LMFDB - Embedded newform 126.3.r.a.23.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [126,3,Mod(11,126)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(126, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 4])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("126.11"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	126.r (of order $6$, degree $2$, 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:	$3.43325133094$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.2
Character	$\chi$	$=$	126.23
Dual form			126.3.r.a.11.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.41421i q^{2} +(-2.24880 + 1.98568i) q^{3} -2.00000 q^{4} +(1.84316 - 1.06415i) q^{5} +(2.80817 + 3.18028i) q^{6} +(6.16730 - 3.31125i) q^{7} +2.82843i q^{8} +(1.11417 - 8.93077i) q^{9} +(-1.50493 - 2.60662i) q^{10} +(7.75793 + 4.47904i) q^{11} +(4.49759 - 3.97135i) q^{12} +(10.4189 - 18.0461i) q^{13} +(-4.68282 - 8.72188i) q^{14} +(-2.03183 + 6.05296i) q^{15} +4.00000 q^{16} +(9.01197 - 5.20307i) q^{17} +(-12.6300 - 1.57568i) q^{18} +(6.15121 - 10.6542i) q^{19} +(-3.68631 + 2.12829i) q^{20} +(-7.29392 + 19.6926i) q^{21} +(6.33432 - 10.9714i) q^{22} +(-16.5455 + 9.55254i) q^{23} +(-5.61634 - 6.36056i) q^{24} +(-10.2352 + 17.7279i) q^{25} +(-25.5210 - 14.7346i) q^{26} +(15.2281 + 22.2959i) q^{27} +(-12.3346 + 6.62251i) q^{28} +(-28.3968 + 16.3949i) q^{29} +(8.56018 + 2.87344i) q^{30} +37.8877 q^{31} -5.65685i q^{32} +(-26.3399 + 5.33229i) q^{33} +(-7.35825 - 12.7449i) q^{34} +(7.84364 - 12.6661i) q^{35} +(-2.22834 + 17.8615i) q^{36} +(16.9479 - 29.3546i) q^{37} +(-15.0673 - 8.69913i) q^{38} +(12.4037 + 61.2705i) q^{39} +(3.00986 + 5.21323i) q^{40} +(-28.7819 - 16.6172i) q^{41} +(27.8495 + 10.3152i) q^{42} +(10.3473 + 17.9220i) q^{43} +(-15.5159 - 8.95808i) q^{44} +(-7.45006 - 17.6464i) q^{45} +(13.5093 + 23.3988i) q^{46} +66.2205i q^{47} +(-8.99519 + 7.94271i) q^{48} +(27.0712 - 40.8430i) q^{49} +(25.0710 + 14.4747i) q^{50} +(-9.93449 + 29.5955i) q^{51} +(-20.8378 + 36.0921i) q^{52} +(2.72252 - 1.57185i) q^{53} +(31.5311 - 21.5358i) q^{54} +19.0654 q^{55} +(9.36564 + 17.4438i) q^{56} +(7.32300 + 36.1735i) q^{57} +(23.1859 + 40.1591i) q^{58} -84.2461i q^{59} +(4.06366 - 12.1059i) q^{60} -92.0227 q^{61} -53.5813i q^{62} +(-22.7006 - 58.7680i) q^{63} -8.00000 q^{64} -44.3490i q^{65} +(7.54099 + 37.2503i) q^{66} -66.7710 q^{67} +(-18.0239 + 10.4061i) q^{68} +(18.2392 - 54.3357i) q^{69} +(-17.9125 - 11.0926i) q^{70} +115.837i q^{71} +(25.2600 + 3.15135i) q^{72} +(-19.6033 - 33.9540i) q^{73} +(-41.5136 - 23.9679i) q^{74} +(-12.1850 - 60.1901i) q^{75} +(-12.3024 + 21.3084i) q^{76} +(62.6767 + 1.93513i) q^{77} +(86.6496 - 17.5415i) q^{78} +52.4167 q^{79} +(7.37263 - 4.25659i) q^{80} +(-78.5172 - 19.9008i) q^{81} +(-23.5003 + 40.7037i) q^{82} +(9.25626 - 5.34410i) q^{83} +(14.5878 - 39.3852i) q^{84} +(11.0737 - 19.1801i) q^{85} +(25.3456 - 14.6333i) q^{86} +(31.3036 - 93.2556i) q^{87} +(-12.6686 + 21.9427i) q^{88} +(-61.9503 - 35.7670i) q^{89} +(-24.9558 + 10.5360i) q^{90} +(4.50139 - 145.795i) q^{91} +(33.0910 - 19.1051i) q^{92} +(-85.2017 + 75.2327i) q^{93} +93.6500 q^{94} -26.1832i q^{95} +(11.2327 + 12.7211i) q^{96} +(64.5880 + 111.870i) q^{97} +(-57.7607 - 38.2845i) q^{98} +(48.6449 - 64.2938i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 64 q^{4} + 8 q^{6} + 2 q^{7} - 20 q^{9} - 36 q^{11} + 10 q^{13} + 36 q^{14} + 10 q^{15} + 128 q^{16} - 54 q^{17} + 28 q^{19} + 28 q^{21} - 126 q^{23} - 16 q^{24} + 80 q^{25} - 72 q^{26} - 126 q^{27}+ \cdots + 394 q^{99}+O(q^{100}) $ 32 * q - 64 * q^4 + 8 * q^6 + 2 * q^7 - 20 * q^9 - 36 * q^11 + 10 * q^13 + 36 * q^14 + 10 * q^15 + 128 * q^16 - 54 * q^17 + 28 * q^19 + 28 * q^21 - 126 * q^23 - 16 * q^24 + 80 * q^25 - 72 * q^26 - 126 * q^27 - 4 * q^28 + 36 * q^29 + 76 * q^30 + 16 * q^31 - 40 * q^33 - 90 * q^35 + 40 * q^36 + 22 * q^37 + 46 * q^39 + 72 * q^41 + 120 * q^42 + 16 * q^43 + 72 * q^44 + 464 * q^45 - 12 * q^46 + 2 * q^49 - 288 * q^50 - 286 * q^51 - 20 * q^52 - 72 * q^53 - 160 * q^54 - 24 * q^55 - 72 * q^56 - 282 * q^57 - 24 * q^58 - 20 * q^60 + 124 * q^61 + 66 * q^63 - 256 * q^64 - 16 * q^66 - 140 * q^67 + 108 * q^68 + 218 * q^69 + 72 * q^70 + 196 * q^73 + 216 * q^74 + 658 * q^75 - 56 * q^76 + 486 * q^77 + 32 * q^78 + 76 * q^79 - 380 * q^81 - 56 * q^84 + 60 * q^85 - 144 * q^86 - 740 * q^87 - 486 * q^89 + 296 * q^90 - 122 * q^91 + 252 * q^92 + 238 * q^93 - 336 * q^94 + 32 * q^96 - 38 * q^97 + 288 * q^98 + 394 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$		−	1.41421i		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$	−2.24880	+	1.98568i	−0.749599	+	0.661892i
$3$	−2.24880	+	1.98568i	−0.749599	+	0.661892i
$4$	−2.00000			−0.500000
$5$	1.84316	−	1.06415i	0.368631	−	0.212829i	−0.304229	−	0.952599i	$-0.598399\pi$
$5$	1.84316	−	1.06415i	0.368631	−	0.212829i	0.672860	+	0.739770i	$0.265065\pi$
$6$	2.80817	+	3.18028i	0.468029	+	0.530046i
$7$	6.16730	−	3.31125i	0.881043	−	0.473036i
$7$	6.16730	−	3.31125i	0.881043	−	0.473036i
$8$			2.82843i			0.353553i
$9$	1.11417	−	8.93077i	0.123797	−	0.992308i
$10$	−1.50493	−	2.60662i	−0.150493	−	0.260662i
$11$	7.75793	+	4.47904i	0.705266	+	0.407185i	0.809306	−	0.587388i	$-0.199844\pi$
$11$	7.75793	+	4.47904i	0.705266	+	0.407185i	−0.104040	+	0.994573i	$0.533177\pi$
$12$	4.49759	−	3.97135i	0.374799	−	0.330946i
$13$	10.4189	−	18.0461i	0.801454	−	1.38816i	−0.117205	−	0.993108i	$-0.537393\pi$
$13$	10.4189	−	18.0461i	0.801454	−	1.38816i	0.918659	−	0.395051i	$-0.129273\pi$
$14$	−4.68282	−	8.72188i	−0.334487	−	0.622991i
$15$	−2.03183	+	6.05296i	−0.135455	+	0.403531i
$16$	4.00000			0.250000
$17$	9.01197	−	5.20307i	0.530116	−	0.306063i	−0.210948	−	0.977497i	$-0.567655\pi$
$17$	9.01197	−	5.20307i	0.530116	−	0.306063i	0.741064	+	0.671435i	$0.234322\pi$
$18$	−12.6300	−	1.57568i	−0.701667	−	0.0875375i
$19$	6.15121	−	10.6542i	0.323748	−	0.560748i	−0.657510	−	0.753446i	$-0.728390\pi$
$19$	6.15121	−	10.6542i	0.323748	−	0.560748i	0.981258	+	0.192698i	$0.0617237\pi$
$20$	−3.68631	+	2.12829i	−0.184316	+	0.106415i
$21$	−7.29392	+	19.6926i	−0.347330	+	0.937743i
$22$	6.33432	−	10.9714i	0.287924	−	0.498698i
$23$	−16.5455	+	9.55254i	−0.719369	+	0.415328i	−0.814520	−	0.580135i	$-0.803000\pi$
$23$	−16.5455	+	9.55254i	−0.719369	+	0.415328i	0.0951515	+	0.995463i	$0.469666\pi$
$24$	−5.61634	−	6.36056i	−0.234014	−	0.265023i
$25$	−10.2352	+	17.7279i	−0.409407	+	0.709114i
$26$	−25.5210	−	14.7346i	−0.981577	−	0.566714i
$27$	15.2281	+	22.2959i	0.564003	+	0.825773i
$28$	−12.3346	+	6.62251i	−0.440521	+	0.236518i
$29$	−28.3968	+	16.3949i	−0.979199	+	0.565341i	−0.902028	−	0.431677i	$-0.857922\pi$
$29$	−28.3968	+	16.3949i	−0.979199	+	0.565341i	−0.0771708	+	0.997018i	$0.524589\pi$
$30$	8.56018	+	2.87344i	0.285339	+	0.0957814i
$31$	37.8877			1.22218			0.611092	−	0.791560i	$-0.290731\pi$
$31$	37.8877			1.22218			0.611092	+	0.791560i	$0.290731\pi$
$32$		−	5.65685i		−	0.176777i
$33$	−26.3399	+	5.33229i	−0.798179	+	0.161584i
$34$	−7.35825	−	12.7449i	−0.216419	−	0.374849i
$35$	7.84364	−	12.6661i	0.224104	−	0.361888i
$36$	−2.22834	+	17.8615i	−0.0618984	+	0.496154i
$37$	16.9479	−	29.3546i	0.458051	−	0.793367i	−0.540807	−	0.841146i	$-0.681881\pi$
$37$	16.9479	−	29.3546i	0.458051	−	0.793367i	0.998858	+	0.0477797i	$0.0152145\pi$
$38$	−15.0673	−	8.69913i	−0.396509	−	0.228924i
$39$	12.4037	+	61.2705i	0.318043	+	1.57104i
$40$	3.00986	+	5.21323i	0.0752465	+	0.130331i
$41$	−28.7819	−	16.6172i	−0.701997	−	0.405298i	0.106094	−	0.994356i	$-0.466166\pi$
$41$	−28.7819	−	16.6172i	−0.701997	−	0.405298i	−0.808091	+	0.589058i	$0.799499\pi$
$42$	27.8495	+	10.3152i	0.663085	+	0.245599i
$43$	10.3473	+	17.9220i	0.240634	+	0.416791i	0.960895	−	0.276912i	$-0.0893112\pi$
$43$	10.3473	+	17.9220i	0.240634	+	0.416791i	−0.720261	+	0.693703i	$0.755978\pi$
$44$	−15.5159	−	8.95808i	−0.352633	−	0.203593i
$45$	−7.45006	−	17.6464i	−0.165557	−	0.392143i
$46$	13.5093	+	23.3988i	0.293681	+	0.508671i
$47$			66.2205i			1.40895i	0.709730	+	0.704474i	$0.248817\pi$
$47$			66.2205i			1.40895i	−0.709730	+	0.704474i	$0.751183\pi$
$48$	−8.99519	+	7.94271i	−0.187400	+	0.165473i
$49$	27.0712	−	40.8430i	0.552473	−	0.833531i
$50$	25.0710	+	14.4747i	0.501420	+	0.289495i
$51$	−9.93449	+	29.5955i	−0.194794	+	0.580304i
$52$	−20.8378	+	36.0921i	−0.400727	+	0.694080i
$53$	2.72252	−	1.57185i	0.0513684	−	0.0296575i	−0.474096	−	0.880473i	$-0.657225\pi$
$53$	2.72252	−	1.57185i	0.0513684	−	0.0296575i	0.525464	+	0.850816i	$0.323892\pi$
$54$	31.5311	−	21.5358i	0.583910	−	0.398810i
$55$	19.0654			0.346644
$56$	9.36564	+	17.4438i	0.167244	+	0.311496i
$57$	7.32300	+	36.1735i	0.128474	+	0.634622i
$58$	23.1859	+	40.1591i	0.399756	+	0.692398i
$59$		−	84.2461i		−	1.42790i	−0.700197	−	0.713950i	$-0.746904\pi$
$59$		−	84.2461i		−	1.42790i	0.700197	−	0.713950i	$-0.253096\pi$
$60$	4.06366	−	12.1059i	0.0677277	−	0.201765i
$61$	−92.0227			−1.50857			−0.754285	−	0.656547i	$-0.772016\pi$
$61$	−92.0227			−1.50857			−0.754285	+	0.656547i	$0.772016\pi$
$62$		−	53.5813i		−	0.864214i
$63$	−22.7006	−	58.7680i	−0.360327	−	0.932826i
$64$	−8.00000			−0.125000
$65$		−	44.3490i		−	0.682292i
$66$	7.54099	+	37.2503i	0.114257	+	0.564398i
$67$	−66.7710			−0.996582			−0.498291	−	0.867010i	$-0.666039\pi$
$67$	−66.7710			−0.996582			−0.498291	+	0.867010i	$0.666039\pi$
$68$	−18.0239	+	10.4061i	−0.265058	+	0.153031i
$69$	18.2392	−	54.3357i	0.264336	−	0.787474i
$70$	−17.9125	−	11.0926i	−0.255893	−	0.158465i
$71$			115.837i			1.63151i	0.578397	+	0.815755i	$0.303678\pi$
$71$			115.837i			1.63151i	−0.578397	+	0.815755i	$0.696322\pi$
$72$	25.2600	+	3.15135i	0.350834	+	0.0437688i
$73$	−19.6033	−	33.9540i	−0.268539	−	0.465123i	0.699946	−	0.714196i	$-0.253207\pi$
$73$	−19.6033	−	33.9540i	−0.268539	−	0.465123i	−0.968485	+	0.249073i	$0.919874\pi$
$74$	−41.5136	−	23.9679i	−0.560995	−	0.323891i
$75$	−12.1850	−	60.1901i	−0.162466	−	0.802535i
$76$	−12.3024	+	21.3084i	−0.161874	+	0.280374i
$77$	62.6767	+	1.93513i	0.813983	+	0.0251315i
$78$	86.6496	−	17.5415i	1.11089	−	0.224890i
$79$	52.4167			0.663503			0.331752	−	0.943367i	$-0.392360\pi$
$79$	52.4167			0.663503			0.331752	+	0.943367i	$0.392360\pi$
$80$	7.37263	−	4.25659i	0.0921578	−	0.0532073i
$81$	−78.5172	−	19.9008i	−0.969349	−	0.245689i
$82$	−23.5003	+	40.7037i	−0.286589	+	0.496387i
$83$	9.25626	−	5.34410i	0.111521	−	0.0643868i	−0.443202	−	0.896422i	$-0.646158\pi$
$83$	9.25626	−	5.34410i	0.111521	−	0.0643868i	0.554723	+	0.832035i	$0.312824\pi$
$84$	14.5878	−	39.3852i	0.173665	−	0.468872i
$85$	11.0737	−	19.1801i	0.130278	−	0.225649i
$86$	25.3456	−	14.6333i	0.294716	−	0.170154i
$87$	31.3036	−	93.2556i	0.359812	−	1.07190i
$88$	−12.6686	+	21.9427i	−0.143962	+	0.249349i
$89$	−61.9503	−	35.7670i	−0.696071	−	0.401877i	0.109811	−	0.993952i	$-0.464975\pi$
$89$	−61.9503	−	35.7670i	−0.696071	−	0.401877i	−0.805882	+	0.592076i	$0.798309\pi$
$90$	−24.9558	+	10.5360i	−0.277287	+	0.117066i
$91$	4.50139	−	145.795i	0.0494658	−	1.60214i
$92$	33.0910	−	19.1051i	0.359684	−	0.207664i
$93$	−85.2017	+	75.2327i	−0.916147	+	0.808954i
$94$	93.6500			0.996276
$95$		−	26.1832i		−	0.275612i
$96$	11.2327	+	12.7211i	0.117007	+	0.132512i
$97$	64.5880	+	111.870i	0.665855	+	1.15330i	0.979053	+	0.203607i	$0.0652666\pi$
$97$	64.5880	+	111.870i	0.665855	+	1.15330i	−0.313197	+	0.949688i	$0.601400\pi$
$98$	−57.7607	−	38.2845i	−0.589395	−	0.390658i
$99$	48.6449	−	64.2938i	0.491363	−	0.649432i
$100$	20.4704	−	35.4557i	0.204704	−	0.354557i
$101$	54.1471	+	31.2619i	0.536110	+	0.309523i	0.743501	−	0.668735i	$-0.233164\pi$
$101$	54.1471	+	31.2619i	0.536110	+	0.309523i	−0.207391	+	0.978258i	$0.566497\pi$
$102$	41.8544	+	14.0495i	0.410337	+	0.137740i
$103$	70.6270	+	122.330i	0.685699	+	1.18767i	0.973216	+	0.229891i	$0.0738369\pi$
$103$	70.6270	+	122.330i	0.685699	+	1.18767i	−0.287517	+	0.957776i	$0.592830\pi$
$104$	51.0420	+	29.4691i	0.490788	+	0.283357i
$105$	7.51198	+	44.0584i	0.0715427	+	0.419603i
$106$	−2.22293	−	3.85023i	−0.0209710	−	0.0363229i
$107$	28.1441	+	16.2490i	0.263029	+	0.151860i	0.625715	−	0.780051i	$-0.284807\pi$
$107$	28.1441	+	16.2490i	0.263029	+	0.151860i	−0.362687	+	0.931911i	$0.618140\pi$
$108$	−30.4562	−	44.5917i	−0.282001	−	0.412886i
$109$	−39.6151	−	68.6153i	−0.363441	−	0.629499i	0.625084	−	0.780558i	$-0.285065\pi$
$109$	−39.6151	−	68.6153i	−0.363441	−	0.629499i	−0.988525	+	0.151059i	$0.951732\pi$
$110$		−	26.9626i		−	0.245114i
$111$	20.1764	+	99.6655i	0.181769	+	0.897887i
$112$	24.6692	−	13.2450i	0.220261	−	0.118259i
$113$	165.260	+	95.4129i	1.46248	+	0.844362i	0.999125	−	0.0418121i	$-0.0133131\pi$
$113$	165.260	+	95.4129i	1.46248	+	0.844362i	0.463352	+	0.886174i	$0.346646\pi$
$114$	51.1570	−	10.3563i	0.448746	−	0.0908447i
$115$	−20.3306	+	35.2136i	−0.176788	+	0.306206i
$116$	56.7935	−	32.7898i	0.489600	−	0.282670i
$117$	−149.557	−	113.155i	−1.27826	−	0.967139i
$118$	−119.142			−1.00968
$119$	38.3509	−	61.9298i	0.322276	−	0.520419i
$120$	−17.1204	−	5.74689i	−0.142670	−	0.0478907i
$121$	−20.3764	−	35.2930i	−0.168400	−	0.291677i
$122$			130.140i			1.06672i
$123$	97.7210	−	19.7828i	0.794480	−	0.160835i
$124$	−75.7753			−0.611092
$125$			96.7743i			0.774194i
$126$	−83.1106	+	32.1035i	−0.659608	+	0.254790i
$127$	−188.069			−1.48086			−0.740430	−	0.672134i	$-0.765378\pi$
$127$	−188.069			−1.48086			−0.740430	+	0.672134i	$0.765378\pi$
$128$			11.3137i			0.0883883i
$129$	−58.8563	−	19.7566i	−0.456250	−	0.153152i
$130$	−62.7189			−0.482453
$131$	−70.2146	+	40.5384i	−0.535989	+	0.309454i	−0.743452	−	0.668789i	$-0.766813\pi$
$131$	−70.2146	+	40.5384i	−0.535989	+	0.309454i	0.207463	+	0.978243i	$0.433479\pi$
$132$	52.6798	−	10.6646i	0.399090	−	0.0807922i
$133$	2.65757	−	86.0759i	0.0199818	−	0.647188i
$134$			94.4285i			0.704690i
$135$	51.7938	+	24.8899i	0.383658	+	0.184369i
$136$	14.7165	+	25.4897i	0.108210	+	0.187424i
$137$	131.502	+	75.9226i	0.959867	+	0.554180i	0.896132	−	0.443787i	$-0.146365\pi$
$137$	131.502	+	75.9226i	0.959867	+	0.554180i	0.0637351	+	0.997967i	$0.479699\pi$
$138$	−76.8423	−	25.7941i	−0.556828	−	0.186914i
$139$	−35.1300	+	60.8469i	−0.252734	+	0.437747i	−0.964277	−	0.264894i	$-0.914663\pi$
$139$	−35.1300	+	60.8469i	−0.252734	+	0.437747i	0.711544	+	0.702642i	$0.247996\pi$
$140$	−15.6873	+	25.3321i	−0.112052	+	0.180944i
$141$	−131.493	−	148.917i	−0.932572	−	1.05615i
$142$	163.819			1.15365
$143$	161.658	−	93.3334i	1.13048	−	0.652681i
$144$	4.45668	−	35.7231i	0.0309492	−	0.248077i
$145$	−34.8931	+	60.4367i	−0.240642	+	0.416805i
$146$	−48.0182	+	27.7233i	−0.328892	+	0.189886i
$147$	20.2234	+	145.602i	0.137574	+	0.990491i
$148$	−33.8957	+	58.7091i	−0.229025	+	0.396683i
$149$	−179.108	+	103.408i	−1.20207	+	0.694013i	−0.961014	−	0.276500i	$-0.910826\pi$
$149$	−179.108	+	103.408i	−1.20207	+	0.694013i	−0.241051	+	0.970512i	$0.577492\pi$
$150$	−85.1217	+	17.2321i	−0.567478	+	0.114881i
$151$	−94.9961	+	164.538i	−0.629113	+	1.08966i	0.358617	+	0.933485i	$0.383248\pi$
$151$	−94.9961	+	164.538i	−0.629113	+	1.08966i	−0.987730	+	0.156171i	$0.950085\pi$
$152$	30.1347	+	17.3983i	0.198254	+	0.114462i
$153$	−36.4265	−	86.2810i	−0.238082	−	0.563928i
$154$	2.73668	−	88.6382i	0.0177707	−	0.575573i
$155$	69.8329	−	40.3180i	0.450535	−	0.260116i
$156$	−24.8074	−	122.541i	−0.159022	−	0.785519i
$157$	89.3468			0.569088			0.284544	−	0.958663i	$-0.408158\pi$
$157$	89.3468			0.569088			0.284544	+	0.958663i	$0.408158\pi$
$158$		−	74.1285i		−	0.469168i
$159$	−3.00121	+	8.94082i	−0.0188756	+	0.0562316i
$160$	−6.01972	−	10.4265i	−0.0376233	−	0.0651654i
$161$	−70.4101	+	113.700i	−0.437330	+	0.706209i
$162$	−28.1440	+	111.040i	−0.173728	+	0.685433i
$163$	−71.0871	+	123.126i	−0.436117	+	0.755377i	−0.997386	−	0.0722564i	$-0.976980\pi$
$163$	−71.0871	+	123.126i	−0.436117	+	0.755377i	0.561269	+	0.827634i	$0.310313\pi$
$164$	57.5638	+	33.2344i	0.350999	+	0.202649i
$165$	−42.8743	+	37.8578i	−0.259844	+	0.229441i
$166$	−7.55770	−	13.0903i	−0.0455283	−	0.0788574i
$167$	−78.5277	−	45.3380i	−0.470226	−	0.271485i	0.246108	−	0.969242i	$-0.420848\pi$
$167$	−78.5277	−	45.3380i	−0.470226	−	0.271485i	−0.716334	+	0.697757i	$0.754181\pi$
$168$	−55.6991	−	20.6303i	−0.331542	−	0.122800i
$169$	−132.607	−	229.682i	−0.784657	−	1.35907i
$170$	−27.1248	−	15.6605i	−0.159558	−	0.0921206i
$171$	−88.2968	−	66.8057i	−0.516356	−	0.390676i
$172$	−20.6946	−	35.8440i	−0.120317	−	0.208395i
$173$		−	50.8580i		−	0.293977i	−0.989138	−	0.146988i	$-0.953042\pi$
$173$		−	50.8580i		−	0.293977i	0.989138	−	0.146988i	$-0.0469580\pi$
$174$	−131.883	−	44.2700i	−0.757950	−	0.254425i
$175$	−4.42202	+	143.224i	−0.0252687	+	0.818425i
$176$	31.0317	+	17.9162i	0.176316	+	0.101796i
$177$	167.286	+	189.452i	0.945116	+	1.07035i
$178$	−50.5822	+	87.6110i	−0.284170	+	0.492196i
$179$	32.9549	−	19.0265i	0.184106	−	0.106293i	−0.405115	−	0.914266i	$-0.632768\pi$
$179$	32.9549	−	19.0265i	0.184106	−	0.106293i	0.589220	+	0.807972i	$0.299435\pi$
$180$	14.9001	+	35.2929i	0.0827784	+	0.196072i
$181$	123.528			0.682475			0.341237	−	0.939977i	$-0.389154\pi$
$181$	123.528			0.682475			0.341237	+	0.939977i	$0.389154\pi$
$182$	−206.185	−	6.36593i	−1.13289	−	0.0349776i
$183$	206.940	−	182.727i	1.13082	−	0.998511i
$184$	−27.0187	−	46.7977i	−0.146841	−	0.254335i
$185$		−	72.1401i		−	0.389946i
$186$	106.395	+	120.493i	0.572017	+	0.647814i
$187$	93.2190			0.498497
$188$		−	132.441i		−	0.704474i
$189$	167.743	+	87.0813i	0.887531	+	0.460747i
$190$	−37.0286			−0.194887
$191$		−	277.694i		−	1.45390i	−0.686692	−	0.726949i	$-0.740938\pi$
$191$		−	277.694i		−	1.45390i	0.686692	−	0.726949i	$-0.259062\pi$
$192$	17.9904	−	15.8854i	0.0936999	−	0.0827366i
$193$	213.818			1.10786			0.553932	−	0.832562i	$-0.313127\pi$
$193$	213.818			1.10786			0.553932	+	0.832562i	$0.313127\pi$
$194$	158.208	−	91.3412i	0.815503	−	0.470831i
$195$	88.0627	+	99.7318i	0.451604	+	0.511445i
$196$	−54.1424	+	81.6860i	−0.276237	+	0.416765i
$197$			332.031i			1.68544i	0.538356	+	0.842718i	$0.319046\pi$
$197$			332.031i			1.68544i	−0.538356	+	0.842718i	$0.680954\pi$
$198$	−90.9252	−	68.7943i	−0.459218	−	0.347446i
$199$	45.1355	+	78.1769i	0.226811	+	0.392849i	0.956861	−	0.290545i	$-0.0938366\pi$
$199$	45.1355	+	78.1769i	0.226811	+	0.392849i	−0.730050	+	0.683394i	$0.760503\pi$
$200$	−50.1420	−	28.9495i	−0.250710	−	0.144747i
$201$	150.154	−	132.586i	0.747037	−	0.659630i
$202$	44.2109	−	76.5756i	0.218866	−	0.379087i
$203$	−120.844	+	195.141i	−0.595290	+	0.961286i
$204$	19.8690	−	59.1910i	0.0973969	−	0.290152i
$205$	−70.7327			−0.345037
$206$	173.000	−	99.8817i	0.839807	−	0.484863i
$207$	66.8770	+	158.407i	0.323077	+	0.765251i
$208$	41.6756	−	72.1843i	0.200364	−	0.347040i
$209$	95.4413	−	55.1031i	0.456657	−	0.263651i
$210$	62.3079	−	10.6236i	0.296704	−	0.0505883i
$211$	40.3852	−	69.9492i	0.191399	−	0.331513i	−0.754315	−	0.656513i	$-0.772031\pi$
$211$	40.3852	−	69.9492i	0.191399	−	0.331513i	0.945714	+	0.325000i	$0.105364\pi$
$212$	−5.44505	+	3.14370i	−0.0256842	+	0.0148288i
$213$	−230.015	−	260.494i	−1.07988	−	1.22298i
$214$	22.9795	−	39.8017i	0.107381	−	0.185989i
$215$	38.1433	+	22.0220i	0.177411	+	0.102428i
$216$	−63.0622	+	43.0715i	−0.291955	+	0.199405i
$217$	233.665	−	125.456i	1.07680	−	0.578137i
$218$	−97.0367	+	56.0242i	−0.445123	+	0.256992i
$219$	111.506	+	37.4297i	0.509158	+	0.170912i
$220$	−38.1309			−0.173322
$221$		−	216.841i		−	0.981181i
$222$	140.948	−	28.5337i	0.634902	−	0.128530i
$223$	157.577	+	272.932i	0.706624	+	1.22391i	0.966102	+	0.258160i	$0.0831160\pi$
$223$	157.577	+	272.932i	0.706624	+	1.22391i	−0.259478	+	0.965749i	$0.583551\pi$
$224$	−18.7313	−	34.8875i	−0.0836218	−	0.155748i
$225$	146.920	+	111.160i	0.652976	+	0.494044i
$226$	134.934	−	233.713i	0.597054	−	1.03413i
$227$	−243.851	−	140.787i	−1.07423	−	0.620208i	−0.144897	−	0.989447i	$-0.546285\pi$
$227$	−243.851	−	140.787i	−1.07423	−	0.620208i	−0.929335	+	0.369239i	$0.879619\pi$
$228$	−14.6460	−	72.3469i	−0.0642369	−	0.317311i
$229$	−90.0637	−	155.995i	−0.393291	−	0.681201i	0.599590	−	0.800307i	$-0.295330\pi$
$229$	−90.0637	−	155.995i	−0.393291	−	0.681201i	−0.992881	+	0.119107i	$0.961997\pi$
$230$	49.7996	+	28.7518i	0.216520	+	0.125008i
$231$	−144.790	+	120.104i	−0.626795	+	0.519931i
$232$	−46.3717	−	80.3182i	−0.199878	−	0.346199i
$233$	−185.936	−	107.350i	−0.798009	−	0.460731i	0.0447652	−	0.998998i	$-0.485746\pi$
$233$	−185.936	−	107.350i	−0.798009	−	0.460731i	−0.842775	+	0.538267i	$0.819079\pi$
$234$	−160.026	+	211.505i	−0.683870	+	0.903869i
$235$	70.4684	+	122.055i	0.299865	+	0.519382i
$236$			168.492i			0.713950i
$237$	−117.875	+	104.083i	−0.497361	+	0.439168i
$238$	−87.5820	−	54.2363i	−0.367992	−	0.227884i
$239$	−395.735	−	228.477i	−1.65579	−	0.955973i	−0.974625	−	0.223846i	$-0.928139\pi$
$239$	−395.735	−	228.477i	−1.65579	−	0.955973i	−0.681169	−	0.732127i	$-0.738528\pi$
$240$	−8.12733	+	24.2119i	−0.0338639	+	0.100883i
$241$	−161.681	+	280.041i	−0.670877	+	1.16199i	0.306778	+	0.951781i	$0.400749\pi$
$241$	−161.681	+	280.041i	−0.670877	+	1.16199i	−0.977656	+	0.210213i	$0.932584\pi$
$242$	−49.9118	+	28.8166i	−0.206247	+	0.119077i
$243$	216.086	−	111.157i	0.889242	−	0.457436i
$244$	184.045			0.754285
$245$	6.43350	−	104.088i	0.0262592	−	0.424848i
$246$	−27.9771	−	138.198i	−0.113728	−	0.561782i
$247$	−128.178	−	222.010i	−0.518938	−	0.898827i
$248$			107.163i			0.432107i
$249$	−10.2038	+	30.3977i	−0.0409790	+	0.122079i
$250$	136.860			0.547438
$251$		−	382.763i		−	1.52495i	−0.647017	−	0.762476i	$-0.723984\pi$
$251$		−	382.763i		−	1.52495i	0.647017	−	0.762476i	$-0.276016\pi$
$252$	45.4012	+	117.536i	0.180164	+	0.466413i
$253$	−171.145			−0.676462
$254$			265.970i			1.04713i
$255$	13.1832	+	65.1209i	0.0516987	+	0.255376i
$256$	16.0000			0.0625000
$257$	289.608	−	167.205i	1.12688	−	0.650605i	0.183732	−	0.982976i	$-0.441182\pi$
$257$	289.608	−	167.205i	1.12688	−	0.650605i	0.943149	+	0.332371i	$0.107849\pi$
$258$	−27.9401	+	83.2353i	−0.108295	+	0.322618i
$259$	7.32217	−	237.157i	0.0282709	−	0.915665i
$260$			88.6979i			0.341146i
$261$	114.780	+	271.872i	0.439770	+	1.04165i
$262$	57.3300	+	99.2984i	0.218817	+	0.379002i
$263$	−36.4925	−	21.0689i	−0.138755	−	0.0801100i	0.429016	−	0.903297i	$-0.358861\pi$
$263$	−36.4925	−	21.0689i	−0.138755	−	0.0801100i	−0.567770	+	0.823187i	$0.692194\pi$
$264$	−15.0820	−	74.5006i	−0.0571287	−	0.282199i
$265$	3.34536	−	5.79433i	0.0126240	−	0.0218654i
$266$	−121.730	−	3.75838i	−0.457631	−	0.0141292i
$267$	210.335	−	42.5806i	0.787773	−	0.159478i
$268$	133.542			0.498291
$269$	70.7724	−	40.8605i	0.263094	−	0.151898i	−0.362651	−	0.931925i	$-0.618128\pi$
$269$	70.7724	−	40.8605i	0.263094	−	0.151898i	0.625745	+	0.780027i	$0.284795\pi$
$270$	35.1996	−	73.2475i	0.130369	−	0.271287i
$271$	−121.924	+	211.178i	−0.449903	+	0.779256i	−0.998379	−	0.0569108i	$-0.981875\pi$
$271$	−121.924	+	211.178i	−0.449903	+	0.779256i	0.548476	+	0.836166i	$0.315208\pi$
$272$	36.0479	−	20.8123i	0.132529	−	0.0765157i
$273$	279.379	+	336.802i	1.02337	+	1.23371i
$274$	107.371	−	185.972i	0.391864	−	0.678729i
$275$	−158.808	+	91.6876i	−0.577482	+	0.333409i
$276$	−36.4783	+	108.671i	−0.132168	+	0.393737i
$277$	223.980	−	387.945i	0.808593	−	1.40052i	−0.105246	−	0.994446i	$-0.533563\pi$
$277$	223.980	−	387.945i	0.808593	−	1.40052i	0.913839	−	0.406078i	$-0.133104\pi$
$278$	86.0505	+	49.6813i	0.309534	+	0.178710i
$279$	42.2133	−	338.366i	0.151302	−	1.21278i
$280$	35.8251	+	22.1852i	0.127947	+	0.0792327i
$281$	−63.8589	+	36.8690i	−0.227256	+	0.131206i	−0.609305	−	0.792936i	$-0.708552\pi$
$281$	−63.8589	+	36.8690i	−0.227256	+	0.131206i	0.382050	+	0.924142i	$0.375218\pi$
$282$	−210.600	+	185.959i	−0.746808	+	0.659428i
$283$	−73.4556			−0.259560			−0.129780	−	0.991543i	$-0.541427\pi$
$283$	−73.4556			−0.259560			−0.129780	+	0.991543i	$0.541427\pi$
$284$		−	231.675i		−	0.815755i
$285$	51.9913	+	58.8806i	0.182426	+	0.206599i
$286$	−131.993	−	228.619i	−0.461515	−	0.799368i
$287$	−232.530	−	7.17932i	−0.810210	−	0.0250150i
$288$	−50.5201	−	6.30270i	−0.175417	−	0.0218844i
$289$	−90.3562	+	156.502i	−0.312651	+	0.541528i
$290$	85.4704	+	49.3463i	0.294725	+	0.170160i
$291$	−367.382	−	123.321i	−1.26248	−	0.423784i
$292$	39.2067	+	67.9080i	0.134269	+	0.232562i
$293$	−329.350	−	190.150i	−1.12406	−	0.648977i	−0.181626	−	0.983368i	$-0.558136\pi$
$293$	−329.350	−	190.150i	−1.12406	−	0.648977i	−0.942434	+	0.334391i	$0.891469\pi$
$294$	205.913	−	28.6002i	0.700383	−	0.0972796i
$295$	−89.6502	−	155.279i	−0.303899	−	0.526369i
$296$	83.0273	+	47.9358i	0.280498	+	0.161945i
$297$	18.2742	+	241.177i	0.0615294	+	0.812043i
$298$	146.241	+	253.297i	0.490741	+	0.849989i
$299$			398.108i			1.33146i
$300$	24.3699	+	120.380i	0.0812331	+	0.401267i
$301$	123.159	+	76.2680i	0.409166	+	0.253382i
$302$	232.692	+	134.345i	0.770503	+	0.444850i
$303$	−183.842	+	37.2172i	−0.606739	+	0.122829i
$304$	24.6048	−	42.6168i	0.0809370	−	0.140187i
$305$	−169.612	+	97.9257i	−0.556106	+	0.321068i
$306$	−122.020	+	51.5148i	−0.398757	+	0.168349i
$307$	171.378			0.558235			0.279118	−	0.960257i	$-0.409958\pi$
$307$	171.378			0.558235			0.279118	+	0.960257i	$0.409958\pi$
$308$	−125.353	−	3.87026i	−0.406992	−	0.0125658i
$309$	−401.733	−	134.852i	−1.30011	−	0.436414i
$310$	−57.0183	−	98.7586i	−0.183930	−	0.318576i
$311$		−	168.397i		−	0.541470i	−0.962654	−	0.270735i	$-0.912733\pi$
$311$		−	168.397i		−	0.541470i	0.962654	−	0.270735i	$-0.0872666\pi$
$312$	−173.299	+	35.0829i	−0.555446	+	0.112445i
$313$	207.059			0.661531			0.330766	−	0.943713i	$-0.392693\pi$
$313$	207.059			0.661531			0.330766	+	0.943713i	$0.392693\pi$
$314$		−	126.355i		−	0.402406i
$315$	−104.379	−	84.1619i	−0.331361	−	0.267181i
$316$	−104.833			−0.331752
$317$		−	129.922i		−	0.409850i	−0.978778	−	0.204925i	$-0.934305\pi$
$317$		−	129.922i		−	0.409850i	0.978778	−	0.204925i	$-0.0656950\pi$
$318$	12.6442	+	4.24436i	0.0397617	+	0.0133470i
$319$	−293.733			−0.920794
$320$	−14.7453	+	8.51317i	−0.0460789	+	0.0266037i
$321$	−95.5555	+	19.3444i	−0.297681	+	0.0602628i
$322$	160.796	+	99.5749i	0.499365	+	0.309239i
$323$		−	128.021i		−	0.396349i
$324$	157.034	+	39.8016i	0.484674	+	0.122844i
$325$	213.279	+	369.410i	0.656242	+	1.13665i
$326$	174.127	+	100.532i	0.534132	+	0.308381i
$327$	225.334	+	75.6392i	0.689095	+	0.231312i
$328$	47.0006	−	81.4074i	0.143295	−	0.248193i
$329$	219.273	+	408.402i	0.666483	+	1.24134i
$330$	53.5390	+	60.6334i	0.162239	+	0.183737i
$331$	43.0801			0.130151			0.0650756	−	0.997880i	$-0.479271\pi$
$331$	43.0801			0.130151			0.0650756	+	0.997880i	$0.479271\pi$
$332$	−18.5125	+	10.6882i	−0.0557606	+	0.0321934i
$333$	−243.276	−	184.064i	−0.730559	−	0.552743i
$334$	−64.1176	+	111.055i	−0.191969	+	0.332500i
$335$	−123.069	+	71.0542i	−0.367371	+	0.212102i
$336$	−29.1757	+	78.7704i	−0.0868324	+	0.234436i
$337$	−104.291	+	180.638i	−0.309469	+	0.536017i	−0.978246	−	0.207446i	$-0.933485\pi$
$337$	−104.291	+	180.638i	−0.309469	+	0.536017i	0.668777	+	0.743463i	$0.266818\pi$
$338$	−324.820	+	187.535i	−0.961005	+	0.554836i
$339$	−561.095	+	113.589i	−1.65515	+	0.335070i
$340$	−22.1473	+	38.3603i	−0.0651391	+	0.112824i
$341$	293.930	+	169.700i	0.861964	+	0.497655i
$342$	−94.4775	+	124.871i	−0.276250	+	0.365118i
$343$	31.7147	−	341.531i	0.0924626	−	0.995716i
$344$	−50.6911	+	29.2665i	−0.147358	+	0.0850771i
$345$	−24.2035	−	119.558i	−0.0701552	−	0.346546i
$346$	−71.9240			−0.207873
$347$			427.035i			1.23065i	0.788274	+	0.615324i	$0.210975\pi$
$347$			427.035i			1.23065i	−0.788274	+	0.615324i	$0.789025\pi$
$348$	−62.6072	+	186.511i	−0.179906	+	0.535952i
$349$	−286.863	−	496.862i	−0.821957	−	1.42367i	−0.904223	−	0.427061i	$-0.859549\pi$
$349$	−286.863	−	496.862i	−0.821957	−	1.42367i	0.0822652	−	0.996610i	$-0.473785\pi$
$350$	202.550	+	6.25368i	0.578714	+	0.0178676i
$351$	561.013	−	42.5086i	1.59833	−	0.121107i
$352$	25.3373	−	43.8855i	0.0719809	−	0.124675i
$353$	266.085	+	153.624i	0.753782	+	0.435196i	0.827059	−	0.562115i	$-0.190012\pi$
$353$	266.085	+	153.624i	0.753782	+	0.435196i	−0.0732768	+	0.997312i	$0.523346\pi$
$354$	267.926	−	236.578i	0.756853	−	0.668298i
$355$	123.268	+	213.506i	0.347233	+	0.601426i
$356$	123.901	+	71.5340i	0.348035	+	0.200938i
$357$	36.7293	+	215.420i	0.102883	+	0.603417i
$358$	−26.9076	−	46.6053i	−0.0751609	−	0.130182i
$359$	−315.969	−	182.425i	−0.880137	−	0.508147i	−0.00943342	−	0.999956i	$-0.503003\pi$
$359$	−315.969	−	182.425i	−0.880137	−	0.508147i	−0.870704	+	0.491808i	$0.836336\pi$
$360$	49.9117	−	21.0719i	0.138644	−	0.0585332i
$361$	104.825	+	181.563i	0.290374	+	0.502943i
$362$		−	174.695i		−	0.482583i
$363$	115.903	+	38.9057i	0.319291	+	0.107178i
$364$	−9.00278	+	291.590i	−0.0247329	+	0.801072i
$365$	−72.2641	−	41.7217i	−0.197984	−	0.114306i
$366$	−258.416	−	292.658i	−0.706054	−	0.799612i
$367$	−252.978	+	438.171i	−0.689313	+	1.19393i	0.282747	+	0.959194i	$0.408754\pi$
$367$	−252.978	+	438.171i	−0.689313	+	1.19393i	−0.972060	+	0.234731i	$0.924579\pi$
$368$	−66.1819	+	38.2102i	−0.179842	+	0.103832i
$369$	−180.473	+	238.530i	−0.489085	+	0.646422i
$370$	−102.021			−0.275734
$371$	11.5858	−	18.7090i	0.0312286	−	0.0504287i
$372$	170.403	−	150.465i	0.458073	−	0.404477i
$373$	−119.155	−	206.382i	−0.319450	−	0.553303i	0.660924	−	0.750453i	$-0.270165\pi$
$373$	−119.155	−	206.382i	−0.319450	−	0.553303i	−0.980373	+	0.197150i	$0.936831\pi$
$374$		−	131.832i		−	0.352491i
$375$	−192.163	−	217.626i	−0.512433	−	0.580335i
$376$	−187.300			−0.498138
$377$			683.267i			1.81238i
$378$	123.151	−	237.225i	0.325798	−	0.627579i
$379$	−308.529			−0.814061			−0.407031	−	0.913415i	$-0.633436\pi$
$379$	−308.529			−0.814061			−0.407031	+	0.913415i	$0.633436\pi$
$380$			52.3663i			0.137806i
$381$	422.929	−	373.445i	1.11005	−	0.980170i
$382$	−392.719			−1.02806
$383$	348.921	−	201.450i	0.911021	−	0.525978i	0.0302615	−	0.999542i	$-0.490366\pi$
$383$	348.921	−	201.450i	0.911021	−	0.525978i	0.880760	+	0.473564i	$0.157033\pi$
$384$	−22.4654	−	25.4422i	−0.0585036	−	0.0662558i
$385$	117.582	−	63.1305i	0.305408	−	0.163975i
$386$		−	302.384i		−	0.783377i
$387$	171.586	−	72.4410i	0.443375	−	0.187186i
$388$	−129.176	−	223.739i	−0.332928	−	0.576648i
$389$	187.262	+	108.116i	0.481394	+	0.277933i	0.720997	−	0.692938i	$-0.243684\pi$
$389$	187.262	+	108.116i	0.481394	+	0.277933i	−0.239603	+	0.970871i	$0.577017\pi$
$390$	141.042	−	124.540i	0.361646	−	0.319332i
$391$	−99.4050	+	172.174i	−0.254233	+	0.440344i
$392$	115.521	+	76.5689i	0.294698	+	0.195329i
$393$	77.4021	−	230.586i	0.196952	−	0.586733i
$394$	469.562			1.19178
$395$	96.6123	−	55.7791i	0.244588	−	0.141213i
$396$	−97.2899	+	128.588i	−0.245681	+	0.324716i
$397$	130.421	−	225.896i	0.328516	−	0.569007i	−0.653701	−	0.756753i	$-0.726785\pi$
$397$	130.421	−	225.896i	0.328516	−	0.569007i	0.982218	+	0.187746i	$0.0601181\pi$
$398$	110.559	−	63.8312i	0.277786	−	0.160380i
$399$	164.943	+	198.844i	0.413390	+	0.498357i
$400$	−40.9407	+	70.9114i	−0.102352	+	0.177279i
$401$	631.146	−	364.392i	1.57393	−	0.908709i	0.578251	−	0.815859i	$-0.303736\pi$
$401$	631.146	−	364.392i	1.57393	−	0.908709i	0.995680	−	0.0928504i	$-0.0295978\pi$
$402$	−187.504	−	212.350i	−0.466429	−	0.528235i
$403$	394.748	−	683.724i	0.979524	−	1.69658i
$404$	−108.294	−	62.5237i	−0.268055	−	0.154762i
$405$	−165.897	+	46.8736i	−0.409622	+	0.115737i
$406$	275.971	+	170.899i	0.679732	+	0.420933i
$407$	262.961	−	151.820i	0.646095	−	0.373023i
$408$	−83.7087	−	28.0990i	−0.205168	−	0.0688700i
$409$	236.165			0.577421			0.288711	−	0.957416i	$-0.406773\pi$
$409$	236.165			0.577421			0.288711	+	0.957416i	$0.406773\pi$
$410$			100.031i			0.243978i
$411$	−446.479	+	90.3857i	−1.08632	+	0.219917i
$412$	−141.254	−	244.659i	−0.342850	−	0.593833i
$413$	−278.960	−	519.571i	−0.675448	−	1.25804i
$414$	224.021	−	94.5784i	0.541114	−	0.228450i
$415$	11.3738	−	19.7000i	0.0274068	−	0.0474700i
$416$	−102.084	−	58.9382i	−0.245394	−	0.141678i
$417$	−41.8221	−	206.589i	−0.100293	−	0.495417i
$418$	−77.9275	−	134.974i	−0.186429	−	0.322905i
$419$	22.4520	+	12.9626i	0.0535846	+	0.0309371i	0.526553	−	0.850142i	$-0.323484\pi$
$419$	22.4520	+	12.9626i	0.0535846	+	0.0309371i	−0.472968	+	0.881079i	$0.656818\pi$
$420$	−15.0240	−	88.1167i	−0.0357714	−	0.209802i
$421$	163.113	+	282.520i	0.387442	+	0.671069i	0.992105	−	0.125413i	$-0.0400255\pi$
$421$	163.113	+	282.520i	0.387442	+	0.671069i	−0.604663	+	0.796481i	$0.706692\pi$
$422$	−98.9231	−	57.1133i	−0.234415	−	0.135340i
$423$	591.400	+	73.7810i	1.39811	+	0.174423i
$424$	4.44586	+	7.70046i	0.0104855	+	0.0181615i
$425$			213.017i			0.501217i
$426$	−368.395	+	325.291i	−0.864776	+	0.763594i
$427$	−567.532	+	304.711i	−1.32911	+	0.713608i
$428$	−56.2881	−	32.4980i	−0.131514	−	0.0759298i
$429$	−178.206	+	530.889i	−0.415399	+	1.23750i
$430$	31.1439	−	53.9428i	0.0724276	−	0.125448i
$431$	356.337	−	205.731i	0.826768	−	0.477335i	−0.0259770	−	0.999663i	$-0.508270\pi$
$431$	356.337	−	205.731i	0.826768	−	0.477335i	0.852745	+	0.522328i	$0.174936\pi$
$432$	60.9123	+	89.1835i	0.141001	+	0.206443i
$433$	407.282			0.940605			0.470303	−	0.882505i	$-0.344145\pi$
$433$	407.282			0.940605			0.470303	+	0.882505i	$0.344145\pi$
$434$	−177.421	−	330.452i	−0.408805	−	0.761410i
$435$	−41.5402	−	205.196i	−0.0954947	−	0.471716i
$436$	79.2302	+	137.231i	0.181721	+	0.314749i
$437$			235.039i			0.537846i
$438$	52.9336	−	157.693i	0.120853	−	0.360029i
$439$	−153.542			−0.349753			−0.174877	−	0.984590i	$-0.555953\pi$
$439$	−153.542			−0.349753			−0.174877	+	0.984590i	$0.555953\pi$
$440$			53.9252i			0.122557i
$441$	−334.597	−	287.273i	−0.758724	−	0.651412i
$442$	−306.659			−0.693800
$443$		−	86.7223i		−	0.195761i	−0.995198	−	0.0978807i	$-0.968794\pi$
$443$		−	86.7223i		−	0.195761i	0.995198	−	0.0978807i	$-0.0312064\pi$
$444$	−40.3528	−	199.331i	−0.0908847	−	0.448944i
$445$	−152.245			−0.342125
$446$	385.984	−	222.848i	0.865434	−	0.499659i
$447$	197.442	−	588.194i	0.441705	−	1.31587i
$448$	−49.3384	+	26.4900i	−0.110130	+	0.0591295i
$449$			745.441i			1.66022i	0.557596	+	0.830112i	$0.311724\pi$
$449$			745.441i			1.66022i	−0.557596	+	0.830112i	$0.688276\pi$
$450$	157.204	−	207.776i	0.349342	−	0.461724i
$451$	−148.858	−	257.830i	−0.330063	−	0.571686i
$452$	−330.520	−	190.826i	−0.731239	−	0.422181i
$453$	−113.093	−	558.644i	−0.249653	−	1.23321i
$454$	−199.103	+	344.857i	−0.438553	+	0.759597i
$455$	−146.851	−	273.513i	−0.322749	−	0.601128i
$456$	−102.314	+	20.7126i	−0.224373	+	0.0454223i
$457$	463.102			1.01335			0.506677	−	0.862136i	$-0.330874\pi$
$457$	463.102			1.01335			0.506677	+	0.862136i	$0.330874\pi$
$458$	−220.610	+	127.369i	−0.481682	+	0.278099i
$459$	253.242	+	121.697i	0.551725	+	0.265135i
$460$	40.6612	−	70.4273i	0.0883939	−	0.153103i
$461$	407.470	−	235.253i	0.883883	−	0.510310i	0.0119464	−	0.999929i	$-0.496197\pi$
$461$	407.470	−	235.253i	0.883883	−	0.510310i	0.871937	+	0.489618i	$0.162864\pi$
$462$	169.853	+	204.764i	0.367647	+	0.443211i
$463$	−103.171	+	178.698i	−0.222832	+	0.385956i	−0.955667	−	0.294451i	$-0.904863\pi$
$463$	−103.171	+	178.698i	−0.222832	+	0.385956i	0.732835	+	0.680406i	$0.238197\pi$
$464$	−113.587	+	65.5795i	−0.244800	+	0.141335i
$465$	−76.9814	+	229.333i	−0.165551	+	0.493189i
$466$	−151.816	+	262.954i	−0.325786	+	0.564278i
$467$	−286.525	−	165.425i	−0.613544	−	0.354230i	0.160807	−	0.986986i	$-0.448590\pi$
$467$	−286.525	−	165.425i	−0.613544	−	0.354230i	−0.774351	+	0.632756i	$0.781924\pi$
$468$	299.114	+	226.310i	0.639132	+	0.483569i
$469$	−411.797	+	221.096i	−0.878032	+	0.471420i
$470$	172.612	−	99.6573i	0.367259	−	0.212037i
$471$	−200.923	+	177.414i	−0.426587	+	0.376675i
$472$	238.284			0.504839
$473$			185.384i			0.391931i
$474$	147.195	+	166.700i	0.310538	+	0.351687i
$475$	125.918	+	218.096i	0.265090	+	0.459149i
$476$	−76.7018	+	123.860i	−0.161138	+	0.260209i
$477$	−11.0045	−	26.0655i	−0.0230702	−	0.0546447i
$478$	−323.116	+	559.653i	−0.675975	+	1.17082i
$479$	−645.847	−	372.880i	−1.34832	−	0.778455i	−0.360312	−	0.932832i	$-0.617330\pi$
$479$	−645.847	−	372.880i	−1.34832	−	0.778455i	−0.988012	+	0.154377i	$0.950663\pi$
$480$	34.2407	+	11.4938i	0.0713349	+	0.0239454i
$481$	−353.156	−	611.685i	−0.734213	−	1.27169i
$482$	396.037	+	228.652i	0.821654	+	0.474382i
$483$	−67.4329	−	395.499i	−0.139613	−	0.818839i
$484$	40.7528	+	70.5859i	0.0842000	+	0.145839i
$485$	238.091	+	137.462i	0.490910	+	0.283427i
$486$	−157.200	−	305.592i	−0.323456	−	0.628789i
$487$	211.707	+	366.687i	0.434717	+	0.752951i	0.997272	−	0.0738079i	$-0.0235152\pi$
$487$	211.707	+	366.687i	0.434717	+	0.752951i	−0.562556	+	0.826759i	$0.690182\pi$
$488$		−	260.280i		−	0.533360i
$489$	−84.6290	−	418.042i	−0.173065	−	0.854892i
$490$	−147.202	−	9.09835i	−0.300413	−	0.0185681i
$491$	464.317	+	268.074i	0.945656	+	0.545975i	0.891729	−	0.452570i	$-0.149493\pi$
$491$	464.317	+	268.074i	0.945656	+	0.545975i	0.0539270	+	0.998545i	$0.482826\pi$
$492$	−195.442	+	39.5655i	−0.397240	+	0.0804177i
$493$	−170.607	+	295.501i	−0.346060	+	0.599393i
$494$	−313.970	+	181.271i	−0.635567	+	0.366945i
$495$	21.2421	−	170.269i	0.0429134	−	0.343978i
$496$	151.551			0.305546
$497$	383.567	+	714.403i	0.771764	+	1.43743i
$498$	42.9889	+	14.4303i	0.0863231	+	0.0289765i
$499$	−158.970	−	275.344i	−0.318577	−	0.551791i	0.661615	−	0.749844i	$-0.269871\pi$
$499$	−158.970	−	275.344i	−0.318577	−	0.551791i	−0.980191	+	0.198053i	$0.936538\pi$
$500$		−	193.549i		−	0.387097i
$501$	266.619	−	53.9748i	0.532174	−	0.107734i
$502$	−541.308			−1.07830
$503$			347.660i			0.691173i	0.938387	+	0.345587i	$0.112320\pi$
$503$			347.660i			0.691173i	−0.938387	+	0.345587i	$0.887680\pi$
$504$	166.221	−	64.2070i	0.329804	−	0.127395i
$505$	133.069			0.263503
$506$			242.035i			0.478331i
$507$	754.281	+	253.194i	1.48773	+	0.499396i
$508$	376.138			0.740430
$509$	−100.375	+	57.9514i	−0.197200	+	0.113853i	−0.595349	−	0.803467i	$-0.702986\pi$
$509$	−100.375	+	57.9514i	−0.197200	+	0.113853i	0.398149	+	0.917321i	$0.369653\pi$
$510$	92.0949	−	18.6438i	0.180578	−	0.0365565i
$511$	−233.330	−	144.493i	−0.456614	−	0.282765i
$512$		−	22.6274i		−	0.0441942i
$513$	331.216	−	25.0966i	0.645645	−	0.0489213i
$514$	−236.464	−	409.568i	−0.460047	−	0.796825i
$515$	260.353	+	150.315i	0.505541	+	0.291874i
$516$	117.713	+	39.5132i	0.228125	+	0.0765760i
$517$	−296.604	+	513.734i	−0.573703	+	0.993683i
$518$	−335.391	−	10.3551i	−0.647473	−	0.0199906i
$519$	100.988	+	114.369i	0.194581	+	0.220365i
$520$	125.438			0.241227
$521$	708.353	−	408.968i	1.35960	−	0.784967i	0.370033	−	0.929018i	$-0.379346\pi$
$521$	708.353	−	408.968i	1.35960	−	0.784967i	0.989570	+	0.144051i	$0.0460129\pi$
$522$	384.485	−	162.324i	0.736561	−	0.310965i
$523$	−162.739	+	281.873i	−0.311165	+	0.538954i	−0.978615	−	0.205701i	$-0.934053\pi$
$523$	−162.739	+	281.873i	−0.311165	+	0.538954i	0.667450	+	0.744655i	$0.267386\pi$
$524$	140.429	−	81.0768i	0.267995	−	0.154727i
$525$	−274.453	−	330.863i	−0.522768	−	0.630215i
$526$	−29.7960	+	51.6082i	−0.0566463	+	0.0981144i
$527$	341.443	−	197.132i	0.647899	−	0.374065i
$528$	−105.360	+	21.3291i	−0.199545	+	0.0403961i
$529$	−81.9980	+	142.025i	−0.155006	+	0.268478i
$530$	−8.19442	−	4.73105i	−0.0154612	−	0.00892651i
$531$	−752.382	−	93.8646i	−1.41692	−	0.176769i
$532$	−5.31515	+	172.152i	−0.00999088	+	0.323594i
$533$	−599.751	+	346.266i	−1.12524	+	0.649656i
$534$	−60.2180	−	297.459i	−0.112768	−	0.557040i
$535$	69.1652			0.129281
$536$		−	188.857i		−	0.352345i
$537$	−36.3284	+	108.225i	−0.0676506	+	0.201536i
$538$	−57.7854	−	100.087i	−0.107408	−	0.186036i
$539$	392.954	−	195.604i	0.729042	−	0.362902i
$540$	−103.588	−	49.7797i	−0.191829	−	0.0921846i
$541$	−335.424	+	580.972i	−0.620008	+	1.07389i	0.369475	+	0.929241i	$0.379537\pi$
$541$	−335.424	+	580.972i	−0.620008	+	1.07389i	−0.989484	+	0.144645i	$0.953796\pi$
$542$	298.651	+	172.426i	0.551017	+	0.318130i
$543$	−277.789	+	245.287i	−0.511582	+	0.451725i
$544$	−29.4330	−	50.9794i	−0.0541048	−	0.0937122i
$545$	−146.034	−	84.3125i	−0.267952	−	0.154702i
$546$	476.310	−	395.102i	0.872362	−	0.723630i
$547$	212.349	+	367.799i	0.388207	+	0.672393i	0.992208	−	0.124589i	$-0.0397614\pi$
$547$	212.349	+	367.799i	0.388207	+	0.672393i	−0.604002	+	0.796983i	$0.706428\pi$
$548$	−263.004	−	151.845i	−0.479934	−	0.277090i
$549$	−102.529	+	821.834i	−0.186756	+	1.49696i
$550$	129.666	+	224.588i	0.235756	+	0.408341i
$551$			403.394i			0.732112i
$552$	153.685	+	51.5881i	0.278414	+	0.0934568i
$553$	323.270	−	173.565i	0.584575	−	0.313861i
$554$	−548.637	−	316.756i	−0.990320	−	0.571761i
$555$	143.247	+	162.228i	0.258103	+	0.292303i
$556$	70.2599	−	121.694i	0.126367	−	0.218874i
$557$	−352.922	+	203.759i	−0.633611	+	0.365816i	−0.782149	−	0.623091i	$-0.785877\pi$
$557$	−352.922	+	203.759i	−0.633611	+	0.365816i	0.148538	+	0.988907i	$0.452543\pi$
$558$	−478.522	−	59.6987i	−0.857566	−	0.106987i
$559$	431.229			0.771430
$560$	31.3746	−	50.6643i	0.0560260	−	0.0904719i
$561$	−209.630	+	185.103i	−0.373673	+	0.329952i
$562$	52.1406	+	90.3101i	0.0927768	+	0.160694i
$563$			387.796i			0.688803i	0.938822	+	0.344402i	$0.111918\pi$
$563$			387.796i			0.688803i	−0.938822	+	0.344402i	$0.888082\pi$
$564$	262.985	+	297.833i	0.466286	+	0.528073i
$565$	406.133			0.718820
$566$			103.882i			0.183537i
$567$	−550.136	+	137.256i	−0.970258	+	0.242075i
$568$	−327.637			−0.576826
$569$		−	682.994i		−	1.20034i	−0.799872	−	0.600170i	$-0.795100\pi$
$569$		−	682.994i		−	1.20034i	0.799872	−	0.600170i	$-0.204900\pi$
$570$	83.2698	−	73.5268i	0.146087	−	0.128994i
$571$	790.279			1.38403			0.692013	−	0.721885i	$-0.256724\pi$
$571$	790.279			1.38403			0.692013	+	0.721885i	$0.256724\pi$
$572$	−323.316	+	186.667i	−0.565238	+	0.326340i
$573$	551.412	+	624.478i	0.962324	+	1.08984i
$574$	−10.1531	+	328.848i	−0.0176883	+	0.572905i
$575$		−	391.088i		−	0.680153i
$576$	−8.91337	+	71.4461i	−0.0154746	+	0.124038i
$577$	−478.802	−	829.310i	−0.829813	−	1.43728i	−0.898185	−	0.439619i	$-0.855114\pi$
$577$	−478.802	−	829.310i	−0.829813	−	1.43728i	0.0683714	−	0.997660i	$-0.478220\pi$
$578$	221.327	+	127.783i	0.382918	+	0.221078i
$579$	−480.832	+	424.573i	−0.830453	+	0.733286i
$580$	69.7863	−	120.873i	0.120321	−	0.208402i
$581$	39.3905	−	63.6085i	0.0677977	−	0.109481i
$582$	−174.403	+	519.557i	−0.299661	+	0.892710i
$583$	28.1615			0.0483045
$584$	96.0364	−	55.4466i	0.164446	−	0.0949429i
$585$	−396.070	−	49.4123i	−0.677043	−	0.0844655i
$586$	−268.913	+	465.771i	−0.458896	+	0.794831i
$587$	−790.499	+	456.395i	−1.34668	+	0.777504i	−0.987777	−	0.155872i	$-0.950181\pi$
$587$	−790.499	+	456.395i	−1.34668	+	0.777504i	−0.358899	+	0.933376i	$0.616848\pi$
$588$	−40.4468	−	291.204i	−0.0687871	−	0.495246i
$589$	233.055	−	403.663i	0.395679	−	0.685337i
$590$	−219.597	+	126.785i	−0.372199	+	0.214889i
$591$	−659.306	−	746.670i	−1.11558	−	1.26340i
$592$	67.7915	−	117.418i	0.114513	−	0.198342i
$593$	−650.841	−	375.763i	−1.09754	−	0.633665i	−0.161966	−	0.986796i	$-0.551783\pi$
$593$	−650.841	−	375.763i	−1.09754	−	0.633665i	−0.935574	+	0.353132i	$0.885117\pi$
$594$	341.076	−	25.8437i	0.574201	−	0.0435079i
$595$	4.78427	−	154.957i	0.00804079	−	0.260432i
$596$	358.215	−	206.816i	0.601033	−	0.347006i
$597$	−256.735	−	86.1795i	−0.430041	−	0.144354i
$598$	563.010			0.941488
$599$			837.451i			1.39808i	0.715081	+	0.699041i	$0.246390\pi$
$599$			837.451i			1.39808i	−0.715081	+	0.699041i	$0.753610\pi$
$600$	170.243	−	34.4643i	0.283739	−	0.0574405i
$601$	−178.129	−	308.529i	−0.296388	−	0.513359i	0.678919	−	0.734213i	$-0.262449\pi$
$601$	−178.129	−	308.529i	−0.296388	−	0.513359i	−0.975307	+	0.220855i	$0.929115\pi$
$602$	107.859	−	174.173i	0.179168	−	0.289324i
$603$	−74.3943	+	596.316i	−0.123374	+	0.988916i
$604$	189.992	−	329.076i	0.314557	−	0.544828i
$605$	−75.1138	−	43.3670i	−0.124155	−	0.0716809i
$606$	52.6330	+	259.992i	0.0868532	+	0.429029i
$607$	−288.539	−	499.764i	−0.475352	−	0.823334i	0.524249	−	0.851565i	$-0.324346\pi$
$607$	−288.539	−	499.764i	−0.475352	−	0.823334i	−0.999601	+	0.0282308i	$0.991013\pi$
$608$	−60.2693	−	34.7965i	−0.0991272	−	0.0572311i
$609$	−115.734	−	678.789i	−0.190040	−	1.11460i
$610$	138.488	+	239.868i	0.227029	+	0.393226i
$611$	1195.02	+	689.945i	1.95584	+	1.12921i
$612$	72.8530	+	172.562i	0.119041	+	0.281964i
$613$	−493.390	−	854.577i	−0.804878	−	1.39409i	−0.916373	−	0.400325i	$-0.868897\pi$
$613$	−493.390	−	854.577i	−0.804878	−	1.39409i	0.111495	−	0.993765i	$-0.464436\pi$
$614$		−	242.365i		−	0.394732i
$615$	159.063	−	140.452i	0.258640	−	0.228378i
$616$	−5.47337	+	177.276i	−0.00888534	+	0.287786i
$617$	−683.671	−	394.718i	−1.10806	−	0.639737i	−0.169732	−	0.985490i	$-0.554290\pi$
$617$	−683.671	−	394.718i	−1.10806	−	0.639737i	−0.938325	+	0.345753i	$0.887623\pi$
$618$	−190.709	+	568.136i	−0.308591	+	0.919314i
$619$	80.1860	−	138.886i	0.129541	−	0.224372i	−0.793958	−	0.607973i	$-0.791983\pi$
$619$	80.1860	−	138.886i	0.129541	−	0.224372i	0.923499	+	0.383601i	$0.125316\pi$
$620$	−139.666	+	80.6361i	−0.225267	+	0.130058i
$621$	−464.938	−	223.429i	−0.748692	−	0.359789i
$622$	−238.149			−0.382877
$623$	−500.500	−	15.4528i	−0.803371	−	0.0248039i
$624$	49.6147	+	245.082i	0.0795108	+	0.392760i
$625$	−152.898	−	264.826i	−0.244636	−	0.423722i
$626$		−	292.826i		−	0.467773i
$627$	−105.211	+	313.431i	−0.167801	+	0.499890i
$628$	−178.694			−0.284544
$629$		−	352.724i		−	0.560769i
$630$	−119.023	+	147.614i	−0.188925	+	0.234307i
$631$	836.748			1.32607			0.663033	−	0.748590i	$-0.269269\pi$
$631$	836.748			1.32607			0.663033	+	0.748590i	$0.269269\pi$
$632$			148.257i			0.234584i
$633$	48.0785	+	237.493i	0.0759533	+	0.375187i
$634$	−183.738			−0.289807
$635$	−346.641	+	200.133i	−0.545891	+	0.315170i
$636$	6.00243	−	17.8816i	0.00943778	−	0.0281158i
$637$	−455.003	−	914.068i	−0.714291	−	1.43496i
$638$			415.402i			0.651100i
$639$	1034.52	+	129.063i	1.61896	+	0.201976i
$640$	12.0394	+	20.8529i	0.0188116	+	0.0325827i
$641$	−129.348	−	74.6790i	−0.201791	−	0.116504i	0.395700	−	0.918380i	$-0.370502\pi$
$641$	−129.348	−	74.6790i	−0.201791	−	0.116504i	−0.597490	+	0.801876i	$0.703835\pi$
$642$	27.3571	+	135.136i	0.0426123	+	0.210492i
$643$	−5.29334	+	9.16834i	−0.00823226	+	0.0142587i	−0.870112	−	0.492854i	$-0.835954\pi$
$643$	−5.29334	+	9.16834i	−0.00823226	+	0.0142587i	0.861880	+	0.507112i	$0.169287\pi$
$644$	140.820	−	227.399i	0.218665	−	0.353105i
$645$	−129.505	+	26.2172i	−0.200783	+	0.0406468i
$646$	−181.049			−0.280261
$647$	−698.353	+	403.194i	−1.07937	+	0.623175i	−0.930727	−	0.365716i	$-0.880824\pi$
$647$	−698.353	+	403.194i	−1.07937	+	0.623175i	−0.148644	+	0.988891i	$0.547491\pi$
$648$	56.2880	−	222.080i	0.0868642	−	0.342717i
$649$	377.342	−	653.575i	0.581420	−	1.00705i
$650$	522.424	−	301.622i	0.803729	−	0.464033i
$651$	−276.350	+	746.107i	−0.424500	+	1.14609i
$652$	142.174	−	246.253i	0.218059	−	0.377689i
$653$	96.8368	−	55.9088i	0.148295	−	0.0856183i	−0.424016	−	0.905655i	$-0.639380\pi$
$653$	96.8368	−	55.9088i	0.148295	−	0.0856183i	0.572312	+	0.820036i	$0.306047\pi$
$654$	106.970	−	318.671i	0.163563	−	0.487264i
$655$	−86.2777	+	149.437i	−0.131722	+	0.228149i
$656$	−115.128	−	66.4689i	−0.175499	−	0.101325i
$657$	−325.077	+	137.242i	−0.494789	+	0.208893i
$658$	577.568	−	310.099i	0.877762	−	0.471275i
$659$	510.814	−	294.918i	0.775135	−	0.447524i	−0.0595686	−	0.998224i	$-0.518972\pi$
$659$	510.814	−	294.918i	0.775135	−	0.447524i	0.834703	+	0.550700i	$0.185639\pi$
$660$	85.7485	−	75.7156i	0.129922	−	0.114721i
$661$	448.693			0.678810			0.339405	−	0.940640i	$-0.389774\pi$
$661$	448.693			0.678810			0.339405	+	0.940640i	$0.389774\pi$
$662$		−	60.9244i		−	0.0920309i
$663$	430.576	+	487.631i	0.649436	+	0.735492i
$664$	15.1154	+	26.1807i	0.0227642	+	0.0394287i
$665$	−86.6991	−	161.479i	−0.130375	−	0.242826i
$666$	−260.305	+	344.044i	−0.390849	+	0.516583i
$667$	313.226	−	542.523i	0.469603	−	0.813377i
$668$	157.055	+	90.6760i	0.235113	+	0.135742i
$669$	−896.313	−	300.870i	−1.33978	−	0.449731i
$670$	100.486	+	174.046i	0.149979	+	0.259771i
$671$	−713.905	−	412.174i	−1.06394	−	0.614268i
$672$	111.398	+	41.2607i	0.165771	+	0.0613998i
$673$	466.228	+	807.530i	0.692760	+	1.19990i	0.970930	+	0.239364i	$0.0769389\pi$
$673$	466.228	+	807.530i	0.692760	+	1.19990i	−0.278170	+	0.960532i	$0.589728\pi$
$674$	255.460	+	147.490i	0.379021	+	0.218828i
$675$	−551.120	+	41.7590i	−0.816474	+	0.0618652i
$676$	265.214	+	459.364i	0.392329	+	0.679533i
$677$		−	253.972i		−	0.375143i	−0.982251	−	0.187571i	$-0.939938\pi$
$677$		−	253.972i		−	0.375143i	0.982251	−	0.187571i	$-0.0600616\pi$
$678$	160.639	+	793.509i	0.236930	+	1.17037i
$679$	768.762	+	476.067i	1.13220	+	0.701129i
$680$	54.2496	+	31.3210i	0.0797788	+	0.0460603i
$681$	827.928	−	167.607i	1.21575	−	0.246119i
$682$	239.993	−	415.679i	0.351895	−	0.609501i
$683$	956.390	−	552.172i	1.40028	−	0.808451i	0.405857	−	0.913936i	$-0.366973\pi$
$683$	956.390	−	552.172i	1.40028	−	0.808451i	0.994421	+	0.105485i	$0.0336396\pi$
$684$	176.594	+	133.611i	0.258178	+	0.195338i
$685$	323.171			0.471783
$686$	−482.997	−	44.8513i	−0.704078	−	0.0653809i
$687$	512.291	+	171.963i	0.745692	+	0.250311i
$688$	41.3891	+	71.6880i	0.0601586	+	0.104198i
$689$		−	65.5078i		−	0.0950766i
$690$	−169.081	+	34.2290i	−0.245045	+	0.0496072i
$691$	4.23924			0.00613494			0.00306747	−	0.999995i	$-0.499024\pi$
$691$	4.23924			0.00613494			0.00306747	+	0.999995i	$0.499024\pi$
$692$			101.716i			0.146988i
$693$	87.1147	−	557.595i	0.125707	−	0.804610i
$694$	603.919			0.870200
$695$			149.534i			0.215156i
$696$	263.767	+	88.5400i	0.378975	+	0.127213i
$697$	−345.842			−0.496187
$698$	−702.668	+	405.686i	−1.00669	+	0.581212i
$699$	631.296	−	127.800i	0.903141	−	0.182833i
$700$	8.84403	−	286.449i	0.0126343	−	0.409212i
$701$		−	811.266i		−	1.15730i	−0.815576	−	0.578649i	$-0.803580\pi$
$701$		−	811.266i		−	1.15730i	0.815576	−	0.578649i	$-0.196420\pi$
$702$	−60.1162	−	793.392i	−0.0856356	−	1.13019i
$703$	−208.500	−	361.132i	−0.296586	−	0.513702i
$704$	−62.0634	−	35.8323i	−0.0881582	−	0.0508982i
$705$	−400.830	−	134.549i	−0.568554	−	0.190850i
$706$	217.258	−	376.301i	0.307730	−	0.533004i
$707$	437.458	+	13.5064i	0.618752	+	0.0191038i
$708$	−334.571	−	378.905i	−0.472558	−	0.535176i
$709$	−679.761			−0.958761			−0.479380	−	0.877607i	$-0.659139\pi$
$709$	−679.761			−0.958761			−0.479380	+	0.877607i	$0.659139\pi$
$710$	301.943	−	174.327i	0.425272	−	0.245531i
$711$	58.4012	−	468.122i	0.0821395	−	0.658399i
$712$	101.164	−	175.222i	0.142085	−	0.246098i
$713$	−626.870	+	361.923i	−0.879200	+	0.507607i
$714$	304.650	−	51.9431i	0.426681	−	0.0727494i
$715$	198.641	−	344.056i	0.277819	−	0.481197i
$716$	−65.9099	+	38.0531i	−0.0920529	+	0.0531467i
$717$	1343.61	−	272.002i	1.87393	−	0.379361i
$718$	−257.988	+	446.848i	−0.359314	+	0.622351i
$719$	93.3734	+	53.9092i	0.129866	+	0.0749780i	0.563525	−	0.826099i	$-0.309445\pi$
$719$	93.3734	+	53.9092i	0.129866	+	0.0749780i	−0.433660	+	0.901077i	$0.642778\pi$
$720$	−29.8002	−	70.5858i	−0.0413892	−	0.0980358i
$721$	840.643	+	520.579i	1.16594	+	0.722024i
$722$	256.768	−	148.245i	0.355635	−	0.205326i
$723$	−192.481	−	950.801i	−0.266226	−	1.31508i
$724$	−247.056			−0.341237
$725$		−	671.219i		−	0.925819i
$726$	55.0210	−	163.911i	0.0757865	−	0.225773i
$727$	−220.335	−	381.632i	−0.303075	−	0.524941i	0.673756	−	0.738954i	$-0.264680\pi$
$727$	−220.335	−	381.632i	−0.303075	−	0.524941i	−0.976831	+	0.214013i	$0.931346\pi$
$728$	412.371	+	12.7319i	0.566444	+	0.0174888i
$729$	−265.211	+	679.046i	−0.363801	+	0.931477i
$730$	−59.0034	+	102.197i	−0.0808265	+	0.139996i
$731$	186.499	+	107.675i	0.255128	+	0.147298i
$732$	−413.881	+	365.455i	−0.565411	+	0.499255i
$733$	112.200	+	194.337i	0.153070	+	0.265125i	0.932355	−	0.361545i	$-0.117751\pi$
$733$	112.200	+	194.337i	0.153070	+	0.265125i	−0.779284	+	0.626670i	$0.784417\pi$
$734$	619.667	+	357.765i	0.844233	+	0.487418i
$735$	192.217	+	246.847i	0.261520	+	0.335846i
$736$	54.0373	+	93.5954i	0.0734203	+	0.127168i
$737$	−518.005	−	299.070i	−0.702856	−	0.405794i
$738$	337.332	+	255.227i	0.457090	+	0.345836i
$739$	−351.064	−	608.061i	−0.475053	−	0.822816i	0.524539	−	0.851387i	$-0.324238\pi$
$739$	−351.064	−	608.061i	−0.475053	−	0.822816i	−0.999592	+	0.0285707i	$0.990904\pi$
$740$			144.280i			0.194973i
$741$	729.087	+	244.736i	0.983923	+	0.330279i
$742$	−26.4586	−	16.3848i	−0.0356584	−	0.0220820i
$743$	627.910	+	362.524i	0.845100	+	0.487919i	0.858995	−	0.511985i	$-0.171089\pi$
$743$	627.910	+	362.524i	0.845100	+	0.487919i	−0.0138943	+	0.999903i	$0.504423\pi$
$744$	−212.790	−	240.987i	−0.286008	−	0.323907i
$745$	−220.082	+	381.194i	−0.295413	+	0.511670i
$746$	−291.868	+	168.510i	−0.391244	+	0.225885i
$747$	−37.4139	−	88.6198i	−0.0500855	−	0.118634i
$748$	−186.438			−0.249249
$749$	227.377	+	7.02022i	0.303575	+	0.00937279i
$750$	−307.769	+	271.759i	−0.410359	+	0.362345i
$751$	−158.250	−	274.097i	−0.210719	−	0.364976i	0.741221	−	0.671261i	$-0.234247\pi$
$751$	−158.250	−	274.097i	−0.210719	−	0.364976i	−0.951940	+	0.306286i	$0.900914\pi$
$752$			264.882i			0.352237i
$753$	760.043	+	860.756i	1.00935	+	1.14310i
$754$	966.285			1.28155
$755$			404.359i			0.535575i
$756$	−335.487	−	174.163i	−0.443766	−	0.230374i
$757$	351.377			0.464171			0.232085	−	0.972695i	$-0.425445\pi$
$757$	351.377			0.464171			0.232085	+	0.972695i	$0.425445\pi$
$758$			436.326i			0.575628i
$759$	384.870	−	339.838i	0.507075	−	0.447745i
$760$	74.0572			0.0974437
$761$	114.692	−	66.2177i	0.150713	−	0.0870141i	−0.422747	−	0.906248i	$-0.638934\pi$
$761$	114.692	−	66.2177i	0.150713	−	0.0870141i	0.573460	+	0.819234i	$0.305601\pi$
$762$	−528.131	−	598.112i	−0.693085	−	0.784924i
$763$	−471.521	−	291.996i	−0.617983	−	0.382694i
$764$			555.389i			0.726949i
$765$	−158.955	−	120.266i	−0.207785	−	0.157211i
$766$	−284.893	−	493.449i	−0.371923	−	0.644189i
$767$	−1520.31	−	877.752i	−1.98215	−	1.14440i
$768$	−35.9807	+	31.7708i	−0.0468499	+	0.0413683i
$769$	−190.808	+	330.489i	−0.248125	+	0.429765i	−0.963006	−	0.269482i	$-0.913148\pi$
$769$	−190.808	+	330.489i	−0.248125	+	0.429765i	0.714881	+	0.699246i	$0.246481\pi$
$770$	−89.2800	−	166.286i	−0.115948	−	0.215956i
$771$	−319.254	+	951.080i	−0.414078	+	1.23357i
$772$	−427.635			−0.553932
$773$	−935.432	+	540.072i	−1.21013	+	0.698670i	−0.962788	−	0.270258i	$-0.912891\pi$
$773$	−935.432	+	540.072i	−1.21013	+	0.698670i	−0.247344	+	0.968928i	$0.579558\pi$
$774$	−102.447	−	242.659i	−0.132360	−	0.313513i
$775$	−387.787	+	671.667i	−0.500371	+	0.866667i
$776$	−316.415	+	182.682i	−0.407751	+	0.235415i
$777$	454.452	+	547.858i	0.584880	+	0.705094i
$778$	152.899	−	264.829i	0.196528	−	0.340397i
$779$	−354.087	+	204.432i	−0.454540	+	0.262429i
$780$	−176.125	−	199.464i	−0.225802	−	0.255723i
$781$	−518.840	+	898.657i	−0.664328	+	1.15065i
$782$	243.491	+	140.580i	0.311370	+	0.179770i
$783$	−797.966	−	383.468i	−1.01911	−	0.489742i
$784$	108.285	−	163.372i	0.138118	−	0.208383i
$785$	164.680	−	95.0781i	0.209783	−	0.121119i
$786$	−326.098	−	109.463i	−0.414883	−	0.139266i
$787$	1412.73			1.79509			0.897544	−	0.440925i	$-0.145349\pi$
$787$	1412.73			1.79509			0.897544	+	0.440925i	$0.145349\pi$
$788$		−	664.062i		−	0.842718i
$789$	123.900	−	25.0825i	0.157035	−	0.0317903i
$790$	−78.8836	−	136.630i	−0.0998526	−	0.172950i
$791$	1335.14	+	41.2223i	1.68792	+	0.0521141i
$792$	181.850	+	137.589i	0.229609	+	0.173723i
$793$	−958.776	+	1660.65i	−1.20905	+	2.09413i
$794$	−319.465	−	184.443i	−0.402349	−	0.232296i
$795$	3.98264	+	19.6731i	0.00500961	+	0.0247460i
$796$	−90.2709	−	156.354i	−0.113406	−	0.196424i
$797$	−590.806	−	341.102i	−0.741287	−	0.427982i	0.0812501	−	0.996694i	$-0.474109\pi$
$797$	−590.806	−	341.102i	−0.741287	−	0.427982i	−0.822537	+	0.568711i	$0.807442\pi$
$798$	281.208	−	233.264i	0.352391	−	0.292311i
$799$	344.550	+	596.778i	0.431226	+	0.746906i
$800$	100.284	+	57.8989i	0.125355	+	0.0723737i
$801$	−388.450	+	513.413i	−0.484957	+	0.640965i
$802$	−515.329	−	892.576i	−0.642555	−	1.11294i
$803$		−	351.217i		−	0.437381i
$804$	−300.309	+	265.171i	−0.373518	+	0.329815i
$805$	−8.78365	+	284.493i	−0.0109114	+	0.353407i
$806$	−966.931	−	558.258i	−1.19967	−	0.692628i
$807$	−78.0170	+	232.418i	−0.0966753	+	0.288002i
$808$	−88.4219	+	153.151i	−0.109433	+	0.189544i
$809$	−717.748	+	414.392i	−0.887204	+	0.512227i	−0.873027	−	0.487672i	$-0.837846\pi$
$809$	−717.748	+	414.392i	−0.887204	+	0.512227i	−0.0141768	+	0.999900i	$0.504513\pi$
$810$	66.2893	+	234.614i	0.0818386	+	0.289647i
$811$	−269.981			−0.332898			−0.166449	−	0.986050i	$-0.553230\pi$
$811$	−269.981			−0.332898			−0.166449	+	0.986050i	$0.553230\pi$
$812$	241.688	−	390.282i	0.297645	−	0.480643i
$813$	−145.150	−	716.998i	−0.178536	−	0.881917i
$814$	−214.706	−	371.882i	−0.263767	−	0.456858i
$815$			302.588i			0.371274i
$816$	−39.7379	+	118.382i	−0.0486985	+	0.145076i
$817$	254.593			0.311620
$818$		−	333.988i		−	0.408298i
$819$	−1297.05	−	202.642i	−1.58370	−	0.247426i
$820$	141.465			0.172519
$821$			540.660i			0.658538i	0.944236	+	0.329269i	$0.106802\pi$
$821$			540.660i			0.658538i	−0.944236	+	0.329269i	$0.893198\pi$
$822$	127.825	+	631.416i	0.155504	+	0.768146i
$823$	−31.8686			−0.0387225			−0.0193612	−	0.999813i	$-0.506163\pi$
$823$	−31.8686			−0.0387225			−0.0193612	+	0.999813i	$0.506163\pi$
$824$	−346.000	+	199.763i	−0.419903	+	0.242431i
$825$	175.064	−	521.527i	0.212199	−	0.632154i
$826$	−734.784	+	394.509i	−0.889569	+	0.477614i
$827$		−	1309.68i		−	1.58365i	−0.610749	−	0.791824i	$-0.709131\pi$
$827$		−	1309.68i		−	1.58365i	0.610749	−	0.791824i	$-0.290869\pi$
$828$	−133.754	−	316.814i	−0.161539	−	0.382626i
$829$	−458.707	−	794.505i	−0.553326	−	0.958389i	−0.998032	−	0.0627123i	$-0.980025\pi$
$829$	−458.707	−	794.505i	−0.553326	−	0.958389i	0.444705	−	0.895677i	$-0.353308\pi$
$830$	−27.8601	−	16.0850i	−0.0335663	−	0.0193795i
$831$	266.648	+	1317.16i	0.320876	+	1.58503i
$832$	−83.3512	+	144.369i	−0.100182	+	0.173520i
$833$	31.4561	−	508.929i	0.0377625	−	0.610960i
$834$	−292.161	+	59.1454i	−0.350313	+	0.0709178i
$835$	−192.985			−0.231120
$836$	−190.883	+	110.206i	−0.228328	+	0.131825i
$837$	576.957	+	844.738i	0.689315	+	1.00925i
$838$	18.3320	−	31.7519i	0.0218758	−	0.0378901i
$839$	1092.02	−	630.476i	1.30157	−	0.751461i	0.320896	−	0.947114i	$-0.396016\pi$
$839$	1092.02	−	630.476i	1.30157	−	0.751461i	0.980673	+	0.195653i	$0.0626827\pi$
$840$	−124.616	+	21.2471i	−0.148352	+	0.0252942i
$841$	117.084	−	202.796i	0.139221	−	0.241137i
$842$	399.543	−	230.676i	0.474517	−	0.273963i
$843$	70.3958	−	209.714i	0.0835063	−	0.248771i
$844$	−80.7704	+	139.898i	−0.0956995	+	0.165756i
$845$	−488.831	−	282.227i	−0.578498	−	0.333996i
$846$	104.342	−	836.366i	0.123336	−	0.988613i
$847$	−242.531	−	150.191i	−0.286342	−	0.177321i
$848$	10.8901	−	6.28740i	0.0128421	−	0.00741438i
$849$	165.187	−	145.859i	0.194566	−	0.171801i
$850$	301.252			0.354414
$851$			647.581i			0.760964i
$852$	460.031	+	520.989i	0.539942	+	0.611489i
$853$	150.056	+	259.905i	0.175916	+	0.304696i	0.940478	−	0.339855i	$-0.110378\pi$
$853$	150.056	+	259.905i	0.175916	+	0.304696i	−0.764562	+	0.644550i	$0.777045\pi$
$854$	430.926	+	802.611i	0.504597	+	0.939826i
$855$	−233.836	−	29.1725i	−0.273492	−	0.0341199i
$856$	−45.9591	+	79.6034i	−0.0536905	+	0.0929947i
$857$	442.157	+	255.280i	0.515936	+	0.297876i	0.735270	−	0.677774i	$-0.237055\pi$
$857$	442.157	+	255.280i	0.515936	+	0.297876i	−0.219334	+	0.975650i	$0.570388\pi$
$858$	750.790	+	252.022i	0.875047	+	0.293732i
$859$	659.044	+	1141.50i	0.767223	+	1.32887i	0.939063	+	0.343744i	$0.111695\pi$
$859$	659.044	+	1141.50i	0.767223	+	1.32887i	−0.171841	+	0.985125i	$0.554971\pi$
$860$	−76.2866	−	44.0441i	−0.0887054	−	0.0512141i
$861$	537.169	−	445.585i	0.623890	−	0.517521i
$862$	−290.948	−	503.936i	−0.337527	−	0.584613i
$863$	348.229	+	201.050i	0.403509	+	0.232966i	0.687997	−	0.725713i	$-0.258490\pi$
$863$	348.229	+	201.050i	0.403509	+	0.232966i	−0.284488	+	0.958680i	$0.591824\pi$
$864$	126.124	−	86.1430i	0.145977	−	0.0997026i
$865$	−54.1204	−	93.7392i	−0.0625669	−	0.108369i
$866$		−	575.984i		−	0.665109i
$867$	−107.569	−	531.358i	−0.124070	−	0.612870i
$868$	−467.329	+	250.911i	−0.538398	+	0.289068i
$869$	406.645	+	234.777i	0.467946	+	0.270169i
$870$	−290.191	+	58.7467i	−0.333553	+	0.0675249i
$871$	−695.681	+	1204.95i	−0.798715	+	1.38341i
$872$	194.073	−	112.048i	0.222561	−	0.128496i
$873$	1071.04	−	452.178i	1.22685	−	0.517959i
$874$	332.395			0.380315
$875$	320.444	+	596.836i	0.366222	+	0.682098i
$876$	−223.011	−	74.8594i	−0.254579	−	0.0854559i
$877$	403.270	+	698.484i	0.459829	+	0.796446i	0.998952	−	0.0457806i	$-0.0145775\pi$
$877$	403.270	+	698.484i	0.459829	+	0.796446i	−0.539123	+	0.842227i	$0.681244\pi$
$878$			217.141i			0.247313i
$879$	1118.22	−	226.373i	1.27215	−	0.257535i
$880$	76.2617			0.0866610
$881$		−	463.240i		−	0.525812i	−0.964821	−	0.262906i	$-0.915319\pi$
$881$		−	463.240i		−	0.525812i	0.964821	−	0.262906i	$-0.0846809\pi$
$882$	−406.265	+	473.192i	−0.460618	+	0.536499i
$883$	−390.166			−0.441864			−0.220932	−	0.975289i	$-0.570910\pi$
$883$	−390.166			−0.441864			−0.220932	+	0.975289i	$0.570910\pi$
$884$			433.682i			0.490590i
$885$	509.939	+	171.174i	0.576202	+	0.193417i
$886$	−122.644			−0.138424
$887$	−508.211	+	293.416i	−0.572954	+	0.330795i	−0.758328	−	0.651873i	$-0.773984\pi$
$887$	−508.211	+	293.416i	−0.572954	+	0.330795i	0.185374	+	0.982668i	$0.440650\pi$
$888$	−281.896	+	57.0675i	−0.317451	+	0.0642652i
$889$	−1159.88	+	622.745i	−1.30470	+	0.700500i
$890$			215.308i			0.241919i
$891$	−519.994	−	506.071i	−0.583608	−	0.567981i
$892$	−315.154	−	545.863i	−0.353312	−	0.611954i
$893$	705.528	+	407.337i	0.790064	+	0.456144i
$894$	−831.831	−	279.225i	−0.930460	−	0.312333i
$895$	40.4941	−	70.1378i	0.0452448	−	0.0783662i
$896$	37.4626	+	69.7750i	0.0418109	+	0.0778739i
$897$	−790.514	−	895.264i	−0.881286	−	0.998064i
$898$	1054.21			1.17396
$899$	−1075.89	+	621.164i	−1.19676	+	0.690950i
$900$	−293.839	−	222.320i	−0.326488	−	0.247022i
$901$	16.3569	−	28.3309i	0.0181541	−	0.0314439i
$902$	−364.627	+	210.518i	−0.404243	+	0.233390i
$903$	−428.403	+	73.0431i	−0.474422	+	0.0808894i
$904$	−269.868	+	467.426i	−0.298527	+	0.517064i
$905$	227.681	−	131.452i	0.251582	−	0.145251i
$906$	−790.042	+	159.937i	−0.872011	+	0.176531i
$907$	639.983	−	1108.48i	0.705604	−	1.22214i	−0.260869	−	0.965374i	$-0.584009\pi$
$907$	639.983	−	1108.48i	0.705604	−	1.22214i	0.966473	−	0.256768i	$-0.0826576\pi$
$908$	487.701	+	281.574i	0.537116	+	0.310104i
$909$	339.522	−	448.744i	0.373511	−	0.493668i
$910$	−386.806	+	207.678i	−0.425062	+	0.228218i
$911$	−843.131	+	486.782i	−0.925501	+	0.534338i	−0.885386	−	0.464857i	$-0.846106\pi$
$911$	−843.131	+	486.782i	−0.925501	+	0.534338i	−0.0401151	+	0.999195i	$0.512772\pi$
$912$	29.2920	+	144.694i	0.0321184	+	0.158656i
$913$	95.7458			0.104869
$914$		−	654.926i		−	0.716549i
$915$	186.975	−	557.010i	0.204344	−	0.608754i
$916$	180.127	+	311.990i	0.196646	+	0.340600i
$917$	−298.802	+	482.511i	−0.325847	+	0.526184i
$918$	172.106	−	358.138i	0.187479	−	0.390129i
$919$	−478.115	+	828.120i	−0.520256	+	0.901110i	0.479466	+	0.877560i	$0.340830\pi$
$919$	−478.115	+	828.120i	−0.520256	+	0.901110i	−0.999723	+	0.0235500i	$0.992503\pi$
$920$	−99.5992	−	57.5036i	−0.108260	−	0.0625040i
$921$	−385.395	+	340.302i	−0.418453	+	0.369492i
$922$	−332.698	−	576.250i	−0.360844	−	0.625000i
$923$	2090.41	+	1206.90i	2.26480	+	1.30758i
$924$	289.579	−	240.208i	0.313398	−	0.259965i
$925$	346.929	+	600.899i	0.375058	+	0.649620i
$926$	252.716	+	145.906i	0.272912	+	0.157566i
$927$	1171.19	−	494.458i	1.26342	−	0.533395i
$928$	92.7435	+	160.636i	0.0999391	+	0.173100i
$929$			542.404i			0.583857i	0.956440	+	0.291929i	$0.0942970\pi$
$929$			542.404i			0.583857i	−0.956440	+	0.291929i	$0.905703\pi$
$930$	324.325	+	108.868i	0.348737	+	0.117062i
$931$	−268.629	−	539.656i	−0.288538	−	0.579652i
$932$	371.872	+	214.701i	0.399005	+	0.230365i
$933$	334.382	+	378.691i	0.358395	+	0.405885i
$934$	−233.947	+	405.208i	−0.250478	+	0.433841i
$935$	171.817	−	99.1987i	0.183762	−	0.106095i
$936$	320.051	−	423.011i	0.341935	−	0.451934i
$937$	−1094.99			−1.16862			−0.584308	−	0.811532i	$-0.698634\pi$
$937$	−1094.99			−1.16862			−0.584308	+	0.811532i	$0.698634\pi$
$938$	312.677	+	582.369i	0.333344	+	0.620862i
$939$	−465.634	+	411.153i	−0.495883	+	0.437863i
$940$	−140.937	−	244.110i	−0.149933	−	0.259691i
$941$			15.0511i			0.0159947i	0.999968	+	0.00799737i	$0.00254567\pi$
$941$			15.0511i			0.0159947i	−0.999968	+	0.00799737i	$0.997454\pi$
$942$	250.901	+	284.148i	0.266349	+	0.301643i
$943$	634.947			0.673326
$944$		−	336.984i		−	0.356975i
$945$	401.845	−	17.9993i	0.425232	−	0.0190468i
$946$	262.172			0.277137
$947$		−	844.311i		−	0.891564i	−0.895142	−	0.445782i	$-0.852926\pi$
$947$		−	844.311i		−	0.891564i	0.895142	−	0.445782i	$-0.147074\pi$
$948$	235.749	−	208.166i	0.248681	−	0.219584i
$949$	−816.981			−0.860887
$950$	308.434	−	178.074i	0.324667	−	0.187447i
$951$	257.984	+	292.169i	0.271276	+	0.307223i
$952$	175.164	+	108.473i	0.183996	+	0.113942i
$953$		−	1313.93i		−	1.37873i	−0.724413	−	0.689367i	$-0.757889\pi$
$953$		−	1313.93i		−	1.37873i	0.724413	−	0.689367i	$-0.242111\pi$
$954$	−36.8622	+	15.5627i	−0.0386396	+	0.0163131i
$955$	−295.508	−	511.834i	−0.309432	−	0.535952i
$956$	791.469	+	456.955i	0.827897	+	0.477986i
$957$	660.547	−	583.260i	0.690226	−	0.609467i
$958$	−527.332	+	913.366i	−0.550451	+	0.953409i
$959$	1062.41	+	32.8017i	1.10783	+	0.0342040i
$960$	16.2547	−	48.4237i	0.0169319	−	0.0504414i
$961$	474.476			0.493731
$962$	−865.053	+	499.439i	−0.899224	+	0.519167i
$963$	176.473	−	233.244i	0.183254	−	0.242206i
$964$	323.363	−	560.081i	0.335439	−	0.580997i
$965$	394.099	−	227.533i	0.408393	−	0.235786i
$966$	−559.320	+	95.3645i	−0.579006	+	0.0987211i
$967$	440.465	−	762.908i	0.455496	−	0.788943i	−0.543220	−	0.839590i	$-0.682795\pi$
$967$	440.465	−	762.908i	0.455496	−	0.788943i	0.998717	+	0.0506473i	$0.0161284\pi$
$968$	99.8236	−	57.6332i	0.103124	−	0.0595384i
$969$	254.208	+	287.892i	0.262340	+	0.297103i
$970$	194.401	−	336.712i	0.200413	−	0.347126i
$971$	−853.170	−	492.578i	−0.878651	−	0.507289i	−0.00843742	−	0.999964i	$-0.502686\pi$
$971$	−853.170	−	492.578i	−0.878651	−	0.507289i	−0.870213	+	0.492675i	$0.836019\pi$
$972$	−432.172	+	222.314i	−0.444621	+	0.228718i
$973$	−15.1776	+	491.585i	−0.0155987	+	0.505226i
$974$	518.574	−	299.399i	0.532417	−	0.307391i
$975$	−1213.15	−	407.224i	−1.24426	−	0.417666i
$976$	−368.091			−0.377142
$977$			132.173i			0.135284i	0.997710	+	0.0676421i	$0.0215476\pi$
$977$			132.173i			0.135284i	−0.997710	+	0.0676421i	$0.978452\pi$
$978$	−591.201	+	119.684i	−0.604500	+	0.122376i
$979$	−320.404	−	554.956i	−0.327277	−	0.566860i
$980$	−12.8670	+	208.176i	−0.0131296	+	0.212424i
$981$	−656.926	+	277.344i	−0.669649	+	0.282716i
$982$	379.113	−	656.643i	0.386062	−	0.668680i
$983$	−1278.76	−	738.290i	−1.30087	−	0.751058i	−0.320318	−	0.947310i	$-0.603790\pi$
$983$	−1278.76	−	738.290i	−1.30087	−	0.751058i	−0.980554	+	0.196252i	$0.937123\pi$
$984$	55.9541	+	276.397i	0.0568639	+	0.280891i
$985$	353.329	+	611.985i	0.358710	+	0.621304i
$986$	417.901	+	241.275i	0.423835	+	0.244701i
$987$	−1304.05	−	483.007i	−1.32123	−	0.489369i
$988$	256.356	+	444.021i	0.259469	+	0.449414i
$989$	−342.401	−	197.686i	−0.346210	−	0.199884i
$990$	−240.797	−	30.0409i	−0.243229	−	0.0303444i
$991$	436.313	+	755.716i	0.440275	+	0.762579i	0.997710	−	0.0676421i	$-0.0215476\pi$
$991$	436.313	+	755.716i	0.440275	+	0.762579i	−0.557435	+	0.830221i	$0.688214\pi$
$992$		−	214.325i		−	0.216053i
$993$	−96.8783	+	85.5431i	−0.0975612	+	0.0861461i
$994$	1010.32	−	542.445i	1.01642	−	0.545719i
$995$	166.383	+	96.0615i	0.167220	+	0.0965442i
$996$	20.4076	−	60.7955i	0.0204895	−	0.0610397i
$997$	190.155	−	329.359i	0.190727	−	0.330350i	−0.754764	−	0.655996i	$-0.772249\pi$
$997$	190.155	−	329.359i	0.190727	−	0.330350i	0.945492	+	0.325647i	$0.105582\pi$
$998$	−389.395	+	224.817i	−0.390175	+	0.225268i
$999$	912.569	−	69.1464i	0.913483	−	0.0692156i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.3.r.a.23.2	yes	32
3.2	odd	2		378.3.r.a.233.12		32
7.4	even	3		126.3.i.a.95.15	yes	32
9.2	odd	6		126.3.i.a.65.15	✓	32
9.7	even	3		378.3.i.a.359.5		32
21.11	odd	6		378.3.i.a.179.4		32
63.11	odd	6	inner	126.3.r.a.11.10	yes	32
63.25	even	3		378.3.r.a.305.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.i.a.65.15	✓	32	9.2	odd	6
126.3.i.a.95.15	yes	32	7.4	even	3
126.3.r.a.11.10	yes	32	63.11	odd	6	inner
126.3.r.a.23.2	yes	32	1.1	even	1	trivial
378.3.i.a.179.4		32	21.11	odd	6
378.3.i.a.359.5		32	9.7	even	3
378.3.r.a.233.12		32	3.2	odd	2
378.3.r.a.305.4		32	63.25	even	3

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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	126.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +(-2.24880 + 1.98568i) q^{3} -2.00000 q^{4} +(1.84316 - 1.06415i) q^{5} +(2.80817 + 3.18028i) q^{6} +(6.16730 - 3.31125i) q^{7} +2.82843i q^{8} +(1.11417 - 8.93077i) q^{9} +(-1.50493 - 2.60662i) q^{10} +(7.75793 + 4.47904i) q^{11} +(4.49759 - 3.97135i) q^{12} +(10.4189 - 18.0461i) q^{13} +(-4.68282 - 8.72188i) q^{14} +(-2.03183 + 6.05296i) q^{15} +4.00000 q^{16} +(9.01197 - 5.20307i) q^{17} +(-12.6300 - 1.57568i) q^{18} +(6.15121 - 10.6542i) q^{19} +(-3.68631 + 2.12829i) q^{20} +(-7.29392 + 19.6926i) q^{21} +(6.33432 - 10.9714i) q^{22} +(-16.5455 + 9.55254i) q^{23} +(-5.61634 - 6.36056i) q^{24} +(-10.2352 + 17.7279i) q^{25} +(-25.5210 - 14.7346i) q^{26} +(15.2281 + 22.2959i) q^{27} +(-12.3346 + 6.62251i) q^{28} +(-28.3968 + 16.3949i) q^{29} +(8.56018 + 2.87344i) q^{30} +37.8877 q^{31} -5.65685i q^{32} +(-26.3399 + 5.33229i) q^{33} +(-7.35825 - 12.7449i) q^{34} +(7.84364 - 12.6661i) q^{35} +(-2.22834 + 17.8615i) q^{36} +(16.9479 - 29.3546i) q^{37} +(-15.0673 - 8.69913i) q^{38} +(12.4037 + 61.2705i) q^{39} +(3.00986 + 5.21323i) q^{40} +(-28.7819 - 16.6172i) q^{41} +(27.8495 + 10.3152i) q^{42} +(10.3473 + 17.9220i) q^{43} +(-15.5159 - 8.95808i) q^{44} +(-7.45006 - 17.6464i) q^{45} +(13.5093 + 23.3988i) q^{46} +66.2205i q^{47} +(-8.99519 + 7.94271i) q^{48} +(27.0712 - 40.8430i) q^{49} +(25.0710 + 14.4747i) q^{50} +(-9.93449 + 29.5955i) q^{51} +(-20.8378 + 36.0921i) q^{52} +(2.72252 - 1.57185i) q^{53} +(31.5311 - 21.5358i) q^{54} +19.0654 q^{55} +(9.36564 + 17.4438i) q^{56} +(7.32300 + 36.1735i) q^{57} +(23.1859 + 40.1591i) q^{58} -84.2461i q^{59} +(4.06366 - 12.1059i) q^{60} -92.0227 q^{61} -53.5813i q^{62} +(-22.7006 - 58.7680i) q^{63} -8.00000 q^{64} -44.3490i q^{65} +(7.54099 + 37.2503i) q^{66} -66.7710 q^{67} +(-18.0239 + 10.4061i) q^{68} +(18.2392 - 54.3357i) q^{69} +(-17.9125 - 11.0926i) q^{70} +115.837i q^{71} +(25.2600 + 3.15135i) q^{72} +(-19.6033 - 33.9540i) q^{73} +(-41.5136 - 23.9679i) q^{74} +(-12.1850 - 60.1901i) q^{75} +(-12.3024 + 21.3084i) q^{76} +(62.6767 + 1.93513i) q^{77} +(86.6496 - 17.5415i) q^{78} +52.4167 q^{79} +(7.37263 - 4.25659i) q^{80} +(-78.5172 - 19.9008i) q^{81} +(-23.5003 + 40.7037i) q^{82} +(9.25626 - 5.34410i) q^{83} +(14.5878 - 39.3852i) q^{84} +(11.0737 - 19.1801i) q^{85} +(25.3456 - 14.6333i) q^{86} +(31.3036 - 93.2556i) q^{87} +(-12.6686 + 21.9427i) q^{88} +(-61.9503 - 35.7670i) q^{89} +(-24.9558 + 10.5360i) q^{90} +(4.50139 - 145.795i) q^{91} +(33.0910 - 19.1051i) q^{92} +(-85.2017 + 75.2327i) q^{93} +93.6500 q^{94} -26.1832i q^{95} +(11.2327 + 12.7211i) q^{96} +(64.5880 + 111.870i) q^{97} +(-57.7607 - 38.2845i) q^{98} +(48.6449 - 64.2938i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 64 q^{4} + 8 q^{6} + 2 q^{7} - 20 q^{9} - 36 q^{11} + 10 q^{13} + 36 q^{14} + 10 q^{15} + 128 q^{16} - 54 q^{17} + 28 q^{19} + 28 q^{21} - 126 q^{23} - 16 q^{24} + 80 q^{25} - 72 q^{26} - 126 q^{27}+ \cdots + 394 q^{99}+O(q^{100}) \) 32 * q - 64 * q^4 + 8 * q^6 + 2 * q^7 - 20 * q^9 - 36 * q^11 + 10 * q^13 + 36 * q^14 + 10 * q^15 + 128 * q^16 - 54 * q^17 + 28 * q^19 + 28 * q^21 - 126 * q^23 - 16 * q^24 + 80 * q^25 - 72 * q^26 - 126 * q^27 - 4 * q^28 + 36 * q^29 + 76 * q^30 + 16 * q^31 - 40 * q^33 - 90 * q^35 + 40 * q^36 + 22 * q^37 + 46 * q^39 + 72 * q^41 + 120 * q^42 + 16 * q^43 + 72 * q^44 + 464 * q^45 - 12 * q^46 + 2 * q^49 - 288 * q^50 - 286 * q^51 - 20 * q^52 - 72 * q^53 - 160 * q^54 - 24 * q^55 - 72 * q^56 - 282 * q^57 - 24 * q^58 - 20 * q^60 + 124 * q^61 + 66 * q^63 - 256 * q^64 - 16 * q^66 - 140 * q^67 + 108 * q^68 + 218 * q^69 + 72 * q^70 + 196 * q^73 + 216 * q^74 + 658 * q^75 - 56 * q^76 + 486 * q^77 + 32 * q^78 + 76 * q^79 - 380 * q^81 - 56 * q^84 + 60 * q^85 - 144 * q^86 - 740 * q^87 - 486 * q^89 + 296 * q^90 - 122 * q^91 + 252 * q^92 + 238 * q^93 - 336 * q^94 + 32 * q^96 - 38 * q^97 + 288 * q^98 + 394 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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