LMFDB - Embedded newform 108.3.j.a.31.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [108,3,Mod(7,108)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(108, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 16])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("108.7"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	108.j (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:	$2.94278685509$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			31.13
Character	$\chi$	$=$	108.31
Dual form			108.3.j.a.7.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00307 + 1.73027i) q^{2} +(-2.96394 - 0.463733i) q^{3} +(-1.98770 - 3.47117i) q^{4} +(0.608002 - 3.44815i) q^{5} +(3.77543 - 4.66328i) q^{6} +(5.71739 + 6.81372i) q^{7} +(7.99989 + 0.0425704i) q^{8} +(8.56990 + 2.74895i) q^{9} +(5.35638 + 4.51075i) q^{10} +(-5.38256 + 0.949091i) q^{11} +(4.28173 + 11.2101i) q^{12} +(21.3373 - 7.76615i) q^{13} +(-17.5245 + 3.05801i) q^{14} +(-3.40111 + 9.93818i) q^{15} +(-8.09811 + 13.7993i) q^{16} +(-8.12631 + 14.0752i) q^{17} +(-13.3527 + 12.0709i) q^{18} +(19.5372 - 11.2798i) q^{19} +(-13.1777 + 4.74341i) q^{20} +(-13.7863 - 22.8468i) q^{21} +(3.75690 - 10.2653i) q^{22} +(22.1707 - 26.4221i) q^{23} +(-23.6915 - 3.83599i) q^{24} +(11.9722 + 4.35753i) q^{25} +(-7.96527 + 44.7094i) q^{26} +(-24.1259 - 12.1219i) q^{27} +(12.2872 - 33.3897i) q^{28} +(24.1480 + 8.78914i) q^{29} +(-13.7842 - 15.8535i) q^{30} +(-14.3967 + 17.1573i) q^{31} +(-15.7536 - 27.8536i) q^{32} +(16.3937 - 0.316980i) q^{33} +(-16.2027 - 28.1791i) q^{34} +(26.9709 - 15.5717i) q^{35} +(-7.49228 - 35.2117i) q^{36} +(7.88574 - 13.6585i) q^{37} +(-0.0800315 + 45.1192i) q^{38} +(-66.8440 + 13.1236i) q^{39} +(5.01074 - 27.5590i) q^{40} +(-49.6190 + 18.0598i) q^{41} +(53.3598 - 0.937056i) q^{42} +(-9.61800 + 1.69591i) q^{43} +(13.9934 + 16.7973i) q^{44} +(14.6893 - 27.8790i) q^{45} +(23.4786 + 64.8646i) q^{46} +(-14.9904 - 17.8648i) q^{47} +(30.4015 - 37.1450i) q^{48} +(-5.22945 + 29.6577i) q^{49} +(-19.5487 + 16.3443i) q^{50} +(30.6130 - 37.9496i) q^{51} +(-69.3698 - 58.6288i) q^{52} +4.09859 q^{53} +(45.1742 - 29.5853i) q^{54} +19.1370i q^{55} +(45.4484 + 54.7523i) q^{56} +(-63.1380 + 24.3727i) q^{57} +(-39.4297 + 32.9665i) q^{58} +(-28.0094 - 4.93882i) q^{59} +(41.2575 - 7.94826i) q^{60} +(-31.1357 + 26.1260i) q^{61} +(-15.2459 - 42.1201i) q^{62} +(30.2669 + 74.1097i) q^{63} +(63.9964 + 0.681117i) q^{64} +(-13.8057 - 78.2962i) q^{65} +(-15.8956 + 28.6836i) q^{66} +(30.9299 + 84.9793i) q^{67} +(65.0100 + 0.230627i) q^{68} +(-77.9656 + 68.0321i) q^{69} +(-0.110483 + 62.2866i) q^{70} +(87.8991 + 50.7486i) q^{71} +(68.4412 + 22.3561i) q^{72} +(-16.0025 - 27.7171i) q^{73} +(15.7230 + 27.3449i) q^{74} +(-33.4642 - 18.4674i) q^{75} +(-77.9884 - 45.3963i) q^{76} +(-37.2410 - 31.2489i) q^{77} +(44.3418 - 128.822i) q^{78} +(8.65102 - 23.7685i) q^{79} +(42.6584 + 36.3135i) q^{80} +(65.8865 + 47.1165i) q^{81} +(18.5229 - 103.970i) q^{82} +(16.3859 - 45.0198i) q^{83} +(-51.9023 + 93.2671i) q^{84} +(43.5925 + 36.5785i) q^{85} +(6.71314 - 18.3429i) q^{86} +(-67.4973 - 37.2487i) q^{87} +(-43.1003 + 7.36348i) q^{88} +(45.0663 + 78.0571i) q^{89} +(33.5038 + 53.3812i) q^{90} +(174.910 + 100.984i) q^{91} +(-135.784 - 24.4394i) q^{92} +(50.6272 - 44.1769i) q^{93} +(45.9475 - 8.01777i) q^{94} +(-27.0159 - 74.2255i) q^{95} +(33.7761 + 89.8620i) q^{96} +(-25.7741 - 146.172i) q^{97} +(-46.0705 - 38.7972i) q^{98} +(-48.7371 - 6.66280i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 39 q^{12} - 12 q^{13} + 39 q^{14} - 6 q^{16} - 6 q^{17} - 27 q^{18} - 69 q^{20} - 12 q^{21} - 6 q^{22} - 138 q^{24} - 12 q^{25}+ \cdots + 510 q^{98}+O(q^{100}) $ 204 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 39 * q^12 - 12 * q^13 + 39 * q^14 - 6 * q^16 - 6 * q^17 - 27 * q^18 - 69 * q^20 - 12 * q^21 - 6 * q^22 - 138 * q^24 - 12 * q^25 - 174 * q^26 - 12 * q^28 + 60 * q^29 - 153 * q^30 - 96 * q^32 + 48 * q^33 + 6 * q^34 + 24 * q^36 - 6 * q^37 + 72 * q^38 + 69 * q^40 - 192 * q^41 - 126 * q^42 - 219 * q^44 - 132 * q^45 - 3 * q^46 - 219 * q^48 - 12 * q^49 - 165 * q^50 + 21 * q^52 - 24 * q^53 + 78 * q^54 + 99 * q^56 - 150 * q^57 - 141 * q^58 + 210 * q^60 - 12 * q^61 + 294 * q^62 - 3 * q^64 - 156 * q^65 + 393 * q^66 + 375 * q^68 - 60 * q^69 - 165 * q^70 + 228 * q^72 - 6 * q^73 + 447 * q^74 - 54 * q^76 + 132 * q^77 + 750 * q^78 + 798 * q^80 + 228 * q^81 - 12 * q^82 + 762 * q^84 + 138 * q^85 + 606 * q^86 - 198 * q^88 - 114 * q^89 + 894 * q^90 + 723 * q^92 - 1020 * q^93 - 357 * q^94 + 474 * q^96 + 168 * q^97 + 510 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.00307	+	1.73027i	−0.501535	+	0.865137i
$2$	−1.00307	+	1.73027i	−0.501535	+	0.865137i
$3$	−2.96394	−	0.463733i	−0.987981	−	0.154578i
$3$	−2.96394	−	0.463733i	−0.987981	−	0.154578i
$4$	−1.98770	−	3.47117i	−0.496925	−	0.867794i
$5$	0.608002	−	3.44815i	0.121600	−	0.689631i	−0.861669	−	0.507471i	$-0.830580\pi$
$5$	0.608002	−	3.44815i	0.121600	−	0.689631i	0.983269	−	0.182159i	$-0.0583086\pi$
$6$	3.77543	−	4.66328i	0.629238	−	0.777213i
$7$	5.71739	+	6.81372i	0.816769	+	0.973388i	0.999953	−	0.00969079i	$-0.00308472\pi$
$7$	5.71739	+	6.81372i	0.816769	+	0.973388i	−0.183184	+	0.983079i	$0.558640\pi$
$8$	7.99989	+	0.0425704i	0.999986	+	0.00532130i
$9$	8.56990	+	2.74895i	0.952212	+	0.305439i
$10$	5.35638	+	4.51075i	0.535638	+	0.451075i
$11$	−5.38256	+	0.949091i	−0.489324	+	0.0862810i	−0.412866	−	0.910792i	$-0.635472\pi$
$11$	−5.38256	+	0.949091i	−0.489324	+	0.0862810i	−0.0764579	+	0.997073i	$0.524361\pi$
$12$	4.28173	+	11.2101i	0.356810	+	0.934177i
$13$	21.3373	−	7.76615i	1.64133	−	0.597396i	0.654061	−	0.756442i	$-0.273064\pi$
$13$	21.3373	−	7.76615i	1.64133	−	0.597396i	0.987271	+	0.159046i	$0.0508418\pi$
$14$	−17.5245	+	3.05801i	−1.25175	+	0.218429i
$15$	−3.40111	+	9.93818i	−0.226740	+	0.662545i
$16$	−8.09811	+	13.7993i	−0.506132	+	0.862456i
$17$	−8.12631	+	14.0752i	−0.478018	+	0.827951i	−0.999682	−	0.0251993i	$-0.991978\pi$
$17$	−8.12631	+	14.0752i	−0.478018	+	0.827951i	0.521664	+	0.853151i	$0.325311\pi$
$18$	−13.3527	+	12.0709i	−0.741815	+	0.670605i
$19$	19.5372	−	11.2798i	1.02828	−	0.593675i	0.111785	−	0.993732i	$-0.464343\pi$
$19$	19.5372	−	11.2798i	1.02828	−	0.593675i	0.916490	+	0.400057i	$0.131010\pi$
$20$	−13.1777	+	4.74341i	−0.658883	+	0.237170i
$21$	−13.7863	−	22.8468i	−0.656488	−	1.08794i
$22$	3.75690	−	10.2653i	0.170768	−	0.466605i
$23$	22.1707	−	26.4221i	0.963945	−	1.14879i	−0.0248778	−	0.999690i	$-0.507920\pi$
$23$	22.1707	−	26.4221i	0.963945	−	1.14879i	0.988823	−	0.149095i	$-0.0476359\pi$
$24$	−23.6915	−	3.83599i	−0.987144	−	0.159833i
$25$	11.9722	+	4.35753i	0.478889	+	0.174301i
$26$	−7.96527	+	44.7094i	−0.306357	+	1.71959i
$27$	−24.1259	−	12.1219i	−0.893553	−	0.448959i
$28$	12.2872	−	33.3897i	0.438827	−	1.19249i
$29$	24.1480	+	8.78914i	0.832688	+	0.303074i	0.722962	−	0.690888i	$-0.242780\pi$
$29$	24.1480	+	8.78914i	0.832688	+	0.303074i	0.109727	+	0.993962i	$0.465002\pi$
$30$	−13.7842	−	15.8535i	−0.459474	−	0.528451i
$31$	−14.3967	+	17.1573i	−0.464408	+	0.553460i	−0.946518	−	0.322651i	$-0.895426\pi$
$31$	−14.3967	+	17.1573i	−0.464408	+	0.553460i	0.482110	+	0.876111i	$0.339871\pi$
$32$	−15.7536	−	27.8536i	−0.492300	−	0.870426i
$33$	16.3937	−	0.316980i	0.496780	−	0.00960546i
$34$	−16.2027	−	28.1791i	−0.476549	−	0.828798i
$35$	26.9709	−	15.5717i	0.770598	−	0.444905i
$36$	−7.49228	−	35.2117i	−0.208119	−	0.978104i
$37$	7.88574	−	13.6585i	0.213128	−	0.369149i	−0.739564	−	0.673086i	$-0.764968\pi$
$37$	7.88574	−	13.6585i	0.213128	−	0.369149i	0.952692	+	0.303938i	$0.0983015\pi$
$38$	−0.0800315	+	45.1192i	−0.00210609	+	1.18735i
$39$	−66.8440	+	13.1236i	−1.71395	+	0.336503i
$40$	5.01074	−	27.5590i	0.125268	−	0.688974i
$41$	−49.6190	+	18.0598i	−1.21022	+	0.440484i	−0.866780	−	0.498691i	$-0.833814\pi$
$41$	−49.6190	+	18.0598i	−1.21022	+	0.440484i	−0.343439	+	0.939175i	$0.611592\pi$
$42$	53.3598	−	0.937056i	1.27047	−	0.0223109i
$43$	−9.61800	+	1.69591i	−0.223674	+	0.0394398i	−0.284362	−	0.958717i	$-0.591782\pi$
$43$	−9.61800	+	1.69591i	−0.223674	+	0.0394398i	0.0606877	+	0.998157i	$0.480671\pi$
$44$	13.9934	+	16.7973i	0.318031	+	0.381757i
$45$	14.6893	−	27.8790i	0.326430	−	0.619533i
$46$	23.4786	+	64.8646i	0.510404	+	1.41010i
$47$	−14.9904	−	17.8648i	−0.318944	−	0.380103i	0.582623	−	0.812743i	$-0.302027\pi$
$47$	−14.9904	−	17.8648i	−0.318944	−	0.380103i	−0.901567	+	0.432640i	$0.857582\pi$
$48$	30.4015	−	37.1450i	0.633365	−	0.773853i
$49$	−5.22945	+	29.6577i	−0.106724	+	0.605259i
$50$	−19.5487	+	16.3443i	−0.390974	+	0.326886i
$51$	30.6130	−	37.9496i	0.600255	−	0.744109i
$52$	−69.3698	−	58.6288i	−1.33403	−	1.12748i
$53$	4.09859			0.0773318			0.0386659	−	0.999252i	$-0.487689\pi$
$53$	4.09859			0.0773318			0.0386659	+	0.999252i	$0.487689\pi$
$54$	45.1742	−	29.5853i	0.836559	−	0.547877i
$55$			19.1370i			0.347945i
$56$	45.4484	+	54.7523i	0.811578	+	0.977720i
$57$	−63.1380	+	24.3727i	−1.10769	+	0.427591i
$58$	−39.4297	+	32.9665i	−0.679823	+	0.568387i
$59$	−28.0094	−	4.93882i	−0.474736	−	0.0837088i	−0.0688395	−	0.997628i	$-0.521930\pi$
$59$	−28.0094	−	4.93882i	−0.474736	−	0.0837088i	−0.405897	+	0.913919i	$0.633041\pi$
$60$	41.2575	−	7.94826i	0.687625	−	0.132471i
$61$	−31.1357	+	26.1260i	−0.510422	+	0.428295i	−0.861278	−	0.508135i	$-0.830335\pi$
$61$	−31.1357	+	26.1260i	−0.510422	+	0.428295i	0.350856	+	0.936430i	$0.385891\pi$
$62$	−15.2459	−	42.1201i	−0.245902	−	0.679357i
$63$	30.2669	+	74.1097i	0.480426	+	1.17634i
$64$	63.9964	+	0.681117i	0.999943	+	0.0106425i
$65$	−13.8057	−	78.2962i	−0.212396	−	1.20456i
$66$	−15.8956	+	28.6836i	−0.240843	+	0.434600i
$67$	30.9299	+	84.9793i	0.461641	+	1.26835i	0.924251	+	0.381785i	$0.124691\pi$
$67$	30.9299	+	84.9793i	0.461641	+	1.26835i	−0.462610	+	0.886562i	$0.653087\pi$
$68$	65.0100	+	0.230627i	0.956030	+	0.00339158i
$69$	−77.9656	+	68.0321i	−1.12994	+	0.985973i
$70$	−0.110483	+	62.2866i	−0.00157832	+	0.889808i
$71$	87.8991	+	50.7486i	1.23802	+	0.714769i	0.968688	−	0.248280i	$-0.0798652\pi$
$71$	87.8991	+	50.7486i	1.23802	+	0.714769i	0.269328	+	0.963049i	$0.413199\pi$
$72$	68.4412	+	22.3561i	0.950573	+	0.310502i
$73$	−16.0025	−	27.7171i	−0.219212	−	0.379687i	0.735355	−	0.677682i	$-0.237015\pi$
$73$	−16.0025	−	27.7171i	−0.219212	−	0.379687i	−0.954567	+	0.297995i	$0.903682\pi$
$74$	15.7230	+	27.3449i	0.212473	+	0.369526i
$75$	−33.4642	−	18.4674i	−0.446190	−	0.246232i
$76$	−77.9884	−	45.3963i	−1.02616	−	0.597319i
$77$	−37.2410	−	31.2489i	−0.483650	−	0.405830i
$78$	44.3418	−	128.822i	0.568485	−	1.65157i
$79$	8.65102	−	23.7685i	0.109507	−	0.300867i	−0.872820	−	0.488042i	$-0.837711\pi$
$79$	8.65102	−	23.7685i	0.109507	−	0.300867i	0.982326	+	0.187176i	$0.0599334\pi$
$80$	42.6584	+	36.3135i	0.533230	+	0.453919i
$81$	65.8865	+	47.1165i	0.813414	+	0.581686i
$82$	18.5229	−	103.970i	0.225889	−	1.26792i
$83$	16.3859	−	45.0198i	0.197420	−	0.542408i	−0.800996	−	0.598670i	$-0.795696\pi$
$83$	16.3859	−	45.0198i	0.197420	−	0.542408i	0.998416	+	0.0562623i	$0.0179183\pi$
$84$	−51.9023	+	93.2671i	−0.617885	+	1.11032i
$85$	43.5925	+	36.5785i	0.512853	+	0.430335i
$86$	6.71314	−	18.3429i	0.0780597	−	0.213289i
$87$	−67.4973	−	37.2487i	−0.775832	−	0.428146i
$88$	−43.1003	+	7.36348i	−0.489776	+	0.0836759i
$89$	45.0663	+	78.0571i	0.506363	+	0.877047i	0.999973	+	0.00736306i	$0.00234375\pi$
$89$	45.0663	+	78.0571i	0.506363	+	0.877047i	−0.493610	+	0.869683i	$0.664323\pi$
$90$	33.5038	+	53.3812i	0.372265	+	0.593124i
$91$	174.910	+	100.984i	1.92209	+	1.10972i
$92$	−135.784	−	24.4394i	−1.47592	−	0.265646i
$93$	50.6272	−	44.1769i	0.544379	−	0.475021i
$94$	45.9475	−	8.01777i	0.488803	−	0.0852954i
$95$	−27.0159	−	74.2255i	−0.284378	−	0.781321i
$96$	33.7761	+	89.8620i	0.351834	+	0.936062i
$97$	−25.7741	−	146.172i	−0.265713	−	1.50693i	−0.766998	−	0.641650i	$-0.778250\pi$
$97$	−25.7741	−	146.172i	−0.265713	−	1.50693i	0.501285	−	0.865282i	$-0.332861\pi$
$98$	−46.0705	−	38.7972i	−0.470107	−	0.395889i
$99$	−48.7371	−	6.66280i	−0.492293	−	0.0673010i
$100$	−8.67141	−	50.2191i	−0.0867141	−	0.502191i
$101$	7.81270	−	6.55563i	0.0773534	−	0.0649072i	−0.603291	−	0.797521i	$-0.706144\pi$
$101$	7.81270	−	6.55563i	0.0773534	−	0.0649072i	0.680645	+	0.732614i	$0.261700\pi$
$102$	34.9561	+	91.0350i	0.342707	+	0.892500i
$103$	−14.2078	−	2.50522i	−0.137940	−	0.0243226i	0.104252	−	0.994551i	$-0.466755\pi$
$103$	−14.2078	−	2.50522i	−0.137940	−	0.0243226i	−0.242192	+	0.970228i	$0.577866\pi$
$104$	171.027	−	61.2200i	1.64449	−	0.588653i
$105$	−87.1613	+	33.6462i	−0.830108	+	0.320440i
$106$	−4.11117	+	7.09168i	−0.0387846	+	0.0669026i
$107$		−	81.7160i		−	0.763701i	−0.924224	−	0.381851i	$-0.875287\pi$
$107$		−	81.7160i		−	0.763701i	0.924224	−	0.381851i	$-0.124713\pi$
$108$	5.87787	+	107.840i	0.0544247	+	0.998518i
$109$	−193.369			−1.77402			−0.887012	−	0.461747i	$-0.847223\pi$
$109$	−193.369			−1.77402			−0.887012	+	0.461747i	$0.847223\pi$
$110$	−33.1122	−	19.1957i	−0.301020	−	0.174506i
$111$	−29.7068	+	36.8261i	−0.267628	+	0.331767i
$112$	−140.325	+	23.7177i	−1.25290	+	0.211765i
$113$	0.255201	−	1.44731i	0.00225841	−	0.0128081i	−0.983658	−	0.180049i	$-0.942375\pi$
$113$	0.255201	−	1.44731i	0.00225841	−	0.0128081i	0.985916	+	0.167240i	$0.0534856\pi$
$114$	21.1605	−	133.694i	0.185618	−	1.17275i
$115$	−77.6274	−	92.5128i	−0.675021	−	0.804459i
$116$	−17.4902	−	101.292i	−0.150778	−	0.873206i
$117$	204.208	−	7.89985i	1.74536	−	0.0675201i
$118$	36.6410	−	43.5100i	0.310517	−	0.368729i
$119$	−142.365	+	25.1029i	−1.19635	+	0.210949i
$120$	−27.6315	+	79.3595i	−0.230263	+	0.661329i
$121$	−85.6316	+	31.1674i	−0.707699	+	0.257581i
$122$	−13.9738	−	80.0796i	−0.114539	−	0.656390i
$123$	155.443	−	30.5184i	1.26376	−	0.248117i
$124$	88.1721	+	15.8698i	0.711065	+	0.127983i
$125$	66.0714	−	114.439i	0.528571	−	0.915512i
$126$	−158.590	−	21.9673i	−1.25865	−	0.174344i
$127$	−136.000	+	78.5197i	−1.07087	+	0.618266i	−0.928418	−	0.371537i	$-0.878831\pi$
$127$	−136.000	+	78.5197i	−1.07087	+	0.618266i	−0.142449	+	0.989802i	$0.545498\pi$
$128$	−65.3714	+	110.048i	−0.510714	+	0.859751i
$129$	29.2936	−	0.566406i	0.227082	−	0.00439074i
$130$	149.322	+	54.6489i	1.14863	+	0.420376i
$131$	32.6480	−	38.9084i	0.249222	−	0.297011i	−0.626901	−	0.779099i	$-0.715677\pi$
$131$	32.6480	−	38.9084i	0.249222	−	0.297011i	0.876123	+	0.482088i	$0.160121\pi$
$132$	−33.6861	−	56.2754i	−0.255198	−	0.426329i
$133$	188.559	+	68.6300i	1.41774	+	0.516015i
$134$	−178.062	−	31.7230i	−1.32882	−	0.236738i
$135$	−56.4667	+	75.8197i	−0.418272	+	0.561628i
$136$	−65.6087	+	112.254i	−0.482417	+	0.825396i
$137$	83.6505	+	30.4463i	0.610588	+	0.222236i	0.628760	−	0.777599i	$-0.283563\pi$
$137$	83.6505	+	30.4463i	0.610588	+	0.222236i	−0.0181727	+	0.999835i	$0.505785\pi$
$138$	−39.5093	−	203.143i	−0.286299	−	1.47205i
$139$	44.4026	−	52.9170i	0.319443	−	0.380698i	−0.582297	−	0.812976i	$-0.697846\pi$
$139$	44.4026	−	52.9170i	0.319443	−	0.380698i	0.901740	+	0.432279i	$0.142290\pi$
$140$	−107.662	−	62.6690i	−0.769015	−	0.447636i
$141$	36.1461	+	59.9018i	0.256355	+	0.424836i
$142$	−175.978	+	101.185i	−1.23928	+	0.712572i
$143$	−107.479	+	62.0528i	−0.751599	+	0.433936i
$144$	−107.334	+	95.9973i	−0.745373	+	0.666648i
$145$	44.9883	−	77.9220i	0.310264	−	0.537393i
$146$	64.0099	+	0.113539i	0.438424	+	0.000777666i
$147$	29.2530	−	85.4786i	0.199000	−	0.581487i
$148$	−63.0855	−	0.223800i	−0.426253	−	0.00151216i
$149$	−200.510	+	72.9797i	−1.34571	+	0.489797i	−0.911605	−	0.411067i	$-0.865156\pi$
$149$	−200.510	+	72.9797i	−1.34571	+	0.489797i	−0.434101	+	0.900864i	$0.642934\pi$
$150$	65.5206	−	39.3782i	0.436804	−	0.262521i
$151$	−70.6394	+	12.4556i	−0.467811	+	0.0824877i	−0.402585	−	0.915383i	$-0.631888\pi$
$151$	−70.6394	+	12.4556i	−0.467811	+	0.0824877i	−0.0652263	+	0.997870i	$0.520777\pi$
$152$	156.776	−	89.4056i	1.03142	−	0.588195i
$153$	−108.334	+	98.2841i	−0.708063	+	0.642379i
$154$	91.4246	−	33.0923i	0.593666	−	0.214885i
$155$	50.4077	+	60.0735i	0.325211	+	0.387571i
$156$	178.420	+	205.941i	1.14372	+	1.32014i
$157$	−45.4824	+	257.943i	−0.289697	+	1.64295i	0.398312	+	0.917250i	$0.369596\pi$
$157$	−45.4824	+	257.943i	−0.289697	+	1.64295i	−0.688009	+	0.725702i	$0.741515\pi$
$158$	32.4484	+	38.8101i	0.205370	+	0.245634i
$159$	−12.1480	−	1.90065i	−0.0764023	−	0.0119538i
$160$	−105.622	+	37.3857i	−0.660136	+	0.233661i
$161$	306.791			1.90553
$162$	−147.613	+	66.7405i	−0.911194	+	0.411978i
$163$		−	302.114i		−	1.85346i	−0.375725	−	0.926731i	$-0.622606\pi$
$163$		−	302.114i		−	1.85346i	0.375725	−	0.926731i	$-0.377394\pi$
$164$	161.316	+	136.339i	0.983637	+	0.831333i
$165$	8.87443	−	56.7208i	0.0537844	−	0.343762i
$166$	61.4605	+	73.5102i	0.370244	+	0.442832i
$167$	111.528	+	19.6654i	0.667833	+	0.117757i	0.497278	−	0.867591i	$-0.334333\pi$
$167$	111.528	+	19.6654i	0.667833	+	0.117757i	0.170555	+	0.985348i	$0.445444\pi$
$168$	−109.316	−	183.359i	−0.650690	−	1.09142i
$169$	265.506	−	222.786i	1.57104	−	1.31826i
$170$	−107.017	+	38.7362i	−0.629513	+	0.227860i
$171$	198.440	−	42.9601i	1.16047	−	0.251229i
$172$	25.0045	+	30.0148i	0.145375	+	0.174505i
$173$	−47.6724	−	270.364i	−0.275563	−	1.56280i	−0.737168	−	0.675710i	$-0.763837\pi$
$173$	−47.6724	−	270.364i	−0.275563	−	1.56280i	0.461605	−	0.887086i	$-0.347274\pi$
$174$	132.155	−	79.4258i	0.759512	−	0.456470i
$175$	38.7588	+	106.489i	0.221479	+	0.608509i
$176$	30.4918	−	81.9614i	0.173249	−	0.465690i
$177$	80.7280	+	27.6273i	0.456091	+	0.156086i
$178$	−180.265	−	0.319750i	−1.01272	−	0.00179635i
$179$	42.5533	+	24.5682i	0.237728	+	0.137252i	0.614132	−	0.789203i	$-0.289506\pi$
$179$	42.5533	+	24.5682i	0.237728	+	0.137252i	−0.376404	+	0.926456i	$0.622840\pi$
$180$	−125.971	+	4.42573i	−0.699838	+	0.0245874i
$181$	−71.8830	−	124.505i	−0.397144	−	0.687873i	0.596229	−	0.802815i	$-0.296665\pi$
$181$	−71.8830	−	124.505i	−0.397144	−	0.687873i	−0.993372	+	0.114942i	$0.963332\pi$
$182$	−350.178	+	201.348i	−1.92405	+	1.10631i
$183$	104.400	−	62.9973i	0.570492	−	0.344247i
$184$	178.488	−	210.430i	0.970044	−	1.14364i
$185$	−42.3020	−	35.4956i	−0.228660	−	0.191868i
$186$	25.6555	+	131.912i	0.137933	+	0.709202i
$187$	30.3817	−	83.4731i	0.162469	−	0.446380i
$188$	−32.2156	+	87.5441i	−0.171360	+	0.465660i
$189$	−55.3421	−	233.693i	−0.292815	−	1.23647i
$190$	155.529	+	27.7086i	0.818576	+	0.145835i
$191$	−96.1293	+	264.113i	−0.503295	+	1.38279i	0.384744	+	0.923023i	$0.374290\pi$
$191$	−96.1293	+	264.113i	−0.503295	+	1.38279i	−0.888039	+	0.459768i	$0.847933\pi$
$192$	−189.366	−	31.6960i	−0.986280	−	0.165083i
$193$	133.817	+	112.286i	0.693352	+	0.581791i	0.919874	−	0.392215i	$-0.128291\pi$
$193$	133.817	+	112.286i	0.693352	+	0.581791i	−0.226522	+	0.974006i	$0.572735\pi$
$194$	278.772	+	102.025i	1.43697	+	0.525902i
$195$	4.61088	+	238.467i	0.0236455	+	1.22291i
$196$	113.342	−	40.7982i	0.578274	−	0.208154i
$197$	75.0398	+	129.973i	0.380913	+	0.659761i	0.991193	−	0.132425i	$-0.0422764\pi$
$197$	75.0398	+	129.973i	0.380913	+	0.659761i	−0.610280	+	0.792186i	$0.708943\pi$
$198$	60.4152	−	77.6452i	0.305127	−	0.392148i
$199$	−144.287	−	83.3043i	−0.725062	−	0.418615i	0.0915512	−	0.995800i	$-0.470817\pi$
$199$	−144.287	−	83.3043i	−0.725062	−	0.418615i	−0.816613	+	0.577186i	$0.804151\pi$
$200$	95.5909	+	35.3694i	0.477955	+	0.176847i
$201$	−52.2668	−	266.217i	−0.260034	−	1.32446i
$202$	3.50635	+	20.0939i	0.0173582	+	0.0994746i
$203$	78.1765	+	214.788i	0.385106	+	1.05807i
$204$	−192.579	−	30.8308i	−0.944015	−	0.151132i
$205$	32.1046	+	182.074i	0.156608	+	0.888167i
$206$	18.5862	−	22.0705i	0.0902242	−	0.107138i
$207$	262.634	−	165.488i	1.26876	−	0.799460i
$208$	−65.6246	+	357.331i	−0.315503	+	1.71794i
$209$	−94.4548	+	79.2570i	−0.451937	+	0.379220i
$210$	29.2118	−	184.563i	0.139104	−	0.878869i
$211$	−305.846	−	53.9289i	−1.44951	−	0.255587i	−0.607184	−	0.794561i	$-0.707701\pi$
$211$	−305.846	−	53.9289i	−1.44951	−	0.255587i	−0.842323	+	0.538974i	$0.818812\pi$
$212$	−8.14675	−	14.2269i	−0.0384281	−	0.0671081i
$213$	−236.994	−	191.178i	−1.11265	−	0.897547i
$214$	141.391	+	81.9670i	0.660706	+	0.383023i
$215$			34.1954i			0.159049i
$216$	−192.489	−	98.0008i	−0.891151	−	0.453707i
$217$	−199.216			−0.918046
$218$	193.962	−	334.581i	0.889736	−	1.53477i
$219$	34.5771	+	89.5729i	0.157886	+	0.409008i
$220$	66.4277	−	38.0385i	0.301944	−	0.172902i
$221$	−64.0837	+	363.437i	−0.289971	+	1.64451i
$222$	−33.9213	−	88.3400i	−0.152799	−	0.397928i
$223$	−12.9953	−	15.4873i	−0.0582751	−	0.0694496i	0.736119	−	0.676852i	$-0.236656\pi$
$223$	−12.9953	−	15.4873i	−0.0582751	−	0.0694496i	−0.794395	+	0.607402i	$0.792212\pi$
$224$	99.7173	−	266.590i	0.445166	−	1.19014i
$225$	90.6221	+	70.2547i	0.402765	+	0.312243i
$226$	2.24827	+	1.89333i	0.00994808	+	0.00837754i
$227$	−46.8151	+	8.25477i	−0.206234	+	0.0363646i	−0.275811	−	0.961212i	$-0.588946\pi$
$227$	−46.8151	+	8.25477i	−0.206234	+	0.0363646i	0.0695767	+	0.997577i	$0.477835\pi$
$228$	210.101	+	170.718i	0.921497	+	0.748762i
$229$	66.3275	−	24.1412i	0.289640	−	0.105420i	−0.193114	−	0.981176i	$-0.561859\pi$
$229$	66.3275	−	24.1412i	0.289640	−	0.105420i	0.482754	+	0.875756i	$0.339637\pi$
$230$	237.938	−	41.5199i	1.03451	−	0.180521i
$231$	95.8891	+	109.890i	0.415104	+	0.475714i
$232$	192.807	+	71.3401i	0.831064	+	0.307500i
$233$	−191.622	+	331.898i	−0.822411	+	1.42446i	0.0814716	+	0.996676i	$0.474038\pi$
$233$	−191.622	+	331.898i	−0.822411	+	1.42446i	−0.903882	+	0.427781i	$0.859295\pi$
$234$	−191.166	+	361.259i	−0.816947	+	1.54384i
$235$	−70.7149	+	40.8272i	−0.300914	+	0.173733i
$236$	38.5308	+	107.043i	0.163266	+	0.453570i
$237$	−36.6633	+	66.4366i	−0.154698	+	0.280323i
$238$	99.3678	−	271.511i	0.417512	−	1.14080i
$239$	−220.713	+	263.036i	−0.923486	+	1.10057i	0.0711850	+	0.997463i	$0.477322\pi$
$239$	−220.713	+	263.036i	−0.923486	+	1.10057i	−0.994671	+	0.103104i	$0.967122\pi$
$240$	−109.597	−	127.413i	−0.456655	−	0.530889i
$241$	−226.848	−	82.5658i	−0.941276	−	0.342597i	−0.174607	−	0.984638i	$-0.555865\pi$
$241$	−226.848	−	82.5658i	−0.941276	−	0.342597i	−0.766670	+	0.642042i	$0.778088\pi$
$242$	31.9665	−	179.429i	0.132093	−	0.741443i
$243$	−173.434	−	170.204i	−0.713721	−	0.700430i
$244$	152.576	+	56.1470i	0.625313	+	0.230111i
$245$	99.0848	+	36.0639i	0.404428	+	0.147200i
$246$	−103.115	+	299.571i	−0.419166	+	1.21777i
$247$	329.271	−	392.410i	1.33308	−	1.58871i
$248$	−115.902	+	136.643i	−0.467347	+	0.550981i
$249$	−69.4440	+	125.838i	−0.278892	+	0.505372i
$250$	131.737	+	229.112i	0.526947	+	0.916448i
$251$	36.5452	−	21.0994i	0.145598	−	0.0840612i	−0.425431	−	0.904991i	$-0.639878\pi$
$251$	36.5452	−	21.0994i	0.145598	−	0.0840612i	0.571029	+	0.820930i	$0.306544\pi$
$252$	197.086	−	252.369i	0.782089	−	1.00147i
$253$	−94.2584	+	163.260i	−0.372563	+	0.645298i
$254$	0.557105	−	314.078i	0.00219333	−	1.23653i
$255$	−112.243	−	128.632i	−0.440169	−	0.504438i
$256$	−124.841	−	223.496i	−0.487661	−	0.873033i
$257$	201.446	−	73.3205i	0.783838	−	0.285294i	0.0810661	−	0.996709i	$-0.474168\pi$
$257$	201.446	−	73.3205i	0.783838	−	0.285294i	0.702772	+	0.711415i	$0.251945\pi$
$258$	−28.4035	+	51.2542i	−0.110091	+	0.198660i
$259$	138.151	−	24.3597i	0.533401	−	0.0940530i
$260$	−244.338	+	203.551i	−0.939762	+	0.782889i
$261$	182.785	+	141.704i	0.700325	+	0.542926i
$262$	34.5739	+	95.5179i	0.131962	+	0.364572i
$263$	68.4293	+	81.5508i	0.260187	+	0.310079i	0.880285	−	0.474446i	$-0.157351\pi$
$263$	68.4293	+	81.5508i	0.260187	+	0.310079i	−0.620098	+	0.784525i	$0.712907\pi$
$264$	131.161	−	1.83792i	0.496824	−	0.00696181i
$265$	2.49195	−	14.1326i	0.00940359	−	0.0533304i
$266$	−307.887	+	257.419i	−1.15747	+	0.967740i
$267$	−97.3763	−	252.256i	−0.364705	−	0.944777i
$268$	233.498	−	276.276i	0.871263	−	1.03088i
$269$	−443.421			−1.64841			−0.824203	−	0.566294i	$-0.808377\pi$
$269$	−443.421			−1.64841			−0.824203	+	0.566294i	$0.808377\pi$
$270$	−74.5488	−	173.755i	−0.276107	−	0.643539i
$271$			315.051i			1.16255i	0.813707	+	0.581275i	$0.197446\pi$
$271$			315.051i			1.16255i	−0.813707	+	0.581275i	$0.802554\pi$
$272$	−128.420	−	226.120i	−0.472132	−	0.831322i
$273$	−471.593	−	380.423i	−1.72745	−	1.39349i
$274$	−136.588	+	114.199i	−0.498496	+	0.416783i
$275$	−68.5769	−	12.0920i	−0.249371	−	0.0439708i
$276$	391.123	+	135.405i	1.41711	+	0.490597i
$277$	123.961	−	104.016i	0.447514	−	0.375509i	−0.390999	−	0.920391i	$-0.627870\pi$
$277$	123.961	−	104.016i	0.447514	−	0.375509i	0.838512	+	0.544883i	$0.183426\pi$
$278$	47.0219	+	129.908i	0.169144	+	0.467296i
$279$	−170.542	+	107.460i	−0.611263	+	0.385163i
$280$	216.427	−	123.423i	0.772954	−	0.440798i
$281$	−72.5198	−	411.280i	−0.258078	−	1.46363i	−0.788048	−	0.615614i	$-0.788908\pi$
$281$	−72.5198	−	411.280i	−0.258078	−	1.46363i	0.529970	−	0.848016i	$-0.322203\pi$
$282$	−139.904	+	2.45686i	−0.496112	+	0.00871227i
$283$	−18.4189	−	50.6056i	−0.0650845	−	0.178818i	0.902887	−	0.429878i	$-0.141443\pi$
$283$	−18.4189	−	50.6056i	−0.0650845	−	0.178818i	−0.967972	+	0.251059i	$0.919221\pi$
$284$	1.44026	−	405.986i	0.00507135	−	1.42953i
$285$	45.6527	+	232.528i	0.160185	+	0.815889i
$286$	0.440271	−	248.211i	0.00153941	−	0.867870i
$287$	−406.745	−	234.835i	−1.41723	−	0.818239i
$288$	−58.4385	−	282.009i	−0.202911	−	0.979197i
$289$	12.4263	+	21.5230i	0.0429976	+	0.0744741i
$290$	89.7001	+	156.003i	0.309311	+	0.537943i
$291$	8.60812	+	445.199i	0.0295812	+	1.52989i
$292$	−64.4029	+	110.641i	−0.220558	+	0.378907i
$293$	−188.522	−	158.189i	−0.643419	−	0.539893i	0.261647	−	0.965164i	$-0.415734\pi$
$293$	−188.522	−	158.189i	−0.643419	−	0.539893i	−0.905066	+	0.425271i	$0.860179\pi$
$294$	118.559	+	136.357i	0.403261	+	0.463799i
$295$	−34.0596	+	93.5780i	−0.115456	+	0.317214i
$296$	63.6664	−	108.931i	0.215089	−	0.368009i
$297$	141.364	+	42.3491i	0.475973	+	0.142590i
$298$	74.8509	−	420.142i	0.251178	−	1.40987i
$299$	267.866	−	735.957i	0.895874	−	2.46139i
$300$	2.41330	+	152.868i	0.00804432	+	0.509559i
$301$	−66.5453	−	55.8381i	−0.221081	−	0.185509i
$302$	49.3047	−	134.719i	0.163261	−	0.446091i
$303$	−26.1964	+	15.8075i	−0.0864569	+	0.0521700i
$304$	−2.56099	+	360.945i	−0.00842430	+	1.18732i
$305$	71.1558	+	123.245i	0.233298	+	0.404084i
$306$	−61.3921	−	286.033i	−0.200628	−	0.934748i
$307$	−237.614	−	137.186i	−0.773987	−	0.446861i	0.0603082	−	0.998180i	$-0.480792\pi$
$307$	−237.614	−	137.186i	−0.773987	−	0.446861i	−0.834295	+	0.551318i	$0.814125\pi$
$308$	−34.4466	+	191.384i	−0.111840	+	0.621375i
$309$	40.9494	+	14.0140i	0.132522	+	0.0453527i
$310$	−154.506	+	26.9611i	−0.498407	+	0.0869713i
$311$	4.91549	+	13.5052i	0.0158054	+	0.0434251i	0.947344	−	0.320216i	$-0.103756\pi$
$311$	4.91549	+	13.5052i	0.0158054	+	0.0434251i	−0.931539	+	0.363641i	$0.881533\pi$
$312$	−535.303	+	102.142i	−1.71571	+	0.327377i
$313$	3.07623	+	17.4462i	0.00982822	+	0.0557386i	0.989327	−	0.145709i	$-0.0465464\pi$
$313$	3.07623	+	17.4462i	0.00982822	+	0.0557386i	−0.979499	+	0.201448i	$0.935435\pi$
$314$	−400.691	−	337.433i	−1.27609	−	1.07463i
$315$	273.944	−	59.3059i	0.869663	−	0.188273i
$316$	−99.7001	+	17.2154i	−0.315507	+	0.0544790i
$317$	20.5145	−	17.2137i	0.0647144	−	0.0543018i	−0.609857	−	0.792512i	$-0.708773\pi$
$317$	20.5145	−	17.2137i	0.0647144	−	0.0543018i	0.674571	+	0.738210i	$0.264329\pi$
$318$	15.4739	−	19.1128i	0.0486601	−	0.0601033i
$319$	−138.320	−	24.3895i	−0.433604	−	0.0764560i
$320$	41.2585	−	220.255i	0.128933	−	0.688297i
$321$	−37.8944	+	242.202i	−0.118051	+	0.754522i
$322$	−307.733	+	530.833i	−0.955693	+	1.64855i
$323$			366.653i			1.13515i
$324$	32.5872	−	322.357i	0.100578	−	0.994929i
$325$	289.296			0.890143
$326$	522.741	+	303.042i	1.60350	+	0.929577i
$327$	573.133	+	89.6713i	1.75270	+	0.274224i
$328$	−397.715	+	142.364i	−1.21255	+	0.434038i
$329$	36.0201	−	204.280i	0.109484	−	0.620913i
$330$	89.2409	+	72.2502i	0.270427	+	0.218940i
$331$	171.799	+	204.742i	0.519031	+	0.618557i	0.960351	−	0.278793i	$-0.0899342\pi$
$331$	171.799	+	204.742i	0.519031	+	0.618557i	−0.441320	+	0.897350i	$0.645490\pi$
$332$	−188.842	+	32.6076i	−0.568801	+	0.0982157i
$333$	105.127	−	95.3745i	0.315695	−	0.286410i
$334$	−145.897	+	173.248i	−0.436818	+	0.518708i
$335$	311.827	−	54.9835i	0.930827	−	0.164130i
$336$	426.912	−	5.22479i	1.27057	−	0.0155500i
$337$	−45.3861	+	16.5192i	−0.134677	+	0.0490184i	−0.408479	−	0.912768i	$-0.633941\pi$
$337$	−45.3861	+	16.5192i	−0.134677	+	0.0490184i	0.273802	+	0.961786i	$0.411719\pi$
$338$	119.160	+	682.869i	0.352544	+	2.02032i
$339$	−1.42757	+	4.17141i	−0.00421111	+	0.0123050i
$340$	40.3215	−	224.024i	0.118593	−	0.658895i
$341$	61.2071	−	106.014i	0.179493	−	0.310891i
$342$	−124.717	+	386.448i	−0.364668	+	1.12996i
$343$	145.470	−	83.9870i	0.424110	−	0.244860i
$344$	−77.0151	+	13.1577i	−0.223881	+	0.0382490i
$345$	187.182	+	310.201i	0.542557	+	0.899133i
$346$	515.622	+	188.707i	1.49024	+	0.545397i
$347$	−132.441	+	157.837i	−0.381673	+	0.454860i	−0.922342	−	0.386375i	$-0.873727\pi$
$347$	−132.441	+	157.837i	−0.381673	+	0.454860i	0.540668	+	0.841236i	$0.318171\pi$
$348$	4.86761	+	308.334i	0.0139874	+	0.886018i
$349$	−154.612	−	56.2741i	−0.443013	−	0.161244i	0.110875	−	0.993834i	$-0.464635\pi$
$349$	−154.612	−	56.2741i	−0.443013	−	0.161244i	−0.553889	+	0.832591i	$0.686857\pi$
$350$	−223.133	−	39.7526i	−0.637523	−	0.113579i
$351$	−608.923	−	71.2830i	−1.73482	−	0.203086i
$352$	111.230	+	134.972i	0.315995	+	0.383444i
$353$	448.666	+	163.301i	1.27101	+	0.462609i	0.887449	−	0.460907i	$-0.152476\pi$
$353$	448.666	+	163.301i	1.27101	+	0.462609i	0.383560	+	0.923516i	$0.374698\pi$
$354$	−128.779	+	111.970i	−0.363782	+	0.316298i
$355$	228.432	−	272.234i	0.643470	−	0.766857i
$356$	181.372	−	311.587i	0.509471	−	0.875245i
$357$	433.604	−	8.38393i	1.21458	−	0.0234844i
$358$	−85.1937	+	48.9853i	−0.237971	+	0.136831i
$359$	361.309	−	208.602i	1.00643	−	0.581064i	0.0962869	−	0.995354i	$-0.469303\pi$
$359$	361.309	−	208.602i	1.00643	−	0.581064i	0.910145	+	0.414290i	$0.135970\pi$
$360$	118.700	−	222.403i	0.329722	−	0.617787i
$361$	73.9690	−	128.118i	0.204900	−	0.354898i
$362$	287.532	+	0.510017i	0.794286	+	0.00140889i
$363$	268.260	−	52.6681i	0.739009	−	0.145091i
$364$	2.86597	−	807.870i	0.00787355	−	2.21942i
$365$	−105.302	+	38.3270i	−0.288500	+	0.105005i
$366$	4.28194	+	243.831i	0.0116993	+	0.666206i
$367$	−46.8441	+	8.25989i	−0.127641	+	0.0225065i	−0.237104	−	0.971484i	$-0.576198\pi$
$367$	−46.8441	+	8.25989i	−0.127641	+	0.0225065i	0.109463	+	0.993991i	$0.465087\pi$
$368$	185.065	+	519.909i	0.502893	+	1.41280i
$369$	−474.876	+	18.3707i	−1.28693	+	0.0497852i
$370$	103.849	−	37.5895i	0.280673	−	0.101593i
$371$	23.4332	+	27.9266i	0.0631623	+	0.0752739i
$372$	−253.978	−	87.9255i	−0.682735	−	0.236359i
$373$	−3.14422	+	17.8318i	−0.00842956	+	0.0478064i	−0.988732	−	0.149694i	$-0.952171\pi$
$373$	−3.14422	+	17.8318i	−0.00842956	+	0.0478064i	0.980303	+	0.197500i	$0.0632823\pi$
$374$	113.956	+	136.298i	0.304696	+	0.364434i
$375$	−248.901	+	308.551i	−0.663736	+	0.822803i
$376$	−119.161	−	143.555i	−0.316917	−	0.381795i
$377$	583.510			1.54777
$378$	459.864	+	138.653i	1.21657	+	0.366807i
$379$			492.502i			1.29948i	0.760157	+	0.649739i	$0.225122\pi$
$379$			492.502i			1.29948i	−0.760157	+	0.649739i	$0.774878\pi$
$380$	−203.950	+	241.315i	−0.536712	+	0.635039i
$381$	439.509	−	169.660i	1.15357	−	0.445302i
$382$	−360.564	−	431.254i	−0.943884	−	1.12894i
$383$	−43.2067	−	7.61850i	−0.112811	−	0.0198916i	0.116958	−	0.993137i	$-0.462686\pi$
$383$	−43.2067	−	7.61850i	−0.112811	−	0.0198916i	−0.229769	+	0.973245i	$0.573797\pi$
$384$	244.790	−	295.861i	0.637474	−	0.770472i
$385$	−130.394	+	109.413i	−0.338685	+	0.284190i
$386$	−328.513	+	118.909i	−0.851070	+	0.308056i
$387$	−87.0873	−	11.9056i	−0.225032	−	0.0307639i
$388$	−456.159	+	380.013i	−1.17567	+	0.979415i
$389$	−43.7808	−	248.293i	−0.112547	−	0.638286i	−0.987936	−	0.154866i	$-0.950505\pi$
$389$	−43.7808	−	248.293i	−0.112547	−	0.638286i	0.875388	−	0.483420i	$-0.160606\pi$
$390$	−417.239	−	231.222i	−1.06984	−	0.592876i
$391$	191.729	+	526.771i	0.490355	+	1.34724i
$392$	−43.0976	+	237.036i	−0.109943	+	0.604683i
$393$	−114.810	+	100.182i	−0.292137	+	0.254917i
$394$	−300.159	−	0.532415i	−0.761825	−	0.00135131i
$395$	−76.6975	−	44.2813i	−0.194171	−	0.112105i
$396$	73.7468	+	182.418i	0.186229	+	0.460653i
$397$	62.6518	+	108.516i	0.157813	+	0.273340i	0.934080	−	0.357064i	$-0.116222\pi$
$397$	62.6518	+	108.516i	0.157813	+	0.273340i	−0.776267	+	0.630405i	$0.782889\pi$
$398$	288.870	−	166.096i	0.725803	−	0.417328i
$399$	−527.053	−	290.857i	−1.32094	−	0.728964i
$400$	−157.083	+	129.920i	−0.392708	+	0.324801i
$401$	390.899	+	328.004i	0.974812	+	0.817964i	0.983299	−	0.182000i	$-0.0582571\pi$
$401$	390.899	+	328.004i	0.974812	+	0.817964i	−0.00848695	+	0.999964i	$0.502702\pi$
$402$	513.055	+	176.598i	1.27626	+	0.439299i
$403$	−173.940	+	477.896i	−0.431613	+	1.18585i
$404$	−38.2850	−	14.0886i	−0.0947649	−	0.0348728i
$405$	202.524	−	198.540i	0.500060	−	0.490222i
$406$	−450.059	−	80.1810i	−1.10852	−	0.197490i
$407$	−29.4823	+	81.0020i	−0.0724381	+	0.199022i
$408$	246.516	−	302.289i	0.604206	−	0.740904i
$409$	−518.054	−	434.699i	−1.26664	−	1.06283i	−0.994942	−	0.100451i	$-0.967972\pi$
$409$	−518.054	−	434.699i	−1.26664	−	1.06283i	−0.271694	−	0.962384i	$-0.587584\pi$
$410$	−347.242	−	127.084i	−0.846931	−	0.309960i
$411$	−233.816	−	129.033i	−0.568896	−	0.313948i
$412$	19.5448	+	54.2975i	0.0474389	+	0.131790i
$413$	−126.489	−	219.085i	−0.306269	−	0.530473i
$414$	22.8993	+	620.425i	0.0553124	+	1.49861i
$415$	−145.273	−	83.8732i	−0.350055	−	0.202104i
$416$	−552.455	−	471.977i	−1.32802	−	1.13456i
$417$	−156.146	+	136.252i	−0.374451	+	0.326743i
$418$	−42.3915	−	242.933i	−0.101415	−	0.581180i
$419$	−13.5624	−	37.2623i	−0.0323684	−	0.0889315i	0.922456	−	0.386103i	$-0.126179\pi$
$419$	−13.5624	−	37.2623i	−0.0323684	−	0.0889315i	−0.954824	+	0.297171i	$0.903957\pi$
$420$	290.042	+	235.674i	0.690577	+	0.561128i
$421$	4.01215	+	22.7540i	0.00953005	+	0.0540476i	0.989202	−	0.146559i	$-0.0468198\pi$
$421$	4.01215	+	22.7540i	0.00953005	+	0.0540476i	−0.979672	+	0.200607i	$0.935709\pi$
$422$	400.097	−	475.103i	0.948097	−	1.12584i
$423$	−79.3565	−	194.308i	−0.187604	−	0.459356i
$424$	32.7882	+	0.174479i	0.0773307	+	0.000411506i
$425$	−158.623	+	133.100i	−0.373231	+	0.313178i
$426$	568.511	−	218.300i	1.33453	−	0.512442i
$427$	−356.030	−	62.7777i	−0.833794	−	0.147020i
$428$	−283.651	+	162.427i	−0.662735	+	0.379502i
$429$	347.336	−	134.080i	0.809642	−	0.312540i
$430$	−59.1675	−	34.3004i	−0.137599	−	0.0797685i
$431$		−	617.967i		−	1.43380i	−0.697177	−	0.716899i	$-0.745561\pi$
$431$		−	617.967i		−	1.43380i	0.697177	−	0.716899i	$-0.254439\pi$
$432$	362.648	−	234.756i	0.839463	−	0.543417i
$433$	135.919			0.313902			0.156951	−	0.987606i	$-0.449834\pi$
$433$	135.919			0.313902			0.156951	+	0.987606i	$0.449834\pi$
$434$	199.828	−	344.698i	0.460432	−	0.794235i
$435$	−169.478	+	210.094i	−0.389604	+	0.482974i
$436$	384.358	+	671.216i	0.881556	+	1.53949i
$437$	135.119	−	766.296i	0.309196	−	1.75354i
$438$	−189.669	−	30.0200i	−0.433034	−	0.0685388i
$439$	217.856	+	259.631i	0.496255	+	0.591414i	0.954797	−	0.297259i	$-0.0960725\pi$
$439$	217.856	+	259.631i	0.496255	+	0.591414i	−0.458542	+	0.888673i	$0.651628\pi$
$440$	−0.814668	+	153.093i	−0.00185152	+	0.347940i
$441$	−126.344	+	239.788i	−0.286493	+	0.543737i
$442$	−564.564	−	475.435i	−1.27730	−	1.07564i
$443$	−329.343	+	58.0721i	−0.743439	+	0.131088i	−0.532523	−	0.846416i	$-0.678756\pi$
$443$	−329.343	+	58.0721i	−0.743439	+	0.131088i	−0.210916	+	0.977504i	$0.567645\pi$
$444$	186.878	+	29.9181i	0.420896	+	0.0673832i
$445$	296.553	−	107.937i	0.666412	−	0.242554i
$446$	39.8324	−	6.95071i	0.0893104	−	0.0155845i
$447$	628.144	−	123.325i	1.40524	−	0.275894i
$448$	361.251	+	439.947i	0.806364	+	0.982025i
$449$	33.3868	−	57.8276i	0.0743581	−	0.128792i	−0.826449	−	0.563012i	$-0.809643\pi$
$449$	33.3868	−	57.8276i	0.0743581	−	0.128792i	0.900807	+	0.434220i	$0.142976\pi$
$450$	−212.460	+	86.3307i	−0.472134	+	0.191846i
$451$	249.937	−	144.301i	0.554184	−	0.319958i
$452$	−5.53114	+	1.99098i	−0.0122370	+	0.00440482i
$453$	215.147	−	4.15997i	0.474939	−	0.00918316i
$454$	32.6759	−	89.2831i	0.0719732	−	0.196659i
$455$	454.555	−	541.718i	0.999022	−	1.19059i
$456$	−506.135	+	192.291i	−1.10994	+	0.421691i
$457$	400.777	+	145.871i	0.876974	+	0.319192i	0.740988	−	0.671518i	$-0.234358\pi$
$457$	400.777	+	145.871i	0.876974	+	0.319192i	0.135986	+	0.990711i	$0.456580\pi$
$458$	−24.7602	+	138.980i	−0.0540616	+	0.303450i
$459$	366.672	−	241.070i	0.798850	−	0.525208i
$460$	−166.828	+	453.346i	−0.362670	+	0.985535i
$461$	−107.797	−	39.2350i	−0.233834	−	0.0851084i	0.222446	−	0.974945i	$-0.428596\pi$
$461$	−107.797	−	39.2350i	−0.233834	−	0.0851084i	−0.456279	+	0.889837i	$0.650818\pi$
$462$	−286.323	+	55.6871i	−0.619747	+	0.120535i
$463$	203.177	−	242.137i	0.438827	−	0.522973i	−0.500621	−	0.865667i	$-0.666895\pi$
$463$	203.177	−	242.137i	0.438827	−	0.522973i	0.939447	+	0.342694i	$0.111339\pi$
$464$	−316.837	+	262.049i	−0.682838	+	0.564762i
$465$	−121.547	−	201.430i	−0.261392	−	0.433183i
$466$	−382.065	−	664.476i	−0.819883	−	1.42591i
$467$	−368.289	+	212.632i	−0.788627	+	0.455314i	−0.839479	−	0.543392i	$-0.817140\pi$
$467$	−368.289	+	212.632i	−0.788627	+	0.455314i	0.0508517	+	0.998706i	$0.483806\pi$
$468$	−433.325	−	693.138i	−0.925907	−	1.48106i
$469$	−402.186	+	696.607i	−0.857540	+	1.48530i
$470$	0.289673	−	163.309i	0.000616326	−	0.347465i
$471$	254.424	−	743.438i	0.540178	−	1.57842i
$472$	−223.862	−	40.7024i	−0.474284	−	0.0862338i
$473$	50.1599	−	18.2567i	0.106046	−	0.0385977i
$474$	−78.1777	−	130.078i	−0.164932	−	0.274427i
$475$	283.056	−	49.9105i	0.595908	−	0.105075i
$476$	370.116	+	444.278i	0.777555	+	0.933358i
$477$	35.1245	+	11.2668i	0.0736362	+	0.0236202i
$478$	−233.733	−	645.737i	−0.488981	−	1.35092i
$479$	−100.261	−	119.487i	−0.209314	−	0.249450i	0.651166	−	0.758936i	$-0.274280\pi$
$479$	−100.261	−	119.487i	−0.209314	−	0.249450i	−0.860479	+	0.509485i	$0.829836\pi$
$480$	330.394	−	61.8289i	0.688320	−	0.128810i
$481$	62.1865	−	352.677i	0.129286	−	0.733217i
$482$	370.406	−	309.689i	0.768476	−	0.642509i
$483$	−909.311	−	142.269i	−1.88263	−	0.294553i
$484$	278.397	+	235.291i	0.575201	+	0.486138i
$485$	−519.696			−1.07154
$486$	468.467	−	129.362i	0.963924	−	0.266177i
$487$		−	545.789i		−	1.12072i	−0.828250	−	0.560359i	$-0.810663\pi$
$487$		−	545.789i		−	1.12072i	0.828250	−	0.560359i	$-0.189337\pi$
$488$	−250.195	+	207.680i	−0.512694	+	0.425573i
$489$	−140.100	+	895.449i	−0.286504	+	1.83118i
$490$	−161.790	+	135.269i	−0.330183	+	0.276060i
$491$	193.358	+	34.0942i	0.393804	+	0.0694383i	0.367044	−	0.930204i	$-0.380370\pi$
$491$	193.358	+	34.0942i	0.393804	+	0.0694383i	0.0267601	+	0.999642i	$0.491481\pi$
$492$	−414.908	−	478.908i	−0.843309	−	0.973389i
$493$	−319.942	+	268.464i	−0.648970	+	0.544551i
$494$	348.695	+	963.345i	0.705860	+	1.95009i
$495$	−52.6066	+	164.002i	−0.106276	+	0.331317i
$496$	−120.172	−	337.605i	−0.242283	−	0.680655i
$497$	156.767	+	889.069i	0.315426	+	1.78887i
$498$	−148.076	−	246.381i	−0.297342	−	0.494741i
$499$	329.193	+	904.449i	0.659705	+	1.81252i	0.578270	+	0.815845i	$0.303728\pi$
$499$	329.193	+	904.449i	0.659705	+	1.81252i	0.0814345	+	0.996679i	$0.474050\pi$
$500$	−528.568	−	1.87513i	−1.05714	−	0.00375026i
$501$	−321.443	−	110.006i	−0.641604	−	0.219574i
$502$	−0.149702	+	84.3973i	−0.000298211	+	0.168122i
$503$	379.909	+	219.340i	0.755285	+	0.436064i	0.827600	−	0.561318i	$-0.189705\pi$
$503$	379.909	+	219.340i	0.755285	+	0.436064i	−0.0723150	+	0.997382i	$0.523039\pi$
$504$	238.977	+	594.158i	0.474160	+	1.17888i
$505$	−17.8547	−	30.9252i	−0.0353558	−	0.0612380i
$506$	−187.937	−	326.855i	−0.371418	−	0.645958i
$507$	−890.259	+	537.202i	−1.75594	+	1.05957i
$508$	542.883	+	316.007i	1.06867	+	0.622061i
$509$	−193.632	−	162.477i	−0.380417	−	0.319208i	0.432449	−	0.901658i	$-0.357650\pi$
$509$	−193.632	−	162.477i	−0.380417	−	0.319208i	−0.812866	+	0.582450i	$0.802094\pi$
$510$	335.156	−	65.1846i	0.657169	−	0.127813i
$511$	97.3642	−	267.506i	0.190537	−	0.523495i
$512$	511.935	+	8.17321i	0.999873	+	0.0159633i
$513$	−608.086	+	35.3081i	−1.18535	+	0.0688267i
$514$	−75.2004	+	422.103i	−0.146304	+	0.821213i
$515$	−17.2768	+	47.4676i	−0.0335472	+	0.0921701i
$516$	−60.1930	−	100.557i	−0.116653	−	0.194879i
$517$	97.6420	+	81.9313i	0.188863	+	0.158475i
$518$	−96.4261	+	263.473i	−0.186151	+	0.508636i
$519$	15.9218	+	823.449i	0.0306778	+	1.58661i
$520$	−107.111	−	626.948i	−0.205983	−	1.20567i
$521$	−364.963	−	632.134i	−0.700504	−	1.21331i	−0.968290	−	0.249830i	$-0.919625\pi$
$521$	−364.963	−	632.134i	−0.700504	−	1.21331i	0.267785	−	0.963479i	$-0.413708\pi$
$522$	−428.532	+	174.129i	−0.820943	+	0.333580i
$523$	405.945	+	234.373i	0.776186	+	0.448131i	0.835077	−	0.550133i	$-0.185423\pi$
$523$	405.945	+	234.373i	0.776186	+	0.448131i	−0.0588911	+	0.998264i	$0.518756\pi$
$524$	−199.952	−	35.9888i	−0.381588	−	0.0686810i
$525$	−65.4965	−	333.601i	−0.124755	−	0.635430i
$526$	−209.745	+	36.6002i	−0.398754	+	0.0695821i
$527$	−124.500	−	342.061i	−0.236243	−	0.649071i
$528$	−128.384	+	228.789i	−0.243152	+	0.433312i
$529$	−114.724	−	650.630i	−0.216869	−	1.22992i
$530$	21.9536	+	18.4877i	0.0414219	+	0.0348825i
$531$	−226.462	−	119.322i	−0.426481	−	0.224712i
$532$	−136.572	−	790.939i	−0.256715	−	1.48673i
$533$	−918.481	+	770.697i	−1.72323	+	1.44596i
$534$	534.147	+	84.5425i	1.00027	+	0.158319i
$535$	−281.769	−	49.6836i	−0.526672	−	0.0928665i
$536$	243.818	+	681.141i	0.454885	+	1.27079i
$537$	−114.733	−	92.5521i	−0.213655	−	0.172350i
$538$	444.783	−	767.241i	0.826734	−	1.42610i
$539$		−	164.598i		−	0.305376i
$540$	375.422	+	45.2992i	0.695227	+	0.0838873i
$541$	578.608			1.06952			0.534758	−	0.845005i	$-0.320403\pi$
$541$	578.608			1.06952			0.534758	+	0.845005i	$0.320403\pi$
$542$	−545.125	−	316.019i	−1.00577	−	0.583060i
$543$	155.320	+	402.360i	0.286041	+	0.740995i
$544$	520.063	+	4.61250i	0.955998	+	0.00847886i
$545$	−117.569	+	666.765i	−0.215722	+	1.22342i
$546$	1131.28	−	434.394i	2.07194	−	0.795594i
$547$	−163.148	−	194.432i	−0.298259	−	0.355451i	0.596013	−	0.802975i	$-0.296751\pi$
$547$	−163.148	−	194.432i	−0.298259	−	0.355451i	−0.894272	+	0.447524i	$0.852306\pi$
$548$	−60.5876	−	350.884i	−0.110561	−	0.640299i
$549$	−338.650	+	138.307i	−0.616848	+	0.251924i
$550$	89.7099	−	106.528i	0.163109	−	0.193687i
$551$	570.924	−	100.669i	1.03616	−	0.182703i
$552$	−626.612	+	540.930i	−1.13517	+	0.979946i
$553$	211.413	−	76.9480i	0.382302	−	0.139146i
$554$	55.6341	+	318.822i	0.100422	+	0.575492i
$555$	108.920	+	124.824i	0.196253	+	0.224908i
$556$	−271.943	−	48.9463i	−0.489106	−	0.0880328i
$557$	65.6464	−	113.703i	0.117857	−	0.204135i	−0.801061	−	0.598583i	$-0.795731\pi$
$557$	65.6464	−	113.703i	0.117857	−	0.204135i	0.918918	+	0.394448i	$0.129064\pi$
$558$	−14.8698	−	402.876i	−0.0266483	−	0.721999i
$559$	−192.052	+	110.881i	−0.343563	+	0.198356i
$560$	−3.53541	+	498.281i	−0.00631324	+	0.889787i
$561$	−128.759	+	233.320i	−0.229517	+	0.415901i
$562$	784.370	+	287.064i	1.39568	+	0.510790i
$563$	233.686	−	278.496i	0.415072	−	0.494664i	−0.517482	−	0.855694i	$-0.673130\pi$
$563$	233.686	−	278.496i	0.415072	−	0.494664i	0.932554	+	0.361030i	$0.117575\pi$
$564$	136.082	−	244.536i	0.241281	−	0.433575i
$565$	−4.83540	−	1.75994i	−0.00855823	−	0.00311494i
$566$	106.037	+	18.8912i	0.187344	+	0.0333766i
$567$	55.6599	+	718.315i	0.0981656	+	1.26687i
$568$	701.023	+	409.725i	1.23419	+	0.721347i
$569$	−285.161	−	103.790i	−0.501161	−	0.182408i	0.0790551	−	0.996870i	$-0.474810\pi$
$569$	−285.161	−	103.790i	−0.501161	−	0.182408i	−0.580216	+	0.814463i	$0.697032\pi$
$570$	−448.131	−	154.251i	−0.786194	−	0.270615i
$571$	−186.268	+	221.985i	−0.326213	+	0.388765i	−0.904078	−	0.427367i	$-0.859441\pi$
$571$	−186.268	+	221.985i	−0.326213	+	0.388765i	0.577866	+	0.816132i	$0.303886\pi$
$572$	429.031	+	249.735i	0.750055	+	0.436599i
$573$	407.400	−	738.238i	0.710994	−	1.28837i
$574$	814.323	−	468.226i	1.41868	−	0.815724i
$575$	380.568	−	219.721i	0.661857	−	0.382124i
$576$	546.570	+	181.760i	0.948907	+	0.315556i
$577$	493.417	−	854.624i	0.855143	−	1.48115i	−0.0213695	−	0.999772i	$-0.506803\pi$
$577$	493.417	−	854.624i	0.855143	−	1.48115i	0.876512	−	0.481379i	$-0.159864\pi$
$578$	−49.7052	−	0.0881659i	−0.0859951	−	0.000152536i
$579$	−344.555	−	394.864i	−0.595087	−	0.681975i
$580$	−359.904	−	1.27678i	−0.620525	−	0.00220135i
$581$	400.437	−	145.747i	0.689220	−	0.250856i
$582$	−778.951	−	431.671i	−1.33840	−	0.741703i
$583$	−22.0609	+	3.88993i	−0.0378403	+	0.00667227i
$584$	−126.838	−	222.415i	−0.217189	−	0.380848i
$585$	96.9188	−	708.942i	0.165673	−	1.21187i
$586$	462.810	−	167.520i	0.789779	−	0.285870i
$587$	183.011	+	218.104i	0.311773	+	0.371557i	0.899062	−	0.437820i	$-0.144249\pi$
$587$	183.011	+	218.104i	0.311773	+	0.371557i	−0.587289	+	0.809377i	$0.699805\pi$
$588$	−354.858	+	68.3633i	−0.603499	+	0.116264i
$589$	−87.7398	+	497.597i	−0.148964	+	0.844817i
$590$	−127.751	−	152.798i	−0.216528	−	0.258979i
$591$	−162.141	−	420.030i	−0.274350	−	0.710711i
$592$	124.618	+	219.426i	0.210504	+	0.370651i
$593$	−669.113			−1.12835			−0.564176	−	0.825654i	$-0.690806\pi$
$593$	−669.113			−1.12835			−0.564176	+	0.825654i	$0.690806\pi$
$594$	−215.074	+	202.119i	−0.362077	+	0.340268i
$595$			506.161i			0.850690i
$596$	651.879	+	550.944i	1.09376	+	0.924403i
$597$	389.028	+	313.820i	0.651638	+	0.525661i
$598$	1004.72	+	1201.70i	1.68013	+	2.00953i
$599$	−363.236	−	64.0483i	−0.606404	−	0.106925i	−0.137989	−	0.990434i	$-0.544064\pi$
$599$	−363.236	−	64.0483i	−0.606404	−	0.106925i	−0.468415	+	0.883508i	$0.655175\pi$
$600$	−266.924	−	149.162i	−0.444873	−	0.248603i
$601$	−489.063	+	410.373i	−0.813750	+	0.682817i	−0.951500	−	0.307650i	$-0.900457\pi$
$601$	−489.063	+	410.373i	−0.813750	+	0.682817i	0.137750	+	0.990467i	$0.456013\pi$
$602$	163.365	−	59.1320i	0.271370	−	0.0982259i
$603$	31.4624	+	813.289i	0.0521764	+	1.34874i
$604$	183.646	+	220.444i	0.304049	+	0.364973i
$605$	55.4056	+	314.221i	0.0915795	+	0.519373i
$606$	−1.07444	−	61.1831i	−0.00177300	−	0.100962i
$607$	38.7649	+	106.506i	0.0638631	+	0.175463i	0.967520	−	0.252795i	$-0.0813498\pi$
$607$	38.7649	+	106.506i	0.0638631	+	0.175463i	−0.903657	+	0.428258i	$0.859128\pi$
$608$	−621.966	−	366.485i	−1.02297	−	0.602771i
$609$	−132.106	−	672.873i	−0.216923	−	1.10488i
$610$	−284.623	−	0.504858i	−0.466595	−	0.000827635i
$611$	−458.595	−	264.770i	−0.750565	−	0.433339i
$612$	556.496	+	180.686i	0.909307	+	0.295239i
$613$	132.437	+	229.387i	0.216047	+	0.374204i	0.953596	−	0.301089i	$-0.0973502\pi$
$613$	132.437	+	229.387i	0.216047	+	0.374204i	−0.737549	+	0.675294i	$0.764017\pi$
$614$	475.714	−	273.530i	0.774778	−	0.445488i
$615$	−10.7224	−	554.546i	−0.0174348	−	0.901700i
$616$	−296.594	−	251.573i	−0.481483	−	0.408398i
$617$	616.167	+	517.025i	0.998649	+	0.837966i	0.986797	−	0.161964i	$-0.0517827\pi$
$617$	616.167	+	517.025i	0.998649	+	0.837966i	0.0118524	+	0.999930i	$0.496227\pi$
$618$	−65.3232	+	56.7967i	−0.105701	+	0.0919041i
$619$	266.035	−	730.924i	0.429781	−	1.18081i	−0.516164	−	0.856490i	$-0.672641\pi$
$619$	266.035	−	730.924i	0.429781	−	1.18081i	0.945946	−	0.324325i	$-0.105137\pi$
$620$	108.330	−	294.382i	0.174727	−	0.474809i
$621$	−855.174	+	368.705i	−1.37709	+	0.593728i
$622$	−28.2983	−	5.04152i	−0.0454956	−	0.00810534i
$623$	−274.198	+	753.352i	−0.440125	+	1.20923i
$624$	360.213	−	1028.68i	0.577265	−	1.64852i
$625$	−110.436	−	92.6665i	−0.176697	−	0.148266i
$626$	−33.2724	−	12.1770i	−0.0531507	−	0.0194521i
$627$	316.713	−	191.111i	0.505124	−	0.304803i
$628$	985.772	−	354.836i	1.56970	−	0.565026i
$629$	128.164	+	221.986i	0.203758	+	0.352919i
$630$	−172.170	+	533.486i	−0.273285	+	0.846804i
$631$	56.8376	+	32.8152i	0.0900754	+	0.0520051i	0.544361	−	0.838851i	$-0.316772\pi$
$631$	56.8376	+	32.8152i	0.0900754	+	0.0520051i	−0.454286	+	0.890856i	$0.650105\pi$
$632$	70.2190	−	189.777i	0.111106	−	0.300280i
$633$	881.501	+	301.673i	1.39258	+	0.476576i
$634$	9.20692	+	52.7622i	0.0145220	+	0.0832211i
$635$	188.060	+	516.690i	0.296157	+	0.813684i
$636$	17.5490	+	45.9456i	0.0275928	+	0.0722416i
$637$	118.744	+	673.429i	0.186411	+	1.05719i
$638$	180.945	−	214.866i	0.283613	−	0.336781i
$639$	613.782	+	676.541i	0.960535	+	1.05875i
$640$	339.717	+	292.320i	0.530807	+	0.456750i
$641$	593.381	−	497.905i	0.925711	−	0.776764i	−0.0493316	−	0.998782i	$-0.515709\pi$
$641$	593.381	−	497.905i	0.925711	−	0.776764i	0.975042	+	0.222019i	$0.0712647\pi$
$642$	−381.064	−	308.513i	−0.593558	−	0.480550i
$643$	−1077.13	−	189.927i	−1.67516	−	0.295376i	−0.746247	−	0.665670i	$-0.768146\pi$
$643$	−1077.13	−	189.927i	−1.67516	−	0.295376i	−0.928915	+	0.370293i	$0.879257\pi$
$644$	−609.808	−	1064.93i	−0.946907	−	1.65361i
$645$	15.8575	−	101.353i	0.0245853	−	0.157137i
$646$	−634.411	−	367.779i	−0.982060	−	0.569318i
$647$			1076.11i			1.66323i	0.555356	+	0.831613i	$0.312582\pi$
$647$			1076.11i			1.66323i	−0.555356	+	0.831613i	$0.687418\pi$
$648$	525.079	+	379.732i	0.810307	+	0.586006i
$649$	155.450			0.239522
$650$	−290.185	+	500.562i	−0.446438	+	0.770095i
$651$	590.464	+	92.3829i	0.907011	+	0.141909i
$652$	−1048.69	+	600.512i	−1.60842	+	0.921031i
$653$	−44.4135	+	251.881i	−0.0680145	+	0.385729i	0.931731	+	0.363150i	$0.118299\pi$
$653$	−44.4135	+	251.881i	−0.0680145	+	0.385729i	−0.999745	+	0.0225791i	$0.992812\pi$
$654$	−730.049	+	901.731i	−1.11628	+	1.37879i
$655$	−114.312	−	136.232i	−0.174522	−	0.207987i
$656$	152.607	−	830.958i	0.232633	−	1.26670i
$657$	−60.9467	−	281.523i	−0.0927652	−	0.428498i
$658$	317.330	+	267.232i	0.482265	+	0.406128i
$659$	−672.381	+	118.559i	−1.02030	+	0.179907i	−0.658685	−	0.752418i	$-0.728887\pi$
$659$	−672.381	+	118.559i	−1.02030	+	0.179907i	−0.361620	+	0.932326i	$0.617776\pi$
$660$	−214.528	+	81.9392i	−0.325042	+	0.124150i
$661$	−296.947	+	108.080i	−0.449239	+	0.163510i	−0.556725	−	0.830697i	$-0.687942\pi$
$661$	−296.947	+	108.080i	−0.449239	+	0.163510i	0.107486	+	0.994207i	$0.465720\pi$
$662$	−526.587	+	91.8888i	−0.795449	+	0.138805i
$663$	358.478	−	1047.49i	0.540690	−	1.57992i
$664$	133.002	−	359.456i	0.200304	−	0.541350i
$665$	351.291	−	608.455i	0.528258	−	0.914969i
$666$	59.5746	+	277.565i	0.0894514	+	0.416764i
$667$	767.605	−	443.177i	1.15083	−	0.664433i
$668$	−153.422	−	426.223i	−0.229674	−	0.638058i
$669$	31.3355	+	51.9297i	0.0468393	+	0.0776228i
$670$	−217.648	+	594.698i	−0.324848	+	0.887610i
$671$	142.794	−	170.175i	0.212808	−	0.253615i
$672$	−419.183	+	743.916i	−0.623784	+	1.10702i
$673$	−161.836	−	58.9034i	−0.240469	−	0.0875236i	0.218974	−	0.975731i	$-0.429729\pi$
$673$	−161.836	−	58.9034i	−0.240469	−	0.0875236i	−0.459444	+	0.888207i	$0.651951\pi$
$674$	16.9427	−	95.1003i	0.0251376	−	0.141098i
$675$	−236.019	−	250.255i	−0.349658	−	0.370749i
$676$	−1301.08	−	478.787i	−1.92467	−	0.708265i
$677$	−723.236	−	263.236i	−1.06829	−	0.388828i	−0.252756	−	0.967530i	$-0.581337\pi$
$677$	−723.236	−	263.236i	−1.06829	−	0.388828i	−0.815539	+	0.578702i	$0.803559\pi$
$678$	−5.78573	−	6.65430i	−0.00853353	−	0.00981460i
$679$	848.616	−	1011.34i	1.24980	−	1.48946i
$680$	347.178	+	294.480i	0.510556	+	0.433058i
$681$	142.585	−	2.75695i	0.209376	−	0.00404839i
$682$	122.038	+	212.244i	0.178941	+	0.311209i
$683$	−534.500	+	308.594i	−0.782577	+	0.451821i	−0.837343	−	0.546678i	$-0.815892\pi$
$683$	−534.500	+	308.594i	−0.782577	+	0.451821i	0.0547656	+	0.998499i	$0.482559\pi$
$684$	−543.561	−	603.428i	−0.794679	−	0.882205i
$685$	155.843	−	269.928i	0.227508	−	0.394056i
$686$	−0.595896	+	335.947i	−0.000868653	+	0.489719i
$687$	−207.786	+	40.7950i	−0.302454	+	0.0593813i
$688$	54.4852	−	146.455i	0.0791936	−	0.212871i
$689$	87.4528	−	31.8302i	0.126927	−	0.0461977i
$690$	−724.489	+	12.7228i	−1.04998	+	0.0184389i
$691$	−1107.65	+	195.308i	−1.60296	+	0.282645i	−0.902384	−	0.430933i	$-0.858185\pi$
$691$	−1107.65	+	195.308i	−1.60296	+	0.282645i	−0.700576	+	0.713578i	$0.747074\pi$
$692$	−843.721	+	702.881i	−1.21925	+	1.01572i
$693$	−233.250	−	370.174i	−0.336580	−	0.534162i
$694$	−140.253	−	387.480i	−0.202094	−	0.558328i
$695$	−155.469	−	185.281i	−0.223696	−	0.266591i
$696$	−538.385	−	300.859i	−0.773542	−	0.432268i
$697$	149.024	−	845.156i	0.213807	−	1.21256i
$698$	252.456	−	211.074i	0.361685	−	0.302398i
$699$	721.868	−	894.867i	1.03271	−	1.28021i
$700$	292.601	−	346.207i	0.418002	−	0.494581i
$701$	368.048			0.525032			0.262516	−	0.964928i	$-0.415448\pi$
$701$	368.048			0.525032			0.262516	+	0.964928i	$0.415448\pi$
$702$	734.132	−	982.101i	1.04577	−	1.39900i
$703$		−	355.799i		−	0.506115i
$704$	−345.111	+	57.0722i	−0.490214	+	0.0810685i
$705$	228.528	−	88.2168i	0.324153	−	0.125130i
$706$	−732.599	+	612.513i	−1.03768	+	0.867582i
$707$	89.3364	+	15.7524i	0.126360	+	0.0222806i
$708$	−64.5639	−	335.136i	−0.0911920	−	0.473356i
$709$	−565.166	+	474.230i	−0.797131	+	0.668872i	−0.947499	−	0.319758i	$-0.896398\pi$
$709$	−565.166	+	474.230i	−0.797131	+	0.668872i	0.150369	+	0.988630i	$0.451954\pi$
$710$	241.907	+	668.320i	0.340714	+	0.941296i
$711$	139.477	−	179.912i	0.196170	−	0.253041i
$712$	357.202	+	626.367i	0.501689	+	0.879729i
$713$	134.146	+	760.778i	0.188143	+	1.06701i
$714$	−420.429	+	758.664i	−0.588836	+	1.06255i
$715$	148.620	+	408.331i	0.207861	+	0.571092i
$716$	0.697254	−	196.544i	0.000973818	−	0.274503i
$717$	776.159	−	677.270i	1.08251	−	0.944589i
$718$	−1.48005	+	834.406i	−0.00206135	+	1.16213i
$719$	1138.67	+	657.410i	1.58368	+	0.914340i	0.994315	+	0.106475i	$0.0339563\pi$
$719$	1138.67	+	657.410i	1.58368	+	0.914340i	0.589367	+	0.807865i	$0.299377\pi$
$720$	265.754	+	428.470i	0.369103	+	0.595097i
$721$	−64.1618	−	111.131i	−0.0889900	−	0.154135i
$722$	147.483	+	256.498i	0.204270	+	0.355260i
$723$	634.075	+	349.917i	0.877005	+	0.483979i
$724$	−289.297	+	496.997i	−0.399581	+	0.686460i
$725$	250.806	+	210.451i	0.345939	+	0.290277i
$726$	−177.954	+	516.994i	−0.245116	+	0.712113i
$727$	−64.9919	+	178.564i	−0.0893974	+	0.245617i	−0.976332	−	0.216278i	$-0.930608\pi$
$727$	−64.9919	+	178.564i	−0.0893974	+	0.245617i	0.886934	+	0.461895i	$0.152830\pi$
$728$	1394.96	+	815.309i	1.91616	+	1.11993i
$729$	435.120	+	584.903i	0.596872	+	0.802336i
$730$	39.3097	−	220.647i	0.0538489	−	0.302256i
$731$	54.2885	−	149.156i	0.0742661	−	0.204044i
$732$	−426.190	−	237.171i	−0.582227	−	0.324004i
$733$	42.1532	+	35.3708i	0.0575078	+	0.0482548i	0.671089	−	0.741377i	$-0.265827\pi$
$733$	42.1532	+	35.3708i	0.0575078	+	0.0482548i	−0.613581	+	0.789632i	$0.710271\pi$
$734$	32.6961	−	89.3385i	0.0445451	−	0.121715i
$735$	−276.958	−	152.840i	−0.376813	−	0.207946i
$736$	−1085.22	−	201.293i	−1.47448	−	0.273496i
$737$	−247.135	−	428.051i	−0.335326	−	0.580802i
$738$	444.547	−	840.092i	0.602368	−	1.13834i
$739$	−190.459	−	109.961i	−0.257725	−	0.148798i	0.365571	−	0.930783i	$-0.380874\pi$
$739$	−190.459	−	109.961i	−0.257725	−	0.148798i	−0.623296	+	0.781986i	$0.714207\pi$
$740$	−39.1278	+	217.392i	−0.0528754	+	0.293773i
$741$	−1157.91	+	1010.39i	−1.56264	+	1.36355i
$742$	−71.8258	+	12.5335i	−0.0968003	+	0.0168915i
$743$	−324.288	−	890.974i	−0.436458	−	1.19916i	−0.941781	−	0.336228i	$-0.890849\pi$
$743$	−324.288	−	890.974i	−0.436458	−	1.19916i	0.505323	−	0.862930i	$-0.331373\pi$
$744$	406.893	−	351.255i	0.546899	−	0.472117i
$745$	129.735	+	735.762i	0.174140	+	0.987600i
$746$	−27.7000	−	23.3269i	−0.0371314	−	0.0312693i
$747$	264.183	−	340.772i	0.353659	−	0.456187i
$748$	−350.139	+	60.4591i	−0.468101	+	0.0808276i
$749$	556.790	−	467.202i	0.743378	−	0.623768i
$750$	−284.213	−	740.166i	−0.378951	−	0.986887i
$751$	−462.740	−	81.5936i	−0.616166	−	0.108647i	−0.143150	−	0.989701i	$-0.545723\pi$
$751$	−462.740	−	81.5936i	−0.616166	−	0.108647i	−0.473015	+	0.881054i	$0.656834\pi$
$752$	367.916	−	62.1852i	0.489250	−	0.0826931i
$753$	−118.102	+	45.5901i	−0.156842	+	0.0605446i
$754$	−585.302	+	1009.63i	−0.776263	+	1.33904i
$755$			251.149i			0.332647i
$756$	−701.185	+	656.613i	−0.927493	+	0.868535i
$757$	503.693			0.665380			0.332690	−	0.943036i	$-0.392044\pi$
$757$	503.693			0.665380			0.332690	+	0.943036i	$0.392044\pi$
$758$	−852.164	−	494.015i	−1.12423	−	0.651734i
$759$	355.086	−	440.184i	0.467834	−	0.579952i
$760$	−212.964	−	594.946i	−0.280216	−	0.782824i
$761$	223.541	−	1267.76i	0.293746	−	1.66592i	−0.378509	−	0.925598i	$-0.623563\pi$
$761$	223.541	−	1267.76i	0.293746	−	1.66592i	0.672255	−	0.740320i	$-0.265326\pi$
$762$	−147.300	+	930.652i	−0.193307	+	1.22133i
$763$	−1105.56	−	1317.56i	−1.44897	−	1.72681i
$764$	1107.86	−	191.296i	1.45008	−	0.250387i
$765$	273.031	+	433.308i	0.356904	+	0.566416i
$766$	56.5214	−	67.1175i	0.0737878	−	0.0876207i
$767$	−636.002	+	112.144i	−0.829207	+	0.146212i
$768$	266.379	+	720.324i	0.346848	+	0.937921i
$769$	1172.81	−	426.869i	1.52511	−	0.555096i	0.562695	−	0.826665i	$-0.309765\pi$
$769$	1172.81	−	426.869i	1.52511	−	0.555096i	0.962419	+	0.271569i	$0.0875425\pi$
$770$	−58.5209	−	335.366i	−0.0760012	−	0.435541i
$771$	−631.077	+	123.900i	−0.818517	+	0.160701i
$772$	123.776	−	687.692i	0.160331	−	0.890793i
$773$	−192.043	+	332.627i	−0.248438	+	0.430307i	−0.963093	−	0.269170i	$-0.913251\pi$
$773$	−192.043	+	332.627i	−0.248438	+	0.430307i	0.714655	+	0.699477i	$0.246584\pi$
$774$	107.955	−	138.743i	0.139476	−	0.179254i
$775$	−247.123	+	142.677i	−0.318869	+	0.184099i
$776$	−199.968	−	1170.46i	−0.257690	−	1.50832i
$777$	−420.768	+	8.13574i	−0.541529	+	0.0104707i
$778$	473.531	+	173.303i	0.608651	+	0.222754i
$779$	−765.706	+	912.533i	−0.982934	+	1.17142i
$780$	818.597	−	490.007i	1.04948	−	0.628214i
$781$	−521.288	−	189.733i	−0.667462	−	0.242936i
$782$	−1103.78	−	196.645i	−1.41148	−	0.251464i
$783$	−476.051	−	504.765i	−0.607983	−	0.644655i
$784$	−366.907	−	312.334i	−0.467993	−	0.398385i
$785$	861.775	+	313.661i	1.09780	+	0.399568i
$786$	−58.1803	−	299.143i	−0.0740208	−	0.380589i
$787$	−446.143	+	531.692i	−0.566890	+	0.675594i	−0.970990	−	0.239121i	$-0.923141\pi$
$787$	−446.143	+	531.692i	−0.566890	+	0.675594i	0.404099	+	0.914715i	$0.367585\pi$
$788$	302.002	−	518.823i	0.383251	−	0.658405i
$789$	−165.003	−	273.445i	−0.209129	−	0.346571i
$790$	153.552	−	88.2904i	0.194369	−	0.111760i
$791$	11.3207	−	6.53599i	0.0143118	−	0.00826294i
$792$	−389.607	−	55.3764i	−0.491928	−	0.0699197i
$793$	−461.455	+	799.263i	−0.581910	+	1.00790i
$794$	−250.607	−	0.444521i	−0.315626	−	0.000559850i
$795$	−13.9397	+	40.7325i	−0.0175342	+	0.0512358i
$796$	−2.36421	+	666.430i	−0.00297011	+	0.837224i
$797$	1135.48	−	413.283i	1.42470	−	0.518548i	0.489291	−	0.872120i	$-0.337256\pi$
$797$	1135.48	−	413.283i	1.42470	−	0.518548i	0.935407	+	0.353573i	$0.115033\pi$
$798$	1031.93	−	620.197i	1.29315	−	0.777189i
$799$	373.267	−	65.8170i	0.467168	−	0.0823743i
$800$	−67.2324	−	402.117i	−0.0840405	−	0.502646i
$801$	171.638	+	792.827i	0.214280	+	0.989797i
$802$	−959.636	+	347.352i	−1.19655	+	0.433108i
$803$	112.441	+	134.001i	0.140026	+	0.166876i
$804$	−820.194	+	710.586i	−1.02014	+	0.883813i
$805$	186.530	−	1057.86i	0.231714	−	1.31411i
$806$	−652.418	−	780.328i	−0.809451	−	0.968149i
$807$	1314.28	+	205.629i	1.62859	+	0.254807i
$808$	62.7798	−	52.1117i	0.0776977	−	0.0644947i
$809$	−270.237			−0.334038			−0.167019	−	0.985954i	$-0.553414\pi$
$809$	−270.237			−0.334038			−0.167019	+	0.985954i	$0.553414\pi$
$810$	140.382	+	549.572i	0.173311	+	0.678484i
$811$		−	207.241i		−	0.255538i	−0.991804	−	0.127769i	$-0.959218\pi$
$811$		−	207.241i		−	0.255538i	0.991804	−	0.127769i	$-0.0407816\pi$
$812$	590.176	−	698.299i	0.726818	−	0.859974i
$813$	146.100	−	933.793i	0.179704	−	1.14858i
$814$	−110.583	−	132.263i	−0.135851	−	0.162486i
$815$	−1041.74	−	183.686i	−1.27820	−	0.225382i
$816$	275.770	+	729.758i	0.337953	+	0.894311i
$817$	−168.779	+	141.623i	−0.206584	+	0.173345i
$818$	1271.79	−	460.342i	1.55476	−	0.562765i
$819$	1221.36	+	1346.25i	1.49128	+	1.64377i
$820$	568.197	−	473.349i	0.692924	−	0.577255i
$821$	176.322	+	999.970i	0.214765	+	1.21799i	0.881315	+	0.472530i	$0.156659\pi$
$821$	176.322	+	999.970i	0.214765	+	1.21799i	−0.666550	+	0.745460i	$0.732230\pi$
$822$	457.796	−	275.138i	0.556929	−	0.334717i
$823$	−5.31063	−	14.5908i	−0.00645277	−	0.0177288i	0.936424	−	0.350869i	$-0.114114\pi$
$823$	−5.31063	−	14.5908i	−0.00645277	−	0.0177288i	−0.942877	+	0.333141i	$0.891892\pi$
$824$	−113.554	−	20.6463i	−0.137809	−	0.0250562i
$825$	197.651	+	67.6412i	0.239576	+	0.0819894i
$826$	505.955	+	0.897452i	0.612537	+	0.00108650i
$827$	327.468	+	189.064i	0.395971	+	0.228614i	0.684744	−	0.728784i	$-0.259914\pi$
$827$	327.468	+	189.064i	0.395971	+	0.228614i	−0.288773	+	0.957398i	$0.593247\pi$
$828$	−1096.48	−	582.708i	−1.32425	−	0.703754i
$829$	258.295	+	447.381i	0.311575	+	0.539663i	0.978703	−	0.205279i	$-0.0658102\pi$
$829$	258.295	+	447.381i	0.311575	+	0.539663i	−0.667129	+	0.744942i	$0.732477\pi$
$830$	290.842	−	167.231i	0.350413	−	0.201483i
$831$	−415.650	+	250.812i	−0.500180	+	0.301820i
$832$	1370.80	−	482.472i	1.64760	−	0.579894i
$833$	−374.941	−	314.613i	−0.450110	−	0.377687i
$834$	−79.1276	−	406.846i	−0.0948772	−	0.487825i
$835$	135.619	−	372.610i	0.162418	−	0.446239i
$836$	462.863	+	170.330i	0.553663	+	0.203744i
$837$	555.311	−	239.420i	0.663454	−	0.286046i
$838$	78.0780	+	13.9101i	0.0931719	+	0.0165992i
$839$	−328.333	+	902.088i	−0.391339	+	1.07519i	0.575052	+	0.818117i	$0.304982\pi$
$839$	−328.333	+	902.088i	−0.391339	+	1.07519i	−0.966391	+	0.257077i	$0.917241\pi$
$840$	−698.713	+	265.455i	−0.831801	+	0.316018i
$841$	−138.368	−	116.105i	−0.164528	−	0.138056i
$842$	−43.3952	−	15.8818i	−0.0515382	−	0.0188620i
$843$	24.2204	+	1252.64i	0.0287312	+	1.48593i
$844$	420.733	+	1168.84i	0.498499	+	1.38488i
$845$	−606.773	−	1050.96i	−0.718075	−	1.24374i
$846$	415.806	+	57.5959i	0.491496	+	0.0680803i
$847$	−701.954	−	405.274i	−0.828754	−	0.478481i
$848$	−33.1908	+	56.5576i	−0.0391401	+	0.0666953i
$849$	31.1251	+	158.533i	0.0366610	+	0.186730i
$850$	−71.1903	−	407.970i	−0.0837533	−	0.479965i
$851$	−186.053	−	511.176i	−0.218629	−	0.600677i
$852$	−192.538	+	1202.65i	−0.225983	+	1.41156i
$853$	−112.090	−	635.694i	−0.131407	−	0.745245i	−0.977295	−	0.211884i	$-0.932040\pi$
$853$	−112.090	−	635.694i	−0.131407	−	0.745245i	0.845888	−	0.533361i	$-0.179071\pi$
$854$	465.746	−	553.059i	0.545370	−	0.647611i
$855$	−27.4810	−	710.371i	−0.0321415	−	0.830843i
$856$	3.47869	−	653.719i	0.00406389	−	0.763691i
$857$	−61.7208	+	51.7899i	−0.0720196	+	0.0604316i	−0.678087	−	0.734982i	$-0.737191\pi$
$857$	−61.7208	+	51.7899i	−0.0720196	+	0.0604316i	0.606067	+	0.795413i	$0.292746\pi$
$858$	−116.408	+	735.479i	−0.135674	+	0.857201i
$859$	−152.417	−	26.8752i	−0.177435	−	0.0312866i	0.0842245	−	0.996447i	$-0.473159\pi$
$859$	−152.417	−	26.8752i	−0.177435	−	0.0312866i	−0.261660	+	0.965160i	$0.584270\pi$
$860$	118.698	−	67.9702i	0.138021	−	0.0790351i
$861$	1096.67	+	884.657i	1.27372	+	1.02748i
$862$	1069.25	+	619.865i	1.24043	+	0.719100i
$863$		−	29.9557i		−	0.0347111i	−0.999849	−	0.0173556i	$-0.994475\pi$
$863$		−	29.9557i		−	0.0347111i	0.999849	−	0.0173556i	$-0.00552472\pi$
$864$	42.4315	+	862.957i	0.0491105	+	0.998793i
$865$	−961.240			−1.11126
$866$	−136.337	+	235.178i	−0.157433	+	0.271568i
$867$	−26.8499	−	69.5554i	−0.0309688	−	0.0802254i
$868$	395.981	+	691.513i	0.456200	+	0.796674i
$869$	−24.0062	+	136.146i	−0.0276251	+	0.156670i
$870$	−193.522	−	503.982i	−0.222439	−	0.579290i
$871$	1319.92	+	1573.02i	1.51541	+	1.80600i
$872$	−1546.93	−	8.23178i	−1.77400	−	0.00944012i
$873$	180.939	−	1323.54i	0.207261	−	1.51608i
$874$	1190.37	+	1002.44i	1.36198	+	1.14696i
$875$	1157.51	−	204.100i	1.32287	−	0.233258i
$876$	242.194	−	298.067i	0.276477	−	0.340259i
$877$	−1523.86	+	554.639i	−1.73758	+	0.632428i	−0.999123	−	0.0418712i	$-0.986668\pi$
$877$	−1523.86	+	554.639i	−1.73758	+	0.632428i	−0.738458	+	0.674299i	$0.764446\pi$
$878$	−667.757	+	116.523i	−0.760543	+	0.132714i
$879$	485.410	+	556.286i	0.552230	+	0.632862i
$880$	−264.076	−	154.973i	−0.300087	−	0.176106i
$881$	−123.078	+	213.177i	−0.139703	+	0.241972i	−0.927384	−	0.374111i	$-0.877948\pi$
$881$	−123.078	+	213.177i	−0.139703	+	0.241972i	0.787681	+	0.616083i	$0.211281\pi$
$882$	−288.168	−	459.134i	−0.326721	−	0.520560i
$883$	649.429	−	374.948i	0.735481	−	0.424630i	−0.0849433	−	0.996386i	$-0.527071\pi$
$883$	649.429	−	374.948i	0.735481	−	0.424630i	0.820424	+	0.571756i	$0.193738\pi$
$884$	1388.93	−	499.957i	1.57119	−	0.565562i
$885$	144.346	−	261.565i	0.163103	−	0.295554i
$886$	229.874	−	628.105i	0.259451	−	0.708922i
$887$	102.658	−	122.344i	0.115737	−	0.137930i	−0.705065	−	0.709142i	$-0.749082\pi$
$887$	102.658	−	122.344i	0.115737	−	0.137930i	0.820802	+	0.571213i	$0.193527\pi$
$888$	−239.218	+	293.340i	−0.269390	+	0.330338i
$889$	−1312.58	−	477.739i	−1.47646	−	0.537389i
$890$	−110.704	+	621.387i	−0.124387	+	0.698187i
$891$	−399.356	−	191.075i	−0.448211	−	0.214451i
$892$	−27.9281	+	75.8931i	−0.0313096	+	0.0850820i
$893$	−494.383	−	179.941i	−0.553620	−	0.201501i
$894$	−416.687	+	1210.56i	−0.466093	+	1.35410i
$895$	110.587	−	131.793i	0.123561	−	0.147255i
$896$	−1123.59	+	183.765i	−1.25401	+	0.205095i
$897$	−1135.23	+	2057.12i	−1.26558	+	2.29333i
$898$	66.5683	+	115.773i	0.0741295	+	0.128924i
$899$	−498.447	+	287.779i	−0.554446	+	0.320110i
$900$	63.7369	−	454.210i	0.0708188	−	0.504678i
$901$	−33.3064	+	57.6883i	−0.0369660	+	0.0640270i
$902$	−1.02383	+	577.204i	−0.00113507	+	0.639915i
$903$	171.342	+	196.360i	0.189748	+	0.217453i
$904$	2.10319	−	11.5675i	0.00232654	−	0.0127959i
$905$	−473.017	+	172.164i	−0.522671	+	0.190237i
$906$	−208.610	+	376.437i	−0.230254	+	0.415493i
$907$	372.598	−	65.6990i	0.410802	−	0.0724355i	0.0355719	−	0.999367i	$-0.488675\pi$
$907$	372.598	−	65.6990i	0.410802	−	0.0724355i	0.375230	+	0.926932i	$0.377564\pi$
$908$	121.708	+	146.095i	0.134040	+	0.160898i
$909$	84.9752	−	34.7044i	0.0934820	−	0.0381786i
$910$	481.369	+	1329.89i	0.528977	+	1.46141i
$911$	−819.489	−	976.629i	−0.899549	−	1.07204i	−0.997046	−	0.0768047i	$-0.975528\pi$
$911$	−819.489	−	976.629i	−0.899549	−	1.07204i	0.0974974	−	0.995236i	$-0.468916\pi$
$912$	174.973	−	1068.63i	0.191856	−	1.17175i
$913$	−45.4701	+	257.874i	−0.0498030	+	0.282447i
$914$	−654.404	+	547.135i	−0.715979	+	0.598616i
$915$	−153.749	−	398.290i	−0.168031	−	0.435289i
$916$	−215.637	−	182.249i	−0.235412	−	0.198962i
$917$	451.772			0.492663
$918$	49.3197	+	876.254i	0.0537252	+	0.954525i
$919$		−	552.951i		−	0.601687i	−0.953673	−	0.300844i	$-0.902732\pi$
$919$		−	552.951i		−	0.601687i	0.953673	−	0.300844i	$-0.0972682\pi$
$920$	−617.072	−	743.396i	−0.670731	−	0.808040i
$921$	640.656	+	516.802i	0.695609	+	0.561131i
$922$	176.016	−	147.163i	0.190906	−	0.159613i
$923$	2269.65	+	400.201i	2.45900	+	0.433587i
$924$	190.848	−	551.276i	0.206546	−	0.596619i
$925$	153.927	−	129.160i	0.166408	−	0.139633i
$926$	215.162	+	594.432i	0.232356	+	0.641935i
$927$	−114.873	−	60.5262i	−0.123919	−	0.0652925i
$928$	−135.608	−	811.069i	−0.146129	−	0.873996i
$929$	37.1959	+	210.948i	0.0400386	+	0.227070i	0.998261	−	0.0589551i	$-0.0187769\pi$
$929$	37.1959	+	210.948i	0.0400386	+	0.227070i	−0.958222	+	0.286026i	$0.907666\pi$
$930$	470.450	−	8.26161i	0.505860	−	0.00888345i
$931$	232.365	+	638.417i	0.249586	+	0.685732i
$932$	1532.96	+	5.43829i	1.64481	+	0.00583508i
$933$	−8.30643	−	42.3081i	−0.00890292	−	0.0453463i
$934$	1.50864	−	850.526i	0.00161525	−	0.910627i
$935$	−269.356	−	155.513i	−0.288081	−	0.166324i
$936$	1633.97	−	54.5047i	1.74570	−	0.0582315i
$937$	245.511	+	425.237i	0.262018	+	0.453829i	0.966778	−	0.255617i	$-0.0822787\pi$
$937$	245.511	+	425.237i	0.262018	+	0.453829i	−0.704760	+	0.709446i	$0.748945\pi$
$938$	−801.900	−	1394.64i	−0.854904	−	1.48682i
$939$	−1.02741	−	53.1360i	−0.00109415	−	0.0565879i
$940$	282.278	+	164.311i	0.300296	+	0.174799i
$941$	−1364.30	−	1144.79i	−1.44984	−	1.21656i	−0.932694	−	0.360668i	$-0.882549\pi$
$941$	−1364.30	−	1144.79i	−1.44984	−	1.21656i	−0.517150	−	0.855895i	$-0.673007\pi$
$942$	1031.15	+	1185.94i	1.09463	+	1.25896i
$943$	−622.912	+	1711.44i	−0.660564	+	1.81488i
$944$	294.976	−	346.515i	0.312474	−	0.367071i
$945$	−839.456	+	48.7424i	−0.888313	+	0.0515793i
$946$	−18.7248	+	105.103i	−0.0197937	+	0.111103i
$947$	282.162	−	775.235i	0.297954	−	0.818622i	−0.696887	−	0.717180i	$-0.745432\pi$
$947$	282.162	−	775.235i	0.297954	−	0.818622i	0.994842	−	0.101441i	$-0.0323455\pi$
$948$	303.489	−	4.79112i	0.320136	−	0.00505392i
$949$	−556.706	−	467.131i	−0.586623	−	0.492236i
$950$	−197.567	+	539.829i	−0.207965	+	0.568241i
$951$	−68.7862	+	41.5071i	−0.0723304	+	0.0436457i
$952$	−1139.98	+	194.760i	−1.19745	+	0.204579i
$953$	857.960	+	1486.03i	0.900273	+	1.55932i	0.827140	+	0.561996i	$0.189966\pi$
$953$	857.960	+	1486.03i	0.900273	+	1.55932i	0.0731332	+	0.997322i	$0.476700\pi$
$954$	−54.7270	+	49.4736i	−0.0573659	+	0.0518591i
$955$	852.256	+	492.050i	0.892414	+	0.515236i
$956$	1351.75	+	243.298i	1.41397	+	0.254496i
$957$	398.661	+	136.432i	0.416574	+	0.142563i
$958$	307.314	−	53.6259i	0.320787	−	0.0559769i
$959$	270.810	+	744.044i	0.282388	+	0.775854i
$960$	−224.427	+	633.691i	−0.233779	+	0.660094i
$961$	79.7679	+	452.386i	0.0830050	+	0.470745i
$962$	547.851	+	461.360i	0.569492	+	0.479584i
$963$	224.634	−	700.299i	0.233264	−	0.727205i
$964$	164.304	+	951.543i	0.170440	+	0.987078i
$965$	468.540	−	393.151i	0.485533	−	0.407411i
$966$	1158.27	−	1430.65i	1.19903	−	1.48101i
$967$	−254.880	−	44.9423i	−0.263578	−	0.0464760i	0.0402972	−	0.999188i	$-0.487170\pi$
$967$	−254.880	−	44.9423i	−0.263578	−	0.0464760i	−0.303875	+	0.952712i	$0.598281\pi$
$968$	−686.370	+	245.690i	−0.709060	+	0.253812i
$969$	170.029	−	1086.74i	0.175469	−	1.12151i
$970$	521.291	−	899.216i	0.537414	−	0.927027i
$971$		−	1362.29i		−	1.40298i	−0.712681	−	0.701488i	$-0.752519\pi$
$971$		−	1362.29i		−	1.40298i	0.712681	−	0.701488i	$-0.247481\pi$
$972$	−246.074	+	940.336i	−0.253163	+	0.967424i
$973$	614.428			0.631478
$974$	944.365	+	547.465i	0.969574	+	0.562079i
$975$	−857.457	−	134.156i	−0.879444	−	0.137596i
$976$	−108.380	−	641.223i	−0.111045	−	0.656990i
$977$	−185.676	+	1053.02i	−0.190047	+	1.07781i	0.729251	+	0.684246i	$0.239869\pi$
$977$	−185.676	+	1053.02i	−0.190047	+	1.07781i	−0.919298	+	0.393562i	$0.871243\pi$
$978$	−1408.84	−	1140.61i	−1.44053	−	1.16627i
$979$	−316.656	−	377.375i	−0.323448	−	0.385470i
$980$	−71.7665	−	415.625i	−0.0732311	−	0.424107i
$981$	−1657.15	−	531.561i	−1.68925	−	0.541857i
$982$	−252.944	+	300.363i	−0.257580	+	0.305869i
$983$	−427.195	+	75.3260i	−0.434583	+	0.0766287i	−0.386660	−	0.922222i	$-0.626371\pi$
$983$	−427.195	+	75.3260i	−0.434583	+	0.0766287i	−0.0479229	+	0.998851i	$0.515260\pi$
$984$	1244.82	−	237.526i	1.26506	−	0.241388i
$985$	493.791	−	179.725i	0.501310	−	0.182462i
$986$	−143.591	−	822.876i	−0.145630	−	0.834560i
$987$	−201.493	+	588.771i	−0.204147	+	0.596526i
$988$	−2016.62	−	362.965i	−2.04111	−	0.367374i
$989$	−168.429	+	291.727i	−0.170302	+	0.294972i
$990$	−231.000	−	255.529i	−0.233333	−	0.258110i
$991$	−866.750	+	500.419i	−0.874622	+	0.504963i	−0.868881	−	0.495020i	$-0.835161\pi$
$991$	−866.750	+	500.419i	−0.874622	+	0.504963i	−0.00574052	+	0.999984i	$0.501827\pi$
$992$	704.691	+	130.710i	0.710374	+	0.131765i
$993$	−414.257	−	686.514i	−0.417178	−	0.691353i
$994$	−1695.58	−	620.549i	−1.70582	−	0.624295i
$995$	−374.973	+	446.875i	−0.376857	+	0.449121i
$996$	574.838	−	9.07486i	0.577146	−	0.00911130i
$997$	834.713	+	303.811i	0.837225	+	0.304725i	0.724820	−	0.688938i	$-0.241923\pi$
$997$	834.713	+	303.811i	0.837225	+	0.304725i	0.112404	+	0.993663i	$0.464145\pi$
$998$	−1895.15	−	337.633i	−1.89895	−	0.338310i
$999$	−355.817	+	233.934i	−0.356173	+	0.234168i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.3.j.a.31.13	yes	204
3.2	odd	2		324.3.j.a.307.22		204
4.3	odd	2	inner	108.3.j.a.31.20	yes	204
12.11	even	2		324.3.j.a.307.15		204
27.7	even	9	inner	108.3.j.a.7.20	yes	204
27.20	odd	18		324.3.j.a.19.15		204
108.7	odd	18	inner	108.3.j.a.7.13	✓	204
108.47	even	18		324.3.j.a.19.22		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.j.a.7.13	✓	204	108.7	odd	18	inner
108.3.j.a.7.20	yes	204	27.7	even	9	inner
108.3.j.a.31.13	yes	204	1.1	even	1	trivial
108.3.j.a.31.20	yes	204	4.3	odd	2	inner
324.3.j.a.19.15		204	27.20	odd	18
324.3.j.a.19.22		204	108.47	even	18
324.3.j.a.307.15		204	12.11	even	2
324.3.j.a.307.22		204	3.2	odd	2

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	108.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00307 + 1.73027i) q^{2} +(-2.96394 - 0.463733i) q^{3} +(-1.98770 - 3.47117i) q^{4} +(0.608002 - 3.44815i) q^{5} +(3.77543 - 4.66328i) q^{6} +(5.71739 + 6.81372i) q^{7} +(7.99989 + 0.0425704i) q^{8} +(8.56990 + 2.74895i) q^{9} +(5.35638 + 4.51075i) q^{10} +(-5.38256 + 0.949091i) q^{11} +(4.28173 + 11.2101i) q^{12} +(21.3373 - 7.76615i) q^{13} +(-17.5245 + 3.05801i) q^{14} +(-3.40111 + 9.93818i) q^{15} +(-8.09811 + 13.7993i) q^{16} +(-8.12631 + 14.0752i) q^{17} +(-13.3527 + 12.0709i) q^{18} +(19.5372 - 11.2798i) q^{19} +(-13.1777 + 4.74341i) q^{20} +(-13.7863 - 22.8468i) q^{21} +(3.75690 - 10.2653i) q^{22} +(22.1707 - 26.4221i) q^{23} +(-23.6915 - 3.83599i) q^{24} +(11.9722 + 4.35753i) q^{25} +(-7.96527 + 44.7094i) q^{26} +(-24.1259 - 12.1219i) q^{27} +(12.2872 - 33.3897i) q^{28} +(24.1480 + 8.78914i) q^{29} +(-13.7842 - 15.8535i) q^{30} +(-14.3967 + 17.1573i) q^{31} +(-15.7536 - 27.8536i) q^{32} +(16.3937 - 0.316980i) q^{33} +(-16.2027 - 28.1791i) q^{34} +(26.9709 - 15.5717i) q^{35} +(-7.49228 - 35.2117i) q^{36} +(7.88574 - 13.6585i) q^{37} +(-0.0800315 + 45.1192i) q^{38} +(-66.8440 + 13.1236i) q^{39} +(5.01074 - 27.5590i) q^{40} +(-49.6190 + 18.0598i) q^{41} +(53.3598 - 0.937056i) q^{42} +(-9.61800 + 1.69591i) q^{43} +(13.9934 + 16.7973i) q^{44} +(14.6893 - 27.8790i) q^{45} +(23.4786 + 64.8646i) q^{46} +(-14.9904 - 17.8648i) q^{47} +(30.4015 - 37.1450i) q^{48} +(-5.22945 + 29.6577i) q^{49} +(-19.5487 + 16.3443i) q^{50} +(30.6130 - 37.9496i) q^{51} +(-69.3698 - 58.6288i) q^{52} +4.09859 q^{53} +(45.1742 - 29.5853i) q^{54} +19.1370i q^{55} +(45.4484 + 54.7523i) q^{56} +(-63.1380 + 24.3727i) q^{57} +(-39.4297 + 32.9665i) q^{58} +(-28.0094 - 4.93882i) q^{59} +(41.2575 - 7.94826i) q^{60} +(-31.1357 + 26.1260i) q^{61} +(-15.2459 - 42.1201i) q^{62} +(30.2669 + 74.1097i) q^{63} +(63.9964 + 0.681117i) q^{64} +(-13.8057 - 78.2962i) q^{65} +(-15.8956 + 28.6836i) q^{66} +(30.9299 + 84.9793i) q^{67} +(65.0100 + 0.230627i) q^{68} +(-77.9656 + 68.0321i) q^{69} +(-0.110483 + 62.2866i) q^{70} +(87.8991 + 50.7486i) q^{71} +(68.4412 + 22.3561i) q^{72} +(-16.0025 - 27.7171i) q^{73} +(15.7230 + 27.3449i) q^{74} +(-33.4642 - 18.4674i) q^{75} +(-77.9884 - 45.3963i) q^{76} +(-37.2410 - 31.2489i) q^{77} +(44.3418 - 128.822i) q^{78} +(8.65102 - 23.7685i) q^{79} +(42.6584 + 36.3135i) q^{80} +(65.8865 + 47.1165i) q^{81} +(18.5229 - 103.970i) q^{82} +(16.3859 - 45.0198i) q^{83} +(-51.9023 + 93.2671i) q^{84} +(43.5925 + 36.5785i) q^{85} +(6.71314 - 18.3429i) q^{86} +(-67.4973 - 37.2487i) q^{87} +(-43.1003 + 7.36348i) q^{88} +(45.0663 + 78.0571i) q^{89} +(33.5038 + 53.3812i) q^{90} +(174.910 + 100.984i) q^{91} +(-135.784 - 24.4394i) q^{92} +(50.6272 - 44.1769i) q^{93} +(45.9475 - 8.01777i) q^{94} +(-27.0159 - 74.2255i) q^{95} +(33.7761 + 89.8620i) q^{96} +(-25.7741 - 146.172i) q^{97} +(-46.0705 - 38.7972i) q^{98} +(-48.7371 - 6.66280i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 39 q^{12} - 12 q^{13} + 39 q^{14} - 6 q^{16} - 6 q^{17} - 27 q^{18} - 69 q^{20} - 12 q^{21} - 6 q^{22} - 138 q^{24} - 12 q^{25}+ \cdots + 510 q^{98}+O(q^{100}) \) 204 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 39 * q^12 - 12 * q^13 + 39 * q^14 - 6 * q^16 - 6 * q^17 - 27 * q^18 - 69 * q^20 - 12 * q^21 - 6 * q^22 - 138 * q^24 - 12 * q^25 - 174 * q^26 - 12 * q^28 + 60 * q^29 - 153 * q^30 - 96 * q^32 + 48 * q^33 + 6 * q^34 + 24 * q^36 - 6 * q^37 + 72 * q^38 + 69 * q^40 - 192 * q^41 - 126 * q^42 - 219 * q^44 - 132 * q^45 - 3 * q^46 - 219 * q^48 - 12 * q^49 - 165 * q^50 + 21 * q^52 - 24 * q^53 + 78 * q^54 + 99 * q^56 - 150 * q^57 - 141 * q^58 + 210 * q^60 - 12 * q^61 + 294 * q^62 - 3 * q^64 - 156 * q^65 + 393 * q^66 + 375 * q^68 - 60 * q^69 - 165 * q^70 + 228 * q^72 - 6 * q^73 + 447 * q^74 - 54 * q^76 + 132 * q^77 + 750 * q^78 + 798 * q^80 + 228 * q^81 - 12 * q^82 + 762 * q^84 + 138 * q^85 + 606 * q^86 - 198 * q^88 - 114 * q^89 + 894 * q^90 + 723 * q^92 - 1020 * q^93 - 357 * q^94 + 474 * q^96 + 168 * q^97 + 510 * q^98

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