LMFDB - Embedded newform 196.3.o.a.11.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [196,3,Mod(11,196)] 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("196.11"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(196, base_ring=CyclotomicField(42)) chi = DirichletCharacter(H, H._module([21, 40])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	196.o (of order $42$, degree $12$, 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:	$5.34061318146$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$54$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			11.9
Character	$\chi$	$=$	196.11
Dual form			196.3.o.a.107.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.76080 + 0.948456i) q^{2} +(0.805611 + 5.34488i) q^{3} +(2.20086 - 3.34009i) q^{4} +(2.78087 - 7.08553i) q^{5} +(-6.48790 - 8.64719i) q^{6} +(0.694514 + 6.96546i) q^{7} +(-0.707355 + 7.96867i) q^{8} +(-19.3185 + 5.95898i) q^{9} +(1.82376 + 15.1138i) q^{10} +(-0.991613 + 3.21473i) q^{11} +(19.6254 + 9.07252i) q^{12} +(4.20668 + 18.4307i) q^{13} +(-7.82934 - 11.6061i) q^{14} +(40.1116 + 9.15521i) q^{15} +(-6.31242 - 14.7022i) q^{16} +(-1.92101 + 1.30972i) q^{17} +(28.3643 - 28.8154i) q^{18} +(-24.2216 + 13.9844i) q^{19} +(-17.5460 - 24.8826i) q^{20} +(-36.6700 + 9.32354i) q^{21} +(-1.30299 - 6.60101i) q^{22} +(1.89872 - 2.78491i) q^{23} +(-43.1614 + 2.63892i) q^{24} +(-24.1453 - 22.4035i) q^{25} +(-24.8878 - 28.4629i) q^{26} +(-26.3060 - 54.6250i) q^{27} +(24.7938 + 13.0103i) q^{28} +(35.9152 + 17.2958i) q^{29} +(-79.3120 + 21.9236i) q^{30} +(3.29227 + 1.90079i) q^{31} +(25.0593 + 19.9006i) q^{32} +(-17.9812 - 2.71023i) q^{33} +(2.14031 - 4.12816i) q^{34} +(51.2854 + 14.4490i) q^{35} +(-22.6139 + 77.6406i) q^{36} +(-4.01768 - 53.6122i) q^{37} +(29.3860 - 47.5968i) q^{38} +(-95.1206 + 37.3321i) q^{39} +(54.4952 + 27.1718i) q^{40} +(10.7940 + 13.5352i) q^{41} +(55.7258 - 51.1968i) q^{42} +(-0.880502 - 0.702177i) q^{43} +(8.55509 + 10.3872i) q^{44} +(-11.4997 + 153.453i) q^{45} +(-0.701907 + 6.70453i) q^{46} +(4.79537 + 5.16818i) q^{47} +(73.4959 - 45.5833i) q^{48} +(-48.0353 + 9.67523i) q^{49} +(63.7639 + 16.5475i) q^{50} +(-8.54789 - 9.21244i) q^{51} +(70.8184 + 26.5126i) q^{52} +(-2.08787 + 27.8606i) q^{53} +(98.1292 + 71.2338i) q^{54} +(20.0205 + 15.9658i) q^{55} +(-55.9967 + 0.607301i) q^{56} +(-94.2578 - 118.196i) q^{57} +(-79.6439 + 3.60939i) q^{58} +(57.4630 - 22.5526i) q^{59} +(118.859 - 113.827i) q^{60} +(-0.870448 - 11.6153i) q^{61} +(-7.59986 - 0.224349i) q^{62} +(-54.9241 - 130.424i) q^{63} +(-62.9993 - 11.2733i) q^{64} +(142.289 + 21.4466i) q^{65} +(34.2319 - 12.2822i) q^{66} +(88.7130 + 51.2185i) q^{67} +(0.146716 + 9.29887i) q^{68} +(16.4146 + 7.90486i) q^{69} +(-104.008 + 23.2000i) q^{70} +(-24.0343 - 49.9078i) q^{71} +(-33.8201 - 158.158i) q^{72} +(18.7519 + 17.3992i) q^{73} +(57.9231 + 90.5899i) q^{74} +(100.292 - 147.102i) q^{75} +(-6.59939 + 111.680i) q^{76} +(-23.0808 - 4.67436i) q^{77} +(132.081 - 155.952i) q^{78} +(-38.0545 + 21.9708i) q^{79} +(-121.727 + 3.84212i) q^{80} +(120.437 - 82.1125i) q^{81} +(-31.8437 - 13.5953i) q^{82} +(-1.86865 - 0.426506i) q^{83} +(-49.5642 + 143.001i) q^{84} +(3.93801 + 17.2535i) q^{85} +(2.21638 + 0.401278i) q^{86} +(-63.5105 + 205.896i) q^{87} +(-24.9157 - 10.1758i) q^{88} +(88.8490 - 27.4063i) q^{89} +(-125.295 - 281.108i) q^{90} +(-125.456 + 42.1018i) q^{91} +(-5.12303 - 12.4711i) q^{92} +(-7.50721 + 19.1281i) q^{93} +(-13.3455 - 4.55195i) q^{94} +(31.7295 + 210.512i) q^{95} +(-86.1780 + 149.971i) q^{96} +72.5196 q^{97} +(75.4042 - 62.5956i) q^{98} -68.0129i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q - 13 q^{2} - 13 q^{4} - 26 q^{5} - 2 q^{6} - 16 q^{8} - 176 q^{9} - 12 q^{10} + 45 q^{12} - 4 q^{13} + 89 q^{14} - 25 q^{16} - 26 q^{17} - 48 q^{18} - 166 q^{20} + 50 q^{21} + 10 q^{22} - 96 q^{24}+ \cdots + 771 q^{98}+O(q^{100}) $ 648 * q - 13 * q^2 - 13 * q^4 - 26 * q^5 - 2 * q^6 - 16 * q^8 - 176 * q^9 - 12 * q^10 + 45 * q^12 - 4 * q^13 + 89 * q^14 - 25 * q^16 - 26 * q^17 - 48 * q^18 - 166 * q^20 + 50 * q^21 + 10 * q^22 - 96 * q^24 + 212 * q^25 - 70 * q^26 + 188 * q^28 + 100 * q^29 + 57 * q^30 + 57 * q^32 - 14 * q^33 - 230 * q^34 - 44 * q^36 - 346 * q^37 - 40 * q^38 - 258 * q^40 - 36 * q^41 - 82 * q^42 - 366 * q^44 - 184 * q^45 - 100 * q^46 - 540 * q^48 - 136 * q^49 - 112 * q^50 + 50 * q^52 - 34 * q^53 - 259 * q^54 + 600 * q^56 + 34 * q^57 + 100 * q^58 + 562 * q^60 + 278 * q^61 + 490 * q^62 - 100 * q^64 + 64 * q^65 + 1340 * q^66 + 61 * q^68 + 160 * q^69 + 666 * q^70 - 412 * q^72 + 206 * q^73 - 202 * q^74 - 177 * q^76 + 234 * q^77 - 632 * q^78 - 364 * q^80 + 618 * q^81 - 2246 * q^82 - 1988 * q^84 - 264 * q^85 - 1025 * q^86 - 1283 * q^88 - 34 * q^89 - 1124 * q^90 - 910 * q^92 - 268 * q^93 + 94 * q^94 - 814 * q^96 - 800 * q^97 + 771 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$-1$	$e\left(\frac{20}{21}\right)$

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 $

$2$	−1.76080	+	0.948456i	−0.880402	+	0.474228i
$2$	−1.76080	+	0.948456i	−0.880402	+	0.474228i
$3$	0.805611	+	5.34488i	0.268537	+	1.78163i	0.563499	+	0.826117i	$0.309455\pi$
$3$	0.805611	+	5.34488i	0.268537	+	1.78163i	−0.294962	+	0.955509i	$0.595307\pi$
$4$	2.20086	−	3.34009i	0.550215	−	0.835023i
$5$	2.78087	−	7.08553i	0.556173	−	1.41711i	−0.325634	−	0.945496i	$-0.605578\pi$
$5$	2.78087	−	7.08553i	0.556173	−	1.41711i	0.881807	−	0.471611i	$-0.156327\pi$
$6$	−6.48790	−	8.64719i	−1.08132	−	1.44120i
$7$	0.694514	+	6.96546i	0.0992163	+	0.995066i
$7$	0.694514	+	6.96546i	0.0992163	+	0.995066i
$8$	−0.707355	+	7.96867i	−0.0884193	+	0.996083i
$9$	−19.3185	+	5.95898i	−2.14651	+	0.662109i
$10$	1.82376	+	15.1138i	0.182376	+	1.51138i
$11$	−0.991613	+	3.21473i	−0.0901466	+	0.292248i	−0.989408	−	0.145164i	$-0.953629\pi$
$11$	−0.991613	+	3.21473i	−0.0901466	+	0.292248i	0.899261	+	0.437413i	$0.144105\pi$
$12$	19.6254	+	9.07252i	1.63545	+	0.756043i
$13$	4.20668	+	18.4307i	0.323590	+	1.41774i	0.831113	+	0.556104i	$0.187704\pi$
$13$	4.20668	+	18.4307i	0.323590	+	1.41774i	−0.507522	+	0.861639i	$0.669439\pi$
$14$	−7.82934	−	11.6061i	−0.559239	−	0.829007i
$15$	40.1116	+	9.15521i	2.67411	+	0.610347i
$16$	−6.31242	−	14.7022i	−0.394526	−	0.918885i
$17$	−1.92101	+	1.30972i	−0.113001	+	0.0770425i	−0.618502	−	0.785783i	$-0.712260\pi$
$17$	−1.92101	+	1.30972i	−0.113001	+	0.0770425i	0.505501	+	0.862826i	$0.331308\pi$
$18$	28.3643	−	28.8154i	1.57580	−	1.60086i
$19$	−24.2216	+	13.9844i	−1.27482	+	0.736019i	−0.975891	−	0.218257i	$-0.929963\pi$
$19$	−24.2216	+	13.9844i	−1.27482	+	0.736019i	−0.298930	+	0.954275i	$0.596630\pi$
$20$	−17.5460	−	24.8826i	−0.877301	−	1.24413i
$21$	−36.6700	+	9.32354i	−1.74619	+	0.443978i
$22$	−1.30299	−	6.60101i	−0.0592270	−	0.300046i
$23$	1.89872	−	2.78491i	0.0825529	−	0.121083i	−0.782741	−	0.622347i	$-0.786179\pi$
$23$	1.89872	−	2.78491i	0.0825529	−	0.121083i	0.865294	+	0.501264i	$0.167132\pi$
$24$	−43.1614	+	2.63892i	−1.79839	+	0.109955i
$25$	−24.1453	−	22.4035i	−0.965811	−	0.896141i
$26$	−24.8878	−	28.4629i	−0.957223	−	1.09473i
$27$	−26.3060	−	54.6250i	−0.974297	−	2.02315i
$28$	24.7938	+	13.0103i	0.885493	+	0.464653i
$29$	35.9152	+	17.2958i	1.23845	+	0.596408i	0.934393	−	0.356245i	$-0.115943\pi$
$29$	35.9152	+	17.2958i	1.23845	+	0.596408i	0.304061	+	0.952653i	$0.401657\pi$
$30$	−79.3120	+	21.9236i	−2.64373	+	0.730786i
$31$	3.29227	+	1.90079i	0.106202	+	0.0613159i	0.552160	−	0.833738i	$-0.313804\pi$
$31$	3.29227	+	1.90079i	0.106202	+	0.0613159i	−0.445958	+	0.895054i	$0.647137\pi$
$32$	25.0593	+	19.9006i	0.783103	+	0.621892i
$33$	−17.9812	−	2.71023i	−0.544884	−	0.0821281i
$34$	2.14031	−	4.12816i	0.0629502	−	0.121416i
$35$	51.2854	+	14.4490i	1.46530	+	0.412829i
$36$	−22.6139	+	77.6406i	−0.628164	+	2.15668i
$37$	−4.01768	−	53.6122i	−0.108586	−	1.44898i	−0.739517	−	0.673138i	$-0.764946\pi$
$37$	−4.01768	−	53.6122i	−0.108586	−	1.44898i	0.630931	−	0.775839i	$-0.282673\pi$
$38$	29.3860	−	47.5968i	0.773315	−	1.25255i
$39$	−95.1206	+	37.3321i	−2.43899	+	0.957233i
$40$	54.4952	+	27.1718i	1.36238	+	0.679295i
$41$	10.7940	+	13.5352i	0.263268	+	0.330128i	0.895842	−	0.444372i	$-0.146573\pi$
$41$	10.7940	+	13.5352i	0.263268	+	0.330128i	−0.632574	+	0.774500i	$0.718002\pi$
$42$	55.7258	−	51.1968i	1.32680	−	1.21897i
$43$	−0.880502	−	0.702177i	−0.0204768	−	0.0163297i	0.613198	−	0.789929i	$-0.289883\pi$
$43$	−0.880502	−	0.702177i	−0.0204768	−	0.0163297i	−0.633675	+	0.773600i	$0.718454\pi$
$44$	8.55509	+	10.3872i	0.194434	+	0.236074i
$45$	−11.4997	+	153.453i	−0.255550	+	3.41007i
$46$	−0.701907	+	6.70453i	−0.0152588	+	0.145751i
$47$	4.79537	+	5.16818i	0.102029	+	0.109961i	0.782002	−	0.623276i	$-0.214199\pi$
$47$	4.79537	+	5.16818i	0.102029	+	0.109961i	−0.679973	+	0.733238i	$0.738008\pi$
$48$	73.4959	−	45.5833i	1.53116	−	0.949652i
$49$	−48.0353	+	9.67523i	−0.980312	+	0.197454i
$50$	63.7639	+	16.5475i	1.27528	+	0.330950i
$51$	−8.54789	−	9.21244i	−0.167606	−	0.180636i
$52$	70.8184	+	26.5126i	1.36189	+	0.509858i
$53$	−2.08787	+	27.8606i	−0.0393937	+	0.525672i	0.942245	+	0.334924i	$0.108711\pi$
$53$	−2.08787	+	27.8606i	−0.0393937	+	0.525672i	−0.981639	+	0.190749i	$0.938908\pi$
$54$	98.1292	+	71.2338i	1.81721	+	1.31914i
$55$	20.0205	+	15.9658i	0.364010	+	0.290288i
$56$	−55.9967	+	0.607301i	−0.999941	+	0.0108447i
$57$	−94.2578	−	118.196i	−1.65365	−	2.07361i
$58$	−79.6439	+	3.60939i	−1.37317	+	0.0622309i
$59$	57.4630	−	22.5526i	0.973950	−	0.382247i	0.175614	−	0.984459i	$-0.443809\pi$
$59$	57.4630	−	22.5526i	0.973950	−	0.382247i	0.798336	+	0.602212i	$0.205714\pi$
$60$	118.859	−	113.827i	1.98099	−	1.89712i
$61$	−0.870448	−	11.6153i	−0.0142696	−	0.190415i	−0.999783	−	0.0208189i	$-0.993373\pi$
$61$	−0.870448	−	11.6153i	−0.0142696	−	0.190415i	0.985514	−	0.169596i	$-0.0542464\pi$
$62$	−7.59986	−	0.224349i	−0.122578	−	0.00361854i
$63$	−54.9241	−	130.424i	−0.871811	−	2.07022i
$64$	−62.9993	−	11.2733i	−0.984364	−	0.176146i
$65$	142.289	+	21.4466i	2.18906	+	0.329948i
$66$	34.2319	−	12.2822i	0.518665	−	0.186094i
$67$	88.7130	+	51.2185i	1.32407	+	0.764455i	0.984376	−	0.176080i	$-0.0563416\pi$
$67$	88.7130	+	51.2185i	1.32407	+	0.764455i	0.339698	+	0.940534i	$0.389675\pi$
$68$	0.146716	+	9.29887i	0.00215759	+	0.136748i
$69$	16.4146	+	7.90486i	0.237893	+	0.114563i
$70$	−104.008	+	23.2000i	−1.48582	+	0.331429i
$71$	−24.0343	−	49.9078i	−0.338512	−	0.702927i	0.660334	−	0.750972i	$-0.270415\pi$
$71$	−24.0343	−	49.9078i	−0.338512	−	0.702927i	−0.998845	+	0.0480459i	$0.984701\pi$
$72$	−33.8201	−	158.158i	−0.469723	−	2.19664i
$73$	18.7519	+	17.3992i	0.256876	+	0.238346i	0.798089	−	0.602539i	$-0.205844\pi$
$73$	18.7519	+	17.3992i	0.256876	+	0.238346i	−0.541213	+	0.840885i	$0.682035\pi$
$74$	57.9231	+	90.5899i	0.782745	+	1.22419i
$75$	100.292	−	147.102i	1.33723	−	1.96136i
$76$	−6.59939	+	111.680i	−0.0868341	+	1.46947i
$77$	−23.0808	−	4.67436i	−0.299750	−	0.0607060i
$78$	132.081	−	155.952i	1.69335	−	1.99939i
$79$	−38.0545	+	21.9708i	−0.481703	+	0.278111i	−0.721126	−	0.692804i	$-0.756375\pi$
$79$	−38.0545	+	21.9708i	−0.481703	+	0.278111i	0.239423	+	0.970915i	$0.423042\pi$
$80$	−121.727	+	3.84212i	−1.52158	+	0.0480265i
$81$	120.437	−	82.1125i	1.48688	−	1.01373i
$82$	−31.8437	−	13.5953i	−0.388338	−	0.165796i
$83$	−1.86865	−	0.426506i	−0.0225138	−	0.00513863i	0.211249	−	0.977432i	$-0.432247\pi$
$83$	−1.86865	−	0.426506i	−0.0225138	−	0.00513863i	−0.233763	+	0.972294i	$0.575104\pi$
$84$	−49.5642	+	143.001i	−0.590049	+	1.70239i
$85$	3.93801	+	17.2535i	0.0463295	+	0.202983i
$86$	2.21638	+	0.401278i	0.0257718	+	0.00466602i
$87$	−63.5105	+	205.896i	−0.730005	+	2.36662i
$88$	−24.9157	−	10.1758i	−0.283133	−	0.115634i
$89$	88.8490	−	27.4063i	0.998304	−	0.307936i	0.247806	−	0.968810i	$-0.420290\pi$
$89$	88.8490	−	27.4063i	0.998304	−	0.307936i	0.750497	+	0.660874i	$0.229814\pi$
$90$	−125.295	−	281.108i	−1.39217	−	3.12343i
$91$	−125.456	+	42.1018i	−1.37864	+	0.462657i
$92$	−5.12303	−	12.4711i	−0.0556851	−	0.135555i
$93$	−7.50721	+	19.1281i	−0.0807227	+	0.205678i
$94$	−13.3455	−	4.55195i	−0.141973	−	0.0484250i
$95$	31.7295	+	210.512i	0.333995	+	2.21591i
$96$	−86.1780	+	149.971i	−0.897688	+	1.56220i
$97$	72.5196			0.747624			0.373812	−	0.927504i	$-0.378050\pi$
$97$	72.5196			0.747624			0.373812	+	0.927504i	$0.378050\pi$
$98$	75.4042	−	62.5956i	0.769431	−	0.638730i
$99$		−	68.0129i		−	0.686999i
$100$	−127.970	+	31.3403i	−1.27970	+	0.313403i
$101$	131.386	−	19.8033i	1.30086	−	0.196072i	0.538167	−	0.842838i	$-0.319117\pi$
$101$	131.386	−	19.8033i	1.30086	−	0.196072i	0.762688	+	0.646766i	$0.223879\pi$
$102$	23.7888	+	8.11399i	0.233223	+	0.0795489i
$103$	104.892	+	41.1671i	1.01837	+	0.399680i	0.815024	−	0.579427i	$-0.196724\pi$
$103$	104.892	+	41.1671i	1.01837	+	0.399680i	0.203345	+	0.979107i	$0.434819\pi$
$104$	−149.843	+	20.4846i	−1.44080	+	0.196967i
$105$	−35.9122	+	285.754i	−0.342021	+	2.72147i
$106$	−22.7483	−	51.0374i	−0.214606	−	0.481485i
$107$	−6.98335	−	22.6395i	−0.0652650	−	0.211584i	0.917066	−	0.398735i	$-0.130551\pi$
$107$	−6.98335	−	22.6395i	−0.0652650	−	0.211584i	−0.982331	+	0.187151i	$0.940075\pi$
$108$	−240.348	−	32.3576i	−2.22545	−	0.299607i
$109$	−165.951	−	51.1891i	−1.52249	−	0.469625i	−0.583076	−	0.812418i	$-0.698151\pi$
$109$	−165.951	−	51.1891i	−1.52249	−	0.469625i	−0.939411	+	0.342792i	$0.888627\pi$
$110$	−50.3951	−	9.12411i	−0.458137	−	0.0829465i
$111$	283.314	−	64.6645i	2.55238	−	0.582563i
$112$	98.0232	−	54.1798i	0.875207	−	0.483748i
$113$	36.2284	−	158.727i	0.320605	−	1.40466i	−0.515874	−	0.856664i	$-0.672533\pi$
$113$	36.2284	−	158.727i	0.320605	−	1.40466i	0.836479	−	0.547999i	$-0.184610\pi$
$114$	278.073	+	118.720i	2.43924	+	1.04140i
$115$	−14.4525	−	21.1979i	−0.125674	−	0.184329i
$116$	136.814	−	81.8942i	1.17943	−	0.705984i
$117$	−191.095	−	330.986i	−1.63329	−	2.82894i
$118$	−79.7910	+	94.2119i	−0.676195	+	0.798406i
$119$	−10.4570	−	12.4711i	−0.0878739	−	0.104799i
$120$	−101.328	+	313.160i	−0.844400	+	2.60967i
$121$	90.6237	+	61.7862i	0.748956	+	0.510630i
$122$	12.5493	+	19.6267i	0.102863	+	0.160875i
$123$	−63.6485	+	68.5967i	−0.517467	+	0.557697i
$124$	13.5946	−	6.81310i	0.109634	−	0.0549443i
$125$	−54.4381	+	26.2160i	−0.435505	+	0.209728i
$126$	220.412	+	177.558i	1.74930	+	1.40919i
$127$	−83.1069	+	172.573i	−0.654385	+	1.35884i	0.264526	+	0.964379i	$0.414785\pi$
$127$	−83.1069	+	172.573i	−0.654385	+	1.35884i	−0.918911	+	0.394466i	$0.870930\pi$
$128$	121.622	−	39.9019i	0.950169	−	0.311734i
$129$	3.04371	−	5.27186i	0.0235946	−	0.0408671i
$130$	−270.885	+	97.1917i	−2.08373	+	0.747629i
$131$	23.2214	−	154.064i	0.177263	−	1.17606i	−0.706357	−	0.707856i	$-0.749663\pi$
$131$	23.2214	−	154.064i	0.177263	−	1.17606i	0.883619	−	0.468206i	$-0.155099\pi$
$132$	−48.6265	+	54.0940i	−0.368383	+	0.409803i
$133$	−114.230	−	159.002i	−0.858870	−	1.19551i
$134$	−204.785	−	6.04529i	−1.52824	−	0.0451141i
$135$	−460.201	+	34.4873i	−3.40889	+	0.255461i
$136$	−9.07791	−	16.2343i	−0.0667493	−	0.119370i
$137$	38.8136	+	98.8955i	0.283311	+	0.721865i	0.999708	+	0.0241717i	$0.00769484\pi$
$137$	38.8136	+	98.8955i	0.283311	+	0.721865i	−0.716397	+	0.697693i	$0.754210\pi$
$138$	−36.4003	+	1.64963i	−0.263771	+	0.0119539i
$139$	−69.1963	+	55.1822i	−0.497815	+	0.396994i	−0.839956	−	0.542654i	$-0.817419\pi$
$139$	−69.1963	+	55.1822i	−0.497815	+	0.396994i	0.342141	+	0.939649i	$0.388848\pi$
$140$	161.133	−	139.498i	1.15095	−	0.996411i
$141$	−23.7601	+	29.7942i	−0.168511	+	0.211306i
$142$	89.6551	+	65.0823i	0.631374	+	0.458326i
$143$	−63.4209	−	4.75274i	−0.443503	−	0.0332360i
$144$	209.557	+	246.409i	1.45525	+	1.71117i
$145$	222.425	−	206.381i	1.53397	−	1.42331i
$146$	−49.5209	−	12.8513i	−0.339184	−	0.0880225i
$147$	−90.4106	−	248.948i	−0.615038	−	1.69353i
$148$	−187.912	−	104.574i	−1.26967	−	0.706578i
$149$	−110.436	+	102.470i	−0.741184	+	0.687718i	−0.957444	−	0.288617i	$-0.906804\pi$
$149$	−110.436	+	102.470i	−0.741184	+	0.687718i	0.216260	+	0.976336i	$0.430614\pi$
$150$	−37.0755	+	354.141i	−0.247170	+	2.36094i
$151$	160.146	+	12.0013i	1.06057	+	0.0794788i	0.593574	−	0.804780i	$-0.297717\pi$
$151$	160.146	+	12.0013i	1.06057	+	0.0794788i	0.466998	+	0.884259i	$0.345336\pi$
$152$	−94.3034	−	202.906i	−0.620417	−	1.33491i
$153$	29.3065	−	36.7492i	0.191546	−	0.240191i
$154$	45.0741	−	13.6605i	0.292689	−	0.0887042i
$155$	22.6235	−	18.0416i	0.145958	−	0.116398i
$156$	−84.6547	+	399.874i	−0.542658	+	2.56330i
$157$	−70.3537	−	179.258i	−0.448112	−	1.14177i	−0.959322	−	0.282316i	$-0.908897\pi$
$157$	−70.3537	−	179.258i	−0.448112	−	1.14177i	0.511209	−	0.859456i	$-0.329198\pi$
$158$	46.1682	−	74.7793i	0.292204	−	0.473286i
$159$	−150.594	+	11.2854i	−0.947130	+	0.0709776i
$160$	210.693	−	122.218i	1.31683	−	0.763860i
$161$	20.7168	+	11.2913i	0.128676	+	0.0701322i
$162$	−134.186	+	258.813i	−0.828307	+	1.59761i
$163$	9.29001	−	61.6352i	0.0569939	−	0.378130i	−0.942091	−	0.335358i	$-0.891143\pi$
$163$	9.29001	−	61.6352i	0.0569939	−	0.378130i	0.999085	−	0.0427724i	$-0.0136190\pi$
$164$	68.9651	−	6.26374i	0.420519	−	0.0381935i
$165$	−69.2067	+	119.870i	−0.419434	+	0.726482i
$166$	3.69484	−	1.02133i	0.0222581	−	0.00615262i
$167$	64.0046	−	132.907i	0.383261	−	0.795850i	−0.616701	−	0.787197i	$-0.711531\pi$
$167$	64.0046	−	132.907i	0.383261	−	0.795850i	0.999963	−	0.00865304i	$-0.00275438\pi$
$168$	−48.3575	−	298.806i	−0.287842	−	1.77861i
$169$	−169.729	+	81.7372i	−1.00431	+	0.483652i
$170$	−23.2983	−	26.6451i	−0.137049	−	0.156736i
$171$	384.594	−	414.494i	2.24909	−	2.42394i
$172$	−4.28320	+	1.39556i	−0.0249023	+	0.00811374i
$173$	230.996	+	157.490i	1.33524	+	0.910350i	0.999500	−	0.0316060i	$-0.0100622\pi$
$173$	230.996	+	157.490i	1.33524	+	0.910350i	0.335737	+	0.941956i	$0.391015\pi$
$174$	−83.4537	−	422.779i	−0.479619	−	2.42976i
$175$	139.282	−	183.742i	0.795895	−	1.04996i
$176$	53.5229	−	5.71387i	0.304107	−	0.0324652i
$177$	166.834	+	288.964i	0.942563	+	1.63257i
$178$	−130.452	+	132.527i	−0.732877	+	0.744531i
$179$	−135.995	−	199.468i	−0.759747	−	1.11434i	−0.989980	−	0.141209i	$-0.954901\pi$
$179$	−135.995	−	199.468i	−0.759747	−	1.11434i	0.230233	−	0.973136i	$-0.426051\pi$
$180$	487.239	+	376.140i	2.70688	+	2.08967i
$181$	12.7787	−	55.9870i	0.0706003	−	0.309320i	−0.927282	−	0.374363i	$-0.877861\pi$
$181$	12.7787	−	55.9870i	0.0706003	−	0.309320i	0.997882	+	0.0650430i	$0.0207184\pi$
$182$	180.972	−	193.123i	0.994354	−	1.06111i
$183$	61.3812	−	14.0099i	0.335417	−	0.0765567i
$184$	20.8489	+	17.1002i	0.113309	+	0.0929357i
$185$	−391.043	−	120.621i	−2.11375	−	0.652005i
$186$	−4.92340	−	40.8010i	−0.0264699	−	0.219360i
$187$	−2.30550	−	7.47426i	−0.0123289	−	0.0399693i
$188$	27.8161	−	4.64253i	0.147958	−	0.0246943i
$189$	362.218	−	221.171i	1.91650	−	1.17022i
$190$	−255.531	−	340.576i	−1.34490	−	1.79250i
$191$	99.4663	+	39.0376i	0.520766	+	0.204386i	0.611140	−	0.791522i	$-0.290711\pi$
$191$	99.4663	+	39.0376i	0.520766	+	0.204386i	−0.0903744	+	0.995908i	$0.528806\pi$
$192$	9.50176	−	345.805i	0.0494883	−	1.80107i
$193$	187.632	−	28.2809i	0.972186	−	0.146533i	0.356302	−	0.934371i	$-0.384037\pi$
$193$	187.632	−	28.2809i	0.972186	−	0.146533i	0.615883	+	0.787837i	$0.288799\pi$
$194$	−127.693	+	68.7816i	−0.658210	+	0.354544i
$195$			777.796i			3.98870i
$196$	−73.4029	+	181.736i	−0.374505	+	0.927225i
$197$	−248.271			−1.26026			−0.630129	−	0.776490i	$-0.716998\pi$
$197$	−248.271			−1.26026			−0.630129	+	0.776490i	$0.716998\pi$
$198$	64.5073	+	119.757i	0.325794	+	0.604835i
$199$	−8.56114	−	56.7994i	−0.0430208	−	0.285424i	0.956968	−	0.290194i	$-0.0937198\pi$
$199$	−8.56114	−	56.7994i	−0.0430208	−	0.285424i	−0.999989	+	0.00476969i	$0.998482\pi$
$200$	195.606	−	176.558i	0.978028	−	0.882792i
$201$	−202.288	+	515.422i	−1.00641	+	2.56429i
$202$	−212.563	+	159.484i	−1.05229	+	0.789525i
$203$	−95.5298	+	262.178i	−0.470590	+	1.29152i
$204$	−49.5831	+	8.27544i	−0.243054	+	0.0405659i
$205$	125.921	−	38.8415i	0.614249	−	0.189471i
$206$	−223.739	+	26.9983i	−1.08611	+	0.131060i
$207$	−20.0853	+	65.1148i	−0.0970302	+	0.314564i
$208$	244.416	−	178.189i	1.17508	−	0.856679i
$209$	−20.9375	−	91.7330i	−0.100179	−	0.438914i
$210$	−207.791	−	537.218i	−0.989481	−	2.55818i
$211$	−77.8828	−	17.7762i	−0.369113	−	0.0842476i	0.0339411	−	0.999424i	$-0.489194\pi$
$211$	−77.8828	−	17.7762i	−0.369113	−	0.0842476i	−0.403054	+	0.915176i	$0.632051\pi$
$212$	88.4620	+	68.2911i	0.417273	+	0.322128i
$213$	247.389	−	168.667i	1.16145	−	0.791863i
$214$	33.7689	+	33.2403i	0.157798	+	0.155328i
$215$	−7.42386	+	4.28616i	−0.0345296	+	0.0199357i
$216$	453.896	−	170.985i	2.10137	−	0.791595i
$217$	−10.9534	+	24.2523i	−0.0504763	+	0.111762i
$218$	340.758	−	67.2633i	1.56311	−	0.308547i
$219$	−77.8901	+	114.244i	−0.355663	+	0.521661i
$220$	97.3898	−	31.7318i	0.442681	−	0.144235i
$221$	−32.2201	−	29.8959i	−0.145792	−	0.135276i
$222$	−437.529	+	382.572i	−1.97085	+	1.72330i
$223$	165.113	+	342.861i	0.740417	+	1.53749i	0.840075	+	0.542470i	$0.182511\pi$
$223$	165.113	+	342.861i	0.740417	+	1.53749i	−0.0996578	+	0.995022i	$0.531775\pi$
$224$	−121.213	+	188.371i	−0.541127	+	0.840941i
$225$	599.954	+	288.923i	2.66646	+	1.28410i
$226$	86.7545	+	313.848i	0.383869	+	1.38871i
$227$	50.1966	+	28.9810i	0.221130	+	0.127670i	0.606474	−	0.795104i	$-0.292584\pi$
$227$	50.1966	+	28.9810i	0.221130	+	0.127670i	−0.385343	+	0.922773i	$0.625917\pi$
$228$	−602.232	+	54.6977i	−2.64137	+	0.239902i
$229$	122.462	+	18.4582i	0.534770	+	0.0806036i	0.410875	−	0.911692i	$-0.365223\pi$
$229$	122.462	+	18.4582i	0.534770	+	0.0806036i	0.123895	+	0.992295i	$0.460461\pi$
$230$	45.5532	+	23.6178i	0.198058	+	0.102686i
$231$	6.38979	−	127.130i	0.0276614	−	0.550344i
$232$	−163.229	+	273.962i	−0.703575	+	1.18087i
$233$	−19.1370	−	255.365i	−0.0821330	−	1.09599i	−0.874204	−	0.485560i	$-0.838616\pi$
$233$	−19.1370	−	255.365i	−0.0821330	−	1.09599i	0.792071	−	0.610429i	$-0.209003\pi$
$234$	650.406	+	401.556i	2.77951	+	1.71605i
$235$	49.9546	−	19.6057i	0.212573	−	0.0834286i
$236$	51.1405	−	241.567i	0.216697	−	1.02359i
$237$	−148.088	−	185.697i	−0.624845	−	0.783531i
$238$	30.2410	+	12.0412i	0.127063	+	0.0505931i
$239$	172.953	+	137.925i	0.723652	+	0.577093i	0.914529	−	0.404521i	$-0.132562\pi$
$239$	172.953	+	137.925i	0.723652	+	0.577093i	−0.190877	+	0.981614i	$0.561133\pi$
$240$	−118.600	−	647.519i	−0.494166	−	2.69799i
$241$	−14.2117	+	189.642i	−0.0589697	+	0.786897i	0.886820	+	0.462116i	$0.152910\pi$
$241$	−14.2117	+	189.642i	−0.0589697	+	0.786897i	−0.945789	+	0.324781i	$0.894709\pi$
$242$	−218.172	−	22.8408i	−0.901538	−	0.0943833i
$243$	164.762	+	177.571i	0.678032	+	0.730745i
$244$	−40.7120	−	22.6563i	−0.166852	−	0.0928539i
$245$	−65.0256	+	367.261i	−0.265411	+	1.49903i
$246$	47.0115	−	181.153i	0.191104	−	0.736395i
$247$	−359.633	−	387.592i	−1.45600	−	1.56920i
$248$	−17.4756	+	24.8905i	−0.0704660	+	0.100365i
$249$	0.774222	−	10.3313i	0.00310933	−	0.0414911i
$250$	70.9901	−	97.7934i	0.283960	−	0.391174i
$251$	−228.384	−	182.130i	−0.909896	−	0.725618i	0.0521112	−	0.998641i	$-0.483405\pi$
$251$	−228.384	−	182.130i	−0.909896	−	0.725618i	−0.962007	+	0.273023i	$0.911976\pi$
$252$	−556.508	−	103.594i	−2.20837	−	0.411086i
$253$	7.06993	+	8.86541i	0.0279444	+	0.0350412i
$254$	−17.3432	−	382.691i	−0.0682804	−	1.50666i
$255$	−89.0456	+	34.9478i	−0.349198	+	0.137050i
$256$	−176.307	+	185.612i	−0.688698	+	0.725048i
$257$	−5.30728	−	70.8207i	−0.0206509	−	0.275567i	−0.997965	−	0.0637702i	$-0.979688\pi$
$257$	−5.30728	−	70.8207i	−0.0206509	−	0.275567i	0.977314	−	0.211797i	$-0.0679315\pi$
$258$	−0.359247	+	12.1695i	−0.00139243	+	0.0471687i
$259$	370.643	−	65.2194i	1.43105	−	0.251812i
$260$	384.793	−	428.058i	1.47997	−	1.64638i
$261$	−796.894	−	120.112i	−3.05323	−	0.460201i
$262$	105.235	+	293.301i	0.401659	+	1.11947i
$263$	−251.513	−	145.211i	−0.956324	−	0.552134i	−0.0612844	−	0.998120i	$-0.519520\pi$
$263$	−251.513	−	145.211i	−0.956324	−	0.552134i	−0.895040	+	0.445986i	$0.852853\pi$
$264$	34.3160	−	141.369i	0.129985	−	0.535489i
$265$	191.601	+	92.2704i	0.723024	+	0.348190i
$266$	351.943	+	171.630i	1.32309	+	0.645226i
$267$	218.061	+	452.808i	0.816708	+	1.69591i
$268$	366.319	−	183.585i	1.36686	−	0.685018i
$269$	37.2417	+	34.5552i	0.138445	+	0.128458i	0.746356	−	0.665547i	$-0.231802\pi$
$269$	37.2417	+	34.5552i	0.138445	+	0.128458i	−0.607911	+	0.794005i	$0.707992\pi$
$270$	777.614	−	497.206i	2.88005	−	1.84150i
$271$	140.181	−	205.608i	0.517274	−	0.758701i	−0.475368	−	0.879787i	$-0.657685\pi$
$271$	140.181	−	205.608i	0.517274	−	0.758701i	0.992642	+	0.121086i	$0.0386376\pi$
$272$	31.3820	+	19.9755i	0.115375	+	0.0734392i
$273$	−326.098	−	636.631i	−1.19450	−	2.33198i
$274$	−162.141	−	137.323i	−0.591756	−	0.501177i
$275$	95.9640	−	55.4049i	0.348960	−	0.201472i
$276$	62.5292	−	37.4288i	0.226555	−	0.135612i
$277$	179.222	−	122.192i	0.647012	−	0.441125i	−0.194839	−	0.980835i	$-0.562418\pi$
$277$	179.222	−	122.192i	0.647012	−	0.441125i	0.841851	+	0.539710i	$0.181466\pi$
$278$	69.5032	−	162.795i	0.250012	−	0.585593i
$279$	−74.9286	−	17.1020i	−0.268561	−	0.0612974i
$280$	−151.416	+	398.455i	−0.540773	+	1.42305i
$281$	−6.24856	−	27.3768i	−0.0222369	−	0.0974262i	0.962592	−	0.270956i	$-0.0873398\pi$
$281$	−6.24856	−	27.3768i	−0.0222369	−	0.0974262i	−0.984829	+	0.173530i	$0.944483\pi$
$282$	13.5783	−	74.9971i	0.0481502	−	0.265947i
$283$	82.6934	−	268.085i	0.292203	−	0.947298i	−0.683824	−	0.729647i	$-0.739684\pi$
$283$	82.6934	−	268.085i	0.292203	−	0.947298i	0.976027	−	0.217651i	$-0.0698394\pi$
$284$	−219.593	−	29.5633i	−0.773214	−	0.104096i
$285$	−1099.60	+	339.181i	−3.85824	+	1.19011i
$286$	116.180	−	51.7833i	0.406222	−	0.181061i
$287$	−86.7827	+	84.5856i	−0.302379	+	0.294723i
$288$	−602.696	−	235.122i	−2.09269	−	0.816396i
$289$	−103.609	+	263.991i	−0.358507	+	0.913462i
$290$	−195.905	+	574.357i	−0.675533	+	1.98054i
$291$	58.4225	+	387.608i	0.200765	+	1.33199i
$292$	99.3855	−	24.3398i	0.340361	−	0.0833556i
$293$	−237.938			−0.812074			−0.406037	−	0.913857i	$-0.633090\pi$
$293$	−237.938			−0.812074			−0.406037	+	0.913857i	$0.633090\pi$
$294$	395.312	+	352.599i	1.34460	+	1.19932i
$295$		−	469.872i		−	1.59279i
$296$	430.059	+	5.90730i	1.45290	+	0.0199571i
$297$	201.690	−	30.3999i	0.679091	−	0.102356i
$298$	97.2685	−	285.174i	0.326405	−	0.956959i
$299$	59.3149	+	23.2794i	0.198378	+	0.0778575i
$300$	−270.604	−	658.737i	−0.902014	−	2.19579i
$301$	4.27946	−	6.62077i	0.0142175	−	0.0219959i
$302$	−293.369	+	130.760i	−0.971420	+	0.432979i
$303$	211.693	+	686.290i	0.698655	+	2.26498i
$304$	358.497	+	267.835i	1.17927	+	0.881035i
$305$	−84.7214	−	26.1331i	−0.277775	−	0.0856822i
$306$	−16.7480	+	92.5041i	−0.0547321	+	0.302301i
$307$	−216.024	+	49.3060i	−0.703661	+	0.160606i	−0.559356	−	0.828927i	$-0.688952\pi$
$307$	−216.024	+	49.3060i	−0.703661	+	0.160606i	−0.144304	+	0.989533i	$0.546094\pi$
$308$	−66.4103	+	66.8042i	−0.215618	+	0.216897i
$309$	−135.531	+	593.800i	−0.438611	+	1.92168i
$310$	−22.7238	+	53.2251i	−0.0733027	+	0.171694i
$311$	43.8674	+	64.3416i	0.141053	+	0.206886i	0.890264	−	0.455445i	$-0.150520\pi$
$311$	43.8674	+	64.3416i	0.141053	+	0.206886i	−0.749211	+	0.662331i	$0.769567\pi$
$312$	−230.203	−	784.392i	−0.737830	−	2.51408i
$313$	160.212	+	277.496i	0.511860	+	0.886568i	0.999905	+	0.0137499i	$0.00437686\pi$
$313$	160.212	+	277.496i	0.511860	+	0.886568i	−0.488045	+	0.872818i	$0.662290\pi$
$314$	293.898	+	248.911i	0.935979	+	0.792711i
$315$	−1076.86	+	26.4746i	−3.41860	+	0.0840463i
$316$	−10.3683	+	175.460i	−0.0328110	+	0.555254i
$317$	−77.4734	−	52.8205i	−0.244396	−	0.166626i	0.434927	−	0.900466i	$-0.356774\pi$
$317$	−77.4734	−	52.8205i	−0.244396	−	0.166626i	−0.679323	+	0.733839i	$0.737726\pi$
$318$	254.462	−	162.703i	0.800196	−	0.511645i
$319$	−91.2153	+	98.3067i	−0.285941	+	0.308172i
$320$	−255.070	+	415.034i	−0.797095	+	1.29698i
$321$	115.379	−	55.5637i	0.359437	−	0.173096i
$322$	−47.1876	−	0.232714i	−0.146545	−	0.000722715i
$323$	28.2143	−	58.5877i	0.0873509	−	0.181386i
$324$	−9.19829	−	582.989i	−0.0283898	−	1.79935i
$325$	311.340	−	539.257i	0.957970	−	1.65925i
$326$	42.1004	+	117.339i	0.129142	+	0.359934i
$327$	139.908	−	928.227i	0.427852	−	2.83861i
$328$	−115.493	+	76.4396i	−0.352113	+	0.233047i
$329$	−32.6683	+	36.9913i	−0.0992957	+	0.112436i
$330$	8.16843	−	276.706i	0.0247528	−	0.838504i
$331$	−192.851	+	14.4522i	−0.582632	+	0.0436622i	−0.362786	−	0.931872i	$-0.618174\pi$
$331$	−192.851	+	14.4522i	−0.582632	+	0.0436622i	−0.219846	+	0.975535i	$0.570555\pi$
$332$	−5.53720	+	5.30277i	−0.0166783	+	0.0159722i
$333$	397.090	+	1011.77i	1.19246	+	3.03834i
$334$	13.3569	+	294.729i	0.0399906	+	0.882422i
$335$	609.609	−	486.147i	1.81973	−	1.45119i
$336$	368.553	+	480.274i	1.09688	+	1.42939i
$337$	39.4440	−	49.4612i	0.117044	−	0.146769i	−0.719858	−	0.694122i	$-0.755793\pi$
$337$	39.4440	−	49.4612i	0.117044	−	0.146769i	0.836902	+	0.547353i	$0.184364\pi$
$338$	221.335	−	304.904i	0.654838	−	0.902082i
$339$	877.562	+	65.7642i	2.58868	+	0.193995i
$340$	66.2954	+	24.8193i	0.194987	+	0.0729981i
$341$	−9.37518	+	8.69890i	−0.0274932	+	0.0255100i
$342$	−284.065	+	1094.61i	−0.830600	+	3.20062i
$343$	−100.754	−	327.868i	−0.293742	−	0.955885i
$344$	6.21824	−	6.51974i	0.0180763	−	0.0189527i
$345$	101.657	−	94.3239i	0.294658	−	0.273403i
$346$	−556.112	−	58.2202i	−1.60726	−	0.168266i
$347$	−260.688	−	19.5358i	−0.751261	−	0.0562993i	−0.306405	−	0.951901i	$-0.599126\pi$
$347$	−260.688	−	19.5358i	−0.751261	−	0.0562993i	−0.444856	+	0.895602i	$0.646745\pi$
$348$	547.933	+	665.279i	1.57452	+	1.91172i
$349$	171.350	−	214.866i	0.490974	−	0.615661i	−0.473193	−	0.880959i	$-0.656899\pi$
$349$	171.350	−	214.866i	0.490974	−	0.615661i	0.964167	+	0.265297i	$0.0854701\pi$
$350$	−70.9761	+	455.637i	−0.202789	+	1.30182i
$351$	896.113	−	714.627i	2.55303	−	2.03597i
$352$	−88.8240	+	60.8252i	−0.252341	+	0.172799i
$353$	74.0881	+	188.773i	0.209881	+	0.534769i	0.996586	−	0.0825605i	$-0.0263098\pi$
$353$	74.0881	+	188.773i	0.209881	+	0.534769i	−0.786705	+	0.617330i	$0.788215\pi$
$354$	−567.831	−	350.575i	−1.60404	−	0.990325i
$355$	−420.460	+	31.5091i	−1.18439	+	0.0887580i
$356$	104.005	−	357.081i	0.292148	−	1.00304i
$357$	58.2322	−	65.9382i	0.163115	−	0.184701i
$358$	428.646	+	222.238i	1.19734	+	0.620778i
$359$	−68.5791	+	454.993i	−0.191028	+	1.26739i	0.663576	+	0.748109i	$0.269038\pi$
$359$	−68.5791	+	454.993i	−0.191028	+	1.26739i	−0.854604	+	0.519280i	$0.826200\pi$
$360$	−1214.68	−	200.184i	−3.37412	−	0.556065i
$361$	210.624	−	364.812i	0.583447	−	1.01056i
$362$	30.6005	+	110.702i	0.0845317	+	0.305807i
$363$	−257.232	+	534.148i	−0.708629	+	1.47148i
$364$	−135.488	+	511.696i	−0.372221	+	1.40576i
$365$	175.430	−	84.4824i	0.480629	−	0.231459i
$366$	−94.7926	+	82.8861i	−0.258996	+	0.226465i
$367$	−444.557	+	479.118i	−1.21133	+	1.30550i	−0.272071	+	0.962277i	$0.587709\pi$
$367$	−444.557	+	479.118i	−1.21133	+	1.30550i	−0.939255	+	0.343221i	$0.888482\pi$
$368$	−52.9296	−	10.3357i	−0.143831	−	0.0280862i
$369$	−289.181	−	197.160i	−0.783688	−	0.534309i
$370$	802.955	−	158.498i	2.17015	−	0.428372i
$371$	−195.512	+	4.80666i	−0.526987	+	0.0129560i
$372$	47.3672	+	67.1730i	0.127331	+	0.180573i
$373$	16.2002	+	28.0597i	0.0434323	+	0.0752270i	0.886924	−	0.461915i	$-0.152837\pi$
$373$	16.2002	+	28.0597i	0.0434323	+	0.0752270i	−0.843492	+	0.537142i	$0.819504\pi$
$374$	11.1486	+	10.9740i	0.0298090	+	0.0293424i
$375$	−183.977	−	269.845i	−0.490606	−	0.719587i
$376$	−44.5755	+	34.5570i	−0.118552	+	0.0919068i
$377$	−167.690	+	734.698i	−0.444801	+	1.94880i
$378$	−428.024	+	732.988i	−1.13234	+	1.93912i
$379$	−625.748	+	142.823i	−1.65105	+	0.376842i	−0.943903	−	0.330224i	$-0.892876\pi$
$379$	−625.748	+	142.823i	−1.65105	+	0.376842i	−0.707148	+	0.707065i	$0.750019\pi$
$380$	772.960	+	357.327i	2.03411	+	0.940335i
$381$	−989.334	−	305.169i	−2.59668	−	0.800969i
$382$	−212.166	+	25.6018i	−0.555409	+	0.0670204i
$383$	199.314	+	646.160i	0.520402	+	1.68710i	0.709135	+	0.705073i	$0.249086\pi$
$383$	199.314	+	646.160i	0.520402	+	1.68710i	−0.188733	+	0.982028i	$0.560438\pi$
$384$	311.251	+	617.908i	0.810548	+	1.60913i
$385$	−97.3049	+	150.541i	−0.252740	+	0.391015i
$386$	−303.560	+	227.758i	−0.786424	+	0.590046i
$387$	21.1943	+	8.31814i	0.0547656	+	0.0214939i
$388$	159.605	−	242.222i	0.411354	−	0.624283i
$389$	82.2517	−	12.3975i	0.211444	−	0.0318701i	−0.0424660	−	0.999098i	$-0.513521\pi$
$389$	82.2517	−	12.3975i	0.211444	−	0.0318701i	0.253910	+	0.967228i	$0.418283\pi$
$390$	−737.705	−	1369.55i	−1.89155	−	3.51166i
$391$			7.83663i			0.0200425i
$392$	−43.1207	−	389.621i	−0.110002	−	0.993931i
$393$	842.161			2.14290
$394$	437.156	−	235.474i	1.10953	−	0.597650i
$395$	49.8502	+	330.734i	0.126203	+	0.837302i
$396$	−227.169	−	149.687i	−0.573660	−	0.377997i
$397$	23.6726	−	60.3167i	0.0596286	−	0.151931i	−0.897955	−	0.440088i	$-0.854947\pi$
$397$	23.6726	−	60.3167i	0.0596286	−	0.151931i	0.957583	+	0.288157i	$0.0930425\pi$
$398$	68.9463	+	91.8928i	0.173232	+	0.230886i
$399$	757.823	−	738.638i	1.89931	−	1.85122i
$400$	−176.965	+	496.408i	−0.442413	+	1.24102i
$401$	−40.5217	+	12.4993i	−0.101052	+	0.0311703i	−0.344869	−	0.938651i	$-0.612077\pi$
$401$	−40.5217	+	12.4993i	−0.101052	+	0.0311703i	0.243817	+	0.969821i	$0.421600\pi$
$402$	−132.665	−	1099.42i	−0.330013	−	2.73487i
$403$	−21.1833	+	68.6747i	−0.0525641	+	0.170409i
$404$	223.018	−	482.427i	0.552026	−	1.19413i
$405$	−246.892	−	1081.70i	−0.609610	−	2.67087i
$406$	−80.4549	−	552.250i	−0.198165	−	1.36022i
$407$	176.333	+	40.2468i	0.433250	+	0.0988864i
$408$	79.4572	−	61.5988i	0.194748	−	0.150978i
$409$	55.8952	−	38.1087i	0.136663	−	0.0931753i	−0.493059	−	0.869996i	$-0.664121\pi$
$409$	55.8952	−	38.1087i	0.136663	−	0.0931753i	0.629722	+	0.776821i	$0.283169\pi$
$410$	−184.883	+	187.823i	−0.450934	+	0.458105i
$411$	−497.316	+	287.125i	−1.21001	+	0.698602i
$412$	368.355	−	259.746i	0.894064	−	0.630451i
$413$	196.998	+	384.594i	0.476993	+	0.931219i
$414$	−26.3923	−	133.704i	−0.0637496	−	0.322957i
$415$	−8.21848	+	12.0543i	−0.0198036	+	0.0290465i
$416$	−261.364	+	545.574i	−0.628279	+	1.31148i
$417$	−350.687	−	325.390i	−0.840977	−	0.780313i
$418$	123.871	+	141.666i	0.296343	+	0.338913i
$419$	−200.590	−	416.530i	−0.478736	−	0.994106i	−0.990822	−	0.135171i	$-0.956841\pi$
$419$	−200.590	−	416.530i	−0.478736	−	0.994106i	0.512086	−	0.858934i	$-0.328873\pi$
$420$	875.407	+	748.855i	2.08430	+	1.78299i
$421$	−412.061	−	198.438i	−0.978768	−	0.471350i	−0.125087	−	0.992146i	$-0.539921\pi$
$421$	−412.061	−	198.438i	−0.978768	−	0.471350i	−0.853681	+	0.520796i	$0.825635\pi$
$422$	153.996	−	42.5680i	0.364920	−	0.100872i
$423$	−123.437	−	71.2662i	−0.291812	−	0.168478i
$424$	−220.535	−	36.3449i	−0.520130	−	0.0857190i
$425$	75.7257	+	11.4138i	0.178178	+	0.0268560i
$426$	−275.630	+	531.626i	−0.647019	+	1.24795i
$427$	80.3016	−	14.1301i	0.188060	−	0.0330915i
$428$	−90.9873	−	26.5013i	−0.212587	−	0.0619189i
$429$	−25.6898	−	342.806i	−0.0598829	−	0.799082i
$430$	9.00671	−	14.5883i	0.0209458	−	0.0339263i
$431$	−581.424	+	228.192i	−1.34901	+	0.529448i	−0.926290	−	0.376811i	$-0.877021\pi$
$431$	−581.424	+	228.192i	−1.34901	+	0.529448i	−0.422722	+	0.906259i	$0.638925\pi$
$432$	−637.051	+	731.571i	−1.47465	+	1.69345i
$433$	−24.5518	−	30.7869i	−0.0567015	−	0.0711014i	0.752672	−	0.658396i	$-0.228765\pi$
$433$	−24.5518	−	30.7869i	−0.0567015	−	0.0711014i	−0.809374	+	0.587294i	$0.800193\pi$
$434$	−3.71551	−	53.0923i	−0.00856109	−	0.122333i
$435$	1282.27	+	1022.57i	2.94774	+	2.35075i
$436$	−536.212	+	441.632i	−1.22984	+	1.01292i
$437$	−7.04487	+	94.0073i	−0.0161210	+	0.215120i
$438$	28.7939	−	275.036i	0.0657396	−	0.627937i
$439$	−315.794	−	340.345i	−0.719348	−	0.775273i	0.262502	−	0.964932i	$-0.415452\pi$
$439$	−315.794	−	340.345i	−0.719348	−	0.775273i	−0.981850	+	0.189658i	$0.939262\pi$
$440$	−141.388	+	148.243i	−0.321336	+	0.336917i
$441$	870.318	−	473.153i	1.97351	−	1.07291i
$442$	85.0882	+	22.0814i	0.192507	+	0.0499580i
$443$	0.306211	+	0.330017i	0.000691222	+	0.000744960i	0.733397	−	0.679800i	$-0.237933\pi$
$443$	0.306211	+	0.330017i	0.000691222	+	0.000744960i	−0.732706	+	0.680545i	$0.761743\pi$
$444$	407.549	−	1088.61i	0.917903	−	2.45183i
$445$	52.8891	−	705.756i	0.118852	−	1.58597i
$446$	−615.920	−	447.108i	−1.38099	−	1.00248i
$447$	−636.658	−	507.718i	−1.42429	−	1.13583i
$448$	34.7702	−	446.649i	0.0776119	−	0.996984i
$449$	−325.643	−	408.343i	−0.725262	−	0.909450i	0.273361	−	0.961912i	$-0.411865\pi$
$449$	−325.643	−	408.343i	−0.725262	−	0.909450i	−0.998623	+	0.0524618i	$0.983293\pi$
$450$	−1330.43	+	60.2940i	−2.95651	+	0.133987i
$451$	−54.2156	+	21.2781i	−0.120212	+	0.0471797i
$452$	−450.429	−	470.342i	−0.996524	−	1.04058i
$453$	64.8700	+	865.631i	0.143201	+	1.91088i
$454$	−115.874	−	3.42062i	−0.255228	−	0.00753440i
$455$	−50.5639	+	1006.00i	−0.111129	+	2.21100i
$456$	1008.53	−	667.503i	2.21170	−	1.46382i
$457$	−404.081	−	60.9054i	−0.884204	−	0.133272i	−0.308786	−	0.951132i	$-0.599923\pi$
$457$	−404.081	−	60.9054i	−0.884204	−	0.133272i	−0.575418	+	0.817859i	$0.695161\pi$
$458$	−233.139	+	83.6488i	−0.509037	+	0.182639i
$459$	122.078	+	70.4816i	0.265964	+	0.153555i
$460$	−102.611	+	1.61897i	−0.223067	+	0.00351951i
$461$	558.199	+	268.814i	1.21084	+	0.583111i	0.926748	−	0.375684i	$-0.122592\pi$
$461$	558.199	+	268.814i	1.21084	+	0.583111i	0.284096	+	0.958796i	$0.408307\pi$
$462$	109.326	+	229.911i	0.236636	+	0.497642i
$463$	162.071	+	336.544i	0.350045	+	0.726877i	0.999436	−	0.0335781i	$-0.0106902\pi$
$463$	162.071	+	336.544i	0.350045	+	0.726877i	−0.649391	+	0.760455i	$0.724976\pi$
$464$	27.5744	−	637.209i	0.0594276	−	1.37329i
$465$	114.656	+	106.385i	0.246572	+	0.228785i
$466$	275.899	+	431.498i	0.592059	+	0.925961i
$467$	322.092	−	472.423i	0.689705	−	1.01161i	−0.308470	−	0.951234i	$-0.599817\pi$
$467$	322.092	−	472.423i	0.689705	−	1.01161i	0.998176	−	0.0603779i	$-0.0192306\pi$
$468$	−1526.10	−	90.1800i	−3.26089	−	0.192692i
$469$	−295.148	+	653.499i	−0.629313	+	1.39339i
$470$	−69.3650	+	81.9016i	−0.147585	+	0.174259i
$471$	901.435	−	520.444i	1.91388	−	1.10498i
$472$	139.067	+	473.857i	0.294634	+	1.00393i
$473$	3.13042	−	2.13429i	0.00661823	−	0.00451224i
$474$	436.880	+	186.520i	0.921687	+	0.393503i
$475$	898.136	+	204.994i	1.89081	+	0.431566i
$476$	−64.6690	+	7.48014i	−0.135859	+	0.0157146i
$477$	−125.687	−	550.669i	−0.263494	−	1.15444i
$478$	−435.352	−	78.8212i	−0.910779	−	0.164898i
$479$	257.287	−	834.104i	0.537133	−	1.74134i	−0.125197	−	0.992132i	$-0.539956\pi$
$479$	257.287	−	834.104i	0.537133	−	1.74134i	0.662331	−	0.749212i	$-0.269567\pi$
$480$	822.974	+	1027.67i	1.71453	+	2.14097i
$481$	971.206	−	299.577i	2.01914	−	0.622822i
$482$	−154.843	−	347.402i	−0.321251	−	0.720750i
$483$	−43.6608	+	119.825i	−0.0903951	+	0.248086i
$484$	405.822	−	166.709i	0.838475	−	0.344439i
$485$	201.667	−	513.840i	0.415809	−	1.05946i
$486$	−458.532	−	156.398i	−0.943481	−	0.321807i
$487$	87.7477	+	582.168i	0.180180	+	1.19542i	0.877828	+	0.478976i	$0.158992\pi$
$487$	87.7477	+	582.168i	0.180180	+	1.19542i	−0.697648	+	0.716441i	$0.745770\pi$
$488$	93.1744	+	1.27984i	0.190931	+	0.00262263i
$489$	336.917			0.688991
$490$	−233.834	−	708.349i	−0.477212	−	1.44561i
$491$		−	355.743i		−	0.724528i	−0.932076	−	0.362264i	$-0.882004\pi$
$491$		−	355.743i		−	0.724528i	0.932076	−	0.362264i	$-0.117996\pi$
$492$	89.0379	+	363.564i	0.180971	+	0.738950i
$493$	−91.6461	+	13.8134i	−0.185895	+	0.0280191i
$494$	1000.86	+	341.378i	2.02603	+	0.691048i
$495$	−481.908	−	189.135i	−0.973551	−	0.382091i
$496$	7.16356	−	60.4020i	0.0144427	−	0.121778i
$497$	330.939	−	202.072i	0.665872	−	0.406583i
$498$	8.43551	+	18.9257i	0.0169388	+	0.0380034i
$499$	−43.5290	−	141.118i	−0.0872325	−	0.282801i	0.901437	−	0.432911i	$-0.142513\pi$
$499$	−43.5290	−	141.118i	−0.0872325	−	0.282801i	−0.988669	+	0.150110i	$0.952037\pi$
$500$	−32.2468	+	239.526i	−0.0644937	+	0.479052i
$501$	761.934	+	235.026i	1.52083	+	0.469113i
$502$	574.882	+	104.083i	1.14518	+	0.207337i
$503$	−604.008	+	137.861i	−1.20081	+	0.274077i	−0.775723	−	0.631074i	$-0.782614\pi$
$503$	−604.008	+	137.861i	−1.20081	+	0.274077i	−0.425089	+	0.905151i	$0.639757\pi$
$504$	1078.16	−	345.416i	2.13920	−	0.685348i
$505$	225.051	−	986.013i	0.445646	−	1.95250i
$506$	−20.8572	−	8.90473i	−0.0412198	−	0.0175983i
$507$	−573.611	−	841.333i	−1.13138	−	1.65943i
$508$	393.504	+	657.394i	0.774613	+	1.29408i
$509$	−19.5873	−	33.9263i	−0.0384820	−	0.0666528i	0.846143	−	0.532956i	$-0.178919\pi$
$509$	−19.5873	−	33.9263i	−0.0384820	−	0.0666528i	−0.884625	+	0.466303i	$0.845586\pi$
$510$	123.645	−	145.992i	0.242442	−	0.286259i
$511$	−108.170	+	142.700i	−0.211684	+	0.279256i
$512$	134.396	−	494.046i	0.262493	−	0.964934i
$513$	1401.07	+	955.233i	2.73113	+	1.86205i
$514$	76.5155	+	119.668i	0.148863	+	0.232817i
$515$	583.381	−	628.736i	1.13278	−	1.22085i
$516$	−10.9097	−	21.7689i	−0.0211428	−	0.0421878i
$517$	−21.3694	+	10.2910i	−0.0413335	+	0.0199052i
$518$	−590.772	+	466.377i	−1.14049	+	0.900342i
$519$	−655.674	+	1361.52i	−1.26334	+	2.62336i
$520$	−271.550	+	1118.68i	−0.522212	+	2.15132i
$521$	−339.872	+	588.675i	−0.652345	+	1.12989i	0.330207	+	0.943908i	$0.392881\pi$
$521$	−339.872	+	588.675i	−0.652345	+	1.12989i	−0.982552	+	0.185986i	$0.940452\pi$
$522$	1517.10	−	544.325i	2.90631	−	1.04277i
$523$	115.135	−	763.873i	0.220144	−	1.46056i	−0.556619	−	0.830768i	$-0.687902\pi$
$523$	115.135	−	763.873i	0.220144	−	1.46056i	0.776763	−	0.629792i	$-0.216860\pi$
$524$	−463.481	−	416.635i	−0.884506	−	0.795106i
$525$	1094.29	+	596.419i	2.08436	+	1.13604i
$526$	580.592	+	17.1392i	1.10379	+	0.0325840i
$527$	−8.81399	+	0.660517i	−0.0167248	+	0.00125335i
$528$	73.6586	+	281.470i	0.139505	+	0.533088i
$529$	189.115	+	481.857i	0.357495	+	0.910882i
$530$	−424.887	+	19.2555i	−0.801673	+	0.0363312i
$531$	−975.712	+	778.105i	−1.83750	+	1.46536i
$532$	−782.486	+	31.5956i	−1.47084	+	0.0593902i
$533$	−204.057	+	255.879i	−0.382845	+	0.480073i
$534$	−813.431	−	590.485i	−1.52328	−	1.10578i
$535$	−179.832	−	13.4766i	−0.336135	−	0.0251899i
$536$	−470.894	+	670.695i	−0.878534	+	1.25130i
$537$	956.571	−	887.569i	1.78132	−	1.65283i
$538$	−98.3494	−	25.5229i	−0.182805	−	0.0474403i
$539$	16.5292	−	164.015i	0.0306664	−	0.304294i
$540$	−897.647	+	1613.01i	−1.66231	+	2.98706i
$541$	−114.439	+	106.184i	−0.211532	+	0.196273i	−0.778822	−	0.627245i	$-0.784182\pi$
$541$	−114.439	+	106.184i	−0.211532	+	0.196273i	0.567290	+	0.823518i	$0.307992\pi$
$542$	−51.8213	+	494.991i	−0.0956113	+	0.913268i
$543$	309.538	+	23.1967i	0.570052	+	0.0427195i
$544$	−74.2033	−	5.40847i	−0.136403	−	0.00994203i
$545$	−824.190	+	1033.50i	−1.51228	+	1.89633i
$546$	1178.01	+	811.693i	2.15753	+	1.48662i
$547$	653.080	−	520.814i	1.19393	−	0.952127i	0.194345	−	0.980933i	$-0.437742\pi$
$547$	653.080	−	520.814i	1.19393	−	0.952127i	0.999585	+	0.0288057i	$0.00917042\pi$
$548$	415.743	+	88.0142i	0.758656	+	0.160610i
$549$	86.0313	+	219.204i	0.156705	+	0.399279i
$550$	−116.425	+	188.575i	−0.211681	+	0.342863i
$551$	−1111.79	+	83.3174i	−2.01777	+	0.151211i
$552$	−74.6022	+	125.211i	−0.135149	+	0.226832i
$553$	−179.466	−	249.808i	−0.324532	−	0.451733i
$554$	−199.682	+	385.140i	−0.360437	+	0.695199i
$555$	329.675	−	2187.25i	0.594010	−	3.94100i
$556$	32.0222	+	352.570i	0.0575938	+	0.634119i
$557$	−103.389	+	179.075i	−0.185618	+	0.321500i	−0.943785	−	0.330561i	$-0.892762\pi$
$557$	−103.389	+	179.075i	−0.185618	+	0.321500i	0.758167	+	0.652061i	$0.226095\pi$
$558$	148.155	−	40.9533i	0.265511	−	0.0733930i
$559$	9.23759	−	19.1821i	0.0165252	−	0.0343149i
$560$	−111.303	−	845.214i	−0.198755	−	1.50931i
$561$	38.0917	−	18.3440i	0.0678996	−	0.0326987i
$562$	36.9681	+	42.2786i	0.0657796	+	0.0752288i
$563$	55.6105	−	59.9339i	0.0987753	−	0.106454i	−0.681729	−	0.731605i	$-0.738772\pi$
$563$	55.6105	−	59.9339i	0.0987753	−	0.106454i	0.780505	+	0.625150i	$0.214962\pi$
$564$	47.2227	+	144.934i	0.0837282	+	0.256975i
$565$	−1023.92	−	698.096i	−1.81225	−	1.23557i
$566$	108.660	+	550.477i	0.191979	+	0.972574i
$567$	655.597	+	781.871i	1.15626	+	1.37896i
$568$	414.699	−	156.219i	0.730104	−	0.275033i
$569$	−184.826	−	320.128i	−0.324826	−	0.562616i	0.656651	−	0.754195i	$-0.271973\pi$
$569$	−184.826	−	320.128i	−0.324826	−	0.562616i	−0.981477	+	0.191579i	$0.938639\pi$
$570$	1614.48	−	1640.15i	2.83242	−	2.87746i
$571$	50.9759	+	74.7680i	0.0892749	+	0.130942i	0.868278	−	0.496078i	$-0.165227\pi$
$571$	50.9759	+	74.7680i	0.0892749	+	0.130942i	−0.779003	+	0.627020i	$0.784274\pi$
$572$	−155.455	+	201.372i	−0.271775	+	0.352048i
$573$	−128.520	+	563.084i	−0.224294	+	0.982695i
$574$	72.5815	−	231.248i	0.126449	−	0.402871i
$575$	−108.237	+	24.7043i	−0.188238	+	0.0429641i
$576$	1284.23	−	157.627i	2.22957	−	0.273658i
$577$	−152.198	−	46.9470i	−0.263775	−	0.0813639i	0.160047	−	0.987109i	$-0.448836\pi$
$577$	−152.198	−	46.9470i	−0.263775	−	0.0813639i	−0.423822	+	0.905746i	$0.639312\pi$
$578$	−67.9490	−	563.104i	−0.117559	−	0.974228i
$579$	302.316	+	980.086i	0.522135	+	1.69272i
$580$	−199.803	−	1197.14i	−0.344487	−	2.06403i
$581$	1.67301	−	13.3122i	0.00287954	−	0.0229126i
$582$	−470.500	−	627.091i	−0.808419	−	1.07748i
$583$	−87.4940	−	34.3389i	−0.150076	−	0.0589003i
$584$	−151.913	+	137.120i	−0.260125	+	0.234795i
$585$	−2876.62	+	433.581i	−4.91730	+	0.741164i
$586$	418.962	−	225.674i	0.714952	−	0.385108i
$587$			36.3734i			0.0619648i	0.999520	+	0.0309824i	$0.00986359\pi$
$587$			36.3734i			0.0619648i	−0.999520	+	0.0309824i	$0.990136\pi$
$588$	−1030.49	−	245.921i	−1.75254	−	0.418233i
$589$	−106.325			−0.180518
$590$	445.653	+	827.353i	0.755344	+	1.40229i
$591$	−200.010	−	1326.98i	−0.338426	−	2.24531i
$592$	−762.853	+	397.491i	−1.28860	+	0.671437i
$593$	339.434	−	864.863i	0.572401	−	1.45845i	−0.292379	−	0.956303i	$-0.594447\pi$
$593$	339.434	−	864.863i	0.572401	−	1.45845i	0.864780	−	0.502151i	$-0.167458\pi$
$594$	−326.303	+	244.822i	−0.549332	+	0.412159i
$595$	−117.444	+	39.4129i	−0.197385	+	0.0662401i
$596$	99.2040	+	594.390i	0.166450	+	0.997299i
$597$	296.689	−	91.5165i	0.496967	−	0.153294i
$598$	−126.521	+	15.2672i	−0.211574	+	0.0255304i
$599$	176.078	−	570.830i	0.293953	−	0.952971i	−0.681324	−	0.731982i	$-0.738595\pi$
$599$	176.078	−	570.830i	0.293953	−	0.952971i	0.975276	−	0.220989i	$-0.0709285\pi$
$600$	1101.26	+	903.250i	1.83544	+	1.50542i
$601$	226.933	+	994.258i	0.377592	+	1.65434i	0.704814	+	0.709392i	$0.251030\pi$
$601$	226.933	+	994.258i	0.377592	+	1.65434i	−0.327222	+	0.944948i	$0.606112\pi$
$602$	−1.25578	+	15.7168i	−0.00208602	+	0.0261076i
$603$	−2019.02	−	460.827i	−3.34829	−	0.764224i
$604$	392.545	−	508.490i	0.649909	−	0.841871i
$605$	689.801	−	470.298i	1.14017	−	0.777352i
$606$	−1023.67	−	1007.64i	−1.68922	−	1.66277i
$607$	254.340	−	146.843i	0.419011	−	0.241916i	−0.275643	−	0.961260i	$-0.588891\pi$
$607$	254.340	−	146.843i	0.419011	−	0.241916i	0.694654	+	0.719344i	$0.255557\pi$
$608$	−885.273	−	131.586i	−1.45604	−	0.216424i
$609$	−1478.27	−	299.382i	−2.42737	−	0.491596i
$610$	173.964	−	34.3393i	0.285187	−	0.0562939i
$611$	−75.0803	+	110.123i	−0.122881	+	0.180233i
$612$	−58.2461	−	178.766i	−0.0951734	−	0.292102i
$613$	482.527	+	447.719i	0.787156	+	0.730374i	0.967402	−	0.253248i	$-0.0814987\pi$
$613$	482.527	+	447.719i	0.787156	+	0.730374i	−0.180245	+	0.983622i	$0.557689\pi$
$614$	333.611	−	291.707i	0.543340	−	0.475093i
$615$	309.047	+	641.742i	0.502515	+	1.04348i
$616$	53.5747	−	180.616i	0.0869720	−	0.293209i
$617$	63.6098	+	30.6328i	0.103095	+	0.0496480i	0.484721	−	0.874669i	$-0.338921\pi$
$617$	63.6098	+	30.6328i	0.103095	+	0.0496480i	−0.381625	+	0.924317i	$0.624636\pi$
$618$	−324.550	−	1174.11i	−0.525161	−	1.89985i
$619$	155.037	+	89.5109i	0.250464	+	0.144606i	0.619977	−	0.784620i	$-0.287142\pi$
$619$	155.037	+	89.5109i	0.250464	+	0.144606i	−0.369513	+	0.929226i	$0.620475\pi$
$620$	−10.4695	−	115.272i	−0.0168863	−	0.185922i
$621$	−202.073	−	30.4576i	−0.325400	−	0.0490461i
$622$	−138.267	−	71.6867i	−0.222294	−	0.115252i
$623$	252.604	+	599.840i	0.405464	+	0.962826i
$624$	1149.30	+	1162.82i	1.84183	+	1.86350i
$625$	−27.1672	−	362.521i	−0.0434676	−	0.580034i
$626$	−545.295	−	336.661i	−0.871079	−	0.537798i
$627$	473.434	−	185.809i	0.755078	−	0.296346i
$628$	−753.577	−	159.535i	−1.19996	−	0.254036i
$629$	77.9351	+	97.7275i	0.123903	+	0.155370i
$630$	1871.03	−	1067.97i	2.96989	−	1.69519i
$631$	−316.896	−	252.716i	−0.502213	−	0.400502i	0.339350	−	0.940660i	$-0.389793\pi$
$631$	−316.896	−	252.716i	−0.502213	−	0.400502i	−0.841563	+	0.540159i	$0.818364\pi$
$632$	−148.160	−	318.785i	−0.234430	−	0.504406i
$633$	32.2686	−	430.595i	0.0509773	−	0.680244i
$634$	186.513	+	19.5264i	0.294185	+	0.0307987i
$635$	991.664	+	1068.76i	1.56168	+	1.68309i
$636$	−293.741	+	527.834i	−0.461858	+	0.829928i
$637$	−380.390	−	844.621i	−0.597158	−	1.32594i
$638$	67.3727	−	259.613i	0.105600	−	0.406916i
$639$	761.708	+	820.926i	1.19203	+	1.28470i
$640$	55.4873	−	972.717i	0.0866989	−	1.51987i
$641$	69.5648	−	928.278i	0.108526	−	1.44817i	−0.631386	−	0.775468i	$-0.717514\pi$
$641$	69.5648	−	928.278i	0.108526	−	1.44817i	0.739912	−	0.672704i	$-0.234867\pi$
$642$	−150.461	+	207.269i	−0.234362	+	0.322849i
$643$	311.627	+	248.514i	0.484645	+	0.386492i	0.835109	−	0.550085i	$-0.185405\pi$
$643$	311.627	+	248.514i	0.484645	+	0.386492i	−0.350464	+	0.936576i	$0.613976\pi$
$644$	83.3088	−	44.3456i	0.129362	−	0.0688597i
$645$	−28.8898	−	36.2266i	−0.0447903	−	0.0561653i
$646$	5.88793	+	129.921i	0.00911444	+	0.201117i
$647$	142.430	−	55.8995i	0.220138	−	0.0863980i	−0.252709	−	0.967542i	$-0.581321\pi$
$647$	142.430	−	55.8995i	0.220138	−	0.0863980i	0.472847	+	0.881144i	$0.343226\pi$
$648$	569.136	+	1017.80i	0.878296	+	1.57069i
$649$	15.5194	+	207.092i	0.0239127	+	0.319093i
$650$	−36.7473	+	1244.82i	−0.0565344	+	1.91511i
$651$	−138.450	−	39.0065i	−0.212672	−	0.0599178i
$652$	−185.421	−	166.680i	−0.284388	−	0.255644i
$653$	−28.4890	−	4.29402i	−0.0436278	−	0.00657584i	0.127192	−	0.991878i	$-0.459404\pi$
$653$	−28.4890	−	4.29402i	−0.0436278	−	0.00657584i	−0.170820	+	0.985302i	$0.554642\pi$
$654$	634.033	+	1767.12i	0.969469	+	2.70202i
$655$	−1027.05	−	592.968i	−1.56802	−	0.905295i
$656$	130.861	−	244.135i	0.199483	−	0.372157i
$657$	−465.942	−	224.386i	−0.709196	−	0.341531i
$658$	22.4378	−	96.1189i	0.0341000	−	0.146077i
$659$	−553.833	−	1150.05i	−0.840415	−	1.74514i	−0.644634	−	0.764491i	$-0.722990\pi$
$659$	−553.833	−	1150.05i	−0.840415	−	1.74514i	−0.195780	−	0.980648i	$-0.562724\pi$
$660$	248.061	+	494.973i	0.375850	+	0.749959i
$661$	773.516	+	717.718i	1.17022	+	1.08581i	0.994856	+	0.101303i	$0.0323012\pi$
$661$	773.516	+	717.718i	1.17022	+	1.08581i	0.175366	+	0.984503i	$0.443889\pi$
$662$	325.866	−	208.358i	0.492244	−	0.314741i
$663$	133.833	−	196.297i	0.201860	−	0.296074i
$664$	4.72048	−	14.5889i	0.00710916	−	0.0219713i
$665$	−1444.27	+	367.214i	−2.17184	+	0.552202i
$666$	−1658.81	−	1404.90i	−2.49071	−	2.10946i
$667$	116.360	−	67.1805i	0.174453	−	0.100720i
$668$	−303.056	−	506.291i	−0.453677	−	0.757921i
$669$	−1699.53	+	1158.72i	−2.54041	+	1.73202i
$670$	−612.313	+	1434.20i	−0.913900	+	2.14059i
$671$	38.2033	+	8.71965i	0.0569348	+	0.0129950i
$672$	−1104.47	−	496.113i	−1.64355	−	0.738263i
$673$	−104.957	−	459.846i	−0.155954	−	0.683278i	−0.991085	−	0.133228i	$-0.957466\pi$
$673$	−104.957	−	459.846i	−0.155954	−	0.683278i	0.835132	−	0.550050i	$-0.185391\pi$
$674$	−22.5413	+	124.502i	−0.0334441	+	0.184721i
$675$	−588.627	+	1908.28i	−0.872040	+	2.82709i
$676$	−100.540	+	746.803i	−0.148728	+	1.10474i
$677$	−368.903	+	113.792i	−0.544909	+	0.168082i	−0.554975	−	0.831867i	$-0.687272\pi$
$677$	−368.903	+	113.792i	−0.544909	+	0.168082i	0.0100660	+	0.999949i	$0.496796\pi$
$678$	−1607.59	+	716.531i	−2.37108	+	1.05683i
$679$	50.3659	+	505.132i	0.0741765	+	0.743935i
$680$	−140.273	+	19.1763i	−0.206284	+	0.0282004i
$681$	−114.461	+	291.642i	−0.168078	+	0.428256i
$682$	8.25734	−	24.2090i	0.0121075	−	0.0354971i
$683$	−76.1835	−	505.445i	−0.111542	−	0.740036i	−0.972763	−	0.231804i	$-0.925537\pi$
$683$	−76.1835	−	505.445i	−0.111542	−	0.740036i	0.861220	−	0.508232i	$-0.169701\pi$
$684$	−538.009	−	2196.82i	−0.786562	−	3.21173i
$685$	808.663			1.18053
$686$	488.376	+	481.752i	0.711919	+	0.702262i
$687$			669.416i			0.974405i
$688$	−4.76542	+	17.3777i	−0.00692648	+	0.0252583i
$689$	−522.273	+	78.7199i	−0.758015	+	0.114252i
$690$	−89.5360	+	262.503i	−0.129762	+	0.380439i
$691$	220.178	+	86.4134i	0.318636	+	0.125056i	0.519269	−	0.854611i	$-0.326204\pi$
$691$	220.178	+	86.4134i	0.318636	+	0.125056i	−0.200632	+	0.979667i	$0.564300\pi$
$692$	1034.42	−	424.933i	1.49483	−	0.614066i
$693$	473.741	−	47.2359i	0.683609	−	0.0681615i
$694$	477.549	−	212.852i	0.688111	−	0.306703i
$695$	198.570	+	643.747i	0.285712	+	0.926255i
$696$	−1595.79	−	651.735i	−2.29280	−	0.936401i
$697$	−38.4628	−	11.8642i	−0.0551834	−	0.0170218i
$698$	−97.9225	+	540.854i	−0.140290	+	0.774863i
$699$	1349.48	−	308.010i	1.93059	−	0.440644i
$700$	−307.177	−	869.605i	−0.438824	−	1.24229i
$701$	−186.629	+	817.675i	−0.266232	+	1.16644i	0.648125	+	0.761534i	$0.275553\pi$
$701$	−186.629	+	817.675i	−0.266232	+	1.16644i	−0.914358	+	0.404907i	$0.867304\pi$
$702$	−900.088	+	2108.24i	−1.28218	+	3.00319i
$703$	847.046	+	1242.39i	1.20490	+	1.76727i
$704$	98.7117	−	191.347i	0.140215	−	0.271800i
$705$	145.034	+	251.207i	0.205722	+	0.356321i
$706$	−309.498	−	262.124i	−0.438382	−	0.371280i
$707$	229.189	+	901.413i	0.324171	+	1.27498i
$708$	1332.34	+	78.7309i	1.88184	+	0.111202i
$709$	144.373	+	98.4320i	0.203629	+	0.138832i	0.660841	−	0.750526i	$-0.270200\pi$
$709$	144.373	+	98.4320i	0.203629	+	0.138832i	−0.457212	+	0.889358i	$0.651152\pi$
$710$	710.462	−	454.269i	1.00065	−	0.639815i
$711$	604.234	−	651.210i	0.849837	−	0.915907i
$712$	155.544	+	727.394i	0.218460	+	1.02162i
$713$	11.5446	−	5.55959i	0.0161916	−	0.00779747i
$714$	−39.9961	+	171.335i	−0.0560169	+	0.239965i
$715$	−210.041	+	436.154i	−0.293764	+	0.610006i
$716$	−965.546	+	15.2342i	−1.34853	+	0.0212768i
$717$	−597.861	+	1035.53i	−0.833837	+	1.44425i
$718$	−310.786	−	866.197i	−0.432850	−	1.20640i
$719$	−129.580	+	859.709i	−0.180223	+	1.19570i	0.697519	+	0.716566i	$0.254287\pi$
$719$	−129.580	+	859.709i	−0.180223	+	1.19570i	−0.877742	+	0.479134i	$0.840951\pi$
$720$	2328.69	−	799.591i	3.23429	−	1.11054i
$721$	−213.899	+	759.212i	−0.296669	+	1.05300i
$722$	−24.8599	+	842.130i	−0.0344319	+	1.16638i
$723$	−1025.06	+	76.8178i	−1.41779	+	0.106249i
$724$	−158.878	−	165.901i	−0.219444	−	0.229146i
$725$	−479.693	−	1222.24i	−0.661646	−	1.68585i
$726$	−53.6807	−	1184.50i	−0.0739404	−	1.63155i
$727$	204.882	−	163.388i	0.281818	−	0.224743i	−0.472371	−	0.881400i	$-0.656602\pi$
$727$	204.882	−	163.388i	0.281818	−	0.224743i	0.754189	+	0.656657i	$0.228030\pi$
$728$	−246.753	−	1029.50i	−0.338946	−	1.41415i
$729$	1.58720	−	1.99028i	0.00217722	−	0.00273015i
$730$	−228.769	+	315.144i	−0.313382	+	0.431705i
$731$	2.61111	+	0.195676i	0.00357197	+	0.000267682i
$732$	88.2974	−	235.853i	0.120625	−	0.322203i
$733$	−158.978	+	147.510i	−0.216887	+	0.201242i	−0.781133	−	0.624365i	$-0.785358\pi$
$733$	−158.978	+	147.510i	−0.216887	+	0.201242i	0.564245	+	0.825607i	$0.309167\pi$
$734$	328.354	−	1265.28i	0.447349	−	1.72381i
$735$	−2015.35	−	51.6845i	−2.74197	−	0.0703191i
$736$	103.002	−	32.0022i	0.139948	−	0.0434813i
$737$	−252.622	+	234.399i	−0.342771	+	0.318045i
$738$	696.188	+	72.8850i	0.943345	+	0.0987601i
$739$	−96.1598	−	7.20618i	−0.130122	−	0.00975126i	0.00951012	−	0.999955i	$-0.496973\pi$
$739$	−96.1598	−	7.20618i	−0.130122	−	0.00975126i	−0.139632	+	0.990204i	$0.544592\pi$
$740$	−1263.52	+	1040.65i	−1.70746	+	1.40628i
$741$	1781.91	−	2234.44i	2.40474	−	3.01544i
$742$	339.700	−	193.898i	0.457816	−	0.261319i
$743$	−471.618	+	376.103i	−0.634748	+	0.506195i	−0.887182	−	0.461419i	$-0.847340\pi$
$743$	−471.618	+	376.103i	−0.634748	+	0.506195i	0.252434	+	0.967614i	$0.418769\pi$
$744$	−147.115	−	73.3528i	−0.197735	−	0.0985925i
$745$	418.946	+	1067.46i	0.562343	+	1.43283i
$746$	−55.1388	−	34.0423i	−0.0739126	−	0.0456331i
$747$	38.6411	−	2.89575i	0.0517283	−	0.00387650i
$748$	−30.0388	−	8.74922i	−0.0401588	−	0.0116968i
$749$	152.844	−	64.3657i	0.204064	−	0.0859355i
$750$	579.884	+	300.650i	0.773179	+	0.400866i
$751$	−157.939	+	1047.86i	−0.210305	+	1.39528i	0.595622	+	0.803265i	$0.296906\pi$
$751$	−157.939	+	1047.86i	−0.210305	+	1.39528i	−0.805926	+	0.592016i	$0.798332\pi$
$752$	45.7130	−	103.126i	0.0607885	−	0.137136i
$753$	789.475	−	1367.41i	1.04844	−	1.81595i
$754$	−401.560	−	1452.71i	−0.532572	−	1.92666i
$755$	530.381	−	1101.35i	0.702492	−	1.45874i
$756$	58.4600	−	1696.61i	0.0773280	−	2.24419i
$757$	−951.344	+	458.143i	−1.25673	+	0.605209i	−0.939308	−	0.343076i	$-0.888531\pi$
$757$	−951.344	+	458.143i	−1.25673	+	0.605209i	−0.317421	+	0.948285i	$0.602817\pi$
$758$	966.359	−	844.978i	1.27488	−	1.11475i
$759$	−41.6889	+	44.9300i	−0.0549261	+	0.0591963i
$760$	−1699.94	+	103.936i	−2.23676	+	0.136757i
$761$	1141.60	+	778.327i	1.50013	+	1.02277i	0.986316	+	0.164863i	$0.0527183\pi$
$761$	1141.60	+	778.327i	1.50013	+	1.02277i	0.513809	+	0.857905i	$0.328234\pi$
$762$	2031.46	−	400.997i	2.66596	−	0.526243i
$763$	241.301	−	1191.48i	0.316252	−	1.56157i
$764$	349.301	−	246.310i	0.457200	−	0.322395i
$765$	−178.890	−	309.847i	−0.233843	−	0.405029i
$766$	−963.807	−	948.720i	−1.25823	−	1.23854i
$767$	657.387	+	964.210i	0.857089	+	1.25712i
$768$	−1134.11	−	792.807i	−1.47671	−	1.03230i
$769$	−107.160	+	469.498i	−0.139350	+	0.610530i	0.856229	+	0.516597i	$0.172801\pi$
$769$	−107.160	+	469.498i	−0.139350	+	0.610530i	−0.995578	+	0.0939336i	$0.970056\pi$
$770$	28.5535	−	357.362i	0.0370825	−	0.464107i
$771$	374.253	−	85.4207i	0.485412	−	0.110792i
$772$	318.491	−	688.950i	0.412553	−	0.892422i
$773$	69.6422	+	21.4818i	0.0900935	+	0.0277902i	0.339474	−	0.940615i	$-0.389751\pi$
$773$	69.6422	+	21.4818i	0.0900935	+	0.0277902i	−0.249381	+	0.968406i	$0.580227\pi$
$774$	−45.2084	+	5.45523i	−0.0584087	+	0.00704810i
$775$	−36.9082	−	119.654i	−0.0476235	−	0.154392i
$776$	−51.2971	+	577.884i	−0.0661044	+	0.744696i
$777$	647.184	+	1928.50i	0.832926	+	2.48198i
$778$	−133.071	+	99.8416i	−0.171042	+	0.128331i
$779$	−450.730	−	176.898i	−0.578600	−	0.227084i
$780$	2597.91	+	1711.82i	3.33065	+	2.19464i
$781$	184.273	−	27.7746i	0.235945	−	0.0355629i
$782$	−7.43270	−	13.7988i	−0.00950473	−	0.0176455i
$783$		−	2416.85i		−	3.08665i
$784$	445.466	+	645.148i	0.568196	+	0.822893i
$785$	−1465.78			−1.86724
$786$	−1482.88	+	798.753i	−1.88662	+	1.01623i
$787$	67.0637	+	444.939i	0.0852144	+	0.565361i	0.990172	+	0.139858i	$0.0446646\pi$
$787$	67.0637	+	444.939i	0.0852144	+	0.565361i	−0.904957	+	0.425503i	$0.860097\pi$
$788$	−546.410	+	829.247i	−0.693413	+	1.05234i
$789$	573.515	−	1461.29i	0.726888	−	1.85208i
$790$	−401.463	−	535.077i	−0.508181	−	0.677313i
$791$	1130.77	+	142.109i	1.42954	+	0.179658i
$792$	541.972	+	48.1092i	0.684308	+	0.0607440i
$793$	210.416	−	64.9048i	0.265342	−	0.0818472i
$794$	15.5250	+	128.658i	0.0195529	+	0.162038i
$795$	−338.818	+	1098.42i	−0.426186	+	1.38166i
$796$	−208.557	−	96.4127i	−0.262007	−	0.121121i
$797$	−39.2930	−	172.154i	−0.0493012	−	0.216002i	0.944277	−	0.329153i	$-0.106763\pi$
$797$	−39.2930	−	172.154i	−0.0493012	−	0.216002i	−0.993578	+	0.113150i	$0.963906\pi$
$798$	−633.813	+	2019.36i	−0.794251	+	2.53052i
$799$	−15.9808	−	3.64752i	−0.0200010	−	0.00456511i
$800$	−159.220	−	1041.92i	−0.199025	−	1.30240i
$801$	−1553.12	+	1058.90i	−1.93898	+	1.32197i
$802$	59.4958	−	60.4419i	0.0741843	−	0.0753640i
$803$	−74.5285	+	43.0291i	−0.0928126	+	0.0535854i
$804$	1276.35	+	1810.03i	1.58750	+	2.25129i
$805$	137.616	−	115.390i	0.170951	−	0.143342i
$806$	−27.8352	−	141.014i	−0.0345350	−	0.174955i
$807$	−154.691	+	226.890i	−0.191687	+	0.281153i
$808$	64.8692	+	1060.98i	0.0802837	+	1.31310i
$809$	492.860	+	457.308i	0.609222	+	0.565275i	0.923280	−	0.384129i	$-0.125498\pi$
$809$	492.860	+	457.308i	0.609222	+	0.565275i	−0.314058	+	0.949404i	$0.601689\pi$
$810$	1460.68	+	1670.50i	1.80331	+	2.06235i
$811$	−172.265	−	357.712i	−0.212411	−	0.441075i	0.767355	−	0.641222i	$-0.221572\pi$
$811$	−172.265	−	357.712i	−0.212411	−	0.441075i	−0.979766	+	0.200147i	$0.935858\pi$
$812$	665.450	+	896.095i	0.819520	+	1.10357i
$813$	1211.88	+	583.611i	1.49063	+	0.717849i
$814$	−348.659	+	96.3771i	−0.428328	+	0.118399i
$815$	−410.884	−	237.224i	−0.504152	−	0.291072i
$816$	−81.4848	+	183.825i	−0.0998588	+	0.225276i
$817$	31.1467	+	4.69460i	0.0381232	+	0.00574615i
$818$	−62.2760	+	120.116i	−0.0761321	+	0.146841i
$819$	2172.75	−	1560.94i	2.65293	−	1.90591i
$820$	147.401	−	506.073i	0.179757	−	0.617162i
$821$	−32.8368	−	438.177i	−0.0399962	−	0.533712i	−0.980833	−	0.194851i	$-0.937578\pi$
$821$	−32.8368	−	438.177i	−0.0399962	−	0.533712i	0.940837	−	0.338860i	$-0.110041\pi$
$822$	603.349	−	977.253i	0.734002	−	1.18887i
$823$	1478.50	−	580.270i	1.79648	−	0.705066i	0.802353	−	0.596850i	$-0.203581\pi$
$823$	1478.50	−	580.270i	1.79648	−	0.705066i	0.994127	−	0.108216i	$-0.0345139\pi$
$824$	−402.243	+	806.730i	−0.488158	+	0.979041i
$825$	373.442	+	468.281i	0.452657	+	0.567614i
$826$	−711.645	−	490.350i	−0.861556	−	0.593644i
$827$	526.978	+	420.251i	0.637217	+	0.508164i	0.887978	−	0.459885i	$-0.152110\pi$
$827$	526.978	+	420.251i	0.637217	+	0.508164i	−0.250761	+	0.968049i	$0.580681\pi$
$828$	173.284	+	210.395i	0.209281	+	0.254100i
$829$	80.6030	−	1075.57i	0.0972293	−	1.29743i	−0.708737	−	0.705473i	$-0.750735\pi$
$829$	80.6030	−	1075.57i	0.0972293	−	1.29743i	0.805966	−	0.591961i	$-0.201646\pi$
$830$	3.03816	−	29.0201i	0.00366043	−	0.0349640i
$831$	797.483	+	859.482i	0.959667	+	1.03427i
$832$	−57.2425	−	1208.54i	−0.0688011	−	1.45257i
$833$	79.6044	−	81.4991i	0.0955635	−	0.0978381i
$834$	926.110	+	240.337i	1.11044	+	0.288174i
$835$	−763.729	−	823.104i	−0.914645	−	0.985753i
$836$	−352.477	−	131.959i	−0.421623	−	0.157845i
$837$	17.2243	−	229.842i	0.0205786	−	0.274603i
$838$	748.261	+	543.177i	0.892913	+	0.648182i
$839$	365.724	+	291.655i	0.435905	+	0.347623i	0.816726	−	0.577026i	$-0.195787\pi$
$839$	365.724	+	291.655i	0.435905	+	0.347623i	−0.380820	+	0.924649i	$0.624358\pi$
$840$	−2251.68	−	488.302i	−2.68057	−	0.581312i
$841$	466.398	+	584.845i	0.554576	+	0.695416i
$842$	913.769	−	41.4112i	1.08524	−	0.0491820i
$843$	141.291	−	55.4528i	0.167606	−	0.0657803i
$844$	−230.783	+	221.013i	−0.273440	+	0.261863i
$845$	107.158	+	1429.92i	0.126814	+	1.69221i
$846$	284.941	+	8.41151i	0.336809	+	0.00994268i
$847$	−367.430	+	674.147i	−0.433802	+	0.795924i
$848$	422.791	−	145.172i	0.498574	−	0.171193i
$849$	1499.50	+	226.013i	1.76620	+	0.266211i
$850$	−144.164	+	51.7250i	−0.169604	+	0.0608530i
$851$	−156.933	−	90.6055i	−0.184411	−	0.106469i
$852$	−18.8942	−	1197.51i	−0.0221762	−	1.40553i
$853$	−1397.14	−	672.825i	−1.63791	−	0.788775i	−0.999823	−	0.0188092i	$-0.994012\pi$
$853$	−1397.14	−	672.825i	−1.63791	−	0.788775i	−0.638085	−	0.769966i	$-0.720273\pi$
$854$	−127.994	+	101.043i	−0.149875	+	0.118317i
$855$	−1867.40	−	3877.70i	−2.18410	−	4.53533i
$856$	185.346	−	39.6339i	0.216526	−	0.0463012i
$857$	−470.241	−	436.320i	−0.548706	−	0.509124i	0.356387	−	0.934338i	$-0.384008\pi$
$857$	−470.241	−	436.320i	−0.548706	−	0.509124i	−0.905093	+	0.425214i	$0.860199\pi$
$858$	370.371	+	579.249i	0.431668	+	0.675115i
$859$	146.164	−	214.383i	0.170155	−	0.249572i	−0.731684	−	0.681644i	$-0.761265\pi$
$859$	146.164	−	214.383i	0.170155	−	0.249572i	0.901839	+	0.432072i	$0.142217\pi$
$860$	−2.02269	+	34.2296i	−0.00235197	+	0.0398019i
$861$	−522.013	−	395.700i	−0.606287	−	0.459581i
$862$	807.344	−	953.257i	0.936594	−	1.10587i
$863$	991.198	−	572.269i	1.14855	−	0.663115i	0.200016	−	0.979793i	$-0.435901\pi$
$863$	991.198	−	572.269i	1.14855	−	0.663115i	0.948533	+	0.316677i	$0.102567\pi$
$864$	427.858	−	1892.37i	0.495206	−	2.19024i
$865$	1758.27	−	1198.77i	2.03269	−	1.38586i
$866$	72.4309	+	30.9235i	0.0836384	+	0.0357084i
$867$	−1494.47	−	341.102i	−1.72372	−	0.393428i
$868$	56.8980	+	89.9612i	0.0655507	+	0.103642i
$869$	−32.8948	−	144.121i	−0.0378536	−	0.165847i
$870$	−3227.69	−	584.378i	−3.70999	−	0.671699i
$871$	−570.803	+	1850.50i	−0.655342	+	2.12457i
$872$	525.295	−	1286.20i	0.602403	−	1.47500i
$873$	−1400.97	+	432.143i	−1.60478	+	0.495009i
$874$	−76.7571	−	172.210i	−0.0878228	−	0.197037i
$875$	−220.415	−	360.979i	−0.251902	−	0.412547i
$876$	210.159	+	511.595i	0.239908	+	0.584012i
$877$	54.9206	−	139.935i	0.0626232	−	0.159561i	−0.896137	−	0.443777i	$-0.853638\pi$
$877$	54.9206	−	139.935i	0.0626232	−	0.159561i	0.958760	+	0.284216i	$0.0917333\pi$
$878$	878.853	+	299.764i	1.00097	+	0.341417i
$879$	−191.685	−	1271.75i	−0.218072	−	1.44681i
$880$	108.354	−	395.128i	0.123130	−	0.449009i
$881$	768.537			0.872346			0.436173	−	0.899863i	$-0.356334\pi$
$881$	768.537			0.872346			0.436173	+	0.899863i	$0.356334\pi$
$882$	−1083.69	+	1658.59i	−1.22868	+	1.88049i
$883$		−	1342.74i		−	1.52066i	−0.649537	−	0.760330i	$-0.725037\pi$
$883$		−	1342.74i		−	1.52066i	0.649537	−	0.760330i	$-0.274963\pi$
$884$	−170.767	+	41.8214i	−0.193175	+	0.0473093i
$885$	2511.41	−	378.534i	2.83775	−	0.427722i
$886$	−0.852185	−	0.290668i	−0.000961835	−	0.000328068i
$887$	−476.165	−	186.881i	−0.536827	−	0.210689i	0.0814103	−	0.996681i	$-0.474058\pi$
$887$	−476.165	−	186.881i	−0.536827	−	0.210689i	−0.618237	+	0.785992i	$0.712153\pi$
$888$	314.887	+	2303.37i	0.354602	+	2.59389i
$889$	−1259.77	−	459.023i	−1.41707	−	0.516336i
$890$	576.251	+	1292.86i	0.647473	+	1.45265i
$891$	144.543	+	468.596i	0.162225	+	0.525921i
$892$	1508.58	+	203.096i	1.69123	+	0.227686i
$893$	−188.425	−	58.1215i	−0.211002	−	0.0650856i
$894$	1602.58	+	290.149i	1.79259	+	0.324552i
$895$	−1791.52	+	408.902i	−2.00170	+	0.456874i
$896$	362.403	+	819.439i	0.404468	+	0.914552i
$897$	−76.6408	+	335.785i	−0.0854412	+	0.374342i
$898$	960.688	+	410.154i	1.06981	+	0.456742i
$899$	85.3666	+	125.210i	0.0949572	+	0.139277i
$900$	2285.44	−	1368.02i	2.53938	−	1.52002i
$901$	−32.4789	−	56.2551i	−0.0360476	−	0.0624363i
$902$	75.2818	−	88.8876i	0.0834609	−	0.0985451i
$903$	38.8348	+	17.5394i	0.0430064	+	0.0194235i
$904$	1239.22	+	400.968i	1.37081	+	0.443549i
$905$	−361.162	−	246.236i	−0.399074	−	0.272084i
$906$	−935.236	−	1462.68i	−1.03227	−	1.61444i
$907$	−1038.79	+	1119.55i	−1.14531	+	1.23435i	−0.177100	+	0.984193i	$0.556671\pi$
$907$	−1038.79	+	1119.55i	−1.14531	+	1.23435i	−0.968206	+	0.250153i	$0.919519\pi$
$908$	207.275	−	103.878i	0.228277	−	0.114403i
$909$	−2420.19	+	1165.50i	−2.66247	+	1.28218i
$910$	−865.119	−	1819.34i	−0.950680	−	1.99927i
$911$	−421.623	+	875.509i	−0.462813	+	0.961042i	0.530725	+	0.847544i	$0.321920\pi$
$911$	−421.623	+	875.509i	−0.462813	+	0.961042i	−0.993538	+	0.113498i	$0.963795\pi$
$912$	−1142.73	+	2131.89i	−1.25300	+	2.33760i
$913$	3.22407	−	5.58426i	0.00353130	−	0.00611639i
$914$	769.274	−	276.011i	0.841656	−	0.301981i
$915$	71.4257	−	473.878i	0.0780609	−	0.517900i
$916$	331.175	−	368.411i	0.361544	−	0.402196i
$917$	1089.26	+	54.7482i	1.18785	+	0.0597036i
$918$	−281.804	−	8.31890i	−0.306976	−	0.00906199i
$919$	−303.801	+	22.7667i	−0.330578	+	0.0247734i	−0.238985	−	0.971023i	$-0.576815\pi$
$919$	−303.801	+	22.7667i	−0.330578	+	0.0247734i	−0.0915926	+	0.995797i	$0.529196\pi$
$920$	179.142	−	100.173i	0.194719	−	0.108883i
$921$	−437.566	−	1114.90i	−0.475098	−	1.21053i
$922$	−1237.84	+	56.0978i	−1.34256	+	0.0608435i
$923$	818.728	−	652.914i	0.887030	−	0.707382i
$924$	−410.561	−	301.137i	−0.444330	−	0.325906i
$925$	−1104.09	+	1384.49i	−1.19362	+	1.49675i
$926$	−604.573	−	438.871i	−0.652886	−	0.473942i
$927$	−2271.68	−	170.239i	−2.45057	−	0.183645i
$928$	555.812	+	1148.15i	0.598935	+	1.23723i
$929$	−455.997	+	423.103i	−0.490847	+	0.455439i	−0.886344	−	0.463028i	$-0.846763\pi$
$929$	−455.997	+	423.103i	−0.490847	+	0.455439i	0.395497	+	0.918467i	$0.370572\pi$
$930$	−302.788	−	78.5773i	−0.325579	−	0.0844917i
$931$	1028.19	−	906.092i	1.10439	−	0.973246i
$932$	−895.062	−	498.105i	−0.960367	−	0.534447i
$933$	−308.558	+	286.300i	−0.330716	+	0.306860i
$934$	−119.069	+	1137.33i	−0.127483	+	1.21770i
$935$	−59.3704	−	4.44920i	−0.0634978	−	0.00475850i
$936$	2772.69	−	1288.65i	2.96227	−	1.37676i
$937$	598.541	−	750.546i	0.638784	−	0.801010i	−0.352066	−	0.935975i	$-0.614521\pi$
$937$	598.541	−	750.546i	0.638784	−	0.801010i	0.990850	+	0.134965i	$0.0430922\pi$
$938$	−100.118	−	1430.62i	−0.106735	−	1.52518i
$939$	−1354.11	+	1079.87i	−1.44208	+	1.15002i
$940$	44.4582	−	210.002i	0.0472959	−	0.223407i
$941$	−468.128	−	1192.77i	−0.497479	−	1.26756i	−0.930540	−	0.366191i	$-0.880662\pi$
$941$	−468.128	−	1192.77i	−0.497479	−	1.26756i	0.433060	−	0.901365i	$-0.357434\pi$
$942$	−1093.63	+	1771.37i	−1.16097	+	1.88044i
$943$	58.1892	−	4.36068i	0.0617064	−	0.00462426i
$944$	−694.302	−	702.469i	−0.735490	−	0.744141i
$945$	−559.836	−	3181.56i	−0.592419	−	3.36673i
$946$	−3.48779	+	6.72713i	−0.00368688	+	0.00711113i
$947$	−208.456	+	1383.01i	−0.220122	+	1.46042i	0.556710	+	0.830707i	$0.312064\pi$
$947$	−208.456	+	1383.01i	−0.220122	+	1.46042i	−0.776832	+	0.629708i	$0.783175\pi$
$948$	−946.166	+	85.9354i	−0.998065	+	0.0906491i
$949$	−241.796	+	418.803i	−0.254791	+	0.441310i
$950$	−1775.87	+	490.889i	−1.86934	+	0.516725i
$951$	219.906	−	456.639i	0.231236	−	0.480167i
$952$	106.775	−	74.5068i	0.112158	−	0.0782634i
$953$	1041.53	−	501.576i	1.09290	−	0.526313i	0.201481	−	0.979493i	$-0.435425\pi$
$953$	1041.53	−	501.576i	1.09290	−	0.526313i	0.891419	+	0.453180i	$0.149710\pi$
$954$	743.594	+	850.411i	0.779449	+	0.891416i
$955$	553.205	−	596.213i	0.579272	−	0.624307i
$956$	841.328	−	274.124i	0.880051	−	0.286740i
$957$	−598.922	−	408.338i	−0.625832	−	0.426685i
$958$	338.079	+	1712.72i	0.352901	+	1.78781i
$959$	−661.896	+	339.039i	−0.690194	+	0.353534i
$960$	−2423.79	−	1028.96i	−2.52478	−	1.07184i
$961$	−473.274	−	819.735i	−0.492481	−	0.853002i
$962$	−1425.97	+	1448.64i	−1.48229	+	1.50587i
$963$	269.816	+	395.748i	0.280183	+	0.410953i
$964$	602.144	+	464.844i	0.624631	+	0.482204i
$965$	321.394	−	1408.12i	0.333050	−	1.45919i
$966$	−36.7710	−	252.399i	−0.0380652	−	0.261283i
$967$	1703.02	−	388.703i	1.76114	−	0.401968i	0.785064	−	0.619415i	$-0.212630\pi$
$967$	1703.02	−	388.703i	1.76114	−	0.401968i	0.976072	+	0.217447i	$0.0697730\pi$
$968$	−556.457	+	678.445i	−0.574852	+	0.700873i
$969$	335.874	+	103.603i	0.346619	+	0.106918i
$970$	132.258	+	1096.04i	0.136349	+	1.12994i
$971$	376.204	+	1219.62i	0.387440	+	1.25605i	0.913931	+	0.405869i	$0.133031\pi$
$971$	376.204	+	1219.62i	0.387440	+	1.25605i	−0.526491	+	0.850181i	$0.676493\pi$
$972$	955.721	−	159.510i	0.983252	−	0.164105i
$973$	−432.427	−	443.659i	−0.444427	−	0.455971i
$974$	−706.667	−	941.858i	−0.725531	−	0.967000i
$975$	3133.08	+	1229.64i	3.21342	+	1.26117i
$976$	−165.276	+	86.1183i	−0.169340	+	0.0882359i
$977$	1093.47	−	164.813i	1.11921	−	0.168693i	0.436725	−	0.899595i	$-0.356138\pi$
$977$	1093.47	−	164.813i	1.11921	−	0.168693i	0.682482	+	0.730902i	$0.260900\pi$
$978$	−593.244	+	319.551i	−0.606589	+	0.326739i
$979$			312.802i			0.319512i
$980$	1083.57	+	1025.48i	1.10569	+	1.04641i
$981$	3510.97			3.57897
$982$	337.407	+	626.394i	0.343591	+	0.637876i
$983$	−235.717	−	1563.88i	−0.239794	−	1.59093i	−0.707284	−	0.706930i	$-0.750080\pi$
$983$	−235.717	−	1563.88i	−0.239794	−	1.59093i	0.467490	−	0.883998i	$-0.345158\pi$
$984$	−501.603	−	555.716i	−0.509759	−	0.564752i
$985$	−690.408	+	1759.13i	−0.700922	+	1.78592i
$986$	148.269	−	111.245i	0.150375	−	0.112825i
$987$	−224.032	−	144.807i	−0.226983	−	0.146715i
$988$	−2086.10	+	348.171i	−2.11143	+	0.352399i
$989$	−3.62732	+	1.11888i	−0.00366767	+	0.00113133i
$990$	1027.93	−	124.039i	1.03831	−	0.125292i
$991$	287.439	−	931.853i	0.290049	−	0.940316i	−0.686884	−	0.726768i	$-0.741022\pi$
$991$	287.439	−	931.853i	0.290049	−	0.940316i	0.976933	−	0.213548i	$-0.0685021\pi$
$992$	44.6751	+	113.150i	0.0450353	+	0.114063i
$993$	−232.608	−	1019.12i	−0.234248	−	1.02631i
$994$	−391.062	+	669.690i	−0.393422	+	0.673732i
$995$	−426.262	−	97.2915i	−0.428404	−	0.0977804i
$996$	−32.8035	−	25.3237i	−0.0329352	−	0.0254254i
$997$	471.022	−	321.137i	0.472439	−	0.322104i	−0.303588	−	0.952804i	$-0.598184\pi$
$997$	471.022	−	321.137i	0.472439	−	0.322104i	0.776027	+	0.630700i	$0.217232\pi$
$998$	210.490	+	207.195i	0.210912	+	0.207610i
$999$	−2822.88	+	1629.79i	−2.82570	+	1.63142i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.3.o.a.11.9	✓	648
4.3	odd	2	inner	196.3.o.a.11.18	yes	648
49.9	even	21	inner	196.3.o.a.107.18	yes	648
196.107	odd	42	inner	196.3.o.a.107.9	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
196.3.o.a.11.9	✓	648	1.1	even	1	trivial
196.3.o.a.11.18	yes	648	4.3	odd	2	inner
196.3.o.a.107.9	yes	648	196.107	odd	42	inner
196.3.o.a.107.18	yes	648	49.9	even	21	inner

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:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	196.o (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.76080 + 0.948456i) q^{2} +(0.805611 + 5.34488i) q^{3} +(2.20086 - 3.34009i) q^{4} +(2.78087 - 7.08553i) q^{5} +(-6.48790 - 8.64719i) q^{6} +(0.694514 + 6.96546i) q^{7} +(-0.707355 + 7.96867i) q^{8} +(-19.3185 + 5.95898i) q^{9} +(1.82376 + 15.1138i) q^{10} +(-0.991613 + 3.21473i) q^{11} +(19.6254 + 9.07252i) q^{12} +(4.20668 + 18.4307i) q^{13} +(-7.82934 - 11.6061i) q^{14} +(40.1116 + 9.15521i) q^{15} +(-6.31242 - 14.7022i) q^{16} +(-1.92101 + 1.30972i) q^{17} +(28.3643 - 28.8154i) q^{18} +(-24.2216 + 13.9844i) q^{19} +(-17.5460 - 24.8826i) q^{20} +(-36.6700 + 9.32354i) q^{21} +(-1.30299 - 6.60101i) q^{22} +(1.89872 - 2.78491i) q^{23} +(-43.1614 + 2.63892i) q^{24} +(-24.1453 - 22.4035i) q^{25} +(-24.8878 - 28.4629i) q^{26} +(-26.3060 - 54.6250i) q^{27} +(24.7938 + 13.0103i) q^{28} +(35.9152 + 17.2958i) q^{29} +(-79.3120 + 21.9236i) q^{30} +(3.29227 + 1.90079i) q^{31} +(25.0593 + 19.9006i) q^{32} +(-17.9812 - 2.71023i) q^{33} +(2.14031 - 4.12816i) q^{34} +(51.2854 + 14.4490i) q^{35} +(-22.6139 + 77.6406i) q^{36} +(-4.01768 - 53.6122i) q^{37} +(29.3860 - 47.5968i) q^{38} +(-95.1206 + 37.3321i) q^{39} +(54.4952 + 27.1718i) q^{40} +(10.7940 + 13.5352i) q^{41} +(55.7258 - 51.1968i) q^{42} +(-0.880502 - 0.702177i) q^{43} +(8.55509 + 10.3872i) q^{44} +(-11.4997 + 153.453i) q^{45} +(-0.701907 + 6.70453i) q^{46} +(4.79537 + 5.16818i) q^{47} +(73.4959 - 45.5833i) q^{48} +(-48.0353 + 9.67523i) q^{49} +(63.7639 + 16.5475i) q^{50} +(-8.54789 - 9.21244i) q^{51} +(70.8184 + 26.5126i) q^{52} +(-2.08787 + 27.8606i) q^{53} +(98.1292 + 71.2338i) q^{54} +(20.0205 + 15.9658i) q^{55} +(-55.9967 + 0.607301i) q^{56} +(-94.2578 - 118.196i) q^{57} +(-79.6439 + 3.60939i) q^{58} +(57.4630 - 22.5526i) q^{59} +(118.859 - 113.827i) q^{60} +(-0.870448 - 11.6153i) q^{61} +(-7.59986 - 0.224349i) q^{62} +(-54.9241 - 130.424i) q^{63} +(-62.9993 - 11.2733i) q^{64} +(142.289 + 21.4466i) q^{65} +(34.2319 - 12.2822i) q^{66} +(88.7130 + 51.2185i) q^{67} +(0.146716 + 9.29887i) q^{68} +(16.4146 + 7.90486i) q^{69} +(-104.008 + 23.2000i) q^{70} +(-24.0343 - 49.9078i) q^{71} +(-33.8201 - 158.158i) q^{72} +(18.7519 + 17.3992i) q^{73} +(57.9231 + 90.5899i) q^{74} +(100.292 - 147.102i) q^{75} +(-6.59939 + 111.680i) q^{76} +(-23.0808 - 4.67436i) q^{77} +(132.081 - 155.952i) q^{78} +(-38.0545 + 21.9708i) q^{79} +(-121.727 + 3.84212i) q^{80} +(120.437 - 82.1125i) q^{81} +(-31.8437 - 13.5953i) q^{82} +(-1.86865 - 0.426506i) q^{83} +(-49.5642 + 143.001i) q^{84} +(3.93801 + 17.2535i) q^{85} +(2.21638 + 0.401278i) q^{86} +(-63.5105 + 205.896i) q^{87} +(-24.9157 - 10.1758i) q^{88} +(88.8490 - 27.4063i) q^{89} +(-125.295 - 281.108i) q^{90} +(-125.456 + 42.1018i) q^{91} +(-5.12303 - 12.4711i) q^{92} +(-7.50721 + 19.1281i) q^{93} +(-13.3455 - 4.55195i) q^{94} +(31.7295 + 210.512i) q^{95} +(-86.1780 + 149.971i) q^{96} +72.5196 q^{97} +(75.4042 - 62.5956i) q^{98} -68.0129i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q - 13 q^{2} - 13 q^{4} - 26 q^{5} - 2 q^{6} - 16 q^{8} - 176 q^{9} - 12 q^{10} + 45 q^{12} - 4 q^{13} + 89 q^{14} - 25 q^{16} - 26 q^{17} - 48 q^{18} - 166 q^{20} + 50 q^{21} + 10 q^{22} - 96 q^{24}+ \cdots + 771 q^{98}+O(q^{100}) \) 648 * q - 13 * q^2 - 13 * q^4 - 26 * q^5 - 2 * q^6 - 16 * q^8 - 176 * q^9 - 12 * q^10 + 45 * q^12 - 4 * q^13 + 89 * q^14 - 25 * q^16 - 26 * q^17 - 48 * q^18 - 166 * q^20 + 50 * q^21 + 10 * q^22 - 96 * q^24 + 212 * q^25 - 70 * q^26 + 188 * q^28 + 100 * q^29 + 57 * q^30 + 57 * q^32 - 14 * q^33 - 230 * q^34 - 44 * q^36 - 346 * q^37 - 40 * q^38 - 258 * q^40 - 36 * q^41 - 82 * q^42 - 366 * q^44 - 184 * q^45 - 100 * q^46 - 540 * q^48 - 136 * q^49 - 112 * q^50 + 50 * q^52 - 34 * q^53 - 259 * q^54 + 600 * q^56 + 34 * q^57 + 100 * q^58 + 562 * q^60 + 278 * q^61 + 490 * q^62 - 100 * q^64 + 64 * q^65 + 1340 * q^66 + 61 * q^68 + 160 * q^69 + 666 * q^70 - 412 * q^72 + 206 * q^73 - 202 * q^74 - 177 * q^76 + 234 * q^77 - 632 * q^78 - 364 * q^80 + 618 * q^81 - 2246 * q^82 - 1988 * q^84 - 264 * q^85 - 1025 * q^86 - 1283 * q^88 - 34 * q^89 - 1124 * q^90 - 910 * q^92 - 268 * q^93 + 94 * q^94 - 814 * q^96 - 800 * q^97 + 771 * q^98

Introduction

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