LMFDB - Embedded newform 55.3.h.a.39.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [55,3,Mod(19,55)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(55, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("55.19"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 55 = 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	55.h (of order $10$, degree $4$, 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:	$1.49864145398$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			39.10
Character	$\chi$	$=$	55.39
Dual form			55.3.h.a.24.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.09764 + 3.37818i) q^{2} +(-0.896484 + 1.23390i) q^{3} +(-6.97124 + 5.06490i) q^{4} +(3.42583 - 3.64194i) q^{5} +(-5.15237 - 1.67411i) q^{6} +(0.882039 - 0.640839i) q^{7} +(-13.2675 - 9.63938i) q^{8} +(2.06232 + 6.34716i) q^{9} +(16.0635 + 7.57554i) q^{10} +(3.85595 - 10.3020i) q^{11} -13.1425i q^{12} +(0.270096 + 0.831271i) q^{13} +(3.13303 + 2.27628i) q^{14} +(1.42261 + 7.49209i) q^{15} +(7.34959 - 22.6197i) q^{16} +(-7.21718 + 22.2122i) q^{17} +(-19.1782 + 13.9338i) q^{18} +(14.8922 - 20.4973i) q^{19} +(-5.43620 + 42.7403i) q^{20} +1.66285i q^{21} +(39.0346 + 1.71822i) q^{22} -33.3562i q^{23} +(23.7881 - 7.72924i) q^{24} +(-1.52743 - 24.9533i) q^{25} +(-2.51172 + 1.82487i) q^{26} +(-22.7355 - 7.38721i) q^{27} +(-2.90312 + 8.93489i) q^{28} +(9.90414 + 13.6319i) q^{29} +(-23.7481 + 13.0294i) q^{30} +(-1.97870 - 6.08982i) q^{31} +18.8828 q^{32} +(9.25491 + 13.9935i) q^{33} -82.9587 q^{34} +(0.687817 - 5.40773i) q^{35} +(-46.5246 - 33.8021i) q^{36} +(-38.5475 - 53.0561i) q^{37} +(85.5899 + 27.8099i) q^{38} +(-1.26785 - 0.411949i) q^{39} +(-80.5580 + 15.2965i) q^{40} +(-22.7486 + 31.3107i) q^{41} +(-5.61743 + 1.82521i) q^{42} +15.0656 q^{43} +(25.2980 + 91.3479i) q^{44} +(30.1811 + 14.2334i) q^{45} +(112.683 - 36.6131i) q^{46} +(-34.8531 + 47.9712i) q^{47} +(21.3218 + 29.3469i) q^{48} +(-14.7745 + 45.4713i) q^{49} +(82.6202 - 32.5496i) q^{50} +(-20.9376 - 28.8182i) q^{51} +(-6.09322 - 4.42698i) q^{52} +(22.5056 - 7.31251i) q^{53} -84.9132i q^{54} +(-24.3095 - 49.3361i) q^{55} -17.8797 q^{56} +(11.9411 + 36.7511i) q^{57} +(-35.1798 + 48.4209i) q^{58} +(-30.7715 + 22.3568i) q^{59} +(-47.8640 - 45.0238i) q^{60} +(32.4198 + 10.5338i) q^{61} +(18.4006 - 13.3688i) q^{62} +(5.88655 + 4.27683i) q^{63} +(-8.67190 - 26.6894i) q^{64} +(3.95274 + 1.86412i) q^{65} +(-37.1140 + 46.6246i) q^{66} +43.7033i q^{67} +(-62.1899 - 191.401i) q^{68} +(41.1584 + 29.9033i) q^{69} +(19.0233 - 3.61216i) q^{70} +(11.1969 - 34.4604i) q^{71} +(33.8209 - 104.090i) q^{72} +(68.0006 - 49.4053i) q^{73} +(136.922 - 188.457i) q^{74} +(32.1593 + 20.4855i) q^{75} +218.319i q^{76} +(-3.20083 - 11.5578i) q^{77} -4.73519i q^{78} +(28.8577 - 9.37643i) q^{79} +(-57.2012 - 104.258i) q^{80} +(-19.0958 + 13.8739i) q^{81} +(-130.743 - 42.4810i) q^{82} +(-42.0601 + 129.448i) q^{83} +(-8.42220 - 11.5922i) q^{84} +(56.1706 + 102.380i) q^{85} +(16.5366 + 50.8943i) q^{86} -25.6994 q^{87} +(-150.464 + 99.5127i) q^{88} -8.46901 q^{89} +(-14.9552 + 117.580i) q^{90} +(0.770946 + 0.560125i) q^{91} +(168.946 + 232.534i) q^{92} +(9.28813 + 3.01790i) q^{93} +(-200.312 - 65.0852i) q^{94} +(-23.6320 - 124.457i) q^{95} +(-16.9281 + 23.2995i) q^{96} +(63.3788 - 20.5930i) q^{97} -169.827 q^{98} +(73.3407 + 3.22831i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 22 q^{4} + 2 q^{5} - 10 q^{6} - 4 q^{9} - 16 q^{11} + 38 q^{14} + 4 q^{15} - 138 q^{16} - 10 q^{19} + 72 q^{20} + 30 q^{24} - 138 q^{25} + 172 q^{26} - 10 q^{29} - 290 q^{30} + 128 q^{31} - 112 q^{34}+ \cdots + 882 q^{99}+O(q^{100}) $ 40 * q - 22 * q^4 + 2 * q^5 - 10 * q^6 - 4 * q^9 - 16 * q^11 + 38 * q^14 + 4 * q^15 - 138 * q^16 - 10 * q^19 + 72 * q^20 + 30 * q^24 - 138 * q^25 + 172 * q^26 - 10 * q^29 - 290 * q^30 + 128 * q^31 - 112 * q^34 - 90 * q^35 + 248 * q^36 - 170 * q^39 + 210 * q^40 + 50 * q^41 + 422 * q^44 + 196 * q^45 + 10 * q^46 + 18 * q^49 + 320 * q^50 - 270 * q^51 + 392 * q^55 + 144 * q^56 - 254 * q^59 - 156 * q^60 - 300 * q^61 - 834 * q^64 - 1470 * q^66 + 246 * q^69 - 370 * q^70 + 260 * q^71 + 620 * q^74 - 76 * q^75 + 270 * q^79 - 838 * q^80 + 606 * q^81 + 80 * q^84 - 630 * q^85 + 602 * q^86 - 812 * q^89 - 300 * q^90 + 582 * q^91 + 840 * q^94 + 460 * q^95 + 1610 * q^96 + 882 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/55\mathbb{Z}\right)^\times$.

$n$	$12$	$46$
$\chi(n)$	$-1$	$e\left(\frac{9}{10}\right)$

Coefficient data

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

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

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

$2$	1.09764	+	3.37818i	0.548819	+	1.68909i	0.711732	+	0.702451i	$0.247911\pi$
$2$	1.09764	+	3.37818i	0.548819	+	1.68909i	−0.162913	+	0.986640i	$0.552089\pi$
$3$	−0.896484	+	1.23390i	−0.298828	+	0.411302i	−0.931857	−	0.362827i	$-0.881812\pi$
$3$	−0.896484	+	1.23390i	−0.298828	+	0.411302i	0.633028	+	0.774129i	$0.281812\pi$
$4$	−6.97124	+	5.06490i	−1.74281	+	1.26623i
$5$	3.42583	−	3.64194i	0.685165	−	0.728388i
$5$	3.42583	−	3.64194i	0.685165	−	0.728388i
$6$	−5.15237	−	1.67411i	−0.858729	−	0.279018i
$7$	0.882039	−	0.640839i	0.126006	−	0.0915484i	−0.522997	−	0.852334i	$-0.675186\pi$
$7$	0.882039	−	0.640839i	0.126006	−	0.0915484i	0.649003	+	0.760786i	$0.275186\pi$
$8$	−13.2675	−	9.63938i	−1.65843	−	1.20492i
$9$	2.06232	+	6.34716i	0.229146	+	0.705239i
$10$	16.0635	+	7.57554i	1.60635	+	0.757554i
$11$	3.85595	−	10.3020i	0.350541	−	0.936547i
$11$	3.85595	−	10.3020i	0.350541	−	0.936547i
$12$		−	13.1425i		−	1.09521i
$13$	0.270096	+	0.831271i	0.0207766	+	0.0639440i	0.960907	−	0.276870i	$-0.0892973\pi$
$13$	0.270096	+	0.831271i	0.0207766	+	0.0639440i	−0.940131	+	0.340814i	$0.889297\pi$
$14$	3.13303	+	2.27628i	0.223788	+	0.162591i
$15$	1.42261	+	7.49209i	0.0948404	+	0.499472i
$16$	7.34959	−	22.6197i	0.459349	−	1.41373i
$17$	−7.21718	+	22.2122i	−0.424540	+	1.30660i	0.478894	+	0.877873i	$0.341038\pi$
$17$	−7.21718	+	22.2122i	−0.424540	+	1.30660i	−0.903434	+	0.428727i	$0.858962\pi$
$18$	−19.1782	+	13.9338i	−1.06545	+	0.774098i
$19$	14.8922	−	20.4973i	0.783799	−	1.07881i	−0.211054	−	0.977474i	$-0.567690\pi$
$19$	14.8922	−	20.4973i	0.783799	−	1.07881i	0.994853	−	0.101332i	$-0.0323104\pi$
$20$	−5.43620	+	42.7403i	−0.271810	+	2.13702i
$21$			1.66285i			0.0791835i
$22$	39.0346	+	1.71822i	1.77430	+	0.0781009i
$23$		−	33.3562i		−	1.45027i	−0.688606	−	0.725135i	$-0.741777\pi$
$23$		−	33.3562i		−	1.45027i	0.688606	−	0.725135i	$-0.258223\pi$
$24$	23.7881	−	7.72924i	0.991173	−	0.322052i
$25$	−1.52743	−	24.9533i	−0.0610971	−	0.998132i
$26$	−2.51172	+	1.82487i	−0.0966046	+	0.0701873i
$27$	−22.7355	−	7.38721i	−0.842056	−	0.273600i
$28$	−2.90312	+	8.93489i	−0.103683	+	0.319103i
$29$	9.90414	+	13.6319i	0.341522	+	0.470065i	0.944885	−	0.327402i	$-0.106173\pi$
$29$	9.90414	+	13.6319i	0.341522	+	0.470065i	−0.603363	+	0.797467i	$0.706173\pi$
$30$	−23.7481	+	13.0294i	−0.791604	+	0.434314i
$31$	−1.97870	−	6.08982i	−0.0638291	−	0.196446i	0.914056	−	0.405587i	$-0.132933\pi$
$31$	−1.97870	−	6.08982i	−0.0638291	−	0.196446i	−0.977885	+	0.209142i	$0.932933\pi$
$32$	18.8828			0.590087
$33$	9.25491	+	13.9935i	0.280452	+	0.424045i
$34$	−82.9587			−2.43996
$35$	0.687817	−	5.40773i	0.0196519	−	0.154507i
$36$	−46.5246	−	33.8021i	−1.29235	−	0.938948i
$37$	−38.5475	−	53.0561i	−1.04182	−	1.43395i	−0.895687	−	0.444684i	$-0.853316\pi$
$37$	−38.5475	−	53.0561i	−1.04182	−	1.43395i	−0.146137	−	0.989264i	$-0.546684\pi$
$38$	85.5899	+	27.8099i	2.25237	+	0.731838i
$39$	−1.26785	−	0.411949i	−0.0325089	−	0.0105628i
$40$	−80.5580	+	15.2965i	−2.01395	+	0.382411i
$41$	−22.7486	+	31.3107i	−0.554843	+	0.763676i	−0.990659	−	0.136360i	$-0.956460\pi$
$41$	−22.7486	+	31.3107i	−0.554843	+	0.763676i	0.435817	+	0.900036i	$0.356460\pi$
$42$	−5.61743	+	1.82521i	−0.133748	+	0.0434574i
$43$	15.0656			0.350362			0.175181	−	0.984536i	$-0.443949\pi$
$43$	15.0656			0.350362			0.175181	+	0.984536i	$0.443949\pi$
$44$	25.2980	+	91.3479i	0.574954	+	2.07609i
$45$	30.1811	+	14.2334i	0.670691	+	0.316298i
$46$	112.683	−	36.6131i	2.44964	−	0.795936i
$47$	−34.8531	+	47.9712i	−0.741556	+	1.02066i	0.256971	+	0.966419i	$0.417275\pi$
$47$	−34.8531	+	47.9712i	−0.741556	+	1.02066i	−0.998528	+	0.0542457i	$0.982725\pi$
$48$	21.3218	+	29.3469i	0.444204	+	0.611394i
$49$	−14.7745	+	45.4713i	−0.301521	+	0.927985i
$50$	82.6202	−	32.5496i	1.65240	−	0.650992i
$51$	−20.9376	−	28.8182i	−0.410542	−	0.565063i
$52$	−6.09322	−	4.42698i	−0.117177	−	0.0851343i
$53$	22.5056	−	7.31251i	0.424634	−	0.137972i	−0.0889014	−	0.996040i	$-0.528336\pi$
$53$	22.5056	−	7.31251i	0.424634	−	0.137972i	0.513535	+	0.858069i	$0.328336\pi$
$54$		−	84.9132i		−	1.57247i
$55$	−24.3095	−	49.3361i	−0.441991	−	0.897020i
$56$	−17.8797			−0.319280
$57$	11.9411	+	36.7511i	0.209494	+	0.644755i
$58$	−35.1798	+	48.4209i	−0.606549	+	0.834843i
$59$	−30.7715	+	22.3568i	−0.521550	+	0.378928i	−0.817188	−	0.576372i	$-0.804468\pi$
$59$	−30.7715	+	22.3568i	−0.521550	+	0.378928i	0.295637	+	0.955300i	$0.404468\pi$
$60$	−47.8640	−	45.0238i	−0.797734	−	0.750396i
$61$	32.4198	+	10.5338i	0.531472	+	0.172686i	0.562445	−	0.826834i	$-0.309861\pi$
$61$	32.4198	+	10.5338i	0.531472	+	0.172686i	−0.0309732	+	0.999520i	$0.509861\pi$
$62$	18.4006	−	13.3688i	0.296784	−	0.215626i
$63$	5.88655	+	4.27683i	0.0934372	+	0.0678861i
$64$	−8.67190	−	26.6894i	−0.135499	−	0.417022i
$65$	3.95274	+	1.86412i	0.0608114	+	0.0286787i
$66$	−37.1140	+	46.6246i	−0.562333	+	0.706433i
$67$			43.7033i			0.652288i	0.945320	+	0.326144i	$0.105750\pi$
$67$			43.7033i			0.652288i	−0.945320	+	0.326144i	$0.894250\pi$
$68$	−62.1899	−	191.401i	−0.914558	−	2.81472i
$69$	41.1584	+	29.9033i	0.596499	+	0.433382i
$70$	19.0233	−	3.61216i	0.271761	−	0.0516023i
$71$	11.1969	−	34.4604i	0.157702	−	0.485358i	−0.840722	−	0.541466i	$-0.817869\pi$
$71$	11.1969	−	34.4604i	0.157702	−	0.485358i	0.998425	+	0.0561087i	$0.0178694\pi$
$72$	33.8209	−	104.090i	0.469735	−	1.44570i
$73$	68.0006	−	49.4053i	0.931515	−	0.676785i	−0.0148485	−	0.999890i	$-0.504727\pi$
$73$	68.0006	−	49.4053i	0.931515	−	0.676785i	0.946363	+	0.323105i	$0.104727\pi$
$74$	136.922	−	188.457i	1.85030	−	2.54672i
$75$	32.1593	+	20.4855i	0.428791	+	0.273141i
$76$			218.319i			2.87262i
$77$	−3.20083	−	11.5578i	−0.0415693	−	0.150102i
$78$		−	4.73519i		−	0.0607076i
$79$	28.8577	−	9.37643i	0.365287	−	0.118689i	−0.120621	−	0.992699i	$-0.538489\pi$
$79$	28.8577	−	9.37643i	0.365287	−	0.118689i	0.485909	+	0.874010i	$0.338489\pi$
$80$	−57.2012	−	104.258i	−0.715015	−	1.30322i
$81$	−19.0958	+	13.8739i	−0.235750	+	0.171283i
$82$	−130.743	−	42.4810i	−1.59443	−	0.518061i
$83$	−42.0601	+	129.448i	−0.506748	+	1.55961i	0.291064	+	0.956704i	$0.405991\pi$
$83$	−42.0601	+	129.448i	−0.506748	+	1.55961i	−0.797812	+	0.602906i	$0.794009\pi$
$84$	−8.42220	−	11.5922i	−0.100264	−	0.138002i
$85$	56.1706	+	102.380i	0.660831	+	1.20447i
$86$	16.5366	+	50.8943i	0.192286	+	0.591794i
$87$	−25.6994			−0.295395
$88$	−150.464	+	99.5127i	−1.70982	+	1.13083i
$89$	−8.46901			−0.0951574			−0.0475787	−	0.998867i	$-0.515150\pi$
$89$	−8.46901			−0.0951574			−0.0475787	+	0.998867i	$0.515150\pi$
$90$	−14.9552	+	117.580i	−0.166169	+	1.30645i
$91$	0.770946	+	0.560125i	0.00847194	+	0.00615522i
$92$	168.946	+	232.534i	1.83637	+	2.52755i
$93$	9.28813	+	3.01790i	0.0998724	+	0.0324505i
$94$	−200.312	−	65.0852i	−2.13098	−	0.692396i
$95$	−23.6320	−	124.457i	−0.248758	−	1.31007i
$96$	−16.9281	+	23.2995i	−0.176335	+	0.242704i
$97$	63.3788	−	20.5930i	0.653390	−	0.212299i	0.0364815	−	0.999334i	$-0.488385\pi$
$97$	63.3788	−	20.5930i	0.653390	−	0.212299i	0.616908	+	0.787035i	$0.288385\pi$
$98$	−169.827			−1.73293
$99$	73.3407	+	3.22831i	0.740815	+	0.0326092i
$100$	137.034	+	166.219i	1.37034	+	1.66219i
$101$	−76.0831	+	24.7209i	−0.753298	+	0.244761i	−0.660400	−	0.750914i	$-0.729613\pi$
$101$	−76.0831	+	24.7209i	−0.753298	+	0.244761i	−0.0928981	+	0.995676i	$0.529613\pi$
$102$	74.3712	−	102.363i	0.729129	−	1.00356i
$103$	−65.5454	−	90.2154i	−0.636363	−	0.875878i	0.362052	−	0.932158i	$-0.382076\pi$
$103$	−65.5454	−	90.2154i	−0.636363	−	0.875878i	−0.998415	+	0.0562796i	$0.982076\pi$
$104$	4.42944	−	13.6324i	0.0425908	−	0.131081i
$105$	6.05601	+	5.69665i	0.0576763	+	0.0542538i
$106$	49.4060	+	68.0015i	0.466094	+	0.641524i
$107$	16.9954	+	12.3479i	0.158836	+	0.115401i	0.664364	−	0.747409i	$-0.268702\pi$
$107$	16.9954	+	12.3479i	0.158836	+	0.115401i	−0.505528	+	0.862810i	$0.668702\pi$
$108$	195.910	−	63.6551i	1.81398	−	0.589399i
$109$			118.493i			1.08710i	0.839378	+	0.543548i	$0.182919\pi$
$109$			118.493i			1.08710i	−0.839378	+	0.543548i	$0.817081\pi$
$110$	139.983	−	136.275i	1.27257	−	1.23886i
$111$	100.023			0.901112
$112$	−8.01296	−	24.6614i	−0.0715443	−	0.220191i
$113$	−62.6514	+	86.2322i	−0.554437	+	0.763117i	−0.990606	−	0.136748i	$-0.956335\pi$
$113$	−62.6514	+	86.2322i	−0.554437	+	0.763117i	0.436169	+	0.899865i	$0.356335\pi$
$114$	−111.045	+	80.6787i	−0.974077	+	0.707708i
$115$	−121.481	−	114.273i	−1.05636	−	0.993675i
$116$	−138.088	−	44.8676i	−1.19042	−	0.386790i
$117$	−4.71918	+	3.42869i	−0.0403349	+	0.0293050i
$118$	−109.301	−	79.4120i	−0.926282	−	0.672983i
$119$	7.86860	+	24.2171i	0.0661227	+	0.203505i
$120$	53.3447	−	113.114i	0.444539	−	0.942617i
$121$	−91.2633	−	79.4482i	−0.754242	−	0.656597i
$122$			121.082i			0.992479i
$123$	−18.2407	−	56.1391i	−0.148298	−	0.456416i
$124$	44.6384	+	32.4317i	0.359987	+	0.261546i
$125$	−96.1111	−	79.9229i	−0.768889	−	0.639383i
$126$	−7.98660	+	24.5802i	−0.0633857	+	0.195081i
$127$	39.6357	−	121.986i	0.312092	−	0.960520i	−0.664843	−	0.746983i	$-0.731502\pi$
$127$	39.6357	−	121.986i	0.312092	−	0.960520i	0.976935	−	0.213537i	$-0.0684983\pi$
$128$	141.749	−	102.987i	1.10741	−	0.804583i
$129$	−13.5061	+	18.5895i	−0.104698	+	0.144105i
$130$	−1.95865	+	15.3992i	−0.0150665	+	0.118455i
$131$		−	15.3029i		−	0.116816i	−0.998293	−	0.0584079i	$-0.981398\pi$
$131$		−	15.3029i		−	0.116816i	0.998293	−	0.0584079i	$-0.0186024\pi$
$132$	−135.394	−	50.6767i	−1.02571	−	0.383914i
$133$		−	27.6229i		−	0.207691i
$134$	−147.638	+	47.9704i	−1.10177	+	0.357988i
$135$	−104.792	+	57.4940i	−0.776234	+	0.425881i
$136$	309.865	−	225.130i	2.27842	−	1.65537i
$137$	−26.1310	−	8.49047i	−0.190737	−	0.0619742i	0.212091	−	0.977250i	$-0.431973\pi$
$137$	−26.1310	−	8.49047i	−0.190737	−	0.0619742i	−0.402828	+	0.915276i	$0.631973\pi$
$138$	−55.8419	+	171.864i	−0.404651	+	1.24539i
$139$	−33.0584	−	45.5009i	−0.237830	−	0.327345i	0.673373	−	0.739303i	$-0.264845\pi$
$139$	−33.0584	−	45.5009i	−0.237830	−	0.327345i	−0.911203	+	0.411958i	$0.864845\pi$
$140$	22.5947	+	41.1824i	0.161391	+	0.294160i
$141$	−27.9466	−	86.0109i	−0.198203	−	0.610007i
$142$	128.704			0.906363
$143$	9.60525	+	0.422803i	0.0671696	+	0.00295667i
$144$	158.728			1.10228
$145$	83.5764	+	10.6302i	0.576389	+	0.0733116i
$146$	241.540	+	175.489i	1.65438	+	1.20198i
$147$	−42.8621	−	58.9946i	−0.291579	−	0.401324i
$148$	537.448	+	174.627i	3.63141	+	1.17992i
$149$	225.598	+	73.3012i	1.51408	+	0.491954i	0.944087	−	0.329695i	$-0.106946\pi$
$149$	225.598	+	73.3012i	1.51408	+	0.491954i	0.569993	+	0.821650i	$0.306946\pi$
$150$	−33.9046	+	131.126i	−0.226031	+	0.874172i
$151$	−27.6455	+	38.0508i	−0.183083	+	0.251992i	−0.890687	−	0.454617i	$-0.849776\pi$
$151$	−27.6455	+	38.0508i	−0.183083	+	0.251992i	0.707604	+	0.706609i	$0.249776\pi$
$152$	−395.163	+	128.396i	−2.59975	+	0.844712i
$153$	−155.868			−1.01875
$154$	35.5311	−	23.4993i	0.230721	−	0.152593i
$155$	−28.9574	−	13.6564i	−0.186822	−	0.0881055i
$156$	10.9250	−	3.54973i	0.0700317	−	0.0227547i
$157$	85.7977	−	118.090i	0.546482	−	0.752168i	−0.443048	−	0.896498i	$-0.646103\pi$
$157$	85.7977	−	118.090i	0.546482	−	0.752168i	0.989530	+	0.144330i	$0.0461027\pi$
$158$	63.3506	+	87.1946i	0.400953	+	0.551865i
$159$	−11.1530	+	34.3253i	−0.0701444	+	0.215882i
$160$	64.6891	−	68.7699i	0.404307	−	0.429812i
$161$	−21.3760	−	29.4215i	−0.132770	−	0.182742i
$162$	−67.8288	−	49.2805i	−0.418696	−	0.304201i
$163$	76.6025	−	24.8897i	0.469954	−	0.152697i	−0.0644598	−	0.997920i	$-0.520532\pi$
$163$	76.6025	−	24.8897i	0.469954	−	0.152697i	0.534414	+	0.845223i	$0.320532\pi$
$164$		−	333.494i		−	2.03350i
$165$	82.6691	+	14.2334i	0.501025	+	0.0862631i
$166$	−483.465			−2.91244
$167$	34.6471	+	106.633i	0.207468	+	0.638521i	0.999603	+	0.0281747i	$0.00896949\pi$
$167$	34.6471	+	106.633i	0.207468	+	0.638521i	−0.792135	+	0.610346i	$0.791031\pi$
$168$	16.0289	−	22.0619i	0.0954100	−	0.131321i
$169$	136.106	−	98.8867i	0.805360	−	0.585128i
$170$	−284.202	+	302.130i	−1.67178	+	1.77724i
$171$	160.812	+	52.2510i	0.940421	+	0.305561i
$172$	−105.026	+	76.3057i	−0.610615	+	0.443638i
$173$	152.953	+	111.127i	0.884120	+	0.642351i	0.934338	−	0.356387i	$-0.115992\pi$
$173$	152.953	+	111.127i	0.884120	+	0.642351i	−0.0502182	+	0.998738i	$0.515992\pi$
$174$	−28.2086	−	86.8171i	−0.162118	−	0.498949i
$175$	−17.3383	−	21.0309i	−0.0990759	−	0.120177i
$176$	−204.689	−	162.936i	−1.16301	−	0.925774i
$177$		−	58.0116i		−	0.327749i
$178$	−9.29591	−	28.6099i	−0.0522242	−	0.160730i
$179$	−185.169	−	134.533i	−1.03446	−	0.751581i	−0.0652651	−	0.997868i	$-0.520789\pi$
$179$	−185.169	−	134.533i	−1.03446	−	0.751581i	−0.969197	+	0.246287i	$0.920789\pi$
$180$	−282.491	+	53.6396i	−1.56939	+	0.297998i
$181$	−3.84557	+	11.8355i	−0.0212463	+	0.0653893i	−0.961118	−	0.276140i	$-0.910945\pi$
$181$	−3.84557	+	11.8355i	−0.0212463	+	0.0653893i	0.939871	+	0.341529i	$0.110945\pi$
$182$	−1.04599	+	3.21921i	−0.00574718	+	0.0176880i
$183$	−42.0616	+	30.5595i	−0.229845	+	0.166992i
$184$	−321.533	+	442.552i	−1.74746	+	2.40518i
$185$	−325.284	−	41.3733i	−1.75829	−	0.223640i
$186$			34.6896i			0.186503i
$187$	201.001	+	160.001i	1.07487	+	0.855619i
$188$		−	510.947i		−	2.71780i
$189$	−24.7876	+	8.05398i	−0.131151	+	0.0426137i
$190$	394.498	−	216.441i	2.07631	−	1.13917i
$191$	0.755326	−	0.548777i	0.00395459	−	0.00287318i	−0.585806	−	0.810451i	$-0.699222\pi$
$191$	0.755326	−	0.548777i	0.00395459	−	0.00287318i	0.589761	+	0.807578i	$0.299222\pi$
$192$	40.7064	+	13.2263i	0.212012	+	0.0688870i
$193$	−12.8593	+	39.5768i	−0.0666284	+	0.205061i	−0.978828	−	0.204685i	$-0.934383\pi$
$193$	−12.8593	+	39.5768i	−0.0666284	+	0.205061i	0.912199	+	0.409747i	$0.134383\pi$
$194$	139.134	+	191.502i	0.717186	+	0.987121i
$195$	−5.84372	+	3.20616i	−0.0299678	+	0.0164418i
$196$	−127.311	−	391.823i	−0.649546	−	1.99910i
$197$	85.8608			0.435842			0.217921	−	0.975966i	$-0.430073\pi$
$197$	85.8608			0.435842			0.217921	+	0.975966i	$0.430073\pi$
$198$	69.5958	+	251.302i	0.351494	+	1.26920i
$199$	78.5577			0.394763			0.197381	−	0.980327i	$-0.436756\pi$
$199$	78.5577			0.394763			0.197381	+	0.980327i	$0.436756\pi$
$200$	−220.269	+	345.790i	−1.10135	+	1.72895i
$201$	−53.9258	−	39.1794i	−0.268287	−	0.194922i
$202$	−167.023	−	229.888i	−0.826848	−	1.13806i
$203$	17.4717	+	5.67689i	0.0860674	+	0.0279650i
$204$	291.923	+	94.8515i	1.43099	+	0.464958i
$205$	36.0990	+	190.114i	0.176093	+	0.927385i
$206$	232.819	−	320.448i	1.13019	−	1.55557i
$207$	211.717	−	68.7911i	1.02279	−	0.332324i
$208$	20.7882			0.0999433
$209$	−153.740	−	232.456i	−0.735600	−	1.11223i
$210$	−12.5970	+	26.7112i	−0.0599858	+	0.127196i
$211$	127.520	−	41.4339i	0.604362	−	0.196369i	0.00917715	−	0.999958i	$-0.497079\pi$
$211$	127.520	−	41.4339i	0.604362	−	0.196369i	0.595185	+	0.803589i	$0.297079\pi$
$212$	−119.855	+	164.966i	−0.565353	+	0.778141i
$213$	32.4830	+	44.7091i	0.152503	+	0.209902i
$214$	−23.0586	+	70.9672i	−0.107751	+	0.331622i
$215$	51.6121	−	54.8679i	0.240056	−	0.255200i
$216$	230.434	+	317.166i	1.06683	+	1.46836i
$217$	−5.64788	−	4.10343i	−0.0260271	−	0.0189098i
$218$	−400.293	+	130.063i	−1.83620	+	0.596619i
$219$			128.197i			0.585376i
$220$	419.350	+	220.808i	1.90614	+	1.00367i
$221$	−20.4137			−0.0923697
$222$	109.790	+	337.897i	0.494547	+	1.52206i
$223$	−117.983	+	162.389i	−0.529071	+	0.728204i	−0.986988	−	0.160791i	$-0.948596\pi$
$223$	−117.983	+	162.389i	−0.529071	+	0.728204i	0.457917	+	0.888995i	$0.348596\pi$
$224$	16.6553	−	12.1008i	0.0743542	−	0.0540215i
$225$	155.232	−	61.1564i	0.689922	−	0.271806i
$226$	−360.077	−	116.996i	−1.59326	−	0.517681i
$227$	−6.02475	+	4.37724i	−0.0265408	+	0.0192830i	−0.600977	−	0.799267i	$-0.705222\pi$
$227$	−6.02475	+	4.37724i	−0.0265408	+	0.0192830i	0.574436	+	0.818550i	$0.305222\pi$
$228$	−269.385	−	195.720i	−1.18151	−	0.858420i
$229$	57.4080	+	176.684i	0.250690	+	0.771544i	0.994648	+	0.103318i	$0.0329460\pi$
$229$	57.4080	+	176.684i	0.250690	+	0.771544i	−0.743959	+	0.668226i	$0.767054\pi$
$230$	252.691	−	535.816i	1.09866	−	2.32964i
$231$	17.1308	+	6.41189i	0.0741591	+	0.0277571i
$232$		−	276.330i		−	1.19108i
$233$	−29.2977	−	90.1691i	−0.125741	−	0.386992i	0.868294	−	0.496050i	$-0.165217\pi$
$233$	−29.2977	−	90.1691i	−0.125741	−	0.386992i	−0.994035	+	0.109058i	$0.965217\pi$
$234$	−16.7627	−	12.1788i	−0.0716354	−	0.0520462i
$235$	55.3075	+	291.274i	0.235351	+	1.23946i
$236$	101.280	−	311.709i	0.429154	−	1.32080i
$237$	−14.3008	+	44.0135i	−0.0603411	+	0.185711i
$238$	−73.1728	+	53.1632i	−0.307449	+	0.223375i
$239$	−232.413	+	319.889i	−0.972439	+	1.33845i	−0.0316341	+	0.999500i	$0.510071\pi$
$239$	−232.413	+	319.889i	−0.972439	+	1.33845i	−0.940805	+	0.338948i	$0.889929\pi$
$240$	179.924	+	22.8848i	0.749685	+	0.0953534i
$241$		−	26.3347i		−	0.109273i	−0.998506	−	0.0546364i	$-0.982600\pi$
$241$		−	26.3347i		−	0.109273i	0.998506	−	0.0546364i	$-0.0174000\pi$
$242$	168.217	−	395.509i	0.695110	−	1.63434i
$243$		−	251.150i		−	1.03354i
$244$	−279.359	+	90.7693i	−1.14491	+	0.372005i
$245$	114.989	+	209.585i	0.469342	+	0.855447i
$246$	169.627	−	123.241i	0.689539	−	0.500979i
$247$	21.0612	+	6.84319i	0.0852679	+	0.0277052i
$248$	−32.4497	+	99.8699i	−0.130846	+	0.402701i
$249$	−122.020	−	167.946i	−0.490040	−	0.674482i
$250$	164.499	−	412.407i	0.657995	−	1.64963i
$251$	115.751	+	356.246i	0.461160	+	1.41931i	0.863748	+	0.503924i	$0.168111\pi$
$251$	115.751	+	356.246i	0.461160	+	1.41931i	−0.402588	+	0.915381i	$0.631889\pi$
$252$	−62.6983			−0.248803
$253$	−343.637	−	128.620i	−1.35825	−	0.508379i
$254$	455.597			1.79369
$255$	−176.683	−	22.4725i	−0.692874	−	0.0881276i
$256$	412.683	+	299.832i	1.61204	+	1.17122i
$257$	−150.186	−	206.714i	−0.584382	−	0.804333i	0.409785	−	0.912182i	$-0.365604\pi$
$257$	−150.186	−	206.714i	−0.584382	−	0.804333i	−0.994167	+	0.107849i	$0.965604\pi$
$258$	−77.6235	−	25.2214i	−0.300866	−	0.0977574i
$259$	−68.0008	−	22.0948i	−0.262551	−	0.0853081i
$260$	−36.9971	+	7.02505i	−0.142297	+	0.0270194i
$261$	−66.0982	+	90.9764i	−0.253250	+	0.348569i
$262$	51.6959	−	16.7970i	0.197312	−	0.0641107i
$263$	288.916			1.09854			0.549270	−	0.835645i	$-0.314906\pi$
$263$	288.916			1.09854			0.549270	+	0.835645i	$0.314906\pi$
$264$	12.0992	−	274.870i	0.0458303	−	1.04117i
$265$	50.4685	−	107.015i	0.190447	−	0.403831i
$266$	93.3153	−	30.3200i	0.350809	−	0.113985i
$267$	7.59233	−	10.4500i	0.0284357	−	0.0391384i
$268$	−221.353	−	304.667i	−0.825945	−	1.13682i
$269$	66.9375	−	206.012i	0.248838	−	0.765846i	−0.746143	−	0.665786i	$-0.768097\pi$
$269$	66.9375	−	206.012i	0.248838	−	0.765846i	0.994981	−	0.100060i	$-0.0319035\pi$
$270$	−309.249	−	290.898i	−1.14536	−	1.07740i
$271$	30.9844	+	42.6464i	0.114334	+	0.157367i	0.862348	−	0.506315i	$-0.168993\pi$
$271$	30.9844	+	42.6464i	0.114334	+	0.157367i	−0.748015	+	0.663682i	$0.768993\pi$
$272$	449.390	+	326.501i	1.65217	+	1.20037i
$273$	−1.38228	+	0.449131i	−0.00506331	+	0.00164517i
$274$		−	97.5947i		−	0.356185i
$275$	−262.959	−	80.4831i	−0.956215	−	0.292666i
$276$	−438.383			−1.58834
$277$	50.6866	+	155.997i	0.182984	+	0.563167i	0.999908	−	0.0135787i	$-0.00432236\pi$
$277$	50.6866	+	155.997i	0.182984	+	0.563167i	−0.816924	+	0.576746i	$0.804322\pi$
$278$	117.424	−	161.621i	0.422390	−	0.581370i
$279$	34.5723	−	25.1183i	0.123915	−	0.0900296i
$280$	−61.2528	+	65.1168i	−0.218760	+	0.232560i
$281$	−486.240	−	157.989i	−1.73039	−	0.562239i	−0.736887	−	0.676016i	$-0.763705\pi$
$281$	−486.240	−	157.989i	−1.73039	−	0.562239i	−0.993506	+	0.113778i	$0.963705\pi$
$282$	259.885	−	188.818i	0.921579	−	0.669567i
$283$	−144.379	−	104.898i	−0.510175	−	0.370664i	0.302715	−	0.953081i	$-0.402107\pi$
$283$	−144.379	−	104.898i	−0.510175	−	0.370664i	−0.812890	+	0.582418i	$0.802107\pi$
$284$	96.4826	+	296.943i	0.339727	+	1.04557i
$285$	174.753	+	82.4138i	0.613170	+	0.289171i
$286$	9.11479	+	32.9124i	0.0318699	+	0.115078i
$287$			42.1954i			0.147022i
$288$	38.9422	+	119.852i	0.135216	+	0.416152i
$289$	−207.488	−	150.749i	−0.717951	−	0.521622i
$290$	55.8259	+	294.004i	0.192503	+	1.01381i
$291$	−31.4083	+	96.6647i	−0.107932	+	0.332181i
$292$	−223.815	+	688.833i	−0.766491	+	2.35902i
$293$	46.0759	−	33.4761i	0.157256	−	0.114253i	−0.506375	−	0.862313i	$-0.669015\pi$
$293$	46.0759	−	33.4761i	0.157256	−	0.114253i	0.663630	+	0.748061i	$0.269015\pi$
$294$	152.248	−	209.551i	0.517849	−	0.712758i
$295$	−23.9957	+	188.658i	−0.0813413	+	0.639519i
$296$			1075.49i			3.63342i
$297$	−163.770	+	205.737i	−0.551415	+	0.692717i
$298$			842.569i			2.82741i
$299$	27.7281	−	9.00940i	0.0927360	−	0.0301318i
$300$	−327.948	+	20.0742i	−1.09316	+	0.0669139i
$301$	13.2884	−	9.65461i	0.0441476	−	0.0320751i
$302$	−158.887	−	51.6256i	−0.526117	−	0.170946i
$303$	37.7041	−	116.041i	0.124436	−	0.382974i
$304$	−354.192	−	487.504i	−1.16511	−	1.60363i
$305$	149.428	−	81.9838i	0.489929	−	0.268800i
$306$	−171.087	−	526.552i	−0.559108	−	1.72076i
$307$	−427.615			−1.39288			−0.696442	−	0.717613i	$-0.745234\pi$
$307$	−427.615			−1.39288			−0.696442	+	0.717613i	$0.745234\pi$
$308$	80.8531	+	64.3605i	0.262510	+	0.208963i
$309$	170.078			0.550413
$310$	14.3489	−	112.813i	0.0462867	−	0.363914i
$311$	80.6811	+	58.6183i	0.259425	+	0.188483i	0.709893	−	0.704309i	$-0.248743\pi$
$311$	80.6811	+	58.6183i	0.259425	+	0.188483i	−0.450469	+	0.892792i	$0.648743\pi$
$312$	12.8502	+	17.6868i	0.0411865	+	0.0566884i
$313$	−50.1472	−	16.2938i	−0.160215	−	0.0520569i	0.227812	−	0.973705i	$-0.426843\pi$
$313$	−50.1472	−	16.2938i	−0.160215	−	0.0520569i	−0.388026	+	0.921648i	$0.626843\pi$
$314$	493.106	+	160.220i	1.57040	+	0.510254i
$315$	35.7422	−	6.78677i	0.113467	−	0.0215453i
$316$	−153.683	+	211.527i	−0.486339	+	0.669389i
$317$	309.132	−	100.443i	0.975180	−	0.316855i	0.222275	−	0.974984i	$-0.428652\pi$
$317$	309.132	−	100.443i	0.975180	−	0.316855i	0.752905	+	0.658129i	$0.228652\pi$
$318$	−128.199			−0.403142
$319$	178.626	−	49.4688i	0.559956	−	0.155075i
$320$	−126.909	−	59.8506i	−0.396592	−	0.187033i
$321$	−30.4723	+	9.90104i	−0.0949292	+	0.0308444i
$322$	75.9281	−	104.506i	0.235802	−	0.324553i
$323$	347.811	+	478.721i	1.07681	+	1.48211i
$324$	62.8513	−	193.437i	0.193986	−	0.597026i
$325$	20.3304	−	8.00950i	0.0625551	−	0.0246446i
$326$	168.164	+	231.457i	0.515839	+	0.709992i
$327$	−146.210	−	106.228i	−0.447124	−	0.324855i
$328$	603.631	−	196.132i	1.84034	−	0.597962i
$329$			64.6477i			0.196498i
$330$	42.6577	+	294.895i	0.129266	+	0.893620i
$331$	343.048			1.03640			0.518199	−	0.855260i	$-0.326603\pi$
$331$	343.048			1.03640			0.518199	+	0.855260i	$0.326603\pi$
$332$	−362.429	−	1115.44i	−1.09165	−	3.35976i
$333$	257.258	−	354.085i	0.772547	−	1.06332i
$334$	−322.196	+	234.089i	−0.964657	+	0.700865i
$335$	159.165	+	149.720i	0.475119	+	0.446925i
$336$	37.6133	+	12.2213i	0.111944	+	0.0363729i
$337$	−506.148	+	367.738i	−1.50192	+	1.09121i	−0.532313	+	0.846547i	$0.678677\pi$
$337$	−506.148	+	367.738i	−1.50192	+	1.09121i	−0.969608	+	0.244663i	$0.921323\pi$
$338$	483.452	+	351.249i	1.43033	+	1.03920i
$339$	−50.2364	−	154.612i	−0.148190	−	0.456082i
$340$	−910.122	−	429.214i	−2.67683	−	1.26240i
$341$	−70.3672	−	3.09742i	−0.206356	−	0.00908334i
$342$			600.605i			1.75616i
$343$	32.6166	+	100.384i	0.0950921	+	0.292663i
$344$	−199.882	−	145.223i	−0.581052	−	0.422159i
$345$	249.908	−	47.4528i	0.724370	−	0.137544i
$346$	−207.519	+	638.679i	−0.599767	+	1.84589i
$347$	147.429	−	453.741i	0.424868	−	1.30761i	−0.478252	−	0.878223i	$-0.658729\pi$
$347$	147.429	−	453.741i	0.424868	−	1.30761i	0.903120	−	0.429388i	$-0.141271\pi$
$348$	179.156	−	130.165i	0.514818	−	0.374037i
$349$	−108.085	+	148.766i	−0.309699	+	0.426264i	−0.935287	−	0.353890i	$-0.884859\pi$
$349$	−108.085	+	148.766i	−0.309699	+	0.426264i	0.625589	+	0.780153i	$0.284859\pi$
$350$	52.0152	−	81.6563i	0.148615	−	0.233304i
$351$		−	20.8946i		−	0.0595289i
$352$	72.8111	−	194.531i	0.206850	−	0.552644i
$353$			289.312i			0.819580i	0.912180	+	0.409790i	$0.134398\pi$
$353$			289.312i			0.819580i	−0.912180	+	0.409790i	$0.865602\pi$
$354$	195.974	−	63.6757i	0.553598	−	0.179875i
$355$	−87.1441	−	158.834i	−0.245476	−	0.447419i
$356$	59.0395	−	42.8947i	0.165841	−	0.120491i
$357$	−36.9356	−	12.0011i	−0.103461	−	0.0336166i
$358$	251.229	−	773.202i	0.701756	−	2.15978i
$359$	−197.102	−	271.288i	−0.549032	−	0.755677i	0.440849	−	0.897581i	$-0.354678\pi$
$359$	−197.102	−	271.288i	−0.549032	−	0.755677i	−0.989880	+	0.141904i	$0.954678\pi$
$360$	−263.225	−	479.768i	−0.731181	−	1.33269i
$361$	−86.8081	−	267.168i	−0.240466	−	0.740078i
$362$	−44.2034			−0.122109
$363$	179.848	−	41.3861i	0.495448	−	0.114011i
$364$	−8.21144			−0.0225589
$365$	53.0271	−	416.908i	0.145280	−	1.14221i
$366$	−149.404	−	108.548i	−0.408208	−	0.296581i
$367$	139.799	+	192.417i	0.380924	+	0.524296i	0.955829	−	0.293924i	$-0.0949611\pi$
$367$	139.799	+	192.417i	0.380924	+	0.524296i	−0.574905	+	0.818220i	$0.694961\pi$
$368$	−754.508	−	245.155i	−2.05029	−	0.666181i
$369$	−245.649	−	79.8161i	−0.665714	−	0.216304i
$370$	−217.278	−	1144.28i	−0.587237	−	3.09265i
$371$	15.1647	−	20.8724i	0.0408751	−	0.0562598i
$372$	−80.0352	+	26.0050i	−0.215148	+	0.0699060i
$373$	240.258			0.644124			0.322062	−	0.946719i	$-0.395624\pi$
$373$	240.258			0.644124			0.322062	+	0.946719i	$0.395624\pi$
$374$	−319.885	+	854.642i	−0.855307	+	2.28514i
$375$	184.779	−	46.9423i	0.492745	−	0.125180i
$376$	924.826	−	300.494i	2.45964	−	0.799186i
$377$	−8.65672	+	11.9150i	−0.0229621	+	0.0316047i
$378$	−54.4157	−	74.8967i	−0.143957	−	0.198139i
$379$	−81.0415	+	249.420i	−0.213830	+	0.658101i	0.785405	+	0.618983i	$0.212455\pi$
$379$	−81.0415	+	249.420i	−0.213830	+	0.658101i	−0.999235	+	0.0391181i	$0.987545\pi$
$380$	795.105	+	747.924i	2.09238	+	1.96822i
$381$	114.986	+	158.265i	0.301802	+	0.415394i
$382$	2.68294	+	1.94927i	0.00702341	+	0.00510281i
$383$	−325.896	+	105.890i	−0.850904	+	0.276475i	−0.701825	−	0.712350i	$-0.747631\pi$
$383$	−325.896	+	105.890i	−0.850904	+	0.276475i	−0.149079	+	0.988825i	$0.547631\pi$
$384$			267.231i			0.695913i
$385$	−53.0584	−	27.9379i	−0.137814	−	0.0725659i
$386$	−147.813			−0.382934
$387$	31.0700	+	95.6236i	0.0802842	+	0.247089i
$388$	−337.527	+	464.567i	−0.869916	+	1.19734i
$389$	511.645	−	371.732i	1.31528	−	0.955608i	0.315304	−	0.948991i	$-0.397893\pi$
$389$	511.645	−	371.732i	1.31528	−	0.955608i	0.999978	−	0.00661783i	$-0.00210654\pi$
$390$	−17.2453	−	16.2219i	−0.0442186	−	0.0415947i
$391$	740.915	+	240.738i	1.89492	+	0.615698i
$392$	634.335	−	460.871i	1.61820	−	1.17569i
$393$	18.8823	+	13.7188i	0.0480465	+	0.0349078i
$394$	94.2441	+	290.053i	0.239198	+	0.736176i
$395$	64.7131	−	137.220i	0.163831	−	0.347392i
$396$	−527.627	+	348.958i	−1.33239	+	0.881208i
$397$			335.656i			0.845482i	0.906251	+	0.422741i	$0.138932\pi$
$397$			335.656i			0.845482i	−0.906251	+	0.422741i	$0.861068\pi$
$398$	86.2280	+	265.382i	0.216653	+	0.666790i
$399$	34.0841	+	24.7635i	0.0854237	+	0.0620639i
$400$	−575.662	−	148.846i	−1.43916	−	0.372116i
$401$	216.430	−	666.103i	0.539725	−	1.66110i	−0.193486	−	0.981103i	$-0.561979\pi$
$401$	216.430	−	666.103i	0.539725	−	1.66110i	0.733211	−	0.680001i	$-0.238021\pi$
$402$	73.1641	−	225.176i	0.182000	−	0.560139i
$403$	4.52785	−	3.28968i	0.0112354	−	0.00816297i
$404$	405.185	−	557.689i	1.00293	−	1.38042i
$405$	−14.8909	+	117.075i	−0.0367678	+	0.289075i
$406$			65.2537i			0.160723i
$407$	−695.222	+	192.535i	−1.70816	+	0.473060i
$408$			584.170i			1.43179i
$409$	−17.4090	+	5.65652i	−0.0425648	+	0.0138301i	−0.330222	−	0.943903i	$-0.607124\pi$
$409$	−17.4090	+	5.65652i	−0.0425648	+	0.0138301i	0.287657	+	0.957733i	$0.407124\pi$
$410$	−602.616	+	330.625i	−1.46979	+	0.806403i
$411$	33.9024	−	24.6316i	0.0824877	−	0.0599308i
$412$	913.865	+	296.933i	2.21812	+	0.720711i
$413$	−12.8145	+	39.4391i	−0.0310279	+	0.0954942i
$414$	464.778	+	639.712i	1.12265	+	1.54520i
$415$	327.350	+	596.645i	0.788795	+	1.43770i
$416$	5.10017	+	15.6967i	0.0122600	+	0.0377325i
$417$	85.7801			0.205708
$418$	616.528	−	774.516i	1.47495	−	1.85291i
$419$	−420.944			−1.00464			−0.502320	−	0.864682i	$-0.667520\pi$
$419$	−420.944			−1.00464			−0.502320	+	0.864682i	$0.667520\pi$
$420$	−71.0709	−	9.03960i	−0.169216	−	0.0215229i
$421$	−377.591	−	274.336i	−0.896891	−	0.651629i	0.0407749	−	0.999168i	$-0.487017\pi$
$421$	−377.591	−	274.336i	−0.896891	−	0.651629i	−0.937665	+	0.347539i	$0.887017\pi$
$422$	279.943	+	385.308i	0.663371	+	0.913052i
$423$	−376.359	−	122.286i	−0.889738	−	0.289093i
$424$	−369.080	−	119.921i	−0.870472	−	0.282833i
$425$	565.291	+	146.165i	1.33010	+	0.343917i
$426$	−115.381	+	158.808i	−0.270847	+	0.372789i
$427$	35.3460	−	11.4846i	0.0827776	−	0.0268961i
$428$	−181.020			−0.422944
$429$	−9.13266	+	11.4729i	−0.0212883	+	0.0267434i
$430$	242.005	+	114.130i	0.562803	+	0.265418i
$431$	−227.136	+	73.8008i	−0.526997	+	0.171232i	−0.560418	−	0.828210i	$-0.689360\pi$
$431$	−227.136	+	73.8008i	−0.526997	+	0.171232i	0.0334216	+	0.999441i	$0.489360\pi$
$432$	−334.193	+	459.977i	−0.773595	+	1.06476i
$433$	56.3808	+	77.6015i	0.130210	+	0.179218i	0.869144	−	0.494559i	$-0.164671\pi$
$433$	56.3808	+	77.6015i	0.130210	+	0.179218i	−0.738934	+	0.673778i	$0.764671\pi$
$434$	7.66280	−	23.5837i	0.0176562	−	0.0543402i
$435$	−88.0415	+	93.5955i	−0.202394	+	0.215162i
$436$	−600.158	−	826.047i	−1.37651	−	1.89460i
$437$	−683.713	−	496.747i	−1.56456	−	1.13672i
$438$	−433.074	+	140.714i	−0.988754	+	0.321266i
$439$		−	749.426i		−	1.70712i	−0.520994	−	0.853560i	$-0.674439\pi$
$439$		−	749.426i		−	1.70712i	0.520994	−	0.853560i	$-0.325561\pi$
$440$	−153.044	+	888.893i	−0.347826	+	2.02021i
$441$	−319.083			−0.723544
$442$	−22.4069	−	68.9612i	−0.0506942	−	0.156021i
$443$	27.2384	−	37.4905i	0.0614863	−	0.0846286i	−0.777166	−	0.629295i	$-0.783344\pi$
$443$	27.2384	−	37.4905i	0.0614863	−	0.0846286i	0.838653	+	0.544666i	$0.183344\pi$
$444$	−697.288	+	506.609i	−1.57047	+	1.14101i
$445$	−29.0134	+	30.8436i	−0.0651985	+	0.0693115i
$446$	−678.084	−	220.323i	−1.52037	−	0.493997i
$447$	−292.692	+	212.653i	−0.654791	+	0.475734i
$448$	−24.7525	−	17.9838i	−0.0552512	−	0.0401424i
$449$	15.0043	+	46.1784i	0.0334171	+	0.102847i	0.966374	−	0.257141i	$-0.0827806\pi$
$449$	15.0043	+	46.1784i	0.0334171	+	0.102847i	−0.932957	+	0.359989i	$0.882781\pi$
$450$	376.987	+	457.276i	0.837748	+	1.01617i
$451$	234.846	+	355.089i	0.520723	+	0.787336i
$452$		−	918.469i		−	2.03201i
$453$	−22.1673	−	68.2239i	−0.0489344	−	0.150605i
$454$	−21.4001	−	15.5481i	−0.0471368	−	0.0342469i
$455$	4.68107	−	0.888847i	0.0102881	−	0.00195351i
$456$	195.829	−	602.698i	0.429449	−	1.32171i
$457$	128.400	−	395.176i	0.280964	−	0.864718i	−0.706616	−	0.707598i	$-0.749779\pi$
$457$	128.400	−	395.176i	0.280964	−	0.864718i	0.987579	−	0.157120i	$-0.0502210\pi$
$458$	−533.856	+	387.869i	−1.16562	+	0.846876i
$459$	328.172	−	451.691i	0.714972	−	0.984075i
$460$	1425.66	+	181.331i	3.09925	+	0.394198i
$461$			704.025i			1.52717i	0.645707	+	0.763585i	$0.276563\pi$
$461$			704.025i			1.52717i	−0.645707	+	0.763585i	$0.723437\pi$
$462$	−2.85715	+	64.9088i	−0.00618431	+	0.140495i
$463$		−	506.506i		−	1.09397i	−0.837144	−	0.546983i	$-0.815776\pi$
$463$		−	506.506i		−	1.09397i	0.837144	−	0.546983i	$-0.184224\pi$
$464$	381.141	−	123.840i	0.821424	−	0.266897i
$465$	42.8105	−	23.4880i	0.0920657	−	0.0505119i
$466$	272.449	−	197.946i	0.584655	−	0.424777i
$467$	341.762	+	111.045i	0.731825	+	0.237785i	0.651143	−	0.758955i	$-0.274290\pi$
$467$	341.762	+	111.045i	0.731825	+	0.237785i	0.0806828	+	0.996740i	$0.474290\pi$
$468$	15.5326	−	47.8044i	0.0331893	−	0.102146i
$469$	28.0068	+	38.5480i	0.0597160	+	0.0821920i
$470$	−923.270	+	506.552i	−1.96440	+	1.07777i
$471$	68.7960	+	211.732i	0.146064	+	0.449538i
$472$	623.765			1.32154
$473$	58.0922	−	155.206i	0.122816	−	0.328131i
$474$	−164.383			−0.346799
$475$	−534.222	−	340.301i	−1.12468	−	0.716422i
$476$	−177.511	−	128.969i	−0.372922	−	0.270944i
$477$	92.8272	+	127.766i	0.194606	+	0.267853i
$478$	−1335.75	−	434.011i	−2.79445	−	0.907973i
$479$	−512.144	−	166.406i	−1.06919	−	0.347402i	−0.279020	−	0.960285i	$-0.590010\pi$
$479$	−512.144	−	166.406i	−1.06919	−	0.347402i	−0.790173	+	0.612883i	$0.790010\pi$
$480$	26.8627	+	141.471i	0.0559640	+	0.294732i
$481$	33.6925	−	46.3737i	0.0700467	−	0.0964110i
$482$	88.9635	−	28.9060i	0.184572	−	0.0599710i
$483$	55.4665			0.114838
$484$	1038.62	+	91.6129i	2.14590	+	0.189283i
$485$	142.126	−	301.370i	0.293044	−	0.621381i
$486$	848.430	−	275.672i	1.74574	−	0.567226i
$487$	388.640	−	534.918i	0.798029	−	1.09839i	−0.195032	−	0.980797i	$-0.562481\pi$
$487$	388.640	−	534.918i	0.798029	−	1.09839i	0.993061	−	0.117596i	$-0.0375189\pi$
$488$	−328.589	−	452.264i	−0.673338	−	0.926770i
$489$	−37.9615	+	116.833i	−0.0776308	+	0.238923i
$490$	−581.799	+	618.501i	−1.18735	+	1.26225i
$491$	39.8508	+	54.8499i	0.0811625	+	0.111711i	0.847668	−	0.530527i	$-0.178006\pi$
$491$	39.8508	+	54.8499i	0.0811625	+	0.111711i	−0.766505	+	0.642238i	$0.778006\pi$
$492$	411.500	+	298.972i	0.836381	+	0.607667i
$493$	−374.274	+	121.609i	−0.759177	+	0.246671i
$494$			78.6598i			0.159230i
$495$	263.010	−	256.043i	0.531333	−	0.517258i
$496$	−152.293			−0.307042
$497$	−12.2075	−	37.5708i	−0.0245624	−	0.0755951i
$498$	433.418	−	596.549i	0.870318	−	1.19789i
$499$	−312.340	+	226.929i	−0.625933	+	0.454767i	−0.854989	−	0.518646i	$-0.826436\pi$
$499$	−312.340	+	226.929i	−0.625933	+	0.454767i	0.229056	+	0.973413i	$0.426436\pi$
$500$	1074.82	+	70.3683i	2.14963	+	0.140737i
$501$	−162.636	−	52.8435i	−0.324622	−	0.105476i
$502$	−1076.41	+	782.058i	−2.14424	+	1.55788i
$503$	209.753	+	152.395i	0.417004	+	0.302971i	0.776431	−	0.630202i	$-0.217028\pi$
$503$	209.753	+	152.395i	0.417004	+	0.302971i	−0.359427	+	0.933173i	$0.617028\pi$
$504$	−36.8736	−	113.485i	−0.0731619	−	0.225169i
$505$	−170.615	+	361.779i	−0.337852	+	0.716395i
$506$	57.3133	−	1302.05i	0.113267	−	2.57321i
$507$			256.592i			0.506099i
$508$	341.538	+	1051.14i	0.672318	+	2.06918i
$509$	653.416	+	474.735i	1.28373	+	0.932681i	0.999659	−	0.0261234i	$-0.00831627\pi$
$509$	653.416	+	474.735i	1.28373	+	0.932681i	0.284067	+	0.958805i	$0.408316\pi$
$510$	−118.018	−	621.534i	−0.231407	−	1.21869i
$511$	28.3183	−	87.1548i	0.0554174	−	0.170557i
$512$	−343.337	+	1056.68i	−0.670581	+	2.06383i
$513$	−489.999	+	356.005i	−0.955164	+	0.693967i
$514$	533.466	−	734.253i	1.03787	−	1.42851i
$515$	−553.106	−	70.3503i	−1.07399	−	0.136603i
$516$		−	197.999i		−	0.383719i
$517$	359.809	+	544.033i	0.695955	+	1.05229i
$518$		−	253.971i		−	0.490292i
$519$	−274.240	+	89.1058i	−0.528400	+	0.171688i
$520$	−34.4739	−	62.8341i	−0.0662960	−	0.120835i
$521$	−252.452	+	183.417i	−0.484553	+	0.352048i	−0.803086	−	0.595864i	$-0.796810\pi$
$521$	−252.452	+	183.417i	−0.484553	+	0.352048i	0.318533	+	0.947912i	$0.396810\pi$
$522$	−379.887	−	123.433i	−0.727753	−	0.236461i
$523$	22.7612	−	70.0519i	0.0435205	−	0.133942i	−0.926935	−	0.375221i	$-0.877567\pi$
$523$	22.7612	−	70.0519i	0.0435205	−	0.133942i	0.970456	+	0.241279i	$0.0775668\pi$
$524$	77.5075	+	106.680i	0.147915	+	0.203588i
$525$	41.4937	−	2.53989i	0.0790356	−	0.00483789i
$526$	317.125	+	976.012i	0.602900	+	1.85554i
$527$	149.549			0.283774
$528$	384.548	−	106.497i	0.728311	−	0.201699i
$529$	−583.638			−1.10328
$530$	416.914	+	53.0278i	0.786629	+	0.100052i
$531$	−205.362	−	149.205i	−0.386747	−	0.280988i
$532$	139.907	+	192.566i	0.262984	+	0.361966i
$533$	−32.1720	−	10.4533i	−0.0603602	−	0.0196122i
$534$	43.6355	+	14.1780i	0.0817144	+	0.0265506i
$535$	103.194	−	19.5945i	0.192885	−	0.0366253i
$536$	421.273	−	579.832i	0.785957	−	1.08178i
$537$	332.002	−	107.874i	0.618253	−	0.200882i
$538$	769.421			1.43015
$539$	411.476	+	327.542i	0.763407	+	0.607685i
$540$	439.327	−	931.564i	0.813568	−	1.72512i
$541$	39.3919	−	12.7992i	0.0728132	−	0.0236584i	−0.272384	−	0.962189i	$-0.587812\pi$
$541$	39.3919	−	12.7992i	0.0728132	−	0.0236584i	0.345197	+	0.938530i	$0.387812\pi$
$542$	−110.058	+	151.481i	−0.203059	+	0.279486i
$543$	−11.1563	−	15.3554i	−0.0205457	−	0.0282788i
$544$	−136.280	+	419.428i	−0.250515	+	0.771007i
$545$	431.546	+	405.938i	0.791827	+	0.744840i
$546$	−3.03449	−	4.17662i	−0.00555768	−	0.00764949i
$547$	−521.562	−	378.937i	−0.953495	−	0.692755i	−0.00186448	−	0.999998i	$-0.500593\pi$
$547$	−521.562	−	378.937i	−0.953495	−	0.692755i	−0.951631	+	0.307243i	$0.900593\pi$
$548$	225.169	−	73.1618i	0.410892	−	0.133507i
$549$			227.498i			0.414386i
$550$	−16.7472	−	976.665i	−0.0304495	−	1.77575i
$551$	426.911			0.774794
$552$	−257.818	−	793.483i	−0.467062	−	1.43747i
$553$	19.4448	−	26.7635i	0.0351624	−	0.0483969i
$554$	−471.352	+	342.457i	−0.850815	+	0.618154i
$555$	342.663	−	364.279i	0.617411	−	0.656359i
$556$	460.916	+	149.761i	0.828985	+	0.269354i
$557$	362.970	−	263.713i	0.651652	−	0.473453i	−0.212181	−	0.977230i	$-0.568057\pi$
$557$	362.970	−	263.713i	0.651652	−	0.473453i	0.863834	+	0.503777i	$0.168057\pi$
$558$	122.802	+	89.2209i	0.220075	+	0.159894i
$559$	4.06916	+	12.5236i	0.00727936	+	0.0224036i
$560$	−117.266	−	55.3028i	−0.209404	−	0.0987551i
$561$	−377.620	+	104.578i	−0.673120	+	0.186414i
$562$		−	1816.02i		−	3.23136i
$563$	165.189	+	508.399i	0.293408	+	0.903018i	0.983751	+	0.179536i	$0.0574595\pi$
$563$	165.189	+	508.399i	0.293408	+	0.903018i	−0.690343	+	0.723482i	$0.742540\pi$
$564$	630.460	+	458.056i	1.11784	+	0.812156i
$565$	99.4197	+	523.589i	0.175964	+	0.926706i
$566$	195.888	−	602.880i	0.346091	−	1.06516i
$567$	−7.95229	+	24.4746i	−0.0140252	+	0.0431651i
$568$	−480.731	+	349.271i	−0.846357	+	0.614914i
$569$	−259.513	+	357.190i	−0.456087	+	0.627750i	−0.973692	−	0.227870i	$-0.926824\pi$
$569$	−259.513	+	357.190i	−0.456087	+	0.627750i	0.517605	+	0.855620i	$0.326824\pi$
$570$	−86.5931	+	680.809i	−0.151918	+	1.19440i
$571$		−	935.409i		−	1.63819i	−0.573655	−	0.819097i	$-0.694475\pi$
$571$		−	935.409i		−	1.63819i	0.573655	−	0.819097i	$-0.305525\pi$
$572$	−69.1020	+	45.7022i	−0.120808	+	0.0798990i
$573$			1.42397i			0.00248511i
$574$	−142.544	+	46.3153i	−0.248334	+	0.0806887i
$575$	−832.348	+	50.9492i	−1.44756	+	0.0886074i
$576$	151.517	−	110.084i	0.263051	−	0.191118i
$577$	538.104	+	174.841i	0.932590	+	0.303017i	0.735621	−	0.677393i	$-0.236890\pi$
$577$	538.104	+	174.841i	0.932590	+	0.303017i	0.196968	+	0.980410i	$0.436890\pi$
$578$	281.510	−	866.400i	0.487042	−	1.49896i
$579$	−37.3059	−	51.3471i	−0.0644316	−	0.0886825i
$580$	−636.472	+	349.201i	−1.09737	+	0.602070i
$581$	45.8564	+	141.132i	0.0789267	+	0.242911i
$582$	−361.026			−0.620320
$583$	11.4468	−	260.050i	0.0196344	−	0.446054i
$584$	−1378.43			−2.36033
$585$	−3.68004	+	28.9331i	−0.00629066	+	0.0494582i
$586$	163.663	+	118.908i	0.279289	+	0.202915i
$587$	−575.718	−	792.407i	−0.980780	−	1.34993i	−0.936408	−	0.350912i	$-0.885872\pi$
$587$	−575.718	−	792.407i	−0.980780	−	1.34993i	−0.0443714	−	0.999015i	$-0.514128\pi$
$588$	597.604	+	194.173i	1.01633	+	0.330227i
$589$	−154.292	−	50.1326i	−0.261956	−	0.0851147i
$590$	−663.661	+	126.017i	−1.12485	+	0.213588i
$591$	−76.9729	+	105.944i	−0.130242	+	0.179262i
$592$	−1483.42	+	481.993i	−2.50578	+	0.814177i
$593$	1106.21			1.86544			0.932720	−	0.360600i	$-0.117428\pi$
$593$	1106.21			1.86544			0.932720	+	0.360600i	$0.117428\pi$
$594$	−874.777	−	327.421i	−1.47269	−	0.551214i
$595$	115.154	+	54.3065i	0.193535	+	0.0912714i
$596$	−1943.96	+	631.632i	−3.26168	+	1.05978i
$597$	−70.4258	+	96.9328i	−0.117966	+	0.162366i
$598$	60.8708	+	83.7815i	0.101791	+	0.140103i
$599$	−176.386	+	542.860i	−0.294467	+	0.906276i	0.688933	+	0.724825i	$0.258079\pi$
$599$	−176.386	+	542.860i	−0.294467	+	0.906276i	−0.983400	+	0.181451i	$0.941921\pi$
$600$	−229.205	−	581.787i	−0.382008	−	0.969645i
$601$	−98.4935	−	135.565i	−0.163883	−	0.225565i	0.719176	−	0.694828i	$-0.244520\pi$
$601$	−98.4935	−	135.565i	−0.163883	−	0.225565i	−0.883058	+	0.469263i	$0.844520\pi$
$602$	47.2009	+	34.2935i	0.0784068	+	0.0569659i
$603$	−277.392	+	90.1301i	−0.460020	+	0.149469i
$604$		−	405.283i		−	0.670999i
$605$	−601.998	+	60.1995i	−0.995037	+	0.0995033i
$606$	433.394			0.715171
$607$	260.558	+	801.915i	0.429255	+	1.32111i	0.898860	+	0.438235i	$0.144396\pi$
$607$	260.558	+	801.915i	0.429255	+	1.32111i	−0.469605	+	0.882877i	$0.655604\pi$
$608$	281.206	−	387.046i	0.462509	−	0.636589i
$609$	−22.6678	+	16.4691i	−0.0372214	+	0.0270429i
$610$	440.975	+	414.807i	0.722909	+	0.680012i
$611$	−49.2908	−	16.0156i	−0.0806724	−	0.0262120i
$612$	1086.60	−	789.458i	1.77548	−	1.28996i
$613$	270.652	+	196.640i	0.441520	+	0.320783i	0.786239	−	0.617923i	$-0.212026\pi$
$613$	270.652	+	196.640i	0.441520	+	0.320783i	−0.344718	+	0.938706i	$0.612026\pi$
$614$	−469.367	−	1444.56i	−0.764441	−	2.35271i
$615$	−266.945	−	125.891i	−0.434056	−	0.204701i
$616$	−68.9433	+	184.197i	−0.111921	+	0.299021i
$617$			916.072i			1.48472i	0.670001	+	0.742360i	$0.266294\pi$
$617$			916.072i			1.48472i	−0.670001	+	0.742360i	$0.733706\pi$
$618$	186.684	+	574.554i	0.302077	+	0.929698i
$619$	563.143	+	409.147i	0.909762	+	0.660981i	0.940955	−	0.338532i	$-0.109930\pi$
$619$	563.143	+	409.147i	0.909762	+	0.660981i	−0.0311923	+	0.999513i	$0.509930\pi$
$620$	271.037	−	51.4649i	0.437157	−	0.0830079i
$621$	−246.410	+	758.370i	−0.396795	+	1.22121i
$622$	−109.465	+	336.897i	−0.175988	+	0.541635i
$623$	−7.46999	+	5.42727i	−0.0119904	+	0.00871151i
$624$	−18.6363	+	25.6507i	−0.0298659	+	0.0411069i
$625$	−620.334	+	76.2287i	−0.992534	+	0.121966i
$626$		−	187.291i		−	0.299187i
$627$	424.655	+	18.6924i	0.677280	+	0.0298125i
$628$			1257.79i			2.00286i
$629$	1456.70	−	473.309i	2.31589	−	0.752479i
$630$	62.1590	+	113.294i	0.0986651	+	0.179832i
$631$	355.498	−	258.284i	0.563388	−	0.409325i	−0.269309	−	0.963054i	$-0.586795\pi$
$631$	355.498	−	258.284i	0.563388	−	0.409325i	0.832697	+	0.553728i	$0.186795\pi$
$632$	−473.251	−	153.769i	−0.748815	−	0.243305i
$633$	−63.1946	+	194.493i	−0.0998335	+	0.307256i
$634$	678.630	+	934.055i	1.07039	+	1.47327i
$635$	−308.481	−	562.253i	−0.485796	−	0.885439i
$636$	−96.1043	−	295.779i	−0.151107	−	0.465061i
$637$	−41.7895			−0.0656036
$638$	363.181	+	549.132i	0.569250	+	0.860708i
$639$	241.817			0.378430
$640$	110.536	−	869.055i	0.172713	−	1.35790i
$641$	611.568	+	444.330i	0.954085	+	0.693183i	0.951769	−	0.306814i	$-0.0992630\pi$
$641$	611.568	+	444.330i	0.954085	+	0.693183i	0.00231537	+	0.999997i	$0.499263\pi$
$642$	−66.8951	−	92.0732i	−0.104198	−	0.143416i
$643$	111.604	+	36.2624i	0.173568	+	0.0563957i	0.394512	−	0.918891i	$-0.370914\pi$
$643$	111.604	+	36.2624i	0.173568	+	0.0563957i	−0.220944	+	0.975287i	$0.570914\pi$
$644$	298.034	+	96.8371i	0.462786	+	0.150368i
$645$	21.4324	+	112.873i	0.0332285	+	0.174996i
$646$	−1235.44	+	1700.43i	−1.91244	+	2.63225i
$647$	997.473	−	324.099i	1.54169	−	0.500925i	0.589847	−	0.807515i	$-0.299188\pi$
$647$	997.473	−	324.099i	1.54169	−	0.500925i	0.951842	+	0.306590i	$0.0991879\pi$
$648$	387.088			0.597358
$649$	111.667	+	403.215i	0.172060	+	0.621286i
$650$	49.3730	+	59.8883i	0.0759585	+	0.0921358i
$651$	10.1265	−	3.29029i	0.0155553	−	0.00505421i
$652$	−407.951	+	561.496i	−0.625692	+	0.861191i
$653$	−231.758	−	318.988i	−0.354913	−	0.488496i	0.593810	−	0.804606i	$-0.297623\pi$
$653$	−231.758	−	318.988i	−0.354913	−	0.488496i	−0.948723	+	0.316110i	$0.897623\pi$
$654$	198.371	−	610.522i	0.303319	−	0.933521i
$655$	−55.7321	−	52.4249i	−0.0850871	−	0.0800381i
$656$	541.046	+	744.687i	0.824766	+	1.13519i
$657$	453.822	+	329.721i	0.690749	+	0.501858i
$658$	−218.392	+	70.9598i	−0.331903	+	0.107842i
$659$		−	894.004i		−	1.35661i	−0.734782	−	0.678303i	$-0.762715\pi$
$659$		−	894.004i		−	1.35661i	0.734782	−	0.678303i	$-0.237285\pi$
$660$	−648.397	+	319.487i	−0.982420	+	0.484071i
$661$	−1104.87			−1.67152			−0.835759	−	0.549097i	$-0.814972\pi$
$661$	−1104.87			−1.67152			−0.835759	+	0.549097i	$0.814972\pi$
$662$	376.542	+	1158.88i	0.568795	+	1.75057i
$663$	18.3006	−	25.1886i	0.0276027	−	0.0379918i
$664$	1805.82	−	1312.01i	2.71962	−	1.97592i
$665$	−100.601	−	94.6313i	−0.151280	−	0.142303i
$666$	1478.54	+	480.407i	2.22003	+	0.721332i
$667$	454.708	−	330.365i	0.681721	−	0.495300i
$668$	−781.619	−	567.880i	−1.17009	−	0.850119i
$669$	−94.6034	−	291.159i	−0.141410	−	0.435216i
$670$	−331.076	+	702.026i	−0.494144	+	1.04780i
$671$	233.529	−	293.372i	0.348031	−	0.437215i
$672$			31.3993i			0.0467251i
$673$	−322.533	−	992.653i	−0.479246	−	1.47497i	−0.840145	−	0.542362i	$-0.817530\pi$
$673$	−322.533	−	992.653i	−0.479246	−	1.47497i	0.360899	−	0.932605i	$-0.382470\pi$
$674$	−1797.85	−	1306.22i	−2.66744	−	1.93801i
$675$	−149.608	+	578.609i	−0.221642	+	0.857199i
$676$	−447.975	+	1378.73i	−0.662685	+	2.03954i
$677$	60.9269	−	187.514i	0.0899954	−	0.276977i	−0.895922	−	0.444212i	$-0.853484\pi$
$677$	60.9269	−	187.514i	0.0899954	−	0.276977i	0.985917	+	0.167235i	$0.0534837\pi$
$678$	467.165	−	339.415i	0.689034	−	0.500613i
$679$	42.7058	−	58.7794i	0.0628951	−	0.0865677i
$680$	241.634	−	1899.77i	0.355344	−	2.79378i
$681$		−	11.3581i		−	0.0166786i
$682$	−66.7741	−	241.113i	−0.0979092	−	0.353538i
$683$			779.498i			1.14129i	0.821198	+	0.570643i	$0.193306\pi$
$683$			779.498i			1.14129i	−0.821198	+	0.570643i	$0.806694\pi$
$684$	−1385.71	+	450.243i	−2.02589	+	0.658250i
$685$	−120.442	+	66.0805i	−0.175828	+	0.0964679i
$686$	−303.313	+	220.370i	−0.442147	+	0.321239i
$687$	−269.476	−	87.5581i	−0.392250	−	0.127450i
$688$	110.726	−	340.779i	0.160939	−	0.495318i
$689$	12.1574	+	16.7332i	0.0176449	+	0.0242862i
$690$	434.612	+	792.148i	0.629873	+	1.14804i
$691$	−229.580	−	706.573i	−0.332242	−	1.02254i	−0.968064	−	0.250701i	$-0.919339\pi$
$691$	−229.580	−	706.573i	−0.332242	−	1.02254i	0.635822	−	0.771836i	$-0.280661\pi$
$692$	−1629.12			−2.35422
$693$	66.7582	−	44.1521i	0.0963322	−	0.0637115i
$694$	1694.64			2.44185
$695$	−278.964	−	35.4818i	−0.401387	−	0.0510529i
$696$	340.965	+	247.726i	0.489893	+	0.355928i
$697$	−531.299	−	731.270i	−0.762265	−	1.04917i
$698$	−621.197	−	201.839i	−0.889967	−	0.289168i
$699$	137.525	+	44.6846i	0.196745	+	0.0639265i
$700$	227.389	+	58.7950i	0.324842	+	0.0839929i
$701$	567.996	−	781.779i	0.810265	−	1.11523i	−0.181018	−	0.983480i	$-0.557939\pi$
$701$	567.996	−	781.779i	0.810265	−	1.11523i	0.991282	−	0.131754i	$-0.0420608\pi$
$702$	70.5859	−	22.9347i	0.100550	−	0.0326706i
$703$	−1661.56			−2.36353
$704$	−308.393	−	13.5748i	−0.438058	−	0.0192824i
$705$	−408.987	−	192.879i	−0.580123	−	0.273587i
$706$	−977.348	+	317.560i	−1.38435	+	0.449801i
$707$	−51.2661	+	70.5618i	−0.0725122	+	0.0998045i
$708$	293.823	+	404.413i	0.415004	+	0.571204i
$709$	−109.834	+	338.035i	−0.154914	+	0.476777i	−0.998152	−	0.0607633i	$-0.980647\pi$
$709$	−109.834	+	338.035i	−0.154914	+	0.476777i	0.843238	+	0.537541i	$0.180647\pi$
$710$	440.916	−	468.731i	0.621009	−	0.660184i
$711$	119.027	+	163.827i	0.167408	+	0.230418i
$712$	112.362	+	81.6359i	0.157812	+	0.114657i
$713$	−203.133	+	66.0020i	−0.284900	+	0.0925695i
$714$		−	137.948i		−	0.193205i
$715$	34.4458	−	33.5333i	0.0481759	−	0.0468997i
$716$	1972.25			2.75454
$717$	−186.358	−	573.551i	−0.259914	−	0.799932i
$718$	700.114	−	963.624i	0.975089	−	1.34210i
$719$	−201.778	+	146.600i	−0.280636	+	0.203894i	−0.719195	−	0.694808i	$-0.755489\pi$
$719$	−201.778	+	146.600i	−0.280636	+	0.203894i	0.438558	+	0.898703i	$0.355489\pi$
$720$	543.775	−	578.078i	0.755242	−	0.802885i
$721$	−115.627	−	37.5695i	−0.160370	−	0.0521075i
$722$	807.259	−	586.508i	1.11809	−	0.812337i
$723$	32.4946	+	23.6087i	0.0449441	+	0.0326538i
$724$	−33.1370	−	101.985i	−0.0457694	−	0.140864i
$725$	325.033	−	267.963i	0.448321	−	0.369604i
$726$	337.218	+	562.131i	0.464487	+	0.774285i
$727$		−	883.791i		−	1.21567i	−0.794064	−	0.607834i	$-0.792039\pi$
$727$		−	883.791i		−	1.21567i	0.794064	−	0.607834i	$-0.207961\pi$
$728$	−4.82924	−	14.8629i	−0.00663358	−	0.0204161i
$729$	138.033	+	100.287i	0.189346	+	0.137568i
$730$	1466.60	−	278.479i	2.00904	−	0.381478i
$731$	−108.731	+	334.640i	−0.148743	+	0.457783i
$732$	138.440	−	426.076i	0.189126	−	0.582071i
$733$	765.506	−	556.173i	1.04435	−	0.758763i	0.0732177	−	0.997316i	$-0.476673\pi$
$733$	765.506	−	556.173i	1.04435	−	0.758763i	0.971129	+	0.238553i	$0.0766732\pi$
$734$	−496.570	+	683.471i	−0.676527	+	0.931159i
$735$	−361.693	−	46.0042i	−0.492099	−	0.0625908i
$736$		−	629.858i		−	0.855785i
$737$	450.233	+	168.518i	0.610899	+	0.228654i
$738$		−	917.455i		−	1.24316i
$739$	−450.994	+	146.537i	−0.610277	+	0.198291i	−0.597818	−	0.801632i	$-0.703966\pi$
$739$	−450.994	+	146.537i	−0.610277	+	0.198291i	−0.0124581	+	0.999922i	$0.503966\pi$
$740$	2477.19	−	1359.11i	3.34755	−	1.83663i
$741$	−27.3248	+	19.8527i	−0.0368756	+	0.0267917i
$742$	87.1560	+	28.3187i	0.117461	+	0.0381654i
$743$	−74.4381	+	229.097i	−0.100186	+	0.308340i	−0.988570	−	0.150760i	$-0.951828\pi$
$743$	−74.4381	+	229.097i	−0.100186	+	0.308340i	0.888385	+	0.459100i	$0.151828\pi$
$744$	−94.1393	−	129.572i	−0.126531	−	0.174155i
$745$	1039.82	−	570.497i	1.39573	−	0.765767i
$746$	263.716	+	811.636i	0.353507	+	1.08798i
$747$	−908.365			−1.21602
$748$	−2211.62	−	97.3508i	−2.95671	−	0.130148i
$749$	22.9036			0.0305790
$750$	361.401	+	572.693i	0.481867	+	0.763590i
$751$	−312.684	−	227.179i	−0.416357	−	0.302501i	0.359813	−	0.933024i	$-0.382840\pi$
$751$	−312.684	−	227.179i	−0.416357	−	0.302501i	−0.776171	+	0.630523i	$0.782840\pi$
$752$	828.939	+	1140.94i	1.10231	+	1.51720i
$753$	−543.343	−	176.543i	−0.721570	−	0.234452i
$754$	−49.7528	−	16.1657i	−0.0659852	−	0.0214399i
$755$	43.8699	+	231.039i	0.0581058	+	0.306012i
$756$	132.008	−	181.693i	0.174613	−	0.240335i
$757$	740.817	−	240.706i	0.978622	−	0.317974i	0.224331	−	0.974513i	$-0.427980\pi$
$757$	740.817	−	240.706i	0.978622	−	0.317974i	0.754292	+	0.656540i	$0.227980\pi$
$758$	−931.541			−1.22895
$759$	466.770	−	308.709i	0.614980	−	0.406731i
$760$	−886.148	+	1879.02i	−1.16598	+	2.47240i
$761$	286.870	−	93.2098i	0.376965	−	0.122483i	−0.114405	−	0.993434i	$-0.536496\pi$
$761$	286.870	−	93.2098i	0.376965	−	0.122483i	0.491370	+	0.870951i	$0.336496\pi$
$762$	−408.435	+	562.163i	−0.536004	+	0.737747i
$763$	75.9352	+	104.516i	0.0995219	+	0.136980i
$764$	−2.48606	+	7.65131i	−0.00325401	+	0.0100148i
$765$	−533.978	+	567.663i	−0.698010	+	0.742043i
$766$	−715.432	−	984.708i	−0.933985	−	1.28552i
$767$	−26.8958	−	19.5410i	−0.0350662	−	0.0254771i
$768$	−739.928	+	240.417i	−0.963448	+	0.313043i
$769$			1335.43i			1.73658i	0.496054	+	0.868292i	$0.334782\pi$
$769$			1335.43i			1.73658i	−0.496054	+	0.868292i	$0.665218\pi$
$770$	36.1403	−	209.907i	0.0469355	−	0.272606i
$771$	389.705			0.505453
$772$	−110.808	−	341.031i	−0.143533	−	0.441750i
$773$	−252.654	+	347.748i	−0.326848	+	0.449868i	−0.940543	−	0.339676i	$-0.889683\pi$
$773$	−252.654	+	347.748i	−0.326848	+	0.449868i	0.613695	+	0.789544i	$0.289683\pi$
$774$	−288.930	+	209.920i	−0.373295	+	0.271215i
$775$	−148.939	+	58.6769i	−0.192179	+	0.0757121i
$776$	−1039.38	−	337.715i	−1.33941	−	0.435200i
$777$	88.2245	−	64.0989i	0.113545	−	0.0824953i
$778$	1817.38	+	1320.40i	2.33596	+	1.69718i
$779$	303.010	+	932.569i	0.388973	+	1.19714i
$780$	24.4991	−	51.9488i	0.0314091	−	0.0666010i
$781$	−311.837	−	248.228i	−0.399279	−	0.317833i
$782$			2767.19i			3.53861i
$783$	−124.474	−	383.092i	−0.158971	−	0.489261i
$784$	919.961	+	668.390i	1.17342	+	0.852539i
$785$	−136.150	−	717.027i	−0.173439	−	0.913410i
$786$	−25.6186	+	78.8460i	−0.0325937	+	0.100313i
$787$	−316.259	+	973.345i	−0.401854	+	1.23678i	0.521640	+	0.853166i	$0.325320\pi$
$787$	−316.259	+	973.345i	−0.401854	+	1.23678i	−0.923494	+	0.383613i	$0.874680\pi$
$788$	−598.556	+	434.877i	−0.759589	+	0.551874i
$789$	−259.009	+	356.495i	−0.328275	+	0.451832i
$790$	534.586	+	67.9947i	0.676691	+	0.0860692i
$791$			116.210i			0.146915i
$792$	−941.926	−	749.790i	−1.18930	−	0.946705i
$793$			29.7948i			0.0375723i
$794$	−1133.91	+	368.429i	−1.42810	+	0.464017i
$795$	86.8025	+	158.211i	0.109186	+	0.199007i
$796$	−547.645	+	397.888i	−0.687996	+	0.499859i
$797$	−638.028	−	207.308i	−0.800537	−	0.260110i	−0.119952	−	0.992780i	$-0.538274\pi$
$797$	−638.028	−	207.308i	−0.800537	−	0.260110i	−0.680585	+	0.732669i	$0.738274\pi$
$798$	−46.2437	+	142.324i	−0.0579495	+	0.178350i
$799$	−814.005	−	1120.38i	−1.01878	−	1.40223i
$800$	−28.8421	−	471.187i	−0.0360526	−	0.588984i
$801$	−17.4658	−	53.7541i	−0.0218050	−	0.0671088i
$802$	2487.78			3.10197
$803$	−246.768	−	891.048i	−0.307307	−	1.10965i
$804$	574.369			0.714390
$805$	−180.382	−	22.9430i	−0.224076	−	0.0285006i
$806$	16.0831	+	11.6850i	0.0199542	+	0.0144976i
$807$	194.191	+	267.282i	0.240634	+	0.331204i
$808$	1247.72	+	405.410i	1.54421	+	0.501745i
$809$	−369.452	−	120.042i	−0.456677	−	0.148383i	0.0716398	−	0.997431i	$-0.477177\pi$
$809$	−369.452	−	120.042i	−0.456677	−	0.148383i	−0.528317	+	0.849047i	$0.677177\pi$
$810$	−411.846	+	78.2018i	−0.508452	+	0.0965455i
$811$	589.421	−	811.268i	0.726783	−	1.00033i	−0.272488	−	0.962159i	$-0.587847\pi$
$811$	589.421	−	811.268i	0.726783	−	1.00033i	0.999271	−	0.0381716i	$-0.0121534\pi$
$812$	−150.552	+	48.9174i	−0.185409	+	0.0602431i
$813$	−80.3987			−0.0988914
$814$	−1413.52	−	2137.25i	−1.73651	−	2.62562i
$815$	171.780	−	364.249i	0.210773	−	0.446932i
$816$	−805.742	+	261.802i	−0.987429	+	0.320835i
$817$	224.359	−	308.804i	0.274614	−	0.377973i
$818$	−38.2175	−	52.6019i	−0.0467207	−	0.0643055i
$819$	−1.96527	+	6.04847i	−0.00239959	+	0.00738519i
$820$	−1214.56	−	1142.49i	−1.48118	−	1.39328i
$821$	313.012	+	430.825i	0.381257	+	0.524756i	0.955917	−	0.293637i	$-0.0948656\pi$
$821$	313.012	+	430.825i	0.381257	+	0.524756i	−0.574660	+	0.818393i	$0.694866\pi$
$822$	120.423	+	87.4921i	0.146499	+	0.106438i
$823$	858.981	−	279.100i	1.04372	−	0.339125i	0.263519	−	0.964654i	$-0.415117\pi$
$823$	858.981	−	279.100i	1.04372	−	0.339125i	0.780201	+	0.625529i	$0.215117\pi$
$824$			1828.75i			2.21935i
$825$	335.047	−	252.315i	0.406118	−	0.305836i
$826$	−147.298			−0.178327
$827$	450.181	+	1385.51i	0.544354	+	1.67535i	0.722521	+	0.691349i	$0.242983\pi$
$827$	450.181	+	1385.51i	0.544354	+	1.67535i	−0.178166	+	0.984000i	$0.557017\pi$
$828$	−1127.51	+	1551.89i	−1.36173	+	1.87426i
$829$	685.365	−	497.947i	0.826737	−	0.600660i	−0.0918972	−	0.995768i	$-0.529293\pi$
$829$	685.365	−	497.947i	0.826737	−	0.600660i	0.918634	+	0.395109i	$0.129293\pi$
$830$	−1656.27	+	1760.75i	−1.99550	+	2.12138i
$831$	−237.926	−	77.3067i	−0.286312	−	0.0930285i
$832$	19.8439	−	14.4174i	0.0238508	−	0.0173286i
$833$	−903.387	−	656.349i	−1.08450	−	0.787934i
$834$	94.1556	+	289.781i	0.112896	+	0.347459i
$835$	507.046	+	239.123i	0.607240	+	0.286375i
$836$	2249.13	+	841.829i	2.69035	+	1.00697i
$837$			153.072i			0.182882i
$838$	−462.044	−	1422.03i	−0.551365	−	1.69693i
$839$	773.960	+	562.315i	0.922480	+	0.670221i	0.944140	−	0.329545i	$-0.106895\pi$
$839$	773.960	+	562.315i	0.922480	+	0.670221i	−0.0216603	+	0.999765i	$0.506895\pi$
$840$	−25.4358	−	133.956i	−0.0302807	−	0.159472i
$841$	172.147	−	529.814i	0.204693	−	0.629981i
$842$	512.299	−	1576.69i	0.608431	−	1.87256i
$843$	630.850	−	458.340i	0.748340	−	0.543701i
$844$	−679.117	+	934.724i	−0.804641	+	1.10749i
$845$	106.136	−	834.457i	0.125604	−	0.987524i
$846$		−	1405.64i		−	1.66151i
$847$	−131.411	−	11.5914i	−0.155149	−	0.0136852i
$848$		−	562.814i		−	0.663695i
$849$	258.868	−	84.1112i	0.304909	−	0.0990710i
$850$	126.713	+	2070.09i	0.149075	+	2.43540i
$851$	−1769.75	+	1285.80i	−2.07961	+	1.51093i
$852$	−452.894	−	147.154i	−0.531566	−	0.172716i
$853$	−387.028	+	1191.15i	−0.453726	+	1.39643i	0.418898	+	0.908033i	$0.362416\pi$
$853$	−387.028	+	1191.15i	−0.453726	+	1.39643i	−0.872624	+	0.488392i	$0.837584\pi$
$854$	77.5943	+	106.799i	0.0908598	+	0.125058i
$855$	741.209	−	406.665i	0.866911	−	0.475631i
$856$	−106.460	−	327.651i	−0.124369	−	0.382769i
$857$	−628.293			−0.733131			−0.366565	−	0.930392i	$-0.619466\pi$
$857$	−628.293			−0.733131			−0.366565	+	0.930392i	$0.619466\pi$
$858$	−48.7820	−	18.2587i	−0.0568555	−	0.0212805i
$859$	196.824			0.229132			0.114566	−	0.993416i	$-0.463452\pi$
$859$	196.824			0.229132			0.114566	+	0.993416i	$0.463452\pi$
$860$	−81.8995	+	643.908i	−0.0952320	+	0.748730i
$861$	−52.0651	−	37.8275i	−0.0604705	−	0.0439344i
$862$	−498.625	−	686.299i	−0.578452	−	0.796170i
$863$	774.393	+	251.616i	0.897327	+	0.291559i	0.721133	−	0.692796i	$-0.243622\pi$
$863$	774.393	+	251.616i	0.897327	+	0.291559i	0.176194	+	0.984356i	$0.443622\pi$
$864$	−429.309	−	139.491i	−0.496886	−	0.161448i
$865$	928.706	−	176.344i	1.07365	−	0.203866i
$866$	−200.266	+	275.643i	−0.231254	+	0.318294i
$867$	372.019	−	120.876i	0.429088	−	0.139419i
$868$	60.1563			0.0693044
$869$	14.6777	−	333.448i	0.0168903	−	0.383714i
$870$	−412.820	−	194.686i	−0.474506	−	0.223778i
$871$	−36.3293	+	11.8041i	−0.0417099	+	0.0135524i
$872$	1142.20	−	1572.11i	1.30987	−	1.80288i
$873$	261.414	+	359.806i	0.299444	+	0.412149i
$874$	927.632	−	2854.96i	1.06136	−	3.26654i
$875$	−135.991	−	8.90337i	−0.155419	−	0.0101753i
$876$	−649.307	−	893.695i	−0.741218	−	1.02020i
$877$	−465.237	−	338.015i	−0.530487	−	0.385422i	0.290053	−	0.957011i	$-0.406327\pi$
$877$	−465.237	−	338.015i	−0.530487	−	0.385422i	−0.820540	+	0.571589i	$0.806327\pi$
$878$	2531.70	−	822.598i	2.88348	−	0.936900i
$879$			86.8641i			0.0988215i
$880$	−1294.63	+	187.274i	−1.47117	+	0.212811i
$881$	513.793			0.583193			0.291596	−	0.956541i	$-0.405814\pi$
$881$	513.793			0.583193			0.291596	+	0.956541i	$0.405814\pi$
$882$	−350.238	−	1077.92i	−0.397095	−	1.22213i
$883$	−171.187	+	235.619i	−0.193870	+	0.266839i	−0.894875	−	0.446318i	$-0.852735\pi$
$883$	−171.187	+	235.619i	−0.193870	+	0.266839i	0.701005	+	0.713156i	$0.252735\pi$
$884$	142.309	−	103.393i	0.160983	−	0.116961i
$885$	−211.275	−	198.738i	−0.238728	−	0.224562i
$886$	156.548	+	50.8654i	0.176690	+	0.0574102i
$887$	−941.224	+	683.839i	−1.06113	+	0.770958i	−0.974297	−	0.225265i	$-0.927675\pi$
$887$	−941.224	+	683.839i	−1.06113	+	0.770958i	−0.0868346	+	0.996223i	$0.527675\pi$
$888$	−1327.06	−	964.163i	−1.49443	−	1.08577i
$889$	−43.2132	−	132.996i	−0.0486087	−	0.149602i
$890$	−136.042	−	64.1573i	−0.152856	−	0.0720868i
$891$	69.2967	+	250.222i	0.0777741	+	0.280833i
$892$		−	1729.63i		−	1.93905i
$893$	464.243	+	1428.79i	0.519869	+	1.59999i
$894$	−1039.65	−	755.350i	−1.16292	−	0.844911i
$895$	−1124.32	+	213.487i	−1.25622	+	0.238532i
$896$	59.0302	−	181.676i	0.0658820	−	0.202764i
$897$	−13.7410	+	42.2906i	−0.0153189	+	0.0471467i
$898$	−139.530	+	101.374i	−0.155379	+	0.112889i
$899$	63.4184	−	87.2879i	0.0705432	−	0.0970944i
$900$	−772.412	+	1212.57i	−0.858235	+	1.34730i
$901$			552.674i			0.613401i
$902$	−941.778	+	1183.11i	−1.04410	+	1.31165i
$903$			25.0519i			0.0277429i
$904$	1662.45	−	540.162i	1.83899	−	0.597525i
$905$	29.9297	+	54.5516i	0.0330715	+	0.0602780i
$906$	206.141	−	149.770i	0.227529	−	0.165309i
$907$	−223.231	−	72.5322i	−0.246120	−	0.0799694i	0.183359	−	0.983046i	$-0.441303\pi$
$907$	−223.231	−	72.5322i	−0.246120	−	0.0799694i	−0.429479	+	0.903077i	$0.641303\pi$
$908$	19.8297	−	61.0296i	0.0218389	−	0.0672132i
$909$	−313.815	−	431.929i	−0.345231	−	0.475169i
$910$	8.14081	+	14.8379i	0.00894595	+	0.0163054i
$911$	−173.440	−	533.795i	−0.190385	−	0.585944i	0.809615	−	0.586962i	$-0.199676\pi$
$911$	−173.440	−	533.795i	−0.190385	−	0.585944i	−0.999999	+	0.00101779i	$0.999676\pi$
$912$	919.061			1.00774
$913$	1171.39	+	932.448i	1.28301	+	1.02130i
$914$	1475.91			1.61479
$915$	−32.7998	+	257.877i	−0.0358467	+	0.281833i
$916$	−1295.09	−	940.938i	−1.41385	−	1.02723i
$917$	−9.80667	−	13.4977i	−0.0106943	−	0.0147194i
$918$	1886.11	+	612.834i	2.05458	+	0.667575i
$919$	761.551	+	247.443i	0.828673	+	0.269252i	0.692487	−	0.721431i	$-0.256515\pi$
$919$	761.551	+	247.443i	0.828673	+	0.269252i	0.136187	+	0.990683i	$0.456515\pi$
$920$	510.232	+	2687.11i	0.554600	+	2.92077i
$921$	383.350	−	527.636i	0.416233	−	0.572895i
$922$	−2378.33	+	772.765i	−2.57953	+	0.838140i
$923$	31.6702			0.0343122
$924$	−151.898	+	42.0668i	−0.164392	+	0.0455269i
$925$	−1265.05	+	1042.93i	−1.36762	+	1.12749i
$926$	1711.07	−	555.960i	1.84781	−	0.600389i
$927$	437.436	−	602.079i	0.471884	−	0.649492i
$928$	187.018	+	257.408i	0.201528	+	0.277379i
$929$	−113.874	+	350.469i	−0.122577	+	0.377254i	−0.993452	−	0.114251i	$-0.963553\pi$
$929$	−113.874	+	350.469i	−0.122577	+	0.377254i	0.870875	+	0.491505i	$0.163553\pi$
$930$	126.337	+	118.840i	0.135847	+	0.127785i
$931$	712.015	+	980.004i	0.764785	+	1.05264i
$932$	660.939	+	480.201i	0.709162	+	0.515237i
$933$	−144.659	+	47.0025i	−0.155047	+	0.0503778i
$934$			1276.42i			1.36662i
$935$	1271.31	−	183.900i	1.35969	−	0.196685i
$936$	95.6620			0.102203
$937$	−10.8560	−	33.4113i	−0.0115859	−	0.0356577i	0.945096	−	0.326792i	$-0.105968\pi$
$937$	−10.8560	−	33.4113i	−0.0115859	−	0.0356577i	−0.956682	+	0.291134i	$0.905968\pi$
$938$	−99.4810	+	136.924i	−0.106057	+	0.145974i
$939$	65.0612	−	47.2697i	0.0692877	−	0.0503405i
$940$	−1860.84	−	1750.42i	−1.97961	−	1.86214i
$941$	−897.547	−	291.631i	−0.953823	−	0.309916i	−0.209555	−	0.977797i	$-0.567201\pi$
$941$	−897.547	−	291.631i	−0.953823	−	0.309916i	−0.744268	+	0.667881i	$0.767201\pi$
$942$	−639.757	+	464.811i	−0.679148	+	0.493430i
$943$	1044.41	+	758.806i	1.10754	+	0.804672i
$944$	279.546	+	860.355i	0.296129	+	0.911393i
$945$	−55.5859	+	117.866i	−0.0588211	+	0.124726i
$946$	588.078	+	25.8860i	0.621647	+	0.0273636i
$947$			337.731i			0.356633i	0.983973	+	0.178316i	$0.0570650\pi$
$947$			337.731i			0.356633i	−0.983973	+	0.178316i	$0.942935\pi$
$948$	−123.229	−	379.261i	−0.129989	−	0.400064i
$949$	59.4359	+	43.1827i	0.0626301	+	0.0455034i
$950$	563.215	−	2178.23i	0.592858	−	2.29287i
$951$	−153.195	+	471.485i	−0.161088	+	0.495778i
$952$	129.041	−	397.147i	0.135547	−	0.417172i
$953$	852.521	−	619.393i	0.894566	−	0.649940i	−0.0424986	−	0.999097i	$-0.513532\pi$
$953$	852.521	−	619.393i	0.894566	−	0.649940i	0.937064	+	0.349156i	$0.113532\pi$
$954$	−329.725	+	453.828i	−0.345624	+	0.475711i
$955$	0.589006	−	4.63087i	0.000616760	−	0.00484907i
$956$		−	3407.17i		−	3.56399i
$957$	−99.0955	+	264.755i	−0.103548	+	0.276651i
$958$		−	1912.77i		−	1.99663i
$959$	−28.4896	+	9.25682i	−0.0297076	+	0.00965257i
$960$	187.622	−	102.939i	0.195440	−	0.107228i
$961$	744.295	−	540.762i	0.774500	−	0.562707i
$962$	193.641	+	62.9178i	0.201290	+	0.0654031i
$963$	−43.3241	+	133.338i	−0.0449887	+	0.138461i
$964$	133.383	+	183.586i	0.138364	+	0.190442i
$965$	100.083	+	182.416i	0.103713	+	0.189032i
$966$	60.8822	+	187.376i	0.0630250	+	0.193971i
$967$	200.406			0.207246			0.103623	−	0.994617i	$-0.466957\pi$
$967$	200.406			0.207246			0.103623	+	0.994617i	$0.466957\pi$
$968$	445.001	+	1933.80i	0.459712	+	1.99772i
$969$	−902.503			−0.931376
$970$	1174.09	+	149.334i	1.21040	+	0.153952i
$971$	253.043	+	183.846i	0.260600	+	0.189337i	0.710412	−	0.703787i	$-0.248509\pi$
$971$	253.043	+	183.846i	0.260600	+	0.189337i	−0.449812	+	0.893124i	$0.648509\pi$
$972$	1272.05	+	1750.83i	1.30869	+	1.80126i
$973$	−58.3175	−	18.9485i	−0.0599358	−	0.0194743i
$974$	2233.64	+	725.752i	2.29326	+	0.745126i
$975$	−8.34293	+	32.2662i	−0.00855685	+	0.0330935i
$976$	476.545	−	655.907i	0.488263	−	0.672036i
$977$	−467.459	+	151.887i	−0.478464	+	0.155462i	−0.538313	−	0.842745i	$-0.680938\pi$
$977$	−467.459	+	151.887i	−0.478464	+	0.155462i	0.0598491	+	0.998207i	$0.480938\pi$
$978$	−436.353			−0.446168
$979$	−32.6561	+	87.2479i	−0.0333566	+	0.0891194i
$980$	−1863.14	−	878.658i	−1.90116	−	0.896590i
$981$	−752.096	+	244.371i	−0.766663	+	0.249104i
$982$	−141.551	+	194.829i	−0.144146	+	0.198400i
$983$	−510.884	−	703.172i	−0.519719	−	0.715332i	0.465801	−	0.884889i	$-0.345766\pi$
$983$	−510.884	−	703.172i	−0.519719	−	0.715332i	−0.985520	+	0.169557i	$0.945766\pi$
$984$	−299.138	+	920.653i	−0.304002	+	0.935623i
$985$	294.144	−	312.700i	0.298624	−	0.317462i
$986$	−821.635	−	1130.88i	−0.833301	−	1.14694i
$987$	−79.7692	−	57.9557i	−0.0808198	−	0.0587190i
$988$	−181.483	+	58.9673i	−0.183687	+	0.0596835i
$989$		−	502.531i		−	0.508120i
$990$	1153.65	+	607.453i	1.16530	+	0.613589i
$991$	−901.175			−0.909360			−0.454680	−	0.890655i	$-0.650246\pi$
$991$	−901.175			−0.909360			−0.454680	+	0.890655i	$0.650246\pi$
$992$	−37.3634	−	114.993i	−0.0376647	−	0.115920i
$993$	−307.537	+	423.288i	−0.309705	+	0.426272i
$994$	113.522	−	82.4783i	0.114207	−	0.0829761i
$995$	269.125	−	286.102i	0.270478	−	0.287540i
$996$	1701.26	+	552.773i	1.70809	+	0.554993i
$997$	−1030.21	+	748.492i	−1.03331	+	0.750744i	−0.968969	−	0.247184i	$-0.920495\pi$
$997$	−1030.21	+	748.492i	−1.03331	+	0.750744i	−0.0643420	+	0.997928i	$0.520495\pi$
$998$	−1109.44	−	806.058i	−1.11167	−	0.807673i
$999$	484.460	+	1491.02i	0.484945	+	1.49251i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	55.3.h.a.39.10	yes	40
5.2	odd	4		275.3.x.j.226.1		40
5.3	odd	4		275.3.x.j.226.10		40
5.4	even	2	inner	55.3.h.a.39.1	yes	40
11.2	odd	10	inner	55.3.h.a.24.1	✓	40
11.3	even	5		605.3.d.b.604.38		40
11.8	odd	10		605.3.d.b.604.4		40
55.2	even	20		275.3.x.j.101.1		40
55.13	even	20		275.3.x.j.101.10		40
55.14	even	10		605.3.d.b.604.3		40
55.19	odd	10		605.3.d.b.604.37		40
55.24	odd	10	inner	55.3.h.a.24.10	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.3.h.a.24.1	✓	40	11.2	odd	10	inner
55.3.h.a.24.10	yes	40	55.24	odd	10	inner
55.3.h.a.39.1	yes	40	5.4	even	2	inner
55.3.h.a.39.10	yes	40	1.1	even	1	trivial
275.3.x.j.101.1		40	55.2	even	20
275.3.x.j.101.10		40	55.13	even	20
275.3.x.j.226.1		40	5.2	odd	4
275.3.x.j.226.10		40	5.3	odd	4
605.3.d.b.604.3		40	55.14	even	10
605.3.d.b.604.4		40	11.8	odd	10
605.3.d.b.604.37		40	55.19	odd	10
605.3.d.b.604.38		40	11.3	even	5

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:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	55.h (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.09764 + 3.37818i) q^{2} +(-0.896484 + 1.23390i) q^{3} +(-6.97124 + 5.06490i) q^{4} +(3.42583 - 3.64194i) q^{5} +(-5.15237 - 1.67411i) q^{6} +(0.882039 - 0.640839i) q^{7} +(-13.2675 - 9.63938i) q^{8} +(2.06232 + 6.34716i) q^{9} +(16.0635 + 7.57554i) q^{10} +(3.85595 - 10.3020i) q^{11} -13.1425i q^{12} +(0.270096 + 0.831271i) q^{13} +(3.13303 + 2.27628i) q^{14} +(1.42261 + 7.49209i) q^{15} +(7.34959 - 22.6197i) q^{16} +(-7.21718 + 22.2122i) q^{17} +(-19.1782 + 13.9338i) q^{18} +(14.8922 - 20.4973i) q^{19} +(-5.43620 + 42.7403i) q^{20} +1.66285i q^{21} +(39.0346 + 1.71822i) q^{22} -33.3562i q^{23} +(23.7881 - 7.72924i) q^{24} +(-1.52743 - 24.9533i) q^{25} +(-2.51172 + 1.82487i) q^{26} +(-22.7355 - 7.38721i) q^{27} +(-2.90312 + 8.93489i) q^{28} +(9.90414 + 13.6319i) q^{29} +(-23.7481 + 13.0294i) q^{30} +(-1.97870 - 6.08982i) q^{31} +18.8828 q^{32} +(9.25491 + 13.9935i) q^{33} -82.9587 q^{34} +(0.687817 - 5.40773i) q^{35} +(-46.5246 - 33.8021i) q^{36} +(-38.5475 - 53.0561i) q^{37} +(85.5899 + 27.8099i) q^{38} +(-1.26785 - 0.411949i) q^{39} +(-80.5580 + 15.2965i) q^{40} +(-22.7486 + 31.3107i) q^{41} +(-5.61743 + 1.82521i) q^{42} +15.0656 q^{43} +(25.2980 + 91.3479i) q^{44} +(30.1811 + 14.2334i) q^{45} +(112.683 - 36.6131i) q^{46} +(-34.8531 + 47.9712i) q^{47} +(21.3218 + 29.3469i) q^{48} +(-14.7745 + 45.4713i) q^{49} +(82.6202 - 32.5496i) q^{50} +(-20.9376 - 28.8182i) q^{51} +(-6.09322 - 4.42698i) q^{52} +(22.5056 - 7.31251i) q^{53} -84.9132i q^{54} +(-24.3095 - 49.3361i) q^{55} -17.8797 q^{56} +(11.9411 + 36.7511i) q^{57} +(-35.1798 + 48.4209i) q^{58} +(-30.7715 + 22.3568i) q^{59} +(-47.8640 - 45.0238i) q^{60} +(32.4198 + 10.5338i) q^{61} +(18.4006 - 13.3688i) q^{62} +(5.88655 + 4.27683i) q^{63} +(-8.67190 - 26.6894i) q^{64} +(3.95274 + 1.86412i) q^{65} +(-37.1140 + 46.6246i) q^{66} +43.7033i q^{67} +(-62.1899 - 191.401i) q^{68} +(41.1584 + 29.9033i) q^{69} +(19.0233 - 3.61216i) q^{70} +(11.1969 - 34.4604i) q^{71} +(33.8209 - 104.090i) q^{72} +(68.0006 - 49.4053i) q^{73} +(136.922 - 188.457i) q^{74} +(32.1593 + 20.4855i) q^{75} +218.319i q^{76} +(-3.20083 - 11.5578i) q^{77} -4.73519i q^{78} +(28.8577 - 9.37643i) q^{79} +(-57.2012 - 104.258i) q^{80} +(-19.0958 + 13.8739i) q^{81} +(-130.743 - 42.4810i) q^{82} +(-42.0601 + 129.448i) q^{83} +(-8.42220 - 11.5922i) q^{84} +(56.1706 + 102.380i) q^{85} +(16.5366 + 50.8943i) q^{86} -25.6994 q^{87} +(-150.464 + 99.5127i) q^{88} -8.46901 q^{89} +(-14.9552 + 117.580i) q^{90} +(0.770946 + 0.560125i) q^{91} +(168.946 + 232.534i) q^{92} +(9.28813 + 3.01790i) q^{93} +(-200.312 - 65.0852i) q^{94} +(-23.6320 - 124.457i) q^{95} +(-16.9281 + 23.2995i) q^{96} +(63.3788 - 20.5930i) q^{97} -169.827 q^{98} +(73.3407 + 3.22831i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 22 q^{4} + 2 q^{5} - 10 q^{6} - 4 q^{9} - 16 q^{11} + 38 q^{14} + 4 q^{15} - 138 q^{16} - 10 q^{19} + 72 q^{20} + 30 q^{24} - 138 q^{25} + 172 q^{26} - 10 q^{29} - 290 q^{30} + 128 q^{31} - 112 q^{34}+ \cdots + 882 q^{99}+O(q^{100}) \) 40 * q - 22 * q^4 + 2 * q^5 - 10 * q^6 - 4 * q^9 - 16 * q^11 + 38 * q^14 + 4 * q^15 - 138 * q^16 - 10 * q^19 + 72 * q^20 + 30 * q^24 - 138 * q^25 + 172 * q^26 - 10 * q^29 - 290 * q^30 + 128 * q^31 - 112 * q^34 - 90 * q^35 + 248 * q^36 - 170 * q^39 + 210 * q^40 + 50 * q^41 + 422 * q^44 + 196 * q^45 + 10 * q^46 + 18 * q^49 + 320 * q^50 - 270 * q^51 + 392 * q^55 + 144 * q^56 - 254 * q^59 - 156 * q^60 - 300 * q^61 - 834 * q^64 - 1470 * q^66 + 246 * q^69 - 370 * q^70 + 260 * q^71 + 620 * q^74 - 76 * q^75 + 270 * q^79 - 838 * q^80 + 606 * q^81 + 80 * q^84 - 630 * q^85 + 602 * q^86 - 812 * q^89 - 300 * q^90 + 582 * q^91 + 840 * q^94 + 460 * q^95 + 1610 * q^96 + 882 * q^99

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