LMFDB - Embedded newform 130.3.r.a.23.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [130,3,Mod(17,130)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(130, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 2])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("130.17"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 130 = 2 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	130.r (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,-14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$3.54224343668$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.6
Character	$\chi$	$=$	130.23
Dual form			130.3.r.a.17.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.366025 - 1.36603i) q^{2} +(0.957104 - 3.57196i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(4.99095 + 0.300686i) q^{5} +(-4.52907 - 2.61486i) q^{6} +(9.12999 - 2.44637i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-4.04863 - 2.33748i) q^{9} +(2.23756 - 6.70771i) q^{10} +(-15.1474 + 8.74538i) q^{11} +(-5.22971 + 5.22971i) q^{12} +(-6.39487 - 11.3184i) q^{13} -13.3672i q^{14} +(5.85090 - 17.5397i) q^{15} +(2.00000 + 3.46410i) q^{16} +(1.68190 + 6.27694i) q^{17} +(-4.67495 + 4.67495i) q^{18} +(-16.0822 + 27.8552i) q^{19} +(-8.34389 - 5.51175i) q^{20} -34.9534i q^{21} +(6.40206 + 23.8928i) q^{22} +(-6.59332 + 24.6066i) q^{23} +(5.22971 + 9.05813i) q^{24} +(24.8192 + 3.00142i) q^{25} +(-17.8019 + 4.59275i) q^{26} +(11.3094 - 11.3094i) q^{27} +(-18.2600 - 4.89274i) q^{28} +(43.3970 - 25.0552i) q^{29} +(-21.8181 - 14.4124i) q^{30} -31.1266i q^{31} +(5.46410 - 1.46410i) q^{32} +(16.7405 + 62.4763i) q^{33} +9.19008 q^{34} +(46.3029 - 9.46447i) q^{35} +(4.67495 + 8.09726i) q^{36} +(-2.27781 + 8.50091i) q^{37} +(32.1644 + 32.1644i) q^{38} +(-46.5493 + 12.0094i) q^{39} +(-10.5833 + 9.38053i) q^{40} +(3.28961 - 1.89926i) q^{41} +(-47.7472 - 12.7938i) q^{42} +(-40.7964 + 10.9313i) q^{43} +34.9815 q^{44} +(-19.5037 - 12.8836i) q^{45} +(31.1999 + 18.0133i) q^{46} +(34.7841 + 34.7841i) q^{47} +(14.2878 - 3.82842i) q^{48} +(34.9367 - 20.1707i) q^{49} +(13.1845 - 32.8050i) q^{50} +24.0307 q^{51} +(-0.242126 + 25.9989i) q^{52} +(-26.8795 - 26.8795i) q^{53} +(-11.3094 - 19.5884i) q^{54} +(-78.2297 + 39.0931i) q^{55} +(-13.3672 + 23.1527i) q^{56} +(84.1054 + 84.1054i) q^{57} +(-18.3417 - 68.4522i) q^{58} +(-32.8679 + 56.9288i) q^{59} +(-27.6737 + 24.5287i) q^{60} +(-22.4306 + 38.8509i) q^{61} +(-42.5197 - 11.3931i) q^{62} +(-42.6823 - 11.4367i) q^{63} -8.00000i q^{64} +(-28.5132 - 58.4123i) q^{65} +91.4717 q^{66} +(11.6697 - 43.5518i) q^{67} +(3.36380 - 12.5539i) q^{68} +(81.5833 + 47.1022i) q^{69} +(4.01933 - 66.7152i) q^{70} +(29.4767 + 17.0184i) q^{71} +(12.7722 - 3.42230i) q^{72} +(6.68149 - 6.68149i) q^{73} +(10.7787 + 6.22309i) q^{74} +(34.4755 - 85.7805i) q^{75} +(55.7104 - 32.1644i) q^{76} +(-116.901 + 116.901i) q^{77} +(-0.633125 + 67.9833i) q^{78} -137.747i q^{79} +(8.94030 + 17.8905i) q^{80} +(-50.6097 - 87.6586i) q^{81} +(-1.39035 - 5.18887i) q^{82} +(-29.6651 + 29.6651i) q^{83} +(-34.9534 + 60.5410i) q^{84} +(6.50690 + 31.8336i) q^{85} +59.7300i q^{86} +(-47.9610 - 178.993i) q^{87} +(12.8041 - 47.7856i) q^{88} +(5.93029 + 10.2716i) q^{89} +(-24.7382 + 21.9268i) q^{90} +(-86.0741 - 87.6923i) q^{91} +(36.0266 - 36.0266i) q^{92} +(-111.183 - 29.7914i) q^{93} +(60.2478 - 34.7841i) q^{94} +(-88.6412 + 134.188i) q^{95} -20.9189i q^{96} +(40.0013 - 10.7183i) q^{97} +(-14.7660 - 55.1073i) q^{98} +81.7685 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 14 q^{2} + 8 q^{5} + 4 q^{7} - 56 q^{8} - 48 q^{9} - 12 q^{10} - 12 q^{11} - 24 q^{13} + 10 q^{15} + 56 q^{16} + 50 q^{17} - 92 q^{18} - 36 q^{19} + 8 q^{20} + 12 q^{22} + 68 q^{23} - 6 q^{25} + 42 q^{26}+ \cdots + 16 q^{99}+O(q^{100}) $ 28 * q - 14 * q^2 + 8 * q^5 + 4 * q^7 - 56 * q^8 - 48 * q^9 - 12 * q^10 - 12 * q^11 - 24 * q^13 + 10 * q^15 + 56 * q^16 + 50 * q^17 - 92 * q^18 - 36 * q^19 + 8 * q^20 + 12 * q^22 + 68 * q^23 - 6 * q^25 + 42 * q^26 - 24 * q^27 - 8 * q^28 + 186 * q^29 + 12 * q^30 + 56 * q^32 - 164 * q^33 - 20 * q^34 - 18 * q^35 + 92 * q^36 + 24 * q^37 + 72 * q^38 + 156 * q^39 - 20 * q^40 + 48 * q^41 - 204 * q^42 + 80 * q^43 + 26 * q^45 - 96 * q^46 + 104 * q^47 + 96 * q^49 + 18 * q^50 - 336 * q^51 - 96 * q^52 + 126 * q^53 + 24 * q^54 - 502 * q^55 - 16 * q^56 + 160 * q^57 - 130 * q^58 + 80 * q^59 + 136 * q^60 - 336 * q^61 - 108 * q^62 + 396 * q^63 + 160 * q^65 - 64 * q^66 - 32 * q^67 + 100 * q^68 + 264 * q^69 + 200 * q^70 - 60 * q^71 + 188 * q^72 - 286 * q^73 + 6 * q^74 - 684 * q^75 + 24 * q^76 + 424 * q^77 + 128 * q^78 + 40 * q^80 + 86 * q^81 + 42 * q^82 - 64 * q^83 - 96 * q^84 + 356 * q^85 + 384 * q^87 + 24 * q^88 - 348 * q^89 - 294 * q^90 + 192 * q^91 + 80 * q^92 - 336 * q^93 + 432 * q^94 - 446 * q^95 - 86 * q^97 - 82 * q^98 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/130\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.366025	−	1.36603i	0.183013	−	0.683013i
$2$	0.366025	−	1.36603i	0.183013	−	0.683013i
$3$	0.957104	−	3.57196i	0.319035	−	1.19065i	−0.601139	−	0.799144i	$-0.705286\pi$
$3$	0.957104	−	3.57196i	0.319035	−	1.19065i	0.920174	−	0.391509i	$-0.128047\pi$
$4$	−1.73205	−	1.00000i	−0.433013	−	0.250000i
$5$	4.99095	+	0.300686i	0.998190	+	0.0601372i
$5$	4.99095	+	0.300686i	0.998190	+	0.0601372i
$6$	−4.52907	−	2.61486i	−0.754844	−	0.435809i
$7$	9.12999	−	2.44637i	1.30428	−	0.349482i	0.461215	−	0.887288i	$-0.347414\pi$
$7$	9.12999	−	2.44637i	1.30428	−	0.349482i	0.843068	+	0.537806i	$0.180747\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$	−4.04863	−	2.33748i	−0.449848	−	0.259720i
$10$	2.23756	−	6.70771i	0.223756	−	0.670771i
$11$	−15.1474	+	8.74538i	−1.37704	+	0.795035i	−0.991802	−	0.127783i	$-0.959214\pi$
$11$	−15.1474	+	8.74538i	−1.37704	+	0.795035i	−0.385238	+	0.922817i	$0.625881\pi$
$12$	−5.22971	+	5.22971i	−0.435809	+	0.435809i
$13$	−6.39487	−	11.3184i	−0.491913	−	0.870644i
$13$	−6.39487	−	11.3184i	−0.491913	−	0.870644i
$14$		−	13.3672i		−	0.954802i
$15$	5.85090	−	17.5397i	0.390060	−	1.16931i
$16$	2.00000	+	3.46410i	0.125000	+	0.216506i
$17$	1.68190	+	6.27694i	0.0989353	+	0.369232i	0.997587	−	0.0694319i	$-0.0221187\pi$
$17$	1.68190	+	6.27694i	0.0989353	+	0.369232i	−0.898651	+	0.438664i	$0.855452\pi$
$18$	−4.67495	+	4.67495i	−0.259720	+	0.259720i
$19$	−16.0822	+	27.8552i	−0.846433	+	1.46606i	0.0379387	+	0.999280i	$0.487921\pi$
$19$	−16.0822	+	27.8552i	−0.846433	+	1.46606i	−0.884371	+	0.466784i	$0.845412\pi$
$20$	−8.34389	−	5.51175i	−0.417195	−	0.275588i
$21$		−	34.9534i		−	1.66445i
$22$	6.40206	+	23.8928i	0.291003	+	1.08604i
$23$	−6.59332	+	24.6066i	−0.286666	+	1.06985i	0.660947	+	0.750432i	$0.270155\pi$
$23$	−6.59332	+	24.6066i	−0.286666	+	1.06985i	−0.947613	+	0.319420i	$0.896512\pi$
$24$	5.22971	+	9.05813i	0.217905	+	0.377422i
$25$	24.8192	+	3.00142i	0.992767	+	0.120057i
$26$	−17.8019	+	4.59275i	−0.684687	+	0.176644i
$27$	11.3094	−	11.3094i	0.418866	−	0.418866i
$28$	−18.2600	−	4.89274i	−0.652142	−	0.174741i
$29$	43.3970	−	25.0552i	1.49645	−	0.863974i	0.496455	−	0.868062i	$-0.334635\pi$
$29$	43.3970	−	25.0552i	1.49645	−	0.863974i	0.999992	+	0.00408808i	$0.00130128\pi$
$30$	−21.8181	−	14.4124i	−0.727270	−	0.480415i
$31$		−	31.1266i		−	1.00408i	−0.864844	−	0.502041i	$-0.832583\pi$
$31$		−	31.1266i		−	1.00408i	0.864844	−	0.502041i	$-0.167417\pi$
$32$	5.46410	−	1.46410i	0.170753	−	0.0457532i
$33$	16.7405	+	62.4763i	0.507287	+	1.89322i
$34$	9.19008			0.270296
$35$	46.3029	−	9.46447i	1.32294	−	0.270413i
$36$	4.67495	+	8.09726i	0.129860	+	0.224924i
$37$	−2.27781	+	8.50091i	−0.0615625	+	0.229754i	−0.989852	−	0.142105i	$-0.954613\pi$
$37$	−2.27781	+	8.50091i	−0.0615625	+	0.229754i	0.928289	+	0.371859i	$0.121280\pi$
$38$	32.1644	+	32.1644i	0.846433	+	0.846433i
$39$	−46.5493	+	12.0094i	−1.19357	+	0.307933i
$40$	−10.5833	+	9.38053i	−0.264582	+	0.234513i
$41$	3.28961	−	1.89926i	0.0802344	−	0.0463233i	−0.459346	−	0.888257i	$-0.651916\pi$
$41$	3.28961	−	1.89926i	0.0802344	−	0.0463233i	0.539580	+	0.841934i	$0.318583\pi$
$42$	−47.7472	−	12.7938i	−1.13684	−	0.304615i
$43$	−40.7964	+	10.9313i	−0.948752	+	0.254217i	−0.699833	−	0.714307i	$-0.746742\pi$
$43$	−40.7964	+	10.9313i	−0.948752	+	0.254217i	−0.248920	+	0.968524i	$0.580075\pi$
$44$	34.9815			0.795035
$45$	−19.5037	−	12.8836i	−0.433415	−	0.286302i
$46$	31.1999	+	18.0133i	0.678259	+	0.391593i
$47$	34.7841	+	34.7841i	0.740087	+	0.740087i	0.972595	−	0.232508i	$-0.0746931\pi$
$47$	34.7841	+	34.7841i	0.740087	+	0.740087i	−0.232508	+	0.972595i	$0.574693\pi$
$48$	14.2878	−	3.82842i	0.297663	−	0.0797587i
$49$	34.9367	−	20.1707i	0.712993	−	0.411647i
$50$	13.1845	−	32.8050i	0.263689	−	0.656101i
$51$	24.0307			0.471191
$52$	−0.242126	+	25.9989i	−0.00465627	+	0.499978i
$53$	−26.8795	−	26.8795i	−0.507161	−	0.507161i	0.406493	−	0.913654i	$-0.366752\pi$
$53$	−26.8795	−	26.8795i	−0.507161	−	0.507161i	−0.913654	+	0.406493i	$0.866752\pi$
$54$	−11.3094	−	19.5884i	−0.209433	−	0.362748i
$55$	−78.2297	+	39.0931i	−1.42236	+	0.710784i
$56$	−13.3672	+	23.1527i	−0.238700	+	0.413441i
$57$	84.1054	+	84.1054i	1.47553	+	1.47553i
$58$	−18.3417	−	68.4522i	−0.316236	−	1.18021i
$59$	−32.8679	+	56.9288i	−0.557082	+	0.964895i	0.440656	+	0.897676i	$0.354746\pi$
$59$	−32.8679	+	56.9288i	−0.557082	+	0.964895i	−0.997738	+	0.0672187i	$0.978587\pi$
$60$	−27.6737	+	24.5287i	−0.461229	+	0.408812i
$61$	−22.4306	+	38.8509i	−0.367715	+	0.636901i	−0.989208	−	0.146519i	$-0.953193\pi$
$61$	−22.4306	+	38.8509i	−0.367715	+	0.636901i	0.621493	+	0.783420i	$0.286526\pi$
$62$	−42.5197	−	11.3931i	−0.685801	−	0.183760i
$63$	−42.6823	−	11.4367i	−0.677496	−	0.181535i
$64$		−	8.00000i		−	0.125000i
$65$	−28.5132	−	58.4123i	−0.438665	−	0.898651i
$66$	91.4717			1.38593
$67$	11.6697	−	43.5518i	0.174174	−	0.650027i	−0.822517	−	0.568741i	$-0.807431\pi$
$67$	11.6697	−	43.5518i	0.174174	−	0.650027i	0.996691	−	0.0812859i	$-0.0259027\pi$
$68$	3.36380	−	12.5539i	0.0494677	−	0.184616i
$69$	81.5833	+	47.1022i	1.18237	+	0.682640i
$70$	4.01933	−	66.7152i	0.0574191	−	0.953074i
$71$	29.4767	+	17.0184i	0.415165	+	0.239696i	0.693007	−	0.720931i	$-0.256286\pi$
$71$	29.4767	+	17.0184i	0.415165	+	0.239696i	−0.277841	+	0.960627i	$0.589619\pi$
$72$	12.7722	−	3.42230i	0.177392	−	0.0475320i
$73$	6.68149	−	6.68149i	0.0915273	−	0.0915273i	−0.659861	−	0.751388i	$-0.729385\pi$
$73$	6.68149	−	6.68149i	0.0915273	−	0.0915273i	0.751388	+	0.659861i	$0.229385\pi$
$74$	10.7787	+	6.22309i	0.145658	+	0.0840959i
$75$	34.4755	−	85.7805i	0.459673	−	1.14374i
$76$	55.7104	−	32.1644i	0.733032	−	0.423216i
$77$	−116.901	+	116.901i	−1.51820	+	1.51820i
$78$	−0.633125	+	67.9833i	−0.00811698	+	0.871581i
$79$		−	137.747i		−	1.74363i	−0.489838	−	0.871814i	$-0.662944\pi$
$79$		−	137.747i		−	1.74363i	0.489838	−	0.871814i	$-0.337056\pi$
$80$	8.94030	+	17.8905i	0.111754	+	0.223632i
$81$	−50.6097	−	87.6586i	−0.624811	−	1.08220i
$82$	−1.39035	−	5.18887i	−0.0169555	−	0.0632789i
$83$	−29.6651	+	29.6651i	−0.357410	+	0.357410i	−0.862858	−	0.505447i	$-0.831328\pi$
$83$	−29.6651	+	29.6651i	−0.357410	+	0.357410i	0.505447	+	0.862858i	$0.331328\pi$
$84$	−34.9534	+	60.5410i	−0.416112	+	0.720727i
$85$	6.50690	+	31.8336i	0.0765517	+	0.374513i
$86$			59.7300i			0.694535i
$87$	−47.9610	−	178.993i	−0.551275	−	2.05739i
$88$	12.8041	−	47.7856i	0.145501	−	0.543019i
$89$	5.93029	+	10.2716i	0.0666325	+	0.115411i	0.897417	−	0.441183i	$-0.145441\pi$
$89$	5.93029	+	10.2716i	0.0666325	+	0.115411i	−0.830784	+	0.556594i	$0.812108\pi$
$90$	−24.7382	+	21.9268i	−0.274868	+	0.243631i
$91$	−86.0741	−	87.6923i	−0.945869	−	0.963652i
$92$	36.0266	−	36.0266i	0.391593	−	0.391593i
$93$	−111.183	−	29.7914i	−1.19551	−	0.320337i
$94$	60.2478	−	34.7841i	0.640934	−	0.370043i
$95$	−88.6412	+	134.188i	−0.933066	+	1.41251i
$96$		−	20.9189i		−	0.217905i
$97$	40.0013	−	10.7183i	0.412385	−	0.110498i	−0.0466609	−	0.998911i	$-0.514858\pi$
$97$	40.0013	−	10.7183i	0.412385	−	0.110498i	0.459046	+	0.888413i	$0.348191\pi$
$98$	−14.7660	−	55.1073i	−0.150673	−	0.562320i
$99$	81.7685			0.825944
$100$	−39.9867	−	30.0178i	−0.399867	−	0.300178i
$101$	27.6675	+	47.9215i	0.273935	+	0.474470i	0.969866	−	0.243639i	$-0.0783412\pi$
$101$	27.6675	+	47.9215i	0.273935	+	0.474470i	−0.695931	+	0.718109i	$0.745008\pi$
$102$	8.79586	−	32.8266i	0.0862339	−	0.321829i
$103$	−44.1479	−	44.1479i	−0.428621	−	0.428621i	0.459538	−	0.888158i	$-0.348015\pi$
$103$	−44.1479	−	44.1479i	−0.428621	−	0.428621i	−0.888158	+	0.459538i	$0.848015\pi$
$104$	35.4265	+	9.84700i	0.340639	+	0.0946827i
$105$	10.5100	−	174.451i	0.100095	−	1.66143i
$106$	−46.5567	+	26.8795i	−0.439214	+	0.253580i
$107$	43.6938	+	11.7077i	0.408353	+	0.109418i	0.457147	−	0.889391i	$-0.348871\pi$
$107$	43.6938	+	11.7077i	0.408353	+	0.109418i	−0.0487943	+	0.998809i	$0.515538\pi$
$108$	−30.8978	+	8.27904i	−0.286091	+	0.0766578i
$109$	−31.2382			−0.286589			−0.143294	−	0.989680i	$-0.545770\pi$
$109$	−31.2382			−0.286589			−0.143294	+	0.989680i	$0.545770\pi$
$110$	24.7681	+	121.173i	0.225165	+	1.10157i
$111$	28.1848	+	16.2725i	0.253917	+	0.146599i
$112$	26.7345	+	26.7345i	0.238700	+	0.238700i
$113$	3.02470	−	0.810466i	0.0267673	−	0.00717227i	−0.245411	−	0.969419i	$-0.578923\pi$
$113$	3.02470	−	0.810466i	0.0267673	−	0.00717227i	0.272178	+	0.962247i	$0.412256\pi$
$114$	145.675	−	84.1054i	1.27785	−	0.737767i
$115$	−40.3058	+	120.828i	−0.350485	+	1.05068i
$116$	−100.221			−0.863974
$117$	−0.565964	+	60.7718i	−0.00483730	+	0.519417i
$118$	65.7357	+	65.7357i	0.557082	+	0.557082i
$119$	30.7115	+	53.1938i	0.258079	+	0.447007i
$120$	23.3776	+	46.7812i	0.194813	+	0.389843i
$121$	92.4633	−	160.151i	0.764160	−	1.32356i
$122$	44.8612	+	44.8612i	0.367715	+	0.367715i
$123$	−3.63557	−	13.5681i	−0.0295575	−	0.110310i
$124$	−31.1266	+	53.9128i	−0.251021	+	0.434780i
$125$	122.969	+	22.4427i	0.983750	+	0.179542i
$126$	−31.2456	+	54.1189i	−0.247981	+	0.429515i
$127$	5.19550	+	1.39213i	0.0409095	+	0.0109617i	0.279216	−	0.960228i	$-0.409926\pi$
$127$	5.19550	+	1.39213i	0.0409095	+	0.0109617i	−0.238306	+	0.971190i	$0.576592\pi$
$128$	−10.9282	−	2.92820i	−0.0853766	−	0.0228766i
$129$			156.185i			1.21074i
$130$	−90.2292	+	17.5694i	−0.694071	+	0.135149i
$131$	−153.628			−1.17273			−0.586365	−	0.810047i	$-0.699442\pi$
$131$	−153.628			−1.17273			−0.586365	+	0.810047i	$0.699442\pi$
$132$	33.4810	−	124.953i	0.253644	−	0.946611i
$133$	−78.6862	+	293.661i	−0.591625	+	2.20798i
$134$	−55.2215	−	31.8821i	−0.412101	−	0.237926i
$135$	59.8451	−	53.0440i	0.443297	−	0.392918i
$136$	−15.9177	−	9.19008i	−0.117042	−	0.0675741i
$137$	19.3710	−	5.19046i	0.141395	−	0.0378865i	−0.187428	−	0.982278i	$-0.560015\pi$
$137$	19.3710	−	5.19046i	0.141395	−	0.0378865i	0.328822	+	0.944392i	$0.393348\pi$
$138$	94.2043	−	94.2043i	0.682640	−	0.682640i
$139$	−170.158	−	98.2408i	−1.22416	−	0.706768i	−0.258357	−	0.966050i	$-0.583181\pi$
$139$	−170.158	−	98.2408i	−1.22416	−	0.706768i	−0.965802	+	0.259281i	$0.916514\pi$
$140$	−89.6634	−	29.9100i	−0.640453	−	0.213643i
$141$	157.539	−	90.9554i	1.11730	−	0.645074i
$142$	34.0368	−	34.0368i	0.239696	−	0.239696i
$143$	195.849	+	115.519i	1.36958	+	0.807824i
$144$		−	18.6998i		−	0.129860i
$145$	224.126	−	112.001i	1.54570	−	0.772418i
$146$	−6.68149	−	11.5727i	−0.0457637	−	0.0792650i
$147$	−38.6109	−	144.098i	−0.262659	−	0.980257i
$148$	12.4462	−	12.4462i	0.0840959	−	0.0840959i
$149$	−32.4564	+	56.2161i	−0.217828	+	0.377289i	−0.954144	−	0.299349i	$-0.903231\pi$
$149$	−32.4564	+	56.2161i	−0.217828	+	0.377289i	0.736316	+	0.676638i	$0.236564\pi$
$150$	−104.559	−	78.4922i	−0.697063	−	0.523281i
$151$		−	87.7534i		−	0.581148i	−0.956852	−	0.290574i	$-0.906154\pi$
$151$		−	87.7534i		−	0.581148i	0.956852	−	0.290574i	$-0.0938463\pi$
$152$	−23.5460	−	87.8749i	−0.154908	−	0.578124i
$153$	7.86281	−	29.3444i	0.0513909	−	0.191793i
$154$	116.901	+	202.479i	0.759101	+	1.31480i
$155$	9.35931	−	155.351i	0.0603827	−	1.00227i
$156$	92.6352	+	25.7485i	0.593816	+	0.165054i
$157$	−53.8086	+	53.8086i	−0.342730	+	0.342730i	−0.857393	−	0.514663i	$-0.827917\pi$
$157$	−53.8086	+	53.8086i	−0.342730	+	0.342730i	0.514663	+	0.857393i	$0.327917\pi$
$158$	−188.165	−	50.4187i	−1.19092	−	0.319106i
$159$	−121.739	+	70.2861i	−0.765655	+	0.442051i
$160$	27.7113	−	5.66428i	0.173196	−	0.0354018i
$161$			240.788i			1.49558i
$162$	−138.268	+	37.0489i	−0.853508	+	0.228697i
$163$	15.0912	+	56.3212i	0.0925842	+	0.345529i	0.996642	−	0.0818810i	$-0.0260928\pi$
$163$	15.0912	+	56.3212i	0.0925842	+	0.345529i	−0.904058	+	0.427410i	$0.859426\pi$
$164$	−7.59703			−0.0463233
$165$	64.7652	+	316.850i	0.392516	+	1.92030i
$166$	29.6651	+	51.3814i	0.178705	+	0.309527i
$167$	−49.7377	+	185.624i	−0.297831	+	1.11152i	0.641112	+	0.767447i	$0.278473\pi$
$167$	−49.7377	+	185.624i	−0.297831	+	1.11152i	−0.938943	+	0.344072i	$0.888193\pi$
$168$	69.9068	+	69.9068i	0.416112	+	0.416112i
$169$	−87.2112	+	144.759i	−0.516042	+	0.856563i
$170$	45.8672	+	2.76332i	0.269807	+	0.0162549i
$171$	130.222	−	75.1836i	0.761531	−	0.439670i
$172$	81.5927	+	21.8627i	0.474376	+	0.127109i
$173$	198.617	−	53.2192i	1.14807	−	0.307625i	0.365880	−	0.930662i	$-0.380768\pi$
$173$	198.617	−	53.2192i	1.14807	−	0.307625i	0.782193	+	0.623037i	$0.214101\pi$
$174$	−262.064			−1.50611
$175$	233.941	−	33.3141i	1.33681	−	0.190366i
$176$	−60.5898	−	34.9815i	−0.344260	−	0.198759i
$177$	171.889	+	171.889i	0.971127	+	0.971127i
$178$	16.2019	−	4.34127i	0.0910217	−	0.0243892i
$179$	−152.430	+	88.0056i	−0.851565	+	0.491651i	−0.861179	−	0.508302i	$-0.830273\pi$
$179$	−152.430	+	88.0056i	−0.851565	+	0.491651i	0.00961348	+	0.999954i	$0.496940\pi$
$180$	20.8977	+	41.8187i	0.116099	+	0.232326i
$181$	−89.9927			−0.497197			−0.248599	−	0.968607i	$-0.579970\pi$
$181$	−89.9927			−0.497197			−0.248599	+	0.968607i	$0.579970\pi$
$182$	−151.295	+	85.4817i	−0.831293	+	0.469680i
$183$	117.306	+	117.306i	0.641014	+	0.641014i
$184$	−36.0266	−	62.3998i	−0.195797	−	0.339130i
$185$	−13.9245	+	41.7427i	−0.0752678	+	0.225636i
$186$	−81.3915	+	140.974i	−0.437589	+	0.757926i
$187$	−80.3707	−	80.3707i	−0.429790	−	0.429790i
$188$	−25.4637	−	95.0319i	−0.135445	−	0.505489i
$189$	75.5875	−	130.921i	0.399934	−	0.692706i
$190$	150.860	+	170.203i	0.793999	+	0.895803i
$191$	−42.7010	+	73.9603i	−0.223565	+	0.387227i	−0.955888	−	0.293731i	$-0.905103\pi$
$191$	−42.7010	+	73.9603i	−0.223565	+	0.387227i	0.732323	+	0.680958i	$0.238436\pi$
$192$	−28.5757	−	7.65683i	−0.148832	−	0.0398793i
$193$	36.3198	+	9.73187i	0.188186	+	0.0504242i	0.351681	−	0.936120i	$-0.385610\pi$
$193$	36.3198	+	9.73187i	0.188186	+	0.0504242i	−0.163495	+	0.986544i	$0.552277\pi$
$194$		−	58.5660i		−	0.301887i
$195$	−235.937	+	45.9415i	−1.20993	+	0.235597i
$196$	−80.6828			−0.411647
$197$	36.5358	−	136.353i	0.185461	−	0.692149i	−0.809071	−	0.587711i	$-0.800029\pi$
$197$	36.5358	−	136.353i	0.185461	−	0.692149i	0.994531	−	0.104437i	$-0.0333042\pi$
$198$	29.9293	−	111.698i	0.151158	−	0.564130i
$199$	−271.836	−	156.944i	−1.36601	−	0.788665i	−0.375593	−	0.926785i	$-0.622561\pi$
$199$	−271.836	−	156.944i	−1.36601	−	0.788665i	−0.990416	+	0.138119i	$0.955894\pi$
$200$	−55.6412	+	43.6355i	−0.278206	+	0.218178i
$201$	−144.396	−	83.3672i	−0.718389	−	0.414762i
$202$	75.5890	−	20.2540i	0.374203	−	0.100267i
$203$	334.919	−	334.919i	1.64985	−	1.64985i
$204$	−41.6224	−	24.0307i	−0.204032	−	0.117798i
$205$	16.9894	−	8.48996i	0.0828749	−	0.0414144i
$206$	−76.4664	+	44.1479i	−0.371196	+	0.214310i
$207$	84.2113	−	84.2113i	0.406818	−	0.406818i
$208$	26.4182	−	44.7892i	0.127011	−	0.215333i
$209$		−	562.580i		−	2.69177i
$210$	−234.457	−	78.2103i	−1.11646	−	0.372430i
$211$	42.4591	+	73.5412i	0.201228	+	0.348537i	0.948924	−	0.315504i	$-0.102174\pi$
$211$	42.4591	+	73.5412i	0.201228	+	0.348537i	−0.747697	+	0.664041i	$0.768840\pi$
$212$	19.6772	+	73.4362i	0.0928169	+	0.346397i
$213$	89.0014	−	89.0014i	0.417847	−	0.417847i
$214$	31.9861	−	55.4015i	0.149468	−	0.258885i
$215$	−206.899	+	42.2909i	−0.962323	+	0.196702i
$216$			45.2375i			0.209433i
$217$	−76.1471	−	284.185i	−0.350908	−	1.30961i
$218$	−11.4340	+	42.6721i	−0.0524494	+	0.195744i
$219$	−17.4711	−	30.2609i	−0.0797769	−	0.138178i
$220$	174.591	+	10.5184i	0.793596	+	0.0478111i
$221$	60.2892	−	59.1766i	0.272802	−	0.267767i
$222$	32.5450	−	32.5450i	0.146599	−	0.146599i
$223$	172.234	+	46.1500i	0.772351	+	0.206951i	0.623410	−	0.781895i	$-0.285747\pi$
$223$	172.234	+	46.1500i	0.772351	+	0.206951i	0.148941	+	0.988846i	$0.452414\pi$
$224$	46.3054	−	26.7345i	0.206721	−	0.119350i
$225$	−93.4679	−	70.1659i	−0.415413	−	0.311848i
$226$		−	4.42847i		−	0.0195950i
$227$	−226.448	+	60.6765i	−0.997567	+	0.267297i	−0.720426	−	0.693532i	$-0.756054\pi$
$227$	−226.448	+	60.6765i	−0.997567	+	0.267297i	−0.277141	+	0.960829i	$0.589387\pi$
$228$	−61.5694	−	229.780i	−0.270041	−	1.00781i
$229$	60.3824			0.263678			0.131839	−	0.991271i	$-0.457912\pi$
$229$	60.3824			0.263678			0.131839	+	0.991271i	$0.457912\pi$
$230$	150.301	+	99.2848i	0.653482	+	0.431673i
$231$	305.681	+	529.454i	1.32329	+	2.29201i
$232$	−36.6834	+	136.904i	−0.158118	+	0.590105i
$233$	−200.345	−	200.345i	−0.859852	−	0.859852i	0.131469	−	0.991320i	$-0.458031\pi$
$233$	−200.345	−	200.345i	−0.859852	−	0.859852i	−0.991320	+	0.131469i	$0.958031\pi$
$234$	82.8086	+	23.0171i	0.353883	+	0.0983638i
$235$	163.147	+	184.065i	0.694241	+	0.783254i
$236$	113.858	−	65.7357i	0.482447	−	0.278541i
$237$	−492.025	−	131.838i	−2.07606	−	0.556278i
$238$	83.9053	−	22.4823i	0.352543	−	0.0944636i
$239$	409.344			1.71274			0.856369	−	0.516365i	$-0.172715\pi$
$239$	409.344			1.71274			0.856369	+	0.516365i	$0.172715\pi$
$240$	72.4611	−	14.8113i	0.301921	−	0.0617137i
$241$	−304.085	−	175.563i	−1.26176	−	0.728479i	−0.288348	−	0.957526i	$-0.593106\pi$
$241$	−304.085	−	175.563i	−1.26176	−	0.728479i	−0.973415	+	0.229047i	$0.926439\pi$
$242$	−184.927	−	184.927i	−0.764160	−	0.764160i
$243$	−222.512	+	59.6218i	−0.915686	+	0.245357i
$244$	77.7019	−	44.8612i	0.318450	−	0.183857i
$245$	180.432	−	90.1660i	0.736458	−	0.368024i
$246$	−19.8651			−0.0807526
$247$	418.120	+	3.89392i	1.69279	+	0.0157649i
$248$	62.2531	+	62.2531i	0.251021	+	0.251021i
$249$	77.5699	+	134.355i	0.311526	+	0.539578i
$250$	75.6670	−	159.764i	0.302668	−	0.639056i
$251$	62.1942	−	107.724i	0.247786	−	0.429177i	−0.715125	−	0.698996i	$-0.753630\pi$
$251$	62.1942	−	107.724i	0.247786	−	0.429177i	0.962911	+	0.269819i	$0.0869638\pi$
$252$	62.4912	+	62.4912i	0.247981	+	0.247981i
$253$	−115.322	−	430.388i	−0.455819	−	1.70114i
$254$	3.80337	−	6.58764i	0.0149739	−	0.0259356i
$255$	119.936	+	7.22570i	0.470338	+	0.0283361i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	209.360	+	56.0979i	0.814632	+	0.218280i	0.641998	−	0.766706i	$-0.278106\pi$
$257$	209.360	+	56.0979i	0.814632	+	0.218280i	0.172633	+	0.984986i	$0.444772\pi$
$258$	213.353	+	57.1678i	0.826951	+	0.221581i
$259$			83.1855i			0.321180i
$260$	−9.02593	+	129.686i	−0.0347151	+	0.498793i
$261$	−234.264			−0.897564
$262$	−56.2316	+	209.859i	−0.214624	+	0.800989i
$263$	−36.3137	+	135.524i	−0.138075	+	0.515302i	0.861891	+	0.507093i	$0.169280\pi$
$263$	−36.3137	+	135.524i	−0.138075	+	0.515302i	−0.999966	+	0.00820946i	$0.997387\pi$
$264$	−158.434	−	91.4717i	−0.600127	−	0.346484i
$265$	−126.072	−	142.237i	−0.475744	−	0.536742i
$266$	372.347	+	214.975i	1.39980	+	0.808175i
$267$	42.3655	−	11.3518i	0.158672	−	0.0425161i
$268$	−63.7643	+	63.7643i	−0.237926	+	0.237926i
$269$	−414.112	−	239.088i	−1.53945	−	0.888802i	−0.998871	−	0.0475099i	$-0.984871\pi$
$269$	−414.112	−	239.088i	−1.53945	−	0.888802i	−0.540580	−	0.841293i	$-0.681795\pi$
$270$	−50.5546	−	101.165i	−0.187239	−	0.374687i
$271$	−198.029	+	114.332i	−0.730735	+	0.421890i	−0.818691	−	0.574234i	$-0.805300\pi$
$271$	−198.029	+	114.332i	−0.730735	+	0.421890i	0.0879561	+	0.996124i	$0.471966\pi$
$272$	−18.3802	+	18.3802i	−0.0675741	+	0.0675741i
$273$	−395.615	+	223.523i	−1.44914	+	0.818764i
$274$		−	28.3612i		−	0.103508i
$275$	−402.196	+	171.589i	−1.46253	+	0.623961i
$276$	−94.2043	−	163.167i	−0.341320	−	0.591184i
$277$	25.7815	+	96.2178i	0.0930740	+	0.347357i	0.996720	−	0.0809225i	$-0.0257866\pi$
$277$	25.7815	+	96.2178i	0.0930740	+	0.347357i	−0.903646	+	0.428279i	$0.859120\pi$
$278$	−196.482	+	196.482i	−0.706768	+	0.706768i
$279$	−72.7576	+	126.020i	−0.260780	+	0.451684i
$280$	−73.6769	+	111.535i	−0.263132	+	0.398338i
$281$			238.944i			0.850336i	0.905114	+	0.425168i	$0.139785\pi$
$281$			238.944i			0.850336i	−0.905114	+	0.425168i	$0.860215\pi$
$282$	−66.5840	−	248.495i	−0.236113	−	0.881187i
$283$	138.823	−	518.096i	0.490542	−	1.83073i	−0.0631469	−	0.998004i	$-0.520114\pi$
$283$	138.823	−	518.096i	0.490542	−	1.83073i	0.553689	−	0.832724i	$-0.313220\pi$
$284$	−34.0368	−	58.9535i	−0.119848	−	0.207583i
$285$	394.477	+	445.055i	1.38413	+	1.56160i
$286$	229.488	−	225.253i	0.802404	−	0.787596i
$287$	25.3878	−	25.3878i	0.0884592	−	0.0884592i
$288$	−25.5444	−	6.84461i	−0.0886959	−	0.0237660i
$289$	213.710	−	123.386i	0.739482	−	0.426940i
$290$	−70.9600	−	347.157i	−0.244690	−	1.19709i
$291$		−	153.142i		−	0.526260i
$292$	−18.2542	+	4.89119i	−0.0625143	+	0.0167507i
$293$	56.2709	+	210.006i	0.192051	+	0.716743i	0.993011	+	0.118025i	$0.0376564\pi$
$293$	56.2709	+	210.006i	0.192051	+	0.716743i	−0.800960	+	0.598718i	$0.795677\pi$
$294$	−210.974			−0.717598
$295$	−181.160	+	274.246i	−0.614100	+	0.929647i
$296$	−12.4462	−	21.5574i	−0.0420479	−	0.0728292i
$297$	−72.4033	+	270.213i	−0.243782	+	0.909808i
$298$	64.9128	+	64.9128i	0.217828	+	0.217828i
$299$	320.670	−	82.7305i	1.07248	−	0.276691i
$300$	−145.494	+	114.101i	−0.484979	+	0.380335i
$301$	−345.728	+	199.606i	−1.14860	+	0.663143i
$302$	−119.873	−	32.1200i	−0.396932	−	0.106358i
$303$	197.654	−	52.9613i	0.652325	−	0.174790i
$304$	−128.658			−0.423216
$305$	−123.632	+	187.159i	−0.405351	+	0.613635i
$306$	−37.2072	−	21.4816i	−0.121592	−	0.0702013i
$307$	79.9309	+	79.9309i	0.260361	+	0.260361i	0.825201	−	0.564840i	$-0.191062\pi$
$307$	79.9309	+	79.9309i	0.260361	+	0.260361i	−0.564840	+	0.825201i	$0.691062\pi$
$308$	319.381	−	85.5778i	1.03695	−	0.277850i
$309$	−199.949	+	115.440i	−0.647083	+	0.373594i
$310$	−208.788	−	69.6475i	−0.673509	−	0.224669i
$311$	397.946			1.27957			0.639785	−	0.768554i	$-0.279023\pi$
$311$	397.946			1.27957			0.639785	+	0.768554i	$0.279023\pi$
$312$	69.0799	−	117.117i	0.221410	−	0.375376i
$313$	171.241	+	171.241i	0.547097	+	0.547097i	0.925600	−	0.378503i	$-0.123561\pi$
$313$	171.241	+	171.241i	0.547097	+	0.547097i	−0.378503	+	0.925600i	$0.623561\pi$
$314$	53.8086	+	93.1993i	0.171365	+	0.296813i
$315$	−209.586	−	69.9138i	−0.665353	−	0.221949i
$316$	−137.747	+	238.584i	−0.435907	+	0.755013i
$317$	−252.091	−	252.091i	−0.795238	−	0.795238i	0.187102	−	0.982340i	$-0.440091\pi$
$317$	−252.091	−	252.091i	−0.795238	−	0.795238i	−0.982340	+	0.187102i	$0.940091\pi$
$318$	51.4530	+	192.025i	0.161802	+	0.603853i
$319$	−438.235	+	759.046i	−1.37378	+	2.37945i
$320$	2.40549	−	39.9276i	0.00751714	−	0.124774i
$321$	83.6390	−	144.867i	0.260558	−	0.451299i
$322$	328.922	+	88.1344i	1.02150	+	0.273709i
$323$	−201.894	−	54.0974i	−0.625059	−	0.167484i
$324$			202.439i			0.624811i
$325$	−124.744	−	300.106i	−0.383829	−	0.923404i
$326$	82.4600			0.252945
$327$	−29.8982	+	111.581i	−0.0914317	+	0.341228i
$328$	−2.78071	+	10.3777i	−0.00847776	+	0.0316394i
$329$	402.673	+	232.483i	1.22393	+	0.706636i
$330$	456.531	+	27.5042i	1.38343	+	0.0833461i
$331$	339.553	+	196.041i	1.02584	+	0.592268i	0.915790	−	0.401658i	$-0.131566\pi$
$331$	339.553	+	196.041i	1.02584	+	0.592268i	0.110049	+	0.993926i	$0.464899\pi$
$332$	81.0465	−	21.7163i	0.244116	−	0.0654106i
$333$	29.0927	−	29.0927i	0.0873654	−	0.0873654i
$334$	235.361	+	135.886i	0.704675	+	0.406844i
$335$	71.3382	−	213.856i	0.212950	−	0.638376i
$336$	121.082	−	69.9068i	0.360363	−	0.208056i
$337$	63.1684	−	63.1684i	0.187443	−	0.187443i	−0.607146	−	0.794590i	$-0.707686\pi$
$337$	63.1684	−	63.1684i	0.187443	−	0.187443i	0.794590	+	0.607146i	$0.207686\pi$
$338$	165.823	+	172.118i	0.490601	+	0.509225i
$339$		−	11.5798i		−	0.0341588i
$340$	20.5633	−	61.6443i	0.0604804	−	0.181307i
$341$	272.214	+	471.488i	0.798280	+	1.38266i
$342$	−55.0382	−	205.405i	−0.160931	−	0.600601i
$343$	−57.8709	+	57.8709i	−0.168720	+	0.168720i
$344$	59.7300	−	103.455i	0.173634	−	0.300742i
$345$	393.015	+	259.615i	1.13918	+	0.752509i
$346$		−	290.795i		−	0.840448i
$347$	−39.7590	−	148.382i	−0.114579	−	0.427615i	0.884676	−	0.466206i	$-0.154380\pi$
$347$	−39.7590	−	148.382i	−0.114579	−	0.427615i	−0.999255	+	0.0385914i	$0.987713\pi$
$348$	−95.9219	+	357.985i	−0.275638	+	1.02869i
$349$	−311.759	−	539.982i	−0.893291	−	1.54723i	−0.835906	−	0.548873i	$-0.815057\pi$
$349$	−311.759	−	539.982i	−0.893291	−	1.54723i	−0.0573854	−	0.998352i	$-0.518276\pi$
$350$	40.1206	−	331.764i	0.114630	−	0.947896i
$351$	−200.326	−	55.6817i	−0.570729	−	0.158637i
$352$	−69.9630	+	69.9630i	−0.198759	+	0.198759i
$353$	221.908	+	59.4601i	0.628635	+	0.168442i	0.559050	−	0.829134i	$-0.311166\pi$
$353$	221.908	+	59.4601i	0.628635	+	0.168442i	0.0695849	+	0.997576i	$0.477833\pi$
$354$	297.721	−	171.889i	0.841021	−	0.485563i
$355$	142.000	+	93.8013i	0.399999	+	0.264229i
$356$		−	23.7212i		−	0.0666325i
$357$	219.400	−	58.7881i	0.614567	−	0.164673i
$358$	64.4246	+	240.436i	0.179957	+	0.671608i
$359$	−140.268			−0.390719			−0.195360	−	0.980732i	$-0.562587\pi$
$359$	−140.268			−0.390719			−0.195360	+	0.980732i	$0.562587\pi$
$360$	64.7745	−	13.2401i	0.179929	−	0.0367781i
$361$	−336.776	−	583.312i	−0.932896	−	1.61582i
$362$	−32.9396	+	122.932i	−0.0909934	+	0.339592i
$363$	−483.557	−	483.557i	−1.33211	−	1.33211i
$364$	61.3923	+	237.962i	0.168660	+	0.653741i
$365$	35.3560	−	31.3380i	0.0968658	−	0.0858575i
$366$	203.179	−	117.306i	0.555135	−	0.320507i
$367$	345.102	+	92.4697i	0.940331	+	0.251961i	0.696255	−	0.717795i	$-0.254848\pi$
$367$	345.102	+	92.4697i	0.940331	+	0.251961i	0.244077	+	0.969756i	$0.421515\pi$
$368$	−98.4264	+	26.3733i	−0.267463	+	0.0716665i
$369$	−17.7579			−0.0481243
$370$	51.9248	+	34.3002i	0.140337	+	0.0927031i
$371$	−311.167	−	179.652i	−0.838725	−	0.484238i
$372$	162.783	+	162.783i	0.437589	+	0.437589i
$373$	443.794	−	118.914i	1.18980	−	0.318805i	0.390991	−	0.920395i	$-0.372132\pi$
$373$	443.794	−	118.914i	1.18980	−	0.318805i	0.798805	+	0.601590i	$0.205466\pi$
$374$	−139.206	+	80.3707i	−0.372209	+	0.214895i
$375$	197.858	−	417.760i	0.527622	−	1.11403i
$376$	−139.136			−0.370043
$377$	−561.103	−	330.958i	−1.48834	−	0.877872i
$378$	−151.175	−	151.175i	−0.399934	−	0.399934i
$379$	164.712	+	285.289i	0.434595	+	0.752741i	0.997263	−	0.0739425i	$-0.0235581\pi$
$379$	164.712	+	285.289i	0.434595	+	0.752741i	−0.562667	+	0.826683i	$0.690225\pi$
$380$	287.719	−	143.780i	0.757156	−	0.378368i
$381$	9.94528	−	17.2257i	0.0261031	−	0.0452119i
$382$	85.4020	+	85.4020i	0.223565	+	0.223565i
$383$	−64.4543	−	240.547i	−0.168288	−	0.628059i	−0.997598	−	0.0692705i	$-0.977933\pi$
$383$	−64.4543	−	240.547i	−0.168288	−	0.628059i	0.829310	−	0.558789i	$-0.188734\pi$
$384$	−20.9189	+	36.2325i	−0.0544762	+	0.0943555i
$385$	−618.600	+	548.299i	−1.60675	+	1.42415i
$386$	26.5880	−	46.0517i	0.0688808	−	0.119305i
$387$	190.721	+	51.1035i	0.492819	+	0.132051i
$388$	−80.0027	−	21.4367i	−0.206192	−	0.0552491i
$389$			155.086i			0.398679i	0.979931	+	0.199339i	$0.0638796\pi$
$389$			155.086i			0.398679i	−0.979931	+	0.199339i	$0.936120\pi$
$390$	−23.6015	+	339.111i	−0.0605167	+	0.869516i
$391$	−165.543			−0.423385
$392$	−29.5319	+	110.215i	−0.0753366	+	0.281160i
$393$	−147.038	+	548.752i	−0.374142	+	1.39632i
$394$	−172.889	−	99.8175i	−0.438805	−	0.253344i
$395$	41.4184	−	687.486i	0.104857	−	1.74047i
$396$	−141.627	−	81.7685i	−0.357644	−	0.206486i
$397$	619.115	−	165.891i	1.55948	−	0.417862i	0.626984	−	0.779032i	$-0.284289\pi$
$397$	619.115	−	165.891i	1.55948	−	0.417862i	0.932500	+	0.361170i	$0.117623\pi$
$398$	−313.889	+	313.889i	−0.788665	+	0.788665i
$399$	973.634	+	562.128i	2.44019	+	1.40884i
$400$	39.2411	+	91.9790i	0.0981029	+	0.229947i
$401$	284.878	−	164.474i	0.710419	−	0.410161i	−0.100797	−	0.994907i	$-0.532139\pi$
$401$	284.878	−	164.474i	0.710419	−	0.410161i	0.811216	+	0.584746i	$0.198806\pi$
$402$	−166.734	+	166.734i	−0.414762	+	0.414762i
$403$	−352.302	+	199.050i	−0.874198	+	0.493922i
$404$		−	110.670i		−	0.273935i
$405$	−226.233	−	452.717i	−0.558600	−	1.11782i
$406$	−334.919	−	580.097i	−0.824924	−	1.42881i
$407$	−39.8406	−	148.687i	−0.0978886	−	0.365325i
$408$	−48.0615	+	48.0615i	−0.117798	+	0.117798i
$409$	−124.816	+	216.188i	−0.305174	+	0.528576i	−0.977300	−	0.211860i	$-0.932048\pi$
$409$	−124.816	+	216.188i	−0.305174	+	0.528576i	0.672126	+	0.740436i	$0.265381\pi$
$410$	−5.37896	−	26.3154i	−0.0131194	−	0.0641840i
$411$		−	74.1604i		−	0.180439i
$412$	32.3185	+	120.614i	0.0784430	+	0.292753i
$413$	−160.814	+	600.166i	−0.389380	+	1.45319i
$414$	−84.2113	−	145.858i	−0.203409	−	0.352314i
$415$	−156.977	+	139.137i	−0.378257	+	0.335270i
$416$	−51.5135	−	52.4820i	−0.123831	−	0.126159i
$417$	−513.771	+	513.771i	−1.23207	+	1.23207i
$418$	−768.499	−	205.919i	−1.83851	−	0.492629i
$419$	320.679	−	185.144i	0.765343	−	0.441871i	−0.0658681	−	0.997828i	$-0.520982\pi$
$419$	320.679	−	185.144i	0.765343	−	0.441871i	0.831211	+	0.555958i	$0.187648\pi$
$420$	−192.654	+	291.647i	−0.458701	+	0.694398i
$421$			161.740i			0.384180i	0.981377	+	0.192090i	$0.0615265\pi$
$421$			161.740i			0.384180i	−0.981377	+	0.192090i	$0.938474\pi$
$422$	116.000	−	31.0822i	0.274882	−	0.0736545i
$423$	−59.5208	−	222.135i	−0.140711	−	0.525141i
$424$	107.518			0.253580
$425$	22.9037	+	160.837i	0.0538910	+	0.378439i
$426$	−89.0014	−	154.155i	−0.208923	−	0.361866i
$427$	−109.747	+	409.582i	−0.257019	+	0.959209i
$428$	−63.9721	−	63.9721i	−0.149468	−	0.149468i
$429$	600.077	−	589.003i	1.39878	−	1.37297i
$430$	−17.9600	+	298.109i	−0.0417674	+	0.693278i
$431$	542.607	−	313.274i	1.25895	−	0.726855i	0.286079	−	0.958206i	$-0.407648\pi$
$431$	542.607	−	313.274i	1.25895	−	0.726855i	0.972870	+	0.231351i	$0.0743146\pi$
$432$	61.7956	+	16.5581i	0.143045	+	0.0383289i
$433$	−277.369	+	74.3207i	−0.640574	+	0.171641i	−0.564464	−	0.825458i	$-0.690917\pi$
$433$	−277.369	+	74.3207i	−0.640574	+	0.171641i	−0.0761107	+	0.997099i	$0.524250\pi$
$434$	−416.076			−0.958700
$435$	−185.550	−	907.765i	−0.426552	−	2.08682i
$436$	54.1061	+	31.2382i	0.124096	+	0.0716471i
$437$	−579.387	−	579.387i	−1.32583	−	1.32583i
$438$	−47.7321	+	12.7898i	−0.108977	+	0.0292004i
$439$	233.856	−	135.017i	0.532702	−	0.307556i	−0.209414	−	0.977827i	$-0.567156\pi$
$439$	233.856	−	135.017i	0.532702	−	0.307556i	0.742116	+	0.670271i	$0.233822\pi$
$440$	78.2732	−	234.646i	0.177894	−	0.533286i
$441$	−188.594			−0.427651
$442$	−58.7694	−	104.017i	−0.132962	−	0.235332i
$443$	160.688	+	160.688i	0.362726	+	0.362726i	0.864816	−	0.502089i	$-0.167435\pi$
$443$	160.688	+	160.688i	0.362726	+	0.362726i	−0.502089	+	0.864816i	$0.667435\pi$
$444$	−32.5450	−	56.3696i	−0.0732996	−	0.126959i
$445$	26.5093	+	53.0480i	0.0595714	+	0.119209i
$446$	126.084	−	218.384i	0.282700	−	0.489651i
$447$	169.738	+	169.738i	0.379726	+	0.379726i
$448$	−19.5710	−	73.0399i	−0.0436852	−	0.163035i
$449$	150.462	−	260.607i	0.335104	−	0.580416i	−0.648401	−	0.761299i	$-0.724562\pi$
$449$	150.462	−	260.607i	0.335104	−	0.580416i	0.983505	+	0.180882i	$0.0578953\pi$
$450$	−130.060	+	101.997i	−0.289022	+	0.226660i
$451$	−33.2194	+	57.5378i	−0.0736573	+	0.127578i
$452$	−6.04940	−	1.62093i	−0.0133836	−	0.00358613i
$453$	−313.452	−	83.9891i	−0.691946	−	0.185406i
$454$			331.543i			0.730270i
$455$	−403.224	−	463.549i	−0.886206	−	1.01879i
$456$	−336.422			−0.737767
$457$	−125.976	+	470.150i	−0.275659	+	1.02877i	0.679739	+	0.733454i	$0.262093\pi$
$457$	−125.976	+	470.150i	−0.275659	+	1.02877i	−0.955398	+	0.295320i	$0.904574\pi$
$458$	22.1015	−	82.4839i	0.0482565	−	0.180096i
$459$	90.0095	+	51.9670i	0.196099	+	0.113218i
$460$	190.639	−	168.974i	0.414434	−	0.367335i
$461$	161.057	+	92.9865i	0.349365	+	0.201706i	0.664406	−	0.747372i	$-0.268685\pi$
$461$	161.057	+	92.9865i	0.349365	+	0.201706i	−0.315040	+	0.949078i	$0.602018\pi$
$462$	835.135	−	223.774i	1.80765	−	0.484359i
$463$	−461.114	+	461.114i	−0.995926	+	0.995926i	−0.999992	−	0.00406556i	$-0.998706\pi$
$463$	−461.114	+	461.114i	−0.995926	+	0.995926i	0.00406556	+	0.999992i	$0.498706\pi$
$464$	173.588	+	100.221i	0.374112	+	0.215994i
$465$	−545.950	−	182.118i	−1.17409	−	0.391652i
$466$	−347.008	+	200.345i	−0.744653	+	0.429926i
$467$	304.019	−	304.019i	0.651004	−	0.651004i	−0.302231	−	0.953235i	$-0.597731\pi$
$467$	304.019	−	304.019i	0.651004	−	0.651004i	0.953235	+	0.302231i	$0.0977313\pi$
$468$	61.7520	−	104.694i	0.131949	−	0.223705i
$469$		−	426.176i		−	0.908690i
$470$	311.153	−	155.490i	0.662027	−	0.330830i
$471$	140.702	+	243.703i	0.298730	+	0.517416i
$472$	−48.1219	−	179.593i	−0.101953	−	0.380494i
$473$	522.362	−	522.362i	1.10436	−	1.10436i
$474$	−360.188	+	623.863i	−0.759889	+	1.31617i
$475$	−482.753	+	643.074i	−1.01632	+	1.35384i
$476$		−	122.846i		−	0.258079i
$477$	45.9950	+	171.656i	0.0964255	+	0.359865i
$478$	149.830	−	559.175i	0.313453	−	1.16982i
$479$	−9.56574	−	16.5684i	−0.0199702	−	0.0345895i	0.855868	−	0.517195i	$-0.173024\pi$
$479$	−9.56574	−	16.5684i	−0.0199702	−	0.0345895i	−0.875838	+	0.482606i	$0.839690\pi$
$480$	6.29000	−	104.405i	0.0131042	−	0.217510i
$481$	110.783	−	28.5811i	0.230318	−	0.0594202i
$482$	−351.127	+	351.127i	−0.728479	+	0.728479i
$483$	860.084	+	230.459i	1.78071	+	0.477140i
$484$	−320.302	+	184.927i	−0.661782	+	0.382080i
$485$	202.868	−	41.4668i	0.418284	−	0.0854986i
$486$			325.780i			0.670329i
$487$	319.367	−	85.5740i	0.655784	−	0.175717i	0.0844412	−	0.996428i	$-0.473089\pi$
$487$	319.367	−	85.5740i	0.655784	−	0.175717i	0.571342	+	0.820712i	$0.306423\pi$
$488$	−32.8407	−	122.563i	−0.0672965	−	0.251154i
$489$	215.621			0.440943
$490$	−57.1262	−	279.478i	−0.116584	−	0.570363i
$491$	−109.202	−	189.143i	−0.222407	−	0.385221i	0.733131	−	0.680087i	$-0.238058\pi$
$491$	−109.202	−	189.143i	−0.222407	−	0.385221i	−0.955538	+	0.294867i	$0.904725\pi$
$492$	−7.27115	+	27.1363i	−0.0147788	+	0.0551551i
$493$	230.260	+	230.260i	0.467058	+	0.467058i
$494$	158.362	−	569.737i	0.320570	−	1.15331i
$495$	408.102	+	24.5866i	0.824449	+	0.0496699i
$496$	107.826	−	62.2531i	0.217390	−	0.125510i
$497$	310.756	+	83.2667i	0.625263	+	0.167539i
$498$	211.925	−	56.7851i	0.425552	−	0.114026i
$499$	−256.760			−0.514550			−0.257275	−	0.966338i	$-0.582825\pi$
$499$	−256.760			−0.514550			−0.257275	+	0.966338i	$0.582825\pi$
$500$	−190.546	−	161.841i	−0.381091	−	0.323681i
$501$	615.436	+	355.322i	1.22842	+	0.709226i
$502$	−124.388	−	124.388i	−0.247786	−	0.247786i
$503$	−626.540	+	167.881i	−1.24561	+	0.333759i	−0.820638	−	0.571449i	$-0.806382\pi$
$503$	−626.540	+	167.881i	−1.24561	+	0.333759i	−0.424969	+	0.905208i	$0.639715\pi$
$504$	108.238	−	62.4912i	0.214758	−	0.123990i
$505$	123.678	+	247.493i	0.244906	+	0.490085i
$506$	−630.132			−1.24532
$507$	433.604	+	450.064i	0.855235	+	0.887701i
$508$	−7.60675	−	7.60675i	−0.0149739	−	0.0149739i
$509$	−18.5630	−	32.1521i	−0.0364696	−	0.0631672i	0.847215	−	0.531251i	$-0.178278\pi$
$509$	−18.5630	−	32.1521i	−0.0364696	−	0.0631672i	−0.883684	+	0.468084i	$0.844945\pi$
$510$	53.7702	−	161.191i	0.105432	−	0.316061i
$511$	44.6565	−	77.3474i	0.0873904	−	0.151365i
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	133.145	+	496.905i	0.259543	+	0.968626i
$514$	153.262	−	265.458i	0.298176	−	0.516456i
$515$	−207.065	−	233.615i	−0.402069	−	0.453621i
$516$	156.185	−	270.521i	0.302685	−	0.524266i
$517$	−831.090	−	222.690i	−1.60752	−	0.430735i
$518$	113.634	+	30.4480i	0.219370	+	0.0587799i
$519$		−	760.387i		−	1.46510i
$520$	173.851	+	59.7981i	0.334329	+	0.114996i
$521$	306.347			0.587998			0.293999	−	0.955806i	$-0.405014\pi$
$521$	306.347			0.587998			0.293999	+	0.955806i	$0.405014\pi$
$522$	−85.7467	+	320.011i	−0.164266	+	0.613048i
$523$	200.278	−	747.447i	0.382940	−	1.42915i	−0.458448	−	0.888721i	$-0.651594\pi$
$523$	200.278	−	747.447i	0.382940	−	1.42915i	0.841388	−	0.540431i	$-0.181739\pi$
$524$	266.091	+	153.628i	0.507807	+	0.293182i
$525$	104.910	−	867.514i	0.199828	−	1.65241i
$526$	171.838	+	99.2108i	0.326689	+	0.188614i
$527$	195.379	−	52.3518i	0.370739	−	0.0993392i
$528$	−182.943	+	182.943i	−0.346484	+	0.346484i
$529$	−103.886	−	59.9783i	−0.196381	−	0.113381i
$530$	−240.445	+	120.155i	−0.453669	+	0.226708i
$531$	266.139	−	153.656i	0.501204	−	0.289370i
$532$	429.949	−	429.949i	0.808175	−	0.808175i
$533$	−42.5331	−	25.0875i	−0.0797995	−	0.0470685i
$534$		−	62.0274i		−	0.116156i
$535$	214.553	+	71.5707i	0.401034	+	0.133777i
$536$	63.7643	+	110.443i	0.118963	+	0.206050i
$537$	168.461	+	628.705i	0.313708	+	1.17077i
$538$	−478.176	+	478.176i	−0.888802	+	0.888802i
$539$	−352.801	+	611.069i	−0.654547	+	1.13371i
$540$	−156.699	+	32.0297i	−0.290183	+	0.0593143i
$541$		−	407.027i		−	0.752360i	−0.926547	−	0.376180i	$-0.877237\pi$
$541$		−	407.027i		−	0.752360i	0.926547	−	0.376180i	$-0.122763\pi$
$542$	83.6970	+	312.361i	0.154422	+	0.576312i
$543$	−86.1323	+	321.450i	−0.158623	+	0.591989i
$544$	18.3802	+	31.8354i	0.0337870	+	0.0585209i
$545$	−155.908	−	9.39287i	−0.286070	−	0.0172346i
$546$	160.532	+	622.236i	0.294015	+	1.13963i
$547$	80.1695	−	80.1695i	0.146562	−	0.146562i	−0.630018	−	0.776580i	$-0.716953\pi$
$547$	80.1695	−	80.1695i	0.146562	−	0.146562i	0.776580	+	0.630018i	$0.216953\pi$
$548$	−38.7421	−	10.3809i	−0.0706973	−	0.0189433i
$549$	181.626	−	104.862i	0.330831	−	0.191005i
$550$	87.1816	+	612.215i	0.158512	+	1.11312i
$551$			1611.78i			2.92518i
$552$	−257.371	+	68.9623i	−0.466252	+	0.124932i
$553$	−336.979	−	1257.62i	−0.609366	−	2.27418i
$554$	140.873			0.254283
$555$	135.776	+	89.6900i	0.244642	+	0.161604i
$556$	196.482	+	340.316i	0.353384	+	0.612079i
$557$	−43.1606	+	161.077i	−0.0774876	+	0.289187i	−0.993786	−	0.111309i	$-0.964496\pi$
$557$	−43.1606	+	161.077i	−0.0774876	+	0.289187i	0.916298	+	0.400496i	$0.131162\pi$
$558$	145.515	+	145.515i	0.260780	+	0.260780i
$559$	384.613	+	391.844i	0.688037	+	0.700973i
$560$	125.392	+	141.469i	0.223914	+	0.252623i
$561$	−364.004	+	210.158i	−0.648849	+	0.374613i
$562$	326.404	+	87.4597i	0.580790	+	0.155622i
$563$	−1020.80	+	273.522i	−1.81314	+	0.485830i	−0.995900	−	0.0904650i	$-0.971165\pi$
$563$	−1020.80	+	273.522i	−1.81314	+	0.485830i	−0.817242	+	0.576295i	$0.804498\pi$
$564$	−363.822			−0.645074
$565$	15.3398	−	3.13551i	0.0271501	−	0.00554958i
$566$	−656.919	−	379.273i	−1.16063	−	0.670093i
$567$	−676.511	−	676.511i	−1.19314	−	1.19314i
$568$	−92.9903	+	24.9167i	−0.163715	+	0.0438674i
$569$	−942.817	+	544.336i	−1.65697	+	0.956654i	−0.682872	+	0.730538i	$0.739269\pi$
$569$	−942.817	+	544.336i	−1.65697	+	0.956654i	−0.974100	+	0.226116i	$0.927397\pi$
$570$	752.345	−	375.964i	1.31990	−	0.659585i
$571$	561.397			0.983182			0.491591	−	0.870826i	$-0.336415\pi$
$571$	561.397			0.983182			0.491591	+	0.870826i	$0.336415\pi$
$572$	−223.702	−	395.934i	−0.391088	−	0.692192i
$573$	223.314	+	223.314i	0.389728	+	0.389728i
$574$	−25.3878	−	43.9730i	−0.0442296	−	0.0766079i
$575$	−237.495	+	590.926i	−0.413035	+	1.02770i
$576$	−18.6998	+	32.3890i	−0.0324650	+	0.0562310i
$577$	426.261	+	426.261i	0.738754	+	0.738754i	0.972337	−	0.233583i	$-0.0750449\pi$
$577$	426.261	+	426.261i	0.738754	+	0.738754i	−0.233583	+	0.972337i	$0.575045\pi$
$578$	−90.3245	−	337.096i	−0.156271	−	0.583211i
$579$	69.5237	−	120.419i	0.120076	−	0.207977i
$580$	−500.198	−	30.1350i	−0.862410	−	0.0519569i
$581$	−198.270	+	343.413i	−0.341256	+	0.591073i
$582$	−209.196	−	56.0538i	−0.359443	−	0.0963123i
$583$	642.228	+	172.084i	1.10159	+	0.295171i
$584$			26.7260i			0.0457637i
$585$	−21.0979	+	303.139i	−0.0360648	+	0.518186i
$586$	307.470			0.524693
$587$	−72.7637	+	271.558i	−0.123959	+	0.462620i	−0.999800	−	0.0199785i	$-0.993640\pi$
$587$	−72.7637	+	271.558i	−0.123959	+	0.462620i	0.875842	+	0.482598i	$0.160307\pi$
$588$	−77.2218	+	288.196i	−0.131330	+	0.490129i
$589$	867.037	+	500.584i	1.47205	+	0.849888i
$590$	308.318	+	347.849i	0.522573	+	0.589575i
$591$	−452.080	−	261.009i	−0.764941	−	0.441639i
$592$	−34.0036	+	9.11124i	−0.0574386	+	0.0153906i
$593$	567.870	−	567.870i	0.957622	−	0.957622i	−0.0415159	−	0.999138i	$-0.513219\pi$
$593$	567.870	−	567.870i	0.957622	−	0.957622i	0.999138	+	0.0415159i	$0.0132187\pi$
$594$	342.616	+	197.810i	0.576795	+	0.333013i
$595$	137.285	+	274.722i	0.230731	+	0.461718i
$596$	112.432	−	64.9128i	0.188645	−	0.108914i
$597$	−820.774	+	820.774i	−1.37483	+	1.37483i
$598$	4.36148	−	468.325i	0.00729345	−	0.783152i
$599$			1001.31i			1.67163i	0.549008	+	0.835817i	$0.315006\pi$
$599$			1001.31i			1.67163i	−0.549008	+	0.835817i	$0.684994\pi$
$600$	102.610	+	240.512i	0.171017	+	0.400853i
$601$	−222.873	−	386.027i	−0.370837	−	0.642308i	0.618858	−	0.785503i	$-0.287596\pi$
$601$	−222.873	−	386.027i	−0.370837	−	0.642308i	−0.989694	+	0.143195i	$0.954262\pi$
$602$	146.122	+	545.334i	0.242727	+	0.905871i
$603$	−149.047	+	149.047i	−0.247177	+	0.247177i
$604$	−87.7534	+	151.993i	−0.145287	+	0.251645i
$605$	509.635	−	771.504i	0.842372	−	1.27521i
$606$		−	289.386i		−	0.477535i
$607$	−273.374	−	1020.25i	−0.450370	−	1.68080i	−0.701355	−	0.712812i	$-0.747421\pi$
$607$	−273.374	−	1020.25i	−0.450370	−	1.68080i	0.250985	−	0.967991i	$-0.419245\pi$
$608$	−47.0920	+	175.750i	−0.0774540	+	0.289062i
$609$	−875.766	−	1516.87i	−1.43804	−	2.49076i
$610$	210.411	+	237.389i	0.344936	+	0.389163i
$611$	171.259	−	616.139i	0.280294	−	1.00841i
$612$	−42.9632	+	42.9632i	−0.0702013	+	0.0702013i
$613$	608.358	+	163.009i	0.992428	+	0.265920i	0.718270	−	0.695764i	$-0.244934\pi$
$613$	608.358	+	163.009i	0.992428	+	0.265920i	0.274158	+	0.961685i	$0.411601\pi$
$614$	138.444	−	79.9309i	0.225479	−	0.130181i
$615$	−14.0652	−	68.8111i	−0.0228703	−	0.111888i
$616$		−	467.606i		−	0.759101i
$617$	1121.83	−	300.594i	1.81820	−	0.487186i	0.821639	−	0.570008i	$-0.193060\pi$
$617$	1121.83	−	300.594i	1.81820	−	0.487186i	0.996564	+	0.0828220i	$0.0263933\pi$
$618$	84.5083	+	315.389i	0.136745	+	0.510339i
$619$	−343.534			−0.554983			−0.277491	−	0.960728i	$-0.589503\pi$
$619$	−343.534			−0.554983			−0.277491	+	0.960728i	$0.589503\pi$
$620$	−171.562	+	259.717i	−0.276713	+	0.418898i
$621$	203.719	+	352.852i	0.328050	+	0.568199i
$622$	145.659	−	543.605i	0.234178	−	0.873963i
$623$	79.2715	+	79.2715i	0.127242	+	0.127242i
$624$	−134.700	−	137.233i	−0.215866	−	0.219925i
$625$	606.983	+	148.985i	0.971173	+	0.238377i
$626$	296.598	−	171.241i	0.473799	−	0.273548i
$627$	−2009.52	−	538.448i	−3.20497	−	0.858769i
$628$	147.008	−	39.3907i	0.234089	−	0.0627240i
$629$	−57.1907			−0.0909232
$630$	−172.218	+	260.710i	−0.273362	+	0.413825i
$631$	668.388	+	385.894i	1.05925	+	0.611560i	0.925225	−	0.379418i	$-0.123876\pi$
$631$	668.388	+	385.894i	1.05925	+	0.611560i	0.134027	+	0.990978i	$0.457209\pi$
$632$	275.493	+	275.493i	0.435907	+	0.435907i
$633$	303.324	−	81.2755i	0.479185	−	0.128397i
$634$	−436.634	+	252.091i	−0.688697	+	0.397619i
$635$	25.5119	+	8.51027i	0.0401762	+	0.0134020i
$636$	281.145			0.442051
$637$	−451.715	−	266.437i	−0.709129	−	0.418269i
$638$	876.471	+	876.471i	1.37378	+	1.37378i
$639$	−79.5603	−	137.802i	−0.124507	−	0.215653i
$640$	−53.6617	−	17.9005i	−0.0838463	−	0.0279695i
$641$	−7.30475	+	12.6522i	−0.0113959	+	0.0197382i	−0.871667	−	0.490098i	$-0.836961\pi$
$641$	−7.30475	+	12.6522i	−0.0113959	+	0.0197382i	0.860271	+	0.509837i	$0.170294\pi$
$642$	−167.278	−	167.278i	−0.260558	−	0.260558i
$643$	−86.6236	−	323.284i	−0.134718	−	0.502774i	−0.999999	−	0.00148702i	$-0.999527\pi$
$643$	−86.6236	−	323.284i	−0.134718	−	0.502774i	0.865281	−	0.501287i	$-0.167140\pi$
$644$	240.788	−	417.056i	0.373894	−	0.647603i
$645$	−46.9627	+	779.514i	−0.0728104	+	1.20855i
$646$	−147.797	+	255.992i	−0.228788	+	0.396272i
$647$	270.270	+	72.4186i	0.417728	+	0.111930i	0.461560	−	0.887109i	$-0.347290\pi$
$647$	270.270	+	72.4186i	0.417728	+	0.111930i	−0.0438320	+	0.999039i	$0.513957\pi$
$648$	276.537	+	74.0977i	0.426754	+	0.114348i
$649$		−	1149.77i		−	1.77160i
$650$	−455.613	+	60.5574i	−0.700942	+	0.0931653i
$651$	−1087.98			−1.67124
$652$	30.1825	−	112.642i	0.0462921	−	0.172764i
$653$	−165.312	+	616.953i	−0.253158	+	0.944798i	0.715948	+	0.698153i	$0.245995\pi$
$653$	−165.312	+	616.953i	−0.253158	+	0.944798i	−0.969106	+	0.246645i	$0.920672\pi$
$654$	141.480	+	81.6833i	0.216330	+	0.124898i
$655$	−766.748	−	46.1936i	−1.17061	−	0.0705246i
$656$	13.1584	+	7.59703i	0.0200586	+	0.0115808i
$657$	−42.6687	+	11.4330i	−0.0649448	+	0.0174019i
$658$	464.967	−	464.967i	0.706636	−	0.706636i
$659$	131.955	+	76.1841i	0.200235	+	0.115606i	0.596765	−	0.802416i	$-0.296452\pi$
$659$	131.955	+	76.1841i	0.200235	+	0.115606i	−0.396530	+	0.918022i	$0.629786\pi$
$660$	204.673	−	613.565i	0.310111	−	0.929644i
$661$	−1072.17	+	619.016i	−1.62204	+	0.936484i	−0.635665	+	0.771965i	$0.719274\pi$
$661$	−1072.17	+	619.016i	−1.62204	+	0.936484i	−0.986374	+	0.164519i	$0.947393\pi$
$662$	392.082	−	392.082i	0.592268	−	0.592268i
$663$	−153.674	−	271.989i	−0.231785	−	0.410240i
$664$		−	118.660i		−	0.178705i
$665$	−481.019	+	1441.99i	−0.723336	+	2.16840i
$666$	−29.0927	−	50.3900i	−0.0436827	−	0.0756607i
$667$	330.395	+	1233.05i	0.495344	+	1.84865i
$668$	271.772	−	271.772i	0.406844	−	0.406844i
$669$	329.692	−	571.044i	0.492813	−	0.853578i
$670$	−266.021	−	175.726i	−0.397047	−	0.262278i
$671$		−	784.656i		−	1.16938i
$672$	−51.1753	−	190.989i	−0.0761537	−	0.284210i
$673$	132.439	−	494.268i	0.196789	−	0.734425i	−0.795008	−	0.606599i	$-0.792533\pi$
$673$	132.439	−	494.268i	0.196789	−	0.734425i	0.991797	−	0.127826i	$-0.0408000\pi$
$674$	−63.1684	−	109.411i	−0.0937217	−	0.162331i
$675$	314.634	−	246.745i	0.466124	−	0.365549i
$676$	295.813	−	163.519i	0.437594	−	0.241892i
$677$	−67.6239	+	67.6239i	−0.0998876	+	0.0998876i	−0.755285	−	0.655397i	$-0.772501\pi$
$677$	−67.6239	+	67.6239i	−0.0998876	+	0.0998876i	0.655397	+	0.755285i	$0.272501\pi$
$678$	−15.8183	−	4.23851i	−0.0233309	−	0.00625149i
$679$	338.991	−	195.716i	0.499250	−	0.288242i
$680$	−76.6810	−	50.6534i	−0.112766	−	0.0744903i
$681$			866.936i			1.27303i
$682$	743.701	−	199.274i	1.09047	−	0.292191i
$683$	−275.294	−	1027.41i	−0.403066	−	1.50426i	−0.807596	−	0.589736i	$-0.799232\pi$
$683$	−275.294	−	1027.41i	−0.403066	−	1.50426i	0.404530	−	0.914525i	$-0.367435\pi$
$684$	−300.735			−0.439670
$685$	98.2406	−	20.0807i	0.143417	−	0.0293149i
$686$	57.8709	+	100.235i	0.0843599	+	0.146116i
$687$	57.7922	−	215.683i	0.0841226	−	0.313950i
$688$	−119.460	−	119.460i	−0.173634	−	0.173634i
$689$	−132.341	+	476.124i	−0.192077	+	0.691036i
$690$	498.495	−	441.843i	0.722456	−	0.640352i
$691$	388.292	−	224.180i	0.561928	−	0.324429i	−0.191991	−	0.981397i	$-0.561495\pi$
$691$	388.292	−	224.180i	0.561928	−	0.324429i	0.753919	+	0.656968i	$0.228161\pi$
$692$	−397.233	−	106.438i	−0.574036	−	0.153813i
$693$	746.545	−	200.036i	1.07727	−	0.288652i
$694$	−217.247			−0.313036
$695$	−819.711	−	541.479i	−1.17944	−	0.779106i
$696$	453.907	+	262.064i	0.652166	+	0.376528i
$697$	17.4543	+	17.4543i	0.0250421	+	0.0250421i
$698$	−851.740	+	228.223i	−1.22026	+	0.326967i
$699$	−907.377	+	523.875i	−1.29811	+	0.749463i
$700$	−438.512	−	176.240i	−0.626446	−	0.251771i
$701$	−914.172			−1.30410			−0.652049	−	0.758177i	$-0.726090\pi$
$701$	−914.172			−1.30410			−0.652049	+	0.758177i	$0.726090\pi$
$702$	−149.387	+	253.269i	−0.212802	+	0.360782i
$703$	−200.162	−	200.162i	−0.284726	−	0.284726i
$704$	69.9630	+	121.180i	0.0993793	+	0.172130i
$705$	813.620	−	406.584i	1.15407	−	0.576715i
$706$	162.448	−	281.368i	0.230096	−	0.398539i
$707$	369.838	+	369.838i	0.523108	+	0.523108i
$708$	−125.832	−	469.611i	−0.177729	−	0.663292i
$709$	−219.284	+	379.812i	−0.309287	+	0.535700i	−0.978207	−	0.207634i	$-0.933424\pi$
$709$	−219.284	+	379.812i	−0.309287	+	0.535700i	0.668920	+	0.743335i	$0.266757\pi$
$710$	180.110	−	159.642i	0.253677	−	0.224847i
$711$	−321.979	+	557.685i	−0.452854	+	0.784367i
$712$	−32.4037	−	8.68255i	−0.0455108	−	0.0121946i
$713$	765.919	+	205.227i	1.07422	+	0.287836i
$714$		−	321.224i		−	0.449894i
$715$	942.740	+	635.438i	1.31852	+	0.888724i
$716$	352.022			0.491651
$717$	391.785	−	1462.16i	0.546423	−	2.03928i
$718$	−51.3417	+	191.610i	−0.0715066	+	0.266866i
$719$	−434.435	−	250.821i	−0.604222	−	0.348847i	0.166479	−	0.986045i	$-0.446760\pi$
$719$	−434.435	−	250.821i	−0.604222	−	0.348847i	−0.770701	+	0.637198i	$0.780094\pi$
$720$	5.62277	−	93.3299i	0.00780940	−	0.129625i
$721$	−511.072	−	295.068i	−0.708838	−	0.409248i
$722$	−920.088	+	246.537i	−1.27436	+	0.341464i
$723$	−918.147	+	918.147i	−1.26991	+	1.26991i
$724$	155.872	+	89.9927i	0.215293	+	0.124299i
$725$	1152.28	−	491.598i	1.58935	−	0.678067i
$726$	−837.545	+	483.557i	−1.15364	+	0.666056i
$727$	113.132	−	113.132i	0.155614	−	0.155614i	−0.625006	−	0.780620i	$-0.714903\pi$
$727$	113.132	−	113.132i	0.155614	−	0.155614i	0.780620	+	0.625006i	$0.214903\pi$
$728$	347.533	+	3.23655i	0.477380	+	0.00444581i
$729$		−	59.1073i		−	0.0810800i
$730$	−29.8673	−	59.7677i	−0.0409141	−	0.0818736i
$731$	−137.231	−	237.691i	−0.187730	−	0.325158i
$732$	−85.8737	−	320.485i	−0.117314	−	0.437821i
$733$	−278.092	+	278.092i	−0.379389	+	0.379389i	−0.870882	−	0.491493i	$-0.836451\pi$
$733$	−278.092	+	278.092i	−0.379389	+	0.379389i	0.491493	+	0.870882i	$0.336451\pi$
$734$	252.632	−	437.571i	0.344185	−	0.596146i
$735$	−149.377	−	730.795i	−0.203234	−	0.994279i
$736$			144.106i			0.195797i
$737$	204.111	+	761.754i	0.276949	+	1.03359i
$738$	−6.49983	+	24.2577i	−0.00880736	+	0.0328695i
$739$	−223.070	−	386.368i	−0.301853	−	0.522826i	0.674702	−	0.738090i	$-0.264272\pi$
$739$	−223.070	−	386.368i	−0.301853	−	0.522826i	−0.976556	+	0.215264i	$0.930939\pi$
$740$	65.8607	−	58.3759i	0.0890010	−	0.0788864i
$741$	414.093	−	1489.78i	0.558830	−	2.01050i
$742$	−359.305	+	359.305i	−0.484238	+	0.484238i
$743$	−911.785	−	244.312i	−1.22717	−	0.328818i	−0.413691	−	0.910417i	$-0.635761\pi$
$743$	−911.785	−	244.312i	−1.22717	−	0.328818i	−0.813476	+	0.581599i	$0.802427\pi$
$744$	281.948	−	162.783i	0.378963	−	0.218794i
$745$	−178.892	+	270.813i	−0.240123	+	0.363507i
$746$		−	649.759i		−	0.870991i
$747$	189.444	−	50.7614i	0.253607	−	0.0679537i
$748$	58.8354	+	219.577i	0.0786570	+	0.293552i
$749$	427.565			0.570848
$750$	−498.249	−	423.190i	−0.664332	−	0.564254i
$751$	368.361	+	638.020i	0.490494	+	0.849560i	0.999940	−	0.0109424i	$-0.00348315\pi$
$751$	368.361	+	638.020i	0.490494	+	0.849560i	−0.509446	+	0.860502i	$0.670150\pi$
$752$	−50.9274	+	190.064i	−0.0677226	+	0.252744i
$753$	−325.258	−	325.258i	−0.431949	−	0.431949i
$754$	−657.475	+	645.342i	−0.871982	+	0.855891i
$755$	26.3862	−	437.973i	0.0349486	−	0.580097i
$756$	−261.843	+	151.175i	−0.346353	+	0.199967i
$757$	1151.63	+	308.577i	1.52130	+	0.407632i	0.920170	−	0.391518i	$-0.128050\pi$
$757$	1151.63	+	308.577i	1.52130	+	0.407632i	0.601132	+	0.799150i	$0.294717\pi$
$758$	450.000	−	120.577i	0.593668	−	0.159073i
$759$	−1647.70			−2.17089
$760$	−91.0942	−	445.659i	−0.119861	−	0.586394i
$761$	−601.652	−	347.364i	−0.790608	−	0.456458i	0.0495687	−	0.998771i	$-0.484215\pi$
$761$	−601.652	−	347.364i	−0.790608	−	0.456458i	−0.840176	+	0.542313i	$0.817549\pi$
$762$	−19.8906	−	19.8906i	−0.0261031	−	0.0261031i
$763$	−285.204	+	76.4202i	−0.373793	+	0.100157i
$764$	147.921	−	85.4020i	0.193613	−	0.111783i
$765$	48.0663	−	144.092i	0.0628318	−	0.188356i
$766$	−352.185			−0.459771
$767$	854.527	+	7.95816i	1.11412	+	0.0103757i
$768$	41.8377	+	41.8377i	0.0544762	+	0.0544762i
$769$	518.417	+	897.925i	0.674145	+	1.16765i	0.976718	+	0.214527i	$0.0688209\pi$
$769$	518.417	+	897.925i	0.674145	+	1.16765i	−0.302573	+	0.953126i	$0.597846\pi$
$770$	522.567	+	1045.71i	0.678658	+	1.35807i
$771$	400.759	−	694.135i	0.519791	−	0.900305i
$772$	−53.1759	−	53.1759i	−0.0688808	−	0.0688808i
$773$	157.270	+	586.940i	0.203454	+	0.759301i	0.989915	+	0.141661i	$0.0452444\pi$
$773$	157.270	+	586.940i	0.203454	+	0.759301i	−0.786461	+	0.617640i	$0.788089\pi$
$774$	139.617	−	241.825i	0.180384	−	0.312435i
$775$	93.4237	−	772.535i	0.120547	−	0.996820i
$776$	−58.5660	+	101.439i	−0.0754717	+	0.130721i
$777$	297.135	+	79.6172i	0.382414	+	0.102467i
$778$	211.851	+	56.7654i	0.272303	+	0.0729633i
$779$			122.177i			0.156838i
$780$	454.596	+	156.364i	0.582815	+	0.200466i
$781$	−595.330			−0.762266
$782$	−60.5931	+	226.137i	−0.0774848	+	0.289177i
$783$	207.433	−	774.152i	0.264921	−	0.988700i
$784$	139.747	+	80.6828i	0.178248	+	0.102912i
$785$	−284.736	+	252.377i	−0.362721	+	0.321499i
$786$	695.789	+	401.714i	0.885228	+	0.511087i
$787$	1396.31	−	374.141i	1.77422	−	0.475402i	0.784712	−	0.619860i	$-0.212811\pi$
$787$	1396.31	−	374.141i	1.77422	−	0.475402i	0.989511	+	0.144459i	$0.0461440\pi$
$788$	−199.635	+	199.635i	−0.253344	+	0.253344i
$789$	449.332	+	259.422i	0.569496	+	0.328799i
$790$	−923.964	−	308.216i	−1.16957	−	0.390147i
$791$	25.6328	−	14.7991i	0.0324055	−	0.0187093i
$792$	−163.537	+	163.537i	−0.206486	+	0.206486i
$793$	583.170	+	5.43103i	0.735398	+	0.00684871i
$794$		−	906.447i		−	1.14162i
$795$	−628.728	+	314.189i	−0.790853	+	0.395207i
$796$	313.889	+	543.671i	0.394333	+	0.683004i
$797$	−315.082	−	1175.90i	−0.395335	−	1.47541i	−0.821208	−	0.570629i	$-0.806700\pi$
$797$	−315.082	−	1175.90i	−0.395335	−	1.47541i	0.425873	−	0.904783i	$-0.359967\pi$
$798$	1124.26	−	1124.26i	1.40884	−	1.40884i
$799$	−159.834	+	276.841i	−0.200043	+	0.346484i
$800$	140.009	−	19.9378i	0.175011	−	0.0249222i
$801$		−	55.4477i		−	0.0692231i
$802$	−120.404	−	449.352i	−0.150129	−	0.560290i
$803$	−42.7753	+	159.640i	−0.0532694	+	0.198804i
$804$	166.734	+	288.793i	0.207381	+	0.359195i
$805$	−72.4014	+	1201.76i	−0.0899396	+	1.49287i
$806$	142.956	+	554.111i	0.177365	+	0.687483i
$807$	−1250.36	+	1250.36i	−1.54939	+	1.54939i
$808$	−151.178	−	40.5080i	−0.187101	−	0.0501337i
$809$	319.941	−	184.718i	0.395477	−	0.228329i	−0.289054	−	0.957313i	$-0.593341\pi$
$809$	319.941	−	184.718i	0.395477	−	0.228329i	0.684530	+	0.728984i	$0.260007\pi$
$810$	−701.230	+	143.334i	−0.865716	+	0.176955i
$811$		−	1148.78i		−	1.41650i	−0.705962	−	0.708250i	$-0.749485\pi$
$811$		−	1148.78i		−	1.41650i	0.705962	−	0.708250i	$-0.250515\pi$
$812$	−915.016	+	245.178i	−1.12687	+	0.301943i
$813$	218.856	+	816.780i	0.269195	+	1.00465i
$814$	−217.693			−0.267437
$815$	58.3846	+	285.634i	0.0716375	+	0.350471i
$816$	48.0615	+	83.2449i	0.0588989	+	0.102016i
$817$	351.601	−	1312.19i	0.430356	−	1.60611i
$818$	249.632	+	249.632i	0.305174	+	0.305174i
$819$	143.503	+	556.230i	0.175217	+	0.679157i
$820$	−37.9164	−	2.28432i	−0.0462395	−	0.00278575i
$821$	−320.125	+	184.824i	−0.389921	+	0.225121i	−0.682126	−	0.731235i	$-0.738944\pi$
$821$	−320.125	+	184.824i	−0.389921	+	0.225121i	0.292205	+	0.956356i	$0.405611\pi$
$822$	−101.305	−	27.1446i	−0.123242	−	0.0330226i
$823$	913.862	−	244.869i	1.11040	−	0.297532i	0.343409	−	0.939186i	$-0.388418\pi$
$823$	913.862	−	244.869i	1.11040	−	0.297532i	0.766994	+	0.641654i	$0.221751\pi$
$824$	176.592			0.214310
$825$	227.967	+	1600.86i	0.276324	+	1.94043i
$826$	760.980	+	439.352i	0.921283	+	0.531903i
$827$	−365.329	−	365.329i	−0.441752	−	0.441752i	0.450849	−	0.892600i	$-0.351121\pi$
$827$	−365.329	−	365.329i	−0.441752	−	0.441752i	−0.892600	+	0.450849i	$0.851121\pi$
$828$	−230.069	+	61.6469i	−0.277862	+	0.0744528i
$829$	−446.303	+	257.673i	−0.538363	+	0.310824i	−0.744415	−	0.667717i	$-0.767272\pi$
$829$	−446.303	+	257.673i	−0.538363	+	0.310824i	0.206052	+	0.978541i	$0.433938\pi$
$830$	132.607	+	265.362i	0.159768	+	0.319713i
$831$	368.362			0.443275
$832$	−90.5470	+	51.1590i	−0.108831	+	0.0614892i
$833$	185.370	+	185.370i	0.222533	+	0.222533i
$834$	513.771	+	889.878i	0.616033	+	1.06700i
$835$	−304.053	+	911.483i	−0.364135	+	1.09160i
$836$	−562.580	+	974.418i	−0.672943	+	1.16557i
$837$	−352.022	−	352.022i	−0.420576	−	0.420576i
$838$	−135.535	−	505.822i	−0.161736	−	0.603607i
$839$	−731.619	+	1267.20i	−0.872014	+	1.51037i	−0.0121034	+	0.999927i	$0.503853\pi$
$839$	−731.619	+	1267.20i	−0.872014	+	1.51037i	−0.859910	+	0.510445i	$0.829481\pi$
$840$	327.881	+	369.921i	0.390335	+	0.440382i
$841$	835.031	−	1446.32i	0.992903	−	1.71976i
$842$	220.940	+	59.2008i	0.262400	+	0.0703098i
$843$	853.500	+	228.695i	1.01246	+	0.271287i
$844$		−	169.836i		−	0.201228i
$845$	−478.794	+	696.263i	−0.566620	+	0.823979i
$846$	−325.228			−0.384430
$847$	452.400	−	1688.38i	0.534120	−	1.99336i
$848$	39.3544	−	146.872i	0.0464084	−	0.173199i
$849$	−1717.75	−	991.744i	−2.02326	−	1.16813i
$850$	228.090	+	27.5832i	0.268341	+	0.0324509i
$851$	−194.160	−	112.098i	−0.228155	−	0.131725i
$852$	−243.156	+	65.1535i	−0.285395	+	0.0764713i
$853$	−349.156	+	349.156i	−0.409327	+	0.409327i	−0.881504	−	0.472177i	$-0.843468\pi$
$853$	−349.156	+	349.156i	−0.409327	+	0.409327i	0.472177	+	0.881504i	$0.343468\pi$
$854$	519.329	+	299.835i	0.608114	+	0.351095i
$855$	672.538	−	336.082i	0.786594	−	0.393078i
$856$	−110.803	+	63.9721i	−0.129443	+	0.0747338i
$857$	−561.853	+	561.853i	−0.655605	+	0.655605i	−0.954337	−	0.298732i	$-0.903436\pi$
$857$	−561.853	+	561.853i	−0.655605	+	0.655605i	0.298732	+	0.954337i	$0.403436\pi$
$858$	−584.950	−	1035.31i	−0.681760	−	1.20666i
$859$		−	909.479i		−	1.05877i	−0.848383	−	0.529383i	$-0.822424\pi$
$859$		−	909.479i		−	1.05877i	0.848383	−	0.529383i	$-0.177576\pi$
$860$	400.651	+	133.649i	0.465874	+	0.155406i
$861$	−66.3855	−	114.983i	−0.0771027	−	0.133546i
$862$	−229.333	−	855.882i	−0.266047	−	0.992902i
$863$	580.010	−	580.010i	0.672085	−	0.672085i	−0.286111	−	0.958196i	$-0.592363\pi$
$863$	580.010	−	580.010i	0.672085	−	0.672085i	0.958196	+	0.286111i	$0.0923627\pi$
$864$	45.2375	−	78.3537i	0.0523582	−	0.0906871i
$865$	1007.29	−	205.893i	1.16449	−	0.238027i
$866$			406.096i			0.468933i
$867$	−236.186	−	881.457i	−0.272417	−	1.01668i
$868$	−152.294	+	568.370i	−0.175454	+	0.654804i
$869$	1204.65	+	2086.51i	1.38624	+	2.40105i
$870$	−1307.95	−	78.7988i	−1.50339	−	0.0905733i
$871$	−567.562	+	146.427i	−0.651621	+	0.168113i
$872$	62.4763	−	62.4763i	0.0716471	−	0.0716471i
$873$	−187.004	−	50.1077i	−0.214209	−	0.0573971i
$874$	−1003.53	+	579.387i	−1.14820	+	0.662914i
$875$	1177.61	−	95.9260i	1.34584	−	0.109630i
$876$			69.8846i			0.0797769i
$877$	−752.336	+	201.588i	−0.857852	+	0.229861i	−0.660827	−	0.750538i	$-0.729794\pi$
$877$	−752.336	+	201.588i	−0.857852	+	0.229861i	−0.197024	+	0.980399i	$0.563128\pi$
$878$	−98.8393	−	368.873i	−0.112573	−	0.420129i
$879$	803.990			0.914664
$880$	−291.882	−	192.810i	−0.331684	−	0.219102i
$881$	437.302	+	757.429i	0.496370	+	0.859738i	0.999991	−	0.00418638i	$-0.00133257\pi$
$881$	437.302	+	757.429i	0.496370	+	0.859738i	−0.503621	+	0.863925i	$0.667999\pi$
$882$	−69.0302	+	257.624i	−0.0782656	+	0.292091i
$883$	1029.02	+	1029.02i	1.16537	+	1.16537i	0.983283	+	0.182083i	$0.0582839\pi$
$883$	1029.02	+	1029.02i	1.16537	+	1.16537i	0.182083	+	0.983283i	$0.441716\pi$
$884$	−163.601	+	42.2077i	−0.185068	+	0.0477463i
$885$	806.207	+	909.577i	0.910969	+	1.02777i
$886$	278.319	−	160.688i	0.314130	−	0.181363i
$887$	−561.678	−	150.501i	−0.633233	−	0.169674i	−0.0720969	−	0.997398i	$-0.522969\pi$
$887$	−561.678	−	150.501i	−0.633233	−	0.169674i	−0.561137	+	0.827723i	$0.689636\pi$
$888$	−88.9146	+	23.8246i	−0.100129	+	0.0268295i
$889$	50.8406			0.0571885
$890$	82.1680	−	16.7954i	0.0923236	−	0.0188713i
$891$	1533.21	+	885.202i	1.72078	+	0.993493i
$892$	−252.168	−	252.168i	−0.282700	−	0.282700i
$893$	−1528.32	+	409.513i	−1.71145	+	0.458581i
$894$	293.994	−	169.738i	0.328852	−	0.189863i
$895$	−787.233	+	393.398i	−0.879590	+	0.439551i
$896$	−106.938			−0.119350
$897$	11.4047	−	1224.60i	0.0127142	−	1.36522i
$898$	−300.923	−	300.923i	−0.335104	−	0.335104i
$899$	−779.884	−	1350.80i	−0.867501	−	1.50256i
$900$	91.7253	+	214.999i	0.101917	+	0.238887i
$901$	123.512	−	213.930i	0.137084	−	0.237436i
$902$	66.4389	+	66.4389i	0.0736573	+	0.0736573i
$903$	382.088	+	1425.97i	0.423131	+	1.57915i
$904$	−4.42847	+	7.67034i	−0.00489875	+	0.00848489i
$905$	−449.149	−	27.0595i	−0.496297	−	0.0299000i
$906$	−229.463	+	397.441i	−0.253270	+	0.438676i
$907$	61.2317	+	16.4070i	0.0675101	+	0.0180893i	0.292416	−	0.956291i	$-0.405541\pi$
$907$	61.2317	+	16.4070i	0.0675101	+	0.0180893i	−0.224906	+	0.974380i	$0.572207\pi$
$908$	452.896	+	121.353i	0.498784	+	0.133649i
$909$		−	258.688i		−	0.284586i
$910$	−780.810	+	381.143i	−0.858033	+	0.418838i
$911$	419.896			0.460918			0.230459	−	0.973082i	$-0.425977\pi$
$911$	419.896			0.460918			0.230459	+	0.973082i	$0.425977\pi$
$912$	−123.139	+	459.560i	−0.135021	+	0.503904i
$913$	189.918	−	708.782i	0.208015	−	0.776322i
$914$	596.126	+	344.173i	0.652216	+	0.376557i
$915$	550.194	+	620.739i	0.601305	+	0.678403i
$916$	−104.585	−	60.3824i	−0.114176	−	0.0659196i
$917$	−1402.62	+	375.830i	−1.52957	+	0.409848i
$918$	103.934	−	103.934i	0.113218	−	0.113218i
$919$	822.676	+	474.972i	0.895186	+	0.516836i	0.875635	−	0.482973i	$-0.160443\pi$
$919$	822.676	+	474.972i	0.895186	+	0.516836i	0.0195506	+	0.999809i	$0.493776\pi$
$920$	−161.044	−	322.267i	−0.175048	−	0.350290i
$921$	362.012	−	209.008i	0.393064	−	0.226936i
$922$	185.973	−	185.973i	0.201706	−	0.201706i
$923$	4.12060	−	442.459i	0.00446435	−	0.479371i
$924$		−	1222.72i		−	1.32329i
$925$	−82.0481	+	204.149i	−0.0887007	+	0.220701i
$926$	461.114	+	798.673i	0.497963	+	0.862497i
$927$	75.5438	+	281.933i	0.0814928	+	0.304135i
$928$	200.442	−	200.442i	0.215994	−	0.215994i
$929$	218.968	−	379.264i	0.235703	−	0.408249i	−0.723774	−	0.690037i	$-0.757594\pi$
$929$	218.968	−	379.264i	0.235703	−	0.408249i	0.959477	+	0.281788i	$0.0909274\pi$
$930$	−448.610	+	679.122i	−0.482376	+	0.730239i
$931$			1297.56i			1.39372i
$932$	146.663	+	547.354i	0.157364	+	0.587290i
$933$	380.876	−	1421.45i	0.408227	−	1.52353i
$934$	−304.019	−	526.576i	−0.325502	−	0.563786i
$935$	−376.960	−	425.293i	−0.403166	−	0.454858i
$936$	−120.412	−	122.675i	−0.128645	−	0.131064i
$937$	−987.175	+	987.175i	−1.05355	+	1.05355i	−0.0550653	+	0.998483i	$0.517537\pi$
$937$	−987.175	+	987.175i	−1.05355	+	1.05355i	−0.998483	+	0.0550653i	$0.982463\pi$
$938$	−582.167	−	155.991i	−0.620647	−	0.166302i
$939$	775.563	−	447.771i	0.825945	−	0.476860i
$940$	−98.5134	−	481.956i	−0.104801	−	0.512719i
$941$			1057.32i			1.12361i	0.827270	+	0.561804i	$0.189893\pi$
$941$			1057.32i			1.12361i	−0.827270	+	0.561804i	$0.810107\pi$
$942$	384.405	−	103.001i	0.408073	−	0.109343i
$943$	25.0448	+	93.4685i	0.0265587	+	0.0991183i
$944$	−262.943			−0.278541
$945$	416.620	−	630.694i	0.440867	−	0.667401i
$946$	−522.362	−	904.757i	−0.552179	−	0.956403i
$947$	−152.169	+	567.901i	−0.160685	+	0.599684i	0.837866	+	0.545875i	$0.183803\pi$
$947$	−152.169	+	567.901i	−0.160685	+	0.599684i	−0.998551	+	0.0538088i	$0.982864\pi$
$948$	720.375	+	720.375i	0.759889	+	0.759889i
$949$	−118.351	−	32.8963i	−0.124711	−	0.0346642i
$950$	701.756	+	894.834i	0.738691	+	0.941930i
$951$	−1141.73	+	659.181i	−1.20056	+	0.693145i
$952$	−167.811	−	44.9647i	−0.176272	−	0.0472318i
$953$	−1248.44	+	334.517i	−1.31001	+	0.351015i	−0.845225	−	0.534411i	$-0.820533\pi$
$953$	−1248.44	+	334.517i	−1.31001	+	0.351015i	−0.464781	+	0.885426i	$0.653867\pi$
$954$	251.321			0.263439
$955$	−235.357	+	356.293i	−0.246447	+	0.373081i
$956$	−709.005	−	409.344i	−0.741637	−	0.428184i
$957$	2291.85	+	2291.85i	2.39482	+	2.39482i
$958$	−26.1341	+	7.00261i	−0.0272798	+	0.00730961i
$959$	164.160	−	94.7776i	0.171178	−	0.0988296i
$960$	−140.318	−	46.8072i	−0.146164	−	0.0487575i
$961$	−7.86231			−0.00818138
$962$	1.50677	−	161.793i	0.00156629	−	0.168184i
$963$	−149.533	−	149.533i	−0.155279	−	0.155279i
$964$	351.127	+	608.170i	0.364240	+	0.630881i
$965$	178.344	+	59.4922i	0.184813	+	0.0616499i
$966$	629.625	−	1090.54i	0.651786	−	1.12893i
$967$	1041.20	+	1041.20i	1.07673	+	1.07673i	0.996800	+	0.0799303i	$0.0254698\pi$
$967$	1041.20	+	1041.20i	1.07673	+	1.07673i	0.0799303	+	0.996800i	$0.474530\pi$
$968$	135.376	+	505.229i	0.139851	+	0.521931i
$969$	−386.467	+	669.381i	−0.398831	+	0.690796i
$970$	17.6100	−	292.300i	0.0181546	−	0.301340i
$971$	834.105	−	1444.71i	0.859017	−	1.48786i	−0.0138515	−	0.999904i	$-0.504409\pi$
$971$	834.105	−	1444.71i	0.859017	−	1.48786i	0.872868	−	0.487956i	$-0.162257\pi$
$972$	445.023	+	119.244i	0.457843	+	0.122679i
$973$	−1793.87	−	480.667i	−1.84365	−	0.494005i
$974$		−	467.585i		−	0.480067i
$975$	−1191.36	+	158.349i	−1.22191	+	0.162409i
$976$	−179.445			−0.183857
$977$	356.831	−	1331.71i	0.365232	−	1.36306i	−0.501874	−	0.864940i	$-0.667356\pi$
$977$	356.831	−	1331.71i	0.365232	−	1.36306i	0.867106	−	0.498123i	$-0.165977\pi$
$978$	78.9228	−	294.544i	0.0806982	−	0.301170i
$979$	−179.657	−	103.725i	−0.183511	−	0.105950i
$980$	−402.684	−	24.2602i	−0.410902	−	0.0247553i
$981$	126.472	+	73.0185i	0.128921	+	0.0744327i
$982$	−298.345	+	79.9414i	−0.303814	+	0.0814067i
$983$	84.2583	−	84.2583i	0.0857155	−	0.0857155i	−0.662949	−	0.748665i	$-0.730695\pi$
$983$	84.2583	−	84.2583i	0.0857155	−	0.0857155i	0.748665	+	0.662949i	$0.230695\pi$
$984$	34.4074	+	19.8651i	0.0349669	+	0.0201882i
$985$	223.348	−	669.547i	0.226749	−	0.679743i
$986$	398.821	−	230.260i	0.404484	−	0.233529i
$987$	1215.82	−	1215.82i	1.23184	−	1.23184i
$988$	−720.310	−	424.864i	−0.729059	−	0.430024i
$989$		−	1075.93i		−	1.08790i
$990$	182.962	−	548.479i	0.184810	−	0.554019i
$991$	−887.074	−	1536.46i	−0.895131	−	1.55041i	−0.833643	−	0.552304i	$-0.813749\pi$
$991$	−887.074	−	1536.46i	−0.895131	−	1.55041i	−0.0614876	−	0.998108i	$-0.519584\pi$
$992$	−45.5724	−	170.079i	−0.0459400	−	0.171450i
$993$	1025.24	−	1025.24i	1.03246	−	1.03246i
$994$	227.489	−	394.022i	0.228862	−	0.396401i
$995$	−1309.53	−	865.039i	−1.31611	−	0.869386i
$996$		−	310.280i		−	0.311526i
$997$	316.062	+	1179.56i	0.317013	+	1.18311i	0.922101	+	0.386949i	$0.126471\pi$
$997$	316.062	+	1179.56i	0.317013	+	1.18311i	−0.605088	+	0.796158i	$0.706862\pi$
$998$	−93.9808	+	350.741i	−0.0941692	+	0.351444i
$999$	70.3793	+	121.901i	0.0704498	+	0.122023i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	130.3.r.a.23.6	yes	28
5.2	odd	4		130.3.r.b.127.2	yes	28
13.4	even	6		130.3.r.b.43.2	yes	28
65.17	odd	12	inner	130.3.r.a.17.6	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.3.r.a.17.6	✓	28	65.17	odd	12	inner
130.3.r.a.23.6	yes	28	1.1	even	1	trivial
130.3.r.b.43.2	yes	28	13.4	even	6
130.3.r.b.127.2	yes	28	5.2	odd	4

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:	\( N \)	\(=\)	\( 130 = 2 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	130.r (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 - 1.36603i) q^{2} +(0.957104 - 3.57196i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(4.99095 + 0.300686i) q^{5} +(-4.52907 - 2.61486i) q^{6} +(9.12999 - 2.44637i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-4.04863 - 2.33748i) q^{9} +(2.23756 - 6.70771i) q^{10} +(-15.1474 + 8.74538i) q^{11} +(-5.22971 + 5.22971i) q^{12} +(-6.39487 - 11.3184i) q^{13} -13.3672i q^{14} +(5.85090 - 17.5397i) q^{15} +(2.00000 + 3.46410i) q^{16} +(1.68190 + 6.27694i) q^{17} +(-4.67495 + 4.67495i) q^{18} +(-16.0822 + 27.8552i) q^{19} +(-8.34389 - 5.51175i) q^{20} -34.9534i q^{21} +(6.40206 + 23.8928i) q^{22} +(-6.59332 + 24.6066i) q^{23} +(5.22971 + 9.05813i) q^{24} +(24.8192 + 3.00142i) q^{25} +(-17.8019 + 4.59275i) q^{26} +(11.3094 - 11.3094i) q^{27} +(-18.2600 - 4.89274i) q^{28} +(43.3970 - 25.0552i) q^{29} +(-21.8181 - 14.4124i) q^{30} -31.1266i q^{31} +(5.46410 - 1.46410i) q^{32} +(16.7405 + 62.4763i) q^{33} +9.19008 q^{34} +(46.3029 - 9.46447i) q^{35} +(4.67495 + 8.09726i) q^{36} +(-2.27781 + 8.50091i) q^{37} +(32.1644 + 32.1644i) q^{38} +(-46.5493 + 12.0094i) q^{39} +(-10.5833 + 9.38053i) q^{40} +(3.28961 - 1.89926i) q^{41} +(-47.7472 - 12.7938i) q^{42} +(-40.7964 + 10.9313i) q^{43} +34.9815 q^{44} +(-19.5037 - 12.8836i) q^{45} +(31.1999 + 18.0133i) q^{46} +(34.7841 + 34.7841i) q^{47} +(14.2878 - 3.82842i) q^{48} +(34.9367 - 20.1707i) q^{49} +(13.1845 - 32.8050i) q^{50} +24.0307 q^{51} +(-0.242126 + 25.9989i) q^{52} +(-26.8795 - 26.8795i) q^{53} +(-11.3094 - 19.5884i) q^{54} +(-78.2297 + 39.0931i) q^{55} +(-13.3672 + 23.1527i) q^{56} +(84.1054 + 84.1054i) q^{57} +(-18.3417 - 68.4522i) q^{58} +(-32.8679 + 56.9288i) q^{59} +(-27.6737 + 24.5287i) q^{60} +(-22.4306 + 38.8509i) q^{61} +(-42.5197 - 11.3931i) q^{62} +(-42.6823 - 11.4367i) q^{63} -8.00000i q^{64} +(-28.5132 - 58.4123i) q^{65} +91.4717 q^{66} +(11.6697 - 43.5518i) q^{67} +(3.36380 - 12.5539i) q^{68} +(81.5833 + 47.1022i) q^{69} +(4.01933 - 66.7152i) q^{70} +(29.4767 + 17.0184i) q^{71} +(12.7722 - 3.42230i) q^{72} +(6.68149 - 6.68149i) q^{73} +(10.7787 + 6.22309i) q^{74} +(34.4755 - 85.7805i) q^{75} +(55.7104 - 32.1644i) q^{76} +(-116.901 + 116.901i) q^{77} +(-0.633125 + 67.9833i) q^{78} -137.747i q^{79} +(8.94030 + 17.8905i) q^{80} +(-50.6097 - 87.6586i) q^{81} +(-1.39035 - 5.18887i) q^{82} +(-29.6651 + 29.6651i) q^{83} +(-34.9534 + 60.5410i) q^{84} +(6.50690 + 31.8336i) q^{85} +59.7300i q^{86} +(-47.9610 - 178.993i) q^{87} +(12.8041 - 47.7856i) q^{88} +(5.93029 + 10.2716i) q^{89} +(-24.7382 + 21.9268i) q^{90} +(-86.0741 - 87.6923i) q^{91} +(36.0266 - 36.0266i) q^{92} +(-111.183 - 29.7914i) q^{93} +(60.2478 - 34.7841i) q^{94} +(-88.6412 + 134.188i) q^{95} -20.9189i q^{96} +(40.0013 - 10.7183i) q^{97} +(-14.7660 - 55.1073i) q^{98} +81.7685 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 14 q^{2} + 8 q^{5} + 4 q^{7} - 56 q^{8} - 48 q^{9} - 12 q^{10} - 12 q^{11} - 24 q^{13} + 10 q^{15} + 56 q^{16} + 50 q^{17} - 92 q^{18} - 36 q^{19} + 8 q^{20} + 12 q^{22} + 68 q^{23} - 6 q^{25} + 42 q^{26}+ \cdots + 16 q^{99}+O(q^{100}) \) 28 * q - 14 * q^2 + 8 * q^5 + 4 * q^7 - 56 * q^8 - 48 * q^9 - 12 * q^10 - 12 * q^11 - 24 * q^13 + 10 * q^15 + 56 * q^16 + 50 * q^17 - 92 * q^18 - 36 * q^19 + 8 * q^20 + 12 * q^22 + 68 * q^23 - 6 * q^25 + 42 * q^26 - 24 * q^27 - 8 * q^28 + 186 * q^29 + 12 * q^30 + 56 * q^32 - 164 * q^33 - 20 * q^34 - 18 * q^35 + 92 * q^36 + 24 * q^37 + 72 * q^38 + 156 * q^39 - 20 * q^40 + 48 * q^41 - 204 * q^42 + 80 * q^43 + 26 * q^45 - 96 * q^46 + 104 * q^47 + 96 * q^49 + 18 * q^50 - 336 * q^51 - 96 * q^52 + 126 * q^53 + 24 * q^54 - 502 * q^55 - 16 * q^56 + 160 * q^57 - 130 * q^58 + 80 * q^59 + 136 * q^60 - 336 * q^61 - 108 * q^62 + 396 * q^63 + 160 * q^65 - 64 * q^66 - 32 * q^67 + 100 * q^68 + 264 * q^69 + 200 * q^70 - 60 * q^71 + 188 * q^72 - 286 * q^73 + 6 * q^74 - 684 * q^75 + 24 * q^76 + 424 * q^77 + 128 * q^78 + 40 * q^80 + 86 * q^81 + 42 * q^82 - 64 * q^83 - 96 * q^84 + 356 * q^85 + 384 * q^87 + 24 * q^88 - 348 * q^89 - 294 * q^90 + 192 * q^91 + 80 * q^92 - 336 * q^93 + 432 * q^94 - 446 * q^95 - 86 * q^97 - 82 * q^98 + 16 * q^99

Introduction

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