LMFDB - Embedded newform 55.3.h.a.24.1

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			24.1
Character	$\chi$	$=$	55.24
Dual form			55.3.h.a.39.1

$q$-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} +(-0.630874 + 4.96004i) 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} +(-6.68579 + 3.66816i) 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} +(29.5201 - 31.3823i) q^{20} -1.66285i q^{21} +(-39.0346 + 1.71822i) q^{22} -33.3562i q^{23} +(23.7881 + 7.72924i) q^{24} +(-24.2040 - 6.25832i) 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} +(-5.05314 - 26.6121i) q^{30} +(-1.97870 + 6.08982i) q^{31} -18.8828 q^{32} +(-9.25491 + 13.9935i) q^{33} -82.9587 q^{34} +(3.73504 - 3.97066i) 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} +(39.4416 + 71.8884i) 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} +(47.7090 - 74.8962i) q^{50} +(-20.9376 + 28.8182i) q^{51} +(6.09322 - 4.42698i) q^{52} +(-22.5056 - 7.31251i) q^{53} +84.9132i q^{54} +(-53.5311 + 12.6264i) q^{55} -17.8797 q^{56} +(-11.9411 + 36.7511i) q^{57} +(35.1798 + 48.4209i) q^{58} +(-30.7715 - 22.3568i) q^{59} +(65.1871 + 8.29124i) 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} +(9.31389 + 16.9760i) 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} +(-13.9763 - 35.4759i) q^{75} -218.319i q^{76} +(3.20083 - 11.5578i) q^{77} -4.73519i q^{78} +(28.8577 + 9.37643i) q^{79} +(-116.831 + 22.1841i) 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} +(-114.727 + 21.7844i) q^{85} +(16.5366 - 50.8943i) q^{86} +25.6994 q^{87} +(150.464 + 99.5127i) q^{88} -8.46901 q^{89} +(-81.2110 + 86.3341i) 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} +(-111.063 + 60.9346i) 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 $\left(\mathbb{Z}/55\mathbb{Z}\right)^\times$.

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

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	0.162913	+	0.986640i	$0.447911\pi$
$2$	−1.09764	+	3.37818i	−0.548819	+	1.68909i	−0.711732	+	0.702451i	$0.752089\pi$
$3$	0.896484	+	1.23390i	0.298828	+	0.411302i	0.931857	−	0.362827i	$-0.118188\pi$
$3$	0.896484	+	1.23390i	0.298828	+	0.411302i	−0.633028	+	0.774129i	$0.718188\pi$
$4$	−6.97124	−	5.06490i	−1.74281	−	1.26623i
$5$	−0.630874	+	4.96004i	−0.126175	+	0.992008i
$5$	−0.630874	+	4.96004i	−0.126175	+	0.992008i
$6$	−5.15237	+	1.67411i	−0.858729	+	0.279018i
$7$	−0.882039	−	0.640839i	−0.126006	−	0.0915484i	0.522997	−	0.852334i	$-0.324814\pi$
$7$	−0.882039	−	0.640839i	−0.126006	−	0.0915484i	−0.649003	+	0.760786i	$0.724814\pi$
$8$	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	$-0.910703\pi$
$13$	−0.270096	+	0.831271i	−0.0207766	+	0.0639440i	0.940131	+	0.340814i	$0.110703\pi$
$14$	3.13303	−	2.27628i	0.223788	−	0.162591i
$15$	−6.68579	+	3.66816i	−0.445719	+	0.244544i
$16$	7.34959	+	22.6197i	0.459349	+	1.41373i
$17$	7.21718	+	22.2122i	0.424540	+	1.30660i	0.903434	+	0.428727i	$0.141038\pi$
$17$	7.21718	+	22.2122i	0.424540	+	1.30660i	−0.478894	+	0.877873i	$0.658962\pi$
$18$	19.1782	+	13.9338i	1.06545	+	0.774098i
$19$	14.8922	+	20.4973i	0.783799	+	1.07881i	0.994853	+	0.101332i	$0.0323104\pi$
$19$	14.8922	+	20.4973i	0.783799	+	1.07881i	−0.211054	+	0.977474i	$0.567690\pi$
$20$	29.5201	−	31.3823i	1.47601	−	1.56912i
$21$		−	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
$25$	−24.2040	−	6.25832i	−0.968160	−	0.250333i
$26$	−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	−0.603363	−	0.797467i	$-0.706173\pi$
$29$	9.90414	−	13.6319i	0.341522	−	0.470065i	0.944885	+	0.327402i	$0.106173\pi$
$30$	−5.05314	−	26.6121i	−0.168438	−	0.887071i
$31$	−1.97870	+	6.08982i	−0.0638291	+	0.196446i	−0.977885	−	0.209142i	$-0.932933\pi$
$31$	−1.97870	+	6.08982i	−0.0638291	+	0.196446i	0.914056	+	0.405587i	$0.132933\pi$
$32$	−18.8828			−0.590087
$33$	−9.25491	+	13.9935i	−0.280452	+	0.424045i
$34$	−82.9587			−2.43996
$35$	3.73504	−	3.97066i	0.106715	−	0.113447i
$36$	−46.5246	+	33.8021i	−1.29235	+	0.938948i
$37$	38.5475	−	53.0561i	1.04182	−	1.43395i	0.146137	−	0.989264i	$-0.453316\pi$
$37$	38.5475	−	53.0561i	1.04182	−	1.43395i	0.895687	−	0.444684i	$-0.146684\pi$
$38$	−85.5899	+	27.8099i	−2.25237	+	0.731838i
$39$	−1.26785	+	0.411949i	−0.0325089	+	0.0105628i
$40$	39.4416	+	71.8884i	0.986040	+	1.79721i
$41$	−22.7486	−	31.3107i	−0.554843	−	0.763676i	0.435817	−	0.900036i	$-0.356460\pi$
$41$	−22.7486	−	31.3107i	−0.554843	−	0.763676i	−0.990659	+	0.136360i	$0.956460\pi$
$42$	5.61743	+	1.82521i	0.133748	+	0.0434574i
$43$	−15.0656			−0.350362			−0.175181	−	0.984536i	$-0.556051\pi$
$43$	−15.0656			−0.350362			−0.175181	+	0.984536i	$0.556051\pi$
$44$	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	0.998528	+	0.0542457i	$0.0172754\pi$
$47$	34.8531	+	47.9712i	0.741556	+	1.02066i	−0.256971	+	0.966419i	$0.582725\pi$
$48$	−21.3218	+	29.3469i	−0.444204	+	0.611394i
$49$	−14.7745	−	45.4713i	−0.301521	−	0.927985i
$50$	47.7090	−	74.8962i	0.954180	−	1.49792i
$51$	−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	$-0.471664\pi$
$53$	−22.5056	−	7.31251i	−0.424634	−	0.137972i	−0.513535	+	0.858069i	$0.671664\pi$
$54$			84.9132i			1.57247i
$55$	−53.5311	+	12.6264i	−0.973292	+	0.229571i
$56$	−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	0.295637	−	0.955300i	$-0.404468\pi$
$59$	−30.7715	−	22.3568i	−0.521550	−	0.378928i	−0.817188	+	0.576372i	$0.804468\pi$
$60$	65.1871	+	8.29124i	1.08645	+	0.138187i
$61$	32.4198	−	10.5338i	0.531472	−	0.172686i	−0.0309732	−	0.999520i	$-0.509861\pi$
$61$	32.4198	−	10.5338i	0.531472	−	0.172686i	0.562445	+	0.826834i	$0.309861\pi$
$62$	−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
$70$	9.31389	+	16.9760i	0.133056	+	0.242514i
$71$	11.1969	+	34.4604i	0.157702	+	0.485358i	0.998425	−	0.0561087i	$-0.0178694\pi$
$71$	11.1969	+	34.4604i	0.157702	+	0.485358i	−0.840722	+	0.541466i	$0.817869\pi$
$72$	−33.8209	−	104.090i	−0.469735	−	1.44570i
$73$	−68.0006	−	49.4053i	−0.931515	−	0.676785i	0.0148485	−	0.999890i	$-0.495273\pi$
$73$	−68.0006	−	49.4053i	−0.931515	−	0.676785i	−0.946363	+	0.323105i	$0.895273\pi$
$74$	136.922	+	188.457i	1.85030	+	2.54672i
$75$	−13.9763	−	35.4759i	−0.186351	−	0.473012i
$76$		−	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	0.485909	−	0.874010i	$-0.338489\pi$
$79$	28.8577	+	9.37643i	0.365287	+	0.118689i	−0.120621	+	0.992699i	$0.538489\pi$
$80$	−116.831	+	22.1841i	−1.46039	+	0.277301i
$81$	−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	0.797812	+	0.602906i	$0.205991\pi$
$83$	42.0601	+	129.448i	0.506748	+	1.55961i	−0.291064	+	0.956704i	$0.594009\pi$
$84$	−8.42220	+	11.5922i	−0.100264	+	0.138002i
$85$	−114.727	+	21.7844i	−1.34972	+	0.256287i
$86$	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	$0.515150\pi$
$90$	−81.2110	+	86.3341i	−0.902345	+	0.959268i
$91$	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
$95$	−111.063	+	60.9346i	−1.16908	+	0.641416i
$96$	−16.9281	−	23.2995i	−0.176335	−	0.242704i
$97$	−63.3788	−	20.5930i	−0.653390	−	0.212299i	−0.0364815	−	0.999334i	$-0.511615\pi$
$97$	−63.3788	−	20.5930i	−0.653390	−	0.212299i	−0.616908	+	0.787035i	$0.711615\pi$
$98$	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	−0.0928981	−	0.995676i	$-0.529613\pi$
$101$	−76.0831	−	24.7209i	−0.753298	−	0.244761i	−0.660400	+	0.750914i	$0.729613\pi$
$102$	−74.3712	−	102.363i	−0.729129	−	1.00356i
$103$	65.5454	−	90.2154i	0.636363	−	0.875878i	−0.362052	−	0.932158i	$-0.617924\pi$
$103$	65.5454	−	90.2154i	0.636363	−	0.875878i	0.998415	+	0.0562796i	$0.0179238\pi$
$104$	4.42944	+	13.6324i	0.0425908	+	0.131081i
$105$	8.24782	+	1.04905i	0.0785507	+	0.00999097i
$106$	49.4060	−	68.0015i	0.466094	−	0.641524i
$107$	−16.9954	+	12.3479i	−0.158836	+	0.115401i	−0.664364	−	0.747409i	$-0.731298\pi$
$107$	−16.9954	+	12.3479i	−0.158836	+	0.115401i	0.505528	+	0.862810i	$0.331298\pi$
$108$	−195.910	−	63.6551i	−1.81398	−	0.589399i
$109$		−	118.493i		−	1.08710i	−0.839378	−	0.543548i	$-0.817081\pi$
$109$		−	118.493i		−	1.08710i	0.839378	−	0.543548i	$-0.182919\pi$
$110$	16.1034	−	194.697i	0.146395	−	1.76997i
$111$	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	$-0.0436650\pi$
$113$	62.6514	+	86.2322i	0.554437	+	0.763117i	−0.436169	+	0.899865i	$0.643665\pi$
$114$	−111.045	−	80.6787i	−0.974077	−	0.707708i
$115$	165.448	+	21.0436i	1.43868	+	0.182988i
$116$	−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
$125$	46.3112	−	116.105i	0.370490	−	0.928837i
$126$	−7.98660	−	24.5802i	−0.0633857	−	0.195081i
$127$	−39.6357	−	121.986i	−0.312092	−	0.960520i	−0.976935	−	0.213537i	$-0.931502\pi$
$127$	−39.6357	−	121.986i	−0.312092	−	0.960520i	0.664843	−	0.746983i	$-0.268498\pi$
$128$	−141.749	−	102.987i	−1.10741	−	0.804583i
$129$	−13.5061	−	18.5895i	−0.104698	−	0.144105i
$130$	10.6360	−	11.3070i	0.0818155	−	0.0869766i
$131$			15.3029i			0.116816i	0.998293	+	0.0584079i	$0.0186024\pi$
$131$			15.3029i			0.116816i	−0.998293	+	0.0584079i	$0.981398\pi$
$132$	135.394	−	50.6767i	1.02571	−	0.383914i
$133$		−	27.6229i		−	0.207691i
$134$	−147.638	−	47.9704i	−1.10177	−	0.357988i
$135$	22.2976	+	117.429i	0.165168	+	0.869847i
$136$	309.865	+	225.130i	2.27842	+	1.65537i
$137$	26.1310	−	8.49047i	0.190737	−	0.0619742i	−0.212091	−	0.977250i	$-0.568027\pi$
$137$	26.1310	−	8.49047i	0.190737	−	0.0619742i	0.402828	+	0.915276i	$0.368027\pi$
$138$	55.8419	+	171.864i	0.404651	+	1.24539i
$139$	−33.0584	+	45.5009i	−0.237830	+	0.327345i	−0.911203	−	0.411958i	$-0.864845\pi$
$139$	−33.0584	+	45.5009i	−0.237830	+	0.327345i	0.673373	+	0.739303i	$0.264845\pi$
$140$	−46.1489	+	8.76281i	−0.329635	+	0.0625915i
$141$	−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
$145$	61.3664	+	57.7250i	0.423217	+	0.398103i
$146$	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	0.569993	−	0.821650i	$-0.306946\pi$
$149$	225.598	−	73.3012i	1.51408	−	0.491954i	0.944087	+	0.329695i	$0.106946\pi$
$150$	135.185	−	8.27488i	0.901234	−	0.0551659i
$151$	−27.6455	−	38.0508i	−0.183083	−	0.251992i	0.707604	−	0.706609i	$-0.249776\pi$
$151$	−27.6455	−	38.0508i	−0.183083	−	0.251992i	−0.890687	+	0.454617i	$0.849776\pi$
$152$	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	$-0.353897\pi$
$157$	−85.7977	−	118.090i	−0.546482	−	0.752168i	−0.989530	+	0.144330i	$0.953897\pi$
$158$	−63.3506	+	87.1946i	−0.400953	+	0.551865i
$159$	−11.1530	−	34.3253i	−0.0701444	−	0.215882i
$160$	11.9127	−	93.6593i	0.0744541	−	0.585371i
$161$	−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	$-0.479468\pi$
$163$	−76.6025	−	24.8897i	−0.469954	−	0.152697i	−0.534414	+	0.845223i	$0.679468\pi$
$164$			333.494i			2.03350i
$165$	−63.5695	−	54.7329i	−0.385270	−	0.331714i
$166$	−483.465			−2.91244
$167$	−34.6471	+	106.633i	−0.207468	+	0.638521i	0.792135	+	0.610346i	$0.208969\pi$
$167$	−34.6471	+	106.633i	−0.207468	+	0.638521i	−0.999603	+	0.0281747i	$0.991031\pi$
$168$	−16.0289	−	22.0619i	−0.0954100	−	0.131321i
$169$	136.106	+	98.8867i	0.805360	+	0.585128i
$170$	52.3365	−	411.479i	0.307862	−	2.42046i
$171$	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	$-0.884008\pi$
$173$	−152.953	+	111.127i	−0.884120	+	0.642351i	0.0502182	+	0.998738i	$0.484008\pi$
$174$	−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	−0.969197	−	0.246287i	$-0.920789\pi$
$179$	−185.169	+	134.533i	−1.03446	+	0.751581i	−0.0652651	+	0.997868i	$0.520789\pi$
$180$	−138.309	−	252.089i	−0.768382	−	1.40049i
$181$	−3.84557	−	11.8355i	−0.0212463	−	0.0653893i	0.939871	−	0.341529i	$-0.110945\pi$
$181$	−3.84557	−	11.8355i	−0.0212463	−	0.0653893i	−0.961118	+	0.276140i	$0.910945\pi$
$182$	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
$185$	238.842	+	224.669i	1.29104	+	1.21443i
$186$		−	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
$190$	−83.9415	−	442.074i	−0.441797	−	2.32671i
$191$	0.755326	+	0.548777i	0.00395459	+	0.00287318i	0.589761	−	0.807578i	$-0.299222\pi$
$191$	0.755326	+	0.548777i	0.00395459	+	0.00287318i	−0.585806	+	0.810451i	$0.699222\pi$
$192$	−40.7064	+	13.2263i	−0.212012	+	0.0688870i
$193$	12.8593	+	39.5768i	0.0666284	+	0.205061i	0.978828	−	0.204685i	$-0.0656171\pi$
$193$	12.8593	+	39.5768i	0.0666284	+	0.205061i	−0.912199	+	0.409747i	$0.865617\pi$
$194$	139.134	−	191.502i	0.717186	−	0.987121i
$195$	−1.24343	−	6.54846i	−0.00637656	−	0.0335818i
$196$	−127.311	+	391.823i	−0.649546	+	1.99910i
$197$	−85.8608			−0.435842			−0.217921	−	0.975966i	$-0.569927\pi$
$197$	−85.8608			−0.435842			−0.217921	+	0.975966i	$0.569927\pi$
$198$	−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	$0.436756\pi$
$200$	−381.452	+	150.279i	−1.90726	+	0.751397i
$201$	−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
$205$	169.654	−	93.0806i	0.827580	−	0.454052i
$206$	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	0.595185	−	0.803589i	$-0.297079\pi$
$211$	127.520	+	41.4339i	0.604362	+	0.196369i	0.00917715	+	0.999958i	$0.497079\pi$
$212$	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
$215$	9.50448	−	74.7259i	0.0442069	−	0.347562i
$216$	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
$220$	437.130	+	183.108i	1.98695	+	0.832309i
$221$	−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	$-0.0514045\pi$
$223$	117.983	+	162.389i	0.529071	+	0.728204i	−0.457917	+	0.888995i	$0.651404\pi$
$224$	16.6553	+	12.1008i	0.0743542	+	0.0540215i
$225$	−89.6388	+	140.720i	−0.398395	+	0.625422i
$226$	−360.077	+	116.996i	−1.59326	+	0.517681i
$227$	6.02475	+	4.37724i	0.0265408	+	0.0192830i	0.600977	−	0.799267i	$-0.294778\pi$
$227$	6.02475	+	4.37724i	0.0265408	+	0.0192830i	−0.574436	+	0.818550i	$0.694778\pi$
$228$	269.385	−	195.720i	1.18151	−	0.858420i
$229$	57.4080	−	176.684i	0.250690	−	0.771544i	−0.743959	−	0.668226i	$-0.767054\pi$
$229$	57.4080	−	176.684i	0.250690	−	0.771544i	0.994648	−	0.103318i	$-0.0329460\pi$
$230$	−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	$-0.834783\pi$
$233$	29.2977	−	90.1691i	0.125741	−	0.386992i	0.994035	+	0.109058i	$0.0347834\pi$
$234$	−16.7627	+	12.1788i	−0.0716354	+	0.0520462i
$235$	−259.927	+	142.609i	−1.10607	+	0.606848i
$236$	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	−0.940805	−	0.338948i	$-0.889929\pi$
$239$	−232.413	−	319.889i	−0.972439	−	1.33845i	−0.0316341	−	0.999500i	$-0.510071\pi$
$240$	−132.111	−	124.271i	−0.550460	−	0.517796i
$241$			26.3347i			0.109273i	0.998506	+	0.0546364i	$0.0174000\pi$
$241$			26.3347i			0.109273i	−0.998506	+	0.0546364i	$0.982600\pi$
$242$	−168.217	−	395.509i	−0.695110	−	1.63434i
$243$		−	251.150i		−	1.03354i
$244$	−279.359	−	90.7693i	−1.14491	−	0.372005i
$245$	234.860	−	44.5955i	0.958613	−	0.182023i
$246$	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
$250$	341.390	+	283.889i	1.36556	+	1.13555i
$251$	115.751	−	356.246i	0.461160	−	1.41931i	−0.402588	−	0.915381i	$-0.631889\pi$
$251$	115.751	−	356.246i	0.461160	−	1.41931i	0.863748	−	0.503924i	$-0.168111\pi$
$252$	62.6983			0.248803
$253$	343.637	−	128.620i	1.35825	−	0.508379i
$254$	455.597			1.79369
$255$	−129.730	−	122.032i	−0.508747	−	0.478558i
$256$	412.683	−	299.832i	1.61204	−	1.17122i
$257$	150.186	−	206.714i	0.584382	−	0.804333i	−0.409785	−	0.912182i	$-0.634396\pi$
$257$	150.186	−	206.714i	0.584382	−	0.804333i	0.994167	+	0.107849i	$0.0343963\pi$
$258$	77.6235	−	25.2214i	0.300866	−	0.0977574i
$259$	−68.0008	+	22.0948i	−0.262551	+	0.0853081i
$260$	18.1140	+	33.0155i	0.0696691	+	0.126983i
$261$	−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	$-0.685094\pi$
$263$	−288.916			−1.09854			−0.549270	+	0.835645i	$0.685094\pi$
$264$	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	0.994981	+	0.100060i	$0.0319035\pi$
$269$	66.9375	+	206.012i	0.248838	+	0.765846i	−0.746143	+	0.665786i	$0.768097\pi$
$270$	−421.173	−	53.5695i	−1.55990	−	0.198406i
$271$	30.9844	−	42.6464i	0.114334	−	0.157367i	−0.748015	−	0.663682i	$-0.768993\pi$
$271$	30.9844	−	42.6464i	0.114334	−	0.157367i	0.862348	+	0.506315i	$0.168993\pi$
$272$	−449.390	+	326.501i	−1.65217	+	1.20037i
$273$	1.38228	+	0.449131i	0.00506331	+	0.00164517i
$274$			97.5947i			0.356185i
$275$	−28.8561	−	273.482i	−0.104931	−	0.994479i
$276$	−438.383			−1.58834
$277$	−50.6866	+	155.997i	−0.182984	+	0.563167i	−0.999908	−	0.0135787i	$-0.995678\pi$
$277$	−50.6866	+	155.997i	−0.182984	+	0.563167i	0.816924	+	0.576746i	$0.195678\pi$
$278$	−117.424	−	161.621i	−0.422390	−	0.581370i
$279$	34.5723	+	25.1183i	0.123915	+	0.0900296i
$280$	11.2798	−	88.6840i	0.0402851	−	0.316729i
$281$	−486.240	+	157.989i	−1.73039	+	0.562239i	−0.993506	−	0.113778i	$-0.963705\pi$
$281$	−486.240	+	157.989i	−1.73039	+	0.562239i	−0.736887	+	0.676016i	$0.763705\pi$
$282$	−259.885	−	188.818i	−0.921579	−	0.669567i
$283$	144.379	−	104.898i	0.510175	−	0.370664i	−0.302715	−	0.953081i	$-0.597893\pi$
$283$	144.379	−	104.898i	0.510175	−	0.370664i	0.812890	+	0.582418i	$0.197893\pi$
$284$	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
$290$	−262.364	+	143.946i	−0.904702	+	0.496365i
$291$	−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	$-0.330985\pi$
$293$	−46.0759	−	33.4761i	−0.157256	−	0.114253i	−0.663630	+	0.748061i	$0.730985\pi$
$294$	152.248	+	209.551i	0.517849	+	0.712758i
$295$	130.303	−	138.523i	0.441707	−	0.469571i
$296$		−	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
$300$	−82.2497	+	318.100i	−0.274166	+	1.06033i
$301$	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
$305$	31.7954	+	167.449i	0.104247	+	0.549013i
$306$	−171.087	+	526.552i	−0.559108	+	1.72076i
$307$	427.615			1.39288			0.696442	−	0.717613i	$-0.254766\pi$
$307$	427.615			1.39288			0.696442	+	0.717613i	$0.254766\pi$
$308$	−80.8531	+	64.3605i	−0.262510	+	0.208963i
$309$	170.078			0.550413
$310$	77.9184	−	82.8338i	0.251350	−	0.267206i
$311$	80.6811	−	58.6183i	0.259425	−	0.188483i	−0.450469	−	0.892792i	$-0.648743\pi$
$311$	80.6811	−	58.6183i	0.259425	−	0.188483i	0.709893	+	0.704309i	$0.248743\pi$
$312$	−12.8502	+	17.6868i	−0.0411865	+	0.0566884i
$313$	50.1472	−	16.2938i	0.160215	−	0.0520569i	−0.227812	−	0.973705i	$-0.573157\pi$
$313$	50.1472	−	16.2938i	0.160215	−	0.0520569i	0.388026	+	0.921648i	$0.373157\pi$
$314$	493.106	−	160.220i	1.57040	−	0.510254i
$315$	−17.4996	−	31.8956i	−0.0555542	−	0.101256i
$316$	−153.683	−	211.527i	−0.486339	−	0.669389i
$317$	−309.132	−	100.443i	−0.975180	−	0.316855i	−0.222275	−	0.974984i	$-0.571348\pi$
$317$	−309.132	−	100.443i	−0.975180	−	0.316855i	−0.752905	+	0.658129i	$0.771348\pi$
$318$	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
$325$	11.7398	−	18.4297i	0.0361224	−	0.0567069i
$326$	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
$330$	254.674	−	154.673i	0.771739	−	0.468705i
$331$	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
$335$	−216.770	−	27.5713i	−0.647075	−	0.0823024i
$336$	37.6133	−	12.2213i	0.111944	−	0.0363729i
$337$	506.148	+	367.738i	1.50192	+	1.09121i	0.969608	+	0.244663i	$0.0786772\pi$
$337$	506.148	+	367.738i	1.50192	+	1.09121i	0.532313	+	0.846547i	$0.321323\pi$
$338$	−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
$345$	122.356	+	223.013i	0.354655	+	0.646413i
$346$	−207.519	−	638.679i	−0.599767	−	1.84589i
$347$	−147.429	−	453.741i	−0.424868	−	1.30761i	−0.903120	−	0.429388i	$-0.858729\pi$
$347$	−147.429	−	453.741i	−0.424868	−	1.30761i	0.478252	−	0.878223i	$-0.341271\pi$
$348$	−179.156	−	130.165i	−0.514818	−	0.374037i
$349$	−108.085	−	148.766i	−0.309699	−	0.426264i	0.625589	−	0.780153i	$-0.284859\pi$
$349$	−108.085	−	148.766i	−0.309699	−	0.426264i	−0.935287	+	0.353890i	$0.884859\pi$
$350$	−90.0775	+	35.4876i	−0.257364	+	0.101393i
$351$			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
$355$	−177.989	+	33.7967i	−0.501377	+	0.0952020i
$356$	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	−0.989880	−	0.141904i	$-0.954678\pi$
$359$	−197.102	+	271.288i	−0.549032	+	0.755677i	0.440849	+	0.897581i	$0.354678\pi$
$360$	537.628	−	102.085i	1.49341	−	0.283570i
$361$	−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
$365$	287.952	−	306.117i	0.788910	−	0.838677i
$366$	−149.404	+	108.548i	−0.408208	+	0.296581i
$367$	−139.799	+	192.417i	−0.380924	+	0.524296i	−0.955829	−	0.293924i	$-0.905039\pi$
$367$	−139.799	+	192.417i	−0.380924	+	0.524296i	0.574905	+	0.818220i	$0.305039\pi$
$368$	754.508	−	245.155i	2.05029	−	0.666181i
$369$	−245.649	+	79.8161i	−0.665714	+	0.216304i
$370$	−1021.13	+	560.246i	−2.75982	+	1.51418i
$371$	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	$-0.604376\pi$
$373$	−240.258			−0.644124			−0.322062	+	0.946719i	$0.604376\pi$
$374$	−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	−0.999235	−	0.0391181i	$-0.987545\pi$
$379$	−81.0415	−	249.420i	−0.213830	−	0.658101i	0.785405	−	0.618983i	$-0.212455\pi$
$380$	1082.87	+	137.732i	2.84966	+	0.362453i
$381$	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	$-0.252369\pi$
$383$	325.896	+	105.890i	0.850904	+	0.276475i	0.149079	+	0.988825i	$0.452369\pi$
$384$		−	267.231i		−	0.695913i
$385$	55.3080	+	23.1678i	0.143657	+	0.0601761i
$386$	−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	0.999978	+	0.00661783i	$0.00210654\pi$
$389$	511.645	+	371.732i	1.31528	+	0.955608i	0.315304	+	0.948991i	$0.397893\pi$
$390$	23.4867	+	2.98731i	0.0602224	+	0.00765977i
$391$	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
$400$	−36.3280	−	593.483i	−0.0908200	−	1.48371i
$401$	216.430	+	666.103i	0.539725	+	1.66110i	0.733211	+	0.680001i	$0.238021\pi$
$401$	216.430	+	666.103i	0.539725	+	1.66110i	−0.193486	+	0.981103i	$0.561979\pi$
$402$	−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
$405$	80.8621	−	85.9631i	0.199659	−	0.212255i
$406$		−	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	0.287657	−	0.957733i	$-0.407124\pi$
$409$	−17.4090	−	5.65652i	−0.0425648	−	0.0138301i	−0.330222	+	0.943903i	$0.607124\pi$
$410$	128.225	+	675.291i	0.312744	+	1.64705i
$411$	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
$415$	−668.600	+	126.955i	−1.61108	+	0.305915i
$416$	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	$0.667520\pi$
$420$	−52.1842	−	49.0876i	−0.124248	−	0.116875i
$421$	−377.591	+	274.336i	−0.896891	+	0.651629i	−0.937665	−	0.347539i	$-0.887017\pi$
$421$	−377.591	+	274.336i	−0.896891	+	0.651629i	0.0407749	+	0.999168i	$0.487017\pi$
$422$	−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
$425$	−35.6735	−	582.791i	−0.0839377	−	1.37127i
$426$	−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	0.0334216	−	0.999441i	$-0.489360\pi$
$431$	−227.136	−	73.8008i	−0.526997	−	0.171232i	−0.560418	+	0.828210i	$0.689360\pi$
$432$	334.193	+	459.977i	0.773595	+	1.06476i
$433$	−56.3808	+	77.6015i	−0.130210	+	0.179218i	−0.869144	−	0.494559i	$-0.835329\pi$
$433$	−56.3808	+	77.6015i	−0.130210	+	0.179218i	0.738934	+	0.673778i	$0.235329\pi$
$434$	7.66280	+	23.5837i	0.0176562	+	0.0543402i
$435$	−16.2131	+	127.470i	−0.0372714	+	0.293034i
$436$	−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	$0.325561\pi$
$439$			749.426i			1.70712i	−0.520994	+	0.853560i	$0.674439\pi$
$440$	−588.511	+	683.526i	−1.33752	+	1.55347i
$441$	−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	$-0.216656\pi$
$443$	−27.2384	−	37.4905i	−0.0614863	−	0.0846286i	−0.838653	+	0.544666i	$0.816656\pi$
$444$	−697.288	−	506.609i	−1.57047	−	1.14101i
$445$	5.34288	−	42.0066i	0.0120065	−	0.0943969i
$446$	−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	−0.932957	−	0.359989i	$-0.882781\pi$
$449$	15.0043	−	46.1784i	0.0334171	−	0.102847i	0.966374	+	0.257141i	$0.0827806\pi$
$450$	−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
$455$	2.29187	+	4.17729i	0.00503709	+	0.00918087i
$456$	195.829	+	602.698i	0.429449	+	1.32171i
$457$	−128.400	−	395.176i	−0.280964	−	0.864718i	−0.987579	−	0.157120i	$-0.949779\pi$
$457$	−128.400	−	395.176i	−0.280964	−	0.864718i	0.706616	−	0.707598i	$-0.250221\pi$
$458$	533.856	+	387.869i	1.16562	+	0.846876i
$459$	328.172	+	451.691i	0.714972	+	0.984075i
$460$	−1046.80	−	984.679i	−2.27564	−	2.14061i
$461$		−	704.025i		−	1.52717i	−0.645707	−	0.763585i	$-0.723437\pi$
$461$		−	704.025i		−	1.52717i	0.645707	−	0.763585i	$-0.276563\pi$
$462$	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
$465$	−9.10925	−	47.9734i	−0.0195898	−	0.103169i
$466$	272.449	+	197.946i	0.584655	+	0.424777i
$467$	−341.762	+	111.045i	−0.731825	+	0.237785i	−0.651143	−	0.758955i	$-0.725710\pi$
$467$	−341.762	+	111.045i	−0.731825	+	0.237785i	−0.0806828	+	0.996740i	$0.525710\pi$
$468$	−15.5326	−	47.8044i	−0.0331893	−	0.102146i
$469$	28.0068	−	38.5480i	0.0597160	−	0.0821920i
$470$	−196.454	−	1034.62i	−0.417987	−	2.20131i
$471$	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
$475$	−232.171	−	589.317i	−0.488782	−	1.24067i
$476$	−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	−0.790173	−	0.612883i	$-0.790010\pi$
$479$	−512.144	+	166.406i	−1.06919	+	0.347402i	−0.279020	+	0.960285i	$0.590010\pi$
$480$	126.246	−	69.2650i	0.263013	−	0.144302i
$481$	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	−0.993061	−	0.117596i	$-0.962481\pi$
$487$	−388.640	−	534.918i	−0.798029	−	1.09839i	0.195032	−	0.980797i	$-0.437519\pi$
$488$	328.589	−	452.264i	0.673338	−	0.926770i
$489$	−37.9615	−	116.833i	−0.0776308	−	0.238923i
$490$	−107.140	+	842.351i	−0.218652	+	1.71908i
$491$	39.8508	−	54.8499i	0.0811625	−	0.111711i	−0.766505	−	0.642238i	$-0.778006\pi$
$491$	39.8508	−	54.8499i	0.0811625	−	0.111711i	0.847668	+	0.530527i	$0.178006\pi$
$492$	−411.500	+	298.972i	−0.836381	+	0.607667i
$493$	374.274	+	121.609i	0.759177	+	0.246671i
$494$		−	78.6598i		−	0.159230i
$495$	−30.2562	+	365.810i	−0.0611237	+	0.739009i
$496$	−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	0.229056	−	0.973413i	$-0.426436\pi$
$499$	−312.340	−	226.929i	−0.625933	−	0.454767i	−0.854989	+	0.518646i	$0.826436\pi$
$500$	−910.905	+	574.831i	−1.82181	+	1.14966i
$501$	−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	$-0.782972\pi$
$503$	−209.753	+	152.395i	−0.417004	+	0.302971i	0.359427	+	0.933173i	$0.382972\pi$
$504$	−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	0.284067	−	0.958805i	$-0.408316\pi$
$509$	653.416	−	474.735i	1.28373	−	0.932681i	0.999659	+	0.0261234i	$0.00831627\pi$
$510$	554.644	−	304.306i	1.08754	−	0.596678i
$511$	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
$515$	406.121	+	382.022i	0.788585	+	0.741791i
$516$			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
$520$	−70.4118	+	13.3699i	−0.135407	+	0.0257113i
$521$	−252.452	−	183.417i	−0.484553	−	0.352048i	0.318533	−	0.947912i	$-0.396810\pi$
$521$	−252.452	−	183.417i	−0.484553	−	0.352048i	−0.803086	+	0.595864i	$0.796810\pi$
$522$	379.887	−	123.433i	0.727753	−	0.236461i
$523$	−22.7612	−	70.0519i	−0.0435205	−	0.133942i	0.926935	−	0.375221i	$-0.122433\pi$
$523$	−22.7612	−	70.0519i	−0.0435205	−	0.133942i	−0.970456	+	0.241279i	$0.922433\pi$
$524$	77.5075	−	106.680i	0.147915	−	0.203588i
$525$	−10.4067	+	40.2477i	−0.0198222	+	0.0766623i
$526$	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
$530$	306.121	+	287.956i	0.577587	+	0.543313i
$531$	−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
$535$	−50.5241	−	92.0880i	−0.0944376	−	0.172127i
$536$	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	0.345197	−	0.938530i	$-0.387812\pi$
$541$	39.3919	+	12.7992i	0.0728132	+	0.0236584i	−0.272384	+	0.962189i	$0.587812\pi$
$542$	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
$545$	587.732	+	74.7545i	1.07841	+	0.137164i
$546$	−3.03449	+	4.17662i	−0.00555768	+	0.00764949i
$547$	521.562	−	378.937i	0.953495	−	0.692755i	0.00186448	−	0.999998i	$-0.499407\pi$
$547$	521.562	−	378.937i	0.953495	−	0.692755i	0.951631	+	0.307243i	$0.0994065\pi$
$548$	−225.169	−	73.1618i	−0.410892	−	0.133507i
$549$		−	227.498i		−	0.414386i
$550$	955.545	+	202.703i	1.73736	+	0.368551i
$551$	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
$555$	−63.1022	+	496.120i	−0.113698	+	0.893910i
$556$	460.916	−	149.761i	0.828985	−	0.269354i
$557$	−362.970	−	263.713i	−0.651652	−	0.473453i	0.212181	−	0.977230i	$-0.431943\pi$
$557$	−362.970	−	263.713i	−0.651652	−	0.473453i	−0.863834	+	0.503777i	$0.831943\pi$
$558$	−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	0.690343	+	0.723482i	$0.257460\pi$
$563$	−165.189	+	508.399i	−0.293408	+	0.903018i	−0.983751	+	0.179536i	$0.942540\pi$
$564$	630.460	−	458.056i	1.11784	−	0.812156i
$565$	−467.240	+	256.352i	−0.826974	+	0.453720i
$566$	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	0.517605	−	0.855620i	$-0.326824\pi$
$569$	−259.513	−	357.190i	−0.456087	−	0.627750i	−0.973692	+	0.227870i	$0.926824\pi$
$570$	470.225	−	499.888i	0.824956	−	0.876997i
$571$			935.409i			1.63819i	0.573655	+	0.819097i	$0.305525\pi$
$571$			935.409i			1.63819i	−0.573655	+	0.819097i	$0.694475\pi$
$572$	69.1020	+	45.7022i	0.120808	+	0.0798990i
$573$			1.42397i			0.00248511i
$574$	−142.544	−	46.3153i	−0.248334	−	0.0806887i
$575$	−208.754	+	807.354i	−0.363050	+	1.40409i
$576$	151.517	+	110.084i	0.263051	+	0.191118i
$577$	−538.104	+	174.841i	−0.932590	+	0.303017i	−0.735621	−	0.677393i	$-0.763110\pi$
$577$	−538.104	+	174.841i	−0.932590	+	0.303017i	−0.196968	+	0.980410i	$0.563110\pi$
$578$	−281.510	−	866.400i	−0.487042	−	1.49896i
$579$	−37.3059	+	51.3471i	−0.0644316	+	0.0886825i
$580$	−135.429	−	713.230i	−0.233498	−	1.22971i
$581$	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
$585$	−19.9836	+	21.2443i	−0.0341601	+	0.0363150i
$586$	163.663	−	118.908i	0.279289	−	0.202915i
$587$	575.718	−	792.407i	0.980780	−	1.34993i	0.0443714	−	0.999015i	$-0.485872\pi$
$587$	575.718	−	792.407i	0.980780	−	1.34993i	0.936408	−	0.350912i	$-0.114128\pi$
$588$	−597.604	+	194.173i	−1.01633	+	0.330227i
$589$	−154.292	+	50.1326i	−0.261956	+	0.0851147i
$590$	324.931	+	592.237i	0.550731	+	1.00379i
$591$	−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	$-0.882572\pi$
$593$	−1106.21			−1.86544			−0.932720	+	0.360600i	$0.882572\pi$
$594$	−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	−0.983400	−	0.181451i	$-0.941921\pi$
$599$	−176.386	−	542.860i	−0.294467	−	0.906276i	0.688933	−	0.724825i	$-0.258079\pi$
$600$	−527.396	−	335.952i	−0.878994	−	0.559920i
$601$	−98.4935	+	135.565i	−0.163883	+	0.225565i	−0.883058	−	0.469263i	$-0.844520\pi$
$601$	−98.4935	+	135.565i	−0.163883	+	0.225565i	0.719176	+	0.694828i	$0.244520\pi$
$602$	−47.2009	+	34.2935i	−0.0784068	+	0.0569659i
$603$	277.392	+	90.1301i	0.460020	+	0.149469i
$604$			405.283i			0.670999i
$605$	−336.491	−	502.791i	−0.556183	−	0.831060i
$606$	433.394			0.715171
$607$	−260.558	+	801.915i	−0.429255	+	1.32111i	0.469605	+	0.882877i	$0.344396\pi$
$607$	−260.558	+	801.915i	−0.429255	+	1.32111i	−0.898860	+	0.438235i	$0.855604\pi$
$608$	−281.206	−	387.046i	−0.462509	−	0.636589i
$609$	−22.6678	−	16.4691i	−0.0372214	−	0.0270429i
$610$	−600.573	−	76.3877i	−0.984547	−	0.125226i
$611$	−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	$-0.787974\pi$
$613$	−270.652	+	196.640i	−0.441520	+	0.320783i	0.344718	+	0.938706i	$0.387974\pi$
$614$	−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	−0.0311923	−	0.999513i	$-0.509930\pi$
$619$	563.143	−	409.147i	0.909762	−	0.660981i	0.940955	+	0.338532i	$0.109930\pi$
$620$	132.701	+	241.868i	0.214034	+	0.390110i
$621$	−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
$625$	546.667	+	302.953i	0.874667	+	0.484724i
$626$			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
$630$	126.958	−	24.1068i	0.201520	−	0.0382648i
$631$	355.498	+	258.284i	0.563388	+	0.409325i	0.832697	−	0.553728i	$-0.186795\pi$
$631$	355.498	+	258.284i	0.563388	+	0.409325i	−0.269309	+	0.963054i	$0.586795\pi$
$632$	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
$635$	630.061	−	119.637i	0.992221	−	0.188404i
$636$	−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
$640$	600.243	−	638.109i	0.937880	−	0.997045i
$641$	611.568	−	444.330i	0.954085	−	0.693183i	0.00231537	−	0.999997i	$-0.499263\pi$
$641$	611.568	−	444.330i	0.954085	−	0.693183i	0.951769	+	0.306814i	$0.0992630\pi$
$642$	66.8951	−	92.0732i	0.104198	−	0.143416i
$643$	−111.604	+	36.2624i	−0.173568	+	0.0563957i	−0.394512	−	0.918891i	$-0.629086\pi$
$643$	−111.604	+	36.2624i	−0.173568	+	0.0563957i	0.220944	+	0.975287i	$0.429086\pi$
$644$	298.034	−	96.8371i	0.462786	−	0.150368i
$645$	100.725	−	55.2630i	0.156163	−	0.0856790i
$646$	−1235.44	−	1700.43i	−1.91244	−	2.63225i
$647$	−997.473	−	324.099i	−1.54169	−	0.500925i	−0.589847	−	0.807515i	$-0.700812\pi$
$647$	−997.473	−	324.099i	−1.54169	−	0.500925i	−0.951842	+	0.306590i	$0.900812\pi$
$648$	−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	$-0.702377\pi$
$653$	231.758	−	318.988i	0.354913	−	0.488496i	0.948723	+	0.316110i	$0.102377\pi$
$654$	198.371	+	610.522i	0.303319	+	0.933521i
$655$	−75.9028	−	9.65418i	−0.115882	−	0.0147392i
$656$	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	$0.237285\pi$
$659$			894.004i			1.35661i	−0.734782	+	0.678303i	$0.762715\pi$
$660$	165.942	+	703.530i	0.251427	+	1.06595i
$661$	−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
$665$	137.011	+	17.4266i	0.206031	+	0.0262054i
$666$	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	−0.360899	−	0.932605i	$-0.617530\pi$
$673$	322.533	−	992.653i	0.479246	−	1.47497i	0.840145	−	0.542362i	$-0.182470\pi$
$674$	−1797.85	+	1306.22i	−2.66744	+	1.93801i
$675$	−596.522	+	36.5140i	−0.883736	+	0.0540948i
$676$	−447.975	−	1378.73i	−0.662685	−	2.03954i
$677$	−60.9269	−	187.514i	−0.0899954	−	0.276977i	0.895922	−	0.444212i	$-0.146516\pi$
$677$	−60.9269	−	187.514i	−0.0899954	−	0.276977i	−0.985917	+	0.167235i	$0.946516\pi$
$678$	−467.165	−	339.415i	−0.689034	−	0.500613i
$679$	42.7058	+	58.7794i	0.0628951	+	0.0865677i
$680$	−1312.14	+	1394.92i	−1.92962	+	2.05135i
$681$			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
$685$	25.6277	+	134.967i	0.0374127	+	0.197032i
$686$	−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
$690$	−887.680	+	168.554i	−1.28649	+	0.244281i
$691$	−229.580	+	706.573i	−0.332242	+	1.02254i	0.635822	+	0.771836i	$0.280661\pi$
$691$	−229.580	+	706.573i	−0.332242	+	1.02254i	−0.968064	+	0.250701i	$0.919339\pi$
$692$	1629.12			2.35422
$693$	−66.7582	−	44.1521i	−0.0963322	−	0.0637115i
$694$	1694.64			2.44185
$695$	−204.831	−	192.676i	−0.294721	−	0.277232i
$696$	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
$700$	−14.3497	−	234.429i	−0.0204996	−	0.334898i
$701$	567.996	+	781.779i	0.810265	+	1.11523i	0.991282	+	0.131754i	$0.0420608\pi$
$701$	567.996	+	781.779i	0.810265	+	1.11523i	−0.181018	+	0.983480i	$0.557939\pi$
$702$	−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	0.843238	−	0.537541i	$-0.180647\pi$
$709$	−109.834	−	338.035i	−0.154914	−	0.476777i	−0.998152	+	0.0607633i	$0.980647\pi$
$710$	81.1958	−	638.375i	0.114360	−	0.899120i
$711$	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
$715$	3.96258	−	47.9092i	0.00554208	−	0.0670058i
$716$	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	0.438558	−	0.898703i	$-0.355489\pi$
$719$	−201.778	−	146.600i	−0.280636	−	0.203894i	−0.719195	+	0.694808i	$0.755489\pi$
$720$	−100.137	+	787.297i	−0.139080	+	1.09347i
$721$	−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
$730$	718.052	+	1308.76i	0.983633	+	1.79282i
$731$	−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	$-0.523327\pi$
$733$	−765.506	−	556.173i	−1.04435	−	0.758763i	−0.971129	+	0.238553i	$0.923327\pi$
$734$	−496.570	−	683.471i	−0.676527	−	0.931159i
$735$	265.575	+	249.816i	0.361327	+	0.339886i
$736$			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	−0.0124581	−	0.999922i	$-0.503966\pi$
$739$	−450.994	−	146.537i	−0.610277	−	0.198291i	−0.597818	+	0.801632i	$0.703966\pi$
$740$	−527.097	−	2775.93i	−0.712294	−	3.75126i
$741$	−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	$-0.0481720\pi$
$743$	74.4381	+	229.097i	0.100186	+	0.308340i	−0.888385	+	0.459100i	$0.848172\pi$
$744$	−94.1393	+	129.572i	−0.126531	+	0.174155i
$745$	221.253	+	1165.22i	0.296984	+	1.56405i
$746$	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
$750$	−44.2410	+	675.744i	−0.0589880	+	0.900992i
$751$	−312.684	+	227.179i	−0.416357	+	0.302501i	−0.776171	−	0.630523i	$-0.782840\pi$
$751$	−312.684	+	227.179i	−0.416357	+	0.302501i	0.359813	+	0.933024i	$0.382840\pi$
$752$	−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
$755$	206.174	−	113.118i	0.273079	−	0.149825i
$756$	132.008	+	181.693i	0.174613	+	0.240335i
$757$	−740.817	−	240.706i	−0.978622	−	0.317974i	−0.224331	−	0.974513i	$-0.572020\pi$
$757$	−740.817	−	240.706i	−0.978622	−	0.317974i	−0.754292	+	0.656540i	$0.772020\pi$
$758$	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	0.491370	−	0.870951i	$-0.336496\pi$
$761$	286.870	+	93.2098i	0.376965	+	0.122483i	−0.114405	+	0.993434i	$0.536496\pi$
$762$	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
$765$	−98.3333	+	773.113i	−0.128540	+	1.01061i
$766$	−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	$-0.665218\pi$
$769$		−	1335.43i		−	1.73658i	0.496054	−	0.868292i	$-0.334782\pi$
$770$	−138.973	+	161.411i	−0.180485	+	0.209624i
$771$	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	$-0.110317\pi$
$773$	252.654	+	347.748i	0.326848	+	0.449868i	−0.613695	+	0.789544i	$0.710317\pi$
$774$	−288.930	−	209.920i	−0.373295	−	0.271215i
$775$	86.0045	−	135.015i	0.110974	−	0.174212i
$776$	−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
$785$	639.860	−	351.060i	0.815109	−	0.447210i
$786$	−25.6186	−	78.8460i	−0.0325937	−	0.100313i
$787$	316.259	+	973.345i	0.401854	+	1.23678i	0.923494	+	0.383613i	$0.125320\pi$
$787$	316.259	+	973.345i	0.401854	+	1.23678i	−0.521640	+	0.853166i	$0.674680\pi$
$788$	598.556	+	434.877i	0.759589	+	0.551874i
$789$	−259.009	−	356.495i	−0.328275	−	0.451832i
$790$	−392.523	−	369.230i	−0.496864	−	0.467380i
$791$		−	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
$795$	177.291	−	33.6642i	0.223008	−	0.0423449i
$796$	−547.645	−	397.888i	−0.687996	−	0.499859i
$797$	638.028	−	207.308i	0.800537	−	0.260110i	0.119952	−	0.992780i	$-0.461726\pi$
$797$	638.028	−	207.308i	0.800537	−	0.260110i	0.680585	+	0.732669i	$0.261726\pi$
$798$	46.2437	+	142.324i	0.0579495	+	0.178350i
$799$	−814.005	+	1120.38i	−1.01878	+	1.40223i
$800$	457.039	+	118.174i	0.571298	+	0.147718i
$801$	−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
$805$	−132.446	−	124.587i	−0.164529	−	0.154766i
$806$	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	−0.528317	−	0.849047i	$-0.677177\pi$
$809$	−369.452	+	120.042i	−0.456677	+	0.148383i	0.0716398	+	0.997431i	$0.477177\pi$
$810$	201.642	+	367.523i	0.248941	+	0.453733i
$811$	589.421	+	811.268i	0.726783	+	1.00033i	0.999271	+	0.0381716i	$0.0121534\pi$
$811$	589.421	+	811.268i	0.726783	+	1.00033i	−0.272488	+	0.962159i	$0.587847\pi$
$812$	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
$820$	−1654.14	−	210.393i	−2.01725	−	0.256576i
$821$	313.012	−	430.825i	0.381257	−	0.524756i	−0.574660	−	0.818393i	$-0.694866\pi$
$821$	313.012	−	430.825i	0.381257	−	0.524756i	0.955917	+	0.293637i	$0.0948656\pi$
$822$	−120.423	+	87.4921i	−0.146499	+	0.106438i
$823$	−858.981	−	279.100i	−1.04372	−	0.339125i	−0.263519	−	0.964654i	$-0.584883\pi$
$823$	−858.981	−	279.100i	−1.04372	−	0.339125i	−0.780201	+	0.625529i	$0.784883\pi$
$824$		−	1828.75i		−	2.21935i
$825$	311.582	−	280.778i	0.377675	−	0.340337i
$826$	−147.298			−0.178327
$827$	−450.181	+	1385.51i	−0.544354	+	1.67535i	0.178166	+	0.984000i	$0.442983\pi$
$827$	−450.181	+	1385.51i	−0.544354	+	1.67535i	−0.722521	+	0.691349i	$0.757017\pi$
$828$	1127.51	+	1551.89i	1.36173	+	1.87426i
$829$	685.365	+	497.947i	0.826737	+	0.600660i	0.918634	−	0.395109i	$-0.129293\pi$
$829$	685.365	+	497.947i	0.826737	+	0.600660i	−0.0918972	+	0.995768i	$0.529293\pi$
$830$	305.005	−	2398.00i	0.367476	−	2.88916i
$831$	−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	−0.0216603	−	0.999765i	$-0.506895\pi$
$839$	773.960	−	562.315i	0.922480	−	0.670221i	0.944140	+	0.329545i	$0.106895\pi$
$840$	119.540	−	65.5856i	0.142309	−	0.0780781i
$841$	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
$845$	−576.347	+	612.705i	−0.682068	+	0.725095i
$846$			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
$850$	2007.93	+	519.182i	2.36227	+	0.610803i
$851$	−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	0.872624	+	0.488392i	$0.162416\pi$
$853$	387.028	+	1191.15i	0.453726	+	1.39643i	−0.418898	+	0.908033i	$0.637584\pi$
$854$	77.5943	−	106.799i	0.0908598	−	0.125058i
$855$	157.715	+	830.598i	0.184462	+	0.971460i
$856$	−106.460	+	327.651i	−0.124369	+	0.382769i
$857$	628.293			0.733131			0.366565	−	0.930392i	$-0.380534\pi$
$857$	628.293			0.733131			0.366565	+	0.930392i	$0.380534\pi$
$858$	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	$0.463452\pi$
$860$	−444.738	+	472.793i	−0.517137	+	0.549759i
$861$	−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	$-0.756378\pi$
$863$	−774.393	+	251.616i	−0.897327	+	0.291559i	−0.176194	+	0.984356i	$0.556378\pi$
$864$	−429.309	+	139.491i	−0.496886	+	0.161448i
$865$	−454.699	−	828.759i	−0.525663	−	0.958103i
$866$	−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
$875$	−115.253	+	72.7307i	−0.131717	+	0.0831208i
$876$	−649.307	+	893.695i	−0.741218	+	1.02020i
$877$	465.237	−	338.015i	0.530487	−	0.385422i	−0.290053	−	0.957011i	$-0.593673\pi$
$877$	465.237	−	338.015i	0.530487	−	0.385422i	0.820540	+	0.571589i	$0.193673\pi$
$878$	−2531.70	−	822.598i	−2.88348	−	0.936900i
$879$		−	86.8641i		−	0.0988215i
$880$	−679.037	−	1118.06i	−0.771633	−	1.27052i
$881$	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	$-0.147265\pi$
$883$	171.187	+	235.619i	0.193870	+	0.266839i	−0.701005	+	0.713156i	$0.747265\pi$
$884$	142.309	+	103.393i	0.160983	+	0.116961i
$885$	287.740	+	36.5980i	0.325130	+	0.0413537i
$886$	156.548	−	50.8654i	0.176690	−	0.0574102i
$887$	941.224	+	683.839i	1.06113	+	0.770958i	0.974297	−	0.225265i	$-0.0723248\pi$
$887$	941.224	+	683.839i	1.06113	+	0.770958i	0.0868346	+	0.996223i	$0.472325\pi$
$888$	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
$895$	−550.471	−	1003.32i	−0.615051	−	1.12103i
$896$	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
$900$	1337.63	−	526.980i	1.48625	−	0.585534i
$901$		−	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
$905$	61.1304	−	11.6075i	0.0675474	−	0.0128260i
$906$	206.141	+	149.770i	0.227529	+	0.165309i
$907$	223.231	−	72.5322i	0.246120	−	0.0799694i	−0.183359	−	0.983046i	$-0.558697\pi$
$907$	223.231	−	72.5322i	0.246120	−	0.0799694i	0.429479	+	0.903077i	$0.358697\pi$
$908$	−19.8297	−	61.0296i	−0.0218389	−	0.0672132i
$909$	−313.815	+	431.929i	−0.345231	+	0.475169i
$910$	−16.6273	+	3.15721i	−0.0182718	+	0.00346947i
$911$	−173.440	+	533.795i	−0.190385	+	0.585944i	−0.999999	−	0.00101779i	$-0.999676\pi$
$911$	−173.440	+	533.795i	−0.190385	+	0.585944i	0.809615	+	0.586962i	$0.199676\pi$
$912$	−919.061			−1.00774
$913$	−1171.39	+	932.448i	−1.28301	+	1.02130i
$914$	1475.91			1.61479
$915$	−178.112	+	189.348i	−0.194658	+	0.206938i
$916$	−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	0.136187	−	0.990683i	$-0.456515\pi$
$919$	761.551	−	247.443i	0.828673	−	0.269252i	0.692487	+	0.721431i	$0.256515\pi$
$920$	2397.92	−	1315.62i	2.60644	−	1.43002i
$921$	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	0.870875	−	0.491505i	$-0.163553\pi$
$929$	−113.874	−	350.469i	−0.122577	−	0.377254i	−0.993452	+	0.114251i	$0.963553\pi$
$930$	172.062	+	21.8848i	0.185013	+	0.0235320i
$931$	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
$935$	−666.803	−	1097.92i	−0.713159	−	1.17424i
$936$	95.6620			0.102203
$937$	10.8560	−	33.4113i	0.0115859	−	0.0356577i	−0.945096	−	0.326792i	$-0.894032\pi$
$937$	10.8560	−	33.4113i	0.0115859	−	0.0356577i	0.956682	+	0.291134i	$0.0940325\pi$
$938$	99.4810	+	136.924i	0.106057	+	0.145974i
$939$	65.0612	+	47.2697i	0.0692877	+	0.0503405i
$940$	2534.32	+	322.343i	2.69608	+	0.342918i
$941$	−897.547	+	291.631i	−0.953823	+	0.309916i	−0.744268	−	0.667881i	$-0.767201\pi$
$941$	−897.547	+	291.631i	−0.953823	+	0.309916i	−0.209555	+	0.977797i	$0.567201\pi$
$942$	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
$950$	2245.66	−	137.460i	2.36385	−	0.144695i
$951$	−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	$-0.486468\pi$
$953$	−852.521	−	619.393i	−0.894566	−	0.649940i	−0.937064	+	0.349156i	$0.886468\pi$
$954$	−329.725	−	453.828i	−0.345624	−	0.475711i
$955$	−3.19847	+	3.40024i	−0.00334918	+	0.00356046i
$956$			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
$960$	−39.9224	−	210.249i	−0.0415858	−	0.219010i
$961$	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
$965$	−204.415	+	38.8146i	−0.211829	+	0.0402224i
$966$	60.8822	−	187.376i	0.0630250	−	0.193971i
$967$	−200.406			−0.207246			−0.103623	−	0.994617i	$-0.533043\pi$
$967$	−200.406			−0.207246			−0.103623	+	0.994617i	$0.533043\pi$
$968$	−445.001	+	1933.80i	−0.459712	+	1.99772i
$969$	−902.503			−0.931376
$970$	862.079	+	810.924i	0.888741	+	0.836004i
$971$	253.043	−	183.846i	0.260600	−	0.189337i	−0.449812	−	0.893124i	$-0.648509\pi$
$971$	253.043	−	183.846i	0.260600	−	0.189337i	0.710412	+	0.703787i	$0.248509\pi$
$972$	−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
$975$	33.2651	−	2.03620i	0.0341180	−	0.00208842i
$976$	476.545	+	655.907i	0.488263	+	0.672036i
$977$	467.459	+	151.887i	0.478464	+	0.155462i	0.538313	−	0.842745i	$-0.319062\pi$
$977$	467.459	+	151.887i	0.478464	+	0.155462i	−0.0598491	+	0.998207i	$0.519062\pi$
$978$	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	$-0.654234\pi$
$983$	510.884	−	703.172i	0.519719	−	0.715332i	0.985520	+	0.169557i	$0.0542338\pi$
$984$	−299.138	−	920.653i	−0.304002	−	0.935623i
$985$	54.1674	−	425.873i	0.0549922	−	0.432358i
$986$	−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
$990$	−1202.56	−	503.738i	−1.21471	−	0.508826i
$991$	−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
$995$	−49.5600	+	389.650i	−0.0498091	+	0.391608i
$996$	1701.26	−	552.773i	1.70809	−	0.554993i
$997$	1030.21	+	748.492i	1.03331	+	0.750744i	0.968969	−	0.247184i	$-0.0795051\pi$
$997$	1030.21	+	748.492i	1.03331	+	0.750744i	0.0643420	+	0.997928i	$0.479505\pi$
$998$	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.24.1	✓	40
5.2	odd	4		275.3.x.j.101.1		40
5.3	odd	4		275.3.x.j.101.10		40
5.4	even	2	inner	55.3.h.a.24.10	yes	40
11.4	even	5		605.3.d.b.604.4		40
11.6	odd	10	inner	55.3.h.a.39.10	yes	40
11.7	odd	10		605.3.d.b.604.38		40
55.4	even	10		605.3.d.b.604.37		40
55.17	even	20		275.3.x.j.226.1		40
55.28	even	20		275.3.x.j.226.10		40
55.29	odd	10		605.3.d.b.604.3		40
55.39	odd	10	inner	55.3.h.a.39.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.3.h.a.24.1	✓	40	1.1	even	1	trivial
55.3.h.a.24.10	yes	40	5.4	even	2	inner
55.3.h.a.39.1	yes	40	55.39	odd	10	inner
55.3.h.a.39.10	yes	40	11.6	odd	10	inner
275.3.x.j.101.1		40	5.2	odd	4
275.3.x.j.101.10		40	5.3	odd	4
275.3.x.j.226.1		40	55.17	even	20
275.3.x.j.226.10		40	55.28	even	20
605.3.d.b.604.3		40	55.29	odd	10
605.3.d.b.604.4		40	11.4	even	5
605.3.d.b.604.37		40	55.4	even	10
605.3.d.b.604.38		40	11.7	odd	10

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} +(-0.630874 + 4.96004i) 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} +(-6.68579 + 3.66816i) 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} +(29.5201 - 31.3823i) q^{20} -1.66285i q^{21} +(-39.0346 + 1.71822i) q^{22} -33.3562i q^{23} +(23.7881 + 7.72924i) q^{24} +(-24.2040 - 6.25832i) 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} +(-5.05314 - 26.6121i) q^{30} +(-1.97870 + 6.08982i) q^{31} -18.8828 q^{32} +(-9.25491 + 13.9935i) q^{33} -82.9587 q^{34} +(3.73504 - 3.97066i) 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} +(39.4416 + 71.8884i) 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} +(47.7090 - 74.8962i) q^{50} +(-20.9376 + 28.8182i) q^{51} +(6.09322 - 4.42698i) q^{52} +(-22.5056 - 7.31251i) q^{53} +84.9132i q^{54} +(-53.5311 + 12.6264i) q^{55} -17.8797 q^{56} +(-11.9411 + 36.7511i) q^{57} +(35.1798 + 48.4209i) q^{58} +(-30.7715 - 22.3568i) q^{59} +(65.1871 + 8.29124i) 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} +(9.31389 + 16.9760i) 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} +(-13.9763 - 35.4759i) q^{75} -218.319i q^{76} +(3.20083 - 11.5578i) q^{77} -4.73519i q^{78} +(28.8577 + 9.37643i) q^{79} +(-116.831 + 22.1841i) 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} +(-114.727 + 21.7844i) q^{85} +(16.5366 - 50.8943i) q^{86} +25.6994 q^{87} +(150.464 + 99.5127i) q^{88} -8.46901 q^{89} +(-81.2110 + 86.3341i) 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} +(-111.063 + 60.9346i) 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

Introduction

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