LMFDB - Embedded newform 189.3.x.a.103.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [189,3,Mod(40,189)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("189.40"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(189, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([8, 15])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	189.x (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.14987699641$
Analytic rank:	$0$
Dimension:	$276$
Relative dimension:	$46$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			103.8
Character	$\chi$	$=$	189.103
Dual form			189.3.x.a.178.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.498156 - 2.82518i) q^{2} +(1.27498 - 2.71559i) q^{3} +(-3.97473 + 1.44668i) q^{4} +(5.42157 + 0.955969i) q^{5} +(-8.30718 - 2.24925i) q^{6} +(6.82445 + 1.55787i) q^{7} +(0.329641 + 0.570956i) q^{8} +(-5.74887 - 6.92463i) q^{9} -15.7931i q^{10} +(-2.53394 - 14.3707i) q^{11} +(-1.13909 + 12.6382i) q^{12} +(-2.45087 + 2.92084i) q^{13} +(1.00162 - 20.0564i) q^{14} +(9.50840 - 13.5039i) q^{15} +(-11.5121 + 9.65977i) q^{16} +10.1803i q^{17} +(-16.6995 + 19.6911i) q^{18} +11.0725i q^{19} +(-22.9322 + 4.04357i) q^{20} +(12.9315 - 16.5462i) q^{21} +(-39.3375 + 14.3177i) q^{22} +(21.5412 + 18.0752i) q^{23} +(1.97077 - 0.167216i) q^{24} +(4.98723 + 1.81520i) q^{25} +(9.47281 + 5.46913i) q^{26} +(-26.1341 + 6.78284i) q^{27} +(-29.3790 + 3.68071i) q^{28} +(20.9105 - 17.5460i) q^{29} +(-42.8877 - 20.1359i) q^{30} +(17.0735 + 46.9091i) q^{31} +(35.0456 + 29.4067i) q^{32} +(-42.2556 - 11.4411i) q^{33} +(28.7611 - 5.07136i) q^{34} +(35.5099 + 14.9700i) q^{35} +(32.8679 + 19.2067i) q^{36} +(-26.1418 - 45.2789i) q^{37} +(31.2820 - 5.51585i) q^{38} +(4.80699 + 10.3796i) q^{39} +(1.24136 + 3.41060i) q^{40} +(-16.0124 + 19.0828i) q^{41} +(-53.1878 - 28.2914i) q^{42} +(-61.8402 - 22.5080i) q^{43} +(30.8615 + 53.4537i) q^{44} +(-24.5482 - 43.0381i) q^{45} +(40.3349 - 69.8621i) q^{46} +(3.05609 - 8.39653i) q^{47} +(11.5544 + 43.5780i) q^{48} +(44.1461 + 21.2632i) q^{49} +(2.64386 - 14.9941i) q^{50} +(27.6455 + 12.9796i) q^{51} +(5.51602 - 15.1551i) q^{52} +(16.5588 + 28.6807i) q^{53} +(32.1816 + 70.4548i) q^{54} -80.3341i q^{55} +(1.36015 + 4.40999i) q^{56} +(30.0685 + 14.1172i) q^{57} +(-59.9873 - 50.3353i) q^{58} +(20.4232 - 24.3394i) q^{59} +(-18.2574 + 67.4300i) q^{60} +(7.47039 - 20.5247i) q^{61} +(124.021 - 71.6038i) q^{62} +(-28.4452 - 56.2127i) q^{63} +(35.5653 - 61.6010i) q^{64} +(-16.0798 + 13.4926i) q^{65} +(-11.2734 + 125.079i) q^{66} +(-14.7693 + 83.7611i) q^{67} +(-14.7276 - 40.4638i) q^{68} +(76.5494 - 35.4516i) q^{69} +(24.6036 - 107.779i) q^{70} +(60.0372 - 103.988i) q^{71} +(2.05859 - 5.56499i) q^{72} +(89.9772 + 51.9484i) q^{73} +(-114.898 + 96.4112i) q^{74} +(11.2879 - 11.2289i) q^{75} +(-16.0184 - 44.0103i) q^{76} +(5.09488 - 102.020i) q^{77} +(26.9295 - 18.7513i) q^{78} +(20.4100 + 115.751i) q^{79} +(-71.6479 + 41.3659i) q^{80} +(-14.9010 + 79.6176i) q^{81} +(61.8891 + 35.7317i) q^{82} +(13.6270 + 16.2401i) q^{83} +(-27.4623 + 84.4742i) q^{84} +(-9.73202 + 55.1931i) q^{85} +(-32.7831 + 185.922i) q^{86} +(-20.9873 - 79.1551i) q^{87} +(7.36973 - 6.18394i) q^{88} +7.15164i q^{89} +(-109.362 + 90.7927i) q^{90} +(-21.2761 + 16.1149i) q^{91} +(-111.769 - 40.6807i) q^{92} +(149.154 + 13.4433i) q^{93} +(-25.2441 - 4.45122i) q^{94} +(-10.5850 + 60.0306i) q^{95} +(124.539 - 57.6765i) q^{96} +(58.8110 - 161.582i) q^{97} +(38.0806 - 135.313i) q^{98} +(-84.9444 + 100.162i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 276 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 36 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9} - 21 q^{11} - 9 q^{12} - 87 q^{14} + 12 q^{15} - 15 q^{16} - 3 q^{18} + 36 q^{20} - 147 q^{21} - 12 q^{22} - 102 q^{23}+ \cdots - 336 q^{99}+O(q^{100}) $ 276 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 36 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9 - 21 * q^11 - 9 * q^12 - 87 * q^14 + 12 * q^15 - 15 * q^16 - 3 * q^18 + 36 * q^20 - 147 * q^21 - 12 * q^22 - 102 * q^23 - 9 * q^24 - 3 * q^25 - 18 * q^26 - 12 * q^28 - 120 * q^29 + 177 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 + 36 * q^34 - 84 * q^35 + 162 * q^36 + 3 * q^37 - 279 * q^38 - 270 * q^39 + 216 * q^40 + 207 * q^42 - 12 * q^43 + 3 * q^44 - 9 * q^45 + 3 * q^46 - 333 * q^47 + 66 * q^49 - 225 * q^50 + 204 * q^51 - 9 * q^52 - 141 * q^53 - 315 * q^54 + 279 * q^56 - 162 * q^57 - 3 * q^58 - 144 * q^59 + 291 * q^60 - 9 * q^61 + 891 * q^62 + 75 * q^63 - 774 * q^64 - 3 * q^65 - 9 * q^66 - 3 * q^67 + 666 * q^68 - 216 * q^69 + 84 * q^70 - 114 * q^71 - 291 * q^72 - 9 * q^73 + 57 * q^74 + 576 * q^75 + 144 * q^76 - 447 * q^77 + 30 * q^78 + 15 * q^79 + 558 * q^80 - 465 * q^81 - 18 * q^82 - 1080 * q^83 + 276 * q^84 + 243 * q^85 + 627 * q^86 + 486 * q^87 + 405 * q^88 + 729 * q^90 + 96 * q^91 - 276 * q^92 - 15 * q^93 - 9 * q^94 + 9 * q^95 + 567 * q^96 + 807 * q^98 - 336 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.498156	−	2.82518i	−0.249078	−	1.41259i	−0.810828	−	0.585284i	$-0.800983\pi$
$2$	−0.498156	−	2.82518i	−0.249078	−	1.41259i	0.561750	−	0.827307i	$-0.310128\pi$
$3$	1.27498	−	2.71559i	0.424992	−	0.905197i
$3$	1.27498	−	2.71559i	0.424992	−	0.905197i
$4$	−3.97473	+	1.44668i	−0.993681	+	0.361670i
$5$	5.42157	+	0.955969i	1.08431	+	0.191194i	0.687122	−	0.726542i	$-0.258874\pi$
$5$	5.42157	+	0.955969i	1.08431	+	0.191194i	0.397192	+	0.917736i	$0.369985\pi$
$6$	−8.30718	−	2.24925i	−1.38453	−	0.374876i
$7$	6.82445	+	1.55787i	0.974921	+	0.222552i
$7$	6.82445	+	1.55787i	0.974921	+	0.222552i
$8$	0.329641	+	0.570956i	0.0412052	+	0.0713695i
$9$	−5.74887	−	6.92463i	−0.638763	−	0.769403i
$10$		−	15.7931i		−	1.57931i
$11$	−2.53394	−	14.3707i	−0.230358	−	1.30643i	−0.852172	−	0.523261i	$-0.824715\pi$
$11$	−2.53394	−	14.3707i	−0.230358	−	1.30643i	0.621814	−	0.783165i	$-0.286396\pi$
$12$	−1.13909	+	12.6382i	−0.0949238	+	1.05318i
$13$	−2.45087	+	2.92084i	−0.188529	+	0.224680i	−0.852027	−	0.523498i	$-0.824627\pi$
$13$	−2.45087	+	2.92084i	−0.188529	+	0.224680i	0.663498	+	0.748178i	$0.269071\pi$
$14$	1.00162	−	20.0564i	0.0715443	−	1.43260i
$15$	9.50840	−	13.5039i	0.633893	−	0.900262i
$16$	−11.5121	+	9.65977i	−0.719504	+	0.603735i
$17$			10.1803i			0.598839i	0.954121	+	0.299420i	$0.0967931\pi$
$17$			10.1803i			0.598839i	−0.954121	+	0.299420i	$0.903207\pi$
$18$	−16.6995	+	19.6911i	−0.927751	+	1.09395i
$19$			11.0725i			0.582765i	0.956607	+	0.291383i	$0.0941153\pi$
$19$			11.0725i			0.582765i	−0.956607	+	0.291383i	$0.905885\pi$
$20$	−22.9322	+	4.04357i	−1.14661	+	0.202179i
$21$	12.9315	−	16.5462i	0.615787	−	0.787912i
$22$	−39.3375	+	14.3177i	−1.78807	+	0.650804i
$23$	21.5412	+	18.0752i	0.936573	+	0.785878i	0.976986	−	0.213305i	$-0.0684227\pi$
$23$	21.5412	+	18.0752i	0.936573	+	0.785878i	−0.0404123	+	0.999183i	$0.512867\pi$
$24$	1.97077	−	0.167216i	0.0821153	−	0.00696734i
$25$	4.98723	+	1.81520i	0.199489	+	0.0726081i
$26$	9.47281	+	5.46913i	0.364339	+	0.210351i
$27$	−26.1341	+	6.78284i	−0.967931	+	0.251216i
$28$	−29.3790	+	3.68071i	−1.04925	+	0.131454i
$29$	20.9105	−	17.5460i	0.721051	−	0.605034i	−0.206625	−	0.978420i	$-0.566248\pi$
$29$	20.9105	−	17.5460i	0.721051	−	0.605034i	0.927676	+	0.373386i	$0.121803\pi$
$30$	−42.8877	−	20.1359i	−1.42959	−	0.671196i
$31$	17.0735	+	46.9091i	0.550758	+	1.51320i	0.832678	+	0.553758i	$0.186807\pi$
$31$	17.0735	+	46.9091i	0.550758	+	1.51320i	−0.281919	+	0.959438i	$0.590971\pi$
$32$	35.0456	+	29.4067i	1.09517	+	0.918960i
$33$	−42.2556	−	11.4411i	−1.28047	−	0.346701i
$34$	28.7611	−	5.07136i	0.845915	−	0.149158i
$35$	35.5099	+	14.9700i	1.01457	+	0.427715i
$36$	32.8679	+	19.2067i	0.912997	+	0.533520i
$37$	−26.1418	−	45.2789i	−0.706534	−	1.22375i	−0.966135	−	0.258037i	$-0.916924\pi$
$37$	−26.1418	−	45.2789i	−0.706534	−	1.22375i	0.259600	−	0.965716i	$-0.416409\pi$
$38$	31.2820	−	5.51585i	0.823209	−	0.145154i
$39$	4.80699	+	10.3796i	0.123256	+	0.266143i
$40$	1.24136	+	3.41060i	0.0310339	+	0.0852651i
$41$	−16.0124	+	19.0828i	−0.390546	+	0.465434i	−0.925113	−	0.379692i	$-0.876030\pi$
$41$	−16.0124	+	19.0828i	−0.390546	+	0.465434i	0.534567	+	0.845126i	$0.320475\pi$
$42$	−53.1878	−	28.2914i	−1.26638	−	0.673604i
$43$	−61.8402	−	22.5080i	−1.43814	−	0.523442i	−0.498891	−	0.866665i	$-0.666259\pi$
$43$	−61.8402	−	22.5080i	−1.43814	−	0.523442i	−0.939254	+	0.343223i	$0.888481\pi$
$44$	30.8615	+	53.4537i	0.701398	+	1.21486i
$45$	−24.5482	−	43.0381i	−0.545515	−	0.956402i
$46$	40.3349	−	69.8621i	0.876845	−	1.51874i
$47$	3.05609	−	8.39653i	0.0650231	−	0.178649i	−0.902926	−	0.429796i	$-0.858585\pi$
$47$	3.05609	−	8.39653i	0.0650231	−	0.178649i	0.967949	+	0.251147i	$0.0808076\pi$
$48$	11.5544	+	43.5780i	0.240716	+	0.907876i
$49$	44.1461	+	21.2632i	0.900941	+	0.433942i
$50$	2.64386	−	14.9941i	0.0528772	−	0.299882i
$51$	27.6455	+	12.9796i	0.542068	+	0.254502i
$52$	5.51602	−	15.1551i	0.106077	−	0.291445i
$53$	16.5588	+	28.6807i	0.312431	+	0.541146i	0.978888	−	0.204397i	$-0.0655235\pi$
$53$	16.5588	+	28.6807i	0.312431	+	0.541146i	−0.666457	+	0.745543i	$0.732190\pi$
$54$	32.1816	+	70.4548i	0.595956	+	1.30472i
$55$		−	80.3341i		−	1.46062i
$56$	1.36015	+	4.40999i	0.0242883	+	0.0787499i
$57$	30.0685	+	14.1172i	0.527518	+	0.247671i
$58$	−59.9873	−	50.3353i	−1.03426	−	0.867850i
$59$	20.4232	−	24.3394i	0.346155	−	0.412532i	−0.564675	−	0.825314i	$-0.690998\pi$
$59$	20.4232	−	24.3394i	0.346155	−	0.412532i	0.910830	+	0.412782i	$0.135443\pi$
$60$	−18.2574	+	67.4300i	−0.304290	+	1.12383i
$61$	7.47039	−	20.5247i	0.122465	−	0.336471i	−0.863278	−	0.504730i	$-0.831592\pi$
$61$	7.47039	−	20.5247i	0.122465	−	0.336471i	0.985743	+	0.168259i	$0.0538144\pi$
$62$	124.021	−	71.6038i	2.00035	−	1.15490i
$63$	−28.4452	−	56.2127i	−0.451511	−	0.892266i
$64$	35.5653	−	61.6010i	0.555708	−	0.962515i
$65$	−16.0798	+	13.4926i	−0.247382	+	0.207578i
$66$	−11.2734	+	125.079i	−0.170810	+	1.89514i
$67$	−14.7693	+	83.7611i	−0.220438	+	1.25017i	0.650779	+	0.759267i	$0.274442\pi$
$67$	−14.7693	+	83.7611i	−0.220438	+	1.25017i	−0.871217	+	0.490898i	$0.836669\pi$
$68$	−14.7276	−	40.4638i	−0.216583	−	0.595056i
$69$	76.5494	−	35.4516i	1.10941	−	0.513791i
$70$	24.6036	−	107.779i	0.351480	−	1.53971i
$71$	60.0372	−	103.988i	0.845595	−	1.46461i	−0.0395092	−	0.999219i	$-0.512579\pi$
$71$	60.0372	−	103.988i	0.845595	−	1.46461i	0.885104	−	0.465394i	$-0.154087\pi$
$72$	2.05859	−	5.56499i	0.0285915	−	0.0772916i
$73$	89.9772	+	51.9484i	1.23257	+	0.711622i	0.967564	−	0.252626i	$-0.0812943\pi$
$73$	89.9772	+	51.9484i	1.23257	+	0.711622i	0.265001	+	0.964248i	$0.414628\pi$
$74$	−114.898	+	96.4112i	−1.55268	+	1.30285i
$75$	11.2879	−	11.2289i	0.150506	−	0.149719i
$76$	−16.0184	−	44.0103i	−0.210769	−	0.579083i
$77$	5.09488	−	102.020i	0.0661673	−	1.32493i
$78$	26.9295	−	18.7513i	0.345250	−	0.240401i
$79$	20.4100	+	115.751i	0.258355	+	1.46520i	0.787313	+	0.616554i	$0.211472\pi$
$79$	20.4100	+	115.751i	0.258355	+	1.46520i	−0.528958	+	0.848648i	$0.677417\pi$
$80$	−71.6479	+	41.3659i	−0.895599	+	0.517074i
$81$	−14.9010	+	79.6176i	−0.183963	+	0.982933i
$82$	61.8891	+	35.7317i	0.754745	+	0.435752i
$83$	13.6270	+	16.2401i	0.164181	+	0.195663i	0.841862	−	0.539692i	$-0.181459\pi$
$83$	13.6270	+	16.2401i	0.164181	+	0.195663i	−0.677681	+	0.735356i	$0.737015\pi$
$84$	−27.4623	+	84.4742i	−0.326932	+	1.00565i
$85$	−9.73202	+	55.1931i	−0.114494	+	0.649330i
$86$	−32.7831	+	185.922i	−0.381199	+	2.16189i
$87$	−20.9873	−	79.1551i	−0.241234	−	0.909828i
$88$	7.36973	−	6.18394i	0.0837470	−	0.0702721i
$89$			7.15164i			0.0803555i	0.999193	+	0.0401777i	$0.0127924\pi$
$89$			7.15164i			0.0803555i	−0.999193	+	0.0401777i	$0.987208\pi$
$90$	−109.362	+	90.7927i	−1.21513	+	1.00881i
$91$	−21.2761	+	16.1149i	−0.233803	+	0.177087i
$92$	−111.769	−	40.6807i	−1.21488	−	0.442182i
$93$	149.154	+	13.4433i	1.60381	+	0.144552i
$94$	−25.2441	−	4.45122i	−0.268555	−	0.0473534i
$95$	−10.5850	+	60.0306i	−0.111421	+	0.631901i
$96$	124.539	−	57.6765i	1.29728	−	0.600797i
$97$	58.8110	−	161.582i	0.606299	−	1.66579i	−0.131943	−	0.991257i	$-0.542121\pi$
$97$	58.8110	−	161.582i	0.606299	−	1.66579i	0.738242	−	0.674536i	$-0.235656\pi$
$98$	38.0806	−	135.313i	0.388578	−	1.38075i
$99$	−84.9444	+	100.162i	−0.858024	+	1.01174i
$100$	−22.4489			−0.224489
$101$	−30.1472	−	35.9280i	−0.298487	−	0.355723i	0.595867	−	0.803083i	$-0.296809\pi$
$101$	−30.1472	−	35.9280i	−0.298487	−	0.355723i	−0.894354	+	0.447360i	$0.852364\pi$
$102$	22.8980	−	84.5693i	0.224490	−	0.829111i
$103$	20.5966	+	3.63173i	0.199967	+	0.0352595i	0.272734	−	0.962089i	$-0.412072\pi$
$103$	20.5966	+	3.63173i	0.199967	+	0.0352595i	−0.0727676	+	0.997349i	$0.523183\pi$
$104$	−2.47558	−	0.436511i	−0.0238036	−	0.00419722i
$105$	85.9268	−	77.3440i	0.818351	−	0.736610i
$106$	72.7794	−	61.0692i	0.686598	−	0.576124i
$107$	−4.46558	+	7.73461i	−0.0417344	+	0.0722861i	−0.886138	−	0.463421i	$-0.846622\pi$
$107$	−4.46558	+	7.73461i	−0.0417344	+	0.0722861i	0.844404	+	0.535707i	$0.179955\pi$
$108$	94.0634	−	64.7677i	0.870957	−	0.599701i
$109$	−13.2097	−	22.8799i	−0.121190	−	0.209907i	0.799047	−	0.601268i	$-0.205338\pi$
$109$	−13.2097	−	22.8799i	−0.121190	−	0.209907i	−0.920237	+	0.391361i	$0.872004\pi$
$110$	−226.958	+	40.0189i	−2.06326	+	0.363808i
$111$	−156.289	+	13.2609i	−1.40801	+	0.119467i
$112$	−93.6121	+	47.9883i	−0.835822	+	0.428467i
$113$	1.02399	−	0.372701i	0.00906183	−	0.00329824i	−0.337485	−	0.941331i	$-0.609576\pi$
$113$	1.02399	−	0.372701i	0.00906183	−	0.00329824i	0.346547	+	0.938033i	$0.387354\pi$
$114$	24.9050	−	91.9816i	0.218465	−	0.806856i
$115$	99.5077	+	118.589i	0.865285	+	1.03121i
$116$	−57.7300	+	99.9913i	−0.497672	+	0.861994i
$117$	34.3154	+	0.179881i	0.293294	+	0.00153744i
$118$	−78.9371	−	45.5744i	−0.668959	−	0.386223i
$119$	−15.8595	+	69.4747i	−0.133273	+	0.583821i
$120$	10.8445	+	0.977419i	0.0903709	+	0.00814515i
$121$	−86.3930	+	31.4445i	−0.713992	+	0.259872i
$122$	−61.7075	−	10.8807i	−0.505799	−	0.0891860i
$123$	31.4057	+	67.8132i	0.255331	+	0.551327i
$124$	−135.725	−	161.751i	−1.09456	−	1.30444i
$125$	−93.8879	−	54.2062i	−0.751103	−	0.433650i
$126$	−144.641	+	108.366i	−1.14795	+	0.860044i
$127$	51.8897	+	89.8757i	0.408581	+	0.707682i	0.994731	−	0.102520i	$-0.0326905\pi$
$127$	51.8897	+	89.8757i	0.408581	+	0.707682i	−0.586150	+	0.810202i	$0.699357\pi$
$128$	−19.7920	−	7.20371i	−0.154625	−	0.0562790i
$129$	−139.967	+	139.236i	−1.08502	+	1.07935i
$130$	46.1292	+	38.7070i	0.354840	+	0.297746i
$131$	8.78896	−	10.4743i	0.0670913	−	0.0799563i	−0.731455	−	0.681890i	$-0.761158\pi$
$131$	8.78896	−	10.4743i	0.0670913	−	0.0799563i	0.798546	+	0.601934i	$0.205603\pi$
$132$	184.506	−	15.6550i	1.39777	−	0.118599i
$133$	−17.2495	+	75.5640i	−0.129696	+	0.568150i
$134$	243.998			1.82088
$135$	−148.172	+	11.7902i	−1.09757	+	0.0873348i
$136$	−5.81248	+	3.35584i	−0.0427388	+	0.0246753i
$137$	−211.472	−	76.9694i	−1.54359	−	0.561820i	−0.576686	−	0.816966i	$-0.695655\pi$
$137$	−211.472	−	76.9694i	−1.54359	−	0.561820i	−0.966903	+	0.255145i	$0.917877\pi$
$138$	−138.291	−	198.606i	−1.00211	−	1.43917i
$139$	−191.084	−	33.6932i	−1.37470	−	0.242397i	−0.562995	−	0.826461i	$-0.690351\pi$
$139$	−191.084	−	33.6932i	−1.37470	−	0.242397i	−0.811708	+	0.584063i	$0.801462\pi$
$140$	−162.799	−	8.13023i	−1.16285	−	0.0580731i
$141$	−18.9051	−	19.0045i	−0.134079	−	0.134783i
$142$	−323.692	−	117.814i	−2.27952	−	0.829677i
$143$	48.1848	+	27.8195i	0.336956	+	0.194542i
$144$	133.072	+	24.1840i	0.924109	+	0.167945i
$145$	130.141	−	75.1370i	0.897525	−	0.518186i
$146$	101.941	−	280.081i	0.698226	−	1.91836i
$147$	114.027	−	92.7727i	0.775696	−	0.631107i
$148$	169.410	+	142.152i	1.14467	+	0.960488i
$149$	−47.1526	+	17.1622i	−0.316461	+	0.115182i	−0.495367	−	0.868684i	$-0.664966\pi$
$149$	−47.1526	+	17.1622i	−0.316461	+	0.115182i	0.178906	+	0.983866i	$0.442744\pi$
$150$	−37.3469	−	26.2967i	−0.248980	−	0.175312i
$151$	−4.50148	−	25.5291i	−0.0298111	−	0.169067i	0.966267	−	0.257541i	$-0.0829122\pi$
$151$	−4.50148	−	25.5291i	−0.0298111	−	0.169067i	−0.996079	+	0.0884737i	$0.971801\pi$
$152$	−6.32193	+	3.64997i	−0.0415917	+	0.0240130i
$153$	70.4946	−	58.5250i	0.460749	−	0.382517i
$154$	−290.762	+	36.4276i	−1.88806	+	0.236543i
$155$	47.7216	+	270.643i	0.307881	+	1.74608i
$156$	−34.1224	−	34.3017i	−0.218733	−	0.219883i
$157$	41.1000	−	48.9811i	0.261784	−	0.311982i	−0.619102	−	0.785310i	$-0.712503\pi$
$157$	41.1000	−	48.9811i	0.261784	−	0.311982i	0.880886	+	0.473329i	$0.156948\pi$
$158$	316.850	−	115.324i	2.00538	−	0.729899i
$159$	98.9972	−	8.39974i	0.622624	−	0.0528285i
$160$	161.890	+	192.933i	1.01181	+	1.20583i
$161$	118.848	+	156.912i	0.738186	+	0.974606i
$162$	232.357	+	2.43609i	1.43430	+	0.0150376i
$163$	−75.8460	+	131.369i	−0.465313	+	0.805946i	−0.999216	−	0.0396003i	$-0.987392\pi$
$163$	−75.8460	+	131.369i	−0.465313	+	0.805946i	0.533903	+	0.845546i	$0.320725\pi$
$164$	36.0380	−	99.0137i	0.219744	−	0.603742i
$165$	−218.154	−	102.424i	−1.32215	−	0.620752i
$166$	39.0928	−	46.5889i	0.235499	−	0.280656i
$167$	−51.2566	−	140.826i	−0.306926	−	0.843271i	−0.993252	−	0.115977i	$-0.963000\pi$
$167$	−51.2566	−	140.826i	−0.306926	−	0.843271i	0.686326	−	0.727294i	$-0.259222\pi$
$168$	13.7099	+	1.92904i	0.0816065	+	0.0114824i
$169$	26.8220	+	152.115i	0.158710	+	0.900091i
$170$	160.778			0.945756
$171$	76.6733	−	63.6546i	0.448382	−	0.372249i
$172$	278.360			1.61837
$173$	202.861	+	241.761i	1.17261	+	1.39746i	0.900311	+	0.435248i	$0.143339\pi$
$173$	202.861	+	241.761i	1.17261	+	1.39746i	0.272298	+	0.962213i	$0.412216\pi$
$174$	−213.173	+	98.7246i	−1.22513	+	0.567383i
$175$	31.2072	+	20.1572i	0.178327	+	0.115184i
$176$	167.988	+	140.959i	0.954479	+	0.800903i
$177$	−40.0568	−	86.4931i	−0.226309	−	0.488662i
$178$	20.2047	−	3.56263i	0.113509	−	0.0200148i
$179$	−174.875			−0.976953			−0.488477	−	0.872577i	$-0.662447\pi$
$179$	−174.875			−0.976953			−0.488477	+	0.872577i	$0.662447\pi$
$180$	159.835	+	135.551i	0.887970	+	0.753063i
$181$	115.098	−	66.4516i	0.635898	−	0.367136i	−0.147134	−	0.989117i	$-0.547005\pi$
$181$	115.098	−	66.4516i	0.635898	−	0.367136i	0.783033	+	0.621980i	$0.213672\pi$
$182$	56.1265	+	52.0811i	0.308387	+	0.286160i
$183$	−46.2122	−	46.4550i	−0.252526	−	0.253853i
$184$	−3.21927	+	18.2574i	−0.0174960	+	0.0992250i
$185$	−98.4442	−	270.473i	−0.532131	−	1.46202i
$186$	−36.3222	−	428.085i	−0.195281	−	2.30153i
$187$	146.297	−	25.7962i	0.782340	−	0.137948i
$188$			37.7951i			0.201038i
$189$	−188.918	+	5.57559i	−0.999565	+	0.0295005i
$190$	174.870			0.920370
$191$	20.8797	+	118.415i	0.109318	+	0.619973i	0.989407	+	0.145165i	$0.0463713\pi$
$191$	20.8797	+	118.415i	0.109318	+	0.619973i	−0.880090	+	0.474808i	$0.842518\pi$
$192$	−121.938	−	175.121i	−0.635094	−	0.912087i
$193$	285.394	−	103.875i	1.47873	−	0.538213i	0.528272	−	0.849075i	$-0.322840\pi$
$193$	285.394	−	103.875i	1.47873	−	0.538213i	0.950455	+	0.310862i	$0.100618\pi$
$194$	−485.796	−	85.6589i	−2.50410	−	0.441541i
$195$	16.1389	+	60.8689i	0.0827635	+	0.312148i
$196$	−206.230	−	20.6498i	−1.05219	−	0.105356i
$197$	−165.865	−	287.286i	−0.841954	−	1.45831i	−0.888241	−	0.459379i	$-0.848072\pi$
$197$	−165.865	−	287.286i	−0.841954	−	1.45831i	0.0462867	−	0.998928i	$-0.485261\pi$
$198$	325.291	+	190.087i	1.64288	+	0.960037i
$199$			252.670i			1.26970i	0.772636	+	0.634850i	$0.218938\pi$
$199$			252.670i			1.26970i	−0.772636	+	0.634850i	$0.781062\pi$
$200$	0.607597	+	3.44585i	0.00303798	+	0.0172293i
$201$	208.630	+	146.901i	1.03796	+	0.730850i
$202$	−86.4852	+	103.069i	−0.428144	+	0.510243i
$203$	170.037	−	87.1659i	0.837620	−	0.429388i
$204$	−128.660	−	11.5962i	−0.630688	−	0.0568441i
$205$	−105.055	+	88.1514i	−0.512462	+	0.430007i
$206$		−	59.9982i		−	0.291254i
$207$	1.32662	−	253.077i	0.00640881	−	1.22259i
$208$		−	57.2997i		−	0.275479i
$209$	159.120	−	28.0572i	0.761340	−	0.134245i
$210$	−261.316	−	204.230i	−1.24436	−	0.972522i
$211$	−265.584	+	96.6646i	−1.25869	+	0.458126i	−0.883330	−	0.468752i	$-0.844704\pi$
$211$	−265.584	+	96.6646i	−1.25869	+	0.458126i	−0.375362	+	0.926878i	$0.622482\pi$
$212$	−107.309	−	90.0426i	−0.506173	−	0.424729i
$213$	−205.842	−	295.618i	−0.966392	−	1.38788i
$214$	24.0762	+	8.76304i	0.112506	+	0.0409488i
$215$	−313.754	−	181.146i	−1.45932	−	0.842540i
$216$	−12.4876	−	12.6855i	−0.0578129	−	0.0587293i
$217$	43.4391	+	346.727i	0.200180	+	1.59782i
$218$	−58.0593	+	48.7176i	−0.266327	+	0.223475i
$219$	255.789	−	178.108i	1.16799	−	0.813280i
$220$	116.218	+	319.306i	0.528263	+	1.45139i
$221$	−29.7349	−	24.9505i	−0.134547	−	0.112898i
$222$	115.321	+	434.939i	0.519462	+	1.95919i
$223$	−100.999	+	17.8088i	−0.452909	+	0.0798601i	−0.395450	−	0.918488i	$-0.629411\pi$
$223$	−100.999	+	17.8088i	−0.452909	+	0.0798601i	−0.0574597	+	0.998348i	$0.518300\pi$
$224$	193.355	+	255.281i	0.863191	+	1.13965i
$225$	−16.1013	−	44.9701i	−0.0715614	−	0.199867i
$226$	−1.56305	−	2.70729i	−0.00691616	−	0.0119791i
$227$	−358.767	+	63.2604i	−1.58047	+	0.278680i	−0.893861	−	0.448344i	$-0.852014\pi$
$227$	−358.767	+	63.2604i	−1.58047	+	0.278680i	−0.686612	+	0.727024i	$0.740903\pi$
$228$	−139.937	−	12.6126i	−0.613759	−	0.0553183i
$229$	23.6170	+	64.8872i	0.103131	+	0.283350i	0.980517	−	0.196435i	$-0.0629366\pi$
$229$	23.6170	+	64.8872i	0.103131	+	0.283350i	−0.877386	+	0.479786i	$0.840714\pi$
$230$	285.464	−	340.203i	1.24115	−	1.47914i
$231$	−270.547	−	143.908i	−1.17120	−	0.622979i
$232$	16.9109	+	6.15508i	0.0728920	+	0.0265305i
$233$	153.248	+	265.433i	0.657717	+	1.13920i	0.981205	+	0.192966i	$0.0618108\pi$
$233$	153.248	+	265.433i	0.657717	+	1.13920i	−0.323489	+	0.946232i	$0.604856\pi$
$234$	−16.5862	−	97.0370i	−0.0708814	−	0.414688i
$235$	24.5956	−	42.6008i	0.104662	−	0.181280i
$236$	−45.9651	+	126.288i	−0.194768	+	0.535119i
$237$	340.354	+	92.1545i	1.43609	+	0.388837i
$238$	204.179	+	10.1968i	0.857896	+	0.0428435i
$239$	6.72337	−	38.1302i	0.0281313	−	0.159540i	−0.967506	−	0.252848i	$-0.918633\pi$
$239$	6.72337	−	38.1302i	0.0281313	−	0.159540i	0.995637	+	0.0933074i	$0.0297439\pi$
$240$	20.9836	+	247.307i	0.0874315	+	1.03045i
$241$	−98.5012	+	270.630i	−0.408719	+	1.12295i	0.549146	+	0.835726i	$0.314953\pi$
$241$	−98.5012	+	270.630i	−0.408719	+	1.12295i	−0.957865	+	0.287219i	$0.907269\pi$
$242$	131.874	+	228.412i	0.544932	+	0.943850i
$243$	197.210	+	141.976i	0.811565	+	0.584262i
$244$			92.3874i			0.378637i
$245$	219.014	+	157.482i	0.893936	+	0.642784i
$246$	175.940	−	122.508i	0.715202	−	0.498001i
$247$	−32.3411	−	27.1374i	−0.130936	−	0.109868i
$248$	−21.1549	+	25.2114i	−0.0853019	+	0.101659i
$249$	61.4755	−	16.2997i	0.246890	−	0.0654608i
$250$	−106.372	+	292.254i	−0.425486	+	1.16901i
$251$	−398.331	+	229.977i	−1.58698	+	0.916241i	−0.593174	+	0.805074i	$0.702126\pi$
$251$	−398.331	+	229.977i	−1.58698	+	0.916241i	−0.993802	+	0.111167i	$0.964541\pi$
$252$	194.384	+	182.279i	0.771364	+	0.723329i
$253$	205.169	−	355.363i	0.810945	−	1.40460i
$254$	228.066	−	191.370i	0.897898	−	0.753426i
$255$	137.474	+	96.7980i	0.539112	+	0.379600i
$256$	38.9146	−	220.695i	0.152010	−	0.862092i
$257$	−77.3954	−	212.642i	−0.301149	−	0.827401i	−0.994301	−	0.106609i	$-0.966001\pi$
$257$	−77.3954	−	212.642i	−0.301149	−	0.827401i	0.693152	−	0.720792i	$-0.256222\pi$
$258$	463.091	+	326.072i	1.79493	+	1.26385i
$259$	−107.865	−	349.729i	−0.416466	−	1.35030i
$260$	44.3934	−	76.8916i	0.170744	−	0.295737i
$261$	−241.711	−	43.9278i	−0.926096	−	0.168306i
$262$	−33.9700	−	19.6126i	−0.129657	−	0.0748572i
$263$	359.543	−	301.693i	1.36708	−	1.14712i	0.393361	−	0.919384i	$-0.371312\pi$
$263$	359.543	−	301.693i	1.36708	−	1.14712i	0.973723	−	0.227736i	$-0.0731322\pi$
$264$	−7.39682	−	27.8976i	−0.0280182	−	0.105673i
$265$	62.3569	+	171.324i	0.235309	+	0.646507i
$266$	222.075	+	11.0905i	0.834868	+	0.0416935i
$267$	19.4209	+	9.11817i	0.0727375	+	0.0341504i
$268$	−62.4716	−	354.294i	−0.233103	−	1.32199i
$269$	12.2504	−	7.07276i	0.0455404	−	0.0262928i	−0.477057	−	0.878872i	$-0.658296\pi$
$269$	12.2504	−	7.07276i	0.0455404	−	0.0262928i	0.522597	+	0.852580i	$0.324963\pi$
$270$	107.122	+	412.740i	0.396749	+	1.52867i
$271$	121.550	+	70.1770i	0.448524	+	0.258956i	0.707207	−	0.707007i	$-0.249955\pi$
$271$	121.550	+	70.1770i	0.448524	+	0.258956i	−0.258682	+	0.965962i	$0.583288\pi$
$272$	−98.3390	−	117.196i	−0.361541	−	0.430867i
$273$	16.6351	+	78.3234i	0.0609343	+	0.286899i
$274$	−112.107	+	635.789i	−0.409149	+	2.32040i
$275$	13.4484	−	76.2695i	0.0489032	−	0.277344i
$276$	−252.976	+	251.653i	−0.916578	+	0.911786i
$277$	−190.921	+	160.202i	−0.689246	+	0.578346i	−0.918692	−	0.394976i	$-0.870753\pi$
$277$	−190.921	+	160.202i	−0.689246	+	0.578346i	0.229446	+	0.973321i	$0.426309\pi$
$278$			556.631i			2.00227i
$279$	226.675	−	387.902i	0.812454	−	1.39033i
$280$	3.15831	+	25.2093i	0.0112797	+	0.0900334i
$281$	−136.660	−	49.7401i	−0.486334	−	0.177011i	0.0872033	−	0.996191i	$-0.472207\pi$
$281$	−136.660	−	49.7401i	−0.486334	−	0.177011i	−0.573537	+	0.819179i	$0.694429\pi$
$282$	−44.2734	+	62.8775i	−0.156998	+	0.222970i
$283$	−11.1361	−	1.96360i	−0.0393502	−	0.00693851i	0.153938	−	0.988080i	$-0.450804\pi$
$283$	−11.1361	−	1.96360i	−0.0393502	−	0.00693851i	−0.193289	+	0.981142i	$0.561915\pi$
$284$	−88.1946	+	500.177i	−0.310544	+	1.76118i
$285$	149.523	+	105.282i	0.524642	+	0.369411i
$286$	54.5916	−	149.989i	0.190880	−	0.524438i
$287$	−139.004	+	105.284i	−0.484335	+	0.366845i
$288$	2.15830	−	411.733i	0.00749409	−	1.42963i
$289$	185.362			0.641391
$290$	−277.106	−	330.242i	−0.955539	−	1.13877i
$291$	−363.808	−	365.720i	−1.25020	−	1.25677i
$292$	−432.788	−	76.3121i	−1.48215	−	0.261343i
$293$	−321.747	−	56.7327i	−1.09811	−	0.193627i	−0.404901	−	0.914360i	$-0.632694\pi$
$293$	−321.747	−	56.7327i	−1.09811	−	0.193627i	−0.693212	+	0.720733i	$0.743805\pi$
$294$	−318.903	−	275.933i	−1.08470	−	0.938546i
$295$	133.993	−	112.434i	0.454215	−	0.381131i
$296$	17.2348	−	29.8516i	0.0582257	−	0.100850i
$297$	163.696	+	358.378i	0.551166	+	1.20666i
$298$	71.9756	+	124.665i	0.241529	+	0.418340i
$299$	−105.589	+	18.6183i	−0.353142	+	0.0622684i
$300$	−28.6218	+	60.9620i	−0.0954060	+	0.203207i
$301$	−386.961	−	249.943i	−1.28558	−	0.830377i
$302$	−69.8820	+	25.4350i	−0.231397	+	0.0842218i
$303$	−136.003	+	36.0600i	−0.448854	+	0.119010i
$304$	−106.958	−	127.468i	−0.351836	−	0.419302i
$305$	60.1222	−	104.135i	0.197122	−	0.341425i
$306$	−200.461	−	170.006i	−0.655102	−	0.555574i
$307$	−9.63477	−	5.56264i	−0.0313836	−	0.0181193i	0.484226	−	0.874943i	$-0.339101\pi$
$307$	−9.63477	−	5.56264i	−0.0313836	−	0.0181193i	−0.515610	+	0.856824i	$0.672435\pi$
$308$	127.339	+	412.870i	0.413438	+	1.34049i
$309$	36.1224	−	51.3015i	0.116901	−	0.166024i
$310$	740.842	−	269.644i	2.38981	−	0.869821i
$311$	−106.736	−	18.8204i	−0.343203	−	0.0605159i	−0.000609675	−	1.00000i	$-0.500194\pi$
$311$	−106.736	−	18.8204i	−0.343203	−	0.0605159i	−0.342593	+	0.939484i	$0.611305\pi$
$312$	−4.34169	+	6.16611i	−0.0139157	+	0.0197632i
$313$	−242.985	−	289.579i	−0.776311	−	0.925172i	0.222449	−	0.974944i	$-0.428595\pi$
$313$	−242.985	−	289.579i	−0.776311	−	0.925172i	−0.998761	+	0.0497723i	$0.984150\pi$
$314$	−158.855	−	91.7148i	−0.505907	−	0.292085i
$315$	−100.480	−	331.954i	−0.318984	−	1.05382i
$316$	−248.579	−	430.551i	−0.786642	−	1.36250i
$317$	−181.980	−	66.2354i	−0.574071	−	0.208945i	0.0386383	−	0.999253i	$-0.487698\pi$
$317$	−181.980	−	66.2354i	−0.574071	−	0.208945i	−0.612709	+	0.790309i	$0.709920\pi$
$318$	−73.0468	−	275.501i	−0.229707	−	0.866355i
$319$	−305.134	−	256.038i	−0.956532	−	0.802626i
$320$	251.709	−	299.975i	0.786589	−	0.937420i
$321$	15.3105	+	21.9881i	0.0476964	+	0.0684989i
$322$	384.099	−	413.933i	1.19285	−	1.28551i
$323$	−112.721			−0.348983
$324$	−55.9539	−	338.015i	−0.172697	−	1.04326i
$325$	−17.5250	+	10.1180i	−0.0539230	+	0.0311324i
$326$	408.925	+	148.837i	1.25437	+	0.456554i
$327$	−78.9745	+	6.70084i	−0.241512	+	0.0204919i
$328$	−16.1738	−	2.85187i	−0.0493103	−	0.00869473i
$329$	33.9368	−	52.5407i	0.103151	−	0.159698i
$330$	−180.692	+	667.349i	−0.547551	+	2.02227i
$331$	−260.747	−	94.9040i	−0.787754	−	0.286719i	−0.0833518	−	0.996520i	$-0.526563\pi$
$331$	−260.747	−	94.9040i	−0.787754	−	0.286719i	−0.704402	+	0.709801i	$0.748785\pi$
$332$	−77.6579	−	44.8358i	−0.233909	−	0.135048i
$333$	−163.254	+	441.324i	−0.490252	+	1.32530i
$334$	−372.326	+	214.963i	−1.11475	+	0.643601i
$335$	−160.146	+	439.998i	−0.478048	+	1.31343i
$336$	10.9634	+	315.396i	0.0326291	+	0.938679i
$337$	−259.493	−	217.741i	−0.770010	−	0.646115i	0.170702	−	0.985323i	$-0.445397\pi$
$337$	−259.493	−	217.741i	−0.770010	−	0.646115i	−0.940712	+	0.339208i	$0.889841\pi$
$338$	416.392	−	151.554i	1.23193	−	0.448385i
$339$	0.293457	−	3.25591i	0.000865653	−	0.00960447i
$340$	−41.1647	−	233.456i	−0.121073	−	0.686636i
$341$	630.853	−	364.223i	1.85001	−	1.06810i
$342$	−218.031	−	184.906i	−0.637518	−	0.540661i
$343$	268.148	+	213.883i	0.781771	+	0.623565i
$344$	−7.53403	−	42.7276i	−0.0219012	−	0.124208i
$345$	448.908	−	119.024i	1.30118	−	0.344998i
$346$	581.962	−	693.555i	1.68197	−	2.00449i
$347$	−400.153	+	145.644i	−1.15318	+	0.419723i	−0.846656	−	0.532140i	$-0.821388\pi$
$347$	−400.153	+	145.644i	−1.15318	+	0.419723i	−0.306523	+	0.951863i	$0.599166\pi$
$348$	197.931	+	284.258i	0.568767	+	0.816832i
$349$	−96.2873	−	114.751i	−0.275895	−	0.328799i	0.610248	−	0.792210i	$-0.291070\pi$
$349$	−96.2873	−	114.751i	−0.275895	−	0.328799i	−0.886143	+	0.463412i	$0.846625\pi$
$350$	41.4017	−	98.2075i	0.118290	−	0.280593i
$351$	44.2399	−	92.9574i	0.126040	−	0.264836i
$352$	333.791	−	578.144i	0.948271	−	1.64245i
$353$	18.6465	−	51.2307i	0.0528228	−	0.145130i	−0.910475	−	0.413564i	$-0.864284\pi$
$353$	18.6465	−	51.2307i	0.0528228	−	0.145130i	0.963298	+	0.268434i	$0.0865062\pi$
$354$	−224.404	+	156.255i	−0.633911	+	0.441397i
$355$	424.905	−	506.382i	1.19691	−	1.42643i
$356$	−10.3461	−	28.4258i	−0.0290622	−	0.0798477i
$357$	168.444	+	131.647i	0.471833	+	0.368758i
$358$	87.1148	+	494.053i	0.243337	+	1.38004i
$359$	−663.602			−1.84847			−0.924236	−	0.381821i	$-0.875297\pi$
$359$	−663.602			−1.84847			−0.924236	+	0.381821i	$0.875297\pi$
$360$	16.4808	−	28.2031i	0.0457799	−	0.0783418i
$361$	238.399			0.660384
$362$	−245.075	−	292.068i	−0.677002	−	0.806819i
$363$	−24.7587	+	274.699i	−0.0682058	+	0.756747i
$364$	61.2535	−	94.8323i	0.168279	−	0.260528i
$365$	438.157	+	367.657i	1.20043	+	1.00728i
$366$	−108.223	+	153.700i	−0.295692	+	0.419944i
$367$	302.275	−	53.2992i	0.823637	−	0.145229i	0.254082	−	0.967183i	$-0.418227\pi$
$367$	302.275	−	53.2992i	0.823637	−	0.145229i	0.569555	+	0.821953i	$0.307116\pi$
$368$	−422.586			−1.14833
$369$	224.194	+	1.17522i	0.607573	+	0.00318489i
$370$	−715.096	+	412.861i	−1.93269	+	1.11584i
$371$	68.3240	+	221.526i	0.184162	+	0.597106i
$372$	−612.295	+	162.345i	−1.64595	+	0.436412i
$373$	−9.00358	+	51.0618i	−0.0241383	+	0.136895i	−0.994495	−	0.104781i	$-0.966586\pi$
$373$	−9.00358	+	51.0618i	−0.0241383	+	0.136895i	0.970357	+	0.241676i	$0.0776970\pi$
$374$	−145.758	−	400.467i	−0.389727	−	1.07077i
$375$	−266.907	+	185.849i	−0.711751	+	0.495599i
$376$	5.80146	−	1.02295i	0.0154294	−	0.00272062i
$377$			104.079i			0.276072i
$378$	109.863	+	530.950i	0.290642	+	1.40463i
$379$	192.980			0.509181			0.254591	−	0.967049i	$-0.418059\pi$
$379$	192.980			0.509181			0.254591	+	0.967049i	$0.418059\pi$
$380$	−44.7726	−	253.918i	−0.117823	−	0.668206i
$381$	310.224	−	26.3219i	0.814236	−	0.0690865i
$382$	324.142	−	117.978i	0.848539	−	0.308843i
$383$	49.4400	+	8.71761i	0.129086	+	0.0227614i	0.237818	−	0.971310i	$-0.423568\pi$
$383$	49.4400	+	8.71761i	0.129086	+	0.0227614i	−0.108732	+	0.994071i	$0.534679\pi$
$384$	−44.7967	+	44.5625i	−0.116658	+	0.116048i
$385$	125.150	−	548.235i	0.325064	−	1.42399i
$386$	−435.637	−	754.545i	−1.12859	−	1.95478i
$387$	199.652	+	557.616i	0.515896	+	1.44087i
$388$			727.325i			1.87455i
$389$	24.8082	+	140.694i	0.0637743	+	0.361682i	0.999949	+	0.0101456i	$0.00322951\pi$
$389$	24.8082	+	140.694i	0.0637743	+	0.361682i	−0.936174	+	0.351536i	$0.885659\pi$
$390$	163.926	−	75.9175i	0.420323	−	0.194660i
$391$	−184.010	+	219.295i	−0.470615	+	0.560857i
$392$	2.41207	+	32.2147i	0.00615323	+	0.0821803i
$393$	−17.2381	−	37.2217i	−0.0438629	−	0.0947117i
$394$	−729.010	+	611.712i	−1.85028	+	1.55257i
$395$			647.063i			1.63813i
$396$	192.728	−	521.003i	0.486688	−	1.31566i
$397$		−	300.259i		−	0.756319i	−0.925740	−	0.378160i	$-0.876557\pi$
$397$		−	300.259i		−	0.756319i	0.925740	−	0.378160i	$-0.123443\pi$
$398$	713.839	−	125.869i	1.79357	−	0.316254i
$399$	183.208	+	143.185i	0.459168	+	0.358860i
$400$	−74.9477	+	27.2787i	−0.187369	+	0.0681968i
$401$	142.337	+	119.435i	0.354954	+	0.297842i	0.802776	−	0.596281i	$-0.203356\pi$
$401$	142.337	+	119.435i	0.354954	+	0.297842i	−0.447822	+	0.894123i	$0.647800\pi$
$402$	311.092	−	662.598i	0.773860	−	1.64825i
$403$	−178.859	−	65.0992i	−0.443818	−	0.161537i
$404$	171.803	+	99.1906i	0.425255	+	0.245521i
$405$	−156.899	+	417.407i	−0.387404	+	1.03064i
$406$	−330.964	−	436.963i	−0.815183	−	1.07626i
$407$	−584.447	+	490.409i	−1.43599	+	1.20494i
$408$	1.70231	+	20.0629i	0.00417232	+	0.0491739i
$409$	−58.0780	−	159.568i	−0.142000	−	0.390142i	0.848222	−	0.529640i	$-0.177673\pi$
$409$	−58.0780	−	159.568i	−0.142000	−	0.390142i	−0.990222	+	0.139499i	$0.955451\pi$
$410$	301.377	+	252.886i	0.735067	+	0.616794i
$411$	−478.639	+	476.136i	−1.16457	+	1.15848i
$412$	−87.1197	+	15.3615i	−0.211455	+	0.0372853i
$413$	177.294	−	134.286i	0.429284	−	0.325148i
$414$	−715.649	+	122.324i	−1.72862	+	0.295468i
$415$	58.3549	+	101.074i	0.140614	+	0.243551i
$416$	−171.784	+	30.2902i	−0.412943	+	0.0728130i
$417$	−335.124	+	475.947i	−0.803655	+	1.14136i
$418$	−158.533	−	435.566i	−0.379266	−	1.04202i
$419$	149.404	−	178.052i	0.356572	−	0.424946i	−0.557703	−	0.830041i	$-0.688317\pi$
$419$	149.404	−	178.052i	0.356572	−	0.424946i	0.914275	+	0.405095i	$0.132762\pi$
$420$	−229.643	+	431.730i	−0.546770	+	1.02793i
$421$	77.0187	+	28.0325i	0.182942	+	0.0665855i	0.431867	−	0.901937i	$-0.357855\pi$
$421$	77.0187	+	28.0325i	0.182942	+	0.0665855i	−0.248925	+	0.968523i	$0.580077\pi$
$422$	405.397	+	702.169i	0.960657	+	1.66391i
$423$	−75.7119	+	27.1083i	−0.178988	+	0.0640857i
$424$	−10.9169	+	18.9087i	−0.0257475	+	0.0445960i
$425$	−18.4793	+	50.7713i	−0.0434806	+	0.119462i
$426$	−732.634	+	728.804i	−1.71980	+	1.71081i
$427$	82.9560	−	128.432i	0.194276	−	0.300777i
$428$	6.55993	−	37.2032i	0.0153269	−	0.0869235i
$429$	136.981	−	95.3809i	0.319303	−	0.222333i
$430$	−355.472	+	976.651i	−0.826679	+	2.27128i
$431$	−26.1487	−	45.2909i	−0.0606699	−	0.105083i	0.834095	−	0.551621i	$-0.185990\pi$
$431$	−26.1487	−	45.2909i	−0.0606699	−	0.105083i	−0.894765	+	0.446537i	$0.852657\pi$
$432$	235.337	−	330.534i	0.544762	−	0.765125i
$433$		−	689.520i		−	1.59242i	−0.605017	−	0.796212i	$-0.706834\pi$
$433$		−	689.520i		−	1.59242i	0.605017	−	0.796212i	$-0.293166\pi$
$434$	957.927	−	295.447i	2.20720	−	0.680754i
$435$	−38.1145	−	449.208i	−0.0876195	−	1.03266i
$436$	85.6049	+	71.8310i	0.196341	+	0.164750i
$437$	−200.138	+	238.516i	−0.457983	+	0.545803i
$438$	−630.612	−	633.926i	−1.43975	−	1.44732i
$439$	−257.324	+	706.993i	−0.586160	+	1.61046i	0.191300	+	0.981532i	$0.438730\pi$
$439$	−257.324	+	706.993i	−0.586160	+	1.61046i	−0.777461	+	0.628931i	$0.783493\pi$
$440$	45.8672	−	26.4814i	0.104244	−	0.0601851i
$441$	−106.551	−	427.935i	−0.241612	−	0.970373i
$442$	−55.6772	+	96.4358i	−0.125967	+	0.218180i
$443$	536.544	−	450.214i	1.21116	−	1.01628i	0.211920	−	0.977287i	$-0.432028\pi$
$443$	536.544	−	450.214i	1.21116	−	1.01628i	0.999239	−	0.0389966i	$-0.0124161\pi$
$444$	602.022	−	278.809i	1.35591	−	0.627948i
$445$	−6.83674	+	38.7731i	−0.0153635	+	0.0871306i
$446$	100.626	+	276.468i	0.225619	+	0.619884i
$447$	−13.5131	+	149.929i	−0.0302307	+	0.335411i
$448$	338.680	−	364.986i	0.755981	−	0.814702i
$449$	36.7734	−	63.6935i	0.0819007	−	0.141856i	−0.822166	−	0.569248i	$-0.807234\pi$
$449$	36.7734	−	63.6935i	0.0819007	−	0.141856i	0.904066	+	0.427392i	$0.140568\pi$
$450$	−119.028	+	67.8913i	−0.264506	+	0.150869i
$451$	314.807	+	181.754i	0.698021	+	0.403002i
$452$	−3.53089	+	2.96277i	−0.00781170	+	0.00655479i
$453$	−75.0660	−	20.3249i	−0.165709	−	0.0448673i
$454$	357.444	+	982.070i	0.787322	+	2.16315i
$455$	−130.755	+	67.0290i	−0.287374	+	0.147317i
$456$	1.85151	+	21.8214i	0.00406032	+	0.0478540i
$457$	−8.31537	−	47.1588i	−0.0181956	−	0.103192i	0.974357	−	0.225006i	$-0.0722401\pi$
$457$	−8.31537	−	47.1588i	−0.0181956	−	0.103192i	−0.992553	+	0.121814i	$0.961129\pi$
$458$	171.553	−	99.0463i	0.374570	−	0.216258i
$459$	−69.0511	−	266.053i	−0.150438	−	0.579635i
$460$	−567.076	−	327.401i	−1.23277	−	0.711742i
$461$	333.871	+	397.892i	0.724233	+	0.863107i	0.995035	−	0.0995279i	$-0.0317333\pi$
$461$	333.871	+	397.892i	0.724233	+	0.863107i	−0.270802	+	0.962635i	$0.587289\pi$
$462$	−271.792	+	836.034i	−0.588294	+	1.80960i
$463$	−20.2846	+	115.040i	−0.0438112	+	0.248466i	−0.998846	−	0.0480282i	$-0.984706\pi$
$463$	−20.2846	+	115.040i	−0.0438112	+	0.248466i	0.955035	+	0.296494i	$0.0958174\pi$
$464$	−71.2327	+	403.981i	−0.153519	+	0.870649i
$465$	795.799	+	215.471i	1.71139	+	0.463378i
$466$	673.556	−	565.180i	1.44540	−	1.21283i
$467$		−	845.102i		−	1.80964i	−0.425794	−	0.904820i	$-0.640005\pi$
$467$		−	845.102i		−	1.80964i	0.425794	−	0.904820i	$-0.359995\pi$
$468$	−136.655	+	48.9285i	−0.291997	+	0.104548i
$469$	−231.281	+	548.614i	−0.493137	+	1.16975i
$470$	−132.608	−	48.2652i	−0.282144	−	0.102692i
$471$	−80.6111	−	174.061i	−0.171149	−	0.369555i
$472$	20.6290	+	3.63745i	0.0437056	+	0.00770647i
$473$	−166.756	+	945.720i	−0.352550	+	1.99941i
$474$	90.8036	−	1007.47i	0.191569	−	2.12547i
$475$	−20.0989	+	55.2213i	−0.0423135	+	0.116255i
$476$	−37.4706	−	299.086i	−0.0787198	−	0.628333i
$477$	103.409	−	279.545i	0.216790	−	0.586049i
$478$	−111.074			−0.232372
$479$	242.221	+	288.668i	0.505681	+	0.602647i	0.957133	−	0.289649i	$-0.0935384\pi$
$479$	242.221	+	288.668i	0.505681	+	0.602647i	−0.451453	+	0.892295i	$0.649094\pi$
$480$	730.333	−	193.642i	1.52153	−	0.403421i
$481$	196.322	+	34.6169i	0.408154	+	0.0719686i
$482$	813.648	+	143.468i	1.68807	+	0.297652i
$483$	577.636	−	122.684i	1.19593	−	0.254004i
$484$	297.898	−	249.966i	0.615492	−	0.516459i
$485$	473.315	−	819.806i	0.975908	−	1.69032i
$486$	302.865	−	627.881i	0.623180	−	1.29194i
$487$	166.740	+	288.803i	0.342382	+	0.593024i	0.984875	−	0.173269i	$-0.0554328\pi$
$487$	166.740	+	288.803i	0.342382	+	0.593024i	−0.642492	+	0.766292i	$0.722100\pi$
$488$	14.1813	−	2.50054i	0.0290599	−	0.00512405i
$489$	260.043	+	373.459i	0.531785	+	0.763721i
$490$	335.812	−	697.206i	0.685331	−	1.42287i
$491$	−202.532	+	73.7156i	−0.412489	+	0.150134i	−0.539925	−	0.841713i	$-0.681547\pi$
$491$	−202.532	+	73.7156i	−0.412489	+	0.150134i	0.127436	+	0.991847i	$0.459325\pi$
$492$	−222.933	−	224.105i	−0.453116	−	0.455497i
$493$	178.623	+	212.874i	0.362318	+	0.431794i
$494$	−60.5572	+	104.888i	−0.122585	+	0.212324i
$495$	−556.284	+	461.830i	−1.12381	+	0.932990i
$496$	−649.682	−	375.094i	−1.30984	−	0.756238i
$497$	571.719	−	616.127i	1.15034	−	1.23969i
$498$	−76.6741	−	165.560i	−0.153964	−	0.332449i
$499$	95.5631	−	34.7821i	0.191509	−	0.0697036i	−0.244485	−	0.969653i	$-0.578619\pi$
$499$	95.5631	−	34.7821i	0.191509	−	0.0697036i	0.435994	+	0.899949i	$0.356397\pi$
$500$	451.598	+	79.6289i	0.903195	+	0.159258i
$501$	−447.778	−	40.3583i	−0.893768	−	0.0805555i
$502$	848.156	+	1010.79i	1.68955	+	2.01353i
$503$	−265.086	−	153.047i	−0.527009	−	0.304269i	0.212789	−	0.977098i	$-0.431745\pi$
$503$	−265.086	−	153.047i	−0.527009	−	0.304269i	−0.739798	+	0.672829i	$0.765079\pi$
$504$	22.7183	−	34.7710i	0.0450759	−	0.0689900i
$505$	−129.099	−	223.606i	−0.255642	−	0.442784i
$506$	−1106.17	−	402.614i	−2.18611	−	0.795679i
$507$	447.280	+	121.106i	0.882210	+	0.238867i
$508$	−336.269	−	282.163i	−0.661947	−	0.555439i
$509$	260.548	−	310.509i	0.511882	−	0.610037i	−0.446760	−	0.894654i	$-0.647422\pi$
$509$	260.548	−	310.509i	0.511882	−	0.610037i	0.958641	+	0.284617i	$0.0918665\pi$
$510$	204.989	−	436.609i	0.401939	−	0.856095i
$511$	533.116	+	494.691i	1.04328	+	0.968085i
$512$	−727.139			−1.42019
$513$	−75.1032	−	289.371i	−0.146400	−	0.564077i
$514$	−562.198	+	324.585i	−1.09377	+	0.631488i
$515$	108.194	+	39.3794i	0.210085	+	0.0764648i
$516$	354.902	−	755.911i	0.687795	−	1.46494i
$517$	−128.408	−	22.6418i	−0.248371	−	0.0437945i
$518$	−934.314	+	478.957i	−1.80369	+	0.924627i
$519$	915.167	−	242.649i	1.76333	−	0.467532i
$520$	−13.0042	−	4.73315i	−0.0250081	−	0.00910221i
$521$	678.887	+	391.956i	1.30305	+	0.752314i	0.980925	−	0.194384i	$-0.0622709\pi$
$521$	678.887	+	391.956i	1.30305	+	0.752314i	0.322121	+	0.946699i	$0.395604\pi$
$522$	−3.69435	+	704.761i	−0.00707729	+	1.35012i
$523$	−392.142	+	226.404i	−0.749794	+	0.432894i	−0.825620	−	0.564227i	$-0.809174\pi$
$523$	−392.142	+	226.404i	−0.749794	+	0.432894i	0.0758252	+	0.997121i	$0.475841\pi$
$524$	−19.7808	+	54.3472i	−0.0377495	+	0.103716i
$525$	94.5272	−	59.0461i	0.180052	−	0.112469i
$526$	−1031.44	−	865.485i	−1.96092	−	1.64541i
$527$	−477.547	+	173.813i	−0.906162	+	0.329816i
$528$	596.968	−	276.468i	1.13062	−	0.523614i
$529$	45.4499	+	257.759i	0.0859167	+	0.487258i
$530$	452.959	−	261.516i	0.854639	−	0.493426i
$531$	−285.951	−	1.49895i	−0.538515	−	0.00282289i
$532$	−40.7548	−	325.301i	−0.0766068	−	0.611467i
$533$	−16.4935	−	93.5390i	−0.0309446	−	0.175495i
$534$	16.0858	−	59.4099i	0.0301233	−	0.111255i
$535$	−31.6045	+	37.6648i	−0.0590739	+	0.0704015i
$536$	−52.6925	+	19.1785i	−0.0983068	+	0.0357808i
$537$	−222.961	+	474.888i	−0.415198	+	0.884335i
$538$	−26.0844	−	31.0862i	−0.0484841	−	0.0577811i
$539$	193.703	−	688.289i	0.359374	−	1.27697i
$540$	571.887	−	261.221i	1.05905	−	0.483742i
$541$	−317.529	+	549.977i	−0.586931	+	1.01659i	0.407701	+	0.913115i	$0.366331\pi$
$541$	−317.529	+	549.977i	−0.586931	+	1.01659i	−0.994632	+	0.103478i	$0.967003\pi$
$542$	137.712	−	378.360i	0.254081	−	0.698082i
$543$	−33.7087	−	397.282i	−0.0620786	−	0.731643i
$544$	−299.368	+	356.773i	−0.550309	+	0.655833i
$545$	−49.7449	−	136.673i	−0.0912750	−	0.250776i
$546$	212.991	−	86.0144i	0.390093	−	0.157535i
$547$	−31.4691	−	178.470i	−0.0575304	−	0.326271i	0.942437	−	0.334385i	$-0.108528\pi$
$547$	−31.4691	−	178.470i	−0.0575304	−	0.326271i	−0.999967	+	0.00811344i	$0.997417\pi$
$548$	951.892			1.73703
$549$	−185.072	+	66.2643i	−0.337108	+	0.120700i
$550$	−222.175			−0.403954
$551$	194.279	+	231.532i	0.352593	+	0.420204i
$552$	45.4751	+	32.0200i	0.0823825	+	0.0580072i
$553$	−41.0375	+	821.732i	−0.0742089	+	1.48595i
$554$	547.708	+	459.581i	0.988642	+	0.829569i
$555$	−860.009	−	77.5129i	−1.54957	−	0.139663i
$556$	808.248	−	142.516i	1.45368	−	0.256324i
$557$	2.34322			0.00420686			0.00210343	−	0.999998i	$-0.499330\pi$
$557$	2.34322			0.00420686			0.00210343	+	0.999998i	$0.499330\pi$
$558$	−1208.81	−	447.162i	−2.16633	−	0.801365i
$559$	217.305	−	125.461i	0.388738	−	0.224438i
$560$	−553.400	+	170.682i	−0.988214	+	0.304789i
$561$	116.474	−	430.174i	0.207618	−	0.766798i
$562$	−72.4470	+	410.867i	−0.128909	+	0.731081i
$563$	55.1203	+	151.442i	0.0979047	+	0.268991i	0.978970	−	0.204003i	$-0.0653954\pi$
$563$	55.1203	+	151.442i	0.0979047	+	0.268991i	−0.881066	+	0.472994i	$0.843173\pi$
$564$	102.636	+	48.1878i	0.181979	+	0.0854394i
$565$	5.90791	−	1.04172i	0.0104565	−	0.00184376i
$566$			32.4397i			0.0573140i
$567$	−225.725	+	520.132i	−0.398104	+	0.917341i
$568$	79.1630			0.139371
$569$	−101.005	−	572.829i	−0.177513	−	1.00673i	−0.935203	−	0.354113i	$-0.884783\pi$
$569$	−101.005	−	572.829i	−0.177513	−	1.00673i	0.757689	−	0.652616i	$-0.226328\pi$
$570$	222.956	−	474.876i	0.391150	−	0.833116i
$571$	−133.548	+	48.6074i	−0.233884	+	0.0851268i	−0.456303	−	0.889824i	$-0.650827\pi$
$571$	−133.548	+	48.6074i	−0.233884	+	0.0851268i	0.222419	+	0.974951i	$0.428605\pi$
$572$	−231.767	−	40.8668i	−0.405187	−	0.0714455i
$573$	348.187	+	94.2753i	0.607657	+	0.164529i
$574$	366.693	+	340.264i	0.638838	+	0.592794i
$575$	74.6207	+	129.247i	0.129775	+	0.224777i
$576$	−631.024	+	107.859i	−1.09553	+	0.187255i
$577$		−	1084.43i		−	1.87943i	−0.341955	−	0.939716i	$-0.611089\pi$
$577$		−	1084.43i		−	1.87943i	0.341955	−	0.939716i	$-0.388911\pi$
$578$	−92.3392	−	523.682i	−0.159756	−	0.906024i
$579$	81.7890	−	907.453i	0.141259	−	1.56728i
$580$	−408.576	+	486.922i	−0.704441	+	0.839520i
$581$	67.6971	+	132.059i	0.116518	+	0.227295i
$582$	−851.992	+	1210.01i	−1.46390	+	2.07905i
$583$	370.203	−	310.637i	0.634996	−	0.532825i
$584$			68.4974i			0.117290i
$585$	185.872	+	33.7797i	0.317729	+	0.0577432i
$586$			937.257i			1.59941i
$587$	452.444	−	79.7782i	0.770774	−	0.135908i	0.225587	−	0.974223i	$-0.427570\pi$
$587$	452.444	−	79.7782i	0.770774	−	0.135908i	0.545187	+	0.838315i	$0.316459\pi$
$588$	−319.014	+	533.707i	−0.542542	+	0.907665i
$589$	−519.403	+	189.047i	−0.881838	+	0.320963i
$590$	−384.395	−	322.546i	−0.651518	−	0.546688i
$591$	−991.626	+	84.1377i	−1.67788	+	0.142365i
$592$	738.329	+	268.730i	1.24718	+	0.453936i
$593$	−528.022	−	304.854i	−0.890426	−	0.514087i	−0.0163439	−	0.999866i	$-0.505203\pi$
$593$	−528.022	−	304.854i	−0.890426	−	0.514087i	−0.874082	+	0.485779i	$0.838536\pi$
$594$	930.937	−	641.000i	1.56723	−	1.07912i
$595$	−152.399	+	361.501i	−0.256133	+	0.607564i
$596$	162.591	−	136.430i	0.272803	−	0.228909i
$597$	686.149	+	322.148i	1.14933	+	0.539612i
$598$	105.200	+	289.034i	0.175920	+	0.483335i
$599$	203.162	+	170.473i	0.339168	+	0.284596i	0.796423	−	0.604740i	$-0.206723\pi$
$599$	203.162	+	170.473i	0.339168	+	0.284596i	−0.457255	+	0.889336i	$0.651167\pi$
$600$	10.1322	+	2.74340i	0.0168870	+	0.00457233i
$601$	935.196	−	164.900i	1.55607	−	0.274376i	0.671576	−	0.740936i	$-0.265618\pi$
$601$	935.196	−	164.900i	1.55607	−	0.274376i	0.884490	+	0.466559i	$0.154507\pi$
$602$	−513.369	+	1217.75i	−0.852772	+	2.02283i
$603$	664.922	−	379.259i	1.10269	−	0.628954i
$604$	54.8247	+	94.9591i	0.0907693	+	0.157217i
$605$	−498.446	+	87.8894i	−0.823877	+	0.145272i
$606$	169.627	+	366.269i	0.279912	+	0.604404i
$607$	182.452	+	501.283i	0.300580	+	0.825838i	0.994399	+	0.105688i	$0.0337045\pi$
$607$	182.452	+	501.283i	0.300580	+	0.825838i	−0.693819	+	0.720149i	$0.744073\pi$
$608$	−325.607	+	388.043i	−0.535538	+	0.638229i
$609$	−19.9139	−	572.885i	−0.0326993	−	0.940698i
$610$	−324.150	−	117.981i	−0.531393	−	0.193411i
$611$	17.0348	+	29.5051i	0.0278802	+	0.0482899i
$612$	−195.530	+	334.604i	−0.319493	+	0.546739i
$613$	254.217	−	440.317i	0.414710	−	0.718298i	−0.580688	−	0.814126i	$-0.697216\pi$
$613$	254.217	−	440.317i	0.414710	−	0.718298i	0.995398	+	0.0958276i	$0.0305498\pi$
$614$	−10.9158	+	29.9910i	−0.0177783	+	0.0488454i
$615$	105.441	+	397.677i	0.171448	+	0.646629i
$616$	59.9281	−	30.7209i	0.0972859	−	0.0498716i
$617$	169.851	−	963.272i	0.275285	−	1.56122i	−0.462771	−	0.886478i	$-0.653145\pi$
$617$	169.851	−	963.272i	0.275285	−	1.56122i	0.738056	−	0.674740i	$-0.235744\pi$
$618$	−162.931	−	76.4963i	−0.263642	−	0.123780i
$619$	275.694	−	757.462i	0.445386	−	1.22369i	−0.490518	−	0.871431i	$-0.663192\pi$
$619$	275.694	−	757.462i	0.445386	−	1.22369i	0.935904	−	0.352256i	$-0.114585\pi$
$620$	−581.214	−	1006.69i	−0.937442	−	1.62370i
$621$	−685.562	−	326.270i	−1.10396	−	0.525394i
$622$			310.924i			0.499878i
$623$	−11.1413	+	48.8060i	−0.0178833	+	0.0783402i
$624$	−155.603	−	73.0558i	−0.249363	−	0.117077i
$625$	−558.841	−	468.923i	−0.894145	−	0.750277i
$626$	−697.068	+	830.734i	−1.11353	+	1.32705i
$627$	126.683	−	467.877i	0.202046	−	0.746216i
$628$	−92.5012	+	254.145i	−0.147295	+	0.404690i
$629$	460.951	−	266.130i	0.732832	−	0.423101i
$630$	−887.776	+	449.239i	−1.40917	+	0.713078i
$631$	292.037	−	505.823i	0.462817	−	0.801622i	−0.536283	−	0.844038i	$-0.680172\pi$
$631$	292.037	−	505.823i	0.462817	−	0.801622i	0.999100	+	0.0424160i	$0.0135055\pi$
$632$	−59.3606	+	49.8095i	−0.0939251	+	0.0788125i
$633$	−76.1117	+	844.462i	−0.120240	+	1.33406i
$634$	−96.4726	+	547.123i	−0.152165	+	0.862971i
$635$	195.406	+	536.872i	0.307725	+	0.845468i
$636$	−381.335	+	176.604i	−0.599583	+	0.277679i
$637$	−170.303	+	76.8302i	−0.267351	+	0.120613i
$638$	−571.349	+	989.605i	−0.895531	+	1.55111i
$639$	−1065.22	+	182.075i	−1.66701	+	0.284938i
$640$	−100.417	−	57.9760i	−0.156902	−	0.0905874i
$641$	−297.452	+	249.592i	−0.464044	+	0.389379i	−0.844616	−	0.535372i	$-0.820171\pi$
$641$	−297.452	+	249.592i	−0.464044	+	0.389379i	0.380573	+	0.924751i	$0.375727\pi$
$642$	54.4935	−	54.2086i	0.0848808	−	0.0844370i
$643$	−80.7402	−	221.832i	−0.125568	−	0.344995i	0.860940	−	0.508706i	$-0.169876\pi$
$643$	−80.7402	−	221.832i	−0.125568	−	0.344995i	−0.986508	+	0.163711i	$0.947654\pi$
$644$	−699.389	−	451.745i	−1.08601	−	0.701468i
$645$	−891.948	+	621.071i	−1.38286	+	0.962900i
$646$	56.1529	+	318.459i	0.0869239	+	0.492970i
$647$	−669.238	+	386.385i	−1.03437	+	0.597194i	−0.918234	−	0.396039i	$-0.870385\pi$
$647$	−669.238	+	386.385i	−1.03437	+	0.597194i	−0.116137	+	0.993233i	$0.537051\pi$
$648$	−50.3701	+	17.7374i	−0.0777316	+	0.0273726i
$649$	−401.525	−	231.820i	−0.618682	−	0.357196i
$650$	37.3155	+	44.4709i	0.0574084	+	0.0684167i
$651$	996.952	+	324.106i	1.53142	+	0.497858i
$652$	111.418	−	631.881i	0.170886	−	0.969143i
$653$	90.3418	−	512.354i	0.138349	−	0.784615i	−0.834120	−	0.551583i	$-0.814024\pi$
$653$	90.3418	−	512.354i	0.138349	−	0.784615i	0.972469	−	0.233033i	$-0.0748649\pi$
$654$	58.2727	+	219.779i	0.0891020	+	0.336054i
$655$	57.6630	−	48.3850i	0.0880352	−	0.0738703i
$656$		−	374.358i		−	0.570668i
$657$	−157.544	−	921.704i	−0.239793	−	1.40290i
$658$	−165.343	−	69.7041i	−0.251281	−	0.105933i
$659$	−70.9626	−	25.8283i	−0.107682	−	0.0391931i	0.287617	−	0.957745i	$-0.407137\pi$
$659$	−70.9626	−	25.8283i	−0.107682	−	0.0391931i	−0.395299	+	0.918552i	$0.629359\pi$
$660$	1015.28	+	91.5074i	1.53830	+	0.138648i
$661$	−1050.91	−	185.304i	−1.58988	−	0.280339i	−0.692442	−	0.721473i	$-0.743465\pi$
$661$	−1050.91	−	185.304i	−1.58988	−	0.280339i	−0.897441	+	0.441134i	$0.854576\pi$
$662$	−138.229	+	783.933i	−0.208805	+	1.18419i
$663$	−105.667	+	48.9365i	−0.159377	+	0.0738107i
$664$	−4.78032	+	13.1338i	−0.00719928	+	0.0197799i
$665$	−165.756	+	393.185i	−0.249258	+	0.591256i
$666$	1328.15	+	241.374i	1.99422	+	0.362423i
$667$	767.584			1.15080
$668$	407.462	+	485.594i	0.609972	+	0.726937i
$669$	−80.4096	+	296.977i	−0.120194	+	0.443912i
$670$	1322.85	+	233.254i	1.97440	+	0.348141i
$671$	−313.884	−	55.3462i	−0.467785	−	0.0824831i
$672$	939.761	−	199.595i	1.39845	−	0.297017i
$673$	−739.467	+	620.487i	−1.09876	+	0.921971i	−0.997341	−	0.0728721i	$-0.976784\pi$
$673$	−739.467	+	620.487i	−1.09876	+	0.921971i	−0.101422	+	0.994844i	$0.532339\pi$
$674$	−485.889	+	841.585i	−0.720904	+	1.24864i
$675$	−142.649	−	13.6112i	−0.211332	−	0.0201647i
$676$	−326.673	−	565.814i	−0.483244	−	0.837002i
$677$	58.1392	−	10.2515i	0.0858777	−	0.0151426i	−0.130544	−	0.991442i	$-0.541672\pi$
$677$	58.1392	−	10.2515i	0.0858777	−	0.0151426i	0.216422	+	0.976300i	$0.430561\pi$
$678$	−9.34474	+	0.792884i	−0.0137828	+	0.00116945i
$679$	653.076	−	1011.09i	0.961820	−	1.48908i
$680$	−34.7209	+	12.6374i	−0.0510601	+	0.0185844i
$681$	−285.631	+	1054.92i	−0.419429	+	1.54908i
$682$	−1343.26	−	1600.83i	−1.96959	−	2.34726i
$683$	354.806	−	614.542i	0.519482	−	0.899768i	−0.480262	−	0.877125i	$-0.659458\pi$
$683$	354.806	−	614.542i	0.519482	−	0.899768i	0.999744	−	0.0226434i	$-0.00720824\pi$
$684$	−212.667	+	363.931i	−0.310917	+	0.532063i
$685$	−1072.93	−	619.455i	−1.56632	−	0.904314i
$686$	470.679	−	864.113i	0.686121	−	1.25964i
$687$	206.318	+	18.5955i	0.300318	+	0.0270677i
$688$	929.330	−	338.249i	1.35077	−	0.491640i
$689$	−124.355	−	21.9272i	−0.180487	−	0.0318246i
$690$	−559.892	−	1208.96i	−0.811438	−	1.75211i
$691$	749.932	+	893.734i	1.08529	+	1.29339i	0.953262	+	0.302146i	$0.0977031\pi$
$691$	749.932	+	893.734i	1.08529	+	1.29339i	0.132024	+	0.991247i	$0.457852\pi$
$692$	−1156.07	−	667.457i	−1.67062	−	0.964533i
$693$	−735.737	+	551.217i	−1.06167	+	0.795406i
$694$	610.809	+	1057.95i	0.880129	+	1.52443i
$695$	−1003.76	−	365.340i	−1.44426	−	0.525669i
$696$	38.2757	−	38.0756i	0.0549939	−	0.0547063i
$697$	−194.268	−	163.010i	−0.278720	−	0.233874i
$698$	−276.226	+	329.193i	−0.395739	+	0.471623i
$699$	916.196	−	77.7376i	1.31072	−	0.111213i
$700$	−153.201	−	34.9724i	−0.218859	−	0.0499605i
$701$	403.488			0.575589			0.287794	−	0.957692i	$-0.407078\pi$
$701$	403.488			0.575589			0.287794	+	0.957692i	$0.407078\pi$
$702$	−284.660	−	78.6785i	−0.405498	−	0.112078i
$703$	501.352	−	289.456i	0.713161	−	0.411744i
$704$	−975.368	−	355.005i	−1.38547	−	0.504269i
$705$	−84.3276	−	121.107i	−0.119614	−	0.171782i
$706$	−154.025	−	27.1588i	−0.218166	−	0.0384685i
$707$	−149.767	−	292.154i	−0.211834	−	0.413231i
$708$	284.343	+	285.837i	0.401614	+	0.403725i
$709$	249.176	+	90.6926i	0.351447	+	0.127916i	0.511710	−	0.859158i	$-0.329012\pi$
$709$	249.176	+	90.6926i	0.351447	+	0.127916i	−0.160263	+	0.987074i	$0.551234\pi$
$710$	−1642.29	−	948.176i	−2.31308	−	1.33546i
$711$	684.198	−	806.769i	0.962303	−	1.13470i
$712$	−4.08327	+	2.35748i	−0.00573493	+	0.00331106i
$713$	−480.108	+	1319.08i	−0.673363	+	1.85005i
$714$	288.014	−	541.467i	0.403381	−	0.758357i
$715$	234.643	+	196.888i	0.328171	+	0.275368i
$716$	695.079	−	252.988i	0.970780	−	0.353335i
$717$	−94.9738	−	66.8730i	−0.132460	−	0.0932678i
$718$	330.577	+	1874.80i	0.460414	+	2.61114i
$719$	205.582	−	118.693i	0.285927	−	0.165080i	−0.350176	−	0.936684i	$-0.613878\pi$
$719$	205.582	−	118.693i	0.285927	−	0.165080i	0.636104	+	0.771604i	$0.280545\pi$
$720$	698.338	+	258.328i	0.969914	+	0.358789i
$721$	134.902	+	56.8713i	0.187105	+	0.0788783i
$722$	−118.760	−	673.520i	−0.164487	−	0.932853i
$723$	609.333	+	612.536i	0.842785	+	0.847214i
$724$	−361.347	+	430.637i	−0.499098	+	0.594802i
$725$	136.135	−	49.5491i	0.187772	−	0.0683435i
$726$	788.408	−	66.8951i	1.08596	−	0.0921420i
$727$	−809.768	−	965.044i	−1.11385	−	1.32743i	−0.939422	−	0.342763i	$-0.888637\pi$
$727$	−809.768	−	965.044i	−1.11385	−	1.32743i	−0.174426	−	0.984670i	$-0.555807\pi$
$728$	−16.2144	−	6.83556i	−0.0222725	−	0.00938951i
$729$	636.986	−	354.527i	0.873781	−	0.486320i
$730$	820.428	−	1421.02i	1.12387	−	1.94661i
$731$	229.137	−	629.550i	0.313458	−	0.861218i
$732$	250.886	+	117.792i	0.342741	+	0.160918i
$733$	−691.844	+	824.508i	−0.943853	+	1.12484i	0.0481768	+	0.998839i	$0.484659\pi$
$733$	−691.844	+	824.508i	−0.943853	+	1.12484i	−0.992030	+	0.126002i	$0.959786\pi$
$734$	−301.160	−	827.430i	−0.410299	−	1.12729i
$735$	706.895	−	393.967i	0.961761	−	0.536010i
$736$	223.391	+	1266.91i	0.303520	+	1.72135i
$737$	1241.13			1.68403
$738$	−108.364	−	633.975i	−0.146834	−	0.859045i
$739$	560.806			0.758871			0.379436	−	0.925218i	$-0.376118\pi$
$739$	560.806			0.758871			0.379436	+	0.925218i	$0.376118\pi$
$740$	782.578	+	932.640i	1.05754	+	1.26032i
$741$	−114.928	+	53.2256i	−0.155099	+	0.0718294i
$742$	591.817	−	303.383i	0.797596	−	0.408871i
$743$	951.553	+	798.448i	1.28069	+	1.07463i	0.993149	+	0.116859i	$0.0372825\pi$
$743$	951.553	+	798.448i	1.28069	+	1.07463i	0.287542	+	0.957768i	$0.407162\pi$
$744$	41.4919	+	89.5919i	0.0557686	+	0.120419i
$745$	−272.048	+	47.9694i	−0.365165	+	0.0643884i
$746$	148.744			0.199389
$747$	34.1164	−	187.724i	0.0456712	−	0.251304i
$748$	−544.173	+	314.179i	−0.727505	+	0.420025i
$749$	−42.5246	+	45.8277i	−0.0567752	+	0.0611851i
$750$	658.020	+	661.478i	0.877360	+	0.881971i
$751$	102.246	−	579.866i	0.136147	−	0.772125i	−0.837908	−	0.545812i	$-0.816221\pi$
$751$	102.246	−	579.866i	0.136147	−	0.772125i	0.974054	−	0.226314i	$-0.0726674\pi$
$752$	45.9266	+	126.182i	0.0610727	+	0.167796i
$753$	116.659	+	1374.92i	0.154926	+	1.82592i
$754$	294.042	−	51.8476i	0.389977	−	0.0687634i
$755$		−	142.711i		−	0.189022i
$756$	742.830	−	295.465i	0.982579	−	0.390827i
$757$	−444.571			−0.587280			−0.293640	−	0.955916i	$-0.594867\pi$
$757$	−444.571			−0.587280			−0.293640	+	0.955916i	$0.594867\pi$
$758$	−96.1340	−	545.203i	−0.126826	−	0.719265i
$759$	−703.435	−	1010.23i	−0.926792	−	1.33101i
$760$	−37.7640	+	13.7450i	−0.0496895	+	0.0180855i
$761$	−584.429	−	103.051i	−0.767975	−	0.135415i	−0.224083	−	0.974570i	$-0.571939\pi$
$761$	−584.429	−	103.051i	−0.767975	−	0.135415i	−0.543892	+	0.839155i	$0.683050\pi$
$762$	−228.904	−	863.326i	−0.300399	−	1.13297i
$763$	−54.5051	−	176.721i	−0.0714353	−	0.231614i
$764$	−254.300	−	440.460i	−0.332853	−	0.576518i
$765$	438.140	−	249.907i	0.572732	−	0.326676i
$766$		−	144.020i		−	0.188015i
$767$	21.0368	+	119.305i	0.0274273	+	0.155548i
$768$	−549.703	−	387.058i	−0.715760	−	0.503981i
$769$	412.972	−	492.161i	0.537025	−	0.640001i	−0.427493	−	0.904019i	$-0.640603\pi$
$769$	412.972	−	492.161i	0.537025	−	0.640001i	0.964518	+	0.264017i	$0.0850476\pi$
$770$	−1611.21	−	80.4642i	−2.09248	−	0.104499i
$771$	−676.126	−	60.9395i	−0.876947	−	0.0790395i
$772$	−984.090	+	825.750i	−1.27473	+	1.06962i
$773$			20.7189i			0.0268032i	0.999910	+	0.0134016i	$0.00426599\pi$
$773$			20.7189i			0.0268032i	−0.999910	+	0.0134016i	$0.995734\pi$
$774$	1475.91	−	841.832i	1.90686	−	1.08764i
$775$			264.938i			0.341856i
$776$	111.643	−	19.6856i	0.143869	−	0.0253681i
$777$	−1087.24	−	152.980i	−1.39929	−	0.196885i
$778$	385.129	−	140.175i	0.495024	−	0.180174i
$779$	−211.295	−	177.298i	−0.271239	−	0.227597i
$780$	−152.206	−	218.589i	−0.195135	−	0.280242i
$781$	−1646.50	−	599.278i	−2.10820	−	0.767321i
$782$	711.215	+	410.620i	0.909482	+	0.525089i
$783$	−427.466	+	600.382i	−0.545934	+	0.766771i
$784$	−713.610	+	181.658i	−0.910216	+	0.231707i
$785$	269.651	−	226.264i	0.343505	−	0.288235i
$786$	−96.5708	+	67.2431i	−0.122864	+	0.0855510i
$787$	484.031	+	1329.86i	0.615033	+	1.68979i	0.718826	+	0.695190i	$0.244680\pi$
$787$	484.031	+	1329.86i	0.615033	+	1.68979i	−0.103793	+	0.994599i	$0.533098\pi$
$788$	1074.88	+	901.931i	1.36406	+	1.14458i
$789$	−360.864	−	1361.02i	−0.457369	−	1.72500i
$790$	1828.07	−	322.338i	2.31401	−	0.408023i
$791$	7.56876	−	0.948241i	0.00956860	−	0.00119879i
$792$	−85.1891	−	15.4820i	−0.107562	−	0.0195480i
$793$	41.6404	+	72.1232i	0.0525099	+	0.0909498i
$794$	−848.285	+	149.576i	−1.06837	+	0.188382i
$795$	544.750	+	49.0985i	0.685220	+	0.0617591i
$796$	−365.533	−	1004.29i	−0.459213	−	1.26168i
$797$	397.648	−	473.898i	0.498931	−	0.594603i	−0.456534	−	0.889706i	$-0.650909\pi$
$797$	397.648	−	473.898i	0.498931	−	0.594603i	0.955465	+	0.295103i	$0.0953539\pi$
$798$	313.258	−	588.925i	0.392553	−	0.738001i
$799$	85.4789	+	31.1118i	0.106982	+	0.0389384i
$800$	121.401	+	210.273i	0.151751	+	0.262841i
$801$	49.5224	−	41.1138i	0.0618258	−	0.0513281i
$802$	266.519	−	461.624i	0.332318	−	0.575591i
$803$	518.537	−	1424.67i	0.645750	−	1.77418i
$804$	−1041.77	−	282.069i	−1.29573	−	0.350832i
$805$	494.340	+	964.322i	0.614087	+	1.19792i
$806$	−94.8177	+	537.738i	−0.117640	+	0.667169i
$807$	−3.58777	−	42.2846i	−0.00444582	−	0.0523973i
$808$	10.5755	−	29.0561i	0.0130885	−	0.0359605i
$809$	213.062	+	369.034i	0.263365	+	0.456161i	0.967134	−	0.254268i	$-0.0818344\pi$
$809$	213.062	+	369.034i	0.263365	+	0.456161i	−0.703769	+	0.710429i	$0.748501\pi$
$810$	1257.41	+	235.334i	1.55236	+	0.290536i
$811$			850.191i			1.04832i	0.851619	+	0.524162i	$0.175621\pi$
$811$			850.191i			1.04832i	−0.851619	+	0.524162i	$0.824379\pi$
$812$	−549.748	+	592.449i	−0.677030	+	0.729618i
$813$	345.546	−	240.606i	0.425025	−	0.295949i
$814$	1676.64	+	1406.87i	2.05976	+	1.72834i
$815$	−536.789	+	639.721i	−0.658637	+	0.784933i
$816$	−443.636	+	117.627i	−0.543672	+	0.144150i
$817$	249.221	−	684.728i	0.305044	−	0.838101i
$818$	−421.877	+	243.571i	−0.515742	+	0.297764i
$819$	233.904	+	54.6865i	0.285597	+	0.0667723i
$820$	290.037	−	502.358i	0.353703	−	0.612632i
$821$	−313.591	+	263.134i	−0.381963	+	0.320505i	−0.813472	−	0.581603i	$-0.802426\pi$
$821$	−313.591	+	263.134i	−0.381963	+	0.320505i	0.431510	+	0.902108i	$0.357981\pi$
$822$	1583.61	+	1115.05i	1.92653	+	1.35651i
$823$	−163.441	+	926.923i	−0.198592	+	1.12627i	0.708617	+	0.705593i	$0.249319\pi$
$823$	−163.441	+	926.923i	−0.198592	+	1.12627i	−0.907209	+	0.420680i	$0.861792\pi$
$824$	4.71592	+	12.9569i	0.00572321	+	0.0157244i
$825$	−189.970	−	133.762i	−0.230267	−	0.162136i
$826$	−467.703	−	433.993i	−0.566227	−	0.525416i
$827$	110.046	−	190.605i	0.133066	−	0.230477i	−0.791791	−	0.610792i	$-0.790851\pi$
$827$	110.046	−	190.605i	0.133066	−	0.230477i	0.924857	+	0.380315i	$0.124184\pi$
$828$	360.849	+	1007.83i	0.435807	+	1.21719i
$829$	−101.359	−	58.5196i	−0.122266	−	0.0705906i	0.437619	−	0.899160i	$-0.355822\pi$
$829$	−101.359	−	58.5196i	−0.122266	−	0.0705906i	−0.559886	+	0.828570i	$0.689155\pi$
$830$	256.482	−	215.214i	0.309014	−	0.259294i
$831$	191.623	+	722.717i	0.230593	+	0.869696i
$832$	92.7602	+	254.857i	0.111491	+	0.306318i
$833$	−216.465	+	449.419i	−0.259862	+	0.539519i
$834$	1511.58	+	709.691i	1.81245	+	0.850949i
$835$	−143.266	−	812.499i	−0.171576	−	0.973053i
$836$	−591.869	+	341.716i	−0.707977	+	0.408751i
$837$	−764.378	−	1110.12i	−0.913235	−	1.32631i
$838$	−577.456	−	333.394i	−0.689088	−	0.397845i
$839$	870.524	+	1037.45i	1.03757	+	1.23653i	0.971082	+	0.238744i	$0.0767357\pi$
$839$	870.524	+	1037.45i	1.03757	+	1.23653i	0.0664905	+	0.997787i	$0.478820\pi$
$840$	72.4850	+	23.5646i	0.0862917	+	0.0280531i
$841$	−16.6511	+	94.4330i	−0.0197992	+	0.112287i
$842$	40.8296	−	231.556i	0.0484912	−	0.275008i
$843$	−309.312	+	307.695i	−0.366918	+	0.365000i
$844$	915.780	−	768.431i	1.08505	−	0.910463i
$845$			850.345i			1.00633i
$846$	114.302	+	200.396i	0.135109	+	0.236874i
$847$	−638.571	+	80.0024i	−0.753920	+	0.0944538i
$848$	−467.675	−	170.220i	−0.551504	−	0.200731i
$849$	−19.5306	+	27.7376i	−0.0230043	+	0.0326709i
$850$	152.644	+	26.9152i	0.179581	+	0.0316650i
$851$	255.300	−	1447.88i	0.300000	−	1.70139i
$852$	1245.83	+	877.214i	1.46224	+	1.02959i
$853$	−53.4660	+	146.897i	−0.0626800	+	0.172212i	−0.967079	−	0.254475i	$-0.918097\pi$
$853$	−53.4660	+	146.897i	−0.0626800	+	0.172212i	0.904399	+	0.426687i	$0.140319\pi$
$854$	−404.169	−	170.387i	−0.473265	−	0.199516i
$855$	476.541	−	271.811i	0.557358	−	0.317907i
$856$	−5.88816			−0.00687869
$857$	−149.107	−	177.699i	−0.173987	−	0.207350i	0.672003	−	0.740549i	$-0.265434\pi$
$857$	−149.107	−	177.699i	−0.173987	−	0.207350i	−0.845990	+	0.533199i	$0.820990\pi$
$858$	−337.706	−	339.481i	−0.393597	−	0.395666i
$859$	169.249	+	29.8431i	0.197030	+	0.0347417i	0.271292	−	0.962497i	$-0.412549\pi$
$859$	169.249	+	29.8431i	0.197030	+	0.0347417i	−0.0742622	+	0.997239i	$0.523660\pi$
$860$	1509.15	+	266.103i	1.75482	+	0.309422i
$861$	108.682	+	511.713i	0.126228	+	0.594324i
$862$	−114.929	+	96.4369i	−0.133328	+	0.111876i
$863$	−453.125	+	784.835i	−0.525058	+	0.909426i	0.474517	+	0.880247i	$0.342623\pi$
$863$	−453.125	+	784.835i	−0.525058	+	0.909426i	−0.999574	+	0.0291799i	$0.990710\pi$
$864$	−1115.35	−	530.811i	−1.29091	−	0.614364i
$865$	868.711	+	1504.65i	1.00429	+	1.73948i
$866$	−1948.02	+	343.488i	−2.24944	+	0.396638i
$867$	236.332	−	503.368i	0.272586	−	0.580585i
$868$	−674.262	−	1315.30i	−0.776799	−	1.51532i
$869$	1611.70	−	586.612i	1.85466	−	0.675042i
$870$	−1250.11	+	331.456i	−1.43690	+	0.380984i
$871$	−208.455	−	248.427i	−0.239328	−	0.285220i
$872$	8.70893	−	15.0843i	0.00998731	−	0.0172985i
$873$	−1456.99	+	521.669i	−1.66895	+	0.597559i
$874$	773.551	+	446.610i	0.885069	+	0.510995i
$875$	−556.287	−	516.192i	−0.635756	−	0.589934i
$876$	−759.027	+	1077.98i	−0.866469	+	1.23057i
$877$	773.729	−	281.614i	0.882245	−	0.321111i	0.139130	−	0.990274i	$-0.455570\pi$
$877$	773.729	−	281.614i	0.882245	−	0.321111i	0.743115	+	0.669163i	$0.233347\pi$
$878$	2125.57	+	374.796i	2.42093	+	0.426874i
$879$	−564.283	+	801.401i	−0.641960	+	0.911719i
$880$	776.008	+	924.811i	0.881828	+	1.05092i
$881$	−609.834	−	352.088i	−0.692207	−	0.399646i	0.112231	−	0.993682i	$-0.464200\pi$
$881$	−609.834	−	352.088i	−0.692207	−	0.399646i	−0.804438	+	0.594036i	$0.797534\pi$
$882$	−1155.91	+	514.203i	−1.31056	+	0.582997i
$883$	−194.991	−	337.735i	−0.220828	−	0.382486i	0.734231	−	0.678899i	$-0.237543\pi$
$883$	−194.991	−	337.735i	−0.220828	−	0.382486i	−0.955060	+	0.296413i	$0.904209\pi$
$884$	154.284	+	56.1546i	0.174529	+	0.0635233i
$885$	−134.486	−	507.222i	−0.151961	−	0.573132i
$886$	−1539.22	−	1291.56i	−1.73727	−	1.45774i
$887$	106.297	−	126.680i	0.119839	−	0.142819i	−0.702789	−	0.711398i	$-0.748062\pi$
$887$	106.297	−	126.680i	0.119839	−	0.142819i	0.822628	+	0.568579i	$0.192507\pi$
$888$	−59.0907	−	84.8628i	−0.0665436	−	0.0955662i
$889$	214.104	+	694.189i	0.240837	+	0.780865i
$890$	112.947			0.126907
$891$	1181.92	+	12.3915i	1.32651	+	0.0139074i
$892$	375.679	−	216.898i	0.421164	−	0.243159i
$893$	92.9709	+	33.8386i	0.104111	+	0.0378932i
$894$	430.307	−	36.5108i	0.481328	−	0.0408398i
$895$	−948.095	−	167.175i	−1.05932	−	0.186787i
$896$	−123.847	−	79.9946i	−0.138222	−	0.0892797i
$897$	−84.0644	+	310.475i	−0.0937173	+	0.346126i
$898$	−198.265	−	72.1624i	−0.220785	−	0.0803590i
$899$	1180.08	+	681.320i	1.31266	+	0.757865i
$900$	129.056	+	155.450i	0.143395	+	0.172722i
$901$	−291.978	+	168.573i	−0.324059	+	0.187096i
$902$	356.665	−	979.930i	0.395416	−	1.08640i
$903$	−1172.11	+	732.155i	−1.29802	+	0.810803i
$904$	0.550344	+	0.461793i	0.000608788	+	0.000510833i
$905$	687.536	−	250.242i	0.759708	−	0.276511i
$906$	−20.0270	+	222.200i	−0.0221048	+	0.245254i
$907$	−130.099	−	737.826i	−0.143438	−	0.813480i	−0.968608	−	0.248594i	$-0.920031\pi$
$907$	−130.099	−	737.826i	−0.143438	−	0.813480i	0.825169	−	0.564886i	$-0.191080\pi$
$908$	1334.48	−	770.465i	1.46970	−	0.848530i
$909$	−75.4760	+	415.304i	−0.0830319	+	0.456880i
$910$	254.506	+	336.017i	0.279677	+	0.369249i
$911$	116.870	+	662.804i	0.128288	+	0.727557i	0.979301	+	0.202412i	$0.0648779\pi$
$911$	116.870	+	662.804i	0.128288	+	0.727557i	−0.851013	+	0.525145i	$0.824011\pi$
$912$	−482.520	+	127.936i	−0.529078	+	0.140281i
$913$	198.851	−	236.981i	0.217799	−	0.259563i
$914$	−129.090	+	46.9849i	−0.141236	+	0.0514058i
$915$	−206.133	−	296.037i	−0.225282	−	0.323537i
$916$	−187.742	−	223.742i	−0.204959	−	0.244260i
$917$	76.2973	−	57.7891i	0.0832032	−	0.0630197i
$918$	−717.249	+	327.618i	−0.781317	+	0.356882i
$919$	−843.661	+	1461.26i	−0.918021	+	1.59006i	−0.115603	+	0.993295i	$0.536880\pi$
$919$	−843.661	+	1461.26i	−0.918021	+	1.59006i	−0.802418	+	0.596763i	$0.796453\pi$
$920$	−34.9070	+	95.9062i	−0.0379424	+	0.104246i
$921$	−27.3900	+	19.0719i	−0.0297394	+	0.0207078i
$922$	957.799	−	1141.46i	1.03883	−	1.23803i
$923$	156.587	+	430.219i	0.169650	+	0.466109i
$924$	1283.54	+	180.599i	1.38911	+	0.195454i
$925$	−48.1846	−	273.269i	−0.0520915	−	0.295426i
$926$	335.113			0.361893
$927$	−93.2586	−	163.502i	−0.100603	−	0.176378i
$928$	1248.79			1.34568
$929$	555.660	+	662.209i	0.598127	+	0.712819i	0.977146	−	0.212569i	$-0.0681831\pi$
$929$	555.660	+	662.209i	0.598127	+	0.712819i	−0.379019	+	0.925389i	$0.623739\pi$
$930$	212.312	−	2355.61i	0.228293	−	2.53292i
$931$	−235.437	+	488.810i	−0.252886	+	0.525037i
$932$	−993.116	−	833.323i	−1.06557	−	0.894124i
$933$	−187.195	+	265.856i	−0.200637	+	0.284947i
$934$	−2387.57	+	420.993i	−2.55628	+	0.450742i
$935$	817.822			0.874676
$936$	11.2091	+	19.6519i	0.0119755	+	0.0209956i
$937$	−627.770	+	362.443i	−0.669979	+	0.386812i	−0.796069	−	0.605206i	$-0.793091\pi$
$937$	−627.770	+	362.443i	−0.669979	+	0.386812i	0.126090	+	0.992019i	$0.459757\pi$
$938$	1665.15	+	380.116i	1.77521	+	0.405241i
$939$	−1096.18	+	290.643i	−1.16739	+	0.309524i
$940$	−36.1309	+	204.909i	−0.0384371	+	0.217988i
$941$	56.7456	+	155.907i	0.0603035	+	0.165683i	0.966186	−	0.257847i	$-0.0830131\pi$
$941$	56.7456	+	155.907i	0.0603035	+	0.165683i	−0.905882	+	0.423530i	$0.860791\pi$
$942$	−451.596	+	314.450i	−0.479401	+	0.333811i
$943$	−689.851	+	121.639i	−0.731549	+	0.128992i
$944$			477.480i			0.505805i
$945$	−1029.56	−	150.371i	−1.08948	−	0.159123i
$946$	2754.90			2.91216
$947$	77.3813	+	438.851i	0.0817120	+	0.463412i	0.998018	+	0.0629325i	$0.0200453\pi$
$947$	77.3813	+	438.851i	0.0817120	+	0.463412i	−0.916306	+	0.400479i	$0.868844\pi$
$948$	−1486.13	+	126.096i	−1.56765	+	0.133012i
$949$	−372.255	+	135.490i	−0.392261	+	0.142771i
$950$	166.023	+	29.2743i	0.174761	+	0.0308150i
$951$	−411.889	+	409.736i	−0.433112	+	0.430847i
$952$	−44.8949	+	13.8467i	−0.0471585	+	0.0145448i
$953$	435.703	+	754.661i	0.457191	+	0.791879i	0.998811	−	0.0487447i	$-0.0155221\pi$
$953$	435.703	+	754.661i	0.457191	+	0.791879i	−0.541620	+	0.840624i	$0.682189\pi$
$954$	−841.280	−	152.892i	−0.881845	−	0.160264i
$955$			661.954i			0.693146i
$956$	28.4386	+	161.283i	0.0297475	+	0.168707i
$957$	−1084.33	+	502.177i	−1.13305	+	0.524740i
$958$	694.875	−	828.120i	0.725339	−	0.864426i
$959$	−1323.27	−	854.718i	−1.37984	−	0.891260i
$960$	−493.686	−	1066.00i	−0.514256	−	1.11041i
$961$	−1172.79	+	984.087i	−1.22038	+	1.02402i
$962$		−	571.891i		−	0.594481i
$963$	79.2314	−	13.5428i	0.0822756	−	0.0140631i
$964$		−	1218.18i		−	1.26367i
$965$	1646.59	−	290.338i	1.70631	−	0.300868i
$966$	−634.357	−	1570.81i	−0.656684	−	1.62610i
$967$	526.396	−	191.593i	0.544360	−	0.198131i	−0.0551788	−	0.998476i	$-0.517573\pi$
$967$	526.396	−	191.593i	0.544360	−	0.198131i	0.599539	+	0.800346i	$0.295351\pi$
$968$	−46.4321	−	38.9612i	−0.0479671	−	0.0402491i
$969$	−143.717	+	306.105i	−0.148315	+	0.315898i
$970$	−2551.89	−	928.811i	−2.63081	−	0.957537i
$971$	1446.40	+	835.079i	1.48960	+	0.860019i	0.999929	−	0.0118902i	$-0.00378484\pi$
$971$	1446.40	+	835.079i	1.48960	+	0.860019i	0.489667	+	0.871909i	$0.337118\pi$
$972$	−989.250	−	279.013i	−1.01775	−	0.287051i
$973$	−1251.55	−	527.620i	−1.28628	−	0.542261i
$974$	732.857	−	614.940i	0.752420	−	0.631355i
$975$	5.13255	+	60.4909i	0.00526415	+	0.0620420i
$976$	112.264	+	308.444i	0.115025	+	0.316029i
$977$	−924.283	−	775.566i	−0.946042	−	0.793824i	0.0325843	−	0.999469i	$-0.489626\pi$
$977$	−924.283	−	775.566i	−0.946042	−	0.793824i	−0.978627	+	0.205645i	$0.934071\pi$
$978$	925.549	−	920.710i	0.946369	−	0.941421i
$979$	102.774	−	18.1218i	0.104978	−	0.0185105i
$980$	−1098.35	−	309.104i	−1.12076	−	0.315412i
$981$	−82.4938	+	223.006i	−0.0840916	+	0.227325i
$982$	309.153	+	535.468i	0.314819	+	0.545283i
$983$	1715.41	−	302.473i	1.74508	−	0.307704i	0.792020	−	0.610495i	$-0.209029\pi$
$983$	1715.41	−	302.473i	1.74508	−	0.307704i	0.953057	+	0.302790i	$0.0979182\pi$
$984$	−28.3657	+	40.2853i	−0.0288269	+	0.0409403i
$985$	−624.611	−	1716.11i	−0.634123	−	1.74224i
$986$	512.427	−	610.687i	0.519703	−	0.619358i
$987$	−99.4104	−	159.146i	−0.100720	−	0.161243i
$988$	167.806	+	61.0764i	0.169844	+	0.0618182i
$989$	−925.275	−	1602.62i	−0.935566	−	1.62045i
$990$	1581.87	+	1341.54i	1.59785	+	1.35509i
$991$	−601.141	+	1041.21i	−0.606600	+	1.05066i	0.385196	+	0.922835i	$0.374134\pi$
$991$	−601.141	+	1041.21i	−0.606600	+	1.05066i	−0.991796	+	0.127827i	$0.959200\pi$
$992$	−781.091	+	2146.03i	−0.787391	+	2.16334i
$993$	−590.166	+	587.081i	−0.594326	+	0.591219i
$994$	−2025.48	−	1308.28i	−2.03770	−	1.31618i
$995$	−241.545	+	1369.87i	−0.242759	+	1.37675i
$996$	−220.768	+	153.723i	−0.221654	+	0.154340i
$997$	457.419	−	1256.75i	0.458795	−	1.26053i	−0.467588	−	0.883947i	$-0.654877\pi$
$997$	457.419	−	1256.75i	0.458795	−	1.26053i	0.926383	−	0.376583i	$-0.122901\pi$
$998$	−145.871	−	252.656i	−0.146163	−	0.253163i
$999$	990.312	+	1006.01i	0.991303	+	1.00702i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.3.x.a.103.8	✓	276
7.3	odd	6		189.3.z.a.157.39	yes	276
27.16	even	9		189.3.z.a.124.39	yes	276
189.178	odd	18	inner	189.3.x.a.178.8	yes	276

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.3.x.a.103.8	✓	276	1.1	even	1	trivial
189.3.x.a.178.8	yes	276	189.178	odd	18	inner
189.3.z.a.124.39	yes	276	27.16	even	9
189.3.z.a.157.39	yes	276	7.3	odd	6

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	189.x (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.498156 - 2.82518i) q^{2} +(1.27498 - 2.71559i) q^{3} +(-3.97473 + 1.44668i) q^{4} +(5.42157 + 0.955969i) q^{5} +(-8.30718 - 2.24925i) q^{6} +(6.82445 + 1.55787i) q^{7} +(0.329641 + 0.570956i) q^{8} +(-5.74887 - 6.92463i) q^{9} -15.7931i q^{10} +(-2.53394 - 14.3707i) q^{11} +(-1.13909 + 12.6382i) q^{12} +(-2.45087 + 2.92084i) q^{13} +(1.00162 - 20.0564i) q^{14} +(9.50840 - 13.5039i) q^{15} +(-11.5121 + 9.65977i) q^{16} +10.1803i q^{17} +(-16.6995 + 19.6911i) q^{18} +11.0725i q^{19} +(-22.9322 + 4.04357i) q^{20} +(12.9315 - 16.5462i) q^{21} +(-39.3375 + 14.3177i) q^{22} +(21.5412 + 18.0752i) q^{23} +(1.97077 - 0.167216i) q^{24} +(4.98723 + 1.81520i) q^{25} +(9.47281 + 5.46913i) q^{26} +(-26.1341 + 6.78284i) q^{27} +(-29.3790 + 3.68071i) q^{28} +(20.9105 - 17.5460i) q^{29} +(-42.8877 - 20.1359i) q^{30} +(17.0735 + 46.9091i) q^{31} +(35.0456 + 29.4067i) q^{32} +(-42.2556 - 11.4411i) q^{33} +(28.7611 - 5.07136i) q^{34} +(35.5099 + 14.9700i) q^{35} +(32.8679 + 19.2067i) q^{36} +(-26.1418 - 45.2789i) q^{37} +(31.2820 - 5.51585i) q^{38} +(4.80699 + 10.3796i) q^{39} +(1.24136 + 3.41060i) q^{40} +(-16.0124 + 19.0828i) q^{41} +(-53.1878 - 28.2914i) q^{42} +(-61.8402 - 22.5080i) q^{43} +(30.8615 + 53.4537i) q^{44} +(-24.5482 - 43.0381i) q^{45} +(40.3349 - 69.8621i) q^{46} +(3.05609 - 8.39653i) q^{47} +(11.5544 + 43.5780i) q^{48} +(44.1461 + 21.2632i) q^{49} +(2.64386 - 14.9941i) q^{50} +(27.6455 + 12.9796i) q^{51} +(5.51602 - 15.1551i) q^{52} +(16.5588 + 28.6807i) q^{53} +(32.1816 + 70.4548i) q^{54} -80.3341i q^{55} +(1.36015 + 4.40999i) q^{56} +(30.0685 + 14.1172i) q^{57} +(-59.9873 - 50.3353i) q^{58} +(20.4232 - 24.3394i) q^{59} +(-18.2574 + 67.4300i) q^{60} +(7.47039 - 20.5247i) q^{61} +(124.021 - 71.6038i) q^{62} +(-28.4452 - 56.2127i) q^{63} +(35.5653 - 61.6010i) q^{64} +(-16.0798 + 13.4926i) q^{65} +(-11.2734 + 125.079i) q^{66} +(-14.7693 + 83.7611i) q^{67} +(-14.7276 - 40.4638i) q^{68} +(76.5494 - 35.4516i) q^{69} +(24.6036 - 107.779i) q^{70} +(60.0372 - 103.988i) q^{71} +(2.05859 - 5.56499i) q^{72} +(89.9772 + 51.9484i) q^{73} +(-114.898 + 96.4112i) q^{74} +(11.2879 - 11.2289i) q^{75} +(-16.0184 - 44.0103i) q^{76} +(5.09488 - 102.020i) q^{77} +(26.9295 - 18.7513i) q^{78} +(20.4100 + 115.751i) q^{79} +(-71.6479 + 41.3659i) q^{80} +(-14.9010 + 79.6176i) q^{81} +(61.8891 + 35.7317i) q^{82} +(13.6270 + 16.2401i) q^{83} +(-27.4623 + 84.4742i) q^{84} +(-9.73202 + 55.1931i) q^{85} +(-32.7831 + 185.922i) q^{86} +(-20.9873 - 79.1551i) q^{87} +(7.36973 - 6.18394i) q^{88} +7.15164i q^{89} +(-109.362 + 90.7927i) q^{90} +(-21.2761 + 16.1149i) q^{91} +(-111.769 - 40.6807i) q^{92} +(149.154 + 13.4433i) q^{93} +(-25.2441 - 4.45122i) q^{94} +(-10.5850 + 60.0306i) q^{95} +(124.539 - 57.6765i) q^{96} +(58.8110 - 161.582i) q^{97} +(38.0806 - 135.313i) q^{98} +(-84.9444 + 100.162i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 276 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 36 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9} - 21 q^{11} - 9 q^{12} - 87 q^{14} + 12 q^{15} - 15 q^{16} - 3 q^{18} + 36 q^{20} - 147 q^{21} - 12 q^{22} - 102 q^{23}+ \cdots - 336 q^{99}+O(q^{100}) \) 276 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 36 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9 - 21 * q^11 - 9 * q^12 - 87 * q^14 + 12 * q^15 - 15 * q^16 - 3 * q^18 + 36 * q^20 - 147 * q^21 - 12 * q^22 - 102 * q^23 - 9 * q^24 - 3 * q^25 - 18 * q^26 - 12 * q^28 - 120 * q^29 + 177 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 + 36 * q^34 - 84 * q^35 + 162 * q^36 + 3 * q^37 - 279 * q^38 - 270 * q^39 + 216 * q^40 + 207 * q^42 - 12 * q^43 + 3 * q^44 - 9 * q^45 + 3 * q^46 - 333 * q^47 + 66 * q^49 - 225 * q^50 + 204 * q^51 - 9 * q^52 - 141 * q^53 - 315 * q^54 + 279 * q^56 - 162 * q^57 - 3 * q^58 - 144 * q^59 + 291 * q^60 - 9 * q^61 + 891 * q^62 + 75 * q^63 - 774 * q^64 - 3 * q^65 - 9 * q^66 - 3 * q^67 + 666 * q^68 - 216 * q^69 + 84 * q^70 - 114 * q^71 - 291 * q^72 - 9 * q^73 + 57 * q^74 + 576 * q^75 + 144 * q^76 - 447 * q^77 + 30 * q^78 + 15 * q^79 + 558 * q^80 - 465 * q^81 - 18 * q^82 - 1080 * q^83 + 276 * q^84 + 243 * q^85 + 627 * q^86 + 486 * q^87 + 405 * q^88 + 729 * q^90 + 96 * q^91 - 276 * q^92 - 15 * q^93 - 9 * q^94 + 9 * q^95 + 567 * q^96 + 807 * q^98 - 336 * q^99

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