LMFDB - Embedded newform 363.3.h.j.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)

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);

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")

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 = [16,0,-10,8,0,33,-6] 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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 12x^{14} + 180x^{12} - 2562x^{10} + 25179x^{8} - 96398x^{6} + 239275x^{4} - 536393x^{2} + 1771561 $ x^16 - 12x^14 + 180x^12 - 2562x^10 + 25179x^8 - 96398x^6 + 239275x^4 - 536393*x^2 + 1771561
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			269.4
Root			$2.91048 - 0.945671i$ of defining polynomial
Character	$\chi$	$=$	363.269
Dual form			363.3.h.j.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+(2.91048 - 0.945671i) q^{2} +(1.65950 - 2.49921i) q^{3} +(4.34051 - 3.15356i) q^{4} +(6.31437 + 2.05166i) q^{5} +(2.46650 - 8.84324i) q^{6} +(-2.47800 + 1.80037i) q^{7} +(2.45561 - 3.37986i) q^{8} +(-3.49213 - 8.29488i) q^{9} +20.3180 q^{10} +(-0.678356 - 16.0812i) q^{12} +(-5.01988 - 15.4496i) q^{13} +(-5.50960 + 7.58331i) q^{14} +(15.6062 - 12.3762i) q^{15} +(-2.68094 + 8.25108i) q^{16} +(0.766216 + 0.248959i) q^{17} +(-18.0080 - 20.8396i) q^{18} +(16.7481 + 12.1682i) q^{19} +(33.8776 - 11.0075i) q^{20} +(0.387274 + 9.18076i) q^{21} +27.3224i q^{23} +(-4.37190 - 11.7460i) q^{24} +(15.4365 + 11.2153i) q^{25} +(-29.2204 - 40.2185i) q^{26} +(-26.5259 - 5.03778i) q^{27} +(-5.07819 + 15.6291i) q^{28} +(-2.22341 - 3.06025i) q^{29} +(33.7177 - 50.7790i) q^{30} +(-6.42137 - 19.7630i) q^{31} +43.2608i q^{32} +2.46549 q^{34} +(-19.3408 + 6.28420i) q^{35} +(-41.3160 - 24.9913i) q^{36} +(-31.1905 + 22.6613i) q^{37} +(60.2520 + 19.5771i) q^{38} +(-46.9423 - 13.0928i) q^{39} +(22.4400 - 16.3036i) q^{40} +(7.86024 - 10.8187i) q^{41} +(9.80913 + 26.3542i) q^{42} -43.4125 q^{43} +(-5.03227 - 59.5416i) q^{45} +(25.8380 + 79.5212i) q^{46} +(11.6912 - 16.0916i) q^{47} +(16.1722 + 20.3929i) q^{48} +(-12.2427 + 37.6791i) q^{49} +(55.5336 + 18.0440i) q^{50} +(1.89374 - 1.50179i) q^{51} +(-70.5100 - 51.2285i) q^{52} +(16.8103 - 5.46201i) q^{53} +(-81.9669 + 10.4224i) q^{54} +12.7963i q^{56} +(58.2044 - 21.6639i) q^{57} +(-9.36516 - 6.80419i) q^{58} +(-25.5837 - 35.2129i) q^{59} +(28.7098 - 102.934i) q^{60} +(-3.29249 + 10.1333i) q^{61} +(-37.3785 - 51.4471i) q^{62} +(23.5874 + 14.2676i) q^{63} +(30.1867 + 92.9052i) q^{64} -107.854i q^{65} +72.2963 q^{67} +(4.11087 - 1.33570i) q^{68} +(68.2845 + 45.3415i) q^{69} +(-50.3481 + 36.5800i) q^{70} +(2.44412 + 0.794142i) q^{71} +(-36.6108 - 8.56611i) q^{72} +(-36.7931 + 26.7318i) q^{73} +(-69.3492 + 95.4510i) q^{74} +(53.6463 - 19.9674i) q^{75} +111.068 q^{76} +(-149.006 + 6.28555i) q^{78} +(30.3585 + 93.4339i) q^{79} +(-33.8569 + 46.6000i) q^{80} +(-56.6101 + 57.9335i) q^{81} +(12.6461 - 38.9207i) q^{82} +(30.3393 + 9.85783i) q^{83} +(30.6331 + 38.6279i) q^{84} +(4.32739 + 3.14404i) q^{85} +(-126.351 + 41.0540i) q^{86} +(-11.3380 + 0.478272i) q^{87} +18.5409i q^{89} +(-70.9531 - 168.536i) q^{90} +(40.2543 + 29.2464i) q^{91} +(86.1629 + 118.593i) q^{92} +(-60.0481 - 16.7482i) q^{93} +(18.8097 - 57.8902i) q^{94} +(80.7886 + 111.196i) q^{95} +(108.118 + 71.7913i) q^{96} +(-19.5614 - 60.2037i) q^{97} +121.242i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 10 q^{3} + 8 q^{4} + 33 q^{6} - 6 q^{7} - 28 q^{9} + 12 q^{10} + 106 q^{12} + 42 q^{13} + 82 q^{15} - 88 q^{16} + 43 q^{18} + 134 q^{19} + 12 q^{21} - 41 q^{24} + 134 q^{25} + 80 q^{27} - 264 q^{28}+ \cdots + 72 q^{97}+O(q^{100}) $ 16 * q - 10 * q^3 + 8 * q^4 + 33 * q^6 - 6 * q^7 - 28 * q^9 + 12 * q^10 + 106 * q^12 + 42 * q^13 + 82 * q^15 - 88 * q^16 + 43 * q^18 + 134 * q^19 + 12 * q^21 - 41 * q^24 + 134 * q^25 + 80 * q^27 - 264 * q^28 + 120 * q^30 + 124 * q^31 - 132 * q^34 - 219 * q^36 + 90 * q^37 + 174 * q^39 + 284 * q^40 - 102 * q^42 + 156 * q^43 - 72 * q^45 + 22 * q^46 + 30 * q^48 - 30 * q^49 - 111 * q^51 - 326 * q^52 - 1046 * q^54 - 281 * q^57 - 116 * q^58 + 54 * q^60 + 126 * q^61 + 138 * q^63 + 236 * q^64 + 368 * q^67 + 198 * q^69 - 322 * q^70 + 562 * q^72 - 24 * q^73 - 21 * q^75 + 900 * q^76 - 492 * q^78 + 314 * q^79 - 388 * q^81 - 270 * q^84 - 318 * q^85 - 132 * q^87 - 176 * q^90 + 374 * q^91 - 10 * q^93 - 990 * q^94 + 332 * q^96 + 72 * 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 $

$2$	2.91048	−	0.945671i	1.45524	−	0.472835i	0.528626	−	0.848855i	$-0.322707\pi$
$2$	2.91048	−	0.945671i	1.45524	−	0.472835i	0.926612	+	0.376020i	$0.122707\pi$
$3$	1.65950	−	2.49921i	0.553166	−	0.833071i
$3$	1.65950	−	2.49921i	0.553166	−	0.833071i
$4$	4.34051	−	3.15356i	1.08513	−	0.788390i
$5$	6.31437	+	2.05166i	1.26287	+	0.410333i	0.862518	−	0.506027i	$-0.168886\pi$
$5$	6.31437	+	2.05166i	1.26287	+	0.410333i	0.400357	+	0.916359i	$0.368886\pi$
$6$	2.46650	−	8.84324i	0.411083	−	1.47387i
$7$	−2.47800	+	1.80037i	−0.354000	+	0.257196i	−0.750545	−	0.660819i	$-0.770209\pi$
$7$	−2.47800	+	1.80037i	−0.354000	+	0.257196i	0.396545	+	0.918015i	$0.370209\pi$
$8$	2.45561	−	3.37986i	0.306951	−	0.422482i
$9$	−3.49213	−	8.29488i	−0.388014	−	0.921653i
$10$	20.3180			2.03180
$11$		0			0
$11$		0			0
$12$	−0.678356	−	16.0812i	−0.0565297	−	1.34010i
$13$	−5.01988	−	15.4496i	−0.386144	−	1.18843i	−0.935647	−	0.352938i	$-0.885183\pi$
$13$	−5.01988	−	15.4496i	−0.386144	−	1.18843i	0.549503	−	0.835492i	$-0.314817\pi$
$14$	−5.50960	+	7.58331i	−0.393543	+	0.541665i
$15$	15.6062	−	12.3762i	1.04042	−	0.825081i
$16$	−2.68094	+	8.25108i	−0.167559	+	0.515693i
$17$	0.766216	+	0.248959i	0.0450715	+	0.0146446i	0.331466	−	0.943467i	$-0.392457\pi$
$17$	0.766216	+	0.248959i	0.0450715	+	0.0146446i	−0.286394	+	0.958112i	$0.592457\pi$
$18$	−18.0080	−	20.8396i	−1.00044	−	1.15776i
$19$	16.7481	+	12.1682i	0.881479	+	0.640432i	0.933642	−	0.358207i	$-0.116612\pi$
$19$	16.7481	+	12.1682i	0.881479	+	0.640432i	−0.0521636	+	0.998639i	$0.516612\pi$
$20$	33.8776	−	11.0075i	1.69388	−	0.550375i
$21$	0.387274	+	9.18076i	0.0184416	+	0.437179i
$22$		0			0
$23$			27.3224i			1.18793i	0.804491	+	0.593965i	$0.202438\pi$
$23$			27.3224i			1.18793i	−0.804491	+	0.593965i	$0.797562\pi$
$24$	−4.37190	−	11.7460i	−0.182163	−	0.489415i
$25$	15.4365	+	11.2153i	0.617462	+	0.448612i
$26$	−29.2204	−	40.2185i	−1.12386	−	1.54687i
$27$	−26.5259	−	5.03778i	−0.982439	−	0.186585i
$28$	−5.07819	+	15.6291i	−0.181364	+	0.558180i
$29$	−2.22341	−	3.06025i	−0.0766691	−	0.105526i	0.768960	−	0.639297i	$-0.220774\pi$
$29$	−2.22341	−	3.06025i	−0.0766691	−	0.105526i	−0.845629	+	0.533771i	$0.820774\pi$
$30$	33.7177	−	50.7790i	1.12392	−	1.69263i
$31$	−6.42137	−	19.7630i	−0.207141	−	0.637515i	−0.999619	−	0.0276136i	$-0.991209\pi$
$31$	−6.42137	−	19.7630i	−0.207141	−	0.637515i	0.792478	−	0.609901i	$-0.208791\pi$
$32$			43.2608i			1.35190i
$33$		0			0
$34$	2.46549			0.0725143
$35$	−19.3408	+	6.28420i	−0.552593	+	0.179548i
$36$	−41.3160	−	24.9913i	−1.14767	−	0.694204i
$37$	−31.1905	+	22.6613i	−0.842988	+	0.612466i	−0.923204	−	0.384311i	$-0.874439\pi$
$37$	−31.1905	+	22.6613i	−0.842988	+	0.612466i	0.0802160	+	0.996778i	$0.474439\pi$
$38$	60.2520	+	19.5771i	1.58558	+	0.515186i
$39$	−46.9423	−	13.0928i	−1.20365	−	0.335714i
$40$	22.4400	−	16.3036i	0.560999	−	0.407590i
$41$	7.86024	−	10.8187i	0.191713	−	0.263871i	−0.702330	−	0.711852i	$-0.747857\pi$
$41$	7.86024	−	10.8187i	0.191713	−	0.263871i	0.894043	+	0.447981i	$0.147857\pi$
$42$	9.80913	+	26.3542i	0.233551	+	0.627480i
$43$	−43.4125			−1.00959			−0.504797	−	0.863238i	$-0.668433\pi$
$43$	−43.4125			−1.00959			−0.504797	+	0.863238i	$0.668433\pi$
$44$		0			0
$45$	−5.03227	−	59.5416i	−0.111828	−	1.32315i
$46$	25.8380	+	79.5212i	0.561695	+	1.72872i
$47$	11.6912	−	16.0916i	0.248749	−	0.342374i	−0.666323	−	0.745663i	$-0.732133\pi$
$47$	11.6912	−	16.0916i	0.248749	−	0.342374i	0.915073	+	0.403289i	$0.132133\pi$
$48$	16.1722	+	20.3929i	0.336921	+	0.424852i
$49$	−12.2427	+	37.6791i	−0.249851	+	0.768962i
$50$	55.5336	+	18.0440i	1.11067	+	0.360880i
$51$	1.89374	−	1.50179i	0.0371321	−	0.0294469i
$52$	−70.5100	−	51.2285i	−1.35596	−	0.985164i
$53$	16.8103	−	5.46201i	0.317176	−	0.103057i	−0.146102	−	0.989269i	$-0.546673\pi$
$53$	16.8103	−	5.46201i	0.317176	−	0.103057i	0.463279	+	0.886213i	$0.346673\pi$
$54$	−81.9669	+	10.4224i	−1.51791	+	0.193007i
$55$		0			0
$56$			12.7963i			0.228505i
$57$	58.2044	−	21.6639i	1.02113	−	0.380069i
$58$	−9.36516	−	6.80419i	−0.161468	−	0.117314i
$59$	−25.5837	−	35.2129i	−0.433621	−	0.596828i	0.535158	−	0.844752i	$-0.320252\pi$
$59$	−25.5837	−	35.2129i	−0.433621	−	0.596828i	−0.968780	+	0.247923i	$0.920252\pi$
$60$	28.7098	−	102.934i	0.478496	−	1.71557i
$61$	−3.29249	+	10.1333i	−0.0539753	+	0.166119i	−0.974410	−	0.224777i	$-0.927835\pi$
$61$	−3.29249	+	10.1333i	−0.0539753	+	0.166119i	0.920435	+	0.390896i	$0.127835\pi$
$62$	−37.3785	−	51.4471i	−0.602879	−	0.829792i
$63$	23.5874	+	14.2676i	0.374403	+	0.226470i
$64$	30.1867	+	92.9052i	0.471667	+	1.45164i
$65$		−	107.854i		−	1.65929i
$66$		0			0
$67$	72.2963			1.07905			0.539525	−	0.841970i	$-0.318604\pi$
$67$	72.2963			1.07905			0.539525	+	0.841970i	$0.318604\pi$
$68$	4.11087	−	1.33570i	0.0604540	−	0.0196427i
$69$	68.2845	+	45.3415i	0.989630	+	0.657123i
$70$	−50.3481	+	36.5800i	−0.719258	+	0.522571i
$71$	2.44412	+	0.794142i	0.0344242	+	0.0111851i	0.326178	−	0.945308i	$-0.394239\pi$
$71$	2.44412	+	0.794142i	0.0344242	+	0.0111851i	−0.291754	+	0.956493i	$0.594239\pi$
$72$	−36.6108	−	8.56611i	−0.508484	−	0.118974i
$73$	−36.7931	+	26.7318i	−0.504015	+	0.366188i	−0.810549	−	0.585671i	$-0.800831\pi$
$73$	−36.7931	+	26.7318i	−0.504015	+	0.366188i	0.306533	+	0.951860i	$0.400831\pi$
$74$	−69.3492	+	95.4510i	−0.937152	+	1.28988i
$75$	53.6463	−	19.9674i	0.715285	−	0.266232i
$76$	111.068			1.46143
$77$		0			0
$78$	−149.006	+	6.28555i	−1.91033	+	0.0805840i
$79$	30.3585	+	93.4339i	0.384285	+	1.18271i	0.936998	+	0.349336i	$0.113593\pi$
$79$	30.3585	+	93.4339i	0.384285	+	1.18271i	−0.552712	+	0.833372i	$0.686407\pi$
$80$	−33.8569	+	46.6000i	−0.423211	+	0.582500i
$81$	−56.6101	+	57.9335i	−0.698890	+	0.715229i
$82$	12.6461	−	38.9207i	0.154221	−	0.474643i
$83$	30.3393	+	9.85783i	0.365534	+	0.118769i	0.486024	−	0.873945i	$-0.338447\pi$
$83$	30.3393	+	9.85783i	0.365534	+	0.118769i	−0.120491	+	0.992714i	$0.538447\pi$
$84$	30.6331	+	38.6279i	0.364679	+	0.459855i
$85$	4.32739	+	3.14404i	0.0509105	+	0.0369887i
$86$	−126.351	+	41.0540i	−1.46920	+	0.477372i
$87$	−11.3380	+	0.478272i	−0.130321	+	0.00549738i
$88$		0			0
$89$			18.5409i			0.208325i	0.994560	+	0.104162i	$0.0332161\pi$
$89$			18.5409i			0.208325i	−0.994560	+	0.104162i	$0.966784\pi$
$90$	−70.9531	−	168.536i	−0.788368	−	1.87262i
$91$	40.2543	+	29.2464i	0.442354	+	0.321389i
$92$	86.1629	+	118.593i	0.936553	+	1.28905i
$93$	−60.0481	−	16.7482i	−0.645678	−	0.180088i
$94$	18.8097	−	57.8902i	0.200103	−	0.615853i
$95$	80.7886	+	111.196i	0.850407	+	1.17048i
$96$	108.118	+	71.7913i	1.12623	+	0.747826i
$97$	−19.5614	−	60.2037i	−0.201664	−	0.620657i	−0.999834	−	0.0182248i	$-0.994199\pi$
$97$	−19.5614	−	60.2037i	−0.201664	−	0.620657i	0.798170	−	0.602432i	$-0.205801\pi$
$98$			121.242i			1.23716i
$99$		0			0
$100$	102.371			1.02371
$101$	−143.000	+	46.4634i	−1.41584	+	0.460034i	−0.914277	−	0.405089i	$-0.867241\pi$
$101$	−143.000	+	46.4634i	−1.41584	+	0.460034i	−0.501561	+	0.865122i	$0.667241\pi$
$102$	4.09147	−	6.16178i	0.0401125	−	0.0604096i
$103$	121.164	−	88.0311i	1.17635	−	0.854671i	0.184597	−	0.982814i	$-0.440902\pi$
$103$	121.164	−	88.0311i	1.17635	−	0.854671i	0.991756	+	0.128144i	$0.0409019\pi$
$104$	−64.5443	−	20.9717i	−0.620618	−	0.201651i
$105$	−16.3904	+	58.7653i	−0.156099	+	0.559670i
$106$	43.7608	−	31.7941i	0.412838	−	0.299944i
$107$	12.1974	−	16.7883i	0.113995	−	0.156900i	−0.748207	−	0.663465i	$-0.769085\pi$
$107$	12.1974	−	16.7883i	0.113995	−	0.156900i	0.862202	+	0.506565i	$0.169085\pi$
$108$	−131.023	+	61.7844i	−1.21317	+	0.572078i
$109$	105.794			0.970583			0.485291	−	0.874352i	$-0.338714\pi$
$109$	105.794			0.970583			0.485291	+	0.874352i	$0.338714\pi$
$110$		0			0
$111$	4.87462	+	115.558i	0.0439155	+	1.04106i
$112$	−8.21165	−	25.2729i	−0.0733183	−	0.225651i
$113$	78.0396	−	107.412i	0.690616	−	0.950552i	−0.309384	−	0.950937i	$-0.600123\pi$
$113$	78.0396	−	107.412i	0.690616	−	0.950552i	1.00000		0.000385488i	$0.000122705\pi$
$114$	148.915	−	118.094i	1.30628	−	1.03592i
$115$	−56.0564	+	172.524i	−0.487447	+	1.50021i
$116$	−19.3014	−	6.27141i	−0.166391	−	0.0540638i
$117$	−110.622	+	95.5912i	−0.945491	+	0.817019i
$118$	−107.760	−	78.2925i	−0.913224	−	0.663496i
$119$	−2.34690	+	0.762555i	−0.0197219	+	0.00640802i
$120$	−3.50703	−	83.1381i	−0.0292253	−	0.692817i
$121$		0			0
$122$			32.6062i			0.267264i
$123$	−13.9942	−	37.5980i	−0.113774	−	0.305675i
$124$	−90.1957	−	65.5310i	−0.727385	−	0.528476i
$125$	−23.1004	−	31.7950i	−0.184803	−	0.254360i
$126$	82.1429	+	19.2196i	0.651928	+	0.152536i
$127$	45.3190	−	139.478i	0.356843	−	1.09825i	−0.598091	−	0.801428i	$-0.704074\pi$
$127$	45.3190	−	139.478i	0.356843	−	1.09825i	0.954933	−	0.296820i	$-0.0959263\pi$
$128$	74.0031	+	101.857i	0.578150	+	0.795755i
$129$	−72.0431	+	108.497i	−0.558473	+	0.841063i
$130$	−101.994	−	313.905i	−0.784569	−	2.41465i
$131$		−	149.467i		−	1.14097i	−0.821309	−	0.570484i	$-0.806756\pi$
$131$		−	149.467i		−	1.14097i	0.821309	−	0.570484i	$-0.193244\pi$
$132$		0			0
$133$	−63.4091			−0.476760
$134$	210.417	−	68.3685i	1.57027	−	0.510213i
$135$	−157.158	−	86.2326i	−1.16414	−	0.638760i
$136$	2.72298	−	1.97836i	0.0200219	−	0.0145467i
$137$	−144.757	−	47.0345i	−1.05662	−	0.343318i	−0.271359	−	0.962478i	$-0.587473\pi$
$137$	−144.757	−	47.0345i	−1.05662	−	0.343318i	−0.785264	+	0.619161i	$0.787473\pi$
$138$	241.618	+	67.3907i	1.75086	+	0.488338i
$139$	90.4769	−	65.7353i	0.650913	−	0.472916i	−0.212669	−	0.977124i	$-0.568216\pi$
$139$	90.4769	−	65.7353i	0.650913	−	0.472916i	0.863582	+	0.504208i	$0.168216\pi$
$140$	−64.1311	+	88.2689i	−0.458079	+	0.630492i
$141$	−20.8147	−	55.9228i	−0.147622	−	0.396616i
$142$	7.86454			0.0553841
$143$		0			0
$144$	77.8039	−	6.57574i	0.540305	−	0.0456649i
$145$	−7.76079	−	23.8853i	−0.0535227	−	0.164726i
$146$	−81.8060	+	112.596i	−0.560315	+	0.771207i
$147$	73.8514	+	93.1256i	0.502391	+	0.633507i
$148$	−63.9190	+	196.723i	−0.431885	+	1.32921i
$149$	−246.985	−	80.2503i	−1.65762	−	0.538592i	−0.677247	−	0.735756i	$-0.736827\pi$
$149$	−246.985	−	80.2503i	−1.65762	−	0.538592i	−0.980371	+	0.197164i	$0.936827\pi$
$150$	137.254	−	108.846i	0.915025	−	0.725643i
$151$	71.2078	+	51.7355i	0.471575	+	0.342619i	0.798055	−	0.602585i	$-0.205863\pi$
$151$	71.2078	+	51.7355i	0.471575	+	0.342619i	−0.326480	+	0.945204i	$0.605863\pi$
$152$	82.2536	−	26.7258i	0.541142	−	0.175828i
$153$	−0.610640	−	7.22507i	−0.00399111	−	0.0472227i
$154$		0			0
$155$		−	137.965i		−	0.890098i
$156$	−245.042	+	91.2058i	−1.57078	+	0.584653i
$157$	6.19326	+	4.49967i	0.0394475	+	0.0286603i	0.607334	−	0.794446i	$-0.292239\pi$
$157$	6.19326	+	4.49967i	0.0394475	+	0.0286603i	−0.567887	+	0.823107i	$0.692239\pi$
$158$	176.715	+	243.228i	1.11845	+	1.53942i
$159$	14.2460	−	51.0768i	0.0895977	−	0.321238i
$160$	−88.7566	+	273.165i	−0.554729	+	1.70728i
$161$	−49.1905	−	67.7049i	−0.305531	−	0.420527i
$162$	−109.976	+	222.149i	−0.678866	+	1.37129i
$163$	81.1315	+	249.697i	0.497739	+	1.53188i	0.812644	+	0.582760i	$0.198027\pi$
$163$	81.1315	+	249.697i	0.497739	+	1.53188i	−0.314905	+	0.949123i	$0.601973\pi$
$164$		−	71.7464i		−	0.437478i
$165$		0			0
$166$	97.6240			0.588096
$167$	152.175	−	49.4447i	0.911228	−	0.296076i	0.184364	−	0.982858i	$-0.440977\pi$
$167$	152.175	−	49.4447i	0.911228	−	0.296076i	0.726863	+	0.686782i	$0.240977\pi$
$168$	31.9807	+	21.2355i	0.190361	+	0.126402i
$169$	−76.7667	+	55.7743i	−0.454241	+	0.330025i
$170$	15.5680	+	5.05835i	0.0915765	+	0.0297550i
$171$	42.4474	−	181.416i	0.248230	−	1.06091i
$172$	−188.432	+	136.904i	−1.09554	+	0.795954i
$173$	97.2924	−	133.912i	0.562384	−	0.774055i	−0.429243	−	0.903189i	$-0.641220\pi$
$173$	97.2924	−	133.912i	0.562384	−	0.774055i	0.991627	+	0.129134i	$0.0412197\pi$
$174$	−32.5466	+	12.1140i	−0.187049	+	0.0696206i
$175$	−58.4435			−0.333963
$176$		0			0
$177$	−130.461	+	5.50325i	−0.737065	+	0.0310918i
$178$	17.5336	+	53.9628i	0.0985032	+	0.303162i
$179$	34.4072	−	47.3575i	0.192219	−	0.264567i	−0.702019	−	0.712158i	$-0.747718\pi$
$179$	34.4072	−	47.3575i	0.192219	−	0.264567i	0.894238	+	0.447591i	$0.147718\pi$
$180$	−209.611	−	242.571i	−1.16450	−	1.34762i
$181$	87.9703	−	270.745i	0.486024	−	1.49583i	−0.344468	−	0.938798i	$-0.611941\pi$
$181$	87.9703	−	270.745i	0.486024	−	1.49583i	0.830492	−	0.557030i	$-0.188059\pi$
$182$	144.817	+	47.0537i	0.795695	+	0.258537i
$183$	19.8613	+	25.0448i	0.108531	+	0.136857i
$184$	92.3459	+	67.0932i	0.501880	+	0.364637i
$185$	−243.442	+	79.0991i	−1.31590	+	0.427563i
$186$	−190.607	+	8.04041i	−1.02477	+	0.0432280i
$187$		0			0
$188$		−	106.715i		−	0.567631i
$189$	74.8009	−	35.2728i	0.395772	−	0.186628i
$190$	340.288	+	247.234i	1.79099	+	1.30123i
$191$	−80.7867	−	111.193i	−0.422967	−	0.582164i	0.543354	−	0.839504i	$-0.317154\pi$
$191$	−80.7867	−	111.193i	−0.422967	−	0.582164i	−0.966321	+	0.257339i	$0.917154\pi$
$192$	282.285	+	78.7330i	1.47023	+	0.410068i
$193$	−92.1162	+	283.505i	−0.477286	+	1.46894i	0.365563	+	0.930786i	$0.380876\pi$
$193$	−92.1162	+	283.505i	−0.477286	+	1.46894i	−0.842850	+	0.538149i	$0.819124\pi$
$194$	−113.866	−	156.723i	−0.586937	−	0.807849i
$195$	−269.549	−	178.983i	−1.38230	−	0.917861i
$196$	65.6840	+	202.155i	0.335122	+	1.03140i
$197$			58.1375i			0.295114i	0.989054	+	0.147557i	$0.0471410\pi$
$197$			58.1375i			0.295114i	−0.989054	+	0.147557i	$0.952859\pi$
$198$		0			0
$199$	−125.049			−0.628385			−0.314193	−	0.949359i	$-0.601734\pi$
$199$	−125.049			−0.628385			−0.314193	+	0.949359i	$0.601734\pi$
$200$	75.8123	−	24.6329i	0.379061	−	0.123165i
$201$	119.976	−	180.684i	0.596894	−	0.898925i
$202$	−372.258	+	270.461i	−1.84286	+	1.33892i
$203$	11.0192	+	3.58035i	0.0542818	+	0.0176372i
$204$	3.48378	−	12.4905i	0.0170774	−	0.0612282i
$205$	71.8288	−	52.1867i	0.350384	−	0.254569i
$206$	269.397	−	370.794i	1.30775	−	1.79997i
$207$	226.636	−	95.4133i	1.09486	−	0.460934i
$208$	140.934			0.677566
$209$		0			0
$210$	7.86865	+	186.535i	0.0374698	+	0.888262i
$211$	14.9542	+	46.0242i	0.0708728	+	0.218124i	0.980219	−	0.197916i	$-0.0634175\pi$
$211$	14.9542	+	46.0242i	0.0708728	+	0.218124i	−0.909346	+	0.416040i	$0.863417\pi$
$212$	55.7406	−	76.7204i	0.262927	−	0.361889i
$213$	6.04074	−	4.79049i	0.0283603	−	0.0224906i
$214$	19.6241	−	60.3967i	0.0917013	−	0.282228i
$215$	−274.123	−	89.0679i	−1.27499	−	0.414269i
$216$	−82.1642	+	77.2828i	−0.380390	+	0.357791i
$217$	51.4928	+	37.4117i	0.237294	+	0.172404i
$218$	307.909	−	100.046i	1.41243	−	0.458926i
$219$	5.75021	+	136.315i	0.0262567	+	0.622444i
$220$		0			0
$221$		−	13.0875i		−	0.0592193i
$222$	123.467	+	331.719i	0.556159	+	1.49423i
$223$	−171.282	−	124.444i	−0.768082	−	0.558044i	0.133297	−	0.991076i	$-0.457444\pi$
$223$	−171.282	−	124.444i	−0.768082	−	0.558044i	−0.901378	+	0.433032i	$0.857444\pi$
$224$	−77.8855	−	107.200i	−0.347703	−	0.478573i
$225$	39.1233	−	167.210i	0.173881	−	0.743153i
$226$	125.556	−	386.421i	0.555556	−	1.70983i
$227$	71.3484	+	98.2027i	0.314310	+	0.432611i	0.936719	−	0.350081i	$-0.113846\pi$
$227$	71.3484	+	98.2027i	0.314310	+	0.432611i	−0.622409	+	0.782692i	$0.713846\pi$
$228$	184.318	−	277.583i	0.808412	−	1.21747i
$229$	99.7951	+	307.138i	0.435786	+	1.34121i	0.892279	+	0.451485i	$0.149106\pi$
$229$	99.7951	+	307.138i	0.435786	+	1.34121i	−0.456492	+	0.889727i	$0.650894\pi$
$230$			555.137i			2.41364i
$231$		0			0
$232$	−15.8030			−0.0681166
$233$	−382.714	+	124.351i	−1.64255	+	0.533697i	−0.977106	−	0.212752i	$-0.931757\pi$
$233$	−382.714	+	124.351i	−1.64255	+	0.533697i	−0.665443	+	0.746449i	$0.731757\pi$
$234$	−231.566	+	382.828i	−0.989599	+	1.63602i
$235$	106.837	−	77.6218i	0.454626	−	0.330305i
$236$	−222.092	−	72.1621i	−0.941068	−	0.305771i
$237$	283.891	+	79.1811i	1.19785	+	0.334098i
$238$	−6.10948	+	4.43879i	−0.0256701	+	0.0186504i
$239$	−0.188940	+	0.260053i	−0.000790543	+	0.00108809i	−0.809412	−	0.587241i	$-0.800214\pi$
$239$	−0.188940	+	0.260053i	−0.000790543	+	0.00108809i	0.808622	+	0.588329i	$0.200214\pi$
$240$	60.2779	+	161.948i	0.251158	+	0.674784i
$241$	−290.799			−1.20664			−0.603318	−	0.797500i	$-0.706155\pi$
$241$	−290.799			−1.20664			−0.603318	+	0.797500i	$0.706155\pi$
$242$		0			0
$243$	50.8438	+	237.621i	0.209234	+	0.977866i
$244$	17.6648	+	54.3665i	0.0723965	+	0.222814i
$245$	−154.610	+	212.802i	−0.631060	+	0.868580i
$246$	−76.2850	−	96.1943i	−0.310102	−	0.391034i
$247$	103.920	−	319.834i	0.420730	−	1.29487i
$248$	−82.5644	−	26.8268i	−0.332921	−	0.108173i
$249$	74.9848	−	59.4653i	0.301144	−	0.238816i
$250$	−97.3007	−	70.6931i	−0.389203	−	0.282772i
$251$	107.109	−	34.8019i	0.426730	−	0.138653i	−0.0877748	−	0.996140i	$-0.527976\pi$
$251$	107.109	−	34.8019i	0.426730	−	0.138653i	0.514505	+	0.857487i	$0.327976\pi$
$252$	147.375	−	12.4557i	0.584821	−	0.0494272i
$253$		0			0
$254$		−	448.803i		−	1.76694i
$255$	15.0389	−	5.59755i	0.0589762	−	0.0219512i
$256$	−4.41230	−	3.20572i	−0.0172355	−	0.0125224i
$257$	−115.540	−	159.027i	−0.449572	−	0.618783i	0.522733	−	0.852496i	$-0.324912\pi$
$257$	−115.540	−	159.027i	−0.449572	−	0.618783i	−0.972306	+	0.233713i	$0.924912\pi$
$258$	−107.077	+	383.907i	−0.415027	+	1.48801i
$259$	36.4915	−	112.309i	0.140894	−	0.433626i
$260$	−340.123	−	468.139i	−1.30816	−	1.80053i
$261$	−17.6200	+	29.1297i	−0.0675097	+	0.111608i
$262$	−141.346	−	435.020i	−0.539490	−	1.66038i
$263$		−	378.327i		−	1.43850i	−0.694749	−	0.719252i	$-0.744485\pi$
$263$		−	378.327i		−	1.43850i	0.694749	−	0.719252i	$-0.255515\pi$
$264$		0			0
$265$	117.353			0.442842
$266$	−184.551	+	59.9641i	−0.693799	+	0.225429i
$267$	46.3376	+	30.7686i	0.173549	+	0.115238i
$268$	313.803	−	227.991i	1.17090	−	0.850712i
$269$	191.309	+	62.1601i	0.711186	+	0.231078i	0.642198	−	0.766539i	$-0.278023\pi$
$269$	191.309	+	62.1601i	0.711186	+	0.231078i	0.0689882	+	0.997617i	$0.478023\pi$
$270$	−538.953	−	102.358i	−1.99612	−	0.379103i
$271$	64.8950	−	47.1490i	0.239465	−	0.173981i	−0.461580	−	0.887099i	$-0.652717\pi$
$271$	64.8950	−	47.1490i	0.239465	−	0.173981i	0.701045	+	0.713117i	$0.252717\pi$
$272$	−4.10836	+	5.65467i	−0.0151043	+	0.0207892i
$273$	139.895	−	52.0695i	0.512436	−	0.190731i
$274$	−465.792			−1.69997
$275$		0			0
$276$	439.376	−	18.5343i	1.59194	−	0.0671533i
$277$	−67.6484	−	208.200i	−0.244218	−	0.751626i	−0.995764	−	0.0919450i	$-0.970692\pi$
$277$	−67.6484	−	208.200i	−0.244218	−	0.751626i	0.751546	−	0.659681i	$-0.229308\pi$
$278$	201.167	−	276.882i	0.723622	−	0.995980i
$279$	−141.507	+	122.279i	−0.507194	+	0.438277i
$280$	−26.2537	+	80.8006i	−0.0937633	+	0.288574i
$281$	472.140	+	153.407i	1.68021	+	0.545934i	0.984953	−	0.172825i	$-0.0552894\pi$
$281$	472.140	+	153.407i	1.68021	+	0.545934i	0.695260	+	0.718759i	$0.255289\pi$
$282$	−113.465	−	143.078i	−0.402359	−	0.507369i
$283$	−248.936	−	180.862i	−0.879632	−	0.639090i	0.0535221	−	0.998567i	$-0.482955\pi$
$283$	−248.936	−	180.862i	−0.879632	−	0.639090i	−0.933154	+	0.359477i	$0.882955\pi$
$284$	13.1131	−	4.26070i	0.0461728	−	0.0150025i
$285$	411.971	−	17.3783i	1.44551	−	0.0609764i
$286$		0			0
$287$			40.9601i			0.142718i
$288$	358.843	−	151.072i	1.24598	−	0.524556i
$289$	−233.281	−	169.488i	−0.807200	−	0.586465i
$290$	−45.1752	−	62.1783i	−0.155777	−	0.214408i
$291$	−182.924	−	51.0200i	−0.628604	−	0.175326i
$292$	−75.4004	+	232.059i	−0.258221	+	0.794721i
$293$	−199.670	−	274.822i	−0.681466	−	0.937957i	0.318484	−	0.947928i	$-0.396826\pi$
$293$	−199.670	−	274.822i	−0.681466	−	0.937957i	−0.999950	+	0.00997075i	$0.996826\pi$
$294$	303.009	+	201.201i	1.03064	+	0.684355i
$295$	−89.2997	−	274.836i	−0.302711	−	0.931648i
$296$			161.067i			0.544145i
$297$		0			0
$298$	−794.734			−2.66689
$299$	422.120	−	137.155i	1.41177	−	0.458712i
$300$	169.884	−	255.846i	0.566279	−	0.852819i
$301$	107.576	−	78.1587i	0.357396	−	0.259664i
$302$	256.173	+	83.2358i	0.848256	+	0.275615i
$303$	−121.186	+	434.492i	−0.399953	+	1.43397i
$304$	−145.301	+	105.568i	−0.477965	+	0.347262i
$305$	−41.5801	+	57.2300i	−0.136328	+	0.187639i
$306$	−8.60979	−	20.4509i	−0.0281366	−	0.0668331i
$307$	396.129			1.29032			0.645161	−	0.764047i	$-0.276790\pi$
$307$	396.129			1.29032			0.645161	+	0.764047i	$0.276790\pi$
$308$		0			0
$309$	−18.9362	−	448.903i	−0.0612821	−	1.45276i
$310$	−130.470	−	401.544i	−0.420870	−	1.29530i
$311$	−51.1584	+	70.4134i	−0.164496	+	0.226410i	−0.883306	−	0.468797i	$-0.844687\pi$
$311$	−51.1584	+	70.4134i	−0.164496	+	0.226410i	0.718809	+	0.695207i	$0.244687\pi$
$312$	−159.524	+	126.507i	−0.511295	+	0.405472i
$313$	−185.075	+	569.601i	−0.591292	+	1.81981i	−0.0189146	+	0.999821i	$0.506021\pi$
$313$	−185.075	+	569.601i	−0.591292	+	1.81981i	−0.572378	+	0.819990i	$0.693979\pi$
$314$	22.2805	+	7.23939i	0.0709572	+	0.0230554i
$315$	119.667	+	138.484i	0.379895	+	0.439632i
$316$	426.421	+	309.813i	1.34943	+	0.980421i
$317$	2.33475	−	0.758605i	0.00736513	−	0.00239308i	−0.305332	−	0.952246i	$-0.598767\pi$
$317$	2.33475	−	0.758605i	0.00736513	−	0.00239308i	0.312697	+	0.949853i	$0.398767\pi$
$318$	−6.83917	−	162.130i	−0.0215068	−	0.509843i
$319$		0			0
$320$			648.571i			2.02678i
$321$	−21.7159	−	58.3441i	−0.0676509	−	0.181757i
$322$	−207.194	−	150.535i	−0.643460	−	0.467501i
$323$	9.80328	+	13.4931i	0.0303507	+	0.0417742i
$324$	−63.0195	+	429.984i	−0.194505	+	1.32711i
$325$	95.7823	−	294.788i	0.294715	−	0.907039i
$326$	472.262	+	650.013i	1.44866	+	1.99391i
$327$	175.564	−	264.400i	0.536894	−	0.808564i
$328$	−17.2640	−	53.1330i	−0.0526340	−	0.161991i
$329$			60.9235i			0.185178i
$330$		0			0
$331$	368.074			1.11200			0.556002	−	0.831181i	$-0.312335\pi$
$331$	368.074			1.11200			0.556002	+	0.831181i	$0.312335\pi$
$332$	162.775	−	52.8888i	0.490286	−	0.159304i
$333$	296.894	+	179.586i	0.891573	+	0.539297i
$334$	396.143	−	287.815i	1.18606	−	0.861721i
$335$	456.506	+	148.328i	1.36270	+	0.442769i
$336$	−76.7895	−	21.4176i	−0.228540	−	0.0637430i
$337$	478.841	−	347.898i	1.42089	−	1.03234i	0.429269	−	0.903177i	$-0.358771\pi$
$337$	478.841	−	347.898i	1.42089	−	1.03234i	0.991624	−	0.129162i	$-0.0412286\pi$
$338$	−170.684	+	234.926i	−0.504981	+	0.695047i
$339$	−138.940	−	373.288i	−0.409851	−	1.10115i
$340$	28.6980			0.0844059
$341$		0			0
$342$	−48.0182	−	568.149i	−0.140404	−	1.66125i
$343$	−83.8781	−	258.150i	−0.244543	−	0.752625i
$344$	−106.604	+	146.728i	−0.309896	+	0.426536i
$345$	338.148	+	426.400i	0.980139	+	1.23594i
$346$	156.531	−	481.753i	0.452402	−	1.39235i
$347$	−280.182	−	91.0367i	−0.807442	−	0.262354i	−0.123928	−	0.992291i	$-0.539549\pi$
$347$	−280.182	−	91.0367i	−0.807442	−	0.262354i	−0.683514	+	0.729938i	$0.739549\pi$
$348$	−47.7042	+	37.8309i	−0.137081	+	0.108710i
$349$	333.322	+	242.172i	0.955076	+	0.693903i	0.952002	−	0.306092i	$-0.0990215\pi$
$349$	333.322	+	242.172i	0.955076	+	0.693903i	0.00307413	+	0.999995i	$0.499021\pi$
$350$	−170.098	+	55.2683i	−0.485995	+	0.157909i
$351$	55.3248	+	435.102i	0.157620	+	1.23961i
$352$		0			0
$353$		−	135.577i		−	0.384070i	−0.981388	−	0.192035i	$-0.938491\pi$
$353$		−	135.577i		−	0.384070i	0.981388	−	0.192035i	$-0.0615086\pi$
$354$	−374.498	+	139.390i	−1.05790	+	0.393756i
$355$	13.8038	+	10.0290i	0.0388838	+	0.0282507i
$356$	58.4698	+	80.4768i	0.164241	+	0.226058i
$357$	−1.98890	+	7.13087i	−0.00557114	+	0.0199744i
$358$	55.3568	−	170.371i	0.154628	−	0.475896i
$359$	163.860	+	225.534i	0.456435	+	0.628229i	0.973765	−	0.227557i	$-0.0730739\pi$
$359$	163.860	+	225.534i	0.456435	+	0.628229i	−0.517330	+	0.855786i	$0.673074\pi$
$360$	−213.600	−	129.203i	−0.593332	−	0.358896i
$361$	20.8784	+	64.2571i	0.0578349	+	0.177997i
$362$		−	871.187i		−	2.40659i
$363$		0			0
$364$	266.954			0.733391
$365$	−287.170	+	93.3072i	−0.786767	+	0.255636i
$366$	81.4898	+	54.1100i	0.222650	+	0.147841i
$367$	142.701	−	103.678i	0.388830	−	0.282502i	−0.376146	−	0.926560i	$-0.622751\pi$
$367$	142.701	−	103.678i	0.388830	−	0.282502i	0.764976	+	0.644059i	$0.222751\pi$
$368$	−225.439	−	73.2497i	−0.612607	−	0.199048i
$369$	−117.189	−	27.4195i	−0.317585	−	0.0743077i
$370$	−633.730	+	460.432i	−1.71278	+	1.24441i
$371$	−31.8224	+	43.7998i	−0.0857746	+	0.118059i
$372$	−313.456	+	116.670i	−0.842623	+	0.313628i
$373$	−163.109			−0.437289			−0.218645	−	0.975805i	$-0.570164\pi$
$373$	−163.109			−0.437289			−0.218645	+	0.975805i	$0.570164\pi$
$374$		0			0
$375$	−117.797	+	4.96908i	−0.314126	+	0.0132509i
$376$	−25.6782	−	79.0293i	−0.0682930	−	0.210184i
$377$	−36.1185	+	49.7128i	−0.0958049	+	0.131864i
$378$	184.350	−	173.398i	0.487698	−	0.458724i
$379$	16.4492	−	50.6253i	0.0434015	−	0.133576i	−0.927008	−	0.375042i	$-0.877628\pi$
$379$	16.4492	−	50.6253i	0.0434015	−	0.133576i	0.970409	+	0.241466i	$0.0776283\pi$
$380$	701.327	+	227.875i	1.84560	+	0.599671i
$381$	−273.377	−	344.725i	−0.717526	−	0.904790i
$382$	−340.280	−	247.228i	−0.890785	−	0.647193i
$383$	−85.2768	+	27.7081i	−0.222655	+	0.0723449i	−0.418220	−	0.908346i	$-0.637346\pi$
$383$	−85.2768	+	27.7081i	−0.222655	+	0.0723449i	0.195565	+	0.980691i	$0.437346\pi$
$384$	377.369	−	15.9187i	0.982733	−	0.0414549i
$385$		0			0
$386$			912.245i			2.36333i
$387$	151.602	+	360.102i	0.391736	+	0.930496i
$388$	−274.762	−	199.626i	−0.708150	−	0.514501i
$389$	−158.468	−	218.112i	−0.407372	−	0.560699i	0.555203	−	0.831715i	$-0.312640\pi$
$389$	−158.468	−	218.112i	−0.407372	−	0.560699i	−0.962575	+	0.271016i	$0.912640\pi$
$390$	−953.774	−	266.021i	−2.44557	−	0.682104i
$391$	−6.80215	+	20.9349i	−0.0173968	+	0.0535419i
$392$	97.2868	+	133.904i	0.248181	+	0.341591i
$393$	−373.549	−	248.040i	−0.950508	−	0.631145i
$394$	54.9789	+	169.208i	0.139540	+	0.429461i
$395$			652.262i			1.65130i
$396$		0			0
$397$	211.490			0.532720			0.266360	−	0.963874i	$-0.414179\pi$
$397$	211.490			0.532720			0.266360	+	0.963874i	$0.414179\pi$
$398$	−363.951	+	118.255i	−0.914450	+	0.297123i
$399$	−105.227	+	158.473i	−0.263728	+	0.397175i
$400$	−133.923	+	97.3006i	−0.334807	+	0.243252i
$401$	−427.784	−	138.995i	−1.06679	−	0.346622i	−0.277555	−	0.960710i	$-0.589524\pi$
$401$	−427.784	−	138.995i	−1.06679	−	0.346622i	−0.789237	+	0.614088i	$0.789524\pi$
$402$	178.319	−	639.333i	0.443579	−	1.59038i
$403$	−273.095	+	198.415i	−0.677655	+	0.492345i
$404$	−474.165	+	652.633i	−1.17368	+	1.61543i
$405$	−476.317	+	249.669i	−1.17609	+	0.616467i
$406$	35.4569			0.0873323
$407$		0			0
$408$	−0.425560	−	10.0884i	−0.00104304	−	0.0247264i
$409$	47.6795	+	146.742i	0.116576	+	0.358783i	0.992272	−	0.124078i	$-0.0395974\pi$
$409$	47.6795	+	146.742i	0.116576	+	0.358783i	−0.875697	+	0.482862i	$0.839597\pi$
$410$	159.705	−	219.814i	0.389523	−	0.536133i
$411$	−357.774	+	283.726i	−0.870496	+	0.690330i
$412$	248.303	−	764.199i	0.602678	−	1.85485i
$413$	126.793	+	41.1974i	0.307004	+	0.0997516i
$414$	569.389	−	492.021i	1.37534	−	1.18846i
$415$	171.349	+	124.492i	0.412888	+	0.299981i
$416$	668.362	−	217.164i	1.60664	−	0.522028i
$417$	−14.1402	−	335.209i	−0.0339093	−	0.803858i
$418$		0			0
$419$			755.530i			1.80317i	0.432599	+	0.901587i	$0.357597\pi$
$419$			755.530i			1.80317i	−0.432599	+	0.901587i	$0.642403\pi$
$420$	114.177	+	306.759i	0.271851	+	0.730380i
$421$	353.452	+	256.798i	0.839553	+	0.609971i	0.922246	−	0.386604i	$-0.126352\pi$
$421$	353.452	+	256.798i	0.839553	+	0.609971i	−0.0826929	+	0.996575i	$0.526352\pi$
$422$	87.0474	+	119.810i	0.206274	+	0.283911i
$423$	−174.305	−	40.7834i	−0.412068	−	0.0964147i
$424$	22.8188	−	70.2292i	0.0538180	−	0.165635i
$425$	9.03558	+	12.4364i	0.0212602	+	0.0292621i
$426$	13.0512	−	19.6552i	0.0306366	−	0.0461389i
$427$	−10.0848	−	31.0379i	−0.0236179	−	0.0726883i
$428$		−	111.335i		−	0.260129i
$429$		0			0
$430$	−882.057			−2.05129
$431$	9.25765	−	3.00799i	0.0214795	−	0.00697910i	−0.298258	−	0.954485i	$-0.596405\pi$
$431$	9.25765	−	3.00799i	0.0214795	−	0.00697910i	0.319737	+	0.947506i	$0.396405\pi$
$432$	112.681	−	205.361i	0.260837	−	0.475373i
$433$	47.9543	−	34.8408i	0.110749	−	0.0804638i	−0.531032	−	0.847352i	$-0.678196\pi$
$433$	47.9543	−	34.8408i	0.110749	−	0.0804638i	0.641781	+	0.766888i	$0.278196\pi$
$434$	185.248	+	60.1907i	0.426838	+	0.138688i
$435$	−72.5734	−	20.2417i	−0.166835	−	0.0465327i
$436$	459.197	−	333.626i	1.05320	−	0.765198i
$437$	−332.465	+	457.598i	−0.760788	+	1.04714i
$438$	145.645	+	391.304i	0.332523	+	0.893388i
$439$	−444.724			−1.01304			−0.506519	−	0.862229i	$-0.669068\pi$
$439$	−444.724			−1.01304			−0.506519	+	0.862229i	$0.669068\pi$
$440$		0			0
$441$	355.297	−	30.0286i	0.805662	−	0.0680920i
$442$	−12.3764	−	38.0908i	−0.0280010	−	0.0861782i
$443$	−314.672	+	433.108i	−0.710320	+	0.977671i	0.289470	+	0.957187i	$0.406521\pi$
$443$	−314.672	+	433.108i	−0.710320	+	0.977671i	−0.999790	+	0.0204842i	$0.993479\pi$
$444$	385.578	+	486.208i	0.868419	+	1.09506i
$445$	−38.0397	+	117.074i	−0.0854824	+	0.263088i
$446$	−616.196	−	200.214i	−1.38160	−	0.448910i
$447$	−610.434	+	484.093i	−1.36562	+	1.08298i
$448$	−242.067	−	175.872i	−0.540327	−	0.392571i
$449$	−731.756	+	237.762i	−1.62975	+	0.529537i	−0.974213	−	0.225629i	$-0.927556\pi$
$449$	−731.756	+	237.762i	−1.62975	+	0.529537i	−0.655534	+	0.755166i	$0.727556\pi$
$450$	−44.2578	−	523.657i	−0.0983508	−	1.16368i
$451$		0			0
$452$		−	712.327i		−	1.57594i
$453$	247.467	−	92.1084i	0.546285	−	0.203330i
$454$	300.525	+	218.344i	0.661950	+	0.480935i
$455$	194.177	+	267.261i	0.426762	+	0.587387i
$456$	69.7063	−	249.921i	0.152865	−	0.548072i
$457$	−52.4263	+	161.352i	−0.114718	+	0.353067i	−0.991888	−	0.127113i	$-0.959429\pi$
$457$	−52.4263	+	161.352i	−0.114718	+	0.353067i	0.877170	+	0.480180i	$0.159429\pi$
$458$	580.902	+	799.543i	1.26835	+	1.74573i
$459$	−19.0703	−	10.4639i	−0.0415476	−	0.0227971i
$460$	300.751	+	925.618i	0.653807	+	2.01221i
$461$			266.355i			0.577777i	0.957363	+	0.288888i	$0.0932857\pi$
$461$			266.355i			0.577777i	−0.957363	+	0.288888i	$0.906714\pi$
$462$		0			0
$463$	−704.848			−1.52235			−0.761175	−	0.648547i	$-0.775377\pi$
$463$	−704.848			−1.52235			−0.761175	+	0.648547i	$0.775377\pi$
$464$	31.2112	−	10.1411i	0.0672656	−	0.0218559i
$465$	−344.804	−	228.953i	−0.741514	−	0.492372i
$466$	−996.284	+	723.843i	−2.13795	+	1.55331i
$467$	642.132	+	208.641i	1.37502	+	0.446770i	0.901028	−	0.433762i	$-0.142814\pi$
$467$	642.132	+	208.641i	1.37502	+	0.446770i	0.473988	+	0.880531i	$0.342814\pi$
$468$	−178.705	+	763.769i	−0.381848	+	1.63198i
$469$	−179.150	+	130.160i	−0.381983	+	0.277527i
$470$	237.542	−	326.949i	0.505409	−	0.695636i
$471$	21.5233	−	8.01109i	0.0456971	−	0.0170087i
$472$	−181.838			−0.385250
$473$		0			0
$474$	901.138	−	38.0129i	1.90113	−	0.0801960i
$475$	122.063	+	375.670i	0.256974	+	0.790884i
$476$	−7.78198	+	10.7110i	−0.0163487	+	0.0225020i
$477$	−104.011	−	120.366i	−0.218052	−	0.252339i
$478$	−0.303980	+	0.935553i	−0.000635941	+	0.00195722i
$479$	665.556	+	216.252i	1.38947	+	0.451466i	0.905771	−	0.423768i	$-0.139293\pi$
$479$	665.556	+	216.252i	1.38947	+	0.451466i	0.483700	+	0.875234i	$0.339293\pi$
$480$	535.405	+	675.138i	1.11543	+	1.40654i
$481$	506.680	+	368.124i	1.05339	+	0.765331i
$482$	−846.365	+	275.001i	−1.75594	+	0.570541i
$483$	−250.841	+	10.5813i	−0.519339	+	0.0219074i
$484$		0			0
$485$		−	420.282i		−	0.866560i
$486$	372.691	+	643.510i	0.766854	+	1.32409i
$487$	528.569	+	384.028i	1.08536	+	0.788558i	0.978609	−	0.205729i	$-0.0659564\pi$
$487$	528.569	+	384.028i	1.08536	+	0.788558i	0.106747	+	0.994286i	$0.465956\pi$
$488$	26.1639	+	36.0115i	0.0536145	+	0.0737941i
$489$	758.683	+	211.607i	1.55150	+	0.432734i
$490$	−248.747	+	765.565i	−0.507647	+	1.56238i
$491$	−36.3470	−	50.0274i	−0.0740265	−	0.101889i	0.770398	−	0.637563i	$-0.220057\pi$
$491$	−36.3470	−	50.0274i	−0.0740265	−	0.101889i	−0.844425	+	0.535674i	$0.820057\pi$
$492$	−179.309	−	119.063i	−0.364450	−	0.241998i
$493$	−0.941732	−	2.89835i	−0.00191021	−	0.00587901i
$494$		−	1029.14i		−	2.08329i
$495$		0			0
$496$	180.281			0.363470
$497$	−7.48628	+	2.43244i	−0.0150629	+	0.00489424i
$498$	162.007	−	243.983i	0.325315	−	0.489926i
$499$	−266.970	+	193.965i	−0.535010	+	0.388707i	−0.822228	−	0.569158i	$-0.807269\pi$
$499$	−266.970	+	193.965i	−0.535010	+	0.388707i	0.287219	+	0.957865i	$0.407269\pi$
$500$	−200.535	−	65.1577i	−0.401069	−	0.130315i
$501$	128.962	−	462.371i	0.257408	−	0.922897i
$502$	278.828	−	202.580i	0.555434	−	0.403547i
$503$	−204.067	+	280.874i	−0.405700	+	0.558398i	−0.962163	−	0.272474i	$-0.912158\pi$
$503$	−204.067	+	280.874i	−0.405700	+	0.558398i	0.556463	+	0.830872i	$0.312158\pi$
$504$	106.144	−	44.6863i	0.210603	−	0.0886633i
$505$	−998.280			−1.97679
$506$		0			0
$507$	11.9975	+	284.414i	0.0236637	+	0.560974i
$508$	−243.144	−	748.320i	−0.478630	−	1.47307i
$509$	503.258	−	692.675i	0.988719	−	1.36086i	0.0567219	−	0.998390i	$-0.481935\pi$
$509$	503.258	−	692.675i	0.988719	−	1.36086i	0.931997	−	0.362465i	$-0.118065\pi$
$510$	38.4770	−	30.5134i	0.0754450	−	0.0598302i
$511$	43.0462	−	132.483i	0.0842391	−	0.259261i
$512$	−494.832	−	160.781i	−0.966468	−	0.314025i
$513$	−382.957	−	407.145i	−0.746504	−	0.793655i
$514$	−486.664	−	353.582i	−0.946817	−	0.687903i
$515$	945.687	−	307.272i	1.83629	−	0.596645i
$516$	29.4492	+	698.125i	0.0570720	+	1.35295i
$517$		0			0
$518$		−	361.382i		−	0.697649i
$519$	−173.217	−	465.381i	−0.333751	−	0.896687i
$520$	−364.530	−	264.846i	−0.701019	−	0.509320i
$521$	418.891	+	576.554i	0.804013	+	1.10663i	0.992220	+	0.124499i	$0.0397325\pi$
$521$	418.891	+	576.554i	0.804013	+	1.10663i	−0.188207	+	0.982129i	$0.560268\pi$
$522$	−23.7356	+	101.444i	−0.0454705	+	0.194337i
$523$	−155.721	+	479.261i	−0.297746	+	0.916369i	0.684539	+	0.728976i	$0.260004\pi$
$523$	−155.721	+	479.261i	−0.297746	+	0.916369i	−0.982285	+	0.187392i	$0.939996\pi$
$524$	−471.353	−	648.762i	−0.899529	−	1.23809i
$525$	−96.9869	+	146.063i	−0.184737	+	0.278215i
$526$	−357.772	−	1101.11i	−0.680176	−	2.09337i
$527$		−	16.7414i		−	0.0317673i
$528$		0			0
$529$	−217.513			−0.411179
$530$	341.553	−	110.977i	0.644440	−	0.209391i
$531$	−202.745	+	335.181i	−0.381818	+	0.631226i
$532$	−275.227	+	199.964i	−0.517345	+	0.375873i
$533$	−206.602	−	67.1290i	−0.387621	−	0.125946i
$534$	163.961	+	45.7311i	0.307044	+	0.0856387i
$535$	111.463	−	80.9826i	0.208342	−	0.151369i
$536$	177.532	−	244.351i	0.331216	−	0.455879i
$537$	−61.2576	−	164.581i	−0.114074	−	0.306482i
$538$	615.583			1.14421
$539$		0			0
$540$	−954.086	+	121.315i	−1.76683	+	0.224658i
$541$	181.281	+	557.925i	0.335085	+	1.03128i	0.966680	+	0.255987i	$0.0824004\pi$
$541$	181.281	+	557.925i	0.335085	+	1.03128i	−0.631596	+	0.775298i	$0.717600\pi$
$542$	144.288	−	198.595i	0.266214	−	0.366412i
$543$	−530.662	−	669.157i	−0.977279	−	1.23233i
$544$	−10.7702	+	33.1471i	−0.0197981	+	0.0609322i
$545$	668.020	+	217.053i	1.22572	+	0.398262i
$546$	357.920	−	283.842i	0.655531	−	0.519856i
$547$	557.289	+	404.894i	1.01881	+	0.740209i	0.966039	−	0.258398i	$-0.0831946\pi$
$547$	557.289	+	404.894i	1.01881	+	0.740209i	0.0527711	+	0.998607i	$0.483195\pi$
$548$	−776.646	+	252.348i	−1.41724	+	0.460489i
$549$	95.5519	−	8.07575i	0.174047	−	0.0147099i
$550$		0			0
$551$		−	78.3083i		−	0.142120i
$552$	320.928	−	119.451i	0.581391	−	0.216396i
$553$	−243.444	−	176.873i	−0.440225	−	0.319842i
$554$	−393.778	−	541.989i	−0.710790	−	0.978319i
$555$	−206.306	+	739.678i	−0.371723	+	1.33275i
$556$	185.415	−	570.649i	0.333480	−	1.02635i
$557$	−363.725	−	500.624i	−0.653007	−	0.898787i	0.346218	−	0.938154i	$-0.387466\pi$
$557$	−363.725	−	500.624i	−0.653007	−	0.898787i	−0.999225	+	0.0393671i	$0.987466\pi$
$558$	−296.217	+	489.710i	−0.530855	+	0.877616i
$559$	217.925	+	670.706i	0.389849	+	1.19983i
$560$		−	176.430i		−	0.315053i
$561$		0			0
$562$	1519.22			2.70325
$563$	541.408	−	175.914i	0.961648	−	0.312458i	0.214208	−	0.976788i	$-0.431283\pi$
$563$	541.408	−	175.914i	0.961648	−	0.312458i	0.747440	+	0.664330i	$0.231283\pi$
$564$	−266.702	−	177.093i	−0.472876	−	0.313994i
$565$	713.145	−	518.130i	1.26220	−	0.917045i
$566$	−895.558	−	290.984i	−1.58226	−	0.514107i
$567$	35.9779	−	245.479i	0.0634531	−	0.432943i
$568$	8.68589	−	6.31067i	0.0152921	−	0.0111103i
$569$	529.905	−	729.352i	0.931292	−	1.28181i	−0.0280618	−	0.999606i	$-0.508934\pi$
$569$	529.905	−	729.352i	0.931292	−	1.28181i	0.959354	−	0.282207i	$-0.0910665\pi$
$570$	1182.60	−	440.168i	2.07473	−	0.772225i
$571$	804.182			1.40837			0.704187	−	0.710014i	$-0.251312\pi$
$571$	804.182			1.40837			0.704187	+	0.710014i	$0.251312\pi$
$572$		0			0
$573$	−411.961	+	17.3779i	−0.718955	+	0.0303279i
$574$	38.7348	+	119.213i	0.0674822	+	0.207689i
$575$	−306.429	+	421.763i	−0.532920	+	0.733501i
$576$	665.221	−	574.832i	1.15490	−	0.997972i
$577$	−243.227	+	748.576i	−0.421538	+	1.29736i	0.484733	+	0.874662i	$0.338917\pi$
$577$	−243.227	+	748.576i	−0.421538	+	1.29736i	−0.906271	+	0.422697i	$0.861083\pi$
$578$	−839.238	−	272.685i	−1.45197	−	0.471773i
$579$	555.671	+	700.694i	0.959709	+	1.21018i
$580$	−109.009	−	79.2000i	−0.187947	−	0.136552i
$581$	−92.9285	+	30.1943i	−0.159946	+	0.0519695i
$582$	−580.643	+	24.4934i	−0.997669	+	0.0420849i
$583$		0			0
$584$			189.998i			0.325340i
$585$	−894.632	+	376.638i	−1.52929	+	0.643826i
$586$	−841.024	−	611.040i	−1.43519	−	1.04273i
$587$	107.287	+	147.667i	0.182771	+	0.251563i	0.890565	−	0.454856i	$-0.150309\pi$
$587$	107.287	+	147.667i	0.182771	+	0.251563i	−0.707794	+	0.706419i	$0.750309\pi$
$588$	614.230	+	171.317i	1.04461	+	0.291355i
$589$	132.934	−	409.128i	0.225694	−	0.694615i
$590$	−519.809	−	715.456i	−0.881033	−	1.21264i
$591$	145.298	+	96.4791i	0.245851	+	0.163247i
$592$	−103.360	−	318.109i	−0.174595	−	0.537347i
$593$			685.071i			1.15526i	0.816297	+	0.577632i	$0.196023\pi$
$593$			685.071i			1.15526i	−0.816297	+	0.577632i	$0.803977\pi$
$594$		0			0
$595$	−16.3837			−0.0275357
$596$	−1325.11	+	430.556i	−2.22335	+	0.722409i
$597$	−207.518	+	312.523i	−0.347602	+	0.523489i
$598$	1098.87	−	798.373i	1.83757	−	1.33507i
$599$	−343.213	−	111.517i	−0.572977	−	0.186171i	0.00817505	−	0.999967i	$-0.497398\pi$
$599$	−343.213	−	111.517i	−0.572977	−	0.186171i	−0.581152	+	0.813795i	$0.697398\pi$
$600$	64.2476	−	230.349i	0.107079	−	0.383915i
$601$	−339.372	+	246.568i	−0.564679	+	0.410264i	−0.833169	−	0.553019i	$-0.813476\pi$
$601$	−339.372	+	246.568i	−0.564679	+	0.410264i	0.268489	+	0.963283i	$0.413476\pi$
$602$	239.186	−	329.211i	0.397318	−	0.546862i
$603$	−252.468	−	599.689i	−0.418686	−	0.994510i
$604$	472.229			0.781836
$605$		0			0
$606$	58.1783	+	1379.18i	0.0960039	+	2.27588i
$607$	−311.403	−	958.400i	−0.513020	−	1.57891i	−0.786856	−	0.617137i	$-0.788293\pi$
$607$	−311.403	−	958.400i	−0.513020	−	1.57891i	0.273836	−	0.961776i	$-0.411707\pi$
$608$	−526.406	+	724.536i	−0.865800	+	1.19167i
$609$	27.2344	−	21.5977i	0.0447199	−	0.0354642i
$610$	−66.8970	+	205.888i	−0.109667	+	0.337521i
$611$	−307.297	−	99.8468i	−0.502941	−	0.163415i
$612$	−25.4352	−	29.4348i	−0.0415608	−	0.0480960i
$613$	−446.778	−	324.603i	−0.728838	−	0.529532i	0.160358	−	0.987059i	$-0.448735\pi$
$613$	−446.778	−	324.603i	−0.728838	−	0.529532i	−0.889196	+	0.457527i	$0.848735\pi$
$614$	1152.92	−	374.608i	1.87773	−	0.610110i
$615$	−11.2258	−	266.119i	−0.0182533	−	0.432714i
$616$		0			0
$617$		−	675.556i		−	1.09490i	−0.836837	−	0.547452i	$-0.815598\pi$
$617$		−	675.556i		−	1.09490i	0.836837	−	0.547452i	$-0.184402\pi$
$618$	−479.628	−	1288.61i	−0.776097	−	2.08514i
$619$	217.722	+	158.184i	0.351732	+	0.255548i	0.749595	−	0.661896i	$-0.230248\pi$
$619$	217.722	+	158.184i	0.351732	+	0.255548i	−0.397863	+	0.917445i	$0.630248\pi$
$620$	−435.082	−	598.838i	−0.701744	−	0.965868i
$621$	137.644	−	724.750i	0.221650	−	1.16707i
$622$	−82.3072	+	253.316i	−0.132327	+	0.407260i
$623$	−33.3805	−	45.9443i	−0.0535802	−	0.0737469i
$624$	233.880	−	352.224i	0.374807	−	0.564461i
$625$	−228.038	−	701.828i	−0.364860	−	1.12292i
$626$			1832.83i			2.92784i
$627$		0			0
$628$	41.0719			0.0654011
$629$	−29.5404	+	9.59826i	−0.0469641	+	0.0152596i
$630$	479.249	+	289.889i	0.760712	+	0.460142i
$631$	−75.5208	+	54.8691i	−0.119684	+	0.0869558i	−0.646017	−	0.763323i	$-0.723567\pi$
$631$	−75.5208	+	54.8691i	−0.119684	+	0.0869558i	0.526333	+	0.850279i	$0.323567\pi$
$632$	390.342	+	126.830i	0.617630	+	0.200680i
$633$	139.841	+	39.0034i	0.220917	+	0.0616168i
$634$	6.07783	−	4.41580i	0.00958649	−	0.00696499i
$635$	572.322	−	787.734i	0.901295	−	1.24053i
$636$	−99.2390	−	266.625i	−0.156036	−	0.419222i
$637$	643.584			1.01034
$638$		0			0
$639$	−1.94785	−	23.0469i	−0.00304828	−	0.0360672i
$640$	258.308	+	794.990i	0.403606	+	1.24217i
$641$	−8.68174	+	11.9494i	−0.0135441	+	0.0186418i	−0.815735	−	0.578425i	$-0.803667\pi$
$641$	−8.68174	+	11.9494i	−0.0135441	+	0.0186418i	0.802191	+	0.597067i	$0.203667\pi$
$642$	−118.378	−	149.273i	−0.184389	−	0.232512i
$643$	−134.744	+	414.698i	−0.209555	+	0.644943i	0.789941	+	0.613183i	$0.210111\pi$
$643$	−134.744	+	414.698i	−0.209555	+	0.644943i	−0.999496	+	0.0317599i	$0.989889\pi$
$644$	−427.023	−	138.748i	−0.663079	−	0.215448i
$645$	−677.506	+	537.283i	−1.05040	+	0.832997i
$646$	41.2922	+	30.0005i	0.0639198	+	0.0464405i
$647$	298.985	−	97.1462i	0.462110	−	0.150149i	−0.0687036	−	0.997637i	$-0.521886\pi$
$647$	298.985	−	97.1462i	0.462110	−	0.150149i	0.530814	+	0.847488i	$0.321886\pi$
$648$	56.7948	+	333.596i	0.0876462	+	0.514809i
$649$		0			0
$650$		−	948.550i		−	1.45931i
$651$	178.952	−	66.6068i	0.274888	−	0.102315i
$652$	1139.59	+	827.958i	1.74783	+	1.26987i
$653$	112.807	+	155.266i	0.172752	+	0.237773i	0.886610	−	0.462517i	$-0.153054\pi$
$653$	112.807	+	155.266i	0.172752	+	0.237773i	−0.713858	+	0.700291i	$0.753054\pi$
$654$	260.940	−	935.557i	0.398990	−	1.43052i
$655$	306.656	−	943.789i	0.468177	−	1.44090i
$656$	68.1931	+	93.8598i	0.103953	+	0.143079i
$657$	350.223	+	211.844i	0.533064	+	0.322441i
$658$	57.6135	+	177.316i	0.0875586	+	0.269478i
$659$		−	127.678i		−	0.193745i	−0.995297	−	0.0968724i	$-0.969116\pi$
$659$		−	127.678i		−	0.193745i	0.995297	−	0.0968724i	$-0.0308839\pi$
$660$		0			0
$661$	580.599			0.878364			0.439182	−	0.898398i	$-0.355268\pi$
$661$	580.599			0.878364			0.439182	+	0.898398i	$0.355268\pi$
$662$	1071.27	−	348.076i	1.61823	−	0.525795i
$663$	−32.7084	−	21.7186i	−0.0493339	−	0.0327581i
$664$	107.820	−	78.3355i	0.162379	−	0.117975i
$665$	−400.388	−	130.094i	−0.602088	−	0.195630i
$666$	1033.93	+	241.917i	1.55245	+	0.363238i
$667$	83.6135	−	60.7488i	0.125358	−	0.0910776i
$668$	504.590	−	694.508i	0.755374	−	1.03968i
$669$	−595.254	+	221.556i	−0.889767	+	0.331175i
$670$	1468.92			2.19241
$671$		0			0
$672$	−397.167	+	16.7538i	−0.591023	+	0.0249313i
$673$	168.866	+	519.715i	0.250915	+	0.772236i	0.994607	+	0.103714i	$0.0330728\pi$
$673$	168.866	+	519.715i	0.250915	+	0.772236i	−0.743692	+	0.668522i	$0.766927\pi$
$674$	1064.66	−	1465.37i	1.57961	−	2.17415i
$675$	−352.967	−	375.261i	−0.522914	−	0.555943i
$676$	−157.319	+	484.177i	−0.232720	+	0.716238i
$677$	−27.7389	−	9.01292i	−0.0409733	−	0.0133130i	0.288459	−	0.957492i	$-0.406857\pi$
$677$	−27.7389	−	9.01292i	−0.0409733	−	0.0133130i	−0.329432	+	0.944179i	$0.606857\pi$
$678$	−757.388	−	955.055i	−1.11709	−	1.40864i
$679$	156.862	+	113.967i	0.231019	+	0.167845i
$680$	21.2528	−	6.90545i	0.0312541	−	0.0101551i
$681$	363.832	−	15.3476i	0.534261	−	0.0225369i
$682$		0			0
$683$		−	82.4506i		−	0.120718i	−0.998177	−	0.0603592i	$-0.980775\pi$
$683$		−	82.4506i		−	0.120718i	0.998177	−	0.0603592i	$-0.0192246\pi$
$684$	−387.865	−	921.299i	−0.567054	−	1.34693i
$685$	−817.553	−	593.987i	−1.19351	−	0.867134i
$686$	−488.251	−	672.019i	−0.711735	−	0.979620i
$687$	933.212	+	260.286i	1.35839	+	0.378873i
$688$	116.386	−	358.200i	0.169166	−	0.520640i
$689$	−168.772	−	232.294i	−0.244952	−	0.337147i
$690$	1387.41	+	921.249i	2.01073	+	1.33514i
$691$	299.041	+	920.352i	0.432765	+	1.33191i	0.895360	+	0.445344i	$0.146918\pi$
$691$	299.041	+	920.352i	0.432765	+	1.33191i	−0.462595	+	0.886570i	$0.653082\pi$
$692$		−	888.061i		−	1.28333i
$693$		0			0
$694$	−901.554			−1.29907
$695$	706.172	−	229.449i	1.01607	−	0.330143i
$696$	−26.2251	+	39.4952i	−0.0376798	+	0.0567459i
$697$	8.71606	−	6.33259i	0.0125051	−	0.00908549i
$698$	1199.14	+	389.624i	1.71796	+	0.558201i
$699$	−324.333	+	1162.84i	−0.463996	+	1.66358i
$700$	−253.674	+	184.305i	−0.362392	+	0.263293i
$701$	−184.624	+	254.112i	−0.263372	+	0.362500i	−0.920138	−	0.391594i	$-0.871924\pi$
$701$	−184.624	+	254.112i	−0.263372	+	0.362500i	0.656766	+	0.754094i	$0.271924\pi$
$702$	572.485	+	1214.04i	0.815506	+	1.72940i
$703$	−798.129			−1.13532
$704$		0			0
$705$	−16.6971	−	395.822i	−0.0236838	−	0.561450i
$706$	−128.211	−	394.592i	−0.181602	−	0.558912i
$707$	270.702	−	372.589i	0.382888	−	0.527000i
$708$	−548.910	+	435.302i	−0.775296	+	0.614834i
$709$	101.157	−	311.330i	0.142676	−	0.439111i	−0.854029	−	0.520226i	$-0.825848\pi$
$709$	101.157	−	311.330i	0.142676	−	0.439111i	0.996705	+	0.0811142i	$0.0258478\pi$
$710$	49.6596	+	16.1354i	0.0699432	+	0.0227259i
$711$	669.008	−	578.103i	0.940939	−	0.813085i
$712$	62.6656	+	45.5292i	0.0880134	+	0.0639455i
$713$	539.971	−	175.447i	0.757323	−	0.246069i
$714$	0.954820	+	22.6351i	0.00133728	+	0.0317018i
$715$		0			0
$716$		−	314.061i		−	0.438632i
$717$	0.336383	+	0.903758i	0.000469153	+	0.00126047i
$718$	690.192	+	501.454i	0.961270	+	0.698404i
$719$	650.211	+	894.939i	0.904327	+	1.24470i	0.969067	+	0.246797i	$0.0793781\pi$
$719$	650.211	+	894.939i	0.904327	+	1.24470i	−0.0647402	+	0.997902i	$0.520622\pi$
$720$	504.774	+	118.106i	0.701075	+	0.164036i
$721$	−141.757	+	436.282i	−0.196611	+	0.605107i
$722$	121.532	+	167.275i	0.168327	+	0.231682i
$723$	−482.581	+	726.770i	−0.667471	+	1.00521i
$724$	−471.975	−	1452.59i	−0.651899	−	2.00634i
$725$		−	72.1759i		−	0.0995530i
$726$		0			0
$727$	577.040			0.793727			0.396864	−	0.917878i	$-0.370099\pi$
$727$	577.040			0.793727			0.396864	+	0.917878i	$0.370099\pi$
$728$	197.698	−	64.2359i	0.271563	−	0.0882361i
$729$	678.241	+	267.263i	0.930372	+	0.366616i
$730$	−747.563	+	543.136i	−1.02406	+	0.744023i
$731$	−33.2634	−	10.8079i	−0.0455040	−	0.0147851i
$732$	165.188	+	46.0732i	0.225667	+	0.0629416i
$733$	501.026	−	364.016i	0.683527	−	0.496612i	−0.190999	−	0.981590i	$-0.561173\pi$
$733$	501.026	−	364.016i	0.683527	−	0.496612i	0.874526	+	0.484979i	$0.161173\pi$
$734$	317.281	−	436.700i	0.432263	−	0.594959i
$735$	275.263	+	739.548i	0.374507	+	1.00619i
$736$	−1181.99			−1.60596
$737$		0			0
$738$	−367.005	+	31.0181i	−0.497297	+	0.0420299i
$739$	345.884	+	1064.52i	0.468044	+	1.44049i	0.855114	+	0.518440i	$0.173487\pi$
$739$	345.884	+	1064.52i	0.468044	+	1.44049i	−0.387070	+	0.922050i	$0.626513\pi$
$740$	−807.217	+	1111.04i	−1.09083	+	1.50140i
$741$	−626.877	−	790.483i	−0.845988	−	1.06678i
$742$	−51.1981	+	157.572i	−0.0690002	+	0.212361i
$743$	−1092.36	−	354.930i	−1.47020	−	0.477698i	−0.539034	−	0.842284i	$-0.681210\pi$
$743$	−1092.36	−	354.930i	−1.47020	−	0.477698i	−0.931170	+	0.364586i	$0.881210\pi$
$744$	−204.061	+	161.827i	−0.274276	+	0.217509i
$745$	−1394.91	−	1013.46i	−1.87236	−	1.36035i
$746$	−474.724	+	154.247i	−0.636360	+	0.206766i
$747$	−24.1791	−	286.086i	−0.0323682	−	0.382979i
$748$		0			0
$749$			63.5613i			0.0848616i
$750$	−338.147	+	125.860i	−0.450863	+	0.167813i
$751$	221.394	+	160.852i	0.294799	+	0.214184i	0.725346	−	0.688384i	$-0.241680\pi$
$751$	221.394	+	160.852i	0.294799	+	0.214184i	−0.430548	+	0.902568i	$0.641680\pi$
$752$	101.430	+	139.606i	0.134880	+	0.185646i
$753$	90.7704	−	325.443i	0.120545	−	0.432195i
$754$	−58.1099	+	178.844i	−0.0770689	+	0.237194i
$755$	343.489	+	472.772i	0.454952	+	0.626188i
$756$	213.439	−	388.991i	0.282327	−	0.514538i
$757$	−172.433	−	530.695i	−0.227785	−	0.701051i	−0.997997	−	0.0632624i	$-0.979850\pi$
$757$	−172.433	−	530.695i	−0.227785	−	0.701051i	0.770212	−	0.637788i	$-0.220150\pi$
$758$		−	162.899i		−	0.214906i
$759$		0			0
$760$	574.212			0.755543
$761$	−401.113	+	130.329i	−0.527086	+	0.171261i	−0.560459	−	0.828182i	$-0.689375\pi$
$761$	−401.113	+	130.329i	−0.527086	+	0.171261i	0.0333725	+	0.999443i	$0.489375\pi$
$762$	−1121.65	−	744.788i	−1.47199	−	0.977412i
$763$	−262.156	+	190.468i	−0.343586	+	0.249630i
$764$	−701.310	−	227.870i	−0.917945	−	0.298259i
$765$	10.9676	−	46.8746i	0.0143367	−	0.0612740i
$766$	−221.993	+	161.287i	−0.289808	+	0.210558i
$767$	−415.598	+	572.021i	−0.541848	+	0.745790i
$768$	−15.3340	+	5.70738i	−0.0199661	+	0.00743148i
$769$	108.997			0.141738			0.0708692	−	0.997486i	$-0.477423\pi$
$769$	108.997			0.141738			0.0708692	+	0.997486i	$0.477423\pi$
$770$		0			0
$771$	−589.181	+	24.8536i	−0.764178	+	0.0322355i
$772$	494.218	+	1521.05i	0.640179	+	1.97027i
$773$	−606.367	+	834.592i	−0.784433	+	1.07968i	0.210346	+	0.977627i	$0.432541\pi$
$773$	−606.367	+	834.592i	−0.784433	+	1.07968i	−0.994779	+	0.102053i	$0.967459\pi$
$774$	781.772	+	904.702i	1.01004	+	1.16887i
$775$	122.524	−	377.089i	0.158095	−	0.486567i
$776$	−251.515	−	81.7222i	−0.324117	−	0.105312i
$777$	−220.127	−	277.577i	−0.283304	−	0.357242i
$778$	−667.478	−	484.951i	−0.857941	−	0.623331i
$779$	263.288	−	85.5475i	0.337982	−	0.109817i
$780$	−1734.41	+	73.1631i	−2.22360	+	0.0937988i
$781$		0			0
$782$			67.3630i			0.0861420i
$783$	43.5608	+	92.3769i	0.0556332	+	0.117978i
$784$	−278.072	−	202.031i	−0.354683	−	0.257692i
$785$	29.8748	+	41.1191i	0.0380570	+	0.0523810i
$786$	−1321.77	−	368.660i	−1.68164	−	0.469033i
$787$	−64.0985	+	197.275i	−0.0814467	+	0.250667i	−0.983485	−	0.180988i	$-0.942070\pi$
$787$	−64.0985	+	197.275i	−0.0814467	+	0.250667i	0.902039	+	0.431655i	$0.142070\pi$
$788$	183.340	+	252.346i	0.232665	+	0.320236i
$789$	−945.519	−	627.833i	−1.19838	−	0.795732i
$790$	616.825	+	1898.39i	0.780791	+	2.40303i
$791$			406.668i			0.514119i
$792$		0			0
$793$	173.082			0.218263
$794$	615.536	−	200.000i	0.775234	−	0.251889i
$795$	194.747	−	293.290i	0.244965	−	0.368918i
$796$	−542.774	+	394.349i	−0.681877	+	0.495413i
$797$	−211.514	−	68.7252i	−0.265388	−	0.0862298i	0.173300	−	0.984869i	$-0.444557\pi$
$797$	−211.514	−	68.7252i	−0.265388	−	0.0862298i	−0.438689	+	0.898639i	$0.644557\pi$
$798$	−156.398	+	560.741i	−0.195988	+	0.702683i
$799$	12.9641	−	9.41900i	0.0162255	−	0.0117885i
$800$	−485.183	+	667.797i	−0.606479	+	0.834746i
$801$	153.794	−	64.7471i	0.192003	−	0.0808328i
$802$	−1376.50			−1.71633
$803$		0			0
$804$	−49.0426	−	1162.61i	−0.0609983	−	1.44603i
$805$	−171.699	−	528.436i	−0.213291	−	0.656443i
$806$	−607.201	+	835.740i	−0.753351	+	1.03690i
$807$	472.828	−	374.967i	0.585909	−	0.464643i
$808$	−194.112	+	597.415i	−0.240237	+	0.739375i
$809$	715.778	+	232.570i	0.884769	+	0.287479i	0.715936	−	0.698166i	$-0.246000\pi$
$809$	715.778	+	232.570i	0.884769	+	0.287479i	0.168833	+	0.985645i	$0.446000\pi$
$810$	−1150.21	+	1177.09i	−1.42001	+	1.45320i
$811$	187.891	+	136.511i	0.231678	+	0.168324i	0.697568	−	0.716519i	$-0.254266\pi$
$811$	187.891	+	136.511i	0.231678	+	0.168324i	−0.465890	+	0.884843i	$0.654266\pi$
$812$	59.1197	−	19.2092i	0.0728076	−	0.0236566i
$813$	−10.1421	−	240.430i	−0.0124749	−	0.295732i
$814$		0			0
$815$			1743.13i			2.13881i
$816$	7.31441	+	19.6516i	0.00896373	+	0.0240828i
$817$	−727.077	−	528.252i	−0.889935	−	0.646576i
$818$	277.540	+	382.001i	0.339291	+	0.466994i
$819$	102.023	−	436.037i	0.124570	−	0.532401i
$820$	147.199	−	453.033i	0.179511	−	0.552480i
$821$	−285.054	−	392.343i	−0.347204	−	0.477885i	0.599324	−	0.800506i	$-0.295436\pi$
$821$	−285.054	−	392.343i	−0.347204	−	0.477885i	−0.946528	+	0.322621i	$0.895436\pi$
$822$	−772.981	+	1164.11i	−0.940367	+	1.41620i
$823$	48.4819	+	149.212i	0.0589088	+	0.181302i	0.976181	−	0.216959i	$-0.0696137\pi$
$823$	48.4819	+	149.212i	0.0589088	+	0.181302i	−0.917272	+	0.398261i	$0.869614\pi$
$824$		−	625.689i		−	0.759331i
$825$		0			0
$826$	407.986			0.493930
$827$	−150.007	+	48.7401i	−0.181386	+	0.0589360i	−0.398302	−	0.917254i	$-0.630400\pi$
$827$	−150.007	+	48.7401i	−0.181386	+	0.0589360i	0.216916	+	0.976190i	$0.430400\pi$
$828$	682.823	−	1128.85i	0.824666	−	1.36335i
$829$	−1057.08	+	768.011i	−1.27512	+	0.926431i	−0.999394	−	0.0348051i	$-0.988919\pi$
$829$	−1057.08	+	768.011i	−1.27512	+	0.926431i	−0.275728	+	0.961236i	$0.588919\pi$
$830$	616.434	+	200.292i	0.742692	+	0.241315i
$831$	−632.599	−	176.441i	−0.761251	−	0.212323i
$832$	1283.81	−	932.745i	1.54304	−	1.12109i
$833$	−18.7611	+	25.8224i	−0.0225223	+	0.0309993i
$834$	−358.152	−	962.245i	−0.429439	−	1.15377i
$835$	1062.33			1.27226
$836$		0			0
$837$	70.7709	+	556.579i	0.0845530	+	0.664969i
$838$	714.482	+	2198.95i	0.852604	+	2.62405i
$839$	754.318	−	1038.23i	0.899068	−	1.23746i	−0.0716959	−	0.997427i	$-0.522841\pi$
$839$	754.318	−	1038.23i	0.899068	−	1.23746i	0.970764	−	0.240035i	$-0.0771589\pi$
$840$	158.370	+	199.702i	0.188536	+	0.237741i
$841$	255.462	−	786.230i	0.303759	−	0.934875i
$842$	1271.56	+	413.154i	1.51016	+	0.490682i
$843$	1166.91	−	925.398i	1.38424	−	1.09774i
$844$	210.049	+	152.609i	0.248873	+	0.180817i
$845$	−599.164	+	194.680i	−0.709069	+	0.230391i
$846$	−545.878	+	46.1359i	−0.645246	+	0.0545342i
$847$		0			0
$848$			153.347i			0.180834i
$849$	−865.123	+	322.002i	−1.01899	+	0.379273i
$850$	38.0586	+	27.6512i	0.0447748	+	0.0325308i
$851$	−619.160	−	852.200i	−0.727567	−	1.00141i
$852$	11.1128	−	39.8430i	0.0130431	−	0.0467641i
$853$	−153.468	+	472.325i	−0.179915	+	0.553723i	−0.999824	−	0.0187721i	$-0.994024\pi$
$853$	−153.468	+	472.325i	−0.179915	+	0.553723i	0.819908	+	0.572495i	$0.194024\pi$
$854$	−58.7033	−	80.7982i	−0.0687392	−	0.0946114i
$855$	640.234	−	1058.44i	0.748811	−	1.23794i
$856$	−26.7900	−	82.4511i	−0.0312967	−	0.0963214i
$857$		−	479.970i		−	0.560059i	−0.959991	−	0.280029i	$-0.909656\pi$
$857$		−	479.970i		−	0.560059i	0.959991	−	0.280029i	$-0.0903442\pi$
$858$		0			0
$859$	658.810			0.766950			0.383475	−	0.923551i	$-0.374727\pi$
$859$	658.810			0.766950			0.383475	+	0.923551i	$0.374727\pi$
$860$	−1470.71	+	477.864i	−1.71013	+	0.555655i
$861$	102.368	+	67.9732i	0.118894	+	0.0789468i
$862$	24.0996	−	17.5094i	0.0279578	−	0.0203125i
$863$	−512.443	−	166.503i	−0.593793	−	0.192935i	−0.00332255	−	0.999994i	$-0.501058\pi$
$863$	−512.443	−	166.503i	−0.593793	−	0.192935i	−0.590470	+	0.807060i	$0.701058\pi$
$864$	217.939	−	1147.53i	0.252244	−	1.32816i
$865$	889.082	−	645.956i	1.02784	−	0.746770i
$866$	106.622	−	146.752i	0.123120	−	0.169460i
$867$	−810.717	+	301.752i	−0.935083	+	0.348042i
$868$	341.485			0.393416
$869$		0			0
$870$	−230.365	+	9.71754i	−0.264787	+	0.0111696i
$871$	−362.918	−	1116.95i	−0.416669	−	1.28237i
$872$	259.788	−	357.567i	0.297922	−	0.410054i
$873$	−431.072	+	372.498i	−0.493782	+	0.426687i
$874$	−534.893	+	1646.23i	−0.612005	+	1.88356i
$875$	114.486	+	37.1986i	0.130841	+	0.0425127i
$876$	454.837	+	573.543i	0.519220	+	0.654729i
$877$	68.5357	+	49.7941i	0.0781479	+	0.0567777i	0.626173	−	0.779684i	$-0.284620\pi$
$877$	68.5357	+	49.7941i	0.0781479	+	0.0567777i	−0.548025	+	0.836462i	$0.684620\pi$
$878$	−1294.36	+	420.562i	−1.47421	+	0.479001i
$879$	−1018.19	+	42.9505i	−1.15835	+	0.0488629i
$880$		0			0
$881$			364.734i			0.414000i	0.978341	+	0.207000i	$0.0663701\pi$
$881$			364.734i			0.414000i	−0.978341	+	0.207000i	$0.933630\pi$
$882$	1005.69	−	423.391i	1.14023	−	0.480035i
$883$	−180.241	−	130.953i	−0.204123	−	0.148304i	0.481027	−	0.876706i	$-0.340264\pi$
$883$	−180.241	−	130.953i	−0.204123	−	0.148304i	−0.685151	+	0.728401i	$0.740264\pi$
$884$	−41.2721	−	56.8062i	−0.0466879	−	0.0642604i
$885$	−835.067	−	232.912i	−0.943578	−	0.263177i
$886$	−506.266	+	1558.13i	−0.571406	+	1.75861i
$887$	801.425	+	1103.07i	0.903523	+	1.24359i	0.969331	+	0.245761i	$0.0790377\pi$
$887$	801.425	+	1103.07i	0.903523	+	1.24359i	−0.0658073	+	0.997832i	$0.520962\pi$
$888$	402.540	+	267.290i	0.453311	+	0.301003i
$889$	138.811	+	427.217i	0.156143	+	0.480559i
$890$			376.714i			0.423274i
$891$		0			0
$892$	−1135.89			−1.27342
$893$	391.611	−	127.242i	0.438534	−	0.142488i
$894$	−1318.86	+	1986.21i	−1.47524	+	2.22171i
$895$	314.422	−	228.441i	0.351309	−	0.255241i
$896$	−366.760	−	119.167i	−0.409330	−	0.132999i
$897$	357.728	−	1282.58i	0.398805	−	1.42985i
$898$	−1904.91	+	1384.00i	−2.12129	+	1.54120i
$899$	−46.2024	+	63.5921i	−0.0513931	+	0.0707365i
$900$	−357.491	−	849.151i	−0.397212	−	0.943502i
$901$	14.2402			0.0158049
$902$		0			0
$903$	−16.8126	−	398.560i	−0.0186186	−	0.441373i
$904$	−171.404	−	527.526i	−0.189606	−	0.583546i
$905$	1110.95	−	1529.10i	1.22757	−	1.68961i
$906$	633.143	−	502.102i	0.698834	−	0.554196i
$907$	203.099	−	625.073i	0.223924	−	0.689166i	−0.774476	−	0.632604i	$-0.781986\pi$
$907$	203.099	−	625.073i	0.223924	−	0.689166i	0.998399	−	0.0565619i	$-0.0180138\pi$
$908$	619.376	+	201.248i	0.682132	+	0.221638i
$909$	884.781	+	1023.91i	0.973357	+	1.12641i
$910$	817.887	+	594.230i	0.898777	+	0.653000i
$911$	−331.388	+	107.674i	−0.363763	+	0.118194i	−0.485195	−	0.874406i	$-0.661251\pi$
$911$	−331.388	+	107.674i	−0.363763	+	0.118194i	0.121432	+	0.992600i	$0.461251\pi$
$912$	22.7085	+	538.329i	0.0248996	+	0.590273i
$913$		0			0
$914$			519.188i			0.568039i
$915$	74.0280	+	198.891i	0.0809049	+	0.217367i
$916$	1401.74	+	1018.42i	1.53028	+	1.11182i
$917$	269.096	+	370.379i	0.293453	+	0.403903i
$918$	−65.3991	−	12.4206i	−0.0712409	−	0.0135301i
$919$	−197.588	+	608.115i	−0.215004	+	0.661714i	0.784150	+	0.620572i	$0.213099\pi$
$919$	−197.588	+	608.115i	−0.215004	+	0.661714i	−0.999153	+	0.0411417i	$0.986901\pi$
$920$	445.453	+	613.114i	0.484188	+	0.666428i
$921$	657.376	−	990.010i	0.713763	−	1.07493i
$922$	251.884	+	775.220i	0.273193	+	0.840803i
$923$		−	41.7471i		−	0.0452298i
$924$		0			0
$925$	−735.627			−0.795272
$926$	−2051.44	+	666.554i	−2.21538	+	0.719821i
$927$	−1153.33	−	697.629i	−1.24415	−	0.752566i
$928$	132.389	−	96.1863i	0.142661	−	0.103649i
$929$	299.056	+	97.1692i	0.321912	+	0.104595i	0.465515	−	0.885040i	$-0.345869\pi$
$929$	299.056	+	97.1692i	0.321912	+	0.104595i	−0.143604	+	0.989635i	$0.545869\pi$
$930$	−1220.06	−	340.291i	−1.31189	−	0.365904i
$931$	−663.529	+	482.082i	−0.712706	+	0.517811i
$932$	−1269.02	+	1746.66i	−1.36161	+	1.87410i
$933$	91.0809	+	244.707i	0.0976215	+	0.262279i
$934$	2066.22			2.21222
$935$		0			0
$936$	51.4389	+	608.623i	0.0549561	+	0.650238i
$937$	−469.735	−	1445.70i	−0.501318	−	1.54290i	−0.806874	−	0.590724i	$-0.798842\pi$
$937$	−469.735	−	1445.70i	−0.501318	−	1.54290i	0.305556	−	0.952174i	$-0.401158\pi$
$938$	−398.324	+	548.245i	−0.424652	+	0.584483i
$939$	1116.42	+	1407.79i	1.18895	+	1.49925i
$940$	218.942	−	673.835i	0.232917	−	0.716846i
$941$	−1067.37	−	346.811i	−1.13430	−	0.368556i	−0.319090	−	0.947724i	$-0.603377\pi$
$941$	−1067.37	−	346.811i	−1.13430	−	0.368556i	−0.815208	+	0.579169i	$0.803377\pi$
$942$	55.0673	−	43.6701i	0.0584579	−	0.0463589i
$943$	295.593	+	214.761i	0.313460	+	0.227742i
$944$	359.133	−	116.689i	0.380437	−	0.123611i
$945$	544.689	−	69.2591i	0.576390	−	0.0732900i
$946$		0			0
$947$		−	865.333i		−	0.913762i	−0.889528	−	0.456881i	$-0.848967\pi$
$947$		−	865.333i		−	0.913762i	0.889528	−	0.456881i	$-0.151033\pi$
$948$	1481.93	−	551.582i	1.56322	−	0.581838i
$949$	597.691	+	434.248i	0.629812	+	0.457585i
$950$	710.520	+	977.947i	0.747916	+	1.02942i
$951$	1.97859	−	7.09393i	0.00208054	−	0.00745945i
$952$	−3.18575	+	9.80474i	−0.00334638	+	0.0102991i
$953$	298.122	+	410.330i	0.312825	+	0.430567i	0.936260	−	0.351309i	$-0.114263\pi$
$953$	298.122	+	410.330i	0.312825	+	0.430567i	−0.623435	+	0.781875i	$0.714263\pi$
$954$	−416.547	−	251.962i	−0.436632	−	0.264111i
$955$	−281.986	−	867.863i	−0.295273	−	0.908757i
$956$			1.72460i			0.00180397i
$957$		0			0
$958$	2141.59			2.23548
$959$	443.388	−	144.066i	0.462345	−	0.150225i
$960$	1620.92	+	1076.30i	1.68845	+	1.12115i
$961$	428.125	−	311.051i	0.445500	−	0.323674i
$962$	1822.80	+	592.265i	1.89481	+	0.615660i
$963$	−181.852	−	42.5493i	−0.188839	−	0.0441841i
$964$	−1262.22	+	917.054i	−1.30935	+	0.951301i
$965$	−1163.31	+	1601.16i	−1.20550	+	1.65924i
$966$	−720.059	+	268.009i	−0.745402	+	0.277442i
$967$	569.116			0.588537			0.294269	−	0.955723i	$-0.404924\pi$
$967$	569.116			0.588537			0.294269	+	0.955723i	$0.404924\pi$
$968$		0			0
$969$	49.9906	−	2.10876i	0.0515899	−	0.00217623i
$970$	−397.448	−	1223.22i	−0.409740	−	1.26105i
$971$	−736.695	+	1013.97i	−0.758697	+	1.04426i	0.238624	+	0.971112i	$0.423304\pi$
$971$	−736.695	+	1013.97i	−0.758697	+	1.04426i	−0.997321	+	0.0731450i	$0.976696\pi$
$972$	970.041	+	871.058i	0.997985	+	0.896150i
$973$	−105.854	+	325.784i	−0.108791	+	0.334825i
$974$	1901.55	+	617.851i	1.95231	+	0.634344i
$975$	−577.786	−	728.580i	−0.592601	−	0.747262i
$976$	−74.7833	−	54.3333i	−0.0766223	−	0.0556693i
$977$	1085.77	−	352.788i	1.11133	−	0.361093i	0.304878	−	0.952391i	$-0.401384\pi$
$977$	1085.77	−	352.788i	1.11133	−	0.361093i	0.806453	+	0.591298i	$0.201384\pi$
$978$	2408.24	−	101.587i	2.46241	−	0.103873i
$979$		0			0
$980$			1411.24i			1.44004i
$981$	−369.444	−	877.545i	−0.376600	−	0.894541i
$982$	−153.097	−	111.231i	−0.155903	−	0.113270i
$983$	−391.031	−	538.208i	−0.397793	−	0.547515i	0.562395	−	0.826869i	$-0.309880\pi$
$983$	−391.031	−	538.208i	−0.397793	−	0.547515i	−0.960188	+	0.279353i	$0.909880\pi$
$984$	−161.440	−	45.0279i	−0.164065	−	0.0457600i
$985$	−119.279	+	367.102i	−0.121095	+	0.372692i
$986$	−5.48178	−	7.54502i	−0.00555961	−	0.00765215i
$987$	152.261	+	101.102i	0.154266	+	0.102434i
$988$	−557.549	−	1715.96i	−0.564321	−	1.73680i
$989$		−	1186.13i		−	1.19933i
$990$		0			0
$991$	−1471.97			−1.48534			−0.742670	−	0.669658i	$-0.766441\pi$
$991$	−1471.97			−1.48534			−0.742670	+	0.669658i	$0.766441\pi$
$992$	854.961	−	277.794i	0.861856	−	0.280034i
$993$	610.818	−	919.894i	0.615124	−	0.926379i
$994$	−19.4883	+	14.1591i	−0.0196060	+	0.0142446i
$995$	−789.604	−	256.558i	−0.793572	−	0.257847i
$996$	137.945	−	494.579i	0.138499	−	0.496565i
$997$	502.232	−	364.893i	0.503743	−	0.365991i	−0.306702	−	0.951806i	$-0.599225\pi$
$997$	502.232	−	364.893i	0.503743	−	0.365991i	0.810445	+	0.585815i	$0.199225\pi$
$998$	−593.582	+	816.996i	−0.594772	+	0.818633i
$999$	941.518	−	443.978i	0.942461	−	0.444422i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.3.h.j.269.4		16
3.2	odd	2	inner	363.3.h.j.269.1		16
11.2	odd	10		33.3.h.b.20.4	yes	16
11.3	even	5		363.3.b.l.122.2		8
11.4	even	5		363.3.h.n.245.4		16
11.5	even	5		363.3.h.n.323.1		16
11.6	odd	10		363.3.h.o.323.4		16
11.7	odd	10		363.3.h.o.245.1		16
11.8	odd	10		363.3.b.m.122.7		8
11.9	even	5	inner	363.3.h.j.251.1		16
11.10	odd	2		33.3.h.b.5.1	✓	16
33.2	even	10		33.3.h.b.20.1	yes	16
33.5	odd	10		363.3.h.n.323.4		16
33.8	even	10		363.3.b.m.122.2		8
33.14	odd	10		363.3.b.l.122.7		8
33.17	even	10		363.3.h.o.323.1		16
33.20	odd	10	inner	363.3.h.j.251.4		16
33.26	odd	10		363.3.h.n.245.1		16
33.29	even	10		363.3.h.o.245.4		16
33.32	even	2		33.3.h.b.5.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.h.b.5.1	✓	16	11.10	odd	2
33.3.h.b.5.4	yes	16	33.32	even	2
33.3.h.b.20.1	yes	16	33.2	even	10
33.3.h.b.20.4	yes	16	11.2	odd	10
363.3.b.l.122.2		8	11.3	even	5
363.3.b.l.122.7		8	33.14	odd	10
363.3.b.m.122.2		8	33.8	even	10
363.3.b.m.122.7		8	11.8	odd	10
363.3.h.j.251.1		16	11.9	even	5	inner
363.3.h.j.251.4		16	33.20	odd	10	inner
363.3.h.j.269.1		16	3.2	odd	2	inner
363.3.h.j.269.4		16	1.1	even	1	trivial
363.3.h.n.245.1		16	33.26	odd	10
363.3.h.n.245.4		16	11.4	even	5
363.3.h.n.323.1		16	11.5	even	5
363.3.h.n.323.4		16	33.5	odd	10
363.3.h.o.245.1		16	11.7	odd	10
363.3.h.o.245.4		16	33.29	even	10
363.3.h.o.323.1		16	33.17	even	10
363.3.h.o.323.4		16	11.6	odd	10

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+(2.91048 - 0.945671i) q^{2} +(1.65950 - 2.49921i) q^{3} +(4.34051 - 3.15356i) q^{4} +(6.31437 + 2.05166i) q^{5} +(2.46650 - 8.84324i) q^{6} +(-2.47800 + 1.80037i) q^{7} +(2.45561 - 3.37986i) q^{8} +(-3.49213 - 8.29488i) q^{9} +20.3180 q^{10} +(-0.678356 - 16.0812i) q^{12} +(-5.01988 - 15.4496i) q^{13} +(-5.50960 + 7.58331i) q^{14} +(15.6062 - 12.3762i) q^{15} +(-2.68094 + 8.25108i) q^{16} +(0.766216 + 0.248959i) q^{17} +(-18.0080 - 20.8396i) q^{18} +(16.7481 + 12.1682i) q^{19} +(33.8776 - 11.0075i) q^{20} +(0.387274 + 9.18076i) q^{21} +27.3224i q^{23} +(-4.37190 - 11.7460i) q^{24} +(15.4365 + 11.2153i) q^{25} +(-29.2204 - 40.2185i) q^{26} +(-26.5259 - 5.03778i) q^{27} +(-5.07819 + 15.6291i) q^{28} +(-2.22341 - 3.06025i) q^{29} +(33.7177 - 50.7790i) q^{30} +(-6.42137 - 19.7630i) q^{31} +43.2608i q^{32} +2.46549 q^{34} +(-19.3408 + 6.28420i) q^{35} +(-41.3160 - 24.9913i) q^{36} +(-31.1905 + 22.6613i) q^{37} +(60.2520 + 19.5771i) q^{38} +(-46.9423 - 13.0928i) q^{39} +(22.4400 - 16.3036i) q^{40} +(7.86024 - 10.8187i) q^{41} +(9.80913 + 26.3542i) q^{42} -43.4125 q^{43} +(-5.03227 - 59.5416i) q^{45} +(25.8380 + 79.5212i) q^{46} +(11.6912 - 16.0916i) q^{47} +(16.1722 + 20.3929i) q^{48} +(-12.2427 + 37.6791i) q^{49} +(55.5336 + 18.0440i) q^{50} +(1.89374 - 1.50179i) q^{51} +(-70.5100 - 51.2285i) q^{52} +(16.8103 - 5.46201i) q^{53} +(-81.9669 + 10.4224i) q^{54} +12.7963i q^{56} +(58.2044 - 21.6639i) q^{57} +(-9.36516 - 6.80419i) q^{58} +(-25.5837 - 35.2129i) q^{59} +(28.7098 - 102.934i) q^{60} +(-3.29249 + 10.1333i) q^{61} +(-37.3785 - 51.4471i) q^{62} +(23.5874 + 14.2676i) q^{63} +(30.1867 + 92.9052i) q^{64} -107.854i q^{65} +72.2963 q^{67} +(4.11087 - 1.33570i) q^{68} +(68.2845 + 45.3415i) q^{69} +(-50.3481 + 36.5800i) q^{70} +(2.44412 + 0.794142i) q^{71} +(-36.6108 - 8.56611i) q^{72} +(-36.7931 + 26.7318i) q^{73} +(-69.3492 + 95.4510i) q^{74} +(53.6463 - 19.9674i) q^{75} +111.068 q^{76} +(-149.006 + 6.28555i) q^{78} +(30.3585 + 93.4339i) q^{79} +(-33.8569 + 46.6000i) q^{80} +(-56.6101 + 57.9335i) q^{81} +(12.6461 - 38.9207i) q^{82} +(30.3393 + 9.85783i) q^{83} +(30.6331 + 38.6279i) q^{84} +(4.32739 + 3.14404i) q^{85} +(-126.351 + 41.0540i) q^{86} +(-11.3380 + 0.478272i) q^{87} +18.5409i q^{89} +(-70.9531 - 168.536i) q^{90} +(40.2543 + 29.2464i) q^{91} +(86.1629 + 118.593i) q^{92} +(-60.0481 - 16.7482i) q^{93} +(18.8097 - 57.8902i) q^{94} +(80.7886 + 111.196i) q^{95} +(108.118 + 71.7913i) q^{96} +(-19.5614 - 60.2037i) q^{97} +121.242i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 10 q^{3} + 8 q^{4} + 33 q^{6} - 6 q^{7} - 28 q^{9} + 12 q^{10} + 106 q^{12} + 42 q^{13} + 82 q^{15} - 88 q^{16} + 43 q^{18} + 134 q^{19} + 12 q^{21} - 41 q^{24} + 134 q^{25} + 80 q^{27} - 264 q^{28}+ \cdots + 72 q^{97}+O(q^{100}) \) 16 * q - 10 * q^3 + 8 * q^4 + 33 * q^6 - 6 * q^7 - 28 * q^9 + 12 * q^10 + 106 * q^12 + 42 * q^13 + 82 * q^15 - 88 * q^16 + 43 * q^18 + 134 * q^19 + 12 * q^21 - 41 * q^24 + 134 * q^25 + 80 * q^27 - 264 * q^28 + 120 * q^30 + 124 * q^31 - 132 * q^34 - 219 * q^36 + 90 * q^37 + 174 * q^39 + 284 * q^40 - 102 * q^42 + 156 * q^43 - 72 * q^45 + 22 * q^46 + 30 * q^48 - 30 * q^49 - 111 * q^51 - 326 * q^52 - 1046 * q^54 - 281 * q^57 - 116 * q^58 + 54 * q^60 + 126 * q^61 + 138 * q^63 + 236 * q^64 + 368 * q^67 + 198 * q^69 - 322 * q^70 + 562 * q^72 - 24 * q^73 - 21 * q^75 + 900 * q^76 - 492 * q^78 + 314 * q^79 - 388 * q^81 - 270 * q^84 - 318 * q^85 - 132 * q^87 - 176 * q^90 + 374 * q^91 - 10 * q^93 - 990 * q^94 + 332 * q^96 + 72 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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