LMFDB - Embedded newform 117.3.n.a.38.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,3,Mod(38,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("117.38");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	117.n (of order $6$, degree $2$, 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:	$3.18801909302$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			38.20
Character	$\chi$	$=$	117.38
Dual form			117.3.n.a.77.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.11386 - 1.92926i) q^{2} +(-2.21197 + 2.02662i) q^{3} +(-0.481371 - 0.833760i) q^{4} +(-4.12144 - 7.13855i) q^{5} +(1.44605 + 6.52485i) q^{6} +(-8.40220 - 4.85102i) q^{7} +6.76616 q^{8} +(0.785636 - 8.96564i) q^{9} -18.3629 q^{10} +(1.25825 - 2.17935i) q^{11} +(2.75449 + 0.868697i) q^{12} +(-8.79176 - 9.57627i) q^{13} +(-18.7178 + 10.8067i) q^{14} +(23.5836 + 7.43767i) q^{15} +(9.46205 - 16.3887i) q^{16} +16.5653i q^{17} +(-16.4220 - 11.5022i) q^{18} +17.7403i q^{19} +(-3.96789 + 6.87258i) q^{20} +(28.4166 - 6.29776i) q^{21} +(-2.80303 - 4.85499i) q^{22} +(34.6120 - 19.9833i) q^{23} +(-14.9666 + 13.7124i) q^{24} +(-21.4726 + 37.1916i) q^{25} +(-28.2679 + 6.29498i) q^{26} +(16.4321 + 21.4239i) q^{27} +9.34056i q^{28} +(-13.9571 - 8.05814i) q^{29} +(40.6181 - 37.2145i) q^{30} +(-3.72176 + 2.14876i) q^{31} +(-7.54648 - 13.0709i) q^{32} +(1.63350 + 7.37066i) q^{33} +(31.9588 + 18.4514i) q^{34} +79.9727i q^{35} +(-7.85338 + 3.66077i) q^{36} -42.9450i q^{37} +(34.2256 + 19.7602i) q^{38} +(38.8546 + 3.36491i) q^{39} +(-27.8864 - 48.3006i) q^{40} +(-8.80660 - 15.2535i) q^{41} +(19.5021 - 61.8379i) q^{42} +(27.9361 - 48.3867i) q^{43} -2.42274 q^{44} +(-67.2396 + 31.3431i) q^{45} -89.0343i q^{46} +(26.3913 - 45.7111i) q^{47} +(12.2840 + 55.4274i) q^{48} +(22.5647 + 39.0832i) q^{49} +(47.8349 + 82.8525i) q^{50} +(-33.5715 - 36.6419i) q^{51} +(-3.75221 + 11.9400i) q^{52} -15.4783i q^{53} +(59.6355 - 7.83864i) q^{54} -20.7432 q^{55} +(-56.8507 - 32.8228i) q^{56} +(-35.9527 - 39.2410i) q^{57} +(-31.0925 + 17.9513i) q^{58} +(30.0606 + 52.0666i) q^{59} +(-5.15125 - 23.2434i) q^{60} +(-14.6963 + 25.4548i) q^{61} +9.57368i q^{62} +(-50.0935 + 71.5200i) q^{63} +42.0735 q^{64} +(-32.1260 + 102.228i) q^{65} +(16.0394 + 5.05843i) q^{66} +(-80.1222 + 46.2585i) q^{67} +(13.8115 - 7.97405i) q^{68} +(-36.0624 + 114.348i) q^{69} +(154.288 + 89.0785i) q^{70} +35.3729 q^{71} +(5.31574 - 60.6630i) q^{72} -59.3591i q^{73} +(-82.8521 - 47.8347i) q^{74} +(-27.8764 - 125.783i) q^{75} +(14.7911 - 8.53965i) q^{76} +(-21.1441 + 12.2076i) q^{77} +(49.7704 - 71.2127i) q^{78} +(-33.1363 + 57.3938i) q^{79} -155.989 q^{80} +(-79.7656 - 14.0875i) q^{81} -39.2373 q^{82} +(20.7644 - 35.9651i) q^{83} +(-18.9297 - 20.6611i) q^{84} +(118.252 - 68.2729i) q^{85} +(-62.2337 - 107.792i) q^{86} +(47.2035 - 10.4614i) q^{87} +(8.51352 - 14.7459i) q^{88} +59.0530 q^{89} +(-14.4265 + 164.635i) q^{90} +(27.4155 + 123.111i) q^{91} +(-33.3225 - 19.2387i) q^{92} +(3.87772 - 12.2956i) q^{93} +(-58.7926 - 101.832i) q^{94} +(126.640 - 73.1155i) q^{95} +(43.1823 + 13.6186i) q^{96} +(-31.2930 - 18.0670i) q^{97} +100.536 q^{98} +(-18.5508 - 12.9932i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 4 q^{3} - 50 q^{4} + 4 q^{9} + 8 q^{10} - 38 q^{12} - 6 q^{13} - 6 q^{14} - 90 q^{16} + 14 q^{22} + 138 q^{23} - 92 q^{25} - 76 q^{27} + 48 q^{29} + 186 q^{30} - 154 q^{36} + 324 q^{38} - 2 q^{39}+ \cdots + 504 q^{95}+O(q^{100}) $ 52 * q - 4 * q^3 - 50 * q^4 + 4 * q^9 + 8 * q^10 - 38 * q^12 - 6 * q^13 - 6 * q^14 - 90 * q^16 + 14 * q^22 + 138 * q^23 - 92 * q^25 - 76 * q^27 + 48 * q^29 + 186 * q^30 - 154 * q^36 + 324 * q^38 - 2 * q^39 - 68 * q^40 - 216 * q^42 + 62 * q^43 + 230 * q^48 + 70 * q^49 + 90 * q^51 - 4 * q^52 + 92 * q^55 - 276 * q^56 + 12 * q^61 + 12 * q^64 - 588 * q^65 + 762 * q^66 - 144 * q^68 - 414 * q^69 + 342 * q^74 - 620 * q^75 - 510 * q^77 - 162 * q^78 - 24 * q^79 + 532 * q^81 - 292 * q^82 - 330 * q^87 - 62 * q^88 + 258 * q^90 + 264 * q^91 - 396 * q^92 - 160 * q^94 + 504 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.11386	−	1.92926i	0.556930	−	0.964632i	−0.440820	−	0.897595i	$-0.645312\pi$
$2$	1.11386	−	1.92926i	0.556930	−	0.964632i	0.997751	−	0.0670362i	$-0.0213543\pi$
$3$	−2.21197	+	2.02662i	−0.737324	+	0.675539i
$3$	−2.21197	+	2.02662i	−0.737324	+	0.675539i
$4$	−0.481371	−	0.833760i	−0.120343	−	0.208440i
$5$	−4.12144	−	7.13855i	−0.824288	−	1.42771i	−0.902462	−	0.430770i	$-0.858242\pi$
$5$	−4.12144	−	7.13855i	−0.824288	−	1.42771i	0.0781734	−	0.996940i	$-0.475091\pi$
$6$	1.44605	+	6.52485i	0.241009	+	1.08747i
$7$	−8.40220	−	4.85102i	−1.20031	−	0.693002i	−0.239690	−	0.970850i	$-0.577046\pi$
$7$	−8.40220	−	4.85102i	−1.20031	−	0.693002i	−0.960625	+	0.277847i	$0.910379\pi$
$8$	6.76616			0.845770
$9$	0.785636	−	8.96564i	0.0872929	−	0.996183i
$10$	−18.3629			−1.83629
$11$	1.25825	−	2.17935i	0.114386	−	0.198123i	−0.803148	−	0.595780i	$-0.796843\pi$
$11$	1.25825	−	2.17935i	0.114386	−	0.198123i	0.917534	+	0.397657i	$0.130177\pi$
$12$	2.75449	+	0.868697i	0.229541	+	0.0723914i
$13$	−8.79176	−	9.57627i	−0.676289	−	0.736636i
$13$	−8.79176	−	9.57627i	−0.676289	−	0.736636i
$14$	−18.7178	+	10.8067i	−1.33698	+	0.771908i
$15$	23.5836	+	7.43767i	1.57224	+	0.495845i
$16$	9.46205	−	16.3887i	0.591378	−	1.02430i
$17$			16.5653i			0.974428i	0.873282	+	0.487214i	$0.161987\pi$
$17$			16.5653i			0.974428i	−0.873282	+	0.487214i	$0.838013\pi$
$18$	−16.4220	−	11.5022i	−0.912333	−	0.639010i
$19$			17.7403i			0.933698i	0.884337	+	0.466849i	$0.154611\pi$
$19$			17.7403i			0.933698i	−0.884337	+	0.466849i	$0.845389\pi$
$20$	−3.96789	+	6.87258i	−0.198394	+	0.343629i
$21$	28.4166	−	6.29776i	1.35317	−	0.299893i
$22$	−2.80303	−	4.85499i	−0.127410	−	0.220681i
$23$	34.6120	−	19.9833i	1.50487	−	0.868837i	0.504886	−	0.863186i	$-0.331534\pi$
$23$	34.6120	−	19.9833i	1.50487	−	0.868837i	0.999984	−	0.00565132i	$-0.00179888\pi$
$24$	−14.9666	+	13.7124i	−0.623607	+	0.571351i
$25$	−21.4726	+	37.1916i	−0.858903	+	1.48766i
$26$	−28.2679	+	6.29498i	−1.08723	+	0.242115i
$27$	16.4321	+	21.4239i	0.608598	+	0.793479i
$28$			9.34056i			0.333591i
$29$	−13.9571	−	8.05814i	−0.481280	−	0.277867i	0.239670	−	0.970854i	$-0.422961\pi$
$29$	−13.9571	−	8.05814i	−0.481280	−	0.277867i	−0.720950	+	0.692988i	$0.756294\pi$
$30$	40.6181	−	37.2145i	1.35394	−	1.24048i
$31$	−3.72176	+	2.14876i	−0.120057	+	0.0693149i	−0.558826	−	0.829285i	$-0.688748\pi$
$31$	−3.72176	+	2.14876i	−0.120057	+	0.0693149i	0.438769	+	0.898600i	$0.355415\pi$
$32$	−7.54648	−	13.0709i	−0.235828	−	0.408465i
$33$	1.63350	+	7.37066i	0.0495001	+	0.223353i
$34$	31.9588	+	18.4514i	0.939965	+	0.542689i
$35$			79.9727i			2.28493i
$36$	−7.85338	+	3.66077i	−0.218149	+	0.101688i
$37$		−	42.9450i		−	1.16067i	−0.814376	−	0.580337i	$-0.802921\pi$
$37$		−	42.9450i		−	1.16067i	0.814376	−	0.580337i	$-0.197079\pi$
$38$	34.2256	+	19.7602i	0.900675	+	0.520005i
$39$	38.8546	+	3.36491i	0.996271	+	0.0862797i
$40$	−27.8864	−	48.3006i	−0.697159	−	1.20751i
$41$	−8.80660	−	15.2535i	−0.214795	−	0.372036i	0.738414	−	0.674348i	$-0.235575\pi$
$41$	−8.80660	−	15.2535i	−0.214795	−	0.372036i	−0.953209	+	0.302312i	$0.902242\pi$
$42$	19.5021	−	61.8379i	0.464336	−	1.47233i
$43$	27.9361	−	48.3867i	0.649676	−	1.12527i	−0.333525	−	0.942741i	$-0.608238\pi$
$43$	27.9361	−	48.3867i	0.649676	−	1.12527i	0.983200	−	0.182530i	$-0.0584286\pi$
$44$	−2.42274			−0.0550623
$45$	−67.2396	+	31.3431i	−1.49421	+	0.696513i
$46$		−	89.0343i		−	1.93553i
$47$	26.3913	−	45.7111i	0.561518	−	0.972578i	−0.435846	−	0.900021i	$-0.643551\pi$
$47$	26.3913	−	45.7111i	0.561518	−	0.972578i	0.997364	−	0.0725565i	$-0.0231158\pi$
$48$	12.2840	+	55.4274i	0.255916	+	1.15474i
$49$	22.5647	+	39.0832i	0.460504	+	0.797616i
$50$	47.8349	+	82.8525i	0.956698	+	1.65705i
$51$	−33.5715	−	36.6419i	−0.658265	−	0.718469i
$52$	−3.75221	+	11.9400i	−0.0721579	+	0.229615i
$53$		−	15.4783i		−	0.292043i	−0.989281	−	0.146021i	$-0.953353\pi$
$53$		−	15.4783i		−	0.292043i	0.989281	−	0.146021i	$-0.0466468\pi$
$54$	59.6355	−	7.83864i	1.10436	−	0.145160i
$55$	−20.7432			−0.377149
$56$	−56.8507	−	32.8228i	−1.01519	−	0.586121i
$57$	−35.9527	−	39.2410i	−0.630750	−	0.688438i
$58$	−31.0925	+	17.9513i	−0.536078	+	0.309505i
$59$	30.0606	+	52.0666i	0.509502	+	0.882484i	0.999939	+	0.0110074i	$0.00350384\pi$
$59$	30.0606	+	52.0666i	0.509502	+	0.882484i	−0.490437	+	0.871477i	$0.663163\pi$
$60$	−5.15125	−	23.2434i	−0.0858542	−	0.387389i
$61$	−14.6963	+	25.4548i	−0.240923	+	0.417291i	−0.960978	−	0.276626i	$-0.910784\pi$
$61$	−14.6963	+	25.4548i	−0.240923	+	0.417291i	0.720054	+	0.693918i	$0.244117\pi$
$62$			9.57368i			0.154414i
$63$	−50.0935	+	71.5200i	−0.795136	+	1.13524i
$64$	42.0735			0.657398
$65$	−32.1260	+	102.228i	−0.494246	+	1.57275i
$66$	16.0394	+	5.05843i	0.243022	+	0.0766428i
$67$	−80.1222	+	46.2585i	−1.19585	+	0.690426i	−0.959628	−	0.281272i	$-0.909244\pi$
$67$	−80.1222	+	46.2585i	−1.19585	+	0.690426i	−0.236225	+	0.971698i	$0.575910\pi$
$68$	13.8115	−	7.97405i	0.203110	−	0.117265i
$69$	−36.0624	+	114.348i	−0.522643	+	1.65721i
$70$	154.288	+	89.0785i	2.20412	+	1.27255i
$71$	35.3729			0.498209			0.249105	−	0.968477i	$-0.419864\pi$
$71$	35.3729			0.498209			0.249105	+	0.968477i	$0.419864\pi$
$72$	5.31574	−	60.6630i	0.0738297	−	0.842542i
$73$		−	59.3591i		−	0.813138i	−0.913620	−	0.406569i	$-0.866725\pi$
$73$		−	59.3591i		−	0.813138i	0.913620	−	0.406569i	$-0.133275\pi$
$74$	−82.8521	−	47.8347i	−1.11962	−	0.646415i
$75$	−27.8764	−	125.783i	−0.371686	−	1.67711i
$76$	14.7911	−	8.53965i	0.194620	−	0.112364i
$77$	−21.1441	+	12.2076i	−0.274599	+	0.158540i
$78$	49.7704	−	71.2127i	0.638082	−	0.912983i
$79$	−33.1363	+	57.3938i	−0.419447	+	0.726504i	−0.995884	−	0.0906378i	$-0.971109\pi$
$79$	−33.1363	+	57.3938i	−0.419447	+	0.726504i	0.576437	+	0.817142i	$0.304443\pi$
$80$	−155.989			−1.94986
$81$	−79.7656	−	14.0875i	−0.984760	−	0.173919i
$82$	−39.2373			−0.478504
$83$	20.7644	−	35.9651i	0.250174	−	0.433314i	−0.713400	−	0.700757i	$-0.752846\pi$
$83$	20.7644	−	35.9651i	0.250174	−	0.433314i	0.963574	+	0.267443i	$0.0861788\pi$
$84$	−18.9297	−	20.6611i	−0.225354	−	0.245965i
$85$	118.252	−	68.2729i	1.39120	−	0.803210i
$86$	−62.2337	−	107.792i	−0.723648	−	1.25340i
$87$	47.2035	−	10.4614i	0.542569	−	0.120245i
$88$	8.51352	−	14.7459i	0.0967446	−	0.167566i
$89$	59.0530			0.663517			0.331758	−	0.943364i	$-0.392358\pi$
$89$	59.0530			0.663517			0.331758	+	0.943364i	$0.392358\pi$
$90$	−14.4265	+	164.635i	−0.160295	+	1.82928i
$91$	27.4155	+	123.111i	0.301269	+	1.35287i
$92$	−33.3225	−	19.2387i	−0.362201	−	0.209117i
$93$	3.87772	−	12.2956i	0.0416959	−	0.132211i
$94$	−58.7926	−	101.832i	−0.625453	−	1.08332i
$95$	126.640	−	73.1155i	1.33305	−	0.769636i
$96$	43.1823	+	13.6186i	0.449816	+	0.141860i
$97$	−31.2930	−	18.0670i	−0.322608	−	0.186258i	0.329946	−	0.944000i	$-0.392969\pi$
$97$	−31.2930	−	18.0670i	−0.322608	−	0.186258i	−0.652554	+	0.757742i	$0.726303\pi$
$98$	100.536			1.02587
$99$	−18.5508	−	12.9932i	−0.187381	−	0.131244i
$100$	41.3451			0.413451
$101$	−53.6919	−	30.9990i	−0.531603	−	0.306921i	0.210066	−	0.977687i	$-0.432632\pi$
$101$	−53.6919	−	30.9990i	−0.531603	−	0.306921i	−0.741669	+	0.670766i	$0.765965\pi$
$102$	−108.086	+	23.9543i	−1.05967	+	0.234846i
$103$	67.7211	+	117.296i	0.657487	+	1.13880i	0.981264	+	0.192667i	$0.0617137\pi$
$103$	67.7211	+	117.296i	0.657487	+	1.13880i	−0.323778	+	0.946133i	$0.604953\pi$
$104$	−59.4865	−	64.7946i	−0.571985	−	0.623025i
$105$	−162.074	−	176.897i	−1.54356	−	1.68474i
$106$	−29.8616	−	17.2406i	−0.281714	−	0.162647i
$107$		−	128.009i		−	1.19635i	−0.801366	−	0.598174i	$-0.795893\pi$
$107$		−	128.009i		−	1.19635i	0.801366	−	0.598174i	$-0.204107\pi$
$108$	9.95245	−	24.0133i	0.0921523	−	0.222346i
$109$			4.07076i			0.0373464i	0.999826	+	0.0186732i	$0.00594421\pi$
$109$			4.07076i			0.0373464i	−0.999826	+	0.0186732i	$0.994056\pi$
$110$	−23.1050	+	40.0191i	−0.210046	+	0.363810i
$111$	87.0330	+	94.9930i	0.784081	+	0.855793i
$112$	−159.004	+	91.8011i	−1.41968	+	0.819653i
$113$	52.9530	−	30.5724i	0.468611	−	0.270553i	−0.247047	−	0.969003i	$-0.579460\pi$
$113$	52.9530	−	30.5724i	0.468611	−	0.270553i	0.715658	+	0.698451i	$0.246127\pi$
$114$	−115.752	+	25.6533i	−1.01537	+	0.225029i
$115$	−285.303	−	164.720i	−2.48089	−	1.43234i
$116$			15.5158i			0.133757i
$117$	−92.7646	+	71.3003i	−0.792860	+	0.609404i
$118$	133.933			1.13503
$119$	80.3584	−	139.185i	0.675281	−	1.16962i
$120$	159.571	+	50.3245i	1.32976	+	0.419371i
$121$	57.3336	+	99.3047i	0.473832	+	0.820700i
$122$	32.7393	+	56.7061i	0.268355	+	0.464804i
$123$	50.3929	+	15.8926i	0.409699	+	0.129208i
$124$	3.58310	+	2.06870i	0.0288960	+	0.0166831i
$125$	147.920			1.18336
$126$	82.1838	+	176.307i	0.652252	+	1.39926i
$127$	−6.65115			−0.0523713			−0.0261856	−	0.999657i	$-0.508336\pi$
$127$	−6.65115			−0.0523713			−0.0261856	+	0.999657i	$0.508336\pi$
$128$	77.0499	−	133.454i	0.601952	−	1.04261i
$129$	36.2675	+	163.646i	0.281144	+	1.26857i
$130$	161.442	+	175.848i	1.24186	+	1.35267i
$131$	209.484	−	120.946i	1.59912	−	0.923250i	0.607458	−	0.794352i	$-0.292189\pi$
$131$	209.484	−	120.946i	1.59912	−	0.923250i	0.991658	−	0.128898i	$-0.0411441\pi$
$132$	5.35903	−	4.90997i	0.0405987	−	0.0371968i
$133$	86.0583	−	149.057i	0.647055	−	1.12073i
$134$			206.102i			1.53808i
$135$	85.2117	−	205.599i	0.631198	−	1.52296i
$136$			112.083i			0.824143i
$137$	−49.1509	+	85.1319i	−0.358766	+	0.621401i	−0.987755	−	0.156013i	$-0.950136\pi$
$137$	−49.1509	+	85.1319i	−0.358766	+	0.621401i	0.628989	+	0.777414i	$0.283469\pi$
$138$	180.438	+	196.941i	1.30753	+	1.42711i
$139$	−48.1124	−	83.3331i	−0.346132	−	0.599518i	0.639427	−	0.768852i	$-0.279172\pi$
$139$	−48.1124	−	83.3331i	−0.346132	−	0.599518i	−0.985559	+	0.169334i	$0.945838\pi$
$140$	66.6780	−	38.4966i	0.476272	−	0.274976i
$141$	34.2622	+	154.597i	0.242994	+	1.09643i
$142$	39.4004	−	68.2436i	0.277468	−	0.480589i
$143$	−31.9323	+	7.11099i	−0.223303	+	0.0497272i
$144$	−139.502	−	97.7090i	−0.968764	−	0.678534i
$145$			132.845i			0.916170i
$146$	−114.519	−	66.1177i	−0.784379	−	0.452861i
$147$	−129.119	−	40.7209i	−0.878362	−	0.277013i
$148$	−35.8058	+	20.6725i	−0.241931	+	0.139679i
$149$	39.9891	+	69.2632i	0.268383	+	0.464854i	0.968445	−	0.249229i	$-0.0801773\pi$
$149$	39.9891	+	69.2632i	0.268383	+	0.464854i	−0.700061	+	0.714083i	$0.746844\pi$
$150$	−273.720	−	86.3242i	−1.82480	−	0.575495i
$151$	−8.07717	−	4.66336i	−0.0534912	−	0.0308832i	0.473016	−	0.881054i	$-0.343165\pi$
$151$	−8.07717	−	4.66336i	−0.0534912	−	0.0308832i	−0.526507	+	0.850171i	$0.676499\pi$
$152$			120.033i			0.789694i
$153$	148.518	+	13.0143i	0.970709	+	0.0850607i
$154$			54.3901i			0.353183i
$155$	30.6781	+	17.7120i	0.197923	+	0.114271i
$156$	−15.8980	−	34.0151i	−0.101910	−	0.218046i
$157$	11.1187	+	19.2582i	0.0708199	+	0.122664i	0.899261	−	0.437413i	$-0.144105\pi$
$157$	11.1187	+	19.2582i	0.0708199	+	0.122664i	−0.828441	+	0.560076i	$0.810772\pi$
$158$	73.8185	+	127.857i	0.467206	+	0.809224i
$159$	31.3685	+	34.2375i	0.197286	+	0.215330i
$160$	−62.2048	+	107.742i	−0.388780	+	0.673387i
$161$	−387.756			−2.40842
$162$	−116.026	+	138.197i	−0.716211	+	0.853070i
$163$			188.492i			1.15639i	0.815898	+	0.578196i	$0.196243\pi$
$163$			188.492i			1.15639i	−0.815898	+	0.578196i	$0.803757\pi$
$164$	−8.47849	+	14.6852i	−0.0516981	+	0.0895437i
$165$	45.8834	−	42.0386i	0.278081	−	0.254779i
$166$	−46.2574	−	80.1201i	−0.278659	−	0.482651i
$167$	−51.5486	−	89.2848i	−0.308674	−	0.534640i	0.669398	−	0.742904i	$-0.266552\pi$
$167$	−51.5486	−	89.2848i	−0.308674	−	0.534640i	−0.978073	+	0.208264i	$0.933219\pi$
$168$	192.271	−	42.6116i	1.14447	−	0.253641i
$169$	−14.4100	+	168.385i	−0.0852665	+	0.996358i
$170$		−	304.186i		−	1.78933i
$171$	159.053	+	13.9374i	0.930134	+	0.0815052i
$172$	−53.7905			−0.312735
$173$	−238.877	−	137.916i	−1.38079	−	0.797202i	−0.388540	−	0.921432i	$-0.627021\pi$
$173$	−238.877	−	137.916i	−1.38079	−	0.797202i	−0.992253	+	0.124230i	$0.960354\pi$
$174$	32.3954	−	102.720i	0.186181	−	0.590348i
$175$	360.834	−	208.328i	2.06191	−	1.19044i
$176$	−23.8112	−	41.2423i	−0.135291	−	0.234331i
$177$	−172.012	−	54.2483i	−0.971821	−	0.306488i
$178$	65.7768	−	113.929i	0.369533	−	0.640049i
$179$		−	11.8276i		−	0.0660761i	−0.999454	−	0.0330381i	$-0.989482\pi$
$179$		−	11.8276i		−	0.0660761i	0.999454	−	0.0330381i	$-0.0105183\pi$
$180$	58.4998	+	40.9740i	0.324999	+	0.227633i
$181$	−64.9356			−0.358760			−0.179380	−	0.983780i	$-0.557409\pi$
$181$	−64.9356			−0.358760			−0.179380	+	0.983780i	$0.557409\pi$
$182$	268.050	+	84.2365i	1.47280	+	0.462838i
$183$	−19.0793	−	86.0891i	−0.104258	−	0.470432i
$184$	234.191	−	135.210i	1.27277	−	0.734837i
$185$	−306.565	+	176.995i	−1.65711	+	0.956731i
$186$	−19.4022	−	21.1767i	−0.104313	−	0.113853i
$187$	36.1016	+	20.8433i	0.193057	+	0.111461i
$188$	−50.8161			−0.270299
$189$	−34.1383	−	259.721i	−0.180626	−	1.37418i
$190$		−	325.762i		−	1.71454i
$191$	125.020	+	72.1804i	0.654555	+	0.377908i	0.790199	−	0.612850i	$-0.209977\pi$
$191$	125.020	+	72.1804i	0.654555	+	0.377908i	−0.135644	+	0.990758i	$0.543310\pi$
$192$	−93.0653	+	85.2669i	−0.484715	+	0.444098i
$193$	86.2173	−	49.7776i	0.446722	−	0.257915i	−0.259723	−	0.965683i	$-0.583631\pi$
$193$	86.2173	−	49.7776i	0.446722	−	0.257915i	0.706445	+	0.707768i	$0.250298\pi$
$194$	−69.7120	+	40.2483i	−0.359340	+	0.207465i
$195$	−136.116	−	291.233i	−0.698032	−	1.49350i
$196$	21.7240	−	37.6271i	0.110837	−	0.191975i
$197$	253.468			1.28664			0.643320	−	0.765598i	$-0.277557\pi$
$197$	253.468			1.28664			0.643320	+	0.765598i	$0.277557\pi$
$198$	−45.7303	+	21.3167i	−0.230961	+	0.107660i
$199$	102.868			0.516924			0.258462	−	0.966021i	$-0.416784\pi$
$199$	102.868			0.516924			0.258462	+	0.966021i	$0.416784\pi$
$200$	−145.287	+	251.644i	−0.726435	+	1.25822i
$201$	83.4795	−	264.700i	0.415321	−	1.31691i
$202$	−119.611	+	69.0572i	−0.592132	+	0.341868i
$203$	78.1803	+	135.412i	0.385125	+	0.667056i
$204$	−14.3902	+	45.6289i	−0.0705402	+	0.223671i
$205$	−72.5918	+	125.733i	−0.354106	+	0.613330i
$206$	301.728			1.46470
$207$	−151.970	−	326.019i	−0.734156	−	1.57497i
$208$	−240.131	+	53.4747i	−1.15448	+	0.257090i
$209$	38.6623	+	22.3217i	0.184987	+	0.106802i
$210$	−521.810	+	115.645i	−2.48481	+	0.550689i
$211$	−93.5578	−	162.047i	−0.443402	−	0.767995i	0.554537	−	0.832159i	$-0.312895\pi$
$211$	−93.5578	−	162.047i	−0.443402	−	0.767995i	−0.997939	+	0.0641641i	$0.979562\pi$
$212$	−12.9052	+	7.45079i	−0.0608734	+	0.0351453i
$213$	−78.2438	+	71.6873i	−0.367342	+	0.336560i
$214$	−246.964	−	142.584i	−1.15404	−	0.666282i
$215$	−460.547			−2.14208
$216$	111.183	+	144.958i	0.514734	+	0.671101i
$217$	41.6947			0.192141
$218$	7.85356	+	4.53426i	0.0360255	+	0.0207993i
$219$	120.298	+	131.301i	0.549307	+	0.599546i
$220$	9.98519	+	17.2949i	0.0453872	+	0.0786130i
$221$	158.634	−	145.638i	0.717799	−	0.658995i
$222$	280.209	−	62.1007i	1.26220	−	0.279733i
$223$	4.74479	+	2.73941i	0.0212771	+	0.0122843i	0.510601	−	0.859818i	$-0.329423\pi$
$223$	4.74479	+	2.73941i	0.0212771	+	0.0122843i	−0.489324	+	0.872102i	$0.662756\pi$
$224$			146.432i			0.653716i
$225$	316.577	+	221.734i	1.40701	+	0.985487i
$226$		−	136.214i		−	0.602716i
$227$	−124.695	+	215.978i	−0.549316	+	0.951443i	0.449005	+	0.893529i	$0.351778\pi$
$227$	−124.695	+	215.978i	−0.549316	+	0.951443i	−0.998322	+	0.0579144i	$0.981555\pi$
$228$	−15.4109	+	48.8654i	−0.0675917	+	0.214322i
$229$	−281.595	+	162.579i	−1.22967	+	0.709951i	−0.966961	−	0.254924i	$-0.917950\pi$
$229$	−281.595	+	162.579i	−1.22967	+	0.709951i	−0.262710	+	0.964875i	$0.584616\pi$
$230$	−635.575	+	366.950i	−2.76337	+	1.59543i
$231$	22.0301	−	69.8539i	0.0953686	−	0.302398i
$232$	−94.4361	−	54.5227i	−0.407052	−	0.235012i
$233$			200.026i			0.858481i	0.903190	+	0.429241i	$0.141219\pi$
$233$			200.026i			0.858481i	−0.903190	+	0.429241i	$0.858781\pi$
$234$	34.2302	+	258.386i	0.146283	+	1.10421i
$235$	−435.082			−1.85141
$236$	28.9407	−	50.1267i	0.122630	−	0.212401i
$237$	−43.0187	−	194.108i	−0.181514	−	0.819022i
$238$	−179.016	−	310.065i	−0.752169	−	1.30279i
$239$	80.9113	+	140.143i	0.338541	+	0.586370i	0.984159	−	0.177291i	$-0.0567332\pi$
$239$	80.9113	+	140.143i	0.338541	+	0.586370i	−0.645617	+	0.763661i	$0.723400\pi$
$240$	345.044	−	316.130i	1.43768	−	1.31721i
$241$	340.380	+	196.518i	1.41237	+	0.815429i	0.995611	−	0.0935898i	$-0.0298342\pi$
$241$	340.380	+	196.518i	1.41237	+	0.815429i	0.416754	+	0.909019i	$0.363168\pi$
$242$	255.447			1.05556
$243$	204.989	−	130.493i	0.843576	−	0.537009i
$244$	28.2976			0.115974
$245$	185.998	−	322.158i	0.759176	−	1.31493i
$246$	86.7918	−	79.5190i	0.352812	−	0.323248i
$247$	169.886	−	155.968i	0.687796	−	0.631450i
$248$	−25.1821	+	14.5389i	−0.101541	+	0.0586245i
$249$	26.9571	+	121.635i	0.108261	+	0.488495i
$250$	164.762	−	285.376i	0.659048	−	1.14150i
$251$			242.343i			0.965510i	0.875755	+	0.482755i	$0.160364\pi$
$251$			242.343i			0.965510i	−0.875755	+	0.482755i	$0.839636\pi$
$252$	83.7441	+	7.33828i	0.332318	+	0.0291202i
$253$		−	100.576i		−	0.397532i
$254$	−7.40846	+	12.8318i	−0.0291672	+	0.0505190i
$255$	−123.207	+	390.669i	−0.483165	+	1.53204i
$256$	−87.4988	−	151.552i	−0.341792	−	0.592001i
$257$	399.900	−	230.882i	1.55603	−	0.898375i	0.558401	−	0.829571i	$-0.311415\pi$
$257$	399.900	−	230.882i	1.55603	−	0.898375i	0.997630	−	0.0688039i	$-0.0219183\pi$
$258$	356.112	+	112.309i	1.38028	+	0.435305i
$259$	−208.327	+	360.832i	−0.804350	+	1.39317i
$260$	100.698	−	22.4245i	0.387302	−	0.0862481i
$261$	−83.2116	+	118.804i	−0.318818	+	0.455187i
$262$		−	538.867i		−	2.05674i
$263$	−2.21094	−	1.27649i	−0.00840661	−	0.00485356i	0.495791	−	0.868442i	$-0.334878\pi$
$263$	−2.21094	−	1.27649i	−0.00840661	−	0.00485356i	−0.504197	+	0.863588i	$0.668212\pi$
$264$	11.0525	+	49.8711i	0.0418657	+	0.188906i
$265$	−110.492	+	63.7928i	−0.416952	+	0.240727i
$266$	−191.714	−	332.058i	−0.720729	−	1.24834i
$267$	−130.624	+	119.678i	−0.489227	+	0.448232i
$268$	77.1370	+	44.5351i	0.287825	+	0.166176i
$269$		−	117.561i		−	0.437030i	−0.975834	−	0.218515i	$-0.929879\pi$
$269$		−	117.561i		−	0.437030i	0.975834	−	0.218515i	$-0.0701212\pi$
$270$	−301.741	−	393.404i	−1.11756	−	1.45705i
$271$			357.409i			1.31885i	0.751770	+	0.659426i	$0.229201\pi$
$271$			357.409i			1.31885i	−0.751770	+	0.659426i	$0.770799\pi$
$272$	271.484	+	156.742i	0.998104	+	0.576256i
$273$	−310.141	−	216.757i	−1.13605	−	0.793981i
$274$	109.495	+	189.650i	0.399615	+	0.692154i
$275$	54.0357	+	93.5926i	0.196493	+	0.340337i
$276$	112.698	−	24.9764i	0.408326	−	0.0904942i
$277$	80.0519	−	138.654i	0.288996	−	0.500556i	−0.684574	−	0.728943i	$-0.740012\pi$
$277$	80.0519	−	138.654i	0.288996	−	0.500556i	0.973570	+	0.228387i	$0.0733452\pi$
$278$	−214.362			−0.771086
$279$	16.3411	+	35.0562i	0.0585702	+	0.125649i
$280$			541.108i			1.93253i
$281$	−146.306	+	253.410i	−0.520662	+	0.901813i	0.479049	+	0.877788i	$0.340982\pi$
$281$	−146.306	+	253.410i	−0.520662	+	0.901813i	−0.999711	+	0.0240253i	$0.992352\pi$
$282$	336.421	+	106.099i	1.19298	+	0.376237i
$283$	168.912	+	292.563i	0.596860	+	1.03379i	0.993281	+	0.115724i	$0.0369187\pi$
$283$	168.912	+	292.563i	0.596860	+	1.03379i	−0.396421	+	0.918069i	$0.629748\pi$
$284$	−17.0275	−	29.4925i	−0.0599559	−	0.103847i
$285$	−131.946	+	418.380i	−0.462969	+	1.46800i
$286$	−21.8492	+	69.5265i	−0.0763956	+	0.243099i
$287$			170.884i			0.595414i
$288$	−123.118	+	57.3901i	−0.427492	+	0.199271i
$289$	14.5914			0.0504893
$290$	256.292	+	147.970i	0.883766	+	0.510243i
$291$	105.834	−	23.4552i	0.363691	−	0.0806021i
$292$	−49.4912	+	28.5738i	−0.169490	+	0.0978554i
$293$	−190.025	−	329.134i	−0.648551	−	1.12332i	−0.983469	−	0.181076i	$-0.942042\pi$
$293$	−190.025	−	329.134i	−0.648551	−	1.12332i	0.334918	−	0.942247i	$-0.391291\pi$
$294$	−222.382	+	203.748i	−0.756402	+	0.693019i
$295$	247.786	−	429.179i	0.839954	−	1.45484i
$296$		−	290.573i		−	0.981664i
$297$	67.3660	−	8.85475i	0.226822	−	0.0298140i
$298$	178.169			0.597883
$299$	−495.666	−	155.766i	−1.65774	−	0.520957i
$300$	−91.4542	+	83.7908i	−0.304847	+	0.279303i
$301$	−469.449	+	271.036i	−1.55963	+	0.900453i
$302$	−17.9937	+	10.3887i	−0.0595817	+	0.0343995i
$303$	181.588	−	40.2440i	0.599301	−	0.132819i
$304$	290.741	+	167.859i	0.956384	+	0.552168i
$305$	242.280			0.794361
$306$	190.537	−	272.035i	0.622669	−	0.889004i
$307$		−	550.690i		−	1.79378i	−0.442254	−	0.896890i	$-0.645821\pi$
$307$		−	550.690i		−	1.79378i	0.442254	−	0.896890i	$-0.354179\pi$
$308$	20.3564	+	11.7528i	0.0660921	+	0.0381583i
$309$	−387.512	−	122.211i	−1.25409	−	0.395506i
$310$	68.3422	−	39.4574i	0.220459	−	0.127282i
$311$	60.5024	−	34.9311i	0.194541	−	0.112319i	−0.399565	−	0.916705i	$-0.630839\pi$
$311$	60.5024	−	34.9311i	0.194541	−	0.112319i	0.594107	+	0.804386i	$0.297506\pi$
$312$	262.896	+	22.7675i	0.842616	+	0.0729728i
$313$	104.282	−	180.622i	0.333170	−	0.577067i	−0.649962	−	0.759967i	$-0.725215\pi$
$313$	104.282	−	180.622i	0.333170	−	0.577067i	0.983132	+	0.182900i	$0.0585484\pi$
$314$	49.5389			0.157767
$315$	717.007	+	62.8294i	2.27621	+	0.199459i
$316$	63.8035			0.201910
$317$	15.9654	−	27.6529i	0.0503640	−	0.0872330i	−0.839744	−	0.542982i	$-0.817295\pi$
$317$	15.9654	−	27.6529i	0.0503640	−	0.0872330i	0.890108	+	0.455749i	$0.150629\pi$
$318$	100.993	−	22.3824i	0.317589	−	0.0703848i
$319$	−35.1230	+	20.2783i	−0.110104	+	0.0635683i
$320$	−173.403	−	300.343i	−0.541886	−	0.938573i
$321$	259.426	+	283.153i	0.808180	+	0.882096i
$322$	−431.907	+	748.084i	−1.34132	+	2.32324i
$323$	−293.872			−0.909822
$324$	26.6513	+	73.2866i	0.0822571	+	0.226193i
$325$	544.938	−	121.352i	1.67673	−	0.373391i
$326$	363.650	+	209.954i	1.11549	+	0.644030i
$327$	−8.24987	−	9.00440i	−0.0252290	−	0.0275364i
$328$	−59.5869	−	103.208i	−0.181667	−	0.314657i
$329$	−443.491	+	256.050i	−1.34800	+	0.778266i
$330$	−29.9958	−	135.346i	−0.0908963	−	0.410140i
$331$	195.507	+	112.876i	0.590654	+	0.341014i	0.765356	−	0.643607i	$-0.222563\pi$
$331$	195.507	+	112.876i	0.590654	+	0.341014i	−0.174702	+	0.984621i	$0.555896\pi$
$332$	−39.9816			−0.120427
$333$	−385.029	−	33.7391i	−1.15624	−	0.101319i
$334$	−229.672			−0.687640
$335$	660.438	+	381.304i	1.97146	+	1.13822i
$336$	165.667	−	525.302i	0.493056	−	1.56340i
$337$	−145.643	−	252.261i	−0.432176	−	0.748550i	0.564885	−	0.825170i	$-0.308921\pi$
$337$	−145.643	−	252.261i	−0.432176	−	0.748550i	−0.997060	+	0.0766195i	$0.975587\pi$
$338$	308.807	+	215.358i	0.913631	+	0.637153i
$339$	−55.1719	+	174.941i	−0.162749	+	0.516050i
$340$	−113.846	−	65.7292i	−0.334842	−	0.193321i
$341$			10.8147i			0.0317147i
$342$	204.052	−	291.331i	0.596642	−	0.851844i
$343$			37.5528i			0.109483i
$344$	189.020	−	327.392i	0.549476	−	0.951721i
$345$	964.906	−	213.845i	2.79683	−	0.619840i
$346$	−532.152	+	307.238i	−1.53801	+	0.887972i
$347$	−271.558	+	156.784i	−0.782587	+	0.451827i	−0.837346	−	0.546673i	$-0.815894\pi$
$347$	−271.558	+	156.784i	−0.782587	+	0.451827i	0.0547595	+	0.998500i	$0.482561\pi$
$348$	−31.4447	−	34.3206i	−0.0903582	−	0.0986224i
$349$	−557.188	−	321.693i	−1.59653	−	0.921755i	−0.992150	−	0.125057i	$-0.960089\pi$
$349$	−557.188	−	321.693i	−1.59653	−	0.921755i	−0.604377	−	0.796698i	$-0.706578\pi$
$350$		−	928.191i		−	2.65198i
$351$	60.6941	−	345.713i	0.172918	−	0.984936i
$352$	−37.9814			−0.107902
$353$	169.330	−	293.288i	0.479688	−	0.830844i	−0.520041	−	0.854142i	$-0.674083\pi$
$353$	169.330	−	293.288i	0.479688	−	0.830844i	0.999729	+	0.0232976i	$0.00741652\pi$
$354$	−296.257	+	271.432i	−0.836884	+	0.766757i
$355$	−145.787	−	252.511i	−0.410668	−	0.711298i
$356$	−28.4264	−	49.2360i	−0.0798495	−	0.138303i
$357$	104.324	+	470.729i	0.292224	+	1.31857i
$358$	−22.8186	−	13.1743i	−0.0637391	−	0.0367998i
$359$	145.561			0.405462			0.202731	−	0.979235i	$-0.435018\pi$
$359$	145.561			0.405462			0.202731	+	0.979235i	$0.435018\pi$
$360$	−454.954	+	212.072i	−1.26376	+	0.589090i
$361$	46.2831			0.128208
$362$	−72.3292	+	125.278i	−0.199804	+	0.346071i
$363$	−328.073	−	103.466i	−0.903783	−	0.285030i
$364$	89.4478	−	82.1199i	0.245736	−	0.225604i
$365$	−423.738	+	244.645i	−1.16092	+	0.670260i
$366$	−187.340	−	59.0823i	−0.511858	−	0.161427i
$367$	−212.079	+	367.332i	−0.577872	+	1.00090i	0.417851	+	0.908516i	$0.362784\pi$
$367$	−212.079	+	367.332i	−0.577872	+	1.00090i	−0.995723	+	0.0923886i	$0.970550\pi$
$368$		−	756.330i		−	2.05525i
$369$	−143.676	+	66.9732i	−0.389366	+	0.181499i
$370$			788.592i			2.13133i
$371$	−75.0853	+	130.052i	−0.202386	+	0.350543i
$372$	−12.1182	+	2.68566i	−0.0325758	+	0.00721953i
$373$	−11.0395	−	19.1209i	−0.0295964	−	0.0512625i	0.850848	−	0.525412i	$-0.176089\pi$
$373$	−11.0395	−	19.1209i	−0.0295964	−	0.0512625i	−0.880444	+	0.474150i	$0.842756\pi$
$374$	80.4243	−	46.4330i	0.215038	−	0.124152i
$375$	−327.194	+	299.777i	−0.872518	+	0.799405i
$376$	178.568	−	309.289i	0.474915	−	0.822577i
$377$	45.5405	+	204.502i	0.120797	+	0.542446i
$378$	−539.095	−	223.431i	−1.42618	−	0.591087i
$379$		−	439.406i		−	1.15938i	−0.814836	−	0.579692i	$-0.803173\pi$
$379$		−	439.406i		−	1.15938i	0.814836	−	0.579692i	$-0.196827\pi$
$380$	−121.921	−	70.3914i	−0.320846	−	0.185240i
$381$	14.7122	−	13.4794i	0.0386146	−	0.0353789i
$382$	278.510	−	160.798i	0.729083	−	0.420936i
$383$	92.9716	+	161.031i	0.242746	+	0.420448i	0.961495	−	0.274821i	$-0.0886186\pi$
$383$	92.9716	+	161.031i	0.242746	+	0.420448i	−0.718750	+	0.695269i	$0.755285\pi$
$384$	100.029	+	451.348i	0.260492	+	1.17539i
$385$	174.289	+	100.626i	0.452698	+	0.261365i
$386$		−	221.781i		−	0.574562i
$387$	−411.870	−	288.479i	−1.06426	−	0.745424i
$388$			34.7878i			0.0896592i
$389$	−122.735	−	70.8611i	−0.315514	−	0.182162i	0.333877	−	0.942617i	$-0.391643\pi$
$389$	−122.735	−	70.8611i	−0.315514	−	0.182162i	−0.649391	+	0.760454i	$0.724976\pi$
$390$	−713.481	−	61.7893i	−1.82944	−	0.158434i
$391$	331.028	+	573.358i	0.846620	+	1.46639i
$392$	152.676	+	264.443i	0.389481	+	0.674600i
$393$	−218.262	+	692.073i	−0.555374	+	1.76100i
$394$	282.328	−	489.006i	0.716568	−	1.24113i
$395$	546.278			1.38298
$396$	−1.90339	+	21.7214i	−0.00480655	+	0.0548521i
$397$		−	128.836i		−	0.324523i	−0.986748	−	0.162261i	$-0.948121\pi$
$397$		−	128.836i		−	0.324523i	0.986748	−	0.162261i	$-0.0518788\pi$
$398$	114.581	−	198.459i	0.287891	−	0.498641i
$399$	111.724	+	504.118i	0.280010	+	1.26345i
$400$	406.349	+	703.817i	1.01587	+	1.75954i
$401$	−191.622	−	331.899i	−0.477861	−	0.827679i	0.521817	−	0.853057i	$-0.325254\pi$
$401$	−191.622	−	331.899i	−0.477861	−	0.827679i	−0.999678	+	0.0253783i	$0.991921\pi$
$402$	−417.691	−	455.892i	−1.03903	−	1.13406i
$403$	53.2980	+	16.7492i	0.132253	+	0.0415614i
$404$			59.6882i			0.147743i
$405$	228.185	+	627.471i	0.563420	+	1.54931i
$406$	348.328			0.857951
$407$	−93.5922	−	54.0355i	−0.229956	−	0.132765i
$408$	−227.150	−	247.925i	−0.556741	−	0.607660i
$409$	90.3177	−	52.1449i	0.220826	−	0.127494i	−0.385507	−	0.922705i	$-0.625973\pi$
$409$	90.3177	−	52.1449i	0.220826	−	0.127494i	0.606332	+	0.795211i	$0.292640\pi$
$410$	161.714	+	280.097i	0.394425	+	0.683164i
$411$	−63.8094	−	287.919i	−0.155254	−	0.700534i
$412$	65.1980	−	112.926i	0.158248	−	0.274093i
$413$		−	583.299i		−	1.41235i
$414$	−798.249	−	69.9485i	−1.92814	−	0.168958i
$415$	−342.318			−0.824862
$416$	−58.8236	+	187.183i	−0.141403	+	0.449960i
$417$	275.307	+	86.8249i	0.660210	+	0.208213i
$418$	86.1288	−	49.7265i	0.206050	−	0.118963i
$419$	91.9581	−	53.0920i	0.219470	−	0.126711i	−0.386235	−	0.922401i	$-0.626224\pi$
$419$	91.9581	−	53.0920i	0.219470	−	0.126711i	0.605705	+	0.795689i	$0.292891\pi$
$420$	−69.4720	+	220.284i	−0.165410	+	0.524486i
$421$	220.358	+	127.224i	0.523416	+	0.302194i	0.738331	−	0.674439i	$-0.235614\pi$
$421$	220.358	+	127.224i	0.523416	+	0.302194i	−0.214915	+	0.976633i	$0.568948\pi$
$422$	−416.842			−0.987776
$423$	−389.096	−	272.528i	−0.919848	−	0.644274i
$424$		−	104.728i		−	0.247001i
$425$	−616.089	−	355.699i	−1.44962	−	0.836939i
$426$	51.1510	+	230.803i	0.120073	+	0.541790i
$427$	246.963	−	142.584i	0.578368	−	0.333921i
$428$	−106.729	+	61.6200i	−0.249367	+	0.143972i
$429$	56.2221	−	80.4439i	0.131054	−	0.187515i
$430$	−512.986	+	888.517i	−1.19299	+	2.06632i
$431$	51.7831			0.120146			0.0600732	−	0.998194i	$-0.480867\pi$
$431$	51.7831			0.120146			0.0600732	+	0.998194i	$0.480867\pi$
$432$	506.593	−	66.5878i	1.17267	−	0.154139i
$433$	−238.438			−0.550664			−0.275332	−	0.961349i	$-0.588788\pi$
$433$	−238.438			−0.550664			−0.275332	+	0.961349i	$0.588788\pi$
$434$	46.4421	−	80.4400i	0.107009	−	0.185346i
$435$	−269.225	−	293.849i	−0.618909	−	0.675514i
$436$	3.39403	−	1.95955i	0.00778448	−	0.00449437i
$437$	354.508	+	614.026i	0.811232	+	1.40509i
$438$	387.309	−	85.8363i	0.884267	−	0.195973i
$439$	236.614	−	409.827i	0.538983	−	0.933546i	−0.459976	−	0.887931i	$-0.652142\pi$
$439$	236.614	−	409.827i	0.538983	−	0.933546i	0.998959	−	0.0456148i	$-0.0145247\pi$
$440$	−140.352			−0.318982
$441$	368.134	−	171.602i	0.834770	−	0.389120i
$442$	−104.278	−	468.267i	−0.235923	−	1.05943i
$443$	63.2547	+	36.5201i	0.142787	+	0.0824381i	0.569692	−	0.821859i	$-0.307063\pi$
$443$	63.2547	+	36.5201i	0.142787	+	0.0824381i	−0.426905	+	0.904297i	$0.640396\pi$
$444$	37.3061	−	118.292i	0.0840228	−	0.266422i
$445$	−243.384	−	421.553i	−0.546929	−	0.947309i
$446$	10.5701	−	6.10264i	0.0236997	−	0.0136830i
$447$	−228.825	−	72.1655i	−0.511912	−	0.161444i
$448$	−353.510	−	204.099i	−0.789085	−	0.455578i
$449$	20.6872			0.0460740			0.0230370	−	0.999735i	$-0.492666\pi$
$449$	20.6872			0.0460740			0.0230370	+	0.999735i	$0.492666\pi$
$450$	780.407	−	363.779i	1.73424	−	0.808398i
$451$	−44.3236			−0.0982785
$452$	−50.9801	−	29.4334i	−0.112788	−	0.0651181i
$453$	27.3173	−	6.05413i	0.0603031	−	0.0133645i
$454$	277.785	+	481.138i	0.611862	+	1.05978i
$455$	765.841	−	703.101i	1.68317	−	1.54528i
$456$	−243.262	−	265.511i	−0.533470	−	0.582260i
$457$	606.146	+	349.959i	1.32636	+	0.765774i	0.984735	−	0.174062i	$-0.0556894\pi$
$457$	606.146	+	349.959i	1.32636	+	0.765774i	0.341625	+	0.939836i	$0.389023\pi$
$458$			724.360i			1.58157i
$459$	−354.894	+	272.203i	−0.773188	+	0.593035i
$460$			317.165i			0.689490i
$461$	68.9796	−	119.476i	0.149630	−	0.259167i	−0.781461	−	0.623955i	$-0.785525\pi$
$461$	68.9796	−	119.476i	0.149630	−	0.259167i	0.931091	+	0.364787i	$0.118858\pi$
$462$	−110.228	−	120.309i	−0.238589	−	0.260410i
$463$	612.880	−	353.846i	1.32371	−	0.764247i	0.339395	−	0.940644i	$-0.389778\pi$
$463$	612.880	−	353.846i	1.32371	−	0.764247i	0.984319	+	0.176397i	$0.0564443\pi$
$464$	−264.126	+	152.493i	−0.569236	+	0.328649i
$465$	−103.754	+	22.9943i	−0.223128	+	0.0494501i
$466$	385.903	+	222.801i	0.828118	+	0.478114i
$467$			566.083i			1.21217i	0.795400	+	0.606085i	$0.207261\pi$
$467$			566.083i			1.21217i	−0.795400	+	0.606085i	$0.792739\pi$
$468$	104.102	+	43.0214i	0.222439	+	0.0919262i
$469$	897.604			1.91387
$470$	−484.620	+	839.387i	−1.03111	+	1.78593i
$471$	−63.6233	−	20.0652i	−0.135081	−	0.0426012i
$472$	203.395	+	352.291i	0.430922	+	0.746379i
$473$	−70.3010	−	121.765i	−0.148628	−	0.257431i
$474$	−422.403	−	133.215i	−0.891145	−	0.281044i
$475$	−659.788	−	380.929i	−1.38903	−	0.801956i
$476$	−154.729			−0.325061
$477$	−138.773	−	12.1603i	−0.290928	−	0.0254932i
$478$	360.496			0.754175
$479$	−358.287	+	620.571i	−0.747989	+	1.29556i	0.200796	+	0.979633i	$0.435647\pi$
$479$	−358.287	+	620.571i	−0.747989	+	1.29556i	−0.948785	+	0.315922i	$0.897686\pi$
$480$	−80.7564	−	364.387i	−0.168243	−	0.759140i
$481$	−411.253	+	377.562i	−0.854995	+	0.784951i
$482$	758.272	−	437.788i	1.57318	−	0.908275i
$483$	857.706	−	785.834i	1.77579	−	1.62699i
$484$	55.1975	−	95.6049i	0.114044	−	0.197531i
$485$			297.848i			0.614121i
$486$	−23.4266	−	540.829i	−0.0482030	−	1.11282i
$487$			206.616i			0.424263i	0.977241	+	0.212131i	$0.0680405\pi$
$487$			206.616i			0.424263i	−0.977241	+	0.212131i	$0.931960\pi$
$488$	−99.4377	+	172.231i	−0.203766	+	0.352933i
$489$	−382.001	−	416.939i	−0.781188	−	0.852635i
$490$	−414.352	−	717.679i	−0.845617	−	1.46465i
$491$	−311.722	+	179.973i	−0.634872	+	0.366543i	−0.782636	−	0.622479i	$-0.786126\pi$
$491$	−311.722	+	179.973i	−0.634872	+	0.366543i	0.147765	+	0.989023i	$0.452792\pi$
$492$	−11.0071	−	49.6658i	−0.0223721	−	0.100947i
$493$	133.485	−	231.203i	0.270761	−	0.468972i
$494$	−111.675	−	501.481i	−0.226062	−	1.01514i
$495$	−16.2966	+	185.976i	−0.0329224	+	0.375710i
$496$			81.3267i			0.163965i
$497$	−297.210	−	171.594i	−0.598008	−	0.345260i
$498$	264.693	+	83.4774i	0.531512	+	0.167625i
$499$	−228.110	+	131.699i	−0.457134	+	0.263926i	−0.710838	−	0.703355i	$-0.751684\pi$
$499$	−228.110	+	131.699i	−0.457134	+	0.263926i	0.253705	+	0.967282i	$0.418351\pi$
$500$	−71.2043	−	123.330i	−0.142409	−	0.246659i
$501$	294.970	+	93.0261i	0.588763	+	0.185681i
$502$	467.543	+	269.936i	0.931361	+	0.537722i
$503$		−	177.364i		−	0.352613i	−0.984335	−	0.176307i	$-0.943585\pi$
$503$		−	177.364i		−	0.352613i	0.984335	−	0.176307i	$-0.0564150\pi$
$504$	−338.941	+	483.916i	−0.672502	+	0.960151i
$505$			511.043i			1.01197i
$506$	−194.037	−	112.027i	−0.383472	−	0.221398i
$507$	−309.377	−	401.665i	−0.610210	−	0.792240i
$508$	3.20168	+	5.54546i	0.00630251	+	0.0109163i
$509$	−445.798	−	772.144i	−0.875830	−	1.51698i	−0.855876	−	0.517182i	$-0.826981\pi$
$509$	−445.798	−	772.144i	−0.875830	−	1.51698i	−0.0199545	−	0.999801i	$-0.506352\pi$
$510$	616.469	+	672.850i	1.20876	+	1.31931i
$511$	−287.952	+	498.747i	−0.563506	+	0.976022i
$512$	226.553			0.442487
$513$	−380.066	+	291.510i	−0.740870	+	0.568246i
$514$		−	1028.68i		−	2.00133i
$515$	558.217	−	966.861i	1.08392	−	1.87740i
$516$	118.983	−	109.013i	0.230587	−	0.211265i
$517$	−66.4138	−	115.032i	−0.128460	−	0.222499i
$518$	464.094	+	803.834i	0.895934	+	1.55180i
$519$	807.893	−	179.047i	1.55663	−	0.344985i
$520$	−217.370	+	691.694i	−0.418018	+	1.33018i
$521$		−	1038.73i		−	1.99373i	−0.0791331	−	0.996864i	$-0.525215\pi$
$521$		−	1038.73i		−	1.99373i	0.0791331	−	0.996864i	$-0.474785\pi$
$522$	136.517	+	292.868i	0.261528	+	0.561050i
$523$	627.155			1.19915			0.599574	−	0.800319i	$-0.295337\pi$
$523$	627.155			1.19915			0.599574	+	0.800319i	$0.295337\pi$
$524$	−201.679	−	116.440i	−0.384884	−	0.222213i
$525$	−375.954	+	1192.09i	−0.716103	+	2.27064i
$526$	−4.92536	+	2.84366i	−0.00936379	+	0.00540619i
$527$	−35.5948	−	61.6521i	−0.0675424	−	0.116987i
$528$	136.252	+	42.9704i	0.258053	+	0.0813834i
$529$	534.161	−	925.194i	1.00976	−	1.74895i
$530$			284.225i			0.536274i
$531$	490.427	−	228.608i	0.923591	−	0.430523i
$532$	−165.704			−0.311474
$533$	−68.6460	+	218.439i	−0.128792	+	0.409830i
$534$	85.3937	+	385.312i	0.159913	+	0.721558i
$535$	−913.800	+	527.583i	−1.70804	+	0.986136i
$536$	−542.120	+	312.993i	−1.01142	+	0.583942i
$537$	23.9701	+	26.1624i	0.0446370	+	0.0487195i
$538$	−226.806	−	130.947i	−0.421573	−	0.243395i
$539$	113.568			0.210701
$540$	−212.439	+	27.9235i	−0.393405	+	0.0517101i
$541$			315.164i			0.582558i	0.956638	+	0.291279i	$0.0940807\pi$
$541$			315.164i			0.582558i	−0.956638	+	0.291279i	$0.905919\pi$
$542$	689.536	+	398.104i	1.27221	+	0.734509i
$543$	143.636	−	131.600i	0.264522	−	0.242357i
$544$	216.523	−	125.010i	0.398020	−	0.229797i
$545$	29.0593	−	16.7774i	0.0533198	−	0.0307842i
$546$	−763.635	+	356.906i	−1.39860	+	0.653675i
$547$	−246.122	+	426.295i	−0.449948	+	0.779334i	−0.998382	−	0.0568605i	$-0.981891\pi$
$547$	−246.122	+	426.295i	−0.449948	+	0.779334i	0.548434	+	0.836194i	$0.315224\pi$
$548$	94.6394			0.172700
$549$	216.672	+	151.760i	0.394668	+	0.276430i
$550$	240.753			0.437733
$551$	142.954	−	247.603i	0.259444	−	0.449370i
$552$	−244.004	+	773.695i	−0.442036	+	1.40162i
$553$	556.837	−	321.490i	1.00694	−	0.581356i
$554$	−178.333	−	308.883i	−0.321901	−	0.557550i
$555$	319.411	−	1012.80i	0.575514	−	1.82486i
$556$	−46.3198	+	80.2283i	−0.0833090	+	0.144295i
$557$	481.165			0.863850			0.431925	−	0.901909i	$-0.357834\pi$
$557$	481.165			0.863850			0.431925	+	0.901909i	$0.357834\pi$
$558$	85.8342	+	7.52143i	0.153825	+	0.0134793i
$559$	−708.971	+	157.880i	−1.26828	+	0.282434i
$560$	1310.65	+	756.706i	2.34045	+	1.35126i
$561$	−122.097	+	27.0594i	−0.217642	+	0.0482343i
$562$	325.929	+	564.526i	0.579945	+	1.00449i
$563$	150.772	−	87.0483i	0.267801	−	0.154615i	−0.360087	−	0.932919i	$-0.617253\pi$
$563$	150.772	−	87.0483i	0.267801	−	0.154615i	0.627888	+	0.778304i	$0.283920\pi$
$564$	112.404	−	102.985i	0.199298	−	0.182597i
$565$	−436.486	−	252.005i	−0.772541	−	0.446027i
$566$	752.576			1.32964
$567$	601.868	+	505.310i	1.06150	+	0.891199i
$568$	239.339			0.421371
$569$	439.176	+	253.559i	0.771839	+	0.445621i	0.833530	−	0.552474i	$-0.186316\pi$
$569$	439.176	+	253.559i	0.771839	+	0.445621i	−0.0616914	+	0.998095i	$0.519649\pi$
$570$	660.195	+	720.576i	1.15824	+	1.26417i
$571$	−529.176	−	916.560i	−0.926753	−	1.60518i	−0.788718	−	0.614756i	$-0.789255\pi$
$571$	−529.176	−	916.560i	−0.926753	−	1.60518i	−0.138035	−	0.990427i	$-0.544079\pi$
$572$	21.3001	+	23.2008i	0.0372380	+	0.0405609i
$573$	−422.823	+	93.7070i	−0.737911	+	0.163538i
$574$	329.680	+	190.341i	0.574355	+	0.331604i
$575$			1716.37i			2.98499i
$576$	33.0544	−	377.216i	0.0573862	−	0.654888i
$577$		−	437.958i		−	0.759026i	−0.925186	−	0.379513i	$-0.876092\pi$
$577$		−	437.958i		−	0.759026i	0.925186	−	0.379513i	$-0.123908\pi$
$578$	16.2528	−	28.1507i	0.0281190	−	0.0487036i
$579$	−89.8300	+	284.836i	−0.155147	+	0.491945i
$580$	110.761	−	63.9476i	0.190966	−	0.110254i
$581$	−348.934	+	201.457i	−0.600575	+	0.346742i
$582$	72.6332	−	230.308i	0.124799	−	0.395718i
$583$	−33.7326	−	19.4755i	−0.0578603	−	0.0334057i
$584$		−	401.633i		−	0.687728i
$585$	891.304	+	368.344i	1.52360	+	0.629648i
$586$	−846.648			−1.44479
$587$	−59.4816	+	103.025i	−0.101331	+	0.175511i	−0.912233	−	0.409671i	$-0.865644\pi$
$587$	−59.4816	+	103.025i	−0.101331	+	0.175511i	0.810902	+	0.585182i	$0.198977\pi$
$588$	28.2028	+	127.256i	0.0479640	+	0.216422i
$589$	−38.1196	−	66.0251i	−0.0647192	−	0.112097i
$590$	−551.999	−	956.090i	−0.935592	−	1.62049i
$591$	−560.664	+	513.683i	−0.948670	+	0.869176i
$592$	−703.814	−	406.347i	−1.18888	−	0.686397i
$593$	−1100.04			−1.85504			−0.927520	−	0.373773i	$-0.878064\pi$
$593$	−1100.04			−1.85504			−0.927520	+	0.373773i	$0.878064\pi$
$594$	57.9532	−	139.830i	0.0975643	−	0.235404i
$595$	−1324.77			−2.22651
$596$	38.4992	−	66.6826i	0.0645960	−	0.111884i
$597$	−227.541	+	208.474i	−0.381141	+	0.349203i
$598$	−852.616	+	782.767i	−1.42578	+	1.30898i
$599$	−459.809	+	265.471i	−0.767627	+	0.443190i	−0.832028	−	0.554734i	$-0.812820\pi$
$599$	−459.809	+	265.471i	−0.767627	+	0.443190i	0.0644003	+	0.997924i	$0.479487\pi$
$600$	−188.617	−	851.071i	−0.314361	−	1.41845i
$601$	403.887	−	699.553i	0.672025	−	1.16398i	−0.305304	−	0.952255i	$-0.598758\pi$
$601$	403.887	−	699.553i	0.672025	−	1.16398i	0.977329	−	0.211726i	$-0.0679085\pi$
$602$			1207.59i			2.00596i
$603$	351.791	+	754.689i	0.583401	+	1.25156i
$604$			8.97922i			0.0148663i
$605$	472.594	−	818.557i	0.781148	−	1.35299i
$606$	124.623	−	395.158i	0.205648	−	0.652076i
$607$	−324.905	−	562.753i	−0.535264	−	0.927105i	−0.999151	−	0.0412100i	$-0.986879\pi$
$607$	−324.905	−	562.753i	−0.535264	−	0.927105i	0.463886	−	0.885895i	$-0.346455\pi$
$608$	231.881	−	133.877i	0.381383	−	0.220192i
$609$	−447.362	−	141.086i	−0.734584	−	0.231669i
$610$	269.866	−	467.422i	0.442404	−	0.766266i
$611$	−669.769	+	149.151i	−1.09618	+	0.244109i
$612$	−60.6417	−	130.093i	−0.0990878	−	0.212571i
$613$		−	190.777i		−	0.311219i	−0.987819	−	0.155609i	$-0.950266\pi$
$613$		−	190.777i		−	0.311219i	0.987819	−	0.155609i	$-0.0497341\pi$
$614$	−1062.43	−	613.392i	−1.73034	−	0.999010i
$615$	−94.2411	−	425.233i	−0.153238	−	0.691436i
$616$	−143.065	+	82.5984i	−0.232248	+	0.134088i
$617$	417.367	+	722.901i	0.676446	+	1.17164i	0.976044	+	0.217573i	$0.0698141\pi$
$617$	417.367	+	722.901i	0.676446	+	1.17164i	−0.299598	+	0.954066i	$0.596853\pi$
$618$	−667.413	+	611.487i	−1.07996	+	0.989461i
$619$	344.598	+	198.954i	0.556702	+	0.321412i	0.751821	−	0.659368i	$-0.229176\pi$
$619$	344.598	+	198.954i	0.556702	+	0.321412i	−0.195119	+	0.980780i	$0.562509\pi$
$620$		−	34.1042i		−	0.0550067i
$621$	996.869	+	413.158i	1.60526	+	0.665311i
$622$		−	155.633i		−	0.250214i
$623$	−496.175	−	286.467i	−0.796429	−	0.459819i
$624$	422.790	−	604.939i	0.677549	−	0.969453i
$625$	−72.8284	−	126.143i	−0.116525	−	0.201828i
$626$	−232.312	−	402.375i	−0.371105	−	0.642772i
$627$	−130.757	+	28.9788i	−0.208544	+	0.0462181i
$628$	10.7045	−	18.5407i	0.0170453	−	0.0295234i
$629$	711.395			1.13099
$630$	919.860	−	1313.31i	1.46010	−	2.08462i
$631$			823.864i			1.30565i	0.757509	+	0.652824i	$0.226416\pi$
$631$			823.864i			1.30565i	−0.757509	+	0.652824i	$0.773584\pi$
$632$	−224.206	+	388.336i	−0.354756	+	0.614456i
$633$	535.354	+	168.837i	0.845742	+	0.266725i
$634$	−35.5664	−	61.6029i	−0.0560985	−	0.0971654i
$635$	27.4123	+	47.4796i	0.0431690	+	0.0747710i
$636$	13.4459	−	42.6348i	0.0211414	−	0.0670358i
$637$	175.888	−	559.696i	0.276119	−	0.878643i
$638$			90.3488i			0.141613i
$639$	27.7902	−	317.141i	0.0434901	−	0.496308i
$640$	−1270.23			−1.98473
$641$	−460.990	−	266.153i	−0.719174	−	0.415215i	0.0952747	−	0.995451i	$-0.469627\pi$
$641$	−460.990	−	266.153i	−0.719174	−	0.415215i	−0.814449	+	0.580236i	$0.802960\pi$
$642$	835.241	−	185.108i	1.30100	−	0.288330i
$643$	45.0664	−	26.0191i	0.0700877	−	0.0404652i	−0.464547	−	0.885549i	$-0.653783\pi$
$643$	45.0664	−	26.0191i	0.0700877	−	0.0404652i	0.534634	+	0.845084i	$0.320449\pi$
$644$	186.655	+	323.296i	0.289837	+	0.502012i
$645$	1018.72	−	933.354i	1.57941	−	1.44706i
$646$	−327.333	+	566.957i	−0.506707	+	0.877643i
$647$		−	27.7907i		−	0.0429531i	−0.999769	−	0.0214766i	$-0.993163\pi$
$647$		−	27.7907i		−	0.0429531i	0.999769	−	0.0214766i	$-0.00683673\pi$
$648$	−539.707	−	95.3181i	−0.832881	−	0.147096i
$649$	151.295			0.233120
$650$	372.865	−	1186.50i	0.573639	−	1.82538i
$651$	−92.2275	+	84.4992i	−0.141670	+	0.129799i
$652$	157.157	−	90.7346i	0.241038	−	0.139163i
$653$	496.796	−	286.825i	0.760791	−	0.439243i	−0.0687890	−	0.997631i	$-0.521914\pi$
$653$	496.796	−	286.825i	0.760791	−	0.439243i	0.829579	+	0.558389i	$0.188580\pi$
$654$	−26.5611	+	5.88653i	−0.0406132	+	0.00900081i
$655$	−1726.75	−	996.942i	−2.63627	−	1.52205i
$656$	−333.314			−0.508100
$657$	−532.192	−	46.6346i	−0.810034	−	0.0709812i
$658$			1140.81i			1.73376i
$659$	−354.829	−	204.861i	−0.538435	−	0.310866i	0.206009	−	0.978550i	$-0.433952\pi$
$659$	−354.829	−	204.861i	−0.538435	−	0.310866i	−0.744445	+	0.667684i	$0.767286\pi$
$660$	−57.1370	−	18.0196i	−0.0865712	−	0.0273024i
$661$	747.052	−	431.311i	1.13018	−	0.652513i	0.186204	−	0.982511i	$-0.440382\pi$
$661$	747.052	−	431.311i	1.13018	−	0.652513i	0.943981	+	0.329999i	$0.107048\pi$
$662$	435.534	−	251.456i	0.657906	−	0.379842i
$663$	−55.7407	+	643.637i	−0.0840734	+	0.970795i
$664$	140.496	−	243.345i	0.211590	−	0.366484i
$665$	−1418.74			−2.13344
$666$	−493.961	+	705.242i	−0.741682	+	1.05892i
$667$	−644.112			−0.965684
$668$	−49.6280	+	85.9583i	−0.0742935	+	0.128680i
$669$	−16.0471	+	3.55639i	−0.0239867	+	0.00531598i
$670$	1471.27	−	849.439i	2.19593	−	1.26782i
$671$	36.9833	+	64.0569i	0.0551166	+	0.0954648i
$672$	−296.763	−	323.904i	−0.441611	−	0.482000i
$673$	−602.341	+	1043.29i	−0.895009	+	1.55020i	−0.0612150	+	0.998125i	$0.519498\pi$
$673$	−602.341	+	1043.29i	−0.895009	+	1.55020i	−0.833794	+	0.552076i	$0.813836\pi$
$674$	−648.905			−0.962767
$675$	−1149.63	+	151.110i	−1.70316	+	0.223867i
$676$	147.329	−	69.0410i	0.217942	−	0.102132i
$677$	−253.793	−	146.527i	−0.374879	−	0.216436i	0.300709	−	0.953716i	$-0.402777\pi$
$677$	−253.793	−	146.527i	−0.374879	−	0.216436i	−0.675588	+	0.737280i	$0.736110\pi$
$678$	276.053	+	301.301i	0.407158	+	0.444397i
$679$	175.287	+	303.605i	0.258154	+	0.447136i
$680$	800.113	−	461.945i	1.17664	−	0.679331i
$681$	−161.883	−	730.445i	−0.237714	−	1.07261i
$682$	20.8644	+	12.0461i	0.0305930	+	0.0176629i
$683$	791.335			1.15862			0.579308	−	0.815109i	$-0.303323\pi$
$683$	791.335			1.15862			0.579308	+	0.815109i	$0.303323\pi$
$684$	−64.9431	−	139.321i	−0.0949460	−	0.203686i
$685$	810.291			1.18291
$686$	72.4492	+	41.8286i	0.105611	+	0.0609746i
$687$	293.394	−	930.304i	0.427066	−	1.35415i
$688$	−528.665	−	915.674i	−0.768408	−	1.33092i
$689$	−148.224	+	136.081i	−0.215129	+	0.197505i
$690$	662.208	−	2099.75i	0.959721	−	3.04312i
$691$	1127.60	+	651.022i	1.63184	+	0.942145i	0.983524	+	0.180776i	$0.0578610\pi$
$691$	1127.60	+	651.022i	1.63184	+	0.942145i	0.648319	+	0.761369i	$0.275472\pi$
$692$			265.555i			0.383750i
$693$	92.8372	+	199.162i	0.133964	+	0.287390i
$694$			698.542i			1.00654i
$695$	−396.585	+	686.905i	−0.570625	+	0.988352i
$696$	319.387	−	70.7832i	0.458889	−	0.101700i
$697$	252.678	−	145.884i	0.362522	−	0.209302i
$698$	−1241.26	+	716.641i	−1.77831	+	1.02671i
$699$	−405.377	−	442.452i	−0.579938	−	0.632979i
$700$	−347.390	−	200.566i	−0.496272	−	0.286523i
$701$		−	43.1832i		−	0.0616023i	−0.999526	−	0.0308012i	$-0.990194\pi$
$701$		−	43.1832i		−	0.0616023i	0.999526	−	0.0308012i	$-0.00980586\pi$
$702$	−599.366	−	502.171i	−0.853798	−	0.715343i
$703$	761.855			1.08372
$704$	52.9389	−	91.6929i	0.0751973	−	0.130246i
$705$	962.388	−	881.744i	1.36509	−	1.25070i
$706$	−377.220	−	653.364i	−0.534306	−	0.925444i
$707$	300.754	+	520.921i	0.425394	+	0.736804i
$708$	37.5718	+	169.531i	0.0530675	+	0.239450i
$709$	−177.188	−	102.300i	−0.249913	−	0.144287i	0.369811	−	0.929107i	$-0.379422\pi$
$709$	−177.188	−	102.300i	−0.249913	−	0.144287i	−0.619724	+	0.784820i	$0.712756\pi$
$710$	−649.547			−0.914854
$711$	488.540	+	342.179i	0.687116	+	0.481265i
$712$	399.562			0.561183
$713$	−85.8785	+	148.746i	−0.120447	+	0.208620i
$714$	1024.36	+	323.058i	1.43468	+	0.452462i
$715$	182.369	+	198.643i	0.255062	+	0.277822i
$716$	−9.86140	+	5.69348i	−0.0137729	+	0.00795179i
$717$	−462.989	−	146.015i	−0.645731	−	0.203647i
$718$	162.134	−	280.825i	0.225814	−	0.391121i
$719$			801.662i			1.11497i	0.830187	+	0.557484i	$0.188233\pi$
$719$			801.662i			1.11497i	−0.830187	+	0.557484i	$0.811767\pi$
$720$	−122.551	+	1398.54i	−0.170209	+	1.94242i
$721$		−	1314.06i		−	1.82256i
$722$	51.5530	−	89.2923i	0.0714030	−	0.123674i
$723$	−1151.18	+	255.127i	−1.59223	+	0.352873i
$724$	31.2581	+	54.1407i	0.0431742	+	0.0747799i
$725$	599.390	−	346.058i	0.826745	−	0.477321i
$726$	−565.041	+	517.693i	−0.778293	+	0.713076i
$727$	−461.472	+	799.294i	−0.634763	+	1.09944i	0.351803	+	0.936074i	$0.385569\pi$
$727$	−461.472	+	799.294i	−0.634763	+	1.09944i	−0.986565	+	0.163367i	$0.947765\pi$
$728$	185.498	+	832.987i	0.254804	+	1.14421i
$729$	−188.970	+	704.082i	−0.259218	+	0.965819i
$730$			1090.00i			1.49315i
$731$	801.539	+	462.769i	1.09650	+	0.633062i
$732$	−62.5934	+	57.3483i	−0.0855101	+	0.0783447i
$733$	909.418	−	525.053i	1.24068	−	0.716306i	0.271447	−	0.962454i	$-0.412498\pi$
$733$	909.418	−	525.053i	1.24068	−	0.716306i	0.969232	+	0.246147i	$0.0791646\pi$
$734$	472.453	+	818.313i	0.643669	+	1.11487i
$735$	241.469	+	1089.55i	0.328530	+	1.48238i
$736$	−522.398	−	301.607i	−0.709780	−	0.409792i
$737$			232.819i			0.315901i
$738$	−30.8262	+	351.788i	−0.0417700	+	0.476677i
$739$			594.008i			0.803799i	0.915684	+	0.401900i	$0.131650\pi$
$739$			594.008i			0.803799i	−0.915684	+	0.401900i	$0.868350\pi$
$740$	295.143	+	170.401i	0.398842	+	0.230271i
$741$	−59.6944	+	689.290i	−0.0805592	+	0.930216i
$742$	167.269	+	289.719i	0.225430	+	0.390456i
$743$	−108.652	−	188.191i	−0.146234	−	0.253285i	0.783598	−	0.621268i	$-0.213382\pi$
$743$	−108.652	−	188.191i	−0.146234	−	0.253285i	−0.929833	+	0.367982i	$0.880049\pi$
$744$	26.2373	−	83.1940i	0.0352651	−	0.111820i
$745$	329.626	−	570.928i	0.442451	−	0.766347i
$746$	−49.1857			−0.0659326
$747$	−306.137	−	214.422i	−0.409822	−	0.287044i
$748$		−	40.1334i		−	0.0536543i
$749$	−620.975	+	1075.56i	−0.829072	+	1.43599i
$750$	213.900	+	965.154i	0.285200	+	1.28687i
$751$	418.499	+	724.861i	0.557255	+	0.965194i	0.997724	+	0.0674264i	$0.0214788\pi$
$751$	418.499	+	724.861i	0.557255	+	0.965194i	−0.440469	+	0.897768i	$0.645188\pi$
$752$	−499.432	−	865.042i	−0.664139	−	1.15032i
$753$	−491.137	−	536.056i	−0.652240	−	0.711893i
$754$	445.265	+	139.927i	0.590537	+	0.185580i
$755$			76.8790i			0.101826i
$756$	−200.112	+	153.485i	−0.264698	+	0.203023i
$757$	−1313.32			−1.73490			−0.867450	−	0.497524i	$-0.834243\pi$
$757$	−1313.32			−1.73490			−0.867450	+	0.497524i	$0.834243\pi$
$758$	−847.731	−	489.437i	−1.11838	−	0.645696i
$759$	203.829	+	222.471i	0.268549	+	0.293110i
$760$	856.865	−	494.711i	1.12745	−	0.650936i
$761$	608.861	+	1054.58i	0.800080	+	1.38578i	0.919563	+	0.392943i	$0.128543\pi$
$761$	608.861	+	1054.58i	0.800080	+	1.38578i	−0.119483	+	0.992836i	$0.538124\pi$
$762$	−9.61792	−	43.3978i	−0.0126219	−	0.0569524i
$763$	19.7473	−	34.2033i	0.0258811	−	0.0448274i
$764$		−	138.982i		−	0.181914i
$765$	−519.207	−	1113.84i	−0.678702	−	1.45600i
$766$	414.229			0.540770
$767$	234.318	−	745.625i	0.305499	−	0.972132i
$768$	500.684	+	157.903i	0.651932	+	0.205603i
$769$	−234.211	+	135.222i	−0.304565	+	0.175841i	−0.644492	−	0.764611i	$-0.722931\pi$
$769$	−234.211	+	135.222i	−0.304565	+	0.175841i	0.339927	+	0.940452i	$0.389598\pi$
$770$	388.267	−	224.166i	0.504242	−	0.291124i
$771$	−416.657	+	1321.15i	−0.540411	+	1.71355i
$772$	−83.0051	−	47.9230i	−0.107520	−	0.0620764i
$773$	862.333			1.11557			0.557784	−	0.829986i	$-0.311652\pi$
$773$	862.333			1.11557			0.557784	+	0.829986i	$0.311652\pi$
$774$	−1015.32	+	473.280i	−1.31178	+	0.611473i
$775$		−	184.558i		−	0.238139i
$776$	−211.733	−	122.244i	−0.272852	−	0.157531i
$777$	−270.457	−	1220.35i	−0.348078	−	1.57059i
$778$	−273.419	+	157.859i	−0.351439	+	0.202903i
$779$	270.601	−	156.231i	0.347369	−	0.200554i
$780$	−177.296	+	253.680i	−0.227303	+	0.325230i
$781$	44.5079	−	77.0899i	0.0569883	−	0.0987067i
$782$	1474.88			1.88603
$783$	−56.7080	−	431.429i	−0.0724240	−	0.550994i
$784$	854.033			1.08933
$785$	91.6504	−	158.743i	0.116752	−	0.202221i
$786$	1092.08	+	1191.96i	1.38941	+	1.51649i
$787$	−764.929	+	441.632i	−0.971956	+	0.561159i	−0.899832	−	0.436237i	$-0.856311\pi$
$787$	−764.929	+	441.632i	−0.971956	+	0.561159i	−0.0721241	+	0.997396i	$0.522978\pi$
$788$	−122.012	−	211.331i	−0.154838	−	0.268187i
$789$	7.47748	−	1.65718i	0.00947716	−	0.00210035i
$790$	608.478	−	1053.91i	0.770225	−	1.33407i
$791$	−593.229			−0.749974
$792$	−125.518	−	87.9141i	−0.158482	−	0.111003i
$793$	372.968	−	83.0562i	0.470326	−	0.104737i
$794$	−248.558	−	143.505i	−0.313045	−	0.180737i
$795$	115.122	−	365.034i	0.144808	−	0.459162i
$796$	−49.5177	−	85.7671i	−0.0622081	−	0.107748i
$797$	156.092	−	90.1197i	0.195849	−	0.113074i	−0.398869	−	0.917008i	$-0.630597\pi$
$797$	156.092	−	90.1197i	0.195849	−	0.113074i	0.594718	+	0.803934i	$0.297264\pi$
$798$	1097.02	+	345.972i	1.37471	+	0.433549i
$799$	757.218	+	437.180i	0.947707	+	0.547159i
$800$	648.170			0.810212
$801$	46.3942	−	529.448i	0.0579203	−	0.660984i
$802$	−853.762			−1.06454
$803$	−129.364	−	74.6885i	−0.161101	−	0.0930119i
$804$	−260.881	+	57.8170i	−0.324478	+	0.0719117i
$805$	1598.12	+	2768.02i	1.98524	+	3.43853i
$806$	91.6802	−	84.1695i	0.113747	−	0.104429i
$807$	238.251	+	260.041i	0.295231	+	0.322232i
$808$	−363.288	−	209.745i	−0.449614	−	0.259585i
$809$		−	1144.26i		−	1.41441i	−0.707008	−	0.707205i	$-0.749956\pi$
$809$		−	1144.26i		−	1.41441i	0.707008	−	0.707205i	$-0.250044\pi$
$810$	1464.72	+	258.686i	1.80830	+	0.319365i
$811$		−	1404.71i		−	1.73207i	−0.499980	−	0.866037i	$-0.666659\pi$
$811$		−	1404.71i		−	1.73207i	0.499980	−	0.866037i	$-0.333341\pi$
$812$	75.2675	−	130.367i	0.0926940	−	0.160551i
$813$	−724.331	−	790.578i	−0.890936	−	0.972421i
$814$	−208.497	+	120.376i	−0.256139	+	0.147882i
$815$	1345.56	−	776.858i	1.65099	−	0.953200i
$816$	−918.171	+	203.487i	−1.12521	+	0.249372i
$817$	858.392	+	495.593i	1.05066	+	0.606601i
$818$		−	232.329i		−	0.284020i
$819$	1125.31	−	149.077i	1.37400	−	0.182024i
$820$	139.774			0.170457
$821$	−520.694	+	901.868i	−0.634219	+	1.09850i	0.352461	+	0.935826i	$0.385345\pi$
$821$	−520.694	+	901.868i	−0.634219	+	1.09850i	−0.986680	+	0.162673i	$0.947989\pi$
$822$	−626.547	−	197.597i	−0.762223	−	0.240386i
$823$	360.507	+	624.416i	0.438040	+	0.758707i	0.997538	−	0.0701244i	$-0.0223396\pi$
$823$	360.507	+	624.416i	0.438040	+	0.758707i	−0.559499	+	0.828831i	$0.689006\pi$
$824$	458.212	+	793.647i	0.556083	+	0.963164i
$825$	−309.202	−	97.5144i	−0.374790	−	0.118199i
$826$	−1125.34	−	649.713i	−1.36239	−	0.786578i
$827$	−998.957			−1.20793			−0.603964	−	0.797011i	$-0.706413\pi$
$827$	−998.957			−1.20793			−0.603964	+	0.797011i	$0.706413\pi$
$828$	−198.667	+	283.643i	−0.239936	+	0.342564i
$829$	1511.17			1.82288			0.911441	−	0.411431i	$-0.134971\pi$
$829$	1511.17			1.82288			0.911441	+	0.411431i	$0.134971\pi$
$830$	−381.294	+	660.421i	−0.459391	+	0.795688i
$831$	103.926	+	468.934i	0.125062	+	0.564300i
$832$	−369.900	−	402.907i	−0.444591	−	0.484263i
$833$	−647.424	+	373.791i	−0.777220	+	0.448728i
$834$	474.162	−	434.430i	0.568540	−	0.520899i
$835$	−424.909	+	735.964i	−0.508873	+	0.881394i
$836$		−	42.9801i		−	0.0514116i
$837$	−107.191	−	44.4261i	−0.128066	−	0.0530778i
$838$		−	236.549i		−	0.282277i
$839$	301.720	−	522.595i	0.359619	−	0.622878i	−0.628278	−	0.777989i	$-0.716240\pi$
$839$	301.720	−	522.595i	0.359619	−	0.622878i	0.987897	+	0.155111i	$0.0495734\pi$
$840$	−1096.62	−	1196.92i	−1.30550	−	1.42490i
$841$	−290.633	−	503.391i	−0.345580	−	0.598562i
$842$	490.896	−	283.419i	0.583012	−	0.336602i
$843$	−189.940	−	857.041i	−0.225314	−	1.01666i
$844$	−90.0721	+	156.009i	−0.106721	+	0.184845i
$845$	1261.41	−	591.120i	1.49279	−	0.699551i
$846$	−959.176	+	447.111i	−1.13378	+	0.528499i
$847$		−	1112.50i		−	1.31347i
$848$	−253.669	−	146.456i	−0.299138	−	0.172708i
$849$	−966.542	−	304.823i	−1.13845	−	0.359037i
$850$	−1372.47	+	792.399i	−1.61468	+	0.932234i
$851$	−858.180	−	1486.41i	−1.00844	−	1.74666i
$852$	97.4343	+	30.7283i	0.114360	+	0.0360661i
$853$	300.891	+	173.720i	0.352745	+	0.203657i	0.665894	−	0.746047i	$-0.268050\pi$
$853$	300.891	+	173.720i	0.352745	+	0.203657i	−0.313149	+	0.949704i	$0.601384\pi$
$854$		−	635.275i		−	0.743882i
$855$	−556.035	−	1192.85i	−0.650333	−	1.39514i
$856$		−	866.131i		−	1.01184i
$857$	1017.85	+	587.654i	1.18769	+	0.685710i	0.957780	−	0.287503i	$-0.0928250\pi$
$857$	1017.85	+	587.654i	1.18769	+	0.685710i	0.229905	+	0.973213i	$0.426158\pi$
$858$	−92.5739	−	198.070i	−0.107895	−	0.230851i
$859$	−719.053	−	1245.44i	−0.837082	−	1.44987i	−0.892324	−	0.451396i	$-0.850926\pi$
$859$	−719.053	−	1245.44i	−0.837082	−	1.44987i	0.0552419	−	0.998473i	$-0.482407\pi$
$860$	221.694	+	383.986i	0.257784	+	0.446495i
$861$	−346.316	−	377.990i	−0.402226	−	0.439013i
$862$	57.6792	−	99.9033i	0.0669132	−	0.115897i
$863$	397.085			0.460122			0.230061	−	0.973176i	$-0.426107\pi$
$863$	397.085			0.460122			0.230061	+	0.973176i	$0.426107\pi$
$864$	156.025	−	376.458i	0.180585	−	0.435715i
$865$			2273.65i			2.62850i
$866$	−265.586	+	460.009i	−0.306682	+	0.531188i
$867$	−32.2758	+	29.5712i	−0.0372270	+	0.0341075i
$868$	−20.0706	−	34.7634i	−0.0231228	−	0.0400499i
$869$	83.3876	+	144.431i	0.0959581	+	0.166204i
$870$	−866.791	+	192.100i	−0.996311	+	0.220805i
$871$	1147.40	+	360.578i	1.31734	+	0.413981i
$872$			27.5434i			0.0315865i
$873$	−186.567	+	266.368i	−0.213708	+	0.305117i
$874$	1579.49			1.80720
$875$	−1242.85	−	717.561i	−1.42040	−	0.820070i
$876$	51.5650	−	163.504i	0.0588642	−	0.186649i
$877$	−1320.07	+	762.145i	−1.50521	+	0.869036i	−0.505233	+	0.862983i	$0.668594\pi$
$877$	−1320.07	+	762.145i	−1.50521	+	0.869036i	−0.999982	+	0.00605330i	$0.998073\pi$
$878$	−527.109	−	912.980i	−0.600352	−	1.03984i
$879$	1087.36	+	342.925i	1.23704	+	0.390131i
$880$	−196.273	+	339.955i	−0.223038	+	0.386313i
$881$			1327.68i			1.50701i	0.657440	+	0.753507i	$0.271640\pi$
$881$			1327.68i			1.50701i	−0.657440	+	0.753507i	$0.728360\pi$
$882$	78.9845	−	901.367i	0.0895515	−	1.02196i
$883$	−69.0868			−0.0782410			−0.0391205	−	0.999234i	$-0.512456\pi$
$883$	−69.0868			−0.0782410			−0.0391205	+	0.999234i	$0.512456\pi$
$884$	−197.789	−	62.1564i	−0.223743	−	0.0703127i
$885$	321.685	+	1451.50i	0.363486	+	1.64011i
$886$	140.914	−	81.3566i	0.159045	−	0.0918246i
$887$	452.207	−	261.082i	0.509817	−	0.294343i	−0.222942	−	0.974832i	$-0.571566\pi$
$887$	452.207	−	261.082i	0.509817	−	0.294343i	0.732758	+	0.680489i	$0.238233\pi$
$888$	588.880	+	642.738i	0.663153	+	0.723804i
$889$	55.8844	+	32.2648i	0.0628620	+	0.0362934i
$890$	−1084.38			−1.21841
$891$	−131.066	+	156.112i	−0.147100	+	0.175210i
$892$		−	5.27469i		−	0.00591333i
$893$	810.928	+	468.189i	0.908094	+	0.524288i
$894$	−394.105	+	361.081i	−0.440834	+	0.403894i
$895$	−84.4321	+	48.7469i	−0.0943375	+	0.0544658i
$896$	−1294.78	+	747.541i	−1.44507	+	0.834309i
$897$	1412.08	−	659.974i	1.57422	−	0.735757i
$898$	23.0427	−	39.9111i	0.0256600	−	0.0444444i
$899$	69.2601			0.0770412
$900$	32.4822	−	370.686i	0.0360913	−	0.411873i
$901$	256.402			0.284575
$902$	−49.3703	+	85.5119i	−0.0547343	+	0.0948025i
$903$	489.120	−	1550.92i	0.541661	−	1.71752i
$904$	358.289	−	206.858i	0.396337	−	0.228825i
$905$	267.628	+	463.546i	0.295722	+	0.512205i
$906$	18.7477	−	59.4457i	0.0206928	−	0.0656134i
$907$	−765.275	+	1325.50i	−0.843743	+	1.46141i	0.0429654	+	0.999077i	$0.486319\pi$
$907$	−765.275	+	1325.50i	−0.843743	+	1.46141i	−0.886708	+	0.462329i	$0.847014\pi$
$908$	240.098			0.264425
$909$	−320.109	+	457.029i	−0.352155	+	0.502782i
$910$	−503.426	−	2260.66i	−0.553216	−	2.48425i
$911$	168.355	+	97.1996i	0.184802	+	0.106696i	0.589547	−	0.807734i	$-0.299306\pi$
$911$	168.355	+	97.1996i	0.184802	+	0.106696i	−0.404745	+	0.914430i	$0.632640\pi$
$912$	−983.297	+	217.921i	−1.07818	+	0.238948i
$913$	−52.2537	−	90.5060i	−0.0572330	−	0.0991304i
$914$	1350.33	−	779.611i	1.47738	−	0.852966i
$915$	−535.917	+	491.009i	−0.585701	+	0.536622i
$916$	271.103	+	156.522i	0.295964	+	0.170875i
$917$	−2346.84			−2.55926
$918$	129.849	+	987.879i	0.141448	+	1.07612i
$919$	−361.496			−0.393358			−0.196679	−	0.980468i	$-0.563016\pi$
$919$	−361.496			−0.393358			−0.196679	+	0.980468i	$0.563016\pi$
$920$	−1930.41	−	1114.52i	−2.09827	−	1.21143i
$921$	1116.04	+	1218.11i	1.21177	+	1.32260i
$922$	−153.667	−	266.159i	−0.166667	−	0.288676i
$923$	−310.990	−	338.740i	−0.336934	−	0.366999i
$924$	−68.8460	+	15.2578i	−0.0745087	+	0.0165128i
$925$	1597.19	+	922.139i	1.72669	+	0.996907i
$926$		−	1576.54i		−	1.70253i
$927$	1104.84	−	515.011i	1.19185	−	0.555568i
$928$			243.242i			0.262115i
$929$	819.537	−	1419.48i	0.882171	−	1.52797i	0.0332494	−	0.999447i	$-0.489414\pi$
$929$	819.537	−	1419.48i	0.882171	−	1.52797i	0.848922	−	0.528518i	$-0.177252\pi$
$930$	−71.2059	+	225.782i	−0.0765655	+	0.242776i
$931$	−693.346	+	400.304i	−0.744733	+	0.429972i
$932$	166.774	−	96.2869i	0.178942	−	0.103312i
$933$	−63.0376	+	199.882i	−0.0675644	+	0.214236i
$934$	1092.12	+	630.538i	1.16930	+	0.675094i
$935$		−	343.617i		−	0.367505i
$936$	−627.660	+	482.429i	−0.670577	+	0.515416i
$937$	−598.606			−0.638854			−0.319427	−	0.947611i	$-0.603490\pi$
$937$	−598.606			−0.638854			−0.319427	+	0.947611i	$0.603490\pi$
$938$	999.805	−	1731.71i	1.06589	−	1.84618i
$939$	135.383	+	610.871i	0.144178	+	0.650555i
$940$	209.436	+	362.753i	0.222804	+	0.385908i
$941$	173.305	+	300.174i	0.184171	+	0.318994i	0.943297	−	0.331950i	$-0.107707\pi$
$941$	173.305	+	300.174i	0.184171	+	0.318994i	−0.759126	+	0.650944i	$0.774373\pi$
$942$	−109.579	+	100.396i	−0.116325	+	0.106578i
$943$	−609.628	−	351.969i	−0.646477	−	0.373244i
$944$	1137.74			1.20523
$945$	−1713.33	+	1314.12i	−1.81305	+	1.39061i
$946$	−313.222			−0.331102
$947$	−315.677	+	546.769i	−0.333345	+	0.577370i	−0.983165	−	0.182718i	$-0.941511\pi$
$947$	−315.677	+	546.769i	−0.333345	+	0.577370i	0.649821	+	0.760087i	$0.274844\pi$
$948$	−141.132	+	129.305i	−0.148873	+	0.136398i
$949$	−568.439	+	521.871i	−0.598987	+	0.549916i
$950$	−1469.82	+	848.604i	−1.54718	+	0.893267i
$951$	20.7268	+	93.5231i	0.0217948	+	0.0983418i
$952$	543.718	−	941.748i	0.571133	−	0.989231i
$953$		−	557.092i		−	0.584567i	−0.956332	−	0.292283i	$-0.905585\pi$
$953$		−	557.092i		−	0.584567i	0.956332	−	0.292283i	$-0.0944150\pi$
$954$	−178.034	+	254.184i	−0.186618	+	0.266440i
$955$		−	1189.95i		−	1.24602i
$956$	77.8968	−	134.921i	0.0814820	−	0.141131i
$957$	36.5948	−	116.036i	0.0382391	−	0.121250i
$958$	798.163	+	1382.46i	0.833156	+	1.44307i
$959$	825.952	−	476.864i	0.861264	−	0.497251i
$960$	992.245	+	312.929i	1.03359	+	0.325967i
$961$	−471.266	+	816.256i	−0.490391	+	0.849382i
$962$	270.338	+	1213.97i	0.281016	+	1.26192i
$963$	−1147.69	−	100.569i	−1.19178	−	0.104433i
$964$		−	378.394i		−	0.392524i
$965$	−710.679	−	410.311i	−0.736455	−	0.425192i
$966$	−560.716	−	2530.05i	−0.580451	−	2.61910i
$967$	−251.033	+	144.934i	−0.259600	+	0.149880i	−0.624152	−	0.781303i	$-0.714555\pi$
$967$	−251.033	+	144.934i	−0.259600	+	0.149880i	0.364552	+	0.931183i	$0.381222\pi$
$968$	387.929	+	671.912i	0.400753	+	0.694124i
$969$	650.037	−	595.567i	0.670833	−	0.614621i
$970$	574.628	+	331.762i	0.592400	+	0.342022i
$971$			386.301i			0.397838i	0.980016	+	0.198919i	$0.0637431\pi$
$971$			386.301i			0.397838i	−0.980016	+	0.198919i	$0.936257\pi$
$972$	−207.476	−	108.096i	−0.213453	−	0.111210i
$973$			933.575i			0.959481i
$974$	398.617	+	230.141i	0.409257	+	0.236285i
$975$	−959.454	+	1372.81i	−0.984055	+	1.40801i
$976$	278.115	+	481.709i	0.284953	+	0.493554i
$977$	−277.059	−	479.880i	−0.283581	−	0.491177i	0.688683	−	0.725063i	$-0.258189\pi$
$977$	−277.059	−	479.880i	−0.283581	−	0.491177i	−0.972264	+	0.233886i	$0.924856\pi$
$978$	−1229.88	+	272.569i	−1.25755	+	0.278700i
$979$	74.3034	−	128.697i	0.0758972	−	0.131458i
$980$	−358.137			−0.365446
$981$	36.4970	+	3.19813i	0.0372038	+	0.00326007i
$982$			801.858i			0.816556i
$983$	44.8835	−	77.7405i	0.0456597	−	0.0790849i	−0.842292	−	0.539021i	$-0.818794\pi$
$983$	44.8835	−	77.7405i	0.0456597	−	0.0790849i	0.887952	+	0.459936i	$0.152128\pi$
$984$	340.967	+	107.532i	0.346511	+	0.109281i
$985$	−1044.65	−	1809.39i	−1.06056	−	1.83695i
$986$	−297.368	−	515.057i	−0.301590	−	0.522370i
$987$	462.074	−	1465.16i	0.468161	−	1.48446i
$988$	−211.818	−	66.5652i	−0.214391	−	0.0673737i
$989$		−	2233.01i		−	2.25785i
$990$	340.645	+	238.592i	0.344086	+	0.241002i
$991$	1582.88			1.59726			0.798629	−	0.601824i	$-0.205559\pi$
$991$	1582.88			1.59726			0.798629	+	0.601824i	$0.205559\pi$
$992$	56.1724	+	32.4312i	0.0566255	+	0.0326927i
$993$	−661.211	+	146.539i	−0.665872	+	0.147572i
$994$	−662.101	+	382.264i	−0.666098	+	0.384572i
$995$	−423.964	−	734.327i	−0.426095	−	0.738018i
$996$	88.4382	−	81.0275i	0.0887934	−	0.0813529i
$997$	−650.699	+	1127.04i	−0.652657	+	1.13043i	0.329819	+	0.944044i	$0.393012\pi$
$997$	−650.699	+	1127.04i	−0.652657	+	1.13043i	−0.982476	+	0.186390i	$0.940321\pi$
$998$			586.778i			0.587954i
$999$	920.050	−	705.677i	0.920971	−	0.706384i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.3.n.a.38.20	yes	52
3.2	odd	2		351.3.n.a.116.7		52
9.4	even	3		351.3.n.a.233.20		52
9.5	odd	6	inner	117.3.n.a.77.7	yes	52
13.12	even	2	inner	117.3.n.a.38.7	✓	52
39.38	odd	2		351.3.n.a.116.20		52
117.77	odd	6	inner	117.3.n.a.77.20	yes	52
117.103	even	6		351.3.n.a.233.7		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.3.n.a.38.7	✓	52	13.12	even	2	inner
117.3.n.a.38.20	yes	52	1.1	even	1	trivial
117.3.n.a.77.7	yes	52	9.5	odd	6	inner
117.3.n.a.77.20	yes	52	117.77	odd	6	inner
351.3.n.a.116.7		52	3.2	odd	2
351.3.n.a.116.20		52	39.38	odd	2
351.3.n.a.233.7		52	117.103	even	6
351.3.n.a.233.20		52	9.4	even	3

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	117.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.11386 - 1.92926i) q^{2} +(-2.21197 + 2.02662i) q^{3} +(-0.481371 - 0.833760i) q^{4} +(-4.12144 - 7.13855i) q^{5} +(1.44605 + 6.52485i) q^{6} +(-8.40220 - 4.85102i) q^{7} +6.76616 q^{8} +(0.785636 - 8.96564i) q^{9} -18.3629 q^{10} +(1.25825 - 2.17935i) q^{11} +(2.75449 + 0.868697i) q^{12} +(-8.79176 - 9.57627i) q^{13} +(-18.7178 + 10.8067i) q^{14} +(23.5836 + 7.43767i) q^{15} +(9.46205 - 16.3887i) q^{16} +16.5653i q^{17} +(-16.4220 - 11.5022i) q^{18} +17.7403i q^{19} +(-3.96789 + 6.87258i) q^{20} +(28.4166 - 6.29776i) q^{21} +(-2.80303 - 4.85499i) q^{22} +(34.6120 - 19.9833i) q^{23} +(-14.9666 + 13.7124i) q^{24} +(-21.4726 + 37.1916i) q^{25} +(-28.2679 + 6.29498i) q^{26} +(16.4321 + 21.4239i) q^{27} +9.34056i q^{28} +(-13.9571 - 8.05814i) q^{29} +(40.6181 - 37.2145i) q^{30} +(-3.72176 + 2.14876i) q^{31} +(-7.54648 - 13.0709i) q^{32} +(1.63350 + 7.37066i) q^{33} +(31.9588 + 18.4514i) q^{34} +79.9727i q^{35} +(-7.85338 + 3.66077i) q^{36} -42.9450i q^{37} +(34.2256 + 19.7602i) q^{38} +(38.8546 + 3.36491i) q^{39} +(-27.8864 - 48.3006i) q^{40} +(-8.80660 - 15.2535i) q^{41} +(19.5021 - 61.8379i) q^{42} +(27.9361 - 48.3867i) q^{43} -2.42274 q^{44} +(-67.2396 + 31.3431i) q^{45} -89.0343i q^{46} +(26.3913 - 45.7111i) q^{47} +(12.2840 + 55.4274i) q^{48} +(22.5647 + 39.0832i) q^{49} +(47.8349 + 82.8525i) q^{50} +(-33.5715 - 36.6419i) q^{51} +(-3.75221 + 11.9400i) q^{52} -15.4783i q^{53} +(59.6355 - 7.83864i) q^{54} -20.7432 q^{55} +(-56.8507 - 32.8228i) q^{56} +(-35.9527 - 39.2410i) q^{57} +(-31.0925 + 17.9513i) q^{58} +(30.0606 + 52.0666i) q^{59} +(-5.15125 - 23.2434i) q^{60} +(-14.6963 + 25.4548i) q^{61} +9.57368i q^{62} +(-50.0935 + 71.5200i) q^{63} +42.0735 q^{64} +(-32.1260 + 102.228i) q^{65} +(16.0394 + 5.05843i) q^{66} +(-80.1222 + 46.2585i) q^{67} +(13.8115 - 7.97405i) q^{68} +(-36.0624 + 114.348i) q^{69} +(154.288 + 89.0785i) q^{70} +35.3729 q^{71} +(5.31574 - 60.6630i) q^{72} -59.3591i q^{73} +(-82.8521 - 47.8347i) q^{74} +(-27.8764 - 125.783i) q^{75} +(14.7911 - 8.53965i) q^{76} +(-21.1441 + 12.2076i) q^{77} +(49.7704 - 71.2127i) q^{78} +(-33.1363 + 57.3938i) q^{79} -155.989 q^{80} +(-79.7656 - 14.0875i) q^{81} -39.2373 q^{82} +(20.7644 - 35.9651i) q^{83} +(-18.9297 - 20.6611i) q^{84} +(118.252 - 68.2729i) q^{85} +(-62.2337 - 107.792i) q^{86} +(47.2035 - 10.4614i) q^{87} +(8.51352 - 14.7459i) q^{88} +59.0530 q^{89} +(-14.4265 + 164.635i) q^{90} +(27.4155 + 123.111i) q^{91} +(-33.3225 - 19.2387i) q^{92} +(3.87772 - 12.2956i) q^{93} +(-58.7926 - 101.832i) q^{94} +(126.640 - 73.1155i) q^{95} +(43.1823 + 13.6186i) q^{96} +(-31.2930 - 18.0670i) q^{97} +100.536 q^{98} +(-18.5508 - 12.9932i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 4 q^{3} - 50 q^{4} + 4 q^{9} + 8 q^{10} - 38 q^{12} - 6 q^{13} - 6 q^{14} - 90 q^{16} + 14 q^{22} + 138 q^{23} - 92 q^{25} - 76 q^{27} + 48 q^{29} + 186 q^{30} - 154 q^{36} + 324 q^{38} - 2 q^{39}+ \cdots + 504 q^{95}+O(q^{100}) \) 52 * q - 4 * q^3 - 50 * q^4 + 4 * q^9 + 8 * q^10 - 38 * q^12 - 6 * q^13 - 6 * q^14 - 90 * q^16 + 14 * q^22 + 138 * q^23 - 92 * q^25 - 76 * q^27 + 48 * q^29 + 186 * q^30 - 154 * q^36 + 324 * q^38 - 2 * q^39 - 68 * q^40 - 216 * q^42 + 62 * q^43 + 230 * q^48 + 70 * q^49 + 90 * q^51 - 4 * q^52 + 92 * q^55 - 276 * q^56 + 12 * q^61 + 12 * q^64 - 588 * q^65 + 762 * q^66 - 144 * q^68 - 414 * q^69 + 342 * q^74 - 620 * q^75 - 510 * q^77 - 162 * q^78 - 24 * q^79 + 532 * q^81 - 292 * q^82 - 330 * q^87 - 62 * q^88 + 258 * q^90 + 264 * q^91 - 396 * q^92 - 160 * q^94 + 504 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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