LMFDB - Embedded newform 363.3.h.n.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 = [16,0,5,18,0,-32,34] 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			$2.10855 + 2.90217i$ of defining polynomial
Character	$\chi$	$=$	363.269
Dual form			363.3.h.n.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+(-3.41170 + 1.10853i) q^{2} +(2.93308 + 0.630124i) q^{3} +(7.17480 - 5.21280i) q^{4} +(1.98428 + 0.644731i) q^{5} +(-10.7053 + 1.10160i) q^{6} +(7.17034 - 5.20956i) q^{7} +(-10.2655 + 14.1293i) q^{8} +(8.20589 + 3.69641i) q^{9} -7.48447 q^{10} +(24.3290 - 10.7685i) q^{12} +(0.508273 + 1.56430i) q^{13} +(-18.6881 + 25.7220i) q^{14} +(5.41378 + 3.14139i) q^{15} +(8.39811 - 25.8467i) q^{16} +(11.8154 + 3.83907i) q^{17} +(-32.0936 - 3.51458i) q^{18} +(8.54780 + 6.21034i) q^{19} +(17.5977 - 5.71782i) q^{20} +(24.3138 - 10.7618i) q^{21} -20.3378i q^{23} +(-39.0129 + 34.9738i) q^{24} +(-16.7037 - 12.1360i) q^{25} +(-3.46815 - 4.77350i) q^{26} +(21.7393 + 16.0126i) q^{27} +(24.2894 - 74.7550i) q^{28} +(-6.82340 - 9.39161i) q^{29} +(-21.9525 - 4.71615i) q^{30} +(-7.22737 - 22.2436i) q^{31} +27.6317i q^{32} -44.5665 q^{34} +(17.5867 - 5.71427i) q^{35} +(78.1442 - 16.2546i) q^{36} +(-5.86208 + 4.25905i) q^{37} +(-36.0469 - 11.7123i) q^{38} +(0.505098 + 4.90850i) q^{39} +(-29.4793 + 21.4180i) q^{40} +(22.8512 - 31.4520i) q^{41} +(-71.0217 + 63.6687i) q^{42} +15.8444 q^{43} +(13.8996 + 12.6253i) q^{45} +(22.5450 + 69.3864i) q^{46} +(-26.6317 + 36.6554i) q^{47} +(40.9190 - 70.5186i) q^{48} +(9.13245 - 28.1068i) q^{49} +(70.4413 + 22.8878i) q^{50} +(32.2365 + 18.7055i) q^{51} +(11.8011 + 8.57403i) q^{52} +(38.3428 - 12.4583i) q^{53} +(-91.9184 - 30.5315i) q^{54} +154.791i q^{56} +(21.1581 + 23.6016i) q^{57} +(33.6903 + 24.4774i) q^{58} +(66.5264 + 91.5657i) q^{59} +(55.2182 - 5.68211i) q^{60} +(-23.9538 + 73.7222i) q^{61} +(49.3152 + 67.8766i) q^{62} +(78.0956 - 16.2445i) q^{63} +(2.96194 + 9.11592i) q^{64} +3.43171i q^{65} +62.9082 q^{67} +(104.786 - 34.0470i) q^{68} +(12.8153 - 59.6523i) q^{69} +(-53.6662 + 38.9908i) q^{70} +(9.71270 + 3.15585i) q^{71} +(-136.466 + 77.9979i) q^{72} +(-60.3706 + 43.8618i) q^{73} +(15.2784 - 21.0289i) q^{74} +(-41.3462 - 46.1212i) q^{75} +93.7020 q^{76} +(-7.16445 - 16.1864i) q^{78} +(-26.6720 - 82.0879i) q^{79} +(33.3284 - 45.8726i) q^{80} +(53.6731 + 60.6646i) q^{81} +(-43.0961 + 132.636i) q^{82} +(11.2304 + 3.64896i) q^{83} +(118.348 - 203.957i) q^{84} +(20.9700 + 15.2356i) q^{85} +(-54.0563 + 17.5639i) q^{86} +(-14.0957 - 31.8459i) q^{87} -74.5782i q^{89} +(-61.4167 - 27.6656i) q^{90} +(11.7938 + 8.56870i) q^{91} +(-106.017 - 145.919i) q^{92} +(-7.18222 - 69.7962i) q^{93} +(50.2259 - 154.579i) q^{94} +(12.9572 + 17.8341i) q^{95} +(-17.4114 + 81.0458i) q^{96} +(-23.8462 - 73.3909i) q^{97} +106.016i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 5 q^{3} + 18 q^{4} - 32 q^{6} + 34 q^{7} + 17 q^{9} + 12 q^{10} + 106 q^{12} + 2 q^{13} - 28 q^{15} + 102 q^{16} - 42 q^{18} - 66 q^{19} + 12 q^{21} + 74 q^{24} - 176 q^{25} - 55 q^{27} + 146 q^{28}+ \cdots + 252 q^{97}+O(q^{100}) $ 16 * q + 5 * q^3 + 18 * q^4 - 32 * q^6 + 34 * q^7 + 17 * q^9 + 12 * q^10 + 106 * q^12 + 2 * q^13 - 28 * q^15 + 102 * q^16 - 42 * q^18 - 66 * q^19 + 12 * q^21 + 74 * q^24 - 176 * q^25 - 55 * q^27 + 146 * q^28 - 110 * q^30 - 126 * q^31 - 132 * q^34 + 226 * q^36 - 230 * q^37 - 136 * q^39 - 226 * q^40 - 72 * q^42 + 156 * q^43 - 72 * q^45 - 308 * q^46 + 255 * q^48 + 170 * q^49 + 169 * q^51 + 224 * q^52 - 1046 * q^54 + 259 * q^57 + 184 * q^58 - 316 * q^60 - 104 * q^61 + 108 * q^63 - 184 * q^64 + 368 * q^67 - 22 * q^69 - 52 * q^70 - 73 * q^72 - 354 * q^73 + 54 * q^75 + 900 * q^76 - 492 * q^78 - 566 * q^79 + 377 * q^81 + 200 * q^82 + 720 * q^84 + 162 * q^85 - 132 * q^87 + 774 * q^90 - 226 * q^91 - 370 * q^93 + 530 * q^94 + 67 * q^96 + 252 * 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 $

$2$	−3.41170	+	1.10853i	−1.70585	+	0.554264i	−0.989634	−	0.143614i	$-0.954128\pi$
$2$	−3.41170	+	1.10853i	−1.70585	+	0.554264i	−0.716217	+	0.697878i	$0.754128\pi$
$3$	2.93308	+	0.630124i	0.977692	+	0.210041i
$3$	2.93308	+	0.630124i	0.977692	+	0.210041i
$4$	7.17480	−	5.21280i	1.79370	−	1.30320i
$5$	1.98428	+	0.644731i	0.396856	+	0.128946i	0.500644	−	0.865653i	$-0.333097\pi$
$5$	1.98428	+	0.644731i	0.396856	+	0.128946i	−0.103789	+	0.994599i	$0.533097\pi$
$6$	−10.7053	+	1.10160i	−1.78422	+	0.183601i
$7$	7.17034	−	5.20956i	1.02433	−	0.744222i	0.0571672	−	0.998365i	$-0.481793\pi$
$7$	7.17034	−	5.20956i	1.02433	−	0.744222i	0.967167	+	0.254142i	$0.0817932\pi$
$8$	−10.2655	+	14.1293i	−1.28319	+	1.76616i
$9$	8.20589	+	3.69641i	0.911765	+	0.410712i
$10$	−7.48447			−0.748447
$11$		0			0
$11$		0			0
$12$	24.3290	−	10.7685i	2.02741	−	0.897377i
$13$	0.508273	+	1.56430i	0.0390979	+	0.120331i	0.968700	−	0.248233i	$-0.0798497\pi$
$13$	0.508273	+	1.56430i	0.0390979	+	0.120331i	−0.929603	+	0.368564i	$0.879850\pi$
$14$	−18.6881	+	25.7220i	−1.33486	+	1.83728i
$15$	5.41378	+	3.14139i	0.360919	+	0.209426i
$16$	8.39811	−	25.8467i	0.524882	−	1.61542i
$17$	11.8154	+	3.83907i	0.695026	+	0.225828i	0.635162	−	0.772379i	$-0.280933\pi$
$17$	11.8154	+	3.83907i	0.695026	+	0.225828i	0.0598641	+	0.998207i	$0.480933\pi$
$18$	−32.0936	−	3.51458i	−1.78298	−	0.195254i
$19$	8.54780	+	6.21034i	0.449884	+	0.326860i	0.789550	−	0.613686i	$-0.210314\pi$
$19$	8.54780	+	6.21034i	0.449884	+	0.326860i	−0.339666	+	0.940546i	$0.610314\pi$
$20$	17.5977	−	5.71782i	0.879883	−	0.285891i
$21$	24.3138	−	10.7618i	1.15780	−	0.512468i
$22$		0			0
$23$		−	20.3378i		−	0.884251i	−0.896953	−	0.442126i	$-0.854225\pi$
$23$		−	20.3378i		−	0.884251i	0.896953	−	0.442126i	$-0.145775\pi$
$24$	−39.0129	+	34.9738i	−1.62554	+	1.45724i
$25$	−16.7037	−	12.1360i	−0.668150	−	0.485439i
$26$	−3.46815	−	4.77350i	−0.133390	−	0.183596i
$27$	21.7393	+	16.0126i	0.805159	+	0.593059i
$28$	24.2894	−	74.7550i	0.867478	−	2.66982i
$29$	−6.82340	−	9.39161i	−0.235290	−	0.323849i	0.675002	−	0.737816i	$-0.264143\pi$
$29$	−6.82340	−	9.39161i	−0.235290	−	0.323849i	−0.910292	+	0.413967i	$0.864143\pi$
$30$	−21.9525	−	4.71615i	−0.731751	−	0.157205i
$31$	−7.22737	−	22.2436i	−0.233141	−	0.717534i	−0.997363	−	0.0725803i	$-0.976877\pi$
$31$	−7.22737	−	22.2436i	−0.233141	−	0.717534i	0.764222	−	0.644954i	$-0.223123\pi$
$32$			27.6317i			0.863489i
$33$		0			0
$34$	−44.5665			−1.31078
$35$	17.5867	−	5.71427i	0.502477	−	0.163265i
$36$	78.1442	−	16.2546i	2.17067	−	0.451518i
$37$	−5.86208	+	4.25905i	−0.158435	+	0.115109i	−0.664178	−	0.747575i	$-0.731218\pi$
$37$	−5.86208	+	4.25905i	−0.158435	+	0.115109i	0.505743	+	0.862684i	$0.331218\pi$
$38$	−36.0469	−	11.7123i	−0.948602	−	0.308220i
$39$	0.505098	+	4.90850i	0.0129512	+	0.125859i
$40$	−29.4793	+	21.4180i	−0.736983	+	0.535449i
$41$	22.8512	−	31.4520i	0.557347	−	0.767122i	−0.433639	−	0.901087i	$-0.642771\pi$
$41$	22.8512	−	31.4520i	0.557347	−	0.767122i	0.990986	+	0.133964i	$0.0427707\pi$
$42$	−71.0217	+	63.6687i	−1.69099	+	1.51592i
$43$	15.8444			0.368474			0.184237	−	0.982882i	$-0.441019\pi$
$43$	15.8444			0.368474			0.184237	+	0.982882i	$0.441019\pi$
$44$		0			0
$45$	13.8996	+	12.6253i	0.308879	+	0.280562i
$46$	22.5450	+	69.3864i	0.490109	+	1.50840i
$47$	−26.6317	+	36.6554i	−0.566633	+	0.779903i	−0.992151	−	0.125047i	$-0.960092\pi$
$47$	−26.6317	+	36.6554i	−0.566633	+	0.779903i	0.425518	+	0.904950i	$0.360092\pi$
$48$	40.9190	−	70.5186i	0.852478	−	1.46914i
$49$	9.13245	−	28.1068i	0.186376	−	0.573608i
$50$	70.4413	+	22.8878i	1.40883	+	0.457755i
$51$	32.2365	+	18.7055i	0.632089	+	0.366774i
$52$	11.8011	+	8.57403i	0.226945	+	0.164885i
$53$	38.3428	−	12.4583i	0.723450	−	0.235063i	0.0759315	−	0.997113i	$-0.475807\pi$
$53$	38.3428	−	12.4583i	0.723450	−	0.235063i	0.647518	+	0.762050i	$0.275807\pi$
$54$	−91.9184	−	30.5315i	−1.70219	−	0.565398i
$55$		0			0
$56$			154.791i			2.76412i
$57$	21.1581	+	23.6016i	0.371194	+	0.414063i
$58$	33.6903	+	24.4774i	0.580867	+	0.422024i
$59$	66.5264	+	91.5657i	1.12757	+	1.55196i	0.792611	+	0.609727i	$0.208721\pi$
$59$	66.5264	+	91.5657i	1.12757	+	1.55196i	0.334955	+	0.942234i	$0.391279\pi$
$60$	55.2182	−	5.68211i	0.920304	−	0.0947018i
$61$	−23.9538	+	73.7222i	−0.392685	+	1.20856i	0.538065	+	0.842903i	$0.319156\pi$
$61$	−23.9538	+	73.7222i	−0.392685	+	1.20856i	−0.930750	+	0.365657i	$0.880844\pi$
$62$	49.3152	+	67.8766i	0.795407	+	1.09478i
$63$	78.0956	−	16.2445i	1.23961	−	0.257850i
$64$	2.96194	+	9.11592i	0.0462803	+	0.142436i
$65$			3.43171i			0.0527956i
$66$		0			0
$67$	62.9082			0.938929			0.469464	−	0.882951i	$-0.344447\pi$
$67$	62.9082			0.938929			0.469464	+	0.882951i	$0.344447\pi$
$68$	104.786	−	34.0470i	1.54097	−	0.500691i
$69$	12.8153	−	59.6523i	0.185729	−	0.864526i
$70$	−53.6662	+	38.9908i	−0.766660	+	0.557011i
$71$	9.71270	+	3.15585i	0.136799	+	0.0444486i	0.376616	−	0.926369i	$-0.377088\pi$
$71$	9.71270	+	3.15585i	0.136799	+	0.0444486i	−0.239817	+	0.970818i	$0.577088\pi$
$72$	−136.466	+	77.9979i	−1.89536	+	1.08330i
$73$	−60.3706	+	43.8618i	−0.826995	+	0.600847i	−0.918708	−	0.394938i	$-0.870766\pi$
$73$	−60.3706	+	43.8618i	−0.826995	+	0.600847i	0.0917125	+	0.995786i	$0.470766\pi$
$74$	15.2784	−	21.0289i	0.206465	−	0.284174i
$75$	−41.3462	−	46.1212i	−0.551283	−	0.614949i
$76$	93.7020			1.23292
$77$		0			0
$78$	−7.16445	−	16.1864i	−0.0918519	−	0.207518i
$79$	−26.6720	−	82.0879i	−0.337620	−	1.03909i	−0.965417	−	0.260710i	$-0.916043\pi$
$79$	−26.6720	−	82.0879i	−0.337620	−	1.03909i	0.627797	−	0.778377i	$-0.283957\pi$
$80$	33.3284	−	45.8726i	0.416605	−	0.573407i
$81$	53.6731	+	60.6646i	0.662631	+	0.748946i
$82$	−43.0961	+	132.636i	−0.525562	+	1.61751i
$83$	11.2304	+	3.64896i	0.135305	+	0.0439634i	0.375887	−	0.926666i	$-0.377338\pi$
$83$	11.2304	+	3.64896i	0.135305	+	0.0439634i	−0.240581	+	0.970629i	$0.577338\pi$
$84$	118.348	−	203.957i	1.40890	−	2.42806i
$85$	20.9700	+	15.2356i	0.246705	+	0.179242i
$86$	−54.0563	+	17.5639i	−0.628561	+	0.204232i
$87$	−14.0957	−	31.8459i	−0.162019	−	0.366045i
$88$		0			0
$89$		−	74.5782i		−	0.837957i	−0.907996	−	0.418979i	$-0.862388\pi$
$89$		−	74.5782i		−	0.837957i	0.907996	−	0.418979i	$-0.137612\pi$
$90$	−61.4167	−	27.6656i	−0.682408	−	0.307396i
$91$	11.7938	+	8.56870i	0.129602	+	0.0941616i
$92$	−106.017	−	145.919i	−1.15236	−	1.58608i
$93$	−7.18222	−	69.7962i	−0.0772282	−	0.750497i
$94$	50.2259	−	154.579i	0.534318	−	1.64446i
$95$	12.9572	+	17.8341i	0.136392	+	0.187727i
$96$	−17.4114	+	81.0458i	−0.181369	+	0.844227i
$97$	−23.8462	−	73.3909i	−0.245837	−	0.756608i	−0.995498	−	0.0947856i	$-0.969783\pi$
$97$	−23.8462	−	73.3909i	−0.245837	−	0.756608i	0.749661	−	0.661822i	$-0.230217\pi$
$98$			106.016i			1.08179i
$99$		0			0
$100$	−183.108			−1.83108
$101$	−12.1692	+	3.95400i	−0.120487	+	0.0391485i	−0.368640	−	0.929572i	$-0.620176\pi$
$101$	−12.1692	+	3.95400i	−0.120487	+	0.0391485i	0.248153	+	0.968721i	$0.420176\pi$
$102$	−130.717	−	28.0824i	−1.28154	−	0.275318i
$103$	−57.0875	+	41.4765i	−0.554248	+	0.402685i	−0.829349	−	0.558731i	$-0.811289\pi$
$103$	−57.0875	+	41.4765i	−0.554248	+	0.402685i	0.275101	+	0.961415i	$0.411289\pi$
$104$	−27.3202	−	8.87688i	−0.262694	−	0.0853546i
$105$	55.1839	−	5.67858i	0.525561	−	0.0540817i
$106$	−117.004	+	85.0083i	−1.10381	+	0.801965i
$107$	−108.282	+	149.037i	−1.01198	+	1.39287i	−0.0943034	+	0.995544i	$0.530062\pi$
$107$	−108.282	+	149.037i	−1.01198	+	1.39287i	−0.917677	+	0.397328i	$0.869938\pi$
$108$	239.445	+	1.56448i	2.21709	+	0.0144859i
$109$	58.5394			0.537058			0.268529	−	0.963272i	$-0.413462\pi$
$109$	58.5394			0.537058			0.268529	+	0.963272i	$0.413462\pi$
$110$		0			0
$111$	−19.8777	+	8.79828i	−0.179078	+	0.0792638i
$112$	−74.4327	−	229.080i	−0.664577	−	2.04536i
$113$	−89.3418	+	122.968i	−0.790635	+	1.08822i	0.203393	+	0.979097i	$0.434803\pi$
$113$	−89.3418	+	122.968i	−0.790635	+	1.08822i	−0.994029	+	0.109119i	$0.965197\pi$
$114$	−98.3481	−	57.0672i	−0.862703	−	0.500590i
$115$	13.1124	−	40.3558i	0.114021	−	0.350920i
$116$	−97.9131	−	31.8139i	−0.844078	−	0.274258i
$117$	−1.61147	+	14.7153i	−0.0137733	+	0.125772i
$118$	−328.471	−	238.648i	−2.78366	−	2.02244i
$119$	104.721	−	34.0258i	0.880005	−	0.285931i
$120$	−99.9611	+	44.2449i	−0.833009	+	0.368708i
$121$		0			0
$122$		−	278.071i		−	2.27927i
$123$	86.8431	−	77.8521i	0.706042	−	0.632944i
$124$	−167.806	−	121.918i	−1.35327	−	0.983212i
$125$	−55.9792	−	77.0488i	−0.447834	−	0.616390i
$126$	−248.431	+	141.993i	−1.97168	+	1.12693i
$127$	4.41099	−	13.5756i	0.0347322	−	0.106895i	−0.932187	−	0.361976i	$-0.882102\pi$
$127$	4.41099	−	13.5756i	0.0347322	−	0.106895i	0.966920	+	0.255081i	$0.0821022\pi$
$128$	−85.1764	−	117.235i	−0.665441	−	0.915901i
$129$	46.4728	+	9.98393i	0.360254	+	0.0773948i
$130$	−3.80415	−	11.7080i	−0.0292627	−	0.0900613i
$131$		−	153.686i		−	1.17318i	−0.809885	−	0.586589i	$-0.800471\pi$
$131$		−	153.686i		−	1.17318i	0.809885	−	0.586589i	$-0.199529\pi$
$132$		0			0
$133$	93.6438			0.704088
$134$	−214.624	+	69.7356i	−1.60167	+	0.520415i
$135$	32.8130	+	45.7894i	0.243059	+	0.339181i
$136$	−175.535	+	127.534i	−1.29070	+	0.937750i
$137$	76.6942	+	24.9195i	0.559812	+	0.181894i	0.575237	−	0.817987i	$-0.304910\pi$
$137$	76.6942	+	24.9195i	0.559812	+	0.181894i	−0.0154246	+	0.999881i	$0.504910\pi$
$138$	22.4042	+	217.722i	0.162349	+	1.57769i
$139$	171.464	−	124.576i	1.23356	−	0.896231i	0.236404	−	0.971655i	$-0.424031\pi$
$139$	171.464	−	124.576i	1.23356	−	0.896231i	0.997152	+	0.0754243i	$0.0240311\pi$
$140$	96.3938	−	132.675i	0.688527	−	0.947676i
$141$	−101.210	+	90.7319i	−0.717804	+	0.643489i
$142$	−36.6352			−0.257994
$143$		0			0
$144$	164.454	−	181.052i	1.14204	−	1.25731i
$145$	−7.48447	−	23.0348i	−0.0516170	−	0.158861i
$146$	157.344	−	216.566i	1.07770	−	1.48333i
$147$	44.4970	−	76.6848i	0.302700	−	0.521665i
$148$	−19.8577	+	61.1156i	−0.134173	+	0.412943i
$149$	−215.252	−	69.9397i	−1.44465	−	0.469394i	−0.521303	−	0.853371i	$-0.674554\pi$
$149$	−215.252	−	69.9397i	−1.44465	−	0.469394i	−0.923342	+	0.383978i	$0.874554\pi$
$150$	192.188	+	111.518i	1.28125	+	0.743455i
$151$	220.642	+	160.306i	1.46121	+	1.06163i	0.983046	+	0.183357i	$0.0586964\pi$
$151$	220.642	+	160.306i	1.46121	+	1.06163i	0.478161	+	0.878272i	$0.341304\pi$
$152$	−175.496	+	57.0220i	−1.15458	+	0.375145i
$153$	82.7654	+	75.1777i	0.540951	+	0.491357i
$154$		0			0
$155$		−	48.7971i		−	0.314820i
$156$	29.2110	+	32.5845i	0.187250	+	0.208875i
$157$	−4.90208	−	3.56157i	−0.0312234	−	0.0226852i	0.572064	−	0.820209i	$-0.306143\pi$
$157$	−4.90208	−	3.56157i	−0.0312234	−	0.0226852i	−0.603288	+	0.797524i	$0.706143\pi$
$158$	181.994	+	250.493i	1.15186	+	1.58540i
$159$	120.313	−	12.3805i	0.756684	−	0.0778649i
$160$	−17.8150	+	54.8289i	−0.111344	+	0.342681i
$161$	−105.951	−	145.829i	−0.658079	−	0.905769i
$162$	−250.365	−	147.471i	−1.54546	−	0.910317i
$163$	50.0381	+	154.002i	0.306982	+	0.944795i	0.978930	+	0.204196i	$0.0654580\pi$
$163$	50.0381	+	154.002i	0.306982	+	0.944795i	−0.671947	+	0.740599i	$0.734542\pi$
$164$		−	344.781i		−	2.10232i
$165$		0			0
$166$	−42.3596			−0.255178
$167$	−151.417	+	49.1982i	−0.906686	+	0.294600i	−0.724994	−	0.688755i	$-0.758158\pi$
$167$	−151.417	+	49.1982i	−0.906686	+	0.294600i	−0.181692	+	0.983355i	$0.558158\pi$
$168$	−97.5375	+	454.014i	−0.580581	+	2.70246i
$169$	134.535	−	97.7455i	0.796066	−	0.578376i
$170$	−88.4323	−	28.7334i	−0.520190	−	0.169020i
$171$	47.1863	+	82.5575i	0.275944	+	0.482793i
$172$	113.680	−	82.5935i	0.660931	−	0.480195i
$173$	−22.5826	+	31.0822i	−0.130535	+	0.179666i	−0.869282	−	0.494317i	$-0.835418\pi$
$173$	−22.5826	+	31.0822i	−0.130535	+	0.179666i	0.738746	+	0.673983i	$0.235418\pi$
$174$	83.3924	+	93.0232i	0.479266	+	0.534616i
$175$	−182.995			−1.04568
$176$		0			0
$177$	137.429	+	310.489i	0.776437	+	1.75418i
$178$	82.6721	+	254.439i	0.464450	+	1.42943i
$179$	80.0291	−	110.151i	0.447090	−	0.615367i	−0.524679	−	0.851300i	$-0.675815\pi$
$179$	80.0291	−	110.151i	0.447090	−	0.615367i	0.971769	+	0.235933i	$0.0758147\pi$
$180$	165.540	+	18.1283i	0.919665	+	0.100713i
$181$	−40.2773	+	123.961i	−0.222526	+	0.684865i	0.776007	+	0.630724i	$0.217242\pi$
$181$	−40.2773	+	123.961i	−0.222526	+	0.684865i	−0.998533	+	0.0541412i	$0.982758\pi$
$182$	−49.7356	−	16.1601i	−0.273273	−	0.0887916i
$183$	−116.712	+	201.139i	−0.637773	+	1.09912i
$184$	287.359	+	208.778i	1.56173	+	1.13467i
$185$	−14.3779	+	4.67167i	−0.0777186	+	0.0252523i
$186$	101.875	+	230.162i	0.547713	+	1.23743i
$187$		0			0
$188$			401.821i			2.13735i
$189$	239.297	+	1.56351i	1.26612	+	0.00827254i
$190$	−63.9758	−	46.4811i	−0.336715	−	0.244637i
$191$	−185.493	−	255.309i	−0.971169	−	1.33670i	−0.941454	−	0.337140i	$-0.890540\pi$
$191$	−185.493	−	255.309i	−0.971169	−	1.33670i	−0.0297142	−	0.999558i	$-0.509460\pi$
$192$	2.94344	+	28.6041i	0.0153304	+	0.148980i
$193$	−45.2431	+	139.244i	−0.234420	+	0.721472i	0.762777	+	0.646661i	$0.223835\pi$
$193$	−45.2431	+	139.244i	−0.234420	+	0.721472i	−0.997198	+	0.0748107i	$0.976165\pi$
$194$	162.712	+	223.954i	0.838721	+	1.15440i
$195$	−2.16241	+	10.0655i	−0.0110893	+	0.0516178i
$196$	−80.9915	−	249.266i	−0.413222	−	1.27177i
$197$			229.459i			1.16476i	0.812915	+	0.582382i	$0.197879\pi$
$197$			229.459i			1.16476i	−0.812915	+	0.582382i	$0.802121\pi$
$198$		0			0
$199$	−389.358			−1.95657			−0.978287	−	0.207253i	$-0.933548\pi$
$199$	−389.358			−1.95657			−0.978287	+	0.207253i	$0.933548\pi$
$200$	342.946	−	111.430i	1.71473	−	0.557150i
$201$	184.515	+	39.6400i	0.917984	+	0.197214i
$202$	37.1344	−	26.9797i	0.183834	−	0.133563i
$203$	−97.8522	−	31.7941i	−0.482031	−	0.156621i
$204$	328.799	−	33.8343i	1.61176	−	0.165854i
$205$	65.6213	−	47.6767i	0.320104	−	0.232569i
$206$	148.788	−	204.789i	0.722270	−	0.994120i
$207$	75.1767	−	166.889i	0.363173	−	0.806229i
$208$	44.7006			0.214907
$209$		0			0
$210$	−181.976	+	80.5465i	−0.866553	+	0.383555i
$211$	−63.0362	−	194.005i	−0.298750	−	0.919457i	−0.981936	−	0.189213i	$-0.939406\pi$
$211$	−63.0362	−	194.005i	−0.298750	−	0.919457i	0.683186	−	0.730244i	$-0.260594\pi$
$212$	210.159	−	289.260i	0.991318	−	1.36443i
$213$	26.4995	+	15.3766i	0.124411	+	0.0721904i
$214$	204.213	−	628.504i	0.954268	−	2.93693i
$215$	31.4396	+	10.2154i	0.146231	+	0.0475133i
$216$	−449.413	+	142.784i	−2.08061	+	0.661035i
$217$	−167.702	−	121.842i	−0.772819	−	0.561486i
$218$	−199.719	+	64.8926i	−0.916141	+	0.297672i
$219$	−204.710	+	90.6091i	−0.934750	+	0.413740i
$220$		0			0
$221$			20.4342i			0.0924626i
$222$	58.0635	−	52.0521i	0.261547	−	0.234469i
$223$	13.3648	+	9.71010i	0.0599319	+	0.0435431i	0.617348	−	0.786690i	$-0.288207\pi$
$223$	13.3648	+	9.71010i	0.0599319	+	0.0435431i	−0.557416	+	0.830233i	$0.688207\pi$
$224$	143.949	+	198.128i	0.642628	+	0.884502i
$225$	−92.2095	−	161.330i	−0.409820	−	0.717024i
$226$	168.493	−	518.569i	0.745546	−	2.29456i
$227$	−66.3365	−	91.3043i	−0.292231	−	0.402222i	0.637506	−	0.770445i	$-0.279966\pi$
$227$	−66.3365	−	91.3043i	−0.292231	−	0.402222i	−0.929737	+	0.368224i	$0.879966\pi$
$228$	274.835	+	59.0439i	1.20542	+	0.258965i
$229$	−113.909	−	350.577i	−0.497421	−	1.53090i	−0.813150	−	0.582054i	$-0.802249\pi$
$229$	−113.909	−	350.577i	−0.497421	−	1.53090i	0.315730	−	0.948849i	$-0.397751\pi$
$230$			152.217i			0.661815i
$231$		0			0
$232$	202.743			0.873892
$233$	−165.998	+	53.9359i	−0.712436	+	0.231485i	−0.642741	−	0.766084i	$-0.722203\pi$
$233$	−165.998	+	53.9359i	−0.712436	+	0.231485i	−0.0696955	+	0.997568i	$0.522203\pi$
$234$	−10.8144	−	51.9905i	−0.0462156	−	0.222181i
$235$	−76.4777	+	55.5643i	−0.325437	+	0.236444i
$236$	954.627	+	310.177i	4.04503	+	1.31431i
$237$	−26.5054	−	257.577i	−0.111837	−	1.08682i
$238$	−319.557	+	232.172i	−1.34268	+	0.975511i
$239$	−202.993	+	279.397i	−0.849345	+	1.16902i	0.134661	+	0.990892i	$0.457005\pi$
$239$	−202.993	+	279.397i	−0.849345	+	1.16902i	−0.984007	+	0.178132i	$0.942995\pi$
$240$	126.660	−	113.547i	0.527751	−	0.473112i
$241$	261.447			1.08484			0.542421	−	0.840107i	$-0.317508\pi$
$241$	261.447			1.08484			0.542421	+	0.840107i	$0.317508\pi$
$242$		0			0
$243$	119.201	+	211.755i	0.490540	+	0.871419i
$244$	212.435	+	653.808i	0.870636	+	2.67954i
$245$	36.2426	−	49.8837i	0.147929	−	0.203607i
$246$	−209.981	+	361.876i	−0.853583	+	1.47104i
$247$	−5.37024	+	16.5279i	−0.0217419	+	0.0669146i
$248$	388.479	+	126.224i	1.56645	+	0.508970i
$249$	30.6402	+	17.7792i	0.123053	+	0.0714025i
$250$	276.395	+	200.813i	1.10558	+	0.803251i
$251$	−188.638	+	61.2921i	−0.751544	+	0.244192i	−0.659646	−	0.751577i	$-0.729294\pi$
$251$	−188.638	+	61.2921i	−0.751544	+	0.244192i	−0.0918987	+	0.995768i	$0.529294\pi$
$252$	475.641	−	523.648i	1.88746	−	2.07797i
$253$		0			0
$254$			51.2057i			0.201597i
$255$	51.9062	+	57.9008i	0.203554	+	0.227062i
$256$	389.537	+	283.016i	1.52163	+	1.10553i
$257$	−1.09633	−	1.50897i	−0.00426588	−	0.00587148i	0.806879	−	0.590717i	$-0.201155\pi$
$257$	−1.09633	−	1.50897i	−0.00426588	−	0.00587148i	−0.811145	+	0.584846i	$0.801155\pi$
$258$	−169.619	+	17.4542i	−0.657437	+	0.0676521i
$259$	−19.8453	+	61.0776i	−0.0766229	+	0.235821i
$260$	17.8888	+	24.6218i	0.0688031	+	0.0946994i
$261$	−21.2769	−	102.289i	−0.0815205	−	0.391910i
$262$	170.366	+	524.332i	0.650251	+	2.00127i
$263$		−	27.0901i		−	0.103004i	−0.998673	−	0.0515020i	$-0.983599\pi$
$263$		−	27.0901i		−	0.103004i	0.998673	−	0.0515020i	$-0.0164009\pi$
$264$		0			0
$265$	84.1151			0.317416
$266$	−319.485	+	103.807i	−1.20107	+	0.390251i
$267$	46.9935	−	218.744i	0.176006	−	0.819264i
$268$	451.354	−	327.928i	1.68416	−	1.22361i
$269$	−135.856	−	44.1424i	−0.505042	−	0.164098i	0.0454041	−	0.998969i	$-0.485542\pi$
$269$	−135.856	−	44.1424i	−0.505042	−	0.164098i	−0.550446	+	0.834871i	$0.685542\pi$
$270$	−162.707	−	119.846i	−0.602619	−	0.443873i
$271$	−85.2115	+	61.9098i	−0.314434	+	0.228449i	−0.733797	−	0.679369i	$-0.762254\pi$
$271$	−85.2115	+	61.9098i	−0.314434	+	0.228449i	0.419363	+	0.907819i	$0.362254\pi$
$272$	198.455	−	273.150i	0.729613	−	1.00423i
$273$	29.1928	+	32.5642i	0.106933	+	0.119283i
$274$	−289.282			−1.05577
$275$		0			0
$276$	−219.008	−	494.797i	−0.793507	−	1.79274i
$277$	−75.6843	−	232.932i	−0.273229	−	0.840911i	−0.989683	−	0.143277i	$-0.954236\pi$
$277$	−75.6843	−	232.932i	−0.273229	−	0.840911i	0.716454	−	0.697634i	$-0.245764\pi$
$278$	−446.889	+	615.089i	−1.60751	+	2.21255i
$279$	22.9143	−	209.243i	0.0821300	−	0.749976i
$280$	−99.7985	+	307.148i	−0.356423	+	1.09696i
$281$	−61.9247	−	20.1206i	−0.220373	−	0.0716034i	0.196750	−	0.980454i	$-0.436961\pi$
$281$	−61.9247	−	20.1206i	−0.220373	−	0.0716034i	−0.417122	+	0.908850i	$0.636961\pi$
$282$	244.721	−	421.745i	0.867804	−	1.49555i
$283$	−127.482	−	92.6208i	−0.450465	−	0.327282i	0.339314	−	0.940673i	$-0.389805\pi$
$283$	−127.482	−	92.6208i	−0.450465	−	0.327282i	−0.789779	+	0.613391i	$0.789805\pi$
$284$	86.1375	−	27.9878i	0.303301	−	0.0985485i
$285$	26.7668	+	60.4734i	0.0939187	+	0.212187i
$286$		0			0
$287$		−	344.566i		−	1.20058i
$288$	−102.138	+	226.742i	−0.354645	+	0.787300i
$289$	−108.940	−	79.1493i	−0.376954	−	0.273873i
$290$	51.0695	+	70.2912i	0.176102	+	0.242383i
$291$	−23.6972	−	230.287i	−0.0814337	−	0.791365i
$292$	−204.504	+	629.400i	−0.700358	+	2.15548i
$293$	108.158	+	148.867i	0.369139	+	0.508077i	0.952667	−	0.304017i	$-0.0983279\pi$
$293$	108.158	+	148.867i	0.369139	+	0.508077i	−0.583527	+	0.812094i	$0.698328\pi$
$294$	−66.8030	+	310.952i	−0.227221	+	1.05766i
$295$	72.9716	+	224.584i	0.247361	+	0.761300i
$296$		−	126.549i		−	0.427529i
$297$		0			0
$298$	811.906			2.72452
$299$	31.8144	−	10.3371i	0.106403	−	0.0345724i
$300$	−537.071	−	115.381i	−1.79024	−	0.384604i
$301$	113.610	−	82.5421i	0.377440	−	0.274226i
$302$	−930.469	−	302.328i	−3.08102	−	1.00109i
$303$	−38.1846	+	3.92930i	−0.126022	+	0.0129680i
$304$	232.302	−	168.778i	0.764153	−	0.555189i
$305$	−95.0619	+	130.842i	−0.311679	+	0.428989i
$306$	−365.708	−	164.736i	−1.19512	−	0.538353i
$307$	−386.672			−1.25952			−0.629759	−	0.776790i	$-0.716846\pi$
$307$	−386.672			−1.25952			−0.629759	+	0.776790i	$0.716846\pi$
$308$		0			0
$309$	−193.578	+	85.6816i	−0.626465	+	0.277287i
$310$	54.0930	+	166.481i	0.174494	+	0.537036i
$311$	−54.2185	+	74.6253i	−0.174336	+	0.239953i	−0.887239	−	0.461309i	$-0.847380\pi$
$311$	−54.2185	+	74.6253i	−0.174336	+	0.239953i	0.712903	+	0.701262i	$0.247380\pi$
$312$	−74.5388	−	43.2517i	−0.238906	−	0.138627i
$313$	−22.9902	+	70.7565i	−0.0734510	+	0.226059i	−0.981042	−	0.193797i	$-0.937920\pi$
$313$	−22.9902	+	70.7565i	−0.0734510	+	0.226059i	0.907591	+	0.419856i	$0.137920\pi$
$314$	20.6725	+	6.71691i	0.0658361	+	0.0213914i
$315$	165.437	+	18.1170i	0.525196	+	0.0575143i
$316$	−619.274	−	449.929i	−1.95973	−	1.42382i
$317$	498.144	−	161.857i	1.57143	−	0.510589i	0.611600	−	0.791167i	$-0.290526\pi$
$317$	498.144	−	161.857i	1.57143	−	0.510589i	0.959831	+	0.280578i	$0.0905263\pi$
$318$	−396.747	+	175.609i	−1.24763	+	0.552229i
$319$		0			0
$320$			19.9982i			0.0624943i
$321$	−411.511	+	368.907i	−1.28197	+	1.14924i
$322$	523.128	+	380.075i	1.62462	+	1.18036i
$323$	77.1542	+	106.194i	0.238867	+	0.328773i
$324$	701.326	+	155.469i	2.16459	+	0.479843i
$325$	10.4943	−	32.2981i	0.0322901	−	0.0993787i
$326$	−341.430	−	469.939i	−1.04733	−	1.44153i
$327$	171.701	+	36.8871i	0.525078	+	0.112805i
$328$	209.815	+	645.744i	0.639680	+	1.96873i
$329$			401.571i			1.22058i
$330$		0			0
$331$	251.706			0.760441			0.380221	−	0.924896i	$-0.375848\pi$
$331$	251.706			0.760441			0.380221	+	0.924896i	$0.375848\pi$
$332$	99.5968	−	32.3610i	0.299990	−	0.0974728i
$333$	−63.8467	+	13.2806i	−0.191732	+	0.0398818i
$334$	462.051	−	335.699i	1.38339	−	1.00509i
$335$	124.827	+	40.5589i	0.372619	+	0.121071i
$336$	−73.9677	−	718.812i	−0.220142	−	2.13932i
$337$	−40.1679	+	29.1837i	−0.119193	+	0.0865985i	−0.645785	−	0.763520i	$-0.723470\pi$
$337$	−40.1679	+	29.1837i	−0.119193	+	0.0865985i	0.526592	+	0.850118i	$0.323470\pi$
$338$	−350.640	+	482.615i	−1.03740	+	1.42785i
$339$	−339.532	+	304.379i	−1.00157	+	0.897874i
$340$	229.875			0.676104
$341$		0			0
$342$	−252.503	−	229.354i	−0.738313	−	0.670626i
$343$	53.2613	+	163.922i	0.155281	+	0.477905i
$344$	−162.651	+	223.870i	−0.472823	+	0.650785i
$345$	63.8889	−	110.104i	0.185185	−	0.319143i
$346$	42.5894	−	131.077i	0.123091	−	0.378835i
$347$	−437.276	−	142.079i	−1.26016	−	0.409451i	−0.398609	−	0.917121i	$-0.630507\pi$
$347$	−437.276	−	142.079i	−1.26016	−	0.409451i	−0.861551	+	0.507670i	$0.830507\pi$
$348$	−267.140	−	155.010i	−0.767644	−	0.445431i
$349$	−318.550	−	231.440i	−0.912750	−	0.663152i	0.0289588	−	0.999581i	$-0.490781\pi$
$349$	−318.550	−	231.440i	−0.912750	−	0.663152i	−0.941709	+	0.336429i	$0.890781\pi$
$350$	624.323	−	202.855i	1.78378	−	0.579585i
$351$	−13.9990	+	42.1456i	−0.0398833	+	0.120073i
$352$		0			0
$353$			16.9433i			0.0479980i	0.999712	+	0.0239990i	$0.00763985\pi$
$353$			16.9433i			0.0479980i	−0.999712	+	0.0239990i	$0.992360\pi$
$354$	−813.054	−	906.952i	−2.29676	−	2.56201i
$355$	17.2380	+	12.5242i	0.0485578	+	0.0352793i
$356$	−388.761	−	535.084i	−1.09203	−	1.50304i
$357$	328.594	−	33.8132i	0.920432	−	0.0947150i
$358$	−150.930	+	464.516i	−0.421593	+	1.29753i
$359$	44.6059	+	61.3948i	0.124250	+	0.171016i	0.866611	−	0.498985i	$-0.166294\pi$
$359$	44.6059	+	61.3948i	0.124250	+	0.171016i	−0.742360	+	0.670001i	$0.766294\pi$
$360$	−321.073	+	66.7859i	−0.891871	+	0.185516i
$361$	−77.0586	−	237.162i	−0.213459	−	0.656958i
$362$		−	467.565i		−	1.29162i
$363$		0			0
$364$	129.285			0.355179
$365$	−148.071	+	48.1113i	−0.405675	+	0.131812i
$366$	175.220	−	815.605i	0.478742	−	2.22843i
$367$	−501.030	+	364.020i	−1.36520	+	0.991879i	−0.367109	+	0.930178i	$0.619653\pi$
$367$	−501.030	+	364.020i	−1.36520	+	0.991879i	−0.998095	+	0.0617010i	$0.980347\pi$
$368$	−525.665	−	170.799i	−1.42844	−	0.464127i
$369$	303.774	−	173.624i	0.823236	−	0.470526i
$370$	43.8745	−	31.8767i	0.118580	−	0.0861533i
$371$	210.029	−	289.080i	0.566115	−	0.779190i
$372$	−415.364	−	463.334i	−1.11657	−	1.24552i
$373$	365.674			0.980359			0.490179	−	0.871622i	$-0.336931\pi$
$373$	365.674			0.980359			0.490179	+	0.871622i	$0.336931\pi$
$374$		0			0
$375$	−115.641	−	261.264i	−0.308376	−	0.696704i
$376$	−244.527	−	752.576i	−0.650337	−	2.00153i
$377$	11.2232	−	15.4474i	0.0297697	−	0.0409744i
$378$	−818.142	+	259.933i	−2.16440	+	0.687653i
$379$	−126.661	+	389.823i	−0.334198	+	1.02856i	0.632917	+	0.774220i	$0.281857\pi$
$379$	−126.661	+	389.823i	−0.334198	+	1.02856i	−0.967116	+	0.254337i	$0.918143\pi$
$380$	185.931	+	60.4126i	0.489292	+	0.158981i
$381$	21.4921	−	37.0389i	0.0564098	−	0.0972150i
$382$	915.865	+	665.415i	2.39755	+	1.74192i
$383$	50.3695	−	16.3660i	0.131513	−	0.0427311i	−0.242521	−	0.970146i	$-0.577974\pi$
$383$	50.3695	−	16.3660i	0.131513	−	0.0427311i	0.374034	+	0.927415i	$0.377974\pi$
$384$	−175.956	−	397.532i	−0.458219	−	1.03524i
$385$		0			0
$386$		−	525.213i		−	1.36065i
$387$	130.017	+	58.5673i	0.335962	+	0.151337i
$388$	−553.664	−	402.260i	−1.42697	−	1.03675i
$389$	53.2922	+	73.3504i	0.136998	+	0.188561i	0.872004	−	0.489500i	$-0.162821\pi$
$389$	53.2922	+	73.3504i	0.136998	+	0.188561i	−0.735006	+	0.678061i	$0.762821\pi$
$390$	−3.78039	−	36.7375i	−0.00969330	−	0.0941987i
$391$	78.0782	−	240.300i	0.199688	−	0.614578i
$392$	303.380	+	417.567i	0.773929	+	1.06522i
$393$	96.8415	−	450.774i	0.246416	−	1.14701i
$394$	−254.361	−	782.844i	−0.645587	−	1.98691i
$395$		−	180.081i		−	0.455902i
$396$		0			0
$397$	−335.768			−0.845763			−0.422882	−	0.906185i	$-0.638981\pi$
$397$	−335.768			−0.845763			−0.422882	+	0.906185i	$0.638981\pi$
$398$	1328.37	−	431.615i	3.33762	−	1.08446i
$399$	274.664	+	59.0072i	0.688382	+	0.147888i
$400$	−453.955	+	329.818i	−1.13489	+	0.824544i
$401$	17.9951	+	5.84696i	0.0448755	+	0.0145809i	0.331369	−	0.943501i	$-0.392490\pi$
$401$	17.9951	+	5.84696i	0.0448755	+	0.0145809i	−0.286493	+	0.958082i	$0.592490\pi$
$402$	−673.451	+	69.3000i	−1.67525	+	0.172388i
$403$	31.1222	−	22.6116i	0.0772262	−	0.0561081i
$404$	−66.6999	+	91.8045i	−0.165099	+	0.227239i
$405$	67.3901	+	154.980i	0.166395	+	0.382667i
$406$	369.087			0.909082
$407$		0			0
$408$	−595.221	+	263.458i	−1.45888	+	0.645730i
$409$	36.8542	+	113.426i	0.0901081	+	0.277324i	0.985948	−	0.167053i	$-0.0534250\pi$
$409$	36.8542	+	113.426i	0.0901081	+	0.277324i	−0.895840	+	0.444377i	$0.853425\pi$
$410$	−171.029	+	235.402i	−0.417145	+	0.574150i
$411$	209.248	+	121.418i	0.509119	+	0.295420i
$412$	−193.383	+	595.172i	−0.469376	+	1.44459i
$413$	954.034	+	309.984i	2.31001	+	0.750567i
$414$	−71.4787	+	652.713i	−0.172654	+	1.57660i
$415$	19.9315	+	14.4811i	0.0480278	+	0.0348943i
$416$	−43.2243	+	14.0444i	−0.103905	+	0.0337606i
$417$	581.416	−	257.347i	1.39428	−	0.617140i
$418$		0			0
$419$			412.874i			0.985381i	0.870205	+	0.492690i	$0.163986\pi$
$419$			412.874i			0.985381i	−0.870205	+	0.492690i	$0.836014\pi$
$420$	366.332	−	328.405i	0.872219	−	0.781917i
$421$	−489.408	−	355.576i	−1.16249	−	0.844598i	−0.172399	−	0.985027i	$-0.555152\pi$
$421$	−489.408	−	355.576i	−1.16249	−	0.844598i	−0.990091	+	0.140429i	$0.955152\pi$
$422$	430.121	+	592.011i	1.01924	+	1.40287i
$423$	−354.030	+	202.349i	−0.836951	+	0.478365i
$424$	−217.582	+	669.650i	−0.513166	+	1.57936i
$425$	−150.771	−	207.519i	−0.354756	−	0.488280i
$426$	−107.454	−	23.0847i	−0.252239	−	0.0541895i
$427$	212.303	+	653.401i	0.497197	+	1.53021i
$428$			1633.76i			3.81721i
$429$		0			0
$430$	−118.587			−0.275783
$431$	421.718	−	137.024i	0.978464	−	0.317922i	0.224236	−	0.974535i	$-0.428011\pi$
$431$	421.718	−	137.024i	0.978464	−	0.317922i	0.754228	+	0.656613i	$0.228011\pi$
$432$	596.442	−	427.414i	1.38065	−	0.989385i
$433$	−177.158	+	128.713i	−0.409142	+	0.297259i	−0.773254	−	0.634096i	$-0.781372\pi$
$433$	−177.158	+	128.713i	−0.409142	+	0.297259i	0.364112	+	0.931355i	$0.381372\pi$
$434$	707.214	+	229.788i	1.62953	+	0.529465i
$435$	−7.43772	−	72.2791i	−0.0170982	−	0.166159i
$436$	420.008	−	305.154i	0.963322	−	0.699894i
$437$	126.305	−	173.843i	0.289026	−	0.397811i
$438$	597.967	−	536.058i	1.36522	−	1.22388i
$439$	−171.641			−0.390982			−0.195491	−	0.980705i	$-0.562630\pi$
$439$	−171.641			−0.390982			−0.195491	+	0.980705i	$0.562630\pi$
$440$		0			0
$441$	178.834	−	196.884i	0.405519	−	0.446449i
$442$	−22.6519	−	69.7155i	−0.0512487	−	0.157727i
$443$	−348.285	+	479.374i	−0.786197	+	1.08211i	0.208374	+	0.978049i	$0.433183\pi$
$443$	−348.285	+	479.374i	−0.786197	+	1.08211i	−0.994571	+	0.104059i	$0.966817\pi$
$444$	−96.7546	+	166.744i	−0.217916	+	0.375550i
$445$	48.0829	−	147.984i	0.108051	−	0.332548i
$446$	−56.3607	−	18.3127i	−0.126369	−	0.0410598i
$447$	−587.281	−	340.774i	−1.31383	−	0.762358i
$448$	68.7280	+	49.9338i	0.153411	+	0.111459i
$449$	−414.782	+	134.771i	−0.923791	+	0.300158i	−0.732021	−	0.681282i	$-0.761423\pi$
$449$	−414.782	+	134.771i	−0.923791	+	0.300158i	−0.191770	+	0.981440i	$0.561423\pi$
$450$	493.430	+	448.194i	1.09651	+	0.995986i
$451$		0			0
$452$			1347.99i			2.98229i
$453$	546.148	+	609.222i	1.20563	+	1.34486i
$454$	327.534	+	237.967i	0.721440	+	0.524157i
$455$	17.8777	+	24.6065i	0.0392916	+	0.0540803i
$456$	−550.674	+	56.6658i	−1.20762	+	0.124267i
$457$	−73.7134	+	226.866i	−0.161298	+	0.496425i	−0.998744	−	0.0500945i	$-0.984048\pi$
$457$	−73.7134	+	226.866i	−0.161298	+	0.496425i	0.837446	+	0.546520i	$0.184048\pi$
$458$	777.249	+	1069.79i	1.69705	+	2.33579i
$459$	195.386	+	272.654i	0.425678	+	0.594018i
$460$	−116.288	−	357.897i	−0.252800	−	0.778037i
$461$		−	711.175i		−	1.54268i	−0.636424	−	0.771339i	$-0.719587\pi$
$461$		−	711.175i		−	1.54268i	0.636424	−	0.771339i	$-0.280413\pi$
$462$		0			0
$463$	−461.487			−0.996732			−0.498366	−	0.866967i	$-0.666066\pi$
$463$	−461.487			−0.996732			−0.498366	+	0.866967i	$0.666066\pi$
$464$	−300.046	+	97.4908i	−0.646651	+	0.210110i
$465$	30.7483	−	143.126i	0.0661253	−	0.307797i
$466$	506.545	−	368.026i	1.08701	−	0.789756i
$467$	46.0163	+	14.9516i	0.0985361	+	0.0320163i	0.357870	−	0.933771i	$-0.383503\pi$
$467$	46.0163	+	14.9516i	0.0985361	+	0.0320163i	−0.259334	+	0.965788i	$0.583503\pi$
$468$	65.1457	+	113.979i	0.139200	+	0.243546i
$469$	451.073	−	327.724i	0.961777	−	0.698772i
$470$	199.324	−	274.346i	0.424094	−	0.583716i
$471$	−12.1339	−	13.5353i	−0.0257621	−	0.0287373i
$472$	−1976.69			−4.18790
$473$		0			0
$474$	375.960	+	849.393i	0.793164	+	1.79197i
$475$	−67.4117	−	207.472i	−0.141919	−	0.436783i
$476$	573.980	−	790.015i	1.20584	−	1.65970i
$477$	360.688	+	39.4990i	0.756159	+	0.0828072i
$478$	382.834	−	1178.24i	0.800908	−	2.46494i
$479$	163.035	+	52.9731i	0.340364	+	0.110591i	0.474212	−	0.880411i	$-0.342733\pi$
$479$	163.035	+	52.9731i	0.340364	+	0.110591i	−0.133847	+	0.991002i	$0.542733\pi$
$480$	−86.8018	+	149.592i	−0.180837	+	0.311650i
$481$	−9.64197	−	7.00530i	−0.0200457	−	0.0145640i
$482$	−891.979	+	289.822i	−1.85058	+	0.601290i
$483$	−218.872	−	494.489i	−0.453150	−	1.02379i
$484$		0			0
$485$		−	161.002i		−	0.331964i
$486$	−641.415	−	590.306i	−1.31978	−	1.21462i
$487$	400.866	+	291.247i	0.823134	+	0.598042i	0.917609	−	0.397485i	$-0.130117\pi$
$487$	400.866	+	291.247i	0.823134	+	0.598042i	−0.0944742	+	0.995527i	$0.530117\pi$
$488$	−795.745	−	1095.25i	−1.63062	−	2.24436i
$489$	49.7256	+	483.229i	0.101688	+	0.988198i
$490$	−68.3515	+	210.364i	−0.139493	+	0.429315i
$491$	194.115	+	267.177i	0.395347	+	0.544148i	0.959569	−	0.281475i	$-0.0908237\pi$
$491$	194.115	+	267.177i	0.395347	+	0.544148i	−0.564222	+	0.825623i	$0.690824\pi$
$492$	217.255	−	1011.27i	0.441575	−	2.05542i
$493$	−44.5665	−	137.162i	−0.0903986	−	0.278218i
$494$		−	62.3413i		−	0.126197i
$495$		0			0
$496$	−635.619			−1.28149
$497$	86.0839	−	27.9704i	0.173207	−	0.0562784i
$498$	−124.244	−	26.6918i	−0.249486	−	0.0535980i
$499$	−88.8306	+	64.5392i	−0.178017	+	0.129337i	−0.673226	−	0.739437i	$-0.735092\pi$
$499$	−88.8306	+	64.5392i	−0.178017	+	0.129337i	0.495208	+	0.868774i	$0.335092\pi$
$500$	−803.279	−	261.001i	−1.60656	−	0.522003i
$501$	−475.118	+	48.8909i	−0.948339	+	0.0975867i
$502$	575.631	−	418.220i	1.14668	−	0.833108i
$503$	336.038	−	462.516i	0.668067	−	0.919516i	−0.331647	−	0.943403i	$-0.607604\pi$
$503$	336.038	−	462.516i	0.668067	−	0.919516i	0.999715	+	0.0238878i	$0.00760445\pi$
$504$	−572.170	+	1270.20i	−1.13526	+	2.52023i
$505$	−26.6963			−0.0528639
$506$		0			0
$507$	456.194	−	201.921i	0.899791	−	0.398267i
$508$	−39.1191	−	120.396i	−0.0770060	−	0.237000i
$509$	317.947	−	437.617i	0.624651	−	0.859758i	−0.373031	−	0.927819i	$-0.621681\pi$
$509$	317.947	−	437.617i	0.624651	−	0.859758i	0.997681	+	0.0680613i	$0.0216813\pi$
$510$	−241.273	−	140.001i	−0.473085	−	0.274511i
$511$	−204.377	+	629.008i	−0.399955	+	1.23094i
$512$	−1091.44	−	354.631i	−2.13172	−	0.692639i
$513$	86.3797	+	271.881i	0.168381	+	0.529982i
$514$	5.41310	+	3.93284i	0.0105313	+	0.00765145i
$515$	−140.019	+	45.4949i	−0.271881	+	0.0883395i
$516$	385.477	−	170.620i	0.747049	−	0.330660i
$517$		0			0
$518$		−	230.378i		−	0.444745i
$519$	−85.8221	+	76.9368i	−0.165361	+	0.148240i
$520$	−48.4877	−	35.2284i	−0.0932456	−	0.0677469i
$521$	198.606	+	273.357i	0.381201	+	0.524678i	0.955902	−	0.293685i	$-0.0948818\pi$
$521$	198.606	+	273.357i	0.381201	+	0.524678i	−0.574701	+	0.818363i	$0.694882\pi$
$522$	185.980	+	325.392i	0.356284	+	0.623356i
$523$	−95.0022	+	292.387i	−0.181649	+	0.559057i	−0.999875	−	0.0158400i	$-0.994958\pi$
$523$	−95.0022	+	292.387i	−0.181649	+	0.559057i	0.818226	+	0.574897i	$0.194958\pi$
$524$	−801.135	−	1102.67i	−1.52888	−	2.10433i
$525$	−536.737	−	115.309i	−1.02236	−	0.219637i
$526$	30.0301	+	92.4232i	0.0570915	+	0.175710i
$527$		−	290.564i		−	0.551355i
$528$		0			0
$529$	115.375			0.218100
$530$	−286.976	+	93.2441i	−0.541464	+	0.175932i
$531$	207.444	+	997.287i	0.390666	+	1.87813i
$532$	671.875	−	488.146i	1.26292	−	0.917568i
$533$	60.8151	+	19.7600i	0.114100	+	0.0370732i
$534$	82.1557	+	798.382i	0.153850	+	1.49510i
$535$	−310.950	+	225.919i	−0.581216	+	0.422278i
$536$	−645.788	+	888.850i	−1.20483	+	1.65830i
$537$	304.140	−	272.652i	0.566369	−	0.507732i
$538$	512.434			0.952480
$539$		0			0
$540$	474.118	+	157.482i	0.877996	+	0.291634i
$541$	25.5563	+	78.6541i	0.0472389	+	0.145387i	0.971894	−	0.235420i	$-0.0756465\pi$
$541$	25.5563	+	78.6541i	0.0472389	+	0.145387i	−0.924655	+	0.380806i	$0.875646\pi$
$542$	222.088	−	305.677i	0.409756	−	0.563980i
$543$	−196.247	+	338.206i	−0.361412	+	0.622848i
$544$	−106.080	+	326.480i	−0.195000	+	0.600148i
$545$	116.158	+	37.7422i	0.213135	+	0.0692517i
$546$	−135.696	−	78.7384i	−0.248527	−	0.144209i
$547$	−320.933	−	233.172i	−0.586715	−	0.426273i	0.254424	−	0.967093i	$-0.418114\pi$
$547$	−320.933	−	233.172i	−0.586715	−	0.426273i	−0.841139	+	0.540819i	$0.818114\pi$
$548$	680.166	−	220.999i	1.24118	−	0.403283i
$549$	−469.069	+	516.413i	−0.854407	+	0.940642i
$550$		0			0
$551$		−	122.653i		−	0.222601i
$552$	711.289	+	793.435i	1.28857	+	1.43738i
$553$	−618.888	−	449.649i	−1.11915	−	0.813108i
$554$	516.425	+	710.798i	0.932174	+	1.28303i
$555$	−45.1153	+	4.64249i	−0.0812889	+	0.00836485i
$556$	580.832	−	1787.62i	1.04466	−	3.21514i
$557$	225.174	+	309.925i	0.404262	+	0.556419i	0.961807	−	0.273728i	$-0.0882567\pi$
$557$	225.174	+	309.925i	0.404262	+	0.556419i	−0.557545	+	0.830146i	$0.688257\pi$
$558$	153.776	+	739.277i	0.275584	+	1.32487i
$559$	8.05326	+	24.7854i	0.0144066	+	0.0443388i
$560$		−	502.548i		−	0.897407i
$561$		0			0
$562$	233.573			0.415610
$563$	−137.748	+	44.7570i	−0.244667	+	0.0794973i	−0.428784	−	0.903407i	$-0.641058\pi$
$563$	−137.748	+	44.7570i	−0.244667	+	0.0794973i	0.184116	+	0.982904i	$0.441058\pi$
$564$	−253.197	+	1178.57i	−0.448932	+	2.08967i
$565$	−256.561	+	186.402i	−0.454089	+	0.329915i
$566$	537.602	+	174.677i	0.949827	+	0.308617i
$567$	700.890	+	155.373i	1.23614	+	0.274026i
$568$	−144.296	+	104.837i	−0.254043	+	0.184573i
$569$	542.614	−	746.845i	0.953628	−	1.31256i	0.00373108	−	0.999993i	$-0.498812\pi$
$569$	542.614	−	746.845i	0.953628	−	1.31256i	0.949897	−	0.312563i	$-0.101188\pi$
$570$	−158.357	−	176.645i	−0.277819	−	0.309904i
$571$	−421.725			−0.738573			−0.369287	−	0.929316i	$-0.620398\pi$
$571$	−421.725			−0.738573			−0.369287	+	0.929316i	$0.620398\pi$
$572$		0			0
$573$	−383.189	−	865.726i	−0.668742	−	1.51087i
$574$	381.962	+	1175.56i	0.665439	+	2.04801i
$575$	−246.819	+	339.717i	−0.429250	+	0.590812i
$576$	−9.39080	+	85.7527i	−0.0163035	+	0.148876i
$577$	142.274	−	437.874i	0.246575	−	0.758880i	−0.748798	−	0.662798i	$-0.769369\pi$
$577$	142.274	−	437.874i	0.246575	−	0.758880i	0.995373	−	0.0960821i	$-0.0306311\pi$
$578$	459.409	+	149.271i	0.794825	+	0.258254i
$579$	−220.443	+	379.905i	−0.380730	+	0.656140i
$580$	−173.775	−	126.255i	−0.299613	−	0.217681i
$581$	99.5349	−	32.3409i	0.171317	−	0.0556641i
$582$	336.128	+	759.403i	0.577539	+	1.30482i
$583$		0			0
$584$		−	1303.26i		−	2.23161i
$585$	−12.6850	+	28.1602i	−0.0216838	+	0.0481371i
$586$	−534.025	−	387.992i	−0.911306	−	0.662102i
$587$	24.9599	+	34.3544i	0.0425212	+	0.0585254i	0.829748	−	0.558138i	$-0.188484\pi$
$587$	24.9599	+	34.3544i	0.0425212	+	0.0585254i	−0.787227	+	0.616663i	$0.788484\pi$
$588$	−80.4856	−	782.152i	−0.136880	−	1.33019i
$589$	76.3620	−	235.018i	0.129647	−	0.399012i
$590$	−497.915	−	685.321i	−0.843923	−	1.16156i
$591$	−144.587	+	673.020i	−0.244649	+	1.13878i
$592$	60.8521	+	187.283i	0.102791	+	0.316357i
$593$			106.267i			0.179203i	0.995978	+	0.0896015i	$0.0285593\pi$
$593$			106.267i			0.179203i	−0.995978	+	0.0896015i	$0.971441\pi$
$594$		0			0
$595$	229.732			0.386105
$596$	−1908.97	+	620.263i	−3.20297	+	1.04071i
$597$	−1142.02	−	245.344i	−1.91293	−	0.410962i
$598$	−97.0823	+	70.5344i	−0.162345	+	0.117951i
$599$	−692.381	−	224.968i	−1.15589	−	0.375573i	−0.332534	−	0.943091i	$-0.607904\pi$
$599$	−692.381	−	224.968i	−1.15589	−	0.375573i	−0.823361	+	0.567518i	$0.807904\pi$
$600$	1076.10	−	110.734i	1.79350	−	0.184557i
$601$	−95.9442	+	69.7075i	−0.159641	+	0.115986i	−0.664738	−	0.747077i	$-0.731457\pi$
$601$	−95.9442	+	69.7075i	−0.159641	+	0.115986i	0.505097	+	0.863063i	$0.331457\pi$
$602$	−296.101	+	407.549i	−0.491863	+	0.676991i
$603$	516.218	+	232.535i	0.856083	+	0.385629i
$604$	2418.71			4.00448
$605$		0			0
$606$	125.919	−	55.7343i	0.207787	−	0.0919708i
$607$	−220.392	−	678.296i	−0.363084	−	1.11746i	−0.951172	−	0.308660i	$-0.900119\pi$
$607$	−220.392	−	678.296i	−0.363084	−	1.11746i	0.588089	−	0.808796i	$-0.299881\pi$
$608$	−171.602	+	236.190i	−0.282240	+	0.388470i
$609$	−266.974	−	154.914i	−0.438381	−	0.254374i
$610$	179.281	−	551.771i	0.293904	−	0.904543i
$611$	−70.8764	−	23.0291i	−0.116001	−	0.0376909i
$612$	985.711	+	107.945i	1.61064	+	0.176381i
$613$	556.171	+	404.082i	0.907294	+	0.659188i	0.940329	−	0.340267i	$-0.110517\pi$
$613$	556.171	+	404.082i	0.907294	+	0.659188i	−0.0330350	+	0.999454i	$0.510517\pi$
$614$	1319.21	−	428.637i	2.14855	−	0.698106i
$615$	222.515	−	98.4898i	0.361812	−	0.160146i
$616$		0			0
$617$		−	762.156i		−	1.23526i	−0.786468	−	0.617631i	$-0.788093\pi$
$617$		−	762.156i		−	1.23526i	0.786468	−	0.617631i	$-0.211907\pi$
$618$	565.448	−	506.906i	0.914965	−	0.820237i
$619$	429.344	+	311.937i	0.693609	+	0.503936i	0.877845	−	0.478946i	$-0.158981\pi$
$619$	429.344	+	311.937i	0.693609	+	0.503936i	−0.184236	+	0.982882i	$0.558981\pi$
$620$	−254.369	−	350.110i	−0.410273	−	0.564693i
$621$	325.660	−	442.129i	0.524413	−	0.711963i
$622$	102.253	−	314.702i	0.164394	−	0.505952i
$623$	−388.519	−	534.751i	−0.623626	−	0.858348i
$624$	131.110	+	28.1670i	0.210113	+	0.0451394i
$625$	98.1039	+	301.933i	0.156966	+	0.483093i
$626$		−	266.885i		−	0.426334i
$627$		0			0
$628$	−53.7372			−0.0855688
$629$	−85.6138	+	27.8176i	−0.136111	+	0.0442252i
$630$	−584.504	+	121.582i	−0.927784	+	0.192987i
$631$	−547.258	+	397.607i	−0.867288	+	0.630121i	−0.929858	−	0.367919i	$-0.880070\pi$
$631$	−547.258	+	397.607i	−0.867288	+	0.630121i	0.0625701	+	0.998041i	$0.480070\pi$
$632$	1433.65	+	465.820i	2.26843	+	0.737058i
$633$	−62.6424	−	608.754i	−0.0989612	−	0.961696i
$634$	−1520.09	+	1104.41i	−2.39763	+	1.74198i
$635$	17.5053	−	24.0939i	0.0275674	−	0.0379432i
$636$	798.683	−	715.994i	1.25579	−	1.12578i
$637$	48.6093			0.0763097
$638$		0			0
$639$	68.0360	+	61.7987i	0.106473	+	0.0967115i
$640$	−93.4285	−	287.543i	−0.145982	−	0.449287i
$641$	461.931	−	635.794i	0.720641	−	0.991878i	−0.278861	−	0.960331i	$-0.589957\pi$
$641$	461.931	−	635.794i	0.720641	−	0.991878i	0.999502	−	0.0315462i	$-0.0100431\pi$
$642$	995.009	−	1714.77i	1.54986	−	2.67098i
$643$	−262.574	+	808.119i	−0.408357	+	1.25679i	0.509702	+	0.860351i	$0.329756\pi$
$643$	−262.574	+	808.119i	−0.408357	+	1.25679i	−0.918059	+	0.396443i	$0.870244\pi$
$644$	−1520.35	−	493.992i	−2.36079	−	0.767069i
$645$	85.7780	+	49.7733i	0.132989	+	0.0771680i
$646$	−380.946	−	276.773i	−0.589699	−	0.428441i
$647$	−1112.14	+	361.357i	−1.71892	+	0.558512i	−0.991778	−	0.127971i	$-0.959154\pi$
$647$	−1112.14	+	361.357i	−1.71892	+	0.558512i	−0.727146	+	0.686483i	$0.759154\pi$
$648$	−1408.13	+	135.609i	−2.17305	+	0.209274i
$649$		0			0
$650$			121.825i			0.187423i
$651$	−415.106	−	463.046i	−0.637644	−	0.711284i
$652$	1161.79	+	844.092i	1.78189	+	1.29462i
$653$	314.778	+	433.255i	0.482049	+	0.663484i	0.978897	−	0.204354i	$-0.0655092\pi$
$653$	314.778	+	433.255i	0.482049	+	0.663484i	−0.496848	+	0.867838i	$0.665509\pi$
$654$	−626.681	+	64.4872i	−0.958228	+	0.0986043i
$655$	99.0863	−	304.956i	0.151277	−	0.465582i
$656$	−621.024	−	854.767i	−0.946684	−	1.30300i
$657$	−657.526	+	136.771i	−1.00080	+	0.208175i
$658$	−445.153	−	1370.04i	−0.676525	−	2.08213i
$659$		−	138.756i		−	0.210555i	−0.994443	−	0.105278i	$-0.966427\pi$
$659$		−	138.756i		−	0.210555i	0.994443	−	0.105278i	$-0.0335731\pi$
$660$		0			0
$661$	27.1690			0.0411029			0.0205515	−	0.999789i	$-0.493458\pi$
$661$	27.1690			0.0411029			0.0205515	+	0.999789i	$0.493458\pi$
$662$	−858.746	+	279.023i	−1.29720	+	0.421485i
$663$	−12.8761	+	59.9352i	−0.0194210	+	0.0903999i
$664$	−166.843	+	121.219i	−0.251270	+	0.182558i
$665$	185.815	+	60.3751i	0.279422	+	0.0907895i
$666$	203.104	−	116.085i	0.304961	−	0.174303i
$667$	−191.004	+	138.773i	−0.286363	+	0.208055i
$668$	−829.924	+	1142.29i	−1.24240	+	1.71002i
$669$	33.0814	+	36.9020i	0.0494491	+	0.0551599i
$670$	−470.835			−0.702738
$671$		0			0
$672$	297.367	+	671.831i	0.442511	+	0.999749i
$673$	203.174	+	625.305i	0.301893	+	0.929131i	0.980818	+	0.194924i	$0.0624459\pi$
$673$	203.174	+	625.305i	0.301893	+	0.929131i	−0.678926	+	0.734207i	$0.737554\pi$
$674$	104.690	−	144.093i	0.155326	−	0.213788i
$675$	−168.799	−	531.298i	−0.250073	−	0.787108i
$676$	455.735	−	1402.61i	0.674165	−	2.07487i
$677$	−581.347	−	188.891i	−0.858711	−	0.279012i	−0.153621	−	0.988130i	$-0.549093\pi$
$677$	−581.347	−	188.891i	−0.858711	−	0.279012i	−0.705090	+	0.709118i	$0.749093\pi$
$678$	820.968	−	1414.83i	1.21087	−	2.08677i
$679$	−553.319	−	402.010i	−0.814903	−	0.592062i
$680$	−430.536	+	139.890i	−0.633142	+	0.205720i
$681$	−137.037	−	309.603i	−0.201229	−	0.454630i
$682$		0			0
$683$			990.520i			1.45025i	0.688618	+	0.725124i	$0.258218\pi$
$683$			990.520i			1.45025i	−0.688618	+	0.725124i	$0.741782\pi$
$684$	768.908	+	346.361i	1.12413	+	0.506376i
$685$	136.116	+	98.8943i	0.198710	+	0.144371i
$686$	−363.423	−	500.209i	−0.529772	−	0.729168i
$687$	−113.198	−	1100.05i	−0.164771	−	1.60123i
$688$	133.063	−	409.525i	0.193405	−	0.595240i
$689$	38.9772	+	53.6476i	0.0565707	+	0.0778629i
$690$	−95.9159	+	446.466i	−0.139009	+	0.647052i
$691$	177.091	+	545.029i	0.256282	+	0.788754i	0.993574	+	0.113181i	$0.0361038\pi$
$691$	177.091	+	545.029i	0.256282	+	0.788754i	−0.737293	+	0.675573i	$0.763896\pi$
$692$			340.727i			0.492380i
$693$		0			0
$694$	1649.35			2.37659
$695$	420.551	−	136.645i	0.605109	−	0.196612i
$696$	594.661	+	127.753i	0.854398	+	0.183554i
$697$	390.744	−	283.892i	0.560608	−	0.407306i
$698$	1343.35	+	436.482i	1.92458	+	0.625333i
$699$	−520.870	+	53.5990i	−0.745165	+	0.0766795i
$700$	−1312.95	+	953.913i	−1.87564	+	1.36273i
$701$	−481.412	+	662.606i	−0.686750	+	0.945230i	−0.999990	−	0.00444396i	$-0.998585\pi$
$701$	−481.412	+	662.606i	−0.686750	+	0.945230i	0.313240	+	0.949674i	$0.398585\pi$
$702$	1.04087	−	159.307i	0.00148272	−	0.226932i
$703$	−76.5580			−0.108902
$704$		0			0
$705$	−259.327	+	114.784i	−0.367840	+	0.162814i
$706$	−18.7821	−	57.8054i	−0.0266036	−	0.0818774i
$707$	−66.6584	+	91.7474i	−0.0942834	+	0.129770i
$708$	2604.55	+	1511.31i	3.67874	+	2.13462i
$709$	55.5742	−	171.040i	0.0783840	−	0.241241i	−0.904185	−	0.427142i	$-0.859520\pi$
$709$	55.5742	−	171.040i	0.0783840	−	0.241241i	0.982568	+	0.185901i	$0.0595204\pi$
$710$	−72.6944	−	23.6199i	−0.102387	−	0.0332674i
$711$	84.5631	−	772.194i	0.118935	−	1.08607i
$712$	1053.74	+	765.586i	1.47997	+	1.07526i
$713$	−452.384	+	146.989i	−0.634480	+	0.206155i
$714$	−1083.58	+	479.617i	−1.51762	+	0.671732i
$715$		0			0
$716$		−	1207.48i		−	1.68643i
$717$	−771.450	+	691.581i	−1.07594	+	0.964548i
$718$	−220.240	−	160.014i	−0.306741	−	0.222860i
$719$	−391.663	−	539.078i	−0.544733	−	0.749761i	0.444553	−	0.895753i	$-0.353363\pi$
$719$	−391.663	−	539.078i	−0.544733	−	0.749761i	−0.989286	+	0.145992i	$0.953363\pi$
$720$	443.053	−	253.230i	0.615351	−	0.351708i
$721$	−193.263	+	594.801i	−0.268048	+	0.824967i
$722$	525.802	+	723.704i	0.728257	+	1.00236i
$723$	766.845	+	164.744i	1.06064	+	0.227862i
$724$	357.200	+	1099.35i	0.493371	+	1.51844i
$725$			239.684i			0.330598i
$726$		0			0
$727$	162.429			0.223424			0.111712	−	0.993741i	$-0.464367\pi$
$727$	162.429			0.223424			0.111712	+	0.993741i	$0.464367\pi$
$728$	−242.140	+	78.6760i	−0.332610	+	0.108071i
$729$	216.195	+	696.205i	0.296563	+	0.955013i
$730$	451.842	−	328.283i	0.618962	−	0.449702i
$731$	187.208	+	60.8277i	0.256099	+	0.0832116i
$732$	211.108	+	2051.53i	0.288399	+	2.80264i
$733$	946.453	−	687.638i	1.29120	−	0.938115i	0.291376	−	0.956609i	$-0.405887\pi$
$733$	946.453	−	687.638i	1.29120	−	0.938115i	0.999829	+	0.0184934i	$0.00588696\pi$
$734$	1305.84	−	1797.33i	1.77907	−	2.44868i
$735$	137.735	−	123.475i	0.187395	−	0.167994i
$736$	561.967			0.763542
$737$		0			0
$738$	−843.919	+	929.096i	−1.14352	+	1.25894i
$739$	74.8985	+	230.514i	0.101351	+	0.311927i	0.988857	−	0.148870i	$-0.0475636\pi$
$739$	74.8985	+	230.514i	0.101351	+	0.311927i	−0.887506	+	0.460797i	$0.847564\pi$
$740$	−78.8063	+	108.468i	−0.106495	+	0.146578i
$741$	−26.1660	+	45.0937i	−0.0353117	+	0.0608552i
$742$	−396.102	+	1219.08i	−0.533830	+	1.64296i
$743$	783.342	+	254.523i	1.05430	+	0.342562i	0.784353	−	0.620314i	$-0.212995\pi$
$743$	783.342	+	254.523i	1.05430	+	0.342562i	0.269943	+	0.962876i	$0.412995\pi$
$744$	1059.90	+	615.016i	1.42460	+	0.826635i
$745$	−382.028	−	277.560i	−0.512789	−	0.372563i
$746$	−1247.57	+	405.360i	−1.67235	+	0.543378i
$747$	78.6669	+	71.4549i	0.105310	+	0.0956559i
$748$		0			0
$749$			1632.75i			2.17990i
$750$	684.151	+	763.163i	0.912202	+	1.01755i
$751$	4.96588	+	3.60793i	0.00661236	+	0.00480416i	0.591087	−	0.806608i	$-0.298699\pi$
$751$	4.96588	+	3.60793i	0.00661236	+	0.00480416i	−0.584474	+	0.811412i	$0.698699\pi$
$752$	723.767	+	996.179i	0.962456	+	1.32471i
$753$	−591.910	+	60.9092i	−0.786069	+	0.0808887i
$754$	−21.1662	+	65.1430i	−0.0280719	+	0.0863965i
$755$	334.461	+	460.347i	0.442995	+	0.609731i
$756$	1725.06	−	1236.19i	2.28182	−	1.63517i
$757$	−340.620	−	1048.32i	−0.449961	−	1.38484i	−0.876951	−	0.480580i	$-0.840426\pi$
$757$	−340.620	−	1048.32i	−0.449961	−	1.38484i	0.426990	−	0.904256i	$-0.359574\pi$
$758$		−	1470.37i		−	1.93980i
$759$		0			0
$760$	−384.996			−0.506574
$761$	1141.53	−	370.907i	1.50004	−	0.487394i	0.560013	−	0.828484i	$-0.310796\pi$
$761$	1141.53	−	370.907i	1.50004	−	0.487394i	0.940031	+	0.341090i	$0.110796\pi$
$762$	−32.2660	+	150.190i	−0.0423438	+	0.197100i
$763$	419.747	−	304.964i	0.550127	−	0.399691i
$764$	−2661.75	−	864.856i	−3.48397	−	1.13201i
$765$	115.760	+	202.535i	0.151321	+	0.264752i
$766$	−153.703	+	111.672i	−0.200657	+	0.145786i
$767$	−109.423	+	150.608i	−0.142664	+	0.196360i
$768$	964.209	+	1075.56i	1.25548	+	1.40047i
$769$	1038.16			1.35001			0.675007	−	0.737811i	$-0.264141\pi$
$769$	1038.16			1.35001			0.675007	+	0.737811i	$0.264141\pi$
$770$		0			0
$771$	−2.26479	−	5.11676i	−0.00293747	−	0.00663652i
$772$	401.241	+	1234.89i	0.519742	+	1.59960i
$773$	344.566	−	474.255i	0.445752	−	0.613525i	−0.525726	−	0.850654i	$-0.676206\pi$
$773$	344.566	−	474.255i	0.445752	−	0.613525i	0.971478	+	0.237129i	$0.0762063\pi$
$774$	−508.503	−	55.6863i	−0.656981	−	0.0719461i
$775$	−149.223	+	459.262i	−0.192546	+	0.592596i
$776$	1281.76	+	416.468i	1.65175	+	0.536686i
$777$	−96.6944	+	166.640i	−0.124446	+	0.214466i
$778$	−263.128	−	191.174i	−0.338211	−	0.245725i
$779$	390.656	−	126.932i	0.501483	−	0.162942i
$780$	36.9545	+	83.4899i	0.0473775	+	0.107038i
$781$		0			0
$782$			906.383i			1.15906i
$783$	2.04786	−	313.427i	0.00261541	−	0.400290i
$784$	−649.773	−	472.088i	−0.828792	−	0.602153i
$785$	−7.43084	−	10.2277i	−0.00946603	−	0.0130289i
$786$	169.301	+	1645.26i	0.215396	+	2.09320i
$787$	−115.407	+	355.185i	−0.146641	+	0.451315i	−0.997218	−	0.0745349i	$-0.976253\pi$
$787$	−115.407	+	355.185i	−0.146641	+	0.451315i	0.850577	+	0.525850i	$0.176253\pi$
$788$	1196.12	+	1646.32i	1.51792	+	2.08924i
$789$	17.0701	−	79.4573i	0.0216351	−	0.100706i
$790$	199.626	+	614.384i	0.252691	+	0.777701i
$791$			1347.16i			1.70311i
$792$		0			0
$793$	−127.499			−0.160780
$794$	1145.54	−	372.208i	1.44275	−	0.468776i
$795$	246.716	+	53.0030i	0.310335	+	0.0666704i
$796$	−2793.57	+	2029.65i	−3.50951	+	2.54981i
$797$	795.852	+	258.588i	0.998560	+	0.324452i	0.762290	−	0.647236i	$-0.224075\pi$
$797$	795.852	+	258.588i	0.998560	+	0.324452i	0.236270	+	0.971687i	$0.424075\pi$
$798$	−1002.48	+	103.158i	−1.25625	+	0.129271i
$799$	−455.389	+	330.859i	−0.569948	+	0.414092i
$800$	335.337	−	461.552i	0.419172	−	0.576940i
$801$	275.671	−	611.980i	0.344159	−	0.764020i
$802$	−67.8754			−0.0846326
$803$		0			0
$804$	1530.49	−	677.429i	1.90360	−	0.842573i
$805$	−116.216	−	357.675i	−0.144367	−	0.444316i
$806$	−81.1140	+	111.644i	−0.100638	+	0.138516i
$807$	−370.662	−	215.080i	−0.459309	−	0.266517i
$808$	69.0558	−	212.532i	0.0854650	−	0.263034i
$809$	−493.440	−	160.328i	−0.609938	−	0.198181i	−0.0122700	−	0.999925i	$-0.503906\pi$
$809$	−493.440	−	160.328i	−0.609938	−	0.198181i	−0.597668	+	0.801744i	$0.703906\pi$
$810$	−401.715	−	454.042i	−0.495944	−	0.560546i
$811$	633.194	+	460.042i	0.780757	+	0.567253i	0.905206	−	0.424973i	$-0.139716\pi$
$811$	633.194	+	460.042i	0.780757	+	0.567253i	−0.124449	+	0.992226i	$0.539716\pi$
$812$	−867.806	+	281.967i	−1.06873	+	0.347250i
$813$	−288.943	+	127.892i	−0.355403	+	0.157309i
$814$		0			0
$815$			337.843i			0.414531i
$816$	754.202	−	676.118i	0.924267	−	0.828576i
$817$	135.435	+	98.3990i	0.165771	+	0.120439i
$818$	−251.471	−	346.120i	−0.307422	−	0.423130i
$819$	65.1052	+	113.909i	0.0794936	+	0.139082i
$820$	222.291	−	684.141i	0.271086	−	0.834318i
$821$	324.234	+	446.270i	0.394926	+	0.543569i	0.959462	−	0.281840i	$-0.0909446\pi$
$821$	324.234	+	446.270i	0.394926	+	0.543569i	−0.564535	+	0.825409i	$0.690945\pi$
$822$	−848.486	−	182.284i	−1.03222	−	0.221756i
$823$	−14.2681	−	43.9128i	−0.0173367	−	0.0533570i	0.942014	−	0.335574i	$-0.108930\pi$
$823$	−14.2681	−	43.9128i	−0.0173367	−	0.0533570i	−0.959351	+	0.282217i	$0.908930\pi$
$824$		−	1232.39i		−	1.49562i
$825$		0			0
$826$	−3598.50			−4.35654
$827$	−567.030	+	184.239i	−0.685648	+	0.222780i	−0.631066	−	0.775729i	$-0.717382\pi$
$827$	−567.030	+	184.239i	−0.685648	+	0.222780i	−0.0545813	+	0.998509i	$0.517382\pi$
$828$	−330.583	−	1589.28i	−0.399255	−	1.91942i
$829$	1122.16	−	815.300i	1.35364	−	0.983474i	0.354815	−	0.934937i	$-0.384544\pi$
$829$	1122.16	−	815.300i	1.35364	−	0.983474i	0.998821	−	0.0485378i	$-0.0154561\pi$
$830$	−84.0532	−	27.3105i	−0.101269	−	0.0329043i
$831$	−75.2116	−	730.899i	−0.0905073	−	0.879542i
$832$	−12.7546	+	9.26674i	−0.0153300	+	0.0111379i
$833$	215.808	−	297.034i	0.259073	−	0.356584i
$834$	−1698.34	+	1522.51i	−2.03638	+	1.82555i
$835$	−332.172			−0.397811
$836$		0			0
$837$	199.059	−	599.288i	0.237824	−	0.715995i
$838$	−457.683	−	1408.60i	−0.546161	−	1.68091i
$839$	978.665	−	1347.02i	1.16647	−	1.60550i	0.482739	−	0.875764i	$-0.339642\pi$
$839$	978.665	−	1347.02i	1.16647	−	1.60550i	0.683727	−	0.729738i	$-0.260358\pi$
$840$	−486.258	+	838.004i	−0.578879	+	0.997624i
$841$	218.240	−	671.673i	0.259500	−	0.798660i
$842$	2063.88	+	670.595i	2.45116	+	0.796432i
$843$	−168.951	−	98.0354i	−0.200417	−	0.116293i
$844$	−1463.58	−	1063.36i	−1.73410	−	1.25990i
$845$	329.975	−	107.215i	0.390503	−	0.126882i
$846$	983.537	−	1082.81i	1.16257	−	1.27991i
$847$		0			0
$848$		−	1095.66i		−	1.29206i
$849$	−315.551	−	351.993i	−0.371673	−	0.414597i
$850$	744.427	+	540.858i	0.875797	+	0.636303i
$851$	86.6196	+	119.222i	0.101786	+	0.140096i
$852$	270.284	−	27.8130i	0.317234	−	0.0326443i
$853$	251.091	−	772.780i	0.294363	−	0.905956i	−0.689072	−	0.724693i	$-0.741982\pi$
$853$	251.091	−	772.780i	0.294363	−	0.905956i	0.983435	−	0.181263i	$-0.0580184\pi$
$854$	−1448.63	−	1993.87i	−1.69629	−	2.33474i
$855$	40.4034	+	194.240i	0.0472555	+	0.227181i
$856$	−994.221	−	3059.90i	−1.16147	−	3.57465i
$857$			551.421i			0.643431i	0.946836	+	0.321716i	$0.104260\pi$
$857$			551.421i			0.643431i	−0.946836	+	0.321716i	$0.895740\pi$
$858$		0			0
$859$	−1196.04			−1.39236			−0.696180	−	0.717868i	$-0.745118\pi$
$859$	−1196.04			−1.39236			−0.696180	+	0.717868i	$0.745118\pi$
$860$	278.824	−	90.5953i	0.324214	−	0.105343i
$861$	217.120	−	1010.64i	0.252172	−	1.17380i
$862$	−1286.88	+	934.973i	−1.49290	+	1.08466i
$863$	681.319	+	221.374i	0.789478	+	0.256517i	0.675882	−	0.737010i	$-0.263763\pi$
$863$	681.319	+	221.374i	0.789478	+	0.256517i	0.113596	+	0.993527i	$0.463763\pi$
$864$	−442.454	+	600.693i	−0.512100	+	0.695247i
$865$	−64.8498	+	47.1161i	−0.0749709	+	0.0544695i
$866$	461.729	−	635.516i	0.533175	−	0.733852i
$867$	−269.654	−	300.796i	−0.311020	−	0.346939i
$868$	−1838.37			−2.11793
$869$		0			0
$870$	105.499	+	238.350i	0.121263	+	0.273965i
$871$	31.9745	+	98.4075i	0.0367101	+	0.112982i
$872$	−600.939	+	827.121i	−0.689150	+	0.948534i
$873$	75.6040	−	690.383i	0.0866025	−	0.790817i
$874$	−238.203	+	733.114i	−0.272544	+	0.838803i
$875$	−802.780	−	260.839i	−0.917463	−	0.298102i
$876$	−996.428	+	1717.22i	−1.13747	+	1.96029i
$877$	802.250	+	582.869i	0.914766	+	0.664616i	0.942216	−	0.335007i	$-0.108739\pi$
$877$	802.250	+	582.869i	0.914766	+	0.664616i	−0.0274497	+	0.999623i	$0.508739\pi$
$878$	585.588	−	190.269i	0.666957	−	0.216707i
$879$	223.431	+	504.790i	0.254188	+	0.574278i
$880$		0			0
$881$			1256.55i			1.42628i	0.701021	+	0.713140i	$0.252728\pi$
$881$			1256.55i			1.42628i	−0.701021	+	0.713140i	$0.747272\pi$
$882$	−391.877	+	869.951i	−0.444305	+	0.986339i
$883$	−225.170	−	163.596i	−0.255006	−	0.185273i	0.452936	−	0.891543i	$-0.350376\pi$
$883$	−225.170	−	163.596i	−0.255006	−	0.185273i	−0.707943	+	0.706270i	$0.750376\pi$
$884$	106.519	+	146.611i	0.120497	+	0.165850i
$885$	72.5158	+	704.702i	0.0819388	+	0.796274i
$886$	656.846	−	2021.56i	0.741361	−	2.28168i
$887$	−690.062	−	949.789i	−0.777973	−	1.07079i	−0.995503	−	0.0947346i	$-0.969800\pi$
$887$	−690.062	−	949.789i	−0.777973	−	1.07079i	0.217529	−	0.976054i	$-0.430200\pi$
$888$	79.7414	−	371.177i	0.0897988	−	0.417992i
$889$	−39.0947	−	120.321i	−0.0439761	−	0.135344i
$890$			558.178i			0.627166i
$891$		0			0
$892$	146.507			0.164245
$893$	−455.286	+	147.931i	−0.509838	+	0.165656i
$894$	2381.38	+	511.602i	2.66374	+	0.572262i
$895$	229.818	−	166.972i	0.256779	−	0.186561i
$896$	−1221.49	−	396.885i	−1.36327	−	0.442953i
$897$	99.8279	−	10.2726i	0.111291	−	0.0114521i
$898$	1265.71	−	919.596i	1.40948	−	1.02405i
$899$	−159.587	+	219.653i	−0.177517	+	0.244331i
$900$	−1502.57	−	676.843i	−1.66952	−	0.752048i
$901$	500.866			0.555900
$902$		0			0
$903$	385.237	−	170.514i	0.426619	−	0.188831i
$904$	−820.317	−	2524.68i	−0.907430	−	2.79278i
$905$	−159.843	+	220.004i	−0.176622	+	0.243099i
$906$	−2538.63	−	1473.06i	−2.80203	−	1.62590i
$907$	44.9979	−	138.489i	0.0496118	−	0.152690i	−0.923181	−	0.384365i	$-0.874421\pi$
$907$	44.9979	−	138.489i	0.0496118	−	0.152690i	0.972793	+	0.231675i	$0.0744206\pi$
$908$	−951.902	−	309.292i	−1.04835	−	0.340630i
$909$	−114.474	−	12.5361i	−0.125934	−	0.0137911i
$910$	−88.2704	−	64.1322i	−0.0970004	−	0.0704749i
$911$	1024.00	−	332.718i	1.12404	−	0.365223i	0.312732	−	0.949841i	$-0.398756\pi$
$911$	1024.00	−	332.718i	1.12404	−	0.365223i	0.811308	+	0.584619i	$0.198756\pi$
$912$	787.712	−	348.658i	0.863719	−	0.382301i
$913$		0			0
$914$		−	855.714i		−	0.936230i
$915$	−361.271	+	323.868i	−0.394831	+	0.353954i
$916$	−2644.76	−	1921.53i	−2.88730	−	2.09774i
$917$	−800.637	−	1101.98i	−0.873105	−	1.20173i
$918$	−968.844	−	713.624i	−1.05539	−	0.777369i
$919$	−97.6839	+	300.640i	−0.106294	+	0.327138i	−0.990032	−	0.140843i	$-0.955019\pi$
$919$	−97.6839	+	300.640i	−0.106294	+	0.327138i	0.883738	+	0.467982i	$0.155019\pi$
$920$	435.594	+	599.544i	0.473472	+	0.651678i
$921$	−1134.14	−	243.652i	−1.23142	−	0.264551i
$922$	788.358	+	2426.32i	0.855052	+	2.63158i
$923$			16.7976i			0.0181990i
$924$		0			0
$925$	149.606			0.161737
$926$	1574.45	−	511.571i	1.70028	−	0.552453i
$927$	−621.768	+	129.333i	−0.670731	+	0.139518i
$928$	259.506	−	188.542i	0.279640	−	0.203170i
$929$	−1063.90	−	345.682i	−1.14521	−	0.372101i	−0.325872	−	0.945414i	$-0.605658\pi$
$929$	−1063.90	−	345.682i	−1.14521	−	0.372101i	−0.819337	+	0.573313i	$0.805658\pi$
$930$	53.7551	+	522.387i	0.0578012	+	0.561707i
$931$	252.615	−	183.536i	0.271337	−	0.197138i
$932$	−909.843	+	1252.29i	−0.976226	+	1.34366i
$933$	−206.050	+	184.717i	−0.220847	+	0.197982i
$934$	−173.568			−0.185833
$935$		0			0
$936$	−191.374	−	173.829i	−0.204459	−	0.185715i
$937$	−324.843	−	999.765i	−0.346684	−	1.06699i	−0.960676	−	0.277672i	$-0.910437\pi$
$937$	−324.843	−	999.765i	−0.346684	−	1.06699i	0.613991	−	0.789313i	$-0.289563\pi$
$938$	−1175.64	+	1618.12i	−1.25334	+	1.72508i
$939$	−112.017	+	193.048i	−0.119294	+	0.205588i
$940$	−259.067	+	797.325i	−0.275603	+	0.848218i
$941$	304.866	+	99.0570i	0.323981	+	0.105268i	0.466492	−	0.884525i	$-0.345518\pi$
$941$	304.866	+	99.0570i	0.323981	+	0.105268i	−0.142511	+	0.989793i	$0.545518\pi$
$942$	56.4016	+	32.7275i	0.0598744	+	0.0347426i
$943$	−639.664	−	464.743i	−0.678329	−	0.492835i
$944$	2925.37	−	950.510i	3.09891	−	1.00690i
$945$	473.823	+	157.384i	0.501400	+	0.166544i
$946$		0			0
$947$		−	689.980i		−	0.728596i	−0.931283	−	0.364298i	$-0.881309\pi$
$947$		−	689.980i		−	0.728596i	0.931283	−	0.364298i	$-0.118691\pi$
$948$	−1532.87	−	1709.89i	−1.61695	−	1.80369i
$949$	−99.2979	−	72.1442i	−0.104634	−	0.0760213i
$950$	459.977	+	633.104i	0.484187	+	0.666426i
$951$	1563.08	−	160.846i	1.64362	−	0.169133i
$952$	−594.253	+	1828.92i	−0.624216	+	1.92114i
$953$	788.855	+	1085.77i	0.827760	+	1.13931i	0.988336	+	0.152290i	$0.0486647\pi$
$953$	788.855	+	1085.77i	0.827760	+	1.13931i	−0.160576	+	0.987023i	$0.551335\pi$
$954$	−1274.35	+	265.074i	−1.33579	+	0.277856i
$955$	−203.464	−	626.198i	−0.213051	−	0.655705i
$956$			3062.78i			3.20374i
$957$		0			0
$958$	−614.947			−0.641907
$959$	679.743	−	220.862i	0.708804	−	0.230304i
$960$	−12.6013	+	58.6562i	−0.0131264	+	0.0611002i
$961$	334.925	−	243.337i	0.348517	−	0.253212i
$962$	40.6611	+	13.2116i	0.0422673	+	0.0137335i
$963$	−1439.45	+	822.728i	−1.49476	+	0.854339i
$964$	1875.83	−	1362.87i	1.94588	−	1.41377i
$965$	−179.550	+	247.129i	−0.186062	+	0.256093i
$966$	1294.88	+	1444.42i	1.34046	+	1.49526i
$967$	−1283.30			−1.32709			−0.663546	−	0.748135i	$-0.730949\pi$
$967$	−1283.30			−1.32709			−0.663546	+	0.748135i	$0.730949\pi$
$968$		0			0
$969$	159.384	+	360.091i	0.164483	+	0.371611i
$970$	178.476	+	549.292i	0.183996	+	0.566281i
$971$	−500.100	+	688.328i	−0.515036	+	0.708886i	−0.984758	−	0.173928i	$-0.944354\pi$
$971$	−500.100	+	688.328i	−0.515036	+	0.708886i	0.469722	+	0.882814i	$0.344354\pi$
$972$	1959.08	+	897.926i	2.01551	+	0.923792i
$973$	580.471	−	1786.50i	0.596578	−	1.83608i
$974$	−1690.49	−	549.274i	−1.73562	−	0.563936i
$975$	51.1324	−	88.1201i	0.0524435	−	0.0903796i
$976$	1704.31	+	1238.25i	1.74622	+	1.26870i
$977$	1153.28	−	374.724i	1.18043	−	0.383545i	0.347904	−	0.937530i	$-0.386893\pi$
$977$	1153.28	−	374.724i	1.18043	−	0.383545i	0.832527	+	0.553985i	$0.186893\pi$
$978$	−705.322	−	1593.51i	−0.721188	−	1.62936i
$979$		0			0
$980$		−	546.831i		−	0.557991i
$981$	480.367	+	216.385i	0.489671	+	0.220576i
$982$	−958.436	−	696.345i	−0.976004	−	0.709109i
$983$	267.240	+	367.825i	0.271862	+	0.374186i	0.923017	−	0.384759i	$-0.125715\pi$
$983$	267.240	+	367.825i	0.271862	+	0.374186i	−0.651155	+	0.758945i	$0.725715\pi$
$984$	208.504	+	2026.23i	0.211895	+	2.05917i
$985$	−147.939	+	455.310i	−0.150192	+	0.462243i
$986$	304.095	+	418.551i	0.308413	+	0.424494i
$987$	−253.040	+	1177.84i	−0.256373	+	1.19335i
$988$	47.6262	+	146.578i	0.0482046	+	0.148359i
$989$		−	322.239i		−	0.325823i
$990$		0			0
$991$	697.554			0.703889			0.351945	−	0.936021i	$-0.385521\pi$
$991$	697.554			0.703889			0.351945	+	0.936021i	$0.385521\pi$
$992$	614.626	−	199.704i	0.619583	−	0.201315i
$993$	738.273	+	158.606i	0.743478	+	0.159724i
$994$	−262.687	+	190.853i	−0.264272	+	0.192005i
$995$	−772.595	−	251.031i	−0.776478	−	0.252293i
$996$	312.517	−	32.1588i	0.313772	−	0.0322880i
$997$	529.077	−	384.397i	0.530669	−	0.385553i	−0.289939	−	0.957045i	$-0.593635\pi$
$997$	529.077	−	384.397i	0.530669	−	0.385553i	0.820608	+	0.571492i	$0.193635\pi$
$998$	231.520	−	318.660i	0.231984	−	0.319299i
$999$	−195.636	−	1.27824i	−0.195832	−	0.00127952i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.3.h.n.269.1		16
3.2	odd	2	inner	363.3.h.n.269.4		16
11.2	odd	10		363.3.h.o.251.1		16
11.3	even	5		363.3.b.l.122.8		8
11.4	even	5		363.3.h.j.245.1		16
11.5	even	5		363.3.h.j.323.4		16
11.6	odd	10		33.3.h.b.26.1	yes	16
11.7	odd	10		33.3.h.b.14.4	yes	16
11.8	odd	10		363.3.b.m.122.1		8
11.9	even	5	inner	363.3.h.n.251.4		16
11.10	odd	2		363.3.h.o.269.4		16
33.2	even	10		363.3.h.o.251.4		16
33.5	odd	10		363.3.h.j.323.1		16
33.8	even	10		363.3.b.m.122.8		8
33.14	odd	10		363.3.b.l.122.1		8
33.17	even	10		33.3.h.b.26.4	yes	16
33.20	odd	10	inner	363.3.h.n.251.1		16
33.26	odd	10		363.3.h.j.245.4		16
33.29	even	10		33.3.h.b.14.1	✓	16
33.32	even	2		363.3.h.o.269.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.h.b.14.1	✓	16	33.29	even	10
33.3.h.b.14.4	yes	16	11.7	odd	10
33.3.h.b.26.1	yes	16	11.6	odd	10
33.3.h.b.26.4	yes	16	33.17	even	10
363.3.b.l.122.1		8	33.14	odd	10
363.3.b.l.122.8		8	11.3	even	5
363.3.b.m.122.1		8	11.8	odd	10
363.3.b.m.122.8		8	33.8	even	10
363.3.h.j.245.1		16	11.4	even	5
363.3.h.j.245.4		16	33.26	odd	10
363.3.h.j.323.1		16	33.5	odd	10
363.3.h.j.323.4		16	11.5	even	5
363.3.h.n.251.1		16	33.20	odd	10	inner
363.3.h.n.251.4		16	11.9	even	5	inner
363.3.h.n.269.1		16	1.1	even	1	trivial
363.3.h.n.269.4		16	3.2	odd	2	inner
363.3.h.o.251.1		16	11.2	odd	10
363.3.h.o.251.4		16	33.2	even	10
363.3.h.o.269.1		16	33.32	even	2
363.3.h.o.269.4		16	11.10	odd	2

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+(-3.41170 + 1.10853i) q^{2} +(2.93308 + 0.630124i) q^{3} +(7.17480 - 5.21280i) q^{4} +(1.98428 + 0.644731i) q^{5} +(-10.7053 + 1.10160i) q^{6} +(7.17034 - 5.20956i) q^{7} +(-10.2655 + 14.1293i) q^{8} +(8.20589 + 3.69641i) q^{9} -7.48447 q^{10} +(24.3290 - 10.7685i) q^{12} +(0.508273 + 1.56430i) q^{13} +(-18.6881 + 25.7220i) q^{14} +(5.41378 + 3.14139i) q^{15} +(8.39811 - 25.8467i) q^{16} +(11.8154 + 3.83907i) q^{17} +(-32.0936 - 3.51458i) q^{18} +(8.54780 + 6.21034i) q^{19} +(17.5977 - 5.71782i) q^{20} +(24.3138 - 10.7618i) q^{21} -20.3378i q^{23} +(-39.0129 + 34.9738i) q^{24} +(-16.7037 - 12.1360i) q^{25} +(-3.46815 - 4.77350i) q^{26} +(21.7393 + 16.0126i) q^{27} +(24.2894 - 74.7550i) q^{28} +(-6.82340 - 9.39161i) q^{29} +(-21.9525 - 4.71615i) q^{30} +(-7.22737 - 22.2436i) q^{31} +27.6317i q^{32} -44.5665 q^{34} +(17.5867 - 5.71427i) q^{35} +(78.1442 - 16.2546i) q^{36} +(-5.86208 + 4.25905i) q^{37} +(-36.0469 - 11.7123i) q^{38} +(0.505098 + 4.90850i) q^{39} +(-29.4793 + 21.4180i) q^{40} +(22.8512 - 31.4520i) q^{41} +(-71.0217 + 63.6687i) q^{42} +15.8444 q^{43} +(13.8996 + 12.6253i) q^{45} +(22.5450 + 69.3864i) q^{46} +(-26.6317 + 36.6554i) q^{47} +(40.9190 - 70.5186i) q^{48} +(9.13245 - 28.1068i) q^{49} +(70.4413 + 22.8878i) q^{50} +(32.2365 + 18.7055i) q^{51} +(11.8011 + 8.57403i) q^{52} +(38.3428 - 12.4583i) q^{53} +(-91.9184 - 30.5315i) q^{54} +154.791i q^{56} +(21.1581 + 23.6016i) q^{57} +(33.6903 + 24.4774i) q^{58} +(66.5264 + 91.5657i) q^{59} +(55.2182 - 5.68211i) q^{60} +(-23.9538 + 73.7222i) q^{61} +(49.3152 + 67.8766i) q^{62} +(78.0956 - 16.2445i) q^{63} +(2.96194 + 9.11592i) q^{64} +3.43171i q^{65} +62.9082 q^{67} +(104.786 - 34.0470i) q^{68} +(12.8153 - 59.6523i) q^{69} +(-53.6662 + 38.9908i) q^{70} +(9.71270 + 3.15585i) q^{71} +(-136.466 + 77.9979i) q^{72} +(-60.3706 + 43.8618i) q^{73} +(15.2784 - 21.0289i) q^{74} +(-41.3462 - 46.1212i) q^{75} +93.7020 q^{76} +(-7.16445 - 16.1864i) q^{78} +(-26.6720 - 82.0879i) q^{79} +(33.3284 - 45.8726i) q^{80} +(53.6731 + 60.6646i) q^{81} +(-43.0961 + 132.636i) q^{82} +(11.2304 + 3.64896i) q^{83} +(118.348 - 203.957i) q^{84} +(20.9700 + 15.2356i) q^{85} +(-54.0563 + 17.5639i) q^{86} +(-14.0957 - 31.8459i) q^{87} -74.5782i q^{89} +(-61.4167 - 27.6656i) q^{90} +(11.7938 + 8.56870i) q^{91} +(-106.017 - 145.919i) q^{92} +(-7.18222 - 69.7962i) q^{93} +(50.2259 - 154.579i) q^{94} +(12.9572 + 17.8341i) q^{95} +(-17.4114 + 81.0458i) q^{96} +(-23.8462 - 73.3909i) q^{97} +106.016i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 5 q^{3} + 18 q^{4} - 32 q^{6} + 34 q^{7} + 17 q^{9} + 12 q^{10} + 106 q^{12} + 2 q^{13} - 28 q^{15} + 102 q^{16} - 42 q^{18} - 66 q^{19} + 12 q^{21} + 74 q^{24} - 176 q^{25} - 55 q^{27} + 146 q^{28}+ \cdots + 252 q^{97}+O(q^{100}) \) 16 * q + 5 * q^3 + 18 * q^4 - 32 * q^6 + 34 * q^7 + 17 * q^9 + 12 * q^10 + 106 * q^12 + 2 * q^13 - 28 * q^15 + 102 * q^16 - 42 * q^18 - 66 * q^19 + 12 * q^21 + 74 * q^24 - 176 * q^25 - 55 * q^27 + 146 * q^28 - 110 * q^30 - 126 * q^31 - 132 * q^34 + 226 * q^36 - 230 * q^37 - 136 * q^39 - 226 * q^40 - 72 * q^42 + 156 * q^43 - 72 * q^45 - 308 * q^46 + 255 * q^48 + 170 * q^49 + 169 * q^51 + 224 * q^52 - 1046 * q^54 + 259 * q^57 + 184 * q^58 - 316 * q^60 - 104 * q^61 + 108 * q^63 - 184 * q^64 + 368 * q^67 - 22 * q^69 - 52 * q^70 - 73 * q^72 - 354 * q^73 + 54 * q^75 + 900 * q^76 - 492 * q^78 - 566 * q^79 + 377 * q^81 + 200 * q^82 + 720 * q^84 + 162 * q^85 - 132 * q^87 + 774 * q^90 - 226 * q^91 - 370 * q^93 + 530 * q^94 + 67 * q^96 + 252 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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