LMFDB - Embedded newform 117.3.n.a.38.7

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			38.7
Character	$\chi$	$=$	117.38
Dual form			117.3.n.a.77.7

$q$-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} +(-3.89742 - 12.4020i) 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} +(33.7551 + 19.5343i) 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} +(-8.46420 + 9.21949i) 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} +(72.4694 - 78.9361i) 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} +(-75.2854 + 43.3640i) 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	$0.354688\pi$
$2$	−1.11386	+	1.92926i	−0.556930	+	0.964632i	−0.997751	+	0.0670362i	$0.978646\pi$
$3$	−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	$0.141758\pi$
$5$	4.12144	+	7.13855i	0.824288	+	1.42771i	−0.0781734	+	0.996940i	$0.524909\pi$
$6$	−1.44605	−	6.52485i	−0.241009	−	1.08747i
$7$	8.40220	+	4.85102i	1.20031	+	0.693002i	0.960625	−	0.277847i	$-0.0896210\pi$
$7$	8.40220	+	4.85102i	1.20031	+	0.693002i	0.239690	+	0.970850i	$0.422954\pi$
$8$	−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	−0.917534	−	0.397657i	$-0.869823\pi$
$11$	−1.25825	+	2.17935i	−0.114386	+	0.198123i	0.803148	+	0.595780i	$0.203157\pi$
$12$	2.75449	+	0.868697i	0.229541	+	0.0723914i
$13$	−3.89742	−	12.4020i	−0.299801	−	0.954002i
$13$	−3.89742	−	12.4020i	−0.299801	−	0.954002i
$14$	−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	$-0.845389\pi$
$19$		−	17.7403i		−	0.933698i	0.884337	−	0.466849i	$-0.154611\pi$
$20$	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	−0.438769	−	0.898600i	$-0.644585\pi$
$31$	3.72176	−	2.14876i	0.120057	−	0.0693149i	0.558826	+	0.829285i	$0.311252\pi$
$32$	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	$0.197079\pi$
$37$			42.9450i			1.16067i	−0.814376	+	0.580337i	$0.802921\pi$
$38$	34.2256	+	19.7602i	0.900675	+	0.520005i
$39$	33.7551	+	19.5343i	0.865516	+	0.500880i
$40$	−27.8864	−	48.3006i	−0.697159	−	1.20751i
$41$	8.80660	+	15.2535i	0.214795	+	0.372036i	0.953209	−	0.302312i	$-0.0977583\pi$
$41$	8.80660	+	15.2535i	0.214795	+	0.372036i	−0.738414	+	0.674348i	$0.764425\pi$
$42$	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	$0.356449\pi$
$47$	−26.3913	+	45.7111i	−0.561518	+	0.972578i	−0.997364	+	0.0725565i	$0.976884\pi$
$48$	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
$52$	−8.46420	+	9.21949i	−0.162773	+	0.177298i
$53$		−	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	$-0.996496\pi$
$59$	−30.0606	−	52.0666i	−0.509502	−	0.882484i	0.490437	−	0.871477i	$-0.336837\pi$
$60$	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
$65$	72.4694	−	78.9361i	1.11491	−	1.21440i
$66$	16.0394	+	5.05843i	0.243022	+	0.0766428i
$67$	80.1222	−	46.2585i	1.19585	−	0.690426i	0.236225	−	0.971698i	$-0.424090\pi$
$67$	80.1222	−	46.2585i	1.19585	−	0.690426i	0.959628	+	0.281272i	$0.0907564\pi$
$68$	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	$-0.580136\pi$
$71$	−35.3729			−0.498209			−0.249105	+	0.968477i	$0.580136\pi$
$72$	−5.31574	+	60.6630i	−0.0738297	+	0.842542i
$73$			59.3591i			0.813138i	0.913620	+	0.406569i	$0.133275\pi$
$73$			59.3591i			0.813138i	−0.913620	+	0.406569i	$0.866725\pi$
$74$	−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
$78$	−75.2854	+	43.3640i	−0.965198	+	0.555949i
$79$	−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	−0.963574	−	0.267443i	$-0.913821\pi$
$83$	−20.7644	+	35.9651i	−0.250174	+	0.433314i	0.713400	+	0.700757i	$0.247154\pi$
$84$	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	$-0.607642\pi$
$89$	−59.0530			−0.663517			−0.331758	+	0.943364i	$0.607642\pi$
$90$	−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	0.652554	−	0.757742i	$-0.273697\pi$
$97$	31.2930	+	18.0670i	0.322608	+	0.186258i	−0.329946	+	0.944000i	$0.607031\pi$
$98$	−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	$0.604953\pi$
$104$	26.3706	+	83.9141i	0.253563	+	0.806866i
$105$	−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	$-0.994056\pi$
$109$		−	4.07076i		−	0.0373464i	0.999826	−	0.0186732i	$-0.00594421\pi$
$110$	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
$117$	−114.254	+	25.1994i	−0.976530	+	0.215379i
$118$	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
$130$	71.5677	+	227.736i	0.550521	+	1.75182i
$131$	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	−0.628989	−	0.777414i	$-0.716531\pi$
$137$	49.1509	−	85.1319i	0.358766	−	0.621401i	0.987755	+	0.156013i	$0.0498643\pi$
$138$	−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	0.700061	−	0.714083i	$-0.253156\pi$
$149$	−39.9891	−	69.2632i	−0.268383	−	0.464854i	−0.968445	+	0.249229i	$0.919823\pi$
$150$	273.720	+	86.3242i	1.82480	+	0.575495i
$151$	8.07717	+	4.66336i	0.0534912	+	0.0308832i	0.526507	−	0.850171i	$-0.323501\pi$
$151$	8.07717	+	4.66336i	0.0534912	+	0.0308832i	−0.473016	+	0.881054i	$0.656835\pi$
$152$			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
$156$	0.0381841	−	37.5469i	0.000244770	−	0.240686i
$157$	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	$-0.803757\pi$
$163$		−	188.492i		−	1.15639i	0.815898	−	0.578196i	$-0.196243\pi$
$164$	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	0.978073	−	0.208264i	$-0.0667814\pi$
$167$	51.5486	+	89.2848i	0.308674	+	0.534640i	−0.669398	+	0.742904i	$0.733448\pi$
$168$	192.271	−	42.6116i	1.14447	−	0.253641i
$169$	−138.620	+	96.6717i	−0.820238	+	0.572022i
$170$		−	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	$0.557409\pi$
$182$	206.976	+	190.020i	1.13723	+	1.04407i
$183$	−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	−0.706445	−	0.707768i	$-0.749702\pi$
$193$	−86.2173	+	49.7776i	−0.446722	+	0.257915i	0.259723	+	0.965683i	$0.416369\pi$
$194$	−69.7120	+	40.2483i	−0.359340	+	0.207465i
$195$	−0.326928	+	321.472i	−0.00167655	+	1.64858i
$196$	21.7240	−	37.6271i	0.110837	−	0.191975i
$197$	−253.468			−1.28664			−0.643320	−	0.765598i	$-0.722443\pi$
$197$	−253.468			−1.28664			−0.643320	+	0.765598i	$0.722443\pi$
$198$	−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
$221$	205.443	−	64.5618i	0.929606	−	0.292135i
$222$	280.209	−	62.1007i	1.26220	−	0.279733i
$223$	−4.74479	−	2.73941i	−0.0212771	−	0.0122843i	0.489324	−	0.872102i	$-0.337244\pi$
$223$	−4.74479	−	2.73941i	−0.0212771	−	0.0122843i	−0.510601	+	0.859818i	$0.670577\pi$
$224$			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	$-0.648222\pi$
$227$	124.695	−	215.978i	0.549316	−	0.951443i	0.998322	−	0.0579144i	$-0.0184451\pi$
$228$	15.4109	−	48.8654i	0.0675917	−	0.214322i
$229$	281.595	−	162.579i	1.22967	−	0.709951i	0.262710	−	0.964875i	$-0.415384\pi$
$229$	281.595	−	162.579i	1.22967	−	0.709951i	0.966961	+	0.254924i	$0.0820505\pi$
$230$	−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	$0.858781\pi$
$234$	78.6468	−	248.495i	0.336098	−	1.06194i
$235$	−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	0.645617	−	0.763661i	$-0.276600\pi$
$239$	−80.9113	−	140.143i	−0.338541	−	0.586370i	−0.984159	+	0.177291i	$0.943267\pi$
$240$	−345.044	+	316.130i	−1.43768	+	1.31721i
$241$	−340.380	−	196.518i	−1.41237	−	0.815429i	−0.416754	−	0.909019i	$-0.636832\pi$
$241$	−340.380	−	196.518i	−1.41237	−	0.815429i	−0.995611	+	0.0935898i	$0.970166\pi$
$242$	−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
$247$	−220.015	+	69.1412i	−0.890749	+	0.279924i
$248$	−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	$-0.770799\pi$
$271$		−	357.409i		−	1.31885i	0.751770	−	0.659426i	$-0.229201\pi$
$272$	271.484	+	156.742i	0.998104	+	0.576256i
$273$	188.856	+	327.878i	0.691781	+	1.20102i
$274$	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	$-0.659018\pi$
$281$	146.306	−	253.410i	0.520662	−	0.901813i	0.999711	−	0.0240253i	$-0.00764823\pi$
$282$	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
$286$	−49.2871	+	53.6851i	−0.172333	+	0.187710i
$287$			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	$0.0579581\pi$
$293$	190.025	+	329.134i	0.648551	+	1.12332i	−0.334918	+	0.942247i	$0.608709\pi$
$294$	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
$299$	−382.730	−	351.376i	−1.28003	−	1.17517i
$300$	−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	$0.354179\pi$
$307$			550.690i			1.79378i	−0.442254	+	0.896890i	$0.645821\pi$
$308$	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	$0.297506\pi$
$312$	−228.393	−	132.173i	−0.732028	−	0.423630i
$313$	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	−0.890108	−	0.455749i	$-0.849371\pi$
$317$	−15.9654	+	27.6529i	−0.0503640	+	0.0872330i	0.839744	+	0.542982i	$0.182705\pi$
$318$	−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	0.174702	−	0.984621i	$-0.444104\pi$
$331$	−195.507	−	112.876i	−0.590654	−	0.341014i	−0.765356	+	0.643607i	$0.777437\pi$
$332$	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	$0.975587\pi$
$338$	−32.1016	−	375.114i	−0.0949750	−	1.10980i
$339$	−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	$0.0399114\pi$
$349$	557.188	+	321.693i	1.59653	+	0.921755i	0.604377	+	0.796698i	$0.293422\pi$
$350$		−	928.191i		−	2.65198i
$351$	201.657	−	287.290i	0.574522	−	0.818489i
$352$	−37.9814			−0.107902
$353$	−169.330	+	293.288i	−0.479688	+	0.830844i	−0.999729	−	0.0232976i	$-0.992583\pi$
$353$	−169.330	+	293.288i	−0.479688	+	0.830844i	0.520041	+	0.854142i	$0.325917\pi$
$354$	−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	$-0.564982\pi$
$359$	−145.561			−0.405462			−0.202731	+	0.979235i	$0.564982\pi$
$360$	−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
$364$	−115.842	+	36.4041i	−0.318247	+	0.100011i
$365$	−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	$0.196827\pi$
$379$			439.406i			1.15938i	−0.814836	+	0.579692i	$0.803173\pi$
$380$	−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	0.718750	−	0.695269i	$-0.244715\pi$
$383$	−92.9716	−	161.031i	−0.242746	−	0.420448i	−0.961495	+	0.274821i	$0.911381\pi$
$384$	−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	$0.724976\pi$
$390$	−619.841	−	358.706i	−1.58933	−	0.919759i
$391$	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	$0.0518788\pi$
$397$			128.836i			0.324523i	−0.986748	+	0.162261i	$0.948121\pi$
$398$	−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	0.999678	−	0.0253783i	$-0.00807902\pi$
$401$	191.622	+	331.899i	0.477861	+	0.827679i	−0.521817	+	0.853057i	$0.674746\pi$
$402$	−417.691	−	455.892i	−1.03903	−	1.13406i
$403$	−41.1543	−	37.7828i	−0.102120	−	0.0937538i
$404$			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	−0.606332	−	0.795211i	$-0.707360\pi$
$409$	−90.3177	+	52.1449i	−0.220826	+	0.127494i	0.385507	+	0.922705i	$0.374027\pi$
$410$	−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
$416$	132.694	−	144.534i	0.318975	−	0.347438i
$417$	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	0.214915	−	0.976633i	$-0.431052\pi$
$421$	−220.358	−	127.224i	−0.523416	−	0.302194i	−0.738331	+	0.674439i	$0.764386\pi$
$422$	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
$429$	−85.0446	+	48.9853i	−0.198239	+	0.114185i
$430$	−512.986	+	888.517i	−1.19299	+	2.06632i
$431$	−51.7831			−0.120146			−0.0600732	−	0.998194i	$-0.519133\pi$
$431$	−51.7831			−0.120146			−0.0600732	+	0.998194i	$0.519133\pi$
$432$	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	$-0.507334\pi$
$449$	−20.6872			−0.0460740			−0.0230370	+	0.999735i	$0.507334\pi$
$450$	−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
$455$	991.823	−	311.687i	2.17983	−	0.685027i
$456$	−243.262	−	265.511i	−0.533470	−	0.582260i
$457$	−606.146	−	349.959i	−1.32636	−	0.765774i	−0.341625	−	0.939836i	$-0.610977\pi$
$457$	−606.146	−	349.959i	−1.32636	−	0.765774i	−0.984735	+	0.174062i	$0.944311\pi$
$458$			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	−0.931091	−	0.364787i	$-0.881142\pi$
$461$	−68.9796	+	119.476i	−0.149630	+	0.259167i	0.781461	+	0.623955i	$0.214475\pi$
$462$	110.228	+	120.309i	0.238589	+	0.260410i
$463$	−612.880	+	353.846i	−1.32371	+	0.764247i	−0.984319	−	0.176397i	$-0.943556\pi$
$463$	−612.880	+	353.846i	−1.32371	+	0.764247i	−0.339395	+	0.940644i	$0.610222\pi$
$464$	−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	$0.792739\pi$
$468$	76.0089	+	83.1302i	0.162412	+	0.177629i
$469$	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	$-0.564353\pi$
$479$	358.287	−	620.571i	0.747989	−	1.29556i	0.948785	−	0.315922i	$-0.102314\pi$
$480$	−80.7564	−	364.387i	−0.168243	−	0.759140i
$481$	532.604	−	167.374i	1.10729	−	0.347972i
$482$	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	$-0.931960\pi$
$487$		−	206.616i		−	0.424263i	0.977241	−	0.212131i	$-0.0680405\pi$
$488$	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	−0.253705	−	0.967282i	$-0.581649\pi$
$499$	228.110	−	131.699i	0.457134	−	0.263926i	0.710838	+	0.703355i	$0.248316\pi$
$500$	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
$507$	110.707	−	494.765i	0.218358	−	0.975869i
$508$	3.20168	+	5.54546i	0.00630251	+	0.0109163i
$509$	445.798	+	772.144i	0.875830	+	1.51698i	0.855876	+	0.517182i	$0.173019\pi$
$509$	445.798	+	772.144i	0.875830	+	1.51698i	0.0199545	+	0.999801i	$0.493648\pi$
$510$	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
$520$	−490.340	+	534.095i	−0.942962	+	1.02711i
$521$		−	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
$533$	154.851	−	168.669i	0.290527	−	0.316452i
$534$	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	$-0.905919\pi$
$541$		−	315.164i		−	0.582558i	0.956638	−	0.291279i	$-0.0940807\pi$
$542$	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
$546$	−842.923	−	0.857228i	−1.54381	−	0.00157001i
$547$	−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	$-0.642166\pi$
$557$	−481.165			−0.863850			−0.431925	+	0.901909i	$0.642166\pi$
$558$	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	$-0.544079\pi$
$572$	−9.44244	−	30.0469i	−0.0165078	−	0.0525295i
$573$	−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	$0.123908\pi$
$577$			437.958i			0.759026i	−0.925186	+	0.379513i	$0.876092\pi$
$578$	−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
$585$	−650.779	−	711.750i	−1.11244	−	1.21667i
$586$	−846.648			−1.44479
$587$	59.4816	−	103.025i	0.101331	−	0.175511i	−0.810902	−	0.585182i	$-0.801023\pi$
$587$	59.4816	−	103.025i	0.101331	−	0.175511i	0.912233	+	0.409671i	$0.134356\pi$
$588$	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	$-0.121936\pi$
$593$	1100.04			1.85504			0.927520	+	0.373773i	$0.121936\pi$
$594$	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
$598$	1104.20	−	347.004i	1.84650	−	0.580274i
$599$	−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	$0.0497341\pi$
$613$			190.777i			0.311219i	−0.987819	+	0.155609i	$0.950266\pi$
$614$	−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	$-0.930186\pi$
$617$	−417.367	−	722.901i	−0.676446	−	1.17164i	0.299598	−	0.954066i	$-0.403147\pi$
$618$	667.413	−	611.487i	1.07996	−	0.989461i
$619$	−344.598	−	198.954i	−0.556702	−	0.321412i	0.195119	−	0.980780i	$-0.437491\pi$
$619$	−344.598	−	198.954i	−0.556702	−	0.321412i	−0.751821	+	0.659368i	$0.770824\pi$
$620$		−	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
$624$	639.536	−	368.370i	1.02490	−	0.590336i
$625$	−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	$-0.773584\pi$
$631$		−	823.864i		−	1.30565i	0.757509	−	0.652824i	$-0.226416\pi$
$632$	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
$637$	396.767	−	432.171i	0.622867	−	0.678448i
$638$			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	−0.534634	−	0.845084i	$-0.679551\pi$
$643$	−45.0664	+	26.0191i	−0.0700877	+	0.0404652i	0.464547	+	0.885549i	$0.346217\pi$
$644$	−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
$650$	−841.106	+	916.160i	−1.29401	+	1.40948i
$651$	−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	−0.943981	−	0.329999i	$-0.892952\pi$
$661$	−747.052	+	431.311i	−1.13018	+	0.652513i	−0.186204	+	0.982511i	$0.559618\pi$
$662$	435.534	−	251.456i	0.657906	−	0.379842i
$663$	−323.592	+	559.163i	−0.488072	+	0.843384i
$664$	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	$-0.696677\pi$
$683$	−791.335			−1.15862			−0.579308	+	0.815109i	$0.696677\pi$
$684$	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
$689$	−191.962	+	60.3253i	−0.278609	+	0.0875548i
$690$	662.208	−	2099.75i	0.959721	−	3.04312i
$691$	−1127.60	−	651.022i	−1.63184	−	0.942145i	−0.983524	−	0.180776i	$-0.942139\pi$
$691$	−1127.60	−	651.022i	−1.63184	−	0.942145i	−0.648319	−	0.761369i	$-0.724528\pi$
$692$			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	$-0.00980586\pi$
$702$	329.640	+	709.051i	0.469572	+	1.01004i
$703$	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	0.619724	−	0.784820i	$-0.287244\pi$
$709$	177.188	+	102.300i	0.249913	+	0.144287i	−0.369811	+	0.929107i	$0.620578\pi$
$710$	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
$715$	80.8450	+	257.258i	0.113070	+	0.359801i
$716$	−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	−0.969232	−	0.246147i	$-0.920835\pi$
$733$	−909.418	+	525.053i	−1.24068	+	0.716306i	−0.271447	+	0.962454i	$0.587502\pi$
$734$	−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	$-0.868350\pi$
$739$		−	594.008i		−	0.803799i	0.915684	−	0.401900i	$-0.131650\pi$
$740$	295.143	+	170.401i	0.398842	+	0.230271i
$741$	346.544	−	598.825i	0.467671	−	0.808131i
$742$	167.269	+	289.719i	0.225430	+	0.390456i
$743$	108.652	+	188.191i	0.146234	+	0.253285i	0.929833	−	0.367982i	$-0.119951\pi$
$743$	108.652	+	188.191i	0.146234	+	0.253285i	−0.783598	+	0.621268i	$0.786618\pi$
$744$	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
$754$	−343.813	−	315.647i	−0.455985	−	0.418630i
$755$			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	$-0.871457\pi$
$761$	−608.861	−	1054.58i	−0.800080	−	1.38578i	0.119483	−	0.992836i	$-0.461876\pi$
$762$	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
$767$	−528.572	+	575.738i	−0.689142	+	0.750636i
$768$	500.684	+	157.903i	0.651932	+	0.205603i
$769$	234.211	−	135.222i	0.304565	−	0.175841i	−0.339927	−	0.940452i	$-0.610402\pi$
$769$	234.211	−	135.222i	0.304565	−	0.175841i	0.644492	+	0.764611i	$0.277069\pi$
$770$	388.267	−	224.166i	0.504242	−	0.291124i
$771$	−416.657	+	1321.15i	−0.540411	+	1.71355i

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} +(-3.89742 - 12.4020i) 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} +(33.7551 + 19.5343i) 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} +(-8.46420 + 9.21949i) 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} +(72.4694 - 78.9361i) 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} +(-75.2854 + 43.3640i) 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

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