LMFDB - Embedded newform 378.3.x.a.103.32

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [378,3,Mod(103,378)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("378.103"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(378, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([14, 15])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	378.x (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$10.2997539928$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$48$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			103.32
Character	$\chi$	$=$	378.103
Dual form			378.3.x.a.367.32

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.245576 + 1.39273i) q^{2} +(-1.55222 + 2.56722i) q^{3} +(-1.87939 + 0.684040i) q^{4} +(1.32662 + 0.233919i) q^{5} +(-3.95663 - 1.53137i) q^{6} +(2.77477 - 6.42656i) q^{7} +(-1.41421 - 2.44949i) q^{8} +(-4.18124 - 7.96977i) q^{9} +1.90506i q^{10} +(-1.44720 - 8.20750i) q^{11} +(1.16113 - 5.88658i) q^{12} +(-4.73332 + 5.64095i) q^{13} +(9.63187 + 2.28630i) q^{14} +(-2.65972 + 3.04263i) q^{15} +(3.06418 - 2.57115i) q^{16} -22.9520i q^{17} +(10.0729 - 7.78052i) q^{18} -29.3193i q^{19} +(-2.65324 + 0.467837i) q^{20} +(12.1913 + 17.0989i) q^{21} +(11.0754 - 4.03112i) q^{22} +(-6.08869 - 5.10902i) q^{23} +(8.48355 + 0.171542i) q^{24} +(-21.7871 - 7.92986i) q^{25} +(-9.01870 - 5.20695i) q^{26} +(26.9504 + 1.63664i) q^{27} +(-0.818842 + 13.9760i) q^{28} +(3.35575 - 2.81580i) q^{29} +(-4.89072 - 2.95707i) q^{30} +(16.9266 + 46.5055i) q^{31} +(4.33340 + 3.63616i) q^{32} +(23.3168 + 9.02453i) q^{33} +(31.9658 - 5.63644i) q^{34} +(5.18435 - 7.87652i) q^{35} +(13.3098 + 12.1181i) q^{36} +(24.7875 + 42.9333i) q^{37} +(40.8339 - 7.20011i) q^{38} +(-7.13443 - 20.9075i) q^{39} +(-1.30314 - 3.58035i) q^{40} +(27.7456 - 33.0659i) q^{41} +(-20.8202 + 21.1783i) q^{42} +(2.78284 + 1.01287i) q^{43} +(8.33411 + 14.4351i) q^{44} +(-3.68264 - 11.5509i) q^{45} +(5.62024 - 9.73454i) q^{46} +(-22.4221 + 61.6041i) q^{47} +(1.84444 + 11.8574i) q^{48} +(-33.6013 - 35.6645i) q^{49} +(5.69376 - 32.2909i) q^{50} +(58.9227 + 35.6264i) q^{51} +(5.03709 - 13.8393i) q^{52} +(-48.0478 - 83.2212i) q^{53} +(4.33896 + 37.9364i) q^{54} -11.2267i q^{55} +(-19.6659 + 2.29175i) q^{56} +(75.2692 + 45.5100i) q^{57} +(4.74574 + 3.98215i) q^{58} +(31.6904 - 37.7671i) q^{59} +(2.91736 - 7.53763i) q^{60} +(11.9718 - 32.8922i) q^{61} +(-60.6128 + 34.9948i) q^{62} +(-62.8202 + 4.75671i) q^{63} +(-4.00000 + 6.92820i) q^{64} +(-7.59883 + 6.37618i) q^{65} +(-6.84267 + 34.6902i) q^{66} +(13.1192 - 74.4025i) q^{67} +(15.7001 + 43.1356i) q^{68} +(22.5669 - 7.70070i) q^{69} +(12.2430 + 5.28612i) q^{70} +(-25.4862 + 44.1433i) q^{71} +(-13.6087 + 21.5129i) q^{72} +(-40.5988 - 23.4397i) q^{73} +(-53.7072 + 45.0657i) q^{74} +(54.1760 - 43.6235i) q^{75} +(20.0556 + 55.1023i) q^{76} +(-56.7616 - 13.4734i) q^{77} +(27.3664 - 15.0707i) q^{78} +(16.8035 + 95.2976i) q^{79} +(4.66643 - 2.69417i) q^{80} +(-46.0344 + 66.6471i) q^{81} +(52.8654 + 30.5219i) q^{82} +(-85.8298 - 102.288i) q^{83} +(-34.6085 - 23.7960i) q^{84} +(5.36889 - 30.4485i) q^{85} +(-0.727255 + 4.12447i) q^{86} +(2.01995 + 12.9857i) q^{87} +(-18.0575 + 15.1521i) q^{88} -132.887i q^{89} +(15.1829 - 7.96553i) q^{90} +(23.1180 + 46.0713i) q^{91} +(14.9378 + 5.43690i) q^{92} +(-145.664 - 28.7323i) q^{93} +(-91.3041 - 16.0994i) q^{94} +(6.85834 - 38.8956i) q^{95} +(-16.0612 + 5.48070i) q^{96} +(23.1162 - 63.5113i) q^{97} +(41.4193 - 55.5558i) q^{98} +(-59.3607 + 45.8514i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 36 q^{6} - 12 q^{9} + 36 q^{11} + 36 q^{14} - 24 q^{15} + 186 q^{21} + 126 q^{23} + 36 q^{29} - 72 q^{30} + 162 q^{35} - 48 q^{36} + 246 q^{39} - 48 q^{42} + 324 q^{47} - 72 q^{49} + 288 q^{50}+ \cdots - 216 q^{99}+O(q^{100}) $ 288 * q - 36 * q^6 - 12 * q^9 + 36 * q^11 + 36 * q^14 - 24 * q^15 + 186 * q^21 + 126 * q^23 + 36 * q^29 - 72 * q^30 + 162 * q^35 - 48 * q^36 + 246 * q^39 - 48 * q^42 + 324 * q^47 - 72 * q^49 + 288 * q^50 - 198 * q^51 + 270 * q^53 + 432 * q^54 - 144 * q^56 + 354 * q^57 + 270 * q^59 + 72 * q^60 + 138 * q^63 - 1152 * q^64 - 360 * q^65 + 72 * q^69 + 180 * q^70 + 216 * q^71 - 96 * q^72 + 216 * q^74 - 1170 * q^75 + 234 * q^77 - 96 * q^78 - 36 * q^79 + 324 * q^81 - 24 * q^84 - 360 * q^85 + 144 * q^86 - 990 * q^87 - 198 * q^91 - 180 * q^92 + 168 * q^93 - 72 * q^95 + 216 * q^98 - 216 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.245576	+	1.39273i	0.122788	+	0.696364i
$2$	0.245576	+	1.39273i	0.122788	+	0.696364i
$3$	−1.55222	+	2.56722i	−0.517406	+	0.855740i
$3$	−1.55222	+	2.56722i	−0.517406	+	0.855740i
$4$	−1.87939	+	0.684040i	−0.469846	+	0.171010i
$5$	1.32662	+	0.233919i	0.265324	+	0.0467837i	0.304727	−	0.952440i	$-0.401435\pi$
$5$	1.32662	+	0.233919i	0.265324	+	0.0467837i	−0.0394036	+	0.999223i	$0.512546\pi$
$6$	−3.95663	−	1.53137i	−0.659438	−	0.255228i
$7$	2.77477	−	6.42656i	0.396396	−	0.918080i
$7$	2.77477	−	6.42656i	0.396396	−	0.918080i
$8$	−1.41421	−	2.44949i	−0.176777	−	0.306186i
$9$	−4.18124	−	7.96977i	−0.464583	−	0.885530i
$10$			1.90506i			0.190506i
$11$	−1.44720	−	8.20750i	−0.131564	−	0.746136i	−0.977191	−	0.212362i	$-0.931884\pi$
$11$	−1.44720	−	8.20750i	−0.131564	−	0.746136i	0.845627	−	0.533774i	$-0.179227\pi$
$12$	1.16113	−	5.88658i	0.0967610	−	0.490548i
$13$	−4.73332	+	5.64095i	−0.364102	+	0.433919i	−0.916729	−	0.399509i	$-0.869181\pi$
$13$	−4.73332	+	5.64095i	−0.364102	+	0.433919i	0.552628	+	0.833428i	$0.313625\pi$
$14$	9.63187	+	2.28630i	0.687990	+	0.163307i
$15$	−2.65972	+	3.04263i	−0.177315	+	0.202842i
$16$	3.06418	−	2.57115i	0.191511	−	0.160697i
$17$		−	22.9520i		−	1.35012i	−0.737765	−	0.675058i	$-0.764119\pi$
$17$		−	22.9520i		−	1.35012i	0.737765	−	0.675058i	$-0.235881\pi$
$18$	10.0729	−	7.78052i	0.559606	−	0.432251i
$19$		−	29.3193i		−	1.54312i	−0.636155	−	0.771562i	$-0.719476\pi$
$19$		−	29.3193i		−	1.54312i	0.636155	−	0.771562i	$-0.280524\pi$
$20$	−2.65324	+	0.467837i	−0.132662	+	0.0233919i
$21$	12.1913	+	17.0989i	0.580540	+	0.814232i
$22$	11.0754	−	4.03112i	0.503428	−	0.183233i
$23$	−6.08869	−	5.10902i	−0.264726	−	0.222131i	0.500757	−	0.865588i	$-0.333055\pi$
$23$	−6.08869	−	5.10902i	−0.264726	−	0.222131i	−0.765482	+	0.643457i	$0.777500\pi$
$24$	8.48355	+	0.171542i	0.353481	+	0.00714757i
$25$	−21.7871	−	7.92986i	−0.871485	−	0.317195i
$26$	−9.01870	−	5.20695i	−0.346873	−	0.200267i
$27$	26.9504	+	1.63664i	0.998161	+	0.0606161i
$28$	−0.818842	+	13.9760i	−0.0292443	+	0.499144i
$29$	3.35575	−	2.81580i	0.115715	−	0.0970967i	−0.583094	−	0.812405i	$-0.698158\pi$
$29$	3.35575	−	2.81580i	0.115715	−	0.0970967i	0.698809	+	0.715308i	$0.253714\pi$
$30$	−4.89072	−	2.95707i	−0.163024	−	0.0985691i
$31$	16.9266	+	46.5055i	0.546020	+	1.50018i	0.839039	+	0.544071i	$0.183118\pi$
$31$	16.9266	+	46.5055i	0.546020	+	1.50018i	−0.293019	+	0.956107i	$0.594660\pi$
$32$	4.33340	+	3.63616i	0.135419	+	0.113630i
$33$	23.3168	+	9.02453i	0.706571	+	0.273471i
$34$	31.9658	−	5.63644i	0.940172	−	0.165778i
$35$	5.18435	−	7.87652i	0.148124	−	0.225043i
$36$	13.3098	+	12.1181i	0.369717	+	0.336615i
$37$	24.7875	+	42.9333i	0.669934	+	1.16036i	0.977922	+	0.208969i	$0.0670108\pi$
$37$	24.7875	+	42.9333i	0.669934	+	1.16036i	−0.307989	+	0.951390i	$0.599656\pi$
$38$	40.8339	−	7.20011i	1.07458	−	0.189477i
$39$	−7.13443	−	20.9075i	−0.182934	−	0.536089i
$40$	−1.30314	−	3.58035i	−0.0325785	−	0.0895087i
$41$	27.7456	−	33.0659i	0.676721	−	0.806485i	−0.312961	−	0.949766i	$-0.601321\pi$
$41$	27.7456	−	33.0659i	0.676721	−	0.806485i	0.989682	+	0.143281i	$0.0457654\pi$
$42$	−20.8202	+	21.1783i	−0.495719	+	0.504245i
$43$	2.78284	+	1.01287i	0.0647171	+	0.0235551i	0.374176	−	0.927358i	$-0.377926\pi$
$43$	2.78284	+	1.01287i	0.0647171	+	0.0235551i	−0.309459	+	0.950913i	$0.600148\pi$
$44$	8.33411	+	14.4351i	0.189412	+	0.328071i
$45$	−3.68264	−	11.5509i	−0.0818364	−	0.256687i
$46$	5.62024	−	9.73454i	0.122179	−	0.211620i
$47$	−22.4221	+	61.6041i	−0.477065	+	1.31073i	0.434908	+	0.900475i	$0.356781\pi$
$47$	−22.4221	+	61.6041i	−0.477065	+	1.31073i	−0.911973	+	0.410251i	$0.865441\pi$
$48$	1.84444	+	11.8574i	0.0384259	+	0.247029i
$49$	−33.6013	−	35.6645i	−0.685740	−	0.727846i
$50$	5.69376	−	32.2909i	0.113875	−	0.645818i
$51$	58.9227	+	35.6264i	1.15535	+	0.698557i
$52$	5.03709	−	13.8393i	0.0968672	−	0.266140i
$53$	−48.0478	−	83.2212i	−0.906562	−	1.57021i	−0.818806	−	0.574070i	$-0.805364\pi$
$53$	−48.0478	−	83.2212i	−0.906562	−	1.57021i	−0.0877557	−	0.996142i	$-0.527969\pi$
$54$	4.33896	+	37.9364i	0.0803511	+	0.702527i
$55$		−	11.2267i		−	0.204123i
$56$	−19.6659	+	2.29175i	−0.351177	+	0.0409241i
$57$	75.2692	+	45.5100i	1.32051	+	0.798421i
$58$	4.74574	+	3.98215i	0.0818231	+	0.0686577i
$59$	31.6904	−	37.7671i	0.537125	−	0.640120i	−0.427416	−	0.904055i	$-0.640576\pi$
$59$	31.6904	−	37.7671i	0.537125	−	0.640120i	0.964541	+	0.263935i	$0.0850204\pi$
$60$	2.91736	−	7.53763i	0.0486226	−	0.125627i
$61$	11.9718	−	32.8922i	0.196259	−	0.539216i	−0.802056	−	0.597249i	$-0.796260\pi$
$61$	11.9718	−	32.8922i	0.196259	−	0.539216i	0.998315	+	0.0580325i	$0.0184827\pi$
$62$	−60.6128	+	34.9948i	−0.977625	+	0.564432i
$63$	−62.8202	+	4.75671i	−0.997146	+	0.0755034i
$64$	−4.00000	+	6.92820i	−0.0625000	+	0.108253i
$65$	−7.59883	+	6.37618i	−0.116905	+	0.0980950i
$66$	−6.84267	+	34.6902i	−0.103677	+	0.525609i
$67$	13.1192	−	74.4025i	0.195808	−	1.11048i	−0.715454	−	0.698659i	$-0.753780\pi$
$67$	13.1192	−	74.4025i	0.195808	−	1.11048i	0.911263	−	0.411825i	$-0.135109\pi$
$68$	15.7001	+	43.1356i	0.230883	+	0.634347i
$69$	22.5669	−	7.70070i	0.327057	−	0.111604i
$70$	12.2430	+	5.28612i	0.174900	+	0.0755159i
$71$	−25.4862	+	44.1433i	−0.358960	+	0.621737i	−0.987787	−	0.155808i	$-0.950202\pi$
$71$	−25.4862	+	44.1433i	−0.358960	+	0.621737i	0.628827	+	0.777545i	$0.283535\pi$
$72$	−13.6087	+	21.5129i	−0.189010	+	0.298790i
$73$	−40.5988	−	23.4397i	−0.556148	−	0.321092i	0.195450	−	0.980714i	$-0.437383\pi$
$73$	−40.5988	−	23.4397i	−0.556148	−	0.321092i	−0.751598	+	0.659621i	$0.770717\pi$
$74$	−53.7072	+	45.0657i	−0.725773	+	0.608996i
$75$	54.1760	−	43.6235i	0.722347	−	0.581646i
$76$	20.0556	+	55.1023i	0.263890	+	0.725031i
$77$	−56.7616	−	13.4734i	−0.737164	−	0.174979i
$78$	27.3664	−	15.0707i	0.350851	−	0.193214i
$79$	16.8035	+	95.2976i	0.212703	+	1.20630i	0.884848	+	0.465880i	$0.154262\pi$
$79$	16.8035	+	95.2976i	0.212703	+	1.20630i	−0.672145	+	0.740420i	$0.734627\pi$
$80$	4.66643	−	2.69417i	0.0583304	−	0.0336771i
$81$	−46.0344	+	66.6471i	−0.568326	+	0.822804i
$82$	52.8654	+	30.5219i	0.644700	+	0.372218i
$83$	−85.8298	−	102.288i	−1.03409	−	1.23238i	−0.972163	−	0.234304i	$-0.924719\pi$
$83$	−85.8298	−	102.288i	−1.03409	−	1.23238i	−0.0619300	−	0.998080i	$-0.519726\pi$
$84$	−34.6085	−	23.7960i	−0.412006	−	0.283286i
$85$	5.36889	−	30.4485i	0.0631634	−	0.358217i
$86$	−0.727255	+	4.12447i	−0.00845646	+	0.0479590i
$87$	2.01995	+	12.9857i	0.0232178	+	0.149261i
$88$	−18.0575	+	15.1521i	−0.205199	+	0.172183i
$89$		−	132.887i		−	1.49311i	−0.665324	−	0.746554i	$-0.731707\pi$
$89$		−	132.887i		−	1.49311i	0.665324	−	0.746554i	$-0.268293\pi$
$90$	15.1829	−	7.96553i	0.168699	−	0.0885059i
$91$	23.1180	+	46.0713i	0.254044	+	0.506278i
$92$	14.9378	+	5.43690i	0.162367	+	0.0590968i
$93$	−145.664	−	28.7323i	−1.56628	−	0.308949i
$94$	−91.3041	−	16.0994i	−0.971320	−	0.171270i
$95$	6.85834	−	38.8956i	0.0721930	−	0.409427i
$96$	−16.0612	+	5.48070i	−0.167304	+	0.0570906i
$97$	23.1162	−	63.5113i	0.238311	−	0.654755i	−0.761665	−	0.647970i	$-0.775618\pi$
$97$	23.1162	−	63.5113i	0.238311	−	0.654755i	0.999977	−	0.00678500i	$-0.00215975\pi$
$98$	41.4193	−	55.5558i	0.422646	−	0.566896i
$99$	−59.3607	+	45.8514i	−0.599603	+	0.463146i
$100$	46.3707			0.463707
$101$	−87.4570	−	104.227i	−0.865911	−	1.03195i	−0.999164	−	0.0408707i	$-0.986987\pi$
$101$	−87.4570	−	104.227i	−0.865911	−	1.03195i	0.133253	−	0.991082i	$-0.457458\pi$
$102$	−35.1479	+	90.8124i	−0.344588	+	0.890317i
$103$	120.511	+	21.2494i	1.17001	+	0.206305i	0.724697	−	0.689068i	$-0.241980\pi$
$103$	120.511	+	21.2494i	1.17001	+	0.206305i	0.445317	+	0.895373i	$0.353091\pi$
$104$	20.5114	+	3.61671i	0.197225	+	0.0347761i
$105$	12.1735	+	25.5354i	0.115938	+	0.243195i
$106$	104.105	−	87.3546i	0.982124	−	0.824100i
$107$	−71.7646	+	124.300i	−0.670697	+	1.16168i	0.307010	+	0.951706i	$0.400672\pi$
$107$	−71.7646	+	124.300i	−0.670697	+	1.16168i	−0.977707	+	0.209975i	$0.932662\pi$
$108$	−51.7696	+	15.3593i	−0.479348	+	0.142215i
$109$	48.0551	+	83.2338i	0.440872	+	0.763613i	0.997754	−	0.0669785i	$-0.0213359\pi$
$109$	48.0551	+	83.2338i	0.440872	+	0.763613i	−0.556882	+	0.830591i	$0.688003\pi$
$110$	15.6358	−	2.75701i	0.142144	−	0.0250638i
$111$	−148.695	−	3.00669i	−1.33959	−	0.0270873i
$112$	−8.02125	−	26.8265i	−0.0716183	−	0.239522i
$113$	−28.6798	+	10.4386i	−0.253803	+	0.0923768i	−0.465789	−	0.884896i	$-0.654229\pi$
$113$	−28.6798	+	10.4386i	−0.253803	+	0.0923768i	0.211985	+	0.977273i	$0.432007\pi$
$114$	−44.8988	+	116.006i	−0.393849	+	1.01759i
$115$	−6.88227	−	8.20197i	−0.0598458	−	0.0713215i
$116$	−4.38061	+	7.58745i	−0.0377639	+	0.0654090i
$117$	64.7482	+	14.1373i	0.553404	+	0.120831i
$118$	60.3817	+	34.8614i	0.511709	+	0.295436i
$119$	−147.502	−	63.6865i	−1.23951	−	0.535180i
$120$	11.2143	+	2.21203i	0.0934525	+	0.0184336i
$121$	48.4342	−	17.6286i	0.400282	−	0.145691i
$122$	48.7499	+	8.59592i	0.399589	+	0.0704583i
$123$	41.8203	+	122.554i	0.340002	+	0.996377i
$124$	−63.6233	−	75.8233i	−0.513091	−	0.611478i
$125$	−56.2134	−	32.4548i	−0.449708	−	0.259639i
$126$	−22.0519	−	86.3233i	−0.175015	−	0.685106i
$127$	84.6492	+	146.617i	0.666529	+	1.15446i	0.978868	+	0.204491i	$0.0655541\pi$
$127$	84.6492	+	146.617i	0.666529	+	1.15446i	−0.312339	+	0.949971i	$0.601113\pi$
$128$	−10.6314	−	3.86952i	−0.0830579	−	0.0302306i
$129$	−6.91982	+	5.57196i	−0.0536420	+	0.0431935i
$130$	−10.7464	−	9.01727i	−0.0826644	−	0.0693636i
$131$	41.6908	−	49.6852i	0.318250	−	0.379276i	−0.583075	−	0.812418i	$-0.698151\pi$
$131$	41.6908	−	49.6852i	0.318250	−	0.379276i	0.901326	+	0.433142i	$0.142595\pi$
$132$	−49.9945	−	1.01091i	−0.378746	−	0.00765844i
$133$	−188.422	−	81.3545i	−1.41671	−	0.611688i
$134$	106.844			0.797345
$135$	35.3700	+	8.47538i	0.262000	+	0.0627806i
$136$	−56.2206	+	32.4590i	−0.413387	+	0.238669i
$137$	−138.294	−	50.3348i	−1.00944	−	0.367407i	−0.216224	−	0.976344i	$-0.569374\pi$
$137$	−138.294	−	50.3348i	−1.00944	−	0.367407i	−0.793219	+	0.608936i	$0.791596\pi$
$138$	16.2669	+	29.5385i	0.117876	+	0.214047i
$139$	72.3260	+	12.7530i	0.520331	+	0.0917484i	0.427645	−	0.903947i	$-0.359343\pi$
$139$	72.3260	+	12.7530i	0.520331	+	0.0917484i	0.0926864	+	0.995695i	$0.470455\pi$
$140$	−4.35554	+	18.3493i	−0.0311110	+	0.131067i
$141$	−123.347	−	153.185i	−0.874804	−	1.08642i
$142$	−67.7384	−	24.6548i	−0.477031	−	0.173625i
$143$	53.1482	+	30.6851i	0.371666	+	0.214581i
$144$	−33.3035	−	13.6702i	−0.231275	−	0.0949318i
$145$	5.11046	−	2.95053i	0.0352446	−	0.0203485i
$146$	22.6751	−	62.2994i	0.155309	−	0.426708i
$147$	143.715	−	30.9029i	0.977653	−	0.210224i
$148$	−75.9534	−	63.7325i	−0.513199	−	0.430625i
$149$	126.932	−	46.1994i	0.851891	−	0.310063i	0.121080	−	0.992643i	$-0.461364\pi$
$149$	126.932	−	46.1994i	0.851891	−	0.310063i	0.730811	+	0.682580i	$0.239142\pi$
$150$	74.0600	+	64.7397i	0.493733	+	0.431598i
$151$	−24.6270	−	139.667i	−0.163093	−	0.924944i	−0.951009	−	0.309162i	$-0.899951\pi$
$151$	−24.6270	−	139.667i	−0.163093	−	0.924944i	0.787917	−	0.615782i	$-0.211160\pi$
$152$	−71.8174	+	41.4638i	−0.472483	+	0.272788i
$153$	−182.922	+	95.9677i	−1.19557	+	0.627240i
$154$	4.82552	−	82.3623i	0.0313346	−	0.534820i
$155$	11.5767	+	65.6545i	0.0746881	+	0.423577i
$156$	27.7099	+	34.4129i	0.177627	+	0.220596i
$157$	81.4205	−	97.0332i	0.518602	−	0.618046i	−0.441648	−	0.897189i	$-0.645606\pi$
$157$	81.4205	−	97.0332i	0.518602	−	0.618046i	0.960250	+	0.279143i	$0.0900503\pi$
$158$	−128.597	+	46.8055i	−0.813906	+	0.296238i
$159$	288.228	+	5.82812i	1.81275	+	0.0366548i
$160$	4.89820	+	5.83745i	0.0306138	+	0.0364841i
$161$	−49.7281	+	24.9529i	−0.308870	+	0.154987i
$162$	−104.126	−	47.7465i	−0.642754	−	0.294732i
$163$	−78.0156	+	135.127i	−0.478623	+	0.829000i	−0.999700	−	0.0245101i	$-0.992197\pi$
$163$	−78.0156	+	135.127i	−0.478623	+	0.829000i	0.521076	+	0.853510i	$0.325531\pi$
$164$	−29.5262	+	81.1226i	−0.180038	+	0.494650i
$165$	28.8215	+	17.4263i	0.174676	+	0.105614i
$166$	121.382	−	144.657i	0.731214	−	0.871427i
$167$	51.8039	+	142.330i	0.310203	+	0.852275i	0.992615	+	0.121308i	$0.0387088\pi$
$167$	51.8039	+	142.330i	0.310203	+	0.852275i	−0.682412	+	0.730968i	$0.739069\pi$
$168$	24.6423	−	54.0440i	0.146681	−	0.321691i
$169$	19.9305	+	113.032i	0.117932	+	0.668826i
$170$	43.7249			0.257205
$171$	−233.668	+	122.591i	−1.36648	+	0.716908i
$172$	−5.92286			−0.0344352
$173$	161.938	+	192.990i	0.936056	+	1.11555i	0.993111	+	0.117178i	$0.0373847\pi$
$173$	161.938	+	192.990i	0.936056	+	1.11555i	−0.0570546	+	0.998371i	$0.518171\pi$
$174$	−17.5895	+	6.00220i	−0.101089	+	0.0344954i
$175$	−111.416	+	118.013i	−0.636663	+	0.674358i
$176$	−25.5372	−	21.4283i	−0.145098	−	0.121751i
$177$	47.7662	+	139.979i	0.269865	+	0.790841i
$178$	185.075	−	32.6337i	1.03975	−	0.183336i
$179$	−51.6708			−0.288664			−0.144332	−	0.989529i	$-0.546103\pi$
$179$	−51.6708			−0.288664			−0.144332	+	0.989529i	$0.546103\pi$
$180$	14.8224	+	19.1895i	0.0823465	+	0.106609i
$181$	38.4771	−	22.2148i	0.212581	−	0.122734i	−0.389929	−	0.920845i	$-0.627501\pi$
$181$	38.4771	−	22.2148i	0.212581	−	0.122734i	0.602510	+	0.798111i	$0.294167\pi$
$182$	−58.4876	+	43.5111i	−0.321360	+	0.239072i
$183$	65.8587	+	81.7900i	0.359884	+	0.446940i
$184$	−3.90378	+	22.1394i	−0.0212162	+	0.120323i
$185$	22.8407	+	62.7543i	0.123463	+	0.339213i
$186$	4.24481	−	209.926i	0.0228216	−	1.12863i
$187$	−188.378	+	33.2162i	−1.00737	+	0.177626i
$188$		−	131.115i		−	0.697423i
$189$	85.2990	−	168.657i	0.451318	−	0.892363i
$190$	55.8552			0.293975
$191$	−5.77085	−	32.7281i	−0.0302139	−	0.171351i	0.965967	−	0.258665i	$-0.0832827\pi$
$191$	−5.77085	−	32.7281i	−0.0302139	−	0.171351i	−0.996181	+	0.0873142i	$0.972172\pi$
$192$	−11.5774	−	21.0230i	−0.0602987	−	0.109495i
$193$	−40.3592	+	14.6895i	−0.209115	+	0.0761116i	−0.444454	−	0.895802i	$-0.646602\pi$
$193$	−40.3592	+	14.6895i	−0.209115	+	0.0761116i	0.235339	+	0.971913i	$0.424380\pi$
$194$	94.1307	+	16.5978i	0.485210	+	0.0855556i
$195$	−4.57402	−	29.4051i	−0.0234565	−	0.150795i
$196$	87.5457	+	44.0426i	0.446662	+	0.224707i
$197$	−136.580	−	236.563i	−0.693299	−	1.20083i	−0.970751	−	0.240089i	$-0.922823\pi$
$197$	−136.580	−	236.563i	−0.693299	−	1.20083i	0.277452	−	0.960739i	$-0.410510\pi$
$198$	−78.4361	−	71.4134i	−0.396142	−	0.360674i
$199$		−	67.2514i		−	0.337947i	−0.985621	−	0.168973i	$-0.945955\pi$
$199$		−	67.2514i		−	0.337947i	0.985621	−	0.168973i	$-0.0540452\pi$
$200$	11.3875	+	64.5818i	0.0569376	+	0.322909i
$201$	170.644	+	149.169i	0.848974	+	0.742132i
$202$	123.683	−	147.400i	0.612292	−	0.729701i
$203$	−8.78450	−	29.3791i	−0.0432734	−	0.144725i
$204$	−135.108	−	26.6502i	−0.662296	−	0.130638i
$205$	44.5425	−	37.3756i	0.217280	−	0.182320i
$206$			173.058i			0.840088i
$207$	−15.2594	+	69.8875i	−0.0737168	+	0.337621i
$208$			29.4550i			0.141610i
$209$	−240.638	+	42.4310i	−1.15138	+	0.203019i
$210$	−32.5744	+	23.2253i	−0.155116	+	0.110597i
$211$	−65.7799	+	23.9419i	−0.311753	+	0.113469i	−0.493158	−	0.869940i	$-0.664158\pi$
$211$	−65.7799	+	23.9419i	−0.311753	+	0.113469i	0.181405	+	0.983408i	$0.441935\pi$
$212$	147.227	+	123.538i	0.694467	+	0.582727i
$213$	−73.7656	−	133.949i	−0.346317	−	0.628867i
$214$	−190.740	−	69.4236i	−0.891307	−	0.324409i
$215$	3.45483	+	1.99465i	0.0160690	+	0.00927743i
$216$	−34.1046	−	68.3292i	−0.157892	−	0.316339i
$217$	345.838	+	20.2623i	1.59372	+	0.0933746i
$218$	−104.121	+	87.3679i	−0.477619	+	0.400770i
$219$	123.193	−	67.8426i	0.562526	−	0.309783i
$220$	7.67954	+	21.0994i	0.0349070	+	0.0959062i
$221$	129.471	+	108.639i	0.585841	+	0.491579i
$222$	−32.3283	−	207.830i	−0.145623	−	0.936171i
$223$	−89.0012	+	15.6933i	−0.399109	+	0.0703736i	−0.369600	−	0.929191i	$-0.620505\pi$
$223$	−89.0012	+	15.6933i	−0.399109	+	0.0703736i	−0.0295085	+	0.999565i	$0.509394\pi$
$224$	35.3922	−	17.7594i	0.158001	−	0.0792828i
$225$	27.8981	+	206.795i	0.123992	+	0.919089i
$226$	−21.5812	−	37.3797i	−0.0954918	−	0.165397i
$227$	244.443	−	43.1019i	1.07684	−	0.189876i	0.393023	−	0.919528i	$-0.371429\pi$
$227$	244.443	−	43.1019i	1.07684	−	0.189876i	0.683818	+	0.729652i	$0.260318\pi$
$228$	−172.591	−	34.0436i	−0.756976	−	0.149314i
$229$	−110.295	−	303.034i	−0.481639	−	1.32329i	−0.908087	−	0.418781i	$-0.862457\pi$
$229$	−110.295	−	303.034i	−0.481639	−	1.32329i	0.426448	−	0.904512i	$-0.359765\pi$
$230$	9.73300	−	11.5993i	0.0423174	−	0.0504319i
$231$	122.696	−	124.806i	0.531150	−	0.540286i
$232$	−11.6430	−	4.23771i	−0.0501855	−	0.0182660i
$233$	120.973	+	209.531i	0.519197	+	0.899275i	0.999751	+	0.0223102i	$0.00710213\pi$
$233$	120.973	+	209.531i	0.519197	+	0.899275i	−0.480554	+	0.876965i	$0.659565\pi$
$234$	−3.78879	+	93.6485i	−0.0161914	+	0.400207i
$235$	−44.1559	+	76.4802i	−0.187897	+	0.325448i
$236$	−33.7242	+	92.6564i	−0.142899	+	0.392612i
$237$	−270.733	−	104.784i	−1.14233	−	0.442127i
$238$	52.4750	−	221.070i	0.220483	−	0.928866i
$239$	−21.0519	+	119.391i	−0.0880834	+	0.499546i	0.908565	+	0.417743i	$0.137179\pi$
$239$	−21.0519	+	119.391i	−0.0880834	+	0.499546i	−0.996649	+	0.0818027i	$0.973932\pi$
$240$	−0.326798	+	16.1617i	−0.00136166	+	0.0673404i
$241$	−112.672	+	309.564i	−0.467519	+	1.28450i	0.452199	+	0.891917i	$0.350640\pi$
$241$	−112.672	+	309.564i	−0.467519	+	1.28450i	−0.919718	+	0.392581i	$0.871582\pi$
$242$	36.4461	+	63.1265i	0.150604	+	0.260853i
$243$	−99.6424	−	221.631i	−0.410051	−	0.912063i
$244$			70.0063i			0.286911i
$245$	−36.2335	−	55.1731i	−0.147892	−	0.225196i
$246$	−160.415	+	88.3406i	−0.652093	+	0.359108i
$247$	165.389	+	138.778i	0.669591	+	0.561854i
$248$	89.9769	−	107.230i	0.362810	−	0.432380i
$249$	395.822	−	61.5709i	1.58965	−	0.247273i
$250$	31.3961	−	86.2602i	0.125585	−	0.345041i
$251$	319.094	−	184.229i	1.27129	−	0.733980i	0.296060	−	0.955169i	$-0.404327\pi$
$251$	319.094	−	184.229i	1.27129	−	0.733980i	0.975231	+	0.221189i	$0.0709939\pi$
$252$	114.810	−	51.9112i	0.455593	−	0.205997i
$253$	−33.1207	+	57.3667i	−0.130912	+	0.226746i
$254$	−183.409	+	153.899i	−0.722084	+	0.605901i
$255$	69.8343	+	61.0458i	0.273860	+	0.239395i
$256$	2.77837	−	15.7569i	0.0108530	−	0.0615505i
$257$	−11.6081	−	31.8929i	−0.0451676	−	0.124097i	0.915058	−	0.403322i	$-0.132145\pi$
$257$	−11.6081	−	31.8929i	−0.0451676	−	0.124097i	−0.960226	+	0.279225i	$0.909922\pi$
$258$	−9.45957	−	8.26910i	−0.0366650	−	0.0320508i
$259$	344.693	−	40.1685i	1.33086	−	0.155091i
$260$	9.91957	−	17.1812i	0.0381522	−	0.0660815i
$261$	−36.4725	−	14.9709i	−0.139741	−	0.0573599i
$262$	79.4362	+	45.8625i	0.303192	+	0.175048i
$263$	204.683	−	171.750i	0.778264	−	0.653041i	−0.164547	−	0.986369i	$-0.552616\pi$
$263$	204.683	−	171.750i	0.778264	−	0.653041i	0.942811	+	0.333329i	$0.108172\pi$
$264$	−10.8695	−	69.8770i	−0.0411723	−	0.264685i
$265$	−44.2741	−	121.642i	−0.167072	−	0.459027i
$266$	67.0328	−	282.400i	0.252003	−	1.06165i
$267$	341.149	+	206.269i	1.27771	+	0.772543i
$268$	26.2383	+	148.805i	0.0979042	+	0.555242i
$269$	9.95325	−	5.74651i	0.0370009	−	0.0213625i	−0.481385	−	0.876509i	$-0.659866\pi$
$269$	9.95325	−	5.74651i	0.0370009	−	0.0213625i	0.518386	+	0.855147i	$0.326533\pi$
$270$	−3.11789	+	51.3421i	−0.0115478	+	0.190156i
$271$	123.954	+	71.5651i	0.457396	+	0.264078i	0.710949	−	0.703244i	$-0.248266\pi$
$271$	123.954	+	71.5651i	0.457396	+	0.264078i	−0.253553	+	0.967322i	$0.581599\pi$
$272$	−59.0129	−	70.3289i	−0.216959	−	0.258562i
$273$	−154.159	−	12.1636i	−0.564686	−	0.0445554i
$274$	36.1411	−	204.967i	0.131902	−	0.748053i
$275$	−33.5539	+	190.294i	−0.122014	+	0.691978i
$276$	−37.1444	+	29.9093i	−0.134581	+	0.108367i
$277$	−328.221	+	275.410i	−1.18491	+	0.994259i	−0.184978	+	0.982743i	$0.559221\pi$
$277$	−328.221	+	275.410i	−1.18491	+	0.994259i	−0.999934	+	0.0115163i	$0.996334\pi$
$278$			103.862i			0.373606i
$279$	299.864	−	329.352i	1.07478	−	1.18047i
$280$	−26.6252	−	1.55995i	−0.0950901	−	0.00557123i
$281$	−126.590	−	46.0748i	−0.450497	−	0.163967i	0.106801	−	0.994280i	$-0.465939\pi$
$281$	−126.590	−	46.0748i	−0.450497	−	0.163967i	−0.557297	+	0.830313i	$0.688162\pi$
$282$	183.054	−	209.408i	0.649129	−	0.742582i
$283$	−150.878	−	26.6038i	−0.533136	−	0.0940063i	−0.0994024	−	0.995047i	$-0.531693\pi$
$283$	−150.878	−	26.6038i	−0.533136	−	0.0940063i	−0.433734	+	0.901041i	$0.642804\pi$
$284$	17.7025	−	100.396i	0.0623327	−	0.353507i
$285$	89.2079	+	77.9812i	0.313010	+	0.273618i
$286$	−29.6841	+	81.5565i	−0.103791	+	0.285163i
$287$	−135.512	−	270.059i	−0.472168	−	0.940971i
$288$	10.8603	−	49.7399i	0.0377094	−	0.172708i
$289$	−237.792			−0.822811
$290$	5.36429	+	6.39291i	0.0184975	+	0.0220445i
$291$	127.166	+	157.928i	0.436997	+	0.542707i
$292$	92.3345	+	16.2811i	0.316214	+	0.0557571i
$293$	233.545	+	41.1803i	0.797082	+	0.140547i	0.557334	−	0.830288i	$-0.311824\pi$
$293$	233.545	+	41.1803i	0.797082	+	0.140547i	0.239748	+	0.970835i	$0.422935\pi$
$294$	78.3323	+	192.567i	0.266436	+	0.654990i
$295$	50.8754	−	42.6896i	0.172459	−	0.144710i
$296$	70.1098	−	121.434i	0.236857	−	0.410249i
$297$	−25.5700	−	223.564i	−0.0860941	−	0.752739i
$298$	95.5145	+	165.436i	0.320518	+	0.555154i
$299$	57.6394	−	10.1634i	0.192774	−	0.0339913i
$300$	−71.9774	+	119.044i	−0.239925	+	0.396813i
$301$	14.2310	−	15.0736i	0.0472791	−	0.0500783i
$302$	188.470	−	68.5974i	0.624072	−	0.227144i
$303$	403.327	−	62.7382i	1.33111	−	0.207057i
$304$	−75.3844	−	89.8397i	−0.247975	−	0.295525i
$305$	23.5761	−	40.8350i	0.0772986	−	0.133885i
$306$	−178.578	−	231.193i	−0.583589	−	0.755533i
$307$	387.282	+	223.597i	1.26150	+	0.728330i	0.973366	−	0.229259i	$-0.0736302\pi$
$307$	387.282	+	223.597i	1.26150	+	0.728330i	0.288139	+	0.957589i	$0.406963\pi$
$308$	115.893	−	13.5055i	0.376277	−	0.0438491i
$309$	−241.612	+	276.396i	−0.781915	+	0.894485i
$310$	−88.5959	+	32.2463i	−0.285793	+	0.104020i
$311$	97.4245	+	17.1786i	0.313262	+	0.0552365i	0.328069	−	0.944654i	$-0.393602\pi$
$311$	97.4245	+	17.1786i	0.313262	+	0.0552365i	−0.0148068	+	0.999890i	$0.504713\pi$
$312$	−41.1230	+	47.0433i	−0.131804	+	0.150780i
$313$	12.2741	+	14.6277i	0.0392143	+	0.0467338i	0.785295	−	0.619122i	$-0.212511\pi$
$313$	12.2741	+	14.6277i	0.0392143	+	0.0467338i	−0.746081	+	0.665855i	$0.768067\pi$
$314$	155.136	+	89.5677i	0.494063	+	0.285247i
$315$	−84.4510	−	8.38446i	−0.268099	−	0.0266173i
$316$	−96.7678	−	167.607i	−0.306227	−	0.530401i
$317$	244.507	+	88.9934i	0.771317	+	0.280736i	0.697547	−	0.716539i	$-0.254275\pi$
$317$	244.507	+	88.9934i	0.771317	+	0.280736i	0.0737696	+	0.997275i	$0.476497\pi$
$318$	62.6647	+	402.854i	0.197059	+	1.26684i
$319$	−27.9672	−	23.4672i	−0.0876713	−	0.0735650i
$320$	−6.92711	+	8.25540i	−0.0216472	+	0.0257981i
$321$	−207.711	−	377.176i	−0.647075	−	1.17500i
$322$	−46.9647	−	63.1299i	−0.145853	−	0.196056i
$323$	−672.936			−2.08339
$324$	40.9271	−	156.745i	0.126318	−	0.483781i
$325$	147.857	−	85.3655i	0.454946	−	0.262663i
$326$	−207.354	−	75.4707i	−0.636055	−	0.231505i
$327$	−288.271	−	5.82900i	−0.881564	−	0.0178257i
$328$	−120.233	−	21.2003i	−0.366563	−	0.0646349i
$329$	333.686	+	315.034i	1.01424	+	0.957550i
$330$	−17.1923	+	44.4200i	−0.0520979	+	0.134606i
$331$	−71.9218	−	26.1774i	−0.217286	−	0.0790858i	0.231083	−	0.972934i	$-0.425773\pi$
$331$	−71.9218	−	26.1774i	−0.217286	−	0.0790858i	−0.448370	+	0.893848i	$0.647995\pi$
$332$	231.276	+	133.527i	0.696615	+	0.402191i
$333$	238.526	−	377.066i	0.716293	−	1.13233i
$334$	−185.505	+	107.101i	−0.555405	+	0.320663i
$335$	34.8082	−	95.6348i	0.103905	−	0.285477i
$336$	81.3202	+	21.0482i	0.242024	+	0.0626434i
$337$	382.722	+	321.142i	1.13567	+	0.952944i	0.999289	−	0.0377122i	$-0.0120070\pi$
$337$	382.722	+	321.142i	1.13567	+	0.952944i	0.136385	+	0.990656i	$0.456451\pi$
$338$	−152.528	+	55.5156i	−0.451266	+	0.164247i
$339$	17.7191	−	89.8302i	0.0522687	−	0.264986i
$340$	10.7378	+	60.8970i	0.0315817	+	0.179109i
$341$	357.198	−	206.228i	1.04750	−	0.604775i
$342$	−228.120	−	295.331i	−0.667017	−	0.863541i
$343$	−322.436	+	116.980i	−0.940046	+	0.341049i
$344$	−1.45451	−	8.24894i	−0.00422823	−	0.0239795i
$345$	31.7390	−	4.93707i	0.0919972	−	0.0143103i
$346$	−229.015	+	272.929i	−0.661892	+	0.788812i
$347$	109.196	−	39.7441i	0.314686	−	0.114536i	−0.179849	−	0.983694i	$-0.557561\pi$
$347$	109.196	−	39.7441i	0.314686	−	0.114536i	0.494534	+	0.869158i	$0.335339\pi$
$348$	−12.6790	−	23.0234i	−0.0364339	−	0.0661591i
$349$	−242.182	−	288.622i	−0.693932	−	0.826996i	0.297893	−	0.954599i	$-0.403716\pi$
$349$	−242.182	−	288.622i	−0.693932	−	0.826996i	−0.991825	+	0.127603i	$0.959272\pi$
$350$	−191.721	−	126.191i	−0.547773	−	0.360546i
$351$	−136.797	+	144.279i	−0.389735	+	0.411051i
$352$	23.5724	−	40.8286i	0.0669671	−	0.115990i
$353$	−4.41406	+	12.1275i	−0.0125044	+	0.0343556i	−0.945788	−	0.324785i	$-0.894708\pi$
$353$	−4.41406	+	12.1275i	−0.0125044	+	0.0343556i	0.933283	+	0.359141i	$0.116930\pi$
$354$	−183.222	+	100.901i	−0.517577	+	0.285030i
$355$	−44.1363	+	52.5996i	−0.124328	+	0.148168i
$356$	90.8999	+	249.745i	0.255337	+	0.701532i
$357$	392.452	−	279.815i	1.09931	−	0.783796i
$358$	−12.6891	−	71.9634i	−0.0354444	−	0.201015i
$359$	−176.208			−0.490831			−0.245416	−	0.969418i	$-0.578924\pi$
$359$	−176.208			−0.490831			−0.245416	+	0.969418i	$0.578924\pi$
$360$	−23.0858	+	25.3560i	−0.0641272	+	0.0704334i
$361$	−498.624			−1.38123
$362$	40.3882	+	48.1328i	0.111570	+	0.132964i
$363$	−29.9239	+	151.705i	−0.0824349	+	0.417919i
$364$	−74.9623	−	70.7721i	−0.205940	−	0.194429i
$365$	−48.3761	−	40.5924i	−0.132537	−	0.111212i
$366$	−97.7380	+	111.809i	−0.267044	+	0.305489i
$367$	−337.714	+	59.5481i	−0.920201	+	0.162256i	−0.613632	−	0.789592i	$-0.710292\pi$
$367$	−337.714	+	59.5481i	−0.920201	+	0.162256i	−0.306569	+	0.951848i	$0.599181\pi$
$368$	−31.7929			−0.0863937
$369$	−379.538	−	82.8692i	−1.02856	−	0.224578i
$370$	−81.7906	+	47.2218i	−0.221056	+	0.127627i
$371$	−668.148	+	77.8620i	−1.80094	+	0.209871i
$372$	293.412	−	45.6408i	0.788743	−	0.122690i
$373$	−93.0474	+	527.698i	−0.249457	+	1.41474i	0.560454	+	0.828186i	$0.310627\pi$
$373$	−93.0474	+	527.698i	−0.249457	+	1.41474i	−0.809910	+	0.586554i	$0.800484\pi$
$374$	−92.5222	−	254.203i	−0.247385	−	0.679686i
$375$	170.574	−	93.9353i	0.454865	−	0.250494i
$376$	182.608	−	32.1988i	0.485660	−	0.0856350i
$377$			32.2577i			0.0855642i
$378$	255.840	+	77.3804i	0.676826	+	0.204710i
$379$	558.240			1.47293			0.736464	−	0.676477i	$-0.236494\pi$
$379$	558.240			1.47293			0.736464	+	0.676477i	$0.236494\pi$
$380$	13.7167	+	77.7911i	0.0360965	+	0.204713i
$381$	−507.791	−	10.2678i	−1.33279	−	0.0269496i
$382$	44.1642	−	16.0744i	0.115613	−	0.0420797i
$383$	579.412	+	102.166i	1.51282	+	0.266752i	0.867608	−	0.497248i	$-0.165656\pi$
$383$	579.412	+	102.166i	1.51282	+	0.266752i	0.645216	+	0.764000i	$0.276767\pi$
$384$	26.4362	−	21.2868i	0.0688442	−	0.0554345i
$385$	−72.1493	−	31.1517i	−0.187401	−	0.0809134i
$386$	−30.3698	−	52.6020i	−0.0786782	−	0.136275i
$387$	−3.56338	−	26.4136i	−0.00920770	−	0.0682522i
$388$			135.175i			0.348388i
$389$	40.6192	+	230.363i	0.104420	+	0.592193i	0.991451	+	0.130483i	$0.0416529\pi$
$389$	40.6192	+	230.363i	0.104420	+	0.592193i	−0.887031	+	0.461710i	$0.847236\pi$
$390$	39.8300	−	13.5915i	0.102128	−	0.0348501i
$391$	−117.262	+	139.747i	−0.299903	+	0.357410i
$392$	−39.8404	+	132.743i	−0.101634	+	0.338631i
$393$	62.8396	+	184.152i	0.159897	+	0.468579i
$394$	295.928	−	248.313i	0.751086	−	0.630236i
$395$			130.354i			0.330011i
$396$	80.1975	−	126.778i	0.202519	−	0.320146i
$397$		−	505.262i		−	1.27270i	−0.771400	−	0.636351i	$-0.780443\pi$
$397$		−	505.262i		−	1.27270i	0.771400	−	0.636351i	$-0.219557\pi$
$398$	93.6629	−	16.5153i	0.235334	−	0.0414957i
$399$	501.327	−	357.442i	1.25646	−	0.895845i
$400$	−87.1485	+	31.7195i	−0.217871	+	0.0792986i
$401$	−169.268	−	142.032i	−0.422114	−	0.354196i	0.406853	−	0.913494i	$-0.366626\pi$
$401$	−169.268	−	142.032i	−0.422114	−	0.354196i	−0.828967	+	0.559298i	$0.811071\pi$
$402$	−165.845	+	274.293i	−0.412551	+	0.682320i
$403$	−342.454	−	124.643i	−0.849763	−	0.309288i
$404$	235.661	+	136.059i	0.583319	+	0.336780i
$405$	−76.6600	+	77.6469i	−0.189284	+	0.191721i
$406$	38.7599	−	19.4492i	0.0954676	−	0.0479045i
$407$	316.502	−	265.577i	0.777647	−	0.652523i
$408$	3.93722	−	194.714i	0.00965005	−	0.477240i
$409$	−163.648	−	449.618i	−0.400116	−	1.09931i	−0.962227	−	0.272249i	$-0.912233\pi$
$409$	−163.648	−	449.618i	−0.400116	−	1.09931i	0.562110	−	0.827062i	$-0.309990\pi$
$410$	62.9926	+	52.8571i	0.153640	+	0.128920i
$411$	343.882	−	276.900i	0.836697	−	0.673722i
$412$	−241.023	+	42.4988i	−0.585007	+	0.103153i
$413$	−154.779	−	308.455i	−0.374767	−	0.746865i
$414$	−101.082	−	4.08952i	−0.244158	−	0.00987806i
$415$	−89.9362	−	155.774i	−0.216714	−	0.375359i
$416$	−41.0228	+	7.23342i	−0.0986124	+	0.0173880i
$417$	−145.006	+	165.881i	−0.347735	+	0.397797i
$418$	−118.190	−	324.724i	−0.282751	−	0.776852i
$419$	−174.481	+	207.939i	−0.416423	+	0.496274i	−0.932954	−	0.359994i	$-0.882779\pi$
$419$	−174.481	+	207.939i	−0.416423	+	0.496274i	0.516531	+	0.856268i	$0.327223\pi$
$420$	−40.3460	−	39.6638i	−0.0960619	−	0.0944375i
$421$	−686.954	−	250.031i	−1.63172	−	0.593897i	−0.646156	−	0.763205i	$-0.723624\pi$
$421$	−686.954	−	250.031i	−1.63172	−	0.593897i	−0.985563	+	0.169308i	$0.945847\pi$
$422$	−49.4985	−	85.7340i	−0.117295	−	0.203161i
$423$	584.723	−	78.8832i	1.38232	−	0.186485i
$424$	−135.900	+	235.385i	−0.320518	+	0.555154i
$425$	−182.006	+	500.057i	−0.428249	+	1.17660i
$426$	168.439	−	135.630i	0.395397	−	0.318380i
$427$	−178.165	−	168.206i	−0.417247	−	0.393924i
$428$	49.8472	−	282.697i	0.116465	−	0.660508i
$429$	−161.273	+	88.8131i	−0.375928	+	0.207024i
$430$	−1.92958	+	5.30148i	−0.00448739	+	0.0123290i
$431$	−345.101	−	597.733i	−0.800699	−	1.38685i	−0.919157	−	0.393892i	$-0.871128\pi$
$431$	−345.101	−	597.733i	−0.800699	−	1.38685i	0.118458	−	0.992959i	$-0.462205\pi$
$432$	86.7887	−	64.2785i	0.200900	−	0.148793i
$433$			620.459i			1.43293i	0.697622	+	0.716466i	$0.254241\pi$
$433$			620.459i			1.43293i	−0.697622	+	0.716466i	$0.745759\pi$
$434$	56.7095	+	486.634i	0.130667	+	1.12128i
$435$	−0.357894	+	17.6995i	−0.000822745	+	0.0406886i
$436$	−147.249	−	123.557i	−0.337728	−	0.283387i
$437$	−149.793	+	178.516i	−0.342776	+	0.408504i
$438$	124.739	+	154.914i	0.284793	+	0.353685i
$439$	−225.444	+	619.402i	−0.513540	+	1.41094i	0.363984	+	0.931405i	$0.381416\pi$
$439$	−225.444	+	619.402i	−0.513540	+	1.41094i	−0.877524	+	0.479533i	$0.840806\pi$
$440$	−27.4998	+	15.8770i	−0.0624995	+	0.0360841i
$441$	−143.742	+	416.916i	−0.325946	+	0.945388i
$442$	−119.510	+	206.997i	−0.270384	+	0.468319i
$443$	−171.504	+	143.909i	−0.387143	+	0.324852i	−0.815499	−	0.578758i	$-0.803537\pi$
$443$	−171.504	+	143.909i	−0.387143	+	0.324852i	0.428356	+	0.903610i	$0.359093\pi$
$444$	281.512	−	96.0626i	0.634035	−	0.216357i
$445$	31.0847	−	176.290i	0.0698532	−	0.396157i
$446$	−43.7131	−	120.101i	−0.0980114	−	0.269284i
$447$	−78.4216	+	397.573i	−0.175440	+	0.889425i
$448$	33.4254	+	44.9304i	0.0746103	+	0.100291i
$449$	93.3901	−	161.756i	0.207996	−	0.360259i	−0.743087	−	0.669194i	$-0.766639\pi$
$449$	93.3901	−	161.756i	0.207996	−	0.360259i	0.951083	+	0.308935i	$0.0999727\pi$
$450$	−281.158	+	89.6383i	−0.624796	+	0.199196i
$451$	−311.542	−	179.869i	−0.690780	−	0.398822i
$452$	46.7599	−	39.2362i	0.103451	−	0.0868058i
$453$	396.781	+	153.570i	0.875897	+	0.339007i
$454$	120.059	+	329.858i	0.264446	+	0.726560i
$455$	19.8918	+	66.5268i	0.0437183	+	0.146213i
$456$	5.02949	−	248.732i	0.0110296	−	0.545465i
$457$	50.4235	+	285.966i	0.110336	+	0.625745i	0.988954	+	0.148221i	$0.0473547\pi$
$457$	50.4235	+	285.966i	0.110336	+	0.625745i	−0.878618	+	0.477524i	$0.841534\pi$
$458$	394.958	−	228.029i	0.862355	−	0.497881i
$459$	37.5640	−	618.563i	0.0818387	−	1.34763i
$460$	18.5449	+	10.7069i	0.0403150	+	0.0232759i
$461$	302.787	+	360.847i	0.656804	+	0.782748i	0.986923	−	0.161191i	$-0.0515334\pi$
$461$	302.787	+	360.847i	0.656804	+	0.782748i	−0.330119	+	0.943939i	$0.607089\pi$
$462$	203.952	+	140.232i	0.441454	+	0.303533i
$463$	−12.9444	+	73.4112i	−0.0279576	+	0.158555i	−0.995590	−	0.0938069i	$-0.970096\pi$
$463$	−12.9444	+	73.4112i	−0.0279576	+	0.158555i	0.967633	+	0.252362i	$0.0812075\pi$
$464$	3.04274	−	17.2563i	0.00655764	−	0.0371902i
$465$	−186.519	−	72.1902i	−0.401116	−	0.155248i
$466$	−262.112	+	219.938i	−0.562472	+	0.471970i
$467$		−	166.417i		−	0.356354i	−0.983998	−	0.178177i	$-0.942980\pi$
$467$		−	166.417i		−	0.356354i	0.983998	−	0.178177i	$-0.0570200\pi$
$468$	−131.357	+	17.7210i	−0.280678	+	0.0378654i
$469$	−441.749	−	290.761i	−0.941896	−	0.619959i
$470$	−117.360	−	42.7154i	−0.249702	−	0.0908839i
$471$	122.723	+	359.641i	0.260559	+	0.763569i
$472$	−137.327	−	24.2145i	−0.290947	−	0.0513018i
$473$	4.28579	−	24.3059i	0.00906087	−	0.0513868i
$474$	79.4506	−	402.790i	0.167617	−	0.849767i
$475$	−232.498	+	638.784i	−0.489470	+	1.34481i
$476$	320.777	+	18.7940i	0.673902	+	0.0394832i
$477$	−462.354	+	730.898i	−0.969296	+	1.53228i
$478$	−171.450			−0.358682
$479$	116.478	+	138.813i	0.243169	+	0.289798i	0.873800	−	0.486285i	$-0.161648\pi$
$479$	116.478	+	138.813i	0.243169	+	0.289798i	−0.630631	+	0.776083i	$0.717204\pi$
$480$	−22.5891	+	3.51378i	−0.0470606	+	0.00732037i
$481$	−359.512	−	63.3917i	−0.747426	−	0.131791i
$482$	−458.808	−	80.9002i	−0.951884	−	0.167843i
$483$	13.1291	−	166.395i	0.0271824	−	0.344504i
$484$	−78.9678	+	66.2619i	−0.163157	+	0.136905i
$485$	45.5228	−	78.8479i	0.0938615	−	0.162573i
$486$	284.202	−	193.202i	0.584779	−	0.397535i
$487$	389.912	+	675.347i	0.800640	+	1.38675i	0.919195	+	0.393802i	$0.128840\pi$
$487$	389.912	+	675.347i	0.800640	+	1.38675i	−0.118555	+	0.992947i	$0.537826\pi$
$488$	−97.4997	+	17.1918i	−0.199795	+	0.0352292i
$489$	−225.804	−	410.030i	−0.461766	−	0.838507i
$490$	67.9431	−	64.0126i	0.138659	−	0.130638i
$491$	−108.424	+	39.4629i	−0.220822	+	0.0803726i	−0.450062	−	0.892997i	$-0.648598\pi$
$491$	−108.424	+	39.4629i	−0.220822	+	0.0803726i	0.229240	+	0.973370i	$0.426376\pi$
$492$	−162.429	−	201.720i	−0.330139	−	0.410000i
$493$	−64.6282	−	77.0209i	−0.131092	−	0.156229i
$494$	−152.664	+	264.422i	−0.309037	+	0.535268i
$495$	−89.4745	+	46.9417i	−0.180757	+	0.0948318i
$496$	171.439	+	98.9803i	0.345643	+	0.199557i
$497$	212.971	+	286.276i	0.428514	+	0.576008i
$498$	182.956	+	536.152i	0.367381	+	1.07661i
$499$	734.610	−	267.376i	1.47216	−	0.535824i	0.523477	−	0.852040i	$-0.324634\pi$
$499$	734.610	−	267.376i	1.47216	−	0.535824i	0.948687	+	0.316215i	$0.102412\pi$
$500$	127.847	+	22.5429i	0.255694	+	0.0450858i
$501$	−445.803	−	87.9350i	−0.889827	−	0.175519i
$502$	334.943	+	399.169i	0.667216	+	0.795158i
$503$	−40.2943	−	23.2639i	−0.0801079	−	0.0462503i	0.459411	−	0.888224i	$-0.348061\pi$
$503$	−40.2943	−	23.2639i	−0.0801079	−	0.0462503i	−0.539519	+	0.841973i	$0.681394\pi$
$504$	100.493	+	147.150i	0.199390	+	0.291965i
$505$	−91.6414	−	158.728i	−0.181468	−	0.314312i
$506$	−88.0298	−	32.0402i	−0.173972	−	0.0633206i
$507$	−321.114	−	124.284i	−0.633360	−	0.245135i
$508$	−259.380	−	217.646i	−0.510591	−	0.428437i
$509$	−529.444	+	630.966i	−1.04016	+	1.23962i	−0.0699046	+	0.997554i	$0.522269\pi$
$509$	−529.444	+	630.966i	−1.04016	+	1.23962i	−0.970260	+	0.242066i	$0.922175\pi$
$510$	−67.8706	+	112.252i	−0.133080	+	0.220101i
$511$	−263.289	+	195.871i	−0.515243	+	0.383309i
$512$	22.6274			0.0441942
$513$	47.9851	−	790.166i	0.0935381	−	1.54029i
$514$	41.5675	−	23.9990i	0.0808707	−	0.0466907i
$515$	154.902	+	56.3797i	0.300781	+	0.109475i
$516$	9.19357	−	15.2053i	0.0178170	−	0.0294676i
$517$	538.065	+	94.8754i	1.04074	+	0.183511i
$518$	140.592	+	470.199i	0.271413	+	0.907721i
$519$	−746.810	+	116.168i	−1.43894	+	0.223830i
$520$	26.3647	+	9.59598i	0.0507014	+	0.0184538i
$521$	−201.450	−	116.307i	−0.386660	−	0.223238i	0.294052	−	0.955789i	$-0.404996\pi$
$521$	−201.450	−	116.307i	−0.386660	−	0.223238i	−0.680712	+	0.732551i	$0.738330\pi$
$522$	11.8937	−	54.4728i	0.0227849	−	0.104354i
$523$	−657.194	+	379.431i	−1.25659	+	0.725490i	−0.972409	−	0.233282i	$-0.925053\pi$
$523$	−657.194	+	379.431i	−1.25659	+	0.725490i	−0.284176	+	0.958772i	$0.591720\pi$
$524$	−44.3664	+	121.896i	−0.0846688	+	0.232626i
$525$	−130.023	−	469.211i	−0.247662	−	0.893735i
$526$	289.466	+	242.891i	0.550315	+	0.461769i
$527$	1067.39	−	388.499i	2.02541	−	0.737190i
$528$	94.6503	−	32.2983i	0.179262	−	0.0611711i
$529$	−80.8898	−	458.749i	−0.152911	−	0.867200i
$530$	158.542	−	91.5341i	0.299135	−	0.172706i
$531$	−433.500	−	94.6514i	−0.816385	−	0.178251i
$532$	409.768	+	24.0079i	0.770241	+	0.0451276i
$533$	55.1944	+	313.023i	0.103554	+	0.587285i
$534$	−203.499	+	525.783i	−0.381084	+	0.984613i
$535$	−124.280	+	148.111i	−0.232300	+	0.276844i
$536$	−200.801	+	73.0857i	−0.374629	+	0.136354i
$537$	80.2043	−	132.650i	0.149356	−	0.247021i
$538$	10.4476	+	12.4510i	0.0194193	+	0.0231431i
$539$	−244.088	+	327.396i	−0.452854	+	0.607414i
$540$	−72.2713	+	8.26599i	−0.133836	+	0.0153074i
$541$	283.649	−	491.294i	0.524305	−	0.908123i	−0.475295	−	0.879827i	$-0.657659\pi$
$541$	283.649	−	491.294i	0.524305	−	0.908123i	0.999600	−	0.0282961i	$-0.00900812\pi$
$542$	−69.2305	+	190.209i	−0.127732	+	0.350940i
$543$	−2.69462	+	133.261i	−0.00496246	+	0.245417i
$544$	83.4569	−	99.4601i	0.153413	−	0.182831i
$545$	44.2808	+	121.660i	0.0812491	+	0.223230i
$546$	−20.9171	−	217.689i	−0.0383098	−	0.398698i
$547$	−120.661	−	684.303i	−0.220587	−	1.25101i	−0.870944	−	0.491382i	$-0.836492\pi$
$547$	−120.661	−	684.303i	−0.220587	−	1.25101i	0.650357	−	0.759629i	$-0.274619\pi$
$548$	294.338			0.537113
$549$	−312.200	+	42.1180i	−0.568670	+	0.0767176i
$550$	−273.268			−0.496850
$551$	−82.5575	−	98.3882i	−0.149832	−	0.178563i
$552$	−50.7773	−	44.3870i	−0.0919878	−	0.0804113i
$553$	659.062	+	156.440i	1.19179	+	0.282894i
$554$	−464.174	−	389.488i	−0.837859	−	0.703047i
$555$	−196.558	−	38.7712i	−0.354158	−	0.0698580i
$556$	−144.652	+	25.5061i	−0.260166	+	0.0458742i
$557$	−23.8691			−0.0428529			−0.0214264	−	0.999770i	$-0.506821\pi$
$557$	−23.8691			−0.0428529			−0.0214264	+	0.999770i	$0.506821\pi$
$558$	532.337	+	336.748i	0.954009	+	0.603491i
$559$	−18.8856	+	10.9036i	−0.0337846	+	0.0195056i
$560$	−4.36593	−	37.4648i	−0.00779630	−	0.0669014i
$561$	207.131	−	535.167i	0.369217	−	0.953952i
$562$	33.0824	−	187.620i	0.0588655	−	0.333843i
$563$	−24.7076	−	67.8835i	−0.0438856	−	0.120575i	0.915814	−	0.401603i	$-0.131547\pi$
$563$	−24.7076	−	67.8835i	−0.0438856	−	0.120575i	−0.959700	+	0.281028i	$0.909325\pi$
$564$	336.602	+	203.520i	0.596813	+	0.360850i
$565$	−40.4889	+	7.13928i	−0.0716617	+	0.0126359i
$566$		−	216.665i		−	0.382800i
$567$	300.576	+	480.773i	0.530117	+	0.847925i
$568$	144.171			0.253823
$569$	−84.2644	−	477.887i	−0.148092	−	0.839872i	−0.964832	−	0.262866i	$-0.915332\pi$
$569$	−84.2644	−	477.887i	−0.148092	−	0.839872i	0.816740	−	0.577006i	$-0.195779\pi$
$570$	−86.6994	+	143.393i	−0.152104	+	0.251566i
$571$	374.077	−	136.153i	0.655127	−	0.238447i	0.00699580	−	0.999976i	$-0.497773\pi$
$571$	374.077	−	136.153i	0.655127	−	0.238447i	0.648131	+	0.761529i	$0.275551\pi$
$572$	−120.876	−	21.3137i	−0.211321	−	0.0372616i
$573$	92.9778	+	35.9861i	0.162265	+	0.0628029i
$574$	342.840	−	255.051i	0.597282	−	0.444340i
$575$	92.1412	+	159.593i	0.160246	+	0.277553i
$576$	71.9411	+	2.91056i	0.124898	+	0.00505306i
$577$		−	482.649i		−	0.836480i	−0.908336	−	0.418240i	$-0.862647\pi$
$577$		−	482.649i		−	0.836480i	0.908336	−	0.418240i	$-0.137353\pi$
$578$	−58.3960	−	331.180i	−0.101031	−	0.572976i
$579$	24.9349	−	126.412i	0.0430655	−	0.218329i
$580$	−7.58625	+	9.04094i	−0.0130797	+	0.0155878i
$581$	−895.517	+	267.764i	−1.54134	+	0.460868i
$582$	−188.722	+	215.891i	−0.324264	+	0.370947i
$583$	−613.503	+	514.790i	−1.05232	+	0.883002i
$584$			132.595i			0.227047i
$585$	82.5892	+	33.9006i	0.141178	+	0.0579497i
$586$			335.378i			0.572317i
$587$	879.007	−	154.993i	1.49746	−	0.264042i	0.635927	−	0.771749i	$-0.280618\pi$
$587$	879.007	−	154.993i	1.49746	−	0.264042i	0.861530	+	0.507707i	$0.169507\pi$
$588$	−248.957	+	156.385i	−0.423396	+	0.265961i
$589$	1363.51	−	496.277i	2.31496	−	0.842576i
$590$	71.9487	+	60.3721i	0.121947	+	0.102326i
$591$	819.312	+	16.5669i	1.38631	+	0.0280320i
$592$	186.341	+	67.8227i	0.314766	+	0.114565i
$593$	476.506	+	275.111i	0.803551	+	0.463931i	0.844711	−	0.535222i	$-0.179772\pi$
$593$	476.506	+	275.111i	0.803551	+	0.463931i	−0.0411600	+	0.999153i	$0.513105\pi$
$594$	305.084	−	90.5138i	0.513609	−	0.152380i
$595$	−180.781	−	118.991i	−0.303834	−	0.199985i
$596$	−206.951	+	173.653i	−0.347234	+	0.291364i
$597$	172.649	+	104.389i	0.289195	+	0.174856i
$598$	28.3097	+	77.7802i	0.0473406	+	0.130067i
$599$	−32.1963	−	27.0159i	−0.0537502	−	0.0451017i	0.615517	−	0.788124i	$-0.288947\pi$
$599$	−32.1963	−	27.0159i	−0.0537502	−	0.0451017i	−0.669267	+	0.743022i	$0.733392\pi$
$600$	−183.472	−	71.0108i	−0.305786	−	0.118351i
$601$	1016.73	−	179.276i	1.69173	−	0.298297i	0.756934	−	0.653492i	$-0.226697\pi$
$601$	1016.73	−	179.276i	1.69173	−	0.298297i	0.934792	+	0.355195i	$0.115586\pi$
$602$	24.4882	+	16.1182i	0.0406780	+	0.0267744i
$603$	−647.825	+	206.538i	−1.07434	+	0.342518i
$604$	141.821	+	245.641i	0.234803	+	0.406691i
$605$	68.3773	−	12.0568i	0.113020	−	0.0199285i
$606$	186.424	+	546.317i	0.307631	+	0.901514i
$607$	−36.9761	−	101.591i	−0.0609162	−	0.167366i	0.905501	−	0.424344i	$-0.139495\pi$
$607$	−36.9761	−	101.591i	−0.0609162	−	0.167366i	−0.966417	+	0.256978i	$0.917273\pi$
$608$	106.610	−	127.052i	0.175345	−	0.208968i
$609$	89.0581	+	23.0510i	0.146237	+	0.0378506i
$610$	62.6617	+	22.8070i	0.102724	+	0.0373885i
$611$	−241.375	−	418.074i	−0.395049	−	0.684245i
$612$	278.135	−	305.486i	0.454468	−	0.499161i
$613$	419.829	−	727.165i	0.684876	−	1.18624i	−0.288600	−	0.957450i	$-0.593190\pi$
$613$	419.829	−	727.165i	0.684876	−	1.18624i	0.973476	−	0.228790i	$-0.0734770\pi$
$614$	−216.303	+	594.289i	−0.352286	+	0.967897i
$615$	26.8118	+	172.365i	0.0435964	+	0.280269i
$616$	47.2701	+	158.091i	0.0767372	+	0.256642i
$617$	15.0798	−	85.5219i	0.0244406	−	0.138609i	−0.970146	−	0.242522i	$-0.922025\pi$
$617$	15.0798	−	85.5219i	0.0244406	−	0.138609i	0.994586	+	0.103913i	$0.0331364\pi$
$618$	−444.278	−	268.624i	−0.718897	−	0.434666i
$619$	46.3652	−	127.387i	0.0749034	−	0.205795i	−0.896590	−	0.442861i	$-0.853963\pi$
$619$	46.3652	−	127.387i	0.0749034	−	0.205795i	0.971494	+	0.237066i	$0.0761857\pi$
$620$	−66.6673	−	115.471i	−0.107528	−	0.186244i
$621$	−155.731	−	147.655i	−0.250774	−	0.237769i
$622$			139.904i			0.224927i
$623$	−854.004	−	368.730i	−1.37079	−	0.591862i
$624$	−75.6174	−	45.7205i	−0.121182	−	0.0732700i
$625$	377.044	+	316.377i	0.603270	+	0.506203i
$626$	−17.3582	+	20.6867i	−0.0277287	+	0.0330458i
$627$	264.593	−	683.634i	0.421999	−	1.09033i
$628$	−86.6459	+	238.058i	−0.137971	+	0.379073i
$629$	985.403	−	568.923i	1.56662	−	0.904488i
$630$	−9.06184	−	119.676i	−0.0143839	−	0.189963i
$631$	156.314	−	270.744i	0.247724	−	0.429071i	−0.715170	−	0.698951i	$-0.753651\pi$
$631$	156.314	−	270.744i	0.247724	−	0.429071i	0.962894	+	0.269880i	$0.0869840\pi$
$632$	209.667	−	175.931i	0.331751	−	0.278372i
$633$	40.6405	−	206.035i	0.0642030	−	0.325489i
$634$	−63.8986	+	362.387i	−0.100786	+	0.571588i
$635$	78.0008	+	214.305i	0.122836	+	0.337489i
$636$	−545.678	+	186.206i	−0.857984	+	0.292777i
$637$	360.227	−	20.7318i	0.565506	−	0.0325461i
$638$	25.8154	−	44.7136i	0.0404631	−	0.0700841i
$639$	458.376	+	18.5448i	0.717333	+	0.0290216i
$640$	−13.1987	−	7.62025i	−0.0206229	−	0.0119066i
$641$	495.250	−	415.564i	0.772621	−	0.648306i	−0.168758	−	0.985658i	$-0.553976\pi$
$641$	495.250	−	415.564i	0.772621	−	0.648306i	0.941379	+	0.337352i	$0.109531\pi$
$642$	474.295	−	381.910i	0.738777	−	0.594876i
$643$	142.096	+	390.407i	0.220990	+	0.607164i	0.999798	−	0.0200978i	$-0.00639776\pi$
$643$	142.096	+	390.407i	0.220990	+	0.607164i	−0.778808	+	0.627262i	$0.784176\pi$
$644$	76.3894	−	80.9122i	0.118617	−	0.125640i
$645$	−10.4833	+	5.77319i	−0.0162532	+	0.00895068i
$646$	−165.257	−	937.218i	−0.255815	−	1.45080i
$647$	908.890	−	524.748i	1.40478	−	0.811048i	0.409898	−	0.912131i	$-0.365564\pi$
$647$	908.890	−	524.748i	1.40478	−	0.811048i	0.994878	+	0.101083i	$0.0322309\pi$
$648$	228.354	+	18.5076i	0.352398	+	0.0285611i
$649$	−355.836	−	205.442i	−0.548283	−	0.316552i
$650$	155.201	+	184.961i	0.238771	+	0.284556i
$651$	−588.833	+	856.391i	−0.904506	+	1.31550i
$652$	54.1891	−	307.322i	0.0831121	−	0.471352i
$653$	10.7797	−	61.1348i	0.0165080	−	0.0936214i	−0.975441	−	0.220263i	$-0.929309\pi$
$653$	10.7797	−	61.1348i	0.0165080	−	0.0936214i	0.991949	+	0.126641i	$0.0404197\pi$
$654$	−62.6742	−	402.915i	−0.0958321	−	0.616078i
$655$	66.9301	−	56.1610i	0.102183	−	0.0857420i
$656$		−	172.658i		−	0.263198i
$657$	−17.0557	+	421.570i	−0.0259600	+	0.641660i
$658$	−356.812	+	542.099i	−0.542267	+	0.823859i
$659$	−526.151	−	191.503i	−0.798409	−	0.290597i	−0.0895819	−	0.995979i	$-0.528553\pi$
$659$	−526.151	−	191.503i	−0.798409	−	0.290597i	−0.708827	+	0.705382i	$0.750775\pi$
$660$	−66.0871	−	13.0357i	−0.100132	−	0.0197511i
$661$	−52.8470	−	9.31834i	−0.0799500	−	0.0140973i	0.133530	−	0.991045i	$-0.457369\pi$
$661$	−52.8470	−	9.31834i	−0.0799500	−	0.0140973i	−0.213480	+	0.976947i	$0.568480\pi$
$662$	18.7958	−	106.596i	0.0283924	−	0.161021i
$663$	−479.867	+	163.749i	−0.723782	+	0.246982i
$664$	−129.172	+	354.896i	−0.194536	+	0.534482i
$665$	−230.934	−	152.002i	−0.347270	−	0.228574i
$666$	583.726	+	239.603i	0.876465	+	0.359765i
$667$	−34.8181			−0.0522010
$668$	−194.719	−	232.057i	−0.291495	−	0.347391i
$669$	97.8610	−	252.845i	0.146280	−	0.377945i
$670$	141.741	+	24.9928i	0.211554	+	0.0373027i
$671$	−287.288	−	50.6567i	−0.428149	−	0.0754943i
$672$	−9.34415	+	118.426i	−0.0139050	+	0.176229i
$673$	154.943	−	130.012i	0.230227	−	0.193183i	−0.520375	−	0.853938i	$-0.674208\pi$
$673$	154.943	−	130.012i	0.230227	−	0.193183i	0.750602	+	0.660754i	$0.229763\pi$
$674$	−353.276	+	611.893i	−0.524149	+	0.907853i
$675$	−574.192	−	249.370i	−0.850655	−	0.369437i
$676$	−114.775	−	198.797i	−0.169786	−	0.294078i
$677$	687.442	−	121.215i	1.01542	−	0.179047i	0.358919	−	0.933369i	$-0.383145\pi$
$677$	687.442	−	121.215i	1.01542	−	0.179047i	0.656505	+	0.754322i	$0.272034\pi$
$678$	129.460	+	2.61776i	0.190945	+	0.00386100i
$679$	−344.017	−	324.787i	−0.506652	−	0.478331i
$680$	−82.1760	+	29.9096i	−0.120847	+	0.0439847i
$681$	−268.777	+	694.443i	−0.394679	+	1.01974i
$682$	374.939	+	446.835i	0.549764	+	0.655183i
$683$	−377.617	+	654.052i	−0.552880	+	0.957616i	0.445185	+	0.895439i	$0.353138\pi$
$683$	−377.617	+	654.052i	−0.552880	+	0.957616i	−0.998065	+	0.0621776i	$0.980195\pi$
$684$	355.295	−	390.235i	0.519438	−	0.570519i
$685$	−171.689	−	99.1245i	−0.250640	−	0.144707i
$686$	−242.103	−	420.338i	−0.352920	−	0.612737i
$687$	949.158	+	187.222i	1.38160	+	0.272521i
$688$	11.1313	−	4.05148i	0.0161793	−	0.00588877i
$689$	696.872	+	122.877i	1.01143	+	0.178342i
$690$	14.6703	+	42.9914i	0.0212613	+	0.0623064i
$691$	−783.727	−	934.009i	−1.13419	−	1.35168i	−0.927743	−	0.373220i	$-0.878254\pi$
$691$	−783.727	−	934.009i	−1.13419	−	1.35168i	−0.206449	−	0.978457i	$-0.566191\pi$
$692$	−436.356	−	251.930i	−0.630573	−	0.364061i
$693$	129.954	+	508.713i	0.187524	+	0.734073i
$694$	82.1686	+	142.320i	0.118399	+	0.205072i
$695$	92.9658	+	33.8368i	0.133764	+	0.0486860i
$696$	28.9517	−	23.3124i	0.0415972	−	0.0334948i
$697$	−758.927	−	636.815i	−1.08885	−	0.913651i
$698$	342.498	−	408.173i	0.490684	−	0.584775i
$699$	−725.689	−	14.6738i	−1.03818	−	0.0209926i
$700$	128.668	−	298.004i	0.183812	−	0.425720i
$701$	−872.387			−1.24449			−0.622245	−	0.782823i	$-0.713779\pi$
$701$	−872.387			−1.24449			−0.622245	+	0.782823i	$0.713779\pi$
$702$	−234.535	−	155.089i	−0.334096	−	0.220925i
$703$	1258.78	−	726.754i	1.79058	−	1.03379i
$704$	62.6520	+	22.8035i	0.0889944	+	0.0323913i
$705$	−127.802	−	232.072i	−0.181279	−	0.329180i
$706$	−17.9743	−	3.16936i	−0.0254594	−	0.00448918i
$707$	−912.496	+	272.841i	−1.29066	+	0.385913i
$708$	−185.522	−	230.400i	−0.262037	−	0.325424i
$709$	−223.288	−	81.2702i	−0.314934	−	0.114626i	0.179717	−	0.983718i	$-0.442482\pi$
$709$	−223.288	−	81.2702i	−0.314934	−	0.114626i	−0.494651	+	0.869092i	$0.664704\pi$
$710$	−84.0958	−	48.5527i	−0.118445	−	0.0683841i
$711$	689.240	−	532.383i	0.969396	−	0.748781i
$712$	−325.505	+	187.930i	−0.457169	+	0.263947i
$713$	134.536	−	369.636i	0.188691	−	0.518423i
$714$	486.083	+	477.864i	0.680789	+	0.669277i
$715$	63.3295	+	53.1398i	0.0885727	+	0.0743213i
$716$	97.1094	−	35.3449i	0.135628	−	0.0493644i
$717$	−273.827	−	239.367i	−0.381907	−	0.333844i
$718$	−43.2725	−	245.410i	−0.0602681	−	0.341797i
$719$	−738.700	+	426.489i	−1.02740	+	0.593169i	−0.916239	−	0.400633i	$-0.868790\pi$
$719$	−738.700	+	426.489i	−1.02740	+	0.593169i	−0.111161	+	0.993802i	$0.535457\pi$
$720$	−40.9834	−	25.9254i	−0.0569214	−	0.0360075i
$721$	470.952	−	715.511i	0.653193	−	0.992388i
$722$	−122.450	−	694.447i	−0.169598	−	0.961838i
$723$	−619.828	−	769.765i	−0.857299	−	1.06468i
$724$	−57.1175	+	68.0700i	−0.0788916	+	0.0940194i
$725$	−95.4410	+	34.7377i	−0.131643	+	0.0479140i
$726$	−218.632	−	4.42085i	−0.301146	−	0.00608933i
$727$	558.888	+	666.057i	0.768760	+	0.916172i	0.998368	−	0.0571110i	$-0.0181889\pi$
$727$	558.888	+	666.057i	0.768760	+	0.916172i	−0.229608	+	0.973283i	$0.573744\pi$
$728$	80.1574	−	121.782i	0.110106	−	0.167283i
$729$	723.643	+	88.2158i	0.992651	+	0.121009i
$730$	44.6542	−	77.3433i	0.0611701	−	0.105950i
$731$	23.2473	−	63.8715i	0.0318021	−	0.0873755i
$732$	−179.722	−	108.665i	−0.245521	−	0.148449i
$733$	−6.59708	+	7.86210i	−0.00900011	+	0.0107259i	−0.770526	−	0.637409i	$-0.780006\pi$
$733$	−6.59708	+	7.86210i	−0.00900011	+	0.0107259i	0.761526	+	0.648135i	$0.224451\pi$
$734$	−165.869	−	455.720i	−0.225979	−	0.620872i
$735$	197.884	−	7.37874i	0.269230	−	0.0100391i
$736$	−7.80755	−	44.2788i	−0.0106081	−	0.0601615i
$737$	−629.644			−0.854334
$738$	22.2090	−	548.944i	0.0300934	−	0.743827i
$739$	745.545			1.00886			0.504428	−	0.863454i	$-0.331703\pi$
$739$	745.545			1.00886			0.504428	+	0.863454i	$0.331703\pi$
$740$	−85.8530	−	102.316i	−0.116018	−	0.138264i
$741$	−612.993	+	209.177i	−0.827251	+	0.282290i
$742$	−272.521	−	911.427i	−0.367279	−	1.22834i
$743$	579.579	+	486.324i	0.780052	+	0.654541i	0.943262	−	0.332050i	$-0.107740\pi$
$743$	579.579	+	486.324i	0.780052	+	0.654541i	−0.163210	+	0.986591i	$0.552185\pi$
$744$	135.620	+	397.435i	0.182285	+	0.534187i
$745$	179.197	−	31.5972i	0.240533	−	0.0424124i
$746$	−757.790			−1.01580
$747$	−456.336	+	1111.73i	−0.610891	+	1.48826i
$748$	331.314	−	191.284i	0.442933	−	0.255728i
$749$	599.690	+	806.103i	0.800654	+	1.07624i
$750$	172.715	+	214.495i	0.230287	+	0.285994i
$751$	22.4795	−	127.487i	0.0299327	−	0.169757i	−0.966177	−	0.257880i	$-0.916976\pi$
$751$	22.4795	−	127.487i	0.0299327	−	0.169757i	0.996110	+	0.0881236i	$0.0280870\pi$
$752$	89.6882	+	246.416i	0.119266	+	0.327681i
$753$	−22.3467	+	1105.15i	−0.0296768	+	1.46766i
$754$	−44.9262	+	7.92171i	−0.0595838	+	0.0105062i
$755$		−	191.045i		−	0.253040i
$756$	−44.9417	+	375.319i	−0.0594467	+	0.496454i
$757$	844.969			1.11621			0.558104	−	0.829771i	$-0.311529\pi$
$757$	844.969			1.11621			0.558104	+	0.829771i	$0.311529\pi$
$758$	137.090	+	777.477i	0.180858	+	1.02569i
$759$	−95.8625	−	174.074i	−0.126301	−	0.229346i
$760$	−104.973	+	38.2072i	−0.138123	+	0.0502726i
$761$	18.5193	+	3.26546i	0.0243355	+	0.00429101i	0.185803	−	0.982587i	$-0.440511\pi$
$761$	18.5193	+	3.26546i	0.0243355	+	0.00429101i	−0.161467	+	0.986878i	$0.551623\pi$
$762$	−110.401	−	709.737i	−0.144883	−	0.931413i
$763$	668.249	−	77.8738i	0.875817	−	0.102063i
$764$	33.2330	+	57.5612i	0.0434987	+	0.0753419i
$765$	−265.116	+	84.5237i	−0.346557	+	0.110489i
$766$			832.053i			1.08623i
$767$	63.0418	+	357.528i	0.0821926	+	0.466138i
$768$	36.1389	+	31.5909i	0.0470558	+	0.0411339i
$769$	728.264	−	867.912i	0.947028	−	1.12862i	−0.0445366	−	0.999008i	$-0.514181\pi$
$769$	728.264	−	867.912i	0.947028	−	1.12862i	0.991564	−	0.129616i	$-0.0413744\pi$
$770$	25.6677	−	108.134i	0.0333347	−	0.140434i
$771$	99.8944	+	19.7043i	0.129565	+	0.0255568i
$772$	65.8022	−	55.2146i	0.0852361	−	0.0715215i
$773$			803.377i			1.03930i	0.854380	+	0.519649i	$0.173937\pi$
$773$			803.377i			1.03930i	−0.854380	+	0.519649i	$0.826063\pi$
$774$	35.9119	−	11.4494i	0.0463978	−	0.0147925i
$775$		−	1147.45i		−	1.48058i
$776$	−188.261	+	33.1956i	−0.242605	+	0.0427778i
$777$	−431.917	+	947.253i	−0.555878	+	1.21912i
$778$	−310.858	+	113.143i	−0.399561	+	0.145428i
$779$	−969.470	−	813.482i	−1.24451	−	1.04426i
$780$	28.7106	+	52.1347i	0.0368085	+	0.0668393i
$781$	399.190	+	145.293i	0.511127	+	0.186035i
$782$	−223.427	−	128.995i	−0.285712	−	0.164956i
$783$	95.0470	−	70.3948i	0.121388	−	0.0899040i
$784$	−194.659	−	22.8883i	−0.248290	−	0.0291943i
$785$	130.712	−	109.680i	0.166512	−	0.139720i
$786$	−241.041	+	132.742i	−0.306668	+	0.168883i
$787$	309.469	+	850.259i	0.393226	+	1.08038i	0.965519	+	0.260331i	$0.0838317\pi$
$787$	309.469	+	850.259i	0.393226	+	1.08038i	−0.572293	+	0.820049i	$0.693946\pi$
$788$	418.505	+	351.167i	0.531098	+	0.445644i
$789$	123.206	+	792.060i	0.156155	+	1.00388i
$790$	−181.548	+	32.0118i	−0.229808	+	0.0405213i
$791$	−12.4957	+	213.277i	−0.0157973	+	0.269629i
$792$	196.261	+	80.5598i	0.247805	+	0.101717i
$793$	128.877	+	223.222i	0.162518	+	0.281490i
$794$	703.693	−	124.080i	0.886264	−	0.156272i
$795$	381.005	+	75.1535i	0.479251	+	0.0945327i
$796$	46.0027	+	126.391i	0.0577923	+	0.158783i
$797$	414.269	−	493.706i	0.519785	−	0.619456i	−0.440745	−	0.897632i	$-0.645286\pi$
$797$	414.269	−	493.706i	0.519785	−	0.619456i	0.960530	+	0.278177i	$0.0897301\pi$
$798$	620.934	+	610.434i	0.778112	+	0.764955i
$799$	1413.94	+	514.630i	1.76963	+	0.644093i
$800$	−65.5781	−	113.585i	−0.0819727	−	0.141981i
$801$	−1059.08	+	555.632i	−1.32219	+	0.693672i
$802$	156.245	−	270.624i	0.194819	−	0.337436i
$803$	−133.627	+	367.137i	−0.166410	+	0.457206i
$804$	−422.743	−	163.618i	−0.525799	−	0.203505i
$805$	−71.8072	+	21.4707i	−0.0892014	+	0.0266717i
$806$	89.4957	−	507.555i	0.111037	−	0.629721i
$807$	−0.697042	+	34.4720i	−0.000863745	+	0.0427163i
$808$	−131.621	+	361.625i	−0.162897	+	0.447555i
$809$	395.895	+	685.711i	0.489364	+	0.847603i	0.999925	−	0.0122382i	$-0.00389563\pi$
$809$	395.895	+	685.711i	0.489364	+	0.847603i	−0.510561	+	0.859841i	$0.670562\pi$
$810$	−126.967	−	87.6984i	−0.156749	−	0.108270i
$811$			860.536i			1.06108i	0.847660	+	0.530540i	$0.178011\pi$
$811$			860.536i			1.06108i	−0.847660	+	0.530540i	$0.821989\pi$
$812$	36.6060	+	49.2057i	0.0450812	+	0.0605982i
$813$	−376.127	+	207.134i	−0.462641	+	0.254777i
$814$	447.602	+	375.583i	0.549879	+	0.461404i
$815$	−135.106	+	161.013i	−0.165774	+	0.197561i
$816$	272.151	−	42.3335i	0.333518	−	0.0518793i
$817$	29.6967	−	81.5909i	0.0363484	−	0.0998664i
$818$	586.008	−	338.332i	0.716391	−	0.413609i
$819$	270.516	−	376.881i	0.330300	−	0.460172i
$820$	−58.1461	+	100.712i	−0.0709099	+	0.122819i
$821$	−311.954	+	261.761i	−0.379968	+	0.318831i	−0.812690	−	0.582696i	$-0.801998\pi$
$821$	−311.954	+	261.761i	−0.379968	+	0.318831i	0.432722	+	0.901528i	$0.357553\pi$
$822$	470.096	+	410.935i	0.571892	+	0.499921i
$823$	−237.212	+	1345.30i	−0.288229	+	1.63463i	0.405291	+	0.914188i	$0.367170\pi$
$823$	−237.212	+	1345.30i	−0.288229	+	1.63463i	−0.693520	+	0.720438i	$0.743941\pi$
$824$	−118.379	−	325.243i	−0.143663	−	0.394712i
$825$	−436.443	−	381.518i	−0.529022	−	0.462446i
$826$	391.584	−	291.314i	0.474073	−	0.352680i
$827$	−165.208	+	286.149i	−0.199768	+	0.346009i	−0.948453	−	0.316917i	$-0.897352\pi$
$827$	−165.208	+	286.149i	−0.199768	+	0.346009i	0.748685	+	0.662926i	$0.230686\pi$
$828$	−19.1276	−	141.784i	−0.0231010	−	0.171236i
$829$	−820.568	−	473.755i	−0.989829	−	0.571478i	−0.0846056	−	0.996415i	$-0.526963\pi$
$829$	−820.568	−	473.755i	−0.989829	−	0.571478i	−0.905223	+	0.424937i	$0.860296\pi$
$830$	194.865	−	163.511i	0.234777	−	0.197001i
$831$	−197.568	−	1270.11i	−0.237747	−	1.52841i
$832$	−20.1484	−	55.3572i	−0.0242168	−	0.0665351i
$833$	−818.569	+	771.215i	−0.982676	+	0.925829i
$834$	−266.638	−	161.217i	−0.319709	−	0.193306i
$835$	35.4303	+	200.935i	0.0424315	+	0.240641i
$836$	423.228	−	244.351i	0.506253	−	0.292285i
$837$	380.066	+	1281.04i	0.454081	+	1.53052i
$838$	−332.451	−	191.940i	−0.396719	−	0.229046i
$839$	−867.615	−	1033.98i	−1.03411	−	1.23240i	−0.972160	−	0.234320i	$-0.924714\pi$
$839$	−867.615	−	1033.98i	−1.03411	−	1.23240i	−0.0619461	−	0.998079i	$-0.519731\pi$
$840$	45.3329	−	65.9315i	0.0539677	−	0.0784898i
$841$	−142.706	+	809.325i	−0.169686	+	0.962337i
$842$	179.526	−	1018.14i	0.213214	−	1.20919i
$843$	314.779	−	253.465i	0.373403	−	0.300670i
$844$	107.248	−	89.9922i	0.127072	−	0.106626i
$845$			154.612i			0.182973i
$846$	253.456	+	794.988i	0.299594	+	0.939702i
$847$	21.1026	−	360.180i	0.0249145	−	0.425242i
$848$	−361.201	−	131.467i	−0.425945	−	0.155031i
$849$	302.493	−	346.041i	0.356293	−	0.407587i
$850$	−741.140	−	130.683i	−0.871929	−	0.153745i
$851$	68.4232	−	388.047i	0.0804033	−	0.455990i
$852$	230.260	+	201.282i	0.270258	+	0.236247i
$853$	−41.6226	+	114.357i	−0.0487955	+	0.134065i	−0.961696	−	0.274117i	$-0.911615\pi$
$853$	−41.6226	+	114.357i	−0.0487955	+	0.134065i	0.912901	+	0.408181i	$0.133837\pi$
$854$	190.512	−	289.442i	0.223082	−	0.338925i
$855$	−338.665	+	107.972i	−0.396099	+	0.126284i
$856$	405.962			0.474255
$857$	−436.277	−	519.935i	−0.509075	−	0.606692i	0.448886	−	0.893589i	$-0.351821\pi$
$857$	−436.277	−	519.935i	−0.509075	−	0.606692i	−0.957962	+	0.286897i	$0.907376\pi$
$858$	−163.297	−	202.799i	−0.190323	−	0.236363i
$859$	1039.52	+	183.296i	1.21015	+	0.213383i	0.742083	−	0.670308i	$-0.233838\pi$
$859$	1039.52	+	183.296i	1.21015	+	0.213383i	0.468071	+	0.883691i	$0.344949\pi$
$860$	−7.85738	−	1.38547i	−0.00913648	−	0.00161101i
$861$	903.645	+	71.3003i	1.04953	+	0.0828110i
$862$	747.731	−	627.421i	0.867437	−	0.727866i
$863$	82.0848	−	142.175i	0.0951157	−	0.164745i	−0.814541	−	0.580106i	$-0.803011\pi$
$863$	82.0848	−	142.175i	0.0951157	−	0.164745i	0.909657	+	0.415361i	$0.136345\pi$
$864$	110.836	+	105.088i	0.128282	+	0.121629i
$865$	169.686	+	293.904i	0.196168	+	0.339774i
$866$	−864.131	+	152.370i	−0.997842	+	0.175946i
$867$	369.106	−	610.466i	0.425727	−	0.704113i
$868$	−663.823	+	198.486i	−0.764773	+	0.228671i
$869$	757.837	−	275.830i	0.872079	−	0.317411i
$870$	−24.7385	+	3.84813i	−0.0284351	+	0.00442313i
$871$	357.604	+	426.175i	0.410567	+	0.489294i
$872$	135.920	−	235.421i	0.155872	−	0.269978i
$873$	−602.825	+	81.3253i	−0.690521	+	0.0931561i
$874$	−285.410	−	164.782i	−0.326556	−	0.188537i
$875$	−364.552	+	271.204i	−0.416631	+	0.309948i
$876$	−185.120	+	211.771i	−0.211325	+	0.241748i
$877$	−6.96482	+	2.53499i	−0.00794164	+	0.00289052i	−0.345988	−	0.938239i	$-0.612456\pi$
$877$	−6.96482	+	2.53499i	−0.00794164	+	0.00289052i	0.338046	+	0.941129i	$0.390234\pi$
$878$	−918.022	−	161.872i	−1.04558	−	0.184365i
$879$	−468.232	+	535.641i	−0.532687	+	0.609376i
$880$	−28.8656	−	34.4007i	−0.0328019	−	0.0390917i
$881$	863.867	+	498.754i	0.980553	+	0.566122i	0.902437	−	0.430822i	$-0.141776\pi$
$881$	863.867	+	498.754i	0.980553	+	0.566122i	0.0781158	+	0.996944i	$0.475110\pi$
$882$	−615.951	−	97.8096i	−0.698357	−	0.110895i
$883$	−804.506	−	1393.44i	−0.911105	−	1.57808i	−0.812506	−	0.582953i	$-0.801897\pi$
$883$	−804.506	−	1393.44i	−0.911105	−	1.57808i	−0.0985992	−	0.995127i	$-0.531436\pi$
$884$	−317.639	−	115.611i	−0.359320	−	0.130782i
$885$	30.6238	+	196.872i	0.0346032	+	0.222454i
$886$	−242.544	−	203.518i	−0.273752	−	0.229705i
$887$	−306.716	+	365.530i	−0.345791	+	0.412097i	−0.910708	−	0.413050i	$-0.864463\pi$
$887$	−306.716	+	365.530i	−0.345791	+	0.412097i	0.564918	+	0.825147i	$0.308908\pi$
$888$	202.921	+	368.479i	0.228515	+	0.414953i
$889$	1177.12	−	137.175i	1.32410	−	0.154303i
$890$	253.158			0.284447
$891$	613.627	+	281.375i	0.688695	+	0.315797i
$892$	156.533	−	90.3742i	0.175485	−	0.101316i
$893$	1806.19	+	657.400i	2.02261	+	0.736170i
$894$	−572.970	−	11.5857i	−0.640906	−	0.0129594i
$895$	−68.5474	−	12.0868i	−0.0765893	−	0.0135048i
$896$	−54.3674	+	57.5863i	−0.0606779	+	0.0642705i
$897$	−63.3772	+	163.749i	−0.0706547	+	0.182552i
$898$	248.217	+	90.3436i	0.276411	+	0.100605i
$899$	187.752	+	108.399i	0.208845	+	0.120577i
$900$	−193.887	−	369.564i	−0.215430	−	0.410627i
$901$	−1910.09	+	1102.79i	−2.11997	+	1.22396i
$902$	174.001	−	478.064i	0.192906	−	0.530005i
$903$	16.6076	+	59.9316i	0.0183916	+	0.0663694i
$904$	66.1285	+	55.4884i	0.0731510	+	0.0613810i
$905$	56.2409	−	20.4700i	0.0621446	−	0.0226188i
$906$	−116.441	+	590.322i	−0.128523	+	0.651569i
$907$	9.53153	+	54.0560i	0.0105089	+	0.0595987i	0.989611	−	0.143769i	$-0.0459223\pi$
$907$	9.53153	+	54.0560i	0.0105089	+	0.0595987i	−0.979102	+	0.203368i	$0.934811\pi$
$908$	−429.919	+	248.214i	−0.473479	+	0.273363i
$909$	−464.988	+	1132.81i	−0.511538	+	1.24622i
$910$	−87.7688	+	44.0413i	−0.0964492	+	0.0483970i
$911$	−113.053	−	641.153i	−0.124097	−	0.703790i	−0.981840	−	0.189711i	$-0.939245\pi$
$911$	−113.053	−	641.153i	−0.124097	−	0.703790i	0.857743	−	0.514079i	$-0.171866\pi$
$912$	347.651	−	54.0778i	0.381197	−	0.0592958i
$913$	−715.315	+	852.479i	−0.783477	+	0.933712i
$914$	−385.890	+	140.452i	−0.422199	+	0.153668i
$915$	68.2372	+	123.910i	0.0745761	+	0.135420i
$916$	414.575	+	494.071i	0.452593	+	0.539379i
$917$	−203.622	−	405.793i	−0.222052	−	0.442523i
$918$	870.716	−	99.5877i	0.948492	−	0.108483i
$919$	−238.753	+	413.533i	−0.259797	+	0.449981i	−0.966187	−	0.257841i	$-0.916989\pi$
$919$	−238.753	+	413.533i	−0.259797	+	0.449981i	0.706391	+	0.707822i	$0.250322\pi$
$920$	−10.3576	+	28.4574i	−0.0112583	+	0.0309319i
$921$	−1175.17	+	647.166i	−1.27597	+	0.702678i
$922$	−428.205	+	510.315i	−0.464430	+	0.553487i
$923$	−128.376	−	352.711i	−0.139086	−	0.382135i
$924$	−145.220	+	318.487i	−0.157164	+	0.344683i
$925$	−199.594	−	1131.95i	−0.215777	−	1.22373i
$926$	−105.421			−0.113845
$927$	−334.535	−	1049.30i	−0.360879	−	1.13193i
$928$	24.7805			0.0267031
$929$	860.490	+	1025.49i	0.926254	+	1.10387i	0.994346	+	0.106188i	$0.0338645\pi$
$929$	860.490	+	1025.49i	0.926254	+	1.10387i	−0.0680917	+	0.997679i	$0.521691\pi$
$930$	54.7368	−	277.499i	0.0588568	−	0.298386i
$931$	−1045.66	+	985.167i	−1.12316	+	1.05818i
$932$	−370.682	−	311.039i	−0.397728	−	0.333733i
$933$	−195.325	+	223.445i	−0.209352	+	0.239491i
$934$	231.774	−	40.8681i	0.248152	−	0.0437560i
$935$	−257.676			−0.275589
$936$	−56.9387	−	178.593i	−0.0608320	−	0.190805i
$937$	488.435	−	281.998i	0.521275	−	0.300958i	−0.216181	−	0.976353i	$-0.569360\pi$
$937$	488.435	−	281.998i	0.521275	−	0.300958i	0.737456	+	0.675395i	$0.236027\pi$
$938$	296.468	−	686.640i	0.316064	−	0.732026i
$939$	−56.6045	+	8.80494i	−0.0602817	+	0.00937693i
$940$	30.6703	−	173.940i	0.0326280	−	0.185043i
$941$	380.480	+	1045.36i	0.404336	+	1.11090i	0.960123	+	0.279579i	$0.0901948\pi$
$941$	380.480	+	1045.36i	0.404336	+	1.11090i	−0.555787	+	0.831325i	$0.687583\pi$
$942$	−470.744	+	259.239i	−0.499729	+	0.275201i
$943$	−337.868	+	59.5753i	−0.358291	+	0.0631763i
$944$		−	197.206i		−	0.208904i
$945$	152.611	−	203.790i	0.161493	−	0.215651i
$946$	34.9041			0.0368965
$947$	−313.893	−	1780.17i	−0.331460	−	1.87980i	−0.459721	−	0.888063i	$-0.652051\pi$
$947$	−313.893	−	1780.17i	−0.331460	−	1.87980i	0.128261	−	0.991740i	$-0.459061\pi$
$948$	580.488	+	11.7378i	0.612329	+	0.0123816i
$949$	324.390	−	118.068i	0.341823	−	0.124413i
$950$	−946.748	−	166.937i	−0.996577	−	0.175723i
$951$	−607.994	+	489.567i	−0.639321	+	0.514792i
$952$	52.6001	+	451.371i	0.0552522	+	0.474129i
$953$	−275.108	−	476.502i	−0.288676	−	0.500002i	0.684818	−	0.728714i	$-0.259882\pi$
$953$	−275.108	−	476.502i	−0.288676	−	0.500002i	−0.973494	+	0.228713i	$0.926548\pi$
$954$	−1131.49	−	464.443i	−1.18604	−	0.486838i
$955$		−	44.7676i		−	0.0468770i
$956$	−42.1039	−	238.783i	−0.0440417	−	0.249773i
$957$	103.657	−	35.3716i	0.108314	−	0.0369609i
$958$	−164.725	+	196.311i	−0.171947	+	0.204918i
$959$	−707.213	+	749.085i	−0.737448	+	0.781110i
$960$	−10.4411	−	30.5976i	−0.0108761	−	0.0318725i
$961$	−1140.08	+	956.643i	−1.18635	+	0.995466i
$962$		−	516.270i		−	0.536663i
$963$	1290.71	+	52.2189i	1.34030	+	0.0542252i
$964$		−	658.862i		−	0.683467i
$965$	−56.9774	+	10.0467i	−0.0590439	+	0.0104110i
$966$	234.968	−	22.5774i	0.243238	−	0.0233720i
$967$	1250.37	−	455.098i	1.29304	−	0.470629i	0.398318	−	0.917248i	$-0.369594\pi$
$967$	1250.37	−	455.098i	1.29304	−	0.470629i	0.894724	+	0.446619i	$0.147372\pi$
$968$	−111.677	−	93.7084i	−0.115369	−	0.0968062i
$969$	1044.54	−	1727.58i	1.07796	−	1.78284i
$970$	120.993	+	44.0378i	0.124735	+	0.0453998i
$971$	657.990	+	379.891i	0.677642	+	0.391237i	0.798966	−	0.601376i	$-0.205381\pi$
$971$	657.990	+	379.891i	0.677642	+	0.391237i	−0.121324	+	0.992613i	$0.538714\pi$
$972$	338.871	+	348.371i	0.348633	+	0.358406i
$973$	282.646	−	429.421i	0.290489	−	0.441337i
$974$	−844.822	+	708.890i	−0.867374	+	0.727813i
$975$	−10.3547	+	512.088i	−0.0106202	+	0.525219i
$976$	−47.8871	−	131.569i	−0.0490647	−	0.134804i
$977$	−714.502	−	599.539i	−0.731323	−	0.613653i	0.199169	−	0.979965i	$-0.436176\pi$
$977$	−714.502	−	599.539i	−0.731323	−	0.613653i	−0.930492	+	0.366312i	$0.880620\pi$
$978$	515.608	−	415.177i	0.527207	−	0.424516i
$979$	−1090.67	+	192.314i	−1.11406	+	0.196439i
$980$	105.837	+	78.9063i	0.107997	+	0.0805166i
$981$	462.424	−	731.009i	0.471380	−	0.745167i
$982$	−81.5873	−	141.313i	−0.0830828	−	0.143904i
$983$	−130.229	+	22.9629i	−0.132481	+	0.0233600i	−0.239495	−	0.970897i	$-0.576982\pi$
$983$	−130.229	+	22.9629i	−0.132481	+	0.0233600i	0.107014	+	0.994257i	$0.465871\pi$
$984$	241.053	−	275.756i	0.244973	−	0.280240i
$985$	−125.853	−	345.778i	−0.127769	−	0.351043i
$986$	91.3981	−	108.924i	0.0926959	−	0.110471i
$987$	−1326.72	+	367.645i	−1.34419	+	0.372487i
$988$	−405.759	−	147.684i	−0.410687	−	0.149478i
$989$	−11.7691	−	20.3846i	−0.0119000	−	0.0206113i
$990$	−87.3499	−	113.086i	−0.0882322	−	0.114228i
$991$	575.089	−	996.083i	0.580311	−	1.00513i	−0.415131	−	0.909762i	$-0.636264\pi$
$991$	575.089	−	996.083i	0.580311	−	1.00513i	0.995442	−	0.0953671i	$-0.0304025\pi$
$992$	−95.7514	+	263.075i	−0.0965236	+	0.265196i
$993$	178.841	−	144.006i	0.180102	−	0.145021i
$994$	−346.404	+	366.914i	−0.348495	+	0.369128i
$995$	15.7313	−	89.2169i	0.0158104	−	0.0896652i
$996$	−701.785	+	386.474i	−0.704604	+	0.388026i
$997$	−111.851	+	307.307i	−0.112187	+	0.308232i	−0.983062	−	0.183273i	$-0.941331\pi$
$997$	−111.851	+	307.307i	−0.112187	+	0.308232i	0.870875	+	0.491505i	$0.163553\pi$
$998$	552.785	+	957.452i	0.553893	+	0.959370i
$999$	597.767	+	1197.64i	0.598365	+	1.19883i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.3.x.a.103.32	✓	288
7.3	odd	6		378.3.be.a.157.1	yes	288
27.16	even	9		378.3.be.a.313.1	yes	288
189.178	odd	18	inner	378.3.x.a.367.32	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.3.x.a.103.32	✓	288	1.1	even	1	trivial
378.3.x.a.367.32	yes	288	189.178	odd	18	inner
378.3.be.a.157.1	yes	288	7.3	odd	6
378.3.be.a.313.1	yes	288	27.16	even	9

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	378.x (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.245576 + 1.39273i) q^{2} +(-1.55222 + 2.56722i) q^{3} +(-1.87939 + 0.684040i) q^{4} +(1.32662 + 0.233919i) q^{5} +(-3.95663 - 1.53137i) q^{6} +(2.77477 - 6.42656i) q^{7} +(-1.41421 - 2.44949i) q^{8} +(-4.18124 - 7.96977i) q^{9} +1.90506i q^{10} +(-1.44720 - 8.20750i) q^{11} +(1.16113 - 5.88658i) q^{12} +(-4.73332 + 5.64095i) q^{13} +(9.63187 + 2.28630i) q^{14} +(-2.65972 + 3.04263i) q^{15} +(3.06418 - 2.57115i) q^{16} -22.9520i q^{17} +(10.0729 - 7.78052i) q^{18} -29.3193i q^{19} +(-2.65324 + 0.467837i) q^{20} +(12.1913 + 17.0989i) q^{21} +(11.0754 - 4.03112i) q^{22} +(-6.08869 - 5.10902i) q^{23} +(8.48355 + 0.171542i) q^{24} +(-21.7871 - 7.92986i) q^{25} +(-9.01870 - 5.20695i) q^{26} +(26.9504 + 1.63664i) q^{27} +(-0.818842 + 13.9760i) q^{28} +(3.35575 - 2.81580i) q^{29} +(-4.89072 - 2.95707i) q^{30} +(16.9266 + 46.5055i) q^{31} +(4.33340 + 3.63616i) q^{32} +(23.3168 + 9.02453i) q^{33} +(31.9658 - 5.63644i) q^{34} +(5.18435 - 7.87652i) q^{35} +(13.3098 + 12.1181i) q^{36} +(24.7875 + 42.9333i) q^{37} +(40.8339 - 7.20011i) q^{38} +(-7.13443 - 20.9075i) q^{39} +(-1.30314 - 3.58035i) q^{40} +(27.7456 - 33.0659i) q^{41} +(-20.8202 + 21.1783i) q^{42} +(2.78284 + 1.01287i) q^{43} +(8.33411 + 14.4351i) q^{44} +(-3.68264 - 11.5509i) q^{45} +(5.62024 - 9.73454i) q^{46} +(-22.4221 + 61.6041i) q^{47} +(1.84444 + 11.8574i) q^{48} +(-33.6013 - 35.6645i) q^{49} +(5.69376 - 32.2909i) q^{50} +(58.9227 + 35.6264i) q^{51} +(5.03709 - 13.8393i) q^{52} +(-48.0478 - 83.2212i) q^{53} +(4.33896 + 37.9364i) q^{54} -11.2267i q^{55} +(-19.6659 + 2.29175i) q^{56} +(75.2692 + 45.5100i) q^{57} +(4.74574 + 3.98215i) q^{58} +(31.6904 - 37.7671i) q^{59} +(2.91736 - 7.53763i) q^{60} +(11.9718 - 32.8922i) q^{61} +(-60.6128 + 34.9948i) q^{62} +(-62.8202 + 4.75671i) q^{63} +(-4.00000 + 6.92820i) q^{64} +(-7.59883 + 6.37618i) q^{65} +(-6.84267 + 34.6902i) q^{66} +(13.1192 - 74.4025i) q^{67} +(15.7001 + 43.1356i) q^{68} +(22.5669 - 7.70070i) q^{69} +(12.2430 + 5.28612i) q^{70} +(-25.4862 + 44.1433i) q^{71} +(-13.6087 + 21.5129i) q^{72} +(-40.5988 - 23.4397i) q^{73} +(-53.7072 + 45.0657i) q^{74} +(54.1760 - 43.6235i) q^{75} +(20.0556 + 55.1023i) q^{76} +(-56.7616 - 13.4734i) q^{77} +(27.3664 - 15.0707i) q^{78} +(16.8035 + 95.2976i) q^{79} +(4.66643 - 2.69417i) q^{80} +(-46.0344 + 66.6471i) q^{81} +(52.8654 + 30.5219i) q^{82} +(-85.8298 - 102.288i) q^{83} +(-34.6085 - 23.7960i) q^{84} +(5.36889 - 30.4485i) q^{85} +(-0.727255 + 4.12447i) q^{86} +(2.01995 + 12.9857i) q^{87} +(-18.0575 + 15.1521i) q^{88} -132.887i q^{89} +(15.1829 - 7.96553i) q^{90} +(23.1180 + 46.0713i) q^{91} +(14.9378 + 5.43690i) q^{92} +(-145.664 - 28.7323i) q^{93} +(-91.3041 - 16.0994i) q^{94} +(6.85834 - 38.8956i) q^{95} +(-16.0612 + 5.48070i) q^{96} +(23.1162 - 63.5113i) q^{97} +(41.4193 - 55.5558i) q^{98} +(-59.3607 + 45.8514i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 36 q^{6} - 12 q^{9} + 36 q^{11} + 36 q^{14} - 24 q^{15} + 186 q^{21} + 126 q^{23} + 36 q^{29} - 72 q^{30} + 162 q^{35} - 48 q^{36} + 246 q^{39} - 48 q^{42} + 324 q^{47} - 72 q^{49} + 288 q^{50}+ \cdots - 216 q^{99}+O(q^{100}) \) 288 * q - 36 * q^6 - 12 * q^9 + 36 * q^11 + 36 * q^14 - 24 * q^15 + 186 * q^21 + 126 * q^23 + 36 * q^29 - 72 * q^30 + 162 * q^35 - 48 * q^36 + 246 * q^39 - 48 * q^42 + 324 * q^47 - 72 * q^49 + 288 * q^50 - 198 * q^51 + 270 * q^53 + 432 * q^54 - 144 * q^56 + 354 * q^57 + 270 * q^59 + 72 * q^60 + 138 * q^63 - 1152 * q^64 - 360 * q^65 + 72 * q^69 + 180 * q^70 + 216 * q^71 - 96 * q^72 + 216 * q^74 - 1170 * q^75 + 234 * q^77 - 96 * q^78 - 36 * q^79 + 324 * q^81 - 24 * q^84 - 360 * q^85 + 144 * q^86 - 990 * q^87 - 198 * q^91 - 180 * q^92 + 168 * q^93 - 72 * q^95 + 216 * q^98 - 216 * q^99

Introduction

L-functions

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