LMFDB - Embedded newform 164.5.d.f.163.15

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			163.15
Character	$\chi$	$=$	164.163
Dual form			164.5.d.f.163.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.77609 + 2.87981i) q^{2} -3.48340 q^{3} +(-0.586657 - 15.9892i) q^{4} -32.0896 q^{5} +(9.67024 - 10.0316i) q^{6} -52.0073 q^{7} +(47.6747 + 42.6981i) q^{8} -68.8659 q^{9} +O(q^{10})$	\(q+(-2.77609 + 2.87981i) q^{2} -3.48340 q^{3} +(-0.586657 - 15.9892i) q^{4} -32.0896 q^{5} +(9.67024 - 10.0316i) q^{6} -52.0073 q^{7} +(47.6747 + 42.6981i) q^{8} -68.8659 q^{9} +(89.0837 - 92.4122i) q^{10} -157.592 q^{11} +(2.04356 + 55.6970i) q^{12} +127.683i q^{13} +(144.377 - 149.771i) q^{14} +111.781 q^{15} +(-255.312 + 18.7604i) q^{16} -315.348i q^{17} +(191.178 - 198.321i) q^{18} +283.013 q^{19} +(18.8256 + 513.089i) q^{20} +181.162 q^{21} +(437.490 - 453.836i) q^{22} +252.922i q^{23} +(-166.070 - 148.735i) q^{24} +404.744 q^{25} +(-367.704 - 354.460i) q^{26} +522.044 q^{27} +(30.5104 + 831.556i) q^{28} -1225.37i q^{29} +(-310.314 + 321.909i) q^{30} +689.617i q^{31} +(654.742 - 787.331i) q^{32} +548.957 q^{33} +(908.144 + 875.435i) q^{34} +1668.89 q^{35} +(40.4006 + 1101.11i) q^{36} -2124.23 q^{37} +(-785.670 + 815.025i) q^{38} -444.772i q^{39} +(-1529.86 - 1370.17i) q^{40} +(820.299 + 1467.27i) q^{41} +(-502.923 + 521.714i) q^{42} +3329.61i q^{43} +(92.4525 + 2519.78i) q^{44} +2209.88 q^{45} +(-728.368 - 702.134i) q^{46} +3329.41 q^{47} +(889.354 - 65.3500i) q^{48} +303.754 q^{49} +(-1123.61 + 1165.59i) q^{50} +1098.49i q^{51} +(2041.56 - 74.9061i) q^{52} -2756.37i q^{53} +(-1449.24 + 1503.39i) q^{54} +5057.07 q^{55} +(-2479.43 - 2220.61i) q^{56} -985.849 q^{57} +(3528.83 + 3401.73i) q^{58} +34.4901i q^{59} +(-65.5772 - 1787.30i) q^{60} -3317.16 q^{61} +(-1985.97 - 1914.44i) q^{62} +3581.53 q^{63} +(449.745 + 4071.23i) q^{64} -4097.30i q^{65} +(-1523.95 + 1580.89i) q^{66} -241.095 q^{67} +(-5042.18 + 185.001i) q^{68} -881.029i q^{69} +(-4633.00 + 4806.10i) q^{70} -7337.81 q^{71} +(-3283.16 - 2940.44i) q^{72} +3857.16 q^{73} +(5897.04 - 6117.37i) q^{74} -1409.89 q^{75} +(-166.032 - 4525.17i) q^{76} +8195.93 q^{77} +(1280.86 + 1234.73i) q^{78} -3083.28 q^{79} +(8192.86 - 602.014i) q^{80} +3759.65 q^{81} +(-6502.68 - 1710.96i) q^{82} -8910.57i q^{83} +(-106.280 - 2896.65i) q^{84} +10119.4i q^{85} +(-9588.65 - 9243.28i) q^{86} +4268.45i q^{87} +(-7513.15 - 6728.88i) q^{88} -10160.1i q^{89} +(-6134.83 + 6364.05i) q^{90} -6640.45i q^{91} +(4044.03 - 148.378i) q^{92} -2402.21i q^{93} +(-9242.73 + 9588.07i) q^{94} -9081.79 q^{95} +(-2280.73 + 2742.59i) q^{96} -13659.4i q^{97} +(-843.249 + 874.756i) q^{98} +10852.7 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 $

$2$	−2.77609	+	2.87981i	−0.694022	+	0.719953i
$2$	−2.77609	+	2.87981i	−0.694022	+	0.719953i
$3$	−3.48340			−0.387045			−0.193522	−	0.981096i	$-0.561991\pi$
$3$	−3.48340			−0.387045			−0.193522	+	0.981096i	$0.561991\pi$
$4$	−0.586657	−	15.9892i	−0.0366660	−	0.999328i
$5$	−32.0896			−1.28359			−0.641793	−	0.766878i	$-0.721809\pi$
$5$	−32.0896			−1.28359			−0.641793	+	0.766878i	$0.721809\pi$
$6$	9.67024	−	10.0316i	0.268618	−	0.278654i
$7$	−52.0073			−1.06137			−0.530686	−	0.847568i	$-0.678066\pi$
$7$	−52.0073			−1.06137			−0.530686	+	0.847568i	$0.678066\pi$
$8$	47.6747	+	42.6981i	0.744916	+	0.667158i
$9$	−68.8659			−0.850196
$10$	89.0837	−	92.4122i	0.890837	−	0.924122i
$11$	−157.592			−1.30241			−0.651207	−	0.758900i	$-0.725737\pi$
$11$	−157.592			−1.30241			−0.651207	+	0.758900i	$0.725737\pi$
$12$	2.04356	+	55.6970i	0.0141914	+	0.386785i
$13$			127.683i			0.755521i	0.925903	+	0.377761i	$0.123306\pi$
$13$			127.683i			0.755521i	−0.925903	+	0.377761i	$0.876694\pi$
$14$	144.377	−	149.771i	0.736616	−	0.764139i
$15$	111.781			0.496805
$16$	−255.312	+	18.7604i	−0.997311	+	0.0732828i
$17$		−	315.348i		−	1.09117i	−0.838055	−	0.545585i	$-0.816307\pi$
$17$		−	315.348i		−	1.09117i	0.838055	−	0.545585i	$-0.183693\pi$
$18$	191.178	−	198.321i	0.590055	−	0.612102i
$19$	283.013			0.783970			0.391985	−	0.919972i	$-0.371789\pi$
$19$	283.013			0.783970			0.391985	+	0.919972i	$0.371789\pi$
$20$	18.8256	+	513.089i	0.0470640	+	1.28272i
$21$	181.162			0.410799
$22$	437.490	−	453.836i	0.903905	−	0.937678i
$23$			252.922i			0.478113i	0.971006	+	0.239057i	$0.0768382\pi$
$23$			252.922i			0.478113i	−0.971006	+	0.239057i	$0.923162\pi$
$24$	−166.070	−	148.735i	−0.288316	−	0.258220i
$25$	404.744			0.647591
$26$	−367.704	−	354.460i	−0.543940	−	0.524349i
$27$	522.044			0.716109
$28$	30.5104	+	831.556i	0.0389163	+	1.06066i
$29$		−	1225.37i		−	1.45703i	−0.685027	−	0.728517i	$-0.740210\pi$
$29$		−	1225.37i		−	1.45703i	0.685027	−	0.728517i	$-0.259790\pi$
$30$	−310.314	+	321.909i	−0.344794	+	0.357677i
$31$			689.617i			0.717603i	0.933414	+	0.358802i	$0.116815\pi$
$31$			689.617i			0.717603i	−0.933414	+	0.358802i	$0.883185\pi$
$32$	654.742	−	787.331i	0.639396	−	0.768878i
$33$	548.957			0.504093
$34$	908.144	+	875.435i	0.785592	+	0.757297i
$35$	1668.89			1.36236
$36$	40.4006	+	1101.11i	0.0311733	+	0.849625i
$37$	−2124.23			−1.55166			−0.775831	−	0.630941i	$-0.782669\pi$
$37$	−2124.23			−1.55166			−0.775831	+	0.630941i	$0.782669\pi$
$38$	−785.670	+	815.025i	−0.544093	+	0.564422i
$39$		−	444.772i		−	0.292421i
$40$	−1529.86	−	1370.17i	−0.956164	−	0.856354i
$41$	820.299	+	1467.27i	0.487982	+	0.872853i
$41$	820.299	+	1467.27i	0.487982	+	0.872853i
$42$	−502.923	+	521.714i	−0.285104	+	0.295756i
$43$			3329.61i			1.80076i	0.435104	+	0.900380i	$0.356712\pi$
$43$			3329.61i			1.80076i	−0.435104	+	0.900380i	$0.643288\pi$
$44$	92.4525	+	2519.78i	0.0477544	+	1.30154i
$45$	2209.88			1.09130
$46$	−728.368	−	702.134i	−0.344219	−	0.331821i
$47$	3329.41			1.50720			0.753600	−	0.657333i	$-0.228315\pi$
$47$	3329.41			1.50720			0.753600	+	0.657333i	$0.228315\pi$
$48$	889.354	−	65.3500i	0.386004	−	0.0283637i
$49$	303.754			0.126512
$50$	−1123.61	+	1165.59i	−0.449443	+	0.466235i
$51$			1098.49i			0.422332i
$52$	2041.56	−	74.9061i	0.755013	−	0.0277020i
$53$		−	2756.37i		−	0.981264i	−0.871367	−	0.490632i	$-0.836766\pi$
$53$		−	2756.37i		−	0.981264i	0.871367	−	0.490632i	$-0.163234\pi$
$54$	−1449.24	+	1503.39i	−0.496996	+	0.515565i
$55$	5057.07			1.67176
$56$	−2479.43	−	2220.61i	−0.790634	−	0.708103i
$57$	−985.849			−0.303432
$58$	3528.83	+	3401.73i	1.04900	+	1.01121i
$59$			34.4901i			0.00990809i	0.999988	+	0.00495404i	$0.00157693\pi$
$59$			34.4901i			0.00990809i	−0.999988	+	0.00495404i	$0.998423\pi$
$60$	−65.5772	−	1787.30i	−0.0182159	−	0.496471i
$61$	−3317.16			−0.891470			−0.445735	−	0.895165i	$-0.647058\pi$
$61$	−3317.16			−0.891470			−0.445735	+	0.895165i	$0.647058\pi$
$62$	−1985.97	−	1914.44i	−0.516641	−	0.498033i
$63$	3581.53			0.902375
$64$	449.745	+	4071.23i	0.109801	+	0.993954i
$65$		−	4097.30i		−	0.969776i
$66$	−1523.95	+	1580.89i	−0.349852	+	0.362923i
$67$	−241.095			−0.0537080			−0.0268540	−	0.999639i	$-0.508549\pi$
$67$	−241.095			−0.0537080			−0.0268540	+	0.999639i	$0.508549\pi$
$68$	−5042.18	+	185.001i	−1.09044	+	0.0400089i
$69$		−	881.029i		−	0.185051i
$70$	−4633.00	+	4806.10i	−0.945510	+	0.980837i
$71$	−7337.81			−1.45563			−0.727813	−	0.685775i	$-0.759463\pi$
$71$	−7337.81			−1.45563			−0.727813	+	0.685775i	$0.759463\pi$
$72$	−3283.16	−	2940.44i	−0.633325	−	0.567215i
$73$	3857.16			0.723805			0.361902	−	0.932216i	$-0.382127\pi$
$73$	3857.16			0.723805			0.361902	+	0.932216i	$0.382127\pi$
$74$	5897.04	−	6117.37i	1.07689	−	1.11712i
$75$	−1409.89			−0.250647
$76$	−166.032	−	4525.17i	−0.0287451	−	0.783443i
$77$	8195.93			1.38235
$78$	1280.86	+	1234.73i	0.210529	+	0.202946i
$79$	−3083.28			−0.494036			−0.247018	−	0.969011i	$-0.579451\pi$
$79$	−3083.28			−0.494036			−0.247018	+	0.969011i	$0.579451\pi$
$80$	8192.86	−	602.014i	1.28013	−	0.0940647i
$81$	3759.65			0.573030
$82$	−6502.68	−	1710.96i	−0.967085	−	0.254455i
$83$		−	8910.57i		−	1.29345i	−0.762724	−	0.646724i	$-0.776138\pi$
$83$		−	8910.57i		−	1.29345i	0.762724	−	0.646724i	$-0.223862\pi$
$84$	−106.280	−	2896.65i	−0.0150624	−	0.410523i
$85$			10119.4i			1.40061i
$86$	−9588.65	−	9243.28i	−1.29646	−	1.24977i
$87$			4268.45i			0.563938i
$88$	−7513.15	−	6728.88i	−0.970190	−	0.868916i
$89$		−	10160.1i		−	1.28268i	−0.767259	−	0.641338i	$-0.778380\pi$
$89$		−	10160.1i		−	1.28268i	0.767259	−	0.641338i	$-0.221620\pi$
$90$	−6134.83	+	6364.05i	−0.757386	+	0.785685i
$91$		−	6640.45i		−	0.801890i
$92$	4044.03	−	148.378i	0.477792	−	0.0175305i
$93$		−	2402.21i		−	0.277745i
$94$	−9242.73	+	9588.07i	−1.04603	+	1.08511i
$95$	−9081.79			−1.00629
$96$	−2280.73	+	2742.59i	−0.247475	+	0.297590i
$97$		−	13659.4i		−	1.45173i	−0.687835	−	0.725867i	$-0.741439\pi$
$97$		−	13659.4i		−	1.45173i	0.687835	−	0.725867i	$-0.258561\pi$
$98$	−843.249	+	874.756i	−0.0878018	+	0.0910824i
$99$	10852.7			1.10731
$100$	−237.446	−	6471.56i	−0.0237446	−	0.647156i
$101$		−	1977.85i		−	0.193888i	−0.995290	−	0.0969438i	$-0.969093\pi$
$101$		−	1977.85i		−	0.193888i	0.995290	−	0.0969438i	$-0.0309067\pi$
$102$	−3163.43	−	3049.49i	−0.304059	−	0.293108i
$103$		−	4117.25i		−	0.388090i	−0.980993	−	0.194045i	$-0.937839\pi$
$103$		−	4117.25i		−	0.388090i	0.980993	−	0.194045i	$-0.0621608\pi$
$104$	−5451.83	+	6087.25i	−0.504052	+	0.562800i
$105$	−5813.43			−0.527295
$106$	7937.83	+	7651.93i	0.706464	+	0.681019i
$107$			18374.6i			1.60491i	0.596713	+	0.802455i	$0.296473\pi$
$107$			18374.6i			1.60491i	−0.596713	+	0.802455i	$0.703527\pi$
$108$	−306.260	−	8347.08i	−0.0262569	−	0.715628i
$109$			11306.6i			0.951650i	0.879540	+	0.475825i	$0.157850\pi$
$109$			11306.6i			0.951650i	−0.879540	+	0.475825i	$0.842150\pi$
$110$	−14038.9	+	14563.4i	−1.16024	+	1.20359i
$111$	7399.53			0.600563
$112$	13278.1	−	975.676i	1.05852	−	0.0777803i
$113$	−6444.37			−0.504688			−0.252344	−	0.967638i	$-0.581202\pi$
$113$	−6444.37			−0.504688			−0.252344	+	0.967638i	$0.581202\pi$
$114$	2736.81	−	2839.06i	0.210588	−	0.218457i
$115$		−	8116.17i		−	0.613699i
$116$	−19592.7	+	718.869i	−1.45605	+	0.0534237i
$117$		−	8793.01i		−	0.642341i
$118$	−99.3250	−	95.7475i	−0.00713336	−	0.00687644i
$119$			16400.4i			1.15814i
$120$	5329.13	+	4772.84i	0.370078	+	0.331447i
$121$	10194.3			0.696283
$122$	9208.73	−	9552.81i	0.618700	−	0.641817i
$123$	−2857.43	−	5111.08i	−0.188871	−	0.337833i
$124$	11026.5	−	404.568i	0.717121	−	0.0263117i
$125$	7067.92			0.452347
$126$	−9942.64	+	10314.1i	−0.626268	+	0.649668i
$127$			6956.41i			0.431298i	0.976471	+	0.215649i	$0.0691867\pi$
$127$			6956.41i			0.431298i	−0.976471	+	0.215649i	$0.930813\pi$
$128$	−12972.9	−	10006.9i	−0.791805	−	0.610774i
$129$		−	11598.4i		−	0.696975i
$130$	11799.5	+	11374.5i	0.698194	+	0.673046i
$131$			5767.10i			0.336059i	0.985782	+	0.168029i	$0.0537403\pi$
$131$			5767.10i			0.336059i	−0.985782	+	0.168029i	$0.946260\pi$
$132$	−322.049	−	8777.41i	−0.0184831	−	0.503754i
$133$	−14718.7			−0.832084
$134$	669.301	−	694.309i	0.0372745	−	0.0386672i
$135$	−16752.2			−0.919187
$136$	13464.8	−	15034.1i	0.727983	−	0.812831i
$137$		−	27262.2i		−	1.45251i	−0.687425	−	0.726256i	$-0.741259\pi$
$137$		−	27262.2i		−	1.45251i	0.687425	−	0.726256i	$-0.258741\pi$
$138$	2537.20	+	2445.82i	0.133228	+	0.128430i
$139$			10258.1i			0.530928i	0.964121	+	0.265464i	$0.0855251\pi$
$139$			10258.1i			0.530928i	−0.964121	+	0.265464i	$0.914475\pi$
$140$	−979.067	−	26684.3i	−0.0499524	−	1.36145i
$141$	−11597.7			−0.583354
$142$	20370.4	−	21131.5i	1.01024	−	1.04798i
$143$		−	20121.8i		−	0.984002i
$144$	17582.3	−	1291.95i	0.847910	−	0.0623047i
$145$			39321.5i			1.87023i
$146$	−10707.8	+	11107.9i	−0.502337	+	0.521106i
$147$	−1058.10			−0.0489656
$148$	1246.19	+	33964.7i	0.0568933	+	1.55062i
$149$			22353.9i			1.00689i	0.864029	+	0.503443i	$0.167934\pi$
$149$			22353.9i			1.00689i	−0.864029	+	0.503443i	$0.832066\pi$
$150$	3913.98	−	4060.22i	0.173955	−	0.180454i
$151$	19793.5			0.868096			0.434048	−	0.900890i	$-0.357085\pi$
$151$	19793.5			0.868096			0.434048	+	0.900890i	$0.357085\pi$
$152$	13492.6	+	12084.1i	0.583992	+	0.523032i
$153$			21716.7i			0.927709i
$154$	−22752.6	+	23602.8i	−0.959379	+	0.995225i
$155$		−	22129.6i		−	0.921105i
$156$	−7111.56	+	260.928i	−0.292224	+	0.0107219i
$157$			36016.7i			1.46118i	0.682815	+	0.730591i	$0.260755\pi$
$157$			36016.7i			1.46118i	−0.682815	+	0.730591i	$0.739245\pi$
$158$	8559.46	−	8879.27i	0.342872	−	0.355683i
$159$			9601.55i			0.379793i
$160$	−21010.4	+	25265.1i	−0.820719	+	0.986920i
$161$		−	13153.8i		−	0.507456i
$162$	−10437.1	+	10827.1i	−0.397695	+	0.412555i
$163$		−	42870.9i		−	1.61357i	−0.590845	−	0.806785i	$-0.701206\pi$
$163$		−	42870.9i		−	1.61357i	0.590845	−	0.806785i	$-0.298794\pi$
$164$	22979.2	−	13976.7i	0.854374	−	0.519658i
$165$	−17615.8			−0.647046
$166$	25660.8	+	24736.5i	0.931223	+	0.897682i
$167$	19069.6			0.683767			0.341883	−	0.939742i	$-0.388935\pi$
$167$	19069.6			0.683767			0.341883	+	0.939742i	$0.388935\pi$
$168$	8636.85	+	7735.29i	0.306011	+	0.274068i
$169$	12258.0			0.429188
$170$	−29142.0	−	28092.4i	−1.00837	−	0.972055i
$171$	−19490.0			−0.666528
$172$	53237.9	−	1953.34i	1.79955	−	0.0660268i
$173$	−26655.0			−0.890609			−0.445304	−	0.895379i	$-0.646904\pi$
$173$	−26655.0			−0.890609			−0.445304	+	0.895379i	$0.646904\pi$
$174$	−12292.3	−	11849.6i	−0.406009	−	0.391385i
$175$	−21049.6			−0.687335
$176$	40235.1	−	2956.49i	1.29891	−	0.0954445i
$177$		−	120.143i		−	0.00383488i
$178$	29259.1	+	28205.3i	0.923466	+	0.890205i
$179$	−4.67721			−0.000145976			−7.29879e−5	−	1.00000i	$-0.500023\pi$
$179$	−4.67721			−0.000145976			−7.29879e−5		1.00000i	$0.500023\pi$
$180$	−1296.44	−	35334.3i	−0.0400136	−	1.09057i
$181$			54672.3i			1.66882i	0.551143	+	0.834411i	$0.314192\pi$
$181$			54672.3i			1.66882i	−0.551143	+	0.834411i	$0.685808\pi$
$182$	19123.3	+	18434.5i	0.577323	+	0.556529i
$183$	11555.0			0.345039
$184$	−10799.3	+	12058.0i	−0.318977	+	0.356154i
$185$	68165.6			1.99169
$186$	6917.93	+	6668.76i	0.199963	+	0.192761i
$187$			49696.4i			1.42116i
$188$	−1953.22	−	53234.7i	−0.0552631	−	1.50619i
$189$	−27150.0			−0.760058
$190$	25211.9	−	26153.9i	0.698389	−	0.724484i
$191$	−23514.6			−0.644571			−0.322285	−	0.946643i	$-0.604451\pi$
$191$	−23514.6			−0.644571			−0.322285	+	0.946643i	$0.604451\pi$
$192$	−1566.64	−	14181.8i	−0.0424979	−	0.384705i
$193$		−	34607.4i		−	0.929083i	−0.885551	−	0.464542i	$-0.846219\pi$
$193$		−	34607.4i		−	0.929083i	0.885551	−	0.464542i	$-0.153781\pi$
$194$	39336.5	+	37919.6i	1.04518	+	1.00754i
$195$			14272.6i			0.375347i
$196$	−178.199	−	4856.80i	−0.00463868	−	0.126426i
$197$	5075.74			0.130788			0.0653939	−	0.997860i	$-0.479170\pi$
$197$	5075.74			0.130788			0.0653939	+	0.997860i	$0.479170\pi$
$198$	−30128.1	+	31253.8i	−0.768496	+	0.797210i
$199$	1185.46			0.0299351			0.0149675	−	0.999888i	$-0.495236\pi$
$199$	1185.46			0.0299351			0.0149675	+	0.999888i	$0.495236\pi$
$200$	19296.1	+	17281.8i	0.482401	+	0.432045i
$201$	839.832			0.0207874
$202$	5695.83	+	5490.68i	0.139590	+	0.134562i
$203$			63727.9i			1.54646i
$204$	17564.0	−	644.434i	0.422048	−	0.0154852i
$205$	−26323.1	−	47084.0i	−0.626367	−	1.12038i
$206$	11856.9	+	11429.8i	0.279407	+	0.269343i
$207$		−	17417.7i		−	0.406490i
$208$	−2395.38	−	32599.0i	−0.0553667	−	0.753490i
$209$	−44600.6			−1.02105
$210$	16138.6	−	16741.6i	0.365955	−	0.379628i
$211$	46926.6			1.05403			0.527017	−	0.849855i	$-0.323310\pi$
$211$	46926.6			1.05403			0.527017	+	0.849855i	$0.323310\pi$
$212$	−44072.3	+	1617.04i	−0.980604	+	0.0359791i
$213$	25560.6			0.563393
$214$	−52915.5	−	51009.6i	−1.15546	−	1.11384i
$215$		−	106846.i		−	2.31143i
$216$	24888.2	+	22290.3i	0.533441	+	0.477758i
$217$		−	35865.1i		−	0.761645i
$218$	−32560.8	−	31388.0i	−0.685144	−	0.660466i
$219$	−13436.0			−0.280145
$220$	−2966.77	−	80858.8i	−0.0612968	−	1.67064i
$221$	40264.6			0.824403
$222$	−20541.8	+	21309.3i	−0.416804	+	0.432377i
$223$		−	35947.1i		−	0.722861i	−0.932399	−	0.361430i	$-0.882289\pi$
$223$		−	35947.1i		−	0.722861i	0.932399	−	0.361430i	$-0.117711\pi$
$224$	−34051.3	+	40946.9i	−0.678637	+	0.816065i
$225$	−27873.1			−0.550580
$226$	17890.1	−	18558.6i	0.350265	−	0.363352i
$227$	−55291.8			−1.07302			−0.536511	−	0.843893i	$-0.680258\pi$
$227$	−55291.8			−1.07302			−0.536511	+	0.843893i	$0.680258\pi$
$228$	578.355	+	15763.0i	0.0111256	+	0.303228i
$229$			23749.3i			0.452877i	0.974026	+	0.226438i	$0.0727082\pi$
$229$			23749.3i			0.452877i	−0.974026	+	0.226438i	$0.927292\pi$
$230$	23373.1	+	22531.2i	0.441835	+	0.425921i
$231$	−28549.7			−0.535030
$232$	52320.8	−	58418.9i	0.972072	−	1.08537i
$233$			41293.1i			0.760617i	0.924860	+	0.380308i	$0.124182\pi$
$233$			41293.1i			0.760617i	−0.924860	+	0.380308i	$0.875818\pi$
$234$	25322.2	+	24410.2i	0.462456	+	0.445799i
$235$	−106839.			−1.93462
$236$	551.470	−	20.2338i	0.00990143	−	0.000363290i
$237$	10740.3			0.191214
$238$	−47230.1	−	45529.0i	−0.833806	−	0.803774i
$239$	103173.			1.80622			0.903109	−	0.429411i	$-0.141279\pi$
$239$	103173.			1.80622			0.903109	+	0.429411i	$0.141279\pi$
$240$	−28539.0	+	2097.06i	−0.495469	+	0.0364073i
$241$	−15911.9			−0.273961			−0.136980	−	0.990574i	$-0.543740\pi$
$241$	−15911.9			−0.273961			−0.136980	+	0.990574i	$0.543740\pi$
$242$	−28300.2	+	29357.6i	−0.483236	+	0.501291i
$243$	−55381.9			−0.937897
$244$	1946.03	+	53038.9i	0.0326867	+	0.890871i
$245$	−9747.36			−0.162388
$246$	22651.5	+	5959.95i	0.374305	+	0.0984856i
$247$			36136.0i			0.592306i
$248$	−29445.3	+	32877.2i	−0.478755	+	0.534555i
$249$			31039.1i			0.500623i
$250$	−19621.2	+	20354.3i	−0.313939	+	0.325669i
$251$		−	18165.3i		−	0.288334i	−0.989553	−	0.144167i	$-0.953950\pi$
$251$		−	18165.3i		−	0.288334i	0.989553	−	0.144167i	$-0.0460502\pi$
$252$	−2101.13	−	57265.9i	−0.0330865	−	0.901768i
$253$		−	39858.5i		−	0.622701i
$254$	−20033.2	−	19311.6i	−0.310515	−	0.299330i
$255$		−	35250.0i		−	0.542099i
$256$	64832.1	−	9579.49i	0.989259	−	0.146171i
$257$		−	27715.6i		−	0.419622i	−0.977742	−	0.209811i	$-0.932715\pi$
$257$		−	27715.6i		−	0.419622i	0.977742	−	0.209811i	$-0.0672848\pi$
$258$	33401.1	+	32198.1i	0.501790	+	0.483716i
$259$	110475.			1.64689
$260$	−65512.8	+	2403.71i	−0.969124	+	0.0355578i
$261$			84385.9i			1.23877i
$262$	−16608.2	−	16010.0i	−0.241947	−	0.233232i
$263$	−17280.5			−0.249831			−0.124915	−	0.992167i	$-0.539866\pi$
$263$	−17280.5			−0.249831			−0.124915	+	0.992167i	$0.539866\pi$
$264$	26171.3	+	23439.4i	0.375507	+	0.336309i
$265$			88450.9i			1.25954i
$266$	40860.5	−	42387.2i	0.577485	−	0.599062i
$267$			35391.6i			0.496453i
$268$	141.440	+	3854.93i	0.00196926	+	0.0536719i
$269$	23673.0			0.327151			0.163576	−	0.986531i	$-0.447697\pi$
$269$	23673.0			0.327151			0.163576	+	0.986531i	$0.447697\pi$
$270$	46505.6	−	48243.2i	0.637936	−	0.661772i
$271$			24955.4i			0.339803i	0.985461	+	0.169901i	$0.0543449\pi$
$271$			24955.4i			0.339803i	−0.985461	+	0.169901i	$0.945655\pi$
$272$	5916.06	+	80512.1i	0.0799640	+	1.08824i
$273$			23131.4i			0.310367i
$274$	78510.0	+	75682.3i	1.04574	+	1.00808i
$275$	−63784.5			−0.843432
$276$	−14087.0	+	516.862i	−0.184927	+	0.00678510i
$277$	−101653.			−1.32483			−0.662415	−	0.749137i	$-0.730468\pi$
$277$	−101653.			−1.32483			−0.662415	+	0.749137i	$0.730468\pi$
$278$	−29541.3	−	28477.3i	−0.382243	−	0.368476i
$279$		−	47491.1i		−	0.610104i
$280$	79563.9	+	71258.6i	1.01485	+	0.908910i
$281$		−	29234.6i		−	0.370241i	−0.982716	−	0.185120i	$-0.940732\pi$
$281$		−	29234.6i		−	0.370241i	0.982716	−	0.185120i	$-0.0592675\pi$
$282$	32196.2	−	33399.1i	0.404861	−	0.419988i
$283$			81841.8i			1.02189i	0.859615	+	0.510943i	$0.170704\pi$
$283$			81841.8i			1.02189i	−0.859615	+	0.510943i	$0.829296\pi$
$284$	4304.78	+	117326.i	0.0533721	+	1.45465i
$285$	31635.5			0.389480
$286$	57947.2	+	55860.1i	0.708435	+	0.682919i
$287$	−42661.5	−	76308.5i	−0.517931	−	0.926423i
$288$	−45089.4	+	54220.2i	−0.543612	+	0.653697i
$289$	−15923.5			−0.190653
$290$	−113239.	−	109160.i	−1.34648	−	1.29798i
$291$			47581.1i			0.561887i
$292$	−2262.83	−	61673.0i	−0.0265391	−	0.723318i
$293$			114232.i			1.33061i	0.746571	+	0.665306i	$0.231699\pi$
$293$			114232.i			1.33061i	−0.746571	+	0.665306i	$0.768301\pi$
$294$	2937.38	−	3047.13i	0.0339833	−	0.0352530i
$295$		−	1106.77i		−	0.0127179i
$296$	−101272.	−	90700.4i	−1.15586	−	1.03520i
$297$	−82269.9			−0.932671
$298$	−64375.0	−	62056.3i	−0.724911	−	0.698801i
$299$	−32293.9			−0.361225
$300$	827.121	+	22543.0i	0.00919023	+	0.250478i
$301$		−	173164.i		−	1.91128i
$302$	−54948.4	+	57001.5i	−0.602478	+	0.624989i
$303$			6889.64i			0.0750432i
$304$	−72256.6	+	5309.44i	−0.781862	+	0.0574515i
$305$	106446.			1.14428
$306$	−62540.2	−	60287.6i	−0.667907	−	0.643851i
$307$		−	109161.i		−	1.15822i	−0.815249	−	0.579111i	$-0.803400\pi$
$307$		−	109161.i		−	1.15822i	0.815249	−	0.579111i	$-0.196600\pi$
$308$	−4808.20	−	131047.i	−0.0506852	−	1.38142i
$309$			14342.0i			0.150208i
$310$	63729.0	+	61433.6i	0.663153	+	0.639268i
$311$	−56986.7			−0.589187			−0.294593	−	0.955623i	$-0.595184\pi$
$311$	−56986.7			−0.589187			−0.294593	+	0.955623i	$0.595184\pi$
$312$	18990.9	−	21204.3i	0.195091	−	0.217829i
$313$		−	99187.1i		−	1.01243i	−0.862406	−	0.506217i	$-0.831044\pi$
$313$		−	99187.1i		−	1.01243i	0.862406	−	0.506217i	$-0.168956\pi$
$314$	−103721.	−	99985.5i	−1.05198	−	1.01409i
$315$	−114930.			−1.15828
$316$	1808.83	+	49299.3i	0.0181143	+	0.493704i
$317$		−	133733.i		−	1.33082i	−0.746479	−	0.665409i	$-0.768257\pi$
$317$		−	133733.i		−	1.33082i	0.746479	−	0.665409i	$-0.231743\pi$
$318$	−27650.7	−	26654.8i	−0.273433	−	0.263585i
$319$			193108.i			1.89766i
$320$	−14432.1	−	130644.i	−0.140939	−	1.27582i
$321$		−	64006.2i		−	0.621172i
$322$	37880.4	+	36516.0i	0.365345	+	0.352186i
$323$		−	89247.7i		−	0.855445i
$324$	−2205.62	−	60113.9i	−0.0210107	−	0.572645i
$325$			51679.0i			0.489269i
$326$	123460.	+	119014.i	1.16170	+	1.11985i
$327$		−	39385.3i		−	0.368331i
$328$	−23542.1	+	104977.i	−0.218825	+	0.975764i
$329$	−173153.			−1.59970
$330$	48903.1	−	50730.3i	0.449064	−	0.465843i
$331$	191344.			1.74646			0.873231	−	0.487307i	$-0.162021\pi$
$331$	191344.			1.74646			0.873231	+	0.487307i	$0.162021\pi$
$332$	−142473.	+	5227.44i	−1.29258	+	0.0474256i
$333$	146287.			1.31922
$334$	−52938.8	+	54916.8i	−0.474549	+	0.492280i
$335$	7736.65			0.0689388
$336$	−46252.8	+	3398.68i	−0.409694	+	0.0301045i
$337$	175972.			1.54948			0.774738	−	0.632283i	$-0.217882\pi$
$337$	175972.			1.54948			0.774738	+	0.632283i	$0.217882\pi$
$338$	−34029.4	+	35300.8i	−0.297866	+	0.308995i
$339$	22448.3			0.195337
$340$	161802.	−	5936.62i	1.39967	−	0.0513548i
$341$		−	108678.i		−	0.934617i
$342$	54105.9	−	56127.4i	0.462586	−	0.479869i
$343$	109072.			0.927097
$344$	−142168.	+	158738.i	−1.20139	+	1.34142i
$345$			28271.9i			0.237529i
$346$	73996.7	−	76761.5i	0.618102	−	0.641197i
$347$	131437.			1.09159			0.545794	−	0.837919i	$-0.316228\pi$
$347$	131437.			1.09159			0.545794	+	0.837919i	$0.316228\pi$
$348$	68249.2	−	2504.11i	0.563559	−	0.0206774i
$349$	156997.			1.28896			0.644480	−	0.764621i	$-0.277074\pi$
$349$	156997.			1.28896			0.644480	+	0.764621i	$0.277074\pi$
$350$	58435.7	−	60619.1i	0.477026	−	0.494850i
$351$			66656.1i			0.541036i
$352$	−103182.	+	124077.i	−0.832758	+	1.00140i
$353$	202655.			1.62633			0.813164	−	0.582035i	$-0.197743\pi$
$353$	202655.			1.62633			0.813164	+	0.582035i	$0.197743\pi$
$354$	345.989	+	333.527i	0.00276093	+	0.00266149i
$355$	235468.			1.86842
$356$	−162452.	+	5960.47i	−1.28181	+	0.0470306i
$357$		−	57129.2i		−	0.448252i
$358$	12.9844	−	13.4695i	0.000101310	−	0.000105096i
$359$			64917.8i			0.503703i	0.967766	+	0.251852i	$0.0810395\pi$
$359$			64917.8i			0.503703i	−0.967766	+	0.251852i	$0.918960\pi$
$360$	105355.	+	94357.7i	0.812927	+	0.728069i
$361$	−50224.6			−0.385391
$362$	−157446.	−	151775.i	−1.20147	−	1.15820i
$363$	−35510.8			−0.269493
$364$	−106176.	+	3895.66i	−0.801350	+	0.0294021i
$365$	−123775.			−0.929065
$366$	−32077.7	+	33276.3i	−0.239465	+	0.248412i
$367$			76838.8i			0.570491i	0.958455	+	0.285245i	$0.0920751\pi$
$367$			76838.8i			0.570491i	−0.958455	+	0.285245i	$0.907925\pi$
$368$	−4744.91	−	64573.9i	−0.0350375	−	0.476828i
$369$	−56490.6	−	101045.i	−0.414881	−	0.742097i
$370$	−189234.	+	196304.i	−1.38228	+	1.43392i
$371$			143351.i			1.04149i
$372$	−38409.6	+	1409.28i	−0.277558	+	0.0101838i
$373$	123491.			0.887602			0.443801	−	0.896125i	$-0.353630\pi$
$373$	123491.			0.887602			0.443801	+	0.896125i	$0.353630\pi$
$374$	−143116.	−	137962.i	−1.02317	−	0.986314i
$375$	−24620.4			−0.175079
$376$	158728.	+	142159.i	1.12274	+	1.00554i
$377$	156459.			1.10082
$378$	75371.0	−	78187.1i	0.527498	−	0.547207i
$379$		−	69405.0i		−	0.483184i	−0.970378	−	0.241592i	$-0.922330\pi$
$379$		−	69405.0i		−	0.483184i	0.970378	−	0.241592i	$-0.0776695\pi$
$380$	5327.89	+	145211.i	0.0368968	+	1.00562i
$381$		−	24232.0i		−	0.166932i
$382$	65278.6	−	67717.6i	0.447346	−	0.464061i
$383$	−38538.5			−0.262723			−0.131361	−	0.991335i	$-0.541935\pi$
$383$	−38538.5			−0.262723			−0.131361	+	0.991335i	$0.541935\pi$
$384$	45190.0	+	34858.2i	0.306464	+	0.236397i
$385$	−263004.			−1.77436
$386$	99663.0	+	96073.3i	0.668897	+	0.644805i
$387$		−	229296.i		−	1.53100i
$388$	−218403.	+	8013.36i	−1.45076	+	0.0532294i
$389$	−129963.			−0.858858			−0.429429	−	0.903101i	$-0.641285\pi$
$389$	−129963.			−0.858858			−0.429429	+	0.903101i	$0.641285\pi$
$390$	−41102.3	−	39621.9i	−0.270232	−	0.260499i
$391$	79758.5			0.521703
$392$	14481.4	+	12969.7i	0.0942405	+	0.0844032i
$393$		−	20089.2i		−	0.130070i
$394$	−14090.7	+	14617.2i	−0.0907697	+	0.0941612i
$395$	98941.3			0.634137
$396$	−6366.82	−	173527.i	−0.0406006	−	1.10656i
$397$		−	11336.1i		−	0.0719257i	−0.999353	−	0.0359628i	$-0.988550\pi$
$397$		−	11336.1i		−	0.0719257i	0.999353	−	0.0359628i	$-0.0114498\pi$
$398$	−3290.94	+	3413.90i	−0.0207756	+	0.0215519i
$399$	51271.3			0.322054
$400$	−103336.	+	7593.16i	−0.645850	+	0.0474573i
$401$	112847.			0.701783			0.350892	−	0.936416i	$-0.385879\pi$
$401$	112847.			0.701783			0.350892	+	0.936416i	$0.385879\pi$
$402$	−2331.45	+	2418.56i	−0.0144269	+	0.0149660i
$403$	−88052.4			−0.542165
$404$	−31624.3	+	1160.32i	−0.193757	+	0.00710909i
$405$	−120646.			−0.735533
$406$	−183525.	−	176914.i	−1.11338	−	1.07328i
$407$	334761.			2.02091
$408$	−46903.2	+	52369.9i	−0.281762	+	0.314602i
$409$	47369.7			0.283174			0.141587	−	0.989926i	$-0.454779\pi$
$409$	47369.7			0.283174			0.141587	+	0.989926i	$0.454779\pi$
$410$	208669.	+	54903.9i	1.24134	+	0.326615i
$411$			94965.2i			0.562187i
$412$	−65831.7	+	2415.41i	−0.387829	+	0.0142297i
$413$		−	1793.73i		−	0.0105162i
$414$	50159.7	+	48353.1i	0.292654	+	0.282113i
$415$			285937.i			1.66025i
$416$	100529.	+	83599.4i	0.580903	+	0.483077i
$417$		−	35733.0i		−	0.205493i
$418$	123815.	−	128442.i	0.708634	−	0.735111i
$419$			259957.i			1.48072i	0.672209	+	0.740361i	$0.265346\pi$
$419$			259957.i			1.48072i	−0.672209	+	0.740361i	$0.734654\pi$
$420$	3410.49	+	92952.4i	0.0193338	+	0.526941i
$421$			240330.i			1.35595i	0.735084	+	0.677976i	$0.237143\pi$
$421$			240330.i			1.35595i	−0.735084	+	0.677976i	$0.762857\pi$
$422$	−130273.	+	135140.i	−0.731523	+	0.758855i
$423$	−229283.			−1.28142
$424$	117692.	−	131409.i	0.654658	−	0.730960i
$425$		−	127635.i		−	0.706632i
$426$	−70958.4	+	73609.7i	−0.391007	+	0.405617i
$427$	172516.			0.946182
$428$	293796.	−	10779.6i	1.60383	−	0.0588457i
$429$			70092.5i			0.380853i
$430$	307696.	+	296614.i	1.66412	+	1.60418i
$431$			42436.3i			0.228446i	0.993455	+	0.114223i	$0.0364378\pi$
$431$			42436.3i			0.228446i	−0.993455	+	0.114223i	$0.963562\pi$
$432$	−133284.	+	9793.74i	−0.714184	+	0.0524785i
$433$	215092.			1.14722			0.573612	−	0.819127i	$-0.305542\pi$
$433$	215092.			1.14722			0.573612	+	0.819127i	$0.305542\pi$
$434$	103285.	+	99564.7i	0.548349	+	0.528598i
$435$		−	136973.i		−	0.723862i
$436$	180783.	−	6633.06i	0.951010	−	0.0348932i
$437$			71580.2i			0.374826i
$438$	37299.6	−	38693.3i	0.194427	−	0.201691i
$439$	−7410.63			−0.0384526			−0.0192263	−	0.999815i	$-0.506120\pi$
$439$	−7410.63			−0.0384526			−0.0192263	+	0.999815i	$0.506120\pi$
$440$	241094.	+	215927.i	1.24532	+	1.11533i
$441$	−20918.3			−0.107560
$442$	−111778.	+	115955.i	−0.572154	+	0.593532i
$443$		−	299791.i		−	1.52760i	−0.645451	−	0.763802i	$-0.723331\pi$
$443$		−	299791.i		−	1.52760i	0.645451	−	0.763802i	$-0.276669\pi$
$444$	−4340.99	−	118313.i	−0.0220203	−	0.600159i
$445$			326033.i			1.64642i
$446$	103521.	+	99792.5i	0.520426	+	0.501682i
$447$		−	77867.6i		−	0.389710i
$448$	−23390.0	−	211734.i	−0.116540	−	1.05495i
$449$	−101915.			−0.505526			−0.252763	−	0.967528i	$-0.581339\pi$
$449$	−101915.			−0.505526			−0.252763	+	0.967528i	$0.581339\pi$
$450$	77378.2	−	80269.3i	0.382114	−	0.396392i
$451$	−129273.	−	231230.i	−0.635555	−	1.13682i
$452$	3780.63	+	103041.i	0.0185049	+	0.504349i
$453$	−68948.6			−0.335992
$454$	153495.	−	159230.i	0.744701	−	0.772526i
$455$			213089.i			1.02929i
$456$	−47000.0	−	42093.9i	−0.226031	−	0.202437i
$457$		−	97497.1i		−	0.466830i	−0.972377	−	0.233415i	$-0.925010\pi$
$457$		−	97497.1i		−	0.466830i	0.972377	−	0.233415i	$-0.0749901\pi$
$458$	−68393.6	−	65930.2i	−0.326050	−	0.314307i
$459$		−	164626.i		−	0.781397i
$460$	−129771.	+	4761.41i	−0.613286	+	0.0225019i
$461$	−230353.			−1.08391			−0.541953	−	0.840409i	$-0.682315\pi$
$461$	−230353.			−1.08391			−0.541953	+	0.840409i	$0.682315\pi$
$462$	79256.6	−	82218.0i	0.371323	−	0.385197i
$463$	−247551.			−1.15479			−0.577394	−	0.816465i	$-0.695931\pi$
$463$	−247551.			−1.15479			−0.577394	+	0.816465i	$0.695931\pi$
$464$	22988.3	+	312850.i	0.106776	+	1.45312i
$465$			77086.2i			0.356509i
$466$	−118917.	−	114633.i	−0.547609	−	0.527885i
$467$			393243.i			1.80313i	0.432642	+	0.901566i	$0.357582\pi$
$467$			393243.i			1.80313i	−0.432642	+	0.901566i	$0.642418\pi$
$468$	−140594.	+	5158.48i	−0.641909	+	0.0235521i
$469$	12538.7			0.0570042
$470$	296596.	−	307678.i	1.34267	−	1.39284i
$471$		−	125461.i		−	0.565543i
$472$	−1472.66	+	1644.30i	−0.00661026	+	0.00738070i
$473$		−	524720.i		−	2.34534i
$474$	−29816.1	+	30930.1i	−0.132707	+	0.137665i
$475$	114548.			0.507692
$476$	262230.	−	9621.40i	1.15736	−	0.0424643i
$477$			189820.i			0.834267i
$478$	−286417.	+	297119.i	−1.25356	+	1.30039i
$479$	81662.3			0.355919			0.177959	−	0.984038i	$-0.443050\pi$
$479$	81662.3			0.355919			0.177959	+	0.984038i	$0.443050\pi$
$480$	73187.8	−	88008.7i	0.317655	−	0.381982i
$481$		−	271228.i		−	1.17231i
$482$	44172.9	−	45823.3i	0.190135	−	0.197239i
$483$			45819.9i			0.196408i
$484$	−5980.54	−	162999.i	−0.0255299	−	0.695814i
$485$			438324.i			1.86343i
$486$	153745.	−	159490.i	0.650922	−	0.675242i
$487$			79721.8i			0.336139i	0.985775	+	0.168070i	$0.0537533\pi$
$487$			79721.8i			0.336139i	−0.985775	+	0.168070i	$0.946247\pi$
$488$	−158144.	−	141636.i	−0.664071	−	0.594751i
$489$			149337.i			0.624524i
$490$	27059.5	−	28070.6i	0.112701	−	0.116912i
$491$			153190.i			0.635430i	0.948186	+	0.317715i	$0.102916\pi$
$491$			153190.i			0.635430i	−0.948186	+	0.317715i	$0.897084\pi$
$492$	−80046.0	+	48686.6i	−0.330681	+	0.201131i
$493$	−386417.			−1.58987
$494$	−104065.	−	100317.i	−0.426433	−	0.411074i
$495$	−348260.			−1.42132
$496$	−12937.5	−	176067.i	−0.0525880	−	0.715674i
$497$	381620.			1.54496
$498$	−89386.8	−	86167.3i	−0.360425	−	0.347443i
$499$	−154097.			−0.618860			−0.309430	−	0.950922i	$-0.600138\pi$
$499$	−154097.			−0.618860			−0.309430	+	0.950922i	$0.600138\pi$
$500$	−4146.44	−	113011.i	−0.0165858	−	0.452043i
$501$	−66427.0			−0.264648
$502$	52312.7	+	50428.5i	0.207587	+	0.200110i
$503$	−16527.9			−0.0653254			−0.0326627	−	0.999466i	$-0.510399\pi$
$503$	−16527.9			−0.0653254			−0.0326627	+	0.999466i	$0.510399\pi$
$504$	170748.	+	152924.i	0.672194	+	0.602026i
$505$			63468.4i			0.248871i
$506$	114785.	+	110651.i	0.448316	+	0.432169i
$507$	−42699.7			−0.166115
$508$	111228.	−	4081.02i	0.431008	−	0.0158140i
$509$		−	112669.i		−	0.434881i	−0.976074	−	0.217440i	$-0.930229\pi$
$509$		−	112669.i		−	0.434881i	0.976074	−	0.217440i	$-0.0697708\pi$
$510$	101513.	+	97857.1i	0.390286	+	0.376229i
$511$	−200600.			−0.768227
$512$	−152393.	+	213298.i	−0.581331	+	0.813667i
$513$	147745.			0.561408
$514$	79815.7	+	76941.0i	0.302108	+	0.291227i
$515$			132121.i			0.498147i
$516$	−185449.	+	6804.26i	−0.696507	+	0.0255553i
$517$	−524688.			−1.96300
$518$	−306689.	+	318148.i	−1.14298	+	1.18569i
$519$	92850.2			0.344706
$520$	174947.	−	195338.i	0.646994	−	0.722402i
$521$		−	50031.7i		−	0.184319i	−0.995744	−	0.0921594i	$-0.970623\pi$
$521$		−	50031.7i		−	0.184319i	0.995744	−	0.0921594i	$-0.0293769\pi$
$522$	−243016.	−	234263.i	−0.891853	−	0.859731i
$523$		−	542367.i		−	1.98285i	−0.130673	−	0.991426i	$-0.541714\pi$
$523$		−	542367.i		−	1.98285i	0.130673	−	0.991426i	$-0.458286\pi$
$524$	92211.6	−	3383.31i	0.335833	−	0.0123219i
$525$	73324.4			0.266030
$526$	47972.3	−	49764.7i	0.173388	−	0.179866i
$527$	217469.			0.783028
$528$	−140155.	+	10298.6i	−0.502737	+	0.0369413i
$529$	215872.			0.771408
$530$	−254722.	−	245548.i	−0.906807	−	0.874146i
$531$		−	2375.19i		−	0.00842382i
$532$	8634.84	+	235341.i	0.0305092	+	0.831525i
$533$	−187345.	+	104738.i	−0.659459	+	0.368681i
$534$	−101921.	−	98250.3i	−0.357423	−	0.344549i
$535$		−	589635.i		−	2.06004i
$536$	−11494.1	−	10294.3i	−0.0400079	−	0.0358317i
$537$	16.2926			5.64992e−5
$538$	−65718.4	+	68173.9i	−0.227050	+	0.235534i
$539$	−47869.3			−0.164770
$540$	9827.78	+	267855.i	0.0337029	+	0.918569i
$541$	322002.			1.10018			0.550090	−	0.835105i	$-0.314593\pi$
$541$	322002.			1.10018			0.550090	+	0.835105i	$0.314593\pi$
$542$	−71867.0	−	69278.5i	−0.244642	−	0.235831i
$543$		−	190446.i		−	0.645909i
$544$	−248283.	−	206472.i	−0.838977	−	0.697690i
$545$		−	362823.i		−	1.22152i
$546$	−66614.0	−	64214.7i	−0.223450	−	0.215402i
$547$	−152951.			−0.511184			−0.255592	−	0.966785i	$-0.582270\pi$
$547$	−152951.			−0.511184			−0.255592	+	0.966785i	$0.582270\pi$
$548$	−435902.	+	15993.5i	−1.45153	+	0.0532578i
$549$	228439.			0.757925
$550$	177072.	−	183688.i	0.585361	−	0.607232i
$551$		−	346795.i		−	1.14227i
$552$	37618.3	−	42002.8i	0.123458	−	0.137848i
$553$	160353.			0.524356
$554$	282197.	−	292741.i	0.919461	−	0.953816i
$555$	−237448.			−0.770874
$556$	164019.	−	6017.96i	0.530571	−	0.0194670i
$557$			357266.i			1.15154i	0.817610	+	0.575772i	$0.195298\pi$
$557$			357266.i			1.15154i	−0.817610	+	0.575772i	$0.804702\pi$
$558$	136765.	+	131839.i	0.439246	+	0.423426i
$559$	−425134.			−1.36051
$560$	−426088.	+	31309.1i	−1.35870	+	0.0998377i
$561$		−	173113.i		−	0.550051i
$562$	84190.2	+	81157.8i	0.266556	+	0.256955i
$563$	38766.8			0.122305			0.0611523	−	0.998128i	$-0.480522\pi$
$563$	38766.8			0.122305			0.0611523	+	0.998128i	$0.480522\pi$
$564$	6803.85	+	185438.i	0.0213893	+	0.582962i
$565$	206797.			0.647811
$566$	−235689.	−	227200.i	−0.735710	−	0.709211i
$567$	−195529.			−0.608198
$568$	−349828.	−	313311.i	−1.08432	−	0.971133i
$569$	−467523.			−1.44404			−0.722018	−	0.691874i	$-0.756785\pi$
$569$	−467523.			−1.44404			−0.722018	+	0.691874i	$0.756785\pi$
$570$	−87823.1	+	91104.5i	−0.270308	+	0.280408i
$571$	−462156.			−1.41748			−0.708740	−	0.705470i	$-0.750736\pi$
$571$	−462156.			−1.41748			−0.708740	+	0.705470i	$0.750736\pi$
$572$	−321733.	+	11804.6i	−0.983340	+	0.0360794i
$573$	81910.8			0.249478
$574$	338186.	+	88982.1i	1.02644	+	0.270072i
$575$			102369.i			0.309622i
$576$	−30972.1	−	280369.i	−0.0933524	−	0.845056i
$577$			93499.1i			0.280838i	0.990092	+	0.140419i	$0.0448449\pi$
$577$			93499.1i			0.280838i	−0.990092	+	0.140419i	$0.955155\pi$
$578$	44205.2	−	45856.8i	0.132318	−	0.137261i
$579$			120552.i			0.359597i
$580$	628722.	−	23068.2i	1.86897	−	0.0685739i
$581$			463414.i			1.37283i
$582$	−137025.	−	132089.i	−0.404532	−	0.389962i
$583$			434382.i			1.27801i
$584$	183889.	+	164693.i	0.539174	+	0.482892i
$585$			282164.i			0.824500i
$586$	−328966.	−	317117.i	−0.957978	−	0.923474i
$587$	−255537.			−0.741614			−0.370807	−	0.928710i	$-0.620919\pi$
$587$	−255537.			−0.741614			−0.370807	+	0.928710i	$0.620919\pi$
$588$	620.741	+	16918.2i	0.00179538	+	0.0489327i
$589$			195171.i			0.562580i
$590$	3187.30	+	3072.50i	0.00915628	+	0.00882649i
$591$	−17680.9			−0.0506208
$592$	542339.	−	39851.3i	1.54749	−	0.113710i
$593$		−	668030.i		−	1.89971i	−0.312696	−	0.949853i	$-0.601232\pi$
$593$		−	668030.i		−	1.89971i	0.312696	−	0.949853i	$-0.398768\pi$
$594$	228389.	−	236922.i	0.647294	−	0.671479i
$595$		−	526283.i		−	1.48657i
$596$	357421.	−	13114.0i	1.00621	−	0.0369185i
$597$	−4129.44			−0.0115862
$598$	89650.6	−	93000.3i	0.250698	−	0.260065i
$599$		−	640472.i		−	1.78503i	−0.451015	−	0.892516i	$-0.648938\pi$
$599$		−	640472.i		−	1.78503i	0.451015	−	0.892516i	$-0.351062\pi$
$600$	−67215.9	−	60199.6i	−0.186711	−	0.167221i
$601$			471877.i			1.30641i	0.757181	+	0.653205i	$0.226576\pi$
$601$			471877.i			1.30641i	−0.757181	+	0.653205i	$0.773424\pi$
$602$	498679.	+	480718.i	1.37603	+	1.32647i
$603$	16603.2			0.0456623
$604$	−11612.0	−	316483.i	−0.0318297	−	0.867513i
$605$	−327131.			−0.893738
$606$	−19840.9	−	19126.3i	−0.0540276	−	0.0520817i
$607$			22269.9i			0.0604422i	0.999543	+	0.0302211i	$0.00962114\pi$
$607$			22269.9i			0.0604422i	−0.999543	+	0.0302211i	$0.990379\pi$
$608$	185300.	−	222825.i	0.501267	−	0.602777i
$609$		−	221990.i		−	0.598548i
$610$	−295505.	+	306546.i	−0.794154	+	0.823827i
$611$			425109.i			1.13872i
$612$	347234.	−	12740.3i	0.927085	−	0.0340154i
$613$	−435542.			−1.15907			−0.579534	−	0.814948i	$-0.696765\pi$
$613$	−435542.			−1.15907			−0.579534	+	0.814948i	$0.696765\pi$
$614$	314364.	+	303041.i	0.833866	+	0.803832i
$615$	91693.9	+	164013.i	0.242432	+	0.433638i
$616$	390738.	+	349951.i	1.02973	+	0.922243i
$617$	560342.			1.47192			0.735958	−	0.677027i	$-0.236732\pi$
$617$	560342.			1.47192			0.735958	+	0.677027i	$0.236732\pi$
$618$	−41302.4	−	39814.8i	−0.108143	−	0.104248i
$619$			361826.i			0.944317i	0.881514	+	0.472159i	$0.156525\pi$
$619$			361826.i			0.944317i	−0.881514	+	0.472159i	$0.843475\pi$
$620$	−353835.	+	12982.4i	−0.920486	+	0.0337733i
$621$			132036.i			0.342381i
$622$	158200.	−	164111.i	0.408909	−	0.424187i
$623$			528397.i			1.36140i
$624$	8344.09	+	113555.i	0.0214294	+	0.291634i
$625$	−479772.			−1.22822
$626$	285640.	+	275352.i	0.728905	+	0.702652i
$627$	155362.			0.395194
$628$	575879.	−	21129.4i	1.46020	−	0.0535758i
$629$			669871.i			1.69313i
$630$	319056.	−	330977.i	0.803869	−	0.833904i
$631$		−	13114.2i		−	0.0329369i	−0.999864	−	0.0164685i	$-0.994758\pi$
$631$		−	13114.2i		−	0.0329369i	0.999864	−	0.0164685i	$-0.00524231\pi$
$632$	−146994.	−	131650.i	−0.368016	−	0.329600i
$633$	−163464.			−0.407959
$634$	385125.	+	371254.i	0.958127	+	0.923617i
$635$		−	223229.i		−	0.553608i
$636$	153522.	−	5632.82i	0.379538	−	0.0139255i
$637$			38784.3i			0.0955822i
$638$	−556115.	−	536085.i	−1.36623	−	1.31702i
$639$	505325.			1.23757
$640$	416296.	+	321119.i	1.01635	+	0.783981i
$641$		−	463484.i		−	1.12803i	−0.825766	−	0.564013i	$-0.809257\pi$
$641$		−	463484.i		−	1.12803i	0.825766	−	0.564013i	$-0.190743\pi$
$642$	184326.	+	177687.i	0.447215	+	0.431107i
$643$	−480367.			−1.16185			−0.580926	−	0.813956i	$-0.697309\pi$
$643$	−480367.			−1.16185			−0.580926	+	0.813956i	$0.697309\pi$
$644$	−210319.	+	7716.75i	−0.507115	+	0.0186064i
$645$			372187.i			0.894627i
$646$	257017.	+	247760.i	0.615881	+	0.593698i
$647$		−	530549.i		−	1.26741i	−0.773575	−	0.633705i	$-0.781533\pi$
$647$		−	530549.i		−	1.26741i	0.773575	−	0.633705i	$-0.218467\pi$
$648$	179240.	+	160530.i	0.426859	+	0.382301i
$649$		−	5435.36i		−	0.0129044i
$650$	−148826.	−	143466.i	−0.352251	−	0.339564i
$651$			124933.i			0.294791i
$652$	−685474.	+	25150.5i	−1.61248	+	0.0591632i
$653$		−	400782.i		−	0.939900i	−0.882693	−	0.469950i	$-0.844272\pi$
$653$		−	400782.i		−	0.939900i	0.882693	−	0.469950i	$-0.155728\pi$
$654$	113422.	+	109337.i	0.265181	+	0.255630i
$655$		−	185064.i		−	0.431360i
$656$	−236958.	−	359221.i	−0.550635	−	0.834746i
$657$	−265627.			−0.615376
$658$	480689.	−	498649.i	1.11023	−	1.15171i
$659$	461867.			1.06352			0.531760	−	0.846895i	$-0.321531\pi$
$659$	461867.			1.06352			0.531760	+	0.846895i	$0.321531\pi$
$660$	10334.4	+	281664.i	0.0237246	+	0.646611i
$661$	−800073.			−1.83116			−0.915581	−	0.402135i	$-0.868268\pi$
$661$	−800073.			−1.83116			−0.915581	+	0.402135i	$0.868268\pi$
$662$	−531188.	+	551035.i	−1.21208	+	1.25737i
$663$	−140258.			−0.319081
$664$	380464.	−	424808.i	0.862934	−	0.963511i
$665$	472319.			1.06805
$666$	−406105.	+	421278.i	−0.915566	+	0.949775i
$667$	309922.			0.696628
$668$	−11187.3	−	304908.i	−0.0250710	−	0.683307i
$669$			125218.i			0.279780i
$670$	−21477.6	+	22280.1i	−0.0478450	+	0.0496327i
$671$	522758.			1.16106
$672$	118614.	−	142635.i	0.262663	−	0.315854i
$673$		−	104565.i		−	0.230864i	−0.993315	−	0.115432i	$-0.963175\pi$
$673$		−	104565.i		−	0.230864i	0.993315	−	0.115432i	$-0.0368252\pi$
$674$	−488515.	+	506768.i	−1.07537	+	1.11555i
$675$	211294.			0.463746
$676$	−7191.25	−	195997.i	−0.0157366	−	0.428899i
$677$	693239.			1.51254			0.756268	−	0.654262i	$-0.227021\pi$
$677$	693239.			1.51254			0.756268	+	0.654262i	$0.227021\pi$
$678$	−62318.6	+	64647.0i	−0.135568	+	0.140634i
$679$			710386.i			1.54083i
$680$	−432080.	+	482439.i	−0.934428	+	1.04334i
$681$	192604.			0.415308
$682$	312973.	+	301700.i	0.672881	+	0.648645i
$683$	−29926.6			−0.0641528			−0.0320764	−	0.999485i	$-0.510212\pi$
$683$	−29926.6			−0.0641528			−0.0320764	+	0.999485i	$0.510212\pi$
$684$	11433.9	+	311630.i	0.0244390	+	0.666080i
$685$			874833.i			1.86442i
$686$	−302794.	+	314107.i	−0.643426	+	0.667466i
$687$		−	82728.4i		−	0.175284i
$688$	−62464.7	−	850087.i	−0.131965	−	1.79592i
$689$	351942.			0.741366
$690$	−81417.8	−	78485.3i	−0.171010	−	0.164851i
$691$	229464.			0.480572			0.240286	−	0.970702i	$-0.422759\pi$
$691$	229464.			0.480572			0.240286	+	0.970702i	$0.422759\pi$
$692$	15637.3	+	426194.i	0.0326551	+	0.890010i
$693$	−564420.			−1.17527
$694$	−364881.	+	378514.i	−0.757587	+	0.785893i
$695$		−	329177.i		−	0.681491i
$696$	−182255.	+	203497.i	−0.376236	+	0.420087i
$697$	462700.	−	258680.i	0.952432	−	0.532472i
$698$	−435837.	+	452121.i	−0.894567	+	0.927991i
$699$		−	143841.i		−	0.294393i
$700$	12348.9	+	336568.i	0.0252019	+	0.686873i
$701$	363642.			0.740011			0.370005	−	0.929030i	$-0.379356\pi$
$701$	363642.			0.740011			0.370005	+	0.929030i	$0.379356\pi$
$702$	−191957.	−	185043.i	−0.389521	−	0.375491i
$703$	−601184.			−1.21646
$704$	−70876.2	−	641594.i	−0.143006	−	1.29454i
$705$	372165.			0.748785
$706$	−562588.	+	583609.i	−1.12871	+	1.17088i
$707$			102862.i			0.205787i
$708$	−1920.99	+	70.4826i	−0.00383230	+	0.000140610i
$709$		−	289108.i		−	0.575132i	−0.957761	−	0.287566i	$-0.907154\pi$
$709$		−	289108.i		−	0.575132i	0.957761	−	0.287566i	$-0.0928460\pi$
$710$	−653680.	+	678103.i	−1.29673	+	1.34518i
$711$	212333.			0.420028
$712$	433816.	−	484378.i	0.855747	−	0.955486i
$713$	−174419.			−0.343096
$714$	164522.	+	158596.i	0.322720	+	0.311097i
$715$			645703.i			1.26305i
$716$	2.74392	+	74.7851i	5.35236e−6	+	0.000145878i
$717$	−359393.			−0.699088
$718$	−186951.	−	180218.i	−0.362643	−	0.349581i
$719$	558642.			1.08063			0.540314	−	0.841464i	$-0.318306\pi$
$719$	558642.			1.08063			0.540314	+	0.841464i	$0.318306\pi$
$720$	−564208.	+	41458.2i	−1.08837	+	0.0799734i
$721$			214127.i			0.411908i
$722$	139428.	−	144637.i	0.267470	−	0.277464i
$723$	55427.6			0.106035
$724$	874168.	−	32073.9i	1.66770	−	0.0611891i
$725$		−	495960.i		−	0.943563i
$726$	98581.1	−	102264.i	0.187034	−	0.194022i
$727$	515470.			0.975291			0.487646	−	0.873042i	$-0.337856\pi$
$727$	515470.			0.975291			0.487646	+	0.873042i	$0.337856\pi$
$728$	283534.	−	316581.i	0.534987	−	0.597341i
$729$	−111614.			−0.210021
$730$	343610.	−	356448.i	0.644792	−	0.668884i
$731$	1.04999e6			1.96494
$732$	−6778.82	−	184756.i	−0.0126512	−	0.344807i
$733$	−129073.			−0.240230			−0.120115	−	0.992760i	$-0.538326\pi$
$733$	−129073.			−0.240230			−0.120115	+	0.992760i	$0.538326\pi$
$734$	−221281.	−	213311.i	−0.410727	−	0.395933i
$735$	33954.0			0.0628516
$736$	199133.	+	165598.i	0.367611	+	0.305704i
$737$	37994.7			0.0699500
$738$	447813.	+	117827.i	0.822212	+	0.216337i
$739$			242229.i			0.443544i	0.975099	+	0.221772i	$0.0711840\pi$
$739$			242229.i			0.443544i	−0.975099	+	0.221772i	$0.928816\pi$
$740$	−39989.8	−	1.08992e6i	−0.0730274	−	1.99035i
$741$		−	125876.i		−	0.229249i
$742$	−412825.	−	397956.i	−0.749822	−	0.722815i
$743$			959310.i			1.73773i	0.495053	+	0.868863i	$0.335149\pi$
$743$			959310.i			1.73773i	−0.495053	+	0.868863i	$0.664851\pi$
$744$	102570.	−	114525.i	0.185300	−	0.206897i
$745$		−	717327.i		−	1.29242i
$746$	−342823.	+	355632.i	−0.616016	+	0.639032i
$747$			613634.i			1.09968i
$748$	794608.	−	29154.7i	1.42020	−	0.0521082i
$749$		−	955613.i		−	1.70341i
$750$	68348.5	−	70902.2i	0.121508	−	0.126048i
$751$	118013.			0.209242			0.104621	−	0.994512i	$-0.466637\pi$
$751$	118013.			0.209242			0.104621	+	0.994512i	$0.466637\pi$
$752$	−850036.	+	62461.0i	−1.50315	+	0.110452i
$753$			63277.1i			0.111598i
$754$	−434343.	+	450571.i	−0.763994	+	0.792540i
$755$	−635165.			−1.11428
$756$	15927.8	+	434109.i	0.0278683	+	0.759547i
$757$		−	373355.i		−	0.651523i	−0.945452	−	0.325762i	$-0.894379\pi$
$757$		−	373355.i		−	0.651523i	0.945452	−	0.325762i	$-0.105621\pi$
$758$	199873.	+	192674.i	0.347870	+	0.335340i
$759$			138843.i			0.241013i
$760$	−432971.	−	387775.i	−0.749604	−	0.671356i
$761$	264183.			0.456180			0.228090	−	0.973640i	$-0.426752\pi$
$761$	264183.			0.456180			0.228090	+	0.973640i	$0.426752\pi$
$762$	69783.6	+	67270.1i	0.120183	+	0.115854i
$763$		−	588023.i		−	1.01005i
$764$	13795.0	+	375980.i	0.0236339	+	0.644137i
$765$		−	696882.i		−	1.19079i
$766$	106986.	−	110984.i	0.182336	−	0.189148i
$767$	−4403.80			−0.00748577
$768$	−225836.	+	33369.2i	−0.382888	+	0.0565749i
$769$	−416691.			−0.704630			−0.352315	−	0.935882i	$-0.614605\pi$
$769$	−416691.			−0.704630			−0.352315	+	0.935882i	$0.614605\pi$
$770$	730124.	−	757404.i	1.23145	−	1.27746i
$771$			96544.6i			0.162412i
$772$	−553347.	+	20302.7i	−0.928459	+	0.0340658i
$773$			140596.i			0.235296i	0.993055	+	0.117648i	$0.0375355\pi$
$773$			140596.i			0.235296i	−0.993055	+	0.117648i	$0.962464\pi$
$774$	660331.	+	636547.i	1.10225	+	1.06255i
$775$			279119.i			0.464714i
$776$	583229.	−	651206.i	0.968536	−	1.08142i
$777$	−384829.			−0.637421
$778$	360790.	−	374270.i	0.596067	−	0.618338i
$779$	232155.	+	415256.i	0.382564	+	0.684291i
$780$	228207.	−	8373.10i	0.375094	−	0.0137625i
$781$	1.15638e6			1.89583
$782$	−221417.	+	229690.i	−0.362074	+	0.375602i
$783$		−	639694.i		−	1.04340i
$784$	−77552.0	+	5698.55i	−0.126171	+	0.00927112i
$785$		−	1.15576e6i		−	1.87555i
$786$	57853.0	+	55769.3i	0.0936442	+	0.0902714i
$787$			354852.i			0.572925i	0.958091	+	0.286463i	$0.0924794\pi$
$787$			354852.i			0.572925i	−0.958091	+	0.286463i	$0.907521\pi$
$788$	−2977.72	−	81157.3i	−0.00479547	−	0.130700i
$789$	60195.1			0.0966957
$790$	−274670.	+	284932.i	−0.440105	+	0.456549i
$791$	335154.			0.535662
$792$	517400.	+	463391.i	0.824852	+	0.738749i
$793$		−	423545.i		−	0.673525i
$794$	32646.0	+	31470.1i	0.0517831	+	0.0499180i
$795$		−	308110.i		−	0.487497i
$796$	−695.458	−	18954.6i	−0.00109760	−	0.0299150i
$797$	−246279.			−0.387713			−0.193856	−	0.981030i	$-0.562100\pi$
$797$	−246279.			−0.387713			−0.193856	+	0.981030i	$0.562100\pi$
$798$	−142334.	+	147652.i	−0.223513	+	0.231864i
$799$		−	1.04992e6i		−	1.64461i
$800$	265003.	−	318668.i	0.414067	−	0.497918i
$801$			699682.i			1.09053i
$802$	−313275.	+	324980.i	−0.487053	+	0.505251i
$803$	−607857.			−0.942694
$804$	−492.693	−	13428.3i	−0.000762192	−	0.0207734i
$805$			422100.i			0.651363i
$806$	244441.	−	253575.i	0.376274	−	0.390333i
$807$	−82462.7			−0.126622
$808$	84450.3	−	94293.2i	0.129354	−	0.144430i
$809$			9807.71i			0.0149855i	0.999972	+	0.00749274i	$0.00238503\pi$
$809$			9807.71i			0.0149855i	−0.999972	+	0.00749274i	$0.997615\pi$
$810$	334923.	−	347437.i	0.510476	−	0.529549i
$811$		−	1.13037e6i		−	1.71862i	−0.511457	−	0.859309i	$-0.670894\pi$
$811$		−	1.13037e6i		−	1.71862i	0.511457	−	0.859309i	$-0.329106\pi$
$812$	1.01896e6	−	37386.4i	1.54542	−	0.0567024i
$813$		−	86929.9i		−	0.131519i
$814$	−929327.	+	964050.i	−1.40255	+	1.45496i
$815$			1.37571e6i			2.07115i
$816$	−20608.0	−	280456.i	−0.0309497	−	0.421196i
$817$			942322.i			1.41174i
$818$	−131503.	+	136416.i	−0.196529	+	0.203872i
$819$			457300.i			0.681763i
$820$	−737396.	+	448508.i	−1.09666	+	0.667026i
$821$	679193.			1.00764			0.503822	−	0.863808i	$-0.331927\pi$
$821$	679193.			1.00764			0.503822	+	0.863808i	$0.331927\pi$
$822$	−273482.	−	263632.i	−0.404749	−	0.390170i
$823$	−1.00435e6			−1.48281			−0.741405	−	0.671057i	$-0.765840\pi$
$823$	−1.00435e6			−1.48281			−0.741405	+	0.671057i	$0.765840\pi$
$824$	175799.	−	196288.i	0.258917	−	0.289095i
$825$	222187.			0.326446
$826$	5165.62	+	4979.56i	0.00757116	+	0.00729846i
$827$	1.17254e6			1.71442			0.857211	−	0.514966i	$-0.172195\pi$
$827$	1.17254e6			1.71442			0.857211	+	0.514966i	$0.172195\pi$
$828$	−278496.	+	10218.2i	−0.406217	+	0.0149044i
$829$	257967.			0.375367			0.187683	−	0.982230i	$-0.439902\pi$
$829$	257967.			0.375367			0.187683	+	0.982230i	$0.439902\pi$
$830$	−823445.	−	793786.i	−1.19530	−	1.15225i
$831$	354098.			0.512769
$832$	−519828.	+	57424.8i	−0.750953	+	0.0829570i
$833$		−	95788.4i		−	0.138046i
$834$	102904.	+	99197.9i	0.147945	+	0.142617i
$835$	−611935.			−0.877673
$836$	26165.3	+	713130.i	0.0374380	+	1.02037i
$837$			360010.i			0.513882i
$838$	−748628.	−	721664.i	−1.06605	−	1.02765i
$839$	−1.00831e6			−1.43243			−0.716213	−	0.697882i	$-0.754126\pi$
$839$	−1.00831e6			−1.43243			−0.716213	+	0.697882i	$0.754126\pi$
$840$	−277153.	−	248222.i	−0.392791	−	0.351789i
$841$	−794241.			−1.12295
$842$	−692107.	−	667179.i	−0.976223	−	0.941061i
$843$			101836.i			0.143300i
$844$	−27529.8	−	750322.i	−0.0386473	−	1.05333i
$845$	−393356.			−0.550899
$846$	636509.	−	660291.i	0.889332	−	0.922560i
$847$	−530176.			−0.739015
$848$	51710.6	+	703734.i	0.0719097	+	0.978626i
$849$		−	285088.i		−	0.395516i
$850$	367566.	+	354327.i	0.508742	+	0.490419i
$851$		−	537263.i		−	0.741870i
$852$	−14995.3	−	408694.i	−0.0206574	−	0.563014i
$853$	415576.			0.571153			0.285577	−	0.958356i	$-0.407815\pi$
$853$	415576.			0.571153			0.285577	+	0.958356i	$0.407815\pi$
$854$	−478921.	+	496815.i	−0.656671	+	0.681207i
$855$	625425.			0.855546
$856$	−784561.	+	876003.i	−1.07073	+	1.19552i
$857$	623946.			0.849543			0.424771	−	0.905301i	$-0.360355\pi$
$857$	623946.			0.849543			0.424771	+	0.905301i	$0.360355\pi$
$858$	−201853.	−	194583.i	−0.274196	−	0.264320i
$859$		−	728776.i		−	0.987661i	−0.869558	−	0.493830i	$-0.835596\pi$
$859$		−	728776.i		−	0.987661i	0.869558	−	0.493830i	$-0.164404\pi$
$860$	−1.70838e6	+	62681.8i	−2.30988	+	0.0847510i
$861$	148607.	+	265813.i	0.200463	+	0.358567i
$862$	−122209.	−	117807.i	−0.164470	−	0.158546i
$863$		−	502935.i		−	0.675290i	−0.941274	−	0.337645i	$-0.890370\pi$
$863$		−	502935.i		−	0.675290i	0.941274	−	0.337645i	$-0.109630\pi$
$864$	341804.	−	411021.i	0.457877	−	0.550600i
$865$	855350.			1.14317
$866$	−597114.	+	619425.i	−0.796199	+	0.825948i
$867$	55468.1			0.0737913
$868$	−573455.	+	21040.5i	−0.761132	+	0.0279265i
$869$	485900.			0.643440
$870$	394456.	+	380249.i	0.521147	+	0.502377i
$871$		−	30783.8i		−	0.0405775i
$872$	−482768.	+	539036.i	−0.634901	+	0.708900i
$873$			940665.i			1.23426i
$874$	−206138.	−	198713.i	−0.269858	−	0.260138i
$875$	−367583.			−0.480108
$876$	7882.34	+	214832.i	0.0102718	+	0.279957i
$877$	−628014.			−0.816527			−0.408263	−	0.912864i	$-0.633865\pi$
$877$	−628014.			−0.816527			−0.408263	+	0.912864i	$0.633865\pi$
$878$	20572.6	−	21341.2i	0.0266870	−	0.0276841i
$879$		−	397915.i		−	0.515006i
$880$	−1.29113e6	+	94872.7i	−1.66726	+	0.122511i
$881$	−1.36691e6			−1.76112			−0.880560	−	0.473935i	$-0.842833\pi$
$881$	−1.36691e6			−1.76112			−0.880560	+	0.473935i	$0.842833\pi$
$882$	58071.1	−	60240.8i	0.0746488	−	0.0774379i
$883$	372511.			0.477769			0.238884	−	0.971048i	$-0.423218\pi$
$883$	372511.			0.477769			0.238884	+	0.971048i	$0.423218\pi$
$884$	−23621.5	−	643801.i	−0.0302276	−	0.823848i
$885$			3855.34i			0.00492239i
$886$	863341.	+	832245.i	1.09980	+	1.06019i
$887$	713116.			0.906385			0.453193	−	0.891413i	$-0.350285\pi$
$887$	713116.			0.906385			0.453193	+	0.891413i	$0.350285\pi$
$888$	352770.	+	315946.i	0.447369	+	0.400670i
$889$		−	361784.i		−	0.457768i
$890$	−938914.	−	905096.i	−1.18535	−	1.14265i
$891$	−592491.			−0.746322
$892$	−574768.	+	21088.6i	−0.722375	+	0.0265044i
$893$	942266.			1.18160
$894$	224244.	+	216167.i	0.280573	+	0.270467i
$895$	150.090			0.000187372
$896$	674686.	+	520433.i	0.840400	+	0.648259i
$897$	112493.			0.139810
$898$	282924.	−	293495.i	0.350846	−	0.363955i
$899$	845033.			1.04557
$900$	16351.9	+	445670.i	0.0201876	+	0.550209i
$901$	−869217.			−1.07073
$902$	1.02477e6	+	269633.i	1.25954	+	0.331406i
$903$			603199.i			0.739750i
$904$	−307233.	−	275162.i	−0.375951	−	0.336707i
$905$		−	1.75441e6i		−	2.14208i
$906$	191408.	−	198559.i	0.233186	−	0.241899i
$907$		−	153338.i		−	0.186396i	−0.995648	−	0.0931979i	$-0.970291\pi$
$907$		−	153338.i		−	0.186396i	0.995648	−	0.0931979i	$-0.0297089\pi$
$908$	32437.3	+	884073.i	0.0393435	+	1.07230i
$909$			136206.i			0.164843i
$910$	−613658.	−	591555.i	−0.741043	−	0.714353i
$911$			812496.i			0.979004i	0.872002	+	0.489502i	$0.162821\pi$
$911$			812496.i			0.979004i	−0.872002	+	0.489502i	$0.837179\pi$
$912$	251699.	−	18494.9i	0.302616	−	0.0222363i
$913$			1.40423e6i			1.68461i
$914$	280773.	+	270661.i	0.336096	+	0.323991i
$915$	−370796.			−0.442887
$916$	379733.	−	13932.7i	0.452572	−	0.0166052i
$917$		−	299931.i		−	0.356684i
$918$	474091.	+	457015.i	0.562570	+	0.542307i
$919$	−97664.7			−0.115640			−0.0578198	−	0.998327i	$-0.518415\pi$
$919$	−97664.7			−0.115640			−0.0578198	+	0.998327i	$0.518415\pi$
$920$	346545.	−	386936.i	0.409434	−	0.457155i
$921$			380253.i			0.448284i
$922$	639479.	−	663373.i	0.752254	−	0.780361i
$923$		−	936915.i		−	1.09976i
$924$	16748.9	+	456489.i	0.0196174	+	0.534670i
$925$	−859768.			−1.00484
$926$	687224.	−	712901.i	0.801449	−	0.831394i
$927$			283538.i			0.329953i
$928$	−964768.	−	802298.i	−1.12028	−	0.931622i
$929$		−	19245.5i		−	0.0222997i	−0.999938	−	0.0111498i	$-0.996451\pi$
$929$		−	19245.5i		−	0.0222997i	0.999938	−	0.0111498i	$-0.00354918\pi$
$930$	−221994.	−	213998.i	−0.256670	−	0.247425i
$931$	85966.4			0.0991812
$932$	660246.	−	24224.9i	0.760105	−	0.0278888i
$933$	198508.			0.228042
$934$	−1.13247e6	−	1.09168e6i	−1.29817	−	1.25141i
$935$		−	1.59474e6i		−	1.82417i
$936$	375445.	−	419204.i	0.428543	−	0.478491i
$937$		−	219618.i		−	0.250143i	−0.992148	−	0.125072i	$-0.960084\pi$
$937$		−	219618.i		−	0.250143i	0.992148	−	0.125072i	$-0.0399160\pi$
$938$	−34808.5	+	36109.1i	−0.0395622	+	0.0410403i
$939$			345509.i			0.391857i
$940$	62678.1	+	1.70828e6i	0.0709349	+	1.93332i
$941$	−843971.			−0.953122			−0.476561	−	0.879141i	$-0.658117\pi$
$941$	−843971.			−0.953122			−0.476561	+	0.879141i	$0.658117\pi$
$942$	361303.	+	348290.i	0.407165	+	0.392500i
$943$	−371104.	+	207471.i	−0.417323	+	0.233311i
$944$	−647.047	−	8805.71i	−0.000726092	−	0.00988145i
$945$	871235.			0.975600
$946$	1.51109e6	+	1.45667e6i	1.68853	+	1.62772i
$947$			504035.i			0.562032i	0.959703	+	0.281016i	$0.0906714\pi$
$947$			504035.i			0.562032i	−0.959703	+	0.281016i	$0.909329\pi$
$948$	−6300.87	−	171729.i	−0.00701107	−	0.191086i
$949$			492494.i			0.546850i
$950$	−317995.	+	329877.i	−0.352350	+	0.365515i
$951$			465845.i			0.515086i
$952$	−700266.	+	781883.i	−0.772661	+	0.862716i
$953$	169107.			0.186198			0.0930990	−	0.995657i	$-0.470323\pi$
$953$	169107.			0.186198			0.0930990	+	0.995657i	$0.470323\pi$
$954$	−546646.	−	526957.i	−0.600633	−	0.579000i
$955$	754574.			0.827362
$956$	−60527.1	−	1.64966e6i	−0.0662269	−	1.80500i
$957$		−	672673.i		−	0.734481i
$958$	−226702.	+	235172.i	−0.247015	+	0.256245i
$959$			1.41783e6i			1.54166i
$960$	50273.0	+	455087.i	0.0545497	+	0.493801i
$961$	447950.			0.485045
$962$	781085.	+	752952.i	0.844011	+	0.813612i
$963$		−	1.26538e6i		−	1.36449i
$964$	9334.82	+	254419.i	0.0100450	+	0.273776i
$965$			1.11054e6i			1.19256i
$966$	−131953.	−	127200.i	−0.141405	−	0.136312i
$967$	−68712.0			−0.0734817			−0.0367409	−	0.999325i	$-0.511698\pi$
$967$	−68712.0			−0.0734817			−0.0367409	+	0.999325i	$0.511698\pi$
$968$	486008.	+	435276.i	0.518672	+	0.464530i
$969$			310886.i			0.331096i
$970$	−1.26229e6	−	1.21683e6i	−1.34158	−	1.29326i
$971$	−365507.			−0.387665			−0.193833	−	0.981035i	$-0.562092\pi$
$971$	−365507.			−0.387665			−0.193833	+	0.981035i	$0.562092\pi$
$972$	32490.2	+	885515.i	0.0343890	+	0.937267i
$973$		−	533493.i		−	0.563512i
$974$	−229584.	−	221315.i	−0.242004	−	0.233288i
$975$		−	180019.i		−	0.189369i
$976$	846910.	−	62231.2i	0.889073	−	0.0653294i
$977$		−	768500.i		−	0.805110i	−0.915396	−	0.402555i	$-0.868122\pi$
$977$		−	768500.i		−	0.805110i	0.915396	−	0.402555i	$-0.131878\pi$
$978$	−430062.	−	414572.i	−0.449628	−	0.433434i
$979$			1.60115e6i			1.67057i
$980$	5718.35	+	155853.i	0.00595414	+	0.162279i
$981$		−	778636.i		−	0.809089i
$982$	−441159.	−	425269.i	−0.457480	−	0.441003i
$983$			974269.i			1.00826i	0.863628	+	0.504129i	$0.168186\pi$
$983$			974269.i			1.00826i	−0.863628	+	0.504129i	$0.831814\pi$
$984$	82006.5	−	365676.i	0.0846950	−	0.377665i
$985$	−162879.			−0.167877
$986$	1.07273e6	−	1.11281e6i	1.10341	−	1.14463i
$987$	603163.			0.619156
$988$	577787.	−	21199.4i	0.591908	−	0.0217175i
$989$	−842130.			−0.860967
$990$	966800.	−	1.00292e6i	0.986430	−	1.02329i
$991$	−425212.			−0.432970			−0.216485	−	0.976286i	$-0.569459\pi$
$991$	−425212.			−0.432970			−0.216485	+	0.976286i	$0.569459\pi$
$992$	542956.	+	451521.i	0.551749	+	0.458833i
$993$	−666529.			−0.675959
$994$	−1.05941e6	+	1.09899e6i	−1.07224	+	1.11230i
$995$	−38041.0			−0.0384243
$996$	496292.	−	18209.3i	0.500286	−	0.0183559i
$997$		−	1.06584e6i		−	1.07226i	−0.844135	−	0.536131i	$-0.819885\pi$
$997$		−	1.06584e6i		−	1.07226i	0.844135	−	0.536131i	$-0.180115\pi$
$998$	427787.	−	443770.i	0.429503	−	0.445551i
$999$	−1.10894e6			−1.11116

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	164.5.d.f.163.15	yes	72
4.3	odd	2	inner	164.5.d.f.163.14	yes	72
41.40	even	2	inner	164.5.d.f.163.16	yes	72
164.163	odd	2	inner	164.5.d.f.163.13	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
164.5.d.f.163.13	✓	72	164.163	odd	2	inner
164.5.d.f.163.14	yes	72	4.3	odd	2	inner
164.5.d.f.163.15	yes	72	1.1	even	1	trivial
164.5.d.f.163.16	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)

\(f(q)\)	\(=\)	\(q+(-2.77609 + 2.87981i) q^{2} -3.48340 q^{3} +(-0.586657 - 15.9892i) q^{4} -32.0896 q^{5} +(9.67024 - 10.0316i) q^{6} -52.0073 q^{7} +(47.6747 + 42.6981i) q^{8} -68.8659 q^{9} +O(q^{10})\)	\(q+(-2.77609 + 2.87981i) q^{2} -3.48340 q^{3} +(-0.586657 - 15.9892i) q^{4} -32.0896 q^{5} +(9.67024 - 10.0316i) q^{6} -52.0073 q^{7} +(47.6747 + 42.6981i) q^{8} -68.8659 q^{9} +(89.0837 - 92.4122i) q^{10} -157.592 q^{11} +(2.04356 + 55.6970i) q^{12} +127.683i q^{13} +(144.377 - 149.771i) q^{14} +111.781 q^{15} +(-255.312 + 18.7604i) q^{16} -315.348i q^{17} +(191.178 - 198.321i) q^{18} +283.013 q^{19} +(18.8256 + 513.089i) q^{20} +181.162 q^{21} +(437.490 - 453.836i) q^{22} +252.922i q^{23} +(-166.070 - 148.735i) q^{24} +404.744 q^{25} +(-367.704 - 354.460i) q^{26} +522.044 q^{27} +(30.5104 + 831.556i) q^{28} -1225.37i q^{29} +(-310.314 + 321.909i) q^{30} +689.617i q^{31} +(654.742 - 787.331i) q^{32} +548.957 q^{33} +(908.144 + 875.435i) q^{34} +1668.89 q^{35} +(40.4006 + 1101.11i) q^{36} -2124.23 q^{37} +(-785.670 + 815.025i) q^{38} -444.772i q^{39} +(-1529.86 - 1370.17i) q^{40} +(820.299 + 1467.27i) q^{41} +(-502.923 + 521.714i) q^{42} +3329.61i q^{43} +(92.4525 + 2519.78i) q^{44} +2209.88 q^{45} +(-728.368 - 702.134i) q^{46} +3329.41 q^{47} +(889.354 - 65.3500i) q^{48} +303.754 q^{49} +(-1123.61 + 1165.59i) q^{50} +1098.49i q^{51} +(2041.56 - 74.9061i) q^{52} -2756.37i q^{53} +(-1449.24 + 1503.39i) q^{54} +5057.07 q^{55} +(-2479.43 - 2220.61i) q^{56} -985.849 q^{57} +(3528.83 + 3401.73i) q^{58} +34.4901i q^{59} +(-65.5772 - 1787.30i) q^{60} -3317.16 q^{61} +(-1985.97 - 1914.44i) q^{62} +3581.53 q^{63} +(449.745 + 4071.23i) q^{64} -4097.30i q^{65} +(-1523.95 + 1580.89i) q^{66} -241.095 q^{67} +(-5042.18 + 185.001i) q^{68} -881.029i q^{69} +(-4633.00 + 4806.10i) q^{70} -7337.81 q^{71} +(-3283.16 - 2940.44i) q^{72} +3857.16 q^{73} +(5897.04 - 6117.37i) q^{74} -1409.89 q^{75} +(-166.032 - 4525.17i) q^{76} +8195.93 q^{77} +(1280.86 + 1234.73i) q^{78} -3083.28 q^{79} +(8192.86 - 602.014i) q^{80} +3759.65 q^{81} +(-6502.68 - 1710.96i) q^{82} -8910.57i q^{83} +(-106.280 - 2896.65i) q^{84} +10119.4i q^{85} +(-9588.65 - 9243.28i) q^{86} +4268.45i q^{87} +(-7513.15 - 6728.88i) q^{88} -10160.1i q^{89} +(-6134.83 + 6364.05i) q^{90} -6640.45i q^{91} +(4044.03 - 148.378i) q^{92} -2402.21i q^{93} +(-9242.73 + 9588.07i) q^{94} -9081.79 q^{95} +(-2280.73 + 2742.59i) q^{96} -13659.4i q^{97} +(-843.249 + 874.756i) q^{98} +10852.7 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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Database

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