LMFDB - Embedded newform 126.3.r.a.23.15

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			23.15
Character	$\chi$	$=$	126.23
Dual form			126.3.r.a.11.7

$q$-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} +(2.36405 - 1.84696i) q^{3} -2.00000 q^{4} +(1.22482 - 0.707152i) q^{5} +(2.61199 + 3.34328i) q^{6} +(3.10205 + 6.27513i) q^{7} -2.82843i q^{8} +(2.17750 - 8.73261i) q^{9} +(1.00006 + 1.73216i) q^{10} +(15.1176 + 8.72813i) q^{11} +(-4.72811 + 3.69391i) q^{12} +(8.59030 - 14.8788i) q^{13} +(-8.87438 + 4.38696i) q^{14} +(1.58947 - 3.93394i) q^{15} +4.00000 q^{16} +(-20.8700 + 12.0493i) q^{17} +(12.3498 + 3.07945i) q^{18} +(11.7810 - 20.4053i) q^{19} +(-2.44965 + 1.41430i) q^{20} +(18.9233 + 9.10540i) q^{21} +(-12.3434 + 21.3795i) q^{22} +(-27.1025 + 15.6476i) q^{23} +(-5.22398 - 6.68655i) q^{24} +(-11.4999 + 19.9184i) q^{25} +(21.0419 + 12.1485i) q^{26} +(-10.9810 - 24.6661i) q^{27} +(-6.20409 - 12.5503i) q^{28} +(-13.7563 + 7.94218i) q^{29} +(5.56344 + 2.24785i) q^{30} -32.1938 q^{31} +5.65685i q^{32} +(51.8592 - 7.28773i) q^{33} +(-17.0403 - 29.5146i) q^{34} +(8.23694 + 5.49231i) q^{35} +(-4.35500 + 17.4652i) q^{36} +(15.7030 - 27.1985i) q^{37} +(28.8574 + 16.6608i) q^{38} +(-7.17265 - 51.0403i) q^{39} +(-2.00013 - 3.46433i) q^{40} +(8.67466 + 5.00832i) q^{41} +(-12.8770 + 26.7616i) q^{42} +(-31.6891 - 54.8871i) q^{43} +(-30.2351 - 17.4563i) q^{44} +(-3.50824 - 12.2357i) q^{45} +(-22.1291 - 38.3287i) q^{46} -4.27193i q^{47} +(9.45621 - 7.38783i) q^{48} +(-29.7546 + 38.9315i) q^{49} +(-28.1688 - 16.2633i) q^{50} +(-27.0832 + 67.0311i) q^{51} +(-17.1806 + 29.7577i) q^{52} +(-45.3154 + 26.1629i) q^{53} +(34.8831 - 15.5295i) q^{54} +24.6885 q^{55} +(17.7488 - 8.77391i) q^{56} +(-9.83677 - 69.9981i) q^{57} +(-11.2319 - 19.4543i) q^{58} -42.1881i q^{59} +(-3.17894 + 7.86789i) q^{60} -12.4785 q^{61} -45.5289i q^{62} +(61.5530 - 13.4249i) q^{63} -8.00000 q^{64} -24.2986i q^{65} +(10.3064 + 73.3400i) q^{66} +96.1382 q^{67} +(41.7399 - 24.0986i) q^{68} +(-35.1712 + 87.0489i) q^{69} +(-7.76730 + 11.6488i) q^{70} +20.8017i q^{71} +(-24.6996 - 6.15889i) q^{72} +(41.6824 + 72.1961i) q^{73} +(38.4644 + 22.2075i) q^{74} +(9.60205 + 68.3278i) q^{75} +(-23.5620 + 40.8105i) q^{76} +(-7.87478 + 121.940i) q^{77} +(72.1819 - 10.1437i) q^{78} -45.1639 q^{79} +(4.89930 - 2.82861i) q^{80} +(-71.5170 - 38.0305i) q^{81} +(-7.08283 + 12.2678i) q^{82} +(3.73381 - 2.15572i) q^{83} +(-37.8466 - 18.2108i) q^{84} +(-17.0414 + 29.5165i) q^{85} +(77.6221 - 44.8151i) q^{86} +(-17.8517 + 44.1830i) q^{87} +(24.6869 - 42.7589i) q^{88} +(123.803 + 71.4779i) q^{89} +(17.3039 - 4.96139i) q^{90} +(120.014 + 7.75043i) q^{91} +(54.2049 - 31.2952i) q^{92} +(-76.1079 + 59.4606i) q^{93} +6.04143 q^{94} -33.3238i q^{95} +(10.4480 + 13.3731i) q^{96} +(-17.5457 - 30.3901i) q^{97} +(-55.0575 - 42.0794i) q^{98} +(109.138 - 113.010i) 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
$3$	2.36405	−	1.84696i	0.788018	−	0.615652i
$3$	2.36405	−	1.84696i	0.788018	−	0.615652i
$4$	−2.00000			−0.500000
$5$	1.22482	−	0.707152i	0.244965	−	0.141430i	−0.372492	−	0.928036i	$-0.621496\pi$
$5$	1.22482	−	0.707152i	0.244965	−	0.141430i	0.617456	+	0.786605i	$0.288163\pi$
$6$	2.61199	+	3.34328i	0.435332	+	0.557213i
$7$	3.10205	+	6.27513i	0.443150	+	0.896448i
$7$	3.10205	+	6.27513i	0.443150	+	0.896448i
$8$		−	2.82843i		−	0.353553i
$9$	2.17750	−	8.73261i	0.241944	−	0.970290i
$10$	1.00006	+	1.73216i	0.100006	+	0.173216i
$11$	15.1176	+	8.72813i	1.37432	+	0.793466i	0.991469	−	0.130343i	$-0.0416077\pi$
$11$	15.1176	+	8.72813i	1.37432	+	0.793466i	0.382855	+	0.923809i	$0.374941\pi$
$12$	−4.72811	+	3.69391i	−0.394009	+	0.307826i
$13$	8.59030	−	14.8788i	0.660793	−	1.14453i	−0.319615	−	0.947547i	$-0.603554\pi$
$13$	8.59030	−	14.8788i	0.660793	−	1.14453i	0.980408	−	0.196979i	$-0.0631130\pi$
$14$	−8.87438	+	4.38696i	−0.633884	+	0.313354i
$15$	1.58947	−	3.93394i	0.105965	−	0.262263i
$16$	4.00000			0.250000
$17$	−20.8700	+	12.0493i	−1.22765	+	0.708781i	−0.966537	−	0.256528i	$-0.917421\pi$
$17$	−20.8700	+	12.0493i	−1.22765	+	0.708781i	−0.261109	+	0.965309i	$0.584088\pi$
$18$	12.3498	+	3.07945i	0.686099	+	0.171080i
$19$	11.7810	−	20.4053i	0.620051	−	1.07396i	−0.369424	−	0.929261i	$-0.620445\pi$
$19$	11.7810	−	20.4053i	0.620051	−	1.07396i	0.989476	−	0.144700i	$-0.0462216\pi$
$20$	−2.44965	+	1.41430i	−0.122482	+	0.0707152i
$21$	18.9233	+	9.10540i	0.901110	+	0.433591i
$22$	−12.3434	+	21.3795i	−0.561065	+	0.971794i
$23$	−27.1025	+	15.6476i	−1.17837	+	0.680331i	−0.955636	−	0.294549i	$-0.904831\pi$
$23$	−27.1025	+	15.6476i	−1.17837	+	0.680331i	−0.222731	+	0.974880i	$0.571497\pi$
$24$	−5.22398	−	6.68655i	−0.217666	−	0.278606i
$25$	−11.4999	+	19.9184i	−0.459995	+	0.796734i
$26$	21.0419	+	12.1485i	0.809302	+	0.467251i
$27$	−10.9810	−	24.6661i	−0.406705	−	0.913560i
$28$	−6.20409	−	12.5503i	−0.221575	−	0.448224i
$29$	−13.7563	+	7.94218i	−0.474354	+	0.273868i	−0.718061	−	0.695981i	$-0.754970\pi$
$29$	−13.7563	+	7.94218i	−0.474354	+	0.273868i	0.243707	+	0.969849i	$0.421637\pi$
$30$	5.56344	+	2.24785i	0.185448	+	0.0749283i
$31$	−32.1938			−1.03851			−0.519255	−	0.854619i	$-0.673791\pi$
$31$	−32.1938			−1.03851			−0.519255	+	0.854619i	$0.673791\pi$
$32$			5.65685i			0.176777i
$33$	51.8592	−	7.28773i	1.57149	−	0.220840i
$34$	−17.0403	−	29.5146i	−0.501184	−	0.868076i
$35$	8.23694	+	5.49231i	0.235341	+	0.156923i
$36$	−4.35500	+	17.4652i	−0.120972	+	0.485145i
$37$	15.7030	−	27.1985i	0.424407	−	0.735094i	−0.571958	−	0.820283i	$-0.693816\pi$
$37$	15.7030	−	27.1985i	0.424407	−	0.735094i	0.996365	+	0.0851890i	$0.0271494\pi$
$38$	28.8574	+	16.6608i	0.759405	+	0.438443i
$39$	−7.17265	−	51.0403i	−0.183914	−	1.30873i
$40$	−2.00013	−	3.46433i	−0.0500032	−	0.0866081i
$41$	8.67466	+	5.00832i	0.211577	+	0.122154i	0.602044	−	0.798463i	$-0.294353\pi$
$41$	8.67466	+	5.00832i	0.211577	+	0.122154i	−0.390467	+	0.920617i	$0.627686\pi$
$42$	−12.8770	+	26.7616i	−0.306595	+	0.637181i
$43$	−31.6891	−	54.8871i	−0.736956	−	1.27644i	−0.953860	−	0.300252i	$-0.902929\pi$
$43$	−31.6891	−	54.8871i	−0.736956	−	1.27644i	0.216904	−	0.976193i	$-0.430404\pi$
$44$	−30.2351	−	17.4563i	−0.687162	−	0.396733i
$45$	−3.50824	−	12.2357i	−0.0779608	−	0.271905i
$46$	−22.1291	−	38.3287i	−0.481067	−	0.833232i
$47$		−	4.27193i		−	0.0908922i	−0.998967	−	0.0454461i	$-0.985529\pi$
$47$		−	4.27193i		−	0.0908922i	0.998967	−	0.0454461i	$-0.0144709\pi$
$48$	9.45621	−	7.38783i	0.197004	−	0.153913i
$49$	−29.7546	+	38.9315i	−0.607237	+	0.794521i
$50$	−28.1688	−	16.2633i	−0.563376	−	0.325265i
$51$	−27.0832	+	67.0311i	−0.531044	+	1.31434i
$52$	−17.1806	+	29.7577i	−0.330396	+	0.572263i
$53$	−45.3154	+	26.1629i	−0.855008	+	0.493639i	−0.862337	−	0.506334i	$-0.831000\pi$
$53$	−45.3154	+	26.1629i	−0.855008	+	0.493639i	0.00732944	+	0.999973i	$0.497667\pi$
$54$	34.8831	−	15.5295i	0.645984	−	0.287584i
$55$	24.6885			0.448881
$56$	17.7488	−	8.77391i	0.316942	−	0.156677i
$57$	−9.83677	−	69.9981i	−0.172575	−	1.22804i
$58$	−11.2319	−	19.4543i	−0.193654	−	0.335419i
$59$		−	42.1881i		−	0.715053i	−0.933903	−	0.357527i	$-0.883620\pi$
$59$		−	42.1881i		−	0.715053i	0.933903	−	0.357527i	$-0.116380\pi$
$60$	−3.17894	+	7.86789i	−0.0529823	+	0.131131i
$61$	−12.4785			−0.204565			−0.102282	−	0.994755i	$-0.532615\pi$
$61$	−12.4785			−0.204565			−0.102282	+	0.994755i	$0.532615\pi$
$62$		−	45.5289i		−	0.734338i
$63$	61.5530	−	13.4249i	0.977032	−	0.213093i
$64$	−8.00000			−0.125000
$65$		−	24.2986i		−	0.373825i
$66$	10.3064	+	73.3400i	0.156158	+	1.11121i
$67$	96.1382			1.43490			0.717449	−	0.696611i	$-0.245310\pi$
$67$	96.1382			1.43490			0.717449	+	0.696611i	$0.245310\pi$
$68$	41.7399	−	24.0986i	0.613823	−	0.354391i
$69$	−35.1712	+	87.0489i	−0.509727	+	1.26158i
$70$	−7.76730	+	11.6488i	−0.110961	+	0.166411i
$71$			20.8017i			0.292982i	0.989212	+	0.146491i	$0.0467980\pi$
$71$			20.8017i			0.292982i	−0.989212	+	0.146491i	$0.953202\pi$
$72$	−24.6996	−	6.15889i	−0.343049	−	0.0855402i
$73$	41.6824	+	72.1961i	0.570992	+	0.988987i	0.996464	+	0.0840158i	$0.0267746\pi$
$73$	41.6824	+	72.1961i	0.570992	+	0.988987i	−0.425472	+	0.904971i	$0.639892\pi$
$74$	38.4644	+	22.2075i	0.519790	+	0.300101i
$75$	9.60205	+	68.3278i	0.128027	+	0.911038i
$76$	−23.5620	+	40.8105i	−0.310026	+	0.536980i
$77$	−7.87478	+	121.940i	−0.102270	+	1.58363i
$78$	72.1819	−	10.1437i	0.925409	−	0.130047i
$79$	−45.1639			−0.571695			−0.285848	−	0.958275i	$-0.592275\pi$
$79$	−45.1639			−0.571695			−0.285848	+	0.958275i	$0.592275\pi$
$80$	4.89930	−	2.82861i	0.0612412	−	0.0353576i
$81$	−71.5170	−	38.0305i	−0.882926	−	0.469512i
$82$	−7.08283	+	12.2678i	−0.0863760	+	0.149608i
$83$	3.73381	−	2.15572i	0.0449856	−	0.0259725i	−0.477339	−	0.878719i	$-0.658398\pi$
$83$	3.73381	−	2.15572i	0.0449856	−	0.0259725i	0.522324	+	0.852747i	$0.325065\pi$
$84$	−37.8466	−	18.2108i	−0.450555	−	0.216795i
$85$	−17.0414	+	29.5165i	−0.200487	+	0.347253i
$86$	77.6221	−	44.8151i	0.902583	−	0.521106i
$87$	−17.8517	+	44.1830i	−0.205192	+	0.507850i
$88$	24.6869	−	42.7589i	0.280533	−	0.485897i
$89$	123.803	+	71.4779i	1.39105	+	0.803122i	0.993431	−	0.114430i	$-0.0365041\pi$
$89$	123.803	+	71.4779i	1.39105	+	0.803122i	0.397617	+	0.917552i	$0.369837\pi$
$90$	17.3039	−	4.96139i	0.192266	−	0.0551266i
$91$	120.014	+	7.75043i	1.31884	+	0.0851696i
$92$	54.2049	−	31.2952i	0.589184	−	0.340165i
$93$	−76.1079	+	59.4606i	−0.818365	+	0.639361i
$94$	6.04143			0.0642705
$95$		−	33.3238i		−	0.350777i
$96$	10.4480	+	13.3731i	0.108833	+	0.139303i
$97$	−17.5457	−	30.3901i	−0.180884	−	0.313300i	0.761298	−	0.648402i	$-0.224562\pi$
$97$	−17.5457	−	30.3901i	−0.180884	−	0.313300i	−0.942182	+	0.335102i	$0.891229\pi$
$98$	−55.0575	−	42.0794i	−0.561811	−	0.429381i
$99$	109.138	−	113.010i	1.10240	−	1.14152i
$100$	22.9997	−	39.8367i	0.229997	−	0.398367i
$101$	−35.9483	−	20.7548i	−0.355924	−	0.205493i	0.311367	−	0.950290i	$-0.399213\pi$
$101$	−35.9483	−	20.7548i	−0.355924	−	0.205493i	−0.667291	+	0.744797i	$0.732546\pi$
$102$	−94.7963	−	38.3015i	−0.929375	−	0.375504i
$103$	16.9344	+	29.3312i	0.164412	+	0.284769i	0.936446	−	0.350811i	$-0.114094\pi$
$103$	16.9344	+	29.3312i	0.164412	+	0.284769i	−0.772035	+	0.635580i	$0.780761\pi$
$104$	−42.0837	−	24.2970i	−0.404651	−	0.233625i
$105$	29.6166	−	2.22915i	0.282063	−	0.0212300i
$106$	−36.9999	−	64.0857i	−0.349056	−	0.604582i
$107$	−39.7440	−	22.9462i	−0.371439	−	0.214450i	0.302648	−	0.953102i	$-0.402129\pi$
$107$	−39.7440	−	22.9462i	−0.371439	−	0.214450i	−0.674087	+	0.738652i	$0.735463\pi$
$108$	21.9621	+	49.3322i	0.203353	+	0.456780i
$109$	21.6535	+	37.5049i	0.198656	+	0.344082i	0.948093	−	0.317994i	$-0.103009\pi$
$109$	21.6535	+	37.5049i	0.198656	+	0.344082i	−0.749437	+	0.662075i	$0.769676\pi$
$110$			34.9148i			0.317407i
$111$	−13.1116	−	93.3015i	−0.118122	−	0.840554i
$112$	12.4082	+	25.1005i	0.110787	+	0.224112i
$113$	−78.3902	−	45.2586i	−0.693719	−	0.400519i	0.111285	−	0.993789i	$-0.464503\pi$
$113$	−78.3902	−	45.2586i	−0.693719	−	0.400519i	−0.805004	+	0.593270i	$0.797837\pi$
$114$	98.9922	−	13.9113i	0.868353	−	0.122029i
$115$	−22.1305	+	38.3311i	−0.192439	+	0.333314i
$116$	27.5125	−	15.8844i	0.237177	−	0.136934i
$117$	−111.226	−	107.414i	−0.950648	−	0.918072i
$118$	59.6630			0.505619
$119$	−140.351	−	93.5844i	−1.17942	−	0.786424i
$120$	−11.1269	−	4.49570i	−0.0927239	−	0.0374641i
$121$	91.8604	+	159.107i	0.759177	+	1.31493i
$122$		−	17.6472i		−	0.144649i
$123$	29.7575	−	4.18180i	0.241931	−	0.0339983i
$124$	64.3877			0.519255
$125$			67.8863i			0.543090i
$126$	18.9856	+	87.0491i	0.150680	+	0.690866i
$127$	−135.543			−1.06727			−0.533635	−	0.845715i	$-0.679174\pi$
$127$	−135.543			−1.06727			−0.533635	+	0.845715i	$0.679174\pi$
$128$		−	11.3137i		−	0.0883883i
$129$	−176.289	−	71.2277i	−1.36658	−	0.552153i
$130$	34.3634			0.264334
$131$	192.988	−	111.422i	1.47319	−	0.850546i	0.473645	−	0.880716i	$-0.342938\pi$
$131$	192.988	−	111.422i	1.47319	−	0.850546i	0.999545	+	0.0301696i	$0.00960475\pi$
$132$	−103.718	+	14.5755i	−0.785745	+	0.110420i
$133$	164.591	+	10.6292i	1.23753	+	0.0799185i
$134$			135.960i			1.01463i
$135$	−30.8925	−	22.4464i	−0.228834	−	0.166269i
$136$	34.0805	+	59.0292i	0.250592	+	0.434038i
$137$	−74.8448	−	43.2117i	−0.546313	−	0.315414i	0.201321	−	0.979525i	$-0.435477\pi$
$137$	−74.8448	−	43.2117i	−0.546313	−	0.315414i	−0.747633	+	0.664112i	$0.768810\pi$
$138$	−123.106	−	49.7396i	−0.892070	−	0.360432i
$139$	1.61343	−	2.79455i	0.0116074	−	0.0201047i	−0.860163	−	0.510019i	$-0.829638\pi$
$139$	1.61343	−	2.79455i	0.0116074	−	0.0201047i	0.871771	+	0.489914i	$0.162972\pi$
$140$	−16.4739	−	10.9846i	−0.117671	−	0.0784616i
$141$	−7.89008	−	10.0991i	−0.0559580	−	0.0716247i
$142$	−29.4181			−0.207170
$143$	259.729	−	149.955i	1.81629	−	1.04863i
$144$	8.70999	−	34.9304i	0.0604861	−	0.242573i
$145$	−11.2327	+	19.4555i	−0.0774667	+	0.134176i
$146$	−102.101	+	58.9478i	−0.699320	+	0.403752i
$147$	1.56337	+	146.992i	0.0106352	+	0.999943i
$148$	−31.4061	+	54.3969i	−0.212203	+	0.367547i
$149$	−169.581	+	97.9078i	−1.13813	+	0.657100i	−0.945967	−	0.324264i	$-0.894884\pi$
$149$	−169.581	+	97.9078i	−1.13813	+	0.657100i	−0.192163	+	0.981363i	$0.561550\pi$
$150$	−96.6302	+	13.5793i	−0.644201	+	0.0905290i
$151$	15.7499	−	27.2796i	0.104304	−	0.180659i	−0.809150	−	0.587602i	$-0.800072\pi$
$151$	15.7499	−	27.2796i	0.104304	−	0.180659i	0.913454	+	0.406943i	$0.133405\pi$
$152$	−57.7148	−	33.3216i	−0.379702	−	0.219221i
$153$	59.7774	+	208.487i	0.390702	+	1.36266i
$154$	−172.449	−	11.1366i	−1.11980	−	0.0723157i
$155$	−39.4318	+	22.7659i	−0.254399	+	0.146877i
$156$	14.3453	+	102.081i	0.0919570	+	0.654363i
$157$	89.3761			0.569274			0.284637	−	0.958635i	$-0.408127\pi$
$157$	89.3761			0.569274			0.284637	+	0.958635i	$0.408127\pi$
$158$		−	63.8714i		−	0.404249i
$159$	−58.8064	+	145.546i	−0.369851	+	0.915384i
$160$	4.00026	+	6.92865i	0.0250016	+	0.0433041i
$161$	−182.264	−	121.532i	−1.13207	−	0.754857i
$162$	53.7832	−	101.140i	0.331995	−	0.624323i
$163$	105.258	−	182.312i	0.645755	−	1.11848i	−0.338372	−	0.941012i	$-0.609876\pi$
$163$	105.258	−	182.312i	0.645755	−	1.11848i	0.984127	−	0.177467i	$-0.0567904\pi$
$164$	−17.3493	−	10.0166i	−0.105789	−	0.0610770i
$165$	58.3649	−	45.5985i	0.353726	−	0.276355i
$166$	3.04864	+	5.28040i	0.0183653	+	0.0318097i
$167$	97.8810	+	56.5116i	0.586114	+	0.338393i	0.763559	−	0.645738i	$-0.223450\pi$
$167$	97.8810	+	56.5116i	0.586114	+	0.338393i	−0.177446	+	0.984131i	$0.556783\pi$
$168$	25.7540	−	53.5232i	0.153297	−	0.318590i
$169$	−63.0866	−	109.269i	−0.373294	−	0.646564i
$170$	−41.7426	−	24.1001i	−0.245545	−	0.141765i
$171$	−152.538	−	147.311i	−0.892036	−	0.861468i
$172$	63.3782	+	109.774i	0.368478	+	0.638222i
$173$		−	51.8246i		−	0.299564i	−0.988719	−	0.149782i	$-0.952143\pi$
$173$		−	51.8246i		−	0.299564i	0.988719	−	0.149782i	$-0.0478572\pi$
$174$	−62.4842	−	25.2461i	−0.359104	−	0.145092i
$175$	−160.664	−	10.3755i	−0.918077	−	0.0592888i
$176$	60.4702	+	34.9125i	0.343581	+	0.198367i
$177$	−77.9197	−	99.7350i	−0.440224	−	0.563475i
$178$	−101.085	+	175.084i	−0.567893	+	0.983620i
$179$	167.471	−	96.6894i	0.935592	−	0.540164i	0.0470161	−	0.998894i	$-0.485029\pi$
$179$	167.471	−	96.6894i	0.935592	−	0.540164i	0.888576	+	0.458730i	$0.151695\pi$
$180$	7.01647	+	24.4715i	0.0389804	+	0.135953i
$181$	175.825			0.971411			0.485705	−	0.874123i	$-0.338563\pi$
$181$	175.825			0.971411			0.485705	+	0.874123i	$0.338563\pi$
$182$	−10.9608	+	169.726i	−0.0602240	+	0.932559i
$183$	−29.4997	+	23.0472i	−0.161201	+	0.125941i
$184$	44.2581	+	76.6573i	0.240533	+	0.416616i
$185$		−	44.4178i		−	0.240096i
$186$	−84.0900	−	107.633i	−0.452097	−	0.578671i
$187$	−420.671			−2.24958
$188$			8.54387i			0.0454461i
$189$	120.719	−	145.423i	0.638727	−	0.769433i
$190$	47.1270			0.248037
$191$			23.2901i			0.121938i	0.998140	+	0.0609690i	$0.0194191\pi$
$191$			23.2901i			0.121938i	−0.998140	+	0.0609690i	$0.980581\pi$
$192$	−18.9124	+	14.7757i	−0.0985022	+	0.0769566i
$193$	84.8341			0.439555			0.219777	−	0.975550i	$-0.429467\pi$
$193$	84.8341			0.439555			0.219777	+	0.975550i	$0.429467\pi$
$194$	42.9780	−	24.8134i	0.221536	−	0.127904i
$195$	−44.8785	−	57.4432i	−0.230146	−	0.294581i
$196$	59.5092	−	77.8630i	0.303618	−	0.397260i
$197$			153.183i			0.777579i	0.921327	+	0.388789i	$0.127107\pi$
$197$			153.183i			0.777579i	−0.921327	+	0.388789i	$0.872893\pi$
$198$	159.821	+	154.344i	0.807175	+	0.779516i
$199$	0.561812	+	0.973087i	0.00282317	+	0.00488988i	0.867434	−	0.497553i	$-0.165768\pi$
$199$	0.561812	+	0.973087i	0.00282317	+	0.00488988i	−0.864610	+	0.502443i	$0.832435\pi$
$200$	56.3376	+	32.5265i	0.281688	+	0.162633i
$201$	227.276	−	177.563i	1.13073	−	0.883399i
$202$	29.3517	−	50.8386i	0.145305	−	0.251676i
$203$	−92.5108	−	61.6854i	−0.455718	−	0.303869i
$204$	54.1664	−	134.062i	0.265522	−	0.657168i
$205$	14.1666			0.0691053
$206$	−41.4806	+	23.9488i	−0.201362	+	0.116257i
$207$	77.6290	+	270.748i	0.375019	+	1.30796i
$208$	34.3612	−	59.5154i	0.165198	−	0.286132i
$209$	356.199	−	205.652i	1.70430	−	0.983980i
$210$	3.15249	+	41.8842i	0.0150119	+	0.199449i
$211$	−78.9195	+	136.693i	−0.374026	+	0.647832i	−0.990181	−	0.139793i	$-0.955356\pi$
$211$	−78.9195	+	136.693i	−0.374026	+	0.647832i	0.616155	+	0.787625i	$0.288690\pi$
$212$	90.6308	−	52.3257i	0.427504	−	0.246820i
$213$	38.4199	+	49.1764i	0.180375	+	0.230875i
$214$	32.4508	−	56.2064i	0.151639	−	0.262647i
$215$	−77.6271	−	44.8180i	−0.361056	−	0.208456i
$216$	−69.7663	+	31.0591i	−0.322992	+	0.143792i
$217$	−99.8668	−	202.021i	−0.460215	−	0.930970i
$218$	−53.0399	+	30.6226i	−0.243302	+	0.140471i
$219$	231.883	+	93.6897i	1.05882	+	0.427807i
$220$	−49.3769			−0.224441
$221$			414.028i			1.87343i
$222$	131.948	−	18.5426i	0.594361	−	0.0835251i
$223$	52.8284	+	91.5014i	0.236899	+	0.410320i	0.959823	−	0.280607i	$-0.0905358\pi$
$223$	52.8284	+	91.5014i	0.236899	+	0.410320i	−0.722924	+	0.690927i	$0.757202\pi$
$224$	−35.4975	+	17.5478i	−0.158471	+	0.0783385i
$225$	148.898	+	143.796i	0.661770	+	0.639094i
$226$	64.0053	−	110.860i	0.283209	−	0.490533i
$227$	52.0479	+	30.0498i	0.229286	+	0.132378i	0.610243	−	0.792215i	$-0.291072\pi$
$227$	52.0479	+	30.0498i	0.229286	+	0.132378i	−0.380957	+	0.924593i	$0.624405\pi$
$228$	19.6735	+	139.996i	0.0862874	+	0.614018i
$229$	−25.5005	−	44.1681i	−0.111356	−	0.192874i	0.804961	−	0.593327i	$-0.202186\pi$
$229$	−25.5005	−	44.1681i	−0.111356	−	0.192874i	−0.916317	+	0.400453i	$0.868853\pi$
$230$	−54.2084	−	31.2972i	−0.235689	−	0.136075i
$231$	206.601	+	302.817i	0.894377	+	1.31089i
$232$	22.4639	+	38.9086i	0.0968271	+	0.167709i
$233$	19.7391	+	11.3964i	0.0847171	+	0.0489114i	0.541760	−	0.840533i	$-0.317758\pi$
$233$	19.7391	+	11.3964i	0.0847171	+	0.0489114i	−0.457043	+	0.889445i	$0.651091\pi$
$234$	151.907	−	157.297i	0.649175	−	0.672209i
$235$	−3.02091	−	5.23237i	−0.0128549	−	0.0222654i
$236$			84.3763i			0.357527i
$237$	−106.770	+	83.4158i	−0.450506	+	0.351965i
$238$	132.348	−	198.486i	0.556086	−	0.833973i
$239$	350.226	+	202.203i	1.46538	+	0.846039i	0.999252	−	0.0386769i	$-0.0123143\pi$
$239$	350.226	+	202.203i	1.46538	+	0.846039i	0.466131	+	0.884716i	$0.345648\pi$
$240$	6.35788	−	15.7358i	0.0264912	−	0.0655657i
$241$	151.820	−	262.961i	0.629961	−	1.09112i	−0.357599	−	0.933875i	$-0.616404\pi$
$241$	151.820	−	262.961i	0.629961	−	1.09112i	0.987559	−	0.157248i	$-0.0502623\pi$
$242$	−225.011	+	129.910i	−0.929798	+	0.536819i
$243$	−239.311	+	42.1827i	−0.984818	+	0.173591i
$244$	24.9569			0.102282
$245$	−8.91364	+	68.7253i	−0.0363822	+	0.280511i
$246$	5.91395	+	42.0835i	0.0240405	+	0.171071i
$247$	−202.404	−	350.575i	−0.819451	−	1.41933i
$248$			91.0579i			0.367169i
$249$	4.84541	−	11.9924i	0.0194595	−	0.0481623i
$250$	−96.0057			−0.384023
$251$		−	233.378i		−	0.929793i	−0.885365	−	0.464897i	$-0.846092\pi$
$251$		−	233.378i		−	0.929793i	0.885365	−	0.464897i	$-0.153908\pi$
$252$	−123.106	+	26.8498i	−0.488516	+	0.106547i
$253$	−546.297			−2.15928
$254$		−	191.687i		−	0.754674i
$255$	14.2290	+	101.253i	0.0558001	+	0.397072i
$256$	16.0000			0.0625000
$257$	−163.518	+	94.4073i	−0.636258	+	0.367344i	−0.783172	−	0.621806i	$-0.786399\pi$
$257$	−163.518	+	94.4073i	−0.636258	+	0.367344i	0.146914	+	0.989149i	$0.453066\pi$
$258$	100.731	−	249.310i	0.390431	−	0.966318i
$259$	219.386	+	14.1678i	0.847049	+	0.0547018i
$260$			48.5972i			0.186912i
$261$	39.4018	+	137.422i	0.150965	+	0.526522i
$262$	157.574	+	272.926i	0.601427	+	1.04170i
$263$	−154.166	−	89.0076i	−0.586181	−	0.338432i	0.177405	−	0.984138i	$-0.443230\pi$
$263$	−154.166	−	89.0076i	−0.586181	−	0.338432i	−0.763586	+	0.645706i	$0.776563\pi$
$264$	−20.6128	−	146.680i	−0.0780788	−	0.555606i
$265$	−37.0023	+	64.0898i	−0.139631	+	0.241848i
$266$	−15.0319	+	232.767i	−0.0565109	+	0.875062i
$267$	424.694	−	59.6819i	1.59061	−	0.223528i
$268$	−192.276			−0.717449
$269$	446.874	−	258.003i	1.66124	−	0.959119i	0.689120	−	0.724647i	$-0.257997\pi$
$269$	446.874	−	258.003i	1.66124	−	0.959119i	0.972123	−	0.234472i	$-0.0753362\pi$
$270$	31.7440	−	43.6886i	0.117570	−	0.161810i
$271$	−117.718	+	203.894i	−0.434385	+	0.752377i	−0.997245	−	0.0741751i	$-0.976368\pi$
$271$	−117.718	+	203.894i	−0.434385	+	0.752377i	0.562860	+	0.826552i	$0.309701\pi$
$272$	−83.4799	+	48.1971i	−0.306911	+	0.177195i
$273$	298.035	−	203.339i	1.09170	−	0.744831i
$274$	61.1106	−	105.847i	0.223031	−	0.386301i
$275$	−347.700	+	200.745i	−1.26436	+	0.729981i
$276$	70.3424	−	174.098i	0.254864	−	0.630789i
$277$	−254.239	+	440.354i	−0.917830	+	1.58973i	−0.115125	+	0.993351i	$0.536727\pi$
$277$	−254.239	+	440.354i	−0.917830	+	1.58973i	−0.802705	+	0.596376i	$0.796607\pi$
$278$	3.95209	+	2.28174i	0.0142161	+	0.00820769i
$279$	−70.1020	+	281.136i	−0.251262	+	1.00766i
$280$	15.5346	−	23.2976i	0.0554807	−	0.0832056i
$281$	−13.5306	+	7.81192i	−0.0481517	+	0.0278004i	−0.523883	−	0.851790i	$-0.675517\pi$
$281$	−13.5306	+	7.81192i	−0.0481517	+	0.0278004i	0.475731	+	0.879591i	$0.342184\pi$
$282$	14.2823	−	11.1583i	0.0506463	−	0.0395683i
$283$	−509.979			−1.80205			−0.901023	−	0.433772i	$-0.857182\pi$
$283$	−509.979			−1.80205			−0.901023	+	0.433772i	$0.857182\pi$
$284$		−	41.6035i		−	0.146491i
$285$	−61.5476	−	78.7792i	−0.215957	−	0.276418i
$286$	212.068	+	367.312i	0.741496	+	1.28431i
$287$	−4.51866	+	69.9707i	−0.0157444	+	0.243800i
$288$	49.3991	+	12.3178i	0.171525	+	0.0427701i
$289$	145.870	−	252.655i	0.504742	−	0.874239i
$290$	−27.5143	−	15.8854i	−0.0948769	−	0.0547772i
$291$	−97.6081	−	39.4375i	−0.335423	−	0.135524i
$292$	−83.3648	−	144.392i	−0.285496	−	0.494494i
$293$	−378.046	−	218.265i	−1.29026	−	0.744932i	−0.311560	−	0.950226i	$-0.600852\pi$
$293$	−378.046	−	218.265i	−1.29026	−	0.744932i	−0.978700	+	0.205294i	$0.934185\pi$
$294$	−207.878	+	2.21094i	−0.707067	+	0.00752020i
$295$	−29.8334	−	51.6730i	−0.101130	−	0.175163i
$296$	−76.9289	−	44.4149i	−0.259895	−	0.150050i
$297$	49.2824	−	468.735i	0.165934	−	1.57823i
$298$	−138.463	−	239.824i	−0.464640	−	0.804779i
$299$			537.671i			1.79823i
$300$	−19.2041	−	136.656i	−0.0640137	−	0.455519i
$301$	246.123	−	369.116i	0.817684	−	1.22630i
$302$	38.5791	+	22.2737i	0.127745	+	0.0737539i
$303$	−123.317	+	17.3296i	−0.406986	+	0.0571934i
$304$	47.1239	−	81.6210i	0.155013	−	0.268490i
$305$	−15.2839	+	8.82417i	−0.0501112	+	0.0289317i
$306$	−294.845	+	84.5380i	−0.963545	+	0.276268i
$307$	−402.350			−1.31059			−0.655294	−	0.755374i	$-0.727455\pi$
$307$	−402.350			−1.31059			−0.655294	+	0.755374i	$0.727455\pi$
$308$	15.7496	−	243.880i	0.0511349	−	0.791817i
$309$	94.2073	+	38.0635i	0.304878	+	0.123183i
$310$	−32.1959	−	55.7649i	−0.103858	−	0.179887i
$311$		−	93.9460i		−	0.302077i	−0.988528	−	0.151039i	$-0.951738\pi$
$311$		−	93.9460i		−	0.302077i	0.988528	−	0.151039i	$-0.0482618\pi$
$312$	−144.364	+	20.2873i	−0.462704	+	0.0650234i
$313$	404.222			1.29144			0.645722	−	0.763572i	$-0.276556\pi$
$313$	404.222			1.29144			0.645722	+	0.763572i	$0.276556\pi$
$314$			126.397i			0.402538i
$315$	65.8982	−	59.9705i	0.209201	−	0.190382i
$316$	90.3278			0.285848
$317$			116.706i			0.368157i	0.982912	+	0.184078i	$0.0589300\pi$
$317$			116.706i			0.368157i	−0.982912	+	0.184078i	$0.941070\pi$
$318$	−205.833	−	83.1648i	−0.647274	−	0.261524i
$319$	−277.281			−0.869221
$320$	−9.79859	+	5.65722i	−0.0306206	+	0.0176788i
$321$	−136.337	+	19.1594i	−0.424727	+	0.0596865i
$322$	171.872	−	257.760i	0.533764	−	0.800497i
$323$			567.809i			1.75792i
$324$	143.034	+	76.0610i	0.441463	+	0.234756i
$325$	197.575	+	342.210i	0.607922	+	1.05295i
$326$	257.828	+	148.857i	0.790885	+	0.456617i
$327$	120.460	+	48.6706i	0.368379	+	0.148840i
$328$	14.1657	−	24.5356i	0.0431880	−	0.0748038i
$329$	26.8070	−	13.2517i	0.0814801	−	0.0402788i
$330$	64.4861	+	82.5404i	0.195412	+	0.250122i
$331$	611.339			1.84695			0.923474	−	0.383662i	$-0.125337\pi$
$331$	611.339			1.84695			0.923474	+	0.383662i	$0.125337\pi$
$332$	−7.46762	+	4.31143i	−0.0224928	+	0.0129862i
$333$	−203.320	−	196.353i	−0.610571	−	0.589649i
$334$	−79.9195	+	138.425i	−0.239280	+	0.414445i
$335$	117.752	−	67.9844i	0.351500	−	0.202938i
$336$	75.6932	+	36.4216i	0.225277	+	0.108398i
$337$	3.59903	−	6.23370i	0.0106796	−	0.0184976i	−0.860636	−	0.509220i	$-0.829934\pi$
$337$	3.59903	−	6.23370i	0.0106796	−	0.0184976i	0.871316	+	0.490723i	$0.163267\pi$
$338$	154.530	−	89.2180i	0.457190	−	0.263959i
$339$	−268.909	+	37.7896i	−0.793243	+	0.111474i
$340$	34.0827	−	59.0330i	0.100243	−	0.173626i
$341$	−486.692	−	280.992i	−1.42725	−	0.824023i
$342$	208.329	−	215.721i	0.609150	−	0.630764i
$343$	−336.601	−	65.9467i	−0.981343	−	0.192265i
$344$	−155.244	+	89.6303i	−0.451291	+	0.260553i
$345$	18.4783	+	131.491i	0.0535603	+	0.381133i
$346$	73.2911			0.211824
$347$		−	546.466i		−	1.57483i	−0.616422	−	0.787416i	$-0.711419\pi$
$347$		−	546.466i		−	1.57483i	0.616422	−	0.787416i	$-0.288581\pi$
$348$	35.7033	−	88.3659i	0.102596	−	0.253925i
$349$	−65.1506	−	112.844i	−0.186678	−	0.323336i	0.757463	−	0.652878i	$-0.226439\pi$
$349$	−65.1506	−	112.844i	−0.186678	−	0.323336i	−0.944141	+	0.329543i	$0.893105\pi$
$350$	14.6732	−	227.213i	0.0419235	−	0.649179i
$351$	−461.334	−	48.5042i	−1.31434	−	0.138189i
$352$	−49.3737	+	85.5178i	−0.140266	+	0.242948i
$353$	19.1736	+	11.0699i	0.0543162	+	0.0313595i	0.526912	−	0.849920i	$-0.323350\pi$
$353$	19.1736	+	11.0699i	0.0543162	+	0.0313595i	−0.472596	+	0.881279i	$0.656683\pi$
$354$	141.047	−	110.195i	0.398437	−	0.311285i
$355$	14.7100	+	25.4785i	0.0414366	+	0.0717703i
$356$	−247.607	−	142.956i	−0.695524	−	0.401561i
$357$	−504.643	+	37.9828i	−1.41356	+	0.106394i
$358$	136.739	+	236.840i	0.381954	+	0.661563i
$359$	52.1828	+	30.1278i	0.145356	+	0.0839214i	0.570914	−	0.821010i	$-0.306589\pi$
$359$	52.1828	+	30.1278i	0.145356	+	0.0839214i	−0.425558	+	0.904931i	$0.639922\pi$
$360$	−34.6079	+	9.92279i	−0.0961330	+	0.0275633i
$361$	−97.0829	−	168.152i	−0.268928	−	0.465796i
$362$			248.655i			0.686891i
$363$	511.027	+	206.475i	1.40779	+	0.568802i
$364$	−240.029	−	15.5009i	−0.659419	−	0.0425848i
$365$	102.107	+	58.9516i	0.279746	+	0.161511i
$366$	−32.5936	−	41.7189i	−0.0890536	−	0.113986i
$367$	3.71386	−	6.43260i	0.0101195	−	0.0175275i	−0.860921	−	0.508738i	$-0.830112\pi$
$367$	3.71386	−	6.43260i	0.0101195	−	0.0175275i	0.871041	+	0.491211i	$0.163445\pi$
$368$	−108.410	+	62.5904i	−0.294592	+	0.170083i
$369$	62.6248	−	64.8468i	0.169715	−	0.175737i
$370$	62.8162			0.169774
$371$	−304.746	−	203.202i	−0.821418	−	0.547714i
$372$	152.216	−	118.921i	0.409182	−	0.319681i
$373$	297.356	+	515.036i	0.797201	+	1.38079i	0.921432	+	0.388540i	$0.127020\pi$
$373$	297.356	+	515.036i	0.797201	+	1.38079i	−0.124230	+	0.992253i	$0.539646\pi$
$374$		−	594.918i		−	1.59069i
$375$	125.383	+	160.487i	0.334355	+	0.427965i
$376$	−12.0829			−0.0321352
$377$			272.903i			0.723881i
$378$	205.659	+	170.723i	0.544072	+	0.451648i
$379$	651.058			1.71783			0.858915	−	0.512118i	$-0.171139\pi$
$379$	651.058			1.71783			0.858915	+	0.512118i	$0.171139\pi$
$380$			66.6476i			0.175388i
$381$	−320.432	+	250.343i	−0.841028	+	0.657068i
$382$	−32.9372			−0.0862231
$383$	287.209	−	165.820i	0.749893	−	0.432951i	−0.0757623	−	0.997126i	$-0.524139\pi$
$383$	287.209	−	165.820i	0.749893	−	0.432951i	0.825655	+	0.564175i	$0.190806\pi$
$384$	−20.8959	−	26.7462i	−0.0544165	−	0.0696516i
$385$	76.5848	+	154.923i	0.198922	+	0.402398i
$386$			119.973i			0.310812i
$387$	−548.311	+	157.212i	−1.41682	+	0.406232i
$388$	35.0914	+	60.7801i	0.0904418	+	0.156650i
$389$	18.0923	+	10.4456i	0.0465098	+	0.0268524i	0.523075	−	0.852287i	$-0.324785\pi$
$389$	18.0923	+	10.4456i	0.0465098	+	0.0268524i	−0.476565	+	0.879139i	$0.658118\pi$
$390$	81.2370	−	63.4678i	0.208300	−	0.162738i
$391$	377.085	−	653.130i	0.964412	−	1.67041i
$392$	110.115	+	84.1587i	0.280906	+	0.214691i
$393$	250.443	−	619.847i	0.637259	−	1.57722i
$394$	−216.633			−0.549831
$395$	−55.3178	+	31.9378i	−0.140045	+	0.0808551i
$396$	−218.276	+	226.021i	−0.551201	+	0.570759i
$397$	−309.823	+	536.629i	−0.780410	+	1.35171i	0.151292	+	0.988489i	$0.451657\pi$
$397$	−309.823	+	536.629i	−0.780410	+	1.35171i	−0.931703	+	0.363222i	$0.881677\pi$
$398$	−1.37615	+	0.794522i	−0.00345767	+	0.00199629i
$399$	408.733	−	278.864i	1.02439	−	0.698908i
$400$	−45.9995	+	79.6734i	−0.114999	+	0.199184i
$401$	−248.826	+	143.660i	−0.620513	+	0.358253i	−0.777069	−	0.629416i	$-0.783294\pi$
$401$	−248.826	+	143.660i	−0.620513	+	0.358253i	0.156556	+	0.987669i	$0.449961\pi$
$402$	251.112	+	321.417i	0.624657	+	0.799544i
$403$	−276.555	+	479.007i	−0.686240	+	1.18860i
$404$	71.8966	+	41.5095i	0.177962	+	0.102746i
$405$	−114.489	+	3.99277i	−0.282689	+	0.00985869i
$406$	87.2363	−	130.830i	0.214868	−	0.322242i
$407$	474.783	−	274.116i	1.16654	−	0.673504i
$408$	189.593	+	76.6029i	0.464688	+	0.187752i
$409$	441.994			1.08067			0.540335	−	0.841450i	$-0.318297\pi$
$409$	441.994			1.08067			0.540335	+	0.841450i	$0.318297\pi$
$410$			20.0346i			0.0488648i
$411$	−256.747	+	36.0805i	−0.624689	+	0.0877870i
$412$	−33.8688	−	58.6624i	−0.0822058	−	0.142385i
$413$	264.736	−	130.870i	0.641008	−	0.316875i
$414$	−382.895	+	109.784i	−0.924868	+	0.265179i
$415$	3.04884	−	5.28074i	0.00734660	−	0.0127247i
$416$	84.1674	+	48.5941i	0.202326	+	0.116813i
$417$	−1.34717	−	9.58640i	−0.00323062	−	0.0229890i
$418$	290.835	+	503.742i	0.695779	+	1.20512i
$419$	281.777	+	162.684i	0.672500	+	0.388268i	0.797023	−	0.603949i	$-0.206407\pi$
$419$	281.777	+	162.684i	0.672500	+	0.388268i	−0.124523	+	0.992217i	$0.539740\pi$
$420$	−59.2333	+	4.45830i	−0.141032	+	0.0106150i
$421$	−201.041	−	348.214i	−0.477533	−	0.827111i	0.522136	−	0.852862i	$-0.325135\pi$
$421$	−201.041	−	348.214i	−0.477533	−	0.827111i	−0.999668	+	0.0257517i	$0.991802\pi$
$422$	−193.312	−	111.609i	−0.458086	−	0.264476i
$423$	−37.3051	−	9.30213i	−0.0881918	−	0.0219908i
$424$	73.9998	+	128.171i	0.174528	+	0.302291i
$425$		−	554.261i		−	1.30414i
$426$	−69.5459	+	54.3340i	−0.163253	+	0.127545i
$427$	−38.7087	−	78.3039i	−0.0906528	−	0.183382i
$428$	79.4879	+	45.8924i	0.185719	+	0.107225i
$429$	337.053	−	834.209i	0.785672	−	1.94454i
$430$	63.3823	−	109.781i	0.147401	−	0.255305i
$431$	148.166	−	85.5439i	0.343774	−	0.198478i	−0.318166	−	0.948035i	$-0.603067\pi$
$431$	148.166	−	85.5439i	0.343774	−	0.198478i	0.661939	+	0.749557i	$0.269734\pi$
$432$	−43.9242	−	98.6644i	−0.101676	−	0.228390i
$433$	−225.192			−0.520075			−0.260038	−	0.965599i	$-0.583735\pi$
$433$	−225.192			−0.520075			−0.260038	+	0.965599i	$0.583735\pi$
$434$	285.700	−	141.233i	0.658295	−	0.325422i
$435$	9.37894	+	66.7402i	0.0215608	+	0.153426i
$436$	−43.3069	−	75.0098i	−0.0993278	−	0.172041i
$437$			737.377i			1.68736i
$438$	−132.497	+	327.931i	−0.302505	+	0.748702i
$439$	−59.3313			−0.135151			−0.0675755	−	0.997714i	$-0.521526\pi$
$439$	−59.3313			−0.135151			−0.0675755	+	0.997714i	$0.521526\pi$
$440$		−	69.8295i		−	0.158703i
$441$	275.183	+	344.609i	0.623998	+	0.781426i
$442$	−585.524			−1.32472
$443$		−	306.058i		−	0.690875i	−0.938442	−	0.345438i	$-0.887730\pi$
$443$		−	306.058i		−	0.690875i	0.938442	−	0.345438i	$-0.112270\pi$
$444$	26.2231	+	186.603i	0.0590611	+	0.420277i
$445$	202.183			0.454344
$446$	−129.403	+	74.7106i	−0.290140	+	0.167513i
$447$	−220.068	+	544.669i	−0.492322	+	1.21850i
$448$	−24.8164	−	50.2011i	−0.0553937	−	0.112056i
$449$			446.116i			0.993578i	0.867871	+	0.496789i	$0.165488\pi$
$449$			446.116i			0.993578i	−0.867871	+	0.496789i	$0.834512\pi$
$450$	−203.358	+	210.574i	−0.451908	+	0.467942i
$451$	87.4265	+	151.427i	0.193850	+	0.335759i
$452$	156.780	+	90.5172i	0.346859	+	0.200259i
$453$	−13.1507	−	93.5797i	−0.0290302	−	0.206578i
$454$	−42.4969	+	73.6068i	−0.0936055	+	0.162129i
$455$	152.477	−	75.3755i	0.335114	−	0.165660i
$456$	−197.984	+	27.8226i	−0.434176	+	0.0610144i
$457$	317.688			0.695160			0.347580	−	0.937650i	$-0.387004\pi$
$457$	317.688			0.695160			0.347580	+	0.937650i	$0.387004\pi$
$458$	62.4632	−	36.0631i	0.136382	−	0.0787404i
$459$	526.383	+	382.467i	1.14680	+	0.833262i
$460$	44.2610	−	76.6623i	0.0962195	−	0.166657i
$461$	−66.3830	+	38.3263i	−0.143998	+	0.0831372i	−0.570268	−	0.821459i	$-0.693161\pi$
$461$	−66.3830	+	38.3263i	−0.143998	+	0.0831372i	0.426270	+	0.904596i	$0.359827\pi$
$462$	−428.247	+	292.178i	−0.926942	+	0.632420i
$463$	155.730	−	269.733i	0.336350	−	0.582576i	−0.647393	−	0.762156i	$-0.724141\pi$
$463$	155.730	−	269.733i	0.336350	−	0.582576i	0.983743	+	0.179580i	$0.0574740\pi$
$464$	−55.0250	+	31.7687i	−0.118588	+	0.0684671i
$465$	−51.1711	+	126.649i	−0.110045	+	0.272363i
$466$	−16.1169	+	27.9153i	−0.0345856	+	0.0599040i
$467$	265.027	+	153.013i	0.567510	+	0.327652i	0.756154	−	0.654394i	$-0.227076\pi$
$467$	265.027	+	153.013i	0.567510	+	0.327652i	−0.188644	+	0.982045i	$0.560409\pi$
$468$	222.452	+	214.829i	0.475324	+	0.459036i
$469$	298.225	+	603.280i	0.635875	+	1.28631i
$470$	7.39968	−	4.27221i	0.0157440	−	0.00908981i
$471$	211.290	−	165.074i	0.448598	−	0.350475i
$472$	−119.326			−0.252809
$473$		−	1106.35i		−	2.33900i
$474$	−117.968	−	150.995i	−0.248877	−	0.318556i
$475$	270.959	+	469.316i	0.570441	+	0.988033i
$476$	280.701	+	187.169i	0.589708	+	0.393212i
$477$	129.796	+	452.692i	0.272109	+	0.949039i
$478$	−285.959	+	495.295i	−0.598240	+	1.03618i
$479$	−408.566	−	235.886i	−0.852956	−	0.492454i	0.00869133	−	0.999962i	$-0.497233\pi$
$479$	−408.566	−	235.886i	−0.852956	−	0.492454i	−0.861647	+	0.507508i	$0.830567\pi$
$480$	22.2537	+	8.99139i	0.0463620	+	0.0187321i
$481$	−269.788	−	467.286i	−0.560889	−	0.971489i
$482$	371.883	+	214.707i	0.771541	+	0.445449i
$483$	−655.346	+	49.3258i	−1.35682	+	0.102124i
$484$	−183.721	−	318.214i	−0.379588	−	0.657466i
$485$	−42.9808	−	24.8150i	−0.0886202	−	0.0511649i
$486$	−59.6554	−	338.436i	−0.122748	−	0.696371i
$487$	195.229	+	338.146i	0.400880	+	0.694345i	0.993832	−	0.110893i	$-0.0353710\pi$
$487$	195.229	+	338.146i	0.400880	+	0.694345i	−0.592952	+	0.805238i	$0.702038\pi$
$488$			35.2944i			0.0723246i
$489$	−87.8873	−	625.403i	−0.179729	−	1.27894i
$490$	−97.1923	−	12.6058i	−0.198352	−	0.0257261i
$491$	−498.578	−	287.854i	−1.01543	−	0.586261i	−0.102656	−	0.994717i	$-0.532734\pi$
$491$	−498.578	−	287.854i	−1.01543	−	0.586261i	−0.912778	+	0.408456i	$0.866067\pi$
$492$	−59.5150	+	8.36359i	−0.120965	+	0.0169992i
$493$	191.395	−	331.506i	0.388226	−	0.672426i
$494$	495.787	−	286.243i	1.00362	−	0.579439i
$495$	53.7591	−	215.595i	0.108604	−	0.435545i
$496$	−128.775			−0.259628
$497$	−130.534	+	64.5280i	−0.262643	+	0.129835i
$498$	16.9598	+	6.85244i	0.0340559	+	0.0137599i
$499$	359.065	+	621.919i	0.719569	+	1.24633i	0.961171	+	0.275954i	$0.0889939\pi$
$499$	359.065	+	621.919i	0.719569	+	1.24633i	−0.241602	+	0.970375i	$0.577673\pi$
$500$		−	135.773i		−	0.271545i
$501$	335.770	−	47.1855i	0.670200	−	0.0941826i
$502$	330.046			0.657463
$503$		−	475.997i		−	0.946316i	−0.880978	−	0.473158i	$-0.843114\pi$
$503$		−	475.997i		−	0.946316i	0.880978	−	0.473158i	$-0.156886\pi$
$504$	−37.9713	−	174.098i	−0.0753399	−	0.345433i
$505$	−58.7071			−0.116252
$506$		−	772.581i		−	1.52684i
$507$	−350.956	−	141.800i	−0.692221	−	0.279685i
$508$	271.087			0.533635
$509$	439.257	−	253.605i	0.862981	−	0.498242i	−0.00202828	−	0.999998i	$-0.500646\pi$
$509$	439.257	−	253.605i	0.862981	−	0.498242i	0.865009	+	0.501756i	$0.167312\pi$
$510$	−143.194	+	20.1229i	−0.280772	+	0.0394566i
$511$	−323.739	+	485.518i	−0.633540	+	0.950134i
$512$			22.6274i			0.0441942i
$513$	−632.685	−	66.5200i	−1.23331	−	0.129669i
$514$	−133.512	−	231.250i	−0.259751	−	0.449902i
$515$	41.4833	+	23.9504i	0.0805501	+	0.0465056i
$516$	352.578	+	142.455i	0.683290	+	0.276076i
$517$	37.2860	−	64.5812i	0.0721199	−	0.124915i
$518$	−20.0362	+	310.258i	−0.0386800	+	0.598954i
$519$	−95.7178	−	122.516i	−0.184427	−	0.236062i
$520$	−68.7269			−0.132167
$521$	−332.558	+	192.003i	−0.638308	+	0.368527i	−0.783962	−	0.620808i	$-0.786805\pi$
$521$	−332.558	+	192.003i	−0.638308	+	0.368527i	0.145655	+	0.989336i	$0.453471\pi$
$522$	−194.344	+	55.7225i	−0.372307	+	0.106748i
$523$	182.193	−	315.567i	0.348361	−	0.603379i	−0.637597	−	0.770370i	$-0.720072\pi$
$523$	182.193	−	315.567i	0.348361	−	0.603379i	0.985959	+	0.166990i	$0.0534049\pi$
$524$	−385.976	+	222.843i	−0.736595	+	0.425273i
$525$	−398.980	+	272.210i	−0.759963	+	0.518496i
$526$	125.876	−	218.023i	0.239308	−	0.414493i
$527$	671.884	−	387.913i	1.27492	−	0.736077i
$528$	207.437	−	29.1509i	0.392873	−	0.0552100i
$529$	225.195	−	390.050i	0.425700	−	0.737335i
$530$	−90.6367	−	52.3291i	−0.171013	−	0.0987342i
$531$	−368.413	−	91.8646i	−0.693809	−	0.173003i
$532$	−329.182	−	21.2583i	−0.618763	−	0.0399592i
$533$	149.036	−	86.0459i	0.279617	−	0.161437i
$534$	84.4029	+	600.608i	0.158058	+	1.12473i
$535$	−64.9058			−0.121319
$536$		−	271.920i		−	0.507313i
$537$	217.329	−	537.891i	0.404710	−	1.00166i
$538$	364.871	+	631.976i	0.678200	+	1.17468i
$539$	−789.616	+	328.848i	−1.46497	+	0.610107i
$540$	61.7851	+	44.8927i	0.114417	+	0.0831347i
$541$	473.259	−	819.709i	0.874786	−	1.51517i	0.0177960	−	0.999842i	$-0.494335\pi$
$541$	473.259	−	819.709i	0.874786	−	1.51517i	0.856990	−	0.515333i	$-0.172332\pi$
$542$	−288.350	−	166.479i	−0.532011	−	0.307157i
$543$	415.661	−	324.742i	0.765489	−	0.598051i
$544$	−68.1610	−	118.058i	−0.125296	−	0.217019i
$545$	53.0434	+	30.6246i	0.0973273	+	0.0561919i
$546$	287.564	+	421.485i	0.526675	+	0.771950i
$547$	−294.515	−	510.116i	−0.538419	−	0.932570i	−0.998989	−	0.0449464i	$-0.985688\pi$
$547$	−294.515	−	510.116i	−0.538419	−	0.932570i	0.460570	−	0.887623i	$-0.347645\pi$
$548$	149.690	+	86.4234i	0.273156	+	0.157707i
$549$	−27.1718	+	108.969i	−0.0494933	+	0.198487i
$550$	−283.896	−	491.722i	−0.516174	−	0.894040i
$551$			374.267i			0.679250i
$552$	246.211	+	99.4792i	0.446035	+	0.180216i
$553$	−140.101	−	283.410i	−0.253346	−	0.512495i
$554$	−622.755	−	359.548i	−1.12411	−	0.649003i
$555$	−82.0377	−	105.006i	−0.147816	−	0.189200i
$556$	−3.22687	+	5.58910i	−0.00580372	+	0.0100523i
$557$	−531.266	+	306.727i	−0.953799	+	0.550676i	−0.894259	−	0.447550i	$-0.852297\pi$
$557$	−531.266	+	306.727i	−0.953799	+	0.550676i	−0.0595401	+	0.998226i	$0.518963\pi$
$558$	−397.587	−	99.1392i	−0.712521	−	0.177669i
$559$	−1088.88			−1.94790
$560$	32.9478	+	21.9693i	0.0588353	+	0.0392308i
$561$	−994.488	+	776.961i	−1.77271	+	1.38496i
$562$	−11.0477	−	19.1352i	−0.0196579	−	0.0340484i
$563$			208.343i			0.370059i	0.982733	+	0.185030i	$0.0592381\pi$
$563$			208.343i			0.370059i	−0.982733	+	0.185030i	$0.940762\pi$
$564$	15.7802	+	20.1982i	0.0279790	+	0.0358123i
$565$	−128.019			−0.226582
$566$		−	721.219i		−	1.27424i
$567$	16.7973	−	566.751i	0.0296249	−	0.999561i
$568$	58.8362			0.103585
$569$			944.539i			1.66000i	0.557765	+	0.829999i	$0.311659\pi$
$569$			944.539i			1.66000i	−0.557765	+	0.829999i	$0.688341\pi$
$570$	111.411	−	87.0415i	0.195457	−	0.152704i
$571$	−114.520			−0.200561			−0.100280	−	0.994959i	$-0.531974\pi$
$571$	−114.520			−0.200561			−0.100280	+	0.994959i	$0.531974\pi$
$572$	−519.458	+	299.909i	−0.908143	+	0.524317i
$573$	43.0159	+	55.0592i	0.0750714	+	0.0960893i
$574$	−98.9535	−	6.39035i	−0.172393	−	0.0111330i
$575$		−	719.782i		−	1.25179i
$576$	−17.4200	+	69.8609i	−0.0302430	+	0.121286i
$577$	493.595	+	854.932i	0.855451	+	1.48168i	0.876226	+	0.481900i	$0.160053\pi$
$577$	493.595	+	854.932i	0.855451	+	1.48168i	−0.0207756	+	0.999784i	$0.506614\pi$
$578$	357.308	+	206.292i	0.618180	+	0.356907i
$579$	200.552	−	156.685i	0.346377	−	0.270613i
$580$	22.4653	−	38.9111i	0.0387333	−	0.0670881i
$581$	25.1099	+	16.7430i	0.0432183	+	0.0288176i
$582$	55.7731	−	138.039i	0.0958301	−	0.237180i
$583$	−913.411			−1.56674
$584$	204.201	−	117.896i	0.349660	−	0.201876i
$585$	−212.190	−	52.9102i	−0.362719	−	0.0904448i
$586$	308.674	−	534.638i	0.526747	−	0.912352i
$587$	−439.957	+	254.009i	−0.749501	+	0.432725i	−0.825514	−	0.564382i	$-0.809115\pi$
$587$	−439.957	+	254.009i	−0.749501	+	0.432725i	0.0760123	+	0.997107i	$0.475781\pi$
$588$	−3.12674	−	293.983i	−0.00531759	−	0.499972i
$589$	−379.275	+	656.923i	−0.643930	+	1.11532i
$590$	73.0767	−	42.1909i	0.123859	−	0.0715099i
$591$	282.922	+	362.133i	0.478718	+	0.612746i
$592$	62.8122	−	108.794i	0.106102	−	0.183773i
$593$	105.925	+	61.1560i	0.178626	+	0.103130i	0.586647	−	0.809843i	$-0.300448\pi$
$593$	105.925	+	61.1560i	0.178626	+	0.103130i	−0.408021	+	0.912973i	$0.633781\pi$
$594$	662.892	+	69.6959i	1.11598	+	0.117333i
$595$	−238.083	−	15.3752i	−0.400140	−	0.0258407i
$596$	339.163	−	195.816i	0.569065	−	0.328550i
$597$	3.12540	+	1.26279i	0.00523518	+	0.00211522i
$598$	−760.382			−1.27154
$599$			934.348i			1.55985i	0.625875	+	0.779923i	$0.284742\pi$
$599$			934.348i			1.55985i	−0.625875	+	0.779923i	$0.715258\pi$
$600$	193.260	−	27.1587i	0.322101	−	0.0452645i
$601$	109.192	+	189.127i	0.181685	+	0.314687i	0.942454	−	0.334335i	$-0.108512\pi$
$601$	109.192	+	189.127i	0.181685	+	0.314687i	−0.760770	+	0.649022i	$0.775178\pi$
$602$	522.009	+	348.070i	0.867124	+	0.578190i
$603$	209.341	−	839.538i	0.347165	−	1.39227i
$604$	−31.4997	+	54.5591i	−0.0521519	+	0.0903297i
$605$	225.026	+	129.919i	0.371943	+	0.214742i
$606$	−24.5078	−	174.396i	−0.0404419	−	0.287783i
$607$	532.851	+	922.924i	0.877843	+	1.52047i	0.853703	+	0.520760i	$0.174351\pi$
$607$	532.851	+	922.924i	0.877843	+	1.52047i	0.0241397	+	0.999709i	$0.492315\pi$
$608$	115.430	+	66.6433i	0.189851	+	0.109611i
$609$	−332.631	+	25.0360i	−0.546192	+	0.0411101i
$610$	−12.4793	−	21.6147i	−0.0204578	−	0.0354339i
$611$	−63.5614	−	36.6972i	−0.104029	−	0.0600609i
$612$	−119.555	−	416.973i	−0.195351	−	0.681329i
$613$	−146.885	−	254.412i	−0.239616	−	0.415027i	0.720988	−	0.692947i	$-0.243688\pi$
$613$	−146.885	−	254.412i	−0.239616	−	0.415027i	−0.960604	+	0.277920i	$0.910355\pi$
$614$		−	569.009i		−	0.926725i
$615$	33.4905	−	26.1651i	0.0544562	−	0.0425448i
$616$	344.898	+	22.2732i	0.559899	+	0.0361579i
$617$	−103.145	−	59.5509i	−0.167172	−	0.0965168i	0.414080	−	0.910241i	$-0.364103\pi$
$617$	−103.145	−	59.5509i	−0.167172	−	0.0965168i	−0.581252	+	0.813724i	$0.697437\pi$
$618$	−53.8299	+	133.229i	−0.0871034	+	0.215581i
$619$	211.746	−	366.755i	0.342077	−	0.592495i	−0.642741	−	0.766084i	$-0.722203\pi$
$619$	211.746	−	366.755i	0.342077	−	0.592495i	0.984818	+	0.173588i	$0.0555362\pi$
$620$	78.8635	−	45.5319i	0.127199	−	0.0734385i
$621$	683.579	+	496.685i	1.10077	+	0.799815i
$622$	132.860			0.213601
$623$	−64.4895	+	998.610i	−0.103514	+	1.60290i
$624$	−28.6906	−	204.161i	−0.0459785	−	0.327181i
$625$	−239.491	−	414.810i	−0.383185	−	0.663696i
$626$			571.657i			0.913189i
$627$	462.244	−	1144.06i	0.737231	−	1.82465i
$628$	−178.752			−0.284637
$629$			756.842i			1.20325i
$630$	84.8111	+	93.1941i	0.134621	+	0.147927i
$631$	1159.89			1.83818			0.919091	−	0.394046i	$-0.128925\pi$
$631$	1159.89			1.83818			0.919091	+	0.394046i	$0.128925\pi$
$632$			127.743i			0.202125i
$633$	65.8954	+	468.909i	0.104100	+	0.740773i
$634$	−165.047			−0.260326
$635$	−166.017	+	95.8498i	−0.261444	+	0.150945i
$636$	117.613	−	291.092i	0.184926	−	0.457692i
$637$	323.655	+	777.148i	0.508092	+	1.22001i
$638$		−	392.135i		−	0.614632i
$639$	181.653	+	45.2957i	0.284278	+	0.0708853i
$640$	−8.00052	−	13.8573i	−0.0125008	−	0.0216520i
$641$	−320.420	−	184.994i	−0.499875	−	0.288603i	0.228787	−	0.973476i	$-0.426524\pi$
$641$	−320.420	−	184.994i	−0.499875	−	0.288603i	−0.728662	+	0.684874i	$0.759857\pi$
$642$	−27.0955	−	192.810i	−0.0422048	−	0.300328i
$643$	223.115	−	386.446i	0.346990	−	0.601005i	−0.638723	−	0.769437i	$-0.720537\pi$
$643$	223.115	−	386.446i	0.346990	−	0.601005i	0.985713	+	0.168432i	$0.0538704\pi$
$644$	364.528	+	243.064i	0.566037	+	0.377428i
$645$	−266.292	+	37.4217i	−0.412855	+	0.0580182i
$646$	−803.004			−1.24304
$647$	−287.119	+	165.768i	−0.443770	+	0.256210i	−0.705195	−	0.709013i	$-0.749141\pi$
$647$	−287.119	+	165.768i	−0.443770	+	0.256210i	0.261426	+	0.965224i	$0.415807\pi$
$648$	−107.566	+	202.281i	−0.165998	+	0.312161i
$649$	368.223	−	637.782i	0.567370	−	0.982714i
$650$	−483.957	+	279.413i	−0.744550	+	0.429866i
$651$	−609.214	−	293.138i	−0.935812	−	0.450288i
$652$	−210.516	+	364.624i	−0.322877	+	0.559240i
$653$	−689.144	+	397.877i	−1.05535	+	0.609307i	−0.924143	−	0.382048i	$-0.875219\pi$
$653$	−689.144	+	397.877i	−1.05535	+	0.609307i	−0.131208	+	0.991355i	$0.541886\pi$
$654$	−68.8306	+	170.356i	−0.105246	+	0.260483i
$655$	157.584	−	272.944i	0.240586	−	0.416708i
$656$	34.6986	+	20.0333i	0.0528943	+	0.0305385i
$657$	721.224	−	206.790i	1.09775	−	0.314748i
$658$	18.7408	+	37.9108i	0.0284814	+	0.0576151i
$659$	−647.026	+	373.560i	−0.981830	+	0.566860i	−0.902822	−	0.430014i	$-0.858508\pi$
$659$	−647.026	+	373.560i	−0.981830	+	0.566860i	−0.0790076	+	0.996874i	$0.525175\pi$
$660$	−116.730	+	91.1971i	−0.176863	+	0.138177i
$661$	−1126.89			−1.70482			−0.852411	−	0.522872i	$-0.824861\pi$
$661$	−1126.89			−1.70482			−0.852411	+	0.522872i	$0.824861\pi$
$662$			864.565i			1.30599i
$663$	764.692	+	978.784i	1.15338	+	1.47630i
$664$	−6.09728	−	10.5608i	−0.00918266	−	0.0159048i
$665$	209.111	−	103.372i	0.314453	−	0.155447i
$666$	277.685	−	287.538i	0.416945	−	0.431739i
$667$	248.552	−	430.505i	0.372642	−	0.645435i
$668$	−195.762	−	113.023i	−0.293057	−	0.169196i
$669$	293.888	+	118.743i	0.439295	+	0.177493i
$670$	96.1444	+	166.527i	0.143499	+	0.248548i
$671$	−188.644	−	108.913i	−0.281138	−	0.162315i
$672$	−51.5079	+	107.046i	−0.0766487	+	0.159295i
$673$	264.569	+	458.246i	0.393118	+	0.680901i	0.992859	−	0.119294i	$-0.0380630\pi$
$673$	264.569	+	458.246i	0.393118	+	0.680901i	−0.599741	+	0.800194i	$0.704730\pi$
$674$	8.81578	+	5.08979i	0.0130798	+	0.00755162i
$675$	617.589	+	64.9328i	0.914947	+	0.0961967i
$676$	126.173	+	218.539i	0.186647	+	0.323282i
$677$		−	188.228i		−	0.278032i	−0.990290	−	0.139016i	$-0.955606\pi$
$677$		−	188.228i		−	0.278032i	0.990290	−	0.139016i	$-0.0443940\pi$
$678$	−53.4425	−	380.295i	−0.0788238	−	0.560907i
$679$	136.274	−	204.373i	0.200698	−	0.300991i
$680$	83.4853	+	48.2002i	0.122772	+	0.0708827i
$681$	178.545	−	25.0907i	0.262180	−	0.0368439i
$682$	397.382	−	688.287i	0.582672	−	1.00922i
$683$	300.248	−	173.348i	0.439601	−	0.253804i	−0.263827	−	0.964570i	$-0.584985\pi$
$683$	300.248	−	173.348i	0.439601	−	0.253804i	0.703429	+	0.710766i	$0.251652\pi$
$684$	305.076	+	294.622i	0.446018	+	0.430734i
$685$	−122.229			−0.178436
$686$	93.2628	−	476.025i	0.135952	−	0.693914i
$687$	−141.861	−	57.3175i	−0.206494	−	0.0834316i
$688$	−126.756	−	219.548i	−0.184239	−	0.319111i
$689$			898.988i			1.30477i
$690$	−185.956	+	26.1323i	−0.269502	+	0.0378728i
$691$	795.908			1.15182			0.575910	−	0.817513i	$-0.304648\pi$
$691$	795.908			1.15182			0.575910	+	0.817513i	$0.304648\pi$
$692$			103.649i			0.149782i
$693$	1047.71	+	334.291i	1.51184	+	0.482382i
$694$	772.820			1.11357
$695$		−	4.56377i		−	0.00656658i
$696$	124.968	+	50.4921i	0.179552	+	0.0725462i
$697$	−241.387			−0.346322
$698$	159.586	−	92.1368i	0.228633	−	0.132001i
$699$	67.7128	−	9.51562i	0.0968710	−	0.0136132i
$700$	321.327	+	20.7511i	0.459039	+	0.0296444i
$701$		−	1048.99i		−	1.49643i	−0.663459	−	0.748213i	$-0.730912\pi$
$701$		−	1048.99i		−	1.49643i	0.663459	−	0.748213i	$-0.269088\pi$
$702$	68.5953	−	652.424i	0.0977141	−	0.929379i
$703$	−369.994	−	640.849i	−0.526308	−	0.911592i
$704$	−120.940	−	69.8250i	−0.171790	−	0.0991833i
$705$	−16.8055	−	6.79011i	−0.0238377	−	0.00963136i
$706$	−15.6552	+	27.1156i	−0.0221745	+	0.0384074i
$707$	18.7256	−	289.963i	0.0264860	−	0.410131i
$708$	155.839	+	199.470i	0.220112	+	0.281737i
$709$	−1020.18			−1.43890			−0.719448	−	0.694547i	$-0.755605\pi$
$709$	−1020.18			−1.43890			−0.719448	+	0.694547i	$0.755605\pi$
$710$	−36.0320	+	20.8031i	−0.0507493	+	0.0293001i
$711$	−98.3443	+	394.399i	−0.138318	+	0.554710i
$712$	202.170	−	350.169i	0.283946	−	0.491810i
$713$	872.532	−	503.756i	1.22375	−	0.706531i
$714$	−53.7158	−	713.672i	−0.0752322	−	0.999541i
$715$	212.081	−	367.336i	0.296617	−	0.513756i
$716$	−334.942	+	193.379i	−0.467796	+	0.270082i
$717$	1201.41	−	168.834i	1.67561	−	0.235472i
$718$	−42.6071	+	73.7977i	−0.0593414	+	0.102782i
$719$	−836.024	−	482.679i	−1.16276	−	0.671320i	−0.210796	−	0.977530i	$-0.567606\pi$
$719$	−836.024	−	482.679i	−1.16276	−	0.671320i	−0.951964	+	0.306210i	$0.900939\pi$
$720$	−14.0329	−	48.9429i	−0.0194902	−	0.0679763i
$721$	−131.526	+	197.252i	−0.182422	+	0.273582i
$722$	237.803	−	137.296i	0.329368	−	0.190161i
$723$	−126.766	−	902.059i	−0.175333	−	1.24766i
$724$	−351.651			−0.485705
$725$		−	365.336i		−	0.503912i
$726$	−292.000	+	722.701i	−0.402203	+	0.995455i
$727$	−679.328	−	1176.63i	−0.934426	−	1.61847i	−0.775654	−	0.631159i	$-0.782580\pi$
$727$	−679.328	−	1176.63i	−0.934426	−	1.61847i	−0.158773	−	0.987315i	$-0.550754\pi$
$728$	21.9215	−	339.452i	0.0301120	−	0.466280i
$729$	−487.834	+	541.719i	−0.669182	+	0.743099i
$730$	−83.3702	+	144.401i	−0.114206	+	0.197810i
$731$	1322.70	+	763.662i	1.80944	+	1.04468i
$732$	58.9994	−	46.0943i	0.0806003	−	0.0629704i
$733$	106.923	+	185.196i	0.145871	+	0.252655i	0.929697	−	0.368324i	$-0.120068\pi$
$733$	106.923	+	185.196i	0.145871	+	0.252655i	−0.783827	+	0.620980i	$0.786735\pi$
$734$	9.09707	+	5.25220i	0.0123938	+	0.00715558i
$735$	105.860	+	178.933i	0.144028	+	0.243447i
$736$	−88.5163	−	153.315i	−0.120267	−	0.208308i
$737$	1453.38	+	839.106i	1.97201	+	1.13854i
$738$	91.7073	+	88.5648i	0.124265	+	0.120006i
$739$	−23.9766	−	41.5286i	−0.0324446	−	0.0561957i	0.849347	−	0.527835i	$-0.176996\pi$
$739$	−23.9766	−	41.5286i	−0.0324446	−	0.0561957i	−0.881792	+	0.471639i	$0.843663\pi$
$740$			88.8356i			0.120048i
$741$	−1125.99	−	454.945i	−1.51956	−	0.613961i
$742$	287.371	−	430.976i	0.387292	−	0.580830i
$743$	646.371	+	373.182i	0.869947	+	0.502264i	0.867331	−	0.497732i	$-0.165834\pi$
$743$	646.371	+	373.182i	0.869947	+	0.502264i	0.00261651	+	0.999997i	$0.499167\pi$
$744$	168.180	+	215.266i	0.226048	+	0.289336i
$745$	−138.472	+	239.840i	−0.185868	+	0.321932i
$746$	−728.371	+	420.525i	−0.976368	+	0.563707i
$747$	−10.6947	−	37.3000i	−0.0143168	−	0.0499330i
$748$	841.341			1.12479
$749$	20.7027	−	320.579i	0.0276405	−	0.428009i
$750$	−226.963	+	177.318i	−0.302617	+	0.236425i
$751$	538.756	+	933.153i	0.717385	+	1.24255i	0.962032	+	0.272935i	$0.0879945\pi$
$751$	538.756	+	933.153i	0.717385	+	1.24255i	−0.244647	+	0.969612i	$0.578672\pi$
$752$		−	17.0877i		−	0.0227230i
$753$	−431.039	−	551.718i	−0.572429	−	0.732694i
$754$	−385.943			−0.511861
$755$		−	44.5502i		−	0.0590069i
$756$	−241.439	+	290.846i	−0.319364	+	0.384717i
$757$	50.0542			0.0661217			0.0330609	−	0.999453i	$-0.489474\pi$
$757$	50.0542			0.0661217			0.0330609	+	0.999453i	$0.489474\pi$
$758$			920.734i			1.21469i
$759$	−1291.48	+	1008.99i	−1.70155	+	1.32936i
$760$	−94.2539			−0.124018
$761$	13.0930	−	7.55923i	0.0172050	−	0.00993329i	−0.491373	−	0.870949i	$-0.663505\pi$
$761$	13.0930	−	7.55923i	0.0172050	−	0.00993329i	0.508578	+	0.861016i	$0.330171\pi$
$762$	−354.038	−	453.159i	−0.464617	−	0.594697i
$763$	−168.178	+	252.220i	−0.220417	+	0.330564i
$764$		−	46.5803i		−	0.0609690i
$765$	220.649	+	213.088i	0.288430	+	0.278546i
$766$	234.505	+	406.175i	0.306142	+	0.530254i
$767$	−627.711	−	362.409i	−0.818397	−	0.472502i
$768$	37.8249	−	29.5513i	0.0492511	−	0.0384783i
$769$	−268.317	+	464.739i	−0.348917	+	0.604342i	−0.986057	−	0.166406i	$-0.946784\pi$
$769$	−268.317	+	464.739i	−0.348917	+	0.604342i	0.637140	+	0.770748i	$0.280117\pi$
$770$	−219.095	+	108.307i	−0.284539	+	0.140659i
$771$	−212.200	+	525.195i	−0.275227	+	0.681187i
$772$	−169.668			−0.219777
$773$	−965.601	+	557.490i	−1.24916	+	0.721203i	−0.970942	−	0.239315i	$-0.923077\pi$
$773$	−965.601	+	557.490i	−1.24916	+	0.721203i	−0.278219	+	0.960518i	$0.589744\pi$
$774$	−222.331	−	775.429i	−0.287250	−	1.00185i
$775$	370.225	−	641.248i	0.477709	−	0.827417i
$776$	−85.9561	+	49.6267i	−0.110768	+	0.0639520i
$777$	544.807	−	371.702i	0.701167	−	0.478382i
$778$	−14.7723	+	25.5864i	−0.0189875	+	0.0328874i
$779$	204.392	−	118.006i	0.262377	−	0.151484i
$780$	89.7570	+	114.886i	0.115073	+	0.147290i
$781$	−181.560	+	314.471i	−0.232471	+	0.402652i
$782$	923.666	+	533.279i	1.18116	+	0.681942i
$783$	346.961	+	252.100i	0.443117	+	0.321967i
$784$	−119.018	+	155.726i	−0.151809	+	0.198630i
$785$	109.470	−	63.2025i	0.139452	−	0.0805127i
$786$	876.596	+	354.179i	1.11526	+	0.450610i
$787$	−512.099			−0.650698			−0.325349	−	0.945594i	$-0.605482\pi$
$787$	−512.099			−0.650698			−0.325349	+	0.945594i	$0.605482\pi$
$788$		−	306.366i		−	0.388789i
$789$	−528.849	+	74.3187i	−0.670278	+	0.0941935i
$790$	−45.1668	−	78.2312i	−0.0571732	−	0.0990269i
$791$	40.8337	−	632.303i	0.0516229	−	0.799372i
$792$	−319.641	−	308.688i	−0.403588	−	0.389758i
$793$	−107.194	+	185.665i	−0.135175	+	0.234130i
$794$	−758.908	−	438.156i	−0.955804	−	0.551834i
$795$	30.8958	+	219.853i	0.0388626	+	0.276545i
$796$	−1.12362	−	1.94617i	−0.00141159	−	0.00244494i
$797$	−205.675	−	118.747i	−0.258061	−	0.148992i	0.365388	−	0.930855i	$-0.380936\pi$
$797$	−205.675	−	118.747i	−0.258061	−	0.148992i	−0.623450	+	0.781863i	$0.714269\pi$
$798$	394.374	+	578.036i	0.494203	+	0.724356i
$799$	51.4737	+	89.1551i	0.0644227	+	0.111583i
$800$	−112.675	−	65.0531i	−0.140844	−	0.0813164i
$801$	893.770	−	925.483i	1.11582	−	1.15541i
$802$	−203.165	−	351.892i	−0.253323	−	0.438769i
$803$			1455.24i			1.81225i
$804$	−454.552	+	355.126i	−0.565363	+	0.441699i
$805$	−309.183	−	19.9668i	−0.384078	−	0.0248035i
$806$	−677.418	−	391.107i	−0.840469	−	0.485245i
$807$	579.914	−	1435.29i	0.718605	−	1.77855i
$808$	−58.7033	+	101.677i	−0.0726526	+	0.125838i
$809$	227.210	−	131.180i	0.280853	−	0.162150i	−0.352957	−	0.935640i	$-0.614824\pi$
$809$	227.210	−	131.180i	0.280853	−	0.162150i	0.633809	+	0.773489i	$0.281490\pi$
$810$	−5.64663	−	161.912i	−0.00697115	−	0.199891i
$811$	241.274			0.297502			0.148751	−	0.988875i	$-0.452475\pi$
$811$	241.274			0.297502			0.148751	+	0.988875i	$0.452475\pi$
$812$	185.022	+	123.371i	0.227859	+	0.151934i
$813$	98.2913	+	699.438i	0.120900	+	0.860317i
$814$	387.659	+	671.445i	0.476240	+	0.824871i
$815$		−	297.734i		−	0.365317i
$816$	−108.333	+	268.124i	−0.132761	+	0.328584i
$817$	−1493.31			−1.82780
$818$			625.074i			0.764150i
$819$	329.012	−	1031.16i	0.401724	−	1.25905i
$820$	−28.3332			−0.0345526
$821$		−	928.640i		−	1.13111i	−0.824711	−	0.565554i	$-0.808662\pi$
$821$		−	928.640i		−	1.13111i	0.824711	−	0.565554i	$-0.191338\pi$
$822$	−51.0255	−	363.096i	−0.0620748	−	0.441722i
$823$	−133.546			−0.162268			−0.0811339	−	0.996703i	$-0.525854\pi$
$823$	−133.546			−0.162268			−0.0811339	+	0.996703i	$0.525854\pi$
$824$	82.9612	−	47.8977i	0.100681	−	0.0581283i
$825$	−451.215	+	1116.76i	−0.546927	+	1.35365i
$826$	185.078	+	374.394i	0.224065	+	0.453261i
$827$		−	880.144i		−	1.06426i	−0.846662	−	0.532130i	$-0.821392\pi$
$827$		−	880.144i		−	1.06426i	0.846662	−	0.532130i	$-0.178608\pi$
$828$	−155.258	−	541.496i	−0.187510	−	0.653980i
$829$	−268.250	−	464.622i	−0.323582	−	0.560461i	0.657642	−	0.753330i	$-0.271554\pi$
$829$	−268.250	−	464.622i	−0.323582	−	0.560461i	−0.981224	+	0.192870i	$0.938221\pi$
$830$	7.46810	+	4.31171i	0.00899771	+	0.00519483i
$831$	212.282	+	1510.59i	0.255453	+	1.81780i
$832$	−68.7224	+	119.031i	−0.0825991	+	0.143066i
$833$	151.881	−	1171.02i	0.182330	−	1.40579i
$834$	13.5572	−	1.90518i	0.0162557	−	0.00228439i
$835$	159.849			0.191436
$836$	−712.399	+	411.303i	−0.852151	+	0.491990i
$837$	353.522	+	794.096i	0.422368	+	0.948741i
$838$	−230.070	+	398.493i	−0.274547	+	0.475529i
$839$	1336.23	−	771.471i	1.59264	−	0.919513i	0.599791	−	0.800157i	$-0.295250\pi$
$839$	1336.23	−	771.471i	1.59264	−	0.919513i	0.992852	−	0.119356i	$-0.0380830\pi$
$840$	−6.30498	−	83.7685i	−0.00750593	−	0.0997244i
$841$	−294.344	+	509.818i	−0.349992	+	0.606204i
$842$	492.448	−	284.315i	0.584856	−	0.337666i
$843$	−17.5589	+	43.4583i	−0.0208290	+	0.0515520i
$844$	157.839	−	273.385i	0.187013	−	0.323916i
$845$	−154.540	−	89.2237i	−0.182888	−	0.105590i
$846$	13.1552	−	52.7574i	0.0155499	−	0.0623610i
$847$	−713.462	+	1069.99i	−0.842340	+	1.26327i
$848$	−181.262	+	104.651i	−0.213752	+	0.123410i
$849$	−1205.62	+	941.909i	−1.42004	+	1.10943i
$850$	783.843			0.922168
$851$			982.860i			1.15495i
$852$	−76.8398	−	98.3528i	−0.0901876	−	0.115438i
$853$	−470.293	−	814.571i	−0.551340	−	0.954948i	−0.998178	−	0.0603337i	$-0.980784\pi$
$853$	−470.293	−	814.571i	−0.551340	−	0.954948i	0.446839	−	0.894615i	$-0.352550\pi$
$854$	110.739	−	54.7424i	0.129670	−	0.0641012i
$855$	−291.004	−	72.5625i	−0.340355	−	0.0848684i
$856$	−64.9016	+	112.413i	−0.0758196	+	0.131323i
$857$	−553.341	−	319.471i	−0.645672	−	0.372779i	0.141124	−	0.989992i	$-0.454928\pi$
$857$	−553.341	−	319.471i	−0.645672	−	0.372779i	−0.786796	+	0.617213i	$0.788262\pi$
$858$	1179.75	+	476.665i	1.37500	+	0.555554i
$859$	−149.147	−	258.330i	−0.173628	−	0.300733i	0.766057	−	0.642772i	$-0.222216\pi$
$859$	−149.147	−	258.330i	−0.173628	−	0.300733i	−0.939686	+	0.342039i	$0.888882\pi$
$860$	155.254	+	89.6361i	0.180528	+	0.104228i
$861$	118.551	+	173.760i	0.137689	+	0.201812i
$862$	120.977	+	209.539i	0.140345	+	0.243085i
$863$	−949.481	−	548.183i	−1.10021	−	0.635207i	−0.163934	−	0.986471i	$-0.552418\pi$
$863$	−949.481	−	548.183i	−1.10021	−	0.635207i	−0.936276	+	0.351265i	$0.885752\pi$
$864$	139.533	−	62.1181i	0.161496	−	0.0718960i
$865$	−36.6479	−	63.4760i	−0.0423675	−	0.0733827i
$866$		−	318.470i		−	0.367749i
$867$	−121.798	−	866.707i	−0.140482	−	0.999662i
$868$	199.734	+	404.041i	0.230108	+	0.465485i
$869$	−682.768	−	394.196i	−0.785694	−	0.453621i
$870$	−94.3849	+	13.2638i	−0.108488	+	0.0152458i
$871$	825.856	−	1430.43i	0.948170	−	1.64228i
$872$	106.080	−	61.2452i	0.121651	−	0.0702354i
$873$	−303.590	+	87.0455i	−0.347755	+	0.0997085i
$874$	−1042.81			−1.19314
$875$	−425.995	+	210.586i	−0.486852	+	0.240670i
$876$	−463.765	−	187.379i	−0.529412	−	0.213903i
$877$	−91.0649	−	157.729i	−0.103837	−	0.179851i	0.809426	−	0.587223i	$-0.199779\pi$
$877$	−91.0649	−	157.729i	−0.103837	−	0.179851i	−0.913262	+	0.407372i	$0.866445\pi$
$878$		−	83.9072i		−	0.0955662i
$879$	−1296.85	+	182.245i	−1.47537	+	0.207332i
$880$	98.7539			0.112220
$881$			447.835i			0.508325i	0.967161	+	0.254163i	$0.0817999\pi$
$881$			447.835i			0.508325i	−0.967161	+	0.254163i	$0.918200\pi$
$882$	−487.350	+	389.168i	−0.552551	+	0.441233i
$883$	576.635			0.653040			0.326520	−	0.945190i	$-0.394124\pi$
$883$	576.635			0.653040			0.326520	+	0.945190i	$0.394124\pi$
$884$		−	828.056i		−	0.936715i
$885$	−165.966	−	67.0567i	−0.187532	−	0.0757703i
$886$	432.831			0.488523
$887$	1412.61	−	815.571i	1.59257	−	0.919471i	0.599707	−	0.800220i	$-0.295284\pi$
$887$	1412.61	−	815.571i	1.59257	−	0.919471i	0.992864	−	0.119252i	$-0.0380495\pi$
$888$	−263.896	+	37.0851i	−0.297181	+	0.0417625i
$889$	−420.462	−	850.553i	−0.472961	−	0.956752i
$890$			285.930i			0.321270i
$891$	−749.228	−	1199.14i	−0.840884	−	1.34583i
$892$	−105.657	−	183.003i	−0.118449	−	0.205160i
$893$	−87.1699	−	50.3275i	−0.0976146	−	0.0563578i
$894$	−770.278	−	311.223i	−0.861609	−	0.348124i
$895$	136.748	−	236.855i	0.152791	−	0.264642i
$896$	70.9950	−	35.0957i	0.0792355	−	0.0391693i
$897$	993.055	+	1271.08i	1.10708	+	1.41704i
$898$	−630.904			−0.702566
$899$	442.867	−	255.689i	0.492621	−	0.284415i
$900$	−297.797	−	287.592i	−0.330885	−	0.319547i
$901$	630.488	−	1092.04i	0.699764	−	1.21203i
$902$	−214.150	+	123.640i	−0.237417	+	0.137073i
$903$	−99.8931	−	1327.19i	−0.110624	−	1.46975i
$904$	−128.011	+	221.721i	−0.141605	+	0.245267i
$905$	215.355	−	124.335i	0.237961	−	0.137387i
$906$	132.342	−	18.5979i	0.146072	−	0.0205274i
$907$	477.583	−	827.199i	0.526553	−	0.912016i	−0.472969	−	0.881079i	$-0.656818\pi$
$907$	477.583	−	827.199i	0.526553	−	0.912016i	0.999521	−	0.0309368i	$-0.00984906\pi$
$908$	−104.096	−	60.0997i	−0.114643	−	0.0661891i
$909$	−259.521	+	268.729i	−0.285501	+	0.295632i
$910$	106.597	+	215.635i	0.117140	+	0.236962i
$911$	198.257	−	114.464i	0.217625	−	0.125646i	−0.387225	−	0.921985i	$-0.626566\pi$
$911$	198.257	−	114.464i	0.217625	−	0.125646i	0.604850	+	0.796339i	$0.293233\pi$
$912$	−39.3471	−	279.992i	−0.0431437	−	0.307009i
$913$	75.2614			0.0824331
$914$			449.279i			0.491552i
$915$	−19.8341	+	49.0895i	−0.0216766	+	0.0536497i
$916$	51.0009	+	88.3362i	0.0556779	+	0.0964369i
$917$	1297.84	+	865.389i	1.41531	+	0.943718i
$918$	−540.890	+	744.418i	−0.589205	+	0.810913i
$919$	−431.028	+	746.563i	−0.469019	+	0.812364i	−0.999373	−	0.0354120i	$-0.988726\pi$
$919$	−431.028	+	746.563i	−0.469019	+	0.812364i	0.530354	+	0.847776i	$0.322059\pi$
$920$	108.417	+	62.5945i	0.117844	+	0.0680375i
$921$	−951.178	+	743.124i	−1.03277	+	0.806866i
$922$	−54.2015	−	93.8798i	−0.0587869	−	0.101822i
$923$	309.506	+	178.693i	0.335326	+	0.193600i
$924$	−413.202	−	605.633i	−0.447189	−	0.655447i
$925$	361.166	+	625.558i	0.390450	+	0.676279i
$926$	381.460	+	220.236i	0.411943	+	0.237836i
$927$	293.013	−	84.0128i	0.316087	−	0.0906287i
$928$	−44.9278	−	77.8172i	−0.0484135	−	0.0838547i
$929$		−	1396.41i		−	1.50313i	−0.659658	−	0.751566i	$-0.729299\pi$
$929$		−	1396.41i		−	1.50313i	0.659658	−	0.751566i	$-0.270701\pi$
$930$	−179.108	−	72.3668i	−0.192590	−	0.0778138i
$931$	443.869	+	1065.80i	0.476766	+	1.14479i
$932$	−39.4781	−	22.7927i	−0.0423585	−	0.0244557i
$933$	−173.514	−	222.093i	−0.185975	−	0.238042i
$934$	−216.394	+	374.805i	−0.231685	+	0.401290i
$935$	−515.248	+	297.478i	−0.551067	+	0.318159i
$936$	−303.814	+	314.594i	−0.324588	+	0.336105i
$937$	−744.918			−0.795003			−0.397501	−	0.917602i	$-0.630123\pi$
$937$	−744.918			−0.795003			−0.397501	+	0.917602i	$0.630123\pi$
$938$	−853.167	+	421.754i	−0.909560	+	0.449631i
$939$	955.603	−	746.581i	1.01768	−	0.795081i
$940$	6.04182	+	10.4647i	0.00642746	+	0.0111327i
$941$		−	1615.42i		−	1.71671i	−0.513056	−	0.858355i	$-0.671487\pi$
$941$		−	1615.42i		−	1.71671i	0.513056	−	0.858355i	$-0.328513\pi$
$942$	233.450	+	298.809i	0.247823	+	0.317207i
$943$	−313.473			−0.332421
$944$		−	168.753i		−	0.178763i
$945$	45.0239	−	263.484i	0.0476443	−	0.278820i
$946$	1564.61			1.65392
$947$			685.435i			0.723796i	0.932218	+	0.361898i	$0.117871\pi$
$947$			685.435i			0.723796i	−0.932218	+	0.361898i	$0.882129\pi$
$948$	213.540	−	166.832i	0.225253	−	0.175983i
$949$	1432.26			1.50923
$950$	−663.712	+	383.195i	−0.698645	+	0.403363i
$951$	215.550	+	275.898i	0.226657	+	0.290114i
$952$	−264.697	+	396.971i	−0.278043	+	0.416987i
$953$		−	988.352i		−	1.03710i	−0.855049	−	0.518548i	$-0.826473\pi$
$953$		−	988.352i		−	1.03710i	0.855049	−	0.518548i	$-0.173527\pi$
$954$	−640.203	+	183.559i	−0.671072	+	0.192410i
$955$	16.4697	+	28.5263i	0.0172457	+	0.0298705i
$956$	−700.453	−	404.407i	−0.732691	−	0.423019i
$957$	−655.508	+	512.127i	−0.684962	+	0.535138i
$958$	333.593	−	577.799i	0.348218	−	0.603131i
$959$	38.9869	−	603.706i	0.0406537	−	0.629516i
$960$	−12.7158	+	31.4715i	−0.0132456	+	0.0327829i
$961$	75.4424			0.0785040
$962$	660.842	−	381.538i	0.686946	−	0.396609i
$963$	−286.923	+	297.103i	−0.297947	+	0.308518i
$964$	−303.641	+	525.922i	−0.314980	+	0.545562i
$965$	103.907	−	59.9906i	0.107675	−	0.0621664i
$966$	−69.7572	−	926.799i	−0.0722124	−	0.959419i
$967$	−252.350	+	437.083i	−0.260962	+	0.451999i	−0.966498	−	0.256675i	$-0.917373\pi$
$967$	−252.350	+	437.083i	−0.260962	+	0.451999i	0.705536	+	0.708674i	$0.250706\pi$
$968$	450.022	−	259.820i	0.464899	−	0.268410i
$969$	1048.72	+	1342.33i	1.08227	+	1.38528i
$970$	35.0937	−	60.7840i	0.0361790	−	0.0626640i
$971$	−1011.31	−	583.878i	−1.04151	−	0.601316i	−0.121250	−	0.992622i	$-0.538690\pi$
$971$	−1011.31	−	583.878i	−1.04151	−	0.601316i	−0.920261	+	0.391306i	$0.872024\pi$
$972$	478.621	−	84.3655i	0.492409	−	0.0867957i
$973$	22.5411	+	1.45569i	0.0231666	+	0.00149608i
$974$	−478.211	+	276.095i	−0.490976	+	0.283465i
$975$	1099.12	+	444.090i	1.12731	+	0.455476i
$976$	−49.9138			−0.0511412
$977$			294.617i			0.301552i	0.988568	+	0.150776i	$0.0481773\pi$
$977$			294.617i			0.301552i	−0.988568	+	0.150776i	$0.951823\pi$
$978$	884.453	−	124.291i	0.904349	−	0.127087i
$979$	1247.74	+	2161.14i	1.27450	+	2.20750i
$980$	17.8273	−	137.451i	0.0181911	−	0.140256i
$981$	374.666	−	107.424i	0.381923	−	0.109505i
$982$	407.087	−	705.096i	0.414549	−	0.718020i
$983$	−539.646	−	311.565i	−0.548978	−	0.316953i	0.199731	−	0.979851i	$-0.435993\pi$
$983$	−539.646	−	311.565i	−0.548978	−	0.316953i	−0.748710	+	0.662898i	$0.769326\pi$
$984$	−11.8279	−	84.1670i	−0.0120202	−	0.0855355i
$985$	108.324	+	187.622i	0.109973	+	0.190479i
$986$	468.821	+	270.674i	0.475477	+	0.274517i
$987$	38.8977	−	80.8391i	0.0394100	−	0.0819039i
$988$	404.809	+	701.149i	0.409725	+	0.709665i
$989$	1717.70	+	991.717i	1.73681	+	1.00275i
$990$	304.897	+	76.0268i	0.307977	+	0.0767948i
$991$	272.200	+	471.464i	0.274672	+	0.475746i	0.970052	−	0.242896i	$-0.0780974\pi$
$991$	272.200	+	471.464i	0.274672	+	0.475746i	−0.695380	+	0.718642i	$0.744764\pi$
$992$		−	182.116i		−	0.183584i
$993$	1445.24	−	1129.12i	1.45543	−	1.13708i
$994$	−91.2563	−	184.602i	−0.0918072	−	0.185717i
$995$	1.37624	+	0.794573i	0.00138316	+	0.000798566i
$996$	−9.69082	+	23.9848i	−0.00972974	+	0.0240811i
$997$	523.979	−	907.559i	0.525556	−	0.910290i	−0.474001	−	0.880524i	$-0.657191\pi$
$997$	523.979	−	907.559i	0.525556	−	0.910290i	0.999557	−	0.0297653i	$-0.00947600\pi$
$998$	−879.526	+	507.794i	−0.881288	+	0.508812i
$999$	−843.316	−	88.6655i	−0.844160	−	0.0887543i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.3.r.a.23.15	yes	32
3.2	odd	2		378.3.r.a.233.4		32
7.4	even	3		126.3.i.a.95.1	yes	32
9.2	odd	6		126.3.i.a.65.1	✓	32
9.7	even	3		378.3.i.a.359.13		32
21.11	odd	6		378.3.i.a.179.12		32
63.11	odd	6	inner	126.3.r.a.11.7	yes	32
63.25	even	3		378.3.r.a.305.12		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.i.a.65.1	✓	32	9.2	odd	6
126.3.i.a.95.1	yes	32	7.4	even	3
126.3.r.a.11.7	yes	32	63.11	odd	6	inner
126.3.r.a.23.15	yes	32	1.1	even	1	trivial
378.3.i.a.179.12		32	21.11	odd	6
378.3.i.a.359.13		32	9.7	even	3
378.3.r.a.233.4		32	3.2	odd	2
378.3.r.a.305.12		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} +(2.36405 - 1.84696i) q^{3} -2.00000 q^{4} +(1.22482 - 0.707152i) q^{5} +(2.61199 + 3.34328i) q^{6} +(3.10205 + 6.27513i) q^{7} -2.82843i q^{8} +(2.17750 - 8.73261i) q^{9} +(1.00006 + 1.73216i) q^{10} +(15.1176 + 8.72813i) q^{11} +(-4.72811 + 3.69391i) q^{12} +(8.59030 - 14.8788i) q^{13} +(-8.87438 + 4.38696i) q^{14} +(1.58947 - 3.93394i) q^{15} +4.00000 q^{16} +(-20.8700 + 12.0493i) q^{17} +(12.3498 + 3.07945i) q^{18} +(11.7810 - 20.4053i) q^{19} +(-2.44965 + 1.41430i) q^{20} +(18.9233 + 9.10540i) q^{21} +(-12.3434 + 21.3795i) q^{22} +(-27.1025 + 15.6476i) q^{23} +(-5.22398 - 6.68655i) q^{24} +(-11.4999 + 19.9184i) q^{25} +(21.0419 + 12.1485i) q^{26} +(-10.9810 - 24.6661i) q^{27} +(-6.20409 - 12.5503i) q^{28} +(-13.7563 + 7.94218i) q^{29} +(5.56344 + 2.24785i) q^{30} -32.1938 q^{31} +5.65685i q^{32} +(51.8592 - 7.28773i) q^{33} +(-17.0403 - 29.5146i) q^{34} +(8.23694 + 5.49231i) q^{35} +(-4.35500 + 17.4652i) q^{36} +(15.7030 - 27.1985i) q^{37} +(28.8574 + 16.6608i) q^{38} +(-7.17265 - 51.0403i) q^{39} +(-2.00013 - 3.46433i) q^{40} +(8.67466 + 5.00832i) q^{41} +(-12.8770 + 26.7616i) q^{42} +(-31.6891 - 54.8871i) q^{43} +(-30.2351 - 17.4563i) q^{44} +(-3.50824 - 12.2357i) q^{45} +(-22.1291 - 38.3287i) q^{46} -4.27193i q^{47} +(9.45621 - 7.38783i) q^{48} +(-29.7546 + 38.9315i) q^{49} +(-28.1688 - 16.2633i) q^{50} +(-27.0832 + 67.0311i) q^{51} +(-17.1806 + 29.7577i) q^{52} +(-45.3154 + 26.1629i) q^{53} +(34.8831 - 15.5295i) q^{54} +24.6885 q^{55} +(17.7488 - 8.77391i) q^{56} +(-9.83677 - 69.9981i) q^{57} +(-11.2319 - 19.4543i) q^{58} -42.1881i q^{59} +(-3.17894 + 7.86789i) q^{60} -12.4785 q^{61} -45.5289i q^{62} +(61.5530 - 13.4249i) q^{63} -8.00000 q^{64} -24.2986i q^{65} +(10.3064 + 73.3400i) q^{66} +96.1382 q^{67} +(41.7399 - 24.0986i) q^{68} +(-35.1712 + 87.0489i) q^{69} +(-7.76730 + 11.6488i) q^{70} +20.8017i q^{71} +(-24.6996 - 6.15889i) q^{72} +(41.6824 + 72.1961i) q^{73} +(38.4644 + 22.2075i) q^{74} +(9.60205 + 68.3278i) q^{75} +(-23.5620 + 40.8105i) q^{76} +(-7.87478 + 121.940i) q^{77} +(72.1819 - 10.1437i) q^{78} -45.1639 q^{79} +(4.89930 - 2.82861i) q^{80} +(-71.5170 - 38.0305i) q^{81} +(-7.08283 + 12.2678i) q^{82} +(3.73381 - 2.15572i) q^{83} +(-37.8466 - 18.2108i) q^{84} +(-17.0414 + 29.5165i) q^{85} +(77.6221 - 44.8151i) q^{86} +(-17.8517 + 44.1830i) q^{87} +(24.6869 - 42.7589i) q^{88} +(123.803 + 71.4779i) q^{89} +(17.3039 - 4.96139i) q^{90} +(120.014 + 7.75043i) q^{91} +(54.2049 - 31.2952i) q^{92} +(-76.1079 + 59.4606i) q^{93} +6.04143 q^{94} -33.3238i q^{95} +(10.4480 + 13.3731i) q^{96} +(-17.5457 - 30.3901i) q^{97} +(-55.0575 - 42.0794i) q^{98} +(109.138 - 113.010i) 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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