LMFDB - Embedded newform 54.4.e.b.13.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [54,4,Mod(7,54)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(54, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([16])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("54.7"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	54.e (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [30] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.18610314031$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			13.2
Character	$\chi$	$=$	54.13
Dual form			54.4.e.b.25.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.347296 - 1.96962i) q^{2} +(-3.45245 - 3.88337i) q^{3} +(-3.75877 + 1.36808i) q^{4} +(0.657259 + 0.551505i) q^{5} +(-6.44973 + 8.14868i) q^{6} +(-20.5288 - 7.47187i) q^{7} +(4.00000 + 6.92820i) q^{8} +(-3.16120 + 26.8143i) q^{9} +(0.857990 - 1.48608i) q^{10} +(-37.2066 + 31.2201i) q^{11} +(18.2897 + 9.87349i) q^{12} +(9.56100 - 54.2231i) q^{13} +(-7.58714 + 43.0288i) q^{14} +(-0.127449 - 4.45643i) q^{15} +(12.2567 - 10.2846i) q^{16} +(39.6041 - 68.5963i) q^{17} +(53.9117 - 3.08617i) q^{18} +(-55.0156 - 95.2899i) q^{19} +(-3.22499 - 1.17380i) q^{20} +(41.8585 + 105.517i) q^{21} +(74.4132 + 62.4401i) q^{22} +(-42.5012 + 15.4692i) q^{23} +(13.0950 - 39.4528i) q^{24} +(-21.5782 - 122.376i) q^{25} -110.119 q^{26} +(115.044 - 80.2989i) q^{27} +87.3852 q^{28} +(21.6890 + 123.004i) q^{29} +(-8.73318 + 1.79873i) q^{30} +(125.635 - 45.7274i) q^{31} +(-24.5134 - 20.5692i) q^{32} +(249.693 + 36.7016i) q^{33} +(-148.863 - 54.1816i) q^{34} +(-9.37195 - 16.2327i) q^{35} +(-24.8019 - 105.114i) q^{36} +(-84.1614 + 145.772i) q^{37} +(-168.578 + 141.453i) q^{38} +(-243.578 + 150.074i) q^{39} +(-1.19191 + 6.75964i) q^{40} +(-3.71508 + 21.0693i) q^{41} +(193.291 - 119.091i) q^{42} +(-128.831 + 108.102i) q^{43} +(97.1396 - 168.251i) q^{44} +(-16.8660 + 15.8805i) q^{45} +(45.2289 + 78.3387i) q^{46} +(-298.913 - 108.795i) q^{47} +(-82.2546 - 12.0903i) q^{48} +(102.849 + 86.3009i) q^{49} +(-233.540 + 85.0015i) q^{50} +(-403.116 + 83.0276i) q^{51} +(38.2440 + 216.893i) q^{52} +463.685 q^{53} +(-198.112 - 198.705i) q^{54} -41.6724 q^{55} +(-30.3485 - 172.115i) q^{56} +(-180.108 + 542.630i) q^{57} +(234.739 - 85.4380i) q^{58} +(415.527 + 348.668i) q^{59} +(6.57580 + 16.5763i) q^{60} +(-648.554 - 236.054i) q^{61} +(-133.698 - 231.571i) q^{62} +(265.249 - 526.845i) q^{63} +(-32.0000 + 55.4256i) q^{64} +(36.1884 - 30.3657i) q^{65} +(-14.4295 - 504.546i) q^{66} +(111.664 - 633.280i) q^{67} +(-55.0174 + 312.019i) q^{68} +(206.806 + 111.642i) q^{69} +(-28.7173 + 24.0967i) q^{70} +(524.772 - 908.932i) q^{71} +(-198.420 + 85.3558i) q^{72} +(480.157 + 831.656i) q^{73} +(316.343 + 115.140i) q^{74} +(-400.734 + 506.293i) q^{75} +(337.155 + 282.907i) q^{76} +(997.080 - 362.907i) q^{77} +(380.181 + 427.634i) q^{78} +(39.7859 + 225.637i) q^{79} +13.7278 q^{80} +(-709.014 - 169.531i) q^{81} +42.7886 q^{82} +(-29.5416 - 167.539i) q^{83} +(-301.693 - 339.349i) q^{84} +(63.8613 - 23.2436i) q^{85} +(257.663 + 216.205i) q^{86} +(402.792 - 508.893i) q^{87} +(-365.125 - 132.895i) q^{88} +(379.679 + 657.623i) q^{89} +(37.1360 + 27.7042i) q^{90} +(-601.424 + 1041.70i) q^{91} +(138.589 - 116.290i) q^{92} +(-611.324 - 330.016i) q^{93} +(-110.474 + 626.528i) q^{94} +(16.3934 - 92.9715i) q^{95} +(4.75341 + 166.209i) q^{96} +(1232.17 - 1033.92i) q^{97} +(134.260 - 232.546i) q^{98} +(-719.527 - 1096.36i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 12 q^{5} + 30 q^{6} + 33 q^{7} + 120 q^{8} + 42 q^{9} - 30 q^{10} - 39 q^{11} + 24 q^{12} - 60 q^{13} - 66 q^{14} - 153 q^{15} + 102 q^{17} + 168 q^{18} - 171 q^{19} + 96 q^{20} + 78 q^{21} + 78 q^{22}+ \cdots + 10296 q^{99}+O(q^{100}) $ 30 * q - 12 * q^5 + 30 * q^6 + 33 * q^7 + 120 * q^8 + 42 * q^9 - 30 * q^10 - 39 * q^11 + 24 * q^12 - 60 * q^13 - 66 * q^14 - 153 * q^15 + 102 * q^17 + 168 * q^18 - 171 * q^19 + 96 * q^20 + 78 * q^21 + 78 * q^22 + 48 * q^23 - 432 * q^25 - 468 * q^26 - 675 * q^27 + 336 * q^28 - 381 * q^29 - 486 * q^30 - 801 * q^31 + 954 * q^33 - 222 * q^34 + 624 * q^35 + 132 * q^36 - 555 * q^37 + 606 * q^38 + 363 * q^39 + 96 * q^40 + 1401 * q^41 - 420 * q^42 + 648 * q^43 + 132 * q^44 + 2583 * q^45 - 348 * q^46 + 540 * q^47 + 192 * q^48 + 15 * q^49 - 828 * q^50 - 2376 * q^51 - 240 * q^52 - 1794 * q^53 - 522 * q^54 + 3906 * q^55 - 264 * q^56 - 1656 * q^57 - 444 * q^58 - 1500 * q^59 + 1332 * q^60 - 378 * q^61 + 744 * q^62 + 840 * q^63 - 960 * q^64 + 3666 * q^65 + 1710 * q^66 + 3087 * q^67 - 24 * q^68 + 1665 * q^69 + 2118 * q^70 + 120 * q^71 + 672 * q^72 - 2604 * q^73 - 1974 * q^74 - 2643 * q^75 - 1212 * q^76 - 6504 * q^77 - 5220 * q^78 - 2625 * q^79 - 480 * q^80 - 7614 * q^81 + 3408 * q^82 - 5211 * q^83 - 1548 * q^84 - 1395 * q^85 - 1296 * q^86 + 4914 * q^87 - 912 * q^88 + 2604 * q^89 + 1512 * q^90 - 3399 * q^91 + 372 * q^92 - 222 * q^93 + 4500 * q^94 + 7545 * q^95 + 384 * q^96 + 8940 * q^97 + 4002 * q^98 + 10296 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

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 $

$2$	−0.347296	−	1.96962i	−0.122788	−	0.696364i
$2$	−0.347296	−	1.96962i	−0.122788	−	0.696364i
$3$	−3.45245	−	3.88337i	−0.664424	−	0.747356i
$3$	−3.45245	−	3.88337i	−0.664424	−	0.747356i
$4$	−3.75877	+	1.36808i	−0.469846	+	0.171010i
$5$	0.657259	+	0.551505i	0.0587870	+	0.0493282i	0.671708	−	0.740816i	$-0.265561\pi$
$5$	0.657259	+	0.551505i	0.0587870	+	0.0493282i	−0.612921	+	0.790144i	$0.710006\pi$
$6$	−6.44973	+	8.14868i	−0.438849	+	0.554447i
$7$	−20.5288	−	7.47187i	−1.10845	−	0.403443i	−0.278026	−	0.960574i	$-0.589680\pi$
$7$	−20.5288	−	7.47187i	−1.10845	−	0.403443i	−0.830425	+	0.557130i	$0.811902\pi$
$8$	4.00000	+	6.92820i	0.176777	+	0.306186i
$9$	−3.16120	+	26.8143i	−0.117081	+	0.993122i
$10$	0.857990	−	1.48608i	0.0271320	−	0.0469941i
$11$	−37.2066	+	31.2201i	−1.01984	+	0.855746i	−0.989607	−	0.143797i	$-0.954069\pi$
$11$	−37.2066	+	31.2201i	−1.01984	+	0.855746i	−0.0302309	+	0.999543i	$0.509624\pi$
$12$	18.2897	+	9.87349i	0.439983	+	0.237519i
$13$	9.56100	−	54.2231i	0.203980	−	1.15683i	−0.695056	−	0.718956i	$-0.744620\pi$
$13$	9.56100	−	54.2231i	0.203980	−	1.15683i	0.899036	−	0.437874i	$-0.144269\pi$
$14$	−7.58714	+	43.0288i	−0.144839	+	0.821423i
$15$	−0.127449	−	4.45643i	−0.00219382	−	0.0767096i
$16$	12.2567	−	10.2846i	0.191511	−	0.160697i
$17$	39.6041	−	68.5963i	0.565024	−	0.978649i	−0.432024	−	0.901862i	$-0.642200\pi$
$17$	39.6041	−	68.5963i	0.565024	−	0.978649i	0.997047	−	0.0767873i	$-0.0244662\pi$
$18$	53.9117	−	3.08617i	0.705951	−	0.0404120i
$19$	−55.0156	−	95.2899i	−0.664287	−	1.15058i	−0.979478	−	0.201550i	$-0.935402\pi$
$19$	−55.0156	−	95.2899i	−0.664287	−	1.15058i	0.315191	−	0.949028i	$-0.397931\pi$
$20$	−3.22499	−	1.17380i	−0.0360565	−	0.0131235i
$21$	41.8585	+	105.517i	0.434966	+	1.09646i
$22$	74.4132	+	62.4401i	0.721134	+	0.605104i
$23$	−42.5012	+	15.4692i	−0.385310	+	0.140241i	−0.527410	−	0.849611i	$-0.676837\pi$
$23$	−42.5012	+	15.4692i	−0.385310	+	0.140241i	0.142100	+	0.989852i	$0.454614\pi$
$24$	13.0950	−	39.4528i	0.111375	−	0.335553i
$25$	−21.5782	−	122.376i	−0.172626	−	0.979008i
$26$	−110.119			−0.830621
$27$	115.044	−	80.2989i	0.820007	−	0.572353i
$28$	87.3852			0.589794
$29$	21.6890	+	123.004i	0.138881	+	0.787633i	0.972078	+	0.234657i	$0.0753967\pi$
$29$	21.6890	+	123.004i	0.138881	+	0.787633i	−0.833197	+	0.552976i	$0.813492\pi$
$30$	−8.73318	+	1.79873i	−0.0531485	+	0.0109467i
$31$	125.635	−	45.7274i	0.727893	−	0.264931i	0.0486205	−	0.998817i	$-0.484518\pi$
$31$	125.635	−	45.7274i	0.727893	−	0.264931i	0.679273	+	0.733886i	$0.262295\pi$
$32$	−24.5134	−	20.5692i	−0.135419	−	0.113630i
$33$	249.693	+	36.7016i	1.31715	+	0.193604i
$34$	−148.863	−	54.1816i	−0.750874	−	0.273296i
$35$	−9.37195	−	16.2327i	−0.0452614	−	0.0783950i
$36$	−24.8019	−	105.114i	−0.114824	−	0.486637i
$37$	−84.1614	+	145.772i	−0.373947	+	0.647696i	−0.990169	−	0.139877i	$-0.955329\pi$
$37$	−84.1614	+	145.772i	−0.373947	+	0.647696i	0.616222	+	0.787573i	$0.288663\pi$
$38$	−168.578	+	141.453i	−0.719655	+	0.603863i
$39$	−243.578	+	150.074i	−1.00009	+	0.616180i
$40$	−1.19191	+	6.75964i	−0.00471143	+	0.0267198i
$41$	−3.71508	+	21.0693i	−0.0141512	+	0.0802554i	−0.991065	−	0.133376i	$-0.957418\pi$
$41$	−3.71508	+	21.0693i	−0.0141512	+	0.0802554i	0.976914	+	0.213632i	$0.0685292\pi$
$42$	193.291	−	119.091i	0.710130	−	0.437527i
$43$	−128.831	+	108.102i	−0.456898	+	0.383383i	−0.841988	−	0.539496i	$-0.818615\pi$
$43$	−128.831	+	108.102i	−0.456898	+	0.383383i	0.385090	+	0.922879i	$0.374170\pi$
$44$	97.1396	−	168.251i	0.332826	−	0.576472i
$45$	−16.8660	+	15.8805i	−0.0558717	+	0.0526073i
$46$	45.2289	+	78.3387i	0.144970	+	0.251096i
$47$	−298.913	−	108.795i	−0.927680	−	0.337648i	−0.166390	−	0.986060i	$-0.553211\pi$
$47$	−298.913	−	108.795i	−0.927680	−	0.337648i	−0.761289	+	0.648412i	$0.775433\pi$
$48$	−82.2546	−	12.0903i	−0.247342	−	0.0363561i
$49$	102.849	+	86.3009i	0.299853	+	0.251606i
$50$	−233.540	+	85.0015i	−0.660550	+	0.240420i
$51$	−403.116	+	83.0276i	−1.10681	+	0.227965i
$52$	38.2440	+	216.893i	0.101990	+	0.578415i
$53$	463.685			1.20174			0.600869	−	0.799348i	$-0.294822\pi$
$53$	463.685			1.20174			0.600869	+	0.799348i	$0.294822\pi$
$54$	−198.112	−	198.705i	−0.499253	−	0.500746i
$55$	−41.6724			−0.102166
$56$	−30.3485	−	172.115i	−0.0724196	−	0.410712i
$57$	−180.108	+	542.630i	−0.418523	+	1.26093i
$58$	234.739	−	85.4380i	0.531427	−	0.193423i
$59$	415.527	+	348.668i	0.916898	+	0.769369i	0.973419	−	0.229033i	$-0.0735562\pi$
$59$	415.527	+	348.668i	0.916898	+	0.769369i	−0.0565206	+	0.998401i	$0.518001\pi$
$60$	6.57580	+	16.5763i	0.0141489	+	0.0356666i
$61$	−648.554	−	236.054i	−1.36129	−	0.495470i	−0.444838	−	0.895611i	$-0.646739\pi$
$61$	−648.554	−	236.054i	−1.36129	−	0.495470i	−0.916453	+	0.400141i	$0.868961\pi$
$62$	−133.698	−	231.571i	−0.273865	−	0.474349i
$63$	265.249	−	526.845i	0.530447	−	1.05359i
$64$	−32.0000	+	55.4256i	−0.0625000	+	0.108253i
$65$	36.1884	−	30.3657i	0.0690557	−	0.0579446i
$66$	−14.4295	−	504.546i	−0.0269113	−	0.940989i
$67$	111.664	−	633.280i	0.203611	−	1.15474i	−0.695998	−	0.718043i	$-0.745038\pi$
$67$	111.664	−	633.280i	0.203611	−	1.15474i	0.899610	−	0.436695i	$-0.143851\pi$
$68$	−55.0174	+	312.019i	−0.0981153	+	0.556440i
$69$	206.806	+	111.642i	0.360819	+	0.194784i
$70$	−28.7173	+	24.0967i	−0.0490340	+	0.0411444i
$71$	524.772	−	908.932i	0.877169	−	1.51930i	0.0227353	−	0.999742i	$-0.492763\pi$
$71$	524.772	−	908.932i	0.877169	−	1.51930i	0.854434	−	0.519560i	$-0.173904\pi$
$72$	−198.420	+	85.3558i	−0.324778	+	0.139712i
$73$	480.157	+	831.656i	0.769837	+	1.33340i	0.937651	+	0.347578i	$0.112996\pi$
$73$	480.157	+	831.656i	0.769837	+	1.33340i	−0.167814	+	0.985819i	$0.553671\pi$
$74$	316.343	+	115.140i	0.496948	+	0.180874i
$75$	−400.734	+	506.293i	−0.616971	+	0.779489i
$76$	337.155	+	282.907i	0.508873	+	0.426995i
$77$	997.080	−	362.907i	1.47569	−	0.537105i
$78$	380.181	+	427.634i	0.551885	+	0.620770i
$79$	39.7859	+	225.637i	0.0566616	+	0.321344i	0.999943	−	0.0106497i	$-0.00338996\pi$
$79$	39.7859	+	225.637i	0.0566616	+	0.321344i	−0.943282	+	0.331993i	$0.892279\pi$
$80$	13.7278			0.0191852
$81$	−709.014	−	169.531i	−0.972584	−	0.232552i
$82$	42.7886			0.0576246
$83$	−29.5416	−	167.539i	−0.0390676	−	0.221564i	0.959023	−	0.283328i	$-0.0914384\pi$
$83$	−29.5416	−	167.539i	−0.0390676	−	0.221564i	−0.998091	+	0.0617642i	$0.980327\pi$
$84$	−301.693	−	339.349i	−0.391874	−	0.440786i
$85$	63.8613	−	23.2436i	0.0814910	−	0.0296603i
$86$	257.663	+	216.205i	0.323075	+	0.271092i
$87$	402.792	−	508.893i	0.496366	−	0.627116i
$88$	−365.125	−	132.895i	−0.442301	−	0.160984i
$89$	379.679	+	657.623i	0.452201	+	0.783235i	0.998522	−	0.0543405i	$-0.0173057\pi$
$89$	379.679	+	657.623i	0.452201	+	0.783235i	−0.546322	+	0.837576i	$0.683972\pi$
$90$	37.1360	+	27.7042i	0.0434942	+	0.0324476i
$91$	−601.424	+	1041.70i	−0.692817	+	1.19999i
$92$	138.589	−	116.290i	0.157054	−	0.131784i
$93$	−611.324	−	330.016i	−0.681628	−	0.367968i
$94$	−110.474	+	626.528i	−0.121218	+	0.687462i
$95$	16.3934	−	92.9715i	0.0177045	−	0.100407i
$96$	4.75341	+	166.209i	0.00505357	+	0.176704i
$97$	1232.17	−	1033.92i	1.28978	−	1.08225i	0.297961	−	0.954578i	$-0.403694\pi$
$97$	1232.17	−	1033.92i	1.28978	−	1.08225i	0.991816	−	0.127673i	$-0.0407509\pi$
$98$	134.260	−	232.546i	0.138391	−	0.239701i
$99$	−719.527	−	1096.36i	−0.730456	−	1.11302i
$100$	248.528	+	430.463i	0.248528	+	0.430463i
$101$	−1527.30	−	555.893i	−1.50468	−	0.547657i	−0.547410	−	0.836865i	$-0.684386\pi$
$101$	−1527.30	−	555.893i	−1.50468	−	0.547657i	−0.957267	+	0.289207i	$0.906608\pi$
$102$	303.533	+	765.148i	0.294650	+	0.742755i
$103$	−5.96157	−	5.00235i	−0.00570302	−	0.00478540i	0.639932	−	0.768432i	$-0.278963\pi$
$103$	−5.96157	−	5.00235i	−0.00570302	−	0.00478540i	−0.645635	+	0.763646i	$0.723407\pi$
$104$	413.913	−	150.652i	0.390264	−	0.142045i
$105$	−30.6815	+	92.4374i	−0.0285162	+	0.0859139i
$106$	−161.036	−	913.282i	−0.147559	−	0.836847i
$107$	−1846.09			−1.66792			−0.833962	−	0.551822i	$-0.813933\pi$
$107$	−1846.09			−1.66792			−0.833962	+	0.551822i	$0.813933\pi$
$108$	−322.568	+	459.214i	−0.287399	+	0.409147i
$109$	−1637.48			−1.43892			−0.719461	−	0.694532i	$-0.755611\pi$
$109$	−1637.48			−1.43892			−0.719461	+	0.694532i	$0.755611\pi$
$110$	14.4727	+	82.0786i	0.0125447	+	0.0711445i
$111$	856.650	−	176.439i	0.732519	−	0.150873i
$112$	−328.461	+	119.550i	−0.277113	+	0.100861i
$113$	300.868	+	252.458i	0.250471	+	0.210170i	0.759375	−	0.650653i	$-0.225505\pi$
$113$	300.868	+	252.458i	0.250471	+	0.210170i	−0.508904	+	0.860823i	$0.669949\pi$
$114$	1131.32	+	166.289i	0.929457	+	0.136618i
$115$	−36.4656	−	13.2724i	−0.0295690	−	0.0107622i
$116$	−249.804	−	432.673i	−0.199946	−	0.346316i
$117$	1423.73	+	427.782i	1.12499	+	0.338021i
$118$	542.432	−	939.519i	0.423177	−	0.732964i
$119$	−1325.57	+	1112.28i	−1.02113	+	0.856830i
$120$	30.3652	−	18.7087i	0.0230996	−	0.0142322i
$121$	178.515	−	1012.41i	0.134121	−	0.760637i
$122$	−239.696	+	1359.38i	−0.177877	+	1.00879i
$123$	94.6461	−	58.3136i	0.0693817	−	0.0427476i
$124$	−409.674	+	343.757i	−0.296692	+	0.248954i
$125$	106.933	−	185.213i	0.0765150	−	0.132528i
$126$	−1129.80	−	339.466i	−0.798816	−	0.240016i
$127$	315.575	+	546.591i	0.220494	+	0.381907i	0.954958	−	0.296741i	$-0.0958998\pi$
$127$	315.575	+	546.591i	0.220494	+	0.381907i	−0.734464	+	0.678647i	$0.762566\pi$
$128$	120.281	+	43.7786i	0.0830579	+	0.0302306i
$129$	864.585	+	127.083i	0.590097	+	0.0867364i
$130$	−72.3768	−	60.7314i	−0.0488297	−	0.0409730i
$131$	−1695.44	+	617.090i	−1.13077	+	0.411568i	−0.838573	−	0.544789i	$-0.816610\pi$
$131$	−1695.44	+	617.090i	−1.13077	+	0.411568i	−0.292200	+	0.956357i	$0.594387\pi$
$132$	−988.750	+	203.648i	−0.651967	+	0.134282i
$133$	417.411	+	2367.26i	0.272136	+	1.54336i
$134$	−1286.10			−0.829119
$135$	119.899	+	10.6702i	0.0764389	+	0.00680254i
$136$	633.665			0.399532
$137$	−39.3700	−	223.278i	−0.0245518	−	0.139240i	0.970068	−	0.242834i	$-0.0780770\pi$
$137$	−39.3700	−	223.278i	−0.0245518	−	0.139240i	−0.994620	+	0.103594i	$0.966966\pi$
$138$	148.068	−	446.101i	0.0913362	−	0.275179i
$139$	1267.23	−	461.235i	0.773275	−	0.281449i	0.0749093	−	0.997190i	$-0.476133\pi$
$139$	1267.23	−	461.235i	0.773275	−	0.281449i	0.698365	+	0.715741i	$0.253911\pi$
$140$	57.4347	+	48.1934i	0.0346722	+	0.0290935i
$141$	609.488	+	1536.40i	0.364030	+	0.917648i
$142$	−1972.50	−	717.931i	−1.16569	−	0.424278i
$143$	1337.12	+	2315.95i	0.781926	+	1.35433i
$144$	237.029	+	361.167i	0.137169	+	0.209009i
$145$	−53.5824	+	92.8074i	−0.0306881	+	0.0531533i
$146$	1471.29	−	1234.56i	0.834003	−	0.699812i
$147$	−19.9436	−	697.352i	−0.0111899	−	0.391270i
$148$	116.916	−	663.062i	0.0649353	−	0.368266i
$149$	300.894	−	1706.46i	0.165438	−	0.938244i	−0.783174	−	0.621802i	$-0.786401\pi$
$149$	300.894	−	1706.46i	0.165438	−	0.938244i	0.948612	−	0.316442i	$-0.102488\pi$
$150$	1136.38	+	613.459i	0.618565	+	0.333925i
$151$	2448.86	−	2054.84i	1.31977	−	1.10742i	0.333419	−	0.942779i	$-0.391798\pi$
$151$	2448.86	−	2054.84i	1.31977	−	1.10742i	0.986353	−	0.164642i	$-0.0526468\pi$
$152$	440.125	−	762.319i	0.234861	−	0.406791i
$153$	1714.16	+	1278.80i	0.905765	+	0.675719i
$154$	−1061.07	−	1837.83i	−0.555217	−	0.961664i
$155$	107.794	+	39.2336i	0.0558592	+	0.0203311i
$156$	710.240	−	897.326i	0.364517	−	0.460536i
$157$	−2697.72	−	2263.65i	−1.37134	−	1.15069i	−0.972293	−	0.233766i	$-0.924895\pi$
$157$	−2697.72	−	2263.65i	−1.37134	−	1.15069i	−0.399052	−	0.916928i	$-0.630661\pi$
$158$	430.601	−	156.726i	0.216815	−	0.0789142i
$159$	−1600.85	−	1800.66i	−0.798463	−	0.898125i
$160$	−4.76763	−	27.0386i	−0.00235571	−	0.0133599i
$161$	988.083			0.483676
$162$	−87.6722	+	1455.36i	−0.0425196	+	0.705827i
$163$	3109.36			1.49414			0.747068	−	0.664747i	$-0.231461\pi$
$163$	3109.36			1.49414			0.747068	+	0.664747i	$0.231461\pi$
$164$	−14.8603	−	84.2772i	−0.00707559	−	0.0401277i
$165$	143.872	+	161.830i	0.0678813	+	0.0763540i
$166$	−319.727	+	116.371i	−0.149492	+	0.0544106i
$167$	−354.144	−	297.162i	−0.164099	−	0.137695i	0.557041	−	0.830485i	$-0.311937\pi$
$167$	−354.144	−	297.162i	−0.164099	−	0.137695i	−0.721139	+	0.692790i	$0.756381\pi$
$168$	−563.611	+	712.074i	−0.258830	+	0.327010i
$169$	−784.231	−	285.437i	−0.356955	−	0.129921i
$170$	−67.9598	−	117.710i	−0.0306605	−	0.0531055i
$171$	2729.05	−	1173.98i	1.22044	−	0.525007i
$172$	336.355	−	582.584i	0.149109	−	0.258265i
$173$	−723.942	+	607.459i	−0.318152	+	0.266961i	−0.787852	−	0.615865i	$-0.788807\pi$
$173$	−723.942	+	607.459i	−0.318152	+	0.266961i	0.469700	+	0.882826i	$0.344362\pi$
$174$	−1142.21	−	616.609i	−0.497649	−	0.268650i
$175$	−471.403	+	2673.46i	−0.203627	+	1.15483i
$176$	−134.945	+	765.311i	−0.0577946	+	0.327770i
$177$	−80.5750	−	2817.41i	−0.0342169	−	1.19644i
$178$	1163.40	−	976.212i	0.489892	−	0.411068i
$179$	−2112.20	+	3658.44i	−0.881974	+	1.52762i	−0.0328318	+	0.999461i	$0.510453\pi$
$179$	−2112.20	+	3658.44i	−0.881974	+	1.52762i	−0.849143	+	0.528164i	$0.822881\pi$
$180$	41.6694	−	82.7652i	0.0172548	−	0.0342720i
$181$	−1580.71	−	2737.87i	−0.649135	−	1.12433i	−0.983330	−	0.181830i	$-0.941798\pi$
$181$	−1580.71	−	2737.87i	−0.649135	−	1.12433i	0.334195	−	0.942504i	$-0.391535\pi$
$182$	2260.62	+	822.797i	0.920703	+	0.335109i
$183$	1322.41	+	3333.54i	0.534183	+	1.34657i
$184$	−277.179	−	232.580i	−0.111054	−	0.0931851i
$185$	−135.710	+	49.3943i	−0.0539329	+	0.0196300i
$186$	−437.694	+	1318.69i	−0.172544	+	0.519843i
$187$	668.046	+	3788.68i	0.261243	+	1.48158i
$188$	1272.39			0.493608
$189$	−2961.69	+	788.847i	−1.13985	+	0.303599i
$190$	−188.811			−0.0720938
$191$	−101.947	−	578.168i	−0.0386209	−	0.219030i	0.959389	−	0.282086i	$-0.0910264\pi$
$191$	−101.947	−	578.168i	−0.0386209	−	0.219030i	−0.998010	+	0.0630561i	$0.979915\pi$
$192$	325.717	−	67.0861i	0.122430	−	0.0252163i
$193$	−1246.84	+	453.811i	−0.465022	+	0.169254i	−0.563896	−	0.825846i	$-0.690698\pi$
$193$	−1246.84	+	453.811i	−0.465022	+	0.169254i	0.0988741	+	0.995100i	$0.468476\pi$
$194$	−2464.35	−	2067.83i	−0.912010	−	0.765267i
$195$	−242.860	−	35.6972i	−0.0891875	−	0.0131094i
$196$	−504.654	−	183.679i	−0.183912	−	0.0669384i
$197$	−1120.32	−	1940.45i	−0.405174	−	0.701782i	0.589168	−	0.808011i	$-0.299456\pi$
$197$	−1120.32	−	1940.45i	−0.405174	−	0.701782i	−0.994342	+	0.106229i	$0.966122\pi$
$198$	−1909.52	+	1797.95i	−0.685373	+	0.645328i
$199$	273.150	−	473.109i	0.0973019	−	0.168532i	−0.813265	−	0.581893i	$-0.802312\pi$
$199$	273.150	−	473.109i	0.0973019	−	0.168532i	0.910567	+	0.413362i	$0.135645\pi$
$200$	761.533	−	639.002i	0.269243	−	0.225921i
$201$	−2844.78	+	1752.73i	−0.998284	+	0.615065i
$202$	−564.468	+	3201.26i	−0.196613	+	1.11505i
$203$	473.824	−	2687.19i	0.163822	−	0.929083i
$204$	1401.63	−	863.577i	0.481048	−	0.296385i
$205$	−14.0616	+	11.7991i	−0.00479075	+	0.00401992i
$206$	−7.78227	+	13.4793i	−0.00263212	+	0.00455896i
$207$	−280.441	−	1188.54i	−0.0941641	−	0.399079i
$208$	−440.477	−	762.928i	−0.146835	−	0.254325i
$209$	5021.90	+	1827.82i	1.66207	+	0.604943i
$210$	192.722	+	28.3275i	0.0633288	+	0.00930850i
$211$	2303.93	+	1933.23i	0.751703	+	0.630754i	0.935953	−	0.352126i	$-0.114541\pi$
$211$	2303.93	+	1933.23i	0.751703	+	0.630754i	−0.184250	+	0.982879i	$0.558985\pi$
$212$	−1742.89	+	634.359i	−0.564632	+	0.205509i
$213$	−5341.47	+	1100.15i	−1.71827	+	0.353903i
$214$	641.139	+	3636.08i	0.204801	+	1.16148i
$215$	−144.295			−0.0457712
$216$	1016.50	+	475.852i	0.320205	+	0.149896i
$217$	−2920.80			−0.913719
$218$	568.692	+	3225.22i	0.176682	+	1.00201i
$219$	1571.92	−	4735.88i	0.485024	−	1.46128i
$220$	156.637	−	57.0112i	0.0480021	−	0.0174713i
$221$	−3340.85	−	2803.31i	−1.01688	−	0.853261i
$222$	−645.029	−	1625.99i	−0.195007	−	0.491575i
$223$	461.585	+	168.003i	0.138610	+	0.0504499i	0.410394	−	0.911908i	$-0.365391\pi$
$223$	461.585	+	168.003i	0.138610	+	0.0504499i	−0.271784	+	0.962358i	$0.587614\pi$
$224$	349.541	+	605.422i	0.104262	+	0.180587i
$225$	3349.64	−	191.749i	0.992486	−	0.0568147i
$226$	392.755	−	680.271i	0.115600	−	0.200225i
$227$	2585.27	−	2169.30i	0.755905	−	0.634280i	−0.181152	−	0.983455i	$-0.557983\pi$
$227$	2585.27	−	2169.30i	0.755905	−	0.634280i	0.937057	+	0.349175i	$0.113538\pi$
$228$	−65.3779	−	2286.02i	−0.0189902	−	0.664015i
$229$	89.6481	−	508.420i	0.0258695	−	0.146713i	−0.969137	−	0.246522i	$-0.920712\pi$
$229$	89.6481	−	508.420i	0.0258695	−	0.146713i	0.995007	+	0.0998092i	$0.0318232\pi$
$230$	−13.4772	+	76.4328i	−0.00386373	+	0.0219123i
$231$	−4851.67	−	2619.11i	−1.38189	−	0.745996i
$232$	−765.444	+	642.284i	−0.216611	+	0.181759i
$233$	659.917	−	1143.01i	0.185548	−	0.321378i	−0.758213	−	0.652007i	$-0.773927\pi$
$233$	659.917	−	1143.01i	0.185548	−	0.321378i	0.943761	+	0.330629i	$0.107261\pi$
$234$	348.109	−	2952.77i	0.0972503	−	0.824909i
$235$	−136.462	−	236.359i	−0.0378800	−	0.0656100i
$236$	−2038.88	−	742.090i	−0.562371	−	0.204686i
$237$	738.874	−	933.504i	0.202511	−	0.255855i
$238$	2651.13	+	2224.56i	0.722048	+	0.605870i
$239$	688.559	−	250.615i	0.186357	−	0.0678282i	−0.247156	−	0.968976i	$-0.579496\pi$
$239$	688.559	−	250.615i	0.186357	−	0.0678282i	0.433513	+	0.901147i	$0.357274\pi$
$240$	−47.3947	−	53.3104i	−0.0127471	−	0.0143382i
$241$	678.306	+	3846.87i	0.181301	+	1.02821i	0.930616	+	0.365996i	$0.119272\pi$
$241$	678.306	+	3846.87i	0.181301	+	1.02821i	−0.749315	+	0.662213i	$0.769617\pi$
$242$	−2056.05			−0.546148
$243$	1789.48	+	3338.66i	0.472409	+	0.881380i
$244$	2760.71			0.724328
$245$	20.0032	+	113.444i	0.00521617	+	0.0295823i
$246$	−147.726	−	166.164i	−0.0382871	−	0.0430660i
$247$	−5692.92	+	2072.05i	−1.46653	+	0.533772i
$248$	819.348	+	687.515i	0.209793	+	0.176037i
$249$	−548.625	+	693.140i	−0.139629	+	0.176410i
$250$	−401.937	−	146.293i	−0.101683	−	0.0370095i
$251$	1383.12	+	2395.63i	0.347816	+	0.602435i	0.985861	−	0.167564i	$-0.0535901\pi$
$251$	1383.12	+	2395.63i	0.347816	+	0.602435i	−0.638045	+	0.769999i	$0.720257\pi$
$252$	−276.242	+	2343.17i	−0.0690539	+	0.585738i
$253$	1098.38	−	1902.45i	0.272943	−	0.472750i
$254$	966.977	−	811.390i	0.238872	−	0.200438i
$255$	−310.742	−	167.750i	−0.0763114	−	0.0411958i
$256$	44.4539	−	252.111i	0.0108530	−	0.0615505i
$257$	811.001	−	4599.42i	0.196844	−	1.11636i	−0.712925	−	0.701241i	$-0.752630\pi$
$257$	811.001	−	4599.42i	0.196844	−	1.11636i	0.909768	−	0.415116i	$-0.136259\pi$
$258$	−49.9635	−	1747.04i	−0.0120566	−	0.421573i
$259$	2816.92	−	2363.68i	0.675811	−	0.567072i
$260$	−94.4812	+	163.646i	−0.0225364	+	0.0390343i
$261$	−3366.84	+	192.734i	−0.798476	+	0.0457086i
$262$	1804.25	+	3125.05i	0.425446	+	0.736895i
$263$	−2955.79	−	1075.82i	−0.693011	−	0.252236i	−0.0285873	−	0.999591i	$-0.509101\pi$
$263$	−2955.79	−	1075.82i	−0.693011	−	0.252236i	−0.664424	+	0.747356i	$0.731323\pi$
$264$	744.497	+	1876.73i	0.173563	+	0.437518i
$265$	304.761	+	255.725i	0.0706465	+	0.0592795i
$266$	4517.62	−	1644.28i	1.04133	−	0.379012i
$267$	1242.98	−	3744.85i	0.284902	−	0.858355i
$268$	446.657	+	2533.12i	0.101806	+	0.577369i
$269$	6454.02			1.46286			0.731428	−	0.681919i	$-0.238854\pi$
$269$	6454.02			1.46286			0.731428	+	0.681919i	$0.238854\pi$
$270$	−20.6243	−	239.860i	−0.00464872	−	0.0540646i
$271$	535.232			0.119974			0.0599871	−	0.998199i	$-0.480894\pi$
$271$	535.232			0.119974			0.0599871	+	0.998199i	$0.480894\pi$
$272$	−220.070	−	1248.08i	−0.0490577	−	0.278220i
$273$	6121.69	−	1260.85i	1.35715	−	0.279524i
$274$	−426.099	+	155.087i	−0.0939474	+	0.0341941i
$275$	4623.44	+	3879.53i	1.01383	+	0.850706i
$276$	−930.071	−	136.708i	−0.202839	−	0.0298147i
$277$	−1257.77	−	457.791i	−0.272824	−	0.0992997i	0.201985	−	0.979389i	$-0.435261\pi$
$277$	−1257.77	−	457.791i	−0.272824	−	0.0992997i	−0.474809	+	0.880089i	$0.657483\pi$
$278$	−1348.56	−	2335.77i	−0.290940	−	0.503922i
$279$	828.991	+	3513.37i	0.177887	+	0.753906i
$280$	74.9756	−	129.862i	0.0160023	−	0.0277168i
$281$	1310.99	−	1100.05i	0.278316	−	0.233535i	−0.492935	−	0.870066i	$-0.664076\pi$
$281$	1310.99	−	1100.05i	0.278316	−	0.233535i	0.771251	+	0.636531i	$0.219631\pi$
$282$	2814.45	−	1734.04i	0.594319	−	0.366173i
$283$	89.3278	−	506.603i	0.0187632	−	0.106411i	−0.973988	−	0.226600i	$-0.927239\pi$
$283$	89.3278	−	506.603i	0.0187632	−	0.106411i	0.992751	+	0.120189i	$0.0383500\pi$
$284$	−729.006	+	4134.40i	−0.152319	+	0.863843i
$285$	−417.640	+	257.318i	−0.0868031	+	0.0534813i
$286$	4097.16	−	3437.93i	0.847099	−	0.710801i
$287$	233.693	−	404.769i	0.0480644	−	0.0832499i
$288$	629.041	−	592.287i	0.128703	−	0.121183i
$289$	−680.466	−	1178.60i	−0.138503	−	0.239894i
$290$	201.404	+	73.3050i	0.0407822	+	0.0148435i
$291$	−8269.11	−	1215.45i	−1.66579	−	0.244848i
$292$	−2942.57	−	2469.11i	−0.589729	−	0.494842i
$293$	−6134.57	+	2232.80i	−1.22316	+	0.445193i	−0.871249	−	0.490841i	$-0.836689\pi$
$293$	−6134.57	+	2232.80i	−1.22316	+	0.445193i	−0.351909	+	0.936034i	$0.614467\pi$
$294$	−1366.59	+	281.469i	−0.271092	+	0.0558354i
$295$	80.8161	+	458.331i	0.0159501	+	0.0904578i
$296$	−1346.58			−0.264421
$297$	−1773.46	+	6579.33i	−0.346486	+	1.28543i
$298$	−3465.56			−0.673674
$299$	432.433	+	2452.45i	0.0836397	+	0.474344i
$300$	813.618	−	2451.28i	0.156581	−	0.471748i
$301$	3452.48	−	1256.60i	0.661122	−	0.240629i
$302$	−4897.73	−	4109.68i	−0.933220	−	0.783065i
$303$	3114.20	+	7850.28i	0.590448	+	1.48841i
$304$	−1654.33	−	602.126i	−0.312113	−	0.113600i
$305$	−296.082	−	512.830i	−0.0555857	−	0.0962772i
$306$	1923.43	−	3820.37i	0.359330	−	0.713712i
$307$	2137.01	−	3701.42i	0.397283	−	0.688114i	−0.596107	−	0.802905i	$-0.703287\pi$
$307$	2137.01	−	3701.42i	0.397283	−	0.688114i	0.993390	+	0.114791i	$0.0366198\pi$
$308$	−3251.31	+	2728.17i	−0.601495	+	0.504714i
$309$	1.15601	+	40.4213i	0.000212826	+	0.00744172i
$310$	39.8389	−	225.937i	0.00729902	−	0.0413948i
$311$	88.5028	−	501.924i	0.0161368	−	0.0915161i	−0.975676	−	0.219219i	$-0.929649\pi$
$311$	88.5028	−	501.924i	0.0161368	−	0.0915161i	0.991813	+	0.127703i	$0.0407603\pi$
$312$	−2014.05	−	1087.26i	−0.365459	−	0.197289i
$313$	2293.96	−	1924.86i	0.414257	−	0.347603i	−0.411716	−	0.911312i	$-0.635070\pi$
$313$	2293.96	−	1924.86i	0.414257	−	0.347603i	0.825973	+	0.563709i	$0.190626\pi$
$314$	−3521.62	+	6099.62i	−0.632918	+	1.09625i
$315$	464.895	−	199.988i	0.0831551	−	0.0357715i
$316$	−458.236	−	793.687i	−0.0815752	−	0.141292i
$317$	5173.58	+	1883.03i	0.916648	+	0.333632i	0.756904	−	0.653526i	$-0.226711\pi$
$317$	5173.58	+	1883.03i	0.916648	+	0.333632i	0.159744	+	0.987159i	$0.448933\pi$
$318$	−2990.65	+	3778.42i	−0.527381	+	0.666300i
$319$	−4647.18	−	3899.45i	−0.815650	−	0.684411i
$320$	−51.5998	+	18.7808i	−0.00901412	+	0.00328087i
$321$	6373.52	+	7169.04i	1.10821	+	1.24653i
$322$	−343.158	−	1946.14i	−0.0593895	−	0.336815i
$323$	−8715.37			−1.50135
$324$	2896.95	−	332.761i	0.496734	−	0.0570578i
$325$	−6841.92			−1.16776
$326$	−1079.87	−	6124.25i	−0.183462	−	1.04046i
$327$	5653.33	+	6358.97i	0.956055	+	1.07539i
$328$	−160.833	+	58.5383i	−0.0270747	+	0.00985438i
$329$	5323.42	+	4466.88i	0.892066	+	0.748532i
$330$	268.776	−	339.575i	0.0448352	−	0.0566454i
$331$	−10127.9	−	3686.26i	−1.68182	−	0.612131i	−0.688258	−	0.725466i	$-0.741624\pi$
$331$	−10127.9	−	3686.26i	−1.68182	−	0.612131i	−0.993557	+	0.113335i	$0.963847\pi$
$332$	340.247	+	589.325i	0.0562454	+	0.0974198i
$333$	−3642.72	−	2717.54i	−0.599459	−	0.447209i
$334$	−462.302	+	800.731i	−0.0757367	+	0.131180i
$335$	422.650	−	354.645i	0.0689308	−	0.0578398i
$336$	1598.25	+	862.796i	0.259499	+	0.140087i
$337$	834.960	−	4735.29i	0.134965	−	0.765424i	−0.839919	−	0.542711i	$-0.817398\pi$
$337$	834.960	−	4735.29i	0.134965	−	0.765424i	0.974884	−	0.222712i	$-0.0714911\pi$
$338$	−289.840	+	1643.76i	−0.0466427	+	0.264524i
$339$	−58.3413	−	2039.98i	−0.00934710	−	0.326833i
$340$	−208.241	+	174.735i	−0.0332160	+	0.0278716i
$341$	−3246.84	+	5623.69i	−0.515619	+	0.893079i
$342$	−3260.07	−	4967.45i	−0.515451	−	0.785407i
$343$	2280.09	+	3949.24i	0.358931	+	0.621687i
$344$	−1264.28	−	460.160i	−0.198155	−	0.0721226i
$345$	74.3540	+	187.432i	0.0116031	+	0.0292493i
$346$	1447.88	+	1214.92i	0.224967	+	0.188770i
$347$	−322.471	+	117.370i	−0.0498880	+	0.0181577i	−0.366844	−	0.930283i	$-0.619562\pi$
$347$	−322.471	+	117.370i	−0.0498880	+	0.0181577i	0.316956	+	0.948440i	$0.397339\pi$
$348$	−817.797	+	2463.86i	−0.125973	+	0.379532i
$349$	−342.291	−	1941.23i	−0.0524997	−	0.297741i	0.947241	−	0.320523i	$-0.103859\pi$
$349$	−342.291	−	1941.23i	−0.0524997	−	0.297741i	−0.999740	+	0.0227823i	$0.992748\pi$
$350$	5429.41			0.829183
$351$	−3254.12	−	7005.78i	−0.494850	−	1.06536i
$352$	1554.23			0.235344
$353$	132.796	+	753.122i	0.0200227	+	0.113554i	0.993181	−	0.116582i	$-0.0371939\pi$
$353$	132.796	+	753.122i	0.0200227	+	0.113554i	−0.973158	+	0.230136i	$0.926083\pi$
$354$	−5521.22	+	1137.18i	−0.828954	+	0.170735i
$355$	846.192	−	307.989i	0.126510	−	0.0460460i
$356$	−2326.81	−	1952.42i	−0.346406	−	0.290669i
$357$	8895.86	+	1307.57i	1.31882	+	0.193849i
$358$	7939.28	+	2889.66i	1.17208	+	0.426602i
$359$	−4076.65	−	7060.97i	−0.599325	−	1.03806i	−0.992921	−	0.118777i	$-0.962103\pi$
$359$	−4076.65	−	7060.97i	−0.599325	−	1.03806i	0.393596	−	0.919283i	$-0.371231\pi$
$360$	−177.487	−	53.3287i	−0.0259844	−	0.00780742i
$361$	−2623.94	+	4544.79i	−0.382554	+	0.662603i
$362$	−4843.58	+	4064.25i	−0.703240	+	0.590089i
$363$	−4547.87	+	2802.04i	−0.657579	+	0.405149i
$364$	835.490	−	4738.30i	0.120306	−	0.682292i
$365$	−143.076	+	811.422i	−0.0205176	+	0.116361i
$366$	6106.53	−	3762.37i	0.872113	−	0.537328i
$367$	2251.99	−	1889.64i	0.320308	−	0.268770i	−0.468429	−	0.883501i	$-0.655180\pi$
$367$	2251.99	−	1889.64i	0.320308	−	0.268770i	0.788737	+	0.614731i	$0.210735\pi$
$368$	−361.831	+	626.710i	−0.0512547	+	0.0887758i
$369$	−553.214	−	166.222i	−0.0780466	−	0.0234503i
$370$	144.419	+	250.142i	0.0202919	+	0.0351466i
$371$	−9518.90	−	3464.60i	−1.33207	−	0.484833i
$372$	2749.32	+	404.113i	0.383187	+	0.0563234i
$373$	1766.21	+	1482.03i	0.245177	+	0.205728i	0.757092	−	0.653308i	$-0.226619\pi$
$373$	1766.21	+	1482.03i	0.245177	+	0.205728i	−0.511915	+	0.859036i	$0.671064\pi$
$374$	7230.23	−	2631.59i	0.999642	−	0.363840i
$375$	−1088.43	+	224.179i	−0.149884	+	0.0308708i
$376$	−441.895	−	2506.11i	−0.0606090	−	0.343731i
$377$	6877.06			0.939487
$378$	2582.31	+	5559.44i	0.351375	+	0.756472i
$379$	10193.5			1.38154			0.690769	−	0.723075i	$-0.257272\pi$
$379$	10193.5			1.38154			0.690769	+	0.723075i	$0.257272\pi$
$380$	65.5735	+	371.886i	0.00885224	+	0.0502036i
$381$	1033.11	−	3112.57i	0.138919	−	0.418535i
$382$	−1103.36	+	401.591i	−0.147783	+	0.0537885i
$383$	4508.54	+	3783.11i	0.601503	+	0.504721i	0.891928	−	0.452177i	$-0.149352\pi$
$383$	4508.54	+	3783.11i	0.601503	+	0.504721i	−0.290425	+	0.956898i	$0.593797\pi$
$384$	−245.254	−	618.238i	−0.0325926	−	0.0821597i
$385$	855.485	+	311.371i	0.113246	+	0.0412180i
$386$	1326.86	+	2298.18i	0.174962	+	0.303042i
$387$	−2491.43	−	3796.26i	−0.327252	−	0.498642i
$388$	−3216.98	+	5571.97i	−0.420921	+	0.729057i
$389$	−2291.32	+	1922.65i	−0.298649	+	0.250596i	−0.779782	−	0.626051i	$-0.784670\pi$
$389$	−2291.32	+	1922.65i	−0.298649	+	0.250596i	0.481133	+	0.876648i	$0.340226\pi$
$390$	14.0346	+	490.738i	0.00182223	+	0.0637166i
$391$	−622.094	+	3528.07i	−0.0804620	+	0.456323i
$392$	−186.513	+	1057.77i	−0.0240314	+	0.136289i
$393$	8249.81	+	4453.56i	1.05890	+	0.571634i
$394$	−3432.85	+	2880.51i	−0.438946	+	0.368319i
$395$	−98.2904	+	170.244i	−0.0125203	+	0.0216858i
$396$	4204.45	+	3136.60i	0.533539	+	0.398031i
$397$	1459.68	+	2528.24i	0.184532	+	0.319619i	0.943419	−	0.331604i	$-0.107590\pi$
$397$	1459.68	+	2528.24i	0.184532	+	0.319619i	−0.758887	+	0.651223i	$0.774256\pi$
$398$	−1026.71	−	373.691i	−0.129307	−	0.0470639i
$399$	7751.85	−	9793.79i	0.972626	−	1.22883i
$400$	−1523.07	−	1278.00i	−0.190383	−	0.159751i
$401$	−5558.14	+	2023.00i	−0.692170	+	0.251929i	−0.664064	−	0.747676i	$-0.731170\pi$
$401$	−5558.14	+	2023.00i	−0.692170	+	0.251929i	−0.0281059	+	0.999605i	$0.508948\pi$
$402$	4440.19	+	4994.40i	0.550887	+	0.619647i
$403$	−1278.29	−	7249.52i	−0.158005	−	0.896090i
$404$	6501.29			0.800622
$405$	−372.508	−	502.450i	−0.0457039	−	0.0616468i
$406$	−5457.29			−0.667096
$407$	−1419.64	−	8051.20i	−0.172897	−	0.980549i
$408$	−2187.70	−	2460.76i	−0.265459	−	0.298593i
$409$	2898.68	−	1055.03i	0.350441	−	0.127550i	−0.160801	−	0.986987i	$-0.551408\pi$
$409$	2898.68	−	1055.03i	0.350441	−	0.127550i	0.511242	+	0.859437i	$0.329186\pi$
$410$	28.1232	+	23.5982i	0.00338757	+	0.00284251i
$411$	−731.150	+	923.745i	−0.0877493	+	0.110864i
$412$	29.2518	+	10.6468i	0.00349789	+	0.00127313i
$413$	−5925.06	−	10262.5i	−0.705940	−	1.22272i
$414$	−2243.58	+	965.137i	−0.266342	+	0.114575i
$415$	72.9821	−	126.409i	0.00863265	−	0.0149522i
$416$	−1349.70	+	1132.53i	−0.159073	+	0.133478i
$417$	−6166.20	−	3328.75i	−0.724125	−	0.390910i
$418$	1856.02	−	10526.0i	0.217179	−	1.23168i
$419$	−2367.66	+	13427.7i	−0.276056	+	1.56559i	0.459529	+	0.888163i	$0.348018\pi$
$419$	−2367.66	+	13427.7i	−0.276056	+	1.56559i	−0.735586	+	0.677431i	$0.763093\pi$
$420$	−11.1372	−	389.425i	−0.00129390	−	0.0452429i
$421$	−4008.80	+	3363.78i	−0.464078	+	0.389408i	−0.844629	−	0.535352i	$-0.820179\pi$
$421$	−4008.80	+	3363.78i	−0.464078	+	0.389408i	0.380551	+	0.924760i	$0.375734\pi$
$422$	3007.57	−	5209.27i	0.346934	−	0.600908i
$423$	3862.20	−	7671.22i	0.443940	−	0.881767i
$424$	1854.74	+	3212.51i	0.212439	+	0.367955i
$425$	−9249.12	−	3366.41i	−1.05564	−	0.384223i
$426$	4021.96	+	10138.6i	0.457428	+	1.15309i
$427$	11550.3	+	9691.82i	1.30903	+	1.09841i
$428$	6939.01	−	2525.59i	0.783668	−	0.285232i
$429$	4377.39	−	13188.2i	0.492640	−	1.48423i
$430$	50.1130	+	284.205i	0.00562014	+	0.0318734i
$431$	1533.38			0.171370			0.0856851	−	0.996322i	$-0.472692\pi$
$431$	1533.38			0.171370			0.0856851	+	0.996322i	$0.472692\pi$
$432$	584.217	−	2167.38i	0.0650652	−	0.241385i
$433$	11955.1			1.32684			0.663422	−	0.748245i	$-0.269103\pi$
$433$	11955.1			1.32684			0.663422	+	0.748245i	$0.269103\pi$
$434$	1014.38	+	5752.86i	0.112194	+	0.636281i
$435$	545.396	−	112.332i	0.0601143	−	0.0123814i
$436$	6154.93	−	2240.21i	0.676073	−	0.246070i
$437$	3812.29	+	3198.89i	0.417315	+	0.350169i
$438$	−9873.78	−	1451.31i	−1.07714	−	0.158325i
$439$	−13930.3	−	5070.23i	−1.51449	−	0.551228i	−0.554721	−	0.832036i	$-0.687175\pi$
$439$	−13930.3	−	5070.23i	−1.51449	−	0.551228i	−0.959764	+	0.280809i	$0.909397\pi$
$440$	−166.690	−	288.715i	−0.0180605	−	0.0312817i
$441$	−2639.23	+	2485.02i	−0.284983	+	0.268332i
$442$	−4361.17	+	7553.77i	−0.469321	+	0.812887i
$443$	7445.43	−	6247.46i	0.798517	−	0.670035i	−0.149321	−	0.988789i	$-0.547709\pi$
$443$	7445.43	−	6247.46i	0.798517	−	0.670035i	0.947838	+	0.318754i	$0.103264\pi$
$444$	−2978.57	+	1835.16i	−0.318370	+	0.196155i
$445$	−113.136	+	641.624i	−0.0120520	+	0.0683503i
$446$	170.595	−	967.492i	0.0181119	−	0.102718i
$447$	−7665.63	+	4722.97i	−0.811123	+	0.499751i
$448$	1071.05	−	898.722i	0.112952	−	0.0947781i
$449$	6100.99	−	10567.2i	0.641255	−	1.11069i	−0.343898	−	0.939007i	$-0.611747\pi$
$449$	6100.99	−	10567.2i	0.641255	−	1.11069i	0.985153	−	0.171679i	$-0.0549192\pi$
$450$	−1540.99	−	6530.91i	−0.161429	−	0.684156i
$451$	−519.559	−	899.902i	−0.0542463	−	0.0939573i
$452$	−1476.27	−	537.320i	−0.153624	−	0.0559146i
$453$	−16434.3	−	2415.62i	−1.70453	−	0.250543i
$454$	−5170.54	−	4338.60i	−0.534506	−	0.448504i
$455$	−969.793	+	352.976i	−0.0999222	+	0.0363687i
$456$	−4479.88	+	922.696i	−0.460065	+	0.0947571i
$457$	1221.09	+	6925.13i	0.124989	+	0.708849i	0.981314	+	0.192412i	$0.0616310\pi$
$457$	1221.09	+	6925.13i	0.124989	+	0.708849i	−0.856325	+	0.516437i	$0.827258\pi$
$458$	−1032.53			−0.105342
$459$	−951.999	−	11071.7i	−0.0968094	−	1.12589i
$460$	155.224			0.0157334
$461$	1578.69	+	8953.18i	0.159494	+	0.904536i	0.954561	+	0.298015i	$0.0963245\pi$
$461$	1578.69	+	8953.18i	0.159494	+	0.904536i	−0.795067	+	0.606522i	$0.792564\pi$
$462$	−3473.68	+	10465.5i	−0.349806	+	1.05390i
$463$	931.412	−	339.006i	0.0934911	−	0.0340280i	−0.294851	−	0.955543i	$-0.595270\pi$
$463$	931.412	−	339.006i	0.0934911	−	0.0340280i	0.388342	+	0.921515i	$0.373048\pi$
$464$	1530.89	+	1284.57i	0.153167	+	0.128523i
$465$	−219.793	−	554.055i	−0.0219197	−	0.0552552i
$466$	−2480.48	−	902.820i	−0.246579	−	0.0897475i
$467$	−3257.02	−	5641.32i	−0.322734	−	0.558992i	0.658317	−	0.752741i	$-0.271269\pi$
$467$	−3257.02	−	5641.32i	−0.322734	−	0.558992i	−0.981051	+	0.193749i	$0.937935\pi$
$468$	−5936.72	+	339.846i	−0.586378	+	0.0335671i
$469$	−7024.12	+	12166.1i	−0.691564	+	1.19782i
$470$	−418.143	+	350.864i	−0.0410373	+	0.0344344i
$471$	523.115	+	18291.4i	0.0511759	+	1.78943i
$472$	−753.538	+	4273.53i	−0.0734839	+	0.416748i
$473$	1418.42	−	8044.25i	0.137884	−	0.781976i
$474$	−2095.25	−	1131.10i	−0.203034	−	0.109605i
$475$	−10474.1	+	8788.78i	−1.01175	+	0.848961i
$476$	3460.81	−	5994.30i	0.333248	−	0.577202i
$477$	−1465.80	+	12433.4i	−0.140701	+	1.19347i
$478$	−732.750	−	1269.16i	−0.0701155	−	0.121444i
$479$	17270.9	+	6286.09i	1.64745	+	0.599622i	0.988318	−	0.152407i	$-0.0487024\pi$
$479$	17270.9	+	6286.09i	1.64745	+	0.599622i	0.659130	+	0.752029i	$0.270925\pi$
$480$	−88.5409	+	111.864i	−0.00841942	+	0.0106372i
$481$	7099.54	+	5957.22i	0.672996	+	0.564711i
$482$	7341.28	−	2672.01i	0.693747	−	0.252503i
$483$	−3411.31	−	3837.10i	−0.321366	−	0.361478i
$484$	714.059	+	4049.63i	0.0670604	+	0.380318i
$485$	1380.07			0.129208
$486$	5954.40	−	4684.10i	0.555755	−	0.437191i
$487$	−13583.7			−1.26394			−0.631968	−	0.774994i	$-0.717753\pi$
$487$	−13583.7			−1.26394			−0.631968	+	0.774994i	$0.717753\pi$
$488$	−958.783	−	5437.53i	−0.0889387	−	0.504396i
$489$	−10734.9	−	12074.8i	−0.992740	−	1.11665i
$490$	216.494	−	78.7974i	0.0199596	−	0.00726470i
$491$	6381.87	+	5355.02i	0.586578	+	0.492197i	0.887100	−	0.461578i	$-0.152716\pi$
$491$	6381.87	+	5355.02i	0.586578	+	0.492197i	−0.300522	+	0.953775i	$0.597161\pi$
$492$	−275.975	+	348.671i	−0.0252885	+	0.0319498i
$493$	9296.62	+	3383.69i	0.849288	+	0.309115i
$494$	6058.28	+	10493.2i	0.551771	+	0.955695i
$495$	131.735	−	1117.42i	0.0119617	−	0.101463i
$496$	1069.58	−	1852.57i	0.0968260	−	0.167708i
$497$	−17564.4	+	14738.3i	−1.58525	+	1.33018i
$498$	1555.76	+	839.855i	0.139990	+	0.0755719i
$499$	−2896.15	+	16424.9i	−0.259818	+	1.47350i	0.523577	+	0.851978i	$0.324597\pi$
$499$	−2896.15	+	16424.9i	−0.259818	+	1.47350i	−0.783395	+	0.621524i	$0.786514\pi$
$500$	−148.550	+	842.467i	−0.0132867	+	0.0753526i
$501$	68.6722	+	2401.21i	0.00612385	+	0.214128i
$502$	4238.12	−	3556.21i	0.376806	−	0.316178i
$503$	5539.21	−	9594.19i	0.491016	−	0.850464i	−0.508931	−	0.860808i	$-0.669959\pi$
$503$	5539.21	−	9594.19i	0.491016	−	0.850464i	0.999947	+	0.0103431i	$0.00329238\pi$
$504$	4711.09	−	269.685i	0.416366	−	0.0238348i
$505$	−697.255	−	1207.68i	−0.0614405	−	0.106418i
$506$	−4128.55	−	1502.67i	−0.362721	−	0.132019i
$507$	1599.06	+	4030.92i	0.140072	+	0.353095i
$508$	−1933.95	−	1622.78i	−0.168908	−	0.141731i
$509$	−8874.08	+	3229.90i	−0.772764	+	0.281263i	−0.698152	−	0.715950i	$-0.745994\pi$
$509$	−8874.08	+	3229.90i	−0.772764	+	0.281263i	−0.0746117	+	0.997213i	$0.523772\pi$
$510$	−222.484	+	670.301i	−0.0193171	+	0.0581989i
$511$	−3643.02	−	20660.6i	−0.315377	−	1.78859i
$512$	−512.000			−0.0441942
$513$	−13980.9	−	6544.82i	−1.20326	−	0.563276i
$514$	−9340.74			−0.801561
$515$	−1.15947	−	6.57567i	−9.92083e−5	−	0.000562638i
$516$	−3423.64	+	705.148i	−0.292088	+	0.0601597i
$517$	14518.1	−	5284.17i	1.23502	−	0.449512i
$518$	−5633.84	−	4727.35i	−0.477870	−	0.400981i
$519$	4858.36	+	714.115i	0.410903	+	0.0603973i
$520$	355.133	+	129.258i	0.0299493	+	0.0109006i
$521$	4490.89	+	7778.45i	0.377638	+	0.654088i	0.990718	−	0.135932i	$-0.0434030\pi$
$521$	4490.89	+	7778.45i	0.377638	+	0.654088i	−0.613080	+	0.790021i	$0.710070\pi$
$522$	1548.90	+	6564.45i	0.129873	+	0.550418i
$523$	5147.16	−	8915.14i	0.430343	−	0.745376i	−0.566560	−	0.824021i	$-0.691726\pi$
$523$	5147.16	−	8915.14i	0.430343	−	0.745376i	0.996903	+	0.0786445i	$0.0250592\pi$
$524$	5528.54	−	4639.00i	0.460907	−	0.386747i
$525$	12009.5	−	7399.35i	0.998361	−	0.615113i
$526$	−1092.42	+	6195.40i	−0.0905545	+	0.513560i
$527$	1838.93	−	10429.1i	0.152002	−	0.862045i
$528$	3437.88	−	2118.15i	0.283361	−	0.174585i
$529$	−7753.40	+	6505.88i	−0.637249	+	0.534715i
$530$	397.837	−	689.075i	0.0326056	−	0.0564745i
$531$	−10662.9	+	10039.9i	−0.871429	+	0.820513i
$532$	−4807.55	−	8326.92i	−0.391793	−	0.678605i
$533$	1106.92	+	402.887i	0.0899553	+	0.0327410i
$534$	−7807.59	−	1147.61i	−0.632710	−	0.0930000i
$535$	−1213.36	−	1018.13i	−0.0980523	−	0.0822756i
$536$	4834.15	−	1759.49i	0.389559	−	0.141788i
$537$	21499.4	−	4428.11i	1.72768	−	0.355842i
$538$	−2241.46	−	12711.9i	−0.179621	−	1.01868i
$539$	−6521.00			−0.521112
$540$	−465.270	+	123.925i	−0.0370778	+	0.00987567i
$541$	11967.5			0.951059			0.475530	−	0.879700i	$-0.342256\pi$
$541$	11967.5			0.951059			0.475530	+	0.879700i	$0.342256\pi$
$542$	−185.884	−	1054.20i	−0.0147314	−	0.0835458i
$543$	−5174.86	+	15590.9i	−0.408977	+	1.23217i
$544$	−2381.80	+	866.905i	−0.187719	+	0.0683240i
$545$	−1076.25	−	903.082i	−0.0845900	−	0.0709794i
$546$	−4609.43	−	11619.5i	−0.361292	−	0.910747i
$547$	15758.3	+	5735.55i	1.23177	+	0.448326i	0.874202	−	0.485562i	$-0.161385\pi$
$547$	15758.3	+	5735.55i	1.23177	+	0.448326i	0.357564	+	0.933889i	$0.383607\pi$
$548$	453.445	+	785.390i	0.0353471	+	0.0612230i
$549$	8379.84	−	16644.3i	0.651444	−	1.29392i
$550$	6035.47	−	10453.7i	0.467915	−	0.810453i
$551$	10527.8	−	8833.91i	0.813977	−	0.683008i
$552$	53.7478	+	1879.36i	0.00414431	+	0.144911i
$553$	869.174	−	4929.33i	0.0668373	−	0.379053i
$554$	−464.853	+	2636.31i	−0.0356493	+	0.202177i
$555$	660.348	+	356.481i	0.0505049	+	0.0272644i
$556$	−4132.23	+	3467.35i	−0.315190	+	0.264476i
$557$	3779.27	−	6545.88i	0.287491	−	0.497950i	−0.685719	−	0.727866i	$-0.740512\pi$
$557$	3779.27	−	6545.88i	0.287491	−	0.497950i	0.973210	+	0.229917i	$0.0738454\pi$
$558$	6632.07	−	2852.97i	0.503151	−	0.216444i
$559$	4629.89	+	8019.21i	0.350310	+	0.606755i
$560$	−281.816	−	102.573i	−0.0212659	−	0.00774016i
$561$	12406.5	−	15674.5i	0.933692	−	1.17964i
$562$	−2621.97	−	2200.10i	−0.196799	−	0.165134i
$563$	−8043.34	+	2927.54i	−0.602107	+	0.219149i	−0.625046	−	0.780588i	$-0.714920\pi$
$563$	−8043.34	+	2927.54i	−0.602107	+	0.219149i	0.0229391	+	0.999737i	$0.492698\pi$
$564$	−4392.85	−	4941.15i	−0.327965	−	0.368901i
$565$	58.5159	+	331.860i	0.00435714	+	0.0247106i
$566$	−1028.84			−0.0764050
$567$	13288.5	+	8777.92i	0.984240	+	0.650155i
$568$	8396.36			0.620252
$569$	1667.17	+	9454.99i	0.122832	+	0.696615i	0.982572	+	0.185883i	$0.0595144\pi$
$569$	1667.17	+	9454.99i	0.122832	+	0.696615i	−0.859740	+	0.510732i	$0.829374\pi$
$570$	651.862	+	733.226i	0.0479009	+	0.0538797i
$571$	1512.51	−	550.508i	0.110852	−	0.0403468i	−0.285999	−	0.958230i	$-0.592325\pi$
$571$	1512.51	−	550.508i	0.110852	−	0.0403468i	0.396851	+	0.917883i	$0.370103\pi$
$572$	−8194.33	−	6875.86i	−0.598990	−	0.502612i
$573$	−1893.28	+	2391.99i	−0.138033	+	0.174392i
$574$	−878.399	−	319.711i	−0.0638740	−	0.0232482i
$575$	2810.16	+	4867.33i	0.203812	+	0.353012i
$576$	−1385.04	−	1033.27i	−0.100191	−	0.0747446i
$577$	6690.66	−	11588.6i	0.482731	−	0.836115i	−0.517072	−	0.855942i	$-0.672978\pi$
$577$	6690.66	−	11588.6i	0.482731	−	0.836115i	0.999803	+	0.0198268i	$0.00631146\pi$
$578$	−2085.07	+	1749.58i	−0.150047	+	0.125905i
$579$	6066.96	+	3275.17i	0.435465	+	0.235080i
$580$	74.4358	−	422.147i	0.00532893	−	0.0302219i
$581$	−645.375	+	3660.10i	−0.0460837	+	0.261354i
$582$	477.863	+	16709.1i	0.0340345	+	1.19006i
$583$	−17252.2	+	14476.3i	−1.22558	+	1.02838i
$584$	−3841.25	+	6653.25i	−0.272178	+	0.471427i
$585$	699.836	+	1066.36i	0.0494609	+	0.0753650i
$586$	6528.27	+	11307.3i	0.460205	+	0.797099i
$587$	−1415.97	−	515.370i	−0.0995626	−	0.0362378i	0.291759	−	0.956492i	$-0.405760\pi$
$587$	−1415.97	−	515.370i	−0.0995626	−	0.0362378i	−0.391321	+	0.920254i	$0.627982\pi$
$588$	1029.00	+	2593.90i	0.0721686	+	0.181923i
$589$	−11269.2	−	9456.01i	−0.788354	−	0.661508i
$590$	874.668	−	318.353i	0.0610331	−	0.0222142i
$591$	−3667.64	+	11049.9i	−0.255274	+	0.769090i
$592$	467.663	+	2652.25i	0.0324676	+	0.184133i
$593$	−14995.5			−1.03844			−0.519218	−	0.854642i	$-0.673777\pi$
$593$	−14995.5			−1.03844			−0.519218	+	0.854642i	$0.673777\pi$
$594$	13574.7	+	1208.05i	0.937668	+	0.0834461i
$595$	−1484.67			−0.102295
$596$	1203.58	+	6825.83i	0.0827189	+	0.469122i
$597$	−2780.30	+	572.642i	−0.190603	+	0.0392574i
$598$	4680.20	−	1703.45i	0.320046	−	0.116487i
$599$	2085.81	+	1750.20i	0.142277	+	0.119384i	0.711148	−	0.703042i	$-0.248175\pi$
$599$	2085.81	+	1750.20i	0.142277	+	0.119384i	−0.568872	+	0.822426i	$0.692620\pi$
$600$	−5110.64	−	751.196i	−0.347735	−	0.0511124i
$601$	13275.2	+	4831.78i	0.901009	+	0.327941i	0.750657	−	0.660692i	$-0.229737\pi$
$601$	13275.2	+	4831.78i	0.901009	+	0.327941i	0.150352	+	0.988632i	$0.451959\pi$
$602$	−3674.05	−	6363.64i	−0.248743	−	0.430835i
$603$	16628.0	+	4996.12i	1.12296	+	0.337409i
$604$	−6393.53	+	11073.9i	−0.430710	+	0.746012i
$605$	675.678	−	566.962i	0.0454053	−	0.0380996i
$606$	14380.5	−	8860.14i	0.963973	−	0.593925i
$607$	1504.53	−	8532.61i	0.100605	−	0.570557i	−0.892281	−	0.451481i	$-0.850896\pi$
$607$	1504.53	−	8532.61i	0.100605	−	0.570557i	0.992885	−	0.119076i	$-0.0379931\pi$
$608$	−611.415	+	3467.51i	−0.0407832	+	0.231293i
$609$	−12071.2	+	7437.35i	−0.803203	+	0.494872i
$610$	−907.249	+	761.272i	−0.0602187	+	0.0505295i
$611$	−8757.14	+	15167.8i	−0.579830	+	1.00429i
$612$	−8192.66	−	2461.61i	−0.541125	−	0.162589i
$613$	−7949.88	−	13769.6i	−0.523805	−	0.907258i	−0.999616	−	0.0277098i	$-0.991179\pi$
$613$	−7949.88	−	13769.6i	−0.523805	−	0.907258i	0.475811	−	0.879548i	$-0.342155\pi$
$614$	−8032.55	−	2923.61i	−0.527960	−	0.192162i
$615$	94.3672	+	13.8707i	0.00618740	+	0.000909466i
$616$	6502.61	+	5456.34i	0.425321	+	0.356887i
$617$	−25497.4	+	9280.31i	−1.66368	+	0.605528i	−0.990934	−	0.134349i	$-0.957106\pi$
$617$	−25497.4	+	9280.31i	−1.66368	+	0.605528i	−0.672742	+	0.739877i	$0.734883\pi$
$618$	79.2130	−	16.3151i	0.00515601	−	0.00106196i
$619$	−1712.87	−	9714.14i	−0.111221	−	0.630766i	−0.988552	−	0.150880i	$-0.951789\pi$
$619$	−1712.87	−	9714.14i	−0.111221	−	0.630766i	0.877331	−	0.479886i	$-0.159322\pi$
$620$	−458.846			−0.0297221
$621$	−3647.35	+	5192.44i	−0.235689	+	0.335532i
$622$	−1019.33			−0.0657099
$623$	−2880.68	−	16337.1i	−0.185252	−	1.05061i
$624$	−1442.01	+	4344.51i	−0.0925108	+	0.278717i
$625$	−14423.8	+	5249.83i	−0.923123	+	0.335989i
$626$	−4587.93	−	3849.73i	−0.292924	−	0.245793i
$627$	−10239.7	−	25812.4i	−0.652210	−	1.64409i
$628$	13237.0	+	4817.86i	0.841102	+	0.306136i
$629$	6666.27	+	11546.3i	0.422578	+	0.731927i
$630$	−555.355	−	846.209i	−0.0351204	−	0.0535140i
$631$	8889.21	−	15396.6i	0.560814	−	0.971359i	−0.436611	−	0.899650i	$-0.643821\pi$
$631$	8889.21	−	15396.6i	0.560814	−	0.971359i	0.997426	−	0.0717088i	$-0.0228452\pi$
$632$	−1404.12	+	1178.19i	−0.0883746	+	0.0741551i
$633$	−446.757	−	15621.4i	−0.0280521	−	0.980878i
$634$	1912.08	−	10843.9i	0.119777	−	0.679287i
$635$	−94.0340	+	533.293i	−0.00587657	+	0.0333277i
$636$	8480.68	+	4578.19i	0.528743	+	0.285436i
$637$	5662.85	−	4751.70i	0.352230	−	0.295556i
$638$	−6066.47	+	10507.4i	−0.376448	+	0.652027i
$639$	22713.5	+	16944.7i	1.40615	+	1.04902i
$640$	54.9114	+	95.1093i	0.00339150	+	0.00587426i
$641$	7457.28	+	2714.23i	0.459508	+	0.167247i	0.561394	−	0.827549i	$-0.310265\pi$
$641$	7457.28	+	2714.23i	0.459508	+	0.167247i	−0.101885	+	0.994796i	$0.532488\pi$
$642$	11906.8	−	15043.2i	0.731966	−	0.924776i
$643$	−13696.9	−	11493.0i	−0.840050	−	0.704886i	0.117525	−	0.993070i	$-0.462504\pi$
$643$	−13696.9	−	11493.0i	−0.840050	−	0.704886i	−0.957575	+	0.288184i	$0.906948\pi$
$644$	−3713.98	+	1351.78i	−0.227253	+	0.0827135i
$645$	498.170	+	560.350i	0.0304115	+	0.0342074i
$646$	3026.82	+	17165.9i	0.184348	+	1.04549i
$647$	2356.45			0.143186			0.0715931	−	0.997434i	$-0.477192\pi$
$647$	2356.45			0.143186			0.0715931	+	0.997434i	$0.477192\pi$
$648$	−1661.51	−	5590.31i	−0.100726	−	0.338902i
$649$	−26345.8			−1.59347
$650$	2376.17	+	13476.0i	0.143386	+	0.813185i
$651$	10083.9	+	11342.6i	0.607097	+	0.682873i
$652$	−11687.4	+	4253.86i	−0.702014	+	0.255512i
$653$	−20131.3	−	16892.2i	−1.20643	−	1.01232i	−0.999423	−	0.0339767i	$-0.989183\pi$
$653$	−20131.3	−	16892.2i	−1.20643	−	1.01232i	−0.207008	−	0.978339i	$-0.566373\pi$
$654$	10561.3	−	13343.3i	0.631469	−	0.797807i
$655$	−1454.67	−	529.457i	−0.0867766	−	0.0315841i
$656$	171.155	+	296.448i	0.0101867	+	0.0176438i
$657$	−23818.1	+	10246.0i	−1.41436	+	0.608426i
$658$	6949.23	−	12036.4i	0.411716	−	0.713113i
$659$	4826.44	−	4049.86i	0.285298	−	0.239393i	−0.488896	−	0.872342i	$-0.662600\pi$
$659$	4826.44	−	4049.86i	0.285298	−	0.239393i	0.774194	+	0.632949i	$0.218156\pi$
$660$	−762.177	−	411.452i	−0.0449511	−	0.0242663i
$661$	−1279.64	+	7257.19i	−0.0752983	+	0.427038i	0.923733	+	0.383037i	$0.125122\pi$
$661$	−1279.64	+	7257.19i	−0.0752983	+	0.427038i	−0.999031	+	0.0440013i	$0.985989\pi$
$662$	−3743.13	+	21228.3i	−0.219760	+	1.24632i
$663$	647.826	+	22652.0i	0.0379479	+	1.32690i
$664$	1042.58	−	874.825i	0.0609334	−	0.0511292i
$665$	−1031.21	+	1786.10i	−0.0601331	+	0.104154i
$666$	−4087.41	+	8118.55i	−0.237814	+	0.472353i
$667$	−2824.59	−	4892.33i	−0.163971	−	0.284006i
$668$	1737.69	+	632.467i	0.100648	+	0.0366330i
$669$	−941.179	−	2372.53i	−0.0543918	−	0.137111i
$670$	−845.299	−	709.290i	−0.0487414	−	0.0408989i
$671$	31500.1	−	11465.1i	1.81229	−	0.659621i
$672$	1144.31	−	3447.59i	0.0656886	−	0.197907i
$673$	−3374.45	−	19137.4i	−0.193277	−	1.09613i	−0.914851	−	0.403791i	$-0.867692\pi$
$673$	−3374.45	−	19137.4i	−0.193277	−	1.09613i	0.721574	−	0.692337i	$-0.243419\pi$
$674$	−9616.68			−0.549586
$675$	−12309.1	−	12345.9i	−0.701892	−	0.703991i
$676$	3338.24			0.189932
$677$	−3076.42	−	17447.3i	−0.174648	−	0.990477i	−0.938550	−	0.345144i	$-0.887830\pi$
$677$	−3076.42	−	17447.3i	−0.174648	−	0.990477i	0.763902	−	0.645333i	$-0.223281\pi$
$678$	−3997.71	+	823.387i	−0.226447	+	0.0466401i
$679$	−33020.4	+	12018.4i	−1.86628	+	0.679271i
$680$	416.482	+	349.470i	0.0234873	+	0.0197082i
$681$	−17349.7	−	2550.18i	−0.976274	−	0.143499i
$682$	12204.1	+	4441.94i	0.685220	+	0.249400i
$683$	3496.02	+	6055.29i	0.195859	+	0.339238i	0.947182	−	0.320697i	$-0.103917\pi$
$683$	3496.02	+	6055.29i	0.195859	+	0.339238i	−0.751323	+	0.659935i	$0.770584\pi$
$684$	−8651.77	+	8146.26i	−0.483638	+	0.455380i
$685$	97.2629	−	168.464i	0.00542514	−	0.00939662i
$686$	6986.61	−	5862.46i	0.388848	−	0.326283i
$687$	−2283.89	+	1407.16i	−0.126835	+	0.0781460i
$688$	−467.259	+	2649.96i	−0.0258926	+	0.146844i
$689$	4433.30	−	25142.5i	0.245131	−	1.39021i
$690$	343.346	−	211.543i	0.0189434	−	0.0116715i
$691$	12868.3	−	10797.8i	0.708441	−	0.594453i	−0.215720	−	0.976455i	$-0.569210\pi$
$691$	12868.3	−	10797.8i	0.708441	−	0.594453i	0.924161	+	0.382003i	$0.124765\pi$
$692$	1890.08	−	3273.71i	0.103829	−	0.179838i
$693$	6579.14	+	27883.2i	0.360636	+	1.52842i
$694$	343.166	+	594.381i	0.0187700	+	0.0325107i
$695$	1087.27	+	395.735i	0.0593419	+	0.0215987i
$696$	5136.88	+	755.054i	0.279760	+	0.0411210i
$697$	1298.14	+	1089.27i	0.0705461	+	0.0591952i
$698$	−3704.60	+	1348.36i	−0.200890	+	0.0731179i
$699$	−6717.07	+	1383.48i	−0.363466	+	0.0748612i
$700$	−1885.61	−	10693.8i	−0.101814	−	0.577413i
$701$	−18157.5			−0.978315			−0.489158	−	0.872195i	$-0.662696\pi$
$701$	−18157.5			−0.978315			−0.489158	+	0.872195i	$0.662696\pi$
$702$	−12668.5	+	8842.45i	−0.681116	+	0.475409i
$703$	18520.8			0.993633
$704$	−539.780	−	3061.24i	−0.0288973	−	0.163885i
$705$	−446.743	+	1345.95i	−0.0238657	+	0.0719027i
$706$	1437.24	−	523.113i	0.0766165	−	0.0278861i
$707$	27200.1	+	22823.6i	1.44691	+	1.21410i
$708$	4157.30	+	10479.8i	0.220679	+	0.556290i
$709$	23930.9	+	8710.13i	1.26762	+	0.461376i	0.886320	−	0.463074i	$-0.153254\pi$
$709$	23930.9	+	8710.13i	1.26762	+	0.461376i	0.381302	+	0.924451i	$0.375476\pi$
$710$	−900.499	−	1559.71i	−0.0475988	−	0.0824435i
$711$	−6176.07	+	353.548i	−0.325768	+	0.0186485i
$712$	−3037.43	+	5260.99i	−0.159877	+	0.276915i
$713$	−4632.27	+	3886.94i	−0.243310	+	0.204161i
$714$	−514.082	−	17975.5i	−0.0269454	−	0.942182i
$715$	−398.430	+	2259.61i	−0.0208398	+	0.118188i
$716$	2934.24	−	16640.9i	0.153153	−	0.868575i
$717$	−3350.45	−	1808.70i	−0.174512	−	0.0942079i
$718$	−12491.6	+	10481.7i	−0.649279	+	0.544809i
$719$	−15455.2	+	26769.1i	−0.801642	+	1.38848i	0.116893	+	0.993145i	$0.462707\pi$
$719$	−15455.2	+	26769.1i	−0.801642	+	1.38848i	−0.918535	+	0.395340i	$0.870627\pi$
$720$	−43.3964	+	368.103i	−0.00224623	+	0.0190533i
$721$	85.0069	+	147.236i	0.00439088	+	0.00760522i
$722$	9862.78	+	3589.76i	0.508386	+	0.185037i
$723$	12597.0	−	15915.2i	0.647978	−	0.818664i
$724$	9687.16	+	8128.49i	0.497266	+	0.417256i
$725$	14584.8	−	5308.43i	0.747125	−	0.271931i
$726$	7098.41	+	7984.41i	0.362874	+	0.408167i
$727$	−2502.44	−	14192.0i	−0.127662	−	0.724007i	−0.979691	−	0.200513i	$-0.935739\pi$
$727$	−2502.44	−	14192.0i	−0.127662	−	0.724007i	0.852029	−	0.523494i	$-0.175372\pi$
$728$	−9622.79			−0.489896
$729$	6787.18	−	18475.8i	0.344824	−	0.938667i
$730$	1647.88			0.0835490
$731$	2313.17	+	13118.6i	0.117039	+	0.663763i
$732$	−9531.20	−	10720.9i	−0.481261	−	0.541331i
$733$	9569.46	−	3483.00i	0.482205	−	0.175508i	−0.0894684	−	0.995990i	$-0.528517\pi$
$733$	9569.46	−	3483.00i	0.482205	−	0.175508i	0.571673	+	0.820482i	$0.306295\pi$
$734$	−4503.98	−	3779.29i	−0.226492	−	0.190049i
$735$	371.486	−	469.340i	0.0186428	−	0.0235536i
$736$	1360.04	+	495.014i	0.0681138	+	0.0247914i
$737$	15616.4	+	27048.4i	0.780511	+	1.35189i
$738$	−135.263	+	1147.35i	−0.00674676	+	0.0572282i
$739$	−4804.30	+	8321.29i	−0.239146	+	0.414213i	−0.960469	−	0.278385i	$-0.910201\pi$
$739$	−4804.30	+	8321.29i	−0.239146	+	0.414213i	0.721323	+	0.692598i	$0.243534\pi$
$740$	442.527	−	371.324i	0.0219832	−	0.0184461i
$741$	27701.1	+	14954.1i	1.37331	+	0.741366i
$742$	−3518.04	+	19951.8i	−0.174059	+	0.987135i
$743$	4955.96	−	28106.6i	0.244706	−	1.38780i	−0.576469	−	0.817119i	$-0.695570\pi$
$743$	4955.96	−	28106.6i	0.244706	−	1.38780i	0.821175	−	0.570677i	$-0.193319\pi$
$744$	−158.880	−	5555.44i	−0.00782907	−	0.273753i
$745$	1138.89	−	955.639i	0.0560074	−	0.0469958i
$746$	2305.63	−	3993.47i	0.113157	−	0.195994i
$747$	4585.82	−	262.515i	0.224614	−	0.0128580i
$748$	−7694.25	−	13326.8i	−0.376109	−	0.651440i
$749$	37897.9	+	13793.7i	1.84881	+	0.672913i
$750$	819.555	+	2065.94i	0.0399012	+	0.100583i
$751$	−2949.90	−	2475.26i	−0.143333	−	0.120271i	0.568302	−	0.822820i	$-0.307601\pi$
$751$	−2949.90	−	2475.26i	−0.143333	−	0.120271i	−0.711635	+	0.702549i	$0.752045\pi$
$752$	−4782.61	+	1740.73i	−0.231920	+	0.0844119i
$753$	4527.99	−	13642.0i	0.219136	−	0.660214i
$754$	−2388.38	−	13545.2i	−0.115357	−	0.654225i
$755$	2742.79			0.132212
$756$	10053.1	−	7016.93i	0.483636	−	0.337571i
$757$	−22515.6			−1.08104			−0.540518	−	0.841332i	$-0.681772\pi$
$757$	−22515.6			−1.08104			−0.540518	+	0.841332i	$0.681772\pi$
$758$	−3540.15	−	20077.2i	−0.169636	−	0.962054i
$759$	−11180.0	+	2302.69i	−0.534662	+	0.110122i
$760$	709.699	−	258.309i	0.0338730	−	0.0123288i
$761$	−15419.0	−	12938.1i	−0.734479	−	0.616301i	0.196869	−	0.980430i	$-0.436922\pi$
$761$	−15419.0	−	12938.1i	−0.734479	−	0.616301i	−0.931349	+	0.364128i	$0.881367\pi$
$762$	−6489.37	−	953.851i	−0.308511	−	0.0453470i
$763$	33615.6	+	12235.1i	1.59498	+	0.580524i
$764$	1174.17	+	2033.73i	0.0556023	+	0.0963059i
$765$	421.383	+	1785.88i	0.0199152	+	0.0844032i
$766$	5885.48	−	10194.0i	0.277612	−	0.480839i
$767$	22878.7	−	19197.6i	1.07706	−	0.903759i
$768$	−1132.52	+	697.768i	−0.0532111	+	0.0327846i
$769$	5018.25	−	28459.9i	0.235322	−	1.33458i	−0.606613	−	0.794997i	$-0.707472\pi$
$769$	5018.25	−	28459.9i	0.235322	−	1.33458i	0.841935	−	0.539579i	$-0.181417\pi$
$770$	316.174	−	1793.11i	0.0147976	−	0.0839212i
$771$	−20661.2	+	12729.8i	−0.965103	+	0.594622i
$772$	4065.72	−	3411.54i	0.189545	−	0.159047i
$773$	20093.2	−	34802.5i	0.934932	−	1.61935i	0.160177	−	0.987088i	$-0.448794\pi$
$773$	20093.2	−	34802.5i	0.934932	−	1.61935i	0.774755	−	0.632261i	$-0.217873\pi$
$774$	−6611.90	+	6225.58i	−0.307054	+	0.289113i
$775$	−8306.91	−	14388.0i	−0.385023	−	0.666879i
$776$	12091.9	+	4401.09i	0.559373	+	0.203595i
$777$	−18904.3	−	2778.68i	−0.872830	−	0.128294i
$778$	4582.64	+	3845.29i	0.211177	+	0.177198i
$779$	2212.08	−	805.130i	0.101741	−	0.0370305i
$780$	961.691	−	198.074i	0.0441462	−	0.00909256i
$781$	8851.92	+	50201.7i	0.405565	+	2.30008i
$782$	7164.99			0.327647
$783$	12372.3	+	12409.3i	0.564687	+	0.566376i
$784$	2148.17			0.0978574
$785$	−524.680	−	2975.61i	−0.0238556	−	0.135292i
$786$	5906.67	−	17795.7i	0.268046	−	0.807570i
$787$	−12441.4	+	4528.31i	−0.563518	+	0.205104i	−0.608043	−	0.793904i	$-0.708045\pi$
$787$	−12441.4	+	4528.31i	−0.563518	+	0.205104i	0.0445242	+	0.999008i	$0.485823\pi$
$788$	6865.70	+	5761.01i	0.310381	+	0.260441i
$789$	6026.91	+	15192.7i	0.271944	+	0.685517i
$790$	369.451	+	134.469i	0.0166386	+	0.00605595i
$791$	−4290.12	−	7430.70i	−0.192843	−	0.334014i
$792$	4717.71	−	9370.48i	0.211662	−	0.420411i
$793$	−19000.4	+	32909.7i	−0.850851	+	1.47372i
$794$	4472.72	−	3753.06i	0.199913	−	0.167747i
$795$	−59.0964	−	2066.38i	−0.00263639	−	0.0921848i
$796$	−379.456	+	2152.00i	−0.0168963	+	0.0958236i
$797$	−4406.01	+	24987.7i	−0.195820	+	1.11055i	0.715425	+	0.698690i	$0.246233\pi$
$797$	−4406.01	+	24987.7i	−0.195820	+	1.11055i	−0.911245	+	0.411864i	$0.864878\pi$
$798$	−21982.2	−	11866.8i	−0.975139	−	0.526417i
$799$	−19301.1	+	16195.6i	−0.854600	+	0.717094i
$800$	−1988.22	+	3443.70i	−0.0878678	+	0.152192i
$801$	−18833.9	+	8101.95i	−0.830792	+	0.357389i
$802$	5914.85	+	10244.8i	0.260425	+	0.451069i
$803$	−43829.4	−	15952.6i	−1.92616	−	0.701064i
$804$	8294.99	−	10480.0i	0.363858	−	0.459703i
$805$	649.426	+	544.933i	0.0284339	+	0.0238589i
$806$	−13834.8	+	5035.46i	−0.604604	+	0.220058i
$807$	−22282.2	−	25063.4i	−0.971957	−	1.09327i
$808$	−2257.87	−	12805.0i	−0.0983066	−	0.557524i
$809$	13345.4			0.579976			0.289988	−	0.957030i	$-0.406349\pi$
$809$	13345.4			0.579976			0.289988	+	0.957030i	$0.406349\pi$
$810$	−860.263	+	908.197i	−0.0373168	+	0.0393961i
$811$	33175.7			1.43644			0.718222	−	0.695815i	$-0.244956\pi$
$811$	33175.7			1.43644			0.718222	+	0.695815i	$0.244956\pi$
$812$	1895.30	+	10748.8i	0.0819112	+	0.464542i
$813$	−1847.86	−	2078.51i	−0.0797138	−	0.0896635i
$814$	−15364.7	+	5592.31i	−0.661589	+	0.240799i
$815$	2043.66	+	1714.83i	0.0878358	+	0.0737030i
$816$	−4086.97	+	5163.53i	−0.175334	+	0.221519i
$817$	17388.8	+	6329.00i	0.744623	+	0.271021i
$818$	−3084.71	−	5342.87i	−0.131851	−	0.228373i
$819$	−26031.2	−	19419.8i	−1.11063	−	0.828549i
$820$	36.7122	−	63.5874i	0.00156347	−	0.00270801i
$821$	−13847.4	+	11619.4i	−0.588646	+	0.493933i	−0.887774	−	0.460280i	$-0.847749\pi$
$821$	−13847.4	+	11619.4i	−0.588646	+	0.493933i	0.299127	+	0.954213i	$0.403304\pi$
$822$	2073.35	+	1119.27i	0.0879760	+	0.0474928i
$823$	−4271.08	+	24222.5i	−0.180900	+	1.02593i	0.750212	+	0.661198i	$0.229952\pi$
$823$	−4271.08	+	24222.5i	−0.180900	+	1.02593i	−0.931111	+	0.364735i	$0.881159\pi$
$824$	10.8110	−	61.3123i	0.000457063	−	0.00259213i
$825$	−896.533	−	31348.4i	−0.0378343	−	1.32292i
$826$	−18155.4	+	15234.2i	−0.764780	+	0.641727i
$827$	3860.28	−	6686.21i	0.162316	−	0.281139i	−0.773383	−	0.633939i	$-0.781437\pi$
$827$	3860.28	−	6686.21i	0.162316	−	0.281139i	0.935699	+	0.352800i	$0.114770\pi$
$828$	2680.13	+	4083.79i	0.112489	+	0.171403i
$829$	6380.71	+	11051.7i	0.267323	+	0.463018i	0.968170	−	0.250295i	$-0.0805275\pi$
$829$	6380.71	+	11051.7i	0.267323	+	0.463018i	−0.700846	+	0.713312i	$0.747194\pi$
$830$	−274.323	−	99.8454i	−0.0114722	−	0.00417552i
$831$	2564.62	+	6464.90i	0.107058	+	0.269873i
$832$	2699.40	+	2265.06i	0.112482	+	0.0943834i
$833$	9993.18	−	3637.22i	0.415658	−	0.151287i
$834$	−4414.85	+	13301.1i	−0.183302	+	0.552254i
$835$	−68.8777	−	390.625i	−0.00285462	−	0.0161894i
$836$	−21376.8			−0.884368
$837$	10781.7	−	15349.0i	0.445244	−	0.633858i
$838$	27269.6			1.12412
$839$	310.479	+	1760.81i	0.0127758	+	0.0724553i	0.990529	−	0.137303i	$-0.0438434\pi$
$839$	310.479	+	1760.81i	0.0127758	+	0.0724553i	−0.977753	+	0.209758i	$0.932732\pi$
$840$	−763.151	+	157.182i	−0.0313467	+	0.00645630i
$841$	8258.48	−	3005.84i	0.338615	−	0.123246i
$842$	8017.60	+	6727.56i	0.328153	+	0.275353i
$843$	−8798.01	−	1293.19i	−0.359454	−	0.0528350i
$844$	−11304.8	−	4114.60i	−0.461050	−	0.167809i
$845$	−358.023	−	620.113i	−0.0145756	−	0.0252456i
$846$	−16450.7	−	4942.86i	−0.668541	−	0.200873i
$847$	−11229.3	+	19449.7i	−0.455540	+	0.789018i
$848$	5683.26	−	4768.82i	0.230146	−	0.193115i
$849$	−2275.73	+	1402.13i	−0.0919939	+	0.0566795i
$850$	−3418.34	+	19386.4i	−0.137939	+	0.782290i
$851$	1321.99	−	7497.39i	0.0532518	−	0.302006i
$852$	18572.3	−	11442.8i	0.746802	−	0.460122i
$853$	−17839.3	+	14968.9i	−0.716067	+	0.600852i	−0.926294	−	0.376801i	$-0.877024\pi$
$853$	−17839.3	+	14968.9i	−0.716067	+	0.600852i	0.210227	+	0.977653i	$0.432580\pi$
$854$	15077.8	−	26115.5i	0.604159	−	1.04643i
$855$	2441.14	+	733.478i	0.0976437	+	0.0293385i
$856$	−7384.34	−	12790.1i	−0.294850	−	0.510695i
$857$	−9309.08	−	3388.23i	−0.371053	−	0.135052i	0.149762	−	0.988722i	$-0.452149\pi$
$857$	−9309.08	−	3388.23i	−0.371053	−	0.135052i	−0.520814	+	0.853670i	$0.674372\pi$
$858$	−27496.0	−	4041.55i	−1.09405	−	0.160812i
$859$	5179.55	+	4346.16i	0.205732	+	0.172630i	0.739832	−	0.672791i	$-0.234905\pi$
$859$	5179.55	+	4346.16i	0.205732	+	0.172630i	−0.534100	+	0.845421i	$0.679349\pi$
$860$	542.370	−	197.407i	0.0215054	−	0.00782733i
$861$	−2378.68	+	489.924i	−0.0941524	+	0.0193921i
$862$	−532.539	−	3020.18i	−0.0210422	−	0.119336i
$863$	6733.15			0.265584			0.132792	−	0.991144i	$-0.457606\pi$
$863$	6733.15			0.265584			0.132792	+	0.991144i	$0.457606\pi$
$864$	−4471.80	−	397.960i	−0.176081	−	0.0156700i
$865$	−810.834			−0.0318719
$866$	−4151.95	−	23546.9i	−0.162920	−	0.923967i
$867$	−2227.68	+	6711.57i	−0.0872617	+	0.262903i
$868$	10978.6	−	3995.89i	0.429307	−	0.156255i
$869$	−8524.70	−	7153.07i	−0.332774	−	0.279231i
$870$	−410.665	−	1035.21i	−0.0160033	−	0.0403412i
$871$	−33270.8	−	12109.6i	−1.29430	−	0.471088i
$872$	−6549.94	−	11344.8i	−0.254368	−	0.440578i
$873$	23828.6	+	36308.3i	0.923799	+	1.40762i
$874$	4976.59	−	8619.71i	0.192604	−	0.333599i
$875$	−3579.10	+	3003.22i	−0.138281	+	0.116031i
$876$	570.595	+	19951.6i	0.0220076	+	0.769522i
$877$	3348.73	−	18991.6i	0.128938	−	0.731244i	−0.849953	−	0.526859i	$-0.823370\pi$
$877$	3348.73	−	18991.6i	0.128938	−	0.731244i	0.978891	−	0.204385i	$-0.0655193\pi$
$878$	−5148.45	+	29198.3i	−0.197895	+	1.12232i
$879$	29850.1	+	16114.2i	1.14541	+	0.618337i
$880$	−510.767	+	428.584i	−0.0195658	+	0.0164177i
$881$	−19079.7	+	33047.0i	−0.729638	+	1.26377i	0.227398	+	0.973802i	$0.426978\pi$
$881$	−19079.7	+	33047.0i	−0.729638	+	1.26377i	−0.957036	+	0.289969i	$0.906355\pi$
$882$	5811.13	+	4335.22i	0.221849	+	0.165504i
$883$	7602.93	+	13168.7i	0.289761	+	0.501881i	0.973753	−	0.227609i	$-0.0730909\pi$
$883$	7602.93	+	13168.7i	0.289761	+	0.501881i	−0.683992	+	0.729490i	$0.739758\pi$
$884$	16392.6	+	5966.43i	0.623692	+	0.227005i
$885$	1500.86	−	1896.20i	0.0570065	−	0.0720228i
$886$	−14890.9	−	12494.9i	−0.564637	−	0.473786i
$887$	−31508.2	+	11468.1i	−1.19272	+	0.434115i	−0.860678	−	0.509149i	$-0.829960\pi$
$887$	−31508.2	+	11468.1i	−1.19272	+	0.434115i	−0.332043	+	0.943264i	$0.607738\pi$
$888$	4649.01	+	5229.28i	0.175687	+	0.197616i
$889$	−2394.31	−	13578.8i	−0.0903290	−	0.512281i
$890$	1303.04			0.0490765
$891$	31672.8	−	15827.8i	1.19088	−	0.595119i
$892$	−1964.83			−0.0737528
$893$	6077.78	+	34468.8i	0.227755	+	1.29166i
$894$	11964.7	+	13458.1i	0.447605	+	0.503474i
$895$	−3405.91	+	1239.65i	−0.127204	+	0.0462983i
$896$	−2142.11	−	1797.44i	−0.0798693	−	0.0670183i
$897$	8030.83	−	10146.3i	0.298932	−	0.377674i
$898$	−22932.2	−	8346.64i	−0.852180	−	0.310168i
$899$	8349.57	+	14461.9i	0.309759	+	0.536519i
$900$	−12328.2	+	5303.32i	−0.456600	+	0.196419i
$901$	18363.8	−	31807.1i	0.679010	−	1.17608i
$902$	−1592.02	+	1335.86i	−0.0587677	+	0.0493120i
$903$	−16799.4	−	9068.92i	−0.619100	−	0.334214i
$904$	−545.609	+	3094.30i	−0.0200738	+	0.113844i
$905$	471.015	−	2671.26i	0.0173006	−	0.0981168i
$906$	949.720	+	33208.2i	0.0348260	+	1.21773i
$907$	35183.3	−	29522.3i	1.28803	−	1.08078i	0.295944	−	0.955205i	$-0.404366\pi$
$907$	35183.3	−	29522.3i	1.28803	−	1.08078i	0.992084	−	0.125578i	$-0.0400785\pi$
$908$	−6749.67	+	11690.8i	−0.246691	+	0.427281i
$909$	19734.0	−	39196.3i	0.720060	−	1.43021i
$910$	1032.03	+	1787.53i	0.0375951	+	0.0651166i
$911$	−42041.8	−	15302.0i	−1.52899	−	0.556506i	−0.565615	−	0.824670i	$-0.691361\pi$
$911$	−42041.8	−	15302.0i	−1.52899	−	0.556506i	−0.963373	+	0.268163i	$0.913583\pi$
$912$	3373.20	+	8503.19i	0.122476	+	0.308738i
$913$	6329.72	+	5311.26i	0.229445	+	0.192527i
$914$	13215.8	−	4810.15i	0.478270	−	0.174076i
$915$	−969.301	+	2920.32i	−0.0350209	+	0.105511i
$916$	358.592	+	2033.68i	0.0129347	+	0.0733566i
$917$	39416.2			1.41945
$918$	−21476.5	+	5720.25i	−0.772144	+	0.205660i
$919$	−24618.1			−0.883651			−0.441826	−	0.897101i	$-0.645669\pi$
$919$	−24618.1			−0.883651			−0.441826	+	0.897101i	$0.645669\pi$
$920$	−53.9086	−	305.731i	−0.00193186	−	0.0109561i
$921$	−21751.9	+	4480.13i	−0.778230	+	0.160288i
$922$	17086.1	−	6218.82i	0.610303	−	0.222132i
$923$	−44267.8	−	37145.1i	−1.57865	−	1.32464i
$924$	21819.5	+	3207.17i	0.776849	+	0.114186i
$925$	19655.0	+	7153.84i	0.698652	+	0.254289i
$926$	−991.188	−	1716.79i	−0.0351754	−	0.0609257i
$927$	152.980	−	144.042i	0.00542020	−	0.00510351i
$928$	1998.43	−	3461.39i	0.0706915	−	0.122441i
$929$	−13710.8	+	11504.7i	−0.484214	+	0.406304i	−0.851947	−	0.523627i	$-0.824578\pi$
$929$	−13710.8	+	11504.7i	−0.484214	+	0.406304i	0.367733	+	0.929931i	$0.380134\pi$
$930$	−1014.94	+	625.328i	−0.0357863	+	0.0220487i
$931$	2565.28	−	14548.4i	0.0903046	−	0.512143i
$932$	−916.748	+	5199.13i	−0.0322200	+	0.182729i
$933$	−2254.71	+	1389.18i	−0.0791168	+	0.0487456i
$934$	−9980.09	+	8374.29i	−0.349634	+	0.293378i
$935$	−1650.40	+	2858.57i	−0.0577260	+	0.0999843i
$936$	2731.17	+	11575.0i	0.0953750	+	0.404211i
$937$	5441.89	+	9425.63i	0.189732	+	0.328625i	0.945161	−	0.326605i	$-0.105905\pi$
$937$	5441.89	+	9425.63i	0.189732	+	0.328625i	−0.755429	+	0.655231i	$0.772571\pi$
$938$	26402.0	+	9609.56i	0.919038	+	0.334502i
$939$	−15394.8	−	2262.83i	−0.535026	−	0.0786417i
$940$	836.287	+	701.728i	0.0290177	+	0.0243488i
$941$	13465.7	−	4901.12i	0.466493	−	0.169789i	−0.0980702	−	0.995179i	$-0.531267\pi$
$941$	13465.7	−	4901.12i	0.466493	−	0.169789i	0.564563	+	0.825390i	$0.309045\pi$
$942$	35845.3	−	7382.87i	1.23981	−	0.255357i
$943$	−168.029	−	952.940i	−0.00580252	−	0.0329077i
$944$	8678.91			0.299231
$945$	−2381.65	−	1114.91i	−0.0819843	−	0.0383790i
$946$	−16336.7			−0.561471
$947$	5576.29	+	31624.7i	0.191346	+	1.08518i	0.917526	+	0.397675i	$0.130183\pi$
$947$	5576.29	+	31624.7i	0.191346	+	1.08518i	−0.726180	+	0.687505i	$0.758706\pi$
$948$	−1500.15	+	4519.67i	−0.0513952	+	0.154844i
$949$	49685.8	−	18084.1i	1.69955	−	0.618584i
$950$	20948.1	+	17577.6i	0.715417	+	0.600306i
$951$	−10549.0	−	26592.0i	−0.359701	−	0.906735i
$952$	−13008.4	−	4734.67i	−0.442862	−	0.161188i
$953$	−23715.8	−	41077.0i	−0.806118	−	1.39624i	−0.915534	−	0.402241i	$-0.868232\pi$
$953$	−23715.8	−	41077.0i	−0.806118	−	1.39624i	0.109417	−	0.993996i	$-0.465102\pi$
$954$	24998.1	−	1431.01i	0.848368	−	0.0485646i
$955$	251.857	−	436.230i	0.00853394	−	0.0147812i
$956$	−2245.28	+	1884.01i	−0.0759596	+	0.0637377i
$957$	901.137	+	31509.4i	0.0304385	+	1.06432i
$958$	6383.07	−	36200.2i	0.215269	−	1.22085i
$959$	−860.088	+	4877.80i	−0.0289611	+	0.164246i
$960$	251.079	+	135.542i	0.00844117	+	0.00455686i
$961$	−9128.10	+	7659.38i	−0.306404	+	0.257104i
$962$	9267.79	−	16052.3i	0.310609	−	0.537990i
$963$	5835.84	−	49501.5i	0.195283	−	1.65645i
$964$	−7812.42	−	13531.5i	−0.261018	−	0.452096i
$965$	−1069.77	−	389.366i	−0.0356862	−	0.0129887i
$966$	−6372.87	+	8051.57i	−0.212261	+	0.268173i
$967$	−616.492	−	517.298i	−0.0205016	−	0.0172029i	0.632479	−	0.774577i	$-0.282037\pi$
$967$	−616.492	−	517.298i	−0.0205016	−	0.0172029i	−0.652981	+	0.757374i	$0.726482\pi$
$968$	7728.22	−	2812.84i	0.256606	−	0.0933969i
$969$	30089.4	+	33845.1i	0.997534	+	1.12204i
$970$	−479.293	−	2718.20i	−0.0158651	−	0.0899755i
$971$	5884.04			0.194467			0.0972337	−	0.995262i	$-0.469001\pi$
$971$	5884.04			0.194467			0.0972337	+	0.995262i	$0.469001\pi$
$972$	−11293.8	−	10101.1i	−0.372684	−	0.333326i
$973$	−29461.0			−0.970686
$974$	4717.58	+	26754.7i	0.155196	+	0.880160i
$975$	23621.4	+	26569.7i	0.775887	+	0.872731i
$976$	−10376.9	+	3776.87i	−0.340323	+	0.123867i
$977$	27422.2	+	23009.9i	0.897966	+	0.753483i	0.969792	−	0.243934i	$-0.0784380\pi$
$977$	27422.2	+	23009.9i	0.897966	+	0.753483i	−0.0718255	+	0.997417i	$0.522882\pi$
$978$	−20054.6	+	25337.2i	−0.655700	+	0.828420i
$979$	−34657.6	−	12614.3i	−1.13142	−	0.411804i
$980$	−230.388	−	399.044i	−0.00750968	−	0.0130071i
$981$	5176.41	−	43908.0i	0.168471	−	1.42903i
$982$	8330.94	−	14429.6i	0.270724	−	0.468908i
$983$	−3166.54	+	2657.04i	−0.102744	+	0.0862121i	−0.692712	−	0.721214i	$-0.743584\pi$
$983$	−3166.54	+	2657.04i	−0.102744	+	0.0862121i	0.589969	+	0.807426i	$0.299140\pi$
$984$	782.593	+	422.473i	0.0253538	+	0.0136869i
$985$	333.829	−	1893.24i	0.0107986	−	0.0612422i
$986$	3435.89	−	19485.9i	0.110975	−	0.629369i
$987$	−1032.27	−	36094.5i	−0.0332902	−	1.16403i
$988$	18563.6	−	15576.7i	0.597761	−	0.501581i
$989$	3803.24	−	6587.40i	0.122281	−	0.211797i
$990$	−2246.63	+	128.608i	−0.0721239	+	0.00412872i
$991$	−4653.74	−	8060.52i	−0.149174	−	0.258376i	0.781749	−	0.623594i	$-0.214328\pi$
$991$	−4653.74	−	8060.52i	−0.149174	−	0.258376i	−0.930922	+	0.365217i	$0.880995\pi$
$992$	−4020.32	−	1463.28i	−0.128675	−	0.0468337i
$993$	20651.0	+	52057.1i	0.659959	+	1.66363i
$994$	35128.7	+	29476.5i	1.12094	+	0.940582i
$995$	440.452	−	160.312i	0.0140334	−	0.00510776i
$996$	1113.88	−	3355.92i	0.0354365	−	0.106763i
$997$	−4637.89	−	26302.8i	−0.147325	−	0.835524i	−0.965471	−	0.260512i	$-0.916109\pi$
$997$	−4637.89	−	26302.8i	−0.147325	−	0.835524i	0.818145	−	0.575012i	$-0.195003\pi$
$998$	33356.5			1.05800
$999$	2023.06	+	23528.2i	0.0640710	+	0.745145i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	54.4.e.b.13.2	✓	30
3.2	odd	2		162.4.e.b.91.3		30
27.2	odd	18		162.4.e.b.73.3		30
27.5	odd	18		1458.4.a.j.1.7		15
27.22	even	9		1458.4.a.i.1.9		15
27.25	even	9	inner	54.4.e.b.25.2	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.4.e.b.13.2	✓	30	1.1	even	1	trivial
54.4.e.b.25.2	yes	30	27.25	even	9	inner
162.4.e.b.73.3		30	27.2	odd	18
162.4.e.b.91.3		30	3.2	odd	2
1458.4.a.i.1.9		15	27.22	even	9
1458.4.a.j.1.7		15	27.5	odd	18

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:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	54.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.347296 - 1.96962i) q^{2} +(-3.45245 - 3.88337i) q^{3} +(-3.75877 + 1.36808i) q^{4} +(0.657259 + 0.551505i) q^{5} +(-6.44973 + 8.14868i) q^{6} +(-20.5288 - 7.47187i) q^{7} +(4.00000 + 6.92820i) q^{8} +(-3.16120 + 26.8143i) q^{9} +(0.857990 - 1.48608i) q^{10} +(-37.2066 + 31.2201i) q^{11} +(18.2897 + 9.87349i) q^{12} +(9.56100 - 54.2231i) q^{13} +(-7.58714 + 43.0288i) q^{14} +(-0.127449 - 4.45643i) q^{15} +(12.2567 - 10.2846i) q^{16} +(39.6041 - 68.5963i) q^{17} +(53.9117 - 3.08617i) q^{18} +(-55.0156 - 95.2899i) q^{19} +(-3.22499 - 1.17380i) q^{20} +(41.8585 + 105.517i) q^{21} +(74.4132 + 62.4401i) q^{22} +(-42.5012 + 15.4692i) q^{23} +(13.0950 - 39.4528i) q^{24} +(-21.5782 - 122.376i) q^{25} -110.119 q^{26} +(115.044 - 80.2989i) q^{27} +87.3852 q^{28} +(21.6890 + 123.004i) q^{29} +(-8.73318 + 1.79873i) q^{30} +(125.635 - 45.7274i) q^{31} +(-24.5134 - 20.5692i) q^{32} +(249.693 + 36.7016i) q^{33} +(-148.863 - 54.1816i) q^{34} +(-9.37195 - 16.2327i) q^{35} +(-24.8019 - 105.114i) q^{36} +(-84.1614 + 145.772i) q^{37} +(-168.578 + 141.453i) q^{38} +(-243.578 + 150.074i) q^{39} +(-1.19191 + 6.75964i) q^{40} +(-3.71508 + 21.0693i) q^{41} +(193.291 - 119.091i) q^{42} +(-128.831 + 108.102i) q^{43} +(97.1396 - 168.251i) q^{44} +(-16.8660 + 15.8805i) q^{45} +(45.2289 + 78.3387i) q^{46} +(-298.913 - 108.795i) q^{47} +(-82.2546 - 12.0903i) q^{48} +(102.849 + 86.3009i) q^{49} +(-233.540 + 85.0015i) q^{50} +(-403.116 + 83.0276i) q^{51} +(38.2440 + 216.893i) q^{52} +463.685 q^{53} +(-198.112 - 198.705i) q^{54} -41.6724 q^{55} +(-30.3485 - 172.115i) q^{56} +(-180.108 + 542.630i) q^{57} +(234.739 - 85.4380i) q^{58} +(415.527 + 348.668i) q^{59} +(6.57580 + 16.5763i) q^{60} +(-648.554 - 236.054i) q^{61} +(-133.698 - 231.571i) q^{62} +(265.249 - 526.845i) q^{63} +(-32.0000 + 55.4256i) q^{64} +(36.1884 - 30.3657i) q^{65} +(-14.4295 - 504.546i) q^{66} +(111.664 - 633.280i) q^{67} +(-55.0174 + 312.019i) q^{68} +(206.806 + 111.642i) q^{69} +(-28.7173 + 24.0967i) q^{70} +(524.772 - 908.932i) q^{71} +(-198.420 + 85.3558i) q^{72} +(480.157 + 831.656i) q^{73} +(316.343 + 115.140i) q^{74} +(-400.734 + 506.293i) q^{75} +(337.155 + 282.907i) q^{76} +(997.080 - 362.907i) q^{77} +(380.181 + 427.634i) q^{78} +(39.7859 + 225.637i) q^{79} +13.7278 q^{80} +(-709.014 - 169.531i) q^{81} +42.7886 q^{82} +(-29.5416 - 167.539i) q^{83} +(-301.693 - 339.349i) q^{84} +(63.8613 - 23.2436i) q^{85} +(257.663 + 216.205i) q^{86} +(402.792 - 508.893i) q^{87} +(-365.125 - 132.895i) q^{88} +(379.679 + 657.623i) q^{89} +(37.1360 + 27.7042i) q^{90} +(-601.424 + 1041.70i) q^{91} +(138.589 - 116.290i) q^{92} +(-611.324 - 330.016i) q^{93} +(-110.474 + 626.528i) q^{94} +(16.3934 - 92.9715i) q^{95} +(4.75341 + 166.209i) q^{96} +(1232.17 - 1033.92i) q^{97} +(134.260 - 232.546i) q^{98} +(-719.527 - 1096.36i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 12 q^{5} + 30 q^{6} + 33 q^{7} + 120 q^{8} + 42 q^{9} - 30 q^{10} - 39 q^{11} + 24 q^{12} - 60 q^{13} - 66 q^{14} - 153 q^{15} + 102 q^{17} + 168 q^{18} - 171 q^{19} + 96 q^{20} + 78 q^{21} + 78 q^{22}+ \cdots + 10296 q^{99}+O(q^{100}) \) 30 * q - 12 * q^5 + 30 * q^6 + 33 * q^7 + 120 * q^8 + 42 * q^9 - 30 * q^10 - 39 * q^11 + 24 * q^12 - 60 * q^13 - 66 * q^14 - 153 * q^15 + 102 * q^17 + 168 * q^18 - 171 * q^19 + 96 * q^20 + 78 * q^21 + 78 * q^22 + 48 * q^23 - 432 * q^25 - 468 * q^26 - 675 * q^27 + 336 * q^28 - 381 * q^29 - 486 * q^30 - 801 * q^31 + 954 * q^33 - 222 * q^34 + 624 * q^35 + 132 * q^36 - 555 * q^37 + 606 * q^38 + 363 * q^39 + 96 * q^40 + 1401 * q^41 - 420 * q^42 + 648 * q^43 + 132 * q^44 + 2583 * q^45 - 348 * q^46 + 540 * q^47 + 192 * q^48 + 15 * q^49 - 828 * q^50 - 2376 * q^51 - 240 * q^52 - 1794 * q^53 - 522 * q^54 + 3906 * q^55 - 264 * q^56 - 1656 * q^57 - 444 * q^58 - 1500 * q^59 + 1332 * q^60 - 378 * q^61 + 744 * q^62 + 840 * q^63 - 960 * q^64 + 3666 * q^65 + 1710 * q^66 + 3087 * q^67 - 24 * q^68 + 1665 * q^69 + 2118 * q^70 + 120 * q^71 + 672 * q^72 - 2604 * q^73 - 1974 * q^74 - 2643 * q^75 - 1212 * q^76 - 6504 * q^77 - 5220 * q^78 - 2625 * q^79 - 480 * q^80 - 7614 * q^81 + 3408 * q^82 - 5211 * q^83 - 1548 * q^84 - 1395 * q^85 - 1296 * q^86 + 4914 * q^87 - 912 * q^88 + 2604 * q^89 + 1512 * q^90 - 3399 * q^91 + 372 * q^92 - 222 * q^93 + 4500 * q^94 + 7545 * q^95 + 384 * q^96 + 8940 * q^97 + 4002 * q^98 + 10296 * q^99

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