LMFDB - Embedded newform 126.3.o.a.13.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [126,3,Mod(13,126)] 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([2, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("126.13"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	126.o (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			13.15
Character	$\chi$	$=$	126.13
Dual form			126.3.o.a.97.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 1.22474i) q^{2} +(2.44188 + 1.74276i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-2.71575 - 1.56794i) q^{5} +(-0.407766 + 4.22300i) q^{6} +(4.10149 + 5.67255i) q^{7} -2.82843 q^{8} +(2.92557 + 8.51123i) q^{9} -4.43480i q^{10} +(3.92650 + 6.80090i) q^{11} +(-5.46043 + 2.48670i) q^{12} +(-2.50339 - 1.44533i) q^{13} +(-4.04723 + 9.03437i) q^{14} +(-3.89899 - 8.56162i) q^{15} +(-2.00000 - 3.46410i) q^{16} -32.9734i q^{17} +(-8.35539 + 9.60143i) q^{18} +10.7355i q^{19} +(5.43150 - 3.13588i) q^{20} +(0.129453 + 20.9996i) q^{21} +(-5.55291 + 9.61792i) q^{22} +(14.1547 - 24.5167i) q^{23} +(-6.90668 - 4.92927i) q^{24} +(-7.58314 - 13.1344i) q^{25} -4.08801i q^{26} +(-7.68914 + 25.8820i) q^{27} +(-13.9266 + 1.43144i) q^{28} +(0.0795224 + 0.137737i) q^{29} +(7.72879 - 10.8293i) q^{30} +(37.8990 + 21.8810i) q^{31} +(2.82843 - 4.89898i) q^{32} +(-2.26429 + 23.4499i) q^{33} +(40.3840 - 23.3157i) q^{34} +(-2.24440 - 21.8361i) q^{35} +(-17.6675 - 3.44399i) q^{36} +47.5168 q^{37} +(-13.1483 + 7.59116i) q^{38} +(-3.59411 - 7.89213i) q^{39} +(7.68130 + 4.43480i) q^{40} +(-50.7432 - 29.2966i) q^{41} +(-25.6276 + 15.0075i) q^{42} +(-27.2812 - 47.2525i) q^{43} -15.7060 q^{44} +(5.39997 - 27.7015i) q^{45} +40.0356 q^{46} +(13.0561 - 7.53793i) q^{47} +(1.15334 - 11.9444i) q^{48} +(-15.3556 + 46.5318i) q^{49} +(10.7242 - 18.5748i) q^{50} +(57.4647 - 80.5170i) q^{51} +(5.00677 - 2.89066i) q^{52} +15.3779 q^{53} +(-37.1359 + 8.88409i) q^{54} -24.6260i q^{55} +(-11.6008 - 16.0444i) q^{56} +(-18.7094 + 26.2149i) q^{57} +(-0.112462 + 0.194789i) q^{58} +(-21.7837 - 12.5768i) q^{59} +(18.7281 + 1.80836i) q^{60} +(7.06108 - 4.07672i) q^{61} +61.8889i q^{62} +(-36.2812 + 51.5041i) q^{63} +8.00000 q^{64} +(4.53238 + 7.85031i) q^{65} +(-30.3213 + 13.8084i) q^{66} +(-6.86107 + 11.8837i) q^{67} +(57.1115 + 32.9734i) q^{68} +(77.2909 - 35.1986i) q^{69} +(25.1566 - 18.1893i) q^{70} -68.9659 q^{71} +(-8.27476 - 24.0734i) q^{72} +120.030i q^{73} +(33.5994 + 58.1959i) q^{74} +(4.37296 - 45.2882i) q^{75} +(-18.5945 - 10.7355i) q^{76} +(-22.4739 + 50.1671i) q^{77} +(7.12443 - 9.98244i) q^{78} +(-9.05179 - 15.6782i) q^{79} +12.5435i q^{80} +(-63.8821 + 49.8004i) q^{81} -82.8633i q^{82} +(-69.1319 + 39.9133i) q^{83} +(-36.5018 - 20.7754i) q^{84} +(-51.7002 + 89.5473i) q^{85} +(38.5815 - 66.8251i) q^{86} +(-0.0458581 + 0.474926i) q^{87} +(-11.1058 - 19.2358i) q^{88} +0.921292i q^{89} +(37.7456 - 12.9743i) q^{90} +(-2.06890 - 20.1286i) q^{91} +(28.3094 + 49.0334i) q^{92} +(54.4116 + 119.480i) q^{93} +(18.4641 + 10.6602i) q^{94} +(16.8326 - 29.1550i) q^{95} +(15.4444 - 7.03346i) q^{96} +(-66.2984 + 38.2774i) q^{97} +(-67.8476 + 14.0962i) q^{98} +(-46.3968 + 53.3159i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{4} - 2 q^{7} + 24 q^{9} - 12 q^{11} - 12 q^{14} + 48 q^{15} - 64 q^{16} - 54 q^{21} + 12 q^{23} + 80 q^{25} + 8 q^{28} - 48 q^{29} - 168 q^{30} + 348 q^{35} - 72 q^{36} - 88 q^{37} + 252 q^{39}+ \cdots - 684 q^{99}+O(q^{100}) $ 32 * q - 32 * q^4 - 2 * q^7 + 24 * q^9 - 12 * q^11 - 12 * q^14 + 48 * q^15 - 64 * q^16 - 54 * q^21 + 12 * q^23 + 80 * q^25 + 8 * q^28 - 48 * q^29 - 168 * q^30 + 348 * q^35 - 72 * q^36 - 88 * q^37 + 252 * q^39 + 32 * q^43 + 48 * q^44 + 48 * q^46 + 50 * q^49 + 48 * q^50 - 372 * q^51 - 864 * q^53 - 24 * q^56 + 372 * q^57 + 48 * q^58 - 24 * q^60 - 114 * q^63 + 256 * q^64 + 120 * q^65 - 140 * q^67 - 108 * q^70 + 552 * q^71 + 96 * q^72 + 144 * q^74 - 258 * q^77 + 288 * q^78 - 176 * q^79 - 360 * q^81 - 60 * q^85 + 96 * q^86 + 372 * q^91 + 24 * q^92 - 456 * q^93 + 528 * q^95 + 624 * q^98 - 684 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$3$	2.44188	+	1.74276i	0.813961	+	0.580920i
$3$	2.44188	+	1.74276i	0.813961	+	0.580920i
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$	−2.71575	−	1.56794i	−0.543150	−	0.313588i	0.203205	−	0.979136i	$-0.434864\pi$
$5$	−2.71575	−	1.56794i	−0.543150	−	0.313588i	−0.746354	+	0.665549i	$0.768198\pi$
$6$	−0.407766	+	4.22300i	−0.0679610	+	0.703833i
$7$	4.10149	+	5.67255i	0.585927	+	0.810364i
$7$	4.10149	+	5.67255i	0.585927	+	0.810364i
$8$	−2.82843			−0.353553
$9$	2.92557	+	8.51123i	0.325063	+	0.945692i
$10$		−	4.43480i		−	0.443480i
$11$	3.92650	+	6.80090i	0.356955	+	0.618264i	0.987450	−	0.157929i	$-0.0504817\pi$
$11$	3.92650	+	6.80090i	0.356955	+	0.618264i	−0.630496	+	0.776193i	$0.717148\pi$
$12$	−5.46043	+	2.48670i	−0.455036	+	0.207225i
$13$	−2.50339	−	1.44533i	−0.192568	−	0.111179i	0.400616	−	0.916246i	$-0.368796\pi$
$13$	−2.50339	−	1.44533i	−0.192568	−	0.111179i	−0.593184	+	0.805067i	$0.702129\pi$
$14$	−4.04723	+	9.03437i	−0.289088	+	0.645312i
$15$	−3.89899	−	8.56162i	−0.259933	−	0.570774i
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$		−	32.9734i		−	1.93961i	−0.243882	−	0.969805i	$-0.578421\pi$
$17$		−	32.9734i		−	1.93961i	0.243882	−	0.969805i	$-0.421579\pi$
$18$	−8.35539	+	9.60143i	−0.464189	+	0.533413i
$19$			10.7355i			0.565027i	0.959263	+	0.282514i	$0.0911682\pi$
$19$			10.7355i			0.565027i	−0.959263	+	0.282514i	$0.908832\pi$
$20$	5.43150	−	3.13588i	0.271575	−	0.156794i
$21$	0.129453	+	20.9996i	0.00616443	+	0.999981i
$22$	−5.55291	+	9.61792i	−0.252405	+	0.437178i
$23$	14.1547	−	24.5167i	0.615422	−	1.06594i	−0.374888	−	0.927070i	$-0.622319\pi$
$23$	14.1547	−	24.5167i	0.615422	−	1.06594i	0.990310	−	0.138873i	$-0.0443479\pi$
$24$	−6.90668	−	4.92927i	−0.287778	−	0.205386i
$25$	−7.58314	−	13.1344i	−0.303326	−	0.525376i
$26$		−	4.08801i		−	0.157231i
$27$	−7.68914	+	25.8820i	−0.284783	+	0.958592i
$28$	−13.9266	+	1.43144i	−0.497380	+	0.0511227i
$29$	0.0795224	+	0.137737i	0.00274215	+	0.00474955i	0.867393	−	0.497623i	$-0.165794\pi$
$29$	0.0795224	+	0.137737i	0.00274215	+	0.00474955i	−0.864651	+	0.502373i	$0.832460\pi$
$30$	7.72879	−	10.8293i	0.257626	−	0.360975i
$31$	37.8990	+	21.8810i	1.22255	+	0.705839i	0.965461	−	0.260548i	$-0.0839033\pi$
$31$	37.8990	+	21.8810i	1.22255	+	0.705839i	0.257089	+	0.966388i	$0.417237\pi$
$32$	2.82843	−	4.89898i	0.0883883	−	0.153093i
$33$	−2.26429	+	23.4499i	−0.0686148	+	0.710604i
$34$	40.3840	−	23.3157i	1.18776	−	0.685756i
$35$	−2.24440	−	21.8361i	−0.0641258	−	0.623888i
$36$	−17.6675	−	3.44399i	−0.490763	−	0.0956665i
$37$	47.5168			1.28424			0.642118	−	0.766606i	$-0.278056\pi$
$37$	47.5168			1.28424			0.642118	+	0.766606i	$0.278056\pi$
$38$	−13.1483	+	7.59116i	−0.346007	+	0.199767i
$39$	−3.59411	−	7.89213i	−0.0921566	−	0.202362i
$40$	7.68130	+	4.43480i	0.192032	+	0.110870i
$41$	−50.7432	−	29.2966i	−1.23764	−	0.714551i	−0.269028	−	0.963132i	$-0.586702\pi$
$41$	−50.7432	−	29.2966i	−1.23764	−	0.714551i	−0.968611	+	0.248581i	$0.920036\pi$
$42$	−25.6276	+	15.0075i	−0.610181	+	0.357322i
$43$	−27.2812	−	47.2525i	−0.634448	−	1.09890i	−0.986632	−	0.162965i	$-0.947894\pi$
$43$	−27.2812	−	47.2525i	−0.634448	−	1.09890i	0.352184	−	0.935931i	$-0.385439\pi$
$44$	−15.7060			−0.356955
$45$	5.39997	−	27.7015i	0.119999	−	0.615588i
$46$	40.0356			0.870339
$47$	13.0561	−	7.53793i	0.277789	−	0.160381i	−0.354633	−	0.935006i	$-0.615394\pi$
$47$	13.0561	−	7.53793i	0.277789	−	0.160381i	0.632422	+	0.774624i	$0.282061\pi$
$48$	1.15334	−	11.9444i	0.0240279	−	0.248843i
$49$	−15.3556	+	46.5318i	−0.313380	+	0.949628i
$50$	10.7242	−	18.5748i	0.214484	−	0.371497i
$51$	57.4647	−	80.5170i	1.12676	−	1.57877i
$52$	5.00677	−	2.89066i	0.0962841	−	0.0555897i
$53$	15.3779			0.290150			0.145075	−	0.989421i	$-0.453658\pi$
$53$	15.3779			0.290150			0.145075	+	0.989421i	$0.453658\pi$
$54$	−37.1359	+	8.88409i	−0.687701	+	0.164520i
$55$		−	24.6260i		−	0.447746i
$56$	−11.6008	−	16.0444i	−0.207156	−	0.286507i
$57$	−18.7094	+	26.2149i	−0.328236	+	0.459910i
$58$	−0.112462	+	0.194789i	−0.00193899	+	0.00335844i
$59$	−21.7837	−	12.5768i	−0.369216	−	0.213167i	0.303900	−	0.952704i	$-0.401711\pi$
$59$	−21.7837	−	12.5768i	−0.369216	−	0.213167i	−0.673116	+	0.739537i	$0.735044\pi$
$60$	18.7281	+	1.80836i	0.312136	+	0.0301393i
$61$	7.06108	−	4.07672i	0.115755	−	0.0668314i	−0.441004	−	0.897505i	$-0.645378\pi$
$61$	7.06108	−	4.07672i	0.115755	−	0.0668314i	0.556760	+	0.830674i	$0.312044\pi$
$62$			61.8889i			0.998208i
$63$	−36.2812	+	51.5041i	−0.575892	+	0.817526i
$64$	8.00000			0.125000
$65$	4.53238	+	7.85031i	0.0697289	+	0.120774i
$66$	−30.3213	+	13.8084i	−0.459413	+	0.209219i
$67$	−6.86107	+	11.8837i	−0.102404	+	0.177369i	−0.912675	−	0.408687i	$-0.865987\pi$
$67$	−6.86107	+	11.8837i	−0.102404	+	0.177369i	0.810271	+	0.586056i	$0.199320\pi$
$68$	57.1115	+	32.9734i	0.839876	+	0.484902i
$69$	77.2909	−	35.1986i	1.12016	−	0.510124i
$70$	25.1566	−	18.1893i	0.359380	−	0.259847i
$71$	−68.9659			−0.971351			−0.485675	−	0.874139i	$-0.661426\pi$
$71$	−68.9659			−0.971351			−0.485675	+	0.874139i	$0.661426\pi$
$72$	−8.27476	−	24.0734i	−0.114927	−	0.334353i
$73$			120.030i			1.64424i	0.569311	+	0.822122i	$0.307210\pi$
$73$			120.030i			1.64424i	−0.569311	+	0.822122i	$0.692790\pi$
$74$	33.5994	+	58.1959i	0.454046	+	0.786431i
$75$	4.37296	−	45.2882i	0.0583061	−	0.603843i
$76$	−18.5945	−	10.7355i	−0.244664	−	0.141257i
$77$	−22.4739	+	50.1671i	−0.291869	+	0.651520i
$78$	7.12443	−	9.98244i	0.0913388	−	0.127980i
$79$	−9.05179	−	15.6782i	−0.114580	−	0.198458i	0.803032	−	0.595936i	$-0.203219\pi$
$79$	−9.05179	−	15.6782i	−0.114580	−	0.198458i	−0.917612	+	0.397478i	$0.869885\pi$
$80$			12.5435i			0.156794i
$81$	−63.8821	+	49.8004i	−0.788668	+	0.614820i
$82$		−	82.8633i		−	1.01053i
$83$	−69.1319	+	39.9133i	−0.832914	+	0.480883i	−0.854849	−	0.518876i	$-0.826351\pi$
$83$	−69.1319	+	39.9133i	−0.832914	+	0.480883i	0.0219353	+	0.999759i	$0.493017\pi$
$84$	−36.5018	−	20.7754i	−0.434546	−	0.247326i
$85$	−51.7002	+	89.5473i	−0.608237	+	1.05350i
$86$	38.5815	−	66.8251i	0.448622	−	0.777036i
$87$	−0.0458581	+	0.474926i	−0.000527104	+	0.00545891i
$88$	−11.1058	−	19.2358i	−0.126203	−	0.218589i
$89$			0.921292i			0.0103516i	0.999987	+	0.00517580i	$0.00164751\pi$
$89$			0.921292i			0.0103516i	−0.999987	+	0.00517580i	$0.998352\pi$
$90$	37.7456	−	12.9743i	0.419395	−	0.144159i
$91$	−2.06890	−	20.1286i	−0.0227352	−	0.221193i
$92$	28.3094	+	49.0334i	0.307711	+	0.532971i
$93$	54.4116	+	119.480i	0.585071	+	1.28473i
$94$	18.4641	+	10.6602i	0.196426	+	0.113407i
$95$	16.8326	−	29.1550i	0.177185	−	0.306894i
$96$	15.4444	−	7.03346i	0.160880	−	0.0732652i
$97$	−66.2984	+	38.2774i	−0.683489	+	0.394613i	−0.801168	−	0.598439i	$-0.795788\pi$
$97$	−66.2984	+	38.2774i	−0.683489	+	0.394613i	0.117679	+	0.993052i	$0.462455\pi$
$98$	−67.8476	+	14.0962i	−0.692322	+	0.143839i
$99$	−46.3968	+	53.3159i	−0.468654	+	0.538544i
$100$	30.3326			0.303326
$101$	−11.1783	+	6.45380i	−0.110676	+	0.0638990i	−0.554316	−	0.832306i	$-0.687020\pi$
$101$	−11.1783	+	6.45380i	−0.110676	+	0.0638990i	0.443640	+	0.896205i	$0.353687\pi$
$102$	139.247	+	13.4454i	1.36516	+	0.131818i
$103$	−135.255	−	78.0896i	−1.31316	−	0.758151i	−0.330539	−	0.943792i	$-0.607230\pi$
$103$	−135.255	−	78.0896i	−1.31316	−	0.758151i	−0.982618	+	0.185641i	$0.940564\pi$
$104$	7.08065	+	4.08801i	0.0680831	+	0.0393078i
$105$	32.5745	−	57.2326i	0.310233	−	0.545072i
$106$	10.8738	+	18.8340i	0.102583	+	0.177680i
$107$	141.343			1.32097			0.660483	−	0.750841i	$-0.270352\pi$
$107$	141.343			1.32097			0.660483	+	0.750841i	$0.270352\pi$
$108$	−37.1398	−	39.2000i	−0.343887	−	0.362963i
$109$	18.8235			0.172693			0.0863464	−	0.996265i	$-0.472481\pi$
$109$	18.8235			0.172693			0.0863464	+	0.996265i	$0.472481\pi$
$110$	30.1606	−	17.4132i	0.274187	−	0.158302i
$111$	116.030	+	82.8103i	1.04532	+	0.746039i
$112$	11.4473	−	25.5531i	0.102208	−	0.228152i
$113$	−64.9119	+	112.431i	−0.574442	+	0.994963i	0.421660	+	0.906754i	$0.361448\pi$
$113$	−64.9119	+	112.431i	−0.574442	+	0.994963i	−0.996102	+	0.0882087i	$0.971886\pi$
$114$	−45.3361	−	4.37758i	−0.397685	−	0.0383998i
$115$	−76.8813	+	44.3874i	−0.668533	+	0.385978i
$116$	−0.318090			−0.00274215
$117$	4.97771	−	25.5353i	0.0425445	−	0.218251i
$118$		−	35.5727i		−	0.301464i
$119$	187.043	−	135.240i	1.57179	−	1.13647i
$120$	11.0280	+	24.2159i	0.0919002	+	0.201799i
$121$	29.6652	−	51.3816i	0.245167	−	0.424641i
$122$	9.98588	+	5.76535i	0.0818514	+	0.0472570i
$123$	−72.8519	−	159.972i	−0.592292	−	1.30059i
$124$	−75.7981	+	43.7620i	−0.611275	+	0.352920i
$125$			125.956i			1.00765i
$126$	−88.7341	−	8.01625i	−0.704239	−	0.0636210i
$127$	74.1282			0.583686			0.291843	−	0.956466i	$-0.405731\pi$
$127$	74.1282			0.583686			0.291843	+	0.956466i	$0.405731\pi$
$128$	5.65685	+	9.79796i	0.0441942	+	0.0765466i
$129$	15.7322	−	162.930i	0.121955	−	1.26302i
$130$	−6.40975	+	11.1020i	−0.0493058	+	0.0854001i
$131$	140.094	+	80.8832i	1.06942	+	0.617429i	0.928023	−	0.372524i	$-0.121508\pi$
$131$	140.094	+	80.8832i	1.06942	+	0.617429i	0.141396	+	0.989953i	$0.454841\pi$
$132$	−38.3522	−	27.3718i	−0.290547	−	0.207362i
$133$	−60.8977	+	44.0316i	−0.457878	+	0.331065i
$134$	−19.4060			−0.144821
$135$	61.4631	−	58.2329i	0.455282	−	0.431354i
$136$			93.2628i			0.685756i
$137$	−91.1018	−	157.793i	−0.664977	−	1.15177i	−0.979292	−	0.202455i	$-0.935108\pi$
$137$	−91.1018	−	157.793i	−0.664977	−	1.15177i	0.314315	−	0.949319i	$-0.398225\pi$
$138$	97.7621	+	69.7724i	0.708421	+	0.505597i
$139$	−209.411	−	120.903i	−1.50655	−	0.869808i	−0.999971	−	0.00761466i	$-0.997576\pi$
$139$	−209.411	−	120.903i	−1.50655	−	0.869808i	−0.506580	−	0.862193i	$-0.669091\pi$
$140$	40.0656	+	17.9487i	0.286183	+	0.128205i
$141$	45.0182	+	4.34689i	0.319278	+	0.0308290i
$142$	−48.7663	−	84.4656i	−0.343424	−	0.594828i
$143$		−	22.7004i		−	0.158744i
$144$	23.6326	−	27.1569i	0.164115	−	0.188590i
$145$		−	0.498745i		−	0.00343962i
$146$	−147.006	+	84.8739i	−1.00689	+	0.581328i
$147$	−118.590	+	86.8639i	−0.806737	+	0.590911i
$148$	−47.5168	+	82.3014i	−0.321059	+	0.556091i
$149$	−26.4982	+	45.8963i	−0.177841	+	0.308029i	−0.941141	−	0.338015i	$-0.890244\pi$
$149$	−26.4982	+	45.8963i	−0.177841	+	0.308029i	0.763300	+	0.646044i	$0.223578\pi$
$150$	58.5587	−	26.6678i	0.390391	−	0.177786i
$151$	−79.7500	−	138.131i	−0.528146	−	0.914775i	−0.999462	−	0.0328107i	$-0.989554\pi$
$151$	−79.7500	−	138.131i	−0.528146	−	0.914775i	0.471316	−	0.881964i	$-0.343779\pi$
$152$		−	30.3646i		−	0.199767i
$153$	280.644	−	96.4659i	1.83427	−	0.630496i
$154$	−77.3333	+	7.94864i	−0.502164	+	0.0516145i
$155$	−68.6162	−	118.847i	−0.442685	−	0.766753i
$156$	17.2637	+	1.66695i	0.110665	+	0.0106856i
$157$	173.153	+	99.9698i	1.10288	+	0.636751i	0.936977	−	0.349391i	$-0.113611\pi$
$157$	173.153	+	99.9698i	1.10288	+	0.636751i	0.165907	+	0.986141i	$0.446945\pi$
$158$	12.8012	−	22.1723i	0.0810201	−	0.140331i
$159$	37.5511	+	26.8000i	0.236170	+	0.168554i
$160$	−15.3626	+	8.86960i	−0.0960162	+	0.0554350i
$161$	197.127	−	20.2616i	1.22439	−	0.125848i
$162$	−106.164	−	43.0250i	−0.655335	−	0.265587i
$163$	117.271			0.719451			0.359726	−	0.933058i	$-0.382870\pi$
$163$	117.271			0.719451			0.359726	+	0.933058i	$0.382870\pi$
$164$	101.486	−	58.5932i	0.618819	−	0.357276i
$165$	42.9173	−	60.1339i	0.260105	−	0.364448i
$166$	−97.7672	−	56.4459i	−0.588959	−	0.340036i
$167$	109.057	+	62.9642i	0.653037	+	0.377031i	0.789619	−	0.613598i	$-0.210278\pi$
$167$	109.057	+	62.9642i	0.653037	+	0.377031i	−0.136582	+	0.990629i	$0.543612\pi$
$168$	−0.366148	−	59.3958i	−0.00217945	−	0.353547i
$169$	−80.3220	−	139.122i	−0.475278	−	0.823206i
$170$	−146.230			−0.860178
$171$	−91.3724	+	31.4075i	−0.534342	+	0.183670i
$172$	109.125			0.634448
$173$	−241.131	+	139.217i	−1.39382	+	0.804724i	−0.993736	−	0.111753i	$-0.964353\pi$
$173$	−241.131	+	139.217i	−1.39382	+	0.804724i	−0.400087	+	0.916477i	$0.631020\pi$
$174$	−0.614089	+	0.279659i	−0.00352925	+	0.00160723i
$175$	43.4033	−	96.8863i	0.248019	−	0.553636i
$176$	15.7060	−	27.2036i	0.0892387	−	0.154566i
$177$	−31.2749	−	68.6750i	−0.176694	−	0.387994i
$178$	−1.12835	+	0.651452i	−0.00633903	+	0.00365984i
$179$	−140.932			−0.787331			−0.393666	−	0.919254i	$-0.628793\pi$
$179$	−140.932			−0.787331			−0.393666	+	0.919254i	$0.628793\pi$
$180$	42.5804	+	37.0545i	0.236558	+	0.205858i
$181$		−	270.055i		−	1.49202i	−0.665936	−	0.746009i	$-0.731967\pi$
$181$		−	270.055i		−	1.49202i	0.665936	−	0.746009i	$-0.268033\pi$
$182$	23.1895	−	16.7669i	0.127415	−	0.0921260i
$183$	24.3471	+	2.35091i	0.133044	+	0.0128465i
$184$	−40.0356	+	69.3437i	−0.217585	+	0.376868i
$185$	−129.044	−	74.5033i	−0.697533	−	0.402721i
$186$	−107.857	+	151.125i	−0.579879	+	0.812502i
$187$	224.249	−	129.470i	1.19919	−	0.692353i
$188$			30.1517i			0.160381i
$189$	−178.354	+	62.5376i	−0.943670	+	0.330887i
$190$	47.6098			0.250578
$191$	43.7715	+	75.8145i	0.229170	+	0.396935i	0.957562	−	0.288226i	$-0.0930654\pi$
$191$	43.7715	+	75.8145i	0.229170	+	0.396935i	−0.728392	+	0.685161i	$0.759732\pi$
$192$	19.5351	+	13.9421i	0.101745	+	0.0726150i
$193$	−93.1992	+	161.426i	−0.482898	+	0.836403i	−0.999807	−	0.0196368i	$-0.993749\pi$
$193$	−93.1992	+	161.426i	−0.482898	+	0.836403i	0.516910	+	0.856040i	$0.327082\pi$
$194$	−93.7602	−	54.1325i	−0.483300	−	0.279033i
$195$	−2.61368	+	27.0684i	−0.0134035	+	0.138812i
$196$	−65.2398	−	73.1285i	−0.332856	−	0.373104i
$197$	365.315			1.85439			0.927196	−	0.374575i	$-0.122212\pi$
$197$	365.315			1.85439			0.927196	+	0.374575i	$0.122212\pi$
$198$	−98.1058	−	19.1242i	−0.495484	−	0.0965868i
$199$			88.1657i			0.443044i	0.975155	+	0.221522i	$0.0711024\pi$
$199$			88.1657i			0.443044i	−0.975155	+	0.221522i	$0.928898\pi$
$200$	21.4484	+	37.1497i	0.107242	+	0.185748i
$201$	−37.4644	+	17.0614i	−0.186390	+	0.0848828i
$202$	−15.8085	−	9.12705i	−0.0782600	−	0.0451834i
$203$	−0.455159	+	1.01602i	−0.00224216	+	0.00500503i
$204$	81.9949	+	180.049i	0.401936	+	0.882592i
$205$	91.8705	+	159.124i	0.448149	+	0.776216i
$206$		−	220.871i		−	1.07219i
$207$	250.078	+	48.7487i	1.20811	+	0.235501i
$208$			11.5626i			0.0555897i
$209$	−73.0112	+	42.1530i	−0.349336	+	0.201689i
$210$	93.1290	−	0.574098i	0.443471	−	0.00273380i
$211$	−64.6561	+	111.988i	−0.306427	+	0.530747i	−0.977578	−	0.210574i	$-0.932467\pi$
$211$	−64.6561	+	111.988i	−0.306427	+	0.530747i	0.671151	+	0.741320i	$0.265800\pi$
$212$	−15.3779	+	26.6353i	−0.0725374	+	0.125638i
$213$	−168.407	−	120.191i	−0.790641	−	0.564277i
$214$	99.9448	+	173.110i	0.467032	+	0.808923i
$215$			171.101i			0.795819i
$216$	21.7482	−	73.2053i	0.100686	−	0.338913i
$217$	31.3213	+	304.729i	0.144338	+	1.40428i
$218$	13.3102	+	23.0540i	0.0610561	+	0.105752i
$219$	−209.183	+	293.099i	−0.955175	+	1.33835i
$220$	42.6535	+	24.6260i	0.193880	+	0.111937i
$221$	−47.6574	+	82.5451i	−0.215644	+	0.373507i
$222$	−19.3757	+	200.663i	−0.0872780	+	0.903888i
$223$	162.872	−	94.0345i	0.730370	−	0.421679i	−0.0881876	−	0.996104i	$-0.528108\pi$
$223$	162.872	−	94.0345i	0.730370	−	0.421679i	0.818557	+	0.574425i	$0.194774\pi$
$224$	39.3905	−	4.04871i	0.175850	−	0.0180746i
$225$	89.6048	−	102.967i	0.398243	−	0.457633i
$226$	−183.599			−0.812384
$227$	151.042	−	87.2040i	0.665382	−	0.384158i	−0.128943	−	0.991652i	$-0.541158\pi$
$227$	151.042	−	87.2040i	0.665382	−	0.384158i	0.794325	+	0.607494i	$0.207825\pi$
$228$	−26.6960	−	58.6206i	−0.117088	−	0.257108i
$229$	305.017	+	176.102i	1.33195	+	0.769004i	0.985599	−	0.169100i	$-0.0540860\pi$
$229$	305.017	+	176.102i	1.33195	+	0.769004i	0.346355	+	0.938104i	$0.387419\pi$
$230$	−108.727	−	62.7733i	−0.472724	−	0.272927i
$231$	−142.308	+	83.3353i	−0.616051	+	0.360759i
$232$	−0.224923	−	0.389579i	−0.000969497	−	0.00167922i
$233$	−210.886			−0.905091			−0.452546	−	0.891741i	$-0.649484\pi$
$233$	−210.886			−0.905091			−0.452546	+	0.891741i	$0.649484\pi$
$234$	34.7940	−	11.9598i	0.148692	−	0.0511101i
$235$	−47.2760			−0.201175
$236$	43.5675	−	25.1537i	0.184608	−	0.106583i
$237$	5.21988	−	54.0593i	0.0220248	−	0.228098i
$238$	297.894	+	133.451i	1.25165	+	0.560718i
$239$	−127.803	+	221.362i	−0.534742	+	0.926200i	0.464434	+	0.885608i	$0.346258\pi$
$239$	−127.803	+	221.362i	−0.534742	+	0.926200i	−0.999176	+	0.0405923i	$0.987076\pi$
$240$	−21.8603	+	30.6297i	−0.0910847	+	0.127624i
$241$	246.362	−	142.237i	1.02225	−	0.590197i	0.107495	−	0.994206i	$-0.465717\pi$
$241$	246.362	−	142.237i	1.02225	−	0.590197i	0.914755	+	0.404009i	$0.132384\pi$
$242$	83.9058			0.346718
$243$	−242.783	+	10.2755i	−0.999106	+	0.0422861i
$244$			16.3069i			0.0668314i
$245$	114.661	−	102.292i	0.468004	−	0.417518i
$246$	144.411	−	202.342i	0.587036	−	0.822530i
$247$	15.5164	−	26.8751i	0.0628193	−	0.108806i
$248$	−107.195	−	61.8889i	−0.432237	−	0.249552i
$249$	−238.371	−	23.0167i	−0.957314	−	0.0924367i
$250$	−154.265	+	89.0647i	−0.617058	+	0.356259i
$251$			252.178i			1.00469i	0.864666	+	0.502347i	$0.167530\pi$
$251$			252.178i			1.00469i	−0.864666	+	0.502347i	$0.832470\pi$
$252$	−52.9266	−	114.345i	−0.210026	−	0.453750i
$253$	222.314			0.878711
$254$	52.4165	+	90.7881i	0.206364	+	0.357433i
$255$	−282.305	+	128.563i	−1.10708	+	0.504168i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−140.650	−	81.2044i	−0.547277	−	0.315970i	0.200746	−	0.979643i	$-0.435663\pi$
$257$	−140.650	−	81.2044i	−0.547277	−	0.315970i	−0.748023	+	0.663673i	$0.768997\pi$
$258$	210.672	−	95.9407i	0.816557	−	0.371863i
$259$	194.889	+	269.541i	0.752469	+	1.04070i
$260$	−18.1295			−0.0697289
$261$	−0.939661	+	1.07979i	−0.00360024	+	0.00413713i
$262$			228.772i			0.873177i
$263$	81.1707	+	140.592i	0.308634	+	0.534570i	0.978064	−	0.208306i	$-0.0667948\pi$
$263$	81.1707	+	140.592i	0.308634	+	0.534570i	−0.669430	+	0.742875i	$0.733462\pi$
$264$	6.40438	−	66.3264i	0.0242590	−	0.251237i
$265$	−41.7626	−	24.1116i	−0.157595	−	0.0909873i
$266$	−96.9887	−	43.4492i	−0.364619	−	0.163343i
$267$	−1.60559	+	2.24969i	−0.00601345	+	0.00842579i
$268$	−13.7221	−	23.7674i	−0.0512020	−	0.0886845i
$269$		−	235.258i		−	0.874566i	−0.899324	−	0.437283i	$-0.855941\pi$
$269$		−	235.258i		−	0.874566i	0.899324	−	0.437283i	$-0.144059\pi$
$270$	114.781	+	34.0998i	0.425116	+	0.126295i
$271$		−	485.944i		−	1.79315i	−0.442892	−	0.896575i	$-0.646048\pi$
$271$		−	485.944i		−	1.79315i	0.442892	−	0.896575i	$-0.353952\pi$
$272$	−114.223	+	65.9467i	−0.419938	+	0.242451i
$273$	30.0273	−	52.7572i	0.109990	−	0.193250i
$274$	128.837	−	223.153i	0.470210	−	0.814427i
$275$	59.5504	−	103.144i	0.216547	−	0.375070i
$276$	−16.3252	+	169.070i	−0.0591491	+	0.612573i
$277$	−38.0297	−	65.8694i	−0.137291	−	0.237796i	0.789179	−	0.614163i	$-0.210506\pi$
$277$	−38.0297	−	65.8694i	−0.137291	−	0.237796i	−0.926470	+	0.376367i	$0.877173\pi$
$278$		−	341.966i		−	1.23009i
$279$	−75.3581	+	386.582i	−0.270101	+	1.38560i
$280$	6.34813	+	61.7618i	0.0226719	+	0.220578i
$281$	−257.770	−	446.471i	−0.917331	−	1.58886i	−0.803452	−	0.595370i	$-0.797006\pi$
$281$	−257.770	−	446.471i	−0.917331	−	1.58886i	−0.113879	−	0.993495i	$-0.536328\pi$
$282$	26.5089	+	58.2095i	0.0940030	+	0.206417i
$283$	229.497	+	132.500i	0.810945	+	0.468199i	0.847284	−	0.531140i	$-0.178236\pi$
$283$	229.497	+	132.500i	0.810945	+	0.468199i	−0.0363388	+	0.999340i	$0.511570\pi$
$284$	68.9659	−	119.452i	0.242838	−	0.420607i
$285$	91.9134	−	41.8577i	0.322503	−	0.146869i
$286$	27.8022	−	16.0516i	0.0972104	−	0.0561244i
$287$	−41.9362	−	408.003i	−0.146119	−	1.42161i
$288$	49.9711	+	9.74108i	0.173511	+	0.0338232i
$289$	−798.243			−2.76209
$290$	0.610835	−	0.352666i	0.00210633	−	0.00121609i
$291$	−228.601	−	22.0734i	−0.785572	−	0.0758536i
$292$	−207.898	−	120.030i	−0.711979	−	0.411061i
$293$	−266.276	−	153.735i	−0.908793	−	0.524692i	−0.0287506	−	0.999587i	$-0.509153\pi$
$293$	−266.276	−	153.735i	−0.908793	−	0.524692i	−0.880043	+	0.474895i	$0.842486\pi$
$294$	−190.242	−	83.8208i	−0.647082	−	0.285105i
$295$	39.4394	+	68.3111i	0.133693	+	0.231563i
$296$	−134.398			−0.454046
$297$	−206.212	+	49.3326i	−0.694317	+	0.166103i
$298$	−74.9483			−0.251504
$299$	−70.8694	+	40.9165i	−0.237022	+	0.136844i
$300$	74.0685	+	52.8624i	0.246895	+	0.176208i
$301$	156.148	−	348.560i	0.518765	−	1.15801i
$302$	112.784	−	195.347i	0.373455	−	0.646844i
$303$	−38.5435	−	3.72170i	−0.127206	−	0.0122829i
$304$	37.1889	−	21.4710i	0.122332	−	0.0706284i
$305$	−25.5682			−0.0838300
$306$	316.591	+	275.505i	1.03461	+	0.900345i
$307$		−	353.190i		−	1.15046i	−0.817993	−	0.575228i	$-0.804913\pi$
$307$		−	353.190i		−	1.15046i	0.817993	−	0.575228i	$-0.195087\pi$
$308$	−64.4180	−	89.0931i	−0.209149	−	0.289263i
$309$	−194.185	−	426.403i	−0.628432	−	1.37994i
$310$	97.0379	−	168.075i	0.313026	−	0.542176i
$311$	322.707	+	186.315i	1.03764	+	0.599084i	0.919165	−	0.393872i	$-0.128865\pi$
$311$	322.707	+	186.315i	1.03764	+	0.599084i	0.118479	+	0.992957i	$0.462198\pi$
$312$	10.1657	+	22.3223i	0.0325823	+	0.0715459i
$313$	81.1943	−	46.8776i	0.259407	−	0.149769i	−0.364657	−	0.931142i	$-0.618814\pi$
$313$	81.1943	−	46.8776i	0.259407	−	0.149769i	0.624064	+	0.781373i	$0.285480\pi$
$314$			282.757i			0.900501i
$315$	179.286	−	82.9857i	0.569161	−	0.263447i
$316$	36.2072			0.114580
$317$	67.8015	+	117.436i	0.213885	+	0.370459i	0.952927	−	0.303200i	$-0.0980550\pi$
$317$	67.8015	+	117.436i	0.213885	+	0.370459i	−0.739042	+	0.673659i	$0.764722\pi$
$318$	−6.27060	+	64.9410i	−0.0197189	+	0.204217i
$319$	−0.624489	+	1.08165i	−0.00195765	+	0.00339074i
$320$	−21.7260	−	12.5435i	−0.0678937	−	0.0391984i
$321$	345.144	+	246.328i	1.07521	+	0.767376i
$322$	164.205	+	227.104i	0.509955	+	0.705291i
$323$	353.986			1.09593
$324$	−22.3748	−	160.447i	−0.0690579	−	0.495208i
$325$			43.8406i			0.134894i
$326$	82.9228	+	143.627i	0.254364	+	0.440572i
$327$	45.9648	+	32.8049i	0.140565	+	0.100321i
$328$	143.523	+	82.8633i	0.437571	+	0.252632i
$329$	96.3086	+	43.1445i	0.292731	+	0.131138i
$330$	103.996	+	10.0417i	0.315139	+	0.0304293i
$331$	167.475	+	290.076i	0.505967	+	0.876361i	0.999976	+	0.00690439i	$0.00219775\pi$
$331$	167.475	+	290.076i	0.505967	+	0.876361i	−0.494009	+	0.869457i	$0.664469\pi$
$332$		−	159.653i		−	0.480883i
$333$	139.014	+	404.426i	0.417458	+	1.21449i
$334$			178.090i			0.533202i
$335$	37.2659	−	21.5155i	0.111241	−	0.0642252i
$336$	72.4858	−	42.4476i	0.215732	−	0.126332i
$337$	274.990	−	476.297i	0.815995	−	1.41335i	−0.0926154	−	0.995702i	$-0.529523\pi$
$337$	274.990	−	476.297i	0.815995	−	1.41335i	0.908611	−	0.417644i	$-0.137144\pi$
$338$	113.593	−	196.748i	0.336073	−	0.582095i
$339$	−354.447	+	161.417i	−1.04557	+	0.476155i
$340$	−103.400	−	179.095i	−0.304119	−	0.526749i
$341$			343.663i			1.00781i
$342$	−103.076	−	89.6995i	−0.301393	−	0.262279i
$343$	−326.934	+	103.744i	−0.953162	+	0.302461i
$344$	77.1630	+	133.650i	0.224311	+	0.388518i
$345$	−265.092	−	25.5968i	−0.768382	−	0.0741937i
$346$	−341.011	−	196.883i	−0.985582	−	0.569026i
$347$	−51.7856	+	89.6953i	−0.149238	+	0.258488i	−0.930946	−	0.365157i	$-0.881015\pi$
$347$	−51.7856	+	89.6953i	−0.149238	+	0.258488i	0.781708	+	0.623645i	$0.214349\pi$
$348$	−0.776737	−	0.554354i	−0.00223200	−	0.00159297i
$349$	−449.229	+	259.363i	−1.28719	+	0.743159i	−0.978152	−	0.207891i	$-0.933340\pi$
$349$	−449.229	+	259.363i	−1.28719	+	0.743159i	−0.309038	+	0.951050i	$0.600007\pi$
$350$	149.352	−	15.3510i	0.426719	−	0.0438600i
$351$	56.6569	−	53.6793i	0.161416	−	0.152932i
$352$	44.4233			0.126203
$353$	139.032	−	80.2699i	0.393857	−	0.227393i	−0.289973	−	0.957035i	$-0.593646\pi$
$353$	139.032	−	80.2699i	0.393857	−	0.227393i	0.683830	+	0.729641i	$0.260313\pi$
$354$	61.9947	−	86.8643i	0.175126	−	0.245379i
$355$	187.294	+	108.134i	0.527589	+	0.304604i
$356$	−1.59572	−	0.921292i	−0.00448237	−	0.00258790i
$357$	692.427	−	4.26850i	1.93957	−	0.0119566i
$358$	−99.6542	−	172.606i	−0.278364	−	0.482140i
$359$	−447.910			−1.24766			−0.623830	−	0.781560i	$-0.714424\pi$
$359$	−447.910			−1.24766			−0.623830	+	0.781560i	$0.714424\pi$
$360$	−15.2734	+	78.3516i	−0.0424261	+	0.217643i
$361$	245.749			0.680744
$362$	330.749	−	190.958i	0.913671	−	0.527508i
$363$	161.985	−	73.7685i	0.446239	−	0.203219i
$364$	36.9326	+	16.5451i	0.101463	+	0.0454537i
$365$	188.199	−	325.971i	0.515615	−	0.893071i
$366$	14.3367	+	31.4813i	0.0391713	+	0.0860144i
$367$	−366.184	+	211.416i	−0.997776	+	0.576066i	−0.907589	−	0.419859i	$-0.862080\pi$
$367$	−366.184	+	211.416i	−0.997776	+	0.576066i	−0.0901863	+	0.995925i	$0.528746\pi$
$368$	−113.238			−0.307711
$369$	100.897	−	517.596i	0.273434	−	1.40270i
$370$		−	210.727i		−	0.569533i
$371$	63.0724	+	87.2320i	0.170006	+	0.235127i
$372$	−261.357	−	25.2362i	−0.702572	−	0.0678392i
$373$	−42.5654	+	73.7254i	−0.114116	+	0.197655i	−0.917426	−	0.397906i	$-0.869737\pi$
$373$	−42.5654	+	73.7254i	−0.114116	+	0.197655i	0.803310	+	0.595561i	$0.203070\pi$
$374$	317.135	+	183.098i	0.847955	+	0.489567i
$375$	−219.512	+	307.571i	−0.585365	+	0.820189i
$376$	−36.9282	+	21.3205i	−0.0982132	+	0.0567034i
$377$		−	0.459745i		−	0.00121948i
$378$	−202.708	−	174.217i	−0.536264	−	0.460892i
$379$	−385.337			−1.01672			−0.508360	−	0.861145i	$-0.669748\pi$
$379$	−385.337			−1.01672			−0.508360	+	0.861145i	$0.669748\pi$
$380$	33.6652	+	58.3099i	0.0885927	+	0.153447i
$381$	181.012	+	129.188i	0.475098	+	0.339075i
$382$	−61.9023	+	107.218i	−0.162048	+	0.280675i
$383$	−186.245	−	107.529i	−0.486280	−	0.280754i	0.236750	−	0.971571i	$-0.423918\pi$
$383$	−186.245	−	107.529i	−0.486280	−	0.280754i	−0.723030	+	0.690817i	$0.757251\pi$
$384$	−3.26213	+	33.7840i	−0.00849513	+	0.0879792i
$385$	139.692	−	101.003i	0.362837	−	0.262346i
$386$	−263.607			−0.682920
$387$	322.364	−	370.437i	0.832981	−	0.957203i
$388$		−	153.110i		−	0.394613i
$389$	3.36450	+	5.82748i	0.00864909	+	0.0149807i	0.870318	−	0.492491i	$-0.163914\pi$
$389$	3.36450	+	5.82748i	0.00864909	+	0.0149807i	−0.861668	+	0.507472i	$0.830580\pi$
$390$	−35.0000	+	15.9391i	−0.0897436	+	0.0408696i
$391$	−808.398	−	466.729i	−2.06751	−	1.19368i
$392$	43.4322	−	131.612i	0.110796	−	0.335744i
$393$	201.132	+	441.657i	0.511788	+	1.12381i
$394$	258.317	+	447.418i	0.655627	+	1.13558i
$395$			56.7706i			0.143723i
$396$	−45.9490	−	133.677i	−0.116033	−	0.337569i
$397$			601.337i			1.51470i	0.653007	+	0.757352i	$0.273507\pi$
$397$			601.337i			1.51470i	−0.653007	+	0.757352i	$0.726493\pi$
$398$	−107.980	+	62.3426i	−0.271308	+	0.156640i
$399$	−225.442	+	1.38974i	−0.565016	+	0.00348307i
$400$	−30.3326	+	52.5376i	−0.0758314	+	0.131344i
$401$	−174.618	+	302.448i	−0.435457	+	0.754233i	−0.997333	−	0.0729881i	$-0.976746\pi$
$401$	−174.618	+	302.448i	−0.435457	+	0.754233i	0.561876	+	0.827222i	$0.310080\pi$
$402$	−47.3872	−	33.8201i	−0.117879	−	0.0841295i
$403$	−63.2506	−	109.553i	−0.156949	−	0.271844i
$404$		−	25.8152i		−	0.0638990i
$405$	251.572	−	35.0822i	0.621164	−	0.0866228i
$406$	−1.56621	+	0.160982i	−0.00385766	+	0.000396507i
$407$	186.575	+	323.157i	0.458414	+	0.793997i
$408$	−162.535	+	227.737i	−0.398369	+	0.558178i
$409$	49.2615	+	28.4412i	0.120444	+	0.0695383i	0.559012	−	0.829160i	$-0.311181\pi$
$409$	49.2615	+	28.4412i	0.120444	+	0.0695383i	−0.438568	+	0.898698i	$0.644514\pi$
$410$	−129.924	+	225.036i	−0.316889	+	0.548868i
$411$	52.5356	−	544.081i	0.127824	−	1.32380i
$412$	270.510	−	156.179i	0.656578	−	0.379076i
$413$	−18.0030	−	175.153i	−0.0435907	−	0.424100i
$414$	117.127	+	340.752i	0.282915	+	0.823073i
$415$	250.326			0.603196
$416$	−14.1613	+	8.17603i	−0.0340416	+	0.0196539i
$417$	−300.650	−	660.184i	−0.720984	−	1.58317i
$418$	−103.253	−	59.6134i	−0.247018	−	0.142616i
$419$	345.034	+	199.205i	0.823470	+	0.475430i	0.851612	−	0.524173i	$-0.175626\pi$
$419$	345.034	+	199.205i	0.823470	+	0.475430i	−0.0281418	+	0.999604i	$0.508959\pi$
$420$	66.5553	+	113.653i	0.158465	+	0.270603i
$421$	240.359	+	416.313i	0.570923	+	0.988868i	0.996471	+	0.0839320i	$0.0267478\pi$
$421$	240.359	+	416.313i	0.570923	+	0.988868i	−0.425549	+	0.904936i	$0.639919\pi$
$422$	−182.875			−0.433353
$423$	102.354	+	89.0705i	0.241971	+	0.210569i
$424$	−43.4953			−0.102583
$425$	−433.085	+	250.042i	−1.01902	+	0.588333i
$426$	28.1220	−	291.243i	0.0660140	−	0.683669i
$427$	52.0863	+	23.3337i	0.121982	+	0.0546457i
$428$	−141.343	+	244.814i	−0.330241	+	0.571995i
$429$	39.5613	−	55.4316i	0.0922175	−	0.129211i
$430$	−209.555	+	120.987i	−0.487338	+	0.281365i
$431$	149.122			0.345991			0.172995	−	0.984923i	$-0.444655\pi$
$431$	149.122			0.345991			0.172995	+	0.984923i	$0.444655\pi$
$432$	105.036	−	25.1280i	0.243139	−	0.0581667i
$433$			114.348i			0.264083i	0.991244	+	0.132042i	$0.0421532\pi$
$433$			114.348i			0.264083i	−0.991244	+	0.132042i	$0.957847\pi$
$434$	−351.068	+	253.836i	−0.808912	+	0.584877i
$435$	0.869193	−	1.21788i	0.00199814	−	0.00279971i
$436$	−18.8235	+	32.6033i	−0.0431732	+	0.0747782i
$437$	263.199	+	151.958i	0.602287	+	0.347730i
$438$	−506.886	−	48.9441i	−1.15727	−	0.111745i
$439$	−151.734	+	87.6039i	−0.345637	+	0.199553i	−0.662762	−	0.748830i	$-0.730616\pi$
$439$	−151.734	+	87.6039i	−0.345637	+	0.199553i	0.317125	+	0.948384i	$0.397282\pi$
$440$			69.6529i			0.158302i
$441$	−440.966	+	5.43692i	−0.999924	+	0.0123286i
$442$	−134.796			−0.304967
$443$	−6.04017	−	10.4619i	−0.0136347	−	0.0236160i	0.859128	−	0.511762i	$-0.171007\pi$
$443$	−6.04017	−	10.4619i	−0.0136347	−	0.0236160i	−0.872762	+	0.488146i	$0.837674\pi$
$444$	−259.462	+	118.160i	−0.584374	+	0.266126i
$445$	1.44453	−	2.50200i	0.00324613	−	0.00562246i
$446$	230.336	+	132.985i	0.516449	+	0.298172i
$447$	−144.692	+	65.8932i	−0.323695	+	0.147412i
$448$	32.8119	+	45.3804i	0.0732408	+	0.101295i
$449$	−63.2131			−0.140786			−0.0703932	−	0.997519i	$-0.522425\pi$
$449$	−63.2131			−0.140786			−0.0703932	+	0.997519i	$0.522425\pi$
$450$	189.469	+	36.9340i	0.421042	+	0.0820756i
$451$		−	460.132i		−	1.02025i
$452$	−129.824	−	224.862i	−0.287221	−	0.497481i
$453$	45.9893	−	476.285i	0.101522	−	1.05140i
$454$	213.605	+	123.325i	0.470496	+	0.271641i
$455$	−25.9418	+	57.9081i	−0.0570149	+	0.127270i
$456$	52.9183	−	74.1468i	0.116049	−	0.162603i
$457$	−26.8766	−	46.5516i	−0.0588109	−	0.101864i	0.835121	−	0.550066i	$-0.185398\pi$
$457$	−26.8766	−	46.5516i	−0.0588109	−	0.101864i	−0.893932	+	0.448203i	$0.852064\pi$
$458$			498.091i			1.08754i
$459$	853.416	+	253.537i	1.85929	+	0.552368i
$460$		−	177.550i		−	0.385978i
$461$	−185.734	+	107.234i	−0.402895	+	0.232611i	−0.687732	−	0.725964i	$-0.741394\pi$
$461$	−185.734	+	107.234i	−0.402895	+	0.232611i	0.284837	+	0.958576i	$0.408060\pi$
$462$	−202.691	−	115.364i	−0.438726	−	0.249705i
$463$	−171.552	+	297.136i	−0.370522	+	0.641763i	−0.989646	−	0.143530i	$-0.954154\pi$
$463$	−171.552	+	297.136i	−0.370522	+	0.641763i	0.619124	+	0.785293i	$0.287488\pi$
$464$	0.318090	−	0.550947i	0.000685538	−	0.00118739i
$465$	39.5688	−	409.791i	0.0850941	−	0.881271i
$466$	−149.119	−	258.282i	−0.319998	−	0.554253i
$467$			440.960i			0.944241i	0.881534	+	0.472120i	$0.156511\pi$
$467$			440.960i			0.944241i	−0.881534	+	0.472120i	$0.843489\pi$
$468$	39.2508	+	34.1570i	0.0838691	+	0.0729850i
$469$	−95.5515	+	9.82118i	−0.203735	+	0.0209407i
$470$	−33.4292	−	57.9011i	−0.0711260	−	0.123194i
$471$	248.595	+	545.878i	0.527803	+	1.15898i
$472$	61.6137	+	35.5727i	0.130538	+	0.0753659i
$473$	214.240	−	371.074i	0.452938	−	0.784511i
$474$	69.8999	−	31.8327i	0.147468	−	0.0671576i
$475$	141.004	−	81.4089i	0.296851	−	0.171387i
$476$	47.1993	+	459.208i	0.0991582	+	0.964722i
$477$	44.9892	+	130.885i	0.0943170	+	0.274392i
$478$	−361.482			−0.756239
$479$	310.764	−	179.420i	0.648776	−	0.374571i	−0.139211	−	0.990263i	$-0.544457\pi$
$479$	310.764	−	179.420i	0.648776	−	0.374571i	0.787987	+	0.615692i	$0.211123\pi$
$480$	−52.9712	−	5.11482i	−0.110357	−	0.0106559i
$481$	−118.953	−	68.6774i	−0.247303	−	0.142781i
$482$	348.409	+	201.154i	0.722840	+	0.417332i
$483$	516.673	+	294.070i	1.06972	+	0.608840i
$484$	59.3304	+	102.763i	0.122583	+	0.212321i
$485$	240.066			0.494982
$486$	−184.258	−	290.081i	−0.379132	−	0.596874i
$487$	414.530			0.851191			0.425595	−	0.904914i	$-0.360065\pi$
$487$	414.530			0.851191			0.425595	+	0.904914i	$0.360065\pi$
$488$	−19.9718	+	11.5307i	−0.0409257	+	0.0236285i
$489$	286.361	+	204.375i	0.585605	+	0.417944i
$490$	206.359	+	68.0990i	0.421141	+	0.138978i
$491$	−196.276	+	339.960i	−0.399747	+	0.692382i	−0.993694	−	0.112122i	$-0.964235\pi$
$491$	−196.276	+	339.960i	−0.399747	+	0.692382i	0.593947	+	0.804504i	$0.297569\pi$
$492$	349.932	+	33.7888i	0.711243	+	0.0686765i
$493$	4.54165	−	2.62212i	0.00921226	−	0.00531870i
$494$	43.8869			0.0888399
$495$	209.598	−	72.0452i	0.423430	−	0.145546i
$496$		−	175.048i		−	0.352920i
$497$	−282.863	−	391.212i	−0.569140	−	0.787148i
$498$	−140.364	−	308.219i	−0.281856	−	0.618914i
$499$	481.752	−	834.418i	0.965434	−	1.67218i	0.256991	−	0.966414i	$-0.417269\pi$
$499$	481.752	−	834.418i	0.965434	−	1.67218i	0.708444	−	0.705767i	$-0.249398\pi$
$500$	−218.163	−	125.956i	−0.436326	−	0.251913i
$501$	156.573	+	343.811i	0.312521	+	0.686250i
$502$	−308.854	+	178.317i	−0.615247	+	0.355213i
$503$		−	475.660i		−	0.945647i	−0.881157	−	0.472823i	$-0.843235\pi$
$503$		−	475.660i		−	0.945647i	0.881157	−	0.472823i	$-0.156765\pi$
$504$	102.619	−	145.676i	0.203608	−	0.289039i
$505$	40.4766			0.0801518
$506$	157.200	+	272.278i	0.310671	+	0.538099i
$507$	46.3192	−	479.701i	0.0913593	−	0.946156i
$508$	−74.1282	+	128.394i	−0.145922	+	0.252744i
$509$	−100.863	−	58.2331i	−0.198158	−	0.114407i	0.397638	−	0.917542i	$-0.369830\pi$
$509$	−100.863	−	58.2331i	−0.198158	−	0.114407i	−0.595796	+	0.803136i	$0.703163\pi$
$510$	−357.077	−	254.844i	−0.700151	−	0.499695i
$511$	−680.875	+	492.301i	−1.33244	+	0.963407i
$512$	−22.6274			−0.0441942
$513$	−277.856	−	82.5469i	−0.541631	−	0.160910i
$514$		−	229.681i		−	0.446850i
$515$	244.879	+	424.143i	0.475493	+	0.823579i
$516$	266.470	+	190.179i	0.516415	+	0.368563i
$517$	102.529	+	59.1954i	0.198316	+	0.114498i
$518$	−192.311	+	429.284i	−0.371258	+	0.828734i
$519$	−831.436	−	80.2822i	−1.60200	−	0.154686i
$520$	−12.8195	−	22.2040i	−0.0246529	−	0.0427001i
$521$			536.626i			1.02999i	0.857192	+	0.514997i	$0.172207\pi$
$521$			536.626i			1.02999i	−0.857192	+	0.514997i	$0.827793\pi$
$522$	−1.98691	−	0.387317i	−0.00380634	−	0.000741987i
$523$			734.057i			1.40355i	0.712398	+	0.701776i	$0.247609\pi$
$523$			734.057i			1.40355i	−0.712398	+	0.701776i	$0.752391\pi$
$524$	−280.188	+	161.766i	−0.534709	+	0.308715i
$525$	274.835	−	160.943i	0.523496	−	0.306559i
$526$	−114.793	+	198.827i	−0.218237	+	0.377998i
$527$	721.491	−	1249.66i	1.36905	−	2.37127i
$528$	85.7616	−	39.0562i	0.162427	−	0.0739700i
$529$	−136.212	−	235.926i	−0.257489	−	0.445985i
$530$		−	68.1980i		−	0.128675i
$531$	43.3146	−	222.201i	0.0815717	−	0.418457i
$532$	−15.3672	−	149.510i	−0.0288857	−	0.281033i
$533$	84.6865	+	146.681i	0.158887	+	0.275200i
$534$	−3.89062	−	0.375672i	−0.00728580	−	0.000703505i
$535$	−383.853	−	221.618i	−0.717482	−	0.414238i
$536$	19.4060	−	33.6122i	0.0362053	−	0.0627094i
$537$	−344.140	−	245.611i	−0.640857	−	0.457377i
$538$	288.131	−	166.353i	0.535560	−	0.309206i
$539$	−376.752	+	78.2751i	−0.698983	+	0.145223i
$540$	39.3992	+	164.690i	0.0729614	+	0.304982i
$541$	−384.174			−0.710118			−0.355059	−	0.934844i	$-0.615539\pi$
$541$	−384.174			−0.710118			−0.355059	+	0.934844i	$0.615539\pi$
$542$	595.157	−	343.614i	1.09808	−	0.633974i
$543$	470.642	−	659.443i	0.866744	−	1.21444i
$544$	−161.536	−	93.2628i	−0.296941	−	0.171439i
$545$	−51.1199	−	29.5141i	−0.0937980	−	0.0541543i
$546$	85.8466	−	0.529205i	0.157228	−	0.000969241i
$547$	−160.326	−	277.692i	−0.293100	−	0.507663i	0.681441	−	0.731873i	$-0.261353\pi$
$547$	−160.326	−	277.692i	−0.293100	−	0.507663i	−0.974541	+	0.224209i	$0.928020\pi$
$548$	364.407			0.664977
$549$	55.3556	+	48.1718i	0.100830	+	0.0877445i
$550$	168.434			0.306244
$551$	−1.47868	+	0.853714i	−0.00268362	+	0.00154939i
$552$	−218.612	+	99.5566i	−0.396035	+	0.180356i
$553$	51.8093	−	115.651i	0.0936878	−	0.209133i
$554$	53.7822	−	93.1534i	0.0970797	−	0.168147i
$555$	−185.268	−	406.820i	−0.333815	−	0.733009i
$556$	418.821	−	241.807i	0.753275	−	0.434904i
$557$	−172.215			−0.309183			−0.154591	−	0.987979i	$-0.549406\pi$
$557$	−172.215			−0.309183			−0.154591	+	0.987979i	$0.549406\pi$
$558$	−526.750	+	181.060i	−0.943997	+	0.324481i
$559$			157.722i			0.282150i
$560$	−71.1536	+	51.4470i	−0.127060	+	0.0918697i
$561$	773.223	+	74.6612i	1.37829	+	0.133086i
$562$	364.542	−	631.405i	0.648651	−	1.12350i
$563$	−518.332	−	299.259i	−0.920660	−	0.531543i	−0.0368145	−	0.999322i	$-0.511721\pi$
$563$	−518.332	−	299.259i	−0.920660	−	0.531543i	−0.883846	+	0.467779i	$0.845054\pi$
$564$	−52.5472	+	73.6269i	−0.0931689	+	0.130544i
$565$	352.569	−	203.556i	0.624016	−	0.360276i
$566$			374.768i			0.662134i
$567$	−544.507	−	158.118i	−0.960329	−	0.278868i
$568$	195.065			0.343424
$569$	−55.3811	−	95.9229i	−0.0973306	−	0.168582i	0.813248	−	0.581917i	$-0.197697\pi$
$569$	−55.3811	−	95.9229i	−0.0973306	−	0.168582i	−0.910579	+	0.413335i	$0.864364\pi$
$570$	116.258	+	82.9726i	0.203961	+	0.145566i
$571$	−230.516	+	399.266i	−0.403706	+	0.699239i	−0.994170	−	0.107825i	$-0.965611\pi$
$571$	−230.516	+	399.266i	−0.403706	+	0.699239i	0.590464	+	0.807064i	$0.298945\pi$
$572$	39.3182	+	22.7004i	0.0687381	+	0.0396860i
$573$	−25.2417	+	261.413i	−0.0440518	+	0.456219i
$574$	470.046	−	339.863i	0.818895	−	0.592095i
$575$	−429.349			−0.746694
$576$	23.4046	+	68.0898i	0.0406329	+	0.118212i
$577$		−	125.230i		−	0.217037i	−0.994094	−	0.108519i	$-0.965389\pi$
$577$		−	125.230i		−	0.217037i	0.994094	−	0.108519i	$-0.0346107\pi$
$578$	−564.443	−	977.644i	−0.976545	−	1.69142i
$579$	−508.908	+	231.759i	−0.878943	+	0.400274i
$580$	0.863851	+	0.498745i	0.00148940	+	0.000859905i
$581$	−509.954	−	228.450i	−0.877717	−	0.393201i
$582$	−134.611	−	295.587i	−0.231291	−	0.507881i
$583$	60.3814	+	104.584i	0.103570	+	0.179389i
$584$		−	339.496i		−	0.581328i
$585$	−53.5560	+	61.5427i	−0.0915487	+	0.105201i
$586$		−	434.828i		−	0.742027i
$587$	336.969	−	194.549i	0.574053	−	0.331430i	−0.184713	−	0.982792i	$-0.559136\pi$
$587$	336.969	−	194.549i	0.574053	−	0.331430i	0.758766	+	0.651363i	$0.225802\pi$
$588$	−31.8624	−	292.268i	−0.0541878	−	0.497055i
$589$	−234.904	+	406.866i	−0.398818	+	0.690774i
$590$	−55.7758	+	96.6065i	−0.0945352	+	0.163740i
$591$	892.057	+	636.657i	1.50940	+	1.07725i
$592$	−95.0335	−	164.603i	−0.160530	−	0.278045i
$593$		−	232.608i		−	0.392256i	−0.980578	−	0.196128i	$-0.937163\pi$
$593$		−	232.608i		−	0.392256i	0.980578	−	0.196128i	$-0.0628368\pi$
$594$	−206.234	−	217.674i	−0.347195	−	0.366454i
$595$	−720.009	+	74.0055i	−1.21010	+	0.124379i
$596$	−52.9965	−	91.7926i	−0.0889203	−	0.154014i
$597$	−153.652	+	215.290i	−0.257373	+	0.360620i
$598$	−100.225	−	57.8647i	−0.167600	−	0.0967637i
$599$	213.695	−	370.130i	0.356752	−	0.617913i	−0.630664	−	0.776056i	$-0.717217\pi$
$599$	213.695	−	370.130i	0.356752	−	0.617913i	0.987416	+	0.158143i	$0.0505507\pi$
$600$	−12.3686	+	128.094i	−0.0206143	+	0.213491i
$601$	−521.460	+	301.065i	−0.867655	+	0.500941i	−0.866568	−	0.499059i	$-0.833679\pi$
$601$	−521.460	+	301.065i	−0.867655	+	0.500941i	−0.00108646	+	0.999999i	$0.500346\pi$
$602$	537.310	−	55.2270i	0.892542	−	0.0917392i
$603$	−121.218	−	23.6295i	−0.201024	−	0.0391865i
$604$	319.000			0.528146
$605$	−161.126	+	93.0263i	−0.266325	+	0.153763i
$606$	−22.6963	−	49.8376i	−0.0374526	−	0.0822403i
$607$	747.808	+	431.747i	1.23197	+	0.711280i	0.967441	−	0.253097i	$-0.0814490\pi$
$607$	747.808	+	431.747i	1.23197	+	0.711280i	0.264533	+	0.964377i	$0.414782\pi$
$608$	52.5931	+	30.3646i	0.0865018	+	0.0499418i
$609$	−2.88212	+	1.68777i	−0.00473255	+	0.00277138i
$610$	−18.0794	−	31.3145i	−0.0296384	−	0.0513352i
$611$	−43.5792			−0.0713244
$612$	−113.560	+	582.555i	−0.185556	+	0.951888i
$613$	949.122			1.54832			0.774161	−	0.632988i	$-0.218172\pi$
$613$	949.122			1.54832			0.774161	+	0.632988i	$0.218172\pi$
$614$	432.567	−	249.743i	0.704507	−	0.406747i
$615$	−52.9788	+	548.671i	−0.0861444	+	0.892148i
$616$	63.5659	−	141.894i	0.103191	−	0.230347i
$617$	−500.196	+	866.364i	−0.810690	+	1.40416i	0.101692	+	0.994816i	$0.467574\pi$
$617$	−500.196	+	866.364i	−0.810690	+	1.40416i	−0.912382	+	0.409340i	$0.865759\pi$
$618$	384.925	−	539.340i	0.622855	−	0.872718i
$619$	344.819	−	199.081i	0.557059	−	0.321618i	−0.194906	−	0.980822i	$-0.562440\pi$
$619$	344.819	−	199.081i	0.557059	−	0.321618i	0.751964	+	0.659204i	$0.229107\pi$
$620$	274.465			0.442685
$621$	525.703	+	554.864i	0.846543	+	0.893501i
$622$			526.979i			0.847233i
$623$	−5.22607	+	3.77867i	−0.00838856	+	0.00606528i
$624$	−20.1509	+	28.2346i	−0.0322932	+	0.0452478i
$625$	7.91335	−	13.7063i	0.0126614	−	0.0219301i
$626$	114.826	+	66.2949i	0.183428	+	0.105902i
$627$	−251.747	−	24.3083i	−0.401511	−	0.0387692i
$628$	−346.306	+	199.940i	−0.551442	+	0.318375i
$629$		−	1566.79i		−	2.49092i
$630$	228.410	+	160.900i	0.362556	+	0.255396i
$631$	−17.6413			−0.0279577			−0.0139788	−	0.999902i	$-0.504450\pi$
$631$	−17.6413			−0.0279577			−0.0139788	+	0.999902i	$0.504450\pi$
$632$	25.6023	+	44.3445i	0.0405100	+	0.0701654i
$633$	−353.050	+	160.780i	−0.557741	+	0.253997i
$634$	−95.8857	+	166.079i	−0.151239	+	0.261954i
$635$	−201.313	−	116.228i	−0.317029	−	0.183037i
$636$	−83.9701	+	38.2403i	−0.132028	+	0.0601263i
$637$	105.695	−	94.2931i	0.165926	−	0.148027i
$638$	−1.76632			−0.00276853
$639$	−201.765	−	586.985i	−0.315751	−	0.918599i
$640$		−	35.4784i		−	0.0554350i
$641$	256.854	+	444.885i	0.400709	+	0.694048i	0.993812	−	0.111079i	$-0.0354305\pi$
$641$	256.854	+	444.885i	0.400709	+	0.694048i	−0.593103	+	0.805127i	$0.702097\pi$
$642$	−57.6350	+	596.893i	−0.0897742	+	0.929740i
$643$	800.066	+	461.918i	1.24427	+	0.718380i	0.969961	−	0.243261i	$-0.0782173\pi$
$643$	800.066	+	461.918i	1.24427	+	0.718380i	0.274310	+	0.961641i	$0.411551\pi$
$644$	−162.033	+	361.696i	−0.251605	+	0.561640i
$645$	−298.188	+	417.809i	−0.462308	+	0.647766i
$646$	250.306	+	433.543i	0.387471	+	0.671119i
$647$		−	753.800i		−	1.16507i	−0.812806	−	0.582535i	$-0.802061\pi$
$647$		−	753.800i		−	1.16507i	0.812806	−	0.582535i	$-0.197939\pi$
$648$	180.686	−	140.857i	0.278836	−	0.217372i
$649$		−	197.532i		−	0.304364i
$650$	−53.6935	+	31.0000i	−0.0826055	+	0.0476923i
$651$	−454.587	+	798.697i	−0.698290	+	1.22688i
$652$	−117.271	+	203.119i	−0.179863	+	0.311532i
$653$	−419.466	+	726.536i	−0.642367	+	1.11261i	0.342536	+	0.939505i	$0.388714\pi$
$653$	−419.466	+	726.536i	−0.642367	+	1.11261i	−0.984903	+	0.173107i	$0.944619\pi$
$654$	−7.67559	+	79.4917i	−0.0117364	+	0.121547i
$655$	−253.640	−	439.317i	−0.387236	−	0.670713i
$656$			234.373i			0.357276i
$657$	−1021.60	+	351.156i	−1.55495	+	0.534484i
$658$	15.2595	+	148.461i	0.0231907	+	0.225625i
$659$	−406.108	−	703.400i	−0.616249	−	1.06737i	−0.990164	−	0.139912i	$-0.955318\pi$
$659$	−406.108	−	703.400i	−0.616249	−	1.06737i	0.373915	−	0.927463i	$-0.378015\pi$
$660$	61.2376	+	134.469i	0.0927843	+	0.203741i
$661$	−479.930	−	277.088i	−0.726067	−	0.419195i	0.0909149	−	0.995859i	$-0.471021\pi$
$661$	−479.930	−	277.088i	−0.726067	−	0.419195i	−0.816981	+	0.576664i	$0.804354\pi$
$662$	−236.846	+	410.229i	−0.357773	+	0.619681i
$663$	−260.230	+	118.510i	−0.392504	+	0.178748i
$664$	195.534	−	112.892i	0.294480	−	0.170018i
$665$	234.422	−	24.0948i	0.352514	−	0.0362328i
$666$	−397.021	+	456.229i	−0.596128	+	0.685028i
$667$	4.50247			0.00675033
$668$	−218.114	+	125.928i	−0.326518	+	0.188515i
$669$	561.595	+	54.2267i	0.839454	+	0.0810564i
$670$	52.7019	+	30.4274i	0.0786595	+	0.0454141i
$671$	55.4507	+	32.0145i	0.0826389	+	0.0477116i
$672$	103.243	+	58.7617i	0.153635	+	0.0874429i
$673$	−30.4512	−	52.7431i	−0.0452470	−	0.0783701i	0.842515	−	0.538673i	$-0.181074\pi$
$673$	−30.4512	−	52.7431i	−0.0452470	−	0.0783701i	−0.887762	+	0.460303i	$0.847741\pi$
$674$	777.791			1.15399
$675$	398.252	−	95.2746i	0.590003	−	0.141148i
$676$	321.288			0.475278
$677$	497.492	−	287.227i	0.734849	−	0.424265i	−0.0853448	−	0.996351i	$-0.527199\pi$
$677$	497.492	−	287.227i	0.734849	−	0.424265i	0.820193	+	0.572086i	$0.193866\pi$
$678$	−448.326	−	319.969i	−0.661248	−	0.471930i
$679$	−489.053	−	219.087i	−0.720254	−	0.322661i
$680$	146.230	−	253.278i	0.215044	−	0.372468i
$681$	520.801	+	50.2878i	0.764760	+	0.0738440i
$682$	−420.900	+	243.007i	−0.617155	+	0.356315i
$683$	−368.025			−0.538837			−0.269418	−	0.963023i	$-0.586831\pi$
$683$	−368.025			−0.538837			−0.269418	+	0.963023i	$0.586831\pi$
$684$	36.9730	−	189.669i	0.0540542	−	0.277294i
$685$			571.368i			0.834114i
$686$	−358.238	−	327.053i	−0.522212	−	0.476754i
$687$	437.913	+	961.592i	0.637428	+	1.39970i
$688$	−109.125	+	189.010i	−0.158612	+	0.274724i
$689$	−38.4969	−	22.2262i	−0.0558736	−	0.0322586i
$690$	−156.099	−	342.769i	−0.226230	−	0.496767i
$691$	738.344	−	426.283i	1.06852	−	0.616908i	0.140740	−	0.990047i	$-0.455052\pi$
$691$	738.344	−	426.283i	1.06852	−	0.616908i	0.927776	+	0.373139i	$0.121718\pi$
$692$		−	556.869i		−	0.804724i
$693$	−492.732	−	44.5135i	−0.711014	−	0.0642331i
$694$	−146.472			−0.211054
$695$	379.138	+	656.686i	0.545522	+	0.944871i
$696$	0.129706	−	1.34329i	0.000186359	−	0.00193002i
$697$	−966.007	+	1673.17i	−1.38595	+	2.40054i
$698$	−635.306	−	366.794i	−0.910181	−	0.525493i
$699$	−514.959	−	367.524i	−0.736708	−	0.525786i
$700$	124.409	+	172.063i	0.177727	+	0.245804i
$701$	1027.42			1.46565			0.732824	−	0.680418i	$-0.238202\pi$
$701$	1027.42			1.46565			0.732824	+	0.680418i	$0.238202\pi$
$702$	105.806	+	31.4333i	0.150721	+	0.0447768i
$703$			510.117i			0.725629i
$704$	31.4120	+	54.4072i	0.0446193	+	0.0772829i
$705$	−115.442	−	82.3908i	−0.163748	−	0.116866i
$706$	196.620	+	113.519i	0.278499	+	0.160791i
$707$	−82.4572	−	36.9393i	−0.116630	−	0.0522480i
$708$	150.224	+	14.5053i	0.212180	+	0.0204878i
$709$	80.9252	+	140.166i	0.114140	+	0.197696i	0.917436	−	0.397884i	$-0.130255\pi$
$709$	80.9252	+	140.166i	0.114140	+	0.197696i	−0.803296	+	0.595580i	$0.796922\pi$
$710$			305.850i			0.430774i
$711$	106.959	−	122.909i	0.150434	−	0.172868i
$712$		−	2.60581i		−	0.00365984i
$713$	1072.90	−	619.439i	1.50477	−	0.868779i
$714$	494.848	+	845.029i	0.693064	+	1.18351i
$715$	−35.5928	+	61.6485i	−0.0497801	+	0.0862217i
$716$	140.932	−	244.102i	0.196833	−	0.340924i
$717$	−697.861	+	317.809i	−0.973307	+	0.443248i
$718$	−316.720	−	548.576i	−0.441115	−	0.764033i
$719$		−	307.062i		−	0.427068i	−0.976936	−	0.213534i	$-0.931503\pi$
$719$		−	307.062i		−	0.427068i	0.976936	−	0.213534i	$-0.0684974\pi$
$720$	−106.761	+	36.6969i	−0.148279	+	0.0509679i
$721$	−111.780	−	1087.52i	−0.155035	−	1.50836i
$722$	173.771	+	300.979i	0.240679	+	0.416869i
$723$	849.473	+	82.0238i	1.17493	+	0.113449i
$724$	467.750	+	270.055i	0.646063	+	0.373005i
$725$	1.20606	−	2.08896i	0.00166353	−	0.00288132i
$726$	204.888	+	146.228i	0.282215	+	0.201416i
$727$	277.114	−	159.992i	0.381175	−	0.220071i	−0.297155	−	0.954829i	$-0.596038\pi$
$727$	277.114	−	159.992i	0.381175	−	0.220071i	0.678329	+	0.734758i	$0.262704\pi$
$728$	5.85173	+	56.9322i	0.00803809	+	0.0782036i
$729$	−610.754	−	398.020i	−0.837797	−	0.545981i
$730$	532.308			0.729189
$731$	−1558.07	+	899.554i	−2.13143	+	1.23058i
$732$	−28.4190	+	39.8194i	−0.0388237	+	0.0543981i
$733$	−147.657	−	85.2496i	−0.201441	−	0.116302i	0.395886	−	0.918300i	$-0.370437\pi$
$733$	−147.657	−	85.2496i	−0.201441	−	0.116302i	−0.597328	+	0.801997i	$0.703771\pi$
$734$	−517.862	−	298.988i	−0.705534	−	0.407340i
$735$	458.259	−	49.9583i	0.623481	−	0.0679705i
$736$	−80.0712	−	138.687i	−0.108792	−	0.188434i
$737$	−107.760			−0.146214
$738$	705.268	−	242.422i	0.955648	−	0.328486i
$739$	1106.86			1.49778			0.748888	−	0.662697i	$-0.230588\pi$
$739$	1106.86			1.49778			0.748888	+	0.662697i	$0.230588\pi$
$740$	258.087	−	149.007i	0.348766	−	0.201360i
$741$	84.7261	−	38.5846i	0.114340	−	0.0520710i
$742$	−62.2381	+	138.930i	−0.0838788	+	0.187237i
$743$	135.692	−	235.025i	0.182627	−	0.316319i	−0.760147	−	0.649751i	$-0.774873\pi$
$743$	135.692	−	235.025i	0.182627	−	0.316319i	0.942774	+	0.333432i	$0.108207\pi$
$744$	−153.899	−	337.940i	−0.206854	−	0.454220i
$745$	143.925	−	83.0952i	0.193188	−	0.111537i
$746$	−120.393			−0.161385
$747$	−541.961	−	471.628i	−0.725517	−	0.631363i
$748$			517.880i			0.692353i
$749$	579.718	+	801.777i	0.773989	+	1.07046i
$750$	−531.914	−	51.3608i	−0.709219	−	0.0684811i
$751$	345.456	−	598.348i	0.459995	−	0.796735i	−0.538965	−	0.842328i	$-0.681184\pi$
$751$	345.456	−	598.348i	0.459995	−	0.796735i	0.998960	+	0.0455932i	$0.0145178\pi$
$752$	−52.2243	−	30.1517i	−0.0694472	−	0.0400954i
$753$	−439.486	+	615.789i	−0.583647	+	0.817781i
$754$	0.563070	−	0.325089i	0.000746777	−	0.000431152i
$755$			500.172i			0.662480i
$756$	70.0354	−	371.455i	0.0926394	−	0.491343i
$757$	−26.8713			−0.0354972			−0.0177486	−	0.999842i	$-0.505650\pi$
$757$	−26.8713			−0.0354972			−0.0177486	+	0.999842i	$0.505650\pi$
$758$	−272.474	−	471.939i	−0.359465	−	0.622611i
$759$	542.864	+	387.440i	0.715236	+	0.510461i
$760$	−47.6098	+	82.4627i	−0.0626445	+	0.108504i
$761$	15.8485	+	9.15015i	0.0208259	+	0.0120238i	0.510377	−	0.859951i	$-0.329506\pi$
$761$	15.8485	+	9.15015i	0.0208259	+	0.0120238i	−0.489551	+	0.871975i	$0.662839\pi$
$762$	−30.2270	+	313.043i	−0.0396679	+	0.410818i
$763$	77.2044	+	106.777i	0.101185	+	0.139944i
$764$	−175.086			−0.229170
$765$	−913.411	−	178.055i	−1.19400	−	0.232752i
$766$		−	304.137i		−	0.397046i
$767$	36.3554	+	62.9694i	0.0473995	+	0.0820983i
$768$	−43.6835	+	19.8936i	−0.0568795	+	0.0259031i
$769$	569.190	+	328.622i	0.740169	+	0.427337i	0.822131	−	0.569298i	$-0.192785\pi$
$769$	569.190	+	328.622i	0.740169	+	0.427337i	−0.0819614	+	0.996636i	$0.526118\pi$
$770$	222.481	+	99.6673i	0.288936	+	0.129438i
$771$	−201.931	−	443.411i	−0.261908	−	0.575112i
$772$	−186.398	−	322.852i	−0.241449	−	0.418202i
$773$			1480.42i			1.91517i	0.288159	+	0.957583i	$0.406957\pi$
$773$			1480.42i			1.91517i	−0.288159	+	0.957583i	$0.593043\pi$
$774$	681.637	+	132.874i	0.880668	+	0.171672i
$775$		−	663.708i		−	0.856397i
$776$	187.520	−	108.265i	0.241650	−	0.139517i
$777$	6.15118	+	997.833i	0.00791658	+	1.28421i
$778$	−4.75812	+	8.24130i	−0.00611583	+	0.0105929i
$779$	314.514	−	544.754i	0.403741	−	0.699299i
$780$	−44.2701	−	31.5954i	−0.0567566	−	0.0405069i
$781$	−270.795	−	469.030i	−0.346728	−	0.600551i
$782$		−	1320.11i		−	1.68812i
$783$	−4.17636	+	0.999120i	−0.00533379	+	0.00127601i
$784$	191.902	−	39.8702i	0.244773	−	0.0508548i
$785$	−313.493	−	542.986i	−0.399354	−	0.691702i
$786$	−398.695	+	558.635i	−0.507246	+	0.710731i
$787$	695.382	+	401.479i	0.883585	+	0.510138i	0.871839	−	0.489793i	$-0.162928\pi$
$787$	695.382	+	401.479i	0.883585	+	0.510138i	0.0117465	+	0.999931i	$0.496261\pi$
$788$	−365.315	+	632.745i	−0.463598	+	0.802976i
$789$	−46.8086	+	484.770i	−0.0593265	+	0.614410i
$790$	−69.5295	+	40.1429i	−0.0880120	+	0.0508138i
$791$	−904.005	+	92.9173i	−1.14286	+	0.117468i
$792$	131.230	−	150.800i	0.165694	−	0.190404i
$793$	−23.5688			−0.0297211
$794$	−736.485	+	425.210i	−0.927563	+	0.535529i
$795$	−59.9584	−	131.660i	−0.0754194	−	0.165610i
$796$	−152.707	−	88.1657i	−0.191844	−	0.110761i
$797$	172.823	+	99.7795i	0.216842	+	0.125194i	0.604487	−	0.796615i	$-0.293378\pi$
$797$	172.823	+	99.7795i	0.216842	+	0.125194i	−0.387645	+	0.921809i	$0.626711\pi$
$798$	−161.113	−	275.126i	−0.201896	−	0.344769i
$799$	−248.551	−	430.503i	−0.311077	−	0.538802i
$800$	−85.7935			−0.107242
$801$	−7.84133	+	2.69530i	−0.00978942	+	0.00336492i
$802$	−493.895			−0.615829
$803$	−816.311	+	471.297i	−1.01658	+	0.586921i
$804$	7.91312	−	81.9517i	0.00984219	−	0.101930i
$805$	−567.117	−	254.058i	−0.704494	−	0.315600i
$806$	89.4499	−	154.932i	0.110980	−	0.192223i
$807$	409.999	−	574.473i	0.508053	−	0.711862i
$808$	31.6170	−	18.2541i	0.0391300	−	0.0225917i
$809$	449.356			0.555447			0.277723	−	0.960661i	$-0.410420\pi$
$809$	449.356			0.555447			0.277723	+	0.960661i	$0.410420\pi$
$810$	220.855	+	283.304i	0.272660	+	0.349758i
$811$			523.569i			0.645585i	0.946470	+	0.322793i	$0.104622\pi$
$811$			523.569i			0.645585i	−0.946470	+	0.322793i	$0.895378\pi$
$812$	−1.30464	−	1.80438i	−0.00160670	−	0.00222214i
$813$	846.883	−	1186.62i	1.04168	−	1.45955i
$814$	−263.856	+	457.012i	−0.324148	+	0.561440i
$815$	−318.477	−	183.873i	−0.390770	−	0.225611i
$816$	−393.849	−	38.0294i	−0.482658	−	0.0466047i
$817$	507.280	−	292.878i	0.620906	−	0.358480i
$818$			80.4437i			0.0983420i
$819$	165.266	−	76.4965i	0.201790	−	0.0934023i
$820$	−367.482			−0.448149
$821$	−694.072	−	1202.17i	−0.845398	−	1.46427i	−0.885275	−	0.465068i	$-0.846030\pi$
$821$	−694.072	−	1202.17i	−0.845398	−	1.46427i	0.0398766	−	0.999205i	$-0.487304\pi$
$822$	703.508	−	320.380i	0.855849	−	0.389757i
$823$	−143.562	+	248.656i	−0.174437	+	0.302134i	−0.939966	−	0.341267i	$-0.889144\pi$
$823$	−143.562	+	248.656i	−0.174437	+	0.302134i	0.765529	+	0.643401i	$0.222477\pi$
$824$	382.559	+	220.871i	0.464271	+	0.268047i
$825$	325.171	−	148.084i	0.394147	−	0.179496i
$826$	201.788	−	145.901i	0.244295	−	0.176636i
$827$	−1246.27			−1.50698			−0.753490	−	0.657460i	$-0.771631\pi$
$827$	−1246.27			−1.50698			−0.753490	+	0.657460i	$0.771631\pi$
$828$	−334.513	+	384.399i	−0.404001	+	0.464250i
$829$		−	595.590i		−	0.718444i	−0.933252	−	0.359222i	$-0.883042\pi$
$829$		−	595.590i		−	0.718444i	0.933252	−	0.359222i	$-0.116958\pi$
$830$	177.007	+	306.586i	0.213262	+	0.369381i
$831$	21.9305	−	227.122i	0.0263905	−	0.273312i
$832$	−20.0271	−	11.5626i	−0.0240710	−	0.0138974i
$833$	1534.31	+	506.326i	1.84191	+	0.607834i
$834$	595.965	−	835.041i	0.714586	−	1.00125i
$835$	−197.448	−	341.990i	−0.236464	−	0.409568i
$836$		−	168.612i		−	0.201689i
$837$	−857.735	+	812.656i	−1.02477	+	0.970915i
$838$			563.438i			0.672360i
$839$	803.641	−	463.982i	0.957855	−	0.553018i	0.0623431	−	0.998055i	$-0.480143\pi$
$839$	803.641	−	463.982i	0.957855	−	0.553018i	0.895512	+	0.445037i	$0.146809\pi$
$840$	−92.1346	+	161.878i	−0.109684	+	0.192712i
$841$	420.487	−	728.305i	0.499985	−	0.865999i
$842$	−339.918	+	588.756i	−0.403704	+	0.699235i
$843$	148.648	−	1539.46i	0.176332	−	1.82617i
$844$	−129.312	−	223.975i	−0.153213	−	0.265373i
$845$			503.760i			0.596165i
$846$	−36.7138	+	188.339i	−0.0433969	+	0.222623i
$847$	413.136	−	42.4638i	0.487764	−	0.0501344i
$848$	−30.7559	−	53.2707i	−0.0362687	−	0.0628192i
$849$	329.489	+	723.510i	0.388091	+	0.852190i
$850$	−612.475	−	353.612i	−0.720558	−	0.416015i
$851$	672.586	−	1164.95i	0.790348	−	1.36892i
$852$	376.584	−	171.498i	0.442000	−	0.201288i
$853$	−247.781	+	143.056i	−0.290482	+	0.167710i	−0.638159	−	0.769905i	$-0.720304\pi$
$853$	−247.781	+	143.056i	−0.290482	+	0.167710i	0.347677	+	0.937614i	$0.386970\pi$
$854$	8.25273	+	80.2919i	0.00966362	+	0.0940186i
$855$	297.390	+	57.9714i	0.347824	+	0.0678028i
$856$	−399.779			−0.467032
$857$	−552.193	+	318.809i	−0.644333	+	0.372006i	−0.786282	−	0.617868i	$-0.787997\pi$
$857$	−552.193	+	318.809i	−0.644333	+	0.372006i	0.141949	+	0.989874i	$0.454663\pi$
$858$	95.8637	+	9.25644i	0.111729	+	0.0107884i
$859$	453.550	+	261.857i	0.527997	+	0.304839i	0.740201	−	0.672386i	$-0.234731\pi$
$859$	453.550	+	261.857i	0.527997	+	0.304839i	−0.212203	+	0.977226i	$0.568064\pi$
$860$	−296.356	−	171.101i	−0.344600	−	0.198955i
$861$	608.648	−	1069.38i	0.706908	−	1.24202i
$862$	105.445	+	182.637i	0.122326	+	0.211875i
$863$	821.844			0.952310			0.476155	−	0.879361i	$-0.342030\pi$
$863$	821.844			0.952310			0.476155	+	0.879361i	$0.342030\pi$
$864$	105.047	+	110.874i	0.121582	+	0.128327i
$865$	873.136			1.00941
$866$	−140.047	+	80.8562i	−0.161717	+	0.0933675i
$867$	−1949.21	−	1391.15i	−2.24823	−	1.60455i
$868$	−559.127	−	250.479i	−0.644156	−	0.288570i
$869$	71.0837	−	123.121i	0.0817995	−	0.141681i
$870$	2.10620	+	0.203371i	0.00242092	+	0.000233760i
$871$	34.3518	−	19.8330i	0.0394395	−	0.0227704i
$872$	−53.2410			−0.0610561
$873$	−519.749	−	452.298i	−0.595359	−	0.518096i
$874$			429.803i			0.491765i
$875$	−714.494	+	516.609i	−0.816565	+	0.590410i
$876$	−298.478	−	655.415i	−0.340729	−	0.748190i
$877$	−90.6785	+	157.060i	−0.103396	+	0.179088i	−0.913082	−	0.407776i	$-0.866304\pi$
$877$	−90.6785	+	157.060i	−0.103396	+	0.179088i	0.809686	+	0.586864i	$0.199638\pi$
$878$	−214.585	−	123.891i	−0.244402	−	0.141106i
$879$	−382.293	−	839.458i	−0.434918	−	0.955015i
$880$	−85.3071	+	49.2521i	−0.0969399	+	0.0559683i
$881$		−	260.901i		−	0.296142i	−0.988977	−	0.148071i	$-0.952694\pi$
$881$		−	260.901i		−	0.296142i	0.988977	−	0.148071i	$-0.0473063\pi$
$882$	−318.469	−	536.227i	−0.361076	−	0.607967i
$883$	1306.75			1.47990			0.739949	−	0.672663i	$-0.234850\pi$
$883$	1306.75			1.47990			0.739949	+	0.672663i	$0.234850\pi$
$884$	−95.3148	−	165.090i	−0.107822	−	0.186754i
$885$	−22.7435	+	235.541i	−0.0256988	+	0.266148i
$886$	8.54209	−	14.7953i	0.00964118	−	0.0166990i
$887$	457.566	+	264.176i	0.515858	+	0.297831i	0.735238	−	0.677809i	$-0.237070\pi$
$887$	457.566	+	264.176i	0.515858	+	0.297831i	−0.219380	+	0.975639i	$0.570404\pi$
$888$	−328.183	−	234.223i	−0.369576	−	0.263765i
$889$	304.036	+	420.496i	0.341997	+	0.472998i
$890$	4.08574			0.00459072
$891$	−589.521	−	238.914i	−0.661639	−	0.268142i
$892$			376.138i			0.421679i
$893$	80.9236	+	140.164i	0.0906199	+	0.156958i
$894$	−183.015	−	130.617i	−0.204715	−	0.146104i
$895$	382.737	+	220.973i	0.427639	+	0.246897i
$896$	−32.3779	+	72.2750i	−0.0361360	+	0.0806640i
$897$	−244.362	−	23.5953i	−0.272422	−	0.0263046i
$898$	−44.6984	−	77.4199i	−0.0497755	−	0.0862137i
$899$			6.96012i			0.00774207i
$900$	88.7401	+	258.167i	0.0986001	+	0.286853i
$901$		−	507.062i		−	0.562777i
$902$	563.545	−	325.363i	0.624772	−	0.360713i
$903$	988.752	−	579.012i	1.09496	−	0.641210i
$904$	183.599	−	318.002i	0.203096	−	0.351772i
$905$	−423.430	+	733.402i	−0.467878	+	0.810389i
$906$	615.847	−	280.459i	0.679743	−	0.309557i
$907$	−348.635	−	603.853i	−0.384382	−	0.665769i	0.607301	−	0.794472i	$-0.292252\pi$
$907$	−348.635	−	603.853i	−0.384382	−	0.665769i	−0.991683	+	0.128702i	$0.958919\pi$
$908$			348.816i			0.384158i
$909$	−87.6327	−	76.2601i	−0.0964056	−	0.0838945i
$910$	−89.2662	+	9.17515i	−0.0980947	+	0.0100826i
$911$	560.877	+	971.468i	0.615672	+	1.06638i	0.990266	+	0.139186i	$0.0444487\pi$
$911$	560.877	+	971.468i	0.615672	+	1.06638i	−0.374594	+	0.927189i	$0.622218\pi$
$912$	128.230	+	12.3817i	0.140603	+	0.0135764i
$913$	−542.893	−	313.439i	−0.594625	−	0.343307i
$914$	38.0093	−	65.8340i	0.0415856	−	0.0720284i
$915$	−62.4344	−	44.5592i	−0.0682343	−	0.0486985i
$916$	−610.035	+	352.204i	−0.665977	+	0.384502i
$917$	115.779	+	1126.43i	0.126259	+	1.22839i
$918$	292.938	+	1224.49i	0.319105	+	1.33387i
$919$	−1158.80			−1.26094			−0.630469	−	0.776214i	$-0.717138\pi$
$919$	−1158.80			−1.26094			−0.630469	+	0.776214i	$0.717138\pi$
$920$	217.453	−	125.547i	0.236362	−	0.136464i
$921$	615.525	−	862.448i	0.668323	−	0.936425i
$922$	−262.668	−	151.652i	−0.284890	−	0.164481i
$923$	172.648	+	99.6786i	0.187051	+	0.107994i
$924$	−2.03319	−	329.820i	−0.00220042	−	0.356948i
$925$	−360.326	−	624.103i	−0.389542	−	0.674706i
$926$	−485.221			−0.523997
$927$	268.940	−	1379.64i	0.290119	−	1.48829i
$928$	0.899693			0.000969497
$929$	600.748	−	346.842i	0.646661	−	0.373350i	−0.140515	−	0.990079i	$-0.544876\pi$
$929$	600.748	−	346.842i	0.646661	−	0.373350i	0.787176	+	0.616729i	$0.211542\pi$
$930$	529.869	−	241.304i	0.569751	−	0.259467i
$931$	−499.543	−	164.850i	−0.536566	−	0.177068i
$932$	210.886	−	365.266i	0.226273	−	0.391916i
$933$	463.311	+	1017.36i	0.496581	+	1.09042i
$934$	−540.064	+	311.806i	−0.578227	+	0.333839i
$935$	−812.003			−0.868453
$936$	−14.0791	+	72.2248i	−0.0150418	+	0.0771632i
$937$			1241.64i			1.32512i	0.749007	+	0.662562i	$0.230531\pi$
$937$			1241.64i			1.32512i	−0.749007	+	0.662562i	$0.769469\pi$
$938$	−79.5936	−	110.082i	−0.0848546	−	0.117358i
$939$	279.963	+	27.0328i	0.298151	+	0.0287889i
$940$	47.2760	−	81.8845i	0.0502936	−	0.0871111i
$941$	651.336	+	376.049i	0.692175	+	0.399627i	0.804426	−	0.594053i	$-0.202473\pi$
$941$	651.336	+	376.049i	0.692175	+	0.399627i	−0.112251	+	0.993680i	$0.535806\pi$
$942$	−492.778	+	690.460i	−0.523119	+	0.732972i
$943$	−1436.51	+	829.370i	−1.52334	+	0.879501i
$944$			100.615i			0.106583i
$945$	582.419	+	109.811i	0.616316	+	0.116202i
$946$	605.961			0.640551
$947$	164.226	+	284.448i	0.173417	+	0.300367i	0.939612	−	0.342241i	$-0.111186\pi$
$947$	164.226	+	284.448i	0.173417	+	0.300367i	−0.766195	+	0.642608i	$0.777852\pi$
$948$	88.4136	+	63.1004i	0.0932633	+	0.0665616i
$949$	173.483	−	300.481i	0.182806	−	0.316629i
$950$	199.410	+	115.130i	0.209906	+	0.121189i
$951$	−39.0990	+	404.925i	−0.0411135	+	0.425789i
$952$	−529.037	+	382.516i	−0.555712	+	0.401803i
$953$	1487.60			1.56097			0.780483	−	0.625177i	$-0.214973\pi$
$953$	1487.60			1.56097			0.780483	+	0.625177i	$0.214973\pi$
$954$	−128.489	+	147.650i	−0.134684	+	0.154769i
$955$		−	274.524i		−	0.287460i
$956$	−255.607	−	442.724i	−0.267371	−	0.463100i
$957$	−3.40998	+	1.55292i	−0.00356320	+	0.00162270i
$958$	439.487	+	253.738i	0.458754	+	0.264862i
$959$	521.435	−	1163.97i	0.543728	−	1.21373i
$960$	−31.1920	−	68.4929i	−0.0324916	−	0.0713468i
$961$	477.058	+	826.289i	0.496419	+	0.859822i
$962$		−	194.249i		−	0.201922i
$963$	413.510	+	1203.01i	0.429398	+	1.24923i
$964$			568.950i			0.590197i
$965$	506.211	−	292.261i	0.524571	−	0.302861i
$966$	5.18272	+	840.731i	0.00536514	+	0.870322i
$967$	−621.111	+	1075.80i	−0.642307	+	1.11251i	0.342609	+	0.939478i	$0.388689\pi$
$967$	−621.111	+	1075.80i	−0.642307	+	1.11251i	−0.984916	+	0.173031i	$0.944644\pi$
$968$	−83.9058	+	145.329i	−0.0866796	+	0.150133i
$969$	864.392	+	616.913i	0.892045	+	0.636649i
$970$	169.753	+	294.020i	0.175003	+	0.303114i
$971$			1010.61i			1.04079i	0.853924	+	0.520397i	$0.174216\pi$
$971$			1010.61i			1.04079i	−0.853924	+	0.520397i	$0.825784\pi$
$972$	224.985	−	430.787i	0.231466	−	0.443197i
$973$	−173.065	−	1683.77i	−0.177868	−	1.73050i
$974$	293.117	+	507.693i	0.300941	+	0.521246i
$975$	−76.4037	+	107.054i	−0.0783627	+	0.109799i
$976$	−28.2443	−	16.3069i	−0.0289389	−	0.0167079i
$977$	−573.800	+	993.851i	−0.587308	+	1.01725i	0.407275	+	0.913306i	$0.366479\pi$
$977$	−573.800	+	993.851i	−0.587308	+	1.01725i	−0.994583	+	0.103942i	$0.966854\pi$
$978$	−47.8190	+	495.234i	−0.0488947	+	0.506374i
$979$	−6.26561	+	3.61745i	−0.00640001	+	0.00369505i
$980$	62.5140	+	300.890i	0.0637897	+	0.307031i
$981$	55.0695	+	160.211i	0.0561361	+	0.163314i
$982$	−555.152			−0.565328
$983$	380.121	−	219.463i	0.386695	−	0.223259i	−0.294032	−	0.955796i	$-0.594997\pi$
$983$	380.121	−	219.463i	0.386695	−	0.223259i	0.680727	+	0.732537i	$0.261664\pi$
$984$	206.056	+	452.469i	0.209407	+	0.459826i
$985$	−992.105	−	572.792i	−1.00721	−	0.581515i
$986$	6.42286	+	3.70824i	0.00651405	+	0.00376089i
$987$	159.984	+	273.197i	0.162091	+	0.276795i
$988$	31.0327	+	53.7503i	0.0314097	+	0.0544031i
$989$	−1544.63			−1.56181
$990$	236.445	+	205.760i	0.238833	+	0.207839i
$991$	−126.283			−0.127430			−0.0637151	−	0.997968i	$-0.520295\pi$
$991$	−126.283			−0.127430			−0.0637151	+	0.997968i	$0.520295\pi$
$992$	214.389	−	123.778i	0.216118	−	0.124776i
$993$	−96.5777	+	1000.20i	−0.0972585	+	1.00725i
$994$	279.121	−	623.064i	0.280806	−	0.626825i
$995$	138.238	−	239.436i	0.138933	−	0.240639i
$996$	278.237	−	389.854i	0.279355	−	0.391420i
$997$	714.603	−	412.576i	0.716753	−	0.413818i	−0.0968032	−	0.995304i	$-0.530862\pi$
$997$	714.603	−	412.576i	0.716753	−	0.413818i	0.813557	+	0.581486i	$0.197528\pi$
$998$	1362.60			1.36533
$999$	−365.363	+	1229.83i	−0.365729	+	1.23106i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.3.o.a.13.15	yes	32
3.2	odd	2		378.3.o.a.307.6		32
7.6	odd	2	inner	126.3.o.a.13.10	✓	32
9.2	odd	6		378.3.o.a.181.3		32
9.4	even	3		1134.3.c.e.811.6		16
9.5	odd	6		1134.3.c.d.811.11		16
9.7	even	3	inner	126.3.o.a.97.10	yes	32
21.20	even	2		378.3.o.a.307.3		32
63.13	odd	6		1134.3.c.e.811.3		16
63.20	even	6		378.3.o.a.181.6		32
63.34	odd	6	inner	126.3.o.a.97.15	yes	32
63.41	even	6		1134.3.c.d.811.14		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.o.a.13.10	✓	32	7.6	odd	2	inner
126.3.o.a.13.15	yes	32	1.1	even	1	trivial
126.3.o.a.97.10	yes	32	9.7	even	3	inner
126.3.o.a.97.15	yes	32	63.34	odd	6	inner
378.3.o.a.181.3		32	9.2	odd	6
378.3.o.a.181.6		32	63.20	even	6
378.3.o.a.307.3		32	21.20	even	2
378.3.o.a.307.6		32	3.2	odd	2
1134.3.c.d.811.11		16	9.5	odd	6
1134.3.c.d.811.14		16	63.41	even	6
1134.3.c.e.811.3		16	63.13	odd	6
1134.3.c.e.811.6		16	9.4	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.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 1.22474i) q^{2} +(2.44188 + 1.74276i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-2.71575 - 1.56794i) q^{5} +(-0.407766 + 4.22300i) q^{6} +(4.10149 + 5.67255i) q^{7} -2.82843 q^{8} +(2.92557 + 8.51123i) q^{9} -4.43480i q^{10} +(3.92650 + 6.80090i) q^{11} +(-5.46043 + 2.48670i) q^{12} +(-2.50339 - 1.44533i) q^{13} +(-4.04723 + 9.03437i) q^{14} +(-3.89899 - 8.56162i) q^{15} +(-2.00000 - 3.46410i) q^{16} -32.9734i q^{17} +(-8.35539 + 9.60143i) q^{18} +10.7355i q^{19} +(5.43150 - 3.13588i) q^{20} +(0.129453 + 20.9996i) q^{21} +(-5.55291 + 9.61792i) q^{22} +(14.1547 - 24.5167i) q^{23} +(-6.90668 - 4.92927i) q^{24} +(-7.58314 - 13.1344i) q^{25} -4.08801i q^{26} +(-7.68914 + 25.8820i) q^{27} +(-13.9266 + 1.43144i) q^{28} +(0.0795224 + 0.137737i) q^{29} +(7.72879 - 10.8293i) q^{30} +(37.8990 + 21.8810i) q^{31} +(2.82843 - 4.89898i) q^{32} +(-2.26429 + 23.4499i) q^{33} +(40.3840 - 23.3157i) q^{34} +(-2.24440 - 21.8361i) q^{35} +(-17.6675 - 3.44399i) q^{36} +47.5168 q^{37} +(-13.1483 + 7.59116i) q^{38} +(-3.59411 - 7.89213i) q^{39} +(7.68130 + 4.43480i) q^{40} +(-50.7432 - 29.2966i) q^{41} +(-25.6276 + 15.0075i) q^{42} +(-27.2812 - 47.2525i) q^{43} -15.7060 q^{44} +(5.39997 - 27.7015i) q^{45} +40.0356 q^{46} +(13.0561 - 7.53793i) q^{47} +(1.15334 - 11.9444i) q^{48} +(-15.3556 + 46.5318i) q^{49} +(10.7242 - 18.5748i) q^{50} +(57.4647 - 80.5170i) q^{51} +(5.00677 - 2.89066i) q^{52} +15.3779 q^{53} +(-37.1359 + 8.88409i) q^{54} -24.6260i q^{55} +(-11.6008 - 16.0444i) q^{56} +(-18.7094 + 26.2149i) q^{57} +(-0.112462 + 0.194789i) q^{58} +(-21.7837 - 12.5768i) q^{59} +(18.7281 + 1.80836i) q^{60} +(7.06108 - 4.07672i) q^{61} +61.8889i q^{62} +(-36.2812 + 51.5041i) q^{63} +8.00000 q^{64} +(4.53238 + 7.85031i) q^{65} +(-30.3213 + 13.8084i) q^{66} +(-6.86107 + 11.8837i) q^{67} +(57.1115 + 32.9734i) q^{68} +(77.2909 - 35.1986i) q^{69} +(25.1566 - 18.1893i) q^{70} -68.9659 q^{71} +(-8.27476 - 24.0734i) q^{72} +120.030i q^{73} +(33.5994 + 58.1959i) q^{74} +(4.37296 - 45.2882i) q^{75} +(-18.5945 - 10.7355i) q^{76} +(-22.4739 + 50.1671i) q^{77} +(7.12443 - 9.98244i) q^{78} +(-9.05179 - 15.6782i) q^{79} +12.5435i q^{80} +(-63.8821 + 49.8004i) q^{81} -82.8633i q^{82} +(-69.1319 + 39.9133i) q^{83} +(-36.5018 - 20.7754i) q^{84} +(-51.7002 + 89.5473i) q^{85} +(38.5815 - 66.8251i) q^{86} +(-0.0458581 + 0.474926i) q^{87} +(-11.1058 - 19.2358i) q^{88} +0.921292i q^{89} +(37.7456 - 12.9743i) q^{90} +(-2.06890 - 20.1286i) q^{91} +(28.3094 + 49.0334i) q^{92} +(54.4116 + 119.480i) q^{93} +(18.4641 + 10.6602i) q^{94} +(16.8326 - 29.1550i) q^{95} +(15.4444 - 7.03346i) q^{96} +(-66.2984 + 38.2774i) q^{97} +(-67.8476 + 14.0962i) q^{98} +(-46.3968 + 53.3159i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{4} - 2 q^{7} + 24 q^{9} - 12 q^{11} - 12 q^{14} + 48 q^{15} - 64 q^{16} - 54 q^{21} + 12 q^{23} + 80 q^{25} + 8 q^{28} - 48 q^{29} - 168 q^{30} + 348 q^{35} - 72 q^{36} - 88 q^{37} + 252 q^{39}+ \cdots - 684 q^{99}+O(q^{100}) \) 32 * q - 32 * q^4 - 2 * q^7 + 24 * q^9 - 12 * q^11 - 12 * q^14 + 48 * q^15 - 64 * q^16 - 54 * q^21 + 12 * q^23 + 80 * q^25 + 8 * q^28 - 48 * q^29 - 168 * q^30 + 348 * q^35 - 72 * q^36 - 88 * q^37 + 252 * q^39 + 32 * q^43 + 48 * q^44 + 48 * q^46 + 50 * q^49 + 48 * q^50 - 372 * q^51 - 864 * q^53 - 24 * q^56 + 372 * q^57 + 48 * q^58 - 24 * q^60 - 114 * q^63 + 256 * q^64 + 120 * q^65 - 140 * q^67 - 108 * q^70 + 552 * q^71 + 96 * q^72 + 144 * q^74 - 258 * q^77 + 288 * q^78 - 176 * q^79 - 360 * q^81 - 60 * q^85 + 96 * q^86 + 372 * q^91 + 24 * q^92 - 456 * q^93 + 528 * q^95 + 624 * q^98 - 684 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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