LMFDB - Embedded newform 164.5.d.f.163.19

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			163.19
Character	$\chi$	$=$	164.163
Dual form			164.5.d.f.163.17

$q$-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} +(4499.04 - 4997.08i) 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	$-0.627948\pi$
$3$	−7.04202			−0.782447			−0.391224	+	0.920296i	$0.627948\pi$
$4$	−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	$-0.251650\pi$
$7$	68.9363			1.40686			0.703432	+	0.710763i	$0.251650\pi$
$8$	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	$-0.730338\pi$
$11$	−160.230			−1.32421			−0.662107	+	0.749409i	$0.730338\pi$
$12$	30.4594	+	108.477i	0.211524	+	0.753313i
$13$			55.6139i			0.329077i	0.986371	+	0.164538i	$0.0526134\pi$
$13$			55.6139i			0.329077i	−0.986371	+	0.164538i	$0.947387\pi$
$14$	−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	$0.0889508\pi$
$17$			159.426i			0.551649i	−0.961208	+	0.275824i	$0.911049\pi$
$18$	75.8880	−	100.132i	0.234222	−	0.309048i
$19$	157.094			0.435163			0.217582	−	0.976042i	$-0.430183\pi$
$19$	157.094			0.435163			0.217582	+	0.976042i	$0.430183\pi$
$20$	−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	$0.138290\pi$
$29$			707.975i			0.841825i	−0.907101	+	0.420913i	$0.861710\pi$
$30$	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	$-0.833544\pi$
$47$	−3827.56			−1.73271			−0.866357	+	0.499426i	$0.833544\pi$
$48$	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	$-0.651221\pi$
$53$		−	4995.85i		−	1.77852i	0.457405	−	0.889258i	$-0.348779\pi$
$54$	−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	$-0.186737\pi$
$67$	7476.87			1.66560			0.832799	+	0.553576i	$0.186737\pi$
$68$	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	$-0.644651\pi$
$71$	−4425.53			−0.877907			−0.438954	+	0.898510i	$0.644651\pi$
$72$	−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	$-0.597215\pi$
$79$	−3753.15			−0.601370			−0.300685	+	0.953723i	$0.597215\pi$
$80$	−1727.21	+	1052.99i	−0.269876	+	0.164530i
$81$	−3030.21			−0.461853
$82$	4499.04	−	4997.08i	0.669101	−	0.743171i
$83$			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	$-0.884289\pi$
$89$		−	5632.85i		−	0.711128i	0.934652	−	0.355564i	$-0.115711\pi$
$90$	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	$-0.969431\pi$
$97$		−	1804.41i		−	0.191775i	0.995392	−	0.0958877i	$-0.0305690\pi$
$98$	−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	$-0.739068\pi$
$101$		−	14913.3i		−	1.46194i	0.682409	−	0.730970i	$-0.260932\pi$
$102$	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	$0.113075\pi$
$109$			8264.68i			0.695622i	−0.937565	+	0.347811i	$0.886925\pi$
$110$	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	$0.234107\pi$
$137$			25185.5i			1.34187i	−0.741517	+	0.670934i	$0.765893\pi$
$138$	−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	$0.162953\pi$
$149$			21750.9i			0.979727i	−0.871799	+	0.489864i	$0.837047\pi$
$150$	−9571.35	+	12629.1i	−0.425393	+	0.561292i
$151$	9221.07			0.404415			0.202208	−	0.979343i	$-0.435188\pi$
$151$	9221.07			0.404415			0.202208	+	0.979343i	$0.435188\pi$
$152$	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	$-0.813313\pi$
$157$		−	27283.8i		−	1.10689i	0.832885	−	0.553445i	$-0.186687\pi$
$158$	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	$0.921369\pi$
$164$	5060.29	+	26415.7i	0.188143	+	0.982142i
$165$	8916.00			0.327493
$166$	−2657.42	−	2014.01i	−0.0964370	−	0.0730879i
$167$	16454.3			0.589993			0.294997	−	0.955498i	$-0.404681\pi$
$167$	16454.3			0.589993			0.294997	+	0.955498i	$0.404681\pi$
$168$	−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	$-0.460855\pi$
$179$	7860.89			0.245338			0.122669	+	0.992448i	$0.460855\pi$
$180$	1073.55	+	3823.28i	0.0331341	+	0.118003i
$181$		−	27046.1i		−	0.825558i	−0.910831	−	0.412779i	$-0.864558\pi$
$181$		−	27046.1i		−	0.825558i	0.910831	−	0.412779i	$-0.135442\pi$
$182$	−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	$-0.584154\pi$
$191$	−19065.5			−0.522614			−0.261307	+	0.965256i	$0.584154\pi$
$192$	−21113.4	−	19652.2i	−0.572737	−	0.533100i
$193$		−	15408.7i		−	0.413668i	−0.978376	−	0.206834i	$-0.933684\pi$
$193$		−	15408.7i		−	0.413668i	0.978376	−	0.206834i	$-0.0663159\pi$
$194$	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	$-0.591880\pi$
$199$	−22545.5			−0.569316			−0.284658	+	0.958629i	$0.591880\pi$
$200$	−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	$-0.539236\pi$
$211$	−10947.7			−0.245900			−0.122950	+	0.992413i	$0.539236\pi$
$212$	−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	$-0.446210\pi$
$227$	17332.6			0.336366			0.168183	+	0.985756i	$0.446210\pi$
$228$	4784.99	+	17041.1i	0.0920474	+	0.327814i
$229$		−	7392.56i		−	0.140969i	−0.997513	−	0.0704845i	$-0.977545\pi$
$229$		−	7392.56i		−	0.140969i	0.997513	−	0.0704845i	$-0.0224545\pi$
$230$	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	$0.199689\pi$
$233$			63734.7i			1.17399i	−0.809591	+	0.586995i	$0.800311\pi$
$234$	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	$-0.754551\pi$
$239$	−81928.1			−1.43429			−0.717145	+	0.696924i	$0.754551\pi$
$240$	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
$246$	−31682.3	+	35189.6i	−0.523536	+	0.581492i
$247$			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	$0.219143\pi$
$257$			83928.1i			1.27069i	−0.772226	+	0.635347i	$0.780857\pi$
$258$	−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	$-0.234941\pi$
$263$	102336.			1.47951			0.739756	+	0.672875i	$0.234941\pi$
$264$	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	$-0.849180\pi$
$281$		−	72057.5i		−	0.912570i	0.889834	−	0.456285i	$-0.150820\pi$
$282$	−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	$0.220441\pi$
$293$			109627.i			1.27698i	−0.769630	+	0.638490i	$0.779559\pi$
$294$	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	$-0.835038\pi$
$311$	−168041.			−1.73738			−0.868690	+	0.495356i	$0.835038\pi$
$312$	9175.46	−	23324.8i	0.0942581	−	0.239612i
$313$			179258.i			1.82974i	0.403747	+	0.914870i	$0.367707\pi$
$313$			179258.i			1.82974i	−0.403747	+	0.914870i	$0.632293\pi$
$314$	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	$-0.732695\pi$
$317$		−	149625.i		−	1.48897i	0.667639	−	0.744485i	$-0.267305\pi$
$318$	−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
$328$	−96436.4	−	47690.0i	−0.896382	−	0.443282i
$329$	−263858.			−2.43769
$330$	−21541.5	+	28423.3i	−0.197810	+	0.261004i
$331$	−106563.			−0.972634			−0.486317	−	0.873782i	$-0.661660\pi$
$331$	−106563.			−0.972634			−0.486317	+	0.873782i	$0.661660\pi$
$332$	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	$-0.483354\pi$
$347$	12588.0			0.104544			0.0522718	+	0.998633i	$0.483354\pi$
$348$	−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	$-0.383519\pi$
$383$	104978.			0.715648			0.357824	+	0.933789i	$0.383519\pi$
$384$	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	$0.181031\pi$
$397$			169764.i			1.07712i	−0.842587	+	0.538560i	$0.818969\pi$
$398$	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	$0.408152\pi$
$410$	35550.7	−	39486.3i	0.211486	−	0.234897i
$411$		−	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	$0.0852250\pi$
$421$			93779.9i			0.529110i	−0.964371	+	0.264555i	$0.914775\pi$
$422$	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	$-0.665341\pi$
$439$	−191329.			−0.992776			−0.496388	+	0.868101i	$0.665341\pi$
$440$	−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	$-0.761859\pi$
$457$		−	284151.i		−	1.36056i	0.732954	−	0.680278i	$-0.238141\pi$
$458$	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	$-0.384344\pi$
$463$	152375.			0.710806			0.355403	+	0.934713i	$0.384344\pi$
$464$	−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	$-0.302648\pi$
$479$	266626.			1.16207			0.581034	+	0.813879i	$0.302648\pi$
$480$	−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	$0.843438\pi$
$492$	−35634.7	−	186020.i	−0.147212	−	0.768474i
$493$	−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	$-0.293739\pi$
$499$	300586.			1.20717			0.603583	+	0.797300i	$0.293739\pi$
$500$	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	$-0.551295\pi$
$503$	−81191.6			−0.320904			−0.160452	+	0.987044i	$0.551295\pi$
$504$	−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	$0.360999\pi$
$509$			469537.i			1.81232i	−0.422937	+	0.906159i	$0.639001\pi$
$510$	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	$0.140885\pi$
$521$			232513.i			0.856589i	−0.903639	+	0.428294i	$0.859115\pi$
$522$	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	$-0.427270\pi$
$547$	135545.			0.453011			0.226505	+	0.974010i	$0.427270\pi$
$548$	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	$-0.797969\pi$
$557$		−	367916.i		−	1.18587i	0.805249	−	0.592936i	$-0.202031\pi$
$558$	−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	$-0.362345\pi$
$563$	265685.			0.838205			0.419102	+	0.907939i	$0.362345\pi$
$564$	−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	$-0.531729\pi$
$571$	−64892.1			−0.199031			−0.0995153	+	0.995036i	$0.531729\pi$
$572$	−137268.	+	38543.5i	−0.419542	+	0.117804i
$573$	134260.			0.408918
$574$	310147.	−	344481.i	0.941334	−	1.04554i
$575$			534935.i			1.61795i
$576$	−94173.2	−	87655.7i	−0.283846	−	0.264201i
$577$		−	274309.i		−	0.823926i	−0.911201	−	0.411963i	$-0.864843\pi$
$577$		−	274309.i		−	0.823926i	0.911201	−	0.411963i	$-0.135157\pi$
$578$	−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	$-0.612700\pi$
$587$	−238929.			−0.693415			−0.346707	+	0.937973i	$0.612700\pi$
$588$	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	$-0.639742\pi$
$593$		−	636605.i		−	1.81034i	0.425047	−	0.905172i	$-0.360258\pi$
$594$	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	$-0.931295\pi$
$601$		−	154718.i		−	0.428343i	0.976796	−	0.214172i	$-0.0687052\pi$
$602$	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	$0.120864\pi$
$641$			304584.i			0.741295i	−0.928774	+	0.370647i	$0.879136\pi$
$642$	259896.	+	196971.i	0.630565	+	0.477894i
$643$	−508615.			−1.23018			−0.615088	−	0.788459i	$-0.710879\pi$
$643$	−508615.			−1.23018			−0.615088	+	0.788459i	$0.710879\pi$
$644$	−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	$0.114122\pi$
$653$			299249.i			0.701788i	−0.936415	+	0.350894i	$0.885878\pi$
$654$	185536.	+	140615.i	0.433783	+	0.328757i
$655$			109816.i			0.255967i
$656$	385026.	−	192208.i	0.894711	−	0.446646i
$657$	50498.9			0.116991
$658$	637495.	−	841153.i	1.47240	−	1.94278i
$659$	−401275.			−0.924000			−0.462000	−	0.886880i	$-0.652868\pi$
$659$	−401275.			−0.924000			−0.462000	+	0.886880i	$0.652868\pi$
$660$	−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	$0.0640822\pi$
$673$			181138.i			0.399926i	−0.979803	+	0.199963i	$0.935918\pi$
$674$	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	$-0.643639\pi$
$683$	−406868.			−0.872192			−0.436096	+	0.899900i	$0.643639\pi$
$684$	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	$-0.453167\pi$
$691$	139996.			0.293197			0.146598	+	0.989196i	$0.453167\pi$
$692$	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	$0.0243271\pi$
$709$			76760.9i			0.152703i	−0.997081	+	0.0763515i	$0.975673\pi$
$710$	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	$-0.256942\pi$
$719$	714976.			1.38304			0.691518	+	0.722359i	$0.256942\pi$
$720$	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	$-0.594247\pi$
$727$	−308427.			−0.583557			−0.291779	+	0.956486i	$0.594247\pi$
$728$	−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
$738$	−141314.	+	156958.i	−0.259462	+	0.288185i
$739$			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	$-0.671327\pi$
$751$	−578243.			−1.02525			−0.512626	+	0.858612i	$0.671327\pi$
$752$	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	$-0.913874\pi$
$757$		−	306334.i		−	0.534569i	0.963618	−	0.267285i	$-0.0861264\pi$
$758$	−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	$0.137808\pi$
$773$			501373.i			0.839078i	−0.907737	+	0.419539i	$0.862192\pi$
$774$	−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	$-0.917153\pi$
$809$		−	336852.i		−	0.514686i	0.966320	−	0.257343i	$-0.0828470\pi$
$810$	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
$820$	39985.7	+	208733.i	0.0594671	+	0.310430i
$821$	−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	$-0.763590\pi$
$823$	−997899.			−1.47329			−0.736643	+	0.676282i	$0.763590\pi$
$824$	−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	$-0.280449\pi$
$827$	870417.			1.27267			0.636336	+	0.771412i	$0.280449\pi$
$828$	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	$-0.550738\pi$
$839$	−223458.			−0.317448			−0.158724	+	0.987323i	$0.550738\pi$
$840$	−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	$-0.346735\pi$
$883$	722157.			0.926212			0.463106	+	0.886303i	$0.346735\pi$
$884$	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	$-0.800092\pi$
$887$	−1.27329e6			−1.61837			−0.809187	+	0.587551i	$0.800092\pi$
$888$	−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
$902$	−720880.	+	800682.i	−0.886033	+	0.984118i
$903$			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	$-0.522830\pi$
$919$	−121046.			−0.143324			−0.0716621	+	0.997429i	$0.522830\pi$
$920$	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	$0.162195\pi$
$929$			841957.i			0.975571i	−0.872964	+	0.487785i	$0.837805\pi$
$930$	−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	$0.354776\pi$
$937$			1.57634e6i			1.79544i	−0.440571	+	0.897718i	$0.645224\pi$
$938$	−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	$-0.659980\pi$
$967$	−900861.			−0.963396			−0.481698	+	0.876337i	$0.659980\pi$
$968$	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	$-0.753629\pi$
$971$	−1.34849e6			−1.43024			−0.715121	+	0.699000i	$0.753629\pi$
$972$	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	$-0.902974\pi$
$977$		−	572943.i		−	0.600236i	0.953902	−	0.300118i	$-0.0970261\pi$
$978$	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	$-0.175438\pi$
$984$	679107.	+	335834.i	0.701372	+	0.346844i
$985$	−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	$-0.829085\pi$
$991$	−1.68775e6			−1.71855			−0.859274	+	0.511515i	$0.829085\pi$
$992$	−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	$-0.907170\pi$
$997$		−	571588.i		−	0.575033i	0.957776	−	0.287517i	$-0.0928297\pi$
$998$	−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.163.19	yes	72
4.3	odd	2	inner	164.5.d.f.163.18	yes	72
41.40	even	2	inner	164.5.d.f.163.20	yes	72
164.163	odd	2	inner	164.5.d.f.163.17	✓	72

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

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} +(4499.04 - 4997.08i) 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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