LMFDB - Embedded newform 130.4.n.a.9.10

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			9.10
Character	$\chi$	$=$	130.9
Dual form			130.4.n.a.29.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.73205 - 1.00000i) q^{2} +(6.95834 + 4.01740i) q^{3} +(2.00000 + 3.46410i) q^{4} +(10.8454 - 2.71598i) q^{5} +(-8.03480 - 13.9167i) q^{6} +(8.29606 - 4.78973i) q^{7} -8.00000i q^{8} +(18.7790 + 32.5262i) q^{9} +(-21.5008 - 6.14122i) q^{10} +(34.0317 - 58.9446i) q^{11} +32.1392i q^{12} +(-38.2106 + 27.1468i) q^{13} -19.1589 q^{14} +(86.3774 + 24.6717i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(-87.2341 + 50.3646i) q^{17} -75.1159i q^{18} +(30.1273 + 52.1821i) q^{19} +(31.0993 + 32.1377i) q^{20} +76.9690 q^{21} +(-117.889 + 68.0634i) q^{22} +(56.6958 + 32.7333i) q^{23} +(32.1392 - 55.6667i) q^{24} +(110.247 - 58.9119i) q^{25} +(93.3295 - 8.80905i) q^{26} +84.8311i q^{27} +(33.1842 + 19.1589i) q^{28} +(64.7097 - 112.080i) q^{29} +(-124.938 - 129.110i) q^{30} -78.5244 q^{31} +(27.7128 - 16.0000i) q^{32} +(473.608 - 273.438i) q^{33} +201.459 q^{34} +(76.9655 - 74.4786i) q^{35} +(-75.1159 + 130.105i) q^{36} +(-74.1123 - 42.7887i) q^{37} -120.509i q^{38} +(-374.942 + 35.3894i) q^{39} +(-21.7278 - 86.7635i) q^{40} +(-183.664 + 318.115i) q^{41} +(-133.314 - 76.9690i) q^{42} +(5.24321 - 3.02717i) q^{43} +272.254 q^{44} +(292.007 + 301.757i) q^{45} +(-65.4667 - 113.392i) q^{46} +422.460i q^{47} +(-111.333 + 64.2784i) q^{48} +(-125.617 + 217.575i) q^{49} +(-249.865 - 8.20852i) q^{50} -809.339 q^{51} +(-170.461 - 78.0718i) q^{52} -114.165i q^{53} +(84.8311 - 146.932i) q^{54} +(208.996 - 731.709i) q^{55} +(-38.3178 - 66.3684i) q^{56} +484.134i q^{57} +(-224.161 + 129.419i) q^{58} +(-196.735 - 340.755i) q^{59} +(87.2893 + 348.563i) q^{60} +(-212.351 - 367.802i) q^{61} +(136.008 + 78.5244i) q^{62} +(311.583 + 179.892i) q^{63} -64.0000 q^{64} +(-340.681 + 398.198i) q^{65} -1093.75 q^{66} +(-894.283 - 516.314i) q^{67} +(-348.936 - 201.459i) q^{68} +(263.006 + 455.539i) q^{69} +(-207.787 + 52.0352i) q^{70} +(391.159 + 677.507i) q^{71} +(260.209 - 150.232i) q^{72} -244.377i q^{73} +(85.5775 + 148.225i) q^{74} +(1003.81 + 32.9769i) q^{75} +(-120.509 + 208.728i) q^{76} -652.010i q^{77} +(684.808 + 313.646i) q^{78} -1133.43 q^{79} +(-49.1298 + 172.007i) q^{80} +(166.232 - 287.923i) q^{81} +(636.230 - 367.327i) q^{82} -215.241i q^{83} +(153.938 + 266.628i) q^{84} +(-809.303 + 783.152i) q^{85} -12.1087 q^{86} +(900.544 - 519.929i) q^{87} +(-471.557 - 272.254i) q^{88} +(554.980 - 961.253i) q^{89} +(-204.013 - 814.665i) q^{90} +(-186.971 + 408.230i) q^{91} +261.867i q^{92} +(-546.400 - 315.464i) q^{93} +(422.460 - 731.723i) q^{94} +(468.469 + 484.112i) q^{95} +257.114 q^{96} +(1289.47 - 744.473i) q^{97} +(435.150 - 251.234i) q^{98} +2556.32 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
$3$	6.95834	+	4.01740i	1.33913	+	0.773149i	0.986679	−	0.162680i	$-0.0520140\pi$
$3$	6.95834	+	4.01740i	1.33913	+	0.773149i	0.352454	+	0.935829i	$0.385347\pi$
$4$	2.00000	+	3.46410i	0.250000	+	0.433013i
$5$	10.8454	−	2.71598i	0.970045	−	0.242924i
$5$	10.8454	−	2.71598i	0.970045	−	0.242924i
$6$	−8.03480	−	13.9167i	−0.546699	−	0.946910i
$7$	8.29606	−	4.78973i	0.447945	−	0.258621i	−0.259017	−	0.965873i	$-0.583399\pi$
$7$	8.29606	−	4.78973i	0.447945	−	0.258621i	0.706962	+	0.707252i	$0.250065\pi$
$8$		−	8.00000i		−	0.353553i
$9$	18.7790	+	32.5262i	0.695518	+	1.20467i
$10$	−21.5008	−	6.14122i	−0.679916	−	0.194203i
$11$	34.0317	−	58.9446i	0.932813	−	1.61568i	0.154324	−	0.988020i	$-0.450680\pi$
$11$	34.0317	−	58.9446i	0.932813	−	1.61568i	0.778489	−	0.627659i	$-0.215987\pi$
$12$			32.1392i			0.773149i
$13$	−38.2106	+	27.1468i	−0.815209	+	0.579167i
$13$	−38.2106	+	27.1468i	−0.815209	+	0.579167i
$14$	−19.1589			−0.365745
$15$	86.3774	+	24.6717i	1.48684	+	0.424681i
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−87.2341	+	50.3646i	−1.24455	+	0.718542i	−0.970018	−	0.243035i	$-0.921857\pi$
$17$	−87.2341	+	50.3646i	−1.24455	+	0.718542i	−0.274534	+	0.961577i	$0.588524\pi$
$18$		−	75.1159i		−	0.983611i
$19$	30.1273	+	52.1821i	0.363773	+	0.630073i	0.988578	−	0.150707i	$-0.0481551\pi$
$19$	30.1273	+	52.1821i	0.363773	+	0.630073i	−0.624806	+	0.780780i	$0.714822\pi$
$20$	31.0993	+	32.1377i	0.347701	+	0.359311i
$21$	76.9690			0.799810
$22$	−117.889	+	68.0634i	−1.14246	+	0.659598i
$23$	56.6958	+	32.7333i	0.513995	+	0.296755i	0.734474	−	0.678636i	$-0.237429\pi$
$23$	56.6958	+	32.7333i	0.513995	+	0.296755i	−0.220479	+	0.975392i	$0.570762\pi$
$24$	32.1392	−	55.6667i	0.273349	−	0.473455i
$25$	110.247	−	58.9119i	0.881975	−	0.471295i
$26$	93.3295	−	8.80905i	0.703978	−	0.0664460i
$27$			84.8311i			0.604657i
$28$	33.1842	+	19.1589i	0.223972	+	0.129311i
$29$	64.7097	−	112.080i	0.414355	−	0.717683i	−0.581006	−	0.813899i	$-0.697341\pi$
$29$	64.7097	−	112.080i	0.414355	−	0.717683i	0.995360	+	0.0962161i	$0.0306740\pi$
$30$	−124.938	−	129.110i	−0.760350	−	0.785739i
$31$	−78.5244			−0.454948			−0.227474	−	0.973784i	$-0.573047\pi$
$31$	−78.5244			−0.454948			−0.227474	+	0.973784i	$0.573047\pi$
$32$	27.7128	−	16.0000i	0.153093	−	0.0883883i
$33$	473.608	−	273.438i	2.49832	−	1.44241i
$34$	201.459			1.01617
$35$	76.9655	−	74.4786i	0.371701	−	0.359691i
$36$	−75.1159	+	130.105i	−0.347759	+	0.602336i
$37$	−74.1123	−	42.7887i	−0.329297	−	0.190120i	0.326232	−	0.945290i	$-0.394221\pi$
$37$	−74.1123	−	42.7887i	−0.329297	−	0.190120i	−0.655529	+	0.755170i	$0.727554\pi$
$38$		−	120.509i		−	0.514452i
$39$	−374.942	+	35.3894i	−1.53946	+	0.145304i
$40$	−21.7278	−	86.7635i	−0.0858867	−	0.342963i
$41$	−183.664	+	318.115i	−0.699596	+	1.21174i	0.269010	+	0.963137i	$0.413303\pi$
$41$	−183.664	+	318.115i	−0.699596	+	1.21174i	−0.968606	+	0.248599i	$0.920030\pi$
$42$	−133.314	−	76.9690i	−0.489782	−	0.282776i
$43$	5.24321	−	3.02717i	0.0185949	−	0.0107358i	−0.490674	−	0.871343i	$-0.663249\pi$
$43$	5.24321	−	3.02717i	0.0185949	−	0.0107358i	0.509269	+	0.860608i	$0.329916\pi$
$44$	272.254			0.932813
$45$	292.007	+	301.757i	0.967328	+	0.999628i
$46$	−65.4667	−	113.392i	−0.209838	−	0.363450i
$47$			422.460i			1.31111i	0.755147	+	0.655555i	$0.227565\pi$
$47$			422.460i			1.31111i	−0.755147	+	0.655555i	$0.772435\pi$
$48$	−111.333	+	64.2784i	−0.334783	+	0.193287i
$49$	−125.617	+	217.575i	−0.366230	+	0.634329i
$50$	−249.865	−	8.20852i	−0.706726	−	0.0232172i
$51$	−809.339			−2.22216
$52$	−170.461	−	78.0718i	−0.454589	−	0.208204i
$53$		−	114.165i		−	0.295882i	−0.988996	−	0.147941i	$-0.952736\pi$
$53$		−	114.165i		−	0.295882i	0.988996	−	0.147941i	$-0.0472645\pi$
$54$	84.8311	−	146.932i	0.213779	−	0.370276i
$55$	208.996	−	731.709i	0.512383	−	1.79388i
$56$	−38.3178	−	66.3684i	−0.0914364	−	0.158372i
$57$			484.134i			1.12500i
$58$	−224.161	+	129.419i	−0.507479	+	0.292993i
$59$	−196.735	−	340.755i	−0.434114	−	0.751908i	0.563109	−	0.826383i	$-0.309605\pi$
$59$	−196.735	−	340.755i	−0.434114	−	0.751908i	−0.997223	+	0.0744750i	$0.976272\pi$
$60$	87.2893	+	348.563i	0.187817	+	0.749989i
$61$	−212.351	−	367.802i	−0.445716	−	0.772003i	0.552385	−	0.833589i	$-0.313718\pi$
$61$	−212.351	−	367.802i	−0.445716	−	0.772003i	−0.998102	+	0.0615854i	$0.980384\pi$
$62$	136.008	+	78.5244i	0.278598	+	0.160849i
$63$	311.583	+	179.892i	0.623107	+	0.359751i
$64$	−64.0000			−0.125000
$65$	−340.681	+	398.198i	−0.650096	+	0.759852i
$66$	−1093.75			−2.03987
$67$	−894.283	−	516.314i	−1.63066	−	0.941460i	−0.983891	−	0.178772i	$-0.942788\pi$
$67$	−894.283	−	516.314i	−1.63066	−	0.941460i	−0.646766	−	0.762688i	$-0.723879\pi$
$68$	−348.936	−	201.459i	−0.622276	−	0.359271i
$69$	263.006	+	455.539i	0.458872	+	0.794790i
$70$	−207.787	+	52.0352i	−0.354790	+	0.0888485i
$71$	391.159	+	677.507i	0.653831	+	1.13247i	0.982185	+	0.187914i	$0.0601727\pi$
$71$	391.159	+	677.507i	0.653831	+	1.13247i	−0.328354	+	0.944555i	$0.606494\pi$
$72$	260.209	−	150.232i	0.425916	−	0.245903i
$73$		−	244.377i		−	0.391810i	−0.980623	−	0.195905i	$-0.937236\pi$
$73$		−	244.377i		−	0.391810i	0.980623	−	0.195905i	$-0.0627644\pi$
$74$	85.5775	+	148.225i	0.134435	+	0.232848i
$75$	1003.81	+	32.9769i	1.54546	+	0.0507712i
$76$	−120.509	+	208.728i	−0.181886	+	0.315036i
$77$		−	652.010i		−	0.964980i
$78$	684.808	+	313.646i	0.994093	+	0.455300i
$79$	−1133.43			−1.61419			−0.807096	−	0.590420i	$-0.798962\pi$
$79$	−1133.43			−1.61419			−0.807096	+	0.590420i	$0.798962\pi$
$80$	−49.1298	+	172.007i	−0.0686610	+	0.240387i
$81$	166.232	−	287.923i	0.228028	−	0.394956i
$82$	636.230	−	367.327i	0.856827	−	0.494689i
$83$		−	215.241i		−	0.284648i	−0.989820	−	0.142324i	$-0.954542\pi$
$83$		−	215.241i		−	0.284648i	0.989820	−	0.142324i	$-0.0454575\pi$
$84$	153.938	+	266.628i	0.199953	+	0.346328i
$85$	−809.303	+	783.152i	−1.03272	+	0.999351i
$86$	−12.1087			−0.0151827
$87$	900.544	−	519.929i	1.10975	−	0.640715i
$88$	−471.557	−	272.254i	−0.571229	−	0.329799i
$89$	554.980	−	961.253i	0.660986	−	1.14486i	−0.319371	−	0.947630i	$-0.603472\pi$
$89$	554.980	−	961.253i	0.660986	−	1.14486i	0.980357	−	0.197231i	$-0.0631950\pi$
$90$	−204.013	−	814.665i	−0.238943	−	0.954147i
$91$	−186.971	+	408.230i	−0.215384	+	0.470265i
$92$			261.867i			0.296755i
$93$	−546.400	−	315.464i	−0.609236	−	0.351743i
$94$	422.460	−	731.723i	0.463548	−	0.802888i
$95$	468.469	+	484.112i	0.505936	+	0.522830i
$96$	257.114			0.273349
$97$	1289.47	−	744.473i	1.34975	−	0.779276i	0.361533	−	0.932359i	$-0.382254\pi$
$97$	1289.47	−	744.473i	1.34975	−	0.779276i	0.988213	+	0.153083i	$0.0489202\pi$
$98$	435.150	−	251.234i	0.448539	−	0.258964i
$99$	2556.32			2.59515
$100$	424.571	+	264.083i	0.424571	+	0.264083i
$101$	−295.526	+	511.866i	−0.291148	+	0.504283i	−0.974081	−	0.226197i	$-0.927371\pi$
$101$	−295.526	+	511.866i	−0.291148	+	0.504283i	0.682934	+	0.730481i	$0.260704\pi$
$102$	1401.82	+	809.339i	1.36079	+	0.785652i
$103$			1106.67i			1.05867i	0.848412	+	0.529337i	$0.177559\pi$
$103$			1106.67i			1.05867i	−0.848412	+	0.529337i	$0.822441\pi$
$104$	217.174	+	305.685i	0.204766	+	0.288220i
$105$	834.762	−	209.046i	0.775852	−	0.194293i
$106$	−114.165	+	197.739i	−0.104610	+	0.181190i
$107$	286.863	+	165.620i	0.259178	+	0.149637i	0.623960	−	0.781457i	$-0.285523\pi$
$107$	286.863	+	165.620i	0.259178	+	0.149637i	−0.364781	+	0.931093i	$0.618856\pi$
$108$	−293.864	+	169.662i	−0.261824	+	0.151164i
$109$	−342.249			−0.300748			−0.150374	−	0.988629i	$-0.548048\pi$
$109$	−342.249			−0.300748			−0.150374	+	0.988629i	$0.548048\pi$
$110$	−1093.70	+	1058.36i	−0.948003	+	0.917371i
$111$	−343.799	−	595.477i	−0.293982	−	0.509191i
$112$			153.271i			0.129311i
$113$	82.8677	−	47.8437i	0.0689871	−	0.0398297i	−0.465110	−	0.885253i	$-0.653985\pi$
$113$	82.8677	−	47.8437i	0.0689871	−	0.0398297i	0.534097	+	0.845423i	$0.320652\pi$
$114$	484.134	−	838.544i	0.397748	−	0.688920i
$115$	703.794	+	201.023i	0.570688	+	0.163004i
$116$	517.677			0.414355
$117$	−1600.54	−	733.055i	−1.26470	−	0.579239i
$118$			786.941i			0.613930i
$119$	−482.466	+	835.656i	−0.371660	+	0.643735i
$120$	197.374	−	691.019i	0.150147	−	0.525676i
$121$	−1650.81	−	2859.29i	−1.24028	−	2.14823i
$122$			849.402i			0.630338i
$123$	−2555.99	+	1475.70i	−1.87370	+	1.08178i
$124$	−157.049	−	272.017i	−0.113737	−	0.196998i
$125$	1035.67	−	938.353i	0.741067	−	0.671431i
$126$	−359.785	−	623.166i	−0.254383	−	0.440603i
$127$	−2004.79	−	1157.47i	−1.40076	−	0.808728i	−0.406287	−	0.913745i	$-0.633177\pi$
$127$	−2004.79	−	1157.47i	−1.40076	−	0.808728i	−0.994470	+	0.105018i	$0.966510\pi$
$128$	110.851	+	64.0000i	0.0765466	+	0.0441942i
$129$	48.6454			0.0332014
$130$	988.274	−	349.019i	0.666749	−	0.235469i
$131$	−622.423			−0.415125			−0.207562	−	0.978222i	$-0.566553\pi$
$131$	−622.423			−0.415125			−0.207562	+	0.978222i	$0.566553\pi$
$132$	1894.43	+	1093.75i	1.24916	+	0.721203i
$133$	499.876	+	288.603i	0.325900	+	0.188159i
$134$	1032.63	+	1788.57i	0.665713	+	1.15305i
$135$	230.399	+	920.030i	0.146886	+	0.586545i
$136$	402.917	+	697.873i	0.254043	+	0.440016i
$137$	−5.27768	+	3.04707i	−0.00329126	+	0.00190021i	−0.501645	−	0.865074i	$-0.667272\pi$
$137$	−5.27768	+	3.04707i	−0.00329126	+	0.00190021i	0.498353	+	0.866974i	$0.333938\pi$
$138$		−	1052.02i		−	0.648943i
$139$	−388.854	−	673.516i	−0.237282	−	0.410985i	0.722651	−	0.691213i	$-0.242923\pi$
$139$	−388.854	−	673.516i	−0.237282	−	0.410985i	−0.959933	+	0.280228i	$0.909590\pi$
$140$	411.933	+	117.659i	0.248676	+	0.0710287i
$141$	−1697.19	+	2939.62i	−1.01368	+	1.75575i
$142$		−	1564.64i		−	0.924657i
$143$	299.787	+	3176.16i	0.175311	+	1.85737i
$144$	−600.927			−0.347759
$145$	397.397	−	1391.31i	0.227600	−	0.796842i
$146$	−244.377	+	423.273i	−0.138526	+	0.239934i
$147$	−1748.17	+	1009.31i	−0.980862	+	0.566301i
$148$		−	342.310i		−	0.190120i
$149$	751.757	+	1302.08i	0.413331	+	0.715911i	0.995252	−	0.0973350i	$-0.0310318\pi$
$149$	751.757	+	1302.08i	0.413331	+	0.715911i	−0.581920	+	0.813246i	$0.697699\pi$
$150$	−1705.67	−	1060.93i	−0.928449	−	0.577495i
$151$	2294.62			1.23665			0.618323	−	0.785924i	$-0.287812\pi$
$151$	2294.62			1.23665			0.618323	+	0.785924i	$0.287812\pi$
$152$	417.456	−	241.019i	0.222764	−	0.128613i
$153$	−3276.34	−	1891.59i	−1.73122	−	0.999518i
$154$	−652.010	+	1129.32i	−0.341172	+	0.590927i
$155$	−851.632	+	213.271i	−0.441321	+	0.110518i
$156$	−872.476	−	1228.06i	−0.447782	−	0.630278i
$157$			653.595i			0.332246i	0.986105	+	0.166123i	$0.0531248\pi$
$157$			653.595i			0.332246i	−0.986105	+	0.166123i	$0.946875\pi$
$158$	1963.16	+	1133.43i	0.988487	+	0.570703i
$159$	458.645	−	794.396i	0.228760	−	0.396225i
$160$	257.102	−	248.794i	0.127036	−	0.122931i
$161$	627.136			0.306989
$162$	−575.845	+	332.464i	−0.279276	+	0.161240i
$163$	3463.44	−	1999.62i	1.66428	−	0.960873i	0.693645	−	0.720317i	$-0.256004\pi$
$163$	3463.44	−	1999.62i	1.66428	−	0.960873i	0.970635	−	0.240555i	$-0.0773296\pi$
$164$	−1469.31			−0.699596
$165$	4393.83	−	4251.86i	2.07309	−	2.00610i
$166$	−215.241	+	372.809i	−0.100638	+	0.174311i
$167$	58.2969	+	33.6577i	0.0270129	+	0.0155959i	0.513446	−	0.858122i	$-0.328369\pi$
$167$	58.2969	+	33.6577i	0.0270129	+	0.0155959i	−0.486433	+	0.873718i	$0.661702\pi$
$168$		−	615.752i		−	0.282776i
$169$	723.101	−	2074.59i	0.329131	−	0.944284i
$170$	2184.91	−	547.157i	0.985733	−	0.246853i
$171$	−1131.52	+	1959.85i	−0.506021	+	0.876454i
$172$	20.9728	+	12.1087i	0.00929747	+	0.00536790i
$173$	1397.67	−	806.945i	0.614236	−	0.354629i	−0.160385	−	0.987054i	$-0.551274\pi$
$173$	1397.67	−	806.945i	0.614236	−	0.354629i	0.774622	+	0.632425i	$0.217940\pi$
$174$	−2079.72			−0.906108
$175$	632.443	−	1016.79i	0.273190	−	0.439212i
$176$	544.507	+	943.114i	0.233203	+	0.403920i
$177$		−	3161.45i		−	1.34254i
$178$	−1922.51	+	1109.96i	−0.809539	+	0.467387i
$179$	−728.749	+	1262.23i	−0.304298	+	0.527059i	−0.977105	−	0.212759i	$-0.931755\pi$
$179$	−728.749	+	1262.23i	−0.304298	+	0.527059i	0.672807	+	0.739818i	$0.265088\pi$
$180$	−461.304	+	1615.05i	−0.191020	+	0.668772i
$181$	−2186.35			−0.897846			−0.448923	−	0.893570i	$-0.648192\pi$
$181$	−2186.35			−0.897846			−0.448923	+	0.893570i	$0.648192\pi$
$182$	732.074	−	520.104i	0.298159	−	0.211828i
$183$		−	3412.39i		−	1.37842i
$184$	261.867	−	453.567i	0.104919	−	0.181725i
$185$	−919.993	−	262.775i	−0.365618	−	0.104430i
$186$	630.928	+	1092.80i	0.248720	+	0.430795i
$187$			6855.97i			2.68106i
$188$	−1463.45	+	844.921i	−0.567727	+	0.327778i
$189$	406.318	+	703.763i	0.156377	+	0.270853i
$190$	−327.300	−	1306.98i	−0.124973	−	0.499042i
$191$	2518.18	+	4361.61i	0.953973	+	1.65233i	0.736700	+	0.676220i	$0.236383\pi$
$191$	2518.18	+	4361.61i	0.953973	+	1.65233i	0.217273	+	0.976111i	$0.430284\pi$
$192$	−445.334	−	257.114i	−0.167392	−	0.0966436i
$193$	1881.45	+	1086.25i	0.701707	+	0.405131i	0.807983	−	0.589206i	$-0.200559\pi$
$193$	1881.45	+	1086.25i	0.701707	+	0.405131i	−0.106276	+	0.994337i	$0.533893\pi$
$194$	−2977.89			−1.10206
$195$	−3970.29	+	1402.15i	−1.45804	+	0.514922i
$196$	−1004.94			−0.366230
$197$	−2911.16	−	1680.76i	−1.05285	−	0.607863i	−0.129404	−	0.991592i	$-0.541306\pi$
$197$	−2911.16	−	1680.76i	−1.05285	−	0.607863i	−0.923446	+	0.383729i	$0.874640\pi$
$198$	−4427.68	−	2556.32i	−1.58920	−	0.917525i
$199$	516.173	+	894.038i	0.183872	+	0.318476i	0.943196	−	0.332237i	$-0.107803\pi$
$199$	516.173	+	894.038i	0.183872	+	0.318476i	−0.759324	+	0.650713i	$0.774470\pi$
$200$	−471.295	−	881.975i	−0.166628	−	0.311825i
$201$	−4148.48	−	7185.38i	−1.45578	−	2.52148i
$202$	1023.73	−	591.052i	0.356582	−	0.205873i
$203$		−	1239.77i		−	0.428643i
$204$	−1618.68	−	2803.63i	−0.555540	−	0.962224i
$205$	−1127.92	+	3948.92i	−0.384280	+	1.34539i
$206$	1106.67	−	1916.81i	0.374298	−	0.648303i
$207$			2458.80i			0.825595i
$208$	−70.4724	−	746.636i	−0.0234922	−	0.248894i
$209$	4101.13			1.35733
$210$	−1654.90	−	472.684i	−0.543804	−	0.155325i
$211$	−1241.53	+	2150.40i	−0.405074	+	0.701609i	−0.994330	−	0.106338i	$-0.966088\pi$
$211$	−1241.53	+	2150.40i	−0.405074	+	0.701609i	0.589256	+	0.807946i	$0.299421\pi$
$212$	395.478	−	228.329i	0.128120	−	0.0739704i
$213$			6285.76i			2.02204i
$214$	−331.240	−	573.725i	−0.105809	−	0.183267i
$215$	48.6432	−	47.0714i	0.0154299	−	0.0149314i
$216$	678.649			0.213779
$217$	−651.443	+	376.111i	−0.203792	+	0.117659i
$218$	592.793	+	342.249i	0.184170	+	0.106331i
$219$	981.759	−	1700.46i	0.302927	−	0.524686i
$220$	2952.71	−	739.434i	0.904871	−	0.226603i
$221$	1966.03	−	4292.59i	0.598414	−	1.30657i
$222$			1375.20i			0.415753i
$223$	2582.81	+	1491.19i	0.775596	+	0.447791i	0.834867	−	0.550451i	$-0.185544\pi$
$223$	2582.81	+	1491.19i	0.775596	+	0.447791i	−0.0592713	+	0.998242i	$0.518878\pi$
$224$	153.271	−	265.474i	0.0457182	−	0.0791862i
$225$	3986.50	+	2479.60i	1.18119	+	0.734697i
$226$	−191.375			−0.0563277
$227$	132.609	−	76.5621i	0.0387736	−	0.0223859i	−0.480488	−	0.877001i	$-0.659540\pi$
$227$	132.609	−	76.5621i	0.0387736	−	0.0223859i	0.519261	+	0.854615i	$0.326207\pi$
$228$	−1677.09	+	968.268i	−0.487140	+	0.281250i
$229$	−4516.58			−1.30334			−0.651668	−	0.758504i	$-0.725931\pi$
$229$	−4516.58			−1.30334			−0.651668	+	0.758504i	$0.725931\pi$
$230$	−1017.98	−	1051.98i	−0.291843	−	0.301588i
$231$	2619.39	−	4536.91i	0.746073	−	1.29224i
$232$	−896.643	−	517.677i	−0.253739	−	0.146496i
$233$		−	1258.34i		−	0.353805i	−0.984228	−	0.176902i	$-0.943392\pi$
$233$		−	1258.34i		−	0.353805i	0.984228	−	0.176902i	$-0.0566077\pi$
$234$	2039.16	+	2870.23i	0.569675	+	0.801848i
$235$	1147.39	+	4581.77i	0.318501	+	1.27184i
$236$	786.941	−	1363.02i	0.217057	−	0.375954i
$237$	−7886.81	−	4553.45i	−2.16162	−	1.24801i
$238$	1671.31	−	964.932i	0.455189	−	0.262804i
$239$	−1814.62			−0.491122			−0.245561	−	0.969381i	$-0.578972\pi$
$239$	−1814.62			−0.491122			−0.245561	+	0.969381i	$0.578972\pi$
$240$	−1032.88	+	999.506i	−0.277801	+	0.268824i
$241$	2427.51	+	4204.57i	0.648837	+	1.12382i	0.983401	+	0.181445i	$0.0580775\pi$
$241$	2427.51	+	4204.57i	0.648837	+	1.12382i	−0.334564	+	0.942373i	$0.608589\pi$
$242$			6603.25i			1.75402i
$243$	4296.98	−	2480.86i	1.13437	−	0.654927i
$244$	849.402	−	1471.21i	0.222858	−	0.386002i
$245$	−771.442	+	2700.87i	−0.201166	+	0.704294i
$246$	5902.80			1.52987
$247$	−2567.76	−	1176.05i	−0.661468	−	0.302956i
$248$			628.195i			0.160849i
$249$	864.710	−	1497.72i	0.220075	−	0.381182i
$250$	−2732.19	+	589.603i	−0.691196	+	0.149159i
$251$	286.351	+	495.974i	0.0720091	+	0.124723i	0.899782	−	0.436340i	$-0.143726\pi$
$251$	286.351	+	495.974i	0.0720091	+	0.124723i	−0.827773	+	0.561064i	$0.810392\pi$
$252$			1439.14i			0.359751i
$253$	3858.91	−	2227.94i	0.958923	−	0.553634i
$254$	2314.93	+	4009.58i	0.571857	+	0.990485i
$255$	−8777.64	+	2198.15i	−2.15560	+	0.539817i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	2507.75	+	1447.85i	0.608673	+	0.351418i	0.772446	−	0.635081i	$-0.219033\pi$
$257$	2507.75	+	1447.85i	0.608673	+	0.351418i	−0.163773	+	0.986498i	$0.552366\pi$
$258$	−84.2563	−	48.6454i	−0.0203317	−	0.0117385i
$259$	−819.786			−0.196676
$260$	−2060.76	−	383.756i	−0.491550	−	0.0915367i
$261$	4860.73			1.15276
$262$	1078.07	+	622.423i	0.254211	+	0.146769i
$263$	−2460.87	−	1420.79i	−0.576973	−	0.333116i	0.182956	−	0.983121i	$-0.441433\pi$
$263$	−2460.87	−	1420.79i	−0.576973	−	0.333116i	−0.759930	+	0.650005i	$0.774767\pi$
$264$	−2187.50	−	3788.86i	−0.509968	−	0.883290i
$265$	−310.069	−	1238.17i	−0.0718768	−	0.287018i
$266$	−577.207	−	999.752i	−0.133048	−	0.230446i
$267$	7723.47	−	4459.15i	1.77030	−	1.02208i
$268$		−	4130.51i		−	0.941460i
$269$	3483.38	+	6033.39i	0.789536	+	1.36752i	0.926251	+	0.376906i	$0.123012\pi$
$269$	3483.38	+	6033.39i	0.789536	+	1.36752i	−0.136715	+	0.990610i	$0.543655\pi$
$270$	520.967	−	1823.94i	0.117426	−	0.411116i
$271$	−1900.31	+	3291.43i	−0.425961	+	0.737786i	−0.996510	−	0.0834780i	$-0.973397\pi$
$271$	−1900.31	+	3291.43i	−0.425961	+	0.737786i	0.570549	+	0.821264i	$0.306731\pi$
$272$		−	1611.67i		−	0.359271i
$273$	−2941.03	+	2089.46i	−0.652012	+	0.463224i
$274$	12.1883			0.00268730
$275$	279.350	−	8503.33i	0.0612561	−	1.86462i
$276$	−1052.02	+	1822.16i	−0.229436	+	0.397395i
$277$	201.240	−	116.186i	0.0436511	−	0.0252020i	−0.478016	−	0.878351i	$-0.658644\pi$
$277$	201.240	−	116.186i	0.0436511	−	0.0252020i	0.521667	+	0.853149i	$0.325310\pi$
$278$			1555.42i			0.335567i
$279$	−1474.61	−	2554.10i	−0.316425	−	0.548064i
$280$	−595.829	−	615.724i	−0.127170	−	0.131416i
$281$	2201.89			0.467451			0.233726	−	0.972303i	$-0.424908\pi$
$281$	2201.89			0.467451			0.233726	+	0.972303i	$0.424908\pi$
$282$	5879.25	−	3394.38i	1.24150	−	0.716782i
$283$	2234.11	+	1289.86i	0.469272	+	0.270934i	0.715935	−	0.698167i	$-0.246001\pi$
$283$	2234.11	+	1289.86i	0.469272	+	0.270934i	−0.246663	+	0.969101i	$0.579334\pi$
$284$	−1564.64	+	2710.03i	−0.326916	+	0.566234i
$285$	1314.90	+	5250.64i	0.273290	+	1.09130i
$286$	2656.92	−	5801.06i	0.549324	−	1.19938i
$287$			3518.80i			0.723722i
$288$	1040.84	+	600.927i	0.212958	+	0.122951i
$289$	2616.69	−	4532.25i	0.532606	−	0.922501i
$290$	−2079.62	+	2012.42i	−0.421102	+	0.407495i
$291$	11963.4			2.40999
$292$	846.546	−	488.753i	0.169659	−	0.0979525i
$293$	1556.41	−	898.592i	0.310328	−	0.179168i	−0.336745	−	0.941596i	$-0.609326\pi$
$293$	1556.41	−	898.592i	0.310328	−	0.179168i	0.647073	+	0.762428i	$0.275993\pi$
$294$	4037.23			0.800870
$295$	−3059.16	−	3161.31i	−0.603767	−	0.623928i
$296$	−342.310	+	592.898i	−0.0672174	+	0.116424i
$297$	5000.34	+	2886.95i	0.976932	+	0.564032i
$298$		−	3007.03i		−	0.584539i
$299$	−3054.99	+	288.350i	−0.590885	+	0.0557715i
$300$	1893.38	+	3543.25i	0.364381	+	0.681898i
$301$	28.9986	−	50.2271i	0.00555300	−	0.00961808i
$302$	−3974.40	−	2294.62i	−0.757288	−	0.437221i
$303$	−4112.74	+	2374.49i	−0.779772	+	0.450201i
$304$	−964.074			−0.181886
$305$	−3301.98	−	3412.23i	−0.619904	−	0.640603i
$306$	3783.19	+	6552.67i	0.706766	+	1.22415i
$307$		−	4628.92i		−	0.860543i	−0.902700	−	0.430271i	$-0.858418\pi$
$307$		−	4628.92i		−	0.860543i	0.902700	−	0.430271i	$-0.141582\pi$
$308$	2258.63	−	1304.02i	0.417849	−	0.241245i
$309$	−4445.94	+	7700.59i	−0.818513	+	1.41771i
$310$	1688.34	+	482.236i	0.309327	+	0.0883522i
$311$	8245.59			1.50342			0.751711	−	0.659493i	$-0.229229\pi$
$311$	8245.59			1.50342			0.751711	+	0.659493i	$0.229229\pi$
$312$	283.116	+	2999.54i	0.0513726	+	0.544280i
$313$			6905.03i			1.24695i	0.781843	+	0.623475i	$0.214280\pi$
$313$			6905.03i			1.24695i	−0.781843	+	0.623475i	$0.785720\pi$
$314$	653.595	−	1132.06i	0.117467	−	0.203458i
$315$	3867.84	+	1104.76i	0.691835	+	0.197607i
$316$	−2266.87	−	3926.33i	−0.403548	−	0.698966i
$317$		−	6551.17i		−	1.16073i	−0.814358	−	0.580363i	$-0.802911\pi$
$317$		−	6551.17i		−	1.16073i	0.814358	−	0.580363i	$-0.197089\pi$
$318$	−1588.79	+	917.290i	−0.280173	+	0.161758i
$319$	−4404.36	−	7628.57i	−0.773031	−	1.33893i
$320$	−694.108	+	173.823i	−0.121256	+	0.0303655i
$321$	1330.72	+	2304.88i	0.231383	+	0.400766i
$322$	−1086.23	−	627.136i	−0.187992	−	0.108537i
$323$	−5256.26	−	3034.70i	−0.905468	−	0.522772i
$324$	1329.86			0.228028
$325$	−2613.33	+	5243.91i	−0.446036	+	0.895015i
$326$	−7998.48			−1.35888
$327$	−2381.49	−	1374.95i	−0.402742	−	0.232523i
$328$	2544.92	+	1469.31i	0.428414	+	0.247345i
$329$	2023.47	+	3504.76i	0.339081	+	0.587305i
$330$	−11862.2	+	2970.60i	−1.97877	+	0.495534i
$331$	−482.637	−	835.951i	−0.0801453	−	0.138816i	0.823167	−	0.567799i	$-0.192205\pi$
$331$	−482.637	−	835.951i	−0.0801453	−	0.138816i	−0.903312	+	0.428984i	$0.858872\pi$
$332$	745.618	−	430.483i	0.123256	−	0.0711621i
$333$		−	3214.12i		−	0.528926i
$334$	−67.3155	−	116.594i	−0.0110280	−	0.0191010i
$335$	−11101.2	−	3170.80i	−1.81051	−	0.517133i
$336$	−615.752	+	1066.51i	−0.0999763	+	0.173164i
$337$			2233.82i			0.361081i	0.983568	+	0.180540i	$0.0577846\pi$
$337$			2233.82i			0.361081i	−0.983568	+	0.180540i	$0.942215\pi$
$338$	−3327.04	+	2870.20i	−0.535406	+	0.461888i
$339$	768.829			0.123177
$340$	−4331.52	−	1237.20i	−0.690911	−	0.197343i
$341$	−2672.32	+	4628.59i	−0.424382	+	0.735051i
$342$	3919.70	−	2263.04i	0.619746	−	0.357811i
$343$			5692.44i			0.896102i
$344$	−24.2174	−	41.9457i	−0.00379568	−	0.00657430i
$345$	4089.65	+	4226.21i	0.638201	+	0.659511i
$346$	−3227.78			−0.501522
$347$	5584.79	−	3224.38i	0.863998	−	0.498830i	−0.00135101	−	0.999999i	$-0.500430\pi$
$347$	5584.79	−	3224.38i	0.863998	−	0.498830i	0.865349	+	0.501170i	$0.167097\pi$
$348$	3602.17	+	2079.72i	0.554876	+	0.320358i
$349$	1703.23	−	2950.08i	0.261238	−	0.452477i	−0.705333	−	0.708876i	$-0.749203\pi$
$349$	1703.23	−	2950.08i	0.261238	−	0.452477i	0.966571	+	0.256399i	$0.0825361\pi$
$350$	−2112.21	+	1128.69i	−0.322579	+	0.172374i
$351$	−2302.89	−	3241.45i	−0.350198	−	0.492922i
$352$		−	2178.03i		−	0.329799i
$353$	9237.36	+	5333.19i	1.39279	+	0.804128i	0.993623	−	0.112751i	$-0.0359662\pi$
$353$	9237.36	+	5333.19i	1.39279	+	0.804128i	0.399167	+	0.916878i	$0.369299\pi$
$354$	−3161.45	+	5475.80i	−0.474659	+	0.822134i
$355$	6082.38	+	6285.48i	0.909350	+	0.939715i
$356$	4439.84			0.660986
$357$	−6714.32	+	3876.52i	−0.995405	+	0.574698i
$358$	2524.46	−	1457.50i	0.372687	−	0.215171i
$359$	−4063.90			−0.597449			−0.298725	−	0.954339i	$-0.596561\pi$
$359$	−4063.90			−0.597449			−0.298725	+	0.954339i	$0.596561\pi$
$360$	2414.06	−	2336.05i	0.353422	−	0.342002i
$361$	1614.19	−	2795.86i	0.235339	−	0.407619i
$362$	3786.87	+	2186.35i	0.549816	+	0.317437i
$363$		−	26527.9i		−	3.83568i
$364$	−1788.09	+	168.772i	−0.257477	+	0.0243023i
$365$	−663.722	−	2650.37i	−0.0951802	−	0.380073i
$366$	−3412.39	+	5910.43i	−0.487345	+	0.844107i
$367$	−2481.71	−	1432.82i	−0.352982	−	0.203794i	0.313016	−	0.949748i	$-0.398661\pi$
$367$	−2481.71	−	1432.82i	−0.352982	−	0.203794i	−0.665998	+	0.745954i	$0.731994\pi$
$368$	−907.133	+	523.734i	−0.128499	+	0.0741889i
$369$	−13796.1			−1.94633
$370$	1330.70	+	1375.13i	0.186972	+	0.193216i
$371$	−546.818	−	947.116i	−0.0765212	−	0.132539i
$372$		−	2523.71i		−	0.351743i
$373$	−10249.4	+	5917.47i	−1.42277	+	0.821435i	−0.996535	−	0.0831793i	$-0.973493\pi$
$373$	−10249.4	+	5917.47i	−1.42277	+	0.821435i	−0.426232	+	0.904614i	$0.640159\pi$
$374$	6855.97	−	11874.9i	0.947898	−	1.64181i
$375$	10976.3	−	2368.67i	1.51150	−	0.326180i
$376$	3379.68			0.463548
$377$	570.030	+	6039.32i	0.0778728	+	0.825042i
$378$		−	1625.27i		−	0.221151i
$379$	−3411.82	+	5909.44i	−0.462410	+	0.800917i	−0.999080	−	0.0428748i	$-0.986348\pi$
$379$	−3411.82	+	5909.44i	−0.462410	+	0.800917i	0.536671	+	0.843792i	$0.319682\pi$
$380$	−740.075	+	2591.05i	−0.0999080	+	0.349784i
$381$	−9300.00	−	16108.1i	−1.25053	−	2.16599i
$382$		−	10072.7i		−	1.34912i
$383$	−2701.51	+	1559.71i	−0.360419	+	0.208088i	−0.669265	−	0.743024i	$-0.733391\pi$
$383$	−2701.51	+	1559.71i	−0.360419	+	0.208088i	0.308846	+	0.951112i	$0.400057\pi$
$384$	514.227	+	890.667i	0.0683373	+	0.118364i
$385$	−1770.85	−	7071.34i	−0.234417	−	0.936074i
$386$	−2172.51	−	3762.89i	−0.286471	−	0.496182i
$387$	196.924	+	113.694i	0.0258662	+	0.0149339i
$388$	5157.86	+	2977.89i	0.674873	+	0.389638i
$389$	357.665			0.0466179			0.0233089	−	0.999728i	$-0.492580\pi$
$389$	357.665			0.0466179			0.0233089	+	0.999728i	$0.492580\pi$
$390$	8278.89	+	1541.70i	1.07492	+	0.200172i
$391$	−6594.41			−0.852925
$392$	1740.60	+	1004.94i	0.224269	+	0.129482i
$393$	−4331.03	−	2500.52i	−0.555908	−	0.320953i
$394$	3361.51	+	5822.31i	0.429824	+	0.744477i
$395$	−12292.6	+	3078.38i	−1.56584	+	0.392127i
$396$	5112.64	+	8855.36i	0.648788	+	1.12373i
$397$	−1109.79	+	640.740i	−0.140300	+	0.0810021i	−0.568507	−	0.822679i	$-0.692479\pi$
$397$	−1109.79	+	640.740i	−0.140300	+	0.0810021i	0.428207	+	0.903681i	$0.359145\pi$
$398$		−	2064.69i		−	0.260034i
$399$	2318.87	+	4016.40i	0.290949	+	0.503939i
$400$	−65.6681	+	1998.92i	−0.00820852	+	0.249865i
$401$	2494.99	−	4321.45i	0.310708	−	0.538162i	−0.667808	−	0.744334i	$-0.732767\pi$
$401$	2494.99	−	4321.45i	0.310708	−	0.538162i	0.978516	+	0.206172i	$0.0661005\pi$
$402$			16593.9i			2.05878i
$403$	3000.47	−	2131.69i	0.370878	−	0.263491i
$404$	−2364.21			−0.291148
$405$	1020.87	−	3574.13i	0.125253	−	0.438518i
$406$	−1239.77	+	2147.34i	−0.151548	+	0.262489i
$407$	−5044.33	+	2912.35i	−0.614345	+	0.354692i
$408$			6474.71i			0.785652i
$409$	1433.46	+	2482.83i	0.173301	+	0.300166i	0.939572	−	0.342351i	$-0.111223\pi$
$409$	1433.46	+	2482.83i	0.173301	+	0.300166i	−0.766271	+	0.642517i	$0.777890\pi$
$410$	5902.54	−	5711.81i	0.710989	−	0.688015i
$411$	−48.9651			−0.00587658
$412$	−3833.62	+	2213.34i	−0.458419	+	0.264669i
$413$	−3264.25	−	1884.62i	−0.388918	−	0.224542i
$414$	2458.80	−	4258.76i	0.291892	−	0.505571i
$415$	−584.591	−	2334.39i	−0.0691480	−	0.276122i
$416$	−624.574	+	1363.68i	−0.0736113	+	0.160721i
$417$		−	6248.73i		−	0.733817i
$418$	−7103.37	−	4101.13i	−0.831190	−	0.479888i
$419$	4464.28	−	7732.36i	0.520512	−	0.901552i	−0.479204	−	0.877704i	$-0.659075\pi$
$419$	4464.28	−	7732.36i	0.520512	−	0.901552i	0.999716	−	0.0238489i	$-0.00759205\pi$
$420$	2393.68	+	2473.61i	0.278095	+	0.287380i
$421$	15373.5			1.77971			0.889854	−	0.456245i	$-0.150806\pi$
$421$	15373.5			1.77971			0.889854	+	0.456245i	$0.150806\pi$
$422$	4300.79	−	2483.06i	0.496112	−	0.286430i
$423$	−13741.0	+	7933.38i	−1.57946	+	0.911901i
$424$	−913.317			−0.104610
$425$	−6650.22	+	10691.7i	−0.759019	+	1.22029i
$426$	6285.76	−	10887.3i	0.714897	−	1.23824i
$427$	−3523.34	−	2034.20i	−0.399313	−	0.230543i
$428$			1324.96i			0.149637i
$429$	−10673.9	+	23305.2i	−1.20126	+	2.62281i
$430$	−131.324	+	32.8869i	−0.0147279	+	0.00368825i
$431$	−3836.00	+	6644.14i	−0.428709	+	0.742545i	−0.996759	−	0.0804488i	$-0.974365\pi$
$431$	−3836.00	+	6644.14i	−0.428709	+	0.742545i	0.568050	+	0.822994i	$0.307698\pi$
$432$	−1175.45	−	678.649i	−0.130912	−	0.0755822i
$433$	7839.41	−	4526.08i	0.870065	−	0.502332i	0.00269485	−	0.999996i	$-0.499142\pi$
$433$	7839.41	−	4526.08i	0.870065	−	0.502332i	0.867370	+	0.497664i	$0.165809\pi$
$434$	1504.44			0.166395
$435$	8354.67	−	8084.71i	0.920864	−	0.891109i
$436$	−684.499	−	1185.59i	−0.0751870	−	0.130228i
$437$			3944.67i			0.431806i
$438$	−3400.91	+	1963.52i	−0.371009	+	0.214202i
$439$	88.6836	−	153.604i	0.00964154	−	0.0166996i	−0.861164	−	0.508327i	$-0.830264\pi$
$439$	88.6836	−	153.604i	0.00964154	−	0.0166996i	0.870806	+	0.491627i	$0.163598\pi$
$440$	−5853.67	−	1671.97i	−0.634234	−	0.181155i
$441$	−9435.84			−1.01888
$442$	−7697.85	+	5468.96i	−0.828393	+	0.588533i
$443$		−	3093.98i		−	0.331827i	−0.986140	−	0.165914i	$-0.946943\pi$
$443$		−	3093.98i		−	0.331827i	0.986140	−	0.165914i	$-0.0530573\pi$
$444$	1375.20	−	2381.91i	0.146991	−	0.254595i
$445$	3408.25	−	11932.5i	0.363071	−	1.27114i
$446$	−2982.37	−	5165.62i	−0.316636	−	0.548429i
$447$			12080.4i			1.27827i
$448$	−530.948	+	306.543i	−0.0559931	+	0.0323276i
$449$	−8772.67	−	15194.7i	−0.922067	−	1.59707i	−0.796212	−	0.605018i	$-0.793166\pi$
$449$	−8772.67	−	15194.7i	−0.922067	−	1.59707i	−0.125855	−	0.992049i	$-0.540167\pi$
$450$	−4425.22	−	8281.30i	−0.463571	−	0.867521i
$451$	12500.8	+	21652.0i	1.30518	+	2.26065i
$452$	331.471	+	191.375i	0.0344935	+	0.0199148i
$453$	15966.8	+	9218.41i	1.65603	+	0.956112i
$454$	−306.249			−0.0316585
$455$	−919.044	+	4935.24i	−0.0946932	+	0.508500i
$456$	3873.07			0.397748
$457$	275.809	+	159.238i	0.0282315	+	0.0162995i	0.514049	−	0.857761i	$-0.328145\pi$
$457$	275.809	+	159.238i	0.0282315	+	0.0162995i	−0.485818	+	0.874060i	$0.661478\pi$
$458$	7822.95	+	4516.58i	0.798127	+	0.460799i
$459$	−4272.49	−	7400.17i	−0.434472	−	0.752528i
$460$	711.224	+	2840.06i	0.0720891	+	0.287866i
$461$	−5613.22	−	9722.38i	−0.567101	−	0.982248i	−0.996851	−	0.0792998i	$-0.974732\pi$
$461$	−5613.22	−	9722.38i	−0.567101	−	0.982248i	0.429750	−	0.902948i	$-0.358602\pi$
$462$	−9073.82	+	5238.77i	−0.913749	+	0.527553i
$463$			6101.76i			0.612469i	0.951956	+	0.306234i	$0.0990691\pi$
$463$			6101.76i			0.612469i	−0.951956	+	0.306234i	$0.900931\pi$
$464$	1035.35	+	1793.29i	0.103589	+	0.179421i
$465$	−6782.73	−	1937.33i	−0.676434	−	0.193208i
$466$	−1258.34	+	2179.51i	−0.125089	+	0.216660i
$467$		−	8845.77i		−	0.876517i	−0.898849	−	0.438258i	$-0.855596\pi$
$467$		−	8845.77i		−	0.876517i	0.898849	−	0.438258i	$-0.144404\pi$
$468$	−661.700	−	7010.53i	−0.0653570	−	0.692440i
$469$	−9892.02			−0.973926
$470$	2594.42	−	9083.25i	0.254621	−	0.891444i
$471$	−2625.75	+	4547.94i	−0.256875	+	0.444921i
$472$	−2726.04	+	1573.88i	−0.265840	+	0.153483i
$473$		−	412.079i		−	0.0400579i
$474$	9106.91	+	15773.6i	0.882477	+	1.52850i
$475$	6395.59	+	3978.05i	0.617789	+	0.384264i
$476$	−3859.73			−0.371660
$477$	3713.34	−	2143.90i	0.356440	−	0.205791i
$478$	3143.02	+	1814.62i	0.300749	+	0.173638i
$479$	2441.31	−	4228.48i	0.232873	−	0.403349i	−0.725779	−	0.687928i	$-0.758521\pi$
$479$	2441.31	−	4228.48i	0.232873	−	0.403349i	0.958653	+	0.284579i	$0.0918539\pi$
$480$	2788.51	−	698.314i	0.265161	−	0.0664032i
$481$	3993.45	−	376.928i	0.378557	−	0.0357306i
$482$		−	9710.04i		−	0.917594i
$483$	4363.82	+	2519.45i	0.411099	+	0.237348i
$484$	6603.25	−	11437.2i	0.620140	−	1.07411i
$485$	11962.8	−	11576.3i	1.12001	−	1.08382i
$486$	−9923.45			−0.926207
$487$	−15146.9	+	8745.09i	−1.40939	+	0.813712i	−0.995329	−	0.0965364i	$-0.969224\pi$
$487$	−15146.9	+	8745.09i	−1.40939	+	0.813712i	−0.414062	+	0.910249i	$0.635890\pi$
$488$	−2942.42	+	1698.80i	−0.272944	+	0.157585i
$489$	32133.1			2.97159
$490$	4037.05	−	3906.60i	0.372194	−	0.360168i
$491$	−981.047	+	1699.22i	−0.0901712	+	0.156181i	−0.907583	−	0.419873i	$-0.862075\pi$
$491$	−981.047	+	1699.22i	−0.0901712	+	0.156181i	0.817412	+	0.576054i	$0.195408\pi$
$492$	−10224.0	−	5902.80i	−0.936852	−	0.540892i
$493$			13036.3i			1.19093i
$494$	3271.44	+	4604.73i	0.297954	+	0.419386i
$495$	27724.4	−	6942.91i	2.51741	−	0.630426i
$496$	628.195	−	1088.07i	0.0568686	−	0.0984992i
$497$	6490.15	+	3747.09i	0.585761	+	0.338189i
$498$	−2995.44	+	1729.42i	−0.269536	+	0.155617i
$499$	13167.7			1.18130			0.590650	−	0.806928i	$-0.298872\pi$
$499$	13167.7			1.18130			0.590650	+	0.806928i	$0.298872\pi$
$500$	5321.90	+	1710.97i	0.476005	+	0.153034i
$501$	270.433	+	468.404i	0.0241159	+	0.0417699i
$502$		−	1145.40i		−	0.101836i
$503$	7033.91	−	4061.03i	0.623512	−	0.359985i	−0.154723	−	0.987958i	$-0.549449\pi$
$503$	7033.91	−	4061.03i	0.623512	−	0.359985i	0.778235	+	0.627973i	$0.216115\pi$
$504$	1439.14	−	2492.66i	0.127191	−	0.220302i
$505$	−1814.89	+	6354.05i	−0.159924	+	0.559904i
$506$	−8911.77			−0.782957
$507$	13366.0	−	11530.7i	1.17082	−	1.01005i
$508$		−	9259.72i		−	0.808728i
$509$	7917.74	−	13713.9i	0.689485	−	1.19422i	−0.282520	−	0.959261i	$-0.591170\pi$
$509$	7917.74	−	13713.9i	0.689485	−	1.19422i	0.972005	−	0.234961i	$-0.0754963\pi$
$510$	17401.5	+	4970.33i	1.51088	+	0.431549i
$511$	−1170.50	−	2027.36i	−0.101330	−	0.175509i
$512$			512.000i			0.0441942i
$513$	−4426.66	+	2555.73i	−0.380978	+	0.219958i
$514$	−2895.70	−	5015.49i	−0.248490	−	0.430397i
$515$	3005.69	+	12002.3i	0.257178	+	1.02696i
$516$	97.2908	+	168.513i	0.00830036	+	0.0143766i
$517$	24901.8	+	14377.0i	2.11833	+	1.22302i
$518$	1419.91	+	819.786i	0.120439	+	0.0695354i
$519$	12967.3			1.09673
$520$	3185.58	+	2725.44i	0.268648	+	0.229844i
$521$	−23211.6			−1.95186			−0.975931	−	0.218081i	$-0.930020\pi$
$521$	−23211.6			−1.95186			−0.975931	+	0.218081i	$0.930020\pi$
$522$	−8419.03	−	4860.73i	−0.705921	−	0.407564i
$523$	−10442.9	−	6029.23i	−0.873113	−	0.504092i	−0.00473125	−	0.999989i	$-0.501506\pi$
$523$	−10442.9	−	6029.23i	−0.873113	−	0.504092i	−0.868381	+	0.495897i	$0.834839\pi$
$524$	−1244.85	−	2156.14i	−0.103781	−	0.179754i
$525$	8485.60	−	4534.39i	0.705413	−	0.376947i
$526$	2841.57	+	4921.75i	0.235548	+	0.407982i
$527$	6850.01	−	3954.85i	0.566207	−	0.326900i
$528$			8750.01i			0.721203i
$529$	−3940.56	−	6825.24i	−0.323872	−	0.560964i
$530$	−701.111	+	2454.63i	−0.0574610	+	0.201174i
$531$	7388.97	−	12798.1i	0.603868	−	1.04593i
$532$			2308.83i			0.188159i
$533$	−1617.90	−	17141.2i	−0.131481	−	1.39300i
$534$	−17836.6			−1.44544
$535$	3560.97	+	1017.11i	0.287765	+	0.0821935i
$536$	−4130.51	+	7154.26i	−0.332856	+	0.576524i
$537$	−10141.8	+	5855.35i	−0.814990	+	0.470535i
$538$		−	13933.5i		−	1.11657i
$539$	8549.92	+	14808.9i	0.683248	+	1.18342i
$540$	−2726.28	+	2638.19i	−0.217260	+	0.210240i
$541$	7803.98			0.620184			0.310092	−	0.950707i	$-0.399640\pi$
$541$	7803.98			0.620184			0.310092	+	0.950707i	$0.399640\pi$
$542$	6582.85	−	3800.61i	0.521693	−	0.301200i
$543$	−15213.4	−	8783.44i	−1.20234	−	0.694169i
$544$	−1611.67	+	2791.49i	−0.127022	+	0.220008i
$545$	−3711.84	+	929.542i	−0.291739	+	0.0730591i
$546$	7183.48	−	678.024i	0.563049	−	0.0531442i
$547$			593.410i			0.0463846i	0.999731	+	0.0231923i	$0.00738300\pi$
$547$			593.410i			0.0463846i	−0.999731	+	0.0231923i	$0.992617\pi$
$548$	−21.1107	−	12.1883i	−0.00164563	−	0.000950104i
$549$	7975.45	−	13813.9i	0.620007	−	1.07388i
$550$	−8987.18	+	14448.9i	−0.696754	+	1.12018i
$551$	7798.12			0.602924
$552$	3644.32	−	2104.05i	0.281001	−	0.162236i
$553$	−9403.03	+	5428.84i	−0.723069	+	0.417464i
$554$	−464.745			−0.0356410
$555$	−5345.95	−	5524.46i	−0.408870	−	0.422523i
$556$	1555.42	−	2694.06i	0.118641	−	0.205492i
$557$	10832.7	+	6254.27i	0.824052	+	0.475767i	0.851812	−	0.523848i	$-0.175504\pi$
$557$	10832.7	+	6254.27i	0.824052	+	0.475767i	−0.0277597	+	0.999615i	$0.508837\pi$
$558$			5898.44i			0.447492i
$559$	−118.168	+	258.006i	−0.00894094	+	0.0195215i
$560$	416.281	+	1662.29i	0.0314127	+	0.125437i
$561$	−27543.2	+	47706.2i	−2.07286	+	3.59030i
$562$	−3813.79	−	2201.89i	−0.286254	−	0.165269i
$563$	12113.5	−	6993.74i	0.906792	−	0.523537i	0.0273946	−	0.999625i	$-0.491279\pi$
$563$	12113.5	−	6993.74i	0.906792	−	0.523537i	0.879398	+	0.476088i	$0.157946\pi$
$564$	−13577.5			−1.01368
$565$	768.794	−	743.952i	0.0572450	−	0.0553952i
$566$	−2579.73	−	4468.22i	−0.191580	−	0.331825i
$567$		−	3184.83i		−	0.235891i
$568$	5420.06	−	3129.27i	0.400388	−	0.231164i
$569$	−4056.80	+	7026.58i	−0.298892	+	0.517697i	−0.975883	−	0.218295i	$-0.929951\pi$
$569$	−4056.80	+	7026.58i	−0.298892	+	0.517697i	0.676990	+	0.735992i	$0.263284\pi$
$570$	2973.18	−	10409.3i	0.218478	−	0.764906i
$571$	−21177.3			−1.55209			−0.776046	−	0.630677i	$-0.782777\pi$
$571$	−21177.3			−1.55209			−0.776046	+	0.630677i	$0.782777\pi$
$572$	−10403.0	+	7390.81i	−0.760437	+	0.540254i
$573$			40466.1i			2.95025i
$574$	3518.80	−	6094.74i	0.255874	−	0.443187i
$575$	8178.92	+	268.692i	0.593191	+	0.0194874i
$576$	−1201.85	−	2081.67i	−0.0869397	−	0.150584i
$577$		−	3634.90i		−	0.262258i	−0.991365	−	0.131129i	$-0.958140\pi$
$577$		−	3634.90i		−	0.262258i	0.991365	−	0.131129i	$-0.0418602\pi$
$578$	−9064.49	+	5233.39i	−0.652307	+	0.376609i
$579$	8727.83	+	15117.0i	0.626453	+	1.08505i
$580$	5614.44	−	1406.00i	0.401943	−	0.100657i
$581$	−1030.95	−	1785.65i	−0.0736161	−	0.127507i
$582$	−20721.2	−	11963.4i	−1.47581	−	0.852059i
$583$	−6729.39	−	3885.22i	−0.478050	−	0.276002i
$584$	−1955.01			−0.138526
$585$	−19349.5	−	3603.27i	−1.36753	−	0.254662i
$586$	−3594.37			−0.253382
$587$	5368.62	+	3099.58i	0.377490	+	0.217944i	0.676726	−	0.736235i	$-0.263398\pi$
$587$	5368.62	+	3099.58i	0.377490	+	0.217944i	−0.299235	+	0.954179i	$0.596732\pi$
$588$	−6992.68	−	4037.23i	−0.490431	−	0.283150i
$589$	−2365.73	−	4097.57i	−0.165498	−	0.286651i
$590$	2137.31	+	8534.71i	0.149139	+	0.595540i
$591$	−13504.5	−	23390.6i	−0.939937	−	1.62802i
$592$	1185.80	−	684.620i	0.0823242	−	0.0475299i
$593$			26416.9i			1.82936i	0.404179	+	0.914680i	$0.367557\pi$
$593$			26416.9i			1.82936i	−0.404179	+	0.914680i	$0.632443\pi$
$594$	−5773.89	−	10000.7i	−0.398831	−	0.690796i
$595$	−2962.93	+	10373.4i	−0.204149	+	0.714737i
$596$	−3007.03	+	5208.33i	−0.206666	+	0.357955i
$597$			8294.69i			0.568641i
$598$	5579.74	+	2555.55i	0.381560	+	0.174756i
$599$	−3580.00			−0.244199			−0.122099	−	0.992518i	$-0.538963\pi$
$599$	−3580.00			−0.244199			−0.122099	+	0.992518i	$0.538963\pi$
$600$	263.815	−	8030.46i	0.0179503	−	0.546404i
$601$	−2332.81	+	4040.55i	−0.158332	+	0.274239i	−0.934267	−	0.356574i	$-0.883945\pi$
$601$	−2332.81	+	4040.55i	−0.158332	+	0.274239i	0.775935	+	0.630812i	$0.217278\pi$
$602$	−100.454	+	57.9973i	−0.00680101	+	0.00392657i
$603$		−	38783.4i		−	2.61921i
$604$	4589.24	+	7948.80i	0.309162	+	0.535484i
$605$	−25669.5	−	26526.7i	−1.72498	−	1.78258i
$606$	9497.97			0.636681
$607$	−5918.94	+	3417.30i	−0.395787	+	0.228507i	−0.684664	−	0.728859i	$-0.740051\pi$
$607$	−5918.94	+	3417.30i	−0.395787	+	0.228507i	0.288878	+	0.957366i	$0.406718\pi$
$608$	1669.83	+	964.074i	0.111382	+	0.0643065i
$609$	4980.64	−	8626.72i	0.331405	−	0.574010i
$610$	2306.96	+	9212.14i	0.153125	+	0.611457i
$611$	−11468.5	−	16142.5i	−0.759352	−	1.06883i
$612$		−	15132.7i		−	0.999518i
$613$	8035.53	+	4639.31i	0.529448	+	0.305677i	0.740792	−	0.671735i	$-0.234450\pi$
$613$	8035.53	+	4639.31i	0.529448	+	0.305677i	−0.211343	+	0.977412i	$0.567784\pi$
$614$	−4628.92	+	8017.53i	−0.304248	+	0.526973i
$615$	−23712.8	+	22946.6i	−1.55479	+	1.50455i
$616$	−5216.08			−0.341172
$617$	25419.4	−	14675.9i	1.65859	−	0.957585i	0.685217	−	0.728339i	$-0.259708\pi$
$617$	25419.4	−	14675.9i	1.65859	−	0.957585i	0.973369	−	0.229245i	$-0.0736258\pi$
$618$	15401.2	−	8891.87i	1.00247	−	0.578776i
$619$	−14552.4			−0.944927			−0.472464	−	0.881350i	$-0.656635\pi$
$619$	−14552.4			−0.944927			−0.472464	+	0.881350i	$0.656635\pi$
$620$	−2442.05	−	2523.60i	−0.158186	−	0.163468i
$621$	−2776.81	+	4809.57i	−0.179435	+	0.310791i
$622$	−14281.8	−	8245.59i	−0.920654	−	0.531540i
$623$		−	10632.8i		−	0.683779i
$624$	2509.16	−	5478.46i	0.160973	−	0.351465i
$625$	8683.77	−	12989.7i	0.555762	−	0.831342i
$626$	6905.03	−	11959.9i	0.440863	−	0.763598i
$627$	28537.1	+	16475.9i	1.81764	+	1.04942i
$628$	−2264.12	+	1307.19i	−0.143867	+	0.0830614i
$629$	8620.16			0.546436
$630$	−5594.53	−	5781.34i	−0.353796	−	0.365610i
$631$	3520.36	+	6097.45i	0.222097	+	0.384684i	0.955445	−	0.295170i	$-0.0953764\pi$
$631$	3520.36	+	6097.45i	0.222097	+	0.384684i	−0.733347	+	0.679854i	$0.762043\pi$
$632$			9067.47i			0.570703i
$633$	−17278.0	+	9975.46i	−1.08490	+	0.626365i
$634$	−6551.17	+	11347.0i	−0.410379	+	0.710797i
$635$	−24886.5	−	7108.25i	−1.55526	−	0.444224i
$636$	3669.16			0.228760
$637$	−1106.57	−	11723.8i	−0.0688285	−	0.729219i
$638$			17617.4i			1.09323i
$639$	−14691.1	+	25445.8i	−0.909503	+	1.57530i
$640$	1376.05	+	393.038i	0.0849895	+	0.0242753i
$641$	3053.24	+	5288.36i	0.188137	+	0.325862i	0.944629	−	0.328140i	$-0.106422\pi$
$641$	3053.24	+	5288.36i	0.188137	+	0.325862i	−0.756492	+	0.654003i	$0.773089\pi$
$642$		−	5322.90i		−	0.327224i
$643$	−8402.69	+	4851.29i	−0.515349	+	0.297537i	−0.735030	−	0.678035i	$-0.762832\pi$
$643$	−8402.69	+	4851.29i	−0.515349	+	0.297537i	0.219680	+	0.975572i	$0.429499\pi$
$644$	1254.27	+	2172.46i	0.0767472	+	0.132930i
$645$	527.580	−	132.120i	0.0322069	−	0.00806544i
$646$	6069.41	+	10512.5i	0.369656	+	0.640263i
$647$	12666.5	+	7313.01i	0.769662	+	0.444365i	0.832754	−	0.553643i	$-0.186763\pi$
$647$	12666.5	+	7313.01i	0.769662	+	0.444365i	−0.0630919	+	0.998008i	$0.520096\pi$
$648$	−2303.38	−	1329.86i	−0.139638	−	0.0806200i
$649$	−26780.9			−1.61979
$650$	9770.34	−	6469.39i	0.589576	−	0.390385i
$651$	−6043.95			−0.363872
$652$	13853.8	+	7998.48i	0.832140	+	0.480436i
$653$	−12738.6	−	7354.61i	−0.763397	−	0.440748i	0.0671169	−	0.997745i	$-0.478620\pi$
$653$	−12738.6	−	7354.61i	−0.763397	−	0.440748i	−0.830514	+	0.556998i	$0.811953\pi$
$654$	2749.90	+	4762.97i	0.164419	+	0.284781i
$655$	−6750.45	+	1690.49i	−0.402690	+	0.100844i
$656$	−2938.62	−	5089.84i	−0.174899	−	0.302934i
$657$	7948.63	−	4589.15i	0.472003	−	0.272511i
$658$		−	8093.89i		−	0.479533i
$659$	3889.58	+	6736.96i	0.229919	+	0.398231i	0.957784	−	0.287489i	$-0.0928205\pi$
$659$	3889.58	+	6736.96i	0.229919	+	0.398231i	−0.727865	+	0.685721i	$0.759487\pi$
$660$	23516.5	+	6716.97i	1.38694	+	0.396148i
$661$	−5713.70	+	9896.42i	−0.336213	+	0.582339i	−0.983717	−	0.179724i	$-0.942480\pi$
$661$	−5713.70	+	9896.42i	−0.336213	+	0.582339i	0.647504	+	0.762062i	$0.275813\pi$
$662$			1930.55i			0.113343i
$663$	30925.3	−	21971.0i	1.81152	−	1.28700i
$664$	−1721.93			−0.100638
$665$	6205.21	+	1772.38i	0.361846	+	0.103353i
$666$	−3214.12	+	5567.01i	−0.187004	+	0.323900i
$667$	7337.54	−	4236.33i	0.425953	−	0.245924i
$668$			269.262i			0.0155959i
$669$	11981.4	+	20752.4i	0.692417	+	1.19930i
$670$	16057.0	+	16593.2i	0.925875	+	0.956791i
$671$	−28906.6			−1.66308
$672$	2133.03	−	1231.50i	0.122445	−	0.0706939i
$673$	7532.63	+	4348.96i	0.431443	+	0.249094i	0.699961	−	0.714181i	$-0.253201\pi$
$673$	7532.63	+	4348.96i	0.431443	+	0.249094i	−0.268518	+	0.963275i	$0.586534\pi$
$674$	2233.82	−	3869.10i	0.127661	−	0.221116i
$675$	4997.56	+	9352.37i	0.284972	+	0.533293i
$676$	8632.80	−	1644.29i	0.491170	−	0.0935530i
$677$		−	15755.1i		−	0.894412i	−0.894431	−	0.447206i	$-0.852419\pi$
$677$		−	15755.1i		−	0.894412i	0.894431	−	0.447206i	$-0.147581\pi$
$678$	−1331.65	−	768.829i	−0.0754303	−	0.0435497i
$679$	7131.65	−	12352.4i	0.403075	−	0.698146i
$680$	6265.22	+	6474.42i	0.353324	+	0.365122i
$681$	1230.32			0.0692306
$682$	9257.18	−	5344.64i	0.519759	−	0.300083i
$683$	19651.2	−	11345.6i	1.10093	−	0.635621i	0.164463	−	0.986383i	$-0.447411\pi$
$683$	19651.2	−	11345.6i	1.10093	−	0.635621i	0.936465	+	0.350762i	$0.114077\pi$
$684$	−9052.17			−0.506021
$685$	−48.9629	+	47.3808i	−0.00273106	+	0.00264281i
$686$	5692.44	−	9859.60i	0.316820	−	0.548748i
$687$	−31427.9	−	18144.9i	−1.74534	−	1.00767i
$688$			96.8694i			0.00536790i
$689$	3099.21	+	4362.30i	0.171365	+	0.241205i
$690$	−2857.27	−	11409.6i	−0.157644	−	0.629504i
$691$	15470.7	−	26796.0i	0.851710	−	1.47521i	−0.0279533	−	0.999609i	$-0.508899\pi$
$691$	15470.7	−	26796.0i	0.851710	−	1.47521i	0.879664	−	0.475596i	$-0.157768\pi$
$692$	5590.68	+	3227.78i	0.307118	+	0.177315i
$693$	21207.4	−	12244.1i	1.16248	−	0.671161i
$694$	−12897.5			−0.705451
$695$	−6046.55	−	6248.45i	−0.330012	−	0.341032i
$696$	−4159.43	−	7204.35i	−0.226527	−	0.392356i
$697$		−	37000.6i		−	2.01076i
$698$	−5900.17	+	3406.46i	−0.319949	+	0.184723i
$699$	5055.25	−	8755.95i	0.273544	−	0.473792i
$700$	4787.15	+	157.266i	0.258482	+	0.00849158i
$701$	28187.1			1.51870			0.759352	−	0.650680i	$-0.225516\pi$
$701$	28187.1			1.51870			0.759352	+	0.650680i	$0.225516\pi$
$702$	747.281	+	7917.25i	0.0401771	+	0.425666i
$703$		−	5156.44i		−	0.276641i
$704$	−2178.03	+	3772.46i	−0.116602	+	0.201960i
$705$	−10422.8	+	36491.0i	−0.556804	+	1.94941i
$706$	−10666.4	−	18474.7i	−0.568604	−	0.984851i
$707$			5661.96i			0.301188i
$708$	10951.6	−	6322.91i	0.581337	−	0.335635i
$709$	−8172.65	−	14155.4i	−0.432906	−	0.749815i	0.564216	−	0.825627i	$-0.309178\pi$
$709$	−8172.65	−	14155.4i	−0.432906	−	0.749815i	−0.997122	+	0.0758122i	$0.975845\pi$
$710$	−4249.51	−	16969.2i	−0.224622	−	0.896959i
$711$	−21284.7	−	36866.2i	−1.12270	−	1.94457i
$712$	−7690.02	−	4439.84i	−0.404769	−	0.233694i
$713$	−4452.01	−	2570.37i	−0.233841	−	0.135008i
$714$	15506.1			0.812745
$715$	11877.7	+	33632.6i	0.621260	+	1.75915i
$716$	−5829.99			−0.304298
$717$	−12626.7	−	7290.05i	−0.657677	−	0.379710i
$718$	7038.88	+	4063.90i	0.365862	+	0.211230i
$719$	1538.85	+	2665.37i	0.0798185	+	0.138250i	0.903172	−	0.429280i	$-0.141233\pi$
$719$	1538.85	+	2665.37i	0.0798185	+	0.138250i	−0.823353	+	0.567530i	$0.807899\pi$
$720$	−6517.32	+	1632.11i	−0.337342	+	0.0844791i
$721$	5300.65	+	9181.00i	0.273796	+	0.474228i
$722$	−5591.71	+	3228.38i	−0.288230	+	0.166410i
$723$			39009.1i			2.00659i
$724$	−4372.70	−	7573.74i	−0.224462	−	0.388779i
$725$	531.170	−	16168.7i	0.0272099	−	0.828262i
$726$	−26527.9	+	45947.6i	−1.35612	+	2.34887i
$727$			7072.83i			0.360821i	0.983591	+	0.180410i	$0.0577426\pi$
$727$			7072.83i			0.360821i	−0.983591	+	0.180410i	$0.942257\pi$
$728$	3265.84	+	1495.77i	0.166264	+	0.0761497i
$729$	30889.9			1.56937
$730$	−1500.77	+	5254.30i	−0.0760905	+	0.266398i
$731$	−304.925	+	528.145i	−0.0154282	+	0.0267225i
$732$	11820.9	−	6824.77i	0.596874	−	0.344605i
$733$		−	29455.2i		−	1.48425i	−0.670263	−	0.742123i	$-0.733819\pi$
$733$		−	29455.2i		−	1.48425i	0.670263	−	0.742123i	$-0.266181\pi$
$734$	2865.64	+	4963.43i	0.144104	+	0.249596i
$735$	−16218.4	+	15694.4i	−0.813912	+	0.787613i
$736$	2094.93			0.104919
$737$	−60867.9	+	35142.1i	−3.04219	+	1.75641i
$738$	23895.5	+	13796.1i	1.19188	+	0.688131i
$739$	9941.65	−	17219.4i	0.494871	−	0.857141i	−0.505112	−	0.863054i	$-0.668549\pi$
$739$	9941.65	−	17219.4i	0.494871	−	0.857141i	0.999983	+	0.00591278i	$0.00188211\pi$
$740$	−929.706	−	3712.50i	−0.0461847	−	0.184425i
$741$	−13142.7	−	18499.1i	−0.651564	−	0.917111i
$742$			2187.27i			0.108217i
$743$	−23888.8	−	13792.2i	−1.17954	−	0.681006i	−0.223629	−	0.974674i	$-0.571790\pi$
$743$	−23888.8	−	13792.2i	−1.17954	−	0.681006i	−0.955907	+	0.293669i	$0.905124\pi$
$744$	−2523.71	+	4371.20i	−0.124360	+	0.215398i
$745$	11689.6	+	12079.9i	0.574862	+	0.594058i
$746$	23669.9			1.16168
$747$	7000.97	−	4042.01i	0.342908	−	0.197978i
$748$	−23749.8	+	13711.9i	−1.16093	+	0.670265i
$749$	3173.10			0.154797
$750$	−21380.2	−	6873.64i	−1.04093	−	0.334653i
$751$	−18792.9	+	32550.2i	−0.913132	+	1.58159i	−0.103519	+	0.994627i	$0.533010\pi$
$751$	−18792.9	+	32550.2i	−0.913132	+	1.58159i	−0.809613	+	0.586964i	$0.800323\pi$
$752$	−5853.78	−	3379.68i	−0.283864	−	0.163889i
$753$			4601.54i			0.222695i
$754$	5052.00	−	11030.4i	0.244009	−	0.532765i
$755$	24886.2	−	6232.14i	1.19960	−	0.300412i
$756$	−1625.27	+	2815.05i	−0.0781886	+	0.135427i
$757$	23965.3	+	13836.4i	1.15064	+	0.664322i	0.949043	−	0.315146i	$-0.102054\pi$
$757$	23965.3	+	13836.4i	1.15064	+	0.664322i	0.201597	+	0.979469i	$0.435387\pi$
$758$	11818.9	−	6823.63i	0.566334	−	0.326973i
$759$	35802.1			1.71217
$760$	3872.90	−	3747.75i	0.184848	−	0.178875i
$761$	11099.8	+	19225.3i	0.528733	+	0.915793i	0.999439	+	0.0335023i	$0.0106661\pi$
$761$	11099.8	+	19225.3i	0.528733	+	0.915793i	−0.470705	+	0.882290i	$0.656001\pi$
$762$			37200.0i			1.76852i
$763$	−2839.32	+	1639.28i	−0.134719	+	0.0777798i
$764$	−10072.7	+	17446.4i	−0.476987	+	0.826165i
$765$	−40670.8	−	11616.7i	−1.92217	−	0.549023i
$766$	6238.86			0.294281
$767$	16767.8	+	7679.74i	0.789374	+	0.361537i
$768$		−	2056.91i		−	0.0966436i
$769$	14548.3	−	25198.4i	0.682218	−	1.18164i	−0.292085	−	0.956392i	$-0.594349\pi$
$769$	14548.3	−	25198.4i	0.682218	−	1.18164i	0.974303	−	0.225243i	$-0.0723177\pi$
$770$	−4004.14	+	14018.8i	−0.187402	+	0.656105i
$771$	11633.2	+	20149.2i	0.543396	+	0.941190i
$772$			8690.03i			0.405131i
$773$	−23252.7	+	13424.9i	−1.08194	+	0.624659i	−0.931419	−	0.363948i	$-0.881429\pi$
$773$	−23252.7	+	13424.9i	−1.08194	+	0.624659i	−0.150522	+	0.988607i	$0.548095\pi$
$774$	−227.389	−	393.849i	−0.0105598	−	0.0182902i
$775$	−8657.08	+	4626.02i	−0.401253	+	0.214415i
$776$	−5955.79	−	10315.7i	−0.275516	−	0.477207i
$777$	−5704.35	−	3293.41i	−0.263375	−	0.152060i
$778$	−619.495	−	357.665i	−0.0285475	−	0.0164819i
$779$	−22133.2			−1.01798
$780$	−12797.8	−	10949.2i	−0.587479	−	0.502621i
$781$	53247.2			2.43961
$782$	11421.9	+	6594.41i	0.522308	+	0.301555i
$783$	9507.91	+	5489.39i	0.433953	+	0.250543i
$784$	−2009.87	−	3481.20i	−0.0915576	−	0.158582i
$785$	1775.15	+	7088.53i	0.0807106	+	0.322293i
$786$	5001.04	+	8662.06i	0.226948	+	0.393086i
$787$	−23132.9	+	13355.8i	−1.04778	+	0.604934i	−0.922026	−	0.387128i	$-0.873467\pi$
$787$	−23132.9	+	13355.8i	−1.04778	+	0.604934i	−0.125750	+	0.992062i	$0.540134\pi$
$788$		−	13446.1i		−	0.607863i
$789$	−11415.7	−	19772.6i	−0.515096	−	0.892172i
$790$	24369.8	+	6960.67i	1.09752	+	0.313480i
$791$	458.317	−	793.828i	0.0206016	−	0.0356830i
$792$		−	20450.6i		−	0.917525i
$793$	18098.7	+	8289.30i	0.810471	+	0.371200i
$794$	2562.96			0.114554
$795$	2816.64	−	9861.24i	0.125655	−	0.439927i
$796$	−2064.69	+	3576.15i	−0.0919360	+	0.159238i
$797$	−23083.0	+	13327.0i	−1.02590	+	0.592302i	−0.915807	−	0.401619i	$-0.868448\pi$
$797$	−23083.0	+	13327.0i	−1.02590	+	0.592302i	−0.110091	+	0.993922i	$0.535114\pi$
$798$		−	9275.48i		−	0.411464i
$799$	−21277.1	−	36853.0i	−0.942088	−	1.63174i
$800$	2112.66	−	3396.57i	0.0933674	−	0.150108i
$801$	41687.8			1.83891
$802$	−8642.90	+	4989.98i	−0.380538	+	0.219704i
$803$	−14404.7	−	8316.55i	−0.633039	−	0.365485i
$804$	16593.9	−	28741.5i	0.727889	−	1.26074i
$805$	6801.56	−	1703.29i	0.297793	−	0.0745751i
$806$	−7328.65	+	691.725i	−0.320274	+	0.0302295i
$807$			55976.5i			2.44172i
$808$	4094.93	+	2364.21i	0.178291	+	0.102936i
$809$	6219.57	−	10772.6i	0.270295	−	0.468164i	−0.698643	−	0.715471i	$-0.746212\pi$
$809$	6219.57	−	10772.6i	0.270295	−	0.468164i	0.968937	+	0.247307i	$0.0795455\pi$
$810$	−5342.33	+	5169.70i	−0.231741	+	0.224253i
$811$	−3092.84			−0.133914			−0.0669571	−	0.997756i	$-0.521329\pi$
$811$	−3092.84			−0.133914			−0.0669571	+	0.997756i	$0.521329\pi$
$812$	4294.68	−	2479.53i	0.185608	−	0.107161i
$813$	−26445.9	+	15268.6i	−1.14084	+	0.658662i
$814$	11649.4			0.501610
$815$	32131.6	−	31093.4i	1.38101	−	1.33638i
$816$	6474.71	−	11214.5i	0.277770	−	0.481112i
$817$	315.928	+	182.401i	0.0135287	+	0.00781078i
$818$		−	5733.84i		−	0.245085i
$819$	−16789.3	+	1584.68i	−0.716319	+	0.0676108i
$820$	−15935.3	+	3990.61i	−0.678640	+	0.169949i
$821$	13615.5	−	23582.7i	0.578787	−	1.00249i	−0.416832	−	0.908984i	$-0.636860\pi$
$821$	13615.5	−	23582.7i	0.578787	−	1.00249i	0.995619	−	0.0935051i	$-0.0298071\pi$
$822$	84.8101	+	48.9651i	0.00359865	+	0.00207768i
$823$	−12365.1	+	7139.01i	−0.523719	+	0.302370i	−0.738455	−	0.674303i	$-0.764444\pi$
$823$	−12365.1	+	7139.01i	−0.523719	+	0.302370i	0.214736	+	0.976672i	$0.431111\pi$
$824$	8853.36			0.374298
$825$	36105.1	−	58046.8i	1.52366	−	2.44961i
$826$	3769.23	+	6528.50i	0.158775	+	0.275007i
$827$			16329.8i			0.686631i	0.939220	+	0.343315i	$0.111550\pi$
$827$			16329.8i			0.686631i	−0.939220	+	0.343315i	$0.888450\pi$
$828$	−8517.52	+	4917.59i	−0.357493	+	0.206399i
$829$	−12130.8	+	21011.2i	−0.508229	+	0.880278i	0.491726	+	0.870750i	$0.336366\pi$
$829$	−12130.8	+	21011.2i	−0.508229	+	0.880278i	−0.999955	+	0.00952773i	$0.996967\pi$
$830$	−1321.85	+	4627.87i	−0.0552794	+	0.193537i
$831$	1867.06			0.0779395
$832$	2445.48	−	1737.40i	0.101901	−	0.0723959i
$833$		−	25306.6i		−	1.05261i
$834$	−6248.73	+	10823.1i	−0.259444	+	0.449369i
$835$	723.669	+	206.700i	0.0299923	+	0.00856663i
$836$	8202.27	+	14206.7i	0.339332	+	0.587740i
$837$		−	6661.31i		−	0.275088i
$838$	−15464.7	+	8928.56i	−0.637494	+	0.368057i
$839$	13481.2	+	23350.2i	0.554737	+	0.960832i	0.997924	+	0.0644030i	$0.0205143\pi$
$839$	13481.2	+	23350.2i	0.554737	+	0.960832i	−0.443187	+	0.896429i	$0.646152\pi$
$840$	−1672.37	−	6678.10i	−0.0686931	−	0.274305i
$841$	3819.82	+	6616.12i	0.156621	+	0.271275i
$842$	−26627.6	−	15373.5i	−1.08984	−	0.629222i
$843$	15321.5	+	8845.87i	0.625979	+	0.361409i
$844$	−9932.26			−0.405074
$845$	2207.80	−	24463.8i	0.0898825	−	0.995952i
$846$	31733.5			1.28962
$847$	−27390.4	−	15813.9i	−1.11115	−	0.641525i
$848$	1581.91	+	913.317i	0.0640602	+	0.0369852i
$849$	10363.8	+	17950.6i	0.418945	+	0.725634i
$850$	22210.2	−	11868.3i	0.896239	−	0.478917i
$851$	−2801.24	−	4851.89i	−0.112838	−	0.195441i
$852$	−21774.5	+	12571.5i	−0.875567	+	0.505509i
$853$		−	12910.4i		−	0.518222i	−0.965847	−	0.259111i	$-0.916570\pi$
$853$		−	12910.4i		−	0.518222i	0.965847	−	0.259111i	$-0.0834296\pi$
$854$	4068.41	+	7046.69i	0.163019	+	0.282357i
$855$	−6948.92	+	24328.6i	−0.277951	+	0.973125i
$856$	1324.96	−	2294.90i	0.0529045	−	0.0916333i
$857$		−	21634.5i		−	0.862333i	−0.902272	−	0.431166i	$-0.858102\pi$
$857$		−	21634.5i		−	0.862333i	0.902272	−	0.431166i	$-0.141898\pi$
$858$	41792.9	−	29691.8i	1.66292	−	1.18143i
$859$	−35110.6			−1.39460			−0.697299	−	0.716781i	$-0.745615\pi$
$859$	−35110.6			−1.39460			−0.697299	+	0.716781i	$0.745615\pi$
$860$	260.347	+	74.3621i	0.0103230	+	0.00294852i
$861$	−14136.4	+	24485.0i	−0.559544	+	0.969159i
$862$	13288.3	−	7671.99i	0.525059	−	0.303143i
$863$		−	15465.3i		−	0.610019i	−0.952349	−	0.305009i	$-0.901340\pi$
$863$		−	15465.3i		−	0.610019i	0.952349	−	0.305009i	$-0.0986596\pi$
$864$	1357.30	+	2350.91i	0.0534447	+	0.0925689i
$865$	12966.7	−	12547.7i	0.509689	−	0.493220i
$866$	−18104.3			−0.710405
$867$	36415.7	−	21024.6i	1.42646	−	0.823567i
$868$	−2605.77	−	1504.44i	−0.101896	−	0.0588296i
$869$	−38572.7	+	66809.8i	−1.50574	+	2.60802i
$870$	−22555.4	+	5648.46i	−0.878966	+	0.220116i
$871$	48187.4	−	4548.24i	1.87459	−	0.176936i
$872$			2738.00i			0.106331i
$873$	48429.7	+	27960.9i	1.87755	+	1.08400i
$874$	3944.67	−	6832.37i	0.152667	−	0.264426i
$875$	4097.54	−	12745.2i	0.158311	−	0.492420i
$876$	7854.07			0.302927
$877$	22077.3	−	12746.3i	0.850054	−	0.490779i	−0.0106151	−	0.999944i	$-0.503379\pi$
$877$	22077.3	−	12746.3i	0.850054	−	0.490779i	0.860669	+	0.509165i	$0.170046\pi$
$878$	−307.209	+	177.367i	−0.0118084	+	0.00681760i
$879$	14440.0			0.554095
$880$	8466.89	+	8749.61i	0.324340	+	0.335170i
$881$	1112.31	−	1926.58i	0.0425366	−	0.0736756i	−0.843973	−	0.536385i	$-0.819789\pi$
$881$	1112.31	−	1926.58i	0.0425366	−	0.0736756i	0.886510	+	0.462710i	$0.153123\pi$
$882$	16343.3	+	9435.84i	0.623933	+	0.360228i
$883$		−	29463.4i		−	1.12290i	−0.827510	−	0.561451i	$-0.810243\pi$
$883$		−	29463.4i		−	1.12290i	0.827510	−	0.561451i	$-0.189757\pi$
$884$	18802.0	−	1774.66i	0.715363	−	0.0675206i
$885$	−8586.44	−	34287.3i	−0.326136	−	1.30232i
$886$	−3093.98	+	5358.93i	−0.117319	+	0.203202i
$887$	41854.0	+	24164.4i	1.58435	+	0.914726i	0.994213	+	0.107423i	$0.0342600\pi$
$887$	41854.0	+	24164.4i	1.58435	+	0.914726i	0.590138	+	0.807302i	$0.299073\pi$
$888$	−4763.82	+	2750.39i	−0.180026	+	0.103938i
$889$	−22175.8			−0.836616
$890$	−17835.8	+	17259.5i	−0.671749	+	0.650044i
$891$	−11314.3	−	19597.0i	−0.425414	−	0.736839i
$892$			11929.5i			0.447791i
$893$	−22044.9	+	12727.6i	−0.826095	+	0.476946i
$894$	12080.4	−	20923.9i	0.451935	−	0.782775i
$895$	−4475.41	+	15668.7i	−0.167147	+	0.585192i
$896$	1226.17			0.0457182
$897$	−22416.1	−	10266.7i	−0.834393	−	0.382156i
$898$			35090.7i			1.30400i
$899$	−5081.29	+	8801.05i	−0.188510	+	0.326509i
$900$	−616.590	+	18768.9i	−0.0228367	+	0.695143i
$901$	5749.86	+	9959.05i	0.212603	+	0.368240i
$902$		−	50003.1i		−	1.84581i
$903$	403.565	−	232.998i	0.0148724	−	0.00858660i
$904$	−382.749	−	662.942i	−0.0140819	−	0.0243906i
$905$	−23711.9	+	5938.08i	−0.870951	+	0.218109i
$906$	−18436.8	−	31933.5i	−0.676073	−	1.17099i
$907$	−27998.8	−	16165.1i	−1.02501	−	0.591791i	−0.109460	−	0.993991i	$-0.534912\pi$
$907$	−27998.8	−	16165.1i	−1.02501	−	0.591791i	−0.915552	+	0.402201i	$0.868245\pi$
$908$	530.438	+	306.249i	0.0193868	+	0.0111930i
$909$	−22198.7			−0.809994
$910$	6527.07	−	7629.05i	0.237770	−	0.277913i
$911$	−11873.9			−0.431831			−0.215916	−	0.976412i	$-0.569274\pi$
$911$	−11873.9			−0.431831			−0.215916	+	0.976412i	$0.569274\pi$
$912$	−6708.36	−	3873.07i	−0.243570	−	0.140625i
$913$	−12687.3	−	7325.03i	−0.459900	−	0.265524i
$914$	−318.476	−	551.617i	−0.0115255	−	0.0199627i
$915$	−9267.97	−	37008.8i	−0.334852	−	1.33713i
$916$	−9033.16	−	15645.9i	−0.325834	−	0.564361i
$917$	−5163.66	+	2981.24i	−0.185953	+	0.107360i
$918$			17090.0i			0.614436i
$919$	7858.91	+	13612.0i	0.282091	+	0.488596i	0.971900	−	0.235396i	$-0.0756387\pi$
$919$	7858.91	+	13612.0i	0.282091	+	0.488596i	−0.689809	+	0.723992i	$0.742305\pi$
$920$	1608.18	−	5630.35i	0.0576307	−	0.201769i
$921$	18596.2	−	32209.6i	0.665327	−	1.15238i
$922$			22452.9i			0.802002i
$923$	−33338.6	−	15269.2i	−1.18890	−	0.544521i
$924$	20955.1			0.746073
$925$	−10691.4	−	351.232i	−0.380034	−	0.0124848i
$926$	6101.76	−	10568.6i	0.216540	−	0.375059i
$927$	−35995.7	+	20782.1i	−1.27536	+	0.736327i
$928$		−	4141.42i		−	0.146496i
$929$	−17935.2	−	31064.6i	−0.633406	−	1.09709i	−0.986851	−	0.161635i	$-0.948323\pi$
$929$	−17935.2	−	31064.6i	−0.633406	−	1.09709i	0.353445	−	0.935455i	$-0.385010\pi$
$930$	9810.70	+	10138.3i	0.345920	+	0.357471i
$931$	−15138.0			−0.532898
$932$	4359.01	−	2516.68i	0.153202	−	0.0884512i
$933$	57375.6	+	33125.8i	2.01328	+	1.16237i
$934$	−8845.77	+	15321.3i	−0.309895	+	0.536755i
$935$	18620.7	+	74356.0i	0.651295	+	2.60075i
$936$	−5864.44	+	12804.3i	−0.204792	+	0.447139i
$937$			8883.82i			0.309735i	0.987935	+	0.154868i	$0.0494951\pi$
$937$			8883.82i			0.309735i	−0.987935	+	0.154868i	$0.950505\pi$
$938$	17133.5	+	9892.02i	0.596405	+	0.344335i
$939$	−27740.3	+	48047.5i	−0.964078	+	1.66983i
$940$	−13576.9	+	13138.2i	−0.471096	+	0.455874i
$941$	−1525.20			−0.0528377			−0.0264188	−	0.999651i	$-0.508410\pi$
$941$	−1525.20			−0.0528377			−0.0264188	+	0.999651i	$0.508410\pi$
$942$	9095.88	−	5251.51i	0.314607	−	0.181638i
$943$	−20825.9	+	12023.9i	−0.719179	+	0.415218i
$944$	6295.53			0.217057
$945$	6318.10	+	6529.07i	0.217490	+	0.224752i
$946$	−412.079	+	713.741i	−0.0141626	+	0.0245304i
$947$	21544.4	+	12438.7i	0.739281	+	0.426824i	0.821808	−	0.569765i	$-0.192966\pi$
$947$	21544.4	+	12438.7i	0.739281	+	0.426824i	−0.0825266	+	0.996589i	$0.526299\pi$
$948$		−	36427.6i		−	1.24801i
$949$	6634.05	+	9337.78i	0.226923	+	0.319407i
$950$	−7099.43	−	13285.8i	−0.242459	−	0.453734i
$951$	26318.6	−	45585.2i	0.897414	−	1.55437i
$952$	6685.25	+	3859.73i	0.227595	+	0.131402i
$953$	−4956.88	+	2861.86i	−0.168488	+	0.0972766i	−0.581873	−	0.813280i	$-0.697680\pi$
$953$	−4956.88	+	2861.86i	−0.168488	+	0.0972766i	0.413385	+	0.910556i	$0.364346\pi$
$954$	−8575.58			−0.291032
$955$	39156.8	+	40464.3i	1.32679	+	1.37109i
$956$	−3629.24	−	6286.03i	−0.122780	−	0.212662i
$957$		−	70776.3i		−	2.39067i
$958$	−8456.95	+	4882.62i	−0.285211	+	0.164666i
$959$	−29.1893	+	50.5573i	−0.000982868	+	0.00170238i
$960$	−5528.15	−	1578.99i	−0.185855	−	0.0530851i
$961$	−23624.9			−0.793022
$962$	−7293.79	−	3340.60i	−0.244450	−	0.111960i
$963$			12440.7i			0.416300i
$964$	−9710.04	+	16818.3i	−0.324418	+	0.561909i
$965$	23355.3	+	6670.93i	0.779104	+	0.222533i
$966$	−5038.91	−	8727.64i	−0.167830	−	0.290691i
$967$			34970.8i			1.16296i	0.813560	+	0.581482i	$0.197527\pi$
$967$			34970.8i			1.16296i	−0.813560	+	0.581482i	$0.802473\pi$
$968$	−22874.3	+	13206.5i	−0.759513	+	0.438505i
$969$	−24383.2	−	42233.0i	−0.808361	−	1.40012i
$970$	−32296.5	+	8087.89i	−1.06905	+	0.267718i
$971$	19093.1	+	33070.1i	0.631025	+	1.09297i	0.987342	+	0.158603i	$0.0506989\pi$
$971$	19093.1	+	33070.1i	0.631025	+	1.09297i	−0.356317	+	0.934365i	$0.615968\pi$
$972$	17187.9	+	9923.45i	0.567184	+	0.327464i
$973$	−6451.92	−	3725.02i	−0.212579	−	0.122732i
$974$	34980.4			1.15076
$975$	−39251.3	+	25990.1i	−1.28928	+	0.853692i
$976$	6795.22			0.222858
$977$	−52725.8	−	30441.3i	−1.72656	−	0.996830i	−0.903063	−	0.429509i	$-0.858687\pi$
$977$	−52725.8	−	30441.3i	−1.72656	−	0.996830i	−0.823497	−	0.567321i	$-0.807980\pi$
$978$	−55656.1	−	32133.1i	−1.81972	−	1.05062i
$979$	−37773.8	−	65426.1i	−1.23315	−	2.13588i
$980$	−10899.0	+	2729.38i	−0.355260	+	0.0889663i
$981$	−6427.10	−	11132.1i	−0.209176	−	0.362303i
$982$	3398.45	−	1962.09i	0.110437	−	0.0637607i
$983$			24089.2i			0.781612i	0.920473	+	0.390806i	$0.127804\pi$
$983$			24089.2i			0.781612i	−0.920473	+	0.390806i	$0.872196\pi$
$984$	11805.6	+	20447.9i	0.382468	+	0.662455i
$985$	−36137.7	−	10321.9i	−1.16898	−	0.333892i
$986$	13036.3	−	22579.6i	0.421056	−	0.729290i
$987$			32516.4i			1.04864i
$988$	−1061.57	−	11247.1i	−0.0341833	−	0.362163i
$989$	396.358			0.0127436
$990$	−54963.0	−	15698.9i	−1.76448	−	0.503985i
$991$	13033.7	−	22575.0i	0.417789	−	0.723631i	−0.577928	−	0.816088i	$-0.696139\pi$
$991$	13033.7	−	22575.0i	0.417789	−	0.723631i	0.995717	+	0.0924565i	$0.0294719\pi$
$992$	−2176.13	+	1256.39i	−0.0696495	+	0.0402121i
$993$		−	7755.77i		−	0.247857i
$994$	−7494.18	−	12980.3i	−0.239136	−	0.414195i
$995$	8026.30	+	8294.31i	0.255730	+	0.264269i
$996$	6917.68			0.220075
$997$	29557.5	−	17065.1i	0.938914	−	0.542082i	0.0492940	−	0.998784i	$-0.484303\pi$
$997$	29557.5	−	17065.1i	0.938914	−	0.542082i	0.889620	+	0.456702i	$0.150970\pi$
$998$	−22807.2	−	13167.7i	−0.723395	−	0.417652i
$999$	3629.82	−	6287.03i	0.114957	−	0.199112i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	130.4.n.a.9.10	✓	44
5.4	even	2	inner	130.4.n.a.9.13	yes	44
13.3	even	3	inner	130.4.n.a.29.13	yes	44
65.29	even	6	inner	130.4.n.a.29.10	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.4.n.a.9.10	✓	44	1.1	even	1	trivial
130.4.n.a.9.13	yes	44	5.4	even	2	inner
130.4.n.a.29.10	yes	44	65.29	even	6	inner
130.4.n.a.29.13	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} +(6.95834 + 4.01740i) q^{3} +(2.00000 + 3.46410i) q^{4} +(10.8454 - 2.71598i) q^{5} +(-8.03480 - 13.9167i) q^{6} +(8.29606 - 4.78973i) q^{7} -8.00000i q^{8} +(18.7790 + 32.5262i) q^{9} +(-21.5008 - 6.14122i) q^{10} +(34.0317 - 58.9446i) q^{11} +32.1392i q^{12} +(-38.2106 + 27.1468i) q^{13} -19.1589 q^{14} +(86.3774 + 24.6717i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(-87.2341 + 50.3646i) q^{17} -75.1159i q^{18} +(30.1273 + 52.1821i) q^{19} +(31.0993 + 32.1377i) q^{20} +76.9690 q^{21} +(-117.889 + 68.0634i) q^{22} +(56.6958 + 32.7333i) q^{23} +(32.1392 - 55.6667i) q^{24} +(110.247 - 58.9119i) q^{25} +(93.3295 - 8.80905i) q^{26} +84.8311i q^{27} +(33.1842 + 19.1589i) q^{28} +(64.7097 - 112.080i) q^{29} +(-124.938 - 129.110i) q^{30} -78.5244 q^{31} +(27.7128 - 16.0000i) q^{32} +(473.608 - 273.438i) q^{33} +201.459 q^{34} +(76.9655 - 74.4786i) q^{35} +(-75.1159 + 130.105i) q^{36} +(-74.1123 - 42.7887i) q^{37} -120.509i q^{38} +(-374.942 + 35.3894i) q^{39} +(-21.7278 - 86.7635i) q^{40} +(-183.664 + 318.115i) q^{41} +(-133.314 - 76.9690i) q^{42} +(5.24321 - 3.02717i) q^{43} +272.254 q^{44} +(292.007 + 301.757i) q^{45} +(-65.4667 - 113.392i) q^{46} +422.460i q^{47} +(-111.333 + 64.2784i) q^{48} +(-125.617 + 217.575i) q^{49} +(-249.865 - 8.20852i) q^{50} -809.339 q^{51} +(-170.461 - 78.0718i) q^{52} -114.165i q^{53} +(84.8311 - 146.932i) q^{54} +(208.996 - 731.709i) q^{55} +(-38.3178 - 66.3684i) q^{56} +484.134i q^{57} +(-224.161 + 129.419i) q^{58} +(-196.735 - 340.755i) q^{59} +(87.2893 + 348.563i) q^{60} +(-212.351 - 367.802i) q^{61} +(136.008 + 78.5244i) q^{62} +(311.583 + 179.892i) q^{63} -64.0000 q^{64} +(-340.681 + 398.198i) q^{65} -1093.75 q^{66} +(-894.283 - 516.314i) q^{67} +(-348.936 - 201.459i) q^{68} +(263.006 + 455.539i) q^{69} +(-207.787 + 52.0352i) q^{70} +(391.159 + 677.507i) q^{71} +(260.209 - 150.232i) q^{72} -244.377i q^{73} +(85.5775 + 148.225i) q^{74} +(1003.81 + 32.9769i) q^{75} +(-120.509 + 208.728i) q^{76} -652.010i q^{77} +(684.808 + 313.646i) q^{78} -1133.43 q^{79} +(-49.1298 + 172.007i) q^{80} +(166.232 - 287.923i) q^{81} +(636.230 - 367.327i) q^{82} -215.241i q^{83} +(153.938 + 266.628i) q^{84} +(-809.303 + 783.152i) q^{85} -12.1087 q^{86} +(900.544 - 519.929i) q^{87} +(-471.557 - 272.254i) q^{88} +(554.980 - 961.253i) q^{89} +(-204.013 - 814.665i) q^{90} +(-186.971 + 408.230i) q^{91} +261.867i q^{92} +(-546.400 - 315.464i) q^{93} +(422.460 - 731.723i) q^{94} +(468.469 + 484.112i) q^{95} +257.114 q^{96} +(1289.47 - 744.473i) q^{97} +(435.150 - 251.234i) q^{98} +2556.32 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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