133151	−	0.183266i
$867$	1323.18	−	1249.34i	1.52616	−	1.44099i
$868$	−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
$873$	98.1308	−	1707.90i	0.112406	−	1.95636i
$874$	60.3503	−	185.739i	0.0690507	−	0.212516i
$875$	455.503	+	148.002i	0.520575	+	0.169145i
$876$	870.401	+	475.430i	0.993608	+	0.542728i
$877$	−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	$0.321994\pi$
$881$			1493.59i			1.69534i	−0.530526	+	0.847668i	$0.678006\pi$
$882$	86.0831	−	220.924i	0.0975999	−	0.250480i
$883$	−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
$885$	−785.263	+	101.372i	−0.887303	+	0.114544i
$886$	−59.1502	+	182.046i	−0.0667609	+	0.205469i
$887$	−489.520	−	673.766i	−0.551882	−	0.759601i	0.438384	−	0.898788i	$-0.355551\pi$
$887$	−489.520	−	673.766i	−0.551882	−	0.759601i	−0.990266	+	0.139187i	$0.955551\pi$
$888$	220.174	+	41.3802i	0.247943	+	0.0465994i
$889$	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
$894$	−74.6392	+	397.136i	−0.0834890	+	0.444224i
$895$	455.464	−	330.914i	0.508898	−	0.369736i
$896$	1133.20	+	368.198i	1.26473	+	0.410935i
$897$	44.6771	+	346.085i	0.0498072	+	0.385825i
$898$	−152.888	+	111.079i	−0.170253	+	0.123696i
$899$	167.652	−	230.753i	0.186487	−	0.256677i
$900$	507.789	+	197.861i	0.564210	+	0.219845i
$901$	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
$906$	−87.0173	+	159.308i	−0.0960456	+	0.175837i
$907$	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
$909$	−427.729	−	24.5760i	−0.470548	−	0.0270363i
$910$	−139.590	−	101.418i	−0.153396	−	0.111448i
$911$	−53.0058	+	17.2226i	−0.0581842	+	0.0189052i	−0.337964	−	0.941159i	$-0.609738\pi$
$911$	−53.0058	+	17.2226i	−0.0581842	+	0.0189052i	0.279780	+	0.960064i	$0.409738\pi$
$912$	140.909	+	297.345i	0.154505	+	0.326037i
$913$		0			0
$914$			235.612i			0.257781i
$915$	−314.247	−	332.820i	−0.343439	−	0.363738i
$916$	1008.44	+	732.677i	1.10092	+	0.799866i
$917$	958.662	+	1319.49i	1.04543	+	1.43892i
$918$	−290.838	+	466.657i	−0.316817	+	0.508341i
$919$	−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
$921$	268.287	−	1427.49i	0.291300	−	1.54993i
$922$	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
$927$	458.537	−	120.394i	0.494646	−	0.129875i
$928$	−362.797	+	263.587i	−0.390945	+	0.284038i
$929$	−800.150	−	259.984i	−0.861302	−	0.279854i	−0.155130	−	0.987894i	$-0.549580\pi$
$929$	−800.150	−	259.984i	−0.861302	−	0.279854i	−0.706172	+	0.708040i	$0.749580\pi$
$930$	232.087	−	29.9607i	0.249556	−	0.0322158i
$931$	−322.330	+	234.186i	−0.346219	+	0.251543i
$932$	73.5992	−	101.301i	0.0789691	−	0.108692i
$933$	692.332	+	733.254i	0.742050	+	0.785910i
$934$	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
$939$	1287.71	+	703.371i	1.37136	+	0.749064i
$940$	74.1714	−	228.276i	0.0789057	−	0.242847i
$941$	1298.15	+	421.795i	1.37954	+	0.448241i	0.902520	−	0.430649i	$-0.141715\pi$
$941$	1298.15	+	421.795i	1.37954	+	0.448241i	0.477025	+	0.878890i	$0.341715\pi$
$942$	65.3125	−	119.572i	0.0693338	−	0.126934i
$943$	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	$0.238452\pi$
$947$			1289.80i			1.36199i	−0.732289	+	0.680994i	$0.761548\pi$
$948$	872.392	−	823.706i	0.920245	−	0.868888i
$949$	−315.435	−	229.177i	−0.332387	−	0.241493i
$950$	70.4786	+	97.0055i	0.0741880	+	0.102111i
$951$	60.0416	+	465.104i	0.0631352	+	0.489069i
$952$	444.224	−	1367.18i	0.466622	−	1.43611i
$953$	−389.907	−	536.661i	−0.409137	−	0.563128i	0.553871	−	0.832602i	$-0.313150\pi$
$953$	−389.907	−	536.661i	−0.409137	−	0.563128i	−0.963008	+	0.269474i	$0.913150\pi$
$954$	−357.810	+	93.9470i	−0.375063	+	0.0984769i
$955$	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
$960$	454.114	+	85.3479i	0.473036	+	0.0889041i
$961$	525.103	−	381.510i	0.546413	−	0.396992i
$962$	−39.3076	−	12.7718i	−0.0408602	−	0.0132763i
$963$	517.348	−	332.279i	0.537225	−	0.345046i
$964$	384.933	−	279.670i	0.399308	−	0.290115i
$965$	48.4271	−	66.6541i	0.0501835	−	0.0690716i
$966$	−387.667	+	366.032i	−0.401312	+	0.378915i
$967$	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	−0.958038	−	0.286641i	$-0.907461\pi$
$971$	−378.084	+	520.388i	−0.389376	+	0.535930i	0.568662	+	0.822571i	$0.307461\pi$
$972$	−254.453	+	820.936i	−0.261783	+	0.844584i
$973$	−1.97096	+	6.06599i	−0.00202565	+	0.00623432i
$974$	−13.3065	−	4.32354i	−0.0136617	−	0.00443896i
$975$	−188.026	−	102.703i	−0.192847	−	0.105337i
$976$	−202.697	−	147.268i	−0.207682	−	0.150890i
$977$	1428.41	−	464.118i	1.46204	−	0.475044i	0.533345	−	0.845898i	$-0.320935\pi$
$977$	1428.41	−	464.118i	1.46204	−	0.475044i	0.928691	+	0.370854i	$0.120935\pi$
$978$	257.995	−	122.261i	0.263798	−	0.125011i
$979$		0			0
$980$			888.634i			0.906769i
$981$	−316.361	−	123.270i	−0.322488	−	0.125658i
$982$	−263.489	−	191.436i	−0.268319	−	0.194945i
$983$	428.555	+	589.856i	0.435967	+	0.600057i	0.969310	−	0.245842i	$-0.0790645\pi$
$983$	428.555	+	589.856i	0.435967	+	0.600057i	−0.533343	+	0.845899i	$0.679065\pi$
$984$	534.192	−	68.9603i	0.542878	−	0.0700816i
$985$	−675.245	+	2078.19i	−0.685528	+	2.10984i
$986$	193.317	+	266.078i	0.196062	+	0.269856i
$987$	−288.736	−	54.2661i	−0.292539	−	0.0549808i
$988$	−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
$993$	22.3199	−	118.758i	0.0224772	−	0.119596i
$994$	−5.13383	+	3.72995i	−0.00516482	+	0.00375246i
$995$	1134.87	+	368.741i	1.14057	+	0.370594i
$996$	141.379	+	1095.17i	0.141947	+	1.09957i
$997$	−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
$999$	−27.8830	−	392.120i	−0.0279109	−	0.392513i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-0.647210 + 0.210291i) q^{2} +(0.554129 - 2.94838i) q^{3} +(-2.86141 + 2.07894i) q^{4} +(6.17237 + 2.00553i) q^{5} +(0.261380 + 2.02475i) q^{6} +(-7.57686 + 5.50491i) q^{7} +(3.01474 - 4.14944i) q^{8} +(-8.38588 - 3.26757i) q^{9} -4.41657 q^{10} +(4.54390 + 9.58852i) q^{12} +(-1.28903 - 3.96722i) q^{13} +(3.74618 - 5.15618i) q^{14} +(9.33334 - 17.0872i) q^{15} +(3.29326 - 10.1356i) q^{16} +(-28.4618 - 9.24781i) q^{17} +(6.11457 + 0.351324i) q^{18} +(-8.32617 - 6.04932i) q^{19} +(-21.8311 + 7.09334i) q^{20} +(12.0320 + 25.3899i) q^{21} -27.8850i q^{23} +(-10.5636 - 11.1879i) q^{24} +(13.8506 + 10.0631i) q^{25} +(1.66854 + 2.29655i) q^{26} +(-14.2809 + 22.9141i) q^{27} +(10.2361 - 31.5036i) q^{28} +(9.49235 + 13.0651i) q^{29} +(-2.44735 + 13.0217i) q^{30} +(-5.45778 - 16.7973i) q^{31} +27.7684i q^{32} +20.3655 q^{34} +(-57.8074 + 18.7828i) q^{35} +(30.7885 - 8.08386i) q^{36} +(-11.7790 + 8.55794i) q^{37} +(6.66090 + 2.16426i) q^{38} +(-12.4112 + 1.60219i) q^{39} +(26.9299 - 19.5657i) q^{40} +(-20.5756 + 28.3199i) q^{41} +(-13.1265 - 13.9024i) q^{42} -64.3417 q^{43} +(-45.2076 - 36.9867i) q^{45} +(5.86397 + 18.0474i) q^{46} +(-6.14617 + 8.45948i) q^{47} +(-28.0588 - 15.3262i) q^{48} +(11.9629 - 36.8181i) q^{49} +(-11.0804 - 3.60026i) q^{50} +(-43.0376 + 78.7918i) q^{51} +(11.9360 + 8.67204i) q^{52} +(-57.4452 + 18.6651i) q^{53} +(4.42410 - 17.8334i) q^{54} +48.0356i q^{56} +(-22.4495 + 21.1966i) q^{57} +(-8.89102 - 6.45971i) q^{58} +(-23.9032 - 32.8999i) q^{59} +(8.81663 + 68.2968i) q^{60} +(7.26488 - 22.3590i) q^{61} +(7.06466 + 9.72367i) q^{62} +(81.5263 - 21.4056i) q^{63} +(7.33362 + 22.5705i) q^{64} -27.0724i q^{65} +30.8376 q^{67} +(100.667 - 32.7086i) q^{68} +(-82.2155 - 15.4519i) q^{69} +(33.4637 - 24.3128i) q^{70} +(-0.946935 - 0.307678i) q^{71} +(-38.8398 + 24.9458i) q^{72} +(75.6188 - 54.9403i) q^{73} +(5.82382 - 8.01580i) q^{74} +(37.3448 - 35.2607i) q^{75} +36.4007 q^{76} +(7.69570 - 3.64691i) q^{78} +(-34.9425 - 107.542i) q^{79} +(40.6545 - 55.9561i) q^{80} +(59.6460 + 54.8029i) q^{81} +(7.36131 - 22.6558i) q^{82} +(98.9769 + 32.1595i) q^{83} +(-87.2124 - 47.6371i) q^{84} +(-157.130 - 114.162i) q^{85} +(41.6426 - 13.5305i) q^{86} +(43.7809 - 20.7473i) q^{87} +20.3993i q^{89} +(37.0368 + 14.4314i) q^{90} +(31.6060 + 22.9631i) q^{91} +(57.9711 + 79.7904i) q^{92} +(-52.5492 + 6.78372i) q^{93} +(2.19891 - 6.76754i) q^{94} +(-39.2602 - 54.0370i) q^{95} +(81.8717 + 15.3873i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more