LMFDB - Embedded newform 363.3.h.j.269.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

sage:traces = [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			269.1
Root			$-2.91048 + 0.945671i$ of defining polynomial
Character	$\chi$	$=$	363.269
Dual form			363.3.h.j.251.1

$q$-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} +(-1.86408 + 2.35058i) q^{3} +(4.34051 - 3.15356i) q^{4} +(-6.31437 - 2.05166i) q^{5} +(3.20248 - 8.60410i) q^{6} +(-2.47800 + 1.80037i) q^{7} +(-2.45561 + 3.37986i) q^{8} +(-2.05042 - 8.76332i) q^{9} +20.3180 q^{10} +(-0.678356 + 16.0812i) q^{12} +(-5.01988 - 15.4496i) q^{13} +(5.50960 - 7.58331i) q^{14} +(16.5931 - 11.0180i) q^{15} +(-2.68094 + 8.25108i) q^{16} +(-0.766216 - 0.248959i) q^{17} +(14.2549 + 23.5664i) q^{18} +(16.7481 + 12.1682i) q^{19} +(-33.8776 + 11.0075i) q^{20} +(0.387274 - 9.18076i) q^{21} -27.3224i q^{23} +(-3.36716 - 12.0724i) q^{24} +(15.4365 + 11.2153i) q^{25} +(29.2204 + 40.2185i) q^{26} +(24.4210 + 11.5159i) q^{27} +(-5.07819 + 15.6291i) q^{28} +(2.22341 + 3.06025i) q^{29} +(-37.8744 + 47.7591i) q^{30} +(-6.42137 - 19.7630i) q^{31} -43.2608i q^{32} +2.46549 q^{34} +(19.3408 - 6.28420i) q^{35} +(-36.5355 - 31.5711i) q^{36} +(-31.1905 + 22.6613i) q^{37} +(-60.2520 - 19.5771i) q^{38} +(45.6729 + 16.9996i) q^{39} +(22.4400 - 16.3036i) q^{40} +(-7.86024 + 10.8187i) q^{41} +(7.55483 + 27.0866i) q^{42} -43.4125 q^{43} +(-5.03227 + 59.5416i) q^{45} +(25.8380 + 79.5212i) q^{46} +(-11.6912 + 16.0916i) q^{47} +(-14.3973 - 21.6824i) q^{48} +(-12.2427 + 37.6791i) q^{49} +(-55.5336 - 18.0440i) q^{50} +(2.01348 - 1.33697i) q^{51} +(-70.5100 - 51.2285i) q^{52} +(-16.8103 + 5.46201i) q^{53} +(-81.9669 - 10.4224i) q^{54} -12.7963i q^{56} +(-59.8221 + 16.6852i) q^{57} +(-9.36516 - 6.80419i) q^{58} +(25.5837 + 35.2129i) q^{59} +(37.2766 - 100.151i) q^{60} +(-3.29249 + 10.1333i) q^{61} +(37.3785 + 51.4471i) q^{62} +(20.8582 + 18.0240i) q^{63} +(30.1867 + 92.9052i) q^{64} +107.854i q^{65} +72.2963 q^{67} +(-4.11087 + 1.33570i) q^{68} +(64.2234 + 50.9311i) q^{69} +(-50.3481 + 36.5800i) q^{70} +(-2.44412 - 0.794142i) q^{71} +(34.6538 + 14.5892i) q^{72} +(-36.7931 + 26.7318i) q^{73} +(69.3492 - 95.4510i) q^{74} +(-55.1374 + 15.3786i) q^{75} +111.068 q^{76} +(-149.006 - 6.28555i) q^{78} +(30.3585 + 93.4339i) q^{79} +(33.8569 - 46.6000i) q^{80} +(-72.5916 + 35.9370i) q^{81} +(12.6461 - 38.9207i) q^{82} +(-30.3393 - 9.85783i) q^{83} +(-27.2711 - 41.0704i) q^{84} +(4.32739 + 3.14404i) q^{85} +(126.351 - 41.0540i) q^{86} +(-11.3380 - 0.478272i) q^{87} -18.5409i q^{89} +(-41.6605 - 178.053i) q^{90} +(40.2543 + 29.2464i) q^{91} +(-86.1629 - 118.593i) q^{92} +(58.4243 + 21.7458i) q^{93} +(18.8097 - 57.8902i) q^{94} +(-80.7886 - 111.196i) q^{95} +(101.688 + 80.6415i) 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	−0.926612	−	0.376020i	$-0.877293\pi$
$2$	−2.91048	+	0.945671i	−1.45524	+	0.472835i	−0.528626	+	0.848855i	$0.677293\pi$
$3$	−1.86408	+	2.35058i	−0.621360	+	0.783526i
$3$	−1.86408	+	2.35058i	−0.621360	+	0.783526i
$4$	4.34051	−	3.15356i	1.08513	−	0.788390i
$5$	−6.31437	−	2.05166i	−1.26287	−	0.410333i	−0.400357	−	0.916359i	$-0.631114\pi$
$5$	−6.31437	−	2.05166i	−1.26287	−	0.410333i	−0.862518	+	0.506027i	$0.831114\pi$
$6$	3.20248	−	8.60410i	0.533747	−	1.43402i
$7$	−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
$9$	−2.05042	−	8.76332i	−0.227824	−	0.973702i
$10$	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
$15$	16.5931	−	11.0180i	1.10621	−	0.734530i
$16$	−2.68094	+	8.25108i	−0.167559	+	0.515693i
$17$	−0.766216	−	0.248959i	−0.0450715	−	0.0146446i	0.286394	−	0.958112i	$-0.407543\pi$
$17$	−0.766216	−	0.248959i	−0.0450715	−	0.0146446i	−0.331466	+	0.943467i	$0.607543\pi$
$18$	14.2549	+	23.5664i	0.791940	+	1.30924i
$19$	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	$-0.797562\pi$
$23$		−	27.3224i		−	1.18793i	0.804491	−	0.593965i	$-0.202438\pi$
$24$	−3.36716	−	12.0724i	−0.140299	−	0.503018i
$25$	15.4365	+	11.2153i	0.617462	+	0.448612i
$26$	29.2204	+	40.2185i	1.12386	+	1.54687i
$27$	24.4210	+	11.5159i	0.904481	+	0.426513i
$28$	−5.07819	+	15.6291i	−0.181364	+	0.558180i
$29$	2.22341	+	3.06025i	0.0766691	+	0.105526i	0.845629	−	0.533771i	$-0.179226\pi$
$29$	2.22341	+	3.06025i	0.0766691	+	0.105526i	−0.768960	+	0.639297i	$0.779226\pi$
$30$	−37.8744	+	47.7591i	−1.26248	+	1.59197i
$31$	−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
$36$	−36.5355	−	31.5711i	−1.01488	−	0.876975i
$37$	−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
$39$	45.6729	+	16.9996i	1.17110	+	0.435888i
$40$	22.4400	−	16.3036i	0.560999	−	0.407590i
$41$	−7.86024	+	10.8187i	−0.191713	+	0.263871i	−0.894043	−	0.447981i	$-0.852143\pi$
$41$	−7.86024	+	10.8187i	−0.191713	+	0.263871i	0.702330	+	0.711852i	$0.252143\pi$
$42$	7.55483	+	27.0866i	0.179877	+	0.644920i
$43$	−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	−0.915073	−	0.403289i	$-0.867867\pi$
$47$	−11.6912	+	16.0916i	−0.248749	+	0.342374i	0.666323	+	0.745663i	$0.267867\pi$
$48$	−14.3973	−	21.6824i	−0.299944	−	0.451717i
$49$	−12.2427	+	37.6791i	−0.249851	+	0.768962i
$50$	−55.5336	−	18.0440i	−1.11067	−	0.360880i
$51$	2.01348	−	1.33697i	0.0394801	−	0.0262151i
$52$	−70.5100	−	51.2285i	−1.35596	−	0.985164i
$53$	−16.8103	+	5.46201i	−0.317176	+	0.103057i	−0.463279	−	0.886213i	$-0.653327\pi$
$53$	−16.8103	+	5.46201i	−0.317176	+	0.103057i	0.146102	+	0.989269i	$0.453327\pi$
$54$	−81.9669	−	10.4224i	−1.51791	−	0.193007i
$55$		0			0
$56$		−	12.7963i		−	0.228505i
$57$	−59.8221	+	16.6852i	−1.04951	+	0.292723i
$58$	−9.36516	−	6.80419i	−0.161468	−	0.117314i
$59$	25.5837	+	35.2129i	0.433621	+	0.596828i	0.968780	−	0.247923i	$-0.0797481\pi$
$59$	25.5837	+	35.2129i	0.433621	+	0.596828i	−0.535158	+	0.844752i	$0.679748\pi$
$60$	37.2766	−	100.151i	0.621276	−	1.66918i
$61$	−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
$63$	20.8582	+	18.0240i	0.331082	+	0.286095i
$64$	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
$69$	64.2234	+	50.9311i	0.930774	+	0.738132i
$70$	−50.3481	+	36.5800i	−0.719258	+	0.522571i
$71$	−2.44412	−	0.794142i	−0.0344242	−	0.0111851i	0.291754	−	0.956493i	$-0.405761\pi$
$71$	−2.44412	−	0.794142i	−0.0344242	−	0.0111851i	−0.326178	+	0.945308i	$0.605761\pi$
$72$	34.6538	+	14.5892i	0.481303	+	0.202627i
$73$	−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
$75$	−55.1374	+	15.3786i	−0.735165	+	0.205047i
$76$	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
$81$	−72.5916	+	35.9370i	−0.896192	+	0.443666i
$82$	12.6461	−	38.9207i	0.154221	−	0.474643i
$83$	−30.3393	−	9.85783i	−0.365534	−	0.118769i	0.120491	−	0.992714i	$-0.461553\pi$
$83$	−30.3393	−	9.85783i	−0.365534	−	0.118769i	−0.486024	+	0.873945i	$0.661553\pi$
$84$	−27.2711	−	41.0704i	−0.324656	−	0.488934i
$85$	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	$-0.966784\pi$
$89$		−	18.5409i		−	0.208325i	0.994560	−	0.104162i	$-0.0332161\pi$
$90$	−41.6605	−	178.053i	−0.462894	−	1.97837i
$91$	40.2543	+	29.2464i	0.442354	+	0.321389i
$92$	−86.1629	−	118.593i	−0.936553	−	1.28905i
$93$	58.4243	+	21.7458i	0.628218	+	0.233826i
$94$	18.8097	−	57.8902i	0.200103	−	0.615853i
$95$	−80.7886	−	111.196i	−0.850407	−	1.17048i
$96$	101.688	+	80.6415i	1.05925	+	0.840016i
$97$	−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	0.501561	−	0.865122i	$-0.332759\pi$
$101$	143.000	−	46.4634i	1.41584	−	0.460034i	0.914277	+	0.405089i	$0.132759\pi$
$102$	−4.59586	+	5.79532i	−0.0450575	+	0.0568168i
$103$	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
$105$	−21.2812	+	57.1762i	−0.202678	+	0.544535i
$106$	43.7608	−	31.7941i	0.412838	−	0.299944i
$107$	−12.1974	+	16.7883i	−0.113995	+	0.156900i	−0.862202	−	0.506565i	$-0.830915\pi$
$107$	−12.1974	+	16.7883i	−0.113995	+	0.156900i	0.748207	+	0.663465i	$0.230915\pi$
$108$	142.315	−	27.0285i	1.31774	−	0.250264i
$109$	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	−1.00000		0.000385488i	$-0.999877\pi$
$113$	−78.0396	+	107.412i	−0.690616	+	0.950552i	0.309384	+	0.950937i	$0.399877\pi$
$114$	158.332	−	105.134i	1.38888	−	0.922226i
$115$	−56.0564	+	172.524i	−0.487447	+	1.50021i
$116$	19.3014	+	6.27141i	0.166391	+	0.0540638i
$117$	−125.097	+	75.6689i	−1.06920	+	0.646743i
$118$	−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
$123$	−10.7781	−	38.6430i	−0.0876265	−	0.314171i
$124$	−90.1957	−	65.5310i	−0.727385	−	0.528476i
$125$	23.1004	+	31.7950i	0.184803	+	0.254360i
$126$	−77.7520	−	32.7334i	−0.617079	−	0.259789i
$127$	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
$129$	80.9244	−	102.044i	0.627321	−	0.791042i
$130$	−101.994	−	313.905i	−0.784569	−	2.41465i
$131$			149.467i			1.14097i	0.821309	+	0.570484i	$0.193244\pi$
$131$			149.467i			1.14097i	−0.821309	+	0.570484i	$0.806756\pi$
$132$		0			0
$133$	−63.4091			−0.476760
$134$	−210.417	+	68.3685i	−1.57027	+	0.510213i
$135$	−130.577	−	122.819i	−0.967234	−	0.909771i
$136$	2.72298	−	1.97836i	0.0200219	−	0.0145467i
$137$	144.757	+	47.0345i	1.05662	+	0.343318i	0.785264	−	0.619161i	$-0.212527\pi$
$137$	144.757	+	47.0345i	1.05662	+	0.343318i	0.271359	+	0.962478i	$0.412527\pi$
$138$	−235.085	−	87.4995i	−1.70351	−	0.634055i
$139$	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
$141$	−16.0311	−	57.4771i	−0.113696	−	0.407639i
$142$	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
$147$	−65.7463	−	99.0142i	−0.447254	−	0.673566i
$148$	−63.9190	+	196.723i	−0.431885	+	1.32921i
$149$	246.985	+	80.2503i	1.65762	+	0.538592i	0.980371	−	0.197164i	$-0.0631730\pi$
$149$	246.985	+	80.2503i	1.65762	+	0.538592i	0.677247	+	0.735756i	$0.263173\pi$
$150$	145.933	−	96.9007i	0.972886	−	0.646005i
$151$	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
$156$	251.853	−	70.2452i	1.61444	−	0.450290i
$157$	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
$159$	18.4969	−	49.6956i	0.116333	−	0.312551i
$160$	−88.7566	+	273.165i	−0.554729	+	1.70728i
$161$	49.1905	+	67.7049i	0.305531	+	0.420527i
$162$	177.291	−	173.241i	1.09439	−	1.06939i
$163$	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	−0.726863	−	0.686782i	$-0.759023\pi$
$167$	−152.175	+	49.4447i	−0.911228	+	0.296076i	−0.184364	+	0.982858i	$0.559023\pi$
$168$	30.0787	+	23.8533i	0.179040	+	0.141984i
$169$	−76.7667	+	55.7743i	−0.454241	+	0.330025i
$170$	−15.5680	−	5.05835i	−0.0915765	−	0.0297550i
$171$	72.2932	−	171.719i	0.422767	−	1.00420i
$172$	−188.432	+	136.904i	−1.09554	+	0.795954i
$173$	−97.2924	+	133.912i	−0.562384	+	0.774055i	−0.991627	−	0.129134i	$-0.958780\pi$
$173$	−97.2924	+	133.912i	−0.562384	+	0.774055i	0.429243	+	0.903189i	$0.358780\pi$
$174$	33.4512	−	9.32998i	0.192248	−	0.0536206i
$175$	−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	−0.894238	−	0.447591i	$-0.852282\pi$
$179$	−34.4072	+	47.3575i	−0.192219	+	0.264567i	0.702019	+	0.712158i	$0.252282\pi$
$180$	165.926	+	274.310i	0.921809	+	1.52395i
$181$	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
$183$	−17.6815	−	26.6284i	−0.0966203	−	0.145511i
$184$	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
$189$	−81.2481	+	15.4306i	−0.429884	+	0.0816435i
$190$	340.288	+	247.234i	1.79099	+	1.30123i
$191$	80.7867	+	111.193i	0.422967	+	0.582164i	0.966321	−	0.257339i	$-0.0828459\pi$
$191$	80.7867	+	111.193i	0.422967	+	0.582164i	−0.543354	+	0.839504i	$0.682846\pi$
$192$	−274.651	−	102.226i	−1.43047	−	0.532429i
$193$	−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
$195$	−253.518	−	201.047i	−1.30009	−	1.03101i
$196$	65.6840	+	202.155i	0.335122	+	1.03140i
$197$		−	58.1375i		−	0.295114i	−0.989054	−	0.147557i	$-0.952859\pi$
$197$		−	58.1375i		−	0.295114i	0.989054	−	0.147557i	$-0.0471410\pi$
$198$		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
$201$	−134.766	+	169.938i	−0.670478	+	0.845463i
$202$	−372.258	+	270.461i	−1.84286	+	1.33892i
$203$	−11.0192	−	3.58035i	−0.0542818	−	0.0176372i
$204$	4.52332	−	12.1528i	0.0221731	−	0.0595724i
$205$	71.8288	−	52.1867i	0.350384	−	0.254569i
$206$	−269.397	+	370.794i	−1.30775	+	1.79997i
$207$	−239.435	+	56.0224i	−1.15669	+	0.270640i
$208$	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
$213$	6.42272	−	4.26474i	0.0301536	−	0.0200223i
$214$	19.6241	−	60.3967i	0.0917013	−	0.282228i
$215$	274.123	+	89.0679i	1.27499	+	0.414269i
$216$	−98.8904	+	54.2611i	−0.457826	+	0.251209i
$217$	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
$222$	95.0925	+	340.939i	0.428345	+	1.53576i
$223$	−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
$225$	66.6319	−	158.271i	0.296142	−	0.703428i
$226$	125.556	−	386.421i	0.555556	−	1.70983i
$227$	−71.3484	−	98.2027i	−0.314310	−	0.432611i	0.622409	−	0.782692i	$-0.286154\pi$
$227$	−71.3484	−	98.2027i	−0.314310	−	0.432611i	−0.936719	+	0.350081i	$0.886154\pi$
$228$	−207.040	+	261.075i	−0.908071	+	1.14506i
$229$	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	0.665443	−	0.746449i	$-0.268243\pi$
$233$	382.714	−	124.351i	1.64255	−	0.533697i	0.977106	+	0.212752i	$0.0682427\pi$
$234$	292.533	−	338.533i	1.25014	−	1.44672i
$235$	106.837	−	77.6218i	0.454626	−	0.330305i
$236$	222.092	+	72.1621i	0.941068	+	0.305771i
$237$	−276.214	−	102.808i	−1.16546	−	0.433790i
$238$	−6.10948	+	4.43879i	−0.0256701	+	0.0186504i
$239$	0.188940	−	0.260053i	0.000790543	−	0.00108809i	−0.808622	−	0.588329i	$-0.799786\pi$
$239$	0.188940	−	0.260053i	0.000790543	−	0.00108809i	0.809412	+	0.587241i	$0.199786\pi$
$240$	46.4250	+	166.449i	0.193437	+	0.693539i
$241$	−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
$246$	67.9128	+	102.277i	0.276068	+	0.415760i
$247$	103.920	−	319.834i	0.420730	−	1.29487i
$248$	82.5644	+	26.8268i	0.332921	+	0.108173i
$249$	79.7264	−	52.9390i	0.320186	−	0.212607i
$250$	−97.3007	−	70.6931i	−0.389203	−	0.282772i
$251$	−107.109	+	34.8019i	−0.426730	+	0.138653i	−0.514505	−	0.857487i	$-0.672024\pi$
$251$	−107.109	+	34.8019i	−0.426730	+	0.138653i	0.0877748	+	0.996140i	$0.472024\pi$
$252$	147.375	+	12.4557i	0.584821	+	0.0494272i
$253$		0			0
$254$			448.803i			1.76694i
$255$	−15.4569	+	4.31114i	−0.0606153	+	0.0169064i
$256$	−4.41230	−	3.20572i	−0.0172355	−	0.0125224i
$257$	115.540	+	159.027i	0.449572	+	0.618783i	0.972306	−	0.233713i	$-0.0750877\pi$
$257$	115.540	+	159.027i	0.449572	+	0.618783i	−0.522733	+	0.852496i	$0.675088\pi$
$258$	−139.028	+	373.526i	−0.538868	+	1.44777i
$259$	36.4915	−	112.309i	0.140894	−	0.433626i
$260$	340.123	+	468.139i	1.30816	+	1.80053i
$261$	22.2591	−	25.7592i	0.0852838	−	0.0986943i
$262$	−141.346	−	435.020i	−0.539490	−	1.66038i
$263$			378.327i			1.43850i	0.694749	+	0.719252i	$0.255515\pi$
$263$			378.327i			1.43850i	−0.694749	+	0.719252i	$0.744485\pi$
$264$		0			0
$265$	117.353			0.442842
$266$	184.551	−	59.9641i	0.693799	−	0.225429i
$267$	43.5818	+	34.5617i	0.163228	+	0.129444i
$268$	313.803	−	227.991i	1.17090	−	0.850712i
$269$	−191.309	−	62.1601i	−0.711186	−	0.231078i	−0.0689882	−	0.997617i	$-0.521977\pi$
$269$	−191.309	−	62.1601i	−0.711186	−	0.231078i	−0.642198	+	0.766539i	$0.721977\pi$
$270$	496.186	+	233.979i	1.83773	+	0.866590i
$271$	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
$273$	−143.783	+	40.1031i	−0.526678	+	0.146898i
$274$	−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
$279$	−160.023	+	96.7949i	−0.573558	+	0.346935i
$280$	−26.2537	+	80.8006i	−0.0937633	+	0.288574i
$281$	−472.140	−	153.407i	−1.68021	−	0.545934i	−0.695260	−	0.718759i	$-0.744711\pi$
$281$	−472.140	−	153.407i	−1.68021	−	0.545934i	−0.984953	+	0.172825i	$0.944711\pi$
$282$	101.013	+	152.125i	0.358201	+	0.539452i
$283$	−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
$288$	−379.108	+	88.7028i	−1.31635	+	0.307996i
$289$	−233.281	−	169.488i	−0.807200	−	0.586465i
$290$	45.1752	+	62.1783i	0.155777	+	0.214408i
$291$	177.977	+	66.2439i	0.611606	+	0.227642i
$292$	−75.4004	+	232.059i	−0.258221	+	0.794721i
$293$	199.670	+	274.822i	0.681466	+	0.937957i	0.999950	−	0.00997075i	$-0.00317384\pi$
$293$	199.670	+	274.822i	0.681466	+	0.937957i	−0.318484	+	0.947928i	$0.603174\pi$
$294$	284.988	+	226.004i	0.969347	+	0.768721i
$295$	−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
$300$	−190.827	+	240.630i	−0.636089	+	0.802099i
$301$	107.576	−	78.1587i	0.357396	−	0.259664i
$302$	−256.173	−	83.2358i	−0.848256	−	0.275615i
$303$	−157.347	+	422.743i	−0.519296	+	1.39519i
$304$	−145.301	+	105.568i	−0.477965	+	0.347262i
$305$	41.5801	−	57.2300i	0.136328	−	0.187639i
$306$	−5.05528	−	21.6058i	−0.0165205	−	0.0706073i
$307$	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	−0.718809	−	0.695207i	$-0.755313\pi$
$311$	51.1584	−	70.4134i	0.164496	−	0.226410i	0.883306	+	0.468797i	$0.155313\pi$
$312$	−169.611	+	112.623i	−0.543626	+	0.360972i
$313$	−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
$315$	−94.7271	−	156.604i	−0.300721	−	0.497156i
$316$	426.421	+	309.813i	1.34943	+	0.980421i
$317$	−2.33475	+	0.758605i	−0.00736513	+	0.00239308i	−0.312697	−	0.949853i	$-0.601233\pi$
$317$	−2.33475	+	0.758605i	−0.00736513	+	0.00239308i	0.305332	+	0.952246i	$0.401233\pi$
$318$	−6.83917	+	162.130i	−0.0215068	+	0.509843i
$319$		0			0
$320$		−	648.571i		−	2.02678i
$321$	−16.7253	−	59.9657i	−0.0521036	−	0.186809i
$322$	−207.194	−	150.535i	−0.643460	−	0.467501i
$323$	−9.80328	−	13.4931i	−0.0303507	−	0.0417742i
$324$	−201.755	+	384.907i	−0.622699	+	1.18798i
$325$	95.7823	−	294.788i	0.294715	−	0.907039i
$326$	−472.262	−	650.013i	−1.44866	−	1.99391i
$327$	−197.207	+	248.676i	−0.603081	+	0.760476i
$328$	−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
$333$	262.542	+	226.868i	0.788413	+	0.681284i
$334$	396.143	−	287.815i	1.18606	−	0.861721i
$335$	−456.506	−	148.328i	−1.36270	−	0.442769i
$336$	74.7130	+	27.8085i	0.222360	+	0.0827634i
$337$	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
$339$	−107.009	−	383.663i	−0.315661	−	1.13175i
$340$	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
$345$	−301.037	−	453.363i	−0.872571	−	1.31409i
$346$	156.531	−	481.753i	0.452402	−	1.39235i
$347$	280.182	+	91.0367i	0.807442	+	0.262354i	0.683514	−	0.729938i	$-0.260451\pi$
$347$	280.182	+	91.0367i	0.807442	+	0.262354i	0.123928	+	0.992291i	$0.460451\pi$
$348$	−50.7208	+	33.6790i	−0.145749	+	0.0967788i
$349$	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	$0.0615086\pi$
$353$			135.577i			0.384070i	−0.981388	+	0.192035i	$0.938491\pi$
$354$	384.906	−	107.356i	1.08731	−	0.303264i
$355$	13.8038	+	10.0290i	0.0388838	+	0.0282507i
$356$	−58.4698	−	80.4768i	−0.164241	−	0.226058i
$357$	−2.58237	+	6.93804i	−0.00723352	+	0.0194343i
$358$	55.3568	−	170.371i	0.154628	−	0.475896i
$359$	−163.860	−	225.534i	−0.456435	−	0.628229i	0.517330	−	0.855786i	$-0.326926\pi$
$359$	−163.860	−	225.534i	−0.456435	−	0.628229i	−0.973765	+	0.227557i	$0.926926\pi$
$360$	−188.885	−	163.219i	−0.524681	−	0.453387i
$361$	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
$366$	76.6434	+	60.7805i	0.209408	+	0.166067i
$367$	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
$369$	110.924	+	46.6990i	0.300608	+	0.126555i
$370$	−633.730	+	460.432i	−1.71278	+	1.24441i
$371$	31.8224	−	43.7998i	0.0857746	−	0.118059i
$372$	322.168	−	89.8569i	0.866042	−	0.241551i
$373$	−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
$378$	221.878	−	121.744i	0.586979	−	0.322075i
$379$	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
$381$	243.375	+	366.523i	0.638778	+	0.962003i
$382$	−340.280	−	247.228i	−0.890785	−	0.647193i
$383$	85.2768	−	27.7081i	0.222655	−	0.0723449i	−0.195565	−	0.980691i	$-0.562654\pi$
$383$	85.2768	−	27.7081i	0.222655	−	0.0723449i	0.418220	+	0.908346i	$0.362654\pi$
$384$	377.369	+	15.9187i	0.982733	+	0.0414549i
$385$		0			0
$386$		−	912.245i		−	2.36333i
$387$	89.0139	+	380.438i	0.230010	+	0.983044i
$388$	−274.762	−	199.626i	−0.708150	−	0.514501i
$389$	158.468	+	218.112i	0.407372	+	0.560699i	0.962575	−	0.271016i	$-0.0873595\pi$
$389$	158.468	+	218.112i	0.407372	+	0.560699i	−0.555203	+	0.831715i	$0.687360\pi$
$390$	927.983	+	345.399i	2.37944	+	0.885639i
$391$	−6.80215	+	20.9349i	−0.0173968	+	0.0535419i
$392$	−97.2868	−	133.904i	−0.248181	−	0.341591i
$393$	−351.333	−	278.618i	−0.893978	−	0.708952i
$394$	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
$399$	118.200	−	149.048i	0.296239	−	0.373554i
$400$	−133.923	+	97.3006i	−0.334807	+	0.243252i
$401$	427.784	+	138.995i	1.06679	+	0.346622i	0.789237	−	0.614088i	$-0.210476\pi$
$401$	427.784	+	138.995i	1.06679	+	0.346622i	0.277555	+	0.960710i	$0.410476\pi$
$402$	231.528	−	622.045i	0.575940	−	1.54737i
$403$	−273.095	+	198.415i	−0.677655	+	0.492345i
$404$	474.165	−	652.633i	1.17368	−	1.61543i
$405$	532.101	−	77.9859i	1.31383	−	0.192558i
$406$	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
$411$	−380.397	+	252.587i	−0.925541	+	0.614568i
$412$	248.303	−	764.199i	0.602678	−	1.85485i
$413$	−126.793	−	41.1974i	−0.307004	−	0.0997516i
$414$	643.891	−	389.478i	1.55529	−	0.940769i
$415$	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	$-0.642403\pi$
$419$		−	755.530i		−	1.80317i	0.432599	−	0.901587i	$-0.357597\pi$
$420$	87.9374	+	315.285i	0.209375	+	0.750679i
$421$	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
$423$	164.988	+	69.4594i	0.390042	+	0.164207i
$424$	22.8188	−	70.2292i	0.0538180	−	0.165635i
$425$	−9.03558	−	12.4364i	−0.0212602	−	0.0292621i
$426$	−14.6601	+	18.4862i	−0.0344134	+	0.0433949i
$427$	−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	−0.319737	−	0.947506i	$-0.603595\pi$
$431$	−9.25765	+	3.00799i	−0.0214795	+	0.00697910i	0.298258	+	0.954485i	$0.403595\pi$
$432$	−160.489	+	170.626i	−0.371503	+	0.394968i
$433$	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
$435$	70.6109	+	26.2817i	0.162324	+	0.0604177i
$436$	459.197	−	333.626i	1.05320	−	0.765198i
$437$	332.465	−	457.598i	0.760788	−	1.04714i
$438$	112.173	+	402.180i	0.256104	+	0.918218i
$439$	−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	$-0.593479\pi$
$443$	314.672	−	433.108i	0.710320	−	0.977671i	0.999790	−	0.0204842i	$-0.00652079\pi$
$444$	−343.261	−	516.953i	−0.773111	−	1.16431i
$445$	−38.0397	+	117.074i	−0.0854824	+	0.263088i
$446$	616.196	+	200.214i	1.38160	+	0.448910i
$447$	−649.034	+	430.964i	−1.45198	+	0.964126i
$448$	−242.067	−	175.872i	−0.540327	−	0.392571i
$449$	731.756	−	237.762i	1.62975	−	0.529537i	0.655534	−	0.755166i	$-0.272444\pi$
$449$	731.756	−	237.762i	1.62975	−	0.529537i	0.974213	+	0.225629i	$0.0724438\pi$
$450$	−44.2578	+	523.657i	−0.0983508	+	1.16368i
$451$		0			0
$452$			712.327i			1.57594i
$453$	−254.345	+	70.9404i	−0.561469	+	0.156601i
$454$	300.525	+	218.344i	0.661950	+	0.480935i
$455$	−194.177	−	267.261i	−0.426762	−	0.587387i
$456$	90.5062	−	243.162i	0.198478	−	0.533251i
$457$	−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
$459$	−15.8448	−	14.9035i	−0.0345203	−	0.0324694i
$460$	300.751	+	925.618i	0.653807	+	2.01221i
$461$		−	266.355i		−	0.577777i	−0.957363	−	0.288888i	$-0.906714\pi$
$461$		−	266.355i		−	0.577777i	0.957363	−	0.288888i	$-0.0932857\pi$
$462$		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
$465$	−324.298	−	257.178i	−0.697414	−	0.553071i
$466$	−996.284	+	723.843i	−2.13795	+	1.55331i
$467$	−642.132	−	208.641i	−1.37502	−	0.446770i	−0.473988	−	0.880531i	$-0.657186\pi$
$467$	−642.132	−	208.641i	−1.37502	−	0.446770i	−0.901028	+	0.433762i	$0.857186\pi$
$468$	−304.357	+	722.942i	−0.650335	+	1.54475i
$469$	−179.150	+	130.160i	−0.381983	+	0.277527i
$470$	−237.542	+	326.949i	−0.505409	+	0.695636i
$471$	−22.1216	+	6.17000i	−0.0469672	+	0.0130998i
$472$	−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
$477$	82.3336	+	136.115i	0.172607	+	0.285356i
$478$	−0.303980	+	0.935553i	−0.000635941	+	0.00195722i
$479$	−665.556	−	216.252i	−1.38947	−	0.451466i	−0.483700	−	0.875234i	$-0.660707\pi$
$479$	−665.556	−	216.252i	−1.38947	−	0.451466i	−0.905771	+	0.423768i	$0.860707\pi$
$480$	−476.645	−	717.830i	−0.993011	−	1.49548i
$481$	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
$486$	76.7320	+	739.673i	0.157885	+	1.52196i
$487$	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
$489$	−738.167	−	274.749i	−1.50954	−	0.561859i
$490$	−248.747	+	765.565i	−0.507647	+	1.56238i
$491$	36.3470	+	50.0274i	0.0740265	+	0.101889i	0.844425	−	0.535674i	$-0.179943\pi$
$491$	36.3470	+	50.0274i	0.0740265	+	0.101889i	−0.770398	+	0.637563i	$0.779943\pi$
$492$	−168.645	−	133.741i	−0.342775	−	0.271831i
$493$	−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
$498$	−181.979	+	229.473i	−0.365419	+	0.460789i
$499$	−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
$501$	167.443	−	449.868i	0.334217	−	0.897940i
$502$	278.828	−	202.580i	0.555434	−	0.403547i
$503$	204.067	−	280.874i	0.405700	−	0.558398i	−0.556463	−	0.830872i	$-0.687842\pi$
$503$	204.067	−	280.874i	0.405700	−	0.558398i	0.962163	+	0.272474i	$0.0878420\pi$
$504$	−112.138	+	26.2378i	−0.222496	+	0.0520591i
$505$	−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	$0.518065\pi$
$509$	−503.258	+	692.675i	−0.988719	+	1.36086i	−0.931997	+	0.362465i	$0.881935\pi$
$510$	40.9100	−	27.1646i	0.0802157	−	0.0532639i
$511$	43.0462	−	132.483i	0.0842391	−	0.259261i
$512$	494.832	+	160.781i	0.966468	+	0.314025i
$513$	268.878	+	490.028i	0.524129	+	0.955221i
$514$	−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
$519$	−133.409	−	478.315i	−0.257049	−	0.921609i
$520$	−364.530	−	264.846i	−0.701019	−	0.509320i
$521$	−418.891	−	576.554i	−0.804013	−	1.10663i	−0.992220	−	0.124499i	$-0.960268\pi$
$521$	−418.891	−	576.554i	−0.804013	−	1.10663i	0.188207	−	0.982129i	$-0.439732\pi$
$522$	−40.4248	+	96.0213i	−0.0774421	+	0.183949i
$523$	−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
$525$	108.943	−	137.376i	0.207511	−	0.261668i
$526$	−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
$531$	256.124	−	296.399i	0.482344	−	0.558190i
$532$	−275.227	+	199.964i	−0.517345	+	0.375873i
$533$	206.602	+	67.1290i	0.387621	+	0.125946i
$534$	−159.528	−	59.3769i	−0.298741	−	0.111193i
$535$	111.463	−	80.9826i	0.208342	−	0.151369i
$536$	−177.532	+	244.351i	−0.331216	+	0.455879i
$537$	−47.1796	−	169.155i	−0.0878577	−	0.315000i
$538$	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
$543$	472.423	+	711.471i	0.870024	+	1.31026i
$544$	−10.7702	+	33.1471i	−0.0197981	+	0.0609322i
$545$	−668.020	−	217.053i	−1.22572	−	0.398262i
$546$	380.553	−	252.690i	0.696983	−	0.462803i
$547$	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
$552$	−329.848	+	91.9990i	−0.597550	+	0.166665i
$553$	−243.444	−	176.873i	−0.440225	−	0.319842i
$554$	393.778	+	541.989i	0.710790	+	0.978319i
$555$	−267.867	+	719.676i	−0.482642	+	1.29671i
$556$	185.415	−	570.649i	0.333480	−	1.02635i
$557$	363.725	+	500.624i	0.653007	+	0.898787i	0.999225	−	0.0393671i	$-0.0125342\pi$
$557$	363.725	+	500.624i	0.653007	+	0.898787i	−0.346218	+	0.938154i	$0.612534\pi$
$558$	374.206	−	433.048i	0.670619	−	0.776071i
$559$	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	−0.747440	−	0.664330i	$-0.768717\pi$
$563$	−541.408	+	175.914i	−0.961648	+	0.312458i	−0.214208	+	0.976788i	$0.568717\pi$
$564$	−250.841	−	198.924i	−0.444753	−	0.352703i
$565$	713.145	−	518.130i	1.26220	−	0.917045i
$566$	895.558	+	290.984i	1.58226	+	0.514107i
$567$	115.182	−	219.744i	0.203143	−	0.387555i
$568$	8.68589	−	6.31067i	0.0152921	−	0.0111103i
$569$	−529.905	+	729.352i	−0.931292	+	1.28181i	0.0280618	+	0.999606i	$0.491066\pi$
$569$	−529.905	+	729.352i	−0.931292	+	1.28181i	−0.959354	+	0.282207i	$0.908934\pi$
$570$	−1215.47	+	339.010i	−2.13240	+	0.594754i
$571$	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
$576$	752.262	−	455.030i	1.30601	−	0.789983i
$577$	−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
$579$	−494.687	−	745.001i	−0.854382	−	1.28670i
$580$	−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
$585$	945.155	−	221.145i	1.61565	−	0.378026i
$586$	−841.024	−	611.040i	−1.43519	−	1.04273i
$587$	−107.287	−	147.667i	−0.182771	−	0.251563i	0.707794	−	0.706419i	$-0.249691\pi$
$587$	−107.287	−	147.667i	−0.182771	−	0.251563i	−0.890565	+	0.454856i	$0.849691\pi$
$588$	−597.620	−	222.437i	−1.01636	−	0.378294i
$589$	132.934	−	409.128i	0.225694	−	0.694615i
$590$	519.809	+	715.456i	0.881033	+	1.21264i
$591$	136.657	+	108.373i	0.231230	+	0.183372i
$592$	−103.360	−	318.109i	−0.174595	−	0.537347i
$593$		−	685.071i		−	1.15526i	−0.816297	−	0.577632i	$-0.803977\pi$
$593$		−	685.071i		−	1.15526i	0.816297	−	0.577632i	$-0.196023\pi$
$594$		0			0
$595$	−16.3837			−0.0275357
$596$	1325.11	−	430.556i	2.22335	−	0.722409i
$597$	233.101	−	293.936i	0.390453	−	0.492356i
$598$	1098.87	−	798.373i	1.83757	−	1.33507i
$599$	343.213	+	111.517i	0.572977	+	0.186171i	0.581152	−	0.813795i	$-0.302602\pi$
$599$	343.213	+	111.517i	0.572977	+	0.186171i	−0.00817505	+	0.999967i	$0.502602\pi$
$600$	83.4186	−	224.120i	0.139031	−	0.373534i
$601$	−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
$603$	−148.238	−	633.556i	−0.245834	−	1.05067i
$604$	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
$609$	28.9565	−	19.2274i	0.0475477	−	0.0315721i
$610$	−66.8970	+	205.888i	−0.109667	+	0.337521i
$611$	307.297	+	99.8468i	0.502941	+	0.163415i
$612$	20.1342	+	33.2861i	0.0328990	+	0.0543891i
$613$	−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	$0.184402\pi$
$617$			675.556i			1.09490i	−0.836837	+	0.547452i	$0.815598\pi$
$618$	−369.401	−	1324.43i	−0.597736	−	2.14309i
$619$	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
$621$	314.641	−	667.240i	0.506668	−	1.07446i
$622$	−82.3072	+	253.316i	−0.132327	+	0.407260i
$623$	33.3805	+	45.9443i	0.0535802	+	0.0737469i
$624$	−262.712	+	331.276i	−0.421012	+	0.530891i
$625$	−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
$630$	423.797	+	366.212i	0.672694	+	0.581288i
$631$	−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
$633$	−136.059	−	50.6418i	−0.214943	−	0.0800028i
$634$	6.07783	−	4.41580i	0.00958649	−	0.00696499i
$635$	−572.322	+	787.734i	−0.901295	+	1.24053i
$636$	−76.4322	−	274.035i	−0.120176	−	0.430873i
$637$	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	−0.802191	−	0.597067i	$-0.796333\pi$
$641$	8.68174	−	11.9494i	0.0135441	−	0.0186418i	0.815735	+	0.578425i	$0.196333\pi$
$642$	105.386	+	158.712i	0.164153	+	0.247215i
$643$	−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
$645$	−720.348	+	478.317i	−1.11682	+	0.741577i
$646$	41.2922	+	30.0005i	0.0639198	+	0.0464405i
$647$	−298.985	+	97.1462i	−0.462110	+	0.150149i	−0.530814	−	0.847488i	$-0.678114\pi$
$647$	−298.985	+	97.1462i	−0.462110	+	0.150149i	0.0687036	+	0.997637i	$0.478114\pi$
$648$	56.7948	−	333.596i	0.0876462	−	0.514809i
$649$		0			0
$650$			948.550i			1.45931i
$651$	−183.926	+	51.2994i	−0.282528	+	0.0788010i
$652$	1139.59	+	827.958i	1.74783	+	1.26987i
$653$	−112.807	−	155.266i	−0.172752	−	0.237773i	0.713858	−	0.700291i	$-0.246946\pi$
$653$	−112.807	−	155.266i	−0.172752	−	0.237773i	−0.886610	+	0.462517i	$0.846946\pi$
$654$	338.802	−	910.258i	0.518046	−	1.39183i
$655$	306.656	−	943.789i	0.468177	−	1.44090i
$656$	−68.1931	−	93.8598i	−0.103953	−	0.143079i
$657$	309.700	+	267.618i	0.471386	+	0.407334i
$658$	57.6135	+	177.316i	0.0875586	+	0.269478i
$659$			127.678i			0.193745i	0.995297	+	0.0968724i	$0.0308839\pi$
$659$			127.678i			0.193745i	−0.995297	+	0.0968724i	$0.969116\pi$
$660$		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
$663$	−30.7631	−	24.3961i	−0.0463998	−	0.0367965i
$664$	107.820	−	78.3355i	0.162379	−	0.117975i
$665$	400.388	+	130.094i	0.602088	+	0.195630i
$666$	−978.663	−	412.015i	−1.46946	−	0.618641i
$667$	83.6135	−	60.7488i	0.125358	−	0.0910776i
$668$	−504.590	+	694.508i	−0.755374	+	1.03968i
$669$	611.798	−	170.639i	0.914497	−	0.255066i
$670$	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
$675$	247.822	+	451.654i	0.367144	+	0.669117i
$676$	−157.319	+	484.177i	−0.232720	+	0.716238i
$677$	27.7389	+	9.01292i	0.0409733	+	0.0133130i	0.329432	−	0.944179i	$-0.393143\pi$
$677$	27.7389	+	9.01292i	0.0409733	+	0.0133130i	−0.288459	+	0.957492i	$0.593143\pi$
$678$	674.266	+	1015.45i	0.994492	+	1.49771i
$679$	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	$0.0192246\pi$
$683$			82.4506i			0.120718i	−0.998177	+	0.0603592i	$0.980775\pi$
$684$	−227.737	−	973.328i	−0.332949	−	1.42299i
$685$	−817.553	−	593.987i	−1.19351	−	0.867134i
$686$	488.251	+	672.019i	0.711735	+	0.979620i
$687$	−907.976	−	337.953i	−1.32165	−	0.491926i
$688$	116.386	−	358.200i	0.169166	−	0.520640i
$689$	168.772	+	232.294i	0.244952	+	0.337147i
$690$	1304.89	+	1034.82i	1.89115	+	1.49974i
$691$	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
$696$	29.4581	−	37.1463i	0.0423249	−	0.0533711i
$697$	8.71606	−	6.33259i	0.0125051	−	0.00908549i
$698$	−1199.14	−	389.624i	−1.71796	−	0.558201i
$699$	−421.112	+	1131.40i	−0.602449	+	1.61860i
$700$	−253.674	+	184.305i	−0.362392	+	0.263293i
$701$	184.624	−	254.112i	0.263372	−	0.362500i	−0.656766	−	0.754094i	$-0.728076\pi$
$701$	184.624	−	254.112i	0.263372	−	0.362500i	0.920138	+	0.391594i	$0.128076\pi$
$702$	250.442	+	1318.67i	0.356755	+	1.87845i
$703$	−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
$708$	−583.619	+	387.528i	−0.824321	+	0.547356i
$709$	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
$711$	756.544	−	457.620i	1.06406	−	0.643629i
$712$	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
$717$	0.259076	+	0.928877i	0.000361334	+	0.00129550i
$718$	690.192	+	501.454i	0.961270	+	0.698404i
$719$	−650.211	−	894.939i	−0.904327	−	1.24470i	−0.969067	−	0.246797i	$-0.920622\pi$
$719$	−650.211	−	894.939i	−0.904327	−	1.24470i	0.0647402	−	0.997902i	$-0.479378\pi$
$720$	−477.792	−	201.149i	−0.663600	−	0.279374i
$721$	−141.757	+	436.282i	−0.196611	+	0.605107i
$722$	−121.532	−	167.275i	−0.168327	−	0.231682i
$723$	542.073	−	683.546i	0.749755	−	0.945431i
$724$	−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
$729$	463.770	+	562.457i	0.636173	+	0.771546i
$730$	−747.563	+	543.136i	−1.02406	+	0.744023i
$731$	33.2634	+	10.8079i	0.0455040	+	0.0147851i
$732$	−160.721	−	59.8211i	−0.219564	−	0.0817229i
$733$	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
$735$	212.003	+	760.102i	0.288439	+	1.03415i
$736$	−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
$741$	558.079	+	840.469i	0.753142	+	1.13424i
$742$	−51.1981	+	157.572i	−0.0690002	+	0.212361i
$743$	1092.36	+	354.930i	1.47020	+	0.477698i	0.931170	−	0.364586i	$-0.118790\pi$
$743$	1092.36	+	354.930i	1.47020	+	0.477698i	0.539034	+	0.842284i	$0.318790\pi$
$744$	−216.965	+	144.067i	−0.291620	+	0.193638i
$745$	−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
$750$	347.546	−	96.9352i	0.463394	−	0.129247i
$751$	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
$753$	117.856	−	316.642i	0.156515	−	0.420508i
$754$	−58.1099	+	178.844i	−0.0770689	+	0.237194i
$755$	−343.489	−	472.772i	−0.454952	−	0.626188i
$756$	−303.996	+	323.197i	−0.402111	+	0.427510i
$757$	−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	−0.0333725	−	0.999443i	$-0.510625\pi$
$761$	401.113	−	130.329i	0.527086	−	0.171261i	0.560459	+	0.828182i	$0.310625\pi$
$762$	−1054.95	−	836.604i	−1.38444	−	1.09791i
$763$	−262.156	+	190.468i	−0.343586	+	0.249630i
$764$	701.310	+	227.870i	0.917945	+	0.298259i
$765$	18.6792	−	44.3689i	0.0244173	−	0.0579986i
$766$	−221.993	+	161.287i	−0.289808	+	0.210558i
$767$	415.598	−	572.021i	0.541848	−	0.745790i
$768$	15.7602	−	4.39573i	0.0205211	−	0.00572360i
$769$	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	$-0.567459\pi$
$773$	606.367	−	834.592i	0.784433	−	1.07968i	0.994779	−	0.102053i	$-0.0325410\pi$
$774$	−618.842	−	1023.08i	−0.799537	−	1.32181i
$775$	122.524	−	377.089i	0.158095	−	0.486567i
$776$	251.515	+	81.7222i	0.324117	+	0.105312i
$777$	195.968	+	295.129i	0.252212	+	0.379832i
$778$	−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
$783$	19.0563	+	100.339i	0.0243376	+	0.128147i
$784$	−278.072	−	202.031i	−0.354683	−	0.257692i
$785$	−29.8748	−	41.1191i	−0.0380570	−	0.0523810i
$786$	1286.03	+	478.665i	1.63617	+	0.608989i
$787$	−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
$789$	−889.286	−	705.231i	−1.12710	−	0.893829i
$790$	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
$795$	−218.755	+	275.847i	−0.275164	+	0.346978i
$796$	−542.774	+	394.349i	−0.681877	+	0.495413i
$797$	211.514	+	68.7252i	0.265388	+	0.0862298i	0.438689	−	0.898639i	$-0.355443\pi$
$797$	211.514	+	68.7252i	0.265388	+	0.0862298i	−0.173300	+	0.984869i	$0.555443\pi$
$798$	−203.067	+	545.578i	−0.254469	+	0.683682i
$799$	12.9641	−	9.41900i	0.0162255	−	0.0117885i
$800$	485.183	−	667.797i	0.606479	−	0.834746i
$801$	−162.480	+	38.0166i	−0.202846	+	0.0474614i
$802$	−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
$807$	502.727	−	333.815i	0.622958	−	0.413649i
$808$	−194.112	+	597.415i	−0.240237	+	0.739375i
$809$	−715.778	−	232.570i	−0.884769	−	0.287479i	−0.168833	−	0.985645i	$-0.554000\pi$
$809$	−715.778	−	232.570i	−0.884769	−	0.287479i	−0.715936	+	0.698166i	$0.754000\pi$
$810$	−1474.92	+	730.168i	−1.82088	+	0.901442i
$811$	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
$816$	5.63343	+	20.1978i	0.00690372	+	0.0247522i
$817$	−727.077	−	528.252i	−0.889935	−	0.646576i
$818$	−277.540	−	382.001i	−0.339291	−	0.466994i
$819$	173.758	−	412.728i	0.212158	−	0.503942i
$820$	147.199	−	453.033i	0.179511	−	0.552480i
$821$	285.054	+	392.343i	0.347204	+	0.477885i	0.946528	−	0.322621i	$-0.104564\pi$
$821$	285.054	+	392.343i	0.347204	+	0.477885i	−0.599324	+	0.800506i	$0.704564\pi$
$822$	868.273	−	1094.88i	1.05629	−	1.33197i
$823$	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	−0.216916	−	0.976190i	$-0.569600\pi$
$827$	150.007	−	48.7401i	0.181386	−	0.0589360i	0.398302	+	0.917254i	$0.369600\pi$
$828$	−862.598	+	998.238i	−1.04179	+	1.20560i
$829$	−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
$831$	615.493	+	229.089i	0.740665	+	0.275679i
$832$	1283.81	−	932.745i	1.54304	−	1.12109i
$833$	18.7611	−	25.8224i	0.0225223	−	0.0309993i
$834$	−275.842	−	988.989i	−0.330746	−	1.18584i
$835$	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	$0.477159\pi$
$839$	−754.318	+	1038.23i	−0.899068	+	1.23746i	−0.970764	+	0.240035i	$0.922841\pi$
$840$	−140.989	−	212.330i	−0.167844	−	0.252774i
$841$	255.462	−	786.230i	0.303759	−	0.934875i
$842$	−1271.56	−	413.154i	−1.51016	−	0.490682i
$843$	1240.70	−	823.837i	1.47177	−	0.977268i
$844$	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
$849$	889.167	−	248.001i	1.04731	−	0.292109i
$850$	38.0586	+	27.6512i	0.0447748	+	0.0325308i
$851$	619.160	+	852.200i	0.727567	+	1.00141i
$852$	14.4287	−	38.7656i	0.0169351	−	0.0454995i
$853$	−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
$855$	−808.796	+	935.975i	−0.945960	+	1.09471i
$856$	−26.7900	−	82.4511i	−0.0312967	−	0.0963214i
$857$			479.970i			0.560059i	0.959991	+	0.280029i	$0.0903442\pi$
$857$			479.970i			0.560059i	−0.959991	+	0.280029i	$0.909656\pi$
$858$		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
$861$	96.2798	+	76.3528i	0.111823	+	0.0886793i
$862$	24.0996	−	17.5094i	0.0279578	−	0.0203125i
$863$	512.443	+	166.503i	0.593793	+	0.192935i	0.590470	−	0.807060i	$-0.298942\pi$
$863$	512.443	+	166.503i	0.593793	+	0.192935i	0.00332255	+	0.999994i	$0.498942\pi$
$864$	498.185	−	1056.47i	0.576603	−	1.22277i
$865$	889.082	−	645.956i	1.02784	−	0.746770i
$866$	−106.622	+	146.752i	−0.123120	+	0.169460i
$867$	833.249	−	232.405i	0.961072	−	0.268056i
$868$	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
$873$	−487.475	+	294.865i	−0.558391	+	0.337761i
$874$	−534.893	+	1646.23i	−0.612005	+	1.88356i
$875$	−114.486	−	37.1986i	−0.130841	−	0.0425127i
$876$	−404.919	−	609.810i	−0.462237	−	0.696130i
$877$	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	$-0.933630\pi$
$881$		−	364.734i		−	0.414000i	0.978341	−	0.207000i	$-0.0663701\pi$
$882$	−1062.48	+	248.596i	−1.20463	+	0.281855i
$883$	−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
$885$	812.485	+	302.411i	0.918063	+	0.341707i
$886$	−506.266	+	1558.13i	−0.571406	+	1.75861i
$887$	−801.425	−	1103.07i	−0.903523	−	1.24359i	−0.969331	−	0.245761i	$-0.920962\pi$
$887$	−801.425	−	1103.07i	−0.903523	−	1.24359i	0.0658073	−	0.997832i	$-0.479038\pi$
$888$	378.600	+	300.241i	0.426351	+	0.338110i
$889$	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
$894$	1481.45	−	1868.08i	1.65710	−	2.08958i
$895$	314.422	−	228.441i	0.351309	−	0.255241i
$896$	366.760	+	119.167i	0.409330	+	0.132999i
$897$	464.471	−	1247.89i	0.517805	−	1.39118i
$898$	−1904.91	+	1384.00i	−2.12129	+	1.54120i
$899$	46.2024	−	63.5921i	0.0513931	−	0.0707365i
$900$	−209.903	−	897.106i	−0.233225	−	0.996784i
$901$	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
$906$	673.179	−	446.997i	0.743024	−	0.493374i
$907$	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
$909$	−700.383	−	1157.88i	−0.770498	−	1.27380i
$910$	817.887	+	594.230i	0.898777	+	0.653000i
$911$	331.388	−	107.674i	0.363763	−	0.118194i	−0.121432	−	0.992600i	$-0.538749\pi$
$911$	331.388	−	107.674i	0.363763	−	0.118194i	0.485195	+	0.874406i	$0.338749\pi$
$912$	22.7085	−	538.329i	0.0248996	−	0.590273i
$913$		0			0
$914$		−	519.188i		−	0.568039i
$915$	57.0151	+	204.418i	0.0623116	+	0.223408i
$916$	1401.74	+	1018.42i	1.53028	+	1.11182i
$917$	−269.096	−	370.379i	−0.293453	−	0.403903i
$918$	60.2096	+	28.3922i	0.0655879	+	0.0309283i
$919$	−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
$921$	−738.416	+	931.131i	−0.801754	+	1.01100i
$922$	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
$927$	−1019.88	−	881.301i	−1.10020	−	0.950703i
$928$	132.389	−	96.1863i	0.142661	−	0.103649i
$929$	−299.056	−	97.1692i	−0.321912	−	0.104595i	0.143604	−	0.989635i	$-0.454131\pi$
$929$	−299.056	−	97.1692i	−0.321912	−	0.104595i	−0.465515	+	0.885040i	$0.654131\pi$
$930$	1187.07	+	441.831i	1.27641	+	0.475087i
$931$	−663.529	+	482.082i	−0.712706	+	0.517811i
$932$	1269.02	−	1746.66i	1.36161	−	1.87410i
$933$	70.1490	+	251.508i	0.0751865	+	0.269569i
$934$	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
$939$	−993.897	−	1496.81i	−1.05846	−	1.59405i
$940$	218.942	−	673.835i	0.232917	−	0.716846i
$941$	1067.37	+	346.811i	1.13430	+	0.368556i	0.815208	−	0.579169i	$-0.196623\pi$
$941$	1067.37	+	346.811i	1.13430	+	0.368556i	0.319090	+	0.947724i	$0.396623\pi$
$942$	58.5494	−	38.8773i	0.0621544	−	0.0412711i
$943$	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	$0.151033\pi$
$947$			865.333i			0.913762i	−0.889528	+	0.456881i	$0.848967\pi$
$948$	−1523.12	+	424.819i	−1.60667	+	0.448122i
$949$	597.691	+	434.248i	0.629812	+	0.457585i
$950$	−710.520	−	977.947i	−0.747916	−	1.02942i
$951$	2.56899	−	6.90210i	0.00270136	−	0.00725773i
$952$	−3.18575	+	9.80474i	−0.00334638	+	0.0102991i
$953$	−298.122	−	410.330i	−0.312825	−	0.430567i	0.623435	−	0.781875i	$-0.285737\pi$
$953$	−298.122	−	410.330i	−0.312825	−	0.430567i	−0.936260	+	0.351309i	$0.885737\pi$
$954$	−368.350	−	318.299i	−0.386111	−	0.333647i
$955$	−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
$960$	1524.52	+	1208.99i	1.58804	+	1.25936i
$961$	428.125	−	311.051i	0.445500	−	0.323674i
$962$	−1822.80	−	592.265i	−1.89481	−	0.615660i
$963$	172.131	+	72.4668i	0.178745	+	0.0752511i
$964$	−1262.22	+	917.054i	−1.30935	+	0.951301i
$965$	1163.31	−	1601.16i	1.20550	−	1.65924i
$966$	740.071	−	206.416i	0.766120	−	0.213681i
$967$	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	$-0.576696\pi$
$971$	736.695	−	1013.97i	0.758697	−	1.04426i	0.997321	−	0.0731450i	$-0.0233036\pi$
$972$	−528.666	−	1191.74i	−0.543895	−	1.22607i
$973$	−105.854	+	325.784i	−0.108791	+	0.334825i
$974$	−1901.55	−	617.851i	−1.95231	−	0.634344i
$975$	514.375	+	774.651i	0.527564	+	0.794514i
$976$	−74.7833	−	54.3333i	−0.0766223	−	0.0556693i
$977$	−1085.77	+	352.788i	−1.11133	+	0.361093i	−0.806453	−	0.591298i	$-0.798616\pi$
$977$	−1085.77	+	352.788i	−1.11133	+	0.361093i	−0.304878	+	0.952391i	$0.598616\pi$
$978$	2408.24	+	101.587i	2.46241	+	0.103873i
$979$		0			0
$980$		−	1411.24i		−	1.44004i
$981$	−216.921	−	927.102i	−0.221122	−	0.945059i
$982$	−153.097	−	111.231i	−0.155903	−	0.113270i
$983$	391.031	+	538.208i	0.397793	+	0.547515i	0.960188	−	0.279353i	$-0.0901200\pi$
$983$	391.031	+	538.208i	0.397793	+	0.547515i	−0.562395	+	0.826869i	$0.690120\pi$
$984$	157.075	+	58.4639i	0.159629	+	0.0594145i
$985$	−119.279	+	367.102i	−0.121095	+	0.372692i
$986$	5.48178	+	7.54502i	0.00555961	+	0.00765215i
$987$	143.205	+	113.566i	0.145091	+	0.115062i
$988$	−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
$993$	−686.118	+	865.185i	−0.690955	+	0.871284i
$994$	−19.4883	+	14.1591i	−0.0196060	+	0.0142446i
$995$	789.604	+	256.558i	0.793572	+	0.257847i
$996$	179.106	−	481.204i	0.179826	−	0.483137i
$997$	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
$999$	−1022.67	+	194.225i	−1.02369	+	0.194419i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.h.b.5.1	✓	16	33.32	even	2
33.3.h.b.5.4	yes	16	11.10	odd	2
33.3.h.b.20.1	yes	16	11.2	odd	10
33.3.h.b.20.4	yes	16	33.2	even	10
363.3.b.l.122.2		8	33.14	odd	10
363.3.b.l.122.7		8	11.3	even	5
363.3.b.m.122.2		8	11.8	odd	10
363.3.b.m.122.7		8	33.8	even	10
363.3.h.j.251.1		16	33.20	odd	10	inner
363.3.h.j.251.4		16	11.9	even	5	inner
363.3.h.j.269.1		16	1.1	even	1	trivial
363.3.h.j.269.4		16	3.2	odd	2	inner
363.3.h.n.245.1		16	11.4	even	5
363.3.h.n.245.4		16	33.26	odd	10
363.3.h.n.323.1		16	33.5	odd	10
363.3.h.n.323.4		16	11.5	even	5
363.3.h.o.245.1		16	33.29	even	10
363.3.h.o.245.4		16	11.7	odd	10
363.3.h.o.323.1		16	11.6	odd	10
363.3.h.o.323.4		16	33.17	even	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} +(-1.86408 + 2.35058i) q^{3} +(4.34051 - 3.15356i) q^{4} +(-6.31437 - 2.05166i) q^{5} +(3.20248 - 8.60410i) q^{6} +(-2.47800 + 1.80037i) q^{7} +(-2.45561 + 3.37986i) q^{8} +(-2.05042 - 8.76332i) q^{9} +20.3180 q^{10} +(-0.678356 + 16.0812i) q^{12} +(-5.01988 - 15.4496i) q^{13} +(5.50960 - 7.58331i) q^{14} +(16.5931 - 11.0180i) q^{15} +(-2.68094 + 8.25108i) q^{16} +(-0.766216 - 0.248959i) q^{17} +(14.2549 + 23.5664i) q^{18} +(16.7481 + 12.1682i) q^{19} +(-33.8776 + 11.0075i) q^{20} +(0.387274 - 9.18076i) q^{21} -27.3224i q^{23} +(-3.36716 - 12.0724i) q^{24} +(15.4365 + 11.2153i) q^{25} +(29.2204 + 40.2185i) q^{26} +(24.4210 + 11.5159i) q^{27} +(-5.07819 + 15.6291i) q^{28} +(2.22341 + 3.06025i) q^{29} +(-37.8744 + 47.7591i) q^{30} +(-6.42137 - 19.7630i) q^{31} -43.2608i q^{32} +2.46549 q^{34} +(19.3408 - 6.28420i) q^{35} +(-36.5355 - 31.5711i) q^{36} +(-31.1905 + 22.6613i) q^{37} +(-60.2520 - 19.5771i) q^{38} +(45.6729 + 16.9996i) q^{39} +(22.4400 - 16.3036i) q^{40} +(-7.86024 + 10.8187i) q^{41} +(7.55483 + 27.0866i) q^{42} -43.4125 q^{43} +(-5.03227 + 59.5416i) q^{45} +(25.8380 + 79.5212i) q^{46} +(-11.6912 + 16.0916i) q^{47} +(-14.3973 - 21.6824i) q^{48} +(-12.2427 + 37.6791i) q^{49} +(-55.5336 - 18.0440i) q^{50} +(2.01348 - 1.33697i) q^{51} +(-70.5100 - 51.2285i) q^{52} +(-16.8103 + 5.46201i) q^{53} +(-81.9669 - 10.4224i) q^{54} -12.7963i q^{56} +(-59.8221 + 16.6852i) q^{57} +(-9.36516 - 6.80419i) q^{58} +(25.5837 + 35.2129i) q^{59} +(37.2766 - 100.151i) q^{60} +(-3.29249 + 10.1333i) q^{61} +(37.3785 + 51.4471i) q^{62} +(20.8582 + 18.0240i) q^{63} +(30.1867 + 92.9052i) q^{64} +107.854i q^{65} +72.2963 q^{67} +(-4.11087 + 1.33570i) q^{68} +(64.2234 + 50.9311i) q^{69} +(-50.3481 + 36.5800i) q^{70} +(-2.44412 - 0.794142i) q^{71} +(34.6538 + 14.5892i) q^{72} +(-36.7931 + 26.7318i) q^{73} +(69.3492 - 95.4510i) q^{74} +(-55.1374 + 15.3786i) q^{75} +111.068 q^{76} +(-149.006 - 6.28555i) q^{78} +(30.3585 + 93.4339i) q^{79} +(33.8569 - 46.6000i) q^{80} +(-72.5916 + 35.9370i) q^{81} +(12.6461 - 38.9207i) q^{82} +(-30.3393 - 9.85783i) q^{83} +(-27.2711 - 41.0704i) q^{84} +(4.32739 + 3.14404i) q^{85} +(126.351 - 41.0540i) q^{86} +(-11.3380 - 0.478272i) q^{87} -18.5409i q^{89} +(-41.6605 - 178.053i) q^{90} +(40.2543 + 29.2464i) q^{91} +(-86.1629 - 118.593i) q^{92} +(58.4243 + 21.7458i) q^{93} +(18.8097 - 57.8902i) q^{94} +(-80.7886 - 111.196i) q^{95} +(101.688 + 80.6415i) 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

Groups

Database

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