LMFDB - Embedded newform 187.3.q.a.138.18

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			138.18
Character	$\chi$	$=$	187.138
Dual form			187.3.q.a.145.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.144987 + 0.0738746i) q^{2} +(-3.69599 - 0.887328i) q^{3} +(-2.33558 - 3.21465i) q^{4} +(0.691295 - 0.0544061i) q^{5} +(-0.470320 - 0.401691i) q^{6} +(-4.14682 + 0.995564i) q^{7} +(-0.202970 - 1.28150i) q^{8} +(4.85392 + 2.47320i) q^{9} +(0.104248 + 0.0431810i) q^{10} +(9.93913 + 4.71315i) q^{11} +(5.77982 + 13.9537i) q^{12} +(5.21929 + 16.0633i) q^{13} +(-0.674783 - 0.162001i) q^{14} +(-2.60329 - 0.412321i) q^{15} +(-4.84630 + 14.9154i) q^{16} +(-16.9018 + 1.82481i) q^{17} +(0.521050 + 0.717164i) q^{18} +(7.19575 - 1.13970i) q^{19} +(-1.78947 - 2.09520i) q^{20} +16.2100 q^{21} +(1.09286 + 1.41760i) q^{22} +(15.4753 + 6.41008i) q^{23} +(-0.386938 + 4.91651i) q^{24} +(-24.2173 + 3.83564i) q^{25} +(-0.429942 + 2.71455i) q^{26} +(10.2673 + 8.76910i) q^{27} +(12.8856 + 11.0053i) q^{28} +(-10.4401 + 17.0366i) q^{29} +(-0.346984 - 0.252099i) q^{30} +(6.11382 + 7.15837i) 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} +(-3.38626 - 21.3800i) q^{36} +(-1.27153 + 2.07496i) q^{37} +(1.12749 + 0.366342i) q^{38} +(-5.03700 - 64.0011i) q^{39} +(-0.210033 - 0.874852i) q^{40} +(-38.6929 - 63.1411i) q^{41} +(2.35024 + 1.19751i) q^{42} +(27.3417 + 27.3417i) q^{43} +(-8.06249 - 42.9587i) q^{44} +(3.49005 + 1.44563i) q^{45} +(1.77018 + 2.07261i) q^{46} +(-10.7190 + 14.7534i) q^{47} +(31.1467 - 50.8268i) q^{48} +(-27.4543 + 13.9887i) q^{49} +(-3.79455 - 1.23292i) q^{50} +(64.0880 + 8.25295i) q^{51} +(39.4479 - 54.2953i) q^{52} +(-27.6693 + 54.3040i) q^{53} +(0.840812 + 2.02990i) q^{54} +(7.12729 + 2.71743i) q^{55} +(2.11749 + 5.11208i) q^{56} +(-27.6067 - 2.17269i) q^{57} +(-2.77225 + 1.69884i) q^{58} +(3.04505 - 19.2257i) q^{59} +(4.75473 + 9.33168i) q^{60} +(49.9327 - 58.4637i) q^{61} +(0.357604 + 1.48953i) q^{62} +(-22.5906 - 5.42352i) q^{63} +(58.4634 - 18.9959i) q^{64} +(4.48201 + 10.8205i) q^{65} +(-2.78134 - 6.20915i) q^{66} -124.848 q^{67} +(45.3415 + 50.0712i) q^{68} +(-51.5087 - 37.4232i) q^{69} +(-0.475288 - 0.0752782i) q^{70} +(8.91029 + 113.216i) q^{71} +(2.18420 - 6.72229i) q^{72} +(-18.9220 + 30.8778i) q^{73} +(-0.337643 + 0.206908i) q^{74} +(92.9103 + 7.31220i) q^{75} +(-20.4700 - 20.4700i) q^{76} +(-45.9080 - 9.64955i) q^{77} +(3.99776 - 9.65145i) q^{78} +(56.9495 + 4.48202i) q^{79} +(-2.53873 + 10.5746i) q^{80} +(-58.9854 - 81.1864i) q^{81} +(-0.945449 - 12.0131i) q^{82} +(29.2698 + 57.4452i) q^{83} +(-37.8597 - 52.1094i) q^{84} +(-11.5848 + 2.18104i) q^{85} +(1.94434 + 5.98405i) q^{86} +(53.7034 - 53.7034i) q^{87} +(4.02256 - 13.6936i) q^{88} +106.211i q^{89} +(0.399217 + 0.467423i) q^{90} +(-37.6355 - 61.4156i) q^{91} +(-15.5376 - 64.7188i) q^{92} +(-16.2448 - 31.8822i) q^{93} +(-2.64402 + 1.34720i) q^{94} +(4.91238 - 1.17936i) q^{95} +(25.0906 - 15.3755i) q^{96} +(19.3764 - 16.5490i) q^{97} -5.01394 q^{98} +(36.5872 + 47.4587i) 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 $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{8}\right)$

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 $

$2$	0.144987	+	0.0738746i	0.0724936	+	0.0369373i	0.489861	−	0.871800i	$-0.337047\pi$
$2$	0.144987	+	0.0738746i	0.0724936	+	0.0369373i	−0.417368	+	0.908738i	$0.637047\pi$
$3$	−3.69599	−	0.887328i	−1.23200	−	0.295776i	−0.435372	−	0.900251i	$-0.643383\pi$
$3$	−3.69599	−	0.887328i	−1.23200	−	0.295776i	−0.796624	+	0.604475i	$0.793383\pi$
$4$	−2.33558	−	3.21465i	−0.583894	−	0.803662i
$5$	0.691295	−	0.0544061i	0.138259	−	0.0108812i	−0.00914076	−	0.999958i	$-0.502910\pi$
$5$	0.691295	−	0.0544061i	0.138259	−	0.0108812i	0.147400	+	0.989077i	$0.452910\pi$
$6$	−0.470320	−	0.401691i	−0.0783866	−	0.0669485i
$7$	−4.14682	+	0.995564i	−0.592403	+	0.142223i	−0.518552	−	0.855046i	$-0.673529\pi$
$7$	−4.14682	+	0.995564i	−0.592403	+	0.142223i	−0.0738508	+	0.997269i	$0.523529\pi$
$8$	−0.202970	−	1.28150i	−0.0253712	−	0.160188i
$9$	4.85392	+	2.47320i	0.539325	+	0.274800i
$10$	0.104248	+	0.0431810i	0.0104248	+	0.00431810i
$11$	9.93913	+	4.71315i	0.903557	+	0.428468i
$11$	9.93913	+	4.71315i	0.903557	+	0.428468i
$12$	5.77982	+	13.9537i	0.481652	+	1.16281i
$13$	5.21929	+	16.0633i	0.401484	+	1.23564i	0.923796	+	0.382886i	$0.125070\pi$
$13$	5.21929	+	16.0633i	0.401484	+	1.23564i	−0.522312	+	0.852755i	$0.674930\pi$
$14$	−0.674783	−	0.162001i	−0.0481988	−	0.0115715i
$15$	−2.60329	−	0.412321i	−0.173553	−	0.0274881i
$16$	−4.84630	+	14.9154i	−0.302894	+	0.932211i
$17$	−16.9018	+	1.82481i	−0.994222	+	0.107342i
$17$	−16.9018	+	1.82481i	−0.994222	+	0.107342i
$18$	0.521050	+	0.717164i	0.0289472	+	0.0398424i
$19$	7.19575	−	1.13970i	0.378724	−	0.0599840i	0.0358294	−	0.999358i	$-0.488593\pi$
$19$	7.19575	−	1.13970i	0.378724	−	0.0599840i	0.342894	+	0.939374i	$0.388593\pi$
$20$	−1.78947	−	2.09520i	−0.0894734	−	0.104760i
$21$	16.2100			0.771905
$22$	1.09286	+	1.41760i	0.0496756	+	0.0644362i
$23$	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	$0.506364\pi$
$24$	−0.386938	+	4.91651i	−0.0161224	+	0.204855i
$25$	−24.2173	+	3.83564i	−0.968691	+	0.153426i
$26$	−0.429942	+	2.71455i	−0.0165362	+	0.104406i
$27$	10.2673	+	8.76910i	0.380270	+	0.324781i
$28$	12.8856	+	11.0053i	0.460200	+	0.393048i
$29$	−10.4401	+	17.0366i	−0.360002	+	0.587470i	−0.980448	−	0.196780i	$-0.936952\pi$
$29$	−10.4401	+	17.0366i	−0.360002	+	0.587470i	0.620446	+	0.784249i	$0.286952\pi$
$30$	−0.346984	−	0.252099i	−0.0115661	−	0.00840329i
$31$	6.11382	+	7.15837i	0.197220	+	0.230915i	0.850200	−	0.526461i	$-0.176481\pi$
$31$	6.11382	+	7.15837i	0.197220	+	0.230915i	−0.652979	+	0.757376i	$0.726481\pi$
$32$	−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
$36$	−3.38626	−	21.3800i	−0.0940627	−	0.593889i
$37$	−1.27153	+	2.07496i	−0.0343658	+	0.0560799i	−0.869362	−	0.494176i	$-0.835470\pi$
$37$	−1.27153	+	2.07496i	−0.0343658	+	0.0560799i	0.834996	+	0.550256i	$0.185470\pi$
$38$	1.12749	+	0.366342i	0.0296707	+	0.00964059i
$39$	−5.03700	−	64.0011i	−0.129154	−	1.64105i
$40$	−0.210033	−	0.874852i	−0.00525083	−	0.0218713i
$41$	−38.6929	−	63.1411i	−0.943729	−	1.54003i	−0.838027	−	0.545628i	$-0.816291\pi$
$41$	−38.6929	−	63.1411i	−0.943729	−	1.54003i	−0.105702	−	0.994398i	$-0.533709\pi$
$42$	2.35024	+	1.19751i	0.0559581	+	0.0285121i
$43$	27.3417	+	27.3417i	0.635854	+	0.635854i	0.949530	−	0.313676i	$-0.101561\pi$
$43$	27.3417	+	27.3417i	0.635854	+	0.635854i	−0.313676	+	0.949530i	$0.601561\pi$
$44$	−8.06249	−	42.9587i	−0.183238	−	0.976334i
$45$	3.49005	+	1.44563i	0.0775566	+	0.0321250i
$46$	1.77018	+	2.07261i	0.0384821	+	0.0450568i
$47$	−10.7190	+	14.7534i	−0.228064	+	0.313903i	−0.907678	−	0.419667i	$-0.862147\pi$
$47$	−10.7190	+	14.7534i	−0.228064	+	0.313903i	0.679615	+	0.733569i	$0.262147\pi$
$48$	31.1467	−	50.8268i	0.648890	−	1.05889i
$49$	−27.4543	+	13.9887i	−0.560293	+	0.285483i
$50$	−3.79455	−	1.23292i	−0.0758910	−	0.0246585i
$51$	64.0880	+	8.25295i	1.25663	+	0.161822i
$52$	39.4479	−	54.2953i	0.758613	−	1.04414i
$53$	−27.6693	+	54.3040i	−0.522062	+	1.02460i	0.467968	+	0.883746i	$0.344986\pi$
$53$	−27.6693	+	54.3040i	−0.522062	+	1.02460i	−0.990030	+	0.140859i	$0.955014\pi$
$54$	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
$57$	−27.6067	−	2.17269i	−0.484328	−	0.0381175i
$58$	−2.77225	+	1.69884i	−0.0477974	+	0.0292903i
$59$	3.04505	−	19.2257i	0.0516110	−	0.325859i	−0.948352	−	0.317221i	$-0.897250\pi$
$59$	3.04505	−	19.2257i	0.0516110	−	0.325859i	0.999963	−	0.00863815i	$-0.00274964\pi$
$60$	4.75473	+	9.33168i	0.0792454	+	0.155528i
$61$	49.9327	−	58.4637i	0.818569	−	0.958421i	−0.181118	−	0.983461i	$-0.557971\pi$
$61$	49.9327	−	58.4637i	0.818569	−	0.958421i	0.999686	+	0.0250404i	$0.00797145\pi$
$62$	0.357604	+	1.48953i	0.00576781	+	0.0240246i
$63$	−22.5906	−	5.42352i	−0.358581	−	0.0860876i
$64$	58.4634	−	18.9959i	0.913490	−	0.296811i
$65$	4.48201	+	10.8205i	0.0689540	+	0.166470i
$66$	−2.78134	−	6.20915i	−0.0421415	−	0.0940780i
$67$	−124.848			−1.86341			−0.931704	−	0.363219i	$-0.881678\pi$
$67$	−124.848			−1.86341			−0.931704	+	0.363219i	$0.881678\pi$
$68$	45.3415	+	50.0712i	0.666787	+	0.736342i
$69$	−51.5087	−	37.4232i	−0.746503	−	0.542366i
$70$	−0.475288	−	0.0752782i	−0.00678982	−	0.00107540i
$71$	8.91029	+	113.216i	0.125497	+	1.59459i	0.661216	+	0.750195i	$0.270041\pi$
$71$	8.91029	+	113.216i	0.125497	+	1.59459i	−0.535719	+	0.844396i	$0.679959\pi$
$72$	2.18420	−	6.72229i	0.0303362	−	0.0933651i
$73$	−18.9220	+	30.8778i	−0.259205	+	0.422984i	−0.955597	−	0.294678i	$-0.904788\pi$
$73$	−18.9220	+	30.8778i	−0.259205	+	0.422984i	0.696392	+	0.717662i	$0.254788\pi$
$74$	−0.337643	+	0.206908i	−0.00456274	+	0.00279605i
$75$	92.9103	+	7.31220i	1.23880	+	0.0974960i
$76$	−20.4700	−	20.4700i	−0.269341	−	0.269341i
$77$	−45.9080	−	9.64955i	−0.596208	−	0.125319i
$78$	3.99776	−	9.65145i	0.0512533	−	0.123736i
$79$	56.9495	+	4.48202i	0.720879	+	0.0567344i	0.433591	−	0.901110i	$-0.357246\pi$
$79$	56.9495	+	4.48202i	0.720879	+	0.0567344i	0.287288	+	0.957844i	$0.407246\pi$
$80$	−2.53873	+	10.5746i	−0.0317342	+	0.132182i
$81$	−58.9854	−	81.1864i	−0.728214	−	1.00230i
$82$	−0.945449	−	12.0131i	−0.0115299	−	0.146501i
$83$	29.2698	+	57.4452i	0.352648	+	0.692110i	0.997383	−	0.0722955i	$-0.0230325\pi$
$83$	29.2698	+	57.4452i	0.352648	+	0.692110i	−0.644735	+	0.764406i	$0.723032\pi$
$84$	−37.8597	−	52.1094i	−0.450711	−	0.620350i
$85$	−11.5848	+	2.18104i	−0.136292	+	0.0256593i
$86$	1.94434	+	5.98405i	0.0226086	+	0.0695820i
$87$	53.7034	−	53.7034i	0.617280	−	0.617280i
$88$	4.02256	−	13.6936i	0.0457109	−	0.155609i
$89$			106.211i			1.19338i	0.802470	+	0.596692i	$0.203519\pi$
$89$			106.211i			1.19338i	−0.802470	+	0.596692i	$0.796481\pi$
$90$	0.399217	+	0.467423i	0.00443575	+	0.00519359i
$91$	−37.6355	−	61.4156i	−0.413577	−	0.674897i
$92$	−15.5376	−	64.7188i	−0.168887	−	0.703466i
$93$	−16.2448	−	31.8822i	−0.174675	−	0.342820i
$94$	−2.64402	+	1.34720i	−0.0281279	+	0.0143319i
$95$	4.91238	−	1.17936i	0.0517092	−	0.0124143i
$96$	25.0906	−	15.3755i	0.261360	−	0.160162i
$97$	19.3764	−	16.5490i	0.199757	−	0.170608i	−0.543943	−	0.839122i	$-0.683069\pi$
$97$	19.3764	−	16.5490i	0.199757	−	0.170608i	0.743700	+	0.668514i	$0.233069\pi$
$98$	−5.01394			−0.0511626
$99$	36.5872	+	47.4587i	0.369568	+	0.479381i
$100$	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	$0.672339\pi$
$102$	8.68225	+	5.93105i	0.0851201	+	0.0581475i
$103$	−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	$0.339077\pi$
$104$	19.5258	−	9.94889i	0.187748	−	0.0956624i
$105$	11.2059	−	0.881922i	0.106723	−	0.00839926i
$106$	−8.02338	+	5.82933i	−0.0756923	+	0.0549937i
$107$	−129.120	−	30.9990i	−1.20673	−	0.289710i	−0.420297	−	0.907386i	$-0.638074\pi$
$107$	−129.120	−	30.9990i	−1.20673	−	0.289710i	−0.786433	+	0.617676i	$0.788074\pi$
$108$	4.20949	−	53.4866i	0.0389767	−	0.495246i
$109$	−61.4264	−	25.4436i	−0.563545	−	0.233428i	0.0826784	−	0.996576i	$-0.473653\pi$
$109$	−61.4264	−	25.4436i	−0.563545	−	0.233428i	−0.646223	+	0.763148i	$0.723653\pi$
$110$	0.832617	+	0.920518i	0.00756924	+	0.00836834i
$111$	6.54074	−	6.54074i	0.0589256	−	0.0589256i
$112$	5.24753	−	66.6762i	0.0468530	−	0.595323i
$113$	65.9304	+	107.589i	0.583455	+	0.952112i	0.999093	+	0.0425816i	$0.0135582\pi$
$113$	65.9304	+	107.589i	0.583455	+	0.952112i	−0.415638	+	0.909530i	$0.636442\pi$
$114$	−3.84211	−	2.35445i	−0.0337027	−	0.0206531i
$115$	11.0467	+	3.58930i	0.0960586	+	0.0312113i
$116$	79.1503	−	6.22926i	0.682330	−	0.0537005i
$117$	−14.3937	+	90.8785i	−0.123023	+	0.776740i
$118$	1.86178	−	2.56252i	0.0157778	−	0.0217163i
$119$	68.2719	−	24.3940i	0.573714	−	0.204991i
$120$			3.41981i			0.0284984i
$121$	76.5725	+	93.6891i	0.632830	+	0.774290i
$122$	11.5586	−	4.78772i	0.0947425	−	0.0392436i
$123$	86.9817	+	267.702i	0.707168	+	2.17644i
$124$	8.73231	−	36.3727i	0.0704219	−	0.293328i
$125$	−33.3894	+	8.01609i	−0.267115	+	0.0641287i
$126$	−2.87468	−	2.45521i	−0.0228150	−	0.0194858i
$127$	41.0604	−	20.9213i	0.323310	−	0.164735i	−0.284801	−	0.958587i	$-0.591927\pi$
$127$	41.0604	−	20.9213i	0.323310	−	0.164735i	0.608111	+	0.793852i	$0.291927\pi$
$128$	40.4660	+	6.40918i	0.316141	+	0.0500717i
$129$	−76.7936	−	125.316i	−0.595299	−	0.971439i
$130$	−0.149529	+	1.89995i	−0.00115022	+	0.0146150i
$131$	21.3691	−	8.85138i	0.163123	−	0.0675678i	−0.299628	−	0.954056i	$-0.596862\pi$
$131$	21.3691	−	8.85138i	0.163123	−	0.0675678i	0.462751	+	0.886488i	$0.346862\pi$
$132$	−8.31958	+	165.929i	−0.0630272	+	1.25704i
$133$	−28.7049	+	11.8899i	−0.215826	+	0.0893981i
$134$	−18.1014	−	9.22312i	−0.135085	−	0.0688293i
$135$	7.57482	+	5.50343i	0.0561098	+	0.0407661i
$136$	5.76904	+	21.2893i	0.0424194	+	0.156539i
$137$	−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	$0.154390\pi$
$138$	−4.70347	−	9.23108i	−0.0340831	−	0.0668919i
$139$	−165.889	−	101.657i	−1.19345	−	0.731344i	−0.223509	−	0.974702i	$-0.571751\pi$
$139$	−165.889	−	101.657i	−1.19345	−	0.731344i	−0.969937	+	0.243358i	$0.921751\pi$
$140$	9.50651	+	6.90688i	0.0679036	+	0.0493349i
$141$	52.7084	−	45.0172i	0.373819	−	0.319271i
$142$	−7.07191	+	17.0731i	−0.0498022	+	0.120233i
$143$	−23.8336	+	184.255i	−0.166669	+	1.28849i
$144$	−60.4123	+	60.4123i	−0.419530	+	0.419530i
$145$	−6.29026	+	12.3453i	−0.0433811	+	0.0851402i
$146$	−5.02453	+	3.07904i	−0.0344146	+	0.0210893i
$147$	113.883	−	27.3410i	0.774718	−	0.185993i
$148$	9.64001	−	0.758686i	0.0651352	−	0.00512625i
$149$	−18.3738	+	56.5488i	−0.123314	+	0.379522i	−0.993590	−	0.113042i	$-0.963940\pi$
$149$	−18.3738	+	56.5488i	−0.123314	+	0.379522i	0.870276	+	0.492565i	$0.163940\pi$
$150$	12.9306	+	7.92389i	0.0862041	+	0.0528259i
$151$	−4.48113	+	0.709741i	−0.0296763	+	0.00470027i	−0.171255	−	0.985227i	$-0.554782\pi$
$151$	−4.48113	+	0.709741i	−0.0296763	+	0.00470027i	0.141579	+	0.989927i	$0.454782\pi$
$152$	−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
$156$	−193.977	+	165.672i	−1.24344	+	1.06200i
$157$	45.1278	−	62.1131i	0.287438	−	0.395625i	−0.640742	−	0.767757i	$-0.721373\pi$
$157$	45.1278	−	62.1131i	0.287438	−	0.395625i	0.928180	+	0.372132i	$0.121373\pi$
$158$	7.92583	+	4.85696i	0.0501635	+	0.0307402i
$159$	150.451	−	176.155i	0.946232	−	1.10790i
$160$	−3.48654	+	4.08221i	−0.0217909	+	0.0255138i
$161$	−70.5549	−	11.1748i	−0.438229	−	0.0694087i
$162$	−2.55450	−	16.1285i	−0.0157685	−	0.0995587i
$163$	251.205	+	19.7703i	1.54113	+	0.121290i	0.820347	−	0.571866i	$-0.193780\pi$
$163$	251.205	+	19.7703i	1.54113	+	0.121290i	0.720788	+	0.693156i	$0.243780\pi$
$164$	−112.606	+	271.855i	−0.686622	+	1.65765i
$165$	−23.9311	−	16.3678i	−0.145037	−	0.0991989i
$166$			10.4911i			0.0631994i
$167$	105.953	−	90.4927i	0.634451	−	0.541873i	−0.273009	−	0.962012i	$-0.588019\pi$
$167$	105.953	−	90.4927i	0.634451	−	0.541873i	0.907460	+	0.420139i	$0.138019\pi$
$168$	−3.29014	−	20.7731i	−0.0195842	−	0.123650i
$169$	−94.0657	+	68.3427i	−0.556602	+	0.404395i
$170$	−1.84077	−	0.539602i	−0.0108281	−	0.00317413i
$171$	37.7463	+	12.2645i	0.220739	+	0.0717224i
$172$	24.0352	−	151.753i	0.139740	−	0.882282i
$173$	−11.2682	+	46.9354i	−0.0651340	+	0.271303i	−0.995428	−	0.0955112i	$-0.969551\pi$
$173$	−11.2682	+	46.9354i	−0.0651340	+	0.271303i	0.930294	+	0.366814i	$0.119551\pi$
$174$	11.7536	−	3.81898i	0.0675496	−	0.0219482i
$175$	96.6061	−	40.0156i	0.552035	−	0.228660i
$176$	−118.466	+	125.404i	−0.673104	+	0.712526i
$177$	−28.3140	+	68.3559i	−0.159966	+	0.386192i
$178$	−7.84632	+	15.3993i	−0.0440804	+	0.0865127i
$179$	189.502	−	30.0142i	1.05867	−	0.167677i	0.397264	−	0.917704i	$-0.369960\pi$
$179$	189.502	−	30.0142i	1.05867	−	0.167677i	0.661407	+	0.750028i	$0.269960\pi$
$180$	−3.50410	−	14.5956i	−0.0194672	−	0.0810869i
$181$	213.953	−	250.507i	1.18206	−	1.38401i	0.275842	−	0.961203i	$-0.411043\pi$
$181$	213.953	−	250.507i	1.18206	−	1.38401i	0.906218	−	0.422811i	$-0.138957\pi$
$182$	−0.919613	−	11.6848i	−0.00505282	−	0.0642021i
$183$	−236.427	+	171.774i	−1.29195	+	0.938658i
$184$	5.07350	−	21.1327i	0.0275734	−	0.114851i
$185$	−0.766115	+	1.50358i	−0.00414116	+	0.00812749i
$186$		−	5.82259i		−	0.0313043i
$187$	−176.590	−	61.5236i	−0.944329	−	0.329003i
$188$	72.4621			0.385437
$189$	−51.3068	−	26.1421i	−0.271465	−	0.138318i
$190$	0.799356	+	0.191909i	0.00420714	+	0.00101004i
$191$	−19.1414	−	26.3459i	−0.100217	−	0.137937i	0.755963	−	0.654614i	$-0.227169\pi$
$191$	−19.1414	−	26.3459i	−0.100217	−	0.137937i	−0.856180	+	0.516677i	$0.827169\pi$
$192$	−232.936	+	18.3324i	−1.21321	+	0.0954814i
$193$	73.6728	+	62.9225i	0.381724	+	0.326023i	0.819519	−	0.573051i	$-0.194240\pi$
$193$	73.6728	+	62.9225i	0.381724	+	0.326023i	−0.437795	+	0.899075i	$0.644240\pi$
$194$	4.03188	−	0.967970i	0.0207829	−	0.00498953i
$195$	−6.96410	−	43.9696i	−0.0357133	−	0.225485i
$196$	109.090	+	55.5843i	0.556584	+	0.283594i
$197$	−169.807	−	70.3362i	−0.861963	−	0.357037i	−0.0924879	−	0.995714i	$-0.529482\pi$
$197$	−169.807	−	70.3362i	−0.861963	−	0.357037i	−0.769475	+	0.638677i	$0.779482\pi$
$198$	1.79868	+	9.58377i	0.00908426	+	0.0484029i
$199$	−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
$201$	461.438	+	110.781i	2.29571	+	0.551152i
$202$	−24.5097	−	3.88196i	−0.121335	−	0.0192176i
$203$	26.3320	−	81.0416i	0.129714	−	0.399219i
$204$	−123.152	−	225.296i	−0.603687	−	1.10439i
$205$	−30.1835	−	41.5440i	−0.147236	−	0.202653i
$206$	−4.05426	+	0.642131i	−0.0196809	+	0.00311714i
$207$	59.2625	+	69.3875i	0.286292	+	0.335205i
$208$	−264.885			−1.27349
$209$	76.8910	+	22.5871i	0.367900	+	0.108072i
$210$	1.68986	+	0.699963i	0.00804696	+	0.00333316i
$211$	20.8144	−	264.473i	0.0986466	−	1.25342i	−0.725968	−	0.687729i	$-0.758608\pi$
$211$	20.8144	−	264.473i	0.0986466	−	1.25342i	0.824614	−	0.565696i	$-0.191392\pi$
$212$	239.192	−	37.8843i	1.12826	−	0.178699i
$213$	67.5274	−	426.352i	0.317030	−	2.00165i
$214$	−16.4307	−	14.0332i	−0.0767790	−	0.0655755i
$215$	20.3887	+	17.4136i	0.0948313	+	0.0809936i
$216$	9.15365	−	14.9374i	0.0423780	−	0.0691546i
$217$	−32.4796	−	23.5978i	−0.149675	−	0.108746i
$218$	−7.02640	−	8.22686i	−0.0322312	−	0.0377379i
$219$	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
$223$	13.0786	+	82.5748i	0.0586483	+	0.370291i	0.999504	+	0.0314839i	$0.0100233\pi$
$223$	13.0786	+	82.5748i	0.0586483	+	0.370291i	−0.940856	+	0.338807i	$0.889977\pi$
$224$	17.2510	−	28.1511i	0.0770135	−	0.125675i
$225$	−127.035	−	41.2762i	−0.564601	−	0.183450i
$226$	1.61099	+	20.4695i	0.00712827	+	0.0905732i
$227$	−9.57940	−	39.9011i	−0.0422000	−	0.175776i	0.947290	−	0.320378i	$-0.103810\pi$
$227$	−9.57940	−	39.9011i	−0.0422000	−	0.175776i	−0.989490	+	0.144602i	$0.953810\pi$
$228$	57.4931	+	93.8203i	0.252163	+	0.411492i
$229$	202.412	+	103.134i	0.883896	+	0.450368i	0.836156	−	0.548492i	$-0.184798\pi$
$229$	202.412	+	103.134i	0.883896	+	0.450368i	0.0477405	+	0.998860i	$0.484798\pi$
$230$	1.33648	+	1.33648i	0.00581077	+	0.00581077i
$231$	161.113	+	76.4001i	0.697460	+	0.330736i
$232$	23.9514	+	9.92101i	0.103239	+	0.0427630i
$233$	11.8736	+	13.9022i	0.0509596	+	0.0596660i	0.785300	−	0.619115i	$-0.212509\pi$
$233$	11.8736	+	13.9022i	0.0509596	+	0.0596660i	−0.734341	+	0.678781i	$0.762509\pi$
$234$	−8.80053	+	12.1129i	−0.0376091	+	0.0517645i
$235$	−6.60731	+	10.7821i	−0.0281162	+	0.0458815i
$236$	−68.9157	+	35.1143i	−0.292016	+	0.148789i
$237$	−206.508	−	67.0984i	−0.871340	−	0.283115i
$238$	11.7006	+	1.50675i	0.0491624	+	0.00633090i
$239$	−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	$0.251625\pi$
$240$	18.7663	−	36.8309i	0.0781928	−	0.153462i
$241$	−142.172	−	343.234i	−0.589925	−	1.42421i	−0.883574	−	0.468292i	$-0.844869\pi$
$241$	−142.172	−	343.234i	−0.589925	−	1.42421i	0.293648	−	0.955914i	$-0.405131\pi$
$242$	4.18077	+	19.2405i	0.0172759	+	0.0795061i
$243$	99.4660	+	240.132i	0.409325	+	0.988198i
$244$	−304.562	−	23.9695i	−1.24820	−	0.0982358i
$245$	−18.2180	+	11.1640i	−0.0743591	+	0.0455673i
$246$	−7.16517	+	45.2391i	−0.0291267	+	0.183899i
$247$	55.8640	+	109.639i	0.226170	+	0.443884i
$248$	7.93253	−	9.28780i	0.0319860	−	0.0374508i
$249$	−57.2080	−	238.289i	−0.229751	−	0.956982i
$250$	−5.43322	−	1.30440i	−0.0217329	−	0.00521760i
$251$	−7.25375	+	2.35689i	−0.0288994	+	0.00938998i	−0.323431	−	0.946252i	$-0.604836\pi$
$251$	−7.25375	+	2.35689i	−0.0288994	+	0.00938998i	0.294532	+	0.955642i	$0.404836\pi$
$252$	35.3274	+	85.2878i	0.140188	+	0.338444i
$253$	123.599	+	136.648i	0.488535	+	0.540110i
$254$	7.49879			0.0295228
$255$	44.7527	+	2.21844i	0.175501	+	0.00869978i
$256$	−193.534	−	140.611i	−0.755993	−	0.549261i
$257$	−414.095	−	65.5861i	−1.61126	−	0.255199i	−0.715132	−	0.698989i	$-0.753634\pi$
$257$	−414.095	−	65.5861i	−1.61126	−	0.255199i	−0.896131	+	0.443790i	$0.853634\pi$
$258$	−1.87643	−	23.8423i	−0.00727297	−	0.0924119i
$259$	3.20708	−	9.87036i	0.0123825	−	0.0381095i
$260$	24.3161	−	39.6803i	0.0935235	−	0.152616i
$261$	−92.8102	+	56.8741i	−0.355594	+	0.217909i
$262$	3.75214	+	0.295300i	0.0143212	+	0.00112710i
$263$	−17.8793	−	17.8793i	−0.0679821	−	0.0679821i	0.672298	−	0.740280i	$-0.265307\pi$
$263$	−17.8793	−	17.8793i	−0.0679821	−	0.0679821i	−0.740280	+	0.672298i	$0.765307\pi$
$264$	−27.0181	+	47.0421i	−0.102341	+	0.178190i
$265$	−16.1732	+	39.0455i	−0.0610308	+	0.147341i
$266$	−5.04020	−	0.396672i	−0.0189481	−	0.00149125i
$267$	94.2442	−	392.555i	0.352975	−	1.47025i
$268$	291.593	+	401.343i	1.08803	+	1.49755i
$269$	−19.1061	−	242.766i	−0.0710265	−	0.902477i	−0.924461	−	0.381277i	$-0.875485\pi$
$269$	−19.1061	−	242.766i	−0.0710265	−	0.902477i	0.853435	−	0.521200i	$-0.174515\pi$
$270$	0.691687	+	1.35751i	0.00256181	+	0.00502783i
$271$	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	$0.553995\pi$
$272$	54.6933	−	260.940i	0.201078	−	0.959338i
$273$	84.6047	+	260.387i	0.309907	+	0.953797i
$274$	−5.36087	+	5.36087i	−0.0195652	+	0.0195652i
$275$	−258.777	−	76.0167i	−0.941006	−	0.276424i
$276$			252.987i			0.916620i
$277$	256.563	+	300.396i	0.926219	+	1.08446i	0.996216	+	0.0869155i	$0.0277010\pi$
$277$	256.563	+	300.396i	0.926219	+	1.08446i	−0.0699971	+	0.997547i	$0.522299\pi$
$278$	−16.5419	−	26.9939i	−0.0595032	−	0.0971004i
$279$	11.9720	+	49.8669i	0.0429103	+	0.178734i
$280$	1.74194	+	3.41875i	0.00622122	+	0.0122098i
$281$	−176.018	+	89.6857i	−0.626399	+	0.319166i	−0.738218	−	0.674562i	$-0.764332\pi$
$281$	−176.018	+	89.6857i	−0.626399	+	0.319166i	0.111819	+	0.993729i	$0.464332\pi$
$282$	10.9677	−	2.63311i	0.0388925	−	0.00933726i
$283$	−252.193	+	154.544i	−0.891142	+	0.546092i	−0.891049	−	0.453908i	$-0.850030\pi$
$283$	−252.193	+	154.544i	−0.891142	+	0.546092i	−9.30988e−5		1.00000i	$0.500030\pi$
$284$	343.139	−	293.068i	1.20824	−	1.03193i
$285$	−19.2026			−0.0673775
$286$	−17.0673	+	24.9539i	−0.0596760	+	0.0872513i
$287$	223.313	+	223.313i	0.778096	+	0.778096i
$288$	−40.1111	+	13.0329i	−0.139275	+	0.0452531i
$289$	282.340	−	61.6851i	0.976955	−	0.213443i
$290$	−1.82401	+	1.32522i	−0.00628970	+	0.00456974i
$291$	−86.2994	+	43.9718i	−0.296562	+	0.151106i
$292$	143.455	−	11.2902i	0.491284	−	0.0386649i
$293$	−441.019	+	320.419i	−1.50519	+	1.09358i	−0.536928	+	0.843628i	$0.680415\pi$
$293$	−441.019	+	320.419i	−1.50519	+	1.09358i	−0.968258	+	0.249953i	$0.919585\pi$
$294$	18.5315	+	4.44901i	0.0630321	+	0.0151327i
$295$	1.05903	−	13.4563i	0.00358994	−	0.0456145i
$296$	2.91714	+	1.20832i	0.00985520	+	0.00408216i
$297$	60.7179	+	135.548i	0.204437	+	0.456392i
$298$	−6.84149	+	6.84149i	−0.0229580	+	0.0229580i
$299$	−22.1971	+	282.041i	−0.0742378	+	0.943281i
$300$	−193.493	−	315.752i	−0.644977	−	1.05251i
$301$	−140.602	−	86.1607i	−0.467115	−	0.286248i
$302$	−0.702138	−	0.228138i	−0.00232496	−	0.000755425i
$303$	577.868	−	45.4792i	1.90715	−	0.150096i
$304$	−17.8738	+	112.851i	−0.0587954	+	0.371219i
$305$	31.3374	−	43.1323i	0.102746	−	0.141417i
$306$	−10.1154	−	11.1705i	−0.0330567	−	0.0365050i
$307$		−	428.553i		−	1.39594i	−0.716129	−	0.697968i	$-0.754088\pi$
$307$		−	428.553i		−	1.39594i	0.716129	−	0.697968i	$-0.245912\pi$
$308$	76.2018	+	170.115i	0.247409	+	0.552322i
$309$	88.5844	−	36.6928i	0.286681	−	0.118747i
$310$	0.328249	+	1.01025i	0.00105887	+	0.00325886i
$311$	−122.066	+	508.441i	−0.392495	+	1.63486i	0.330357	+	0.943856i	$0.392831\pi$
$311$	−122.066	+	508.441i	−0.392495	+	1.63486i	−0.722852	+	0.691003i	$0.757169\pi$
$312$	−80.9951	+	19.4452i	−0.259600	+	0.0623244i
$313$	221.994	+	189.600i	0.709245	+	0.605752i	0.929121	−	0.369775i	$-0.120565\pi$
$313$	221.994	+	189.600i	0.709245	+	0.605752i	−0.219876	+	0.975528i	$0.570565\pi$
$314$	11.1315	−	5.67180i	0.0354507	−	0.0180631i
$315$	−15.9118	−	2.52019i	−0.0505137	−	0.00800059i
$316$	−118.602	−	193.540i	−0.375322	−	0.612470i
$317$	−8.22218	+	104.473i	−0.0259375	+	0.329567i	0.970236	+	0.242163i	$0.0778570\pi$
$317$	−8.22218	+	104.473i	−0.0259375	+	0.329567i	−0.996173	+	0.0874036i	$0.972143\pi$
$318$	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
$321$	449.720	+	229.144i	1.40100	+	0.713844i
$322$	−9.40402	−	6.83242i	−0.0292050	−	0.0212187i
$323$	−119.541	+	32.3938i	−0.370097	+	0.100290i
$324$	−123.221	+	379.234i	−0.380311	+	1.17048i
$325$	−188.010	−	368.991i	−0.578493	−	1.13536i
$326$	34.9610	+	21.4241i	0.107242	+	0.0657181i
$327$	204.454	+	148.545i	0.625243	+	0.454266i
$328$	−73.0618	+	62.4007i	−0.222749	+	0.190246i
$329$	29.7618	−	71.8513i	0.0904613	−	0.218393i
$330$	−2.26054	−	4.14103i	−0.00685012	−	0.0125486i
$331$	−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	$0.364001\pi$
$332$	116.304	−	228.260i	0.350313	−	0.687529i
$333$	−11.3037	+	6.92692i	−0.0339451	+	0.0208016i
$334$	22.0470	−	5.29301i	0.0660090	−	0.0158473i
$335$	−86.3070	+	6.79251i	−0.257633	+	0.0202761i
$336$	−78.5585	+	241.778i	−0.233805	+	0.719578i
$337$	371.935	+	227.922i	1.10367	+	0.676327i	0.950142	−	0.311818i	$-0.100938\pi$
$337$	371.935	+	227.922i	1.10367	+	0.676327i	0.153523	+	0.988145i	$0.450938\pi$
$338$	−18.6871	+	2.95975i	−0.0552873	+	0.00875665i
$339$	−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
$343$	258.822	−	221.055i	0.754584	−	0.644475i
$344$	29.4889	−	40.5879i	0.0857234	−	0.117988i
$345$	−37.6437	−	23.0681i	−0.109112	−	0.0668641i
$346$	−5.10108	+	5.97259i	−0.0147430	+	0.0172618i
$347$	−225.582	+	264.122i	−0.650091	+	0.761159i	−0.983359	−	0.181673i	$-0.941849\pi$
$347$	−225.582	+	264.122i	−0.650091	+	0.761159i	0.333268	+	0.942832i	$0.391849\pi$
$348$	−298.066	−	47.2090i	−0.856511	−	0.135658i
$349$	−24.5281	−	154.864i	−0.0702811	−	0.443737i	−0.997587	−	0.0694322i	$-0.977881\pi$
$349$	−24.5281	−	154.864i	−0.0702811	−	0.443737i	0.927306	−	0.374305i	$-0.122119\pi$
$350$	16.9628	+	1.33500i	0.0484651	+	0.00381429i
$351$	−87.2729	+	210.695i	−0.248641	+	0.600272i
$352$	−80.2114	+	28.6087i	−0.227873	+	0.0812748i
$353$		−	338.465i		−	0.958824i	−0.877590	−	0.479412i	$-0.840850\pi$
$353$		−	338.465i		−	0.958824i	0.877590	−	0.479412i	$-0.159150\pi$
$354$	−9.15493	+	7.81905i	−0.0258614	+	0.0220877i
$355$	12.3193	+	77.7809i	0.0347022	+	0.219101i
$356$	341.431	−	248.064i	0.959077	−	0.696810i
$357$	−273.978	+	29.5802i	−0.767445	+	0.0828576i
$358$	29.6926	+	9.64772i	0.0829403	+	0.0269489i
$359$	65.1991	−	411.651i	0.181613	−	1.14666i	−0.713445	−	0.700711i	$-0.752866\pi$
$359$	65.1991	−	411.651i	0.181613	−	1.14666i	0.895058	−	0.445949i	$-0.147134\pi$
$360$	1.14420	−	4.76592i	0.00317832	−	0.0132387i
$361$	−292.851	+	95.1532i	−0.811223	+	0.263582i
$362$	49.5265	−	20.5145i	0.136813	−	0.0566700i
$363$	−199.878	−	414.219i	−0.550628	−	1.14110i
$364$	−109.529	+	264.426i	−0.300903	+	0.726445i
$365$	−11.4007	+	22.3751i	−0.0312348	+	0.0613018i
$366$	−46.9687	+	7.43911i	−0.128330	+	0.0203254i
$367$	137.406	+	572.337i	0.374403	+	1.55950i	0.768143	+	0.640278i	$0.221181\pi$
$367$	137.406	+	572.337i	0.374403	+	1.55950i	−0.393740	+	0.919222i	$0.628819\pi$
$368$	−170.607	+	199.755i	−0.463605	+	0.542812i
$369$	−31.6520	−	402.177i	−0.0857779	−	1.08991i
$370$	−0.222154	+	0.161404i	−0.000600415	+	0.000436227i
$371$	60.6765	−	252.736i	0.163548	−	0.681228i
$372$	−64.5491	+	126.685i	−0.173519	+	0.340550i
$373$			206.316i			0.553126i	0.960996	+	0.276563i	$0.0891955\pi$
$373$			206.316i			0.553126i	−0.960996	+	0.276563i	$0.910805\pi$
$374$	−21.0582	−	21.9656i	−0.0563053	−	0.0587316i
$375$	130.520			0.348053
$376$	21.0822	+	10.7419i	0.0560696	+	0.0285689i
$377$	−328.155	−	78.7829i	−0.870436	−	0.208973i
$378$	−5.50759	−	7.58055i	−0.0145703	−	0.0200544i
$379$	256.502	−	20.1871i	0.676785	−	0.0532642i	0.264592	−	0.964360i	$-0.414763\pi$
$379$	256.502	−	20.1871i	0.676785	−	0.0532642i	0.412194	+	0.911096i	$0.364763\pi$
$380$	−15.2645	−	13.0371i	−0.0401696	−	0.0343081i
$381$	−170.323	+	40.8909i	−0.447042	+	0.107325i
$382$	−0.828966	−	5.23389i	−0.00217007	−	0.0137013i
$383$	249.144	+	126.945i	0.650506	+	0.331449i	0.747914	−	0.663795i	$-0.231055\pi$
$383$	249.144	+	126.945i	0.650506	+	0.331449i	−0.0974084	+	0.995244i	$0.531055\pi$
$384$	−143.875	−	59.5949i	−0.374674	−	0.155195i
$385$	−32.2610	−	4.17301i	−0.0837947	−	0.0108390i
$386$	6.03323	+	14.5655i	0.0156301	+	0.0377345i
$387$	65.0931	+	200.336i	0.168199	+	0.517664i
$388$	−98.4543	−	23.6368i	−0.253748	−	0.0609196i
$389$	262.165	+	41.5228i	0.673945	+	0.106742i	0.484021	−	0.875056i	$-0.339176\pi$
$389$	262.165	+	41.5228i	0.673945	+	0.106742i	0.189924	+	0.981799i	$0.439176\pi$
$390$	2.23853	−	6.88950i	0.00573983	−	0.0176654i
$391$	−273.257	−	80.1022i	−0.698868	−	0.204865i
$392$	23.4989	+	32.3435i	0.0599462	+	0.0825088i
$393$	−86.8341	+	13.7532i	−0.220952	+	0.0349954i
$394$	−19.4237	−	22.7423i	−0.0492988	−	0.0577215i
$395$	39.6127			0.100285
$396$	67.1106	−	228.458i	0.169471	−	0.576915i
$397$	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	$0.593912\pi$
$398$	4.15582	−	52.8047i	0.0104418	−	0.132675i
$399$	116.643	−	18.4745i	0.292339	−	0.0463019i
$400$	60.1542	−	379.799i	0.150385	−	0.949496i
$401$	164.081	+	140.138i	0.409179	+	0.349472i	0.830089	−	0.557630i	$-0.188289\pi$
$401$	164.081	+	140.138i	0.409179	+	0.349472i	−0.420911	+	0.907102i	$0.638289\pi$
$402$	58.7186	+	50.1505i	0.146066	+	0.124752i
$403$	−83.0774	+	135.570i	−0.206147	+	0.336402i
$404$	490.234	+	356.176i	1.21345	+	0.881623i
$405$	−45.1933	−	52.9146i	−0.111588	−	0.130653i
$406$	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	$0.589068\pi$
$410$	−1.30717	−	8.25313i	−0.00318821	−	0.0201296i
$411$	92.5307	−	150.996i	0.225136	−	0.367388i
$412$	95.3289	+	30.9742i	0.231381	+	0.0751802i
$413$	6.51312	+	82.7570i	0.0157703	+	0.200380i
$414$	3.46633	+	14.4383i	0.00837277	+	0.0348751i
$415$	23.3594	+	38.1191i	0.0562877	+	0.0918532i
$416$	−116.508	−	59.3639i	−0.280068	−	0.142702i
$417$	522.920	+	522.920i	1.25401	+	1.25401i
$418$	9.47960	+	8.95513i	0.0226785	+	0.0214238i
$419$	−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	$0.717605\pi$
$420$	−29.0073	−	33.9632i	−0.0690650	−	0.0808647i
$421$	−422.986	+	582.190i	−1.00472	+	1.38287i	−0.0823296	+	0.996605i	$0.526236\pi$
$421$	−422.986	+	582.190i	−1.00472	+	1.38287i	−0.922387	+	0.386268i	$0.873764\pi$
$422$	22.5556	−	36.8075i	0.0534494	−	0.0872215i
$423$	−88.5173	+	45.1018i	−0.209261	+	0.106624i
$424$	75.2066	+	24.4361i	0.177374	+	0.0576324i
$425$	402.316	−	109.021i	0.946625	−	0.256520i
$426$	41.2872	−	56.8269i	0.0969183	−	0.133397i
$427$	−148.858	+	292.150i	−0.348613	+	0.684191i
$428$	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
$431$	15.0076	+	1.18112i	0.0348203	+	0.00274042i	0.0958573	−	0.995395i	$-0.469441\pi$
$431$	15.0076	+	1.18112i	0.0348203	+	0.00274042i	−0.0610370	+	0.998136i	$0.519441\pi$
$432$	−180.553	+	110.643i	−0.417946	+	0.256118i
$433$	99.7957	−	630.085i	0.230475	−	1.45516i	−0.552710	−	0.833374i	$-0.686406\pi$
$433$	99.7957	−	630.085i	0.230475	−	1.45516i	0.783185	−	0.621789i	$-0.213594\pi$
$434$	−2.96584	−	5.82079i	−0.00683373	−	0.0134120i
$435$	34.2031	−	40.0467i	0.0786278	−	0.0920613i
$436$	61.6738	+	256.890i	0.141454	+	0.589197i
$437$	118.662	+	28.4882i	0.271538	+	0.0651904i
$438$	21.3027	−	6.92167i	0.0486363	−	0.0158029i
$439$	−94.1941	−	227.405i	−0.214565	−	0.518006i	0.779549	−	0.626341i	$-0.215448\pi$
$439$	−94.1941	−	227.405i	−0.214565	−	0.518006i	−0.994114	+	0.108335i	$0.965448\pi$
$440$	2.03576	−	9.68518i	0.00462672	−	0.0220118i
$441$	−167.858			−0.380631
$442$	2.31325	−	46.6653i	0.00523360	−	0.105578i
$443$	−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	$0.828151\pi$
$444$	−36.3026	−	5.74976i	−0.0817626	−	0.0129499i
$445$	5.77854	+	73.4233i	0.0129855	+	0.164996i
$446$	−4.20396	+	12.9385i	−0.00942592	+	0.0290100i
$447$	118.087	−	192.700i	0.264176	−	0.431097i
$448$	−223.526	+	136.977i	−0.498941	+	0.305751i
$449$	−200.150	−	15.7521i	−0.445767	−	0.0350826i	−0.146411	−	0.989224i	$-0.546772\pi$
$449$	−200.150	−	15.7521i	−0.445767	−	0.0350826i	−0.299357	+	0.954141i	$0.596772\pi$
$450$	−15.3692	−	15.3692i	−0.0341538	−	0.0341538i
$451$	−86.9804	−	809.932i	−0.192861	−	1.79586i
$452$	191.874	−	463.224i	0.424500	−	1.02483i
$453$	17.1920	+	1.35304i	0.0379514	+	0.00298684i
$454$	1.55879	−	6.49282i	0.00343345	−	0.0143014i
$455$	−29.3586	−	40.4087i	−0.0645245	−	0.0888103i
$456$	2.81902	+	35.8190i	0.00618205	+	0.0785504i
$457$	102.928	+	202.008i	0.225226	+	0.442030i	0.975773	−	0.218787i	$-0.0702099\pi$
$457$	102.928	+	202.008i	0.225226	+	0.442030i	−0.750547	+	0.660817i	$0.770210\pi$
$458$	21.7282	+	29.9063i	0.0474414	+	0.0652975i
$459$	−189.537	−	129.477i	−0.412936	−	0.282086i
$460$	−14.2622	−	43.8944i	−0.0310047	−	0.0954227i
$461$	275.492	−	275.492i	0.597597	−	0.597597i	−0.342075	−	0.939672i	$-0.611130\pi$
$461$	275.492	−	275.492i	0.597597	−	0.597597i	0.939672	+	0.342075i	$0.111130\pi$
$462$	17.7153	+	22.9792i	0.0383448	+	0.0497386i
$463$			82.2263i			0.177595i	0.996050	+	0.0887973i	$0.0283023\pi$
$463$			82.2263i			0.177595i	−0.996050	+	0.0887973i	$0.971698\pi$
$464$	−203.512	−	238.282i	−0.438603	−	0.513539i
$465$	−12.9645	−	21.1562i	−0.0278807	−	0.0454972i
$466$	0.694499	+	2.89280i	0.00149034	+	0.00620772i
$467$	333.272	+	654.082i	0.713644	+	1.40060i	0.907702	+	0.419615i	$0.137835\pi$
$467$	333.272	+	654.082i	0.713644	+	1.40060i	−0.194058	+	0.980990i	$0.562165\pi$
$468$	325.760	−	165.983i	0.696068	−	0.354665i
$469$	517.724	−	124.294i	1.10389	−	0.265020i
$470$	−1.75450	+	1.07516i	−0.00373298	+	0.00228757i
$471$	−221.907	+	189.526i	−0.471139	+	0.402391i
$472$	−25.2558			−0.0535080
$473$	142.887	+	400.618i	0.302087	+	0.846973i
$474$	−24.9841	−	24.9841i	−0.0527090	−	0.0527090i
$475$	−169.890	+	55.2006i	−0.357663	+	0.116212i
$476$	−237.872	−	162.496i	−0.499732	−	0.341378i
$477$	−268.609	+	195.156i	−0.563122	+	0.409132i
$478$	−11.1907	+	5.70196i	−0.0234116	+	0.0119288i
$479$	255.781	−	20.1304i	0.533989	−	0.0420259i	0.191402	−	0.981512i	$-0.438697\pi$
$479$	255.781	−	20.1304i	0.533989	−	0.0420259i	0.342588	+	0.939486i	$0.388697\pi$
$480$	16.5085	−	11.9941i	0.0343927	−	0.0249877i
$481$	−39.9672	−	9.59528i	−0.0830919	−	0.0199486i
$482$	4.74315	−	60.2674i	0.00984055	−	0.125036i
$483$	250.855	+	103.907i	0.519368	+	0.215129i
$484$	122.337	−	464.972i	0.252761	−	0.960685i
$485$	12.4944	−	12.4944i	0.0257617	−	0.0257617i
$486$	−3.31839	+	42.1641i	−0.00682796	+	0.0867574i
$487$	233.837	+	381.587i	0.480157	+	0.783545i	0.997383	−	0.0723038i	$-0.0230351\pi$
$487$	233.837	+	381.587i	0.480157	+	0.783545i	−0.517225	+	0.855849i	$0.673035\pi$
$488$	−85.0561	−	52.1224i	−0.174295	−	0.106808i
$489$	−910.908	−	295.972i	−1.86280	−	0.605260i
$490$	−3.46611	+	0.272789i	−0.00707369	+	0.000556711i
$491$	86.8940	−	548.627i	0.176973	−	1.11737i	−0.726008	−	0.687686i	$-0.758626\pi$
$491$	86.8940	−	548.627i	0.176973	−	1.11737i	0.902981	−	0.429680i	$-0.141374\pi$
$492$	657.415	−	904.854i	1.33621	−	1.83913i
$493$	145.367	−	307.000i	0.294862	−	0.622719i
$494$			20.0232i			0.0405329i
$495$	27.8746	+	30.8174i	0.0563123	+	0.0622573i
$496$	−136.399	+	56.4984i	−0.274998	+	0.113908i
$497$	−149.663	−	460.616i	−0.301133	−	0.926792i
$498$	9.30905	−	38.7750i	0.0186929	−	0.0778615i
$499$	−269.027	+	64.5878i	−0.539133	+	0.129434i	−0.493862	−	0.869540i	$-0.664415\pi$
$499$	−269.027	+	64.5878i	−0.539133	+	0.129434i	−0.0452712	+	0.998975i	$0.514415\pi$
$500$	103.752	+	88.6130i	0.207505	+	0.177226i
$501$	−471.899	+	240.445i	−0.941914	+	0.479929i
$502$	−1.22581	−	0.194150i	−0.00244186	−	0.000386753i
$503$	−334.370	−	545.642i	−0.664751	−	1.08477i	−0.990259	−	0.139236i	$-0.955535\pi$
$503$	−334.370	−	545.642i	−0.664751	−	1.08477i	0.325508	−	0.945539i	$-0.394465\pi$
$504$	−2.36504	+	30.0507i	−0.00469253	+	0.0596243i
$505$	−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
$508$	−163.154	−	83.1313i	−0.321170	−	0.163644i
$509$	−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	$0.869600\pi$
$510$	6.32468	+	3.62774i	0.0124013	+	0.00711321i
$511$	47.7251	−	146.883i	0.0933956	−	0.287442i
$512$	−92.0731	−	180.704i	−0.179830	−	0.352937i
$513$	83.8750	+	51.3987i	0.163499	+	0.100192i
$514$	−55.1932	−	40.1002i	−0.107380	−	0.0780160i
$515$	−13.3012	+	11.3603i	−0.0258277	+	0.0220589i
$516$	−223.488	+	539.549i	−0.433117	+	1.04564i
$517$	−176.073	+	96.1160i	−0.340566	+	0.185911i
$518$	1.19415	−	1.19415i	0.00230532	−	0.00230532i
$519$	83.2942	−	163.474i	0.160490	−	0.314979i
$520$	12.9568	−	7.93994i	0.0249169	−	0.0152691i
$521$	268.137	−	64.3740i	0.514659	−	0.123559i	0.0322070	−	0.999481i	$-0.489746\pi$
$521$	268.137	−	64.3740i	0.514659	−	0.123559i	0.482452	+	0.875923i	$0.339746\pi$
$522$	−17.6578	+	1.38970i	−0.0338273	+	0.00266226i
$523$	204.690	−	629.972i	0.391377	−	1.20453i	−0.540370	−	0.841427i	$-0.681716\pi$
$523$	204.690	−	629.972i	0.391377	−	1.20453i	0.931747	−	0.363107i	$-0.118284\pi$
$524$	−78.3633	−	48.0211i	−0.149548	−	0.0916433i
$525$	−392.562	+	62.1757i	−0.747737	+	0.118430i
$526$	−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
$530$	−5.22937	+	4.46630i	−0.00986673	+	0.00842699i
$531$	62.3293	−	85.7890i	0.117381	−	0.161561i
$532$	105.264	+	64.5061i	0.197865	+	0.121252i
$533$	812.306	−	951.089i	1.52403	−	1.78441i
$534$	42.6641	−	49.9532i	0.0798953	−	0.0935454i
$535$	−90.9466	−	14.4045i	−0.169994	−	0.0269243i
$536$	25.3404	+	159.993i	0.0472769	+	0.298495i
$537$	−727.030	−	57.2185i	−1.35387	−	0.106552i
$538$	15.1641	−	36.6094i	0.0281861	−	0.0680473i
$539$	−338.803	+	9.63894i	−0.628577	+	0.0178830i
$540$		−	37.2040i		−	0.0688964i
$541$	−62.9605	+	53.7734i	−0.116378	+	0.0993963i	−0.705733	−	0.708478i	$-0.749382\pi$
$541$	−62.9605	+	53.7734i	−0.116378	+	0.0993963i	0.589355	+	0.807874i	$0.299382\pi$
$542$	9.63264	+	60.8181i	0.0177724	+	0.112211i
$543$	−1013.05	+	736.023i	−1.86565	+	1.35548i
$544$	82.5363	−	102.516i	0.151721	−	0.188448i
$545$	−43.8480	−	14.2471i	−0.0804551	−	0.0261415i
$546$	−6.96937	+	44.0029i	−0.0127644	+	0.0805913i
$547$	−186.015	+	774.808i	−0.340064	+	1.41647i	0.496232	+	0.868190i	$0.334717\pi$
$547$	−186.015	+	774.808i	−0.340064	+	1.41647i	−0.836296	+	0.548279i	$0.815283\pi$
$548$	176.069	−	57.2084i	0.321294	−	0.104395i
$549$	386.962	−	160.285i	0.704848	−	0.291958i
$550$	−31.9036	−	30.1385i	−0.0580065	−	0.0547972i
$551$	−55.7075	+	134.490i	−0.101103	+	0.244083i
$552$	−37.5032	+	73.6042i	−0.0679406	+	0.133341i
$553$	−240.621	+	38.1107i	−0.435120	+	0.0689162i
$554$	15.0066	+	62.5071i	0.0270878	+	0.112829i
$555$	4.16573	−	4.87744i	0.00750581	−	0.00878818i
$556$	60.6555	+	770.701i	0.109093	+	1.38615i
$557$	191.199	−	138.914i	0.343265	−	0.249397i	−0.402773	−	0.915300i	$-0.631954\pi$
$557$	191.199	−	138.914i	0.343265	−	0.249397i	0.746038	+	0.665903i	$0.231954\pi$
$558$	−1.94811	+	8.11448i	−0.00349125	+	0.0145421i
$559$	−296.494	+	581.903i	−0.530402	+	1.04097i
$560$		−	46.3784i		−	0.0828186i
$561$	598.081	+	384.083i	1.06610	+	0.684640i
$562$	−32.1459			−0.0571990
$563$	30.9888	+	15.7896i	0.0550423	+	0.0280455i	0.481295	−	0.876559i	$-0.340167\pi$
$563$	30.9888	+	15.7896i	0.0550423	+	0.0280455i	−0.426253	+	0.904604i	$0.640167\pi$
$564$	−267.819	−	64.2977i	−0.474857	−	0.114003i
$565$	51.4308	+	70.7884i	0.0910280	+	0.125289i
$566$	−47.9817	+	3.77624i	−0.0847733	+	0.00667180i
$567$	325.428	+	277.942i	0.573947	+	0.490197i
$568$	143.278	−	34.3980i	0.252250	−	0.0605598i
$569$	106.344	+	671.428i	0.186896	+	1.18001i	0.885547	+	0.464551i	$0.153784\pi$
$569$	106.344	+	671.428i	0.186896	+	1.18001i	−0.698651	+	0.715463i	$0.746216\pi$
$570$	−2.78413	−	1.41858i	−0.00488443	−	0.00248874i
$571$	769.379	+	318.687i	1.34742	+	0.558121i	0.935574	−	0.353131i	$-0.114883\pi$
$571$	769.379	+	318.687i	1.34742	+	0.558121i	0.411850	+	0.911252i	$0.364883\pi$
$572$	647.979	−	353.725i	1.13283	−	0.618399i
$573$	47.3691	+	114.359i	0.0826685	+	0.199579i
$574$	15.8804	+	48.8748i	0.0276662	+	0.0851477i
$575$	−399.356	−	95.8770i	−0.694533	−	0.166743i
$576$	330.758	+	52.3868i	0.574232	+	0.0909494i
$577$	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	$0.0621168\pi$
$578$	45.4927	+	11.9142i	0.0787070	+	0.0206129i
$579$	−216.461	−	297.933i	−0.373853	−	0.514565i
$580$	54.3772	−	8.61251i	0.0937539	−	0.0148492i
$581$	−178.567	−	209.075i	−0.307344	−	0.359854i
$582$	−15.7607			−0.0270802
$583$	−530.951	+	409.325i	−0.910723	+	0.702101i
$584$	43.4105	+	17.9812i	0.0743331	+	0.0307898i
$585$	−5.00598	+	63.6070i	−0.00855722	+	0.108730i
$586$	−87.6130	+	13.8765i	−0.149510	+	0.0236801i
$587$	−125.207	+	790.526i	−0.213300	+	1.34672i	0.615924	+	0.787806i	$0.288783\pi$
$587$	−125.207	+	790.526i	−0.213300	+	1.34672i	−0.829224	+	0.558917i	$0.811217\pi$
$588$	−353.875	−	302.238i	−0.601829	−	0.514010i
$589$	52.1519	+	44.5419i	0.0885432	+	0.0756230i
$590$	1.14762	−	1.87275i	0.00194513	−	0.00317416i
$591$	565.192	+	410.636i	0.956332	+	0.694816i
$592$	−24.7865	−	29.0213i	−0.0418691	−	0.0490224i
$593$	−138.796	+	138.796i	−0.234058	+	0.234058i	−0.814384	−	0.580326i	$-0.802925\pi$
$593$	−138.796	+	138.796i	−0.234058	+	0.234058i	0.580326	+	0.814384i	$0.302925\pi$
$594$	−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
$597$	193.551	+	1222.04i	0.324207	+	2.04696i
$598$	−24.0540	+	39.2525i	−0.0402240	+	0.0656396i
$599$	1025.04	+	333.056i	1.71126	+	0.556021i	0.990542	−	0.137211i	$-0.0438140\pi$
$599$	1025.04	+	333.056i	1.71126	+	0.556021i	0.720714	+	0.693232i	$0.243814\pi$
$600$	−9.48739	−	120.549i	−0.0158123	−	0.200915i
$601$	247.546	+	1031.10i	0.411890	+	1.71564i	0.663814	+	0.747897i	$0.268936\pi$
$601$	247.546	+	1031.10i	0.411890	+	1.71564i	−0.251925	+	0.967747i	$0.581064\pi$
$602$	−14.0203	−	22.8791i	−0.0232896	−	0.0380051i
$603$	−606.004	−	308.775i	−1.00498	−	0.512064i
$604$	12.7476	+	12.7476i	0.0211053	+	0.0211053i
$605$	58.0314	+	60.6008i	0.0959197	+	0.100167i
$606$	87.1431	+	36.0959i	0.143801	+	0.0595641i
$607$	−456.830	−	534.880i	−0.752604	−	0.881186i	0.243452	−	0.969913i	$-0.421720\pi$
$607$	−456.830	−	534.880i	−0.752604	−	0.881186i	−0.996056	+	0.0887273i	$0.971720\pi$
$608$	−33.1529	+	45.6310i	−0.0545277	+	0.0750510i
$609$	−169.233	+	276.164i	−0.277887	+	0.453471i
$610$	7.72991	−	3.93858i	0.0126720	−	0.00645670i
$611$	−292.935	−	95.1803i	−0.479435	−	0.155778i
$612$	96.2482	+	355.181i	0.157268	+	0.580360i
$613$	−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	$0.303367\pi$
$614$	31.6592	−	62.1346i	0.0515622	−	0.101196i
$615$	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	$0.870368\pi$
$618$	15.5543	+	1.22415i	0.0251687	+	0.00198082i
$619$	842.863	−	516.507i	1.36165	−	0.834422i	0.366280	−	0.930505i	$-0.380631\pi$
$619$	842.863	−	516.507i	1.36165	−	0.834422i	0.995373	+	0.0960829i	$0.0306314\pi$
$620$	4.05771	−	25.6193i	0.00654469	−	0.0413215i
$621$	102.679	+	201.519i	0.165344	+	0.324506i
$622$	−55.2589	+	64.6999i	−0.0888407	+	0.104019i
$623$	−105.740	−	440.439i	−0.169727	−	0.706965i
$624$	979.012	+	235.040i	1.56893	+	0.376667i
$625$	560.332	−	182.063i	0.896531	−	0.291300i
$626$	18.1796	+	43.8893i	0.0290408	+	0.0701108i
$627$	−264.146	−	151.709i	−0.421286	−	0.241960i
$628$	−305.071			−0.485782
$629$	17.7048	−	37.3907i	0.0281475	−	0.0594447i
$630$	−2.12083	−	1.54087i	−0.00336640	−	0.00244583i
$631$	1228.25	+	194.536i	1.94652	+	0.308298i	0.999901	−	0.0140635i	$-0.00447671\pi$
$631$	1228.25	+	194.536i	1.94652	+	0.308298i	0.946617	+	0.322362i	$0.104477\pi$
$632$	−5.81531	−	73.8905i	−0.00920143	−	0.116915i
$633$	−311.604	+	959.018i	−0.492265	+	1.51504i
$634$	−8.90999	+	14.5398i	−0.0140536	+	0.0229334i
$635$	27.2466	−	16.6967i	0.0429080	−	0.0262941i
$636$	−917.667	−	72.2219i	−1.44287	−	0.113556i
$637$	−367.997	−	367.997i	−0.577703	−	0.577703i
$638$	−35.5606	+	3.81893i	−0.0557376	+	0.00598578i
$639$	−236.756	+	571.579i	−0.370510	+	0.894490i
$640$	28.3226	+	2.22904i	0.0442541	+	0.00348287i
$641$	−195.988	+	816.350i	−0.305754	+	1.27356i	0.581981	+	0.813202i	$0.302278\pi$
$641$	−195.988	+	816.350i	−0.305754	+	1.27356i	−0.887735	+	0.460355i	$0.847722\pi$
$642$	48.2757	+	66.4458i	0.0751958	+	0.103498i
$643$	0.421850	+	5.36011i	0.000656065	+	0.00833609i	0.997237	−	0.0742904i	$-0.0236692\pi$
$643$	0.421850	+	5.36011i	0.000656065	+	0.00833609i	−0.996581	+	0.0826265i	$0.973669\pi$
$644$	128.863	+	252.909i	0.200099	+	0.392715i
$645$	−59.9049	−	82.4520i	−0.0928758	−	0.127833i
$646$	−19.7250	−	4.13439i	−0.0305341	−	0.00639998i
$647$	−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
$649$	120.879	−	176.735i	0.186254	−	0.272318i
$650$		−	67.3881i		−	0.103674i
$651$	99.1051	+	116.037i	0.152235	+	0.178244i
$652$	−523.154	−	853.710i	−0.802384	−	1.30937i
$653$	−181.480	−	755.918i	−0.277917	−	1.15761i	−0.920296	−	0.391222i	$-0.872053\pi$
$653$	−181.480	−	755.918i	−0.277917	−	1.15761i	0.642379	−	0.766387i	$-0.277947\pi$
$654$	18.6696	+	36.6411i	0.0285467	+	0.0560261i
$655$	14.2908	−	7.28152i	0.0218180	−	0.0111168i
$656$	1129.29	−	271.119i	1.72148	−	0.413291i
$657$	−168.213	+	103.081i	−0.256032	+	0.156896i
$658$	9.62306	−	8.21887i	0.0146247	−	0.0124907i
$659$	−401.718			−0.609587			−0.304793	−	0.952419i	$-0.598587\pi$
$659$	−401.718			−0.609587			−0.304793	+	0.952419i	$0.598587\pi$
$660$	3.27626	+	115.158i	0.00496403	+	0.174482i
$661$	−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
$663$	201.924	+	1072.54i	0.304561	+	1.61771i
$664$	67.6751	−	49.1688i	0.101920	−	0.0740495i
$665$	−19.1966	+	9.78117i	−0.0288671	+	0.0147085i
$666$	−2.15062	+	0.169257i	−0.00322915	+	0.000254140i
$667$	−270.769	+	196.725i	−0.405951	+	0.294940i
$668$	−538.364	−	129.250i	−0.805935	−	0.193488i
$669$	24.9328	−	316.801i	0.0372687	−	0.473544i
$670$	−13.0152	−	5.39107i	−0.0194257	−	0.00804637i
$671$	771.835	−	345.738i	1.15028	−	0.515257i
$672$	−88.7389	+	88.7389i	−0.132052	+	0.132052i
$673$	23.7514	−	301.791i	0.0352919	−	0.448426i	−0.953731	−	0.300662i	$-0.902792\pi$
$673$	23.7514	−	301.791i	0.0352919	−	0.448426i	0.989023	−	0.147764i	$-0.0472076\pi$
$674$	37.0881	+	60.5224i	0.0550269	+	0.0897958i
$675$	−282.281	−	172.982i	−0.418194	−	0.256270i
$676$	439.395	+	142.768i	0.649993	+	0.211196i
$677$	−768.441	+	60.4776i	−1.13507	+	0.0893317i	−0.632038	−	0.774937i	$-0.717781\pi$
$677$	−768.441	+	60.4776i	−1.13507	+	0.0893317i	−0.503030	+	0.864269i	$0.667781\pi$
$678$	12.2090	−	77.0847i	0.0180074	−	0.113694i
$679$	−63.8749	+	87.9163i	−0.0940720	+	0.129479i
$680$	5.14637	+	14.4033i	0.00756820	+	0.0211813i
$681$			155.974i			0.229037i
$682$	−3.46609	+	16.4900i	−0.00508225	+	0.0241790i
$683$	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
$685$	−7.54208	+	31.4150i	−0.0110103	+	0.0458613i
$686$	53.8563	−	12.9297i	0.0785077	−	0.0188480i
$687$	−656.599	−	560.789i	−0.955749	−	0.816287i
$688$	−540.318	+	275.306i	−0.785346	+	0.400154i
$689$	−1016.72	−	161.032i	−1.47564	−	0.233719i
$690$	−3.75371	−	6.12550i	−0.00544016	−	0.00887753i
$691$	−50.4135	+	640.565i	−0.0729573	+	0.927011i	0.846135	+	0.532969i	$0.178924\pi$
$691$	−50.4135	+	640.565i	−0.0729573	+	0.927011i	−0.919092	+	0.394042i	$0.871076\pi$
$692$	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
$695$	−120.209	−	61.2495i	−0.172962	−	0.0881287i
$696$	−79.7211	−	57.9208i	−0.114542	−	0.0832195i
$697$	769.199	+	996.589i	1.10359	+	1.42983i
$698$	7.88429	−	24.2653i	0.0112955	−	0.0347641i
$699$	−31.5488	−	61.9181i	−0.0451343	−	0.0885810i
$700$	−354.267	−	217.095i	−0.506096	−	0.310136i
$701$	356.984	+	259.364i	0.509249	+	0.369991i	0.812539	−	0.582907i	$-0.198085\pi$
$701$	356.984	+	259.364i	0.509249	+	0.369991i	−0.303289	+	0.952899i	$0.598085\pi$
$702$	−28.2185	+	24.1009i	−0.0401973	+	0.0343317i
$703$	−6.78483	+	16.3800i	−0.00965125	+	0.0233002i
$704$	670.606	+	86.7439i	0.952565	+	0.123216i
$705$	33.9878	−	33.9878i	0.0482097	−	0.0482097i
$706$	25.0040	−	49.0730i	0.0354164	−	0.0695086i
$707$	554.523	−	339.812i	0.784333	−	0.480640i
$708$	285.870	−	68.6312i	0.403771	−	0.0969368i
$709$	−299.044	+	23.5353i	−0.421783	+	0.0331950i	−0.287575	−	0.957758i	$-0.592849\pi$
$709$	−299.044	+	23.5353i	−0.421783	+	0.0331950i	−0.134208	+	0.990953i	$0.542849\pi$
$710$	−3.95990	+	12.1873i	−0.00557732	+	0.0171652i
$711$	265.343	+	162.603i	0.373198	+	0.228696i
$712$	136.110	−	21.5577i	0.191165	−	0.0302776i
$713$	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
$717$	223.087	−	190.534i	0.311139	−	0.265738i
$718$	39.8636	−	54.8675i	0.0555203	−	0.0764172i
$719$	1.39744	+	0.856355i	0.00194360	+	0.00119104i	0.523470	−	0.852044i	$-0.324637\pi$
$719$	1.39744	+	0.856355i	0.00194360	+	0.00119104i	−0.521526	+	0.853235i	$0.674637\pi$
$720$	−38.4759	+	45.0495i	−0.0534387	+	0.0625687i
$721$	69.8668	−	81.8035i	0.0969026	−	0.113458i
$722$	−49.4891	−	7.83830i	−0.0685445	−	0.0108564i
$723$	220.905	+	1394.74i	0.305540	+	1.92910i
$724$	−1304.99	−	102.705i	−1.80248	−	0.141858i
$725$	187.483	−	452.625i	0.258598	−	0.624310i
$726$	1.62054	−	74.8223i	0.00223215	−	0.103061i
$727$		−	1287.32i		−	1.77073i	−0.464897	−	0.885365i	$-0.653909\pi$
$727$		−	1287.32i		−	1.77073i	0.464897	−	0.885365i	$-0.346091\pi$
$728$	−71.0653	+	60.6955i	−0.0976171	+	0.0833729i
$729$	−13.2627	−	83.7375i	−0.0181930	−	0.114866i
$730$	−3.30591	+	2.40189i	−0.00452865	+	0.00329025i
$731$	−512.017	−	412.230i	−0.700433	−	0.563926i
$732$	1104.39	+	358.837i	1.50873	+	0.490215i
$733$	108.091	−	682.461i	0.147464	−	0.931052i	−0.797367	−	0.603494i	$-0.793775\pi$
$733$	108.091	−	682.461i	0.147464	−	0.931052i	0.944831	−	0.327557i	$-0.106225\pi$
$734$	−22.3591	+	93.1323i	−0.0304620	+	0.126883i
$735$	77.2395	−	25.0966i	0.105088	−	0.0341451i
$736$	−119.808	+	49.6260i	−0.162782	+	0.0674266i
$737$	−1240.88	−	588.429i	−1.68369	−	0.798411i
$738$	25.1216	−	60.6488i	0.0340401	−	0.0821800i
$739$	588.155	−	1154.32i	0.795880	−	1.56200i	−0.0309303	−	0.999522i	$-0.509847\pi$
$739$	588.155	−	1154.32i	0.795880	−	1.56200i	0.826810	−	0.562481i	$-0.190153\pi$
$740$	6.62281	−	1.04895i	0.00894975	−	0.00141750i
$741$	−109.187	−	454.796i	−0.147351	−	0.613759i
$742$	27.4681	−	32.1610i	0.0370189	−	0.0433436i
$743$	41.4780	+	527.028i	0.0558251	+	0.709325i	0.959609	+	0.281336i	$0.0907776\pi$
$743$	41.4780	+	527.028i	0.0558251	+	0.709325i	−0.903784	+	0.427988i	$0.859222\pi$
$744$	−37.5599	+	27.2888i	−0.0504837	+	0.0366786i
$745$	−9.62513	+	40.0915i	−0.0129196	+	0.0538142i
$746$	−15.2415	+	29.9132i	−0.0204310	+	0.0400981i
$747$			351.224i			0.470180i
$748$	214.662	+	711.366i	0.286981	+	0.951024i
$749$	566.299			0.756074
$750$	18.9237	+	9.64210i	0.0252316	+	0.0128561i
$751$	177.931	+	42.7174i	0.236925	+	0.0568806i	0.350169	−	0.936687i	$-0.386124\pi$
$751$	177.931	+	42.7174i	0.236925	+	0.0568806i	−0.113244	+	0.993567i	$0.536124\pi$
$752$	−168.105	−	231.377i	−0.223545	−	0.307683i
$753$	28.9011	−	2.27457i	0.0383813	−	0.00302067i
$754$	−41.7581	−	35.6648i	−0.0553821	−	0.0473008i
$755$	−3.05917	+	0.734441i	−0.00405187	+	0.000972769i
$756$	35.7933	+	225.990i	0.0473457	+	0.298929i
$757$	−877.925	−	447.325i	−1.15974	−	0.590919i	−0.235181	−	0.971951i	$-0.575568\pi$
$757$	−877.925	−	447.325i	−1.15974	−	0.590919i	−0.924561	+	0.381033i	$0.875568\pi$
$758$	38.6808	+	16.0221i	0.0510300	+	0.0211373i
$759$	−335.570	−	614.722i	−0.442121	−	0.809911i
$760$	−2.50841	−	6.05584i	−0.00330054	−	0.00796821i
$761$	−213.776	−	657.935i	−0.280915	−	0.864566i	−0.987594	−	0.157032i	$-0.949807\pi$
$761$	−213.776	−	657.935i	−0.280915	−	0.864566i	0.706679	−	0.707534i	$-0.250193\pi$
$762$	−27.7154	−	6.65389i	−0.0363720	−	0.00873214i
$763$	280.055	+	44.3564i	0.367045	+	0.0581342i
$764$	−39.9865	+	123.066i	−0.0523384	+	0.161081i
$765$	−61.6260	−	18.0650i	−0.0805569	−	0.0236143i
$766$	26.7446	+	36.8108i	0.0349147	+	0.0480559i
$767$	324.721	−	51.4308i	0.423366	−	0.0670545i
$768$	590.532	+	691.424i	0.768922	+	0.900292i
$769$	340.547			0.442844			0.221422	−	0.975178i	$-0.428930\pi$
$769$	340.547			0.442844			0.221422	+	0.975178i	$0.428930\pi$
$770$	−4.36915	−	2.98830i	−0.00567422	−	0.00388091i
$771$	1472.29	+	609.844i	1.90959	+	0.790977i
$772$	30.2051	−	383.792i	0.0391258	−	0.497140i
$773$	941.034	−	149.045i	1.21738	−	0.192814i	0.485493	−	0.874241i	$-0.338640\pi$
$773$	941.034	−	149.045i	1.21738	−	0.192814i	0.731886	+	0.681427i	$0.238640\pi$
$774$	−5.36209	+	33.8549i	−0.00692776	+	0.0437401i
$775$	−175.517	−	149.906i	−0.226474	−	0.193427i
$776$	−25.1404	−	21.4719i	−0.0323974	−	0.0276700i
$777$	−20.6116	+	33.6350i	−0.0265271	+	0.0432883i
$778$	34.9430	+	25.3876i	0.0449139	+	0.0326319i
$779$	−350.386	−	410.249i	−0.449790	−	0.526636i
$780$	−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
$784$	−75.5945	−	477.285i	−0.0964216	−	0.608782i
$785$	27.8173	−	45.3937i	0.0354360	−	0.0578263i
$786$	−13.6058	−	4.42081i	−0.0173102	−	0.00562444i
$787$	−42.2861	−	537.296i	−0.0537307	−	0.682714i	−0.963519	−	0.267641i	$-0.913756\pi$
$787$	−42.2861	−	537.296i	−0.0537307	−	0.682714i	0.909788	−	0.415073i	$-0.136244\pi$
$788$	170.490	+	710.144i	0.216359	+	0.901198i
$789$	50.2169	+	81.9465i	0.0636462	+	0.103861i
$790$	5.74333	+	2.92637i	0.00727004	+	0.00370427i
$791$	−380.513	−	380.513i	−0.481053	−	0.481053i
$792$	53.3922	−	56.5192i	0.0674144	−	0.0713626i
$793$	1199.73	+	496.946i	1.51291	+	0.626666i
$794$	8.18203	+	9.57993i	0.0103048	+	0.0120654i
$795$	94.4220	−	129.961i	0.118770	−	0.163473i
$796$	−675.811	+	1102.82i	−0.849009	+	1.38546i
$797$	444.771	−	226.622i	0.558056	−	0.284344i	−0.152127	−	0.988361i	$-0.548612\pi$
$797$	444.771	−	226.622i	0.558056	−	0.284344i	0.710183	+	0.704017i	$0.248612\pi$
$798$	18.2765	+	5.93841i	0.0229029	+	0.00744162i
$799$	154.248	−	268.919i	0.193051	−	0.336570i
$800$	111.576	−	153.571i	0.139470	−	0.191964i
$801$	−262.681	+	515.541i	−0.327942	+	0.643622i
$802$	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
$805$	−49.3822	−	3.88647i	−0.0613444	−	0.00482791i
$806$	−22.0603	+	13.5186i	−0.0273702	+	0.0167725i
$807$	−144.797	+	914.215i	−0.179427	+	1.13286i
$808$	89.8288	+	176.299i	0.111174	+	0.218192i
$809$	−491.275	+	575.209i	−0.607262	+	0.711012i	−0.975816	−	0.218594i	$-0.929853\pi$
$809$	−491.275	+	575.209i	−0.607262	+	0.711012i	0.368554	+	0.929606i	$0.379853\pi$
$810$	−2.64340	−	11.0106i	−0.00326346	−	0.0135933i
$811$	766.250	+	183.960i	0.944822	+	0.226832i	0.676454	−	0.736485i	$-0.263516\pi$
$811$	766.250	+	183.960i	0.944822	+	0.226832i	0.268368	+	0.963317i	$0.413516\pi$
$812$	−322.020	+	104.631i	−0.396577	+	0.128856i
$813$	−550.431	−	1328.86i	−0.677037	−	1.63451i
$814$	−4.33106	+	0.465122i	−0.00532071	+	0.000571403i
$815$	174.732			0.214395
$816$	−433.685	+	915.900i	−0.531477	+	1.12243i
$817$	227.905	+	165.583i	0.278954	+	0.202672i
$818$	−73.5774	−	11.6535i	−0.0899480	−	0.0142464i
$819$	−30.7871	−	391.187i	−0.0375911	−	0.477640i
$820$	−63.0533	+	194.058i	−0.0768943	+	0.236656i
$821$	694.373	−	1133.11i	0.845765	−	1.38016i	−0.0778999	−	0.996961i	$-0.524821\pi$
$821$	694.373	−	1133.11i	0.845765	−	1.38016i	0.923665	−	0.383202i	$-0.125179\pi$
$822$	24.5706	−	15.0569i	0.0298912	−	0.0183174i
$823$	665.880	+	52.4059i	0.809089	+	0.0636767i	0.476253	−	0.879308i	$-0.341995\pi$
$823$	665.880	+	52.4059i	0.809089	+	0.0636767i	0.332836	+	0.942985i	$0.391995\pi$
$824$	23.1434	+	23.1434i	0.0280866	+	0.0280866i
$825$	888.984	+	510.577i	1.07756	+	0.618881i
$826$	−5.16933	+	12.4799i	−0.00625826	+	0.0151088i
$827$	456.503	+	35.9275i	0.551998	+	0.0434432i	0.351392	−	0.936229i	$-0.385709\pi$
$827$	456.503	+	35.9275i	0.551998	+	0.0434432i	0.200607	+	0.979672i	$0.435709\pi$
$828$	84.6441	−	352.568i	0.102227	−	0.425807i
$829$	172.385	+	237.267i	0.207943	+	0.286209i	0.900231	−	0.435412i	$-0.143397\pi$
$829$	172.385	+	237.267i	0.207943	+	0.286209i	−0.692288	+	0.721621i	$0.743397\pi$
$830$	0.570780	+	7.25244i	0.000687686	+	0.00873788i
$831$	−681.702	−	1337.92i	−0.820340	−	1.61001i
$832$	610.275	+	839.972i	0.733504	+	1.00958i
$833$	438.500	−	286.533i	0.526411	−	0.343977i
$834$	37.1862	+	114.447i	0.0445878	+	0.137227i
$835$	68.3216	−	68.3216i	0.0818223	−	0.0818223i
$836$	−106.976	−	299.931i	−0.127961	−	0.358770i
$837$			127.110i			0.151864i
$838$	−25.4025	−	29.7425i	−0.0303133	−	0.0354923i
$839$	262.561	+	428.460i	0.312945	+	0.510680i	0.969981	−	0.243179i	$-0.0781903\pi$
$839$	262.561	+	428.460i	0.312945	+	0.510680i	−0.657036	+	0.753859i	$0.728190\pi$
$840$	−3.40464	−	14.1813i	−0.00405314	−	0.0168826i
$841$	200.554	+	393.610i	0.238471	+	0.468026i
$842$	−104.337	+	53.1621i	−0.123915	+	0.0631379i
$843$	730.141	−	175.291i	0.866123	−	0.207938i
$844$	−898.799	+	550.785i	−1.06493	+	0.652589i
$845$	−61.3089	+	52.3627i	−0.0725549	+	0.0619677i
$846$	−16.1658			−0.0191085
$847$	−410.806	−	312.279i	−0.485013	−	0.368689i
$848$	−675.871	−	675.871i	−0.797018	−	0.797018i
$849$	1069.23	−	347.415i	1.25940	−	0.409205i
$850$	66.3845	+	13.9143i	0.0780994	+	0.0163697i
$851$	−32.9780	+	23.9599i	−0.0387521	+	0.0281550i
$852$	−1528.28	+	778.700i	−1.79376	+	0.913967i
$853$	−386.656	+	30.4305i	−0.453289	+	0.0356746i	−0.303049	−	0.952975i	$-0.598005\pi$
$853$	−386.656	+	30.4305i	−0.453289	+	0.0356746i	−0.150240	+	0.988650i	$0.548005\pi$
$854$	−43.1649	+	31.3611i	−0.0505444	+	0.0367226i
$855$	26.7611	+	6.42477i	0.0312995	+	0.00751435i
$856$	−13.5178	+	171.759i	−0.0157918	+	0.200653i
$857$	56.4173	+	23.3688i	0.0658311	+	0.0272682i	0.415356	−	0.909659i	$-0.363657\pi$
$857$	56.4173	+	23.3688i	0.0658311	+	0.0272682i	−0.349525	+	0.936927i	$0.613657\pi$
$858$	85.2229	−	77.0849i	0.0993274	−	0.0898426i
$859$	−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	$0.377096\pi$
$860$	8.35918	−	106.213i	0.00971997	−	0.123504i
$861$	−627.212	−	1023.52i	−0.728469	−	1.18875i
$862$	2.08865	+	1.27993i	0.00242303	+	0.00148483i
$863$	−1019.18	−	331.152i	−1.18097	−	0.383722i	−0.348246	−	0.937403i	$-0.613223\pi$
$863$	−1019.18	−	331.152i	−1.18097	−	0.383722i	−0.832729	+	0.553681i	$0.813223\pi$
$864$	−104.212	+	8.20162i	−0.120615	+	0.00949262i
$865$	−5.23607	+	33.0592i	−0.00605326	+	0.0382188i
$866$	61.0164	−	83.9819i	0.0704578	−	0.0969768i
$867$	−1098.26	−	22.5410i	−1.26674	−	0.0259989i
$868$			159.525i			0.183784i
$869$	544.903	+	312.959i	0.627047	+	0.360136i
$870$	7.91744	−	3.27951i	0.00910051	−	0.00376955i
$871$	−651.620	−	2005.48i	−0.748128	−	2.30250i
$872$	−20.1383	+	83.8822i	−0.0230944	+	0.0961952i
$873$	134.981	−	32.4060i	0.154617	−	0.0371203i
$874$	15.0999	+	12.8965i	0.0172768	+	0.0147558i
$875$	130.479	−	66.4826i	0.149119	−	0.0759801i
$876$	−540.226	−	85.5634i	−0.616696	−	0.0976751i
$877$	−244.854	−	399.565i	−0.279195	−	0.455604i	0.682048	−	0.731307i	$-0.261089\pi$
$877$	−244.854	−	399.565i	−0.279195	−	0.455604i	−0.961243	+	0.275703i	$0.911089\pi$
$878$	3.14250	−	39.9293i	0.00357916	−	0.0454776i
$879$	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	$0.127639\pi$
$882$	−24.3373	−	12.4005i	−0.0275933	−	0.0140595i
$883$	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	$0.597949\pi$
$884$	−567.660	+	989.672i	−0.642150	+	1.11954i
$885$	−15.8543	+	48.7946i	−0.0179145	+	0.0551351i
$886$	−25.6451	−	50.3314i	−0.0289448	−	0.0568075i
$887$	−782.105	−	479.275i	−0.881742	−	0.540332i	0.00635935	−	0.999980i	$-0.497976\pi$
$887$	−782.105	−	479.275i	−0.881742	−	0.540332i	−0.888101	+	0.459648i	$0.847976\pi$
$888$	−9.70954	−	7.05439i	−0.0109342	−	0.00794414i
$889$	−149.442	+	127.635i	−0.168101	+	0.143572i
$890$	−4.58630	+	11.0723i	−0.00515315	+	0.0124408i
$891$	−203.620	−	1084.93i	−0.228529	−	1.21765i
$892$	234.903	−	234.903i	0.263344	−	0.263344i
$893$	−60.3168	+	118.378i	−0.0675440	+	0.132563i
$894$	31.3567	−	19.2154i	0.0350746	−	0.0214938i
$895$	129.369	−	31.0587i	0.144546	−	0.0347025i
$896$	−174.186	+	13.7087i	−0.194404	+	0.0152999i
$897$	332.303	−	1022.72i	0.370461	−	1.14016i
$898$	−27.8554	−	17.0698i	−0.0310194	−	0.0190087i
$899$	−185.783	+	29.4251i	−0.206655	+	0.0327310i
$900$	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
$904$	124.493	−	106.327i	0.137713	−	0.117618i
$905$	134.275	−	184.814i	0.148371	−	0.204215i
$906$	2.39266	+	1.46622i	0.00264090	+	0.00161835i
$907$	500.240	−	585.706i	0.551532	−	0.645762i	−0.412685	−	0.910874i	$-0.635409\pi$
$907$	500.240	−	585.706i	0.551532	−	0.645762i	0.964218	+	0.265112i	$0.0854090\pi$
$908$	−105.894	+	123.986i	−0.116624	+	0.136549i
$909$	−820.544	−	129.961i	−0.902689	−	0.142972i
$910$	−1.27145	−	8.02760i	−0.00139719	−	0.00882154i
$911$	−640.405	−	50.4009i	−0.702969	−	0.0553248i	−0.278064	−	0.960563i	$-0.589693\pi$
$911$	−640.405	−	50.4009i	−0.702969	−	0.0553248i	−0.424905	+	0.905238i	$0.639693\pi$
$912$	166.197	−	401.235i	0.182233	−	0.439951i
$913$	20.1684	+	708.907i	0.0220903	+	0.776459i
$914$			36.8923i			0.0403636i
$915$	−154.095	+	131.610i	−0.168410	+	0.143836i
$916$	−141.209	−	891.562i	−0.154159	−	0.973320i
$917$	−79.8018	+	57.9794i	−0.0870249	+	0.0632273i
$918$	−17.9154	−	32.7746i	−0.0195157	−	0.0357022i
$919$	−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	$0.626231\pi$
$920$	2.35754	−	14.8849i	0.00256254	−	0.0161793i
$921$	−380.267	+	1583.93i	−0.412885	+	1.71979i
$922$	60.2947	−	19.5909i	0.0653956	−	0.0212483i
$923$	−1772.12	+	734.037i	−1.91996	+	0.795272i
$924$	−130.693	−	696.360i	−0.141443	−	0.753637i
$925$	22.8343	−	55.1269i	0.0246857	−	0.0595967i
$926$	−6.07444	+	11.9218i	−0.00655987	+	0.0128745i
$927$	−135.730	+	21.4975i	−0.146418	+	0.0231904i
$928$	−36.1118	−	150.416i	−0.0389136	−	0.162087i
$929$	−813.158	+	952.085i	−0.875304	+	1.02485i	0.124165	+	0.992262i	$0.460375\pi$
$929$	−813.158	+	952.085i	−0.875304	+	1.02485i	−0.999469	+	0.0325878i	$0.989625\pi$
$930$	−0.316784	−	4.02513i	−0.000340628	−	0.00432809i
$931$	−181.612	+	131.949i	−0.195072	+	0.141728i
$932$	16.9589	−	70.6390i	0.0181963	−	0.0757929i
$933$	902.309	−	1770.88i	0.967105	−	1.89805i
$934$			119.454i			0.127895i
$935$	−125.423	−	32.9234i	−0.134142	−	0.0352122i
$936$	119.382			0.127545
$937$	1067.36	+	543.847i	1.13913	+	0.580413i	0.918687	−	0.394987i	$-0.129251\pi$
$937$	1067.36	+	543.847i	1.13913	+	0.580413i	0.220439	+	0.975401i	$0.429251\pi$
$938$	84.2455	+	20.2256i	0.0898140	+	0.0215624i
$939$	−652.248	−	897.743i	−0.694620	−	0.956062i
$940$	50.0927	−	3.94238i	0.0532901	−	0.00419402i
$941$	987.518	+	843.420i	1.04943	+	0.896302i	0.994764	−	0.102203i	$-0.0325890\pi$
$941$	987.518	+	843.420i	1.04943	+	0.896302i	0.0546709	+	0.998504i	$0.482589\pi$
$942$	−46.1748	+	11.0856i	−0.0490178	+	0.0117681i
$943$	−194.045	−	1225.15i	−0.205774	−	1.29921i
$944$	272.001	+	138.591i	0.288137	+	0.146813i
$945$	−36.8904	−	15.2805i	−0.0390375	−	0.0161699i
$946$	−8.87872	+	68.6402i	−0.00938554	+	0.0725584i
$947$	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
$949$	−594.760	−	142.789i	−0.626723	−	0.150463i
$950$	−28.7098	−	4.54719i	−0.0302208	−	0.00478651i
$951$	123.091	−	378.834i	0.129433	−	0.398354i
$952$	−45.1180	−	82.5393i	−0.0473929	−	0.0867009i
$953$	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	$0.724441\pi$
$954$	−53.3620	+	8.45170i	−0.0559350	+	0.00885923i
$955$	−14.6658	−	17.1714i	−0.0153568	−	0.0179805i
$956$	306.693			0.320809
$957$	786.877	−	280.653i	0.822233	−	0.293263i
$958$	38.5721	+	15.9771i	0.0402631	+	0.0166775i
$959$	15.5894	−	198.082i	0.0162559	−	0.206550i
$960$	−160.030	+	25.3462i	−0.166698	+	0.0264023i
$961$	136.470	−	861.638i	0.142008	−	0.896606i
$962$	−5.08588	−	4.34375i	−0.00528678	−	0.00451534i
$963$	−550.073	−	469.806i	−0.571207	−	0.487857i
$964$	−771.321	+	1258.68i	−0.800126	+	1.30569i
$965$	54.3530	+	39.4898i	0.0563243	+	0.0409220i
$966$	28.6946	+	33.5970i	0.0297045	+	0.0347795i
$967$	−1152.03	+	1152.03i	−1.19134	+	1.19134i	−0.214655	+	0.976690i	$0.568863\pi$
$967$	−1152.03	+	1152.03i	−1.19134	+	1.19134i	−0.976690	+	0.214655i	$0.931137\pi$
$968$	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
$971$	132.892	+	839.046i	0.136861	+	0.864105i	0.956608	+	0.291379i	$0.0941141\pi$
$971$	132.892	+	839.046i	0.136861	+	0.864105i	−0.819747	+	0.572726i	$0.805886\pi$
$972$	539.630	−	880.595i	0.555174	−	0.905962i
$973$	789.117	+	256.400i	0.811015	+	0.263515i
$974$	5.71372	+	72.5998i	0.00586625	+	0.0745377i
$975$	367.468	+	1530.61i	0.376890	+	1.56986i
$976$	630.019	+	1028.10i	0.645511	+	1.05338i
$977$	1664.35	+	848.030i	1.70353	+	0.867994i	0.985011	+	0.172489i	$0.0551809\pi$
$977$	1664.35	+	848.030i	1.70353	+	0.867994i	0.718522	+	0.695504i	$0.244819\pi$
$978$	−110.205	−	110.205i	−0.112684	−	0.112684i
$979$	−500.589	+	1055.65i	−0.511327	+	1.07829i
$980$	78.4377	+	32.4900i	0.0800385	+	0.0331530i
$981$	−235.232	−	275.421i	−0.239788	−	0.280756i
$982$	53.1281	−	73.1246i	0.0541020	−	0.0744649i
$983$	−746.249	+	1217.77i	−0.759154	+	1.23883i	0.206360	+	0.978476i	$0.433838\pi$
$983$	−746.249	+	1217.77i	−0.759154	+	1.23883i	−0.965514	+	0.260351i	$0.916162\pi$
$984$	325.406	−	165.802i	0.330697	−	0.168498i
$985$	−121.213	−	39.3845i	−0.123059	−	0.0399843i
$986$	43.7559	−	33.7722i	0.0443771	−	0.0342517i
$987$	−173.755	+	239.153i	−0.176043	+	0.242303i
$988$	221.977	−	435.654i	0.224673	−	0.440946i
$989$	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	$0.857672\pi$
$992$	−72.6564	−	5.71818i	−0.0732423	−	0.00576430i
$993$	752.066	−	460.866i	0.757367	−	0.464115i
$994$	12.3286	−	77.8397i	0.0124030	−	0.0783095i
$995$	−102.474	−	201.117i	−0.102989	−	0.202128i
$996$	−632.400	+	740.445i	−0.634939	+	0.743419i
$997$	−266.764	−	1111.15i	−0.267566	−	1.11449i	−0.930639	−	0.365939i	$-0.880748\pi$
$997$	−266.764	−	1111.15i	−0.267566	−	1.11449i	0.663072	−	0.748555i	$-0.269252\pi$
$998$	−43.7769	−	10.5099i	−0.0438647	−	0.0105310i
$999$	−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.138.18	yes	544
11.2	odd	10	inner	187.3.q.a.2.18	✓	544
17.9	even	8	inner	187.3.q.a.94.18	yes	544
187.145	odd	40	inner	187.3.q.a.145.18	yes	544

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.3.q.a.2.18	✓	544	11.2	odd	10	inner
187.3.q.a.94.18	yes	544	17.9	even	8	inner
187.3.q.a.138.18	yes	544	1.1	even	1	trivial
187.3.q.a.145.18	yes	544	187.145	odd	40	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+(0.144987 + 0.0738746i) q^{2} +(-3.69599 - 0.887328i) q^{3} +(-2.33558 - 3.21465i) q^{4} +(0.691295 - 0.0544061i) q^{5} +(-0.470320 - 0.401691i) q^{6} +(-4.14682 + 0.995564i) q^{7} +(-0.202970 - 1.28150i) q^{8} +(4.85392 + 2.47320i) q^{9} +(0.104248 + 0.0431810i) q^{10} +(9.93913 + 4.71315i) q^{11} +(5.77982 + 13.9537i) q^{12} +(5.21929 + 16.0633i) q^{13} +(-0.674783 - 0.162001i) q^{14} +(-2.60329 - 0.412321i) q^{15} +(-4.84630 + 14.9154i) q^{16} +(-16.9018 + 1.82481i) q^{17} +(0.521050 + 0.717164i) q^{18} +(7.19575 - 1.13970i) q^{19} +(-1.78947 - 2.09520i) q^{20} +16.2100 q^{21} +(1.09286 + 1.41760i) q^{22} +(15.4753 + 6.41008i) q^{23} +(-0.386938 + 4.91651i) q^{24} +(-24.2173 + 3.83564i) q^{25} +(-0.429942 + 2.71455i) q^{26} +(10.2673 + 8.76910i) q^{27} +(12.8856 + 11.0053i) q^{28} +(-10.4401 + 17.0366i) q^{29} +(-0.346984 - 0.252099i) q^{30} +(6.11382 + 7.15837i) 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} +(-3.38626 - 21.3800i) q^{36} +(-1.27153 + 2.07496i) q^{37} +(1.12749 + 0.366342i) q^{38} +(-5.03700 - 64.0011i) q^{39} +(-0.210033 - 0.874852i) q^{40} +(-38.6929 - 63.1411i) q^{41} +(2.35024 + 1.19751i) q^{42} +(27.3417 + 27.3417i) q^{43} +(-8.06249 - 42.9587i) q^{44} +(3.49005 + 1.44563i) q^{45} +(1.77018 + 2.07261i) q^{46} +(-10.7190 + 14.7534i) q^{47} +(31.1467 - 50.8268i) q^{48} +(-27.4543 + 13.9887i) q^{49} +(-3.79455 - 1.23292i) q^{50} +(64.0880 + 8.25295i) q^{51} +(39.4479 - 54.2953i) q^{52} +(-27.6693 + 54.3040i) q^{53} +(0.840812 + 2.02990i) q^{54} +(7.12729 + 2.71743i) q^{55} +(2.11749 + 5.11208i) q^{56} +(-27.6067 - 2.17269i) q^{57} +(-2.77225 + 1.69884i) q^{58} +(3.04505 - 19.2257i) q^{59} +(4.75473 + 9.33168i) q^{60} +(49.9327 - 58.4637i) q^{61} +(0.357604 + 1.48953i) q^{62} +(-22.5906 - 5.42352i) q^{63} +(58.4634 - 18.9959i) q^{64} +(4.48201 + 10.8205i) q^{65} +(-2.78134 - 6.20915i) q^{66} -124.848 q^{67} +(45.3415 + 50.0712i) q^{68} +(-51.5087 - 37.4232i) q^{69} +(-0.475288 - 0.0752782i) q^{70} +(8.91029 + 113.216i) q^{71} +(2.18420 - 6.72229i) q^{72} +(-18.9220 + 30.8778i) q^{73} +(-0.337643 + 0.206908i) q^{74} +(92.9103 + 7.31220i) q^{75} +(-20.4700 - 20.4700i) q^{76} +(-45.9080 - 9.64955i) q^{77} +(3.99776 - 9.65145i) q^{78} +(56.9495 + 4.48202i) q^{79} +(-2.53873 + 10.5746i) q^{80} +(-58.9854 - 81.1864i) q^{81} +(-0.945449 - 12.0131i) q^{82} +(29.2698 + 57.4452i) q^{83} +(-37.8597 - 52.1094i) q^{84} +(-11.5848 + 2.18104i) q^{85} +(1.94434 + 5.98405i) q^{86} +(53.7034 - 53.7034i) q^{87} +(4.02256 - 13.6936i) q^{88} +106.211i q^{89} +(0.399217 + 0.467423i) q^{90} +(-37.6355 - 61.4156i) q^{91} +(-15.5376 - 64.7188i) q^{92} +(-16.2448 - 31.8822i) q^{93} +(-2.64402 + 1.34720i) q^{94} +(4.91238 - 1.17936i) q^{95} +(25.0906 - 15.3755i) q^{96} +(19.3764 - 16.5490i) q^{97} -5.01394 q^{98} +(36.5872 + 47.4587i) 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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more