LMFDB - Embedded newform 164.5.d.f.163.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [164,5,Mod(163,164)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(164, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 5, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("164.163");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 164 = 2^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	164.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$16.9526739458$
Analytic rank:	$0$
Dimension:	$72$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			163.20
Character	$\chi$	$=$	164.163
Dual form			164.5.d.f.163.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.41605 + 3.18790i) q^{2} +7.04202 q^{3} +(-4.32538 - 15.4043i) q^{4} +7.90186 q^{5} +(-17.0139 + 22.4492i) q^{6} -68.9363 q^{7} +(59.5575 + 23.4286i) q^{8} -31.4099 q^{9} +O(q^{10})$	\(q+(-2.41605 + 3.18790i) q^{2} +7.04202 q^{3} +(-4.32538 - 15.4043i) q^{4} +7.90186 q^{5} +(-17.0139 + 22.4492i) q^{6} -68.9363 q^{7} +(59.5575 + 23.4286i) q^{8} -31.4099 q^{9} +(-19.0913 + 25.1903i) q^{10} +160.230 q^{11} +(-30.4594 - 108.477i) q^{12} -55.6139i q^{13} +(166.554 - 219.762i) q^{14} +55.6451 q^{15} +(-218.582 + 133.259i) q^{16} -159.426i q^{17} +(75.8880 - 100.132i) q^{18} -157.094 q^{19} +(-34.1785 - 121.722i) q^{20} -485.451 q^{21} +(-387.124 + 510.796i) q^{22} -950.893i q^{23} +(419.406 + 164.985i) q^{24} -562.561 q^{25} +(177.292 + 134.366i) q^{26} -791.593 q^{27} +(298.176 + 1061.91i) q^{28} -707.975i q^{29} +(-134.441 + 177.391i) q^{30} -896.050i q^{31} +(103.291 - 1018.78i) q^{32} +1128.34 q^{33} +(508.235 + 385.183i) q^{34} -544.725 q^{35} +(135.860 + 483.846i) q^{36} +1343.53 q^{37} +(379.547 - 500.799i) q^{38} -391.635i q^{39} +(470.615 + 185.130i) q^{40} +(-1675.01 + 141.828i) q^{41} +(1172.88 - 1547.57i) q^{42} -2248.24i q^{43} +(-693.055 - 2468.22i) q^{44} -248.197 q^{45} +(3031.35 + 2297.41i) q^{46} +3827.56 q^{47} +(-1539.26 + 938.410i) q^{48} +2351.21 q^{49} +(1359.18 - 1793.39i) q^{50} -1122.68i q^{51} +(-856.691 + 240.551i) q^{52} +4995.85i q^{53} +(1912.53 - 2523.52i) q^{54} +1266.11 q^{55} +(-4105.68 - 1615.08i) q^{56} -1106.26 q^{57} +(2256.95 + 1710.50i) q^{58} -6423.39i q^{59} +(-240.686 - 857.171i) q^{60} -3861.65 q^{61} +(2856.51 + 2164.90i) q^{62} +2165.28 q^{63} +(2998.20 + 2790.70i) q^{64} -439.453i q^{65} +(-2726.14 + 3597.04i) q^{66} -7476.87 q^{67} +(-2455.85 + 689.580i) q^{68} -6696.21i q^{69} +(1316.08 - 1736.53i) q^{70} +4425.53 q^{71} +(-1870.70 - 735.891i) q^{72} -1607.74 q^{73} +(-3246.03 + 4283.03i) q^{74} -3961.56 q^{75} +(679.491 + 2419.91i) q^{76} -11045.7 q^{77} +(1248.49 + 946.210i) q^{78} +3753.15 q^{79} +(-1727.21 + 1052.99i) q^{80} -3030.21 q^{81} +(3594.77 - 5682.41i) q^{82} +833.596i q^{83} +(2099.76 + 7478.01i) q^{84} -1259.77i q^{85} +(7167.17 + 5431.87i) q^{86} -4985.58i q^{87} +(9542.90 + 3753.97i) q^{88} +5632.85i q^{89} +(599.656 - 791.226i) q^{90} +3833.82i q^{91} +(-14647.8 + 4112.97i) q^{92} -6310.00i q^{93} +(-9247.60 + 12201.9i) q^{94} -1241.33 q^{95} +(727.381 - 7174.25i) q^{96} +1804.41i q^{97} +(-5680.65 + 7495.43i) q^{98} -5032.81 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 6 q^{2} - 162 q^{4} - 8 q^{5} + 162 q^{8} + 1728 q^{9}+O(q^{10}) $ 72 * q + 6 * q^2 - 162 * q^4 - 8 * q^5 + 162 * q^8 + 1728 * q^9	$ 72 q + 6 q^{2} - 162 q^{4} - 8 q^{5} + 162 q^{8} + 1728 q^{9} - 272 q^{10} - 2842 q^{16} - 298 q^{18} - 584 q^{20} + 280 q^{21} + 4264 q^{25} + 66 q^{32} + 3512 q^{33} - 11338 q^{36} + 5720 q^{37} - 4648 q^{40} - 7928 q^{41} - 10140 q^{42} - 9528 q^{45} - 5680 q^{46} + 6624 q^{49} + 554 q^{50} + 29864 q^{57} + 11712 q^{61} - 3936 q^{62} - 34554 q^{64} + 24852 q^{66} - 12166 q^{72} + 16632 q^{73} - 11120 q^{74} + 84456 q^{77} - 20496 q^{78} - 12104 q^{80} + 13408 q^{81} - 51114 q^{82} - 948 q^{84} - 20400 q^{86} + 64976 q^{90} - 2784 q^{92} + 2902 q^{98}+O(q^{100}) $ 72 * q + 6 * q^2 - 162 * q^4 - 8 * q^5 + 162 * q^8 + 1728 * q^9 - 272 * q^10 - 2842 * q^16 - 298 * q^18 - 584 * q^20 + 280 * q^21 + 4264 * q^25 + 66 * q^32 + 3512 * q^33 - 11338 * q^36 + 5720 * q^37 - 4648 * q^40 - 7928 * q^41 - 10140 * q^42 - 9528 * q^45 - 5680 * q^46 + 6624 * q^49 + 554 * q^50 + 29864 * q^57 + 11712 * q^61 - 3936 * q^62 - 34554 * q^64 + 24852 * q^66 - 12166 * q^72 + 16632 * q^73 - 11120 * q^74 + 84456 * q^77 - 20496 * q^78 - 12104 * q^80 + 13408 * q^81 - 51114 * q^82 - 948 * q^84 - 20400 * q^86 + 64976 * q^90 - 2784 * q^92 + 2902 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/164\mathbb{Z}\right)^\times$.

$n$	$83$	$129$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−2.41605	+	3.18790i	−0.604013	+	0.796974i
$2$	−2.41605	+	3.18790i	−0.604013	+	0.796974i
$3$	7.04202			0.782447			0.391224	−	0.920296i	$-0.372052\pi$
$3$	7.04202			0.782447			0.391224	+	0.920296i	$0.372052\pi$
$4$	−4.32538	−	15.4043i	−0.270336	−	0.962766i
$5$	7.90186			0.316074			0.158037	−	0.987433i	$-0.449483\pi$
$5$	7.90186			0.316074			0.158037	+	0.987433i	$0.449483\pi$
$6$	−17.0139	+	22.4492i	−0.472608	+	0.623590i
$7$	−68.9363			−1.40686			−0.703432	−	0.710763i	$-0.748350\pi$
$7$	−68.9363			−1.40686			−0.703432	+	0.710763i	$0.748350\pi$
$8$	59.5575	+	23.4286i	0.930586	+	0.366072i
$9$	−31.4099			−0.387777
$10$	−19.0913	+	25.1903i	−0.190913	+	0.251903i
$11$	160.230			1.32421			0.662107	−	0.749409i	$-0.269662\pi$
$11$	160.230			1.32421			0.662107	+	0.749409i	$0.269662\pi$
$12$	−30.4594	−	108.477i	−0.211524	−	0.753313i
$13$		−	55.6139i		−	0.329077i	−0.986371	−	0.164538i	$-0.947387\pi$
$13$		−	55.6139i		−	0.329077i	0.986371	−	0.164538i	$-0.0526134\pi$
$14$	166.554	−	219.762i	0.849764	−	1.12123i
$15$	55.6451			0.247311
$16$	−218.582	+	133.259i	−0.853837	+	0.520541i
$17$		−	159.426i		−	0.551649i	−0.961208	−	0.275824i	$-0.911049\pi$
$17$		−	159.426i		−	0.551649i	0.961208	−	0.275824i	$-0.0889508\pi$
$18$	75.8880	−	100.132i	0.234222	−	0.309048i
$19$	−157.094			−0.435163			−0.217582	−	0.976042i	$-0.569817\pi$
$19$	−157.094			−0.435163			−0.217582	+	0.976042i	$0.569817\pi$
$20$	−34.1785	−	121.722i	−0.0854464	−	0.304306i
$21$	−485.451			−1.10080
$22$	−387.124	+	510.796i	−0.799843	+	1.05536i
$23$		−	950.893i		−	1.79753i	−0.438432	−	0.898765i	$-0.644466\pi$
$23$		−	950.893i		−	1.79753i	0.438432	−	0.898765i	$-0.355534\pi$
$24$	419.406	+	164.985i	0.728135	+	0.286432i
$25$	−562.561			−0.900097
$26$	177.292	+	134.366i	0.262266	+	0.198767i
$27$	−791.593			−1.08586
$28$	298.176	+	1061.91i	0.380326	+	1.35448i
$29$		−	707.975i		−	0.841825i	−0.907101	−	0.420913i	$-0.861710\pi$
$29$		−	707.975i		−	0.841825i	0.907101	−	0.420913i	$-0.138290\pi$
$30$	−134.441	+	177.391i	−0.149379	+	0.197101i
$31$		−	896.050i		−	0.932414i	−0.884676	−	0.466207i	$-0.845620\pi$
$31$		−	896.050i		−	0.932414i	0.884676	−	0.466207i	$-0.154380\pi$
$32$	103.291	−	1018.78i	0.100871	−	0.994900i
$33$	1128.34			1.03613
$34$	508.235	+	385.183i	0.439650	+	0.333203i
$35$	−544.725			−0.444673
$36$	135.860	+	483.846i	0.104830	+	0.373338i
$37$	1343.53			0.981394			0.490697	−	0.871330i	$-0.336742\pi$
$37$	1343.53			0.981394			0.490697	+	0.871330i	$0.336742\pi$
$38$	379.547	−	500.799i	0.262844	−	0.346814i
$39$		−	391.635i		−	0.257485i
$40$	470.615	+	185.130i	0.294135	+	0.115706i
$41$	−1675.01	+	141.828i	−0.996434	+	0.0843711i
$41$	−1675.01	+	141.828i	−0.996434	+	0.0843711i
$42$	1172.88	−	1547.57i	0.664895	−	0.877306i
$43$		−	2248.24i		−	1.21592i	−0.793966	−	0.607962i	$-0.791987\pi$
$43$		−	2248.24i		−	1.21592i	0.793966	−	0.607962i	$-0.208013\pi$
$44$	−693.055	−	2468.22i	−0.357983	−	1.27491i
$45$	−248.197			−0.122566
$46$	3031.35	+	2297.41i	1.43258	+	1.08573i
$47$	3827.56			1.73271			0.866357	−	0.499426i	$-0.166456\pi$
$47$	3827.56			1.73271			0.866357	+	0.499426i	$0.166456\pi$
$48$	−1539.26	+	938.410i	−0.668082	+	0.407296i
$49$	2351.21			0.979264
$50$	1359.18	−	1793.39i	0.543670	−	0.717354i
$51$		−	1122.68i		−	0.431636i
$52$	−856.691	+	240.551i	−0.316824	+	0.0889613i
$53$			4995.85i			1.77852i	0.457405	+	0.889258i	$0.348779\pi$
$53$			4995.85i			1.77852i	−0.457405	+	0.889258i	$0.651221\pi$
$54$	1912.53	−	2523.52i	0.655875	−	0.865404i
$55$	1266.11			0.418550
$56$	−4105.68	−	1615.08i	−1.30921	−	0.515014i
$57$	−1106.26			−0.340492
$58$	2256.95	+	1710.50i	0.670913	+	0.508474i
$59$		−	6423.39i		−	1.84527i	−0.385673	−	0.922636i	$-0.626031\pi$
$59$		−	6423.39i		−	1.84527i	0.385673	−	0.922636i	$-0.373969\pi$
$60$	−240.686	−	857.171i	−0.0668572	−	0.238103i
$61$	−3861.65			−1.03780			−0.518900	−	0.854835i	$-0.673658\pi$
$61$	−3861.65			−1.03780			−0.518900	+	0.854835i	$0.673658\pi$
$62$	2856.51	+	2164.90i	0.743110	+	0.563190i
$63$	2165.28			0.545549
$64$	2998.20	+	2790.70i	0.731982	+	0.681324i
$65$		−	439.453i		−	0.104013i
$66$	−2726.14	+	3597.04i	−0.625834	+	0.825767i
$67$	−7476.87			−1.66560			−0.832799	−	0.553576i	$-0.813263\pi$
$67$	−7476.87			−1.66560			−0.832799	+	0.553576i	$0.813263\pi$
$68$	−2455.85	+	689.580i	−0.531109	+	0.149131i
$69$		−	6696.21i		−	1.40647i
$70$	1316.08	−	1736.53i	0.268589	−	0.354393i
$71$	4425.53			0.877907			0.438954	−	0.898510i	$-0.355349\pi$
$71$	4425.53			0.877907			0.438954	+	0.898510i	$0.355349\pi$
$72$	−1870.70	−	735.891i	−0.360860	−	0.141954i
$73$	−1607.74			−0.301696			−0.150848	−	0.988557i	$-0.548200\pi$
$73$	−1607.74			−0.301696			−0.150848	+	0.988557i	$0.548200\pi$
$74$	−3246.03	+	4283.03i	−0.592775	+	0.782145i
$75$	−3961.56			−0.704278
$76$	679.491	+	2419.91i	0.117640	+	0.418960i
$77$	−11045.7			−1.86299
$78$	1248.49	+	946.210i	0.205209	+	0.155524i
$79$	3753.15			0.601370			0.300685	−	0.953723i	$-0.402785\pi$
$79$	3753.15			0.601370			0.300685	+	0.953723i	$0.402785\pi$
$80$	−1727.21	+	1052.99i	−0.269876	+	0.164530i
$81$	−3030.21			−0.461853
$82$	3594.77	−	5682.41i	0.534618	−	0.845094i
$83$			833.596i			0.121004i	0.998168	+	0.0605020i	$0.0192701\pi$
$83$			833.596i			0.121004i	−0.998168	+	0.0605020i	$0.980730\pi$
$84$	2099.76	+	7478.01i	0.297585	+	1.05981i
$85$		−	1259.77i		−	0.174362i
$86$	7167.17	+	5431.87i	0.969060	+	0.734434i
$87$		−	4985.58i		−	0.658684i
$88$	9542.90	+	3753.97i	1.23230	+	0.484758i
$89$			5632.85i			0.711128i	0.934652	+	0.355564i	$0.115711\pi$
$89$			5632.85i			0.711128i	−0.934652	+	0.355564i	$0.884289\pi$
$90$	599.656	−	791.226i	0.0740316	−	0.0976822i
$91$			3833.82i			0.462966i
$92$	−14647.8	+	4112.97i	−1.73060	+	0.485937i
$93$		−	6310.00i		−	0.729564i
$94$	−9247.60	+	12201.9i	−1.04658	+	1.38093i
$95$	−1241.33			−0.137544
$96$	727.381	−	7174.25i	0.0789259	−	0.778456i
$97$			1804.41i			0.191775i	0.995392	+	0.0958877i	$0.0305690\pi$
$97$			1804.41i			0.191775i	−0.995392	+	0.0958877i	$0.969431\pi$
$98$	−5680.65	+	7495.43i	−0.591488	+	0.780448i
$99$	−5032.81			−0.513499
$100$	2433.29	+	8665.83i	0.243329	+	0.866583i
$101$			14913.3i			1.46194i	0.682409	+	0.730970i	$0.260932\pi$
$101$			14913.3i			1.46194i	−0.682409	+	0.730970i	$0.739068\pi$
$102$	3579.00	+	2712.47i	0.344003	+	0.260714i
$103$			9906.08i			0.933743i	0.884325	+	0.466871i	$0.154619\pi$
$103$			9906.08i			0.933743i	−0.884325	+	0.466871i	$0.845381\pi$
$104$	1302.96	−	3312.23i	0.120466	−	0.306234i
$105$	−3835.97			−0.347933
$106$	−15926.3	−	12070.2i	−1.41743	−	1.07425i
$107$			11577.1i			1.01118i	0.862772	+	0.505592i	$0.168726\pi$
$107$			11577.1i			1.01118i	−0.862772	+	0.505592i	$0.831274\pi$
$108$	3423.94	+	12193.9i	0.293548	+	1.04543i
$109$		−	8264.68i		−	0.695622i	−0.937565	−	0.347811i	$-0.886925\pi$
$109$		−	8264.68i		−	0.695622i	0.937565	−	0.347811i	$-0.113075\pi$
$110$	−3059.00	+	4036.24i	−0.252810	+	0.333574i
$111$	9461.15			0.767888
$112$	15068.2	−	9186.35i	1.20123	−	0.732330i
$113$	−7682.65			−0.601664			−0.300832	−	0.953677i	$-0.597264\pi$
$113$	−7682.65			−0.601664			−0.300832	+	0.953677i	$0.597264\pi$
$114$	2672.78	−	3526.64i	0.205662	−	0.271364i
$115$		−	7513.82i		−	0.568153i
$116$	−10905.8	+	3062.26i	−0.810481	+	0.227576i
$117$			1746.83i			0.127608i
$118$	20477.1	+	15519.2i	1.47063	+	1.11457i
$119$			10990.3i			0.776094i
$120$	3314.08	+	1303.69i	0.230145	+	0.0905338i
$121$	11032.6			0.753543
$122$	9329.95	−	12310.5i	0.626844	−	0.827099i
$123$	−11795.4	+	998.755i	−0.779657	+	0.0660159i
$124$	−13803.0	+	3875.76i	−0.897696	+	0.252065i
$125$	−9383.94			−0.600572
$126$	−5231.44	+	6902.70i	−0.329519	+	0.434788i
$127$		−	28974.4i		−	1.79641i	−0.439572	−	0.898207i	$-0.644870\pi$
$127$		−	28974.4i		−	1.79641i	0.439572	−	0.898207i	$-0.355130\pi$
$128$	−16140.3	+	2815.47i	−0.985124	+	0.171843i
$129$		−	15832.2i		−	0.951396i
$130$	1400.93	+	1061.74i	0.0828954	+	0.0628250i
$131$			13897.5i			0.809830i	0.914354	+	0.404915i	$0.132699\pi$
$131$			13897.5i			0.809830i	−0.914354	+	0.404915i	$0.867301\pi$
$132$	−4880.51	−	17381.3i	−0.280103	−	0.997548i
$133$	10829.5			0.612215
$134$	18064.5	−	23835.5i	1.00604	−	1.32744i
$135$	−6255.06			−0.343213
$136$	3735.14	−	9495.05i	0.201943	−	0.513357i
$137$		−	25185.5i		−	1.34187i	−0.741517	−	0.670934i	$-0.765893\pi$
$137$		−	25185.5i		−	1.34187i	0.741517	−	0.670934i	$-0.234107\pi$
$138$	21346.8	+	16178.4i	1.12092	+	0.849527i
$139$		−	19397.0i		−	1.00393i	−0.864887	−	0.501967i	$-0.832610\pi$
$139$		−	19397.0i		−	1.00393i	0.864887	−	0.501967i	$-0.167390\pi$
$140$	2356.14	+	8391.08i	0.120211	+	0.428116i
$141$	26953.8			1.35576
$142$	−10692.3	+	14108.1i	−0.530268	+	0.699670i
$143$		−	8911.02i		−	0.435768i
$144$	6865.65	−	4185.64i	0.331098	−	0.201854i
$145$		−	5594.32i		−	0.266079i
$146$	3884.38	−	5125.31i	0.182228	−	0.240444i
$147$	16557.3			0.766222
$148$	−5811.27	−	20696.0i	−0.265306	−	0.944852i
$149$		−	21750.9i		−	0.979727i	−0.871799	−	0.489864i	$-0.837047\pi$
$149$		−	21750.9i		−	0.979727i	0.871799	−	0.489864i	$-0.162953\pi$
$150$	9571.35	−	12629.1i	0.425393	−	0.561292i
$151$	−9221.07			−0.404415			−0.202208	−	0.979343i	$-0.564812\pi$
$151$	−9221.07			−0.404415			−0.202208	+	0.979343i	$0.564812\pi$
$152$	−9356.13	−	3680.49i	−0.404957	−	0.159301i
$153$			5007.57i			0.213917i
$154$	26686.9	−	35212.4i	1.12527	−	1.48475i
$155$		−	7080.46i		−	0.294712i
$156$	−6032.84	+	1693.97i	−0.247898	+	0.0696075i
$157$			27283.8i			1.10689i	0.832885	+	0.553445i	$0.186687\pi$
$157$			27283.8i			1.10689i	−0.832885	+	0.553445i	$0.813313\pi$
$158$	−9067.81	+	11964.7i	−0.363236	+	0.479277i
$159$			35180.9i			1.39160i
$160$	816.195	−	8050.23i	0.0318826	−	0.314462i
$161$			65551.0i			2.52888i
$162$	7321.16	−	9660.01i	0.278965	−	0.368085i
$163$			12993.5i			0.489046i	0.969643	+	0.244523i	$0.0786314\pi$
$163$			12993.5i			0.489046i	−0.969643	+	0.244523i	$0.921369\pi$
$164$	9429.79	+	25188.8i	0.350602	+	0.936525i
$165$	8916.00			0.327493
$166$	−2657.42	−	2014.01i	−0.0964370	−	0.0730879i
$167$	−16454.3			−0.589993			−0.294997	−	0.955498i	$-0.595319\pi$
$167$	−16454.3			−0.589993			−0.294997	+	0.955498i	$0.595319\pi$
$168$	−28912.3	−	11373.4i	−1.02439	−	0.402971i
$169$	25468.1			0.891709
$170$	4016.00	+	3043.66i	0.138962	+	0.105317i
$171$	4934.31			0.168746
$172$	−34632.5	+	9724.51i	−1.17065	+	0.328708i
$173$	−10541.3			−0.352211			−0.176106	−	0.984371i	$-0.556350\pi$
$173$	−10541.3			−0.352211			−0.176106	+	0.984371i	$0.556350\pi$
$174$	15893.5	+	12045.4i	0.524954	+	0.397854i
$175$	38780.8			1.26631
$176$	−35023.4	+	21352.0i	−1.13066	+	0.689308i
$177$		−	45233.7i		−	1.44383i
$178$	−17956.9	−	13609.3i	−0.566751	−	0.429531i
$179$	−7860.89			−0.245338			−0.122669	−	0.992448i	$-0.539145\pi$
$179$	−7860.89			−0.245338			−0.122669	+	0.992448i	$0.539145\pi$
$180$	1073.55	+	3823.28i	0.0331341	+	0.118003i
$181$			27046.1i			0.825558i	0.910831	+	0.412779i	$0.135442\pi$
$181$			27046.1i			0.825558i	−0.910831	+	0.412779i	$0.864558\pi$
$182$	−12221.8	−	9262.71i	−0.368972	−	0.279637i
$183$	−27193.8			−0.812023
$184$	22278.1	−	56632.8i	0.658025	−	1.67276i
$185$	10616.4			0.310193
$186$	20115.6	+	15245.3i	0.581444	+	0.440666i
$187$		−	25544.9i		−	0.730501i
$188$	−16555.7	−	58960.8i	−0.468415	−	1.66820i
$189$	54569.5			1.52766
$190$	2999.13	−	3957.25i	0.0830783	−	0.109619i
$191$	19065.5			0.522614			0.261307	−	0.965256i	$-0.415846\pi$
$191$	19065.5			0.522614			0.261307	+	0.965256i	$0.415846\pi$
$192$	21113.4	+	19652.2i	0.572737	+	0.533100i
$193$			15408.7i			0.413668i	0.978376	+	0.206834i	$0.0663159\pi$
$193$			15408.7i			0.413668i	−0.978376	+	0.206834i	$0.933684\pi$
$194$	−5752.29	−	4359.56i	−0.152840	−	0.115835i
$195$		−	3094.64i		−	0.0813844i
$196$	−10169.9	−	36218.7i	−0.264731	−	0.942802i
$197$	−5016.71			−0.129267			−0.0646333	−	0.997909i	$-0.520588\pi$
$197$	−5016.71			−0.129267			−0.0646333	+	0.997909i	$0.520588\pi$
$198$	12159.5	−	16044.1i	0.310160	−	0.409246i
$199$	22545.5			0.569316			0.284658	−	0.958629i	$-0.408120\pi$
$199$	22545.5			0.569316			0.284658	+	0.958629i	$0.408120\pi$
$200$	−33504.7	−	13180.0i	−0.837618	−	0.329500i
$201$	−52652.3			−1.30324
$202$	−47541.9	−	36031.2i	−1.16513	−	0.883031i
$203$			48805.2i			1.18433i
$204$	−17294.1	+	4856.04i	−0.415564	+	0.116687i
$205$	−13235.7	+	1120.70i	−0.314947	+	0.0266675i
$206$	−31579.6	−	23933.6i	−0.744169	−	0.563993i
$207$			29867.5i			0.697040i
$208$	7411.03	+	12156.2i	0.171298	+	0.280978i
$209$	−25171.1			−0.576249
$210$	9267.89	−	12228.7i	0.210156	−	0.277294i
$211$	10947.7			0.245900			0.122950	−	0.992413i	$-0.460764\pi$
$211$	10947.7			0.245900			0.122950	+	0.992413i	$0.460764\pi$
$212$	76957.4	−	21609.0i	1.71230	−	0.480798i
$213$	31164.7			0.686916
$214$	−36906.5	−	27970.8i	−0.805888	−	0.610769i
$215$		−	17765.3i		−	0.384322i
$216$	−47145.3	−	18545.9i	−1.01049	−	0.397504i
$217$			61770.3i			1.31178i
$218$	26347.0	+	19967.9i	0.554393	+	0.420165i
$219$	−11321.7			−0.236061
$220$	−5476.42	−	19503.5i	−0.113149	−	0.402966i
$221$	−8866.33			−0.181535
$222$	−22858.6	+	30161.2i	−0.463815	+	0.611987i
$223$			42305.1i			0.850713i	0.905026	+	0.425357i	$0.139851\pi$
$223$			42305.1i			0.850713i	−0.905026	+	0.425357i	$0.860149\pi$
$224$	−7120.53	+	70230.7i	−0.141911	+	1.39969i
$225$	17670.0			0.349037
$226$	18561.7	−	24491.5i	0.363413	−	0.479511i
$227$	−17332.6			−0.336366			−0.168183	−	0.985756i	$-0.553790\pi$
$227$	−17332.6			−0.336366			−0.168183	+	0.985756i	$0.553790\pi$
$228$	4784.99	+	17041.1i	0.0920474	+	0.327814i
$229$			7392.56i			0.140969i	0.997513	+	0.0704845i	$0.0224545\pi$
$229$			7392.56i			0.140969i	−0.997513	+	0.0704845i	$0.977545\pi$
$230$	23953.3	+	18153.8i	0.452803	+	0.343172i
$231$	−77783.8			−1.45769
$232$	16586.9	−	42165.2i	0.308169	−	0.783391i
$233$		−	63734.7i		−	1.17399i	−0.809591	−	0.586995i	$-0.800311\pi$
$233$		−	63734.7i		−	1.17399i	0.809591	−	0.586995i	$-0.199689\pi$
$234$	−5568.71	−	4220.43i	−0.101700	−	0.0770770i
$235$	30244.9			0.547666
$236$	−98947.5	+	27783.6i	−1.77656	+	0.498844i
$237$	26429.8			0.470540
$238$	−35035.9	−	26553.1i	−0.618527	−	0.468771i
$239$	81928.1			1.43429			0.717145	−	0.696924i	$-0.245449\pi$
$239$	81928.1			1.43429			0.717145	+	0.696924i	$0.245449\pi$
$240$	−12163.0	+	7415.18i	−0.211164	+	0.128736i
$241$	24452.4			0.421006			0.210503	−	0.977593i	$-0.432490\pi$
$241$	24452.4			0.421006			0.210503	+	0.977593i	$0.432490\pi$
$242$	−26655.4	+	35170.9i	−0.455150	+	0.600554i
$243$	42780.2			0.724487
$244$	16703.1	+	59485.9i	0.280555	+	0.999158i
$245$	18579.0			0.309520
$246$	25314.5	−	40015.7i	0.418310	−	0.661241i
$247$			8736.61i			0.143202i
$248$	20993.2	−	53366.5i	0.341331	−	0.867692i
$249$			5870.20i			0.0946791i
$250$	22672.1	−	29915.0i	0.362753	−	0.478640i
$251$			69987.4i			1.11089i	0.831552	+	0.555447i	$0.187453\pi$
$251$			69987.4i			1.11089i	−0.831552	+	0.555447i	$0.812547\pi$
$252$	−9365.67	−	33354.6i	−0.147482	−	0.525236i
$253$		−	152361.i		−	2.38031i
$254$	92367.3	+	70003.6i	1.43170	+	1.08506i
$255$		−	8871.30i		−	0.136429i
$256$	30020.3	−	58255.9i	0.458074	−	0.888914i
$257$		−	83928.1i		−	1.27069i	−0.772226	−	0.635347i	$-0.780857\pi$
$257$		−	83928.1i		−	1.27069i	0.772226	−	0.635347i	$-0.219143\pi$
$258$	50471.4	+	38251.4i	0.758238	+	0.574656i
$259$	−92617.8			−1.38069
$260$	−6769.45	+	1900.80i	−0.100140	+	0.0281184i
$261$			22237.4i			0.326440i
$262$	−44303.8	−	33577.1i	−0.645414	−	0.489148i
$263$	−102336.			−1.47951			−0.739756	−	0.672875i	$-0.765059\pi$
$263$	−102336.			−1.47951			−0.739756	+	0.672875i	$0.765059\pi$
$264$	67201.3	+	26435.5i	0.964206	+	0.379297i
$265$			39476.5i			0.562144i
$266$	−26164.6	+	34523.3i	−0.369786	+	0.487920i
$267$			39666.6i			0.556420i
$268$	32340.3	+	115176.i	0.450272	+	1.60358i
$269$	40115.4			0.554379			0.277190	−	0.960815i	$-0.410597\pi$
$269$	40115.4			0.554379			0.277190	+	0.960815i	$0.410597\pi$
$270$	15112.5	−	19940.5i	0.207305	−	0.273532i
$271$		−	7340.29i		−	0.0999481i	−0.998751	−	0.0499740i	$-0.984086\pi$
$271$		−	7340.29i		−	0.0999481i	0.998751	−	0.0499740i	$-0.0159139\pi$
$272$	21244.9	+	34847.8i	0.287156	+	0.471018i
$273$			26997.8i			0.362246i
$274$	80288.8	+	60849.5i	1.06943	+	0.810506i
$275$	−90139.0			−1.19192
$276$	−103150.	+	28963.7i	−1.35410	+	0.380220i
$277$	−12251.3			−0.159670			−0.0798351	−	0.996808i	$-0.525439\pi$
$277$	−12251.3			−0.159670			−0.0798351	+	0.996808i	$0.525439\pi$
$278$	61835.6	+	46864.2i	0.800109	+	0.606389i
$279$			28144.8i			0.361568i
$280$	−32442.5	−	12762.2i	−0.413807	−	0.162783i
$281$			72057.5i			0.912570i	0.889834	+	0.456285i	$0.150820\pi$
$281$			72057.5i			0.912570i	−0.889834	+	0.456285i	$0.849180\pi$
$282$	−65121.8	+	85925.9i	−0.818895	+	1.08050i
$283$		−	63657.0i		−	0.794828i	−0.917639	−	0.397414i	$-0.869908\pi$
$283$		−	63657.0i		−	0.794828i	0.917639	−	0.397414i	$-0.130092\pi$
$284$	−19142.1	−	68172.0i	−0.237330	−	0.845219i
$285$	−8741.50			−0.107621
$286$	28407.4	+	21529.5i	0.347296	+	0.263209i
$287$	115469.	−	9777.09i	1.40185	−	0.118699i
$288$	−3244.38	+	31999.7i	−0.0391153	+	0.385799i
$289$	58104.2			0.695684
$290$	17834.1	+	13516.2i	0.212058	+	0.160715i
$291$			12706.7i			0.150054i
$292$	6954.08	+	24766.0i	0.0815594	+	0.290463i
$293$		−	109627.i		−	1.27698i	−0.769630	−	0.638490i	$-0.779559\pi$
$293$		−	109627.i		−	1.27698i	0.769630	−	0.638490i	$-0.220441\pi$
$294$	−40003.3	+	52783.0i	−0.462808	+	0.610659i
$295$		−	50756.7i		−	0.583243i
$296$	80017.2	+	31477.0i	0.913272	+	0.359261i
$297$	−126837.			−1.43791
$298$	69339.7	+	52551.4i	0.780818	+	0.591768i
$299$	−52882.9			−0.591525
$300$	17135.3	+	61025.0i	0.190392	+	0.678055i
$301$			154986.i			1.71064i
$302$	22278.6	−	29395.8i	0.244272	−	0.322308i
$303$			105019.i			1.14389i
$304$	34337.9	−	20934.1i	0.371558	−	0.226520i
$305$	−30514.2			−0.328022
$306$	−15963.6	−	12098.6i	−0.170486	−	0.129208i
$307$		−	55004.8i		−	0.583612i	−0.956478	−	0.291806i	$-0.905744\pi$
$307$		−	55004.8i		−	0.583612i	0.956478	−	0.291806i	$-0.0942561\pi$
$308$	47776.7	+	170150.i	0.503633	+	1.79362i
$309$			69758.8i			0.730604i
$310$	22571.8	+	17106.8i	0.234878	+	0.178010i
$311$	168041.			1.73738			0.868690	−	0.495356i	$-0.164962\pi$
$311$	168041.			1.73738			0.868690	+	0.495356i	$0.164962\pi$
$312$	9175.46	−	23324.8i	0.0942581	−	0.239612i
$313$		−	179258.i		−	1.82974i	−0.403747	−	0.914870i	$-0.632293\pi$
$313$		−	179258.i		−	1.82974i	0.403747	−	0.914870i	$-0.367707\pi$
$314$	−86977.8	−	65919.0i	−0.882164	−	0.668577i
$315$	17109.8			0.172434
$316$	−16233.8	−	57814.5i	−0.162572	−	0.578979i
$317$			149625.i			1.48897i	0.667639	+	0.744485i	$0.267305\pi$
$317$			149625.i			1.48897i	−0.667639	+	0.744485i	$0.732695\pi$
$318$	−112153.	−	84998.9i	−1.10907	−	0.840542i
$319$		−	113439.i		−	1.11476i
$320$	23691.3	+	22051.7i	0.231361	+	0.215349i
$321$			81525.9i			0.791199i
$322$	−208970.	−	158375.i	−2.01545	−	1.52748i
$323$			25044.9i			0.240057i
$324$	13106.8	+	46678.2i	0.124856	+	0.444656i
$325$			31286.2i			0.296201i
$326$	−41421.9	−	31392.9i	−0.389757	−	0.295390i
$327$		−	58200.1i		−	0.544287i
$328$	−103082.	−	30796.2i	−0.958154	−	0.286252i
$329$	−263858.			−2.43769
$330$	−21541.5	+	28423.3i	−0.197810	+	0.261004i
$331$	106563.			0.972634			0.486317	−	0.873782i	$-0.338340\pi$
$331$	106563.			0.972634			0.486317	+	0.873782i	$0.338340\pi$
$332$	12840.9	−	3605.62i	0.116498	−	0.0327117i
$333$	−42200.1			−0.380562
$334$	39754.5	−	52454.7i	0.356364	−	0.470209i
$335$	−59081.2			−0.526453
$336$	106111.	−	64690.5i	0.939900	−	0.573010i
$337$	−38652.9			−0.340347			−0.170173	−	0.985414i	$-0.554433\pi$
$337$	−38652.9			−0.340347			−0.170173	+	0.985414i	$0.554433\pi$
$338$	−61532.2	+	81189.7i	−0.538604	+	0.710669i
$339$	−54101.4			−0.470770
$340$	−19405.7	+	5448.97i	−0.167870	+	0.0471364i
$341$		−	143574.i		−	1.23472i
$342$	−11921.5	+	15730.1i	−0.101925	+	0.134486i
$343$	3432.13			0.0291726
$344$	52673.2	−	133900.i	0.445116	−	1.13152i
$345$		−	52912.5i		−	0.444549i
$346$	25468.4	−	33604.7i	0.212740	−	0.280703i
$347$	−12588.0			−0.104544			−0.0522718	−	0.998633i	$-0.516646\pi$
$347$	−12588.0			−0.104544			−0.0522718	+	0.998633i	$0.516646\pi$
$348$	−76799.1	+	21564.5i	−0.634158	+	0.178066i
$349$	227009.			1.86377			0.931883	−	0.362759i	$-0.118165\pi$
$349$	227009.			1.86377			0.931883	+	0.362759i	$0.118165\pi$
$350$	−93696.6	+	123629.i	−0.764870	+	1.00922i
$351$			44023.6i			0.357332i
$352$	16550.4	−	163239.i	0.133574	−	1.31746i
$353$	−144435.			−1.15911			−0.579553	−	0.814935i	$-0.696773\pi$
$353$	−144435.			−1.15911			−0.579553	+	0.814935i	$0.696773\pi$
$354$	144200.	+	109287.i	1.15069	+	0.872090i
$355$	34969.9			0.277484
$356$	86769.8	−	24364.2i	0.684650	−	0.192244i
$357$			77393.7i			0.607253i
$358$	18992.3	−	25059.7i	0.148188	−	0.195528i
$359$		−	135558.i		−	1.05181i	−0.850544	−	0.525903i	$-0.823727\pi$
$359$		−	135558.i		−	1.05181i	0.850544	−	0.525903i	$-0.176273\pi$
$360$	−14782.0	−	5814.91i	−0.114058	−	0.0448681i
$361$	−105642.			−0.810633
$362$	−86220.2	−	65344.8i	−0.657949	−	0.498648i
$363$	77692.0			0.589607
$364$	59057.1	−	16582.7i	0.445728	−	0.125156i
$365$	−12704.1			−0.0953584
$366$	65701.7	−	86691.1i	0.490472	−	0.647161i
$367$		−	12293.8i		−	0.0912758i	−0.998958	−	0.0456379i	$-0.985468\pi$
$367$		−	12293.8i		−	0.0912758i	0.998958	−	0.0456379i	$-0.0145320\pi$
$368$	126715.	+	207848.i	0.935688	+	1.53480i
$369$	52611.8	−	4454.80i	0.386394	−	0.0327172i
$370$	−25649.7	+	33843.9i	−0.187361	+	0.247216i
$371$		−	344396.i		−	2.50213i
$372$	−97200.9	+	27293.2i	−0.702400	+	0.197228i
$373$	−25572.9			−0.183807			−0.0919037	−	0.995768i	$-0.529295\pi$
$373$	−25572.9			−0.183807			−0.0919037	+	0.995768i	$0.529295\pi$
$374$	81434.5	+	61717.8i	0.582191	+	0.441232i
$375$	−66081.9			−0.469916
$376$	227960.	+	89674.5i	1.61244	+	0.634298i
$377$	−39373.3			−0.277025
$378$	−131843.	+	173962.i	−0.922726	+	1.21750i
$379$			43511.2i			0.302916i	0.988464	+	0.151458i	$0.0483968\pi$
$379$			43511.2i			0.302916i	−0.988464	+	0.151458i	$0.951603\pi$
$380$	5369.24	+	19121.8i	0.0371831	+	0.132423i
$381$		−	204038.i		−	1.40560i
$382$	−46063.2	+	60778.8i	−0.315666	+	0.416510i
$383$	−104978.			−0.715648			−0.357824	−	0.933789i	$-0.616481\pi$
$383$	−104978.			−0.715648			−0.357824	+	0.933789i	$0.616481\pi$
$384$	−113660.	+	19826.6i	−0.770808	+	0.134458i
$385$	−87281.2			−0.588843
$386$	−49121.4	−	37228.2i	−0.329683	−	0.249861i
$387$			70617.1i			0.471507i
$388$	27795.7	−	7804.78i	0.184635	−	0.0518438i
$389$	103329.			0.682849			0.341425	−	0.939909i	$-0.389091\pi$
$389$	103329.			0.682849			0.341425	+	0.939909i	$0.389091\pi$
$390$	9865.40	+	7476.82i	0.0648613	+	0.0491572i
$391$	−151598.			−0.991605
$392$	140032.	+	55085.7i	0.911290	+	0.358481i
$393$			97866.5i			0.633649i
$394$	12120.6	−	15992.8i	0.0780787	−	0.103022i
$395$	29656.9			0.190078
$396$	21768.8	+	77526.6i	0.138817	+	0.494380i
$397$		−	169764.i		−	1.07712i	−0.842587	−	0.538560i	$-0.818969\pi$
$397$		−	169764.i		−	1.07712i	0.842587	−	0.538560i	$-0.181031\pi$
$398$	−54471.1	+	71872.7i	−0.343875	+	0.453731i
$399$	76261.4			0.479026
$400$	122966.	−	74966.0i	0.768536	−	0.468538i
$401$	149492.			0.929669			0.464835	−	0.885398i	$-0.346114\pi$
$401$	149492.			0.929669			0.464835	+	0.885398i	$0.346114\pi$
$402$	127211.	−	167850.i	0.787175	−	1.03865i
$403$	−49832.9			−0.306836
$404$	229728.	−	64505.5i	1.40751	−	0.395216i
$405$	−23944.3			−0.145980
$406$	−155586.	−	117916.i	−0.943883	−	0.715353i
$407$	215273.			1.29958
$408$	26303.0	−	66864.3i	0.158010	−	0.401675i
$409$	95203.1			0.569121			0.284560	−	0.958658i	$-0.408152\pi$
$409$	95203.1			0.569121			0.284560	+	0.958658i	$0.408152\pi$
$410$	28405.4	−	44901.6i	0.168979	−	0.267113i
$411$		−	177357.i		−	1.04994i
$412$	152596.	−	42847.6i	0.898976	−	0.252425i
$413$			442805.i			2.59604i
$414$	−95214.4	−	72161.4i	−0.555523	−	0.421021i
$415$			6586.96i			0.0382462i
$416$	−56658.2	−	5744.45i	−0.327398	−	0.0331941i
$417$		−	136594.i		−	0.785524i
$418$	60814.8	−	80243.0i	0.348062	−	0.459256i
$419$		−	143344.i		−	0.816491i	−0.912872	−	0.408245i	$-0.866141\pi$
$419$		−	143344.i		−	0.816491i	0.912872	−	0.408245i	$-0.133859\pi$
$420$	16592.0	+	59090.2i	0.0940590	+	0.334978i
$421$		−	93779.9i		−	0.529110i	−0.964371	−	0.264555i	$-0.914775\pi$
$421$		−	93779.9i		−	0.529110i	0.964371	−	0.264555i	$-0.0852250\pi$
$422$	−26450.3	+	34900.3i	−0.148527	+	0.195976i
$423$	−120223.			−0.671906
$424$	−117046.	+	297541.i	−0.651066	+	1.65506i
$425$			89687.1i			0.496537i
$426$	−75295.5	+	99349.8i	−0.414906	+	0.547454i
$427$	266208.			1.46004
$428$	178336.	−	50075.2i	0.973534	−	0.273360i
$429$		−	62751.6i		−	0.340965i
$430$	56634.0	+	42921.9i	0.306295	+	0.232136i
$431$		−	178261.i		−	0.959627i	−0.877370	−	0.479814i	$-0.840704\pi$
$431$		−	178261.i		−	0.959627i	0.877370	−	0.479814i	$-0.159296\pi$
$432$	173028.	−	105487.i	0.927148	−	0.565236i
$433$	−157517.			−0.840141			−0.420070	−	0.907492i	$-0.637995\pi$
$433$	−157517.			−0.840141			−0.420070	+	0.907492i	$0.637995\pi$
$434$	−196918.	−	149240.i	−1.04545	−	0.792332i
$435$		−	39395.3i		−	0.208193i
$436$	−127311.	+	35747.9i	−0.669721	+	0.188052i
$437$			149379.i			0.782219i
$438$	27353.9	−	36092.5i	0.142584	−	0.188135i
$439$	191329.			0.992776			0.496388	−	0.868101i	$-0.334659\pi$
$439$	191329.			0.992776			0.496388	+	0.868101i	$0.334659\pi$
$440$	75406.6	+	29663.3i	0.389497	+	0.153220i
$441$	−73851.4			−0.379736
$442$	21421.5	−	28265.0i	0.109649	−	0.144678i
$443$		−	269956.i		−	1.37558i	−0.725910	−	0.687790i	$-0.758581\pi$
$443$		−	269956.i		−	1.37558i	0.725910	−	0.687790i	$-0.241419\pi$
$444$	−40923.1	−	145742.i	−0.207588	−	0.739297i
$445$			44510.0i			0.224769i
$446$	−134864.	−	102211.i	−0.677997	−	0.513842i
$447$		−	153171.i		−	0.766585i
$448$	−206685.	−	192381.i	−1.02980	−	0.958529i
$449$	188124.			0.933148			0.466574	−	0.884482i	$-0.345488\pi$
$449$	188124.			0.933148			0.466574	+	0.884482i	$0.345488\pi$
$450$	−42691.6	+	56330.1i	−0.210823	+	0.278173i
$451$	−268386.	+	22725.1i	−1.31949	+	0.111725i
$452$	33230.4	+	118345.i	0.162652	+	0.579261i
$453$	−64935.0			−0.316433
$454$	41876.5	−	55254.6i	0.203170	−	0.268075i
$455$			30294.3i			0.146332i
$456$	−65886.1	−	25918.1i	−0.316857	−	0.124645i
$457$			284151.i			1.36056i	0.732954	+	0.680278i	$0.238141\pi$
$457$			284151.i			1.36056i	−0.732954	+	0.680278i	$0.761859\pi$
$458$	−23566.7	−	17860.8i	−0.112349	−	0.0851471i
$459$			126201.i			0.599014i
$460$	−115745.	+	32500.1i	−0.546998	+	0.153592i
$461$	−52071.9			−0.245020			−0.122510	−	0.992467i	$-0.539094\pi$
$461$	−52071.9			−0.245020			−0.122510	+	0.992467i	$0.539094\pi$
$462$	187930.	−	247967.i	0.880464	−	1.16174i
$463$	−152375.			−0.710806			−0.355403	−	0.934713i	$-0.615656\pi$
$463$	−152375.			−0.710806			−0.355403	+	0.934713i	$0.615656\pi$
$464$	94343.7	+	154751.i	0.438205	+	0.718781i
$465$		−	49860.7i		−	0.230597i
$466$	203180.	+	153986.i	0.935640	+	0.709105i
$467$			155399.i			0.712549i	0.934381	+	0.356275i	$0.115953\pi$
$467$			155399.i			0.712549i	−0.934381	+	0.356275i	$0.884047\pi$
$468$	26908.6	−	7555.70i	0.122857	−	0.0344971i
$469$	515428.			2.34327
$470$	−73073.2	+	96417.5i	−0.330798	+	0.436476i
$471$			192133.i			0.866084i
$472$	150491.	−	382561.i	0.675502	−	1.71718i
$473$		−	360236.i		−	1.61014i
$474$	−63855.7	+	84255.4i	−0.284213	+	0.375009i
$475$	88374.9			0.391689
$476$	169297.	−	47537.1i	0.747197	−	0.209806i
$477$		−	156919.i		−	0.689667i
$478$	−197942.	+	261178.i	−0.866330	+	1.14309i
$479$	−266626.			−1.16207			−0.581034	−	0.813879i	$-0.697352\pi$
$479$	−266626.			−1.16207			−0.581034	+	0.813879i	$0.697352\pi$
$480$	5747.66	−	56689.9i	0.0249464	−	0.246050i
$481$		−	74718.9i		−	0.322954i
$482$	−59078.4	+	77951.9i	−0.254293	+	0.335531i
$483$			461612.i			1.97871i
$484$	−47720.3	−	169949.i	−0.203710	−	0.725485i
$485$			14258.2i			0.0606153i
$486$	−103359.	+	136379.i	−0.437599	+	0.577397i
$487$			50271.4i			0.211964i	0.994368	+	0.105982i	$0.0337987\pi$
$487$			50271.4i			0.211964i	−0.994368	+	0.105982i	$0.966201\pi$
$488$	−229990.	−	90473.1i	−0.965762	−	0.379909i
$489$			91500.3i			0.382653i
$490$	−44887.7	+	59227.8i	−0.186954	+	0.246680i
$491$			227706.i			0.944520i	0.881459	+	0.472260i	$0.156562\pi$
$491$			227706.i			0.944520i	−0.881459	+	0.472260i	$0.843438\pi$
$492$	66404.8	+	177380.i	0.274328	+	0.732781i
$493$	−112870.			−0.464392
$494$	−27851.4	−	21108.1i	−0.114128	−	0.0864959i
$495$	−39768.5			−0.162304
$496$	119406.	+	195860.i	0.485360	+	0.796129i
$497$	−305080.			−1.23510
$498$	−18713.6	−	14182.7i	−0.0754568	−	0.0571874i
$499$	−300586.			−1.20717			−0.603583	−	0.797300i	$-0.706261\pi$
$499$	−300586.			−1.20717			−0.603583	+	0.797300i	$0.706261\pi$
$500$	40589.1	+	144553.i	0.162356	+	0.578210i
$501$	−115872.			−0.461638
$502$	−223113.	−	169093.i	−0.885353	−	0.670994i
$503$	81191.6			0.320904			0.160452	−	0.987044i	$-0.448705\pi$
$503$	81191.6			0.320904			0.160452	+	0.987044i	$0.448705\pi$
$504$	128959.	+	50729.6i	0.507680	+	0.199710i
$505$			117842.i			0.462082i
$506$	485713.	+	368113.i	1.89705	+	1.43774i
$507$	179347.			0.697715
$508$	−446329.	+	125325.i	−1.72953	+	0.485636i
$509$		−	469537.i		−	1.81232i	−0.422937	−	0.906159i	$-0.639001\pi$
$509$		−	469537.i		−	1.81232i	0.422937	−	0.906159i	$-0.360999\pi$
$510$	28280.8	+	21433.5i	0.108730	+	0.0824049i
$511$	110832.			0.424445
$512$	113183.	+	236451.i	0.431759	+	0.901989i
$513$	124354.			0.472527
$514$	267554.	+	202775.i	1.01271	+	0.767516i
$515$			78276.4i			0.295132i
$516$	−243883.	+	68480.2i	−0.915972	+	0.257197i
$517$	613290.			2.29448
$518$	223770.	−	295256.i	0.833953	−	1.10037i
$519$	−74232.3			−0.275587
$520$	10295.8	−	26172.8i	0.0380761	−	0.0967928i
$521$		−	232513.i		−	0.856589i	−0.903639	−	0.428294i	$-0.859115\pi$
$521$		−	232513.i		−	0.856589i	0.903639	−	0.428294i	$-0.140885\pi$
$522$	−70890.7	−	53726.8i	−0.260164	−	0.197174i
$523$			243189.i			0.889080i	0.895759	+	0.444540i	$0.146633\pi$
$523$			243189.i			0.889080i	−0.895759	+	0.444540i	$0.853367\pi$
$524$	214081.	−	60112.0i	0.779677	−	0.218927i
$525$	273096.			0.990823
$526$	247250.	−	326238.i	0.893645	−	1.17913i
$527$	−142854.			−0.514365
$528$	−246636.	+	150361.i	−0.884683	+	0.539347i
$529$	−624356.			−2.23111
$530$	−125847.	−	95377.4i	−0.448014	−	0.339542i
$531$			201758.i			0.715553i
$532$	−46841.6	−	166820.i	−0.165504	−	0.589420i
$533$	7887.61	+	93153.7i	0.0277646	+	0.327903i
$534$	−126453.	−	95836.7i	−0.443453	−	0.336085i
$535$			91480.3i			0.319610i
$536$	−445304.	−	175173.i	−1.54998	−	0.609729i
$537$	−55356.6			−0.191964
$538$	−96921.0	+	127884.i	−0.334852	+	0.441826i
$539$	376735.			1.29676
$540$	27055.5	+	96354.5i	0.0927829	+	0.330434i
$541$	409172.			1.39801			0.699007	−	0.715115i	$-0.253626\pi$
$541$	409172.			1.39801			0.699007	+	0.715115i	$0.253626\pi$
$542$	23400.1	+	17734.5i	0.0796560	+	0.0603699i
$543$			190459.i			0.645955i
$544$	−162420.	−	16467.4i	−0.548835	−	0.0556451i
$545$		−	65306.4i		−	0.219868i
$546$	−86066.4	−	65228.2i	−0.288701	−	0.218801i
$547$	−135545.			−0.453011			−0.226505	−	0.974010i	$-0.572730\pi$
$547$	−135545.			−0.453011			−0.226505	+	0.974010i	$0.572730\pi$
$548$	−387964.	+	108937.i	−1.29190	+	0.362755i
$549$	121294.			0.402434
$550$	217781.	−	287354.i	0.719936	−	0.949931i
$551$			111219.i			0.366331i
$552$	156883.	−	398810.i	0.514870	−	1.30884i
$553$	−258728.			−0.846046
$554$	29599.9	−	39056.0i	0.0964430	−	0.127253i
$555$	74760.7			0.242710
$556$	−298796.	+	83899.4i	−0.966553	+	0.271400i
$557$			367916.i			1.18587i	0.805249	+	0.592936i	$0.202031\pi$
$557$			367916.i			1.18587i	−0.805249	+	0.592936i	$0.797969\pi$
$558$	−89722.9	−	67999.4i	−0.288161	−	0.218392i
$559$	−125034.			−0.400132
$560$	119067.	−	72589.2i	0.379678	−	0.231471i
$561$		−	179888.i		−	0.571578i
$562$	−229712.	−	174095.i	−0.727295	−	0.551204i
$563$	−265685.			−0.838205			−0.419102	−	0.907939i	$-0.637655\pi$
$563$	−265685.			−0.838205			−0.419102	+	0.907939i	$0.637655\pi$
$564$	−116585.	−	415203.i	−0.366510	−	1.30528i
$565$	−60707.2			−0.190171
$566$	202932.	+	153799.i	0.633458	+	0.480087i
$567$	208892.			0.649763
$568$	263574.	+	103684.i	0.816969	+	0.321377i
$569$	−394347.			−1.21802			−0.609010	−	0.793163i	$-0.708433\pi$
$569$	−394347.			−1.21802			−0.609010	+	0.793163i	$0.708433\pi$
$570$	21119.9	−	27867.0i	0.0650044	−	0.0857710i
$571$	64892.1			0.199031			0.0995153	−	0.995036i	$-0.468271\pi$
$571$	64892.1			0.199031			0.0995153	+	0.995036i	$0.468271\pi$
$572$	−137268.	+	38543.5i	−0.419542	+	0.117804i
$573$	134260.			0.408918
$574$	−247810.	+	391724.i	−0.752134	+	1.18893i
$575$			534935.i			1.61795i
$576$	−94173.2	−	87655.7i	−0.283846	−	0.264201i
$577$			274309.i			0.823926i	0.911201	+	0.411963i	$0.135157\pi$
$577$			274309.i			0.823926i	−0.911201	+	0.411963i	$0.864843\pi$
$578$	−140383.	+	185230.i	−0.420202	+	0.554442i
$579$			108508.i			0.323673i
$580$	−86176.3	+	24197.6i	−0.256172	+	0.0719309i
$581$		−	57465.0i		−	0.170236i
$582$	−40507.7	−	30700.1i	−0.119589	−	0.0906346i
$583$			800485.i			2.35514i
$584$	−95753.0	−	37667.1i	−0.280754	−	0.110443i
$585$			13803.2i			0.0403337i
$586$	349481.	+	264866.i	1.01772	+	0.771313i
$587$	238929.			0.693415			0.346707	−	0.937973i	$-0.387300\pi$
$587$	238929.			0.693415			0.346707	+	0.937973i	$0.387300\pi$
$588$	−71616.6	−	255053.i	−0.207138	−	0.737693i
$589$			140764.i			0.405752i
$590$	161807.	+	122631.i	0.464830	+	0.352286i
$591$	−35327.8			−0.101144
$592$	−293671.	+	179037.i	−0.837950	+	0.510856i
$593$			636605.i			1.81034i	0.425047	+	0.905172i	$0.360258\pi$
$593$			636605.i			1.81034i	−0.425047	+	0.905172i	$0.639742\pi$
$594$	306445.	−	404343.i	0.868519	−	1.14598i
$595$			86843.6i			0.245303i
$596$	−335057.	+	94081.0i	−0.943248	+	0.264856i
$597$	158766.			0.445460
$598$	127768.	−	168585.i	0.357289	−	0.471430i
$599$		−	14707.9i		−	0.0409917i	−0.999790	−	0.0204959i	$-0.993476\pi$
$599$		−	14707.9i		−	0.0409917i	0.999790	−	0.0204959i	$-0.00652450\pi$
$600$	−235941.	−	92814.0i	−0.655392	−	0.257817i
$601$			154718.i			0.428343i	0.976796	+	0.214172i	$0.0687052\pi$
$601$			154718.i			0.428343i	−0.976796	+	0.214172i	$0.931295\pi$
$602$	−494078.	−	374453.i	−1.36334	−	1.03325i
$603$	234848.			0.645880
$604$	39884.6	+	142044.i	0.109328	+	0.389357i
$605$	87178.2			0.238176
$606$	−334791.	−	253733.i	−0.911652	−	0.690925i
$607$		−	372621.i		−	1.01132i	−0.862732	−	0.505662i	$-0.831248\pi$
$607$		−	372621.i		−	1.01132i	0.862732	−	0.505662i	$-0.168752\pi$
$608$	−16226.5	+	160044.i	−0.0438952	+	0.432944i
$609$			343687.i			0.926678i
$610$	73723.9	−	97276.2i	0.198129	−	0.261425i
$611$		−	212866.i		−	0.570195i
$612$	77137.9	−	21659.7i	0.205952	−	0.0578294i
$613$	−553891.			−1.47402			−0.737010	−	0.675881i	$-0.763763\pi$
$613$	−553891.			−1.47402			−0.737010	+	0.675881i	$0.763763\pi$
$614$	175350.	+	132895.i	0.465124	+	0.352509i
$615$	−93205.8	+	7892.02i	−0.246430	+	0.0208659i
$616$	−657852.	−	258784.i	−1.73367	−	0.681988i
$617$	505823.			1.32870			0.664352	−	0.747420i	$-0.268708\pi$
$617$	505823.			1.32870			0.664352	+	0.747420i	$0.268708\pi$
$618$	−222384.	−	168541.i	−0.582273	−	0.441295i
$619$		−	271382.i		−	0.708271i	−0.935194	−	0.354136i	$-0.884775\pi$
$619$		−	271382.i		−	0.708271i	0.935194	−	0.354136i	$-0.115225\pi$
$620$	−109069.	+	30625.7i	−0.283739	+	0.0796714i
$621$			752720.i			1.95187i
$622$	−405996.	+	535698.i	−1.04940	+	1.38465i
$623$		−	388308.i		−	1.00046i
$624$	52188.7	+	85604.3i	0.134032	+	0.219850i
$625$	277450.			0.710272
$626$	571456.	+	433096.i	1.45826	+	1.10519i
$627$	−177256.			−0.450885
$628$	420286.	−	118013.i	1.06568	−	0.299233i
$629$		−	214194.i		−	0.541384i
$630$	−41338.1	+	54544.2i	−0.104152	+	0.137425i
$631$		−	61994.6i		−	0.155702i	−0.996965	−	0.0778511i	$-0.975194\pi$
$631$		−	61994.6i		−	0.155702i	0.996965	−	0.0778511i	$-0.0248059\pi$
$632$	223528.	+	87931.2i	0.559627	+	0.220145i
$633$	77094.2			0.192404
$634$	−476989.	−	361502.i	−1.18667	−	0.899357i
$635$		−	228951.i		−	0.567801i
$636$	541936.	−	152171.i	1.33978	−	0.376199i
$637$		−	130760.i		−	0.322253i
$638$	361631.	+	274074.i	0.888433	+	0.673328i
$639$	−139006.			−0.340432
$640$	−127538.	+	22247.4i	−0.311373	+	0.0543151i
$641$		−	304584.i		−	0.741295i	−0.928774	−	0.370647i	$-0.879136\pi$
$641$		−	304584.i		−	0.741295i	0.928774	−	0.370647i	$-0.120864\pi$
$642$	−259896.	−	196971.i	−0.630565	−	0.477894i
$643$	508615.			1.23018			0.615088	−	0.788459i	$-0.289121\pi$
$643$	508615.			1.23018			0.615088	+	0.788459i	$0.289121\pi$
$644$	1.00976e6	−	283533.i	2.43472	−	0.683647i
$645$		−	125104.i		−	0.300712i
$646$	−79840.7	−	60509.9i	−0.191319	−	0.144998i
$647$		−	421539.i		−	1.00700i	−0.863996	−	0.503499i	$-0.832046\pi$
$647$		−	421539.i		−	1.00700i	0.863996	−	0.503499i	$-0.167954\pi$
$648$	−180472.	−	70993.8i	−0.429794	−	0.169071i
$649$		−	1.02922e6i		−	2.44353i
$650$	−99737.2	−	75589.1i	−0.236064	−	0.178909i
$651$			434988.i			1.02640i
$652$	200155.	−	56201.7i	0.470837	−	0.132207i
$653$		−	299249.i		−	0.701788i	−0.936415	−	0.350894i	$-0.885878\pi$
$653$		−	299249.i		−	0.701788i	0.936415	−	0.350894i	$-0.114122\pi$
$654$	185536.	+	140615.i	0.433783	+	0.328757i
$655$			109816.i			0.255967i
$656$	347227.	−	254210.i	0.806874	−	0.590724i
$657$	50498.9			0.116991
$658$	637495.	−	841153.i	1.47240	−	1.94278i
$659$	401275.			0.924000			0.462000	−	0.886880i	$-0.347132\pi$
$659$	401275.			0.924000			0.462000	+	0.886880i	$0.347132\pi$
$660$	−38565.1	−	137344.i	−0.0885333	−	0.315299i
$661$	483374.			1.10632			0.553159	−	0.833075i	$-0.313422\pi$
$661$	483374.			1.10632			0.553159	+	0.833075i	$0.313422\pi$
$662$	−257461.	+	339711.i	−0.587484	+	0.775165i
$663$	−62436.9			−0.142041
$664$	−19530.0	+	49646.9i	−0.0442962	+	0.112605i
$665$	85573.0			0.193505
$666$	101958.	−	134530.i	0.229864	−	0.303298i
$667$	−673208.			−1.51321
$668$	71171.2	+	253467.i	0.159497	+	0.568025i
$669$			297914.i			0.665638i
$670$	142743.	−	188345.i	0.317984	−	0.419569i
$671$	−618752.			−1.37427
$672$	−50142.9	+	494566.i	−0.111038	+	1.09518i
$673$		−	181138.i		−	0.399926i	−0.979803	−	0.199963i	$-0.935918\pi$
$673$		−	181138.i		−	0.399926i	0.979803	−	0.199963i	$-0.0640822\pi$
$674$	93387.3	−	123221.i	0.205574	−	0.271248i
$675$	445319.			0.977381
$676$	−110159.	−	392317.i	−0.241061	−	0.858507i
$677$	−49477.9			−0.107953			−0.0539764	−	0.998542i	$-0.517190\pi$
$677$	−49477.9			−0.107953			−0.0539764	+	0.998542i	$0.517190\pi$
$678$	130712.	−	172470.i	0.284351	−	0.375192i
$679$		−	124390.i		−	0.269802i
$680$	29514.6	−	75028.5i	0.0638291	−	0.162259i
$681$	−122057.			−0.263189
$682$	457699.	+	346882.i	0.984037	+	0.745784i
$683$	406868.			0.872192			0.436096	−	0.899900i	$-0.356361\pi$
$683$	406868.			0.872192			0.436096	+	0.899900i	$0.356361\pi$
$684$	−21342.8	−	76009.3i	−0.0456182	−	0.162463i
$685$		−	199012.i		−	0.424130i
$686$	−8292.21	+	10941.3i	−0.0176207	+	0.0232498i
$687$			52058.5i			0.110301i
$688$	299598.	+	491426.i	0.632938	+	1.03820i
$689$	277839.			0.585268
$690$	168680.	+	127839.i	0.354295	+	0.268514i
$691$	−139996.			−0.293197			−0.146598	−	0.989196i	$-0.546833\pi$
$691$	−139996.			−0.293197			−0.146598	+	0.989196i	$0.546833\pi$
$692$	45595.3	+	162381.i	0.0952155	+	0.339097i
$693$	346943.			0.722423
$694$	30413.2	−	40129.2i	0.0631457	−	0.0833185i
$695$		−	153272.i		−	0.317317i
$696$	116805.	−	296929.i	0.241126	−	0.612962i
$697$	22611.1	+	267040.i	0.0465432	+	0.549682i
$698$	−548465.	+	723680.i	−1.12574	+	1.48537i
$699$		−	448821.i		−	0.918585i
$700$	−167742.	−	597390.i	−0.342330	−	1.21916i
$701$	58045.3			0.118122			0.0590610	−	0.998254i	$-0.481189\pi$
$701$	58045.3			0.118122			0.0590610	+	0.998254i	$0.481189\pi$
$702$	−140343.	−	106363.i	−0.284784	−	0.215833i
$703$	−211060.			−0.427066
$704$	480401.	+	447154.i	0.969301	+	0.902218i
$705$	212985.			0.428520
$706$	348962.	−	460444.i	0.700115	−	0.923777i
$707$		−	1.02806e6i		−	2.05675i
$708$	−696791.	+	195653.i	−1.39007	+	0.390319i
$709$		−	76760.9i		−	0.152703i	−0.997081	−	0.0763515i	$-0.975673\pi$
$709$		−	76760.9i		−	0.152703i	0.997081	−	0.0763515i	$-0.0243271\pi$
$710$	−84489.2	+	111481.i	−0.167604	+	0.221148i
$711$	−117886.			−0.233197
$712$	−131970.	+	335478.i	−0.260324	+	0.661766i
$713$	−852047.			−1.67604
$714$	−246723.	−	186987.i	−0.483965	−	0.366789i
$715$		−	70413.6i		−	0.137735i
$716$	34001.3	+	121091.i	0.0663239	+	0.236204i
$717$	576939.			1.12226
$718$	432145.	+	327515.i	0.838263	+	0.635305i
$719$	−714976.			−1.38304			−0.691518	−	0.722359i	$-0.743058\pi$
$719$	−714976.			−1.38304			−0.691518	+	0.722359i	$0.743058\pi$
$720$	54251.4	−	33074.3i	0.104652	−	0.0638008i
$721$		−	682888.i		−	1.31365i
$722$	255238.	−	336777.i	0.489633	−	0.646054i
$723$	172195.			0.329415
$724$	416625.	−	116985.i	0.794819	−	0.223178i
$725$			398279.i			0.757724i
$726$	−187708.	+	247674.i	−0.356131	+	0.469902i
$727$	308427.			0.583557			0.291779	−	0.956486i	$-0.405753\pi$
$727$	308427.			0.583557			0.291779	+	0.956486i	$0.405753\pi$
$728$	−89821.1	+	228333.i	−0.169479	+	0.430830i
$729$	546707.			1.02872
$730$	30693.8	−	40499.5i	0.0575978	−	0.0759982i
$731$	−358430.			−0.670763
$732$	117624.	+	418901.i	0.219519	+	0.781788i
$733$	−594431.			−1.10635			−0.553176	−	0.833064i	$-0.686584\pi$
$733$	−594431.			−1.10635			−0.553176	+	0.833064i	$0.686584\pi$
$734$	39191.5	+	29702.6i	0.0727444	+	0.0551318i
$735$	130833.			0.242183
$736$	−968748.	−	98219.1i	−1.78836	−	0.181318i
$737$	−1.19802e6			−2.20561
$738$	−112911.	+	178484.i	−0.207312	+	0.327708i
$739$			521604.i			0.955107i	0.878603	+	0.477554i	$0.158476\pi$
$739$			521604.i			0.955107i	−0.878603	+	0.477554i	$0.841524\pi$
$740$	−45919.8	−	163537.i	−0.0838565	−	0.298644i
$741$			61523.4i			0.112048i
$742$	1.09790e6	+	832078.i	1.99413	+	1.51132i
$743$		−	1.00240e6i		−	1.81578i	−0.419204	−	0.907892i	$-0.637691\pi$
$743$		−	1.00240e6i		−	1.81578i	0.419204	−	0.907892i	$-0.362309\pi$
$744$	147835.	−	375808.i	0.267073	−	0.678923i
$745$		−	171873.i		−	0.309667i
$746$	61785.6	−	81523.9i	0.111022	−	0.146490i
$747$		−	26183.2i		−	0.0469225i
$748$	−393500.	+	110491.i	−0.703301	+	0.197481i
$749$		−	798079.i		−	1.42260i
$750$	159657.	−	210662.i	0.283835	−	0.374511i
$751$	578243.			1.02525			0.512626	−	0.858612i	$-0.328673\pi$
$751$	578243.			1.02525			0.512626	+	0.858612i	$0.328673\pi$
$752$	−836637.	+	510056.i	−1.47945	+	0.901949i
$753$			492853.i			0.869215i
$754$	95127.9	−	125518.i	0.167327	−	0.220782i
$755$	−72863.6			−0.127825
$756$	−236034.	−	840603.i	−0.412982	−	1.47078i
$757$			306334.i			0.534569i	0.963618	+	0.267285i	$0.0861264\pi$
$757$			306334.i			0.534569i	−0.963618	+	0.267285i	$0.913874\pi$
$758$	−138709.	−	105125.i	−0.241416	−	0.182965i
$759$		−	1.07293e6i		−	1.86247i
$760$	−73930.8	−	29082.7i	−0.127997	−	0.0503510i
$761$	−730380.			−1.26119			−0.630593	−	0.776113i	$-0.717188\pi$
$761$	−730380.			−1.26119			−0.630593	+	0.776113i	$0.717188\pi$
$762$	650453.	+	492967.i	1.12023	+	0.849000i
$763$			569737.i			0.978645i
$764$	−82465.5	−	293690.i	−0.141282	−	0.503155i
$765$			39569.1i			0.0676135i
$766$	253631.	−	334658.i	0.432261	−	0.570353i
$767$	−357230.			−0.607235
$768$	211404.	−	410239.i	0.358419	−	0.695528i
$769$	−220202.			−0.372364			−0.186182	−	0.982515i	$-0.559611\pi$
$769$	−220202.			−0.372364			−0.186182	+	0.982515i	$0.559611\pi$
$770$	210876.	−	278244.i	0.355669	−	0.469293i
$771$		−	591024.i		−	0.994251i
$772$	237360.	−	66648.5i	0.398265	−	0.111829i
$773$		−	501373.i		−	0.839078i	−0.907737	−	0.419539i	$-0.862192\pi$
$773$		−	501373.i		−	0.839078i	0.907737	−	0.419539i	$-0.137808\pi$
$774$	−225120.	−	170615.i	−0.375779	−	0.284796i
$775$			504082.i			0.839263i
$776$	−42274.9	+	107466.i	−0.0702036	+	0.178464i
$777$	−652217.			−1.08031
$778$	−249649.	+	329404.i	−0.412450	+	0.544213i
$779$	263133.	−	22280.3i	0.433612	−	0.0367152i
$780$	−47670.6	+	13385.5i	−0.0783541	+	0.0220012i
$781$	709102.			1.16254
$782$	366268.	−	483277.i	0.598942	−	0.790283i
$783$			560428.i			0.914106i
$784$	−513933.	+	313319.i	−0.836131	+	0.509747i
$785$			215592.i			0.349860i
$786$	−311988.	−	236451.i	−0.505002	−	0.382733i
$787$			460772.i			0.743938i	0.928245	+	0.371969i	$0.121317\pi$
$787$			460772.i			0.743938i	−0.928245	+	0.371969i	$0.878683\pi$
$788$	21699.2	+	77278.7i	0.0349455	+	0.124454i
$789$	−720655.			−1.15764
$790$	−71652.6	+	94543.1i	−0.114809	+	0.151487i
$791$	529613.			0.846459
$792$	−299742.	−	117912.i	−0.477855	−	0.187978i
$793$			214762.i			0.341515i
$794$	541190.	+	410158.i	0.858437	+	0.650595i
$795$			277995.i			0.439848i
$796$	−97517.9	−	347297.i	−0.153907	−	0.548119i
$797$	−33724.2			−0.0530915			−0.0265457	−	0.999648i	$-0.508451\pi$
$797$	−33724.2			−0.0530915			−0.0265457	+	0.999648i	$0.508451\pi$
$798$	−184252.	+	243114.i	−0.289338	+	0.381771i
$799$		−	610215.i		−	0.955849i
$800$	−58107.7	+	573124.i	−0.0907933	+	0.895506i
$801$		−	176927.i		−	0.275759i
$802$	−361180.	+	476564.i	−0.561532	+	0.740922i
$803$	−257608.			−0.399510
$804$	227741.	+	811069.i	0.352314	+	1.25472i
$805$			517975.i			0.799313i
$806$	120399.	−	158862.i	0.185333	−	0.244540i
$807$	282494.			0.433772
$808$	−349397.	+	888197.i	−0.535176	+	1.36046i
$809$			336852.i			0.514686i	0.966320	+	0.257343i	$0.0828470\pi$
$809$			336852.i			0.514686i	−0.966320	+	0.257343i	$0.917153\pi$
$810$	57850.8	−	76332.1i	0.0881737	−	0.116342i
$811$		−	994330.i		−	1.51178i	−0.654698	−	0.755891i	$-0.727204\pi$
$811$		−	994330.i		−	1.51178i	0.654698	−	0.755891i	$-0.272796\pi$
$812$	751807.	−	211101.i	1.14024	−	0.320168i
$813$		−	51690.5i		−	0.0782041i
$814$	−520112.	+	686269.i	−0.784960	+	1.03573i
$815$			102673.i			0.154575i
$816$	149607.	+	245399.i	0.224684	+	0.368547i
$817$			353185.i			0.529125i
$818$	−230016.	+	303498.i	−0.343756	+	0.453575i
$819$		−	120420.i		−	0.179527i
$820$	74512.9	+	199038.i	0.110816	+	0.296011i
$821$	−714855.			−1.06055			−0.530276	−	0.847825i	$-0.677912\pi$
$821$	−714855.			−1.06055			−0.530276	+	0.847825i	$0.677912\pi$
$822$	565396.	+	428504.i	0.836776	+	0.634178i
$823$	997899.			1.47329			0.736643	−	0.676282i	$-0.236410\pi$
$823$	997899.			1.47329			0.736643	+	0.676282i	$0.236410\pi$
$824$	−232086.	+	589982.i	−0.341817	+	0.868929i
$825$	−634761.			−0.932615
$826$	−1.41162e6	−	1.06984e6i	−2.06898	−	1.56804i
$827$	−870417.			−1.27267			−0.636336	−	0.771412i	$-0.719551\pi$
$827$	−870417.			−1.27267			−0.636336	+	0.771412i	$0.719551\pi$
$828$	460086.	−	129188.i	0.671086	−	0.188435i
$829$	−227604.			−0.331185			−0.165593	−	0.986194i	$-0.552954\pi$
$829$	−227604.			−0.331185			−0.165593	+	0.986194i	$0.552954\pi$
$830$	−20998.5	−	15914.4i	−0.0304813	−	0.0231012i
$831$	−86274.2			−0.124934
$832$	155202.	−	166742.i	0.224208	−	0.240878i
$833$		−	374846.i		−	0.540210i
$834$	435448.	+	330018.i	0.626043	+	0.474467i
$835$	−130020.			−0.186482
$836$	108875.	+	387743.i	0.155781	+	0.554793i
$837$			709307.i			1.01247i
$838$	456966.	+	346326.i	0.650722	+	0.493171i
$839$	223458.			0.317448			0.158724	−	0.987323i	$-0.449262\pi$
$839$	223458.			0.317448			0.158724	+	0.987323i	$0.449262\pi$
$840$	−228461.	−	89871.4i	−0.323782	−	0.127369i
$841$	206052.			0.291330
$842$	298961.	+	226577.i	0.421687	+	0.319589i
$843$			507430.i			0.714038i
$844$	−47353.1	−	168642.i	−0.0664758	−	0.236745i
$845$	201245.			0.281846
$846$	290466.	−	383260.i	0.405840	−	0.535492i
$847$	−760548.			−1.06013
$848$	−665740.	−	1.09200e6i	−0.925791	−	1.51856i
$849$		−	448274.i		−	0.621911i
$850$	−285913.	−	216689.i	−0.395728	−	0.299915i
$851$		−	1.27755e6i		−	1.76408i
$852$	−134799.	−	480069.i	−0.185698	−	0.661339i
$853$	482897.			0.663677			0.331838	−	0.943336i	$-0.392331\pi$
$853$	482897.			0.663677			0.331838	+	0.943336i	$0.392331\pi$
$854$	−643172.	+	848643.i	−0.881884	+	1.16362i
$855$	38990.2			0.0533363
$856$	−271234.	+	689501.i	−0.370167	+	0.940995i
$857$	−1.07346e6			−1.46159			−0.730795	−	0.682597i	$-0.760850\pi$
$857$	−1.07346e6			−1.46159			−0.730795	+	0.682597i	$0.760850\pi$
$858$	200046.	+	151611.i	0.271741	+	0.205947i
$859$			1.13699e6i			1.54088i	0.637510	+	0.770442i	$0.279964\pi$
$859$			1.13699e6i			1.54088i	−0.637510	+	0.770442i	$0.720036\pi$
$860$	−273661.	+	76841.7i	−0.370012	+	0.103896i
$861$	813133.	−	68850.5i	1.09687	−	0.0928754i
$862$	568279.	+	430689.i	0.764798	+	0.579627i
$863$			418187.i			0.561499i	0.959781	+	0.280749i	$0.0905830\pi$
$863$			418187.i			0.561499i	−0.959781	+	0.280749i	$0.909417\pi$
$864$	−81764.8	+	806457.i	−0.109532	+	1.08032i
$865$	−83296.1			−0.111325
$866$	380570.	−	502148.i	0.507456	−	0.669570i
$867$	409171.			0.544336
$868$	951526.	−	267180.i	1.26294	−	0.354621i
$869$	601367.			0.796343
$870$	125588.	+	95181.2i	0.165924	+	0.125751i
$871$			415818.i			0.548109i
$872$	193630.	−	492224.i	0.254648	−	0.647336i
$873$		−	56676.5i		−	0.0743660i
$874$	−476207.	−	360909.i	−0.623408	−	0.472470i
$875$	646894.			0.844923
$876$	48970.8	+	174403.i	0.0638159	+	0.227272i
$877$	181899.			0.236500			0.118250	−	0.992984i	$-0.462272\pi$
$877$	181899.			0.236500			0.118250	+	0.992984i	$0.462272\pi$
$878$	−462261.	+	609937.i	−0.599650	+	0.791217i
$879$		−	771999.i		−	0.999169i
$880$	−276750.	+	168720.i	−0.357373	+	0.217873i
$881$	174889.			0.225326			0.112663	−	0.993633i	$-0.464062\pi$
$881$	174889.			0.225326			0.112663	+	0.993633i	$0.464062\pi$
$882$	178429.	−	235431.i	0.229365	−	0.302640i
$883$	−722157.			−0.926212			−0.463106	−	0.886303i	$-0.653265\pi$
$883$	−722157.			−0.926212			−0.463106	+	0.886303i	$0.653265\pi$
$884$	38350.3	+	136579.i	0.0490754	+	0.174775i
$885$		−	357430.i		−	0.456357i
$886$	860592.	+	652228.i	1.09630	+	0.830868i
$887$	1.27329e6			1.61837			0.809187	−	0.587551i	$-0.199908\pi$
$887$	1.27329e6			1.61837			0.809187	+	0.587551i	$0.199908\pi$
$888$	563483.	+	221662.i	0.714587	+	0.281103i
$889$			1.99739e6i			2.52731i
$890$	−141893.	−	107538.i	−0.179135	−	0.135764i
$891$	−485531.			−0.611592
$892$	651679.	−	182986.i	0.819038	−	0.229979i
$893$	−601287.			−0.754013
$894$	488292.	+	370068.i	0.610948	+	0.463027i
$895$	−62115.6			−0.0775452
$896$	1.11265e6	−	194088.i	1.38594	−	0.241759i
$897$	−372403.			−0.462837
$898$	−454516.	+	599719.i	−0.563634	+	0.743695i
$899$	−634381.			−0.784930
$900$	−76429.4	−	272193.i	−0.0943573	−	0.336041i
$901$	796471.			0.981117
$902$	575990.	−	910492.i	0.707948	−	1.11909i
$903$			1.09141e6i			1.33848i
$904$	−457559.	−	179994.i	−0.559900	−	0.220252i
$905$			213715.i			0.260938i
$906$	156886.	−	207006.i	0.191130	−	0.252189i
$907$			724061.i			0.880157i	0.897959	+	0.440079i	$0.145049\pi$
$907$			724061.i			0.880157i	−0.897959	+	0.440079i	$0.854951\pi$
$908$	74970.1	+	266996.i	0.0909320	+	0.323842i
$909$		−	468424.i		−	0.566906i
$910$	−96575.1	−	73192.6i	−0.116623	−	0.0883862i
$911$		−	778657.i		−	0.938231i	−0.883137	−	0.469115i	$-0.844573\pi$
$911$		−	778657.i		−	0.938231i	0.883137	−	0.469115i	$-0.155427\pi$
$912$	241809.	−	147418.i	0.290725	−	0.177240i
$913$			133567.i			0.160235i
$914$	−905844.	−	686524.i	−1.08433	−	0.821794i
$915$	−214882.			−0.256660
$916$	113877.	−	31975.6i	0.135720	−	0.0381090i
$917$		−	958042.i		−	1.13932i
$918$	−402316.	−	304908.i	−0.477399	−	0.361812i
$919$	121046.			0.143324			0.0716621	−	0.997429i	$-0.477170\pi$
$919$	121046.			0.143324			0.0716621	+	0.997429i	$0.477170\pi$
$920$	176038.	−	447505.i	0.207985	−	0.528715i
$921$		−	387345.i		−	0.456645i
$922$	125808.	−	166000.i	0.147995	−	0.195275i
$923$		−	246121.i		−	0.288899i
$924$	336444.	+	1.19820e6i	0.394066	+	1.40341i
$925$	−755816.			−0.883349
$926$	368146.	−	485755.i	0.429336	−	0.566495i
$927$		−	311149.i		−	0.362084i
$928$	−721269.	−	73127.8i	−0.837532	−	0.0849154i
$929$		−	841957.i		−	0.975571i	−0.872964	−	0.487785i	$-0.837805\pi$
$929$		−	841957.i		−	0.975571i	0.872964	−	0.487785i	$-0.162195\pi$
$930$	158951.	+	120466.i	0.183780	+	0.139283i
$931$	−369361.			−0.426140
$932$	−981786.	+	275677.i	−1.13028	+	0.317372i
$933$	1.18335e6			1.35941
$934$	−495396.	−	375452.i	−0.567883	−	0.430389i
$935$		−	201852.i		−	0.230893i
$936$	−40925.8	+	104037.i	−0.0467138	+	0.118750i
$937$		−	1.57634e6i		−	1.79544i	−0.440571	−	0.897718i	$-0.645224\pi$
$937$		−	1.57634e6i		−	1.79544i	0.440571	−	0.897718i	$-0.354776\pi$
$938$	−1.24530e6	+	1.64313e6i	−1.41536	+	1.86752i
$939$		−	1.26234e6i		−	1.43168i
$940$	−130821.	−	465900.i	−0.148054	−	0.527274i
$941$	47974.9			0.0541795			0.0270898	−	0.999633i	$-0.491376\pi$
$941$	47974.9			0.0541795			0.0270898	+	0.999633i	$0.491376\pi$
$942$	−612500.	−	464203.i	−0.690246	−	0.523126i
$943$	134863.	+	1.59275e6i	0.151660	+	1.79112i
$944$	855971.	+	1.40404e6i	0.960539	+	1.57556i
$945$	431200.			0.482854
$946$	1.14839e6	+	870349.i	1.28324	+	0.972548i
$947$		−	266665.i		−	0.297348i	−0.988886	−	0.148674i	$-0.952499\pi$
$947$		−	266665.i		−	0.297348i	0.988886	−	0.148674i	$-0.0475006\pi$
$948$	−114319.	−	407131.i	−0.127204	−	0.453020i
$949$			89412.7i			0.0992812i
$950$	−213518.	+	281730.i	−0.236585	+	0.312166i
$951$			1.05366e6i			1.16504i
$952$	−257487.	+	654553.i	−0.284107	+	0.722223i
$953$	462835.			0.509613			0.254807	−	0.966992i	$-0.417988\pi$
$953$	462835.			0.509613			0.254807	+	0.966992i	$0.417988\pi$
$954$	500243.	+	379125.i	0.549647	+	0.416568i
$955$	150653.			0.165185
$956$	−354370.	−	1.26204e6i	−0.387741	−	1.38089i
$957$		−	798838.i		−	0.872238i
$958$	644183.	−	849977.i	0.701905	−	0.926139i
$959$			1.73620e6i			1.88782i
$960$	166835.	+	155289.i	0.181028	+	0.168499i
$961$	120616.			0.130604
$962$	238196.	+	180525.i	0.257386	+	0.195068i
$963$		−	363634.i		−	0.392114i
$964$	−105766.	−	376672.i	−0.113813	−	0.405330i
$965$			121757.i			0.130750i
$966$	−1.47157e6	−	1.11528e6i	−1.57698	−	1.19517i
$967$	900861.			0.963396			0.481698	−	0.876337i	$-0.340020\pi$
$967$	900861.			0.963396			0.481698	+	0.876337i	$0.340020\pi$
$968$	657076.	+	258479.i	0.701237	+	0.275851i
$969$			176367.i			0.187832i
$970$	−45453.8	−	34448.6i	−0.0483088	−	0.0366124i
$971$	1.34849e6			1.43024			0.715121	−	0.699000i	$-0.246371\pi$
$971$	1.34849e6			1.43024			0.715121	+	0.699000i	$0.246371\pi$
$972$	−185041.	−	658997.i	−0.195855	−	0.697511i
$973$			1.33716e6i			1.41240i
$974$	−160260.	−	121458.i	−0.168930	−	0.128029i
$975$			220318.i			0.231761i
$976$	844088.	−	514598.i	0.886111	−	0.540217i
$977$			572943.i			0.600236i	0.953902	+	0.300118i	$0.0970261\pi$
$977$			572943.i			0.600236i	−0.953902	+	0.300118i	$0.902974\pi$
$978$	−291694.	−	221070.i	−0.304964	−	0.231127i
$979$			902550.i			0.941686i
$980$	−80361.0	−	286195.i	−0.0836746	−	0.297996i
$981$			259593.i			0.269746i
$982$	−725903.	−	550149.i	−0.752758	−	0.570502i
$983$		−	1.01204e6i		−	1.04734i	−0.851921	−	0.523671i	$-0.824562\pi$
$983$		−	1.01204e6i		−	1.04734i	0.851921	−	0.523671i	$-0.175438\pi$
$984$	−725906.	−	216867.i	−0.749705	−	0.223977i
$985$	−39641.3			−0.0408579
$986$	272700.	−	359818.i	0.280499	−	0.370108i
$987$	−1.85809e6			−1.90736
$988$	134581.	−	37789.2i	0.137870	−	0.0387127i
$989$	−2.13784e6			−2.18566
$990$	96082.8	−	126778.i	0.0980337	−	0.129352i
$991$	1.68775e6			1.71855			0.859274	−	0.511515i	$-0.170915\pi$
$991$	1.68775e6			1.71855			0.859274	+	0.511515i	$0.170915\pi$
$992$	−912875.	−	92554.3i	−0.927658	−	0.0940531i
$993$	750418.			0.761035
$994$	737089.	−	972563.i	0.746014	−	0.984339i
$995$	178151.			0.179946
$996$	90426.1	−	25390.9i	0.0911539	−	0.0255952i
$997$			571588.i			0.575033i	0.957776	+	0.287517i	$0.0928297\pi$
$997$			571588.i			0.575033i	−0.957776	+	0.287517i	$0.907170\pi$
$998$	726230.	−	958236.i	0.729144	−	0.962080i
$999$	−1.06353e6			−1.06566

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	164.5.d.f.163.20	yes	72
4.3	odd	2	inner	164.5.d.f.163.17	✓	72
41.40	even	2	inner	164.5.d.f.163.19	yes	72
164.163	odd	2	inner	164.5.d.f.163.18	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
164.5.d.f.163.17	✓	72	4.3	odd	2	inner
164.5.d.f.163.18	yes	72	164.163	odd	2	inner
164.5.d.f.163.19	yes	72	41.40	even	2	inner
164.5.d.f.163.20	yes	72	1.1	even	1	trivial

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 164 = 2^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	164.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.41605 + 3.18790i) q^{2} +7.04202 q^{3} +(-4.32538 - 15.4043i) q^{4} +7.90186 q^{5} +(-17.0139 + 22.4492i) q^{6} -68.9363 q^{7} +(59.5575 + 23.4286i) q^{8} -31.4099 q^{9} +O(q^{10})\)	\(q+(-2.41605 + 3.18790i) q^{2} +7.04202 q^{3} +(-4.32538 - 15.4043i) q^{4} +7.90186 q^{5} +(-17.0139 + 22.4492i) q^{6} -68.9363 q^{7} +(59.5575 + 23.4286i) q^{8} -31.4099 q^{9} +(-19.0913 + 25.1903i) q^{10} +160.230 q^{11} +(-30.4594 - 108.477i) q^{12} -55.6139i q^{13} +(166.554 - 219.762i) q^{14} +55.6451 q^{15} +(-218.582 + 133.259i) q^{16} -159.426i q^{17} +(75.8880 - 100.132i) q^{18} -157.094 q^{19} +(-34.1785 - 121.722i) q^{20} -485.451 q^{21} +(-387.124 + 510.796i) q^{22} -950.893i q^{23} +(419.406 + 164.985i) q^{24} -562.561 q^{25} +(177.292 + 134.366i) q^{26} -791.593 q^{27} +(298.176 + 1061.91i) q^{28} -707.975i q^{29} +(-134.441 + 177.391i) q^{30} -896.050i q^{31} +(103.291 - 1018.78i) q^{32} +1128.34 q^{33} +(508.235 + 385.183i) q^{34} -544.725 q^{35} +(135.860 + 483.846i) q^{36} +1343.53 q^{37} +(379.547 - 500.799i) q^{38} -391.635i q^{39} +(470.615 + 185.130i) q^{40} +(-1675.01 + 141.828i) q^{41} +(1172.88 - 1547.57i) q^{42} -2248.24i q^{43} +(-693.055 - 2468.22i) q^{44} -248.197 q^{45} +(3031.35 + 2297.41i) q^{46} +3827.56 q^{47} +(-1539.26 + 938.410i) q^{48} +2351.21 q^{49} +(1359.18 - 1793.39i) q^{50} -1122.68i q^{51} +(-856.691 + 240.551i) q^{52} +4995.85i q^{53} +(1912.53 - 2523.52i) q^{54} +1266.11 q^{55} +(-4105.68 - 1615.08i) q^{56} -1106.26 q^{57} +(2256.95 + 1710.50i) q^{58} -6423.39i q^{59} +(-240.686 - 857.171i) q^{60} -3861.65 q^{61} +(2856.51 + 2164.90i) q^{62} +2165.28 q^{63} +(2998.20 + 2790.70i) q^{64} -439.453i q^{65} +(-2726.14 + 3597.04i) q^{66} -7476.87 q^{67} +(-2455.85 + 689.580i) q^{68} -6696.21i q^{69} +(1316.08 - 1736.53i) q^{70} +4425.53 q^{71} +(-1870.70 - 735.891i) q^{72} -1607.74 q^{73} +(-3246.03 + 4283.03i) q^{74} -3961.56 q^{75} +(679.491 + 2419.91i) q^{76} -11045.7 q^{77} +(1248.49 + 946.210i) q^{78} +3753.15 q^{79} +(-1727.21 + 1052.99i) q^{80} -3030.21 q^{81} +(3594.77 - 5682.41i) q^{82} +833.596i q^{83} +(2099.76 + 7478.01i) q^{84} -1259.77i q^{85} +(7167.17 + 5431.87i) q^{86} -4985.58i q^{87} +(9542.90 + 3753.97i) q^{88} +5632.85i q^{89} +(599.656 - 791.226i) q^{90} +3833.82i q^{91} +(-14647.8 + 4112.97i) q^{92} -6310.00i q^{93} +(-9247.60 + 12201.9i) q^{94} -1241.33 q^{95} +(727.381 - 7174.25i) q^{96} +1804.41i q^{97} +(-5680.65 + 7495.43i) q^{98} -5032.81 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 6 q^{2} - 162 q^{4} - 8 q^{5} + 162 q^{8} + 1728 q^{9}+O(q^{10}) \) 72 * q + 6 * q^2 - 162 * q^4 - 8 * q^5 + 162 * q^8 + 1728 * q^9	\( 72 q + 6 q^{2} - 162 q^{4} - 8 q^{5} + 162 q^{8} + 1728 q^{9} - 272 q^{10} - 2842 q^{16} - 298 q^{18} - 584 q^{20} + 280 q^{21} + 4264 q^{25} + 66 q^{32} + 3512 q^{33} - 11338 q^{36} + 5720 q^{37} - 4648 q^{40} - 7928 q^{41} - 10140 q^{42} - 9528 q^{45} - 5680 q^{46} + 6624 q^{49} + 554 q^{50} + 29864 q^{57} + 11712 q^{61} - 3936 q^{62} - 34554 q^{64} + 24852 q^{66} - 12166 q^{72} + 16632 q^{73} - 11120 q^{74} + 84456 q^{77} - 20496 q^{78} - 12104 q^{80} + 13408 q^{81} - 51114 q^{82} - 948 q^{84} - 20400 q^{86} + 64976 q^{90} - 2784 q^{92} + 2902 q^{98}+O(q^{100}) \) 72 * q + 6 * q^2 - 162 * q^4 - 8 * q^5 + 162 * q^8 + 1728 * q^9 - 272 * q^10 - 2842 * q^16 - 298 * q^18 - 584 * q^20 + 280 * q^21 + 4264 * q^25 + 66 * q^32 + 3512 * q^33 - 11338 * q^36 + 5720 * q^37 - 4648 * q^40 - 7928 * q^41 - 10140 * q^42 - 9528 * q^45 - 5680 * q^46 + 6624 * q^49 + 554 * q^50 + 29864 * q^57 + 11712 * q^61 - 3936 * q^62 - 34554 * q^64 + 24852 * q^66 - 12166 * q^72 + 16632 * q^73 - 11120 * q^74 + 84456 * q^77 - 20496 * q^78 - 12104 * q^80 + 13408 * q^81 - 51114 * q^82 - 948 * q^84 - 20400 * q^86 + 64976 * q^90 - 2784 * q^92 + 2902 * q^98

Introduction

L-functions

Modular forms

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Representations

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Database

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