LMFDB - Embedded newform 99.8.f.a.64.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [99,8,Mod(37,99)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("99.37"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(99, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	99.f (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$30.9261175229$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 11)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			64.5
Character	$\chi$	$=$	99.64
Dual form			99.8.f.a.82.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.78266 - 11.6418i) q^{2} +(-17.6695 - 12.8376i) q^{4} +(-31.6803 - 97.5020i) q^{5} +(601.350 + 436.906i) q^{7} +(1051.31 - 763.821i) q^{8} -1254.94 q^{10} +(401.213 + 4396.16i) q^{11} +(-2230.19 + 6863.81i) q^{13} +(7361.09 - 5348.14i) q^{14} +(-5779.42 - 17787.2i) q^{16} +(8334.56 + 25651.1i) q^{17} +(-20825.3 + 15130.5i) q^{19} +(-691.919 + 2129.51i) q^{20} +(52697.0 + 11958.3i) q^{22} +103362. q^{23} +(54701.5 - 39742.9i) q^{25} +(71471.3 + 51926.9i) q^{26} +(-5016.70 - 15439.8i) q^{28} +(-86363.5 - 62746.8i) q^{29} +(-15762.2 + 48511.1i) q^{31} -62602.6 q^{32} +330153. q^{34} +(23548.3 - 72474.1i) q^{35} +(226043. + 164230. i) q^{37} +(97371.5 + 299679. i) q^{38} +(-107780. - 78306.7i) q^{40} +(86569.6 - 62896.5i) q^{41} +399488. q^{43} +(49347.0 - 82828.4i) q^{44} +(390984. - 1.20333e6i) q^{46} +(-28842.7 + 20955.4i) q^{47} +(-83754.2 - 257769. i) q^{49} +(-255763. - 787159. i) q^{50} +(127521. - 92649.6i) q^{52} +(312401. - 961471. i) q^{53} +(415924. - 178391. i) q^{55} +965923. q^{56} +(-1.05717e6 + 768080. i) q^{58} +(-1.44375e6 - 1.04894e6i) q^{59} +(-63755.2 - 196218. i) q^{61} +(505135. + 367002. i) q^{62} +(502961. - 1.54796e6i) q^{64} +739889. q^{65} +1.61162e6 q^{67} +(182032. - 560238. i) q^{68} +(-754656. - 548290. i) q^{70} +(666655. + 2.05175e6i) q^{71} +(1.30220e6 + 946107. i) q^{73} +(2.76698e6 - 2.01033e6i) q^{74} +562212. q^{76} +(-1.67944e6 + 2.81892e6i) q^{77} +(313917. - 966136. i) q^{79} +(-1.55120e6 + 1.12701e6i) q^{80} +(-404767. - 1.24574e6i) q^{82} +(1.44767e6 + 4.45546e6i) q^{83} +(2.23699e6 - 1.62527e6i) q^{85} +(1.51113e6 - 4.65077e6i) q^{86} +(3.77968e6 + 4.31527e6i) q^{88} -5.83358e6 q^{89} +(-4.33997e6 + 3.15317e6i) q^{91} +(-1.82636e6 - 1.32692e6i) q^{92} +(134858. + 415049. i) q^{94} +(2.13501e6 + 1.55117e6i) q^{95} +(-4.59200e6 + 1.41327e7i) q^{97} -3.31771e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{2} - 505 q^{4} + 72 q^{5} + 68 q^{7} + 4545 q^{8} + 4240 q^{10} - 5952 q^{11} - 16564 q^{13} + 29544 q^{14} + 13279 q^{16} + 65592 q^{17} - 37804 q^{19} - 120702 q^{20} + 246233 q^{22} + 26304 q^{23}+ \cdots + 51534036 q^{98}+O(q^{100}) $ 24 * q - 3 * q^2 - 505 * q^4 + 72 * q^5 + 68 * q^7 + 4545 * q^8 + 4240 * q^10 - 5952 * q^11 - 16564 * q^13 + 29544 * q^14 + 13279 * q^16 + 65592 * q^17 - 37804 * q^19 - 120702 * q^20 + 246233 * q^22 + 26304 * q^23 - 210646 * q^25 + 336384 * q^26 + 92334 * q^28 + 231048 * q^29 + 141004 * q^31 + 260892 * q^32 + 1512162 * q^34 + 342588 * q^35 - 836112 * q^37 + 2387040 * q^38 - 1906028 * q^40 - 1930344 * q^41 + 2877456 * q^43 - 5822808 * q^44 - 4951876 * q^46 + 2462532 * q^47 - 6581826 * q^49 + 2698797 * q^50 + 1655498 * q^52 - 6157836 * q^53 + 11721612 * q^55 - 11431080 * q^56 - 15150140 * q^58 + 2480268 * q^59 - 4195044 * q^61 + 6436524 * q^62 + 11301151 * q^64 - 11117640 * q^65 + 16682528 * q^67 + 14718306 * q^68 - 16625944 * q^70 + 20942628 * q^71 - 456824 * q^73 - 8747736 * q^74 + 18091206 * q^76 - 13904988 * q^77 - 12976692 * q^79 + 11893596 * q^80 - 32706099 * q^82 + 4471404 * q^83 + 25528128 * q^85 - 20374383 * q^86 + 25246815 * q^88 + 2477316 * q^89 - 18339604 * q^91 - 1026678 * q^92 - 4961738 * q^94 + 25328772 * q^95 - 34034202 * q^97 + 51534036 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

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 $

$2$	3.78266	−	11.6418i	0.334343	−	1.02900i	−0.632702	−	0.774396i	$-0.718054\pi$
$2$	3.78266	−	11.6418i	0.334343	−	1.02900i	0.967045	−	0.254606i	$-0.0819459\pi$
$3$		0			0
$3$		0			0
$4$	−17.6695	−	12.8376i	−0.138043	−	0.100294i
$5$	−31.6803	−	97.5020i	−0.113343	−	0.348834i	0.878255	−	0.478193i	$-0.158708\pi$
$5$	−31.6803	−	97.5020i	−0.113343	−	0.348834i	−0.991598	+	0.129359i	$0.958708\pi$
$6$		0			0
$7$	601.350	+	436.906i	0.662650	+	0.481443i	0.867557	−	0.497338i	$-0.165689\pi$
$7$	601.350	+	436.906i	0.662650	+	0.481443i	−0.204907	+	0.978781i	$0.565689\pi$
$8$	1051.31	−	763.821i	0.725965	−	0.527445i
$9$		0			0
$10$	−1254.94			−0.396846
$11$	401.213	+	4396.16i	0.0908868	+	0.995861i
$11$	401.213	+	4396.16i	0.0908868	+	0.995861i
$12$		0			0
$13$	−2230.19	+	6863.81i	−0.281540	+	0.866491i	0.705875	+	0.708337i	$0.250554\pi$
$13$	−2230.19	+	6863.81i	−0.281540	+	0.866491i	−0.987414	+	0.158154i	$0.949446\pi$
$14$	7361.09	−	5348.14i	0.716958	−	0.520901i
$15$		0			0
$16$	−5779.42	−	17787.2i	−0.352748	−	1.08565i
$17$	8334.56	+	25651.1i	0.411444	+	1.26630i	0.915393	+	0.402562i	$0.131880\pi$
$17$	8334.56	+	25651.1i	0.411444	+	1.26630i	−0.503948	+	0.863734i	$0.668120\pi$
$18$		0			0
$19$	−20825.3	+	15130.5i	−0.696554	+	0.506076i	−0.878808	−	0.477175i	$-0.841661\pi$
$19$	−20825.3	+	15130.5i	−0.696554	+	0.506076i	0.182254	+	0.983251i	$0.441661\pi$
$20$	−691.919	+	2129.51i	−0.0193397	+	0.0595216i
$21$		0			0
$22$	52697.0	+	11958.3i	1.05513	+	0.239437i
$23$	103362.			1.77139			0.885695	−	0.464267i	$-0.153682\pi$
$23$	103362.			1.77139			0.885695	+	0.464267i	$0.153682\pi$
$24$		0			0
$25$	54701.5	−	39742.9i	0.700179	−	0.508710i
$26$	71471.3	+	51926.9i	0.797490	+	0.579410i
$27$		0			0
$28$	−5016.70	−	15439.8i	−0.0431882	−	0.132919i
$29$	−86363.5	−	62746.8i	−0.657563	−	0.477748i	0.208276	−	0.978070i	$-0.433215\pi$
$29$	−86363.5	−	62746.8i	−0.657563	−	0.477748i	−0.865839	+	0.500323i	$0.833215\pi$
$30$		0			0
$31$	−15762.2	+	48511.1i	−0.0950279	+	0.292466i	−0.987261	−	0.159109i	$-0.949138\pi$
$31$	−15762.2	+	48511.1i	−0.0950279	+	0.292466i	0.892233	+	0.451575i	$0.149138\pi$
$32$	−62602.6			−0.337728
$33$		0			0
$34$	330153.			1.44058
$35$	23548.3	−	72474.1i	0.0928370	−	0.285723i
$36$		0			0
$37$	226043.	+	164230.i	0.733644	+	0.533024i	0.890714	−	0.454564i	$-0.150205\pi$
$37$	226043.	+	164230.i	0.733644	+	0.533024i	−0.157070	+	0.987587i	$0.550205\pi$
$38$	97371.5	+	299679.i	0.287865	+	0.885958i
$39$		0			0
$40$	−107780.	−	78306.7i	−0.266273	−	0.193459i
$41$	86569.6	−	62896.5i	0.196165	−	0.142522i	−0.485367	−	0.874311i	$-0.661314\pi$
$41$	86569.6	−	62896.5i	0.196165	−	0.142522i	0.681532	+	0.731788i	$0.261314\pi$
$42$		0			0
$43$	399488.			0.766239			0.383120	−	0.923699i	$-0.374850\pi$
$43$	399488.			0.766239			0.383120	+	0.923699i	$0.374850\pi$
$44$	49347.0	−	82828.4i	0.0873325	−	0.146587i
$45$		0			0
$46$	390984.	−	1.20333e6i	0.592252	−	1.82276i
$47$	−28842.7	+	20955.4i	−0.0405222	+	0.0294411i	−0.607862	−	0.794043i	$-0.707973\pi$
$47$	−28842.7	+	20955.4i	−0.0405222	+	0.0294411i	0.567340	+	0.823484i	$0.307973\pi$
$48$		0			0
$49$	−83754.2	−	257769.i	−0.101700	−	0.313000i
$50$	−255763.	−	787159.i	−0.289363	−	0.890569i
$51$		0			0
$52$	127521.	−	92649.6i	0.125768	−	0.0913760i
$53$	312401.	−	961471.i	0.288235	−	0.887096i	−0.697175	−	0.716901i	$-0.745560\pi$
$53$	312401.	−	961471.i	0.288235	−	0.887096i	0.985410	−	0.170195i	$-0.0544399\pi$
$54$		0			0
$55$	415924.	−	178391.i	0.337089	−	0.144578i
$56$	965923.			0.734995
$57$		0			0
$58$	−1.05717e6	+	768080.i	−0.711455	+	0.516902i
$59$	−1.44375e6	−	1.04894e6i	−0.915185	−	0.664921i	0.0271359	−	0.999632i	$-0.491361\pi$
$59$	−1.44375e6	−	1.04894e6i	−0.915185	−	0.664921i	−0.942321	+	0.334711i	$0.891361\pi$
$60$		0			0
$61$	−63755.2	−	196218.i	−0.0359635	−	0.110684i	0.931463	−	0.363835i	$-0.118533\pi$
$61$	−63755.2	−	196218.i	−0.0359635	−	0.110684i	−0.967427	+	0.253151i	$0.918533\pi$
$62$	505135.	+	367002.i	0.269176	+	0.195568i
$63$		0			0
$64$	502961.	−	1.54796e6i	0.239831	−	0.738123i
$65$	739889.			0.334172
$66$		0			0
$67$	1.61162e6			0.654637			0.327319	−	0.944914i	$-0.393855\pi$
$67$	1.61162e6			0.654637			0.327319	+	0.944914i	$0.393855\pi$
$68$	182032.	−	560238.i	0.0702048	−	0.216068i
$69$		0			0
$70$	−754656.	−	548290.i	−0.262970	−	0.191059i
$71$	666655.	+	2.05175e6i	0.221053	+	0.680332i	0.998668	+	0.0515915i	$0.0164294\pi$
$71$	666655.	+	2.05175e6i	0.221053	+	0.680332i	−0.777615	+	0.628741i	$0.783571\pi$
$72$		0			0
$73$	1.30220e6	+	946107.i	0.391786	+	0.284649i	0.766187	−	0.642618i	$-0.222152\pi$
$73$	1.30220e6	+	946107.i	0.391786	+	0.284649i	−0.374401	+	0.927267i	$0.622152\pi$
$74$	2.76698e6	−	2.01033e6i	0.793771	−	0.576708i
$75$		0			0
$76$	562212.			0.146911
$77$	−1.67944e6	+	2.81892e6i	−0.419225	+	0.703664i
$78$		0			0
$79$	313917.	−	966136.i	0.0716341	−	0.220467i	−0.908830	−	0.417168i	$-0.863023\pi$
$79$	313917.	−	966136.i	0.0716341	−	0.220467i	0.980464	+	0.196701i	$0.0630228\pi$
$80$	−1.55120e6	+	1.12701e6i	−0.338728	+	0.246101i
$81$		0			0
$82$	−404767.	−	1.24574e6i	−0.0810693	−	0.249506i
$83$	1.44767e6	+	4.45546e6i	0.277904	+	0.855301i	0.988436	+	0.151636i	$0.0484542\pi$
$83$	1.44767e6	+	4.45546e6i	0.277904	+	0.855301i	−0.710532	+	0.703665i	$0.751546\pi$
$84$		0			0
$85$	2.23699e6	−	1.62527e6i	0.395092	−	0.287051i
$86$	1.51113e6	−	4.65077e6i	0.256187	−	0.788462i
$87$		0			0
$88$	3.77968e6	+	4.31527e6i	0.591242	+	0.675023i
$89$	−5.83358e6			−0.877142			−0.438571	−	0.898697i	$-0.644515\pi$
$89$	−5.83358e6			−0.877142			−0.438571	+	0.898697i	$0.644515\pi$
$90$		0			0
$91$	−4.33997e6	+	3.15317e6i	−0.603728	+	0.438634i
$92$	−1.82636e6	−	1.32692e6i	−0.244528	−	0.177660i
$93$		0			0
$94$	134858.	+	415049.i	0.0167466	+	0.0515409i
$95$	2.13501e6	+	1.55117e6i	0.255486	+	0.185621i
$96$		0			0
$97$	−4.59200e6	+	1.41327e7i	−0.510859	+	1.57226i	0.279834	+	0.960048i	$0.409721\pi$
$97$	−4.59200e6	+	1.41327e7i	−0.510859	+	1.57226i	−0.790693	+	0.612213i	$0.790279\pi$
$98$	−3.31771e6			−0.356080
$99$		0			0
$100$	−1.47675e6			−0.147675
$101$	−2.37590e6	+	7.31227e6i	−0.229458	+	0.706200i	0.768350	+	0.640030i	$0.221078\pi$
$101$	−2.37590e6	+	7.31227e6i	−0.229458	+	0.706200i	−0.997808	+	0.0661700i	$0.978922\pi$
$102$		0			0
$103$	9.83134e6	+	7.14289e6i	0.886507	+	0.644085i	0.934965	−	0.354740i	$-0.115431\pi$
$103$	9.83134e6	+	7.14289e6i	0.886507	+	0.644085i	−0.0484576	+	0.998825i	$0.515431\pi$
$104$	2.89811e6	+	8.91946e6i	0.252638	+	0.777539i
$105$		0			0
$106$	−1.00116e7	−	7.27384e6i	−0.816454	−	0.593189i
$107$	1.29955e7	−	9.44178e6i	1.02553	−	0.745093i	0.0581229	−	0.998309i	$-0.481488\pi$
$107$	1.29955e7	−	9.44178e6i	1.02553	−	0.745093i	0.967410	+	0.253216i	$0.0814885\pi$
$108$		0			0
$109$	−2.07604e7			−1.53547			−0.767737	−	0.640765i	$-0.778617\pi$
$109$	−2.07604e7			−1.53547			−0.767737	+	0.640765i	$0.778617\pi$
$110$	−503498.	−	5.51690e6i	−0.0360681	−	0.395204i
$111$		0			0
$112$	4.29590e6	−	1.32214e7i	0.288929	−	0.889231i
$113$	−4.98010e6	+	3.61825e6i	−0.324686	+	0.235898i	−0.738172	−	0.674612i	$-0.764311\pi$
$113$	−4.98010e6	+	3.61825e6i	−0.324686	+	0.235898i	0.413486	+	0.910510i	$0.364311\pi$
$114$		0			0
$115$	−3.27455e6	−	1.00780e7i	−0.200775	−	0.617921i
$116$	720478.	+	2.21740e6i	0.0428566	+	0.131899i
$117$		0			0
$118$	−1.76728e7	+	1.28401e7i	−0.990190	+	0.719415i
$119$	−6.19515e6	+	1.90667e7i	−0.337006	+	1.03720i
$120$		0			0
$121$	−1.91652e7	+	3.52759e6i	−0.983479	+	0.181021i
$122$	−2.52551e6			−0.125918
$123$		0			0
$124$	901277.	−	654816.i	0.0424504	−	0.0308421i
$125$	−1.20877e7	−	8.78221e6i	−0.553551	−	0.402178i
$126$		0			0
$127$	763181.	+	2.34883e6i	0.0330609	+	0.101751i	0.966225	−	0.257699i	$-0.0829643\pi$
$127$	763181.	+	2.34883e6i	0.0330609	+	0.101751i	−0.933164	+	0.359450i	$0.882964\pi$
$128$	−2.26013e7	−	1.64208e7i	−0.952572	−	0.692084i
$129$		0			0
$130$	2.79875e6	−	8.61366e6i	0.111728	−	0.343863i
$131$	6.36488e6			0.247367			0.123683	−	0.992322i	$-0.460529\pi$
$131$	6.36488e6			0.247367			0.123683	+	0.992322i	$0.460529\pi$
$132$		0			0
$133$	−1.91339e7			−0.705218
$134$	6.09621e6	−	1.87622e7i	0.218873	−	0.673623i
$135$		0			0
$136$	2.83551e7	+	2.06012e7i	0.966595	+	0.702273i
$137$	−3.33698e6	−	1.02702e7i	−0.110874	−	0.341236i	0.880190	−	0.474622i	$-0.157415\pi$
$137$	−3.33698e6	−	1.02702e7i	−0.110874	−	0.341236i	−0.991064	+	0.133386i	$0.957415\pi$
$138$		0			0
$139$	−1.68414e7	−	1.22360e7i	−0.531896	−	0.386445i	0.289170	−	0.957278i	$-0.406621\pi$
$139$	−1.68414e7	−	1.22360e7i	−0.531896	−	0.386445i	−0.821067	+	0.570832i	$0.806621\pi$
$140$	−1.34648e6	+	978276.i	−0.0414717	+	0.0301310i
$141$		0			0
$142$	2.64079e7			0.773971
$143$	−3.10692e7	−	7.05041e6i	−0.888493	−	0.201622i
$144$		0			0
$145$	−3.38191e6	+	1.04085e7i	−0.0921243	+	0.283530i
$146$	1.59402e7	−	1.15812e7i	0.423896	−	0.307978i
$147$		0			0
$148$	−1.88574e6	−	5.80371e6i	−0.0478152	−	0.147160i
$149$	−2.48940e6	−	7.66159e6i	−0.0616514	−	0.189744i	0.915487	−	0.402347i	$-0.131806\pi$
$149$	−2.48940e6	−	7.66159e6i	−0.0616514	−	0.189744i	−0.977138	+	0.212604i	$0.931806\pi$
$150$		0			0
$151$	−1.49263e7	+	1.08446e7i	−0.352803	+	0.256326i	−0.750044	−	0.661388i	$-0.769968\pi$
$151$	−1.49263e7	+	1.08446e7i	−0.352803	+	0.256326i	0.397241	+	0.917714i	$0.369968\pi$
$152$	−1.03369e7	+	3.18137e7i	−0.238747	+	0.734787i
$153$		0			0
$154$	2.64646e7	+	3.02148e7i	0.583907	+	0.666648i
$155$	5.22928e6			0.112793
$156$		0			0
$157$	3.50337e7	−	2.54534e7i	0.722498	−	0.524925i	−0.164683	−	0.986346i	$-0.552660\pi$
$157$	3.50337e7	−	2.54534e7i	0.722498	−	0.524925i	0.887181	+	0.461421i	$0.152660\pi$
$158$	−1.00602e7	−	7.30913e6i	−0.202911	−	0.147423i
$159$		0			0
$160$	1.98327e6	+	6.10388e6i	0.0382791	+	0.117811i
$161$	6.21569e7	+	4.51596e7i	1.17381	+	0.852824i
$162$		0			0
$163$	3.05975e7	−	9.41694e7i	0.553388	−	1.70315i	−0.146776	−	0.989170i	$-0.546890\pi$
$163$	3.05975e7	−	9.41694e7i	0.553388	−	1.70315i	0.700164	−	0.713982i	$-0.253110\pi$
$164$	−2.33708e6			−0.0413733
$165$		0			0
$166$	5.73457e7			0.973021
$167$	−2.20091e7	+	6.77370e7i	−0.365674	+	1.12543i	0.583884	+	0.811837i	$0.301532\pi$
$167$	−2.20091e7	+	6.77370e7i	−0.365674	+	1.12543i	−0.949558	+	0.313592i	$0.898468\pi$
$168$		0			0
$169$	8.62641e6	+	6.26745e6i	0.137476	+	0.0998821i
$170$	−1.04593e7	−	3.21906e7i	−0.163280	−	0.502525i
$171$		0			0
$172$	−7.05874e6	−	5.12848e6i	−0.105774	−	0.0768491i
$173$	4.51110e7	−	3.27751e7i	0.662402	−	0.481263i	−0.205071	−	0.978747i	$-0.565743\pi$
$173$	4.51110e7	−	3.27751e7i	0.662402	−	0.481263i	0.867473	+	0.497484i	$0.165743\pi$
$174$		0			0
$175$	5.02586e7			0.708888
$176$	7.58766e7	−	3.25437e7i	1.04909	−	0.449959i
$177$		0			0
$178$	−2.20664e7	+	6.79135e7i	−0.293266	+	0.902581i
$179$	3.08572e7	−	2.24191e7i	0.402134	−	0.292168i	−0.368275	−	0.929717i	$-0.620052\pi$
$179$	3.08572e7	−	2.24191e7i	0.402134	−	0.292168i	0.770410	+	0.637549i	$0.220052\pi$
$180$		0			0
$181$	−1.48317e7	−	4.56472e7i	−0.185915	−	0.572188i	0.814048	−	0.580798i	$-0.197259\pi$
$181$	−1.48317e7	−	4.56472e7i	−0.185915	−	0.572188i	−0.999963	+	0.00860977i	$0.997259\pi$
$182$	2.02921e7	+	6.24525e7i	0.249503	+	0.767892i
$183$		0			0
$184$	1.08666e8	−	7.89503e7i	1.28597	−	0.934310i
$185$	8.85163e6	−	2.72425e7i	0.102783	−	0.316334i
$186$		0			0
$187$	−1.09422e8	+	4.69316e7i	−1.22366	+	0.524831i
$188$	778653.			0.00854656
$189$		0			0
$190$	2.61345e7	−	1.89878e7i	0.276425	−	0.200834i
$191$	5.73733e7	+	4.16842e7i	0.595790	+	0.432867i	0.844382	−	0.535741i	$-0.179968\pi$
$191$	5.73733e7	+	4.16842e7i	0.595790	+	0.432867i	−0.248592	+	0.968608i	$0.579968\pi$
$192$		0			0
$193$	2.39574e7	+	7.37334e7i	0.239878	+	0.738267i	0.996437	+	0.0843423i	$0.0268789\pi$
$193$	2.39574e7	+	7.37334e7i	0.239878	+	0.738267i	−0.756559	+	0.653925i	$0.773121\pi$
$194$	1.47161e8	+	1.06919e8i	1.44706	+	1.05135i
$195$		0			0
$196$	−1.82925e6	+	5.62984e6i	−0.0173531	+	0.0534072i
$197$	−1.52795e8			−1.42389			−0.711947	−	0.702233i	$-0.752186\pi$
$197$	−1.52795e8			−1.42389			−0.711947	+	0.702233i	$0.752186\pi$
$198$		0			0
$199$	−1.32401e8			−1.19098			−0.595491	−	0.803362i	$-0.703043\pi$
$199$	−1.32401e8			−1.19098			−0.595491	+	0.803362i	$0.703043\pi$
$200$	2.71517e7	−	8.35643e7i	0.239989	−	0.738611i
$201$		0			0
$202$	7.61410e7	+	5.53197e7i	0.649963	+	0.472226i
$203$	−2.45202e7	−	7.54655e7i	−0.205726	−	0.633159i
$204$		0			0
$205$	−8.87509e6	−	6.44813e6i	−0.0719506	−	0.0522751i
$206$	1.20345e8	−	8.74357e7i	0.959163	−	0.696872i
$207$		0			0
$208$	1.34977e8			1.04001
$209$	−7.48715e7	−	8.54810e7i	−0.567289	−	0.647675i
$210$		0			0
$211$	3.56662e7	−	1.09769e8i	0.261377	−	0.804437i	−0.731128	−	0.682240i	$-0.761006\pi$
$211$	3.56662e7	−	1.09769e8i	0.261377	−	0.804437i	0.992506	−	0.122197i	$-0.0389940\pi$
$212$	−1.78630e7	+	1.29782e7i	−0.128759	+	0.0935489i
$213$		0			0
$214$	−6.07620e7	−	1.87006e8i	−0.423823	−	1.30439i
$215$	−1.26559e7	−	3.89509e7i	−0.0868478	−	0.267290i
$216$		0			0
$217$	−3.06734e7	+	2.22855e7i	−0.203776	+	0.148052i
$218$	−7.85294e7	+	2.41689e8i	−0.513375	+	1.58001i
$219$		0			0
$220$	−9.63926e6	−	2.18740e6i	−0.0610329	−	0.0138500i
$221$	−1.94652e8			−1.21307
$222$		0			0
$223$	−1.41324e8	+	1.02678e8i	−0.853392	+	0.620026i	−0.926079	−	0.377329i	$-0.876843\pi$
$223$	−1.41324e8	+	1.02678e8i	−0.853392	+	0.620026i	0.0726873	+	0.997355i	$0.476843\pi$
$224$	−3.76460e7	−	2.73515e7i	−0.223795	−	0.162597i
$225$		0			0
$226$	2.32851e7	+	7.16641e7i	0.134183	+	0.412973i
$227$	−1.00926e8	−	7.33272e7i	−0.572682	−	0.416078i	0.263396	−	0.964688i	$-0.415157\pi$
$227$	−1.00926e8	−	7.33272e7i	−0.572682	−	0.416078i	−0.836079	+	0.548610i	$0.815157\pi$
$228$		0			0
$229$	5.26141e7	−	1.61930e8i	0.289520	−	0.891050i	−0.695488	−	0.718538i	$-0.744812\pi$
$229$	5.26141e7	−	1.61930e8i	0.289520	−	0.891050i	0.985007	−	0.172512i	$-0.0551883\pi$
$230$	−1.29713e8			−0.702969
$231$		0			0
$232$	−1.38722e8			−0.729353
$233$	7.80393e7	−	2.40180e8i	0.404173	−	1.24392i	−0.517411	−	0.855737i	$-0.673104\pi$
$233$	7.80393e7	−	2.40180e8i	0.404173	−	1.24392i	0.921584	−	0.388180i	$-0.126896\pi$
$234$		0			0
$235$	2.95694e6	+	2.14834e6i	0.0148630	+	0.0107986i
$236$	1.20443e7	+	3.70685e7i	0.0596471	+	0.183575i
$237$		0			0
$238$	1.98537e8	+	1.44246e8i	0.954603	+	0.693560i
$239$	−3.67919e7	+	2.67309e7i	−0.174325	+	0.126654i	−0.671526	−	0.740981i	$-0.734361\pi$
$239$	−3.67919e7	+	2.67309e7i	−0.174325	+	0.126654i	0.497201	+	0.867635i	$0.334361\pi$
$240$		0			0
$241$	−1.50043e8			−0.690489			−0.345244	−	0.938513i	$-0.612204\pi$
$241$	−1.50043e8			−0.690489			−0.345244	+	0.938513i	$0.612204\pi$
$242$	−3.14279e7	+	2.36462e8i	−0.142548	+	1.07253i
$243$		0			0
$244$	−1.39246e6	+	4.28554e6i	−0.00613645	+	0.0188861i
$245$	−2.24796e7	+	1.63324e7i	−0.0976580	+	0.0709527i
$246$		0			0
$247$	−5.74085e7	−	1.76685e8i	−0.242402	−	0.746038i
$248$	2.04828e7	+	6.30397e7i	0.0852726	+	0.262442i
$249$		0			0
$250$	−1.47965e8	+	1.07503e8i	−0.598918	+	0.435140i
$251$	3.10836e7	−	9.56656e7i	0.124072	−	0.381854i	−0.869659	−	0.493653i	$-0.835661\pi$
$251$	3.10836e7	−	9.56656e7i	0.124072	−	0.381854i	0.993731	+	0.111799i	$0.0356612\pi$
$252$		0			0
$253$	4.14703e7	+	4.54397e8i	0.160996	+	1.76406i
$254$	3.02315e7			0.115756
$255$		0			0
$256$	−1.08114e8	+	7.85495e7i	−0.402757	+	0.292620i
$257$	−9.73577e7	−	7.07345e7i	−0.357770	−	0.259935i	0.394351	−	0.918960i	$-0.370969\pi$
$257$	−9.73577e7	−	7.07345e7i	−0.357770	−	0.259935i	−0.752121	+	0.659025i	$0.770969\pi$
$258$		0			0
$259$	6.41779e7	+	1.97519e8i	0.229528	+	0.706416i
$260$	−1.30734e7	−	9.49841e6i	−0.0461300	−	0.0335154i
$261$		0			0
$262$	2.40762e7	−	7.40989e7i	0.0827053	−	0.254541i
$263$	−1.77779e8			−0.602610			−0.301305	−	0.953528i	$-0.597422\pi$
$263$	−1.77779e8			−0.602610			−0.301305	+	0.953528i	$0.597422\pi$
$264$		0			0
$265$	−1.03642e8			−0.342119
$266$	−7.23771e7	+	2.22754e8i	−0.235785	+	0.725671i
$267$		0			0
$268$	−2.84765e7	−	2.06894e7i	−0.0903679	−	0.0656561i
$269$	−9.52997e7	−	2.93302e8i	−0.298510	−	0.918718i	−0.982020	−	0.188777i	$-0.939548\pi$
$269$	−9.52997e7	−	2.93302e8i	−0.298510	−	0.918718i	0.683510	−	0.729941i	$-0.260452\pi$
$270$		0			0
$271$	−4.69097e8	−	3.40819e8i	−1.43176	−	1.04023i	−0.989686	−	0.143255i	$-0.954243\pi$
$271$	−4.69097e8	−	3.40819e8i	−1.43176	−	1.04023i	−0.442073	−	0.896979i	$-0.645757\pi$
$272$	4.08093e8	−	2.96497e8i	1.22961	−	0.893366i
$273$		0			0
$274$	−1.32186e8			−0.388203
$275$	1.96663e8	+	2.24531e8i	0.570241	+	0.651046i
$276$		0			0
$277$	−2.73857e7	+	8.42845e7i	−0.0774185	+	0.238270i	−0.982275	−	0.187448i	$-0.939978\pi$
$277$	−2.73857e7	+	8.42845e7i	−0.0774185	+	0.238270i	0.904856	+	0.425718i	$0.139978\pi$
$278$	−2.06155e8	+	1.49780e8i	−0.575489	+	0.418117i
$279$		0			0
$280$	−3.06008e7	−	9.41794e7i	−0.0833065	−	0.256391i
$281$	1.21296e8	+	3.73311e8i	0.326118	+	1.00369i	0.970934	+	0.239349i	$0.0769341\pi$
$281$	1.21296e8	+	3.73311e8i	0.326118	+	1.00369i	−0.644816	+	0.764338i	$0.723066\pi$
$282$		0			0
$283$	5.30672e8	−	3.85556e8i	1.39179	−	1.01119i	0.396122	−	0.918198i	$-0.370356\pi$
$283$	5.30672e8	−	3.85556e8i	1.39179	−	1.01119i	0.995666	−	0.0929960i	$-0.0296444\pi$
$284$	1.45602e7	−	4.48117e7i	0.0377184	−	0.116085i
$285$		0			0
$286$	−1.99604e8	+	3.35033e8i	−0.504531	+	0.846850i
$287$	7.95385e7			0.198605
$288$		0			0
$289$	−2.56545e8	+	1.86390e8i	−0.625202	+	0.454236i
$290$	1.08381e8	+	7.87433e7i	0.260951	+	0.189592i
$291$		0			0
$292$	−1.08635e7	−	3.34344e7i	−0.0255346	−	0.0785875i
$293$	4.41284e8	+	3.20612e8i	1.02490	+	0.744634i	0.967282	−	0.253705i	$-0.0816493\pi$
$293$	4.41284e8	+	3.20612e8i	1.02490	+	0.744634i	0.0576185	+	0.998339i	$0.481649\pi$
$294$		0			0
$295$	−5.65357e7	+	1.73999e8i	−0.128217	+	0.394612i
$296$	3.63084e8			0.813740
$297$		0			0
$298$	−9.86115e7			−0.215859
$299$	−2.30517e8	+	7.09459e8i	−0.498717	+	1.53489i
$300$		0			0
$301$	2.40232e8	+	1.74539e8i	0.507748	+	0.368901i
$302$	6.97897e7	+	2.14791e8i	0.145803	+	0.448736i
$303$		0			0
$304$	3.89488e8	+	2.82980e8i	0.795127	+	0.577694i
$305$	−1.71119e7	+	1.24325e7i	−0.0345342	+	0.0250905i
$306$		0			0
$307$	−1.57160e8			−0.309998			−0.154999	−	0.987915i	$-0.549537\pi$
$307$	−1.57160e8			−0.309998			−0.154999	+	0.987915i	$0.549537\pi$
$308$	6.58630e7	−	2.82488e7i	0.128444	−	0.0550900i
$309$		0			0
$310$	1.97806e7	−	6.08784e7i	0.0377114	−	0.116064i
$311$	1.38961e8	−	1.00961e8i	0.261957	−	0.190323i	−0.449052	−	0.893505i	$-0.648238\pi$
$311$	1.38961e8	−	1.00961e8i	0.261957	−	0.190323i	0.711009	+	0.703183i	$0.248238\pi$
$312$		0			0
$313$	−5.99115e7	−	1.84389e8i	−0.110434	−	0.339882i	0.880533	−	0.473985i	$-0.157185\pi$
$313$	−5.99115e7	−	1.84389e8i	−0.110434	−	0.339882i	−0.990967	+	0.134102i	$0.957185\pi$
$314$	−1.63804e8	−	5.04137e8i	−0.298587	−	0.918957i
$315$		0			0
$316$	−1.79496e7	+	1.30412e7i	−0.0320000	+	0.0232494i
$317$	1.53171e8	−	4.71411e8i	0.270065	−	0.831175i	−0.720418	−	0.693540i	$-0.756050\pi$
$317$	1.53171e8	−	4.71411e8i	0.270065	−	0.831175i	0.990483	−	0.137635i	$-0.0439500\pi$
$318$		0			0
$319$	2.41195e8	−	4.04842e8i	0.416006	−	0.698262i
$320$	−1.66863e8			−0.284665
$321$		0			0
$322$	7.60858e8	−	5.52796e8i	1.27001	−	0.922719i
$323$	−5.61684e8	−	4.08088e8i	−0.927435	−	0.673821i
$324$		0			0
$325$	1.50794e8	+	4.64095e8i	0.243664	+	0.749920i
$326$	−9.80565e8	−	7.12422e8i	−1.56753	−	1.13887i
$327$		0			0
$328$	4.29698e7	−	1.32247e8i	0.0672364	−	0.206933i
$329$	−2.65001e7			−0.0410263
$330$		0			0
$331$	−1.01012e9			−1.53099			−0.765496	−	0.643440i	$-0.777507\pi$
$331$	−1.01012e9			−1.53099			−0.765496	+	0.643440i	$0.777507\pi$
$332$	3.16180e7	−	9.73101e7i	0.0474188	−	0.145940i
$333$		0			0
$334$	7.05330e8	+	5.12452e8i	1.03581	+	0.752559i
$335$	−5.10566e7	−	1.57136e8i	−0.0741985	−	0.228360i
$336$		0			0
$337$	7.31547e8	+	5.31500e8i	1.04121	+	0.756482i	0.970521	−	0.241017i	$-0.0774808\pi$
$337$	7.31547e8	+	5.31500e8i	1.04121	+	0.756482i	0.0706871	+	0.997499i	$0.477481\pi$
$338$	1.05595e8	−	7.67195e7i	0.148743	−	0.108068i
$339$		0			0
$340$	−6.03911e7			−0.0833291
$341$	−2.19586e8	−	4.98299e7i	−0.299892	−	0.0680533i
$342$		0			0
$343$	2.51419e8	−	7.73789e8i	0.336410	−	1.03536i
$344$	4.19986e8	−	3.05138e8i	0.556263	−	0.404149i
$345$		0			0
$346$	−2.10922e8	−	6.49152e8i	−0.273751	−	0.842520i
$347$	4.72029e8	+	1.45276e9i	0.606479	+	1.86655i	0.486285	+	0.873800i	$0.338352\pi$
$347$	4.72029e8	+	1.45276e9i	0.606479	+	1.86655i	0.120195	+	0.992750i	$0.461648\pi$
$348$		0			0
$349$	9.94789e8	−	7.22756e8i	1.25268	−	0.910129i	0.254310	−	0.967123i	$-0.418152\pi$
$349$	9.94789e8	−	7.22756e8i	1.25268	−	0.910129i	0.998375	+	0.0569940i	$0.0181516\pi$
$350$	1.90111e8	−	5.85103e8i	0.237012	−	0.729447i
$351$		0			0
$352$	−2.51170e7	−	2.75211e8i	−0.0306950	−	0.336330i
$353$	−4.99236e7			−0.0604080			−0.0302040	−	0.999544i	$-0.509616\pi$
$353$	−4.99236e7			−0.0604080			−0.0302040	+	0.999544i	$0.509616\pi$
$354$		0			0
$355$	1.78930e8	−	1.30000e8i	0.212268	−	0.154222i
$356$	1.03076e8	+	7.48892e7i	0.121083	+	0.0879720i
$357$		0			0
$358$	−1.44277e8	−	4.44038e8i	−0.166190	−	0.511481i
$359$	−6.76838e7	−	4.91751e7i	−0.0772065	−	0.0560938i	0.548512	−	0.836142i	$-0.315194\pi$
$359$	−6.76838e7	−	4.91751e7i	−0.0772065	−	0.0560938i	−0.625719	+	0.780049i	$0.715194\pi$
$360$		0			0
$361$	−7.14585e7	+	2.19927e8i	−0.0799426	+	0.246038i
$362$	−5.87520e8			−0.650942
$363$		0			0
$364$	1.17164e8			0.127333
$365$	5.09930e7	−	1.56940e8i	0.0548891	−	0.168931i
$366$		0			0
$367$	−2.58978e7	−	1.88159e7i	−0.0273484	−	0.0198698i	0.574027	−	0.818836i	$-0.305380\pi$
$367$	−2.58978e7	−	1.88159e7i	−0.0273484	−	0.0198698i	−0.601375	+	0.798967i	$0.705380\pi$
$368$	−5.97374e8	−	1.83853e9i	−0.624854	−	1.92310i
$369$		0			0
$370$	−2.83670e8	−	2.06098e8i	−0.291144	−	0.211528i
$371$	6.07935e8	−	4.41691e8i	0.618085	−	0.449065i
$372$		0			0
$373$	−1.75838e9			−1.75441			−0.877205	−	0.480115i	$-0.840595\pi$
$373$	−1.75838e9			−1.75441			−0.877205	+	0.480115i	$0.840595\pi$
$374$	1.32462e8	+	1.45140e9i	0.130930	+	1.43462i
$375$		0			0
$376$	−1.43164e7	+	4.40613e7i	−0.0138892	+	0.0427464i
$377$	6.23289e8	−	4.52846e8i	0.599094	−	0.435267i
$378$		0			0
$379$	−2.22930e8	−	6.86109e8i	−0.210345	−	0.647375i	−0.999451	−	0.0331188i	$-0.989456\pi$
$379$	−2.22930e8	−	6.86109e8i	−0.210345	−	0.647375i	0.789106	−	0.614256i	$-0.210544\pi$
$380$	−1.78111e7	−	5.48168e7i	−0.0166513	−	0.0512473i
$381$		0			0
$382$	7.02304e8	−	5.10253e8i	0.644619	−	0.468343i
$383$	−2.08217e8	+	6.40825e8i	−0.189374	+	0.582833i	−0.999996	−	0.00273659i	$-0.999129\pi$
$383$	−2.08217e8	+	6.40825e8i	−0.189374	+	0.582833i	0.810622	+	0.585569i	$0.199129\pi$
$384$		0			0
$385$	3.28056e8	+	7.44443e7i	0.292978	+	0.0664843i
$386$	9.49014e8			0.839880
$387$		0			0
$388$	2.62569e8	−	1.90767e8i	0.228209	−	0.165803i
$389$	1.59442e9	+	1.15841e9i	1.37334	+	0.997790i	0.997468	+	0.0711189i	$0.0226570\pi$
$389$	1.59442e9	+	1.15841e9i	1.37334	+	0.997790i	0.375873	+	0.926671i	$0.377343\pi$
$390$		0			0
$391$	8.61478e8	+	2.65136e9i	0.728829	+	2.24311i
$392$	−2.84941e8	−	2.07022e8i	−0.238921	−	0.173586i
$393$		0			0
$394$	−5.77972e8	+	1.77881e9i	−0.476069	+	1.46519i
$395$	−1.04145e8			−0.0850255
$396$		0			0
$397$	1.79667e9			1.44112			0.720561	−	0.693391i	$-0.243884\pi$
$397$	1.79667e9			1.44112			0.720561	+	0.693391i	$0.243884\pi$
$398$	−5.00828e8	+	1.54139e9i	−0.398197	+	1.22552i
$399$		0			0
$400$	−1.02306e9	−	7.43296e8i	−0.799265	−	0.580700i
$401$	−3.82289e8	−	1.17656e9i	−0.296064	−	0.911193i	−0.982862	−	0.184344i	$-0.940984\pi$
$401$	−3.82289e8	−	1.17656e9i	−0.296064	−	0.911193i	0.686797	−	0.726849i	$-0.259016\pi$
$402$		0			0
$403$	−2.97818e8	−	2.16378e8i	−0.226665	−	0.164682i
$404$	1.35853e8	−	9.87030e7i	0.102503	−	0.0744725i
$405$		0			0
$406$	−9.71308e8			−0.720304
$407$	−6.31289e8	+	1.05961e9i	−0.464139	+	0.779053i
$408$		0			0
$409$	−1.20413e8	+	3.70592e8i	−0.0870242	+	0.267833i	−0.985093	−	0.172022i	$-0.944970\pi$
$409$	−1.20413e8	+	3.70592e8i	−0.0870242	+	0.267833i	0.898069	+	0.439855i	$0.144970\pi$
$410$	−1.08639e8	+	7.89312e7i	−0.0778474	+	0.0565594i
$411$		0			0
$412$	−8.20169e7	−	2.52422e8i	−0.0577781	−	0.177823i
$413$	−4.09907e8	−	1.26156e9i	−0.286325	−	0.881219i
$414$		0			0
$415$	3.88553e8	−	2.82301e8i	0.266859	−	0.193885i
$416$	1.39616e8	−	4.29692e8i	0.0950839	−	0.292638i
$417$		0			0
$418$	−1.27837e9	+	5.48295e8i	−0.856128	+	0.367196i
$419$	2.14825e9			1.42671			0.713355	−	0.700803i	$-0.247175\pi$
$419$	2.14825e9			1.42671			0.713355	+	0.700803i	$0.247175\pi$
$420$		0			0
$421$	1.89969e8	−	1.38020e8i	0.124078	−	0.0901480i	−0.524015	−	0.851709i	$-0.675567\pi$
$421$	1.89969e8	−	1.38020e8i	0.124078	−	0.0901480i	0.648094	+	0.761561i	$0.275567\pi$
$422$	−1.14300e9	−	8.30439e8i	−0.740378	−	0.537916i
$423$		0			0
$424$	−4.05962e8	−	1.24942e9i	−0.258645	−	0.796029i
$425$	1.47536e9	+	1.07191e9i	0.932261	+	0.677328i
$426$		0			0
$427$	4.73899e7	−	1.45851e8i	0.0294570	−	0.0906592i
$428$	−3.50833e8			−0.216296
$429$		0			0
$430$	−5.01333e8			−0.304079
$431$	−7.71035e7	+	2.37300e8i	−0.0463878	+	0.142767i	−0.971568	−	0.236762i	$-0.923914\pi$
$431$	−7.71035e7	+	2.37300e8i	−0.0463878	+	0.142767i	0.925180	+	0.379529i	$0.123914\pi$
$432$		0			0
$433$	−5.62888e8	−	4.08962e8i	−0.333207	−	0.242089i	0.408583	−	0.912721i	$-0.366023\pi$
$433$	−5.62888e8	−	4.08962e8i	−0.333207	−	0.242089i	−0.741790	+	0.670632i	$0.766023\pi$
$434$	1.43417e8	+	4.41393e8i	0.0842146	+	0.259186i
$435$		0			0
$436$	3.66825e8	+	2.66514e8i	0.211961	+	0.153999i
$437$	−2.15255e9	+	1.56392e9i	−1.23387	+	0.896458i
$438$		0			0
$439$	3.16156e9			1.78351			0.891756	−	0.452516i	$-0.149473\pi$
$439$	3.16156e9			1.78351			0.891756	+	0.452516i	$0.149473\pi$
$440$	3.01006e8	−	5.05235e8i	0.168458	−	0.282754i
$441$		0			0
$442$	−7.36303e8	+	2.26611e9i	−0.405582	+	1.24825i
$443$	−3.24127e8	+	2.35492e8i	−0.177134	+	0.128695i	−0.672819	−	0.739807i	$-0.734917\pi$
$443$	−3.24127e8	+	2.35492e8i	−0.177134	+	0.128695i	0.495685	+	0.868502i	$0.334917\pi$
$444$		0			0
$445$	1.84810e8	+	5.68785e8i	0.0994179	+	0.305977i
$446$	6.60777e8	+	2.03366e9i	0.352682	+	1.08544i
$447$		0			0
$448$	9.78767e8	−	7.11116e8i	0.514288	−	0.373652i
$449$	−2.63362e6	+	8.10546e6i	−0.00137307	+	0.00422586i	−0.951741	−	0.306903i	$-0.900707\pi$
$449$	−2.63362e6	+	8.10546e6i	−0.00137307	+	0.00422586i	0.950368	+	0.311129i	$0.100707\pi$
$450$		0			0
$451$	3.11236e8	+	3.55339e8i	0.159761	+	0.182400i
$452$	1.34445e8			0.0684797
$453$		0			0
$454$	−1.23543e9	+	8.97594e8i	−0.619617	+	0.450178i
$455$	4.44932e8	+	3.23262e8i	0.221439	+	0.160885i
$456$		0			0
$457$	4.83215e7	+	1.48718e8i	0.0236828	+	0.0728882i	0.962199	−	0.272346i	$-0.0877995\pi$
$457$	4.83215e7	+	1.48718e8i	0.0236828	+	0.0728882i	−0.938517	+	0.345234i	$0.887800\pi$
$458$	−1.68613e9	−	1.22505e9i	−0.820093	−	0.595832i
$459$		0			0
$460$	−7.15183e7	+	2.20111e8i	−0.0342582	+	0.105436i
$461$	−2.07419e9			−0.986041			−0.493021	−	0.870018i	$-0.664107\pi$
$461$	−2.07419e9			−0.986041			−0.493021	+	0.870018i	$0.664107\pi$
$462$		0			0
$463$	−1.63176e9			−0.764051			−0.382025	−	0.924152i	$-0.624773\pi$
$463$	−1.63176e9			−0.764051			−0.382025	+	0.924152i	$0.624773\pi$
$464$	−6.16960e8	+	1.89881e9i	−0.286711	+	0.882405i
$465$		0			0
$466$	−2.50094e9	−	1.81704e9i	−1.14486	−	0.831790i
$467$	−1.05692e9	−	3.25288e9i	−0.480214	−	1.47795i	−0.838794	−	0.544448i	$-0.816739\pi$
$467$	−1.05692e9	−	3.25288e9i	−0.480214	−	1.47795i	0.358580	−	0.933499i	$-0.383261\pi$
$468$		0			0
$469$	9.69147e8	+	7.04127e8i	0.433795	+	0.315171i
$470$	3.61958e7	−	2.62978e7i	0.0160811	−	0.0116836i
$471$		0			0
$472$	−2.31903e9			−1.01510
$473$	1.60280e8	+	1.75621e9i	0.0696410	+	0.763068i
$474$		0			0
$475$	−5.37846e8	+	1.65532e9i	−0.230266	+	0.708687i
$476$	3.54236e8	−	2.57368e8i	0.150546	−	0.109378i
$477$		0			0
$478$	1.72025e8	+	5.29438e8i	0.0720433	+	0.221727i
$479$	−1.24957e9	−	3.84577e9i	−0.519499	−	1.59885i	−0.774944	−	0.632030i	$-0.782222\pi$
$479$	−1.24957e9	−	3.84577e9i	−0.519499	−	1.59885i	0.255445	−	0.966824i	$-0.417778\pi$
$480$		0			0
$481$	−1.63136e9	+	1.18525e9i	−0.668410	+	0.485628i
$482$	−5.67562e8	+	1.74678e9i	−0.230860	+	0.710514i
$483$		0			0
$484$	3.83925e8	+	1.83705e8i	0.153917	+	0.0736483i
$485$	1.52345e9			0.606360
$486$		0			0
$487$	−6.36476e8	+	4.62427e8i	−0.249707	+	0.181423i	−0.705597	−	0.708613i	$-0.749321\pi$
$487$	−6.36476e8	+	4.62427e8i	−0.249707	+	0.181423i	0.455890	+	0.890036i	$0.349321\pi$
$488$	−2.16902e8	−	1.57589e8i	−0.0844879	−	0.0613841i
$489$		0			0
$490$	1.05106e8	+	3.23484e8i	0.0403592	+	0.124213i
$491$	−2.33621e9	−	1.69736e9i	−0.890692	−	0.647126i	0.0453665	−	0.998970i	$-0.485554\pi$
$491$	−2.33621e9	−	1.69736e9i	−0.890692	−	0.647126i	−0.936058	+	0.351845i	$0.885554\pi$
$492$		0			0
$493$	8.89724e8	−	2.73829e9i	0.334419	−	1.02924i
$494$	−2.27410e9			−0.848720
$495$		0			0
$496$	9.53974e8			0.351035
$497$	−4.95531e8	+	1.52509e9i	−0.181060	+	0.557247i
$498$		0			0
$499$	−2.34471e9	−	1.70353e9i	−0.844768	−	0.613760i	0.0789301	−	0.996880i	$-0.474850\pi$
$499$	−2.34471e9	−	1.70353e9i	−0.844768	−	0.613760i	−0.923699	+	0.383120i	$0.874850\pi$
$500$	1.00840e8	+	3.10354e8i	0.0360777	+	0.111036i
$501$		0			0
$502$	−9.96143e8	−	7.23740e8i	−0.351446	−	0.255341i
$503$	1.17663e9	−	8.54869e8i	0.412241	−	0.299510i	−0.362268	−	0.932074i	$-0.617997\pi$
$503$	1.17663e9	−	8.54869e8i	0.412241	−	0.299510i	0.774508	+	0.632564i	$0.217997\pi$
$504$		0			0
$505$	7.88230e8			0.272354
$506$	5.44687e9	+	1.23604e9i	1.86905	+	0.424136i
$507$		0			0
$508$	1.66684e7	−	5.13000e7i	0.00564119	−	0.0173618i
$509$	1.92568e9	−	1.39909e9i	0.647250	−	0.470254i	−0.215083	−	0.976596i	$-0.569002\pi$
$509$	1.92568e9	−	1.39909e9i	0.647250	−	0.470254i	0.862333	+	0.506341i	$0.169002\pi$
$510$		0			0
$511$	3.69720e8	+	1.13788e9i	0.122575	+	0.377246i
$512$	−5.99512e8	−	1.84511e9i	−0.197403	−	0.607543i
$513$		0			0
$514$	−1.19175e9	+	8.65857e8i	−0.387092	+	0.281239i
$515$	3.84986e8	−	1.18486e9i	0.124199	−	0.382246i
$516$		0			0
$517$	−1.03695e8	−	1.18389e8i	−0.0330022	−	0.0376787i
$518$	2.54225e9			0.803645
$519$		0			0
$520$	7.77852e8	−	5.65143e8i	0.242597	−	0.176257i
$521$	−1.86357e9	−	1.35397e9i	−0.577317	−	0.419446i	0.260439	−	0.965490i	$-0.416133\pi$
$521$	−1.86357e9	−	1.35397e9i	−0.577317	−	0.419446i	−0.837756	+	0.546045i	$0.816133\pi$
$522$		0			0
$523$	−1.81572e9	−	5.58822e9i	−0.555001	−	1.70812i	−0.695941	−	0.718099i	$-0.745013\pi$
$523$	−1.81572e9	−	5.58822e9i	−0.555001	−	1.70812i	0.140941	−	0.990018i	$-0.454987\pi$
$524$	−1.12464e8	−	8.17100e7i	−0.0341471	−	0.0248094i
$525$		0			0
$526$	−6.72479e8	+	2.06968e9i	−0.201478	+	0.620087i
$527$	−1.37574e9			−0.409447
$528$		0			0
$529$	7.27892e9			2.13783
$530$	−3.92044e8	+	1.20659e9i	−0.114385	+	0.352041i
$531$		0			0
$532$	3.38086e8	+	2.45634e8i	0.0973502	+	0.0707291i
$533$	2.38643e8	+	7.34469e8i	0.0682660	+	0.210101i
$534$		0			0
$535$	−1.33229e9	−	9.67968e8i	−0.376150	−	0.273289i
$536$	1.69431e9	−	1.23099e9i	0.475244	−	0.345285i
$537$		0			0
$538$	−3.77506e9			−1.04517
$539$	1.09959e9	−	4.71617e8i	0.302461	−	0.129727i
$540$		0			0
$541$	−8.38525e8	+	2.58071e9i	−0.227680	+	0.700728i	0.770328	+	0.637648i	$0.220092\pi$
$541$	−8.38525e8	+	2.58071e9i	−0.227680	+	0.700728i	−0.998008	+	0.0630804i	$0.979908\pi$
$542$	−5.74219e9	+	4.17194e9i	−1.54910	+	1.12549i
$543$		0			0
$544$	−5.21765e8	−	1.60583e9i	−0.138956	−	0.427664i
$545$	6.57695e8	+	2.02418e9i	0.174035	+	0.535625i
$546$		0			0
$547$	3.51536e9	−	2.55406e9i	0.918362	−	0.667229i	−0.0247540	−	0.999694i	$-0.507880\pi$
$547$	3.51536e9	−	2.55406e9i	0.918362	−	0.667229i	0.943116	+	0.332465i	$0.107880\pi$
$548$	−7.28818e7	+	2.24307e8i	−0.0189185	+	0.0582252i
$549$		0			0
$550$	3.35786e9	−	1.44019e9i	0.860583	−	0.369107i
$551$	2.74794e9			0.699805
$552$		0			0
$553$	6.10885e8	−	4.43834e8i	0.153611	−	0.111605i
$554$	8.77635e8	+	6.37639e8i	0.219296	+	0.159328i
$555$		0			0
$556$	1.40498e8	+	4.32407e8i	0.0346663	+	0.106692i
$557$	1.54363e9	+	1.12151e9i	0.378486	+	0.274986i	0.760721	−	0.649079i	$-0.224846\pi$
$557$	1.54363e9	+	1.12151e9i	0.378486	+	0.274986i	−0.382235	+	0.924065i	$0.624846\pi$
$558$		0			0
$559$	−8.90934e8	+	2.74201e9i	−0.215727	+	0.663939i
$560$	−1.42521e9			−0.342942
$561$		0			0
$562$	4.80484e9			1.14183
$563$	−1.34565e9	+	4.14147e9i	−0.317798	+	0.978082i	0.656789	+	0.754074i	$0.271914\pi$
$563$	−1.34565e9	+	4.14147e9i	−0.317798	+	0.978082i	−0.974587	+	0.224008i	$0.928086\pi$
$564$		0			0
$565$	5.10558e8	+	3.70942e8i	0.119090	+	0.0865240i
$566$	−2.48122e9	−	7.63641e9i	−0.575185	−	1.77024i
$567$		0			0
$568$	2.26803e9	+	1.64782e9i	0.519315	+	0.377304i
$569$	5.34719e9	−	3.88496e9i	1.21684	−	0.884085i	0.221004	−	0.975273i	$-0.429066\pi$
$569$	5.34719e9	−	3.88496e9i	1.21684	−	0.884085i	0.995834	+	0.0911881i	$0.0290665\pi$
$570$		0			0
$571$	−5.10068e8			−0.114657			−0.0573287	−	0.998355i	$-0.518258\pi$
$571$	−5.10068e8			−0.114657			−0.0573287	+	0.998355i	$0.518258\pi$
$572$	4.58466e8	+	5.23431e8i	0.102428	+	0.116943i
$573$		0			0
$574$	3.00867e8	−	9.25973e8i	0.0664023	−	0.204365i
$575$	5.65406e9	−	4.10792e9i	1.24029	−	0.901123i
$576$		0			0
$577$	6.13855e8	+	1.88925e9i	0.133030	+	0.409425i	0.995278	−	0.0970610i	$-0.0309442\pi$
$577$	6.13855e8	+	1.88925e9i	0.133030	+	0.409425i	−0.862248	+	0.506486i	$0.830944\pi$
$578$	1.19951e9	+	3.69170e9i	0.258378	+	0.795204i
$579$		0			0
$580$	1.93376e8	−	1.40496e8i	0.0411534	−	0.0298997i
$581$	−1.07606e9	+	3.31178e9i	−0.227626	+	0.700560i
$582$		0			0
$583$	4.35212e9	+	9.87609e8i	0.909621	+	0.206417i
$584$	2.09168e9			0.434560
$585$		0			0
$586$	5.40173e9	−	3.92459e9i	1.10890	−	0.805661i
$587$	−6.91785e9	−	5.02611e9i	−1.41168	−	1.02565i	−0.993075	−	0.117482i	$-0.962518\pi$
$587$	−6.91785e9	−	5.02611e9i	−1.41168	−	1.02565i	−0.418609	−	0.908167i	$-0.637482\pi$
$588$		0			0
$589$	−4.05744e8	−	1.24875e9i	−0.0818179	−	0.251810i
$590$	1.81181e9	+	1.31636e9i	0.363188	+	0.263871i
$591$		0			0
$592$	1.61480e9	−	4.96983e9i	0.319884	−	0.984501i
$593$	−3.11643e9			−0.613714			−0.306857	−	0.951756i	$-0.599277\pi$
$593$	−3.11643e9			−0.613714			−0.306857	+	0.951756i	$0.599277\pi$
$594$		0			0
$595$	2.05531e9			0.400007
$596$	−5.43702e7	+	1.67334e8i	−0.0105196	+	0.0323760i
$597$		0			0
$598$	7.38743e9	+	5.36728e9i	1.41267	+	1.02636i
$599$	2.51412e9	+	7.73766e9i	0.477960	+	1.47101i	0.841924	+	0.539597i	$0.181423\pi$
$599$	2.51412e9	+	7.73766e9i	0.477960	+	1.47101i	−0.363964	+	0.931413i	$0.618577\pi$
$600$		0			0
$601$	−2.10681e9	−	1.53068e9i	−0.395880	−	0.287624i	0.371981	−	0.928241i	$-0.378679\pi$
$601$	−2.10681e9	−	1.53068e9i	−0.395880	−	0.287624i	−0.767861	+	0.640617i	$0.778679\pi$
$602$	2.94067e9	−	2.13652e9i	0.549362	−	0.399135i
$603$		0			0
$604$	4.02958e8			0.0744099
$605$	9.51108e8	+	1.75689e9i	0.174617	+	0.322553i
$606$		0			0
$607$	−1.40278e9	+	4.31730e9i	−0.254582	+	0.783524i	0.739329	+	0.673344i	$0.235143\pi$
$607$	−1.40278e9	+	4.31730e9i	−0.254582	+	0.783524i	−0.993912	+	0.110180i	$0.964857\pi$
$608$	1.30372e9	−	9.47208e8i	0.235246	−	0.170916i
$609$		0			0
$610$	8.00088e7	+	2.46242e8i	0.0142720	+	0.0439246i
$611$	−7.95096e7	−	2.44705e8i	−0.0141018	−	0.0434010i
$612$		0			0
$613$	−4.08679e9	+	2.96923e9i	−0.716590	+	0.520633i	−0.885293	−	0.465034i	$-0.846042\pi$
$613$	−4.08679e9	+	2.96923e9i	−0.716590	+	0.520633i	0.168703	+	0.985667i	$0.446042\pi$
$614$	−5.94484e8	+	1.82963e9i	−0.103646	+	0.318989i
$615$		0			0
$616$	3.87541e8	+	4.24635e9i	0.0668014	+	0.731953i
$617$	7.95634e9			1.36369			0.681844	−	0.731497i	$-0.261178\pi$
$617$	7.95634e9			1.36369			0.681844	+	0.731497i	$0.261178\pi$
$618$		0			0
$619$	−1.08653e9	+	7.89409e8i	−0.184130	+	0.133778i	−0.676032	−	0.736873i	$-0.736302\pi$
$619$	−1.08653e9	+	7.89409e8i	−0.184130	+	0.133778i	0.491902	+	0.870650i	$0.336302\pi$
$620$	−9.23986e7	−	6.71315e7i	−0.0155702	−	0.0113124i
$621$		0			0
$622$	−6.49727e8	−	1.99965e9i	−0.108259	−	0.333187i
$623$	−3.50802e9	−	2.54873e9i	−0.581238	−	0.422294i
$624$		0			0
$625$	1.15901e9	−	3.56706e9i	0.189892	−	0.584428i
$626$	−2.37324e9			−0.386663
$627$		0			0
$628$	−9.45787e8			−0.152382
$629$	−2.32871e9	+	7.16705e9i	−0.373112	+	1.14832i
$630$		0			0
$631$	−9.33777e9	−	6.78429e9i	−1.47959	−	1.07498i	−0.977690	−	0.210055i	$-0.932636\pi$
$631$	−9.33777e9	−	6.78429e9i	−1.47959	−	1.07498i	−0.501897	−	0.864928i	$-0.667364\pi$
$632$	−4.07932e8	−	1.25548e9i	−0.0642803	−	0.197834i
$633$		0			0
$634$	−4.90869e9	−	3.56637e9i	−0.764986	−	0.555795i
$635$	2.04838e8	−	1.48823e8i	0.0317470	−	0.0230655i
$636$		0			0
$637$	1.95607e9			0.299844
$638$	−3.80075e9	−	4.33933e9i	−0.579425	−	0.661531i
$639$		0			0
$640$	−8.85043e8	+	2.72388e9i	−0.133455	+	0.410732i
$641$	−7.22558e6	+	5.24969e6i	−0.00108360	+	0.000787283i	−0.588327	−	0.808623i	$-0.700213\pi$
$641$	−7.22558e6	+	5.24969e6i	−0.00108360	+	0.000787283i	0.587243	+	0.809410i	$0.300213\pi$
$642$		0			0
$643$	−1.11963e9	−	3.44587e9i	−0.166087	−	0.511164i	0.833027	−	0.553232i	$-0.186606\pi$
$643$	−1.11963e9	−	3.44587e9i	−0.166087	−	0.511164i	−0.999115	+	0.0420673i	$0.986606\pi$
$644$	−5.18537e8	−	1.59589e9i	−0.0765031	−	0.235452i
$645$		0			0
$646$	−6.87555e9	+	4.99538e9i	−1.00344	+	0.729045i
$647$	1.88219e9	−	5.79278e9i	0.273211	−	0.840856i	−0.716476	−	0.697611i	$-0.754246\pi$
$647$	1.88219e9	−	5.79278e9i	0.273211	−	0.840856i	0.989687	−	0.143245i	$-0.0457537\pi$
$648$		0			0
$649$	4.03207e9	−	6.76779e9i	0.578991	−	0.971830i
$650$	5.97331e9			0.853137
$651$		0			0
$652$	−1.74955e9	+	1.27112e9i	−0.247207	+	0.179606i
$653$	−5.21351e9	−	3.78784e9i	−0.732713	−	0.532347i	0.157707	−	0.987486i	$-0.449590\pi$
$653$	−5.21351e9	−	3.78784e9i	−0.732713	−	0.532347i	−0.890421	+	0.455139i	$0.849590\pi$
$654$		0			0
$655$	−2.01642e8	−	6.20589e8i	−0.0280373	−	0.0862898i
$656$	−1.61908e9	−	1.17633e9i	−0.223926	−	0.162691i
$657$		0			0
$658$	−1.00241e8	+	3.08510e8i	−0.0137168	+	0.0422161i
$659$	−4.17157e9			−0.567807			−0.283904	−	0.958853i	$-0.591630\pi$
$659$	−4.17157e9			−0.567807			−0.283904	+	0.958853i	$0.591630\pi$
$660$		0			0
$661$	−1.61108e9			−0.216976			−0.108488	−	0.994098i	$-0.534601\pi$
$661$	−1.61108e9			−0.216976			−0.108488	+	0.994098i	$0.534601\pi$
$662$	−3.82092e9	+	1.17596e10i	−0.511877	+	1.57539i
$663$		0			0
$664$	4.92512e9	+	3.57831e9i	0.652872	+	0.474340i
$665$	6.06169e8	+	1.86560e9i	0.0799315	+	0.246004i
$666$		0			0
$667$	−8.92673e9	−	6.48565e9i	−1.16480	−	0.846278i
$668$	1.25847e9	−	9.14332e8i	0.163352	−	0.118682i
$669$		0			0
$670$	−2.02248e9			−0.259790
$671$	8.37028e8	−	3.59003e8i	0.106957	−	0.0458743i
$672$		0			0
$673$	−2.58261e9	+	7.94844e9i	−0.326592	+	1.00515i	0.644125	+	0.764920i	$0.277222\pi$
$673$	−2.58261e9	+	7.94844e9i	−0.326592	+	1.00515i	−0.970717	+	0.240226i	$0.922778\pi$
$674$	8.95482e9	−	6.50606e9i	1.12654	−	0.818481i
$675$		0			0
$676$	−7.19648e7	−	2.21485e8i	−0.00895998	−	0.0275760i
$677$	3.79789e8	+	1.16887e9i	0.0470416	+	0.144779i	0.971818	−	0.235731i	$-0.0757484\pi$
$677$	3.79789e8	+	1.16887e9i	0.0470416	+	0.144779i	−0.924777	+	0.380510i	$0.875748\pi$
$678$		0			0
$679$	−8.93607e9	+	6.49244e9i	−1.09548	+	0.795909i
$680$	1.11036e9	−	3.41733e9i	0.135420	−	0.416779i
$681$		0			0
$682$	−1.41073e9	+	2.36790e9i	−0.170294	+	0.285836i
$683$	−1.27446e10			−1.53057			−0.765286	−	0.643690i	$-0.777403\pi$
$683$	−1.27446e10			−1.53057			−0.765286	+	0.643690i	$0.777403\pi$
$684$		0			0
$685$	−8.95644e8	+	6.50724e8i	−0.106468	+	0.0773534i
$686$	−8.05728e9	−	5.85396e9i	−0.952915	−	0.692333i
$687$		0			0
$688$	−2.30881e9	−	7.10578e9i	−0.270289	−	0.831864i
$689$	5.90265e9	+	4.28852e9i	0.687511	+	0.499506i
$690$		0			0
$691$	−9.68318e8	+	2.98018e9i	−0.111646	+	0.343612i	−0.991233	−	0.132127i	$-0.957819\pi$
$691$	−9.68318e8	+	2.98018e9i	−0.111646	+	0.343612i	0.879586	+	0.475739i	$0.157819\pi$
$692$	−1.21784e9			−0.139707
$693$		0			0
$694$	1.86983e10			2.12346
$695$	−6.59494e8	+	2.02971e9i	−0.0745184	+	0.229344i
$696$		0			0
$697$	2.33489e9	+	1.69639e9i	0.261187	+	0.189763i
$698$	−4.65126e9	−	1.43151e10i	−0.517698	−	1.59331i
$699$		0			0
$700$	−8.88043e8	−	6.45201e8i	−0.0978568	−	0.0710971i
$701$	−4.68775e9	+	3.40585e9i	−0.513986	+	0.373433i	−0.814334	−	0.580397i	$-0.802897\pi$
$701$	−4.68775e9	+	3.40585e9i	−0.513986	+	0.373433i	0.300348	+	0.953830i	$0.402897\pi$
$702$		0			0
$703$	−7.19231e9			−0.780773
$704$	7.00685e9	+	1.59004e9i	0.756865	+	0.171752i
$705$		0			0
$706$	−1.88844e8	+	5.81202e8i	−0.0201970	+	0.0621599i
$707$	−4.62353e9	+	3.35919e9i	−0.492046	+	0.357492i
$708$		0			0
$709$	−8.06095e8	−	2.48091e9i	−0.0849424	−	0.261426i	0.899560	−	0.436797i	$-0.143887\pi$
$709$	−8.06095e8	−	2.48091e9i	−0.0849424	−	0.261426i	−0.984502	+	0.175372i	$0.943887\pi$
$710$	−8.36611e8	−	2.57482e9i	−0.0877242	−	0.269987i
$711$		0			0
$712$	−6.13290e9	+	4.45581e9i	−0.636774	+	0.462644i
$713$	−1.62922e9	+	5.01421e9i	−0.168332	+	0.518071i
$714$		0			0
$715$	2.96853e8	+	3.25267e9i	0.0303718	+	0.332789i
$716$	−8.33038e8			−0.0848143
$717$		0			0
$718$	−8.28513e8	+	6.01950e8i	−0.0835341	+	0.0606911i
$719$	−3.20611e9	−	2.32937e9i	−0.321682	−	0.233716i	0.415211	−	0.909725i	$-0.363708\pi$
$719$	−3.20611e9	−	2.32937e9i	−0.321682	−	0.233716i	−0.736893	+	0.676009i	$0.763708\pi$
$720$		0			0
$721$	2.79130e9	+	8.59075e9i	0.277353	+	0.853606i
$722$	2.29004e9	+	1.66381e9i	0.226445	+	0.164522i
$723$		0			0
$724$	−3.23933e8	+	9.96965e8i	−0.0317227	+	0.0976326i
$725$	−7.21795e9			−0.703446
$726$		0			0
$727$	2.85430e9			0.275505			0.137752	−	0.990467i	$-0.456012\pi$
$727$	2.85430e9			0.275505			0.137752	+	0.990467i	$0.456012\pi$
$728$	−2.15419e9	+	6.62992e9i	−0.206930	+	0.636866i
$729$		0			0
$730$	−1.63418e9	−	1.18730e9i	−0.155479	−	0.112962i
$731$	3.32956e9	+	1.02473e10i	0.315265	+	0.970286i
$732$		0			0
$733$	1.32240e9	+	9.60783e8i	0.124022	+	0.0901076i	0.648067	−	0.761583i	$-0.275578\pi$
$733$	1.32240e9	+	9.60783e8i	0.124022	+	0.0901076i	−0.524045	+	0.851691i	$0.675578\pi$
$734$	−3.17014e8	+	2.30324e8i	−0.0295898	+	0.0214982i
$735$		0			0
$736$	−6.47074e9			−0.598248
$737$	6.46603e8	+	7.08493e9i	0.0594979	+	0.651928i
$738$		0			0
$739$	−1.36427e9	+	4.19879e9i	−0.124350	+	0.382709i	−0.993782	−	0.111343i	$-0.964485\pi$
$739$	−1.36427e9	+	4.19879e9i	−0.124350	+	0.382709i	0.869432	+	0.494052i	$0.164485\pi$
$740$	−5.06133e8	+	3.67727e8i	−0.0459149	+	0.0333591i
$741$		0			0
$742$	−2.84248e9	−	8.74824e9i	−0.255437	−	0.786153i
$743$	−4.78895e9	−	1.47389e10i	−0.428331	−	1.31827i	−0.899769	−	0.436367i	$-0.856265\pi$
$743$	−4.78895e9	−	1.47389e10i	−0.428331	−	1.31827i	0.471438	−	0.881899i	$-0.343735\pi$
$744$		0			0
$745$	−6.68155e8	+	4.85443e8i	−0.0592012	+	0.0430122i
$746$	−6.65134e9	+	2.04707e10i	−0.586575	+	1.80529i
$747$		0			0
$748$	2.53593e9	+	5.75468e8i	0.221555	+	0.0502765i
$749$	1.19400e10			1.03829
$750$		0			0
$751$	4.75946e9	−	3.45795e9i	0.410032	−	0.297906i	−0.363583	−	0.931562i	$-0.618447\pi$
$751$	4.75946e9	−	3.45795e9i	0.410032	−	0.297906i	0.773615	+	0.633656i	$0.218447\pi$
$752$	5.39433e8	+	3.91921e8i	0.0462567	+	0.0336075i
$753$		0			0
$754$	−2.91427e9	−	8.96919e9i	−0.247588	−	0.761997i
$755$	1.53024e9	+	1.11178e9i	0.129403	+	0.0940168i
$756$		0			0
$757$	−5.69713e9	+	1.75339e10i	−0.477332	+	1.46908i	0.365456	+	0.930829i	$0.380913\pi$
$757$	−5.69713e9	+	1.75339e10i	−0.477332	+	1.46908i	−0.842787	+	0.538247i	$0.819087\pi$
$758$	−8.83084e9			−0.736478
$759$		0			0
$760$	3.42937e9			0.283379
$761$	−5.16417e8	+	1.58937e9i	−0.0424770	+	0.130731i	−0.970046	−	0.242921i	$-0.921894\pi$
$761$	−5.16417e8	+	1.58937e9i	−0.0424770	+	0.130731i	0.927569	+	0.373652i	$0.121894\pi$
$762$		0			0
$763$	−1.24843e10	−	9.07034e9i	−1.01748	−	0.739244i
$764$	−4.78631e8	−	1.47307e9i	−0.0388306	−	0.119508i
$765$		0			0
$766$	6.67276e9	+	4.84805e9i	0.536420	+	0.389732i
$767$	1.04196e10	−	7.57027e9i	0.833809	−	0.605797i
$768$		0			0
$769$	2.39264e10			1.89730			0.948649	−	0.316329i	$-0.102450\pi$
$769$	2.39264e10			1.89730			0.948649	+	0.316329i	$0.102450\pi$
$770$	2.10759e9	−	3.53757e9i	0.166368	−	0.279246i
$771$		0			0
$772$	5.23246e8	−	1.61039e9i	0.0409304	−	0.125971i
$773$	1.15639e10	−	8.40167e9i	0.900485	−	0.654240i	−0.0381058	−	0.999274i	$-0.512132\pi$
$773$	1.15639e10	−	8.40167e9i	0.900485	−	0.654240i	0.938590	+	0.345033i	$0.112132\pi$
$774$		0			0
$775$	1.06576e9	+	3.28006e9i	0.0822436	+	0.253120i
$776$	5.96726e9	+	1.83653e10i	0.458415	+	1.41086i
$777$		0			0
$778$	1.95172e10	−	1.41800e10i	1.48589	−	1.07957i
$779$	−8.51187e8	+	2.61968e9i	−0.0645125	+	0.198549i
$780$		0			0
$781$	−8.75236e9	+	3.75391e9i	−0.657426	+	0.281972i
$782$	3.41253e10			2.55184
$783$		0			0
$784$	−4.10094e9	+	2.97951e9i	−0.303933	+	0.220820i
$785$	−3.59164e9	−	2.60948e9i	−0.265002	−	0.192535i
$786$		0			0
$787$	6.86381e8	+	2.11246e9i	0.0501942	+	0.154482i	0.973012	−	0.230755i	$-0.0741196\pi$
$787$	6.86381e8	+	2.11246e9i	0.0501942	+	0.154482i	−0.922818	+	0.385237i	$0.874120\pi$
$788$	2.69981e9	+	1.96153e9i	0.196558	+	0.142808i
$789$		0			0
$790$	−3.93946e8	+	1.21244e9i	−0.0284277	+	0.0874914i
$791$	−4.57562e9			−0.328725
$792$		0			0
$793$	1.48899e9			0.106032
$794$	6.79618e9	−	2.09165e10i	0.481829	−	1.48292i
$795$		0			0
$796$	2.33945e9	+	1.69971e9i	0.164406	+	0.119448i
$797$	−3.90568e9	−	1.20205e10i	−0.273271	−	0.841040i	−0.989672	−	0.143352i	$-0.954212\pi$
$797$	−3.90568e9	−	1.20205e10i	−0.273271	−	0.841040i	0.716401	−	0.697689i	$-0.245788\pi$
$798$		0			0
$799$	−7.77922e8	−	5.65193e8i	−0.0539538	−	0.0391997i
$800$	−3.42445e9	+	2.48801e9i	−0.236470	+	0.171806i
$801$		0			0
$802$	−1.51434e10			−1.03661
$803$	−3.63677e9	+	6.10428e9i	−0.247863	+	0.416035i
$804$		0			0
$805$	2.43400e9	−	7.49109e9i	0.164451	−	0.506127i
$806$	−3.64558e9	+	2.64867e9i	−0.245241	+	0.178178i
$807$		0			0
$808$	3.08746e9	+	9.50223e9i	0.205903	+	0.633703i
$809$	2.82268e9	+	8.68732e9i	0.187431	+	0.576854i	0.999982	−	0.00603683i	$-0.00192160\pi$
$809$	2.82268e9	+	8.68732e9i	0.187431	+	0.576854i	−0.812551	+	0.582891i	$0.801922\pi$
$810$		0			0
$811$	5.33354e9	−	3.87505e9i	0.351110	−	0.255096i	−0.398225	−	0.917288i	$-0.630374\pi$
$811$	5.33354e9	−	3.87505e9i	0.351110	−	0.255096i	0.749334	+	0.662192i	$0.230374\pi$
$812$	−5.35538e8	+	1.64822e9i	−0.0351030	+	0.108036i
$813$		0			0
$814$	9.94788e9	+	1.13575e10i	0.646465	+	0.738071i
$815$	−1.01510e10			−0.656840
$816$		0			0
$817$	−8.31948e9	+	6.04446e9i	−0.533727	+	0.387775i
$818$	3.85888e9	+	2.80364e9i	0.246505	+	0.179096i
$819$		0			0
$820$	7.40394e7	+	2.27870e8i	0.00468937	+	0.0144324i
$821$	−8.04374e9	−	5.84412e9i	−0.507291	−	0.368568i	0.304504	−	0.952511i	$-0.401509\pi$
$821$	−8.04374e9	−	5.84412e9i	−0.507291	−	0.368568i	−0.811795	+	0.583943i	$0.801509\pi$
$822$		0			0
$823$	7.92385e9	−	2.43871e10i	0.495492	−	1.52497i	−0.320696	−	0.947182i	$-0.603917\pi$
$823$	7.92385e9	−	2.43871e10i	0.495492	−	1.52497i	0.816188	−	0.577786i	$-0.196083\pi$
$824$	1.57917e10			0.983293
$825$		0			0
$826$	−1.62374e10			−1.00251
$827$	2.36224e9	−	7.27023e9i	0.145229	−	0.446970i	−0.851811	−	0.523849i	$-0.824496\pi$
$827$	2.36224e9	−	7.27023e9i	0.145229	−	0.446970i	0.997040	+	0.0768790i	$0.0244955\pi$
$828$		0			0
$829$	−7.51054e9	−	5.45672e9i	−0.457857	−	0.332653i	0.334833	−	0.942278i	$-0.391320\pi$
$829$	−7.51054e9	−	5.45672e9i	−0.457857	−	0.332653i	−0.792690	+	0.609625i	$0.791320\pi$
$830$	−1.81673e9	−	5.59132e9i	−0.110285	−	0.339423i
$831$		0			0
$832$	9.50318e9	+	6.90447e9i	0.572055	+	0.415622i
$833$	5.91401e9	−	4.29678e9i	0.354507	−	0.257564i
$834$		0			0
$835$	7.30175e9			0.434034
$836$	2.25567e8	+	2.47157e9i	0.0133522	+	0.146302i
$837$		0			0
$838$	8.12610e9	−	2.50096e10i	0.477011	−	1.46809i
$839$	3.42837e7	−	2.49085e7i	0.00200411	−	0.00145607i	−0.586783	−	0.809744i	$-0.699606\pi$
$839$	3.42837e7	−	2.49085e7i	0.00200411	−	0.00145607i	0.588787	+	0.808288i	$0.299606\pi$
$840$		0			0
$841$	−1.80900e9	−	5.56754e9i	−0.104871	−	0.322758i
$842$	−8.88223e8	−	2.73367e9i	−0.0512778	−	0.157817i
$843$		0			0
$844$	−2.03938e9	+	1.48170e9i	−0.116761	+	0.0848321i
$845$	3.37802e8	−	1.03965e9i	0.0192603	−	0.0592771i
$846$		0			0
$847$	−1.30662e10	−	6.25209e9i	−0.738854	−	0.353536i
$848$	−1.89074e10			−1.06475
$849$		0			0
$850$	1.80598e10	−	1.31212e10i	1.00867	−	0.732839i
$851$	2.33643e10	+	1.69752e10i	1.29957	+	0.944193i
$852$		0			0
$853$	7.43930e9	+	2.28958e10i	0.410403	+	1.26309i	0.916299	+	0.400495i	$0.131162\pi$
$853$	7.43930e9	+	2.28958e10i	0.410403	+	1.26309i	−0.505896	+	0.862595i	$0.668838\pi$
$854$	−1.51871e9	−	1.10341e9i	−0.0834397	−	0.0606225i
$855$		0			0
$856$	6.45046e9	−	1.98525e10i	0.351506	−	1.08182i
$857$	−1.40911e9			−0.0764734			−0.0382367	−	0.999269i	$-0.512174\pi$
$857$	−1.40911e9			−0.0764734			−0.0382367	+	0.999269i	$0.512174\pi$
$858$		0			0
$859$	−1.31310e10			−0.706840			−0.353420	−	0.935465i	$-0.614981\pi$
$859$	−1.31310e10			−0.706840			−0.353420	+	0.935465i	$0.614981\pi$
$860$	−2.76414e8	+	8.50713e8i	−0.0148189	+	0.0456078i
$861$		0			0
$862$	2.47095e9	+	1.79525e9i	0.131398	+	0.0954663i
$863$	−1.85717e9	−	5.71578e9i	−0.0983590	−	0.302718i	0.889756	−	0.456437i	$-0.150875\pi$
$863$	−1.85717e9	−	5.71578e9i	−0.0983590	−	0.302718i	−0.988115	+	0.153720i	$0.950875\pi$
$864$		0			0
$865$	−4.62477e9	−	3.36009e9i	−0.242959	−	0.176520i
$866$	−6.89028e9	+	5.00608e9i	−0.360516	+	0.261930i
$867$		0			0
$868$	8.28076e8			0.0429785
$869$	4.37323e9	+	9.92400e8i	0.226065	+	0.0513000i
$870$		0			0
$871$	−3.59422e9	+	1.10619e10i	−0.184306	+	0.567237i
$872$	−2.18256e10	+	1.58572e10i	−1.11470	+	0.809877i
$873$		0			0
$874$	1.00645e10	+	3.09755e10i	0.509922	+	1.56938i
$875$	−3.43192e9	−	1.05624e10i	−0.173184	−	0.533007i
$876$		0			0
$877$	2.85863e10	−	2.07692e10i	1.43106	−	1.03973i	0.441248	−	0.897385i	$-0.354536\pi$
$877$	2.85863e10	−	2.07692e10i	1.43106	−	1.03973i	0.989817	−	0.142344i	$-0.0454639\pi$
$878$	1.19591e10	−	3.68064e10i	0.596305	−	1.83524i
$879$		0			0
$880$	−5.57687e9	−	6.36713e9i	−0.275868	−	0.314959i
$881$	−2.47432e10			−1.21910			−0.609551	−	0.792747i	$-0.708650\pi$
$881$	−2.47432e10			−1.21910			−0.609551	+	0.792747i	$0.708650\pi$
$882$		0			0
$883$	1.02288e10	−	7.43163e9i	0.499989	−	0.363263i	−0.309024	−	0.951054i	$-0.600002\pi$
$883$	1.02288e10	−	7.43163e9i	0.499989	−	0.363263i	0.809013	+	0.587791i	$0.200002\pi$
$884$	3.43940e9	+	2.49887e9i	0.167456	+	0.121664i
$885$		0			0
$886$	1.51549e9	+	4.66421e9i	0.0732043	+	0.225300i
$887$	−1.63938e10	−	1.19108e10i	−0.788764	−	0.573070i	0.118833	−	0.992914i	$-0.462085\pi$
$887$	−1.63938e10	−	1.19108e10i	−0.788764	−	0.573070i	−0.907596	+	0.419844i	$0.862085\pi$
$888$		0			0
$889$	−5.67280e8	+	1.74591e9i	−0.0270795	+	0.0833422i
$890$	7.32077e9			0.348090
$891$		0			0
$892$	3.81526e9			0.179989
$893$	2.83593e8	−	8.72809e8i	0.0133265	−	0.0410146i
$894$		0			0
$895$	−3.16347e9	−	2.29840e9i	−0.147497	−	0.107163i
$896$	−6.41693e9	−	1.97493e10i	−0.298022	−	0.917219i
$897$		0			0
$898$	8.44003e7	+	6.13204e7i	0.00388935	+	0.00282578i
$899$	4.40519e9	−	3.20056e9i	0.202212	−	0.146915i
$900$		0			0
$901$	2.72665e10			1.24192
$902$	5.31409e9	−	2.27923e9i	0.241105	−	0.103411i
$903$		0			0
$904$	−2.47193e9	+	7.60781e9i	−0.111287	+	0.342508i
$905$	−3.98082e9	+	2.89223e9i	−0.178526	+	0.129707i
$906$		0			0
$907$	−1.28611e10	−	3.95824e10i	−0.572339	−	1.76148i	−0.645068	−	0.764126i	$-0.723171\pi$
$907$	−1.28611e10	−	3.95824e10i	−0.572339	−	1.76148i	0.0727289	−	0.997352i	$-0.476829\pi$
$908$	8.41966e8	+	2.59131e9i	0.0373245	+	0.114873i
$909$		0			0
$910$	5.44639e9	−	3.95703e9i	0.239587	−	0.174070i
$911$	5.96668e9	−	1.83635e10i	0.261468	−	0.804715i	−0.731018	−	0.682358i	$-0.760955\pi$
$911$	5.96668e9	−	1.83635e10i	0.261468	−	0.804715i	0.992486	−	0.122357i	$-0.0390454\pi$
$912$		0			0
$913$	−1.90061e10	+	8.15175e9i	−0.826503	+	0.354489i
$914$	1.91413e9			0.0829203
$915$		0			0
$916$	−3.00845e9	+	2.18577e9i	−0.129333	+	0.0939658i
$917$	3.82752e9	+	2.78086e9i	0.163917	+	0.119093i
$918$		0			0
$919$	−3.90949e9	−	1.20322e10i	−0.166156	−	0.511376i	0.832964	−	0.553328i	$-0.186642\pi$
$919$	−3.90949e9	−	1.20322e10i	−0.166156	−	0.511376i	−0.999120	+	0.0419521i	$0.986642\pi$
$920$	−1.11404e10	−	8.09395e9i	−0.471674	−	0.342692i
$921$		0			0
$922$	−7.84595e9	+	2.41474e10i	−0.329676	+	1.01464i
$923$	−1.55696e10			−0.651737
$924$		0			0
$925$	1.88919e10			0.784836
$926$	−6.17239e9	+	1.89966e10i	−0.255455	+	0.786210i
$927$		0			0
$928$	5.40658e9	+	3.92811e9i	0.222078	+	0.161349i
$929$	3.54368e9	+	1.09063e10i	0.145010	+	0.446296i	0.997012	−	0.0772424i	$-0.0246115\pi$
$929$	3.54368e9	+	1.09063e10i	0.145010	+	0.446296i	−0.852002	+	0.523539i	$0.824612\pi$
$930$		0			0
$931$	5.64438e9	+	4.10088e9i	0.229241	+	0.166553i
$932$	−4.46225e9	+	3.24202e9i	−0.180550	+	0.131178i
$933$		0			0
$934$	−4.18674e10			−1.68137
$935$	8.04246e9	+	9.18210e9i	0.321772	+	0.367368i
$936$		0			0
$937$	−1.21922e10	+	3.75239e10i	−0.484167	+	1.49011i	0.349017	+	0.937117i	$0.386516\pi$
$937$	−1.21922e10	+	3.75239e10i	−0.484167	+	1.49011i	−0.833184	+	0.552996i	$0.813484\pi$
$938$	1.18633e10	−	8.61917e9i	0.469348	−	0.341001i
$939$		0			0
$940$	−2.46680e7	−	7.59202e7i	−0.000968693	−	0.00298133i
$941$	−3.56273e8	−	1.09650e9i	−0.0139386	−	0.0428986i	0.943845	−	0.330388i	$-0.107179\pi$
$941$	−3.56273e8	−	1.09650e9i	−0.0139386	−	0.0428986i	−0.957784	+	0.287489i	$0.907179\pi$
$942$		0			0
$943$	8.94803e9	−	6.50112e9i	0.347485	−	0.252463i
$944$	−1.03138e10	+	3.17425e10i	−0.399039	+	1.22812i
$945$		0			0
$946$	2.10518e10	+	4.77720e9i	0.808482	+	0.183466i
$947$	2.63741e9			0.100914			0.0504572	−	0.998726i	$-0.483932\pi$
$947$	2.63741e9			0.100914			0.0504572	+	0.998726i	$0.483932\pi$
$948$		0			0
$949$	−9.39806e9	+	6.82809e9i	−0.356949	+	0.259339i
$950$	1.72365e10	+	1.25230e10i	0.652253	+	0.473889i
$951$		0			0
$952$	8.05054e9	+	2.47770e10i	0.302410	+	0.930721i
$953$	3.17157e10	+	2.30428e10i	1.18699	+	0.862402i	0.992943	−	0.118590i	$-0.0378373\pi$
$953$	3.17157e10	+	2.30428e10i	1.18699	+	0.862402i	0.194051	+	0.980991i	$0.437837\pi$
$954$		0			0
$955$	2.24668e9	−	6.91458e9i	0.0834699	−	0.256894i
$956$	9.93253e8			0.0367669
$957$		0			0
$958$	−4.94985e10			−1.81891
$959$	2.48041e9	−	7.63390e9i	0.0908150	−	0.279500i
$960$		0			0
$961$	2.01533e10	+	1.46422e10i	0.732511	+	0.532200i
$962$	7.62764e9	+	2.34755e10i	0.276234	+	0.850162i
$963$		0			0
$964$	2.65118e9	+	1.92620e9i	0.0953169	+	0.0692518i
$965$	6.43018e9	−	4.67180e9i	0.230344	−	0.167355i
$966$		0			0
$967$	−3.73048e10			−1.32670			−0.663349	−	0.748310i	$-0.730866\pi$
$967$	−3.73048e10			−1.32670			−0.663349	+	0.748310i	$0.730866\pi$
$968$	−1.74541e10	+	1.83474e10i	−0.618493	+	0.650146i
$969$		0			0
$970$	5.76267e9	−	1.77357e10i	0.202732	−	0.623946i
$971$	−1.20420e10	+	8.74899e9i	−0.422114	+	0.306684i	−0.778488	−	0.627660i	$-0.784013\pi$
$971$	−1.20420e10	+	8.74899e9i	−0.422114	+	0.306684i	0.356374	+	0.934343i	$0.384013\pi$
$972$		0			0
$973$	−4.78160e9	−	1.47162e10i	−0.166409	−	0.512156i
$974$	2.97592e9	+	9.15895e9i	0.103197	+	0.317606i
$975$		0			0
$976$	−3.12171e9	+	2.26806e9i	−0.107478	+	0.0780871i
$977$	9.01513e9	−	2.77457e10i	0.309272	−	0.951842i	−0.668776	−	0.743464i	$-0.733181\pi$
$977$	9.01513e9	−	2.77457e10i	0.309272	−	0.951842i	0.978048	−	0.208378i	$-0.0668185\pi$
$978$		0			0
$979$	−2.34051e9	−	2.56453e10i	−0.0797206	−	0.873512i
$980$	6.06872e8			0.0205971
$981$		0			0
$982$	−2.85975e10	+	2.07773e10i	−0.963690	+	0.700162i
$983$	1.75961e10	+	1.27843e10i	0.590852	+	0.429279i	0.842620	−	0.538508i	$-0.181012\pi$
$983$	1.75961e10	+	1.27843e10i	0.590852	+	0.429279i	−0.251768	+	0.967788i	$0.581012\pi$
$984$		0			0
$985$	4.84060e9	+	1.48978e10i	0.161388	+	0.496702i
$986$	−2.85132e10	−	2.07160e10i	−0.947275	−	0.688236i
$987$		0			0
$988$	−1.25384e9	+	3.85892e9i	−0.0413612	+	0.127297i
$989$	4.12920e10			1.35731
$990$		0			0
$991$	−5.54420e10			−1.80959			−0.904797	−	0.425844i	$-0.859977\pi$
$991$	−5.54420e10			−1.80959			−0.904797	+	0.425844i	$0.859977\pi$
$992$	9.86755e8	−	3.03692e9i	0.0320936	−	0.0987739i
$993$		0			0
$994$	1.58804e10	+	1.15378e10i	0.512872	+	0.372623i
$995$	4.19450e9	+	1.29094e10i	0.134989	+	0.415455i
$996$		0			0
$997$	4.60132e10	+	3.34305e10i	1.47045	+	1.06834i	0.980484	+	0.196599i	$0.0629896\pi$
$997$	4.60132e10	+	3.34305e10i	1.47045	+	1.06834i	0.489963	+	0.871743i	$0.337010\pi$
$998$	−2.87015e10	+	2.08529e10i	−0.914003	+	0.664062i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.8.f.a.64.5		24
3.2	odd	2		11.8.c.a.9.2	yes	24
11.5	even	5	inner	99.8.f.a.82.5		24
33.5	odd	10		11.8.c.a.5.2	✓	24
33.26	odd	10		121.8.a.i.1.3		12
33.29	even	10		121.8.a.g.1.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.8.c.a.5.2	✓	24	33.5	odd	10
11.8.c.a.9.2	yes	24	3.2	odd	2
99.8.f.a.64.5		24	1.1	even	1	trivial
99.8.f.a.82.5		24	11.5	even	5	inner
121.8.a.g.1.10		12	33.29	even	10
121.8.a.i.1.3		12	33.26	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	99.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(3.78266 - 11.6418i) q^{2} +(-17.6695 - 12.8376i) q^{4} +(-31.6803 - 97.5020i) q^{5} +(601.350 + 436.906i) q^{7} +(1051.31 - 763.821i) q^{8} -1254.94 q^{10} +(401.213 + 4396.16i) q^{11} +(-2230.19 + 6863.81i) q^{13} +(7361.09 - 5348.14i) q^{14} +(-5779.42 - 17787.2i) q^{16} +(8334.56 + 25651.1i) q^{17} +(-20825.3 + 15130.5i) q^{19} +(-691.919 + 2129.51i) q^{20} +(52697.0 + 11958.3i) q^{22} +103362. q^{23} +(54701.5 - 39742.9i) q^{25} +(71471.3 + 51926.9i) q^{26} +(-5016.70 - 15439.8i) q^{28} +(-86363.5 - 62746.8i) q^{29} +(-15762.2 + 48511.1i) q^{31} -62602.6 q^{32} +330153. q^{34} +(23548.3 - 72474.1i) q^{35} +(226043. + 164230. i) q^{37} +(97371.5 + 299679. i) q^{38} +(-107780. - 78306.7i) q^{40} +(86569.6 - 62896.5i) q^{41} +399488. q^{43} +(49347.0 - 82828.4i) q^{44} +(390984. - 1.20333e6i) q^{46} +(-28842.7 + 20955.4i) q^{47} +(-83754.2 - 257769. i) q^{49} +(-255763. - 787159. i) q^{50} +(127521. - 92649.6i) q^{52} +(312401. - 961471. i) q^{53} +(415924. - 178391. i) q^{55} +965923. q^{56} +(-1.05717e6 + 768080. i) q^{58} +(-1.44375e6 - 1.04894e6i) q^{59} +(-63755.2 - 196218. i) q^{61} +(505135. + 367002. i) q^{62} +(502961. - 1.54796e6i) q^{64} +739889. q^{65} +1.61162e6 q^{67} +(182032. - 560238. i) q^{68} +(-754656. - 548290. i) q^{70} +(666655. + 2.05175e6i) q^{71} +(1.30220e6 + 946107. i) q^{73} +(2.76698e6 - 2.01033e6i) q^{74} +562212. q^{76} +(-1.67944e6 + 2.81892e6i) q^{77} +(313917. - 966136. i) q^{79} +(-1.55120e6 + 1.12701e6i) q^{80} +(-404767. - 1.24574e6i) q^{82} +(1.44767e6 + 4.45546e6i) q^{83} +(2.23699e6 - 1.62527e6i) q^{85} +(1.51113e6 - 4.65077e6i) q^{86} +(3.77968e6 + 4.31527e6i) q^{88} -5.83358e6 q^{89} +(-4.33997e6 + 3.15317e6i) q^{91} +(-1.82636e6 - 1.32692e6i) q^{92} +(134858. + 415049. i) q^{94} +(2.13501e6 + 1.55117e6i) q^{95} +(-4.59200e6 + 1.41327e7i) q^{97} -3.31771e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{2} - 505 q^{4} + 72 q^{5} + 68 q^{7} + 4545 q^{8} + 4240 q^{10} - 5952 q^{11} - 16564 q^{13} + 29544 q^{14} + 13279 q^{16} + 65592 q^{17} - 37804 q^{19} - 120702 q^{20} + 246233 q^{22} + 26304 q^{23}+ \cdots + 51534036 q^{98}+O(q^{100}) \) 24 * q - 3 * q^2 - 505 * q^4 + 72 * q^5 + 68 * q^7 + 4545 * q^8 + 4240 * q^10 - 5952 * q^11 - 16564 * q^13 + 29544 * q^14 + 13279 * q^16 + 65592 * q^17 - 37804 * q^19 - 120702 * q^20 + 246233 * q^22 + 26304 * q^23 - 210646 * q^25 + 336384 * q^26 + 92334 * q^28 + 231048 * q^29 + 141004 * q^31 + 260892 * q^32 + 1512162 * q^34 + 342588 * q^35 - 836112 * q^37 + 2387040 * q^38 - 1906028 * q^40 - 1930344 * q^41 + 2877456 * q^43 - 5822808 * q^44 - 4951876 * q^46 + 2462532 * q^47 - 6581826 * q^49 + 2698797 * q^50 + 1655498 * q^52 - 6157836 * q^53 + 11721612 * q^55 - 11431080 * q^56 - 15150140 * q^58 + 2480268 * q^59 - 4195044 * q^61 + 6436524 * q^62 + 11301151 * q^64 - 11117640 * q^65 + 16682528 * q^67 + 14718306 * q^68 - 16625944 * q^70 + 20942628 * q^71 - 456824 * q^73 - 8747736 * q^74 + 18091206 * q^76 - 13904988 * q^77 - 12976692 * q^79 + 11893596 * q^80 - 32706099 * q^82 + 4471404 * q^83 + 25528128 * q^85 - 20374383 * q^86 + 25246815 * q^88 + 2477316 * q^89 - 18339604 * q^91 - 1026678 * q^92 - 4961738 * q^94 + 25328772 * q^95 - 34034202 * q^97 + 51534036 * q^98

Introduction

L-functions

Modular forms

Varieties

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