LMFDB - Embedded newform 187.3.q.a.94.18

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			94.18
Character	$\chi$	$=$	187.94
Dual form			187.3.q.a.2.18

$q$-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 $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{8}\right)$

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	−0.871800	−	0.489861i	$-0.837047\pi$
$2$	0.0738746	−	0.144987i	0.0369373	−	0.0724936i	0.908738	+	0.417368i	$0.137047\pi$
$3$	−1.98602	−	3.24089i	−0.662008	−	1.08030i	−0.990727	−	0.135871i	$-0.956617\pi$
$3$	−1.98602	−	3.24089i	−0.662008	−	1.08030i	0.328719	−	0.944428i	$-0.393383\pi$
$4$	2.33558	+	3.21465i	0.583894	+	0.803662i
$5$	−0.527290	−	0.450348i	−0.105458	−	0.0900697i	0.595156	−	0.803610i	$-0.297090\pi$
$5$	−0.527290	−	0.450348i	−0.105458	−	0.0900697i	−0.700614	+	0.713541i	$0.747090\pi$
$6$	−0.616605	+	0.0485279i	−0.102767	+	0.00808798i
$7$	2.22828	−	3.63622i	0.318325	−	0.519459i	−0.652956	−	0.757396i	$-0.726471\pi$
$7$	2.22828	−	3.63622i	0.318325	−	0.519459i	0.971281	+	0.237937i	$0.0764712\pi$
$8$	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	−0.923796	−	0.382886i	$-0.874930\pi$
$13$	−5.21929	−	16.0633i	−0.401484	−	1.23564i	0.522312	−	0.852755i	$-0.325070\pi$
$14$	−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	−0.999358	−	0.0358294i	$-0.988593\pi$
$19$	−1.13970	−	7.19575i	−0.0599840	−	0.378724i	0.939374	−	0.342894i	$-0.111407\pi$
$20$	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	−0.0199908	−	0.999800i	$-0.506364\pi$
$23$	15.4753	−	6.41008i	0.672839	−	0.278699i	0.692830	+	0.721101i	$0.256364\pi$
$24$	−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	0.115826	−	0.993269i	$-0.463048\pi$
$29$	19.4289	−	4.66448i	0.669964	−	0.160844i	0.554137	+	0.832425i	$0.313048\pi$
$30$	0.346984	+	0.252099i	0.0115661	+	0.00840329i
$31$	−0.738604	+	9.38486i	−0.0238259	+	0.302737i	0.973446	+	0.228918i	$0.0735188\pi$
$31$	−0.738604	+	9.38486i	−0.0238259	+	0.302737i	−0.997272	+	0.0738193i	$0.976481\pi$
$32$	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	−0.265296	−	0.964167i	$-0.585470\pi$
$37$	−2.36633	+	0.568104i	−0.0639547	+	0.0153542i	0.201342	+	0.979521i	$0.435470\pi$
$38$	−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	0.978392	−	0.206757i	$-0.0662911\pi$
$41$	72.0075	+	17.2875i	1.75628	+	0.421646i	0.777888	+	0.628403i	$0.216291\pi$
$42$	−1.19751	+	2.35024i	−0.0285121	+	0.0559581i
$43$	−27.3417	+	27.3417i	−0.635854	+	0.635854i	−0.949530	−	0.313676i	$-0.898439\pi$
$43$	−27.3417	+	27.3417i	−0.635854	+	0.635854i	0.313676	+	0.949530i	$0.398439\pi$
$44$	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	−0.679615	−	0.733569i	$-0.737853\pi$
$47$	10.7190	−	14.7534i	0.228064	−	0.313903i	0.907678	+	0.419667i	$0.137853\pi$
$48$	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	0.883746	−	0.467968i	$-0.155014\pi$
$53$	54.3040	+	27.6693i	1.02460	+	0.522062i	0.140859	+	0.990030i	$0.455014\pi$
$54$	−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	0.317221	−	0.948352i	$-0.397250\pi$
$59$	19.2257	+	3.04505i	0.325859	+	0.0516110i	0.00863815	+	0.999963i	$0.497250\pi$
$60$	−9.33168	+	4.75473i	−0.155528	+	0.0792454i
$61$	6.03231	+	76.6478i	0.0988904	+	1.25652i	0.823482	+	0.567343i	$0.192029\pi$
$61$	6.03231	+	76.6478i	0.0988904	+	1.25652i	−0.724591	+	0.689179i	$0.757971\pi$
$62$	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	−0.0629179	+	0.998019i	$0.520041\pi$
$71$	−73.7553	+	86.3563i	−1.03881	+	1.21629i	−0.975889	+	0.218268i	$0.929959\pi$
$72$	−2.18420	+	6.72229i	−0.0303362	+	0.0933651i
$73$	35.2138	−	8.45408i	0.482380	−	0.115809i	0.0150402	−	0.999887i	$-0.495212\pi$
$73$	35.2138	−	8.45408i	0.482380	−	0.115809i	0.467340	+	0.884078i	$0.345212\pi$
$74$	−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	−0.330586	−	0.943776i	$-0.607246\pi$
$79$	43.4386	−	37.1001i	0.549856	−	0.469621i	0.880442	+	0.474155i	$0.157246\pi$
$80$	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	−0.0722955	−	0.997383i	$-0.523032\pi$
$83$	57.4452	−	29.2698i	0.692110	−	0.352648i	0.764406	+	0.644735i	$0.223032\pi$
$84$	−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	$-0.796481\pi$
$89$		−	106.211i		−	1.19338i	0.802470	−	0.596692i	$-0.203519\pi$
$90$	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	−0.0531646	−	0.998586i	$-0.516931\pi$
$97$	−25.4031	−	1.99927i	−0.261888	−	0.0206110i	−0.208723	+	0.977975i	$0.566931\pi$
$98$	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	−0.920648	−	0.390393i	$-0.872339\pi$
$101$	−145.036	+	47.1251i	−1.43600	+	0.466585i	−0.515353	+	0.856978i	$0.672339\pi$
$102$	8.32373	+	6.42452i	0.0816052	+	0.0629855i
$103$	−20.4080	+	14.8273i	−0.198136	+	0.143954i	−0.682430	−	0.730951i	$-0.739077\pi$
$103$	−20.4080	+	14.8273i	−0.198136	+	0.143954i	0.484294	+	0.874905i	$0.339077\pi$
$104$	−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	0.992855	+	0.119329i	$0.0380742\pi$
$107$	69.3821	+	113.221i	0.648431	+	1.05814i	−0.344424	+	0.938814i	$0.611926\pi$
$108$	−34.8442	−	40.7973i	−0.322631	−	0.377753i
$109$	61.4264	−	25.4436i	0.563545	−	0.233428i	−0.0826784	−	0.996576i	$-0.526347\pi$
$109$	61.4264	−	25.4436i	0.563545	−	0.233428i	0.646223	+	0.763148i	$0.276347\pi$
$110$	−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	0.736575	−	0.676356i	$-0.236442\pi$
$113$	122.696	+	29.4568i	1.08581	+	0.260680i	0.349234	+	0.937035i	$0.386442\pi$
$114$	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	0.958587	−	0.284801i	$-0.0919275\pi$
$127$	20.9213	+	41.0604i	0.164735	+	0.323310i	−0.793852	+	0.608111i	$0.791927\pi$
$128$	−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	0.299628	−	0.954056i	$-0.403138\pi$
$131$	−21.3691	−	8.85138i	−0.163123	−	0.0675678i	−0.462751	+	0.886488i	$0.653138\pi$
$132$	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	−0.989752	−	0.142799i	$-0.954390\pi$
$137$	−14.3974	+	44.3106i	−0.105091	+	0.323435i	0.884661	+	0.466234i	$0.154390\pi$
$138$	−9.23108	+	4.70347i	−0.0668919	+	0.0340831i
$139$	−45.4189	−	189.183i	−0.326755	−	1.36103i	−0.857929	−	0.513769i	$-0.828249\pi$
$139$	−45.4189	−	189.183i	−0.326755	−	1.36103i	0.531174	−	0.847263i	$-0.321751\pi$
$140$	−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	−0.870276	−	0.492565i	$-0.836060\pi$
$149$	18.3738	−	56.5488i	0.123314	−	0.379522i	0.993590	+	0.113042i	$0.0360596\pi$
$150$	3.54029	+	14.7464i	0.0236019	+	0.0983090i
$151$	0.709741	+	4.48113i	0.00470027	+	0.0296763i	0.989927	−	0.141579i	$-0.0452178\pi$
$151$	0.709741	+	4.48113i	0.00470027	+	0.0296763i	−0.985227	+	0.171255i	$0.945218\pi$
$152$	−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	−0.928180	−	0.372132i	$-0.878627\pi$
$157$	−45.1278	+	62.1131i	−0.287438	+	0.395625i	0.640742	+	0.767757i	$0.278627\pi$
$158$	−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	−0.175703	+	0.984443i	$0.556220\pi$
$163$	−191.608	+	163.649i	−1.17551	+	1.00398i	−0.999809	+	0.0195386i	$0.993780\pi$
$164$	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	0.487199	−	0.873291i	$-0.338019\pi$
$167$	138.908	+	10.9323i	0.831786	+	0.0654630i	0.344588	+	0.938754i	$0.388019\pi$
$168$	−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	−0.636338	−	0.771411i	$-0.719551\pi$
$173$	−41.1561	+	25.2205i	−0.237897	+	0.145783i	0.398441	+	0.917194i	$0.369551\pi$
$174$	−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	0.917704	+	0.397264i	$0.130040\pi$
$179$	30.0142	+	189.502i	0.167677	+	1.05867i	−0.750028	+	0.661407i	$0.769960\pi$
$180$	12.7985	+	7.84290i	0.0711025	+	0.0435717i
$181$	−25.8474	−	328.422i	−0.142803	−	1.81449i	−0.484624	−	0.874723i	$-0.661043\pi$
$181$	−25.8474	−	328.422i	−0.142803	−	1.81449i	0.341820	−	0.939765i	$-0.388957\pi$
$182$	−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	0.856180	−	0.516677i	$-0.172831\pi$
$191$	19.1414	+	26.3459i	0.100217	+	0.137937i	−0.755963	+	0.654614i	$0.772831\pi$
$192$	177.673	+	151.747i	0.925382	+	0.790351i
$193$	96.5875	−	7.60160i	0.500453	−	0.0393865i	0.174279	−	0.984696i	$-0.444240\pi$
$193$	96.5875	−	7.60160i	0.500453	−	0.0393865i	0.326174	+	0.945310i	$0.394240\pi$
$194$	−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	0.0924879	−	0.995714i	$-0.470518\pi$
$197$	169.807	−	70.3362i	0.861963	−	0.357037i	0.769475	+	0.638677i	$0.220518\pi$
$198$	8.04861	+	5.50489i	0.0406495	+	0.0278025i
$199$	−124.567	+	300.732i	−0.625967	+	1.51122i	0.218626	+	0.975809i	$0.429842\pi$
$199$	−124.567	+	300.732i	−0.625967	+	1.51122i	−0.844593	+	0.535409i	$0.820158\pi$
$200$	−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	0.999634	−	0.0270388i	$-0.00860775\pi$
$211$	172.292	+	201.728i	0.816551	+	0.956059i	−0.183083	+	0.983097i	$0.558608\pi$
$212$	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	0.0314839	−	0.999504i	$-0.489977\pi$
$223$	82.5748	−	13.0786i	0.370291	−	0.0586483i	0.338807	+	0.940856i	$0.389977\pi$
$224$	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	0.443294	−	0.896376i	$-0.353810\pi$
$227$	−34.9880	−	21.4407i	−0.154132	−	0.0944523i	−0.597426	+	0.801924i	$0.703810\pi$
$228$	−106.995	−	25.6872i	−0.469275	−	0.112663i
$229$	−103.134	+	202.412i	−0.450368	+	0.883896i	0.548492	+	0.836156i	$0.315202\pi$
$229$	−103.134	+	202.412i	−0.450368	+	0.883896i	−0.998860	+	0.0477405i	$0.984798\pi$
$230$	−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	−0.993072	−	0.117511i	$-0.962509\pi$
$233$	1.43443	−	18.2262i	0.00615637	−	0.0782241i	0.999228	+	0.0392866i	$0.0125085\pi$
$234$	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	−0.893312	−	0.449437i	$-0.851625\pi$
$239$	−45.3678	+	62.4434i	−0.189823	+	0.261269i	0.703489	+	0.710707i	$0.251625\pi$
$240$	−36.8309	−	18.7663i	−0.153462	−	0.0781928i
$241$	142.172	−	343.234i	0.589925	−	1.42421i	−0.293648	−	0.955914i	$-0.594869\pi$
$241$	142.172	−	343.234i	0.589925	−	1.42421i	0.883574	−	0.468292i	$-0.155131\pi$
$242$	−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	−0.294532	−	0.955642i	$-0.595164\pi$
$251$	7.25375	−	2.35689i	0.0288994	−	0.00938998i	0.323431	+	0.946252i	$0.395164\pi$
$252$	−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	0.443790	+	0.896131i	$0.353634\pi$
$257$	−65.5861	+	414.095i	−0.255199	+	1.61126i	−0.698989	+	0.715132i	$0.746366\pi$
$258$	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	−0.672298	−	0.740280i	$-0.734693\pi$
$263$	17.8793	−	17.8793i	0.0679821	−	0.0679821i	0.740280	+	0.672298i	$0.234693\pi$
$264$	−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	−0.384089	−	0.923296i	$-0.625485\pi$
$269$	158.152	−	185.172i	0.587924	−	0.688371i	0.972013	+	0.234925i	$0.0754845\pi$
$270$	1.35751	−	0.691687i	0.00502783	−	0.00256181i
$271$	222.425	+	306.141i	0.820755	+	1.12967i	0.989574	+	0.144026i	$0.0460048\pi$
$271$	222.425	+	306.141i	0.820755	+	1.12967i	−0.168819	+	0.985647i	$0.553995\pi$
$272$	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	−0.642972	−	0.765889i	$-0.722299\pi$
$277$	30.9950	−	393.829i	0.111895	−	1.42177i	0.754868	−	0.655877i	$-0.227701\pi$
$278$	−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	0.674562	−	0.738218i	$-0.264332\pi$
$281$	−89.6857	−	176.018i	−0.319166	−	0.626399i	−0.993729	+	0.111819i	$0.964332\pi$
$282$	−5.89343	+	9.61720i	−0.0208987	+	0.0341036i
$283$	−69.0483	+	287.607i	−0.243987	+	1.01628i	0.707041	+	0.707173i	$0.250030\pi$
$283$	−69.0483	+	287.607i	−0.243987	+	1.01628i	−0.951028	+	0.309106i	$0.899970\pi$
$284$	−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	0.536928	−	0.843628i	$-0.319585\pi$
$293$	441.019	−	320.419i	1.50519	−	1.09358i	0.968258	−	0.249953i	$-0.0804153\pi$
$294$	−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	$-0.754088\pi$
$307$		−	428.553i		−	1.39594i	0.716129	−	0.697968i	$-0.245912\pi$
$308$	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	0.433809	−	0.901005i	$-0.357169\pi$
$311$	445.836	−	273.209i	1.43356	−	0.878484i	0.999746	+	0.0225206i	$0.00716915\pi$
$312$	−43.5223	+	71.0220i	−0.139495	+	0.227635i
$313$	−291.041	+	22.9054i	−0.929843	+	0.0731803i	−0.534326	−	0.845278i	$-0.679435\pi$
$313$	−291.041	+	22.9054i	−0.929843	+	0.0731803i	−0.395517	+	0.918459i	$0.629435\pi$
$314$	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	0.857295	−	0.514825i	$-0.172143\pi$
$317$	68.0594	+	79.6873i	0.214698	+	0.251380i	−0.642597	+	0.766204i	$0.722143\pi$
$318$	−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	0.414374	−	0.910107i	$-0.364001\pi$
$331$	−164.088	−	164.088i	−0.495733	−	0.495733i	−0.910107	+	0.414374i	$0.864001\pi$
$332$	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	0.892340	+	0.451363i	$0.149062\pi$
$337$	101.833	+	424.163i	0.302174	+	1.25864i	−0.590167	+	0.807281i	$0.700938\pi$
$338$	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	−0.902339	−	0.431027i	$-0.858151\pi$
$347$	−27.2523	−	346.273i	−0.0785368	−	0.997904i	0.823802	−	0.566877i	$-0.191849\pi$
$348$	47.2090	−	298.066i	0.135658	−	0.856511i
$349$	154.864	−	24.5281i	0.443737	−	0.0702811i	0.0694322	−	0.997587i	$-0.477881\pi$
$349$	154.864	−	24.5281i	0.443737	−	0.0702811i	0.374305	+	0.927306i	$0.377881\pi$
$350$	−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	$0.159150\pi$
$353$			338.465i			0.958824i	−0.877590	+	0.479412i	$0.840850\pi$
$354$	−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	−0.445949	−	0.895058i	$-0.647134\pi$
$359$	−411.651	−	65.1991i	−1.14666	−	0.181613i	−0.700711	+	0.713445i	$0.747134\pi$
$360$	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	−0.371572	−	0.928404i	$-0.621181\pi$
$367$	−501.864	−	307.542i	−1.36748	−	0.837990i	−0.995904	+	0.0904140i	$0.971181\pi$
$368$	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	$0.0891955\pi$
$373$			206.316i			0.553126i	−0.960996	+	0.276563i	$0.910805\pi$
$374$	−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	0.352778	−	0.935707i	$-0.385237\pi$
$379$	−195.649	−	167.100i	−0.516223	−	0.440896i	−0.869001	+	0.494811i	$0.835237\pi$
$380$	−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	−0.995244	−	0.0974084i	$-0.968945\pi$
$383$	−126.945	+	249.144i	−0.331449	+	0.650506i	0.663795	+	0.747914i	$0.268945\pi$
$384$	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	−0.875056	−	0.484021i	$-0.839176\pi$
$389$	41.5228	−	262.165i	0.106742	−	0.673945i	0.981799	−	0.189924i	$-0.0608242\pi$
$390$	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	−0.290773	−	0.956792i	$-0.593912\pi$
$397$	71.5292	−	29.6284i	0.180174	−	0.0746307i	0.470947	+	0.882162i	$0.343912\pi$
$398$	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	−0.343789	−	0.939047i	$-0.611711\pi$
$401$	−215.115	+	16.9299i	−0.536447	+	0.0422193i	−0.192657	+	0.981266i	$0.561711\pi$
$402$	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	−0.788356	−	0.615219i	$-0.789068\pi$
$409$	−435.394	+	141.468i	−1.06453	+	0.345888i	−0.276177	+	0.961107i	$0.589068\pi$
$410$	−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	−0.631608	−	0.775288i	$-0.717605\pi$
$419$	−222.075	+	91.9864i	−0.530011	+	0.219538i	0.101597	+	0.994826i	$0.467605\pi$
$420$	−3.50434	+	44.5268i	−0.00834366	+	0.106016i
$421$	422.986	−	582.190i	1.00472	−	1.38287i	0.0823296	−	0.996605i	$-0.473764\pi$
$421$	422.986	−	582.190i	1.00472	−	1.38287i	0.922387	−	0.386268i	$-0.126236\pi$
$422$	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	−0.636069	−	0.771632i	$-0.719441\pi$
$431$	11.4471	−	9.77678i	0.0265595	−	0.0226839i	0.662629	+	0.748948i	$0.269441\pi$
$432$	49.4338	−	205.906i	0.114430	−	0.476635i
$433$	630.085	+	99.7957i	1.45516	+	0.230475i	0.833374	−	0.552710i	$-0.186406\pi$
$433$	630.085	+	99.7957i	1.45516	+	0.230475i	0.621789	+	0.783185i	$0.286406\pi$
$434$	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	−0.779549	−	0.626341i	$-0.784552\pi$
$439$	94.1941	−	227.405i	0.214565	−	0.518006i	0.994114	+	0.108335i	$0.0345519\pi$
$440$	−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	0.223808	−	0.974633i	$-0.428151\pi$
$443$	−280.845	−	204.046i	−0.633962	−	0.460601i	−0.857771	+	0.514033i	$0.828151\pi$
$444$	−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	−0.463003	−	0.886357i	$-0.653228\pi$
$449$	152.666	−	130.389i	0.340012	−	0.290398i	0.803015	+	0.595959i	$0.203228\pi$
$450$	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	−0.218787	−	0.975773i	$-0.570210\pi$
$457$	202.008	−	102.928i	0.442030	−	0.225226i	0.660817	+	0.750547i	$0.270210\pi$
$458$	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	0.342075	−	0.939672i	$-0.388870\pi$
$461$	−275.492	−	275.492i	−0.597597	−	0.597597i	−0.939672	+	0.342075i	$0.888870\pi$
$462$	−3.72214	+	28.7754i	−0.00805658	+	0.0622844i
$463$		−	82.2263i		−	0.177595i	−0.996050	−	0.0887973i	$-0.971698\pi$
$463$		−	82.2263i		−	0.177595i	0.996050	−	0.0887973i	$-0.0283023\pi$
$464$	−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	−0.980990	−	0.194058i	$-0.937835\pi$
$467$	−654.082	+	333.272i	−1.40060	+	0.713644i	−0.419615	+	0.907702i	$0.637835\pi$
$468$	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	0.829375	−	0.558692i	$-0.188697\pi$
$479$	195.099	+	166.630i	0.407304	+	0.347871i	−0.422071	+	0.906563i	$0.638697\pi$
$480$	−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	0.654130	−	0.756383i	$-0.273035\pi$
$487$	435.170	+	104.475i	0.893573	+	0.214528i	0.239443	+	0.970910i	$0.423035\pi$
$488$	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	−0.429680	−	0.902981i	$-0.641374\pi$
$491$	−548.627	−	86.8940i	−1.11737	−	0.176973i	−0.687686	+	0.726008i	$0.741374\pi$
$492$	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	−0.964071	−	0.265645i	$-0.914415\pi$
$499$	−144.561	+	235.902i	−0.289701	+	0.472749i	0.674370	+	0.738393i	$0.264415\pi$
$500$	−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	0.798674	−	0.601765i	$-0.205535\pi$
$503$	622.262	+	149.392i	1.23710	+	0.297002i	0.438428	+	0.898766i	$0.355535\pi$
$504$	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	0.0953592	−	0.995443i	$-0.469600\pi$
$509$	−418.345	−	303.945i	−0.821896	−	0.597142i	−0.917255	+	0.398301i	$0.869600\pi$
$510$	−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	−0.683966	−	0.729514i	$-0.739746\pi$
$521$	144.082	−	235.121i	0.276549	−	0.451288i	0.960516	+	0.278226i	$0.0897464\pi$
$522$	13.4686	+	11.5033i	0.0258020	+	0.0220370i
$523$	−204.690	+	629.972i	−0.391377	+	1.20453i	0.540370	+	0.841427i	$0.318284\pi$
$523$	−204.690	+	629.972i	−0.391377	+	1.20453i	−0.931747	+	0.363107i	$0.881716\pi$
$524$	−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	0.00194128	−	0.999998i	$-0.499382\pi$
$541$	−82.5433	−	6.49630i	−0.152576	−	0.0120080i	−0.154517	+	0.987990i	$0.549382\pi$
$542$	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	−0.979042	−	0.203659i	$-0.934717\pi$
$547$	−679.405	+	416.340i	−1.24206	+	0.761133i	−0.263014	+	0.964792i	$0.584717\pi$
$548$	−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	−0.746038	−	0.665903i	$-0.768046\pi$
$557$	−191.199	+	138.914i	−0.343265	+	0.249397i	0.402773	+	0.915300i	$0.368046\pi$
$558$	−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	−0.876559	−	0.481295i	$-0.840167\pi$
$563$	15.7896	−	30.9888i	0.0280455	−	0.0550423i	0.904604	+	0.426253i	$0.140167\pi$
$564$	−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	−0.715463	−	0.698651i	$-0.753784\pi$
$569$	−671.428	+	106.344i	−1.18001	+	0.186896i	−0.464551	+	0.885547i	$0.653784\pi$
$570$	1.41858	−	2.78413i	0.00248874	−	0.00488443i
$571$	−769.379	+	318.687i	−1.34742	+	0.558121i	−0.935574	−	0.353131i	$-0.885117\pi$
$571$	−769.379	+	318.687i	−1.34742	+	0.558121i	−0.411850	+	0.911252i	$0.635117\pi$
$572$	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	−0.907638	−	0.419753i	$-0.862117\pi$
$577$	42.3408	−	130.312i	0.0733810	−	0.225844i	0.981019	+	0.193909i	$0.0621168\pi$
$578$	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	−0.558917	−	0.829224i	$-0.688783\pi$
$587$	−790.526	−	125.207i	−1.34672	−	0.213300i	−0.787806	+	0.615924i	$0.788783\pi$
$588$	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	0.814384	−	0.580326i	$-0.197075\pi$
$593$	138.796	+	138.796i	0.234058	+	0.234058i	−0.580326	+	0.814384i	$0.697075\pi$
$594$	−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	−0.720714	−	0.693232i	$-0.756186\pi$
$599$	−1025.04	−	333.056i	−1.71126	−	0.556021i	−0.990542	+	0.137211i	$0.956186\pi$
$600$	−78.5322	+	91.9494i	−0.130887	+	0.153249i
$601$	904.141	+	554.058i	1.50439	+	0.921894i	0.998231	+	0.0594556i	$0.0189365\pi$
$601$	904.141	+	554.058i	1.50439	+	0.921894i	0.506163	+	0.862438i	$0.331064\pi$
$602$	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	0.767058	+	0.641578i	$0.221720\pi$
$607$	−55.1892	+	701.245i	−0.0909212	+	1.15526i	−0.857979	+	0.513685i	$0.828280\pi$
$608$	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	−0.954272	−	0.298938i	$-0.903367\pi$
$613$	−229.923	+	316.462i	−0.375079	+	0.516252i	0.579194	+	0.815190i	$0.303367\pi$
$614$	−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	−0.918214	−	0.396086i	$-0.870368\pi$
$617$	6.87116	−	16.5884i	0.0111364	−	0.0268857i	0.929350	+	0.369200i	$0.120368\pi$
$618$	11.8641	−	10.1329i	0.0191976	−	0.0163963i
$619$	−230.768	+	961.220i	−0.372809	+	1.55286i	0.398968	+	0.916965i	$0.369369\pi$
$619$	−230.768	+	961.220i	−0.372809	+	1.55286i	−0.771776	+	0.635894i	$0.780631\pi$
$620$	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	−0.0140635	−	0.999901i	$-0.504477\pi$
$631$	194.536	−	1228.25i	0.308298	−	1.94652i	0.322362	−	0.946617i	$-0.395523\pi$
$632$	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	0.163498	−	0.986544i	$-0.447722\pi$
$641$	715.831	−	438.662i	1.11674	−	0.684340i	0.953243	+	0.302204i	$0.0977222\pi$
$642$	−48.2757	−	66.4458i	−0.0751958	−	0.103498i
$643$	−3.49188	+	4.08846i	−0.00543060	+	0.00635842i	−0.763115	−	0.646263i	$-0.776331\pi$
$643$	−3.49188	+	4.08846i	−0.00543060	+	0.00635842i	0.757684	+	0.652622i	$0.226331\pi$
$644$	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	−0.973865	−	0.227126i	$-0.927067\pi$
$647$	−206.712	−	636.194i	−0.319493	−	0.983298i	0.654373	−	0.756172i	$-0.272933\pi$
$648$	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	0.927383	−	0.374112i	$-0.122053\pi$
$653$	662.841	+	406.189i	1.01507	+	0.622036i	0.0876868	+	0.996148i	$0.472053\pi$
$654$	−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	−0.968159	−	0.250335i	$-0.919459\pi$
$661$	−474.482	+	474.482i	−0.717824	+	0.717824i	0.250335	+	0.968159i	$0.419459\pi$
$662$	−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	0.886990	−	0.461789i	$-0.152792\pi$
$673$	196.603	+	230.193i	0.292130	+	0.342040i	−0.594860	+	0.803830i	$0.702792\pi$
$674$	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	0.101045	−	0.994882i	$-0.467781\pi$
$677$	−586.134	−	500.606i	−0.865781	−	0.739447i	−0.966826	+	0.255435i	$0.917781\pi$
$678$	−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	0.553436	−	0.832891i	$-0.313316\pi$
$683$	243.033	+	100.668i	0.355832	+	0.147390i	−0.197604	+	0.980282i	$0.563316\pi$
$684$	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	0.975174	−	0.221442i	$-0.0710763\pi$
$691$	417.300	+	488.595i	0.603907	+	0.707084i	−0.371266	+	0.928526i	$0.621076\pi$
$692$	−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	0.303289	−	0.952899i	$-0.401915\pi$
$701$	−356.984	−	259.364i	−0.509249	−	0.369991i	−0.812539	+	0.582907i	$0.801915\pi$
$702$	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	0.795609	−	0.605810i	$-0.207151\pi$
$709$	228.098	+	194.814i	0.321718	+	0.274773i	−0.473891	+	0.880583i	$0.657151\pi$
$710$	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	0.972103	−	0.234553i	$-0.0753628\pi$
$719$	−0.382608	−	1.59368i	−0.000532139	−	0.00221652i	−0.972635	+	0.232337i	$0.925363\pi$
$720$	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	$0.346091\pi$
$727$			1287.32i			1.77073i	−0.464897	+	0.885365i	$0.653909\pi$
$728$	−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	−0.327557	−	0.944831i	$-0.606225\pi$
$733$	−682.461	−	108.091i	−0.931052	−	0.147464i	−0.603494	+	0.797367i	$0.706225\pi$
$734$	−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	0.999522	−	0.0309303i	$-0.00984700\pi$
$739$	1154.32	+	588.155i	1.56200	+	0.795880i	0.562481	+	0.826810i	$0.309847\pi$
$740$	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	−0.479612	−	0.877481i	$-0.659222\pi$
$743$	343.336	−	401.995i	0.462094	−	0.541042i	0.941705	+	0.336438i	$0.109222\pi$
$744$	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	0.909944	−	0.414731i	$-0.136124\pi$
$751$	95.6102	+	156.022i	0.127311	+	0.207752i	−0.782634	+	0.622482i	$0.786124\pi$
$752$	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	−0.381033	−	0.924561i	$-0.624432\pi$
$757$	447.325	−	877.925i	0.590919	−	1.15974i	0.971951	−	0.235181i	$-0.0755684\pi$
$758$	−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	0.987594	+	0.157032i	$0.0501926\pi$
$761$	213.776	+	657.935i	0.280915	+	0.864566i	−0.706679	+	0.707534i	$0.749807\pi$
$762$	−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	0.874241	+	0.485493i	$0.161360\pi$
$773$	149.045	+	941.034i	0.192814	+	1.21738i	−0.681427	+	0.731886i	$0.738640\pi$
$774$	−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	−0.936818	−	0.349816i	$-0.886244\pi$
$787$	−350.025	+	409.826i	−0.444758	+	0.520745i	0.492060	+	0.870561i	$0.336244\pi$
$788$	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	0.704017	−	0.710183i	$-0.251388\pi$
$797$	−226.622	−	444.771i	−0.284344	−	0.558056i	−0.988361	+	0.152127i	$0.951388\pi$
$798$	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	−0.917938	−	0.396724i	$-0.870147\pi$
$809$	−59.3503	−	754.118i	−0.0733626	−	0.932160i	0.844576	−	0.535436i	$-0.179853\pi$
$810$	−9.65482	−	5.91648i	−0.0119195	−	0.00730430i
$811$	−411.741	−	671.901i	−0.507696	−	0.828484i	0.491403	−	0.870932i	$-0.336484\pi$
$811$	−411.741	−	671.901i	−0.507696	−	0.828484i	−0.999099	+	0.0424482i	$0.986484\pi$
$812$	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	−0.924094	−	0.382165i	$-0.875179\pi$
$821$	−1292.23	+	310.237i	−1.57397	+	0.377876i	−0.649874	+	0.760042i	$0.725179\pi$
$822$	6.72721	−	28.0208i	0.00818395	−	0.0340886i
$823$	−507.905	+	433.792i	−0.617138	+	0.527086i	−0.902141	−	0.431441i	$-0.858005\pi$
$823$	−507.905	+	433.792i	−0.617138	+	0.527086i	0.285003	+	0.958527i	$0.408005\pi$
$824$	−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	−0.413542	−	0.910485i	$-0.635709\pi$
$827$	348.201	−	297.392i	0.421041	−	0.359603i	0.834583	+	0.550882i	$0.185709\pi$
$828$	−309.156	+	189.451i	−0.373376	+	0.228805i
$829$	−172.385	−	237.267i	−0.207943	−	0.286209i	0.692288	−	0.721621i	$-0.256603\pi$
$829$	−172.385	−	237.267i	−0.207943	−	0.286209i	−0.900231	+	0.435412i	$0.856603\pi$
$830$	−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	0.513927	−	0.857834i	$-0.328190\pi$
$839$	488.626	+	117.309i	0.582391	+	0.139820i	0.0684637	+	0.997654i	$0.478190\pi$
$840$	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	0.459567	−	0.888143i	$-0.348005\pi$
$853$	−294.924	−	251.889i	−0.345750	−	0.295298i	−0.805317	+	0.592845i	$0.798005\pi$
$854$	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	−0.415356	−	0.909659i	$-0.636343\pi$
$857$	−56.4173	+	23.3688i	−0.0658311	+	0.0272682i	0.349525	+	0.936927i	$0.386343\pi$
$858$	77.0849	+	85.2229i	0.0898426	+	0.0993274i
$859$	−472.268	−	472.268i	−0.549788	−	0.549788i	0.376591	−	0.926379i	$-0.377096\pi$
$859$	−472.268	−	472.268i	−0.549788	−	0.549788i	−0.926379	+	0.376591i	$0.877096\pi$
$860$	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	0.832729	−	0.553681i	$-0.186777\pi$
$863$	1019.18	+	331.152i	1.18097	+	0.383722i	0.348246	+	0.937403i	$0.386777\pi$
$864$	−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	0.484750	−	0.874653i	$-0.338911\pi$
$877$	455.673	+	109.397i	0.519582	+	0.124740i	0.0348315	+	0.999393i	$0.488911\pi$
$878$	−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	0.920675	−	0.390330i	$-0.127639\pi$
$881$	1141.50	+	472.825i	1.29569	+	0.536691i	0.375011	+	0.927020i	$0.377639\pi$
$882$	−12.4005	+	24.3373i	−0.0140595	+	0.0275933i
$883$	450.245	+	327.122i	0.509903	+	0.370466i	0.812787	−	0.582561i	$-0.197949\pi$
$883$	450.245	+	327.122i	0.509903	+	0.370466i	−0.302884	+	0.953028i	$0.597949\pi$
$884$	−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	−0.953002	−	0.302963i	$-0.902024\pi$
$887$	−214.134	−	891.930i	−0.241413	−	1.00556i	0.711589	−	0.702596i	$-0.247976\pi$
$888$	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	−0.935897	−	0.352273i	$-0.885409\pi$
$907$	−60.4334	−	767.880i	−0.0666300	−	0.846615i	0.869267	−	0.494342i	$-0.164591\pi$
$908$	−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	−0.339646	−	0.940553i	$-0.610307\pi$
$911$	488.473	−	417.196i	0.536195	−	0.457953i	0.875841	+	0.482600i	$0.160307\pi$
$912$	−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	0.229682	−	0.973266i	$-0.426231\pi$
$919$	−143.890	−	46.7527i	−0.156572	−	0.0508735i	−0.386254	+	0.922392i	$0.626231\pi$
$920$	−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	0.789433	+	0.613837i	$0.210375\pi$
$929$	98.2367	+	1248.22i	0.105745	+	1.34361i	−0.683688	+	0.729774i	$0.739625\pi$
$930$	−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	−0.394987	−	0.918687i	$-0.629251\pi$
$937$	543.847	−	1067.36i	0.580413	−	1.13913i	0.975401	−	0.220439i	$-0.0707489\pi$
$938$	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	0.631136	−	0.775672i	$-0.282589\pi$
$941$	1294.67	−	101.893i	1.37584	−	0.108281i	0.744707	+	0.667391i	$0.232589\pi$
$942$	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	−0.714561	−	0.699574i	$-0.753373\pi$
$947$	270.258	−	652.460i	0.285383	−	0.688976i	0.999944	+	0.0105974i	$0.00337331\pi$
$948$	−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	0.924550	−	0.381061i	$-0.124441\pi$
$953$	263.445	+	362.601i	0.276437	+	0.380484i	−0.648112	+	0.761545i	$0.724441\pi$
$954$	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	0.976690	+	0.214655i	$0.0688627\pi$
$967$	1152.03	+	1152.03i	1.19134	+	1.19134i	0.214655	+	0.976690i	$0.431137\pi$
$968$	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	0.291379	−	0.956608i	$-0.405886\pi$
$971$	839.046	−	132.892i	0.864105	−	0.136861i	0.572726	+	0.819747i	$0.305886\pi$
$972$	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	−0.172489	+	0.985011i	$0.555181\pi$
$977$	−848.030	+	1664.35i	−0.867994	+	1.70353i	−0.695504	+	0.718522i	$0.744819\pi$
$978$	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	−0.866817	−	0.498626i	$-0.833838\pi$
$983$	−1388.77	+	333.414i	−1.41279	+	0.339180i	−0.545969	+	0.837806i	$0.683838\pi$
$984$	−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	−0.901690	−	0.432384i	$-0.857672\pi$
$991$	41.2681	−	99.6301i	0.0416429	−	0.100535i	0.943332	+	0.331849i	$0.107672\pi$
$992$	−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	−0.0604455	−	0.998171i	$-0.519252\pi$
$997$	−974.333	−	597.072i	−0.977265	−	0.598868i	−0.916819	+	0.399303i	$0.869252\pi$
$998$	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.94.18	yes	544
11.2	odd	10	inner	187.3.q.a.145.18	yes	544
17.2	even	8	inner	187.3.q.a.138.18	yes	544
187.2	odd	40	inner	187.3.q.a.2.18	✓	544

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.3.q.a.2.18	✓	544	187.2	odd	40	inner
187.3.q.a.94.18	yes	544	1.1	even	1	trivial
187.3.q.a.138.18	yes	544	17.2	even	8	inner
187.3.q.a.145.18	yes	544	11.2	odd	10	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

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Database

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