LMFDB - Embedded newform 363.3.h.n.251.1

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			251.1
Root			$2.10855 - 2.90217i$ of defining polynomial
Character	$\chi$	$=$	363.251
Dual form			363.3.h.n.269.1

$q$-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 $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{3}{5}\right)$

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	−0.716217	−	0.697878i	$-0.754128\pi$
$2$	−3.41170	−	1.10853i	−1.70585	−	0.554264i	−0.989634	+	0.143614i	$0.954128\pi$
$3$	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	−0.103789	−	0.994599i	$-0.533097\pi$
$5$	1.98428	−	0.644731i	0.396856	−	0.128946i	0.500644	+	0.865653i	$0.333097\pi$
$6$	−10.7053	−	1.10160i	−1.78422	−	0.183601i
$7$	7.17034	+	5.20956i	1.02433	+	0.744222i	0.967167	−	0.254142i	$-0.0817932\pi$
$7$	7.17034	+	5.20956i	1.02433	+	0.744222i	0.0571672	+	0.998365i	$0.481793\pi$
$8$	−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	−0.929603	−	0.368564i	$-0.879850\pi$
$13$	0.508273	−	1.56430i	0.0390979	−	0.120331i	0.968700	+	0.248233i	$0.0798497\pi$
$14$	−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	0.0598641	−	0.998207i	$-0.480933\pi$
$17$	11.8154	−	3.83907i	0.695026	−	0.225828i	0.635162	+	0.772379i	$0.280933\pi$
$18$	−32.0936	+	3.51458i	−1.78298	+	0.195254i
$19$	8.54780	−	6.21034i	0.449884	−	0.326860i	−0.339666	−	0.940546i	$-0.610314\pi$
$19$	8.54780	−	6.21034i	0.449884	−	0.326860i	0.789550	+	0.613686i	$0.210314\pi$
$20$	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	$0.145775\pi$
$23$			20.3378i			0.884251i	−0.896953	+	0.442126i	$0.854225\pi$
$24$	−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	−0.910292	−	0.413967i	$-0.864143\pi$
$29$	−6.82340	+	9.39161i	−0.235290	+	0.323849i	0.675002	+	0.737816i	$0.264143\pi$
$30$	−21.9525	+	4.71615i	−0.731751	+	0.157205i
$31$	−7.22737	+	22.2436i	−0.233141	+	0.717534i	0.764222	+	0.644954i	$0.223123\pi$
$31$	−7.22737	+	22.2436i	−0.233141	+	0.717534i	−0.997363	+	0.0725803i	$0.976877\pi$
$32$		−	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	0.505743	−	0.862684i	$-0.331218\pi$
$37$	−5.86208	−	4.25905i	−0.158435	−	0.115109i	−0.664178	+	0.747575i	$0.731218\pi$
$38$	−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	0.990986	−	0.133964i	$-0.0427707\pi$
$41$	22.8512	+	31.4520i	0.557347	+	0.767122i	−0.433639	+	0.901087i	$0.642771\pi$
$42$	−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	0.425518	−	0.904950i	$-0.360092\pi$
$47$	−26.6317	−	36.6554i	−0.566633	−	0.779903i	−0.992151	+	0.125047i	$0.960092\pi$
$48$	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	0.647518	−	0.762050i	$-0.275807\pi$
$53$	38.3428	+	12.4583i	0.723450	+	0.235063i	0.0759315	+	0.997113i	$0.475807\pi$
$54$	−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	0.334955	−	0.942234i	$-0.391279\pi$
$59$	66.5264	−	91.5657i	1.12757	−	1.55196i	0.792611	−	0.609727i	$-0.208721\pi$
$60$	55.2182	+	5.68211i	0.920304	+	0.0947018i
$61$	−23.9538	−	73.7222i	−0.392685	−	1.20856i	−0.930750	−	0.365657i	$-0.880844\pi$
$61$	−23.9538	−	73.7222i	−0.392685	−	1.20856i	0.538065	−	0.842903i	$-0.319156\pi$
$62$	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	−0.239817	−	0.970818i	$-0.577088\pi$
$71$	9.71270	−	3.15585i	0.136799	−	0.0444486i	0.376616	+	0.926369i	$0.377088\pi$
$72$	−136.466	−	77.9979i	−1.89536	−	1.08330i
$73$	−60.3706	−	43.8618i	−0.826995	−	0.600847i	0.0917125	−	0.995786i	$-0.470766\pi$
$73$	−60.3706	−	43.8618i	−0.826995	−	0.600847i	−0.918708	+	0.394938i	$0.870766\pi$
$74$	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	0.627797	+	0.778377i	$0.283957\pi$
$79$	−26.6720	+	82.0879i	−0.337620	+	1.03909i	−0.965417	+	0.260710i	$0.916043\pi$
$80$	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	−0.240581	−	0.970629i	$-0.577338\pi$
$83$	11.2304	−	3.64896i	0.135305	−	0.0439634i	0.375887	+	0.926666i	$0.377338\pi$
$84$	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	$0.137612\pi$
$89$			74.5782i			0.837957i	−0.907996	+	0.418979i	$0.862388\pi$
$90$	−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	0.749661	+	0.661822i	$0.230217\pi$
$97$	−23.8462	+	73.3909i	−0.245837	+	0.756608i	−0.995498	+	0.0947856i	$0.969783\pi$
$98$		−	106.016i		−	1.08179i
$99$		0			0
$100$	−183.108			−1.83108
$101$	−12.1692	−	3.95400i	−0.120487	−	0.0391485i	0.248153	−	0.968721i	$-0.420176\pi$
$101$	−12.1692	−	3.95400i	−0.120487	−	0.0391485i	−0.368640	+	0.929572i	$0.620176\pi$
$102$	−130.717	+	28.0824i	−1.28154	+	0.275318i
$103$	−57.0875	−	41.4765i	−0.554248	−	0.402685i	0.275101	−	0.961415i	$-0.411289\pi$
$103$	−57.0875	−	41.4765i	−0.554248	−	0.402685i	−0.829349	+	0.558731i	$0.811289\pi$
$104$	−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	−0.917677	−	0.397328i	$-0.869938\pi$
$107$	−108.282	−	149.037i	−1.01198	−	1.39287i	−0.0943034	−	0.995544i	$-0.530062\pi$
$108$	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	−0.994029	−	0.109119i	$-0.965197\pi$
$113$	−89.3418	−	122.968i	−0.790635	−	1.08822i	0.203393	−	0.979097i	$-0.434803\pi$
$114$	−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	0.966920	−	0.255081i	$-0.0821022\pi$
$127$	4.41099	+	13.5756i	0.0347322	+	0.106895i	−0.932187	+	0.361976i	$0.882102\pi$
$128$	−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	$0.199529\pi$
$131$			153.686i			1.17318i	−0.809885	+	0.586589i	$0.800471\pi$
$132$		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	−0.0154246	−	0.999881i	$-0.504910\pi$
$137$	76.6942	−	24.9195i	0.559812	−	0.181894i	0.575237	+	0.817987i	$0.304910\pi$
$138$	22.4042	−	217.722i	0.162349	−	1.57769i
$139$	171.464	+	124.576i	1.23356	+	0.896231i	0.997152	−	0.0754243i	$-0.0240311\pi$
$139$	171.464	+	124.576i	1.23356	+	0.896231i	0.236404	+	0.971655i	$0.424031\pi$
$140$	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	−0.923342	−	0.383978i	$-0.874554\pi$
$149$	−215.252	+	69.9397i	−1.44465	+	0.469394i	−0.521303	+	0.853371i	$0.674554\pi$
$150$	192.188	−	111.518i	1.28125	−	0.743455i
$151$	220.642	−	160.306i	1.46121	−	1.06163i	0.478161	−	0.878272i	$-0.341304\pi$
$151$	220.642	−	160.306i	1.46121	−	1.06163i	0.983046	−	0.183357i	$-0.0586964\pi$
$152$	−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	−0.603288	−	0.797524i	$-0.706143\pi$
$157$	−4.90208	+	3.56157i	−0.0312234	+	0.0226852i	0.572064	+	0.820209i	$0.306143\pi$
$158$	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	−0.671947	−	0.740599i	$-0.734542\pi$
$163$	50.0381	−	154.002i	0.306982	−	0.944795i	0.978930	−	0.204196i	$-0.0654580\pi$
$164$			344.781i			2.10232i
$165$		0			0
$166$	−42.3596			−0.255178
$167$	−151.417	−	49.1982i	−0.906686	−	0.294600i	−0.181692	−	0.983355i	$-0.558158\pi$
$167$	−151.417	−	49.1982i	−0.906686	−	0.294600i	−0.724994	+	0.688755i	$0.758158\pi$
$168$	−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	0.738746	−	0.673983i	$-0.235418\pi$
$173$	−22.5826	−	31.0822i	−0.130535	−	0.179666i	−0.869282	+	0.494317i	$0.835418\pi$
$174$	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	0.971769	−	0.235933i	$-0.0758147\pi$
$179$	80.0291	+	110.151i	0.447090	+	0.615367i	−0.524679	+	0.851300i	$0.675815\pi$
$180$	165.540	−	18.1283i	0.919665	−	0.100713i
$181$	−40.2773	−	123.961i	−0.222526	−	0.684865i	−0.998533	−	0.0541412i	$-0.982758\pi$
$181$	−40.2773	−	123.961i	−0.222526	−	0.684865i	0.776007	−	0.630724i	$-0.217242\pi$
$182$	−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	−0.0297142	+	0.999558i	$0.509460\pi$
$191$	−185.493	+	255.309i	−0.971169	+	1.33670i	−0.941454	+	0.337140i	$0.890540\pi$
$192$	2.94344	−	28.6041i	0.0153304	−	0.148980i
$193$	−45.2431	−	139.244i	−0.234420	−	0.721472i	−0.997198	−	0.0748107i	$-0.976165\pi$
$193$	−45.2431	−	139.244i	−0.234420	−	0.721472i	0.762777	−	0.646661i	$-0.223835\pi$
$194$	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	$-0.802121\pi$
$197$		−	229.459i		−	1.16476i	0.812915	−	0.582382i	$-0.197879\pi$
$198$		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	0.683186	+	0.730244i	$0.260594\pi$
$211$	−63.0362	+	194.005i	−0.298750	+	0.919457i	−0.981936	+	0.189213i	$0.939406\pi$
$212$	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	−0.557416	−	0.830233i	$-0.688207\pi$
$223$	13.3648	−	9.71010i	0.0599319	−	0.0435431i	0.617348	+	0.786690i	$0.288207\pi$
$224$	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	−0.929737	−	0.368224i	$-0.879966\pi$
$227$	−66.3365	+	91.3043i	−0.292231	+	0.402222i	0.637506	+	0.770445i	$0.279966\pi$
$228$	274.835	−	59.0439i	1.20542	−	0.258965i
$229$	−113.909	+	350.577i	−0.497421	+	1.53090i	0.315730	+	0.948849i	$0.397751\pi$
$229$	−113.909	+	350.577i	−0.497421	+	1.53090i	−0.813150	+	0.582054i	$0.802249\pi$
$230$		−	152.217i		−	0.661815i
$231$		0			0
$232$	202.743			0.873892
$233$	−165.998	−	53.9359i	−0.712436	−	0.231485i	−0.0696955	−	0.997568i	$-0.522203\pi$
$233$	−165.998	−	53.9359i	−0.712436	−	0.231485i	−0.642741	+	0.766084i	$0.722203\pi$
$234$	−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	−0.984007	−	0.178132i	$-0.942995\pi$
$239$	−202.993	−	279.397i	−0.849345	−	1.16902i	0.134661	−	0.990892i	$-0.457005\pi$
$240$	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	−0.0918987	−	0.995768i	$-0.529294\pi$
$251$	−188.638	−	61.2921i	−0.751544	−	0.244192i	−0.659646	+	0.751577i	$0.729294\pi$
$252$	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	−0.811145	−	0.584846i	$-0.801155\pi$
$257$	−1.09633	+	1.50897i	−0.00426588	+	0.00587148i	0.806879	+	0.590717i	$0.201155\pi$
$258$	−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	$0.0164009\pi$
$263$			27.0901i			0.103004i	−0.998673	+	0.0515020i	$0.983599\pi$
$264$		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	−0.550446	−	0.834871i	$-0.685542\pi$
$269$	−135.856	+	44.1424i	−0.505042	+	0.164098i	0.0454041	+	0.998969i	$0.485542\pi$
$270$	−162.707	+	119.846i	−0.602619	+	0.443873i
$271$	−85.2115	−	61.9098i	−0.314434	−	0.228449i	0.419363	−	0.907819i	$-0.362254\pi$
$271$	−85.2115	−	61.9098i	−0.314434	−	0.228449i	−0.733797	+	0.679369i	$0.762254\pi$
$272$	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	0.716454	+	0.697634i	$0.245764\pi$
$277$	−75.6843	+	232.932i	−0.273229	+	0.840911i	−0.989683	+	0.143277i	$0.954236\pi$
$278$	−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	−0.417122	−	0.908850i	$-0.636961\pi$
$281$	−61.9247	+	20.1206i	−0.220373	+	0.0716034i	0.196750	+	0.980454i	$0.436961\pi$
$282$	244.721	+	421.745i	0.867804	+	1.49555i
$283$	−127.482	+	92.6208i	−0.450465	+	0.327282i	−0.789779	−	0.613391i	$-0.789805\pi$
$283$	−127.482	+	92.6208i	−0.450465	+	0.327282i	0.339314	+	0.940673i	$0.389805\pi$
$284$	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	−0.583527	−	0.812094i	$-0.698328\pi$
$293$	108.158	−	148.867i	0.369139	−	0.508077i	0.952667	+	0.304017i	$0.0983279\pi$
$294$	−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	0.712903	−	0.701262i	$-0.247380\pi$
$311$	−54.2185	−	74.6253i	−0.174336	−	0.239953i	−0.887239	+	0.461309i	$0.847380\pi$
$312$	−74.5388	+	43.2517i	−0.238906	+	0.138627i
$313$	−22.9902	−	70.7565i	−0.0734510	−	0.226059i	0.907591	−	0.419856i	$-0.137920\pi$
$313$	−22.9902	−	70.7565i	−0.0734510	−	0.226059i	−0.981042	+	0.193797i	$0.937920\pi$
$314$	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	0.959831	−	0.280578i	$-0.0905263\pi$
$317$	498.144	+	161.857i	1.57143	+	0.510589i	0.611600	+	0.791167i	$0.290526\pi$
$318$	−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	0.526592	−	0.850118i	$-0.323470\pi$
$337$	−40.1679	−	29.1837i	−0.119193	−	0.0865985i	−0.645785	+	0.763520i	$0.723470\pi$
$338$	−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	−0.861551	−	0.507670i	$-0.830507\pi$
$347$	−437.276	+	142.079i	−1.26016	+	0.409451i	−0.398609	+	0.917121i	$0.630507\pi$
$348$	−267.140	+	155.010i	−0.767644	+	0.445431i
$349$	−318.550	+	231.440i	−0.912750	+	0.663152i	−0.941709	−	0.336429i	$-0.890781\pi$
$349$	−318.550	+	231.440i	−0.912750	+	0.663152i	0.0289588	+	0.999581i	$0.490781\pi$
$350$	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	$-0.992360\pi$
$353$		−	16.9433i		−	0.0479980i	0.999712	−	0.0239990i	$-0.00763985\pi$
$354$	−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	−0.742360	−	0.670001i	$-0.766294\pi$
$359$	44.6059	−	61.3948i	0.124250	−	0.171016i	0.866611	+	0.498985i	$0.166294\pi$
$360$	−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	−0.998095	−	0.0617010i	$-0.980347\pi$
$367$	−501.030	−	364.020i	−1.36520	−	0.991879i	−0.367109	−	0.930178i	$-0.619653\pi$
$368$	−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	−0.967116	−	0.254337i	$-0.918143\pi$
$379$	−126.661	−	389.823i	−0.334198	−	1.02856i	0.632917	−	0.774220i	$-0.281857\pi$
$380$	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	0.374034	−	0.927415i	$-0.377974\pi$
$383$	50.3695	+	16.3660i	0.131513	+	0.0427311i	−0.242521	+	0.970146i	$0.577974\pi$
$384$	−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	−0.735006	−	0.678061i	$-0.762821\pi$
$389$	53.2922	−	73.3504i	0.136998	−	0.188561i	0.872004	+	0.489500i	$0.162821\pi$
$390$	−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	−0.286493	−	0.958082i	$-0.592490\pi$
$401$	17.9951	−	5.84696i	0.0448755	−	0.0145809i	0.331369	+	0.943501i	$0.392490\pi$
$402$	−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	−0.895840	−	0.444377i	$-0.853425\pi$
$409$	36.8542	−	113.426i	0.0901081	−	0.277324i	0.985948	+	0.167053i	$0.0534250\pi$
$410$	−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	$-0.836014\pi$
$419$		−	412.874i		−	0.985381i	0.870205	−	0.492690i	$-0.163986\pi$
$420$	366.332	+	328.405i	0.872219	+	0.781917i
$421$	−489.408	+	355.576i	−1.16249	+	0.844598i	−0.990091	−	0.140429i	$-0.955152\pi$
$421$	−489.408	+	355.576i	−1.16249	+	0.844598i	−0.172399	+	0.985027i	$0.555152\pi$
$422$	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	0.754228	−	0.656613i	$-0.228011\pi$
$431$	421.718	+	137.024i	0.978464	+	0.317922i	0.224236	+	0.974535i	$0.428011\pi$
$432$	596.442	+	427.414i	1.38065	+	0.989385i
$433$	−177.158	−	128.713i	−0.409142	−	0.297259i	0.364112	−	0.931355i	$-0.381372\pi$
$433$	−177.158	−	128.713i	−0.409142	−	0.297259i	−0.773254	+	0.634096i	$0.781372\pi$
$434$	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	−0.994571	−	0.104059i	$-0.966817\pi$
$443$	−348.285	−	479.374i	−0.786197	−	1.08211i	0.208374	−	0.978049i	$-0.433183\pi$
$444$	−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	−0.191770	−	0.981440i	$-0.561423\pi$
$449$	−414.782	−	134.771i	−0.923791	−	0.300158i	−0.732021	+	0.681282i	$0.761423\pi$
$450$	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	0.837446	−	0.546520i	$-0.184048\pi$
$457$	−73.7134	−	226.866i	−0.161298	−	0.496425i	−0.998744	+	0.0500945i	$0.984048\pi$
$458$	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	$0.280413\pi$
$461$			711.175i			1.54268i	−0.636424	+	0.771339i	$0.719587\pi$
$462$		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	−0.259334	−	0.965788i	$-0.583503\pi$
$467$	46.0163	−	14.9516i	0.0985361	−	0.0320163i	0.357870	+	0.933771i	$0.383503\pi$
$468$	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	−0.133847	−	0.991002i	$-0.542733\pi$
$479$	163.035	−	52.9731i	0.340364	−	0.110591i	0.474212	+	0.880411i	$0.342733\pi$
$480$	−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	−0.0944742	−	0.995527i	$-0.530117\pi$
$487$	400.866	−	291.247i	0.823134	−	0.598042i	0.917609	+	0.397485i	$0.130117\pi$
$488$	−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	−0.564222	−	0.825623i	$-0.690824\pi$
$491$	194.115	−	267.177i	0.395347	−	0.544148i	0.959569	+	0.281475i	$0.0908237\pi$
$492$	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	0.495208	−	0.868774i	$-0.335092\pi$
$499$	−88.8306	−	64.5392i	−0.178017	−	0.129337i	−0.673226	+	0.739437i	$0.735092\pi$
$500$	−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	0.999715	−	0.0238878i	$-0.00760445\pi$
$503$	336.038	+	462.516i	0.668067	+	0.919516i	−0.331647	+	0.943403i	$0.607604\pi$
$504$	−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	0.997681	−	0.0680613i	$-0.0216813\pi$
$509$	317.947	+	437.617i	0.624651	+	0.859758i	−0.373031	+	0.927819i	$0.621681\pi$
$510$	−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	−0.574701	−	0.818363i	$-0.694882\pi$
$521$	198.606	−	273.357i	0.381201	−	0.524678i	0.955902	+	0.293685i	$0.0948818\pi$
$522$	185.980	−	325.392i	0.356284	−	0.623356i
$523$	−95.0022	−	292.387i	−0.181649	−	0.559057i	0.818226	−	0.574897i	$-0.194958\pi$
$523$	−95.0022	−	292.387i	−0.181649	−	0.559057i	−0.999875	+	0.0158400i	$0.994958\pi$
$524$	−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	−0.924655	−	0.380806i	$-0.875646\pi$
$541$	25.5563	−	78.6541i	0.0472389	−	0.145387i	0.971894	+	0.235420i	$0.0756465\pi$
$542$	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	−0.841139	−	0.540819i	$-0.818114\pi$
$547$	−320.933	+	233.172i	−0.586715	+	0.426273i	0.254424	+	0.967093i	$0.418114\pi$
$548$	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	−0.557545	−	0.830146i	$-0.688257\pi$
$557$	225.174	−	309.925i	0.404262	−	0.556419i	0.961807	+	0.273728i	$0.0882567\pi$
$558$	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	0.184116	−	0.982904i	$-0.441058\pi$
$563$	−137.748	−	44.7570i	−0.244667	−	0.0794973i	−0.428784	+	0.903407i	$0.641058\pi$
$564$	−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	0.949897	+	0.312563i	$0.101188\pi$
$569$	542.614	+	746.845i	0.953628	+	1.31256i	0.00373108	+	0.999993i	$0.498812\pi$
$570$	−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	0.995373	+	0.0960821i	$0.0306311\pi$
$577$	142.274	+	437.874i	0.246575	+	0.758880i	−0.748798	+	0.662798i	$0.769369\pi$
$578$	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	−0.787227	−	0.616663i	$-0.788484\pi$
$587$	24.9599	−	34.3544i	0.0425212	−	0.0585254i	0.829748	+	0.558138i	$0.188484\pi$
$588$	−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	$-0.971441\pi$
$593$		−	106.267i		−	0.179203i	0.995978	−	0.0896015i	$-0.0285593\pi$
$594$		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	−0.823361	−	0.567518i	$-0.807904\pi$
$599$	−692.381	+	224.968i	−1.15589	+	0.375573i	−0.332534	+	0.943091i	$0.607904\pi$
$600$	1076.10	+	110.734i	1.79350	+	0.184557i
$601$	−95.9442	−	69.7075i	−0.159641	−	0.115986i	0.505097	−	0.863063i	$-0.331457\pi$
$601$	−95.9442	−	69.7075i	−0.159641	−	0.115986i	−0.664738	+	0.747077i	$0.731457\pi$
$602$	−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	0.588089	+	0.808796i	$0.299881\pi$
$607$	−220.392	+	678.296i	−0.363084	+	1.11746i	−0.951172	+	0.308660i	$0.900119\pi$
$608$	−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	−0.0330350	−	0.999454i	$-0.510517\pi$
$613$	556.171	−	404.082i	0.907294	−	0.659188i	0.940329	+	0.340267i	$0.110517\pi$
$614$	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	$0.211907\pi$
$617$			762.156i			1.23526i	−0.786468	+	0.617631i	$0.788093\pi$
$618$	565.448	+	506.906i	0.914965	+	0.820237i
$619$	429.344	−	311.937i	0.693609	−	0.503936i	−0.184236	−	0.982882i	$-0.558981\pi$
$619$	429.344	−	311.937i	0.693609	−	0.503936i	0.877845	+	0.478946i	$0.158981\pi$
$620$	−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	0.0625701	−	0.998041i	$-0.480070\pi$
$631$	−547.258	−	397.607i	−0.867288	−	0.630121i	−0.929858	+	0.367919i	$0.880070\pi$
$632$	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	0.999502	+	0.0315462i	$0.0100431\pi$
$641$	461.931	+	635.794i	0.720641	+	0.991878i	−0.278861	+	0.960331i	$0.589957\pi$
$642$	995.009	+	1714.77i	1.54986	+	2.67098i
$643$	−262.574	−	808.119i	−0.408357	−	1.25679i	−0.918059	−	0.396443i	$-0.870244\pi$
$643$	−262.574	−	808.119i	−0.408357	−	1.25679i	0.509702	−	0.860351i	$-0.329756\pi$
$644$	−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	−0.727146	−	0.686483i	$-0.759154\pi$
$647$	−1112.14	−	361.357i	−1.71892	−	0.558512i	−0.991778	+	0.127971i	$0.959154\pi$
$648$	−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	−0.496848	−	0.867838i	$-0.665509\pi$
$653$	314.778	−	433.255i	0.482049	−	0.663484i	0.978897	+	0.204354i	$0.0655092\pi$
$654$	−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	$0.0335731\pi$
$659$			138.756i			0.210555i	−0.994443	+	0.105278i	$0.966427\pi$
$660$		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	−0.678926	−	0.734207i	$-0.737554\pi$
$673$	203.174	−	625.305i	0.301893	−	0.929131i	0.980818	−	0.194924i	$-0.0624459\pi$
$674$	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	−0.705090	−	0.709118i	$-0.749093\pi$
$677$	−581.347	+	188.891i	−0.858711	+	0.279012i	−0.153621	+	0.988130i	$0.549093\pi$
$678$	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	$-0.741782\pi$
$683$		−	990.520i		−	1.45025i	0.688618	−	0.725124i	$-0.258218\pi$
$684$	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	−0.737293	−	0.675573i	$-0.763896\pi$
$691$	177.091	−	545.029i	0.256282	−	0.788754i	0.993574	−	0.113181i	$-0.0361038\pi$
$692$		−	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	0.313240	−	0.949674i	$-0.398585\pi$
$701$	−481.412	−	662.606i	−0.686750	−	0.945230i	−0.999990	+	0.00444396i	$0.998585\pi$
$702$	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	0.982568	−	0.185901i	$-0.0595204\pi$
$709$	55.5742	+	171.040i	0.0783840	+	0.241241i	−0.904185	+	0.427142i	$0.859520\pi$
$710$	−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	−0.989286	−	0.145992i	$-0.953363\pi$
$719$	−391.663	+	539.078i	−0.544733	+	0.749761i	0.444553	+	0.895753i	$0.353363\pi$
$720$	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	0.999829	−	0.0184934i	$-0.00588696\pi$
$733$	946.453	+	687.638i	1.29120	+	0.938115i	0.291376	+	0.956609i	$0.405887\pi$
$734$	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	−0.887506	−	0.460797i	$-0.847564\pi$
$739$	74.8985	−	230.514i	0.101351	−	0.311927i	0.988857	+	0.148870i	$0.0475636\pi$
$740$	−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	0.269943	−	0.962876i	$-0.412995\pi$
$743$	783.342	−	254.523i	1.05430	−	0.342562i	0.784353	+	0.620314i	$0.212995\pi$
$744$	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	−0.584474	−	0.811412i	$-0.698699\pi$
$751$	4.96588	−	3.60793i	0.00661236	−	0.00480416i	0.591087	+	0.806608i	$0.298699\pi$
$752$	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	0.426990	+	0.904256i	$0.359574\pi$
$757$	−340.620	+	1048.32i	−0.449961	+	1.38484i	−0.876951	+	0.480580i	$0.840426\pi$
$758$			1470.37i			1.93980i
$759$		0			0
$760$	−384.996			−0.506574
$761$	1141.53	+	370.907i	1.50004	+	0.487394i	0.940031	−	0.341090i	$-0.110796\pi$
$761$	1141.53	+	370.907i	1.50004	+	0.487394i	0.560013	+	0.828484i	$0.310796\pi$
$762$	−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	0.971478	−	0.237129i	$-0.0762063\pi$
$773$	344.566	+	474.255i	0.445752	+	0.613525i	−0.525726	+	0.850654i	$0.676206\pi$
$774$	−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	0.850577	−	0.525850i	$-0.176253\pi$
$787$	−115.407	−	355.185i	−0.146641	−	0.451315i	−0.997218	+	0.0745349i	$0.976253\pi$
$788$	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	0.236270	−	0.971687i	$-0.424075\pi$
$797$	795.852	−	258.588i	0.998560	−	0.324452i	0.762290	+	0.647236i	$0.224075\pi$
$798$	−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	−0.597668	−	0.801744i	$-0.703906\pi$
$809$	−493.440	+	160.328i	−0.609938	+	0.198181i	−0.0122700	+	0.999925i	$0.503906\pi$
$810$	−401.715	+	454.042i	−0.495944	+	0.560546i
$811$	633.194	−	460.042i	0.780757	−	0.567253i	−0.124449	−	0.992226i	$-0.539716\pi$
$811$	633.194	−	460.042i	0.780757	−	0.567253i	0.905206	+	0.424973i	$0.139716\pi$
$812$	−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	−0.564535	−	0.825409i	$-0.690945\pi$
$821$	324.234	−	446.270i	0.394926	−	0.543569i	0.959462	+	0.281840i	$0.0909446\pi$
$822$	−848.486	+	182.284i	−1.03222	+	0.221756i
$823$	−14.2681	+	43.9128i	−0.0173367	+	0.0533570i	−0.959351	−	0.282217i	$-0.908930\pi$
$823$	−14.2681	+	43.9128i	−0.0173367	+	0.0533570i	0.942014	+	0.335574i	$0.108930\pi$
$824$			1232.39i			1.49562i
$825$		0			0
$826$	−3598.50			−4.35654
$827$	−567.030	−	184.239i	−0.685648	−	0.222780i	−0.0545813	−	0.998509i	$-0.517382\pi$
$827$	−567.030	−	184.239i	−0.685648	−	0.222780i	−0.631066	+	0.775729i	$0.717382\pi$
$828$	−330.583	+	1589.28i	−0.399255	+	1.91942i
$829$	1122.16	+	815.300i	1.35364	+	0.983474i	0.998821	+	0.0485378i	$0.0154561\pi$
$829$	1122.16	+	815.300i	1.35364	+	0.983474i	0.354815	+	0.934937i	$0.384544\pi$
$830$	−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	0.683727	+	0.729738i	$0.260358\pi$
$839$	978.665	+	1347.02i	1.16647	+	1.60550i	0.482739	+	0.875764i	$0.339642\pi$
$840$	−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	0.983435	+	0.181263i	$0.0580184\pi$
$853$	251.091	+	772.780i	0.294363	+	0.905956i	−0.689072	+	0.724693i	$0.741982\pi$
$854$	−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	$-0.895740\pi$
$857$		−	551.421i		−	0.643431i	0.946836	−	0.321716i	$-0.104260\pi$
$858$		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	0.113596	−	0.993527i	$-0.463763\pi$
$863$	681.319	−	221.374i	0.789478	−	0.256517i	0.675882	+	0.737010i	$0.263763\pi$
$864$	−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	−0.0274497	−	0.999623i	$-0.508739\pi$
$877$	802.250	−	582.869i	0.914766	−	0.664616i	0.942216	+	0.335007i	$0.108739\pi$
$878$	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	$-0.747272\pi$
$881$		−	1256.55i		−	1.42628i	0.701021	−	0.713140i	$-0.252728\pi$
$882$	−391.877	−	869.951i	−0.444305	−	0.986339i
$883$	−225.170	+	163.596i	−0.255006	+	0.185273i	−0.707943	−	0.706270i	$-0.750376\pi$
$883$	−225.170	+	163.596i	−0.255006	+	0.185273i	0.452936	+	0.891543i	$0.350376\pi$
$884$	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	0.217529	+	0.976054i	$0.430200\pi$
$887$	−690.062	+	949.789i	−0.777973	+	1.07079i	−0.995503	+	0.0947346i	$0.969800\pi$
$888$	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	0.972793	−	0.231675i	$-0.0744206\pi$
$907$	44.9979	+	138.489i	0.0496118	+	0.152690i	−0.923181	+	0.384365i	$0.874421\pi$
$908$	−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	0.811308	−	0.584619i	$-0.198756\pi$
$911$	1024.00	+	332.718i	1.12404	+	0.365223i	0.312732	+	0.949841i	$0.398756\pi$
$912$	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	0.883738	−	0.467982i	$-0.155019\pi$
$919$	−97.6839	−	300.640i	−0.106294	−	0.327138i	−0.990032	+	0.140843i	$0.955019\pi$
$920$	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	−0.819337	−	0.573313i	$-0.805658\pi$
$929$	−1063.90	+	345.682i	−1.14521	+	0.372101i	−0.325872	+	0.945414i	$0.605658\pi$
$930$	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	0.613991	+	0.789313i	$0.289563\pi$
$937$	−324.843	+	999.765i	−0.346684	+	1.06699i	−0.960676	+	0.277672i	$0.910437\pi$
$938$	−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	−0.142511	−	0.989793i	$-0.545518\pi$
$941$	304.866	−	99.0570i	0.323981	−	0.105268i	0.466492	+	0.884525i	$0.345518\pi$
$942$	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	$0.118691\pi$
$947$			689.980i			0.728596i	−0.931283	+	0.364298i	$0.881309\pi$
$948$	−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	−0.160576	−	0.987023i	$-0.551335\pi$
$953$	788.855	−	1085.77i	0.827760	−	1.13931i	0.988336	−	0.152290i	$-0.0486647\pi$
$954$	−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	0.469722	−	0.882814i	$-0.344354\pi$
$971$	−500.100	−	688.328i	−0.515036	−	0.708886i	−0.984758	+	0.173928i	$0.944354\pi$
$972$	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	0.832527	−	0.553985i	$-0.186893\pi$
$977$	1153.28	+	374.724i	1.18043	+	0.383545i	0.347904	+	0.937530i	$0.386893\pi$
$978$	−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	−0.651155	−	0.758945i	$-0.725715\pi$
$983$	267.240	−	367.825i	0.271862	−	0.374186i	0.923017	+	0.384759i	$0.125715\pi$
$984$	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	0.820608	−	0.571492i	$-0.193635\pi$
$997$	529.077	+	384.397i	0.530669	+	0.385553i	−0.289939	+	0.957045i	$0.593635\pi$
$998$	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.251.1		16
3.2	odd	2	inner	363.3.h.n.251.4		16
11.2	odd	10		33.3.h.b.14.1	✓	16
11.3	even	5		363.3.h.j.323.1		16
11.4	even	5		363.3.b.l.122.1		8
11.5	even	5	inner	363.3.h.n.269.4		16
11.6	odd	10		363.3.h.o.269.1		16
11.7	odd	10		363.3.b.m.122.8		8
11.8	odd	10		33.3.h.b.26.4	yes	16
11.9	even	5		363.3.h.j.245.4		16
11.10	odd	2		363.3.h.o.251.4		16
33.2	even	10		33.3.h.b.14.4	yes	16
33.5	odd	10	inner	363.3.h.n.269.1		16
33.8	even	10		33.3.h.b.26.1	yes	16
33.14	odd	10		363.3.h.j.323.4		16
33.17	even	10		363.3.h.o.269.4		16
33.20	odd	10		363.3.h.j.245.1		16
33.26	odd	10		363.3.b.l.122.8		8
33.29	even	10		363.3.b.m.122.1		8
33.32	even	2		363.3.h.o.251.1		16

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

Fields

Representations

Groups

Database

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