LMFDB - Embedded newform 130.4.n.a.9.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [130,4,Mod(9,130)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("130.9"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(130, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 4])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 130 = 2 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	130.n (of order $6$, degree $2$, 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:	$7.67024830075$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			9.7
Character	$\chi$	$=$	130.9
Dual form			130.4.n.a.29.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.73205 - 1.00000i) q^{2} +(2.13838 + 1.23459i) q^{3} +(2.00000 + 3.46410i) q^{4} +(-10.7802 + 2.96444i) q^{5} +(-2.46918 - 4.27675i) q^{6} +(0.660166 - 0.381147i) q^{7} -8.00000i q^{8} +(-10.4516 - 18.1026i) q^{9} +(21.6362 + 5.64562i) q^{10} +(31.0198 - 53.7278i) q^{11} +9.87674i q^{12} +(30.9407 + 35.2090i) q^{13} -1.52459 q^{14} +(-26.7119 - 6.97004i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(89.1952 - 51.4968i) q^{17} +41.8063i q^{18} +(-38.8754 - 67.3341i) q^{19} +(-31.8295 - 31.4147i) q^{20} +1.88224 q^{21} +(-107.456 + 62.0395i) q^{22} +(-0.835838 - 0.482571i) q^{23} +(9.87674 - 17.1070i) q^{24} +(107.424 - 63.9143i) q^{25} +(-18.3818 - 91.9245i) q^{26} -118.282i q^{27} +(2.64066 + 1.52459i) q^{28} +(52.8488 - 91.5368i) q^{29} +(39.2964 + 38.7844i) q^{30} -125.714 q^{31} +(27.7128 - 16.0000i) q^{32} +(132.664 - 76.5935i) q^{33} -205.987 q^{34} +(-5.98682 + 6.06585i) q^{35} +(41.8063 - 72.4106i) q^{36} +(-294.412 - 169.979i) q^{37} +155.501i q^{38} +(22.6941 + 113.489i) q^{39} +(23.7155 + 86.2414i) q^{40} +(83.9935 - 145.481i) q^{41} +(-3.26014 - 1.88224i) q^{42} +(126.469 - 73.0171i) q^{43} +248.158 q^{44} +(166.334 + 164.167i) q^{45} +(0.965143 + 1.67168i) q^{46} -73.0270i q^{47} +(-34.2140 + 19.7535i) q^{48} +(-171.209 + 296.543i) q^{49} +(-249.979 + 3.27849i) q^{50} +254.310 q^{51} +(-60.0862 + 177.600i) q^{52} +680.487i q^{53} +(-118.282 + 204.870i) q^{54} +(-175.126 + 671.151i) q^{55} +(-3.04917 - 5.28133i) q^{56} -191.981i q^{57} +(-183.074 + 105.698i) q^{58} +(329.694 + 571.047i) q^{59} +(-29.2790 - 106.473i) q^{60} +(-74.0351 - 128.233i) q^{61} +(217.743 + 125.714i) q^{62} +(-13.7995 - 7.96716i) q^{63} -64.0000 q^{64} +(-437.921 - 287.837i) q^{65} -306.374 q^{66} +(329.372 + 190.163i) q^{67} +(356.781 + 205.987i) q^{68} +(-1.19156 - 2.06384i) q^{69} +(16.4353 - 4.51954i) q^{70} +(-458.764 - 794.602i) q^{71} +(-144.821 + 83.6125i) q^{72} +92.0384i q^{73} +(339.958 + 588.824i) q^{74} +(308.622 - 4.04760i) q^{75} +(155.501 - 269.336i) q^{76} -47.2923i q^{77} +(74.1819 - 219.263i) q^{78} +422.098 q^{79} +(45.1650 - 173.090i) q^{80} +(-136.163 + 235.841i) q^{81} +(-290.962 + 167.987i) q^{82} -1236.65i q^{83} +(3.76449 + 6.52028i) q^{84} +(-808.880 + 819.558i) q^{85} -292.068 q^{86} +(226.021 - 130.493i) q^{87} +(-429.822 - 248.158i) q^{88} +(480.091 - 831.542i) q^{89} +(-123.932 - 450.679i) q^{90} +(33.8458 + 11.4508i) q^{91} -3.86057i q^{92} +(-268.824 - 155.206i) q^{93} +(-73.0270 + 126.486i) q^{94} +(618.691 + 610.630i) q^{95} +79.0139 q^{96} +(-110.626 + 63.8702i) q^{97} +(593.087 - 342.419i) q^{98} -1296.82 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 88 q^{4} - 12 q^{5} + 266 q^{9} + 28 q^{10} + 2 q^{11} - 216 q^{14} - 64 q^{15} - 352 q^{16} + 14 q^{19} - 24 q^{20} - 32 q^{21} + 504 q^{25} + 336 q^{26} + 308 q^{29} + 104 q^{30} + 792 q^{31} - 352 q^{34}+ \cdots + 2916 q^{99}+O(q^{100}) $ 44 * q + 88 * q^4 - 12 * q^5 + 266 * q^9 + 28 * q^10 + 2 * q^11 - 216 * q^14 - 64 * q^15 - 352 * q^16 + 14 * q^19 - 24 * q^20 - 32 * q^21 + 504 * q^25 + 336 * q^26 + 308 * q^29 + 104 * q^30 + 792 * q^31 - 352 * q^34 + 106 * q^35 - 1064 * q^36 + 120 * q^39 + 224 * q^40 + 140 * q^41 + 16 * q^44 - 522 * q^45 - 320 * q^46 + 536 * q^49 - 96 * q^50 - 256 * q^51 + 552 * q^54 + 1188 * q^55 - 432 * q^56 - 500 * q^59 - 512 * q^60 - 2352 * q^61 - 2816 * q^64 - 2924 * q^65 + 496 * q^66 + 376 * q^69 - 1008 * q^70 - 1268 * q^71 + 436 * q^74 + 3560 * q^75 - 56 * q^76 - 264 * q^79 + 96 * q^80 - 6326 * q^81 - 64 * q^84 + 606 * q^85 + 336 * q^86 + 4730 * q^89 + 3560 * q^90 + 5866 * q^91 + 1732 * q^94 + 2224 * q^95 + 2916 * q^99

Character values

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

$n$	$27$	$41$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.73205	−	1.00000i	−0.612372	−	0.353553i
$2$	−1.73205	−	1.00000i	−0.612372	−	0.353553i
$3$	2.13838	+	1.23459i	0.411531	+	0.237597i	0.691447	−	0.722427i	$-0.256973\pi$
$3$	2.13838	+	1.23459i	0.411531	+	0.237597i	−0.279916	+	0.960024i	$0.590307\pi$
$4$	2.00000	+	3.46410i	0.250000	+	0.433013i
$5$	−10.7802	+	2.96444i	−0.964208	+	0.265147i
$5$	−10.7802	+	2.96444i	−0.964208	+	0.265147i
$6$	−2.46918	−	4.27675i	−0.168007	−	0.290996i
$7$	0.660166	−	0.381147i	0.0356456	−	0.0205800i	−0.482071	−	0.876132i	$-0.660115\pi$
$7$	0.660166	−	0.381147i	0.0356456	−	0.0205800i	0.517717	+	0.855552i	$0.326782\pi$
$8$		−	8.00000i		−	0.353553i
$9$	−10.4516	−	18.1026i	−0.387095	−	0.670468i
$10$	21.6362	+	5.64562i	0.684198	+	0.178530i
$11$	31.0198	−	53.7278i	0.850255	−	1.47269i	−0.0307226	−	0.999528i	$-0.509781\pi$
$11$	31.0198	−	53.7278i	0.850255	−	1.47269i	0.880978	−	0.473157i	$-0.156886\pi$
$12$			9.87674i			0.237597i
$13$	30.9407	+	35.2090i	0.660108	+	0.751171i
$13$	30.9407	+	35.2090i	0.660108	+	0.751171i
$14$	−1.52459			−0.0291045
$15$	−26.7119	−	6.97004i	−0.459799	−	0.119977i
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	89.1952	−	51.4968i	1.27253	−	0.734695i	0.297066	−	0.954857i	$-0.403992\pi$
$17$	89.1952	−	51.4968i	1.27253	−	0.734695i	0.975463	+	0.220162i	$0.0706585\pi$
$18$			41.8063i			0.547435i
$19$	−38.8754	−	67.3341i	−0.469401	−	0.813027i	0.529987	−	0.848006i	$-0.322197\pi$
$19$	−38.8754	−	67.3341i	−0.469401	−	0.813027i	−0.999388	+	0.0349792i	$0.988863\pi$
$20$	−31.8295	−	31.4147i	−0.355864	−	0.351227i
$21$	1.88224			0.0195590
$22$	−107.456	+	62.0395i	−1.04135	+	0.601221i
$23$	−0.835838	−	0.482571i	−0.00757758	−	0.00437492i	0.496206	−	0.868205i	$-0.334726\pi$
$23$	−0.835838	−	0.482571i	−0.00757758	−	0.00437492i	−0.503784	+	0.863830i	$0.668059\pi$
$24$	9.87674	−	17.1070i	0.0840034	−	0.145498i
$25$	107.424	−	63.9143i	0.859394	−	0.511314i
$26$	−18.3818	−	91.9245i	−0.138653	−	0.693380i
$27$		−	118.282i		−	0.843086i
$28$	2.64066	+	1.52459i	0.0178228	+	0.0102900i
$29$	52.8488	−	91.5368i	0.338406	−	0.586137i	−0.645727	−	0.763568i	$-0.723446\pi$
$29$	52.8488	−	91.5368i	0.338406	−	0.586137i	0.984133	+	0.177432i	$0.0567789\pi$
$30$	39.2964	+	38.7844i	0.239150	+	0.236034i
$31$	−125.714			−0.728353			−0.364176	−	0.931330i	$-0.618649\pi$
$31$	−125.714			−0.728353			−0.364176	+	0.931330i	$0.618649\pi$
$32$	27.7128	−	16.0000i	0.153093	−	0.0883883i
$33$	132.664	−	76.5935i	0.699812	−	0.404037i
$34$	−205.987			−1.03902
$35$	−5.98682	+	6.06585i	−0.0289130	+	0.0292947i
$36$	41.8063	−	72.4106i	0.193547	−	0.335234i
$37$	−294.412	−	169.979i	−1.30814	−	0.755253i	−0.326351	−	0.945249i	$-0.605819\pi$
$37$	−294.412	−	169.979i	−1.30814	−	0.755253i	−0.981785	+	0.189996i	$0.939152\pi$
$38$			155.501i			0.663833i
$39$	22.6941	+	113.489i	0.0931785	+	0.465970i
$40$	23.7155	+	86.2414i	0.0937437	+	0.340899i
$41$	83.9935	−	145.481i	0.319941	−	0.554154i	−0.660534	−	0.750796i	$-0.729670\pi$
$41$	83.9935	−	145.481i	0.319941	−	0.554154i	0.980475	+	0.196642i	$0.0630035\pi$
$42$	−3.26014	−	1.88224i	−0.0119774	−	0.00691516i
$43$	126.469	−	73.0171i	0.448520	−	0.258953i	−0.258685	−	0.965962i	$-0.583289\pi$
$43$	126.469	−	73.0171i	0.448520	−	0.258953i	0.707205	+	0.707008i	$0.249956\pi$
$44$	248.158			0.850255
$45$	166.334	+	164.167i	0.551013	+	0.543834i
$46$	0.965143	+	1.67168i	0.00309353	+	0.00535816i
$47$		−	73.0270i		−	0.226640i	−0.993559	−	0.113320i	$-0.963851\pi$
$47$		−	73.0270i		−	0.226640i	0.993559	−	0.113320i	$-0.0361485\pi$
$48$	−34.2140	+	19.7535i	−0.102883	+	0.0593993i
$49$	−171.209	+	296.543i	−0.499153	+	0.864558i
$50$	−249.979	+	3.27849i	−0.707046	+	0.00927298i
$51$	254.310			0.698247
$52$	−60.0862	+	177.600i	−0.160240	+	0.473628i
$53$			680.487i			1.76363i	0.471600	+	0.881813i	$0.343677\pi$
$53$			680.487i			1.76363i	−0.471600	+	0.881813i	$0.656323\pi$
$54$	−118.282	+	204.870i	−0.298076	+	0.516282i
$55$	−175.126	+	671.151i	−0.429345	+	1.64542i
$56$	−3.04917	−	5.28133i	−0.00727613	−	0.0126026i
$57$		−	191.981i		−	0.446114i
$58$	−183.074	+	105.698i	−0.414461	+	0.239289i
$59$	329.694	+	571.047i	0.727500	+	1.26007i	0.957937	+	0.286980i	$0.0926513\pi$
$59$	329.694	+	571.047i	0.727500	+	1.26007i	−0.230437	+	0.973087i	$0.574015\pi$
$60$	−29.2790	−	106.473i	−0.0629983	−	0.229093i
$61$	−74.0351	−	128.233i	−0.155397	−	0.269156i	0.777806	−	0.628504i	$-0.216332\pi$
$61$	−74.0351	−	128.233i	−0.155397	−	0.269156i	−0.933204	+	0.359348i	$0.882999\pi$
$62$	217.743	+	125.714i	0.446023	+	0.257512i
$63$	−13.7995	−	7.96716i	−0.0275965	−	0.0159328i
$64$	−64.0000			−0.125000
$65$	−437.921	−	287.837i	−0.835652	−	0.549259i
$66$	−306.374			−0.571394
$67$	329.372	+	190.163i	0.600586	+	0.346748i	0.769272	−	0.638921i	$-0.220619\pi$
$67$	329.372	+	190.163i	0.600586	+	0.346748i	−0.168686	+	0.985670i	$0.553952\pi$
$68$	356.781	+	205.987i	0.636265	+	0.367348i
$69$	−1.19156	−	2.06384i	−0.00207894	−	0.00360083i
$70$	16.4353	−	4.51954i	0.0280628	−	0.00771698i
$71$	−458.764	−	794.602i	−0.766834	−	1.32820i	−0.939271	−	0.343176i	$-0.888497\pi$
$71$	−458.764	−	794.602i	−0.766834	−	1.32820i	0.172437	−	0.985021i	$-0.444836\pi$
$72$	−144.821	+	83.6125i	−0.237046	+	0.136859i
$73$			92.0384i			0.147566i	0.997274	+	0.0737828i	$0.0235071\pi$
$73$			92.0384i			0.147566i	−0.997274	+	0.0737828i	$0.976493\pi$
$74$	339.958	+	588.824i	0.534044	+	0.924992i
$75$	308.622	−	4.04760i	0.475154	−	0.00623169i
$76$	155.501	−	269.336i	0.234701	−	0.406513i
$77$		−	47.2923i		−	0.0699930i
$78$	74.1819	−	219.263i	0.107685	−	0.318291i
$79$	422.098			0.601135			0.300568	−	0.953760i	$-0.402824\pi$
$79$	422.098			0.601135			0.300568	+	0.953760i	$0.402824\pi$
$80$	45.1650	−	173.090i	0.0631199	−	0.241901i
$81$	−136.163	+	235.841i	−0.186780	+	0.323512i
$82$	−290.962	+	167.987i	−0.391846	+	0.226233i
$83$		−	1236.65i		−	1.63542i	−0.575627	−	0.817712i	$-0.695242\pi$
$83$		−	1236.65i		−	1.63542i	0.575627	−	0.817712i	$-0.304758\pi$
$84$	3.76449	+	6.52028i	0.00488975	+	0.00846930i
$85$	−808.880	+	819.558i	−1.03218	+	1.04581i
$86$	−292.068			−0.366215
$87$	226.021	−	130.493i	0.278529	−	0.160809i
$88$	−429.822	−	248.158i	−0.520673	−	0.300611i
$89$	480.091	−	831.542i	0.571792	−	0.990373i	−0.424590	−	0.905386i	$-0.639582\pi$
$89$	480.091	−	831.542i	0.571792	−	0.990373i	0.996382	−	0.0849875i	$-0.0270850\pi$
$90$	−123.932	−	450.679i	−0.145151	−	0.527841i
$91$	33.8458	+	11.4508i	0.0389890	+	0.0131909i
$92$		−	3.86057i		−	0.00437492i
$93$	−268.824	−	155.206i	−0.299740	−	0.173055i
$94$	−73.0270	+	126.486i	−0.0801293	+	0.138788i
$95$	618.691	+	610.630i	0.668172	+	0.659466i
$96$	79.0139			0.0840034
$97$	−110.626	+	63.8702i	−0.115798	+	0.0668560i	−0.556780	−	0.830660i	$-0.687963\pi$
$97$	−110.626	+	63.8702i	−0.115798	+	0.0668560i	0.440982	+	0.897516i	$0.354630\pi$
$98$	593.087	−	342.419i	0.611335	−	0.352954i
$99$	−1296.82			−1.31652
$100$	436.254	+	244.300i	0.436254	+	0.244300i
$101$	771.264	−	1335.87i	0.759838	−	1.31608i	−0.183095	−	0.983095i	$-0.558611\pi$
$101$	771.264	−	1335.87i	0.759838	−	1.31608i	0.942933	−	0.332983i	$-0.108055\pi$
$102$	−440.479	−	254.310i	−0.427587	−	0.246867i
$103$			1514.88i			1.44918i	0.689179	+	0.724591i	$0.257971\pi$
$103$			1514.88i			1.44918i	−0.689179	+	0.724591i	$0.742029\pi$
$104$	281.672	−	247.526i	0.265579	−	0.233383i
$105$	−20.2909	+	5.57979i	−0.0188590	+	0.00518602i
$106$	680.487	−	1178.64i	0.623536	−	1.08000i
$107$	213.462	+	123.242i	0.192861	+	0.111348i	0.593321	−	0.804966i	$-0.297816\pi$
$107$	213.462	+	123.242i	0.192861	+	0.111348i	−0.400460	+	0.916314i	$0.631150\pi$
$108$	409.740	−	236.563i	0.365067	−	0.210771i
$109$	−660.193			−0.580138			−0.290069	−	0.957006i	$-0.593678\pi$
$109$	−660.193			−0.580138			−0.290069	+	0.957006i	$0.593678\pi$
$110$	974.478	−	987.342i	0.844662	−	0.855812i
$111$	−419.709	−	726.957i	−0.358892	−	0.621619i
$112$			12.1967i			0.0102900i
$113$	−1820.83	+	1051.26i	−1.51583	+	0.875166i	−0.516005	+	0.856586i	$0.672581\pi$
$113$	−1820.83	+	1051.26i	−1.51583	+	0.875166i	−0.999827	+	0.0185806i	$0.994085\pi$
$114$	−191.981	+	332.521i	−0.157725	+	0.273188i
$115$	10.4410	+	2.72441i	0.00846636	+	0.00220916i
$116$	422.790			0.338406
$117$	313.997	−	928.097i	0.248112	−	0.733356i
$118$		−	1318.78i		−	1.02884i
$119$	39.2557	−	67.9929i	0.0302401	−	0.0523773i
$120$	−55.7603	+	213.695i	−0.0424183	+	0.162564i
$121$	−1258.95	−	2180.57i	−0.945868	−	1.63829i
$122$			296.141i			0.219765i
$123$	359.220	−	207.395i	0.263331	−	0.152034i
$124$	−251.428	−	435.487i	−0.182088	−	0.315386i
$125$	−968.582	+	1007.46i	−0.693061	+	0.720879i
$126$	15.9343	+	27.5991i	0.0112662	+	0.0195136i
$127$	2211.50	+	1276.81i	1.54519	+	0.892114i	0.998499	+	0.0547778i	$0.0174451\pi$
$127$	2211.50	+	1276.81i	1.54519	+	0.892114i	0.546688	+	0.837336i	$0.315888\pi$
$128$	110.851	+	64.0000i	0.0765466	+	0.0441942i
$129$	360.585			0.246107
$130$	470.664	+	936.470i	0.317538	+	0.631799i
$131$	1281.48			0.854679			0.427340	−	0.904091i	$-0.359451\pi$
$131$	1281.48			0.854679			0.427340	+	0.904091i	$0.359451\pi$
$132$	530.655	+	306.374i	0.349906	+	0.202018i
$133$	−51.3284	−	29.6345i	−0.0334642	−	0.0193205i
$134$	−380.327	−	658.745i	−0.245188	−	0.424678i
$135$	350.638	+	1275.10i	0.223542	+	0.812910i
$136$	−411.975	−	713.561i	−0.259754	−	0.449907i
$137$	−1055.49	+	609.388i	−0.658224	+	0.380026i	−0.791600	−	0.611040i	$-0.790752\pi$
$137$	−1055.49	+	609.388i	−0.658224	+	0.380026i	0.133376	+	0.991065i	$0.457418\pi$
$138$			4.76623i			0.00294006i
$139$	−160.848	−	278.596i	−0.0981505	−	0.170002i	0.812769	−	0.582587i	$-0.197959\pi$
$139$	−160.848	−	278.596i	−0.0981505	−	0.170002i	−0.910919	+	0.412585i	$0.864626\pi$
$140$	−32.9863	−	8.60724i	−0.0199132	−	0.00519603i
$141$	90.1585	−	156.159i	0.0538491	−	0.0932693i
$142$			1835.06i			1.08447i
$143$	2851.47	−	570.200i	1.66750	−	0.333444i
$144$	334.450			0.193547
$145$	−298.364	+	1143.45i	−0.170881	+	0.654885i
$146$	92.0384	−	159.415i	0.0521723	−	0.0903651i
$147$	−732.221	+	422.748i	−0.410834	+	0.237195i
$148$		−	1359.83i		−	0.755253i
$149$	921.755	+	1596.53i	0.506800	+	0.877803i	0.999969	+	0.00786939i	$0.00250493\pi$
$149$	921.755	+	1596.53i	0.506800	+	0.877803i	−0.493169	+	0.869933i	$0.664162\pi$
$150$	−538.596	−	301.611i	−0.293174	−	0.164176i
$151$	−527.652			−0.284369			−0.142184	−	0.989840i	$-0.545413\pi$
$151$	−527.652			−0.284369			−0.142184	+	0.989840i	$0.545413\pi$
$152$	−538.673	+	311.003i	−0.287448	+	0.165958i
$153$	−1864.46	−	1076.45i	−0.985180	−	0.568794i
$154$	−47.2923	+	81.9127i	−0.0247463	+	0.0428618i
$155$	1355.22	−	372.672i	0.702284	−	0.193121i
$156$	−347.750	+	305.593i	−0.178476	+	0.156840i
$157$		−	3040.22i		−	1.54545i	−0.634739	−	0.772726i	$-0.718893\pi$
$157$		−	3040.22i		−	1.54545i	0.634739	−	0.772726i	$-0.281107\pi$
$158$	−731.094	−	422.098i	−0.368119	−	0.212533i
$159$	−840.124	+	1455.14i	−0.419033	+	0.725786i
$160$	−251.318	+	254.636i	−0.124178	+	0.125817i
$161$	−0.735722			−0.000360143
$162$	471.681	−	272.325i	0.228758	−	0.132073i
$163$	−908.091	+	524.287i	−0.436363	+	0.251934i	−0.702054	−	0.712124i	$-0.747733\pi$
$163$	−908.091	+	524.287i	−0.436363	+	0.251934i	0.265691	+	0.964058i	$0.414400\pi$
$164$	671.948			0.319941
$165$	−1203.08	+	1218.96i	−0.567635	+	0.575129i
$166$	−1236.65	+	2141.95i	−0.578210	+	1.00149i
$167$	−320.668	−	185.138i	−0.148587	−	0.0857868i	0.423863	−	0.905726i	$-0.360674\pi$
$167$	−320.668	−	185.138i	−0.148587	−	0.0857868i	−0.572450	+	0.819939i	$0.694007\pi$
$168$		−	15.0580i		−	0.00691516i
$169$	−282.348	+	2178.78i	−0.128515	+	0.991708i
$170$	2220.58	−	610.636i	1.00183	−	0.275492i
$171$	−812.617	+	1407.49i	−0.363406	+	0.629437i
$172$	505.877	+	292.068i	0.224260	+	0.129477i
$173$	−1264.88	+	730.278i	−0.555878	+	0.320936i	−0.751489	−	0.659745i	$-0.770664\pi$
$173$	−1264.88	+	730.278i	−0.555878	+	0.320936i	0.195611	+	0.980681i	$0.437331\pi$
$174$	−521.974			−0.227418
$175$	46.5571	−	83.1384i	0.0201108	−	0.0359124i
$176$	496.316	+	859.645i	0.212564	+	0.368171i
$177$			1628.15i			0.691408i
$178$	−1663.08	+	960.181i	−0.700300	+	0.404318i
$179$	1847.53	−	3200.02i	0.771458	−	1.33620i	−0.165306	−	0.986242i	$-0.552861\pi$
$179$	1847.53	−	3200.02i	0.771458	−	1.33620i	0.936764	−	0.349962i	$-0.113806\pi$
$180$	−236.022	+	904.530i	−0.0977337	+	0.374554i
$181$	192.170			0.0789166			0.0394583	−	0.999221i	$-0.487437\pi$
$181$	192.170			0.0789166			0.0394583	+	0.999221i	$0.487437\pi$
$182$	−47.1718	−	53.6792i	−0.0192121	−	0.0218625i
$183$		−	365.613i		−	0.147688i
$184$	−3.86057	+	6.68670i	−0.00154677	+	0.00267908i
$185$	3677.70	+	959.636i	1.46157	+	0.381372i
$186$	310.412	+	537.649i	0.122368	+	0.211948i
$187$		−	6389.68i		−	2.49871i
$188$	252.973	−	146.054i	0.0981380	−	0.0566600i
$189$	−45.0827	−	78.0855i	−0.0173507	−	0.0300523i
$190$	−460.974	−	1676.33i	−0.176014	−	0.640073i
$191$	402.994	+	698.007i	0.152668	+	0.264429i	0.932208	−	0.361924i	$-0.117880\pi$
$191$	402.994	+	698.007i	0.152668	+	0.264429i	−0.779539	+	0.626353i	$0.784547\pi$
$192$	−136.856	−	79.0139i	−0.0514413	−	0.0296997i
$193$	−1045.92	−	603.865i	−0.390090	−	0.225218i	0.292109	−	0.956385i	$-0.405643\pi$
$193$	−1045.92	−	603.865i	−0.390090	−	0.225218i	−0.682199	+	0.731167i	$0.738976\pi$
$194$	255.481			0.0945487
$195$	−581.078	−	1156.16i	−0.213394	−	0.424586i
$196$	−1369.68			−0.499153
$197$	−395.873	−	228.558i	−0.143172	−	0.0826602i	0.426703	−	0.904392i	$-0.359675\pi$
$197$	−395.873	−	228.558i	−0.143172	−	0.0826602i	−0.569875	+	0.821732i	$0.693008\pi$
$198$	2246.16	+	1296.82i	0.806199	+	0.465459i
$199$	1060.43	+	1836.71i	0.377747	+	0.654277i	0.990734	−	0.135816i	$-0.0433656\pi$
$199$	1060.43	+	1836.71i	0.377747	+	0.654277i	−0.612987	+	0.790093i	$0.710032\pi$
$200$	−511.314	−	859.394i	−0.180777	−	0.303842i
$201$	469.548	+	813.281i	0.164773	+	0.285395i
$202$	−2671.74	+	1542.53i	−0.930608	+	0.537287i
$203$		−	80.5726i		−	0.0278576i
$204$	508.621	+	880.957i	0.174562	+	0.302350i
$205$	−474.195	+	1817.30i	−0.161557	+	0.619151i
$206$	1514.88	−	2623.85i	0.512363	−	0.887439i
$207$			20.1745i			0.00677403i
$208$	−735.396	+	147.055i	−0.245147	+	0.0490212i
$209$	−4823.62			−1.59644
$210$	40.7247	+	10.6264i	0.0133822	+	0.00349187i
$211$	−1747.28	+	3026.38i	−0.570084	+	0.987414i	0.426473	+	0.904500i	$0.359756\pi$
$211$	−1747.28	+	3026.38i	−0.570084	+	0.987414i	−0.996557	+	0.0829139i	$0.973577\pi$
$212$	−2357.28	+	1360.97i	−0.763672	+	0.440906i
$213$		−	2265.54i		−	0.728791i
$214$	−246.484	−	426.924i	−0.0787352	−	0.136373i
$215$	−1146.91	+	1162.05i	−0.363806	+	0.368609i
$216$	−946.253			−0.298076
$217$	−82.9922	+	47.9156i	−0.0259626	+	0.0149895i
$218$	1143.49	+	660.193i	0.355260	+	0.205110i
$219$	−113.630	+	196.813i	−0.0350612	+	0.0607278i
$220$	−2675.19	+	735.649i	−0.819823	+	0.225443i
$221$	4572.91	+	1547.12i	1.39189	+	0.470909i
$222$			1678.84i			0.507550i
$223$	3685.10	+	2127.60i	1.10660	+	0.638898i	0.937948	−	0.346776i	$-0.112724\pi$
$223$	3685.10	+	2127.60i	1.10660	+	0.638898i	0.168657	+	0.985675i	$0.446057\pi$
$224$	12.1967	−	21.1253i	0.00363806	−	0.00630131i
$225$	−2279.77	−	1276.66i	−0.675487	−	0.378269i
$226$	4205.02			1.23767
$227$	2663.55	−	1537.80i	0.778794	−	0.449637i	−0.0572084	−	0.998362i	$-0.518220\pi$
$227$	2663.55	−	1537.80i	0.778794	−	0.449637i	0.836003	+	0.548725i	$0.184887\pi$
$228$	665.041	−	383.962i	0.193173	−	0.111528i
$229$	2227.59			0.642809			0.321405	−	0.946942i	$-0.395845\pi$
$229$	2227.59			0.642809			0.321405	+	0.946942i	$0.395845\pi$
$230$	−15.3600	−	15.1599i	−0.00440351	−	0.00434614i
$231$	58.3867	−	101.129i	0.0166302	−	0.0288043i
$232$	−732.294	−	422.790i	−0.207231	−	0.119645i
$233$		−	2100.43i		−	0.590575i	−0.955408	−	0.295287i	$-0.904585\pi$
$233$		−	2100.43i		−	0.590575i	0.955408	−	0.295287i	$-0.0954154\pi$
$234$	−1471.96	+	1293.51i	−0.411217	+	0.361366i
$235$	216.484	+	787.243i	0.0600929	+	0.218528i
$236$	−1318.78	+	2284.19i	−0.363750	+	0.630034i
$237$	902.604	+	521.118i	0.247386	+	0.142828i
$238$	−135.986	+	78.5115i	−0.0370364	+	0.0213829i
$239$	2433.29			0.658563			0.329282	−	0.944232i	$-0.393193\pi$
$239$	2433.29			0.658563			0.329282	+	0.944232i	$0.393193\pi$
$240$	310.275	−	314.371i	0.0834507	−	0.0845524i
$241$	310.242	+	537.354i	0.0829229	+	0.143627i	0.904504	−	0.426465i	$-0.140241\pi$
$241$	310.242	+	537.354i	0.0829229	+	0.143627i	−0.821581	+	0.570091i	$0.806908\pi$
$242$			5035.80i			1.33766i
$243$	−3348.08	+	1933.01i	−0.883865	+	0.510300i
$244$	296.141	−	512.930i	0.0776986	−	0.134578i
$245$	966.583	−	3704.33i	0.252052	−	0.965963i
$246$	−829.582			−0.215009
$247$	1167.94	−	3452.13i	0.300866	−	0.889286i
$248$			1005.71i			0.257512i
$249$	1526.76	−	2644.43i	0.388573	−	0.673028i
$250$	2685.09	−	776.388i	0.679281	−	0.196412i
$251$	−614.724	−	1064.73i	−0.154586	−	0.267750i	0.778322	−	0.627865i	$-0.216071\pi$
$251$	−614.724	−	1064.73i	−0.154586	−	0.267750i	−0.932908	+	0.360115i	$0.882738\pi$
$252$		−	63.7373i		−	0.0159328i
$253$	−51.8550	+	29.9385i	−0.0128858	+	0.00743959i
$254$	−2553.62	−	4423.00i	−0.630820	−	1.09261i
$255$	−2741.51	+	753.887i	−0.673255	+	0.185138i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	2208.81	+	1275.26i	0.536117	+	0.309527i	0.743504	−	0.668732i	$-0.233163\pi$
$257$	2208.81	+	1275.26i	0.536117	+	0.309527i	−0.207387	+	0.978259i	$0.566496\pi$
$258$	−624.552	−	360.585i	−0.150709	−	0.0870118i
$259$	−259.148			−0.0621724
$260$	121.257	−	2092.68i	0.0289231	−	0.499163i
$261$	−2209.41			−0.523981
$262$	−2219.58	−	1281.48i	−0.523382	−	0.302175i
$263$	4873.96	+	2813.98i	1.14274	+	0.659762i	0.947108	−	0.320915i	$-0.103990\pi$
$263$	4873.96	+	2813.98i	1.14274	+	0.659762i	0.195634	+	0.980677i	$0.437324\pi$
$264$	−612.748	−	1061.31i	−0.142849	−	0.247421i
$265$	−2017.26	−	7335.77i	−0.467620	−	1.70050i
$266$	59.2689	+	102.657i	0.0136617	+	0.0236627i
$267$	2053.23	−	1185.43i	0.470620	−	0.271713i
$268$			1521.31i			0.346748i
$269$	−2310.10	−	4001.20i	−0.523602	−	0.906906i	−0.999623	−	0.0274716i	$-0.991254\pi$
$269$	−2310.10	−	4001.20i	−0.523602	−	0.906906i	0.476020	−	0.879434i	$-0.342079\pi$
$270$	667.773	−	2559.17i	0.150516	−	0.576838i
$271$	−2394.15	+	4146.79i	−0.536658	+	0.929519i	0.462423	+	0.886659i	$0.346980\pi$
$271$	−2394.15	+	4146.79i	−0.536658	+	0.929519i	−0.999081	+	0.0428597i	$0.986353\pi$
$272$			1647.90i			0.367348i
$273$	58.2379	+	66.2719i	0.0129111	+	0.0146922i
$274$	2437.55			0.537437
$275$	−101.698	−	7754.27i	−0.0223004	−	1.70036i
$276$	4.76623	−	8.25535i	0.00103947	−	0.00180041i
$277$	3012.31	−	1739.16i	0.653401	−	0.377241i	−0.136357	−	0.990660i	$-0.543539\pi$
$277$	3012.31	−	1739.16i	0.653401	−	0.377241i	0.789758	+	0.613419i	$0.210206\pi$
$278$			643.391i			0.138806i
$279$	1313.91	+	2275.76i	0.281942	+	0.488337i
$280$	48.5268	+	47.8945i	0.0103572	+	0.0102223i
$281$	2509.09			0.532668			0.266334	−	0.963881i	$-0.414188\pi$
$281$	2509.09			0.532668			0.266334	+	0.963881i	$0.414188\pi$
$282$	−312.318	+	180.317i	−0.0659514	+	0.0380770i
$283$	7120.68	+	4111.13i	1.49569	+	0.863538i	0.999988	−	0.00495406i	$-0.00157693\pi$
$283$	7120.68	+	4111.13i	1.49569	+	0.863538i	0.495704	+	0.868492i	$0.334910\pi$
$284$	1835.06	−	3178.41i	0.383417	−	0.664098i
$285$	569.115	+	2069.59i	0.118286	+	0.430147i
$286$	−5509.10	−	1863.86i	−1.13902	−	0.385358i
$287$		−	128.055i		−	0.0263375i
$288$	−579.284	−	334.450i	−0.118523	−	0.0684294i
$289$	2847.35	−	4931.76i	0.579554	−	1.00382i
$290$	1660.23	−	1682.15i	0.336180	−	0.340618i
$291$	−315.414			−0.0635393
$292$	−318.830	+	184.077i	−0.0638978	+	0.0368914i
$293$	−6861.45	+	3961.46i	−1.36809	+	0.789867i	−0.990684	−	0.136181i	$-0.956517\pi$
$293$	−6861.45	+	3961.46i	−1.36809	+	0.789867i	−0.377406	+	0.926048i	$0.623184\pi$
$294$	1690.99			0.335444
$295$	−5246.99	−	5178.63i	−1.03556	−	1.02207i
$296$	−1359.83	+	2355.30i	−0.267022	+	0.462496i
$297$	−6355.01	−	3669.07i	−1.24160	−	0.716838i
$298$		−	3687.02i		−	0.716723i
$299$	−8.87055	−	44.3601i	−0.00171571	−	0.00857997i
$300$	631.264	+	1061.00i	0.121487	+	0.204190i
$301$	55.6604	−	96.4067i	0.0106585	−	0.0184611i
$302$	913.920	+	527.652i	0.174140	+	0.100540i
$303$	3298.51	−	1904.39i	0.625394	−	0.361071i
$304$	1244.01			0.234701
$305$	1178.25	+	1162.90i	0.221201	+	0.218319i
$306$	2152.89	+	3728.92i	0.402198	+	0.696627i
$307$			929.515i			0.172802i	0.996260	+	0.0864010i	$0.0275366\pi$
$307$			929.515i			0.172802i	−0.996260	+	0.0864010i	$0.972463\pi$
$308$	163.825	−	94.5847i	0.0303079	−	0.0174983i
$309$	−1870.26	+	3239.39i	−0.344322	+	0.596383i
$310$	−2719.98	−	709.735i	−0.498338	−	0.130033i
$311$	−2559.71			−0.466713			−0.233356	−	0.972391i	$-0.574971\pi$
$311$	−2559.71			−0.466713			−0.233356	+	0.972391i	$0.574971\pi$
$312$	907.914	−	181.553i	0.164745	−	0.0329436i
$313$		−	2292.82i		−	0.414051i	−0.978336	−	0.207025i	$-0.933622\pi$
$313$		−	2292.82i		−	0.414051i	0.978336	−	0.207025i	$-0.0663783\pi$
$314$	−3040.22	+	5265.82i	−0.546400	+	0.946392i
$315$	172.379	+	44.9796i	0.0308333	+	0.00804543i
$316$	844.195	+	1462.19i	0.150284	+	0.260299i
$317$		−	99.3043i		−	0.0175946i	−0.999961	−	0.00879729i	$-0.997200\pi$
$317$		−	99.3043i		−	0.0175946i	0.999961	−	0.00879729i	$-0.00280030\pi$
$318$	2910.28	−	1680.25i	0.513208	−	0.296301i
$319$	−3278.71	−	5678.90i	−0.575463	−	0.996731i
$320$	689.931	−	189.724i	0.120526	−	0.0331434i
$321$	304.308	+	527.077i	0.0529122	+	0.0916466i
$322$	1.27431	+	0.735722i	0.000220542	+	0.000127330i
$323$	−6934.99	−	4003.92i	−1.19465	−	0.689734i
$324$	−1089.30			−0.186780
$325$	5574.14	+	1804.75i	0.951377	+	0.308029i
$326$	2097.15			0.356289
$327$	−1411.74	−	815.069i	−0.238744	−	0.137839i
$328$	−1163.85	−	671.948i	−0.195923	−	0.113116i
$329$	−27.8340	−	48.2099i	−0.00466425	−	0.00807872i
$330$	3302.76	−	908.226i	0.550943	−	0.151504i
$331$	4885.08	+	8461.20i	0.811203	+	1.40504i	0.912023	+	0.410140i	$0.134520\pi$
$331$	4885.08	+	8461.20i	0.811203	+	1.40504i	−0.100820	+	0.994905i	$0.532147\pi$
$332$	4283.89	−	2473.31i	0.708160	−	0.408856i
$333$			7106.18i			1.16942i
$334$	370.276	+	641.337i	0.0606605	+	0.105067i
$335$	−4114.42	−	1073.59i	−0.671029	−	0.175094i
$336$	−15.0580	+	26.0811i	−0.00244488	+	0.00423465i
$337$			7747.81i			1.25237i	0.779673	+	0.626187i	$0.215386\pi$
$337$			7747.81i			1.25237i	−0.779673	+	0.626187i	$0.784614\pi$
$338$	2667.82	−	3491.41i	0.429321	−	0.561857i
$339$	−5191.49			−0.831749
$340$	−4456.79	−	1162.93i	−0.710893	−	0.185496i
$341$	−3899.62	+	6754.35i	−0.619286	+	1.07263i
$342$	2814.99	−	1625.23i	0.445079	−	0.256967i
$343$			522.491i			0.0822503i
$344$	−584.136	−	1011.75i	−0.0915538	−	0.158576i
$345$	18.9633	+	18.7162i	0.00295928	+	0.00292072i
$346$	2921.11			0.453872
$347$	−8144.74	+	4702.37i	−1.26004	+	0.727482i	−0.973081	−	0.230462i	$-0.925976\pi$
$347$	−8144.74	+	4702.37i	−1.26004	+	0.727482i	−0.286955	+	0.957944i	$0.592643\pi$
$348$	904.085	+	521.974i	0.139265	+	0.0804044i
$349$	2620.03	−	4538.02i	0.401854	−	0.696031i	−0.592096	−	0.805868i	$-0.701699\pi$
$349$	2620.03	−	4538.02i	0.401854	−	0.696031i	0.993950	+	0.109836i	$0.0350327\pi$
$350$	−163.778	+	97.4429i	−0.0250122	+	0.0148815i
$351$	4164.58	−	3659.72i	0.633301	−	0.556528i
$352$		−	1985.26i		−	0.300611i
$353$	5574.65	+	3218.53i	0.840535	+	0.485283i	0.857446	−	0.514574i	$-0.172050\pi$
$353$	5574.65	+	3218.53i	0.840535	+	0.485283i	−0.0169111	+	0.999857i	$0.505383\pi$
$354$	1628.15	−	2820.04i	0.244450	−	0.423400i
$355$	7301.10	+	7205.97i	1.09156	+	1.07733i
$356$	3840.73			0.571792
$357$	167.887	−	96.9296i	0.0248894	−	0.0143699i
$358$	−6400.04	+	3695.06i	−0.944839	+	0.545503i
$359$	2761.93			0.406042			0.203021	−	0.979174i	$-0.434924\pi$
$359$	2761.93			0.406042			0.203021	+	0.979174i	$0.434924\pi$
$360$	1313.33	−	1330.67i	0.192274	−	0.194812i
$361$	406.911	−	704.791i	0.0593252	−	0.102754i
$362$	−332.849	−	192.170i	−0.0483264	−	0.0279012i
$363$		−	6217.16i		−	0.898943i
$364$	28.0247	+	140.147i	0.00403543	+	0.0201805i
$365$	−272.842	−	992.190i	−0.0391266	−	0.142284i
$366$	−365.613	+	633.260i	−0.0522155	+	0.0904400i
$367$	4487.03	+	2590.59i	0.638205	+	0.368468i	0.783923	−	0.620858i	$-0.213216\pi$
$367$	4487.03	+	2590.59i	0.638205	+	0.368468i	−0.145718	+	0.989326i	$0.546549\pi$
$368$	13.3734	−	7.72114i	0.00189439	−	0.00109373i
$369$	−3511.45			−0.495390
$370$	−5410.33	−	5339.84i	−0.760189	−	0.750284i
$371$	259.366	+	449.234i	0.0362954	+	0.0628655i
$372$		−	1241.65i		−	0.173055i
$373$	−1999.94	+	1154.66i	−0.277621	+	0.160285i	−0.632346	−	0.774686i	$-0.717908\pi$
$373$	−1999.94	+	1154.66i	−0.277621	+	0.160285i	0.354725	+	0.934971i	$0.384575\pi$
$374$	−6389.68	+	11067.2i	−0.883429	+	1.53014i
$375$	−3314.99	+	958.522i	−0.456495	+	0.131994i
$376$	−584.216			−0.0801293
$377$	4858.10	−	971.458i	0.663673	−	0.132713i
$378$			180.331i			0.0245376i
$379$	−1596.02	+	2764.39i	−0.216312	+	0.374663i	−0.953678	−	0.300831i	$-0.902736\pi$
$379$	−1596.02	+	2764.39i	−0.216312	+	0.374663i	0.737366	+	0.675494i	$0.236069\pi$
$380$	−877.902	+	3364.47i	−0.118514	+	0.454194i
$381$	3152.68	+	5460.60i	0.423928	+	0.734265i
$382$		−	1611.98i		−	0.215906i
$383$	−4540.19	+	2621.28i	−0.605726	+	0.349716i	−0.771291	−	0.636483i	$-0.780389\pi$
$383$	−4540.19	+	2621.28i	−0.605726	+	0.349716i	0.165565	+	0.986199i	$0.447055\pi$
$384$	158.028	+	273.712i	0.0210008	+	0.0363745i
$385$	140.195	+	509.819i	0.0185584	+	0.0674878i
$386$	1207.73	+	2091.85i	0.159253	+	0.275835i
$387$	−2643.60	−	1526.28i	−0.347240	−	0.200479i
$388$	−442.506	−	255.481i	−0.0578990	−	0.0334280i
$389$	−9400.46			−1.22525			−0.612625	−	0.790374i	$-0.709886\pi$
$389$	−9400.46			−1.22525			−0.612625	+	0.790374i	$0.709886\pi$
$390$	−149.702	+	2583.60i	−0.0194371	+	0.335451i
$391$	−99.4036			−0.0128569
$392$	2372.35	+	1369.68i	0.305667	+	0.176477i
$393$	2740.28	+	1582.10i	0.351727	+	0.203070i
$394$	457.115	+	791.747i	0.0584496	+	0.101238i
$395$	−4550.28	+	1251.28i	−0.579619	+	0.159389i
$396$	−2593.64	−	4492.32i	−0.329130	−	0.570069i
$397$	7347.44	−	4242.05i	0.928860	−	0.536277i	0.0424090	−	0.999100i	$-0.486497\pi$
$397$	7347.44	−	4242.05i	0.928860	−	0.536277i	0.886451	+	0.462823i	$0.153163\pi$
$398$		−	4241.71i		−	0.534215i
$399$	−73.1729	−	126.739i	−0.00918102	−	0.0159020i
$400$	26.2279	+	1999.83i	0.00327849	+	0.249979i
$401$	−4851.80	+	8403.57i	−0.604208	+	1.04652i	0.387968	+	0.921673i	$0.373177\pi$
$401$	−4851.80	+	8403.57i	−0.604208	+	1.04652i	−0.992176	+	0.124846i	$0.960156\pi$
$402$		−	1878.19i		−	0.233024i
$403$	−3889.68	−	4426.27i	−0.480791	−	0.547117i
$404$	6170.11			0.759838
$405$	768.722	−	2946.05i	0.0943163	−	0.361457i
$406$	−80.5726	+	139.556i	−0.00984914	+	0.0170592i
$407$	−18265.2	+	10545.4i	−2.22450	+	1.28431i
$408$		−	2034.48i		−	0.246867i
$409$	5340.83	+	9250.59i	0.645690	+	1.11837i	0.984142	+	0.177384i	$0.0567633\pi$
$409$	5340.83	+	9250.59i	0.645690	+	1.11837i	−0.338452	+	0.940984i	$0.609903\pi$
$410$	2638.63	−	2673.47i	0.317836	−	0.322032i
$411$	−3009.38			−0.361172
$412$	−5247.70	+	3029.76i	−0.627514	+	0.362295i
$413$	435.305	+	251.324i	0.0518644	+	0.0299439i
$414$	20.1745	−	34.9433i	0.00239498	−	0.00414823i
$415$	3665.98	+	13331.3i	0.433628	+	1.57689i
$416$	1420.80	+	480.689i	0.167453	+	0.0566532i
$417$		−	794.325i		−	0.0932812i
$418$	8354.75	+	4823.62i	0.977618	+	0.564428i
$419$	1161.55	−	2011.86i	0.135430	−	0.234572i	−0.790332	−	0.612679i	$-0.790092\pi$
$419$	1161.55	−	2011.86i	0.135430	−	0.234572i	0.925762	+	0.378107i	$0.123425\pi$
$420$	−59.9108	−	59.1302i	−0.00696035	−	0.00686966i
$421$	2908.50			0.336702			0.168351	−	0.985727i	$-0.446156\pi$
$421$	2908.50			0.336702			0.168351	+	0.985727i	$0.446156\pi$
$422$	6052.76	−	3494.56i	0.698207	−	0.403110i
$423$	−1321.98	+	763.246i	−0.151955	+	0.0877312i
$424$	5443.90			0.623536
$425$	6290.34	−	11232.9i	0.717944	−	1.28205i
$426$	−2265.54	+	3924.04i	−0.257667	+	0.446292i
$427$	−97.7509	−	56.4365i	−0.0110785	−	0.00639615i
$428$			985.938i			0.111348i
$429$	6801.49	+	2301.11i	0.765452	+	0.258971i
$430$	3148.55	−	865.817i	0.353108	−	0.0971010i
$431$	−4989.31	+	8641.73i	−0.557602	+	0.965795i	0.440094	+	0.897952i	$0.354945\pi$
$431$	−4989.31	+	8641.73i	−0.557602	+	0.965795i	−0.997696	+	0.0678431i	$0.978388\pi$
$432$	1638.96	+	946.253i	0.182533	+	0.105386i
$433$	−2679.27	+	1546.88i	−0.297362	+	0.171682i	−0.641257	−	0.767326i	$-0.721587\pi$
$433$	−2679.27	+	1546.88i	−0.297362	+	0.171682i	0.343895	+	0.939008i	$0.388253\pi$
$434$	191.662			0.0211984
$435$	−2049.71	+	2076.77i	−0.225922	+	0.228904i
$436$	−1320.39	−	2286.97i	−0.145034	−	0.251207i
$437$			75.0406i			0.00821436i
$438$	393.626	−	227.260i	0.0429410	−	0.0247920i
$439$	6697.19	−	11599.9i	0.728108	−	1.26112i	−0.229574	−	0.973291i	$-0.573733\pi$
$439$	6697.19	−	11599.9i	0.728108	−	1.26112i	0.957682	−	0.287828i	$-0.0929333\pi$
$440$	5369.21	+	1401.01i	0.581743	+	0.151796i
$441$	7157.63			0.772878
$442$	−6373.39	−	7252.61i	−0.685863	−	0.780478i
$443$		−	2578.96i		−	0.276592i	−0.990391	−	0.138296i	$-0.955837\pi$
$443$		−	2578.96i		−	0.276592i	0.990391	−	0.138296i	$-0.0441625\pi$
$444$	1678.84	−	2907.83i	0.179446	−	0.310810i
$445$	−2710.41	+	10387.4i	−0.288732	+	1.10653i
$446$	−4255.19	−	7370.21i	−0.451769	−	0.782488i
$447$			4551.97i			0.481657i
$448$	−42.2506	+	24.3934i	−0.00445570	+	0.00257250i
$449$	6878.53	+	11914.0i	0.722980	+	1.25224i	0.959800	+	0.280684i	$0.0905614\pi$
$449$	6878.53	+	11914.0i	0.722980	+	1.25224i	−0.236820	+	0.971553i	$0.576105\pi$
$450$	2672.02	+	4491.01i	0.279911	+	0.470462i
$451$	−5210.92	−	9025.57i	−0.544063	−	0.942345i
$452$	−7283.31	−	4205.02i	−0.757916	−	0.437583i
$453$	−1128.32	−	651.435i	−0.117027	−	0.0675653i
$454$	−6151.22			−0.635883
$455$	−398.809	−	23.1083i	−0.0410911	−	0.00238095i
$456$	−1535.85			−0.157725
$457$	3256.72	+	1880.27i	0.333354	+	0.192462i	0.657329	−	0.753604i	$-0.271686\pi$
$457$	3256.72	+	1880.27i	0.333354	+	0.192462i	−0.323975	+	0.946066i	$0.605019\pi$
$458$	−3858.30	−	2227.59i	−0.393639	−	0.227267i
$459$	−6091.13	−	10550.2i	−0.619411	−	1.07285i
$460$	11.4444	+	41.6176i	0.00116000	+	0.00421833i
$461$	−7148.97	−	12382.4i	−0.722257	−	1.25099i	−0.960093	−	0.279681i	$-0.909771\pi$
$461$	−7148.97	−	12382.4i	−0.722257	−	1.25099i	0.237836	−	0.971305i	$-0.423562\pi$
$462$	−202.258	+	116.773i	−0.0203677	+	0.0117593i
$463$		−	3597.59i		−	0.361110i	−0.983565	−	0.180555i	$-0.942211\pi$
$463$		−	3597.59i		−	0.361110i	0.983565	−	0.180555i	$-0.0577894\pi$
$464$	845.581	+	1464.59i	0.0846015	+	0.146534i
$465$	3358.07	+	876.233i	0.334896	+	0.0873856i
$466$	−2100.43	+	3638.06i	−0.208800	+	0.361652i
$467$			2291.67i			0.227079i	0.993533	+	0.113539i	$0.0362188\pi$
$467$			2291.67i			0.227079i	−0.993533	+	0.113539i	$0.963781\pi$
$468$	3843.02	−	768.476i	0.379580	−	0.0759035i
$469$	289.921			0.0285443
$470$	412.282	−	1580.03i	0.0404621	−	0.155067i
$471$	3753.43	−	6501.14i	0.367195	−	0.636001i
$472$	4568.37	−	2637.55i	0.445501	−	0.257210i
$473$		−	9059.88i		−	0.880706i
$474$	−1042.24	−	1805.21i	−0.100995	−	0.174928i
$475$	−8479.77	−	4748.63i	−0.819112	−	0.458699i
$476$	314.046			0.0302401
$477$	12318.6	−	7112.16i	1.18245	−	0.682690i
$478$	−4214.59	−	2433.29i	−0.403286	−	0.232837i
$479$	−4593.75	+	7956.60i	−0.438191	+	0.758969i	−0.997550	−	0.0699562i	$-0.977714\pi$
$479$	−4593.75	+	7956.60i	−0.438191	+	0.758969i	0.559359	+	0.828926i	$0.311047\pi$
$480$	−851.784	+	234.232i	−0.0809967	+	0.0222733i
$481$	−3124.52	−	15625.2i	−0.296187	−	1.48118i
$482$		−	1240.97i		−	0.117271i
$483$	−1.57325	−	0.908317i	−0.000148210	−	8.55691e-5i
$484$	5035.80	−	8722.26i	0.472934	−	0.819146i
$485$	1003.23	−	1016.48i	0.0939267	−	0.0951666i
$486$	7732.05			0.721673
$487$	5122.29	−	2957.35i	0.476618	−	0.275175i	−0.242388	−	0.970179i	$-0.577931\pi$
$487$	5122.29	−	2957.35i	0.476618	−	0.275175i	0.719006	+	0.695004i	$0.244597\pi$
$488$	−1025.86	+	592.281i	−0.0951609	+	0.0549412i
$489$	−2589.12			−0.239436
$490$	−5378.50	+	5449.50i	−0.495869	+	0.502415i
$491$	9188.91	−	15915.7i	0.844581	−	1.46286i	−0.0414027	−	0.999143i	$-0.513183\pi$
$491$	9188.91	−	15915.7i	0.844581	−	1.46286i	0.885984	−	0.463716i	$-0.153484\pi$
$492$	1436.88	+	829.582i	0.131666	+	0.0760172i
$493$		−	10886.2i		−	0.994501i
$494$	−5475.05	+	4811.32i	−0.498652	+	0.438202i
$495$	13979.9	−	3844.34i	1.26940	−	0.349071i
$496$	1005.71	−	1741.95i	0.0910441	−	0.157693i
$497$	−605.720	−	349.713i	−0.0546685	−	0.0315629i
$498$	−5288.86	+	3053.52i	−0.475902	+	0.274762i
$499$	3123.66			0.280229			0.140115	−	0.990135i	$-0.455253\pi$
$499$	3123.66			0.280229			0.140115	+	0.990135i	$0.455253\pi$
$500$	−5427.10	−	1340.35i	−0.485415	−	0.119884i
$501$	−457.140	−	791.789i	−0.0407655	−	0.0706078i
$502$			2458.89i			0.218617i
$503$	9510.17	−	5490.70i	0.843017	−	0.486716i	−0.0152718	−	0.999883i	$-0.504861\pi$
$503$	9510.17	−	5490.70i	0.843017	−	0.486716i	0.858288	+	0.513167i	$0.171528\pi$
$504$	−63.7373	+	110.396i	−0.00563310	+	0.00975682i
$505$	−4354.26	+	16687.3i	−0.383688	+	1.47044i
$506$	119.754			0.0105212
$507$	−3293.67	+	4310.47i	−0.288515	+	0.377583i
$508$			10214.5i			0.892114i
$509$	2680.91	−	4643.48i	0.233457	−	0.404359i	−0.725366	−	0.688363i	$-0.758330\pi$
$509$	2680.91	−	4643.48i	0.233457	−	0.404359i	0.958823	+	0.284004i	$0.0916630\pi$
$510$	5502.32	+	1435.74i	0.477739	+	0.124658i
$511$	35.0802	+	60.7606i	0.00303690	+	0.00526006i
$512$			512.000i			0.0441942i
$513$	−7964.39	+	4598.24i	−0.685451	+	0.395745i
$514$	−2550.52	−	4417.63i	−0.218869	−	0.379092i
$515$	−4490.77	−	16330.7i	−0.384246	−	1.39731i
$516$	721.170	+	1249.10i	0.0615266	+	0.106567i
$517$	−3923.58	−	2265.28i	−0.333769	−	0.192702i
$518$	448.857	+	259.148i	0.0380727	+	0.0219813i
$519$	−3606.38			−0.305014
$520$	−2302.70	+	3503.37i	−0.194192	+	0.295448i
$521$	−2082.78			−0.175140			−0.0875701	−	0.996158i	$-0.527910\pi$
$521$	−2082.78			−0.175140			−0.0875701	+	0.996158i	$0.527910\pi$
$522$	3826.81	+	2209.41i	0.320872	+	0.185255i
$523$	−13983.6	−	8073.43i	−1.16914	−	0.675003i	−0.215662	−	0.976468i	$-0.569191\pi$
$523$	−13983.6	−	8073.43i	−1.16914	−	0.675003i	−0.953477	+	0.301466i	$0.902524\pi$
$524$	2562.95	+	4439.16i	0.213670	+	0.370087i
$525$	202.199	−	120.302i	0.0168089	−	0.0100008i
$526$	−5627.96	−	9747.92i	−0.466522	−	0.808041i
$527$	−11213.1	+	6473.89i	−0.926851	+	0.535117i
$528$			2450.99i			0.202018i
$529$	−6083.03	−	10536.1i	−0.499962	−	0.865959i
$530$	−3841.77	+	14723.2i	−0.314860	+	1.20667i
$531$	6891.64	−	11936.7i	0.563223	−	0.975531i
$532$		−	237.076i		−	0.0193205i
$533$	7721.06	−	1543.96i	0.627460	−	0.125471i
$534$	−4741.73			−0.384260
$535$	−2666.50	−	695.779i	−0.215482	−	0.0562264i
$536$	1521.31	−	2634.98i	0.122594	−	0.212339i
$537$	7901.44	−	4561.90i	0.634958	−	0.366593i
$538$			9240.38i			0.740486i
$539$	10621.8	+	18397.4i	0.848815	+	1.47019i
$540$	−3715.79	+	3764.84i	−0.296115	+	0.300024i
$541$	1521.93			0.120948			0.0604740	−	0.998170i	$-0.480739\pi$
$541$	1521.93			0.120948			0.0604740	+	0.998170i	$0.480739\pi$
$542$	8293.58	−	4788.30i	0.657269	−	0.379475i
$543$	410.933	+	237.252i	0.0324766	+	0.0187504i
$544$	1647.90	−	2854.25i	0.129877	−	0.224954i
$545$	7116.99	−	1957.10i	0.559373	−	0.153822i
$546$	−34.5991	−	173.024i	−0.00271191	−	0.0135618i
$547$			319.733i			0.0249923i	0.999922	+	0.0124961i	$0.00397775\pi$
$547$			319.733i			0.0249923i	−0.999922	+	0.0124961i	$0.996022\pi$
$548$	−4221.96	−	2437.55i	−0.329112	−	0.190013i
$549$	−1547.57	+	2680.46i	−0.120307	+	0.208378i
$550$	−7578.13	+	13532.5i	−0.587513	+	1.04914i
$551$	−8218.07			−0.635393
$552$	−16.5107	+	9.53246i	−0.00127308	+	0.000735015i
$553$	278.654	−	160.881i	0.0214278	−	0.0123714i
$554$	−6956.63			−0.533500
$555$	6679.55	+	6592.53i	0.510867	+	0.504211i
$556$	643.391	−	1114.39i	0.0490753	−	0.0850008i
$557$	5384.82	+	3108.93i	0.409627	+	0.236498i	0.690629	−	0.723209i	$-0.257334\pi$
$557$	5384.82	+	3108.93i	0.409627	+	0.236498i	−0.281003	+	0.959707i	$0.590667\pi$
$558$		−	5255.64i		−	0.398726i
$559$	6483.90	+	2193.66i	0.490590	+	0.165978i
$560$	−36.1563	−	131.483i	−0.00272836	−	0.00992170i
$561$	7888.65	−	13663.5i	0.593688	−	1.02830i
$562$	−4345.87	−	2509.09i	−0.326191	−	0.188327i
$563$	14730.5	−	8504.68i	1.10270	−	0.636642i	0.165768	−	0.986165i	$-0.446990\pi$
$563$	14730.5	−	8504.68i	1.10270	−	0.636642i	0.936928	+	0.349523i	$0.113656\pi$
$564$	721.268			0.0538491
$565$	16512.5	−	16730.4i	1.22953	−	1.24576i
$566$	−8222.26	−	14241.4i	−0.610613	−	1.05761i
$567$			207.592i			0.0153757i
$568$	−6356.82	+	3670.11i	−0.469588	+	0.271117i
$569$	−1290.14	+	2234.59i	−0.0950536	+	0.164638i	−0.909631	−	0.415417i	$-0.863636\pi$
$569$	−1290.14	+	2234.59i	−0.0950536	+	0.164638i	0.814577	+	0.580055i	$0.196969\pi$
$570$	1083.85	−	4153.75i	0.0796448	−	0.305230i
$571$	−7562.68			−0.554270			−0.277135	−	0.960831i	$-0.589385\pi$
$571$	−7562.68			−0.554270			−0.277135	+	0.960831i	$0.589385\pi$
$572$	7678.18	+	8737.40i	0.561260	+	0.638687i
$573$			1990.13i			0.145094i
$574$	−128.055	+	221.799i	−0.00931173	+	0.0161284i
$575$	−120.632	+	1.58211i	−0.00874908	+	0.000114745i
$576$	668.900	+	1158.57i	0.0483869	+	0.0838085i
$577$			22883.2i			1.65102i	0.564385	+	0.825512i	$0.309113\pi$
$577$			22883.2i			1.65102i	−0.564385	+	0.825512i	$0.690887\pi$
$578$	−9863.51	+	5694.70i	−0.709806	+	0.409807i
$579$	−1491.05	−	2582.58i	−0.107023	−	0.185369i
$580$	−4557.75	+	1253.33i	−0.326294	+	0.0897274i
$581$	−471.346	−	816.396i	−0.0336570	−	0.0582957i
$582$	546.314	+	315.414i	0.0389097	+	0.0224645i
$583$	36561.1	+	21108.6i	2.59726	+	1.49953i
$584$	736.307			0.0521723
$585$	−633.660	+	10935.9i	−0.0447840	+	0.772894i
$586$	15845.8			1.11704
$587$	−22919.3	−	13232.5i	−1.61155	−	0.930430i	−0.989011	−	0.147843i	$-0.952767\pi$
$587$	−22919.3	−	13232.5i	−1.61155	−	0.930430i	−0.622541	−	0.782587i	$-0.713900\pi$
$588$	−2928.88	−	1690.99i	−0.205417	−	0.118597i
$589$	4887.19	+	8464.85i	0.341890	+	0.592170i
$590$	3909.43	+	14216.6i	0.272794	+	0.992016i
$591$	−564.351	−	977.485i	−0.0392797	−	0.0680344i
$592$	4710.59	−	2719.66i	0.327034	−	0.188813i
$593$			6505.12i			0.450477i	0.974304	+	0.225239i	$0.0723162\pi$
$593$			6505.12i			0.450477i	−0.974304	+	0.225239i	$0.927684\pi$
$594$	7338.14	+	12710.0i	0.506881	+	0.877944i
$595$	−221.623	+	849.346i	−0.0152700	+	0.0585207i
$596$	−3687.02	+	6386.11i	−0.253400	+	0.438901i
$597$			5236.78i			0.359007i
$598$	−28.9959	+	85.7045i	−0.00198283	+	0.00586073i
$599$	−23131.1			−1.57781			−0.788906	−	0.614514i	$-0.789352\pi$
$599$	−23131.1			−1.57781			−0.788906	+	0.614514i	$0.789352\pi$
$600$	−32.3808	−	2468.97i	−0.00220323	−	0.167992i
$601$	−12953.5	+	22436.1i	−0.879173	+	1.52277i	−0.0269221	+	0.999638i	$0.508571\pi$
$601$	−12953.5	+	22436.1i	−0.879173	+	1.52277i	−0.852250	+	0.523134i	$0.824763\pi$
$602$	−192.813	+	111.321i	−0.0130540	+	0.00753671i
$603$		−	7950.01i		−	0.536898i
$604$	−1055.30	−	1827.84i	−0.0710922	−	0.123135i
$605$	20035.9	+	19774.8i	1.34640	+	1.32886i
$606$	−7617.57			−0.510632
$607$	−3001.39	+	1732.85i	−0.200696	+	0.115872i	−0.596980	−	0.802256i	$-0.703633\pi$
$607$	−3001.39	+	1732.85i	−0.200696	+	0.115872i	0.396284	+	0.918128i	$0.370300\pi$
$608$	−2154.69	−	1244.01i	−0.143724	−	0.0829792i
$609$	99.4743	−	172.295i	0.00661889	−	0.0114643i
$610$	−877.889	−	3192.45i	−0.0582700	−	0.211899i
$611$	2571.21	−	2259.50i	0.170245	−	0.149607i
$612$		−	8611.56i		−	0.568794i
$613$	−4792.23	−	2766.80i	−0.315753	−	0.182300i	0.333745	−	0.942663i	$-0.391687\pi$
$613$	−4792.23	−	2766.80i	−0.315753	−	0.182300i	−0.649498	+	0.760363i	$0.725021\pi$
$614$	929.515	−	1609.97i	0.0610947	−	0.105819i
$615$	−3257.64	+	3300.64i	−0.213595	+	0.216414i
$616$	−378.339			−0.0247463
$617$	−3063.88	+	1768.93i	−0.199914	+	0.115420i	−0.596615	−	0.802527i	$-0.703488\pi$
$617$	−3063.88	+	1768.93i	−0.199914	+	0.115420i	0.396701	+	0.917948i	$0.370155\pi$
$618$	6478.77	−	3740.52i	0.421706	−	0.243472i
$619$	24275.8			1.57629			0.788147	−	0.615487i	$-0.211041\pi$
$619$	24275.8			1.57629			0.788147	+	0.615487i	$0.211041\pi$
$620$	4001.41	+	3949.28i	0.259195	+	0.255818i
$621$	−57.0793	+	98.8643i	−0.00368843	+	0.00638855i
$622$	4433.54	+	2559.71i	0.285802	+	0.165008i
$623$		−	731.940i		−	0.0470699i
$624$	−1754.11	−	593.455i	−0.112533	−	0.0380725i
$625$	7454.94	−	13731.9i	0.477116	−	0.878840i
$626$	−2292.82	+	3971.28i	−0.146389	+	0.253553i
$627$	−10314.7	−	5955.20i	−0.656985	−	0.379311i
$628$	10531.6	−	6080.44i	0.669201	−	0.386363i
$629$	−35013.5			−2.21952
$630$	−253.590	−	250.286i	−0.0160370	−	0.0158280i
$631$	9823.65	+	17015.1i	0.619768	+	1.07347i	0.989528	+	0.144342i	$0.0461066\pi$
$631$	9823.65	+	17015.1i	0.619768	+	1.07347i	−0.369760	+	0.929127i	$0.620560\pi$
$632$		−	3376.78i		−	0.212533i
$633$	−7472.68	+	4314.36i	−0.469214	+	0.270901i
$634$	−99.3043	+	172.000i	−0.00622063	+	0.0107744i
$635$	−27625.3	−	7208.38i	−1.72642	−	0.450482i
$636$	−6721.00			−0.419033
$637$	−15738.3	+	3147.15i	−0.978926	+	0.195753i
$638$			13114.9i			0.813828i
$639$	−9589.60	+	16609.7i	−0.593675	+	1.02828i
$640$	−1384.72	−	361.320i	−0.0855248	−	0.0223163i
$641$	−7447.06	−	12898.7i	−0.458879	−	0.794801i	0.540023	−	0.841650i	$-0.318415\pi$
$641$	−7447.06	−	12898.7i	−0.458879	−	0.794801i	−0.998902	+	0.0468488i	$0.985082\pi$
$642$		−	1217.23i		−	0.0748291i
$643$	−12712.3	+	7339.46i	−0.779666	+	0.450140i	−0.836312	−	0.548254i	$-0.815293\pi$
$643$	−12712.3	+	7339.46i	−0.779666	+	0.450140i	0.0566462	+	0.998394i	$0.481959\pi$
$644$	−1.47144	−	2.54862i	−9.00358e−5	−	0.000155947i
$645$	−3887.17	+	1068.93i	−0.237298	+	0.0652545i
$646$	8007.84	+	13870.0i	0.487715	+	0.844748i
$647$	23224.1	+	13408.4i	1.41118	+	0.814744i	0.995499	−	0.0947679i	$-0.0302109\pi$
$647$	23224.1	+	13408.4i	1.41118	+	0.814744i	0.415678	+	0.909512i	$0.363544\pi$
$648$	1886.72	+	1089.30i	0.114379	+	0.0660367i
$649$	40908.1			2.47424
$650$	−7849.94	−	8700.05i	−0.473692	−	0.524991i
$651$	−236.625			−0.0142459
$652$	−3632.36	−	2097.15i	−0.218182	−	0.125967i
$653$	−27706.6	−	15996.4i	−1.66040	−	0.958634i	−0.972522	−	0.232811i	$-0.925208\pi$
$653$	−27706.6	−	15996.4i	−1.66040	−	0.958634i	−0.687881	−	0.725823i	$-0.741459\pi$
$654$	1630.14	+	2823.48i	0.0974670	+	0.168818i
$655$	−13814.5	+	3798.85i	−0.824089	+	0.226616i
$656$	1343.90	+	2327.70i	0.0799853	+	0.138539i
$657$	1666.14	−	961.946i	0.0989380	−	0.0571219i
$658$			111.336i			0.00659624i
$659$	7455.05	+	12912.5i	0.440679	+	0.763279i	0.997740	−	0.0671928i	$-0.0214043\pi$
$659$	7455.05	+	12912.5i	0.440679	+	0.763279i	−0.557061	+	0.830472i	$0.688071\pi$
$660$	−6628.78	−	1729.67i	−0.390947	−	0.102011i
$661$	9348.15	−	16191.5i	0.550077	−	0.952761i	−0.448192	−	0.893937i	$-0.647932\pi$
$661$	9348.15	−	16191.5i	0.550077	−	0.952761i	0.998268	−	0.0588233i	$-0.0187349\pi$
$662$		−	19540.3i		−	1.14721i
$663$	7868.54	+	8954.02i	0.460918	+	0.524503i
$664$	−9893.22			−0.578210
$665$	641.178	+	167.305i	0.0373892	+	0.00975610i
$666$	7106.18	−	12308.3i	0.413452	−	0.716119i
$667$	−88.3461	+	51.0066i	−0.00512860	+	0.00296100i
$668$		−	1481.10i		−	0.0857868i
$669$	5253.43	+	9099.20i	0.303601	+	0.525853i
$670$	6052.79	+	5973.93i	0.349015	+	0.344467i
$671$	−9186.21			−0.528509
$672$	52.1623	−	30.1159i	0.00299435	−	0.00172879i
$673$	−19992.7	−	11542.8i	−1.14512	−	0.661133i	−0.197423	−	0.980318i	$-0.563257\pi$
$673$	−19992.7	−	11542.8i	−1.14512	−	0.661133i	−0.947692	+	0.319186i	$0.896591\pi$
$674$	7747.81	−	13419.6i	0.442781	−	0.766920i
$675$	−7559.88	−	12706.3i	−0.431082	−	0.724543i
$676$	−8112.22	+	3379.48i	−0.461551	+	0.192278i
$677$			19019.0i			1.07970i	0.841760	+	0.539852i	$0.181520\pi$
$677$			19019.0i			1.07970i	−0.841760	+	0.539852i	$0.818480\pi$
$678$	8991.92	+	5191.49i	0.509340	+	0.294068i
$679$	−48.6878	+	84.3298i	−0.00275179	+	0.00476625i
$680$	6556.47	+	6471.04i	0.369748	+	0.364931i
$681$	7594.24			0.427330
$682$	13508.7	−	7799.25i	0.758467	−	0.437901i
$683$	26578.9	−	15345.3i	1.48904	−	0.859696i	0.489115	−	0.872219i	$-0.337320\pi$
$683$	26578.9	−	15345.3i	1.48904	−	0.859696i	0.999922	+	0.0125236i	$0.00398651\pi$
$684$	−6500.93			−0.363406
$685$	9571.88	−	9698.24i	0.533902	−	0.540950i
$686$	522.491	−	904.980i	0.0290799	−	0.0503678i
$687$	4763.43	+	2750.17i	0.264536	+	0.152730i
$688$			2336.55i			0.129477i
$689$	−23959.3	+	21054.7i	−1.32478	+	1.16418i
$690$	−14.1292	−	51.3808i	−0.000779549	−	0.00283483i
$691$	2798.97	−	4847.96i	0.154092	−	0.266896i	−0.778636	−	0.627476i	$-0.784088\pi$
$691$	2798.97	−	4847.96i	0.154092	−	0.266896i	0.932728	+	0.360580i	$0.117421\pi$
$692$	−5059.51	−	2921.11i	−0.277939	−	0.160468i
$693$	−856.116	+	494.279i	−0.0469281	+	0.0270939i
$694$	18809.5			1.02881
$695$	2559.85	+	2526.49i	0.139713	+	0.137893i
$696$	−1043.95	−	1808.17i	−0.0568545	−	0.0984749i
$697$		−	17301.6i		−	0.940237i
$698$	−9076.05	+	5240.06i	−0.492168	+	0.284154i
$699$	2593.18	−	4491.52i	0.140319	−	0.243040i
$700$	381.114	−	4.99835i	0.0205782	−	0.000269885i
$701$	17788.7			0.958443			0.479222	−	0.877694i	$-0.340919\pi$
$701$	17788.7			0.958443			0.479222	+	0.877694i	$0.340919\pi$
$702$	−10873.0	+	2174.23i	−0.584579	+	0.116896i
$703$			26432.0i			1.41807i
$704$	−1985.26	+	3438.58i	−0.106282	+	0.184086i
$705$	−509.001	+	1950.69i	−0.0271916	+	0.104209i
$706$	−6437.05	−	11149.3i	−0.343147	−	0.594348i
$707$		−	1175.86i		−	0.0625499i
$708$	−5640.08	+	3256.30i	−0.299389	+	0.172852i
$709$	−11150.3	−	19312.9i	−0.590632	−	1.02300i	−0.994147	−	0.108031i	$-0.965545\pi$
$709$	−11150.3	−	19312.9i	−0.590632	−	1.02300i	0.403516	−	0.914973i	$-0.367788\pi$
$710$	−5439.90	−	19782.2i	−0.287544	−	1.04565i
$711$	−4411.58	−	7641.08i	−0.232696	−	0.403042i
$712$	−6652.33	−	3840.73i	−0.350150	−	0.202159i
$713$	105.077	+	60.6661i	0.00551915	+	0.00318648i
$714$	−387.719			−0.0203221
$715$	−29049.1	+	14599.9i	−1.51940	+	0.763642i
$716$	14780.3			0.771458
$717$	5203.29	+	3004.12i	0.271019	+	0.156473i
$718$	−4783.80	−	2761.93i	−0.248649	−	0.143557i
$719$	−6284.12	−	10884.4i	−0.325950	−	0.564562i	0.655754	−	0.754974i	$-0.272351\pi$
$719$	−6284.12	−	10884.4i	−0.325950	−	0.564562i	−0.981704	+	0.190413i	$0.939017\pi$
$720$	−3605.43	+	991.456i	−0.186620	+	0.0513186i
$721$	577.392	+	1000.07i	0.0298241	+	0.0516569i
$722$	−1409.58	+	813.822i	−0.0726582	+	0.0419492i
$723$			1532.09i			0.0788090i
$724$	384.341	+	665.698i	0.0197292	+	0.0341719i
$725$	−173.264	−	13211.1i	−0.00887569	−	0.676754i
$726$	−6217.16	+	10768.4i	−0.317824	+	0.550488i
$727$		−	533.809i		−	0.0272323i	−0.999907	−	0.0136162i	$-0.995666\pi$
$727$		−	533.809i		−	0.0272323i	0.999907	−	0.0136162i	$-0.00433429\pi$
$728$	91.6066	−	270.766i	0.00466369	−	0.0137847i
$729$	−2193.15			−0.111424
$730$	−519.614	+	1991.37i	−0.0263449	+	0.100964i
$731$	7520.30	−	13025.5i	0.380504	−	0.659052i
$732$	1266.52	−	731.226i	0.0639507	−	0.0369220i
$733$			5164.01i			0.260214i	0.991500	+	0.130107i	$0.0415321\pi$
$733$			5164.01i			0.260214i	−0.991500	+	0.130107i	$0.958468\pi$
$734$	−5181.18	−	8974.07i	−0.260546	−	0.451279i
$735$	6640.26	−	6727.91i	0.333237	−	0.337637i
$736$	−30.8846			−0.00154677
$737$	20434.1	−	11797.6i	1.02130	−	0.589649i
$738$	6082.02	+	3511.45i	0.303363	+	0.175147i
$739$	5972.38	−	10344.5i	0.297290	−	0.514922i	−0.678225	−	0.734854i	$-0.737250\pi$
$739$	5972.38	−	10344.5i	0.297290	−	0.514922i	0.975515	+	0.219933i	$0.0705838\pi$
$740$	4031.13	+	14659.2i	0.200253	+	0.728221i
$741$	6759.46	−	5940.02i	0.335108	−	0.294483i
$742$		−	1037.46i		−	0.0513294i
$743$	32254.5	+	18622.1i	1.59260	+	0.919489i	0.992859	+	0.119296i	$0.0380638\pi$
$743$	32254.5	+	18622.1i	1.59260	+	0.919489i	0.599743	+	0.800193i	$0.295270\pi$
$744$	−1241.65	+	2150.59i	−0.0611841	+	0.105974i
$745$	−14669.5	−	14478.4i	−0.721407	−	0.712008i
$746$	4618.65			0.226677
$747$	−22386.7	+	12925.0i	−1.09650	+	0.633065i
$748$	22134.5	−	12779.4i	1.08198	−	0.624679i
$749$	187.894			0.00916620
$750$	6700.26	+	1654.78i	0.326212	+	0.0805656i
$751$	2158.36	−	3738.39i	0.104873	−	0.181645i	−0.808813	−	0.588066i	$-0.799890\pi$
$751$	2158.36	−	3738.39i	0.104873	−	0.181645i	0.913686	+	0.406420i	$0.133223\pi$
$752$	1011.89	+	584.216i	0.0490690	+	0.0283300i
$753$		−	3035.73i		−	0.146917i
$754$	−9385.93	−	3175.48i	−0.453336	−	0.153374i
$755$	5688.18	−	1564.19i	0.274191	−	0.0753996i
$756$	180.331	−	312.342i	0.00867535	−	0.0150261i
$757$	10998.7	+	6350.10i	0.528077	+	0.304886i	0.740233	−	0.672350i	$-0.234715\pi$
$757$	10998.7	+	6350.10i	0.528077	+	0.304886i	−0.212156	+	0.977236i	$0.568048\pi$
$758$	5528.78	−	3192.05i	0.264927	−	0.152956i
$759$	−147.847			−0.00707051
$760$	4885.04	−	4949.53i	0.233157	−	0.236234i
$761$	9732.17	+	16856.6i	0.463588	+	0.802959i	0.999137	−	0.0415459i	$-0.0132283\pi$
$761$	9732.17	+	16856.6i	0.463588	+	0.802959i	−0.535548	+	0.844505i	$0.679895\pi$
$762$		−	12610.7i		−	0.599525i
$763$	−435.837	+	251.630i	−0.0206794	+	0.0119392i
$764$	−1611.98	+	2792.03i	−0.0763342	+	0.132215i
$765$	23290.2	+	6077.20i	1.10073	+	0.287218i
$766$	10485.1			0.494573
$767$	−9905.03	+	29276.8i	−0.466297	+	1.37826i
$768$		−	632.111i		−	0.0296997i
$769$	9041.43	−	15660.2i	0.423982	−	0.734358i	−0.572343	−	0.820014i	$-0.693965\pi$
$769$	9041.43	−	15660.2i	0.423982	−	0.734358i	0.996325	+	0.0856561i	$0.0272987\pi$
$770$	266.995	−	1023.23i	0.0124959	−	0.0478891i
$771$	3148.85	+	5453.97i	0.147086	+	0.254760i
$772$		−	4830.92i		−	0.225218i
$773$	−17404.4	+	10048.4i	−0.809822	+	0.467551i	−0.846894	−	0.531762i	$-0.821530\pi$
$773$	−17404.4	+	10048.4i	−0.809822	+	0.467551i	0.0370721	+	0.999313i	$0.488197\pi$
$774$	3052.57	+	5287.21i	0.141760	+	0.245536i
$775$	−13504.8	+	8034.93i	−0.625942	+	0.372417i
$776$	510.961	+	885.011i	0.0236372	+	0.0409408i
$777$	−554.155	−	319.942i	−0.0255858	−	0.0147720i
$778$	16282.1	+	9400.46i	0.750309	+	0.433191i
$779$	−13061.1			−0.600723
$780$	2842.89	−	4325.23i	0.130503	−	0.198549i
$781$	−56923.0			−2.60802
$782$	172.172	+	99.4036i	0.00787323	+	0.00454561i
$783$	−10827.1	−	6251.04i	−0.494163	−	0.285305i
$784$	−2739.35	−	4744.70i	−0.124788	−	0.216140i
$785$	9012.54	+	32774.1i	0.409772	+	1.49014i
$786$	−3164.20	−	5480.55i	−0.143592	−	0.248708i
$787$	10526.6	−	6077.55i	0.476790	−	0.275275i	−0.242288	−	0.970204i	$-0.577898\pi$
$787$	10526.6	−	6077.55i	0.476790	−	0.275275i	0.719078	+	0.694930i	$0.244564\pi$
$788$		−	1828.46i		−	0.0826602i
$789$	6948.24	+	12034.7i	0.313516	+	0.543025i
$790$	9132.61	+	2383.00i	0.411296	+	0.107321i
$791$	−801.365	+	1388.01i	−0.0360218	+	0.0623916i
$792$			10374.6i			0.465459i
$793$	2224.24	−	6574.31i	0.0996031	−	0.294402i
$794$	−16968.2			−0.758411
$795$	4743.02	−	18177.1i	0.211595	−	0.810914i
$796$	−4241.71	+	7346.85i	−0.188873	+	0.327138i
$797$	−21798.0	+	12585.1i	−0.968791	+	0.559332i	−0.898867	−	0.438221i	$-0.855609\pi$
$797$	−21798.0	+	12585.1i	−0.968791	+	0.559332i	−0.0699234	+	0.997552i	$0.522275\pi$
$798$			292.692i			0.0129839i
$799$	−3760.66	−	6513.65i	−0.166511	−	0.288406i
$800$	1954.40	−	3490.03i	0.0863731	−	0.154239i
$801$	−20070.8			−0.885352
$802$	16807.1	−	9703.60i	0.740001	−	0.427240i
$803$	4945.02	+	2855.01i	0.217318	+	0.125468i
$804$	−1878.19	+	3253.13i	−0.0823865	+	0.142698i
$805$	7.93121	−	2.18100i	0.000347253	−	9.54909e-5i
$806$	2310.86	+	11556.2i	0.100988	+	0.505025i
$807$		−	11408.1i		−	0.497626i
$808$	−10687.0	−	6170.11i	−0.465304	−	0.268643i
$809$	17666.9	−	30599.9i	0.767780	−	1.32983i	−0.170984	−	0.985274i	$-0.554695\pi$
$809$	17666.9	−	30599.9i	0.767780	−	1.32983i	0.938764	−	0.344561i	$-0.111972\pi$
$810$	−4277.51	+	4333.98i	−0.185551	+	0.188001i
$811$	−26854.0			−1.16273			−0.581363	−	0.813644i	$-0.697480\pi$
$811$	−26854.0			−1.16273			−0.581363	+	0.813644i	$0.697480\pi$
$812$	279.112	−	161.145i	0.0120627	−	0.00696440i
$813$	−10239.2	+	5911.60i	−0.441703	+	0.255017i
$814$	42181.6			1.81630
$815$	8235.16	−	8343.88i	0.353945	−	0.358617i
$816$	−2034.48	+	3523.83i	−0.0872808	+	0.151175i
$817$	−9833.08	−	5677.13i	−0.421072	−	0.243106i
$818$		−	21363.3i		−	0.913143i
$819$	−146.451	−	732.377i	−0.00624837	−	0.0312470i
$820$	−7243.72	+	1991.95i	−0.308490	+	0.0848315i
$821$	−5817.98	+	10077.0i	−0.247319	+	0.428369i	−0.962781	−	0.270283i	$-0.912883\pi$
$821$	−5817.98	+	10077.0i	−0.247319	+	0.428369i	0.715462	+	0.698651i	$0.246216\pi$
$822$	5212.40	+	3009.38i	0.221172	+	0.127694i
$823$	28747.9	−	16597.6i	1.21761	−	0.702986i	0.253201	−	0.967414i	$-0.418517\pi$
$823$	28747.9	−	16597.6i	1.21761	−	0.702986i	0.964405	+	0.264428i	$0.0851832\pi$
$824$	12119.0			0.512363
$825$	9355.90	−	16707.1i	0.394825	−	0.705051i
$826$	−502.647	−	870.611i	−0.0211735	−	0.0366736i
$827$		−	31994.0i		−	1.34527i	−0.739973	−	0.672637i	$-0.765162\pi$
$827$		−	31994.0i		−	1.34527i	0.739973	−	0.672637i	$-0.234838\pi$
$828$	−69.8865	+	40.3490i	−0.00293324	+	0.00169351i
$829$	13325.7	−	23080.8i	0.558289	−	0.966985i	−0.439351	−	0.898316i	$-0.644791\pi$
$829$	13325.7	−	23080.8i	0.558289	−	0.966985i	0.997639	−	0.0686690i	$-0.0218752\pi$
$830$	6981.67	−	26756.5i	0.291973	−	1.11895i
$831$	8588.60			0.358526
$832$	−1980.20	−	2253.38i	−0.0825135	−	0.0938963i
$833$			35267.0i			1.46690i
$834$	−794.325	+	1375.81i	−0.0329799	+	0.0571229i
$835$	4005.69	+	1045.22i	0.166015	+	0.0433189i
$836$	−9647.24	−	16709.5i	−0.399111	−	0.691280i
$837$			14869.7i			0.614064i
$838$	−4023.71	+	2323.09i	−0.165867	+	0.0957636i
$839$	−4554.60	−	7888.80i	−0.187416	−	0.324614i	0.756972	−	0.653447i	$-0.226678\pi$
$839$	−4554.60	−	7888.80i	−0.187416	−	0.324614i	−0.944388	+	0.328833i	$0.893345\pi$
$840$	44.6383	+	162.327i	0.00183353	+	0.00666765i
$841$	6608.51	+	11446.3i	0.270963	+	0.469321i
$842$	−5037.67	−	2908.50i	−0.206187	−	0.119042i
$843$	5365.38	+	3097.70i	0.219209	+	0.126561i
$844$	−13978.2			−0.570084
$845$	−3415.10	−	24324.6i	−0.139033	−	0.990288i
$846$	3052.98			0.124071
$847$	−1662.23	−	959.690i	−0.0674321	−	0.0389319i
$848$	−9429.11	−	5443.90i	−0.381836	−	0.220453i
$849$	10151.1	+	17582.3i	0.410349	+	0.710745i
$850$	−22128.0	+	13165.5i	−0.892924	+	0.531263i
$851$	164.054	+	284.150i	0.00660833	+	0.0114460i
$852$	7848.08	−	4531.09i	0.315576	−	0.182198i
$853$			6196.34i			0.248720i	0.992237	+	0.124360i	$0.0396878\pi$
$853$			6196.34i			0.248720i	−0.992237	+	0.124360i	$0.960312\pi$
$854$	112.873	+	195.502i	0.00452276	+	0.00783365i
$855$	4587.73	−	17582.0i	0.183505	−	0.703264i
$856$	985.938	−	1707.69i	0.0393676	−	0.0681867i
$857$		−	5042.07i		−	0.200973i	−0.994938	−	0.100486i	$-0.967960\pi$
$857$		−	5042.07i		−	0.200973i	0.994938	−	0.100486i	$-0.0320399\pi$
$858$	−9479.42	−	10787.1i	−0.377182	−	0.429215i
$859$	1176.58			0.0467338			0.0233669	−	0.999727i	$-0.492561\pi$
$859$	1176.58			0.0467338			0.0233669	+	0.999727i	$0.492561\pi$
$860$	−6319.26	−	1648.91i	−0.250564	−	0.0653805i
$861$	158.096	−	273.831i	0.00625773	−	0.0108387i
$862$	17283.5	−	9978.61i	0.682920	−	0.394284i
$863$			15621.2i			0.616167i	0.951359	+	0.308084i	$0.0996876\pi$
$863$			15621.2i			0.616167i	−0.951359	+	0.308084i	$0.900312\pi$
$864$	−1892.51	−	3277.92i	−0.0745190	−	0.129071i
$865$	11470.7	−	11622.2i	0.450887	−	0.456839i
$866$	6187.52			0.242795
$867$	12177.4	−	7030.63i	0.477009	−	0.275401i
$868$	−331.969	−	191.662i	−0.0129813	−	0.00749475i
$869$	13093.4	−	22678.4i	0.511118	−	0.885283i
$870$	5626.97	−	1547.36i	0.219278	−	0.0602992i
$871$	3495.55	+	17480.7i	0.135984	+	0.680034i
$872$			5281.54i			0.205110i
$873$	2312.44	+	1335.09i	0.0896497	+	0.0517593i
$874$	75.0406	−	129.974i	0.00290422	−	0.00503025i
$875$	−255.435	+	1034.26i	−0.00986889	+	0.0399594i
$876$	−909.039			−0.0350612
$877$	−24243.2	+	13996.8i	−0.933448	+	0.538926i	−0.887900	−	0.460036i	$-0.847837\pi$
$877$	−24243.2	+	13996.8i	−0.933448	+	0.538926i	−0.0455474	+	0.998962i	$0.514503\pi$
$878$	−23199.7	+	13394.4i	−0.891746	+	0.514850i
$879$	−19563.2			−0.750681
$880$	−7898.73	−	7795.82i	−0.302575	−	0.298633i
$881$	−4259.65	+	7377.93i	−0.162896	+	0.282144i	−0.935906	−	0.352250i	$-0.885417\pi$
$881$	−4259.65	+	7377.93i	−0.162896	+	0.282144i	0.773010	+	0.634394i	$0.218750\pi$
$882$	−12397.4	−	7157.63i	−0.473289	−	0.273254i
$883$		−	34533.5i		−	1.31613i	−0.752960	−	0.658067i	$-0.771374\pi$
$883$		−	34533.5i		−	1.31613i	0.752960	−	0.658067i	$-0.228626\pi$
$884$	3786.43	+	18935.3i	0.144063	+	0.720433i
$885$	−4826.55	−	17551.7i	−0.183325	−	0.666662i
$886$	−2578.96	+	4466.90i	−0.0977900	+	0.169377i
$887$	−22901.0	−	13221.9i	−0.866899	−	0.500504i	−0.000582639	−	1.00000i	$-0.500185\pi$
$887$	−22901.0	−	13221.9i	−0.866899	−	0.500504i	−0.866317	+	0.499495i	$0.833519\pi$
$888$	−5815.66	+	3357.67i	−0.219776	+	0.126888i
$889$	1946.61			0.0734388
$890$	15081.9	−	15281.0i	0.568031	−	0.575529i
$891$	8447.46	+	14631.4i	0.317621	+	0.550136i
$892$			17020.8i			0.638898i
$893$	−4917.21	+	2838.95i	−0.184264	+	0.106385i
$894$	4551.97	−	7884.24i	0.170291	−	0.294954i
$895$	−10430.5	+	39973.6i	−0.389555	+	1.49293i
$896$	97.5736			0.00363806
$897$	35.7981	−	105.810i	0.00133251	−	0.00393857i
$898$		−	27514.1i		−	1.02245i
$899$	−6643.85	+	11507.5i	−0.246479	+	0.426914i
$900$	−137.061	−	10450.7i	−0.00507635	−	0.387062i
$901$	35043.0	+	60696.2i	1.29573	+	2.24427i
$902$			20843.7i			0.769422i
$903$	238.046	−	137.436i	0.00877262	−	0.00506487i
$904$	8410.04	+	14566.6i	0.309418	+	0.535928i
$905$	−2071.63	+	569.677i	−0.0760921	+	0.0209245i
$906$	1302.87	+	2256.64i	0.0477759	+	0.0827503i
$907$	−9023.85	−	5209.92i	−0.330355	−	0.190731i	0.325644	−	0.945493i	$-0.394419\pi$
$907$	−9023.85	−	5209.92i	−0.330355	−	0.190731i	−0.655999	+	0.754762i	$0.727752\pi$
$908$	10654.2	+	6151.22i	0.389397	+	0.224819i
$909$	−32243.7			−1.17652
$910$	667.649	+	438.833i	0.0243212	+	0.0159859i
$911$	52607.0			1.91322			0.956612	−	0.291364i	$-0.0941091\pi$
$911$	52607.0			1.91322			0.956612	+	0.291364i	$0.0941091\pi$
$912$	2660.17	+	1535.85i	0.0965865	+	0.0557642i
$913$	−66442.6	−	38360.7i	−2.40847	−	1.39053i
$914$	−3760.53	−	6513.43i	−0.136091	−	0.235717i
$915$	1083.84	+	3941.37i	0.0391590	+	0.142402i
$916$	4455.18	+	7716.60i	0.160702	+	0.278345i
$917$	845.986	−	488.430i	0.0304656	−	0.0175893i
$918$			24364.5i			0.875980i
$919$	11317.0	+	19601.6i	0.406216	+	0.703586i	0.994462	−	0.105095i	$-0.0335148\pi$
$919$	11317.0	+	19601.6i	0.406216	+	0.703586i	−0.588246	+	0.808682i	$0.700181\pi$
$920$	21.7953	−	83.5282i	0.000781055	−	0.00299331i
$921$	−1147.57	+	1987.65i	−0.0410573	+	0.0711133i
$922$			28595.9i			1.02143i
$923$	13782.7	−	40738.2i	0.491509	−	1.45278i
$924$	467.094			0.0166302
$925$	−42491.0	+	557.274i	−1.51038	+	0.0198087i
$926$	−3597.59	+	6231.20i	−0.127672	+	0.221134i
$927$	27423.3	−	15832.9i	0.971630	−	0.560971i
$928$		−	3382.32i		−	0.119645i
$929$	14272.9	+	24721.4i	0.504068	+	0.873071i	0.999989	+	0.00470362i	$0.00149722\pi$
$929$	14272.9	+	24721.4i	0.504068	+	0.873071i	−0.495921	+	0.868368i	$0.665169\pi$
$930$	−4940.11	−	4875.75i	−0.174186	−	0.171916i
$931$	26623.3			0.937212
$932$	7276.11	−	4200.87i	0.255726	−	0.147644i
$933$	−5473.62	−	3160.19i	−0.192067	−	0.110890i
$934$	2291.67	−	3969.29i	0.0802845	−	0.139057i
$935$	18941.8	+	68881.8i	0.662527	+	2.40928i
$936$	−7424.78	−	2511.98i	−0.259280	−	0.0877207i
$937$		−	35965.7i		−	1.25395i	−0.779041	−	0.626973i	$-0.784293\pi$
$937$		−	35965.7i		−	1.25395i	0.779041	−	0.626973i	$-0.215707\pi$
$938$	−502.157	−	289.921i	−0.0174798	−	0.0100919i
$939$	2830.70	−	4902.91i	0.0983774	−	0.170395i
$940$	−2294.12	+	2324.41i	−0.0796022	+	0.0806530i
$941$	−15840.0			−0.548746			−0.274373	−	0.961623i	$-0.588470\pi$
$941$	−15840.0			−0.548746			−0.274373	+	0.961623i	$0.588470\pi$
$942$	−13002.3	+	7506.87i	−0.449721	+	0.259646i
$943$	−140.410	+	81.0657i	−0.00484876	+	0.00279943i
$944$	−10550.2			−0.363750
$945$	717.479	+	708.130i	0.0246980	+	0.0243762i
$946$	−9059.88	+	15692.2i	−0.311377	+	0.539320i
$947$	39118.6	+	22585.1i	1.34233	+	0.774992i	0.987148	−	0.159807i	$-0.0510871\pi$
$947$	39118.6	+	22585.1i	1.34233	+	0.774992i	0.355177	+	0.934799i	$0.384420\pi$
$948$			4168.95i			0.142828i
$949$	−3240.58	+	2847.73i	−0.110847	+	0.0974092i
$950$	9938.76	+	16704.6i	0.339427	+	0.570494i
$951$	122.600	−	212.350i	0.00418043	−	0.00724071i
$952$	−543.943	−	314.046i	−0.0185182	−	0.0106915i
$953$	4781.53	−	2760.62i	0.162528	−	0.0938354i	−0.416530	−	0.909122i	$-0.636754\pi$
$953$	4781.53	−	2760.62i	0.162528	−	0.0938354i	0.579058	+	0.815287i	$0.303421\pi$
$954$	−28448.6			−0.965470
$955$	−6413.55	−	6329.98i	−0.217317	−	0.214485i
$956$	4866.58	+	8429.17i	0.164641	+	0.285166i
$957$		−	16191.5i		−	0.546914i
$958$	15913.2	−	9187.49i	0.536672	−	0.309848i
$959$	−464.533	+	804.594i	−0.0156419	+	0.0270925i
$960$	1709.56	+	446.082i	0.0574749	+	0.0149971i
$961$	−13986.9			−0.469502
$962$	−10213.4	+	30188.2i	−0.342300	+	1.01175i
$963$		−	5152.30i		−	0.172410i
$964$	−1240.97	+	2149.42i	−0.0414614	+	0.0718133i
$965$	13065.4	+	3409.19i	0.435844	+	0.113726i
$966$	1.81663	+	3.14650i	6.05065e−5	+	0.000104800i
$967$			19462.9i			0.647245i	0.946186	+	0.323622i	$0.104901\pi$
$967$			19462.9i			0.647245i	−0.946186	+	0.323622i	$0.895099\pi$
$968$	−17444.5	+	10071.6i	−0.579224	+	0.334415i
$969$	−9886.41	−	17123.8i	−0.327758	−	0.567693i
$970$	−2754.13	+	757.356i	−0.0911646	+	0.0250693i
$971$	17055.4	+	29540.9i	0.563682	+	0.976325i	0.997171	+	0.0751667i	$0.0239489\pi$
$971$	17055.4	+	29540.9i	0.563682	+	0.976325i	−0.433489	+	0.901159i	$0.642718\pi$
$972$	−13392.3	−	7732.05i	−0.441933	−	0.255150i
$973$	−212.372	−	122.613i	−0.00699727	−	0.00403987i
$974$	−11829.4			−0.389157
$975$	9691.47	+	10741.0i	0.318334	+	0.352808i
$976$	2369.12			0.0776986
$977$	−11672.1	−	6738.88i	−0.382214	−	0.220671i	0.296567	−	0.955012i	$-0.404158\pi$
$977$	−11672.1	−	6738.88i	−0.382214	−	0.220671i	−0.678781	+	0.734341i	$0.737491\pi$
$978$	4484.49	+	2589.12i	0.146624	+	0.0846533i
$979$	−29784.6	−	51588.4i	−0.972339	−	1.68414i
$980$	14765.3	−	4060.32i	0.481287	−	0.132349i
$981$	6900.05	+	11951.2i	0.224568	+	0.388964i
$982$	−31831.3	+	18377.8i	−1.03440	+	0.597209i
$983$		−	18218.9i		−	0.591141i	−0.955321	−	0.295571i	$-0.904490\pi$
$983$		−	18218.9i		−	0.591141i	0.955321	−	0.295571i	$-0.0955097\pi$
$984$	−1659.16	−	2873.76i	−0.0537523	−	0.0931016i
$985$	4945.13	+	1290.35i	0.159964	+	0.0417401i
$986$	−10886.2	+	18855.4i	−0.351609	+	0.609005i
$987$		−	137.455i		−	0.00443285i
$988$	14294.4	−	2858.40i	0.460289	−	0.0920424i
$989$	−140.944			−0.00453160
$990$	−28058.3	−	7321.35i	−0.900759	−	0.235038i
$991$	−21768.9	+	37704.9i	−0.697792	+	1.20861i	0.271438	+	0.962456i	$0.412501\pi$
$991$	−21768.9	+	37704.9i	−0.697792	+	1.20861i	−0.969230	+	0.246156i	$0.920833\pi$
$992$	−3483.89	+	2011.43i	−0.111506	+	0.0643779i
$993$			24124.3i			0.770959i
$994$	699.425	+	1211.44i	0.0223183	+	0.0386565i
$995$	−16876.4	−	16656.5i	−0.537706	−	0.530700i
$996$	12214.1			0.388573
$997$	2503.58	−	1445.44i	0.0795277	−	0.0459153i	−0.459709	−	0.888070i	$-0.652046\pi$
$997$	2503.58	−	1445.44i	0.0795277	−	0.0459153i	0.539237	+	0.842154i	$0.318713\pi$
$998$	−5410.34	−	3123.66i	−0.171605	−	0.0990760i
$999$	−20105.4	+	34823.5i	−0.636743	+	1.10287i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	130.4.n.a.9.7	✓	44
5.4	even	2	inner	130.4.n.a.9.16	yes	44
13.3	even	3	inner	130.4.n.a.29.16	yes	44
65.29	even	6	inner	130.4.n.a.29.7	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.4.n.a.9.7	✓	44	1.1	even	1	trivial
130.4.n.a.9.16	yes	44	5.4	even	2	inner
130.4.n.a.29.7	yes	44	65.29	even	6	inner
130.4.n.a.29.16	yes	44	13.3	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 130 = 2 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	130.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.73205 - 1.00000i) q^{2} +(2.13838 + 1.23459i) q^{3} +(2.00000 + 3.46410i) q^{4} +(-10.7802 + 2.96444i) q^{5} +(-2.46918 - 4.27675i) q^{6} +(0.660166 - 0.381147i) q^{7} -8.00000i q^{8} +(-10.4516 - 18.1026i) q^{9} +(21.6362 + 5.64562i) q^{10} +(31.0198 - 53.7278i) q^{11} +9.87674i q^{12} +(30.9407 + 35.2090i) q^{13} -1.52459 q^{14} +(-26.7119 - 6.97004i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(89.1952 - 51.4968i) q^{17} +41.8063i q^{18} +(-38.8754 - 67.3341i) q^{19} +(-31.8295 - 31.4147i) q^{20} +1.88224 q^{21} +(-107.456 + 62.0395i) q^{22} +(-0.835838 - 0.482571i) q^{23} +(9.87674 - 17.1070i) q^{24} +(107.424 - 63.9143i) q^{25} +(-18.3818 - 91.9245i) q^{26} -118.282i q^{27} +(2.64066 + 1.52459i) q^{28} +(52.8488 - 91.5368i) q^{29} +(39.2964 + 38.7844i) q^{30} -125.714 q^{31} +(27.7128 - 16.0000i) q^{32} +(132.664 - 76.5935i) q^{33} -205.987 q^{34} +(-5.98682 + 6.06585i) q^{35} +(41.8063 - 72.4106i) q^{36} +(-294.412 - 169.979i) q^{37} +155.501i q^{38} +(22.6941 + 113.489i) q^{39} +(23.7155 + 86.2414i) q^{40} +(83.9935 - 145.481i) q^{41} +(-3.26014 - 1.88224i) q^{42} +(126.469 - 73.0171i) q^{43} +248.158 q^{44} +(166.334 + 164.167i) q^{45} +(0.965143 + 1.67168i) q^{46} -73.0270i q^{47} +(-34.2140 + 19.7535i) q^{48} +(-171.209 + 296.543i) q^{49} +(-249.979 + 3.27849i) q^{50} +254.310 q^{51} +(-60.0862 + 177.600i) q^{52} +680.487i q^{53} +(-118.282 + 204.870i) q^{54} +(-175.126 + 671.151i) q^{55} +(-3.04917 - 5.28133i) q^{56} -191.981i q^{57} +(-183.074 + 105.698i) q^{58} +(329.694 + 571.047i) q^{59} +(-29.2790 - 106.473i) q^{60} +(-74.0351 - 128.233i) q^{61} +(217.743 + 125.714i) q^{62} +(-13.7995 - 7.96716i) q^{63} -64.0000 q^{64} +(-437.921 - 287.837i) q^{65} -306.374 q^{66} +(329.372 + 190.163i) q^{67} +(356.781 + 205.987i) q^{68} +(-1.19156 - 2.06384i) q^{69} +(16.4353 - 4.51954i) q^{70} +(-458.764 - 794.602i) q^{71} +(-144.821 + 83.6125i) q^{72} +92.0384i q^{73} +(339.958 + 588.824i) q^{74} +(308.622 - 4.04760i) q^{75} +(155.501 - 269.336i) q^{76} -47.2923i q^{77} +(74.1819 - 219.263i) q^{78} +422.098 q^{79} +(45.1650 - 173.090i) q^{80} +(-136.163 + 235.841i) q^{81} +(-290.962 + 167.987i) q^{82} -1236.65i q^{83} +(3.76449 + 6.52028i) q^{84} +(-808.880 + 819.558i) q^{85} -292.068 q^{86} +(226.021 - 130.493i) q^{87} +(-429.822 - 248.158i) q^{88} +(480.091 - 831.542i) q^{89} +(-123.932 - 450.679i) q^{90} +(33.8458 + 11.4508i) q^{91} -3.86057i q^{92} +(-268.824 - 155.206i) q^{93} +(-73.0270 + 126.486i) q^{94} +(618.691 + 610.630i) q^{95} +79.0139 q^{96} +(-110.626 + 63.8702i) q^{97} +(593.087 - 342.419i) q^{98} -1296.82 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 88 q^{4} - 12 q^{5} + 266 q^{9} + 28 q^{10} + 2 q^{11} - 216 q^{14} - 64 q^{15} - 352 q^{16} + 14 q^{19} - 24 q^{20} - 32 q^{21} + 504 q^{25} + 336 q^{26} + 308 q^{29} + 104 q^{30} + 792 q^{31} - 352 q^{34}+ \cdots + 2916 q^{99}+O(q^{100}) \) 44 * q + 88 * q^4 - 12 * q^5 + 266 * q^9 + 28 * q^10 + 2 * q^11 - 216 * q^14 - 64 * q^15 - 352 * q^16 + 14 * q^19 - 24 * q^20 - 32 * q^21 + 504 * q^25 + 336 * q^26 + 308 * q^29 + 104 * q^30 + 792 * q^31 - 352 * q^34 + 106 * q^35 - 1064 * q^36 + 120 * q^39 + 224 * q^40 + 140 * q^41 + 16 * q^44 - 522 * q^45 - 320 * q^46 + 536 * q^49 - 96 * q^50 - 256 * q^51 + 552 * q^54 + 1188 * q^55 - 432 * q^56 - 500 * q^59 - 512 * q^60 - 2352 * q^61 - 2816 * q^64 - 2924 * q^65 + 496 * q^66 + 376 * q^69 - 1008 * q^70 - 1268 * q^71 + 436 * q^74 + 3560 * q^75 - 56 * q^76 - 264 * q^79 + 96 * q^80 - 6326 * q^81 - 64 * q^84 + 606 * q^85 + 336 * q^86 + 4730 * q^89 + 3560 * q^90 + 5866 * q^91 + 1732 * q^94 + 2224 * q^95 + 2916 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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