LMFDB - Embedded newform 187.3.q.a.2.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [187,3,Mod(2,187)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("187.2"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(187, base_ring=CyclotomicField(40)) chi = DirichletCharacter(H, H._module([4, 35])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	187.q (of order $40$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.09538094354$
Analytic rank:	$0$
Dimension:	$544$
Relative dimension:	$34$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			2.18
Character	$\chi$	$=$	187.2
Dual form			187.3.q.a.94.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0738746 + 0.144987i) q^{2} +(-1.98602 + 3.24089i) q^{3} +(2.33558 - 3.21465i) q^{4} +(-0.527290 + 0.450348i) q^{5} +(-0.616605 - 0.0485279i) q^{6} +(2.22828 + 3.63622i) q^{7} +(1.28150 + 0.202970i) q^{8} +(-2.47320 - 4.85392i) q^{9} +(-0.104248 - 0.0431810i) q^{10} +(10.3607 + 3.69532i) q^{11} +(5.77982 + 13.9537i) q^{12} +(-5.21929 + 16.0633i) q^{13} +(-0.362591 + 0.591695i) q^{14} +(-0.412321 - 2.60329i) q^{15} +(-4.84630 - 14.9154i) q^{16} +(-12.6012 + 11.4109i) q^{17} +(0.521050 - 0.717164i) q^{18} +(-1.13970 + 7.19575i) q^{19} +(0.216184 + 2.74687i) q^{20} -16.2100 q^{21} +(0.229620 + 1.77516i) q^{22} +(15.4753 + 6.41008i) q^{23} +(-3.20289 + 3.75011i) q^{24} +(-3.83564 + 24.2173i) q^{25} +(-2.71455 + 0.429942i) q^{26} +(-13.4608 - 1.05938i) q^{27} +(16.8935 + 1.32954i) q^{28} +(19.4289 + 4.66448i) q^{29} +(0.346984 - 0.252099i) q^{30} +(-0.738604 - 9.38486i) q^{31} +(5.47433 - 5.47433i) q^{32} +(-32.5528 + 26.2390i) q^{33} +(-2.58535 - 0.984039i) q^{34} +(-2.81251 - 0.913840i) q^{35} +(-21.3800 - 3.38626i) q^{36} +(-2.36633 - 0.568104i) q^{37} +(-1.12749 + 0.366342i) q^{38} +(-41.6939 - 48.8173i) q^{39} +(-0.767129 + 0.470098i) q^{40} +(72.0075 - 17.2875i) q^{41} +(-1.19751 - 2.35024i) q^{42} +(-27.3417 - 27.3417i) q^{43} +(36.0774 - 24.6753i) q^{44} +(3.49005 + 1.44563i) q^{45} +(0.213853 + 2.71726i) q^{46} +(10.7190 + 14.7534i) q^{47} +(57.9640 + 13.9159i) q^{48} +(13.9887 - 27.4543i) q^{49} +(-3.79455 + 1.23292i) q^{50} +(-11.9553 - 63.5016i) q^{51} +(39.4479 + 54.2953i) q^{52} +(54.3040 - 27.6693i) q^{53} +(-0.840812 - 2.02990i) q^{54} +(-7.12729 + 2.71743i) q^{55} +(2.11749 + 5.11208i) q^{56} +(-21.0572 - 17.9846i) q^{57} +(0.759017 + 3.16153i) q^{58} +(19.2257 - 3.04505i) q^{59} +(-9.33168 - 4.75473i) q^{60} +(6.03231 - 76.6478i) q^{61} +(1.30612 - 0.800391i) q^{62} +(12.1389 - 19.8090i) q^{63} +(-58.4634 - 18.9959i) q^{64} +(-4.48201 - 10.8205i) q^{65} +(-6.20915 - 2.78134i) q^{66} -124.848 q^{67} +(7.25092 + 67.1596i) q^{68} +(-51.5087 + 37.4232i) q^{69} +(-0.0752782 - 0.475288i) q^{70} +(-73.7553 - 86.3563i) q^{71} +(-2.18420 - 6.72229i) q^{72} +(35.2138 + 8.45408i) q^{73} +(-0.0924436 - 0.385055i) q^{74} +(-70.8680 - 60.5270i) q^{75} +(20.4700 + 20.4700i) q^{76} +(9.64955 + 45.9080i) q^{77} +(3.99776 - 9.65145i) q^{78} +(43.4386 + 37.1001i) q^{79} +(9.27252 + 5.68221i) q^{80} +(58.9854 - 81.1864i) q^{81} +(7.82599 + 9.16306i) q^{82} +(57.4452 + 29.2698i) q^{83} +(-37.8597 + 52.1094i) q^{84} +(1.50562 - 11.6918i) q^{85} +(1.94434 - 5.98405i) q^{86} +(-53.7034 + 53.7034i) q^{87} +(12.5272 + 6.83847i) q^{88} +106.211i q^{89} +(0.0482290 + 0.612807i) q^{90} +(-70.0398 + 16.8151i) q^{91} +(56.7499 - 34.7764i) q^{92} +(31.8822 + 16.2448i) q^{93} +(-1.34720 + 2.64402i) q^{94} +(-2.63964 - 4.30751i) q^{95} +(6.86958 + 28.6139i) q^{96} +(-25.4031 + 1.99927i) q^{97} +5.01394 q^{98} +(-7.68729 - 59.4294i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 544 q - 20 q^{2} - 12 q^{3} - 20 q^{5} - 20 q^{6} - 20 q^{7} - 20 q^{8} + 36 q^{9} + 28 q^{11} - 200 q^{12} + 36 q^{14} + 108 q^{15} + 424 q^{16} - 180 q^{17} - 40 q^{18} - 20 q^{19} - 140 q^{20} + 32 q^{22}+ \cdots - 72 q^{99}+O(q^{100}) $ 544 * q - 20 * q^2 - 12 * q^3 - 20 * q^5 - 20 * q^6 - 20 * q^7 - 20 * q^8 + 36 * q^9 + 28 * q^11 - 200 * q^12 + 36 * q^14 + 108 * q^15 + 424 * q^16 - 180 * q^17 - 40 * q^18 - 20 * q^19 - 140 * q^20 + 32 * q^22 - 48 * q^23 + 460 * q^24 - 84 * q^25 + 132 * q^26 - 228 * q^27 - 20 * q^28 - 20 * q^29 - 100 * q^31 + 24 * q^33 + 96 * q^34 - 40 * q^35 + 164 * q^36 - 332 * q^37 - 20 * q^39 - 760 * q^40 - 560 * q^41 + 276 * q^42 - 240 * q^44 - 32 * q^45 - 20 * q^46 + 252 * q^48 - 472 * q^49 - 40 * q^50 - 20 * q^51 + 280 * q^52 + 92 * q^53 - 160 * q^56 + 1060 * q^57 - 1348 * q^58 - 260 * q^59 - 748 * q^60 - 320 * q^61 - 20 * q^62 + 580 * q^63 + 292 * q^66 + 160 * q^67 - 20 * q^68 - 192 * q^69 - 628 * q^70 - 268 * q^71 - 20 * q^73 - 20 * q^74 + 1116 * q^75 + 732 * q^77 + 1232 * q^78 - 20 * q^79 - 936 * q^80 - 684 * q^82 - 380 * q^83 + 1240 * q^84 - 1320 * q^85 - 632 * q^86 - 412 * q^88 - 20 * q^90 + 1204 * q^91 + 540 * q^92 + 1108 * q^93 - 3800 * q^94 + 360 * q^95 - 20 * q^96 + 652 * q^97 - 72 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{8}\right)$

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 $

$2$	0.0738746	+	0.144987i	0.0369373	+	0.0724936i	0.908738	−	0.417368i	$-0.137047\pi$
$2$	0.0738746	+	0.144987i	0.0369373	+	0.0724936i	−0.871800	+	0.489861i	$0.837047\pi$
$3$	−1.98602	+	3.24089i	−0.662008	+	1.08030i	0.328719	+	0.944428i	$0.393383\pi$
$3$	−1.98602	+	3.24089i	−0.662008	+	1.08030i	−0.990727	+	0.135871i	$0.956617\pi$
$4$	2.33558	−	3.21465i	0.583894	−	0.803662i
$5$	−0.527290	+	0.450348i	−0.105458	+	0.0900697i	−0.700614	−	0.713541i	$-0.747090\pi$
$5$	−0.527290	+	0.450348i	−0.105458	+	0.0900697i	0.595156	+	0.803610i	$0.297090\pi$
$6$	−0.616605	−	0.0485279i	−0.102767	−	0.00808798i
$7$	2.22828	+	3.63622i	0.318325	+	0.519459i	0.971281	−	0.237937i	$-0.0764712\pi$
$7$	2.22828	+	3.63622i	0.318325	+	0.519459i	−0.652956	+	0.757396i	$0.726471\pi$
$8$	1.28150	+	0.202970i	0.160188	+	0.0253712i
$9$	−2.47320	−	4.85392i	−0.274800	−	0.539325i
$10$	−0.104248	−	0.0431810i	−0.0104248	−	0.00431810i
$11$	10.3607	+	3.69532i	0.941884	+	0.335939i
$11$	10.3607	+	3.69532i	0.941884	+	0.335939i
$12$	5.77982	+	13.9537i	0.481652	+	1.16281i
$13$	−5.21929	+	16.0633i	−0.401484	+	1.23564i	0.522312	+	0.852755i	$0.325070\pi$
$13$	−5.21929	+	16.0633i	−0.401484	+	1.23564i	−0.923796	+	0.382886i	$0.874930\pi$
$14$	−0.362591	+	0.591695i	−0.0258994	+	0.0422640i
$15$	−0.412321	−	2.60329i	−0.0274881	−	0.173553i
$16$	−4.84630	−	14.9154i	−0.302894	−	0.932211i
$17$	−12.6012	+	11.4109i	−0.741249	+	0.671230i
$17$	−12.6012	+	11.4109i	−0.741249	+	0.671230i
$18$	0.521050	−	0.717164i	0.0289472	−	0.0398424i
$19$	−1.13970	+	7.19575i	−0.0599840	+	0.378724i	0.939374	+	0.342894i	$0.111407\pi$
$19$	−1.13970	+	7.19575i	−0.0599840	+	0.378724i	−0.999358	+	0.0358294i	$0.988593\pi$
$20$	0.216184	+	2.74687i	0.0108092	+	0.137344i
$21$	−16.2100			−0.771905
$22$	0.229620	+	1.77516i	0.0104373	+	0.0806892i
$23$	15.4753	+	6.41008i	0.672839	+	0.278699i	0.692830	−	0.721101i	$-0.256364\pi$
$23$	15.4753	+	6.41008i	0.672839	+	0.278699i	−0.0199908	+	0.999800i	$0.506364\pi$
$24$	−3.20289	+	3.75011i	−0.133454	+	0.156254i
$25$	−3.83564	+	24.2173i	−0.153426	+	0.968691i
$26$	−2.71455	+	0.429942i	−0.104406	+	0.0165362i
$27$	−13.4608	−	1.05938i	−0.498547	−	0.0392365i
$28$	16.8935	+	1.32954i	0.603338	+	0.0474837i
$29$	19.4289	+	4.66448i	0.669964	+	0.160844i	0.554137	−	0.832425i	$-0.313048\pi$
$29$	19.4289	+	4.66448i	0.669964	+	0.160844i	0.115826	+	0.993269i	$0.463048\pi$
$30$	0.346984	−	0.252099i	0.0115661	−	0.00840329i
$31$	−0.738604	−	9.38486i	−0.0238259	−	0.302737i	−0.997272	−	0.0738193i	$-0.976481\pi$
$31$	−0.738604	−	9.38486i	−0.0238259	−	0.302737i	0.973446	−	0.228918i	$-0.0735188\pi$
$32$	5.47433	−	5.47433i	0.171073	−	0.171073i
$33$	−32.5528	+	26.2390i	−0.986448	+	0.795122i
$34$	−2.58535	−	0.984039i	−0.0760396	−	0.0289423i
$35$	−2.81251	−	0.913840i	−0.0803575	−	0.0261097i
$36$	−21.3800	−	3.38626i	−0.593889	−	0.0940627i
$37$	−2.36633	−	0.568104i	−0.0639547	−	0.0153542i	0.201342	−	0.979521i	$-0.435470\pi$
$37$	−2.36633	−	0.568104i	−0.0639547	−	0.0153542i	−0.265296	+	0.964167i	$0.585470\pi$
$38$	−1.12749	+	0.366342i	−0.0296707	+	0.00964059i
$39$	−41.6939	−	48.8173i	−1.06908	−	1.25173i
$40$	−0.767129	+	0.470098i	−0.0191782	+	0.0117524i
$41$	72.0075	−	17.2875i	1.75628	−	0.421646i	0.777888	−	0.628403i	$-0.216291\pi$
$41$	72.0075	−	17.2875i	1.75628	−	0.421646i	0.978392	+	0.206757i	$0.0662911\pi$
$42$	−1.19751	−	2.35024i	−0.0285121	−	0.0559581i
$43$	−27.3417	−	27.3417i	−0.635854	−	0.635854i	0.313676	−	0.949530i	$-0.398439\pi$
$43$	−27.3417	−	27.3417i	−0.635854	−	0.635854i	−0.949530	+	0.313676i	$0.898439\pi$
$44$	36.0774	−	24.6753i	0.819942	−	0.560803i
$45$	3.49005	+	1.44563i	0.0775566	+	0.0321250i
$46$	0.213853	+	2.71726i	0.00464898	+	0.0590709i
$47$	10.7190	+	14.7534i	0.228064	+	0.313903i	0.907678	−	0.419667i	$-0.137853\pi$
$47$	10.7190	+	14.7534i	0.228064	+	0.313903i	−0.679615	+	0.733569i	$0.737853\pi$
$48$	57.9640	+	13.9159i	1.20758	+	0.289915i
$49$	13.9887	−	27.4543i	0.285483	−	0.560293i
$50$	−3.79455	+	1.23292i	−0.0758910	+	0.0246585i
$51$	−11.9553	−	63.5016i	−0.234417	−	1.24513i
$52$	39.4479	+	54.2953i	0.758613	+	1.04414i
$53$	54.3040	−	27.6693i	1.02460	−	0.522062i	0.140859	−	0.990030i	$-0.455014\pi$
$53$	54.3040	−	27.6693i	1.02460	−	0.522062i	0.883746	+	0.467968i	$0.155014\pi$
$54$	−0.840812	−	2.02990i	−0.0155706	−	0.0375907i
$55$	−7.12729	+	2.71743i	−0.129587	+	0.0494077i
$56$	2.11749	+	5.11208i	0.0378124	+	0.0912872i
$57$	−21.0572	−	17.9846i	−0.369425	−	0.315519i
$58$	0.759017	+	3.16153i	0.0130865	+	0.0545092i
$59$	19.2257	−	3.04505i	0.325859	−	0.0516110i	0.00863815	−	0.999963i	$-0.497250\pi$
$59$	19.2257	−	3.04505i	0.325859	−	0.0516110i	0.317221	+	0.948352i	$0.397250\pi$
$60$	−9.33168	−	4.75473i	−0.155528	−	0.0792454i
$61$	6.03231	−	76.6478i	0.0988904	−	1.25652i	−0.724591	−	0.689179i	$-0.757971\pi$
$61$	6.03231	−	76.6478i	0.0988904	−	1.25652i	0.823482	−	0.567343i	$-0.192029\pi$
$62$	1.30612	−	0.800391i	0.0210664	−	0.0129095i
$63$	12.1389	−	19.8090i	0.192682	−	0.314428i
$64$	−58.4634	−	18.9959i	−0.913490	−	0.296811i
$65$	−4.48201	−	10.8205i	−0.0689540	−	0.166470i
$66$	−6.20915	−	2.78134i	−0.0940780	−	0.0421415i
$67$	−124.848			−1.86341			−0.931704	−	0.363219i	$-0.881678\pi$
$67$	−124.848			−1.86341			−0.931704	+	0.363219i	$0.881678\pi$
$68$	7.25092	+	67.1596i	0.106631	+	0.987641i
$69$	−51.5087	+	37.4232i	−0.746503	+	0.542366i
$70$	−0.0752782	−	0.475288i	−0.00107540	−	0.00678982i
$71$	−73.7553	−	86.3563i	−1.03881	−	1.21629i	−0.975889	−	0.218268i	$-0.929959\pi$
$71$	−73.7553	−	86.3563i	−1.03881	−	1.21629i	−0.0629179	−	0.998019i	$-0.520041\pi$
$72$	−2.18420	−	6.72229i	−0.0303362	−	0.0933651i
$73$	35.2138	+	8.45408i	0.482380	+	0.115809i	0.467340	−	0.884078i	$-0.345212\pi$
$73$	35.2138	+	8.45408i	0.482380	+	0.115809i	0.0150402	+	0.999887i	$0.495212\pi$
$74$	−0.0924436	−	0.385055i	−0.00124924	−	0.00520345i
$75$	−70.8680	−	60.5270i	−0.944907	−	0.807026i
$76$	20.4700	+	20.4700i	0.269341	+	0.269341i
$77$	9.64955	+	45.9080i	0.125319	+	0.596208i
$78$	3.99776	−	9.65145i	0.0512533	−	0.123736i
$79$	43.4386	+	37.1001i	0.549856	+	0.469621i	0.880442	−	0.474155i	$-0.157246\pi$
$79$	43.4386	+	37.1001i	0.549856	+	0.469621i	−0.330586	+	0.943776i	$0.607246\pi$
$80$	9.27252	+	5.68221i	0.115907	+	0.0710276i
$81$	58.9854	−	81.1864i	0.728214	−	1.00230i
$82$	7.82599	+	9.16306i	0.0954389	+	0.111745i
$83$	57.4452	+	29.2698i	0.692110	+	0.352648i	0.764406	−	0.644735i	$-0.223032\pi$
$83$	57.4452	+	29.2698i	0.692110	+	0.352648i	−0.0722955	+	0.997383i	$0.523032\pi$
$84$	−37.8597	+	52.1094i	−0.450711	+	0.620350i
$85$	1.50562	−	11.6918i	0.0177131	−	0.137551i
$86$	1.94434	−	5.98405i	0.0226086	−	0.0695820i
$87$	−53.7034	+	53.7034i	−0.617280	+	0.617280i
$88$	12.5272	+	6.83847i	0.142355	+	0.0777099i
$89$			106.211i			1.19338i	0.802470	+	0.596692i	$0.203519\pi$
$89$			106.211i			1.19338i	−0.802470	+	0.596692i	$0.796481\pi$
$90$	0.0482290	+	0.612807i	0.000535878	+	0.00680897i
$91$	−70.0398	+	16.8151i	−0.769668	+	0.184781i
$92$	56.7499	−	34.7764i	0.616847	−	0.378004i
$93$	31.8822	+	16.2448i	0.342820	+	0.174675i
$94$	−1.34720	+	2.64402i	−0.0143319	+	0.0281279i
$95$	−2.63964	−	4.30751i	−0.0277857	−	0.0453422i
$96$	6.86958	+	28.6139i	0.0715582	+	0.298061i
$97$	−25.4031	+	1.99927i	−0.261888	+	0.0206110i	−0.208723	−	0.977975i	$-0.566931\pi$
$97$	−25.4031	+	1.99927i	−0.261888	+	0.0206110i	−0.0531646	+	0.998586i	$0.516931\pi$
$98$	5.01394			0.0511626
$99$	−7.68729	−	59.4294i	−0.0776494	−	0.600297i
$100$	68.8916	+	68.8916i	0.688916	+	0.688916i
$101$	−145.036	−	47.1251i	−1.43600	−	0.466585i	−0.515353	−	0.856978i	$-0.672339\pi$
$101$	−145.036	−	47.1251i	−1.43600	−	0.466585i	−0.920648	+	0.390393i	$0.872339\pi$
$102$	8.32373	−	6.42452i	0.0816052	−	0.0629855i
$103$	−20.4080	−	14.8273i	−0.198136	−	0.143954i	0.484294	−	0.874905i	$-0.339077\pi$
$103$	−20.4080	−	14.8273i	−0.198136	−	0.143954i	−0.682430	+	0.730951i	$0.739077\pi$
$104$	−9.94889	+	19.5258i	−0.0956624	+	0.187748i
$105$	8.54737	−	7.30014i	0.0814035	−	0.0695252i
$106$	8.02338	+	5.82933i	0.0756923	+	0.0549937i
$107$	69.3821	−	113.221i	0.648431	−	1.05814i	−0.344424	−	0.938814i	$-0.611926\pi$
$107$	69.3821	−	113.221i	0.648431	−	1.05814i	0.992855	−	0.119329i	$-0.0380742\pi$
$108$	−34.8442	+	40.7973i	−0.322631	+	0.377753i
$109$	61.4264	+	25.4436i	0.563545	+	0.233428i	0.646223	−	0.763148i	$-0.276347\pi$
$109$	61.4264	+	25.4436i	0.563545	+	0.233428i	−0.0826784	+	0.996576i	$0.526347\pi$
$110$	−0.920518	−	0.832617i	−0.00836834	−	0.00756924i
$111$	6.54074	−	6.54074i	0.0589256	−	0.0589256i
$112$	43.4366	−	50.8578i	0.387827	−	0.454087i
$113$	122.696	−	29.4568i	1.08581	−	0.260680i	0.349234	−	0.937035i	$-0.386442\pi$
$113$	122.696	−	29.4568i	1.08581	−	0.260680i	0.736575	+	0.676356i	$0.236442\pi$
$114$	1.05194	−	4.38163i	0.00922751	−	0.0384353i
$115$	−11.0467	+	3.58930i	−0.0960586	+	0.0312113i
$116$	60.3724	−	51.5629i	0.520452	−	0.444508i
$117$	90.8785	−	14.3937i	0.776740	−	0.123023i
$118$	1.86178	+	2.56252i	0.0157778	+	0.0217163i
$119$	−69.5716	−	20.3941i	−0.584635	−	0.171379i
$120$		−	3.41981i		−	0.0284984i
$121$	93.6891	+	76.5725i	0.774290	+	0.632830i
$122$	11.5586	−	4.78772i	0.0947425	−	0.0392436i
$123$	−86.9817	+	267.702i	−0.707168	+	2.17644i
$124$	−31.8941	−	19.5447i	−0.257210	−	0.157619i
$125$	−17.9416	−	29.2781i	−0.143533	−	0.234225i
$126$	3.76881	+	0.296611i	0.0299112	+	0.00235406i
$127$	20.9213	−	41.0604i	0.164735	−	0.323310i	−0.793852	−	0.608111i	$-0.791927\pi$
$127$	20.9213	−	41.0604i	0.164735	−	0.323310i	0.958587	+	0.284801i	$0.0919275\pi$
$128$	−6.40918	−	40.4660i	−0.0500717	−	0.316141i
$129$	142.913	−	34.3103i	1.10785	−	0.265972i
$130$	1.23773	−	1.44920i	0.00952101	−	0.0111477i
$131$	−21.3691	+	8.85138i	−0.163123	+	0.0675678i	−0.462751	−	0.886488i	$-0.653138\pi$
$131$	−21.3691	+	8.85138i	−0.163123	+	0.0675678i	0.299628	+	0.954056i	$0.403138\pi$
$132$	8.31958	+	165.929i	0.0630272	+	1.25704i
$133$	−28.7049	+	11.8899i	−0.215826	+	0.0893981i
$134$	−9.22312	−	18.1014i	−0.0688293	−	0.135085i
$135$	7.57482	−	5.50343i	0.0561098	−	0.0407661i
$136$	−18.4645	+	12.0654i	−0.135769	+	0.0887164i
$137$	−14.3974	−	44.3106i	−0.105091	−	0.323435i	0.884661	−	0.466234i	$-0.154390\pi$
$137$	−14.3974	−	44.3106i	−0.105091	−	0.323435i	−0.989752	+	0.142799i	$0.954390\pi$
$138$	−9.23108	−	4.70347i	−0.0668919	−	0.0340831i
$139$	−45.4189	+	189.183i	−0.326755	+	1.36103i	0.531174	+	0.847263i	$0.321751\pi$
$139$	−45.4189	+	189.183i	−0.326755	+	1.36103i	−0.857929	+	0.513769i	$0.828249\pi$
$140$	−9.50651	+	6.90688i	−0.0679036	+	0.0493349i
$141$	−69.1025	+	5.43848i	−0.490088	+	0.0385708i
$142$	7.07191	−	17.0731i	0.0498022	−	0.120233i
$143$	−113.435	+	147.141i	−0.793251	+	1.02896i
$144$	−60.4123	+	60.4123i	−0.419530	+	0.419530i
$145$	−12.3453	+	6.29026i	−0.0851402	+	0.0433811i
$146$	1.37567	+	5.73009i	0.00942241	+	0.0392472i
$147$	61.1948	+	99.8608i	0.416291	+	0.679325i
$148$	−7.35299	+	6.28005i	−0.0496824	+	0.0424328i
$149$	18.3738	+	56.5488i	0.123314	+	0.379522i	0.993590	−	0.113042i	$-0.0360596\pi$
$149$	18.3738	+	56.5488i	0.123314	+	0.379522i	−0.870276	+	0.492565i	$0.836060\pi$
$150$	3.54029	−	14.7464i	0.0236019	−	0.0983090i
$151$	0.709741	−	4.48113i	0.00470027	−	0.0296763i	−0.985227	−	0.171255i	$-0.945218\pi$
$151$	0.709741	−	4.48113i	0.00470027	−	0.0296763i	0.989927	+	0.141579i	$0.0452178\pi$
$152$	−2.92104	+	8.99003i	−0.0192174	+	0.0591450i
$153$	86.5531	+	32.9439i	0.565706	+	0.215320i
$154$	−5.94322	+	4.79050i	−0.0385923	+	0.0311071i
$155$	4.61591	+	4.61591i	0.0297801	+	0.0297801i
$156$	−254.310	+	20.0146i	−1.63019	+	0.128299i
$157$	−45.1278	−	62.1131i	−0.287438	−	0.395625i	0.640742	−	0.767757i	$-0.278627\pi$
$157$	−45.1278	−	62.1131i	−0.287438	−	0.395625i	−0.928180	+	0.372132i	$0.878627\pi$
$158$	−2.17002	+	9.03880i	−0.0137343	+	0.0572076i
$159$	−18.1758	+	230.945i	−0.114313	+	1.45249i
$160$	−0.421205	+	5.35192i	−0.00263253	+	0.0334495i
$161$	11.1748	+	70.5549i	0.0694087	+	0.438229i
$162$	16.1285	+	2.55450i	0.0995587	+	0.0157685i
$163$	−191.608	−	163.649i	−1.17551	−	1.00398i	−0.999809	−	0.0195386i	$-0.993780\pi$
$163$	−191.608	−	163.649i	−1.17551	−	1.00398i	−0.175703	−	0.984443i	$-0.556220\pi$
$164$	112.606	−	271.855i	0.686622	−	1.65765i
$165$	5.34807	−	28.4957i	0.0324125	−	0.172701i
$166$			10.4911i			0.0631994i
$167$	138.908	−	10.9323i	0.831786	−	0.0654630i	0.344588	−	0.938754i	$-0.388019\pi$
$167$	138.908	−	10.9323i	0.831786	−	0.0654630i	0.487199	+	0.873291i	$0.338019\pi$
$168$	−20.7731	−	3.29014i	−0.123650	−	0.0195842i
$169$	−94.0657	−	68.3427i	−0.556602	−	0.404395i
$170$	1.80639	−	0.645433i	0.0106258	−	0.00379667i
$171$	37.7463	−	12.2645i	0.220739	−	0.0717224i
$172$	−151.753	+	24.0352i	−0.882282	+	0.139740i
$173$	−41.1561	−	25.2205i	−0.237897	−	0.145783i	0.398441	−	0.917194i	$-0.369551\pi$
$173$	−41.1561	−	25.2205i	−0.237897	−	0.145783i	−0.636338	+	0.771411i	$0.719551\pi$
$174$	−11.7536	−	3.81898i	−0.0675496	−	0.0219482i
$175$	−96.6061	+	40.0156i	−0.552035	+	0.228660i
$176$	4.90600	−	172.443i	0.0278750	−	0.979788i
$177$	−28.3140	+	68.3559i	−0.159966	+	0.386192i
$178$	−15.3993	+	7.84632i	−0.0865127	+	0.0440804i
$179$	30.0142	−	189.502i	0.167677	−	1.05867i	−0.750028	−	0.661407i	$-0.769960\pi$
$179$	30.0142	−	189.502i	0.167677	−	1.05867i	0.917704	−	0.397264i	$-0.130040\pi$
$180$	12.7985	−	7.84290i	0.0711025	−	0.0435717i
$181$	−25.8474	+	328.422i	−0.142803	+	1.81449i	0.341820	+	0.939765i	$0.388957\pi$
$181$	−25.8474	+	328.422i	−0.142803	+	1.81449i	−0.484624	+	0.874723i	$0.661043\pi$
$182$	−7.61213	−	8.91266i	−0.0418249	−	0.0489706i
$183$	236.427	+	171.774i	1.29195	+	0.938658i
$184$	18.5305	+	11.3555i	0.100709	+	0.0617149i
$185$	1.50358	−	0.766115i	0.00812749	−	0.00414116i
$186$			5.82259i			0.0313043i
$187$	−172.725	+	71.6597i	−0.923662	+	0.383207i
$188$	72.4621			0.385437
$189$	−26.1421	−	51.3068i	−0.138318	−	0.271465i
$190$	0.429531	−	0.700930i	0.00226069	−	0.00368911i
$191$	19.1414	−	26.3459i	0.100217	−	0.137937i	−0.755963	−	0.654614i	$-0.772831\pi$
$191$	19.1414	−	26.3459i	0.100217	−	0.137937i	0.856180	+	0.516677i	$0.172831\pi$
$192$	177.673	−	151.747i	0.925382	−	0.790351i
$193$	96.5875	+	7.60160i	0.500453	+	0.0393865i	0.326174	−	0.945310i	$-0.394240\pi$
$193$	96.5875	+	7.60160i	0.500453	+	0.0393865i	0.174279	+	0.984696i	$0.444240\pi$
$194$	−2.16651	−	3.53543i	−0.0111676	−	0.0182239i
$195$	43.9696	+	6.96410i	0.225485	+	0.0357133i
$196$	−55.5843	−	109.090i	−0.283594	−	0.556584i
$197$	169.807	+	70.3362i	0.861963	+	0.357037i	0.769475	−	0.638677i	$-0.220518\pi$
$197$	169.807	+	70.3362i	0.861963	+	0.357037i	0.0924879	+	0.995714i	$0.470518\pi$
$198$	8.04861	−	5.50489i	0.0406495	−	0.0278025i
$199$	−124.567	−	300.732i	−0.625967	−	1.51122i	−0.844593	−	0.535409i	$-0.820158\pi$
$199$	−124.567	−	300.732i	−0.625967	−	1.51122i	0.218626	−	0.975809i	$-0.429842\pi$
$200$	−9.83075	+	30.2559i	−0.0491537	+	0.151280i
$201$	247.952	−	404.620i	1.23359	−	2.01304i
$202$	−3.88196	−	24.5097i	−0.0192176	−	0.121335i
$203$	26.3320	+	81.0416i	0.129714	+	0.399219i
$204$	−232.058	−	109.881i	−1.13754	−	0.538632i
$205$	−30.1835	+	41.5440i	−0.147236	+	0.202653i
$206$	0.642131	−	4.05426i	0.00311714	−	0.0196809i
$207$	−7.15944	−	90.9693i	−0.0345867	−	0.439465i
$208$	264.885			1.27349
$209$	−38.3987	+	70.3416i	−0.183726	+	0.336563i
$210$	1.68986	+	0.699963i	0.00804696	+	0.00333316i
$211$	172.292	−	201.728i	0.816551	−	0.956059i	−0.183083	−	0.983097i	$-0.558608\pi$
$211$	172.292	−	201.728i	0.816551	−	0.956059i	0.999634	+	0.0270388i	$0.00860775\pi$
$212$	37.8843	−	239.192i	0.178699	−	1.12826i
$213$	426.352	−	67.5274i	2.00165	−	0.317030i
$214$	21.5412	+	1.69533i	0.100660	+	0.00792210i
$215$	26.7303	+	2.10372i	0.124327	+	0.00978474i
$216$	−17.0349	−	4.08973i	−0.0788655	−	0.0189339i
$217$	32.4796	−	23.5978i	0.149675	−	0.108746i
$218$	0.848851	+	10.7857i	0.00389381	+	0.0494756i
$219$	−97.3341	+	97.3341i	−0.444448	+	0.444448i
$220$	−7.91077	+	29.2585i	−0.0359581	+	0.132993i
$221$	−117.528	−	261.975i	−0.531800	−	1.18541i
$222$	1.43152	+	0.465129i	0.00644828	+	0.00209517i
$223$	82.5748	+	13.0786i	0.370291	+	0.0586483i	0.338807	−	0.940856i	$-0.389977\pi$
$223$	82.5748	+	13.0786i	0.370291	+	0.0586483i	0.0314839	+	0.999504i	$0.489977\pi$
$224$	32.1042	+	7.70753i	0.143322	+	0.0344086i
$225$	127.035	−	41.2762i	0.564601	−	0.183450i
$226$	13.3350	+	15.6133i	0.0590045	+	0.0690854i
$227$	−34.9880	+	21.4407i	−0.154132	+	0.0944523i	−0.597426	−	0.801924i	$-0.703810\pi$
$227$	−34.9880	+	21.4407i	−0.154132	+	0.0944523i	0.443294	+	0.896376i	$0.353810\pi$
$228$	−106.995	+	25.6872i	−0.469275	+	0.112663i
$229$	−103.134	−	202.412i	−0.450368	−	0.883896i	−0.998860	−	0.0477405i	$-0.984798\pi$
$229$	−103.134	−	202.412i	−0.450368	−	0.883896i	0.548492	−	0.836156i	$-0.315202\pi$
$230$	−1.33648	−	1.33648i	−0.00581077	−	0.00581077i
$231$	−167.947	−	59.9012i	−0.727045	−	0.259313i
$232$	23.9514	+	9.92101i	0.103239	+	0.0427630i
$233$	1.43443	+	18.2262i	0.00615637	+	0.0782241i	0.999228	−	0.0392866i	$-0.0125085\pi$
$233$	1.43443	+	18.2262i	0.00615637	+	0.0782241i	−0.993072	+	0.117511i	$0.962509\pi$
$234$	8.80053	+	12.1129i	0.0376091	+	0.0517645i
$235$	−12.2962	−	2.95206i	−0.0523243	−	0.0125619i
$236$	35.1143	−	68.9157i	0.148789	−	0.292016i
$237$	−206.508	+	67.0984i	−0.871340	+	0.283115i
$238$	−2.18269	−	11.5936i	−0.00917097	−	0.0487126i
$239$	−45.3678	−	62.4434i	−0.189823	−	0.261269i	0.703489	−	0.710707i	$-0.251625\pi$
$239$	−45.3678	−	62.4434i	−0.189823	−	0.261269i	−0.893312	+	0.449437i	$0.851625\pi$
$240$	−36.8309	+	18.7663i	−0.153462	+	0.0781928i
$241$	142.172	+	343.234i	0.589925	+	1.42421i	0.883574	+	0.468292i	$0.155131\pi$
$241$	142.172	+	343.234i	0.589925	+	1.42421i	−0.293648	+	0.955914i	$0.594869\pi$
$242$	−4.18077	+	19.2405i	−0.0172759	+	0.0795061i
$243$	99.4660	+	240.132i	0.409325	+	0.988198i
$244$	−232.307	−	198.409i	−0.952077	−	0.813150i
$245$	4.98792	+	20.7762i	0.0203589	+	0.0848007i
$246$	−45.2391	+	7.16517i	−0.183899	+	0.0291267i
$247$	−109.639	−	55.8640i	−0.443884	−	0.226170i
$248$	0.958320	−	12.1766i	0.00386419	−	0.0490992i
$249$	−208.948	+	128.043i	−0.839147	+	0.514230i
$250$	2.91952	−	4.76422i	0.0116781	−	0.0190569i
$251$	7.25375	+	2.35689i	0.0288994	+	0.00938998i	0.323431	−	0.946252i	$-0.395164\pi$
$251$	7.25375	+	2.35689i	0.0288994	+	0.00938998i	−0.294532	+	0.955642i	$0.595164\pi$
$252$	−35.3274	−	85.2878i	−0.140188	−	0.338444i
$253$	136.648	+	123.599i	0.540110	+	0.488535i
$254$	7.49879			0.0295228
$255$	34.9017	+	28.0997i	0.136870	+	0.110195i
$256$	−193.534	+	140.611i	−0.755993	+	0.549261i
$257$	−65.5861	−	414.095i	−0.255199	−	1.61126i	−0.698989	−	0.715132i	$-0.746366\pi$
$257$	−65.5861	−	414.095i	−0.255199	−	1.61126i	0.443790	−	0.896131i	$-0.353634\pi$
$258$	15.5322	+	18.1859i	0.0602023	+	0.0704878i
$259$	−3.20708	−	9.87036i	−0.0123825	−	0.0381095i
$260$	−45.2523	−	10.8641i	−0.174047	−	0.0417850i
$261$	−25.4106	−	105.843i	−0.0973586	−	0.405528i
$262$	−2.86197	−	2.44436i	−0.0109236	−	0.00932960i
$263$	17.8793	+	17.8793i	0.0679821	+	0.0679821i	0.740280	−	0.672298i	$-0.234693\pi$
$263$	17.8793	+	17.8793i	0.0679821	+	0.0679821i	−0.672298	+	0.740280i	$0.734693\pi$
$264$	−47.0421	+	27.0181i	−0.178190	+	0.102341i
$265$	−16.1732	+	39.0455i	−0.0610308	+	0.147341i
$266$	−3.84445	−	3.28347i	−0.0144528	−	0.0123439i
$267$	−344.219	−	210.938i	−1.28921	−	0.790030i
$268$	−291.593	+	401.343i	−1.08803	+	1.49755i
$269$	158.152	+	185.172i	0.587924	+	0.688371i	0.972013	−	0.234925i	$-0.0754845\pi$
$269$	158.152	+	185.172i	0.587924	+	0.688371i	−0.384089	+	0.923296i	$0.625485\pi$
$270$	1.35751	+	0.691687i	0.00502783	+	0.00256181i
$271$	222.425	−	306.141i	0.820755	−	1.12967i	−0.168819	−	0.985647i	$-0.553995\pi$
$271$	222.425	−	306.141i	0.820755	−	1.12967i	0.989574	−	0.144026i	$-0.0460048\pi$
$272$	231.267	+	132.651i	0.850248	+	0.487689i
$273$	84.6047	−	260.387i	0.309907	−	0.953797i
$274$	5.36087	−	5.36087i	0.0195652	−	0.0195652i
$275$	−129.231	+	236.735i	−0.469930	+	0.860853i
$276$			252.987i			0.916620i
$277$	30.9950	+	393.829i	0.111895	+	1.42177i	0.754868	+	0.655877i	$0.227701\pi$
$277$	30.9950	+	393.829i	0.111895	+	1.42177i	−0.642972	+	0.765889i	$0.722299\pi$
$278$	−30.7845	+	7.39070i	−0.110735	+	0.0265852i
$279$	−43.7267	+	26.7957i	−0.156726	+	0.0960421i
$280$	−3.41875	−	1.74194i	−0.0122098	−	0.00622122i
$281$	−89.6857	+	176.018i	−0.319166	+	0.626399i	−0.993729	−	0.111819i	$-0.964332\pi$
$281$	−89.6857	+	176.018i	−0.319166	+	0.626399i	0.674562	+	0.738218i	$0.264332\pi$
$282$	−5.89343	−	9.61720i	−0.0208987	−	0.0341036i
$283$	−69.0483	−	287.607i	−0.243987	−	1.01628i	−0.951028	−	0.309106i	$-0.899970\pi$
$283$	−69.0483	−	287.607i	−0.243987	−	1.01628i	0.707041	−	0.707173i	$-0.250030\pi$
$284$	−449.866	+	35.4052i	−1.58404	+	0.124666i
$285$	19.2026			0.0673775
$286$	−29.7135	−	5.57663i	−0.103893	−	0.0194987i
$287$	223.313	+	223.313i	0.778096	+	0.778096i
$288$	−40.1111	−	13.0329i	−0.139275	−	0.0452531i
$289$	28.5819	−	287.583i	0.0988993	−	0.995097i
$290$	−1.82401	−	1.32522i	−0.00628970	−	0.00456974i
$291$	43.9718	−	86.2994i	0.151106	−	0.296562i
$292$	109.421	−	93.4546i	0.374731	−	0.320050i
$293$	441.019	+	320.419i	1.50519	+	1.09358i	0.968258	+	0.249953i	$0.0804153\pi$
$293$	441.019	+	320.419i	1.50519	+	1.09358i	0.536928	+	0.843628i	$0.319585\pi$
$294$	−9.95779	+	16.2496i	−0.0338700	+	0.0552709i
$295$	−8.76618	+	10.2639i	−0.0297159	+	0.0347928i
$296$	−2.91714	−	1.20832i	−0.00985520	−	0.00408216i
$297$	−135.548	−	60.7179i	−0.456392	−	0.204437i
$298$	−6.84149	+	6.84149i	−0.0229580	+	0.0229580i
$299$	−183.737	+	215.129i	−0.614506	+	0.719494i
$300$	−360.090	+	86.4501i	−1.20030	+	0.288167i
$301$	38.4955	−	160.345i	0.127892	−	0.532708i
$302$	0.702138	−	0.228138i	0.00232496	−	0.000755425i
$303$	440.773	−	376.455i	1.45470	−	1.24243i
$304$	112.851	−	17.8738i	0.371219	−	0.0587954i
$305$	31.3374	+	43.1323i	0.102746	+	0.141417i
$306$	1.61763	+	14.9828i	0.00528637	+	0.0489634i
$307$			428.553i			1.39594i	0.716129	+	0.697968i	$0.245912\pi$
$307$			428.553i			1.39594i	−0.716129	+	0.697968i	$0.754088\pi$
$308$	170.115	+	76.2018i	0.552322	+	0.247409i
$309$	88.5844	−	36.6928i	0.286681	−	0.118747i
$310$	−0.328249	+	1.01025i	−0.00105887	+	0.00325886i
$311$	445.836	+	273.209i	1.43356	+	0.878484i	0.999746	−	0.0225206i	$-0.00716915\pi$
$311$	445.836	+	273.209i	1.43356	+	0.878484i	0.433809	+	0.901005i	$0.357169\pi$
$312$	−43.5223	−	71.0220i	−0.139495	−	0.227635i
$313$	−291.041	−	22.9054i	−0.929843	−	0.0731803i	−0.395517	−	0.918459i	$-0.629435\pi$
$313$	−291.041	−	22.9054i	−0.929843	−	0.0731803i	−0.534326	+	0.845278i	$0.679435\pi$
$314$	5.67180	−	11.1315i	0.0180631	−	0.0354507i
$315$	2.52019	+	15.9118i	0.00800059	+	0.0505137i
$316$	220.718	−	52.9897i	0.698474	−	0.167689i
$317$	68.0594	−	79.6873i	0.214698	−	0.251380i	−0.642597	−	0.766204i	$-0.722143\pi$
$317$	68.0594	−	79.6873i	0.214698	−	0.251380i	0.857295	+	0.514825i	$0.172143\pi$
$318$	−34.8269	+	14.4258i	−0.109518	+	0.0453640i
$319$	184.061	+	120.124i	0.576994	+	0.376563i
$320$	39.3819	−	16.3125i	0.123069	−	0.0509767i
$321$	229.144	+	449.720i	0.713844	+	1.40100i
$322$	−9.40402	+	6.83242i	−0.0292050	+	0.0212187i
$323$	−67.7486	−	103.680i	−0.209748	−	0.320992i
$324$	−123.221	−	379.234i	−0.380311	−	1.17048i
$325$	−368.991	−	188.010i	−1.13536	−	0.578493i
$326$	9.57201	−	39.8703i	0.0293620	−	0.122301i
$327$	−204.454	+	148.545i	−0.625243	+	0.454266i
$328$	95.7865	−	7.53856i	0.292032	−	0.0229834i
$329$	−29.7618	+	71.8513i	−0.0904613	+	0.218393i
$330$	4.52659	−	1.32971i	0.0137169	−	0.00402941i
$331$	−164.088	+	164.088i	−0.495733	+	0.495733i	−0.910107	−	0.414374i	$-0.864001\pi$
$331$	−164.088	+	164.088i	−0.495733	+	0.495733i	0.414374	+	0.910107i	$0.364001\pi$
$332$	228.260	−	116.304i	0.687529	−	0.350313i
$333$	3.09486	+	12.8910i	0.00929386	+	0.0387117i
$334$	11.8469	+	19.3323i	0.0354696	+	0.0578811i
$335$	65.8313	−	56.2252i	0.196511	−	0.167836i
$336$	78.5585	+	241.778i	0.233805	+	0.719578i
$337$	101.833	−	424.163i	0.302174	−	1.25864i	−0.590167	−	0.807281i	$-0.700938\pi$
$337$	101.833	−	424.163i	0.302174	−	1.25864i	0.892340	−	0.451363i	$-0.149062\pi$
$338$	2.95975	−	18.6871i	0.00875665	−	0.0552873i
$339$	−148.212	+	456.148i	−0.437202	+	1.34557i
$340$	−34.0685	−	32.1471i	−0.100202	−	0.0945504i
$341$	27.0276	−	99.9633i	0.0792599	−	0.293147i
$342$	4.56669	+	4.56669i	0.0133529	+	0.0133529i
$343$	339.324	−	26.7054i	0.989284	−	0.0778583i
$344$	−29.4889	−	40.5879i	−0.0857234	−	0.117988i
$345$	10.3065	−	42.9298i	0.0298740	−	0.124434i
$346$	0.616255	−	7.83027i	0.00178108	−	0.0226308i
$347$	−27.2523	+	346.273i	−0.0785368	+	0.997904i	0.823802	+	0.566877i	$0.191849\pi$
$347$	−27.2523	+	346.273i	−0.0785368	+	0.997904i	−0.902339	+	0.431027i	$0.858151\pi$
$348$	47.2090	+	298.066i	0.135658	+	0.856511i
$349$	154.864	+	24.5281i	0.443737	+	0.0702811i	0.374305	−	0.927306i	$-0.377881\pi$
$349$	154.864	+	24.5281i	0.443737	+	0.0702811i	0.0694322	+	0.997587i	$0.477881\pi$
$350$	−12.9385	−	11.0505i	−0.0369671	−	0.0315729i
$351$	87.2729	−	210.695i	0.248641	−	0.600272i
$352$	76.9475	−	36.4886i	0.218601	−	0.103661i
$353$		−	338.465i		−	0.958824i	−0.877590	−	0.479412i	$-0.840850\pi$
$353$		−	338.465i		−	0.958824i	0.877590	−	0.479412i	$-0.159150\pi$
$354$	−12.0024	+	0.944611i	−0.0339051	+	0.00266839i
$355$	77.7809	+	12.3193i	0.219101	+	0.0347022i
$356$	341.431	+	248.064i	0.959077	+	0.696810i
$357$	204.266	−	184.971i	0.572173	−	0.518126i
$358$	29.6926	−	9.64772i	0.0829403	−	0.0269489i
$359$	−411.651	+	65.1991i	−1.14666	+	0.181613i	−0.700711	−	0.713445i	$-0.747134\pi$
$359$	−411.651	+	65.1991i	−1.14666	+	0.181613i	−0.445949	+	0.895058i	$0.647134\pi$
$360$	4.17908	+	2.56094i	0.0116086	+	0.00711373i
$361$	292.851	+	95.1532i	0.811223	+	0.263582i
$362$	−49.5265	+	20.5145i	−0.136813	+	0.0566700i
$363$	−434.232	+	151.562i	−1.19623	+	0.417526i
$364$	−109.529	+	264.426i	−0.300903	+	0.726445i
$365$	−22.3751	+	11.4007i	−0.0613018	+	0.0312348i
$366$	−7.43911	+	46.9687i	−0.0203254	+	0.128330i
$367$	−501.864	+	307.542i	−1.36748	+	0.837990i	−0.995904	−	0.0904140i	$-0.971181\pi$
$367$	−501.864	+	307.542i	−1.36748	+	0.837990i	−0.371572	+	0.928404i	$0.621181\pi$
$368$	20.6108	−	261.885i	0.0560076	−	0.711644i
$369$	−262.001	−	306.764i	−0.710029	−	0.831338i
$370$	0.222154	+	0.161404i	0.000600415	+	0.000436227i
$371$	221.616	+	135.806i	0.597347	+	0.366055i
$372$	126.685	−	64.5491i	0.340550	−	0.173519i
$373$		−	206.316i		−	0.553126i	−0.960996	−	0.276563i	$-0.910805\pi$
$373$		−	206.316i		−	0.553126i	0.960996	−	0.276563i	$-0.0891955\pi$
$374$	−23.1497	−	19.7491i	−0.0618977	−	0.0528050i
$375$	130.520			0.348053
$376$	10.7419	+	21.0822i	0.0285689	+	0.0560696i
$377$	−176.332	+	287.748i	−0.467725	+	0.763258i
$378$	5.50759	−	7.58055i	0.0145703	−	0.0200544i
$379$	−195.649	+	167.100i	−0.516223	+	0.440896i	−0.869001	−	0.494811i	$-0.835237\pi$
$379$	−195.649	+	167.100i	−0.516223	+	0.440896i	0.352778	+	0.935707i	$0.385237\pi$
$380$	−20.0122	−	1.57499i	−0.0526637	−	0.00414472i
$381$	91.5223	+	149.351i	0.240216	+	0.391997i
$382$	5.23389	+	0.828966i	0.0137013	+	0.00217007i
$383$	−126.945	−	249.144i	−0.331449	−	0.650506i	0.663795	−	0.747914i	$-0.268945\pi$
$383$	−126.945	−	249.144i	−0.331449	−	0.650506i	−0.995244	+	0.0974084i	$0.968945\pi$
$384$	143.875	+	59.5949i	0.374674	+	0.155195i
$385$	−25.7627	−	19.8612i	−0.0669161	−	0.0515875i
$386$	6.03323	+	14.5655i	0.0156301	+	0.0377345i
$387$	−65.0931	+	200.336i	−0.168199	+	0.517664i
$388$	−52.9040	+	86.3315i	−0.136351	+	0.222504i
$389$	41.5228	+	262.165i	0.106742	+	0.673945i	0.981799	+	0.189924i	$0.0608242\pi$
$389$	41.5228	+	262.165i	0.106742	+	0.673945i	−0.875056	+	0.484021i	$0.839176\pi$
$390$	2.23853	+	6.88950i	0.00573983	+	0.0176654i
$391$	−268.153	+	95.8125i	−0.685812	+	0.245045i
$392$	23.4989	−	32.3435i	0.0599462	−	0.0825088i
$393$	13.7532	−	86.8341i	0.0349954	−	0.220952i
$394$	2.34656	+	29.8158i	0.00595573	+	0.0756747i
$395$	−39.6127			−0.100285
$396$	−208.999	−	114.090i	−0.527775	−	0.288106i
$397$	71.5292	+	29.6284i	0.180174	+	0.0746307i	0.470947	−	0.882162i	$-0.343912\pi$
$397$	71.5292	+	29.6284i	0.180174	+	0.0746307i	−0.290773	+	0.956792i	$0.593912\pi$
$398$	34.3999	−	40.2772i	0.0864320	−	0.101199i
$399$	18.4745	−	116.643i	0.0463019	−	0.292339i
$400$	379.799	−	60.1542i	0.949496	−	0.150385i
$401$	−215.115	−	16.9299i	−0.536447	−	0.0422193i	−0.192657	−	0.981266i	$-0.561711\pi$
$401$	−215.115	−	16.9299i	−0.536447	−	0.0422193i	−0.343789	+	0.939047i	$0.611711\pi$
$402$	76.9821	+	6.05862i	0.191498	+	0.0150712i
$403$	154.607	+	37.1179i	0.383640	+	0.0921039i
$404$	−490.234	+	356.176i	−1.21345	+	0.881623i
$405$	5.45975	+	69.3727i	0.0134809	+	0.171291i
$406$	−9.80472	+	9.80472i	−0.0241496	+	0.0241496i
$407$	−22.4175	−	14.6303i	−0.0550799	−	0.0359467i
$408$	−2.43177	−	83.8039i	−0.00596021	−	0.205402i
$409$	−435.394	−	141.468i	−1.06453	−	0.345888i	−0.276177	−	0.961107i	$-0.589068\pi$
$409$	−435.394	−	141.468i	−1.06453	−	0.345888i	−0.788356	+	0.615219i	$0.789068\pi$
$410$	−8.25313	−	1.30717i	−0.0201296	−	0.00318821i
$411$	172.200	+	41.3415i	0.418977	+	0.100588i
$412$	−95.3289	+	30.9742i	−0.231381	+	0.0751802i
$413$	53.9126	+	63.1235i	0.130539	+	0.152841i
$414$	12.6605	−	7.75835i	0.0305809	−	0.0187400i
$415$	−43.4719	+	10.4367i	−0.104751	+	0.0251486i
$416$	59.3639	+	116.508i	0.142702	+	0.280068i
$417$	−522.920	−	522.920i	−1.25401	−	1.25401i
$418$	−13.0353	−	0.370855i	−0.0311850	−	0.000887213i
$419$	−222.075	−	91.9864i	−0.530011	−	0.219538i	0.101597	−	0.994826i	$-0.467605\pi$
$419$	−222.075	−	91.9864i	−0.530011	−	0.219538i	−0.631608	+	0.775288i	$0.717605\pi$
$420$	−3.50434	−	44.5268i	−0.00834366	−	0.106016i
$421$	422.986	+	582.190i	1.00472	+	1.38287i	0.922387	+	0.386268i	$0.126236\pi$
$421$	422.986	+	582.190i	1.00472	+	1.38287i	0.0823296	+	0.996605i	$0.473764\pi$
$422$	41.9761	+	10.0776i	0.0994693	+	0.0238805i
$423$	45.1018	−	88.5173i	0.106624	−	0.209261i
$424$	75.2066	−	24.4361i	0.177374	−	0.0576324i
$425$	−228.008	−	348.936i	−0.536489	−	0.821025i
$426$	41.2872	+	56.8269i	0.0969183	+	0.133397i
$427$	292.150	−	148.858i	0.684191	−	0.348613i
$428$	−201.919	−	487.476i	−0.471774	−	1.13896i
$429$	−251.583	−	659.855i	−0.586441	−	1.53812i
$430$	1.66968	+	4.03096i	0.00388297	+	0.00937433i
$431$	11.4471	+	9.77678i	0.0265595	+	0.0226839i	0.662629	−	0.748948i	$-0.269441\pi$
$431$	11.4471	+	9.77678i	0.0265595	+	0.0226839i	−0.636069	+	0.771632i	$0.719441\pi$
$432$	49.4338	+	205.906i	0.114430	+	0.476635i
$433$	630.085	−	99.7957i	1.45516	−	0.230475i	0.621789	−	0.783185i	$-0.286406\pi$
$433$	630.085	−	99.7957i	1.45516	−	0.230475i	0.833374	+	0.552710i	$0.186406\pi$
$434$	5.82079	+	2.96584i	0.0134120	+	0.00683373i
$435$	4.13204	−	52.5025i	0.00949894	−	0.120695i
$436$	225.258	−	138.039i	0.516648	−	0.316602i
$437$	−63.7625	+	104.051i	−0.145909	+	0.238103i
$438$	−21.3027	−	6.92167i	−0.0486363	−	0.0158029i
$439$	94.1941	+	227.405i	0.214565	+	0.518006i	0.994114	−	0.108335i	$-0.0345519\pi$
$439$	94.1941	+	227.405i	0.214565	+	0.518006i	−0.779549	+	0.626341i	$0.784552\pi$
$440$	−9.68518	+	2.03576i	−0.0220118	+	0.00462672i
$441$	−167.858			−0.380631
$442$	29.3006	−	36.3933i	0.0662910	−	0.0823378i
$443$	−280.845	+	204.046i	−0.633962	+	0.460601i	−0.857771	−	0.514033i	$-0.828151\pi$
$443$	−280.845	+	204.046i	−0.633962	+	0.460601i	0.223808	+	0.974633i	$0.428151\pi$
$444$	−5.74976	−	36.3026i	−0.0129499	−	0.0817626i
$445$	−47.8320	−	56.0041i	−0.107488	−	0.125852i
$446$	4.20396	+	12.9385i	0.00942592	+	0.0290100i
$447$	−219.760	−	52.7596i	−0.491632	−	0.118030i
$448$	−61.1993	−	254.914i	−0.136606	−	0.569004i
$449$	152.666	+	130.389i	0.340012	+	0.290398i	0.803015	−	0.595959i	$-0.203228\pi$
$449$	152.666	+	130.389i	0.340012	+	0.290398i	−0.463003	+	0.886357i	$0.653228\pi$
$450$	15.3692	+	15.3692i	0.0341538	+	0.0341538i
$451$	809.932	+	86.9804i	1.79586	+	0.192861i
$452$	191.874	−	463.224i	0.424500	−	1.02483i
$453$	13.1133	+	11.1998i	0.0289477	+	0.0247237i
$454$	−5.69335	−	3.48889i	−0.0125404	−	0.00768477i
$455$	29.3586	−	40.4087i	0.0645245	−	0.0888103i
$456$	−23.3345	−	27.3212i	−0.0511722	−	0.0599149i
$457$	202.008	+	102.928i	0.442030	+	0.225226i	0.660817	−	0.750547i	$-0.270210\pi$
$457$	202.008	+	102.928i	0.442030	+	0.225226i	−0.218787	+	0.975773i	$0.570210\pi$
$458$	21.7282	−	29.9063i	0.0474414	−	0.0652975i
$459$	181.711	−	140.250i	0.395884	−	0.305556i
$460$	−14.2622	+	43.8944i	−0.0310047	+	0.0954227i
$461$	−275.492	+	275.492i	−0.597597	+	0.597597i	−0.939672	−	0.342075i	$-0.888870\pi$
$461$	−275.492	+	275.492i	−0.597597	+	0.597597i	0.342075	+	0.939672i	$0.388870\pi$
$462$	−3.72214	−	28.7754i	−0.00805658	−	0.0622844i
$463$			82.2263i			0.177595i	0.996050	+	0.0887973i	$0.0283023\pi$
$463$			82.2263i			0.177595i	−0.996050	+	0.0887973i	$0.971698\pi$
$464$	−24.5861	−	312.395i	−0.0529872	−	0.673266i
$465$	−24.1270	+	5.79238i	−0.0518860	+	0.0124567i
$466$	−2.53660	+	1.55443i	−0.00544335	+	0.00333569i
$467$	−654.082	−	333.272i	−1.40060	−	0.713644i	−0.419615	−	0.907702i	$-0.637835\pi$
$467$	−654.082	−	333.272i	−1.40060	−	0.713644i	−0.980990	+	0.194058i	$0.937835\pi$
$468$	165.983	−	325.760i	0.354665	−	0.696068i
$469$	−278.196	−	453.975i	−0.593169	−	0.967965i
$470$	−0.480367	−	2.00087i	−0.00102206	−	0.00425718i
$471$	290.927	−	22.8964i	0.617679	−	0.0486124i
$472$	25.2558			0.0535080
$473$	−182.243	−	384.316i	−0.385292	−	0.812508i
$474$	−24.9841	−	24.9841i	−0.0527090	−	0.0527090i
$475$	−169.890	−	55.2006i	−0.357663	−	0.116212i
$476$	−228.050	+	176.016i	−0.479096	+	0.369781i
$477$	−268.609	−	195.156i	−0.563122	−	0.409132i
$478$	5.70196	−	11.1907i	0.0119288	−	0.0234116i
$479$	195.099	−	166.630i	0.407304	−	0.347871i	−0.422071	−	0.906563i	$-0.638697\pi$
$479$	195.099	−	166.630i	0.407304	−	0.347871i	0.829375	+	0.558692i	$0.188697\pi$
$480$	−16.5085	−	11.9941i	−0.0343927	−	0.0249877i
$481$	21.4762	−	35.0460i	0.0446491	−	0.0728606i
$482$	−39.2616	+	45.9694i	−0.0814555	+	0.0953722i
$483$	−250.855	−	103.907i	−0.519368	−	0.215129i
$484$	464.972	−	122.337i	0.960685	−	0.252761i
$485$	12.4944	−	12.4944i	0.0257617	−	0.0257617i
$486$	−27.4681	+	32.1610i	−0.0565187	+	0.0661748i
$487$	435.170	−	104.475i	0.893573	−	0.214528i	0.239443	−	0.970910i	$-0.423035\pi$
$487$	435.170	−	104.475i	0.893573	−	0.214528i	0.654130	+	0.756383i	$0.273035\pi$
$488$	23.2876	−	96.9998i	0.0477205	−	0.198770i
$489$	910.908	−	295.972i	1.86280	−	0.605260i
$490$	−2.64380	+	2.25802i	−0.00539551	+	0.00460820i
$491$	−548.627	+	86.8940i	−1.11737	+	0.176973i	−0.687686	−	0.726008i	$-0.741374\pi$
$491$	−548.627	+	86.8940i	−1.11737	+	0.176973i	−0.429680	+	0.902981i	$0.641374\pi$
$492$	657.415	+	904.854i	1.33621	+	1.83913i
$493$	−298.054	+	162.924i	−0.604573	+	0.330475i
$494$		−	20.0232i		−	0.0405329i
$495$	30.8174	+	27.8746i	0.0622573	+	0.0563123i
$496$	−136.399	+	56.4984i	−0.274998	+	0.113908i
$497$	149.663	−	460.616i	0.301133	−	0.926792i
$498$	−34.0006	−	20.8356i	−0.0682742	−	0.0418385i
$499$	−144.561	−	235.902i	−0.289701	−	0.472749i	0.674370	−	0.738393i	$-0.264415\pi$
$499$	−144.561	−	235.902i	−0.289701	−	0.472749i	−0.964071	+	0.265645i	$0.914415\pi$
$500$	−136.023	−	10.7052i	−0.272046	−	0.0214105i
$501$	−240.445	+	471.899i	−0.479929	+	0.941914i
$502$	0.194150	+	1.22581i	0.000386753	+	0.00244186i
$503$	622.262	−	149.392i	1.23710	−	0.297002i	0.438428	−	0.898766i	$-0.355535\pi$
$503$	622.262	−	149.392i	1.23710	−	0.297002i	0.798674	+	0.601765i	$0.205535\pi$
$504$	19.5767	−	22.9214i	0.0388426	−	0.0454789i
$505$	97.6989	−	40.4682i	0.193463	−	0.0801350i
$506$	−7.82549	+	28.9430i	−0.0154654	+	0.0571997i
$507$	408.308	−	169.127i	0.805342	−	0.333583i
$508$	−83.1313	−	163.154i	−0.163644	−	0.321170i
$509$	−418.345	+	303.945i	−0.821896	+	0.597142i	−0.917255	−	0.398301i	$-0.869600\pi$
$509$	−418.345	+	303.945i	−0.821896	+	0.597142i	0.0953592	+	0.995443i	$0.469600\pi$
$510$	−1.49575	+	7.13616i	−0.00293284	+	0.0139925i
$511$	47.7251	+	146.883i	0.0933956	+	0.287442i
$512$	−180.704	−	92.0731i	−0.352937	−	0.179830i
$513$	22.9642	−	95.6529i	0.0447646	−	0.186458i
$514$	55.1932	−	40.1002i	0.107380	−	0.0780160i
$515$	17.4384	−	1.37243i	0.0338609	−	0.00266491i
$516$	223.488	−	539.549i	0.433117	−	1.04564i
$517$	56.5378	+	192.466i	0.109357	+	0.372275i
$518$	1.19415	−	1.19415i	0.00230532	−	0.00230532i
$519$	163.474	−	83.2942i	0.314979	−	0.160490i
$520$	−3.54746	−	14.7762i	−0.00682204	−	0.0284158i
$521$	144.082	+	235.121i	0.276549	+	0.451288i	0.960516	−	0.278226i	$-0.0897464\pi$
$521$	144.082	+	235.121i	0.276549	+	0.451288i	−0.683966	+	0.729514i	$0.739746\pi$
$522$	13.4686	−	11.5033i	0.0258020	−	0.0220370i
$523$	−204.690	−	629.972i	−0.391377	−	1.20453i	−0.931747	−	0.363107i	$-0.881716\pi$
$523$	−204.690	−	629.972i	−0.391377	−	1.20453i	0.540370	−	0.841427i	$-0.318284\pi$
$524$	−21.4552	+	89.3673i	−0.0409450	+	0.170548i
$525$	62.1757	−	392.562i	0.118430	−	0.747737i
$526$	−1.27144	+	3.91309i	−0.00241719	+	0.00743934i
$527$	116.397	+	109.833i	0.220867	+	0.208411i
$528$	549.125	+	358.375i	1.04001	+	0.678741i
$529$	−175.664	−	175.664i	−0.332068	−	0.332068i
$530$	−6.85588	+	0.539569i	−0.0129356	+	0.00101806i
$531$	−62.3293	−	85.7890i	−0.117381	−	0.161561i
$532$	−28.8205	+	120.046i	−0.0541738	+	0.225650i
$533$	−98.1338	+	1246.91i	−0.184116	+	2.33942i
$534$	5.15420	−	65.4904i	0.00965206	−	0.122641i
$535$	14.4045	+	90.9466i	0.0269243	+	0.169994i
$536$	−159.993	−	25.3404i	−0.298495	−	0.0472769i
$537$	554.547	+	473.628i	1.03268	+	0.881989i
$538$	−15.1641	+	36.6094i	−0.0281861	+	0.0680473i
$539$	246.386	−	232.754i	0.457116	−	0.431826i
$540$		−	37.2040i		−	0.0688964i
$541$	−82.5433	+	6.49630i	−0.152576	+	0.0120080i	−0.154517	−	0.987990i	$-0.549382\pi$
$541$	−82.5433	+	6.49630i	−0.152576	+	0.0120080i	0.00194128	+	0.999998i	$0.499382\pi$
$542$	60.8181	+	9.63264i	0.112211	+	0.0177724i
$543$	−1013.05	−	736.023i	−1.86565	−	1.35548i
$544$	−6.51615	+	131.450i	−0.0119782	+	0.241637i
$545$	−43.8480	+	14.2471i	−0.0804551	+	0.0261415i
$546$	44.0029	−	6.96937i	0.0805913	−	0.0127644i
$547$	−679.405	−	416.340i	−1.24206	−	0.761133i	−0.263014	−	0.964792i	$-0.584717\pi$
$547$	−679.405	−	416.340i	−1.24206	−	0.761133i	−0.979042	+	0.203659i	$0.934717\pi$
$548$	−176.069	−	57.2084i	−0.321294	−	0.104395i
$549$	−386.962	+	160.285i	−0.704848	+	0.291958i
$550$	−43.8703	−	1.24811i	−0.0797643	−	0.00226929i
$551$	−55.7075	+	134.490i	−0.101103	+	0.244083i
$552$	−73.6042	+	37.5032i	−0.133341	+	0.0679406i
$553$	−38.1107	+	240.621i	−0.0689162	+	0.435120i
$554$	−54.8104	+	33.5879i	−0.0989358	+	0.0606279i
$555$	−0.503257	+	6.39448i	−0.000906769	+	0.0115216i
$556$	502.078	+	587.858i	0.903018	+	1.05730i
$557$	−191.199	−	138.914i	−0.343265	−	0.249397i	0.402773	−	0.915300i	$-0.368046\pi$
$557$	−191.199	−	138.914i	−0.343265	−	0.249397i	−0.746038	+	0.665903i	$0.768046\pi$
$558$	−7.11533	−	4.36028i	−0.0127515	−	0.00781412i
$559$	581.903	−	296.494i	1.04097	−	0.530402i
$560$			46.3784i			0.0828186i
$561$	110.794	−	702.101i	0.197494	−	1.25152i
$562$	−32.1459			−0.0571990
$563$	15.7896	+	30.9888i	0.0280455	+	0.0550423i	0.904604	−	0.426253i	$-0.140167\pi$
$563$	15.7896	+	30.9888i	0.0280455	+	0.0550423i	−0.876559	+	0.481295i	$0.840167\pi$
$564$	−143.911	+	234.842i	−0.255162	+	0.416387i
$565$	−51.4308	+	70.7884i	−0.0910280	+	0.125289i
$566$	36.5984	−	31.2580i	0.0646614	−	0.0552261i
$567$	426.647	+	33.5778i	0.752464	+	0.0592202i
$568$	−76.9897	−	125.636i	−0.135545	−	0.221190i
$569$	−671.428	−	106.344i	−1.18001	−	0.186896i	−0.464551	−	0.885547i	$-0.653784\pi$
$569$	−671.428	−	106.344i	−1.18001	−	0.186896i	−0.715463	+	0.698651i	$0.753784\pi$
$570$	1.41858	+	2.78413i	0.00248874	+	0.00488443i
$571$	−769.379	−	318.687i	−1.34742	−	0.558121i	−0.411850	−	0.911252i	$-0.635117\pi$
$571$	−769.379	−	318.687i	−1.34742	−	0.558121i	−0.935574	+	0.353131i	$0.885117\pi$
$572$	208.070	+	708.312i	0.363758	+	1.23831i
$573$	47.3691	+	114.359i	0.0826685	+	0.199579i
$574$	−15.8804	+	48.8748i	−0.0276662	+	0.0851477i
$575$	−214.592	+	350.183i	−0.373204	+	0.609014i
$576$	52.3868	+	330.758i	0.0909494	+	0.574232i
$577$	42.3408	+	130.312i	0.0733810	+	0.225844i	0.981019	−	0.193909i	$-0.0621168\pi$
$577$	42.3408	+	130.312i	0.0733810	+	0.225844i	−0.907638	+	0.419753i	$0.862117\pi$
$578$	43.8073	−	17.1011i	0.0757912	−	0.0295867i
$579$	−216.461	+	297.933i	−0.373853	+	0.514565i
$580$	−8.61251	+	54.3772i	−0.0148492	+	0.0937539i
$581$	21.5725	+	274.104i	0.0371299	+	0.471780i
$582$	15.7607			0.0270802
$583$	664.876	−	86.0027i	1.14044	−	0.147518i
$584$	43.4105	+	17.9812i	0.0743331	+	0.0307898i
$585$	−41.4372	+	48.5167i	−0.0708327	+	0.0829345i
$586$	−13.8765	+	87.6130i	−0.0236801	+	0.149510i
$587$	−790.526	+	125.207i	−1.34672	+	0.213300i	−0.787806	−	0.615924i	$-0.788783\pi$
$587$	−790.526	+	125.207i	−1.34672	+	0.213300i	−0.558917	+	0.829224i	$0.688783\pi$
$588$	463.942	+	36.5130i	0.789017	+	0.0620970i
$589$	68.3729	+	5.38106i	0.116083	+	0.00913593i
$590$	−2.13573	−	0.512743i	−0.00361988	−	0.000869056i
$591$	−565.192	+	410.636i	−0.956332	+	0.694816i
$592$	2.99443	+	38.0478i	0.00505816	+	0.0642700i
$593$	138.796	−	138.796i	0.234058	−	0.234058i	−0.580326	−	0.814384i	$-0.697075\pi$
$593$	138.796	−	138.796i	0.234058	−	0.234058i	0.814384	+	0.580326i	$0.197075\pi$
$594$	−1.21028	−	24.1383i	−0.00203751	−	0.0406369i
$595$	45.8688	−	20.5778i	0.0770905	−	0.0345846i
$596$	224.698	+	73.0088i	0.377010	+	0.122498i
$597$	1222.04	+	193.551i	2.04696	+	0.324207i
$598$	−44.7644	−	10.7470i	−0.0748569	−	0.0179716i
$599$	−1025.04	+	333.056i	−1.71126	+	0.556021i	−0.990542	−	0.137211i	$-0.956186\pi$
$599$	−1025.04	+	333.056i	−1.71126	+	0.556021i	−0.720714	+	0.693232i	$0.756186\pi$
$600$	−78.5322	−	91.9494i	−0.130887	−	0.153249i
$601$	904.141	−	554.058i	1.50439	−	0.921894i	0.506163	−	0.862438i	$-0.331064\pi$
$601$	904.141	−	554.058i	1.50439	−	0.921894i	0.998231	−	0.0594556i	$-0.0189365\pi$
$602$	26.0918	−	6.26409i	0.0433419	−	0.0104055i
$603$	308.775	+	606.004i	0.512064	+	1.00498i
$604$	−12.7476	−	12.7476i	−0.0211053	−	0.0211053i
$605$	−83.8856	+	1.81684i	−0.138654	+	0.00300304i
$606$	87.1431	+	36.0959i	0.143801	+	0.0595641i
$607$	−55.1892	−	701.245i	−0.0909212	−	1.15526i	−0.857979	−	0.513685i	$-0.828280\pi$
$607$	−55.1892	−	701.245i	−0.0909212	−	1.15526i	0.767058	−	0.641578i	$-0.221720\pi$
$608$	33.1529	+	45.6310i	0.0545277	+	0.0750510i
$609$	−314.943	−	75.6112i	−0.517148	−	0.124156i
$610$	−3.93858	+	7.72991i	−0.00645670	+	0.0126720i
$611$	−292.935	+	95.1803i	−0.479435	+	0.155778i
$612$	308.054	−	201.294i	0.503357	−	0.328912i
$613$	−229.923	−	316.462i	−0.375079	−	0.516252i	0.579194	−	0.815190i	$-0.303367\pi$
$613$	−229.923	−	316.462i	−0.375079	−	0.516252i	−0.954272	+	0.298938i	$0.903367\pi$
$614$	−62.1346	+	31.6592i	−0.101196	+	0.0515622i
$615$	−74.6946	−	180.329i	−0.121455	−	0.293217i
$616$	3.04796	+	60.7897i	0.00494799	+	0.0986846i
$617$	6.87116	+	16.5884i	0.0111364	+	0.0268857i	0.929350	−	0.369200i	$-0.120368\pi$
$617$	6.87116	+	16.5884i	0.0111364	+	0.0268857i	−0.918214	+	0.396086i	$0.870368\pi$
$618$	11.8641	+	10.1329i	0.0191976	+	0.0163963i
$619$	−230.768	−	961.220i	−0.372809	−	1.55286i	−0.771776	−	0.635894i	$-0.780631\pi$
$619$	−230.768	−	961.220i	−0.372809	−	1.55286i	0.398968	−	0.916965i	$-0.369369\pi$
$620$	25.6193	−	4.05771i	0.0413215	−	0.00654469i
$621$	−201.519	−	102.679i	−0.324506	−	0.165344i
$622$	−6.67577	+	84.8237i	−0.0107327	+	0.136372i
$623$	−386.207	+	236.668i	−0.619915	+	0.379884i
$624$	−526.067	+	858.464i	−0.843057	+	1.37574i
$625$	−560.332	−	182.063i	−0.896531	−	0.291300i
$626$	−18.1796	−	43.8893i	−0.0290408	−	0.0701108i
$627$	−151.709	−	264.146i	−0.241960	−	0.421286i
$628$	−305.071			−0.485782
$629$	36.3012	−	19.8431i	0.0577126	−	0.0315471i
$630$	−2.12083	+	1.54087i	−0.00336640	+	0.00244583i
$631$	194.536	+	1228.25i	0.308298	+	1.94652i	0.322362	+	0.946617i	$0.395523\pi$
$631$	194.536	+	1228.25i	0.308298	+	1.94652i	−0.0140635	+	0.999901i	$0.504477\pi$
$632$	48.1364	+	56.3605i	0.0761652	+	0.0891780i
$633$	311.604	+	959.018i	0.492265	+	1.51504i
$634$	16.5815	+	3.98087i	0.0261538	+	0.00627897i
$635$	7.45988	+	31.0726i	0.0117478	+	0.0489333i
$636$	699.957	+	597.820i	1.10056	+	0.939968i
$637$	367.997	+	367.997i	0.577703	+	0.577703i
$638$	−3.81893	+	35.5606i	−0.00598578	+	0.0557376i
$639$	−236.756	+	571.579i	−0.370510	+	0.894490i
$640$	21.6033	+	18.4509i	0.0337551	+	0.0288296i
$641$	715.831	+	438.662i	1.11674	+	0.684340i	0.953243	−	0.302204i	$-0.0977222\pi$
$641$	715.831	+	438.662i	1.11674	+	0.684340i	0.163498	+	0.986544i	$0.447722\pi$
$642$	−48.2757	+	66.4458i	−0.0751958	+	0.103498i
$643$	−3.49188	−	4.08846i	−0.00543060	−	0.00635842i	0.757684	−	0.652622i	$-0.226331\pi$
$643$	−3.49188	−	4.08846i	−0.00543060	−	0.00635842i	−0.763115	+	0.646263i	$0.776331\pi$
$644$	252.909	+	128.863i	0.392715	+	0.200099i
$645$	−59.9049	+	82.4520i	−0.0928758	+	0.127833i
$646$	10.0274	−	17.4820i	0.0155223	−	0.0270619i
$647$	−206.712	+	636.194i	−0.319493	+	0.983298i	0.654373	+	0.756172i	$0.272933\pi$
$647$	−206.712	+	636.194i	−0.319493	+	0.983298i	−0.973865	+	0.227126i	$0.927067\pi$
$648$	92.0681	−	92.0681i	0.142080	−	0.142080i
$649$	210.444	+	39.4962i	0.324259	+	0.0608571i
$650$		−	67.3881i		−	0.103674i
$651$	11.9728	+	152.129i	0.0183914	+	0.233684i
$652$	−973.590	+	233.738i	−1.49324	+	0.358494i
$653$	662.841	−	406.189i	1.01507	−	0.622036i	0.0876868	−	0.996148i	$-0.472053\pi$
$653$	662.841	−	406.189i	1.01507	−	0.622036i	0.927383	+	0.374112i	$0.122053\pi$
$654$	−36.6411	−	18.6696i	−0.0560261	−	0.0285467i
$655$	7.28152	−	14.2908i	0.0111168	−	0.0218180i
$656$	−606.819	−	990.239i	−0.925029	−	1.50951i
$657$	−46.0552	−	191.834i	−0.0700992	−	0.291984i
$658$	−12.6162	+	0.992913i	−0.0191735	+	0.00150899i
$659$	401.718			0.609587			0.304793	−	0.952419i	$-0.401413\pi$
$659$	401.718			0.609587			0.304793	+	0.952419i	$0.401413\pi$
$660$	−79.1127	−	83.7460i	−0.119868	−	0.126888i
$661$	−474.482	−	474.482i	−0.717824	−	0.717824i	0.250335	−	0.968159i	$-0.419459\pi$
$661$	−474.482	−	474.482i	−0.717824	−	0.717824i	−0.968159	+	0.250335i	$0.919459\pi$
$662$	−35.9125	−	11.6687i	−0.0542485	−	0.0176264i
$663$	1082.45	+	139.392i	1.63265	+	0.210245i
$664$	67.6751	+	49.1688i	0.101920	+	0.0740495i
$665$	9.78117	−	19.1966i	0.0147085	−	0.0288671i
$666$	−1.64040	+	1.40103i	−0.00246306	+	0.00210365i
$667$	270.769	+	196.725i	0.405951	+	0.294940i
$668$	289.288	−	472.074i	0.433065	−	0.706698i
$669$	−206.382	+	241.642i	−0.308493	+	0.361199i
$670$	13.0152	+	5.39107i	0.0194257	+	0.00804637i
$671$	345.738	−	771.835i	0.515257	−	1.15028i
$672$	−88.7389	+	88.7389i	−0.132052	+	0.132052i
$673$	196.603	−	230.193i	0.292130	−	0.342040i	−0.594860	−	0.803830i	$-0.702792\pi$
$673$	196.603	−	230.193i	0.292130	−	0.342040i	0.886990	+	0.461789i	$0.152792\pi$
$674$	69.0211	−	16.5705i	0.102405	−	0.0245853i
$675$	77.2861	−	321.920i	0.114498	−	0.476918i
$676$	−439.395	+	142.768i	−0.649993	+	0.211196i
$677$	−586.134	+	500.606i	−0.865781	+	0.739447i	−0.966826	−	0.255435i	$-0.917781\pi$
$677$	−586.134	+	500.606i	−0.865781	+	0.739447i	0.101045	+	0.994882i	$0.467781\pi$
$678$	−77.0847	+	12.2090i	−0.113694	+	0.0180074i
$679$	−63.8749	−	87.9163i	−0.0940720	−	0.129479i
$680$	4.30253	−	14.6775i	0.00632725	−	0.0215845i
$681$		−	155.974i		−	0.229037i
$682$	16.4900	−	3.46609i	0.0241790	−	0.00508225i
$683$	243.033	−	100.668i	0.355832	−	0.147390i	−0.197604	−	0.980282i	$-0.563316\pi$
$683$	243.033	−	100.668i	0.355832	−	0.147390i	0.553436	+	0.832891i	$0.313316\pi$
$684$	48.7334	−	149.986i	0.0712476	−	0.219278i
$685$	27.5468	+	16.8807i	0.0402143	+	0.0246434i
$686$	28.9394	+	47.2248i	0.0421857	+	0.0688409i
$687$	860.824	+	67.7483i	1.25302	+	0.0986147i
$688$	−275.306	+	540.318i	−0.400154	+	0.785346i
$689$	161.032	+	1016.72i	0.233719	+	1.47564i
$690$	6.98565	−	1.67711i	0.0101241	−	0.00243059i
$691$	417.300	−	488.595i	0.603907	−	0.707084i	−0.371266	−	0.928526i	$-0.621076\pi$
$691$	417.300	−	488.595i	0.603907	−	0.707084i	0.975174	+	0.221442i	$0.0710763\pi$
$692$	−177.198	+	73.3980i	−0.256067	+	0.106066i
$693$	198.969	−	160.378i	0.287112	−	0.231425i
$694$	−52.2184	+	21.6296i	−0.0752426	+	0.0311665i
$695$	−61.2495	−	120.209i	−0.0881287	−	0.172962i
$696$	−79.7211	+	57.9208i	−0.114542	+	0.0832195i
$697$	−710.117	+	1039.51i	−1.01882	+	1.49141i
$698$	7.88429	+	24.2653i	0.0112955	+	0.0347641i
$699$	−61.9181	−	31.5488i	−0.0885810	−	0.0451343i
$700$	−96.9952	+	404.014i	−0.138565	+	0.577163i
$701$	−356.984	+	259.364i	−0.509249	+	0.369991i	−0.812539	−	0.582907i	$-0.801915\pi$
$701$	−356.984	+	259.364i	−0.509249	+	0.369991i	0.303289	+	0.952899i	$0.401915\pi$
$702$	36.9954	−	2.91160i	0.0527000	−	0.00414758i
$703$	6.78483	−	16.3800i	0.00965125	−	0.0233002i
$704$	−535.527	−	412.853i	−0.760692	−	0.586438i
$705$	33.9878	−	33.9878i	0.0482097	−	0.0482097i
$706$	49.0730	−	25.0040i	0.0695086	−	0.0354164i
$707$	−151.824	−	632.391i	−0.214743	−	0.894470i
$708$	153.611	+	250.670i	0.216964	+	0.354054i
$709$	228.098	−	194.814i	0.321718	−	0.274773i	−0.473891	−	0.880583i	$-0.657151\pi$
$709$	228.098	−	194.814i	0.321718	−	0.274773i	0.795609	+	0.605810i	$0.207151\pi$
$710$	3.95990	+	12.1873i	0.00557732	+	0.0171652i
$711$	72.6487	−	302.604i	0.102178	−	0.425603i
$712$	−21.5577	+	136.110i	−0.0302776	+	0.191165i
$713$	48.7275	−	149.968i	0.0683416	−	0.210334i
$714$	41.9085	+	15.9513i	0.0586954	+	0.0223407i
$715$	−6.45149	−	128.671i	−0.00902307	−	0.179960i
$716$	−539.081	−	539.081i	−0.752907	−	0.752907i
$717$	292.474	−	23.0182i	0.407914	−	0.0321035i
$718$	−39.8636	−	54.8675i	−0.0555203	−	0.0764172i
$719$	−0.382608	+	1.59368i	−0.000532139	+	0.00221652i	−0.972635	−	0.232337i	$-0.925363\pi$
$719$	−0.382608	+	1.59368i	−0.000532139	+	0.00221652i	0.972103	+	0.234553i	$0.0753628\pi$
$720$	4.64823	−	59.0613i	0.00645587	−	0.0820296i
$721$	8.44053	−	107.247i	0.0117067	−	0.148748i
$722$	7.83830	+	49.4891i	0.0108564	+	0.0685445i
$723$	−1394.74	−	220.905i	−1.92910	−	0.305540i
$724$	995.393	+	850.146i	1.37485	+	1.17423i
$725$	−187.483	+	452.625i	−0.258598	+	0.624310i
$726$	−54.0533	−	51.7615i	−0.0744536	−	0.0712968i
$727$		−	1287.32i		−	1.77073i	−0.464897	−	0.885365i	$-0.653909\pi$
$727$		−	1287.32i		−	1.77073i	0.464897	−	0.885365i	$-0.346091\pi$
$728$	−93.1689	+	7.33255i	−0.127979	+	0.0100722i
$729$	−83.7375	−	13.2627i	−0.114866	−	0.0181930i
$730$	−3.30591	−	2.40189i	−0.00452865	−	0.00329025i
$731$	656.533	+	32.5451i	0.898130	+	0.0445213i
$732$	1104.39	−	358.837i	1.50873	−	0.490215i
$733$	−682.461	+	108.091i	−0.931052	+	0.147464i	−0.603494	−	0.797367i	$-0.706225\pi$
$733$	−682.461	+	108.091i	−0.931052	+	0.147464i	−0.327557	+	0.944831i	$0.606225\pi$
$734$	−81.6647	−	50.0442i	−0.111260	−	0.0681801i
$735$	−77.2395	−	25.0966i	−0.105088	−	0.0341451i
$736$	119.808	−	49.6260i	0.162782	−	0.0674266i
$737$	−1293.52	−	461.355i	−1.75511	−	0.625991i
$738$	25.1216	−	60.6488i	0.0340401	−	0.0821800i
$739$	1154.32	−	588.155i	1.56200	−	0.795880i	0.562481	−	0.826810i	$-0.309847\pi$
$739$	1154.32	−	588.155i	1.56200	−	0.795880i	0.999522	+	0.0309303i	$0.00984700\pi$
$740$	1.04895	−	6.62281i	0.00141750	−	0.00894975i
$741$	398.796	−	244.382i	0.538186	−	0.329801i
$742$	−3.31839	+	42.1641i	−0.00447222	+	0.0568249i
$743$	343.336	+	401.995i	0.462094	+	0.541042i	0.941705	−	0.336438i	$-0.109222\pi$
$743$	343.336	+	401.995i	0.462094	+	0.541042i	−0.479612	+	0.877481i	$0.659222\pi$
$744$	37.5599	+	27.2888i	0.0504837	+	0.0366786i
$745$	−35.1550	−	21.5430i	−0.0471879	−	0.0289168i
$746$	29.9132	−	15.2415i	0.0400981	−	0.0204310i
$747$		−	351.224i		−	0.470180i
$748$	−173.052	+	722.616i	−0.231352	+	0.966064i
$749$	566.299			0.756074
$750$	9.64210	+	18.9237i	0.0128561	+	0.0252316i
$751$	95.6102	−	156.022i	0.127311	−	0.207752i	−0.782634	−	0.622482i	$-0.786124\pi$
$751$	95.6102	−	156.022i	0.127311	−	0.207752i	0.909944	+	0.414731i	$0.136124\pi$
$752$	168.105	−	231.377i	0.223545	−	0.307683i
$753$	−22.0445	+	18.8278i	−0.0292756	+	0.0250037i
$754$	−54.7463	−	4.30863i	−0.0726078	−	0.00571436i
$755$	1.64383	+	2.68248i	0.00217726	+	0.00355296i
$756$	−225.990	−	35.7933i	−0.298929	−	0.0473457i
$757$	447.325	+	877.925i	0.590919	+	1.15974i	0.971951	+	0.235181i	$0.0755684\pi$
$757$	447.325	+	877.925i	0.590919	+	1.15974i	−0.381033	+	0.924561i	$0.624432\pi$
$758$	−38.6808	−	16.0221i	−0.0510300	−	0.0211373i
$759$	−671.958	+	197.391i	−0.885320	+	0.260067i
$760$	−2.50841	−	6.05584i	−0.00330054	−	0.00796821i
$761$	213.776	−	657.935i	0.280915	−	0.864566i	−0.706679	−	0.707534i	$-0.749807\pi$
$761$	213.776	−	657.935i	0.280915	−	0.864566i	0.987594	−	0.157032i	$-0.0501926\pi$
$762$	−14.8928	+	24.3028i	−0.0195443	+	0.0318934i
$763$	44.3564	+	280.055i	0.0581342	+	0.367045i
$764$	−39.9865	−	123.066i	−0.0523384	−	0.161081i
$765$	−60.4748	+	21.6080i	−0.0790521	+	0.0282458i
$766$	26.7446	−	36.8108i	0.0349147	−	0.0480559i
$767$	−51.4308	+	324.721i	−0.0670545	+	0.423366i
$768$	−71.3415	−	906.480i	−0.0928926	−	1.18031i
$769$	−340.547			−0.442844			−0.221422	−	0.975178i	$-0.571070\pi$
$769$	−340.547			−0.442844			−0.221422	+	0.975178i	$0.571070\pi$
$770$	0.976406	−	5.20250i	0.00126806	−	0.00675649i
$771$	1472.29	+	609.844i	1.90959	+	0.790977i
$772$	250.024	−	292.740i	0.323865	−	0.379197i
$773$	149.045	−	941.034i	0.192814	−	1.21738i	−0.681427	−	0.731886i	$-0.738640\pi$
$773$	149.045	−	941.034i	0.192814	−	1.21738i	0.874241	−	0.485493i	$-0.161360\pi$
$774$	−33.8549	+	5.36209i	−0.0437401	+	0.00692776i
$775$	230.109	+	18.1100i	0.296915	+	0.0233677i
$776$	−32.9599	−	2.59400i	−0.0424741	−	0.00334278i
$777$	38.3581	+	9.20897i	0.0493670	+	0.0118520i
$778$	−34.9430	+	25.3876i	−0.0449139	+	0.0326319i
$779$	42.3297	+	537.850i	0.0543386	+	0.690437i
$780$	125.081	−	125.081i	0.160361	−	0.160361i
$781$	−445.043	−	1167.26i	−0.569838	−	1.49458i
$782$	−33.7013	−	31.8006i	−0.0430962	−	0.0406657i
$783$	−256.587	−	83.3701i	−0.327697	−	0.106475i
$784$	−477.285	−	75.5945i	−0.608782	−	0.0964216i
$785$	51.7680	+	12.4284i	0.0659464	+	0.0158323i
$786$	13.6058	−	4.42081i	0.0173102	−	0.00562444i
$787$	−350.025	−	409.826i	−0.444758	−	0.520745i	0.492060	−	0.870561i	$-0.336244\pi$
$787$	−350.025	−	409.826i	−0.444758	−	0.520745i	−0.936818	+	0.349816i	$0.886244\pi$
$788$	622.703	−	381.593i	0.790232	−	0.484255i
$789$	−93.4536	+	22.4362i	−0.118446	+	0.0284363i
$790$	−2.92637	−	5.74333i	−0.00370427	−	0.00727004i
$791$	380.513	+	380.513i	0.481053	+	0.481053i
$792$	2.21111	−	77.7191i	0.00279180	−	0.0981302i
$793$	1199.73	+	496.946i	1.51291	+	0.626666i
$794$	0.988462	+	12.5596i	0.00124491	+	0.0158181i
$795$	−94.4220	−	129.961i	−0.118770	−	0.163473i
$796$	−1257.68	−	301.943i	−1.58001	−	0.379326i
$797$	−226.622	+	444.771i	−0.284344	+	0.558056i	−0.988361	−	0.152127i	$-0.951388\pi$
$797$	−226.622	+	444.771i	−0.284344	+	0.558056i	0.704017	+	0.710183i	$0.251388\pi$
$798$	18.2765	−	5.93841i	0.0229029	−	0.00744162i
$799$	−303.423	−	63.5978i	−0.379753	−	0.0795967i
$800$	111.576	+	153.571i	0.139470	+	0.191964i
$801$	515.541	−	262.681i	0.643622	−	0.327942i
$802$	−13.4369	−	32.4396i	−0.0167543	−	0.0404484i
$803$	333.599	+	217.717i	0.415441	+	0.271129i
$804$	−721.601	−	1742.10i	−0.897513	−	2.16679i
$805$	−37.6667	−	32.1704i	−0.0467909	−	0.0399632i
$806$	6.03993	+	25.1581i	0.00749371	+	0.0312135i
$807$	−914.215	+	144.797i	−1.13286	+	0.179427i
$808$	−176.299	−	89.8288i	−0.218192	−	0.111174i
$809$	−59.3503	+	754.118i	−0.0733626	+	0.932160i	0.844576	+	0.535436i	$0.179853\pi$
$809$	−59.3503	+	754.118i	−0.0733626	+	0.932160i	−0.917938	+	0.396724i	$0.870147\pi$
$810$	−9.65482	+	5.91648i	−0.0119195	+	0.00730430i
$811$	−411.741	+	671.901i	−0.507696	+	0.828484i	−0.999099	−	0.0424482i	$-0.986484\pi$
$811$	−411.741	+	671.901i	−0.507696	+	0.828484i	0.491403	+	0.870932i	$0.336484\pi$
$812$	322.020	+	104.631i	0.396577	+	0.128856i
$813$	550.431	+	1328.86i	0.677037	+	1.63451i
$814$	0.465122	−	4.33106i	0.000571403	−	0.00532071i
$815$	174.732			0.214395
$816$	−889.212	+	486.065i	−1.08972	+	0.595668i
$817$	227.905	−	165.583i	0.278954	−	0.202672i
$818$	−11.6535	−	73.5774i	−0.0142464	−	0.0899480i
$819$	254.841	+	298.381i	0.311161	+	0.364323i
$820$	63.0533	+	194.058i	0.0768943	+	0.236656i
$821$	−1292.23	−	310.237i	−1.57397	−	0.377876i	−0.649874	−	0.760042i	$-0.725179\pi$
$821$	−1292.23	−	310.237i	−1.57397	−	0.377876i	−0.924094	+	0.382165i	$0.875179\pi$
$822$	6.72721	+	28.0208i	0.00818395	+	0.0340886i
$823$	−507.905	−	433.792i	−0.617138	−	0.527086i	0.285003	−	0.958527i	$-0.408005\pi$
$823$	−507.905	−	433.792i	−0.617138	−	0.527086i	−0.902141	+	0.431441i	$0.858005\pi$
$824$	−23.1434	−	23.1434i	−0.0280866	−	0.0280866i
$825$	−510.577	−	888.984i	−0.618881	−	1.07756i
$826$	−5.16933	+	12.4799i	−0.00625826	+	0.0151088i
$827$	348.201	+	297.392i	0.421041	+	0.359603i	0.834583	−	0.550882i	$-0.185709\pi$
$827$	348.201	+	297.392i	0.421041	+	0.359603i	−0.413542	+	0.910485i	$0.635709\pi$
$828$	−309.156	−	189.451i	−0.373376	−	0.228805i
$829$	−172.385	+	237.267i	−0.207943	+	0.286209i	−0.900231	−	0.435412i	$-0.856603\pi$
$829$	−172.385	+	237.267i	−0.207943	+	0.286209i	0.692288	+	0.721621i	$0.256603\pi$
$830$	−4.72465	−	5.53185i	−0.00569235	−	0.00666489i
$831$	−1337.92	−	681.702i	−1.61001	−	0.820340i
$832$	610.275	−	839.972i	0.733504	−	1.00958i
$833$	137.005	+	505.582i	0.164471	+	0.606941i
$834$	37.1862	−	114.447i	0.0445878	−	0.137227i
$835$	−68.3216	+	68.3216i	−0.0818223	+	0.0818223i
$836$	136.440	+	287.727i	0.163206	+	0.344171i
$837$			127.110i			0.151864i
$838$	−3.06885	−	38.9935i	−0.00366211	−	0.0465316i
$839$	488.626	−	117.309i	0.582391	−	0.139820i	0.0684637	−	0.997654i	$-0.478190\pi$
$839$	488.626	−	117.309i	0.582391	−	0.139820i	0.513927	+	0.857834i	$0.328190\pi$
$840$	12.4352	−	7.62028i	0.0148038	−	0.00907176i
$841$	−393.610	−	200.554i	−0.468026	−	0.238471i
$842$	−53.1621	+	104.337i	−0.0631379	+	0.123915i
$843$	−392.338	−	640.238i	−0.465407	−	0.759475i
$844$	−246.083	−	1025.01i	−0.291568	−	1.21447i
$845$	80.3779	−	6.32588i	0.0951218	−	0.00748625i
$846$	16.1658			0.0191085
$847$	−69.6688	+	511.299i	−0.0822535	+	0.603658i
$848$	−675.871	−	675.871i	−0.797018	−	0.797018i
$849$	1069.23	+	347.415i	1.25940	+	0.409205i
$850$	33.7472	−	58.8357i	0.0397026	−	0.0692184i
$851$	−32.9780	−	23.9599i	−0.0387521	−	0.0281550i
$852$	778.700	−	1528.28i	0.913967	−	1.79376i
$853$	−294.924	+	251.889i	−0.345750	+	0.295298i	−0.805317	−	0.592845i	$-0.798005\pi$
$853$	−294.924	+	251.889i	−0.345750	+	0.295298i	0.459567	+	0.888143i	$0.348005\pi$
$854$	43.1649	+	31.3611i	0.0505444	+	0.0367226i
$855$	−14.3800	+	23.4660i	−0.0168187	+	0.0274456i
$856$	111.894	−	131.011i	0.130717	−	0.153050i
$857$	−56.4173	−	23.3688i	−0.0658311	−	0.0272682i	0.349525	−	0.936927i	$-0.386343\pi$
$857$	−56.4173	−	23.3688i	−0.0658311	−	0.0272682i	−0.415356	+	0.909659i	$0.636343\pi$
$858$	77.0849	−	85.2229i	0.0898426	−	0.0993274i
$859$	−472.268	+	472.268i	−0.549788	+	0.549788i	−0.926379	−	0.376591i	$-0.877096\pi$
$859$	−472.268	+	472.268i	−0.549788	+	0.549788i	0.376591	+	0.926379i	$0.377096\pi$
$860$	69.1934	−	81.0150i	0.0804574	−	0.0942035i
$861$	−1167.24	+	280.230i	−1.35568	+	0.325470i
$862$	−0.571854	+	2.38194i	−0.000663404	+	0.00276327i
$863$	1019.18	−	331.152i	1.18097	−	0.383722i	0.348246	−	0.937403i	$-0.386777\pi$
$863$	1019.18	−	331.152i	1.18097	−	0.383722i	0.832729	+	0.553681i	$0.186777\pi$
$864$	−79.4881	+	67.8892i	−0.0920001	+	0.0785755i
$865$	33.0592	−	5.23607i	0.0382188	−	0.00605326i
$866$	61.0164	+	83.9819i	0.0704578	+	0.0969768i
$867$	875.263	+	663.778i	1.00953	+	0.765603i
$868$		−	159.525i		−	0.183784i
$869$	312.959	+	544.903i	0.360136	+	0.627047i
$870$	7.91744	−	3.27951i	0.00910051	−	0.00376955i
$871$	651.620	−	2005.48i	0.748128	−	2.30250i
$872$	73.5537	+	45.0737i	0.0843505	+	0.0516901i
$873$	72.5312	+	118.360i	0.0830827	+	0.135579i
$874$	−19.7965	−	1.55802i	−0.0226504	−	0.00178263i
$875$	66.4826	−	130.479i	0.0759801	−	0.149119i
$876$	85.5634	+	540.226i	0.0976751	+	0.616696i
$877$	455.673	−	109.397i	0.519582	−	0.124740i	0.0348315	−	0.999393i	$-0.488911\pi$
$877$	455.673	−	109.397i	0.519582	−	0.124740i	0.484750	+	0.874653i	$0.338911\pi$
$878$	−26.0122	+	30.4564i	−0.0296266	+	0.0346883i
$879$	−1914.32	+	792.937i	−2.17784	+	0.902090i
$880$	75.0724	+	93.1368i	0.0853096	+	0.105837i
$881$	1141.50	−	472.825i	1.29569	−	0.536691i	0.375011	−	0.927020i	$-0.377639\pi$
$881$	1141.50	−	472.825i	1.29569	−	0.536691i	0.920675	+	0.390330i	$0.127639\pi$
$882$	−12.4005	−	24.3373i	−0.0140595	−	0.0275933i
$883$	450.245	−	327.122i	0.509903	−	0.370466i	−0.302884	−	0.953028i	$-0.597949\pi$
$883$	450.245	−	327.122i	0.509903	−	0.370466i	0.812787	+	0.582561i	$0.197949\pi$
$884$	−1116.65	−	234.051i	−1.26318	−	0.264764i
$885$	−15.8543	−	48.7946i	−0.0179145	−	0.0551351i
$886$	−50.3314	−	25.6451i	−0.0568075	−	0.0289448i
$887$	−214.134	+	891.930i	−0.241413	+	1.00556i	0.711589	+	0.702596i	$0.247976\pi$
$887$	−214.134	+	891.930i	−0.241413	+	1.00556i	−0.953002	+	0.302963i	$0.902024\pi$
$888$	9.70954	−	7.05439i	0.0109342	−	0.00794414i
$889$	195.923	−	15.4195i	0.220386	−	0.0173447i
$890$	4.58630	−	11.0723i	0.00515315	−	0.0124408i
$891$	911.141	−	623.180i	1.02260	−	0.699416i
$892$	234.903	−	234.903i	0.263344	−	0.263344i
$893$	−118.378	+	60.3168i	−0.132563	+	0.0675440i
$894$	−8.58520	−	35.7599i	−0.00960313	−	0.0399999i
$895$	69.5157	+	113.439i	0.0776712	+	0.126748i
$896$	132.862	−	113.475i	0.148283	−	0.126646i
$897$	−332.303	−	1022.72i	−0.370461	−	1.14016i
$898$	−7.62657	+	31.7670i	−0.00849284	+	0.0353752i
$899$	29.4251	−	185.783i	0.0327310	−	0.206655i
$900$	164.012	−	504.777i	0.182235	−	0.560863i
$901$	−368.565	+	968.326i	−0.409063	+	1.07472i
$902$	47.2224	+	123.855i	0.0523530	+	0.137312i
$903$	443.209	+	443.209i	0.490818	+	0.490818i
$904$	163.214	−	12.8453i	0.180547	−	0.0142093i
$905$	−134.275	−	184.814i	−0.148371	−	0.204215i
$906$	−0.655089	+	2.72864i	−0.000723056	+	0.00301175i
$907$	−60.4334	+	767.880i	−0.0666300	+	0.846615i	0.869267	+	0.494342i	$0.164591\pi$
$907$	−60.4334	+	767.880i	−0.0666300	+	0.846615i	−0.935897	+	0.352273i	$0.885409\pi$
$908$	−12.7930	+	162.550i	−0.0140892	+	0.179020i
$909$	129.961	+	820.544i	0.142972	+	0.902689i
$910$	8.02760	+	1.27145i	0.00882154	+	0.00139719i
$911$	488.473	+	417.196i	0.536195	+	0.457953i	0.875841	−	0.482600i	$-0.160307\pi$
$911$	488.473	+	417.196i	0.536195	+	0.457953i	−0.339646	+	0.940553i	$0.610307\pi$
$912$	−166.197	+	401.235i	−0.182233	+	0.439951i
$913$	487.012	+	515.534i	0.533420	+	0.564660i
$914$			36.8923i			0.0403636i
$915$	−202.024	+	15.8996i	−0.220791	+	0.0173767i
$916$	−891.562	−	141.209i	−0.973320	−	0.154159i
$917$	−79.8018	−	57.9794i	−0.0870249	−	0.0632273i
$918$	33.7583	+	15.9848i	0.0367737	+	0.0174126i
$919$	−143.890	+	46.7527i	−0.156572	+	0.0508735i	−0.386254	−	0.922392i	$-0.626231\pi$
$919$	−143.890	+	46.7527i	−0.156572	+	0.0508735i	0.229682	+	0.973266i	$0.426231\pi$
$920$	−14.8849	+	2.35754i	−0.0161793	+	0.00256254i
$921$	−1388.89	−	851.115i	−1.50803	−	0.924121i
$922$	−60.2947	−	19.5909i	−0.0653956	−	0.0212483i
$923$	1772.12	−	734.037i	1.91996	−	0.795272i
$924$	−584.815	+	399.987i	−0.632917	+	0.432887i
$925$	22.8343	−	55.1269i	0.0246857	−	0.0595967i
$926$	−11.9218	+	6.07444i	−0.0128745	+	0.00655987i
$927$	−21.4975	+	135.730i	−0.0231904	+	0.146418i
$928$	131.895	−	80.8256i	0.142129	−	0.0870965i
$929$	98.2367	−	1248.22i	0.105745	−	1.34361i	−0.683688	−	0.729774i	$-0.739625\pi$
$929$	98.2367	−	1248.22i	0.105745	−	1.34361i	0.789433	−	0.613837i	$-0.210375\pi$
$930$	−2.62219	−	3.07019i	−0.00281956	−	0.00330128i
$931$	181.612	+	131.949i	0.195072	+	0.141728i
$932$	61.9411	+	37.9576i	0.0664604	+	0.0407270i
$933$	−1770.88	+	902.309i	−1.89805	+	0.967105i
$934$		−	119.454i		−	0.127895i
$935$	58.8043	−	115.572i	0.0628923	−	0.123606i
$936$	119.382			0.127545
$937$	543.847	+	1067.36i	0.580413	+	1.13913i	0.975401	+	0.220439i	$0.0707489\pi$
$937$	543.847	+	1067.36i	0.580413	+	1.13913i	−0.394987	+	0.918687i	$0.629251\pi$
$938$	45.2689	−	73.8722i	0.0482611	−	0.0787550i
$939$	652.248	−	897.743i	0.694620	−	0.956062i
$940$	−38.2085	+	32.6332i	−0.0406474	+	0.0347161i
$941$	1294.67	+	101.893i	1.37584	+	0.108281i	0.744707	−	0.667391i	$-0.232589\pi$
$941$	1294.67	+	101.893i	1.37584	+	0.108281i	0.631136	+	0.775672i	$0.282589\pi$
$942$	24.8118	+	40.4892i	0.0263395	+	0.0429821i
$943$	1225.15	+	194.045i	1.29921	+	0.205774i
$944$	−138.591	−	272.001i	−0.146813	−	0.288137i
$945$	36.8904	+	15.2805i	0.0390375	+	0.0161699i
$946$	42.2578	−	54.8142i	0.0446699	−	0.0579431i
$947$	270.258	+	652.460i	0.285383	+	0.688976i	0.999944	−	0.0105974i	$-0.00337331\pi$
$947$	270.258	+	652.460i	0.285383	+	0.688976i	−0.714561	+	0.699574i	$0.753373\pi$
$948$	−266.617	+	820.562i	−0.281241	+	0.865572i
$949$	−319.592	+	521.526i	−0.336767	+	0.549553i
$950$	−4.54719	−	28.7098i	−0.00478651	−	0.0302208i
$951$	123.091	+	378.834i	0.129433	+	0.398354i
$952$	−85.0166	−	40.2560i	−0.0893032	−	0.0422857i
$953$	263.445	−	362.601i	0.276437	−	0.380484i	−0.648112	−	0.761545i	$-0.724441\pi$
$953$	263.445	−	362.601i	0.276437	−	0.380484i	0.924550	+	0.381061i	$0.124441\pi$
$954$	8.45170	−	53.3620i	0.00885923	−	0.0559350i
$955$	1.77175	+	22.5123i	0.00185524	+	0.0235730i
$956$	−306.693			−0.320809
$957$	−754.858	+	357.955i	−0.788775	+	0.374038i
$958$	38.5721	+	15.9771i	0.0402631	+	0.0166775i
$959$	129.042	−	151.088i	0.134559	−	0.157548i
$960$	−25.3462	+	160.030i	−0.0264023	+	0.166698i
$961$	861.638	−	136.470i	0.896606	−	0.142008i
$962$	6.66776	+	0.524764i	0.00693114	+	0.000545493i
$963$	−721.163	−	56.7568i	−0.748872	−	0.0589375i
$964$	1435.43	+	344.616i	1.48903	+	0.357485i
$965$	−54.3530	+	39.4898i	−0.0563243	+	0.0409220i
$966$	−3.46656	−	44.0468i	−0.00358857	−	0.0455971i
$967$	1152.03	−	1152.03i	1.19134	−	1.19134i	0.214655	−	0.976690i	$-0.431137\pi$
$967$	1152.03	−	1152.03i	1.19134	−	1.19134i	0.976690	−	0.214655i	$-0.0688627\pi$
$968$	104.521	+	117.144i	0.107976	+	0.121016i
$969$	470.567	−	13.6546i	0.485621	−	0.0140914i
$970$	2.73456	+	0.888511i	0.00281913	+	0.000915991i
$971$	839.046	+	132.892i	0.864105	+	0.136861i	0.572726	−	0.819747i	$-0.305886\pi$
$971$	839.046	+	132.892i	0.864105	+	0.136861i	0.291379	+	0.956608i	$0.405886\pi$
$972$	1004.25	+	241.099i	1.03318	+	0.248044i
$973$	−789.117	+	256.400i	−0.811015	+	0.263515i
$974$	47.2956	+	55.3760i	0.0485581	+	0.0568542i
$975$	1342.15	−	822.468i	1.37656	−	0.843557i
$976$	−1172.47	+	281.484i	−1.20130	+	0.288406i
$977$	−848.030	−	1664.35i	−0.867994	−	1.70353i	−0.695504	−	0.718522i	$-0.744819\pi$
$977$	−848.030	−	1664.35i	−0.867994	−	1.70353i	−0.172489	−	0.985011i	$-0.555181\pi$
$978$	110.205	+	110.205i	0.112684	+	0.112684i
$979$	−392.485	+	1100.42i	−0.400904	+	1.12403i
$980$	78.4377	+	32.4900i	0.0800385	+	0.0331530i
$981$	−28.4181	−	361.086i	−0.0289685	−	0.368080i
$982$	−53.1281	−	73.1246i	−0.0541020	−	0.0744649i
$983$	−1388.77	−	333.414i	−1.41279	−	0.339180i	−0.545969	−	0.837806i	$-0.683838\pi$
$983$	−1388.77	−	333.414i	−1.41279	−	0.339180i	−0.866817	+	0.498626i	$0.833838\pi$
$984$	−165.802	+	325.406i	−0.168498	+	0.330697i
$985$	−121.213	+	39.3845i	−0.123059	+	0.0399843i
$986$	−45.6405	−	31.1781i	−0.0462886	−	0.0316208i
$987$	−173.755	−	239.153i	−0.176043	−	0.242303i
$988$	−435.654	+	221.977i	−0.440946	+	0.224673i
$989$	−247.859	−	598.383i	−0.250615	−	0.605039i
$990$	−1.76484	+	6.52735i	−0.00178266	+	0.00659328i
$991$	41.2681	+	99.6301i	0.0416429	+	0.100535i	0.943332	−	0.331849i	$-0.107672\pi$
$991$	41.2681	+	99.6301i	0.0416429	+	0.100535i	−0.901690	+	0.432384i	$0.857672\pi$
$992$	−55.4192	−	47.3325i	−0.0558661	−	0.0477142i
$993$	−205.909	−	857.673i	−0.207360	−	0.863719i
$994$	77.8397	−	12.3286i	0.0783095	−	0.0124030i
$995$	201.117	+	102.474i	0.202128	+	0.102989i
$996$	−76.3995	+	970.748i	−0.0767063	+	0.974646i
$997$	−974.333	+	597.072i	−0.977265	+	0.598868i	−0.916819	−	0.399303i	$-0.869252\pi$
$997$	−974.333	+	597.072i	−0.977265	+	0.598868i	−0.0604455	+	0.998171i	$0.519252\pi$
$998$	23.5233	−	38.3866i	0.0235705	−	0.0384635i
$999$	31.2507	+	10.1540i	0.0312820	+	0.0101641i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.3.q.a.2.18	✓	544
11.6	odd	10	inner	187.3.q.a.138.18	yes	544
17.9	even	8	inner	187.3.q.a.145.18	yes	544
187.94	odd	40	inner	187.3.q.a.94.18	yes	544

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.3.q.a.2.18	✓	544	1.1	even	1	trivial
187.3.q.a.94.18	yes	544	187.94	odd	40	inner
187.3.q.a.138.18	yes	544	11.6	odd	10	inner
187.3.q.a.145.18	yes	544	17.9	even	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	187.q (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0738746 + 0.144987i) q^{2} +(-1.98602 + 3.24089i) q^{3} +(2.33558 - 3.21465i) q^{4} +(-0.527290 + 0.450348i) q^{5} +(-0.616605 - 0.0485279i) q^{6} +(2.22828 + 3.63622i) q^{7} +(1.28150 + 0.202970i) q^{8} +(-2.47320 - 4.85392i) q^{9} +(-0.104248 - 0.0431810i) q^{10} +(10.3607 + 3.69532i) q^{11} +(5.77982 + 13.9537i) q^{12} +(-5.21929 + 16.0633i) q^{13} +(-0.362591 + 0.591695i) q^{14} +(-0.412321 - 2.60329i) q^{15} +(-4.84630 - 14.9154i) q^{16} +(-12.6012 + 11.4109i) q^{17} +(0.521050 - 0.717164i) q^{18} +(-1.13970 + 7.19575i) q^{19} +(0.216184 + 2.74687i) q^{20} -16.2100 q^{21} +(0.229620 + 1.77516i) q^{22} +(15.4753 + 6.41008i) q^{23} +(-3.20289 + 3.75011i) q^{24} +(-3.83564 + 24.2173i) q^{25} +(-2.71455 + 0.429942i) q^{26} +(-13.4608 - 1.05938i) q^{27} +(16.8935 + 1.32954i) q^{28} +(19.4289 + 4.66448i) q^{29} +(0.346984 - 0.252099i) q^{30} +(-0.738604 - 9.38486i) q^{31} +(5.47433 - 5.47433i) q^{32} +(-32.5528 + 26.2390i) q^{33} +(-2.58535 - 0.984039i) q^{34} +(-2.81251 - 0.913840i) q^{35} +(-21.3800 - 3.38626i) q^{36} +(-2.36633 - 0.568104i) q^{37} +(-1.12749 + 0.366342i) q^{38} +(-41.6939 - 48.8173i) q^{39} +(-0.767129 + 0.470098i) q^{40} +(72.0075 - 17.2875i) q^{41} +(-1.19751 - 2.35024i) q^{42} +(-27.3417 - 27.3417i) q^{43} +(36.0774 - 24.6753i) q^{44} +(3.49005 + 1.44563i) q^{45} +(0.213853 + 2.71726i) q^{46} +(10.7190 + 14.7534i) q^{47} +(57.9640 + 13.9159i) q^{48} +(13.9887 - 27.4543i) q^{49} +(-3.79455 + 1.23292i) q^{50} +(-11.9553 - 63.5016i) q^{51} +(39.4479 + 54.2953i) q^{52} +(54.3040 - 27.6693i) q^{53} +(-0.840812 - 2.02990i) q^{54} +(-7.12729 + 2.71743i) q^{55} +(2.11749 + 5.11208i) q^{56} +(-21.0572 - 17.9846i) q^{57} +(0.759017 + 3.16153i) q^{58} +(19.2257 - 3.04505i) q^{59} +(-9.33168 - 4.75473i) q^{60} +(6.03231 - 76.6478i) q^{61} +(1.30612 - 0.800391i) q^{62} +(12.1389 - 19.8090i) q^{63} +(-58.4634 - 18.9959i) q^{64} +(-4.48201 - 10.8205i) q^{65} +(-6.20915 - 2.78134i) q^{66} -124.848 q^{67} +(7.25092 + 67.1596i) q^{68} +(-51.5087 + 37.4232i) q^{69} +(-0.0752782 - 0.475288i) q^{70} +(-73.7553 - 86.3563i) q^{71} +(-2.18420 - 6.72229i) q^{72} +(35.2138 + 8.45408i) q^{73} +(-0.0924436 - 0.385055i) q^{74} +(-70.8680 - 60.5270i) q^{75} +(20.4700 + 20.4700i) q^{76} +(9.64955 + 45.9080i) q^{77} +(3.99776 - 9.65145i) q^{78} +(43.4386 + 37.1001i) q^{79} +(9.27252 + 5.68221i) q^{80} +(58.9854 - 81.1864i) q^{81} +(7.82599 + 9.16306i) q^{82} +(57.4452 + 29.2698i) q^{83} +(-37.8597 + 52.1094i) q^{84} +(1.50562 - 11.6918i) q^{85} +(1.94434 - 5.98405i) q^{86} +(-53.7034 + 53.7034i) q^{87} +(12.5272 + 6.83847i) q^{88} +106.211i q^{89} +(0.0482290 + 0.612807i) q^{90} +(-70.0398 + 16.8151i) q^{91} +(56.7499 - 34.7764i) q^{92} +(31.8822 + 16.2448i) q^{93} +(-1.34720 + 2.64402i) q^{94} +(-2.63964 - 4.30751i) q^{95} +(6.86958 + 28.6139i) q^{96} +(-25.4031 + 1.99927i) q^{97} +5.01394 q^{98} +(-7.68729 - 59.4294i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 544 q - 20 q^{2} - 12 q^{3} - 20 q^{5} - 20 q^{6} - 20 q^{7} - 20 q^{8} + 36 q^{9} + 28 q^{11} - 200 q^{12} + 36 q^{14} + 108 q^{15} + 424 q^{16} - 180 q^{17} - 40 q^{18} - 20 q^{19} - 140 q^{20} + 32 q^{22}+ \cdots - 72 q^{99}+O(q^{100}) \) 544 * q - 20 * q^2 - 12 * q^3 - 20 * q^5 - 20 * q^6 - 20 * q^7 - 20 * q^8 + 36 * q^9 + 28 * q^11 - 200 * q^12 + 36 * q^14 + 108 * q^15 + 424 * q^16 - 180 * q^17 - 40 * q^18 - 20 * q^19 - 140 * q^20 + 32 * q^22 - 48 * q^23 + 460 * q^24 - 84 * q^25 + 132 * q^26 - 228 * q^27 - 20 * q^28 - 20 * q^29 - 100 * q^31 + 24 * q^33 + 96 * q^34 - 40 * q^35 + 164 * q^36 - 332 * q^37 - 20 * q^39 - 760 * q^40 - 560 * q^41 + 276 * q^42 - 240 * q^44 - 32 * q^45 - 20 * q^46 + 252 * q^48 - 472 * q^49 - 40 * q^50 - 20 * q^51 + 280 * q^52 + 92 * q^53 - 160 * q^56 + 1060 * q^57 - 1348 * q^58 - 260 * q^59 - 748 * q^60 - 320 * q^61 - 20 * q^62 + 580 * q^63 + 292 * q^66 + 160 * q^67 - 20 * q^68 - 192 * q^69 - 628 * q^70 - 268 * q^71 - 20 * q^73 - 20 * q^74 + 1116 * q^75 + 732 * q^77 + 1232 * q^78 - 20 * q^79 - 936 * q^80 - 684 * q^82 - 380 * q^83 + 1240 * q^84 - 1320 * q^85 - 632 * q^86 - 412 * q^88 - 20 * q^90 + 1204 * q^91 + 540 * q^92 + 1108 * q^93 - 3800 * q^94 + 360 * q^95 - 20 * q^96 + 652 * q^97 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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