LMFDB - Embedded newform 363.3.h.n.251.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 8]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("363.245");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.89103359628$
Analytic rank:	$0$
Dimension:	$16$
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			251.4
Root			$-2.10855 + 2.90217i$ of defining polynomial
Character	$\chi$	$=$	363.251
Dual form			363.3.h.n.269.4

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.41170 + 1.10853i) q^{2} +(1.50565 - 2.59480i) q^{3} +(7.17480 + 5.21280i) q^{4} +(-1.98428 + 0.644731i) q^{5} +(8.01326 - 7.18363i) q^{6} +(7.17034 + 5.20956i) q^{7} +(10.2655 + 14.1293i) q^{8} +(-4.46601 - 7.81376i) q^{9} -7.48447 q^{10} +(24.3290 - 10.7685i) q^{12} +(0.508273 - 1.56430i) q^{13} +(18.6881 + 25.7220i) q^{14} +(-1.31469 + 6.11955i) q^{15} +(8.39811 + 25.8467i) q^{16} +(-11.8154 + 3.83907i) q^{17} +(-6.57491 - 31.6089i) q^{18} +(8.54780 - 6.21034i) q^{19} +(-17.5977 - 5.71782i) q^{20} +(24.3138 - 10.7618i) q^{21} -20.3378i q^{23} +(52.1192 - 5.36321i) q^{24} +(-16.7037 + 12.1360i) q^{25} +(3.46815 - 4.77350i) q^{26} +(-26.9994 - 0.176408i) q^{27} +(24.2894 + 74.7550i) q^{28} +(6.82340 - 9.39161i) q^{29} +(-11.2690 + 19.4207i) q^{30} +(-7.22737 + 22.2436i) q^{31} +27.6317i q^{32} -44.5665 q^{34} +(-17.5867 - 5.71427i) q^{35} +(8.68881 - 79.3425i) q^{36} +(-5.86208 - 4.25905i) q^{37} +(36.0469 - 11.7123i) q^{38} +(-3.29377 - 3.67417i) q^{39} +(-29.4793 - 21.4180i) q^{40} +(-22.8512 - 31.4520i) q^{41} +(94.8813 - 9.76355i) q^{42} +15.8444 q^{43} +(13.8996 + 12.6253i) q^{45} +(22.5450 - 69.3864i) q^{46} +(26.6317 + 36.6554i) q^{47} +(79.7118 + 17.1248i) q^{48} +(9.13245 + 28.1068i) q^{49} +(-70.4413 + 22.8878i) q^{50} +(-7.82835 + 36.4391i) q^{51} +(11.8011 - 8.57403i) q^{52} +(-38.3428 - 12.4583i) q^{53} +(-91.9184 - 30.5315i) q^{54} +154.791i q^{56} +(-3.24458 - 31.5305i) q^{57} +(33.6903 - 24.4774i) q^{58} +(-66.5264 + 91.5657i) q^{59} +(-41.3326 + 37.0534i) q^{60} +(-23.9538 - 73.7222i) q^{61} +(-49.3152 + 67.8766i) q^{62} +(8.68341 - 79.2932i) q^{63} +(2.96194 - 9.11592i) q^{64} +3.43171i q^{65} +62.9082 q^{67} +(-104.786 - 34.0470i) q^{68} +(-52.7725 - 30.6217i) q^{69} +(-53.6662 - 38.9908i) q^{70} +(-9.71270 + 3.15585i) q^{71} +(64.5570 - 143.314i) q^{72} +(-60.3706 - 43.8618i) q^{73} +(-15.2784 - 21.0289i) q^{74} +(6.34041 + 61.6155i) q^{75} +93.7020 q^{76} +(-7.16445 - 16.1864i) q^{78} +(-26.6720 + 82.0879i) q^{79} +(-33.3284 - 45.8726i) q^{80} +(-41.1096 + 69.7926i) q^{81} +(-43.0961 - 132.636i) q^{82} +(-11.2304 + 3.64896i) q^{83} +(230.546 + 49.5291i) q^{84} +(20.9700 - 15.2356i) q^{85} +(54.0563 + 17.5639i) q^{86} +(-14.0957 - 31.8459i) q^{87} -74.5782i q^{89} +(33.4257 + 58.4818i) q^{90} +(11.7938 - 8.56870i) q^{91} +(106.017 - 145.919i) q^{92} +(46.8357 + 52.2447i) q^{93} +(50.2259 + 154.579i) q^{94} +(-12.9572 + 17.8341i) q^{95} +(71.6987 + 41.6037i) 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	0.989634	−	0.143614i	$-0.0458722\pi$
$2$	3.41170	+	1.10853i	1.70585	+	0.554264i	0.716217	+	0.697878i	$0.245872\pi$
$3$	1.50565	−	2.59480i	0.501885	−	0.864934i
$3$	1.50565	−	2.59480i	0.501885	−	0.864934i
$4$	7.17480	+	5.21280i	1.79370	+	1.30320i
$5$	−1.98428	+	0.644731i	−0.396856	+	0.128946i	−0.500644	−	0.865653i	$-0.666903\pi$
$5$	−1.98428	+	0.644731i	−0.396856	+	0.128946i	0.103789	+	0.994599i	$0.466903\pi$
$6$	8.01326	−	7.18363i	1.33554	−	1.19727i
$7$	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
$9$	−4.46601	−	7.81376i	−0.496223	−	0.868195i
$10$	−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
$15$	−1.31469	+	6.11955i	−0.0876459	+	0.407970i
$16$	8.39811	+	25.8467i	0.524882	+	1.61542i
$17$	−11.8154	+	3.83907i	−0.695026	+	0.225828i	−0.635162	−	0.772379i	$-0.719067\pi$
$17$	−11.8154	+	3.83907i	−0.695026	+	0.225828i	−0.0598641	+	0.998207i	$0.519067\pi$
$18$	−6.57491	−	31.6089i	−0.365273	−	1.75605i
$19$	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	$-0.854225\pi$
$23$		−	20.3378i		−	0.884251i	0.896953	−	0.442126i	$-0.145775\pi$
$24$	52.1192	−	5.36321i	2.17163	−	0.223467i
$25$	−16.7037	+	12.1360i	−0.668150	+	0.485439i
$26$	3.46815	−	4.77350i	0.133390	−	0.183596i
$27$	−26.9994	−	0.176408i	−0.999979	−	0.00653363i
$28$	24.2894	+	74.7550i	0.867478	+	2.66982i
$29$	6.82340	−	9.39161i	0.235290	−	0.323849i	−0.675002	−	0.737816i	$-0.735857\pi$
$29$	6.82340	−	9.39161i	0.235290	−	0.323849i	0.910292	+	0.413967i	$0.135857\pi$
$30$	−11.2690	+	19.4207i	−0.375634	+	0.647357i
$31$	−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
$36$	8.68881	−	79.3425i	0.241356	−	2.20396i
$37$	−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
$39$	−3.29377	−	3.67417i	−0.0844557	−	0.0942094i
$40$	−29.4793	−	21.4180i	−0.736983	−	0.535449i
$41$	−22.8512	−	31.4520i	−0.557347	−	0.767122i	0.433639	−	0.901087i	$-0.357229\pi$
$41$	−22.8512	−	31.4520i	−0.557347	−	0.767122i	−0.990986	+	0.133964i	$0.957229\pi$
$42$	94.8813	−	9.76355i	2.25908	−	0.232465i
$43$	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	$-0.0399082\pi$
$47$	26.6317	+	36.6554i	0.566633	+	0.779903i	−0.425518	+	0.904950i	$0.639908\pi$
$48$	79.7118	+	17.1248i	1.66066	+	0.356767i
$49$	9.13245	+	28.1068i	0.186376	+	0.573608i
$50$	−70.4413	+	22.8878i	−1.40883	+	0.457755i
$51$	−7.82835	+	36.4391i	−0.153497	+	0.714492i
$52$	11.8011	−	8.57403i	0.226945	−	0.164885i
$53$	−38.3428	−	12.4583i	−0.723450	−	0.235063i	−0.0759315	−	0.997113i	$-0.524193\pi$
$53$	−38.3428	−	12.4583i	−0.723450	−	0.235063i	−0.647518	+	0.762050i	$0.724193\pi$
$54$	−91.9184	−	30.5315i	−1.70219	−	0.565398i
$55$		0			0
$56$			154.791i			2.76412i
$57$	−3.24458	−	31.5305i	−0.0569224	−	0.553167i
$58$	33.6903	−	24.4774i	0.580867	−	0.422024i
$59$	−66.5264	+	91.5657i	−1.12757	+	1.55196i	−0.334955	+	0.942234i	$0.608721\pi$
$59$	−66.5264	+	91.5657i	−1.12757	+	1.55196i	−0.792611	+	0.609727i	$0.791279\pi$
$60$	−41.3326	+	37.0534i	−0.688877	+	0.617556i
$61$	−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
$63$	8.68341	−	79.2932i	0.137832	−	1.25862i
$64$	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
$69$	−52.7725	−	30.6217i	−0.764819	−	0.443792i
$70$	−53.6662	−	38.9908i	−0.766660	−	0.557011i
$71$	−9.71270	+	3.15585i	−0.136799	+	0.0444486i	−0.376616	−	0.926369i	$-0.622912\pi$
$71$	−9.71270	+	3.15585i	−0.136799	+	0.0444486i	0.239817	+	0.970818i	$0.422912\pi$
$72$	64.5570	−	143.314i	0.896625	−	1.99047i
$73$	−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
$75$	6.34041	+	61.6155i	0.0845388	+	0.821540i
$76$	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
$81$	−41.1096	+	69.7926i	−0.507525	+	0.861637i
$82$	−43.0961	−	132.636i	−0.525562	−	1.61751i
$83$	−11.2304	+	3.64896i	−0.135305	+	0.0439634i	−0.375887	−	0.926666i	$-0.622662\pi$
$83$	−11.2304	+	3.64896i	−0.135305	+	0.0439634i	0.240581	+	0.970629i	$0.422662\pi$
$84$	230.546	+	49.5291i	2.74460	+	0.589632i
$85$	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	$-0.137612\pi$
$90$	33.4257	+	58.4818i	0.371397	+	0.649798i
$91$	11.7938	−	8.56870i	0.129602	−	0.0941616i
$92$	106.017	−	145.919i	1.15236	−	1.58608i
$93$	46.8357	+	52.2447i	0.503610	+	0.561771i
$94$	50.2259	+	154.579i	0.534318	+	1.64446i
$95$	−12.9572	+	17.8341i	−0.136392	+	0.187727i
$96$	71.6987	+	41.6037i	0.746862	+	0.433372i
$97$	−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	0.368640	−	0.929572i	$-0.379824\pi$
$101$	12.1692	+	3.95400i	0.120487	+	0.0391485i	−0.248153	+	0.968721i	$0.579824\pi$
$102$	−67.1017	+	115.641i	−0.657860	+	1.13374i
$103$	−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
$105$	−41.3069	+	37.0303i	−0.393399	+	0.352670i
$106$	−117.004	−	85.0083i	−1.10381	−	0.801965i
$107$	108.282	+	149.037i	1.01198	+	1.39287i	0.917677	+	0.397328i	$0.130062\pi$
$107$	108.282	+	149.037i	1.01198	+	1.39287i	0.0943034	+	0.995544i	$0.469938\pi$
$108$	−192.796	−	142.008i	−1.78515	−	1.31489i
$109$	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	$0.0348030\pi$
$113$	89.3418	+	122.968i	0.790635	+	1.08822i	−0.203393	+	0.979097i	$0.565197\pi$
$114$	23.8829	−	111.169i	0.209500	−	0.975170i
$115$	13.1124	+	40.3558i	0.114021	+	0.350920i
$116$	97.9131	−	31.8139i	0.844078	−	0.274258i
$117$	−14.4930	+	3.01467i	−0.123872	+	0.0257664i
$118$	−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
$123$	−116.018	+	11.9386i	−0.943235	+	0.0970615i
$124$	−167.806	+	121.918i	−1.35327	+	0.983212i
$125$	55.9792	−	77.0488i	0.447834	−	0.616390i
$126$	117.524	−	260.899i	0.932730	−	2.07063i
$127$	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
$129$	23.8562	−	41.1130i	0.184931	−	0.318706i
$130$	−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
$135$	53.6881	−	17.0573i	0.397690	−	0.126351i
$136$	−175.535	−	127.534i	−1.29070	−	0.937750i
$137$	−76.6942	+	24.9195i	−0.559812	+	0.181894i	−0.575237	−	0.817987i	$-0.695090\pi$
$137$	−76.6942	+	24.9195i	−0.559812	+	0.181894i	0.0154246	+	0.999881i	$0.495090\pi$
$138$	−146.099	−	162.972i	−1.05869	−	1.18096i
$139$	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
$141$	135.212	−	13.9137i	0.958949	−	0.0986785i
$142$	−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
$147$	86.6819	+	18.6222i	0.589673	+	0.126682i
$148$	−19.8577	−	61.1156i	−0.134173	−	0.412943i
$149$	215.252	−	69.9397i	1.44465	−	0.469394i	0.521303	−	0.853371i	$-0.325446\pi$
$149$	215.252	−	69.9397i	1.44465	−	0.469394i	0.923342	+	0.383978i	$0.125446\pi$
$150$	−46.6710	+	217.242i	−0.311140	+	1.44828i
$151$	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
$156$	−4.47948	−	43.5312i	−0.0287146	−	0.279046i
$157$	−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
$159$	−90.0580	+	80.7341i	−0.566403	+	0.507762i
$160$	−17.8150	−	54.8289i	−0.111344	−	0.342681i
$161$	105.951	−	145.829i	0.658079	−	0.905769i
$162$	−217.621	+	192.540i	−1.34334	+	1.18852i
$163$	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	0.724994	−	0.688755i	$-0.241842\pi$
$167$	151.417	+	49.1982i	0.906686	+	0.294600i	0.181692	+	0.983355i	$0.441842\pi$
$168$	401.652	+	233.062i	2.39079	+	1.38727i
$169$	134.535	+	97.7455i	0.796066	+	0.578376i
$170$	88.4323	−	28.7334i	0.520190	−	0.169020i
$171$	−86.7006	−	39.0550i	−0.507021	−	0.228392i
$172$	113.680	+	82.5935i	0.660931	+	0.480195i
$173$	22.5826	+	31.0822i	0.130535	+	0.179666i	0.869282	−	0.494317i	$-0.164582\pi$
$173$	22.5826	+	31.0822i	0.130535	+	0.179666i	−0.738746	+	0.673983i	$0.764582\pi$
$174$	−12.7882	−	124.274i	−0.0734952	−	0.714219i
$175$	−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	$-0.324185\pi$
$179$	−80.0291	−	110.151i	−0.447090	−	0.615367i	−0.971769	+	0.235933i	$0.924185\pi$
$180$	33.9136	+	163.040i	0.188409	+	0.905776i
$181$	−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
$183$	−227.361	−	48.8448i	−1.24241	−	0.266911i
$184$	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
$189$	−192.676	−	141.920i	−1.01945	−	0.750899i
$190$	−63.9758	+	46.4811i	−0.336715	+	0.244637i
$191$	185.493	−	255.309i	0.971169	−	1.33670i	0.0297142	−	0.999558i	$-0.490540\pi$
$191$	185.493	−	255.309i	0.971169	−	1.33670i	0.941454	−	0.337140i	$-0.109460\pi$
$192$	−19.1943	−	21.4111i	−0.0999706	−	0.111516i
$193$	−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
$195$	8.90461	+	5.16697i	0.0456647	+	0.0264973i
$196$	−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
$201$	94.7181	−	163.235i	0.471234	−	0.812112i
$202$	37.1344	+	26.9797i	0.183834	+	0.133563i
$203$	97.8522	−	31.7941i	0.482031	−	0.156621i
$204$	−246.116	+	220.635i	−1.20645	+	1.08155i
$205$	65.6213	+	47.6767i	0.320104	+	0.232569i
$206$	−148.788	−	204.789i	−0.722270	−	0.994120i
$207$	−158.914	+	90.8287i	−0.767703	+	0.438786i
$208$	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
$213$	−6.43517	+	29.9542i	−0.0302121	+	0.140630i
$214$	204.213	+	628.504i	0.954268	+	2.93693i
$215$	−31.4396	+	10.2154i	−0.146231	+	0.0475133i
$216$	−274.671	−	383.294i	−1.27163	−	1.77451i
$217$	−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
$222$	−77.5698	+	7.98214i	−0.349413	+	0.0359556i
$223$	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
$225$	169.427	+	76.3196i	0.753007	+	0.339198i
$226$	168.493	+	518.569i	0.745546	+	2.29456i
$227$	66.3365	−	91.3043i	0.292231	−	0.402222i	−0.637506	−	0.770445i	$-0.720034\pi$
$227$	66.3365	−	91.3043i	0.292231	−	0.402222i	0.929737	+	0.368224i	$0.120034\pi$
$228$	141.083	−	243.138i	0.618785	−	1.06640i
$229$	−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	0.642741	−	0.766084i	$-0.277797\pi$
$233$	165.998	+	53.9359i	0.712436	+	0.231485i	0.0696955	+	0.997568i	$0.477797\pi$
$234$	−52.7877	−	5.78079i	−0.225589	−	0.0247042i
$235$	−76.4777	−	55.5643i	−0.325437	−	0.236444i
$236$	−954.627	+	310.177i	−4.04503	+	1.31431i
$237$	172.843	+	192.805i	0.729296	+	0.813521i
$238$	−319.557	−	232.172i	−1.34268	−	0.975511i
$239$	202.993	+	279.397i	0.849345	+	1.16902i	0.984007	+	0.178132i	$0.0570053\pi$
$239$	202.993	+	279.397i	0.849345	+	1.16902i	−0.134661	+	0.990892i	$0.542995\pi$
$240$	−169.211	+	17.4123i	−0.705047	+	0.0725513i
$241$	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
$246$	−409.052	−	87.8783i	−1.66282	−	0.357229i
$247$	−5.37024	−	16.5279i	−0.0217419	−	0.0669146i
$248$	−388.479	+	126.224i	−1.56645	+	0.508970i
$249$	−7.44069	+	34.6346i	−0.0298823	+	0.139095i
$250$	276.395	−	200.813i	1.10558	−	0.803251i
$251$	188.638	+	61.2921i	0.751544	+	0.244192i	0.659646	−	0.751577i	$-0.270706\pi$
$251$	188.638	+	61.2921i	0.751544	+	0.244192i	0.0918987	+	0.995768i	$0.470706\pi$
$252$	475.641	−	523.648i	1.88746	−	2.07797i
$253$		0			0
$254$			51.2057i			0.201597i
$255$	−7.95978	−	77.3524i	−0.0312148	−	0.303343i
$256$	389.537	−	283.016i	1.52163	−	1.10553i
$257$	1.09633	−	1.50897i	0.00426588	−	0.00587148i	−0.806879	−	0.590717i	$-0.798845\pi$
$257$	1.09633	−	1.50897i	0.00426588	−	0.00587148i	0.811145	+	0.584846i	$0.198845\pi$
$258$	126.965	−	113.820i	0.492113	−	0.441163i
$259$	−19.8453	−	61.0776i	−0.0766229	−	0.235821i
$260$	−17.8888	+	24.6218i	−0.0688031	+	0.0946994i
$261$	−103.857	−	11.3734i	−0.397920	−	0.0435763i
$262$	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
$267$	−193.516	−	112.289i	−0.724778	−	0.420558i
$268$	451.354	+	327.928i	1.68416	+	1.22361i
$269$	135.856	−	44.1424i	0.505042	−	0.164098i	−0.0454041	−	0.998969i	$-0.514458\pi$
$269$	135.856	−	44.1424i	0.505042	−	0.164098i	0.550446	+	0.834871i	$0.314458\pi$
$270$	202.076	+	1.32032i	0.748431	+	0.00489008i
$271$	−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
$273$	−4.47669	−	43.5041i	−0.0163981	−	0.159356i
$274$	−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
$279$	206.083	−	42.8670i	0.738649	−	0.153645i
$280$	−99.7985	−	307.148i	−0.356423	−	1.09696i
$281$	61.9247	−	20.1206i	0.220373	−	0.0716034i	−0.196750	−	0.980454i	$-0.563039\pi$
$281$	61.9247	−	20.1206i	0.220373	−	0.0716034i	0.417122	+	0.908850i	$0.363039\pi$
$282$	476.726	+	102.417i	1.69052	+	0.363181i
$283$	−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
$288$	215.907	−	123.403i	0.749677	−	0.428483i
$289$	−108.940	+	79.1493i	−0.376954	+	0.273873i
$290$	−51.0695	+	70.2912i	−0.176102	+	0.242383i
$291$	154.531	+	172.378i	0.531034	+	0.592363i
$292$	−204.504	−	629.400i	−0.700358	−	2.15548i
$293$	−108.158	+	148.867i	−0.369139	+	0.508077i	−0.952667	−	0.304017i	$-0.901672\pi$
$293$	−108.158	+	148.867i	−0.369139	+	0.508077i	0.583527	+	0.812094i	$0.301672\pi$
$294$	275.089	+	159.623i	0.935678	+	0.542935i
$295$	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
$300$	−275.698	+	475.130i	−0.918994	+	1.58377i
$301$	113.610	+	82.5421i	0.377440	+	0.274226i
$302$	930.469	−	302.328i	3.08102	−	1.00109i
$303$	28.5824	−	25.6232i	0.0943313	−	0.0845650i
$304$	232.302	+	168.778i	0.764153	+	0.555189i
$305$	95.0619	+	130.842i	0.311679	+	0.428989i
$306$	199.034	+	348.232i	0.650439	+	1.13801i
$307$	−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	$-0.152620\pi$
$311$	54.2185	+	74.6253i	0.174336	+	0.239953i	−0.712903	+	0.701262i	$0.752620\pi$
$312$	18.1011	−	84.2561i	0.0580162	−	0.270052i
$313$	−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
$315$	33.8925	+	162.938i	0.107595	+	0.517264i
$316$	−619.274	+	449.929i	−1.95973	+	1.42382i
$317$	−498.144	−	161.857i	−1.57143	−	0.510589i	−0.611600	−	0.791167i	$-0.709474\pi$
$317$	−498.144	−	161.857i	−1.57143	−	0.510589i	−0.959831	+	0.280578i	$0.909474\pi$
$318$	−396.747	+	175.609i	−1.24763	+	0.552229i
$319$		0			0
$320$			19.9982i			0.0624943i
$321$	549.757	−	56.5716i	1.71264	−	0.176235i
$322$	523.128	−	380.075i	1.62462	−	1.18036i
$323$	−77.1542	+	106.194i	−0.238867	+	0.328773i
$324$	−658.767	+	286.452i	−2.03323	+	0.884111i
$325$	10.4943	+	32.2981i	0.0322901	+	0.0993787i
$326$	341.430	−	469.939i	1.04733	−	1.44153i
$327$	88.1401	−	151.898i	0.269542	−	0.464520i
$328$	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
$333$	−7.09908	+	64.8258i	−0.0213186	+	0.194672i
$334$	462.051	+	335.699i	1.38339	+	1.00509i
$335$	−124.827	+	40.5589i	−0.372619	+	0.121071i
$336$	482.348	+	538.054i	1.43556	+	1.60135i
$337$	−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
$339$	453.597	−	46.6764i	1.33804	−	0.137688i
$340$	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
$345$	124.458	+	26.7378i	0.360748	+	0.0775010i
$346$	42.5894	+	131.077i	0.123091	+	0.378835i
$347$	437.276	−	142.079i	1.26016	−	0.409451i	0.398609	−	0.917121i	$-0.369493\pi$
$347$	437.276	−	142.079i	1.26016	−	0.409451i	0.861551	+	0.507670i	$0.169493\pi$
$348$	64.8725	−	301.966i	0.186415	−	0.867718i
$349$	−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	$0.00763985\pi$
$353$			16.9433i			0.0479980i	−0.999712	+	0.0239990i	$0.992360\pi$
$354$	124.681	+	1211.64i	0.352207	+	3.42271i
$355$	17.2380	−	12.5242i	0.0485578	−	0.0352793i
$356$	388.761	−	535.084i	1.09203	−	1.50304i
$357$	−245.963	+	220.498i	−0.688973	+	0.617642i
$358$	−150.930	−	464.516i	−0.421593	−	1.29753i
$359$	−44.6059	+	61.3948i	−0.124250	+	0.171016i	−0.866611	−	0.498985i	$-0.833706\pi$
$359$	−44.6059	+	61.3948i	−0.124250	+	0.171016i	0.742360	+	0.670001i	$0.233706\pi$
$360$	−35.7000	+	325.997i	−0.0991666	+	0.905547i
$361$	−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
$366$	−721.541	−	418.680i	−1.97142	−	1.14393i
$367$	−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
$369$	−143.705	+	319.019i	−0.389443	+	0.864550i
$370$	43.8745	+	31.8767i	0.118580	+	0.0861533i
$371$	−210.029	−	289.080i	−0.566115	−	0.779190i
$372$	63.6958	+	618.990i	0.171225	+	1.66395i
$373$	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
$378$	−500.031	−	697.775i	−1.32283	−	1.84597i
$379$	−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
$381$	41.8675	+	8.99457i	0.109889	+	0.0236078i
$382$	915.865	−	665.415i	2.39755	−	1.74192i
$383$	−50.3695	−	16.3660i	−0.131513	−	0.0427311i	0.242521	−	0.970146i	$-0.422026\pi$
$383$	−50.3695	−	16.3660i	−0.131513	−	0.0427311i	−0.374034	+	0.927415i	$0.622026\pi$
$384$	−175.956	−	397.532i	−0.458219	−	1.03524i
$385$		0			0
$386$		−	525.213i		−	1.36065i
$387$	−70.7611	−	123.804i	−0.182845	−	0.319907i
$388$	−553.664	+	402.260i	−1.42697	+	1.03675i
$389$	−53.2922	+	73.3504i	−0.136998	+	0.188561i	−0.872004	−	0.489500i	$-0.837179\pi$
$389$	−53.2922	+	73.3504i	−0.136998	+	0.188561i	0.735006	+	0.678061i	$0.237179\pi$
$390$	24.6521	+	27.4992i	0.0632106	+	0.0705107i
$391$	78.0782	+	240.300i	0.199688	+	0.614578i
$392$	−303.380	+	417.567i	−0.773929	+	1.06522i
$393$	−398.786	−	231.398i	−1.01472	−	0.588800i
$394$	−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
$399$	140.995	−	242.987i	0.353371	−	0.608990i
$400$	−453.955	−	329.818i	−1.13489	−	0.824544i
$401$	−17.9951	+	5.84696i	−0.0448755	+	0.0145809i	−0.331369	−	0.943501i	$-0.607510\pi$
$401$	−17.9951	+	5.84696i	−0.0448755	+	0.0145809i	0.286493	+	0.958082i	$0.407510\pi$
$402$	504.100	−	451.910i	1.25398	−	1.12415i
$403$	31.1222	+	22.6116i	0.0772262	+	0.0561081i
$404$	66.6999	+	91.8045i	0.165099	+	0.227239i
$405$	36.5754	−	164.993i	0.0903095	−	0.407389i
$406$	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
$411$	−50.8139	+	236.527i	−0.123635	+	0.575490i
$412$	−193.383	−	595.172i	−0.469376	−	1.44459i
$413$	−954.034	+	309.984i	−2.31001	+	0.750567i
$414$	−642.855	+	133.719i	−1.55279	+	0.322993i
$415$	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	$0.836014\pi$
$420$	−489.401	+	50.3607i	−1.16524	+	0.119906i
$421$	−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
$423$	167.479	−	371.797i	0.395932	−	0.878953i
$424$	−217.582	−	669.650i	−0.513166	−	1.57936i
$425$	150.771	−	207.519i	0.354756	−	0.488280i
$426$	−55.1600	+	95.0611i	−0.129483	+	0.223148i
$427$	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	$-0.571989\pi$
$431$	−421.718	−	137.024i	−0.978464	−	0.317922i	−0.754228	+	0.656613i	$0.771989\pi$
$432$	−222.185	−	699.328i	−0.514316	−	1.61882i
$433$	−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
$435$	48.5018	+	54.1032i	0.111498	+	0.124375i
$436$	420.008	+	305.154i	0.963322	+	0.699894i
$437$	−126.305	−	173.843i	−0.289026	−	0.397811i
$438$	−798.853	+	82.2042i	−1.82386	+	0.187681i
$439$	−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	$0.0331830\pi$
$443$	348.285	+	479.374i	0.786197	+	1.08211i	−0.208374	+	0.978049i	$0.566817\pi$
$444$	−188.482	−	40.4923i	−0.424509	−	0.0911989i
$445$	48.0829	+	147.984i	0.108051	+	0.332548i
$446$	56.3607	−	18.3127i	0.126369	−	0.0410598i
$447$	142.616	−	663.842i	0.319051	−	1.48511i
$448$	68.7280	−	49.9338i	0.153411	−	0.111459i
$449$	414.782	+	134.771i	0.923791	+	0.300158i	0.732021	−	0.681282i	$-0.238577\pi$
$449$	414.782	+	134.771i	0.923791	+	0.300158i	0.191770	+	0.981440i	$0.438577\pi$
$450$	493.430	+	448.194i	1.09651	+	0.995986i
$451$		0			0
$452$			1347.99i			2.98229i
$453$	−83.7514	−	813.889i	−0.184882	−	1.79666i
$454$	327.534	−	237.967i	0.721440	−	0.524157i
$455$	−17.8777	+	24.6065i	−0.0392916	+	0.0540803i
$456$	412.197	−	369.521i	0.903941	−	0.810354i
$457$	−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
$459$	319.687	−	101.568i	0.696487	−	0.221282i
$460$	−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
$465$	−126.619	−	73.4716i	−0.272299	−	0.158003i
$466$	506.545	+	368.026i	1.08701	+	0.789756i
$467$	−46.0163	+	14.9516i	−0.0985361	+	0.0320163i	−0.357870	−	0.933771i	$-0.616497\pi$
$467$	−46.0163	+	14.9516i	−0.0985361	+	0.0320163i	0.259334	+	0.965788i	$0.416497\pi$
$468$	−119.699	−	53.9196i	−0.255768	−	0.115213i
$469$	451.073	+	327.724i	0.961777	+	0.698772i
$470$	−199.324	−	274.346i	−0.424094	−	0.583716i
$471$	1.86073	+	18.0824i	0.00395060	+	0.0383916i
$472$	−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
$477$	73.8929	+	355.241i	0.154912	+	0.744739i
$478$	382.834	+	1178.24i	0.800908	+	2.46494i
$479$	−163.035	+	52.9731i	−0.340364	+	0.110591i	−0.474212	−	0.880411i	$-0.657267\pi$
$479$	−163.035	+	52.9731i	−0.340364	+	0.110591i	0.133847	+	0.991002i	$0.457267\pi$
$480$	−169.093	−	36.3270i	−0.352278	−	0.0756813i
$481$	−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
$486$	171.943	+	854.582i	0.353792	+	1.75840i
$487$	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
$489$	−324.264	−	361.712i	−0.663116	−	0.739698i
$490$	−68.3515	−	210.364i	−0.139493	−	0.429315i
$491$	−194.115	+	267.177i	−0.395347	+	0.544148i	−0.959569	−	0.281475i	$-0.909176\pi$
$491$	−194.115	+	267.177i	−0.395347	+	0.544148i	0.564222	+	0.825623i	$0.309176\pi$
$492$	−894.638	−	519.121i	−1.81837	−	1.05512i
$493$	−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
$498$	−63.7789	+	109.915i	−0.128070	+	0.220712i
$499$	−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
$501$	355.641	−	318.821i	0.709862	−	0.636369i
$502$	575.631	+	418.220i	1.14668	+	0.833108i
$503$	−336.038	−	462.516i	−0.668067	−	0.919516i	0.331647	−	0.943403i	$-0.392396\pi$
$503$	−336.038	−	462.516i	−0.668067	−	0.919516i	−0.999715	+	0.0238878i	$0.992396\pi$
$504$	1209.50	−	691.297i	2.39980	−	1.37162i
$505$	−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	$-0.378319\pi$
$509$	−317.947	−	437.617i	−0.624651	−	0.859758i	−0.997681	+	0.0680613i	$0.978319\pi$
$510$	58.5910	−	272.727i	0.114884	−	0.534759i
$511$	−204.377	−	629.008i	−0.399955	−	1.23094i
$512$	1091.44	−	354.631i	2.13172	−	0.692639i
$513$	−231.881	+	166.168i	−0.452010	+	0.323914i
$514$	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
$519$	114.654	−	11.7982i	0.220913	−	0.0227326i
$520$	−48.4877	+	35.2284i	−0.0932456	+	0.0677469i
$521$	−198.606	+	273.357i	−0.381201	+	0.524678i	−0.955902	−	0.293685i	$-0.905118\pi$
$521$	−198.606	+	273.357i	−0.381201	+	0.524678i	0.574701	+	0.818363i	$0.305118\pi$
$522$	−341.722	−	153.931i	−0.654639	−	0.294887i
$523$	−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
$525$	−275.527	+	474.835i	−0.524813	+	0.904447i
$526$	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
$531$	1012.58	+	110.888i	1.90693	+	0.208828i
$532$	671.875	+	488.146i	1.26292	+	0.917568i
$533$	−60.8151	+	19.7600i	−0.114100	+	0.0370732i
$534$	−535.742	−	597.614i	−1.00326	−	1.11913i
$535$	−310.950	−	225.919i	−0.581216	−	0.422278i
$536$	645.788	+	888.850i	1.20483	+	1.65830i
$537$	−406.315	+	41.8110i	−0.756639	+	0.0778603i
$538$	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
$543$	−382.297	−	82.1304i	−0.704046	−	0.151253i
$544$	−106.080	−	326.480i	−0.195000	−	0.600148i
$545$	−116.158	+	37.7422i	−0.213135	+	0.0692517i
$546$	32.9524	−	153.386i	0.0603524	−	0.280926i
$547$	−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
$552$	−109.076	−	1059.99i	−0.197601	−	1.92027i
$553$	−618.888	+	449.649i	−1.11915	+	0.813108i
$554$	−516.425	+	710.798i	−0.932174	+	1.28303i
$555$	33.7703	−	30.2740i	0.0608473	−	0.0545477i
$556$	580.832	+	1787.62i	1.04466	+	3.21514i
$557$	−225.174	+	309.925i	−0.404262	+	0.556419i	−0.961807	−	0.273728i	$-0.911743\pi$
$557$	−225.174	+	309.925i	−0.404262	+	0.556419i	0.557545	+	0.830146i	$0.311743\pi$
$558$	750.613	+	82.1998i	1.34519	+	0.147312i
$559$	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	$-0.358942\pi$
$563$	137.748	+	44.7570i	0.244667	+	0.0794973i	−0.184116	+	0.982904i	$0.558942\pi$
$564$	1042.65	+	605.004i	1.84866	+	1.07270i
$565$	−256.561	−	186.402i	−0.454089	−	0.329915i
$566$	−537.602	+	174.677i	−0.949827	+	0.308617i
$567$	−658.358	+	286.274i	−1.16112	+	0.504892i
$568$	−144.296	−	104.837i	−0.254043	−	0.184573i
$569$	−542.614	−	746.845i	−0.953628	−	1.31256i	−0.949897	−	0.312563i	$-0.898812\pi$
$569$	−542.614	−	746.845i	−0.953628	−	1.31256i	−0.00373108	−	0.999993i	$-0.501188\pi$
$570$	24.2839	+	235.989i	0.0426034	+	0.414016i
$571$	−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
$576$	−84.4576	+	17.5679i	−0.146628	+	0.0304998i
$577$	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
$579$	−429.432	−	92.2565i	−0.741678	−	0.159338i
$580$	−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
$585$	26.8146	−	15.3260i	0.0458368	−	0.0261984i
$586$	−534.025	+	387.992i	−0.911306	+	0.662102i
$587$	−24.9599	+	34.3544i	−0.0425212	+	0.0585254i	−0.829748	−	0.558138i	$-0.811516\pi$
$587$	−24.9599	+	34.3544i	−0.0425212	+	0.0585254i	0.787227	+	0.616663i	$0.211516\pi$
$588$	524.851	+	585.466i	0.892604	+	0.995690i
$589$	76.3620	+	235.018i	0.129647	+	0.399012i
$590$	497.915	−	685.321i	0.843923	−	1.16156i
$591$	595.400	+	345.485i	1.00744	+	0.584578i
$592$	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
$597$	−586.239	+	1010.31i	−0.981975	+	1.69231i
$598$	−97.0823	−	70.5344i	−0.162345	−	0.117951i
$599$	692.381	−	224.968i	1.15589	−	0.375573i	0.332534	−	0.943091i	$-0.392096\pi$
$599$	692.381	−	224.968i	1.15589	−	0.375573i	0.823361	+	0.567518i	$0.192096\pi$
$600$	−805.497	+	722.103i	−1.34250	+	1.20350i
$601$	−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
$603$	−280.949	−	491.550i	−0.465918	−	0.815173i
$604$	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
$609$	64.8322	−	301.778i	0.106457	−	0.495531i
$610$	179.281	+	551.771i	0.293904	+	0.904543i
$611$	70.8764	−	23.0291i	0.116001	−	0.0376909i
$612$	201.939	+	970.824i	0.329966	+	1.58631i
$613$	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	$-0.788093\pi$
$617$		−	762.156i		−	1.23526i	0.786468	−	0.617631i	$-0.211907\pi$
$618$	−755.409	+	77.7337i	−1.22235	+	0.125783i
$619$	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
$621$	−3.58775	+	549.108i	−0.00577737	+	0.884232i
$622$	102.253	+	314.702i	0.164394	+	0.505952i
$623$	388.519	−	534.751i	0.623626	−	0.858348i
$624$	67.3037	−	115.989i	0.107858	−	0.185880i
$625$	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
$630$	−64.9907	+	593.467i	−0.103160	+	0.942012i
$631$	−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
$633$	408.495	+	455.672i	0.645332	+	0.719861i
$634$	−1520.09	−	1104.41i	−2.39763	−	1.74198i
$635$	−17.5053	−	24.0939i	−0.0275674	−	0.0379432i
$636$	−1067.00	+	109.797i	−1.67767	+	0.172637i
$637$	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	$-0.989957\pi$
$641$	−461.931	−	635.794i	−0.720641	−	0.991878i	0.278861	−	0.960331i	$-0.410043\pi$
$642$	1938.32	+	416.417i	3.01919	+	0.648624i
$643$	−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
$645$	−20.8304	+	96.9605i	−0.0322952	+	0.150326i
$646$	−380.946	+	276.773i	−0.589699	+	0.428441i
$647$	1112.14	+	361.357i	1.71892	+	0.558512i	0.991778	−	0.127971i	$-0.0408463\pi$
$647$	1112.14	+	361.357i	1.71892	+	0.558512i	0.727146	+	0.686483i	$0.240846\pi$
$648$	−1408.13	+	135.609i	−2.17305	+	0.209274i
$649$		0			0
$650$			121.825i			0.187423i
$651$	63.6562	+	618.606i	0.0977822	+	0.950239i
$652$	1161.79	−	844.092i	1.78189	−	1.29462i
$653$	−314.778	+	433.255i	−0.482049	+	0.663484i	−0.978897	−	0.204354i	$-0.934491\pi$
$653$	−314.778	+	433.255i	−0.482049	+	0.663484i	0.496848	+	0.867838i	$0.334491\pi$
$654$	469.091	−	420.525i	0.717265	−	0.643005i
$655$	99.0863	+	304.956i	0.151277	+	0.465582i
$656$	621.024	−	854.767i	0.946684	−	1.30300i
$657$	−73.1100	+	667.609i	−0.111278	+	1.01615i
$658$	−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
$663$	53.0228	+	30.7669i	0.0799740	+	0.0464056i
$664$	−166.843	−	121.219i	−0.251270	−	0.182558i
$665$	−185.815	+	60.3751i	−0.279422	+	0.0907895i
$666$	−96.0812	+	213.297i	−0.144266	+	0.320265i
$667$	−191.004	−	138.773i	−0.286363	−	0.208055i
$668$	829.924	+	1142.29i	1.24240	+	1.71002i
$669$	−5.07302	−	49.2991i	−0.00758298	−	0.0736908i
$670$	−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
$675$	453.132	−	324.718i	0.671307	−	0.481063i
$676$	455.735	+	1402.61i	0.674165	+	2.07487i
$677$	581.347	−	188.891i	0.858711	−	0.279012i	0.153621	−	0.988130i	$-0.450907\pi$
$677$	581.347	−	188.891i	0.858711	−	0.279012i	0.705090	+	0.709118i	$0.250907\pi$
$678$	1599.28	+	343.579i	2.35882	+	0.506754i
$679$	−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	$0.741782\pi$
$684$	−418.474	−	732.165i	−0.611804	−	1.07042i
$685$	136.116	−	98.8943i	0.198710	−	0.144371i
$686$	363.423	−	500.209i	0.529772	−	0.729168i
$687$	738.170	+	823.420i	1.07448	+	1.19857i
$688$	133.063	+	409.525i	0.193405	+	0.595240i
$689$	−38.9772	+	53.6476i	−0.0565707	+	0.0778629i
$690$	394.974	+	229.187i	0.572427	+	0.332155i
$691$	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
$696$	305.261	−	526.078i	0.438593	−	0.755859i
$697$	390.744	+	283.892i	0.560608	+	0.407306i
$698$	−1343.35	+	436.482i	−1.92458	+	0.625333i
$699$	389.888	−	349.522i	0.557780	−	0.500032i
$700$	−1312.95	−	953.913i	−1.87564	−	1.36273i
$701$	481.412	+	662.606i	0.686750	+	0.945230i	0.999990	−	0.00444396i	$-0.00141456\pi$
$701$	481.412	+	662.606i	0.686750	+	0.945230i	−0.313240	+	0.949674i	$0.601415\pi$
$702$	−94.4801	+	128.270i	−0.134587	+	0.182721i
$703$	−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
$708$	−632.490	+	2944.09i	−0.893348	+	4.15832i
$709$	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
$711$	760.532	−	158.197i	1.06967	−	0.222499i
$712$	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
$717$	1030.62	−	106.053i	1.43740	−	0.147913i
$718$	−220.240	+	160.014i	−0.306741	+	0.222860i
$719$	391.663	−	539.078i	0.544733	−	0.749761i	−0.444553	−	0.895753i	$-0.646637\pi$
$719$	391.663	−	539.078i	0.544733	−	0.749761i	0.989286	+	0.145992i	$0.0466373\pi$
$720$	−209.592	+	465.287i	−0.291100	+	0.646232i
$721$	−193.263	−	594.801i	−0.268048	−	0.824967i
$722$	−525.802	+	723.704i	−0.728257	+	1.00236i
$723$	393.649	−	678.404i	0.544466	−	0.938318i
$724$	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
$729$	728.938	+	9.52583i	0.999915	+	0.0130670i
$730$	451.842	+	328.283i	0.618962	+	0.449702i
$731$	−187.208	+	60.8277i	−0.256099	+	0.0832116i
$732$	−1376.65	−	1535.64i	−1.88067	−	2.09786i
$733$	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
$735$	−184.007	+	18.9349i	−0.250350	+	0.0257617i
$736$	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
$741$	−50.9724	−	10.9506i	−0.0687886	−	0.0147781i
$742$	−396.102	−	1219.08i	−0.533830	−	1.64296i
$743$	−783.342	+	254.523i	−1.05430	+	0.342562i	−0.784353	−	0.620314i	$-0.787005\pi$
$743$	−783.342	+	254.523i	−1.05430	+	0.342562i	−0.269943	+	0.962876i	$0.587005\pi$
$744$	−257.388	+	1198.08i	−0.345951	+	1.61032i
$745$	−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
$750$	−104.914	−	1019.55i	−0.139885	−	1.35939i
$751$	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
$753$	443.064	−	397.193i	0.588398	−	0.527480i
$754$	−21.1662	−	65.1430i	−0.0280719	−	0.0863965i
$755$	−334.461	+	460.347i	−0.442995	+	0.609731i
$756$	−642.612	−	2022.63i	−0.850016	−	2.67543i
$757$	−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	−0.560013	−	0.828484i	$-0.689204\pi$
$761$	−1141.53	−	370.907i	−1.50004	−	0.487394i	−0.940031	+	0.341090i	$0.889204\pi$
$762$	132.869	+	77.0981i	0.174368	+	0.101179i
$763$	419.747	+	304.964i	0.550127	+	0.399691i
$764$	2661.75	−	864.856i	3.48397	−	1.13201i
$765$	−212.699	−	95.8120i	−0.278038	−	0.125244i
$766$	−153.703	−	111.672i	−0.200657	−	0.145786i
$767$	109.423	+	150.608i	0.142664	+	0.196360i
$768$	−147.861	−	1436.90i	−0.192527	−	1.87096i
$769$	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	$-0.323794\pi$
$773$	−344.566	−	474.255i	−0.445752	−	0.613525i	−0.971478	+	0.237129i	$0.923794\pi$
$774$	−104.175	−	500.823i	−0.134593	−	0.647058i
$775$	−149.223	−	459.262i	−0.192546	−	0.592596i
$776$	−1281.76	+	416.468i	−1.65175	+	0.536686i
$777$	−188.365	−	40.4671i	−0.242426	−	0.0520812i
$778$	−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
$783$	−185.885	+	252.364i	−0.237401	+	0.322304i
$784$	−649.773	+	472.088i	−0.828792	+	0.602153i
$785$	7.43084	−	10.2277i	0.00946603	−	0.0130289i
$786$	−1104.03	−	1231.53i	−1.40461	−	1.56683i
$787$	−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
$789$	−70.2934	−	40.7883i	−0.0890917	−	0.0516962i
$790$	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
$795$	126.648	−	218.262i	0.159306	−	0.274544i
$796$	−2793.57	−	2029.65i	−3.50951	−	2.54981i
$797$	−795.852	+	258.588i	−0.998560	+	0.324452i	−0.762290	−	0.647236i	$-0.775925\pi$
$797$	−795.852	+	258.588i	−0.998560	+	0.324452i	−0.236270	+	0.971687i	$0.575925\pi$
$798$	750.392	−	672.702i	0.940340	−	0.842985i
$799$	−455.389	−	330.859i	−0.569948	−	0.414092i
$800$	−335.337	−	461.552i	−0.419172	−	0.576940i
$801$	−582.736	+	333.067i	−0.727510	+	0.415814i
$802$	−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
$807$	90.0119	−	418.984i	0.111539	−	0.519187i
$808$	69.0558	+	212.532i	0.0854650	+	0.263034i
$809$	493.440	−	160.328i	0.609938	−	0.198181i	0.0122700	−	0.999925i	$-0.496094\pi$
$809$	493.440	−	160.328i	0.609938	−	0.198181i	0.597668	+	0.801744i	$0.296094\pi$
$810$	307.683	−	522.360i	0.379856	−	0.644889i
$811$	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
$816$	−1007.57	+	103.682i	−1.23477	+	0.127061i
$817$	135.435	−	98.3990i	0.165771	−	0.120439i
$818$	251.471	−	346.120i	0.307422	−	0.423130i
$819$	−119.625	−	53.8860i	−0.146062	−	0.0657949i
$820$	222.291	+	684.141i	0.271086	+	0.834318i
$821$	−324.234	+	446.270i	−0.394926	+	0.543569i	−0.959462	−	0.281840i	$-0.909055\pi$
$821$	−324.234	+	446.270i	−0.394926	+	0.543569i	0.564535	+	0.825409i	$0.309055\pi$
$822$	−435.558	+	750.629i	−0.529877	+	0.913174i
$823$	−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	0.631066	−	0.775729i	$-0.282618\pi$
$827$	567.030	+	184.239i	0.685648	+	0.222780i	0.0545813	+	0.998509i	$0.482618\pi$
$828$	−1613.65	−	176.711i	−1.94885	−	0.213419i
$829$	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
$831$	490.459	+	547.102i	0.590204	+	0.658366i
$832$	−12.7546	−	9.26674i	−0.0153300	−	0.0111379i
$833$	−215.808	−	297.034i	−0.259073	−	0.356584i
$834$	2268.90	−	233.476i	2.72050	−	0.279947i
$835$	−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	$-0.739642\pi$
$839$	−978.665	−	1347.02i	−1.16647	−	1.60550i	−0.482739	−	0.875764i	$-0.660358\pi$
$840$	−947.251	−	203.502i	−1.12768	−	0.242264i
$841$	218.240	+	671.673i	0.259500	+	0.798660i
$842$	−2063.88	+	670.595i	−2.45116	+	0.796432i
$843$	41.0283	−	190.977i	0.0486694	−	0.226545i
$844$	−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
$849$	48.3895	+	470.245i	0.0569958	+	0.553880i
$850$	744.427	−	540.858i	0.875797	−	0.636303i
$851$	−86.6196	+	119.222i	−0.101786	+	0.140096i
$852$	−202.316	+	181.370i	−0.237460	+	0.212876i
$853$	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
$855$	197.218	+	21.5974i	0.230665	+	0.0252601i
$856$	−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
$861$	−894.082	−	518.798i	−1.03842	−	0.602553i
$862$	−1286.88	−	934.973i	−1.49290	−	1.08466i
$863$	−681.319	+	221.374i	−0.789478	+	0.256517i	−0.675882	−	0.737010i	$-0.736237\pi$
$863$	−681.319	+	221.374i	−0.789478	+	0.256517i	−0.113596	+	0.993527i	$0.536237\pi$
$864$	4.87445	−	746.039i	0.00564172	−	0.863471i
$865$	−64.8498	−	47.1161i	−0.0749709	−	0.0544695i
$866$	−461.729	−	635.516i	−0.533175	−	0.733852i
$867$	41.3513	+	401.848i	0.0476947	+	0.463493i
$868$	−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
$873$	679.956	−	141.436i	0.778873	−	0.162012i
$874$	−238.203	−	733.114i	−0.272544	−	0.838803i
$875$	802.780	−	260.839i	0.917463	−	0.298102i
$876$	−1941.08	−	417.010i	−2.21585	−	0.476039i
$877$	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	$0.252728\pi$
$881$			1256.55i			1.42628i	−0.701021	+	0.713140i	$0.747272\pi$
$882$	828.379	−	473.466i	0.939206	−	0.536810i
$883$	−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
$885$	−472.880	−	527.492i	−0.534328	−	0.596036i
$886$	656.846	+	2021.56i	0.741361	+	2.28168i
$887$	690.062	−	949.789i	0.777973	−	1.07079i	−0.217529	−	0.976054i	$-0.569800\pi$
$887$	690.062	−	949.789i	0.777973	−	1.07079i	0.995503	−	0.0947346i	$-0.0302003\pi$
$888$	−328.369	−	190.538i	−0.369785	−	0.214570i
$889$	−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
$894$	1222.45	−	2106.74i	1.36739	−	2.35653i
$895$	229.818	+	166.972i	0.256779	+	0.186561i
$896$	1221.49	−	396.885i	1.36327	−	0.442953i
$897$	−74.7244	+	66.9880i	−0.0833048	+	0.0746801i
$898$	1265.71	+	919.596i	1.40948	+	1.02405i
$899$	159.587	+	219.653i	0.177517	+	0.244331i
$900$	817.764	+	1430.76i	0.908626	+	1.58974i
$901$	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
$906$	616.484	−	2869.59i	0.680446	−	3.16731i
$907$	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
$909$	−23.4520	−	112.745i	−0.0257997	−	0.124032i
$910$	−88.2704	+	64.1322i	−0.0970004	+	0.0704749i
$911$	−1024.00	−	332.718i	−1.12404	−	0.365223i	−0.312732	−	0.949841i	$-0.601244\pi$
$911$	−1024.00	−	332.718i	−1.12404	−	0.365223i	−0.811308	+	0.584619i	$0.801244\pi$
$912$	787.712	−	348.658i	0.863719	−	0.382301i
$913$		0			0
$914$		−	855.714i		−	0.936230i
$915$	482.639	−	49.6648i	0.527474	−	0.0542785i
$916$	−2644.76	+	1921.53i	−2.88730	+	2.09774i
$917$	800.637	−	1101.98i	0.873105	−	1.20173i
$918$	1203.27	+	7.86189i	1.31075	+	0.00856415i
$919$	−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
$921$	−582.195	+	1003.34i	−0.632133	+	1.08940i
$922$	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
$927$	−69.1341	+	631.303i	−0.0745783	+	0.681017i
$928$	259.506	+	188.542i	0.279640	+	0.203170i
$929$	1063.90	−	345.682i	1.14521	−	0.372101i	0.325872	−	0.945414i	$-0.394342\pi$
$929$	1063.90	−	345.682i	1.14521	−	0.372101i	0.819337	+	0.573313i	$0.194342\pi$
$930$	−350.540	−	391.024i	−0.376925	−	0.420456i
$931$	252.615	+	183.536i	0.271337	+	0.197138i
$932$	909.843	+	1252.29i	0.976226	+	1.34366i
$933$	275.272	−	28.3263i	0.295040	−	0.0303604i
$934$	−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
$939$	−218.214	−	46.8798i	−0.232390	−	0.0499253i
$940$	−259.067	−	797.325i	−0.275603	−	0.848218i
$941$	−304.866	+	99.0570i	−0.323981	+	0.105268i	−0.466492	−	0.884525i	$-0.654482\pi$
$941$	−304.866	+	99.0570i	−0.323981	+	0.105268i	0.142511	+	0.989793i	$0.454482\pi$
$942$	−13.6966	+	63.7545i	−0.0145399	+	0.0676799i
$943$	−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	$-0.118691\pi$
$948$	235.064	+	2284.33i	0.247958	+	2.40963i
$949$	−99.2979	+	72.1442i	−0.104634	+	0.0760213i
$950$	−459.977	+	633.104i	−0.484187	+	0.666426i
$951$	−1170.02	+	1048.88i	−1.23030	+	1.10293i
$952$	−594.253	−	1828.92i	−0.624216	−	1.92114i
$953$	−788.855	+	1085.77i	−0.827760	+	1.13931i	0.160576	+	0.987023i	$0.448665\pi$
$953$	−788.855	+	1085.77i	−0.827760	+	1.13931i	−0.988336	+	0.152290i	$0.951335\pi$
$954$	−141.694	+	1293.89i	−0.148526	+	1.35628i
$955$	−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
$960$	51.8913	+	30.1103i	0.0540535	+	0.0313649i
$961$	334.925	+	243.337i	0.348517	+	0.253212i
$962$	−40.6611	+	13.2116i	−0.0422673	+	0.0137335i
$963$	680.953	−	1511.69i	0.707116	−	1.56977i
$964$	1875.83	+	1362.87i	1.94588	+	1.41377i
$965$	179.550	+	247.129i	0.186062	+	0.256093i
$966$	−198.569	−	1929.67i	−0.205558	−	1.99759i
$967$	−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	$-0.0556460\pi$
$971$	500.100	+	688.328i	0.515036	+	0.708886i	−0.469722	+	0.882814i	$0.655646\pi$
$972$	−248.590	+	2140.67i	−0.255751	+	2.20234i
$973$	580.471	+	1786.50i	0.596578	+	1.83608i
$974$	1690.49	−	549.274i	1.73562	−	0.563936i
$975$	99.6080	+	21.3992i	0.102162	+	0.0219479i
$976$	1704.31	−	1238.25i	1.74622	−	1.26870i
$977$	−1153.28	−	374.724i	−1.18043	−	0.383545i	−0.347904	−	0.937530i	$-0.613107\pi$
$977$	−1153.28	−	374.724i	−1.18043	−	0.383545i	−0.832527	+	0.553985i	$0.813107\pi$
$978$	−705.322	−	1593.51i	−0.721188	−	1.62936i
$979$		0			0
$980$		−	546.831i		−	0.557991i
$981$	−261.437	−	457.412i	−0.266501	−	0.466272i
$982$	−958.436	+	696.345i	−0.976004	+	0.709109i
$983$	−267.240	+	367.825i	−0.271862	+	0.374186i	−0.923017	−	0.384759i	$-0.874285\pi$
$983$	−267.240	+	367.825i	−0.271862	+	0.374186i	0.651155	+	0.758945i	$0.274285\pi$
$984$	−1359.67	−	1516.70i	−1.38178	−	1.54136i
$985$	−147.939	−	455.310i	−0.150192	−	0.462243i
$986$	−304.095	+	418.551i	−0.308413	+	0.424494i
$987$	1042.00	+	604.628i	1.05572	+	0.612591i
$988$	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
$993$	378.982	−	653.128i	0.381654	−	0.657732i
$994$	−262.687	−	190.853i	−0.264272	−	0.192005i
$995$	772.595	−	251.031i	0.776478	−	0.252293i
$996$	−233.929	+	209.710i	−0.234868	+	0.210552i
$997$	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
$999$	157.521	+	116.026i	0.157679	+	0.116142i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(3.41170 + 1.10853i) q^{2} +(1.50565 - 2.59480i) q^{3} +(7.17480 + 5.21280i) q^{4} +(-1.98428 + 0.644731i) q^{5} +(8.01326 - 7.18363i) q^{6} +(7.17034 + 5.20956i) q^{7} +(10.2655 + 14.1293i) q^{8} +(-4.46601 - 7.81376i) q^{9} -7.48447 q^{10} +(24.3290 - 10.7685i) q^{12} +(0.508273 - 1.56430i) q^{13} +(18.6881 + 25.7220i) q^{14} +(-1.31469 + 6.11955i) q^{15} +(8.39811 + 25.8467i) q^{16} +(-11.8154 + 3.83907i) q^{17} +(-6.57491 - 31.6089i) q^{18} +(8.54780 - 6.21034i) q^{19} +(-17.5977 - 5.71782i) q^{20} +(24.3138 - 10.7618i) q^{21} -20.3378i q^{23} +(52.1192 - 5.36321i) q^{24} +(-16.7037 + 12.1360i) q^{25} +(3.46815 - 4.77350i) q^{26} +(-26.9994 - 0.176408i) q^{27} +(24.2894 + 74.7550i) q^{28} +(6.82340 - 9.39161i) q^{29} +(-11.2690 + 19.4207i) q^{30} +(-7.22737 + 22.2436i) q^{31} +27.6317i q^{32} -44.5665 q^{34} +(-17.5867 - 5.71427i) q^{35} +(8.68881 - 79.3425i) q^{36} +(-5.86208 - 4.25905i) q^{37} +(36.0469 - 11.7123i) q^{38} +(-3.29377 - 3.67417i) q^{39} +(-29.4793 - 21.4180i) q^{40} +(-22.8512 - 31.4520i) q^{41} +(94.8813 - 9.76355i) q^{42} +15.8444 q^{43} +(13.8996 + 12.6253i) q^{45} +(22.5450 - 69.3864i) q^{46} +(26.6317 + 36.6554i) q^{47} +(79.7118 + 17.1248i) q^{48} +(9.13245 + 28.1068i) q^{49} +(-70.4413 + 22.8878i) q^{50} +(-7.82835 + 36.4391i) q^{51} +(11.8011 - 8.57403i) q^{52} +(-38.3428 - 12.4583i) q^{53} +(-91.9184 - 30.5315i) q^{54} +154.791i q^{56} +(-3.24458 - 31.5305i) q^{57} +(33.6903 - 24.4774i) q^{58} +(-66.5264 + 91.5657i) q^{59} +(-41.3326 + 37.0534i) q^{60} +(-23.9538 - 73.7222i) q^{61} +(-49.3152 + 67.8766i) q^{62} +(8.68341 - 79.2932i) q^{63} +(2.96194 - 9.11592i) q^{64} +3.43171i q^{65} +62.9082 q^{67} +(-104.786 - 34.0470i) q^{68} +(-52.7725 - 30.6217i) q^{69} +(-53.6662 - 38.9908i) q^{70} +(-9.71270 + 3.15585i) q^{71} +(64.5570 - 143.314i) q^{72} +(-60.3706 - 43.8618i) q^{73} +(-15.2784 - 21.0289i) q^{74} +(6.34041 + 61.6155i) q^{75} +93.7020 q^{76} +(-7.16445 - 16.1864i) q^{78} +(-26.6720 + 82.0879i) q^{79} +(-33.3284 - 45.8726i) q^{80} +(-41.1096 + 69.7926i) q^{81} +(-43.0961 - 132.636i) q^{82} +(-11.2304 + 3.64896i) q^{83} +(230.546 + 49.5291i) q^{84} +(20.9700 - 15.2356i) q^{85} +(54.0563 + 17.5639i) q^{86} +(-14.0957 - 31.8459i) q^{87} -74.5782i q^{89} +(33.4257 + 58.4818i) q^{90} +(11.7938 - 8.56870i) q^{91} +(106.017 - 145.919i) q^{92} +(46.8357 + 52.2447i) q^{93} +(50.2259 + 154.579i) q^{94} +(-12.9572 + 17.8341i) q^{95} +(71.6987 + 41.6037i) 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

Properties

Related objects

Downloads

Learn more