LMFDB - Embedded newform 384.3.u.a.235.30

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,3,Mod(19,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([16, 23, 0]))

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

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

chi := DirichletCharacter("384.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	384.u (of order $32$, degree $16$, 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:	$10.4632421514$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			235.30
Character	$\chi$	$=$	384.235
Dual form			384.3.u.a.67.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.229020 - 1.98684i) q^{2} +(1.09880 - 1.33889i) q^{3} +(-3.89510 + 0.910053i) q^{4} +(0.643049 + 2.11985i) q^{5} +(-2.91182 - 1.87651i) q^{6} +(-0.669346 + 3.36503i) q^{7} +(2.70019 + 7.53054i) q^{8} +(-0.585271 - 2.94236i) q^{9} +O(q^{10})$	\(q+(-0.229020 - 1.98684i) q^{2} +(1.09880 - 1.33889i) q^{3} +(-3.89510 + 0.910053i) q^{4} +(0.643049 + 2.11985i) q^{5} +(-2.91182 - 1.87651i) q^{6} +(-0.669346 + 3.36503i) q^{7} +(2.70019 + 7.53054i) q^{8} +(-0.585271 - 2.94236i) q^{9} +(4.06454 - 1.76313i) q^{10} +(15.8415 + 1.56025i) q^{11} +(-3.06148 + 6.21509i) q^{12} +(-0.630919 - 0.191387i) q^{13} +(6.83908 + 0.559228i) q^{14} +(3.54484 + 1.46832i) q^{15} +(14.3436 - 7.08949i) q^{16} +(-0.591278 - 1.42747i) q^{17} +(-5.71196 + 1.83670i) q^{18} +(20.1849 - 10.7891i) q^{19} +(-4.43392 - 7.67182i) q^{20} +(3.76994 + 4.59368i) q^{21} +(-0.528036 - 31.8318i) q^{22} +(-3.36507 - 2.24847i) q^{23} +(13.0496 + 4.65930i) q^{24} +(16.7065 - 11.1629i) q^{25} +(-0.235764 + 1.29737i) q^{26} +(-4.58260 - 2.44945i) q^{27} +(-0.455184 - 13.7163i) q^{28} +(23.9449 - 2.35837i) q^{29} +(2.10548 - 7.37931i) q^{30} +(-15.4286 + 15.4286i) q^{31} +(-17.3707 - 26.8749i) q^{32} +(19.4956 - 19.4956i) q^{33} +(-2.70075 + 1.50170i) q^{34} +(-7.56377 + 0.744967i) q^{35} +(4.95739 + 10.9281i) q^{36} +(29.5819 + 15.8119i) q^{37} +(-26.0590 - 37.6334i) q^{38} +(-0.949501 + 0.634437i) q^{39} +(-14.2272 + 10.5665i) q^{40} +(3.99697 + 2.67069i) q^{41} +(8.26354 - 8.54232i) q^{42} +(-6.22436 - 7.58440i) q^{43} +(-63.1240 + 8.33924i) q^{44} +(5.86099 - 3.13277i) q^{45} +(-3.69669 + 7.20082i) q^{46} +(-3.66832 - 8.85611i) q^{47} +(6.26870 - 26.9945i) q^{48} +(34.3947 + 14.2468i) q^{49} +(-26.0051 - 30.6367i) q^{50} +(-2.56093 - 0.776849i) q^{51} +(2.63166 + 0.171303i) q^{52} +(-74.8279 - 7.36990i) q^{53} +(-3.81717 + 9.66588i) q^{54} +(6.87935 + 34.5848i) q^{55} +(-27.1478 + 4.04567i) q^{56} +(7.73382 - 38.8805i) q^{57} +(-10.1696 - 47.0347i) q^{58} +(17.8189 + 58.7411i) q^{59} +(-15.1437 - 2.49326i) q^{60} +(47.2776 - 57.6079i) q^{61} +(34.1876 + 27.1207i) q^{62} +10.2929 q^{63} +(-49.4180 + 40.6677i) q^{64} -1.46052i q^{65} +(-43.1996 - 34.2699i) q^{66} +(22.0763 + 18.1175i) q^{67} +(3.60216 + 5.02205i) q^{68} +(-6.70800 + 2.03485i) q^{69} +(3.21239 + 14.8574i) q^{70} +(-63.9848 - 12.7274i) q^{71} +(20.5772 - 12.3523i) q^{72} +(66.3820 - 13.2042i) q^{73} +(24.6409 - 62.3959i) q^{74} +(3.41116 - 34.6340i) q^{75} +(-68.8038 + 60.3939i) q^{76} +(-15.8537 + 52.2626i) q^{77} +(1.47798 + 1.74121i) q^{78} +(0.238866 - 0.576674i) q^{79} +(24.2523 + 25.8474i) q^{80} +(-8.31492 + 3.44415i) q^{81} +(4.39086 - 8.55299i) q^{82} +(-40.3032 - 75.4020i) q^{83} +(-18.8648 - 14.4620i) q^{84} +(2.64580 - 2.17135i) q^{85} +(-13.6435 + 14.1038i) q^{86} +(23.1531 - 34.6511i) q^{87} +(31.0254 + 123.508i) q^{88} +(-22.9784 - 34.3897i) q^{89} +(-7.56660 - 10.9274i) q^{90} +(1.06633 - 1.99496i) q^{91} +(15.1535 + 5.69562i) q^{92} +(3.70427 + 37.6101i) q^{93} +(-16.7556 + 9.31660i) q^{94} +(35.8511 + 35.8511i) q^{95} +(-55.0695 - 6.27266i) q^{96} +(99.8490 + 99.8490i) q^{97} +(20.4290 - 71.5997i) q^{98} +(-4.68074 - 47.5244i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q+O(q^{10}) $ 1024 * q	$ 1024 q + 1248 q^{50} + 1056 q^{52} + 288 q^{54} + 1568 q^{56} + 576 q^{60} + 192 q^{62} - 192 q^{64} - 576 q^{66} - 960 q^{68} - 1344 q^{70} - 2464 q^{74} - 416 q^{76} - 1440 q^{78} - 1632 q^{80}+O(q^{100}) $ 1024 * q + 1248 * q^50 + 1056 * q^52 + 288 * q^54 + 1568 * q^56 + 576 * q^60 + 192 * q^62 - 192 * q^64 - 576 * q^66 - 960 * q^68 - 1344 * q^70 - 2464 * q^74 - 416 * q^76 - 1440 * q^78 - 1632 * q^80

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$-1$	$e\left(\frac{13}{32}\right)$	$1$

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 $

$2$	−0.229020	−	1.98684i	−0.114510	−	0.993422i
$2$	−0.229020	−	1.98684i	−0.114510	−	0.993422i
$3$	1.09880	−	1.33889i	0.366267	−	0.446298i
$3$	1.09880	−	1.33889i	0.366267	−	0.446298i
$4$	−3.89510	+	0.910053i	−0.973775	+	0.227513i
$5$	0.643049	+	2.11985i	0.128610	+	0.423970i	0.997470	−	0.0710876i	$-0.0226470\pi$
$5$	0.643049	+	2.11985i	0.128610	+	0.423970i	−0.868860	+	0.495057i	$0.835147\pi$
$6$	−2.91182	−	1.87651i	−0.485303	−	0.312752i
$7$	−0.669346	+	3.36503i	−0.0956208	+	0.480718i	0.903067	+	0.429500i	$0.141310\pi$
$7$	−0.669346	+	3.36503i	−0.0956208	+	0.480718i	−0.998688	+	0.0512179i	$0.983690\pi$
$8$	2.70019	+	7.53054i	0.337523	+	0.941317i
$9$	−0.585271	−	2.94236i	−0.0650301	−	0.326928i
$10$	4.06454	−	1.76313i	0.406454	−	0.176313i
$11$	15.8415	+	1.56025i	1.44013	+	0.141841i	0.787725	−	0.616027i	$-0.211259\pi$
$11$	15.8415	+	1.56025i	1.44013	+	0.141841i	0.652408	+	0.757868i	$0.273759\pi$
$12$	−3.06148	+	6.21509i	−0.255123	+	0.517924i
$13$	−0.630919	−	0.191387i	−0.0485322	−	0.0147221i	0.265925	−	0.963994i	$-0.414323\pi$
$13$	−0.630919	−	0.191387i	−0.0485322	−	0.0147221i	−0.314457	+	0.949272i	$0.601823\pi$
$14$	6.83908	+	0.559228i	0.488506	+	0.0399449i
$15$	3.54484	+	1.46832i	0.236322	+	0.0978879i
$16$	14.3436	−	7.08949i	0.896476	−	0.443093i
$17$	−0.591278	−	1.42747i	−0.0347811	−	0.0839689i	0.905535	−	0.424273i	$-0.139470\pi$
$17$	−0.591278	−	1.42747i	−0.0347811	−	0.0839689i	−0.940316	+	0.340304i	$0.889470\pi$
$18$	−5.71196	+	1.83670i	−0.317331	+	0.102039i
$19$	20.1849	−	10.7891i	1.06237	−	0.567846i	0.154882	−	0.987933i	$-0.450500\pi$
$19$	20.1849	−	10.7891i	1.06237	−	0.567846i	0.907484	+	0.420087i	$0.138000\pi$
$20$	−4.43392	−	7.67182i	−0.221696	−	0.383591i
$21$	3.76994	+	4.59368i	0.179521	+	0.218747i
$22$	−0.528036	−	31.8318i	−0.0240016	−	1.44690i
$23$	−3.36507	−	2.24847i	−0.146307	−	0.0977595i	0.480262	−	0.877125i	$-0.340542\pi$
$23$	−3.36507	−	2.24847i	−0.146307	−	0.0977595i	−0.626570	+	0.779366i	$0.715542\pi$
$24$	13.0496	+	4.65930i	0.543731	+	0.194138i
$25$	16.7065	−	11.1629i	0.668260	−	0.446517i
$26$	−0.235764	+	1.29737i	−0.00906783	+	0.0498988i
$27$	−4.58260	−	2.44945i	−0.169726	−	0.0907203i
$28$	−0.455184	−	13.7163i	−0.0162566	−	0.489866i
$29$	23.9449	−	2.35837i	0.825686	−	0.0813230i	0.323658	−	0.946174i	$-0.395087\pi$
$29$	23.9449	−	2.35837i	0.825686	−	0.0813230i	0.502028	+	0.864851i	$0.332587\pi$
$30$	2.10548	−	7.37931i	0.0701828	−	0.245977i
$31$	−15.4286	+	15.4286i	−0.497695	+	0.497695i	−0.910720	−	0.413024i	$-0.864472\pi$
$31$	−15.4286	+	15.4286i	−0.497695	+	0.497695i	0.413024	+	0.910720i	$0.364472\pi$
$32$	−17.3707	−	26.8749i	−0.542834	−	0.839840i
$33$	19.4956	−	19.4956i	0.590776	−	0.590776i
$34$	−2.70075	+	1.50170i	−0.0794338	+	0.0441675i
$35$	−7.56377	+	0.744967i	−0.216108	+	0.0212848i
$36$	4.95739	+	10.9281i	0.137705	+	0.303560i
$37$	29.5819	+	15.8119i	0.799511	+	0.427348i	0.819944	−	0.572444i	$-0.194004\pi$
$37$	29.5819	+	15.8119i	0.799511	+	0.427348i	−0.0204330	+	0.999791i	$0.506504\pi$
$38$	−26.0590	−	37.6334i	−0.685762	−	0.990353i
$39$	−0.949501	+	0.634437i	−0.0243462	+	0.0162676i
$40$	−14.2272	+	10.5665i	−0.355681	+	0.264162i
$41$	3.99697	+	2.67069i	0.0974870	+	0.0651387i	0.603358	−	0.797470i	$-0.293829\pi$
$41$	3.99697	+	2.67069i	0.0974870	+	0.0651387i	−0.505871	+	0.862609i	$0.668829\pi$
$42$	8.26354	−	8.54232i	0.196751	−	0.203389i
$43$	−6.22436	−	7.58440i	−0.144752	−	0.176381i	0.695587	−	0.718442i	$-0.255144\pi$
$43$	−6.22436	−	7.58440i	−0.144752	−	0.176381i	−0.840339	+	0.542060i	$0.817644\pi$
$44$	−63.1240	+	8.33924i	−1.43464	+	0.189528i
$45$	5.86099	−	3.13277i	0.130244	−	0.0696170i
$46$	−3.69669	+	7.20082i	−0.0803628	+	0.156539i
$47$	−3.66832	−	8.85611i	−0.0780494	−	0.188428i	0.880038	−	0.474902i	$-0.157517\pi$
$47$	−3.66832	−	8.85611i	−0.0780494	−	0.188428i	−0.958088	+	0.286475i	$0.907517\pi$
$48$	6.26870	−	26.9945i	0.130598	−	0.562386i
$49$	34.3947	+	14.2468i	0.701933	+	0.290750i
$50$	−26.0051	−	30.6367i	−0.520102	−	0.612733i
$51$	−2.56093	−	0.776849i	−0.0502143	−	0.0152323i
$52$	2.63166	+	0.171303i	0.0506089	+	0.00329428i
$53$	−74.8279	−	7.36990i	−1.41185	−	0.139055i	−0.636834	−	0.771001i	$-0.719756\pi$
$53$	−74.8279	−	7.36990i	−1.41185	−	0.139055i	−0.775013	+	0.631946i	$0.782256\pi$
$54$	−3.81717	+	9.66588i	−0.0706883	+	0.178998i
$55$	6.87935	+	34.5848i	0.125079	+	0.628815i
$56$	−27.1478	+	4.04567i	−0.484783	+	0.0722442i
$57$	7.73382	−	38.8805i	0.135681	−	0.682115i
$58$	−10.1696	−	47.0347i	−0.175337	−	0.810943i
$59$	17.8189	+	58.7411i	0.302015	+	0.995612i	0.968274	+	0.249891i	$0.0803947\pi$
$59$	17.8189	+	58.7411i	0.302015	+	0.995612i	−0.666259	+	0.745721i	$0.732105\pi$
$60$	−15.1437	−	2.49326i	−0.252396	−	0.0415544i
$61$	47.2776	−	57.6079i	0.775043	−	0.944392i	−0.224505	−	0.974473i	$-0.572076\pi$
$61$	47.2776	−	57.6079i	0.775043	−	0.944392i	0.999547	+	0.0300808i	$0.00957646\pi$
$62$	34.1876	+	27.1207i	0.551413	+	0.437431i
$63$	10.2929			0.163379
$64$	−49.4180	+	40.6677i	−0.772156	+	0.635433i
$65$		−	1.46052i		−	0.0224696i
$66$	−43.1996	−	34.2699i	−0.654540	−	0.519241i
$67$	22.0763	+	18.1175i	0.329496	+	0.270411i	0.784566	−	0.620045i	$-0.212886\pi$
$67$	22.0763	+	18.1175i	0.329496	+	0.270411i	−0.455070	+	0.890456i	$0.650386\pi$
$68$	3.60216	+	5.02205i	0.0529729	+	0.0738537i
$69$	−6.70800	+	2.03485i	−0.0972175	+	0.0294906i
$70$	3.21239	+	14.8574i	0.0458912	+	0.212249i
$71$	−63.9848	−	12.7274i	−0.901194	−	0.179259i	−0.277315	−	0.960779i	$-0.589444\pi$
$71$	−63.9848	−	12.7274i	−0.901194	−	0.179259i	−0.623880	+	0.781520i	$0.714444\pi$
$72$	20.5772	−	12.3523i	0.285794	−	0.171560i
$73$	66.3820	−	13.2042i	0.909342	−	0.180879i	0.281810	−	0.959470i	$-0.409065\pi$
$73$	66.3820	−	13.2042i	0.909342	−	0.180879i	0.627532	+	0.778591i	$0.284065\pi$
$74$	24.6409	−	62.3959i	0.332985	−	0.843187i
$75$	3.41116	−	34.6340i	0.0454821	−	0.461787i
$76$	−68.8038	+	60.3939i	−0.905313	+	0.794657i
$77$	−15.8537	+	52.2626i	−0.205892	+	0.678735i
$78$	1.47798	+	1.74121i	0.0189485	+	0.0223232i
$79$	0.238866	−	0.576674i	0.00302362	−	0.00729967i	−0.922361	−	0.386330i	$-0.873742\pi$
$79$	0.238866	−	0.576674i	0.00302362	−	0.00729967i	0.925384	+	0.379031i	$0.123742\pi$
$80$	24.2523	+	25.8474i	0.303154	+	0.323092i
$81$	−8.31492	+	3.44415i	−0.102653	+	0.0425204i
$82$	4.39086	−	8.55299i	0.0535470	−	0.104305i
$83$	−40.3032	−	75.4020i	−0.485581	−	0.908458i	−0.998741	−	0.0501653i	$-0.984025\pi$
$83$	−40.3032	−	75.4020i	−0.485581	−	0.908458i	0.513160	−	0.858293i	$-0.328475\pi$
$84$	−18.8648	−	14.4620i	−0.224581	−	0.172167i
$85$	2.64580	−	2.17135i	0.0311271	−	0.0255453i
$86$	−13.6435	+	14.1038i	−0.158646	+	0.163998i
$87$	23.1531	−	34.6511i	0.266128	−	0.398288i
$88$	31.0254	+	123.508i	0.352561	+	1.40350i
$89$	−22.9784	−	34.3897i	−0.258185	−	0.386401i	0.679620	−	0.733565i	$-0.262145\pi$
$89$	−22.9784	−	34.3897i	−0.258185	−	0.386401i	−0.937804	+	0.347164i	$0.887145\pi$
$90$	−7.56660	−	10.9274i	−0.0840733	−	0.121416i
$91$	1.06633	−	1.99496i	0.0117179	−	0.0219226i
$92$	15.1535	+	5.69562i	0.164712	+	0.0619089i
$93$	3.70427	+	37.6101i	0.0398309	+	0.404410i
$94$	−16.7556	+	9.31660i	−0.178251	+	0.0991128i
$95$	35.8511	+	35.8511i	0.377380	+	0.377380i
$96$	−55.0695	−	6.27266i	−0.573641	−	0.0653402i
$97$	99.8490	+	99.8490i	1.02937	+	1.02937i	0.999555	+	0.0298160i	$0.00949214\pi$
$97$	99.8490	+	99.8490i	1.02937	+	1.02937i	0.0298160	+	0.999555i	$0.490508\pi$
$98$	20.4290	−	71.5997i	0.208459	−	0.730609i
$99$	−4.68074	−	47.5244i	−0.0472802	−	0.480044i
$100$	−54.9146	+	58.6845i	−0.549146	+	0.586845i
$101$	−13.7280	+	25.6834i	−0.135921	+	0.254291i	−0.940669	−	0.339327i	$-0.889801\pi$
$101$	−13.7280	+	25.6834i	−0.135921	+	0.254291i	0.804747	+	0.593617i	$0.202301\pi$
$102$	−0.956975	+	5.26608i	−0.00938211	+	0.0516282i
$103$	−11.0086	−	16.4755i	−0.106880	−	0.159957i	0.774174	−	0.632972i	$-0.218165\pi$
$103$	−11.0086	−	16.4755i	−0.106880	−	0.159957i	−0.881054	+	0.473016i	$0.843165\pi$
$104$	−0.262351	−	5.26794i	−0.00252261	−	0.0506533i
$105$	−7.31365	+	10.9457i	−0.0696538	+	0.104244i
$106$	2.49420	+	150.359i	0.0235302	+	1.41848i
$107$	−81.8420	+	67.1660i	−0.764879	+	0.627720i	−0.933753	−	0.357918i	$-0.883487\pi$
$107$	−81.8420	+	67.1660i	−0.764879	+	0.627720i	0.168874	+	0.985638i	$0.445987\pi$
$108$	20.0788	+	5.37045i	0.185915	+	0.0497263i
$109$	40.0600	+	74.9470i	0.367523	+	0.687587i	0.995914	−	0.0903108i	$-0.0287860\pi$
$109$	40.0600	+	74.9470i	0.367523	+	0.687587i	−0.628391	+	0.777898i	$0.716286\pi$
$110$	67.1391	−	21.5888i	0.610356	−	0.196262i
$111$	53.6750	−	22.2329i	0.483559	−	0.200297i
$112$	14.2555	+	53.0120i	0.127281	+	0.473321i
$113$	72.3215	−	174.600i	0.640013	−	1.54513i	−0.186647	−	0.982427i	$-0.559762\pi$
$113$	72.3215	−	174.600i	0.640013	−	1.54513i	0.826660	−	0.562702i	$-0.190238\pi$
$114$	−79.0208	−	6.46149i	−0.693165	−	0.0566797i
$115$	2.60251	−	8.57932i	0.0226305	−	0.0746028i
$116$	−91.1216	+	30.9772i	−0.785531	+	0.267045i
$117$	−0.193871	+	1.96840i	−0.00165701	+	0.0168239i
$118$	112.629	−	48.8563i	0.954479	−	0.414036i
$119$	5.19925	−	1.03420i	0.0436912	−	0.00869071i
$120$	−1.48551	+	30.6592i	−0.0123793	+	0.255494i
$121$	129.842	+	25.8273i	1.07308	+	0.213448i
$122$	−125.285	−	80.7399i	−1.02693	−	0.661802i
$123$	7.96764	−	2.41696i	0.0647776	−	0.0196501i
$124$	46.0550	−	74.1366i	0.371411	−	0.597876i
$125$	77.2168	+	63.3702i	0.617735	+	0.506962i
$126$	−2.35727	−	20.4503i	−0.0187085	−	0.162304i
$127$			121.745i			0.958623i	0.877645	+	0.479312i	$0.159114\pi$
$127$			121.745i			0.958623i	−0.877645	+	0.479312i	$0.840886\pi$
$128$	92.1181	+	88.8721i	0.719673	+	0.694313i
$129$	−16.9940			−0.131737
$130$	−2.90183	+	0.334489i	−0.0223218	+	0.00257299i
$131$	−9.01280	+	10.9821i	−0.0688000	+	0.0838331i	−0.806273	−	0.591543i	$-0.798519\pi$
$131$	−9.01280	+	10.9821i	−0.0688000	+	0.0838331i	0.737473	+	0.675376i	$0.236019\pi$
$132$	−58.1953	+	93.6794i	−0.440874	+	0.709693i
$133$	22.7948	+	75.1445i	0.171390	+	0.564996i
$134$	30.9408	−	48.0114i	0.230901	−	0.358294i
$135$	2.24563	−	11.2895i	0.0166343	−	0.0836262i
$136$	9.15306	−	8.30708i	0.0673019	−	0.0610815i
$137$	27.5862	+	138.685i	0.201359	+	1.01230i	0.940770	+	0.339046i	$0.110104\pi$
$137$	27.5862	+	138.685i	0.201359	+	1.01230i	−0.739411	+	0.673254i	$0.764896\pi$
$138$	5.57920	+	12.8617i	0.0404290	+	0.0932010i
$139$	−35.0805	−	3.45513i	−0.252378	−	0.0248571i	−0.0289630	−	0.999580i	$-0.509221\pi$
$139$	−35.0805	−	3.45513i	−0.252378	−	0.0248571i	−0.223415	+	0.974723i	$0.571721\pi$
$140$	28.7837	−	9.78515i	0.205598	−	0.0698939i
$141$	−15.8881	−	4.81962i	−0.112682	−	0.0341817i
$142$	−10.6335	+	130.043i	−0.0748840	+	0.915793i
$143$	−9.69606	−	4.01624i	−0.0678046	−	0.0280856i
$144$	−29.2547	−	38.0547i	−0.203158	−	0.264269i
$145$	20.3971	+	49.2430i	0.140670	+	0.339607i
$146$	−41.4375	−	128.867i	−0.283818	−	0.882648i
$147$	56.8678	−	30.3965i	0.386856	−	0.206779i
$148$	−129.614	−	34.6677i	−0.875771	−	0.234241i
$149$	104.034	+	126.766i	0.698218	+	0.850781i	0.994545	−	0.104306i	$-0.0332620\pi$
$149$	104.034	+	126.766i	0.698218	+	0.850781i	−0.296328	+	0.955086i	$0.595762\pi$
$150$	−69.5937	+	1.15444i	−0.463958	+	0.00769628i
$151$	−31.2723	−	20.8955i	−0.207102	−	0.138381i	0.447694	−	0.894187i	$-0.352245\pi$
$151$	−31.2723	−	20.8955i	−0.207102	−	0.138381i	−0.654796	+	0.755806i	$0.727245\pi$
$152$	135.751	+	122.871i	0.893097	+	0.808362i
$153$	−3.85407	+	2.57521i	−0.0251900	+	0.0168314i
$154$	107.468	+	19.5296i	0.697847	+	0.126816i
$155$	−42.6275	−	22.7849i	−0.275016	−	0.146999i
$156$	3.12103	−	3.33529i	0.0200066	−	0.0213801i
$157$	−133.497	+	13.1483i	−0.850297	+	0.0837470i	−0.513771	−	0.857927i	$-0.671752\pi$
$157$	−133.497	+	13.1483i	−0.850297	+	0.0837470i	−0.336526	+	0.941674i	$0.609252\pi$
$158$	−1.20047	−	0.342520i	−0.00759789	−	0.00216785i
$159$	−92.0885	+	92.0885i	−0.579173	+	0.579173i
$160$	45.8005	−	54.1051i	0.286253	−	0.338157i
$161$	9.81856	−	9.81856i	0.0609848	−	0.0609848i
$162$	8.74727	+	15.7317i	0.0539955	+	0.0971090i
$163$	−273.597	+	26.9469i	−1.67851	+	0.165319i	−0.891930	−	0.452173i	$-0.850649\pi$
$163$	−273.597	+	26.9469i	−1.67851	+	0.165319i	−0.786578	+	0.617491i	$0.788149\pi$
$164$	−17.9991	−	6.76515i	−0.109750	−	0.0412509i
$165$	53.8644	+	28.7911i	0.326451	+	0.174492i
$166$	−140.582	+	97.3448i	−0.846879	+	0.586414i
$167$	−142.102	+	94.9494i	−0.850909	+	0.568559i	−0.902784	−	0.430094i	$-0.858480\pi$
$167$	−142.102	+	94.9494i	−0.850909	+	0.568559i	0.0518750	+	0.998654i	$0.483480\pi$
$168$	−24.4133	+	40.7934i	−0.145318	+	0.242818i
$169$	−140.157	−	93.6499i	−0.829331	−	0.554141i
$170$	−4.92008	−	4.75952i	−0.0289417	−	0.0279971i
$171$	−43.5590	−	53.0768i	−0.254731	−	0.310390i
$172$	31.1467	+	23.8775i	0.181085	+	0.138823i
$173$	−81.7055	+	43.6725i	−0.472286	+	0.252442i	−0.690327	−	0.723497i	$-0.742533\pi$
$173$	−81.7055	+	43.6725i	−0.472286	+	0.252442i	0.218041	+	0.975940i	$0.430033\pi$
$174$	−74.1488	−	38.0658i	−0.426142	−	0.218769i
$175$	26.3811	+	63.6897i	0.150749	+	0.363941i
$176$	238.285	−	89.9283i	1.35389	−	0.510956i
$177$	98.2275	+	40.6872i	0.554958	+	0.229871i
$178$	−63.0644	+	53.5305i	−0.354294	+	0.300733i
$179$	−270.771	−	82.1375i	−1.51269	−	0.458869i	−0.578509	−	0.815676i	$-0.696365\pi$
$179$	−270.771	−	82.1375i	−1.51269	−	0.458869i	−0.934178	+	0.356807i	$0.883865\pi$
$180$	−19.9782	+	17.5362i	−0.110990	+	0.0974236i
$181$	245.684	+	24.1977i	1.35737	+	0.133689i	0.750372	−	0.661016i	$-0.229874\pi$
$181$	245.684	+	24.1977i	1.35737	+	0.133689i	0.606996	+	0.794705i	$0.292374\pi$
$182$	−4.20787	−	1.66174i	−0.0231202	−	0.00913044i
$183$	−25.1822	−	126.599i	−0.137607	−	0.691800i
$184$	7.84585	−	31.4121i	0.0426405	−	0.170718i
$185$	−14.4961	+	72.8770i	−0.0783575	+	0.393930i
$186$	73.8771	−	15.9733i	0.397189	−	0.0858778i
$187$	−7.13950	−	23.5358i	−0.0381791	−	0.125860i
$188$	22.3480	+	31.1571i	0.118872	+	0.165729i
$189$	11.3098	−	13.7810i	0.0598402	−	0.0729156i
$190$	63.0200	−	79.4412i	0.331684	−	0.418112i
$191$	32.0691			0.167901			0.0839506	−	0.996470i	$-0.473246\pi$
$191$	32.0691			0.167901			0.0839506	+	0.996470i	$0.473246\pi$
$192$	0.149200	+	110.851i	0.000777082	+	0.577350i
$193$		−	186.455i		−	0.966088i	−0.875596	−	0.483044i	$-0.839531\pi$
$193$		−	186.455i		−	0.966088i	0.875596	−	0.483044i	$-0.160469\pi$
$194$	175.517	−	221.252i	0.904727	−	1.14047i
$195$	−1.95549	−	1.60483i	−0.0100281	−	0.00822988i
$196$	−146.936	−	24.1915i	−0.749674	−	0.123426i
$197$	−237.110	+	71.9265i	−1.20360	+	0.365109i	−0.827499	−	0.561467i	$-0.810237\pi$
$197$	−237.110	+	71.9265i	−1.20360	+	0.365109i	−0.376106	+	0.926577i	$0.622737\pi$
$198$	−93.3515	+	20.1839i	−0.471472	+	0.101939i
$199$	−95.9954	−	19.0947i	−0.482389	−	0.0959531i	−0.0520953	−	0.998642i	$-0.516590\pi$
$199$	−95.9954	−	19.0947i	−0.482389	−	0.0959531i	−0.430294	+	0.902689i	$0.641590\pi$
$200$	129.173	+	95.6669i	0.645867	+	0.478334i
$201$	48.5149	−	9.65020i	0.241367	−	0.0480110i
$202$	54.1728	+	21.3935i	0.268182	+	0.105908i
$203$	−8.09145	+	82.1538i	−0.0398593	+	0.404699i
$204$	10.6820	+	0.695325i	0.0523630	+	0.00340846i
$205$	−3.09121	+	10.1904i	−0.0150791	+	0.0497090i
$206$	−30.2131	+	25.6456i	−0.146666	+	0.124493i
$207$	−4.64632	+	11.2172i	−0.0224460	+	0.0541894i
$208$	−10.4065	+	1.72771i	−0.0500312	+	0.00830631i
$209$	336.593	−	139.421i	1.61049	−	0.667087i
$210$	23.4223	+	12.0243i	0.111535	+	0.0572587i
$211$	−166.903	−	312.253i	−0.791007	−	1.47987i	−0.875380	−	0.483436i	$-0.839389\pi$
$211$	−166.903	−	312.253i	−0.791007	−	1.47987i	0.0843726	−	0.996434i	$-0.473111\pi$
$212$	298.169	−	39.3908i	1.40646	−	0.185806i
$213$	−87.3472	+	71.6840i	−0.410081	+	0.336544i
$214$	152.192	+	147.225i	0.711177	+	0.687967i
$215$	12.0752	−	18.0718i	0.0561638	−	0.0840551i
$216$	6.07180	−	41.1234i	0.0281102	−	0.190386i
$217$	−41.5905	−	62.2446i	−0.191661	−	0.286841i
$218$	139.733	−	96.7573i	0.640979	−	0.443841i
$219$	55.2616	−	103.387i	0.252336	−	0.472088i
$220$	−58.2697	−	128.451i	−0.264862	−	0.583867i
$221$	0.0998487	+	1.01378i	0.000451804	+	0.00458725i
$222$	−56.4660	−	101.552i	−0.254351	−	0.457442i
$223$	264.363	+	264.363i	1.18548	+	1.18548i	0.978302	+	0.207182i	$0.0664291\pi$
$223$	264.363	+	264.363i	1.18548	+	1.18548i	0.207182	+	0.978302i	$0.433571\pi$
$224$	102.062	−	40.4643i	0.455633	−	0.180644i
$225$	−42.6231	−	42.6231i	−0.189436	−	0.189436i
$226$	−363.465	−	103.705i	−1.60825	−	0.458871i
$227$	−8.80838	−	89.4330i	−0.0388034	−	0.393978i	−0.994895	−	0.100911i	$-0.967824\pi$
$227$	−8.80838	−	89.4330i	−0.0388034	−	0.393978i	0.956092	−	0.293067i	$-0.0946758\pi$
$228$	5.25934	+	158.482i	0.0230673	+	0.695096i
$229$	106.578	−	199.393i	0.465405	−	0.870711i	−0.534272	−	0.845312i	$-0.679414\pi$
$229$	106.578	−	199.393i	0.465405	−	0.870711i	0.999677	−	0.0253990i	$-0.00808563\pi$
$230$	−17.6418	−	3.20595i	−0.0767035	−	0.0139389i
$231$	52.5540	+	78.6526i	0.227506	+	0.340488i
$232$	82.4155	+	173.950i	0.355239	+	0.749784i
$233$	−73.1390	+	109.460i	−0.313901	+	0.469786i	−0.954551	−	0.298047i	$-0.903665\pi$
$233$	−73.1390	+	109.460i	−0.313901	+	0.469786i	0.640650	+	0.767833i	$0.278665\pi$
$234$	3.95531	−	0.0656118i	0.0169030	−	0.000280392i
$235$	16.4147	−	13.4712i	0.0698498	−	0.0573243i
$236$	−122.864	−	212.586i	−0.520610	−	0.900789i
$237$	−0.509638	−	0.953466i	−0.00215037	−	0.00402306i
$238$	−3.24551	−	10.0932i	−0.0136366	−	0.0424086i
$239$	−44.9563	+	18.6215i	−0.188102	+	0.0779143i	−0.474746	−	0.880123i	$-0.657460\pi$
$239$	−44.9563	+	18.6215i	−0.188102	+	0.0779143i	0.286644	+	0.958037i	$0.407460\pi$
$240$	61.2554	−	4.07009i	0.255231	−	0.0169587i
$241$	145.051	−	350.185i	0.601872	−	1.45305i	−0.269779	−	0.962922i	$-0.586951\pi$
$241$	145.051	−	350.185i	0.601872	−	1.45305i	0.871652	−	0.490126i	$-0.163049\pi$
$242$	21.5783	−	263.892i	0.0891664	−	1.09046i
$243$	−4.52509	+	14.9172i	−0.0186218	+	0.0613878i
$244$	−131.725	+	267.414i	−0.539855	+	1.09596i
$245$	−8.08348	+	82.0730i	−0.0329938	+	0.334992i
$246$	−6.62686	−	15.2769i	−0.0269385	−	0.0621013i
$247$	−14.8000	+	2.94389i	−0.0599188	+	0.0119186i
$248$	−157.845	−	74.5253i	−0.636473	−	0.300505i
$249$	−145.241	−	28.8901i	−0.583295	−	0.116025i
$250$	108.223	−	167.931i	0.432890	−	0.671723i
$251$	−82.2710	+	24.9566i	−0.327773	+	0.0994288i	−0.449882	−	0.893088i	$-0.648534\pi$
$251$	−82.2710	+	24.9566i	−0.327773	+	0.0994288i	0.122110	+	0.992517i	$0.461034\pi$
$252$	−40.0917	+	9.36704i	−0.159094	+	0.0371708i
$253$	−49.7995	−	40.8694i	−0.196836	−	0.161539i
$254$	241.889	−	27.8820i	0.952318	−	0.109772i
$255$		−	5.92833i		−	0.0232484i
$256$	155.478	−	203.378i	0.607337	−	0.794445i
$257$	−234.872			−0.913898			−0.456949	−	0.889493i	$-0.651058\pi$
$257$	−234.872			−0.913898			−0.456949	+	0.889493i	$0.651058\pi$
$258$	3.89197	+	33.7645i	0.0150851	+	0.130870i
$259$	−73.0079	+	88.9603i	−0.281884	+	0.343476i
$260$	1.32915	+	5.68889i	0.00511213	+	0.0218803i
$261$	−20.9534	−	69.0742i	−0.0802813	−	0.264652i
$262$	23.8839	+	15.3919i	0.0911599	+	0.0587478i
$263$	68.9919	−	346.846i	0.262327	−	1.31880i	−0.594873	−	0.803820i	$-0.702798\pi$
$263$	68.9919	−	346.846i	0.262327	−	1.31880i	0.857199	−	0.514985i	$-0.172202\pi$
$264$	199.454	+	94.1707i	0.755509	+	0.356707i
$265$	−32.4949	−	163.363i	−0.122622	−	0.616464i
$266$	144.080	−	62.4994i	0.541654	−	0.234960i
$267$	−71.2928	−	7.02173i	−0.267014	−	0.0262986i
$268$	−102.477	−	50.4790i	−0.382377	−	0.188354i
$269$	−262.916	−	79.7548i	−0.977384	−	0.296486i	−0.239114	−	0.970992i	$-0.576857\pi$
$269$	−262.916	−	79.7548i	−0.977384	−	0.296486i	−0.738270	+	0.674505i	$0.764357\pi$
$270$	−22.9448	−	1.87619i	−0.0849809	−	0.00694884i
$271$	−82.6995	−	34.2553i	−0.305164	−	0.126403i	0.224846	−	0.974394i	$-0.427812\pi$
$271$	−82.6995	−	34.2553i	−0.305164	−	0.126403i	−0.530011	+	0.847991i	$0.677812\pi$
$272$	−18.6011	−	16.2832i	−0.0683864	−	0.0598648i
$273$	−1.49935	−	3.61976i	−0.00549213	−	0.0132592i
$274$	269.228	−	86.5711i	0.982584	−	0.315953i
$275$	282.072	−	150.771i	1.02572	−	0.548257i
$276$	24.2765	−	14.0306i	0.0879584	−	0.0508355i
$277$	−143.404	−	174.738i	−0.517704	−	0.630824i	0.446882	−	0.894593i	$-0.352534\pi$
$277$	−143.404	−	174.738i	−0.517704	−	0.630824i	−0.964586	+	0.263769i	$0.915034\pi$
$278$	1.16932	+	70.4909i	0.00420620	+	0.253564i
$279$	54.4262	+	36.3664i	0.195076	+	0.130346i
$280$	−26.0336	−	54.9477i	−0.0929772	−	0.196242i
$281$	−68.5711	+	45.8177i	−0.244025	+	0.163052i	−0.671569	−	0.740942i	$-0.734379\pi$
$281$	−68.5711	+	45.8177i	−0.244025	+	0.163052i	0.427543	+	0.903995i	$0.359379\pi$
$282$	−5.93713	+	32.6710i	−0.0210536	+	0.115855i
$283$	−443.900	−	237.270i	−1.56855	−	0.838408i	−0.999874	−	0.0158476i	$-0.994955\pi$
$283$	−443.900	−	237.270i	−1.56855	−	0.838408i	−0.568677	−	0.822561i	$-0.692545\pi$
$284$	260.810	−	8.65517i	0.918344	−	0.0304759i
$285$	87.3941	−	8.60757i	0.306646	−	0.0302020i
$286$	−5.75906	+	20.1844i	−0.0201366	+	0.0705747i
$287$	−11.6623	+	11.6623i	−0.0406352	+	0.0406352i
$288$	−68.9089	+	66.8398i	−0.239267	+	0.232083i
$289$	202.666	−	202.666i	0.701266	−	0.701266i
$290$	93.1669	−	51.8036i	0.321265	−	0.178633i
$291$	243.401	−	23.9730i	0.836431	−	0.0823813i
$292$	−246.548	+	111.843i	−0.844342	+	0.383023i
$293$	−335.992	−	179.591i	−1.14673	−	0.612940i	−0.215187	−	0.976573i	$-0.569036\pi$
$293$	−335.992	−	179.591i	−1.14673	−	0.612940i	−0.931542	+	0.363633i	$0.881536\pi$
$294$	−73.4169	−	106.026i	−0.249718	−	0.360633i
$295$	−113.064	+	75.5468i	−0.383267	+	0.256091i
$296$	−39.1951	+	265.463i	−0.132416	+	0.896833i
$297$	−68.7733	−	45.9528i	−0.231560	−	0.154723i
$298$	228.039	−	235.732i	0.765232	−	0.791048i
$299$	1.69276	+	2.06263i	0.00566140	+	0.00689844i
$300$	18.2320	+	138.007i	0.0607734	+	0.460025i
$301$	29.6880	−	15.8685i	0.0986311	−	0.0527194i
$302$	−34.3541	+	66.9187i	−0.113755	+	0.221585i
$303$	19.3029	+	46.6013i	0.0637059	+	0.153800i
$304$	213.036	−	297.855i	0.700776	−	0.979787i
$305$	152.522	+	63.1767i	0.500072	+	0.207137i
$306$	5.99919	+	7.06766i	0.0196052	+	0.0230969i
$307$	−70.4071	−	21.3578i	−0.229339	−	0.0695692i	0.173524	−	0.984830i	$-0.444485\pi$
$307$	−70.4071	−	21.3578i	−0.229339	−	0.0695692i	−0.402863	+	0.915260i	$0.631985\pi$
$308$	14.1900	−	217.996i	0.0460713	−	0.707778i
$309$	−34.1552	−	3.36400i	−0.110535	−	0.0108867i
$310$	−35.5075	+	89.9125i	−0.114540	+	0.290040i
$311$	−15.5784	−	78.3177i	−0.0500912	−	0.251825i	0.947624	−	0.319389i	$-0.103478\pi$
$311$	−15.5784	−	78.3177i	−0.0500912	−	0.251825i	−0.997715	+	0.0675633i	$0.978478\pi$
$312$	−7.34148	−	5.43716i	−0.0235304	−	0.0174268i
$313$	−21.3483	+	107.325i	−0.0682055	+	0.342892i	−0.999787	−	0.0206405i	$-0.993429\pi$
$313$	−21.3483	+	107.325i	−0.0682055	+	0.342892i	0.931581	+	0.363533i	$0.118429\pi$
$314$	56.6969	+	262.226i	0.180563	+	0.835114i
$315$	6.61881	+	21.8193i	0.0210121	+	0.0692676i
$316$	−0.405604	+	2.46358i	−0.00128356	+	0.00779615i
$317$	−311.577	+	379.657i	−0.982892	+	1.19766i	−0.00262094	+	0.999997i	$0.500834\pi$
$317$	−311.577	+	379.657i	−0.982892	+	1.19766i	−0.980271	+	0.197660i	$0.936666\pi$
$318$	204.056	+	161.875i	0.641684	+	0.509042i
$319$	383.002			1.20063
$320$	−117.988	−	78.6073i	−0.368711	−	0.245648i
$321$			183.380i			0.571277i
$322$	−21.7566	−	17.2593i	−0.0675670	−	0.0536003i
$323$	−27.3360	−	22.4341i	−0.0846316	−	0.0694554i
$324$	29.2531	−	20.9823i	0.0902873	−	0.0647603i
$325$	−12.6769	+	3.84549i	−0.0390058	+	0.0118323i
$326$	116.198	+	537.423i	0.356437	+	1.64854i
$327$	144.364	+	28.7158i	0.441480	+	0.0878159i
$328$	−9.31916	+	37.3107i	−0.0284121	+	0.113752i
$329$	32.2564	−	6.41620i	0.0980439	−	0.0195021i
$330$	44.8675	−	113.614i	0.135962	−	0.344285i
$331$	−43.6448	+	443.133i	−0.131857	+	1.33877i	0.670493	+	0.741916i	$0.266083\pi$
$331$	−43.6448	+	443.133i	−0.131857	+	1.33877i	−0.802350	+	0.596854i	$0.796417\pi$
$332$	225.605	+	257.020i	0.679533	+	0.774158i
$333$	29.2107	−	96.2947i	0.0877198	−	0.289173i
$334$	221.194	+	260.589i	0.662257	+	0.780206i
$335$	−24.2103	+	58.4488i	−0.0722695	+	0.174474i
$336$	86.6413	+	39.1630i	0.257861	+	0.116557i
$337$	277.384	−	114.896i	0.823097	−	0.340938i	0.0689309	−	0.997621i	$-0.478041\pi$
$337$	277.384	−	114.896i	0.823097	−	0.340938i	0.754166	+	0.656683i	$0.228041\pi$
$338$	−153.969	+	299.918i	−0.455530	+	0.887330i
$339$	−154.303	−	288.681i	−0.455172	−	0.851566i
$340$	−8.32962	+	10.8655i	−0.0244989	+	0.0319572i
$341$	−268.483	+	220.338i	−0.787341	+	0.646154i
$342$	−95.4794	+	98.7005i	−0.279180	+	0.288598i
$343$	−164.363	+	245.987i	−0.479193	+	0.717163i
$344$	40.3077	−	67.3520i	0.117173	−	0.195791i
$345$	−8.62715	−	12.9114i	−0.0250062	−	0.0374245i
$346$	105.483	+	152.334i	0.304863	+	0.440273i
$347$	−248.734	+	465.349i	−0.716813	+	1.34106i	0.214457	+	0.976733i	$0.431202\pi$
$347$	−248.734	+	465.349i	−0.716813	+	1.34106i	−0.931270	+	0.364329i	$0.881298\pi$
$348$	−58.6493	+	156.040i	−0.168533	+	0.448390i
$349$	29.6937	+	301.485i	0.0850822	+	0.863854i	0.939108	+	0.343623i	$0.111654\pi$
$349$	29.6937	+	301.485i	0.0850822	+	0.863854i	−0.854025	+	0.520231i	$0.825846\pi$
$350$	120.500	−	67.0014i	0.344285	−	0.191432i
$351$	2.42245	+	2.42245i	0.00690158	+	0.00690158i
$352$	−233.245	−	452.840i	−0.662629	−	1.28648i
$353$	124.305	+	124.305i	0.352140	+	0.352140i	0.860905	−	0.508765i	$-0.169898\pi$
$353$	124.305	+	124.305i	0.352140	+	0.352140i	−0.508765	+	0.860905i	$0.669898\pi$
$354$	58.3430	−	204.481i	0.164811	−	0.577630i
$355$	−14.1653	−	143.822i	−0.0399022	−	0.405134i
$356$	120.800	+	113.040i	0.339325	+	0.317527i
$357$	4.32827	−	8.09762i	0.0121240	−	0.0226824i
$358$	−101.183	+	556.791i	−0.282633	+	1.55528i
$359$	174.373	+	260.967i	0.485718	+	0.726928i	0.990679	−	0.136214i	$-0.0434934\pi$
$359$	174.373	+	260.967i	0.485718	+	0.726928i	−0.504962	+	0.863142i	$0.668493\pi$
$360$	39.4172	+	35.6774i	0.109492	+	0.0991038i
$361$	90.4670	−	135.393i	0.250601	−	0.375051i
$362$	−8.18927	−	493.677i	−0.0226223	−	1.36375i
$363$	177.251	−	145.466i	0.488295	−	0.400733i
$364$	−2.33793	+	8.74096i	−0.00642289	+	0.0240136i
$365$	70.6778	+	132.229i	0.193638	+	0.362271i
$366$	−245.766	+	79.0268i	−0.671492	+	0.215920i
$367$	249.733	−	103.443i	0.680471	−	0.281860i	−0.0155528	−	0.999879i	$-0.504951\pi$
$367$	249.733	−	103.443i	0.680471	−	0.281860i	0.696024	+	0.718019i	$0.254951\pi$
$368$	−64.2078	−	8.39451i	−0.174478	−	0.0228112i
$369$	5.51881	−	13.3236i	0.0149561	−	0.0361073i
$370$	148.115	+	12.1113i	0.400311	+	0.0327332i
$371$	74.8857	−	246.865i	0.201848	−	0.665404i
$372$	−48.6557	−	143.124i	−0.130795	−	0.384742i
$373$	26.2945	−	266.972i	0.0704946	−	0.715743i	−0.893365	−	0.449332i	$-0.851662\pi$
$373$	26.2945	−	266.972i	0.0704946	−	0.715743i	0.963859	−	0.266411i	$-0.0858380\pi$
$374$	−45.1268	+	19.5752i	−0.120660	+	0.0523402i
$375$	169.692	−	33.7538i	0.452512	−	0.0900102i
$376$	56.7861	−	51.5376i	0.151027	−	0.137068i
$377$	−15.5587	−	3.09481i	−0.0412696	−	0.00820904i
$378$	−29.9709	−	19.3147i	−0.0792882	−	0.0510971i
$379$	−210.532	+	63.8640i	−0.555492	+	0.168507i	−0.555535	−	0.831493i	$-0.687486\pi$
$379$	−210.532	+	63.8640i	−0.555492	+	0.168507i	4.26369e−5		1.00000i	$0.499986\pi$
$380$	−172.270	−	107.017i	−0.453343	−	0.281625i
$381$	163.004	+	133.774i	0.427832	+	0.351112i
$382$	−7.34446	−	63.7164i	−0.0192263	−	0.166797i
$383$		−	689.453i		−	1.80014i	−0.435748	−	0.900069i	$-0.643516\pi$
$383$		−	689.453i		−	1.80014i	0.435748	−	0.900069i	$-0.356484\pi$
$384$	220.210	−	25.6835i	0.573463	−	0.0668842i
$385$	−120.984			−0.314243
$386$	−370.457	+	42.7019i	−0.959733	+	0.110627i
$387$	−18.6731	+	22.7532i	−0.0482508	+	0.0587938i
$388$	−479.790	−	298.054i	−1.23657	−	0.768181i
$389$	−171.342	−	564.839i	−0.440468	−	1.45203i	−0.843642	−	0.536906i	$-0.819593\pi$
$389$	−171.342	−	564.839i	−0.440468	−	1.45203i	0.403174	−	0.915123i	$-0.367907\pi$
$390$	−2.74069	+	4.25278i	−0.00702742	+	0.0109046i
$391$	−1.21993	+	6.13301i	−0.00312003	+	0.0156855i
$392$	−14.4136	+	297.480i	−0.0367693	+	0.758876i
$393$	4.80062	+	24.1344i	0.0122153	+	0.0614106i
$394$	197.210	+	454.628i	0.500532	+	1.15388i
$395$	1.37606	+	0.135531i	0.00348371	+	0.000343115i
$396$	61.4816	+	180.852i	0.155257	+	0.456698i
$397$	332.695	+	100.922i	0.838022	+	0.254211i	0.679989	−	0.733222i	$-0.261985\pi$
$397$	332.695	+	100.922i	0.838022	+	0.254211i	0.158034	+	0.987434i	$0.449485\pi$
$398$	−15.9533	+	195.101i	−0.0400837	+	0.490203i
$399$	125.658	+	52.0490i	0.314931	+	0.130449i
$400$	160.492	−	278.557i	0.401230	−	0.696393i
$401$	180.228	+	435.108i	0.449445	+	1.08506i	0.972530	+	0.232776i	$0.0747810\pi$
$401$	180.228	+	435.108i	0.449445	+	1.08506i	−0.523085	+	0.852281i	$0.675219\pi$
$402$	−30.2843	−	94.1814i	−0.0753341	−	0.234282i
$403$	12.6870	−	6.78134i	0.0314814	−	0.0168271i
$404$	30.0989	−	112.532i	0.0745022	−	0.278546i
$405$	−12.6480	−	15.4116i	−0.0312296	−	0.0380534i
$406$	165.080	−	2.73840i	0.406601	−	0.00674482i
$407$	443.950	+	296.638i	1.09079	+	0.728840i
$408$	−1.06490	−	21.3828i	−0.00261004	−	0.0524088i
$409$	−367.304	+	245.425i	−0.898054	+	0.600061i	−0.916617	−	0.399767i	$-0.869091\pi$
$409$	−367.304	+	245.425i	−0.898054	+	0.600061i	0.0185624	+	0.999828i	$0.494091\pi$
$410$	20.9546	+	3.80796i	0.0511088	+	0.00928771i
$411$	215.996	+	115.452i	0.525539	+	0.280906i
$412$	57.8732	+	54.1554i	0.140469	+	0.131445i
$413$	−209.592	+	20.6431i	−0.507488	+	0.0499832i
$414$	23.3509	+	6.66255i	0.0564032	+	0.0160931i
$415$	133.924	−	133.924i	0.322708	−	0.322708i
$416$	5.81599	+	20.2804i	0.0139807	+	0.0487509i
$417$	−43.1726	+	43.1726i	−0.103531	+	0.103531i
$418$	−354.095	−	636.827i	−0.847116	−	1.52351i
$419$	56.2120	−	5.53640i	0.134158	−	0.0132134i	−0.0307154	−	0.999528i	$-0.509779\pi$
$419$	56.2120	−	5.53640i	0.134158	−	0.0132134i	0.164873	+	0.986315i	$0.447279\pi$
$420$	18.5263	−	49.2902i	0.0441102	−	0.117358i
$421$	−507.156	−	271.081i	−1.20465	−	0.643897i	−0.257992	−	0.966147i	$-0.583061\pi$
$421$	−507.156	−	271.081i	−1.20465	−	0.643897i	−0.946655	+	0.322250i	$0.895561\pi$
$422$	−582.173	+	403.121i	−1.37956	+	0.955264i
$423$	−23.9109	+	15.9767i	−0.0565269	+	0.0377700i
$424$	−146.550	−	583.394i	−0.345637	−	1.37593i
$425$	−25.8129	−	17.2476i	−0.0607363	−	0.0405827i
$426$	162.429	+	157.128i	0.381289	+	0.368846i
$427$	162.207	+	197.650i	0.379876	+	0.462881i
$428$	257.658	−	336.099i	0.602005	−	0.785278i
$429$	−16.0314	+	8.56894i	−0.0373691	+	0.0199742i
$430$	−38.6714	−	19.8528i	−0.0899335	−	0.0461692i
$431$	149.648	+	361.283i	0.347212	+	0.838244i	0.996947	+	0.0780830i	$0.0248799\pi$
$431$	149.648	+	361.283i	0.347212	+	0.838244i	−0.649735	+	0.760161i	$0.725120\pi$
$432$	−83.0963	−	2.64565i	−0.192353	−	0.00612420i
$433$	−84.3417	−	34.9355i	−0.194784	−	0.0806824i	0.283159	−	0.959073i	$-0.408618\pi$
$433$	−84.3417	−	34.9355i	−0.194784	−	0.0806824i	−0.477943	+	0.878391i	$0.658618\pi$
$434$	−114.145	+	96.8891i	−0.263007	+	0.223247i
$435$	88.3436	+	26.7987i	0.203089	+	0.0616063i
$436$	−224.243	−	255.469i	−0.514320	−	0.585939i
$437$	−92.1827	−	9.07920i	−0.210944	−	0.0207762i
$438$	−218.070	−	86.1185i	−0.497877	−	0.196618i
$439$	108.086	+	543.383i	0.246209	+	1.23777i	0.883971	+	0.467541i	$0.154860\pi$
$439$	108.086	+	543.383i	0.246209	+	1.23777i	−0.637763	+	0.770233i	$0.720140\pi$
$440$	−241.867	+	145.191i	−0.549697	+	0.329979i
$441$	21.7888	−	109.540i	0.0494077	−	0.248389i
$442$	1.99136	−	0.430560i	0.00450534	−	0.000974117i
$443$	−52.7147	−	173.777i	−0.118995	−	0.392274i	0.877127	−	0.480259i	$-0.159457\pi$
$443$	−52.7147	−	173.777i	−0.118995	−	0.392274i	−0.996122	+	0.0879851i	$0.971957\pi$
$444$	−188.837	+	135.447i	−0.425307	+	0.305060i
$445$	58.1246	−	70.8251i	0.130617	−	0.159157i
$446$	464.704	−	585.792i	1.04194	−	1.31344i
$447$	284.040			0.635436
$448$	−103.770	−	193.514i	−0.231630	−	0.431950i
$449$		−	294.060i		−	0.654923i	−0.944864	−	0.327462i	$-0.893807\pi$
$449$		−	294.060i		−	0.654923i	0.944864	−	0.327462i	$-0.106193\pi$
$450$	−74.9240	+	94.4470i	−0.166498	+	0.209882i
$451$	59.1509	+	48.5438i	0.131155	+	0.107636i
$452$	−122.805	+	745.899i	−0.271692	+	1.65022i
$453$	−62.3389	+	18.9103i	−0.137614	+	0.0417446i
$454$	−175.672	+	37.9828i	−0.386943	+	0.0836625i
$455$	4.91470	+	0.977595i	0.0108015	+	0.00214856i
$456$	313.674	−	46.7449i	0.687882	−	0.102511i
$457$	63.6333	−	12.6574i	0.139241	−	0.0276968i	−0.124978	−	0.992160i	$-0.539886\pi$
$457$	63.6333	−	12.6574i	0.139241	−	0.0276968i	0.264219	+	0.964463i	$0.414886\pi$
$458$	−420.571	−	166.088i	−0.918277	−	0.362639i
$459$	−0.786930	+	7.98983i	−0.00171444	+	0.0174070i
$460$	−2.32940	+	35.7857i	−0.00506391	+	0.0777951i
$461$	−129.768	+	427.789i	−0.281493	+	0.927959i	0.696187	+	0.717861i	$0.254879\pi$
$461$	−129.768	+	427.789i	−0.281493	+	0.927959i	−0.977680	+	0.210099i	$0.932621\pi$
$462$	144.235	−	122.430i	0.312196	−	0.264999i
$463$	−155.765	+	376.051i	−0.336426	+	0.812205i	0.661627	+	0.749833i	$0.269866\pi$
$463$	−155.765	+	376.051i	−0.336426	+	0.812205i	−0.998053	+	0.0623717i	$0.980134\pi$
$464$	326.737	−	203.585i	0.704174	−	0.438760i
$465$	−77.3457	+	32.0377i	−0.166335	+	0.0688982i
$466$	234.231	+	120.247i	0.502641	+	0.258041i
$467$	209.200	+	391.387i	0.447967	+	0.838087i	0.999991	+	0.00425876i	$0.00135561\pi$
$467$	209.200	+	391.387i	0.447967	+	0.838087i	−0.552024	+	0.833828i	$0.686144\pi$
$468$	−1.03620	−	7.84355i	−0.00221411	−	0.0167597i
$469$	−75.7426	+	62.1604i	−0.161498	+	0.132538i
$470$	−30.5245	−	29.5283i	−0.0649457	−	0.0628262i
$471$	−129.082	+	193.185i	−0.274060	+	0.410160i
$472$	−394.238	+	292.798i	−0.835249	+	0.620335i
$473$	−86.7693	−	129.859i	−0.183445	−	0.274544i
$474$	−1.77767	+	1.23093i	−0.00375036	+	0.00259691i
$475$	216.782	−	405.571i	0.456383	−	0.853833i
$476$	−19.3104	+	8.75988i	−0.0405681	+	0.0184031i
$477$	22.1097	+	224.484i	0.0463516	+	0.470616i
$478$	47.2940	+	85.0566i	0.0989413	+	0.177943i
$479$	515.141	+	515.141i	1.07545	+	1.07545i	0.996911	+	0.0785400i	$0.0250258\pi$
$479$	515.141	+	515.141i	1.07545	+	1.07545i	0.0785400	+	0.996911i	$0.474974\pi$
$480$	−22.1153	−	120.773i	−0.0460736	−	0.251610i
$481$	−15.6376	−	15.6376i	−0.0325106	−	0.0325106i
$482$	−728.982	−	207.995i	−1.51241	−	0.431525i
$483$	−2.35736	−	23.9346i	−0.00488066	−	0.0495541i
$484$	−529.253	+	17.5637i	−1.09350	+	0.0362886i
$485$	−147.457	+	275.873i	−0.304035	+	0.568810i
$486$	30.6745	+	5.57431i	0.0631163	+	0.0114698i
$487$	−124.104	−	185.734i	−0.254833	−	0.381385i	0.681891	−	0.731454i	$-0.261158\pi$
$487$	−124.104	−	185.734i	−0.254833	−	0.381385i	−0.936724	+	0.350069i	$0.886158\pi$
$488$	561.477	+	200.474i	1.15057	+	0.410806i
$489$	−264.549	+	395.926i	−0.541001	+	0.809665i
$490$	164.917	−	2.73570i	0.336566	−	0.00558306i
$491$	59.3440	−	48.7023i	0.120863	−	0.0991901i	−0.572020	−	0.820240i	$-0.693840\pi$
$491$	59.3440	−	48.7023i	0.120863	−	0.0991901i	0.692883	+	0.721050i	$0.256340\pi$
$492$	−28.8352	+	16.6653i	−0.0586081	+	0.0338725i
$493$	−17.5246	−	32.7862i	−0.0355468	−	0.0665035i
$494$	9.23854	+	28.7310i	0.0187015	+	0.0581599i
$495$	97.7345	−	40.4830i	0.197444	−	0.0817838i
$496$	−111.921	+	330.682i	−0.225646	+	0.666697i
$497$	85.6559	−	206.792i	0.172346	−	0.416080i
$498$	−24.1373	+	295.187i	−0.0484684	+	0.592745i
$499$	171.457	−	565.217i	0.343600	−	1.13270i	−0.599551	−	0.800336i	$-0.704654\pi$
$499$	171.457	−	565.217i	0.343600	−	1.13270i	0.943152	−	0.332362i	$-0.107846\pi$
$500$	−358.438	−	176.562i	−0.716875	−	0.353124i
$501$	−29.0145	+	294.590i	−0.0579133	+	0.588003i
$502$	68.4266	+	157.744i	0.136308	+	0.314231i
$503$	−513.352	+	102.112i	−1.02058	+	0.203006i	−0.676895	−	0.736079i	$-0.736675\pi$
$503$	−513.352	+	102.112i	−1.02058	+	0.203006i	−0.343685	+	0.939085i	$0.611675\pi$
$504$	27.7926	+	77.5108i	0.0551441	+	0.153791i
$505$	−63.2726	−	12.5857i	−0.125292	−	0.0249222i
$506$	−69.7960	+	108.304i	−0.137937	+	0.214039i
$507$	−279.392	+	84.7526i	−0.551069	+	0.167165i
$508$	−110.795	−	474.210i	−0.218099	−	0.933484i
$509$	64.4900	+	52.9256i	0.126699	+	0.103980i	0.695609	−	0.718421i	$-0.255135\pi$
$509$	64.4900	+	52.9256i	0.126699	+	0.103980i	−0.568910	+	0.822400i	$0.692635\pi$
$510$	−11.7787	+	1.35771i	−0.0230954	+	0.00266217i
$511$			232.215i			0.454433i
$512$	−439.688	−	262.333i	−0.858765	−	0.512370i
$513$	−118.927			−0.231826
$514$	53.7903	+	466.654i	0.104650	+	0.907887i
$515$	27.8466	−	33.9311i	0.0540710	−	0.0658857i
$516$	66.1935	−	15.4655i	0.128282	−	0.0299718i
$517$	−44.2938	−	146.017i	−0.0856747	−	0.282432i
$518$	193.471	+	124.682i	0.373495	+	0.240698i
$519$	−31.3053	+	157.382i	−0.0603185	+	0.303242i
$520$	10.9985	−	3.94369i	0.0211510	−	0.00758402i
$521$	48.9005	+	245.840i	0.0938590	+	0.471861i	0.998915	+	0.0465688i	$0.0148287\pi$
$521$	48.9005	+	245.840i	0.0938590	+	0.471861i	−0.905056	+	0.425292i	$0.860171\pi$
$522$	−132.441	+	57.4505i	−0.253718	+	0.110058i
$523$	79.6455	+	7.84439i	0.152286	+	0.0149988i	0.173873	−	0.984768i	$-0.444372\pi$
$523$	79.6455	+	7.84439i	0.152286	+	0.0149988i	−0.0215869	+	0.999767i	$0.506872\pi$
$524$	25.1114	−	50.9786i	0.0479226	−	0.0972875i
$525$	114.261	+	34.6608i	0.217641	+	0.0660205i
$526$	−704.929	−	57.6417i	−1.34017	−	0.109585i
$527$	31.1464	+	12.9013i	0.0591013	+	0.0244806i
$528$	141.423	−	417.852i	0.267848	−	0.791386i
$529$	−196.171	−	473.600i	−0.370834	−	0.895274i
$530$	−317.135	+	101.976i	−0.598368	+	0.192407i
$531$	162.408	−	86.8090i	0.305854	−	0.163482i
$532$	−157.174	−	271.951i	−0.295439	−	0.511186i
$533$	−2.01063	−	2.44996i	−0.00377228	−	0.00459654i
$534$	2.37637	+	143.256i	0.00445013	+	0.268269i
$535$	−195.010	−	130.302i	−0.364505	−	0.243555i
$536$	−76.8246	+	215.167i	−0.143330	+	0.401431i
$537$	−407.497	+	272.281i	−0.758840	+	0.507041i
$538$	−98.2473	+	540.639i	−0.182616	+	1.00491i
$539$	522.634	+	279.354i	0.969636	+	0.518281i
$540$	1.52712	+	46.0175i	0.00282801	+	0.0852176i
$541$	701.265	−	69.0686i	1.29624	−	0.127668i	0.573738	−	0.819039i	$-0.305493\pi$
$541$	701.265	−	69.0686i	1.29624	−	0.127668i	0.722500	+	0.691370i	$0.242993\pi$
$542$	−49.1201	+	172.156i	−0.0906274	+	0.317631i
$543$	302.356	−	302.356i	0.556825	−	0.556825i
$544$	−28.0922	+	40.6867i	−0.0516401	+	0.0747917i
$545$	−133.116	+	133.116i	−0.244249	+	0.244249i
$546$	−6.84851	+	3.80797i	−0.0125431	+	0.00697431i
$547$	416.283	−	41.0003i	0.761030	−	0.0749549i	0.289946	−	0.957043i	$-0.406363\pi$
$547$	416.283	−	41.0003i	0.761030	−	0.0749549i	0.471084	+	0.882088i	$0.343863\pi$
$548$	−233.662	−	515.088i	−0.426390	−	0.939941i
$549$	−197.173	−	105.391i	−0.359150	−	0.191970i
$550$	−364.158	−	525.904i	−0.662105	−	0.956189i
$551$	457.882	−	305.947i	0.831002	−	0.555258i
$552$	−33.4364	−	45.0204i	−0.0605732	−	0.0815587i
$553$	1.78064	+	1.18979i	0.00321996	+	0.00215151i
$554$	−314.335	+	324.940i	−0.567392	+	0.586534i
$555$	81.6461	+	99.4861i	0.147110	+	0.179254i
$556$	139.787	−	18.4671i	0.251415	−	0.0332141i
$557$	180.698	−	96.5851i	0.324413	−	0.173402i	−0.301148	−	0.953577i	$-0.597370\pi$
$557$	180.698	−	96.5851i	0.324413	−	0.173402i	0.625561	+	0.780175i	$0.284870\pi$
$558$	59.7897	−	116.465i	0.107150	−	0.208719i
$559$	2.47551	+	5.97640i	0.00442846	+	0.0106912i
$560$	−103.210	+	64.3088i	−0.184304	+	0.114837i
$561$	−39.3568	−	16.3021i	−0.0701547	−	0.0290590i
$562$	106.737	+	125.747i	0.189923	+	0.223749i
$563$	308.822	+	93.6800i	0.548529	+	0.166394i	0.552371	−	0.833598i	$-0.313723\pi$
$563$	308.822	+	93.6800i	0.548529	+	0.166394i	−0.00384248	+	0.999993i	$0.501223\pi$
$564$	66.2720	+	4.31384i	0.117504	+	0.00764865i
$565$	416.631	+	41.0346i	0.737400	+	0.0726276i
$566$	−369.756	+	936.300i	−0.653279	+	1.65424i
$567$	−6.02411	−	30.2853i	−0.0106245	−	0.0534131i
$568$	−76.9270	−	516.206i	−0.135435	−	0.908814i
$569$	72.7352	−	365.665i	0.127830	−	0.642644i	−0.862741	−	0.505645i	$-0.831254\pi$
$569$	72.7352	−	365.665i	0.127830	−	0.642644i	0.990571	−	0.136999i	$-0.0437456\pi$
$570$	−37.1169	−	171.667i	−0.0651173	−	0.301171i
$571$	64.2801	+	211.903i	0.112575	+	0.371109i	0.995065	−	0.0992210i	$-0.0316351\pi$
$571$	64.2801	+	211.903i	0.112575	+	0.371109i	−0.882491	+	0.470330i	$0.844135\pi$
$572$	41.4221	+	6.81973i	0.0724163	+	0.0119226i
$573$	35.2376	−	42.9372i	0.0614967	−	0.0749340i
$574$	25.8421	+	20.5003i	0.0450210	+	0.0357147i
$575$	−81.3180			−0.141423
$576$	148.582	+	121.604i	0.257955	+	0.211117i
$577$			243.414i			0.421861i	0.977501	+	0.210931i	$0.0676494\pi$
$577$			243.414i			0.421861i	−0.977501	+	0.210931i	$0.932351\pi$
$578$	−449.080	−	356.251i	−0.776955	−	0.616351i
$579$	−249.643	−	204.877i	−0.431163	−	0.353846i
$580$	−124.263	−	173.244i	−0.214246	−	0.298697i
$581$	280.707	−	85.1515i	0.483144	−	0.146560i
$582$	−103.374	−	478.111i	−0.177619	−	0.821496i
$583$	−1173.88	−	233.500i	−2.01352	−	0.400515i
$584$	278.679	+	464.238i	0.477189	+	0.794928i
$585$	−4.29738	+	0.854802i	−0.00734595	+	0.00146120i
$586$	−279.871	+	708.693i	−0.477596	+	1.20937i
$587$	−51.1115	+	518.944i	−0.0870725	+	0.884062i	0.848092	+	0.529849i	$0.177751\pi$
$587$	−51.1115	+	518.944i	−0.0870725	+	0.884062i	−0.935165	+	0.354213i	$0.884749\pi$
$588$	−193.844	+	170.150i	−0.329666	+	0.289371i
$589$	−144.965	+	477.885i	−0.246120	+	0.811349i
$590$	175.994	+	207.338i	0.298294	+	0.351421i
$591$	−164.235	+	396.498i	−0.277893	+	0.670894i
$592$	536.409	+	17.0784i	0.906097	+	0.0288487i
$593$	845.817	−	350.349i	1.42634	−	0.590808i	0.469892	−	0.882724i	$-0.344293\pi$
$593$	845.817	−	350.349i	1.42634	−	0.590808i	0.956444	+	0.291916i	$0.0942928\pi$
$594$	−75.5507	+	147.166i	−0.127190	+	0.247754i
$595$	5.53571	+	10.3566i	0.00930372	+	0.0174060i
$596$	−520.589	−	399.091i	−0.873471	−	0.669615i
$597$	−131.046	+	107.546i	−0.219507	+	0.180145i
$598$	3.71045	−	3.83563i	0.00620477	−	0.00641410i
$599$	507.192	−	759.067i	0.846732	−	1.26722i	−0.115037	−	0.993361i	$-0.536699\pi$
$599$	507.192	−	759.067i	0.846732	−	1.26722i	0.961769	−	0.273862i	$-0.0883013\pi$
$600$	270.024	−	67.8306i	0.450040	−	0.113051i
$601$	−43.9380	−	65.7579i	−0.0731082	−	0.109414i	0.793114	−	0.609073i	$-0.208459\pi$
$601$	−43.9380	−	65.7579i	−0.0731082	−	0.109414i	−0.866222	+	0.499659i	$0.833459\pi$
$602$	−38.3275	−	55.3511i	−0.0636669	−	0.0919454i
$603$	40.3876	−	75.5599i	0.0669778	−	0.125307i
$604$	140.825	+	52.9306i	0.233154	+	0.0876335i
$605$	28.7452	+	291.854i	0.0475126	+	0.482404i
$606$	88.1688	−	49.0244i	0.145493	−	0.0808984i
$607$	446.445	+	446.445i	0.735495	+	0.735495i	0.971703	−	0.236208i	$-0.0759046\pi$
$607$	446.445	+	446.445i	0.735495	+	0.735495i	−0.236208	+	0.971703i	$0.575905\pi$
$608$	−640.582	−	355.054i	−1.05359	−	0.583971i
$609$	101.104	+	101.104i	0.166017	+	0.166017i
$610$	90.5916	−	317.506i	0.148511	−	0.520502i
$611$	0.619467	+	6.28955i	0.00101386	+	0.0102939i
$612$	12.6684	−	13.5381i	0.0207000	−	0.0221211i
$613$	434.632	−	813.139i	0.709024	−	1.32649i	−0.226772	−	0.973948i	$-0.572817\pi$
$613$	434.632	−	813.139i	0.709024	−	1.32649i	0.935796	−	0.352543i	$-0.114683\pi$
$614$	−26.3099	+	144.779i	−0.0428500	+	0.235797i
$615$	10.2472	+	15.3360i	0.0166621	+	0.0249365i
$616$	−436.373	+	21.7320i	−0.708398	+	0.0352793i
$617$	281.105	−	420.703i	0.455599	−	0.681853i	−0.530561	−	0.847647i	$-0.678019\pi$
$617$	281.105	−	420.703i	0.455599	−	0.681853i	0.986160	+	0.165794i	$0.0530187\pi$
$618$	1.13848	+	68.6315i	0.00184220	+	0.111054i
$619$	530.106	−	435.047i	0.856391	−	0.702822i	−0.0999764	−	0.994990i	$-0.531877\pi$
$619$	530.106	−	435.047i	0.856391	−	0.702822i	0.956367	+	0.292168i	$0.0943767\pi$
$620$	186.774	+	49.9561i	0.301248	+	0.0805744i
$621$	9.91326	+	18.5464i	0.0159634	+	0.0298654i
$622$	−152.037	+	48.8881i	−0.244433	+	0.0785982i
$623$	131.103	−	54.3045i	0.210438	−	0.0871661i
$624$	−9.12144	+	15.8316i	−0.0146177	+	0.0253711i
$625$	107.548	−	259.643i	0.172076	−	0.415429i
$626$	218.128	+	17.8362i	0.348447	+	0.0284923i
$627$	183.178	−	603.858i	0.292150	−	0.963091i
$628$	508.017	−	172.703i	0.808945	−	0.275005i
$629$	5.07984	−	51.5765i	0.00807606	−	0.0819977i
$630$	41.8357	−	18.1476i	0.0664059	−	0.0288057i
$631$	−352.718	+	70.1599i	−0.558982	+	0.111189i	−0.466493	−	0.884525i	$-0.654483\pi$
$631$	−352.718	+	70.1599i	−0.558982	+	0.111189i	−0.0924898	+	0.995714i	$0.529483\pi$
$632$	4.98765	+	0.241663i	0.00789185	+	0.000382378i
$633$	−601.466	−	119.639i	−0.950183	−	0.189003i
$634$	825.677	+	532.105i	1.30233	+	0.839283i
$635$	−258.081	+	78.2881i	−0.406427	+	0.123288i
$636$	274.889	−	442.499i	0.432215	−	0.695754i
$637$	−18.9736	−	15.5712i	−0.0297859	−	0.0244447i
$638$	−87.7149	−	760.965i	−0.137484	−	1.19274i
$639$			195.715i			0.306283i
$640$	−129.159	+	252.426i	−0.201811	+	0.394415i
$641$	491.819			0.767269			0.383634	−	0.923485i	$-0.374672\pi$
$641$	491.819			0.767269			0.383634	+	0.923485i	$0.374672\pi$
$642$	364.347	−	41.9976i	0.567519	−	0.0654168i
$643$	−611.769	+	745.443i	−0.951429	+	1.15932i	0.0356948	+	0.999363i	$0.488636\pi$
$643$	−611.769	+	745.443i	−0.951429	+	1.15932i	−0.987124	+	0.159957i	$0.948864\pi$
$644$	−29.3089	+	47.1797i	−0.0455106	+	0.0732603i
$645$	−10.9280	−	36.0248i	−0.0169426	−	0.0558524i
$646$	−38.3125	+	59.4502i	−0.0593073	+	0.0920282i
$647$	156.125	−	784.894i	0.241306	−	1.21313i	−0.650074	−	0.759871i	$-0.725262\pi$
$647$	156.125	−	784.894i	0.241306	−	1.21313i	0.891380	−	0.453257i	$-0.149738\pi$
$648$	−48.3881	−	53.3159i	−0.0746730	−	0.0822777i
$649$	190.627	+	958.346i	0.293724	+	1.47665i
$650$	10.5436	+	24.3063i	0.0162210	+	0.0373943i
$651$	−129.039	−	12.7092i	−0.198216	−	0.0195226i
$652$	1041.16	−	353.949i	1.59688	−	0.542866i
$653$	−740.440	−	224.610i	−1.13391	−	0.343967i	−0.333101	−	0.942891i	$-0.608095\pi$
$653$	−740.440	−	224.610i	−1.13391	−	0.343967i	−0.800805	+	0.598925i	$0.795595\pi$
$654$	23.9916	−	293.405i	0.0366844	−	0.448632i
$655$	−29.0761	−	12.0437i	−0.0443911	−	0.0183874i
$656$	76.2648	+	9.97084i	0.116257	+	0.0151994i
$657$	−77.7029	−	187.591i	−0.118269	−	0.285527i
$658$	−20.1354	−	62.6191i	−0.0306008	−	0.0951658i
$659$	620.055	−	331.426i	0.940903	−	0.502923i	0.0717259	−	0.997424i	$-0.477149\pi$
$659$	620.055	−	331.426i	0.940903	−	0.502923i	0.869177	+	0.494501i	$0.164649\pi$
$660$	−236.009	−	63.1249i	−0.357589	−	0.0956438i
$661$	−282.989	−	344.823i	−0.428123	−	0.521669i	0.513613	−	0.858022i	$-0.328307\pi$
$661$	−282.989	−	344.823i	−0.428123	−	0.521669i	−0.941736	+	0.336352i	$0.890807\pi$
$662$	890.432	−	14.7708i	1.34506	−	0.0223123i
$663$	1.46706	+	0.980258i	0.00221276	+	0.00147852i
$664$	458.992	−	507.105i	0.691252	−	0.763712i
$665$	−144.637	+	96.6433i	−0.217499	+	0.145328i
$666$	−198.012	−	35.9837i	−0.297316	−	0.0540296i
$667$	−85.8790	−	45.9033i	−0.128754	−	0.0688205i
$668$	467.092	−	499.157i	0.699239	−	0.747242i
$669$	644.436	−	63.4714i	0.963283	−	0.0948751i
$670$	121.673	+	34.7161i	0.181602	+	0.0518151i
$671$	838.829	−	838.829i	1.25012	−	1.25012i
$672$	57.9682	−	181.112i	0.0862623	−	0.269512i
$673$	−42.0548	+	42.0548i	−0.0624885	+	0.0624885i	−0.737660	−	0.675172i	$-0.764069\pi$
$673$	−42.0548	+	42.0548i	−0.0624885	+	0.0624885i	0.675172	+	0.737660i	$0.264069\pi$
$674$	−291.807	−	524.805i	−0.432948	−	0.778642i
$675$	−103.902	+	10.2335i	−0.153929	+	0.0151607i
$676$	631.152	+	237.225i	0.933656	+	0.350925i
$677$	−998.822	−	533.882i	−1.47537	−	0.788599i	−0.479336	−	0.877631i	$-0.659123\pi$
$677$	−998.822	−	533.882i	−1.47537	−	0.788599i	−0.996029	+	0.0890320i	$0.971623\pi$
$678$	−538.226	+	372.690i	−0.793843	+	0.549690i
$679$	−402.828	+	269.161i	−0.593267	+	0.396408i
$680$	23.4956	+	14.0613i	0.0345524	+	0.0206783i
$681$	−129.420	−	86.4756i	−0.190044	−	0.126983i
$682$	499.266	+	482.972i	0.732062	+	0.708171i
$683$	143.504	+	174.861i	0.210109	+	0.256019i	0.867392	−	0.497625i	$-0.165794\pi$
$683$	143.504	+	174.861i	0.210109	+	0.256019i	−0.657283	+	0.753644i	$0.728294\pi$
$684$	217.969	+	167.098i	0.318668	+	0.244296i
$685$	−276.252	+	147.660i	−0.403288	+	0.215562i
$686$	526.380	+	270.228i	0.767318	+	0.393919i
$687$	−149.858	−	361.789i	−0.218134	−	0.526622i
$688$	−143.049	−	64.6601i	−0.207920	−	0.0939827i
$689$	45.7998	+	18.9709i	0.0664729	+	0.0275340i
$690$	−23.6773	+	20.0978i	−0.0343149	+	0.0291272i
$691$	157.577	+	47.8005i	0.228042	+	0.0691759i	0.402238	−	0.915535i	$-0.368232\pi$
$691$	157.577	+	47.8005i	0.228042	+	0.0691759i	−0.174196	+	0.984711i	$0.555732\pi$
$692$	278.507	−	244.465i	0.402467	−	0.353273i
$693$	163.054	+	16.0594i	0.235287	+	0.0231737i
$694$	981.540	+	387.622i	1.41432	+	0.558533i
$695$	−15.2342	−	76.5873i	−0.0219197	−	0.110198i
$696$	323.459	+	80.7909i	0.464740	+	0.116079i
$697$	1.44901	−	7.28467i	0.00207893	−	0.0104515i
$698$	592.204	−	128.043i	0.848429	−	0.183442i
$699$	66.1904	+	218.200i	0.0946929	+	0.312161i
$700$	−160.718	−	224.069i	−0.229597	−	0.320099i
$701$	−255.661	+	311.524i	−0.364709	+	0.444399i	−0.922741	−	0.385420i	$-0.874057\pi$
$701$	−255.661	+	311.524i	−0.364709	+	0.444399i	0.558032	+	0.829819i	$0.311557\pi$
$702$	4.25825	−	5.36783i	0.00606588	−	0.00764648i
$703$	767.705			1.09204
$704$	−846.304	+	567.132i	−1.20214	+	0.805585i
$705$		−	36.7797i		−	0.0521698i
$706$	218.507	−	275.444i	0.309500	−	0.390147i
$707$	−77.2364	−	63.3863i	−0.109245	−	0.0896553i
$708$	−419.633	−	69.0884i	−0.592703	−	0.0975824i
$709$	866.331	−	262.799i	1.22191	−	0.370661i	0.387530	−	0.921857i	$-0.373329\pi$
$709$	866.331	−	262.799i	1.22191	−	0.370661i	0.834376	+	0.551196i	$0.185829\pi$
$710$	−282.509	+	61.0824i	−0.397900	+	0.0860315i
$711$	−1.83658	−	0.365319i	−0.00258310	−	0.000513810i
$712$	196.927	−	265.898i	0.276582	−	0.373453i
$713$	86.6088	−	17.2276i	0.121471	−	0.0241621i
$714$	−17.0800	−	6.74508i	−0.0239215	−	0.00944689i
$715$	2.27878	−	23.1368i	0.00318710	−	0.0323592i
$716$	1129.43	+	73.5179i	1.57742	+	0.102679i
$717$	−24.4659	+	80.6531i	−0.0341225	+	0.112487i
$718$	478.566	−	406.218i	0.666527	−	0.565763i
$719$	334.979	−	808.711i	0.465896	−	1.12477i	−0.500043	−	0.866001i	$-0.666682\pi$
$719$	334.979	−	808.711i	0.465896	−	1.12477i	0.965939	−	0.258771i	$-0.0833176\pi$
$720$	61.8581	−	86.4866i	0.0859140	−	0.120120i
$721$	62.8091	−	26.0164i	0.0871139	−	0.0360838i
$722$	−289.724	−	148.736i	−0.401280	−	0.206006i
$723$	−309.477	−	578.991i	−0.428046	−	0.800818i
$724$	−978.984	+	129.333i	−1.35219	+	0.178636i
$725$	373.709	−	306.695i	0.515461	−	0.423028i
$726$	−329.612	−	318.855i	−0.454012	−	0.439195i
$727$	−131.543	+	196.868i	−0.180939	+	0.270795i	−0.910841	−	0.412757i	$-0.864566\pi$
$727$	−131.543	+	196.868i	−0.180939	+	0.270795i	0.729902	+	0.683552i	$0.239566\pi$
$728$	17.9024	+	2.64325i	0.0245912	+	0.00363084i
$729$	15.0004	+	22.4497i	0.0205767	+	0.0307952i
$730$	246.532	−	170.709i	0.337714	−	0.233848i
$731$	−7.14619	+	13.3696i	−0.00977591	+	0.0182894i
$732$	213.299	+	470.200i	0.291392	+	0.642350i
$733$	98.1110	+	996.138i	0.133849	+	1.35899i	0.794029	+	0.607880i	$0.207980\pi$
$733$	98.1110	+	996.138i	0.133849	+	1.35899i	−0.660180	+	0.751107i	$0.729520\pi$
$734$	−262.718	−	472.490i	−0.357927	−	0.643719i
$735$	101.005	+	101.005i	0.137421	+	0.137421i
$736$	−1.97374	+	129.493i	−0.00268171	+	0.175942i
$737$	321.452	+	321.452i	0.436163	+	0.436163i
$738$	−27.7358	−	7.91365i	−0.0375824	−	0.0107231i
$739$	122.495	+	1243.71i	0.165758	+	1.68296i	0.614198	+	0.789152i	$0.289480\pi$
$739$	122.495	+	1243.71i	0.165758	+	1.68296i	−0.448441	+	0.893813i	$0.648020\pi$
$740$	−9.85801	−	297.055i	−0.0133216	−	0.401426i
$741$	−12.3206	+	23.0503i	−0.0166271	+	0.0311070i
$742$	−507.632	−	92.2492i	−0.684141	−	0.124325i
$743$	−635.611	−	951.259i	−0.855466	−	1.28029i	−0.958349	−	0.285601i	$-0.907807\pi$
$743$	−635.611	−	951.259i	−0.855466	−	1.28029i	0.102883	−	0.994693i	$-0.467193\pi$
$744$	−273.222	+	129.450i	−0.367234	+	0.173991i
$745$	−201.826	+	302.054i	−0.270908	+	0.405442i
$746$	−536.454	+	8.89887i	−0.719108	+	0.0119288i
$747$	−198.271	+	162.717i	−0.265423	+	0.217827i
$748$	49.2278	+	85.1768i	0.0658126	+	0.113873i
$749$	−171.235	−	320.358i	−0.228618	−	0.427714i
$750$	−105.926	−	329.421i	−0.141235	−	0.439228i
$751$	−564.444	+	233.800i	−0.751590	+	0.311319i	−0.725390	−	0.688338i	$-0.758341\pi$
$751$	−564.444	+	233.800i	−0.751590	+	0.311319i	−0.0261997	+	0.999657i	$0.508341\pi$
$752$	−115.402	−	101.022i	−0.153460	−	0.134338i
$753$	−56.9852	+	137.574i	−0.0756775	+	0.182702i
$754$	−2.58567	+	31.6214i	−0.00342926	+	0.0419382i
$755$	24.1857	−	79.7295i	0.0320340	−	0.105602i
$756$	−31.5114	+	63.9710i	−0.0416817	+	0.0846178i
$757$	−75.2719	+	764.248i	−0.0994344	+	1.00957i	0.807944	+	0.589260i	$0.200580\pi$
$757$	−75.2719	+	764.248i	−0.0994344	+	1.00957i	−0.907378	+	0.420315i	$0.861920\pi$
$758$	175.104	+	403.667i	0.231008	+	0.532543i
$759$	−109.439	+	21.7689i	−0.144189	+	0.0286810i
$760$	−173.174	+	366.783i	−0.227860	+	0.482609i
$761$	524.537	+	104.337i	0.689273	+	0.137105i	0.527286	−	0.849688i	$-0.323210\pi$
$761$	524.537	+	104.337i	0.689273	+	0.137105i	0.161987	+	0.986793i	$0.448210\pi$
$762$	228.457	−	354.500i	0.299812	−	0.465223i
$763$	−279.013	+	84.6376i	−0.365679	+	0.110927i
$764$	−124.912	+	29.1846i	−0.163498	+	0.0381997i
$765$	−7.93741	−	6.51406i	−0.0103757	−	0.00851511i
$766$	−1369.84	+	157.898i	−1.78830	+	0.206133i
$767$		−	40.4712i		−	0.0527655i
$768$	−101.462	−	431.641i	−0.132111	−	0.562032i
$769$	−828.713			−1.07765			−0.538825	−	0.842418i	$-0.681132\pi$
$769$	−828.713			−1.07765			−0.538825	+	0.842418i	$0.681132\pi$
$770$	27.7076	+	240.375i	0.0359839	+	0.312176i
$771$	−258.077	+	314.468i	−0.334731	+	0.407871i
$772$	169.684	+	726.261i	0.219798	+	0.940753i
$773$	45.8399	+	151.114i	0.0593014	+	0.195490i	0.981586	−	0.191021i	$-0.0611799\pi$
$773$	45.8399	+	151.114i	0.0593014	+	0.195490i	−0.922285	+	0.386512i	$0.873680\pi$
$774$	49.4836	+	31.8895i	0.0639322	+	0.0412010i
$775$	−85.5293	+	429.985i	−0.110360	+	0.554819i
$776$	−482.306	+	1021.53i	−0.621528	+	1.31640i
$777$	38.8873	+	195.500i	0.0500480	+	0.251608i
$778$	−1083.01	+	469.790i	−1.39204	+	0.603843i
$779$	109.493	+	10.7841i	0.140556	+	0.0138435i
$780$	9.07729	+	4.47136i	0.0116376	+	0.00573252i
$781$	−993.755	−	301.452i	−1.27241	−	0.385982i
$782$	12.4647	+	1.01923i	0.0159395	+	0.00130337i
$783$	−115.507	−	47.8444i	−0.147518	−	0.0611039i
$784$	594.346	−	39.4912i	0.758095	−	0.0503714i
$785$	−113.717	−	274.538i	−0.144863	−	0.349730i
$786$	46.8518	−	15.0653i	0.0596079	−	0.0191671i
$787$	778.346	−	416.035i	0.989004	−	0.528634i	0.104180	−	0.994558i	$-0.466778\pi$
$787$	778.346	−	416.035i	0.989004	−	0.528634i	0.884824	+	0.465925i	$0.154278\pi$
$788$	858.110	−	495.944i	1.08897	−	0.629370i
$789$	−388.581	−	473.487i	−0.492498	−	0.600110i
$790$	−0.0458677	−	2.76506i	−5.80604e−5	−	0.00350008i
$791$	539.124	+	360.231i	0.681573	+	0.455413i
$792$	345.245	−	163.573i	0.435916	−	0.206532i
$793$	−40.8537	+	27.2976i	−0.0515180	+	0.0344232i
$794$	124.322	−	684.126i	0.156577	−	0.861620i
$795$	−254.431	−	135.996i	−0.320039	−	0.171065i
$796$	391.289	−	12.9852i	0.491569	−	0.0163131i
$797$	1548.40	−	152.504i	1.94279	−	0.191348i	0.950089	−	0.311979i	$-0.100992\pi$
$797$	1548.40	−	152.504i	1.94279	−	0.191348i	0.992697	+	0.120632i	$0.0384920\pi$
$798$	74.6353	−	261.582i	0.0935280	−	0.327797i
$799$	−10.4728	+	10.4728i	−0.0131074	+	0.0131074i
$800$	−590.205	−	255.077i	−0.737757	−	0.318847i
$801$	−87.7380	+	87.7380i	−0.109536	+	0.109536i
$802$	823.216	−	457.732i	1.02645	−	0.570739i
$803$	1072.19	−	105.601i	1.33523	−	0.131509i
$804$	−180.188	+	81.7396i	−0.224114	+	0.101666i
$805$	27.1277	+	14.5000i	0.0336990	+	0.0180125i
$806$	−16.3790	−	23.6540i	−0.0203214	−	0.0293474i
$807$	−395.676	+	264.382i	−0.490305	+	0.327611i
$808$	−230.478	−	34.0296i	−0.285245	−	0.0421159i
$809$	−515.167	−	344.224i	−0.636795	−	0.425493i	0.194825	−	0.980838i	$-0.437586\pi$
$809$	−515.167	−	344.224i	−0.636795	−	0.425493i	−0.831620	+	0.555345i	$0.812586\pi$
$810$	−27.7238	+	28.6591i	−0.0342270	+	0.0353816i
$811$	113.712	+	138.558i	0.140212	+	0.170848i	0.838382	−	0.545084i	$-0.183502\pi$
$811$	113.712	+	138.558i	0.140212	+	0.170848i	−0.698170	+	0.715932i	$0.746002\pi$
$812$	−43.2473	−	327.361i	−0.0532603	−	0.403154i
$813$	−136.735	+	73.0861i	−0.168185	+	0.0898968i
$814$	487.700	−	949.996i	0.599140	−	1.16707i
$815$	−233.060	−	562.656i	−0.285963	−	0.690375i
$816$	−42.2404	+	7.01286i	−0.0517652	+	0.00859420i
$817$	−207.467	−	85.9356i	−0.253938	−	0.105184i
$818$	571.741	+	673.569i	0.698950	+	0.823434i
$819$	−6.49396	−	1.96992i	−0.00792913	−	0.00240528i
$820$	2.76681	−	42.5056i	0.00337416	−	0.0518361i
$821$	−337.689	−	33.2594i	−0.411314	−	0.0405109i	−0.109755	−	0.993959i	$-0.535007\pi$
$821$	−337.689	−	33.2594i	−0.411314	−	0.0405109i	−0.301558	+	0.953448i	$0.597507\pi$
$822$	179.919	−	455.592i	0.218879	−	0.554248i
$823$	−200.672	−	1008.85i	−0.243830	−	1.22581i	−0.887607	−	0.460601i	$-0.847634\pi$
$823$	−200.672	−	1008.85i	−0.243830	−	1.22581i	0.643777	−	0.765213i	$-0.277366\pi$
$824$	94.3443	−	127.388i	0.114495	−	0.154597i
$825$	108.075	−	543.331i	0.131000	−	0.658584i
$826$	89.0153	+	411.700i	0.107767	+	0.498426i
$827$	211.554	+	697.401i	0.255809	+	0.843290i	0.986945	+	0.161058i	$0.0514906\pi$
$827$	211.554	+	697.401i	0.255809	+	0.843290i	−0.731136	+	0.682232i	$0.761009\pi$
$828$	7.88962	−	47.9205i	0.00952853	−	0.0578750i
$829$	229.403	−	279.528i	0.276723	−	0.337188i	−0.616040	−	0.787715i	$-0.711264\pi$
$829$	229.403	−	279.528i	0.276723	−	0.337188i	0.892763	+	0.450527i	$0.148764\pi$
$830$	−296.757	−	235.415i	−0.357539	−	0.283632i
$831$	−391.528			−0.471153
$832$	38.9620	−	16.2001i	0.0468293	−	0.0194712i
$833$		−	57.5212i		−	0.0690531i
$834$	95.6646	+	75.8899i	0.114706	+	0.0909951i
$835$	−292.657	−	240.177i	−0.350487	−	0.287637i
$836$	−1184.18	+	849.377i	−1.41648	+	1.01600i
$837$	108.494	−	32.9114i	0.129623	−	0.0393207i
$838$	−23.8736	−	110.417i	−0.0284888	−	0.131762i
$839$	−1203.02	−	239.296i	−1.43388	−	0.285216i	−0.583811	−	0.811889i	$-0.698439\pi$
$839$	−1203.02	−	239.296i	−1.43388	−	0.285216i	−0.850068	+	0.526673i	$0.823439\pi$
$840$	−102.175	−	25.5204i	−0.121637	−	0.0303815i
$841$	−257.044	+	51.1292i	−0.305641	+	0.0607957i
$842$	−422.446	+	1069.72i	−0.501718	+	1.27046i
$843$	−14.0009	+	142.154i	−0.0166085	+	0.168629i
$844$	934.268	+	1064.37i	1.10695	+	1.26110i
$845$	108.396	−	357.333i	0.128279	−	0.422879i
$846$	37.2193	+	43.8482i	0.0439945	+	0.0518300i
$847$	−173.819	+	419.636i	−0.205217	+	0.495438i
$848$	−1125.55	+	424.781i	−1.32730	+	0.500921i
$849$	−805.437	+	333.623i	−0.948689	+	0.392960i
$850$	−28.3567	+	55.2363i	−0.0333608	+	0.0649839i
$851$	−63.9928	−	119.722i	−0.0751971	−	0.140684i
$852$	274.990	−	358.707i	0.322758	−	0.421017i
$853$	−285.005	+	233.897i	−0.334120	+	0.274205i	−0.786461	−	0.617640i	$-0.788089\pi$
$853$	−285.005	+	233.897i	−0.334120	+	0.274205i	0.452341	+	0.891845i	$0.350589\pi$
$854$	355.551	−	367.546i	0.416336	−	0.430382i
$855$	84.5042	−	126.469i	0.0988353	−	0.147917i
$856$	−726.785	−	434.953i	−0.849048	−	0.508123i
$857$	−692.795	−	1036.84i	−0.808396	−	1.20985i	−0.974643	−	0.223766i	$-0.928165\pi$
$857$	−692.795	−	1036.84i	−0.808396	−	1.20985i	0.166247	−	0.986084i	$-0.446835\pi$
$858$	20.6967	+	29.8894i	0.0241220	+	0.0348361i
$859$	−22.6814	+	42.4339i	−0.0264044	+	0.0493992i	−0.894778	−	0.446512i	$-0.852666\pi$
$859$	−22.6814	+	42.4339i	−0.0264044	+	0.0493992i	0.868373	+	0.495911i	$0.165166\pi$
$860$	−30.5878	+	81.3807i	−0.0355673	+	0.0946287i
$861$	2.80002	+	28.4291i	0.00325206	+	0.0330187i
$862$	683.541	−	380.069i	0.792971	−	0.440915i
$863$	−549.378	−	549.378i	−0.636591	−	0.636591i	0.313122	−	0.949713i	$-0.398625\pi$
$863$	−549.378	−	549.378i	−0.636591	−	0.636591i	−0.949713	+	0.313122i	$0.898625\pi$
$864$	13.7742	+	165.705i	0.0159424	+	0.191789i
$865$	−145.120	−	145.120i	−0.167769	−	0.167769i
$866$	−50.0954	+	175.575i	−0.0578469	+	0.202742i
$867$	−48.6584	−	494.037i	−0.0561228	−	0.569824i
$868$	218.645	+	204.599i	0.251895	+	0.235713i
$869$	4.68374	−	8.76266i	0.00538981	−	0.0100836i
$870$	33.0125	−	181.662i	0.0379454	−	0.208807i
$871$	−10.4609	−	15.6558i	−0.0120102	−	0.0179745i
$872$	−456.222	+	504.044i	−0.523190	+	0.578032i
$873$	235.353	−	352.230i	0.269591	−	0.403471i
$874$	3.07268	+	185.232i	0.00351566	+	0.211936i
$875$	−264.927	+	217.420i	−0.302774	+	0.248480i
$876$	−121.162	+	452.994i	−0.138312	+	0.517117i
$877$	470.589	+	880.411i	0.536590	+	1.00389i	0.993441	+	0.114346i	$0.0364773\pi$
$877$	470.589	+	880.411i	0.536590	+	1.00389i	−0.456851	+	0.889543i	$0.651023\pi$
$878$	1054.86	−	339.195i	1.20144	−	0.386326i
$879$	−609.642	+	252.522i	−0.693563	+	0.287283i
$880$	343.863	+	447.300i	0.390754	+	0.508295i
$881$	−171.085	+	413.035i	−0.194194	+	0.468825i	−0.990743	−	0.135748i	$-0.956656\pi$
$881$	−171.085	+	413.035i	−0.194194	+	0.468825i	0.796550	+	0.604573i	$0.206656\pi$
$882$	−222.628	−	18.2042i	−0.252413	−	0.0206397i
$883$	−278.289	+	917.397i	−0.315163	+	1.03895i	0.646084	+	0.763267i	$0.276406\pi$
$883$	−278.289	+	917.397i	−0.315163	+	1.03895i	−0.961247	+	0.275688i	$0.911094\pi$
$884$	−1.31152	−	3.85791i	−0.00148361	−	0.00436415i
$885$	−23.0855	+	234.391i	−0.0260853	+	0.264849i
$886$	−333.196	+	144.534i	−0.376067	+	0.163131i
$887$	−1320.24	+	262.613i	−1.48844	+	0.296069i	−0.871286	−	0.490776i	$-0.836713\pi$
$887$	−1320.24	+	262.613i	−1.48844	+	0.296069i	−0.617152	+	0.786844i	$0.711713\pi$
$888$	312.359	+	344.169i	0.351755	+	0.387577i
$889$	−409.676	−	81.4896i	−0.460828	−	0.0916643i
$890$	−154.030	−	99.2642i	−0.173067	−	0.111533i
$891$	−137.094	+	41.5870i	−0.153865	+	0.0466746i
$892$	−1270.30	−	789.136i	−1.42411	−	0.884682i
$893$	−169.594	−	139.182i	−0.189915	−	0.155859i
$894$	−65.0507	−	564.343i	−0.0727636	−	0.631256i
$895$		−	626.812i		−	0.700349i
$896$	−360.716	+	250.494i	−0.402585	+	0.279569i
$897$	4.62165			0.00515234
$898$	−584.252	+	67.3456i	−0.650615	+	0.0749951i
$899$	−333.049	+	405.822i	−0.370466	+	0.451414i
$900$	204.811	+	127.232i	0.227567	+	0.141369i
$901$	33.7238	+	111.172i	0.0374292	+	0.123388i
$902$	82.9024	−	128.641i	0.0919095	−	0.142618i
$903$	11.3749	−	57.1854i	0.0125968	−	0.0633282i
$904$	1510.11	+	73.1683i	1.67048	+	0.0809383i
$905$	106.691	+	536.373i	0.117891	+	0.592677i
$906$	51.8487	+	119.527i	0.0572281	+	0.131928i
$907$	−1299.24	−	127.964i	−1.43246	−	0.141085i	−0.648177	−	0.761490i	$-0.724468\pi$
$907$	−1299.24	−	127.964i	−1.43246	−	0.141085i	−0.784282	+	0.620405i	$0.786968\pi$
$908$	115.698	+	340.334i	0.127421	+	0.374817i
$909$	83.6042	+	25.3611i	0.0919738	+	0.0278999i
$910$	0.816766	−	9.98864i	0.000897545	−	0.0109765i
$911$	−676.206	−	280.094i	−0.742268	−	0.307457i	−0.0206854	−	0.999786i	$-0.506585\pi$
$911$	−676.206	−	280.094i	−0.742268	−	0.307457i	−0.721582	+	0.692329i	$0.756585\pi$
$912$	−164.712	−	612.516i	−0.180606	−	0.671619i
$913$	−520.816	−	1257.36i	−0.570445	−	1.37718i
$914$	−39.7216	−	123.531i	−0.0434591	−	0.135154i
$915$	252.178	−	134.792i	0.275604	−	0.147314i
$916$	−233.673	+	873.647i	−0.255101	+	0.953763i
$917$	−30.9225	−	37.6792i	−0.0337214	−	0.0410896i
$918$	16.0548	−	0.266321i	0.0174889	−	0.000290111i
$919$	877.210	+	586.133i	0.954527	+	0.637795i	0.932195	−	0.361956i	$-0.117891\pi$
$919$	877.210	+	586.133i	0.954527	+	0.637795i	0.0223320	+	0.999751i	$0.492891\pi$
$920$	71.6341	−	3.56749i	0.0778632	−	0.00387770i
$921$	−105.959	+	70.7996i	−0.115048	+	0.0768726i
$922$	879.670	+	159.858i	0.954089	+	0.173381i
$923$	37.9334	+	20.2758i	0.0410979	+	0.0219673i
$924$	−276.281	−	258.533i	−0.299006	−	0.279798i
$925$	670.716	−	66.0598i	0.725099	−	0.0714160i
$926$	782.828	+	223.359i	0.845387	+	0.241208i
$927$	−42.0338	+	42.0338i	−0.0453439	+	0.0453439i
$928$	−479.320	−	602.550i	−0.516509	−	0.649300i
$929$	−885.622	+	885.622i	−0.953307	+	0.953307i	−0.998957	−	0.0456503i	$-0.985464\pi$
$929$	−885.622	+	885.622i	−0.953307	+	0.953307i	0.0456503	+	0.998957i	$0.485464\pi$
$930$	81.3675	+	146.337i	0.0874920	+	0.157351i
$931$	847.965	−	83.5172i	0.910811	−	0.0897070i
$932$	185.269	−	492.919i	0.198787	−	0.528883i
$933$	−121.977	−	65.1978i	−0.130736	−	0.0698798i
$934$	729.713	−	505.284i	0.781277	−	0.540989i
$935$	45.3012	−	30.2693i	0.0484505	−	0.0323736i
$936$	−15.3466	+	3.85510i	−0.0163959	+	0.00411870i
$937$	845.263	+	564.787i	0.902095	+	0.602761i	0.917768	−	0.397116i	$-0.129989\pi$
$937$	845.263	+	564.787i	0.902095	+	0.602761i	−0.0156729	+	0.999877i	$0.504989\pi$
$938$	140.849	+	136.253i	0.150159	+	0.145259i
$939$	120.239	+	146.512i	0.128051	+	0.156030i
$940$	−51.6774	+	67.4099i	−0.0549760	+	0.0717127i
$941$	843.686	−	450.960i	0.896584	−	0.479234i	0.0423385	−	0.999103i	$-0.486519\pi$
$941$	843.686	−	450.960i	0.896584	−	0.479234i	0.854246	+	0.519869i	$0.174019\pi$
$942$	413.391	+	212.223i	0.438844	+	0.225290i
$943$	−7.44512	−	17.9741i	−0.00789514	−	0.0190606i
$944$	672.032	+	716.232i	0.711898	+	0.758720i
$945$	36.4865	+	15.1132i	0.0386100	+	0.0159928i
$946$	−238.139	+	202.137i	−0.251732	+	0.213676i
$947$	409.525	+	124.228i	0.432445	+	0.131181i	0.499000	−	0.866602i	$-0.333701\pi$
$947$	409.525	+	124.228i	0.432445	+	0.131181i	−0.0665550	+	0.997783i	$0.521201\pi$
$948$	2.85280	+	3.25005i	0.00300928	+	0.00342832i
$949$	−44.4088	−	4.37388i	−0.0467953	−	0.00460894i
$950$	−855.453	−	337.828i	−0.900477	−	0.355609i
$951$	165.960	+	834.336i	0.174511	+	0.877325i
$952$	21.8270	+	36.3606i	0.0229275	+	0.0381939i
$953$	−204.413	+	1027.65i	−0.214494	+	1.07833i	0.712044	+	0.702135i	$0.247770\pi$
$953$	−204.413	+	1027.65i	−0.214494	+	1.07833i	−0.926538	+	0.376200i	$0.877230\pi$
$954$	440.950	−	95.3397i	0.462212	−	0.0999368i
$955$	20.6220	+	67.9817i	0.0215938	+	0.0711851i
$956$	158.163	−	113.445i	0.165442	−	0.118667i
$957$	420.843	−	512.799i	0.439752	−	0.535840i
$958$	905.528	−	1141.48i	0.945227	−	1.19153i
$959$	−485.144			−0.505885
$960$	−234.892	+	71.5990i	−0.244679	+	0.0745823i
$961$			484.919i			0.504599i
$962$	−27.4882	+	34.6508i	−0.0285740	+	0.0360195i
$963$	245.526	+	201.498i	0.254960	+	0.209240i
$964$	−246.303	+	1496.01i	−0.255501	+	1.55188i
$965$	395.257	−	119.900i	0.409592	−	0.124248i
$966$	−47.0145	+	10.1652i	−0.0486693	+	0.0105230i
$967$	−1498.49	−	298.068i	−1.54963	−	0.308240i	−0.655200	−	0.755456i	$-0.727416\pi$
$967$	−1498.49	−	298.068i	−1.54963	−	0.308240i	−0.894426	+	0.447216i	$0.852416\pi$
$968$	156.106	+	1047.52i	0.161266	+	1.08215i
$969$	−60.0737	+	11.9494i	−0.0619956	+	0.0123317i
$970$	581.887	+	229.794i	0.599883	+	0.236901i
$971$	−85.8602	+	871.753i	−0.0884245	+	0.897789i	0.843980	+	0.536374i	$0.180206\pi$
$971$	−85.8602	+	871.753i	−0.0884245	+	0.897789i	−0.932405	+	0.361415i	$0.882294\pi$
$972$	4.05022	−	62.2221i	0.00416689	−	0.0640146i
$973$	35.1076	−	115.734i	0.0360818	−	0.118946i
$974$	−340.603	+	289.112i	−0.349695	+	0.296829i
$975$	−8.78067	+	21.1984i	−0.00900582	+	0.0217420i
$976$	269.720	−	1161.48i	0.276353	−	1.19004i
$977$	838.751	−	347.422i	0.858496	−	0.355601i	0.0903769	−	0.995908i	$-0.471193\pi$
$977$	838.751	−	347.422i	0.858496	−	0.355601i	0.768119	+	0.640307i	$0.221193\pi$
$978$	847.231	+	434.944i	0.866289	+	0.444728i
$979$	−310.356	−	580.634i	−0.317013	−	0.593089i
$980$	−43.2047	−	327.039i	−0.0440865	−	0.333713i
$981$	197.075	−	161.735i	0.200892	−	0.164868i
$982$	−110.355	−	106.753i	−0.112378	−	0.108710i
$983$	−578.901	+	866.387i	−0.588913	+	0.881370i	−0.999537	−	0.0304346i	$-0.990311\pi$
$983$	−578.901	+	866.387i	−0.588913	+	0.881370i	0.410624	+	0.911805i	$0.365311\pi$
$984$	39.7151	+	53.4744i	0.0403609	+	0.0543439i
$985$	−304.947	−	456.385i	−0.309591	−	0.463335i
$986$	−61.1276	+	42.3273i	−0.0619956	+	0.0429283i
$987$	26.8528	−	50.2381i	0.0272065	−	0.0508997i
$988$	54.9682	−	24.9355i	0.0556358	−	0.0252384i
$989$	3.89212	+	39.5173i	0.00393540	+	0.0399568i
$990$	−102.816	−	184.912i	−0.103855	−	0.186780i
$991$	700.214	+	700.214i	0.706573	+	0.706573i	0.965813	−	0.259240i	$-0.0834720\pi$
$991$	700.214	+	700.214i	0.706573	+	0.706573i	−0.259240	+	0.965813i	$0.583472\pi$
$992$	682.645	+	146.636i	0.688151	+	0.147819i
$993$	545.351	+	545.351i	0.549195	+	0.549195i
$994$	−430.480	−	122.826i	−0.433078	−	0.123567i
$995$	−21.2519	−	215.775i	−0.0213587	−	0.216859i
$996$	592.018	−	19.6466i	0.594396	−	0.0197255i
$997$	772.503	−	1445.25i	0.774828	−	1.44960i	−0.115030	−	0.993362i	$-0.536696\pi$
$997$	772.503	−	1445.25i	0.774828	−	1.44960i	0.889857	−	0.456239i	$-0.150804\pi$
$998$	−1162.26	−	211.212i	−1.16459	−	0.211635i
$999$	−96.8316	−	144.919i	−0.0969286	−	0.145064i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.3.u.a.235.30	yes	1024
128.67	odd	32	inner	384.3.u.a.67.30	✓	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.3.u.a.67.30	✓	1024	128.67	odd	32	inner
384.3.u.a.235.30	yes	1024	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	384.u (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.229020 - 1.98684i) q^{2} +(1.09880 - 1.33889i) q^{3} +(-3.89510 + 0.910053i) q^{4} +(0.643049 + 2.11985i) q^{5} +(-2.91182 - 1.87651i) q^{6} +(-0.669346 + 3.36503i) q^{7} +(2.70019 + 7.53054i) q^{8} +(-0.585271 - 2.94236i) q^{9} +O(q^{10})\)	\(q+(-0.229020 - 1.98684i) q^{2} +(1.09880 - 1.33889i) q^{3} +(-3.89510 + 0.910053i) q^{4} +(0.643049 + 2.11985i) q^{5} +(-2.91182 - 1.87651i) q^{6} +(-0.669346 + 3.36503i) q^{7} +(2.70019 + 7.53054i) q^{8} +(-0.585271 - 2.94236i) q^{9} +(4.06454 - 1.76313i) q^{10} +(15.8415 + 1.56025i) q^{11} +(-3.06148 + 6.21509i) q^{12} +(-0.630919 - 0.191387i) q^{13} +(6.83908 + 0.559228i) q^{14} +(3.54484 + 1.46832i) q^{15} +(14.3436 - 7.08949i) q^{16} +(-0.591278 - 1.42747i) q^{17} +(-5.71196 + 1.83670i) q^{18} +(20.1849 - 10.7891i) q^{19} +(-4.43392 - 7.67182i) q^{20} +(3.76994 + 4.59368i) q^{21} +(-0.528036 - 31.8318i) q^{22} +(-3.36507 - 2.24847i) q^{23} +(13.0496 + 4.65930i) q^{24} +(16.7065 - 11.1629i) q^{25} +(-0.235764 + 1.29737i) q^{26} +(-4.58260 - 2.44945i) q^{27} +(-0.455184 - 13.7163i) q^{28} +(23.9449 - 2.35837i) q^{29} +(2.10548 - 7.37931i) q^{30} +(-15.4286 + 15.4286i) q^{31} +(-17.3707 - 26.8749i) q^{32} +(19.4956 - 19.4956i) q^{33} +(-2.70075 + 1.50170i) q^{34} +(-7.56377 + 0.744967i) q^{35} +(4.95739 + 10.9281i) q^{36} +(29.5819 + 15.8119i) q^{37} +(-26.0590 - 37.6334i) q^{38} +(-0.949501 + 0.634437i) q^{39} +(-14.2272 + 10.5665i) q^{40} +(3.99697 + 2.67069i) q^{41} +(8.26354 - 8.54232i) q^{42} +(-6.22436 - 7.58440i) q^{43} +(-63.1240 + 8.33924i) q^{44} +(5.86099 - 3.13277i) q^{45} +(-3.69669 + 7.20082i) q^{46} +(-3.66832 - 8.85611i) q^{47} +(6.26870 - 26.9945i) q^{48} +(34.3947 + 14.2468i) q^{49} +(-26.0051 - 30.6367i) q^{50} +(-2.56093 - 0.776849i) q^{51} +(2.63166 + 0.171303i) q^{52} +(-74.8279 - 7.36990i) q^{53} +(-3.81717 + 9.66588i) q^{54} +(6.87935 + 34.5848i) q^{55} +(-27.1478 + 4.04567i) q^{56} +(7.73382 - 38.8805i) q^{57} +(-10.1696 - 47.0347i) q^{58} +(17.8189 + 58.7411i) q^{59} +(-15.1437 - 2.49326i) q^{60} +(47.2776 - 57.6079i) q^{61} +(34.1876 + 27.1207i) q^{62} +10.2929 q^{63} +(-49.4180 + 40.6677i) q^{64} -1.46052i q^{65} +(-43.1996 - 34.2699i) q^{66} +(22.0763 + 18.1175i) q^{67} +(3.60216 + 5.02205i) q^{68} +(-6.70800 + 2.03485i) q^{69} +(3.21239 + 14.8574i) q^{70} +(-63.9848 - 12.7274i) q^{71} +(20.5772 - 12.3523i) q^{72} +(66.3820 - 13.2042i) q^{73} +(24.6409 - 62.3959i) q^{74} +(3.41116 - 34.6340i) q^{75} +(-68.8038 + 60.3939i) q^{76} +(-15.8537 + 52.2626i) q^{77} +(1.47798 + 1.74121i) q^{78} +(0.238866 - 0.576674i) q^{79} +(24.2523 + 25.8474i) q^{80} +(-8.31492 + 3.44415i) q^{81} +(4.39086 - 8.55299i) q^{82} +(-40.3032 - 75.4020i) q^{83} +(-18.8648 - 14.4620i) q^{84} +(2.64580 - 2.17135i) q^{85} +(-13.6435 + 14.1038i) q^{86} +(23.1531 - 34.6511i) q^{87} +(31.0254 + 123.508i) q^{88} +(-22.9784 - 34.3897i) q^{89} +(-7.56660 - 10.9274i) q^{90} +(1.06633 - 1.99496i) q^{91} +(15.1535 + 5.69562i) q^{92} +(3.70427 + 37.6101i) q^{93} +(-16.7556 + 9.31660i) q^{94} +(35.8511 + 35.8511i) q^{95} +(-55.0695 - 6.27266i) q^{96} +(99.8490 + 99.8490i) q^{97} +(20.4290 - 71.5997i) q^{98} +(-4.68074 - 47.5244i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q+O(q^{10}) \) 1024 * q	\( 1024 q + 1248 q^{50} + 1056 q^{52} + 288 q^{54} + 1568 q^{56} + 576 q^{60} + 192 q^{62} - 192 q^{64} - 576 q^{66} - 960 q^{68} - 1344 q^{70} - 2464 q^{74} - 416 q^{76} - 1440 q^{78} - 1632 q^{80}+O(q^{100}) \) 1024 * q + 1248 * q^50 + 1056 * q^52 + 288 * q^54 + 1568 * q^56 + 576 * q^60 + 192 * q^62 - 192 * q^64 - 576 * q^66 - 960 * q^68 - 1344 * q^70 - 2464 * q^74 - 416 * q^76 - 1440 * q^78 - 1632 * q^80

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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